2025 | Solvation, geometry, and assembly of the tobacco mosaic virus | Ivan Spirandelli, Myfanwy E Evans
Zeitschrift: PNAS Nexus
Band: Vol. 4, No. 3
Link zur Publikation
Solvation, geometry, and assembly of the tobacco mosaic virus
Autoren: Ivan Spirandelli, Myfanwy E Evans
(2025)
Biological self-assembly is a fundamental aspect in the development of complex structures in nature. A paradigm for such a process is the assembly of tobacco mosaic virus (TMV) capsid proteins into helical rods around the viral genome. The self-assembly process of the virus is typically modelled through attractive interactions between protein subunits, however capsid proteins also interact with their aqueous environment through solvation free energy. An open question is what role solvation plays in virus self-assembly. Here, we show that a purely geometric model of nonpolar solvation free energy, the morphometric approach, is sufficient to simulate the assembly of up to three protein subunits of TMV. The lowest solvation free energy states we find in a geometric simulation setting are remarkably close to the correctly assembled states of various experimentally determined structures. This demonstrates that van der Waals forces and entropic considerations are sufficient to guide assembly in the absence of attractive interactions between protein subunits. It further illustrates the impact of the morphometric approach as a computationally efficient model for nonpolar solvation free energy of solutes, in particular those with complicated geometry. This demonstration of the role of solvation raises important questions about the driving forces behind biological self-assembly and the paramount role of geometry.
2025 | The I-Love universal relation for polytropic stars under Newtonian gravity | Rui Xu, Alejandro Torres-Orjuela, Lars Andersson, Pau Amaro Seoane
Link zum Preprint
The I-Love universal relation for polytropic stars under Newtonian gravity
Autoren: Rui Xu, Alejandro Torres-Orjuela, Lars Andersson, Pau Amaro Seoane
(2025)
The moment of inertia and tidal deformability of idealized stars with polytropic equations of state (EOSs) are numerically calculated under both Newtonian gravity and general relativity (GR). The results explicitly confirm that the relation between the moment of inertia and tidal deformability, parameterized by the star's mass, exhibits variations of 1% to 10% for different polytropic indices in Newtonian gravity and GR, respectively. This indicates a more robust I-Love universal relation in the Newtonian framework. The theoretically derived I-Love universal relation for polytropic stars is subsequently tested against observational data for the moment of inertia and tidal deformability of the 8 planets and some moons in our solar system. The analysis reveals that the theoretical I-Love universal relation aligns well with the observational data, suggesting that it can serve as an empirical relation. Consequently, it enables the estimation of either the moment of inertia or the tidal deformability of an exoplanet if one of these quantities, along with the mass of the exoplanet, is known.
2025 | Spectral estimates of dynamically-defined and amenable operator families | Siegfried Beckus, Alberto Takase
Zeitschrift: to appear in Journal of Spectral Theory
Link zum Preprint
Spectral estimates of dynamically-defined and amenable operator families
Autoren: Siegfried Beckus, Alberto Takase
(2025)
We consider kernel operators defined by a dynamical system. The Hausdorff distance of spectra is estimated by the Hausdorff distance of subsystems. We prove that the spectrum map is 1/2-Hölder continuous provided the group action and kernel are Lipschitz continuous and the group has strict polynomial growth. Also, we prove that the continuity can be improved resulting in the spectrum map being Lipschitz continuous provided the kernel is instead locally-constant. This complements a 1990 result by J. Avron; P.H.M.v. Mouche; B. Simon establishing that one-dimensional discrete quasiperiodic Schrödinger operators with Lipschitz continuous potentials, e.g., the Almost Mathieu Operator, exhibit spectral 1/2-Hölder continuity. Also, this complements a 2019 result by S. Beckus; J. Bellissard; H. Cornean establishing that d-dimensional discrete subshift Schrödinger operators with locally-constant potentials, e.g., the Fibonacci Hamiltonian, exhibit spectral Lipschitz continuity.
Our work exposes the connection between the past two results, and the group, e.g., the Heisenberg group, needs not be the integer lattice nor abelian.
Zeitschrift:
to appear in Journal of Spectral Theory
2025 | A review of a work by L. Raymond: Sturmian Hamiltonians with a large coupling constant - periodic approximations and gap labels | Ram Band, Siegfried Beckus, Barak Biber, Laurent Raymond and Yannik Thomas
Zeitschrift: to appear in the Proceedings of the Final Conference of COST Action “CA18232: Mathematical models for interacting dynamics on networks” (in press)
Link zum Preprint
A review of a work by L. Raymond: Sturmian Hamiltonians with a large coupling constant - periodic approximations and gap labels
Autoren: Ram Band, Siegfried Beckus, Barak Biber, Laurent Raymond and Yannik Thomas
(2025)
We present a review of the work L. Raymond from 1995. The review aims at making this work more accessible and offers adaptations of some statements and proofs. In addition, this review forms an applicable framework for the complete solution of the Dry Ten Martini Problem for Sturmian Hamiltonians as appears in the work arXiv:2402.16703 by R. Band, S. Beckus and R. Loewy. A Sturmian Hamiltonian is a one-dimensional Schrödinger operator whose potential is a Sturmian sequence multiplied by a coupling constant, V∈ℝ. The spectrum of such an operator is commonly approximated by the spectra of designated periodic operators. If V>4, then the spectral bands of the periodic operators exhibit a particular combinatorial structure. This structure provides a formula for the integrated density of states. Employing this, it is shown that if V>4, then all the gaps, as predicted by the gap labelling theorem, are there.
Zeitschrift:
to appear in the Proceedings of the Final Conference of COST Action “CA18232: Mathematical models for interacting dynamics on networks” (in press)
2025 | Spectral approximation for substitution systems | Ram Band, Siegfried Beckus, Felix Pogorzelski and Lior Tenenbaum
Zeitschrift: to appear in Journal d'Analyse Mathématique
Link zum Preprint
Spectral approximation for substitution systems
Autoren: Ram Band, Siegfried Beckus, Felix Pogorzelski and Lior Tenenbaum
(2025)
We study periodic approximations of aperiodic Schrödinger operators on lattices in Lie groups with dilation structure. The potentials arise through symbolic substitution systems that have been recently introduced in this setting. We characterize convergence of spectra of associated Schrödinger operators in the Hausdorff distance via properties of finite graphs. As a consequence, new examples of periodic approximations are obtained. We further prove that there are substitution systems that do not admit periodic approximations in higher dimensions, in contrast to the one-dimensional case. On the other hand, if the spectra converge, then we show that the rate of convergence is necessarily exponentially fast. These results are new even for substitutions over ℤd.
Zeitschrift:
to appear in Journal d'Analyse Mathématique
2025 | Some Remarks on Wang-Yau Quasi-Local Mass | Bowen Zhao, Lars Andersson, Shing-Tung Yau
Zeitschrift: Classical and Quantum Gravity
Seiten: 025027
Band: 42 (2)
Link zur Publikation
,
Link zum Preprint
Some Remarks on Wang-Yau Quasi-Local Mass
Autoren: Bowen Zhao, Lars Andersson, Shing-Tung Yau
(2025)
We review Wang-Yau quasi-local definitions along the line of gravitational Hamiltonian. This makes clear the connection and difference between Wang-Yau definition and Brown-York or even global ADM definition. We make a brief comment on admissibility condition in Wang-Yau quasi-lcoal mass. We extend the positivity proof for Wang-Yau quasi-local energy to allow possible presence of strictly stable apparent horizons through establishing solvability of Dirac equation in certain 3-manifolds that possess cylindrical ends, as in the case of Jang's graph blowing up at marginally outer trapped surfaces.
Zeitschrift:
Classical and Quantum Gravity
2025 | Computing Euclidean distance and maximum likelihood retraction maps for constrained optimization | Alexander Heaton and Matthias Himmelmann
Zeitschrift: Computational Geometry
Band: Vol. 126
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Computing Euclidean distance and maximum likelihood retraction maps for constrained optimization
Autoren: Alexander Heaton and Matthias Himmelmann
(2025)
Riemannian optimization uses local methods to solve optimization problems whose constraint set is a smooth manifold. A linear step along some descent direction usually leaves the constraints, and hence retraction maps are used to approximate the exponential map and return to the manifold. For many common matrix manifolds, retraction maps are available, with more or less explicit formulas. For implicitly-defined manifolds, suitable retraction maps are difficult to compute. We therefore develop an algorithm which uses homotopy continuation to compute the Euclidean distance retraction for any implicitly-defined submanifold of Rn, and prove convergence results.
We also consider statistical models as Riemannian submanifolds of the probability simplex with the Fisher metric. Replacing Euclidean distance with maximum likelihood results in a map which we prove is a retraction. In fact, we prove the retraction is second-order; with the Levi-Civita connection associated to the Fisher metric, it approximates geodesics to second-order accuracy.
Zeitschrift:
Computational Geometry
2024 | Can solvents tie knots? Helical folds of biopolymers in liquid environments | Rhoslyn Coles, Myfanwy E. Evans
Link zum Preprint
Can solvents tie knots? Helical folds of biopolymers in liquid environments
Autoren: Rhoslyn Coles, Myfanwy E. Evans
(2024)
Helices are the quintessential geometric motif of microscale self-assembly, from α-helices in proteins to double helices in DNA. Assembly of the helical geometry of biopolymers is a foundational step in a hierarchy of structure that eventually leads to biological activity. Simulating self-assembly in a simplified and controlled setting allows us to probe the relevance of the solvent as a component of the system of collaborative processes governing biomaterials. Using a simulation technique based on the morphometric approach to solvation, we performed computer experiments which fold a short open flexible tube, modelling a biopolymer in an aqueous environment, according to the interaction of the tube with the solvent alone. Different fluid environments may favour quite different solute geometry: We find an array of helical geometries that self-assemble depending on the solvent conditions, including overhand knot shapes and symmetric double helices where the strand folds back on itself. Interestingly these shapes-in all their variety-are energetically favoured over the α-helix. In differentiating the role of solvation in self-assembly our study helps illuminate the energetic background scenery in which all soluble biomolecules live, indeed our results demonstrate that the solvent is capable of quite fundamental rearrangements even up to tying a simple overhand knot.
2024 | Mode stability of Hermitian instantons | Lars Andersson, Bernardo Araneda, Mattias Dahl
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Mode stability of Hermitian instantons
Autoren: Lars Andersson, Bernardo Araneda, Mattias Dahl
(2024)
In this note we prove the Riemannian analog of black hole mode stability for Hermitian, non-self-dual gravitational instantons which are either asymptotically locally flat (ALF) and Ricci-flat, or compact and Einstein with positive cosmological constant. We show that the Teukolsky equation on any such manifold is a positive definite operator. We also discuss the compatibility of the results with the existence of negative modes associated to variational instabilities.
2024 | A proposal of quasi-local mass for 2-surfaces of timelike mean curvature | Bowen Zhao, Shing-Tung Yau, Lars Andersson
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A proposal of quasi-local mass for 2-surfaces of timelike mean curvature
Autoren: Bowen Zhao, Shing-Tung Yau, Lars Andersson
(2024)
A quasi-local mass, typically defined as an integral over a spacelike 2-surface Σ, should encode information about the gravitational field within a finite, extended region bounded by Σ. Therefore, in attempts to quantize gravity, one may consider an infinite dimensional space of 2-surfaces instead of an infinite dimensional space of 4-dimensional Lorentzian spacetimes. However, existing definitions for quasilocal mass only applies to surfaces outside an horizon whose mean curvature vector is spacelike. In this paper, we propose an extension of the Wang-Yau quasi-local energy/mass to surfaces with timelike mean curvature vector, including in particular trapped surfaces. We adopt the same canonical gauge as in the Wang-Yau quasi-local energy but allow the pulled back "killing vector" to the physical spacetime to be spacelike. We define the new quasi-local energy along the Hamiltonian formulation of the Wang-Yau quasi-local energy. The new definition yields a positive definite surface energy density and a new divergence free current. Calculations for coordinate spheres in Kerr family spacetime are shown. In the spherical symmetric case, our definition reduces to a previous definition.
2024 | Elementare Differentialgeometrie (Monografie), 3. Auflage | Christian Bär
Verlag: De Gruyter
Seiten: xiv + 352
Link zur Publikation
Elementare Differentialgeometrie (Monografie), 3. Auflage
Autoren: Christian Bär
(2024)
Die dritte Auflage des bewährten Lehrbuchs bietet, vollständig überarbeitet und aktualisiert, eine fundierte und zugängliche Einführung in die Differentialgeometrie von Kurven und Flächen.
Beginnend mit klassischer euklidischer Geometrie deckt das Lehrbuch wichtige Themen wie Kurven- und Flächentheorie, die zentrale Bedeutung der Krümmung sowie analytische und topologische Aspekte ab. Auch Minimalflächen, hyperbolische Geometrie, Anwendungen in der Kartografie und der Satz von Gauß-Bonnet werden behandelt. Die mathematische Darstellung ist so gewählt, dass sich das Buch als Einstieg in die abstrakte riemannsche Geometrie eignet.
Eine der wichtigsten Erweiterungen in dieser Auflage ist die verbesserte Darstellung der Konstruktion von Triangulierungen. Durch Illustrationen und verständlichere Erklärungen wird nun ein noch tieferes und intuitiveres Verständnis der Materie ermöglicht.
Zu jedem Kapitel finden sich sorgfältig ausgewählte Übungsaufgaben, die das Gelernte vertiefen und anwenden lassen. Die meisten Aufgaben sind mit ausführlichen Lösungshinweisen versehen, die helfen, die Konzepte selbstständig zu meistern und das Wissen zu festigen.
- Anschauliche Einführung in die Differentialgeometrie anhand von Kurven und Flächen.
- Theoretische Zusammenhänge werden mittels zahlreicher Beispiele verständlich erklärt.
- Zu jedem Themenbereich ausgewählte Aufgaben mit sehr guten Lösungshinweisen.
2024 | Inference-Oriented Balanced Truncation for Quadratic Dynamical Systems: Formulation for Bayesian Smoothing and Model Stability Analysis | Melina A. Freitag, Josie König, Elizabeth Qian
Zeitschrift: Proceedings in Applied Mathematics and Mechanics
Verlag: Wiley
Seiten: e202400051
Link zur Publikation
Inference-Oriented Balanced Truncation for Quadratic Dynamical Systems: Formulation for Bayesian Smoothing and Model Stability Analysis
Autoren: Melina A. Freitag, Josie König, Elizabeth Qian
(2024)
The posterior distribution for nonlinear Bayesian inverse problems often has to be estimated via sampling and requires many simulations of the forward model, which can be computationally expensive when the forward model requires simulating a high-dimensional dynamical system. This can be remedied by using a reduced forward model that captures the important dynamics of the high-dimensional dynamical system. In systems theory, balanced truncation methods obtain efficient reduced models by projecting the high-dimensional model operators onto the space spanned by dominant eigenvectors of the system Gramians. In this paper, we consider Bayesian smoothing problems for quadratic dynamical systems and introduce inference-oriented Gramians that define a procedure for model reduction by balanced truncation. We provide a stability analysis of the resulting quadratic nonlinear model and support the analysis with a numerical example.
Zeitschrift:
Proceedings in Applied Mathematics and Mechanics
2024 | The RQR algorithm | Daan Camps, Thomas Mach, Raf Vandebril, David S. Watkins
Zeitschrift: arXiv
Seiten: arXiv:2411.17671
Link zur Publikation
,
Link zum Preprint
The RQR algorithm
Autoren: Daan Camps, Thomas Mach, Raf Vandebril, David S. Watkins
(2024)
Pole-swapping algorithms, generalizations of bulge-chasing algorithms, have been shown to be a viable alternative to the bulge-chasing QZ algorithm for solving the generalized eigenvalue problem for a matrix pencil A - λB. It is natural to try to devise a pole-swapping algorithm that solves the standard eigenvalue problem for a single matrix A. This paper introduces such an algorithm and shows that it is competitive with Francis's bulge-chasing QR algorithm.
2024 | Cocoon microstructures through the lens of topological persistence | Vira Raichenko, Nikolai Rosenthal, Michaela Eder and Myfanwy E. Evans
Zeitschrift: Journal of The Royal Society Interface
Band: Vol. 21, No. 220
Link zur Publikation
Cocoon microstructures through the lens of topological persistence
Autoren: Vira Raichenko, Nikolai Rosenthal, Michaela Eder and Myfanwy E. Evans
(2024)
Biological materials display a wide array of functionality, often dictated by complicated microstructures. New geometric and topological strategies allow one to describe the microstructures in a precise and systematic way. This article describes the application of topological persistence and other geometric methods to the microstructural analysis of three-dimensional X-ray micro-computed tomography scans of the Bombyx mori silkworm cocoons. These methods allow conclusions to be drawn about pore space gradients, silk fibre thickness gradients and fibre alignment within the cocoon. The study demonstrates the applicability of these topological and geometric methods to quantify and characterize fibrous materials.
Zeitschrift:
Journal of The Royal Society Interface
2024 | Understanding Voriconazole Metabolism: A Middle‑Out Physiologically‑Based Pharmacokinetic Modelling Framework Integrating In Vitro and Clinical Insights | A. Saleh, J. Schulz, J.‑F. Schlender, L. B. S. Aulin, A.‑P. Konrad, F. Kluwe, G. Mikus, W. Huisinga, C. Kloft, R. Michelet
Zeitschrift: Clinical Pharmacokinetics
Link zur Publikation
Understanding Voriconazole Metabolism: A Middle‑Out Physiologically‑Based Pharmacokinetic Modelling Framework Integrating In Vitro and Clinical Insights
Autoren: A. Saleh, J. Schulz, J.‑F. Schlender, L. B. S. Aulin, A.‑P. Konrad, F. Kluwe, G. Mikus, W. Huisinga, C. Kloft, R. Michelet
(2024)
Zeitschrift:
Clinical Pharmacokinetics
2024 | A Hands-on Guide to AmoePy — a Python-Based Software Package to Analyze Cell Migration Data | T. Moldenhawer, D. Schindler, M. Holschneider, W. Huisinga, C. Beta
Reihe: Methods in Molecular Biology
Verlag: Springer Nature
Buchtitel: Cell Motility and Chemotaxis
Seiten: 159-184
Band: 2828
Link zur Publikation
A Hands-on Guide to AmoePy — a Python-Based Software Package to Analyze Cell Migration Data
Autoren: T. Moldenhawer, D. Schindler, M. Holschneider, W. Huisinga, C. Beta
(2024)
Reihe:
Methods in Molecular Biology
Buchtitel:
Cell Motility and Chemotaxis
2024 | Strong field behavior of Wang-Yau Quasi-local energy | Bowen Zhao, Lars Andersson, Shing-Tung Yau
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Strong field behavior of Wang-Yau Quasi-local energy
Autoren: Bowen Zhao, Lars Andersson, Shing-Tung Yau
(2024)
We look at the strong field behavior of the Wang-Yau quasi-local energy. In particular, we examine the limit of the Wang-Yau quasi-local energy as the defining spacelike 2-surface \(\Sigma\) approaches an apparent horizon from outside. Assuming that coordinate functions of the isometric embedding are bounded in \(W^{2,1} \)and mean curvature vector of the image surface remains spacelike, we find that the limit falls in two exclusive cases: 1) If the horizon cannot be isometrically embedded into \(R^3 \) , the Wang-Yau quasi-local energy blows up as \(\Sigma\) approaches the horizon while the optimal embedding equation is not solvable for \(\Sigma\) near the horizon; 2) If the horizon can be isometrically embedded into \(R^3 \), the optimal embedding equation is solvable up to the horizon with the unique solution at the horizon corresponding to isometric embedding into \(R^3 \) and the Wang-Yau quasi-local mass admits a finite limit at the horizon. We discuss the implications of our results in the conclusion section.
2024 | Interacting Kerr-Newman Electromagnetic Fields | Sajad Aghapour, Lars Andersson, Kjell Rosquist, Tomasz Smołka
Zeitschrift: Physical Review D
Seiten: 104053
Band: 110
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,
Link zum Preprint
Interacting Kerr-Newman Electromagnetic Fields
Autoren: Sajad Aghapour, Lars Andersson, Kjell Rosquist, Tomasz Smołka
(2024)
In this paper, we study some of the properties of the G→0 limit of the Kerr-Newman solution of Einstein-Maxwell equations. Noting Carter's observation of the near equality between the g=2 gyromagnetic ratio in the Kerr-Newman solution and that of the electron, we discuss additional such coincidences relating to the Kerr-Newman multipoles and properties of the electron. In contrast to the Coulomb field, this spinning Maxwell field has a finite Lagrangian. Moreover, by evaluating the Lagrangian for the superposition of two such Kerr-Newman electromagnetic fields on a flat background, we are able to find their interaction potential. This yields a correction to the Coulomb interaction due to the spin of the field.
Zeitschrift:
Physical Review D
2024 | Cell topology during coarsening of simulated three-dimensional dry liquid foams | Ihab Sabik, Frank H. Lutz and Myfanwy E. Evans
Zeitschrift: Soft Matter
Band: Vol. 20, No. 33
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Cell topology during coarsening of simulated three-dimensional dry liquid foams
Autoren: Ihab Sabik, Frank H. Lutz and Myfanwy E. Evans
(2024)
Cell topology provides a deep insight into the structure of dry liquid foams. This paper analyses the cell topology of simulated 3-dimensional monodisperse dry liquid foams through the process of coarsening, where gas slowly diffuses through the cell interfaces. The coarsened foams are polydisperse, yet show a difference in cell types to annealed, low energy foams of comparable polydispersity. These two types of foams are analysed using average face degree of the cells and a measure of combinatorial roundedness, a new concept from combinatorial topology. We see that the spectrum of cell types changes drastically through the evolution of the foam via coarsening, from cells with a face degree between 12 and 14, with many 4-, 5-, and 6-side faces, to a combination of very large cells with many faces alongside a high frequency of tetrahedra and other cells with low face degree. These results demonstrate the insight that topological methods can give into foams and other complex structures.
2024 | Anchored heat kernel upper bounds on graphs with unbounded geometry and anti-trees | Keller, Matthias; Rose, Christian
Zeitschrift: Calculus of Variations and Partial Differential Equations
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,
Link zum Preprint
Anchored heat kernel upper bounds on graphs with unbounded geometry and anti-trees
Autoren: Keller, Matthias; Rose, Christian
(2024)
Zeitschrift:
Calculus of Variations and Partial Differential Equations
2024 | Rigidity results for initial data sets satisfying the dominant energy condition | Christian Bär, Simon Brendle, Tsz-Kiu Aaron Chow, Bernhard Hanke
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Rigidity results for initial data sets satisfying the dominant energy condition
Autoren: Christian Bär, Simon Brendle, Tsz-Kiu Aaron Chow, Bernhard Hanke
(2024)
Our work proves rigidity theorems for initial data sets associated with compact smooth spin manifolds with boundary and with compact convex polytopes, subject to the dominant energy condition. For manifolds with smooth boundary, this is based on the solution of a boundary value problem for Dirac operators. For convex polytopes we use approximations by manifolds with smooth boundary.
2024 | Novel mathematical approach to accurately quantify 3D endothelial cell morphology and vessel geometry based on fluorescently marked endothelial cell contours: Application to the dorsal aorta of wild-type and Endoglin-deficient zebrafish embryos | D. Seeler, N. Grdseloff, C. J. Rödel, C. Kloft, S. Abdelilah-Seyfried, W. Huisinga
Zeitschrift: PLoS Computational Biology
Link zur Publikation
Novel mathematical approach to accurately quantify 3D endothelial cell morphology and vessel geometry based on fluorescently marked endothelial cell contours: Application to the dorsal aorta of wild-type and Endoglin-deficient zebrafish embryos
Autoren: D. Seeler, N. Grdseloff, C. J. Rödel, C. Kloft, S. Abdelilah-Seyfried, W. Huisinga
(2024)
Zeitschrift:
PLoS Computational Biology
2024 | Calcium kinetic rates in Caucasian males and females from birth to adulthood | N. Hartung, S. A. Abrams, W. Huisinga, K. Weisser
Zeitschrift: Bone
Link zur Publikation
Calcium kinetic rates in Caucasian males and females from birth to adulthood
Autoren: N. Hartung, S. A. Abrams, W. Huisinga, K. Weisser
(2024)
2024 | Linear repetitivity beyond abelian groups | Siegfried Beckus, Tobias Hartnick, Felix Pogorzelski
Zeitschrift: to appear in Ergodic Theory Dynam. Systems
Link zur Publikation
,
Link zum Preprint
Linear repetitivity beyond abelian groups
Autoren: Siegfried Beckus, Tobias Hartnick, Felix Pogorzelski
(2024)
We show that linearly repetitive weighted Delone sets in groups of polynomial growth have a uniquely ergodic hull. This result applies in particular to the linearly repetitive weighted Delone sets in homogeneous Lie groups constructed in the companion paper arXiv:2109.15210 using symbolic substitution methods. More generally, using the quasi-tiling method of Ornstein-Weiss, we establish unique ergodicity of hulls of weighted Delone sets in amenable unimodular lcsc groups under a new repetitivity condition which we call tempered repetitivity. For this purpose, we establish a general sub-additive convergence theorem, which also has applications concerning the existence of Banach densities and uniform approximation of the spectral distribution function of finite hopping range operators on Cayley graphs.
Zeitschrift:
to appear in Ergodic Theory Dynam. Systems
2024 | Dirac eigenvalues and the hyperspherical radius | Christian Bär
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Dirac eigenvalues and the hyperspherical radius
Autoren: Christian Bär
(2024)
For closed connected Riemannian spin manifolds an upper estimate of the smallest eigenvalue of the Dirac operator in terms of the hyperspherical radius is proved. When combined with known lower Dirac eigenvalue estimates, this has a number of geometric consequences. Some are known and include Llarull's scalar curvature rigidity of the standard metric on the sphere, Geroch's conjecture on the impossibility of positive scalar curvature on tori and a mean curvature estimate for spin fill-ins with nonnegative scalar curvature due to Gromov, including its rigidity statement recently proved by Cecchini, Hirsch and Zeidler. New applications provide a comparison of the hyperspherical radius with the Yamabe constant and improved estimates of the hyperspherical radius for Kähler manifolds, Kähler-Einstein manifolds, quaternionic Kähler manifolds and manifolds with a harmonic 1-form of constant length.
2024 | Robust self-assembly of nonconvex shapes in two dimensions | Lukas Mayrhofer, Myfanwy E. Evans, and Gero Friesecke
Zeitschrift: Phys. Rev. E
Band: Vol. 110, No. 1
Link zur Publikation
Robust self-assembly of nonconvex shapes in two dimensions
Autoren: Lukas Mayrhofer, Myfanwy E. Evans, and Gero Friesecke
(2024)
We present fast simulation methods for the self-assembly of complex shapes in two dimensions. The shapes are modeled via a general boundary curve and interact via a standard volume term promoting overlap and an interpenetration penalty. To efficiently realize the Gibbs measure on the space of possible configurations we employ the hybrid Monte Carlo algorithm together with a careful use of signed distance functions for energy evaluation. Motivated by the self-assembly of identical coat proteins of the tobacco mosaic virus which assemble into a helical shell, we design a nonconvex two-dimensional model shape and demonstrate its robust self-assembly into a unique final state. Our numerical experiments reveal certain essential prerequisites for this self-assembly process: blocking and matching (i.e., local repulsion and attraction) of different parts of the boundary, and nonconvexity and handedness of the shape.
Zeitschrift:
Phys. Rev. E
2024 | Nonintrusive model order reduction for stochastic differential equations | M. A. Freitag, J. M. Nicolaus, M. Redmann
Zeitschrift: arXiv
Link zum Preprint
Nonintrusive model order reduction for stochastic differential equations
Autoren: M. A. Freitag, J. M. Nicolaus, M. Redmann
(2024)
A non-intrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional systems. The drift and diffusion coefficients of the ROM are inferred from state observations by solving appropriate least-squares problems. The closeness of the ROM obtained by the presented approach to the intrusive ROM obtained by the proper orthogonal decomposition (POD) method is investigated. Two generalisations of the snapshot-based dominant subspace construction to the stochastic case are presented. Numerical experiments are provided to compare the developed approach to POD.
2024 | Model reduction for Ca2+-induced vesicle fusion dynamics | A. Ernst, U. Falkenhagen, S. Winkelmann
Zeitschrift: Proceedings in Applied Mathematics and Mechanics
Seiten: e202300184
Link zur Publikation
Model reduction for Ca2+-induced vesicle fusion dynamics
Autoren: A. Ernst, U. Falkenhagen, S. Winkelmann
(2024)
Zeitschrift:
Proceedings in Applied Mathematics and Mechanics
2024 | Leveraging QSP Models for MIPD: A Case Study for Warfarin/INR | U. Falkenhagen, L. H. Cavallari, J. D. Duarte, C. Kloft, S. Schmidt, W. Huisinga
Zeitschrift: Clinical Pharmacology & Therapeutics
Seiten: 795-806
Band: 116(3)
Link zur Publikation
,
Corrigendum
Leveraging QSP Models for MIPD: A Case Study for Warfarin/INR
Autoren: U. Falkenhagen, L. H. Cavallari, J. D. Duarte, C. Kloft, S. Schmidt, W. Huisinga
(2024)
Zeitschrift:
Clinical Pharmacology & Therapeutics
2024 | Anisotropic examples of inflation-generating initial conditions for the big bang | Eric Ling, Annachiara Piubello
Link zum Preprint
Anisotropic examples of inflation-generating initial conditions for the big bang
Autoren: Eric Ling, Annachiara Piubello
(2024)
The inflationary scenario, which states that the early universe underwent a brief but dramatic period of accelerated spatial expansion, has become the current paradigm of early universe cosmology. Although inflationary cosmology has its many successes, it does not (as of yet) have the status of an established physical theory. In this paper, we provide mathematical support for the inflationary scenario in a class of anisotropic spacetimes by generalizing the work in [19]. These anisotropic spacetimes satisfy certain initial conditions so that they are perfectly isotropic at the big bang but become less isotropic as time progresses. The resulting inflationary eras are a consequence of the energy-momentum tensor being dominated by a cosmological constant at the big bang.
2024 | Exotic self-assembly of hard spheres in a morphometric solvent | Ivan Spirandelli, Rhoslyn Coles, Gero Friesecke, and Myfanwy E. Evans
Zeitschrift: PNAS
Band: Vol. 121, No. 15
Link zur Publikation
Exotic self-assembly of hard spheres in a morphometric solvent
Autoren: Ivan Spirandelli, Rhoslyn Coles, Gero Friesecke, and Myfanwy E. Evans
(2024)
The self-assembly of spheres into geometric structures, under various theoretical conditions, offers valuable insights into complex self-assembly processes in soft systems. Previous studies have utilized pair potentials between spheres to assemble maximum contact clusters in simulations and experiments. The morphometric approach to solvation free energy that we utilize here goes beyond pair potentials; it is a geometry-based theory that incorporates a weighted combination of geometric measures over the solvent accessible surface for solute configurations in a solvent. In this paper, we demonstrate that employing the morphometric model of solvation free energy in simulating the self-assembly of sphere clusters results, under most conditions, in the previously observed maximum contact clusters. Under other conditions, it unveils an assortment of extraordinary sphere configurations, such as double helices and rhombohedra. These exotic structures arise specifically under conditions where the interactions take multibody potentials into account. This investigation establishes a foundation for comprehending the diverse range of geometric forms in self-assembled structures, emphasizing the significance of the morphometric approach in this context.
2024 | Solution of Linear Ill-Posed Operator Equations by Modified Truncated Singular Value Expansion | L. Dykes, M. Kuian, T. Mach, S. Noschese, L. Reichel
Zeitschrift: Journal of Computational and Applied Mathematics
Seiten: 116621
Band: 467
Link zur Publikation
Solution of Linear Ill-Posed Operator Equations by Modified Truncated Singular Value Expansion
Autoren: L. Dykes, M. Kuian, T. Mach, S. Noschese, L. Reichel
(2024)
In much of the literature on the solution of linear ill-posed operator equations, the operator equation is discretized and regularization methods are developed for the discretized problem so obtained, without discussing the ramification of these methods for the infinite-dimensional problem. In particular, these regularization methods may only be applicable to certain linear ill-posed operator equations. This paper discusses how regularization by a modified truncated singular value decomposition introduced in [21] for finite-dimensional problems can be extended to operator equations. In finite dimensions, this regularization method yields approximate solutions of higher quality than standard truncated singular value decomposition. Our analysis in a Hilbert space setting is of practical interest, because the solution method presented avoids introduction of discretization errors during the solution process. We discuss how to construct such problems with Chebfun.
Zeitschrift:
Journal of Computational and Applied Mathematics
2024 | Optimal Sparse Energy Sampling for X-ray Spectro-Microscopy: Reducing the X-ray Dose and Experiment Time Using Model Order Reduction | P.D. Quinn, M.S. Landman, T. Davis, M.A. Freitag, S. Gazzola, S. Dolgov
Zeitschrift: Chem. Biomed. Imaging
Verlag: ACS Publications
Link zur Publikation
,
https://doi.org/10.1021/cbmi.3c00116
Optimal Sparse Energy Sampling for X-ray Spectro-Microscopy: Reducing the X-ray Dose and Experiment Time Using Model Order Reduction
Autoren: P.D. Quinn, M.S. Landman, T. Davis, M.A. Freitag, S. Gazzola, S. Dolgov
(2024)
The application of X-ray spectro-microscopy to image changes in the chemical state in application areas such as catalysis, environmental science, or biological samples can be limited by factors such as the speed of measurement, the presence of dilute concentrations, radiation damage, and thermal drift during the measurement. We have adapted a reduced-order model approach, known as the discrete empirical interpolation method, which identifies how to optimally subsample the spectroscopic information, accounting for background variations in the signal, to provide an accurate approximation of an equivalent full spectroscopic measurement from the sampled material. This approach uses readily available prior information to guide and significantly reduce the sampling requirements impacting both the total X-ray dose and the acquisition time. The reduced-order model approach can be adapted more broadly to any spectral or spectro-microscopy measurement where a low-rank approximation can be made from prior information on the possible states of a system, and examples of the approach are presented.
Zeitschrift:
Chem. Biomed. Imaging
2024 | Low-rank solutions to the stochastic Helmholtz equation | A. Kaya, M.A. Freitag
Zeitschrift: Journal of Computational and Applied Mathematics
Seiten: In Press
Link zur Publikation
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Link zum Preprint
Low-rank solutions to the stochastic Helmholtz equation
Autoren: A. Kaya, M.A. Freitag
(2024)
In this paper, we consider low-rank approximations for the solutions to the stochastic Helmholtz equation with random coefficients. A Stochastic Galerkin finite element method is used for the discretization of the Helmholtz problem. Existence theory for the low-rank approximation is established when the system matrix is indefinite. The low-rank algorithm does not require the construction of a large system matrix which results in an advantage in terms of CPU time and storage. Numerical results show that, when the operations in a low-rank method are performed efficiently, it is possible to obtain an advantage in terms of storage and CPU time compared to computations in full rank. We also propose a general approach to implement a preconditioner using the low-rank format efficiently.
Zeitschrift:
Journal of Computational and Applied Mathematics
2024 | Diagrammatic representations of 3-periodic entanglements | Toky Andriamanalina, Myfanwy E. Evans, Sonia Mahmoudi
Link zum Preprint
Diagrammatic representations of 3-periodic entanglements
Autoren: Toky Andriamanalina, Myfanwy E. Evans, Sonia Mahmoudi
(2024)
Diagrams enable the use of various algebraic and geometric tools in analysing and classifying knots. In this paper we introduce a new diagrammatic representation of triply periodic entangled structures, which are embeddings of simple curves in R3 that are invariant under translations along three non-coplanar axes. These diagrams require an extended set of new moves in addition to the Reidemeister moves, which we show to preserve ambient isotopies of triply periodic entangled structures. We use the diagrams to define the crossing number and the unknotting number of the triply periodic entanglements, demonstrating the practicality of the diagrammatic representation.
2024 | Local index theory for the Rarita-Schwinger operator | Alberto Richtsfeld
Link zum Preprint
Local index theory for the Rarita-Schwinger operator
Autoren: Alberto Richtsfeld
(2024)
We prove the local index theorem for the Rarita-Schwinger operator and higher Dirac operators using Gilkey's invariance theory. That is, we show that the supertrace of the heat kernel of a given geometric operator converges as time goes to zero, and identifies the limit as the Chern-Weil form of the Atiyah-Singer integrand.
2024 | First-order elliptic boundary value problems on manifolds with non-compact boundary | Christian Bär und Lashi Bandara
Link zum Preprint
First-order elliptic boundary value problems on manifolds with non-compact boundary
Autoren: Christian Bär und Lashi Bandara
(2024)
We consider first-order elliptic differential operators acting on vector bundles over smooth manifolds with smooth boundary, which is permitted to be noncompact. Under very mild assumptions, we obtain a regularity theory for sections in the maximal domain. Under additional geometric assumptions, and assumptions on an adapted boundary operator, we obtain a trace theorem on the maximal domain. This allows us to systematically study both local and nonlocal boundary conditions. In particular, the Atiyah-Patodi-Singer boundary condition occurs as a special case. Furthermore, we study contexts which induce semi-Fredholm and Fredholm extensions.
2024 | A Generalization of Lévy's Theorem on Transition Matrices | Moritz Gerlach
Zeitschrift: submitted
Link zum Preprint
A Generalization of Lévy's Theorem on Transition Matrices
Autoren: Moritz Gerlach
(2024)
We generalize a fundamental theorem on transition matrices stating that each component is either strictly positive for all times or identically zero ("Lévy's Theorem"). Our proof of this fact that does not require the matrices to be Markovian nor to be continuous at time zero. We also provide a formulation of this theorem in the terminology of one-parameter operator semigroups.
2024 | Boundary Value Problems for Dirac Operators on Graphs | Alberto Richtsfeld
Zeitschrift: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Seiten: 23
Band: 20
Link zur Publikation
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Link zum Preprint
Boundary Value Problems for Dirac Operators on Graphs
Autoren: Alberto Richtsfeld
(2024)
We carry the index theory for manifolds with boundary of Bär and Ballmann over to first order differential operators on metric graphs. This results in an elegant proof for the index of such operators. Then the self-adjoint extensions and the spectrum of the Dirac operator on the complex line bundle are studied. We also introduce two types of boundary conditions for the Dirac operator, whose spectrum encodes information of the underlying topology of the graph.
Zeitschrift:
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
2024 | K-cowaist of manifolds with boundary | Christian Bär, Bernhard Hanke
Zeitschrift: Comptes Rendus Mathématique
Seiten: 1349-1356
Band: 362
Link zur Publikation
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Link zum Preprint
K-cowaist of manifolds with boundary
Autoren: Christian Bär, Bernhard Hanke
(2024)
We extend the K-cowaist inequality to generalized Dirac operators in the sense of Gromov and Lawson and study applications to manifolds with boundary.
Zeitschrift:
Comptes Rendus Mathématique
2024 | Scalar curvature rigidity of warped product metrics | Christian Bär, Simon Brendle, Bernhard Hanke, Yipeng Wang
Zeitschrift: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Seiten: article 035, 26 pages
Band: 20
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Link zum Preprint
Scalar curvature rigidity of warped product metrics
Autoren: Christian Bär, Simon Brendle, Bernhard Hanke, Yipeng Wang
(2024)
We show scalar-mean curvature rigidity of warped products of round spheres of dimension at least 2 over compact intervals equipped with strictly log-concave warping functions. This generalizes earlier results of Cecchini-Zeidler to all dimensions.
Moreover, we show scalar curvature rigidity of round spheres of dimension at least 3 minus two antipodal points, thus resolving a problem in Gromov's ``Four Lectures'' in all dimensions.
Our arguments are based on spin geometry.
Zeitschrift:
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Seiten:
article 035, 26 pages
2024 | Diffusion dynamics for an infinite system of two-type spheres and the associated depletion effect | M. Fradon, J. Kern, S. Roelly, A. Zass
Zeitschrift: Stochastic Processes and Applications
Band: 171
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Link zum Preprint
Diffusion dynamics for an infinite system of two-type spheres and the associated depletion effect
Autoren: M. Fradon, J. Kern, S. Roelly, A. Zass
(2024)
We consider a random diffusion dynamics for an infinite system of hard spheres of two different sizes evolving in Rd, its reversible probability measure, and its projection on the subset of the large spheres. The main feature is the occurrence of an attractive short-range dynamical interaction – known in the physics literature as a depletion interaction – between the large spheres, which is induced by the hidden presence of the small ones. By
considering the asymptotic limit for such a system when the density of the particles is high, we also obtain a constructive dynamical approach to the famous discrete geometry problem of maximisation of the contact number of n identical spheres in Rd. As support material, we propose numerical simulations in the form of movies.
Zeitschrift:
Stochastic Processes and Applications
2024 | Robust geometric modeling of 3-periodic tensegrity frameworks using Riemannian optimization | Matthias Himmelmann und Myfanwy E. Evans
Zeitschrift: SIAM Journal on Applied Algebra and Geometry
Band: Vol. 8, No. 2
Link zur Publikation
Robust geometric modeling of 3-periodic tensegrity frameworks using Riemannian optimization
Autoren: Matthias Himmelmann und Myfanwy E. Evans
(2024)
Framework materials composed of rigid bars and joints and their deformations provide a compelling relation between materials science and algebraic geometry. Physical distance constraints within the material transform into quadratic polynomial constraints via the Euclidean distance between two points, enabling associated numerical strategies for finding feasible configurations and deformation pathways. When adding elastic elements, the resulting material is called a tensegrity framework and can be used to model curvilinear cylinder packings. In this paper, we build the necessary geometric formulations to robustly transform rod packings to tensegrity frameworks, leading to a nonlinear optimization problem with polynomial constraints. Since the constraints are smooth almost everywhere, techniques from Riemannian optimization become admissible, allowing us to provide numerical strategies for exploring the deformative behavior of two exemplary 3-periodic cylinder packings. As a result of this investigation, we are able to show that the structures are auxetic by multiple definitions, intuitively meaning that when expanded in a fixed direction, these materials also expand in their lateral directions.
Zeitschrift:
SIAM Journal on Applied Algebra and Geometry
2024 | Index analysis: an approach to understand signal transduction with application to the EGFR signalling pathway | J. Knöchel, C. Kloft, W. Huisinga
Zeitschrift: PLoS Computational Biology
Link zur Publikation
,
Link zum Preprint
Index analysis: an approach to understand signal transduction with application to the EGFR signalling pathway
Autoren: J. Knöchel, C. Kloft, W. Huisinga
(2024)
Zeitschrift:
PLoS Computational Biology
2024 | Three-component contour dynamics model to simulate and analyze amoeboid cell motility in two dimensions | D. Schindler, T. Moldenhawer, C. Beta, W. Huisinga, M. Holschneider
Zeitschrift: PLoS One
Link zur Publikation
,
Link zum Preprint
Three-component contour dynamics model to simulate and analyze amoeboid cell motility in two dimensions
Autoren: D. Schindler, T. Moldenhawer, C. Beta, W. Huisinga, M. Holschneider
(2024)
2024 | On Characteristics of the Range of Kernel Operators | Moritz Gerlach, Jochen Glück
Zeitschrift: Proceedings of the American Mathematical Society
Seiten: 677-690
Band: 152(2)
Link zur Publikation
,
Link zum Preprint
On Characteristics of the Range of Kernel Operators
Autoren: Moritz Gerlach, Jochen Glück
(2024)
We show that a positive operator between L^p-spaces is given by integration against a kernel function if and only if the image of each positive function has a lower semi-continuous representative with respect to a suitable topology. This is a consequence of a new characterization of (abstract) kernel operators on general Banach lattices as those operators whose range can be represented over a fixed countable set of positive vectors. Similar results are shown to hold for operators that merely dominate a non-trivial kernel operator.
Zeitschrift:
Proceedings of the American Mathematical Society
2024 | On microlocalization and the construction of Feynman propagators for normally hyperbolic operators | Onirban Islam, Alexander Strohmaier
Zeitschrift: Communications in Analysis and Geometry
Seiten: 1811-1883
Band: 32 (7)
Link zur Publikation
,
Link zum Preprint
On microlocalization and the construction of Feynman propagators for normally hyperbolic operators
Autoren: Onirban Islam, Alexander Strohmaier
(2024)
This article reviews the microlocal construction of Feynman propagators for normally hyperbolic operators acting on vector bundles over globally hyperbolic spacetimes and its consequences. It is shown that for normally hyperbolic operators that are selfadjoint with respect to a hermitian bundle metric, the Feynman propagators can be constructed to satisfy a positivity property that reflects the existence of Hadamard states in quantum field theory on curved spacetimes. We also give a more direct construction of the Feynman propagator for the Dirac operator on a globally hyperbolic spacetime. Even though the natural bundle metric on spinors is not positive-definite, in this case we can give a direct microlocal construction of a Feynman propagator that satisfies positivity.
Zeitschrift:
Communications in Analysis and Geometry
2024 | Gravitational Instantons and special geometry | Steffen Aksteiner, Lars Andersson
Zeitschrift: J. Differential Geom.
Seiten: 928-958
Band: 128 (3)
Link zur Publikation
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Gravitational Instantons and special geometry
Autoren: Steffen Aksteiner, Lars Andersson
(2024)
The Chen–Teo gravitational instanton is an asymptotically flat, toric, Ricci-flat family of metrics on CP2∖S1, that provides a counter-example to the classical Euclidean Black Hole Uniqueness conjecture. In this paper we show that the Chen–Teo instanton is Hermitian and non-Kähler. It follows that all known examples of gravitational instantons are Hermitian.
Zeitschrift:
J. Differential Geom.
2024 | Local Index Theory for Lorentzian Manifolds | Christian Bär and Alexander Strohmaier
Zeitschrift: Annales scientifiques de l'École normale supérieure
Seiten: 1693-1752
Band: 57
Link zur Publikation
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Link zum Preprint
Local Index Theory for Lorentzian Manifolds
Autoren: Christian Bär and Alexander Strohmaier
(2024)
We prove a local version of the index theorem for Lorentzian Dirac-type operators on globally hyperbolic Lorentzian manifolds with Cauchy boundary. In case the Cauchy hypersurface is compact we do not assume self-adjointness of the Dirac operator on the spacetime or the associated elliptic Dirac operator on the boundary. In this case integration of our local index theorem results in a generalization of previously known index theorems for globally hyperbolic spacetimes that allows for twisting bundles associated with non-compact gauge groups.
Zeitschrift:
Annales scientifiques de l'École normale supérieure
2023 | Optimal Hardy weights on the Euclidean lattice | Keller, Matthias; Lemm, Marius
Zeitschrift: Trans. Amer. Math. Soc.
Link zur Publikation
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Link zum Preprint
Optimal Hardy weights on the Euclidean lattice
Autoren: Keller, Matthias; Lemm, Marius
(2023)
Zeitschrift:
Trans. Amer. Math. Soc.
2023 | An improved discrete p-Hardy inequality | Fischer, Florian; Keller, Matthias; Pogorzelski, Felix
Zeitschrift: Integral Equations Operator Theory
Link zur Publikation
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Link zum Preprint
An improved discrete p-Hardy inequality
Autoren: Fischer, Florian; Keller, Matthias; Pogorzelski, Felix
(2023)
Zeitschrift:
Integral Equations Operator Theory
2023 | Sobolev-type inequalities and eigenvalue growth on graphs with finite measure | Hua, Bobo; Keller, Matthias; Schwarz, Michael; Wirth, Melchior
Zeitschrift: Proc. Amer. Math. Soc.
Link zur Publikation
,
Link zum Preprint
Sobolev-type inequalities and eigenvalue growth on graphs with finite measure
Autoren: Hua, Bobo; Keller, Matthias; Schwarz, Michael; Wirth, Melchior
(2023)
Zeitschrift:
Proc. Amer. Math. Soc.
2023 | Optimal Hardy inequality for fractional Laplacians on the integers | Keller, Matthias; Nietschmann, Marius
Zeitschrift: Annales Henri Poincaré
Link zur Publikation
,
Link zum Preprint
Optimal Hardy inequality for fractional Laplacians on the integers
Autoren: Keller, Matthias; Nietschmann, Marius
(2023)
Zeitschrift:
Annales Henri Poincaré
2023 | MFO Report: The dry ten Martini problem for Sturmian dynamical systems | Ram Band, Siegfried Beckus, Raphael Loewy
Zeitschrift: Oberwolfach Reports - OWR
Link zum Preprint
MFO Report: The dry ten Martini problem for Sturmian dynamical systems
Autoren: Ram Band, Siegfried Beckus, Raphael Loewy
(2023)
This extended Oberwolfach report (to appear in the proceedings of the MFO Workshop 2335: Aspects of Aperiodic Order) announces the full solution to the Dry Ten Martini Problem for Sturmian Hamiltonians. Specifically, we show that all spectral gaps of Sturmian Hamiltonians (as predicted by the gap labeling theorem) are open for all nonzero couplings and all irrational rotations. We present here the proof strategy.
Zeitschrift:
Oberwolfach Reports - OWR
2023 | Towards Model-Informed Precision Dosing of Voriconazole: Challenging Published Voriconazole Nonlinear Mixed-Effects Models with Real-World Clinical Data | F. Kluwe. R. Michelet, W. Huisinga, M. Zeitlinger, G. Mikus, C. Kloft
Zeitschrift: Clinical Pharmacokinetics
Link zur Publikation
Towards Model-Informed Precision Dosing of Voriconazole: Challenging Published Voriconazole Nonlinear Mixed-Effects Models with Real-World Clinical Data
Autoren: F. Kluwe. R. Michelet, W. Huisinga, M. Zeitlinger, G. Mikus, C. Kloft
(2023)
Zeitschrift:
Clinical Pharmacokinetics
2023 | Efficient training of Gaussian processes with tensor product structure | Josie König, Max Pfeffer, Martin Stoll
Zeitschrift: arXiv
Seiten: arXiv:2312.15305
Link zum Preprint
Efficient training of Gaussian processes with tensor product structure
Autoren: Josie König, Max Pfeffer, Martin Stoll
(2023)
To determine the optimal set of hyperparameters of a Gaussian process based on a large number of training data, both a linear system and a trace estimation problem must be solved. In this paper, we focus on establishing numerical methods for the case where the covariance matrix is given as the sum of possibly multiple Kronecker products, i.e., can be identified as a tensor. As such, we will represent this operator and the training data in the tensor train format. Based on the AMEn method and Krylov subspace methods, we derive an efficient scheme for computing the matrix functions required for evaluating the gradient and the objective function in hyperparameter optimization.
2023 | Properties of quasilocal mass in binary black hole mergers | Daniel Pook-Kolb, Bowen Zhao, Lars Andersson, Badri Krishnan, and Shing-Tung Yau
Zeitschrift: Phys. Rev. D
Seiten: 124031
Band: 108
Link zur Publikation
,
Link zum Preprint
Properties of quasilocal mass in binary black hole mergers
Autoren: Daniel Pook-Kolb, Bowen Zhao, Lars Andersson, Badri Krishnan, and Shing-Tung Yau
(2023)
Identifying a general quasilocal notion of energy-momentum and angular momentum would be an important advance in general relativity with potentially important consequences for mathematical and astrophysical studies in general relativity. In this paper, we study a promising approach to this problem first proposed by Wang and Yau in 2009 based on isometric embeddings of closed surfaces in Minkowski space. We study the properties of the Wang-Yau quasilocal mass in high-accuracy numerical simulations of the head-on collisions of two nonspinning black holes within full general relativity. We discuss the behavior of the Wang-Yau quasilocal mass on constant expansion surfaces, and we compare its behavior with the irreducible mass. We investigate the time evolution of the Wang-Yau quasilocal mass in numerical examples. In addition, we discuss mathematical subtleties in defining the Wang-Yau mass for marginally trapped surfaces.
Zeitschrift:
Phys. Rev. D
2023 | C-Reactive Protein as an Early Predictor of Efficacy in Advanced Non-Small-Cell Lung Cancer Patients: A Tumor Dynamics-Biomarker Modeling Framework | Y. M. Nassar, F. W. Ojara, A. Pérez-Pitarch, K. Geiger, W. Huisinga, N. Hartung, R. Michelet, S. Holdenrieder, M. Joerger, C. Kloft
Zeitschrift: Cancers
Seiten: 5429
Band: 15(22)
Link zur Publikation
C-Reactive Protein as an Early Predictor of Efficacy in Advanced Non-Small-Cell Lung Cancer Patients: A Tumor Dynamics-Biomarker Modeling Framework
Autoren: Y. M. Nassar, F. W. Ojara, A. Pérez-Pitarch, K. Geiger, W. Huisinga, N. Hartung, R. Michelet, S. Holdenrieder, M. Joerger, C. Kloft
(2023)
2023 | Sample-based robust model reduction for non-linear systems biology models | U. Falkenhagen, C. Himpe, J. Knöchel, C. Kloft, W. Huisinga
Zeitschrift: Proceedings in Applied Mathematics & Mechanics
Link zur Publikation
Sample-based robust model reduction for non-linear systems biology models
Autoren: U. Falkenhagen, C. Himpe, J. Knöchel, C. Kloft, W. Huisinga
(2023)
Zeitschrift:
Proceedings in Applied Mathematics & Mechanics
2023 | Übungsbuch zur Stochastik: Aufgaben und Lösungen. Grundlegende Konzepte und Anwendungen | T. Ehlen, A. Flöge, F. Göbel, P. Keller, S. Rœlly
Verlag: Universitätsverlag Potsdam, Hrsg.: P. Keller, S. Roelly
Seiten: 1-306
Link zur Publikation
Übungsbuch zur Stochastik: Aufgaben und Lösungen. Grundlegende Konzepte und Anwendungen
Autoren: T. Ehlen, A. Flöge, F. Göbel, P. Keller, S. Rœlly
(2023)
Dieses Buch stellt Übungen zu den Grundbegriffen und Grundsätzen der Stochastik und ihre Lösungen zur Verfügung.
So wie man Tonleitern in der Musik trainiert, so berechnet man Übungsaufgaben in der Mathematik. In diesem Sinne soll dieses Übungsbuch vor allem als Vorlage dienen für das eigenständige, eigenverantwortliche Lernen und Üben.
Die Schönheit und Einzigartigkeit der Wahrscheinlichkeitstheorie besteht darin, dass sie eine Vielzahl von realen Phänomenen modellieren kann. Daher findet man hier Aufgaben mit Verbindungen zur Geometrie, zu Glücksspielen, zur Versicherungsmathematik, zur Demographie und vielen anderen Themen.
Die Zeichnerin Gisela Gurr hat einige Aufgaben des Buches mit Illustrationen bereichert.
Verlag:
Universitätsverlag Potsdam, Hrsg.: P. Keller, S. Roelly
2023 | Sparse grid based Chebyshev HOPGD for parameterized linear systems | S. Correnty, M.A. Freitag, and K. Soodhalter
Zeitschrift: arXiv
Reihe: 2309.14178
Link zum Preprint
Sparse grid based Chebyshev HOPGD for parameterized linear systems
Autoren: S. Correnty, M.A. Freitag, and K. Soodhalter
(2023)
2023 | Extracting Hadamard Coefficients from Green's Operators | Lennart Ronge
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Extracting Hadamard Coefficients from Green's Operators
Autoren: Lennart Ronge
(2023)
We develop a formula for the diagonal values of the Hadamard coefficients associated to a normally hyperbolic operator on a globally hyperbolic spacetime in terms of the advanced and retarded Green's operators. We develop a local formula as well as formulae for integrals over (parts of) the diagonal. Furthermore, we develop analogues of the Hadamard expansion for powers of the advanced/retarded Green's operators and an analogue of a resolvent.
2023 | Hadamard expansions for powers of causal Green’s operators and “resolvents” | Lennart Ronge
Zeitschrift: Annals of Global Analysis and Geometry
Verlag: Springer
Band: 64
Link zur Publikation
,
Link zum Preprint
Hadamard expansions for powers of causal Green’s operators and “resolvents”
Autoren: Lennart Ronge
(2023)
The Hadamard expansion describes the singularity structure of Green’s operators associated with a normally hyperbolic operator P in terms of Riesz distributions (fundamental solutions on Minkowski space, transported to the manifold via the exponential map) and Hadamard coefficients (smooth sections in two variables, corresponding to the heat Kernel coefficients in the Riemannian case). In this paper, we derive an asymptotic expansion analogous to the Hadamard expansion for powers of advanced/retarded Green’s operators associated with P, as well as expansions for advanced/retarded Green’s operators associated with P−z for z∈C. These expansions involve the same Hadamard coefficients as the original Hadamard expansion, as well as the same or analogous (with built-in z-dependence) Riesz distributions.
Zeitschrift:
Annals of Global Analysis and Geometry
2023 | Model order reduction methods applied to neural network training | M.A. Freitag, J.M. Nicolaus, M. Redmann
Zeitschrift: Proceedings in Applied Mathematics and Mechanics
Seiten: e202300078
Link zur Publikation
Model order reduction methods applied to neural network training
Autoren: M.A. Freitag, J.M. Nicolaus, M. Redmann
(2023)
Neural networks have emerged as powerful and versatile tools in the field of deep learning. As the complexity of the task increases, so do size and architectural complexity of the causing compression techniques to become a focus of current research. Parameter truncation can provide a significant reduction in memory and computational complexity. Originating from a model order reduction framework, the Discrete Empirical Interpolation Method is applied to the gradient descent training of neural networks and analyze for important parameters. The approach for various state-of-the-art neural networks is compared to established truncation methods. Further metrics like L2 and Cross-Entropy Loss, as well as accuracy and compression rate are reported.
Zeitschrift:
Proceedings in Applied Mathematics and Mechanics
2023 | Time-limited Balanced Truncation within Incremental Four-Dimensional Variational Data Assimilation | J. König, M.A. Freitag
Zeitschrift: Proceedings in Applied Mathematics and Mechanics
Seiten: e202300019
Link zur Publikation
Time-limited Balanced Truncation within Incremental Four-Dimensional Variational Data Assimilation
Autoren: J. König, M.A. Freitag
(2023)
Four-dimensional variational data assimilation (4D-Var) is a data assimilation method often used in weather forecasting. Based on a numerical model and observations of a system, it predicts the system state beyond the last time of measurement. This requires the minimisation of a functional. At each step of the optimisation algorithm, a full nonlinear model evaluation and its adjoint is required. This quickly becomes very costly, especially in high dimensions. For this reason, a surrogate model is needed that approximates the full model well, but requires significantly less computational effort. In this paper, we propose time-limited balanced truncation to build such a reduced-order model. Our approach is able to deal with unstable system matrices. We demonstrate its performance in experiments and compare it with α-bounded balanced truncation, which is an another reduction approach for unstable systems.
Zeitschrift:
Proceedings in Applied Mathematics and Mechanics
2023 | Can one hear the depth of the water? | M.A. Freitag, P.Kriz, T. Mach, J. M. Nicolaus
Zeitschrift: Proceedings in Applied Mathematics and Mechanics
Seiten: e202300122
Link zur Publikation
Can one hear the depth of the water?
Autoren: M.A. Freitag, P.Kriz, T. Mach, J. M. Nicolaus
(2023)
We discuss discrete-time dynamical systems depending on a parameter μ. Assuming that the system matrix A(μ) is given, but the parameter μ is unknown, we infer the most-likely parameter μm≈μ from an observed trajectory x of the dynamical system. We use parametric eigenpairs (vi(μ),lambdai(μ) of the system matrix A(μ) computed with Newton's method based on a Chebyshev expansion. We then represent x in the eigenvector basis defined by the vi(μ) and compare the decay of the components with predictions based on the lambdai(μ). The resulting estimates for μ are combined using a kernel density estimator to find the most likely value for μm and a corresponding uncertainty quantification.
Zeitschrift:
Proceedings in Applied Mathematics and Mechanics
2023 | Spin Hall effects in the sky | Lars Andersson, Marius A. Oancea
Zeitschrift: Class. Quantum Grav.
Seiten: 154002
Band: 40
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,
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Spin Hall effects in the sky
Autoren: Lars Andersson, Marius A. Oancea
(2023)
In many areas of physics, the propagation of wave packets carrying intrinsic angular momentum is generally influenced by spin-orbit interactions. This is the main mechanism behind spin Hall effects, which result in wave packets following spin-dependent trajectories. Spin Hall effects have been observed in several experiments for electrons in condensed matter systems and for light propagating in inhomogeneous optical media. Similar effects have also been predicted for wave packets propagating in inhomogeneous gravitational fields. We give a brief introduction to gravitational spin Hall effects, emphasizing the analogies with the spin Hall effect of light in optics. Furthermore, we review the most promising astrophysical avenues that could lead to experimental observations of the gravitational spin Hall effect.
Zeitschrift:
Class. Quantum Grav.
2023 | Gravitational instantons with S1 symmetry | Steffen Aksteiner, Lars Andersson, Mattias Dahl, Gustav Nilsson, Walter Simon
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Gravitational instantons with S1 symmetry
Autoren: Steffen Aksteiner, Lars Andersson, Mattias Dahl, Gustav Nilsson, Walter Simon
(2023)
Uniqueness results for asymptotically locally flat and asymptotically flat S1-symmetric gravitational instantons are proved using a divergence identity of the type used in uniqueness proofs for static black holes, combined with results derived from the G-signature theorem. Our results include a proof of the S1-symmetric version of the Euclidean Black Hole Uniqueness conjecture, a uniqueness result for the Taub-bolt family of instantons, as well as a proof that an ALF S1-symmetric instanton with the topology of the Chen-Teo family of instantons is Hermitian.
2023 | Model-Informed Target Morning 17α-Hydroxyprogesterone Concentrations in Dried Blood Spots for Pediatric Congenital Adrenal Hyperplasia Patients | V. Stachanow, U. Neumann, O. Blankenstein, N. Alder-Baerens, D. Bindellini, P. Hindmarsh, R.J. Ross, M.J. Whitaker, J. Melin, W. Huisinga, R. Michelet, C. Kloft
Zeitschrift: Pharmaceuticals
Seiten: 464
Band: 16(3)
Link zur Publikation
Model-Informed Target Morning 17α-Hydroxyprogesterone Concentrations in Dried Blood Spots for Pediatric Congenital Adrenal Hyperplasia Patients
Autoren: V. Stachanow, U. Neumann, O. Blankenstein, N. Alder-Baerens, D. Bindellini, P. Hindmarsh, R.J. Ross, M.J. Whitaker, J. Melin, W. Huisinga, R. Michelet, C. Kloft
(2023)
Zeitschrift:
Pharmaceuticals
2023 | Realisations of elliptic operators on compact manifolds with boundary | Lashi Bandara, Magnus Goffeng, Hemanth Saratchandran
Zeitschrift: Advances in Mathematics
Seiten: 1-123
Band: 420
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Realisations of elliptic operators on compact manifolds with boundary
Autoren: Lashi Bandara, Magnus Goffeng, Hemanth Saratchandran
(2023)
This paper investigates realisations of elliptic differential operators of general order on manifolds with boundary following the approach of Bär-Ballmann to first order elliptic operators. The space of possible boundary values of elements in the maximal domain is described as a Hilbert space densely sandwiched between two mixed order Sobolev spaces. The description uses Calderón projectors which, in the first order case, is equivalent to results of Bär-Bandara using spectral projectors of an adapted boundary operator. Boundary conditions that induce Fredholm as well as regular realisations, and those that admit higher order regularity, are characterised. In addition, results concerning spectral theory, homotopy invariance of the Fredholm index, and well-posedness for higher order elliptic boundary value problems are proven.
Zeitschrift:
Advances in Mathematics
2023 | Tikhonov regularization in general form with Chebfun | A. Alqahtani, T. Mach, L. Reichel
Zeitschrift: PAMM
Seiten: e202200041, 6 pages
Band: 22(1)
Link zur Publikation
Tikhonov regularization in general form with Chebfun
Autoren: A. Alqahtani, T. Mach, L. Reichel
(2023)
Linear ill-posed problems often are analyzed in function spaces using tools from functional analysis, while their numerical solution typically is computed by first discretizing the problem and then applying tools from finite-dimensional linear algebra. The Chebfun package makes it possible to solve linear ill-posed problems without explicit discretization. This work discusses the use of Tikhonov regularization with a fairly general linear regularization operator within the Chebfun framework.
Seiten:
e202200041, 6 pages
2023 | Deriving mechanism-based pharmacodynamic models by reducing quantitative systems pharmacology models: An application to warfarin | U. Falkenhagen, J. Knöchel, C. Kloft, W. Huisinga
Zeitschrift: CPT: Pharmacometrics & Systems Pharmacology
Seiten: 432–443
Band: 12
Link zur Publikation
Deriving mechanism-based pharmacodynamic models by reducing quantitative systems pharmacology models: An application to warfarin
Autoren: U. Falkenhagen, J. Knöchel, C. Kloft, W. Huisinga
(2023)
Zeitschrift:
CPT: Pharmacometrics & Systems Pharmacology
2023 | A prognostic baseline blood biomarker and tumor growth kinetics integrated model in paclitaxel/platinum treated advanced non-small cell lung cancer patients | F. W. Ojara, A. Henrich, N. Frances, Y. M. Nassar, W. Huisinga, N. Hartung, K. Geiger, S. Holdenrieder, M. Joerger, C. Kloft
Zeitschrift: CPT: Pharmacometrics & Systems Pharmacology
Link zur Publikation
A prognostic baseline blood biomarker and tumor growth kinetics integrated model in paclitaxel/platinum treated advanced non-small cell lung cancer patients
Autoren: F. W. Ojara, A. Henrich, N. Frances, Y. M. Nassar, W. Huisinga, N. Hartung, K. Geiger, S. Holdenrieder, M. Joerger, C. Kloft
(2023)
Zeitschrift:
CPT: Pharmacometrics & Systems Pharmacology
2023 | Solving the Parametric Eigenvalue Problem by Taylor Series and Chebyshev Expansion | T. Mach, M.A. Freitag
Zeitschrift: arXiv
Band: 2302.03661
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Solving the Parametric Eigenvalue Problem by Taylor Series and Chebyshev Expansion
Autoren: T. Mach, M.A. Freitag
(2023)
We discuss two approaches to solving the parametric (or stochastic) eigenvalue problem A(μ)λ(μ)=A(μ)v(μ). One of them uses a Taylor expansion and the other a Chebyshev expansion. The parametric eigenvalue problem assumes that the matrix A depends on a parameter μ, where μ might be a random variable. Consequently, the eigenvalues and eigenvectors are also functions of μ. We compute a Taylor approximation of these functions about μ₀ by iteratively computing the Taylor coefficients. The complexity of this approach is O(n³) for all eigenpairs, if the derivatives of A(μ) at μ₀ are given. The Chebyshev expansion works similarly. We first find an initial approximation iteratively which we then refine with Newton's method. This second method is more expensive but provides a good approximation over the whole interval of the expansion instead around a single point.
We present numerical experiments confirming the complexity and demonstrating that the approaches are capable of tracking eigenvalues at intersection points. Further experiments shed light on the limitations of the Taylor expansion approach with respect to the distance from the expansion point μ₀.
2023 | Insights in the maturational processes influencing hydrocortisone pharmacokinetics in congenital adrenal hyperplasia patients using a middle-out approach | R. Michelet, D. Bindellini, J. Melin, U. Neumann, O. Blankenstein, W. Huisinga, T. Johnson, M. J. Whitaker, R. Ross, C. Kloft
Zeitschrift: Frontiers in Pharmacology
Seiten: 1090554
Band: 13
Link zur Publikation
Insights in the maturational processes influencing hydrocortisone pharmacokinetics in congenital adrenal hyperplasia patients using a middle-out approach
Autoren: R. Michelet, D. Bindellini, J. Melin, U. Neumann, O. Blankenstein, W. Huisinga, T. Johnson, M. J. Whitaker, R. Ross, C. Kloft
(2023)
Zeitschrift:
Frontiers in Pharmacology
2023 | On the Rigidity of Cosmological Space-times | Rodrigo Avalos
Zeitschrift: Letters in Mathematical Physics
Verlag: Springer
Seiten: 98
Band: 113
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On the Rigidity of Cosmological Space-times
Autoren: Rodrigo Avalos
(2023)
In this paper we analyse a family of geometrically well-behaved cosmological space-times $(V^{n+1},g)$, which are foliated by \emph{intrinsically isotropic} space-like hypersurfaces $\{M_t\}_{t\in \mathbb{R}}$, which are orthogonal to a family of co-moving observers defined by a global time-like vector field $U$. In particular, this implies such space-times satisfy several of the well-known criteria for isotropic cosmological space-times, although, in the family in question, the simultaneity-spaces $(M_t,g_t)$ associated to $U$ can have as sectional curvature a sign-changing function $k(t)$. Being this clearly impossible in the FLRW family of standard cosmological space-times, it motivates us to revisit the geometric rigidity consequences of different definitions of isotropy available in the literature. In this analysis, we divide such definition according to whether the isometries involved are taken to be (local) space-time (STI space-times) or (local) space isometries (SI space-times) of $(M_t,g_t)$ for each $t$. This subtlety will be shown to be critical, proving that only when space-time isometries are considered one obtains the well-known rigidity properties associated with isotropic cosmological space-times. In particular SI space-times will be shown to be a strictly larger class than the STI ones, allowing a family of basic cosmological curvature change models which are not even locally isometric to any FLRW space-time.
Zeitschrift:
Letters in Mathematical Physics
2023 | Cell-level systems biology model to study inflammatory bowel diseases and their treatment options | S. Stübler, C. Kloft, W. Huisinga
Zeitschrift: CPT: Pharmacometrics & Systems Pharmacology
Seiten: 690-705
Band: 12
Link zur Publikation
Cell-level systems biology model to study inflammatory bowel diseases and their treatment options
Autoren: S. Stübler, C. Kloft, W. Huisinga
(2023)
Zeitschrift:
CPT: Pharmacometrics & Systems Pharmacology
2023 | On reflected diffusions in cones and cylinders | Oleksii Kulyk, Andrey Pilipenko, Sylvie Roelly
Zeitschrift: Ukrains'kyi Matematychnyi Zhurnal
Seiten: 1497-1521
Band: 75 (11)
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On reflected diffusions in cones and cylinders
Autoren: Oleksii Kulyk, Andrey Pilipenko, Sylvie Roelly
(2023)
Let X be a diffusion in a cone with oblique reflection at the boundary. We study the question whether X reaches a vertex of the cone for a finite time with positive probability. We propose new probabilistic method of investigation connected with the long-term behavior of a diffusion reflected in a cylinder.
Zeitschrift:
Ukrains'kyi Matematychnyi Zhurnal
2023 | Time-limited Balanced Truncation for Data Assimilation Problems | J. König, M.A. Freitag
Zeitschrift: Journal of Scientific Computing
Seiten: 22. Article No.: 47
Band: 97
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Time-limited Balanced Truncation for Data Assimilation Problems
Autoren: J. König, M.A. Freitag
(2023)
Balanced truncation is a well-established model order reduction method in system theory that has been applied to a variety of problems. Recently, a connection between linear Gaussian Bayesian inference problems and the system theoretic concept of balanced truncation was drawn for the first time. Although this connection is new, the application of balanced truncation to data assimilation is not a novel concept: It has already been used in four-dimensional variational data assimilation (4D-Var) in its discrete formulation. In this paper, the link between system theory and data assimilation is further strengthened by discussing the application of balanced truncation to standard linear Gaussian Bayesian inference, and, in particular, the 4D-Var method. similarities between both data assimilation problems allow a discussion of established methods as well as a generalisation of the state-of-the-art approach to arbitrary prior covariances as reachability Gramians. Furthermore, we propose an enhanced approach using time-limited balanced truncation that allows to balance Bayesian inference for unstable systems and in addition mproves the numerical results for short observation periods.
Zeitschrift:
Journal of Scientific Computing
Seiten:
22. Article No.: 47
2023 | Local foliations by critical surfaces of the Hawking energy and small sphere limit | Alejandro Penuela Diaz
Zeitschrift: Classical and Quantum Gravity
Seiten: 035002
Band: 40
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Local foliations by critical surfaces of the Hawking energy and small sphere limit
Autoren: Alejandro Penuela Diaz
(2023)
Local foliations of area constrained Willmore surfaces on a 3-dimensional Riemannian manifold were constructed by Lamm, Metzger and Schulze , and Ikoma, Machiodi and Mondino, the leaves of these foliations are in particular critical surfaces of the Hawking energy in case they are contained in a totally geodesic spacelike hypersurface. We generalize these foliations to the general case of a non-totally geodesic spacelike hypersurface, constructing an unique local foliation of area constrained critical surfaces of the Hawking energy. A discrepancy when evaluating the so called small sphere limit of the Hawking energy was found by Friedrich, he studied concentrations of area constrained critical surfaces of the Hawking energy and obtained a result that apparently differs from the well established small sphere limit of the Hawking energy of Horowitz and Schmidt, this small sphere limit in principle must be satisfied by any quasi local energy. We confirm independently the discrepancy and explain the reasons for it to happen. We also prove that these surfaces are suitable to evaluate the Hawking energy in the sense of Lamm, Metzger and Schulze, and we find an indication that these surfaces may induce an excess in the energy measured.
Zeitschrift:
Classical and Quantum Gravity
2023 | POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier-Stokes equations | S. Hijazi, M.A. Freitag, N. Landwehr
Zeitschrift: Advanced Modeling and Simulation in Engineering Sciences
Seiten: 38 pages
Band: 10
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POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier-Stokes equations
Autoren: S. Hijazi, M.A. Freitag, N. Landwehr
(2023)
We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier--Stokes equations (NSE). In the proposed approach, the presence of simulated data for the fluid dynamics fields is assumed. A POD-Galerkin ROM is then constructed by applying POD on the snapshots matrices of the fluid fields and performing a Galerkin projection of the NSE (or the modified equations in case of turbulence modeling) onto the POD reduced basis. A POD-Galerkin PINN ROM is then derived by introducing deep neural networks which approximate the reduced outputs with the input being time and/or parameters of the model. The neural networks incorporate the physical equations (the POD-Galerkin reduced equations) into their structure as part of the loss function. Using this approach, the reduced model is able to approximate unknown parameters such as physical constants or the boundary conditions. A demonstration of the applicability of the proposed ROM is illustrated by two cases which are the steady flow around a backward step and the unsteady turbulent flow around a surface mounted cubic obstacle.
Zeitschrift:
Advanced Modeling and Simulation in Engineering Sciences
2023 | A Gutzwiller Trace formula for Dirac Operators on a Stationary Spacetime | Onirban Islam
Zeitschrift: The Journal of Geometric Analysis
Band: 33: Artikel: 57
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A Gutzwiller Trace formula for Dirac Operators on a Stationary Spacetime
Autoren: Onirban Islam
(2023)
A Duistermaat-Guillemin-Gutzwiller trace formula for Dirac-type operators on a globally hyperbolic spatially compact standard stationary spacetime is achieved by generalising the recent construction by A. Strohmaier and S. Zelditch to a vector bundle setting. We have analysed the spectrum of the Lie derivative with respect to a global timelike Killing vector field on the solution space of the Dirac equation and found that it consists of discrete real eigenvalues. The distributional trace of the time evolution operator has singularities at the periods of induced Killing flow on the space of lightlike geodesics. This gives rise to the Weyl law asymptotic at the vanishing period.
Zeitschrift:
The Journal of Geometric Analysis
2023 | Solution of Ill-posed Problems with Chebfun | A. Alqahtani, T. Mach, L. Reichel
Zeitschrift: Numerical Algorithms
Verlag: Springer
Seiten: 2341‒2364
Band: 92
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Solution of Ill-posed Problems with Chebfun
Autoren: A. Alqahtani, T. Mach, L. Reichel
(2023)
The analysis of linear ill-posed problems often is carried out in function spaces using tools from functional analysis. However, the numerical solution of these problems typically is computed by first discretizing the problem and then applying tools from finite-dimensional linear algebra. The present paper explores the feasibility of applying the Chebfun package to solve ill-posed problems with a regularize-first approach numerically. This allows a user to work with functions instead of vectors and with integral operators instead of matrices. The solution process therefore is much closer to the analysis of ill-posed problems than standard linear algebra-based solution methods. Furthermore, the difficult process of explicitly choosing a suitable discretization is not required.
Zeitschrift:
Numerical Algorithms
2023 | Adaptive Cross Approximation for Tikhonov Regularization in General Form | T. Mach, L. Reichel, M. Van Barel
Zeitschrift: Numerical Algorithms
Verlag: Springer
Seiten: 815‒830
Band: 92
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Adaptive Cross Approximation for Tikhonov Regularization in General Form
Autoren: T. Mach, L. Reichel, M. Van Barel
(2023)
Many problems in Science and Engineering give rise to linear integral equations of the first kind with a smooth kernel. Discretization of the integral operator yields a matrix, whose singular values cluster at the origin. We describe the approximation of such matrices by adaptive cross approximation, which avoids forming the entire matrix. The choice of the number of steps of adaptive cross approximation is discussed. The discretized right-hand side represents data that commonly are contaminated by measurement error. Solution of the linear system of equations so obtained is not meaningful because the matrix determined by adaptive cross approximation is rank-deficient. We remedy this difficulty by using Tikhonov regularization and discuss how a fairly general regularization matrix can be used. Computed examples illustrate that the use of a regularization matrix different from the identity can improve the quality of the computed approximate solutions significantly.
Zeitschrift:
Numerical Algorithms
2023 | Cauchy Problem for Incompressible Neo-Hookean materials | Lars Andersson, Lev Kapitanski
Zeitschrift: Archive for Rational Mechanics and Analysis
Seiten: 21
Band: 247
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Cauchy Problem for Incompressible Neo-Hookean materials
Autoren: Lars Andersson, Lev Kapitanski
(2023)
In this paper we consider the Cauchy problem for neo-Hookean incompressible elasticity in spatial dimension d≥2. We are here interested primarily in the low regularity case, s≤scrit=d/2+1. For d=2,3, we prove existence and uniqueness for s0<s≤scrit, and we can prove well-posedness, but for a smaller range, s1<s≤scrit,
if d=2if d=3,s0=74,s1=74+65√−78,s0=2,s1=1+32−−√
We consider the initial deformations of the form x(0,ξ)=Aξ+φ(ξ), where A is a constant SL(d,R) matrix, and φ∈Hs+1. For the full range (in s) results, as indicated above, we need additional Hölder regularity assumptions on certain combinations of second order derivatives of φ.
A key observation in the proof is that the equations of evolution for the vorticities decomposes into a first-order hyperbolic system, for which a Strichartz estimate holds, and a coupled transport system. This allows one to set up a bootstrap argument to prove local existence and uniqueness. Continuous dependence on initial data is proved using an argument inspired by Bona and Smith, and Kato and Lai, with a modification based on new estimates for Riesz potentials. The results of this paper should be compared to what is known for the ideal fluid equations, where, as shown by Bourgain and Li, the requirement s>scrit is necessary.
Zeitschrift:
Archive for Rational Mechanics and Analysis
2023 | Constructing electrically charged Riemannian manifolds with minimal boundary, prescribed asymptotics, and controlled mass | Armando J. Cabrera Pacheco, Carla Cederbaum, Penelope Gehring, Alejandro Peñuela Diaz
Zeitschrift: Journal of Geometry and Physics
Seiten: 104746
Band: 185
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Constructing electrically charged Riemannian manifolds with minimal boundary, prescribed asymptotics, and controlled mass
Autoren: Armando J. Cabrera Pacheco, Carla Cederbaum, Penelope Gehring, Alejandro Peñuela Diaz
(2023)
In 2015, Mantoulidis and Schoen constructed 3-dimensional asymptotically Euclidean manifolds with non-negative scalar curvature whose ADM mass can be made arbitrarily close to the optimal value of the Riemannian Penrose Inequality, while the intrinsic geometry of the outermost minimal surface can be "far away" from being round. The resulting manifolds, called extensions, are geometrically not "close" to a spatial Schwarzschild manifold. This suggests instability of the Riemannian Penrose Inequality. Their construction was later adapted to \(n+1\) dimensions by Cabrera Pacheco and Miao, suggesting instability of the higher dimensional Riemannian Penrose Inequality. In recent papers by Alaee, Cabrera Pacheco, and Cederbaum and by Cabrera Pacheco, Cederbaum, and McCormick, a similar construction was performed for asymptotically Euclidean, electrically charged Riemannian manifolds and for asymptotically hyperbolic Riemannian manifolds, respectively, obtaining 3-dimensional extensions that suggest instability of the Riemannian Penrose Inequality with electric charge and of the conjectured asymptotically hyperbolic Riemannian Penrose Inequality in 3 dimensions. This paper combines and generalizes all the aforementioned results by constructing suitable asymptotically hyperbolic or asymptotically Euclidean extensions with electric charge in \(n+1\) dimensions for \(n \geq 2\).
Besides suggesting instability of a naturally conjecturally generalized Riemannian Penrose Inequality, the constructed extensions give insights into an ad hoc generalized notion of Bartnik mass, similar to the Bartnik mass estimate for minimal surfaces proven by Mantoulidis and Schoen via their extensions, and unifying the Bartnik mass estimates in the various scenarios mentioned above.
Zeitschrift:
Journal of Geometry and Physics
2023 | Global stability of spacetimes with supersymmetric compactifications | Lars Andersson, Pieter Blue, Zoe Wyatt, Shing-Tung Yau
Seiten: 2079–2107
Band: 9
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Global stability of spacetimes with supersymmetric compactifications
Autoren: Lars Andersson, Pieter Blue, Zoe Wyatt, Shing-Tung Yau
(2023)
This paper proves the stability, with respect to the evolution determined by the vacuum Einstein equations, of the Cartesian product of high-dimensional Minkowski space with a compact, Ricci-flat Riemannian manifold that admits a spin structure and a nonzero parallel spinor. Such a product includes the example of Calabi-Yau and other special holonomy compactifications, which play a central role in supergravity and string theory. The stability proved in this paper provides a counter example to an instability argument by Penrose.
2023 | Boundary conditions for scalar curvature | Christian Bär and Bernhard Hanke
Verlag: World Scientific
Buchtitel: M. Gromov, B. Lawson (eds): Perspectives in Scalar Curvature
Seiten: 325-377
Band: 2
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Boundary conditions for scalar curvature
Autoren: Christian Bär and Bernhard Hanke
(2023)
Based on the Atiyah-Patodi-Singer index formula, we construct an obstruction to positive scalar curvature metrics with mean convex boundaries on spin manifolds of infinite K-area. We also characterize the extremal case. Next we show a general deformation principle for boundary conditions of metrics with lower scalar curvature bounds. This implies that the relaxation of boundary conditions often induces weak homotopy equivalences of spaces of such metrics. This can be used to refine the smoothing of codimension-one singularites a la Miao and the deformation of boundary conditions a la Brendle-Marques-Neves, among others. Finally, we construct compact manifolds for which the spaces of positive scalar curvature metrics with mean convex boundaries have nontrivial higher homotopy groups.
Buchtitel:
M. Gromov, B. Lawson (eds): Perspectives in Scalar Curvature
2023 | Stability of transition semigroups and applications to parabolic equations | Moritz Gerlach, Jochen Glück, Markus Kunze
Zeitschrift: Transactions of the American Mathematical Society
Seiten: 153-180
Band: 376(1)
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Stability of transition semigroups and applications to parabolic equations
Autoren: Moritz Gerlach, Jochen Glück, Markus Kunze
(2023)
The paper deals with the long-term behavior of positive operator semigroups on spaces of bounded functions and of signed measures, which have
applications to parabolic equations with unbounded coefficients and to stochastic analysis. The main results are a Tauberian type theorem characterizing the convergence to equilibrium of strongly Feller semigroups and a generalization of a classical convergence theorem of Doob. None of these results requires any kind of time regularity of the semigroup.
Zeitschrift:
Transactions of the American Mathematical Society
2022 | On Lp Liouville theorems for Dirichlet forms | Hua, Bobo; Keller, Matthias; Lenz, Daniel; Schmidt, Marcel
Zeitschrift: Springer Proc. Math. Stat.
Verlag: Springer
Buchtitel: IWDFRT— INTERNATIONAL conference on Dirichlet Forms and Related Topics
Seiten: 201–221
Band: 394
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On Lp Liouville theorems for Dirichlet forms
Autoren: Hua, Bobo; Keller, Matthias; Lenz, Daniel; Schmidt, Marcel
(2022)
Zeitschrift:
Springer Proc. Math. Stat.
Buchtitel:
IWDFRT— INTERNATIONAL conference on Dirichlet Forms and Related Topics
2022 | Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales | Barbara Schamberger et. al.
Zeitschrift: Advanced Materials
Band: Vol. 35, issue 13
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Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales
Autoren: Barbara Schamberger et. al.
(2022)
Abstract Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.
Zeitschrift:
Advanced Materials
2022 | Symmetric Tangling of Honeycomb Networks | Myfanwy E. Evans and Stephen T. Hyde
Zeitschrift: Symmetry
Band: 14(9)
Link zur Publikation
Symmetric Tangling of Honeycomb Networks
Autoren: Myfanwy E. Evans and Stephen T. Hyde
(2022)
2022 | Exploring dried blood spot cortisol concentrations as an alternative for monitoring pediatric adrenal insufficiency patients: A model-based analysis | V. Stachanow, U. Neumann, O. Blankenstein, D. Bindellini, J. Melin, R. Ross, M.J. Whitaker, W. Huisinga, R. Michelet, C. Kloft
Zeitschrift: Frontiers Pharmacol.
Seiten: 1-8
Band: 13
Link zur Publikation
Exploring dried blood spot cortisol concentrations as an alternative for monitoring pediatric adrenal insufficiency patients: A model-based analysis
Autoren: V. Stachanow, U. Neumann, O. Blankenstein, D. Bindellini, J. Melin, R. Ross, M.J. Whitaker, W. Huisinga, R. Michelet, C. Kloft
(2022)
Zeitschrift:
Frontiers Pharmacol.
2022 | High-dosage fosfomycin results in adequate plasma and target-site exposure in morbidly obese and nonobese nonhyperfiltration patients | D. Busse, P. Simon, D. Petroff, N. El-Najjar, L. Schmitt, D. Bindellini, A. Dietrich, M. Zeitlinger, W. Huisinga, R. Michelet, H. Wrigge, C. Kloft
Zeitschrift: Antimicrob. Agents Chemother.
Seiten: e0230221
Band: 66
Link zur Publikation
High-dosage fosfomycin results in adequate plasma and target-site exposure in morbidly obese and nonobese nonhyperfiltration patients
Autoren: D. Busse, P. Simon, D. Petroff, N. El-Najjar, L. Schmitt, D. Bindellini, A. Dietrich, M. Zeitlinger, W. Huisinga, R. Michelet, H. Wrigge, C. Kloft
(2022)
Zeitschrift:
Antimicrob. Agents Chemother.
2022 | Comparative plasma and interstitial tissue fluid pharmacokinetics of meropenem demonstrate the need for increasing dose and infusion duration in obese and non-obese patients | D. Busse, P. Simon, L. Schmitt, D. Petroff, C. Dorn, A. Dietrich, M. Zeitlinger, W. Huisinga, R. Michelet, H. Wrigge, C. Kloft
Zeitschrift: Clin. Pharmacokinet.
Seiten: 655-672
Band: 61
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Comparative plasma and interstitial tissue fluid pharmacokinetics of meropenem demonstrate the need for increasing dose and infusion duration in obese and non-obese patients
Autoren: D. Busse, P. Simon, L. Schmitt, D. Petroff, C. Dorn, A. Dietrich, M. Zeitlinger, W. Huisinga, R. Michelet, H. Wrigge, C. Kloft
(2022)
Zeitschrift:
Clin. Pharmacokinet.
2022 | Evaluation of a meropenem and piperacillin monitoring program in intensive care unit patients calls for the regular assessment of empirical targets and easy-to-use dosing decision tools | F.A. Weinelt, M.S. Stegemann, A. Theloe, F. Pfäfflin, S. Achterberg, F. Weber, L. Dübel, A. Mikolajewska, A. Uhrig, P. Kiessling, W. Huisinga, R. Michelet, S. Hennig, C. Kloft
Zeitschrift: Antibiotics
Seiten: 758
Band: 11(6)
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Evaluation of a meropenem and piperacillin monitoring program in intensive care unit patients calls for the regular assessment of empirical targets and easy-to-use dosing decision tools
Autoren: F.A. Weinelt, M.S. Stegemann, A. Theloe, F. Pfäfflin, S. Achterberg, F. Weber, L. Dübel, A. Mikolajewska, A. Uhrig, P. Kiessling, W. Huisinga, R. Michelet, S. Hennig, C. Kloft
(2022)
2022 | Quantification of the Time Course of CYP3A Inhibition, Activation, and Induction Using a Population Pharmacokinetic Model of Microdosed Midazolam Continuous Infusion | Y. M. Nasser, N. Hohmann, R. Michelet, K. Gottwalt, A. D. Meid, J. Burhenne, W. Huisinga, W. E. Haefeli, G. Mikus, C. Kloft
Zeitschrift: Clinical Pharmacokinetics
Reihe: 61
Seiten: 1595–1607
Link zur Publikation
Quantification of the Time Course of CYP3A Inhibition, Activation, and Induction Using a Population Pharmacokinetic Model of Microdosed Midazolam Continuous Infusion
Autoren: Y. M. Nasser, N. Hohmann, R. Michelet, K. Gottwalt, A. D. Meid, J. Burhenne, W. Huisinga, W. E. Haefeli, G. Mikus, C. Kloft
(2022)
Zeitschrift:
Clinical Pharmacokinetics
2022 | Dimension-independent Markov chain Monte Carlo on the sphere | Han Cheng Lie, Daniel Rudolf, Bjorn Sprungk, T. J. Sullivan
Link zum Preprint
Dimension-independent Markov chain Monte Carlo on the sphere
Autoren: Han Cheng Lie, Daniel Rudolf, Bjorn Sprungk, T. J. Sullivan
(2022)
2022 | Datenassimilation: Die nahtlose Verschmelzung von Daten und Modellen | M.A. Freitag, S. Reich
Zeitschrift: Mitteilungen der Deutschen Mathematiker-Vereinigung
Verlag: De Gruyter
Seiten: 108‒112
Band: 30
Link zur Publikation
Datenassimilation: Die nahtlose Verschmelzung von Daten und Modellen
Autoren: M.A. Freitag, S. Reich
(2022)
Der Sonderforschungsbereich SFB1294 „Datenassimilation: Die nahtlose Verschmelzung von Daten und Modellen“ wird seit 2017 von der Deutschen Forschungsgemeinschaft an der Universität of Potsdam gefördert und befindet sich gegenwärtig am Beginn der zweiten Förderphase. Gemeinsam mit den Projektpartnern der Humboldt Universität zu Berlin, der Technischen Universität Berlin, dem Weierstraß-Institut für Angewandte Analysis und Stochastik sowie dem Helmholtz-Zentrum Potsdam: Deutsches GeoForschungsZentrum GFZ, werden innerhalb des Verbundes sowohl die statistischen und mathematischen Grundlagen also auch mannigfaltige Anwendungen zeitabhängiger inverser Problemeuntersucht. In diesem Beitrag werden in kurzen Zügen sowohl die grundlegende mathematische Fragestellung also auch die aktuellen wissenschaftlichen Projekte des SFBs vorgestellt
Zeitschrift:
Mitteilungen der Deutschen Mathematiker-Vereinigung
2022 | Well-posedness for rough solutions of the 3D compressible Euler equations | Lars Andersson, Huali Zhang
Link zum Preprint
Well-posedness for rough solutions of the 3D compressible Euler equations
Autoren: Lars Andersson, Huali Zhang
(2022)
In this paper we prove full local well-posedness for the Cauchy problem for the compressible 3D Euler equation, i.e. local existence, uniqueness, and continuous dependence on initial data, with initial velocity, density and vorticity (v0,ρ0,w0)∈H2+×H2+×H2, improving on the regularity conditions of \cite{WQEuler}. The continuous dependence on initial data for rough solutions of the compressible Euler system is new, even with the same regularity conditions as in \cite{WQEuler}. In addition, we prove new local well-posedness results for the 3D compressible Euler system with entropy.
2022 | Mode analysis for the linearized Einstein equations on the Kerr metric : the large \(\mathfrak{a}\) case | Lars Andersson, Dietrich Häfner, Bernard F. Whiting
Link zum Preprint
Mode analysis for the linearized Einstein equations on the Kerr metric : the large \(\mathfrak{a}\) case
Autoren: Lars Andersson, Dietrich Häfner, Bernard F. Whiting
(2022)
We give a complete analysis of mode solutions for the linearized Einstein equations and the 1−form wave operator on the Kerr metric in the large a case. By mode solutions we mean solutions of the form \(e^{-i t_\ast \sigma} \tilde h (r,\theta,\varphi)\) where \(t_\ast\) is a suitable time variable. The corresponding Fourier transformed 1−form wave operator and linearized Einstein operator are shown to be Fredholm between suitable function spaces and \(\tilde h\) has to lie in the domain of these operators. These spaces are constructed following the general framework of Vasy. No mode solutions exist for \(\mathfrak{J} \sigma \geq 0\), \(\sigma \neq 0\). For \(\sigma=0\) mode solutions are Coulomb solutions for the 1−form wave operator and linearized Kerr solutions plus pure gauge terms in the case of the linearized Einstein equations. If we fix a De Turck/wave map gauge, then the zero mode solutions for the linearized Einstein equations lie in a fixed 7−dimensional space. The proof relies on the absence of modes for the Teukolsky equation shown by the third author and a complete classification of the gauge invariants of linearized gravity on the Kerr spacetime due to Aksteiner et al.
2022 | The Cauchy problem for Lorentzian Dirac operators under non-local boundary conditions | Christian Bär and Penelope Gehring
Link zum Preprint
The Cauchy problem for Lorentzian Dirac operators under non-local boundary conditions
Autoren: Christian Bär and Penelope Gehring
(2022)
Non-local boundary conditions, such as the Atiyah-Patodi-Singer (APS) conditions, for Dirac operators on Riemannian manifolds are well under\-stood while not much is known for such operators on spacetimes with timelike boundary. We define a class of Lorentzian boundary conditions that are local in time and non-local in the spatial directions and show that they lead to a well-posed Cauchy problem for the Dirac operator. This applies in particular to the APS conditions imposed on each level set of a given Cauchy temporal function.
2022 | Ulcerative Colitis and Acute Severe Ulcerative Colitis Patients Are Overlooked in Infliximab Population Pharmacokinetic Models: Results from a Comprehensive Review | A. Démaris, E. S. K. Widigson, J. F. K. F. Ilvemark, C. Steenholdt, J. B. Seidelin, W. Huisinga, R. Michelet, L. B. S. Aulin, C. Kloft
Zeitschrift: Pharmaceutics
Seiten: 2095
Band: 14
Link zur Publikation
Ulcerative Colitis and Acute Severe Ulcerative Colitis Patients Are Overlooked in Infliximab Population Pharmacokinetic Models: Results from a Comprehensive Review
Autoren: A. Démaris, E. S. K. Widigson, J. F. K. F. Ilvemark, C. Steenholdt, J. B. Seidelin, W. Huisinga, R. Michelet, L. B. S. Aulin, C. Kloft
(2022)
Ulcerative colitis (UC) is part of the inflammatory bowels diseases, and moderate to severe
UC patients can be treated with anti-tumour necrosis α monoclonal antibodies, including infliximab
(IFX). Even though treatment of UC patients by IFX has been in place for over a decade, many gaps
in modelling of IFX PK in this population remain. This is even more true for acute severe UC (ASUC)
patients for which early prediction of IFX pharmacokinetic (PK) could highly improve treatment
outcome. Thus, this review aims to compile and analyse published population PK models of IFX in
UC and ASUC patients, and to assess the current knowledge on disease activity impact on IFX PK.
For this, a semi-systematic literature search was conducted, from which 26 publications including a
population PK model analysis of UC patients receiving IFX therapy were selected. Amongst those,
only four developed a model specifically for UC patients, and only three populations included se-
vere UC patients. Investigations of disease activity impact on PK were reported in only 4 of the 14
models selected. In addition, the lack of reported model codes and assessment of predictive perfor-
mance make the use of published models in a clinical setting challenging. Thus, more comprehen-
sive investigation of PK in UC and ASUC is needed as well as more adequate reports on developed
models and their evaluation in order to apply them in a clinical setting.
Zeitschrift:
Pharmaceutics
2022 | Local space time constant mean curvature and constant expansion foliations | Jan Metzger, Alejandro Peñuela Diaz
Zeitschrift: Journal of Geometry and Physics Volume 188, June 2023, 104823
Link zur Publikation
,
Link zum Preprint
Local space time constant mean curvature and constant expansion foliations
Autoren: Jan Metzger, Alejandro Peñuela Diaz
(2022)
Inspired by the small sphere-limit for quasi-local energy we study local foliations of surfaces with prescribed mean curvature. Following the strategy used by Ye in 1991 to study local constant mean curvature foliations, we use a Lyapunov Schmidt reduction in an n+1 dimensional manifold equipped with a symmetric 2-tensor to construct the foliations around a point, prove their uniqueness and show their nonexistence conditions. To be specific, we study two foliation conditions. First we consider constant space-time mean curvature surfaces. These foliations were used by Cederbaum and Sakovich to characterize the center of mass in general relativity. Second, we study local foliations of constant expansion surfaces.
Zeitschrift:
Journal of Geometry and Physics Volume 188, June 2023, 104823
2022 | Conditioning analysis for discrete Helmholtz problems | A. Kaya, M.A. Freitag
Zeitschrift: Computers & Mathematics with Applications
Verlag: Elsevier
Seiten: 171‒182
Band: 118
Link zur Publikation
Conditioning analysis for discrete Helmholtz problems
Autoren: A. Kaya, M.A. Freitag
(2022)
In this paper, we examine conditioning of the discretization of the Helmholtz problem. Although the discrete Helmholtz problem has been studied from different perspectives, to the best of our knowledge, there is no conditioning analysis for it. We aim to fill this gap in the literature. We propose a novel method in 1D to observe the near-zero eigenvalues of a symmetric indefinite matrix. Standard classification of ill-conditioning based on the matrix condition number is not true for the discrete Helmholtz problem. We relate the ill-conditioning of the discretization of the Helmholtz problem with the condition number of the matrix. We carry out analytical conditioning analysis in 1D and extend our observations to 2D with numerical observations. We examine several discretizations. We find different regions in which the condition number of the problem shows different characteristics. We also explain the general behavior of the solutions in these regions.
Zeitschrift:
Computers & Mathematics with Applications
2022 | Spontaneous transitions between amoeboid and keratocyte-like modes of migration | T. Moldenhawer, E. Moreno, D. Schindler, S. Flemming, M. Holschneider, W. Huisinga, S. Alonso, C. Beta
Zeitschrift: Front. Cell Dev. Biol.
Seiten: 10:898351
Link zur Publikation
Spontaneous transitions between amoeboid and keratocyte-like modes of migration
Autoren: T. Moldenhawer, E. Moreno, D. Schindler, S. Flemming, M. Holschneider, W. Huisinga, S. Alonso, C. Beta
(2022)
Zeitschrift:
Front. Cell Dev. Biol.
2022 | Huisken-Yau-type uniqueness for area-constrained Willmore spheres | Michael Eichmair, Thomas Koerber, Jan Metzger, Felix Schulze
Link zum Preprint
Huisken-Yau-type uniqueness for area-constrained Willmore spheres
Autoren: Michael Eichmair, Thomas Koerber, Jan Metzger, Felix Schulze
(2022)
Let (M,g) be a Riemannian 3-manifold that is asymptotic to Schwarzschild. We study the existence of large area-constrained Willmore spheres $$\Sigma\subset M$$ with non-negative Hawking mass and inner radius $$\rho$$ dominated by the area radius $$\lambda$$. If the scalar curvature of $$(M,g)$$ is non-negative, we show that no such surfaces with $$\log \lambda \ll \rho$$ exist. This answers a question of G. Huisken.
2022 | Rigidity Theorems for Asymptotically Euclidean $Q$-singular Spaces | R. Avalos, P. Laurain, N. Marque
Link zum Preprint
Rigidity Theorems for Asymptotically Euclidean $Q$-singular Spaces
Autoren: R. Avalos, P. Laurain, N. Marque
(2022)
In this paper we prove some rigidity theorems associated to $Q$-curvature analysis on asymptotically Euclidean (AE) manifolds, which are inspired by the analysis of conservation principles within fourth order gravitational theories. A central object in this analysis is a notion of fourth order energy, previously analysed by the authors, which is subject to a positive energy theorem. We show that this energy can be more geometrically rewritten in terms of a fourth order analogue to the Ricci tensor, which we denote by $J_g$. This allows us to prove that Yamabe positive $J$-flat AE manifolds must be isometric to Euclidean space. As a by product, we prove that this $J$-tensor provides a geometric control for the optimal decay rates at infinity. This last result reinforces the analogy of $J$ as a fourth order analogue to the Ricci tensor.
2022 | Hyperbolic Embedding for Finding Syntax in BERT (short paper) | T. Auyespek, T. Mach, Zh. Assylbekov
Verlag: CEUR Workshop Proceedings
Buchtitel: AIxIA 2021 Discussion Papers
Seiten: 58‒64
Link zur Publikation
Hyperbolic Embedding for Finding Syntax in BERT (short paper)
Autoren: T. Auyespek, T. Mach, Zh. Assylbekov
(2022)
Recent advances in natural language processing have improved our understanding of what kind of linguistic knowledge is encoded in modern word representations. For example, methods for testing the ability to extract syntax trees from a language model architecture were developed by Hewitt and Manning (2019)—they project word vectors into Euclidean subspace in such a way that the corresponding squared Euclidean distance approximates the tree distance between words in the syntax tree. This work proposes a method for assessing whether embedding word representations in hyperbolic space can better reflect the graph structure of syntax trees. We show that the tree distance between words in a syntax tree can be approximated well by the hyperbolic distance between corresponding word vectors.
Verlag:
CEUR Workshop Proceedings
Buchtitel:
AIxIA 2021 Discussion Papers
2022 | Einstein Type Systems on Complete Manifolds | R. Avalos, J. Lira, N. Marque
Link zum Preprint
Einstein Type Systems on Complete Manifolds
Autoren: R. Avalos, J. Lira, N. Marque
(2022)
In the present paper, we study the coupled Einstein Constraint Equations (ECE) on complete manifolds through the conformal method, focusing on non-compact manifolds with flexible asymptotics. In particular, we do not impose any specific model for infinity. First, we prove an existence criteria on compact manifolds with boundary which applies to more general systems and can be seen as a natural extension of known existence theory for the coupled ECE. Building on this, we prove an L^p existence based on existence of appropriate barrier functions for a family of physically well-motivated coupled systems on complete manifolds. We prove existence results for these systems by building barrier functions in the bounded geometry case. We conclude by translating our result to the H^s formulation, making contact with classic works. To this end, we prove several intermediary L^2 regularity results for the coupled systems in dimensions n \le 12 which fills certain gaps in current initial data analysis.
2022 | Nonlinear radiation gauge for near Kerr spacetimes | Lars Andersson, Thomas Bäckdahl, Pieter Blue, Siyuan Ma
Zeitschrift: Communications in Mathematical Physics
Seiten: 45–90
Band: 396
Link zur Publikation
,
Link zum Preprint
Nonlinear radiation gauge for near Kerr spacetimes
Autoren: Lars Andersson, Thomas Bäckdahl, Pieter Blue, Siyuan Ma
(2022)
In this paper, we introduce and explore the properties of a new gauge choice for the vacuum Einstein equation inspired by the ingoing and outgoing radiation gauges (IRG, ORG) for the linearized vacuum Einstein equation introduced by Chrzanowski in his work on metric reconstruction [DOI:10.1103/PhysRevD.11.2042] on the Kerr background. It has been shown by Price, Shankar and Whiting [arXiv:gr-qc/0611070] that IRG/ORG are consistent gauges for the linearized vacuum Einstein equation on Petrov type II backgrounds. In [arXiv:1903.03859] ORG was used in proving linearized stability for the Kerr spacetime, and the new non-linear radiation gauge introduced here is a direct generalization of that gauge condition, and is intended to be used to study the stability of Kerr black holes under the evolution generated by the vacuum Einstein equation.
Zeitschrift:
Communications in Mathematical Physics
2022 | Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes | Max Lewandowski
Zeitschrift: Journal of Mathematical Physics
Seiten: 013501
Band: 63
Link zur Publikation
Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes
Autoren: Max Lewandowski
(2022)
According to Radzikowski’s celebrated results, bisolutions of a wave operator on a globally hyperbolic spacetime are of the Hadamard form iff they are given by a linear combination of distinguished parametrices i2(G˜aF−G˜F+G˜A−G˜R) in the sense of Duistermaat and Hörmander [Acta Math. 128, 183–269 (1972)] and Radzikowski [Commun. Math. Phys. 179, 529 (1996)]. Inspired by the construction of the corresponding advanced and retarded Green operator GA, GR as done by Bär, Ginoux, and Pfäffle {Wave Equations on Lorentzian Manifolds and Quantization [European Mathematical Society (EMS), Zürich, 2007]}, we construct the remaining two Green operators GF, GaF locally in terms of Hadamard series. Afterward, we provide the global construction of i2(G˜aF−G˜F), which relies on new techniques such as a well-posed Cauchy problem for bisolutions and a patching argument using Čech cohomology. This leads to global bisolutions of the Hadamard form, each of which can be chosen to be a Hadamard two-point-function, i.e., the smooth part can be adapted such that, additionally, the symmetry and the positivity condition are exactly satisfied.
Zeitschrift:
Journal of Mathematical Physics
2022 | Symmetric tangled Platonic polyhedra | S. T. Hyde and M. E. Evans
Zeitschrift: Proceedings National Academy of Sciences of the USA
Band: vol. 119, no. 1
Link zur Publikation
Symmetric tangled Platonic polyhedra
Autoren: S. T. Hyde and M. E. Evans
(2022)
Zeitschrift:
Proceedings National Academy of Sciences of the USA
2022 | Enumerating Isotopy Classes of Tilings guided by the symmetry of Triply-Periodic Minimal Surfaces | B. Kolbe and M. E. Evans
Zeitschrift: SIAM Journal on Applied Algebra and Geometry
Band: vol. 6, issue 1
Link zur Publikation
Enumerating Isotopy Classes of Tilings guided by the symmetry of Triply-Periodic Minimal Surfaces
Autoren: B. Kolbe and M. E. Evans
(2022)
Zeitschrift:
SIAM Journal on Applied Algebra and Geometry
2022 | A continued learning approach for model-informed precision dosing: updating models in clinical practice | C. Maier, J. de Wiljes, N. Hartung, C. Kloft, W. Huisinga
Zeitschrift: CPT: Pharmacometrics Syst. Pharmacol.
Seiten: 185-198
Band: 11
Link zur Publikation
,
Link zum Preprint
A continued learning approach for model-informed precision dosing: updating models in clinical practice
Autoren: C. Maier, J. de Wiljes, N. Hartung, C. Kloft, W. Huisinga
(2022)
Zeitschrift:
CPT: Pharmacometrics Syst. Pharmacol.
2022 | Randomised one-step time integration methods for deterministic operator differential equations | Han Cheng Lie, Martin Stahn, T. J. Sullivan
Zeitschrift: Calcolo
Reihe: 59
Seiten: 1-33
Band: 13
Link zur Publikation
,
Link zum Preprint
Randomised one-step time integration methods for deterministic operator differential equations
Autoren: Han Cheng Lie, Martin Stahn, T. J. Sullivan
(2022)
2022 | Gibbs point processes on path space: existence, cluster expansion and uniqueness | Alexander Zass
Zeitschrift: Markov processes and random fields
Link zur Publikation
,
Link zum Preprint
Gibbs point processes on path space: existence, cluster expansion and uniqueness
Autoren: Alexander Zass
(2022)
We study a class of infinite-dimensional diffusions under Gibbsian interactions, in the context of marked point configurations: the starting points belong to ℝd, and the marks are the paths of Langevin diffusions. We use the entropy method to prove existence of an infinite-volume Gibbs point process and use cluster expansion tools to provide an explicit activity domain in which uniqueness holds.
Zeitschrift:
Markov processes and random fields
2022 | Random population dynamics under catastrophic events | Patrick Cattiaux, Jens Fischer, Sylvie Roelly, Samuel Sindayigaya
Zeitschrift: Journal of Applied Probability
Seiten: 962-982
Band: 59 (4)
Link zur Publikation
,
Link zum Preprint
Random population dynamics under catastrophic events
Autoren: Patrick Cattiaux, Jens Fischer, Sylvie Roelly, Samuel Sindayigaya
(2022)
In this paper we introduce new Birth-and-Death processes with partial catastrophe and study their properties. In particular we obtain some estimates for the mean catastrophe time, and the first and second moments of the distribution of the process at a fixed time t. This is completed by some asymptotic results.
Zeitschrift:
Journal of Applied Probability
2022 | A relative trace formula for obstacle scattering | Florian Hanisch, Alexander Strohmaier, Alden Waters
Zeitschrift: Duke Mathematical Journal
Verlag: Duke University Press
Seiten: 2233 - 2274
Band: 171 (11)
Link zur Publikation
,
Link zum Preprint
A relative trace formula for obstacle scattering
Autoren: Florian Hanisch, Alexander Strohmaier, Alden Waters
(2022)
We consider the case of scattering of several obstacles in \(\mathbb{R}^d\) for \(d \geq 2\). Then the absolutely continuous part of the Laplace operator \(\Delta\) with Dirichlet boundary conditions and the free Laplace operator \(\Delta_0\) are unitarily equivalent. For suitable functions that decay sufficiently fast we have that the difference \(g(\Delta) - g(\Delta_0)\) is a trace-class operator and its trace is described by the Krein spectral shift function. In this paper we study the contribution to the trace (and hence the Krein spectral shift function) that arises from assembling several obstacles relative to a setting where the obstacles are completely separated. In the case of two obstacles we consider the Laplace operators \(\Delta_1\) and \(\Delta_2\) obtained by imposing Dirichlet boundary conditions only on one of the objects. Our main result in this case states that then \(g(\Delta) - g(\Delta_1) - g(\Delta_2) + g(\Delta_0)\) is a trace class operator for a much larger class of functions (including functions of polynomial growth) and that this trace may still be computed by a modification of the Birman-Krein formula. In case \(g(x) = x^{\frac{1}{2}}\) the relative trace has a physical meaning as the vacuum energy of the massless scalar field and is expressible as an integral involving boundary layer operators. Such integrals have been derived in the physics literature using non-rigorous path integral derivations and our formula provides both a rigorous justification as well as a generalisation.
Zeitschrift:
Duke Mathematical Journal
Verlag:
Duke University Press
2022 | Concentration of Small Hawking Type Surfaces | Alexander Friedrich
Zeitschrift: Differential Geometry and its Applications
Seiten: 101927
Band: 85
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,
Link zum Preprint
Concentration of Small Hawking Type Surfaces
Autoren: Alexander Friedrich
(2022)
We investigate the Hawking energy of small surfaces in space times without symmetry assumptions by introducing the notion of Hawking type functionals. In particular, we find that Hawking type functionals are generalized Willmore functionals which allows us to find area constrained, minimizing, immersed, haunted bubble trees. These bubble trees are smooth spheres provided their area is small enough. Following a similar analysis of the Willmore functional conducted by T. Lamm and J. Metzger we characterize the concentration points of area constrained, critical surfaces for Hawking type functionals and the Hawking energy. Moreover, we determine their expansion on small surfaces.
Zeitschrift:
Differential Geometry and its Applications
2022 | Boundary value problems for general first-order elliptic differential operators | Christian Bär, Lashi Bandara
Zeitschrift: J. Funct. Analysis
Seiten: 109445
Band: 282
Link zur Publikation
,
Link zum Preprint
,
Video abstract: https://vimeo.com/523211595
Boundary value problems for general first-order elliptic differential operators
Autoren: Christian Bär, Lashi Bandara
(2022)
We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the boundary condition need not be pseudo-local.
We show the equivalence of various characterisations of elliptic boundary conditions and demonstrate how the boundary conditions traditionally considered in the literature fit in our framework. The regularity of the solutions up to the boundary is proven. We provide examples which are conveniently treated by our methods.
Zeitschrift:
J. Funct. Analysis
2022 | Local Flexibility for Open Partial Differential Relations | Christian Bär, Bernhard Hanke
Zeitschrift: Communications on Pure and Applied Mathematics
Seiten: 1377-1415
Band: 75
Link zur Publikation
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Link zum Preprint
Local Flexibility for Open Partial Differential Relations
Autoren: Christian Bär, Bernhard Hanke
(2022)
We show that local deformations, near closed subsets, of solutions to open partial differential relations can be extended to global deformations, provided all but the highest derivatives stay constant along the subset. The applicability of this general result is illustrated by a number of examples, dealing with convex embeddings of hypersurfaces, differential forms, and lapse functions in Lorentzian geometry.
The main application is a general approximation result by sections which have very restrictive local properties an open dense subsets. This shows, for instance, that given any K every manifold of dimension at least two carries a complete C1,1-metric which, on a dense open subset, is smooth with constant sectional curvature K. Of course this is impossible for C2-metrics in general.
Zeitschrift:
Communications on Pure and Applied Mathematics
2022 | The Fermionic integral on loop space and the Pfaffian line bundle | Florian Hanisch, Matthias Ludewig
Zeitschrift: Journal of Mathematical Physics
Band: 61, Issue 12
Link zur Publikation
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Link zum Preprint
The Fermionic integral on loop space and the Pfaffian line bundle
Autoren: Florian Hanisch, Matthias Ludewig
(2022)
As the loop space of a Riemannian manifold is infinite-dimensional, it is a non-trivial problem to make sense of the "top degree component" of a differential form on it. In this paper, we show that a formula from finite dimensions generalizes to assign a sensible "top degree component" to certain composite forms, obtained by wedging with the exponential (in the exterior algebra) of the canonical 2-form on the loop space. The result is a section on the Pfaffian line bundle on the loop space. We then identify this with a section of the line bundle obtained by transgression of the spin lifting gerbe. These results are a crucial ingredient for defining the fermionic part of the supersymmetric path integral on the loop space.
Zeitschrift:
Journal of Mathematical Physics
2022 | A Rigorous Construction of the Supersymmetric Path Integral Associated to a Compact Spin Manifold | Florian Hanisch, Matthias Ludewig
Zeitschrift: Comm. Math. Phys.
Verlag: Springer
Seiten: 1209–1239
Band: 391
Link zur Publikation
,
Link zum Preprint
A Rigorous Construction of the Supersymmetric Path Integral Associated to a Compact Spin Manifold
Autoren: Florian Hanisch, Matthias Ludewig
(2022)
We give a rigorous construction of the path integral in N=1/2 supersymmetry as an integral map for differential forms on the loop space of a compact spin manifold. It is defined on the space of differential forms which can be represented by extended iterated integrals in the sense of Chen and Getzler-Jones-Petrack. Via the iterated integral map, we compare our path integral to the non-commutative loop space Chern character of Güneysu and the second author. Our theory provides a rigorous background to various formal proofs of the Atiyah-Singer index theorem using supersymmetric path integrals, as investigated by Alvarez-Gaumé, Atiyah, Bismut and Witten.
Zeitschrift:
Comm. Math. Phys.
2021 | The APS-Index and the Spectral Flow | Koen van den Dungen, Lennart Ronge
Zeitschrift: Operators and Matrices
Verlag: Ele-Math
Seiten: 1393--1416
Band: 15 - 4
Link zur Publikation
,
Link zum Preprint
The APS-Index and the Spectral Flow
Autoren: Koen van den Dungen, Lennart Ronge
(2021)
We study the Atiyah-Patodi-Singer (APS) index, and its equality to the spectral flow,
in an abstract, functional analytic setting. More precisely, we consider a (suitably continuous or
differentiable) family of self-adjoint Fredholm operators A(t) on a Hilbert space, parametrised
by t in a finite interval. We then consider two different operators, namely D := d/dt + A (the
abstract analogue of a Riemannian Dirac operator) and D := d/dt − iA (the abstract analogue of
a Lorentzian Dirac operator). The latter case is inspired by a recent index theorem by Bär and
Strohmaier (Amer. J. Math. 141 (2019), 1421–1455) for a Lorentzian Dirac operator equipped
with APS boundary conditions. In both cases, we prove that the Fredholm index of the operator
D equipped with APS boundary conditions is equal to the spectral flow of the family A(t) .
Zeitschrift:
Operators and Matrices
2021 | Mit Mathematik zur individuellen Therapie | W. Huisinga, C. Maier
Buchtitel: M. Ehrhardt, M. Günther und W. Schilders: Erfolgsformeln - Anwendungen der Mathematik
Seiten: 27-32
Link zur Publikation
Mit Mathematik zur individuellen Therapie
Autoren: W. Huisinga, C. Maier
(2021)
Buchtitel:
M. Ehrhardt, M. Günther und W. Schilders: Erfolgsformeln - Anwendungen der Mathematik
2021 | Development of a model-informed dosing tool to optimise initial antibiotic dosing - a translational example for intensive care units | F. Weinelt, M. Stegemann, A. Theloe, F. Pfäfflin, S. Achterberg, L. Schmitt, W. Husinga, R. Michelet, S. Hennig, C. Kloft
Zeitschrift: Pharmaceutics
Seiten: 2128
Band: 13
Link zur Publikation
Development of a model-informed dosing tool to optimise initial antibiotic dosing - a translational example for intensive care units
Autoren: F. Weinelt, M. Stegemann, A. Theloe, F. Pfäfflin, S. Achterberg, L. Schmitt, W. Husinga, R. Michelet, S. Hennig, C. Kloft
(2021)
Zeitschrift:
Pharmaceutics
2021 | Fréchet derivatives of expected functionals of solutions to stochastic differential equations | Han Cheng Lie
Link zum Preprint
Fréchet derivatives of expected functionals of solutions to stochastic differential equations
Autoren: Han Cheng Lie
(2021)
2021 | Gamma-convergence of Onsager-Machlup functionals. Part II: Infinite product measures on Banach spaces | Birzhan Ayanbayev, Ilja Klebanov, Han Cheng Lie, T.J. Sullivan
Zeitschrift: Inverse Problems
Reihe: 38
Seiten: 025006
Band: 2
Link zur Publikation
,
Link zum Preprint
Gamma-convergence of Onsager-Machlup functionals. Part II: Infinite product measures on Banach spaces
Autoren: Birzhan Ayanbayev, Ilja Klebanov, Han Cheng Lie, T.J. Sullivan
(2021)
Zeitschrift:
Inverse Problems
2021 | Gamma-convergence of Onsager-Machlup functionals. Part I: With applications to maximum a posteriori estimation in Bayesian inverse problems | Birzhan Ayanbayev, Ilja Klebanov, Han Cheng Lie, T.J. Sullivan
Zeitschrift: Inverse Problems
Reihe: 38
Seiten: 025005
Band: 2
Link zur Publikation
,
Link zum Preprint
Gamma-convergence of Onsager-Machlup functionals. Part I: With applications to maximum a posteriori estimation in Bayesian inverse problems
Autoren: Birzhan Ayanbayev, Ilja Klebanov, Han Cheng Lie, T.J. Sullivan
(2021)
Zeitschrift:
Inverse Problems
2021 | Autonomous Exploration and Identification of High Performing Adsorbents using Active Learning | G. Donval, C. Hand, J. Hook, E. Dupont, M. S. Landman, M.A. Freitag, M. Lennox, T. Düren
Verlag: submitted
Link zum Preprint
Autonomous Exploration and Identification of High Performing Adsorbents using Active Learning
Autoren: G. Donval, C. Hand, J. Hook, E. Dupont, M. S. Landman, M.A. Freitag, M. Lennox, T. Düren
(2021)
MOFs and COFs are porous materials with a large variety of applications including gas storage and separation. Synthesised in a modular fashion from distinct building blocks, a near infinite number of structures can be constructed and the properties of the material can be tailored for a specific application. While this modularity is a very attractive feature it also poses a challenge. Attempting to identify the best performing material(s) for a given application is experimentally intractable. Current research efforts combine molecular simulations and machine learning techniques to evaluate the simulated performance of hundreds of thousands of materials to identify top performing MOFs and COFs for a given application. These approaches typically rely on moderated brute-force screening which is still resource-intensive as typically between 70‒100 % of the hundreds of thousands of materials must be simulated to create a training set for the machine learning models used, restricting screening to relatively simple molecules. In this work we demonstrate our novel Bayesian mining approach to materials screening which allows 62‒92 % of the top 100 porous materials for a range of applications to be readily identified from large materials databases after only assessing less than one percent of all materials. This is a stark contrast to the 0‒1 % achieved by conventional brute-force screening where porous materials are just chosen at random during a high throughput screening. Through this accelerated virtual screening process, the identification of high performing materials can be used to more rapidly inform experimental efforts and hence lead to an acceleration of the entire research and development pipeline of porous materials.
2021 | Correction to: Therapeutic drug monitoring of oral targeted antineoplastic drugs | A. Mueller-Schoell, S.L. Groenland, O. Scherf-Clavel, M. van Dyk, W. Huisinga, R. Michelet, U. Jaehde, N. Steeghs, A.D.R. Huitema, C. Kloft
Zeitschrift: Eur. J. Clin. Pharmacol.
Seiten: 465
Band: 77
Link zur Publikation
Correction to: Therapeutic drug monitoring of oral targeted antineoplastic drugs
Autoren: A. Mueller-Schoell, S.L. Groenland, O. Scherf-Clavel, M. van Dyk, W. Huisinga, R. Michelet, U. Jaehde, N. Steeghs, A.D.R. Huitema, C. Kloft
(2021)
Zeitschrift:
Eur. J. Clin. Pharmacol.
2021 | Therapeutic drug monitoring of oral targeted antineoplastic drugs | A. Mueller-Schoell, S.L. Groenland, O. Scherf-Clavel, M. van Dyk, W. Huisinga, R. Michelet, U. Jaehde, N. Steeghs, A.D.R. Huitema, C. Kloft
Zeitschrift: Eur. J. Clin. Pharmacol.
Seiten: 441-464
Band: 77
Link zur Publikation
Therapeutic drug monitoring of oral targeted antineoplastic drugs
Autoren: A. Mueller-Schoell, S.L. Groenland, O. Scherf-Clavel, M. van Dyk, W. Huisinga, R. Michelet, U. Jaehde, N. Steeghs, A.D.R. Huitema, C. Kloft
(2021)
Zeitschrift:
Eur. J. Clin. Pharmacol.
2021 | Infliximab clearance decreases in second and third trimesters of pregnancy in inflammatory bowel disease | A.M. Grisic, M. Dorn-Rasmussen, B. Ungar, J. Brynskov, J.F. Ilvemark, N. Bolstad, D.J. Warren, M.A. Ainsworth, W. Huisinga, S. Ben-Horin, C. Kloft, C. Steenholdt
Zeitschrift: United Eur. Gastroenterol. J.
Seiten: 91-101
Band: 9
Link zur Publikation
Infliximab clearance decreases in second and third trimesters of pregnancy in inflammatory bowel disease
Autoren: A.M. Grisic, M. Dorn-Rasmussen, B. Ungar, J. Brynskov, J.F. Ilvemark, N. Bolstad, D.J. Warren, M.A. Ainsworth, W. Huisinga, S. Ben-Horin, C. Kloft, C. Steenholdt
(2021)
Zeitschrift:
United Eur. Gastroenterol. J.
2021 | Evaluation of the MeroRisk Calculator, a user-friendly tool to predict the risk of meropenem target non-attainment in critically ill patients | U. Liebchen, M. Klose, M. Paal, M. Vogeser, M. Zoller, I. Schroeder, L. Schmitt, W. Huisinga, R. Michelet, J. Zander, C. Scharf, F. Weinelt, C. Kloft
Zeitschrift: Antibiotics
Reihe: 10
Seiten: 468
Link zur Publikation
Evaluation of the MeroRisk Calculator, a user-friendly tool to predict the risk of meropenem target non-attainment in critically ill patients
Autoren: U. Liebchen, M. Klose, M. Paal, M. Vogeser, M. Zoller, I. Schroeder, L. Schmitt, W. Huisinga, R. Michelet, J. Zander, C. Scharf, F. Weinelt, C. Kloft
(2021)
2021 | Similar piperacillin/tazobactam target attainment in obese versus nonobese patients despite differences in interstitial tissue fluid pharmacokinetics | D. Busse, P. Simon, D. Petroff, C. Dorn, L. Schmitt, D. Bindellini, A. Kratzer, A. Dietrich, M. Zeitlinger, W. Huisinga, R. Michelet, H. Wrigge, C. Kloft
Zeitschrift: Pharmaceuticals
Reihe: 13
Seiten: 1380
Link zur Publikation
Similar piperacillin/tazobactam target attainment in obese versus nonobese patients despite differences in interstitial tissue fluid pharmacokinetics
Autoren: D. Busse, P. Simon, D. Petroff, C. Dorn, L. Schmitt, D. Bindellini, A. Kratzer, A. Dietrich, M. Zeitlinger, W. Huisinga, R. Michelet, H. Wrigge, C. Kloft
(2021)
Zeitschrift:
Pharmaceuticals
2021 | Early survival prediction framework in CD19-specific CAR-T-cell immunotherapy using a population quantitative systems pharmacology model | A. Mueller-Schoell, N. Puebla-Osorio, R. Michelet, M. Green, A. Künkele, W. Huisinga, P. Strati, B. Chasen, S.S. Neelapu, C. Yee, C. Kloft
Zeitschrift: Cancers
Reihe: 13
Seiten: 2782
Link zur Publikation
Early survival prediction framework in CD19-specific CAR-T-cell immunotherapy using a population quantitative systems pharmacology model
Autoren: A. Mueller-Schoell, N. Puebla-Osorio, R. Michelet, M. Green, A. Künkele, W. Huisinga, P. Strati, B. Chasen, S.S. Neelapu, C. Yee, C. Kloft
(2021)
2021 | Simulation-based assessment of the impact of non-adherence on endoxifen target attainment in different tamoxifen dosing strategies | A. Mueller-Schoell, L. Klopp-Schulze, R. Michelet, M. Van Dyk, T.E. Mürdter, M. Schwab, M. Joerger, W. Huisinga, G. Mikus, C. Kloft
Zeitschrift: Pharmaceuticals
Reihe: 14
Seiten: 115
Link zur Publikation
Simulation-based assessment of the impact of non-adherence on endoxifen target attainment in different tamoxifen dosing strategies
Autoren: A. Mueller-Schoell, L. Klopp-Schulze, R. Michelet, M. Van Dyk, T.E. Mürdter, M. Schwab, M. Joerger, W. Huisinga, G. Mikus, C. Kloft
(2021)
Zeitschrift:
Pharmaceuticals
2021 | Computational treatment simulations to assess the need for personalized tamoxifen dosing in breast cancer patients of different biogeographical groups | A. Mueller-Schoell, R. Michelet, L. Klopp-Schulze, M. van Dyk, T.E. Mürdter, M. Schwab, M. Joerger, W. Huisinga, G. Mikus, C. Kloft
Zeitschrift: Cancers
Reihe: 13
Seiten: 2432
Link zur Publikation
Computational treatment simulations to assess the need for personalized tamoxifen dosing in breast cancer patients of different biogeographical groups
Autoren: A. Mueller-Schoell, R. Michelet, L. Klopp-Schulze, M. van Dyk, T.E. Mürdter, M. Schwab, M. Joerger, W. Huisinga, G. Mikus, C. Kloft
(2021)
2021 | On the rough solutions of 3D compressible Euler equations: an alternative proof | Huali Zhang, Lars Andersson
Link zum Preprint
On the rough solutions of 3D compressible Euler equations: an alternative proof
Autoren: Huali Zhang, Lars Andersson
(2021)
The well-posedness of Cauchy problem of 3D compressible Euler equations is studied. By using Smith-Tataru's approach \cite{ST}, we prove the local existence, uniqueness and stability of solutions for Cauchy problem of 3D compressible Euler equations, where the initial data of velocity, density, specific vorticity v,ρ∈Hs,ϖ∈Hs0(2<s0<s). It's an alternative and simplified proof of the result given by Q. Wang in \cite{WQEuler}.
2021 | SPIRE—a software tool for bicontinuous phase recognition: application for plastid cubic membranes | T. M. Hain, M. Bykowski, M. Saba, M. E. Evans, G. E. Schröder-Turk, Ł. Kowalewska
Zeitschrift: Plant Physiology
Band: kiab476
Link zur Publikation
SPIRE—a software tool for bicontinuous phase recognition: application for plastid cubic membranes
Autoren: T. M. Hain, M. Bykowski, M. Saba, M. E. Evans, G. E. Schröder-Turk, Ł. Kowalewska
(2021)
Zeitschrift:
Plant Physiology
2021 | Evaluating prediction methods for glomerular filtration to optimise drug doses in obese and nonobese patients | D. Busse, J.M. Borghardt, D. Petroff, A. Pevzner, C. Dorn, N. El-Najjar, W. Huisinga, H. Wrigge, P. Simon, C. Kloft
Zeitschrift: British Journal of Clinical Pharmacology
Seiten: 2973-2981
Band: 88
Link zur Publikation
Evaluating prediction methods for glomerular filtration to optimise drug doses in obese and nonobese patients
Autoren: D. Busse, J.M. Borghardt, D. Petroff, A. Pevzner, C. Dorn, N. El-Najjar, W. Huisinga, H. Wrigge, P. Simon, C. Kloft
(2021)
Zeitschrift:
British Journal of Clinical Pharmacology
2021 | Re-entrant tensegrity: A three-periodic, chiral, tensegrity structure that is auxetic | M. Oster, M. A. Dias, T. de Wolff and M. E. Evans
Zeitschrift: Science Advances
Band: Vol. 7, Issue 50
Link zur Publikation
Re-entrant tensegrity: A three-periodic, chiral, tensegrity structure that is auxetic
Autoren: M. Oster, M. A. Dias, T. de Wolff and M. E. Evans
(2021)
Zeitschrift:
Science Advances
2021 | Isotopic tiling theory for hyperbolic surfaces | B. Kolbe and M. E. Evans
Zeitschrift: Geometriae Dedicata 212
Seiten: 177–204
Link zur Publikation
Isotopic tiling theory for hyperbolic surfaces
Autoren: B. Kolbe and M. E. Evans
(2021)
Zeitschrift:
Geometriae Dedicata 212
2021 | Constructing electrically charged Riemannian manifolds with minimal boundary, prescribed asymptotics, and controlled mass | Armando J. Cabrera Pacheco, Carla Cederbaum, Penelope Gehring, Alejandro Peñuela Diaz
Zeitschrift: Journal of Geometry and Physics
Seiten: 104746
Link zur Publikation
,
Link zum Preprint
Constructing electrically charged Riemannian manifolds with minimal boundary, prescribed asymptotics, and controlled mass
Autoren: Armando J. Cabrera Pacheco, Carla Cederbaum, Penelope Gehring, Alejandro Peñuela Diaz
(2021)
In 2015, Mantoulidis and Schoen constructed 3-dimensional asymptotically Euclidean manifolds with non-negative scalar curvature whose ADM mass can be made arbitrarily close to the optimal value of the Riemannian Penrose Inequality, while the intrinsic geometry of the outermost minimal surface can be "far away" from being round. The resulting manifolds, called \emph{extensions}, are geometrically not "close" to a spatial Schwarzschild manifold. This suggests instability of the Riemannian Penrose Inequality. Their construction was later adapted to n+1 dimensions by Cabrera Pacheco and Miao, suggesting instability of the higher dimensional Riemannian Penrose Inequality. In recent papers by Alaee, Cabrera Pacheco, and Cederbaum and by Cabrera Pacheco, Cederbaum, and McCormick, a similar construction was performed for asymptotically Euclidean, electrically charged Riemannian manifolds and for asymptotically hyperbolic Riemannian manifolds, respectively, obtaining 3-dimensional extensions that suggest instability of the Riemannian Penrose Inequality with electric charge and of the conjectured asymptotically hyperbolic Riemannian Penrose Inequality in 3 dimensions. This paper combines and generalizes all the aforementioned results by constructing suitable asymptotically hyperbolic or asymptotically Euclidean extensions with electric charge in n+1 dimensions for n≥2.
Besides suggesting instability of a naturally conjecturally generalized Riemannian Penrose Inequality, the constructed extensions give insights into an ad hoc generalized notion of Bartnik mass, similar to the Bartnik mass estimate for minimal surfaces proven by Mantoulidis and Schoen via their extensions, and unifying the Bartnik mass estimates in the various scenarios mentioned above.
Zeitschrift:
Journal of Geometry and Physics
2021 | Graphs and Discrete Dirichlet Spaces | Matthias Keller, Daniel Lenz, Radoslaw Wojciechowski
Reihe: Grundlehren der mathematischen Wissenschaften
Verlag: Springer
Seiten: 668
Band: 358
Link zur Publikation
,
Link zum Preprint
Graphs and Discrete Dirichlet Spaces
Autoren: Matthias Keller, Daniel Lenz, Radoslaw Wojciechowski
(2021)
The spectral geometry of infinite graphs deals with three major themes and their interplay: the spectral theory of the Laplacian, the geometry of the underlying graph, and the heat flow with its probabilistic aspects. In this book, all three themes are brought together coherently under the perspective of Dirichlet forms, providing a powerful and unified approach.
The book gives a complete account of key topics of infinite graphs, such as essential self-adjointness, Markov uniqueness, spectral estimates, recurrence, and stochastic completeness. A major feature of the book is the use of intrinsic metrics to capture the geometry of graphs. As for manifolds, Dirichlet forms in the graph setting offer a structural understanding of the interaction between spectral theory, geometry and probability. For graphs, however, the presentation is much more accessible and inviting thanks to the discreteness of the underlying space, laying bare the main concepts while preserving the deep insights of the manifold case.
Graphs and Discrete Dirichlet Spaces offers a comprehensive treatment of the spectral geometry of graphs, from the very basics to deep and thorough explorations of advanced topics. With modest prerequisites, the book can serve as a basis for a number of topics courses, starting at the undergraduate level.
Reihe:
Grundlehren der mathematischen Wissenschaften
2021 | Riesz Decompositions for Schrödinger Operators on Graphs | Florian Fischer, Matthias Keller
Zeitschrift: Journal of Mathematical Analysis and Applications
Seiten: 22 pp.
Band: 495
Link zur Publikation
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Link zum Preprint
Riesz Decompositions for Schrödinger Operators on Graphs
Autoren: Florian Fischer, Matthias Keller
(2021)
We study superharmonic functions for Schrödinger operators on general weighted graphs. Specifically, we prove two decompositions which both go under the name Riesz decomposition in the literature. The first one decomposes a superharmonic function into a harmonic and a potential part. The second one decomposes a superharmonic function into a sum of superharmonic functions with certain upper bounds given by prescribed superharmonic functions. As application we show a Brelot type theorem.
Zeitschrift:
Journal of Mathematical Analysis and Applications
2021 | Physiology-based toxicokinetic modelling of aluminium in rat and man | C. Hethey, N. Hartung, G. Wangorsch, K. Weisser, W. Huisinga
Zeitschrift: Archives of Toxicology
Seiten: 2977–3000
Band: 95
Link zur Publikation
Physiology-based toxicokinetic modelling of aluminium in rat and man
Autoren: C. Hethey, N. Hartung, G. Wangorsch, K. Weisser, W. Huisinga
(2021)
Zeitschrift:
Archives of Toxicology
2021 | Rationale of a lower dexamethasone dose in prenatal congenital adrenal hyperplasia therapy based on pharmacokinetic modelling | V. Stachanow, U. Neumann, O. Blankenstein, U. Fuhr, W. Huisinga, R. Michelet, N. Reisch, C. Kloft
Zeitschrift: European Journal of Endocrinology
Seiten: 365–374
Band: 185:3
Link zur Publikation
Rationale of a lower dexamethasone dose in prenatal congenital adrenal hyperplasia therapy based on pharmacokinetic modelling
Autoren: V. Stachanow, U. Neumann, O. Blankenstein, U. Fuhr, W. Huisinga, R. Michelet, N. Reisch, C. Kloft
(2021)
Zeitschrift:
European Journal of Endocrinology
2021 | Energy in Fourth Order Gravity | Rodrigo Avalos, Jorge H. Lira, Nicolas Marque
Link zum Preprint
Energy in Fourth Order Gravity
Autoren: Rodrigo Avalos, Jorge H. Lira, Nicolas Marque
(2021)
In this paper we make a detailed analysis of conservation principles in the context of a family of fourth-order gravitational theories generated via a quadratic Lagrangian. In particular, we focus on the associated notion of energy and start a program related to its study. We also exhibit examples of solutions which provide intuitions about this notion of energy which allows us to interpret it, and introduce several study cases where its analysis seems tractable. Finally, positive energy theorems are presented in restricted situations.
2021 | The Tunneling Effect for Schrödinger operators on a Vector Bundle | Markus Klein, Elke Rosenberger
Zeitschrift: Analysis and Mathematical Physics
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,
Link zum Preprint
The Tunneling Effect for Schrödinger operators on a Vector Bundle
Autoren: Markus Klein, Elke Rosenberger
(2021)
In the semiclassical limit \( \hbar\to 0\), we analyze a class of self-adjoint Schr\"odinger operators \( H_\hbar = \hbar^2 L + \hbar W + V\cdot \mathrm{id}_\mathscr{E}\) acting on sections of a vector bundle \(\mathscr{E}\) over an oriented Riemannian manifold \(M\) where \(L\) is a Laplace type operator, \(W\) is an endomorphism field
and the potential energy \(V\) has non-degenerate minima at a finite number of points \(m^1,\ldots m^r \in M\), called potential wells.
Using quasimodes of WKB-type near \(m^j\)
for eigenfunctions associated with the low lying eigenvalues of \(H_\hbar\), we analyze the tunneling effect, i.e. the splitting between low lying eigenvalues, which e.g. arises in certain symmetric configurations.
Technically, we treat the coupling between different potential wells by an interaction matrix and we consider the case of a single minimal geodesic
(with respect to the associated Agmon metric) connecting two potential wells
and the case of a submanifold of minimal geodesics of dimension \(\ell + 1\).
This dimension \(\ell\) determines the polynomial prefactor for exponentially small eigenvalue splitting.
Zeitschrift:
Analysis and Mathematical Physics
2021 | Quantitative relationship between infliximab exposure and inhibition of C‐reactive protein synthesis to support inflammatory bowel disease management | A.‐M. Grisic, A. Eser, W. Huisinga, W. Reinisch, C. Kloft
Zeitschrift: British Journal of Clinical Pharmacology
Seiten: 2374-2384
Band: 87
Link zur Publikation
Quantitative relationship between infliximab exposure and inhibition of C‐reactive protein synthesis to support inflammatory bowel disease management
Autoren: A.‐M. Grisic, A. Eser, W. Huisinga, W. Reinisch, C. Kloft
(2021)
Zeitschrift:
British Journal of Clinical Pharmacology
2021 | Which Analysis Approach Is Adequate to Leverage Clinical Microdialysis Data? A Quantitative Comparison to Investigate Exposure and Reponse Exemplified by Levofloxacin | D. Busse, A. Schaeftlein, A. Solms, L. Ilia, R. Michelet, M. Zeitlinger, W. Huisinga, C. Kloft
Zeitschrift: Pharmaceutical Research
Seiten: 381-395
Band: 38
Link zur Publikation
Which Analysis Approach Is Adequate to Leverage Clinical Microdialysis Data? A Quantitative Comparison to Investigate Exposure and Reponse Exemplified by Levofloxacin
Autoren: D. Busse, A. Schaeftlein, A. Solms, L. Ilia, R. Michelet, M. Zeitlinger, W. Huisinga, C. Kloft
(2021)
Zeitschrift:
Pharmaceutical Research
2021 | Perspectives on model-informed precision dosing in the digital health era: Challenges, opportunities, and recommendations | F. Kluwe, R. Michelet, A. Mueller-Schoell, C. Maier, L. Klopp-Schulze, M. van Dyk, G. Mikus, W. Huisinga, C. Kloft
Zeitschrift: Clinical Pharmacology & Therapeutics
Seiten: 29-36
Band: 109
Link zur Publikation
Perspectives on model-informed precision dosing in the digital health era: Challenges, opportunities, and recommendations
Autoren: F. Kluwe, R. Michelet, A. Mueller-Schoell, C. Maier, L. Klopp-Schulze, M. van Dyk, G. Mikus, W. Huisinga, C. Kloft
(2021)
Zeitschrift:
Clinical Pharmacology & Therapeutics
2021 | Quantification of microdialysis related variability in humans: Clinical trial design recommendations | D. Busse, P. Simon, R. Michelet, L. Ehmann, F. Mehner, C. Dorn, A. Kratzer, W. Huisinga, H. Wrigge, D. Petroff, C. Kloft
Zeitschrift: European Journal of Pharmaceutical Sciences
Seiten: 105607
Band: 157
Link zur Publikation
Quantification of microdialysis related variability in humans: Clinical trial design recommendations
Autoren: D. Busse, P. Simon, R. Michelet, L. Ehmann, F. Mehner, C. Dorn, A. Kratzer, W. Huisinga, H. Wrigge, D. Petroff, C. Kloft
(2021)
Zeitschrift:
European Journal of Pharmaceutical Sciences
2021 | New matrix function approximations and quadratue rules based on the Arnoldi process | N. Eshghi, T. Mach, L. Reichel
Zeitschrift: Journal of Computational and Applied Mathematics
Verlag: Elsevier
Seiten: 113442
Band: 391
Link zur Publikation
New matrix function approximations and quadratue rules based on the Arnoldi process
Autoren: N. Eshghi, T. Mach, L. Reichel
(2021)
The Arnoldi process can be applied to inexpensively approximate matrix functions of the form f(A)v and matrix functionals of the form v∗(f(A))∗g(A)v, where A is a large square non-Hermitian matrix, v is a vector, and the superscript ∗ denotes transposition and complex conjugation. Here f and g are analytic functions that are defined in suitable regions in the complex plane. This paper reviews available approximation methods and describes new ones that provide higher accuracy for essentially the same computational effort by exploiting available, but generally not used, moment information.
Numerical experiments show that in some cases the modifications of the Arnoldi decompositions proposed can improve the accuracy of v∗(f(A))∗g(A)v about as much as performing an additional step of the Arnoldi process.
Zeitschrift:
Journal of Computational and Applied Mathematics
2021 | Optimization based model order reduction for stochastic systems | M. Redmann, M.A. Freitag
Zeitschrift: Appl. Math. Comput., 398
Link zur Publikation
Optimization based model order reduction for stochastic systems
Autoren: M. Redmann, M.A. Freitag
(2021)
Zeitschrift:
Appl. Math. Comput., 398
2021 | Nilpotent symmetries as a mechanism for Grand Unification | Lars Andersson, Andras Laszo, Blazej Ruba
Zeitschrift: Journal of High Energy Physics
Verlag: Springer
Link zur Publikation
,
Link zum Preprint
Nilpotent symmetries as a mechanism for Grand Unification
Autoren: Lars Andersson, Andras Laszo, Blazej Ruba
(2021)
In the classic Coleman--Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact- \(U(1)\)- component, a Lorentz- \(SL(2,\mathbb{C})\) -component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman--Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.
Zeitschrift:
Journal of High Energy Physics
2021 | Propagation of polarized gravitational waves | Lars Andersson, Jérémie Joudioux, Marius A. Oancea, Ayush Raj
Zeitschrift: Phys. Rev. D
Seiten: 044053
Band: 103
Link zur Publikation
,
Link zum Preprint
Propagation of polarized gravitational waves
Autoren: Lars Andersson, Jérémie Joudioux, Marius A. Oancea, Ayush Raj
(2021)
The propagation of high-frequency gravitational waves can be analyzed using the geometrical optics approximation. In the case of large but finite frequencies, the geometrical optics approximation is no longer accurate, and polarization-dependent corrections at first order in wavelength modify the propagation of gravitational waves via a spin-orbit coupling mechanism. We present a covariant derivation from first principles of effective ray equations describing the propagation of polarized gravitational waves, up to first-order terms in wavelength, on arbitrary spacetime backgrounds. The effective ray equations describe a gravitational spin Hall effect for gravitational waves and are of the same form as those describing the gravitational spin Hall effect of light, derived from Maxwell's equations.
Zeitschrift:
Phys. Rev. D
2021 | Helicity, Spin, and Infra-zilch of Light: a Lorentz Covariant Formulation | Sajad Aghapour, Lars Andersson, Kjell Rosquist
Zeitschrift: Ann. Phys.
Seiten: 168535
Band: 432
Link zur Publikation
,
Link zum Preprint
Helicity, Spin, and Infra-zilch of Light: a Lorentz Covariant Formulation
Autoren: Sajad Aghapour, Lars Andersson, Kjell Rosquist
(2021)
The spin part of angular momentum of the electromagnetic field is known since the 1990's to be a separately conserved quantity. Cameron et al. introduced the helicity array, a non-covariant analog of Lipkin's zilch tensor, which expresses the hierarchy of conservation laws including helicity, spin, as well as the spin-flux or infra-zilch. In this paper, a novel conserved Lorentz covariant tensor, termed the helicity tensor, is introduced. The conservation laws arising from the helicity array can be obtained from the helicity tensor. The Lorentz covariance of the helicity tensor is in contrast to previous formulations of the helicity hierarchy of conservation laws, which required the non-Lorentz covariant transverse gauge. The helicity tensor is shown to arise as a Noether current for a variational symmetry of a duality-symmetric Lagrangian for Maxwell theory.
2021 | On the geometry of Petrov type II spacetimes | Steffen Aksteiner, Lars Andersson, Bernardo Araneda, Bernard Whiting
Zeitschrift: Classical and Quantum Gravity
Seiten: 135023
Band: 38
Link zur Publikation
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On the geometry of Petrov type II spacetimes
Autoren: Steffen Aksteiner, Lars Andersson, Bernardo Araneda, Bernard Whiting
(2021)
In general, geometries of Petrov type II do not admit symmetries in terms of Killing vectors or spinors. We introduce a weaker form of Killing equations which do admit solutions. In particular, there is an analog of the Penrose-Walker Killing spinor. Some of its properties, including associated conservation laws, are discussed. Perturbations of Petrov type II Einstein geometries in terms of a complex scalar Debye potential yield complex solutions to the linearized Einstein equations. The complex linearized Weyl tensor is shown to be half Petrov type N. The remaining curvature component on the algebraically special side is reduced to a first order differential operator acting on the potential.
Zeitschrift:
Classical and Quantum Gravity
2021 | Nonparametric goodness-of-fit testing for parametric covariate models in pharmacometric analyses | N. Hartung, M. Wahl, A. Rastogi, W. Huisinga
Zeitschrift: CPT: Pharmacometrics & Systems Pharmacology
Seiten: 564–576
Band: 10
Link zur Publikation
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Link zum Preprint
Nonparametric goodness-of-fit testing for parametric covariate models in pharmacometric analyses
Autoren: N. Hartung, M. Wahl, A. Rastogi, W. Huisinga
(2021)
Zeitschrift:
CPT: Pharmacometrics & Systems Pharmacology
2021 | Wave equations with initial data on compact Cauchy horizons | Oliver Lindblad Petersen
Zeitschrift: Analysis and PDE
Seiten: 2363-2408
Band: 14
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Wave equations with initial data on compact Cauchy horizons
Autoren: Oliver Lindblad Petersen
(2021)
We study the following problem: Given initial data on a compact Cauchy horizon, does there exist a unique solution to wave equations on the globally hyperbolic region? Our main results apply to any spacetime satisfying the null energy condition and containing a compact Cauchy horizon with surface gravity that can be normalised to a non-zero constant. Examples include the Misner spacetime and the Taub-NUT spacetime. We prove an energy estimate close to the Cauchy horizon for wave equations acting on sections of vector bundles. Using this estimate we prove that if a linear wave equation can be solved up to any order at the Cauchy horizon, then there exists a unique solution on the globally hyperbolic region. As a consequence, we prove several existence and uniqueness results for linear and non-linear wave equations without assuming analyticity or symmetry of the spacetime and without assuming that the generators close. We overcome in particular the essential remaining difficulty in proving that vacuum spacetimes with a compact Cauchy horizon with constant non-zero surface gravity necessarily admits a Killing vector field. This work is therefore related to the strong cosmic censorship conjecture.
Zeitschrift:
Analysis and PDE
2021 | The Faddeev-LeVerrier algorithm and the Pfaffian | Christian Bär
Zeitschrift: Linear Algebra and its Applications
Seiten: 39-55
Band: 630
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The Faddeev-LeVerrier algorithm and the Pfaffian
Autoren: Christian Bär
(2021)
We adapt the Faddeev-LeVerrier algorithm for the computation of characteristic polynomials to the computation of the Pfaffian of a skew-symmetric matrix. This yields a very simple, easy to implement and parallelize algorithm of computational cost O(n4) where n is the size of the matrix. We compare its performance to that of other algorithms and show how it can be used to compute the Euler form of a Riemannian manifold.
Zeitschrift:
Linear Algebra and its Applications
2021 | Eigenfunctions growth and R-limits on Graphs | Siegfried Beckus, Latif Eliaz
Zeitschrift: Journal of Spectral Theory
Reihe: 11
Seiten: 1895-1933
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Eigenfunctions growth and R-limits on Graphs
Autoren: Siegfried Beckus, Latif Eliaz
(2021)
A characterization of the essential spectrum of Schrödinger operators on infinite graphs is derived involving the concept of R-limits. This concept, which was introduced previously for operators on the natural numbers and the d-dimensional integer lattice as “right-limits,” captures the behaviour of the operator at infinity. For graphs with sub-exponential growth rate, we show that each point in the essential spectrum of H corresponds to a bounded generalized eigenfunction of a corresponding R-limit of H. If, additionally, the graph is of uniform sub-exponential growth, also the converse inclusion holds.
Zeitschrift:
Journal of Spectral Theory
2021 | Reinforcement learning and Bayesian data assimilation for model-informed precision dosing in oncology | C. Maier, N. Hartung, C. Kloft, W. Huisinga, J. de Wiljes
Zeitschrift: CPT: Pharmacometrics & Systems Pharmacology
Seiten: 241–254
Band: 10
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Reinforcement learning and Bayesian data assimilation for model-informed precision dosing in oncology
Autoren: C. Maier, N. Hartung, C. Kloft, W. Huisinga, J. de Wiljes
(2021)
Zeitschrift:
CPT: Pharmacometrics & Systems Pharmacology
2021 | Analysis of protrusion dynamics in amoeboid cell motility by means of regularized contour flows | D. Schindler, T. Moldenhawer, M. Stange, C. Beta, M. Holschneider, W. Huisinga
Zeitschrift: PLoS Computational Biology
Seiten: e1009268
Band: 17(8)
Link zur Publikation
Analysis of protrusion dynamics in amoeboid cell motility by means of regularized contour flows
Autoren: D. Schindler, T. Moldenhawer, M. Stange, C. Beta, M. Holschneider, W. Huisinga
(2021)
Zeitschrift:
PLoS Computational Biology
2021 | Manifolds with many Rarita-Schwinger fields | Christian Bär, Rafe Mazzeo
Zeitschrift: Commun. Math. Phys.
Verlag: Springer-Verlag
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Manifolds with many Rarita-Schwinger fields
Autoren: Christian Bär, Rafe Mazzeo
(2021)
The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare; it is even more unexpected for there to be large dimensional spaces of solutions.
In this paper we prove the existence of a sequence of compact manifolds in any given dimension greater than or equal to 4 for which the dimension of the space of Rarita-Schwinger fields tends to infinity. These manifolds are either simply connected Kähler-Einstein spin with negative Einstein constant, or products of such spaces with flat tori. Moreover, we construct Calabi-Yau manifolds of even complex dimension with more linearly independent Rarita-Schwinger fields than flat tori of the same dimension.
Zeitschrift:
Commun. Math. Phys.
2021 | Exponential a.s. synchronization of one-dimensional diffusions with non-regular coefficients | Olga Aryasova, Andrey Pilipenko, Sylvie Roelly
Zeitschrift: Stochastic Analysis and Applications
Seiten: 631-642
Band: 39 (4)
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Exponential a.s. synchronization of one-dimensional diffusions with non-regular coefficients
Autoren: Olga Aryasova, Andrey Pilipenko, Sylvie Roelly
(2021)
We study the asymptotic behaviour of a real-valued diffusion whose non-
regular drift is given as a sum of a dissipative term and a bounded measurable one.
We prove that two trajectories of that diffusion converge a.s. to one another at an
exponential explicit rate as soon as the dissipative coefficient is large enough. A
similar result in Lp is obtained.
Zeitschrift:
Stochastic Analysis and Applications
2021 | Convergent discretisation schemes for transition path theory for diffusion processes | Nada Cvetković, Tim Conrad, Han Cheng Lie
Zeitschrift: SIAM J. Multiscale Modeling and Simulation
Verlag: Society for Industrial and Applied Mathematics
Seiten: 242–266
Band: 19(1)
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Convergent discretisation schemes for transition path theory for diffusion processes
Autoren: Nada Cvetković, Tim Conrad, Han Cheng Lie
(2021)
Zeitschrift:
SIAM J. Multiscale Modeling and Simulation
Verlag:
Society for Industrial and Applied Mathematics
2021 | Error bounds for some approximate posterior measures in Bayesian inference | Han Cheng Lie, T. J. Sullivan, Aretha Teckentrup
Zeitschrift: Lecture Notes in Computational Science and Engineering
Verlag: Springer, Cham
Buchtitel: Numerical Mathematics and Advanced Applications ENUMATH 2019
Seiten: 275-283
Band: 139
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Error bounds for some approximate posterior measures in Bayesian inference
Autoren: Han Cheng Lie, T. J. Sullivan, Aretha Teckentrup
(2021)
Zeitschrift:
Lecture Notes in Computational Science and Engineering
Buchtitel:
Numerical Mathematics and Advanced Applications ENUMATH 2019
2021 | Compatibility complex for black hole spacetimes | Steffen Aksteiner, Lars Andersson, Thomas Bäckdahl, Igor Khavkine, Bernard Whiting
Zeitschrift: Communications in Mathematical Physics
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Compatibility complex for black hole spacetimes
Autoren: Steffen Aksteiner, Lars Andersson, Thomas Bäckdahl, Igor Khavkine, Bernard Whiting
(2021)
The set of local gauge invariant quantities for linearized gravity on the Kerr spacetime presented by two of the authors (S.A, T.B.) in (arXiv:1803.05341) is shown to be complete. In particular, any gauge invariant quantity for linearized gravity on Kerr that is local and of finite order in derivatives can be expressed in terms of these gauge invariants and derivatives thereof. The proof is carried out by constructing a complete compatibility complex for the Killing operator, and demonstrating the equivalence of the gauge invariants from (arXiv:1803.05341) with the first compatibility operator from that complex.
Zeitschrift:
Communications in Mathematical Physics
2021 | Generalized eigenfunctions and eigenvalues: a unifying framework for Shnol-type theorems | Siegfried Beckus, Baptiste Devyver
Zeitschrift: Journal d'Analyse Mathematique
Reihe: 146
Seiten: 165-203
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Generalized eigenfunctions and eigenvalues: a unifying framework for Shnol-type theorems
Autoren: Siegfried Beckus, Baptiste Devyver
(2021)
Let H be a generalized Schrödinger operator on a domain of a non-compact connected Riemannian manifold, and a generalized eigenfunction u for H: that is, u satisfies the equation Hu = λu in the weak sense but is not necessarily in L2. The problem is to find conditions on the growth of u, so that λ belongs to the spectrum of H. We unify and generalize known results on this problem. In addition, a variety of examples is provided, illustrating the different nature of the growth conditions.
Zeitschrift:
Journal d'Analyse Mathematique
2021 | Helicity and spin conservation in Maxwell theory and Linearized Gravity | Lars Andersson, Sajad Aghapour, Reebhu Bhattacharyya
Zeitschrift: General Relativity and Gravitation
Seiten: Article number 102
Band: 53
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Helicity and spin conservation in Maxwell theory and Linearized Gravity
Autoren: Lars Andersson, Sajad Aghapour, Reebhu Bhattacharyya
(2021)
A duality symmetric formulation of linearized gravity has been introduced by Barnett and used to show the conservation of helicity. However, the relation between helicity and spin as well as the separate conservation of the spin and orbital parts of angular momentum, which is known to hold in Maxwell theory, was not considered. These conservation laws are known to follow from the conservation of the so-called helicity array, an analog of the zilch tensor, which includes helicity, spin, and spin-flux or infra-zilch. In the present paper we prove the conservation of spin and orbital angular momentum for linearized gravity on Minkowski space, and construct the analog of the helicity array for linearized gravity.
Zeitschrift:
General Relativity and Gravitation
Seiten:
Article number 102
2020 | A perturbation of the de Rham complex | Ihsane Malass, Nikolai Tarkhanov
Zeitschrift: Journal of Siberian Federal University. Mathematics & Physics
Seiten: 519–532
Band: 13
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A perturbation of the de Rham complex
Autoren: Ihsane Malass, Nikolai Tarkhanov
(2020)
We consider a perturbation of the de Rham complex on a compact manifold with boundary. This perturbation goes beyond the framework of complexes, and so cohomology does not apply to it. On the other hand, its curvature is "small" hence there is a natural way to introduce an Euler characteristic and develop a Lefschetz theory for the perturbation. This work is intended as an attempt to develop a cohomology theory for arbitrary sequences of linear mappings.
Zeitschrift:
Journal of Siberian Federal University. Mathematics & Physics
2020 | Relative entanglement entropy of thermal states of Klein-Gordon and Dirac quantum field theories | Onirban Islam
Link zum Preprint
Relative entanglement entropy of thermal states of Klein-Gordon and Dirac quantum field theories
Autoren: Onirban Islam
(2020)
An upper bound of the relative entanglement entropy of thermal states at an inverse temperature \(\beta\) of linear, massive Klein-Gordon and Dirac quantum field theories across two regions, separated by a nonzero distance \(d\) in a Cauchy hypersurface of an ultrastatic (spin-)spacetime has been computed. This entanglement measure is bounded by a negative constant times \(\mathrm{ln}|\tanh(\pi d/2\beta)|\) which signifies power law decay for asymptotic \(d\) where the exponent depends on \(\beta < \infty\).
2020 | From Hardy to Rellich inequalities on graphs | Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
Zeitschrift: Proceedings of the London Mathematical Society
Seiten: 458-477
Band: 122
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From Hardy to Rellich inequalities on graphs
Autoren: Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
(2020)
We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schrödinger operators afterwards.
Zeitschrift:
Proceedings of the London Mathematical Society
2020 | Feynman path integrals for magnetic Schrödinger operators on infinite weighted graphs | Batu Güneysu, Matthias Keller
Zeitschrift: Journal d'Analyse Mathematique
Verlag: Springer
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Feynman path integrals for magnetic Schrödinger operators on infinite weighted graphs
Autoren: Batu Güneysu, Matthias Keller
(2020)
We prove a Feynman path integral formula for the unitary group exp(−itLv,θ), t≥0, associated with a discrete magnetic Schrödinger operator Lv,θ on a large class of weighted infinite graphs. As a consequence, we get a new Kato-Simon estimate
|exp(−itLv,θ)(x,y)|≤exp(−tL−deg,0)(x,y),
which controls the unitary group uniformly in the potentials in terms of a Schrödinger semigroup, where the potential deg is the weighted degree function of the graph.
Zeitschrift:
Journal d'Analyse Mathematique
2020 | Asymptotic Eigenfunctions for Schrödinger operators on a vector bundle | Matthias Ludewig, Elke Rosenberger
Zeitschrift: Reviews in Mathematical Physics
Verlag: World Scientific
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Asymptotic Eigenfunctions for Schrödinger operators on a vector bundle
Autoren: Matthias Ludewig, Elke Rosenberger
(2020)
In the limit \(\hbar \to 0\), we analyze a class of Schrödinger operators \( H_\hbar = \hbar^2 L + \hbar W + V\cdot id_{\mathscr{E}}\) acting on sections of a vector bundle \(\mathscr{E}\) over a Riemannian manifold \(M\) where \(L\) is a Laplace type operator, \(W\) is an endomorphism field and the potential energy \(V\) has a non-degenerate minimum at some point \(p\in M\). We construct quasimodes of WKB-type near \(p\) for eigenfunctions associated with the low-lying eigenvalues of \(H_\hbar\). These are obtained from eigenfunctions of the associated harmonic oscillator \(H_{p,\hbar}\) at \(p\), acting on smooth functions on the tangent space.
Zeitschrift:
Reviews in Mathematical Physics
2020 | Impact of the Mesoscale Range on Error Growth and the Limits to Atmospheric Predictability | Tsz Yan Leung and Martin Leutbecher and Sebastian Reich and Theodore G. Shepherd
Zeitschrift: Journal of the Atmospheric Sciences 2020-11-01
Impact of the Mesoscale Range on Error Growth and the Limits to Atmospheric Predictability
Autoren: Tsz Yan Leung and Martin Leutbecher and Sebastian Reich and Theodore G. Shepherd
(2020)
Zeitschrift:
Journal of the Atmospheric Sciences 2020-11-01
2020 | A mathematical model of local and global attention in natural scene viewing | Noa Malem-Shinitski (author) Jakob H. Macke (editor) Manfred Opper (author) Sebastian Reich (author) Lisa Schwetlick (author) Stefan A. Seelig (author) Ralf Engbert (author)
Zeitschrift: PLOS Computational Biology 2020-12-14
A mathematical model of local and global attention in natural scene viewing
Autoren: Noa Malem-Shinitski (author) Jakob H. Macke (editor) Manfred Opper (author) Sebastian Reich (author) Lisa Schwetlick (author) Stefan A. Seelig (author) Ralf Engbert (author)
(2020)
Zeitschrift:
PLOS Computational Biology 2020-12-14
2020 | Sequential Data Assimilation of the Stochastic SEIR Epidemic Model for Regional COVID-19 Dynamics | Ralf Engbert, Maximilian M. Rabe, Reinhold Kliegl, Sebastian Reich
Zeitschrift: Bulletin of Mathematical Biology 2021-01
Sequential Data Assimilation of the Stochastic SEIR Epidemic Model for Regional COVID-19 Dynamics
Autoren: Ralf Engbert, Maximilian M. Rabe, Reinhold Kliegl, Sebastian Reich
(2020)
Zeitschrift:
Bulletin of Mathematical Biology 2021-01
2020 | Energy Estimates for the Tracefree Curvature of Willmore Surfaces and Applications | Yann Bernard, Paul Laurain, Nicolas Marque
Link zum Preprint
Energy Estimates for the Tracefree Curvature of Willmore Surfaces and Applications
Autoren: Yann Bernard, Paul Laurain, Nicolas Marque
(2020)
We prove an ϵ-regularity result for the tracefree curvature of a Willmore surface with bounded second fundamental form. For such a surface, we obtain a pointwise control of the tracefree second fundamental form from a small control of its L2-norm.Several applications are investigated. Notably, we derive a gap statement for surfaces of the aforementioned type. We further apply our results to deduce regularity results for conformal minimal spacelike immersions into the de Sitter space S4,1.
2020 | Risk of target non-attainment in obese compared to non-obese patients in calculated linezolid therapy | L. Ehmann, P. Simon, D. Busse, D. Petroff, C. Dorn, W. Huisinga, A. Dietrich, M. Zeitlinger, H. Wrigge, C. Kloft
Zeitschrift: Clinical Microbiology and Infection
Seiten: 1222-1228
Band: 26
Link zur Publikation
Risk of target non-attainment in obese compared to non-obese patients in calculated linezolid therapy
Autoren: L. Ehmann, P. Simon, D. Busse, D. Petroff, C. Dorn, W. Huisinga, A. Dietrich, M. Zeitlinger, H. Wrigge, C. Kloft
(2020)
Zeitschrift:
Clinical Microbiology and Infection
2020 | Response to ‘Hydrocortisone suspension formulations are not necessarily the same in the treatment of children with congenital adrenal hyperplasia’. | R. Michelet, J. Melin, Z.P. Parra-Guillen, U. Neumann, M.J. Whitaker, V. Stachanow, W. Huisinga, J. Porter, O. Blankenstein, R.J. Ross, C. Kloft
Zeitschrift: European Journal of Endocrinology
Seiten: L29-L30
Band: 183
Link zur Publikation
Response to ‘Hydrocortisone suspension formulations are not necessarily the same in the treatment of children with congenital adrenal hyperplasia’.
Autoren: R. Michelet, J. Melin, Z.P. Parra-Guillen, U. Neumann, M.J. Whitaker, V. Stachanow, W. Huisinga, J. Porter, O. Blankenstein, R.J. Ross, C. Kloft
(2020)
Zeitschrift:
European Journal of Endocrinology
2020 | Numerical linear algebra in data assimilation | M.A. Freitag
Zeitschrift: GAMM Mitteilungen
Link zur Publikation
Numerical linear algebra in data assimilation
Autoren: M.A. Freitag
(2020)
Zeitschrift:
GAMM Mitteilungen
2020 | Gravitational spin Hall effect of light | Marius A. Oancea, Jérémie Joudioux, I. Y. Dodin, D. E. Ruiz, Claudio F. Paganini, Lars Andersson
Zeitschrift: Phys. Rev. D
Seiten: 024075
Band: 102
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,
Link zum Preprint
Gravitational spin Hall effect of light
Autoren: Marius A. Oancea, Jérémie Joudioux, I. Y. Dodin, D. E. Ruiz, Claudio F. Paganini, Lars Andersson
(2020)
The propagation of electromagnetic waves in vacuum is often described within the geometrical optics approximation, which predicts that wave rays follow null geodesics. However, this model is valid only in the limit of infinitely high frequencies. At large but finite frequencies, diffraction can still be negligible, but the ray dynamics becomes affected by the evolution of the wave polarization. Hence, rays can deviate from null geodesics, which is known as the gravitational spin Hall effect of light. In the literature, this effect has been calculated ad hoc for a number of special cases, but no general description has been proposed. Here, we present a covariant Wentzel-Kramers-Brillouin analysis from first principles for the propagation of light in arbitrary curved spacetimes. We obtain polarization-dependent ray equations describing the gravitational spin Hall effect of light. We also present numerical examples of polarization-dependent ray dynamics in the Schwarzschild spacetime, and the magnitude of the effect is briefly discussed. The analysis reported here is analogous to that of the spin Hall effect of light in inhomogeneous media, which has been experimentally verified.
Zeitschrift:
Phys. Rev. D
2020 | Time-to-event analysis of paclitaxel-associated peripheral neuropathy in advanced non-small cell lung cancer highlighting key influential treatment/patient factors | F.W. Ojara, A. Henrich, N. Frances, W. Huisinga, N. Hartung, M. Joerger, C. Kloft
Zeitschrift: Journal of Pharmacology and Experimental Therapeutics
Seiten: JPET-AR-2020-000053
Link zur Publikation
Time-to-event analysis of paclitaxel-associated peripheral neuropathy in advanced non-small cell lung cancer highlighting key influential treatment/patient factors
Autoren: F.W. Ojara, A. Henrich, N. Frances, W. Huisinga, N. Hartung, M. Joerger, C. Kloft
(2020)
Zeitschrift:
Journal of Pharmacology and Experimental Therapeutics
Seiten:
JPET-AR-2020-000053
2020 | Semimechanistic Clearance Models of Oncology Biotherapeutics and Impact of Study Design: Cetuximab as a Case Study | A.-M. Grisic, A. Khandelwal, M. Bertolino, W. Huisinga, P. Girard, C. Kloft
Zeitschrift: CPT: Pharmacometrics & Systems Pharmacology
Seiten: 628–638
Band: 9
Link zur Publikation
Semimechanistic Clearance Models of Oncology Biotherapeutics and Impact of Study Design: Cetuximab as a Case Study
Autoren: A.-M. Grisic, A. Khandelwal, M. Bertolino, W. Huisinga, P. Girard, C. Kloft
(2020)
Zeitschrift:
CPT: Pharmacometrics & Systems Pharmacology
2020 | Relative torsion and bordism classes of positive scalar curvature metrics on manifolds with boundary | Simone Cecchini, Mehran Seyedhosseini, Vito Felice Zenobi
Link zum Preprint
Relative torsion and bordism classes of positive scalar curvature metrics on manifolds with boundary
Autoren: Simone Cecchini, Mehran Seyedhosseini, Vito Felice Zenobi
(2020)
In this paper, we define a relative \(L^2\)-\(\rho\)-invariant for Dirac operators on odd-dimensional spin manifolds with boundary and show that they are invariants of the bordism classes of positive scalar curvature metrics which are collared near the boundary. As an application, we show that if a \(4k+3\)-dimensional spin manifold with boundary admits such a metric and if, roughly speaking, there exists a torsion element in the difference of the fundamental groups of the manifold and its boundary, then there are infinitely many bordism classes of such psc metrics on the given manifold. This result in turn implies that the moduli-space of psc metrics on such manifolds has infinitely many path components. We also indicate how to define delocalised \(\eta\)-invariants for odd-dimensional spin manifolds with boundary, which could then be used to obtain similar results for \(4k+1\)-dimensional manifolds.
2020 | An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions | Pierre Houdebert, Alexander Zass
Zeitschrift: Journal of Applied Probability (June 2022)
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An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions
Autoren: Pierre Houdebert, Alexander Zass
(2020)
We present a uniqueness result for Gibbs point processes with interactions that come from a non-negative pair potential; in particular, we provide an explicit uniqueness region in terms of activity z and inverse temperature β. The technique used relies on applying to the continuous setting the classical Dobrushin criterion. We also present a comparison to the two other uniqueness methods of cluster expansion and disagreement percolation, which can also be applied for this type of interactions.
Zeitschrift:
Journal of Applied Probability (June 2022)
2020 | Critical Hardy Inequalities on Manifolds and Graphs | Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
Reihe: London Mathematical Society Lecture Note Series
Verlag: Cambridge University Press
Buchtitel: Analysis and Geometry on Graphs and Manifolds
Seiten: 172-202
Band: 461
Link zur Publikation
Critical Hardy Inequalities on Manifolds and Graphs
Autoren: Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
(2020)
In this expository article we give an overview of recent developments in the study of optimal Hardy-type inequality in the continuum and in the discrete setting. In particular, we present the technique of the supersolution construction that yield “as large as possibleȍ Hardy weights which is made precise in terms of the notion of criticality. Instead of presenting the most general setting possible, we restrict ourselves to the case of the Laplacian on smooth manifolds and bounded combinatorial graphs. Although the results hold in far greater generality, the fundamental phenomena as well as the core ideas of the proofs become especially clear in these basic settings.
Reihe:
London Mathematical Society Lecture Note Series
Verlag:
Cambridge University Press
Buchtitel:
Analysis and Geometry on Graphs and Manifolds
2020 | Analysis and Geometry on Graphs and Manifolds | Matthias Keller, Daniel Lenz, Radoslaw Wojciechowski
Reihe: London Mathematical Society Lecture Note Series
Verlag: Cambridge University Press
Band: 461
Link zur Publikation
Analysis and Geometry on Graphs and Manifolds
Autoren: Matthias Keller, Daniel Lenz, Radoslaw Wojciechowski
(2020)
The interplay of geometry, spectral theory and stochastics has a long and fruitful history, and is the driving force behind many developments in modern mathematics. Bringing together contributions from a 2017 conference at the University of Potsdam, this volume focuses on global effects of local properties. Exploring the similarities and differences between the discrete and the continuous settings is of great interest to both researchers and graduate students in geometric analysis. The range of survey articles presented in this volume give an expository overview of various topics, including curvature, the effects of geometry on the spectrum, geometric group theory, and spectral theory of Laplacian and Schrödinger operators. Also included are shorter articles focusing on specific techniques and problems, allowing the reader to get to the heart of several key topics.
Reihe:
London Mathematical Society Lecture Note Series
Verlag:
Cambridge University Press
2020 | Magnetic sparseness and Schrödinger operators on graphs | Michel Bonnefont, Sylvain Golénia, Matthias Keller, Shiping Liu, Florentin Münch
Zeitschrift: Annales Henri Poincaré volume
Seiten: pages1489–1516
Band: 21
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Magnetic sparseness and Schrödinger operators on graphs
Autoren: Michel Bonnefont, Sylvain Golénia, Matthias Keller, Shiping Liu, Florentin Münch
(2020)
We study magnetic Schrödinger operators on graphs. We extend the notion of sparseness of graphs by including a magnetic quantity called the frustration index. This notion of magnetic-sparseness turns out to be equivalent to the fact that the form domain is an ℓ2 space. As a consequence, we get criteria of discreteness for the spectrum and eigenvalue asymptotics.
Zeitschrift:
Annales Henri Poincaré volume
2020 | Courant's Nodal Domain Theorem for Positivity Preserving Forms | Matthias Keller, Michael Schwarz
Zeitschrift: Journal of Spectral Theory
Seiten: 271–309
Band: 10
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Courant's Nodal Domain Theorem for Positivity Preserving Forms
Autoren: Matthias Keller, Michael Schwarz
(2020)
We introduce a notion of nodal domains for positivity preserving forms. This notion generalizes the classical ones for Laplacians on domains and on graphs. We prove the Courant nodal domain theorem in this generalized setting using purely analytical methods.
Zeitschrift:
Journal of Spectral Theory
2020 | Criticality theory for Schrödinger operators on graphs | Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
Zeitschrift: Journal of Spectral Theory
Seiten: 73-114
Band: 10
Link zur Publikation
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Link zum Preprint
Criticality theory for Schrödinger operators on graphs
Autoren: Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
(2020)
We study Schrödinger operators given by positive quadratic forms on infinite graphs. From there, we develop a criticality theory for Schrödinger operators on general weighted graphs.
Zeitschrift:
Journal of Spectral Theory
2020 | Drift estimation of the threshold Ornstein-Uhlenbeck process from continuous and discrete observations | Sara Mazzonetto and Paolo Pigato
Link zum Preprint
Drift estimation of the threshold Ornstein-Uhlenbeck process from continuous and discrete observations
Autoren: Sara Mazzonetto and Paolo Pigato
(2020)
We refer by threshold Ornstein-Uhlenbeck to a continuous-time threshold autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above or below a fixed level, yet at this level (threshold) its coefficients can be discontinuous. We discuss (quasi)-maximum likelihood estimation of the drift parameters, both assuming continuous and discrete time observations. In the ergodic case, we derive consistency and speed of convergence of these estimators in long time and high frequency. Based on these results, we develop a heuristic test for the presence of a threshold in the dynamics. Finally, we apply these statistical tools to short-term US interest rates modeling.
2020 | Paediatric population pharmacokinetic modelling to assess hydrocortisone replacement dosing regimens in young children | R. Michelet, J. Melin, Z.P. Parra-Guillen, U. Neumann, M.J. Whitaker, V. Stachanow, W. Huisinga, J. Porter, O. Blankenstein, R.J. Ross, C. Kloft
Zeitschrift: European Journal of Endocrinology
Seiten: 357–368
Band: 183
Link zur Publikation
Paediatric population pharmacokinetic modelling to assess hydrocortisone replacement dosing regimens in young children
Autoren: R. Michelet, J. Melin, Z.P. Parra-Guillen, U. Neumann, M.J. Whitaker, V. Stachanow, W. Huisinga, J. Porter, O. Blankenstein, R.J. Ross, C. Kloft
(2020)
Zeitschrift:
European Journal of Endocrinology
2020 | Obesity Alters Endoxifen Plasma Levels in Young Breast Cancer Patients: A Pharmacometric Simulation Approach | A. Mueller‐Schoell, L. Klopp‐Schulze, W. Schroth, T. Mürdter, R. Michelet, H. Brauch, W. Huisinga, M. Joerger, P. Neven, S.L.W. Koolen, R.H.J. Mathijssen, E. Copson, D. Eccles, S. Chen, B. Chowbay, A. Tfayli, N.K. Zgheib, M. Schwab, C. Kloft
Zeitschrift: Clinical Pharmacology & Therapeutics
Link zur Publikation
Obesity Alters Endoxifen Plasma Levels in Young Breast Cancer Patients: A Pharmacometric Simulation Approach
Autoren: A. Mueller‐Schoell, L. Klopp‐Schulze, W. Schroth, T. Mürdter, R. Michelet, H. Brauch, W. Huisinga, M. Joerger, P. Neven, S.L.W. Koolen, R.H.J. Mathijssen, E. Copson, D. Eccles, S. Chen, B. Chowbay, A. Tfayli, N.K. Zgheib, M. Schwab, C. Kloft
(2020)
Zeitschrift:
Clinical Pharmacology & Therapeutics
2020 | Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problems | A. Rastogi, G. Blanchard, P. Mathé.
Zeitschrift: Electronic Journal of Statistics
Seiten: 2798-2841
Band: 14 (2)
Link zur Publikation
,
Link zum Preprint
Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problems
Autoren: A. Rastogi, G. Blanchard, P. Mathé.
(2020)
Zeitschrift:
Electronic Journal of Statistics
2020 | Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems | A. Rastogi
Zeitschrift: Communications on Pure & Applied Analysis
Seiten: 4111-4126
Band: 19 (8)
Link zur Publikation
Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems
Autoren: A. Rastogi
(2020)
Zeitschrift:
Communications on Pure & Applied Analysis
2020 | Inverse learning in Hilbert scales | A. Rastogi, P. Mathé
Link zum Preprint
Inverse learning in Hilbert scales
Autoren: A. Rastogi, P. Mathé
(2020)
2020 | | Sylvie Roelly (Ed.)
Reihe: Lectures in Pure and Applied Mathematics
Verlag: Potsdam University Press
Buchtitel: Proceedings of the XI international conference stochastic and analytic methods in mathematical physics
Band: 6
Link zur Publikation
The XI international conference Stochastic and Analytic Methods in Mathematical Physics was held in Yerevan 2 – 7 September 2019 and was dedicated to the memory of the great mathematician Robert Adol’fovich Minlos, who passed away in January 2018. The present volume collects a large majority of the contributions presented at the conference on the following domains of contemporary interest: classical and quantum statistical physics, mathematical methods in quantum mechanics, stochastic analysis, applications of point processes in statistical mechanics. The authors are specialists from Armenia, Czech Republic, Denmark, France, Germany, Italy, Japan, Lithuania, Russia, UK and Uzbekistan. A particular aim of this volume is to offer young scientists basic material in order to inspire their future research in the wide fields presented here.
Reihe:
Lectures in Pure and Applied Mathematics
Verlag:
Potsdam University Press
Buchtitel:
Proceedings of the XI international conference stochastic and analytic methods in mathematical physics
2020 | A mechanistic framework for a priori pharmacokinetic predictions of orally inhaled drugs | N. Hartung, J. Borghardt
Zeitschrift: PLoS Computational Biology
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A mechanistic framework for a priori pharmacokinetic predictions of orally inhaled drugs
Autoren: N. Hartung, J. Borghardt
(2020)
Zeitschrift:
PLoS Computational Biology
2020 | Free division rings of fractions of crossed products of groups with Conradian left-orders | Gräter, J.
Zeitschrift: Forum Math. 32
Seiten: 739 - 772
Free division rings of fractions of crossed products of groups with Conradian left-orders
Autoren: Gräter, J.
(2020)
Zeitschrift:
Forum Math. 32
2020 | Numerical study for the phase transition of the area-interaction model | Pierre Houdebert
Zeitschrift: Lectures in Pure and Applied Mathematics
Verlag: Potsdam University Press
Buchtitel: Proceedings of the XI international conference Stochastic and Analytic Methods in Mathematical Physics
Seiten: 165 - 174
Band: 6
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Numerical study for the phase transition of the area-interaction model
Autoren: Pierre Houdebert
(2020)
Zeitschrift:
Lectures in Pure and Applied Mathematics
Verlag:
Potsdam University Press
Buchtitel:
Proceedings of the XI international conference Stochastic and Analytic Methods in Mathematical Physics
2020 | On an approximation of 2-D stochastic Navier-Stokes equations | Sara Mazzonetto
Zeitschrift: Lectures in Pure and Applied Mathematics
Verlag: Potsdam University Press
Buchtitel: Proceedings of the XI international conference Stochastic and Analytic Methods in Mathematical Physics
Seiten: 87-96
Band: 6
Link zum Preprint
On an approximation of 2-D stochastic Navier-Stokes equations
Autoren: Sara Mazzonetto
(2020)
We describe a full-discrete explicit approximation scheme for the process solution of the two-dimensional incompressible stochastic Navier-Stokes equations driven by additive noise with periodic boundary conditions. We focus on the properties which play a role in the proof of the strong convergence towards the mild solution of the equation.
Zeitschrift:
Lectures in Pure and Applied Mathematics
Verlag:
Potsdam University Press
Buchtitel:
Proceedings of the XI international conference Stochastic and Analytic Methods in Mathematical Physics
2020 | A Gibbs point process of diffusions: existence and uniqueness | Alexander Zass
Zeitschrift: Lectures in Pure and Applied Mathematics
Verlag: Potsdam University Press
Buchtitel: Proceedings of the XI international conference Stochastic and Analytic Methods in Mathematical Physics
Seiten: 13-22
Band: 6
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Link zum Preprint
A Gibbs point process of diffusions: existence and uniqueness
Autoren: Alexander Zass
(2020)
In this work we consider a system of infinitely many interacting diffusions as a marked Gibbs point process. With this perspective, we show, for a large class of stable and regular interactions, existence and (conjecture) uniqueness of an infinite-volume Gibbs process. In order to prove existence we use the specific entropy as a tightness tool. For the uniqueness problem, we use cluster expansion to prove a Ruelle bound, and conjecture how this would lead to the uniqueness of the Gibbs process as solution of the Kirkwood-Salsburg equation.
Zeitschrift:
Lectures in Pure and Applied Mathematics
Verlag:
Potsdam University Press
Buchtitel:
Proceedings of the XI international conference Stochastic and Analytic Methods in Mathematical Physics
2020 | A Variant of Roe Algebras for Spaces with Cylindrical Ends with Applications in Relative Higher Index Theory | Mehran Seyedhosseini
Zeitschrift: To appear in Journal of Noncommutative Geometry
Link zum Preprint
A Variant of Roe Algebras for Spaces with Cylindrical Ends with Applications in Relative Higher Index Theory
Autoren: Mehran Seyedhosseini
(2020)
In this paper we define a variant of Roe algebras for spaces with cylindrical ends and use this to study questions regarding existence and classification of metrics of positive scalar curvature on such manifolds which are collared on the cylindrical end. We discuss how our constructions are related to relative higher index theory as developed by Chang, Weinberger, and Yu and use this relationship to define higher rho-invariants for positive scalar curvature metrics on manifolds with boundary. This paves the way for classification of these metrics. Finally, we use the machinery developed here to give a concise proof of a result of Schick and the author, which relates the relative higher index with indices defined in the presence of positive scalar curvature on the boundary.
Zeitschrift:
To appear in Journal of Noncommutative Geometry
2020 | Pharmacokinetic/pharmacodynamic evaluation of hydrocortisone therapy in pediatric patients with congenital adrenal hyperplasia | J. Melin, Z.P. Parra-Guillen, R. Michelet, T. Truong, W. Huisinga, N. Hartung, P. Hindmarsh, C. Kloft
Zeitschrift: The Journal of Clinical Endocrinology & Metabolism
Link zur Publikation
Pharmacokinetic/pharmacodynamic evaluation of hydrocortisone therapy in pediatric patients with congenital adrenal hyperplasia
Autoren: J. Melin, Z.P. Parra-Guillen, R. Michelet, T. Truong, W. Huisinga, N. Hartung, P. Hindmarsh, C. Kloft
(2020)
Zeitschrift:
The Journal of Clinical Endocrinology & Metabolism
2020 | Bayesian data assimilation to support informed decision‐making in individualized chemotherapy | C. Maier, N. Hartung, J. de Wiljes, C. Kloft, W. Huisinga
Zeitschrift: CPT: Pharmacometrics & Systems Pharmacology
Link zur Publikation
Bayesian data assimilation to support informed decision‐making in individualized chemotherapy
Autoren: C. Maier, N. Hartung, J. de Wiljes, C. Kloft, W. Huisinga
(2020)
An essential component of therapeutic drug/biomarker monitoring (TDM) is to combine patient data with prior knowledge for model‐based predictions of therapy outcomes. Current Bayesian forecasting tools typically rely only on the most probable model parameters (maximum a‐posteriori (MAP) estimate). This MAP‐based approach, however, does neither necessarily predict the most probable outcome nor does it quantify the risks of treatment inefficacy or toxicity. Bayesian data assimilation (DA) methods overcome these limitations by providing a comprehensive uncertainty quantification. We compare DA methods with MAP‐based approaches and show how probabilistic statements about key markers related to chemotherapy‐induced neutropenia can be leveraged for more informative decision support in individualized chemotherapy. Sequential Bayesian DA proved to be most computational efficient for handling interoccasion variability and integrating TDM data. For new digital monitoring devices enabling more frequent data collection, these features will be of critical importance to improve patient care decisions in various therapeutic areas.
Zeitschrift:
CPT: Pharmacometrics & Systems Pharmacology
2020 | Marked Gibbs point processes with unbounded interaction: an existence result | Sylvie Roelly, Alexander Zass
Zeitschrift: Journal of Statistical Physics
Seiten: 972–996
Band: 179
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,
Link zum Preprint
Marked Gibbs point processes with unbounded interaction: an existence result
Autoren: Sylvie Roelly, Alexander Zass
(2020)
We construct marked Gibbs point processes in ℝd under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded. Indeed, our typical interaction admits an as finite but random range. Secondly, the random marks - attached to the locations in ℝd - belong to a general normed space S. They are not bounded, but their law should admit a super-exponential moment. The approach used here relies on the so-called entropy method and large-deviation tools in order to prove tightness of a family of finite-volume Gibbs point processes. An application to infinite-dimensional interacting diffusions is also presented.
Zeitschrift:
Journal of Statistical Physics
2020 | On an Index Theorem of Chang, Weinberger and Yu | Thomas Schick, Mehran Seyedhosseini
Zeitschrift: Münster Journal of Mathematics
Link zur Publikation
On an Index Theorem of Chang, Weinberger and Yu
Autoren: Thomas Schick, Mehran Seyedhosseini
(2020)
In this paper we prove a strengthening of a theorem of Chang, Weinberger and Yu on obstructions to the existence of positive scalar curvature metrics on compact manifolds with boundary. They construct a relative index for the Dirac operator, which lives in a relative K-theory group, measuring the difference between the fundamental group of the boundary and of the full manifold. Whenever the Riemannian metric has product structure and positive scalar curvature near the boundary, one can define an absolute index of the Dirac operator taking value in the K-theory of the C*-algebra of fundamental group of the full manifold. This index depends on the metric near the boundary. We prove that the relative index of Chang, Weinberger and Yu is the image of this absolute index under the canonical map of K-theory groups. This has the immediate corollary that positive scalar curvature on the whole manifold implies vanishing of the relative index, giving a conceptual and direct proof of the vanishing theorem of Chang, Weinberger, and Yu. To take the fundamental groups of the manifold and its boundary into account requires working with maximal C* completions of the involved *-algebras. A significant part of this paper is devoted to foundational results regarding these completions.
Zeitschrift:
Münster Journal of Mathematics
2020 | On Maxwell's Equations on Globally Hyperbolic Spacetimes with Timelike Boundary | Claudio Dappiaggi, Nicolò Drago, Rubens Longhi
Zeitschrift: Ann. Henri Poincaré
Seiten: 2367–2409
Band: 21
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On Maxwell's Equations on Globally Hyperbolic Spacetimes with Timelike Boundary
Autoren: Claudio Dappiaggi, Nicolò Drago, Rubens Longhi
(2020)
We study Maxwell's equation as a theory for smooth k-forms on globally hyperbolic spacetimes with timelike boundary as defined by Aké, Flores and Sanchez. In particular we start by investigating on these backgrounds the D'Alembert - de Rham wave operator □k and we highlight the boundary conditions which yield a Green's formula for □k. Subsequently, we characterize the space of solutions of the associated initial and boundary value problem under the assumption that advanced and retarded Green operators do exist. This hypothesis is proven to be verified by a large class of boundary conditions using the method of boundary triples and under the additional assumption that the underlying spacetime is ultrastatic. Subsequently we focus on the Maxwell operator. First we construct the boundary conditions which entail a Green's formula for such operator and then we highlight two distinguished cases, dubbed δd-tangential and δd-normal boundary conditions. Associated to these we introduce two different notions of gauge equivalence and we prove that in both cases, every equivalence class admits a representative abiding to the Lorentz gauge. We use this property and the analysis of the operator □k to construct and to classify the space of gauge equivalence classes of solutions of the Maxwell's equations with the prescribed boundary conditions. As a last step and in the spirit of future applications in the framework of algebraic quantum field theory, we construct the associated unital ∗-algebras of observables proving in particular that, as in the case of the Maxwell operator on globally hyperbolic spacetimes with empty boundary, they possess a non-trivial center.
Zeitschrift:
Ann. Henri Poincaré
2020 | The Chiral Anomaly of the Free Fermion in Functorial Field Theory | Matthias Ludewig, Saskia Roos
Zeitschrift: Ann. Henri Poincaré
Verlag: Birkhauser Verlag
Seiten: 1191–1233
Band: 21
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Link zum Preprint
The Chiral Anomaly of the Free Fermion in Functorial Field Theory
Autoren: Matthias Ludewig, Saskia Roos
(2020)
When trying to cast the free fermion in the framework of functorial field theory, its chiral anomaly manifests in the fact that it assigns the determinant of the Dirac operator to a top-dimensional closed spin manifold, which is not a number as expected, but an element of a complex line. In functorial field theory language, this means that the theory is twisted, which gives rise to an anomaly theory. In this paper, we give a detailed construction of this anomaly theory, as a functor that sends manifolds to infinite-dimensional Clifford algebras and bordisms to bimodules.
Zeitschrift:
Ann. Henri Poincaré
Verlag:
Birkhauser Verlag
2020 | Inexact methods for the low-rank solution to large-scale Lyapunov equations | P. Kürschner, M.A. Freitag
Zeitschrift: BIT, 60:1221-1259
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Link zum Preprint
Inexact methods for the low-rank solution to large-scale Lyapunov equations
Autoren: P. Kürschner, M.A. Freitag
(2020)
Zeitschrift:
BIT, 60:1221-1259
2020 | The Zilch Electromagnetic Conservation Law in Variational Characteristic Form | Sajad Aghapour, Lars Andersson, Kjell Rosquist
Zeitschrift: J.Math.Phys.
Seiten: 122902
Band: 61
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The Zilch Electromagnetic Conservation Law in Variational Characteristic Form
Autoren: Sajad Aghapour, Lars Andersson, Kjell Rosquist
(2020)
In this paper we consider the zilch conservation laws for Maxwell theory and demonstrate that in the duality-symmetric version of Maxwell theory, the zilch arises as a Noether current for a variational symmetry of the duality symmetric Lagrangian which we identify through an application of the reverse of the Noether theorem. A variational symmetry leaves Lagrangian invariant up to a total divergence, without restricting to solutions of the field equations. This fact was previously known only for the so-called chirality current, i.e. the 00-component of zilch.
Zeitschrift:
J.Math.Phys.
2020 | Spectral continuity for aperiodic quantum systems: applications of a folklore theorem | Siegfried Beckus, Jean Bellissard, Giuseppe De Nittis
Zeitschrift: Journal of Mathematical Physics
Reihe: 61
Link zur Publikation
,
Link zum Preprint
,
Oberwolfach Preprint
Spectral continuity for aperiodic quantum systems: applications of a folklore theorem
Autoren: Siegfried Beckus, Jean Bellissard, Giuseppe De Nittis
(2020)
This work provides a necessary and sufficient condition for a symbolic dynamical system to admit a sequence of periodic approximations in the Hausdorff topology. The key result proved and applied here uses graphs that are called De Bruijn graphs, Rauzy graphs, or Anderson–Putnam complex, depending on the community. Combining this with a previous result, the present work justifies rigorously the accuracy and reliability of algorithmic methods used to compute numerically the spectra of a large class of self-adjoint operators. The so-called Hamiltonians describe the effective dynamic of a quantum particle in aperiodic media. No restrictions on the structure of these operators other than general regularity assumptions are imposed. In particular, nearest-neighbor correlation is not necessary. Examples for the Fibonacci and the Golay–Rudin–Shapiro sequences are explicitly provided illustrating this discussion. While the first sequence has been thoroughly studied by physicists and mathematicians alike, a shroud of mystery still surrounds the latter when it comes to spectral properties. In light of this, the present paper gives a new result here that might help uncovering a solution.
Zeitschrift:
Journal of Mathematical Physics
2020 | Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundary | Lashi Bandara, Medet Nursultanov, Julie Rowlett
Zeitschrift: To appear in Annali della Scuola Normale Superiore di Pisa. Classe di Scienze
Link zum Preprint
Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundary
Autoren: Lashi Bandara, Medet Nursultanov, Julie Rowlett
(2020)
Our topological setting is a smooth compact manifold of dimension two or higher with smooth boundary. Although this underlying topological structure is smooth, the Riemannian metric tensor is only assumed to be bounded and measurable. This is known as a rough Riemannian manifold. For a large class of boundary conditions we demonstrate a Weyl law for the asymptotics of the eigenvalues of the Laplacian associated to a rough metric. Moreover, we obtain eigenvalue asymptotics for weighted Laplace equations associated to a rough metric. Of particular novelty is that the weight function is not assumed to be of fixed sign, and thus the eigenvalues may be both positive and negative. Key ingredients in the proofs were demonstrated by Birman and Solomjak nearly fifty years ago in their seminal work on eigenvalue asymptotics. In addition to determining the eigenvalue asymptotics in the rough Riemannian manifold setting for weighted Laplace equations, we also wish to promote their achievements which may have further applications to modern problems.
Zeitschrift:
To appear in Annali della Scuola Normale Superiore di Pisa. Classe di Scienze
2020 | The Dirac operator under collapse to a smooth limit space | Saskia Roos
Zeitschrift: Ann. Glob. Anal. Geom.
Verlag: Springer
Seiten: 121–151
Band: 57
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The Dirac operator under collapse to a smooth limit space
Autoren: Saskia Roos
(2020)
Let (Mi,gi)i∈ℕ be a sequence of spin manifolds with uniform bounded curvature and diameter that converges to a lower-dimensional Riemannian manifold (B, h) in the Gromov–Hausdorff topology. Then, it happens that the spectrum of the Dirac operator converges to the spectrum of a certain first-order elliptic differential operator DB on B. We give an explicit description of DB and characterize the special case where DB equals the Dirac operator on B.
Zeitschrift:
Ann. Glob. Anal. Geom.
2020 | Heat kernels and regularity for rough metrics on smooth manifolds | Lashi Bandara, Paul Bryan
Zeitschrift: Mathematische Nachrichten
Reihe: 293
Seiten: 2255-2270
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Heat kernels and regularity for rough metrics on smooth manifolds
Autoren: Lashi Bandara, Paul Bryan
(2020)
We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are H\"older continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with bounded measurable coefficients in weighted Sobolev spaces.
Zeitschrift:
Mathematische Nachrichten
2020 | Pinned diffusions and Markov bridges | Florian Hildebrandt, Sylvie Roelly
Zeitschrift: Journal of Theoretical Probability
Seiten: 906-917
Band: 33
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Pinned diffusions and Markov bridges
Autoren: Florian Hildebrandt, Sylvie Roelly
(2020)
In this article we consider a family of real-valued diffusion processes on the time interval [0; 1] indexed by their prescribed initial value and another point y in space. We first present a condition on their drift and diffusion coefficients ensuring that the diffusion is pinned in y at time 1. Our main result then concerns the following question: can this family of pinned diffusions be obtained as the bridges either of a Gaussian Markov process or of an Ito diffusion? We eventually illustrate our precise answer with several examples.
Zeitschrift:
Journal of Theoretical Probability
2020 | Nonlinear stability of the Milne model with matter | Lars Andersson, David Fajman
Zeitschrift: Commun. Math. Phys.
Seiten: 261–298
Band: 378
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Nonlinear stability of the Milne model with matter
Autoren: Lars Andersson, David Fajman
(2020)
We show that any 3+1-dimensional Milne model is future nonlinearly, asymptotically stable in the set of solutions to the Einstein-Vlasov system. For the analysis of the Einstein equations we use the constant-mean-curvature-spatial-harmonic gauge. For the distribution function the proof makes use of geometric L^2-estimates based on the Sasaki-metric. The resulting estimates on the energy momentum tensor are then upgraded by employing the natural continuity equation for the energy density.
Zeitschrift:
Commun. Math. Phys.
2020 | Morawetz estimate for linearized gravity in Schwarzschild | Lars Andersson, Pieter Blue, Jinhua Wang
Zeitschrift: Annales Henri Poincaré
Verlag: Springer
Seiten: 1–53
Link zur Publikation
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Link zum Preprint
Morawetz estimate for linearized gravity in Schwarzschild
Autoren: Lars Andersson, Pieter Blue, Jinhua Wang
(2020)
The equations governing the perturbations of the Schwarzschild metric satisfy the Regge-Wheeler-Zerilli-Moncrief system. Applying the technique introduced in [2], we prove an integrated local energy decay estimate for both the Regge-Wheeler and Zerilli equations. In these proofs, we use some constants that are computed numerically. Furthermore, we make use of the rp hierarchy estimates [13, 32] to prove that both the Regge-Wheeler and Zerilli variables decay as t-3/2 in fixed regions of r.
Zeitschrift:
Annales Henri Poincaré
2019 | The de Rham cohomology through Hilbert space methods | Ihsane Malass, Nikolai Tarkhanov
Zeitschrift: Journal of Siberian Federal University. Mathematics & Physics
Seiten: 455–465
Band: 12
Link zur Publikation
The de Rham cohomology through Hilbert space methods
Autoren: Ihsane Malass, Nikolai Tarkhanov
(2019)
We discuss canonical representations of the de Rham cohomology on a compact manifold with boundary. They are obtained by minimising the energy integral in a Hilbert space of differential forms that belong along with the exterior derivative to the domain of the adjoint operator. The corresponding Euler–Lagrange equations reduce to an elliptic boundary value problem on the manifold, which is usually referred to as the Neumann problem after Spencer.
Zeitschrift:
Journal of Siberian Federal University. Mathematics & Physics
2019 | Discrete gradients for computational Bayesian inference | Sahani Pathiraja and Sebastian Reich
Zeitschrift: Journal of Computational Dynamics 2019
Discrete gradients for computational Bayesian inference
Autoren: Sahani Pathiraja and Sebastian Reich
(2019)
Zeitschrift:
Journal of Computational Dynamics 2019
2019 | First order convergence of weak Wong–Zakai approximations of Lévy-driven Marcus SDEs | T. Kosenkova, A. Kulik, I. Pavlyukevich
Zeitschrift: Theory Stoch. Process.
Reihe: 24 (40)
Seiten: 32-60
Band: 2
First order convergence of weak Wong–Zakai approximations of Lévy-driven Marcus SDEs
Autoren: T. Kosenkova, A. Kulik, I. Pavlyukevich
(2019)
Zeitschrift:
Theory Stoch. Process.
2019 | Teaching of Computing to Mathematics Students: Programming and Discrete Mathematics | J. Betteridge, J.H. Davenport, M.A. Freitag, W. Heijtljes, S. Kynaston, G. Sankaran, G. Traustason
Zeitschrift: Proceedings of the 3rd Conference on Computing Education Practice, 12, 1-4
Link zur Publikation
Teaching of Computing to Mathematics Students: Programming and Discrete Mathematics
Autoren: J. Betteridge, J.H. Davenport, M.A. Freitag, W. Heijtljes, S. Kynaston, G. Sankaran, G. Traustason
(2019)
Zeitschrift:
Proceedings of the 3rd Conference on Computing Education Practice, 12, 1-4
2019 | Variational principle for the Einstein-Vlasov equations | Lars Andersson, Mikołaj Korzyński
Link zum Preprint
Variational principle for the Einstein-Vlasov equations
Autoren: Lars Andersson, Mikołaj Korzyński
(2019)
The Einstein-Vlasov equations govern Einstein spacetimes filled with matter which interacts only via gravitation. The matter, described by a distribution function on phase space, evolves under the collisionless Boltzmann equation, corresponding to the free geodesic motion of the particles, while the source of the gravitational field is given by the stress-energy tensor defined in terms of momenta of the distribution function. As no variational derivation of the Einstein-Vlasov system appears to exist in the literature, we here set out to fill this gap. In our approach we treat the matter as a generalized type of fluid, flowing in the tangent bundle instead of the spacetime. We present the actions for the Einstein-Vlasov system in both the Lagrangian and Eulerian pictures.
2019 | On the Cauchy problem for the linearised Einstein equation | Oliver Lindblad Petersen
Zeitschrift: Annales Henri Poincaré
Seiten: 3849–3888
Band: 20
Link zur Publikation
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Link zum Preprint
On the Cauchy problem for the linearised Einstein equation
Autoren: Oliver Lindblad Petersen
(2019)
A classical problem in general relativity is the Cauchy problem for the linearised Einstein equation (the initial value problem for gravitational waves) on a globally hyperbolic vacuum spacetime. A well-known result is that it is uniquely solvable up to gauge solutions, given initial data on a spacelike Cauchy hypersurface. The solution map is an isomorphism between initial data (modulo gauge producing initial data) and solutions (modulo gauge solutions). In the first part of this work, we show that the solution map is actually an isomorphism of locally convex topological vector spaces. This implies that the equivalence class of solutions depends continuously on the equivalence class of initial data. We may therefore conclude well-posedness of the Cauchy problem. In the second part, we show that the linearised constraint equations can always be solved on a closed manifold with vanishing scalar curvature. This generalises the classical notion of TT-tensors on flat space used to produce models of gravitational waves. All our results are proven for smooth and distributional initial data of arbitrary real Sobolev regularity.
Zeitschrift:
Annales Henri Poincaré
2019 | Boundary representation of Dirichlet forms on discrete spaces | Matthias Keller, Daniel Lenz, Marcel Schmidt, Michael Schwarz
Zeitschrift: Journal de Mathématique Pure et Appliquée
Seiten: 109-143
Band: 126
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Link zum Preprint
Boundary representation of Dirichlet forms on discrete spaces
Autoren: Matthias Keller, Daniel Lenz, Marcel Schmidt, Michael Schwarz
(2019)
We describe the set of all Dirichlet forms associated to a given infinitegraphin terms of Dirichlet forms on its Royden boundary. Our approach is purely analyticaland uses form methods.
Zeitschrift:
Journal de Mathématique Pure et Appliquée
2019 | Tikhonov regularization with oversmoothing penalty for linear statistical inverse learning problems. | A. Rastogi
Zeitschrift: AIP Conference Proceedings.
Verlag: AIP Publishing LLC
Band: 2183 (1)
Link zur Publikation
Tikhonov regularization with oversmoothing penalty for linear statistical inverse learning problems.
Autoren: A. Rastogi
(2019)
Zeitschrift:
AIP Conference Proceedings.
Verlag:
AIP Publishing LLC
2019 | Rates of convergence to the local time of Oscillating and Skew Brownian Motions | Sara Mazzonetto
Zeitschrift: Preprint
Link zum Preprint
Rates of convergence to the local time of Oscillating and Skew Brownian Motions
Autoren: Sara Mazzonetto
(2019)
In this paper a class of statistics based on high frequency observations of oscillating Brownian motions and skew Brownian motions is considered. Their convergence rate towards the local time of the underling process is obtained in form of a Central Limit Theorem. The convergence speed is the same as in the case of Brownian motion but oscillating and skew Brownian motion have singular coecients and their local time is discontinuous.
2019 | Strong convergence rates of probabilistic integrators for ordinary differential equations | H. C. Lie, A. M. Stuart, T. J. Sullivan
Zeitschrift: Stat Comput
Verlag: Springer
Seiten: 1265-1283
Band: 29
Link zur Publikation
,
Link zum Preprint
Strong convergence rates of probabilistic integrators for ordinary differential equations
Autoren: H. C. Lie, A. M. Stuart, T. J. Sullivan
(2019)
2019 | On a degeneracy ratio for bounded convex polytopes | Nada Cvetković, Han Cheng Lie
Link zum Preprint
On a degeneracy ratio for bounded convex polytopes
Autoren: Nada Cvetković, Han Cheng Lie
(2019)
2019 | The Isoperimetric Inequality: Proofs by Convex and Differential Geometry | Penelope Gehring
Zeitschrift: Rose Hulman Undergraduate Mathematics Journal
Band: 20, no. 2
Link zur Publikation
The Isoperimetric Inequality: Proofs by Convex and Differential Geometry
Autoren: Penelope Gehring
(2019)
The Isoperimetric Inequality has many different proofs using methods from diverse mathematical fields. In the paper, two methods to prove this inequality will be shown and compared. First the 2-dimensional case will be proven by tools of elementary differential geometry and Fourier analysis. Afterwards the theory of convex geometry will briefly be introduced and will be used to prove the Brunn--Minkowski-Inequality. Using this inequality, the Isoperimetric Inquality in n dimensions will be shown.
Zeitschrift:
Rose Hulman Undergraduate Mathematics Journal
2019 | Development of a dosing algorithm for meropenem in critically ill patients based on a population pharmacokinetic/pharmacodynamic analysis. | L. Ehmann, M. Zoller, I.K. Minichmayr, C. Scharf, W. Huisinga, J. Zander, C. Kloft
Zeitschrift: Int. J. Antimicrob. Agents
Seiten: 309-317
Band: 54
Link zur Publikation
Development of a dosing algorithm for meropenem in critically ill patients based on a population pharmacokinetic/pharmacodynamic analysis.
Autoren: L. Ehmann, M. Zoller, I.K. Minichmayr, C. Scharf, W. Huisinga, J. Zander, C. Kloft
(2019)
Zeitschrift:
Int. J. Antimicrob. Agents
2019 | Phase transition of the non-symmetric Continuum Potts model | P. Houdebert
Zeitschrift: arXiv:1908.10066
Link zum Preprint
Phase transition of the non-symmetric Continuum Potts model
Autoren: P. Houdebert
(2019)
Zeitschrift:
arXiv:1908.10066
2019 | A stochastic Gronwall inequality andapplications to moments, strong completeness,strong local Lipschitz continuity, and perturbations | Anselm Hudde, Martin Hutzenthaler, Sara Mazzonetto
Zeitschrift: Accepted in Ann. Inst. H. Poincaré Probab. Statist.
Link zum Preprint
A stochastic Gronwall inequality andapplications to moments, strong completeness,strong local Lipschitz continuity, and perturbations
Autoren: Anselm Hudde, Martin Hutzenthaler, Sara Mazzonetto
(2019)
Zeitschrift:
Accepted in Ann. Inst. H. Poincaré Probab. Statist.
2019 | Statistical inference for Bures-Wasserstein barycenters | Alexey Kroshnin, Vladimir Spokoiny, Alexandra Suvorikova
Zeitschrift: Preprint
Link zum Preprint
Statistical inference for Bures-Wasserstein barycenters
Autoren: Alexey Kroshnin, Vladimir Spokoiny, Alexandra Suvorikova
(2019)
2019 | Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problems | A Rastogi, G Blanchard, P Mathé
Zeitschrift: Preprint
Link zum Preprint
Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problems
Autoren: A Rastogi, G Blanchard, P Mathé
(2019)
2019 | A minimax near-optimal algorithm for adaptive rejection sampling | J Achddou, J Lam-Weil, A Carpentier, G Blanchard
Zeitschrift: ALT
Seiten: 94-126
Link zur Publikation
A minimax near-optimal algorithm for adaptive rejection sampling
Autoren: J Achddou, J Lam-Weil, A Carpentier, G Blanchard
(2019)
2019 | Lepskii Principle in Supervised Learning | G Blanchard, P Mathé, N Mücke
Zeitschrift: Preprint
Link zum Preprint
Lepskii Principle in Supervised Learning
Autoren: G Blanchard, P Mathé, N Mücke
(2019)
2019 | Restless dependent bandits with fading memory | O Zadorozhnyi, G Blanchard, A Carpentier
Zeitschrift: Preprint
Link zum Preprint
Restless dependent bandits with fading memory
Autoren: O Zadorozhnyi, G Blanchard, A Carpentier
(2019)
We study the stochastic multi-armed bandit problem in the case when the arm samples are dependent over time and generated from so-called weak $\cC $-mixing processes. We establish a $\cC-$ Mix Improved UCB agorithm and provide both problem-dependent and independent regret analysis in two different scenarios. In the first, so-called fast-mixing scenario, we show that pseudo-regret enjoys the same upper bound (up to a factor) as for iid observations; whereas in the second, slow mixing scenario, we discover a surprising effect, that the regret upper bound is similar to the independent case, with an incremental {\em additive} term which does not depend on the number of arms. The analysis of slow mixing scenario is supported with a minmax lower bound, which (up to a factor log(T)) matches the obtained upper bound.
2019 | Volume Doubling Condition and a Local Poincar\'e Inequality on Unweighted Random Geometric Graphs | F Göbel, G Blanchard
Zeitschrift: Preprint
Link zum Preprint
Volume Doubling Condition and a Local Poincar\'e Inequality on Unweighted Random Geometric Graphs
Autoren: F Göbel, G Blanchard
(2019)
2019 | 1940 : Wolfgang Döblin, génie du passé, héros d’aujourd’hui. Quand les probabilités rencontrent la physique et l’économie. | Guillaume Peter, Sylvie Roelly
Zeitschrift: Images des Mathématiques
Reihe: Les 80 ans du CNRS
Verlag: Institut Henri Poincaré
Link zur Publikation
1940 : Wolfgang Döblin, génie du passé, héros d’aujourd’hui. Quand les probabilités rencontrent la physique et l’économie.
Autoren: Guillaume Peter, Sylvie Roelly
(2019)
L’histoire ne se compose pas uniquement de guerres ou de règnes de monarques. La science a marqué l’histoire grâce à de nombreuses découvertes, passionnantes tant d’un point de vue scientifique qu’historique. Nous connaissons les grands de ce monde dont les découvertes ont façonné notre société : Pierre (1859-1906) et Marie (1867-1934) Curie, Albert Einstein (1879-1955), Nicolas Tesla (1856-1943), Ernest Rutherford (1871-1937) et bien d’autres encore. Wolfgang Döblin (1915-1940) mérite lui aussi toute notre attention car ses travaux mathématiques avant-gardistes sont méconnus, bien qu’ils aient débouché sur des applications importantes dans nombre de domaines tels la finance ou la physique. Sa vie tourmentée fut dense et finit tragiquement.
Zeitschrift:
Images des Mathématiques
Reihe:
Les 80 ans du CNRS
Verlag:
Institut Henri Poincaré
2019 | Minimizers of Generalized Willmore Functionals | Alexander Friedrich
Link zum Preprint
Minimizers of Generalized Willmore Functionals
Autoren: Alexander Friedrich
(2019)
We introduce a notion of generalized Willmore functionals motivated by the Hawking energy of General Relativity and bending energies of membranes. An example of a bending energy is discussed in detail. Using results of Y. Chen and J. Li, we present a compactness result for branched, immersed, haunted, stratified surface with bounded area and Willmore energy. This allows us to prove the existence of area constrained minimizers for generalized Willmore functionals in the class of haunted, branched, immersed bubble trees by direct minimization. Here a haunted, stratified surfaces are introduced, in order to account for bubbling and vanishing components along the minimization process. Similarly, we obtain the existence of area and volume constrained, minimal, closed membranes for the discussed bending energy. Moreover, we argue that the regularity results of A. Mondino and T. Rivière for Willmore surfaces can be carried over to the setting of generalized Willmore surfaces. In particular, this means that critical points of a generalized Willmore functional are smooth away from finitely many points.
2019 | Hölder Continuity of the Spectra for Aperiodic Hamiltonians | Siegfried Beckus, Jean Bellissard, Horia Cornean
Zeitschrift: Annales Henri Poincaré
Reihe: 20
Seiten: 3603 - 3631
Link zur Publikation
,
Link zum Preprint
,
Oberwolfach Preprint
Hölder Continuity of the Spectra for Aperiodic Hamiltonians
Autoren: Siegfried Beckus, Jean Bellissard, Horia Cornean
(2019)
We study the spectral location of strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to each other" if, up to a translation, they "almost coincide" on a large fixed ball. The larger this ball is, the more similar they are, and this induces a metric on the space of the corresponding dynamical systems. Our main result states that the map which sends a given configuration into the spectrum of its associated Hamiltonian, is Hölder (even Lipschitz) continuous in the usual Hausdorff metric. Specifically, the spectral distance of two Hamiltonians is estimated by the distance of the corresponding dynamical systems.
Zeitschrift:
Annales Henri Poincaré
2019 | Projection methods for weak constraint variational data assimilation | M.A. Freitag, D.L.H. Green
Projection methods for weak constraint variational data assimilation
Autoren: M.A. Freitag, D.L.H. Green
(2019)
2019 | Refined position estimates for surfaces of Willmore type in Riemannian manifolds | Jan Metzger
Zeitschrift: Comm. Anal. Geom.30(2022), no.10, 2315–2346.
Link zur Publikation
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Link zum Preprint
Refined position estimates for surfaces of Willmore type in Riemannian manifolds
Autoren: Jan Metzger
(2019)
In this paper we consider surfaces which are critical points of the Willmore functional subject to constrained area. In the case of small area we calculate the corrections to the intrinsic geometry induced by the ambient curvature. These estimates together with the choice of an adapted geometric center of mass lead to refined position estimates in relation to the scalar curvature of the ambient manifold.
Zeitschrift:
Comm. Anal. Geom.30(2022), no.10, 2315–2346.
2019 | Corrigendum to “Spectral continuity for aperiodic quantum systems I. General theory | Siegfried Beckus, Jean Bellissard, Giuseppe De Nittis
Zeitschrift: Journal of Functional Analysis
Reihe: 277
Seiten: 3351-3353
Link zur Publikation
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Link zum Preprint
Corrigendum to “Spectral continuity for aperiodic quantum systems I. General theory
Autoren: Siegfried Beckus, Jean Bellissard, Giuseppe De Nittis
(2019)
A correct statement of Theorem 4 in [1] is provided. The change does not affect the main results.
Zeitschrift:
Journal of Functional Analysis
2019 | A new discrete Hopf-Rinow theorem | Matthias Keller, Florentin Münch
Zeitschrift: Discrete Mathematics
Seiten: 2751-2757
Band: 342
Link zur Publikation
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Link zum Preprint
A new discrete Hopf-Rinow theorem
Autoren: Matthias Keller, Florentin Münch
(2019)
We prove a version of the Hopf–Rinow theorem with respect to path metrics on discrete spaces. The novel aspect is that we do not a priori assume local finiteness but isolate a local finiteness type condition, called essentially locally finite, that is indeed necessary. As a side product we identify the maximal weight, called the geodesic weight, generating the path metric in the situation when the space is complete with respect to any of the equivalent notions of completeness proven in the Hopf–Rinow theorem. As an application we characterize the graphs for which the resistance metric is a path metric induced by the graph structure.
Zeitschrift:
Discrete Mathematics
2019 | Stability for linearized gravity on the Kerr spacetime | Lars Andersson, Thomas Bäckdahl, Pieter Blue, Siyuan Ma
Zeitschrift: Annals of PDE (to appear)
Link zum Preprint
Stability for linearized gravity on the Kerr spacetime
Autoren: Lars Andersson, Thomas Bäckdahl, Pieter Blue, Siyuan Ma
(2019)
In this paper we prove integrated energy and pointwise decay estimates for solutions of the vacuum linearized Einstein equation on the Kerr black hole exterior. The estimates are valid for the full, subextreme range of Kerr black holes, provided integrated energy estimates for the Teukolsky Master Equation holds. For slowly rotating Kerr backgrounds, such estimates are known to hold, due to the work of one of the authors arXiv:1708.07385. The results in this paper thus provide the first stability results for linearized gravity on the Kerr background, in the slowly rotating case, and reduce the linearized stability problem for the full subextreme range to proving integrated energy estimates for the Teukolsky equation. This constitutes an essential step towards a proof of the black hole stability conjecture, i.e. the statement that the Kerr family is dynamically stable, one of the central open problems in general relativity.
The proof relies on three key steps. First, there are energy decay estimates for the Teukolsky equation, proved by applying weighted multiplier estimates to a system of spin-weighted wave equations derived from the Teukolsky equation, and making use of the pigeonhole principle for the resulting hierarchy of weighted energy estimates. Second, working in the outgoing radiation gauge, the linearized Einstein equations are written as a system of transport equations, driven by one of the Teukolsky scalars. Third, expansions for the relevant curvature, connection, and metric components can be made near null infinity. An analysis of the dynamics on future null infinity, together with the Teukolsky Starobinsky Identity plays an important role in the argument.
Zeitschrift:
Annals of PDE (to appear)
2019 | An overview of the gravitational spin Hall effect | Marius A. Oancea, Claudio F. Paganini, Jérémie Joudioux, Lars Andersson
Link zum Preprint
An overview of the gravitational spin Hall effect
Autoren: Marius A. Oancea, Claudio F. Paganini, Jérémie Joudioux, Lars Andersson
(2019)
In General Relativity, the propagation of electromagnetic waves is usually described by the vacuum Maxwell's equations on a fixed curved background. In the limit of infinitely high frequencies, electromagnetic waves can be localized as point particles, following null geodesics. However, at finite frequencies, electromagnetic waves can no longer be treated as point particles following null geodesics, and the spin angular momentum of light comes into play, via the spin-curvature coupling. We will refer to this effect as the gravitational spin Hall effect of light. Here, we review a series of theoretical results related to the gravitational spin Hall effect of light, and we compare the predictions of different models. The analogy with the spin Hall effect in Optics is also explored, since in this field the effect is well understood, both theoretically and experimentally.
2019 | Comment on Jaki et al., A proposal for a new PhD level curriculum on quantitative methods for drug development. Pharmaceutical Statistics 17 (5):593–606, Sep/Oct 2018, DOI: 10.1002/pst.1873 | A. Krause, C. Kloft, W. Huisinga, M. Karlsson, J. Pinheiro, R. Bies, J. Rogers, F. Mentré, B.J. Musser, ASA Special Interest Group on Statistics and Pharmacometrics/ASA Special Interest Group on Statistics and Pharmacometrics (SIG SxP)
Zeitschrift: Pharmaceutical Statistics
Seiten: 278–281
Band: 18
Link zur Publikation
Comment on Jaki et al., A proposal for a new PhD level curriculum on quantitative methods for drug development. Pharmaceutical Statistics 17 (5):593–606, Sep/Oct 2018, DOI: 10.1002/pst.1873
Autoren: A. Krause, C. Kloft, W. Huisinga, M. Karlsson, J. Pinheiro, R. Bies, J. Rogers, F. Mentré, B.J. Musser, ASA Special Interest Group on Statistics and Pharmacometrics/ASA Special Interest Group on Statistics and Pharmacometrics (SIG SxP)
(2019)
Zeitschrift:
Pharmaceutical Statistics
2019 | The circadian rhythm of corticosteroid-binding globulin has little impact on cortisol exposure after hydrocortisone dosing | J. Melin, N. Hartung, Z.P. Parra-Guillen, M.J. Whitaker, R.J. Ross, C. Kloft
Zeitschrift: Clinical Endocrinology
Link zur Publikation
The circadian rhythm of corticosteroid-binding globulin has little impact on cortisol exposure after hydrocortisone dosing
Autoren: J. Melin, N. Hartung, Z.P. Parra-Guillen, M.J. Whitaker, R.J. Ross, C. Kloft
(2019)
Zeitschrift:
Clinical Endocrinology
2019 | Functional calculus and harmonic analysis in geometry | Lashi Bandara
Zeitschrift: São Paulo Journal of Mathematical Sciences, Special Section: An Homage to Manfredo P. do Carmo
Seiten: 1-34
Link zur Publikation
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Link zum Preprint
Functional calculus and harmonic analysis in geometry
Autoren: Lashi Bandara
(2019)
In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these methods as well as their interplay. This is a succinct survey that hopes to inspire geometers and analysts alike to study these methods so that they can be further developed to be potentially applied to a broader range of questions.
Zeitschrift:
São Paulo Journal of Mathematical Sciences, Special Section: An Homage to Manfredo P. do Carmo
2019 | Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operator | Nicolas Garcia Trillos, Moritz Gerlach, Matthias Hein, Dejan Slepcev
Zeitschrift: Foundations of Computational Mathematics
Link zur Publikation
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Link zum Preprint
Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operator
Autoren: Nicolas Garcia Trillos, Moritz Gerlach, Matthias Hein, Dejan Slepcev
(2019)
We study the convergence of the graph Laplacian of a random geometric graph generated by an i.i.d. sample from a m-dimensional submanifold M in R^d as the sample size n increases and the neighborhood size h tends to zero. We show that eigenvalues and eigenvectors of the graph Laplacian converge with a rate of O\Big(\big(\frac{\log n}{n}\big)^\frac{1}{2m}\Big) to the eigenvalues and eigenfunctions of the weighted Laplace-Beltrami operator of M.
No information on the submanifold M is needed in the construction of the graph or the "out-of-sample extension" of the eigenvectors. Of independent interest is a generalization of the rate of convergence of empirical measures on submanifolds in R^d in infinity transportation distance.
Zeitschrift:
Foundations of Computational Mathematics
2019 | On the asymptotic behavior of static perfect fluids | Lars Andersson, Annegret Y. Burtscher
Zeitschrift: Annales Henri Poincaré
Verlag: Springer
Seiten: 813-857
Band: 20, no. 3
Link zur Publikation
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Link zum Preprint
On the asymptotic behavior of static perfect fluids
Autoren: Lars Andersson, Annegret Y. Burtscher
(2019)
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether solutions have finite extent (stars with a vacuum exterior) or infinite extent. In the latter case, the matter extends globally with the density approaching zero at infinity. The asymptotic behavior largely depends on the equation of state of the fluid and is still poorly understood. While a few such unbounded solutions are known to be asymptotically flat with finite ADM mass, the vast majority are not. We provide a full geometric description of the asymptotic behavior of static spherically symmetric perfect fluid solutions with linear and polytropic-type equations of state. In order to capture the asymptotic behavior we introduce a notion of scaled quasi-asymptotic flatness, which encodes a form of asymptotic conicality. In particular, these spacetimes are asymptotically simple.
Zeitschrift:
Annales Henri Poincaré
2019 | Conditioned point processes with application to Lévy bridges | Giovanni Conforti, Tetiana Kosenkova, Sylvie Roelly
Zeitschrift: Journal of Theoretical Probability
Seiten: 2111-2134
Band: 32
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Link zum Preprint
Conditioned point processes with application to Lévy bridges
Autoren: Giovanni Conforti, Tetiana Kosenkova, Sylvie Roelly
(2019)
Our first result concerns a characterisation by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalised version of Mecke's formula. En passant, it also allows to gain quantitative results about stochastic domination for Poisson point processes under linear constraints.
Since bridges of a pure jump Lévy process in R^d with a height h can be interpreted as a Poisson point process on space-time conditioned by pinning its first moment to h, our approach allows us to characterize bridges of Lévy processes by means of a functional equation.
The latter result has two direct applications:
first we obtain a constructive and simple way to sample Lévy bridge dynamics; second it allows to estimate the number of jumps for such bridges. We finally show that our method remains valid for linearly perturbed Lévy processes like periodic Ornstein-Uhlenbeck processes driven by Lévy noise.
Zeitschrift:
Journal of Theoretical Probability
2019 | Packungen aus Kreisscheiben | Charlotte Dombrowsky, Myriam Fradon, Sylvie Roelly
Zeitschrift: Elemente der Mathematik
Seiten: pp.45-62
Band: 74-2
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Link zum Preprint
Packungen aus Kreisscheiben
Autoren: Charlotte Dombrowsky, Myriam Fradon, Sylvie Roelly
(2019)
Wir beschäftigen uns mit Konfigurationen von gleichgroßen Kreisscheiben in einer Ebene, die sich nicht überlappen. Wir sind insbesondere daran interessiert, die Konfiguration(en) zu finden, die eine minimale quadratische Energie besitzen.
In der Tat, ist die genaue Geometrie der optimalen Konfiguration(en) nur für sehr kleine Systeme schon bekannt. Wir schlagen hier eine wahrscheinlichkeitstheoretische Methode vor, die effizient für Systeme jeder Größe ist.
Zeitschrift:
Elemente der Mathematik
2019 | Concentration of weakly dependent Banach-valued sums and applications to statistical learning methods | Blanchard G., Zadorozhnyi O.
Zeitschrift: Bernoulli
Seiten: 3421-3458
Band: 25
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Concentration of weakly dependent Banach-valued sums and applications to statistical learning methods
Autoren: Blanchard G., Zadorozhnyi O.
(2019)
We obtain a new Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order to investigate in asymptotical regime the error upper bounds for the broad family of spectral regularization methods for reproducing kernel decision rules, when trained on a sample coming from a τ−mixing process.
2019 | Decontamination of Mutual Contamination Models | J. Katz-Samuels, G. Blanchard, C. Scott.
Zeitschrift: Journal of Machine Learning Research
Link zum Preprint
Decontamination of Mutual Contamination Models
Autoren: J. Katz-Samuels, G. Blanchard, C. Scott.
(2019)
Zeitschrift:
Journal of Machine Learning Research
2019 | Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions | Lashi Bandara, Andreas Rosén
Zeitschrift: Comm. Part. Diff. Eq.
Verlag: Taylor & Francis
Band: DOI: 10.1080/03605302.2019.1611847
Link zur Publikation
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Link zum Preprint
Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions
Autoren: Lashi Bandara, Andreas Rosén
(2019)
On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that Atiyah-Singer Dirac operator DB in L2 depends Riesz continuously on L∞ perturbations of local boundary conditions B. The Lipschitz bound for the map B→DB(1+DB2)-1/2 depends on Lipschitz smoothness and ellipticity of B and bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius. More generally, we prove perturbation estimates for functional calculi of elliptic operators on manifolds with local boundary conditions.
Zeitschrift:
Comm. Part. Diff. Eq.
Band:
DOI: 10.1080/03605302.2019.1611847
2019 | Mean ergodicity vs weak almost periodicity | Moritz Gerlach, Jochen Glück
Zeitschrift: Studia Mathematica
Seiten: 45-56
Band: 248
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Link zum Preprint
Mean ergodicity vs weak almost periodicity
Autoren: Moritz Gerlach, Jochen Glück
(2019)
We provide explicit examples of positive and power-bounded operators on $c_0$ and $\ell^\infty$ which are mean ergodic but not weakly almost periodic. As a consequence we prove that a countably order complete Banach lattice on which every positive and power-bounded mean ergodic operator is weakly almost periodic is necessarily a KB-space. This answers several open questions from the literature.
Finally, we prove that if $T$ is a positive mean ergodic operator with zero fixed space on an arbitrary Banach lattice, then so is every power of $T$.
Zeitschrift:
Studia Mathematica
2019 | Convergence of Positive Operator Semigroups | Moritz Gerlach, Jochen Glück
Zeitschrift: Transactions of the American Mathematical Society
Seiten: 6603-6627
Band: 372
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Convergence of Positive Operator Semigroups
Autoren: Moritz Gerlach, Jochen Glück
(2019)
We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw and Glicksberg with a purely algebraic result about positive group representations. Thus we obtain convergence theorems not only for one-parameter semigroups but for a much larger class of semigroup representations.
Our results allow for a unified treatment of various theorems from the literature that, under technical assumptions, a bounded positive $C_0$-semigroup containing or dominating a kernel operator converges strongly as $t \to \infty$. We gain new insights into the structure theoretical background of those theorems and generalise them in several respects; especially we drop any kind of continuity or regularity assumption with respect
to the time parameter.
As applications we derive, inter alia, a generalisation of a famous theorem by Doob for operator semigroups on the space of measures and a Tauberian theorem for positive one-parameter semigroups under rather weak continuity assumptions. We also demonstrate how our results are useful to treat semigroups that do not satisfy any irreducibility conditions.
Zeitschrift:
Transactions of the American Mathematical Society
2019 | The curl operator on odd-dimensional manifolds | Christian Bär
Zeitschrift: J. Math. Phys.
Seiten: 031501
Band: 60
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Link zum Preprint
The curl operator on odd-dimensional manifolds
Autoren: Christian Bär
(2019)
We study the spectral properties of curl, a linear differential operator of first order acting on differential forms of appropriate degree on an odd-dimensional closed oriented Riemannian manifold. In three dimensions its eigenvalues are the electromagnetic oscillation frequencies in vacuum without external sources. In general, the spectrum consists of the eigenvalue 0 with infinite multiplicity and further real discrete eigenvalues of finite multiplicity. We compute the Weyl asymptotics and study the zeta-function. We give a sharp lower eigenvalue bound for positively curved manifolds and analyze the equality case. Finally, we compute the spectrum for flat tori, round spheres and 3-dimensional spherical space forms.
Zeitschrift:
J. Math. Phys.
2019 | New identities for linearized gravity on the Kerr spacetime | Steffen Aksteiner, Lars Andersson, Thomas Bäckdahl
Zeitschrift: Physical Review D
Verlag: American Physical Society
Seiten: 044043
Band: 99
Link zur Publikation
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Link zum Preprint
New identities for linearized gravity on the Kerr spacetime
Autoren: Steffen Aksteiner, Lars Andersson, Thomas Bäckdahl
(2019)
In this paper we derive a differential identity for linearized gravity on the Kerr spacetime and more generally on vacuum spacetimes of Petrov type D. We show that a linear combination of second derivatives of the linearized Weyl tensor can be formed into a complex symmetric 2-tensor Mab which solves the linearized Einstein equations. The identity makes this manifest by relating Mab to two terms solving the linearized Einstein equations by construction. The self-dual Weyl curvature of Mab gives a covariant version of the Teukolsky-Starobinsky identities for linearized gravity which, in addition to the two classical identities for linearized Weyl scalars with extreme spin weights, includes three additional equations. In particular, they are not consequences of the classical Teukolsky-Starobinsky identities, but are additional integrability conditions for linearized gravity. The result has direct application in the construction of symmetry operators and also yields a set of nontrivial gauge invariants for linearized gravity.
Zeitschrift:
Physical Review D
Verlag:
American Physical Society
2019 | Strong Short Time Asymptotics and Convolution Approximation of the Heat Kernel | Matthias Ludewig
Zeitschrift: Annals of Global Analysis and Geometry
Verlag: Springer
Seiten: 371-394
Band: 55, no. 2
Link zur Publikation
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Link zum Preprint
Strong Short Time Asymptotics and Convolution Approximation of the Heat Kernel
Autoren: Matthias Ludewig
(2019)
We give a short proof of a strong version of the short-time asymptotic expansion of heat kernels associated with Laplace-type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the difference of the approximate heat kernel and the true heat kernel. We use this to show that repeated convolution of the approximate heat kernels can be used to approximate the heat kernel on all of M, which is related to expressing the heat kernel as a path integral. This scheme is then applied to obtain a short-time asymptotic expansion of the heat kernel at the cut locus.
Zeitschrift:
Annals of Global Analysis and Geometry
2019 | An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary | Christian Bär, Alexander Strohmaier
Zeitschrift: Amer. J. Math.
Verlag: Johns Hopkins Univ. Press
Seiten: 1421-1455
Band: 141 (5)
Link zur Publikation
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Link zum Preprint
An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary
Autoren: Christian Bär, Alexander Strohmaier
(2019)
We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemannian manifolds with boundary. The index is also shown to equal that of a certain operator constructed from the evolution operator and a spectral projection on the boundary. In case the metric is of product type near the boundary a Feynman parametrix is constructed.
Zeitschrift:
Amer. J. Math.
Verlag:
Johns Hopkins Univ. Press
2018 | Relative entanglement entropy for widely separated regions in curved spacetime | Stefan Hollands, Onirban Islam, Ko Sanders
Zeitschrift: Journal of Mathematical Physics
Band: 59
Link zur Publikation
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Link zum Preprint
Relative entanglement entropy for widely separated regions in curved spacetime
Autoren: Stefan Hollands, Onirban Islam, Ko Sanders
(2018)
We give an upper bound of the relative entanglement entropy of the ground state of a massive Dirac-Majorana field across two widely separated regions \(A\) and \(B\) in a static slice of an ultrastatic Lorentzian spacetime. Our bound decays exponentially in \(\mathrm{dist}(A,B)\) at a rate set by the Compton wavelength and the spatial scalar curvature. The physical interpretation of our result is that, on a manifold with positive spatial scalar curvature, one cannot use the entanglement of the vacuum state to teleport one classical bit from \(A\) to \(B\) if their distance is of the order of the maximum of the curvature radius and the Compton wavelength or greater.
Zeitschrift:
Journal of Mathematical Physics
2018 | Kalman Filter and Its Modern Extensions for the Continuous-Time Nonlinear Filtering Problem | Amirhossein Taghvaei , Jana de Wiljes , Prashant G. Mehta , Sebastian Reich
Zeitschrift: Journal of Dynamic Systems, Measurement, and Control 2018-03-01
Kalman Filter and Its Modern Extensions for the Continuous-Time Nonlinear Filtering Problem
Autoren: Amirhossein Taghvaei , Jana de Wiljes , Prashant G. Mehta , Sebastian Reich
(2018)
Zeitschrift:
Journal of Dynamic Systems, Measurement, and Control 2018-03-01
2018 | The Dirac operator under collapse with bounded curvature and diameter | Saskia Roos
Link zur Publikation
The Dirac operator under collapse with bounded curvature and diameter
Autoren: Saskia Roos
(2018)
A sequence (Mi , gi)i of closed Riemannian manifolds with uniform bounded curvature and diameter collapses if it converges to a lower dimensional compact metric space (B,h). The limit space (B,h) has in general many singularities.
In the first part of this thesis we show that the case, where the limit space (B,h) is at most of one dimension less, can be characterized by a uniform lower bound on the quotient of the volume of the manifoldsi divided by their injectivity radius. In that case the limit space (B,h) is a Riemannian orbifold.
In the second part, we discuss the behavior of Dirac eigenvalues on a collapsing sequence of spin manifolds with bounded curvature and diameter converging to a lower dimensional Riemannian manifold (B,h). Lott showed that the spectrum of Dirac type operators converges to the spectrum of a certain first order elliptic differential operator D on B. We accentuate this result in the case of spin manifolds by giving an explicit description of the differential operator D and conclude that D is self-adjoint. Moreover we characterize the special case where D is the Dirac operator on B.
2018 | Quasi-invariance of countable products of Cauchy measures under non-unitary dilations | Han Cheng Lie, T. J. Sullivan
Zeitschrift: Electron. Commun. Probab.
Seiten: 6 pages
Band: 23, paper no. 8
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Quasi-invariance of countable products of Cauchy measures under non-unitary dilations
Autoren: Han Cheng Lie, T. J. Sullivan
(2018)
Zeitschrift:
Electron. Commun. Probab.
2018 | Equivalence of weak and strong modes of measures on topological vector spaces | Han Cheng Lie, T. J. Sullivan
Zeitschrift: Inverse Problems
Verlag: IOP Publishing
Seiten: 115013
Band: 34
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Equivalence of weak and strong modes of measures on topological vector spaces
Autoren: Han Cheng Lie, T. J. Sullivan
(2018)
Zeitschrift:
Inverse Problems
2018 | Implicit Probabilistic Integrators for ODEs | Onur Teymur, Han Cheng Lie, Tim Sullivan, Ben Calderhead
Buchtitel: Advances in Neural Information Processing Systems 31 (NIPS 2018)
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Implicit Probabilistic Integrators for ODEs
Autoren: Onur Teymur, Han Cheng Lie, Tim Sullivan, Ben Calderhead
(2018)
Buchtitel:
Advances in Neural Information Processing Systems 31 (NIPS 2018)
2018 | Random forward models and log-likelihoods in Bayesian inverse problems | H. C. Lie, T. J. Sullivan, A. L. Teckentrup
Zeitschrift: SIAM/ASA J. Uncertainty Quantification
Verlag: SIAM
Seiten: 1600-1629
Band: 6(4)
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Random forward models and log-likelihoods in Bayesian inverse problems
Autoren: H. C. Lie, T. J. Sullivan, A. L. Teckentrup
(2018)
Zeitschrift:
SIAM/ASA J. Uncertainty Quantification
2018 | Fréchet differentiable drift dependence of Perron--Frobenius and Koopman operators for non-deterministic dynamics | Péter Koltai, Han Cheng Lie, Martin Plonka
Zeitschrift: Nonlinearity
Verlag: IOP Publishing
Seiten: 4232
Band: 32
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Fréchet differentiable drift dependence of Perron--Frobenius and Koopman operators for non-deterministic dynamics
Autoren: Péter Koltai, Han Cheng Lie, Martin Plonka
(2018)
Zeitschrift:
Nonlinearity
2018 | Multivariate Brenier cumulative distribution functions and their application to non-parametric testing | M Boeckel, V Spokoiny, A Suvorikova
Zeitschrift: Preprint
Link zum Preprint
Multivariate Brenier cumulative distribution functions and their application to non-parametric testing
Autoren: M Boeckel, V Spokoiny, A Suvorikova
(2018)
2018 | Parallelizing Spectral Algorithms for Kernel Learning | G. Blanchard, N. Mücke
Zeitschrift: Journal of Machine Learning Research
Seiten: 1-29
Band: 30
Link zur Publikation
Parallelizing Spectral Algorithms for Kernel Learning
Autoren: G. Blanchard, N. Mücke
(2018)
Zeitschrift:
Journal of Machine Learning Research
2018 | On the post selection inference constant under restricted isometry properties. | F. Bachoc, G. Blanchard, P. Neuvial.
Zeitschrift: Electron. J. Statist
Seiten: 3736-3757
Band: 12(2)
Link zur Publikation
On the post selection inference constant under restricted isometry properties.
Autoren: F. Bachoc, G. Blanchard, P. Neuvial.
(2018)
Zeitschrift:
Electron. J. Statist
2018 | Early stopping for statistical inverse problems via truncated SVD estimation | G. Blanchard, M. Hoffmann, M. Reiß.
Zeitschrift: Electron. J. Statist
Seiten: 3204-3231
Band: 12 (2):
Link zur Publikation
Early stopping for statistical inverse problems via truncated SVD estimation
Autoren: G. Blanchard, M. Hoffmann, M. Reiß.
(2018)
Zeitschrift:
Electron. J. Statist
2018 | Optimal adaptation for early stopping in statistical inverse problems | G. Blanchard, M. Hoffmann, M. Reiß
Zeitschrift: SIAM/ASA Journal on Uncertainty Quantification
Seiten: 1043-1075
Band: 6(3)
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Optimal adaptation for early stopping in statistical inverse problems
Autoren: G. Blanchard, M. Hoffmann, M. Reiß
(2018)
Zeitschrift:
SIAM/ASA Journal on Uncertainty Quantification
2018 | Model reduction and approximation: theory and algorithms | M. A. Freitag
Zeitschrift: SIAM Rev.
Seiten: 763–767
Band: 60(3)
(review of book)
Model reduction and approximation: theory and algorithms
Autoren: M. A. Freitag
(2018)
2018 | Balanced model order reduction for linear random dynamical systems driven by Lévy noise | M. Redmann, M.A. Freitag
Zeitschrift: To appear in J. Comput. Dyn.
Link zum Preprint
Balanced model order reduction for linear random dynamical systems driven by Lévy noise
Autoren: M. Redmann, M.A. Freitag
(2018)
Zeitschrift:
To appear in J. Comput. Dyn.
2018 | A low-rank approach to the solution of weak constraint variational data assimilation problems | M.A. Freitag, D.L.H. Green
Zeitschrift: J. Comput. Phys.
Seiten: 263-281
Band: 357
Link zur Publikation
A low-rank approach to the solution of weak constraint variational data assimilation problems
Autoren: M.A. Freitag, D.L.H. Green
(2018)
Zeitschrift:
J. Comput. Phys.
2018 | GMRES convergence bounds for eigenvalue problems | M.A. Freitag, P. Kürschner, J. Pestana
Zeitschrift: Comput. Methods Appl. Math.
Seiten: 203-222
Band: 18(2)
Link zur Publikation
GMRES convergence bounds for eigenvalue problems
Autoren: M.A. Freitag, P. Kürschner, J. Pestana
(2018)
Zeitschrift:
Comput. Methods Appl. Math.
2018 | Shnol-type theorem for the Agmon ground state | Siegfried Beckus, Yehuda Pinchover
Zeitschrift: Journal of Spectral Theory
Reihe: 10
Seiten: 355 - 377
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Shnol-type theorem for the Agmon ground state
Autoren: Siegfried Beckus, Yehuda Pinchover
(2018)
Let H be a Schrödinger operator defined on a noncompact Riemannian manifold Ω, and let W∈L∞(Ω;R). Suppose that the operator H+W is critical in Ω, and let φ be the corresponding Agmon ground state. We prove that if u is a generalized eigenfunction of H satisfying |u|≤φ in Ω, then the corresponding eigenvalue is in the spectrum of H. The conclusion also holds true if for some K⋐Ω the operator H admits a positive solution in Ω'=Ω∖K, and |u|≤ψ in Ω', where ψ is a positive solution of minimal growth in a neighborhood of infinity in Ω.
Under natural assumptions, this result holds true also in the context of infinite graphs, and Dirichlet forms.
Zeitschrift:
Journal of Spectral Theory
2018 | Delone dynamical systems and spectral convergence | Siegfried Beckus, Felix Pogorzelski
Zeitschrift: Ergodic Theory and Dynamical Systems
Reihe: 40
Seiten: 1510-1544
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Delone dynamical systems and spectral convergence
Autoren: Siegfried Beckus, Felix Pogorzelski
(2018)
In the realm of Delone sets in locally compact, second countable Hausdorff groups, we develop a dynamical systems approach in order to study the continuity behavior of measured quantities arising from point sets. A special focus is both on the autocorrelation, as well as on the density of states for random bounded operators. It is shown that for uniquely ergodic limit systems, the latter measures behave continuously with respect to the Chabauty–Fell convergence of hulls. In the special situation of Euclidean spaces, our results complement recent developments in describing spectra as topological limits: we show that the measured quantities under consideration can be approximated via periodic analogs.
Zeitschrift:
Ergodic Theory and Dynamical Systems
2018 | Lineare Algebra und analytische Geometrie | Christian Bär
Verlag: Springer
Link zur Publikation
Lineare Algebra und analytische Geometrie
Autoren: Christian Bär
(2018)
Das Werk bietet eine Einführung in die lineare Algebra und die analytische Geometrie und enthält Material für eine zweisemestrige Vorlesung. Es beginnt mit einem Kapitel, das allgemein in die mathematische Denkweise und Beweistechniken einführt, um dann über lineare Gleichungssysteme zur linearen Algebra überzuleiten. Besonderer Wert wird auf eine enge Verzahnung von algebraischen und geometrischen Konzepten gelegt, zum einen um eine gute geometrische Intuition für algebraische Begriffe zu entwickeln, zum anderen um elegante algebraische Beweismethoden für geometrische Sätze einsetzen zu können. Schließlich sind interaktive Übungsseiten und Illustrationen integriert, die zu einem aktiven Studium anregen.
2018 | Spectral continuity for aperiodic quantum systems I. General theory | Siegfried Beckus, Jean Bellissard, Giuseppe De Nittis
Zeitschrift: Journal of Functional Analysis
Reihe: 275
Seiten: 2917 - 2977
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Spectral continuity for aperiodic quantum systems I. General theory
Autoren: Siegfried Beckus, Jean Bellissard, Giuseppe De Nittis
(2018)
How does the spectrum of a Schrödinger operator vary if the corresponding geometry and dynamics change? Is it possible to define approximations of the spectrum of such operators by defining approximations of the underlying structures? In this work a positive answer is provided using the rather general setting of groupoid C*-algebras. A characterization of the convergence of the spectra by the convergence of the underlying structures is proved. In order to do so, the concept of continuous field of groupoids is slightly extended by adding continuous fields of cocycles. With this at hand, magnetic Schrödinger operators on dynamical systems or Delone systems fall into this unified setting. Various approximations used in computational physics, like the periodic or the finite cluster approximations, are expressed through the tautological groupoid, which provides a universal model for fields of groupoids. The use of the Hausdorff topology turns out to be fundamental in understanding why and how these approximations work.
Zeitschrift:
Journal of Functional Analysis
2018 | Note on spectra of non-selfadjoint operators over dynamical system | Siegfried Beckus, Daniel Lenz,Marko Lindner,Christian Seifert
Zeitschrift: Proceedings of the Edinburgh Mathematical Society
Reihe: 61
Seiten: 371 -386
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Note on spectra of non-selfadjoint operators over dynamical system
Autoren: Siegfried Beckus, Daniel Lenz,Marko Lindner,Christian Seifert
(2018)
We consider equivariant continuous families of discrete one-dimensional operators over arbitrary dynamical systems. We introduce the concept of a pseudo-ergodic element of a dynamical system. We then show that all operators associated to pseudo-ergodic elements have the same spectrum and that this spectrum agrees with their essential spectrum. As a consequence we obtain that the spectrum is constant and agrees with the essential spectrum for all elements in the dynamical system if minimality holds.
Zeitschrift:
Proceedings of the Edinburgh Mathematical Society
2018 | Scattering the Geometry of Weighted Graphs | Güneysu, Batu; Keller, Matthias
Zeitschrift: Math. Phys. Anal. Geom.
Seiten: 21-28
Band: 21
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Scattering the Geometry of Weighted Graphs
Autoren: Güneysu, Batu; Keller, Matthias
(2018)
Given two weighted graphs (X, bk, mk), k = 1,2 with b1 ∼ b2 and m1 ∼ m2, we prove a weighted L1-criterion for the existence and completeness of the wave operators W±(H2, H1, I1,2), where Hk denotes the natural Laplacian in ℓ2(X, mk) w.r.t. (X, bk, mk) and I1,2 the trivial identification of ℓ2(X, m1) with ℓ2(X, m2). In particular, this entails a general criterion for the absolutely continuous spectra of H1 and H2 to be equal.
Zeitschrift:
Math. Phys. Anal. Geom.
2018 | Scalar curvature and the multiconformal class of a direct product Riemannian manifold | Nobuhiko Otoba, Saskia Roos
Link zum Preprint
Scalar curvature and the multiconformal class of a direct product Riemannian manifold
Autoren: Nobuhiko Otoba, Saskia Roos
(2018)
For a closed, connected direct product Riemannian manifold (M,g)=(M1×⋯×Ml,g1⊕⋯⊕gl), we define its multiconformal class [[g]] as the totality {f12g1⊕⋯⊕fl2gl} of all Riemannian metrics obtained from multiplying the metric gi of each factor Mi by a function fi2>0 on the total space M. A multiconformal class [[g]] contains not only all warped product type deformations of g but also the whole conformal class [g~] of every g~∈[[g]]. In this article, we prove that [[g]] carries a metric of positive scalar curvature if and only if the conformal class of some factor (Mi,gi) does, under the technical assumption dimMi≥2. We also show that, even in the case where every factor (Mi,gi) has positive scalar curvature, [[g]] carries a metric of scalar curvature constantly equal to −1 and with arbitrarily large volume, provided l≥2 and dimM≥3. In this case, such negative scalar curvature metrics within [[g]] for l=2 cannot be of any warped product type.
2018 | Dirac operators with W1,∞ -potential on collapsing sequences losing one dimension in the limit | Saskia Roos
Zeitschrift: Manuscripta Mathematica
Verlag: Springer
Seiten: 1-24
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Dirac operators with W1,∞ -potential on collapsing sequences losing one dimension in the limit
Autoren: Saskia Roos
(2018)
We study the behavior of the spectrum of the Dirac operator together with a symmetric W1,∞-potential on a collapsing sequence of spin manifolds with bounded sectional curvature and diameter losing one dimension in the limit. If there is an induced spin or pin− structure on the limit space N, then there are eigenvalues that converge to the spectrum of a first order differential operator D on N together with a symmetric W1,∞-potential. In the case of an orientable limit space N, D is the spin Dirac operator DN on N if the dimension of the limit space is even and if the dimension of the limit space is odd, then D=DN⊕−DN.
Zeitschrift:
Manuscripta Mathematica
2018 | Mass functions of a compact manifold | Andreas Hermann, Emmanuel Humbert
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Mass functions of a compact manifold
Autoren: Andreas Hermann, Emmanuel Humbert
(2018)
Let M be a compact manifold of dimension n. In this paper, we introduce the mass function a≥0→XM+(a) (resp. a≥0→XM-(a)) which is defined as the supremum (resp. infimum) of the masses of all metrics on M whose Yamabe constant is larger than a and which are flat on a ball of radius 1 and centered at a point p∈M. Here, the mass of a metric flat around p is the constant term in the expansion of the Green function of the conformal Laplacian at p. We show that these functions are well defined and have many properties which allow to obtain applications to the Yamabe invariant (i.e. the supremum of Yamabe constants over the set of all metrics on M).
2018 | Optimal Hardy inequalities for Schrödinger operators on graphs | Keller, Matthias; Pinchover, Yehuda; Pogorzelski, Felix
Zeitschrift: Comm. Math. Phys.
Seiten: 767–790
Band: 358
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Optimal Hardy inequalities for Schrödinger operators on graphs
Autoren: Keller, Matthias; Pinchover, Yehuda; Pogorzelski, Felix
(2018)
For a given subcritical discrete Schr\"odinger operator $H$ on a weighted infinite graph $X$, we construct a Hardy-weight $w$ which is {\em optimal} in the following sense. The operator $H - \lambda w$ is subcritical in $X$ for all $\lambda < 1$, null-critical in $X$ for $\lambda = 1$, and supercritical near any neighborhood of infinity in $X$ for any $\lambda > 1$. Our results rely on a criticality theory for Schr\"odinger operators on general weighted graphs.
Zeitschrift:
Comm. Math. Phys.
2018 | The Kazdan-Warner equation on canonically compactifiable graphs | Keller, Matthias; Schwarz, Michael
Zeitschrift: Calc. Var. Partial Differential Equations
Seiten: 18 pp.
Band: 57
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The Kazdan-Warner equation on canonically compactifiable graphs
Autoren: Keller, Matthias; Schwarz, Michael
(2018)
We study the Kazdan-Warner equation on canonically compactifiable graphs. These graphs are distinguished as analytic properties of Laplacians on these graphs carry a strong resemblance to Laplacians on open pre-compact manifolds.
Zeitschrift:
Calc. Var. Partial Differential Equations
2018 | Local foliation of manifolds by surfaces of Willmore type | Tobias Lamm, Jan Metzger, Felix Schulze
Zeitschrift: Ann. Inst. Fourier
Seiten: 1639–1662
Band: 70
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Local foliation of manifolds by surfaces of Willmore type
Autoren: Tobias Lamm, Jan Metzger, Felix Schulze
(2018)
We show the existence of a local foliation of a three dimensional Riemannian manifold by critical points of the Willmore functional subject to a small area constraint around non-degenerate critical points of the scalar curvature. This adapts a method developed by Rugang Ye to construct foliations by surfaces of constant mean curvature.
Zeitschrift:
Ann. Inst. Fourier
2018 | ShapeRotator: An R tool for standardized rigid rotations of articulated three‐dimensional structures with application for geometric morphometrics | Marta Vidal-García, Lashi Bandara, J. Scott Keogh
Zeitschrift: Ecology and Evolution
Verlag: John Wiley & Sons Ltd.
Seiten: 4669-4675
Band: 2018;8
Link zur Publikation
ShapeRotator: An R tool for standardized rigid rotations of articulated three‐dimensional structures with application for geometric morphometrics
Autoren: Marta Vidal-García, Lashi Bandara, J. Scott Keogh
(2018)
The quantification of complex morphological patterns typically involves comprehensive shape and size analyses, usually obtained by gathering morphological data from all the structures that capture the phenotypic diversity of an organism or object. Articulated structures are a critical component of overall phenotypic diversity, but data gathered from these structures are difficult to incorporate into modern analyses because of the complexities associated with jointly quantifying 3D shape in multiple structures. While there are existing methods for analyzing shape variation in articulated structures in two‐dimensional (2D) space, these methods do not work in 3D, a rapidly growing area of capability and research. Here, we describe a simple geometric rigid rotation approach that removes the effect of random translation and rotation, enabling the morphological analysis of 3D articulated structures. Our method is based on Cartesian coordinates in 3D space, so it can be applied to any morphometric problem that also uses 3D coordinates (e.g., spherical harmonics). We demonstrate the method by applying it to a landmark‐based dataset for analyzing shape variation using geometric morphometrics. We have developed an R tool (ShapeRotator) so that the method can be easily implemented in the commonly used R package geomorph and MorphoJ software. This method will be a valuable tool for 3D morphological analyses in articulated structures by allowing an exhaustive examination of shape and size diversity.
Zeitschrift:
Ecology and Evolution
Verlag:
John Wiley & Sons Ltd.
2018 | Understanding and reducing complex systems pharmacology models based on a novel input-response index | J. Knöchel, C. Kloft, W. Huisinga
Zeitschrift: J Pharmacokinet Pharmacodyn
Seiten: 139-157
Band: 45
Link zur Publikation
,
Suppl Material (Matlab code)
Understanding and reducing complex systems pharmacology models based on a novel input-response index
Autoren: J. Knöchel, C. Kloft, W. Huisinga
(2018)
Zeitschrift:
J Pharmacokinet Pharmacodyn
2018 | Stochastic and Deterministic Models for the Metastatic Emission Process: Formalisms and Crosslinks | C. Gomez, N. Hartung
Reihe: Methods Mol. Biol.
Buchtitel: von Stechow L. (eds) Cancer Systems Biology
Seiten: 193-224
Band: 1711
Link zur Publikation
Stochastic and Deterministic Models for the Metastatic Emission Process: Formalisms and Crosslinks
Autoren: C. Gomez, N. Hartung
(2018)
Reihe:
Methods Mol. Biol.
Buchtitel:
von Stechow L. (eds) Cancer Systems Biology
2018 | Focal Points at Infinity for Short-Range Scattering Trajectories | Horst Hohberger, Markus Klein
Zeitschrift: J. Shanghai Jia Tong Univ. (Sci.)
Seiten: 1-12
Band: 23(1)
Link zur Publikation
Focal Points at Infinity for Short-Range Scattering Trajectories
Autoren: Horst Hohberger, Markus Klein
(2018)
Classical scattering trajectories are known to form a Lagrangian manifold in euclidean phase space, which allows the classification of local focal points for sufficiently small dimensions. For the case of a short-range potential, we show that the natural description of focal points at infinity is a Lagrangian manifold in the cotangent bundle of the sphere and establish the relationship between focal points at infinity and the projection singularities of the manifold.
Zeitschrift:
J. Shanghai Jia Tong Univ. (Sci.)
2018 | The Tunneling Effect for a Class of Difference Operators | Markus Klein, Elke Rosenberger
Zeitschrift: Reviews in Mathematical Physics (RMP)
Verlag: World Scientific Publishing
Seiten: 1830002 (1-42)
Band: Vol.30, No. 4
Link zur Publikation
The Tunneling Effect for a Class of Difference Operators
Autoren: Markus Klein, Elke Rosenberger
(2018)
We analyze a general class of self-adjoint difference operators <tex>H_\varepsilon = T_\varepsilon
</tex>
<tex>+ V_\varepsilon</tex> on <tex>\ell^2(\varepsilon\mathbb{Z}^d)</tex>, where<tex> </tex><tex><tex>V_ε</tex></tex> is a multi-well
potential and ε is a small parameter.
We review some preparatory results on tunneling of the authors, needed for
our presentation of new sharp results on tunneling on the level of complete asymptotic expansions.
The wells are decoupled by introducing certain Dirichlet operators on regions containing only one
potential well. Then the eigenvalue problem for the Hamiltonian <tex>H_\varepsilon</tex> is treated as a small perturbation of these comparison
problems.
After constructing a Finslerian distance d induced by <tex>H_\varepsilon</tex> we show that Dirichlet eigenfunctions decay exponentially with a rate
controlled by this distance to the well. It follows with microlocal techniques that the first
n eigenvalues of <tex>H_\varepsilon</tex> converge to
the first n eigenvalues of the direct sum of harmonic oscillators on <tex>\mathbb{R}^d</tex> located
at the several wells.
In a neighborhood of one well, we construct formal asymptotic expansions of WKB-type
for eigenfunctions associated with the low lying eigenvalues of<tex> H_\varepsilon</tex>. These are obtained
from eigenfunctions or quasimodes for the
operator <tex>H_\varepsilon</tex>, acting on <tex>L^2(\mathbb{R}^d)</tex>, via restriction to the lattice <tex>\varepsilon\mathbb{Z}^d</tex>.
Tunneling is then described by a certain interaction matrix, similar to the analysis for the Schrödinger operator, the remainder is exponentially small and roughly quadratic compared with the
interaction matrix.
We give weighted<tex> \ell^2</tex>-estimates for the difference of eigenfunctions of Dirichlet-operators in
neighbourhoods of the different wells and the associated WKB-expansions at the wells.
In the last step, we
derive full asymptotic expansions for interactions between two ``wells'' (minima)
of the potential energy, in particular for the discrete tunneling
effect. Here we essentially use analysis on phase space, complexified in the momentum variable.
These results are as sharp as the classical results for the Schrödinger operator given by Helffer and Sjöstrand.
Zeitschrift:
Reviews in Mathematical Physics (RMP)
Verlag:
World Scientific Publishing
2018 | Tunneling for a class of Difference Operators: Complete Asymptotics | Markus Klein, Elke Rosenberger
Zeitschrift: Annales Henri Poincare
Verlag: Springer Verlag
Seiten: 3511-3559
Band: 19(11)
Link zur Publikation
,
Link zum Preprint
,
https://rdcu.be/9Gyk
Tunneling for a class of Difference Operators: Complete Asymptotics
Autoren: Markus Klein, Elke Rosenberger
(2018)
We analyze a general class of difference operators <tex>H_\varepsilon = T_\varepsilon +V_\varepsilo</tex> on <tex>\ell^2((\varepsilon\mathbb{Z})^d)</tex>, where
<tex>V_\varepsilon</tex> is a multi-well potential and <tex>\varepsilon</tex> is a small parameter. We derive full asymptotic expansions
of the prefactor of the exponentially small eigenvalue splitting due to interactions between two
“wells” (minima) of the potential energy, i.e., for the discrete tunneling effect. We treat both
the case where there is a single minimal geodesic (with respect to the natural Finsler metric
induced by the leading symbol<tex> h_0(x, ξ)</tex> of <tex>H_\varepsilon</tex>) connecting the two minima and the case where
the minimal geodesics form an k+1 dimensional manifold, k ≥ 1. These results on the tunneling
problem are as sharp as the classical results for the Schrödinger operator in [Helffer, Sjöstrand,
1984]. Technically, our approach is pseudodifferential and we adapt techniques from [Helffer,
Sjöstrand, 1988] and [Helffer, Parisse, 1994] to our discrete setting.
Zeitschrift:
Annales Henri Poincare
2018 | Construction of Tight Frames on Graphs and Application to Denoising | G. Blanchard, F. Göbel, U. von Luxburg
Zeitschrift: In Handbook of Big Data Analytics
Verlag: Springer
Buchtitel: Härdle, W., Lu, H.-S. and Xen, S.
Seiten: pp. 503-522
Band: 20
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,
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Construction of Tight Frames on Graphs and Application to Denoising
Autoren: G. Blanchard, F. Göbel, U. von Luxburg
(2018)
Zeitschrift:
In Handbook of Big Data Analytics
Buchtitel:
Härdle, W., Lu, H.-S. and Xen, S.
2018 | Wave and Dirac equations on manifolds | Lars Andersson, Christian Bär
Verlag: de Gruyter
Buchtitel: Space - Time - Matter
Seiten: 324-348
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,
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Wave and Dirac equations on manifolds
Autoren: Lars Andersson, Christian Bär
(2018)
We review some recent results on geometric equations on Lorentzian manifolds such as the wave and Dirac equations. This includes well-posedness and stability for various initial value problems, as well as results on the structure of these equations on black-hole spacetimes (in particular, on the Kerr solution), the index theorem for hyperbolic Dirac operators and properties of the class of Green-hyperbolic operators.
Buchtitel:
Space - Time - Matter
2018 | An improved discrete Hardy inequality | Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
Zeitschrift: American Mathematics Monthly
Seiten: 347–350
Band: 125
Link zur Publikation
,
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An improved discrete Hardy inequality
Autoren: Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
(2018)
We improve the classical discrete Hardy inequality
<nobr>∑n=1∞a2n≥(12)2∑n=1∞(a1+a2+⋯+ann)2,</nobr>
where <nobr>{an}∞n=1</nobr> is any sequence of non-negative real numbers.
Zeitschrift:
American Mathematics Monthly
2018 | Boundary value problems for the Lorentzian Dirac operator | Christian Bär, Sebastian Hannes
Verlag: Oxford Univ. Press
Buchtitel: A. Dancer, J.E. Andersen, O. García-Prada (eds.): Geometry and Physics
Seiten: 3-18
Band: 1
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,
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Boundary value problems for the Lorentzian Dirac operator
Autoren: Christian Bär, Sebastian Hannes
(2018)
On a compact globally hyperbolic Lorentzian spin manifold with smooth spacelike Cauchy boundary the (hyperbolic) Dirac operator is known to be Fredholm when Atiyah-Patodi-Singer boundary conditions are imposed. In this paper we investigate to what extent these boundary conditions can be replaced by more general ones and how the index then changes. There are some differences to the classical case of the elliptic Dirac operator on a Riemannian manifold with boundary.
Verlag:
Oxford Univ. Press
Buchtitel:
A. Dancer, J.E. Andersen, O. García-Prada (eds.): Geometry and Physics
2018 | Empilements de disques ou comment une approche probabiliste peut compléter une analyse géométrique ... | Charlotte Dombrowsky, Myriam Fradon, Sylvie Roelly
Zeitschrift: Quadrature
Band: 107
Link zur Publikation
Empilements de disques ou comment une approche probabiliste peut compléter une analyse géométrique ...
Autoren: Charlotte Dombrowsky, Myriam Fradon, Sylvie Roelly
(2018)
2018 | The stack of Yang-Mills fields on Lorentzian manifolds | Marco Benini, Alexander Schenkel, Urs Schreiber
Zeitschrift: Comm. Math. Phys.
Verlag: Springer
Seiten: 765-820
Band: 359, no. 2
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,
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The stack of Yang-Mills fields on Lorentzian manifolds
Autoren: Marco Benini, Alexander Schenkel, Urs Schreiber
(2018)
We provide an abstract definition and an explicit construction of the stack of non-Abelian Yang-Mills fields on globally hyperbolic Lorentzian manifolds. We also formulate a stacky version of the Yang-Mills Cauchy problem and show that its well-posedness is equivalent to a whole family of parametrized PDE problems. Our work is based on the homotopy theoretical approach to stacks proposed in [S. Hollander, Israel J. Math. 163, 93-124 (2008)], which we shall extend by further constructions that are relevant for our purposes. In particular, we will clarify the concretification of mapping stacks to classifying stacks such as BGcon.
Zeitschrift:
Comm. Math. Phys.
2018 | Hidden symmetries and decay for the Vlasov equation on the Kerr spacetime | Lars Andersson, Pieter Blue, Jeremie Joudioux
Zeitschrift: Commun. Part. Diff. Eq.
Verlag: Taylor & Francis
Seiten: 47-65
Band: 43, no. 1
Link zur Publikation
,
Link zum Preprint
Hidden symmetries and decay for the Vlasov equation on the Kerr spacetime
Autoren: Lars Andersson, Pieter Blue, Jeremie Joudioux
(2018)
This paper proves the existence of a bounded energy and integrated energy decay for solutions of the massless Vlasov equation in the exterior of a very slowly rotating Kerr spacetime. This combines methods previously developed to prove similar results for the wave equation on the exterior of a very slowly rotating Kerr spacetime with recent work applying the vector-field method to the relativistic Vlasov equation.
Zeitschrift:
Commun. Part. Diff. Eq.
2018 | On the geometry and topology of initial data sets with horizons | Lars Andersson, Mattias Dahl, Gregory J. Galloway, Daniel Pollack
Zeitschrift: Asian J. Math.
Verlag: International Press
Seiten: 863-881
Band: 22, no. 5
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,
Link zum Preprint
On the geometry and topology of initial data sets with horizons
Autoren: Lars Andersson, Mattias Dahl, Gregory J. Galloway, Daniel Pollack
(2018)
We study the relationship between initial data sets with horizons and the existence of metrics of positive scalar curvature. We define a Cauchy Domain of Outer Communications (CDOC) to be an asymptotically flat initial set (M,g,K) such that the boundary ∂M of M is a collection of Marginally Outer (or Inner) Trapped Surfaces (MOTSs and/or MITSs) and such that M\∂M contains no MOTSs or MITSs. This definition is meant to capture, on the level of the initial data sets, the well known notion of the domain of outer communications (DOC) as the region of spacetime outside of all the black holes (and white holes). Our main theorem establishes that in dimensions 3 ≤ n ≤ 7, a CDOC which satisfies the dominant energy condition and has a strictly stable boundary has a positive scalar curvature metric which smoothly compactifies the asymptotically flat end and is a Riemannian product metric near the boundary where the cross sectional metric is conformal to a small perturbation of the initial metric on the boundary ∂M induced by g. This result may be viewed as a generalization of Galloway and Schoen's higher dimensional black hole topology theorem to the exterior of the horizon. We also show how this result leads to a number of topological restrictions on the CDOC, which allows one to also view this as an extension of the initial data topological censorship theorem, established by Eichmair, Galloway, and Pollack in dimension n = 3, to higher dimensions.
Zeitschrift:
Asian J. Math.
Verlag:
International Press
2018 | Geometry of black hole spacetimes | Lars Andersson, Thomas Bäckdahl, Pieter Blue
Reihe: London Mathematical Society Lecture Note Series
Verlag: Cambridge University Press
Buchtitel: T. Daudé, D. Häfner, J.-P. Nicolas (eds.): Asymptotic Analysis in General Relativity
Seiten: 9-85
Band: 443
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,
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Geometry of black hole spacetimes
Autoren: Lars Andersson, Thomas Bäckdahl, Pieter Blue
(2018)
These notes, based on lectures given at the summer school on Asymptotic Analysis in General Relativity, collect material on the Einstein equations, the geometry of black hole spacetimes, and the analysis of fields on black hole backgrounds. The Kerr model of a rotating black hole in vacuum is expected to be unique and stable. The problem of proving these fundamental facts provides the background for the material presented in these notes.
Among the many topics which are relevant for the uniqueness and stability problems are the theory of fields on black hole spacetimes, in particular for gravitational perturbations of the Kerr black hole, and more generally, the study of nonlinear field equations in the presence of trapping. The study of these questions requires tools from several different fields, including Lorentzian geometry, hyperbolic differential equations and spin geometry, which are all relevant to the black hole stability problem.
Reihe:
London Mathematical Society Lecture Note Series
Verlag:
Cambridge University Press
Buchtitel:
T. Daudé, D. Häfner, J.-P. Nicolas (eds.): Asymptotic Analysis in General Relativity
2018 | Convergence of Dynamics and the Perron-Frobenius Operator | Moritz Gerlach
Zeitschrift: Israel Journal of Mathematics
Seiten: 451–463
Band: 225(1)
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Convergence of Dynamics and the Perron-Frobenius Operator
Autoren: Moritz Gerlach
(2018)
We complete the picture how the asymptotic behavior of a dynamical system is reflected by properties of the associated Perron-Frobenius operator. Our main result states that strong convergence of the powers of the Perron-Frobenius operator is equivalent to setwise convergence of the underlying dynamic in the measure algebra. This situation is furthermore characterized by a uniform mixing-like property of the system.
Zeitschrift:
Israel Journal of Mathematics
2018 | Heat Kernel Asymptotics, Path Integrals and Infinite-Dimensional Determinants | Matthias Ludewig
Zeitschrift: Journal of Geometry and Physics
Seiten: 66-88
Band: 131
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Heat Kernel Asymptotics, Path Integrals and Infinite-Dimensional Determinants
Autoren: Matthias Ludewig
(2018)
We compare the short-time expansion of the heat kernel on a Riemannian manifold with the formal stationary phase expansion of its representing path integral and prove that these asymptotic expansions coincide. Besides shedding light on the formal properties of quantum mechanical path integrals, this shows that the lowest order term of the heat kernel expansion is given by the Fredholm determinant of the Hessian of the energy functional on the space of finite energy paths. We also relate this to the zeta determinant of the Jacobi operator, considering both the near-diagonal asymptotics as well as the behavior at the cut locus.
Zeitschrift:
Journal of Geometry and Physics
2018 | Lower Bounds and the Asymptotic Behaviour of Positive Operator Semigroups | Moritz Gerlach, Jochen Glück
Zeitschrift: Ergodic Theory and Dynamical Systems
Seiten: 3012-3041
Band: 38(8)
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Link zum Preprint
Lower Bounds and the Asymptotic Behaviour of Positive Operator Semigroups
Autoren: Moritz Gerlach, Jochen Glück
(2018)
If $(T_t)$ is a semigroup of Markov operators on an $L^1$-space that admits a non-trivial lower bound, then a well-known theorem of Lasota and Yorke asserts that the semigroup is strongly convergent as $t \to \infty$. In this article we generalise and improve this result in several respects.
First, we give a new and very simple proof for the fact that the same conclusion also holds if the semigroup is merely assumed to be bounded instead of Markov. As a main result we then prove a version of this theorem for semigroups which only admit certain individual lower bounds. Moreover, we generalise a theorem of Ding on semigroups of Frobenius-Perron operators. We also demonstrate how our results can be adapted to the setting of general Banach lattices and we give some counterexamples to show optimality of our results.
Our methods combine some rather concrete estimates and approximation arguments with abstract functional analytical tools. One of these tools is a theorem which relates the convergence of a time-continuous operator semigroup to the convergence of embedded discrete semigroups.
Zeitschrift:
Ergodic Theory and Dynamical Systems
2017 | A geometric exploration of stress in deformed liquid foams | M. E. Evans, G. E. Schröder-Turk and A. M. Kraynik
Zeitschrift: Journal of Physics: Condensed Matter
Link zur Publikation
A geometric exploration of stress in deformed liquid foams
Autoren: M. E. Evans, G. E. Schröder-Turk and A. M. Kraynik
(2017)
Zeitschrift:
Journal of Physics: Condensed Matter
2017 | Emergence and function of complex form in self-assembly and biological cells | S. T. Hyde, G. E. Schröder-Turk, M. E. Evans and B. D. Wilts
Zeitschrift: Interface Focus 7
Link zur Publikation
Emergence and function of complex form in self-assembly and biological cells
Autoren: S. T. Hyde, G. E. Schröder-Turk, M. E. Evans and B. D. Wilts
(2017)
Zeitschrift:
Interface Focus 7
2017 | Some connections between importance sampling and enhanced sampling methods in molecular dynamics | H. C. Lie, J. Quer
Zeitschrift: J. Chem. Phys.
Verlag: AIP Publishing
Seiten: 194107
Band: 147
Link zur Publikation
Some connections between importance sampling and enhanced sampling methods in molecular dynamics
Autoren: H. C. Lie, J. Quer
(2017)
Zeitschrift:
J. Chem. Phys.
2017 | On the spectrum of operator families on discrete groups over minimal dynamical Systems | Siegfried Beckus, Daniel Lenz, Marko Lindner, Christian Seifert
Zeitschrift: Mathematische Zeitschrift
Reihe: 287
Seiten: 993 - 1007
Link zur Publikation
,
Link zum Preprint
On the spectrum of operator families on discrete groups over minimal dynamical Systems
Autoren: Siegfried Beckus, Daniel Lenz, Marko Lindner, Christian Seifert
(2017)
It is well known that, given an equivariant and continuous (in a suitable sense) family of selfadjoint operators in a Hilbert space over a minimal dynamical system, the spectrum of all operators from that family coincides. As shown recently similar results also hold for suitable families of non-selfadjoint operators in ℓp(ℤ). Here, we generalize this to a large class of bounded linear operator families on Banach-space valued ℓp-spaces over countable discrete groups. We also provide equality of the pseudospectra for operators in such a family. A main tool for our analysis are techniques from limit operator theory.
Zeitschrift:
Mathematische Zeitschrift
2017 | Eigenvalue pinching on spin-c manifolds | Saskia Roos
Zeitschrift: J. Geom. Phys.
Verlag: Elsevier
Seiten: 59-73
Band: 112
Link zur Publikation
,
Link zum Preprint
Eigenvalue pinching on spin-c manifolds
Autoren: Saskia Roos
(2017)
We derive various pinching results for small Dirac eigenvalues using the classification of spinc and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for spinc manifolds which involves a general study on convergence of Riemannian manifolds with a principal S1-bundle. We also analyze the relation between the regularity of the Riemannian metric and the regularity of the curvature of the associated principal S1-bundle on spinc manifolds with Killing spinors.
Zeitschrift:
J. Geom. Phys.
2017 | A Characterization of Codimension One Collapse Under Bounded Curvature and Diameter | Saskia Roos
Zeitschrift: Journal of Geometric Analysis
Verlag: Springer
Seiten: 2707-2724
Band: 28, no. 3
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,
Link zum Preprint
A Characterization of Codimension One Collapse Under Bounded Curvature and Diameter
Autoren: Saskia Roos
(2017)
Let M(n,D) be the space of closed n-dimensional Riemannian manifolds (M,g) with diam(M)≤D and |secM|≤1. In this paper we consider sequences (Mi,gi) in M(n,D) converging in the Gromov–Hausdorff topology to a compact metric space Y. We show, on the one hand, that the limit space of this sequence has at most codimension one if there is a positive number r such that the quotient vol(BMir(x))/injMi(x) can be uniformly bounded from below by a positive constant C(n, r, Y) for all points x∈Mi. On the other hand, we show that if the limit space has at most codimension one then for all positive r there is a positive constant C(n, r, Y) bounding the quotient vol(BMir(x))/injMi(x) uniformly from below for all x∈Mi. As a conclusion, we derive a uniform lower bound on the volume and a bound on the essential supremum of the sectional curvature for the closure of the space consisting of all manifolds in M(n,D) with C≤vol(M)/inj(M).
Zeitschrift:
Journal of Geometric Analysis
2017 | The Cauchy problem for the linearised Einstein equation and the Goursat problem for wave equations | Oliver Lindblad Petersen
Link zur Publikation
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PhD thesis, University of Potsdam
The Cauchy problem for the linearised Einstein equation and the Goursat problem for wave equations
Autoren: Oliver Lindblad Petersen
(2017)
In this thesis, we study two initial value problems arising in general relativity. The first is the Cauchy problem for the linearised Einstein equation on general globally hyperbolic spacetimes, with smooth and distributional initial data. We extend well-known results by showing that given a solution to the linearised constraint equations of arbitrary real Sobolev regularity, there is a globally defined solution, which is unique up to addition of gauge solutions. Two solutions are considered equivalent if they differ by a gauge solution. Our main result is that the equivalence class of solutions depends continuously on the corresponding equivalence class of initial data. We also solve the linearised constraint equations in certain cases and show that there exist arbitrarily irregular (non-gauge) solutions to the linearised Einstein equation on Minkowski spacetime and Kasner spacetime.
In the second part, we study the Goursat problem (the characteristic Cauchy problem) for wave equations. We specify initial data on a smooth compact Cauchy horizon, which is a lightlike hypersurface. This problem has not been studied much, since it is an initial value problem on a non-globally hyperbolic spacetime. Our main result is that given a smooth function on a non-empty, smooth, compact, totally geodesic and non-degenerate Cauchy horizon and a so called admissible linear wave equation, there exists a unique solution that is defined on the globally hyperbolic region and restricts to the given function on the Cauchy horizon. Moreover, the solution depends continuously on the initial data. A linear wave equation is called admissible if the first order part satisfies a certain condition on the Cauchy horizon, for example if it vanishes. Interestingly, both existence of solution and uniqueness are false for general wave equations, as examples show. If we drop the non-degeneracy assumption, examples show that existence of solution fails even for the simplest wave equation. The proof requires precise energy estimates for the wave equation close to the Cauchy horizon. In case the Ricci curvature vanishes on the Cauchy horizon, we show that the energy estimates are strong enough to prove local existence and uniqueness for a class of non-linear wave equations. Our results apply in particular to the Taub-NUT spacetime and the Misner spacetime. It has recently been shown that compact Cauchy horizons in spacetimes satisfying the null energy condition are necessarily smooth and totally geodesic. Our results therefore apply if the spacetime satisfies the null energy condition and the Cauchy horizon is compact and non-degenerate.
2017 | Study of metastatic kinetics in metastatic melanoma treated with B-RAF inhibitors: Introducing mathematical modelling of kinetics into the therapeutic decision | N. Hartung, C.T. Huynh, C. Gaudy-Marqueste, A. Flavian, N. Malissen, M.A. Richard-Lallemand, F. Hubert, J.-J. Grob
Zeitschrift: PLoS ONE
Band: 12(5)
Link zur Publikation
,
e017608074
Study of metastatic kinetics in metastatic melanoma treated with B-RAF inhibitors: Introducing mathematical modelling of kinetics into the therapeutic decision
Autoren: N. Hartung, C.T. Huynh, C. Gaudy-Marqueste, A. Flavian, N. Malissen, M.A. Richard-Lallemand, F. Hubert, J.-J. Grob
(2017)
2017 | Model Description Language (MDL): A Standard for Modelling and Simulation | M. Smith, S. Moodie, R. Bizzotto, E. Blaudez, E. Borella, L. Carrara, P. Chan, M. Chenel, E. Comets, R. Gieschke, K. Harling, L. Harnisch, N. Hartung, A. Hooker, M. Karlsson, R. Kaye, C. Kloft, N. Kokash, M. Lavielle, G. Lestini, P. Magni, A. Mari, F. Men
Zeitschrift: CPT: Pharmacometrics & Systems Pharmacology
Link zur Publikation
,
doi:10.1002/psp4.12222
Model Description Language (MDL): A Standard for Modelling and Simulation
Autoren: M. Smith, S. Moodie, R. Bizzotto, E. Blaudez, E. Borella, L. Carrara, P. Chan, M. Chenel, E. Comets, R. Gieschke, K. Harling, L. Harnisch, N. Hartung, A. Hooker, M. Karlsson, R. Kaye, C. Kloft, N. Kokash, M. Lavielle, G. Lestini, P. Magni, A. Mari, F. Men
(2017)
Zeitschrift:
CPT: Pharmacometrics & Systems Pharmacology
2017 | Magnitude of Increased Infliximab Clearance Imposed by Anti-infliximab Antibodies in Crohn's Disease Is Determined by Their Concentration | H. Edlund, C. Steenholdt, M.A. Ainsworth, E. Goebgen, J. Brynskov, O.Ø. Thomsen, W. Huisinga, C. Kloft
Zeitschrift: AAPS J
Seiten: 223-233
Band: 19(1)
Link zur Publikation
Magnitude of Increased Infliximab Clearance Imposed by Anti-infliximab Antibodies in Crohn's Disease Is Determined by Their Concentration
Autoren: H. Edlund, C. Steenholdt, M.A. Ainsworth, E. Goebgen, J. Brynskov, O.Ø. Thomsen, W. Huisinga, C. Kloft
(2017)
2017 | Towards toxicokinetic modelling of aluminium exposure from adjuvants in medicinal products | K. Weisser, S. Stübler, W. Matheis, W. Huisinga
Zeitschrift: Regul Toxicol Pharmacol
Seiten: 310-321
Band: 88
Link zur Publikation
Towards toxicokinetic modelling of aluminium exposure from adjuvants in medicinal products
Autoren: K. Weisser, S. Stübler, W. Matheis, W. Huisinga
(2017)
Zeitschrift:
Regul Toxicol Pharmacol
2017 | Translational Pharmacometric Evaluation of Typical Antibiotic Broad-Spectrum Combination Therapies Against Staphylococcus Aureus Exploiting In Vitro Information | S. Wicha, W. Huisinga, C. Kloft
Zeitschrift: CPT Pharmacometrics Syst Pharmacol
Seiten: 512-522
Band: 6(8)
Link zur Publikation
Translational Pharmacometric Evaluation of Typical Antibiotic Broad-Spectrum Combination Therapies Against Staphylococcus Aureus Exploiting In Vitro Information
Autoren: S. Wicha, W. Huisinga, C. Kloft
(2017)
Zeitschrift:
CPT Pharmacometrics Syst Pharmacol
2017 | Impact of altered endogenous IgG on unspecific mAb clearance | S. Fuhrmann, C. Kloft, W. Huisinga
Zeitschrift: J Pharmacokinet Pharmacodyn
Seiten: 351-374
Band: 44
Link zur Publikation
,
Suppl Material (Matlab code)
Impact of altered endogenous IgG on unspecific mAb clearance
Autoren: S. Fuhrmann, C. Kloft, W. Huisinga
(2017)
Zeitschrift:
J Pharmacokinet Pharmacodyn
2017 | Semimechanistic Bone Marrow Exhaustion Pharmacokinetic/Pharmacodynamic Model for Chemotherapy-Induced Cumulative Neutropenia | A. Henrich A, M. Jörger, S. Kraff, U. Jaehde U, W. Huisinga, C. Kloft, Z.P. Parra-Guillen
Zeitschrift: J Pharmacol Exp Ther
Seiten: 347-358
Band: 362(2)
Link zur Publikation
Semimechanistic Bone Marrow Exhaustion Pharmacokinetic/Pharmacodynamic Model for Chemotherapy-Induced Cumulative Neutropenia
Autoren: A. Henrich A, M. Jörger, S. Kraff, U. Jaehde U, W. Huisinga, C. Kloft, Z.P. Parra-Guillen
(2017)
Zeitschrift:
J Pharmacol Exp Ther
2017 | Predicting Cortisol Exposure from Paediatric Hydrocortisone Formulation Using a Semi-Mechanistic Pharmacokinetic Model Established in Healthy Adults | J. Melin, Z.P. Parra-Guillen, N. Hartung, W. Huisinga, R.J. Ross, M.J. Whitaker, C. Kloft
Zeitschrift: Clin Pharmacokinet.
Verlag: Springer
Link zur Publikation
Predicting Cortisol Exposure from Paediatric Hydrocortisone Formulation Using a Semi-Mechanistic Pharmacokinetic Model Established in Healthy Adults
Autoren: J. Melin, Z.P. Parra-Guillen, N. Hartung, W. Huisinga, R.J. Ross, M.J. Whitaker, C. Kloft
(2017)
Zeitschrift:
Clin Pharmacokinet.
2017 | Role of renal function in risk assessment of target non-attainment after standard dosing of meropenem in critically ill patients: A prospective observational study | L. Ehmann, M. Zoller, I. K. Minichmayr, C. Scharf, B. Maier, M. V. Schmitt, N. Hartung, W. Huisinga, M. Vogeser, L. Frey, J. Zander, C. Kloft
Zeitschrift: Critical Care
Seiten: 263
Band: 21
Link zur Publikation
Role of renal function in risk assessment of target non-attainment after standard dosing of meropenem in critically ill patients: A prospective observational study
Autoren: L. Ehmann, M. Zoller, I. K. Minichmayr, C. Scharf, B. Maier, M. V. Schmitt, N. Hartung, W. Huisinga, M. Vogeser, L. Frey, J. Zander, C. Kloft
(2017)
Zeitschrift:
Critical Care
2017 | Paracrine and autocrine regulation of gene expression by Wnt-inhibitor Dickkopf in wild-type and mutant hepatocytes | N. Hartung, U. Benary, J. Wolf, B. Kofahl
Zeitschrift: BMC Systems Biology
Seiten: 98
Band: 11
Link zur Publikation
Paracrine and autocrine regulation of gene expression by Wnt-inhibitor Dickkopf in wild-type and mutant hepatocytes
Autoren: N. Hartung, U. Benary, J. Wolf, B. Kofahl
(2017)
Zeitschrift:
BMC Systems Biology
2017 | On a Semigroup of n-ary Operations | Susanti, Y., Koppitz, J.
Zeitschrift: Far East Journal of Mathematical Sciences (FJMS)
Band: 102 no.4
On a Semigroup of n-ary Operations
Autoren: Susanti, Y., Koppitz, J.
(2017)
Zeitschrift:
Far East Journal of Mathematical Sciences (FJMS)
2017 | Regular Semigroups of Partial Transformations Preserving a Fence | Lohapan, L., Koppitz, J.
Zeitschrift: Novi Sad Journal of Mathematics (NSJOM)
Band: 47 no. 2
Regular Semigroups of Partial Transformations Preserving a Fence
Autoren: Lohapan, L., Koppitz, J.
(2017)
Zeitschrift:
Novi Sad Journal of Mathematics (NSJOM)
2017 | Generating Sets of Semigroups of Partial Transformations Preserving a Zig-Zag Order on N | Dimitrova, I, Koppitz, J, Lohapan, L.
Zeitschrift: International Journal of Pure and Applied Mathematics
Band: 12 no. 2
Generating Sets of Semigroups of Partial Transformations Preserving a Zig-Zag Order on N
Autoren: Dimitrova, I, Koppitz, J, Lohapan, L.
(2017)
Zeitschrift:
International Journal of Pure and Applied Mathematics
2017 | Relations on a Semigroup of Sets of Transformations with Restricted Range. | Anantayasethi, A., Koppitz, J.
Zeitschrift: Comptes rendus de l’Acad´emie bulgare des Sciences
Band: 70 n0. 12
Relations on a Semigroup of Sets of Transformations with Restricted Range.
Autoren: Anantayasethi, A., Koppitz, J.
(2017)
Zeitschrift:
Comptes rendus de l’Acad´emie bulgare des Sciences
2017 | A Note on Generators of the endomorphism Semigroup of an infinite countable chain, | Dimitrova, I., Fernandes, V.H. and Koppitz,
Zeitschrift: J. Algebra Appl.
Band: 16
A Note on Generators of the endomorphism Semigroup of an infinite countable chain,
Autoren: Dimitrova, I., Fernandes, V.H. and Koppitz,
(2017)
Zeitschrift:
J. Algebra Appl.
2017 | Klipp Klapp - Würfelnetze einmal anders. Mit digitalen Medien das räumliche Vorstellungsvermögen fördern | Heiko Etzold, Ana Kuzle
Zeitschrift: Grundschulunterricht Mathematik
Reihe: 1
Seiten: 29-32
Klipp Klapp - Würfelnetze einmal anders. Mit digitalen Medien das räumliche Vorstellungsvermögen fördern
Autoren: Heiko Etzold, Ana Kuzle
(2017)
Zeitschrift:
Grundschulunterricht Mathematik
2017 | Raum und Form | Ulrich Kortenkamp, Bernd Wollring
Verlag: Kallmeyer Klett
Buchtitel: Basiswissen Lehrerbildung: Mathematik Unterrichten
Seiten: 99–112
Raum und Form
Autoren: Ulrich Kortenkamp, Bernd Wollring
(2017)
Buchtitel:
Basiswissen Lehrerbildung: Mathematik Unterrichten
2017 | Algunas propiedades básicas de procesos de ramificación | S. Roelly
Reihe: Lectures in pure and applied mathematics
Verlag: Universitätsverlag Potsdam
Buchtitel: Stochastic processes with applications in the natural sciences.international workshop at Universidad de los Andes, Bogotá, Colombia
Seiten: 29-79
Band: 4
Link zur Publikation
Algunas propiedades básicas de procesos de ramificación
Autoren: S. Roelly
(2017)
The interdisciplinary workshop STOCHASTIC PROCESSES WITH APPLICATIONS IN THE NATURAL SCIENCES was held in Bogotá, at Universidad de los Andes from December 5 to December 9, 2016. It brought together researchers from Colombia, Germany, France, Italy, Ukraine, who communicated recent progress in the mathematical research related to stochastic processes with application in biophysics. The present volume collects three of the four courses held at this meeting by Angelo Valleriani, Sylvie Rœlly and Alexei Kulik. A particular aim of this collection is to inspire young scientists in setting up research goals within the wide scope of fields represented in this volume.
Angelo Valleriani, PhD in high energy physics, is group leader of the team "Stochastic processes in complex and biological systems" from the Max-Planck-Institute of Colloids and Interfaces, Potsdam.
Sylvie Rœlly, Docteur en Mathématiques, is the head of the chair of Probability at the University of Potsdam.
Alexei Kulik, Doctor of Sciences, is a Leading researcher at the Institute of Mathematics of Ukrainian National Academy of Sciences.
Reihe:
Lectures in pure and applied mathematics
Verlag:
Universitätsverlag Potsdam
Buchtitel:
Stochastic processes with applications in the natural sciences.international workshop at Universidad de los Andes, Bogotá, Colombia
2017 | The Neumann problem after Spencer | A. Mera and N. Tarkhanov
Zeitschrift: J. of Siberian Federal University
Reihe: Mathematics and Physics
Seiten: 1—20
Band: 10 n.4
Link zur Publikation
,
Link zum Preprint
The Neumann problem after Spencer
Autoren: A. Mera and N. Tarkhanov
(2017)
When trying to extend the Hodge theory for elliptic complexes on compact closed manifolds to the case of compact manifolds with boundary one is led to a boundary value problem for the Laplacian of the complex which is usually referred to as Neumann problem. We study the Neumann problem for a larger class of sequences of differential operators on a compact manifold with boundary. These are sequences of small curvature, i.e., bearing the property that the composition of any two neighbouring operators has order less than two.
Zeitschrift:
J. of Siberian Federal University
Reihe:
Mathematics and Physics
2017 | Isoperimetric structure of asymptotically conical manifolds | Otis Chodosh, Michael Eichmair, and Alexander Volkmann
Zeitschrift: J. Differential Geom.
Seiten: 1-19
Band: 105
Link zur Publikation
Isoperimetric structure of asymptotically conical manifolds
Autoren: Otis Chodosh, Michael Eichmair, and Alexander Volkmann
(2017)
We study the isoperimetric structure of Riemannian manifolds that are asymptotic to cones with non-negative Ricci curvature. Specifically, we generalize to this setting the seminal results of G. Huisken and S.–T. Yau on the existence of a canonical foliation by volume-preserving stable constant mean curvature surfaces at infinity of asymptotically flat manifolds as well as the results of the second-named author with S. Brendle and J. Metzger on the isoperimetric structure of asymptotically flat manifolds. We also include an observation on the isoperimetric cone angle of such manifolds. This result is a natural analogue of the positive mass theorem in this setting.
Zeitschrift:
J. Differential Geom.
2017 | The first mixed problem for the nonstationary Lamé system | O. Makhmudov and N. Tarkhanov
Zeitschrift: Rocky Mountain J. Math.
Link zur Publikation
,
Link zum Preprint
The first mixed problem for the nonstationary Lamé system
Autoren: O. Makhmudov and N. Tarkhanov
(2017)
We find an adequate interpretation of the Lam´e operator within the framework of elliptic complexes and study the first mixed problem for the nonstationary Lam´e system.
Zeitschrift:
Rocky Mountain J. Math.
2017 | The asymptotic content of solutions on spaces with singularities | D.-C. Chang, M. Hedayat Mahmoudi, B.-W. Schulze
Zeitschrift: Applied Analysis and Optimization
Band: 1, issue 2
The asymptotic content of solutions on spaces with singularities
Autoren: D.-C. Chang, M. Hedayat Mahmoudi, B.-W. Schulze
(2017)
Zeitschrift:
Applied Analysis and Optimization
2017 | Singular Degenerate Operators | D.-C. Chang, M. Hedayat Mahmoudi, B.-W. Schulze
Zeitschrift: Applicable Analysis
Band: 96, Issue 14
Link zur Publikation
Singular Degenerate Operators
Autoren: D.-C. Chang, M. Hedayat Mahmoudi, B.-W. Schulze
(2017)
We outline some simplified and more general method for constructing parametrices on higher singular spaces. We also outline basic ideas on operators on manifolds with conical or edge singularities.
Zeitschrift:
Applicable Analysis
2017 | Nonlinear Equations with Small Parameter. Vol. II: Waves and Boundary Problems | S. Glebov, O.M. Kiselev, N. Tarkhanov
Reihe: De Gruyter Series in Nonlinear Analysis and Applications 23/2
Verlag: De Gruyter
Seiten: 390
Link zur Publikation
Nonlinear Equations with Small Parameter. Vol. II: Waves and Boundary Problems
Autoren: S. Glebov, O.M. Kiselev, N. Tarkhanov
(2017)
This is the second volume of Nonlinear Equations with Small Parameter containing new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. They allow one to match asymptotics of various properties with each other in transition regions and to get unified formulas for connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena. These are beginnings of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering constructions and quantum systems. Apart from independent interest the approximate solutions serve as a foolproof basis for testing numerical algorithms. The second volume will be related to partial differential equations.
Reihe:
De Gruyter Series in Nonlinear Analysis and Applications 23/2
2017 | Nonlinear Equations with Small Parameter. Vol. I: Oscillations and Resonances | S. Glebov, O.M. Kiselev, N. Tarkhanov
Reihe: De Gruyter Series in Nonlinear Analysis and Applications 23/1
Verlag: De Gruyter
Seiten: 339
Link zur Publikation
Nonlinear Equations with Small Parameter. Vol. I: Oscillations and Resonances
Autoren: S. Glebov, O.M. Kiselev, N. Tarkhanov
(2017)
This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of characteristic parameters of approximate solutions.
This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena in the natural sciences. These include the outset of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering applications, and quantum systems. Apart from being of independent interest, such approximate solutions serve as a foolproof basis for testing numerical algorithms.
This first volume presents asymptotic methods in oscillation and resonance problems described by ordinary differential equations, whereby the second volume will be devoted to applications of asymptotic methods in waves and boundary value problems.
Reihe:
De Gruyter Series in Nonlinear Analysis and Applications 23/1
2017 | Ellipticity on spaces with higher singularities | Der-Chen Chang, Bert-Wolfgang Schulze
Zeitschrift: Science China Mathematics
Seiten: 2053–2076
Band: 60, Issue 11
Link zur Publikation
Ellipticity on spaces with higher singularities
Autoren: Der-Chen Chang, Bert-Wolfgang Schulze
(2017)
We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata.
Zeitschrift:
Science China Mathematics
2017 | Corner boundary value problems | M. Hedayat Mahmoudi, B.-W. Schulze
Zeitschrift: Asian-European J. Math.
Band: 10
Link zur Publikation
Corner boundary value problems
Autoren: M. Hedayat Mahmoudi, B.-W. Schulze
(2017)
The paper develops some crucial steps in extending the first-order cone or edge calculus to higher singularity orders. We focus here on order 2, but the ideas are motivated by an iterative approach for higher singularities
Zeitschrift:
Asian-European J. Math.
2017 | Construction of series of perfect lattices by layer superposition | S. Vasiliev and N. Tarkhanov
Zeitschrift: J. of Siberian Federal University
Seiten: 352—362
Link zur Publikation
,
Link zum Preprint
Construction of series of perfect lattices by layer superposition
Autoren: S. Vasiliev and N. Tarkhanov
(2017)
We construct a new series of perfect lattices in n dimensions by the layer superposition method of Delaunay-Barnes.
Zeitschrift:
J. of Siberian Federal University
2017 | Calculus on spaces with higher singularities | D.-C. Chang, M. Hedayat Mahmoudi, B.-W. Schulze
Zeitschrift: Journal of Pseudo-Differential Operators and Application
Seiten: 585 - 622
Band: 8, Issue 4
Link zur Publikation
Calculus on spaces with higher singularities
Autoren: D.-C. Chang, M. Hedayat Mahmoudi, B.-W. Schulze
(2017)
We establish extensions of the standard pseudo-differential calculus to specific classes of operators with operator-valued symbols occurring in symbolic hierarchies motivated by manifolds with higher singularities or stratified spaces.
Zeitschrift:
Journal of Pseudo-Differential Operators and Application
2017 | Boundary value problems with global projection conditions | B.-W. Schulze
Reihe: ISAAC, Trend in Math
Verlag: Springer
Buchtitel: Groups, Geometry and Applications
Boundary value problems with global projection conditions
Autoren: B.-W. Schulze
(2017)
Reihe:
ISAAC, Trend in Math
Buchtitel:
Groups, Geometry and Applications
2017 | Boundary Problems on a Manifold with Edge | S. Khalil, B.-W. Schulze
Zeitschrift: Asian-European J. Math.
Band: 10
Link zur Publikation
Boundary Problems on a Manifold with Edge
Autoren: S. Khalil, B.-W. Schulze
(2017)
We establish a calculus of boundary value problems (BVPs) on a manifold NN with boundary and edge, based on Boutet de Monvel’s theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices.
Zeitschrift:
Asian-European J. Math.
2017 | Analytic semigroups of holomorphic mappings and composition operators | M. Elin, D. Shoikhet, and N. Tarkhanov
Zeitschrift: Computational Methods and Function Theory
Seiten: 1-26
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,
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Analytic semigroups of holomorphic mappings and composition operators
Autoren: M. Elin, D. Shoikhet, and N. Tarkhanov
(2017)
- In this paper we study the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators. We also provide a brief review around this topic.
Zeitschrift:
Computational Methods and Function Theory
2017 | A Radó theorem for the porous medium equation | D. Fedchenko and N. Tarkhanov
Zeitschrift: Boletín de la Sociedad Matemática Mexicana
Seiten: 3—13
Link zum Preprint
A Radó theorem for the porous medium equation
Autoren: D. Fedchenko and N. Tarkhanov
(2017)
- We prove that each locally Lipschitz continuous function satisfying the porous medium equation away from the set of its zeroes is actually a weak solution of this equation in the whole domain.
Zeitschrift:
Boletín de la Sociedad Matemática Mexicana
2017 | A nonstandard Cauchy problem for the heat equation | K. Makhmudov, O. Makhmudov, and N. Tarkhanov
Zeitschrift: Math. Notes
Verlag: Springer
Seiten: 250–260
Band: 102
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,
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A nonstandard Cauchy problem for the heat equation
Autoren: K. Makhmudov, O. Makhmudov, and N. Tarkhanov
(2017)
We consider the Cauchy problem for the heat equation in a cylinder C T = X × (0, T) over a domain X in R n , with data on a strip lying on the lateral surface. The strip is of the form S × (0, T), where S is an open subset of the boundary of X. The problem is ill-posed. Under natural restrictions on the configuration of S, we derive an explicit formula for solutions of this problem.
2017 | A New Approach to the Second Order Edge Calculus | M. Hedayat Mahmoudi, B.-W. Schulze
Zeitschrift: Journal of Pseudo-Differential Operators and Applications
Verlag: Springer
Seiten: 1 - 37
Band: 2017
Link zur Publikation
A New Approach to the Second Order Edge Calculus
Autoren: M. Hedayat Mahmoudi, B.-W. Schulze
(2017)
We establish essential steps of an iterative approach to operator algebras, ellipticity and Fredholm property on stratified spaces with singularities of second order. We cover, in particular, corner-degenerate differential operators. Our constructions are focused on the case where no additional conditions of trace and potential type are posed, but this case works well and will be considered in a forthcoming paper as a conclusion of the present calculus.
Zeitschrift:
Journal of Pseudo-Differential Operators and Applications
2017 | Microphysical characterization of long-range transported biomass burning particles from North America at three EARLINET stations | P. Ortiz-Amezcua, Luis Guerrero-Rascado, J., Jose Granados-Munoz, M., Antonio Benavent-Oltra, J., Böckmann, C., et al
Zeitschrift: Atmospheric Chemistry and Physics 17(2017)5931-5946
Microphysical characterization of long-range transported biomass burning particles from North America at three EARLINET stations
Autoren: P. Ortiz-Amezcua, Luis Guerrero-Rascado, J., Jose Granados-Munoz, M., Antonio Benavent-Oltra, J., Böckmann, C., et al
(2017)
Zeitschrift:
Atmospheric Chemistry and Physics 17(2017)5931-5946
2017 | Kalman filter and its modern extensions for the continuous-time filtering problem | A. Taghvaei, J. de Wiljes, P.G. Mehta, S. Reich
Zeitschrift: J. Dyn. Sys. Meas., Control, 140, 030904
Kalman filter and its modern extensions for the continuous-time filtering problem
Autoren: A. Taghvaei, J. de Wiljes, P.G. Mehta, S. Reich
(2017)
Zeitschrift:
J. Dyn. Sys. Meas., Control, 140, 030904
2017 | Likelihood-based parameter estimation and comparison of dynamical cognitive models | H.H. Schuett, L. Rothkegel, H.A. Trukenbrod, S. Reich, F.A. Wichmann, R. Engbert
Zeitschrift: Psychological Review, 124, 505--524
Likelihood-based parameter estimation and comparison of dynamical cognitive models
Autoren: H.H. Schuett, L. Rothkegel, H.A. Trukenbrod, S. Reich, F.A. Wichmann, R. Engbert
(2017)
Zeitschrift:
Psychological Review, 124, 505--524
2017 | A second-order accuate ensemble transform particle filter | J. de Wiljes, W. Acevedo, S. Reich
Zeitschrift: SIAM J. Sci. Comput., 39, A1834-A1850
A second-order accuate ensemble transform particle filter
Autoren: J. de Wiljes, W. Acevedo, S. Reich
(2017)
Zeitschrift:
SIAM J. Sci. Comput., 39, A1834-A1850
2017 | Backscattering effects of raindrops beating the ocean surface on TechDemoSat-1 derived wind speeds: Toward an improved GNSS scatterometry | M. Asgarimehr, J. Wickert, S. Reich, P. Jales, V. U. Zavorotny
Zeitschrift: submitted to Geophysical Review Letters
Backscattering effects of raindrops beating the ocean surface on TechDemoSat-1 derived wind speeds: Toward an improved GNSS scatterometry
Autoren: M. Asgarimehr, J. Wickert, S. Reich, P. Jales, V. U. Zavorotny
(2017)
Zeitschrift:
submitted to Geophysical Review Letters
2017 | Balanced data assimilation for highly oscillatory mechanical systems | M. Reinhardt, G. Hastermann, R. Klein and S. Reich
Zeitschrift: submitted to Nonlinear Science
Balanced data assimilation for highly oscillatory mechanical systems
Autoren: M. Reinhardt, G. Hastermann, R. Klein and S. Reich
(2017)
Zeitschrift:
submitted to Nonlinear Science
2017 | Algebraic Birkhoff factorization and the Euler–Maclaurin formula on cones | L. Guo, S. Paycha, B. Zhang
Zeitschrift: Duke Math. J.
Band: 166, 3
Link zur Publikation
,
Link zum Preprint
Algebraic Birkhoff factorization and the Euler–Maclaurin formula on cones
Autoren: L. Guo, S. Paycha, B. Zhang
(2017)
We equip the space of lattice cones with a coproduct which makes it a cograded, coaugmented, connnected coalgebra. The exponential generating sum and exponential generating integral on lattice cones can be viewed as linear maps on this space with values in the space of meromorphic germs with linear poles at zero. We investigate the subdivision properties—reminiscent of the inclusion-exclusion principle for the cardinal on finite sets—of such linear maps and show that these properties are compatible with the convolution quotient of maps on the coalgebra. Implementing the algebraic Birkhoff factorization procedure on the linear maps under consideration, we factorize the exponential generating sum as a convolution quotient of two maps, with each of the maps in the factorization satisfying a subdivision property. A direct computation shows that the polar decomposition of the exponential generating sum on a smooth lattice cone yields an Euler–Maclaurin formula. The compatibility with subdivisions of the convolution quotient arising in the algebraic Birkhoff factorization then yields the Euler–Maclaurin formula for any lattice cone. This provides a simple formula for the interpolating factor by means of a projection formula.
Zeitschrift:
Duke Math. J.
2017 | An algebraic formulation of the locality principle in renormalisation | Pierre Clavier, Li Guo, Sylvie Paycha, Bin Zhang
Link zum Preprint
An algebraic formulation of the locality principle in renormalisation
Autoren: Pierre Clavier, Li Guo, Sylvie Paycha, Bin Zhang
(2017)
We study the mathematical structure underlying the concept of locality which lies at the heart of classical and quantum field theory, and develop a machinery used to preserve locality during the renormalisation procedure. Viewing renormalisation in the framework of Connes and Kreimer as the algebraic Birkhoff factorisation of characters on a Hopf algebra with values in a Rota-Baxter algebra, we build locality variants of these algebraic structures, leading to a locality variant of the algebraic Birkhoff factorisation. This provides an algebraic formulation of the conservation of locality while renormalising.
As an application in the context of the Euler-Maclaurin formula on cones, we renormalise the exponential generating function which sums over the lattice points in convex cones. For a suitable multivariate regularisation, renormalisation from the algebraic Birkhoff factorisation amounts to composition by a projection onto holomorphic multivariate functions.
2017 | Un destin singulier: Vincent, alias Wolfgang, fils d’Alfred Döblin | Sylvie Roelly
Zeitschrift: Dokumente/Documents
Band: 4/2017
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,
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Un destin singulier: Vincent, alias Wolfgang, fils d’Alfred Döblin
Autoren: Sylvie Roelly
(2017)
Un pli cacheté, envoyé par Wolfgang Döblin (1915-1940) à l’Académie des Sciences de Paris, mais ouvert seulement en 2000, met en évidence l’avant-gardisme du génie probabiliste du fils de l’écrivain Alfred Döblin (1878-1957), auteur notamment de Berlin, Alexanderplatz. Son inspiration mathématique géniale a puisé ses forces dans l’union des deux écoles française et allemande.
Zeitschrift:
Dokumente/Documents
2017 | Two-sample Tests for Random Graphs | Debarghya Ghoshdastidar, Maurilio Gutzeit, Alexandra Carpentier, Ulrike von Luxburg.
Zeitschrift: Preprint
Link zum Preprint
Two-sample Tests for Random Graphs
Autoren: Debarghya Ghoshdastidar, Maurilio Gutzeit, Alexandra Carpentier, Ulrike von Luxburg.
(2017)
2017 | Adaptive estimation of the sparsity in the Gaussian vector model | A. Carpentier, N. Verzelen
Zeitschrift: Preprint
Link zum Preprint
Adaptive estimation of the sparsity in the Gaussian vector model
Autoren: A. Carpentier, N. Verzelen
(2017)
2017 | An iterative hard thresholding estimator for low rank matrix recovery with explicit limiting distribution | A. Carpentier and A.K.H. Kim
Zeitschrift: To appear in Statistica Sinica
Link zum Preprint
An iterative hard thresholding estimator for low rank matrix recovery with explicit limiting distribution
Autoren: A. Carpentier and A.K.H. Kim
(2017)
Zeitschrift:
To appear in Statistica Sinica
2017 | Early stopping for statistical inverse problems via truncated SVD estimation. | G. Blanchard, M. Hoffmann, M. Reiß
Zeitschrift: Preprint
Link zum Preprint
Early stopping for statistical inverse problems via truncated SVD estimation.
Autoren: G. Blanchard, M. Hoffmann, M. Reiß
(2017)
2017 | Optimal adaptation for early stopping in statistical inverse problems | G. Blanchard, M. Hoffmann, M. Reiß.
Zeitschrift: Preprint
Link zum Preprint
Optimal adaptation for early stopping in statistical inverse problems
Autoren: G. Blanchard, M. Hoffmann, M. Reiß.
(2017)
2017 | Compressive Statistical Learning with Random Feature Moments | R. Gribonval, G. Blanchard, N. Keriven, Y. Traonmilin.
Zeitschrift: Preprint
Link zum Preprint
Compressive Statistical Learning with Random Feature Moments
Autoren: R. Gribonval, G. Blanchard, N. Keriven, Y. Traonmilin.
(2017)
2017 | Post hoc inference via joint family-wise error rate control | G. Blanchard, P. Neuvial, E. Roquain
Zeitschrift: Preprint
Link zum Preprint
Post hoc inference via joint family-wise error rate control
Autoren: G. Blanchard, P. Neuvial, E. Roquain
(2017)
2017 | Minimax Euclidean Separation Rates for Testing Convex Hypotheses in R^d | G. Blanchard, A. Carpentier, M. Gutzeit
Zeitschrift: Preprint
Link zum Preprint
Minimax Euclidean Separation Rates for Testing Convex Hypotheses in R^d
Autoren: G. Blanchard, A. Carpentier, M. Gutzeit
(2017)
2017 | Kernel regression, minimax rates and effective dimensionality: beyond the regular case. | G. Blanchard, N. Mücke.
Zeitschrift: Preprint
Link zum Preprint
Kernel regression, minimax rates and effective dimensionality: beyond the regular case.
Autoren: G. Blanchard, N. Mücke.
(2017)
2017 | Adaptive Confidence Sets for Matrix Completion. | A. Carpentier, O. Klopp, M. Loeffler, and R. Nickl.
Zeitschrift: To appear in Bernoulli
Link zum Preprint
Adaptive Confidence Sets for Matrix Completion.
Autoren: A. Carpentier, O. Klopp, M. Loeffler, and R. Nickl.
(2017)
Zeitschrift:
To appear in Bernoulli
2017 | Two-Sample Tests for Large Random Graphs using Network Statistics. | Debarghya Ghoshdastidar, Ulrike von Luxburg, Maurilio Gutzeit and Alexandra Carpentier
Zeitschrift: COLT
Link zur Publikation
,
Link zum Preprint
Two-Sample Tests for Large Random Graphs using Network Statistics.
Autoren: Debarghya Ghoshdastidar, Ulrike von Luxburg, Maurilio Gutzeit and Alexandra Carpentier
(2017)
2017 | Adaptivity to Noise Parameters in Nonparametric Active Learning | Andrea Locatelli, Alexandra Carpentier and Samory Kpotufe
Zeitschrift: COLT 2017
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,
Link zum Preprint
Adaptivity to Noise Parameters in Nonparametric Active Learning
Autoren: Andrea Locatelli, Alexandra Carpentier and Samory Kpotufe
(2017)
2017 | Optimal Rates For Regularization Of Statistical Inverse Learning Problems | G. Blanchard, N. Mücke.
Zeitschrift: Foundations of Computational Mathematics
Verlag: Springer
Link zur Publikation
,
Link zum Preprint
Optimal Rates For Regularization Of Statistical Inverse Learning Problems
Autoren: G. Blanchard, N. Mücke.
(2017)
Zeitschrift:
Foundations of Computational Mathematics
2017 | Remarks on curvature dimension conditions on graphs | Florentin Münch
Zeitschrift: Calculus of Variations and Partial Differential Equations
Reihe: 56
Verlag: Springer
Seiten: 11
Link zum Preprint
Remarks on curvature dimension conditions on graphs
Autoren: Florentin Münch
(2017)
We show a connection between the CDE′ inequality introduced in Horn et al. (Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for nonnegative curvature graphs. arXiv:1411.5087v2, 2014) and the CDψ inequality established in Münch (Li–Yau inequality on finite graphs via non-linear curvature dimension conditions. arXiv:1412.3340v1, 2014). In particular, we introduce a CDφψ inequality as a slight generalization of CDψ which turns out to be equivalent to CDE′ with appropriate choices of φ and ψ. We use this to prove that the CDE′ inequality implies the classical CD inequality on graphs, and that the CDE′ inequality with curvature bound zero holds on Ricci-flat graphs.
Zeitschrift:
Calculus of Variations and Partial Differential Equations
2017 | On the positive mass theorem for closed Riemannian manifolds | Andreas Hermann, Emmanuel Humbert
Verlag: Springer
Buchtitel: Ji, Lizhen, Papadopoulos, Athanase, Yamada, Sumio (Eds.): From Riemann to Differential Geometry and Relativity
Seiten: 515-540
Link zur Publikation
On the positive mass theorem for closed Riemannian manifolds
Autoren: Andreas Hermann, Emmanuel Humbert
(2017)
The Positive Mass Conjecture for asymptotically flat Riemannian manifolds is a famous open problem in geometric analysis. In this article we consider a variant of this conjecture, namely the Positive Mass Conjecture for closed Riemannian manifolds. We explain why the two positive mass conjectures are equivalent. After that we explain our proof of the following result: If one can prove the Positive Mass Conjecture for one closed simply-connected non-spin manifold of dimension n≥5, then the Positive Mass Conjecture is true for all closed manifolds of dimension n.
Buchtitel:
Ji, Lizhen, Papadopoulos, Athanase, Yamada, Sumio (Eds.): From Riemann to Differential Geometry and Relativity
2017 | Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of the metric | Lashi Bandara, Alan McIntosh, Andreas Rosén
Zeitschrift: Math. Ann.
Verlag: Springer
Seiten: 1-53
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,
Link zum Preprint
Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of the metric
Autoren: Lashi Bandara, Alan McIntosh, Andreas Rosén
(2017)
We prove that the Atiyah-Singer Dirac operator Dg in L2 depends Riesz continuously on L∞ perturbations of complete metrics g on a smooth manifold. The Lipschitz bound for the map g→Dg(1+Dg2)-1/2 depends on bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius. Our proof uses harmonic analysis techniques related to Calder\'on's first commutator and the Kato square root problem. We also show perturbation results for more general functions of general Dirac-type operators on vector bundles.
2017 | Geometric singularities and a flow tangent to the Ricci flow | Lashi Bandara, Sajjad Lakzian, Michael Munn
Zeitschrift: Ann. Sc. Norm. Super. Pisa Cl. Sci.
Seiten: 763-804
Band: 17, no. 2
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,
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Geometric singularities and a flow tangent to the Ricci flow
Autoren: Lashi Bandara, Sajjad Lakzian, Michael Munn
(2017)
We consider a geometric flow introduced by Gigli and Mantegazza which, in the case of smooth compact manifolds with smooth metrics, is tangential to the Ricci flow almost-everywhere along geodesics. To study spaces with geometric singularities, we consider this flow in the context of smooth manifolds with rough metrics with sufficiently regular heat kernels. On an appropriate non-singular open region, we provide a family of metric tensors evolving in time and provide a regularity theory for this flow in terms of the regularity of the heat kernel.
When the rough metric induces a metric measure space satisfying a Riemannian Curvature Dimension condition, we demonstrate that the distance induced by the flow is identical to the evolving distance metric defined by Gigli and Mantegazza on appropriate admissible points. Consequently, we demonstrate that a smooth compact manifold with a finite number of geometric conical singularities remains a smooth manifold with a smooth metric away from the cone points for all future times. Moreover, we show that the distance induced by the evolving metric tensor agrees with the flow of RCD(K, N) spaces defined by Gigli-Mantegazza.
Zeitschrift:
Ann. Sc. Norm. Super. Pisa Cl. Sci.
2017 | Continuity of solutions to space-varying pointwise linear elliptic equations | Lashi Bandara
Zeitschrift: Publ. Mat.
Seiten: 239-258
Band: 61, no. 1
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,
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Continuity of solutions to space-varying pointwise linear elliptic equations
Autoren: Lashi Bandara
(2017)
We consider pointwise linear elliptic equations of the form Lxux=ηx on a smooth compact manifold where the operators Lx are in divergence form with real, bounded, measurable coefficients that vary in the space variable x. We establish L2-continuity of the solution at x whenever the coefficients of Lx are L∞-continuous at x and the initial datum is L2-continuous at x. This is obtained by reducing the continuity of solutions to a homogeneous Kato square root problem. As an application, we consider a time evolving family of metrics g<ub>t that is tangential to the Ricci flow almost-everywhere along geodesics when starting with a smooth initial metric. Under the assumption that our initial metric is a rough metric on M with a C1 heat kernel on a "non-singular" nonempty open subset N, we show that x x↦gt(x) is continuous whenever x ∈ N.
2017 | Essential self-adjointness of powers of first-order differential operators on non-compact manifolds with low-regularity metrics | Lashi Bandara, Hemanth Saratchandran
Zeitschrift: Journal of Functional Analysis
Reihe: 273
Seiten: 3719-3758
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,
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Essential self-adjointness of powers of first-order differential operators on non-compact manifolds with low-regularity metrics
Autoren: Lashi Bandara, Hemanth Saratchandran
(2017)
We consider first-order differential operators with locally bounded measurable coefficients on vector bundles with measurable coefficient metrics. Under a mild set of assumptions, we demonstrate the equivalence between the essential self-adjointness of such operators to a negligible boundary property. When the operator possesses higher regularity coefficients, we show that higher powers are essentially self-adjoint if and only if this condition is satisfied. In the case that the low-regularity Riemannian metric induces a complete length space, we demonstrate essential self-adjointness of the operator and its higher powers up to the regularity of its coefficients. We also present applications to Dirac operators on Dirac bundles when the metric is non-smooth.
Zeitschrift:
Journal of Functional Analysis
2017 | On central extensions of SL(2,F) admitting left-orderings | Brungs, H. H.; Gräter, J.
Zeitschrift: Journal of Algebra 486, Seiten: 288-327
On central extensions of SL(2,F) admitting left-orderings
Autoren: Brungs, H. H.; Gräter, J.
(2017)
Zeitschrift:
Journal of Algebra 486, Seiten: 288-327
2017 | Global properties of Dirichlet forms in terms of Green's formula | aeseler, Sebastian; Keller, Matthias; Lenz, Daniel; Masamune, Jun; Schmidt, Marcel;
Zeitschrift: Calc. Var. Partial Differential Equations
Seiten: 56-124.
Band: 56
Link zum Preprint
Global properties of Dirichlet forms in terms of Green's formula
Autoren: aeseler, Sebastian; Keller, Matthias; Lenz, Daniel; Masamune, Jun; Schmidt, Marcel;
(2017)
Zeitschrift:
Calc. Var. Partial Differential Equations
2017 | Geometric and spectral consequences of curvature bounds on tessellations | Matthias Keller
Reihe: Lecture Notes in Mathematics
Verlag: Springer
Buchtitel: Modern Approaches to Discrete Curvature
Band: 2184
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,
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Geometric and spectral consequences of curvature bounds on tessellations
Autoren: Matthias Keller
(2017)
Reihe:
Lecture Notes in Mathematics
Buchtitel:
Modern Approaches to Discrete Curvature
2017 | On a Convergence Theorem for Semigroups of Positive Integral Operators | Moritz Gerlach, Jochen Glück
Zeitschrift: Comptes rendus - Mathematics
Seiten: 973-976
Band: 355(9)
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On a Convergence Theorem for Semigroups of Positive Integral Operators
Autoren: Moritz Gerlach, Jochen Glück
(2017)
We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive c_0-semigroup on an L^p-space is strongly convergent in case that it has a strictly positive fixed point and contains an integral operator. Our proof is a streamlined version of a much more general approach to the asymptotic theory of positive semigroups developed recently by the authors. Under the assumptions of Greiner's theorem, this approach becomes particularly elegant and simple. We also give an outlook on several generalisations of this result.
Zeitschrift:
Comptes rendus - Mathematics
2017 | How close are time series to power tail Lévy diffusions? | Jan Gairing, Michael Hoegele, Tania Kosenkova, and Adam Monahan
Zeitschrift: Chaos: An Interdisciplinary Journal of Nonlinear Sciences
Band: 27 (11) 073112-1--073112-20, DOI: 10.1063/1.4986496
Link zur Publikation
,
Link zum Preprint
How close are time series to power tail Lévy diffusions?
Autoren: Jan Gairing, Michael Hoegele, Tania Kosenkova, and Adam Monahan
(2017)
Zeitschrift:
Chaos: An Interdisciplinary Journal of Nonlinear Sciences
Band:
27 (11) 073112-1--073112-20, DOI: 10.1063/1.4986496
2017 | A new tensorial conservation law for Maxwell fields on the Kerr background | Lars Andersson, Thomas Bäckdahl, Pieter Blue
Zeitschrift: J. Differential Geom.
Verlag: Project Euclid
Seiten: 163-176
Band: 105, no. 2
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,
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A new tensorial conservation law for Maxwell fields on the Kerr background
Autoren: Lars Andersson, Thomas Bäckdahl, Pieter Blue
(2017)
A new, conserved, symmetric tensor field for a source-free Maxwell test field on a four-dimensional spacetime with a conformal Killing–Yano tensor, satisfying a certain compatibility condition, is introduced. In particular, this construction works for the Kerr spacetime.
Zeitschrift:
J. Differential Geom.
2017 | Transportation distances and noise sensitivity of multiplicative Lévy SDE with applications | Jan Gairing, Michael Högele, Tetiana Kosenkova
Zeitschrift: Stochastic Processes and their Applications
Link zur Publikation
Transportation distances and noise sensitivity of multiplicative Lévy SDE with applications
Autoren: Jan Gairing, Michael Högele, Tetiana Kosenkova
(2017)
Zeitschrift:
Stochastic Processes and their Applications
2017 | Sectional curvature of polygonal complexes with planar substructures | Matthias Keller, Norbert Peyerimhoff, Felix Pogorzelski
Zeitschrift: Advances in Mathematics
Seiten: 1070--1107.
Band: 307
Link zur Publikation
,
Link zum Preprint
Sectional curvature of polygonal complexes with planar substructures
Autoren: Matthias Keller, Norbert Peyerimhoff, Felix Pogorzelski
(2017)
In this paper we introduce a class of polygonal complexes for which we can define a notion of sectional combinatorial curvature. These complexes can be viewed as generalizations of 2-dimensional Euclidean and hyperbolic buildings. We focus on the case of non-positive and negative combinatorial curvature. As geometric results we obtain a Hadamard-Cartan type theorem, thinness of bigons, Gromov hyperbolicity and estimates for the Cheeger constant. We employ the latter to get spectral estimates, show discreteness of the spectrum in the sense of a Donnelly-Li type theorem and present corresponding eigenvalue asymptotics. Moreover, we prove a unique continuation theorem for eigenfunctions and the solvability of the Dirichlet problem at infinity.
Zeitschrift:
Advances in Mathematics
2017 | Hadamard states for quantum Abelian duality | Marco Benini, Matteo Capoferri, Claudio Dappiaggi
Zeitschrift: Ann. Henri Poincaré
Verlag: Springer
Seiten: 3325-3370
Band: 18, no. 10
Link zur Publikation
,
Link zum Preprint
Hadamard states for quantum Abelian duality
Autoren: Marco Benini, Matteo Capoferri, Claudio Dappiaggi
(2017)
Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a C*-algebra of observables, which encompasses the simultaneous discretization of both magnetic and electric fluxes. We discuss the assignment of physically well-behaved states to such algebra and the properties of the associated GNS triple. We show that the algebra of observables factorizes as a suitable tensor product of three C*-algebras: the first factor encodes dynamical information, while the other two capture topological data corresponding to electric and magnetic fluxes. On the former factor we exhibit a state whose two-point correlation function has the same singular structure of a Hadamard state. Specifying suitable counterparts also on the topological factors we obtain a state for the full theory, providing ultimately a unitary implementation of Abelian duality.
Zeitschrift:
Ann. Henri Poincaré
2017 | Global Regularity for the 2+1 Dimensional Equivariant Einstein-Wave Map System | Lars Andersson, Nishanth Gudapati, Jeremie Szeftel
Zeitschrift: Ann. PDE
Verlag: Springer
Seiten: Art. 13
Band: 3, no. 2
Link zur Publikation
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Link zum Preprint
Global Regularity for the 2+1 Dimensional Equivariant Einstein-Wave Map System
Autoren: Lars Andersson, Nishanth Gudapati, Jeremie Szeftel
(2017)
In this paper we consider the equivariant 2+1 dimensional Einstein-wave map system and show that if the target satisfies the so called Grillakis condition, then global existence holds. In view of the fact that the 3+1 vacuum Einstein equations with a spacelike translational Killing field reduce to a 2+1 dimensional Einstein-wave map system with target the hyperbolic plane, which in particular satisfies the Grillakis condition, this work proves global existence for the equivariant class of such spacetimes.
2017 | Mode stability on the real axis | Lars Andersson, Siyuan Ma, Claudio Paganini, Bernard F. Whiting
Zeitschrift: J. Math. Phys.
Verlag: AIP Publishing
Seiten: 072501
Band: 58, no. 7
Link zur Publikation
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Link zum Preprint
Mode stability on the real axis
Autoren: Lars Andersson, Siyuan Ma, Claudio Paganini, Bernard F. Whiting
(2017)
A generalization of the mode stability result of Whiting (1989) for the Teukolsky equation is proved for the case of real frequencies. The main result of the paper states that a separated solution of the Teukolsky equation governing massless test fields on the Kerr spacetime, which is purely outgoing at infinity, and purely ingoing at the horizon, must vanish. This has the consequence, that for real frequencies, there are linearly independent fundamental solutions of the radial Teukolsky equation which are purely ingoing at the horizon, and purely outgoing at infinity, respectively. This fact yields a representation formula for solutions of the inhomogenous Teukolsky equation.
Zeitschrift:
J. Math. Phys.
2017 | Quantum field theories on categories fibered in groupoids | Marco Benini, Alexander Schenkel
Zeitschrift: Comm. Math. Phys.
Verlag: Springer
Seiten: 19-64
Band: 356, no. 1
Link zur Publikation
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Link zum Preprint
Quantum field theories on categories fibered in groupoids
Autoren: Marco Benini, Alexander Schenkel
(2017)
We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geometric structures such as bundles, connections and spin structures. Using right Kan extensions, we can assign to any such theory an ordinary quantum field theory defined on the category of spacetimes and we shall clarify under which conditions it satisfies the axioms of locally covariant quantum field theory. The same constructions can be performed in a homotopy theoretic framework by using homotopy right Kan extensions, which allows us to obtain first examples of homotopical quantum field theories resembling some aspects of gauge theories.
Zeitschrift:
Comm. Math. Phys.
2017 | Path Integrals on Manifolds with Boundary | Matthias Ludewig
Zeitschrift: Comm. Math. Phys.
Verlag: Springer
Seiten: 621-640
Band: 354, no. 2
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Path Integrals on Manifolds with Boundary
Autoren: Matthias Ludewig
(2017)
We give time-slicing path integral formulas for solutions to the heat equation corresponding to a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold with boundary. More specifically, we show that such a solution can be approximated by integrals over finite-dimensional path spaces of piecewise geodesics subordinated to increasingly fine partitions of the time interval. We consider a subclass of mixed boundary conditions which includes standard Dirichlet and Neumann boundary conditions.
Zeitschrift:
Comm. Math. Phys.
2017 | Exact simulation of Brownian diffusions with drift admitting jumps | David Dereudre, Sara Mazzonetto, Sylvie Roelly
Zeitschrift: SIAM J. Sci. Comput., 39(3)
Seiten: A711–A740
Link zur Publikation
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Link zum Preprint
Exact simulation of Brownian diffusions with drift admitting jumps
Autoren: David Dereudre, Sara Mazzonetto, Sylvie Roelly
(2017)
Zeitschrift:
SIAM J. Sci. Comput., 39(3)
2017 | Poisson algebras for non-linear field theories in the Cahiers topos | Marco Benini, Alexander Schenkel
Zeitschrift: Ann. Henri Poincare
Verlag: Springer
Seiten: 1435-1464
Band: 18, no. 4
Link zur Publikation
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Link zum Preprint
Poisson algebras for non-linear field theories in the Cahiers topos
Autoren: Marco Benini, Alexander Schenkel
(2017)
We develop an approach to construct Poisson algebras for non-linear scalar field theories that is based on the Cahiers topos model for synthetic differential geometry. In this framework the solution space of the field equation carries a natural smooth structure and, following Zuckerman's ideas, we can endow it with a presymplectic current. We formulate the Hamiltonian vector field equation in this setting and show that it selects a family of observables which forms a Poisson algebra. Our approach provides a clean splitting between geometric and algebraic aspects of the construction of a Poisson algebra, which are sufficient to guarantee existence, and analytical aspects that are crucial to analyze its properties.
Zeitschrift:
Ann. Henri Poincare
2017 | Bridge mixtures of random walks on an Abelian group | G. Conforti and S. Roelly
Zeitschrift: Bernoulli
Seiten: 1518-1537
Band: 23, No. 3
Link zur Publikation
Bridge mixtures of random walks on an Abelian group
Autoren: G. Conforti and S. Roelly
(2017)
2017 | Path-dependent infinite-dimensional SDE with non-regular drift: an existence result. | David Dereudre, Sylvie Roelly
Zeitschrift: Annales de l'Institut Henri Poincaré - Probabilités et Statistiques
Seiten: 641–657
Band: 53 No.2
Link zur Publikation
Path-dependent infinite-dimensional SDE with non-regular drift: an existence result.
Autoren: David Dereudre, Sylvie Roelly
(2017)
Zeitschrift:
Annales de l'Institut Henri Poincaré - Probabilités et Statistiques
2017 | Reciprocal class of jump processes | G. Conforti, P. dai Pra and S. Roelly
Zeitschrift: Journal of Theoretical Probability
Seiten: 551-580
Band: 30-2
Link zur Publikation
Reciprocal class of jump processes
Autoren: G. Conforti, P. dai Pra and S. Roelly
(2017)
Zeitschrift:
Journal of Theoretical Probability
2017 | Abelian duality on globally hyperbolic spacetimes | Christian Becker, Marco Benini, Alexander Schenkel, Richard J. Szabo
Zeitschrift: Comm. Math. Phys.
Verlag: Springer
Seiten: 361-392
Band: 349, no. 1
Link zur Publikation
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Link zum Preprint
Abelian duality on globally hyperbolic spacetimes
Autoren: Christian Becker, Marco Benini, Alexander Schenkel, Richard J. Szabo
(2017)
We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian manifolds. Our approach generalizes previous treatments using the Hamiltonian formalism in a manifestly covariant way and without the assumption of compact Cauchy surfaces. We construct semi-classical configuration spaces and corresponding presymplectic Abelian groups of observables, which are quantized by the CCR-functor to the category of C*-algebras. We demonstrate explicitly how duality is implemented as a natural isomorphism between quantum field theories. We apply this formalism to develop a fully covariant quantum theory of self-dual fields.
Zeitschrift:
Comm. Math. Phys.
2017 | Differential cohomology and locally covariant quantum field theory | Christian Becker, Alexander Schenkel, Richard J. Szabo
Zeitschrift: Rev. Math. Phys.
Verlag: World Scientific
Seiten: 1750003
Band: 29, no. 1
Link zur Publikation
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Link zum Preprint
Differential cohomology and locally covariant quantum field theory
Autoren: Christian Becker, Alexander Schenkel, Richard J. Szabo
(2017)
We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental exact sequences of differential cohomology. We consider smooth Pontryagin duals of differential cohomology groups, which are subgroups of the character groups. We prove that these groups fit into smooth duals of the fundamental exact sequences of differential cohomology and equip them with a natural presymplectic structure derived from a generalized Maxwell Lagrangian. The resulting presymplectic Abelian groups are quantized using the CCR-functor, which yields a covariant functor from our categories of globally hyperbolic Lorentzian manifolds to the category of C*-algebras. We prove that this functor satisfies the causality and time-slice axioms of locally covariant quantum field theory, but that it violates the locality axiom. We show that this violation is precisely due to the fact that our functor has topological subfunctors describing the Pontryagin duals of certain singular cohomology groups. As a byproduct, we develop a Fr\'echet-Lie group structure on differential cohomology groups.
Zeitschrift:
Rev. Math. Phys.
2017 | Magnetic Geodesics via the Heat Flow | Volker Branding, Florian Hanisch
Zeitschrift: Asian Journal of Mathematics
Verlag: International Press
Seiten: 995-1014
Band: 21, no. 6
Link zur Publikation
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Link zum Preprint
Magnetic Geodesics via the Heat Flow
Autoren: Volker Branding, Florian Hanisch
(2017)
Magnetic geodesics describe the trajectory of a particle in a Riemannian manifold under the influence of an external magnetic field. In this article, we use the heat flow method to derive existence results for such curves. We first establish subconvergence of this flow to a magnetic geodesic under certain boundedness assumptions. It is then shown that these conditions are satisfied provided that either the magnetic field admits a global potential or the initial curve is sufficiently small. Finally, we discuss different examples which illustrate our results.
Zeitschrift:
Asian Journal of Mathematics
Verlag:
International Press
2016 | On a strongly convex approximation of a stochastic optimal control problem for importance sampling of metastable diffusions | Han Cheng Lie
Verlag: Dissertation, Freie Universität Berlin
Link zur Publikation
On a strongly convex approximation of a stochastic optimal control problem for importance sampling of metastable diffusions
Autoren: Han Cheng Lie
(2016)
Verlag:
Dissertation, Freie Universität Berlin
2016 | Convexity of a stochastic control functional related to importance sampling of Itô diffusions | Han Cheng Lie
Link zum Preprint
Convexity of a stochastic control functional related to importance sampling of Itô diffusions
Autoren: Han Cheng Lie
(2016)
2016 | Continuity of the Spectrum of a Field of Self-Adjoint Operators | Siegfried Beckus, Jean Bellissard
Zeitschrift: Annales Henri Poincaré
Reihe: 17
Seiten: 3425 - 3442
Link zur Publikation
,
Link zum Preprint
Continuity of the Spectrum of a Field of Self-Adjoint Operators
Autoren: Siegfried Beckus, Jean Bellissard
(2016)
Given a family of self-adjoint operators (At)t∈T indexed by a parameter t in some topological space T, necessary and sufficient conditions are given for the spectrum σ(At) to be Vietoris continuous with respect to t. Equivalently the boundaries and the gap edges are continuous in t. If (T,d) is a complete metric space with metric d, these conditions are extended to guarantee Hölder continuity of the spectral boundaries and of the spectral gap edges. As a corollary, an upper bound is provided for the size of closing gaps.
Zeitschrift:
Annales Henri Poincaré
2016 | Stable varieties of semigroups and groupoids | Koppitz, J. and Shtrakov, Sl.
Zeitschrift: Algebra Universalis
Band: 75 no. 1
Stable varieties of semigroups and groupoids
Autoren: Koppitz, J. and Shtrakov, Sl.
(2016)
Zeitschrift:
Algebra Universalis
2016 | Generating sets of infinite full transformation semigroups with restricted range | Tinpun, K. and Koppitz J
Zeitschrift: Acta Sci. Math. (Szeged)
Band: 82
Generating sets of infinite full transformation semigroups with restricted range
Autoren: Tinpun, K. and Koppitz J
(2016)
Zeitschrift:
Acta Sci. Math. (Szeged)
2016 | Relative Rank of the Finite Full Transformation Semigroup with Restricted Range | Tinpun, K. and Koppitz, J.
Zeitschrift: Acta Math. Univ. Comenianae
Band: Vol. LXXXV, No. 2
Relative Rank of the Finite Full Transformation Semigroup with Restricted Range
Autoren: Tinpun, K. and Koppitz, J.
(2016)
Zeitschrift:
Acta Math. Univ. Comenianae
2016 | Maximal subsemigroups of some semigroups of order-preserving mappings on a countably infinite set | Koppitz, J. and Musunthia, T.
Zeitschrift: Forum Mathematicum
Link zur Publikation
Maximal subsemigroups of some semigroups of order-preserving mappings on a countably infinite set
Autoren: Koppitz, J. and Musunthia, T.
(2016)
Zeitschrift:
Forum Mathematicum
2016 | On a Semigroup of Sets of Transformations with Restricted Range | Anantayasthi, A, and Koppitz, J.
Zeitschrift: Thai Journal of Mathematics
Band: 14, no. 3
On a Semigroup of Sets of Transformations with Restricted Range
Autoren: Anantayasthi, A, and Koppitz, J.
(2016)
Zeitschrift:
Thai Journal of Mathematics
2016 | Zahlverständnis mit dem Tablet unterstützen | Heiko Etzold
Zeitschrift: Inklusiver Mathematikunterricht – Mathematiklernen in ausgewählten Förderschwerpunkten : Tagungsband des AK Grundschule in der GDM 2016
Seiten: 81-84
Zahlverständnis mit dem Tablet unterstützen
Autoren: Heiko Etzold
(2016)
Zeitschrift:
Inklusiver Mathematikunterricht – Mathematiklernen in ausgewählten Förderschwerpunkten : Tagungsband des AK Grundschule in der GDM 2016
2016 | Neue Zugänge zum Winkelbegriff – Vorstellung eines Promotionsprojektes | Heiko Etzold
Zeitschrift: Beiträge zum Mathematikunterricht 2016. Vorträge auf der 50. GDM Tagung für Didaktik der Mathematik. Band 1, 2 und 3.
Seiten: 257-260
Neue Zugänge zum Winkelbegriff – Vorstellung eines Promotionsprojektes
Autoren: Heiko Etzold
(2016)
Zeitschrift:
Beiträge zum Mathematikunterricht 2016. Vorträge auf der 50. GDM Tagung für Didaktik der Mathematik. Band 1, 2 und 3.
2016 | Guck hier - guck dort. Das Klassenzimmer aus verschiedenen Blickwinkeln betrachtet | Heiko Etzold
Zeitschrift: Grundschulunterricht Mathematik
Seiten: 30-34
Guck hier - guck dort. Das Klassenzimmer aus verschiedenen Blickwinkeln betrachtet
Autoren: Heiko Etzold
(2016)
Zeitschrift:
Grundschulunterricht Mathematik
2016 | Die Kraft des Fünfecks. Argumentationsanlässe für dynamische Betrachtungen | Heiko Etzold, Ines Petzschler
Zeitschrift: Praxis der Mathematik in der Schule
Seiten: 30-33
Band: 58
Die Kraft des Fünfecks. Argumentationsanlässe für dynamische Betrachtungen
Autoren: Heiko Etzold, Ines Petzschler
(2016)
Zeitschrift:
Praxis der Mathematik in der Schule
2016 | Touch2Learn: Multi-Touch Lernumgebungen explorativ erforschen. | Christian Dohrmann
Verlag: Hohengehren: Schneider Verlag
Buchtitel: In Peschel, M. (Hrsg.), Mediales Lernen – Beispiele für eine inklusive Mediendidaktik.
Seiten: 95-104
Touch2Learn: Multi-Touch Lernumgebungen explorativ erforschen.
Autoren: Christian Dohrmann
(2016)
Verlag:
Hohengehren: Schneider Verlag
Buchtitel:
In Peschel, M. (Hrsg.), Mediales Lernen – Beispiele für eine inklusive Mediendidaktik.
2016 | Vorwärts-Rückwärts zum Begriff. Konstruktion und Re-Konstruktion von Zugfiguren. | Ulrich Kortenkamp, Christian Dohrmann
Zeitschrift: Mathematik lehren
Seiten: 18-21
Band: 33
Vorwärts-Rückwärts zum Begriff. Konstruktion und Re-Konstruktion von Zugfiguren.
Autoren: Ulrich Kortenkamp, Christian Dohrmann
(2016)
Zusammenfassung: Zugfiguren, d.h. dynamische Realisierungen von Konstruktionen im DGS, sind ein gutes Werkzeug, um die heuristischen Strategien des Vorwärts- und Rückwärtsarbeiten zu unterstützen. Was muss man über ein Parallelogramm (oder ein anderes spezielles Viereck) wissen, um dieses zu (re-)konstruieren? Die Beschäftigung damit führt zu elementaren Konstruktionsschritten wie auch zu den Typ-bestimmenden Eigenschaften spezieller Vierecke.
Zeitschrift:
Mathematik lehren
2016 | Und er ist drin! Drin! Drin! | Ulrich Kortenkam, Jürgen Richter-Gebert
Verlag: Verlag Klaus Seeberger
Buchtitel: Digitale Werkzeuge für den Mathematikunterricht
Seiten: 296-308
Und er ist drin! Drin! Drin!
Autoren: Ulrich Kortenkam, Jürgen Richter-Gebert
(2016)
Verlag:
Verlag Klaus Seeberger
Buchtitel:
Digitale Werkzeuge für den Mathematikunterricht
2016 | Recent research on geometry education: an ICME-13 survey team report | Nathalie Sinclair, Maria G. Bartolini Bussi, Michael de Villiers, Ulrich Kortenkamp, Allen Leung, Kay Owens
Seiten: 1–29
Link zur Publikation
Recent research on geometry education: an ICME-13 survey team report
Autoren: Nathalie Sinclair, Maria G. Bartolini Bussi, Michael de Villiers, Ulrich Kortenkamp, Allen Leung, Kay Owens
(2016)
This survey on the theme of Geometry Education (including new technologies) focuses chiefly on the time span since 2008. Based on our review of the research literature published during this time span (in refereed journal articles, conference proceedings and edited books), we have jointly identified seven major threads of contributions that span from the early years of learning (pre-school and primary school) through to post-compulsory education and to the issue of mathematics teacher education for geometry. These threads are as follows: developments and trends in the use of theories; advances in the understanding of visuo spatial reasoning; the use and role of diagrams and gestures; advances in the understanding of the role of digital technologies; advances in the understanding of the teaching and learning of definitions; advances in the understanding of the teaching and learning of the proving process; and, moving beyond traditional Euclidean approaches. Within each theme, we identify relevant research and also offer commentary on future directions.
2016 | Model Development in Scientific Discovery Learning with a Computer-Based Physics Task | Saskia Kistner, Regina Vollmeyer, Bruce D. Burns, Ulrich Kortenkamp
Zeitschrift: Computers in Human Behaviour
Link zur Publikation
Model Development in Scientific Discovery Learning with a Computer-Based Physics Task
Autoren: Saskia Kistner, Regina Vollmeyer, Bruce D. Burns, Ulrich Kortenkamp
(2016)
Based on theories of scientific discovery learning and conceptual change, this study explores students' preconceptions in the domain of torques in physics and the development of these conceptions while learning with a scientific discovery learning task. Referring to a three-space theory of scientific discovery learning (Burns & Vollmeyer, 2000), the focus was on the content of model space, which is supposed to contain the current conceptualization/model of the learning domain, and on its change through hypothesis testing and experimenting. A multiple-choice test for assessing students' models of torques was developed and used in a study with secondary school students (N=47) who learned about torques using computer simulations. We identified those aspects of torques about which students had physically correct conceptions, and those about which misconceptions were predominant. Working with the computer simulations led to replacement of some misconceptions with physically correct conceptions, though some misconceptions were still common after learning. Analyzing individual differences in model development, we found that an intense use of the simulations was associated with the acquisition of correct conceptions. The three-space theory provided a useful framework for understanding conceptual change in scientific discovery learning.
Zeitschrift:
Computers in Human Behaviour
2016 | Mathematikfortbildungen mit E-Learning gestalten | Axel Blessing, Christian Dohrmann, Ulrich Kortenkamp
Zeitschrift: Beiträge zum Mathematikunterricht
Verlag: WTM Verlag
Mathematikfortbildungen mit E-Learning gestalten
Autoren: Axel Blessing, Christian Dohrmann, Ulrich Kortenkamp
(2016)
Zeitschrift:
Beiträge zum Mathematikunterricht
2016 | Jonathan M Borwein (1951–2016): exploring, experiencing and experimenting in mathematics – an inspiring journey in mathematics. | Ulrich Kortenkamp, John Monaghan,Luc Trouche
Zeitschrift: Educational Studies in Mathematics
Seiten: 131-136
Band: 93
Jonathan M Borwein (1951–2016): exploring, experiencing and experimenting in mathematics – an inspiring journey in mathematics.
Autoren: Ulrich Kortenkamp, John Monaghan,Luc Trouche
(2016)
Summary: Jonathan M Borwein died on August 2nd. He was a major figure in the field of experimental mathematics. His death, at 65, was an astonishment for his family and his colleagues. We three, as mathematics educators who have worked with Jon, have been asked to pay homage to his life and his work. But we three have only shared a part of Jon's tremendous appetite for life and work, so we barely scratch the surface of the significance of his work. Ulli writes about Jon's experimental mathematics, Luc writes about the implications of Jon's work for mathematics education and John writes about Jon, culture and mathematics.
Zeitschrift:
Educational Studies in Mathematics
2016 | Development of a Flexible Understanding of Place Value | Silke Ladel, Ulrich Kortenkamp
Verlag: Springer International Publishing
Buchtitel: Mathematics Education in the Early Years: Results from the POEM2 Conference, 2014
Seiten: 289–307
Link zur Publikation
Development of a Flexible Understanding of Place Value
Autoren: Silke Ladel, Ulrich Kortenkamp
(2016)
Verlag:
Springer International Publishing
Buchtitel:
Mathematics Education in the Early Years: Results from the POEM2 Conference, 2014
2016 | CindyJS. Mathematical visualization on modern devices | Martin von Gagern, Ulrich Kortenkamp, Jürgen Richter-Gebert, Michael Strobel
Zeitschrift: Mathematical Software – ICMS 2016: 5th International Conference
Reihe: Lecture Notes in Computer Science, vol 9725
Verlag: Springer International Publishing
Seiten: 319–326
Link zur Publikation
CindyJS. Mathematical visualization on modern devices
Autoren: Martin von Gagern, Ulrich Kortenkamp, Jürgen Richter-Gebert, Michael Strobel
(2016)
The CindyJS Project brings interactive mathematical visualization to a broad variety of devices. Using projective geometry, homotopy methods and well tuned algorithms the CindyJS project is one of the first real time capable software projects in this field that at the same time approaches high-level mathematical descriptions and performance.
Zeitschrift:
Mathematical Software – ICMS 2016: 5th International Conference
Reihe:
Lecture Notes in Computer Science, vol 9725
Verlag:
Springer International Publishing
2016 | Artifact-Centric Activity Theory—A Framework for the Analysis of the Design and Use of Virtual Manipulatives | Silke Ladel, Ulrich Kortenkamp
Verlag: Springer International Publishing
Buchtitel: International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives
Seiten: 25–40
Link zur Publikation
Artifact-Centric Activity Theory—A Framework for the Analysis of the Design and Use of Virtual Manipulatives
Autoren: Silke Ladel, Ulrich Kortenkamp
(2016)
Verlag:
Springer International Publishing
Buchtitel:
International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives
2016 | Pseudodiffential analysis with twisted symbolic structure | D.-C. Chang, M. Hedayat Mahmoudi and B.-W. Schulze
Zeitschrift: Journal of nonlinear and convex analysis
Seiten: pp. 1889-1937
Band: 17, n.9
Link zur Publikation
Pseudodiffential analysis with twisted symbolic structure
Autoren: D.-C. Chang, M. Hedayat Mahmoudi and B.-W. Schulze
(2016)
Zeitschrift:
Journal of nonlinear and convex analysis
2016 | Deformation quantisation and boundary value problems | Nikolai Tarkhanov
Zeitschrift: Int. J. Geom. Methods Mod. Phys.
Band: 13
Link zur Publikation
,
Link zum Preprint
Deformation quantisation and boundary value problems
Autoren: Nikolai Tarkhanov
(2016)
We describe a natural construction of deformation quantization on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator.
Zeitschrift:
Int. J. Geom. Methods Mod. Phys.
2016 | Jenkins-Serrin-type results for the Jang equation | Michael Eichmair and Jan Metzger
Zeitschrift: J. Differential Geom.
Seiten: 207–242
Band: 102
Link zum Preprint
Jenkins-Serrin-type results for the Jang equation
Autoren: Michael Eichmair and Jan Metzger
(2016)
Zeitschrift:
J. Differential Geom.
2016 | Modified iterative Runge-Kutta-type methods for non-linear ill-posed problems | P. Pornsawad, C. Böckmann
Zeitschrift: Numerical Functional Analysis and Optimization (2016)
Modified iterative Runge-Kutta-type methods for non-linear ill-posed problems
Autoren: P. Pornsawad, C. Böckmann
(2016)
Zeitschrift:
Numerical Functional Analysis and Optimization (2016)
2016 | Microphysical particle properties derived from inversion algorithms developedin the frame of EARLINET | D. Müller, C. Böckmann, A. Kolgotin, L. Schneidenbach, E. Chemyakin, J. Rosemann, P. Znak, and A. Romanov
Zeitschrift: Atmos. Meas. Tech. 9 (2016) 5007-5035
Microphysical particle properties derived from inversion algorithms developedin the frame of EARLINET
Autoren: D. Müller, C. Böckmann, A. Kolgotin, L. Schneidenbach, E. Chemyakin, J. Rosemann, P. Znak, and A. Romanov
(2016)
Zeitschrift:
Atmos. Meas. Tech. 9 (2016) 5007-5035
2016 | Long-time stability and accuracy of the ensemble Kalman-Bucy filter for fully observed processes and small measurement noise | J. de Wiljes, S. Reich, W. Stannat
Zeitschrift: technical report
Long-time stability and accuracy of the ensemble Kalman-Bucy filter for fully observed processes and small measurement noise
Autoren: J. de Wiljes, S. Reich, W. Stannat
(2016)
Zeitschrift:
technical report
2016 | Multilevel ensemble transform particle filter | A. Gregory, C. Cotter, S. Reich
Zeitschrift: SIAM J Scientific Computing, 38, A1317-A1338
Multilevel ensemble transform particle filter
Autoren: A. Gregory, C. Cotter, S. Reich
(2016)
Zeitschrift:
SIAM J Scientific Computing, 38, A1317-A1338
2016 | Elliptic perturbation of dynamical systems with a proper node | O. Sultanov, L. Kalyakin, and N. Tarkhanov
Zeitschrift: Contemporary Mathematics
Band: 67
Link zum Preprint
Elliptic perturbation of dynamical systems with a proper node
Autoren: O. Sultanov, L. Kalyakin, and N. Tarkhanov
(2016)
- The paper is devoted to asymptotic analysis of the Dirichlet problem for a second order partial differential equation containing a small parameter multiplying the highest order derivatives. It corresponds to a small perturbation of a dynamical system having a stationary solution in the domain. We focus on the case where the trajectories of the system go into the domain and the stationary solution is a proper node.
Zeitschrift:
Contemporary Mathematics
2016 | On the convergence rate of continuous Newton method | A. Gibali, D. Shoikhet, and N. Tarkhanov
Reihe: Contemporary Mathematics
Seiten: 1--13
Band: 62
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On the convergence rate of continuous Newton method
Autoren: A. Gibali, D. Shoikhet, and N. Tarkhanov
(2016)
In this paper we study the convergence of continuous Newton method for solving nonlinear equations with holomorphic mappings in complex Banach spaces. Our contribution is based on a recent progress in the geometric theory of spirallike functions. We prove convergence theorems and illustrate them by numerical simulations.
Reihe:
Contemporary Mathematics
2016 | Solving the Dyson–Schwinger equation around its first singularities in the Borel plane | Pierre J. Clavier and Marc P. Bellon
Zeitschrift: Front. Phys.
Band: 11 (6)
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Solving the Dyson–Schwinger equation around its first singularities in the Borel plane
Autoren: Pierre J. Clavier and Marc P. Bellon
(2016)
The Dyson–Schwinger equation of the massless Wess–Zumino model is written as an equation over the anomalous dimension of the theory. Its asymptotic behavior is derived and the procedure to compute the perturbations of this asymptotic behavior is detailed. This procedure uses ill-defined objects. To solve this, the Dyson–Schwinger equation is rewritten for the Borel plane. It is shown that the illdefined procedure in the physical plane can be applied in the Borel plane. Other results obtained in the Borel plane are stated and the proof for one result is described.
Zeitschrift:
Front. Phys.
2016 | A hybrid ensemble transform filter for high dimensional dynamical systems | N. Chustagulprom, S. Reich, M. Reinhardt
Zeitschrift: SIAM/ASA Journal on Uncertainty Quantification, 4, 552-591
A hybrid ensemble transform filter for high dimensional dynamical systems
Autoren: N. Chustagulprom, S. Reich, M. Reinhardt
(2016)
Zeitschrift:
SIAM/ASA Journal on Uncertainty Quantification, 4, 552-591
2016 | Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques | W. Acevedo, S. Reich, U. Cubasch
Zeitschrift: Climate Dynamics, 46 , 1909-1920
Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques
Autoren: W. Acevedo, S. Reich, U. Cubasch
(2016)
Zeitschrift:
Climate Dynamics, 46 , 1909-1920
2016 | Boundary value problems for elliptic complexes | D. Fedchenko and N. Tarkhanov
Zeitschrift: Far East J. of Math. Sci.
Seiten: 1401--1420
Band: 100
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Boundary value problems for elliptic complexes
Autoren: D. Fedchenko and N. Tarkhanov
(2016)
The aim of this paper is to bring together two areas which are of great importance for the study of overdetermined boundary value problems. The first area is homological algebra which is the main tool in constructing the formal theory of overdetermined problems. And the second area is the global calculus of pseudodifferential operators which allows one to develop explicit analysis.
Zeitschrift:
Far East J. of Math. Sci.
2016 | A Radó theorem for p-harmonic functions | I. Ly and N. Tarkhanov
Zeitschrift: Boletín de la Sociedad Matemática Mexicana
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A Radó theorem for p-harmonic functions
Autoren: I. Ly and N. Tarkhanov
(2016)
Let A be a nonlinear differential operator on an open set X ⊂ Rn and S a closed subset of X . Given a class F of functions in X , the set S is said to be removable for F relative to A if any weak solution of A(u) = 0 in X \S of class F satisfies this equation weakly in all of X. For the most extensively studied classes F, we show conditions on S which guarantee that S is removable for F relative to A.
Zeitschrift:
Boletín de la Sociedad Matemática Mexicana
2016 | A Hilbert boundary value problem for generalised Cauchy-Riemann equations | A. Alsaedy and N. Tarkhanov
Zeitschrift: Advances in Applied Clifford Algebras
Seiten: 931–953
Band: 27
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A Hilbert boundary value problem for generalised Cauchy-Riemann equations
Autoren: A. Alsaedy and N. Tarkhanov
(2016)
We elaborate a boundary Fourier method for studying an analogue of the Hilbert problem for analytic functions within the framework of generalised Cauchy–Riemann equations. The boundary value problem need not satisfy the Shapiro–Lopatinskij condition and so it fails to be Fredholm in Sobolev spaces. We show a solvability condition of the Hilbert problem, which looks like those for ill-posed problems, and construct an explicit formula for approximate solutions.
Zeitschrift:
Advances in Applied Clifford Algebras
2016 | Alien calculus and a Schwinger--Dyson equation: two-point function with a nonperturbative mass scale | Marc P. Bellon, Pierre J. Clavier
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Alien calculus and a Schwinger--Dyson equation: two-point function with a nonperturbative mass scale
Autoren: Marc P. Bellon, Pierre J. Clavier
(2016)
Starting from the Schwinger--Dyson equation and the renormalization group equation for the massless Wess--Zumino model, we compute the dominant nonperturbative contributions to the anomalous dimension of the theory, which are related by alien calculus to singularities of the Borel transform on integer points. The sum of these dominant contributions has an analytic expression. When applied to the two-point function, this analysis gives a tame evolution in the deep euclidean domain at this approximation level, making doubtful the arguments on the triviality of the quantum field theory with positive \(\beta\)-function. On the other side, we have a singularity of the propagator for time like momenta of the order of the renormalization group invariant scale of the theory, which has a nonperturbative relationship with the renormalization point of the theory. All these results do not seem to have an interpretation in terms of semiclassical analysis of a Feynman path integral.
2016 | Spectral $\zeta$-invariants lifted to coverings | Sara Azzali, Sylvie Paycha
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Spectral $\zeta$-invariants lifted to coverings
Autoren: Sara Azzali, Sylvie Paycha
(2016)
The canonical trace and the Wodzicki residue on classical pseudodifferential operators on a closed manifold are shown to be preserved under lifting to the universal covering as a result of their local feature. In contrast, regularised traces, such as $\zeta$-regularised traces, are shown to differ from their lifted counterpart by an ordinary trace of an operator with smooth kernel. The latter vanishes for regularised traces of differential operators; the $\Z_2$-graded generalisation of this statement yields back Atiyah's $L^2$-index theorem. In contrast, the eta invariant of an essentially self-adjoint invertible differential operator differs from the $L^2$-eta invariant of its lift by an ordinary trace of some operator with smooth kernel.
More generally, we prove that due to their local feature, defect formula that express discrepancies of regularised traces for integer order classical pseudodifferential on closed manifolds, lift to their universal covering.
2016 | Bivariant K-theory with R/Z-coefficients and rho classes of unitary representations | Paolo Antonini, Sara Azzali and Georges Skandalis
Zeitschrift: J. Funct. Anal.
Verlag: Elsevier
Seiten: 447-481
Band: 270, 1
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Bivariant K-theory with R/Z-coefficients and rho classes of unitary representations
Autoren: Paolo Antonini, Sara Azzali and Georges Skandalis
(2016)
We construct equivariant $KK$-theory with coefficients in $\R$ and $\R/\Z$ as suitable inductive limits over ${\rm II}_1$-factors. We show that the Kasparov product, together with its usual functorial properties, extends to $KK$-theory with real coefficients.
Let $\Gamma$ be a group. We define a $\Gamma$-algebra $A$ to be \emph{$K$-theoretically free and proper} (KFP) if the group trace ${\bf tr}$ of $\Gamma$ acts as the unit element in $KK^\Gamma_\R(A,A)$. We show that free and proper $\Gamma$-algebras (in the sense of Kasparov) have the (KFP) property. Moreover, if $\Gamma$ is torsion free and satisfies the $KK^\Gamma$-form of the Baum-Connes conjecture, then every $\Gamma$-algebra satisfies (KFP).
If $\alpha:\Gamma\to U_n$ is a unitary representation and $A$ satisfies property (KFP), we construct in a canonical way a rho class $\rho_\alpha^A\in KK_{\R/\Z}^{1,\Gamma}(A,A)$. This construction generalizes the Atiyah-Patodi-Singer $K$-theory class with $\R/\Z$ coefficients associated to $\alpha$.
Zeitschrift:
J. Funct. Anal.
2016 | Tight (Lower) Bounds for the Fixed Budget Best Arm Identification Bandit Problem | A. Carpentier and A. Locatelli
Zeitschrift: In the Journal of Machine Learning Research W&CP (COLT)
Seiten: 1–15
Band: 49
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Tight (Lower) Bounds for the Fixed Budget Best Arm Identification Bandit Problem
Autoren: A. Carpentier and A. Locatelli
(2016)
Zeitschrift:
In the Journal of Machine Learning Research W&CP (COLT)
2016 | An optimal algorithm for the Thresholding Bandit Problem | A. Locatelli, M. Gutzeit, A. Carpentier.
Zeitschrift: In the Journal of Machine Learning Research W&CP (ICML)
Seiten: 1690–1698
Band: 48
Link zur Publikation
An optimal algorithm for the Thresholding Bandit Problem
Autoren: A. Locatelli, M. Gutzeit, A. Carpentier.
(2016)
Zeitschrift:
In the Journal of Machine Learning Research W&CP (ICML)
2016 | Pliable Rejection Sampling | A. Erraqabi, M. Valko, A. Carpentier, O. Maillard
Zeitschrift: In the Journal of Machine Learning Research W&CP (ICML)
Seiten: 2121–2129
Band: 48
Link zur Publikation
Pliable Rejection Sampling
Autoren: A. Erraqabi, M. Valko, A. Carpentier, O. Maillard
(2016)
Zeitschrift:
In the Journal of Machine Learning Research W&CP (ICML)
2016 | Revealing Graph Bandits for Maximizing Local Influence | A. Carpentier and M. Valko
Zeitschrift: In the Journal of Machine Learning Research W&CP (AISTATS)
Seiten: 10-18
Band: 51
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Revealing Graph Bandits for Maximizing Local Influence
Autoren: A. Carpentier and M. Valko
(2016)
Zeitschrift:
In the Journal of Machine Learning Research W&CP (AISTATS)
2016 | Learning Relationships between data obtained independently | A. Carpentier and T. Schlueter
Zeitschrift: In the Journal of Machine Learning Research W&CP (AISTATS)
Seiten: 658–666
Band: 51
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Learning Relationships between data obtained independently
Autoren: A. Carpentier and T. Schlueter
(2016)
Zeitschrift:
In the Journal of Machine Learning Research W&CP (AISTATS)
2016 | Convergence rates of Kernel Conjugate Gradient for random design regression. | G. Blanchard, N. Krämer
Zeitschrift: Analysis and Applications
Seiten: 763-794
Band: 14(6)
Link zum Preprint
Convergence rates of Kernel Conjugate Gradient for random design regression.
Autoren: G. Blanchard, N. Krämer
(2016)
Zeitschrift:
Analysis and Applications
2016 | Combining Multiple Hypothesis Testing with Machine Learning Increases the Statistical Power of Genome-wide Association Studies | B. Mieth, M. Kloft, J. A. Rodríguez, S. Sonnenburg, R. Vobruba, C. Morcillo-Suárez, X. Farré, U.M. Marigorta, E. Fehr, T. Dickhaus, G. Blanchard, D. Schunk, A. Navarro & K.-R. Müller
Zeitschrift: Scientific Reports
Seiten: 36671
Band: 6
Link zur Publikation
Combining Multiple Hypothesis Testing with Machine Learning Increases the Statistical Power of Genome-wide Association Studies
Autoren: B. Mieth, M. Kloft, J. A. Rodríguez, S. Sonnenburg, R. Vobruba, C. Morcillo-Suárez, X. Farré, U.M. Marigorta, E. Fehr, T. Dickhaus, G. Blanchard, D. Schunk, A. Navarro & K.-R. Müller
(2016)
Zeitschrift:
Scientific Reports
2016 | Classification with asymmetric label noise: Consistency and maximal denoising | G. Blanchard, M. Flaska, G. Handy, S. Pozzi, C. Scott
Zeitschrift: Electronic Journal of Statistics
Seiten: 2780-2824
Band: 10(2)
Link zur Publikation
Classification with asymmetric label noise: Consistency and maximal denoising
Autoren: G. Blanchard, M. Flaska, G. Handy, S. Pozzi, C. Scott
(2016)
Zeitschrift:
Electronic Journal of Statistics
2016 | Extensions of stability selection using subsamples of observations and covariates | A. Beinrucker, Ü. Dogan, G. Blanchard.
Zeitschrift: Statistics and Computing
Seiten: 1059-1077
Band: 26
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Extensions of stability selection using subsamples of observations and covariates
Autoren: A. Beinrucker, Ü. Dogan, G. Blanchard.
(2016)
Zeitschrift:
Statistics and Computing
2016 | The Kato square root problem on vector bundles with generalised bounded geometry | Lashi Bandara, Alan McIntosh
Zeitschrift: J. Geom. Anal.
Verlag: Springer
Seiten: 428-462
Band: 26, no. 1
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The Kato square root problem on vector bundles with generalised bounded geometry
Autoren: Lashi Bandara, Alan McIntosh
(2016)
We consider smooth, complete Riemannian manifolds which are exponentially locally doubling. Under a uniform Ricci curvature bound and a uniform lower bound on injectivity radius, we prove a Kato square root estimate for certain coercive operators over the bundle of finite rank tensors. These results are obtained as a special case of similar estimates on smooth vector bundles satisfying a criterion which we call generalised bounded geometry. We prove this by establishing quadratic estimates for perturbations of Dirac type operators on such bundles under an appropriate set of assumptions.
Zeitschrift:
J. Geom. Anal.
2016 | Rough metrics on manifolds and quadratic estimates | Lashi Bandara,
Zeitschrift: Math. Z.
Verlag: Springer
Seiten: 1245-1281
Band: 283, no. 3-4
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Rough metrics on manifolds and quadratic estimates
Autoren: Lashi Bandara,
(2016)
We study the persistence of quadratic estimates related to the Kato square root problem across a change of metric on smooth manifolds by defining a class of Riemannian-like metrics that are permitted to be of low regularity and degenerate on sets of measure zero. We also demonstrate how to transmit quadratic estimates between manifolds which are homeomorphic and locally bi-Lipschitz. As a consequence, we demonstrate the invariance of the Kato square root problem under Lipschitz transformations of the space and obtain solutions to this problem on functions and forms on compact manifolds with a continuous metric. Furthermore, we show that a lower bound on the injectivity radius is not a necessary condition to solve the Kato square root problem.
2016 | The 2-D stochastic Keller-Segel particle model : existence and uniqueness | Patrick Cattiaux, Laure Pédèches
Zeitschrift: ALEA, Lat. Am. J. Probab. Math. Stat.
Seiten: 447-463
Band: 13 (1)
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The 2-D stochastic Keller-Segel particle model : existence and uniqueness
Autoren: Patrick Cattiaux, Laure Pédèches
(2016)
Zeitschrift:
ALEA, Lat. Am. J. Probab. Math. Stat.
2016 | Convoluted Brownian motion | Sylvie Roelly, Pierre Vallois
Zeitschrift: Theory of Stochastic Processes
Reihe: 21 (37) no. 2
Seiten: 58–83
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Convoluted Brownian motion
Autoren: Sylvie Roelly, Pierre Vallois
(2016)
Zeitschrift:
Theory of Stochastic Processes
2016 | Spektren verallgemeinerter Hodge-Laplace-Operatoren - Am Beispiel von flachen Tori und runden Sphären | Stine Franziska Beitz
Reihe: BestMasters
Verlag: Springer
Link zur Publikation
Spektren verallgemeinerter Hodge-Laplace-Operatoren - Am Beispiel von flachen Tori und runden Sphären
Autoren: Stine Franziska Beitz
(2016)
2016 | On the Calibration of Lévy Driven Time Series with Coupling Distances and an Application in Paleoclimate | J. Gairing, M. Högele, T. Kosenkova, A. Kulik
Verlag: Springer
Buchtitel: Mathematical Paradigms of Climate Science
Seiten: 115-135
Link zur Publikation
On the Calibration of Lévy Driven Time Series with Coupling Distances and an Application in Paleoclimate
Autoren: J. Gairing, M. Högele, T. Kosenkova, A. Kulik
(2016)
Buchtitel:
Mathematical Paradigms of Climate Science
2016 | Note on short time behavior of semigroups associated to selfadjoint operators | Matthias Keller, Daniel Lenz, Florentin Münch, Marcel Schmidt, Andras Telcs
Zeitschrift: Bullettin of the London Mathematical Society, to appear
Link zum Preprint
Note on short time behavior of semigroups associated to selfadjoint operators
Autoren: Matthias Keller, Daniel Lenz, Florentin Münch, Marcel Schmidt, Andras Telcs
(2016)
We present a simple observation showing that the heat kernel on a locally finite graph behaves for short times $t$ roughly like $t^d$, where $d$ is the combinatorial distance. This is very different from the classical Varadhan type behavior on manifolds. Moreover, this also gives that short time behavior and global behavior of the heat kernel are governed by two different metrics whenever the degree of the graph is not uniformly bounded.
Zeitschrift:
Bullettin of the London Mathematical Society, to appear
2016 | Note on uniformly transient graphs | Matthias Keller, Daniel Lenz, Marcel Schmidt, Radosław K. Wojciechowski
Zeitschrift: Revista Iberoamericana
Seiten: 831–860
Band: 33
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Note on uniformly transient graphs
Autoren: Matthias Keller, Daniel Lenz, Marcel Schmidt, Radosław K. Wojciechowski
(2016)
We study a special class of graphs with a strong transience feature called uniform transience. We characterize uniform transience via a Feller-type property and via validity of an isoperimetric inequality. We then give a further characterization via equality of the Royden boundary and the harmonic boundary and show that the Dirichlet problem has a unique solution for such graphs. The Markov semigroups and resolvents (with Dirichlet boundary conditions) on these graphs are shown to be ultracontractive. Moreover, if the underlying measure is finite, the semigroups and resolvents are trace class and their generators have $\ell^p$ independent pure point spectra (for $1 \leq p \leq \infty$). Examples of uniformly transient graphs include Cayley graphs of hyperbolic groups as well as trees and Euclidean lattices of dimension at least three. As a surprising consequence, the Royden compactification of such lattices turns out to be the one-point compacitifcation and the Laplacians of such lattices have pure point spectrum if the underlying measure is chosen to be finite.
Zeitschrift:
Revista Iberoamericana
2016 | General Cheeger inequalities for p-Laplacians on graphs | Matthias Keller, Delio Mugnolo
Zeitschrift: Nonlinear Analysis: Theory, Methods & Applications
Seiten: 80–95
Band: 147
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General Cheeger inequalities for p-Laplacians on graphs
Autoren: Matthias Keller, Delio Mugnolo
(2016)
We prove Cheeger inequalities for p-Laplacians on finite and infinite weighted graphs. Unlike in previous works, we do not impose boundedness of the vertex degree, nor do we restrict ourselves to the normalized Laplacian and, more generally, we do not impose any boundedness assumption on the geometry. This is achieved by a novel definition of the measure of the boundary which is using the idea of intrinsic metrics. For the non-normalized case, our bounds on the spectral gap of p-Laplacians are already significantly better for finite graphs and for infinite graphs they yield non-trivial bounds even in the case of unbounded vertex degree. We, furthermore, give upper bounds by the Cheeger constant and by the exponential volume growth of distance balls.
Zeitschrift:
Nonlinear Analysis: Theory, Methods & Applications
2016 | Dynamical compact elastic bodies in general relativity | Lars Andersson, Todd A. Oliynyk, Bernd G. Schmidt
Zeitschrift: Archive for Rational Mechanics and Analysis
Verlag: Springer
Seiten: 849-887
Band: 220, no. 2
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Dynamical compact elastic bodies in general relativity
Autoren: Lars Andersson, Todd A. Oliynyk, Bernd G. Schmidt
(2016)
We prove the local existence of solutions to the Einstein-Elastic equations that represent self-gravitating, relativistic elastic bodies with compact support.
Zeitschrift:
Archive for Rational Mechanics and Analysis
2016 | Decay of solutions to the Maxwell equation on the Schwarzschild background | Lars Andersson, Thomas Bäckdahl, Pieter Blue
Zeitschrift: Class. Quantum Grav.
Verlag: IOP Publishing
Seiten: 085010
Band: 33, no. 8
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Decay of solutions to the Maxwell equation on the Schwarzschild background
Autoren: Lars Andersson, Thomas Bäckdahl, Pieter Blue
(2016)
A new Morawetz or integrated local energy decay estimate for Maxwell test fields on the exterior of a Schwarzschild black hole spacetime is proved. The proof makes use of a new superenergy tensor $H_{ab}$ defined in terms of the Maxwell field and its first derivatives. The superenergy tensor, although not conserved, yields a conserved higher order energy current $H_{ab}(\partial_t)^ b$. The tensor $H_{ab}$ vanishes for the static Coulomb field, and the Morawetz estimate proved here therefore yields integrated decay for the Maxwell field to the Coulomb solution on the Schwarzschild exterior.
Zeitschrift:
Class. Quantum Grav.
2016 | Gauge-invariant perturbations of Schwarzschild spacetime | Abhay G. Shaw, Bernard F. Whiting, Steffen Aksteiner, Lars Andersson, Thomas Bäckdahl
Link zum Preprint
Gauge-invariant perturbations of Schwarzschild spacetime
Autoren: Abhay G. Shaw, Bernard F. Whiting, Steffen Aksteiner, Lars Andersson, Thomas Bäckdahl
(2016)
We study perturbations of Schwarzschild spacetime in a coordinate-free, covariant form. The GHP formulation, having the advantage of not only being covariant but also tetrad-rotation invariant, is used to write down the previously known odd- and even-parity gauge-invariants and the equations they satisfy. Additionally, in the even-parity sector, a new invariant and the second order hyperbolic equation it satisfies are presented. Chandrasekhar's work on transformations of solutions for perturbation equations on Schwarzschild spacetime is translated into the GHP form, i.e., solutions for the equations of the even- and odd-parity invariants are written in terms of one another, and the extreme Weyl scalars; and solutions for the equations of these latter invariants are also written in terms of one another. Recently, further gauge invariants previously used by Steven Detweiler have been described. His method is translated into GHP form and his basic invariants are presented here. We also show how these invariants can be written in terms of curvature invariants.
2016 | Criticising with Foucault: Towards a guiding framework for socio-political studies in mathematics education | David Kollosche
Zeitschrift: Educational Studies in Mathematics
Link zur Publikation
Criticising with Foucault: Towards a guiding framework for socio-political studies in mathematics education
Autoren: David Kollosche
(2016)
Zeitschrift:
Educational Studies in Mathematics
2016 | A socio-critical analysis of students’ perceptions of mathematics | David Kollosche
Buchtitel: Straehler-Pohl, Bohlmann & Pais (Hg.) The disorder of mathematics education. Challenging the socio-political dimensions of research
Link zur Publikation
A socio-critical analysis of students’ perceptions of mathematics
Autoren: David Kollosche
(2016)
Buchtitel:
Straehler-Pohl, Bohlmann & Pais (Hg.) The disorder of mathematics education. Challenging the socio-political dimensions of research
2016 | Social and Political Dimensions of Mathematics Education | Murad Jurdak, Renuka Vithal, Elizabeth de Freitas, Peter Gates & David Kollosche
Verlag: Springer
Social and Political Dimensions of Mathematics Education
Autoren: Murad Jurdak, Renuka Vithal, Elizabeth de Freitas, Peter Gates & David Kollosche
(2016)
2016 | A Feynman–Kac–Itô formula for magnetic Schrödinger operators on graphs | Batu Güneysu, Matthias Keller, Marcel Schmidt
Zeitschrift: Probability Theory and Related Fields
Seiten: 365-399
Band: 165
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A Feynman–Kac–Itô formula for magnetic Schrödinger operators on graphs
Autoren: Batu Güneysu, Matthias Keller, Marcel Schmidt
(2016)
In this paper we prove a Feynman–Kac–Itô formula for magnetic Schrödinger operators on arbitrary weighted graphs. To do so, we have to provide a natural and general framework both on the operator theoretic and the probabilistic side of the equation. On the operator side we identify a very general class of potentials that allows the definition of magnetic Schrödinger operators. On the probabilistic side, we introduce an appropriate notion of stochastic line integrals with respect to magnetic potentials. Apart from linking the world of discrete magnetic operators with the probabilistic world through the Feynman–Kac–Itô formula, the insights from this paper gained on both sides should be of an independent interest. As applications of the Feynman–Kac–Itô formula, we prove a Kato inequality, a Golden–Thompson inequality and an explicit representation of the quadratic form domains corresponding to a large class of potentials.
Zeitschrift:
Probability Theory and Related Fields
2016 | An explicit representation of the transition densities of the skew Brownian motion with drift and two semipermeable barriers | David Dereudre, Sara Mazzonetto, Sylvie Roelly
Zeitschrift: Monte Carlo Methods and Applications Vol. 22-1 (2016)
Seiten: 1-23
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An explicit representation of the transition densities of the skew Brownian motion with drift and two semipermeable barriers
Autoren: David Dereudre, Sara Mazzonetto, Sylvie Roelly
(2016)
Zeitschrift:
Monte Carlo Methods and Applications Vol. 22-1 (2016)
2016 | Noncommutative Geometry and the Physics of the LHC Era | Christoph Stephan
Verlag: Birkhäuser Basel
Buchtitel: F. Finster, J. Kleiner, C. Röken, J. Tolksdorf (eds.): Quantum mathematical physics
Seiten: 471-495
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Noncommutative Geometry and the Physics of the LHC Era
Autoren: Christoph Stephan
(2016)
Noncommutative geometry allows to unify the basic building blocks of particle physics, Yang-Mills-Higgs theory and general relativity, into a single geometrical framework. The resulting effective theory constrains the couplings of the standard model and reduces the number of degrees of freedom. After an introduction of the basic ideas of Noncommutative geometry, I will present its predictions for the standard model and the few known models beyond the standard model based on a classification scheme for finite spectral triples. Most of these models, including the Standard Model, are now ruled out by LHC data. But interesting extensions of the standard model which agree with the presumed Higgs mass, predict new particles (Fermions, Scalars and Bosons) and await further experimental data.
Buchtitel:
F. Finster, J. Kleiner, C. Röken, J. Tolksdorf (eds.): Quantum mathematical physics
2016 | Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies | Marco Benini
Zeitschrift: J. Math. Phys.
Verlag: American Institute of Physics
Seiten: 053502
Band: 57
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Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies
Autoren: Marco Benini
(2016)
Being motivated by open questions in gauge field theories, we consider non-standard de Rham cohomology groups for timelike compact and spacelike compact support systems. These cohomology groups are shown to be isomorphic respectively to the usual de Rham cohomology of a spacelike Cauchy surface and its counterpart with compact support. Furthermore, an analog of the usual Poincaré duality for de Rham cohomology is shown to hold for the case with non-standard supports as well. We apply these results to find optimal spaces of linear observables for analogs of arbitrary degree k of both the vector potential and the Faraday tensor. The term optimal has to be intended in the following sense: The spaces of linear observables we consider distinguish between different configurations; in addition to that, there are no redundant observables. This last point in particular heavily relies on the analog of Poincaré duality for the new cohomology groups.
Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
2016 | The mode solution of the wave equation in Kasner spacetimes and redshift | Oliver Lindblad Petersen
Zeitschrift: Math. Phys. Anal. Geom.
Verlag: Springer
Seiten: Art.: 26
Band: 19, no. 4
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The mode solution of the wave equation in Kasner spacetimes and redshift
Autoren: Oliver Lindblad Petersen
(2016)
We study the mode solution to the Cauchy problem of the scalar wave equation ◻φ = 0 in Kasner spacetimes. As a first result, we give the explicit mode solution in axisymmetric Kasner spacetimes, of which flat Kasner spacetimes are special cases. Furthermore, we give the small and large time asymptotics of the modes in general Kasner spacetimes. Generically, the modes in non-flat Kasner spacetimes grow logarithmically for small times, while the modes in flat Kasner spacetimes stay bounded for small times. For large times, however, the modes in general Kasner spacetimes oscillate with a polynomially decreasing amplitude. This gives a notion of large time frequency of the modes, which we use to model the wavelength of light rays in Kasner spacetimes. We show that the redshift one obtains in this way actually coincides with the usual cosmological redshift.
Zeitschrift:
Math. Phys. Anal. Geom.
2016 | A rigorous geometric derivation of the chiral anomaly in curved backgrounds | Christian Bär, Alexander Strohmaier
Zeitschrift: Comm. Math. Phys.
Verlag: Springer
Seiten: 703-721
Band: 347, no. 3
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A rigorous geometric derivation of the chiral anomaly in curved backgrounds
Autoren: Christian Bär, Alexander Strohmaier
(2016)
We discuss the chiral anomaly for a Weyl field in a curved background and show that a novel index theorem for the Lorentzian Dirac operator can be applied to describe the gravitational chiral anomaly. A formula for the total charge generated by the gravitational and gauge field background is derived in a mathematically rigorous manner. It contains a term identical to the integrand in the Atiyah-Singer index theorem and another term involving the η-invariant of the Cauchy hypersurfaces.
Zeitschrift:
Comm. Math. Phys.
2016 | Long time behavior of stochastic hard ball systems | P. Cattiaux, M. Fradon, A. Kulik, S. Roelly
Zeitschrift: Bernoulli 22-2 (2016)
Seiten: 681-710
Link zur Publikation
,
Link zum Preprint
Long time behavior of stochastic hard ball systems
Autoren: P. Cattiaux, M. Fradon, A. Kulik, S. Roelly
(2016)
Zeitschrift:
Bernoulli 22-2 (2016)
2016 | Supergeometry in locally covariant quantum field theory | Thomas Paul Hack, Florian Hanisch, Alexander Schenkel
Zeitschrift: Comm. Math. Phys.
Verlag: Springer
Seiten: 615-673
Band: 342, no. 2
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,
Link zum Preprint
Supergeometry in locally covariant quantum field theory
Autoren: Thomas Paul Hack, Florian Hanisch, Alexander Schenkel
(2016)
In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor A : SLoc→S*Alg to the category of super-*-algebras which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct super-quantum field theories in terms of enriched functors eA : eSLoc→eS*Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the enriched framework. As examples we analyze the superparticle in 1|1-dimensions and the free Wess-Zumino model in 3|2-dimensions.
Zeitschrift:
Comm. Math. Phys.
2016 | Cheeger-Chern-Simons theory and differential String classes | Christian Becker
Zeitschrift: Ann. Henri Poincaré
Verlag: Springer
Seiten: 1-66
Link zur Publikation
,
Link zum Preprint
Cheeger-Chern-Simons theory and differential String classes
Autoren: Christian Becker
(2016)
We introduce certain relative differential characters which we call Cheeger-Chern-Simons characters. These combine the well-known Cheeger-Simons characters with Chern-Simons forms. In the same way as the Cheeger-Simons characters generalize Chern-Simons invariants of oriented closed manifolds, the Cheeger-Chern-Simons characters generalize Chern-Simons invariants of oriented manifolds with boundary.
Using Cheeger-Chern-Simons characters, we introduce the notion of differential trivializations of universal characteristic classes. Specializing to the class ½ p1 ∈ H4(BSpinn, Z) this yields a notion of differential String classes. Differential String classes turn out to be stable isomorphism classes of geometric String structures.
Zeitschrift:
Ann. Henri Poincaré
2016 | About the mass of certain second order elliptic operators | Andreas Hermann, Emmanuel Humbert
Zeitschrift: Adv. Math.
Verlag: Elsevier
Seiten: 596-633
Band: 294
Link zur Publikation
,
Link zum Preprint
About the mass of certain second order elliptic operators
Autoren: Andreas Hermann, Emmanuel Humbert
(2016)
Let (M,g) be a closed Riemannian manifold of dimension n ≥ 3 and let f ∈ C∞(M), such that the operator Pf := Δg + f is positive. If g is flat near some point p and f vanishes around p, we can define the mass of Pf as the constant term in the expansion of the Green function of Pf at p. In this paper, we establish many results on the mass of such operators. In particular, if f = \frac{n-2}{4(n-1)}\scal_g, i.e. if Pf is the Yamabe operator, we show the following result: assume that there exists a closed simply connected non-spin manifold M such that the mass is non-negative for every metric g as above on M, then the mass is non-negative for every such metric on every closed manifold of the same dimension as M.
2016 | Guide to Boundary Value Problems for Dirac-Type Operators | Werner Ballmann, Christian Bär
Reihe: Progress in Mathematics
Verlag: Springer-Verlag
Buchtitel: Arbeitstagung Bonn 2013
Seiten: 43-80
Band: 319
Link zur Publikation
,
Link zum Preprint
Guide to Boundary Value Problems for Dirac-Type Operators
Autoren: Werner Ballmann, Christian Bär
(2016)
We present an introduction to boundary value problems for Dirac-type operators on complete Riemannian manifolds with compact boundary. We introduce a very general class of boundary conditions which contains local elliptic boundary conditions in the sense of Lopatinskij and Shapiro as well as the Atiyah-Patodi-Singer boundary conditions. We discuss boundary regularity of solutions and also spectral and index theory. The emphasis is on providing the reader with a working knowledge.
Reihe:
Progress in Mathematics
Buchtitel:
Arbeitstagung Bonn 2013
2015 | In a material world: hyperbolic geometry in biological materials | M. E. Evans and G. E. Schröder-Turk
Zeitschrift: Asia Pacific Mathematics Newsletter 5(2)
Seiten: 21-30 (popular science, not referreed)
Link zur Publikation
In a material world: hyperbolic geometry in biological materials
Autoren: M. E. Evans and G. E. Schröder-Turk
(2015)
Zeitschrift:
Asia Pacific Mathematics Newsletter 5(2)
Seiten:
21-30 (popular science, not referreed)
2015 | Ideal geometry of periodic entanglements | M. E. Evans, V. Robins and S. T. Hyde
Zeitschrift: Proceedings of the Royal Society A. 471(2181)
Link zur Publikation
Ideal geometry of periodic entanglements
Autoren: M. E. Evans, V. Robins and S. T. Hyde
(2015)
Zeitschrift:
Proceedings of the Royal Society A. 471(2181)
2015 | Periodic entanglement III: tangled degree-3 finite and layer net intergrowths from rare forests | M. E. Evans and S. T. Hyde
Zeitschrift: Acta Crystallographica A71
Seiten: 599-611
Link zur Publikation
Periodic entanglement III: tangled degree-3 finite and layer net intergrowths from rare forests
Autoren: M. E. Evans and S. T. Hyde
(2015)
Zeitschrift:
Acta Crystallographica A71
2015 | Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration | M.A. Freitag, P. Kürschner
Zeitschrift: Numer. Linear Algebra Appl.
Seiten: 175–196
Band: 22(1)
Link zur Publikation
Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration
Autoren: M.A. Freitag, P. Kürschner
(2015)
Zeitschrift:
Numer. Linear Algebra Appl.
2015 | The effect of numerical model error on data assimilation | S.E. Jenkins, C.J. Budd, M.A. Freitag, N.D. Smith
Zeitschrift: J. Comput. Appl. Math.
Seiten: 567 – 588
Band: 290
Link zur Publikation
The effect of numerical model error on data assimilation
Autoren: S.E. Jenkins, C.J. Budd, M.A. Freitag, N.D. Smith
(2015)
Zeitschrift:
J. Comput. Appl. Math.
2015 | Estimates for eigensections of Riemannian vector bundles | Saskia Roos
Link zum Preprint
Estimates for eigensections of Riemannian vector bundles
Autoren: Saskia Roos
(2015)
We derive a bound on the L∞-norm of the covariant derivative of Laplace eigensections on general Riemannian vector bundles depending on the diameter, the dimension, the Ricci curvature of the underlying manifold, and the curvature of the Riemannian vector bundle. Our result implies that eigensections with small eigenvalues are almost parallel.
2015 | Target driven pharmacokinetics of biopharmaceutics | W. Huisinga, S. Fuhrmann, L. Fronton, B.F. Krippendorff
Verlag: Wiley
Buchtitel: 'Therapeutic Proteins – ADME and translational PK/PD in discovery and development', H. Zhou and F.-P. Theil (Eds.), ISBN 978-1-118-89864-2
Link zur Publikation
Target driven pharmacokinetics of biopharmaceutics
Autoren: W. Huisinga, S. Fuhrmann, L. Fronton, B.F. Krippendorff
(2015)
Buchtitel:
'Therapeutic Proteins – ADME and translational PK/PD in discovery and development', H. Zhou and F.-P. Theil (Eds.), ISBN 978-1-118-89864-2
2015 | Gröbner-Shirshov bases and embedding of a semigroup in a group | Karpuz, E.G., Cevik, A.S., Firat, A. and Koppitz, J.
Zeitschrift: Adv. Stud. Contemp. Math. (Kyugshang)
Band: 25 n0. 4
Gröbner-Shirshov bases and embedding of a semigroup in a group
Autoren: Karpuz, E.G., Cevik, A.S., Firat, A. and Koppitz, J.
(2015)
Zeitschrift:
Adv. Stud. Contemp. Math. (Kyugshang)
2015 | Separation of On from its proper subsemigroups by a single identity | Koppitz, J.
Zeitschrift: Semigroup Forum
Band: 91, No. 1
Separation of On from its proper subsemigroups by a single identity
Autoren: Koppitz, J.
(2015)
Zeitschrift:
Semigroup Forum
2015 | A Note on finite generated subsemigroups of T(X,Y), | Lekkoksung, N. and Koppitz, J.
Zeitschrift: Math. Appl
Band: 4
A Note on finite generated subsemigroups of T(X,Y),
Autoren: Lekkoksung, N. and Koppitz, J.
(2015)
2015 | The merger of small and large black holes | P. Mösta; L. Andersson; J. Metzger; B. Szilágyi; J. Winicour
Zeitschrift: Classical Quantum Gravity
Seiten: 235003, 20 pp.
Band: 32
The merger of small and large black holes
Autoren: P. Mösta; L. Andersson; J. Metzger; B. Szilágyi; J. Winicour
(2015)
We present simulations of binary black-hole mergers in which, after the common outer horizon has formed, the marginally outer trapped surfaces (MOTSs) corresponding to the individual black holes continue to approach and eventually penetrate each other. This has very interesting consequences according to recent results in the theory of MOTSs. Uniqueness and stability theorems imply that two MOTSs which touch with a common outer normal must be identical. This suggests a possible dramatic consequence of the collision between a small and large black hole. If the penetration were to continue to completion, then the two MOTSs would have to coalesce, by some combination of the small one growing and the big one shrinking. Here we explore the relationship between theory and numerical simulations, in which a small black hole has halfway penetrated a large one.
Zeitschrift:
Classical Quantum Gravity
2015 | Null mean curvature flow and outermost MOTS | Theodora Bourni, Kristen Moore
Link zum Preprint
Null mean curvature flow and outermost MOTS
Autoren: Theodora Bourni, Kristen Moore
(2015)
We study the evolution of hypersurfaces in spacetime initial data sets by their null mean curvature. A theory of weak solutions is developed using the level-set approach. Starting from an arbitrary mean convex, outer untapped hypersurface $\partial\Omega_0$, we show that there exists a weak solution to the null mean curvature flow, given as a limit of approximate solutions that are defined using the $\varepsilon$-regularization method. We show that the approximate solutions blow up on the outermost MOTS and the weak solution converges (as boundaries of finite perimeter sets) to a generalized MOTS.
2015 | Traces of holomorphic families of operators on the noncommutative torus and on Hilbert modules | Sara Azzali, Cyril Levy, Carolina Neira and Sylvie Paycha
Reihe: Geometric Methods in Physics, Trends in Mathematics
Verlag: Birkäuser
Buchtitel: Geometric Methods in Physics
Seiten: 3-38
Link zur Publikation
,
Link zum Preprint
Traces of holomorphic families of operators on the noncommutative torus and on Hilbert modules
Autoren: Sara Azzali, Cyril Levy, Carolina Neira and Sylvie Paycha
(2015)
We revisit traces of holomorphic families of pseudodifferential operators on a closed manifold in view of geometric applications. We then transpose the corresponding analytic constructions to two different geometric frameworks; the noncommutative torus and Hilbert modules. These traces are meromorphic functions whose residues at the poles as well as the constant term of the Laurent expansion at zero (the latter when the family at zero is a differential operator) can be expressed in terms of Wodzicki residues and extended Wodzicki residues involving logarithmic operators. They are therefore local and contain geometric information. For holomorphic families leading to zeta regularised traces, they relate to the heat-kernel asymptotic coefficients via an inverse Mellin mapping theorem. We revisit Atiyah's L^2-index theorem by means of the (extended) Wodzicki residue and interpret the scalar curvature on the noncommutative two torus as an (extended) Wodzicki residue.
Reihe:
Geometric Methods in Physics, Trends in Mathematics
Buchtitel:
Geometric Methods in Physics
2015 | Large time limit and local L^2-index theorems for families | Sara Azzali, Sebastian Goette, Thomas Schick
Zeitschrift: J. Noncommut. Geom.
Verlag: EMS
Seiten: 621–664
Band: 9, Issue 2
Link zur Publikation
,
Link zum Preprint
Large time limit and local L^2-index theorems for families
Autoren: Sara Azzali, Sebastian Goette, Thomas Schick
(2015)
We compute explicitly, and without any extra regularity assumptions, the large time limit of the fibrewise heat operator for Bismut-Lott type superconnections in the $L^2$-setting. This is motivated by index theory on certain non-compact spaces (families of manifolds with cocompact group action) where the convergence of the heat operator at large time implies refined $L^2$-index formulas. As applications, we prove a local $L^2$-index theorem for families of signature operators and an $L^2$-Bismut-Lott theorem, expressing the Becker-Gottlieb transfer of flat bundles in terms of Kamber-Tandeur classes. With slightly stronger regularity we obtain the respective refined versions: we construct $L^2$-eta forms and $L^2$-torsion forms as transgression forms.
Zeitschrift:
J. Noncommut. Geom.
2015 | Self-adjointness of the Gaffney Laplacian on vector bundles | Lashi Bandara, Ognjen Milatovic
Zeitschrift: Math. Phys. Anal. Geom.
Verlag: Springer
Seiten: 14 pp.
Band: 18, no. 1, Art. 17
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,
Link zum Preprint
Self-adjointness of the Gaffney Laplacian on vector bundles
Autoren: Lashi Bandara, Ognjen Milatovic
(2015)
We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boundary is a necessary and sufficient condition for the self-adjointness of this operator.
Zeitschrift:
Math. Phys. Anal. Geom.
2015 | Hidden symmetries and decay for the wave equation on the Kerr spacetime | Lars Andersson, Pieter Blue
Zeitschrift: Annals of Mathematics
Verlag: Princeton University
Seiten: 787-853
Band: 182, no. 3
Link zur Publikation
,
Link zum Preprint
Hidden symmetries and decay for the wave equation on the Kerr spacetime
Autoren: Lars Andersson, Pieter Blue
(2015)
Energy and decay estimates for the wave equation on the exterior region of slowly rotating Kerr spacetimes are proved. The method used is a generalisation of the vector-field method that allows the use of higher-order symmetry operators. In particular, our method makes use of the second-order Carter operator, which is a hidden symmetry in the sense that it does not correspond to a Killing symmetry of the spacetime.
Zeitschrift:
Annals of Mathematics
Verlag:
Princeton University
2015 | Fast L_2-approximation of integral-type functionals of Markov processes | Iu. Ganychenko
Zeitschrift: Modern Stochastics: Theory and Applications
Reihe: 2
Seiten: 165-171
Band: 2
Link zur Publikation
Fast L_2-approximation of integral-type functionals of Markov processes
Autoren: Iu. Ganychenko
(2015)
Zeitschrift:
Modern Stochastics: Theory and Applications
2015 | Weak approximation rates for integral functionals of Markov processes | Iu. Ganychenko, A. Kulik
Zeitschrift: Modern Stochastics: Theory and Applications
Reihe: 3
Seiten: 251-266
Band: 2
Link zur Publikation
Weak approximation rates for integral functionals of Markov processes
Autoren: Iu. Ganychenko, A. Kulik
(2015)
Zeitschrift:
Modern Stochastics: Theory and Applications
2015 | Accuracy of discrete approximation for integral functionals of Markov processes | Iu. Ganychenko, V. Knopova, A. Kulik
Zeitschrift: Modern Stochastics: Theory and Applications
Reihe: 4
Seiten: 401-420
Band: 2
Link zur Publikation
Accuracy of discrete approximation for integral functionals of Markov processes
Autoren: Iu. Ganychenko, V. Knopova, A. Kulik
(2015)
Zeitschrift:
Modern Stochastics: Theory and Applications
2015 | Geometry and spectrum of rapidly branching graphs | Matthias Keller, Felix Pogorzelski, Florentin Münch
Zeitschrift: Mathematische Nachrichten
Seiten: 1636–1647
Band: 289
Link zur Publikation
,
Link zum Preprint
Geometry and spectrum of rapidly branching graphs
Autoren: Matthias Keller, Felix Pogorzelski, Florentin Münch
(2015)
We study graphs whose vertex degree tends and which are, therefore, called rapidly branching. We prove spectral estimates, discreteness of spectrum, first order eigenvalue and Weyl asymptotics solely in terms of the vertex degree growth. The underlying techniques are estimates on the isoperimetric constant. Furthermore, we give lower volume growth bounds and we provide a new criterion for stochastic incompleteness.
Zeitschrift:
Mathematische Nachrichten
2015 | Self-gravitating elastic bodies | Lars Andersson
Reihe: Fundamental Theories of Physics
Verlag: Springer
Buchtitel: D. Puetzfeld, C. Lämmerzahl, B. Schutz (eds.): Equations of Motion in Relativistic Gravity
Seiten: 543-559
Band: Volume 179
Link zur Publikation
,
Link zum Preprint
Self-gravitating elastic bodies
Autoren: Lars Andersson
(2015)
Extended objects in GR are often modelled using distributional solutions of the Einstein equations with point-like sources, or as the limit of infinitesimally small "test" objects. In this note, I will consider models of finite self-gravitating extended objects, which make it possible to give a rigorous treatment of the initial value problem for (finite) extended objects.
Reihe:
Fundamental Theories of Physics
Buchtitel:
D. Puetzfeld, C. Lämmerzahl, B. Schutz (eds.): Equations of Motion in Relativistic Gravity
2015 | Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior | Lars Andersson, Pieter Blue
Zeitschrift: J. Hyperbolic Differ. Equ.
Verlag: World Scientific
Seiten: 689-743
Band: 12, no. 4
Link zur Publikation
,
Link zum Preprint
Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior
Autoren: Lars Andersson, Pieter Blue
(2015)
We consider the Maxwell equation in the exterior of a very slowly rotating Kerr black hole. For this system, we prove the boundedness of a positive definite energy on each hypersurface of constant $t$. We also prove the convergence of each solution to a stationary Coulomb solution. We separate a general solution into the charged, Coulomb part and the uncharged part. Convergence to the Coulomb solutions follows from the fact that the uncharged part satisfies a Morawetz estimate, i.e. that a spatially localised energy density is integrable in time. For the unchanged part, we study both the full Maxwell equation and the Fackerell-Ipser equation for one component. To treat the Fackerell-Ipser equation, we use a Fourier transform in $t$. For the Fackerell-Ipser equation, we prove a refined Morawetz estimate that controls 3/2 derivatives with no loss near the orbiting null geodesics.
Zeitschrift:
J. Hyperbolic Differ. Equ.
2015 | The Merger of Small and Large Black Holes | P. Mösta, L. Andersson, J. Metzger, B. Szilágyi, J. Winicour
Zeitschrift: Class. Quantum Grav.
Verlag: IOP Publishing
Seiten: 235003
Band: 32, no. 23
Link zur Publikation
,
Link zum Preprint
The Merger of Small and Large Black Holes
Autoren: P. Mösta, L. Andersson, J. Metzger, B. Szilágyi, J. Winicour
(2015)
We present simulations of binary black holes mergers in which, after the common outer horizon has formed, the marginally outer trapped surfaces (MOTSs) corresponding to the individual black holes continue to approach and eventually penetrate each other. This has very interesting consequences according to recent results in the theory of MOTSs. Uniqueness and stability theorems imply that two MOTSs which touch with a common outer normal must be identical. This suggests a possible dramatic consequence of the collision between a small and large black hole. If the penetration were to continue to completion then the two MOTSs would have to coalesce, by some combination of the small one growing and the big one shrinking. Here we explore the relationship between theory and numerical simulations, in which a small black hole has halfway penetrated a large one.
Zeitschrift:
Class. Quantum Grav.
2015 | Spin geometry and conservation laws in the Kerr spacetime | Lars Andersson, Thomas Bäckdahl, Pieter Blue
Reihe: Surveys in Differential Geometry
Verlag: International Press of Boston
Buchtitel: L. Bieri, S.-T. Yau (eds.): One hundred years of general relativity
Seiten: 183-226
Band: Volume 20
Link zur Publikation
,
Link zum Preprint
Spin geometry and conservation laws in the Kerr spacetime
Autoren: Lars Andersson, Thomas Bäckdahl, Pieter Blue
(2015)
In this paper we will review some facts, both classical and recent, concerning the geometry and analysis of the Kerr and related black hole spacetimes. This includes the analysis of test fields on these spacetimes. Central to our analysis is the existence of a valence $(2,0)$ Killing spinor, which we use to construct symmetry operators and conserved currents as well as a new energy momentum tensor for the Maxwell test fields on a class of spacetimes containing the Kerr spacetime. We then outline how this new energy momentum tensor can be used to obtain decay estimated for Maxwell test fields. An important motivation for this work is the black hole stability problem, where fields with non-zero spin present interesting new challenges. The main tool in the analysis is the 2-spinor calculus, and for completeness we introduce its main features.
Reihe:
Surveys in Differential Geometry
Verlag:
International Press of Boston
Buchtitel:
L. Bieri, S.-T. Yau (eds.): One hundred years of general relativity
2015 | Is there proof that backreaction of inhomogeneities is irrelevant in cosmology? | T. Buchert, M. Carfora, G.F.R. Ellis, E.W. Kolb, M.A.H. MacCallum, J.J. Ostrowski, S. Räsänen, B.F. Roukema, L. Andersson, A.A. Coley, D.L. Wiltshire
Zeitschrift: Class. Quantum Grav.
Verlag: IOP Publishing
Seiten: 215021
Band: 32, no. 21
Link zur Publikation
,
Link zum Preprint
Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?
Autoren: T. Buchert, M. Carfora, G.F.R. Ellis, E.W. Kolb, M.A.H. MacCallum, J.J. Ostrowski, S. Räsänen, B.F. Roukema, L. Andersson, A.A. Coley, D.L. Wiltshire
(2015)
No. In a number of papers Green and Wald argue that the standard FLRW model approximates our Universe extremely well on all scales, except close to strong field astrophysical objects. In particular, they argue that the effect of inhomogeneities on average properties of the Universe (backreaction) is irrelevant. We show that this latter claim is not valid. Specifically, we demonstrate, referring to their recent review paper, that (i) their two-dimensional example used to illustrate the fitting problem differs from the actual problem in important respects, and it assumes what is to be proven; (ii) the proof of the trace-free property of backreaction is unphysical and the theorem about it fails to be a mathematically general statement; (iii) the scheme that underlies the trace-free theorem does not involve averaging and therefore does not capture crucial non-local effects; (iv) their arguments are to a large extent coordinate-dependent, and (v) many of their criticisms of backreaction frameworks do not apply to the published definitions of these frameworks. It is therefore incorrect to infer that Green and Wald have proven a general result that addresses the essential physical questions of backreaction in cosmology.
Zeitschrift:
Class. Quantum Grav.
2015 | School mathematics and bureaucracy | David Kollosche
Buchtitel: Krainer & Vondrová (Hg.) Proceedings of the 9th Congress of the European Society for Research in Mathematics Education
School mathematics and bureaucracy
Autoren: David Kollosche
(2015)
Buchtitel:
Krainer & Vondrová (Hg.) Proceedings of the 9th Congress of the European Society for Research in Mathematics Education
2015 | Mathematics education as a disciplinary institution | David Kollosche
Buchtitel: Mukhopadhyay & Greer (Hg.) Proceedings of the Eighth International Mathematics Education and Society Conference
Mathematics education as a disciplinary institution
Autoren: David Kollosche
(2015)
Buchtitel:
Mukhopadhyay & Greer (Hg.) Proceedings of the Eighth International Mathematics Education and Society Conference
2015 | Mathematik und Bildung aus kritischer Sicht | David Kollosche
Zeitschrift: mathematica didactica
Link zur Publikation
Mathematik und Bildung aus kritischer Sicht
Autoren: David Kollosche
(2015)
Zeitschrift:
mathematica didactica
2015 | Instability of Pre-Existing Resonances Under a Small Constant Electric Field | Ira Herbst, Juliane Rama
Zeitschrift: Annales Henri Poincare
Verlag: Springer Basel
Seiten: 2783 - 2835
Band: 16
Link zur Publikation
Instability of Pre-Existing Resonances Under a Small Constant Electric Field
Autoren: Ira Herbst, Juliane Rama
(2015)
Two simple model operators are considered which have pre-existing resonances. A potential corresponding to a small electric field, f, is then introduced and the resonances of the resulting operator are considered as<tex> <tex>f\to 0</tex>. </tex>
It is shown that these resonances are not continuous in this limit. It is conjectured that a similar behavior will appear in more complicated models of atoms and molecules. Numerical results are presented.
Zeitschrift:
Annales Henri Poincare
2015 | Eigenvalue asymptotics for Schrödinger operators on sparse graphs | Michel Bonnefont, Sylvain Golénia, Matthias Keller
Zeitschrift: Annales de l'Institut Fourier
Seiten: 1969-1998
Band: 65
Link zur Publikation
,
Link zum Preprint
Eigenvalue asymptotics for Schrödinger operators on sparse graphs
Autoren: Michel Bonnefont, Sylvain Golénia, Matthias Keller
(2015)
We consider Schrödinger operators on sparse graphs. The geometric definition of sparseness turn out to be equivalent to a functional inequality for the Laplacian. In consequence, sparseness has in turn strong spectral and functional analytic consequences. Specifically, one consequence is that it allows to completely describe the form domain. Moreover, as another consequence it leads to a characterization for discreteness of the spectrum. In this case we determine the first order of the corresponding eigenvalue asymptotics.
Zeitschrift:
Annales de l'Institut Fourier
2015 | Diffussion determines the recurrent graph | Matthias Keller, Daniel Lenz, Marcel Schmidt, Melchior Wirth
Zeitschrift: Advances in Mathematics
Seiten: 364–398
Band: 269
Link zur Publikation
,
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Diffussion determines the recurrent graph
Autoren: Matthias Keller, Daniel Lenz, Marcel Schmidt, Melchior Wirth
(2015)
We consider diffusion on discrete measure spaces as encoded by Markovian semigroups arising from weighted graphs. We study whether the graph is uniquely determined if the diffusion is given up to order isomorphism. If the graph is recurrent then the complete graph structure and the measure space are determined (up to an overall scaling). As shown by counterexamples this result is optimal. Without the recurrence assumption, the graph still turns out to be determined in the case of normalized diffusion on graphs with standard weights and in the case of arbitrary graphs over spaces in which each point has the same mass. These investigations provide discrete counterparts to studies of diffusion on Euclidean domains and manifolds initiated by Arendt and continued by Arendt/Biegert/ter Elst and Arendt/ter Elst. A crucial step in our considerations shows that order isomorphisms are actually unitary maps (up to a scaling) in our context.
Zeitschrift:
Advances in Mathematics
2015 | Graphs of finite measure | Agelos Georgakopoulos, Sebastian Haeseler, Matthias Keller, Daniel Lenz, Radosław Wojciechowski
Zeitschrift: Journal de Mathématiques Pures et Appliquées
Seiten: 1093–1131
Band: 103
Link zur Publikation
,
Link zum Preprint
Graphs of finite measure
Autoren: Agelos Georgakopoulos, Sebastian Haeseler, Matthias Keller, Daniel Lenz, Radosław Wojciechowski
(2015)
We consider weighted graphs with an infinite set of vertices. We show that boundedness of all functions of finite energy can be seen as a notion of ‘relative compactness’ for such graphs and study sufficient and necessary conditions for this property in terms of various metrics. We then equip graphs satisfying this property with a finite measure and investigate the associated Laplacian and its semigroup. In this context, our results include the trace class property for the semigroup, uniqueness and existence of solutions to the Dirichlet Problem with boundary arising from the natural compactification, an explicit description of the domain of the Dirichlet Laplacian, convergence of the heat semigroup for large times as well as stochastic incompleteness and transience of the corresponding random walk in continuous time.
Zeitschrift:
Journal de Mathématiques Pures et Appliquées
2015 | Intrinsic Metrics on Graphs: A Survey | Matthias Keller
Reihe: Springer Proceedings in Mathematics & Statistics
Verlag: Springer
Buchtitel: Mathematical Technology of Networks
Seiten: 81-119
Band: 128
Intrinsic Metrics on Graphs: A Survey
Autoren: Matthias Keller
(2015)
A few years ago various disparities for Laplacians on graphs and manifolds were discovered. The corresponding results are mostly related to volume growth in the context of unbounded geometry. Indeed, these disparities can now be resolved by using so called intrinsic metrics instead of the combinatorial graph distance. In this article we give an introduction to this topic and survey recent results in this direction. Specifically, we cover topics such as Liouville type theorems for harmonic functions, essential selfadjointness, stochastic completeness and upper escape rates. Furthermore, we determine the spectrum as a set via solutions, discuss upper and lower spectral bounds by isoperimetric constants and volume growth and study p-independence of spectra under a volume growth assumption.
Reihe:
Springer Proceedings in Mathematics & Statistics
Buchtitel:
Mathematical Technology of Networks
2015 | An invitation to trees of finite cone type: random and deterministic operators | Matthias Keller, Daniel Lenz, Simone Warzel
Zeitschrift: Markov Processes and Related Filelds
Seiten: 557-574
Band: 21
Link zur Publikation
,
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An invitation to trees of finite cone type: random and deterministic operators
Autoren: Matthias Keller, Daniel Lenz, Simone Warzel
(2015)
Trees of finite cone type have appeared in various contexts. In particular, they come up as simplified models of regular tessellations of the hyperbolic plane. The spectral theory of the associated Laplacians can thus be seen as induced by geometry. Here we give an introduction focusing on background and then turn to recent results for (random) perturbations of trees of finite cone type and their spectral theory.
Zeitschrift:
Markov Processes and Related Filelds
2015 | Note on basic features of large time behaviour of heat kernels | Matthias Keller, Daniel Lenz, Hendrik Vogt, Radoslaw Wojciechowski
Zeitschrift: Journal für die reine und angewandte Mathematik (Crelle's Journal)
Seiten: 73–95
Band: 2015
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Note on basic features of large time behaviour of heat kernels
Autoren: Matthias Keller, Daniel Lenz, Hendrik Vogt, Radoslaw Wojciechowski
(2015)
Large time behaviour of heat semigroups (and, more generally, of positive selfadjoint semigroups) is studied. Convergence of the semigroup to the ground state and of averaged logarithms of kernels to the ground state energy is shown in the general framework of positivity improving selfadjoint semigroups. This framework encompasses all irreducible semigroups coming from Dirichlet forms as well as suitable perturbations thereof. It includes, in particular, Laplacians on connected manifolds, metric graphs and discrete graphs.
Zeitschrift:
Journal für die reine und angewandte Mathematik (Crelle's Journal)
2015 | Cheeger inequalities for unbounded graph Laplacians | Frank Bauer, Matthias Keller, Radoslaw Wojciechowski
Zeitschrift: Journal of the European Mathematical Society
Seiten: 259–271
Band: 17
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Cheeger inequalities for unbounded graph Laplacians
Autoren: Frank Bauer, Matthias Keller, Radoslaw Wojciechowski
(2015)
We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate for the bottom of the spectrum which is nontrivial even if the vertex degrees are unbounded.
Zeitschrift:
Journal of the European Mathematical Society
2015 | Agmon estimates for the difference of exact and approximate Dirichlet eigenfunctions for difference operators | Markus Klein, Elke Rosenberger
Zeitschrift: Asymptotic Analysis
Verlag: IOS Press
Seiten: 61-89
Band: 97
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Agmon estimates for the difference of exact and approximate Dirichlet eigenfunctions for difference operators
Autoren: Markus Klein, Elke Rosenberger
(2015)
We analyze a general class of difference operators <tex>H_\varepsilon = T_\varepsilon + V_\varepsilon</tex> on <tex>\ell^2(\varepsilon \mathbb{Z}^d</tex>), where <tex>V_\varepsilon</tex> is a multi-well
potential and <tex>\varepsilon</tex> is a small parameter. We construct approximate eigenfunctions in
neighbourhoods of the different wells and give weighted <tex>\ell^2</tex>-estimates for the difference of these
and the exact eigenfunctions of the associated Dirichlet-operators.
Zeitschrift:
Asymptotic Analysis
2015 | On the lattice structure of kernel operators | Moritz Gerlach, Markus Kunze
Zeitschrift: Mathematische Nachrichten
Seiten: 584-592
Band: 288
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On the lattice structure of kernel operators
Autoren: Moritz Gerlach, Markus Kunze
(2015)
Consider the lattice of bounded linear operators on the space of Borel measures on a Polish space. We prove that the operators which are continuous with respect to the weak topology induced by the bounded measurable functions form a sublattice that is lattice isomorphic to the space of transition kernels. As an application we present a purely analytic proof of Doob's theorem concerning stability of transition semigroups.
Zeitschrift:
Mathematische Nachrichten
2015 | Relative Cauchy evolution for the vector potential on globally hyperbolic spacetimes | Marco Benini
Zeitschrift: Mathematics and Mechanics of Complex Systems
Verlag: Mathematical Science Publishers
Seiten: 177-210
Band: 3, no. 2
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Relative Cauchy evolution for the vector potential on globally hyperbolic spacetimes
Autoren: Marco Benini
(2015)
The dynamics of the electromagnetic vector potential is analyzed in full detail in view of the principle of general local covariance of Brunetti, Fredenhagen and Verch. Exploiting this result, the relative Cauchy evolution for the vector potential is introduced and its relation with the energy-momentum tensor is established, extending the well known results for Klein–Gordon and Dirac fields.
Zeitschrift:
Mathematics and Mechanics of Complex Systems
Verlag:
Mathematical Science Publishers
2015 | Homotopy colimits and global observables in Abelian gauge theory | Marco Benini, Alexander Schenkel, Richard J. Szabo
Zeitschrift: Lett. Math. Phys.
Verlag: Springer
Seiten: 1193-1222
Band: 105, no. 9
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Homotopy colimits and global observables in Abelian gauge theory
Autoren: Marco Benini, Alexander Schenkel, Richard J. Szabo
(2015)
We study chain complexes of field configurations and observables for Abelian gauge theory on contractible manifolds, and show that they can be extended to non-contractible manifolds by using techniques from homotopy theory. The extension prescription yields functors from a category of manifolds to suitable categories of chain complexes. The extended functors properly describe the global field and observable content of Abelian gauge theory, while the original gauge field configurations and observables on contractible manifolds are recovered up to a natural weak equivalence.
Zeitschrift:
Lett. Math. Phys.
2015 | Models of free quantum field theories on curved backgrounds | Marco Benini, Claudio Dappiaggi
Verlag: Springer
Buchtitel: R. Brunetti, C. Dappiaggi, K. Fredenhagen, J. Yngvason (eds.): Advances in Algebraic Quantum Field Theory
Seiten: 75-124
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Models of free quantum field theories on curved backgrounds
Autoren: Marco Benini, Claudio Dappiaggi
(2015)
Free quantum field theories on curved backgrounds are discussed via three explicit examples: the real scalar field, the Dirac field and the Proca field. The first step consists of outlining the main properties of globally hyperbolic spacetimes, that is the class of manifolds on which the classical dynamics of all physically relevant free fields can be written in terms of a Cauchy problem. The set of all smooth solutions of the latter encompasses the dynamically allowed configurations which are used to identify via a suitable pairing a collection of classical observables. As a last step we use such collection to construct a *-algebra which encodes the information on the dynamics and on the canonical commutation or anti-commutation relations depending whether the underlying field is a Fermion or a Boson.
Buchtitel:
R. Brunetti, C. Dappiaggi, K. Fredenhagen, J. Yngvason (eds.): Advances in Algebraic Quantum Field Theory
2015 | Cheeger-Simons differential characters with compact support and Pontryagin duality | Christian Becker, Marco Benini, Alexander Schenkel, Richard J. Szabo
Link zum Preprint
Cheeger-Simons differential characters with compact support and Pontryagin duality
Autoren: Christian Becker, Marco Benini, Alexander Schenkel, Richard J. Szabo
(2015)
By adapting the Cheeger-Simons approach to differential cohomology, we establish a notion of differential cohomology with compact support. We show that it is functorial with respect to open embeddings and that it fits into a natural diagram of exact sequences which compare it to compactly supported singular cohomology and differential forms with compact support, in full analogy to ordinary differential cohomology. By extending some results for relative differential cohomology we prove an excision theorem for differential cohomology. We further establish Pontryagin duality for differential cohomology: On any oriented manifold, ordinary differential cohomology is isomorphic to the smooth Pontryagin dual of compactly supported differential cohomology. For manifolds of finite-type, a similar result is obtained interchanging ordinary with compactly supported differential cohomology.
2015 | Large-scale modelling via alpha-regularization for atmospheric simulations | V. Aizinger, P. Korn, P. Giorgetta, S. Reich
Zeitschrift: Journal of Turbulence, (to appear)
Large-scale modelling via alpha-regularization for atmospheric simulations
Autoren: V. Aizinger, P. Korn, P. Giorgetta, S. Reich
(2015)
Zeitschrift:
Journal of Turbulence, (to appear)
2015 | Multiple-time-stepping generalized hybrid Monte Carlo methods | B. Escribano, E. Akhmatskaya, S. Reich, J.M. Azprioz
Zeitschrift: Journal of Computational Physics,
Seiten: 1--20
Band: 280
Link zur Publikation
Multiple-time-stepping generalized hybrid Monte Carlo methods
Autoren: B. Escribano, E. Akhmatskaya, S. Reich, J.M. Azprioz
(2015)
Zeitschrift:
Journal of Computational Physics,
2015 | Data assimilation: a dynamical system perspective | Y. Cheng and S. Reich
Reihe: Frontiers in Applied Dynamics: Reviews and Tutorials
Verlag: Springer-Verlag
Seiten: in press
Band: 1
Link zur Publikation
Data assimilation: a dynamical system perspective
Autoren: Y. Cheng and S. Reich
(2015)
Reihe:
Frontiers in Applied Dynamics: Reviews and Tutorials
2015 | On embedding left-ordered groups into division rings | Gräter, J.; Sperner, R.P.
Zeitschrift: Forum Math.27
Seiten: 485-518
On embedding left-ordered groups into division rings
Autoren: Gräter, J.; Sperner, R.P.
(2015)
Zeitschrift:
Forum Math.27
2015 | On Elementary Bounds for ... | Gräter, J.; Wirths, K.-J.
Zeitschrift: Amer. Math. Monthly 122
Seiten: 155-158
On Elementary Bounds for ...
Autoren: Gräter, J.; Wirths, K.-J.
(2015)
Zeitschrift:
Amer. Math. Monthly 122
2015 | Development of Conceptual Understanding of Place Value | Silke Ladel, Ulrich Kortenkamp
Buchtitel: ICME Study 23
Development of Conceptual Understanding of Place Value
Autoren: Silke Ladel, Ulrich Kortenkamp
(2015)
2015 | Coupling distances between Lévy measures and applications to noise sensitivity of SDE | J. Gairing, M. Högele, T. Kosenkova, A. Kulik
Zeitschrift: Stochastics and Dynamics 2 (2015)
Link zur Publikation
Coupling distances between Lévy measures and applications to noise sensitivity of SDE
Autoren: J. Gairing, M. Högele, T. Kosenkova, A. Kulik
(2015)
Zeitschrift:
Stochastics and Dynamics 2 (2015)
2015 | Winkel in der Sekundarstufe I – Schülervorstellungen erforschen | Christian Dohrmann, Ana Kuzle
Zeitschrift: Geometrie zwischen Grundbegriffen und Grundvorstellungen
Verlag: Springer
Seiten: 62-76
Band: Jubiläumsband des Arbeitskreises der Geometrie in der Gesellschaft für Didaktik der Mathematik
Winkel in der Sekundarstufe I – Schülervorstellungen erforschen
Autoren: Christian Dohrmann, Ana Kuzle
(2015)
Zeitschrift:
Geometrie zwischen Grundbegriffen und Grundvorstellungen
Band:
Jubiläumsband des Arbeitskreises der Geometrie in der Gesellschaft für Didaktik der Mathematik
2015 | On small-noise equations with degenerate limiting system arising from volatility models | G. Conforti, J.-D. Deuschel, S. de Marco
Reihe: Proceedings in Mathematics & Statistics
Verlag: Springer
Buchtitel: Large Deviations and Asymptotic methods in Finance
Band: 110
Link zur Publikation
On small-noise equations with degenerate limiting system arising from volatility models
Autoren: G. Conforti, J.-D. Deuschel, S. de Marco
(2015)
Reihe:
Proceedings in Mathematics & Statistics
Buchtitel:
Large Deviations and Asymptotic methods in Finance
2015 | Bridges of Markov counting processes. Reciprocal classes and duality formulae | G. Conforti, C. Léonard, R. Murr, S. Roelly
Zeitschrift: Electron. Commun. Probab. 20-18 (2015)
Seiten: 1-12
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Bridges of Markov counting processes. Reciprocal classes and duality formulae
Autoren: G. Conforti, C. Léonard, R. Murr, S. Roelly
(2015)
Zeitschrift:
Electron. Commun. Probab. 20-18 (2015)
2015 | A quasi Random Walk to model a biological transport process | P. Keller, S. Roelly, A. Valleriani
Zeitschrift: Methodology and Computing in Applied Probability 17 (2015)
Seiten: 125-137
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A quasi Random Walk to model a biological transport process
Autoren: P. Keller, S. Roelly, A. Valleriani
(2015)
Zeitschrift:
Methodology and Computing in Applied Probability 17 (2015)
2015 | On time duality for Markov chains | P. Keller, S. Roelly, A. Valleriani
Zeitschrift: Stochastic Models 31-1 (2015)
Seiten: 98-118
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On time duality for Markov chains
Autoren: P. Keller, S. Roelly, A. Valleriani
(2015)
Zeitschrift:
Stochastic Models 31-1 (2015)
2015 | Averaging along Lévy diffusions in foliated spaces | M. Högele, P. Ruffino
Zeitschrift: Nonlinear An.
Band: 112
Link zum Preprint
Averaging along Lévy diffusions in foliated spaces
Autoren: M. Högele, P. Ruffino
(2015)
Zeitschrift:
Nonlinear An.
2015 | Metastability of Morse-Smale dynamical systems perturbed by heavy-tailed Lévy type noise | M. Högele, I. Pavlyukevich
Zeitschrift: Stoch. Dyn.
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Link zum Preprint
Metastability of Morse-Smale dynamical systems perturbed by heavy-tailed Lévy type noise
Autoren: M. Högele, I. Pavlyukevich
(2015)
2015 | Weakly differentiable functions on varifolds | Ulrich Menne
Zeitschrift: Indiana Univ. Math. J. (to appear)
Seiten: 1-102
Link zum Preprint
Weakly differentiable functions on varifolds
Autoren: Ulrich Menne
(2015)
The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept proposed here is defined by means of integration by parts identities for certain compositions with smooth functions. In this class the idea of zero boundary values is realised using the relative perimeter of superlevel sets. Results include a variety of Sobolev Poincaré type embeddings, embeddings into spaces of continuous and sometimes Hölder continuous functions, pointwise differentiability results both of approximate and integral type as well as coarea formulae.
As prerequisite for this study decomposition properties of such varifolds and a relative isoperimetric inequality are established. Both involve a concept of distributional boundary of a set introduced for this purpose.
As applications the finiteness of the geodesic distance associated to varifolds with suitable summability of the mean curvature and a charac- terisation of curvature varifolds are obtained.
Zeitschrift:
Indiana Univ. Math. J. (to appear)
2015 | Decay rates for the quadratic and super-quadratic tilt-excess of integral varifolds | Sławomir Kolasiński, Ulrich Menne
Seiten: 1-53
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Decay rates for the quadratic and super-quadratic tilt-excess of integral varifolds
Autoren: Sławomir Kolasiński, Ulrich Menne
(2015)
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space satisfying integrability conditions on their first variation. Firstly, the study of pointwise power decay rates almost everywhere of the quadratic tilt-excess is completed by establishing the precise decay rate for two-dimensional integral varifolds of locally bounded first variation. In order to obtain the exact decay rate, a coercive estimate involving a height-excess quantity measured in Orlicz spaces is established. Moreover, counter-examples to pointwise power decay rates almost everywhere of the super-quadratic tilt-excess are obtained. These examples are optimal in terms of the dimension of the varifold and the exponent of the integrability condition in most cases, for example if the varifold is not two-dimensional. These examples also demonstrate that within the scale of Lebesgue spaces no local higher integrability of the second fundamental form, of an at least two-dimensional curvature varifold, may be deduced from boundedness of its generalised mean curvature vector.
Amongst the tools are Cartesian products of curvature varifolds.
2015 | Sobolev functions on varifolds | Ulrich Menne
Seiten: 1-51
Link zum Preprint
Sobolev functions on varifolds
Autoren: Ulrich Menne
(2015)
This paper introduces first order Sobolev spaces on certain rectifiable varifolds. These complete locally convex spaces are contained in the generally nonlinear class of generalised weakly differentiable functions and share key functional analytic properties with their Euclidean counterparts.
Assuming the varifold to satisfy a uniform lower density bound and a dimensionally critical summability condition on its mean curvature, the following statements hold. Firstly, continuous and compact embeddings of Sobolev spaces into Lebesgue spaces and spaces of continuous functions are available. Secondly, the geodesic distance associated to the varifold is a continuous, not necessarily Höolder continuous Sobolev function with bounded derivative. Thirdly, if the varifold additionally has bounded mean curvature and finite measure, the present Sobolev spaces are isomorphic to those previously available for finite Radon measures yielding many new results for those classes as well.
Suitable versions of the embedding results obtained for Sobolev functions hold in the larger class of generalised weakly differentiable functions.
2015 | Geometrically formal 4-manifolds with nonnegative sectional curvature | Christian Bär
Zeitschrift: Comm. Anal. Geom.
Verlag: International Press
Seiten: 479-497
Band: 23, no. 3
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Geometrically formal 4-manifolds with nonnegative sectional curvature
Autoren: Christian Bär
(2015)
A Riemannian manifold is called geometrically formal if the wedge product of any two harmonic forms is again harmonic. We classify geometrically formal compact 4-manifolds with nonnegative sectional curvature. If the sectional curvature is strictly positive, the manifold must be homeomorphic to S^4 or diffeomorphic to CP^2. This conclusion stills holds true if the sectional curvature is strictly positive and we relax the condition of geometric formality to the requirement that the length of harmonic 2-forms is not too nonconstant. In particular, the Hopf conjecture on S^2 x S^2 holds in this class of manifolds.
Zeitschrift:
Comm. Anal. Geom.
Verlag:
International Press
2015 | Green-hyperbolic operators on globally hyperbolic spacetimes | Christian Bär
Zeitschrift: Comm. Math. Phys.
Verlag: Springer
Seiten: 1585-1615
Band: 333, no. 3
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Link zum Preprint
Green-hyperbolic operators on globally hyperbolic spacetimes
Autoren: Christian Bär
(2015)
Green-hyperbolic operators are linear differential operators acting on sections of a vector bundle over a Lorentzian manifold which possess advanced and retarded Green's operators. The most prominent examples are wave operators and Dirac-type operators. This paper is devoted to a systematic study of this class of differential operators. For instance, we show that this class is closed under taking restrictions to suitable subregions of the manifold, under composition, under taking "square roots", and under the direct sum construction. Symmetric hyperbolic systems are studied in detail.
Zeitschrift:
Comm. Math. Phys.
2015 | On infinitesimal Einstein deformations | Klaus Kröncke
Zeitschrift: Differential Geom. Appl.
Verlag: Elsevier
Seiten: 41-57
Band: 38
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On infinitesimal Einstein deformations
Autoren: Klaus Kröncke
(2015)
We study infinitesimal Einstein deformations on compact flat manifolds and on product manifolds. Moreover, we prove refinements of results by Koiso and Bourguignon which yield obstructions on the existence of infinitesimal Einstein deformations under certain curvature conditions.
Zeitschrift:
Differential Geom. Appl.
2015 | On the stability of Einstein manifolds | Klaus Kröncke
Zeitschrift: Ann. Global Anal. Geom.
Verlag: Springer
Seiten: 81-98
Band: 47, no. 1
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On the stability of Einstein manifolds
Autoren: Klaus Kröncke
(2015)
Certain curvature conditions for stability of Einstein manifolds with respect to the Einstein-Hilbert action are given. These conditions are given in terms of quantities involving the Weyl tensor and the Bochner tensor. In dimension six, a stability criterion involving the Euler characteristic is given.
Zeitschrift:
Ann. Global Anal. Geom.
2015 | Initial value problems for wave equations on manifolds | Christian Bär, Roger Tagne Wafo
Zeitschrift: Math. Phys. Anal. Geom.
Verlag: Springer
Seiten: Art.:7
Band: 18, no. 1
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Initial value problems for wave equations on manifolds
Autoren: Christian Bär, Roger Tagne Wafo
(2015)
We study the global theory of linear wave equations for sections of vector bundles over globally hyperbolic Lorentz manifolds. We introduce spaces of finite energy sections and show well-posedness of the Cauchy problem in those spaces. These spaces depend in general on the choice of a time function but it turns out that certain spaces of finite energy solutions are independent of this choice and hence invariantly defined.
We also show existence and uniqueness of solutions for the Goursat problem where one prescribes initial data on a characteristic partial Cauchy hypersurface. This extends classical results due to H\"ormander.
Zeitschrift:
Math. Phys. Anal. Geom.
2015 | Stability and instability of Ricci solitons | Klaus Kröncke
Zeitschrift: Calc. Var. Partial Differ. Equ.
Verlag: Springer
Seiten: 265-287
Band: 53, no.1-2
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Stability and instability of Ricci solitons
Autoren: Klaus Kröncke
(2015)
We consider the volume-normalized Ricci flow close to compact shrinking Ricci solitons. We show that if a compact Ricci soliton (M,g) is a local maximum of Perelman's shrinker entropy, any normalized Ricci flow starting close to it exists for all time and converges towards a Ricci soliton. If g is not a local maximum of the shrinker entropy, we show that there exists a nontrivial normalized Ricci flow emerging from it. These theorems are analogues of results in the Ricci-flat and in the Einstein case.
Zeitschrift:
Calc. Var. Partial Differ. Equ.
2015 | Rigidity and infinitesimal deformability of Ricci solitons | Klaus Kröncke
Zeitschrift: J. Geom. Anal.
Verlag: Springer
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Rigidity and infinitesimal deformability of Ricci solitons
Autoren: Klaus Kröncke
(2015)
In this paper, an obstruction against the integrability of certain infinitesimal solitonic deformations is given. Using this obstruction, we show that the complex projective spaces of even complex dimension are rigid as Ricci solitons although they have infinitesimal solitonic deformations.
Zeitschrift:
J. Geom. Anal.
2015 | A Semiclassical Heat Kernel Proof of the Poincaré-Hopf Theorem | Matthias Ludewig
Zeitschrift: Manuscripta Math.
Verlag: Springer
Seiten: 29-58
Band: 148, no. 1-2
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A Semiclassical Heat Kernel Proof of the Poincaré-Hopf Theorem
Autoren: Matthias Ludewig
(2015)
We treat the Witten operator on the de Rham complex with semiclassical heat kernel methods to derive the Poincar\'e-Hopf theorem and degenerate generalizations of it. Thereby, we see how the semiclassical asymptotics of the Witten heat kernel are related to approaches using the Thom form of Mathai and Quillen.
Zeitschrift:
Manuscripta Math.
2015 | A confidence ellipse for the net reclassification improvement | Kristin Mhlenbruch, Olga Kuxhaus, Matthias Schulz, Heiner Boeing, Hannelore Liero, Michael Pencina
Zeitschrift: European Journal of Epidemiology
A confidence ellipse for the net reclassification improvement
Autoren: Kristin Mhlenbruch, Olga Kuxhaus, Matthias Schulz, Heiner Boeing, Hannelore Liero, Michael Pencina
(2015)
Zeitschrift:
European Journal of Epidemiology
2014 | Solvation of a sponge-like geometry | M. E. Evans and R. Roth
Zeitschrift: Pure and Applied Chemistry 86(2)
Seiten: 173-179
Link zur Publikation
Solvation of a sponge-like geometry
Autoren: M. E. Evans and R. Roth
(2014)
Zeitschrift:
Pure and Applied Chemistry 86(2)
2014 | Shaping the skin: the interplay of mesoscale geometry and corneocyte swelling | M. E. Evans and R. Roth
Zeitschrift: Physical Review Letters 112(3)
Link zur Publikation
Shaping the skin: the interplay of mesoscale geometry and corneocyte swelling
Autoren: M. E. Evans and R. Roth
(2014)
Zeitschrift:
Physical Review Letters 112(3)
2014 | Hierarchical self-assembly of a striped Gyroid formed by threaded chiral mesoscale networks | J. J. K. Kirkensgaard, M. E. Evans, L. de Campo and S. T. Hyde
Zeitschrift: Proceedings of the National Academy of Sciences USA 111(4)
Seiten: 1271-1276
Link zur Publikation
Hierarchical self-assembly of a striped Gyroid formed by threaded chiral mesoscale networks
Autoren: J. J. K. Kirkensgaard, M. E. Evans, L. de Campo and S. T. Hyde
(2014)
Zeitschrift:
Proceedings of the National Academy of Sciences USA 111(4)
2014 | In a material world: Hyperbolische Geometrie in biologischen Materialien | M. E. Evans and G. E. Schröder-Turk
Zeitschrift: Mitteilungen der Deutschen Mathematiker-Vereinigung 22(3)
Seiten: 158-166 (popular science, not referreed)
Link zur Publikation
In a material world: Hyperbolische Geometrie in biologischen Materialien
Autoren: M. E. Evans and G. E. Schröder-Turk
(2014)
Zeitschrift:
Mitteilungen der Deutschen Mathematiker-Vereinigung 22(3)
Seiten:
158-166 (popular science, not referreed)
2014 | Towards breaking the curse of dimensionality in computational methods for the conformational analysis of molecules | Han Cheng Lie
Zeitschrift: BMC Bioinformatics
Verlag: BioMed Central
Band: 15, A2
Link zur Publikation
Towards breaking the curse of dimensionality in computational methods for the conformational analysis of molecules
Autoren: Han Cheng Lie
(2014)
Zeitschrift:
BMC Bioinformatics
2014 | Calculating the $H_\infty$-norm using the implicit determinant method | M.A. Freitag, A Spence, P. Van Dooren
Zeitschrift: SIAM J. Matrix Anal. Appl.
Seiten: 619-635
Band: 35(2)
Link zur Publikation
Calculating the $H_\infty$-norm using the implicit determinant method
Autoren: M.A. Freitag, A Spence, P. Van Dooren
(2014)
Zeitschrift:
SIAM J. Matrix Anal. Appl.
2014 | A new approach for calculating the real stability radius | M.A. Freitag, A. Spence
Zeitschrift: BIT
Verlag: Springer
Seiten: 381-400
Band: 54(2)
Link zur Publikation
A new approach for calculating the real stability radius
Autoren: M.A. Freitag, A. Spence
(2014)
2014 | The computation of Jordan blocks in parameter-dependent matrices | R.O. Akinola, M.A. Freitag, A. Spence
Zeitschrift: IMA J. Numer. Anal.
Verlag: Oxford University Press
Seiten: 955-976
Band: 34(3)
Link zur Publikation
The computation of Jordan blocks in parameter-dependent matrices
Autoren: R.O. Akinola, M.A. Freitag, A. Spence
(2014)
Zeitschrift:
IMA J. Numer. Anal.
Verlag:
Oxford University Press
2014 | The calculation of the distance to a nearby defective matrix | R.O. Akinola, M.A. Freitag, A. Spence
Zeitschrift: Numer. Linear Algebra Appl.
Seiten: 403-414
Band: 21(3)
Link zur Publikation
The calculation of the distance to a nearby defective matrix
Autoren: R.O. Akinola, M.A. Freitag, A. Spence
(2014)
Zeitschrift:
Numer. Linear Algebra Appl.
2014 | Meta-analysis for diagnostic accuracy studies: A new statistical model using beta-binomial distributions and bivariate copulas | O. Kuß, A. Hoyer, A. Solms
Zeitschrift: Statistics in Medicine
Seiten: 17-30
Band: 33
Link zur Publikation
Meta-analysis for diagnostic accuracy studies: A new statistical model using beta-binomial distributions and bivariate copulas
Autoren: O. Kuß, A. Hoyer, A. Solms
(2014)
Zeitschrift:
Statistics in Medicine
2014 | Monoclonal antibody disposition: a simplified PBPK model and its implications for the derivation and interpretation of classical compartment models | L. Fronton, S. Pilari, W. Huisinga
Zeitschrift: J. Pharmacokinet. Pharmacodyn.
Seiten: 87-107
Band: 41
Link zur Publikation
,
Suppl Material (Matlab code)
Monoclonal antibody disposition: a simplified PBPK model and its implications for the derivation and interpretation of classical compartment models
Autoren: L. Fronton, S. Pilari, W. Huisinga
(2014)
Zeitschrift:
J. Pharmacokinet. Pharmacodyn.
2014 | Quantifying the degree of persistence in random amoeboid motion based on the Hurst exponent of fractional Brownian motion | N. Makarava, S. Menz, M. Theves, W. Huisinga, C. Beta, M. Holschneider
Zeitschrift: Phys Rev E 90, 042703
Link zur Publikation
Quantifying the degree of persistence in random amoeboid motion based on the Hurst exponent of fractional Brownian motion
Autoren: N. Makarava, S. Menz, M. Theves, W. Huisinga, C. Beta, M. Holschneider
(2014)
Zeitschrift:
Phys Rev E 90, 042703
2014 | Estimating HIV-1 Fitness Characteristics from Cross-sectional Genotype Data | S. Gopalakrishnan, H. Montazeri, S. Menz, N. Beerenwinkel, W. Huisinga
Zeitschrift: PLoS Computational Biology
Seiten: 1-14
Band: 10
Link zur Publikation
,
e1003886, Suppl Material (R and Matlab code)
Estimating HIV-1 Fitness Characteristics from Cross-sectional Genotype Data
Autoren: S. Gopalakrishnan, H. Montazeri, S. Menz, N. Beerenwinkel, W. Huisinga
(2014)
Zeitschrift:
PLoS Computational Biology
2014 | he subsemigroups of the full transformation semigroup T_n in the ideal K(n,2) satisfying x^k=x | Jende, A., Koppitz, J. and Musunthia, T.
Zeitschrift: Southeast Asian Bulletin of Mathematics
Band: 34
he subsemigroups of the full transformation semigroup T_n in the ideal K(n,2) satisfying x^k=x
Autoren: Jende, A., Koppitz, J. and Musunthia, T.
(2014)
Zeitschrift:
Southeast Asian Bulletin of Mathematics
2014 | Maximal Subsemigroups containing a particular semigroup | Koppitz, J. and Musunthia, T.
Zeitschrift: Mathematica Slovaca
Band: 64
Maximal Subsemigroups containing a particular semigroup
Autoren: Koppitz, J. and Musunthia, T.
(2014)
Zeitschrift:
Mathematica Slovaca
2014 | Density problems on vector bundles and manifolds | Lashi Bandara
Zeitschrift: Proc. Amer. Math. Soc.
Verlag: AMS
Seiten: 2683-2695
Band: 142, no. 8
Link zur Publikation
,
Link zum Preprint
Density problems on vector bundles and manifolds
Autoren: Lashi Bandara
(2014)
We study some canonical differential operators on vector bundles over smooth, complete Riemannian manifolds. Under very general assumptions, we show that smooth, compactly supported sections are dense in the domains of these operators. Furthermore, we show that smooth, compactly supported functions are dense in second order Sobolev spaces on such manifolds under the sole additional assumption that the Ricci curvature is uniformly bounded from below.
Zeitschrift:
Proc. Amer. Math. Soc.
2014 | An estimate of the rate of convergence of a sequence of additive functionals of difference approximations for a multidimensional diffusion process | Iu. Ganychenko
Zeitschrift: Theory of Probability and Mathematical Statistics
Band: 90
Link zur Publikation
An estimate of the rate of convergence of a sequence of additive functionals of difference approximations for a multidimensional diffusion process
Autoren: Iu. Ganychenko
(2014)
Zeitschrift:
Theory of Probability and Mathematical Statistics
2014 | Rates of approximation of nonsmooth integral-type functionals of Markov processes | Iu. Ganychenko, A. Kulik
Zeitschrift: Modern Stochastics: Theory and Applications
Reihe: 2
Seiten: 117-126
Band: 1
Link zur Publikation
Rates of approximation of nonsmooth integral-type functionals of Markov processes
Autoren: Iu. Ganychenko, A. Kulik
(2014)
Zeitschrift:
Modern Stochastics: Theory and Applications
2014 | Didactical desiderata from a sociological approach to logic | David Kollosche
Buchtitel: Aldon, Di Paola & Fazio (Hg.) Mathematics and Reality. Proceedings of CIEAEM 66
Didactical desiderata from a sociological approach to logic
Autoren: David Kollosche
(2014)
Buchtitel:
Aldon, Di Paola & Fazio (Hg.) Mathematics and Reality. Proceedings of CIEAEM 66
2014 | Mean ergodic theorems on norming dual pairs | Moritz Gerlach, Markus Kunze
Zeitschrift: Ergodic Theory and Dynamical Systems
Seiten: 1210–1229
Band: 34
Link zur Publikation
,
Link zum Preprint
Mean ergodic theorems on norming dual pairs
Autoren: Moritz Gerlach, Markus Kunze
(2014)
We extend the classical mean ergodic theorem to the setting of norming dual pairs. It turns out that, in general, not all equivalences from the Banach space setting remain valid in our situation. However, for Markovian semigroups on the norming dual pair (C_b(E), M(E)) all classical equivalences hold true under an additional assumption which is slightly weaker than the e-property.
Zeitschrift:
Ergodic Theory and Dynamical Systems
2014 | A Tauberian theorem for strong Feller semigroups | Moritz Gerlach
Zeitschrift: Archiv der Mathematik
Seiten: 245-255
Band: 3
Link zur Publikation
,
Link zum Preprint
A Tauberian theorem for strong Feller semigroups
Autoren: Moritz Gerlach
(2014)
We prove that a weakly ergodic, eventually strong Feller semigroup on the space of measures on a Polish space converges strongly to a projection onto its fixed space.
Zeitschrift:
Archiv der Mathematik
2014 | Quantized Abelian principal connections on Lorentzian manifolds | Marco Benini, Claudio Dappiaggi, Alexander Schenkel
Zeitschrift: Commun. Math. Phys.
Verlag: Springer
Seiten: 123-152
Band: 330, no. 1
Link zur Publikation
,
Link zum Preprint
Quantized Abelian principal connections on Lorentzian manifolds
Autoren: Marco Benini, Claudio Dappiaggi, Alexander Schenkel
(2014)
We construct a covariant functor from a category of Abelian principal bundles over globally hyperbolic spacetimes to a category of *-algebras that describes quantized principal connections. We work within an appropriate differential geometric setting by using the bundle of connections and we study the full gauge group, namely the group of vertical principal bundle automorphisms. Properties of our functor are investigated in detail and, similar to earlier works, it is found that due to topological obstructions the locality property of locally covariant quantum field theory is violated. Furthermore, we prove that, for Abelian structure groups containing a nontrivial compact factor, the gauge invariant Borchers-Uhlmann algebra of the vector dual of the bundle of connections is not separating on gauge equivalence classes of principal connections. We introduce a topological generalization of the concept of locally covariant quantum fields. As examples, we construct for the category of principal U(1)-bundles two natural transformations from singular homology functors to the quantum field theory functor that can be interpreted as the Chern class and the electric charge. In this case we also prove that the electric charges can be consistently set to zero, which yields another quantum field theory functor that satisfies all axioms of locally covariant quantum field theory.
Zeitschrift:
Commun. Math. Phys.
2014 | A C*-algebra for quantized Abelian principal U(1)-connections on globally hyperbolic Lorentzian manifolds | Marco Benini, Claudio Dappiaggi, Thomas-Paul Hack, Alexander Schenkel
Zeitschrift: Commun. Math. Phys.
Verlag: Springer
Seiten: 477-504
Band: 332, no. 1
Link zur Publikation
,
Link zum Preprint
A C*-algebra for quantized Abelian principal U(1)-connections on globally hyperbolic Lorentzian manifolds
Autoren: Marco Benini, Claudio Dappiaggi, Thomas-Paul Hack, Alexander Schenkel
(2014)
The aim of this work is to complete our program on the quantization of connections on arbitrary principal U(1)-bundles over globally hyperbolic Lorentzian manifolds. In particular, we show that one can assign via a covariant functor to any such bundle an algebra of observables which separates gauge equivalence classes of connections. The C*-algebra we construct generalizes the usual CCR-algebras since, contrary to the standard field-theoretic models, it is based on a presymplectic Abelian group instead of a symplectic vector space. We prove a no-go theorem according to which neither this functor, nor any of its quotients, satisfies the strict axioms of general local covariance. As a byproduct, we prove that a morphism violates the locality axiom if and only if a certain induced morphism of cohomology groups is non-injective. We then show that fixing any principal U(1)-bundle, there exists a suitable category of sub-bundles for which a quotient of our functor yields a quantum field theory in the sense of Haag and Kastler. We shall provide a physical interpretation of this feature and we obtain some new insights concerning electric charges in locally covariant quantum field theory.
Zeitschrift:
Commun. Math. Phys.
2014 | Radiative observables for linearized gravity on asymptotically flat spacetimes and their boundary induced states | Marco Benini, Claudio Dappiaggi, Simone Murro
Zeitschrift: J. Math. Phys.
Verlag: American Institute of Physics
Seiten: Art. ID: 082301
Link zur Publikation
,
Link zum Preprint
Radiative observables for linearized gravity on asymptotically flat spacetimes and their boundary induced states
Autoren: Marco Benini, Claudio Dappiaggi, Simone Murro
(2014)
We discuss the quantization of linearized gravity on globally hyperbolic, asymptotically flat, vacuum spacetimes and the construction of distinguished states which are both of Hadamard form and invariant under the action of all bulk isometries. The procedure, we follow, consists of looking for a realization of the observables of the theory as a sub-algebra of an auxiliary, non-dynamical algebra constructed on future null infinity ℑ+. The applicability of this scheme is tantamount to proving that a solution of the equations of motion for linearized gravity can be extended smoothly to ℑ+. This has been claimed to be possible provided that a suitable gauge fixing condition, first written by Geroch and Xanthopoulos, is imposed. We review its definition critically showing that there exists a previously unnoticed obstruction in its implementation leading us to introducing the concept of radiative observables. These constitute an algebra for which a Hadamard state induced from null infinity and invariant under the action of all spacetime isometries exists and it is explicitly constructed.
Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
2014 | Locality in Abelian gauge theories over globally hyperbolic spacetimes | Marco Benini
Zeitschrift: PhD thesis
Verlag: University of Pavia
Link zum Preprint
Locality in Abelian gauge theories over globally hyperbolic spacetimes
Autoren: Marco Benini
(2014)
The thesis investigates the locality axiom of general local covariance for Abelian gauge theories. Two models, Maxwell k-forms (higher analogues of the electromagnetic vector potential) and the U(1) Yang-Mills model are analyzed over globally hyperbolic spacetimes. Our attention is mainly focused on the locality axiom of general local covariance, which states that a causal embedding between spacetimes should induce an inclusion at the level of observables. Both at the classical and at the quantum level, it turns out that the models we consider violate locality depending on certain global features of the background spacetime. For Maxwell k-forms, we prove that there is no coherent way to recover the locality axiom. For the U(1) Yang-Mills model we adopt two different approaches: in the first one locality can be recovered coherently, but the class of observables we consider fails in detecting those field configurations which correspond to the Aharonov-Bohm effect; conversely, in our second approach observables are defined in the spirit of Wilson loops (hence capturing also Aharonov-Bohm configurations), but a no-go theorem shows that locality cannot be recovered in a coherent way.
Verlag:
University of Pavia
2014 | The largest expected earthquake magnitudes in Japan: The statistical perspective | Gert Zöller, Sebastian Hainzl, Matthias Holschneider, Jianzang Zhuang
Zeitschrift: Bull. Seismol. Soc. Am.
Verlag: Seismological Society of America
Seiten: 769-779
Band: 104
Link zur Publikation
The largest expected earthquake magnitudes in Japan: The statistical perspective
Autoren: Gert Zöller, Sebastian Hainzl, Matthias Holschneider, Jianzang Zhuang
(2014)
Zeitschrift:
Bull. Seismol. Soc. Am.
Verlag:
Seismological Society of America
2014 | Can we test for the maximum possible earthquake magnitude? | Matthias Holschneider, Gert Zöller, Robert Clements, Danijel Schorlemmer
Zeitschrift: J. Geophys. Res.
Verlag: American Geophysical Union
Seiten: 2019-2028
Band: 119
Link zur Publikation
Can we test for the maximum possible earthquake magnitude?
Autoren: Matthias Holschneider, Gert Zöller, Robert Clements, Danijel Schorlemmer
(2014)
Zeitschrift:
J. Geophys. Res.
Verlag:
American Geophysical Union
2014 | Large earthquake hazard of the San Jacinto fault zone, CA, from long record of simulated seismicity assimilating the available instrumental and paleoseismic data | Gert Zöller, Yehuda Ben-Zion
Zeitschrift: Pure Appl. Geophys
Verlag: Springer
Seiten: 2955-2965
Band: 171
Link zur Publikation
Large earthquake hazard of the San Jacinto fault zone, CA, from long record of simulated seismicity assimilating the available instrumental and paleoseismic data
Autoren: Gert Zöller, Yehuda Ben-Zion
(2014)
Zeitschrift:
Pure Appl. Geophys
2014 | Assessment of stress coupling among the inter-, co- and post- seismic phases related to the 2004 M6 Parkfield earthquake | Lifeng Wang, Sebastian Hainzl, Gert Zöller
Zeitschrift: Geophys. J. Int.
Verlag: Oxford Journals
Seiten: 1858-1868
Band: 197
Link zur Publikation
Assessment of stress coupling among the inter-, co- and post- seismic phases related to the 2004 M6 Parkfield earthquake
Autoren: Lifeng Wang, Sebastian Hainzl, Gert Zöller
(2014)
Zeitschrift:
Geophys. J. Int.
2014 | Joint determination of slip and stress drop in a Bayesian inversion approach: A case study for the 2010 M8.8 Maule earthquake | Lifeng Wang, Gert Zöller, Sebastian Hainzl
Zeitschrift: Pure Appl. Geophys
Verlag: Springer
Seiten: 375-388
Band: 172
Link zur Publikation
Joint determination of slip and stress drop in a Bayesian inversion approach: A case study for the 2010 M8.8 Maule earthquake
Autoren: Lifeng Wang, Gert Zöller, Sebastian Hainzl
(2014)
Zeitschrift:
Pure Appl. Geophys
2014 | Induced seismicity: What is the size of the largest expected earthquake? | Gert Zöller, Matthias Holschneider
Zeitschrift: Bull. Seismol. Soc. Am.
Verlag: Seismological Society of America
Seiten: 3153-3158
Band: 104
Link zur Publikation
Induced seismicity: What is the size of the largest expected earthquake?
Autoren: Gert Zöller, Matthias Holschneider
(2014)
Zeitschrift:
Bull. Seismol. Soc. Am.
Verlag:
Seismological Society of America
2014 | Schonend melken ohne Haftvakuum | Ulrich Ströbel, Sandra Rose-Meierhöfer, Reiner Brunsch, Toni Luhdo
Zeitschrift: agrarmanager
Seiten: 58-61
Band: 11
Schonend melken ohne Haftvakuum
Autoren: Ulrich Ströbel, Sandra Rose-Meierhöfer, Reiner Brunsch, Toni Luhdo
(2014)
Zeitschrift:
agrarmanager
2014 | Analytical calculation of flow profiles and forces between teatcup and teat | Toni Luhdo, Ulrich Ströbel, Sandra Rose-Meierhöfer
Zeitschrift: Proceedings. International Conference of Agricultural Engineering AgEng 2014
Link zur Publikation
Analytical calculation of flow profiles and forces between teatcup and teat
Autoren: Toni Luhdo, Ulrich Ströbel, Sandra Rose-Meierhöfer
(2014)
Zeitschrift:
Proceedings. International Conference of Agricultural Engineering AgEng 2014
2014 | Development of a vacuum control system and vacuum adaption system for the teat-end vacuum in modern milking systems | Ulrich Ströbel, Sandra Rose-Meierhöfer, Toni Luhdo, Reiner Brunsch
Zeitschrift: Proceedings. ASABE and CSBE - SCGAB Annual International Meeting 2014
Link zur Publikation
Development of a vacuum control system and vacuum adaption system for the teat-end vacuum in modern milking systems
Autoren: Ulrich Ströbel, Sandra Rose-Meierhöfer, Toni Luhdo, Reiner Brunsch
(2014)
Zeitschrift:
Proceedings. ASABE and CSBE - SCGAB Annual International Meeting 2014
2014 | Analytical calculation of flow profiles and forces between teatcup and teat | Toni Luhdo, Ulrich Ströbel, Sandra Rose-Meierhöfer
Zeitschrift: Proceedings. ASABE and CSBE - SCGAB Annual International Meeting 2014
Link zur Publikation
Analytical calculation of flow profiles and forces between teatcup and teat
Autoren: Toni Luhdo, Ulrich Ströbel, Sandra Rose-Meierhöfer
(2014)
Zeitschrift:
Proceedings. ASABE and CSBE - SCGAB Annual International Meeting 2014
2014 | Bayesian inversion for the filtered flow at the Earth's core-mantle boundary | Julien Baerenzung, Matthias Holschneider, Vincent Lesur
Zeitschrift: Journal of Geophysical Research: Solid Earth
Seiten: 2695-2720
Band: 119
Link zur Publikation
Bayesian inversion for the filtered flow at the Earth's core-mantle boundary
Autoren: Julien Baerenzung, Matthias Holschneider, Vincent Lesur
(2014)
Zeitschrift:
Journal of Geophysical Research: Solid Earth
2014 | Inverse Sturm-Liouville Problems with Pseudospectral Methods | H. Altundag, C. Böckmann, H. Taseli
Zeitschrift: International Journal of Computer Mathematics
Seiten: 1--13
Band: 91
Link zur Publikation
Inverse Sturm-Liouville Problems with Pseudospectral Methods
Autoren: H. Altundag, C. Böckmann, H. Taseli
(2014)
Zeitschrift:
International Journal of Computer Mathematics
2014 | Runge-Kutta type regularization method for inversion of spheroidal particle distribution from limited optical data | C. Böckmann, L. Osterloh
Zeitschrift: Inverse Problems in Science and Engineering
Seiten: 150-165
Band: 22
Link zur Publikation
Runge-Kutta type regularization method for inversion of spheroidal particle distribution from limited optical data
Autoren: C. Böckmann, L. Osterloh
(2014)
Zeitschrift:
Inverse Problems in Science and Engineering
2014 | On the theory of mass conserving transformations for Lagrangian methods in 3D atmosphere-chemistry models | V. Grewe, S. Brinkop, P. Joeckel, S. Shin, S. Reich, H. Yserentant,
Zeitschrift: Meteorologische Zeitschrift
Seiten: 441-447
Band: 23
Link zur Publikation
On the theory of mass conserving transformations for Lagrangian methods in 3D atmosphere-chemistry models
Autoren: V. Grewe, S. Brinkop, P. Joeckel, S. Shin, S. Reich, H. Yserentant,
(2014)
Zeitschrift:
Meteorologische Zeitschrift
2014 | On the consistency of ensemble transform filter formulations. Journal of Computational Dynamics | S. Reich and S. Shin
Zeitschrift: Journal of Computational Dynamics
Seiten: 177-189
Band: 1
Link zur Publikation
On the consistency of ensemble transform filter formulations. Journal of Computational Dynamics
Autoren: S. Reich and S. Shin
(2014)
Zeitschrift:
Journal of Computational Dynamics
2014 | Ensemble transform Kalman-Bucy filter | J. Amezcua, E. Kalnay, K. Ide, S. Reich
Zeitschrift: Q.J. Royal Meteorological Soc
Seiten: 995-1004
Band: 140
Link zur Publikation
Ensemble transform Kalman-Bucy filter
Autoren: J. Amezcua, E. Kalnay, K. Ide, S. Reich
(2014)
Zeitschrift:
Q.J. Royal Meteorological Soc
2014 | A class of elliptic operators on a manifold with edge and boundary | N. Habal, B.-W. Schulze, and W. Rungrottheera
Zeitschrift: Trends in Mathematics, Fourier Analysis
A class of elliptic operators on a manifold with edge and boundary
Autoren: N. Habal, B.-W. Schulze, and W. Rungrottheera
(2014)
Zeitschrift:
Trends in Mathematics, Fourier Analysis
2014 | An extremal problem related to analytic continuation | O. Makhmudov and N. Tarkhanov
Zeitschrift: Mathematics and Physics 7
Reihe: no. 1
Seiten: 79--90
An extremal problem related to analytic continuation
Autoren: O. Makhmudov and N. Tarkhanov
(2014)
Zeitschrift:
Mathematics and Physics 7
2014 | Asymptotic solutions of the Dirichlet problem for the heat equation at a characteristic point | A, Antoniouk, O. Kiselev and N. Tarkhanov
Zeitschrift: Ukrainian Math. J. 66
Reihe: no. 10
Seiten: 1299--1317
Asymptotic solutions of the Dirichlet problem for the heat equation at a characteristic point
Autoren: A, Antoniouk, O. Kiselev and N. Tarkhanov
(2014)
Zeitschrift:
Ukrainian Math. J. 66
2014 | Asymptotics in weighted corner spaces | X. Lyu
Zeitschrift: Asian-European Journal of Mathematics
Reihe: Vol.7
Seiten: 1450050-1-1450050-36
Asymptotics in weighted corner spaces
Autoren: X. Lyu
(2014)
Zeitschrift:
Asian-European Journal of Mathematics
Seiten:
1450050-1-1450050-36
2014 | Conical zeta values and their double subdivision relations | L. Guo, S. Paycha and B. Zhang
Zeitschrift: Adv. in Math.
Seiten: p. 343-381
Conical zeta values and their double subdivision relations
Autoren: L. Guo, S. Paycha and B. Zhang
(2014)
Zeitschrift:
Adv. in Math.
2014 | Counterterms in the context of the universal Hopf algebra of renormalization | A. Shojaei-Fard
Zeitschrift: International Journal of Modern Physics A,
Reihe: Vol. 29
Seiten: 1450045 (15 pages)
Counterterms in the context of the universal Hopf algebra of renormalization
Autoren: A. Shojaei-Fard
(2014)
Zeitschrift:
International Journal of Modern Physics A,
Seiten:
1450045 (15 pages)
2014 | Differential invariants of a class of Lagrangian systems with two degrees of freedom | Yu. Bagderina and N. Tarkhanov
Zeitschrift: J. Math. Anal. Appl. 410
Seiten: 733--749
Differential invariants of a class of Lagrangian systems with two degrees of freedom
Autoren: Yu. Bagderina and N. Tarkhanov
(2014)
Zeitschrift:
J. Math. Anal. Appl. 410
2014 | Flat bundles, von Neumann algebras and K-theory with R/Z - coefficients | Paolo Antonini, Sara Azzali, Georges Skandalis
Zeitschrift: Journal of K-theory vol 13
Reihe: Issue 2
Seiten: pp. 275-303
Flat bundles, von Neumann algebras and K-theory with R/Z - coefficients
Autoren: Paolo Antonini, Sara Azzali, Georges Skandalis
(2014)
Zeitschrift:
Journal of K-theory vol 13
2014 | Generalised Beltrami equations | I. Ly and N. Tarkhanov
Zeitschrift: Complex Variables and Elliptic Equations 59
Generalised Beltrami equations
Autoren: I. Ly and N. Tarkhanov
(2014)
Zeitschrift:
Complex Variables and Elliptic Equations 59
2014 | Iterative properties of pseudo-differential operators on edge spaces | W. Rungrottheera and B.-W. Schulze, and M.W. Wong
Zeitschrift: J. Pseudo-Differ. Oper. Appl. (2014) textbf{5}
Seiten: 455?479
Iterative properties of pseudo-differential operators on edge spaces
Autoren: W. Rungrottheera and B.-W. Schulze, and M.W. Wong
(2014)
Zeitschrift:
J. Pseudo-Differ. Oper. Appl. (2014) textbf{5}
2014 | Normally solvable nonlinear boundary value problems | A. Alsaedy and N. Tarkhanov
Zeitschrift: Nonlinear Analysis 95
Seiten: 468--482
Normally solvable nonlinear boundary value problems
Autoren: A. Alsaedy and N. Tarkhanov
(2014)
Zeitschrift:
Nonlinear Analysis 95
2014 | Scattering of trajectories at a separatrix under autoresonance | O. Kiselev and N. Tarkhanov.
Zeitschrift: J. Math. Phys. 55
Reihe: Issue 5
Scattering of trajectories at a separatrix under autoresonance
Autoren: O. Kiselev and N. Tarkhanov.
(2014)
Zeitschrift:
J. Math. Phys. 55
2014 | The canonical trace and the noncommutative residue on the noncommutative torus | C. Lévy, C. Neira-Jimenez, S. Paycha
Zeitschrift: To appear in Trans. Amer. Math. Soc.
The canonical trace and the noncommutative residue on the noncommutative torus
Autoren: C. Lévy, C. Neira-Jimenez, S. Paycha
(2014)
Zeitschrift:
To appear in Trans. Amer. Math. Soc.
2014 | The capture of a particle into resonance at potential hole with dissipative perturbation | O. Kiselev and N. Tarkhanov
Zeitschrift: Chaos, Solitons and Fractals 58 (2014)
Seiten: 27--39
The capture of a particle into resonance at potential hole with dissipative perturbation
Autoren: O. Kiselev and N. Tarkhanov
(2014)
Zeitschrift:
Chaos, Solitons and Fractals 58 (2014)
2014 | The edge algebra structure of the Zaremba problem | D.-C. Chang, N. Habal, and B.-W. Schulze
Zeitschrift: J. Pseudo-Differ. Oper. Appl. 5,
Seiten: 69-155
The edge algebra structure of the Zaremba problem
Autoren: D.-C. Chang, N. Habal, and B.-W. Schulze
(2014)
Zeitschrift:
J. Pseudo-Differ. Oper. Appl. 5,
2014 | Weighted spaces on corner manifolds | W. Rungrottheera and B.-W. Schulze
Zeitschrift: Complex Variables and Elliptic Equations, 59, 12
Seiten: 1706-1738
Weighted spaces on corner manifolds
Autoren: W. Rungrottheera and B.-W. Schulze
(2014)
Zeitschrift:
Complex Variables and Elliptic Equations, 59, 12
2014 | Mathe verstehen durch Papierfalten. Anleitungen und Arbeitsblätter für die Sekundarstufe | Heiko Etzold, Ines Petzschler
Verlag: Mülheim an der Ruhr
Mathe verstehen durch Papierfalten. Anleitungen und Arbeitsblätter für die Sekundarstufe
Autoren: Heiko Etzold, Ines Petzschler
(2014)
Verlag:
Mülheim an der Ruhr
2014 | Intelligentes Üben im Spiel | Heiko Etzold, Ines Petzschler
Zeitschrift: mathematik lehren
Verlag: Friedrich Verlag
Seiten: 6-9
Band: 186
Intelligentes Üben im Spiel
Autoren: Heiko Etzold, Ines Petzschler
(2014)
Zeitschrift:
mathematik lehren
2014 | On the evolution of hypersurfaces by their inverse null mean curvature | Kristen Moore
Zeitschrift: J. Differential Geom.
Seiten: 425-466
Band: 98
Link zur Publikation
On the evolution of hypersurfaces by their inverse null mean curvature
Autoren: Kristen Moore
(2014)
Zeitschrift:
J. Differential Geom.
2014 | Eine Stadt von allen Seiten - MatheWelt-Heft | Heiko Etzold, Thomas Krohn, Ines Petzschler, Silvia Schöneburg
Zeitschrift: mathematik lehren
Verlag: Friedrich Verlag
Band: 186
Eine Stadt von allen Seiten - MatheWelt-Heft
Autoren: Heiko Etzold, Thomas Krohn, Ines Petzschler, Silvia Schöneburg
(2014)
Zeitschrift:
mathematik lehren
2014 | An Explorative Study of Search of Model Space in Problem Solving | Saskia Kistner, Bruce Burns, Regina Vollmeyer, Ulrich Kortenkamp
Zeitschrift: Journal of Cognitive Psychology
Link zur Publikation
An Explorative Study of Search of Model Space in Problem Solving
Autoren: Saskia Kistner, Bruce Burns, Regina Vollmeyer, Ulrich Kortenkamp
(2014)
Zeitschrift:
Journal of Cognitive Psychology
2014 | Early Mathematics Learning - Selected Papers of the POEM 2012 Conference | Ulrich Kortenkamp, Birgit Brandt, Christiane Benz, Götz Krummheuer, Silke Ladel, Rose Vogel
Verlag: Springer-Verlag
Link zur Publikation
Early Mathematics Learning - Selected Papers of the POEM 2012 Conference
Autoren: Ulrich Kortenkamp, Birgit Brandt, Christiane Benz, Götz Krummheuer, Silke Ladel, Rose Vogel
(2014)
2014 | „Ist das dann noch ein Zehner oder ist das dann ein Einer?'' - Zu einem flexiblen Verständnis von Stellenwerten | Silke Ladel, Ulrich Kortenkamp
Verlag: WTM Verlag
Buchtitel: Beiträge zum Mathematikunterricht. Vorträge auf der 48. Tagung für Didaktik der Mathematik in Koblenz
„Ist das dann noch ein Zehner oder ist das dann ein Einer?'' - Zu einem flexiblen Verständnis von Stellenwerten
Autoren: Silke Ladel, Ulrich Kortenkamp
(2014)
Buchtitel:
Beiträge zum Mathematikunterricht. Vorträge auf der 48. Tagung für Didaktik der Mathematik in Koblenz
2014 | Number concepts - processes of internalization and externalization by the use of multi-touch technology | Silke Ladel, Ulrich Kortenkamp
Buchtitel: Early Mathematics Learning
Number concepts - processes of internalization and externalization by the use of multi-touch technology
Autoren: Silke Ladel, Ulrich Kortenkamp
(2014)
Buchtitel:
Early Mathematics Learning
2014 | Open Discovery Space - Austausch von Open Educational Resources in einem zentralen Netzwerk | Christoph Bail, Ulrich Kortenkamp, Paul Libbrecht
Zeitschrift: Friedrich-Ebert-Stiftung
Buchtitel: Schöne neue Welt? Open Educational Resources an Schulen
Link zur Publikation
Open Discovery Space - Austausch von Open Educational Resources in einem zentralen Netzwerk
Autoren: Christoph Bail, Ulrich Kortenkamp, Paul Libbrecht
(2014)
Zeitschrift:
Friedrich-Ebert-Stiftung
Buchtitel:
Schöne neue Welt? Open Educational Resources an Schulen
2014 | So rechnet Deutschland - Ergebnisse und Hypothesen einer Umfrage | Ulrich Kortenkamp, Anselm Lambert
Verlag: WTM Verlag
So rechnet Deutschland - Ergebnisse und Hypothesen einer Umfrage
Autoren: Ulrich Kortenkamp, Anselm Lambert
(2014)
2014 | Tätigkeitsorientiert zu einem flexiblen Verständnis von Stellenwerten - Ein Ansatz aus Sicht der Artefact-Centric Activity Theory | Silke Ladel, Ulrich Kortenkamp
Buchtitel: Lernen, Lehren und Forschen mit digitalen Medien
Band: 2
Tätigkeitsorientiert zu einem flexiblen Verständnis von Stellenwerten - Ein Ansatz aus Sicht der Artefact-Centric Activity Theory
Autoren: Silke Ladel, Ulrich Kortenkamp
(2014)
Buchtitel:
Lernen, Lehren und Forschen mit digitalen Medien
2014 | Mathematics and Power: An Alliance in the Foundations of Mathematics and its Teaching | David Kollosche
Zeitschrift: ZDM. The International Journal on Mathematics Education
Mathematics and Power: An Alliance in the Foundations of Mathematics and its Teaching
Autoren: David Kollosche
(2014)
Zeitschrift:
ZDM. The International Journal on Mathematics Education
2014 | Gesellschaftliche Funktionen des Mathematikunterrichts. Ein soziologischer Beitrag zum kritischen Verständnis mathematischer Bildung | David Kollosche
Verlag: Springer
Gesellschaftliche Funktionen des Mathematikunterrichts. Ein soziologischer Beitrag zum kritischen Verständnis mathematischer Bildung
Autoren: David Kollosche
(2014)
2014 | Propagation of Gibbsianness for infinite-dimensional diffusions with space-time interaction | S. Roelly, W. Ruszel
Zeitschrift: Markov Proc. Rel. Fields
Seiten: 653-674
Band: 20
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,
Link zum Preprint
Propagation of Gibbsianness for infinite-dimensional diffusions with space-time interaction
Autoren: S. Roelly, W. Ruszel
(2014)
Zeitschrift:
Markov Proc. Rel. Fields
2014 | The exit problem from the neighborhood of a global attractor for heavy-tailed Lévy diffusions | M. Högele, I. Pavlyukevich
Zeitschrift: Stoch. Anal. Appl.
Seiten: 163-190
Band: 32-1
Link zum Preprint
The exit problem from the neighborhood of a global attractor for heavy-tailed Lévy diffusions
Autoren: M. Högele, I. Pavlyukevich
(2014)
Zeitschrift:
Stoch. Anal. Appl.
2014 | Begriffsbildung zum Winkel in der Sek I: Auf der Suche nach Grundvorstellungen | Christian Dohrmann, Ana Kuzle
Zeitschrift: Tagungsband der 48. Jahrestagung der Gesellschaft für Didaktik der Mathematik
Seiten: 301-304
Begriffsbildung zum Winkel in der Sek I: Auf der Suche nach Grundvorstellungen
Autoren: Christian Dohrmann, Ana Kuzle
(2014)
Zeitschrift:
Tagungsband der 48. Jahrestagung der Gesellschaft für Didaktik der Mathematik
2014 | Reciprocal processes: A measure-theoretical point of view | C. Léonard, S. Roelly, J.C. Zambrini
Zeitschrift: Probability Surveys
Seiten: 237-269
Band: 11
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,
Link zum Preprint
Reciprocal processes: A measure-theoretical point of view
Autoren: C. Léonard, S. Roelly, J.C. Zambrini
(2014)
Zeitschrift:
Probability Surveys
2014 | Unpacking Children's Angle Grundvorstellungen: The Case of Distance “Grundvorstellung of 1° Angle | Ana Kuzle, Christian Dohrmann
Zeitschrift: Proceedings of PME 38
Unpacking Children's Angle Grundvorstellungen: The Case of Distance “Grundvorstellung of 1° Angle
Autoren: Ana Kuzle, Christian Dohrmann
(2014)
Zeitschrift:
Proceedings of PME 38
2014 | Asymptotic Properties of Coupled Forward Backward Stochastic Differential Equations | A. B. Cruzeiro, A.Oliveira Gomes, L. Zhang
Zeitschrift: Stoch. Dyn.
Band: 14
Link zur Publikation
Asymptotic Properties of Coupled Forward Backward Stochastic Differential Equations
Autoren: A. B. Cruzeiro, A.Oliveira Gomes, L. Zhang
(2014)
2014 | Fermi verbindet - Die Fußball-WM 2014 in Brasilien und der Mathematikunterricht | Silke Fleckenstein
Zeitschrift: Zeitschrift Grundschule
Seiten: 15 - 20
Band: 2
Fermi verbindet - Die Fußball-WM 2014 in Brasilien und der Mathematikunterricht
Autoren: Silke Fleckenstein
(2014)
Zeitschrift:
Zeitschrift Grundschule
2014 | Transportation distance between the Lévy measures and stochastic equations for Lévy-type processes | T. Kosenkova, A. Kulik
Zeitschrift: Modern Stochastics: Theory and Applications No 1, Vol. 1, (2014)
Link zur Publikation
Transportation distance between the Lévy measures and stochastic equations for Lévy-type processes
Autoren: T. Kosenkova, A. Kulik
(2014)
Zeitschrift:
Modern Stochastics: Theory and Applications No 1, Vol. 1, (2014)
2014 | Mass endomorphism, surgery and perturbations | Bernd Ammann, Mattias Dahl, Andreas Hermann, Emmanuel Humbert
Zeitschrift: Ann. Inst. Fourier
Verlag: UJF Grenoble
Seiten: 467-487
Band: 64, no. 2
Link zur Publikation
,
Link zum Preprint
Mass endomorphism, surgery and perturbations
Autoren: Bernd Ammann, Mattias Dahl, Andreas Hermann, Emmanuel Humbert
(2014)
We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.
Zeitschrift:
Ann. Inst. Fourier
2014 | Differential Characters and Geometric Chains | Christian Bär, Christian Becker
Reihe: Lecture Notes in Mathematics
Verlag: Springer
Buchtitel: C. Bär, C. Becker: Differential Characters
Seiten: 1-90
Band: 2112
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,
Link zum Preprint
Differential Characters and Geometric Chains
Autoren: Christian Bär, Christian Becker
(2014)
We study Cheeger-Simons differential characters and provide geometric descriptions of the ring structure and of the fiber integration map. The uniqueness of differential cohomology (up to unique natural transformation) is proved by deriving an explicit formula for any natural transformation between a differential cohomology theory and the model given by differential characters. Fiber integration for fibers with boundary is treated in the context of relative differential characters. As applications we treat higher-dimensional holonomy, parallel transport, and transgression.
Reihe:
Lecture Notes in Mathematics
Buchtitel:
C. Bär, C. Becker: Differential Characters
2014 | Differential Characters | Christian Bär, Christian Becker
Reihe: Lecture Notes in Mathematics
Verlag: Springer
Band: 2112
Link zur Publikation
Differential Characters
Autoren: Christian Bär, Christian Becker
(2014)
This text provides a systematic introduction to differential characters, as introduced by Cheeger and Simons. Differential characters form a model of what is nowadays called differential cohomology. In degree 2, integral cohomology of a space X classifies U(1)-bundles over X via the first Chern class, while differential characters correspond to U(1)-bundles with a connection. Similarly, in degree 3, integral cohomology classes classify gerbes over X while differential characters correspond to gerbes with additional geometric structure. We construct the product which provides differential cohomology with a ring structure and we describe the fiber integration map. In both cases, we show uniqueness in the sense that these operations are determined by certain natural axioms. This shows in particular that the various very different descriptions in the literature are equivalent. We present natural and explicit geometric formulas for both the product and the fiber integration map. The underlying space X may be more general than a finite-dimensional manifold. We allow for “smooth spaces” which contains loop spaces of manifolds, for instance. This is important for applications like the transgression map. Up to now, there does not exist much literature on the relative version of differential characters. We investigate them in detail. In degree 2, a relative differential character corresponds to a U(1)-bundle with connection and a section over a subspace. We derive long exact sequences which relate absolute and relative differential characters. Fiber integration for fibers with boundary is naturally considered in the relative framework. The module structure of relative differential cohomology over the ring of absolute differential characters is derived. We discuss various applications including chain field theories and higher dimensional holonomies which occur as actions in string theory.
Reihe:
Lecture Notes in Mathematics
2014 | Relative differential cohomology | Christian Becker
Reihe: Lecture Notes in Mathematics
Verlag: Springer
Buchtitel: C. Bär, C. Becker: Differential Characters
Seiten: 91-180
Band: 2112
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,
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Relative differential cohomology
Autoren: Christian Becker
(2014)
We study two notions of relative differential cohomology, using the model of differential characters. The two notions arise from the two options to construct relative homology, either by cycles of a quotient complex or of a mapping cone complex. We discuss the relation of the two notions of relative differential cohomology to each other. We discuss long exact sequences for both notions, thereby clarifying their relation to absolute differential cohomology. We construct the external and internal product of relative and absolute characters and show that relative differential cohomology is a right module over the absolute differential cohomology ring. Finally we construct fiber integration and transgression for relative differential characters.
Reihe:
Lecture Notes in Mathematics
Buchtitel:
C. Bär, C. Becker: Differential Characters
2014 | The subsemigroups of the full transformation semigroup T_n in the ideal K(n,2) satisfying x^k=x | Jörg Koppitz, Alexander Jende, Tiwadee Musunthia
Zeitschrift: Asian Bulletin of Mathematics
Seiten: 369-382
Band: 38
The subsemigroups of the full transformation semigroup T_n in the ideal K(n,2) satisfying x^k=x
Autoren: Jörg Koppitz, Alexander Jende, Tiwadee Musunthia
(2014)
Zeitschrift:
Asian Bulletin of Mathematics
2014 | Maximal subsemigroups containing a particular semigroup | Jörg Koppitz, Tiwadee Musunthia
Zeitschrift: Mathematica Slovaca
Seiten: 1369-1380
Band: 64/6
Maximal subsemigroups containing a particular semigroup
Autoren: Jörg Koppitz, Tiwadee Musunthia
(2014)
Zeitschrift:
Mathematica Slovaca
2014 | A Supermanifold structure on Spaces of Morphisms between Supermanifolds | Florian Hanisch
Link zum Preprint
A Supermanifold structure on Spaces of Morphisms between Supermanifolds
Autoren: Florian Hanisch
(2014)
The aim of this work is the construction of a "supermanifold of morphisms X→Y", given two finite-dimensional supermanifolds X and Y. More precisely, we will define an object SC∞(X,Y) in the category of supermanifolds proposed by Molotkov and Sachse. Initially, it is given by the set-valued functor characterised by the adjunction formula Hom(PxX, Y) ≅ Hom(P, SC∞(X,Y)) where P ranges over all superpoints. We determine the structure of this functor in purely geometric terms: We show that it takes values in the set of certain differential operators and establish a bijective correspondence to the set of sections in certain vector bundles associated to X and Y. Equipping these spaces of sections with infinite-dimensional manifold structures using the convenient setting by Kriegl and Michor, we obtain at a supersmooth structure on SC∞(X,Y), i.e. a supermanifold of all morphisms X→Y.
2014 | Zero sets of eigenspinors for generic metrics | Andreas Hermann
Zeitschrift: Comm. Anal. Geom.
Verlag: International Press
Seiten: 177-218
Band: 22, no. 2
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,
Link zum Preprint
Zero sets of eigenspinors for generic metrics
Autoren: Andreas Hermann
(2014)
Let M be a closed connected spin manifold of dimension 2 or 3 with a fixed orientation and a fixed spin structure. We prove that for a generic Riemannian metric on M the non-harmonic eigenspinors of the Dirac operator are nowhere zero. The proof is based on a transversality theorem and the unique continuation property of the Dirac operator.
Zeitschrift:
Comm. Anal. Geom.
Verlag:
International Press
2014 | Agmon-type estimates for a class of jump processes | Markus Klein, Christian Leonard, Elke Rosenberger
Zeitschrift: Mathematische Nachrichten
Seiten: 2021 – 2039
Band: 287, Nr. 1
Link zur Publikation
Agmon-type estimates for a class of jump processes
Autoren: Markus Klein, Christian Leonard, Elke Rosenberger
(2014)
In the limit <tex>\varepsilon \to 0</tex> we analyze the generators <tex>H_\varepsilon</tex> of families of reversible jump processes in <tex>R^d </tex>associated with a class of symmetric non-local Dirichlet-forms and show exponential decay of the eigenfunctions.
The exponential rate function is a Finsler distance, given as solution of a certain eikonal equation. Fine results are sensitive to the rate function being <tex>C^2</tex> or just Lipschitz.
Our estimates are analogous to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice <tex>\varepsilon Z^d</tex>.
Although our final interest is in the (sub)stochastic jump process, technically this is a pure analysis paper, inspired by PDE techniques.
Zeitschrift:
Mathematische Nachrichten
2014 | Time asymptotics of exp(ith) for analytic matrices and analytic perturbation theory | Markus Klein, Juliane Rama
Zeitschrift: Asymptotic Analysis
Seiten: 189 – 233
Band: 89, Nr. 3-
Time asymptotics of exp(ith) for analytic matrices and analytic perturbation theory
Autoren: Markus Klein, Juliane Rama
(2014)
Zeitschrift:
Asymptotic Analysis
2014 | Vector Fields with a non-degenerate Source | Matthias Ludewig
Zeitschrift: J. Geom. Phys.
Verlag: Elsevier
Seiten: 59-76
Band: 79
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Vector Fields with a non-degenerate Source
Autoren: Matthias Ludewig
(2014)
We discuss the solution theory of operators of the form ∇X + A, acting on smooth sections of a vector bundle with connection ∇ over a manifold M, where X is a vector field having a critical point with positive linearization at some point p ∈ M. As an operator on a suitable space of smooth sections Γ∞(U, V), it fulfills a Fredholm alternative, and the same is true for the adjoint operator. Furthermore, we show that the solutions depend smoothly on the data ∇, X and A.
Zeitschrift:
J. Geom. Phys.
2014 | A Dark Sector Extension of the Almost-Commutative Standard Model | Christoph Stephan
Zeitschrift: Int. J. Mod. Phys. A
Verlag: World Scientific
Seiten: Art. ID 1450005
Band: 29, no. 1
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,
Link zum Preprint
A Dark Sector Extension of the Almost-Commutative Standard Model
Autoren: Christoph Stephan
(2014)
We consider an extension of the Standard Model within the frame work of Noncommutative Geometry. The model is based on an older model [St09] which extends the Standard Model by new fermions, a new U(1)-gauge group and, crucially, a new scalar field which couples to the Higgs field. This new scalar field allows to lower the mass of the Higgs mass from ~170 GeV, as predicted by the Spectral Action for the Standard Model, to a value of 120-130 GeV. The short-coming of the previous model lay in its inability to meet all the constraints on the gauge couplings implied by the Spectral Action. These shortcomings are cured in the present model which also features a "dark sector" containing fermions and scalar particles.
Zeitschrift:
Int. J. Mod. Phys. A
2014 | Decontamination of mutually contaminated models | Blanchard, G., Scott, C,
Zeitschrift: AISTATS 2014
Verlag: JMLR Workshop and Conference Proceedings
Seiten: 1-9
Band: 33
Decontamination of mutually contaminated models
Autoren: Blanchard, G., Scott, C,
(2014)
Zeitschrift:
AISTATS 2014
Verlag:
JMLR Workshop and Conference Proceedings
2014 | Testing over a continuum of null hypotheses with False Discovery Rate control | Blanchard, G., Delattre, S., Roquain, E.
Zeitschrift: Bernoulli
Verlag: Bernoulli Society for Mathematical Statistics and Probability
Seiten: 304-333
Band: 20
Testing over a continuum of null hypotheses with False Discovery Rate control
Autoren: Blanchard, G., Delattre, S., Roquain, E.
(2014)
Verlag:
Bernoulli Society for Mathematical Statistics and Probability
2014 | Localized Complexities for Transductive Learning | Tolstikhin, I., Blanchard, G., Kloft, M.
Zeitschrift: COLT 2014
Verlag: JMLR Workshop and Conference Proceedings
Seiten: 857-884
Band: 35
Localized Complexities for Transductive Learning
Autoren: Tolstikhin, I., Blanchard, G., Kloft, M.
(2014)
Verlag:
JMLR Workshop and Conference Proceedings
2014 | The f-Adjusted Graph Laplacian: a Diagonal Modification with a Geometric Interpretation | Kurras, S., Luxburg, U., Blanchard, G.
Zeitschrift: ICML 2014
Verlag: JMLR Workshop and Conference Proceedings
Seiten: 1530-1538
Band: 32
The f-Adjusted Graph Laplacian: a Diagonal Modification with a Geometric Interpretation
Autoren: Kurras, S., Luxburg, U., Blanchard, G.
(2014)
Verlag:
JMLR Workshop and Conference Proceedings
2014 | On least favorable configurations for step-up-down tests | Blanchard, G., Dickhaus, T., Roquain, E., Villers, F.
Zeitschrift: Statistica Sinica
Verlag: International Chinese Statistical Association
Seiten: 1-23
Band: 24
On least favorable configurations for step-up-down tests
Autoren: Blanchard, G., Dickhaus, T., Roquain, E., Villers, F.
(2014)
Zeitschrift:
Statistica Sinica
Verlag:
International Chinese Statistical Association
2014 | Decannulation of critically ill patients after long-term mechanical ventilation - predictors from clinical routine data | Maria-Dorothea Heidler, Annett salzwedel, Hannelore Liero, Michael Jöbges, Heinz Völler
Zeitschrift: Advances in Rehabilitation
Verlag: Wydawnictwo AWF Warszawa
Seiten: 5--11
Band: 28--3
Decannulation of critically ill patients after long-term mechanical ventilation - predictors from clinical routine data
Autoren: Maria-Dorothea Heidler, Annett salzwedel, Hannelore Liero, Michael Jöbges, Heinz Völler
(2014)
Zeitschrift:
Advances in Rehabilitation
Verlag:
Wydawnictwo AWF Warszawa
2013 | Polycontinuous geometries for inverse surfactant phases with more than two aqueous network domains | G. Schröder-Turk, L. de Campo, M. E. Evans, M. Saba, S. C. Kapfer, T. Varslot, K. Grosse-Brauckmann, S. Ramsden and S. T. Hyde
Zeitschrift: Faraday Discussions 161
Seiten: 215-247
Link zur Publikation
Polycontinuous geometries for inverse surfactant phases with more than two aqueous network domains
Autoren: G. Schröder-Turk, L. de Campo, M. E. Evans, M. Saba, S. C. Kapfer, T. Varslot, K. Grosse-Brauckmann, S. Ramsden and S. T. Hyde
(2013)
Zeitschrift:
Faraday Discussions 161
2013 | Periodic entanglement I: nets from hyperbolic reticulations | M. E. Evans, V. Robins and S. Hyde
Zeitschrift: Acta Crystallographica A69
Seiten: 241-261
Link zur Publikation
Periodic entanglement I: nets from hyperbolic reticulations
Autoren: M. E. Evans, V. Robins and S. Hyde
(2013)
Zeitschrift:
Acta Crystallographica A69
2013 | Periodic entanglement II: weavings from hyperbolic line patterns | M. E. Evans, V. Robins and S. Hyde
Zeitschrift: Acta Crystallographica A69
Seiten: 262-275
Link zur Publikation
Periodic entanglement II: weavings from hyperbolic line patterns
Autoren: M. E. Evans, V. Robins and S. Hyde
(2013)
Zeitschrift:
Acta Crystallographica A69
2013 | Set Voronoi diagrams of 3D assemblies of aspherical particles | F. M. Schaller, S. C. Kapfer, M. E. Evans, M. J. F. Hoffmann, T. Aste, M. Saadatfar, K. Mecke, G. W. Delaney and G. E. Schröder-Turk
Zeitschrift: Philosophical Magazine 93(31-33)
Seiten: 3993-4017
Link zur Publikation
Set Voronoi diagrams of 3D assemblies of aspherical particles
Autoren: F. M. Schaller, S. C. Kapfer, M. E. Evans, M. J. F. Hoffmann, T. Aste, M. Saadatfar, K. Mecke, G. W. Delaney and G. E. Schröder-Turk
(2013)
Zeitschrift:
Philosophical Magazine 93(31-33)
2013 | Networklike Propagation of Cell-Level Stress in Sheared Random Foams | M. E. Evans, A. M. Kraynik, D. A. Reinelt, K. Mecke and G. E. Schröder-Turk
Zeitschrift: Physical Review Letters 111(13)
Link zur Publikation
Networklike Propagation of Cell-Level Stress in Sheared Random Foams
Autoren: M. E. Evans, A. M. Kraynik, D. A. Reinelt, K. Mecke and G. E. Schröder-Turk
(2013)
Zeitschrift:
Physical Review Letters 111(13)
2013 | A Square Root Approximation of Transition Rates for a Markov State Model | Han Cheng Lie, Konstantin Fackeldey, Marcus Weber
Zeitschrift: SIAM J. Matrix Anal. Appl.
Verlag: SIAM
Seiten: 738-756
Band: 34(2)
Link zur Publikation
A Square Root Approximation of Transition Rates for a Markov State Model
Autoren: Han Cheng Lie, Konstantin Fackeldey, Marcus Weber
(2013)
Zeitschrift:
SIAM J. Matrix Anal. Appl.
2013 | Large Scale Inverse Problems: Computational Methods and Applications in the Earth Sciences | M. Cullen, M.A. Freitag, S. Kindermann and R. Scheichl (Editors)
Reihe: Radon Series on Computational and Applied Mathematics, Vol. 13
Verlag: De Gruyter, Berlin
Link zur Publikation
Large Scale Inverse Problems: Computational Methods and Applications in the Earth Sciences
Autoren: M. Cullen, M.A. Freitag, S. Kindermann and R. Scheichl (Editors)
(2013)
Reihe:
Radon Series on Computational and Applied Mathematics, Vol. 13
Verlag:
De Gruyter, Berlin
2013 | Synergy of inverse problems and data assimilation techniques. Large Scale Inverse Problems | M.A. Freitag, R.W.E Potthast
Zeitschrift: Radon Ser. Comput. Appl. Math.
Verlag: De Gruyter
Band: 13
(Preprint)
Synergy of inverse problems and data assimilation techniques. Large Scale Inverse Problems
Autoren: M.A. Freitag, R.W.E Potthast
(2013)
Zeitschrift:
Radon Ser. Comput. Appl. Math.
2013 | The Origin of Power-Law Emergent Scaling in Large Binary Networks | D.P. Almond, C.J. Budd, M.A. Freitag, G.W. Hunt, N.J. McCullen, N.D. Smith
Zeitschrift: Phys. A
Seiten: 1004-1027
Band: 392(4)
Link zur Publikation
,
Link zum Preprint
The Origin of Power-Law Emergent Scaling in Large Binary Networks
Autoren: D.P. Almond, C.J. Budd, M.A. Freitag, G.W. Hunt, N.J. McCullen, N.D. Smith
(2013)
2013 | Resolution of sharp fronts in the presence of model error in variational data assimilation | M.A. Freitag, N.K. Nichols, C.J. Budd
Zeitschrift: Q. J. R. Meteorol. Soc.
Seiten: 742-757
Band: 139
Link zur Publikation
Resolution of sharp fronts in the presence of model error in variational data assimilation
Autoren: M.A. Freitag, N.K. Nichols, C.J. Budd
(2013)
Zeitschrift:
Q. J. R. Meteorol. Soc.
2013 | Spectrum of Lebesgue Measure Zero for Jacobi Matrices of Quasicrystals | Siegfried Beckus, Felix Pogorzelski
Zeitschrift: Mathematical Physics, Analysis and Geometry
Reihe: 16
Seiten: 289 -308
Link zur Publikation
,
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Spectrum of Lebesgue Measure Zero for Jacobi Matrices of Quasicrystals
Autoren: Siegfried Beckus, Felix Pogorzelski
(2013)
We study one-dimensional random Jacobi operators corresponding to strictly ergodic dynamical systems. We characterize the spectrum of these operators via non-uniformity of the transfer matrices and vanishing of the Lyapunov exponent. For aperiodic, minimal subshifts satisfying the so-called Boshernitzan condition this gives that the spectrum is supported on a Cantor set with Lebesgue measure zero. This generalizes earlier results for Schrödinger operators.
Zeitschrift:
Mathematical Physics, Analysis and Geometry
2013 | Category Equivalences of Clones of Operations Preserving Unary Operations | Koppitz, J. and Supaporn, W.
Zeitschrift: Comptes rendus de l´Acadèmie bulgare des Sciences
Band: 66 no. 2
Category Equivalences of Clones of Operations Preserving Unary Operations
Autoren: Koppitz, J. and Supaporn, W.
(2013)
Zeitschrift:
Comptes rendus de l´Acadèmie bulgare des Sciences
2013 | Some fixed-point results on (generalized) Bruck-Reilly *-extensions of monoids | Karpuz, E.G., Cevik, A.S., Koppitz, J. and Cangul, I.N.
Zeitschrift: Fixed Point Theory Appl.
Link zur Publikation
Some fixed-point results on (generalized) Bruck-Reilly *-extensions of monoids
Autoren: Karpuz, E.G., Cevik, A.S., Koppitz, J. and Cangul, I.N.
(2013)
Zeitschrift:
Fixed Point Theory Appl.
2013 | Willmore flow of surfaces in Riemannian spaces I: Concentration-compactness | J. Metzger, G. Wheeler, and V.-M. Wheeler
Link zum Preprint
Willmore flow of surfaces in Riemannian spaces I: Concentration-compactness
Autoren: J. Metzger, G. Wheeler, and V.-M. Wheeler
(2013)
In this paper we study the local regularity of closed surfaces immersed in a Riemannian 3-manifold flowing by Willmore flow. We establish a pair of concentration-compactness alternatives for the flow, giving a lower bound on the maximal time of existence of the flow proportional to the concentration of the curvature and area at initial time. The estimate from the first theorem is purely in terms of the concentration of curvature at initial time but applies only to ambient spaces with non-positive sectional curvature. The second requires additional information on the concentration of area at initial time but applies in more general background spaces. Applications of these results shall appear in forthcoming work.
2013 | Square roots of perturbed subelliptic operators on Lie groups | Lashi Bandara, A. F. M. ter Elst, Alan McIntosh
Zeitschrift: Studia Math.
Seiten: 193-217
Band: 216, no. 3
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,
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Square roots of perturbed subelliptic operators on Lie groups
Autoren: Lashi Bandara, A. F. M. ter Elst, Alan McIntosh
(2013)
We solve the Kato square root problem for bounded measurable perturbations of subelliptic operators on connected Lie groups. The subelliptic operators are divergence form operators with complex bounded coefficients, which may have lower order terms. In this general setting we deduce inhomogeneous estimates. In case the group is nilpotent and the subelliptic operator is pure second order, then we prove stronger homogeneous estimates. Furthermore, we prove Lipschitz stability of the estimates under small perturbations of the coefficients.
Zeitschrift:
Studia Math.
2013 | Harmonic functions of general graph Laplacians | Bobo Hua, Matthias Keller
Zeitschrift: Calculus of Variations and Partial Differential Equations
Seiten: 343-362
Band: 51
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,
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Harmonic functions of general graph Laplacians
Autoren: Bobo Hua, Matthias Keller
(2013)
We study harmonic functions on general weighted graphs which allow for a compatible intrinsic metric. We prove an \(L^{p}\) Liouville type theorem which is a quantitative integral \(L^{p}\) estimate of harmonic functions analogous to Karp’s theorem for Riemannian manifolds. As corollaries we obtain Yau’s \(L^{p}\)-Liouville type theorem on graphs, identify the domain of the generator of the semigroup on \(L^{p}\) and get a criterion for recurrence. As a side product, we show an analogue of Yau’s \(L^{p}\) Caccioppoli inequality. Furthermore, we derive various Liouville type results for harmonic functions on graphs and harmonic maps from graphs into Hadamard spaces.
Zeitschrift:
Calculus of Variations and Partial Differential Equations
2013 | On the l^p spectrum of Laplacians on graphs | Frank Bauer, Bobo Hua, Matthias Keller
Zeitschrift: Advances in Mathematics
Seiten: 717–735
Band: 248
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,
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On the l^p spectrum of Laplacians on graphs
Autoren: Frank Bauer, Bobo Hua, Matthias Keller
(2013)
We study the p-independence of spectra of Laplace operators on graphs arising from regular Dirichlet forms on discrete spaces. Here, a sufficient criterion is given solely by a uniform subexponential growth condition. Moreover, under a mild assumption on the measure we show a one-sided spectral inclusion without any further assumptions. We study applications to normalized Laplacians including symmetries of the spectrum and a characterization for positivity of the Cheeger constant. Furthermore, we consider Laplacians on planar tessellations for which we relate the spectral p-independence to assumptions on the curvature.
Zeitschrift:
Advances in Mathematics
2013 | Volume growth and bounds for the essential spectrum for Dirichlet forms | Sebastian Haeseler, Matthias Keller, Radoslaw Wojciechowski
Zeitschrift: Journal of the London Mathematical Society
Seiten: 883-898
Band: 88
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,
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Volume growth and bounds for the essential spectrum for Dirichlet forms
Autoren: Sebastian Haeseler, Matthias Keller, Radoslaw Wojciechowski
(2013)
We consider operators arising from regular Dirichlet forms with vanishing killing term. We give bounds for the bottom of the (essential) spectrum in terms of exponential volume growth with respect to an intrinsic metric. As special cases, we discuss operators on graphs. When the volume growth is measured in the natural graph distance (which is not an intrinsic metric), we discuss the threshold for positivity of the bottom of the spectrum and finiteness of the bottom of the essential spectrum of the (unbounded) graph Laplacian. This threshold is shown to lie at cubic polynomial growth.
Zeitschrift:
Journal of the London Mathematical Society
2013 | Spectral Analysis of Certain Spherically Homogeneous Graphs | Jonathan Breuer, Matthias Keller
Zeitschrift: Operators and Matrices
Seiten: 825-847
Band: 7
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Spectral Analysis of Certain Spherically Homogeneous Graphs
Autoren: Jonathan Breuer, Matthias Keller
(2013)
We study operators on rooted graphs with a certain spherical homogeneity. These graphs are called path commuting and allow for a decomposition of the adjacency matrix and the Laplacian into a direct sum of Jacobi matrices which reflect the structure of the graph. Thus, the spectral properties of the adjacency matrix and the Laplacian can be analyzed by means of the elaborated theory of Jacobi matrices. For some examples which include antitrees, we derive the decomposition explicitly and present a zoo of spectral behavior induced by the geometry of the graph. In particular, these examples show that spectral types are not at all stable under rough isometries.
Zeitschrift:
Operators and Matrices
2013 | A note on self-adjoint extensions of the Laplacian on weighted graphs | Xueping Huang, Matthias Keller, Jun Masamune, Radoslaw Wojciechowski
Zeitschrift: Journal of Functional Analysis
Seiten: 1556-1578
Band: 265
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A note on self-adjoint extensions of the Laplacian on weighted graphs
Autoren: Xueping Huang, Matthias Keller, Jun Masamune, Radoslaw Wojciechowski
(2013)
We study the uniqueness of self-adjoint and Markovian exten
sions of the Laplacian
on weighted graphs. We first show that, for locally finite grap
hs and a certain family of metrics,
completeness of the graph implies uniqueness of these exten
sions. Moreover, in the case when the
graph is not metrically complete and the Cauchy boundary has
finite capacity, we characterize
the uniqueness of the Markovian extensions
Zeitschrift:
Journal of Functional Analysis
2013 | On the spectral theory of trees with finite cone type | Matthias Keller, Daniel Lenz, Simone Warzel
Zeitschrift: Israel Journal of Mathematics
Seiten: 107-135
Band: 194
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On the spectral theory of trees with finite cone type
Autoren: Matthias Keller, Daniel Lenz, Simone Warzel
(2013)
We study basic spectral features of graph Laplacians associated with a class of rooted trees which contains all regular trees. Trees in this class can be generated by substitution processes. Their spectra are shown to be purely absolutely continuous and to consist of finitely many bands. The main result gives stability of the absolutely continuous spectrum under sufficiently small radially label symmetric perturbations for non-regular trees in this class. In sharp contrast, the absolutely continuous spectrum can be completely destroyed by arbitrary small radially label symmetric perturbations for regular trees in this class.
Zeitschrift:
Israel Journal of Mathematics
2013 | On the peripheral point spectrum and the asymptotic behavior of irreducible semigroups of Harris operators | Moritz Gerlach
Zeitschrift: Positivity
Seiten: 875–898
Band: 17
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On the peripheral point spectrum and the asymptotic behavior of irreducible semigroups of Harris operators
Autoren: Moritz Gerlach
(2013)
Given a positive, irreducible and bounded C_0-semigroup on a Banach lattice with order continuous norm, we prove that the peripheral point spectrum of its generator is trivial whenever one of its operators dominates a non-trivial compact or kernel operator. For a discrete semigroup, i.e. for powers of a single operator T, we show that the point spectrum of some power T^k intersects the unit circle at most in 1. As a consequence, we obtain a sufficient condition for strong convergence of the C_0-semigroup and for a subsequence of the powers of T, respectively.
2013 | Quantum field theories on affine bundles | Marco Benini, Claudio Dappiaggi, Alexander Schenkel
Zeitschrift: Ann. Henri Poincaré
Verlag: Springer
Seiten: 171-211
Band: 15, no. 1
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,
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Quantum field theories on affine bundles
Autoren: Marco Benini, Claudio Dappiaggi, Alexander Schenkel
(2013)
We develop a general framework for the quantization of bosonic and fermionic field theories on affine bundles over arbitrary globally hyperbolic spacetimes. All concepts and results are formulated using the language of category theory, which allows us to prove that these models satisfy the principle of general local covariance. Our analysis is a preparatory step towards a full-fledged quantization scheme for the Maxwell field, which emphasises the affine bundle structure of the bundle of principal U(1)-connections. As a by-product, our construction provides a new class of exactly tractable locally covariant quantum field theories, which are a mild generalization of the linear ones. We also show the existence of a functorial assignment of linear quantum field theories to affine ones. The identification of suitable algebra homomorphisms enables us to induce whole families of physical states (satisfying the microlocal spectrum condition) for affine quantum field theories by pulling back quasi-free Hadamard states of the underlying linear theories.
Zeitschrift:
Ann. Henri Poincaré
2013 | Quantum field theory on curved backgrounds - A primer | Marco Benini, Claudio Dappiaggi, Thomas-Paul Hack
Zeitschrift: Int. J. Mod. Phys. A
Verlag: World Scientific
Seiten: Art. ID: 1330023
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,
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Quantum field theory on curved backgrounds - A primer
Autoren: Marco Benini, Claudio Dappiaggi, Thomas-Paul Hack
(2013)
Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a suitable algebra of observables is assigned to a physical system, which is meant to encode all algebraic relations among observables, such as commutation relations, while, in the second step, one must select an algebraic state in order to recover the standard Hilbert space interpretation of a quantum system. As quantum field theories possess infinitely many degrees of freedom, many unitarily inequivalent Hilbert space representations exist and the power of such approach is the ability to treat them all in a coherent manner. We will discuss in detail the algebraic approach for free fields in order to give to the reader all necessary information to deal with the recent literature, which focuses on the applications to specific problems, mostly in cosmology.
Zeitschrift:
Int. J. Mod. Phys. A
2013 | The maximum earthquake magnitude in a time horizon: Theory and case studies | Gert Zöller, Sebastian Hainzl, Matthias Holschneider
Zeitschrift: Bull. Seismol. Soc. Am.
Verlag: Seismological Society of America
Seiten: 860-875
Band: 103
Link zur Publikation
The maximum earthquake magnitude in a time horizon: Theory and case studies
Autoren: Gert Zöller, Sebastian Hainzl, Matthias Holschneider
(2013)
Zeitschrift:
Bull. Seismol. Soc. Am.
Verlag:
Seismological Society of America
2013 | Comparison of deterministic and stochastic earthquake simulators for fault interactions in the Lower Rhine Embayment, Germany | Gert Zöller, Sebastian Hainzl, Gilbert Brietzke, Klaus-G. Hinzen
Zeitschrift: Geophys. J. Int.
Verlag: Oxford Journals
Seiten: 684-694
Band: 195
Link zur Publikation
Comparison of deterministic and stochastic earthquake simulators for fault interactions in the Lower Rhine Embayment, Germany
Autoren: Gert Zöller, Sebastian Hainzl, Gilbert Brietzke, Klaus-G. Hinzen
(2013)
Zeitschrift:
Geophys. J. Int.
2013 | Convergence of the frequency-magnitude distribution of global earthquakes: Maybe in 200 years | Gert Zöller
Zeitschrift: Geophys. Res. Lett.
Verlag: American Geophysical Union
Seiten: 3873-3877
Band: 40
Link zur Publikation
Convergence of the frequency-magnitude distribution of global earthquakes: Maybe in 200 years
Autoren: Gert Zöller
(2013)
Zeitschrift:
Geophys. Res. Lett.
Verlag:
American Geophysical Union
2013 | Untersuchung des hydrostatischen Drucks beim Halten eines Melkbechers | Toni Luhdo, Ulrich Ströbel, Sandra Rose-Meierhöfer
Zeitschrift: "Inproceedings:""Bau, Technik und Umwelt in der landwirtschaftlichen Nutztierhaltung"""
Seiten: 426-431
Band: 11
Untersuchung des hydrostatischen Drucks beim Halten eines Melkbechers
Autoren: Toni Luhdo, Ulrich Ströbel, Sandra Rose-Meierhöfer
(2013)
Zeitschrift:
"Inproceedings:""Bau, Technik und Umwelt in der landwirtschaftlichen Nutztierhaltung"""
2013 | Matrix methods for computing eigenvalues of Sturm–Liouville problems of order four | A. Rattana, C. Böckmann
Zeitschrift: Journal of Computational and Applied Mathematics
Seiten: 144-156
Band: 249
Link zur Publikation
Matrix methods for computing eigenvalues of Sturm–Liouville problems of order four
Autoren: A. Rattana, C. Böckmann
(2013)
Zeitschrift:
Journal of Computational and Applied Mathematics
2013 | Regularized Inversion of Microphysical Atmospheric Particle Parameters: Theory and Application | L. Osterloh, C. Böckmann, D. Nicolae, A. Nemuc
Zeitschrift: Journal of Computational Physics
Seiten: 79-94
Band: 237
Link zur Publikation
Regularized Inversion of Microphysical Atmospheric Particle Parameters: Theory and Application
Autoren: L. Osterloh, C. Böckmann, D. Nicolae, A. Nemuc
(2013)
Zeitschrift:
Journal of Computational Physics
2013 | A geometric perspective on counterterms related to Dyson-Schwinger equations | A. Shojaei-Fard
Zeitschrift: International Journal of Modern Physics A
Reihe: Vol. 28, No. 32
Seiten: pages 1350170-1 to 1350170-15
A geometric perspective on counterterms related to Dyson-Schwinger equations
Autoren: A. Shojaei-Fard
(2013)
Zeitschrift:
International Journal of Modern Physics A
Seiten:
pages 1350170-1 to 1350170-15
2013 | A note on Muskhelishvili-Vekua reduction | S. Grudsky and N. Tarkhanov
Zeitschrift: In: Complex Analysis and Dynamical systems, Contemporary Mathematics
Reihe: Vol. 591
Verlag: Amer. Math. Soc., Providence, RI
Seiten: 113—126
A note on Muskhelishvili-Vekua reduction
Autoren: S. Grudsky and N. Tarkhanov
(2013)
Zeitschrift:
In: Complex Analysis and Dynamical systems, Contemporary Mathematics
Verlag:
Amer. Math. Soc., Providence, RI
2013 | Conformal reduction of boundary problems for harmonic functions in a plane domain with strong singularities on the boundary | S. Grudsky and N. Tarkhanov
Zeitschrift: Mathematical Sciences 7
Reihe: no. 14
Seiten: 1—52
Conformal reduction of boundary problems for harmonic functions in a plane domain with strong singularities on the boundary
Autoren: S. Grudsky and N. Tarkhanov
(2013)
Zeitschrift:
Mathematical Sciences 7
2013 | Degeneration of boundary layer at singular points | E. Dyachenko and N. Tarkhanov,
Zeitschrift: Mathematics and Physics 6
Degeneration of boundary layer at singular points
Autoren: E. Dyachenko and N. Tarkhanov,
(2013)
Zeitschrift:
Mathematics and Physics 6
2013 | Holomorphic operator families on a manifold with edge | W. Rungrotheera and B.-W. Schulze
Zeitschrift: J. Pseudo-Differ. Oper. Appl. textbf{4}, 3
Seiten: 297-315
Holomorphic operator families on a manifold with edge
Autoren: W. Rungrotheera and B.-W. Schulze
(2013)
Zeitschrift:
J. Pseudo-Differ. Oper. Appl. textbf{4}, 3
2013 | Mellin quantisation in corner operators | N. Habal a
Zeitschrift: Operator Theory, Advances and Applications
Reihe: Vol. 228
Verlag: Birkhäuser, Basel
Seiten: pp. 151-172
Mellin quantisation in corner operators
Autoren: N. Habal a
(2013)
Zeitschrift:
Operator Theory, Advances and Applications
Verlag:
Birkhäuser, Basel
2013 | Motivic Dyson-Schwinger equations | Ali Shojaei-Fard
Zeitschrift: International Journal of Modern Physics A
Reihe: Vol. 28
Verlag: No. 20
Seiten: 1350102 (19 pages)
Motivic Dyson-Schwinger equations
Autoren: Ali Shojaei-Fard
(2013)
Zeitschrift:
International Journal of Modern Physics A
Seiten:
1350102 (19 pages)
2013 | On completeness of root functions of Sturm–Liouville problems with discontinuous boundary operators | A. Shlapunov and N. Tarkhanov
Zeitschrift: J. Differential Equations 255
Seiten: 3305—3337
On completeness of root functions of Sturm–Liouville problems with discontinuous boundary operators
Autoren: A. Shlapunov and N. Tarkhanov
(2013)
Zeitschrift:
J. Differential Equations 255
2013 | Parameter-dependent corner operators | W. Rungrotheera
Zeitschrift: Asian-Eur. J. Math. 6
Seiten: 1--29
Parameter-dependent corner operators
Autoren: W. Rungrotheera
(2013)
Zeitschrift:
Asian-Eur. J. Math. 6
2013 | A non-parametric ensemble transform method for Bayesian inference | S. Reich
Zeitschrift: SIAM J Sci Comput
Seiten: A2013-A2014
Band: 35
Link zur Publikation
A non-parametric ensemble transform method for Bayesian inference
Autoren: S. Reich
(2013)
Zeitschrift:
SIAM J Sci Comput
2013 | Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles | S. Paycha
Zeitschrift: in Geometric and Topological Methodsfor Quantum Field Theory
Verlag: Cambridge University Press
Seiten: 81-139
Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles
Autoren: S. Paycha
(2013)
Zeitschrift:
in Geometric and Topological Methodsfor Quantum Field Theory
Verlag:
Cambridge University Press
2013 | Ensemble filter techniques for intermittent data assimilation | C.J. Cotter, S. Reich
Reihe: Radon Ser. Comput. Appl. Math.
Verlag: Walter de Gruyter Verlag
Seiten: 91-134
Band: 13
Link zur Publikation
Ensemble filter techniques for intermittent data assimilation
Autoren: C.J. Cotter, S. Reich
(2013)
Reihe:
Radon Ser. Comput. Appl. Math.
Verlag:
Walter de Gruyter Verlag
2013 | Quantisation on a manifold with singular edge | D.-C. Chang, N. Habal, and B.-W. Schulze
Zeitschrift: J. Pseudo-Differ Oper Appl. 4
Seiten: 317-343
Quantisation on a manifold with singular edge
Autoren: D.-C. Chang, N. Habal, and B.-W. Schulze
(2013)
Zeitschrift:
J. Pseudo-Differ Oper Appl. 4
2013 | A guided sequential Monte Carlo method for the assimilation of data into stochastic dynamical systems. | S. Reich
Zeitschrift: Springer Proceedings in Mathematics and Statistics
Seiten: 205-220
Band: B 35
Link zur Publikation
A guided sequential Monte Carlo method for the assimilation of data into stochastic dynamical systems.
Autoren: S. Reich
(2013)
Zeitschrift:
Springer Proceedings in Mathematics and Statistics
2013 | The Dirichlet problem for the heat equation in domains with cuspidal points on the boundary | A. Antoniouk and N. Tarkhanov
Zeitschrift: In: Operator Theory: Advances and Applications
Reihe: Vol. 228
Verlag: Springer, Basel AG
Seiten: 1—20
The Dirichlet problem for the heat equation in domains with cuspidal points on the boundary
Autoren: A. Antoniouk and N. Tarkhanov
(2013)
Zeitschrift:
In: Operator Theory: Advances and Applications
Verlag:
Springer, Basel AG
2013 | The global beta- functions from solutions of Dyson-Schwinger equations | Ali Shojaei-Fard
Zeitschrift: Modern Physics Letters A
Reihe: Vol. 28
Seiten: 1350152 (12 pages)
The global beta- functions from solutions of Dyson-Schwinger equations
Autoren: Ali Shojaei-Fard
(2013)
Zeitschrift:
Modern Physics Letters A
Seiten:
1350152 (12 pages)
2013 | The Mellin-edge quantisation for corner operators | B.-W. Schulze and Y. Wei
Zeitschrift: Complex Analysis and Operator Theory
Seiten: 10.1007/s11785-013-0289-3
The Mellin-edge quantisation for corner operators
Autoren: B.-W. Schulze and Y. Wei
(2013)
Zeitschrift:
Complex Analysis and Operator Theory
Seiten:
10.1007/s11785-013-0289-3
2013 | The method of Fischer-Riesz equations for elliptic boundary value problems | A. Alsaedy and N. Tarkhanov
Zeitschrift: Journal of Complex Analysis 1
Reihe: Issue 1
Seiten: 1—11
The method of Fischer-Riesz equations for elliptic boundary value problems
Autoren: A. Alsaedy and N. Tarkhanov
(2013)
Zeitschrift:
Journal of Complex Analysis 1
2013 | What is a quantum equation of motion? | Ali Shojaei-Fard
Zeitschrift: Electronic Journal of Theoretical Physics
Reihe: Vol. 10, No. 28
What is a quantum equation of motion?
Autoren: Ali Shojaei-Fard
(2013)
Zeitschrift:
Electronic Journal of Theoretical Physics
2013 | Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions | Michael Eichmair and Jan Metzger
Zeitschrift: Invent. Math.
Seiten: 591-630
Band: 194
Link zur Publikation
Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions
Autoren: Michael Eichmair and Jan Metzger
(2013)
Zeitschrift:
Invent. Math.
2013 | Large isoperimetric surfaces in asymptotically flat manifolds | Michael Eichmair and Jan Metzger
Zeitschrift: J. Differential Geom.
Seiten: 159-186
Band: 94
Link zur Publikation
Large isoperimetric surfaces in asymptotically flat manifolds
Autoren: Michael Eichmair and Jan Metzger
(2013)
Zeitschrift:
J. Differential Geom.
2013 | Minimizers of the Willmore functional with a small area constraint | Tobias Lamm and Jan Metzger
Zeitschrift: Annales de l’Institut Henri Poincaré / Analyse non linéaire
Seiten: 497-518
Band: 30
Link zur Publikation
Minimizers of the Willmore functional with a small area constraint
Autoren: Tobias Lamm and Jan Metzger
(2013)
Zeitschrift:
Annales de l’Institut Henri Poincaré / Analyse non linéaire
2013 | Logik, Gesellschaft, Mathematik | David Kollosche
Buchtitel: Rathgeb; Helmerich; Krömer; Lengnink & Nickel (Hg.) Mathematik im Prozess. Philosophische, historische und didaktische Perspektiven.
Logik, Gesellschaft, Mathematik
Autoren: David Kollosche
(2013)
Buchtitel:
Rathgeb; Helmerich; Krömer; Lengnink & Nickel (Hg.) Mathematik im Prozess. Philosophische, historische und didaktische Perspektiven.
2013 | Evolutive two-level population process and large population approximations | S. Méléard, S. Roelly
Zeitschrift: Ann. Univ. Bucharest
Seiten: 37-70
Band: 4
Link zur Publikation
,
Link zum Preprint
Evolutive two-level population process and large population approximations
Autoren: S. Méléard, S. Roelly
(2013)
Zeitschrift:
Ann. Univ. Bucharest
2013 | Characterization of infinite divisibility by duality formulas. Application to Lévy processes and random measures | R. Murr
Zeitschrift: Stoch. Proc. Appl.
Seiten: 1729-1749
Band: 123-5
Link zur Publikation
Characterization of infinite divisibility by duality formulas. Application to Lévy processes and random measures
Autoren: R. Murr
(2013)
Zeitschrift:
Stoch. Proc. Appl.
2013 | Logic, Society and School Mathematics | David Kollosche
Buchtitel: Ubuz; Haser & Mariotto (Hg.) Proceedings of the 8th Congress of the European Society for Research in Mathematics Education
Logic, Society and School Mathematics
Autoren: David Kollosche
(2013)
Buchtitel:
Ubuz; Haser & Mariotto (Hg.) Proceedings of the 8th Congress of the European Society for Research in Mathematics Education
2013 | Reciprocal processes: a stochastic analysis approach | S. Roelly
Reihe: Springer Optimization and Its Applications
Verlag: Springer
Buchtitel: Modern Stochastics and Applications
Seiten: 53-67
Band: 90
Link zur Publikation
,
Link zum Preprint
Reciprocal processes: a stochastic analysis approach
Autoren: S. Roelly
(2013)
Reihe:
Springer Optimization and Its Applications
Buchtitel:
Modern Stochastics and Applications
2013 | On the construction of point processes in statistical mechanics. | B. Nehring, S. Poghosyan, H. Zessin
Zeitschrift: J. Math. Phys.
Band: 54-6
Link zur Publikation
On the construction of point processes in statistical mechanics.
Autoren: B. Nehring, S. Poghosyan, H. Zessin
(2013)
Zeitschrift:
J. Math. Phys.
2013 | The dynamics of nonlinear reaction-diffusion equations with small Lévy noise. | A. Debussche,M. Högele, P. Imkeller
Reihe: LNM 2085
Verlag: Springer
Link zum Preprint
The dynamics of nonlinear reaction-diffusion equations with small Lévy noise.
Autoren: A. Debussche,M. Högele, P. Imkeller
(2013)
2013 | On the construction of point processes for classical and quantum gases | B. Nehring
Zeitschrift: J. Maths. Phys.
Band: 54-5
Link zur Publikation
On the construction of point processes for classical and quantum gases
Autoren: B. Nehring
(2013)
Zeitschrift:
J. Maths. Phys.
2013 | The Pólya Sum Process: Limit Theorems for Conditioned Random Fields | M. Rafler
Zeitschrift: J. Theor. Probab.
Seiten: 1097-1116
Band: 26
Link zur Publikation
The Pólya Sum Process: Limit Theorems for Conditioned Random Fields
Autoren: M. Rafler
(2013)
Zeitschrift:
J. Theor. Probab.
2013 | Begriffsbildung im Mathematikunterricht der Sek I zum Thema Winkel | Christian Dohrmann, Ana Kuzle
Zeitschrift: Tagungsband des GDM-Arbeitskreises Geometrie 2012
Link zur Publikation
Begriffsbildung im Mathematikunterricht der Sek I zum Thema Winkel
Autoren: Christian Dohrmann, Ana Kuzle
(2013)
Zeitschrift:
Tagungsband des GDM-Arbeitskreises Geometrie 2012
2013 | Past-Present-Future: Winkel anschaulich unterrichten! | Christian Dohrmann, Ana Kuzle
Zeitschrift: Tagungsband der 47. Jahrestagung der Gesellschaft für Didaktik der Mathematik
Link zur Publikation
Past-Present-Future: Winkel anschaulich unterrichten!
Autoren: Christian Dohrmann, Ana Kuzle
(2013)
Zeitschrift:
Tagungsband der 47. Jahrestagung der Gesellschaft für Didaktik der Mathematik
2013 | Second order rectifiability of integral varifolds of locally bounded first variation | Ulrich Menne
Zeitschrift: J. Geom. Anal.
Seiten: 709-763
Band: 23(2)
Link zur Publikation
,
Link zum Preprint
Second order rectifiability of integral varifolds of locally bounded first variation
Autoren: Ulrich Menne
(2013)
It is shown that every integral varifold in an open subset of Euclidean space whose first variation with respect to area is representable by integration can be covered by a countable collection of submanifolds of the same dimension of class 2 and that their mean curvature agrees almost everywhere with the variationally defined generalized mean curvature of the varifold.
Zeitschrift:
J. Geom. Anal.
2013 | Strong Markov approximation of Lévy processes and their generalizations in a scheme of series | T. Kosenkova
Zeitschrift: Theory of Probability and Mathematical Statistics 86 (2013)
Link zur Publikation
Strong Markov approximation of Lévy processes and their generalizations in a scheme of series
Autoren: T. Kosenkova
(2013)
Zeitschrift:
Theory of Probability and Mathematical Statistics 86 (2013)
2013 | Some fixed points results on (Generalized Bruck-Reilly *-extensions of monoids | Cevik, A.S., Karpuz, E.G., Koppitz J., I.N. Cangul
Zeitschrift: Fixed Point theory and Applications
Seiten: DOI 10.1186/1687-1812-2013-78
Band: 78
Some fixed points results on (Generalized Bruck-Reilly *-extensions of monoids
Autoren: Cevik, A.S., Karpuz, E.G., Koppitz J., I.N. Cangul
(2013)
Zeitschrift:
Fixed Point theory and Applications
Seiten:
DOI 10.1186/1687-1812-2013-78
2013 | Category Equivalences of Clones of Operations Preserving Unary Operations | Jörk Koppitz, Worakrit Supaprorn
Zeitschrift: Comptes rendus de l´Acadèmie bulgare des Sciences
Seiten: 177-184
Band: 66/2
Category Equivalences of Clones of Operations Preserving Unary Operations
Autoren: Jörk Koppitz, Worakrit Supaprorn
(2013)
Zeitschrift:
Comptes rendus de l´Acadèmie bulgare des Sciences
2013 | Some properties of solutions to weakly hypoelliptic equations | Christian Bär
Zeitschrift: Int. J. Differ. Equ.
Verlag: Hindawi, New York
Seiten: Art. ID 526390
Band: 2013
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,
Link zum Preprint
Some properties of solutions to weakly hypoelliptic equations
Autoren: Christian Bär
(2013)
A linear different operator L is called weakly hypoelliptic if any local solution u of Lu=0 is smooth. We allow for systems, that is, the coefficients may be matrices, not necessarily of square size. This is a huge class of important operators which cover all elliptic, overdetermined elliptic, subelliptic and parabolic equations.
We extend several classical theorems from complex analysis to solutions of any weakly hypoelliptic equation: the Montel theorem providing convergent subsequences, the Vitali theorem ensuring convergence of a given sequence and Riemann's first removable singularity theorem. In the case of constant coefficients we show that Liouville's theorem holds, any bounded solution must be constant and any L^p-solution must vanish.
Zeitschrift:
Int. J. Differ. Equ.
Verlag:
Hindawi, New York
2013 | Ricci flow, Einstein metrics and the Yamabe invariant | Klaus Kröncke
Link zum Preprint
Ricci flow, Einstein metrics and the Yamabe invariant
Autoren: Klaus Kröncke
(2013)
We prove dynamical stability and instability theorems for compact Einstein metrics under the Ricci flow. The stability and instability conditions are given in terms of the conformal Yamabe invariant and the Laplace spectrum. These theorems generalize results recently obtained in the Ricci-flat case.
2013 | Asymptotic eigenfunctions for Schrödinger operators on a vector bundle | Matthias Ludewig, Elke Rosenberger
Link zum Preprint
Asymptotic eigenfunctions for Schrödinger operators on a vector bundle
Autoren: Matthias Ludewig, Elke Rosenberger
(2013)
In the limit ℏ→0, we analyze a class of Schr\"odinger operators Hℏ = ℏ2 L + ℏ W + V idEh acting on sections of a vector bundle Eh over a Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has a non-degenerate minimum at some point p ∈ M. We construct quasimodes of WKB-type near p for eigenfunctions associated with the low lying eigenvalues of Hℏ. These are obtained from eigenfunctions of the associated harmonic oscillator Hp,ℏ at p, acting on C∞(TpM, Ehp).
2013 | Chiral Asymmetry and the Spectral Action | Frank Pfäffle, Christoph Stephan
Zeitschrift: Comm. Math. Phys.
Verlag: Springer
Seiten: 283-310
Band: 321, no. 2
Link zur Publikation
,
Link zum Preprint
Chiral Asymmetry and the Spectral Action
Autoren: Frank Pfäffle, Christoph Stephan
(2013)
We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition to the Einstein-Hilbert action and the bosonic part of the Standard Model Lagrangian we find the Holst term from Loop Quantum Gravity, a coupling of the Holst term to the scalar curvature and a prediction for the value of the Barbero-Immirzi parameter.
Zeitschrift:
Comm. Math. Phys.
2013 | Noncommutative Geometry in the LHC-Era | Christoph Stephan
Buchtitel: Proceedings of the XLVIIIth Rencontres de Moriond EW session
Seiten: 451-458
Link zum Preprint
Noncommutative Geometry in the LHC-Era
Autoren: Christoph Stephan
(2013)
Noncommutative geometry allows to unify the basic building blocks of particle physics, Yang-Mills-Higgs theory and General relativity, into a single geometrical framework. The resulting effective theory constrains the couplings of the particle model and reduces the number of degrees of freedom. After briefly introducing the basic ideas of noncommutative geometry, I will present its predictions for the Standard Model and the few known models beyond the Standard Model. Most of these models, including the Standard Model, are now ruled out by LHC data. But interesting extensions of the Standard Model which agree with the presumed Standard Model Scalar mass and predict new particles are still very much alive and await further experimental data.
Buchtitel:
Proceedings of the XLVIIIth Rencontres de Moriond EW session
2013 | Classification with asymmetric label noise: Consistency and maximal denoising | Scott, C., Blanchard, G., Handy, G.
Zeitschrift: COLT 2013
Verlag: JMLR Workshop and Conference Proceedings
Seiten: 489-511
Band: 30
Classification with asymmetric label noise: Consistency and maximal denoising
Autoren: Scott, C., Blanchard, G., Handy, G.
(2013)
Verlag:
JMLR Workshop and Conference Proceedings
2012 | Trading Spaces: Building three-dimensional nets from two-dimensional tilings | T. Castle, M. E. Evans, S. T. Hyde, S. J. Ramsden and V. Robins
Zeitschrift: Interface Focus 2
Seiten: 555-566
Link zur Publikation
Trading Spaces: Building three-dimensional nets from two-dimensional tilings
Autoren: T. Castle, M. E. Evans, S. T. Hyde, S. J. Ramsden and V. Robins
(2012)
Zeitschrift:
Interface Focus 2
2012 | Deformations of Platonic foam cells: Effect on growth rate | M. E. Evans, J. Zirkelbach, G. E. Schröder-Turk, A. M. Kraynik and K. Mecke
Zeitschrift: Physical Review E85
Link zur Publikation
Deformations of Platonic foam cells: Effect on growth rate
Autoren: M. E. Evans, J. Zirkelbach, G. E. Schröder-Turk, A. M. Kraynik and K. Mecke
(2012)
Zeitschrift:
Physical Review E85
2012 | Predicting the F(ab)-mediated effect of monoclonal antibodies in vivo by combining cell-level kinetic and pharmacokinetic modelling | B.-F. Krippendorff, D. A. Oyarzún, W. Huisinga
Zeitschrift: J. Pharmacokinet. Pharmacodyn.
Seiten: 125-139
Band: 39
Link zur Publikation
Predicting the F(ab)-mediated effect of monoclonal antibodies in vivo by combining cell-level kinetic and pharmacokinetic modelling
Autoren: B.-F. Krippendorff, D. A. Oyarzún, W. Huisinga
(2012)
Zeitschrift:
J. Pharmacokinet. Pharmacodyn.
2012 | Modeling inter-individual variability in physiologically-based pharmacokinetics and its link to mechanistic covariate modeling | W. Huisinga, A. Solms, L. Fronton, S. Pilari
Zeitschrift: CPT: Pharmacometrics & Systems Pharmacology
Band: 1
Link zur Publikation
,
Suppl Material (Data and Matlab code)
Modeling inter-individual variability in physiologically-based pharmacokinetics and its link to mechanistic covariate modeling
Autoren: W. Huisinga, A. Solms, L. Fronton, S. Pilari
(2012)
Zeitschrift:
CPT: Pharmacometrics & Systems Pharmacology
2012 | Hybrid stochastic-deterministic solution of the chemical master equation | S. Menz, J.C. Latorre, C. Schütte, W. Huisinga
Zeitschrift: SIAM Multiscale Modelling and Simulation
Seiten: 1232-1262
Band: 10
Link zur Publikation
Hybrid stochastic-deterministic solution of the chemical master equation
Autoren: S. Menz, J.C. Latorre, C. Schütte, W. Huisinga
(2012)
Zeitschrift:
SIAM Multiscale Modelling and Simulation
2012 | On the Monoid of All Partial Order-preserving Extensive Transformations | Dimitrova, I. and Koppitz, J.
Zeitschrift: Communications in Algebra
Band: 40
On the Monoid of All Partial Order-preserving Extensive Transformations
Autoren: Dimitrova, I. and Koppitz, J.
(2012)
Zeitschrift:
Communications in Algebra
2012 | The maximal subsemigroups of semigroups of transformations preserving or reversing the orientation on a finite chain | Dimitrova, I., Fernandes, V.H. and Koppitz, J.
Zeitschrift: Publications Mathematicae Debrecen
Band: 81 no. 1
The maximal subsemigroups of semigroups of transformations preserving or reversing the orientation on a finite chain
Autoren: Dimitrova, I., Fernandes, V.H. and Koppitz, J.
(2012)
Zeitschrift:
Publications Mathematicae Debrecen
2012 | Finite Symmetric functions with non-trivial arity gap | Shtrakov, Sl. and Koppitz, J.
Zeitschrift: Serdica J. Computing
Band: 6
Finite Symmetric functions with non-trivial arity gap
Autoren: Shtrakov, Sl. and Koppitz, J.
(2012)
Zeitschrift:
Serdica J. Computing
2012 | Real Harmonic Analysis, Lectures by Pascal Auscher with the assistance of Lashi Bandara | Pascal Auscher, Lashi Bandara
Verlag: Australian National University Press
Link zur Publikation
Real Harmonic Analysis, Lectures by Pascal Auscher with the assistance of Lashi Bandara
Autoren: Pascal Auscher, Lashi Bandara
(2012)
This book presents the material covered in graduate lectures delivered at The Australian National University in 2010. Real Harmonic Analysis originates from the seminal works of Zygmund and Calderón, pursued by Stein, Weiss, Fefferman, Coifman, Meyer and many others. Moving from the classical periodic setting to the real line, then to higher dimensional Euclidean spaces and finally to, nowadays, sets with minimal structures, the theory has reached a high level of applicability. This is why it is called real harmonic analysis: the usual exponential functions have disappeared from the picture. Set and function decomposition prevail.
Verlag:
Australian National University Press
2012 | Laplacians on infinite graphs: Dirichlet and Neumann boundary conditions | Sebastian Haeseler, Matthias Keller, Daniel Lenz, Radoslaw Wojciechowski
Zeitschrift: Journal of Spectral theory
Seiten: 397-432
Band: 2
Link zur Publikation
,
Link zum Preprint
Laplacians on infinite graphs: Dirichlet and Neumann boundary conditions
Autoren: Sebastian Haeseler, Matthias Keller, Daniel Lenz, Radoslaw Wojciechowski
(2012)
We study Laplacians associated to a graph and single out a class of such operators with special regularity properties. In the case of locally finite graphs, this class consists of all selfadjoint, non-negative restrictions of the standard formal Laplacian and we can characterize the Dirichlet and Neumann Laplacians as the largest and smallest Markovian restrictions of the standard formal Laplacian. In the case of general graphs, this class contains the Dirichlet and Neumann Laplacians and we describe howthesemay differ fromeach other, characterize when they agree, and study connections to essential selfadjointness and stochastic completeness.
Finally, we study basic common features of all Laplacians associated to a graph. In particular, we characterize when the associated semigroup is positivity improving and present some basic estimates on its long term behavior. We also discuss some situations in which the Laplacian associated to a graph is unique and, in this context, characterize its boundedness.
Zeitschrift:
Journal of Spectral theory
2012 | Absolutely continuous spectrum for multi-type Galton Watson trees | Matthias Keller
Zeitschrift: Annales Henri Poincaré
Seiten: 1745-1766
Band: 13
Link zur Publikation
,
Link zum Preprint
Absolutely continuous spectrum for multi-type Galton Watson trees
Autoren: Matthias Keller
(2012)
We consider multi-type Galton Watson trees that are close to a tree of finite cone type in distribution. Moreover, we impose that each vertex has at least one forward neighbor. Then, we show that the spectrum of the Laplace operator exhibits almost surely a purely absolutely continuous component which is included in the absolutely continuous spectrum of the tree of finite cone type.
Zeitschrift:
Annales Henri Poincaré
2012 | Absolutely continuous spectrum for random operators on trees of finite cone type | Matthias Keller, Daniel Lenz, Simone Warzel
Zeitschrift: Journal d'Analyse Mathematique
Seiten: 363-396.
Band: 118
Link zur Publikation
,
Link zum Preprint
Absolutely continuous spectrum for random operators on trees of finite cone type
Autoren: Matthias Keller, Daniel Lenz, Simone Warzel
(2012)
We study the spectrum of random operators on a large class of trees. These trees have finitely many cone types and they can be constructed by a substitution rule. The random operators are perturbations of Laplace type operators either by random potentials or by random hopping terms, i.e., perturbations of the off-diagonal elements. We prove stability of arbitrary large parts of the absolutely continuous spectrum for sufficiently small but extensive disorder.
Zeitschrift:
Journal d'Analyse Mathematique
2012 | Dirichlet forms and stochastic completeness of graphs and subgraphs | Matthias Keller, Daniel Lenz
Zeitschrift: Journal für die reine und angewandte Mathematik (Crelle's Journal)
Seiten: 189-223
Band: 2012
Link zur Publikation
,
Link zum Preprint
Dirichlet forms and stochastic completeness of graphs and subgraphs
Autoren: Matthias Keller, Daniel Lenz
(2012)
We study Laplacians on graphs and networks via regular Dirichlet forms. We give a sufficient geometric condition for essential selfadjointness and explicitly determine the generators of the associated semigroups on all ℓp, 1 ≦ p < ∞, in this case. We characterize stochastic completeness thereby generalizing all earlier corresponding results for graph Laplacians. Finally, we study how stochastic completeness of a subgraph is related to stochastic completeness of the whole graph.
Zeitschrift:
Journal für die reine und angewandte Mathematik (Crelle's Journal)
2012 | A new proof of Doob's theorem | Moritz Gerlach, Robin Nittka
Zeitschrift: Journal of Mathematical Analysis and Applications
Seiten: 763–774
Band: 388
Link zur Publikation
,
Link zum Preprint
A new proof of Doob's theorem
Autoren: Moritz Gerlach, Robin Nittka
(2012)
We prove that every bounded, positive, irreducible, stochastically continuous semigroup on the space of bounded, measurable functions which is strong Feller, consists of kernel operators and possesses an invariant measure converges pointwise. This differs from Doob's theorem in that we do not require the semigroup to be Markovian and request a fairly weak kind of irreducibility. In addition, we elaborate on the various notions of kernel operators in this context, show the stronger result that the adjoint semigroup converges strongly and discuss as an example diffusion equations on rough domains. The proofs are based on the theory of positive semigroups and do not use probability theory.
Zeitschrift:
Journal of Mathematical Analysis and Applications
2012 | Stress- and aftershock- constrained joint inversions for co- and post- seismic slip applied to the 2004 M6.0 Parkfield earthquake | Lifeng Wang, Sebastian Hainzl, Gert Zöller, Matthias Holschneider
Zeitschrift: J. Geophys. Res.
Verlag: American Geophysical Union
Seiten: B07406
Band: 117
Link zur Publikation
Stress- and aftershock- constrained joint inversions for co- and post- seismic slip applied to the 2004 M6.0 Parkfield earthquake
Autoren: Lifeng Wang, Sebastian Hainzl, Gert Zöller, Matthias Holschneider
(2012)
Zeitschrift:
J. Geophys. Res.
Verlag:
American Geophysical Union
2012 | From alarm-based to rate-based earthquake forecast models | P. Shebalin, C. Narteau, and M. Holschneider
Zeitschrift: BSSA.,102:64--72,2012.
Seiten: 455-462
Band: 18
From alarm-based to rate-based earthquake forecast models
Autoren: P. Shebalin, C. Narteau, and M. Holschneider
(2012)
Zeitschrift:
BSSA.,102:64--72,2012.
2012 | Bayesian analysis of the modified omori law | M. Holschneider, C. Narteau, P. Shebalin, Z. Peng, and D. Schorlemmer
Zeitschrift: Journal of Geophysical Research,
Seiten: B06317
Band: 117
Bayesian analysis of the modified omori law
Autoren: M. Holschneider, C. Narteau, P. Shebalin, Z. Peng, and D. Schorlemmer
(2012)
Zeitschrift:
Journal of Geophysical Research,
2012 | Numerical modeling of solar wind influences on the dynamics of the high-latitude upper atmosphere | B.E. Namgaladze A.A. Holschneider M. Förster, M. Prokhorov
Zeitschrift: Adv. Radio Sci.,
Seiten: 299—312
Band: 10
Numerical modeling of solar wind influences on the dynamics of the high-latitude upper atmosphere
Autoren: B.E. Namgaladze A.A. Holschneider M. Förster, M. Prokhorov
(2012)
Zeitschrift:
Adv. Radio Sci.,
2012 | Bayesian selection of markov models for symbol sequences: Application to microsaccadic eye movements | Mario Bettenbühl, Marco Rusconi, Ralf Engbert, and Matthias Holschneider
Zeitschrift: PloS ONE,
Seiten: e43388
Band: 7(9)
Bayesian selection of markov models for symbol sequences: Application to microsaccadic eye movements
Autoren: Mario Bettenbühl, Marco Rusconi, Ralf Engbert, and Matthias Holschneider
(2012)
2012 | Bayesian estimation of the scaling parameter of fixational eye movements | N. Makarava, M. Bettenbühl, R. Engbert, and M. Holschneider
Zeitschrift: Europhysics Letters,
Seiten: 40003
Band: 100
Bayesian estimation of the scaling parameter of fixational eye movements
Autoren: N. Makarava, M. Bettenbühl, R. Engbert, and M. Holschneider
(2012)
Zeitschrift:
Europhysics Letters,
2012 | Estimation of the hurst exponent from noisy data: a bayesian approach | N. Makarava and M. Holschneider
Zeitschrift: The European Physical Journal B,
Seiten: 1—6
Band: 85
Estimation of the hurst exponent from noisy data: a bayesian approach
Autoren: N. Makarava and M. Holschneider
(2012)
Zeitschrift:
The European Physical Journal B,
2012 | Error distribution in regional modelling of the geomagnetic field {Geophys. J. Int.}, 191:1015--1024, 2012 | Reyko Schachtschneider, Matthias Holschneider, and Mioara Mandea
Seiten: 1015-1024
Band: 191,3
Error distribution in regional modelling of the geomagnetic field {Geophys. J. Int.}, 191:1015--1024, 2012
Autoren: Reyko Schachtschneider, Matthias Holschneider, and Mioara Mandea
(2012)
2012 | Improved daily GRACE gravity field solutions using Kalman smoother | E. Kurtenbach, A. Eicker, M. Holschneider, M. Hayn, M. Fuhrmann, J. Kusche
Zeitschrift: Journal of Geodynamics
Seiten: Pages 39–48
Band: Vol.59-60
Link zur Publikation
Improved daily GRACE gravity field solutions using Kalman smoother
Autoren: E. Kurtenbach, A. Eicker, M. Holschneider, M. Hayn, M. Fuhrmann, J. Kusche
(2012)
Zeitschrift:
Journal of Geodynamics
2012 | Nonlinear force-free extrapolation of emerging flux with a global twist and serpentine fine structures | G. Valori, L.M. Green, P. Demoulin, S. Vargas Dominguez, L. van Driel-Gesztelyi, A. Wallace, D. Baker, M. Fuhrmann
Zeitschrift: Solar Physics
Nonlinear force-free extrapolation of emerging flux with a global twist and serpentine fine structures
Autoren: G. Valori, L.M. Green, P. Demoulin, S. Vargas Dominguez, L. van Driel-Gesztelyi, A. Wallace, D. Baker, M. Fuhrmann
(2012)
Zeitschrift:
Solar Physics
2012 | The retrieval of aerosol extinction coefficient profiles from Raman lidar data by inversion | P. Pornsawad, G. D'Amico, C. Böckmann, A. Amodeo, G. Pappalardo
Zeitschrift: Applied Optics
Seiten: 2035-2044
Band: 51
Link zur Publikation
The retrieval of aerosol extinction coefficient profiles from Raman lidar data by inversion
Autoren: P. Pornsawad, G. D'Amico, C. Böckmann, A. Amodeo, G. Pappalardo
(2012)
Zeitschrift:
Applied Optics
2012 | Remote sensing and in-situ measurements of tropospheric aerosol, a PAMARCMiP case study | A. Hoffmann, L. Osterloh, R. Stone , A. Lampert, C. Ritter,..., C. Böckmann, et al
Zeitschrift: Atmospheric Environment
Seiten: 56-66
Band: 52
Link zur Publikation
Remote sensing and in-situ measurements of tropospheric aerosol, a PAMARCMiP case study
Autoren: A. Hoffmann, L. Osterloh, R. Stone , A. Lampert, C. Ritter,..., C. Böckmann, et al
(2012)
Zeitschrift:
Atmospheric Environment
2012 | A simple numerical approach to the Riemann hypothesis | N. Tarkhanov
Zeitschrift: In: Centre de Recherches Mathématiques, CRM Proceedings and Lecture Notes
Reihe: Vol. 55
Seiten: 21--32
A simple numerical approach to the Riemann hypothesis
Autoren: N. Tarkhanov
(2012)
Zeitschrift:
In: Centre de Recherches Mathématiques, CRM Proceedings and Lecture Notes
2012 | Boris Vasil'evich Fedosov | M. S. Agranovich, N. Tarkhanov et al.
Zeitschrift: Russian Math. Surveys 67 (2012)
Reihe: no. 1
Seiten: 167–174
Boris Vasil'evich Fedosov
Autoren: M. S. Agranovich, N. Tarkhanov et al.
(2012)
Zeitschrift:
Russian Math. Surveys 67 (2012)
2012 | Elliptic quasicomplexes on compact closed manifolds | D. Wallenta
Zeitschrift: Integr. Equ. Oper. Theory 73 (2012)
Seiten: 517--536
Elliptic quasicomplexes on compact closed manifolds
Autoren: D. Wallenta
(2012)
Zeitschrift:
Integr. Equ. Oper. Theory 73 (2012)
2012 | Formal solutions of epidemic equation | V. Stepanenko and N. Tarkhanov
Zeitschrift: In: Mathematics and Life Sciences, Walter de Gruyter, Berlin
Seiten: 71--85
Formal solutions of epidemic equation
Autoren: V. Stepanenko and N. Tarkhanov
(2012)
Zeitschrift:
In: Mathematics and Life Sciences, Walter de Gruyter, Berlin
2012 | Inversion of Two-Dimensional Spheroidal Particle Distributions from Backscatter, Extinction and Depolarization Profiles via Regularization | C. Böckmann, L. Osterloh
Zeitschrift: Proc. 9th International Symposium on Tropospheric Profiling
Seiten: 1--4
Inversion of Two-Dimensional Spheroidal Particle Distributions from Backscatter, Extinction and Depolarization Profiles via Regularization
Autoren: C. Böckmann, L. Osterloh
(2012)
Zeitschrift:
Proc. 9th International Symposium on Tropospheric Profiling
2012 | On spectral projection for the complex Neumann problem | A. Alsaedy and N. Tarkhanov
Zeitschrift: Mathematics and Physics 5
Reihe: no. 4
Seiten: 468--479
On spectral projection for the complex Neumann problem
Autoren: A. Alsaedy and N. Tarkhanov
(2012)
Zeitschrift:
Mathematics and Physics 5
2012 | Microphysical Properties of Burning Biomass from Raman Lidar | C. Böckmann, L. Osterloh, D. Nicolae, L. Belegante
Zeitschrift: Proc. 26th International Lidar Radar Conference
Seiten: 1--4
Microphysical Properties of Burning Biomass from Raman Lidar
Autoren: C. Böckmann, L. Osterloh, D. Nicolae, L. Belegante
(2012)
Zeitschrift:
Proc. 26th International Lidar Radar Conference
2012 | On the instability of the Riemann hypothesis for curves over finite fields | P. M. Gauthier and N. Tarkhanov
Zeitschrift: Journal of Approximation Theory 164
Seiten: 504--515
On the instability of the Riemann hypothesis for curves over finite fields
Autoren: P. M. Gauthier and N. Tarkhanov
(2012)
Zeitschrift:
Journal of Approximation Theory 164
2012 | Optical and Microphysical Properties from Raman Lidar and Depolarization Data | C. Böckmann, L. Osterloh, T. Rother, I. Serikov, H. Linne, S. Kinne,
Zeitschrift: Proc. 26th International Lidar Radar Conference
Seiten: 1--4
Optical and Microphysical Properties from Raman Lidar and Depolarization Data
Autoren: C. Böckmann, L. Osterloh, T. Rother, I. Serikov, H. Linne, S. Kinne,
(2012)
Zeitschrift:
Proc. 26th International Lidar Radar Conference
2012 | The Lefschetz number of sequences of trace class curvature | N. Tarkhanov and D. Wallenta
Zeitschrift: Mathematical Sciences 6
Reihe: no. 44
Seiten: 1--16
The Lefschetz number of sequences of trace class curvature
Autoren: N. Tarkhanov and D. Wallenta
(2012)
Zeitschrift:
Mathematical Sciences 6
2012 | An ensemble Kalman-Bucy filter for continuous data assimilation | K. Bergemann and S. Reich
Zeitschrift: Meteorolog. Zeitschrift
Seiten: 213-219
Band: 21
Link zur Publikation
An ensemble Kalman-Bucy filter for continuous data assimilation
Autoren: K. Bergemann and S. Reich
(2012)
Zeitschrift:
Meteorolog. Zeitschrift
2012 | Hydrostatic Hamiltonian particle-mesh (HPM) methods for atmospheric modeling | S. Shin, S. Reich, and J. Frank
Zeitschrift: Quarterly Journal of the Royal Meteorological Society
Seiten: 1388-1399
Band: 138
Link zur Publikation
Hydrostatic Hamiltonian particle-mesh (HPM) methods for atmospheric modeling
Autoren: S. Shin, S. Reich, and J. Frank
(2012)
Zeitschrift:
Quarterly Journal of the Royal Meteorological Society
2012 | A Gaussian mixture ensemble transform filters | S. Reich
Zeitschrift: Q.J.R. Meteorolog. Soc
Seiten: 222-233
Band: 138
Link zur Publikation
A Gaussian mixture ensemble transform filters
Autoren: S. Reich
(2012)
Zeitschrift:
Q.J.R. Meteorolog. Soc
2012 | On large volume preserving stable constant mean curvature surfaces in initial data sets | Michael Eichmair and Jan Metzger
Zeitschrift: J. Differential Geom.
Seiten: 81-102
Band: 91
Link zur Publikation
On large volume preserving stable constant mean curvature surfaces in initial data sets
Autoren: Michael Eichmair and Jan Metzger
(2012)
Zeitschrift:
J. Differential Geom.
2012 | Foucault und Mathematikdidaktik – eine fruchtbare Mischung? | David Kollosche
Buchtitel: Ludwig & Kleine (Hg.) Beiträge zum Mathematikunterricht 2012. Vorträge auf der 46. Tagung für Didaktik der Mathematik.
Foucault und Mathematikdidaktik – eine fruchtbare Mischung?
Autoren: David Kollosche
(2012)
Buchtitel:
Ludwig & Kleine (Hg.) Beiträge zum Mathematikunterricht 2012. Vorträge auf der 46. Tagung für Didaktik der Mathematik.
2012 | A representation of the moment measures of the general ideal Bose gas | B. Nehring
Zeitschrift: Math. Nach.
Seiten: 878-888
Band: 285-7
Link zur Publikation
A representation of the moment measures of the general ideal Bose gas
Autoren: B. Nehring
(2012)
2012 | Single-molecule stochastic times in a reversible bimolecular reaction. | P. Keller
Zeitschrift: J. Chem. Phys.
Band: 137-8
Link zur Publikation
Single-molecule stochastic times in a reversible bimolecular reaction.
Autoren: P. Keller
(2012)
Zeitschrift:
J. Chem. Phys.
2012 | Decay estimates for the quadratic tilt-excess of integral varifolds | Ulrich Menne
Zeitschrift: Arch. Ration. Mech. Anal.
Seiten: 1-83
Band: 204(1)
Link zur Publikation
,
Link zum Preprint
Decay estimates for the quadratic tilt-excess of integral varifolds
Autoren: Ulrich Menne
(2012)
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space with their first variation given by either a Radon measure or a function in some Lebesgue space. Pointwise decay results for the quadratic tilt-excess are established for those varifolds. The results are optimal in terms of the dimension of the varifold and the exponent of the Lebesgue space in most cases, for example if the varifold is not two-dimensional.
Zeitschrift:
Arch. Ration. Mech. Anal.
2012 | Weak convergence of the series scheme of Markov chains to the solution of Lévy driven SDE | T. Kosenkova
Zeitschrift: Theory of Stochastic Processes 18(34) 1 (2012)
Link zur Publikation
Weak convergence of the series scheme of Markov chains to the solution of Lévy driven SDE
Autoren: T. Kosenkova
(2012)
Zeitschrift:
Theory of Stochastic Processes 18(34) 1 (2012)
2012 | Finite Symmetric Functions with non-trivial arity gap | Jörg Koppitz, Slavcho Shtrakov
Zeitschrift: Serdica J. Computing
Seiten: 419-436
Band: 6
Finite Symmetric Functions with non-trivial arity gap
Autoren: Jörg Koppitz, Slavcho Shtrakov
(2012)
Zeitschrift:
Serdica J. Computing
2012 | On the Monoid of All Partial Order-preserving Extensive Transformations | Ilinka Dimitrova, Jörg Koppitz
Zeitschrift: Communications in Algebra
Seiten: 1821-1826
Band: 40
On the Monoid of All Partial Order-preserving Extensive Transformations
Autoren: Ilinka Dimitrova, Jörg Koppitz
(2012)
Zeitschrift:
Communications in Algebra
2012 | The maximal subsemigroups of semigroups of transformations preserving or reversing the orientation on a finite chain | Ilinka Dimitrova, Vitor Fernandes, Jörg Koppitz
Zeitschrift: Publications Mathematicae Debrecen
Seiten: 11_29
Band: 81/1-2
The maximal subsemigroups of semigroups of transformations preserving or reversing the orientation on a finite chain
Autoren: Ilinka Dimitrova, Vitor Fernandes, Jörg Koppitz
(2012)
Zeitschrift:
Publications Mathematicae Debrecen
2012 | Tunneling for a class of difference operators | Markus Klein, Elke Rosenberger
Zeitschrift: Annales Henri Poincare
Seiten: 1231 – 1269
Band: 13, Nr. 5
Link zur Publikation
Tunneling for a class of difference operators
Autoren: Markus Klein, Elke Rosenberger
(2012)
We analyze a general class of difference operators <tex>H_\varepsilon = T_\varepsilon + V_\varepsilon</tex> acting on the square summable function on <tex>\varepsilon</tex><tex> Z^d</tex>, where <tex>V_\varepsilon</tex> is a multi-well potential and <tex>\varepsilon</tex> is a small parameter.
We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we shall treat the eigenvalue problem for <tex>H_\varepsilon</tex> as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix, similar to the analysis for the Schrödinger operator (see Helffer-Sjöstrand (1982)), and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.
Zeitschrift:
Annales Henri Poincare
2012 | Renormalized Integrals and a Path Integral Formula for the Heat Kernel on a Manifold | Christian Bär
Zeitschrift: Contemp. Math.
Verlag: American Mathematical Society
Buchtitel: C. Aldana, M. Braverman, B. Iochum, C. Neira Jimenez (eds.): Analysis, Geometry and Quantum Field Theory
Seiten: 179-197
Band: 584
Link zur Publikation
,
Link zum Preprint
Renormalized Integrals and a Path Integral Formula for the Heat Kernel on a Manifold
Autoren: Christian Bär
(2012)
We introduce renormalized integrals which generalize conventional measure theoretic integrals. One approximates the integration domain by measure spaces and defines the integral as the limit of integrals over the approximating spaces. This concept is implicitly present in many mathematical contexts such as Cauchy's principal value, the determinant of operators on a Hilbert space and the Fourier transform of an Lp-function.
We use renormalized integrals to define a path integral on manifolds by approximation via geodesic polygons. The main part of the paper is dedicated to the proof of a path integral formula for the heat kernel of any self-adjoint generalized Laplace operator acting on sections of a vector bundle over a compact Riemannian manifold.
Zeitschrift:
Contemp. Math.
Verlag:
American Mathematical Society
Buchtitel:
C. Aldana, M. Braverman, B. Iochum, C. Neira Jimenez (eds.): Analysis, Geometry and Quantum Field Theory
2012 | Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration | Blanchard, G., Mathé, P.
Zeitschrift: Inverse Problems
Verlag: IOP Publishing
Band: 28
Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration
Autoren: Blanchard, G., Mathé, P.
(2012)
Zeitschrift:
Inverse Problems
2012 | Boundary Value Problems for Elliptic Differential Operators of First Order | Werner Ballmann, Christian Bär
Zeitschrift: Surv. Differ. Geom.
Verlag: International Press
Seiten: 1-78
Band: 17
Link zur Publikation
,
Link zum Preprint
Boundary Value Problems for Elliptic Differential Operators of First Order
Autoren: Werner Ballmann, Christian Bär
(2012)
We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncompact, but the boundary is assumed to be compact. We require a symmetry property of the principal symbol of the operator along the boundary. This is satisfied by Dirac type operators, for instance.
We provide a selfcontained introduction to (nonlocal) elliptic boundary conditions, boundary regularity of solutions, and index theory. In particular, we simplify and generalize the traditional theory of elliptic boundary value problems for Dirac type operators. We also prove a related decomposition theorem, a general version of Gromov and Lawson's relative index theorem and a generalization of the cobordism theorem.
Zeitschrift:
Surv. Differ. Geom.
Verlag:
International Press
2012 | On the convergence rate of lp-norm multiple kernel learning | Kloft, M., Blanchard, G.
Zeitschrift: Journal of Machine Learning Research
Verlag: JMLR. org
Seiten: 2465-2502
Band: 13
On the convergence rate of lp-norm multiple kernel learning
Autoren: Kloft, M., Blanchard, G.
(2012)
Zeitschrift:
Journal of Machine Learning Research
2012 | CCR- versus CAR-quantization on curved spacetimes | Christian Bär, Nicolas Ginoux
Verlag: Birkhäuser
Buchtitel: F. Finster, O. Müller, M. Nardmann, J. Tolksdorf, E. Zeidler (Eds.): Quantum Field Theory and Gravity
Seiten: 183-206
Link zur Publikation
,
Link zum Preprint
CCR- versus CAR-quantization on curved spacetimes
Autoren: Christian Bär, Nicolas Ginoux
(2012)
We provide a systematic construction of bosonic and fermionic locally covariant quantum field theories on curved backgrounds for large classes of free fields. It turns out that bosonic quantization is possible under much more general assumptions than fermionic quantization.
Buchtitel:
F. Finster, O. Müller, M. Nardmann, J. Tolksdorf, E. Zeidler (Eds.): Quantum Field Theory and Gravity
2012 | Exemplar-based image inpainting: Fast priority and coherent nearest neighbor search | Martínez-Noriega, R., Roumy, A., Blanchard, G.
Zeitschrift: Machine Learning for Signal Processing (MLSP), 2012 IEEE International Workshop on
Verlag: IEEE
Seiten: 1-6
Exemplar-based image inpainting: Fast priority and coherent nearest neighbor search
Autoren: Martínez-Noriega, R., Roumy, A., Blanchard, G.
(2012)
Zeitschrift:
Machine Learning for Signal Processing (MLSP), 2012 IEEE International Workshop on
2012 | Classical and Quantum Fields on Lorentzian Manifolds | Christian Bär, Nicolas Ginoux
Reihe: Springer Proceedings in Mathematics
Verlag: Springer
Buchtitel: C. Bär, J. Lohkamp, M. Schwarz (Eds.): Global Differential Geometry
Seiten: 359-400
Band: 17
Link zur Publikation
,
Link zum Preprint
Classical and Quantum Fields on Lorentzian Manifolds
Autoren: Christian Bär, Nicolas Ginoux
(2012)
We construct bosonic and fermionic locally covariant quantum field theories on curved backgrounds for large classes of fields. We investigate the quantum field and n-point functions induced by suitable states.
Reihe:
Springer Proceedings in Mathematics
Buchtitel:
C. Bär, J. Lohkamp, M. Schwarz (Eds.): Global Differential Geometry
2012 | A simple extension of stability feature selection | Beinrucker, A., Dogan, Ü., Blanchard, G.
Zeitschrift: Pattern Recognition (DAGM-OAGM 2012)
Verlag: Springer Berlin Heidelberg
Seiten: 256-265
A simple extension of stability feature selection
Autoren: Beinrucker, A., Dogan, Ü., Blanchard, G.
(2012)
Zeitschrift:
Pattern Recognition (DAGM-OAGM 2012)
Verlag:
Springer Berlin Heidelberg
2012 | Global Differential Geometry | Christian Bär, Joachim Lohkamp, Matthias Schwarz
Reihe: Springer Proceedings in Mathematics
Verlag: Springer
Band: 17
Link zur Publikation
Global Differential Geometry
Autoren: Christian Bär, Joachim Lohkamp, Matthias Schwarz
(2012)
This volume contains a collection of surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.
Reihe:
Springer Proceedings in Mathematics
2012 | Early stopping for mutual information based feature selection | Beinrucker, A., Dogan, U., Blanchard, G.
Zeitschrift: Pattern Recognition (ICPR), 2012 21st International Conference on
Verlag: IEEE
Seiten: 975-978
Early stopping for mutual information based feature selection
Autoren: Beinrucker, A., Dogan, U., Blanchard, G.
(2012)
Zeitschrift:
Pattern Recognition (ICPR), 2012 21st International Conference on
2012 | On Gravity, Torsion and the Spectral Action Principle | Frank Pfäffle, Christoph Stephan
Zeitschrift: J. Funct. Anal.
Verlag: Elsevier
Seiten: 1529-1565
Band: 262, no. 4
Link zur Publikation
,
Link zum Preprint
On Gravity, Torsion and the Spectral Action Principle
Autoren: Frank Pfäffle, Christoph Stephan
(2012)
We consider compact Riemannian spin manifolds without boundary equipped with orthogonal connections. We investigate the induced Dirac operators and the associated commutative spectral triples. In case of dimension four and totally anti-symmetric torsion we compute the Chamseddine-Connes spectral action, deduce the equations of motions and discuss critical points.
Zeitschrift:
J. Funct. Anal.
2011 | Entanglement of embedded graphs | T. Castle, M. E. Evans and S. T. Hyde
Zeitschrift: Progress of Theoretical Physics Supplement 191
Seiten: 235-244
Link zur Publikation
Entanglement of embedded graphs
Autoren: T. Castle, M. E. Evans and S. T. Hyde
(2011)
Zeitschrift:
Progress of Theoretical Physics Supplement 191
2011 | From three-dimensional weavings to swollen corneocytes | M. E. Evans and S. T. Hyde
Zeitschrift: Journal of the Royal Society Interface 8(62)
Seiten: 1274-1280
Link zur Publikation
From three-dimensional weavings to swollen corneocytes
Autoren: M. E. Evans and S. T. Hyde
(2011)
Zeitschrift:
Journal of the Royal Society Interface 8(62)
2011 | A Newton-based method for the calculation of the distance to instability | M.A. Freitag, A. Spence
Zeitschrift: Linear Alg. Appl.
Seiten: 3189-3205
Band: 435(12)
Link zur Publikation
A Newton-based method for the calculation of the distance to instability
Autoren: M.A. Freitag, A. Spence
(2011)
Zeitschrift:
Linear Alg. Appl.
2011 | Regularization techniques for ill-posed inverse problems in data assimilation | M.A. Freitag, N.K. Nichols, C.J. Budd
Zeitschrift: Comput. & Fluids
Seiten: 168-173
Band: 46(1)
Link zur Publikation
Regularization techniques for ill-posed inverse problems in data assimilation
Autoren: M.A. Freitag, N.K. Nichols, C.J. Budd
(2011)
Zeitschrift:
Comput. & Fluids
2011 | Gestational Influences on the Pharmacokinetics of Gestagenic Drugs: A Combined In Silico, In Vitro and In Vivo Analysis | S. Pilari, C. Preusse, W. Huisinga
Zeitschrift: Eur J Pharm Sci.
Seiten: 318-331
Band: 42
Link zur Publikation
Gestational Influences on the Pharmacokinetics of Gestagenic Drugs: A Combined In Silico, In Vitro and In Vivo Analysis
Autoren: S. Pilari, C. Preusse, W. Huisinga
(2011)
Zeitschrift:
Eur J Pharm Sci.
2011 | Logarithmic convergence rate of Levenberg_Marquardt method with application to an inverse potential problem | C. Böckmann, A. Kammanee, H.-A. Braunß
Zeitschrift: Journal of Inverse and III-Posed Problems
Seiten: 345-367
Band: 19
Link zur Publikation
Logarithmic convergence rate of Levenberg_Marquardt method with application to an inverse potential problem
Autoren: C. Böckmann, A. Kammanee, H.-A. Braunß
(2011)
Zeitschrift:
Journal of Inverse and III-Posed Problems
2011 | Error-Controlled Global Sensitivity Analysis of Ordinary Differential Equations | A. Y. Weiße, W. Huisinga
Zeitschrift: J. Comput. Phys.
Seiten: 6824-6842
Band: 230
Link zur Publikation
,
Suppl Material (zip)
Error-Controlled Global Sensitivity Analysis of Ordinary Differential Equations
Autoren: A. Y. Weiße, W. Huisinga
(2011)
Zeitschrift:
J. Comput. Phys.
2011 | HIV Quasispecies Dynamics during Pro-Active Treatment Switching: Impact on Multi-Drug Resistance and Resistance Archiving in Latent Reservoirs | M. von Kleist, S. Menz, H. Stocker, K. Arasteh, C. Schütte, W. Huisinga
Zeitschrift: PLoS ONE
Band: 6
Link zur Publikation
,
e18204
HIV Quasispecies Dynamics during Pro-Active Treatment Switching: Impact on Multi-Drug Resistance and Resistance Archiving in Latent Reservoirs
Autoren: M. von Kleist, S. Menz, H. Stocker, K. Arasteh, C. Schütte, W. Huisinga
(2011)
2011 | Intra-aortic balloon pump counterpulsation (IABP) for myocardial infarction complicated by cardiogenic shock | S. Unverzagt, M.-T. Machemer, A. Solms, H. Thiele, D. Burkhoff, M. Seyfarth, A. de Waha, E. Magnus Ohman, Michael Buerke, Johannes Haerting, Karl Werdan, Roland Prondzinsky
Zeitschrift: Cochrane Database of Systematic Reviews 6, CD007398
Link zur Publikation
Intra-aortic balloon pump counterpulsation (IABP) for myocardial infarction complicated by cardiogenic shock
Autoren: S. Unverzagt, M.-T. Machemer, A. Solms, H. Thiele, D. Burkhoff, M. Seyfarth, A. de Waha, E. Magnus Ohman, Michael Buerke, Johannes Haerting, Karl Werdan, Roland Prondzinsky
(2011)
Zeitschrift:
Cochrane Database of Systematic Reviews 6, CD007398
2011 | On the maximal regular subsemigroups of ideals of order-preserving or order-reversing transformations | Dimitrova, I. and Koppitz, J.
Zeitschrift: Semigroup Forum
Band: 82
On the maximal regular subsemigroups of ideals of order-preserving or order-reversing transformations
Autoren: Dimitrova, I. and Koppitz, J.
(2011)
Zeitschrift:
Semigroup Forum
2011 | Coregular Semigroups of full Transformations | Dimitrova, I. and Koppitz, J.
Zeitschrift: Demonstratio Mathematica
Band: Vol. XLIV, No. 4
Coregular Semigroups of full Transformations
Autoren: Dimitrova, I. and Koppitz, J.
(2011)
Zeitschrift:
Demonstratio Mathematica
2011 | Quadratic Estimates and perturbations of Dirac type operators on doubling measure metric spaces | Lashi Bandara
Reihe: Proc. Centre Math. Appl. Austral. Nat. Univ.
Verlag: Austral. Nat. Univ., Canberra
Buchtitel: Proceedings of the AMSI International Conference on Harmonic Analysis and Applications
Seiten: 1-21
Band: 45
Link zur Publikation
,
Link zum Preprint
Quadratic Estimates and perturbations of Dirac type operators on doubling measure metric spaces
Autoren: Lashi Bandara
(2011)
We consider perturbations of Dirac type operators on complete, connected metric spaces equipped with a doubling measure. Under a suitable set of assumptions, we prove quadratic estimates for such operators and hence deduce that these operators have a bounded functional calculus. In particular, we deduce a Kato square root type estimate.
Reihe:
Proc. Centre Math. Appl. Austral. Nat. Univ.
Verlag:
Austral. Nat. Univ., Canberra
Buchtitel:
Proceedings of the AMSI International Conference on Harmonic Analysis and Applications
2011 | Curvature, geometry and spectral properties of planar graphs | Matthias Keller
Zeitschrift: Discrete & Computational Geometry
Seiten: 500-525
Band: 46
Link zur Publikation
,
Link zum Preprint
Curvature, geometry and spectral properties of planar graphs
Autoren: Matthias Keller
(2011)
We introduce a curvature function for planar graphs to study the connection between the curvature and the geometric and spectral properties of the graph. We show that non-positive curvature implies that the graph is infinite and locally similar to a tessellation. We use this to extend several results known for tessellations to general planar graphs. For non-positive curvature, we show that the graph admits no cut locus and we give a description of the boundary structure of distance balls. For negative curvature, we prove that the interiors of minimal bigons are empty and derive explicit bounds for the growth of distance balls and Cheeger’s constant. The latter are used to obtain lower bounds for the bottom of the spectrum of the discrete Laplace operator. Moreover, we give a characterization for triviality of the essential spectrum by uniform decrease of the curvature. Finally, we show that non-positive curvature implies the absence of finitely supported eigenfunctions for nearest neighbor operators.
Zeitschrift:
Discrete & Computational Geometry
2011 | Generalized solutions and spectrum for Dirichlet forms on graphs | Sebastian Haeseler, Matthias Keller
Reihe: Progress in Probability
Verlag: Birkhäuser
Buchtitel: Random Walks, Boundaries and Spectra
Seiten: 181-201
Link zur Publikation
,
Link zum Preprint
Generalized solutions and spectrum for Dirichlet forms on graphs
Autoren: Sebastian Haeseler, Matthias Keller
(2011)
In the framework of regular Dirichlet forms we consider operators on infinite graphs. We study the connection of the existence of solutions with certain properties and the spectrum of the operators. In particular we prove a version of the Allegretto-Piepenbrink theorem which says that positive (super)-solutions to a generalized eigenvalue equation exist exactly for energies not exceeding the infimum of the spectrum. Moreover we show a version of Shnol’s theorem, which says that existence of solutions satisfying a growth condition with respect to a given boundary measure implies that the corresponding energy is in the spectrum.
Reihe:
Progress in Probability
Buchtitel:
Random Walks, Boundaries and Spectra
2011 | Cheeger constants, growth and spectrum of locally tessellating planar graphs (with Norbert Peyerimhoff), | Matthias Keller, Norbert Peyerimhoff
Zeitschrift: Mathematische Zeitschrift
Seiten: 871-886
Band: 268
Link zur Publikation
,
Link zum Preprint
Cheeger constants, growth and spectrum of locally tessellating planar graphs (with Norbert Peyerimhoff),
Autoren: Matthias Keller, Norbert Peyerimhoff
(2011)
In this article, we study relations between the local geometry of planar graphs (combinatorial curvature) and global geometric invariants, namely the Cheeger constants and the exponential growth. We also discuss spectral applications.
Zeitschrift:
Mathematische Zeitschrift
2011 | Relative Cauchy evolution for spin 1 fields | Marco Benini
Zeitschrift: MSc thesis
Verlag: University of Pavia
Link zum Preprint
Relative Cauchy evolution for spin 1 fields
Autoren: Marco Benini
(2011)
In this thesis the generally covariant locality principle for bosonic free fields has been thoroughly analyzed devoting particular attention to the case of spin 1 fields on curved spacetimes (Proca and Maxwell fields). This has been obtained in two steps: In the first place the preliminary study of the corresponding field equations led to the construction of a symplectic space of solutions describing the classical theories of the considered fields. Secondly the locally covariant quantum theory of the field under consideration has been obtained through the assignment of the Weyl algebra associated to the symplectic space describing the classical theory. The last part of the thesis has been devoted to the proof of the relative Cauchy evolution for both the Proca field and the Maxwell field.
Verlag:
University of Pavia
2011 | Estimation of the maximum possible magnitude in the framework of the doubly-truncated Gutenberg-Richter model | Matthias Holschneider, Gert Zöller, Sebastian Hainzl
Zeitschrift: Bull. Seismol. Soc. Am.
Verlag: Seismological Society of America
Seiten: 1649-1659
Band: 101
Link zur Publikation
Estimation of the maximum possible magnitude in the framework of the doubly-truncated Gutenberg-Richter model
Autoren: Matthias Holschneider, Gert Zöller, Sebastian Hainzl
(2011)
Zeitschrift:
Bull. Seismol. Soc. Am.
Verlag:
Seismological Society of America
2011 | Estimation of the maximum possible magnitude in the framework of the doubly-truncated gutenberg-richter model, | M. Holschneider, G. Zöller, and S. Hainzl
Zeitschrift: Bull. Seismol. Soc. Am.,
Seiten: 1649—1659
Band: 101(4):
Estimation of the maximum possible magnitude in the framework of the doubly-truncated gutenberg-richter model,
Autoren: M. Holschneider, G. Zöller, and S. Hainzl
(2011)
Zeitschrift:
Bull. Seismol. Soc. Am.,
2011 | Bayesian estimation of the self-similarity exponent of the Nile River fluctuation | S. Benmehdi, N. Makarava, N. Benhamidouche, and M. Holschneider
Zeitschrift: Nonlinear Processes in Geophysics,
Seiten: 441—446
Band: 18(3):
Bayesian estimation of the self-similarity exponent of the Nile River fluctuation
Autoren: S. Benmehdi, N. Makarava, N. Benhamidouche, and M. Holschneider
(2011)
Zeitschrift:
Nonlinear Processes in Geophysics,
2011 | Short-term earthquake forecasting using early aftershock statistics | P. Shebalin, C. Narteau, M. Holschneider, and D. Schorlemmer
Zeitschrift: BSSA
Seiten: :297--312
Band: 101
Short-term earthquake forecasting using early aftershock statistics
Autoren: P. Shebalin, C. Narteau, M. Holschneider, and D. Schorlemmer
(2011)
2011 | Detection of trend changes in time series using bayesian inference | Nadine Schütz and Matthias Holschneider
Zeitschrift: Phys. Rev. E
Seiten: 21120
Band: 84:
Detection of trend changes in time series using bayesian inference
Autoren: Nadine Schütz and Matthias Holschneider
(2011)
Zeitschrift:
Phys. Rev. E
2011 | Bayesian estimation of self-similarity exponent | Natallia Makarava, Sabah Benmehdi, and Matthias Holschneider
Zeitschrift: Phys. Rev. E
Seiten: 21109
Band: 84:
Bayesian estimation of self-similarity exponent
Autoren: Natallia Makarava, Sabah Benmehdi, and Matthias Holschneider
(2011)
Zeitschrift:
Phys. Rev. E
2011 | Wavelet modeling of the gravity field by domain decomposition methods : an example over japan | I. Panet, Y Kuroishi, and M. Holschneider
Zeitschrift: Geophys. J. Int.
Seiten: 203--219
Band: 184(1):
Wavelet modeling of the gravity field by domain decomposition methods : an example over japan
Autoren: I. Panet, Y Kuroishi, and M. Holschneider
(2011)
Zeitschrift:
Geophys. J. Int.
2011 | A comparison of preprocessing methods for solar force-free magnetic field extrapolation | M. Fuhrmann, N. Seehafer, G. Valori, T. Wiegelmann
Zeitschrift: A&A 526
Seiten: Pages 73-97
Band: A70 Volume
A comparison of preprocessing methods for solar force-free magnetic field extrapolation
Autoren: M. Fuhrmann, N. Seehafer, G. Valori, T. Wiegelmann
(2011)
2011 | An analogue of the Paley-Wiener theorem and its applications to optimal recovering of entire functions | N. Tarkhanov, L.S. Maergoiz
Zeitschrift: Ufimskii Matematicheskii Zhurnal
Reihe: Vol. 3, Issue 1
Seiten: S. 16-30
An analogue of the Paley-Wiener theorem and its applications to optimal recovering of entire functions
Autoren: N. Tarkhanov, L.S. Maergoiz
(2011)
Zeitschrift:
Ufimskii Matematicheskii Zhurnal
2011 | Equations of Maxwell type | N. Tarkhanov, K. Makhmudov, O. Makhmudov
Zeitschrift: Journal of Mathematical Analysis and Applications
Reihe: Vol. 378, Issue 1
Equations of Maxwell type
Autoren: N. Tarkhanov, K. Makhmudov, O. Makhmudov
(2011)
Zeitschrift:
Journal of Mathematical Analysis and Applications
2011 | Forced nonlinear resonance in a system of coupled oscillators | N. Tarkhanov, S. Glebov, O. Kiselev
Zeitschrift: An Interdisciplinary Journal of Nonlinear Science
Reihe: Vol. 21, Issue 2, Article 023109
Seiten: 7 Seiten
Forced nonlinear resonance in a system of coupled oscillators
Autoren: N. Tarkhanov, S. Glebov, O. Kiselev
(2011)
Zeitschrift:
An Interdisciplinary Journal of Nonlinear Science
Reihe:
Vol. 21, Issue 2, Article 023109
2011 | Holomorphic corner symbols | B.-W. Schulze, N. Habal
Zeitschrift: Journal of Pseudo-Differential Operators and Applications
Seiten: S. 419-465
Holomorphic corner symbols
Autoren: B.-W. Schulze, N. Habal
(2011)
Zeitschrift:
Journal of Pseudo-Differential Operators and Applications
2011 | Mellin and Green operators of the corner calculus, | B.-W. Schulze, M.W. Wong
Zeitschrift: Journal of Pseudo-Differential Operators and Applications
Seiten: S. 467-507
Mellin and Green operators of the corner calculus,
Autoren: B.-W. Schulze, M.W. Wong
(2011)
Zeitschrift:
Journal of Pseudo-Differential Operators and Applications
2011 | Mellin Operators with Asymptotics on manifolds with Corners | B.-W. Schulze, M.W. Wong
Zeitschrift: Pseudo-Differential Operators: Analysis, Applications and Computations
Verlag: Birkhäuser Verlag
Seiten: S. 31-78
Mellin Operators with Asymptotics on manifolds with Corners
Autoren: B.-W. Schulze, M.W. Wong
(2011)
Zeitschrift:
Pseudo-Differential Operators: Analysis, Applications and Computations
Verlag:
Birkhäuser Verlag
2011 | Noncommutative formal Taylor expansions and second quantised regularised traces | S. Paycha, Ed.: Ed. K. Ebrahimi-Fard, M. Marcolli, W.D. van Suijlekom
Zeitschrift: in Combinatorics and Physics, Contemporary Mathematics AMS
Reihe: vol. 539
Seiten: S. 349-376
Noncommutative formal Taylor expansions and second quantised regularised traces
Autoren: S. Paycha, Ed.: Ed. K. Ebrahimi-Fard, M. Marcolli, W.D. van Suijlekom
(2011)
Zeitschrift:
in Combinatorics and Physics, Contemporary Mathematics AMS
2011 | Renormalization by Birkhoff factorization and by generalized evaluators | S. Paycha, L.Guo, B. Zhang
Zeitschrift: in Noncommutative Geometry, Arithmetic and Related Topics
Verlag: John Hopkins University Press
Seiten: S. 183-211
Renormalization by Birkhoff factorization and by generalized evaluators
Autoren: S. Paycha, L.Guo, B. Zhang
(2011)
Zeitschrift:
in Noncommutative Geometry, Arithmetic and Related Topics
Verlag:
John Hopkins University Press
2011 | Separation of boundary singularities for holomorphic generators | N. Tarkhanov, M. Elin, D. Shoikhet
Zeitschrift: Annali di Matematica Pura ed Applicata
Seiten: S. 595-618
Separation of boundary singularities for holomorphic generators
Autoren: N. Tarkhanov, M. Elin, D. Shoikhet
(2011)
Zeitschrift:
Annali di Matematica Pura ed Applicata
2011 | Spectral triples and manifolds with boundary | C. Levy, B. Iochum
Zeitschrift: Journal of Functional Analysis 260
Seiten: S. 117-134,
Spectral triples and manifolds with boundary
Autoren: C. Levy, B. Iochum
(2011)
Zeitschrift:
Journal of Functional Analysis 260
2011 | Tadpoles and commutative spectral triples | C. Levy, B. Iochum
Zeitschrift: Journal of Noncommutative Geometry 5,
Seiten: S. 299-329
Tadpoles and commutative spectral triples
Autoren: C. Levy, B. Iochum
(2011)
Zeitschrift:
Journal of Noncommutative Geometry 5,
2011 | The Dirichlet to Neumann operator for elliptic complexes | N. Tarkhanov
Zeitschrift: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 363
Reihe: Volume 363
Seiten: S. 6421-6437
The Dirichlet to Neumann operator for elliptic complexes
Autoren: N. Tarkhanov
(2011)
Zeitschrift:
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 363
2011 | The Dirichlet to Neumann operator for nonlinear elliptic equations | N. Tarkhanov, I. Ly
Zeitschrift: Complex Analysis and Dynamical Systems IV, Contemporary Mathematics
Reihe: vol. 553
Seiten: S. 115-126
The Dirichlet to Neumann operator for nonlinear elliptic equations
Autoren: N. Tarkhanov, I. Ly
(2011)
Zeitschrift:
Complex Analysis and Dynamical Systems IV, Contemporary Mathematics
2011 | The logarithmic residue density of a generalized Laplacian | S. Paycha, J. Mickelsson
Zeitschrift: Journal of the Australian Mathematical Society
Reihe: Vol. 90 n.1
Seiten: S. 53-80
The logarithmic residue density of a generalized Laplacian
Autoren: S. Paycha, J. Mickelsson
(2011)
Zeitschrift:
Journal of the Australian Mathematical Society
2011 | The Schwarz kernel in Clifford analysis | N. Tarkhanov, L. Aizenberg
Zeitschrift: Complex Analysis and Dynamical Systems IV, Contemporary Mathematics
Reihe: vol. 553
Seiten: S. 1-13
The Schwarz kernel in Clifford analysis
Autoren: N. Tarkhanov, L. Aizenberg
(2011)
Zeitschrift:
Complex Analysis and Dynamical Systems IV, Contemporary Mathematics
2011 | Logarithmic convergence rate of Levenberg–Marquardt method with application to an inverse potential problem | C. Böckmann, A. Kammanee, A. Braunß
Zeitschrift: Journal Inverse and Ill-posed Problems
Seiten: 345-367
Band: 19
Link zur Publikation
Logarithmic convergence rate of Levenberg–Marquardt method with application to an inverse potential problem
Autoren: C. Böckmann, A. Kammanee, A. Braunß
(2011)
Zeitschrift:
Journal Inverse and Ill-posed Problems
2011 | An Adaptive Base Point Algorithm for the Retrieval of Aerosol Microphysical Properties | L. Osterloh, C. Böckmann, R. E. Mamouri, A. Papayannis
Zeitschrift: The Open Atmospheric Science Journal
Seiten: 61-73
Band: 5
Link zur Publikation
An Adaptive Base Point Algorithm for the Retrieval of Aerosol Microphysical Properties
Autoren: L. Osterloh, C. Böckmann, R. E. Mamouri, A. Papayannis
(2011)
Zeitschrift:
The Open Atmospheric Science Journal
2011 | Broyden method for inverse non-symmetric Sturm-Liouville problems | C. Böckmann, A. Kammanee
Zeitschrift: BIT
Seiten: 513-528
Band: 51
Link zur Publikation
Broyden method for inverse non-symmetric Sturm-Liouville problems
Autoren: C. Böckmann, A. Kammanee
(2011)
2011 | Corrected potential energy functions for constrained molecular dynamics | R.D. Skeel and S. Reich
Zeitschrift: European Physical Journal Special Topics
Seiten: 55-72
Band: 200
Link zur Publikation
Corrected potential energy functions for constrained molecular dynamics
Autoren: R.D. Skeel and S. Reich
(2011)
Zeitschrift:
European Physical Journal Special Topics
2011 | On the use of constraints in molecular and geophysical fluid dynamics | S. Reich and T. Hundertmark
Zeitschrift: European Physical Journal Special Topics
Seiten: 259-270
Band: 200
Link zur Publikation
On the use of constraints in molecular and geophysical fluid dynamics
Autoren: S. Reich and T. Hundertmark
(2011)
Zeitschrift:
European Physical Journal Special Topics
2011 | New Hybrid Monte Carlo Methods for Efficient Sampling: from Physics to Biology and Statistics | E. Akhmatskaya and S. Reich
Zeitschrift: Progress in Nuclear Science and Technology
Seiten: 447-462
Band: 2
Link zur Publikation
New Hybrid Monte Carlo Methods for Efficient Sampling: from Physics to Biology and Statistics
Autoren: E. Akhmatskaya and S. Reich
(2011)
Zeitschrift:
Progress in Nuclear Science and Technology
2011 | Meso-GSHMC: A stochastic algorithm for meso-scale constant temperature simulations | E. Akhmatskaya and S. Reich
Zeitschrift: Procedia Computer Science
Seiten: 1353-1362
Band: 4
Link zur Publikation
Meso-GSHMC: A stochastic algorithm for meso-scale constant temperature simulations
Autoren: E. Akhmatskaya and S. Reich
(2011)
Zeitschrift:
Procedia Computer Science
2011 | Controlling overestimation of error covariance in ensemble Kalman filters with sparse observations: A variance limiting Kalman filter | G. Gottwald, L. Mitchell and S. Reich,
Zeitschrift: Monthly Weather Review
Seiten: 2650-2667
Band: 139
Link zur Publikation
Controlling overestimation of error covariance in ensemble Kalman filters with sparse observations: A variance limiting Kalman filter
Autoren: G. Gottwald, L. Mitchell and S. Reich,
(2011)
Zeitschrift:
Monthly Weather Review
2011 | A multigrid solver for modeling complex interseismic stress fields | S. Shin, G. Zoeller, M. Holschneider and S. Reich
Zeitschrift: Computers & Geosciences
Seiten: 1075-1082
Band: 37
Link zur Publikation
A multigrid solver for modeling complex interseismic stress fields
Autoren: S. Shin, G. Zoeller, M. Holschneider and S. Reich
(2011)
Zeitschrift:
Computers & Geosciences
2011 | A dynamical systems framework for intermittent data assimilation | S. Reich
Zeitschrift: BIT Numerical Analysis
Seiten: 235-249
Band: 51
Link zur Publikation
A dynamical systems framework for intermittent data assimilation
Autoren: S. Reich
(2011)
Zeitschrift:
BIT Numerical Analysis
2011 | Foliations of asymptotically flat manifolds by surfaces of Willmore type | Tobias Lamm, Jan Metzger and Felix Schulze
Zeitschrift: Math. Ann.
Seiten: 1-78
Band: 350
Link zur Publikation
Foliations of asymptotically flat manifolds by surfaces of Willmore type
Autoren: Tobias Lamm, Jan Metzger and Felix Schulze
(2011)
2011 | Spiele zur Unterrichtsgestaltung. Mathematik | Heiko Etzold, Ines Petzschler
Verlag: Mülheim an der Ruhr
Spiele zur Unterrichtsgestaltung. Mathematik
Autoren: Heiko Etzold, Ines Petzschler
(2011)
Verlag:
Mülheim an der Ruhr
2011 | On type-I singularities in Ricci flow | Jörg Enders, Reto Müller, Peter Topping
Zeitschrift: Comm. Anal. Geom.
Seiten: 905-922
Band: 19
Link zur Publikation
On type-I singularities in Ricci flow
Autoren: Jörg Enders, Reto Müller, Peter Topping
(2011)
Zeitschrift:
Comm. Anal. Geom.
2011 | Continuous-time multitype branching processes conditioned on very late extinction | S. Pénisson
Zeitschrift: ESAIM: P. & S.
Seiten: 417-442
Band: 15
Link zur Publikation
Continuous-time multitype branching processes conditioned on very late extinction
Autoren: S. Pénisson
(2011)
Zeitschrift:
ESAIM: P. & S.
2011 | The Papangelou process. A concept for Gibbs, Fermi and Bose process | B. Nehring
Zeitschrift: Izv. Nats. Akad. Nauk Armenii Mat.
Seiten: 49-66
Band: 46-6
Link zur Publikation
The Papangelou process. A concept for Gibbs, Fermi and Bose process
Autoren: B. Nehring
(2011)
Zeitschrift:
Izv. Nats. Akad. Nauk Armenii Mat.
2011 | Asymptotic first exit times of the Chafee-Infante equation with small heavy-tailed Lévy noise. | A. Debussche,M. Högele, P. Imkeller
Zeitschrift: Electron. Commun. Probab.
Seiten: 213-225
Band: 16
Link zum Preprint
Asymptotic first exit times of the Chafee-Infante equation with small heavy-tailed Lévy noise.
Autoren: A. Debussche,M. Högele, P. Imkeller
(2011)
Zeitschrift:
Electron. Commun. Probab.
2011 | Social Functions of School Mathematics | David Kollosche
Buchtitel: Pytlak; Rowland & Swoboda (Hg.) Proceedings of the 7th Congress of the European Society for Research in Mathematics Education. Uniwersytet Rzeszowski.
Social Functions of School Mathematics
Autoren: David Kollosche
(2011)
Buchtitel:
Pytlak; Rowland & Swoboda (Hg.) Proceedings of the 7th Congress of the European Society for Research in Mathematics Education. Uniwersytet Rzeszowski.
2011 | Surveys in Stochastic Processes | S. Roelly (Ed.)
Reihe: Series of Congress Reports
Verlag: EMS
Buchtitel: Surveys in Stochastic Processes
Link zur Publikation
Surveys in Stochastic Processes
Autoren: S. Roelly (Ed.)
(2011)
Reihe:
Series of Congress Reports
Buchtitel:
Surveys in Stochastic Processes
2011 | Coregular Semigroups of full Transformations | Ilinka Dimitrova, Jörg Koppitz
Zeitschrift: Demonstratio Mathematica
Seiten: 739-753
Band: XLIV/4
Coregular Semigroups of full Transformations
Autoren: Ilinka Dimitrova, Jörg Koppitz
(2011)
Zeitschrift:
Demonstratio Mathematica
2011 | The maximal regular subsemigroups of ideals of order-preserving or order-reversing transformations | Ilinka Dimitrova, Jörg Koppitz
Zeitschrift: Semigroup Forum
Seiten: 172-180
Band: 82
The maximal regular subsemigroups of ideals of order-preserving or order-reversing transformations
Autoren: Ilinka Dimitrova, Jörg Koppitz
(2011)
Zeitschrift:
Semigroup Forum
2011 | Asymptotic Eigenfunctions for a class of difference operators | Markus Klein, Elke Rosenberger
Zeitschrift: Asymptotic Analysis
Seiten: 1 – 36
Band: 73, Nr. 1-2
Link zur Publikation
Asymptotic Eigenfunctions for a class of difference operators
Autoren: Markus Klein, Elke Rosenberger
(2011)
We analyze a general class of difference operators <tex>H_\varepsilon = T_\varepsilon+ V_\varepsilon</tex> on <tex>\ell^2(\varepsilon\mathbb{Z}^d</tex>), where <tex>V_\varepsilon</tex> is a one-well potential and <tex>\varepsilon</tex> is a small parameter.
We construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low lying eigenvalues of <tex>H_\varepsilon</tex>. These are obtained from eigenfunctions or quasimodes for the operator <tex>H_\varepsilon</tex>, acting on <tex>L^2(R^d)</tex>, via restriction to the lattice <tex>\varepsilon Z^d</tex>.
Zeitschrift:
Asymptotic Analysis
2011 | The local Rademacher complexity of lp-norm multiple kernel learning | Kloft, M., Blanchard, G.
Zeitschrift: Advances in Neural Information Processing Systems (NIPS 2011)
Seiten: 2438-2446
The local Rademacher complexity of lp-norm multiple kernel learning
Autoren: Kloft, M., Blanchard, G.
(2011)
Zeitschrift:
Advances in Neural Information Processing Systems (NIPS 2011)
2011 | Wiener Measures on Riemannian Manifolds and the Feynman-Kac Formula | Christian Bär, Frank Pfäffle
Zeitschrift: Mat. Contemp.
Verlag: Sociedade Brasileira de Matematica
Seiten: 37-90
Band: 40
Link zur Publikation
,
Link zum Preprint
Wiener Measures on Riemannian Manifolds and the Feynman-Kac Formula
Autoren: Christian Bär, Frank Pfäffle
(2011)
This is an introduction to Wiener measure and the Feynman-Kac formula on general Riemannian manifolds for Riemannian geometers with little or no background in stochastics. We explain the construction of Wiener measure based on the heat kernel in full detail and we prove the Feynman-Kac formula for Schr\"odinger operators with L∞-potentials. We also consider normal Riemannian coverings and show that projecting and lifting of paths are inverse operations which respect the Wiener measure.
Zeitschrift:
Mat. Contemp.
Verlag:
Sociedade Brasileira de Matematica
2011 | Generalizing from several related classification tasks to a new unlabeled sample | Blanchard, G., Lee, G., Scott, C.
Zeitschrift: Advances in neural information processing systems (NIPS 2011)
Seiten: 2178-2186
Generalizing from several related classification tasks to a new unlabeled sample
Autoren: Blanchard, G., Lee, G., Scott, C.
(2011)
Zeitschrift:
Advances in neural information processing systems (NIPS 2011)
2011 | The Holst Action by the Spectral Action Principle | Frank Pfäffle, Christoph Stephan
Zeitschrift: Comm. Math. Phys.
Verlag: Springer
Seiten: 261-273
Band: 307, no. 1
Link zur Publikation
,
Link zum Preprint
The Holst Action by the Spectral Action Principle
Autoren: Frank Pfäffle, Christoph Stephan
(2011)
We investigate the Holst action for closed Riemannian 4-manifolds with orthogonal connections. For connections whose torsion has zero Cartan type component we show that the Holst action can be recovered from the heat asymptotics for the natural Dirac operator acting on left-handed spinor fields.
Zeitschrift:
Comm. Math. Phys.
2011 | Application of classical Kolmogorov, Cramér-von-Mises-Smirnov and Anderson-Darling Tests for censored samples | Hannelore Liero, Ekatarina Chimitova, Maria Vedernikova
Buchtitel: Proc. Workshop Applied Methods of Statistical Analysis AMSA´2011. Novosibirsk 2011
Seiten: 176-185
Application of classical Kolmogorov, Cramér-von-Mises-Smirnov and Anderson-Darling Tests for censored samples
Autoren: Hannelore Liero, Ekatarina Chimitova, Maria Vedernikova
(2011)
Buchtitel:
Proc. Workshop Applied Methods of Statistical Analysis AMSA´2011. Novosibirsk 2011
2011 | Goodness of Fit, Smoothing and Resampling under Censoring | Hannelore Liero
Buchtitel: Proc. Workshop Applied Methods of Statistical Analysis AMSA´2011}. Novosibirsk 2011
Seiten: 127-132
Goodness of Fit, Smoothing and Resampling under Censoring
Autoren: Hannelore Liero
(2011)
Buchtitel:
Proc. Workshop Applied Methods of Statistical Analysis AMSA´2011}. Novosibirsk 2011
2010 | L1-regularisation for ill-posed problems in variational data assimilation | M.A. Freitag, N.K. Nichols, C.J. Budd
Zeitschrift: PAMM
Seiten: 665-668
Band: 10(1)
Link zur Publikation
L1-regularisation for ill-posed problems in variational data assimilation
Autoren: M.A. Freitag, N.K. Nichols, C.J. Budd
(2010)
2010 | Drug-Class Specific Impact of Antivirals on the Reproductive Capacity of HIV | M. von Kleist, S. Menz, W. Huisinga
Zeitschrift: PLoS Comput Biol
Band: 6(3)
Link zur Publikation
,
e1000720
Drug-Class Specific Impact of Antivirals on the Reproductive Capacity of HIV
Autoren: M. von Kleist, S. Menz, W. Huisinga
(2010)
Zeitschrift:
PLoS Comput Biol
2010 | Quantifying uncertainty, variability and likelihood for ordinary differential equation models | A. Y. Weiße, R. Middleton, W. Huisinga
Zeitschrift: BMC Systems Biology
Band: 4
Link zur Publikation
Quantifying uncertainty, variability and likelihood for ordinary differential equation models
Autoren: A. Y. Weiße, R. Middleton, W. Huisinga
(2010)
Zeitschrift:
BMC Systems Biology
2010 | Lumping of Physiologically Based Pharmacokinetic Models and a Mechanistic Derivation of Classical Compartmental Models | S. Pilari, W. Huisinga
Zeitschrift: J. Pharmacokinet. Pharmacodyn.
Seiten: 365-405
Band: 37
Link zur Publikation
Lumping of Physiologically Based Pharmacokinetic Models and a Mechanistic Derivation of Classical Compartmental Models
Autoren: S. Pilari, W. Huisinga
(2010)
Zeitschrift:
J. Pharmacokinet. Pharmacodyn.
2010 | Eine gute Dosis Mathematik - Modellbasierte Arzneimittelentwicklung am Beispiel therapeutischer Proteine | W. Huisinga, B.-F. Krippendorff
Zeitschrift: Systembiologie.de, Ausg. 02, December 2010
Link zur Publikation
Eine gute Dosis Mathematik - Modellbasierte Arzneimittelentwicklung am Beispiel therapeutischer Proteine
Autoren: W. Huisinga, B.-F. Krippendorff
(2010)
Zeitschrift:
Systembiologie.de, Ausg. 02, December 2010
2010 | On Finite Functions with Non-trivial Arity Gap | Shtrakov, Sl. and Koppitz, J.
Zeitschrift: Discussiones Mathematicae General Algebra and Applications
Band: 30
On Finite Functions with Non-trivial Arity Gap
Autoren: Shtrakov, Sl. and Koppitz, J.
(2010)
Zeitschrift:
Discussiones Mathematicae General Algebra and Applications
2010 | On some Anti-inverse Transformation Semigroups | Dimitrova, I. and Koppitz, J.
Zeitschrift: Comptes redndus de I`Académie bulgare des Sciences
Band: 63 no. 6
On some Anti-inverse Transformation Semigroups
Autoren: Dimitrova, I. and Koppitz, J.
(2010)
Zeitschrift:
Comptes redndus de I`Académie bulgare des Sciences
2010 | he relationship between proper and inner hypersubstitutions for varieties of rings | Koppitz, J. and Musunthia, T.
Zeitschrift: Novi Sad J. Math
Band: 40 n0. 3
he relationship between proper and inner hypersubstitutions for varieties of rings
Autoren: Koppitz, J. and Musunthia, T.
(2010)
Zeitschrift:
Novi Sad J. Math
2010 | Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation | Matthias Keller, Daniel Lenz
Zeitschrift: Mathematical Modeling of Natural Phenomena
Buchtitel: "Spectral Problems"
Seiten: 198-204
Band: 5
Link zur Publikation
,
Link zum Preprint
Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation
Autoren: Matthias Keller, Daniel Lenz
(2010)
We discuss Laplacians on graphs in a framework of regular Dirichlet forms. We focus on phenomena related to unboundedness of the Laplacians. This includes (failure of) essential selfadjointness, absence of essential spectrum and stochastic incompleteness.
Zeitschrift:
Mathematical Modeling of Natural Phenomena
Buchtitel:
"Spectral Problems"
2010 | The essential spectrum of the Laplacian on rapidly branching tessellations | Matthias Keller
Zeitschrift: Mathematische Annalen
Seiten: 51-66
Band: 346
Link zur Publikation
,
Link zum Preprint
The essential spectrum of the Laplacian on rapidly branching tessellations
Autoren: Matthias Keller
(2010)
In this paper, we characterize absence of the essential spectrum of the Laplacian under a hyperbolicity assumption for general graphs. Moreover, we present a characterization for absence of the essential spectrum for planar tessellations in terms of curvature.
Zeitschrift:
Mathematische Annalen
2010 | Impact of the receiver fault distribution on aftershock activity | Sebastian Hainzl, Gert Zöller, and Ronjang Wang
Zeitschrift: J. Geophys. Res.
Verlag: American Geophysical Union
Seiten: B05315
Band: 115
Link zur Publikation
Impact of the receiver fault distribution on aftershock activity
Autoren: Sebastian Hainzl, Gert Zöller, and Ronjang Wang
(2010)
Zeitschrift:
J. Geophys. Res.
Verlag:
American Geophysical Union
2010 | Recurrence of large earthquakes: Bayesian inference from catalogs in the presence of magnitude uncertainties | Gert Zöller, Sebastian Hainzl, Matthias Holschneider
Zeitschrift: Pure Appl. Geophys
Verlag: Springer
Seiten: 845-853
Band: 167
Link zur Publikation
Recurrence of large earthquakes: Bayesian inference from catalogs in the presence of magnitude uncertainties
Autoren: Gert Zöller, Sebastian Hainzl, Matthias Holschneider
(2010)
Zeitschrift:
Pure Appl. Geophys
2010 | A multigrid solver for modeling complex interseismic stress fields | Seoleun Shin, Gert Zöller, Matthias Holschneider, Sebastian Reich
Zeitschrift: Comp. Geosci.
Verlag: Elsevier
Seiten: 1075-1082
Band: 37
Link zur Publikation
A multigrid solver for modeling complex interseismic stress fields
Autoren: Seoleun Shin, Gert Zöller, Matthias Holschneider, Sebastian Reich
(2010)
Zeitschrift:
Comp. Geosci.
2010 | Quantitative earthquake forecasts resulting from static stress-triggering | Sebastian Hainzl, Gilbert Brietzke, Gert Zöller
Zeitschrift: J. Geophys. Res.
Verlag: American Geophysical Union
Seiten: B11311
Band: 115
Link zur Publikation
Quantitative earthquake forecasts resulting from static stress-triggering
Autoren: Sebastian Hainzl, Gilbert Brietzke, Gert Zöller
(2010)
Zeitschrift:
J. Geophys. Res.
Verlag:
American Geophysical Union
2010 | Steady-state solutions of rupture propagation in an earthquake simulator governed by rate and state dependent friction | Gert Zöller, Sebastian Hainzl, Matthias Holschneider, Gilbert Brietzke
Zeitschrift: Eur. Phys. J. Spec. Top.
Verlag: Springer
Seiten: 105-115
Band: 191
Link zur Publikation
Steady-state solutions of rupture propagation in an earthquake simulator governed by rate and state dependent friction
Autoren: Gert Zöller, Sebastian Hainzl, Matthias Holschneider, Gilbert Brietzke
(2010)
Zeitschrift:
Eur. Phys. J. Spec. Top.
2010 | Frames of poisson wavelets on the sphere | I. Iglewska-Nowak and M Holschneider
Zeitschrift: ACHA
Seiten: 227--248
Band: 28(2):
Frames of poisson wavelets on the sphere
Autoren: I. Iglewska-Nowak and M Holschneider
(2010)
2010 | Microsaccade characterization using the continuous wavelet transform and principal component analysis | M. Bettenbühl, C. Paladini, K. Mergenthaler, R. Kliegl, R. Engbert, and M. Holschneider
Zeitschrift: Journal of Eye Movement Research
Seiten: 1--14.
Band: 1(3(5)):
Microsaccade characterization using the continuous wavelet transform and principal component analysis
Autoren: M. Bettenbühl, C. Paladini, K. Mergenthaler, R. Kliegl, R. Engbert, and M. Holschneider
(2010)
Zeitschrift:
Journal of Eye Movement Research
2010 | Error distribution in regional inversion of potential fields from satellite data | Reyko Schachtschneider, Matthias Holschneider, and Mioara Mandea
Zeitschrift: Geophys. J. Int.
Seiten: 1428--1440
Band: 181
Error distribution in regional inversion of potential fields from satellite data
Autoren: Reyko Schachtschneider, Matthias Holschneider, and Mioara Mandea
(2010)
Zeitschrift:
Geophys. J. Int.
2010 | Convergence rate analysis of the first stage Runge-Kutta-type regularizations | P. Pornsawad, C. Böckmann
Zeitschrift: Inverse Problems
Band: 26
Link zur Publikation
Convergence rate analysis of the first stage Runge-Kutta-type regularizations
Autoren: P. Pornsawad, C. Böckmann
(2010)
Zeitschrift:
Inverse Problems
2010 | RETRIEVAL OF AEROSOL EXTINCTION COEFFICIENT PROFILES FROM RAMAN LIDAR SIGNALS | C. Böckmann, P. Pornsawad, G. D’Amico, A. Amodeo, G. Pappalardo
Zeitschrift: Proc. 25th International Lidar Radar Conference
Seiten: 1--4
RETRIEVAL OF AEROSOL EXTINCTION COEFFICIENT PROFILES FROM RAMAN LIDAR SIGNALS
Autoren: C. Böckmann, P. Pornsawad, G. D’Amico, A. Amodeo, G. Pappalardo
(2010)
Zeitschrift:
Proc. 25th International Lidar Radar Conference
2010 | THE COMMON CALCULUS CHAIN DEVELOPED IN THE FRAME OF EARLINET | A. Amodeo, G. D’Amico, I. Mattis,..C. Böckmann, et al
Zeitschrift: Proc. 25th International Lidar Radar Conference
Seiten: 1--4
THE COMMON CALCULUS CHAIN DEVELOPED IN THE FRAME OF EARLINET
Autoren: A. Amodeo, G. D’Amico, I. Mattis,..C. Böckmann, et al
(2010)
Zeitschrift:
Proc. 25th International Lidar Radar Conference
2010 | From LIDAR Signals to Aerosol Microphysics by Regularization | C. Böckmann, P. Pornsawad, L. Osterloh, A. Papayannis, A. Amodeo
Zeitschrift: Proc. International Geoscience and Remote Sensing Symposium
Seiten: 1--4
From LIDAR Signals to Aerosol Microphysics by Regularization
Autoren: C. Böckmann, P. Pornsawad, L. Osterloh, A. Papayannis, A. Amodeo
(2010)
Zeitschrift:
Proc. International Geoscience and Remote Sensing Symposium
2010 | Ensemble Kalman and H_infty filters. | S. Reich
Zeitschrift: AIP Conf. Proc.
Seiten: 19-22
Band: 1281
Link zur Publikation
Ensemble Kalman and H_infty filters.
Autoren: S. Reich
(2010)
Zeitschrift:
AIP Conf. Proc.
2010 | A mollified ensemble Kalman filter. | K. Bergemann and S. Reich,
Zeitschrift: Q.J.R. Meteorolog. Soc.
Seiten: 1636-1643
Band: 136
Link zur Publikation
A mollified ensemble Kalman filter.
Autoren: K. Bergemann and S. Reich,
(2010)
Zeitschrift:
Q.J.R. Meteorolog. Soc.
2010 | A localization technique for ensemble Kalman filters | K. Bergemann and S. Reich
Zeitschrift: Q.J.R. Meterolog. Soc
Seiten: 701-707
Band: 136
Link zur Publikation
A localization technique for ensemble Kalman filters
Autoren: K. Bergemann and S. Reich
(2010)
Zeitschrift:
Q.J.R. Meterolog. Soc
2010 | Evaluation of three spatial discretization schemes with the Galewsky et al. test | S. Shin, M. Sommer, S. Reich and P. Nevir
Zeitschrift: Atmospheric Science Letters
Seiten: 223-228
Band: 11
Link zur Publikation
Evaluation of three spatial discretization schemes with the Galewsky et al. test
Autoren: S. Shin, M. Sommer, S. Reich and P. Nevir
(2010)
Zeitschrift:
Atmospheric Science Letters
2010 | Phase space volume conservation under space and time discretization schemes for the shallow-water equations | M. Sommer and S. Reich
Zeitschrift: Monthly Weather Review
Seiten: 4229-4236
Band: 138
Link zur Publikation
Phase space volume conservation under space and time discretization schemes for the shallow-water equations
Autoren: M. Sommer and S. Reich
(2010)
Zeitschrift:
Monthly Weather Review
2010 | Surfaces with maximal constant mean curvature | Jan Metzger
Zeitschrift: Comm. Anal. Geom.
Seiten: 627-647
Band: 18
Link zur Publikation
Surfaces with maximal constant mean curvature
Autoren: Jan Metzger
(2010)
Zeitschrift:
Comm. Anal. Geom.
2010 | Small surfaces of Willmore type in Riemannian manifolds | Tobias Lamm and Jan Metzger
Zeitschrift: Intl. Math. Res. Notices
Seiten: 3786-3813
Band: 2010
Link zur Publikation
Small surfaces of Willmore type in Riemannian manifolds
Autoren: Tobias Lamm and Jan Metzger
(2010)
Zeitschrift:
Intl. Math. Res. Notices
2010 | Blowup of Jang’s equation at outermost marginally trapped surfaces | Jan Metzger
Zeitschrift: Comm. Math. Phys.
Seiten: 61-72
Band: 294
Link zur Publikation
Blowup of Jang’s equation at outermost marginally trapped surfaces
Autoren: Jan Metzger
(2010)
Zeitschrift:
Comm. Math. Phys.
2010 | Short-time Gibbsianness for Infinite-dimensional Diffusions with Space-Time Interaction | F. Redig, S. Roelly, W. Ruszel
Zeitschrift: J. Stat. Phys.
Seiten: 1124-1144"
Band: 138
Link zur Publikation
,
Link zum Preprint
Short-time Gibbsianness for Infinite-dimensional Diffusions with Space-Time Interaction
Autoren: F. Redig, S. Roelly, W. Ruszel
(2010)
Zeitschrift:
J. Stat. Phys.
2010 | Infinitely many Brownian globules with Brownian radii | M. Fradon, S. Roelly
Zeitschrift: Stoch. Dyn.
Seiten: 591-612
Band: 10
Link zur Publikation
,
Link zum Preprint
Infinitely many Brownian globules with Brownian radii
Autoren: M. Fradon, S. Roelly
(2010)
2010 | User Interface Design for Dynamic Geometry Software | Ulrich Kortenkamp, Christian Dohrmann
Zeitschrift: Proceedings of CADGME 2009
Reihe: 3
Seiten: 59-66
Band: 2
Link zur Publikation
User Interface Design for Dynamic Geometry Software
Autoren: Ulrich Kortenkamp, Christian Dohrmann
(2010)
Zeitschrift:
Proceedings of CADGME 2009
2010 | A Sobolev Poincaré type inequality for integral varifolds | Ulrich Menne
Zeitschrift: Calc. Var. Partial Differential Equations
Seiten: 369-408
Band: 38(3-4)
Link zur Publikation
,
Link zum Preprint
A Sobolev Poincaré type inequality for integral varifolds
Autoren: Ulrich Menne
(2010)
In this work a local inequality is provided which bounds the distance of an integral varifold from a multivalued plane (height) by its tilt and mean curvature. The bounds obtained for the exponents of the Lebesgue spaces involved are shown to be sharp.
Zeitschrift:
Calc. Var. Partial Differential Equations
2010 | M-solid Positive Varieties of Tree Languages | Jörg Koppitz, Klaus Denecke
Zeitschrift: Contributions to General Algebra
Seiten: 57-80
Band: 19
M-solid Positive Varieties of Tree Languages
Autoren: Jörg Koppitz, Klaus Denecke
(2010)
Zeitschrift:
Contributions to General Algebra
2010 | On some Anti-inverse Transformation Semigroups | Ilinka Dimitrova, Jörg Koppitz
Zeitschrift: Comptes redndus de I`Académie bulgare des Sciences
Seiten: 793-798
Band: 63/6
On some Anti-inverse Transformation Semigroups
Autoren: Ilinka Dimitrova, Jörg Koppitz
(2010)
Zeitschrift:
Comptes redndus de I`Académie bulgare des Sciences
2010 | On Finite Functions with Non-trivial Arity Gap | Jörg Koppitz, Slavcho Shtrakov
Zeitschrift: Discussiones Mathematicae, General Algebra and Applications
Seiten: 217-245
Band: 30
On Finite Functions with Non-trivial Arity Gap
Autoren: Jörg Koppitz, Slavcho Shtrakov
(2010)
Zeitschrift:
Discussiones Mathematicae, General Algebra and Applications
2010 | The relationship between proper and inner hypersubstitutions for varieties of rings | Jörg Koppitz Tiwadee Musunthia
Zeitschrift: Novi Sad J. Math
Seiten: 55-65
Band: 40/3
The relationship between proper and inner hypersubstitutions for varieties of rings
Autoren: Jörg Koppitz Tiwadee Musunthia
(2010)
Zeitschrift:
Novi Sad J. Math
2010 | Almost exponential decay of quantum resonance states and Paley-Wiener type estimates in Gevrey spaces | Markus Klein, Juliane Rama
Zeitschrift: Annales Henri Poincare
Seiten: 499 – 537
Band: 11, Nr. 3
Almost exponential decay of quantum resonance states and Paley-Wiener type estimates in Gevrey spaces
Autoren: Markus Klein, Juliane Rama
(2010)
Zeitschrift:
Annales Henri Poincare
2010 | Optimal learning rates for kernel conjugate gradient regression | Blanchard, G., Krämer, N.
Zeitschrift: Advances in Neural Information Processing Systems (NIPS 2010)
Seiten: 226-234
Optimal learning rates for kernel conjugate gradient regression
Autoren: Blanchard, G., Krämer, N.
(2010)
Zeitschrift:
Advances in Neural Information Processing Systems (NIPS 2010)
2010 | Linear Wave Equations on Lorentzian Manifolds | Christian Bär
Verlag: European Mathematical Society
Buchtitel: V. Cortes (ed.): Handbook of Pseudo-Riemannian Geometry and Supersymmetry
Seiten: 897-914
Link zur Publikation
,
Link zum Preprint
Linear Wave Equations on Lorentzian Manifolds
Autoren: Christian Bär
(2010)
We summarize the analytic theory of linear wave equations on globally hyperbolic Lorentzian manifolds.
Verlag:
European Mathematical Society
Buchtitel:
V. Cortes (ed.): Handbook of Pseudo-Riemannian Geometry and Supersymmetry
2010 | Kernel Partial Least Squares is Universally Consistent | Blanchard, G., Krämer, N.
Zeitschrift: AISTATS 2010
Verlag: JMLR Workshop and Conference Proceedings
Seiten: 57-64
Band: 9
Kernel Partial Least Squares is Universally Consistent
Autoren: Blanchard, G., Krämer, N.
(2010)
Zeitschrift:
AISTATS 2010
Verlag:
JMLR Workshop and Conference Proceedings
2010 | Elementare Differentialgeometrie (Monografie), 2. Auflage | Christian Bär
Reihe: de Gruyter Lehrbuch
Verlag: De Gruyter
Seiten: xvi+340 pages
Link zur Publikation
Elementare Differentialgeometrie (Monografie), 2. Auflage
Autoren: Christian Bär
(2010)
Dieses Lehrbuch bietet eine Einführung in die Differentialgeometrie von Kurven und Flächen. Es ist in der vorliegenden zweiten, überarbeiteten Auflage um Lösungshinweise sowie Anwendungen in der Kartografie erweitert. Themen sind u. a. euklidische Geometrie, Kurventheorie, Flächentheorie, Krümmungsbegriffe, Minimalflächen, Riemann'sche Geometrie und der Satz von Gauß-Bonnet.
Reihe:
de Gruyter Lehrbuch
2010 | Conjugate gradient regularization under general smoothness and noise assumptions | Blanchard, G., Mathé, P.
Zeitschrift: Journal of Inverse and Ill-posed Problems
Seiten: 701-726
Band: 18
Conjugate gradient regularization under general smoothness and noise assumptions
Autoren: Blanchard, G., Mathé, P.
(2010)
Zeitschrift:
Journal of Inverse and Ill-posed Problems
2010 | Elementary Differential Geometry (Monografie) | Christian Bär
Reihe: Cambridge University Press
Verlag: Cambridge University Press
Link zur Publikation
Elementary Differential Geometry (Monografie)
Autoren: Christian Bär
(2010)
English translation of the book "Elementare Differentialgeometrie", published by deGruyter.
Reihe:
Cambridge University Press
Verlag:
Cambridge University Press
2010 | Semi-supervised novelty detection | Blanchard, G., Lee, G., Scott, C.
Zeitschrift: Journal of Machine Learning Research
Verlag: JMLR. org
Seiten: 2973-3009
Band: 11
Semi-supervised novelty detection
Autoren: Blanchard, G., Lee, G., Scott, C.
(2010)
Zeitschrift:
Journal of Machine Learning Research
2010 | Stochastic completeness and volume growth | Christian Bär, Gregorio Pacelli Bessa
Zeitschrift: Proc. Amer. Math. Soc.
Verlag: American Mathematical Society
Seiten: 2629-2640
Band: 138, no. 7
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,
Link zum Preprint
Stochastic completeness and volume growth
Autoren: Christian Bär, Gregorio Pacelli Bessa
(2010)
It has been suggested in 1999 that a certain volume growth condition for geodesically complete Riemannian manifolds might imply that the manifold is stochastically complete. This is motivated by a large class of examples and by a known analogous criterion for recurrence of Brownian motion. We show that the suggested implication is not true in general. We also give counter-examples to a converse implication.
Zeitschrift:
Proc. Amer. Math. Soc.
Verlag:
American Mathematical Society
2010 | Some nonasymptotic results on resampling in high dimension, I: Confidence regions | Arlot, S., Blanchard, G., Roquain, E.
Zeitschrift: The Annals of Statistics
Verlag: Institute of Mathematical Statistics
Seiten: 51-82
Band: 38
Some nonasymptotic results on resampling in high dimension, I: Confidence regions
Autoren: Arlot, S., Blanchard, G., Roquain, E.
(2010)
Zeitschrift:
The Annals of Statistics
Verlag:
Institute of Mathematical Statistics
2010 | Asymptotic heat kernel expansion in the semi-classical limit | Christian Bär, Frank Pfäffle
Zeitschrift: Comm. Math. Phys.
Verlag: Springer
Seiten: 731-744
Band: 294, no. 3
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,
Link zum Preprint
Asymptotic heat kernel expansion in the semi-classical limit
Autoren: Christian Bär, Frank Pfäffle
(2010)
Let Hh = h2 L + V where L is a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold and V is a symmetric endomorphism field. We derive an asymptotic expansion for the heat kernel of Hh as h→0. As a consequence we get an asymptotic expansion for the quantum partition function and we see that it is asymptotic to the classical partition function. Moreover, we show how to bound the quantum partition function for positive h by the classical partition function.
Zeitschrift:
Comm. Math. Phys.
2010 | Some non-asymptotic results on resampling in high dimension, II: Multiple tests | Roquain, E., Arlot, S., Blanchard, G.
Zeitschrift: The Annals of Statistics
Verlag: Institute of Mathematical Statistics
Seiten: 83-99
Band: 38
Some non-asymptotic results on resampling in high dimension, II: Multiple tests
Autoren: Roquain, E., Arlot, S., Blanchard, G.
(2010)
Zeitschrift:
The Annals of Statistics
Verlag:
Institute of Mathematical Statistics
2010 | A spectral estimate for the Dirac operator on Riemannian flows | Nicolas Ginoux, Georges Habib
Zeitschrift: Cent. Eur. J. Math.
Verlag: Springer
Seiten: 950-965
Band: 8, no. 5
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,
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A spectral estimate for the Dirac operator on Riemannian flows
Autoren: Nicolas Ginoux, Georges Habib
(2010)
We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on Sasakian and on 3-dimensional manifolds and partially classify those satisfying the limiting case. Finally, we compare our estimate with a lower bound in terms of a natural tensor depending on the eigenspinor.
Zeitschrift:
Cent. Eur. J. Math.
2010 | uTOSS-Multiple hypothesis testing in an open software system. | Blanchard, G., Dickhaus, T., Hack, N., Konietschke, F., Rohmeyer, K., Rosenblatt, J., Scheer, M., Werft, W.
Zeitschrift: Workshop on Applications of Pattern Analysis (WAPA)
Verlag: JMLR Workshop and Conference Proceedings
Seiten: 12-19
Band: 11
uTOSS-Multiple hypothesis testing in an open software system.
Autoren: Blanchard, G., Dickhaus, T., Hack, N., Konietschke, F., Rohmeyer, K., Rosenblatt, J., Scheer, M., Werft, W.
(2010)
Zeitschrift:
Workshop on Applications of Pattern Analysis (WAPA)
Verlag:
JMLR Workshop and Conference Proceedings
2010 | The Spectral Action for Dirac Operators with skew-symmetric Torsion | Florian Hanisch, Frank Pfäffle, Christoph Stephan
Zeitschrift: Comm. Math. Phys.
Verlag: Springer
Seiten: 877-888
Band: 300, no. 3
Link zur Publikation
,
Link zum Preprint
The Spectral Action for Dirac Operators with skew-symmetric Torsion
Autoren: Florian Hanisch, Frank Pfäffle, Christoph Stephan
(2010)
We derive a formula for the gravitational part of the spectral action for Dirac operators on 4-dimensional manifolds with totally anti-symmetric torsion. We find that the torsion becomes dynamical and couples to the traceless part of the Riemann curvature tensor. Finally we deduce the Lagrangian for the Standard Model of particle physics in presence of torsion from the Chamseddine-Connes Dirac operator.
Zeitschrift:
Comm. Math. Phys.
2010 | Generic metrics and the mass endomorphism on spin three-manifolds | Andreas Hermann
Zeitschrift: Ann. Global Anal. Geom.
Verlag: Springer
Seiten: 163-171
Band: 37, no. 2
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Generic metrics and the mass endomorphism on spin three-manifolds
Autoren: Andreas Hermann
(2010)
Let (M,g) be a closed Riemannian spin manifold. The constant term in the expansion of the Green function for the Dirac operator at a fixed point p ∈ M is called the mass endomorphism in p associated to the metric g due to an analogy to the mass in the Yamabe problem. We show that the mass endomorphism of a generic metric on a three-dimensional spin manifold is nonzero. This implies a strict inequality which can be used to avoid bubbling-off phenomena in conformal spin geometry.
Zeitschrift:
Ann. Global Anal. Geom.
2010 | Nonparametric Estimation and Testing the Effect of Covariates in Accelerated Life Time Models under Censoring | Hannelore Liero
Verlag: Birkhauser, Boston
Buchtitel: Mathematical and Statistical Methods in Reliability, Eds. N.Balakrishnan, M. S. Nikulin, and V. Rykov,
Nonparametric Estimation and Testing the Effect of Covariates in Accelerated Life Time Models under Censoring
Autoren: Hannelore Liero
(2010)
Verlag:
Birkhauser, Boston
Buchtitel:
Mathematical and Statistical Methods in Reliability, Eds. N.Balakrishnan, M. S. Nikulin, and V. Rykov,
2009 | All toroidal embeddings of polyhedral graphs in 3-space are chiral | T. Castle, M. E. Evans and S. T. Hyde
Zeitschrift: New Journal of Chemistry 33(10)
Seiten: 2107-2113
Link zur Publikation
All toroidal embeddings of polyhedral graphs in 3-space are chiral
Autoren: T. Castle, M. E. Evans and S. T. Hyde
(2009)
Zeitschrift:
New Journal of Chemistry 33(10)
2009 | Shift-invert Arnoldi's method with preconditioned iterative solves | M.A. Freitag, A. Spence
Zeitschrift: SIAM J. Matrix Anal. Appl.
Seiten: 942-969
Band: 31(3)
Link zur Publikation
Shift-invert Arnoldi's method with preconditioned iterative solves
Autoren: M.A. Freitag, A. Spence
(2009)
Zeitschrift:
SIAM J. Matrix Anal. Appl.
2009 | The calculation of the distance to instability by the computation of a Jordan block | M. Freitag (joint work with A. Spence)
Oberwolfach Report No. 37/2009. (Report)
The calculation of the distance to instability by the computation of a Jordan block
Autoren: M. Freitag (joint work with A. Spence)
(2009)
Oberwolfach Report No. 37/2009. (
Report)
2009 | Using math to optimize medication | W. Huisinga
Zeitschrift: NUI Maynooth Research Magazine, Vol. 1, January 2009
Link zur Publikation
Using math to optimize medication
Autoren: W. Huisinga
(2009)
Zeitschrift:
NUI Maynooth Research Magazine, Vol. 1, January 2009
2009 | Pharmacokinetic-Pharmacodynamic relationship of NRTIs and its connection to viral escape: An example based on Zidovudine | M. von Kleist, and W. Huisinga
Zeitschrift: Eur J Pharm Sci.
Seiten: 532-543
Band: 36
Link zur Publikation
Pharmacokinetic-Pharmacodynamic relationship of NRTIs and its connection to viral escape: An example based on Zidovudine
Autoren: M. von Kleist, and W. Huisinga
(2009)
Zeitschrift:
Eur J Pharm Sci.
2009 | Mechanism-based Inhibition: Deriving KI and kinact directly from Time-Dependent IC50 Values | B.-F. Krippendorff, R. Neuhaus, P. Lienau, A. Reichel, W. Huisinga
Zeitschrift: J Biomol Screen.
Seiten: 913-923
Band: 14
Link zur Publikation
,
Suppl Material
Mechanism-based Inhibition: Deriving KI and kinact directly from Time-Dependent IC50 Values
Autoren: B.-F. Krippendorff, R. Neuhaus, P. Lienau, A. Reichel, W. Huisinga
(2009)
Zeitschrift:
J Biomol Screen.
2009 | Nonlinear Pharmacokinetics of Therapeutic Proteins Resulting from Receptor Mediated Endocytosis | B.-F. Krippendorff, K. Küster, C. Kloft, W. Huisinga
Zeitschrift: J. Pharmacokinet. Pharmacodyn.
Seiten: 239-260
Band: 36
Link zur Publikation
,
Suppl Material
Nonlinear Pharmacokinetics of Therapeutic Proteins Resulting from Receptor Mediated Endocytosis
Autoren: B.-F. Krippendorff, K. Küster, C. Kloft, W. Huisinga
(2009)
Zeitschrift:
J. Pharmacokinet. Pharmacodyn.
2009 | Ligand accumulation counteracts therapeutic inhibition of receptor systems | B.-F. Krippendorff, D. Oyarzun and W. Huisinga
Zeitschrift: Proceedings of Foundations of Systems Biology in Engeneering, FOSBE
Seiten: 173-176
Link zur Publikation
Ligand accumulation counteracts therapeutic inhibition of receptor systems
Autoren: B.-F. Krippendorff, D. Oyarzun and W. Huisinga
(2009)
Zeitschrift:
Proceedings of Foundations of Systems Biology in Engeneering, FOSBE
2009 | Retention of gene products in syncytial spermatids promotes non-Mendelian inheritance as revealed by the t-complex-responder | N. Véron, H. Bauer, A. Y. Weiße, G. Lüder, M. Werber, and B. G. Herrmann
Zeitschrift: Genes & Development
Seiten: 2705-10
Band: 23
Link zur Publikation
Retention of gene products in syncytial spermatids promotes non-Mendelian inheritance as revealed by the t-complex-responder
Autoren: N. Véron, H. Bauer, A. Y. Weiße, G. Lüder, M. Werber, and B. G. Herrmann
(2009)
Zeitschrift:
Genes & Development
2009 | All Reg-solid varieties of commutative semigroups | Koppitz, J.
Zeitschrift: Semigroup Forum
Band: 78 no.1
All Reg-solid varieties of commutative semigroups
Autoren: Koppitz, J.
(2009)
Zeitschrift:
Semigroup Forum
2009 | The maximal subsemigroupoups of the ideals of some semigroups of partial injections | Dimitrova, I. and Koppitz, J.
Zeitschrift: Discussiones Mathematicae General Algebra and Applications
Band: 29 no. 2
The maximal subsemigroupoups of the ideals of some semigroups of partial injections
Autoren: Dimitrova, I. and Koppitz, J.
(2009)
Zeitschrift:
Discussiones Mathematicae General Algebra and Applications
2009 | On extending Prüfer rings in central simple algebras | Gräter, J.
Zeitschrift: Forum Math.21
Seiten: 131-145
On extending Prüfer rings in central simple algebras
Autoren: Gräter, J.
(2009)
Zeitschrift:
Forum Math.21
2009 | Some applications of the isoperimetric inequality for integral varifolds | Ulrich Menne
Zeitschrift: Adv. Calc. Var.
Seiten: 247-269
Band: 2(3)
Link zur Publikation
,
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Some applications of the isoperimetric inequality for integral varifolds
Autoren: Ulrich Menne
(2009)
In this work the isoperimetric inequality for integral varifolds of locally bounded first variation is used to obtain sharp estimates for the size of the set where the density quotient is small and to generalise Calderón’s and Zygmund’s theory of first order differentiability for functions in Lebesgue spaces from Lebesgue measure to integral varifolds.
Zeitschrift:
Adv. Calc. Var.
2009 | Harmonic Approximations of difference operators | Markus Klein, Elke Rosenberger
Zeitschrift: Journal of Functional Analysis
Seiten: 3409 – 3453
Band: 257, Nr. 1
Link zur Publikation
Harmonic Approximations of difference operators
Autoren: Markus Klein, Elke Rosenberger
(2009)
For a general class of difference operators <tex>H_\varepsilon = T_\varepsilon + V_\varepsilon</tex> on <tex>\ell^2(\varepsilon\mathbf{Z}^d)</tex>.
where <tex>V_\varepsilon</tex> is a multi-well potential and <tex>\varepsilon</tex> is a small parameter, we analyze the asymptotic behavior as<tex> \varepsilon\to 0</tex> of the (low-lying) eigenvalues and eigenfunctions.
We show that the first n eigenvalues of <tex>H_\varepsilon</tex> converge to the first n eigenvalues of the direct sum of harmonic oscillators on <tex>\mathbf{R}^d</tex> located at the several wells. Our proof is microlocal.
Zeitschrift:
Journal of Functional Analysis
2009 | Novelty detection: Unlabeled data definitely help | Scott, C., Blanchard, G.
Zeitschrift: AISTATS 2009
Verlag: JMLR Workshop and Conference Proceedings
Seiten: 464-471
Band: 5
Novelty detection: Unlabeled data definitely help
Autoren: Scott, C., Blanchard, G.
(2009)
Zeitschrift:
AISTATS 2009
Verlag:
JMLR Workshop and Conference Proceedings
2009 | How wrong can we get? A review of machine learning approaches and error bars | Schwaighofer, A., Schroeter, T., Mika, S., Blanchard, G.
Zeitschrift: Combinatorial chemistry & high throughput screening
Verlag: Bentham Science Publishers
Seiten: 453-468
Band: 12
How wrong can we get? A review of machine learning approaches and error bars
Autoren: Schwaighofer, A., Schroeter, T., Mika, S., Blanchard, G.
(2009)
Zeitschrift:
Combinatorial chemistry & high throughput screening
Verlag:
Bentham Science Publishers
2009 | Duality between Hyperbolic and de Sitter Geometry | Immanuel Asmus
Zeitschrift: J. Geom.
Verlag: Springer
Seiten: 11-40
Band: 96, no.1-2
Link zur Publikation
,
Link zum Preprint
Duality between Hyperbolic and de Sitter Geometry
Autoren: Immanuel Asmus
(2009)
In this paper we describe trigonometry on the de Sitter surface. For that a characterization of geodesics is given, leading to various types of triangles. We define lengths and angles of these. Then, transferring the concept of polar triangles from spherical geometry into the Minkowski space, we relate hyperbolic with de Sitter triangles such that the proof of the hyperbolic law of cosines for angles becomes much clearer and easier than it is traditionally. Furthermore, polar triangles turn out to be a powerful tool for describing de Sitter trigonometry.
2009 | Adaptive false discovery rate control under independence and dependence | Blanchard, G., Roquain, E.
Zeitschrift: Journal of Machine Learning Research
Verlag: JMLR. org
Seiten: 2837-2871
Band: 10
Adaptive false discovery rate control under independence and dependence
Autoren: Blanchard, G., Roquain, E.
(2009)
Zeitschrift:
Journal of Machine Learning Research
2009 | Spectral Bounds for Dirac Operators on Open Manifolds | Christian Bär
Zeitschrift: Ann. Global Anal. Geom.
Verlag: Springer
Seiten: 67-79
Band: 36, no. 1
Link zur Publikation
,
Link zum Preprint
Spectral Bounds for Dirac Operators on Open Manifolds
Autoren: Christian Bär
(2009)
We extend several classical eigenvalue estimates for Dirac operators on compact manifolds to noncompact, even incomplete manifolds. This includes Friedrich's estimate for manifolds with positive scalar curvature as well as the author's estimate on surfaces.
Zeitschrift:
Ann. Global Anal. Geom.
2009 | C*-algebras | Christian Bär, Christian Becker
Reihe: Lecture Notes in Physics
Verlag: Springer
Buchtitel: C. Bär, K. Fredenhagen (eds.): Quantum Field Theory on Curved Spacetimes
Seiten: 1-37
Band: 786
Link zur Publikation
,
Link zum Preprint
C*-algebras
Autoren: Christian Bär, Christian Becker
(2009)
This is a survey on the theory of C*-algebras as needed for quantum field theory on curved spacetimes. It covers basic definitions, the spectrum, morphisms, states and representations, product states, and Weyl systems.
Reihe:
Lecture Notes in Physics
Buchtitel:
C. Bär, K. Fredenhagen (eds.): Quantum Field Theory on Curved Spacetimes
2009 | Quantum Field Theory on Curved Spacetimes - Concepts and Mathematical Foundations (Monografie) | Christian Bär, Klaus Fredenhagen
Reihe: Lecture Notes in Physics
Verlag: Springer
Band: 786
Link zur Publikation
Quantum Field Theory on Curved Spacetimes - Concepts and Mathematical Foundations (Monografie)
Autoren: Christian Bär, Klaus Fredenhagen
(2009)
After some decades of work a satisfactory theory of quantum gravity is still not available; moreover, there are indications that the original field theoretical approach may be better suited than originally expected. There, to first approximation, one is left with the problem of quantum field theory on Lorentzian manifolds. Surprisingly, this seemingly modest approach leads to far reaching conceptual and mathematical problems and to spectacular predictions, the most famous one being the Hawking radiation of black holes. Ingredients of this approach are the formulation of quantum physics in terms of C*-algebras, the geometry of Lorentzian manifolds, in particular their causal structure, and linear hyperbolic differential equations where the well-posedness of the Cauchy problem plays a distinguished role, as well as more recently the insights from suitable concepts such as microlocal analysis. This primer is an outgrowth of a compact course given by the editors and contributing authors to an audience of advanced graduate students and young researchers in the field, and assumes working knowledge of differential geometry and functional analysis on the part of the reader.
Reihe:
Lecture Notes in Physics
2009 | Das Yang-Mills-Problem. Die mathematische Zähmung des Standardmodells | Christian Bär, Christoph Stephan
Zeitschrift: Spektrum der Wissenschaft
Verlag: Spektrum der Wissenschaft Verlag
Seiten: 66-73
Band: 5
Link zur Publikation
Das Yang-Mills-Problem. Die mathematische Zähmung des Standardmodells
Autoren: Christian Bär, Christoph Stephan
(2009)
Die moderne Theorie der Elementarteilchen, die Quanten-Yang-Mills-Theorie, vermag die experimentellen Befunde mit unerhörter Genauigkeit wiederzugegen, es fehlt ihr jedoch bisher ein solides mathematisches Fundament. Über dessen Gestalt gibt es nur sehr nebelhafte Vorstellungen.
Zeitschrift:
Spektrum der Wissenschaft
Verlag:
Spektrum der Wissenschaft Verlag
2009 | BPS Wilson loops in N=4 SYM: Examples on hyperbolic submanifolds of space-time | Nadav Drukker, Volker Branding
Zeitschrift: Phys. Rev. D
Verlag: American Physical Society
Seiten: 106006
Band: 79, no. 10
Link zur Publikation
,
Link zum Preprint
BPS Wilson loops in N=4 SYM: Examples on hyperbolic submanifolds of space-time
Autoren: Nadav Drukker, Volker Branding
(2009)
In this paper we present a family of supersymmetric Wilson loops of N=4 supersymmetric Yang-Mills theory in Minkowski space. Our examples focus on curves restricted to hyperbolic submanifolds, H_3 and H_2, of space-time. Generically they preserve two supercharges, but in special cases more, including a case which has not been discussed before, of the hyperbolic line, conformal to the straight line and circle, which is half-BPS. We discuss some general properties of these Wilson loops and their string duals and study special examples in more detail. Generically the string duals propagate on a complexification of AdS_5 x S^5 and in some specific examples the compact sphere is effectively replaced by a de-Sitter space.
Zeitschrift:
Phys. Rev. D
Verlag:
American Physical Society
2009 | On a classification of irreducible almost-commutative geometries V | Jan-Hendrik Jureit, Christoph Stephan
Zeitschrift: J. Math. Phys.
Verlag: American Institute of Physics
Seiten: 72301
Band: 50, no. 7
Link zur Publikation
,
Link zum Preprint
On a classification of irreducible almost-commutative geometries V
Autoren: Jan-Hendrik Jureit, Christoph Stephan
(2009)
We extend a classification of irreducible, almost-commutative geometries whose spectral action is dynamically non-degenerate, to internal algebras that have six simple summands. We find essentially four particle models: An extension of the standard model by a new species of fermions with vectorlike coupling to the gauge group and gauge invariant masses, two versions of the electro-strong model and a variety of the electro-strong model with Higgs mechanism.
Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
2009 | On the evolution equation for magnetic geodesics | Dennis Koh
Zeitschrift: Calc. Var. Partial Differ. Equ.
Verlag: Springer
Seiten: 453-480
Band: 36, no. 3
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,
Link zum Preprint
On the evolution equation for magnetic geodesics
Autoren: Dennis Koh
(2009)
Orbits of charged particles under the effect of a magnetic field are mathematically described by magnetic geodesics. They appear as solutions to a system of (nonlinear) ordinary differential equations of second order. But we are only interested in periodic solutions. To this end, we study the corresponding system of (nonlinear) parabolic equations for closed magnetic geodesics and, as a main result, eventually prove the existence of long time solutions. As generalization one can consider a system of elliptic nonlinear partial differential equations whose solutions describe the orbits of closed p-branes under the effect of a "generalized physical force". For the corresponding evolution equation, which is a system of parabolic nonlinear PDEs associated to the elliptic PDE, we can establish existence of short time solutions.
Zeitschrift:
Calc. Var. Partial Differ. Equ.
2009 | Lorentzian Manifolds | Frank Pfäffle
Reihe: Lecture Notes in Physics
Verlag: Springer
Buchtitel: C. Bär, K. Fredenhagen (eds.): Quantum Field Theory on Curved Spacetimes
Seiten: 39-58
Band: 786
Link zur Publikation
,
Link zum Preprint
Lorentzian Manifolds
Autoren: Frank Pfäffle
(2009)
Some basic notions from Lorentzian geometry are reviewed. In particular causality relations are explained, Cauchy hypersurfaces and the concept of global hyperbolic manifoldes are introduced. Finally, the structure of globally hyperbolic manifolds is discussed.
Reihe:
Lecture Notes in Physics
Buchtitel:
C. Bär, K. Fredenhagen (eds.): Quantum Field Theory on Curved Spacetimes
2009 | The Laplacian on hyperbolic 3-manifolds with Dehn surgery type singularities | Frank Pfäffle, Hartmut Weiß
Zeitschrift: Comm. Anal. Geom.
Verlag: International Press
Seiten: 505-528
Band: 17, no. 3
Link zur Publikation
,
Link zum Preprint
The Laplacian on hyperbolic 3-manifolds with Dehn surgery type singularities
Autoren: Frank Pfäffle, Hartmut Weiß
(2009)
We study the spectrum of the Laplacian on hyperbolic 3-manifolds with Dehn surgery type singularities and its dependence on the generalized Dehn surgery coefficients.
Zeitschrift:
Comm. Anal. Geom.
Verlag:
International Press
2009 | Krajewski diagrams and the Standard Model | Christoph Stephan
Zeitschrift: J. Math. Phys
Verlag: American Institute of Physics
Seiten: 43515
Band: 50, no. 4
Link zur Publikation
,
Link zum Preprint
Krajewski diagrams and the Standard Model
Autoren: Christoph Stephan
(2009)
This paper provides a complete list of Krajewski diagrams representing the standard model of particle physics. We will give the possible representations of the algebra and the anomaly free lifts which provide the representation of the standard model gauge group on the fermionic Hilbert space. The algebra representations following from the Krajewski diagrams are not complete in the sense that the corresponding spectral triples do not necessarily obey to the axiom of Poincare duality. This defect may be repaired by adding new particles to the model, i.e. by building models beyond the standard model. The aim of this list of finite spectral triples (up to Poincare duality) is therefore to provide a basis for model building beyond the standard model.
Zeitschrift:
J. Math. Phys
Verlag:
American Institute of Physics
2009 | New Scalar Fields in Noncommutative Geometry | Christoph Stephan
Zeitschrift: Phys. Rev. D
Verlag: American Physical Society
Seiten: 65013
Band: 79, no. 6
Link zur Publikation
,
Link zum Preprint
New Scalar Fields in Noncommutative Geometry
Autoren: Christoph Stephan
(2009)
In this publication we present an extension of the Standard Model within the framework of Connes' noncommutative geometry [1]. The model presented here is based on a minimal spectral triple [7] which contains the Standard Model particles, new vectorlike fermions and a new U(1) gauge subgroup. Additionally a new complex scalar field appears that couples to the right-handed neutrino, the new fermions and the standard Higgs particle. The bosonic part of the action is given by the spectral action [1] which also determines relations among the gauge couplings, the quartic scalar couplings and the Yukawa couplings at a cut-off energy of ca. 10^(17) GeV. We investigate the renormalisation group flow of these relations. The low energy behaviour allows to constrain the Higgs mass, the mass of the new scalar and the mixing between these two scalar fields.
Zeitschrift:
Phys. Rev. D
Verlag:
American Physical Society
2009 | Beyond the Standard Model: A Noncommutative Approach | Christoph Stephan
Buchtitel: Proceedings of the XLIVth Rencontres de Moriond: Electroweak Interactions and Unified Theories
Link zum Preprint
Beyond the Standard Model: A Noncommutative Approach
Autoren: Christoph Stephan
(2009)
During the last two decades Alain Connes developed Noncommutative Geometry (NCG), which allows to unify two of the basic theories of modern physics: General Relativity (GR) and the Standard Model (SM) of Particle Physics as classical field theories. In the noncommutative framework the Higgs boson, which had previously to be put in by hand, and many of the ad hoc features of the standard model appear in a natural way.
The aim of this presentation is to motivate this unification from basic physical principles and to give a flavour of its derivation. One basic prediction of the noncommutative approach to the SM is that the mass of the Higgs Boson should be of the order of 170 GeV if one assumes the Big Desert. This mass range is with reasonable probability excluded by the Tevatron and therefore it is interesting to investigate models beyond the SM that are compatible with NCG. Going beyond the SM is highly non-trivial within the NCG approach but possible extensions have been found and provide for phenomenologically interesting models. We will present in this article a short introduction into the NCG framework and describe one of these extensions of the SM. This model contains new scalar bosons (and fermions) which constitute a second Higgs-like sector mixing with theordinary Higgs sector and thus considerably modifying the mass eigenvalues.
Buchtitel:
Proceedings of the XLIVth Rencontres de Moriond: Electroweak Interactions and Unified Theories
2009 | The Inverse Seesaw Mechanism in Noncommutative Geometry | Christoph Stephan
Zeitschrift: Phys. Rev. D
Verlag: American Physical Society
Seiten: 65007
Band: 80, no. 6
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,
Link zum Preprint
The Inverse Seesaw Mechanism in Noncommutative Geometry
Autoren: Christoph Stephan
(2009)
In this publication we will implement the inverse Seesaw mechanism into the noncommutative framework on the basis of the AC-extension of the Standard Model. The main difference to the classical AC model is the chiral nature of the AC fermions with respect to a U(1) extension of the Standard Model gauge group. It is this extension which allows us to couple the right-handed neutrinos via a gauge invariant mass term to left-handed A-particles. The natural scale of these gauge invariant masses is of the order of 10^17 GeV while the Dirac masses of the neutrino and the AC-particles are generated dynamically and are therefore much smaller (ca. 1 GeV to 10^6 GeV). From this configuration a working inverse Seesaw mechanism for the neutrinos is obtained.
Zeitschrift:
Phys. Rev. D
Verlag:
American Physical Society
2008 | Ravels: knot-free but not free. Novel entanglements of graphs in 3-space | T. Castle, M. E. Evans and S. T. Hyde
Zeitschrift: New Journal of Chemistry 32(9)
Seiten: 1484-1492
Link zur Publikation
Ravels: knot-free but not free. Novel entanglements of graphs in 3-space
Autoren: T. Castle, M. E. Evans and S. T. Hyde
(2008)
Zeitschrift:
New Journal of Chemistry 32(9)
2008 | Rayleigh quotient iteration and simplified Jacobi-Davidson with preconditioned iterative solves for generalised eigenvalue problems | M.A. Freitag, A. Spence, E. Vainikko
(Gzipped PostScript), (PDF)
Rayleigh quotient iteration and simplified Jacobi-Davidson with preconditioned iterative solves for generalised eigenvalue problems
Autoren: M.A. Freitag, A. Spence, E. Vainikko
(2008)
2008 | The Impact of Multiplication Operators on the Ill-Posedness of Inverse Problems | Melina Freitag
168 pages, VDM Verlag Dr. Müller Aktiengesellschaft & Co. KG (2008). (Available online here)
The Impact of Multiplication Operators on the Ill-Posedness of Inverse Problems
Autoren: Melina Freitag
(2008)
168 pages, VDM Verlag Dr. Müller Aktiengesellschaft & Co. KG (2008). (Available online
here)
2008 | Rayleigh Quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves | M.A. Freitag, A. Spence
Zeitschrift: Linear Alg. Appl.
Verlag: Elsevier
Seiten: 2049-2060
Band: 428(8-9)
Link zur Publikation
Rayleigh Quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves
Autoren: M.A. Freitag, A. Spence
(2008)
Zeitschrift:
Linear Alg. Appl.
2008 | A tuned preconditioner for inexact inverse iteration applied to Hermitian eigenvalue problems | M.A. Freitag, A. Spence
Zeitschrift: IMA J. Numer. Anal.
Verlag: Oxford University Press
Seiten: 522-551
Band: 28(3)
Link zur Publikation
A tuned preconditioner for inexact inverse iteration applied to Hermitian eigenvalue problems
Autoren: M.A. Freitag, A. Spence
(2008)
Zeitschrift:
IMA J. Numer. Anal.
Verlag:
Oxford University Press
2008 | A dynamical low-rank approach to the chemical master equation | T. Jahnke, and W. Huisinga
Zeitschrift: Bull. Math. Biol.
Seiten: 2283-2302
Band: 70
Link zur Publikation
A dynamical low-rank approach to the chemical master equation
Autoren: T. Jahnke, and W. Huisinga
(2008)
Zeitschrift:
Bull. Math. Biol.
2008 | Adaptive discrete Galerkin methods applied to the chemical master equation | P. Deuflhard, W. Huisinga, T. Jahnke, and M. Wulkow
Zeitschrift: SIAM J. Sci. Comput.
Seiten: 2990-3011
Band: 30
Link zur Publikation
Adaptive discrete Galerkin methods applied to the chemical master equation
Autoren: P. Deuflhard, W. Huisinga, T. Jahnke, and M. Wulkow
(2008)
Zeitschrift:
SIAM J. Sci. Comput.
2008 | The Greatest Regular-solid Variety of Semigroups | Denecke, K., Koppitz J. and Pabhapote, N.
Zeitschrift: Discussiones Mathematicae General Algebra and Applications
Band: 28
The Greatest Regular-solid Variety of Semigroups
Autoren: Denecke, K., Koppitz J. and Pabhapote, N.
(2008)
Zeitschrift:
Discussiones Mathematicae General Algebra and Applications
2008 | Power Clones and Non-Deterministic Hypersubstitutions, | Denecke, K., Glubudom, P. and Koppitz, J.
Zeitschrift: Asian-European Journal of Mathematics
Band: 1 no. 2
Power Clones and Non-Deterministic Hypersubstitutions,
Autoren: Denecke, K., Glubudom, P. and Koppitz, J.
(2008)
Zeitschrift:
Asian-European Journal of Mathematics
2008 | On the Maximal Subsemigroups of Some Transformation Semigroups | Dimitrova, I. and Koppitz, J.
Zeitschrift: Asian-European Journal of Mathematics
Band: 1 no. 2
On the Maximal Subsemigroups of Some Transformation Semigroups
Autoren: Dimitrova, I. and Koppitz, J.
(2008)
Zeitschrift:
Asian-European Journal of Mathematics
2008 | Testing in Nonparametric Accelerated Life Time Models | Hannelore Liero
Zeitschrift: Austrian Journal of Statistics Vol. 37--1
Band: 37--1
Testing in Nonparametric Accelerated Life Time Models
Autoren: Hannelore Liero
(2008)
Zeitschrift:
Austrian Journal of Statistics Vol. 37--1
2008 | Testing the influence function in accelerated life time models | Hannelore Liero, Matthias Liero
Verlag: Birkhauser, Boston
Buchtitel: Statistical models and methods for biomedical and technical systems, Eds. F.Vonta, M. Nikulin, N. Limnios and C. Huber
Testing the influence function in accelerated life time models
Autoren: Hannelore Liero, Matthias Liero
(2008)
Verlag:
Birkhauser, Boston
Buchtitel:
Statistical models and methods for biomedical and technical systems, Eds. F.Vonta, M. Nikulin, N. Limnios and C. Huber
2008 | Estimation of rescaled distribution. | Henning Läuter, Mikhail Nikulin
Verlag: Birkhäuser
Buchtitel: Statistical Models and Methods for Systems
Seiten: 187-198
Estimation of rescaled distribution.
Autoren: Henning Läuter, Mikhail Nikulin
(2008)
Buchtitel:
Statistical Models and Methods for Systems
2008 | Approximate likelihood in survival models. | Henning Läuter
Verlag: ISTE&J.Wiley
Buchtitel: Mathematical Methods in Survival Analysis
Seiten: 121-130
Approximate likelihood in survival models.
Autoren: Henning Läuter
(2008)
Buchtitel:
Mathematical Methods in Survival Analysis
2008 | Agmon-Type Estimates for a class of Difference Operators | Markus Klein, Elke Rosenberger
Zeitschrift: Ann. Henri Poincare
Verlag: Birkhäuser Verlag Basel
Seiten: 1177 - 1215
Band: 9
Link zur Publikation
Agmon-Type Estimates for a class of Difference Operators
Autoren: Markus Klein, Elke Rosenberger
(2008)
We analyze a general class of self-adjoint difference operators <tex>H_\varepsilon = T_\varepsilon + V_\varepsilon</tex> on <tex>\ell^2(\varepsilon{\mathbf Z}^d)</tex>, where <tex>V_\varepsilon</tex> is a one-well potential and <tex>\varepsilon</tex> is a small parameter.
We construct a Finslerian distance d induced by<tex> H_\varepsilon</tex> and show that short integral curves are geodesics. Then we show that Dirichlet eigenfunctions decay exponentially with a rate controlled by the Finsler distance to the well. This is analog to semiclassical Agmon estimates for Schrödinger operators.
Zeitschrift:
Ann. Henri Poincare
Verlag:
Birkhäuser Verlag Basel
2008 | Two simple sufficient conditions for FDR control | Blanchard, G., Roquain, E.
Zeitschrift: Electronic journal of statistics
Verlag: Institute of Mathematical Statistics
Seiten: 963-992
Band: 2
Two simple sufficient conditions for FDR control
Autoren: Blanchard, G., Roquain, E.
(2008)
Zeitschrift:
Electronic journal of statistics
Verlag:
Institute of Mathematical Statistics
2008 | Finite-dimensional projection for classification and statistical learning | Blanchard, G., Zwald, L.
Zeitschrift: Information Theory, IEEE Transactions on
Verlag: IEEE
Seiten: 4169-4182
Band: 54
Finite-dimensional projection for classification and statistical learning
Autoren: Blanchard, G., Zwald, L.
(2008)
Zeitschrift:
Information Theory, IEEE Transactions on
2008 | Statistical performance of support vector machines | Blanchard, G, Bousquet, O., Massart, P.
Zeitschrift: The Annals of Statistics
Verlag: Institute of Mathematical Statistics
Seiten: 489-531
Band: 36
Statistical performance of support vector machines
Autoren: Blanchard, G, Bousquet, O., Massart, P.
(2008)
Zeitschrift:
The Annals of Statistics
Verlag:
Institute of Mathematical Statistics
2008 | Path integrals on manifolds by finite dimensional approximation | Christian Bär, Frank Pfäffle
Zeitschrift: J. Reine Angew. Math.
Verlag: De Gruyter
Seiten: 29-57
Band: 625
Link zur Publikation
,
Link zum Preprint
Path integrals on manifolds by finite dimensional approximation
Autoren: Christian Bär, Frank Pfäffle
(2008)
Let M be a compact Riemannian manifold without boundary and let H be a self-adjoint generalized Laplace operator acting on sections in a bundle over M. We give a path integral formula for the solution to the corresponding heat equation. This is based on approximating path space by finite dimensional spaces of geodesic polygons. We also show a uniform convergence result for the heat kernels. This yields a simple and natural proof for the Hess-Schrader-Uhlenbrock estimate and a path integral formula for the trace of the heat operator.
Zeitschrift:
J. Reine Angew. Math.
2008 | On the Riemannian geometry of Seiberg-Witten moduli spaces | Christian Becker
Zeitschrift: J. Geom. Phys.
Verlag: Elsevier
Seiten: 1291-1309
Band: 58, no. 10
Link zur Publikation
,
Link zum Preprint
On the Riemannian geometry of Seiberg-Witten moduli spaces
Autoren: Christian Becker
(2008)
We construct natural Riemannian metrics on Seiberg-Witten moduli spaces and study their geometry.
Zeitschrift:
J. Geom. Phys.
2008 | The spectrum of the Dirac operator on SU(2)/Q8 | Nicolas Ginoux
Zeitschrift: Manuscr. Math.
Verlag: Springer
Seiten: 383-409
Band: 125, no. 3
Link zur Publikation
The spectrum of the Dirac operator on SU(2)/Q8
Autoren: Nicolas Ginoux
(2008)
We compute the fundamental Dirac operator for the three-parameter-family of homogeneous Riemannian metrics and the four different spin structures on SU2/Q8, where Q8 denotes the group of quaternions. We deduce its spectrum for the Berger metrics and show the sharpness of Christian Bär’s upper bound for the smallest Dirac eigenvalue in the particular case where SU2/Q8 is a homogeneous minimal hypersurface of S4.
Zeitschrift:
Manuscr. Math.
2008 | Remarques sur les spineurs de Killing transversaux | Nicolas Ginoux, Georges Habib
Zeitschrift: C. R. Math. Acad. Sci. Paris
Verlag: Elsevier
Seiten: 657-659
Band: 346, no. 1
Link zur Publikation
,
Link zum Preprint
Remarques sur les spineurs de Killing transversaux
Autoren: Nicolas Ginoux, Georges Habib
(2008)
We show necessary conditions for the existence of transversal Killing spinors on a spin manifold endowed with a Riemannian flow.
Zeitschrift:
C. R. Math. Acad. Sci. Paris
2008 | Finding the standard model of particle physics: A combinatorial problem | Jan-Hendrik Jureit, Christoph Stephan
Zeitschrift: Comput. Phys. Commun.
Verlag: Elsevier
Seiten: 230-247
Band: 178, no. 3
Link zur Publikation
,
Link zum Preprint
Finding the standard model of particle physics: A combinatorial problem
Autoren: Jan-Hendrik Jureit, Christoph Stephan
(2008)
We present a combinatorial problem which consists in finding irreducible Krajewski diagrams from finite geometries. This problem boils down to placing arrows into a quadratic array with some additional constrains. The Krajewski diagrams play a central role in the description of finite noncommutative geometries. They allow to localise the standard model of particle physics within the set of all Yang-Mills-Higgs models.
Zeitschrift:
Comput. Phys. Commun.
2008 | On a classification of irreducible almost-commutative geometries. IV | Jan-Hendrik Jureit, Christoph Stephan
Zeitschrift: J. Math. Phys.
Verlag: American Institute of Physics
Seiten: 33502
Band: 49, no. 3
Link zur Publikation
,
Link zum Preprint
On a classification of irreducible almost-commutative geometries. IV
Autoren: Jan-Hendrik Jureit, Christoph Stephan
(2008)
In this paper we will classify the finite spectral triples with KO-dimension six, following the classification found in [1,2,3,4], with up to four summands in the matrix algebra. Again, heavy use is made of Krajewski diagrams [5]. Furthermore we will show that any real finite spectral triple in KO-dimension 6 is automatically S 0 -real. This work has been inspired by the recent paper by Alain Connes [6] and John Barrett [7].
In the classification we find that the standard model of particle physics in its minimal version fits the axioms of noncommutative geometry in the case of KO-dimension six. By minimal version it is meant that at least one neutrino has to be massless and mass-terms mixing particles and antiparticles are prohibited
Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
2008 | Gauge unification in noncommutative geometry | Christoph Stephan
Zeitschrift: Europhys. Lett.
Verlag: IOP Publishing
Seiten: 51003
Band: 84
Link zur Publikation
,
Link zum Preprint
Gauge unification in noncommutative geometry
Autoren: Christoph Stephan
(2008)
Gauge unification is widely considered to be a desirable feature for extensions of the standard model. Unfortunately the standard model itself does not exhibit a unification of its running gauge couplings but it is required by grand unified theories as well as the noncommutative version of the standard model [2].
We will consider here the extension of the noncommutative standard model by vector doublets as proposed in [6]. Two consequences of this modification are: 1. the relations of the coupling constants at unification energy are altered with respect to the well known relation from grand unified theories. 2. The extended model allows for unification of the gauge couplings at ~10^(13) GeV.
Zeitschrift:
Europhys. Lett.
2007 | Inner-outer Iterative Methods for Eigenvalue Problems - Convergence and Preconditioning | M. A. Freitag
PhD Thesis, Department of Mathematical Sciences, University of Bath (2007). (Gzipped PostScript), (PDF)
Inner-outer Iterative Methods for Eigenvalue Problems - Convergence and Preconditioning
Autoren: M. A. Freitag
(2007)
2007 | Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem | M.A. Freitag, A. Spence
Zeitschrift: Electron. Trans. Numer. Anal.
Seiten: 40-64
Band: 28
Link zum Preprint
Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem
Autoren: M.A. Freitag, A. Spence
(2007)
Zeitschrift:
Electron. Trans. Numer. Anal.
2007 | The Preissmann box scheme and its modification for transcritical flows | M.A. Freitag, K. W. Morton
Zeitschrift: Internat. J. Numer. Methods Engrg.
Verlag: Wiley
Seiten: 791-811
Band: 70(7)
Link zur Publikation
The Preissmann box scheme and its modification for transcritical flows
Autoren: M.A. Freitag, K. W. Morton
(2007)
Zeitschrift:
Internat. J. Numer. Methods Engrg.
2007 | Convergence rates for inexact inverse iteration with application to preconditioned iterative solves | M.A. Freitag, A. Spence
Zeitschrift: BIT
Verlag: Springer
Seiten: 27-44
Band: 47(1)
Link zur Publikation
Convergence rates for inexact inverse iteration with application to preconditioned iterative solves
Autoren: M.A. Freitag, A. Spence
(2007)
2007 | Optimizing Classification of Drug-Drug Interaction Potential for CYP450 Isoenzyme Inhibition Assays in Early Drug Discovery | B.-F. Krippendorff, P. Lienau, A. Reichel, W. Huisinga
Zeitschrift: J Biomol Screen
Seiten: 92-99
Band: 12
Link zur Publikation
Optimizing Classification of Drug-Drug Interaction Potential for CYP450 Isoenzyme Inhibition Assays in Early Drug Discovery
Autoren: B.-F. Krippendorff, P. Lienau, A. Reichel, W. Huisinga
(2007)
Zeitschrift:
J Biomol Screen
2007 | Solving the chemical master equation for monomolecular reaction systems analytically | T. Jahnke, W. Huisinga
Zeitschrift: J. Math. Biol.
Seiten: 1-26
Band: 54
Link zur Publikation
Solving the chemical master equation for monomolecular reaction systems analytically
Autoren: T. Jahnke, W. Huisinga
(2007)
Zeitschrift:
J. Math. Biol.
2007 | Combining Systems Biology with physiologically-based pharmacokinetics to support the understanding of drug effects | M. von Kleist, C. Kloft and W. Huisinga
Zeitschrift: Proceedings of Foundations of Systems Biology in Engeneering FOSBE
Seiten: 231-236
Combining Systems Biology with physiologically-based pharmacokinetics to support the understanding of drug effects
Autoren: M. von Kleist, C. Kloft and W. Huisinga
(2007)
Zeitschrift:
Proceedings of Foundations of Systems Biology in Engeneering FOSBE
2007 | Hybrid stochastic and deterministic simulations of calcium blips | S. Rüdiger, J.W. Shuai, W. Huisinga, Ch. Nagaiah, G. Warnecke, I. Parker, M. Falcke
Zeitschrift: Biophys. J.
Seiten: 1847-1857
Band: 93
Link zur Publikation
Hybrid stochastic and deterministic simulations of calcium blips
Autoren: S. Rüdiger, J.W. Shuai, W. Huisinga, Ch. Nagaiah, G. Warnecke, I. Parker, M. Falcke
(2007)
2007 | Physiologically based pharmacokinetic modelling: A sub-compartmentalized model of tissue distribution | M. von Kleist and W. Huisinga
Zeitschrift: J. Pharmacokinet. Pharmacodyn.
Seiten: 789-806
Band: 34
Link zur Publikation
Physiologically based pharmacokinetic modelling: A sub-compartmentalized model of tissue distribution
Autoren: M. von Kleist and W. Huisinga
(2007)
Zeitschrift:
J. Pharmacokinet. Pharmacodyn.
2007 | Maximal Submonoids of Monoids of Hypersubstitutions | Dimitrova, I. and Koppitz, J.
Zeitschrift: Discussiones Mathematicae General Algebra and Applications
Band: 27
Maximal Submonoids of Monoids of Hypersubstitutions
Autoren: Dimitrova, I. and Koppitz, J.
(2007)
Zeitschrift:
Discussiones Mathematicae General Algebra and Applications
2007 | he degree of proper hypersubstitutions | Denecke, K., Koppitz, J. and Srithus, R.
Zeitschrift: Sci. Math. Jpn.
Band: 66 no. 2
he degree of proper hypersubstitutions
Autoren: Denecke, K., Koppitz, J. and Srithus, R.
(2007)
Zeitschrift:
Sci. Math. Jpn.
2007 | N-fluid Varieties | Denecke, K., Koppitz, J. and Srithus, R.
Zeitschrift: Sci. Math. Jpn.
Band: 65 no. 1
N-fluid Varieties
Autoren: Denecke, K., Koppitz, J. and Srithus, R.
(2007)
Zeitschrift:
Sci. Math. Jpn.
2007 | Time Evolution of Quantum Resonance States | M. Klein, J. Rama, R. Wüst
Zeitschrift: Asymptotic Analysis 51, no 1
Time Evolution of Quantum Resonance States
Autoren: M. Klein, J. Rama, R. Wüst
(2007)
Let H0 be self-adjoint with E0 a possibly degenerate eigenvalue embedded in the continuous spectrum σc (H0 ) and ψ0 a normalized eigenfunction. For a certain class of perturbations W and H=H0 +W we investigate the asymptotics of the (naive) resonance state e−itH ψ0 in the limit W→0. This amplifies previous results of Merkli and Sigal.
Zeitschrift:
Asymptotic Analysis 51, no 1
2007 | Extending rings of Prüfer type in central simple algebras | Gräter, J.
Zeitschrift: Algebr. Represent. Theory 10
Seiten: 315-331
Extending rings of Prüfer type in central simple algebras
Autoren: Gräter, J.
(2007)
Zeitschrift:
Algebr. Represent. Theory 10
2007 | A new algorithm of non-Gaussian component analysis with radial kernel functions | Kawanabe, M., Sugiyama, M., Blanchard, G., Müller, K-R
Zeitschrift: Annals of the Institute of Statistical Mathematics
Verlag: Springer-Verlag
Seiten: 57-75
Band: 59
A new algorithm of non-Gaussian component analysis with radial kernel functions
Autoren: Kawanabe, M., Sugiyama, M., Blanchard, G., Müller, K-R
(2007)
Zeitschrift:
Annals of the Institute of Statistical Mathematics
2007 | Occam’s hammer | Blanchard, G., Fleuret, F.
Zeitschrift: Learning theory (COLT 2007)
Verlag: Springer Lecture Notes on Computer Science
Seiten: 112-126
Band: 4539
Occam’s hammer
Autoren: Blanchard, G., Fleuret, F.
(2007)
Zeitschrift:
Learning theory (COLT 2007)
Verlag:
Springer Lecture Notes on Computer Science
2007 | Resampling-based confidence regions and multiple tests for a correlated random vector | Arlot, S., Blanchard, G., Roquain, E.
Zeitschrift: Learning theory (COLT 2007)
Verlag: Springer Lecture Notes on Computer Science
Seiten: 127-141
Band: 4539
Resampling-based confidence regions and multiple tests for a correlated random vector
Autoren: Arlot, S., Blanchard, G., Roquain, E.
(2007)
Zeitschrift:
Learning theory (COLT 2007)
Verlag:
Springer Lecture Notes on Computer Science
2007 | Statistical properties of kernel principal component analysis | Blanchard, G., Bousquet, O., Zwald, L.
Zeitschrift: Machine Learning
Verlag: Springer
Seiten: 259-294
Band: 66
Statistical properties of kernel principal component analysis
Autoren: Blanchard, G., Bousquet, O., Zwald, L.
(2007)
Zeitschrift:
Machine Learning
2007 | Optimal dyadic decision trees | Blanchard, G., Schäfer, C., Rozenholc, Y., Müller, K-R
Zeitschrift: Machine Learning
Verlag: Kluwer Academic Publishers
Seiten: 209-241
Band: 66
Optimal dyadic decision trees
Autoren: Blanchard, G., Schäfer, C., Rozenholc, Y., Müller, K-R
(2007)
Zeitschrift:
Machine Learning
Verlag:
Kluwer Academic Publishers
2007 | Conformal structures in noncommutative geometry | Christian Bär
Zeitschrift: J. Noncommut. Geom.
Verlag: European Mathematical Society
Seiten: 385-395
Band: 1, no. 3
Link zur Publikation
,
Link zum Preprint
Conformal structures in noncommutative geometry
Autoren: Christian Bär
(2007)
It is well-known that a compact Riemannian spin manifold can be reconstructed from its canonical spectral triple which consists of the algebra of smooth functions, the Hilbert space of square integrable spinors and the Dirac operator. It seems to be a folklore fact that the metric can be reconstructed up to conformal equivalence if one replaces the Dirac operator D by sign(D). We give a precise formulation and proof of this fact.
Zeitschrift:
J. Noncommut. Geom.
Verlag:
European Mathematical Society
2007 | Wave equations on Lorentzian manifolds and quantization (Monografie) | Christian Bär, Nicolas Ginoux, Frank Pfäffle
Reihe: ESI Lectures in Mathematics and Physics
Verlag: European Mathematical Society
Seiten: viii+194 pages
Link zur Publikation
,
Link zum Preprint
Wave equations on Lorentzian manifolds and quantization (Monografie)
Autoren: Christian Bär, Nicolas Ginoux, Frank Pfäffle
(2007)
This book provides a detailed introduction to linear wave equations on Lorentzian manifolds (for vector-bundle valued fields). After a collection of preliminary material in the first chapter one finds in the second chapter the construction of local fundamental solutions together with their Hadamard expansion. The third chapter establishes the existence and uniqueness of global fundamental solutions on globally hyperbolic spacetimes and discusses Green's operators and well-posedness of the Cauchy problem. The last chapter is devoted to field quantization in the sense of algebraic quantum field theory. The necessary basics on C*-algebras and CCR-representations are developed in full detail.
The text provides a self-contained introduction to these topics addressed to graduate students in mathematics and physics. At the same time it is intended as a reference for researchers in global analysis, general relativity, and quantum field theory.
Reihe:
ESI Lectures in Mathematics and Physics
Verlag:
European Mathematical Society
2007 | A singularity theorem for twistor spinors | Florin Alexandru Belgun, Nicolas Ginoux, Hans-Bert Rademacher
Zeitschrift: Ann. Inst. Fourier
Verlag: UJF Grenoble
Seiten: 1135-1159
Band: 57, no. 4
Link zur Publikation
,
Link zum Preprint
A singularity theorem for twistor spinors
Autoren: Florin Alexandru Belgun, Nicolas Ginoux, Hans-Bert Rademacher
(2007)
We study spin structures on orbifolds. In particular, we show that if the singular set has codimension greater than 2, an orbifold is spin if and only if its smooth part is. On compact orbifolds, we show that any non-trivial twistor spinor admits at most one zero which is singular unless the orbifold is conformally equivalent to a round sphere. We show the sharpness of our results through examples.
Zeitschrift:
Ann. Inst. Fourier
2007 | Seesaw and noncommutative geometry | Jan-Hendrik Jureit, Thomas Krajewski, Thomas Schucker, Christoph Stephan
Zeitschrift: Phys. Lett. B
Verlag: Elsevier
Seiten: 127-132
Band: 654, no. 3
Link zur Publikation
,
Link zum Preprint
Seesaw and noncommutative geometry
Autoren: Jan-Hendrik Jureit, Thomas Krajewski, Thomas Schucker, Christoph Stephan
(2007)
The 1-loop corrections to the seesaw mechanism in the noncommutative standard model are computed. Other consequences of the Lorentzian signature in the inner space are summarised.
Zeitschrift:
Phys. Lett. B
2007 | On the noncommutative standard model | Jan-Hendrik Jureit, Thomas Krajewski, Thomas Schucker, Christoph Stephan
Zeitschrift: Acta Phys. Polon. B
Verlag: Jagiellonian University, Poland
Seiten: 3181-3202
Band: 38, no. 10
Link zur Publikation
,
Link zum Preprint
On the noncommutative standard model
Autoren: Jan-Hendrik Jureit, Thomas Krajewski, Thomas Schucker, Christoph Stephan
(2007)
We propose a pedestrian review of the noncommutative standard model in its present state.
Zeitschrift:
Acta Phys. Polon. B
Verlag:
Jagiellonian University, Poland
2007 | Almost-commutative geometries beyond the Standard Model III: Vector Doublets | Romain Squellari, Christoph Stephan
Zeitschrift: J. Phys. A
Verlag: IOP Publishing
Seiten: 10685-10698
Band: 40, no. 34
Link zur Publikation
,
Link zum Preprint
Almost-commutative geometries beyond the Standard Model III: Vector Doublets
Autoren: Romain Squellari, Christoph Stephan
(2007)
We will present a new extension of the standard model of particle physics in its almostcommutative formulation. This extension has as its basis the algebra of the standard model with four summands [11], and enlarges only the particle content by an arbitrary number of generations of left-right symmetric doublets which couple vectorially to the U(1)YxSU(2)w subgroup of the standard model. As in the model presented in [8], which introduced particles with a new colour, grand unification is no longer required by the spectral action. The new model may also possess a candidate for dark matter in the hundred TeV mass range with neutrino-like cross section.
2007 | Massive neutrinos in almost commutative geometry | Christoph Stephan
Zeitschrift: J. Math. Phys.
Verlag: American Institute of Physics
Seiten: 23513
Band: 48
Link zur Publikation
,
Link zum Preprint
Massive neutrinos in almost commutative geometry
Autoren: Christoph Stephan
(2007)
In the noncommutative formulation of the standard model of particle physics by A. Connes and A. Chamseddine [1] one of the three generations of fermions has to possess a massless neutrino. This formulation is consistent with neutrino oscillation experiments and the known bounds of the Pontecorvo-Maki-Nakagawa-Sakata matrix (PMNS matrix). But future experiments which may be able to detect neutrino masses directly and high-precission measurements of the PMNS matrix might need massive neutrinos in all three generations.
In this publication we present an almost-commutative geometry which allows for a standard model with massive neutrinos in all three generations. This model does not follow in a straight forward way from Connes' and Chamseddine's version since it requires an internal algebra with four summands of matrix algebras, instead of three summands for the model with one massless neutrino.
Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
2007 | Almost-commutative geometries beyond the Standard Model II: New Colours | Christoph Stephan
Zeitschrift: J. Phys. A
Verlag: IOP Publishing
Seiten: 9941-9956
Band: 40, no. 32
Link zur Publikation
,
Link zum Preprint
Almost-commutative geometries beyond the Standard Model II: New Colours
Autoren: Christoph Stephan
(2007)
We will present an extension of the standard model of particle physics in its almost-commutative formulation. This extension is guided by the minimal approach to almost-commutative geometries employed in [13], although the model presented here is not minimal itself.
The corresponding almost-commutative geometry leads to a Yang-Mills-Higgs model which consists of the standard model and two new fermions of opposite electro-magnetic charge which may possess a new colour like gauge group. As a new phenomenon, grand unification is no longer required by the spectral action.
2006 | Computational Physiology | W. Huisinga
Zeitschrift: European Communications in Mathematical and Theoretical Biology, No. 8, January 2006
Seiten: 12-13
Band: 8
Link zur Publikation
Computational Physiology
Autoren: W. Huisinga
(2006)
Zeitschrift:
European Communications in Mathematical and Theoretical Biology, No. 8, January 2006
2006 | The virtual lab approach to pharmacokinetic: Design principles and concepts | W. Huisinga, R. Telgmann, M. Wulkow
Zeitschrift: Drug Discov Today
Seiten: 800-805
Band: 11
Link zur Publikation
The virtual lab approach to pharmacokinetic: Design principles and concepts
Autoren: W. Huisinga, R. Telgmann, M. Wulkow
(2006)
Zeitschrift:
Drug Discov Today
2006 | Adaptive Approach for Modelling Variability in Pharmacokinetics | A. Weiße, I. Horenko, and W. Huisinga
Reihe: Lecture Notes in Computer Science
Verlag: Springer
Buchtitel: 'Computational Life Sciences II', M.R. Berthold, R. Glen, and I. Fischer (Eds.)
Seiten: 194-204
Band: 4216
Link zur Publikation
Adaptive Approach for Modelling Variability in Pharmacokinetics
Autoren: A. Weiße, I. Horenko, and W. Huisinga
(2006)
Reihe:
Lecture Notes in Computer Science
Buchtitel:
'Computational Life Sciences II', M.R. Berthold, R. Glen, and I. Fischer (Eds.)
2006 | Software Supported Modelling in Pharmacokinetics | R. Telgmann, M. von Kleist, and W. Huisinga
Reihe: Lecture Notes in Computer Science
Verlag: Springer
Buchtitel: 'Computational Life Sciences II', M.R. Berthold, R. Glen, and I. Fischer (Eds.)
Seiten: 216-225
Band: 4216
Link zur Publikation
Software Supported Modelling in Pharmacokinetics
Autoren: R. Telgmann, M. von Kleist, and W. Huisinga
(2006)
Reihe:
Lecture Notes in Computer Science
Buchtitel:
'Computational Life Sciences II', M.R. Berthold, R. Glen, and I. Fischer (Eds.)
2006 | Multi-Hypersubstitutions and Colored Solid Varieties | Denecke, K., Koppitz, J. and Shtrakov, Sl.,
Zeitschrift: International Journal of Algebra and Computation
Band: 16 no. 4
Multi-Hypersubstitutions and Colored Solid Varieties
Autoren: Denecke, K., Koppitz, J. and Shtrakov, Sl.,
(2006)
Zeitschrift:
International Journal of Algebra and Computation
2006 | Free Systems of Algebras and Ultraclosed Classes | hron, R. and Koppitz, J.
Zeitschrift: Acta Math. Univ. Comenianae
Band: Vol. LXXV no. 1
Free Systems of Algebras and Ultraclosed Classes
Autoren: hron, R. and Koppitz, J.
(2006)
Zeitschrift:
Acta Math. Univ. Comenianae
2006 | Asymptotic spectral analysis and tunnelling for a class of difference operators | Elke Rosenberger
Buchtitel: Dissertation
Link zur Publikation
Asymptotic spectral analysis and tunnelling for a class of difference operators
Autoren: Elke Rosenberger
(2006)
We analyze the asymptotic behavior in the limit <tex>\varepsilon \to 0</tex> for a wide class of difference operators <tex>H_\varepsilon = T_\varepsilon + V_\varepsilon</tex> with underlying multi-well potential. They act on the square summable functions on the lattice <tex>\varepsilon \mathbb{Z}^d</tex>. We start showing the validity of an harmonic approximation and construct WKB-solutions at the wells. Then we construct a Finslerian distance d induced by <tex>H_\varepsilon</tex> and show that short integral curves are geodesics and d gives the rate for the exponential decay of Dirichlet eigenfunctions. In terms of this distance, we give sharp estimates for the interaction between the wells and construct the interaction matrix.
2006 | Nonparametric estimation and testing in survival models | Henning Läuter, Hannelore Liero
Verlag: Springer
Buchtitel: Probability, Statistics and Modelling in Public Health, Eds. M. Nikulin, D. Commenges and C. Huber
Nonparametric estimation and testing in survival models
Autoren: Henning Läuter, Hannelore Liero
(2006)
Buchtitel:
Probability, Statistics and Modelling in Public Health, Eds. M. Nikulin, D. Commenges and C. Huber
2006 | Algunas consideraciones practicas acera de la estimacion de parametros en el modelo clasico de clases latentes | Adalberto González Debén, Hannelore Liero, Henning Läuter, Jesús Sánchez García
Zeitschrift: Investigación operacional, Ciencia Matemáticas
Seiten: 20-27
Band: 12
Algunas consideraciones practicas acera de la estimacion de parametros en el modelo clasico de clases latentes
Autoren: Adalberto González Debén, Hannelore Liero, Henning Läuter, Jesús Sánchez García
(2006)
Zeitschrift:
Investigación operacional, Ciencia Matemáticas
2006 | Nonparametric estimation and testing in survival models | Henning Läuter, Hannelore Liero
Verlag: Springer
Buchtitel: Probability, Statistics and Modelling
Seiten: 319-331
Nonparametric estimation and testing in survival models
Autoren: Henning Läuter, Hannelore Liero
(2006)
Buchtitel:
Probability, Statistics and Modelling
2006 | Algunas consideraciones practicas acera de la estimacion de parametros en el modelo clasico | Gonzalez Debén, A., Liero, H., Läuter, H.
Zeitschrift: Investigacion operacional, Ciencia Matemáticas
Seiten: 20-27
Band: 12
Algunas consideraciones practicas acera de la estimacion de parametros en el modelo clasico
Autoren: Gonzalez Debén, A., Liero, H., Läuter, H.
(2006)
Zeitschrift:
Investigacion operacional, Ciencia Matemáticas
2006 | Obtaining the best linear unbiased estimator of noisy signals by non-Gaussian component analysis | Sugiyama, M., Kawanabe, M., Blanchard, G., Spokoiny, V., Muller, K-R
Zeitschrift: Acoustics, Speech and Signal Processing, 2006. ICASSP 2006 Proceedings. 2006 IEEE International Conference on
Verlag: IEEE
Seiten: 608-611
Band: 3
Obtaining the best linear unbiased estimator of noisy signals by non-Gaussian component analysis
Autoren: Sugiyama, M., Kawanabe, M., Blanchard, G., Spokoiny, V., Muller, K-R
(2006)
Zeitschrift:
Acoustics, Speech and Signal Processing, 2006. ICASSP 2006 Proceedings. 2006 IEEE International Conference on
2006 | On the convergence of eigenspaces in kernel principal component analysis | Zwald, L., Blanchard, G.
Zeitschrift: Advances in Neural Information Processing Systems (NIPS 2005)
Verlag: MIT Press
Seiten: 1649-1656
Band: 18
On the convergence of eigenspaces in kernel principal component analysis
Autoren: Zwald, L., Blanchard, G.
(2006)
Zeitschrift:
Advances in Neural Information Processing Systems (NIPS 2005)
2006 | A novel dimension reduction procedure for searching non-gaussian subspaces | Kawanabe, M., Blanchard, G., Sugiyama, M., Spokoiny, V., Müller, K-R
Zeitschrift: Independent Component Analysis and Blind Signal Separation
Verlag: Springer Berlin Heidelberg
Seiten: 149-156
A novel dimension reduction procedure for searching non-gaussian subspaces
Autoren: Kawanabe, M., Blanchard, G., Sugiyama, M., Spokoiny, V., Müller, K-R
(2006)
Zeitschrift:
Independent Component Analysis and Blind Signal Separation
Verlag:
Springer Berlin Heidelberg
2006 | In search of non-Gaussian components of a high-dimensional distribution | Blanchard, G., Kawanabe, M., Sugiyama, M., Spokoiny, V., Müller, K-R
Zeitschrift: Journal of Machine Learning Research
Verlag: JMLR. org
Seiten: 247-282
Band: 7
In search of non-Gaussian components of a high-dimensional distribution
Autoren: Blanchard, G., Kawanabe, M., Sugiyama, M., Spokoiny, V., Müller, K-R
(2006)
Zeitschrift:
Journal of Machine Learning Research
2006 | Discussion: Local Rademacher complexities and oracle inequalities in risk minimization | Blanchard, G., Massart, P.
Zeitschrift: The Annals of Statistics
Verlag: Institute of Mathematical Statistics
Seiten: 2664-2671
Band: 34
Discussion: Local Rademacher complexities and oracle inequalities in risk minimization
Autoren: Blanchard, G., Massart, P.
(2006)
Zeitschrift:
The Annals of Statistics
Verlag:
Institute of Mathematical Statistics
2006 | Cold dark matter by heavy double charged leptons? | Daniele Fargion, Maxim Khlopov, Christoph Stephan
Zeitschrift: Class. Quantum Grav.
Verlag: IOP Publishing
Seiten: 7305-7354
Band: 23, no. 24
Link zur Publikation
,
Link zum Preprint
Cold dark matter by heavy double charged leptons?
Autoren: Daniele Fargion, Maxim Khlopov, Christoph Stephan
(2006)
A new candidate of cold dark matter arises by a novel elementary particle model: the almostcommutative AC-geometrical framework. Two heavy leptons are added to the Standard Model, each one sharing a double opposite electric charge and an own lepton flavor number The novel mathematical theory of almost-commutative geometry [1] wishes to unify gauge models with gravity. In this scenario two new heavy (m_L>100GeV), oppositely double charged leptons (A,C),(A with charge -2 and C with charge +2), are born with no twin quark companions. The model naturally involves a new U(1) gauge interaction, possessed only by the AC-leptons and providing a Coulomblike attraction between them. AC-leptons posses electro-magnetic as well as Z-boson interaction and, according to the charge chosen for the new U(1) gauge interaction, a new "invisible light" interaction. Their final cosmic relics are bounded into "neutral" stable atoms (AC) forming the mysterious cold dark matter, in the spirit of the Glashow's Sinister model. An (AC) state is reached in the early Universe along a tail of a few secondary frozen exotic components. They should be now here somehow hidden in the surrounding matter. The two main secondary manifest relics are C (mostly hidden in a neutral (Cee) "anomalous helium" atom, at a 10-8 ratio) and a corresponding "ion" A bounded with an ordinary helium ion (4He); indeed the positive helium ions are able to attract and capture the free A fixing them into a neutral relic cage that has nuclear interaction (4HeA).
Zeitschrift:
Class. Quantum Grav.
2006 | Composite dark matter with invisible light from almost-commutative geometry | Maxim Khlopov, Christoph Stephan
Link zum Preprint
Composite dark matter with invisible light from almost-commutative geometry
Autoren: Maxim Khlopov, Christoph Stephan
(2006)
Almost commutative geometry offers a specific way to unify general relativity, quantum mechanics and gauge symmetries. The AC-model of elementary particles, arising on this way, naturally embeds the Standard model and predicts doubly charged AC-leptons, anion-like A^{--} and cathion-like C^{++}, which can bind in WIMP-like (AC)-atoms, being a nontrivial candidate for cosmological dark matter. This state is reached in the early Universe along a tail of more manifest secondary frozen blocks. They should be now here polluting the surrounding matter. The main secondary relics are C^{++} "anomalous helium" and a bound system of A^{--} with an ordinary helium ion (^4He)^{++}, which is able to attract and capture (in thefirst three minutes) all the free A^{--} fixing them into a neutral OLe-helium (OHe) nuclear interacting "atom" (^4He^{++}A^{--}). The model naturally involves a new U(1) gauge interaction, possessed only by the AC-leptons and providing a Coulomb-like attraction between them. This attraction stimulates the effective A-C recombination into AC-atoms inside dense matter bodies (stars and planets), resulting in a decrease of anomalous isotopes below the experimental upper limits. OLe-helium pollution of terrestrial matter and (OHe) catalysis of nuclear reactions in it is one of the exciting problems (or advantages?) of the present model.
2006 | Almost-commutative geometries beyond the Standard Model | Christoph Stephan
Zeitschrift: J. Phys. A
Verlag: IOP Publishing
Seiten: 9657-9670
Band: 39, no. 30
Link zur Publikation
,
Link zum Preprint
Almost-commutative geometries beyond the Standard Model
Autoren: Christoph Stephan
(2006)
In [7-9] and [10] the conjecture is presented that almost-commutative geometries, with respect to sensible physical constraints, allow only the standard model of particle physics and electro-strong models as Yang-Mills-Higgs theories. In this publication a counter example will be given.
The corresponding almost-commutative geometry leads to a Yang-Mills-Higgs model which consists of the standard model of particle physics and two new fermions of opposite electro-magnetic charge. This is the second Yang-Mills-Higgs model within noncommutative geometry, after the standard model, which could be compatible with experiments. Combined to a hydrogen-like composite particle these new particles provide a novel dark matter candidate.
2006 | Almost-commutative geometry, massive neutrinos and the orientability axiom in KO-dimension 6 | Christoph Stephan
Link zum Preprint
Almost-commutative geometry, massive neutrinos and the orientability axiom in KO-dimension 6
Autoren: Christoph Stephan
(2006)
In recent publications Alain Connes [1] and John Barrett [2] proposed to change the KO-dimension of the internal space of the standard model in its noncommutative representation [3] from zero to six. This apparently minor modification allowed to resolve the fermion doubling problem [4], and the introduction of Majorana mass terms for the right-handed neutrino. The price which had to be paid was that at least the orientability axiom of noncommutative geometry [5,6] may not be obeyed by the underlying geometry. In this publication we review three internal geometries, all three failing to meet the orientability axiom of noncommutative geometry. They will serve as examples to illustrate the nature of this lack of orientability. We will present an extension of the minimal standard model found in [7] by a right-handed neutrino, where only the sub-representation associated to this neutrino is not orientable.
2005 | Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems | M. Freitag, B. Hofmann
Zeitschrift: J. Inverse Ill-Posed Probl.
Seiten: 123-148
Band: 13(2)
Link zur Publikation
Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems
Autoren: M. Freitag, B. Hofmann
(2005)
Zeitschrift:
J. Inverse Ill-Posed Probl.
2005 | Elevated Internal Exposure of Children in Simulated Acute Inhalation of Volatile Organic Compounds: Effects of Concentration and Duration | K. Abraham, H. Mielke, W. Huisinga, U. Gundert-Remy
Zeitschrift: Arch Toxicol
Seiten: 63-73
Band: 79
Link zur Publikation
Elevated Internal Exposure of Children in Simulated Acute Inhalation of Volatile Organic Compounds: Effects of Concentration and Duration
Autoren: K. Abraham, H. Mielke, W. Huisinga, U. Gundert-Remy
(2005)
Zeitschrift:
Arch Toxicol
2005 | Internal exposure of children by simulated acute inhalation of volatile organic compounds: the influence of chemical properties on the child/adult concentration ratio | K. Abraham, H. Mielke, W. Huisinga, U. Gundert-Remy
Zeitschrift: Basic & Clinical Pharmacology & Toxicology
Seiten: 242–243
Band: 96
Link zur Publikation
Internal exposure of children by simulated acute inhalation of volatile organic compounds: the influence of chemical properties on the child/adult concentration ratio
Autoren: K. Abraham, H. Mielke, W. Huisinga, U. Gundert-Remy
(2005)
Zeitschrift:
Basic & Clinical Pharmacology & Toxicology
2005 | Adaptive Approach for Non-Linear Sensitivity Analysis of Reaction Kinetics | I. Horenko, S. Lorenz, C. Schütte, W. Huisinga
Zeitschrift: J. Comp. Chem.
Seiten: 941-948
Band: 26
Link zur Publikation
Adaptive Approach for Non-Linear Sensitivity Analysis of Reaction Kinetics
Autoren: I. Horenko, S. Lorenz, C. Schütte, W. Huisinga
(2005)
Zeitschrift:
J. Comp. Chem.
2005 | Metastability and Dominant Eigenvalues of Transfer Operators | W. Huisinga, B. Schmidt
Reihe: Lecture Notes in Computational Science and Engineering
Verlag: Springer
Buchtitel: 'Advances in Algorithms for Macromolecular Simulation', C. Chipot, R. Elber, A. Laaksonen, B. Leimkuhler, A. Mark, T. Schlick, C. Schütte, and R. Skeel (Eds.)
Band: 49
Link zur Publikation
Metastability and Dominant Eigenvalues of Transfer Operators
Autoren: W. Huisinga, B. Schmidt
(2005)
Reihe:
Lecture Notes in Computational Science and Engineering
Buchtitel:
'Advances in Algorithms for Macromolecular Simulation', C. Chipot, R. Elber, A. Laaksonen, B. Leimkuhler, A. Mark, T. Schlick, C. Schütte, and R. Skeel (Eds.)
2005 | Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems | A. Alfonsi, E. Cances, G. Turinici, B. Di Ventura, W. Huisinga
Zeitschrift: ESAIM: Proc.
Seiten: 1-13
Band: 14
Link zur Publikation
Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems
Autoren: A. Alfonsi, E. Cances, G. Turinici, B. Di Ventura, W. Huisinga
(2005)
Zeitschrift:
ESAIM: Proc.
2005 | Presolid Varieties of n-semigroups | Chantasartrassmee, A. and Koppitz, J.
Zeitschrift: Discussiones Mathematicae General Algebra and Applications
Band: 25
Presolid Varieties of n-semigroups
Autoren: Chantasartrassmee, A. and Koppitz, J.
(2005)
Zeitschrift:
Discussiones Mathematicae General Algebra and Applications
2005 | On mappings of terms determined by hypersubstituions | Koppitz, J. and Shtrakov, Sl.
Zeitschrift: Journal of Algebra and Discrete Mathematics
Band: 3
On mappings of terms determined by hypersubstituions
Autoren: Koppitz, J. and Shtrakov, Sl.
(2005)
Zeitschrift:
Journal of Algebra and Discrete Mathematics
2005 | Introduction to differential manifolds | Christian Bär
Verlag: International Press
Buchtitel: J.-P. Bourguignon et al. (eds.): Dirac operators: yesterday and today
Seiten: 13-25
Link zur Publikation
,
Link zum Preprint
Introduction to differential manifolds
Autoren: Christian Bär
(2005)
We give a very condensed introduction to the theory of differential manifolds.
Verlag:
International Press
Buchtitel:
J.-P. Bourguignon et al. (eds.): Dirac operators: yesterday and today
2005 | The spectrum of the Dirac operator | Christian Bär
Verlag: International Press
Buchtitel: J.-P. Bourguignon et al. (eds.): Dirac operators: yesterday and today
Seiten: 145-162
Link zur Publikation
,
Link zum Preprint
The spectrum of the Dirac operator
Autoren: Christian Bär
(2005)
We survey results on the spectrum of the Dirac operator on compact and on complete noncompact Riemannian spin manifolds.
Verlag:
International Press
Buchtitel:
J.-P. Bourguignon et al. (eds.): Dirac operators: yesterday and today
2005 | Generalized cylinders in semi-Riemannian and Spin geometry | Christian Bär, Paul Gauduchon, Andrei Moroianu
Zeitschrift: Math. Z.
Verlag: Springer
Seiten: 545-580
Band: 249, no. 3
Link zur Publikation
,
Link zum Preprint
Generalized cylinders in semi-Riemannian and Spin geometry
Autoren: Christian Bär, Paul Gauduchon, Andrei Moroianu
(2005)
We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory. It has the advantage of being very simple and the result directly extends to semi-Riemannian manifolds and to embeddings into spaces of constant curvature. We also give a new way to identify spinors for different metrics and to derive the variation formula for the Dirac operator. Moreover, we show that generalized Killing spinors for Codazzi tensors are restrictions of parallel spinors. Finally, we study the space of Lorentzian metrics and give a criterion when two Lorentzian metrics on a manifold can be joined in a natural manner by a 1-parameter family of such metrics.
2005 | Reilly-type spinorial inequalities | Nicolas Ginoux
Verlag: International Press
Buchtitel: J.-P. Bourguignon et al. (eds.): Dirac operators: yesterday and today
Seiten: 263-269
Link zur Publikation
Reilly-type spinorial inequalities
Autoren: Nicolas Ginoux
(2005)
Verlag:
International Press
Buchtitel:
J.-P. Bourguignon et al. (eds.): Dirac operators: yesterday and today
2005 | On a classification of irreducible almost commutative geometries. III | Jan-Hendrik Jureit, Thomas Schucker, Christoph Stephan
Zeitschrift: J. Math. Phys.
Verlag: American Institute of Physics
Seiten: 72303
Band: 46, no. 7
Link zur Publikation
,
Link zum Preprint
On a classification of irreducible almost commutative geometries. III
Autoren: Jan-Hendrik Jureit, Thomas Schucker, Christoph Stephan
(2005)
We extend a classification of irreducible, almost commutative geometries whose spectral action is dynamically non-degenerate to internal algebras that have four simple summands.
Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
2005 | On a classification of irreducible almost commutative geometries, a second helping | Jan-Hendrik Jureit, Christoph Stephan
Zeitschrift: J. Math. Phys.
Verlag: American Institute of Physics
Seiten: 43512
Band: 46, no. 4
Link zur Publikation
,
Link zum Preprint
On a classification of irreducible almost commutative geometries, a second helping
Autoren: Jan-Hendrik Jureit, Christoph Stephan
(2005)
We complete the classification of almost commutative geometries from a particle physics point of view given in hep-th/0312276. Four missing Krajewski diagrams will be presented after a short introduction into irreducible, non-degenerate spectral triples.
Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
2005 | Eigenvalues of Dirac operators for hyperbolic degenerations | Frank Pfäffle
Zeitschrift: Manuscr. Math.
Verlag: Springer
Seiten: 1-29
Band: 116, no. 1
Link zur Publikation
,
Link zum Preprint
Eigenvalues of Dirac operators for hyperbolic degenerations
Autoren: Frank Pfäffle
(2005)
We study the behaviour of the spectrum of the Dirac operator for sequences of compact hyperbolic spin manifolds whose limit is non-compact. If the spectrum of the limit manifold is discrete we show that this spectrum is approximated by the spectra of the compact manifolds.
Zeitschrift:
Manuscr. Math.
2005 | Pattern recognition from one example by chopping | Fleuret, F., Blanchard, G.
Zeitschrift: Advances in Neural Information Processing Systems (NIPS 2005)
Verlag: MIT Press
Seiten: 371-378
Pattern recognition from one example by chopping
Autoren: Fleuret, F., Blanchard, G.
(2005)
Zeitschrift:
Advances in Neural Information Processing Systems (NIPS 2005)
2005 | Non-Gaussian Component Analysis: a Semiparametric Framework for Linear Dimension Reduction | Blanchard, G., Kawanabe, M., Sugiyama, M., Spokoiny, V., Müller, K-R
Zeitschrift: Advances in Neural Information Processing Systems (NIPS 2005)
Verlag: MIT Press
Seiten: 131-138
Band: 18
Non-Gaussian Component Analysis: a Semiparametric Framework for Linear Dimension Reduction
Autoren: Blanchard, G., Kawanabe, M., Sugiyama, M., Spokoiny, V., Müller, K-R
(2005)
Zeitschrift:
Advances in Neural Information Processing Systems (NIPS 2005)
2005 | Hierarchical testing designs for pattern recognition | Blanchard, G., Geman, D.
Zeitschrift: The Annals of Statistics
Verlag: Institute of Mathematical Statistics
Seiten: 1155-1202
Band: 33
Hierarchical testing designs for pattern recognition
Autoren: Blanchard, G., Geman, D.
(2005)
Zeitschrift:
The Annals of Statistics
Verlag:
Institute of Mathematical Statistics
2004 | On the Influence of Multiplication Operators on the Ill-posedness of Inverse Problems | M. Freitag
Diplomarbeit, Fakultät für Mathematik, Technische Universität Chemnitz (2004). (Available online here)
On the Influence of Multiplication Operators on the Ill-posedness of Inverse Problems
Autoren: M. Freitag
(2004)
Diplomarbeit, Fakultät für Mathematik, Technische Universität Chemnitz (2004). (Available online
here)
2004 | Phase Transitions & Metastability in Markovian and Molecular Systems | W. Huisinga, S. Meyn, Ch. Schütte
Zeitschrift: Ann. Appl. Probab.
Seiten: 419-458
Band: 14
Link zur Publikation
Phase Transitions & Metastability in Markovian and Molecular Systems
Autoren: W. Huisinga, S. Meyn, Ch. Schütte
(2004)
Zeitschrift:
Ann. Appl. Probab.
2004 | An Averaging Principle for Fast Degrees of Freedom Exhibiting Long-Term Correlations | Ch. Schütte, J. Walter, C. Hartmann, W. Huisinga
Zeitschrift: SIAM Multiscale Modeling and Simulation 2
Seiten: 501-526
Link zur Publikation
An Averaging Principle for Fast Degrees of Freedom Exhibiting Long-Term Correlations
Autoren: Ch. Schütte, J. Walter, C. Hartmann, W. Huisinga
(2004)
Zeitschrift:
SIAM Multiscale Modeling and Simulation 2
2004 | Hypersubstitutions and Groups | Koppitz, J.
Zeitschrift: Novi Sad Math.
Band: 34 no.2
Hypersubstitutions and Groups
Autoren: Koppitz, J.
(2004)
Zeitschrift:
Novi Sad Math.
2004 | The first Dirac eigenvalues on manifolds with positive scalar curvature | Christian Bär, Mattias Dahl
Zeitschrift: Proc. Amer. Math. Soc.
Verlag: American Mathematical Society
Seiten: 3337-3344 (electronic)
Band: 132, no. 1
Link zur Publikation
,
Link zum Preprint
The first Dirac eigenvalues on manifolds with positive scalar curvature
Autoren: Christian Bär, Mattias Dahl
(2004)
We show that on every compact spin manifold admitting a Riemannian metric of positive scalar curvature Friedrich's eigenvalue estimate for the Dirac operator can be made sharp up to an arbitrarily small given error by choosing the metric suitably.
Zeitschrift:
Proc. Amer. Math. Soc.
Verlag:
American Mathematical Society
Seiten:
3337-3344 (electronic)
2004 | Dirac operators on Lagrangian submanifolds | Nicolas Ginoux
Zeitschrift: J. Geom. Phys.
Verlag: Elsevier
Seiten: 480-498
Band: 52, no. 4
Link zur Publikation
,
Link zum Preprint
Dirac operators on Lagrangian submanifolds
Autoren: Nicolas Ginoux
(2004)
We study a natural Dirac operator on a Lagrangian submanifold of a K\"ahler manifold. We first show that its square coincides with the Hodge-de Rham Laplacian provided the complex structure identifies the Spin structures of the tangent and normal bundles of the submanifold. We then give extrinsic estimates for the eigenvalues of that operator and discuss some examples.
Zeitschrift:
J. Geom. Phys.
2004 | On a classification of irreducible almost commutative geometries | Bruno Iochum, Thomas Schucker, Christoph Stephan
Zeitschrift: J. Math. Phys.
Verlag: American Institute of Physics
Seiten: 5003-5041
Band: 45, no. 12
Link zur Publikation
,
Link zum Preprint
On a classification of irreducible almost commutative geometries
Autoren: Bruno Iochum, Thomas Schucker, Christoph Stephan
(2004)
We classify all irreducible, almost commutative geometries whose spectral action is dynamically non-degenerate. Heavy use is made of Krajewski's diagrammatic language. The motivation for our definition of dynamical non-degeneracy stems from particle physics where the fermion masses are non-degenerate.
Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
2004 | Estimation in partly parametric additive Cox models. | Henning Läuter
Verlag: Birkhäuser
Buchtitel: Parametric and semiparametric models
Estimation in partly parametric additive Cox models.
Autoren: Henning Läuter
(2004)
Buchtitel:
Parametric and semiparametric models
2004 | On the norm equation over function fields | Gräter, J.; Weese, M.
Zeitschrift: J. Lond. Math. Soc, II. Ser. 69
Seiten: 575-592
On the norm equation over function fields
Autoren: Gräter, J.; Weese, M.
(2004)
Zeitschrift:
J. Lond. Math. Soc, II. Ser. 69
2004 | Kernel projection machine: a new tool for pattern recognition | Zwald, L., Blanchard, G., Massart, P., Vert, R.
Zeitschrift: Advances in Neural Information Processing Systems (NIPS 2004)
Verlag: MIT Press
Seiten: 1649-1656
Band: 17
Kernel projection machine: a new tool for pattern recognition
Autoren: Zwald, L., Blanchard, G., Massart, P., Vert, R.
(2004)
Zeitschrift:
Advances in Neural Information Processing Systems (NIPS 2004)
2004 | BCI competition 2003-data set IIa: spatial patterns of self-controlled brain rhythm modulations | Blanchard, G., Blankertz, B.
Zeitschrift: Biomedical Engineering, IEEE Transactions on
Verlag: IEEE
Seiten: 1062-1066
Band: 51
BCI competition 2003-data set IIa: spatial patterns of self-controlled brain rhythm modulations
Autoren: Blanchard, G., Blankertz, B.
(2004)
Zeitschrift:
Biomedical Engineering, IEEE Transactions on
2004 | Statistical properties of kernel principal component analysis | Zwald, L., Bousquet, O., Blanchard, G.
Zeitschrift: Learning theory (COLT 2004)
Verlag: Springer Lecture Notes in Artificial Intelligence
Seiten: 594-608
Band: 3120
Statistical properties of kernel principal component analysis
Autoren: Zwald, L., Bousquet, O., Blanchard, G.
(2004)
Zeitschrift:
Learning theory (COLT 2004)
Verlag:
Springer Lecture Notes in Artificial Intelligence
2004 | Oracle bounds and exact algorithm for dyadic classification trees | Blanchard, G., Schäfer, C., Rozenholc, Y.
Zeitschrift: Learning theory (COLT 2004)
Verlag: Springer Lecture Notes in Artificial Intelligence
Seiten: 378-392
Band: 3120
Oracle bounds and exact algorithm for dyadic classification trees
Autoren: Blanchard, G., Schäfer, C., Rozenholc, Y.
(2004)
Zeitschrift:
Learning theory (COLT 2004)
Verlag:
Springer Lecture Notes in Artificial Intelligence
2004 | Different paradigms for choosing sequential reweighting algorithms | Blanchard, G.
Zeitschrift: Neural Computation
Verlag: MIT Press
Seiten: 811-836
Band: 16
Different paradigms for choosing sequential reweighting algorithms
Autoren: Blanchard, G.
(2004)
Zeitschrift:
Neural Computation
2004 | Un algorithme accéléré d'échantillonnage bayésien pour le modèle CART | Blanchard, G.
Zeitschrift: Revue d'intelligence artificielle
Verlag: Lavoisier
Seiten: 383-410
Band: 18
Un algorithme accéléré d'échantillonnage bayésien pour le modèle CART
Autoren: Blanchard, G.
(2004)
Zeitschrift:
Revue d'intelligence artificielle
2003 | Transcritical flow modelling with the Box Scheme | M. Freitag
MSc Thesis, Department of Mathematical Sciences, University of Bath (2003). (GZipped PostScript), (PDF)
Transcritical flow modelling with the Box Scheme
Autoren: M. Freitag
(2003)
2003 | Biomolecular Conformations can be Identified as Metastable Sets of Molecular Dynamics | Ch. Schütte, W. Huisinga
Buchtitel: 'Handbook of Numerical Analysis' edited by P. G. Ciarlet, Special Volume: Computational Chemistry (Vol X) , guest editor C. Le Bris
Link zur Publikation
Biomolecular Conformations can be Identified as Metastable Sets of Molecular Dynamics
Autoren: Ch. Schütte, W. Huisinga
(2003)
Buchtitel:
'Handbook of Numerical Analysis' edited by P. G. Ciarlet, Special Volume: Computational Chemistry (Vol X) , guest editor C. Le Bris
2003 | Extracting Macroscopic Stochastic Dynamics: Model Problems | W. Huisinga, Ch. Schütte, A. M. Stuart
Zeitschrift: Comm. Pure Appl. Math.
Seiten: 234-269
Band: 56
Link zur Publikation
Extracting Macroscopic Stochastic Dynamics: Model Problems
Autoren: W. Huisinga, Ch. Schütte, A. M. Stuart
(2003)
Zeitschrift:
Comm. Pure Appl. Math.
2003 | Metastability of Diffusion Processes | Ch. Schütte, W. Huisinga, S. Meyn
Buchtitel: Proceeding of the IUTAM Symposium on Nonlinear Stochastic Dynamics (August 26 - August 30, 2002, Illinois/USA)
Link zur Publikation
Metastability of Diffusion Processes
Autoren: Ch. Schütte, W. Huisinga, S. Meyn
(2003)
Buchtitel:
Proceeding of the IUTAM Symposium on Nonlinear Stochastic Dynamics (August 26 - August 30, 2002, Illinois/USA)
2003 | Lattice-theoretically characterized classes of finite bands | Koppitz, J. and Thron, R.
Zeitschrift: Archivum Mathematicum (Brno)
Band: 39
Lattice-theoretically characterized classes of finite bands
Autoren: Koppitz, J. and Thron, R.
(2003)
Zeitschrift:
Archivum Mathematicum (Brno)
2003 | Testing homoscedasticity in nonparametric regression | Hannelore Liero
Zeitschrift: Nonparametric Statistics
Seiten: 31-51
Band: 12
Testing homoscedasticity in nonparametric regression
Autoren: Hannelore Liero
(2003)
Zeitschrift:
Nonparametric Statistics
2003 | Small eigenvalues of the conformal Laplacian | Christian Bär, Mattias Dahl
Zeitschrift: Geom. Funct. Anal.
Verlag: Springer
Seiten: 483-508
Band: 13, no. 3
Link zur Publikation
,
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Small eigenvalues of the conformal Laplacian
Autoren: Christian Bär, Mattias Dahl
(2003)
We introduce a differential topological invariant for compact differentiable manifolds by counting the small eigenvalues of the Conformal Laplace operator. This invariant vanishes if and only if the manifold has a metric of positive scalar curvature. We show that the invariant does not increase under surgery of codimension at least three and we give lower and upper bounds in terms of the α-genus.
Zeitschrift:
Geom. Funct. Anal.
2003 | Heat kernel asymptotics for roots of generalized Laplacians | Christian Bär, Sergiu Moroianu
Zeitschrift: Internat. J. Math.
Verlag: World Scientific
Seiten: 397-412
Band: 14, no. 4
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,
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Heat kernel asymptotics for roots of generalized Laplacians
Autoren: Christian Bär, Sergiu Moroianu
(2003)
We describe the heat kernel asymptotics for roots of a Laplace type operator Δ on a closed manifold. A previously known relation between the Wodzicki residue of Δ and heat trace asymptotics is shown to hold pointwise for the corresponding densities.
Zeitschrift:
Internat. J. Math.
2003 | The Dirac determinant of spherical space forms | Christian Bär, Sven Schopka
Verlag: Springer
Buchtitel: S. Hildebrandt, H. Karcher (Eds.): Geometric analysis and nonlinear partial differential equations
Seiten: 39-67
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,
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The Dirac determinant of spherical space forms
Autoren: Christian Bär, Sven Schopka
(2003)
The ζ-regularized determinants of the Dirac operator and of its square are computed on spherical space forms. On S2 the determinant of Dirac operators twisted by a complex line bundle is also calculated.
Buchtitel:
S. Hildebrandt, H. Karcher (Eds.): Geometric analysis and nonlinear partial differential equations
2003 | Une nouvelle estimation extrinsèque du spectre de l'opérateur de Dirac | Nicolas Ginoux
Zeitschrift: C. R. Math. Acad. Sci. Paris
Verlag: Elsevier
Seiten: 829-832
Band: 336, no. 1
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,
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Une nouvelle estimation extrinsèque du spectre de l'opérateur de Dirac
Autoren: Nicolas Ginoux
(2003)
We prove a new upper bound for the smallest eigenvalues of the Dirac operator on a compact hypersurface of the hyperbolic space.
Zeitschrift:
C. R. Math. Acad. Sci. Paris
2003 | Remarques sur le spectre de l'opérateur de Dirac | Nicolas Ginoux
Zeitschrift: C. R. Math. Acad. Sci. Paris
Verlag: Elsevier
Seiten: 53-56
Band: 337, no. 1
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,
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Remarques sur le spectre de l'opérateur de Dirac
Autoren: Nicolas Ginoux
(2003)
We describe a new family of examples of hypersurfaces in the sphere satisfying the limiting-case in C. B\"ar's extrinsic upper bound for the smallest eigenvalue of the Dirac operator.
Zeitschrift:
C. R. Math. Acad. Sci. Paris
2003 | Estimation in Survival Models. | Henning Läuter
Buchtitel: Statistical Inference for Semiparametric Models
Estimation in Survival Models.
Autoren: Henning Läuter
(2003)
Buchtitel:
Statistical Inference for Semiparametric Models
2003 | Complexity of elements in rings | Dubrovin, N.I.; Gräter, J.; Hanke, T.
Zeitschrift: Algebr. Represent. Theory 6
Seiten: 33-45
Complexity of elements in rings
Autoren: Dubrovin, N.I.; Gräter, J.; Hanke, T.
(2003)
Zeitschrift:
Algebr. Represent. Theory 6
2003 | Characterizing nearly simple chain domains | Brungs, H.H.; Gräter, J.
Zeitschrift: Proc. Am. Math. Soc. 131
Seiten: 1347-1355
Characterizing nearly simple chain domains
Autoren: Brungs, H.H.; Gräter, J.
(2003)
Zeitschrift:
Proc. Am. Math. Soc. 131
2003 | On the rate of convergence of regularized boosting classifiers | Blanchard, G., Lugosi, G., Vayatis, N.
Zeitschrift: Journal of Machine Learning Research
Verlag: JMLR. org
Seiten: 861-894
Band: 4
On the rate of convergence of regularized boosting classifiers
Autoren: Blanchard, G., Lugosi, G., Vayatis, N.
(2003)
Zeitschrift:
Journal of Machine Learning Research
2003 | Generalization error bounds for aggregate classifiers | Blanchard, G.
Zeitschrift: Nonlinear Estimation and Classification
Verlag: Springer Lectures notes in Statistics
Buchtitel: Nonlinear Estimation and Classification
Seiten: 357-368
Band: 171
Generalization error bounds for aggregate classifiers
Autoren: Blanchard, G.
(2003)
Zeitschrift:
Nonlinear Estimation and Classification
Verlag:
Springer Lectures notes in Statistics
Buchtitel:
Nonlinear Estimation and Classification
2002 | Equational Theories generated by Hypersubstitutions of Type (n) | Denecke, K., Koppitz, J. and Niwczyk, St.
Zeitschrift: International Journal of Algebra and Computation
Band: 12 no. 6
Equational Theories generated by Hypersubstitutions of Type (n)
Autoren: Denecke, K., Koppitz, J. and Niwczyk, St.
(2002)
Zeitschrift:
International Journal of Algebra and Computation
2002 | Solid varieties of arbitrary type | Denecke, K., Koppitz, J. and Wismath, S.L.,
Zeitschrift: Algebra Universalis
Band: 48
Solid varieties of arbitrary type
Autoren: Denecke, K., Koppitz, J. and Wismath, S.L.,
(2002)
Zeitschrift:
Algebra Universalis
2002 | The Einstein-Hilbert action as a spectral action | Bernd Ammann, Christian Bär
Reihe: Lecture Notes in Physics
Verlag: Springer
Buchtitel: F. Scheck, H. Upmeier, W. Werner (eds.): Noncommutative geometry and the standard model of elementary particle physics (Hesselberg, 1999)
Seiten: 75-108
Band: 596
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,
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The Einstein-Hilbert action as a spectral action
Autoren: Bernd Ammann, Christian Bär
(2002)
Exposition of heat asymptotics for generalized Laplace operators, Weyl's asymptotics for the eigenvalues, variation of the total scalar curvature functional (Einstein-Hilbert action), and of a theorem by Kalau/Walze and Kastler independently relating the second heat coefficient to the Wodzicki residue.
Reihe:
Lecture Notes in Physics
Buchtitel:
F. Scheck, H. Upmeier, W. Werner (eds.): Noncommutative geometry and the standard model of elementary particle physics (Hesselberg, 1999)
2002 | Dirac eigenvalue estimates on surfaces | Bernd Ammann, Christian Bär
Zeitschrift: Math. Z.
Verlag: Springer
Seiten: 423-449
Band: 240, no. 2
Link zur Publikation
,
Link zum Preprint
Dirac eigenvalue estimates on surfaces
Autoren: Bernd Ammann, Christian Bär
(2002)
We prove lower Dirac eigenvalue bounds for closed surfaces with a spin structure whose Arf invariant equals 1. Besides the area only one geometric quantity enters in these estimates, the spin-cut-diameter which depends on the choice of spin structure. It can be expressed in terms of various distances on the surfaces or, alternatively, by stable norms of certain cohomology classes. In case of the 2-torus we obtain a positive lower bound for all Riemannian metrics and all nontrivial spin structures. The corresponding estimate also holds for the L2-spectrum of the Dirac operator on a noncompact complete surface of finite area. As a corollary we get positive lower bounds on the Willmore integral for all 2-tori embedded in R3.
2002 | Surgery and the Spectrum of the Dirac Operator | Christian Bär, Mattias Dahl
Zeitschrift: J. Reine Angew. Math.
Verlag: De Gruyter
Seiten: 53-76
Band: 552
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,
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Surgery and the Spectrum of the Dirac Operator
Autoren: Christian Bär, Mattias Dahl
(2002)
We show that for generic Riemannian metrics on a simply-connected closed spin manifold of dimension at least 5 the dimension of the space of harmonic spinors is no larger than it must be by the index theorem. The same result holds for periodic fundamental groups of odd order.
The proof is based on a surgery theorem for the Dirac spectrum which says that if one performs surgery of codimension at least 3 on a closed Riemannian spin manifold, then the Dirac spectrum changes arbitrarily little provided the metric on the manifold after surgery is chosen properly.
Zeitschrift:
J. Reine Angew. Math.
2002 | Reilly-type spinorial inequalities | Nicolas Ginoux
Zeitschrift: Math. Z.
Verlag: Springer
Seiten: 513-525
Band: 241, no. 3
Link zur Publikation
Reilly-type spinorial inequalities
Autoren: Nicolas Ginoux
(2002)
We give a new extrinsic upper bound for the smallest eigenvalues of the Dirac operator of a hypersurface. If the ambient manifold is the hyperbolic space, we show that its limiting case is achieved only for geodesic spheres.
2002 | On eigenvalue estimates for the submanifold Dirac operator | Nicolas Ginoux, Bertrand Morel
Zeitschrift: Internat. J. Math.
Verlag: World Scientific
Seiten: 533-548
Band: 13, no. 5
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,
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On eigenvalue estimates for the submanifold Dirac operator
Autoren: Nicolas Ginoux, Bertrand Morel
(2002)
We give lower bounds for the eigenvalues of the submanifold Dirac operator in terms of intrinsic and extrinsic curvature expressions. We also show that the limiting cases give rise to a class generalizing that of Killing spinors. We conclude by translating these results in terms of intrinsic twisted Dirac operators.
Zeitschrift:
Internat. J. Math.
2002 | Le système de renvoi dans l’Encyclopédie: une cartographie des structures de connaissances au XVIIIe siècle | Blanchard, G., Olsen, M.
Zeitschrift: Recherches sur Diderot et sur l'Encyclopédie
Verlag: Société Diderot
Seiten: 45-70
Le système de renvoi dans l’Encyclopédie: une cartographie des structures de connaissances au XVIIIe siècle
Autoren: Blanchard, G., Olsen, M.
(2002)
Zeitschrift:
Recherches sur Diderot et sur l'Encyclopédie
2001 | Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems | Ch. Schütte, W. Huisinga, P. Deuflhard
Buchtitel: 'Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems' edited by B. Fiedler
Seiten: 191-223
Link zur Publikation
Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems
Autoren: Ch. Schütte, W. Huisinga, P. Deuflhard
(2001)
Buchtitel:
'Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems' edited by B. Fiedler
2001 | Closure Operators and Generating Sets | Thron, R. and Koppitz, J.
Zeitschrift: Mathematica Slovaca
Band: 51
Closure Operators and Generating Sets
Autoren: Thron, R. and Koppitz, J.
(2001)
Zeitschrift:
Mathematica Slovaca
2001 | rongly fluid and weakly unsolid varieties | Arworn, Sr., Denecke, K. and Koppitz, J.
Zeitschrift: Scientiae Matematicae Japoniacae
Band: 54 no. 1
rongly fluid and weakly unsolid varieties
Autoren: Arworn, Sr., Denecke, K. and Koppitz, J.
(2001)
Zeitschrift:
Scientiae Matematicae Japoniacae
2001 | The semantical hyperunification problem | Denecke, K., Koppitz, J. and Wismath, S.L
Zeitschrift: Discussiones Mathematicae General Algebra and Applications
Band: 21
The semantical hyperunification problem
Autoren: Denecke, K., Koppitz, J. and Wismath, S.L
(2001)
Zeitschrift:
Discussiones Mathematicae General Algebra and Applications
2001 | The depth of a hypersubstitution | Denecke, K., Koppitz, J. and Shtrakov Sl.,
Zeitschrift: Journal of Automata, Languages and Combinatorics
Band: 6 no. 3
The depth of a hypersubstitution
Autoren: Denecke, K., Koppitz, J. and Shtrakov Sl.,
(2001)
Zeitschrift:
Journal of Automata, Languages and Combinatorics
2001 | Essential variables in hypersubstitutions | Denecke, K. and Koppitz, J.
Zeitschrift: Algebra Universalis
Band: 46
Essential variables in hypersubstitutions
Autoren: Denecke, K. and Koppitz, J.
(2001)
Zeitschrift:
Algebra Universalis
2001 | $L_2$-tests for sparse multinomials. | Hannelore Liero
Zeitschrift: Statistics & Probability Letters
Seiten: 147-158
Band: 55
$L_2$-tests for sparse multinomials.
Autoren: Hannelore Liero
(2001)
Zeitschrift:
Statistics & Probability Letters
2001 | Testing in sparse contingency tables. | Hannelore Liero
Buchtitel: Proceedings of the 6th International Conference on Computer Data Analysis and Modeling Minsk 2001
Testing in sparse contingency tables.
Autoren: Hannelore Liero
(2001)
Buchtitel:
Proceedings of the 6th International Conference on Computer Data Analysis and Modeling Minsk 2001
2001 | Elementare Differentialgeometrie (Monografie) | Christian Bär
Reihe: de Gruyter Lehrbuch
Verlag: De Gruyter
Seiten: xii+281 pages
Link zur Publikation
Elementare Differentialgeometrie (Monografie)
Autoren: Christian Bär
(2001)
Reihe:
de Gruyter Lehrbuch
2001 | Semi-Bounded Restrictions of Dirac Type Operators and the Unique Continuation Property | Christian Bär, Alexander Strohmaier
Zeitschrift: Differential Geom. Appl.
Verlag: Elsevier
Seiten: 175-182
Band: 15, no. 2
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,
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Semi-Bounded Restrictions of Dirac Type Operators and the Unique Continuation Property
Autoren: Christian Bär, Alexander Strohmaier
(2001)
Let M be a connected Riemannian manifold and let D be a Dirac type operator acting on smooth compactly supported sections in a Hermitian vector bundle over M. Suppose D has a self-adjoint extension A in the Hilbert space of square-integrable sections. We show that any L2-section φ contained in a closed A-invariant subspace onto which the restriction of A is semi-bounded has the unique continuation property: if φ vanishes on a non-empty open subset of M, then it vanishes on all of M.
Zeitschrift:
Differential Geom. Appl.
2001 | Die schwachdiskontinuierlichen Raumgruppen | Benno Klotzek, Horst Wendland
Zeitschrift: J. Geom.
Verlag: Springer
Seiten: 85-98
Band: 71, no.1-2
Link zur Publikation
Die schwachdiskontinuierlichen Raumgruppen
Autoren: Benno Klotzek, Horst Wendland
(2001)
The research of discontinuous groups with respect to different geometries has made considerable progress (cf. references). One can state the remarkable fact that conditions which all characterize the same discontinuous motion groups in Euclidean spaces of the same finite dimension define different classes of discontinuous transformation groups in other geometries. Moreover in the earlier paper [15], eight conditions are described which define different classes of generalized discontinuous motion groups in metric spaces, in particular in Euclidean spaces of arbitrary dimension. The increase in models in the Euclidean plane geometry is given in the paper [18]. Now, we will give all classes of weak discontinuous or so-called D' 3-discontinuous motion groups of the Euclidean space.
2001 | Residuals. | Henning Läuter
Verlag: Physica Verlag
Buchtitel: Model-oriented Data Analysis
Seiten: 155-162
Residuals.
Autoren: Henning Läuter
(2001)
Buchtitel:
Model-oriented Data Analysis
2000 | Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains | P. Deuflhard, W. Huisinga, A. Fischer, Ch. Schütte
Zeitschrift: Lin. Alg. Appl.
Seiten: 39-59
Band: 315
Link zur Publikation
Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains
Autoren: P. Deuflhard, W. Huisinga, A. Fischer, Ch. Schütte
(2000)
Zeitschrift:
Lin. Alg. Appl.
2000 | On Conformational Dynamics induced by Langevin Processes | Ch. Schütte, W. Huisinga
Buchtitel: 'International Conference on Differential Equations (EquaDiff 99)', edited by B. Fiedler K. Gröger and J. Sprekels, Vol.2 (2000)
Seiten: 1247-1262
Link zur Publikation
On Conformational Dynamics induced by Langevin Processes
Autoren: Ch. Schütte, W. Huisinga
(2000)
Buchtitel:
'International Conference on Differential Equations (EquaDiff 99)', edited by B. Fiedler K. Gröger and J. Sprekels, Vol.2 (2000)
2000 | Self-Organizing Maps Combined with Eigenmode Analysis for Automated Cluster Identification | T. Galliat, Wilhelm Huisinga, P. Deuflhard
Verlag: Academic Press
Buchtitel: 'Neural Computation' edited by H. Bothe and R. Rojas, ICSC
Seiten: 227-232
Link zur Publikation
Self-Organizing Maps Combined with Eigenmode Analysis for Automated Cluster Identification
Autoren: T. Galliat, Wilhelm Huisinga, P. Deuflhard
(2000)
Buchtitel:
'Neural Computation' edited by H. Bothe and R. Rojas, ICSC
2000 | Biomolecular Conformations as Metastable Sets of Markov Chains | Ch. Schütte, W. Huisinga
Buchtitel: Proceedings of the 38th. Annual Allerton Conference on Communication, Control, and Computing, Oct. 4-6, Allerton House, Monticello, Illinoins/USA (2000)
Seiten: 1106-1115
Link zur Publikation
Biomolecular Conformations as Metastable Sets of Markov Chains
Autoren: Ch. Schütte, W. Huisinga
(2000)
Buchtitel:
Proceedings of the 38th. Annual Allerton Conference on Communication, Control, and Computing, Oct. 4-6, Allerton House, Monticello, Illinoins/USA (2000)
2000 | Hyperidentities for Varieties of Star bands | Koppitz, J. and Wismath, S.L.
Zeitschrift: Sci. Math.
Band: 3
Hyperidentities for Varieties of Star bands
Autoren: Koppitz, J. and Wismath, S.L.
(2000)
2000 | All 2-solid varieties of semigroups | Koppitz, J
Zeitschrift: Semigroup Forum
Band: 60
All 2-solid varieties of semigroups
Autoren: Koppitz, J
(2000)
Zeitschrift:
Semigroup Forum
2000 | Fluid, unsolid and completely unsolid varieties | Denecke, K. and Koppitz, J.
Zeitschrift: Algebra Colloquium
Band: 7 no. 4
Fluid, unsolid and completely unsolid varieties
Autoren: Denecke, K. and Koppitz, J.
(2000)
Zeitschrift:
Algebra Colloquium
2000 | Dirac eigenvalues and total scalar curvature | Bernd Ammann, Christian Bär
Zeitschrift: J. Geom. Phys.
Verlag: Elsevier
Seiten: 229-234
Band: 33, no.3-4
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,
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Dirac eigenvalues and total scalar curvature
Autoren: Bernd Ammann, Christian Bär
(2000)
It has recently been conjectured that the eigenvalues λ of the Dirac operator on a closed Riemannian spin manifold M of dimension n ≥ 3 can be estimated from below by the total scalar curvature:
<tex>\lambda^2\geq\frac{n}{4(n-1)}\cdot\frac{\int_{M} S}{vol(M)}</tex>
We show by example that such an estimate is impossible.
Zeitschrift:
J. Geom. Phys.
2000 | The Dirac Operator on Hyperbolic Manifolds of Finite Volume | Christian Bär
Zeitschrift: J. Differential Geom.
Seiten: 439-488
Band: 54, no. 3
Link zur Publikation
,
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The Dirac Operator on Hyperbolic Manifolds of Finite Volume
Autoren: Christian Bär
(2000)
We study the spectrum of the Dirac operator on hyperbolic manifolds of finite volume. Depending on the spin structure it is either discrete or the whole real line. For link complements in S^3 we give a simple criterion in terms of linking numbers for when essential spectrum can occur. We compute the accumulation rate of the eigenvalues of a sequence of closed hyperbolic 2- or 3-manifolds degenerating into a noncompact hyperbolic manifold of finite volume. It turns out that in three dimensions there is no clustering at all.
Zeitschrift:
J. Differential Geom.
2000 | Dependence of the Dirac spectrum on the spin structure | Christian Bär
Zeitschrift: Semin. Congr.
Verlag: Societe Mathematique de France
Buchtitel: Global Analysis and Harmonic Analysis
Seiten: 17-33
Band: 4
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,
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Dependence of the Dirac spectrum on the spin structure
Autoren: Christian Bär
(2000)
The theme is the influence of the spin structure on the Dirac spectrum of a spin manifold. We survey examples and results related to this question.
Zeitschrift:
Semin. Congr.
Verlag:
Societe Mathematique de France
Buchtitel:
Global Analysis and Harmonic Analysis
2000 | Localization and Semibounded Energy - A Weak Unique Continuation Theorem | Christian Bär
Zeitschrift: J. Geom. Phys.
Verlag: Elsevier
Seiten: 155-161
Band: 34, no. 2
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,
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Localization and Semibounded Energy - A Weak Unique Continuation Theorem
Autoren: Christian Bär
(2000)
Let D be a self-adjoint differential operator of Dirac type acting on sections in a vector bundle over a closed Riemannian manifold M. Let H be a closed D-invariant subspace of the Hilbert space of square integrable sections. Suppose D restricted to H is semibounded. We show that every element u in H has the weak unique continuation property, i.e. if u vanishes on a nonempty open subset of M, then it vanishes on all of M.
Zeitschrift:
J. Geom. Phys.
2000 | The Dirac spectrum of Bieberbach manifolds | Frank Pfäffle
Zeitschrift: J. Geom. Phys.
Verlag: Elsevier
Seiten: 367-385
Band: 35, no. 4
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,
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The Dirac spectrum of Bieberbach manifolds
Autoren: Frank Pfäffle
(2000)
The Dirac spectra and the eta invariants of three-dimensional Bieberbach manifolds are computed. Compact connected three-dimensional spin manifolds admitting parallel non-vanishing spinors are identified as flat tori.
Zeitschrift:
J. Geom. Phys.
2000 | Pre-eclampsia associated alterations of the elastic fibre system. | Thomas Junek, Henning Läuter
Zeitschrift: Anat. Embryol.
Verlag: Springer
Seiten: 291-303
Band: 201
Pre-eclampsia associated alterations of the elastic fibre system.
Autoren: Thomas Junek, Henning Läuter
(2000)
Zeitschrift:
Anat. Embryol.
2000 | Trees and valuation rings | Brungs, H.H.; Gräter, J.
Zeitschrift: Trans. Am. Math. Soc. 352
Seiten: 3357-3379
Trees and valuation rings
Autoren: Brungs, H.H.; Gräter, J.
(2000)
Zeitschrift:
Trans. Am. Math. Soc. 352
1999 | Faber and Newton Polynomial Integrators for Open-System Density Matrix Propagation | W. Huisinga, L. Pesce, R. Kosloff, P. Saalfrank
Zeitschrift: J. Chem. Phys.
Seiten: 5538-5547
Band: 110
Link zur Publikation
Faber and Newton Polynomial Integrators for Open-System Density Matrix Propagation
Autoren: W. Huisinga, L. Pesce, R. Kosloff, P. Saalfrank
(1999)
Zeitschrift:
J. Chem. Phys.
1999 | A Direct Approach to Conformational Dynamics based on Hybrid Monte Carlo | Ch. Schütte, A. Fischer, W. Huisinga, P. Deuflhard
Zeitschrift: J. Comp. Phys.
Seiten: 146-168
Band: 151
Link zur Publikation
A Direct Approach to Conformational Dynamics based on Hybrid Monte Carlo
Autoren: Ch. Schütte, A. Fischer, W. Huisinga, P. Deuflhard
(1999)
Zeitschrift:
J. Comp. Phys.
1999 | From Simulation Data to Conformational Ensembles: Structure and Dynamics based Methods | W. Huisinga, Ch. Best, R. Roitzsch, Ch. Schütte, F. Cordes
Zeitschrift: J. Comp. Chem.
Seiten: 1760-1774
Band: 20
Link zur Publikation
From Simulation Data to Conformational Ensembles: Structure and Dynamics based Methods
Autoren: W. Huisinga, Ch. Best, R. Roitzsch, Ch. Schütte, F. Cordes
(1999)
Zeitschrift:
J. Comp. Chem.
1999 | Finite Relational Disjunctions | Thron, R. and Koppitz, J.
Zeitschrift: Algebra Colloquium
Band: 6 no. 3
Finite Relational Disjunctions
Autoren: Thron, R. and Koppitz, J.
(1999)
Zeitschrift:
Algebra Colloquium
1999 | Elliptic Symbols | Christian Bär
Zeitschrift: Math. Nachr.
Verlag: Wiley-VCH
Seiten: 7-35
Band: 201, no. 1
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,
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Elliptic Symbols
Autoren: Christian Bär
(1999)
If $G$ is the structure group of a manifold $M$ it is shown how a certain ideal in the character ring of $G$ corresponds to the set of geometric elliptic operators on $M$. This provides a simple method to construct these operators. For classical structure groups like $G = O(n)$ (Riemannian manifolds), $G = SO(n)$ (oriented Riemannian manifolds), $G = U(m)$ (almost complex manifolds), $G = Spin(n)$ (spin manifolds), or $G = Spin^c(n)$ (spin$^c$ manifolds) this yields well known classical operators like the Euler-deRham operator, signature operator, Cauchy-Riemann operator, or the Dirac operator. For some less well studied structure groups like $Spin^h(n)$ or $Sp(q)Sp(1)$ we can determine the corresponding operators. As applications, we obtain integrality results for such manifolds by applying the Atiyah-Singer Index Theorem to these operators. Finally, we explain how immersions yield interesting structure groups to which one can apply this method. This yields lower bounds on the codimension of immersions in terms of topological data of the manifolds involved.
Zeitschrift:
Math. Nachr.
1999 | Nonlinear estimation problems. | Henning Läuter
Zeitschrift: Tatra Mt. Math. Publ.
Seiten: 003-012
Band: 17
Nonlinear estimation problems.
Autoren: Henning Läuter
(1999)
Zeitschrift:
Tatra Mt. Math. Publ.
1999 | Zero Sets of Solutions to Semilinear Elliptic Systems of First Order | Christian Bär
Zeitschrift: Invent. Math.
Verlag: Springer
Seiten: 183-202
Band: 138, no. 1
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,
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Zero Sets of Solutions to Semilinear Elliptic Systems of First Order
Autoren: Christian Bär
(1999)
Consider a nontrivial solution to a semilinear elliptic system of first order with smooth coefficients defined over an n-dimensional manifold. Assume the operator has the strong unique continuation property. We show that the zero set of the solution is contained in a countable union of smooth (n-2)-dimensional submanifolds. Hence it is countably (n-2)-rectifiable and its Hausdorff dimension is at most n-2. Moreover, it has locally finite (n-2)-dimensional Hausdorff measure. We show by example that every real number between 0 and n-2 actually occurs as the Hausdorff dimension (for a suitable choice of operator). We also derive results for scalar elliptic equations of second order.
Zeitschrift:
Invent. Math.
1999 | The Dirac Operator and the Scalar Curvature of Continuously Deformed Algebraic Varieties | Christian Bär, David Bleecker
Zeitschrift: Contemp. Math.
Verlag: American Mathematical Society
Seiten: 3-24
Band: 242
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The Dirac Operator and the Scalar Curvature of Continuously Deformed Algebraic Varieties
Autoren: Christian Bär, David Bleecker
(1999)
The Bochner-Lichnerowicz formula and the Atiyah-Singer Index Formula for the Dirac operator have been used to find an obstruction (the $\widehatA$-genus) to producing metrics of positive scalar curvature on spin manifolds. Here the technique is applied to twisted Dirac operators in order to obtain upper bounds on the minimum of the scalar curvature for Riemannian manifolds which admit certain contractive spin mappings into a fixed Riemannian manifold. The principal application is to obtain such upper bounds for algebraic varieties equipped with arbitrary metrics, which admit contractive maps into P^n(C) homotopic to inclusions.
Zeitschrift:
Contemp. Math.
Verlag:
American Mathematical Society
1999 | The progressive mixture estimator for regression trees | Blanchard, G.
Zeitschrift: Annales de l'Institut Henri Poincare (B) Probability and Statistics
Verlag: Elsevier
Seiten: 793-820
Band: 35
The progressive mixture estimator for regression trees
Autoren: Blanchard, G.
(1999)
Zeitschrift:
Annales de l'Institut Henri Poincare (B) Probability and Statistics
1999 | L'estimateur de << mélange progressif >> appliqué aux arbres de régression | Blanchard, G.
Zeitschrift: Comptes Rendus de l'Académie des Sciences-Series I-Mathematics
Verlag: Elsevier Masson
Seiten: 925-928
Band: 328
L'estimateur de << mélange progressif >> appliqué aux arbres de régression
Autoren: Blanchard, G.
(1999)
Zeitschrift:
Comptes Rendus de l'Académie des Sciences-Series I-Mathematics
1998 | Derived theories and derived equational theories | Denecke, K., Koppitz, J. and Marszałek, R.
Zeitschrift: International Journal of Algebra and Computation
Band: 6 no. 2
Derived theories and derived equational theories
Autoren: Denecke, K., Koppitz, J. and Marszałek, R.
(1998)
Zeitschrift:
International Journal of Algebra and Computation
1998 | Finite monoids of hypersubstitutions of type τ = (2) | Denecke, K. and Koppitz, J.
Zeitschrift: Semigroup Forum
Band: 56
Finite monoids of hypersubstitutions of type τ = (2)
Autoren: Denecke, K. and Koppitz, J.
(1998)
Zeitschrift:
Semigroup Forum
1998 | M-solid monoids of hypersubstitutions of type τ = (2) | Denecke, K. and Koppitz, J.
Zeitschrift: Semigroup Forum
Band: 57
M-solid monoids of hypersubstitutions of type τ = (2)
Autoren: Denecke, K. and Koppitz, J.
(1998)
Zeitschrift:
Semigroup Forum
1998 | Nonparametric versus parametric goodness of fit. | Hannelore Liero, Henning Läuter, Valentin Konakov
Zeitschrift: Statistics
Seiten: 115-149
Band: 31
Nonparametric versus parametric goodness of fit.
Autoren: Hannelore Liero, Henning Läuter, Valentin Konakov
(1998)
1998 | Nonparametric versus parametric goodness of fit. | Hannelore Liero, Henning Läuter, V. Konakov
Zeitschrift: Statistics
Verlag: Gordon
Seiten: 115-149
Band: 31
Nonparametric versus parametric goodness of fit.
Autoren: Hannelore Liero, Henning Läuter, V. Konakov
(1998)
1998 | The Dirac Operator on Nilmanifolds and Collapsing Circle Bundles | Bernd Ammann, Christian Bär
Zeitschrift: Ann. Global Anal. Geom.
Verlag: Springer
Seiten: 221-253
Band: 16, no. 3
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The Dirac Operator on Nilmanifolds and Collapsing Circle Bundles
Autoren: Bernd Ammann, Christian Bär
(1998)
We compute the spectrum of the Dirac operator on 3-dimensional Heisenberg manifolds. The behavior under collapse to the 2-torus is studied. Depending on the spin structure either all eigenvalues tend to $\pm\infty$ or there are eigenvalues converging to those of the torus. This is shown to be true in general for collapsing circle bundles with totally geodesic fibers. Using the Hopf fibration we use this fact to compute the Dirac eigenvalues on complex projective space including the multiplicities. Finally, we show that there are 1-parameter families of Riemannian nilmanifolds such that the Laplacian on functions and the Dirac operator for certain spin structures have constant spectrum while the Laplacian on 1-forms and the Dirac operator for the other spin structures have nonconstant spectrum. The marked length spectrum is also constant for these families.
Zeitschrift:
Ann. Global Anal. Geom.
1998 | On Harmonic Spinors | Christian Bär
Zeitschrift: Acta Phys. Polon. B
Verlag: Jagiellonian University, Poland
Seiten: 859-869
Band: 29, no. 4
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,
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On Harmonic Spinors
Autoren: Christian Bär
(1998)
This is a survey. We study the question to what extend classical Hodge-deRham theory for harmonic differential forms carries over to harmonic spinors. Despite some special phenomena in very low dimensions and despite the Atiyah-Singer index theorem which provides a link between harmonic spinors and the topology of the underlying manifold it turns out that in many dimensions harmonic spinors are not topologically obstructed. In this respect harmonic spinors behave very differently from harmonic differential forms. We also discuss parallel spinors and Killing spinors
Zeitschrift:
Acta Phys. Polon. B
Verlag:
Jagiellonian University, Poland
1998 | Extrinsic Bounds for Eigenvalues of the Dirac Operator | Christian Bär
Zeitschrift: Ann. Global Anal. Geom.
Verlag: Springer
Seiten: 573-596
Band: 16, no. 6
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,
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Extrinsic Bounds for Eigenvalues of the Dirac Operator
Autoren: Christian Bär
(1998)
We derive upper eigenvalue bounds for the Dirac operator of a closed hypersurface in a manifold with Killing spinors such as Euclidean space, spheres or hyperbolic space. The bounds involve the Willmore functional. Relations with the Willmore inequality are briefly discussed. In higher codimension we obtain bounds on the eigenvalues of the Dirac operator of the submanifold twisted with the spinor bundle of the normal bundle.
Zeitschrift:
Ann. Global Anal. Geom.
1998 | Heat Operator and Zeta-Function Estimates for Surfaces | Christian Bär
Zeitschrift: Arch. Math.
Verlag: Springer
Seiten: 63-70
Band: 71, no. 1
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,
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Heat Operator and Zeta-Function Estimates for Surfaces
Autoren: Christian Bär
(1998)
Using Kato's comparison principle for heat semi-groups we derive estimates for the trace of the heat operator on surfaces with variable curvature. This estimate is from above for positively curved surfaces of genus 0 and from below for genus $g \ge 2$. It is shown that the estimates are asymptotically sharp for small time and in the case of positive curvature also for large time. As a consequence we can estimate the corresponding $\zeta$-function by the Riemann $\zeta$-function.
1998 | Connections on Soldered Principal Bundles | Christian Bär, David Bleecker
Zeitschrift: Acta Phys. Polon. B
Verlag: Jagiellonian University, Poland
Seiten: 891-903
Band: 29, no. 4
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,
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Connections on Soldered Principal Bundles
Autoren: Christian Bär, David Bleecker
(1998)
In Kaluza-Klein theory one usually computes the scalar curvature of the principal bundle manifold using the Levi-Civita connection. Here we consider a natural family of invariant connections on a soldered principal bundle which is then parallelizable and hence spinable. This 3-parameter family includes the Levi-Civita connection and the flat connection. By varying the connection instead of merely scaling the metric on the fibers, there is greater independence among the coupling constants in the scalar curvature. In particular, a large cosmological constant can be avoided in spite of tiny fibers.
Zeitschrift:
Acta Phys. Polon. B
Verlag:
Jagiellonian University, Poland
1997 | Maps between M-solid Varieties of semigroups | Denecke, K., Koppitz, J. and Wismath, S.L.,
Zeitschrift: Discussiones Mathematicae Algebra and Stochastic Methods
Band: 17
Maps between M-solid Varieties of semigroups
Autoren: Denecke, K., Koppitz, J. and Wismath, S.L.,
(1997)
Zeitschrift:
Discussiones Mathematicae Algebra and Stochastic Methods
1997 | M-solid subvarieties of some varieties of commutative semigroups | Koppitz, J.
Zeitschrift: Serdica Mathematical Journal
Band: 23
M-solid subvarieties of some varieties of commutative semigroups
Autoren: Koppitz, J.
(1997)
Zeitschrift:
Serdica Mathematical Journal
1997 | On Nodal Sets for Dirac and Laplace Operators | Christian Bär
Zeitschrift: Comm. Math. Phys.
Verlag: Springer
Seiten: 709-721
Band: 188, no. 3
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,
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On Nodal Sets for Dirac and Laplace Operators
Autoren: Christian Bär
(1997)
We prove that the nodal set (zero set) of a solution of a generalized Dirac equation on a Riemannian manifold has codimension 2 at least. If the underlying manifold is a surface, then the nodal set is discrete. We obtain a quick proof of the fact that the nodal set of an eigenfunction for the Laplace-Beltrami operator on a Riemannian manifold consists of a smooth hypersurface and a singular set of lower dimension. We also see that the nodal set of a Δ-harmonic differential form on a closed manifold has codimension 2 at least; a fact which is not true if the manifold is not closed. Examples show that all bounds are optimal.
Zeitschrift:
Comm. Math. Phys.
1997 | Harmonic Spinors for Twisted Dirac Operators | Christian Bär
Zeitschrift: Math. Ann.
Verlag: Springer
Seiten: 225-246
Band: 309, no. 2
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Harmonic Spinors for Twisted Dirac Operators
Autoren: Christian Bär
(1997)
We show that for a suitable class of "Dirac-like" operators there holds a Gluing Theorem for connected sums. More precisely, if M1 and M2 are closed Riemannian manifolds of dimension n ≥ 3 together with such operators, then the connected sum M1 # M2 can be given a Riemannian metric such that the spectrum of its associated operator is close to the disjoint union of the spectra of the two original operators. As an application, we show that in dimension n = 3 mod 4 harmonic spinors for the Dirac operator of a spin, Spinc, or Spinh manifold are not topologically obstructed.
1996 | Hyperidentities and Subvarieties of Varieties of commutative nilpotent Semigroups | Koppitz, J.
Zeitschrift: Comptes rendus de l´Acadèmie bulgare des Sciences
Band: 49 no. 7-8
Hyperidentities and Subvarieties of Varieties of commutative nilpotent Semigroups
Autoren: Koppitz, J.
(1996)
Zeitschrift:
Comptes rendus de l´Acadèmie bulgare des Sciences
1996 | Harmonic Spinors and Topology | Christian Bär
Verlag: Springer
Buchtitel: New Developments in Differential Geometry
Seiten: 53-66
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,
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Harmonic Spinors and Topology
Autoren: Christian Bär
(1996)
We survey relations between the dimension of the solution space of the Dirac equation and the topology of the underlying manifold. It is shown that in certain dimensions existence of metrics with harmonic spinors is not topologically obstructed. In this respect the Dirac operator behaves very differently from the Laplace-Beltrami operator.
Buchtitel:
New Developments in Differential Geometry
1996 | Metrics with Harmonic Spinors | Christian Bär
Zeitschrift: Geom. Funct. Anal.
Verlag: Springer
Seiten: 899-942
Band: 6, no. 6
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,
Link zum Preprint
Metrics with Harmonic Spinors
Autoren: Christian Bär
(1996)
We show that every closed spin manifold of dimension n ≡ 3 mod 4 with a fixed spin structure can be given a Riemannian metric with harmonic spinors, i.e. the corresponding Dirac operator has a non-trivial kernel (Theorem A). To prove this we first compute the Dirac spectrum of the Berger spheres Sn, n odd (Theorem 3.1). The second main ingredient is Theorem B which states that the Dirac spectrum of a connected sum M1 # M2 with certain metrics is close to the union of the spectra of M1 and of M2.
Zeitschrift:
Geom. Funct. Anal.
1996 | The Dirac Operator on Space Forms of Positive Curvature | Christian Bär
Zeitschrift: J. Math. Soc. Japan
Verlag: Mathematical Society of Japan
Seiten: 69-83
Band: 48, no. 1
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,
Link zum Preprint
The Dirac Operator on Space Forms of Positive Curvature
Autoren: Christian Bär
(1996)
The spectrum of the Dirac operator on spherical space forms is calculated. Manifolds with many Killing spinors are characterized. In the last section non-isometric space forms with the same Dirac spectrum are constructed.
Zeitschrift:
J. Math. Soc. Japan
Verlag:
Mathematical Society of Japan
1995 | Pre-Solid Varieties of Semigroups | Denecke, K. and Koppitz, J.
Zeitschrift: Archivum Mathematicum (Brno)
Band: 31
Pre-Solid Varieties of Semigroups
Autoren: Denecke, K. and Koppitz, J.
(1995)
Zeitschrift:
Archivum Mathematicum (Brno)
1995 | Pre-Solid Varieties of Commutative Semigroups | Denecke, K. and Koppitz, J.
Zeitschrift: Tatra Mountains Math. Publ.
Band: 5
Pre-Solid Varieties of Commutative Semigroups
Autoren: Denecke, K. and Koppitz, J.
(1995)
Zeitschrift:
Tatra Mountains Math. Publ.
1995 | M-Solid Varieties of Semigroups | Denecke, K. and Koppitz, J.
Zeitschrift: Discussiones Mathematicae Algebra and Stochastic Methods
Band: 15
M-Solid Varieties of Semigroups
Autoren: Denecke, K. and Koppitz, J.
(1995)
Zeitschrift:
Discussiones Mathematicae Algebra and Stochastic Methods
1994 | Hyperassociative Varieties of Semigroups | Denecke, K. and Koppitz, J.
Zeitschrift: Semigroup Forum
Band: 49
Hyperassociative Varieties of Semigroups
Autoren: Denecke, K. and Koppitz, J.
(1994)
Zeitschrift:
Semigroup Forum
1994 | On the representation of the minimax linear estimator in the convex linear model. | Henning Läuter, Hilmar Drygas
Zeitschrift: Proc. LINSTAT '93
Verlag: Kluwer
Seiten: 13-26
On the representation of the minimax linear estimator in the convex linear model.
Autoren: Henning Läuter, Hilmar Drygas
(1994)
Zeitschrift:
Proc. LINSTAT '93
1994 | A Remark on Positively Curved 4-Manifolds | Christian Bär
Zeitschrift: Differential Geom. Appl.
Verlag: Elsevier
Seiten: 71-75
Band: 4, no. 1
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A Remark on Positively Curved 4-Manifolds
Autoren: Christian Bär
(1994)
Let M be an oriented connected compact Riemannian 4-manifold. We show that if the sectional curvature satisfies K ≥ 1 and the covariant differential of the curvature tensor satisfies |∇R|∞ ≤ 2/pi, then the intersection form of M is definite.
Zeitschrift:
Differential Geom. Appl.
1993 | A note on the asymptotic behaviour of the distance of the knth nearest neighbour 24: | Hannelore Liero
Zeitschrift: Satistics
Seiten: 235-243
Band: 24
A note on the asymptotic behaviour of the distance of the knth nearest neighbour 24:
Autoren: Hannelore Liero
(1993)
1993 | Elliptic Operators and Representation Theory of Compact Groups | Christian Bär
Buchtitel: Geometry and Global Analysis, Sendai 1993
Seiten: 151-160
Link zum Preprint
Elliptic Operators and Representation Theory of Compact Groups
Autoren: Christian Bär
(1993)
Let M denote an n-dimensional Riemannian manifold with structure group G. We assume that G acts transitively on the unit sphere in the tangent space and denote by $H \subset G$ the isotropy subgroup for some point in the sphere. We can show Let V_1 and V_2 be two G-Moduls whose restrictions to H are equivalent, then there exists an elliptic pseudo-differential operator from the sections of the bundle associated to V_1 into those for V_2. Consequently, to describe the space of elliptic operators naturally associated to the structure group G we need to determine the kernel R(G,H) of the restriction mapping R(G) -> R(H) of character rings. R(G,H) is a finitely generated ideal in R(G). Here are some examples: i) G = SO(2m), H = SO(2m-1), n=2m, R(G,H) = (1-\Lambda^1\pm\cdots- \Lambda^n-1+1, \Lambda^m_+-\Lambda^m_-). ii) G = Spin(2m), H = Spin(2m-1), R(G,H) = (\Sigma^+-\Sigma^-). iii) G = U(m), H = U(m-1), R(G,H) = (1-\Lambda^1,0\pm\cdots +(-1)^m \Lambda^m,0). We may call the operators corresponding to the generators fundamental. For the above examples this means that for oriented even-dimensional Riemannian manifolds the Euler operator and the signature operator are fundamental, for even-dimensional spin manifolds the Dirac operator is fundamental, and for almost complex manifolds the Cauchy Riemann operator is fundamental. It is interesting to apply this approach to some less well understood structure groups such as G = Sp(q)Sp(1), n=4q. We get elliptic operators for almost quaternionic manifolds and give new integralitiy and vanishing theorems in the case q odd. This method can also be used to study embeddability questions of manifolds into higher dimensional ones.
Buchtitel:
Geometry and Global Analysis, Sendai 1993
1993 | Real Killing Spinors and Holonomy | Christian Bär
Zeitschrift: Comm. Math. Phys.
Seiten: 509-521
Band: 154, no. 3
Link zur Publikation
Real Killing Spinors and Holonomy
Autoren: Christian Bär
(1993)
Zeitschrift:
Comm. Math. Phys.
1993 | Elliptische Operatoren und Darstellungstheorie kompakter Gruppen | Christian Bär
Zeitschrift: Bonner Math. Schr.
Reihe: Habilitationsschrift, Universität Bonn
Seiten: iv+50 pages
Band: 248
Link zur Publikation
Elliptische Operatoren und Darstellungstheorie kompakter Gruppen
Autoren: Christian Bär
(1993)
This is the author's Habilitationsschrift (in German language).
Zeitschrift:
Bonner Math. Schr.
Reihe:
Habilitationsschrift, Universität Bonn
1992 | Asymptotic normality of a weighted integrated square error of kernel regression estimates with data-dependent bandwidth | Hannelore Liero
Zeitschrift: J. Statistical Planning and Inference
Seiten: 307-325
Band: 30
Asymptotic normality of a weighted integrated square error of kernel regression estimates with data-dependent bandwidth
Autoren: Hannelore Liero
(1992)
Zeitschrift:
J. Statistical Planning and Inference
1992 | Asymptotic behavior of conditional U-statistics. | Hannelore Liero
Buchtitel: Order Statistics and Nonparametrics: Theory and Applications} Ed. Sen, P. K. and Salama,
Asymptotic behavior of conditional U-statistics.
Autoren: Hannelore Liero
(1992)
Buchtitel:
Order Statistics and Nonparametrics: Theory and Applications} Ed. Sen, P. K. and Salama,
1992 | Bootstrap and estimation of nonlinear parameters. | Henning Läuter
Verlag: Physica
Buchtitel: Model-oriented Data Analysis
Seiten: 159-168
Bootstrap and estimation of nonlinear parameters.
Autoren: Henning Läuter
(1992)
Buchtitel:
Model-oriented Data Analysis
1992 | The Dirac operator on homogeneous spaces and its spectrum on 3-dimensional lens spaces (Erratum) | Christian Bär
Link zum Preprint
The Dirac operator on homogeneous spaces and its spectrum on 3-dimensional lens spaces (Erratum)
Autoren: Christian Bär
(1992)
1992 | The Dirac operator on homogeneous spaces and its spectrum on 3-dimensional lens spaces | Christian Bär
Zeitschrift: Arch. Math.
Verlag: Springer
Seiten: 65-79
Band: 59, no. 1
Link zur Publikation
The Dirac operator on homogeneous spaces and its spectrum on 3-dimensional lens spaces
Autoren: Christian Bär
(1992)
1992 | Upper Eigenvalue Estimates for Dirac Operators | Christian Bär
Zeitschrift: Ann. Global Anal. Geom.
Verlag: Springer
Seiten: 171-177
Band: 10, no. 2
Link zur Publikation
Upper Eigenvalue Estimates for Dirac Operators
Autoren: Christian Bär
(1992)
Zeitschrift:
Ann. Global Anal. Geom.
1992 | The Dirac Fundamental Tone of the Hyperbolic Space | Christian Bär
Zeitschrift: Geom. Dedicata
Verlag: Springer
Seiten: 103-107
Band: 41, no. 1
Link zur Publikation
The Dirac Fundamental Tone of the Hyperbolic Space
Autoren: Christian Bär
(1992)
Zeitschrift:
Geom. Dedicata
1992 | Lower Eigenvalue Estimates for Dirac Operators | Christian Bär
Zeitschrift: Math. Ann.
Verlag: Springer
Seiten: 39-46
Band: 293, no. 1
Link zur Publikation
,
Link zum Preprint
Lower Eigenvalue Estimates for Dirac Operators
Autoren: Christian Bär
(1992)
1992 | Harmonic Spinors on Riemann Surfaces | Christian Bär, Paul Schmutz
Zeitschrift: Ann. Global Anal. Geom.
Verlag: Springer
Seiten: 263-273
Band: 10, no. 3
Link zur Publikation
Harmonic Spinors on Riemann Surfaces
Autoren: Christian Bär, Paul Schmutz
(1992)
Zeitschrift:
Ann. Global Anal. Geom.
1991 | Bootstrap methods and nonlinear estimation problems. | Henning Läuter
Zeitschrift: IIASA Workshop Model-oriented Data Analysis
Verlag: Springer
Buchtitel: Lecture Notes
Bootstrap methods and nonlinear estimation problems.
Autoren: Henning Läuter
(1991)
Zeitschrift:
IIASA Workshop Model-oriented Data Analysis
1991 | Das Spektrum von Dirac-Operatoren | Christian Bär
Zeitschrift: Bonner Math. Schr.
Reihe: Dissertation, Universität Bonn
Seiten: xii+124 pages
Band: 217
Link zum Preprint
Das Spektrum von Dirac-Operatoren
Autoren: Christian Bär
(1991)
This is the author's dissertation (in German language).
Zeitschrift:
Bonner Math. Schr.
Reihe:
Dissertation, Universität Bonn
1991 | Die Bewegungsgruppen endlicher transitiver Spiegelungsräume | Horst Wendland
Zeitschrift: Wiss. Z. Brandenburg. Landeshochsch.
Seiten: 169-174
Band: 35, no. 2
Die Bewegungsgruppen endlicher transitiver Spiegelungsräume
Autoren: Horst Wendland
(1991)
Ein metrischer Spiegelungsraum, der nur triviale Unterräume besitzt heißt einfach. Jeder einfache Spiegelungsraum ist ein endlicher Raum. Die Bewegungsgruppen transitiver einfacher Spiegelungsräume sind Diedergruppen.
Zeitschrift:
Wiss. Z. Brandenburg. Landeshochsch.
1989 | Asymptotic normality of kernel regression estimates with data-dependent bandwidth | Hannelore Liero
Buchtitel: International Workshop on Theory and Practice in Data Analysis 1988, AdW der DDR
Asymptotic normality of kernel regression estimates with data-dependent bandwidth
Autoren: Hannelore Liero
(1989)
Buchtitel:
International Workshop on Theory and Practice in Data Analysis 1988, AdW der DDR
1989 | Strong uniform consistency of nonparametric regression function estimates | Hannelore Liero
Zeitschrift: Probability Theory and Related Fields
Seiten: 587-614
Band: 82
Strong uniform consistency of nonparametric regression function estimates
Autoren: Hannelore Liero
(1989)
Zeitschrift:
Probability Theory and Related Fields
1989 | Note on the strong consistency of the least squares estimator in nonlinear regression | Henning Läuter
Zeitschrift: Statistics
Verlag: Akademie
Seiten: 199-210
Band: 20
Note on the strong consistency of the least squares estimator in nonlinear regression
Autoren: Henning Läuter
(1989)
1989 | Mathematisch-statistische Datenanalyse. | Henning Läuter, Richard Pincus
Zeitschrift: Monographie
Verlag: Akad./Oldenb.
Mathematisch-statistische Datenanalyse.
Autoren: Henning Läuter, Richard Pincus
(1989)
1988 | Conditioned estimators of nonlinear parameters. | Henning Läuter
Verlag: Springer
Buchtitel: Model-Oriented Data Analysis
Seiten: 106-113
Band: 297
Conditioned estimators of nonlinear parameters.
Autoren: Henning Läuter
(1988)
Buchtitel:
Model-Oriented Data Analysis
1988 | Metrische Spiegelungsräume und symmetrische G-Räume | Horst Wendland
Zeitschrift: Wiss. Z Pädagog. Hochsch. Potsdam
Seiten: 183-185
Band: 32, no. 1
Metrische Spiegelungsräume und symmetrische G-Räume
Autoren: Horst Wendland
(1988)
Jeder symmetrische G-Raum besitzt die Struktur eines Spiegelungsraumes im Sinne von O. Loos. Umgekehrt wird eine Kennzeichnung der symmetrischen G-Räume unter den metrischen Spiegelungsräumen angegegeben.
Zeitschrift:
Wiss. Z Pädagog. Hochsch. Potsdam
1987 | Approximation of surfaces in (p+1)-dimensional spaces. | Henning Läuter
Verlag: Physica
Buchtitel: Compstat 82
Seiten: 300-305
Approximation of surfaces in (p+1)-dimensional spaces.
Autoren: Henning Läuter
(1987)
1985 | Nichtparametrische Schätzungen der Regressionsfunktion | Hannelore Liero
Nichtparametrische Schätzungen der Regressionsfunktion
Autoren: Hannelore Liero
(1985)
1985 | Optimal combinations of classification procedures. | Henning Läuter
Zeitschrift: Statistics
Verlag: Akademie
Seiten: 389-406
Band: 16
Optimal combinations of classification procedures.
Autoren: Henning Läuter
(1985)
1985 | An efficient estimator for the error rate in discriminant anlysis. | Henning Läuter
Zeitschrift: Operationsforsch. u. Statist., Ser. Statistics
Verlag: Akademie
Seiten: 107-119
Band: 16
An efficient estimator for the error rate in discriminant anlysis.
Autoren: Henning Läuter
(1985)
Zeitschrift:
Operationsforsch. u. Statist., Ser. Statistics
1984 | Experimental design methods. | Elisabeth Läuter, Henning Läuter
Zeitschrift: Monographie
Verlag: Wiley
Seiten: 505-568
Experimental design methods.
Autoren: Elisabeth Läuter, Henning Läuter
(1984)
1984 | Estimating linear parameters using additional information. | Henning Läuter
Zeitschrift: Monographie
Verlag: Wiley
Seiten: 166-203
Estimating linear parameters using additional information.
Autoren: Henning Läuter
(1984)
1982 | On the maximal deviation of the kernel regression function estimate. | Hannelore Liero
Zeitschrift: Mathematische Operationsforschung undStatistik, Serie Statistics
Seiten: 171-182
Band: 13
On the maximal deviation of the kernel regression function estimate.
Autoren: Hannelore Liero
(1982)
Zeitschrift:
Mathematische Operationsforschung undStatistik, Serie Statistics
1982 | A strong law for the kernel estimate of a regression function | Hannelore Liero
Verlag: North Holland, New York
Buchtitel: Limit Theorems in Probability and Statistics, Colloquia Matematica Societatis Janos Bolyai 36
Seiten: 25-31
A strong law for the kernel estimate of a regression function
Autoren: Hannelore Liero
(1982)
Verlag:
North Holland, New York
Buchtitel:
Limit Theorems in Probability and Statistics, Colloquia Matematica Societatis Janos Bolyai 36
1982 | Properties of discriminant analysis procedures with an application in estimation problems | Henning Läuter
Verlag: Acad. CSSR
Buchtitel: Conf. on discriminant analysis
Seiten: 89-100
Properties of discriminant analysis procedures with an application in estimation problems
Autoren: Henning Läuter
(1982)
Buchtitel:
Conf. on discriminant analysis
1982 | Approximation and smoothing of surfaces in (p+1)-dimensional spaces | Henning Läuter
Verlag: Reidel
Buchtitel: Pannon. Symp. Bad Tatzmannsdorf
Seiten: 231-238
Approximation and smoothing of surfaces in (p+1)-dimensional spaces
Autoren: Henning Läuter
(1982)
Buchtitel:
Pannon. Symp. Bad Tatzmannsdorf
1982 | Nonparametric analysis of cyclic curves with an application in the psychatrie | Elisabeth Läuter, Henning Läuter
Zeitschrift: Biometrical Journal
Verlag: Akademie
Seiten: 133-144
Band: 24
Nonparametric analysis of cyclic curves with an application in the psychatrie
Autoren: Elisabeth Läuter, Henning Läuter
(1982)
Zeitschrift:
Biometrical Journal
1982 | Some theoretical results on approximation methods. | Fritz Auert, Henning Läuter
Zeitschrift: Mathem. Operationsforsch. u. Statist.
Verlag: Akademie
Seiten: 265-293
Band: 13
Some theoretical results on approximation methods.
Autoren: Fritz Auert, Henning Läuter
(1982)
Zeitschrift:
Mathem. Operationsforsch. u. Statist.
1982 | Estimation of parameters in mixtures of distributions arising in cultivation problems | Henning Läuter
Zeitschrift: Biometrical Journal
Verlag: Akademie
Seiten: 63-70
Band: 24
Estimation of parameters in mixtures of distributions arising in cultivation problems
Autoren: Henning Läuter
(1982)
Zeitschrift:
Biometrical Journal
1981 | Zur Sonderstellung des ebenen Falles beim spiegelungsgeometrischen Aufbau pseudoeuklidischer Räume | Horst Wendland, Martin Schütze
Zeitschrift: Wiss. Z Pädagog. Hochsch. Potsdam
Seiten: 795-798
Band: 25
Zur Sonderstellung des ebenen Falles beim spiegelungsgeometrischen Aufbau pseudoeuklidischer Räume
Autoren: Horst Wendland, Martin Schütze
(1981)
Die Einordnung des ebenen Falles bei gruppentheoretischen Kennzeichnungen pseudoeuklidischer Räume endlicher Dimension unter besonderer Berücksichtigung der Stellung der Dreispiegelungssätze in den verwendeten Axiomensystemen.
Zeitschrift:
Wiss. Z Pädagog. Hochsch. Potsdam
1980 | On kernel estimation of regression functions | Hannelore Wandl (Liero)
Reihe: Wissenschaftliche Sitzungen zur Stochastik
Verlag: AdW DDR
Band: Mrz 80
On kernel estimation of regression functions
Autoren: Hannelore Wandl (Liero)
(1980)
Reihe:
Wissenschaftliche Sitzungen zur Stochastik
1980 | Projection estimators for unknown covariance matrices in linear models | Olaf Bunke Hannelore Wandl (Liero)
Zeitschrift: Mathematische Operationsforschung und Statistik, Serie Statistics
Band: 11
Projection estimators for unknown covariance matrices in linear models
Autoren: Olaf Bunke Hannelore Wandl (Liero)
(1980)
Zeitschrift:
Mathematische Operationsforschung und Statistik, Serie Statistics
1980 | Pseudoeuklidische Räume endlicher Dimension im Aufbau der Geometrie aus dem Spiegelungsbegriff | Horst Wendland
Zeitschrift: Wiss. Z Pädagog. Hochsch. Potsdam
Seiten: 115-127
Band: 24
Pseudoeuklidische Räume endlicher Dimension im Aufbau der Geometrie aus dem Spiegelungsbegriff
Autoren: Horst Wendland
(1980)
Die beschreibt den gruppentheoretischen Aufbau n-dimensionaler pseudoeuklidischer Räume (2 < n) auf der Grundlage des Spiegelungsbegriffs. Als pseudoeuklidische Geometrie bezeichnen wir hier die Geometrie der n-dimensionalen metrischen Räume über Körpern einer Charakteristik ungleich 2. Die Metrik in diesen Räumen wird durch eine symmetrische Bilinearform vom Index > 0 über dem zugehörigen Vektorraum bestimmt.
Zeitschrift:
Wiss. Z Pädagog. Hochsch. Potsdam
1979 | Diplomarbeit, Sektion Mathematik der Humboldt-Universität zu Berlin, 1977 | Hannelore Wandl (Liero)
Diplomarbeit, Sektion Mathematik der Humboldt-Universität zu Berlin, 1977
Autoren: Hannelore Wandl (Liero)
(1979)
1979 | Some tests in dynamic models with a finite number of parameters | Henning Läuter, Norbert Miethe
Zeitschrift: Mathem. Operationsforsch. u. Statist.
Verlag: Akademie
Seiten: 395-414
Band: 10
Some tests in dynamic models with a finite number of parameters
Autoren: Henning Läuter, Norbert Miethe
(1979)
Zeitschrift:
Mathem. Operationsforsch. u. Statist.
1978 | Schätzung von Kovarianzparametern und gemischte lineare Modelle | Hannelore Wandl (Liero)
Schätzung von Kovarianzparametern und gemischte lineare Modelle
Autoren: Hannelore Wandl (Liero)
(1978)
1978 | Properties and comparison of procedures of discriminant analysis | Elisabeth Läuter, Henning Läuter, Dieter Schmidtke
Zeitschrift: Biometrical Journal
Verlag: Akademie
Seiten: 407-424
Band: 20
Properties and comparison of procedures of discriminant analysis
Autoren: Elisabeth Läuter, Henning Läuter, Dieter Schmidtke
(1978)
Zeitschrift:
Biometrical Journal
1977 | Asymptotic properties of classification procedures. | Elisabeth Läuter, Henning Läuter
Buchtitel: Proc. of the 41. session New Delhi,
Seiten: 589-595
Asymptotic properties of classification procedures.
Autoren: Elisabeth Läuter, Henning Läuter
(1977)
Buchtitel:
Proc. of the 41. session New Delhi,
1977 | Methoden der Versuchsplanung. | Elisabeth Läuter, Henning Läuter
Zeitschrift: Monographie KMS Humak
Verlag: Akademie
Seiten: 423-478
Methoden der Versuchsplanung.
Autoren: Elisabeth Läuter, Henning Läuter
(1977)
Zeitschrift:
Monographie KMS Humak
1977 | Schätzung linearer Parameter bei Zusatzinformation. | Henning Läuter
Zeitschrift: Monographie KMS Humak
Verlag: Akademie
Seiten: 129-163
Schätzung linearer Parameter bei Zusatzinformation.
Autoren: Henning Läuter
(1977)
Zeitschrift:
Monographie KMS Humak
1976 | Schätzungen linearer Parameter in eingeschränkten linearen Modellen | Henning Läuter
Zeitschrift: Diss. B
Verlag: Akademie
Schätzungen linearer Parameter in eingeschränkten linearen Modellen
Autoren: Henning Läuter
(1976)
1975 | Linear minimax estimation for inadequate models for the I. Petersen approach | Henning Läuter
Zeitschrift: Mathem. Operationsforsch. u. Statist.
Verlag: Akademie
Seiten: 769-774
Band: 6
Linear minimax estimation for inadequate models for the I. Petersen approach
Autoren: Henning Läuter
(1975)
Zeitschrift:
Mathem. Operationsforsch. u. Statist.
1975 | A minimax linear estimator for linear parameters under restrictions in form of inequalities | Henning Läuter
Zeitschrift: Mathem. Operationsforsch. u. Statist.
Verlag: Akademie
Seiten: 689-695
Band: 6
A minimax linear estimator for linear parameters under restrictions in form of inequalities
Autoren: Henning Läuter
(1975)
Zeitschrift:
Mathem. Operationsforsch. u. Statist.
1974 | On the admissibility and nonadmissibility of the usual estimator for the mean. | Henning Läuter
Zeitschrift: Mathem. Operationsforsch. u. Statist.
Verlag: Akademie
Seiten: 663-669
Band: 5
On the admissibility and nonadmissibility of the usual estimator for the mean.
Autoren: Henning Läuter
(1974)
Zeitschrift:
Mathem. Operationsforsch. u. Statist.
1973 | Stability of approximations of stochastic processes. | Henning Läuter
Zeitschrift: Conf. of probability
Buchtitel: Conf. of probability, Vilnius
Seiten: 15-18
Stability of approximations of stochastic processes.
Autoren: Henning Läuter
(1973)
Zeitschrift:
Conf. of probability
Buchtitel:
Conf. of probability, Vilnius
1973 | Bemerkungen zur optimalen Synthese von Systemen (in russian) | Henning Läuter
Zeitschrift: Teorija verojatnostjei
Verlag: Akad. Moskau
Seiten: 621-627
Band: 18
Bemerkungen zur optimalen Synthese von Systemen (in russian)
Autoren: Henning Läuter
(1973)
Zeitschrift:
Teorija verojatnostjei
1971 | Optimale Schätzung bei stochastischen Prozessen. | Henning Läuter
Zeitschrift: Mathem. Operationsforsch. u. Statist.
Verlag: Akademie
Seiten: 237-246
Band: 2
Optimale Schätzung bei stochastischen Prozessen.
Autoren: Henning Läuter
(1971)
Zeitschrift:
Mathem. Operationsforsch. u. Statist.
1971 | Vorhersage bei stochastischen Prozessen mit linearem Regressionsanteil | Henning Läuter
Zeitschrift: Mathem. Operationsforsch. u. Statist.
Verlag: Akademie
Seiten: 69-166
Band: 2
Vorhersage bei stochastischen Prozessen mit linearem Regressionsanteil
Autoren: Henning Läuter
(1971)
Zeitschrift:
Mathem. Operationsforsch. u. Statist.
1970 | Über verallgemeinerte Inverse von linearen, beschränkten Operatoren | Henning Läuter
Zeitschrift: Monatsberichte AdW
Verlag: Akademie
Seiten: 432-435
Band: 12
Über verallgemeinerte Inverse von linearen, beschränkten Operatoren
Autoren: Henning Läuter
(1970)
Zeitschrift:
Monatsberichte AdW
1970 | Optimale Vorhersage und Schätzung in regulären und singulären Regressionsmodellen | Henning Läuter
Zeitschrift: Mathem. Operationsforsch. u. Statist.
Verlag: Akademie
Seiten: 229-243
Band: 1
Optimale Vorhersage und Schätzung in regulären und singulären Regressionsmodellen
Autoren: Henning Läuter
(1970)
Zeitschrift:
Mathem. Operationsforsch. u. Statist.
1970 | Vorhersage und Schätzung bei stochastischen Prozessen mit linearem Regressionsanteil | Henning Läuter
Zeitschrift: Diss. A
Verlag: Humboldt-Uni
Vorhersage und Schätzung bei stochastischen Prozessen mit linearem Regressionsanteil
Autoren: Henning Läuter
(1970)
0 | On the uniqueness class, stochastic completeness and volume growth for graphs | Xueping Huang, Matthias Keller and Marcel Schmidt
Zeitschrift: Transactions of the American Mathematical Society
Seiten: 8861-8884.
Band: 373
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On the uniqueness class, stochastic completeness and volume growth for graphs
Autoren: Xueping Huang, Matthias Keller and Marcel Schmidt
In this note we prove an optimal volume growth condition for stochastic completeness of graphs under very mild assumptions. This is realized by proving a uniqueness class criterion for the heat equation which is an analogue to a corresponding result of Grigor’yan on manifolds. This uniqueness class criterion is shown to hold for graphs that we call globally local, i.e., graphs where we control the jump size far outside. The transfer from general graphs to globally local graphs is then carried out via so-called refinements.
Zeitschrift:
Transactions of the American Mathematical Society
0 | A note on eigenvalue bounds for non-compact manifolds | Matthias Keller, Shiping Liu, Norbert Peyerimhoff
Zeitschrift: Mathematische Nachrichten
Seiten: 1134-1139
Band: 294
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A note on eigenvalue bounds for non-compact manifolds
Autoren: Matthias Keller, Shiping Liu, Norbert Peyerimhoff
In this article we prove upper bounds for the Laplace eigenvalues below the essential spectrum for strictly negatively curved Cartan–Hadamard manifolds. Our bound is given in terms of k2 and specific geometric data of the manifold. This applies also to the particular case of non-compact manifolds whose sectional curvature tends to −∞, where no essential spectrum is present due to a theorem of Donnelly/Li. The result stands in clear contrast to Laplacians on graphs where such a bound fails to be true in general.
Zeitschrift:
Mathematische Nachrichten
0 | test |
Zeitschrift: test
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