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Singular Behavior of the Solution to the Stochastic Heat Equation on a Polygonal DomainMay 05 2013Jun 07 2013We study the stochastic heat equation with trace class noise and zero Dirichlet boundary condition on a bounded polygonal domain O in R^2. It is shown that the solution u can be decomposed into a regular part u_R and a singular part u_S which incorporates ... More

Malliavin regularity and weak approximation of semilinear SPDE with Lévy noiseAug 26 2018We investigate the weak order of convergence for space-time discrete approximations of semilinear parabolic stochastic evolution equations driven by additive square-integrable L\'evy noise. To this end, the Malliavin regularity of the solution is analyzed ... More

Strong convergence of a half-explicit Euler scheme for constrained stochastic mechanical systemsSep 22 2017This paper is concerned with the numerical approximation of stochastic mechanical systems with nonlinear holonomic constraints. Such systems are described by second order stochastic differential-algebraic equations involving an implicitly given Lagrange ... More

Weak error analysis via functional Itô calculusMar 29 2016Jun 14 2016We consider autonomous stochastic ordinary differential equations (SDEs) and weak approximations of their solutions for a general class of sufficiently smooth path-dependent functionals f. Based on tools from functional It\^o calculus, such as the functional ... More

Poisson Malliavin calculus in Hilbert space with an application to SPDEMar 21 2017In this paper we introduce a Hilbert space-valued Malliavin calculus for Poisson random measures. It is solely based on elementary principles from the theory of point processes and basic moment estimates, and thus allows for a simple treatment of the ... More

Weak convergence rates for temporal numerical approximations of stochastic wave equations with multiplicative noiseJan 16 2019In numerical analysis for stochastic partial differential equations one distinguishes between weak and strong convergence rates. Often the weak convergence rate is twice the strong convergence rate. However, there is no standard way to prove this: to ... More

Weak convergence of finite element approximations of linear stochastic evolution equations with additive Lévy noiseNov 04 2014Feb 03 2015We present an abstract framework to study weak convergence of numerical approximations of linear stochastic partial differential equations driven by additive L\'evy noise. We first derive a representation formula for the error which we then apply to study ... More

On the Lq(Lp)-regularity and Besov smoothness of stochastic parabolic equations on bounded Lipschitz domainsJan 07 2013We investigate the regularity of linear stochastic parabolic equations with zero Dirichlet boundary condition on bounded Lipschitz domains $O \subset R^d$ with both theoretical and numerical purpose. We use N.V. Krylov's framework of stochastic parabolic ... More

An $L_p$-estimate for the stochastic heat equation on an angular domain in $\mathbb{R}^2$Mar 29 2016We prove a weighted $L_p$-estimate for the stochastic convolution associated to the stochastic heat equation with zero Dirichlet boundary condition on a planar angular domain $\mathcal{D}_{\kappa_0}\subset\mathbb{R}^2$ with angle $\kappa_0\in(0,2\pi)$. ... More

Exact results for power spectrum and susceptibility of a leaky integrate-and-fire neuron with two-state noiseOct 17 2016The response properties of excitable systems driven by colored noise are of great interest, but are usually mathematically only accessible via approximations. For this reason, dichotomous noise, a rare example of a colored noise leading often to analytically ... More

On the convergence analysis of the inexact linearly implicit Euler scheme for a class of SPDEsJan 23 2015This paper is concerned with the adaptive numerical treatment of stochastic partial differential equations. Our method of choice is Rothe's method. We use the implicit Euler scheme for the time discretization. Consequently, in each step, an elliptic equation ... More

Weak order for the discretization of the stochastic heat equation driven by impulsive noiseNov 24 2009Mar 10 2010Considering a linear parabolic stochastic partial differential equation driven by impulsive space time noise, dX_t+AX_t dt= Q^{1/2}dZ_t, X_0=x_0\in H, t\in [0,T], we approximate the distribution of X_T. (Z_t)_{t\in[0,T]} is an impulsive cylindrical process ... More

A Formalization of Kant's Second Formulation of the Categorical ImperativeJan 09 2018Mar 21 2018We present a formalization and computational implementation of the second formulation of Kant's categorical imperative. This ethical principle requires an agent to never treat someone merely as a means but always also as an end. Here we interpret this ... More

On the Alekseev-Gröbner formula in Banach spacesOct 23 2018The Alekseev-Gr\"obner formula is a well known tool in numerical analysis for describing the effect that a perturbation of an ordinary differential equation (ODE) has on its solution. In this article we provide an extension of the Alekseev-Gr\"obner formula ... More

Interplay between scintillation and ionization in liquid xenon Dark Matter searchesNov 17 2010Jul 05 2011We provide a new way of constraining the relative scintillation efficiency L_eff for liquid xenon. Using a simple estimate for the electronic and nuclear stopping powers together with an analysis of recombination processes we predict both the ionization ... More

Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutionsDec 12 2018In this article we establish exponential moment bounds, moment bounds in fractional order smoothness spaces, a uniform H\"older continuity in time, and strong convergence rates for a class of fully discrete exponential Euler-type numerical approximations ... More

Circulant matrices: norm, powers, and positivityMar 26 2018Apr 23 2018In their recent paper "The spectral norm of a Horadam circulant matrix", Merikoski, Haukkanen, Mattila and Tossavainen study under which conditions the spectral norm of a general real circulant matrix ${\bf C}$ equals the modulus of its row/column sum. ... More

The Future of low Energy Photon ExperimentsOct 09 2009"Light-shining-through-a-wall" experiments search for Weakly Interacting Sub-eV Particles (WISPs). The necessity and status of such enterprises as well as their future potential are sketched.

Stochastic fiber dynamics in a spatially semi-discrete settingJan 18 2016Feb 16 2016We investigate a spatially discrete surrogate model for the dynamics of a slender, elastic, inextensible fiber in turbulent flows. Deduced from a continuous space-time beam model for which no solution theory is available, it consists of a high-dimensional ... More

Detecting atmospheric neutrino oscillations in the ATLAS detector at CERNMay 17 2007Nov 16 2007We discuss the possibility to study oscillations of atmospheric neutrinos in the ATLAS experiment at CERN. Due to the large total detector mass, a significant number of events is expected, and during the shutdown phases of the LHC, reconstruction of these ... More

On the integer points in a lattice polytope: n-fold Minkowski sum and boundaryJun 10 2010In this article we compare the set of integer points in the homothetic copy $n\Pi$ of a lattice polytope $\Pi\subseteq\R^d$ with the set of all sums $x_1+\cdots+x_n$ with $x_1,...,x_n\in \Pi\cap\Z^d$ and $n\in\N$. We give conditions on the polytope $\Pi$ ... More

A central limit theorem for the sample autocorrelations of a Lévy driven continuous time moving average processJun 14 2012In this article we consider L\'evy driven continuous time moving average processes observed on a lattice, which are stationary time series. We show asymptotic normality of the sample mean, the sample autocovariances and the sample autocorrelations. A ... More

The Main Diagonal of a Permutation MatrixDec 02 2011Dec 15 2011By counting 1's in the "right half" of $2w$ consecutive rows, we locate the main diagonal of any doubly infinite permutation matrix with bandwidth $w$. Then the matrix can be correctly centered and factored into block-diagonal permutation matrices. Part ... More

Viscoelastic surface instabilitiesSep 28 2009We review three different types of viscoelastic surface instabilities: The Rayleigh -- Plateau, the Saffman -- Taylor and the Faraday instability. These instabilities are classical examples of hydrodynamic surface instabilities. The addition of a small ... More

Finite sections of the Fibonacci HamiltonianNov 27 2017We study finite but growing principal square submatrices $A_n$ of the one- or two-sided infinite Fibonacci Hamiltonian $A$. Our results show that such a sequence $(A_n)$, no matter how the points of truncation are chosen, is always stable -- implying ... More

Comment on: "Characterization of subthreshold voltage fluctuations in neuronal membranes" by M. Rudolph and A. DestexheJan 28 2005Jun 15 2005In two recent papers, Rudolph and Destexhe (Neural Comp. {\bf 15}, 2577-2618, 2003; Neural Comp. in press, 2005) studied a leaky integrator model (i.e. an RC-circuit) driven by correlated (``colored'') Gaussian conductance noise and Gaussian current noise. ... More

On exponential functionals of Levy processesJan 15 2013Jun 27 2013Exponential functionals of L\'evy processes appear as stationary distributions of generalized Ornstein-Uhlenbeck (GOU) processes. In this paper we obtain the infinitesimal generator of the GOU process and show that it is a Feller process. Further we use ... More

Spectral Aspects of the Evolution of Gamma-Ray BurstsOct 12 1999A review on the spectral and temporal properties of gamma-ray bursts is given. Special attention is paid to the spectral evolution of their continuum emission and its connection to the time evolution of the intensity. Efforts on systematizing these observations ... More

Smoothly Broken Power Law Spectra of Gamma-Ray BurstsNov 30 1998A five-parameter expression for a smoothly broken power law is presented. It is used to fit Gamma-Ray Burst (GRB) spectra observed by BATSE. The function is compared to previously used four-parameter functions, such as a sharply broken power law and the ... More

A primer on information theory, with applications to neuroscienceApr 08 2013Oct 07 2013Given the constant rise in quantity and quality of data obtained from neural systems on many scales ranging from molecular to systems', information-theoretic analyses became increasingly necessary during the past few decades in the neurosciences. Such ... More

Propensity score matching in SPSSJan 30 2012Propensity score matching is a tool for causal inference in non-randomized studies that allows for conditioning on large sets of covariates. The use of propensity scores in the social sciences is currently experiencing a tremendous increase; however it ... More

Glassiness in a model without energy barriersApr 20 1995Apr 22 1995We propose a microscopic model without energy barriers in order to explain some generic features observed in structural glasses. The statics can be exactly solved while the dynamics has been clarified using Monte Carlo calculations. Although the model ... More

Static chaos and scaling behaviour in the spin-glass phaseApr 09 1994We discuss the problem of static chaos in spin glasses. In the case of magnetic field perturbations, we propose a scaling theory for the spin-glass phase. Using the mean-field approach we argue that some pure states are suppressed by the magnetic field ... More

A natural renormalizable model of metastable SUSY breakingMay 15 2007May 30 2007We propose a model of metastable dynamical supersymmetry breaking in which all scales are generated dynamically. Our construction is a simple variant of the Intriligator-Seiberg-Shih model, with quark masses induced by renormalizable couplings to an auxiliary ... More

Bounds on the Automata Size for Presburger ArithmeticJun 02 2005Automata provide a decision procedure for Presburger arithmetic. However, until now only crude lower and upper bounds were known on the sizes of the automata produced by this approach. In this paper, we prove an upper bound on the the number of states ... More

Set theory and topology. An introduction to the foundations of analysis. Part I: Sets, relations, numbersMay 29 2013We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of number systems. ... More

Increasing Positive Monoids of Ordered Fields Are FF-monoidsOct 27 2016Given an ambient ordered field $K$, a positive monoid is a countably generated additive submonoid of the nonnegative cone of $K$. In this paper, we first generalize a few atomic features exhibited by Puiseux monoids of the field of rational numbers to ... More

The Causal Action in Minkowski Space and Surface Layer IntegralsNov 19 2017The Lagrangian of the causal action principle is computed in Minkowski space for Dirac wave functions interacting with classical electromagnetism and linearized gravity in the limiting case when the ultraviolet cutoff is removed. Various surface layer ... More

Hopf invariants and differential formsNov 13 2017Dec 11 2018Let $f,g:M \rightarrow N$ be two maps between simply-connected smooth manifolds $M$ and $N$, such that $M$ is compact and $N$ is of finite $\mathbb{R}$-type. The goal of this paper is to use integration of certain differential forms to obtain a complete ... More

Systems of sets of lengths of Puiseux monoidsNov 19 2017In this paper we study the system of sets of lengths of non-finitely generated atomic Puiseux monoids (a Puiseux monoid is an additive submonoid of $\mathbb{Q}_{\ge 0}$). We begin by presenting a BF-monoid $M$ with full system of sets of lengths, which ... More

Finite temperature coupled cluster theories for extended systemsJul 24 2018Nov 20 2018At zero temperature coupled cluster theory is widely used to predict total energies, ground state expectation values and even excited states for molecules and extended systems. Generalizations to finite temperature exist, however, they are in practice ... More

Isometry groups of Lorentzian manifolds of finite volume and The local geometry of compact homogeneous Lorentz spacesJun 27 2011Oct 06 2011Based on the work of Adams and Stuck as well as on the work of Zeghib, we classify the Lie groups which can act isometrically and locally effectively on Lorentzian manifolds of finite volume. In the case that the corresponding Lie algebra contains a direct ... More

Explicit Methods for Radical Function Fields over Finite FieldsNov 30 2009We develop explicit formulas and algorithms for arithmetic in radical function fields K/k(x) over finite constant fields. First, we classify which places of k(x) whose local integral bases have an easy monogenic form, and give explicit formulas for these ... More

Tautological relations in moduli spaces of weighted pointed curvesJun 27 2013Sep 29 2015Pandharipande-Pixton have used the geometry of the moduli space of stable quotients to produce relations between tautological Chow classes on the moduli space $M_g$ of smooth genus g curves. We study a natural extension of their methods to the boundary ... More

Embeddings of decomposition spacesMay 31 2016Feb 15 2018Many smoothness spaces in harmonic analysis are decomposition spaces. In this paper we ask: Given two decomposition spaces, is there an embedding between the two? A decomposition space $\mathcal{D}(\mathcal{Q}, L^p, Y)$ can be described using : a covering ... More

Irreducibility and factorizations in monoid ringsMay 17 2019For an integral domain $R$ and a commutative cancellative monoid $M$, the ring consisting of all polynomial expressions with coefficients in $R$ and exponents in $M$ is called the monoid ring of $M$ over $R$. An integral domain is called atomic if every ... More

Embeddings of decomposition spacesMay 31 2016Many smoothness spaces in harmonic analysis are decomposition spaces. Iin this paper we ask: Given two decomposition spaces, is there an embedding between the two? A decomposition space $\mathcal{D}(\mathcal{Q}, L^p, Y)$ can be described using : a covering ... More

Local U(2,2) Symmetry in Relativistic Quantum MechanicsMar 11 1997Feb 07 2007Local gauge freedom in relativistic quantum mechanics is derived from a measurement principle for space and time. For the Dirac equation, one obtains local U(2,2) gauge transformations acting on the spinor index of the wave functions. This local U(2,2) ... More

Hidden Charm Spectroscopy from TevatronMay 03 2011The observation of a narrow structure near the J/psi phi threshold in exclusive B+ to J/psi phi K+ decays produced in p-pbar collisions at sqrt(s) = 1.96 TeV is reported. A signal of 19 +- 6(stat) +- 3(syst) events, with statistical significance of 5.0 ... More

Electron-phonon interaction in Fe-based superconductors: Coupling of magnetic moments with phonons in LaFeAsO$_{1-x}$F$_{x}$Sep 24 2010The coupling of Fe magnetic moments in LaFeAsO$_{1-x}$F$_{x}$ with the As $A_{1g}$ phonon is calculated. We present first principles calculations of the atomic and electronic structure of LaFeAsO as a function of electron doping. We perform calculations ... More

Classical and Quantum Behavior in Mean-Field Glassy SystemsNov 05 1996In this talk I review some recent developments which shed light on the main connections between structural glasses and mean-field spin glass models with a discontinuous transition. I also discuss the role of quantum fluctuations on the dynamical instability ... More

Quantum critical effects in mean-field glassy systemsJul 06 1996We consider the effects of quantum fluctuations in mean-field quantum spin-glass models with pairwise interactions. We examine the nature of the quantum glass transition at zero temperature in a transverse field. In models (such as the random orthogonal ... More

Injective Hulls In a Locally Finite ToposFeb 03 2018We show that in a locally finite topos, every object has an essential extension that is injective, and that this extension is unique up to isomorphism. The construction was motivated by work on Bewl, a software project for doing topos-theoretic calculations. ... More

Uneven Splitting of Ham SandwichesJul 17 2008Let m_1,...,m_n be continuous probability measures on R^n and a_1,...,a_n in [0,1]. When does there exist an oriented hyperplane H such that the positive half-space H^+ has m_i(H^+)=a_i for all i in [n]? It is well known that such a hyperplane does not ... More

Cartan Geometry in Modal Homotopy Type TheoryJun 15 2018Aug 17 2018In this article, some Differential Geometry is developed synthetically in a Modal Homotopy Type Theory. While Homotopy Type Theory is used to reason about general $\infty$-toposes, the "Modal" extension we are using here, is concerned with special $\infty$-toposes ... More

Quantum Theory on a Galois FieldMar 23 2004Systems of free particles in a quantum theory based on a Galois field (GFQT) are discussed in detail. In this approach infinities cannot exist, the cosmological constant problem does not arise and one irreducible representation of the symmetry algebra ... More

Problem of constructing discrete and finite quantum theoryJun 10 2002We consider in detail an approach (proposed by the author earlier) where quantum states are described by elements of a linear space over a Galois field, and operators of physical quantities - by linear operators in this space. The notion of Galois fields ... More

Minimal Stable Sets in TournamentsMar 14 2008Sep 20 2010We propose a systematic methodology for defining tournament solutions as extensions of maximality. The central concepts of this methodology are maximal qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy of tournament solutions, ... More

On measuring unboundedness of the $H^\infty$-calculus for generators of analytic semigroupsFeb 05 2015Sep 28 2016We investigate the boundedness of the $H^\infty$-calculus by estimating the bound $b(\varepsilon)$ of the mapping $H^{\infty}\rightarrow \mathcal{B}(X)$: $f\mapsto f(A)T(\varepsilon)$ for $\varepsilon$ near zero. Here, $-A$ generates the analytic semigroup ... More

Embeddings of Decomposition Spaces into Sobolev and BV SpacesJan 10 2016In the present paper, we investigate whether an embedding of a decomposition space $\mathcal{D}\left(\mathcal{Q},L^{p},Y\right)$ into a given Sobolev space $W^{k,q}(\mathbb{R}^{d})$ exists. As special cases, this includes embeddings into Sobolev spaces ... More

Definition of the Dirac Sea in the Presence of External FieldsMay 02 1997Jan 06 2009It is shown that the Dirac sea can be uniquely defined for the Dirac equation with general interaction, if we impose a causality condition on the Dirac sea. We derive an explicit formula for the Dirac sea in terms of a power series in the bosonic potentials. ... More

Dynamical phase transitions in glasses induced by the ruggedness of the free energy landscapeNov 10 1999We propose damage spreading (DS) as a tool to investigate the topological features related to the ruggedness of the free energy landscape. We argue that DS measures the positiveness of the largest Lyapunov exponent associated to the basins of attraction ... More

Cross-over in scaling laws: A simple example from micromagneticsMay 01 2003Scaling laws for characteristic length scales (in time or in the model parameters) are both experimentally robust and accessible for rigorous analysis. In multiscale situations cross--overs between different scaling laws are observed. We give a simple ... More

Reactor Neutrino Physics -- An UpdateJun 18 1999We review the status and the results of reactor neutrino experiments. Long baseline oscillation experiments at Palo Verde and Chooz have provided limits for the oscillation parameters while the recently proposed Kamland experiment at a baseline of more ... More

Volume preserving embeddings of open subsets of $R^n$ into manifoldsDec 23 2001We consider a connected smooth $n$-dimensional manifold $M$ endowed with a volume form $\Omega$, and we show that an open subset $U$ of $R^n$ of Lebesgue measure $\Vol (U)$ embeds into $M$ by a smooth volume preserving embedding whenever the volume condition ... More

Rational formality of mapping spacesMar 29 2010Let X and Y be finite nilpotent CW complexes with dimension of X less than the connectivity of Y. Generalizing results of Vigu\'e-Poirrier and Yamaguchi, we prove that the mapping space Map(X,Y) is rationally formal if and only if Y has the rational homotopy ... More

A spectral bound for graph irregularityAug 18 2013The imbalance of an edge $e=\{u,v\}$ in a graph is defined as $i(e)=|d(u)-d(v)|$, where $d(\cdot)$ is the vertex degree. The irregularity $I(G)$ of $G$ is then defined as the sum of imbalances over all edges of $G$. This concept was introduced by Albertson ... More

A general version of Price's theoremOct 10 2017Assume that $X_{\Sigma}\in\mathbb{R}^{n}$ is a random vector following a multivariate normal distribution with zero mean and positive definite covariance matrix $\Sigma$. Let $g:\mathbb{R}^{n}\to\mathbb{C}$ be measurable and of moderate growth, e.g., ... More

The Infrastructure of a Global Field of Arbitrary Unit RankSep 09 2008Oct 10 2010In this paper, we show a general way to interpret the infrastructure of a global field of arbitrary unit rank. This interpretation generalizes the prior concepts of the giant step operation and f-representations, and makes it possible to relate the infrastructure ... More

Convergence theorems for graph sequencesApr 03 2013Jan 13 2015In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We examine their ... More

Measurements of the properties of Lambda_c(2595), Lambda_c(2625), Sigma_c(2455), and Sigma_c(2520) baryonsMay 30 2011Jul 28 2011We report measurements of the resonance properties of Lambda_c(2595)+ and Lambda_c(2625)+ baryons in their decays to Lambda_c+ pi+ pi- as well as Sigma_c(2455)++,0 and Sigma_c(2520)++,0 baryons in their decays to Lambda_c+ pi+/- final states. These measurements ... More

Light-Cone Expansion of the Dirac Sea with Light Cone IntegralsJul 13 1997The Dirac sea is calculated in an expansion around the light cone. The method is to analyze the perturbation expansion for the Dirac sea in position space. This leads to integrals over expressions containing distributions which are singular on the light ... More

Derivation of Local Gauge Freedom from a Measurement PrincipleJan 06 1997Apr 07 1999We define operator manifolds as manifolds on which a spectral measure on a Hilbert space is given as additional structure. The spectral measure mathematically describes space as a quantum mechanical observable. We show that the vectors of the Hilbert ... More

Chaos in short-range spin glassesJul 29 1993The nature of static chaos in Ising spin glasses is studied. For the problem of chaos with magnetic field, scaling relations in the case of the SK model and short-range models are presented. Our results also suggest that if there is de Almeida-Thouless ... More

Solvable dynamics in a system of interacting random topsMay 21 1997In this letter a new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops with random precession frequencies. The model allows for an explicit study of orientational effects in synchronized phenomena. ... More

Galactic Sources of High Energy NeutrinosFeb 26 2007The undisputed galactic origin of cosmic rays at energies below the so-called knee implies an existence of a nonthemal population of galactic objects which effectively accelerate protons and nuclei to TeV-PeV energies. The distinct signatures of these ... More

The maximum number of intersections of two polygonsJul 04 2012Feb 10 2015We investigate the maximum number of intersections between two polygons with p and q vertices, respectively, in the plane. The cases where p or q is even or the polygons do not have to be simple are quite easy and already known, but when p and q are both ... More

New results on eigenvalues and degree deviationMar 11 2014Let $G$ be a graph. In a famous paper Collatz and Sinogowitz had proposed to measure its deviation from regularity by the difference of the (adjacency) spectral radius and the average degree: $\epsilon(G)=\rho(G)-\frac{2m}{n}$. We obtain here a new upper ... More

Next generation of IACT arrays: scientific objectives versus energy domainsNov 04 2005Several key motivations and perspectives of ground based gamma-ray astronomy are discussed in the context of the specifics of detection techniques and scientific topics/objectives relevant to four major energy domains -- very-low or \textit{multi-GeV} ... More

A Molecular Mass Gradient is the Key Parameter of the Genetc Code OrganizationJul 21 2009The structure of the genetic code is discussed in formal terms. A rectangular table of the code ("the code matrix"), whose properties reveal its arithmetical content tagged with the information symbols in several notations. New parameters used to analyze ... More

Do You Like What I Like? Similarity Estimation in Proximity-based Mobile Social NetworksMay 19 2018While existing social networking services tend to connect people who know each other, people show a desire to also connect to yet unknown people in physical proximity. Existing research shows that people tend to connect to similar people. Utilizing technology ... More

Time Quasilattices in Dissipative Dynamical SystemsJul 28 2017May 28 2018We establish the existence of `time quasilattices' as stable trajectories in dissipative dynamical systems. These tilings of the time axis, with two unit cells of different durations, can be generated as cuts through a periodic lattice spanned by two ... More

Pell and Clapeyron Words as Stable Trajectories in Dynamical SystemsJul 28 2017Nov 30 2017We establish the existence of `time quasicrystals', tilings of the time axis with two unit cells of different duration. These aperiodic tilings can be constructed as slices through regular tilings of a space spanned by two orthogonal time directions. ... More

Graphs, Ultrafilters and ColourabilityMar 16 2018Let $\beta$ be the functor from Set to CHaus which maps each discrete set X to its Stone-Cech compactification, the set $\beta$ X of ultrafilters on X. Every graph G with vertex set V naturally gives rise to a graph $\beta G$ on the set $\beta V$ of ultrafilters ... More

Tadpole diagrams in constant electromagnetic fieldsSep 12 2017Oct 10 2017We show how all possible one-particle reducible tadpole diagrams in constant electromagnetic fields can be constructed from one-particle irreducible constant-field diagrams. The construction procedure is essentially algebraic and involves differentiations ... More

On the system of sets of lengths and the elasticity of submonoids of $\mathbb{N}^d$Jun 29 2018Let $H$ be an atomic monoid. For $x \in H$, let $\mathsf{L}(x)$ denote the set of all possible lengths of factorizations of $x$ into irreducibles. The system of sets of lengths of $H$ is the set $\mathcal{L}(H) = \{\mathsf{L}(x) \mid x \in H\}$. On the ... More

Positive Functionals Induced by Minimizers of Causal Variational PrinciplesAug 25 2017Feb 18 2018Considering second variations about a given minimizer of a causal variational principle, we derive positive functionals in space-time. It is shown that the strict positivity of these functionals ensures that the minimizer is nonlinearly stable within ... More

Swap-invariant and exchangeable random measuresFeb 24 2016Jul 05 2016In this work we analyze the concept of swap-invariance, which is a weaker variant of exchangeability. A random vector $\xi$ in $\mathbb{R}^n$ is called swap-invariant if $\,{\mathbf E}\,\big| \!\sum_j u_j \xi_j \big|\,$ is invariant under all permutations ... More

The local geometry of compact homogeneous Lorentz spacesFeb 09 2015In 1995, S. Adams and G. Stuck as well as A. Zeghib independently provided a classification of non-compact Lie groups which can act isometrically and locally effectively on compact Lorentzian manifolds. In the case that the corresponding Lie algebra contains ... More

Functional calculus estimates for Tadmor-Ritt operatorsJun 30 2015We show $H^{\infty}$-functional calculus estimates for Tadmor-Ritt operators (also known as Ritt operators), which generalize and improve results by Vitse. These estimates are in conformity with the best known power-bounds for Tadmor-Ritt operators in ... More

Modelling of transport phenomena in gases based on quantum scatteringMay 21 2018A quantum interatomic scattering is implemented in the direct simulation Monte Carlo (DSMC) method applied to transport phenomena in rarefied gases. In contrast to the traditional DSMC method based on the classical scattering, the proposed implementation ... More

An Invitation to Ehrhart Theory: Polyhedral Geometry and its Applications in Enumerative CombinatoricsMay 29 2014Jul 22 2014In this expository article we give an introduction to Ehrhart theory, i.e., the theory of integer points in polyhedra, and take a tour through its applications in enumerative combinatorics. Topics include geometric modeling in combinatorics, Ehrhart's ... More

Structured, compactly supported Banach frame decompositions of decomposition spacesDec 27 2016$\newcommand{mc}[1]{\mathcal{#1}}$ $\newcommand{D}{\mc{D}(\mc{Q},L^p,\ell_w^q)}$ We present a framework for the construction of structured, possibly compactly supported Banach frames and atomic decompositions for decomposition spaces. Such a space $\D$ ... More

Lighting up topological insulators: large surface photocurrents from magnetic superlatticesFeb 28 2014Dec 22 2015The gapless surface states of topological insulators (TI) can potentially be used to detect and harvest low-frequency infrared light. Nonetheless, it was shown that significant surface photocurrents due to light with frequency below the bulk gap are rather ... More

Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearitiesMar 14 2019The explicit Euler scheme and similar explicit approximation schemes (such as the Milstein scheme) are known to diverge strongly and numerically weakly in the case of one-dimensional stochastic ordinary differential equations with superlinearly growing ... More

Comparison of Boltzmann Kinetics with Quantum Dynamics for a Chiral Yukawa Model Far From EquilibriumOct 16 2007Boltzmann equations are often used to describe the non-equilibrium time-evolution of many-body systems in particle physics. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after ... More

An $L_p$-estimate for the stochastic heat equation on an angular domain in $\mathbb{R}^2$Mar 29 2016Oct 20 2016We prove a weighted $L_p$-estimate for the stochastic convolution associated to the stochastic heat equation with zero Dirichlet boundary condition on a planar angular domain $\mathcal{D}_{\kappa_0}\subset\mathbb{R}^2$ with angle $\kappa_0\in(0,2\pi)$. ... More

Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz DomainsNov 08 2010We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0, 1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains O\subset R^d. ... More

Extracting Majorana Properties in the Throat of Neutrinoless Double Beta DecayAug 04 2016Assuming that neutrinos are Majorana particles, we explore what information can be inferred from future strong limits (i.e. non-observation) for neutrinoless double beta decay. Specifically we consider the case where the mass hierarchy is normal and the ... More

Escape rate of an active Brownian particle over a potential barrierMar 30 2012We study the dynamics of an active Brownian particle with a nonlinear friction function located in a spatial cubic potential. For strong but finite damping, the escape rate of the particle over the spatial potential barrier shows a nonmonotonic dependence ... More