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Never look back - A modified EnKF method and its application to the training of neural networks without back propagationMay 21 2018May 31 2018In this work, we present a new derivative-free optimization method and investigate its use for training neural networks. Our method is motivated by the Ensemble Kalman Filter (EnKF), which has been used successfully for solving optimization problems that ... More

Fast Gibbs sampling for high-dimensional Bayesian inversionFeb 27 2016Jul 05 2016Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to explore and ... More

Fast Markov chain Monte Carlo sampling for sparse Bayesian inference in high-dimensional inverse problems using L1-type priorsJun 01 2012Sep 24 2012Sparsity has become a key concept for solving of high-dimensional inverse problems using variational regularization techniques. Recently, using similar sparsity-constraints in the Bayesian framework for inverse problems by encoding them in the prior distribution ... More

On the Adjoint Operator in Photoacoustic TomographyFeb 05 2016Aug 01 2016Photoacoustic Tomography (PAT) is an emerging biomedical "imaging from coupled physics" technique, in which the image contrast is due to optical absorption, but the information is carried to the surface of the tissue as ultrasound pulses. Many algorithms ... More

Bayesian Modelling of Skull Conductivity Uncertainties in EEG Source ImagingMar 27 2017Knowing the correct skull conductivity is crucial for the accuracy of EEG source imaging, but unfortunately, its true value, which is inter- and intra-individually varying, is difficult to determine. In this paper, we propose a statistical method based ... More

Maximum-A-Posteriori Estimates in Linear Inverse Problems with Log-concave Priors are Proper Bayes EstimatorsFeb 21 2014Jun 02 2014A frequent matter of debate in Bayesian inversion is the question, which of the two principle point-estimators, the maximum-a-posteriori (MAP) or the conditional mean (CM) estimate is to be preferred. As the MAP estimate corresponds to the solution given ... More

A hierarchical Bayesian perspective on majorization-minimization for non-convex sparse regression: application to M/EEG source imagingOct 24 2017Jun 06 2018Majorization-minimization (MM) is a standard iterative optimization technique which consists in minimizing a sequence of convex surrogate functionals. MM approaches have been particularly successful to tackle inverse problems and statistical machine learning ... More

Model based learning for accelerated, limited-view 3D photoacoustic tomographyAug 31 2017Recent advances in deep learning for tomographic reconstructions have shown great potential to create accurate and high quality images with a considerable speed-up. In this work we present a deep neural network that is specifically designed to provide ... More

Enhancing Compressed Sensing Photoacoustic Tomography by Simultaneous Motion EstimationFeb 14 2018A crucial limitation of current high-resolution 3D photoacoustic tomography (PAT) devices that employ sequential scanning is their long acquisition time. In previous work, we demonstrated how to use compressed sensing techniques to improve upon this: ... More

Accelerated High-Resolution Photoacoustic Tomography via Compressed SensingApr 30 2016Sep 28 2016Current 3D photoacoustic tomography (PAT) systems offer either high image quality or high frame rates but are not able to deliver high spatial and temporal resolution simultaneously, which limits their ability to image dynamic processes in living tissue. ... 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

Node Theorem for Matrix Schroedinger OperatorsJun 14 1996Mar 12 1997In this paper we study the ground states of a matrix Schroedinger operator, that is an operator of the type (-Laplace) + V acting on m-component wave functions in R^n. We prove in generalization of the classical node theorem that the ground states of ... 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

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

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

On symplectic foldingMar 15 1999We study the rigidity and flexibility of symplectic embeddings of simple shapes. It is first proved that under the condition $r_n^2 \le 2 r_1^2$ the symplectic ellipsoid $E(r_1, ..., r_n)$ with radii $r_1 \le ... \le r_n$ does not embed in a ball of radius ... More

Nonlinear evolution by mean curvature and isoperimetric inequalitiesJun 27 2006Evolving smooth, compact hypersurfaces in R^{n+1} with normal speed equal to a positive power k of the mean curvature improves a certain 'isoperimetric difference' for k >= n-1. As singularities may develop before the volume goes to zero, we develop a ... More

Is Thermal Emission in Gamma-Ray Bursts Ubiquitous?Apr 20 2005The prompt emission of gamma-ray bursts has yet defied any simple explanation, despite the presence of a rich observational material and great theoretical efforts. Here we show that all the types of spectral evolution and spectral shapes that have been ... More

Interpretations of gamma-ray burst spectroscopy. I. Analytical and numerical study of spectral lagsNov 08 2004We describe the strong spectral evolution that occurs during a gamma-ray burst pulse and the means by which it can be analyzed. Based on observed empirical correlations, an analytical model is constructed which is used to describe the pulse shape and ... More

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

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

Stacked polytopes and tight triangulations of manifoldsNov 26 2009Mar 03 2011Tightness of a triangulated manifold is a topological condition, roughly meaning that any simplexwise linear embedding of the triangulation into euclidean space is "as convex as possible". It can thus be understood as a generalization of the concept of ... More

Relations in the Tautological Ring and Frobenius Manifolds near the DiscriminantMay 13 2015Sep 29 2015For generically semisimple cohomological field theories pole cancellation in the Givental-Teleman classification implies relations between classes in the tautological ring of the moduli space of curves. For the theory of the $A_2$-singularity these are ... More

Comparing tautological relations from the equivariant Gromov-Witten theory of projective spaces and spin structuresJul 17 2014Sep 29 2015Pandharipande-Pixton-Zvonkine's proof of Pixton's generalized Faber-Zagier relations in the tautological ring of $\overline M_{g, n}$ has started the study of tautological relations from semisimple cohomological field theories. In this article we compare ... More

Optimal isoperimetric inequalities for surfaces in any codimension in Cartan-Hadamard manifoldsFeb 01 2018Let $(M^n,g)$ be simply connected, complete, with non-positive sectional curvatures, and $\Sigma$ a 2-dimensional closed integral current (or flat chain mod 2) with compact support in $M$. Let $S$ be an area minimising integral 3-current (resp.~flat chain ... More

Holes in the Infrastructure of Global Hyperelliptic Function FieldsNov 23 2009Nov 25 2009We prove that the number of "hole elements" $H(K)$ in the infrastructure of a hyperelliptic function field $K$ of genus $g$ with finite constant field $\F_q$ with $n + 1$ places at infinity, of whom $n' + 1$ are of degree one, satisfies $|\frac{H(K)}{\abs{\Pic^0(K)}} ... 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

Ehrhart f*-coefficients of polytopal complexes are non-negative integersFeb 13 2012Mar 06 2012The Ehrhart polynomial $L_P$ of an integral polytope $P$ counts the number of integer points in integral dilates of $P$. Ehrhart polynomials of polytopes are often described in terms of their Ehrhart $h^*$-vector (aka Ehrhart $\delta$-vector), which is ... 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

A Bernstein Theorem for Minimal Maps with Small Second Fundamental FormNov 27 2017We consider minimal maps $f:M\to N$ between Riemannian manifolds $(M,\mathrm{g}_M)$ and $(N,\mathrm{g}_N)$, where $M$ is compact and where the sectional curvatures satisfy $\sec_N\le \sigma\le \sec_M$ for some $\sigma>0$. Under certain assumptions on ... 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

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

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

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

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

Uniqueness of compact tangent flows in Mean Curvature FlowJul 22 2011Oct 11 2011We show, for mean curvature flows in Euclidean space, that if one of the tangent flows at a given space-time point consists of a closed, multiplicity-one, smoothly embedded self-similar shrinker, then it is the unique tangent flow at that point. That ... More

Circular velocity profiles of dark matter haloesMar 03 2004Dec 19 2005We use a high-resolution simulation of a galaxy-sized dark matter halo, published simulated data as well as four cluster-sized haloes from Fukushige, Kawai & Makino to study the inner halo structure in a Lambda cold dark matter cosmology. We find that ... 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

Phenomenology of Enhanced Light Quark Yukawa Couplings and the $W^\pm h$ Charge AsymmetrySep 21 2016I propose the measurement of the $W^\pm h$ charge asymmetry as a consistency test for the Standard Model (SM) Higgs, which is sensitive to enhanced Yukawa couplings of the first and second generation quarks. I present a collider analysis for the charge ... More

Causal Fermion Systems -- An OverviewMay 19 2015Jul 28 2015The theory of causal fermion systems is an approach to describe fundamental physics. We here introduce the mathematical framework and give an overview of the objectives and current results.

Quantum Ergodicity and the Analysis of Semiclassical Pseudodifferential OperatorsOct 11 2014This undergraduate thesis is concerned with developing the tools of differential geometry and semiclassical analysis needed to understand the the quantum ergodicity theorem of Schnirelman (1974), Zelditch (1987), and Colin de Verdi\`ere (1985) and the ... More

Affine differential geometry and smoothness maximization as tools for identifying geometric movement primitivesSep 02 2014Jan 27 2016Neuroscientific studies of drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole. This work is about ... More

Evolution of area-decreasing maps between two-dimensional Euclidean spacesAug 18 2016We consider the mean curvature flow of the graph of a smooth map $f:\mathbb{R}^2\to\mathbb{R}^2$ between two-dimensional Euclidean spaces. If $f$ satisfies an area-decreasing property, the solution exists for all times and the evolving submanifold stays ... More

Automating Political Bias PredictionAug 07 2016Every day media generate large amounts of text. An unbiased view on media reports requires an understanding of the political bias of media content. Assistive technology for estimating the political bias of texts can be helpful in this context. This study ... More

Quadratic Equations in Three Variables over Gaussian IntegersJul 25 2016We develop an algebraic method of studying of Diophantine quadratic equations in three variables over the ring of Gaussian integers.

Photon propagation in slowly varying electromagnetic fieldsJul 06 2016We study the effective theory of soft photons in slowly varying electromagnetic background fields at one-loop order in QED. This is of relevance for the study of all-optical signatures of quantum vacuum nonlinearity in realistic electromagnetic background ... More

Fermat's Last Theorem: Algebra and Number TheoryMay 02 2016Jul 03 2016In our work we give the examples using Fermat's Last Theorem for solving some problems from algebra and number theory.

The Continuum Limit of Causal Fermion SystemsMay 16 2016Aug 21 2016This monograph introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting cases and is ... More

Anatomizing Exotic Production of the Higgs BosonApr 10 2014We discuss exotic production modes of the Higgs boson and how their phenomenology can be probed in current Higgs analyses. We highlight the importance of differential distributions in disentangling standard production mechanisms from exotic modes. We ... More

Independence and Matching Number in Graphs with Maximum Degree 4Dec 02 2013We prove that $\frac{7}{4}\alpha(G)+\beta(G)\geq n(G)$ and $\alpha(G)+\frac{3}{2}\beta(G)\geq n(G)$ for every triangle-free graph $G$ with maximum degree at most $4$, where $\alpha(G)$ is the independence number and $\beta(G)$ is the matching number of ... More

A Universal Quaternary Quadratic Form over Gaussian IntegersOct 23 2013May 08 2014In this article we show that the form $x^2 + iy^2 + z^2 + iw^2$ represents all gaussian integers. The main tools used in this proof are Fermat's little theorem (over finite field extensions), the Mordell-Niven theorem (representation of some gaussians), ... More

Perturbative Quantum Field Theory in the Framework of the Fermionic ProjectorOct 15 2013Apr 16 2014We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the ... More

Set theory and topology. An introduction to the foundations of analysis. Part II: Topology - Fundamental notionsJun 28 2013We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as well as their ... 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

Diophantine Inequalities with Primes, Auxiliary Inequalities, Evaluations of the Difference between Consecutive PrimesOct 07 2015The goal of the present paper is to present a method of proving of Diophantine inequalities with primes through the use of auxiliary inequalities and available evaluations of the difference between consecutive primes. We study the Legendre - Ingham's ... 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

Relative entropies and their use in quantum information theoryNov 27 2016This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations of the optimal ... More

Set-Monotonicity Implies Kelly-StrategyproofnessMay 26 2010Feb 05 2015This paper studies the strategic manipulation of set-valued social choice functions according to Kelly's preference extension, which prescribes that one set of alternatives is preferred to another if and only if all elements of the former are preferred ... More

Packing symplectic manifolds by handSep 29 2004We construct explicit maximal symplectic packings of minimal rational and ruled symplectic 4-manifolds by few balls in a very simple way.

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 Z' Model for the CDF Dijet AnomalyApr 01 2011Apr 18 2011We adopt a bottom-up approach to constructing a new physics model to explain the CDF excess seen in dijets with an associated lepton and missing transverse energy. We find that the 145 GeV broad feature seen by CDF in the dijet invariant mass distribution ... More

Thermal emission in the prompt phase of gamma-ray burstsApr 25 2005I discuss the interpretation of the prompt phase in gamma-ray bursts as being dominated by quasi-thermal emission, rather than by synchrotron emission. Such an interpretation gives a more natural explanation of (i) the observed variety of spectral shape ... 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

Studies of Neutrino Oscillations at ReactorsMay 09 2000Experiments with reactor neutrinos continue to shed light on our understanding of neutrino oscillations. We review some of the early decisive experiments. We then turn to the recent long baseline oscillation experiments at Palo Verde and Chooz which are ... More

Vacuum Birefringence as a Vacuum Emission ProcessOct 12 2015We argue that the phenomenon of vacuum birefringence in strong inhomogeneous electromagnetic fields can be most efficiently analyzed in terms of a vacuum emission process. In this contribution, we exemplarily stick to the case of vacuum birefringence ... More

Relations on $\overline M_{g,n}$ via equivariant Gromov-Witten theory of $\mathbb P^1$Sep 28 2015We give a proof of Pixton's generalized Faber-Zagier relations in the tautological Chow ring of $\overline M_{g,n}$. The strategy is very similar to the work of Pandharipande-Pixton-Zvonkine, who have given a proof of the same result in cohomology. The ... More

Remarks on the geometric quantization of a class of harmonic oscillator type potentialsJul 22 2016The conditions that must be fulfilled by a certain physical system to apply geometric quantization prescription on it are investigated. These terms are sought as mathematical requirements, which can be traced in an analysis of integrable systems, from ... More

Floer homology of Lagrangians in clean intersectionJun 16 2016We consider Floer homology associated to a pair of closed Lagrangian submanifolds that satisfy a monotonicty assumption. If the Lagrangians intersect cleanly we decribe two spectral sequences which help to compute their Floer homology. The spectral sequences ... More

A Note on Quartic Equations with only Trivial SolutionsNov 06 2013In our notice we propose the classification of some quartic equations with only trivial solutions by the auxiliary equations. For proving trivial solutions of the quartic equations we use method infinite descent based on the number of prime integers of ... More

Longest Paths in Circular Arc GraphsDec 11 2013As observed by Rautenbach and Sereni (arXiv:1302.5503) there is a gap in the proof of the theorem of Balister et al. (Longest paths in circular arc graphs, Combin. Probab. Comput., 13, No. 3, 311-317 (2004)), which states that the intersection of all ... More

The photon polarization tensor in a homogeneous magnetic or electric fieldAug 28 2013Aug 13 2014We revisit the photon polarization tensor in a homogeneous external magnetic or electric field. The starting point of our considerations is the momentum space representation of the one-loop photon polarization tensor in the presence of a homogeneous electromagnetic ... More

Di-jet resonances at future hadron colliders: A Snowmass whitepaperAug 05 2013I investigate the sensitivity of future hadron colliders to di-jet resonances arising from Z' or coloron models. The projected discovery potential and exclusion limits for these resonances is presented in the coupling vs. mass plane, which highlights ... More

Parity linkage and the Erdős-Pósa property of odd cycles through prescribed vertices in highly connected graphsNov 24 2014Feb 16 2016We show the following for every sufficiently connected graph $G$, any vertex subset $S$ of $G$, and given integer $k$: there are $k$ disjoint odd cycles in $G$ each containing a vertex of $S$ or there is set $X$ of at most $2k-2$ vertices such that $G-X$ ... More

Spectral characterization of the hydrogen like atoms confined by oscillating systemsOct 07 2014The spectral characterization of Coulomb systems confined by the homogeneous pseudo-Gaussian oscillator is investigated. This is made using the efficient computational method of generating functional. Also, the method is used for the spectral characterization ... More

Spectral radius minus average degree: a better boundJul 16 2014Collatz and Sinogowitz had proposed to measure the departure of a graph $G$ from regularity by the difference of the (adjacency) spectral radius and the average degree: $\epsilon(G)=\rho(G)-\frac{2m}{n}$. We give here new lower bounds on this quantity, ... More

The Higgs Physics Programme at the International Linear ColliderOct 13 2014The talk summarises the case for Higgs physics in $e^+e^-$ collisions and explains how Higgs parameters can be extracted in a model-independent way at the International Linear Collider (ILC). The expected precision will be discussed in the context of ... More

On Proving of Diophantine Inequalities with Prime Numbers by Evaluations of the Difference between Consecutive PrimesJul 24 2015Using as the working hypothesis of an evaluation of the difference between primes $p_{n+1} - p_n = O(\sqrt{p_n})$ we represent in detail the proofs of Legendre's and Oppermann's conjectures.

Gromov-Witten theory of target curves and the tautological ringAug 28 2013In the Gromov-Witten theory of a target curve we consider descendent integrals against the virtual fundamental class relative to the forgetful morphism to the moduli space of curves. We show that cohomology classes obtained in this way lie in the tautological ... 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

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

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

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

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

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

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

An extension theorem in symplectic geometryDec 31 2001We extend the ``Extension after Restriction Principle'' for symplectic embeddings of bounded starlike domains to a large class of symplectic embeddings of unbounded starlike domains.

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

Induced Matchings in Graphs of Maximum Degree 4Jul 31 2014For a graph $G$, let $\nu_s(G)$ be the induced matching number of $G$. We prove the sharp bound $\nu_s(G)\geq \frac{n(G)}{9}$ for every graph $G$ of maximum degree at most $4$ and without isolated vertices that does not contain a certain blown up $5$-cycle ... More

Fusion rules from root systems I: case ${\rm A}_n$Mar 13 2014Axial algebras are commutative algebras generated by idempotents; they generalise associative algebras by allowing the idempotents to have additional eigenvectors, controlled by fusion rules. If the fusion rules are $\mathbb{Z}/2$-graded, axial algebras ... 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

Pressure induced magnetism in rotated graphene bilayersNov 10 2018Using ab initio methods based on the density functional theory we show that rotated graphene bilayers at angles different from the magic ones can have an electronic spectrum similar to those by applying moderate external pressures. We find that for an ... 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