Results for "Felix Lucka"

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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
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
A Multi-channel DART AlgorithmAug 28 2018Tomography deals with the reconstruction of objects from their projections, acquired along a range of angles. Discrete tomography is concerned with objects that consist of a small number of materials, which makes it possible to compute accurate reconstructions ... More
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
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
A Cone-Beam X-Ray CT Data Collection Designed for Machine LearningMay 12 2019Unlike previous works, this open data collection consists of X-ray cone-beam (CB) computed tomography (CT) datasets specifically designed for machine learning applications and high cone-angle artefact reduction. Forty-two walnuts were scanned with a laboratory ... 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
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
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
Enhancing Compressed Sensing 4D Photoacoustic Tomography by Simultaneous Motion EstimationFeb 14 2018Jun 15 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
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
Risk Estimators for Choosing Regularization Parameters in Ill-Posed Problems - Properties and LimitationsJan 18 2017Oct 10 2017This paper discusses the properties of certain risk estimators recently proposed to choose regularization parameters in ill-posed problems. A simple approach is Stein's unbiased risk estimator (SURE), which estimates the risk in the data space, while ... 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
Real-time Cardiovascular MR with Spatio-temporal Artifact Suppression using Deep Learning - Proof of Concept in Congenital Heart DiseaseMar 14 2018Jun 14 2018PURPOSE: Real-time assessment of ventricular volumes requires high acceleration factors. Residual convolutional neural networks (CNN) have shown potential for removing artifacts caused by data undersampling. In this study we investigated the effect of ... More
Approximate k-space models and Deep Learning for fast photoacoustic reconstructionJul 09 2018We present a framework for accelerated iterative reconstructions using a fast and approximate forward model that is based on k-space methods for photoacoustic tomography. The approximate model introduces aliasing artefacts in the gradient information ... More
Model based learning for accelerated, limited-view 3D photoacoustic tomographyAug 31 2017Mar 26 2018Recent 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
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
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
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
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.
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
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
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
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
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
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
Vacuum birefringence in the head-on collision of XFEL and optical high-intensity laser pulsesJul 09 2018The focus of this article is on providing compact analytical expressions for the differential number of polarization flipped signal photons constituting the signal of vacuum birefringence in the head-on collision of x-ray free electron (XFEL) and optical ... More
Efficient Tree Solver for Hines Matrices on the GPUOct 30 2018Nov 06 2018The human brain consists of a large number of interconnected neurons communicating via exchange of electrical spikes. Simulations play an important role in better understanding electrical activity in the brain and offers a way to to compare measured data ... More
An Alternative View of the Universe Structure (on the invalidity of the four dimensional space-time concept)Nov 08 2007The model of the Universe in this paper uses equations of the unperturbed Keplerian motion. They have been updated, complementied and generalized when the solution of these equations is the characteristic function of a random value from the theory of ... 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
De Sitter Invariance and a Possible Mechanism of GravityJul 20 2008It is believed that gravity will be explained in the framework of the existing quantum theory when one succeeds in eliminating divergencies at large momenta or small distances (although the phenomenon of gravity has been observed only at nonrelativistic ... More
Why is Quantum Physics Based on Complex Numbers?Aug 29 2003May 31 2006The modern quantum theory is based on the assumption that quantum states are represented by elements of a complex Hilbert space. It is expected that in future quantum theory the number field will be not postulated but derived from more general principles. ... More
A Possible Mechanism of GravityJul 09 2003We consider systems of two free particles in de Sitter invariant quantum theory and calculate the mean value of the mass operator for such systems. It is shown that, in addition to the well known relativistic contribution (and de Sitter antigravity which ... 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
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
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
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
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
Evolution of Contractions between Non-Compact ManifoldsMay 29 2018Let $N$ be a complete manifold with bounded geometry, such that $\sec_N\le -\sigma < 0$ for some positive constant $\sigma$. We investigate the mean curvature flow of the graphs of smooth length-decreasing maps $f:\mathbb{R}^m\to N$. In this case, the ... 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
Relativistic pseudo-Gaussian oscillatorsOct 07 2014The quantum models of a massive scalar particle inside of an open bag generated by a pseudo-Gaussian conformaly flat (1+1) metrics are investigated. The potential of a free moving test particle, in the generated metric, has Gaussian asymptotic behavior, ... More
Random Subgraphs in Sparse GraphsDec 03 2013We investigate the threshold probability for connectivity of sparse graphs under weak assumptions. As a corollary this completely solve the problem for Cartesian powers of arbitrary graphs. In detail, let $G$ be a connected graph on $k$ vertices, $G^n$ ... More
A Characterization of Mixed Unit Interval GraphsDec 03 2013Jun 11 2014We give a complete characterization of mixed unit interval graphs, the intersection graphs of closed, open, and half-open unit intervals of the real line. This is a proper superclass of the well known unit interval graphs. Our result solves a problem ... More
An algorithmic proof of Bachet's conjecture and the Lagrange-Euler methodOct 21 2013The goal of this notice is to present a proof of Bachet's conjecture based exclusively on the fundamental theorem of arithmetic. The novelty of this proof consists in its introduction of a partial order on rational integers through the unique factorization ... More
Generalised dihedral subalgebras from the MonsterOct 02 2015The conjugacy classes of the Monster which occur in the McKay observation correspond to the isomorphism types of certain 2-generated subalgebras of the Griess algebra. Sakuma, Ivanov and others showed that these subalgebras match the classification of ... More
The quantum vacuum in electromagnetic fields: From the Heisenberg-Euler effective action to vacuum birefringenceNov 23 2016The focus of these lectures is on the quantum vacuum subjected to classical electromagnetic fields. To this end we explicitly derive the renowned Heisenberg-Euler effective action in constant electromagnetic fields in a rather pedagogical and easy to ... More
Minkowski EndomorphismsOct 27 2016Several open problems concerning Minkowski endomorphisms and Minkowski valuations are solved. More precisely, it is proved that all Minkowski endomorphisms are uniformly continuous but that there exist Minkowski endomorphisms that are not weakly-monotone. ... 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
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
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
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
Goldbach's Conjecture and Euler's $φ$-FunctionApr 24 2017May 04 2017In this paper we propose an alternative formulation of the binary and ternary Goldbach conjectures as the systems of equations involving the Euler $\phi$-function.
Perturbation Theory for Critical Points of Causal Variational PrinciplesMar 15 2017Dec 01 2018The perturbation theory for critical points of causal variational principles is developed. We first analyze the class of perturbations obtained by multiplying the universal measure by a weight function and taking the push-forward under a diffeomorphism. ... More
Jet substructure in high-energy hadron collisionsDec 18 2018In the past years significant progress has been made toward achieving a quantitative understanding of jets and their substructure in high-energy proton-proton collisions from first principles in QCD. Precise measurements have become available from the ... More
Atomic and antimatter semigroup algebras with rational exponentsJan 21 2018Oct 15 2018In this paper, we study the atomic structure of certain classes of semigroup algebras whose sets of exponents are additive submonoids of rational numbers. When studying the atomicity of integral domains, the building blocks by excellence are the irreducible ... More
Lectures on Linear Stability of Rotating Black HolesNov 20 2018These lecture notes are concerned with linear stability of the non-extreme Kerr geometry under perturbations of general spin. After a brief review of the Kerr black hole and its symmetries, we describe these symmetries by Killing fields and work out the ... More
An all-loop result for the strong magnetic field limit of the Heisenberg-Euler effective LagrangianMar 16 2019We provide an explicit expression for the strong magnetic field limit of the Heisenberg-Euler effective Lagrangian for both scalar and spinor quantum electrodynamics. To this end, we show that the strong magnetic field behavior is fully determined by ... More
Puiseux monoids and transfer homomorphismsSep 06 2017May 14 2018There are several families of atomic monoids whose arithmetical invariants have received a great deal of attention during the last two decades. The factorization theory of finitely generated monoids, strongly primary monoids, Krull monoids, and C-monoids ... 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
Adjacent Pairs Exchange correction to the Random Phase ApproximationSep 01 2015The Random Phase Approximation (RPA) is a widely employed post Hartree-Fock or DFT method, capable of capturing van der Waal interactions and other dynamic correlation effects at relatively low costs of $\mathcal O(N^3)$ in time and $\mathcal O(N^2)$ ... 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
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
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
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
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
A lower bound on the entries of the principal eigenvector of a graphMar 06 2014Mar 09 2014We obtain a lower bound on each entry of the principal eigenvector of a non-regular connected graph.
Graph energy estimates via the Chebyshev functionalJul 28 2014Sep 03 2014Let $G$ be a graph with $n$ vertices and $m$ edges. The energy $E$ of the graph $G$ is defined as the sum of the moduli of the adjacency eigenvalues $\lambda_{1} \geq \lambda_{2} \geq \ldots \geq \lambda_{n}$ of $G$: $$ E=\sum_{i=1}^{n}{|\lambda{i}|}. ... 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
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
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
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
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
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