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Results for "Felix L. Opolka"

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Spatio-Temporal Deep Graph InfomaxApr 12 2019Spatio-temporal graphs such as traffic networks or gene regulatory systems present challenges for the existing deep learning methods due to the complexity of structural changes over time. To address these issues, we introduce Spatio-Temporal Deep Graph ... 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
Bayesian inference in decomposable graphical models using sequential Monte Carlo methodsMay 31 2018Jun 02 2018In this study we present a sequential sampling methodology for Bayesian inference in decomposable graphical models. We recast the problem of graph estimation, which in general lacks natural sequential interpretation, into a sequential setting. Specifically, ... 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
A Prior Distribution over Directed Acyclic Graphs for Sparse Bayesian NetworksApr 25 2015The main contribution of this article is a new prior distribution over directed acyclic graphs, which gives larger weight to sparse graphs. This distribution is intended for structured Bayesian networks, where the structure is given by an ordered block ... More
Simulating Forces - Learning Through Touch, Virtual LaboratoriesFeb 20 2019With the expansion of e-learning course curricula and the affordability of haptic devices, at-home virtual laboratories are emerging as an increasingly viable option for e-learners. We outline three novel haptic simulations for the introductory physics ... More
Dark Higgs Bosons at FASEROct 25 2017Apr 25 2018FASER, ForwArd Search ExpeRiment at the LHC, has been proposed as a small, very far forward detector to discover new, light, weakly-coupled particles. Previous work showed that with a total volume of just $\sim 0.1 - 1~\rm{m}^3$, FASER can discover dark ... More
FASER: ForwArd Search ExpeRiment at the LHCAug 30 2017Jun 14 2018New physics has traditionally been expected in the high-$p_T$ region at high-energy collider experiments. If new particles are light and weakly-coupled, however, this focus may be completely misguided: light particles are typically highly concentrated ... More
The Neutral Hydrogen Bridge between M31 and M33May 23 2012The Green Bank Telescope has been used to search for 21cm HI emission over a large area between the galaxies M31 and M33 in an attempt to confirm at 9.1 arcmin angular resolution the detection by Braun and Thilker (2004) of a very extensive neutral gas ... More
Adapting to Unknown Sparsity by controlling the False Discovery RateMay 18 2005We attempt to recover an $n$-dimensional vector observed in white noise, where $n$ is large and the vector is known to be sparse, but the degree of sparsity is unknown. We consider three different ways of defining sparsity of a vector: using the fraction ... More
ALPs at FASER: The LHC as a Photon Beam DumpJun 06 2018The goal of FASER, ForwArd Search ExpeRiment at the LHC, is to discover light, weakly-interacting particles with a small and inexpensive detector placed in the far-forward region of ATLAS or CMS. A promising location in an unused service tunnel 480 m ... More
Enumerating Colorings, Tensions and Flows in Cell ComplexesDec 28 2012Oct 24 2013We study quasipolynomials enumerating proper colorings, nowhere-zero tensions, and nowhere-zero flows in an arbitrary CW-complex $X$, generalizing the chromatic, tension and flow polynomials of a graph. Our colorings, tensions and flows may be either ... More
X3D in Urban Planning - Savannah in 3DFeb 08 2019Urban planning often raises complex issues that are difficult to visualize and challenging to communicate. The increasing availability of 3D modeling standards has provided the opportunity for many developers, engineers, designers, planners, investors, ... More
Three-Body Decays of Sleptons with General Flavor Violation and Left-Right MixingApr 09 2009Jun 30 2009We determine the widths of three-body decays of sleptons, $\tilde{l}^- \to \tilde{l}^{\pm} l^- l^{\mp}, \tilde{l}^- \nu \bar{\nu}, \tilde{l}^- q \bar{q}$, in the presence of arbitrary slepton flavor violation and left-right mixing. These decays are important ... 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
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
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
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
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
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 Numerical Analysis of the Supersymmetric Flavor Problem and Radiative Fermion MassesDec 13 2005Feb 27 2010We study the SUSY flavor problem in the MSSM, we are namely interested in estimating the size of the SUSY flavor problem and its dependence on the MSSM parameters. For that, we made a numerical analysis randomly generating the entries of the sfermion ... More
Electrostatic potential variations on stellarator magnetic surfaces in low collisionality regimesApr 30 2018Aug 21 2018The component of the neoclassical electrostatic potential that is non-constant on the magnetic surface, that we denote by $\tilde\varphi$, can affect radial transport of highly charged impurities, and this has motivated its inclusion in some modern neoclassical ... More
Flow damping in stellarators close to quasisymmetryJul 04 2014Oct 13 2014Quasisymmetric stellarators are a type of optimized stellarators for which flows are undamped to lowest order in an expansion in the normalized Larmor radius. However, perfect quasisymmetry is impossible. Since large flows may be desirable as a means ... More
Optimizing stellarators for large flowsMay 05 2014Plasma flow is damped in stellarators because they are not intrinsically ambipolar, unlike tokamaks, in which the flux-surface averaged radial electric current vanishes for any value of the radial electric field. Only quasisymmetric stellarators are intrinsically ... More
SPICE: Simulation Package for Including Flavor in Collider EventsApr 08 2009Dec 21 2009We describe SPICE: Simulation Package for Including Flavor in Collider Events. SPICE takes as input two ingredients: a standard flavor-conserving supersymmetric spectrum and a set of flavor-violating slepton mass parameters, both of which are specified ... 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
Causal Fermion Systems: Discrete Space-Times, Causation and Finite Propagation SpeedDec 01 2018The theory of causal fermion systems is a recent approach to fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. The dynamics is described by a ... 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
On taut singularities in arbitrary characteristicsMar 25 2013Over $\C$, Henry Laufer classified all taut surface singularities. We adapt and extent his transcendental methods to positive characteristic. With this we show that if a normal surface singularity is taut over $\C$, then the normal surface singularities ... 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
On a question of Dusa McDuffJan 01 2002Consider the $2n$-dimensional closed ball $B$ of radius 1 in the $2n$-dimensional symplectic cylinder $Z = D \times R^{2n-2}$ over the closed disc $D$ of radius 1. We construct for each $\epsilon >0$ a Hamiltonian deformation $\phi$ of $B$ in $Z$ of energy ... More
Chip-firing may be much faster than you thinkNov 06 2014Nov 24 2014A new bound (Theorem \ref{thm:main}) for the duration of the chip-firing game with $N$ chips on a $n$-vertex graph is obtained, by a careful analysis of the pseudo-inverse of the discrete Laplacian matrix of the graph. This new bound is expressed in terms ... More
On monotonicity-preserving perturbations of $M$-matricesAug 04 2013We obtain an explicit analytical sufficient condition on $E$ that ensures the monotonicity of the matrix $M+E$, where $M$ is an $M$-matrix.
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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 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
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
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
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
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
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
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
On the LHC sensitivity for non-thermalised hidden sectorsJan 23 2018We show under rather general assumptions that hidden sectors that never reach thermal equilibrium in the early Universe are also inaccessible for the LHC. In other words, any particle that can be produced at the LHC must either have been in thermal equilibrium ... More
Stability Conditions and Lagrangian CobordismsDec 06 2017Jul 17 2018In this paper we study the interplay between Lagrangian cobordisms and stability conditions. We show that any stability condition on the derived Fukaya category $D\mathcal{F}uk(M)$ of a symplectic manifold $(M,\omega)$ induces a stability condition on ... More
Causal Fermion Systems: A Primer for Lorentzian GeometersSep 13 2017Feb 20 2018We give a brief introduction to causal fermion systems with a focus on the geometric structures in space-time.
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
Algebraic Hopf invariants and rational models for mapping spacesDec 22 2016Dec 11 2018In this paper we will define an invariant $mc_{\infty}(f)$ of maps $f:X \rightarrow Y_{\mathbb{Q}}$ between a finite CW-complex and a rational space $Y_{\mathbb{Q}}$. We prove that this invariant is complete, i.e. $mc_{\infty}(f)=mc_{\infty}(g)$ if an ... 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
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
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.
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
Non-Contact Measurement of Thermal Diffusivity in Ion-Implanted Nuclear MaterialsMay 21 2015Knowledge of mechanical and physical property evolution due to irradiation damage is essential for the development of future fission and fusion reactors. Ion-irradiation provides an excellent proxy for studying irradiation damage, allowing high damage ... More
On Iterated Dominance, Matrix Elimination, and Matched PathsJan 04 2010Feb 03 2010We study computational problems arising from the iterated removal of weakly dominated actions in anonymous games. Our main result shows that it is NP-complete to decide whether an anonymous game with three actions can be solved via iterated weak dominance. ... More
Recognizing Members of the Tournament Equilibrium Set is NP-hardNov 19 2007Jan 07 2008A recurring theme in the mathematical social sciences is how to select the "most desirable" elements given a binary dominance relation on a set of alternatives. Schwartz's tournament equilibrium set (TEQ) ranks among the most intriguing, but also among ... More
Measuring Slepton Masses and Mixings at the LHCOct 08 2009Dec 21 2009Flavor physics may help us understand theories beyond the standard model. In the context of supersymmetry, if we can measure the masses and mixings of sleptons and squarks, we may learn something about supersymmetry and supersymmetry breaking. Here we ... 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
Quasilinear SPDEs via rough pathsMay 31 2016We consider the variable-coefficient uniformly parabolic PDE \begin{equation*} \partial_2u+a(u)\partial_1^2u=\sigma(u)f \end{equation*} with a right hand side $f$ which is only controlled in the low regularity norm of $ C^{\alpha-2}$ for $\alpha > \frac{2}{3}$ ... More
The Regularized Hadamard ExpansionAug 15 2017Aug 29 2017A local expansion is proposed for two-point distributions involving an ultraviolet regularization in a globally hyperbolic space-time. The regularization is described by an infinite number of functions which can be computed iteratively by solving transport ... More
Tilings and matroids on regular subdivisions of a triangleFeb 15 2018Nov 19 2018In this paper we investigate a family of matroids introduced by Ardila and Billey to study one-dimensional intersections of complete flag arrangements of $\mathbb{C}^n$. The set of lattice points $P_n$ inside the equilateral triangle $S_n$ obtained by ... More
Towards an Analytic Construction of the Wavefunction of Boson StarsJun 13 2017Jan 11 2018Light scalar fields can form gravitationally bound compact objects called boson stars. The profile of boson stars in the Newtonian limit is described by the Gross-Pitaevskii-Poisson equations. We present a semi-analytic solution to these equations and ... More
A locally conservative reduced flux reconstruction for elliptic problemsMar 21 2019In the context of model order reduction of parametric elliptic problems, we present a methodology to reconstruct a conforming flux from a given reduced solution, that is locally conservative with respect to the underlying finite element grid. All components ... More
Spanning trees in randomly perturbed graphsMar 13 2018A classical result of Koml\'os, S\'ark\"ozy and Szemer\'edi states that every $n$-vertex graph with minimum degree at least $(1/2+ o(1))n$ contains every $n$-vertex tree with maximum degree $O(n/\log{n})$ as a subgraph, and the bounds on the degree conditions ... More
Heavy Neutral Leptons at FASERJan 26 2018May 24 2018We study the prospects for discovering heavy neutral leptons at ForwArd Search ExpeRiment (FASER), the newly proposed detector at the LHC. Previous studies showed that a relatively small detector with ~10 m length and ~1 m cross sectional area can probe ... More
Simulating the Injection of Magnetized Plasma without Electromagnetic Precursor WaveOct 11 2017Injecting magnetized plasma with changes in magnetization or injection rate necessitate a time variable magnetic field at the boundary of the simulation box. Naive implementation will lead to electromagnetic precursor waves that can affect the simulation ... More
Data-Driven Microstructure Property RelationsMar 26 2019An image based prediction of the effective heat conductivity for highly heterogeneous microstructured materials is presented. The synthetic materials under consideration show different inclusion morphology, orientation, volume fraction and topology. The ... More
On annealed elliptic Green function estimatesJan 13 2014Jan 18 2014We consider a random, uniformly elliptic coefficient field $a$ on the lattice $\mathbb{Z}^d$. The distribution $\langle \cdot \rangle$ of the coefficient field is assumed to be stationary. Delmotte and Deuschel showed that the gradient and second mixed ... More
Annealed estimates on the Green functionApr 16 2013Jan 13 2014We consider a random, uniformly elliptic coefficient field $a(x)$ on the $d$-dimensional integer lattice $\mathbb{Z}^d$. We are interested in the spatial decay of the quenched elliptic Green function $G(a;x,y)$. Next to stationarity, we assume that the ... More
On a game on graphsFeb 22 2013We start with the well-known game below: Two players hold a sheet of paper to their forehead on which a positive integer is written. The numbers are consecutive and each player can only see the number of the other one. In each time step, they either say ... More
Intuitionistic implication makes model checking hardJul 11 2011Apr 25 2012We investigate the complexity of the model checking problem for intuitionistic and modal propositional logics over transitive Kripke models. More specific, we consider intuitionistic logic IPC, basic propositional logic BPL, formal propositional logic ... More
Simplicial blowups and discrete normal surfaces in simpcompMay 26 2011simpcomp is an extension to GAP, the well known system for computational discrete algebra. It allows the user to work with simplicial complexes. In the latest version, support for simplicial blowups and discrete normal surfaces was added, both features ... More
Approximation in $L^p(μ)$ with deep ReLU neural networksApr 09 2019We discuss the expressive power of neural networks which use the non-smooth ReLU activation function $\varrho(x) = \max\{0,x\}$ by analyzing the approximation theoretic properties of such networks. The existing results mainly fall into two categories: ... More
Theoretical results on the Universe structureJun 14 2004This paper discusses an ordinary homogeneous differential equation of the second order with constant real-valued coefficients. The solution of this equation has to satisfy additional conditions. The first of the conditions stems from the analytical research ... More
Restricting unipotent characters in special orthogonal groupsSep 24 2013For all prime powers q we restrict the unipotent characters of the special orthogonal groups SO_5(q) and SO_7(q) to a maximal parabolic subgroup. We determine all irreducible constituents of these restrictions for SO_5(q) and a large part of the irreducible ... More
Local sampling and approximation of operators with bandlimited Kohn-Nirenberg symbolsNov 26 2012Oct 19 2013Recent sampling theorems allow for the recovery of operators with bandlimited Kohn-Nirenberg symbols from their response to a single discretely supported identifier signal. The available results are inherently non-local. For example, we show that in order ... More