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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

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

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

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

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

Stellarators close to quasisymmetryJul 12 2013Feb 06 2014Rotation is favorable for confinement, but a stellarator can rotate at high speeds if and only if it is sufficiently close to quasisymmetry. This article investigates how close it needs to be. For a magnetic field $\mathbf{B} = \mathbf{B}_0 + \alpha \mathbf{B}_1$, ... More

Stellarator impurity flux driven by electric fields tangent to magnetic surfacesMar 15 2018Oct 16 2018The control of impurity accumulation is one of the main challenges for future stellarator fusion reactors. The standard argument to explain this accumulation relies on the, in principle, large inward pinch in the neoclassical impurity flux caused by the ... 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

The effect of tangential drifts on neoclassical transport in stellarators close to omnigeneityOct 19 2016Mar 10 2017In general, the orbit-averaged radial magnetic drift of trapped particles in stellarators is non-zero due to the three-dimensional nature of the magnetic field. Stellarators in which the orbit-averaged radial magnetic drift vanishes are called omnigeneous, ... 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

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 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.

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

On the thermodynamic aspect of zinc oxide polymorphism. Calorimetric study of metastable rock salt ZnOJun 11 2017The enthalpies of dissolution of metastable rock salt and thermodynamically stable wurtzite polymorphs of zinc oxide in aqueous H2SO4 have been measured in direct calorimetric experiments at 303 K and 0.1 MPa and the obtained results enabled determination ... 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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

Phenomenology of Enhanced Light Quark Yukawa Couplings and the $W^\pm h$ Charge AsymmetrySep 21 2016Feb 10 2017I 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

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

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

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

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 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

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

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

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

Rapid flipping of parametric phase statesMay 28 2019Since the invention of the solid-state transistor, the overwhelming majority of computers followed the von Neumann architecture that strictly separates logic operations and memory. Today, there is a revived interest in alternative computation models accompanied ... 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

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

Peering Through the Muck: Notes on the Influence of the Galactic Interstellar Medium on Extragalactic ObservationsNov 17 2003This paper considers some effects of foreground Galactic gas on radiation received from extragalactic objects, with an emphasis on the use of the 21cm line to determine the total N(HI). In general, the opacity of the 21cm line makes it impossible to derive ... More

Evolution of plasma turbulence excited with particle beamsSep 04 2012Sep 12 2012Particles ejected from the Sun that stream through the surrounding plasma of the solar wind are causing instabilities. These generate wavemodes in a certain frequency range especially within shock regions, where particles are accelerated. The aim of this ... More

Polymer state approximations of Schroedinger wave functionsJun 21 2006Aug 25 2006It is shown how states of a quantum mechanical particle in the Schroedinger representation can be approximated by states in the so-called polymer representation. The result may shed some light on the semiclassical limit of loop quantum gravity.

A note on Gorenstein spacesDec 23 2018Associated with an augmented differential graded algebra $R= R^{\geq 0}$ is a homotopy invariant ${\mathcal T}(R)$. This is a graded vector space, and if $H^0(R)$ is the ground field and $H^{>N}(R)= 0$ then dim$\, {\mathcal T}(R)= 1$ if and only if $H(R)$ ... 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

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

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

Stable and robust sampling strategies for compressive imagingOct 08 2012Oct 21 2013In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples. For such applications, overwhelming empirical evidence suggests that ... More

Generators with a closure relationSep 17 2013Assume that a block operator of the form $\left(\begin{smallmatrix}A_{1}\\A_{2}\quad 0\end{smallmatrix}\right)$, acting on the Banach space $X_{1}\times X_{2}$, generates a contraction $C_{0}$-semigroup. We show that the operator $A_{S}$ defined by $A_{S}x=A_{1}\left(\begin{smallmatrix}x\\SA_{2}x\end{smallmatrix}\right)$ ... More

Quantitative results on the corrector equation in stochastic homogenizationSep 02 2014We derive optimal estimates in stochastic homogenization of linear elliptic equations in divergence form in dimensions $d\ge 2$. In previous works we studied the model problem of a discrete elliptic equation on $\mathbb{Z}^d$. Under the assumption that ... 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

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

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

Finite Strain Homogenization Using a Reduced Basis and Efficient SamplingApr 01 2019May 28 2019The computational homogenization of hyperelastic solids in the geometrically nonlinear context has yet to be treated with sufficient efficiency in order to allow for real-world applications in true multiscale settings. This problem is addressed by a problem-specific ... More

Independent individual addressing of multiple neutral atom qubits with a MEMS beam steering systemJun 14 2010We demonstrate a scalable approach to addressing multiple atomic qubits for use in quantum information processing. Individually trapped 87Rb atoms in a linear array are selectively manipulated with a single laser guided by a MEMS beam steering system. ... 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

A Variety of Decays of Gamma-Ray Burst PulsesFeb 23 2001We find and study a variety of the spectral-temporal behavior during the decay phase of the light curve of long and bright pulse structures in gamma-ray bursts. It was earlier found that for about half of these decays, the instantaneous photon flux is ... More

On the Time Evolution of Gamma-Ray Burst Pulses: A Self-Consistent DescriptionDec 16 1999For the first time, the consequences of combining two well-established empirical relations, describing different aspects of the spectral evolution of observed gamma-ray burst (GRB) pulses, are explored. These empirical relations are: i) the hardness-intensity ... More

New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry PropertySep 03 2010Feb 11 2011Consider an m by N matrix Phi with the Restricted Isometry Property of order k and level delta, that is, the norm of any k-sparse vector in R^N is preserved to within a multiplicative factor of 1 +- delta under application of Phi. We show that by randomizing ... More

GPU-accelerated simulation of colloidal suspensions with direct hydrodynamic interactionsMay 29 2012Solvent-mediated hydrodynamic interactions between colloidal particles can significantly alter their dynamics. We discuss the implementation of Stokesian dynamics in leading approximation for streaming processors as provided by the compute unified device ... More

A Simplified Scheme for GUT-inspired Theories with Multiple Abelian FactorsJul 14 2011Jan 09 2012Grand Unified Theories often involve additional Abelian group factors apart from the standard model hypercharge, that generally lead to loop-induced mixing gauge kinetic terms. In this letter, we show that at the one-loop level this effect can be avoided ... More

High energy gamma rays from the massive black hole in the Galactic CenterAug 17 2004Accreting black holes are believed to be sites of possible particle acceleration with favorable conditions also for effective gamma-ray production. However, because of photon-photon pair production, only low energy (MeV) gamma-rays can escape these compact ... More

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

A-posteriori error estimates for the localized reduced basis multi-scale methodJan 28 2014May 27 2014We present a localized a-posteriori error estimate for the localized reduced basis multi-scale (LRBMS) method [Albrecht, Haasdonk, Kaulmann, Ohlberger (2012): The localized reduced basis multiscale method]. The LRBMS is a combination of numerical multi-scale ... More

Anomaly-free Model Building with Algebraic GeometryFeb 22 2019We present a method to find anomaly-free gauged Froggatt-Nielsen type models using results from algebraic geometry. These methods should be of general interest for model building beyond the Standard Model (SM) when rational charges are required. We consider ... More

Bounds on the Coefficients of Tension and Flow PolynomialsApr 20 2010The goal of this article is to obtain bounds on the coefficients of modular and integral flow and tension polynomials of graphs. To this end we make use of the fact that these polynomials can be realized as Ehrhart polynomials of inside-out polytopes. ... More

Gaussian rational points on a singular cubic surfaceMay 13 2011Apr 12 2012Manin's conjecture predicts the asymptotic behavior of the number of rational points of bounded height on algebraic varieties. For toric varieties, it was proved by Batyrev and Tschinkel via height zeta functions and an application of the Poisson formula. ... More

Analysis vs. synthesis sparsity for $α$-shearletsFeb 12 2017There are two notions of sparsity associated to a frame $\Psi=(\psi_i)_{i\in I}$: Analysis sparsity of $f$ means that the analysis coefficients $(\langle f,\psi_i\rangle)_i$ are sparse, while synthesis sparsity means that $f=\sum_i c_i\psi_i$ with sparse ... More

Exponential stability for a coupled system of damped-undamped plate equationsFeb 02 2017We consider the transmission problem for a coupled system of undamped and structurally damped plate equations in two sufficiently smooth and bounded subdomains. It is shown that, independently of the size of the damped part, the damping is strong enough ... More

Modelling the emission from blazar jets - the case of PKS 2155-304May 27 2010A time-dependent Synchrotron Self Compton model (SSC) which is able to motivate the used electron spectra of many SSC models as a balance of acceleration and radiative losses is introduced. Using stochastic acceleration as well as Fermi-I processes even ... More

Can Remote Observing be Good Observing? Reflections on Procrustes and AntaeusJul 06 2005Remote observing seeks to simulate the presence of the astronomer at the telescope. While this is useful, and necessary in some circumstances, simulation is not reality. The drive to abstract the astronomer from the instrument can have unpleasant consequences, ... More

The Hydrogen Clouds in the Galactic HaloNov 10 2003New 21cm observations with the Green Bank Telescope show that a significant fraction of the HI in the inner Galaxy's halo 1 kpc from the midplane exists in the form of discrete clouds. Some look very much like a Spitzer ``standard'' diffuse cloud but ... More

Complex Line Bundles over Simplicial Complexes and their ApplicationsJun 25 2015Jan 18 2017Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete classification of discrete ... More

The magnetization ripple: a nonlocal stochastic PDE perspectiveSep 05 2017The magnetization ripple is a microstructure formed by the magnetization in a thin-film ferromagnet. It is triggered by the random orientation of the grains in the poly-crystalline material. In an approximation of the micromagnetic model, which is sketched ... More

Optimal artificial boundary condition for random elliptic mediaMar 26 2018We are given a uniformly elliptic coefficient field that we regard as a realization of a stationary and finite-range (say, range unity) ensemble of coefficient fields. Given a (deterministic) right-hand-side supported in a ball of size $\ell\gg 1$ and ... More

Dispersive mixed-order systems in $L^p$-Sobolev spaces and application to the thermoelastic plate equationOct 31 2016Feb 02 2018We study dispersive mixed-order systems of pseudodifferential operators in the setting of $L^p$-Sobolev spaces. Under the weak condition of quasi-hyperbolicity, these operators generate a semigroup in the space of tempered distributions. However, if the ... More

Brakke's inequality for the thresholding schemeAug 10 2017Jun 10 2018We continue our analysis of the thresholding scheme from the variational viewpoint and prove a conditional convergence result towards Brakke's notion of mean curvature flow. Our proof is based on a localized version of the minimizing movements interpretation ... More

Convergence of the thresholding scheme for multi-phase mean-curvature flowFeb 18 2016Aug 19 2016We consider the thresholding scheme, a time discretization for mean curvature flow introduced by Merriman, Bence and Osher. We prove a convergence result in the multi-phase case. The result establishes convergence towards a weak formulation of mean curvature ... More

Less than one implies zeroOct 23 2013Feb 13 2015In this paper we show that from the estimate $\sup_{t \geq 0}\|C(t) - \cos(at)I\| <1$ we can conclude that $C(t)$ equals $\cos(at) I$. Here $\left(C(t)\right)_{t \geq 0}$ is a strongly continuous cosine family on a Banach space.

Weakly admissible $H^{\infty}(\C_{-})$-calculus on general Banach spacesJul 26 2012We show that, given a Banach space and a generator of an exponentially stable $C_{0}$-semigroup, a weakly admissible operator $g(A)$ can be defined for any $g$ bounded, analytic function on the left half-plane. This yields an (unbounded) functional calculus. ... More

Error control for the localized reduced basis multi-scale method with adaptive on-line enrichmentJan 21 2015Feb 06 2015In this contribution we consider localized, robust and efficient a-posteriori error estimation of the localized reduced basis multi-scale (LRBMS) method for parametric elliptic problems with possibly heterogeneous diffusion coefficient. The numerical ... More

Galactic Sources of High-Energy Neutrinos: HighlightsDec 16 2011We overview high-energy neutrinos from galactic sources, transparent to their gamma-ray emission. We focus on young supernova remnants and in particular on RX J1713.7-3946, discussing expectations and upper bounds. We also consider the possibility to ... More

Hamiltonian submanifolds of regular polytopesSep 24 2008Apr 21 2009We investigate polyhedral $2k$-manifolds as subcomplexes of the boundary complex of a regular polytope. We call such a subcomplex {\it $k$-Hamiltonian} if it contains the full $k$-skeleton of the polytope. Since the case of the cube is well known and ... More

Socle pairings on tautological ringsMar 29 2013Mar 30 2019We study some aspects of the $\lambda_g$ pairing on the tautological ring of $M_g^c$, the moduli space of genus $g$ stable curves of compact type. We consider pairing kappa classes with pure boundary strata, all tautological classes supported on the boundary, ... More