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Automated Variational Inference in Probabilistic ProgrammingJan 07 2013We present a new algorithm for approximate inference in probabilistic programs, based on a stochastic gradient for variational programs. This method is efficient without restrictions on the probabilistic program; it is particularly practical for distributions ... More

RDCI: A novel method of cluster analysis and applications thereof in sample molecular simulationsJun 14 2013A novel method, termed Reduced Dimensionality Cluster Identification, RDCI, is presented, for the identification and quantitative description of clusters formed by N objects in three dimensional space. The method consists of finding a path, as short as ... More

Correlation Decay in Random Decision NetworksDec 02 2009We consider a decision network on an undirected graph in which each node corresponds to a decision variable, and each node and edge of the graph is associated with a reward function whose value depends only on the variables of the corresponding nodes. ... More

Learning and Querying Fast Generative Models for Reinforcement LearningFeb 08 2018A key challenge in model-based reinforcement learning (RL) is to synthesize computationally efficient and accurate environment models. We show that carefully designed generative models that learn and operate on compact state representations, so-called ... More

Deep Reinforcement Learning in Large Discrete Action SpacesDec 24 2015Apr 04 2016Being able to reason in an environment with a large number of discrete actions is essential to bringing reinforcement learning to a larger class of problems. Recommender systems, industrial plants and language models are only some of the many real-world ... More

Gradient Estimation Using Stochastic Computation GraphsJun 17 2015Jan 05 2016In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external world. Estimating ... More

POLYANA - A tool for the calculation of molecular radial distribution functions based on Molecular Dynamics trajectoriesMay 11 2015We present an application for the calculation of radial distribution functions for molecular centres of mass, based on trajectories generated by molecular simulation methods (Molecular Dynamics, Monte Carlo). When designing this application, the emphasis ... More

Energy-Momentum Localization for a Space-Time Geometry Exterior to a Black Hole in the Brane WorldAug 22 2011May 20 2012In general relativity one of the most fundamental issues consists in defining a generally acceptable definition for the energy-momentum density. As a consequence, many coordinate-dependent definitions have been presented, whereby some of them utilize ... More

Woulda, Coulda, Shoulda: Counterfactually-Guided Policy SearchNov 15 2018Learning policies on data synthesized by models can in principle quench the thirst of reinforcement learning algorithms for large amounts of real experience, which is often costly to acquire. However, simulating plausible experience de novo is a hard ... More

Attend, Infer, Repeat: Fast Scene Understanding with Generative ModelsMar 28 2016Aug 12 2016We present a framework for efficient inference in structured image models that explicitly reason about objects. We achieve this by performing probabilistic inference using a recurrent neural network that attends to scene elements and processes them one ... More

Curvature Estimates for Critical 4-Manifolds with a Lower Ricci Curvature BoundSep 12 2013We draw elliptic regularity results for 4-manifolds with an elliptic system, without Sobolev constant control. Direct use of analysis is circumvented; the results come mainly through geometric and topological arguments. In contrast to our previous paper, ... More

Strategies for Addressing Spreadsheet Compliance ChallengesNov 29 2007Most organizations today use spreadsheets in some form or another to support critical business processes. However the financial resources, and developmental rigor dedicated to them are often minor in comparison to other enterprise technology. The increasing ... More

Regularity and convergence of 4-dimensional extremal Kahler metricsApr 16 2011May 10 2011We establish a regularity result for the metric on any 4-dimensional extremal K\"ahler manifold, and a weak compactness theorem on the space of such metrics. Specifically, the sectional curvature at a point is bounded when the quantity $L^2(|\Riem|)$ ... More

Analysis of aggregated tick returns: evidence for anomalous diffusionJun 18 2006Jun 20 2006In order to investigate the origin of large price fluctuations, we analyze stock price changes of ten frequently traded NASDAQ stocks in the year 2002. Though the influence of the trading frequency on the aggregate return in a certain time interval is ... More

On Mean Values of Dirichlet PolynomialsJul 28 2009We show a general lower bound for Mean-value of Dirichlet polynomials

Fine and hyperfine structure in different bound systemsSep 02 2005We demonstrate that the generalized Gell-Mann-Low theorem permits for a systematic expansion around the nonrelativistic limit when applied to bound states in the Wick-Cutkosky model, Yukawa theory, and QED (in Coulomb gauge). We apply this expansion to ... More

Analysis of the physical Laplacian and the heat flow on a locally finite graphJan 05 2008Jan 01 2010We study the physical Laplacian and the corresponding heat flow on an infinite, locally finite graph with possibly unbounded valence.

Weights in the cohomology of toric varietiesJan 27 2003Jun 16 2004We describe the weight filtration in the cohomology of toric varieties. We present a role of the Frobenius automorphism in an elementary way. We prove that equivariant intersection homology of an arbitrary toric variety is pure. We obtain results concerning ... More

Internal algebra classifiers as codescent objects of crossed internal categoriesMar 26 2015Nov 17 2015Inspired by recent work of Batanin and Berger on the homotopy theory of operads, a general monad-theoretic context for speaking about structures within structures is presented, and the problem of constructing the universal ambient structure containing ... More

Operads within monoidal pseudo algebrasOct 08 2004A general notion of operad is given, which includes as instances, the operads originally conceived to study loop spaces, as well as the higher operads that arise in the globular approach to higher dimensional algebra. In the framework of this paper, one ... More

$L^p$-Spectral theory of locally symmetric spaces with $Q$-rank oneJul 17 2007We study the $L^p$-spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces $M=\Gamma\backslash X$ with finite volume and arithmetic fundamental group $\Gamma$ whose universal covering $X$ is a symmetric space of non-compact ... More

Nuclear and High-Energy AstrophysicsJul 01 2002There has never been a more exciting time in the overlapping areas of nuclear physics, particle physics and relativistic astrophysics than today. Orbiting observatories such as the Hubble Space Telescope, Rossi X-ray Timing Explorer (RXTE), Chandra X-ray ... More

From Neutron Stars to Strange StarsDec 04 2001This paper discusses several most intruigung astrophysical implications connected with the possible absolute stability of strange quark matter.This is followed by a discussion of two astrophysical signals that may point at the existence of quark matter ... More

From Boson Condensation to Quark Deconfinement: The Many Faces of Neutron Star InteriorsOct 20 1999Gravity compresses the matter in the cores of neutron stars to densities which are significantly higher than the density of ordinary atomic nuclei, thus providing a high-pressure environment in which numerous particle processes - from the generation of ... More

On C*-Algebras Generated by Isometries with Twisted Commutation RelationsJul 12 2012In the theory of C*-algebras, interesting noncommutative structures arise as deformations of the tensor product. For instance, the rotation algebra may be seen as a scalar twist deformation of the tensor product of the functions on the circle with itself. ... More

Conley pairs in geometry - Lusternik-Schnirelmann theory and moreSep 14 2017Firstly, we wish to motivate that Conley pairs, realized via Salamon's definition [17], are rather useful building blocks in geometry: Initially we met Conley pairs in an attempt to construct Morse filtrations of free loop spaces [21]. From this fell ... More

Polynomials in categories with pullbacksJun 10 2011May 21 2015The theory developed by Gambino and Kock, of polynomials over a locally cartesian closed category E, is generalised for E just having pullbacks. The 2-categorical analogue of the theory of polynomials and polynomial functors is given, and its relationship ... More

Energy and Asymptotics of Ricci-Flat 4-Manifolds with a Killing FieldAug 22 2013Given a complete, Ricci-flat 4-manifold with a Killing field, we give an estimate on the manifold's energy in terms of a certain asymptotic quantity of the Killing field. If the Killing field has no zeros and satisfies a certain asymptotic condition, ... More

Hybrid Branching-Time LogicsAug 13 2007Hybrid branching-time logics are introduced as extensions of CTL-like logics with state variables and the downarrow-binder. Following recent work in the linear framework, only logics with a single variable are considered. The expressive power and the ... More

SILEM : a new gaseous detector with integrated x-y readout planeJun 11 2007This works reports on gaseous detectors developments made in the frame of the EXO double-beta decay experiment. LEM (Large Electron Multiplication) are electron amplification grids based on GEM. They were developed in Neuchatel and showed remarquable ... More

Pure homology of algebraic varietiesFeb 27 2003Sep 07 2003We show that for a complete complex algebraic variety the pure component of homology coincides with the image of intersection homology. Therefore pure homology is topologically invariant. To obtain slightly more general results we introduce "image homology" ... More

Residue forms on singular hypersurfacesJan 27 2003Apr 05 2005The purpose of this paper is to point out a relation between the canonical sheaf and the intersection complex of a singular algebraic variety. We focus on the hypersurface case. Let $M$ be a complex manifold, $X\subset M$ a singular hypersurface. We study ... More

Formality of equivariant intersection cohomologyJan 23 2001Dec 18 2001We present several approaches to equivariant intersection cohomology. We show that for a complete algebraic variety acted by a connected algebraic group $G$ it is a free module over $H^*(BG)$. The result follows from the decomposition theorem or from ... More

On the short time asymptotic of the stochastic Allen-Cahn equationAug 05 2009A description of the short time behavior of solutions of the Allen-Cahn equation with a smoothened additive noise is presented. The key result is that in the sharp interface limit solutions move according to motion by mean curvature with an additional ... More

Computing equivariant characteristic classes of singular varietiesAug 04 2013The paper is based on a talk. Complete exposition is given in "Equivariant Hirzebruch class for singular varieties". Starting from the classical theory we describe Hirzebruch class and the related Todd genus of a complex singular algebraic varieties. ... More

Equivariant Chern classes and localization theoremOct 25 2011Jun 06 2012For a complex variety with a torus action we propose a new method of computing Chern-Schwartz-MacPherson classes. The method does not apply resolution of singularities. It is based on Localization Theorem in equivariant cohomology.

A Sharp Estimate for Divisors of Bernoulli SumsAug 14 2009Let $S_n=\e_1+...+\e_n$, where $ \e_i $ are i.i.d. Bernoulli r.v.'s. Let $0\le r_d(n)<2d$ be the least residue of $n$ mod$(2d)$, $\bar r_d(n)= 2d -r_d(n)$ and $\b(n,d)=\max ({1\over d}, {1\over \sqrt n})[e^{- {r_d(n)^2/2 n}} +e^{- {\bar r_d(n)^2/2 n}}]$. ... More

Operads as polynomial 2-monadsDec 24 2014Nov 17 2015In this article we give a construction of a polynomial 2-monad from an operad and describe the algebras of the 2-monads which then arise. This construction is different from the standard construction of a monad from an operad in that the algebras of our ... More

Star Products that can not be induced by Drinfel'd TwistsAug 08 2016This is the final version of my master thesis. I prove that there are no twist star products on the 2-sphere and on the higher genus pretzel surfaces deforming a symplectic structure. One of the key arguments is that a connected compact symplectic manifold ... More

The infrared fixed point of Landau gauge Yang-Mills theoryNov 07 2012Over the last decade, the infrared behavior of Yang-Mills theory in the Landau gauge has been scrutinized with the help of Dyson-Schwinger equations and lattice calculations. In this contribution, we describe a technically simple approach to the deep ... More

A bound for Mean values of Fourier transformsMay 16 2011We show that there exists a sequence $\{n_k, k\ge 1\}$ growing at least geometrically such that for any finite non-negative measure $\nu$ such that $\hat \nu\ge 0$, any $T>0$, $$ \int_{-2^{n_k} T}^{2^{n_k} T} \hat \nu(x) \dd x \ll_\e T\,2^{2^{(1+\e)n_k}} ... More

Convergence rates of finite difference schemes for the linear advection and wave equation with rough coefficientJul 02 2016We prove convergence rates of explicit finite difference schemes for the linear advection and wave equation in one space dimension with H\"older continuous coefficient. The obtained convergence rates explicitly depend on the H\"older regularity of the ... More

Optimal Control of the Two-Dimensional Vlasov-Maxwell SystemSep 26 2018The time evolution of a collisionless plasma is modeled by the Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We only consider a 'two-dimensional' version of the problem ... More

Topological Methods in the Quest for Periodic OrbitsFeb 18 2018These are lecture notes on Floer and Rabinowitz-Floer homology written for a graduate course at UNICAMP August-December 2016 and a mini-course held at IMPA in August 2017.

A product estimate, the parabolic Weyl lemma and applicationsOct 14 2009We prove a product estimate that allows to estimate the quadratic first order nonlinearity of the harmonic map flow in the $L^p$ norm. Then the parabolic analogue of Weyl's lemma for the Lapace operator is established. Both results are applied to prove ... More

Partition C*-algebras II - Links to Compact Matrix Quantum GroupsOct 24 2017In a recent article, we gave a definition of partition C*-algebras. These are universal C*-algebras based on algebraic relations which are induced from partitions of sets. In this follow up article, we show that often we can associate a Hopf algebra structure ... More

Divisors of Bernoulli sumsMar 23 2007Feb 22 2008We study the asymptotic behavior of the sums of divisors when the integers are modelled with the Bernoulli random walk; We prealably study the correlation properties of the corresponding system.

Morse homology for the heat flowMar 23 2010We use the heat flow on the loop space of a closed Riemannian manifold to construct an algebraic chain complex. The chain groups are generated by perturbed closed geodesics. The boundary operator is defined in the spirit of Floer theory by counting, modulo ... More

Stable foliations and semi-flow Morse homologyAug 17 2014In case of the heat flow on the free loop space of a closed Riemannian manifold non-triviality of Morse homology for semi-flows is established by constructing a natural isomorphism to singular homology of the loop space. The construction is also new in ... More

Convergence of compact Ricci solitonsApr 07 2008We show that sequences of compact gradient Ricci solitons converge to complete orbifold gradient solitons, assuming constraints on volume, the $L^{n/2}$-norm of curvature, and the auxiliary constant $C_1$. The strongest results are in dimension 4, where ... More

Determination of the Dark Matter profile from the EGRET excess of diffuse Galactic gamma radiationOct 26 2007The excess above 1 GeV in the energy spectrum of the diffuse Galactic gamma radiation, measured with the EGRET experiment, can be interpreted as the annihilation of Dark Matter (DM) particles. The DM is distributed in a halo around the Milky Way. Considering ... More

Classification of polytope metrics and complete scalar-flat Kähler 4-Manifolds with two symmetriesSep 15 2015We study unbounded 2-dimensional metric polytopes such as those arising as K\"ahler quotients of complete K\"ahler 4-manifolds with two commuting symmetries and zero scalar curvature. Under a mild closedness condition, we obtain a complete classification ... More

Supremum of Random Dirichlet Polynomials with Sub-multiplicative CoefficientsApr 15 2009We study the supremum of random Dirichlet polynomials $D_N(t)=\sum_{n=1}^N\varepsilon_n d(n) n^{- s}$, where $(\varepsilon_n)$ is a sequence of independent Rademacher random variables, and $ d $ is a sub-multiplicative function. The approach is gaussian ... More

Relativistic Bound StatesAug 27 2003In this contribution, I will give a brief survey of present techniques to treat the bound state problem in relativistic quantum field theories. In particular, I will discuss the Bethe-Salpeter equation, various quasi-potential equations, the Feynman-Schwinger ... More

Search for excited fermions in ep collisions at HERAJul 15 2002Heavy excited electrons and neutrinos have been sought by the H1 and ZEUS experiments at HERA. For the e* (nu*) searches, 120 pb^-1 (16 pb^-1) of ep collision data have been analysed. No evidence for any excited lepton has been found, and limits on the ... More

Bloch-Wilson Hamiltonian and a Generalization of the Gell-Mann-Low TheoremNov 25 1999The effective Hamiltonian introduced many years ago by Bloch and generalized later by Wilson, appears to be the ideal starting point for Hamiltonian perturbation theory in quantum field theory. The present contribution derives the Bloch-Wilson Hamiltonian ... More

A Morphism of Intersection Homology and Hard LefschetzJan 05 1999We consider a possibility of the existence of intersection homology morphism, which would be associated to a map of analytic varieties. We assume that the map is an inclusion of codimension one. Then the existence of a morphism follows from Saito's decomposition ... More

A morphism of intersection homology induced by an algebraic mapDec 30 1997Let $f:X-->Y$ be a map of algebraic varieties. Barthel, Brasselet, Fieseler, Gabber and Kaup have shown that there exists a homomorphism of intersection homology groups $f^*:IH^*(Y)-->IH^*(X)$ compatible with the induced homomorphism on cohomology. The ... More

The Anderson-Weber strategy is not optimal for symmetric rendezvous search on K4Dec 03 2009We consider the symmetric rendezvous search game on a complete graph of n locations. In 1990, Anderson and Weber proposed a strategy in which, over successive blocks of n-1 steps, the players independently choose either to stay at their initial location ... More

Multitensors as monads on categories of enriched graphsJun 10 2011Sep 17 2013In this paper we unify previous developments on higher operads and multitensors into a single framework in which the interplay between multitensors on a category V, and monads on the category of graphs enriched in V, is taken as fundamental. The material ... More

Algebraic Kan extensions along morphisms of internal algebra classifiersNov 16 2015Nov 26 2015An algebraic left Kan extension is a left Kan extension which interacts well with the algebraic structure present in the given situation, and these appear in various subjects such as the homotopy theory of operads and in the study of conformal field theories. ... More

The Morse-Witten complex via dynamical systemsNov 21 2004Oct 26 2005Given a smooth closed manifold M, the Morse-Witten complex associated to a Morse function f and a Riemannian metric g on M consists of chain groups generated by the critical points of f and a boundary operator counting isolated flow lines of the negative ... More

A backward $λ$-Lemma for the forward heat flowOct 15 2012Feb 07 2014The inclination or $\lambda$-Lemma is a fundamental tool in finite dimensional hyperbolic dynamics. In contrast to finite dimension, we consider the forward semi-flow on the loop space of a closed Riemannian manifold $M$ provided by the heat flow. The ... More

Hirzebruch class and Bialynicki-Birula decompositionNov 24 2014Nov 23 2015Suppose an algebraic torus acts on a complex algebraic variety $X$. Then a great part of information about global invariants of $X$ are encoded in some data localized around the fixed points. The goal of this note is to present a connection between two ... More

Purity of boundaries of open complex varietiesJun 06 2012We study the boundary of an open smooth complex algebraic variety $U$. We ask when the cohomology of the geometric boundary $Z=X\setminus U$ in a smooth compactification $X$ is pure with respect to the mixed Hodge structure. Knowing the dimension of singularity ... More

Criteria of Divergence Almost Everywhere in Ergodic TheoryFeb 29 2016In this expository paper, we survey nowadays classical tools or criteria used in problems of convergence everywhere to build counterexamples: the Stein continuity principle, Bourgain's entropy criteria and Kakutani-Rochlin lemma, most classical device ... More

Instants of small amplitude of Brownian motion and application to the Kubilius modelOct 14 2010Let $W(t), t\ge 0$ be standard Brownian motion. We study the size of the time intervals $I$ which are admissible for the long range of slow increase, namely given a real $z>0$, $$ \sup_{t\in I}{|W(t)|\over \sqrt t} \le z, $$ and we estimate their number ... More

Strict 2-toposesJun 16 2006A 2-categorical generalisation of elementary topos is provided and some of the properties of the yoneda structure it generates are explored. Examples relevant to the globular approach to higher category theory are discussed. This paper also contains some ... More

Cauchy Means of Dirichlet polynomialsDec 25 2014We study Cauchy means of Dirichlet polynomials $$\int_\R \Big|\sum_{n=1}^N \frac{1}{ n^{\s+ ist}} \Big|^{2q} \frac{\dd t}{\pi( t^2+1)}.$$ These integrals were investigated when $q=1,\s= 1, s=1/2 $ by Wilf, using integral operator theory and Widom's eigenvalue ... More

On the Translation Invariance of Wavelet SubspacesSep 22 1999An examination of the translation invariance of $V_0$ under dyadic rationals is presented, generating a new equivalence relation on the collection of wavelets. The equivalence classes under this relation are completely characterized in terms of the support ... More

Harnack Inequalities for Critical 4-manifolds with a Ricci Curvature BoundSep 03 2013Sep 12 2013We study critical Riemannian 4-manifolds with a lower bound on Ricci curvature, but no a priori analytic constraints such as on Sobolev constants. We derive elliptic-type estimates for the local curvature radius, which itself controls sectional curvature. ... More

Generalized Kahler Taub-NUTs and Two Exceptional InstantonsFeb 19 2016We study the one-parameter family of twisted Kahler Taub-NUT metrics (discovered by Donaldson), along with two exceptional Taub-NUT-like instantons, and understand them to the extend that is sufficient for blow-up and gluing-type arguments. In particular ... More

Muonium spectrum beyond the nonrelativistic limitJan 09 2008A generalization of the Gell-Mann-Low theorem is applied to the antimuon-electron system. The bound state spectrum is extracted numerically. As a result, fine and hyperfine structure are reproduced correctly near the nonrelativistic limit (and for arbitrary ... More

Tensor products of recurrent hypercyclic semigroupsOct 01 2008Oct 26 2008We study tensor products of strongly continuous semigroups on Banach spaces that satisfy the hypercyclicity criterion, the recurrent hypercyclicity criterion or are chaotic.

On torsion in homology of singular toric varietiesSep 19 2005Let $X$ be a toric variety. Rationally Borel-Moore homology of $X$ is isomorphic to the homology of the Koszul complex $A^T_*(X)\otimes \Lambda^\x M$, where $A^T_*(X)$ is the equivariant Chow group and $M$ is the character group of $T$. Moreover, the ... More

Orthogonal Frames of TranslatesOct 10 2003Two Bessel sequences are orthogonal if the composition of the synthesis operator of one sequence with the analysis operator of the other sequence is the 0 operator. We characterize when two Bessel sequences are orthogonal when the Bessel sequences have ... More

On an identity of Ky FanApr 09 2008We give several applications of an identity for sums of weakly stationary sequences due to Ky Fan.

The Geometry of Sampling on Unions of LatticesAug 26 2003In this short note we show two results concerning sampling translation invariant subspaces of $\ltwod$ on unions of lattices. The first result shows that the sampling transform on a union of lattices is a constant times an isometry if and only if the ... More

Leray spectral sequence for complements of certain arrangements of smooth submanifoldsMay 06 2015Let Z be an arrangement of submanifolds in a complex compact algebraic manifold X. We allow some kind of singular intersections. We consider the Leray spectral sequence of the embedding of the U=X-Z into X and formulate a condition sufficient for degeneration ... More

Free Products of Higher Operad AlgebrasSep 25 2009One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2-categories. In this paper we continue the developments of [3] and [2] by understanding the natural generalisations ... More

The infrared fixed point of Landau gauge Yang-Mills theory: A renormalization group analysisMay 02 2012The infrared behavior of gluon and ghost propagators in Landau gauge Yang-Mills theory has been at the center of an intense debate over the last decade. Different solutions of the Dyson-Schwinger equations show a different behavior of the propagators ... More

Low-degree Cohomology of Integral Specht ModulesMay 26 2009We introduce a way of describing cohomology of the symmetric groups with coefficients in Specht modules over Z or F_p. We study i-th-degree cohomology for i in {0,1,2}. The focus lies on the isomorphism type of second-degree cohomology of integral Specht ... More

Strange Quark Matter and Compact StarsJul 07 2004Sep 27 2004Astrophysicists distinguish between three different types of compact stars. These are white dwarfs, neutron stars, and black holes. The former contain matter in one of the densest forms found in the Universe which, together with the unprecedented progress ... More

On the classification of easy quantum groupsJan 23 2012Dec 05 2013In 2009, Banica and Speicher began to study the compact quantum subgroups of the free orthogonal quantum group containing the symmetric group S_n. They focused on those whose intertwiner spaces are induced by some partitions. These so-called easy quantum ... More

Idiomatic and Reproducible Software Builds using Containers for Reliable ComputingFeb 09 2017Containers as the unit of application delivery are the 'next big thing' in the software development world. They enable developers to create an executable image containing an application bundled with all its dependencies which a user can run inside a controlled ... More

Equivariant stratifold homology theoriesJun 22 2006We define equivariant homology theories using bordism of stratifolds with a G-action, where G is a discrete group. Stratifolds are a generalization of smooth manifolds which were introduced by Kreck. He defines homology theories using bordism of suitable ... More

Euler homologyJun 22 2006We geometrically construct a homology theory that generalizes the Euler characteristic mod 2 to objects in the unoriented cobordism ring N_*(X) of a topological space X. This homology theory Eh_* has coefficients Z/2 in every nonnegative dimension. There ... More

Classical Morse theory revisited I -- Backward $λ$-Lemma and homotopy typeOct 03 2014Jan 29 2016We introduce two tools, dynamical thickening and flow selectors, to overcome the infamous discontinuity of the gradient flow endpoint map near non-degenerate critical points. More precisely, we interpret the stable fibrations of certain Conley pairs $(N,L)$, ... More

The backward λ-Lemma and Morse filtrationsNov 09 2012Mar 16 2013Consider the infinite dimensional hyperbolic dynamical system provided by the (forward) heat semi-flow on the loop space of a closed Riemannian manifold M. We use the recently discovered backward {\lambda}-Lemma and elements of Conley theory to construct ... More

Perturbed closed geodesics are periodic orbits: Index and TransversalityMay 17 2001We study the classical action functional $\SMC_V$ on the free loop space of a closed, finite dimensional Riemannian manifold $M$ and the symplectic action $\AMC_V$ on the free loop space of its cotangent bundle. The critical points of both functionals ... More

Sharp interface limit for invariant measures of a stochastic Allen-Cahn equationAug 19 2009The invariant measure of a one-dimensional Allen-Cahn equation with an additive space-time white noise is studied. This measure is absolutely continuous with respect to a Brownian bridge with a density which can be interpreted as a potential energy term. ... More

Dirichlet polynomials: some old and recent results, and their interplay in number theoryJul 28 2009Dec 01 2009In the first part of this expository paper, we present and discuss the interplay of Dirichlet polynomials in some classical problems of number theory, notably the Lindel\"of Hypothesis. We review some typical properties of their means and continue with ... More

An extended type system with lambda-typed lambda-expressionsMar 21 2018We present the system $\mathtt{d}$, an extended type system with lambda-typed lambda-expressions. It is related to type systems originating from the Automath project. $\mathtt{d}$ extends existing lambda-typed systems by an existential abstraction operator ... More

Weak Solutions of the Relativistic Vlasov-Maxwell System with External CurrentsFeb 07 2019The time evolution of a collisionless plasma is modeled by the relativistic Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We consider the case that the plasma consists of ... More

$\boldsymbol L^{\boldsymbol 1}$-Norm of Steinhaus chaose on the polydiscNov 26 2014Let $J_n\subset[1,n]$, $n=1,2,\ldots$ be increasing sets of mutually coprime numbers. Under reasonable conditions on the coefficient sequence $\{c^j_n\}_{n,j}$, we show that $$ \lim_{T\to \infty}\frac{1}{T} \int_{0}^T \Big| \sum_{j\in J_n} c^j_n\,j^{it}\Big| ... More

Robertson Type Theorems for FramesAug 14 2001We extend Robertson's theorem to apply to frames generated by the action of a discrete, countable abelian unitary group. Within this setup we use Stone's theorem and the theory of spectral multiplicity to analyze wandering frame collections. Motivated ... More

Applications of the Wavelet Multiplicity FunctionSep 22 1999This paper examines the wavelet multiplicity function. An explicit formula for the multiplicity function is derived. An application to operator interpolation is then presented. We conclude with several remarks regarding the wavelet connectivity problem. ... More

First betti numbers of Kähler manifolds with weakly pseudoconvex boundaryOct 20 2011We study K\"ahler manifolds-with-boundary, not necessarily compact, with weakly pseudoconvex boundary, each component of which is compact. If such a manifold $K$ has $l\ge2$ boundary components (possibly $l=\infty$), it has first betti number at least ... More

Local Suprema of Dirichlet Polynomials and Zerofree Regions of the Riemann Zeta-FunctionMay 21 2010Mar 13 2012A new zerofree region of the Riemann Zeta-function $\zeta$ is identified by using Tur\'an's localization criterion linking zeros of $\zeta$ with uniform local suprema of sets of Dirichlet polynomials expanded over the primes. The proof is based on a randomization ... More

Measurement of Boson Self Couplings at LEP and Search for AnomaliesMay 10 2002Jun 12 2002With center of mass energies up to 209 GeV of LEP II, massive W and Z bosons can be produced in pairs and jointly with photons. This allows to study boson-boson couplings. Since the W and Z bosons are unstable and decay into fermions, two- and four-fermion ... More