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Improving the Coverage and the Generalization Ability of Neural Word Sense Disambiguation through Hypernymy and Hyponymy RelationshipsNov 02 2018In Word Sense Disambiguation (WSD), the predominant approach generally involves a supervised system trained on sense annotated corpora. The limited quantity of such corpora however restricts the coverage and the performance of these systems. In this article, ... More

Automatic Quality Assessment for Speech Translation Using Joint ASR and MT FeaturesSep 20 2016This paper addresses automatic quality assessment of spoken language translation (SLT). This relatively new task is defined and formalized as a sequence labeling problem where each word in the SLT hypothesis is tagged as good or bad according to a large ... More

Disentangling ASR and MT Errors in Speech TranslationSep 03 2017The main aim of this paper is to investigate automatic quality assessment for spoken language translation (SLT). More precisely, we investigate SLT errors that can be due to transcription (ASR) or to translation (MT) modules. This paper investigates automatic ... More

Sense Vocabulary Compression through the Semantic Knowledge of WordNet for Neural Word Sense DisambiguationMay 14 2019In this article, we tackle the issue of the limited quantity of manually sense annotated corpora for the task of word sense disambiguation, by exploiting the semantic relationships between senses such as synonymy, hypernymy and hyponymy, in order to compress ... More

Analyzing Learned Representations of a Deep ASR Performance Prediction ModelAug 26 2018Aug 28 2018This paper addresses a relatively new task: prediction of ASR performance on unseen broadcast programs. In a previous paper, we presented an ASR performance prediction system using CNNs that encode both text (ASR transcript) and speech, in order to predict ... More

Quantum spin pumping with adiabatically modulated magnetic barrier'sMar 29 2003Dec 09 2003A quantum pump device involving magnetic barriers produced by the deposition of ferro magnetic stripes on hetero-structure's is investigated. The device for dc- transport does not provide spin-polarized currents, but in the adiabatic regime, when one ... More

On smooth Gorenstein polytopesMar 08 2013A Gorenstein polytope of index r is a lattice polytope whose r-th dilate is a reflexive polytope. These objects are of interest in combinatorial commutative algebra and enumerative combinatorics, and play a crucial role in Batyrev's and Borisov's computation ... More

Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noiseJul 11 2018We prove the path-by-path well-posedness of stochastic porous media and fast diffusion equations driven by linear, multiplicative noise. As a consequence, we obtain the existence of a random dynamical system. This solves an open problem raised in [Barbu, ... More

A bound for the splitting of smooth Fano polytopes with many verticesSep 25 2014Aug 10 2015The classification of toric Fano manifolds with large Picard number corresponds to the classification of smooth Fano polytopes with large number of vertices. A smooth Fano polytope is a polytope that contains the origin in its interior such that the vertex ... More

Discriminants of stable rank two sheaves on some general type surfacesDec 05 2018Jan 10 2019We prove sharp bounds on the discriminants of stable rank two sheaves on surfaces in three-dimensional projective space. The key technical ingredient is to study them as torsion sheaves in projective space via tilt stability in the derived category. We ... More

The Kernel Quantum Probabilities (KQP) LibraryMar 27 2012Mar 30 2012In this document, we show how the different quantities necessary to compute kernel quantum probabilities can be computed. This document form the basis of the implementation of the Kernel Quantum Probability (KQP) open source project

Smooth Rational Surfaces in Calabi-Yau FourfoldsOct 13 2016Hartshorne conjectured and Ellingsrud-Peskine proved that the smooth rational surfaces in $\mathbb{P}^4$ belong to only finitely many families. We formulate and study a collection of analogous problems in which $\mathbb{P}^4$ is replaced by a smooth fourfold ... More

A structural approach to the locality of pseudovarieties of the form $\mathbf{LH} m \mathbf{V}$Dec 18 2006We show that if $\mathbf H$ is a Fitting pseudovariety of groups and $\mathbf V$ is a local pseudovariety of monoids, then $\mathbf {LH}m \mathbf V$ is local if either $\mathbf V$ contains the six element Brandt monoid, or $\mathbf H$ is a non-trivial ... More

Möbius Functions and Semigroup Representation Theory II: Character formulas and multiplicitiesJul 22 2006Nov 26 2007We generalize the character formulas for multiplicities of irreducible constituents from group theory to semigroup theory using Rota's theory of M\"obius inversion. The technique works for a large class of semigroups including: inverse semigroups, semigroups ... More

Topological dynamics and recognition of languagesJun 06 2013We define compact automata and show that every language has a unique minimal compact automaton. We also define recognition of languages by compact left semitopological monoids and construct the analogue of the syntactic monoid in this context. For rational ... More

An existing, ecologically-successful genus of collectively intelligent artificial creaturesApr 18 2012People sometimes worry about the Singularity [Vinge, 1993; Kurzweil, 2005], or about the world being taken over by artificially intelligent robots. I believe the risks of these are very small. However, few people recognize that we already share our world ... More

Iwasawa theory of Heegner points on abelian varieties of GL_2 typeFeb 28 2012In an earlier paper the author proved one divisibility of Perrin- Riou's Iwasawa main conjecture for Heegner points on elliptic curves. In the present paper, that result is generalized to abelian varieties of GL2-type (i.e. abelian varieties with real ... More

Complex multiplication cycles and Kudla-Rapoport divisors IIMar 03 2013Jul 26 2014This paper is about the arithmetic of Kudla-Rapoport divisors on Shimura varieties of type GU(n-1,1). In the first part of the paper we construct a toroidal compactification of N. Kramer's integral model of the Shimura variety. This extends work of K.-W. ... More

Intersection theory on Shimura surfacesFeb 28 2012Kudla has proposed a general program to relate arithmetic intersection multiplicities of special cycles on Shimura varieties to Fourier coefficients of Eisenstein series. The lowest dimensional case, in which one intersects two codimension one cycles ... More

Supersymmetry - When Theory Inspires Experimental SearchesJan 24 2014Feb 05 2014We review, in the first part of this work, many pioneering works on supersymmetry and organize these results to show how supersymmetric quantum field theories arise from spin-statistics, N{\oe}ther and a series of no-go theorems. We then introduce the ... More

Half-balanced braided monoidal categories and Teichmueller groupoids in genus zeroSep 14 2010Sep 16 2010We introduce the notions of a half-balanced braided monoidal category and of its contraction. These notions give rise to an explicit description of the action of the Galois group of QQ on Teichmueller groupoids in genus 0, equivalent to that of L. Schneps. ... More

Smooth projective planesDec 27 2004Mar 04 2008Using symplectic topology and the Radon transform, we prove that smooth 4-dimensional projective planes are diffeomorphic to $\mathbb{CP}^2$. We define the notion of a plane curve in a smooth projective plane, show that plane curves in high dimensional ... More

Complete projective connectionsApr 05 2005May 27 2006The first examples of complete projective connections are uncovered: normal projective connections on surfaces whose geodesics are all closed and embedded are complete, as are normal projective connections induced from complete affine connections with ... More

Holographic CheckerboardsJul 03 2014Sep 30 2014We construct cohomogeneity-three, finite temperature stationary black brane solutions dual to a field theory exhibiting checkerboard order. The checkerboards form a backreacted part of the bulk solution, and are obtained numerically from the coupled Einstein-Maxwell-scalar ... More

A geometrical dual to relativistic Bohmian mechanics - the multi particle caseJan 27 2009In this article it is shown that the fundamental equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of curved space-time. We further generalize the results to interactions ... More

Relativistic Bohmian mechanics from scalar gravityOct 15 2008Jan 22 2009In this article we show that the fundamental equations of relativistic Bohmian mechanics for a single particle can be derived from a scalar theory of curved space-time.

Formal loops, Tate objects and tangent Lie algebrasNov 29 2014Feb 24 2015If $M$ is a symplectic manifold then the space of smooth loops $\mathrm C^{\infty}(\mathrm S^1,M)$ inherits of a quasi-symplectic form. We will focus in this thesis on an algebraic analogue of that result. Kapranov and Vasserot introduced and studied ... More

Calculus on manifolds of conformal maps and CFTApr 01 2010Aug 03 2012In conformal field theory (CFT) on simply connected domains of the Riemann sphere, the natural conformal symmetries under self-maps are extended, in a certain way, to local symmetries under general conformal maps, and this is at the basis of the powerful ... More

Bi-partite entanglement entropy in massive two-dimensional quantum field theoryMar 13 2008Nov 12 2008Recently, Cardy, Castro Alvaredo and the author obtained the first exponential correction to saturation of the bi-partite entanglement entropy at large region length, in massive two-dimensional integrable quantum field theory. It only depends on the particle ... More

Fabrication of micro-magnetic traps for cold neutral atomsMay 13 2003Many proposals for quantum information processing require precise control over the motion of neutral atoms, as in the manipulation of coherent matter waves or the confinement and localization of individual atoms. Patterns of micron-sized wires, fabricated ... More

Localization and lattice fermionsNov 01 2005I review how the phenomenology of localization applies to fermions in lattice gauge theory, present measurements of the localization length and other quantities, and discuss the consequences for things like the overlap kernel.

The Ising model and bubbles in the quark-gluon plasmaJul 28 1997I review evidence for the stability of bubbles in the quark-gluon plasma near the confinement phase transition. In analogy with the much-studied oil-water emulsions, this raises the possibility that there are many phases between the pure plasma and the ... More

Separate Constraints on Early and Late CosmologyDec 19 2013Since the public release of Planck data, several attempts have been made to explain the observed small tensions with other data-sets, most of them involving an extension of the {\Lambda}CDM Model. We try here an alternative approach to the data analysis, ... More

Twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphsOct 25 2013To each finitely aligned higher-rank graph $\Lambda$ and each $\mathbb{T}$-valued 2-cocycle on $\Lambda$, we associate a family of twisted relative Cuntz-Krieger algebras. We show that each of these algebras carries a gauge action, and prove a gauge-invariant ... More

Limits of dark energy measurements from CMB lensing-ISW-galaxy count correlationsNov 14 2004Mar 10 2005I discuss several issues that arise when trying to constrain the dark energy equation of state using correlations of the integrated Sachs-Wolfe effect with galaxy counts and lensing of the cosmic microwave background. These techniques are complementary ... More

A Refined Count of BPS States in the D1/D5 SystemOct 24 2016We examine the low-lying quarter BPS spectrum of a 2d conformal field theory with target Sym$^N(K3)$ at various points in the moduli space, and look at a more refined count than the ordinary elliptic genus. We compute growth of the spectrum at both the ... More

A Short Proof of Strassen's Theorem Using Convex AnalysisMar 01 2016We give a simple proof of Strassen's theorem on stochastic dominance using linear programming duality, without requiring measure-theoretic arguments. The result extends to generalized inequalities using conic optimization duality and provides an additional, ... More

Fast computation of all maximum acyclic agreement forests for two rooted binary phylogenetic treesDec 17 2015Evolutionary scenarios displaying reticulation events are often represented by rooted phylogenetic networks. Due to biological reasons, those events occur very rarely, and, thus, networks containing a minimum number of such events, so-called minimum hybridization ... More

Refinements of the orthogonality relations for blocksNov 20 2015For a block B of a finite group G there are well-known orthogonality relations for the generalized decomposition numbers. We refine these relations by expressing the generalized decomposition numbers with respect to an integral basis of a certain cyclotomic ... More

Performance of a measurement-driven 'adiabatic-like' quantum 3-SAT solverSep 02 2015I describe one quantum approach to solving 3-satisfiability (3-SAT), the well known problem in computer science. The approach is based on repeatedly measuring the truth value of the clauses forming the 3-SAT proposition using a non-orthogonal basis. If ... More

On a theorem of BlichfeldtJun 08 2016Let $G$ be a permutation group on $n<\infty$ objects. Let $f(g)$ be the number of fixed points of $g\in G$, and let $\{f(g):1\ne g\in G\}=\{f_1,\ldots,f_r\}$. In this expository note we give a character-free proof of a theorem of Blichfeldt which asserts ... More

Optimal Parameter Settings for the $(1+(λ, λ))$ Genetic AlgorithmApr 04 2016Jul 29 2016The $(1+(\lambda,\lambda))$ genetic algorithm is one of the few algorithms for which a super-constant speed-up through the use of crossover could be proven. So far, this algorithm has been used with parameters based also on intuitive considerations. In ... More

Nonlinear conductivity and the ringdown of currents in metallic holographyJun 10 2016Oct 10 2016We study the electric and heat current response resulting from an electric field quench in a holographic model of momentum relaxation at nonzero charge density. After turning the electric field off, currents return to equilibrium as governed by the vector ... More

Homogenization of pathwise Hamilton-Jacobi equationsApr 30 2016Nov 10 2016We present qualitative and quantitative homogenization results for pathwise Hamilton-Jacobi equations with "rough" multiplicative driving signals. When there is only one such signal and the Hamiltonian is convex, we show that the equation, as well as ... More

Multichroic TES Bolometers and Galaxy Cluster Mass Scaling Relations with the South Pole TelescopeJan 20 2016The South Pole Telescope (SPT) is a high-resolution microwave-frequency telescope designed to observe the Cosmic Microwave Background (CMB). To date, two cameras have been installed on the SPT to conduct two surveys of the CMB, the first in intensity ... More

Formal Contact CategoriesNov 15 2015To each oriented surface S, we associate a differential graded category Ko(S). The homotopy category Ho(Ko(S)) is a triangulated category which satisfies properties akin to those of the contact categories studied by K. Honda. These categories are also ... More

Observable Effects of Noncommutative Spacetime on the Hydrogen AtomJan 30 2006We present a brief historical introduction to the motivations behind quantum mechanics and quantum field theory on noncommutative spacetime and provide an insightful technique, readily accessible to the undergraduate student, to examine the measurable ... More

Characterizing Hilbert modular cusp forms by coefficient sizeMay 18 2012Associated to an (adelic) Hilbert modular form is a sequence of `Fourier coefficients' which uniquely determine the form. In this paper we characterize Hilbert modular cusp forms by the size of their Fourier coefficients. This answers in the affirmative ... More

Every continuous action of a compact group on a uniquely arcwise connected continuum has a fixed pointSep 04 2017Dec 22 2017We are dealing with the question whether every group or semigroup action (with some additional property) on a continuum (with some additional property) has a fixed point. One of such results was given in 2009 by Shi and Sun. They proved that every nilpotent ... More

The Eigenvalue Point Process for Symmetric Group Permutation Representations on $k$-tuplesJan 20 2019Equip the symmetric group $\mathfrak{S}_n$ with the Ewens distribution. We study the eigenvalue point process of the permutation representation of $\mathfrak{S}_n$ on $k$-tuples of distinct integers chosen from the set $\{1,2,...,n\}$. Taking $n \to \infty$, ... More

Pseudo Frobenius numbersDec 21 2018For a prime p, we call a positive integer n a Frobenius p-number if there exists a finite group with exactly n subgroups of order p^a for some $a\ge 0$. Extending previous results on Sylow's theorem, we prove in this paper that every Frobenius p-number ... More

Heavy-quark production with $k_t$-factorization: The importance of the sea-quark distributionDec 05 2018Apr 09 2019We discuss the fact that $k_t$-factorization calculations for heavy-quark production include only the $gg\rightarrow Q\bar{Q}$ contribution. The cases of fixed-flavor-number scheme and variable-flavor-number scheme calculations are analyzed separately. ... More

On decomposable correlation matricesDec 04 2018Correlation matrices (positive semidefinite matrices with ones on the diagonal) are of fundamental interest in quantum information theory. In this work we introduce and study the set of $r$-decomposable correlation matrices: those that can be written ... More

Unsupervised learning with sparse space-and-time autoencodersNov 26 2018We use spatially-sparse two, three and four dimensional convolutional autoencoder networks to model sparse structures in 2D space, 3D space, and 3+1=4 dimensional space-time. We evaluate the resulting latent spaces by testing their usefulness for downstream ... More

Physical chemistry of charged interfaces: Multiscale modelling and applications to EnergyNov 22 2018We present the advantages of a multiscale modelling strategy for the understanding of systems with charged interfaces. On the one hand, one can simulate a complex system at different levels, depending on the relevant length and time scales for a given ... More

Morita Equivalent Blocks of Symmetric GroupsSep 20 2018A well-known result of Scopes states that there are only finitely many Morita equivalence classes of $p$-blocks of symmetric groups with a given weight (or defect). In this note we investigate a lower bound on the number of those Morita equivalence classes. ... More

Bounding the number of characters in a block of a finite groupJul 22 2018We present a strong upper bound on the number k(B) of irreducible characters of a p-block B of a finite group G in terms of local invariants. More precisely, the bound depends on a chosen major B-subsection (u,b), its normalizer N_G(\langle u\rangle,b) ... More

Families of explicitly isogenous Jacobians of variable-separated curvesSep 08 2010We construct six infinite series of families of pairs of curves (X,Y) of arbitrarily high genus, defined over number fields, together with an explicit isogeny from the Jacobian of X to the Jacobian of Y splitting multiplication by 2, 3, or 4. For each ... More

Easy scalar decompositions for efficient scalar multiplication on elliptic curves and genus 2 JacobiansOct 19 2013The first step in elliptic curve scalar multiplication algorithms based on scalar decompositions using efficient endomorphisms-including Gallant-Lambert-Vanstone (GLV) and Galbraith-Lin-Scott (GLS) multiplication, as well as higher-dimensional and higher-genus ... More

Computing low-degree isogenies in genus 2 with the Dolgachev-Lehavi methodOct 13 2011Jan 26 2012Let ell be a prime, and H a curve of genus 2 over a field k of characteristic not 2 or ell. If S is a maximal Weil-isotropic subgroup of Jac(H)[ell], then Jac(H)/S is isomorphic to the Jacobian of some (possibly reducible) curve X. We investigate the ... More

Semigroup Actions, Covering Spaces and Schutzenberger GroupsMay 29 2009We associate a 2-complex to the following data: a presentation of a semigroup $S$ and a transitive action of $S$ on a set $V$ by partial transformations. The automorphism group of the action acts properly discontinuously on this 2-complex. A sufficient ... More

2-Blocks with minimal nonabelian defect groupsDec 08 2010We study numerical invariants of 2-blocks with minimal nonabelian defect groups. These groups were classified by R\'edei. If the defect group is also metacyclic, then the block invariants are known. In the remaining cases there are only two (infinite) ... More

The Dynkin diagrams of rational double pointsJun 06 2005Rational double points are the simplest surface singularities. In this essay we will be mainly concerned with the geometry of the exceptional set corresponding to the resolution of a rational double point. We will derive the classification of rational ... More

Squishing dimers on the hexagon latticeAug 13 2008We describe an operation on dimer configurations on the hexagon lattice, called "squishing", and use this operation to explain some of the properties of dimer generating functions.

Computing Cohomology on Toric VarietiesSep 07 2011In these notes a recently developed technique for the computation of line bundle-valued sheaf cohomology group dimensions on toric varieties is reviewed. The key result is a vanishing theorem for the contributing components which depends on the structure ... More

Independence Complexes of Stable Kneser GraphsDec 03 2009For integers n\geq 1, k\geq 0, the stable Kneser graph SG_{n,k} (also called the Schrijver graph) has as vertex set the stable n-subsets of [2n+k] and as edges disjoint pairs of n-subsets, where a stable n-subset is one that does not contain any 2-subset ... More

Tangent of K-theoryApr 17 2019We show that the relative algebraic K-theory functor fully determines the absolute cyclic homology over any field k of characteristic 0. More precisely, we prove that the tangent of K-theory, in terms of (abelian) deformation problems over k, is cyclic ... More

Heavy Meson Physics: What have we learned in Twenty Years?Dec 30 2004Jan 04 2005I give a personal account of the development of the field of heavy quarks. After reviewing the experimental discovery of charm and bottom quarks, I describe how the field's focus shifted towards determination of CKM elements and how this has matured into ... More

Shape and soft functions of HQET and SCET in the 't Hooft ModelJul 13 2006Jul 14 2006The main application of Heavy Quark Effective Theory (HQET) and of Soft Collinear Effective Theory (SCET) is in establishing factorization theorems for exclusive and semi-inclusive decays of heavy mesons. However, the calculation of the soft factors from ... More

Coverings of Configurations, Prime Configurations, and OrbiconfigurationsApr 02 2019This exploratory paper considers the notion of a covering of a configuration. We consider prime configurations, those which cannot cover other configurations, before considering orbiconfigurations. These are a generalized notion of a configuration in ... More

Convergence of Siegel-Veech constantsDec 31 2016Oct 30 2017We show that for any weakly convergent sequence of ergodic $SL_2(\mathbb{R})$-invariant probability measures on a stratum of unit-area translation surfaces, the corresponding Siegel-Veech constants converge to the Siegel-Veech constant of the limit measure. ... More

A splitting formula for the spectral flow of the odd signature operator on 3-manifolds coupled to a path of SU(2) connectionsDec 09 2004Dec 21 2005We establish a splitting formula for the spectral flow of the odd signature operator on a closed 3-manifold M coupled to a path of SU(2) connections, provided M = S cup X, where S is the solid torus. It describes the spectral flow on M in terms of the ... More

On the structure of graphs excluding $K_{4}$, $W_{4}$, $K_{2,4}$ and one other graph as a rooted minorAug 11 2017In this paper we give structural characterizations of graphs not containing rooted $K_{4}$, $W_{4}$, $K_{2,4}$, and a graph we call $L$.

Multi-splits and tropical linear spaces from nested matroidsJul 10 2017In this paper we present an explicit combinatorial description of a special class of facets of the secondary polytopes of hypersimplices. These facets correspond to polytopal subdivisions called multi-splits. We show a relation between the cells in a ... More

A Theory of Transformation Monoids: Combinatorics and Representation TheoryApr 17 2010The aim of this paper is to develop a theory of finite transformation monoids and in particular to study primitive transformation monoids. We introduce the notion of orbitals and orbital digraphs for transformation monoids and prove a monoid version of ... More

A Tight Runtime Analysis for the cGA on Jump Functions---EDAs Can Cross Fitness Valleys at No Extra CostMar 26 2019We prove that the compact genetic algorithm (cGA) with hypothetical population size $\mu = \Omega(\sqrt n \log n) \cap \text{poly}(n)$ with high probability finds the optimum of any $n$-dimensional jump function with jump size $k < \frac 1 {20} \ln n$ ... More

Vulnerability Analysis of GWirelessAug 09 2015Wireless networking has become very popular in recent years due to the increase in adoption of mobile devices. As more and more employees demand for Wi-Fi access for their devices, more companies have been jumping onto the "Bring Your Own Device" (BYOD) ... More

Holomorphic geometric structures on Kaehler-Einstein manifoldsAug 07 2013Nov 23 2013We prove that the compact Kaehler manifolds with first Chern class nonnegative that admit holomorphic parabolic geometries are the flat bundles of rational homogeneous varieties over complex tori. We also prove that the compact Kaehler manifolds with ... More

Extension Phenomena for Holomorphic Geometric StructuresDec 12 2008Jun 08 2009The most commonly encountered types of complex analytic G-structures and Cartan geometries cannot have singularities of complex codimension 2 or more.

Effective Evolution Equations in Quantum PhysicsNov 29 2011In these notes, we review some recent mathematical results concerning the derivation of effective evolution equations from many body quantum mechanics. In particular, we discuss the emergence of the Hartree equation in the so-called mean field regime ... More

Effective equations for quantum dynamicsAug 01 2012We report on recent results concerning the derivation of effective evolution equations starting from many body quantum dynamics. In particular, we obtain rigorous derivations of nonlinear Hartree equations in the bosonic mean field limit, with precise ... More

Derivation of Effective Evolution Equations from Microscopic Quantum DynamicsJul 27 2008In these lecture notes we discuss recent progress in the rigorous derivation of effective evolution equations for the description of the dynamics of quantum mechanical many-body systems.

Global well-posedness for the defocusing, quintic nonlinear Schrödinger equation in one dimensionOct 20 2009In this paper, we prove global well-posedness for low regularity data for the one dimensional quintic defocusing nonlinear Schr\"odinger equation. We show that a unique solution exists for $u_{0} \in H^{s}(\mathbf{R})$, $s > {8/29}$. This improves the ... More

Improved almost Morawetz estimates for the cubic nonlinear Schrodinger equationSep 04 2009Sep 06 2009We prove global well-posedness for the cubic, defocusing, nonlinear Schr{\"o}dinger equation on $\mathbf{R}^{2}$ with data $u_{0} \in H^{s}(\mathbf{R}^{2})$, $s > 1/4$. We accomplish this by improving the almost Morawetz estimates in [9].

Wavelet decomposition techniques and Hardy inequalities for function spaces on cellular domainsJun 13 2013A rather tricky question is the construction of wavelet bases on domains for suitable function spaces (Sobolev, Besov, Triebel-Lizorkin type). In his monograph from 2008, Triebel presented an approach how to construct wavelet (Riesz) bases in function ... More

Atomic representations in function spaces and applications to pointwise multipliers and diffeomorphisms, a new approachNov 29 2011Sep 25 2012In Chapter 4 of [25] Triebel proved two theorems concerning pointwise multipliers and diffeomorphisms in function spaces of Besov and Triebel-Lizorkin type. In each case he presented two approaches, one via atoms and one via local means. While the approach ... More

Higher Laplacians on pseudo-Hermitian symmetric spacesOct 14 2014Let $X=G/H$ be a symmetric space for a real simple Lie group $G$, equipped with a $G$-invariant complex structure. Then, $X$ is a pseudo-Hermitian manifold, and in this geometric setting, higher Laplacians $L_m$ are defined for each positive integer $m$, ... More

Tangent Cones to TT VarietiesMay 29 2017As already done for the matrix case for example in [Joe Harris, Algebraic Geometry - A first course, p.256] we give a parametrization of the Bouligand tangent cone of the variety of tensors of bounded TT rank. We discuss how the proof generalizes to any ... More

Radial Subgradient MethodMar 27 2017Jul 25 2017We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different perspective, leading ... More

On a class of self-similar processes with stationary increments in higher order Wiener chaosesNov 19 2012Jul 31 2013We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise ... More

Modules over etale groupoid algebras as sheavesMay 31 2014The author has previously associated to each commutative ring with unit $\Bbbk$ and \'etale groupoid $\mathscr G$ with locally compact, Hausdorff, totally disconnected unit space a $\Bbbk$-algebra $\Bbbk\mathscr G$. The algebra $\Bbbk\mathscr G$ need ... More

Hilbert series of nearly holomorphic sections on generalized flag manifoldsMar 12 2014Apr 09 2014Let X=G/P be a complex flag manifold and E->X be a G-homogeneous holomorphic vector bundle. Fix a U-invariant Kaehler metric on X with U in G maximal compact. We study the sheaf of nearly holomorphic sections and show that the space of global nearly holomorphic ... More

Nearly holomorphic sections on compact Hermitian symmetric spacesSep 11 2012Let X be a K\"ahler manifold, and E be a Hermitian vector bundle on X. We investigate the space N(X,E) of nearly holomorphic sections in E, which generalizes the notion of nearly holomorphic functions introduced by Shimura. If X=U/K is a compact Hermitian ... More

Generic stabilisers for actions of reductive groupsJun 08 2015Oct 09 2015Let $G$ be a reductive algebraic group over an algebraically closed field and let $V$ be a quasi-projective $G$-variety. We prove that the set of points $v\in V$ such that ${\rm dim}(G_v)$ is minimal and $G_v$ is reductive is open. We also prove some ... More

Unique maximal Betti diagrams for Artinian Gorenstein $k$-algebras with the weak Lefschetz propertyNov 26 2018We give an alternate proof for a theorem of Migliore and Nagel. In particular, we show that if $\mathcal H$ is an SI-sequence, then the collection of Betti diagrams for all Artinian Gorenstein $k$-algebras with the weak Lefschetz property and Hilbert ... More

On the uniqueness of infinity-categorical enhancements of triangulated categoriesDec 04 2018Dec 20 2018We study the problem of when triangulated categories admit unique infinity-categorical enhancements. Our results use Lurie's theory of prestable infinity-categories to give conceptual proofs of, and in many cases strengthen, previous work on the subject ... More

Performance of algebraic multigrid methods for non-symmetric matrices arising in particle methodsMay 18 2009Oct 20 2009Large linear systems with sparse, non-symmetric matrices arise in the modeling of Markov chains or in the discretization of convection-diffusion problems. Due to their potential to solve sparse linear systems with an effort that is linear in the number ... More

Model reduction for transport-dominated problems via online adaptive bases and adaptive samplingDec 05 2018This work presents a model reduction approach for problems with coherent structures that propagate over time such as convection-dominated flows and wave-type phenomena. Traditional model reduction methods have difficulties with these transport-dominated ... More

A Hilbert space approach to approximate diagonals for locally compact quantum groupsOct 08 2014Nov 20 2014For a locally compact quantum group $\mathbb{G}$, the quantum group algebra $L^1(\mathbb{G})$ is operator amenable if and only if it has an operator bounded approximate diagonal. It is known that if $L^1(\mathbb{G})$ is operator biflat and has a bounded ... More