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Cold nuclear matter physics at forward rapidities from d+Au collisions in PHENIXSep 09 2011We present measurements by the PHENIX experiment at RHIC of di-hadron pair production in \dAu collisions where the particles in the pair are varied across a wide range of pseudorapidity, out to $\eta = 3.8$. With di-hadrons, varying the $p_T$ and rapidity ... More

On quadratic variation in the Skorokhod spaceApr 03 2017Jun 21 2018This paper has been withdrawn by the author. The most updated version can be accessed by arXiv:1806.07290.

Speech recognition for medical conversationsNov 20 2017Jun 20 2018In this work we explored building automatic speech recognition models for transcribing doctor patient conversation. We collected a large scale dataset of clinical conversations ($14,000$ hr), designed the task to represent the real word scenario, and ... More

Blazars in Context in the Fermi EraMar 20 2013Blazars are the most plentiful gamma-ray source at GeV energies, and despite detailed study, there is much that is not known about these sources. In this review I explore some recent results on blazars, including the controversy of the "blazar sequence", ... More

Sheaves, Cosheaves and ApplicationsMar 13 2013Dec 17 2014This thesis develops the theory of sheaves and cosheaves with an eye towards applications in science and engineering. To provide a theory that is computable, we focus on a combinatorial version of sheaves and cosheaves called cellular sheaves and cosheaves, ... More

Norm inequalities in generalized Morrey spacesMay 29 2012May 14 2014We prove that Calder\'on-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on weighted Morrey ... More

Topological Data Analysis and CosheavesNov 03 2014Mar 04 2015This paper contains an expository account of persistent homology and its usefulness for topological data analysis. An alternative foundation for level-set persistence is presented using sheaves and cosheaves.

The Mezard-Parisi equation for matchings in pseudo-dimension d>1Sep 09 2014We establish existence and uniqueness of the solution to the cavity equation for the random assignment problem in pseudo-dimension $d>1$, as conjectured by Aldous and Bandyopadhyay (Annals of Applied Probability, 2005) and W\"astlund (Annals of Mathematics, ... More

The interpolation method for random graphs with prescribed degreesApr 26 2014We consider large random graphs with prescribed degrees, such as those generated by the configuration model. In the regime where the empirical degree distribution approaches a limit $\mu$ with finite mean, we establish the systematic convergence of a ... More

Matroids: A Macaulay2 packageNov 14 2015We give an overview of the Macaulay2 package Matroids, which contains functionality to create and compute with matroids. Examples highlighting the use of all major functions in the package are provided, along with explanations of some of the algorithms. ... More

PDE Approaches to Graph AnalysisApr 30 2015This paper surveys and discusses recent work adapting partial differential equation (PDE) models to discrete structures.

Irreducibility of some quantum representations of mapping class groupsSep 22 1999The SU(2) TQFT representation of the mapping class group of a closed surface of genus g, at a root of unity of prime order, is shown to be irreducible. Some examples of reducible representations are also given.

Exotic Branes from del Pezzo SurfacesApr 10 2019We revisit a correspondence between toroidal compactifications of M-theory and del Pezzo surfaces, in which rational curves on the del Pezzo are related to ${1\over 2}$-BPS branes of the corresponding compactification. We argue that curves of higher genus ... More

The Thompson-Lyons transfer lemma for fusion systemsMar 24 2013Apr 25 2014In this note, a generalization of the Thompson transfer lemma and its various extensions, most recently due to Lyons, is proven in the context of saturated fusion systems. A strengthening of Alperin's fusion theorem is also given in this setting, following ... More

The big projective module as a nearby cycles sheafNov 30 2014Aug 22 2016We give a new geometric construction of the big projective module in the principal block of the BGG category $\mathscr{O}$, or rather the corresponding $\mathscr{D}$-module on the flag variety. Namely, given a one-parameter family of nondegenerate additive ... More

Invertible sums of matricesMar 22 2016Apr 19 2016We give an elementary proof of a Caratheodory-type result on the invertibility of a sum of matrices, due first to Facchini and Barioli. The proof yields a polynomial identity, expressing the determinant of a large sum of matrices in terms of determinants ... More

Mono: an algebraic study of torus closuresOct 12 2017Given an ideal I in a polynomial ring, we consider the largest monomial subideal contained in I, denoted mono(I). We study mono as an interesting operation in its own right, guided by questions that arise from comparing the Betti tables of I and mono(I). ... More

Closed points on schemesAug 22 2017This brief note gives a survey on results relating to existence of closed points on schemes, including an elementary topological characterization of the schemes with (at least one) closed point.

Topology of eigenspace posets for unitary reflection groupsAug 09 2012Apr 02 2013The eigenspace theory of unitary reflection groups, initiated by Springer and Lehrer, suggests that the following object is worthy of study: the poset of eigenspaces of elements of a unitary reflection group, for a fixed eigenvalue, ordered by the reverse ... More

Generating mapping class groups with elements of fixed finite orderOct 12 2017We show that for any $k$ at least $6$ and $g$ sufficiently large, the mapping class group of a surface of genus $g$ can be generated by three elements of order $k$. We also show that this can be done with four elements of order $5$. We additionally prove ... More

Brace Bar-Cobar DualitySep 11 2013Sep 12 2013Using Kadeishvili's formulas with appropriate signs, we show that the classical cobar construction from coalgebras to algebras \Omega: CoAlg -> Alg can be enhanced to a functor from Hopf algebras to E_2 algebras (for a certain choice of E_2 operad) \Omega ... More

Seeking the Principles of Sustainable Software EngineeringMay 18 2014Jul 22 2014Like other engineering disciplines, software engineering should also have principles to guide the construction of sustainable computer applications. Tangible properties include a) unlimited scalability, b) maximal reproducibility, and c) optimizable energy ... More

Fibrations on four-folds with trivial canonical bundlesApr 01 2009Four-folds with trivial canonical bundles are divided into six classes according to their holonomy group. We consider examples that are fibred by abelian surfaces over the projective plane. We construct such fibrations in five of the six classes, and ... More

Desingularization of a steady vortex pair in the lake equationNov 17 2017We construct a family of steady solutions of the lake model perturbed by some small Coriolis force, that converge to a singular vortex pair. The desingularized solutions are obtained by maximization of the kinetic energy over a class of rearrangements ... More

Satellite-Mounted Light Sources as Photometric Calibration Standards for Ground-Based TelescopesJan 27 2011A significant and growing portion of systematic error on a number of fundamental parameters in astrophysics and cosmology is due to uncertainties from absolute photometric and flux standards. A path toward achieving major reduction in such uncertainties ... More

Combinatorially Generated Piecewise Activation FunctionsMay 17 2016In the neuroevolution literature, research has primarily focused on evolving the number of nodes, connections, and weights in artificial neural networks. Few attempts have been made to evolve activation functions. Research in evolving activation functions ... More

On the Negative $K$-theory of Singular VarietiesJun 16 2013Let $X$ be an $n$-dimensional variety over a field $k$ of characteristic zero, regular in codimension 1 with singular locus $Z$. In this paper we study the negative $K$-theory of $X$, showing that when $Z$ is sufficiently nice, $K_{1-n}(X)$ is an extension ... More

Up-down asymmetric tokamaksNov 21 2016Bulk toroidal rotation has proven capable of stabilising both dangerous MHD modes and turbulence. In this thesis, we explore a method to drive rotation in large tokamaks: up-down asymmetry in the magnetic equilibrium. We seek to maximise this rotation ... More

Every totally real algebraic integer is a tree eigenvalueFeb 18 2013Sep 04 2014Graph eigenvalues are examples of totally real algebraic integers, i.e. roots of real-rooted monic polynomials with integer coefficients. Conversely, the fact that every totally real algebraic integer occurs as an eigenvalue of some finite graph is a ... More

Compton Dominance and the Blazar SequenceDec 04 2012Does the "blazar sequence" exist, or is it a result of a selection effect, due to the difficulty in measuring the redshifts of blazars with both high synchrotron peak frequencies (\gtrsim 10^{15} Hz) and luminosities (\gtrsim 10^{46} erg s^{-1})? We explore ... More

The cavity method for counting spanning subgraphs subject to local constraintsMar 16 2011Using the theory of negative association for measures and the notion of random weak limits of sparse graphs, we establish the validity of the cavity method for counting spanning subgraphs subject to local constraints in asymptotically tree-like graphs. ... More

Rozansky-Witten theoryDec 19 2001Rozansky and Witten proposed in 1996 a family of new three-dimensional topological quantum field theories, indexed by compact (or asymptotically flat) hyperkaehler manifolds. As a byproduct they proved that hyperkaehler manifolds also give rise to Vassiliev ... More

A finiteness theorem for Lagrangian fibrationsDec 28 2012We consider (holomorphic) Lagrangian fibrations X->P^n that satisfy some natural hypotheses. We prove that there are only finitely many such Lagrangian fibrations up to deformation.

Intrinsic square functions on functions spaces including weighted Morrey spacesMay 01 2012Apr 16 2013We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley $g^{\ast}_{\lambda}$-function as defined by Wilson, are bounded in a class of function spaces include weighted Morrey spaces. The corresponding commutators ... More

Product of functions in $\BMO$ and $\H^{1}$ in non-homogeneous spacesJun 27 2009Aug 11 2010Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition and may not be doubling, we define the product of functions in the regular $BMO$ and the atomic block $\H^{1}$ in the sense of ... More

Homology representations of unitary reflection groupsMar 21 2013Apr 02 2013This paper continues the study of the poset of eigenspaces of elements of a unitary reflection group (for a fixed eigenvalue), which was commenced in [6] and [5]. The emphasis in this paper is on the representation theory of unitary reflection groups. ... More

Source-LDA: Enhancing probabilistic topic models using prior knowledge sourcesJun 02 2016A popular approach to topic modeling involves extracting co-occurring n-grams of a corpus into semantic themes. The set of n-grams in a theme represents an underlying topic, but most topic modeling approaches are not able to label these sets of words ... More

Summary: Acoustic Detection of EHE NeutrinosNov 15 2006Neutrino astronomy was initiated primarily to search for TeV to PeV neutrinos from Active Galactic Nuclei, and the optical Cherenkov technique is well suited for this energy range. Interest has grown recently in detecting EeV neutrinos, particularly the ... More

Products of functions in $\BMO$ and $\H^{1}$ spaces on spaces of homogeneous typeFeb 18 2009We give an extension to certain \textit{RD-space} $\X$, i.e space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property, of the definition and various properties of the product of functions in $\BMO(\X)$ and $\H^{1}(\X)$, ... More

On the Density of Happy NumbersOct 17 2011Mar 01 2015The happy function $H: \mathbb{N} \rightarrow \mathbb{N}$ sends a positive integer to the sum of the squares of its digits. A number $x$ is said to be happy if the sequence $\{H^n(x)\}^\infty_{n=1}$ eventually reaches one. A basic open question regarding ... More

Thermoacoustic Tomography in Elastic MediaMay 04 2011Oct 11 2011We investigate the problem of recovering the initial displacement f for a solution u of a linear, isotropic, non-homogeneous elastic wave equation, given measurements of u on [0,T] x \partial \Omega, where \Omega\subset\R^3 is some bounded domain containing ... More

Chameleon Field TheoriesJun 18 2013Chameleons are light scalar fields with remarkable properties. Through the interplay of self-interactions and coupling to matter, chameleon particles have a mass that depends on the ambient matter density. The manifestation of the fifth force mediated ... More

Comparisons of polychromatic and monochromatic Ramsey theoryMar 06 2012May 17 2012We compare the strength of polychromatic and monochromatic Ramsey theory in several set-theoretic domains. We show that the rainbow Ramsey theorem does not follow from ZF, nor does the rainbow Ramsey theorem imply Ramsey's theorem over ZF. Extending the ... More

Structured Learning via Logistic RegressionJul 03 2014A successful approach to structured learning is to write the learning objective as a joint function of linear parameters and inference messages, and iterate between updates to each. This paper observes that if the inference problem is "smoothed" through ... More

Inflationary Quantum Cosmology: General Framework and Exact Bianchi I SolutionJul 29 2004Sep 11 2004Using the methods of loop quantum gravity, we derive a framework for describing an inflationary, homogeneous universe in a purely quantum theory. The classical model is formulated in terms of the Ashtekar-Sen connection variables for a general subclass ... More

Interpolating factorizations for acyclic Donaldson--Thomas invariantsJul 05 2018Jul 15 2018We prove a family of factorization formulas for the combinatorial Donaldson--Thomas invariant for an acyclic quiver. A quantum dilogarithm identity due to Reineke, later interpreted by Rim\'anyi by counting codimensions of quiver loci, gives two extremal ... More

Kirby calculus in manifolds with boundaryDec 15 1998Suppose there are two framed links in a compact, connected 3-manifold (possibly with boundary, or non-orientable) such that the associated 3-manifolds obtained by surgery are homeomorphic (relative to their common boundary, if there is one.) How are the ... More

On the discriminant locus of a Lagrangian fibrationJul 21 2006Let $X\to\P^n$ be an irreducible holomorphic symplectic manifold of dimension $2n$ fibred over $\P^n$. Matsushita proved that the generic fibre is a holomorphic Lagrangian abelian variety. In this article we study the discriminant locus $\Delta\subset\P^n$ ... More

Deformations of holomorphic Lagrangian fibrationsSep 09 2005Let $X\to\P^n$ be a $2n$-dimensional projective holomorphic symplectic manifold admitting a Lagrangian fibration over $\P^n$. Matsushita proved that the fibration can be deformed in a codimension one family in the moduli space $\mathrm{Def}(X)$ of deformations ... More

H-infinity is not E-infinityOct 19 2009Apr 19 2014We provide an example of a spectrum over S^0 with an H_\infty structure which does not rigidify to an E_3 structure. It follows that in the category of spectra over S^0 not every H_\infty ring spectrum comes from an underlying E_\infty ring spectrum. ... More

Twisted Fourier-Mukai transforms for holomorphic symplectic fourfoldsSep 09 2005We apply the methods of C{\u{a}}ld{\u{a}}raru to construct a twisted Fourier-Mukai transform between a pair of holomorphic symplectic four-folds. More precisely, we obtain an equivalence between the derived category of coherent sheaves on a certain four-fold ... More

The Laplace transform of the lognormal distributionMar 15 2018In this paper, we explore the analytic continuation of the Laplace transform of the lognormal distribution. Two integral expressions of the analytic continuation are provided, one of which takes the form of a Mellin-Barnes integral. As a corollary, we ... More

Tight Algorithms for Vertex Cover with Hard Capacities on Multigraphs and HypergraphsJun 25 2016In this paper we give a f-approximation algorithm for the minimum unweighted Vertex Cover problem with Hard Capacity constraints (VCHC) on f-hypergraphs. This problem generalizes standard vertex cover for which the best known approximation ratio is also ... More

Learning Convex Inference of MarginalsJun 13 2012Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this paper, the inference ... More

Spectral atoms of unimodular random treesSep 29 2016We use the Mass Transport Principle to analyze the local recursion governing the resolvent $(A-z)^{-1}$ of the adjacency operator of unimodular random trees. In the limit where the complex parameter $z$ approaches a given location $\lambda$ on the real ... More

Rationality of motivic zeta-functions for curves with finite abelian group actionsMar 10 2011Let $\mathfrak{Var}_k^G$ denote the category of pairs $(X,\sigma)$, where $X$ is a variety over $k$ and $\sigma$ is a group action on $X$. We define the Grothendieck ring for varieties with group actions as the free abelian group of isomorphism classes ... More

2-subnormal quadratic offenders and Oliver's p-group conjectureDec 07 2011Bob Oliver conjectures that if $p$ is an odd prime and $S$ is a finite $p$-group, then the Oliver subgroup $\X(S)$ contains the Thompson subgroup $J_e(S)$. A positive resolution of this conjecture would give the existence and uniqueness of centric linking ... More

Lagrangian fibrations on Hilbert schemes of points on K3 surfacesSep 09 2005Oct 07 2005Let $\mathrm{Hilb}^gS$ be the Hilbert scheme of $g$ points on a K3 surface $S$. Suppose that $\mathrm{Pic}S\cong\Z C$ where $C$ is a smooth curve with $C^2=2(g-1)n^2$. We prove that $\mathrm{Hilb}^gS$ is a Lagrangian fibration.

Isotrivial elliptic K3 surfaces and Lagrangian fibrationsJun 04 2014A fibration is said to be isotrivial if all of its smooth fibres are isomorphic to a single fixed variety. We classify the elliptic K3 surfaces that are isotrivial, and use them to construct Lagrangian fibrations that are isotrivial. We then modify the ... More

Measurement of gamma and 2 beta + gammaDec 20 2004Jan 26 2005We report on the initial measurements of the angle gamma and the sum of angles 2 beta + gamma of the Unitarity Triangle. When compared with indirect information on the value of gamma from other measurements of CKM parameters, the measurement of these ... More

A $(k + 3)/2$-approximation algorithm for monotone submodular maximization over a $k$-exchange systemAug 25 2011Sep 28 2011We consider the problem of maximizing a monotone submodular function in a $k$-exchange system. These systems, introduced by Feldman et al., generalize the matroid k-parity problem in a wide class of matroids and capture many other combinatorial optimization ... More

Perturbative expansion of Chern-Simons theoryApr 24 2005Mar 13 2009An overview of the perturbative expansion of the Chern--Simons path integral is given. The main goal is to describe how trivalent graphs appear: as they already occur in the perturbative expansion of an analogous finite-dimensional integral, we discuss ... More

Classical 6j-symbols and the tetrahedronDec 15 1998Mar 22 1999A classical 6j-symbol is a real number which can be associated to a labelling of the six edges of a tetrahedron by irreducible representations of SU(2). This abstract association is traditionally used simply to express the symmetry of the 6j-symbol, which ... More

Pseudo-Anosov homeomorphisms and the lower central series of a surface groupFeb 21 2007Let Gamma_k be the lower central series of a surface group Gamma of a compact surface S with one boundary component. A simple question to ponder is whether a mapping class of S can be determined to be pseudo-Anosov given only the data of its action on ... More

Efficient estimation of the error distribution function in heteroskedastic nonparametric regression with missing dataOct 27 2016A residual-based empirical distribution function is proposed to estimate the distribution function of the errors of a heteroskedastic nonparametric regression with responses missing at random based on completely observed data, and this estimator is shown ... More

Steenrod coalgebrasJan 15 2014Mar 06 2015This paper shows that a functorial version of the "higher diagonal" of a space used to compute Steenrod squares actually contains far more topological information --- including (in some cases) the space's integral homotopy type.

Topology of eigenspace posets for imprimitive reflection groupsAug 22 2012Apr 02 2013This paper studies the poset of eigenspaces of elements of an imprimitive unitary reflection group, for a fixed eigenvalue, ordered by the reverse of inclusion. The study of this poset is suggested by the eigenspace theory of Springer and Lehrer. The ... More

Nontrivial surface topological physics from strong and weak topological insulators and superconductorsOct 05 2014We investigate states on the surface of strong and weak topological insulators and superconductors that have been gapped by a symmetry breaking term. The surface of a strong 3D topological insulator gapped by a magnetic material is well known to possess ... More

A rephasing invariant study of neutrino mixingDec 14 2015We derive a set of renormalization group equations (RGE) for Dirac neutrinos using a rephasing invariant parametrization. The symmetric properties of these equations under flavor permutation facilitate the derivation of some exact and approximate RGE ... More

Observables in multi-detector analyses of supernova neutrinosSep 05 2007Mar 16 2010This paper has been withdrawn by the author, due to errors in the figures.

Density profiles of supernova matter and determination of neutrino parametersDec 22 2006Jul 05 2007The flavor conversion of supernova neutrinos can lead to observable signatures related to the unknown neutrino parameters. As one of the determinants in dictating the efficiency of resonant flavor conversion, the local density profile near the MSW resonance ... More

On the Weil-étale cohomology of the ring of $S$-integersDec 01 2011In this article, we first briefly introduce the history of the Weil-\'etale cohomology theory of arithmetic schemes and review some important results established by Lichtenbaum, Flach and Morin. Next we generalize the Weil-etale cohomology to $S$-integers ... More

On pathwise quadratic variation for cadlag functionsJun 19 2018Oct 30 2018We revisit H. Foellmer's concept of quadratic variation of a cadlag function along a sequence of time partitions and discuss its relation with the Skorokhod topology. We show that in order to obtain a robust notion of pathwise quadratic variation applicable ... More

Latent Alignment and Variational AttentionJul 10 2018Nov 07 2018Neural attention has become central to many state-of-the-art models in natural language processing and related domains. Attention networks are an easy-to-train and effective method for softly simulating alignment; however, the approach does not marginalize ... More

Tensor Variable Elimination for Plated Factor GraphsFeb 08 2019A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to ... More

Active Lévy Matter: Anomalous Diffusion, Hydrodynamics and Linear StabilityApr 17 2019Anomalous diffusion, manifest as a nonlinear relationship between the position mean square displacement and the temporal duration, and/or non-Gaussian features of the position statistics, is prevalent in biological transport processes. Likewise, collective ... More

Single-Electron Transport in Nanostructured Dirac MaterialsJan 05 2016The relativistic dynamics of electronic excitations in two-dimensional Dirac materials such as graphene and the surface states of topological insulators gives rise to superb electronic properties relevant to a wide range of applications and fundamental ... More

Helical Majorana edge mode in a superconducting antiferromagnetic quantum spin Hall insulatorAug 18 2017Aug 10 2018A two-dimensional time-reversal symmetric topological superconductor is a fully gapped system possessing a helical Majorana mode on the edges. This helical Majorana edge mode (HMEM), which is a Kramer's pair of two chiral Majorana edge modes in the opposite ... More

Quelques applications de l'Ansatz de Bethe (Some applications of the Bethe Ansatz)Oct 11 1998The Bethe Ansatz is a method that is used in quantum integrable models in order to solve them explicitly. This method is explained here in a general framework, which applies to 1D quantum spin chains, 2D statistical lattice models (vertex models) and ... More

Chameleon CosmologySep 15 2003Dec 01 2003The evidence for the accelerated expansion of the universe and the time-dependence of the fine-structure constant suggests the existence of at least one scalar field with a mass of order H_0. If such a field exists, then it is generally assumed that its ... More

Focusing Quantum Many-body Dynamics: The Rigorous Derivation of the 1D Focusing Cubic Nonlinear Schrödinger EquationAug 18 2013Oct 01 2013We consider the dynamics of N bosons in one dimension. We assume that the pair interaction is attractive and given by N^{\beta -1}V(N^{\beta}\cdot) where \int V\leqslant 0. We develop new techniques in treating the N-body Hamiltonian so that we overcome ... More

Pseudo-Anosov dilatations and the Johnson filtrationJul 23 2013Feb 02 2015Answering a question of Farb-Leininger-Margalit, we give explicit lower bounds for the dilatations of pseudo-Anosov mapping classes lying in the kth term of the Johnson filtration of the mapping class group.

On the Klainerman-Machedon Conjecture of the Quantum BBGKY Hierarchy with Self-interactionMar 21 2013Apr 19 2015We consider the 3D quantum BBGKY hierarchy which corresponds to the $N$-particle Schr\"{o}dinger equation. We assume the pair interaction is $N^{3\beta -1}V(N^{\beta}\bullet).$ For interaction parameter $\beta \in(0,\frac23)$, we prove that, as $N\rightarrow ... More

On the rigorous derivation of the 2D cubic nonlinear Schrödinger equation from 3D quantum many-body dynamicsDec 04 2012Dec 11 2012We consider the 3D quantum many-body dynamics describing a dilute bose gas with strong confining in one direction. We study the corresponding BBGKY hierarchy which contains a diverging coefficient as the strength of the confining potential tends to $\infty$. ... More

Dynamic Compressive Sensing of Time-Varying Signals via Approximate Message PassingMay 18 2012Apr 17 2013In this work the dynamic compressive sensing (CS) problem of recovering sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear measurements is explored from a Bayesian perspective. While there has been a handful of previously ... More

Sketching for Simultaneously Sparse and Low-Rank Covariance MatricesOct 06 2015Oct 08 2015We introduce a technique for estimating a structured covariance matrix from observations of a random vector which have been sketched. Each observed random vector $\boldsymbol{x}_t$ is reduced to a single number by taking its inner product against one ... More

Black Five-Branes and Fluxbranes on Gravitational InstantonsOct 03 2011Sep 10 2012We apply a U-duality based solution-generating technique to construct supergravity solutions which describe nonextremal D5-branes and fluxbranes on various gravitational instantons. This includes an F7-brane wrapped on a sphere, which remains weakly-coupled ... More

Scale Invariance via a Phase of Slow ExpansionApr 21 2011We consider a cosmological scenario in which a scale-invariant spectrum of curvature perturbations is generated by a rapidly-evolving equation of state on a slowly expanding background. This scenario generalizes the "adiabatic ekpyrotic" mechanism proposed ... More

Lifting for Blind Deconvolution in Random Mask Imaging: Identifiability and Convex RelaxationDec 30 2014Apr 06 2015In this paper we analyze the blind deconvolution of an image and an unknown blur in a coded imaging system. The measurements consist of subsampled convolution of an unknown blurring kernel with multiple random binary modulations (coded masks) of the image. ... More

Correlation structures, Many-body Scattering Processes and the Derivation of the Gross-Pitaevskii HierarchySep 04 2014We consider the dynamics of $N$ bosons in three dimensions. We assume the pair interaction is given by $N^{3\beta -1}V(N^{\beta }\cdot )$ . By studying an associated many-body wave operator, we introduce a BBGKY hierarchy which takes into account all ... More

Projecting Ising Model Parameters for Fast MixingJul 03 2014Oct 08 2014Inference in general Ising models is difficult, due to high treewidth making tree-based algorithms intractable. Moreover, when interactions are strong, Gibbs sampling may take exponential time to converge to the stationary distribution. We present an ... More

Projecting Markov Random Field Parameters for Fast MixingNov 05 2014Nov 12 2014Markov chain Monte Carlo (MCMC) algorithms are simple and extremely powerful techniques to sample from almost arbitrary distributions. The flaw in practice is that it can take a large and/or unknown amount of time to converge to the stationary distribution. ... More

Ultrarigid periodic frameworksApr 08 2014Mar 06 2015We give an algebraic characterization of when a $d$-dimensional periodic framework has no non-trivial, symmetry preserving, motion for any choice of periodicity lattice. Our condition is decidable, and we provide a simple algorithm that does not require ... More

Sparse Shape ReconstructionFeb 28 2013This paper introduces a new shape-based image reconstruction technique applicable to a large class of imaging problems formulated in a variational sense. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right ... More

N-body simulations of gravitational dynamicsMay 05 2011We describe the astrophysical and numerical basis of N-body simulations, both of collisional stellar systems (dense star clusters and galactic centres) and collisionless stellar dynamics (galaxies and large-scale structure). We explain and discuss the ... More

Norms inequalities in some subspaces of Morrey spaceNov 15 2012Nov 18 2012We give norm inequalities for some classical operators in amalgams spaces and in some subspace of Morrey space.

Unstable magnetic fluxes in heterotic string theoryAug 01 2002Aug 22 2002We study exact string backgrounds representing a constant magnetic field background in heterotic string theory. These backgrounds are obtained by Kaluza-Klein reduction of a special class of plane wave solutions. For small values of the magnetic field ... More

U(1) gauge invariance from open string field theoryMay 09 2000Sep 26 2000The naive low energy effective action of the tachyon and the U(1) gauge field obtained from string field theory does not correspond to the world volume action of unstable branes in bosonic string theory. We show that there exists a field redefinition ... More

Constraint-Based Synthesis of Coupling ProofsApr 11 2018Proof by coupling is a classical technique for proving properties about pairs of randomized algorithms by carefully relating (or coupling) two probabilistic executions. In this paper, we show how to automatically construct such proofs for probabilistic ... More