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Exponential sum approximations for $t^{-β}$Jun 01 2016Jun 07 2017Given $\beta>0$ and $\delta>0$, the function $t^{-\beta}$ may be approximated for $t$ in a compact interval $[\delta,T]$ by a sum of terms of the form $we^{-at}$, with parameters $w>0$ and $a>0$. One such an approximation, studied by Beylkin and Monz\'on, ... More

Iterative methods for shifted positive definite linear systems and time discretization of the heat equationNov 22 2011In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In application to ... More

Superconvergence of a discontinuous Galerkin method for fractional diffusion and wave equationsJun 12 2012We consider an initial-boundary value problem for $\partial_tu-\partial_t^{-\alpha}\nabla^2u=f(t)$, that is, for a fractional diffusion ($-1<\alpha<0$) or wave ($0<\alpha<1$) equation. A numerical solution is found by applying a piecewise-linear, discontinuous ... More

Solving parabolic equations on the unit sphere via Laplace transforms and radial basis functionsJul 20 2012We propose a method to construct numerical solutions of parabolic equations on the unit sphere. The time discretization uses Laplace transforms and quadrature. The spatial approximation of the solution employs radial basis functions restricted to the ... More

Numerical solution of the time-fractional Fokker-Planck equation with general forcingJul 21 2015We study two schemes for a time-fractional Fokker-Planck equation with space- and time-dependent forcing in one space dimension. The first scheme is continuous in time and is discretized in space using a piecewise-linear Galerkin finite element method. ... More

Existence, uniqueness and regularity of the solution of the time-fractional Fokker-Planck equation with general forcingFeb 07 2019A time-fractional Fokker-Planck initial-boundary value problem is considered, with differential operator $u_t-\nabla\cdot(\partial_t^{1-\alpha}\kappa_\alpha\nabla u-\textbf{F}\partial_t^{1-\alpha}u)$, where $0<\alpha <1$. The forcing function $\textbf{F} ... More

Exponential sum approximations and fast evaluation of fractional integralsJun 01 2016Given $\beta>0$ and $\delta>0$, the function $t^{-\beta}$ may be approximated for $t$ in the interval $[\delta,1]$ by a sum of terms of the form $we^{-at}$, with parameters $w>0$ and $a>0$. A basic approximation is obtained by applying quadratures to ... More

Exponential sum approximations for $t^{-β}$Jun 01 2016Oct 21 2016Given $\beta>0$ and $\delta>0$, the function $t^{-\beta}$ may be approximated for $t$ in a compact interval $[\delta,T]$ by a sum of terms of the form $we^{-at}$, with parameters $w>0$ and $a>0$. One such an approximation, studied by Beylkin and Monz\'on, ... More

Regularity theory for time-fractional advection-diffusion-reaction equationsFeb 03 2019We investigate the behavior of the time derivatives of the solution to a linear time-fractional, advection-diffusion-reaction equation, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. Our focus is ... More

Well-posedness of time-fractional, advection-diffusion-reaction equationsOct 11 2018Feb 05 2019We establish the well-posedness of an initial-boundary value problem for a general class of time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. ... More

Fast summation by interval clustering for an evolution equation with memoryMar 19 2012We solve a fractional diffusion equation using a piecewise-constant, discontinuous Galerkin method in time combined with a continuous, piecewise-linear finite element method in space. If there are $N$ time levels and $M$ spatial degrees of freedom, then ... More

Time-stepping error bounds for fractional diffusion problems with non-smooth initial dataMay 09 2014We apply the piecewise constant, discontinuous Galerkin method to discretize a fractional diffusion equation with respect to time. Using Laplace transform techniques, we show that the method is first order accurate at the \$n\$th time level \$t_n\$, but ... More

A spectral sequence for symplectic homologyNov 10 2010Sep 21 2011We construct a spectral sequence converging to symplectic homology of a Lefschetz fibration whose E1 page is related to Floer homology of the monodromy symplectomorphism and its iterates. We use this to show the existence of fixed points of certain symplectomorphisms. ... More

Computability and the growth rate of symplectic homologySep 21 2011For each n greater than 7 we explicitly construct a sequence of Stein manifolds diffeomorphic to complex affine space of dimension n so that there is no algorithm to tell us in general whether a given such Stein manifold is symplectomorphic to the first ... More

A semidiscrete finite element approximation of a time-fractional Fokker-Planck equation with nonsmooth initial dataFeb 08 2019We present a new stability and convergence analysis for the spatial discretization of a time-fractional Fokker--Planck equation in a convex polyhedral domain, using continuous, piecewise-linear, finite elements. The forcing may depend on time as well ... More

Finite element approximation of a time-fractional diffusion problem in a non-convex polygonal domainJan 29 2016An initial-boundary value problem for the time-fractional diffusion equation is discretized in space using continuous piecewise-linear finite elements on a polygonal domain with a re-entrant corner. Known error bounds for the case of a convex polygon ... More

Fractional Euler Limits and Their ApplicationsSep 10 2016Generalisations of the classical Euler formula to the setting of fractional calculus are discussed. Compound interest and fractional compound interest serve as motivation. Connections to fractional master equations are highlighted. An application to the ... More

Wider contours and adaptive contoursDec 19 2017Contour integrals in the complex plane are the basis of effective numerical methods for computing matrix functions, such as the matrix exponential and the Mittag-Leffler function. These methods provide successful ways to solve partial differential equations, ... More

Anomalous dispersion and negative group velocity in a coherence-free cold atomic mediumMay 20 2008We have observed the propagation of an approximately 35 ns long light pulse with a negative group velocity through a laser-cooled 85Rb atomic medium. The anomalous dispersion results from linear atom-light interaction, and is unrelated to long-lived ground ... More

On a Singular Integrodifferential Equation arising from a Linearised Free Surface ProblemDec 14 2005A problem of linear surface waves discussed by Forbes(1984) initially gave rise to a singular integrodifferential equation over the real line. We have been able to transform this integrodifferential equation into a linear second order differential equation ... More

Lefschetz fibrations and symplectic homologySep 11 2007Feb 11 2009We show that for each k > 3 there are infinitely many finite type Stein manifolds diffeomorphic to Euclidean space R^{2k} which are pairwise distinct as symplectic manifolds.

Far-Ultraviolet Imaging of the Field Star Population in the Large Magellanic Cloud with HSTSep 24 1998We present an analysis of the deepest pure-UV observations with the highest angular resolution ever performed, a set of 12 exposures with the HST WFPC2 and F160BW filter obtained in parallel observing mode, which cover $\sim$12 square arcminutes in the ... More

On the symplectic invariance of log Kodaira dimensionNov 09 2012Suppose that A and B are symplectomorphic smooth affine varieties. If A is acylic of dimension 2 then B has the same log Kodaira dimension as A. If the dimension of A is 3, has log Kodaira dimension 2 and satisfies some other conditions then B cannot ... More

Reeb orbits and the minimal discrepancy of an isolated singularityApr 07 2014Apr 28 2015Let A be an affine variety inside a complex N dimensional vector space which has an isolated singularity at the origin. The intersection of A with a very small sphere turns out to be a contact manifold called the link of A. Any contact manifold contactomorphic ... More

Affine Varieties, Singularities and the Growth Rate of Wrapped Floer CohomologySep 05 2015In this paper, we give partial answers to the following questions: Which contact manifolds are contactomorphic to links of isolated complex singularities? Which symplectic manifolds are symplectomorphic to smooth affine varieties? The invariant that we ... More

Algebras of multiplace functions for signatures containing antidomainJul 22 2015May 19 2016We define antidomain operations for algebras of multiplace partial functions. For all signatures containing composition, the antidomain operations and any subset of intersection, preferential union and fixset, we give finite equational or quasiequational ... More

Complete representation by partial functions for composition, intersection and antidomainJul 04 2014Nov 20 2014For representation by partial functions in the signature with intersection, composition and antidomain, we show that a representation is meet complete if and only if it is join complete. We show that a representation is complete if and only if it is atomic, ... More

Floer Cohomology, Multiplicity and the Log Canonical ThresholdAug 26 2016Let f be a polynomial over the complex numbers with an isolated singularity at 0. We show that the multiplicity and the log canonical threshold of f at 0 are invariants of the link of f viewed as a contact submanifold of the sphere. This is done by first ... More

Single Exponential Approximation of Fourier TransformsDec 14 2005This article is concerned with a new method for the approximate evaluation of Fourier sine and cosine transforms. We develop and analyse a new quadrature rule for Fourier sine and cosine transforms involving transforming the integral to one over the entire ... More

The growth rate of symplectic homology and affine varietiesNov 11 2010Mar 08 2012We will show that the cotangent bundle of a manifold whose free loopspace homology grows exponentially is not symplectomorphic to any smooth affine variety. We will also show that the unit cotangent bundle of such a manifold is not Stein fillable by a ... More

Dynamics of reflection of ultracold atoms from a periodic 1D magnetic lattice potentialOct 06 2009We report on an experimental study of the dynamics of the reflection of ultracold atoms from a periodic one-dimensional magnetic lattice potential. The magnetic lattice potential of period 10 \textmu m is generated by applying a uniform bias magnetic ... More

Near-Infrared Observations of the Environments of Radio Quiet QSOs at z >~ 1Feb 16 1999We present the results of an infrared survey of QSO fields at z=0.95, 0.995 and 1.5. Each z<1 field was imaged to typical continuum limits of J=20.5, Kprime=19 (5 sigma), and line fluxes of 1.3E10{-16}ergs/cm^2/s (1 sigma)in a 1% interference filter. ... More

Local Floer homology and infinitely many simple Reeb orbitsFeb 02 2012Jun 19 2012Let Q be a Riemannian manifold such that the Betti numbers of its free loop space with respect to some coefficient field are unbounded. We show that every contact form on its unit contangent bundle supporting the natural contact structure has infinitely ... More

Straightforward Bibliography Management in R with the RefManageR PackageMar 09 2014This work introduces the R package RefManageR, which provides tools for importing and working with bibliographic references. It extends the bibentry class in R in a number of useful ways, including providing R with previously unavailable support for BibLaTeX. ... More

Disjoint-union partial algebrasDec 01 2016Disjoint union is a partial binary operation returning the union of two sets if they are disjoint and undefined otherwise. A disjoint-union partial algebra of sets is a collection of sets closed under disjoint unions, whenever they are defined. We provide ... More

$B_s\to D_s^{(*)}lν$ Form Factors with Heavy HISQ QuarksJan 15 2019We present progress on an ongoing calculation of the $B_s\to D_s^{(*)} l \nu$ form factors calculated on the $n_f=2+1+1$ MILC ensembles and using the Highly Improved Staggered Quark action for all valence quarks. We perform the calculation at a range ... More

Non-displaceable contact embeddings and infinitely many leaf-wise intersectionsApr 22 2009We construct using Lefschetz fibrations a large family of contact manifolds with the following properties: Any bounding contact embedding into an exact symplectic manifold satisfying a mild topological assumption is non-displaceable and generically has ... More

APF - The Lick Observatory Automated Planet FinderFeb 26 2014The Automated Planet Finder (APF) is a facility purpose-built for the discovery and characterization of extrasolar planets through high-cadence Doppler velocimetry of the reflex barycentric accelerations of their host stars. Located atop Mt. Hamilton, ... More

The finite representation property for composition, intersection, domain and rangeMar 09 2015Mar 04 2016We prove that the finite representation property holds for representation by partial functions for the signature consisting of composition, intersection, domain and range and for any expansion of this signature by the antidomain, fixset, preferential ... More

One dimensional lattice of permanent magnetic microtraps for ultracold atoms on an atom chipJan 04 2008We report on the loading and trapping of ultracold atoms in a one dimensional permanent magnetic lattice of period 10 micron produced on an atom chip. The grooved structure which generates the magnetic lattice potential is fabricated on a silicon substrate ... More

Maximal prime homomorphic images of mod-$p$ Iwasawa algebrasAug 28 2016Let $k$ be a finite field of characteristic $p$, and $G$ a compact $p$-adic analytic group. Write $kG$ for the completed group ring of $G$ over $k$. In this paper, we describe the structure of the ring $kG/P$, where $P$ is a minimal prime ideal of $kG$. ... More

Tsirelson's problem and an embedding theorem for groups arising from non-local gamesJun 09 2016Jul 01 2016Tsirelson's problem asks whether the commuting operator model for two-party quantum correlations is equivalent to the tensor-product model. We give a negative answer to this question by showing that there are non-local games which have perfect commuting-operator ... More

Hausdorff dimension of the spectrum of the square Fibonacci HamiltonianOct 12 2014Oct 22 2014Denoting the Hausdorff dimension of the Fibonacci Hamiltonian with coupling $\lambda$ by $\mathrm{HD}_\lambda$, we prove that for all but countably many $\lambda$, the Hausdorff dimension of the spectrum of the square Fibonacci Hamiltonian with coupling ... More

Q-Systems, Factorization Dynamics, and the Twist AutomorphismOct 24 2013We provide a concrete realization of the cluster algebras associated with Q-systems as amalgamations of cluster structures on double Bruhat cells in simple algebraic groups. For nonsimply-laced groups, this provides a cluster-algebraic formulation of ... More

Finding paths of length k in O*(2^k) timeJul 18 2008Nov 09 2008We give a randomized algorithm that determines if a given graph has a simple path of length at least k in O(2^k poly(n,k)) time.

The quark-gluon vertex in Landau gauge bound-state studiesApr 09 2014Apr 21 2015We present a practical method for the solution of the quark-gluon vertex for use in Bethe--Salpeter and Dyson--Schwinger calculations. The efficient decomposition into the necessary covariants is detailed, with the numerical algorithm outlined for both ... More

Faster all-pairs shortest paths via circuit complexityDec 23 2013May 22 2014We present a new randomized method for computing the min-plus product (a.k.a., tropical product) of two $n \times n$ matrices, yielding a faster algorithm for solving the all-pairs shortest path problem (APSP) in dense $n$-node directed graphs with arbitrary ... More

Episodic mass transfer: A trigger for nova outbursts?Aug 24 2011High resolution spectra of postoutburst novae show multiple components of ejected gas that are kinematically distinct. We interpret the observations in terms of episodes of enhanced mass transfer originating from the secondary star that result in the ... More

Bethe-Salpeter studies of mesons beyond rainbow-ladderDec 17 2009We investigate the masses of light mesons from a coupled system of Dyson-Schwinger and Bethe-Salpeter equations. The dominant non-Abelian and sub-leading Abelian contributions to the dressed quark-gluon vertex are explicitly taken into account. We also ... More

Multi-meson States in Lattice QCDOct 07 2008In this contribution, I summarise the studies of the properties of Bose-Einstein condensed systems composed of up to twelve pions or kaons carried out by the NPLQCD collaboration. These investigations have provided precise determination the I=2 pi-pi ... More

Generators of Noncommutative DynamicsJan 15 2002For a fixed C*-algebra A, we consider all noncommutative dynamical systems that can be generated by A. More precisely, an A-dynamical system is a triple (i,B,\alpha) where $\alpha$ is a *-endomorphism of a C*-algebra B, and i: A --> B is the inclusion ... More

Interactions in noncommutative dynamicsOct 29 1999Nov 07 1999A mathematical notion of interaction is introduced for noncommutative dynamical systems, i.e., for one parameter groups of *-automorphisms of $\Cal B(H)$ endowed with a certain causal structure. With any interaction there is a well-defined "state of the ... More

The index of a quantum dynamical semigroupMay 25 1997A numerical index is introduced for semigroups of completely positive maps of $\Cal B(H)$ which generalizes the index of E_0-semigroups. It is shown that the index of a unital completely positive semigroup agrees with the index of its dilation to an E_0-semigroup, ... More

Multilinear Embedding and Hardy's InequalityNov 26 2013Multilinear trace restriction inequalities are obtained for Hardy's inequality. More generally, detailed development is given for new multilinear forms for Young's convolution inequality, and a new proof for the multilinear Hardy-Littlewood-Sobolev inequality, ... More

Maximal vectors in Hilbert space and quantum entanglementApr 08 2008May 13 2008Let $V$ be a norm-closed subset of the unit sphere of a Hilbert space $H$ that is stable under multiplication by scalars of absolute value 1. A {\em maximal vector} (for $V$) is a unit vector $\xi\in H$ whose distance to $V$ is maximum $d(\xi,V)=\sup_{\|\eta\|=1}d(\eta,V)$, ... More

The probability of entanglementDec 27 2007May 04 2008We show that states on tensor products of matrix algebras whose ranks are relatively small are {\em almost surely} entangled, but that states of maximum rank are not. More precisely, let $M=M_m(\mathbb C)$ and $N=M_n(\mathbb C)$ be full matrix algebras ... More

Yi's Unique Range Set Construction in the Number Field CaseMay 17 2006Feb 18 2013H. X. Yi's construction of unique range sets for entire functions is translated to the number theory setting to illustrate that his construction would work in the number theory setting if one knew a version of Schmidt's Subspace Theorem with truncated ... More

Existence of GCD's and Factorization in Rings of Non-Archimedean Entire FunctionsJul 06 2010Apr 13 2011A detailed proof is given of the well-known facts that greatest common divisors exist in rings of non-Archimedean entire functions of several variables and that these rings of entire functions are almost factorial, in the sense that an entire function ... More

The Gm-equivariant Motivic Cohomology of Stiefel VarietiesMar 26 2012Aug 07 2012We derive a version of the Rothenberg-Steenrod, fiber-to-base, spectral sequence for cohomology theories represented in model categories of simplicial presheaves. We then apply this spectral sequence to calculate the equivariant motivic cohomology of ... More

The Motivic Cohomology of Stiefel VarietiesMay 21 2011The main result of this paper is a computation of the motivic cohomology of varieties of n \times m-matrices of of rank m, including both the ring structure and the action of the reduced power operations. The argument proceeds by a comparison of the general ... More

The Forgetfulness of Balls and BinsApr 29 2010Nov 18 2011We find the asymptotic total variation distance between two distributions on configurations of m balls in n labeled bins: in the first, each ball is placed in a bin uniformly at random; in the second, k balls are planted in an arbitrary but fixed arrangement ... More

Hamiltonicity of the Cayley Digraph on the Symmetric Group Generated by σ = (1 2 ... n) and τ = (1 2)Jul 09 2013Oct 27 2013The symmetric group is generated by {\sigma} = (1 2 ... n) and {\tau} = (1 2). We answer an open problem of Nijenhuis and Wilf by constructing a Hamilton path in the directed Cayley graph for all n, and a Hamilton cycle for odd n.

Metric currents, differentiable structures, and Carnot groupsAug 24 2010Feb 06 2011We examine the theory of metric currents of Ambrosio and Kirchheim in the setting of spaces admitting differentiable structures in the sense of Cheeger and Keith. We prove that metric forms which vanish in the sense of Cheeger on a set must also vanish ... More

On blow-up solutions of the Jang equation in spherical symmetryOct 15 2009We prove some related results concerning blow-up solutions for the Jang equation. First: it has been shown that, given an outermost marginally outer trapped surface (MOTS) \Sigma, there exists a solution to Jang's equation which blows up at \Sigma. Here ... More

Cosmic Superstrings: Dynamics and CuspsOct 21 2009Whilst standard field theoretic Cosmic Strings cannot end, Cosmic Superstrings can form three string junctions, at which each string ends. This opens up a new class of possible boundary conditions for such strings and we show that, at least when the junctions ... More

Static Solutions for 4th order gravityOct 19 2010Nov 05 2010The Lichnerowicz and Israel theorems are extended to higher order theories of gravity. In particular it is shown that Schwarzschild is the unique spherically symmetric, static, asymptotically flat, black-hole solution, provided the spatial curvature is ... More

Universal Schubert polynomialsFeb 15 1997Feb 18 1998We introduce polynomials that represent general degeneracy loci for maps of vector bundles. These polynomials specialize to the known classical and quantum forms of single and double Schubert polynomials. This is the final version of the paper, to appear ... More

On the growth of local intersection multiplicities in holomorphic dynamics: a conjecture of ArnoldDec 20 2012Feb 25 2014We show by explicit example that local intersection multiplicities in holomorphic dynamical systems can grow arbitrarily fast, answering a question of V. I. Arnold. On the other hand, we provide results showing that such behavior is exceptional, and that ... More

Disentangled Representations in Neural ModelsFeb 07 2016Representation learning is the foundation for the recent success of neural network models. However, the distributed representations generated by neural networks are far from ideal. Due to their highly entangled nature, they are di cult to reuse and interpret, ... More

Iterations of Quadratic Polynomials over Finite FieldsJan 22 2012Jan 25 2012Given a map f:Z-->Z and an initial argument alpha, we can iterate the map to get a finite set of iterates modulo a prime p. In particular, for a quadratic map f(z)=z^2 +c, c constant, work by Pollard suggests that this set should have length on the order ... More

Strange attractors in periodically-kicked degenerate Hopf bifurcationsJun 15 2007We prove that spiral sinks (stable foci of vector fields) can be transformed into strange attractors exhibiting sustained, observable chaos if subjected to periodic pulsatile forcing. We show that this phenomenon occurs in the context of periodically-kicked ... More

A p-adic completion of Zagier's Eisenstein seriesNov 20 2017Nov 21 2017This note points out that for any odd prime $p$, Zagier's weight $3/2$ mock Eisenstein series can be completed to a $p$-adic modular form in a way that bears some resemblance to its completion to a harmonic Maass form.

Computations of the slice genus of virtual knotsJun 26 2017Aug 29 2017A virtual knot is an equivalence class of embeddings of $ S^1 $ into thickened (closed oriented) surfaces, up to self-diffeomorphism of the surface and certain handle stabilisations. The slice genus of a virtual knot is defined diagrammatically, in direct ... More

The noncommutative Choquet boundary II: HyperrigidityOct 15 2008May 28 2009A (finite or countably infinite) set G of generators of an abstract C*-algebra A is called hyperrigid if for every faithful representation of A on a Hilbert space $A\subseteq \mathcal B(H)$ and every sequence of unital completely positive linear maps ... More

Bounding Lagrangian widths via geodesic pathsJul 04 2013Apr 24 2014The width of a Lagrangian is the largest capacity of a ball that can be symplectically embedded into the ambient manifold such that the ball intersects the Lagrangian exactly along the real part of the ball. Due to Dimitroglou Rizell, finite width is ... More

Geometric and analytic quasiconformality in metric measure spacesAug 21 2010Feb 06 2011We prove the equivalence between geometric and analytic definitions of quasiconformality for a homeomorphism $f\colon X\rightarrow Y$ between arbitrary locally finite separable metric measure spaces, assuming no metric hypotheses on either space. When ... More

Equidistribution of preimages over nonarchimedean fields for maps of good reductionAug 28 2012Feb 05 2013In this article we prove an analogue of the equidistribution of preimages theorem from complex dynamics for maps of good reduction over nonarchimedean fields. While in general our result is only a partial analogue of the complex equidistribution theorem, ... More

A Sane Proof that COLk \le COL3Jul 18 2014Jan 28 2016Let COLk be the set of all k-colorable graphs. It is easy to show that if a<b then COLa \le COLb (poly time reduction). Using the Cook-Levin theorem it is easy to show that if 3 \le a< b then COLb \le COLa. However this proof is insane in that it translates ... More

Which Unbounded Protocol for Envy Free Cake Cutting is Better?Jul 28 2015Aug 21 2015A division of a cake by n people is envy free if everyone thinks they got the biggest pieces. Note that peoples tastes can differ. There is a discrete protocol for envy free division for n=3 which takes at most 5 cuts. For n=4 and beyond there is a protocol ... More

New algorithms and lower bounds for circuits with linear threshold gatesJan 10 2014Let $ACC \circ THR$ be the class of constant-depth circuits comprised of AND, OR, and MOD$m$ gates (for some constant $m > 1$), with a bottom layer of gates computing arbitrary linear threshold functions. This class of circuits can be seen as a "midpoint" ... More

Cluster Ensembles and Kac-Moody GroupsOct 09 2012Sep 15 2013We study the relationship between two sets of coordinates on a double Bruhat cell, the cluster variables introduced by Berenstein, Fomin, and Zelevinsky and the $\CX$-coordinates defined by the coweight parametrization of Fock and Goncharov. In these ... More

Double Bruhat Cells in Kac-Moody Groups and Integrable SystemsApr 03 2012Feb 21 2013We construct a family of integrable Hamiltonian systems generalizing the relativistic periodic Toda lattice, which is recovered as a special case. The phase spaces of these systems are double Bruhat cells corresponding to pairs of Coxeter elements in ... More

Functionals for Multilinear Fractional EmbeddingMay 21 2014Jun 05 2014A novel representation is developed as a measure for multilinear fractional embedding. Corresponding extensions are given for the Bourgain-Brezis-Mironescu theorem and Pitt's inequality. New results are obtained for diagonal trace restriction on submanifolds ... More

Lectures on Non-Archimedean Function TheorySep 24 2009Lecture 1 discusses non-Archimedean analogs of classical complex function theory based on the Schnirelman integral. Lecture 2 discusses valuation (Newton) polygons and their consequences and presents a non-Archimedean analog of the Poisson-Jensen formula. ... More

Automorphic representations with prescribed ramification for unitary groupsOct 17 2011Let F be a totally real number field, n a prime integer, and G a unitary group of rank n defined over F that is compact at every infinite place. We prove an asymptotic formula for the number of cuspidal automorphic representations of G whose factors at ... More

Complete Shrinking Ricci Solitons have Finite Fundamental GroupApr 03 2007We show that if a complete Riemannian manifold supports a vector field such that the Ricci tensor plus the Lie derivative of the metric with respect to the vector field has a positive lower bound, then the fundamental group is finite. In particular, it ... More

Some curvature pinching results for Riemannian manifolds with densityJan 24 2015In this note we consider versions of both Ricci and sectional curvature pinching for Riemannian manifold with density. In the Ricci curvature case the main result implies a diameter estimate that is new even for compact shrinking Ricci solitons. In the ... More

The forgetful map in rational K-theoryOct 05 2007Let G be a connected reductive algebraic group acting on a scheme X. Let R(G) denote the representation ring of G, and let I be the ideal in R(G) of virtual representations of rank 0. Let G(X) (resp. G(G,X)) denote the Grothendieck group of coherent sheaves ... More

Nonemptiness of symmetric degeneracy lociMay 11 2003Let V be a rank N vector bundle on a d-dimensional complex projective scheme X; assume that V is equipped with a quadratic form with values in a line bundle L and that S^2 V^* \otimes L is ample. Suppose that the maximum rank of the quadratic form at ... More

Comments by William M. Gray (Colorado State University) on the recently published paper in Science by Webster et al., titled "Changes in tropical cyclone number, duration, and intensity in a warming environment." (September 2005, Vol. 309, pp. 1844-1846, ... MoreJan 09 2006Recent US major landfalling hurricanes Katrina and Rita and last year's four U.S. landfalling major hurricanes have spawned an abundance of questions concerning the role that global warming might be playing in these events. This idea has been given added ... More

Stability and noise in biochemical switchesMay 15 2000Many processes in biology, from the regulation of gene expression in bacteria to memory in the brain, involve switches constructed from networks of biochemical reactions. Crucial molecules are present in small numbers, raising questions about noise and ... More

Should you believe that this coin is fair?Aug 30 2005Faced with a sequence of N binary events, such as coin flips (or Ising spins), it is natural to ask whether these events reflect some underlying dynamic signals or are just random. Plausible models for the dynamics of hidden biases lead to surprisingly ... More

A comparison of the performance and scalability of relational and document-based web-systems for large scale applications in a rehabilitation contextOct 01 2015Background: The Virtual Rehabilitation Environment (VRE) provides patients of long term neurological conditions with a platform to review their previous physiotherapy sessions, as well as see their goals and any treatments or exercises that their clinician ... More

Multilinear embedding estimates for the fractional LaplacianApr 13 2010Oct 27 2011Three novel multilinear embedding estimates for the fractional Laplacian are obtained in terms of trace integrals restricted to the diagonal. The resulting sharp inequalities may be viewed as extensions of the Hardy-Littlewood-Sobolev inequality, the ... More

A berndtsson-Andersson operator solving \bar\partial-equation with W^α-estimates on convex domains of finite typeFeb 22 2010In this article, we use a Berndtsson-Andersson operator and the Bergman metric in order to solve the $\bar\partial$ equation on convex domains of finite type for forms satisifying a Carleson condition and get norm estimates of the solution in term of ... More

Non-Archimedean Big Picard TheoremsJul 10 2002A non-Archimedean analog of the classical Big Picard Theorem, which says that a holomorphic map from the punctured disc to a Riemann surface of hyperbolic type extends accross the puncture, is proven using Berkovich's theory of non-Archimedean analytic ... More

Models of Quantum Algorithms in Sets and RelationsMar 19 2015Jul 19 2015We construct abstract models of blackbox quantum algorithms using a model of quantum computation in sets and relations, a setting that is usually considered for nondeterministic classical computation. This alternative model of quantum computation (QCRel), ... More

On the Zeros of the Complex Fourier Transforms of a Class of Exponential FunctionsJan 22 2009A class theorem is presented and proved: the complex Fourier transforms of a certain class of exponential functions have all their zeros on the real line. A class of basis functions is first considered, and the class is then extended via the method of ... More

Structure and conditions in massive star forming giant molecular cloudsMay 21 2001Massive stars form in clusters within self-gravitating molecular clouds. The size scale of these clusters is sufficiently large that non-thermal, or turbulent, motions of the gas must be taken into account when considering their formation. Millimeter ... More

Universal countable Borel quasi-ordersJun 06 2013In recent years, much work in descriptive set theory has been focused on the Borel complexity of naturally occurring classification problems, in particular, the study of countable Borel equivalence relations and their structure under the quasi-order of ... More