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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

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

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

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

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

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

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

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

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

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

A discrete Grönwall inequality with application to numerical schemes for subdiffusion problemsMar 27 2018Nov 22 2018We consider a class of numerical approximations to the Caputo fractional derivative. Our assumptions permit the use of nonuniform time steps, such as is appropriate for accurately resolving the behavior of a solution whose derivatives are singular at~$t=0$. ... 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

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

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

A second-order scheme with nonuniform time steps for a linear reaction-sudiffusion problemMar 27 2018Nov 26 2018Stability and convergence of a time-weighted discrete scheme with nonuniform time steps are established for linear reaction-subdiffusion equations. The Caupto derivative is approximated at an offset point by using linear and quadratic polynomial interpolation. ... 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

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

Non-Negative Networks Against Adversarial AttacksJun 15 2018Jan 03 2019Adversarial attacks against neural networks are a problem of considerable importance, for which effective defenses are not yet readily available. We make progress toward this problem by showing that non-negative weight constraints can be used to improve ... More

Static Malware Detection & Subterfuge: Quantifying the Robustness of Machine Learning and Current Anti-VirusJun 12 2018As machine-learning (ML) based systems for malware detection become more prevalent, it becomes necessary to quantify the benefits compared to the more traditional anti-virus (AV) systems widely used today. It is not practical to build an agreed upon test ... More

LADAR-Based Vehicle Tracking and Trajectory Estimation for Urban DrivingSep 25 2017Safe mobility for unmanned ground vehicles requires reliable detection of other vehicles, along with precise estimates of their locations and trajectories. Here we describe the algorithms and system we have developed for accurate trajectory estimation ... 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

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

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.

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

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

Birational Calabi-Yau manifolds have the same small quantum productsJun 05 2018We show that any two birational projective Calabi-Yau manifolds have isomorphic small quantum cohomology algebras after a certain change of Novikov rings. The key tool used is a version of an algebra called symplectic cohomology, which is constructed ... More

Five classes of monotone linear relations and operatorsNov 05 2012The relationships between five classes of monotonicity, namely 3^*-, 3-cyclic, strictly, para-, and maximal monotonicity, are explored for linear operators and linear relations in Hilbert space. Where classes overlap, examples are given; otherwise their ... 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

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

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

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 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

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

Disjoint-union partial algebrasDec 01 2016Jun 21 2017Disjoint 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

The temporal logic of two-dimensional Minkowski spacetime with slower-than-light accessibility is decidableJun 26 2018We work primarily with the Kripke frame consisting of two-dimensional Minkowski spacetime with the irreflexive accessibility relation 'can reach with a slower-than-light signal'. We show that in the basic temporal language, the set of validities over ... 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

Lattice QCD form factor for $B_s\to D_s^* lν$ at zero recoil with non-perturbative current renormalisationApr 03 2019We present details of a lattice QCD calculation of the $B_s\to D_s^*$ axial form factor at zero recoil using the Highly Improved Staggered Quark (HISQ) formalism on the second generation MILC gluon ensembles that include up, down, strange and charm quarks ... More

The McKay correspondence via Floer theoryFeb 05 2018Feb 19 2018We prove the generalised McKay correspondence for isolated singularities using Floer theory. Given an isolated singularity \C^n/G for a finite subgroup G in SL(n,\C) and any crepant resolution Y, we prove that the rank of positive symplectic cohomology ... 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

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.

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

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

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

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

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

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

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

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

Lipschitz and biLipschitz Maps on Carnot GroupsMar 19 2010Sep 07 2012Suppose A is an open subset of a Carnot group G, where G has a discrete analogue, and H is another Carnot group. We show that a Lipschitz function from A to H whose image has positive Hausdorff measure in the appropriate dimension is biLipschitz on a ... 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 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

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

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

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

On the homotopy type of the complement of an arrangement that is a 2-generic section of the parallel connection of an arrangement and a pencil of linesJul 16 2015Let $\mathcal{A} $ be a complexified-real arrangement of lines in $\mathbb{C}^2.$ Let $H$ be any line in $ \mathcal{A} $. Then, form a new complexified-real arrangement $ \mathcal{B}_H = \mathcal{A} \cup \mathcal{C} $ where $ \mathcal{C} \cup \{H\} $ ... More

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

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.

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

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

On the Provenance of Linked Data StatisticsOct 19 2014As the amount of linked data published on the web grows, attempts are being made to describe and measure it. However even basic statistics about a graph, such as its size, are difficult to express in a uniform and predictable way. In order to be able ... More

On the structure of virtually nilpotent compact $p$-adic analytic groupsAug 10 2016Let $G$ be a compact $p$-adic analytic group. We recall the well-understood finite radical $\Delta^+$ and FC-centre $\Delta$, and introduce a $p$-adic analogue of Roseblade's subgroup $\mathrm{nio}(G)$, the unique largest orbitally sound open normal subgroup ... More

Fast Algorithms for Finding Pattern Avoiders and Counting Pattern Occurrences in PermutationsSep 28 2015Oct 30 2016Given a set $\Pi$ of permutation patterns of length at most $k$, we present an algorithm for building $S_{\le n}(\Pi)$, the set of permutations of length at most $n$ avoiding the patterns in $\Pi$, in time $O(|S_{\le n - 1}(\Pi)| \cdot k + |S_{n}(\Pi)|)$. ... More

Novae Ejecta as Discrete Adiabatically Expanding GlobulesJun 26 2013Available data for novae show that the X-ray and visible spectral regions correlate with each other as they evolve. Large differences in ionization exist simultaneously in the two wavelength regimes, and a straightforward model is proposed that explains ... More

Third Parameter Classification of Transients and Novae Ejecta as Ballistically Ejected GlobulesJan 03 2016Feb 03 2016A third parameter, in addition to luminosity and rate of brightness decline, derived from the spectra of transients is suggested as a means of more accurately classifying objects in outburst. Principal component analysis of the spectra of transients is ... More

QCD inequalities for hadron interactionsAug 29 2014We derive generalisations of the Weingarten--Witten QCD mass inequalities for particular multi-hadron systems. For systems of any number of identical pseudo-scalar mesons of maximal isospin, these inequalities prove that interactions between the constituent ... More

The domain algebra of a CP semigroupMay 24 2000A CP semigroup is a semigroup of normal unit-preserving completely positive maps acting on the algebra B(H) of all operators on a separable Hilbert space H. Such a semigroup has a natural generator L; since the individual maps of the semigroup need not ... More

On the index and dilations of completely positive semigroupsMay 25 1997It is known that every semigroup of normal completely positive maps $P = {P_t: t\geq 0}$ of $B(H)$, satisfying $P_t(1) = 1$ for every $t\geq 0$, has a minimal dilation to an E_0-semigroup acting on $B(K)$ for some Hilbert space K containing H. The minimal ... More

Multilinear Embedding -- convolution estimates on smooth submanifoldsApr 25 2012Multilinear embedding estimates for the fractional Laplacian are obtained in terms of functionals defined over a hyperbolic surface. Convolution estimates used in the proof enlarge the classical framework of the convolution algebra for Riesz potentials ... More

The Two Extended Bodies Problem in General Relativity within the post-Newtonian ApproximationApr 02 2014The dynamics of extended bodies is a fundamental problem in any gravitational theory. In the case of General Relativity, this problem is under study since the theory was published. Several methods have been developed and different approaches are avalaible ... More

Approximate Recall Confidence IntervalsFeb 13 2012Oct 23 2012Recall, the proportion of relevant documents retrieved, is an important measure of effectiveness in information retrieval, particularly in the legal, patent, and medical domains. Where document sets are too large for exhaustive relevance assessment, recall ... More

Comments on "Increasing destructiveness of tropical cyclones over the past 30 years" by Kerry Emanuel, Nature, 31 July 2005, Vol. 436, pp. 686-688Jan 09 2006The near universal references to the above paper by most of the major US media outlets and blogs since Katrina and Rita made US landfall requires a response from a few of us who study hurricanes. Having been involved with hurricane research and forecasting ... More

First Run of the LArIAT Testbeam ExperimentNov 01 2015LArIAT (Liquid Argon In A Testbeam) aims to characterize the response of a liquid argon time projection chamber (LArTPC) to the particles often seen as final-state products of ~1 GeV neutrino interactions in existing and planned detectors. The experiment ... More

The Dimension of the Space of Cusp Forms of Weight OneNov 09 1994A new upper bound is given for the dimension of the space of holomorphic cusp forms of weight one and prime level $q$: $$ \hbox{dim}\, S_1(q) << q^{11/12} \log^4{q} $$ with an absolute implied constant.

Trusted Certificates in Quantum CryptographyMar 10 2006This paper analyzes the performance of Kak's three stage quantum cryptographic protocol based on public key cryptography against a man-in-the-middle attack. A method for protecting against such an attack is presented using certificates distributed by ... More

The Combinatorics of Occam's RazorApr 28 2015Occam's Razor tells us to pick the simplest model that fits our observations. In order to make sense of his process mathematically, we interpret it in the context of posets of functions. Our approach leads to some unusual new combinatorial problems concerning ... More

Do Type-Ia Supernovae Constrain the Total Equation of State?Nov 28 2005Feb 01 2007In this paper, we consider a couple of alternative dark energy models using the total equation of state of the cosmological fluid, $\wt$. These models are fit to the recent type-Ia supernovae data and are compared to previously considered models. The ... More

Exciton Transfer Integrals Between Polymer ChainsMar 26 2007The line-dipole approximation for the evaluation of the exciton transfer integral, $J$, between conjugated polymer chains is rigorously justified. Using this approximation, as well as the plane-wave approximation for the exciton center-of-mass wavefunction, ... More

Theory of the singlet exciton yield in light-emitting polymersOct 26 2004This paper presents a possible explanation for the enhanced singlet exciton yield in light emitting polymers. We propose a theory of electron-hole recombination via inter-molecular inter-conversion from inter-molecular weakly bound polaron pairs (or charge-transfer ... More

Asymptotic Behavior of Spherically Symmetric Marginally Trapped TubesFeb 19 2007Jan 14 2009We give conditions on a general stress-energy tensor T_{\alpha \beta} in a spherically symmetric black hole spacetime which are sufficient to guarantee that the black hole will contain a (spherically symmetric) marginally trapped tube which is eventually ... More

A Comment on Black Hole Entropy in String TheoryJun 03 1994Jun 12 1994In this note, we extend the string theoretic calculation of the black hole entropy, first performed by Susskind and Uglum, away from the infinite mass limit. It is shown that the result agrees with that obtained from the classical action of string theory, ... More