Results for "William McLean"

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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
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
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
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
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
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
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
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
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
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
A second-order scheme with nonuniform time steps for a linear reaction-sudiffusion problemMar 27 2018Apr 28 2019Stability 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
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
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
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
Long-term Multi-wavelength Observations of GRS 1758-258 and the ADAF ModelAug 07 2001We present a long-term multi-wavelength light curve of Galactic black hole candidate GRS 1758-258 by combining previously published and archival data from GRANAT, ROSAT, CGRO, RXTE, SAX, ASCA, EXOSAT, and the VLA. In addition we include first spectral ... 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
KiloGrams: Very Large N-Grams for Malware ClassificationAug 01 2019N-grams have been a common tool for information retrieval and machine learning applications for decades. In nearly all previous works, only a few values of $n$ are tested, with $n > 6$ being exceedingly rare. Larger values of $n$ are not tested due to ... 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
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
Free Kleene algebras with domainJul 24 2019First we identify the free algebras of the class of algebras of binary relations equipped with the composition and domain operations. Elements of the free algebras are pointed labelled finite rooted trees. Then we extend to the analogous case when the ... 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 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
Efficient inference for stochastic differential mixed-effects models using correlated particle pseudo-marginal algorithmsJul 23 2019We perform fully Bayesian inference for stochastic differential equation mixed-effects models (SDEMEMs) using data at discrete times that may be incomplete and subject to measurement error. SDEMEMs are flexible hierarchical models that are able to account ... 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
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
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
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
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
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
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
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
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
Measuring Dielectric Properties and Surface Resistance of Microwave PCBs in the K-bandDec 05 2003Dec 08 2003The theoretical model is fully developed and the test rig is designed for the measurements of microwave parameters of unclad and laminated dielectric substrates. The geometry of the electromagnetic field in the resonator allows dielectric measurements ... 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
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
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
The heat flow of the CCR algebraMay 24 2000Let P and Q be the canonical operators acting on the Hilbert space of all L^2 functions on the real line, defined appropriately on a common dense domain. The derivations D_P(A) = i(PA - AP) and D_Q(A) = i(QA - AQ) act on the *-algebra of all integral ... More
The curvature invariant of a Hilbert module over C[z_1,...,z_d]Aug 23 1998A notion of curvature is introduced in multivariable operator theory and an analogue of the Gauss-Bonnet-Chern theorem is established for graded (contractive) Hilbert modules over the complex polynomial algebra in d variables, d=1,2,3,.... The curvature ... More
Non-commutative spheres and numerical quantum mechanicsNov 30 1992Jan 18 1993We discuss some basic issues that arise when one attempts to model quantum mechanical systems on a computer, and we describe the mathematical structure of the resulting discretized cannonical commutation relations.
Improper filtrations for C*-algebras: spectra of unilateral tridiagonal operatorsNov 23 1992Nov 24 1992We extend the results of our previous paper "C*-algebras and numerical linear algebra" to cover the case of "unilateral" sections. This situation bears a close resemblance to the case of Toeplitz operators on Hardy spaces, in spite of the fact that the ... More
Helson and subdiagonal operator algebrasJan 21 2011This article shows how the work of Henry Helson, especially the two papers of Helson and Lowdenslager, came to influence the development of the theory of non self adjoint operator algebras acting on Hilbert space.
Noncommutative flows I: dynamical invariantsDec 19 1995We show that a noncommutative dynamical system of the type that occurs in quantum theory can often be associated with a dynamical principle; that is, an infinitesimal structure that completely determines the dynamics. The nature of these dynamical principles ... More
C*-algebras and numerical linear algebraNov 22 1992Jan 18 1993We consider problems associated with the computation of spectra of self-adjoint operators in terms of the eigenvalue distributions of their n x n sections. Under rather general circumstances, we show how these eigenvalues accumulate near points of the ... 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
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
Hamiltonicity of the Cayley Digraph on the Symmetric Group Generated by σ = (1 2 ... n) and τ = (1 2)Jul 09 2013Jul 06 2017The 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.
$\mathsf{QMA}$ Lower Bounds for Approximate CountingFeb 06 2019We prove a query complexity lower bound for $\mathsf{QMA}$ protocols that solve approximate counting: estimating the size of a set given a membership oracle. This gives rise to an oracle $A$ such that $\mathsf{SBP}^A \not\subset \mathsf{QMA}^A$, resolving ... 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
EMU and ECB ConflictsJul 21 2018In dynamical framework the conflict between government and the central bank according to the exchange Rate of payment of fixed rates and fixed rates of fixed income (EMU) convergence criteria such that the public debt / GDP ratio The method consists of ... More
The Free Cover of a Row ContractionMar 15 2004Apr 15 2004We establish the existence and uniqueness of finite free resolutions - and their attendant Betti numbers - for graded commuting d-tuples of Hilbert space operators. Our approach is based on the notion of free cover of a (perhaps noncommutative) row contraction. ... 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
The noncommutative Choquet boundary III: Operator systems in matrix algebrasOct 23 2008Oct 25 2008We classify operator systems $S\subseteq \mathcal B(H)$ that act on finite dimensional Hilbert spaces by making use of the noncommutative Choquet boundary. S is said to be {\em reduced} when its boundary ideal is 0. In the category of operator systems, ... More
Self-organized avalanches in globally-coupled phase oscillatorsJun 13 2019Spontaneous desynchronization of coupled oscillators occurs in diverse systems spanning from the mammalian brain to alternating current power grids. Here, we model desynchronization using a generalization of the classical Kuramoto model, which includes ... More
Real-Time Stochastic Predictive Control for Hybrid Vehicle Energy ManagementApr 23 2018This work presents three computational methods for real time energy management in a hybrid hydraulic vehicle (HHV) when driver behavior and vehicle route are not known in advance. These methods, implemented in a receding horizon control (aka model predictive ... More
Syntactic and Semantic Distribution in Quantum MeasurementDec 06 2005The nondistributivity of compound quantum mechanical propositions leads to a theorem that rules out the possibility of microscopic deterministic hidden variables, the Logical No-Go Theorem. We observe that there appear in fact two distinct nondistributivity ... More
A Question of Self-consistent SemifactualityDec 06 2005Dec 07 2005This article is intended as a compendium and guide to the variety of Bell Inequality derivations that have appeared in the literature in recent years, classifying them into six broad categories, revealing the underlying, often hidden, assumption common ... More
Revisiting the Eichten - Feinberg - Gromes Q \bar{Q} Spin-Orbit InteractionJul 01 1996Dec 17 1999Invariant and covariant forms of the quark-antiquark interaction derived by the method of Eichten and Feinberg are considered. Relations between the various terms imposed by Lorentz transformation constraints, here called Gromes relations, are found to ... More
Salpeter amplitudes in a Wilson-loop contextJul 01 1996The bound state problem for a gauge invariant quark-antiquark system is considered in the instantaneous rest frame. Focus here is on the long range non-perturbative interaction. A two-time Green's function is constructed for Salpeter amplitudes. The corresponding ... More
Wilson loop evaluations in the stochastic vacuum modelOct 20 1998Feb 02 2001The stochastic vacuum model description of a heavy meson is discussed in the context of a gauge invariant approach where Wilson loop expectation values appear naturally in the O($v^2$) spin-orbit Hamiltonian. These expectation values have been derived ... More
Extensions of almost faithful prime ideals in virtually nilpotent mod-$p$ Iwasawa algebrasOct 12 2016Apr 25 2017Let $G$ be a nilpotent-by-finite compact $p$-adic analytic group for some $p>2$, and $H = \mathbf{FN}_p(G)$ its finite-by-(nilpotent $p$-valuable) radical. Fix a finite field $k$ of characteristic $p$, and write $kG$ for the completed group ring of $G$ ... 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
Dynamic Time Warping in Strongly Subquadratic Time: Algorithms for the Low-Distance Regime and Approximate EvaluationApr 22 2019May 23 2019Dynamic time warping distance (DTW) is a widely used distance measure between time series. The best known algorithms for computing DTW run in near quadratic time, and conditional lower bounds prohibit the existence of significantly faster algorithms. ... More
Elimination of HIV in South Africa through expanded access to antiretroviral therapy: Cautions, caveats and the importance of parsimonyMar 26 2014In a recent article Hontelez and colleagues investigate the prospects for elimination of HIV in South Africa through expanded access to antiretroviral therapy (ART) using STDSIM, a micro-simulation model. One of the first published models to suggest that ... 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
How many ways can you make change: Some easy proofsJun 19 2014Jul 18 2014Given a dollar, how many ways are there to make change using pennies, nickels, dimes, and quarters? What if you are given a different amount of money? What if you use different coin denominations? This is a well known problem and formulas are known. We ... 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
On the Number of Not Powers in a Finite GroupNov 05 2018Let G be a finite group and let k be a positive integer. We examine the relationship between structural properties of G and the number of elements of G that are not kth powers in G. In particular, we examine a bound on |G| given by Lucido and Pournaki ... 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
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
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
Poincaré square series for the Weil representationApr 22 2017Jun 11 2017We calculate the Jacobi Eisenstein series of weight $k \ge 3$ for a certain representation of the Jacobi group, and evaluate these at $z = 0$ to give coefficient formulas for a family of modular forms $Q_{k,m,\beta}$ of weight $k \ge 5/2$ for the (dual) ... More
Vector-valued Hirzebruch-Zagier series and class number sumsNov 28 2017Mar 11 2018For any number $m \equiv 0,1 \, (4)$ we correct the generating function of Hurwitz class number sums $\sum_r H(4n - mr^2)$ to a modular form (or quasimodular form if $m$ is a square) of weight two for the Weil representation attached to a binary quadratic ... More
Experimental statistics of veering triangulationsOct 03 2017Mar 01 2018Certain fibered hyperbolic 3-manifolds admit a $\mathit{\text{layered veering triangulation}}$, which can be constructed algorithmically given the stable lamination of the monodromy. These triangulations were introduced by Agol in 2011, and have been ... More
Lifting non-ordinary cohomology classes for SL(3)Feb 19 2016Jul 27 2017In this paper, we present a generalisation of a theorem of David and Rob Pollack. In 'A construction of rigid analytic cohomology classes for congruence subgroups of SL(3,Z)', they give a very general argument for lifting ordinary eigenclasses (with respect ... 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
Spheroidal groups, virtual cohomology and lower dimensional G-spacesMay 08 2016A space is defined to be "$n$-spheroidal" if it has the homotopy type of an $n$-dimensional CW-complex $X$ with $H_{n}(X, \mathbb{Z})$ not zero and finitely generated. A group $G$ is called "$n$-spheroidal" if its classifying space $K(G,1)$ is $n$-spheroidal. ... More
New Examples of Torsion-Free Non-unique Product GroupsFeb 01 2013Nov 24 2013We give an infinite family of torsion-free groups that do not satisfy the unique product property. For these examples, we also show that each group contains arbitrarily large sets whose square has no uniquely represented element.