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8-Bit Approximations for Parallelism in Deep LearningNov 14 2015Feb 19 2016The creation of practical deep learning data-products often requires parallelization across processors and computers to make deep learning feasible on large data sets, but bottlenecks in communication bandwidth make it difficult to attain good speedups ... More

Sparse Networks from Scratch: Faster Training without Losing PerformanceJul 10 2019We demonstrate the possibility of what we call sparse learning: accelerated training of deep neural networks that maintain sparse weights throughout training while achieving performance levels competitive with dense networks. We accomplish this by developing ... More

Convolutional 2D Knowledge Graph EmbeddingsJul 05 2017Jul 04 2018Link prediction for knowledge graphs is the task of predicting missing relationships between entities. Previous work on link prediction has focused on shallow, fast models which can scale to large knowledge graphs. However, these models learn less expressive ... More

Network inference in the non-equilibrium steady stateJul 26 2016Non-equilibrium systems lack an explicit characterisation of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of parameters of a model when its dynamics lacks detailed balance. ... More

Jack the Reader - A Machine Reading FrameworkJun 20 2018Many Machine Reading and Natural Language Understanding tasks require reading supporting text in order to answer questions. For example, in Question Answering, the supporting text can be newswire or Wikipedia articles; in Natural Language Inference, premises ... More

On the edge energy of grapheneDec 12 2017Surface/edge energy is typically modeled as a continuous function of orientation, $\gamma({\bf n})$. We put forward a simple geometric argument that suggests this picture is inadequate for crystals with a non-Bravais lattice structure. In the case of ... More

Inferring the parameters of a Markov process from snapshots of the steady stateJul 13 2017Dec 14 2017We seek to infer the parameters of an ergodic Markov process from samples taken independently from the steady state. Our focus is on non-equilibrium processes, where the steady state is not described by the Boltzmann measure, but is generally unknown ... More

The mildly nonlinear imprint of structure on the CMBDec 03 1999Dec 05 1999I outline some nonperturbative relativistic effects that arise from gravitational corrections to the Boltzmann equations. These may be important for the study of CMB temperature anisotropies, particularly their interpretation. These terms are not included ... More

Are pre-main-sequence stars older than we thought?Jul 14 2009We fit the colour-magnitude diagrams of stars between the zero-age main-sequence and terminal-age main sequence in young clusters and associations. The ages we derive are a factor 1.5 to 2 longer than the commonly used ages for these regions, which are ... More

On the equivalence of the discrete nonlinear Schrödinger equation and the discrete isotropic Heisenberg magnetJun 28 1999The equivalence of the discrete isotropic Heisenberg magnet (IHM) model and the discrete nonlinear Schr\"odinger equation (NLSE) given by Ablowitz and Ladik is shown. This is used to derive the equivalence of their discretization with the one by Izergin ... More

A Structured Variational Auto-encoder for Learning Deep Hierarchies of Sparse FeaturesFeb 28 2016In this note we present a generative model of natural images consisting of a deep hierarchy of layers of latent random variables, each of which follows a new type of distribution that we call rectified Gaussian. These rectified Gaussian units allow spike-and-slab ... More

What Bell DidAug 08 2014On the 50th anniversary of Bell's monumental 1964 paper, there is still widespread misunderstanding about exactly what Bell proved. This misunderstanding derives in turn from a failure to appreciate the earlier arguments of Einstein, Podolsky and Rosen. ... More

Reply to WernerAug 08 2014Reinhard Werner authored a comment on my paper "What Bell Did", disputing the conclusion and argumentation of the paper. This is my reply.

Euclidean-valued group cohomology is always reducedOct 11 2013Nov 25 2013If G is a countable discrete group acting linearly on a finite-dimensional vector space over any topological field, then the groups of coboundaries are closed for the product topology in all degrees, and hence the cohomology is reduced in all degrees. ... More

The No-Boundary Probability for the Universe starting at the top of the hillApr 16 2007We use the Hartle-Hawking No-Boundary Proposal to make a comparison between the probabilities of the universe starting near, and at, the top of a hill in the effective potential. In the context of top-down cosmology, our calculation finds that the universe ... More

Correlation functions, null polygonal Wilson loops, and local operatorsOct 18 2011Jul 30 2012We consider the ratio of the correlation function of n+1 local operators over the correlator of the first n of these operators in planar N=4 super-Yang-Mills theory, and consider the limit where the first n operators become pairwise null separated. By ... More

Privacy Implications of Health Information Seeking on the WebApr 07 2014Mar 06 2015This article investigates privacy risks to those visiting health- related web pages. The population of pages analyzed is derived from the 50 top search results for 1,986 common diseases. This yielded a total population of 80,124 unique pages which were ... More

The LSST Data Processing Software Stack: Summer 2015 ReleaseNov 20 2015The Large Synoptic Survey Telescope (LSST) is an 8-m optical ground-based telescope being constructed on Cerro Pachon in Chile. LSST will survey half the sky every few nights in six optical bands. The data will be transferred to NCSA and within 60 seconds ... More

The structure of low-complexity Gibbs measures on product spacesOct 16 2018Mar 04 2019Let $K_1$, $\dots$, $K_n$ be bounded, complete, separable metric spaces. Let $\lambda_i$ be a Borel probability measure on $K_i$ for each $i$. Let $f:\prod_i K_i \to \mathbb{R}$ be a bounded and continuous potential function, and let $$\mu(d \mathbf{x})\ ... More

On the regularity over positively graded algebrasDec 20 2006Aug 30 2007We study the relationship between the Tor-regularity and the local-regularity over a positively graded algebra defined over a field which coincide if the algebra is a standard graded polynomial ring. In this case both are characterizations of the so-called ... More

Homological properties of bigraded algebrasNov 24 2000Sep 23 2001We study the x- and y-regularity of a bigraded K-algebra R. These notions are used to study asymptotic properties of certain finitely generated bigraded modules. As an application we get for any equigenerated graded ideal I upper bounds for the number ... More

A Geometric Embedding for Standard Analytic ModulesMar 28 2005Jun 11 2007In this manuscript we make a general study of the representations realized, for a reductive Lie group of Harish-Chandra class, on the compactly supported sheaf cohomology groups of an irreducible finite-rank polarized homogeneous vector bundle defined ... More

Norm convergence of continuous-time polynomial multiple ergodic averagesMar 01 2011Jul 01 2016For a jointly measurable probability-preserving action $\tau:\mathbb{R}^D\curvearrowright (X,\mu)$ and a tuple of polynomial maps $p_i:\mathbb{R}\to \mathbb{R}^D$, $i=1,2,...,k$, the multiple ergodic averages \[ \frac{1}{T}\int_0^T (f_1\circ \tau^{p_1(t)})(f_2\circ ... More

Uniform stability of linear evolution equations, with applications to parallel transportsFeb 12 2015I prove the bistability of linear evolution equations $x' = A(t)x$ in a Banach space $E$, where the operator-valued function $A$ is of the form $A(t) = f'(t)G(t,f(t))$ for a binary operator-valued function $G$ and a scalar function $f$. The constant that ... More

RectangularityAug 08 2011We introduce a condition on arrays in some way maximally distinct from Latin square condition, as well as some other conditions on algebras, graphs and $0,1$-matrices. We show that these are essentially the same structures, generalising a similar collection ... More

Rational group ring elements with kernels having irrational dimensionSep 12 2009Mar 12 2013We prove that there are examples of finitely generated groups G together with group ring elements Q \in \bbQ G for which the von Neumann dimension \dim_{LG}\ker Q is irrational, so (in conjunction with other known results) answering a question of Atiyah. ... More

The elementary obstruction and the Weil restrictionDec 20 2007Mar 31 2009In this text we investigate the good behaviour of the elementary obstruction, introduced by Colliot-Thelene and Sansuc. This is an obstruction to the existence of a rational points on certain algebraic varieties. Assuming some conditions on the Picard ... More

Discrete Hashimoto surfaces and a doubly discrete smokering flowJul 25 2000B\"acklund transformations for smooth and ``space discrete'' Hashimoto surfaces are discussed and a geometric interpretation is given. It is shown that the complex curvature of a discrete space curve evolves with the discrete nonlinear Schr\"odinger equation ... More

Behaviour of entropy under bounded and integrable orbit equivalenceApr 04 2016Nov 07 2016Let $G$ and $H$ be infinite finitely generated amenable groups. This paper studies two notions of equivalence between actions of such groups on standard Borel probability spaces. They are defined as stable orbit equivalences in which the associated cocycles ... More

The geometry of model spaces for probability-preserving actions of sofic groupsDec 04 2015Jun 06 2016Bowen's notion of sofic entropy is a powerful invariant for classifying probability-preserving actions of sofic groups. It can be defined in terms of the covering numbers of certain metric spaces associated to such an action, the `model spaces'. The metric ... More

An Interesting Gadget for Chain Pair SimplificationJul 22 2016In this paper we present an interesting gadget based on the chain pair simplification problem under the discrete Fr\'echet distance (CPS-3F), which allows the construction of arbitrarily long paths that must be chosen in the simplification of the two ... More

Known Radio Pulsars Do Not Contribute to the Galactic Center Gamma-Ray ExcessSep 09 2015Observations using the Fermi Large Area Telescope (Fermi-LAT) have found a significant gamma-ray excess surrounding the center of the Milky Way (GC). One possible interpretation of this excess invokes gamma-ray emission from an undiscovered population ... More

Constraints on the Size of Extra Dimensions from the Orbital Evolution of the Black-Hole X-Ray Binary XTE J1118+480Dec 03 2008Sep 30 2009In a universe of the Randall-Sundrum type, black holes are unstable and emit gravitational modes in the extra dimension. This leads to dramatically shortened lifetimes of astrophysical black holes and to an observable change of the orbital period of black-hole ... More

Neutralino annihilation processes in the minimal supergravity modelJun 13 2008We study all tree-level neutralino annihilation processes concerning energy-dependence at the mSUGRA benchmark point SPS1a using tree-level calculators MadGraph and CompHEP as well as FormCalc. We further investigate the total tree-level neutralino annihilation ... More

Testing the No-Hair Theorem with Observations of Black Holes in the Electromagnetic SpectrumFeb 24 2016May 20 2016According to the general-relativistic no-hair theorem, astrophysical black holes depend only on their masses and spins and are uniquely described by the Kerr metric. Mass and spin are the first two multipole moments of the Kerr spacetime and completely ... More

Transient Alert Follow-up Planned for CCATFeb 05 2014CCAT is a sub-millimeter telescope to be built on Cerro Chajnantor in Chile near the ALMA site. The remote location means that all observing will be done by remote observers with the future goal of fully autonomous observing using a dynamic scheduler. ... More

The renaissance of radio detection of cosmic raysOct 25 2013Nearly 50 years ago, the first radio signals from cosmic ray air showers were detected. After many successful studies, however, research ceased not even 10 years later. Only a decade ago, the field was revived with the application of powerful digital ... More

Reimplementing the Hierarchical Data System using HDF5Feb 13 2015The Starlink Hierarchical Data System has been a very successful niche astronomy file format and library for over 30 years. Development of the library was frozen ten years ago when funding for Starlink was stopped and almost no-one remains who understands ... More

Real Algebraic Geometry and its ApplicationsJun 23 2016This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to optimization, ... More

Twistor actions for gauge theory and gravityAug 13 2013Oct 09 2013This is a review of recent developments in the study of perturbative gauge theory and gravity using action functionals on twistor space. It is intended to provide a user-friendly introduction to twistor actions, geared towards researchers or graduate ... More

Gravity with a cosmological constant from rational curvesAug 11 2015Nov 19 2015We give a new formula for all tree-level correlators of boundary field insertions in gauged N=8 supergravity in AdS_4; this is an analog of the tree-level S-matrix in anti-de Sitter space. The formula is written in terms of rational maps from the Riemann ... More

Worldsheet factorization for twistor-stringsOct 31 2013Apr 17 2014We study the multiparticle factorization properties of two worldsheet theories which--at tree-level--describe the scattering of massless particles in four dimensions: the Berkovits-Witten twistor-string for N=4 super-Yang-Mills coupled to N=4 conformal ... More

Radio detection of extensive air showersJan 11 2017Radio detection of extensive air showers initiated in the Earth's atmosphere has made tremendous progress in the last decade. Today, radio detection is routinely used in several cosmic-ray observatories. The physics of the radio emission in air showers ... More

Star-Forming Galaxies Significantly Contribute to the Isotropic Gamma-Ray BackgroundDec 09 2016The origin of the isotropic gamma-ray background (IGRB) --- the portion of the extragalactic gamma-ray sky that is not resolvable into individual point sources --- provides a powerful probe into the evolution of the high-energy universe. Star-forming ... More

WebAL-1: Workshop on Artificial Life and the Web 2014 ProceedingsJun 10 2014Aug 07 2014Proceedings of WebAL-1: Workshop on Artificial Life and the Web 2014, held at the 14th International Conference on the Synthesis and Simulation of Living Systems (ALIFE 14), New York, NY, 31 July 2014.

Shape Dynamics and Effective Field TheoryMay 07 2013Shape Dynamics is a gauge theory based on spatial diffeomorphism- and Weyl-invariance which is locally indistinguishable form classical General Relativity. If taken seriously, it suggests that the spacetime--geometry picture that underlies General Relativity ... More

Physical Diffeomorphisms in Loop Quantum GravityOct 05 2006We investigate the action of diffeomorphisms in the context of Hamiltonian Gravity. By considering how the diffeomorphism-invariant Hilbert space of Loop Quantum Gravity should be constructed, we formulate a physical principle by demanding, that the gauge-invariant ... More

On discontinuities of cocycles in cohomology theories for topological groupsDec 07 2011Jun 13 2012This paper studies Moore's measurable cohomology theory for locally compact groups and Polish modules. An elementary dimension-shifting argument is used to show that all classes in that theory have representatives with considerable extra topological structure ... More

On Infinite Words Determined by Indexed LanguagesJun 12 2014Jun 17 2014We characterize the infinite words determined by indexed languages. An infinite language $L$ determines an infinite word $\alpha$ if every string in $L$ is a prefix of $\alpha$. If $L$ is regular or context-free, it is known that $\alpha$ must be ultimately ... More

A remark on Kähler forms on symmetric products of Riemann surfacesJan 31 2005Feb 27 2008Users of Heegaard Floer homology may be reassured to know that it can be made to conform exactly to the standard analytic pattern of Lagrangian Floer homology. This follows from the following remark, which we prove using an argument of J. Varouchas: the ... More

All Difference Family Structures arise from GroupsMay 28 2004Difference families are traditionally built using groups as their basis. This paper looks at what sort of generalised difference family constructions could be made, using the standard basis of translation and difference. The main result is that minimal ... More

Stochastic Heat Equations defined by Fractal Laplacians on Cantor-like SetsFeb 06 2019We study stochastic heat equations defined by fractal Laplacians on Cantor-like sets. For this purpose, we give an improved estimate on the uniform norm of eigenfunctions and resulting heat kernel estimates. Then, we prove existence and uniqueness of ... More

A Robust Method for Treating Astrophysical Mismodeling in Dark Matter Annihilation Searches of Dwarf Spheroidal GalaxiesMay 28 2019Fermi-LAT observations have strongly constrained dark matter annihilation through the joint-likelihood analysis of dwarf spheroidal galaxies (dSphs). These constraints are expected to be robust because dSphs have measurable dark matter content and produce ... More

Complexity Theory, Game Theory, and EconomicsJan 02 2018This document collects the lecture notes from my mini-course "Complexity Theory, Game Theory, and Economics," taught at the Bellairs Research Institute of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th McGill Invitational Workshop ... More

The airglow layer emission altitude cannot be determined unambiguously from temperature comparison with lidarsOct 23 2017Jun 01 2018I investigate the nightly mean emission height and width of the OH*(3-1) layer by comparing nightly mean temperatures measured by the ground-based spectrometer GRIPS 9 and the Na lidar at ALOMAR. The data set contains 42 coincident measurements between ... More

Solvable Base Change and Rankin-Selberg ConvolutionsOct 30 2009Given unitary automorphic cuspidal representations $\pi$ and $\pi'$ defined on $GL_n(\mathbb{A}_E)$ and $GL_m(\mathbb{A}_F)$, respectively, with $E$ and $F$ solvable algebraic number fields we deduce a prime number theorem for the Rankin-Selberg L-function ... More

Pleasant extensions retaining algebraic structure, IIOct 06 2009Sep 16 2014In this paper we combine the general tools developed in (arXiv:0905.0518) with several ideas taken from earlier work on one-dimensional nonconventional ergodic averages by Furstenberg and Weiss, Host and Kra and Ziegler to study the averages $\frac{1}{N}\sum_{n=1}^N(f_1\circ ... More

L'invariant de Suslin en caractéristique positiveJul 28 2009Pour une k-alg\`ebre simple centrale A d'indice inversible dans k, Suslin a d\'efini un invariant cohomologique de SK_1(A). Dans ce texte, nous g\'en\'eralisons cet invariant \`a toute k-alg\`ebre simple centrale par un rel\`evement de la caract\'eristique ... More

A proof of Walsh's convergence theorem using couplingsOct 11 2013Oct 22 2013Walsh has recently proved the norm convergence of all nonconventional ergodic averages involving polynomial sequences in discrete nilpotent acting groups. He deduces this convergence from an equivalent, `finitary' assertion of stability over arbitrarily ... More

Exchangeable random measuresFeb 08 2013Jul 08 2015Let A be a standard Borel space, and consider the space A^{\bbN^{(k)}} of A-valued arrays indexed by all size-k subsets of \bbN. This paper concerns random measures on such a space whose laws are invariant under the natural action of permutations of \bbN. ... More

Partial difference equations over compact Abelian groups, I: modules of solutionsMay 30 2013Oct 25 2014Consider a compact Abelian group $Z$ and closed subgroups $U_1$, \ldots, $U_k \leq Z$. Let $\mathbb{T} := \mathbb{R}/\mathbb{Z}$. This paper examines two kinds of functional equation for measurable functions $Z\to \mathbb{T}$. First, given $f:Z\to \mathbb{T}$ ... More

Uchiyama's conjecture on sums of squaresDec 19 2017Uchiyama showed that every interval $(n, n + c n^{1/4})$ contains an integer that is the sum of two squares, where $c= 2^{3/2}$. He also conjectured a minimal value of $c$ such that the above statement still holds. We investigate this claim.

Betti numbers and shifts in minimal graded free resolutionsJan 06 2007Jul 14 2011Let S be a polynomial ring and R=S/I where I is a graded ideal of S. The Multiplicity Conjecture of Herzog, Huneke, and Srinivasan which was recently proved using the Boij-Soederberg theory states that the multiplicity of R is bounded above by a function ... More

Strictly elliptic operators with Dirichlet boundary conditions on spaces of continuous functions on manifoldsAug 20 2018Jul 11 2019We study strictly elliptic differential operators with Dirichlet boundary conditions on the space $\mathrm{C}(\overline{M})$ of continuous functions on a compact, Riemannian manifold $\overline{M}$ with boundary and prove sectoriality with optimal angle ... More

Generalised Swan modules and the D(2) problemJan 16 2006Feb 26 2009We give a detailed proof that, for any natural number n, each algebraic two complex over C_n \times C_\infty is realised up to congruence by a geometric complex arising from a presentation for the group.

The Effective Cone of Moduli Spaces of Sheaves on a Smooth Quadric SurfaceJul 25 2016Let $\xi$ be a stable Chern character on $\mathbb{P}^1 \times \mathbb{P}^1$, and let $M(\xi)$ be the moduli space of Gieseker semistable sheaves on $\mathbb{P}^1 \times \mathbb{P}^1$ with Chern character $\xi$. In this paper, we provide an approach to ... More

Note on bounds for multiplicitiesNov 03 2003Jun 21 2004Let S=K[x_1,...,x_n] be a polynomial ring and R=S/I be a graded K-algebra where I is a graded ideal in S. Herzog, Huneke and Srinivasan have conjectured that the multiplicity of R is bounded above by a function of the maximal shifts in the minimal graded ... More

Additivity properties of sofic entropy and measures on model spacesOct 08 2015Jun 13 2016Sofic entropy is an invariant for probability-preserving actions of sofic groups. It was introduced a few years ago by Lewis Bowen, and shown to extend the classical Kolmogorov-Sinai entropy from the setting of amenable groups. Some parts of Kolmogorov-Sinai ... More

Entropy of probability kernels from the backwards tail boundaryMay 20 2014Aug 23 2015A number of recent works have sought to generalize the Kolmogorov-Sinai entropy of probability-preserving transformations to the setting of Markov operators acting on the integrable functions on a probability space $(X,\mu)$. These have culminated in ... More

On the failure of concentration for the \ell_\infty-ballSep 12 2013Jun 23 2014Let $(X,d)$ be a compact metric space and $\mu$ a Borel probability on $X$. For each $N\geq 1$ let $d^N_\infty$ be the $\ell_\infty$-product on $X^N$ of copies of $d$, and consider $1$-Lipschitz functions $X^N\to\mathbb{R}$ for $d^N_\infty$. If the support ... More

A CAT(0)-valued pointwise ergodic theoremMay 05 2009Feb 25 2016In this note we prove the a pointwise ergodic theorem for functions taking values in a separable complete CAT(0)-space, analogous to Lindenstrauss' pointwise ergodic theorem for real-valued integrable functions on a probability space subject to a probability-preserving ... More

Scenery entropy as an invariant of RWRS processesMay 06 2014Probabilistic models of random walks in random sceneries give rise to examples of probability-preserving dynamical systems. A point in the state spaces consists of a walk-trajectory and a scenery, and its `motion' corresponds to shifting the time-origin. ... More

Towards a Noether-like conservation law theorem for one dimensional reversible cellular automataDec 01 2003Evidence and results suggesting that a Noether--like theorem for conservation laws in 1D RCA can be obtained. Unlike Noether's theorem, the connection here is to the maximal congruences rather than the automorphisms of the local dynamics. We take the ... More

Electroweak Physics Results from NuTeVMay 22 2002NuTeV has performed precise measurements of neutral-current to charged-current cross section ratios using intense high energy neutrino and anti-neutrino beams on a primarily steel target at the Fermilab Tevatron. A null hypothesis test of the standard ... More

Inner Accretion Disk Edges in a Kerr-Like SpacetimeApr 30 2013Jun 06 2013According to the no-hair theorem, astrophysical black holes are uniquely described by the Kerr metric. In order to test this theorem with observations in either the electromagnetic or gravitational-wave spectra, several Kerr-like spacetimes have been ... More

Beyond the Standard Model Higgs Boson Searches at the TevatronDec 02 2010Results are presented for beyond the Standard Model Higgs boson searches using up to 4.2 fb-1 of data from Run II at the Tevatron. No significant excess is observed in any of the channels so 95% confidence level limits are presented.

Sgr A* and General RelativityDec 11 2015May 09 2016General relativity has been widely tested in weak gravitational fields but still stands largely untested in the strong-field regime. According to the no-hair theorem, black holes in general relativity depend only on their masses and spins and are described ... More

Invariant Set Theory: Violating Measurement Independence without Fine Tuning, Conspiracy, Constraints on Free Will or RetrocausalityJul 07 2015Nov 06 2015Invariant Set (IS) theory is a locally causal ontic theory of physics based on the Cosmological Invariant Set postulate that the universe $U$ can be considered a deterministic dynamical system evolving precisely on a (suitably constructed) fractal dynamically ... More

Observable Equivalence between General Relativity and Shape DynamicsMar 29 2012In this conceptual paper we construct a local version of Shape Dynamics that is equivalent to General Relativity in the sense that the algebras of Dirac observables weakly coincide. This allows us to identify Shape Dynamics observables with General Relativity ... More

Shape DynamicsAug 26 2011General Relativity can be reformulated as a geometrodynamical theory, called Shape Dynamics, that is not based on spacetime (in particular refoliation) symmetry but on spatial diffeomorphism and local spatial conformal symmetry. This leads to a constraint ... More

Reduction of a Quantum TheoryDec 21 2006This paper serves as a preparation of work that focuses on extracting cosmological sectors from Loop Quantum Gravity. We start with studying the extraction of subsystems from classical systems. A classical Hamiltonian system can be reduced to a subsystem ... More

Counting Cliques in Finite Distant GraphsDec 23 2016We state and prove some counting formulas relating to cliques in the distant graphs of projective lines over finite rings. As a preliminary to this, we prove a decomposition theorem for the graphs in terms of the direct-product decomposition of their ... More

Equidistribution of joinings under off-diagonal polynomial flows of nilpotent Lie groupsMay 27 2011Jul 01 2016Let $G$ be a connected nilpotent Lie group. Given probability-preserving $G$-actions $(X_i,\Sigma_i,\mu_i,u_i)$, $i=0,1,...,k$, and also polynomial maps $\phi_i:\mathbb{R}\to G$, $i=1,...,k$, we consider the trajectory of a joining $\lambda$ of the systems ... More

Beyond the RPA on the cheap: improved correlation energies with the efficient "Radial Exchange Hole" kernelAug 27 2012The "ACFD-RPA" correlation energy functional has been widely applied to a variety of systems to successfully predict energy differences, and less successfully predict absolute correlation energies. Here we present a parameter-free exchange-correlation ... More

The one-arm exponent for mean-field long-range percolationNov 11 2014Consider a long-range percolation model on $\mathbb{Z}^d$ where the probability that an edge $\{x,y\} \in \mathbb{Z}^d \times \mathbb{Z}^d$ is open is proportional to $\|x-y\|_2^{-d-\alpha}$ for some $\alpha >0$ and where $d > 3 \min\{2,\alpha\}$. We ... More

The n-homology of representationsApr 01 2008Jun 23 2008This is an expository article, written for a special edition of the journal of the UMA (Union Matematica Argentina) commemorating the mathematician Misha Cotlar. The article gives an introduction to the n-homology groups and surveys some developments, ... More

Strictly elliptic operators with Dirichlet boundary conditions on spaces of continuous functions on manifoldsAug 20 2018Jan 14 2019We study strictly elliptic differential operators with Dirichlet boundary conditions on the space $\mathrm{C}(\overline{M})$ of continuous functions on a compact, Riemannian manifold $\overline{M}$ with boundary and prove sectoriality with optimal angle ... More

Who discovered positron annihilation?Sep 13 2018In the early 1930s, the positron, pair production, and, at last, positron annihilation were discovered. Over the years, several scientists have been credited with the discovery of the annihilation radiation. Commonly, Thibaud and Joliot have received ... More

The ECMWF Ensemble Prediction System: Looking Back (more than) 25 Years and Projecting Forward 25 YearsMar 16 2018This paper has been written to mark 25 years of operational medium-range ensemble forecasting. The origins of the ECMWF Ensemble Prediction System are outlined, including the development of the precursor real-time Met Office monthly ensemble forecast ... More

Modern Python at the Large Synoptic Survey TelescopeDec 01 2017The LSST software systems make extensive use of Python, with almost all of it initially being developed solely in Python 2. Since LSST will be commissioned when Python 2 is end-of-lifed it is critical that we have all our code support Python 3 before ... More

A Discussion on Solving Partial Differential Equations using Neural NetworksApr 15 2019Can neural networks learn to solve partial differential equations (PDEs)? We investigate this question for two (systems of) PDEs, namely, the Poisson equation and the steady Navier--Stokes equations. The contributions of this paper are five-fold. (1) ... More

A Characterization of Morphic Words with Polynomial GrowthMar 24 2019A morphic word is obtained by iterating a morphism to generate an infinite word, and then applying a coding. We characterize morphic words with polynomial growth in terms of a new type of infinite word called a $\textit{zigzag word}$. A zigzag word is ... More

Free Semialgebraic GeometryFeb 28 2019This is a survey article on the currently very active research area of free (=non-commutative) real algebra and geometry. We first review some of the important results from the commutative theory, and then explain similarities and differences as well ... More

Contrastive Explanation: A Structural-Model ApproachNov 07 2018The topic of causal explanation in artificial intelligence has gathered interest in recent years as researchers and practitioners aim to increase trust and understanding of intelligent decision-making and action. While different sub-fields have looked ... More

Gluing and deformations of asymptotically cylindrical special LagrangiansSep 27 2017We study gluings of asymptotically cylindrical special Lagrangian submanifolds in asymptotically cylindrical Calabi--Yau manifolds. We prove both that there is a well-defined gluing map, and, after reviewing the deformation theory for special Lagrangians, ... More

Time Symmetric Quantum Theory Without RetrocausalityJul 24 2017In their recent paper "Is a Time Symmetric Interpretation of Quantum Theory Possible Without Retrocausality?", Matthew Leifer and Matthew Pusey argue that the answer to their title question is "no". Unfortunately, the central proof offered in the paper ... More

An alternative ending to "Pleasant extensions retaining algebraic structure''Oct 06 2009May 24 2010The culmination of the papers (arXiv:0905.0518, arXiv:0910.0909) was a proof of the norm convergence in $L^2(\mu)$ of the quadratic nonconventional ergodic averages \frac{1}{N}\sum_{n=1}^N(f_1\circ T_1^{n^2})(f_2\circ T_1^{n^2}T_2^n)\quad\quad f_1,f_2\in ... More

What Teachers Should Know about the Bootstrap: Resampling in the Undergraduate Statistics CurriculumNov 19 2014I have three goals in this article: (1) To show the enormous potential of bootstrapping and permutation tests to help students understand statistical concepts including sampling distributions, standard errors, bias, confidence intervals, null distributions, ... More

Deducing the Density Hales-Jewett Theorem from an infinitary removal lemmaMar 09 2009Apr 19 2011We offer a new proof of Furstenberg and Katznelson's density version of the Hales-Jewett Theorem: For any $\delta > 0$ there is some $N_0 \geq 1$ such that whenever $A \subseteq [k]^N$ with $N \geq N_0$ and $|A|\geq \delta k^N$, $A$ contains a \textbf{combinatorial ... More

Plethysm and fast matrix multiplicationOct 02 2017Apr 09 2018Motivated by the symmetric version of matrix multiplication we study the plethysm $S^k(\mathfrak{sl}_n)$ of the adjoint representation $\mathfrak{sl}_n$ of the Lie group $SL_n$. In particular, we describe the decomposition of this representation into ... More