Results for "Richard J. Samworth"

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Peter Hall's work on high-dimensional data and classificationJun 03 2016In this article, I summarise Peter Hall's contributions to high-dimensional data, including their geometric representations and variable selection methods based on ranking. I also discuss his work on classification problems, concluding with some personal ... More
Recent progress in log-concave density estimationSep 10 2017In recent years, log-concave density estimation via maximum likelihood estimation has emerged as a fascinating alternative to traditional nonparametric smoothing techniques, such as kernel density estimation, which require the choice of one or more bandwidths. ... More
A Conversation with Jon WellnerAug 15 2018Jon August Wellner was born in Portland, Oregon, in August 1945. He received his Bachelor's degree from the University of Idaho in 1968 and his PhD degree from the University of Washington in 1975. From 1975 until 1983 he was an Assistant Professor and ... More
Generalised additive and index models with shape constraintsApr 10 2014We study generalised additive models, with shape restrictions (e.g. monotonicity, convexity, concavity) imposed on each component of the additive prediction function. We show that this framework facilitates a nonparametric estimator of each additive component, ... More
High-dimensional changepoint estimation via sparse projectionJun 20 2016Mar 17 2017Changepoints are a very common feature of Big Data that arrive in the form of a data stream. In this paper, we study high-dimensional time series in which, at certain time points, the mean structure changes in a sparse subset of the coordinates. The challenge ... More
Independent component analysis via nonparametric maximum likelihood estimationJun 03 2012Independent Component Analysis (ICA) models are very popular semiparametric models in which we observe independent copies of a random vector $X = AS$, where $A$ is a non-singular matrix and $S$ has independent components. We propose a new way of estimating ... More
High-dimensional changepoint estimation via sparse projectionJun 20 2016Changepoints are a very common feature of Big Data that arrive in the form of a data stream. In this paper, we study high-dimensional time series in which, at certain time points, the mean structure changes in a sparse subset of the coordinates. The challenge ... More
Smoothed log-concave maximum likelihood estimation with applicationsFeb 06 2011Jun 10 2012We study the smoothed log-concave maximum likelihood estimator of a probability distribution on $\mathbb{R}^d$. This is a fully automatic nonparametric density estimator, obtained as a canonical smoothing of the log-concave maximum likelihood estimator. ... More
High-dimensional nonparametric density estimation via symmetry and shape constraintsMar 14 2019We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and can mitigate ... More
Global rates of convergence in log-concave density estimationApr 08 2014Sep 26 2015The estimation of a log-concave density on $\mathbb{R}^d$ represents a central problem in the area of nonparametric inference under shape constraints. In this paper, we study the performance of log-concave density estimators with respect to global loss ... More
Sparse principal component analysis via random projectionsDec 15 2017Jul 24 2018We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected random projections of the sample covariance matrix. Unlike most alternative approaches, our algorithm is non-iterative, ... More
Variable selection with error control: Another look at Stability SelectionMay 27 2011Oct 05 2011Stability Selection was recently introduced by Meinshausen and Buhlmann (2010) as a very general technique designed to improve the performance of a variable selection algorithm. It is based on aggregating the results of applying a selection procedure ... More
A useful variant of the Davis--Kahan theorem for statisticiansMay 04 2014The Davis--Kahan theorem is used in the analysis of many statistical procedures to bound the distance between subspaces spanned by population eigenvectors and their sample versions. It relies on an eigenvalue separation condition between certain relevant ... More
Random projection ensemble classificationApr 17 2015We introduce a very general method for high-dimensional classification, based on careful combination of the results of applying an arbitrary base classifier to random projections of the feature vectors into a lower-dimensional space. In one special case ... More
Random-projection ensemble classificationApr 17 2015Jun 05 2017We introduce a very general method for high-dimensional classification, based on careful combination of the results of applying an arbitrary base classifier to random projections of the feature vectors into a lower-dimensional space. In one special case ... More
Nonparametric independence testing via mutual informationNov 17 2017We propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach, which we call MINT, is based on the estimation of mutual information, whose decomposition into joint and marginal entropies ... More
Confidence intervals for high-dimensional Cox modelsMar 03 2018The purpose of this paper is to construct confidence intervals for the regression coefficients in high-dimensional Cox proportional hazards regression models where the number of covariates may be larger than the sample size. Our debiased estimator construction ... More
Statistical and computational trade-offs in estimation of sparse principal componentsAug 22 2014Sep 28 2016In recent years, sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a population covariance ... More
The empirical process in Mallows distance, with application to goodness-of-fit testsApr 21 2005Nov 24 2005This paper has been temporarily withdrawn, pending a revised version taking into account similarities between this paper and the recent work of del Barrio, Gine and Utzet (Bernoulli, 11 (1), 2005, 131-189).
Central Limit Theorem and convergence to stable laws in Mallows distanceJun 10 2004Feb 22 2005We give a new proof of the classical Central Limit Theorem, in the Mallows ($L^r$-Wasserstein) distance. Our proof is elementary in the sense that it does not require complex analysis, but rather makes use of a simple subadditive inequality related to ... More
Adaptation in log-concave density estimationSep 03 2016The log-concave maximum likelihood estimator of a density on the real line based on a sample of size $n$ is known to attain the minimax optimal rate of convergence of $O(n^{-4/5})$ with respect to, e.g., squared Hellinger distance. In this paper, we show ... More
Efficient multivariate entropy estimation via $k$-nearest neighbour distancesJun 01 2016Jul 14 2016Many statistical procedures, including goodness-of-fit tests and methods for independent component analysis, rely critically on the estimation of the entropy of a distribution. In this paper, we seek entropy estimators that are efficient in the sense ... More
Classification with imperfect training labelsMay 29 2018Sep 26 2018We study the effect of imperfect training data labels on the performance of classification methods. In a general setting, where the probability that an observation in the training dataset is mislabelled may depend on both the feature vector and the true ... More
Efficient multivariate entropy estimation via $k$-nearest neighbour distancesJun 01 2016Jun 22 2017Many statistical procedures, including goodness-of-fit tests and methods for independent component analysis, rely critically on the estimation of the entropy of a distribution. In this paper, we seek entropy estimators that are efficient and achieve the ... More
Choice of neighbor order in nearest-neighbor classificationOct 29 2008The $k$th-nearest neighbor rule is arguably the simplest and most intuitively appealing nonparametric classification procedure. However, application of this method is inhibited by lack of knowledge about its properties, in particular, about the manner ... More
Robust inference with knockoffsJan 11 2018Jan 23 2018We consider the variable selection problem, which seeks to identify important variables influencing a response $Y$ out of many candidate features $X_1, \ldots, X_p$. We wish to do so while offering finite-sample guarantees about the fraction of false ... More
Local nearest neighbour classification with applications to semi-supervised learningApr 03 2017Aug 24 2018We derive a new asymptotic expansion for the global excess risk of a local $k$-nearest neighbour classifier, where the choice of $k$ may depend upon the test point. This expansion elucidates conditions under which the dominant contribution to the excess ... More
Importance TemperingJul 28 2007Nov 03 2008Simulated tempering (ST) is an established Markov chain Monte Carlo (MCMC) method for sampling from a multimodal density $\pi(\theta)$. Typically, ST involves introducing an auxiliary variable $k$ taking values in a finite subset of $[0,1]$ and indexing ... More
Convergence of the empirical process in Mallows distance, with an application to bootstrap performanceJun 29 2004We study the rate of convergence of the Mallows distance between the empirical distribution of a sample and the underlying population. The surprising feature of our results is that the convergence rate is slower in the discrete case than in the absolutely ... More
Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional densityAug 30 2009We present theoretical properties of the log-concave maximum likelihood estimator of a density based on an independent and identically distributed sample in $\mathbb{R}^d$. Our study covers both the case where the true underlying density is log-concave, ... More
Isotonic regression in general dimensionsAug 30 2017We study the least squares regression function estimator over the class of real-valued functions on $[0,1]^d$ that are increasing in each coordinate. For uniformly bounded signals and with a fixed, cubic lattice design, we establish that the estimator ... More
Adaptation in multivariate log-concave density estimationDec 30 2018We study the adaptation properties of the multivariate log-concave maximum likelihood estimator over two subclasses of log-concave densities. The first consists of densities with polyhedral support whose logarithms are piecewise affine. The complexity ... More
Ultrahigh dimensional variable selection: beyond the linear modelDec 17 2008Variable selection in high-dimensional space characterizes many contemporary problems in scientific discovery and decision making. Many frequently-used techniques are based on independence screening; examples include correlation ranking (Fan and Lv, 2008) ... More
Stochastic Search for Semiparametric Linear Regression ModelsJun 17 2011Oct 10 2011This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar (1987). The idea is to generate a random finite subset of a parameter space which will automatically contain ... More
Asymptotics and optimal bandwidth selection for highest density region estimationOct 04 2010We study kernel estimation of highest-density regions (HDR). Our main contributions are two-fold. First, we derive a uniform-in-bandwidth asymptotic approximation to a risk that is appropriate for HDR estimation. This approximation is then used to derive ... More
Saddlepoint methods in portfolio theoryDec 30 2011We discuss the use of saddlepoint methods in the analysis of portfolios, with particular reference to credit portfolios. The objective is to proceed from a model of the loss distribution, given through probabilities, correlations and the like, to an analytical ... More
Analytic and Numerical Models of Oxygen and Nutrient Diffusion, Metabolism Dynamics, and Architecture Optimization in Three-Dimensional Tissue Constructs with Applications and Insights in Cerebral OrganoidsDec 21 2015Diffusion models are important in tissue engineering as they enable an understanding of molecular delivery to cells in tissue constructs. As three-dimensional (3D) tissue constructs become larger, more intricate, and more clinically applicable, it will ... More
Universal trading under proportional transaction costsMar 21 2016The theory of optimal trading under proportional transaction costs has been considered from a variety of perspectives. In this paper, we show that all the results can be interpreted using a universal law, illustrating the results in trading algorithm ... More
Modal Decomposition of the von-Kármán Covariance of Atmospheric Turbulence in the Circular Entrance PupilNov 24 2009Nov 04 2010Estimators of outer scales of atmospheric turbulence usually fit the phase screen snapshots derived from local wave front sensors to a Zernike basis, and then compare the spectrum of expansion coefficients in this basis with a narrowing associated with ... More
Wide-band and Air Dispersion Effecting the ABCD Algorithm of Phase-Recovery in Long-baseline InterferometryMay 11 2006Jan 24 2007Long-baseline interferometry detects fringes created by superposition of two beams of light collected by two telescopes pointing into a common direction. The external path difference generated by pointing away from the zenith is commonly compensated by ... More
Orthogonal Linear Combinations of Gaussian Type OrbitalsJul 30 1999Jan 24 2009The set of Gaussian Type Orbitals g(n1,n2,n3) of order (n+1)(n+2)/2, of common n=n1+n2+n3<=7, common center and exponential, is customized to define a set of 2n+1 linear combinations t(n,m) (-n<=m<=n) such that each t(n,m) depends on the azimuthal and ... More
Corrigenda to "Interesting Series Involving the Central Binomial Coefficient" [Am. Math. Monthly vol 92 (1985)]May 02 2009These are seven corrigenda to equations in the Lehmer article in American Mathematical Monthly 92 (1985), pp 449--457, partially reproduced in the Apelblat tables of integrals and series.
Symmetry Analysis of the Kohn-Sham Band Structure of Bulk Lithium FluorideSep 25 2003Kohn-Sham orbitals of face-centered cubic lithium fluoride are calculated in prototypical local-density approximations to the exchange-correlation functional. The symmetry analysis of these Bloch functions in a LCAO basis on a path Gamma-X-W-K-Gamma-L-W ... More
Clustered Star Formation: A ReviewJul 31 2012In this contribution I present a review of star formation in clusters. I begin by discussing the various definitions of what constitutes a star cluster, and then compare the outcome of star formation (IMF, multiplicity, mass segregation and structure ... More
Further Spectroscopy of the Diffuse Ionized Gas in NGC 891 and Evidence for a Secondary Source of IonizationFeb 03 1998Two long-slit spectra of the diffuse ionized gas in NGC 891 are presented. The first reveals variations parallel to the major axis in emission line ratios in the halo gas at z=700 pc. It is found that filaments of Halpha emission show lower values of ... More
Interferometric 12CO Observations of the Central Disk of NGC 4631: An Energetic Molecular OutflowJan 05 2000We present interferometric observations of CO J=1-0 emission in the central regions of the edge-on galaxy NGC 4631, known for its extended gaseous halo and its tidal interactions. Previous single-dish observations revealed that almost all of the CO emission ... More
Instantons, Topological Strings and Enumerative GeometryDec 08 2009Mar 12 2010We review and elaborate on certain aspects of the connections between instanton counting in maximally supersymmetric gauge theories and the computation of enumerative invariants of smooth varieties. We study in detail three instances of gauge theories ... More
Quantum Gravity, Field Theory and Signatures of Noncommutative SpacetimeJun 16 2009Oct 05 2009A pedagogical introduction to some of the main ideas and results of field theories on quantized spacetimes is presented, with emphasis on what such field theories may teach us about the problem of quantizing gravity. We examine to what extent noncommutative ... More
Microscopic Spectrum of the QCD Dirac Operator in Three DimensionsSep 28 2000Dec 05 2000The microscopic spectral correlators of the Dirac operator in three-dimensional Yang-Mills theory coupled to fundamental fermions and with three or more colours are derived from the supersymmetric formulation of partially quenched effective Lagrangians. ... More
Quantization of Higher Abelian Gauge Theory in Generalized Differential CohomologySep 12 2012Oct 01 2012We review and elaborate on some aspects of the quantization of certain classes of higher abelian gauge theories using techniques of generalized differential cohomology. Particular emphasis is placed on the examples of generalized Maxwell theory and Cheeger-Simons ... More
Minimax Robust Function Reconstruction in Reproducing Kernel Hilbert SpacesJun 30 2007Jan 05 2013In this paper, we present a unified approach to function approximation in reproducing kernel Hilbert spaces (RKHS) that establishes a previously unrecognized optimality property for several well-known function approximation techniques, such as minimum-norm ... More
Dynamics versus structure: breaking the density degeneracy in star formationSep 30 2014The initial density of individual star-forming regions (and by extension the birth environment of planetary systems) is difficult to constrain due to the "density degeneracy problem": an initially dense region expands faster than a more quiescent region ... More
The effects of supernovae on the dynamical evolution of binary stars and star clustersSep 19 2016Sep 29 2016In this chapter I review the effects of supernovae explosions on the dynamical evolution of (1) binary stars and (2) star clusters. (1) Supernovae in binaries can drastically alter the orbit of the system, sometimes disrupting it entirely, and are thought ... More
Point Counts of D_k and Some A_k and E_k Integer Lattices Inside HypercubesFeb 19 2010Apr 21 2010Regular integer lattices are characterized by k unit vectors that build up their generator matrices. These have rank k for D-lattices, and are rank-deficient for A-lattices, for E_6 and E_7. We count lattice points inside hypercubes centered at the origin ... More
Elusive multiquark spectroscopyJan 29 2010A review is presented of past and recent attempts to build multiquark states within current models already describing ordinary mesons and baryons. This includes: coherence in the chromomagnetic interaction, tetraquarks with two heavy quarks, Steiner-tree ... More
Perspectives in hadron spectroscopyNov 17 2005Nov 21 2005A brief survey is presented of selected recent results in hadron spectroscopy and related theoretical studies. This includes the pentaquarks and hadrons containing one or two charmed quarks or antiquarks.
Speculations in hadron spectroscopyDec 17 2004A selected survey is presented of the recent progress in hadron spectroscopy. This includes spin-singlet charmonium states, excitations of charmonium and open-charm mesons, double-charm baryons, and pentaquark candidates. Models proposing exotic bound ... More
Review of experimental and theoretical status of the proton radius puzzleFeb 03 2017The discrepancy between the measured Lamb shift in muonic hydrogen and expectations from electron-proton scattering and regular hydrogen spectroscopy has become known as the proton radius puzzle, whose most "mundane" resolution requires a $> 5 \sigma$ ... More
The modern description of semileptonic meson form factorsJun 02 2006Jul 31 2006I describe recent advances in our understanding of the hadronic form factors governing semileptonic meson transitions. The resulting framework provides a systematic approach to the experimental data, as a means of extracting precision observables, testing ... More
Numerical Evaluation Of the Oscillatory Integral over exp(i*pi*x)*x^(1/x) between 1 and infinityDec 18 2009Aug 05 2010Real and imaginary part of the limit 2N->infinity of the integral int_{x=1..2N} exp(i*pi*x)*x^(1/x) dx are evaluated to 20 digits with brute force methods after multiple partial integration, or combining a standard Simpson integration over the first halve ... More
Twenty Digits of Some Integrals of the Prime Zeta FunctionNov 28 2008Sep 18 2018The double sum sum_(s >= 1) sum_p 1/(p^s log p^s) = 2.00666645... over the inverse of the product of prime powers p^s and their logarithms, is computed to 24 decimal digits. The sum covers all primes p and all integer exponents s>=1. The calculational ... More
Tile Count in the Interior of Regular 2n-gons Dissected by Diagonals Parallel to SidesNov 17 2009The regular 2n-gon (square, hexagon, octagon, ...) is subdivided into smaller polygons (tiles) by the subset of diagonals which run parallel to any of the 2n sides. The manuscript reports on the number of tiles up to the 78-gon.
Gruenhage compacta and strictly convex dual normsOct 29 2007We prove that if K is a Gruenhage compact space then C(K)* admits an equivalent, strictly convex dual norm. As a corollary, we show that if X is a Banach space and X* is the |.|-closed linear span of K, where K is a Gruenhage compact in the w*-topology ... More
An Introduction to Nonassociative PhysicsMar 13 2019We give a pedagogical introduction to the nonassociative structures arising from recent developments in quantum mechanics with magnetic monopoles, in string theory and M-theory with non-geometric fluxes, and in M-theory with non-geometric Kaluza-Klein ... More
Interdependent Security with Strategic Agents and Cascades of InfectionFeb 26 2015We investigate cascades in networks consisting of strategic agents with interdependent security. We assume that the strategic agents have choices between i) investing in protecting themselves, ii) purchasing insurance to transfer (some) risks, and iii) ... More
Patterned and Functionalized Nanofiber Scaffolds in Three-Dimensional Hydrogel Constructs Enhance Neurite Outgrowth and Directional ControlJan 07 2015Neural tissue engineering holds incredible potential to restore functional capabilities to damaged neural tissue. It was hypothesized that patterned and functionalized nanofiber scaffolds could control neurite direction and enhance neurite outgrowth. ... More
Scalar and Tensor Couplings in Kaon DecaysMar 30 1999Apr 23 1999In the past few years charged kaon experiments have indicated possible scalar and tensor couplings in semileptonic kaon decays(K --> pi e nu). These couplings, if correct, are not predicted by the Standard Model and may indicate the onset of new physics. ... More
Charged Higgs and Scalar Couplings in Semileptonic Meson DecayJan 15 1999Feb 10 1999We present a new charged Higgs search technique using the effects of scalar dynamics in semileptonic meson decay. Applying this method to a modest sample of B meson decays yields sensitivity to the high tan(beta) region well beyond existing charged Higgs ... More
Statistical Aspects of Baseline Calibration in Earth-Bound Optical Stellar InterferometryJun 14 2009Baseline calibration of a stellar interferometer is a prerequisite to data reduction of astrometric operations. This technique of astrometry is triangulation of star positions. Since angles are deduced from the baseline and delay side of these triangles, ... More
The Wigner 3n-j Graphs up to 12 VerticesSep 11 2011Jan 27 2012The 3-regular graphs representing sums over products of Wigner 3-jm symbols are drawn on up to 12 vertices (complete to 18j-symbols), and the irreducible graphs on up to 14 vertices (complete to 21j-symbols). The Lederer-Coxeter-Frucht notations of the ... More
A Table of Third and Fourth Order Feynman Diagrams of the Interacting Fermion Green's FunctionDec 04 2005Jan 25 2006The Feynman diagrams of the Green's function expansion of fermions interacting with a non-relativistic 2-body interaction are displayed in first, second and third order of the interaction as 2, 10 and 74 diagrams, respectively. A name convention for the ... More
Ionization, Kinematics, and Extent of the Diffuse Ionized Gas Halo of NGC 5775Jun 01 2000We present key results from deep spectra of the Diffuse Ionized Gas (DIG) halo of the edge-on galaxy NGC 5775. [NII]6583 has been detected up to about z=13 kpc above the plane in one of two vertically oriented long slits -- making this the spiral galaxy ... More
Perturbation Theory and TechniquesMay 16 2005May 27 2005Prepared for the Quantum Field Theory section of the Encyclopedia of Mathematical Physics, Elsevier, 2006. A brief introduction to the methodology and techniques of perturbative relativistic quantum field theory is presented.
Strings, Gauge Fields and MembranesMay 31 2004We present an overview of the intimate relationship between string and D-brane dynamics, and the dynamics of gauge and gravitational fields in three spacetime dimensions. The successes, prospects and open problems in describing both perturbative and nonperturbative ... More
String Holonomy and Extrinsic Geometry in Four-dimensional Topological Gauge TheoryApr 22 1998Jul 21 1998The most general gauge-invariant marginal deformation of four-dimensional abelian BF-type topological field theory is studied. It is shown that the deformed quantum field theory is topological and that its observables compute, in addition to the usual ... More
Equivariant Localization of Path IntegralsAug 12 1996We review equivariant localization techniques for the evaluation of Feynman path integrals. We develop systematic geometric methods for studying the semi-classical properties of phase space path integrals for dynamical systems, emphasizing the relations ... More
Matrix Models, Large N Limits and Noncommutative SolitonsDec 06 2005A survey of the interrelationships between matrix models and field theories on the noncommutative torus is presented. The discretization of noncommutative gauge theory by twisted reduced models is described along with a rigorous definition of the large ... More
Finite Volume Gauge Theory Partition Functions in Three DimensionsApr 25 2005Jun 20 2005We determine the fermion mass dependence of Euclidean finite volume partition functions for three-dimensional QCD in the epsilon-regime directly from the effective field theory of the pseudo-Goldstone modes by using zero-dimensional non-linear sigma-models. ... More
Quantum Field Theory on Noncommutative SpacesSep 20 2001Jan 23 2003A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner correspondence, noncommutative ... More
Survey of Dirichlet Series of Multiplicative Arithmetic FunctionsJun 20 2011Jul 04 2012The manuscript reviews Dirichlet Series of important multiplicative arithmetic functions. The aim is to represent these as products and ratios of Riemann zeta-functions, or, if that concise format is not found, to provide the leading factors of the infinite ... More
The Theoretical Agenda in CMB ResearchOct 15 1996The terrain that theorists cover in this CMB golden age is described. We ponder early universe physics in quest of the fluctuation generator. We extoll the virtues of inflation and defects. We transport fields, matter and radiation into the linear (primary ... More
Properties of Space MIMO Communication ChannelsJan 14 2016Jan 20 2016This paper discusses the characteristics of a space-to-space multiple-input, multiple-output (MIMO) communication channel that distinguish it from more common terrestrial MIMO communication channels. These characteristics imply that the channel matrices ... More
Historical Survey of the Quasi-Nuclear BaryoniumJun 02 1999We review ideas and speculations concerning possible bound states or resonances of the nucleon--antinucleon system.
Charmonium singlets, open charm and exotic hadronsJun 01 2007Jun 13 2007Caution is suggested on the comparison of the spin-singlet charmonium P-state with the centre of gravity of triplet states, when the mass splitting is of the order of a few MeV. The physics of new hidden-charm states X and Y is briefly reviewed. Perspectives ... More
Chebyshev Series Representation of Feigenbaum's Period-Doubling FunctionAug 26 2010The Feigenbaum-Cvitanovic equation -lambda * g(x)= g(g(lambda * x)) is solved over the interval 0 <= x <= 1 with a Chebyshev series representation of g(x). Accurate expansion coefficients are tabulated for solutions g(x) = 1+O(x^z) with even exponents ... More
Heavy-to-light meson form factors at large recoilMay 16 2005Jan 06 2006Heavy-to-light meson form factors at large recoil can be described using the same techniques as for hard exclusive processes involving only light hadrons. Two competing mechanisms appear in the large-recoil regime, describing so-called ``soft-overlap'' ... More
Two Integrals of Geodetic Lines in Oblate Ellipsoidal CoordinatesMay 20 2010The manuscript establishes a series expansion of the core integral that relates changes in longitude and latitude along the geodetic line in oblate elliptical coordinates, and of a companion integral which is the path length along this line as a function ... More
The series limit of sum_k 1/[k log k (log log k)^2]Feb 04 2009Feb 14 2009The slowly converging series sum_{k=3}^infinity 1/[k * log k * (log log k)^a] is evaluated to 38.4067680928 at a=2. After some initial terms, the infinite tail of the sum is replaced by the integral of the associated interpolating function, which is available ... More
Topologically Distinct Sets of Non-intersecting Circles in the PlaneFeb 29 2016Sep 19 2016Nested parentheses are forms in an algebra which define orders of evaluations. A class of well-formed sets of associated opening and closing parentheses is well studied in conjunction with Dyck paths and Catalan numbers. Nested parentheses also represent ... More
A C99 Implementation of the Clausen SumsSep 28 2013A C99 program is presented which calculates the Clausen sums for non-negative integer indices j and real arguments x. The implementation is split into three major cases. For large j, a direct, truncated summation of the sum is performed. For smaller j, ... More
Clebsch--Gordan Coefficients of the Quaternion GroupOct 11 2010The Clebsch--Gordan coefficients of the Kronecker products of the irreducible representations of the Quaternion Group Q8, of the Generalized Quaternion Groups Q16 and Q32, and of the factor group (Q32 X Q32)/{(1,1),(-1,-1)} are computed as eigenvectors ... More
Chebyshev Series Expansion of Inverse PolynomialsMar 22 2004Aug 23 2005An inverse polynomial has a Chebyshev series expansion 1/\sum(j=0..k)b_j*T_j(x)=\sum'(n=0..oo) a_n*T_n(x) if the polynomial has no roots in [-1,1]. If the inverse polynomial is decomposed into partial fractions, the a_n are linear combinations of simple ... More
Finite Square Lattice Vertex Cover by a Baseline Set Defined With a Minimum SublatticeNov 14 2008Each straight infinite line defined by two vertices of a finite square point lattice contains (covers) these two points and a - possibly empty - subset of points that happen to be collinear to these. This work documents vertex subsets of minimum order ... More
Tightly Circumscribed Regular PolygonsJan 26 2013A regular polygon circumscribing another regular polygon (with a different side number) may be tightened to minimize the difference of both areas. The manuscripts computes the optimum result under the restriction that both polygons are concentric, and ... More
Multi-Compartmental Biomaterial Scaffolds for Patterning Neural Tissue Organoids in Models of Neurodevelopment and Tissue RegenerationOct 08 2016Biomaterials are becoming an essential tool in the study and application of stem cell research. Various types of biomaterials enable three-dimensional (3D) culture of stem cells, and, more recently, also enable high-resolution patterning and organization ... More
Crystals, instantons and quantum toric geometryFeb 18 2011We describe the statistical mechanics of a melting crystal in three dimensions and its relation to a diverse range of models arising in combinatorics, algebraic geometry, integrable systems, low-dimensional gauge theories, topological string theory and ... More
D-Branes, Tachyons and K-HomologySep 25 2002Nov 12 2002We present an overview of the ways in which D-brane charges are classified in terms of K-theory, emphasizing the natural physical interpretations of a homological classification within a topological setting.
BUSSTEPP Lectures on String TheoryJul 15 2002This paper comprises the written version of the lectures on string theory delivered at the 31st British Universities Summer School on Theoretical Elementary Particle Physics which was held in Manchester, England, August 28 - September 12 2001.
Superconnections, Anomalies and Non-BPS Brane ChargesAug 07 2001Oct 09 2001The properties of brane-antibrane systems and systems of unstable D-branes in Type II superstring theory are investigated using the formalism of superconnections. The low-energy open string dynamics is shown to be probed by generalized Dirac operators. ... More
N=2 gauge theories, instanton moduli spaces and geometric representation theoryJul 02 2015Sep 24 2015We survey some of the AGT relations between N=2 gauge theories in four dimensions and geometric representations of symmetry algebras of two-dimensional conformal field theory on the equivariant cohomology of their instanton moduli spaces. We treat the ... More