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Abstracting Runtime Heaps for Program UnderstandingJan 06 2012Modern programming environments provide extensive support for inspecting, analyzing, and testing programs based on the algorithmic structure of a program. Unfortunately, support for inspecting and understanding runtime data structures during execution ... More

Principal arc analysis on direct product manifoldsApr 18 2011We propose a new approach to analyze data that naturally lie on manifolds. We focus on a special class of manifolds, called direct product manifolds, whose intrinsic dimension could be very high. Our method finds a low-dimensional representation of the ... More

McFly: Time-Travel Debugging for the WebOct 28 2018Time-traveling debuggers offer the promise of simplifying debugging by letting developers freely step forwards and backwards through a program's execution. However, web applications present multiple challenges that make time-travel debugging especially ... More

Are My Invariants Valid? A Learning ApproachMar 14 2019Ensuring that a program operates correctly is a difficult task in large, complex systems. Enshrining invariants -- desired properties of correct execution -- in code or comments can support maintainability and help sustain correctness. Tools that can ... More

Are My Invariants Valid? A Learning ApproachMar 14 2019Mar 15 2019Ensuring that a program operates correctly is a difficult task in large, complex systems. Enshrining invariants -- desired properties of correct execution -- in code or comments can support maintainability and help sustain correctness. Tools that can ... More

A General Framework For Consistency of Principal Component AnalysisNov 12 2012Nov 13 2013A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to investigate interesting ... More

Surprising Asymptotic Conical Structure in Critical Sample Eigen-DirectionsMar 25 2013The aim of this paper is to establish several deep theoretical properties of principal component analysis for multiple-component spike covariance models. Our new results reveal a surprising asymptotic conical structure in critical sample eigendirections ... More

Co-occurrence Matrix and Fractal Dimension for Image SegmentationAug 29 2009Dec 06 2011One of the most important tasks in image processing problem and machine vision is object recognition, and the success of many proposed methods relies on a suitable choice of algorithm for the segmentation of an image. This paper focuses on how to apply ... More

Program Synthesis using Natural LanguageSep 01 2015Interacting with computers is a ubiquitous activity for millions of people. Repetitive or specialized tasks often require creation of small, often one-off, programs. End-users struggle with learning and using the myriad of domain-specific languages (DSLs) ... More

Visualizing genetic constraintsDec 06 2013Principal Components Analysis (PCA) is a common way to study the sources of variation in a high-dimensional data set. Typically, the leading principal components are used to understand the variation in the data or to reduce the dimension of the data for ... More

Estimation of safety areas for epidemic spreadOct 30 2009In this work we study safety areas in epidemic spred. The aim of this work is, given the evolution of epidemic at time $t$, find a safety set at time $t+h$. This is, a random set $K_{t+h}$ such that the probability that infection reaches $K_{t+h}$ at ... More

Irregular sets and Central Limit Theorems for dependent triangular arraysNov 05 2009In previous papers, we studied the asymptotic behaviour of $S_N(A,X)=(2N+1)^{-d/2}\sum_{n \in A_N} X_n,$ where $X$ is a centered, stationary and weakly dependent random field, and $A_N=A \cap [-N,N]^d$, $A \subset \mathbb{Z}^d$. This leads to the definition ... More

Fast algorithms for large scale generalized distance weighted discriminationApr 19 2016Aug 17 2017High dimension low sample size statistical analysis is important in a wide range of applications. In such situations, the highly appealing discrimination method, support vector machine, can be improved to alleviate data piling at the margin. This leads ... More

Object oriented data analysis: Sets of treesNov 20 2007Object oriented data analysis is the statistical analysis of populations of complex objects. In the special case of functional data analysis, these data objects are curves, where standard Euclidean approaches, such as principal component analysis, have ... More

Analysis of nonlinear modes of variation for functional dataDec 17 2007A set of curves or images of similar shape is an increasingly common functional data set collected in the sciences. Principal Component Analysis (PCA) is the most widely used technique to decompose variation in functional data. However, the linear modes ... More

A scale-based approach to finding effective dimensionality in manifold learningOct 29 2007Mar 17 2008The discovering of low-dimensional manifolds in high-dimensional data is one of the main goals in manifold learning. We propose a new approach to identify the effective dimension (intrinsic dimension) of low-dimensional manifolds. The scale space viewpoint ... More

Analyzing Collaborative Forecast and Response NetworksJun 09 2013Collaborative forecasting involves exchanging information on how much of an item will be needed by a buyer and how much can be supplied by a seller or manufacturer in a supply chain. This exchange allows parties to plan their operations based on the needs ... More

PCA consistency in high dimension, low sample size contextNov 19 2009Principal Component Analysis (PCA) is an important tool of dimension reduction especially when the dimension (or the number of variables) is very high. Asymptotic studies where the sample size is fixed, and the dimension grows [i.e., High Dimension, Low ... More

Principal Nested Spheres for Time Warped Functional Data AnalysisApr 25 2013There are often two important types of variation in functional data: the horizontal (or phase) variation and the vertical (or amplitude) variation. These two types of variation have been appropriately separated and modeled through a domain warping method ... More

SiZer for Censored Density and Hazard EstimationJun 10 2008The SiZer method is extended to nonparametric hazard estimation and also to censored density and hazard estimation. The new method allows quick, visual statistical inference about the important issue of statistically significant increases and decreases ... More

A Note on Automatic Data TransformationJan 08 2016Modern data analysis frequently involves variables with highly non-Gaussian marginal distributions. However, commonly used analysis methods are most effective with roughly Gaussian data. This paper introduces an automatic transformation that improves ... More

Relative Optimality Conditions and Algorithms for Treespace Fréchet MeansOct 16 2014Aug 16 2017Recent interest in treespaces as well-founded mathematical domains for phylogenetic inference and statistical analysis for populations of anatomical trees has motivated research into efficient and rigorous methods for optimization problems on treespaces. ... More

Consistency of Sparse PCA in High Dimension, Low Sample Size ContextsApr 21 2011Sparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or the number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most loadings are zero. ... More

Significance Analysis for Pairwise Variable Selection in ClassificationFeb 18 2014The goal of this article is to select important variables that can distinguish one class of data from another. A marginal variable selection method ranks the marginal effects for classification of individual variables, and is a useful and efficient approach ... More

MultiResolution Anomaly Detection Method for Long Range Dependent Time SeriesSep 08 2008Driven by network intrusion detection, we propose a MultiResolution Anomaly Detection (MRAD) method, which effectively utilizes the multiscale properties of Internet features and network anomalies. In this paper, several theoretical properties of the ... More

High velocity gas from the Galactic dark haloNov 13 1998We present the germ of a new model for High Velocity Clouds, derived from the idea that the dark matter halo of our Galaxy is in the form of cold, planetary-mass gas clouds. In this picture HVCs arise as a result of disruptive collisions between dark ... More

Order-Revealing Encryption and the Hardness of Private LearningMay 03 2015An order-revealing encryption scheme gives a public procedure by which two ciphertexts can be compared to reveal the ordering of their underlying plaintexts. We show how to use order-revealing encryption to separate computationally efficient PAC learning ... More

The Cloudy UniverseJul 20 1999Modelling of Extreme Scattering Events suggests that the Galaxy's dark matter is an undetected population of cold, AU-sized, planetary-mass gas clouds. None of the direct observational constraints on this picture -- thermal/non-thermal emission, extinction ... More

A Probabilistic Model of Compound NounsSep 06 1994Compound nouns such as example noun compound are becoming more common in natural language and pose a number of difficult problems for NLP systems, notably increasing the complexity of parsing. In this paper we develop a probabilistic model for syntactically ... More

Relative Optimality Conditions and Algorithms for Treespace Fréchet MeansOct 16 2014Dec 10 2015Recent interest in treespaces as well-founded mathematical domains for phylogenetic inference and statistical analysis for populations of anatomical trees has motivated research into efficient and rigorous methods for optimization problems on treespaces. ... More

Non-iterative Joint and Individual Variation ExplainedDec 13 2015Apr 25 2016Integrative analysis of disparate data blocks measured on a common set of experimental subjects is one major challenge in modern data analysis. This data structure naturally motivates the simultaneous exploration of the joint and individual variation ... More

Object Oriented Data Analysis of Cell-Well Structured DataMar 19 2013Object oriented data analysis (OODA) aims at statistically analyzing populations of complicated objects. This paper is motivated by a study of cell images in cell culture biology, which highlights a common critical issue: choice of data objects. Instead ... More

SiZer for time series: A new approach to the analysis of trendsJun 28 2007Smoothing methods and SiZer are a useful statistical tool for discovering statistically significant structure in data. Based on scale space ideas originally developed in the computer vision literature, SiZer (SIgnificant ZERo crossing of the derivatives) ... More

Nested Nonnegative Cone AnalysisAug 20 2013Sep 06 2013Motivated by the analysis of nonnegative data objects, a novel Nested Nonnegative Cone Analysis (NNCA) approach is proposed to overcome some drawbacks of existing methods. The application of traditional PCA/SVD method to nonnegative data often cause the ... More

Latest Electroweak Results from CDFMay 30 2010The latest results in electroweak physics from proton anti-proton collisions at the Fermilab Tevatron recorded by the CDF detector are presented. The results provide constraints on parton distribution functions, the mass of the Higgs boson and beyond ... More

W Mass and PropertiesNov 15 2005Precise measurements of the mass and width of the W boson are sensitive to radiative corrections and can be used to place limits on new physics beyond the Standard Model and validate the consistency of the model. In particular, the W boson mass constrains ... More

Negative probability in the framework of combined probabilityMay 31 2013Negative probability has found diverse applications in theoretical physics. Thus, construction of sound and rigorous mathematical foundations for negative probability is important for physics. There are different axiomatizations of conventional probability. ... More

Extended Probabilities: Mathematical FoundationsDec 24 2009There are important problems in physics related to the concept of probability. One of these problems is related to negative probabilities used in physics from 1930s. In spite of many demonstrations of usefulness of negative probabilities, physicists looked ... More

Foundations of Information TheoryAug 06 2008Information is the basic concept of information theory. However, there is no definition of this concept that can encompass all uses of the term information in information theories and beyond. Many question a possibility of such a definition. However, ... More

Non-existence of Physical Classical Solutions to Euler's Equations of Rigid Body DynamicsJun 16 2015Nov 23 2015We prove that one cannot construct, for arbitrary initial data, global-in-time physical classical solutions to Euler's equations of continuum rigid body mechanics when the constituent rigid bodies are not perfect spheres. By 'physical' solutions, we mean ... More

Aren't we all nearest neighbors: Spatial trees, high dimensional reductions and batch nearest neighbor searchJul 13 2015We start with a review of the pervasiveness of the nearest neighbor search problem and techniques used to solve it along with some experimental results. In the second chapter, we show reductions between two different classes of geo- metric proximity problems: ... More

Chromatic phenomena in the algebra of BP_{*}BP-comodulesJan 21 2003This paper begins with an exposition of the author's research on the category of BP_*BP-comodules, much of which is joint with Neil Strickland. The main result of that work is that the category of E(n)_*E(n)-comodules is equivalent to a localization of ... More

Observational Signatures of Lyman Alpha Emission from Early Galaxy FormationFeb 15 2011The next generation of telescopes aim to directly observe the first generation of galaxies that initiated the reionization process in our Universe. The Lyman Alpha (Lya) emission line is robustly predicted to be the most prominent intrinsic spectral feature ... More

Massive Black Holes at High RedshiftsMar 15 2003Black holes with masses M_BH~10^{8.5} M_Sun dominate the accretion history of the Universe. These black hole masses are typical of those found in radio-selected galaxies today, suggesting that the giant elliptical hosts of low redshift radio galaxies ... More

The production mechanism of radio jets in AGN and quasar grand unificationOct 31 2002Recent advances in estimating black hole masses for AGN show that radio luminosity is dependent on black hole mass and accretion rate. In this paper we outline a possible scheme for unifying radio-quiet and radio-loud AGN. We take the ``optimistic'' view ... More

The evolution of free wave packetsDec 31 2007We discuss four general features of force-free evolution: (1) The spatial spread of any packet changes with time in a very simple way. (2) Over sufficiently short periods of time (whose duration is related to the spread in momentum of the packet) the ... More

Effective field theories of non-equilibrium physicsAug 19 1998Sep 12 1998Non equilibrium effective field theory is presented as an inhomogeneous field theory, using a formulation which is analogous to that of a gauge theory. This formulation underlines the importance of structural aspects of non-equilibrium, effective field ... More

Effective field theory of resonant 2-level atomsJun 17 1998The phenomenological two-level atom is re-analysed using the methods of effective field theory. By presenting the Dicke-Jaynes-Cummings model in real space, an exact diagonalization is accomplished going beyond the rotating wave approximation. The meaning ... More

QCD with and in nuclei: color transparency and short-range correlations in nuclei - theory, observations, directions for further studiesMar 11 2009Apr 02 2009We summarize basic theoretical ideas which let to the observation of the short-range correlations (SRC) in nuclei using hard probes and outline directions for probing quark-gluon structure of SRCs. Implications of the observations of color transparency ... More

Level Set Method for the Evolution of Defect and Brane NetworksJul 22 2002May 13 2003A theory for studying the dynamic scaling properties of branes and relativistic topological defect networks is presented. The theory, based on a relativistic version of the level set method, well-known in other contexts, possesses self-similar ``scaling'' ... More

Cosmic Strings - Dead Again?Jun 24 1998I report on recent numerical simulations of the simplest field theory with cosmic string solutions, the Abelian Higgs model. We find that random networks of string quickly converge to a scaling solution in which the network scale length $\xi$ increases ... More

Small Scale Microwave Background Fluctuations from Cosmic StringsJul 30 1993Feb 09 1994The Cosmic Microwave Background (CMB) fluctuations at very small angular scales (less than $10'$) induced by matter sources are computed in a simplified way. The result corrects a previous formula appearing in the literature. The small scale power spectrum ... More

Semilocal Topological DefectsJun 17 1992Semilocal defects are those formed in field theories with spontaneously broken symmetries, where the vacuum manifold $M$ is fibred by the action of the gauge group in a non-trivial way. Studied in this paper is the simplest such class of theories, in ... More

Star Formation and the Hall EffectJul 04 2003The breakdown of flux-freezing in molecular clouds and protostellar discs is usually approximated by ambipolar diffusion at low densities or by resistive diffusion at high densities. Here I discuss an intermediate regime in which the Hall term in the ... More

Enhanced OH in C-type shock waves in molecular cloudsAug 16 1999Sep 20 1999Cosmic-ray and X-ray ionisations in molecular gas produce a weak far-ultraviolet flux through the radiative decay of H2 molecules that have been excited by collisions with energetic electrons (the Prasad-Tarafdar mechanism). I consider the effect of this ... More

X-ray echoes of infrared flaring in Sgr A*Jul 11 2010Sgr A* exhibits flaring in the infrared several times each day, occasionally accompanied by flaring in X-rays. The infrared flares are believed to arise through synchrotron emission from a transient population of accelerated electrons. The X-ray flaring ... More

Quantum Oracle Classification - The Case of Group StructureOct 28 2015The Quantum Oracle Classification (QOC) problem is to classify a function, given only quantum black box access, into one of several classes without necessarily determining the entire function. Generally, QOC captures a very wide range of problems in quantum ... More

Evolutionary Algorithm for Drug Discovery Interim Design ReportMar 19 2014A software program which aims to provide an exploration capability over the Search Space of potential drug molecules. The program explores the search space by generating random molecules, determining their fitness and then breeding a new generation from ... More

On extendability of permutationsJun 27 2012Let $V$ be a left vector space over a division ring and let ${\mathcal P}(V)$ be the associated projective space. We describe all finite subsets $X\subset V$ such that every permutation on $X$ can be extended to a linear automorphism of $V$ and all finite ... More

Order preserving transformations of the Hilbert grassmannianMay 14 2006Let $H$ be a separable real Hilbert space. Denote by ${\mathcal G}_{\infty}(H)$ the Grassmannian consisting of closed subspaces with infinite dimension and codimension. This Grassmannian is partially ordered by the inclusion relation. We show that every ... More

On Tits Buildings of Type $A_n$Nov 26 2003Let $P$ and $P'$ be projective spaces having the same dimension $n$ assumed to be finite. Let $\Delta$ and $\Delta'$ be buildings of type $A_n$. We consider mappings of chambers of $\Delta$ into chambers of $\Delta'$ which send appartments to appartments. ... More

On the Observability of Quantum Information Radiated from a Black HoleJul 10 2002We propose a resolution to the black-hole information-loss paradox: in one formulation of physical theory, information is preserved and macroscopic causality is violated; in another, causality is preserved and pure states evolve to mixed states. However, ... More

Spectral statistics of the k-body random-interaction modelJul 08 2002We reconsider the question of the spectral statistics of the k-body random-interaction model, investigated recently by Benet, Rupp, and Weidenmueller, who concluded that the spectral statistics are Poissonian. The binary-correlation method that these ... More

Quantum Chaos and Statistical MechanicsJun 14 1994We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.

Recent constraints on the parton distributions in the proton and the measurement of $α_S$ from ATLAS and CMSJun 06 2014Recent results on cross sections sensitive to the parton distribution functions (PDFs) within the proton from the ATLAS and CMS Collaborations are presented. The potential impact on the inclusion of these data in fits to the PDFs is discussed. Recent ... More

$C^{\infty}$ Stability, Canonical Maps, and Discrete DynamicsOct 31 2014We study a discrete dynamical system designed to find a 'most holomorphic' connection on a smooth complex vector bundle $E$. We examine the relation between the distance of the chern classes of $E$ from the $(p,p)$ axis of the Hodge diamond and singularity ... More

Spectral asymmetry for manifolds of special holonomyFeb 12 2009We define a measure of spectral asymmetry for G_2 and Spin(7) manifolds. We show that this invariant can be computed in terms of characteristic classes and the covariant constant form defining the G_2 or Spin(7) structure.

Conserving Fuel in Statistical Language Learning: Predicting Data RequirementsSep 07 1995In this paper I address the practical concern of predicting how much training data is sufficient for a statistical language learning system. First, I briefly review earlier results and show how these can be combined to bound the expected accuracy of a ... More

Fractional Dynamical SystemsDec 30 2013In this paper the author presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential equations describing ... More

Fractional Standard Map: Riemann-Liouville vs. CaputoMay 06 2013Properties of the phase space of the standard maps with memory obtained from the differential equations with the Riemann-Liouville and Caputo derivatives are considered. Properties of the attractors which these fractional dynamical systems demonstrate ... More

Parametric argument principle and its applications to CR functions and manifoldsJan 09 2014A version of the argument principle is established for varieties of holomorphic mappings from the unit disc to $\mathbb C^n,$ parametrized by points of real manifolds. Applications to characterization of CR functions and estimating CR dimensions of real ... More

Light Hidden U(1)s from String TheoryDec 21 2009The possible masses and kinetic mixings of hidden U(1)s in the LARGE volume scenario are discussed, including the generalisation of the compact manifold to a K3 fibration.

Asymptotic invariants, complexity of groups and related problemsDec 06 2010Mar 21 2011We survey results about computational complexity of the word problem in groups, Dehn functions of groups and related problems.

Classical codes in quantum state spaceJun 11 2015We present a construction of Hermitian operators and quantum states labelled by strings from a finite field. The distance between these operators or states is then simply related (typically, proportional) to the Hamming distance between their corresponding ... More

The quark-gluon plasma, turbulence, and quantum mechanicsJul 12 2008Nov 25 2008Quark-gluon plasmas formed in heavy ion collisions at high energies are well described by ideal classical fluid equations with nearly zero viscosity. It is believed that a similar fluid permeated the entire universe at about three microseconds after the ... More

The loop problem for Rees matrix semigroupsFeb 23 2007We study the relationship between the loop problem of a semigroup, and that of a Rees matrix construction (with or without zero) over the semigroup. This allows us to characterize exactly those completely zero-simple semigroups for which the loop problem ... More

Far Ultraviolet Fluorescence of Molecular Hydrogen in IC 63Apr 16 1998We present observations of H_2 fluorescence at wavelengths between 1000 and 1200 A from the bright reflection nebula IC 63. Observations were performed with the Berkeley spectrograph on the ORFEUS-SPAS II mission. To the best of our knowledge, this is ... More

Business Processes: The Theoretical Impact of Process Thinking on Information Systems DevelopmentSep 19 2004This paper investigates two aspects of process thinking that affect the success rate of IT projects. These two aspects are the changes in the structure of organizations and the epistemology of Information Systems Development. Firstly, the conception of ... More

Spatial birth-death swap chainsJun 30 2010Jul 30 2012Markov chains have long been used for generating random variates from spatial point processes. Broadly speaking, these chains fall into two categories: Metropolis-Hastings type chains running in discrete time and spatial birth-death chains running in ... More

Deconstructing analogyAug 09 2013Analogy has been shown to be important in many key cognitive abilities, including learning, problem solving, creativity and language change. For cognitive models of analogy, the fundamental computational question is how its inherent complexity (its NP-hardness) ... More

How well does NLO pQCD describe strangeness in $p+p$ collisions at $\sqrt{s}$= 200 GeV in STAR?Jan 21 2005Feb 23 2005We present measurements of the transverse momentum spectra for $\mathrm{K^{0}_{S}}$, $\Lambda$, $\Xi$ and their antiparticles in p+p collisions at $\sqrt{s}=200 GeV$. The extracted mid-rapidity yields and $<\mathrm{p_{T}}>$ are in agreement with previous ... More

A New Rule for LTL TableauxSep 14 2016Propositional linear time temporal logic (LTL) is the standard temporal logic for computing applications and many reasoning techniques and tools have been developed for it. Tableaux for deciding satisfiability have existed since the 1980s. However, the ... More

On the scaling of functional spaces, from smart cities to cloud computingFeb 19 2016The study of spacetime, and its role in understanding functional systems has received little attention in information science. Recent work, on the origin of universal scaling in cities and biological systems, provides an intriguing insight into the functional ... More

The Eisenbud-Koh-Stillman Conjecture on Linear SyzygiesFeb 28 1996It is proved, as was conjectured by Eisenbud-Koh-Stillman, that for a finitely generated graded module $M$ over the symmetric algebra $S(V)$, if the Koszul group ${\cal K}_{p,0}(M,V)\ne 0$, then the set of rank 1 relations in $M_0\otimes V$ has dimension ... More

Beauty and Charm Physics at HERAFeb 16 2006Apr 10 2006The most recent beauty and charm results from the ZEUS and H1 collaborations are presented.

TOPCAT's TAP ClientDec 21 2015TAP, the Table Access Protocol, is a Virtual Observatory (VO) protocol for executing queries in remote relational databases using ADQL, an SQL-like query language. It is one of the most powerful components of the VO, but also one of the most complex to ... More

The geometric complexity of special Lagrangian $T^2$-conesJul 09 2003Jan 18 2004We prove a number of results relating various measures (volume, Legendrian index, stability index, and spectral curve genus) of the geometric complexity of special Lagrangian $T^2$-cones. We explain how these results fit into a program to understand the ... More

Semiautomorphic Inverse Property LoopsMar 10 2014Feb 22 2015We define a variety of loops called semiautomorphic, inverse property loops that generalize Moufang and Steiner loops. We first show an equivalence between a previously studied variety of loops. Next we extend several known results for Moufang and Steiner ... More

Local-in-time Physical Solutions of the Incompressible Semi-Geostrophic Equations in Eulerian CoordinatesJul 03 2018Jul 25 2018We prove the existence of local-in-time smooth solutions of the incompressible semi-geostrophic equations expressed in Eulerian co-ordinates in 3-dimensional smooth bounded simply-connected domains. Our solutions adhere to Cullen's Stability Principle ... More

The Cosmic Spiderweb and General Origami Tessellation DesignAug 31 2018The cosmic web (the arrangement of matter in the universe), spider's webs, and origami tessellations are linked by their geometry (specifically, of sectional-Voronoi tessellations). This motivates origami and textile artistic representations of the cosmic ... More

Optimization of Amorphous Germanium Electrical Contacts and Surface Coatings on High Purity Germanium Radiation DetectorsSep 09 2018Semiconductor detector fabrication technologies developed decades ago are widely employed today to produce gamma-ray detectors from large volume, single crystals of high purity Ge (HPGe). Most all of these detectors are used exclusively for spectroscopy ... More

Halving the bounds for the Markov, Chebyshev, and Chernoff Inequalities using smoothingMar 16 2018The Markov, Chebyshev, and Chernoff inequalities are some of the most widely used methods for bounding the tail probabilities of random variables. In all three cases, the bounds are tight in the sense that there exists easy examples where the inequalities ... More

Regularity of Gaussian white noise on the d-dimensional torusOct 29 2010Nov 05 2010In this paper we prove that a Gaussian white noise on the $d$-dimensional torus has paths in the Besov spaces $B^{-d/2}_{p,\infty}(\T^d)$ with $p\in [1, \infty)$. This result is shown to be optimal in several ways. We also show that Gaussian white noise ... More

A Seifert-van Kampen Theorem for Legendrian Submanifolds and Exact Lagrangian CobordismsNov 11 2015Apr 23 2017We prove a Seifert-van Kampen theorem for Legendrian submanifolds and exact Lagrangian cobordisms, and use it to calculate the change in the DGA caused by critical Legendrian ambient surgery.

Decay of correlations for invertible systems with non-Hölder observablesDec 03 2014An invertible dynamical system with some hyperbolic structure is considered. Upper estimates for the correlations of continuous observables is given in terms of modulus of continuity. The result is applied to certain H\'enon maps and Solenoid maps with ... More

Operads within monoidal pseudo algebrasOct 08 2004A general notion of operad is given, which includes as instances, the operads originally conceived to study loop spaces, as well as the higher operads that arise in the globular approach to higher dimensional algebra. In the framework of this paper, one ... More

Geometrical characterization of semilinear isomorphisms of vector spaces and semilinear homeomorphisms of normed spacesApr 05 2013Sep 25 2013Let $V$ and $V'$ be vector spaces over division rings (possible infinite-dimensional) and let ${\mathcal P}(V)$ and ${\mathcal P}(V')$ be the associated projective spaces. We say that $f:{\mathcal P}(V)\to {\mathcal P}(V')$ is a PGL-{\it mapping} if for ... More

A free boundary problem on three-dimensional conesApr 17 2017We consider a free boundary problem on cones depending on a parameter c and study when the free boundary is allowed to pass through the vertex of the cone. We show that when the cone is three-dimensional and c is large enough, the free boundary avoids ... More

The G-Ball, a New Icon for Codon Symmetry and the Genetic CodeFeb 26 2007A codon table is a useful tool for mapping codons to amino acids as they have been assigned by nature. It has become a scientific icon because of the way it embodies our understanding of this natural process and the way it immediately communicates this ... More

A generalized SXP rule proved by bijections and involutionsAug 27 2015Oct 09 2016This paper proves a combinatorial rule expressing the product $s_\tau(s_{\lambda/\mu} \circ p_r)$ of a Schur function and the plethysm of a skew Schur function with a power sum symmetric function as an integral linear combination of Schur functions. This ... More