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Matrix Convex Sets Without Absolute Extreme PointsAug 07 2017This article shows the existence of a class of closed bounded matrix convex sets which do not have absolute extreme points. The sets we consider are noncommutative sets, $K_X$, formed by taking matrix convex combinations of a single tuple $X$. In the ... More

The noncommutative Waring problemMar 14 2019This paper poses and treats a noncommutative version of the classical Waring problem for polynomials. That is, for a homogeneous \nc \ polynomial $p$, we find a condition equivalent to $p$ being expressible as sums of powers of homogeneous \nc \ polynomials. ... More

Arveson extreme points span free spectrahedraJun 23 2018Let $ SM_n(\mathbb{R})^g$ denote $g$-tuples of $n \times n$ real symmetric matrices. Given tuples $X=(X_1, \dots, X_g) \in SM_{n_1}(\mathbb{R})^g$ and $Y=(Y_1, \dots, Y_g) \in SM_{n_2}(\mathbb{R})^g$, a matrix convex combination of $X$ and $Y$ is a sum ... More

Circular Free SpectrahedraApr 19 2016This paper considers matrix convex sets invariant under several types of rotations. It is known that matrix convex sets that are free semialgebraic are solution sets of Linear Matrix Inequalities (LMIs); they are called free spectrahedra. We classify ... More

Extreme points of matrix convex sets, free spectrahedra and dilation theoryNov 30 2016For matrix convex sets a unified geometric interpretation of notions of extreme points and of Arveson boundary points is given. These notions include, in increasing order of strength, the core notions of "Euclidean" extreme points, "matrix" extreme points, ... More

Factor posets of frames and dual frames in finite dimensionsNov 15 2014We consider frames in a finite-dimensional Hilbert space where frames are exactly the spanning sets of the vector space. A factor poset of a frame is defined to be a collection of subsets of $I$, the index set of our vectors, ordered by inclusion so that ... More

Multiple Populations in Globular Clusters: The Possible Contributions of Stellar CollisionsApr 23 2010Globular clusters were thought to be simple stellar populations, but recent photometric and spectroscopic evidence suggests that the clusters' early formation history was more complicated. In particular, clusters show star-to-star abundance variations, ... More

Correlations in the Ising antiferromagnet on the anisotropic kagome latticeJul 07 2011Sep 16 2011We study the correlation function of middle spins, i. e. of spins on intermediate sites between two adjacent parallel lattice axes, of the spatially anisotropic Ising antiferromagnet on the kagome lattice. It is given rigorously by a Toeplitz determinant. ... More

Molybdenum-Rhenium alloy based high-$Q$ superconducting microwave resonatorsNov 18 2014Superconducting microwave resonators (SMR) with high quality factors have become an important technology in a wide range of applications. Molybdenum-Rhenium (MoRe) is a disordered superconducting alloy with a noble surface chemistry and a relatively high ... More

Asymptotically hyperbolic normalized Ricci flow and rotational symmetryJun 22 2015Sep 27 2016We consider the normalized Ricci flow evolving from an initial metric which is conformally compactifiable and asymptotically hyperbolic. We show that there is a unique evolving metric which remains in this class, and that the flow exists up to the time ... More

Asymptotically hyperbolic normalized Ricci flow and rotational symmetryJun 22 2015Dec 05 2018We consider the normalized Ricci flow evolving from an initial metric which is conformally compactifiable and asymptotically hyperbolic. We show that there is a unique evolving metric which remains in this class, and that the flow exists up to the time ... More

Window To The StarsJul 27 2006We present Window To The Stars, a graphical user interface to the popular TWIN single/binary stellar evolution code, for novices, students and professional astrophysicists. It removes the drudgery associated with the traditional approach to running the ... More

Thermohaline mixing and gravitational settling in carbon-enhanced metal-poor starsJul 10 2008We investigate the formation of carbon-enhanced metal-poor (CEMP) stars via the scenario of mass transfer from a carbon-rich asymptotic giant branch (AGB) primary to a low-mass companion in a binary system. We explore the extent to which material accreted ... More

Geometry induced pair condensationOct 09 2013We study a one-dimensional model of interacting bosons on a lattice with two flat bands. Regular condensation is suppressed due to the absence of a well defined minimum in the single particle spectrum. We find that interactions stabilize a number of non-trivial ... More

Realizations of Bialgebras (II) : Duality TheoremFeb 04 2005Feb 22 2005From the method of realization of bialgebras developped in a preceding paper, we obtain the Duality Theorem and apply it to the study of the ideal of relations for each realized bialgebra. This is detailed in the english version of the abstract of this ... More

Density-matrix renormalization group methods for momentum- and frequency-resolved dynamical correlation functionsAug 19 2008Several density-matrix renormalization group methods have been proposed to compute the momentum- and frequency-resolved dynamical correlation functions of low-dimensional strongly correlated systems. The most relevant approaches are discussed in this ... More

Identification of significant features in DNA microarray dataApr 13 2013DNA microarrays are a relatively new technology that can simultaneously measure the expression level of thousands of genes. They have become an important tool for a wide variety of biological experiments. One of the most common goals of DNA microarray ... More

Construction of initial data for 3+1 numerical relativityApr 02 2007Nov 07 2007This lecture is devoted to the problem of computing initial data for the Cauchy problem of 3+1 general relativity. The main task is to solve the constraint equations. The conformal technique, introduced by Lichnerowicz and enhanced by York, is presented. ... More

Generalized Representation Stability and FI_d-modulesJun 08 2016Jun 09 2016In this note we consider the complex representation theory of FI_d, a natural generalization of the category FI of finite sets and injections. We prove that finitely generated FI_d-modules exhibit behaviors in the spirit of Church-Farb representation ... More

Hawking Radiation from a Reisner-Nordström Domain WallSep 30 2009Dec 14 2009We investigate the effect on the Hawking radiation given off during the time of collapse of a Reisner-Nordstr\"om domain wall. Using the functional Schr\"odinger formalism we are able to probe the time-dependent regime, which is out of the reach of the ... More

Local Transformations Requiring Infinite Rounds of Classical CommunicationMay 17 2011In this paper, we study the number of rounds of communication needed to implement certain tasks by local quantum operations and classical communication (LOCC). We find that the class of LOCC operations becomes strictly more powerful as more rounds of ... More

Duality Symmetries and the Type II String Effective ActionSep 26 1995We discuss the duality symmetries of Type II string effective actions in nine, ten and eleven dimensions. As a by-product we give a covariant action underlying the ten--dimensional Type IIB supergravity theory. We apply duality symmetries to construct ... More

Summary of CP Violation in D -> hh Decays at BelleJan 20 2013Although CP violation is predicted to be small in the Standard Model, there exists a continuing theoretical interest within the charm sector due to enhancements of CPV through new physics processes. We present an overview of the measurements of direct ... More

Bar-driven fueling of galactic nuclei: a 2D viewSep 27 2004I discuss evidences for bar-driven gas fueling in the central regions of galaxies, focusing on scales down to about 10 pc. I thus mention the building of inner disks, and the link with resonances, as well as the corresponding kinematic signatures such ... More

Integral Field Spectrographs: a user's viewSep 25 2007We easily tend to think of Integral-Field Spectrographs (IFS) along two opposing trends: as either the beautiful combination between photometry and spectroscopy, or as our worst nightmare including the dark side of both worlds. I favour a view where each ... More

Secular evolution in the central regions of galaxiesSep 10 2001In this paper, I mention a few processes which may play a role in the evolution of the central regions of galaxies. In this context, I briefly discuss some issues regarding the formation of bulges in spirals, the role of supermassive black holes, and ... More

Discrete Torsion, Quotient Stacks, and String OrbifoldsOct 15 2001This is the writeup of a lecture given at the May Wisconsin workshop on mathematical aspects of orbifold string theory. In the first part of this lecture, we review recent work on discrete torsion, and outline how it is currently understood in terms of ... More

Seidel's Mirror Map for the TorusJun 17 2005Jul 25 2005Using only the Fukaya category and the monodromy around large complex structure, we reconstruct the mirror map in the case of a symplectic torus. This realizes an idea described by Paul Seidel.

What Transcription Factors Can't Do: On the Combinatorial Limits of Gene Regulatory NetworksDec 19 2013Jan 27 2014A proof is presented that gene regulatory networks (GRNs) based solely on transcription factors cannot control the development of complex multicellular life. GRNs alone cannot explain the evolution of multicellular life in the Cambrian Explosion. Networks ... More

On the complexity of learning a language: An improvement of Block's algorithmDec 11 2012Language learning is thought to be a highly complex process. One of the hurdles in learning a language is to learn the rules of syntax of the language. Rules of syntax are often ordered in that before one rule can applied one must apply another. It has ... More

Hierarchical Bayesian estimation of inequality measures with nonrectangular censored survey data with an application to wealth distribution of French householdsJul 29 2011We consider the estimation of wealth inequality measures with their confidence interval, based on survey data with interval censoring. We rely on a Bayesian hierarchical model. It consists of a model where, due to survey sampling and unit nonresponse, ... More

Deeply Virtual Compton Scattering at JLab Hall ASep 27 2007The deeply virtual Compton scattering reaction has been investigated in the Hall A of the Jefferson Laboratory by measuring longitudinally polarized (e,e'gamma) cross sections, in the valence quark region, for protons and neutrons. In the proton channel, ... More

Meunier ConjectureSep 01 2012Fr\'ed\'eric Meunier's question about a multicolored Sperner lemma is addressed, leaving the question of connectivity for the color hypergraphs of such a multicolored simplex. Sperner's lemma asserts the existence of a simplex using all the colors for ... More

Color superconductivity in the Nambu Jona-Lasinio model complemented by a Polyakov loopJun 08 2016The color superconductivity was studied with an adaptation of the Nambu and Jona-Lasinio model (NJL). This one was coupled to a Polyakov loop, to form the PNJL model. A $\mu$-dependent Polyakov loop potential was considered. An objective of the presented ... More

Quantum Collapse of a Charged $n$-dimensional BTZ-like Domain WallMay 20 2016We investigate both the classical and quantum gravitational collapse of a charged, non-rotating $n$-dimensional BTZ black hole in AdS space. This is done by first deriving the conserved mass of a "spherically" symmetric domain wall, which is then taken ... More

Bounding the Space of Holographic CFTs with ChaosFeb 26 2016Oct 14 2016Thermal states of quantum systems with many degrees of freedom are subject to a bound on the rate of onset of chaos, including a bound on the Lyapunov exponent, $\lambda_L\leq 2\pi /\beta$. We harness this bound to constrain the space of putative holographic ... More

Closed subgroups of the polynomial automorphism group containing the affine subgroupSep 09 2016We prove that, in characteristic zero, closed subgroups of the polynomial automorphisms group containing the affine group contain the whole tame group.

The rigid Horowitz-Myers conjectureFeb 19 2016The "new positive energy conjecture" Horowitz and Myers (1999) probes a possible nonsupersymmetric AdS/CFT correspondence. We consider a version formulated for complete, asymptotically Poincar\'e-Einstein Riemannian metrics $(M,g)$ with bounded scalar ... More

Theoretical approaches to the statistical physics of interacting non-conservative unitsAug 30 2016The aim of this review is to provide a concise overview of some of the generic approaches that have been developed to deal with the statistical description of large systems of interacting non-conservative 'units'. The latter notion includes, e.g., inelastic ... More

On the Oscillations of Second Order Linear Differential EquationsNov 09 2016This paper extends the discriminant associated to second order linear constant coefficient differential equations to general second order linear differential equations. The main result of this paper is that the discriminant of a second order linear differential ... More

On the covering number of symmetric groups of even degreeOct 28 2014Feb 03 2016If a group $G$ is the union of proper subgroups $H_1, \dots, H_k$, we say that the collection $\{H_1, \dots H_k \}$ is a cover of $G$, and the size of a minimal cover (supposing one exists) is the covering number of $G$, denoted $\sigma(G)$. Mar\'oti ... More

Stability phenomena in the homology of tree braid groupsSep 19 2016For a tree $G$, we study the changing behaviors in the homology groups $H_i(B_nG)$ as $n$ varies, where $B_nG := \pi_1($UConf$_n(G))$. We prove that the ranks of these homologies can be described by a single polynomial for all $n$, and construct this ... More

Sobolev solutions of parabolic equation in a complete riemannian manifoldDec 11 2018Jan 03 2019We study Sobolev estimates for the solutions of parabolic equations acting on a vector bundle, in a complete riemannian manifold $M.$ The idea is to use known estimates in ${\mathbb{R}}^{n}$ to get local estimates on $M$ and then to use our LIR method ... More

Milne-like Spacetimes and their SymmetriesMar 01 2018May 03 2018When developing a quantum theory for a physical system, one determines the system's symmetry group and its irreducible unitary representations. For Minkowski space, the symmetry group is the Poincar\'e group, $\mathbb{R}^4 \rtimes \text{O}(1,3)$, and ... More

Milne-like spacetimes and their role in CosmologyJun 05 2017May 04 2018Milne-like spacetimes are a class of FLRW models which admit $C^0$ spacetime extensions through the big bang. The boundary of a Milne-like spacetime can be identified with a null cone in the extension. We find that the comoving observers all emanate from ... More

Etude d'equations differentielles singulierement perturbees au voisinage d'un point tournantFeb 09 2001Consider a singularly perturbed ordinary differential equation, admitting 0 as turning point of order p. We study the behaviour, in the complex plane, of the solutions of this equation in the neighborhood of 0. We prove that the domain of these solutions ... More

On the homology of open-closed string field theoryDec 13 2004Oct 21 2005The homology of a 2-colored dioperad of decorated Riemann surfaces, relevant to open-closed string field theory, is computed. The structure it describes is realized in an open-closed setting of string topology via an action at the level of topological ... More

A Tropical ToolkitOct 28 2006Apr 04 2008We give an introduction to Tropical Geometry and prove some results in Tropical Intersection Theory. The first part of this paper is an introduction to tropical geometry aimed at researchers in Algebraic Geometry from the point of view of degenerations ... More

Cosets, genericity, and the Weyl groupJan 15 2008Sep 12 2008We prove a non-generosity theorem for proper cosets in groups of finite Morley rank and elaborate on the theory of Weyl groups in this context.

Measuring Differences in Stochastic Network StructureMar 26 2019Mar 31 2019How can one determine whether the realized differences between two stochastic networks are statistically significant? This paper considers a two-sample goodness-of-fit testing problem for network data in which the null hypothesis is that the networks ... More

Quantifying the Loss of Information from Binning List-Mode DataFeb 12 2019List-mode data is increasingly being uesd in SPECT and PET imaging, among other imaging modalities. However, there are still many imaging designs that effectively bin list-mode data before image reconstruction or other estimation tasks are performed. ... More

Solutions of the $\bar \partial $-equation on Kähler manifold with compact supportFeb 07 2019We study the $\bar \partial $-equation in complete K\"ahler manifolds. The aim is to get $L^{r}$ and Sobolev estimates on solutions with compact support. We prove and use estimates on solutions on Poisson equation with compact support and the link with ... More

The Relation Between Bayesian Fisher Information and Shannon Information for Detecting a Change in a ParameterJan 31 2019We derive a connection between performance of estimators the performance of the ideal observer on related detection tasks. Specifically we show how Shannon Information for the task of detecting a change in a parameter is related to the Fisher Information ... More

Linear compactness and combinatorial bialgebrasSep 29 2018We present an expository overview of the monoidal structures in the category of linearly compact vector spaces. Bimonoids in this category are the natural duals of infinite-dimensional bialgebras. We classify the relations on words whose equivalence classes ... More

A few properties of sample varianceSep 11 2018A basic result is that the sample variance for i.i.d. observations is an unbiased estimator of the variance of the underlying distribution (see for instance Casella and Berger (2002)). But what happens if the observations are neither independent nor identically ... More

The Morava E-theory of Eilenberg-Mac Lane spacesSep 27 2011Sep 29 2011We deform the Ravenel-Wilson computation of the Morava K-homology of Eilenberg-Mac Lane spaces to obtain a similar description of their completed Morava E-homology. This yields both a cohomological description and an interpretation on the level of formal ... More

Extinction time of the logistic processMay 22 2018We study the scaling behaviour of the extinction time of the simple logistic birth and death process, as the carrying capacity $n$ tends to $\infty$, when the reproductive rate $r$ and the initial value $X_0$ are allowed to vary arbitrarily with $n$. ... More

Constrained Generative Adversarial Networks for Interactive Image GenerationApr 03 2019Generative Adversarial Networks (GANs) have received a great deal of attention due in part to recent success in generating original, high-quality samples from visual domains. However, most current methods only allow for users to guide this image generation ... More

Tropical Intersection Theory from Toric VarietiesJul 15 2009We apply ideas from intersection theory on toric varieties to tropical intersection theory. We introduce mixed Minkowski weights on toric varieties which interpolate between equivariant and ordinary Chow cohomology classes on complete toric varieties. ... More

A class of hypergraphs that generalizes chordal graphsMar 14 2008Mar 28 2008In this paper we introduce a class of hypergraphs that we call chordal. We also extend the definition of triangulated hypergraphs, given in \cite{VT}, so that a triangulated hypergraph, according to our definition, is a natural generalization of a chordal ... More

A method of realization of bialgebras, and Hopf algebras associated to some realizationsDec 19 2003This article introduces a method, which starting from simple and quite general mathematical data, allows to construct linear algebras of operators which are, each of them, endowed with a bialgebra structure (coproduct and counity). Moreover under some ... More

Order 1 strongly minimal sets in differentially closed fieldsOct 11 2005Jan 19 2007We give a classification of non-orthogonality classes of trivial order 1 strongly minimal sets in differentially closed fields. A central idea is the introduction of $\tau$-forms, functions on the prolongation of a variety which are analogous to 1-forms. ... More

On the Shuffling Algorithm for Domino TilingsFeb 19 2008We study the dynamics of a certain discrete model of interacting particles that comes from the so called shuffling algorithm for sampling a random tiling of an Aztec diamond. It turns out that the transition probabilities have a particularly convenient ... More

Potential for Quantum-Mechanical Tests Using Quasars, as Illuminated by Gemini Archival DataSep 21 2018There has been recent interest in quantum-mechanical tests aided by distant quasars. For two quasars of sufficient redshift at opposite directions on the sky, light-travel-time arguments can assure the acausality of their photons. And if those photons ... More

Teaching practices of graduate teaching assistantsFeb 24 2016Physics education research has consistently shown that students have higher learning outcomes when enrolled in interactive-engagement courses. Consequently, many schools are actively reforming their introductory curricula. For courses where the interactive ... More

Bifurcation delay - the case of the sequence: stable focus - unstable focus - unstable nodeJan 19 2009Let us give a two dimensional family of real vector fields. We suppose that there exists a stationary point where the linearized vector field has successively a stable focus, an unstable focus and an unstable node. When the parameter moves slowly, a bifurcation ... More

On the dual nature of partial theta functions and Appell-Lerch sumsAug 30 2012Jul 14 2014In recent work, Hickerson and the author demonstrated that it is useful to think of Appell--Lerch sums as partial theta functions. This notion can be used to relate identities involving partial theta functions with identities involving Appell--Lerch sums. ... More

Critical Behaviour of the Partner ModelDec 10 2014Jul 18 2015We consider a stochastic model of infection spread incorporating monogamous partnership dynamics. In previous work a basic reproduction number $R_0$ is defined with the property that if $R_0<1$ the infection dies out within $O(\log N)$ units of time, ... More

New Results for the Two-Stage Contact ProcessJan 11 2014Here we continue the work started by Steve Krone on the two-stage contact process. We give a simplified proof of the duality relation, and answer most of the open questions posed in that paper. We also fill in the details of an incomplete proof.

Quenched large deviations for interacting diffusions in random mediaAug 23 2016The aim of the paper is to establish a large deviation principle (LDP) for the empirical measure of mean-field interacting diffusions in a random environment. The point is to derive such a result once the environment has been frozen (quenched model). ... More

Connecting Sharpe ratio and Student t-statistic, and beyondAug 02 2018May 09 2019Sharpe ratio is widely used in asset management to compare and benchmark funds and asset managers. It computes the ratio of the excess return over the strategy standard deviation. However, the elements to compute the Sharpe ratio, namely, the expected ... More

Graphical Condensation Generalizations Involving Pfaffians and DeterminantsMay 05 2006Graphical condensation is a technique used to prove combinatorial identities among numbers of perfect matchings of plane graphs. Propp and Kuo first applied this technique to prove identities for bipartite graphs. Yan, Yeh, and Zhang later applied graphical ... More

Intrinsic characterization for Lipschitz asymptotically hyperbolic metricsNov 21 2007Jul 11 2008Conformally compact asymptotically hyperbolic metrics have been intensively studied. The goal of this note is to understand what intrinsic conditions on a complete Riemannian manifold (M,g) will ensure that g is asymptotically hyperbolic in this sense. ... More

Noncyclic Division Algebras over Fields of Brauer Dimension OneMar 21 2019Let $K$ be a complete discretely valued field of rank one, with residue field $\Q_p$. It is well known that period equals index in $\Br(K)$. We prove that when $p=2$ there exist noncyclic $K$-division algebras of every $2$-power degree divisible by four. ... More

Motivic Steenrod operations in characteristic $p$Mar 26 2019Using the recent work of Frankland and Spitzweck, we define Steenrod operations $P^{n}$ on the mod $p$ motivic cohomology of smooth varieties defined over a base field of characteristic $p$. We show that $P^{n}$ is the $p$th power on $H^{2n,n}(-,\mathbb{F}_{p})$ ... More

Smooth classifying spaces for differential $K$-theoryMay 08 2019We construct a version of differential $K$-theory based on smooth Banach manifold models for the homotopy types $B \mathrm U\times Z$ and $\mathrm U$ that appear in the topological $K$-theory spectrum. These manifolds carry natural differential forms ... More

Lifting Tropical Curves in Space and Linear Systems on GraphsSep 09 2010Aug 20 2011Tropicalization is a procedure for associating a polyhedral complex in Euclidean space to a subvariety of an algebraic torus. We study the question of which graphs arise from tropicalizing algebraic curves. By using Baker's specialization of linear systems ... More

An Andreotti-Grauert theorem with $L^r$ estimatesMar 04 2012Apr 16 2014By a theorem of Andreotti and Grauert if $\omega $ is a $(p,q)$ current, $q < n,$ in a Stein manifold $\displaystyle \Omega,\ \bar \partial $ closed and with compact support, then there is a solution $u$ to $\bar \partial u=\omega $ still with compact ... More

The raising steps method. Applications to the $\bar \partial $ equation in Stein manifoldsDec 30 2013Jan 09 2014In order to get estimates on the solutions of the equation $\bar \partial u=\omega $ on Stein manifold, we introduce a new method the "raising steps method", to get global results from local ones. In particular it allows us to transfer results form open ... More

Estimates $ L^{r}-L^{s}$ for solutions of the $\bar \partial $ equation in strictly pseudo convex domains in ${\mathbb{C}}^{n}.$Dec 26 2013Jan 24 2014We prove estimates for solutions of the $\bar \partial u=\omega $ equation in a strictly pseudo convex domain $ \Omega $ in ${\mathbb{C}}^{n}.$ For instance if the $ (p,q)$ current $\omega $ has its coefficients in $L^{r}(\Omega )$ with $1\leq r<2(n+1)$ ... More

Irreducible Local Systems on Nilpotent OrbitsOct 24 2016Let $G$ be a simple, simply-connected algebraic group over the complex numbers with Lie algebra $\mathfrak g$. The main result of this article is a proof that each irreducible representation of the fundamental group of the orbit $\mathcal O$ through a ... More

Lorentzian Cobordisms, Compact Horizons and the Generic ConditionJun 24 2014We consider the problem of determining which conditions are necessary for cobordisms to admit Lorentzian metrics with certain properties. In particular, we prove a result originally due to Tipler without a smoothness hypothesis necessary in the original ... More

A Concise Resolution to the Two Envelope ParadoxFeb 18 2012Aug 24 2012In this paper, I will demonstrate a new perspective on the Two Envelope Problem. I hope to show with convincing clarity how the paradox results from an inherent problem pertaining to the interpretation of Bayesian probability. Specifically, a subjective ... More

The Semiotic MachineSep 02 2008A semiotic model of the user interface in human-computer interaction. Algorithmic sign, semotics, algorithmic art.

The Stock Market as a Game: An Agent Based Approach to Trading in StocksSep 02 2008Just as war is sometimes fallaciously represented as a zero sum game -- when in fact war is a negative sum game - stock market trading, a positive sum game over time, is often erroneously represented as a zero sum game. This is called the "zero sum fallacy" ... More

Quantum Computing Simulation Optimizations and Operational Errors on Various 2-qubit Multiplier CircuitsAug 15 2002Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates. Additionally, ... More

How to Grow an Organism Inside-Out: Evolution of an internal skeleton from an external skeleton in bilateral organismsJul 16 2012An intriguing unanswered question about the evolution of bilateral animals with internal skeletons is how an internal skeleton evolved in the first place. Computational modeling of the development of bilateral symmetric organisms suggests an answer to ... More

On cyclic CAT(0) domains of discontinuityJun 01 2010Let $X$ be a CAT(0) space, and $G$ a discrete cyclic group of isometries of $X$. We investigate the domain of discontinuity for the action of $G$ on the boundary $\partial X$.

A Density Matrix-based Algorithm for Solving Eigenvalue ProblemsJan 17 2009A new numerical algorithm for solving the symmetric eigenvalue problem is presented. The technique deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques, ... More

Generalized Representation Stability and FI_d-modulesJun 08 2016Oct 04 2016In this note we consider the complex representation theory of FI_d, a natural generalization of the category FI of finite sets and injections. We prove that finitely generated FI_d-modules exhibit behaviors in the spirit of Church-Farb representation ... More

Semi-supervised clustering methodsJul 01 2013Cluster analysis methods seek to partition a data set into homogeneous subgroups. It is useful in a wide variety of applications, including document processing and modern genetics. Conventional clustering methods are unsupervised, meaning that there is ... More

Time Evolution of Entropy of a Charged Domain Wall during Gravitational CollapseFeb 11 2010We study the time evolution of the entropy of a collapsing charged spherical domain wall, from the point of view of an asymptotic observer, by investigating the entropy of the entire system (i.e. charged domain wall and radiation) and induced radiation ... More

Ramanujan's $_{1}ψ_1$ summation, Hecke-type double sums, and Appell-Lerch sumsAug 07 2012We use a specialization of Ramanujan's ${}_1\psi_1$ summation to give a new proof of a recent formula of Hickerson and Mortenson which expands a special family of Hecke-type double sums in terms of Appell-Lerch sums and theta functions.

Graphing and Grafting Graphene: Classifying Finite Topological DefectsJun 30 2011Nov 16 2011The structure of finite-area topological defects in graphene is described in terms of both the direct honeycomb lattice and its dual triangular lattice. Such defects are equivalent to cutting out a patch of graphene and replacing it with a different patch ... More

3+1 Formalism and Bases of Numerical RelativityMar 06 2007These lecture notes provide some introduction to the 3+1 formalism of general relativity, which is the foundation of most modern numerical relativity. The text is rather self-contained, with detailed calculations and numerous examples. Contents: 1. Introduction, ... More

Improved Error Bounds Based on Worst Likely AssignmentsMar 31 2015Error bounds based on worst likely assignments use permutation tests to validate classifiers. Worst likely assignments can produce effective bounds even for data sets with 100 or fewer training examples. This paper introduces a statistic for use in the ... More

An introduction to the hydrodynamics of locomotion on small scalesMar 17 2014In these lecture notes, I will briefly review the fundamental physical principles of locomotion in fluids, with a particular emphasis on the low-Reynolds number world.

All roots of unity are detected by the A-polynomialNov 09 2004Mar 30 2005For an arbitrary positive integer n, we construct infinitely many one-cusped hyperbolic 3-manifolds where each manifold's A-polynomial detects every n-th root of unity. This answers a question of Cooper, Culler, Gillet, Long, and Shalen as to which roots ... More

Two remarks on elementary theories of groups obtained by free constructionsFeb 06 2012May 30 2012We give two slight generalizations of results of Poizat about elementary theories of groups obtained by free constructions. The first-one concerns the non-superstability of such groups in most cases, and the second-one concerns the connectedness of most ... More

How far can stochastic and deterministic views be reconciled?May 22 2012In this short note, we try to provide the reader with a brief pedagogical account of some similarities and differences between stochastic and deterministic processes. A short presentation of some basic notions related to the mathematical description of ... More