Results for "Damek Davis"
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Factorial and Noetherian Subrings of Power Series RingsOct 21 2009Let $F$ be a field. We show that certain subrings contained between the polynomial ring $F[X] = F[X_1, ..., X_n]$ and the power series ring $F[X][[Y]] = F[X_1, ..., X_n][[Y]]$ have Weierstrass Factorization, which allows us to deduce both unique factorization ... More Stochastic model-based minimization of weakly convex functionsMar 17 2018Aug 26 2018We consider a family of algorithms that successively sample and minimize simple stochastic models of the objective function. We show that under reasonable conditions on approximation quality and regularity of the models, any such algorithm drives a natural ... More The nonsmooth landscape of phase retrievalNov 09 2017Jan 07 2018We consider a popular nonsmooth formulation of the real phase retrieval problem. We show that under standard statistical assumptions, a simple subgradient method converges linearly when initialized within a constant relative distance of an optimal solution. ... More Stochastic model-based minimization under high-order growthJul 01 2018Given a nonsmooth, nonconvex minimization problem, we consider algorithms that iteratively sample and minimize stochastic convex models of the objective function. Assuming that the one-sided approximation quality and the variation of the models is controlled ... More Stochastic subgradient method converges on tame functionsApr 20 2018May 26 2018This work considers the question: what convergence guarantees does the stochastic subgradient method have in the absence of smoothness and convexity? We prove that the stochastic subgradient method, on any semialgebraic locally Lipschitz function, produces ... More The Asynchronous PALM Algorithm for Nonsmooth Nonconvex ProblemsApr 02 2016We introduce the Asynchronous PALM algorithm, a new extension of the Proximal Alternating Linearized Minimization (PALM) algorithm for solving nonsmooth, nonconvex optimization problems. Like the PALM algorithm, each step of the Asynchronous PALM algorithm ... More SMART: The Stochastic Monotone Aggregated Root-Finding AlgorithmJan 04 2016Jun 09 2016We introduce the Stochastic Monotone Aggregated Root-Finding (SMART) algorithm, a new randomized operator-splitting scheme for finding roots of finite sums of operators. These algorithms are similar to the growing class of incremental aggregated gradient ... More Composite optimization for robust blind deconvolutionJan 06 2019Jan 18 2019The blind deconvolution problem seeks to recover a pair of vectors from a set of rank one bilinear measurements. We consider a natural nonsmooth formulation of the problem and show that under standard statistical assumptions, its moduli of weak convexity, ... More Convergence rate analysis of primal-dual splitting schemesAug 19 2014Jul 30 2015Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They decompose problems that are built from sums, linear compositions, ... More Subgradient methods for sharp weakly convex functionsMar 06 2018Subgradient methods converge linearly on a convex function that grows sharply away from its solution set. In this work, we show that the same is true for sharp functions that are only weakly convex, provided that the subgradient methods are initialized ... More Convergence rate analysis of several splitting schemesJun 18 2014May 15 2015Splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which the simple pieces of the decomposition are ... More Continuity of KMS States for Quantum Fields on ManifoldsApr 04 2005We show that pure, quasifree states, as well as regular (i.e., those with a unique vacuum) quasifree ground and KMS states, for linear quantum fields in a curved spacetime, are always continuous in the sense of distributions, and provide certain applications ... More Large versus bounded solutions to sublinear elliptic problemsOct 13 2017Dec 31 2018Let $L $ be a second order elliptic operator with smooth coefficients defined on a domain $\Omega \subset \mathbb{R}^d$ (possibly unbounded), $d\geq 3$. We study nonnegative continuous solutions $u$ to the equation $L u(x) - \varphi (x, u(x))=0$ on $\Omega ... More On the Design and Analysis of Multiple View DescriptorsNov 23 2013We propose an extension of popular descriptors based on gradient orientation histograms (HOG, computed in a single image) to multiple views. It hinges on interpreting HOG as a conditional density in the space of sampled images, where the effects of nuisance ... More On the blow-up of four dimensional Ricci flow singularitiesApr 26 2012In this paper we prove a conjecture by Feldman-Ilmanen-Knopf in \cite{FIK} that the gradient shrinking soliton metric they constructed on the tautological line bundle over $\CP^1$ is the uniform limit of blow-ups of a type I Ricci flow singularity on ... More Is the Universe Homogeneous on Large Scales?Oct 19 1996Oct 21 1996This contribution is the affirmative side of a debate held with Dr. L. Pietronero at Princeton in June, 1996. I present the observational evidence that the fractal behavior which characterizes the small scale galaxy distribution does not continue to arbitarily ... More On the Stable Ergodicity of Berger-Carrasco's exampleFeb 19 2018Mar 15 2018We prove the stable ergodicity of an example of a volume-preserving, partially hyperbolic diffeomorphism introduced by Pierre Berger and Pablo Carrasco. This example is robustly non-uniformly hyperbolic, with two dimensional center, almost every point ... More Winograd Schemas and Machine TranslationAug 05 2016Sep 30 2016A Winograd schema is a pair of sentences that differ in a single word and that contain an ambiguous pronoun whose referent is different in the two sentences and requires the use of commonsense knowledge or world knowledge to disambiguate. This paper discusses ... More Universal Graphs at $\aleph_{ω_1+1}$ and Set-theoretic GeologyMay 27 2016This thesis consists of two parts: the construction of a jointly universal family of graphs, and then an exploration of set-theoretic geology. Firstly we shall construct a model in which $2^{\aleph_{\omega_1}}=2^{\aleph_{\omega_1+1}}=\aleph_{\omega_1+3}$ ... More Summability of Superstring TheoryMar 11 1998Mar 20 1998Several arguments are given for the summability of the superstring perturbation series. Whereas the Schottky group coordinatization of moduli space may be used to provide refined estimates of large-order bosonic string amplitudes, the super-Schottky group ... More Scalar Field Theory in Curved Space and the Definition of MomentumFeb 09 1997Dec 22 1997Some general remarks are made about the quantum theory of scalar fields and the definition of momentum in curved space. Special emphasis is given to field theory in anti-de Sitter space, as it represents a maximally symmetric space-time of constant curvature ... More Lines in positive genus: An introduction to flat surfacesJul 09 2015This text is aimed at undergraduates, or anyone else who enjoys thinking about shapes and numbers. The goal is to encourage the student to think deeply about seemingly simple things. The main objects of study are lines, squares, and the effects of simple ... More Distortion in Free Nilpotent GroupsSep 14 2010We prove that a subgroup of a finitely generated free nilpotent group F is undistorted if and only if it is a retract of a subgroup of finite index in F. Types, Tokens, and Hapaxes: A New Heap's LawDec 31 2018Heap's Law states that in a large enough text corpus, the number of types as a function of tokens grows as $N=KM^\beta$ for some free parameters $K,\beta$. Much has been written about how this result and various generalizations can be derived from Zipf's ... More The Four-Point Function on a Surface of Infinite GenusOct 26 1994Jul 30 1996The four-point function arising in the scattering of closed bosonic strings in their tachyonic ground state is evaluated on a surface of infinite genus. The amplitude has poles corresponding to physical intermediate states and divergences at the boundary ... More Non-negative Ricci curvature on closed manifolds under Ricci flowNov 10 2009Dec 01 2009In this short note we show that non-negative Ricci curvature is not preserved under Ricci flow for closed manifolds of dimensions four and above, strengthening a previous result of Knopf in \cite{K} for complete non-compact manifolds of bounded curvature. ... More Generalized Topological Sigma ModelMar 16 1997Apr 21 1997In this article we will examine a "generalized topological sigma model." This so-called "generalized topological sigma model" is the M-Theoretic analog of the standard topological sigma model of string theory. We find that the observables of the theory ... More Connections and Generalized Gauge TransformationsFeb 01 1996Mar 11 1996Elimination of the fibre coordinate dependence from the connection form transformation rule for a bundle with a coset manifold standard fibre reduces the structure group. The nonlinear SU(4) action on an $S^7$ bundle is applied to the dimensional reduction ... More Infinite-genus surfaces and the universal GrassmannianMay 26 1995Mar 29 1996Correlation functions can be calculated on Riemann surfaces using the operator formalism. The state in the Hilbert space of the free field theory on the punctured disc, corresponding to the Riemann surface, is constructed at infinite genus, verifying ... More Cutting sequences on translation surfacesSep 18 2013Sep 20 2013We analyze the cutting sequences associated to geodesic flow on a large class of translation surfaces, including Bouw-Moller surfaces. We give a combinatorial rule that relates a cutting sequence corresponding to a given trajectory, to the cutting sequence ... More Cutting sequences, regular polygons, and the Veech groupAug 31 2017We describe the cutting sequences associated to geodesic flow on regular polygons, in terms of a combinatorial process called "derivation." This work is an extension of some of the ideas and results in Smillie and Ulcigrai's recent paper, where the analysis ... More Some Basic Radio System OPSEC ConsiderationsAug 03 2014This is an unscientific introduction to basic radio frequency system OPSEC aspects that I have found to be overlooked and lacking in high security system deployments that may have benefited from them. Length Functions for Semigroup EmbeddingsSep 14 2010Following the work done by Olshanskii for groups, we describe, for a given semigroup $S$, which functions $l : S \rightarrow \mathbb{N}$ can be realized up to equivalence as length functions $g \mapsto |g|_{H}$ by embedding $S$ into a finitely generated ... More Order of Magnitude Comparisons of DistanceMay 27 2011Order of magnitude reasoning - reasoning by rough comparisons of the sizes of quantities - is often called 'back of the envelope calculation', with the implication that the calculations are quick though approximate. This paper exhibits an interesting ... More Universal graphs at $\aleph_{ω_1+1}$May 02 2016Starting from a supercompact cardinal we build a model in which $2^{\aleph_{\omega_1}}=2^{\aleph_{\omega_1+1}}=\aleph_{\omega_1+3}$ but there is a jointly universal family of size $\aleph_{\omega_1+2}$ of graphs on $\aleph_{\omega_1+1}$. The same technique ... More Symmetries of vector fields: the diffeomorphism centralizerMar 14 2019In this paper we study the diffeomorphism centralizer of a vector field: given a vector field it is the set of diffeomorphisms that commutes with the flow. Our main theorem states that for a $C^1$-generic diffeomorphism having at most finitely many sinks ... More On the p-typical de Rham-Witt complex over W(k)Jun 18 2017Hesselholt and Madsen in [7] define and study the (absolute, p-typical) de Rham-Witt complex in mixed characteristic, where p is an odd prime. They give as an example an elementary algebraic description of the de Rham-Witt complex over Z_(p). The main ... More Higher-Derivative Quantum CosmologyNov 06 1999Nov 10 1999The quantum cosmology of a higher-derivative derivative gravity theory arising from the heterotic string effective action is reviewed. A new type of Wheeler-DeWitt equation is obtained when the dilaton is coupled to the quadratic curvature terms. Techniques ... More A Proof of the Odd Perfect Number ConjectureJan 08 2004May 31 2008It is sufficient to prove that there is an excess of prime factors in the product of repunits with odd prime bases defined by the sum of divisors of the integer $N=(4k+1)^{4m+1}\prod_{i=1}^\ell ~ q_i^{2\alpha_i}$ to establish that there do not exist any ... More A class of nonsymmetric harmonic Riemannian spacesJul 01 1992Certain solvable extensions of $H$-type groups provide noncompact counterexamples to the so-called Lichnerowicz conjecture, which asserted that ``harmonic'' Riemannian spaces must be rank 1 symmetric spaces. Iterated random functions and regularly varying tailsJun 13 2017We consider solutions to so-called stochastic fixed point equation $R \stackrel{d}{=} \Psi(R)$, where $\Psi $ is a random Lipschitz function and $R$ is a random variable independent of $\Psi$. Under the assumption that $\Psi$ can be approximated by the ... More Stochastic recursions: between Kesten's and Grey's assumptionsJan 10 2017Feb 08 2019We study the stochastic recursion $X_n=\Psi_n(X_{n-1})$, where $(\Psi_n)_{n\geq 1}$ is a sequence of i.i.d. random Lipschitz mappings close to the random affine transformation $x\mapsto Ax+B$. We describe the tail behavior of the stationary solution $X$ ... More Winograd Schemas and Machine TranslationAug 05 2016A Winograd schema is a pair of sentences that differ in a single word and that contain an ambiguous pronoun whose referent is different in the two sentences and requires the use of commonsense knowledge or world knowledge to disambiguate. This paper discusses ... More Separability of multi-charge black holes in supergravityJul 11 2006Oct 23 2006In this paper, we show that some five-dimensional rotating black hole solutions of both gauged and ungauged supergravity, with independent rotation parameters and three charges admit separable solutions to the massless Hamilton-Jacobi and Klein-Gordon ... More Unlabeled Signed Graph ColoringNov 24 2015We extend the work of Hanlon on the chromatic polynomial of an unlabeled graph to an unlabeled signed graph. Explicit formulas are presented for labeled and unlabeled signed chromatic polynomials as summations over distinguished order-ideals of the signed ... More A Covert Channel Based on Web Read-time ModulationOct 07 2014Oct 08 2014A network covert channel is created that operates by modulating the time between web resource accesses, with an 'average web user' read-time used as a reference. While the covert channel may be classified as timing based, it does not operate by changing ... More Inquiry-based learning in a first-year honors courseJun 28 2016Aug 31 2017We describe a case study of a problem-solving section, using the "Harkness" discussion method, of an honors multivariable calculus course. Students in the problem-solving section had equivalent outcomes on exams, reported higher ratings in self-assessments ... More M-Theory and String-String DualityJan 19 1996In this article we examine the compatibility of some recent results, results relating M-Theory to String Theory, with the string-string duality conjecture in six-dimensions. In particular, we rederive the relation between M-Theory and Type IIA strings. ... More Spin Structures on Riemann Surfaces and the Perfect NumbersDec 28 1998Dec 23 1999The equality between the number of odd spin structures on a Riemann surface of genus g, with $2^g - 1$ being a Mersenne prime, and the even perfect numbers, is an indication that the action of the modular group on the set of spin structures has special ... More Modular Invariance and the Finiteness of Superstring TheoryApr 01 1995Apr 03 1996The genus-dependence of multi-loop superstring amplitudes is bounded at large orders in perturbation theory using the super-Schottky group parametrization of supermoduli space. Partial estimates of supermoduli space integrals suggest an exponential dependence ... More Plausible inference from the idea of estimationJul 26 2016The probability axioms by R. T. Cox can be regarded as the modern foundations of Bayesian inference, the idea of assigning degrees of belief to logical propositions in a manner consistent with Boolean logic. In this work it is shown that one can start ... More Affine stochastic equation with triangular matricesJun 23 2018We study solution X of the stochastic equation X = AX +B, where A is a random matrix and B,X are random vectors, the law of (A,B) is given and X is independent of (A,B). The equation is meant in law, the matrix A is 2x2 upper triangular, A_{11}=A_{22}>0, ... More A renewal theorem and supremum of a perturbed random walkDec 10 2018We study tails of the supremum of a perturbed random walk under regime which was not yet considered in the literature. Our approach is based on a new renewal theorem, which is of independent interest. We obtain first and second order asymptotics of the ... More Microphysics of SO(10) Cosmic StringsAug 01 1996Feb 07 1997We uncover a rich microphysical structure for SO(10) cosmic strings. For the abelian string the electroweak symmetry is restored around it in a region depending on the electroweak scale. A rich structure of nonabelian strings is found. Some of these also ... More Studies on access: a reviewDec 20 2009A review of the empirical literature on access to scholarly information. This review focuses on surveys of authors, article download and citation analysis. Random Walks on Homogeneous Spaces by Sparse Solvable MeasuresOct 09 2015The paper analyzes a specific class of random walks on quotients of $X:=\text{SL}(k,{\Bbb R})/ \Gamma$ for a lattice $\Gamma$. Consider a one parameter diagonal subgroup, $\{g_t\}$, with an associated abelian expanding horosphere, $U\cong {\Bbb R}^k$, ... More A Brief State of the Art for Ontology AuthoringJun 11 2014Jun 12 2014One of the main challenges for building the Semantic web is Ontology Authoring. Controlled Natural Languages CNLs offer a user friendly means for non-experts to author ontologies. This paper provides a snapshot of the state-of-the-art for the core CNLs ... More