Results for "Damek Davis"
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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 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 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 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 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 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 On multidimensional Mandelbrot's cascadesSep 08 2011Mar 13 2014Let $Z$ be a random variable with values in a proper closed convex cone $C\subset \mathbb{R}^d$, $A$ a random endomorphism of $C$ and $N$ a random integer. We assume that $Z$, $A$, $N$ are independent. Given $N$ independent copies $(A_i,Z_i)$ of $(A,Z)$ ... 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 Heavy tailed solutions of multivariate smoothing transformsJun 08 2012Feb 05 2013Let $N > 1$ be a fixed integer and $(C_1,..., C_N,Q)$ a random element of $GL(d, \R)^N x \R^d$. We consider solutions of multivariate smoothing transforms, i.e. random variables $R$ satisfying $$R \eqdist \sum_{i=1}^N C_i R_i +Q $$ where $\eqdist$ denotes ... 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. 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 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 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 Inquiry-based learning in a first-year honors courseJun 28 2016We report on a pilot problem-solving section of an honors multivariable calculus course. The course consisted of students doing problems for homework, and then spending class time discussing solutions, using the "Harkness method." There were no lectures, ... 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 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 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 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 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 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 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 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 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 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 A Note on Tensionless Strings in M-TheoryAug 30 1996In this article we examine the appearance of tensionless strings in M-Theory. We subsequently interpret these tensionless strings in a String Theory context. In particular, we examine tensionless strings appearing in M-Theory on $S^{1}$, M-Theory on $S^{1} ... More Enhanced Gauge Symmetry in M-TheoryAug 16 1996In this article we examine some points in the moduli space of M-Theory at which there arise enhanced gauge symmetries. In particular, we examine the ``trivial" points of enhanced gauge symmetry in the moduli space of M-Theory on $S^{ 1 } \times S^{ 1 ... 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. Function spectra and continuous G-spectraJan 29 2011Let G be a profinite group, {X_alpha}_alpha a cofiltered diagram of discrete G-spectra, and Z a spectrum with trivial G-action. We show how to define the homotopy fixed point spectrum F(Z, holim_alpha X_alpha)^{hG} and that when G has finite virtual cohomological ... 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 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 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 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 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 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 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 Quadrant Marked Mesh Patterns and the r-Stirling NumbersDec 01 2014Dec 18 2014Marked mesh patterns are a very general type of permutation pattern. We examine a particular marked mesh pattern originally defined by Kitaev and Remmel, and show that its generating function is described by the $r$-Stirling numbers. We examine some ramifications ... 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 Solar System Constraints on Gauss-Bonnet Dark EnergyAug 15 2007Quadratic curvature Gauss-Bonnet gravity may be the solution to the dark energy problem, but a large coupling strength is required. This can lead to conflict with laboratory and planetary tests of Newton's law, as well as light bending. The corresponding ... More Gravity on a Dilatonic Gauss-Bonnet Brane WorldAug 18 2004The effective four-dimensional, linearised gravity of a Randall-Sundrum-like brane world model is analysed. The model includes higher order curvature terms (such as the Gauss-Bonnet term) and a scalar field. The resulting brane worlds can have better ... More Destruction of Fermion Zero Modes on Cosmic StringsJan 26 1999Dec 18 2000I examine the existence of zero energy fermion solutions (zero modes) on cosmic strings in an SO(10) grand unified theory. The current carrying capability of a cosmic string formed at one phase transition can be modified at subsequent phase transitions. ... More Solar System Constraints on f(G) Dark EnergySep 27 2007Jan 30 2008Corrections to solar system gravity are derived for f(G) gravity theories, in which a function of the Gauss-Bonnet curvature term is added to the gravitational action. Their effects on Newton's law, as felt by the planets, and on the frequency shift of ... More A Fermionic Hodge Star OperatorSep 21 1998A fermionic analogue of the Hodge star operation is shown to have an explicit operator representation in models with fermions, in spacetimes of any dimension. This operator realizes a conjugation (pairing) not used explicitly in field-theory, and induces ... More Zitterbewegung and the Magnetic Moment of the ElectronJul 04 2013Zitterbewegung of a Dirac electron is an oscillation between positive and negative energy states, and is thus distinct from the analogous phenomena exhibited by spin half charged particles in electric and magnetic fields. Quantum field theory offers an ... More Verified AIG Algorithms in ACL2Apr 30 2013And-Inverter Graphs (AIGs) are a popular way to represent Boolean functions (like circuits). AIG simplification algorithms can dramatically reduce an AIG, and play an important role in modern hardware verification tools like equivalence checkers. In practice, ... More INDICATIONS OF DARK MATTER DERIVED FROM LARGE SCALE FLOWSJan 09 1995Recent progress in the measurement of relative distances to galaxies has been quite substantial, and catalogs of 3000 galaxies with distances are soon to become available. The peculiar {\it velocity} field (deviations from Hubble flow) derivable from ... More Axiomatic TQFT, Axiomatic DQFT, and Exotic 4-ManifoldsJun 12 2011Oct 07 2011In this article we prove that any unitary, axiomatic topological quantum field theory in four-dimensions can not detect changes in the smooth structure of M, a simply connected, closed (compact without boundary), oriented smooth manifold. However, as ... More Orbits of the Kepler problem via polar reciprocalsJul 05 2011It is argued that, for motion in a central force field, polar reciprocals of trajectories are an elegant alternative to hodographs. The principal advantage of polar reciprocals is that the transformation from a trajectory to its polar reciprocal is its ... More Which alternating and symmetric groups are unit groups?Mar 30 2013We prove there is no ring with unit group isomorphic to S_n for n \geq 5 and that there is no ring with unit group isomorphic to A_n for n \geq 5, n \neq 8. We give examples of rings with unit groups isomorphic to S_1, S_2, S_3, S_4, A_1, A_2, A_3, A_4, ... More Pattern-Avoiding PolytopesSep 06 2016The permutohedron and the Birkhoff polytope are two well-studied polytopes related to many areas of mathematics. In this paper, we generalize these polytopes by considering convex hulls of subsets of their vertices. The vertices chosen correspond to avoidance ... More Hamiltonian formalism and path entropy maximizationApr 11 2014Sep 07 2015Maximization of the path information entropy is a clear prescription for constructing models in non-equilibrium statistical mechanics. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous constraints on position ... More A Direct Construction of Non-Transitive Dice SetsOct 27 2016In this paper, we give a direct construction for a set of dice realizing any given tournament $T$. The construction for a tournament with $n$ vertices requires a number of sides on the order of $n$, which appears to be the best general construction to ... More Excited random walks with non-nearest neighbor stepsApr 20 2015Jun 10 2016Let $W$ be an integer valued random variable satisfying $E[W] =: \delta \geq 0$ and $P(W<0)>0$, and consider a self-interacting random walk that behaves like a simple symmetric random walk with the exception that on the first visit to any integer $x\in ... More On the cohomology classes of planar polygon spacesApr 14 2016We obtain an explicit formula for the Poincare duality isomorphism H^{n-3}(Mbar(ell)) to Z/2 for the space of isometry classes of n-gons with specified side lengths, if ell is monogenic in the sense of Hausmann-Rodriguez. This has potential application ... More Divisibility by 2 of partial Stirling numbersSep 22 2011The partial Stirling numbers T_n(k) used here are defined as the sum over odd values of i of (n choose i) i^k. Their 2-exponents nu(T_n(k)) are important in algebraic topology. We provide many specific results, applying to all values of n, stating that, ... More Projective product spacesAug 04 2009Aug 07 2009Let nbar=(n_1,...,n_r). The quotient space P_nbar:=(S^{n_1} x...x S^{n_r})/(x ~ -x)is what we call a projective product space. We determine the integral cohomology ring and the action of the Steenrod algebra. We give a splitting of Sigma P_nbar in terms ... More