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
Stochastic subgradient method converges at the rate $O(k^{-1/4})$ on weakly convex functionsFeb 08 2018We prove that the projected stochastic subgradient method, applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$.
The Sound of APALM Clapping: Faster Nonsmooth Nonconvex Optimization with Stochastic Asynchronous PALMJun 07 2016We introduce the Stochastic Asynchronous Proximal Alternating Linearized Minimization (SAPALM) method, a block coordinate stochastic proximal-gradient method for solving nonconvex, nonsmooth optimization problems. SAPALM is the first asynchronous parallel ... 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 the forward-Douglas-Rachford splitting schemeOct 09 2014Jul 08 2015Operator splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which all simple pieces of the decomposition ... More
An $O(n\log(n))$ Algorithm for Projecting Onto the Ordered Weighted $\ell_1$ Norm BallMay 05 2015Jun 26 2015The ordered weighted $\ell_1$ (OWL) norm is a newly developed generalization of the Octogonal Shrinkage and Clustering Algorithm for Regression (OSCAR) norm. This norm has desirable statistical properties and can be used to perform simultaneous clustering ... 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
A SMART Stochastic Algorithm for Nonconvex Optimization with Applications to Robust Machine LearningOct 04 2016Machine learning theory typically assumes that training data is unbiased and not adversarially generated. When real training data deviates from these assumptions, trained models make erroneous predictions, sometimes with disastrous effects. Robust losses, ... More
A Three-Operator Splitting Scheme and its Optimization ApplicationsApr 04 2015Operator splitting schemes have been successfully used in computational sciences to reduce complex problems into a series of simpler subproblems. Since 1950s, these schemes have been widely used to solve problems in PDE and control. Recently, large-scale ... More
Faster convergence rates of relaxed Peaceman-Rachford and ADMM under regularity assumptionsJul 19 2014May 01 2015Splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion 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 processed ... More
Precise tail index of fixed points of the two-sided smoothing transformJun 18 2012We consider real-valued random variables R satisfying the distributional equation R \eqdist \sum_{k=1}^{N}T_k R_k + Q, where R_1,R_2,... are iid copies of R and independent of T=(Q, (T_k)_{k \ge 1}). N is the number of nonzero weights T_k and assumed ... More
Beating level-set methods for 3D seismic data interpolation: a primal-dual alternating approachJul 09 2016Acquisition cost is a crucial bottleneck for seismic workflows, and low-rank formulations for data interpolation allow practitioners to `fill in' data volumes from critically subsampled data acquired in the field. Tremendous size of seismic data volumes ... 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
Maximum boundary regularity of bounded Hua-harmonic functions on tube domainsFeb 03 2004In this paper we prove that bounded Hua-harmonic functions on tube domains that satisfy some boundary regularity condition are necessarily pluriharmonic. In doing so, we show that a similar theorem is true on one-dimensional extensions of the Heisenberg ... 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.
A simple proof of heavy tail estimates for affine type Lipschitz recursionsApr 23 2016We study the affine recursion $X_n = A_nX_{n-1}+B_n$ where $(A_n,B_n)\in {\mathbb R}^+ \times {\mathbb R} $ is an i.i.d. sequence and recursions $X_n = \Phi_n(X_{n-1})$ defined by Lipschitz transformations such that $\Phi (x)\geq Ax+B$. It is known that ... 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
The Bosonic String Measure at Two and Three Loops and Symplectic Transformations of the Volume FormOct 28 1994Oct 29 1994Symplectic modular invariance of the bosonic string partition function has been verified at genus 2 and 3 using the period matrix coordinatization of moduli space. A calculation of the transformation of the holomorphic part of the differential volume ... More
Effectively Closed Infinite-Genus Surfaces and the String CouplingDec 09 2003Dec 10 2003The class of effectively closed infinite-genus surfaces, defining the completion of the domain of string perturbation theory, can be included in the category $O_G$, which is characterized by the vanishing capacity of the ideal boundary. The cardinality ... 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
Representations of Rank Two Affine Hecke Algebras at Roots of UnityApr 26 2011In this paper, we will fully describe the representations of the crystallographic rank two affine Hecke algebras using elementary methods, for all possible values of q. The focus is on the case when q is a root of unity of small order.
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
Ehrhart Series of Polytopes Related to Symmetric Doubly-Stochastic MatricesSep 09 2014Apr 27 2015In Ehrhart theory, the $h^*$-vector of a rational polytope often provide insights into properties of the polytope that may be otherwise obscured. As an example, the Birkhoff polytope, also known as the polytope of real doubly-stochastic matrices, has ... 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
A Proposed System for Covert Communication to Distant and Broad Geographical AreasAug 20 2014Aug 23 2014A covert communication system is developed that modulates Morse code characteristics and that delivers its mes- sage economically and to geographically remote areas using radio and EchoLink. Our system allows a covert message to be sent to a receiving ... 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
Symmetric Variations of the Metric and Extrema of the Action for Pure GravityAug 10 1996Sep 10 1996Symmetries of generalized gravitational actions, yielding field equations which typically involve at most second-order derivatives of the metric, are considered. The field equations for several different higher-derivative theories in the first-order formalism ... 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
The Quantum Cosmological Wavefunction at Very Early Times for a Quadratic Gravity TheoryMay 28 2003The quantum cosmological wavefunction for a quadratic gravity theory derived from the heterotic string effective action is obtained near the inflationary epoch and during the initial Planck era. Neglecting derivatives with respect to the scalar field, ... More
Divergences in the Moduli Space Integral and Accumulating Handles in the Infinite-Genus LimitOct 24 1994The symmetries associated with the closed bosonic string partition function are examined so that the integration region in Teichmuller space can be determined. The conditions on the period matrix defining the fundamental region can be translated to relations ... 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
Configurations of Handles and the Classification of Divergences in the String Partition FunctionApr 13 1994Apr 22 1994The divergences that arise in the regularized partition function for closed bosonic string theory in flat space lead to three types of perturbation series expansions, distinguished by their genus dependence. This classification of infinities can be traced ... 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 Killing tensor for higher dimensional Kerr-AdS black holes with NUT chargeFeb 13 2006May 01 2006In this paper, we study the recently discovered family of higher dimensional Kerr-AdS black holes with an extra NUT-like parameter. We show that the inverse metric is additively separable after multiplication by a simple function. This allows us to separate ... More
A Rationality Condition for the Existence of Odd Perfect NumbersNov 24 2000A rationality condition is derived for the existence of odd perfect numbers involving the square root of a product, which consists of a sequence of repunits, multiplied by twice the base of one of the repunits. This constraint also provides an upper bound ... 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
The Relevance of Proofs of the Rationality of Probability Theory to Automated Reasoning and Cognitive ModelsOct 04 2013A number of well-known theorems, such as Cox's theorem and de Finetti's theorem. prove that any model of reasoning with uncertain information that satisfies specified conditions of "rationality" must satisfy the axioms of probability theory. I argue here ... More
Exponential Family Models from Bayes' Theorem under Expectation ConstraintsMar 11 2015Apr 29 2016It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy principle, ... 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
Citation advantage of Open Access articles likely explained by quality differential and media effectsJan 16 2007In a study of articles published in the Proceedings of the National Academy of Sciences, Gunther Eysenbach discovered a significant citation advantage for those articles made freely-available upon publication (Eysenbach 2006). While the author attempted ... More
A Large Deviations Result for Aggregation of Independent Noisy ObservationsFeb 15 2011Sensing and aggregation of noisy observations should not be considered as separate issues. The quality of collective estimation involves a difficult tradeoff between sensing quality which increases by increasing the number of sensors, and aggregation ... More
Universal Behavior in Large-scale Aggregation of Independent Noisy ObservationsDec 15 2008Aggregation of noisy observations involves a difficult tradeoff between observation quality, which can be increased by increasing the number of observations, and aggregation quality which decreases if the number of observations is too large. We clarify ... More
Nonlinear dynamics of autonomous vehicles with limits on accelerationOct 31 2013The stability of autonomous vehicle platoons with limits on acceleration and deceleration is determined. If the leading-vehicle acceleration remains within the limits, all vehicles in the platoon remain within the limits when the relative-velocity feedback ... More
The Effects of Powertrain Mechanical Response on the Dynamics and String Stability of a Platoon of Adaptive Cruise Control VehiclesJan 09 2013The dynamics of a platoon of adaptive cruise control vehicles is analyzed for a general mechanical response of the vehicle's power-train. Effects of acceleration-feedback control that were not previously studied are found. For small acceleration-feedback ... 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
Generalised Israel Junction Conditions for a Gauss-Bonnet Brane WorldAug 28 2002Dec 18 2002In spacetimes of dimension greater than four it is natural to consider higher order (in R) corrections to the Einstein equations. In this letter generalized Israel junction conditions for a membrane in such a theory are derived. This is achieved by generalising ... 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
Modified Large Distance Newton Potential on a Gauss-Bonnet Brane WorldOct 06 2004Jul 28 2005Gravity on a brane world with higher order curvature terms and a conformally coupled bulk scalar field is investigated. Solutions with non-standard large distance gravity are described. It is not necessary to include a scalar field potential in order ... 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
The Moduli Space and Phase Structure of Heterotic Strings in Two DimensionsNov 29 2005Jun 19 2006We explore the moduli space of heterotic strings in two dimensions. In doing so, we introduce new lines of compactified theories with Spin(24) gauge symmetry and discuss compactifications with Wilson lines. The phase structure of d=2 heterotic string ... 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
Transition to the Most Probable Kinetic State in a Pre-Steady State SystemApr 22 1997Apr 23 1997A system containing a pre-steady state standard (non-autocatalytic) reaction, with multiple paths, evolves toward a kinetic state with the minimum attainable activation free energy. Displacement of the path frequency distribution in this transition was ... 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
Growth of a Bose-Einstein condensate: A detailed comparison of theory and experimentNov 23 2001We extend the earlier model of condensate growth of Davis et al [Davis MJ, Gardiner CW and Ballagh RJ 2000, Phys. Rev. A 62, 063608] to include the effect of gravity in a magnetic trap. We carry out calculations to model the experiment reported by K\"{o}hl ... 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
A figure of merit for black hole mass measurements with molecular gasJun 10 2014In this work we discuss the technique of using molecular gas kinematics (or the kinematics of any dynamically cold tracer) to estimate black hole masses. We present a figure of merit that will be useful in defining future observational campaigns, and ... 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
Implications of the Oklo phenomenon in a chiral approach to nuclear matterJun 28 2014It has been customary to use data from the Oklo natural nuclear reactor to place bounds on the change that has occurred in the electromagnetic fine structure constant $\alpha$ over the last 2 billion years. Alternatively, an analysis could be based on ... 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
Dynamic origin-to-destination routing of wirelessly connected, autonomous vehicles on a congested networkNov 30 2016Up-to-date information wirelessly communicated among vehicles can be used to select the optimal route between a given origin and destination. To elucidate how to make use of such information, simulations are performed for autonomous vehicles traveling ... 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
Liouville's Theorem from the Principle of Maximum Caliber in Phase SpaceFeb 08 2016One of the cornerstones in non--equilibrium statistical mechanics (NESM) is Liouville's theorem, a differential equation for the phase space probability $\rho(q,p; t)$. This is usually derived considering the flow in or out of a given surface for a physical ... 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
Topological complexity of 2-torsion lens spaces and ku-(co)homologyAug 15 2014Feb 12 2015We use ku-cohomology to determine lower bounds for the topological complexity of 2-torsion lens spaces. In the process, we give an almost-complete description of the tensor product of two copies of the ku-homology of infinite mod 2^e lens space, proving ... 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