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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 2016Feb 05 2017In this paper, we show how to transform any optimization problem that arises from fitting a machine learning model into one that (1) detects and removes contaminated data from the training set while (2) simultaneously fitting the trimmed model on the ... 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

Forward-Backward-Half Forward Algorithm for Solving Monotone InclusionsMar 09 2017Mar 23 2018Tseng's algorithm finds a zero of the sum of a maximally monotone operator and a monotone continuous operator by evaluating the latter twice per iteration. In this paper, we modify Tseng's algorithm for finding a zero of the sum of three operators, where ... 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

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

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

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

Graphical Convergence of Subgradients in Nonconvex Optimization and LearningOct 17 2018Dec 17 2018We investigate the stochastic optimization problem of minimizing population risk, where the loss defining the risk is assumed to be weakly convex. Compositions of Lipschitz convex functions with smooth maps are the primary examples of such losses. We ... More

Stochastic subgradient method converges at the rate $O(k^{-1/4})$ on weakly convex functionsFeb 08 2018Feb 19 2018We prove that the proximal stochastic subgradient method, applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$. As a consequence, we resolve an open question on the convergence rate of the proximal ... 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 $O(k^{-1/4})$.

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

Proximally Guided Stochastic Subgradient Method for Nonsmooth, Nonconvex ProblemsJul 12 2017Sep 18 2018In this paper, we introduce a stochastic projected subgradient method for weakly convex (i.e., uniformly prox-regular) nonsmooth, nonconvex functions---a wide class of functions which includes the additive and convex composite classes. At a high-level, ... More

Complexity of finding near-stationary points of convex functions stochasticallyFeb 21 2018In a recent paper, we showed that the stochastic subgradient method applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$. In this supplementary note, we present a stochastic subgradient method ... 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

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

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

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

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

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

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

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

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

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

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

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

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

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

On the invariant measure of the random difference equation $X_n=A_n X_{n-1}+ B_n$ in the critical caseSep 10 2008Nov 10 2008We consider the autoregressive model on $\R^d$ defined by the following stochastic recursion $X_n = A_n X_{n-1}+B_n$, where $\{(B_n,A_n)\}$ are i.i.d. random variables valued in $\R^d\times \R^+$. The critical case, when $\E\big[\log A_1\big]=0$, was ... 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

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.

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

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

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

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

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

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

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

Absolute Continuity of Complex Martingales and of Solutions to Complex Smoothing EquationsApr 06 2018Let $X$ be a $\mathbb{C}$-valued random variable with the property that $$X \ \text{ has the same law as }\ \sum_{j\ge1} T_j X_j$$ where $X_j$ are i.i.d.\ copies of $X$, which are independent of the (given) $\mathbb{C}$-valued random variables $ (T_j)_{j\ge1}$. ... 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

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.

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.

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

Local Scale Invariance and General RelativityDec 04 2003Dec 05 2003According to the theory of unimodular relativity developed by Anderson and Finkelstein, the equations of general relativity with a cosmological constant are composed of two independent equations, one which determines the null-cone structure of space-time, ... More

Brane Cosmology Solutions with Bulk Scalar FieldsNov 27 2001Apr 11 2002Brane cosmologies with static, five-dimensional and Z_2 symmetric bulks are analysed. A general solution generating mechanism is outlined. The qualatitive cosmological behaviour of all such solutions is determined. Conditions for avoiding naked bulk singularities ... More

Brane World Linearized Cosmic String GravityOct 21 2000Dec 14 2000The gravitational properties of cosmic strings in the Randall-Sundrum brane world scenario are investigated. Using a gauge in which the brane remains straight, the leading order corrections to the metric on the brane are determined. In contrast to their ... More

The quantum theory of a quadratic gravity action for heterotic stringsDec 31 2001Feb 13 2002The wave function for the quadratic gravity theory derived from the heterotic string effective action is deduced to first order in ${{e^{-\Phi}}\over {g_4^2}}$ by solving a perturbed second-order Wheeler-DeWitt equation, assuming that the potential is ... More

Microphysics of Cosmic Strings in Supersymmetric and Grand Unified TheoriesDec 19 2006In this thesis we investigate the microphysics of cosmic strings in non-minimal quantum field theories. In particular we consider theories in which fermion fields couple to the strings, and those with larger symmetry groups, such as grand unified and ... More

Brane World Cosmic String InteractionAug 16 2006It is shown that brane world gravity produces an attractive force between cosmic strings, in contrast to conventional Einstein gravity. This force is sufficient for stable bound states of Type II strings (which normally repel each other) to form. There ... More

An $O^*(1.0821^n)$-Time Algorithm for Computing Maximum Independent Set in Graphs with Bounded Degree 3Aug 06 2013Apr 12 2015We give an $O^*(1.0821^n)$-time, polynomial space algorithm for computing Maximum Independent Set in graphs with bounded degree 3. This improves all the previous running time bounds known for the problem.

Determining the value of the fine-structure constant from a current balance: getting acquainted with some upcoming changes to the SIOct 10 2016The revised International System of Units (SI), expected to be approved late in 2018, has implications for physics pedagogy; the ampere definition which dates from 1948 will be replaced by a definition that fixes the numerical value of the elementary ... More

Realizing Wardrop Equilbria with Real-Time Traffic InformationMay 08 2009A Wardrop equilibrium for multiple routes requires equal travel time on each path used. With real-time traffic data regarding travel times, it is important to analyze how to use the information provided. In particular, can a Wardrop equilibrium be realized? ... More

Effect of adaptive cruise control systems on mixed traffic flow near an on-rampJun 16 2005Mixed traffic flow consisting of vehicles equipped with adaptive cruise control (ACC) and manually driven vehicles is analyzed using car-following simulations. Unlike simulations that show suppression of jams due to increased string stability, simulations ... More

Driver Choice Compared to Controlled Diversion for a Freeway Double On-RampApr 30 2008Two diversion schemes that apportion demand between two on-ramps to reduce congestion and improve throughput on a freeway are analyzed. In the first scheme, drivers choose to merge or to divert to a downstream on-ramp based on information about average ... More

Electronic Access to Information and the Privacy Paradox: Rethinking :'Practical Obscurity'Sep 24 2001This article addresses the U.S. Supreme Court's central purpose formulation in Reporters Committee v. Department of Justice under the federal Freedom of Information Act. By examining all lower federal court opinions interpreting Reporters Committee and ... More

Mining the Sky with Redshift SurveysApr 25 2001Since the late 1970's, redshift surveys have been vital for progress in understanding large-scale structure in the Universe. The original CfA redshift survey collected spectra of 20-30 galaxies per clear night on a 1.5 meter telescope; over a two year ... More

Estimation of Peculiar Velocity from the Inverse Tully-Fisher RelationJul 30 1994Aug 08 1994We present a method for deriving a smoothed estimate of the peculiar velocity field of a set of galaxies with measured circular velocities $\eta\equiv {\rm log} \Delta v$ and apparent magnitudes $m$. The method is based on minimizing the scatter of a ... More

The Origin of the Magellanic StreamJan 07 1994SHORTENED ABSTRACT: We present numerical investigations designed to critically test models of the origin of the Magellanic Stream. The most developed model is the tidal model which fails to reproduce several of its characteristic properties. We suggest ... More

Jump-Diffusion Risk-Sensitive Asset Management I: Diffusion Factor ModelJan 08 2010Nov 13 2010This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion factor process. The criterion, following ... More

The work of Tom Farrell and Lowell Jones in topology and geometryJun 08 2010Aug 08 2010This is a survey of some of the work of Tom Farrell and Lowell Jones. This is the lead article of a special issue of the Pure and Applied Mathematics Quarterly. This issue is published in conjunction with the conference "Geometry,Topology, and their Interactions" ... More

Dark Matter vs. Neutrinos: The effect of astrophysical uncertainties and timing information on the neutrino floorDec 03 2014Mar 09 2015Future multi-tonne Direct Detection experiments will be sensitive to solar neutrino induced nuclear recoils which form an irreducible background to light Dark Matter searches. Indeed for masses around 6 GeV the spectra of neutrinos and Dark Matter are ... More

S_3 x S_3 acts freely on S^3 x S^3Jun 06 1998A free action of the direct product of two copies of the symmetric group on 3 elements on the cartesian product of two copies of the 3-sphere is constructed. This nonlinear action is constructed using surgery. The action provides a counterexample to a ... More

Darwinian Aspects of Molecular Evolution at Sublinear Propagation RatesFeb 24 1999The symmetric distribution and all other states in the symmetry sector of the frequency trajectory increase mean fitness during competitive replication at sublinear propagation rates (parabolic time course). States in the non-symmetry sector, by contrast, ... More

Subgroup Distortion in Wreath Products of Cyclic GroupsSep 22 2010Apr 08 2011We study the effects of subgroup distortion in the wreath products A wr Z, where A is finitely generated abelian. We show that every finitely generated subgroup of A wr Z has distortion function equivalent to some polynomial. Moreover, for A infinite, ... More