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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

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 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

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 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

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 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 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

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

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

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

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

Low-rank matrix recovery with composite optimization: good conditioning and rapid convergenceApr 22 2019The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem often exhibit an undesirable phenomenon: the condition number, classically defined, scales poorly ... 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

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

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

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

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

Pointwise estimates for exceedance times of perpetuity sequencesDec 10 2015We consider large exceedence probabilities of the perpetuity sequence $$Y_n = B_1 + A_1 B_2 + \cdots + (A_1\ldots A_{n-1})B_n, $$ where $(A_n,B_n)$ are i.i.d. random variables with values in ${\mathbf R} ^+\times {\mathbf R}$ and the exceedance times ... 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

Absolute continuity of the martingale limit in branching processes in random environmentJun 13 2018We consider a supercritical branching process $Z_n$ in a stationary and ergodic random environment $\xi =(\xi_n)_{n\ge0}$. Due to the martingale convergence theorem, it is known that the normalized population size $W_n=Z_n/ (\mathbb E (Z_n|\xi ))$ converges ... 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

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

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

On the stable ergodicity of diffeomorphisms with dominated splittingJun 08 2018In this paper we obtain two criteria of stable ergodicity outside the partially hyperbolic scenario. In both criteria, we use a weak form of hyperbolicity called chain-hyperbolicity. It is obtained one criterion for diffeomorphisms with dominated splitting ... 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.

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

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

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

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

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

A Centroid for Sections of a Cube in a Function Space, with application to ColorimetryNov 02 2018Feb 28 2019The definition of the centroid in finite dimensions does not apply in a function space because of the lack of a translation invariant measure. Another approach, suggested by Nik Weaver, is to use a suitable collection of finite-dimensional subspaces. ... 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

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

The Limitations of Standardized Science Tests as Benchmarks for Artificial Intelligence Research: Position PaperNov 06 2014Oct 16 2015In this position paper, I argue that standardized tests for elementary science such as SAT or Regents tests are not very good benchmarks for measuring the progress of artificial intelligence systems in understanding basic science. The primary problem ... 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

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

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

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

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 Centroid for Sections of a Cube in a Function Space, with application to ColorimetryNov 02 2018The definition of the centroid in finite dimensions does not apply in a function space because of the lack of a translation invariant measure. Another approach, suggested by Nik Weaver, is to use a suitable collection of finite-dimensional subspaces. ... 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

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

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

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

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

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

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

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

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

Projections for measuring the size of the solar core with neutrino-electron scatteringJun 08 2016Jun 20 2016We quantify the amount of data needed in order to measure the size of the solar core with future experiments looking at elastic scattering between electrons and solar neutrinos. The directions of the electrons immediately after scattering are strongly ... 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.

Hawking mass and local rigidity of minimal two-spheres in three-manifoldsJun 24 2012We study rigidity of minimal two-spheres $\Sigma$ that locally maximize the Hawking mass on a Riemannian three-manifold with a positive lower bound on its scalar curvature. After assuming strict stability of $\Sigma$, we prove that a neighborhood of it ... More

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

Societal and ethical interactions with nanotechnology ("SEIN") -- an introductionApr 01 2005We identify 6 important issues tied to the continued development of nantechnology: (1) environmental issues, (2) equity issues relating to the possible emergence of a "nanodivide", (3) legal, regulatory and insurance challenges, (4) privacy issues, (5) ... 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

Donald Burkholder's work in martingales and analysisDec 22 2010Overview of Burkholder's work on martingales and analysis

Systematic variation of the 12CO/13CO ratio as a function of star-formation rate surface densitySep 05 2014We show that the12CO/13CO intensity ratio in nearby galaxies varies systematically as a function of the star formation rate surface density and gas surface density. The same effect is observed in different transitions, and in the 12CO/C18O ratio, while ... More

The Abundance Pattern in the Hot ISM of NGC 4472: Insights and AnomaliesApr 20 2010Important clues to the chemical and dynamical history of elliptical galaxies are encoded in the abundances of heavy elements in the X-ray emitting plasma. We derive the hot ISM abundance pattern in inner and outer regions of NGC 4472 from analysis of ... More