A Note on Gauge Invariant Operators in Noncommutative Gauge Theories and the Matrix Model

In this note we discuss local gauge-invariant operators in noncommutative gauge theories. Inspired by the connection of these theories with the Matrix model, we give a simple construction of a complete set of gauge-invariant operators. We make connection with the recent discussions of candidate operators which are dual to closed strings modes. We also discuss large Wilson loops which in the limit of vanishing noncommutativity, reduce to the closed Wilson loops of the ordinary gauge theory

Noncritical Strings, RG Flows and Holography

We derive an RG flow equation that is satisfied by the regularized partition function for noncritical strings in background fields. The flow refers to change in the position of a ``boundary'' in the liouville direction. The boundary is required to regularize the ultraviolet divergences in the partition function coming from integration over world-sheets of arbitrarily small area. From the point of view of the target space effective gravitational action that the partition function evaluates on-shell, the boundary regularizes {\it infrared} divergences coming from the infinite volume of the liouville direction. The RG flow equation that we obtain looks very much like the Hamilton-Jacobi constraint equation that an on-shell gauge-fixed gravitational action must satisfy

The properties of some substitute bearing alloys

A bearing is a means for supporting a load between rela-tively moving surfaces with as little friction as possible .' The plain bearings, used in the automobile , aircraft and other engineering industries, consist of two surfaces, the shaft and the hearing, generally separated by a film of lubricant. The so-called bear- ing alloys utilised for the purpose have to satisfy some primary requirements such as suitable chemical make up giving rise to a hard constituent embedded in a soft matrix , and a certain range of physical ( melting point , density, thermal conductivity, etc.) and mechanical (hardness , modulus of elasticity, tensile strength, impact resistance and age-hardening characteristics) properties. Besides these, certain service properties such as wear, seizure-resistance , conformability , embeddability corrosion-resistance, etc. are also to be complied with

Gauge/Gravity Duality and Some Applications

We discuss the AdS/CFT correspondence in which space-time emerges from an interacting theory of D-branes and open strings. These ideas have a historical continuity with QCD which is an interacting theory of quarks and gluons. In particular we review the classic case of D3 branes and the non-conformal D1 brane system. We outline by some illustrative examples the calculations that are enabled in a strongly coupled gauge theory by correspondence with dynamical horizons in semi-classical gravity in one higher dimension. We also discuss implications of the gauge-fluid/gravity correspondence for the information paradox of black hole physics.Comment: 19 pages, 2 figures, Contribution to "Conference in Honor of Murray Gell-Mann's 80th Birthday

Supersymmetric Chern-Simons Theories with Vector Matter

In this paper we discuss SU(N) Chern-Simons theories at level k with both fermionic and bosonic vector matter. In particular we present an exact calculation of the free energy of the N=2 supersymmetric model (with one chiral field) for all values of the 't Hooft coupling in the large N limit. This is done by using a generalization of the standard Hubbard-Stratanovich method because the SUSY model contains higher order polynomial interactions.Comment: 46 pages, 24 figures, v2: comments and references added, v3: a footnote in Section 3.5 adde

A Gentle Introduction to Gradient-Based Optimization and Variational Inequalities for Machine Learning

The rapid progress in machine learning in recent years has been based on a highly productive connection to gradient-based optimization. Further progress hinges in part on a shift in focus from pattern recognition to decision-making and multi-agent problems. In these broader settings, new mathematical challenges emerge that involve equilibria and game theory instead of optima. Gradient-based methods remain essential -- given the high dimensionality and large scale of machine-learning problems -- but simple gradient descent is no longer the point of departure for algorithm design. We provide a gentle introduction to a broader framework for gradient-based algorithms in machine learning, beginning with saddle points and monotone games, and proceeding to general variational inequalities. While we provide convergence proofs for several of the algorithms that we present, our main focus is that of providing motivation and intuition.Comment: 36 pages, 7 figure

Quark Confinement and Dual Representation in 2+1 Dimensional Pure Yang-Mills Theory

We study the quark confinement problem in 2+1 dimensional pure Yang-Mills theory using euclidean instanton methods. The instantons are regularized and dressed Wu-Yang monopoles. The dressing of a monopole is due to the mean field of the rest of the monopoles. We argue that such configurations are stable to small perturbations unlike the case of singular, undressed monopoles. Using exact non-perturbative results for the 3-dim. Coulomb gas, where Debye screening holds for arbitrarily low temperatures, we show in a self-consistent way that a mass gap is dynamically generated in the gauge theory. The mass gap also determines the size of the monopoles. In a sense the pure Yang-Mills theory generates a dynamical Higgs effect. We also identify the disorder operator of the model in terms of the Sine-Gordon field of the Coulomb gas.Comment: 26 pages, RevTex, Title changed, a new section added, the discussion on stability of dressed monopole expanded. Version to appear in Physical Review

Acute effects of sex steroids on visual processing in male goldfish

Elevations of sex steroids induced by social cues can rapidly modulate social behavior, but we know little about where they act within the nervous system to produce such effects. In male goldfish, testosterone (T) rapidly increases approach responses to the visual cues of females through its conversion to estradiol. Because aromatase is expressed in the retina, we tested if T can acutely influence retina responses to visual stimuli, and investigated the receptor mechanisms that may mediate such effects. Specifically, we measured FOS protein immunoreactivity to determine if T affects cellular responses to visual stimuli that include females, and used electrophysiology to investigate whether T can generally affect light sensitivity. We found that T acutely increased FOS responses to the simultaneous onset of light and the presence of female visual stimuli, both of which would normally be associated with early morning spawning, and increased electrophysiological responses to low intensity light pulses. Both effects were blocked by an estrogen receptor beta (ERβ) antagonist, indicating that T is likely being converted to estradiol (E2) and acting through an ERβ mediated mechanism to acutely modulate visual processing. Changes in sensory processing could subsequently influence approach behavior to increase reproductive success in competitive mating environments