Evaluation of the Free Energy of Two-Dimensional Yang-Mills Theory

The free energy in the weak-coupling phase of two-dimensional Yang-Mills theory on a sphere for SO(N) and Sp(N) is evaluated in the 1/N expansion using the techniques of Gross and Matytsin. Many features of Yang-Mills theory are universal among different gauge groups in the large N limit, but significant differences arise in subleading order in 1/N.Comment: 10 pages; no figures; LaTe

Asymptotic Learning Curve and Renormalizable Condition in Statistical Learning Theory

Bayes statistics and statistical physics have the common mathematical structure, where the log likelihood function corresponds to the random Hamiltonian. Recently, it was discovered that the asymptotic learning curves in Bayes estimation are subject to a universal law, even if the log likelihood function can not be approximated by any quadratic form. However, it is left unknown what mathematical property ensures such a universal law. In this paper, we define a renormalizable condition of the statistical estimation problem, and show that, under such a condition, the asymptotic learning curves are ensured to be subject to the universal law, even if the true distribution is unrealizable and singular for a statistical model. Also we study a nonrenormalizable case, in which the learning curves have the different asymptotic behaviors from the universal law

Some New/Old Approaches to QCD

This is a talk delivered at the Meeting on Integrable Quantum Field Theories, Villa Olmo and at STRINGS 1992, Rome, September 1992. I discuss some recent attempts to revive two old ideas regarding an analytic approach to QCD-the development of a string representation of the theory and the large N limit of QCD.Comment: 20 page

A preliminary factor analytic investigation into the first-order factor structure of the Fifteen Factor Plus (15FQ+) on a sample of Black South African managers

The original publication is available at http://www.sajip.co.zaMoyo, S. & Theron, C. 2011. A preliminary factor analytic investigation into the first-order factor structure of the Fifteen Factor Plus (15FQ+) on a sample of Black South African managers. SA Journal of Industrial Psychology, 37(1), 1-22, doi: 10.4102/sajip.v37i1.934.Orientation: The Fifteen Factor Questionnaire Plus (15FQ+) is a prominent personality questionnaire that organisations frequently use in personnel selection in South Africa. Research purpose: The primary objective of this study was to undertake a factor analytic investigation of the first-order factor structure of the 15FQ+. Motivation for the study: The construct validity of the 15FQ+, as a measure of personality, is necessary even though it is insufficient to justify its use in personnel selection. Research design, approach and method: The researchers evaluated the fit of the measurement model, which the structure and scoring key of the 15FQ+ implies, in a quantitative study that used an ex post facto correlation design through structural equation modelling. They conducted a secondary data analysis. They selected a sample of 241 Black South African managers from a large 15FQ+ database. Main findings: The researchers found good measurement model fit. The measurement model parameter estimates were worrying. The magnitude of the estimated model parameters suggests that the items generally do not reflect the latent personality dimensions the designers intended them to with a great degree of precision. The items are reasonably noisy measures of the latent variables they represent. Practical/managerial implications: Organisations should use the 15FQ+ carefully on Black South African managers until further local research evidence becomes available. Contribution/value-add: The study is a catalyst to trigger the necessary additional research we need to establish convincingly the psychometric credentials of the 15FQ+ as a valuable assessment tool in South Africa.Publisher's versio

Summing Over Inequivalent Maps in the String Theory Interpretation of Two Dimensional QCD

Following some recent work by Gross, we consider the partition function for QCD on a two dimensional torus and study its stringiness. We present strong evidence that the free energy corresponds to a sum over branched surfaces with small handles mapped into the target space. The sum is modded out by all diffeomorphisms on the world-sheet. This leaves a sum over disconnected classes of maps. We prove that the free energy gives a consistent result for all smooth maps of the torus into the torus which cover the target space $p$ times, where $p$ is prime, and conjecture that this is true for all coverings. Each class can also contain integrations over the positions of branch points and small handles which act as ``moduli'' on the surface. We show that the free energy is consistent for any number of handles and that the first few leading terms are consistent with contributions from maps with branch points.Comment: 17 pages, 5 eps figures contained in a uuencoded file, UVA-HET-92-1

Density Correlation Functions in Calogero Sutherland Models

Using arguments from two dimensional Yang-Mills theory and the collective coordinate formulation of the Calogero-Sutherland model, we conjecture the dynamical density correlation function for coupling $l$ and $1/l$, where $l$ is an integer. We present overwhelming evidence that the conjecture is indeed correct.Comment: 12 pages phyzzx, CERN-TH/94.7243 One reference change

Open Wilson Lines and Group Theory of Noncommutative Yang-Mills Theory in Two Dimensions

The correlation functions of open Wilson line operators in two-dimensional Yang-Mills theory on the noncommutative torus are computed exactly. The correlators are expressed in two equivalent forms. An instanton expansion involves only topological numbers of Heisenberg modules and enables extraction of the weak-coupling limit of the gauge theory. A dual algebraic expansion involves only group theoretic quantities, winding numbers and translational zero modes, and enables analysis of the strong-coupling limit of the gauge theory and the high-momentum behaviour of open Wilson lines. The dual expressions can be interpreted physically as exact sums over contributions from virtual electric dipole quanta.Comment: 37 pages. References adde

Neuronal adaptation involves rapid expansion of the action potential initiation site

Action potential (AP) generation is the key to information processing in the brain. Although APs are normally initiated in the axonal initial segment, developmental adaptation or prolonged network activity may alter the initiation site geometry thus affecting cell excitability. Here we find that hippocampal dentate granule cells adapt their spiking threshold to the kinetics of the ongoing dendrosomatic excitatory input by expanding the AP initiation area away from the soma while also decelerating local axonal spikes. Dual-patch soma-axon recordings combined with axonal Na+ and Ca2+ imaging and biophysical modeling show that the underlying mechanism involves distance-dependent inactivation of axonal Na+ channels due to somatic depolarization propagating into the axon. Thus the ensuing changes in the AP initiation zone and local AP propagation could provide activity-dependent control of cell excitability and spiking on a relatively rapid time scale

Template synthesis and magnetic characterization of FeNi nanotubes

Iron-nickel nanotubes consisting of 20% Ni and 80% Fe with an aspect ratio of about 100 were synthesized by electrochemical deposition in the pores of polyethylene terephthalate ion-track membranes. The main morphological parameters such as composition, wall thickness and structural characteristics were defined. Macro- and micromagnetic parameters of FeNi nanotubes were determined. © 2017, Electromagnetics Academy. All rights reserved

Localization for Yang-Mills Theory on the Fuzzy Sphere

We present a new model for Yang-Mills theory on the fuzzy sphere in which the configuration space of gauge fields is given by a coadjoint orbit. In the classical limit it reduces to ordinary Yang-Mills theory on the sphere. We find all classical solutions of the gauge theory and use nonabelian localization techniques to write the partition function entirely as a sum over local contributions from critical points of the action, which are evaluated explicitly. The partition function of ordinary Yang-Mills theory on the sphere is recovered in the classical limit as a sum over instantons. We also apply abelian localization techniques and the geometry of symmetric spaces to derive an explicit combinatorial expression for the partition function, and compare the two approaches. These extend the standard techniques for solving gauge theory on the sphere to the fuzzy case in a rigorous framework.Comment: 55 pages. V2: references added; V3: minor corrections, reference added; Final version to be published in Communications in Mathematical Physic