Fine structure in the large n limit of the non-hermitian Penner matrix model

In this paper we apply results on the asymptotic zero distribution of the Laguerre polynomials to discuss generalizations of the standard large $n$ limit in the non-hermitian Penner matrix model. In these generalizations $g_n n\to t$, but the product $g_n n$ is not necessarily fixed to the value of the 't Hooft coupling $t$. If $t>1$ and the limit $l = \lim_{n\rightarrow \infty} |\sin(\pi/g_n)|^{1/n}$ exists, then the large $n$ limit is well-defined but depends both on $t$ and on $l$. This result implies that for $t>1$ the standard large $n$ limit with $g_n n=t$ fixed is not well-defined. The parameter $l$ determines a fine structure of the asymptotic eigenvalue support: for $l\neq 0$ the support consists of an interval on the real axis with charge fraction $Q=1-1/t$ and an $l$-dependent oval around the origin with charge fraction $1/t$. For $l=1$ these two components meet, and for $l=0$ the oval collapses to the origin. We also calculate the total electrostatic energy $\mathcal{E}$, which turns out to be independent of $l$, and the free energy $\mathcal{F}=\mathcal{E}-Q\ln l$, which does depend of the fine structure parameter $l$. The existence of large $n$ asymptotic expansions of $\mathcal{F}$ beyond the planar limit as well as the double-scaling limit are also discussed

Spectral curves in gauge/string dualities: integrability, singular sectors and regularization

We study the moduli space of the spectral curves $y^2=W'(z)^2+f(z)$ which characterize the vacua of $\mathcal{N}=1$ U(n) supersymmetric gauge theories with an adjoint Higgs field and a polynomial tree level potential $W(z)$. It is shown that there is a direct way to associate a spectral density and a prepotential functional to these spectral curves. The integrable structure of the Whitham equations is used to determine the spectral curves from their moduli. An alternative characterization of the spectral curves in terms of critical points of a family of polynomial solutions $\mathbb{W}$ to Euler-Poisson-Darboux equations is provided. The equations for these critical points are a generalization of the planar limit equations for one-cut random matrix models. Moreover, singular spectral curves with higher order branch points turn out to be described by degenerate critical points of $\mathbb{W}$. As a consequence we propose a multiple scaling limit method of regularization and show that, in the simplest cases, it leads to the Painlev\`{e}-I equation and its multi-component generalizations.Comment: 29 pages, 4 figure

Soliton motion in the case of a nonzero reflection coefficient

A method is given for finding the shifts in position of the solitons for the case of nonzero reflection coefficient. Expressions for boost generators in terms of scattering data play a prominent role in the analysis. Phase-shift formulas which show the effect of the radiation component on the soliton motion are deduced for the nonlinear Schrodinger equation, the Korteweg —de Vries equation, and the sine-Gordon equation

Measuring the Pro-Activity of Software Agents

Despite having well-defined characteristics, software agents do not have a developed set of measures defining their quality. Attempts at evaluating software agent quality have focused on some agent aspects, like the development process, whereas others focusing on the agent as a software product have basically adopted measures associated with other software paradigms, like procedural and object-oriented concepts. Here we propose a set of measures for evaluating software agent pro-activity, the software agent's goal-driven behavioral ability to take the initiative and satisfy its goal

On the testability of WCAG 2.0 for beginners

Web accessibility for people with disabilities is a highly visible area of research in the field of ICT accessibility, including many policy activities across many countries. The commonly accepted guidelines for web accessibility (WCAG 1.0) were published in 1999 and have been extensively used by designers, evaluators and legislators. W3C-WAI published a new version of these guidelines (WCAG 2.0) in December 2008. One of the main goals of WCAG 2.0 was testability, that is, WCAG 2.0 should be either machine testable or reliably human testable. In this paper we present an educational experiment performed during an intensive web accessibility course. The goal of the experiment was to assess the testability of the 25 level-A success criteria of WCAG 2.0 by beginners. To do this, the students had to manually evaluate the accessibility of the same web page. The result was that only eight success criteria could be considered to be reliably human testable when evaluators were beginners. We also compare our experiment with a similar study published recently. Our work is not a conclusive experiment, but it does suggest some parts of WCAG 2.0 to which special attention should be paid when training accessibility evaluator

Les personificacions instrumentals locals: estat de la qüestió

En la primera part d"aquest article s"analitza el fenomen de les personificacions instrumentals locals (PIL), tant de les funcionals (organismes autònoms, entitats públiques empresarials i societats mercantils locals), com de les cooperatives (mancomunitats, consorcis i societats mercantils constituïdes per diversos ens locals). L"estudi inclou dues dimensions: la quantitativa, que centra el seu objectiu en determinar el nombre de personificacions existents i classificar-les; i la qualitativa, en la qual l"anàlisi persegueix descriure i caracteritzar el fenomen i explicar els seus problemes i dificultats de funcionament, com també els criteris de funcionalitat i les alternatives a la seva constitució. La segona part del treball revela com s"ha invertit la tendència al creixement que havia caracteritzat el fenomen de les PIL. L"estudi dels projectes de llei aprovats el mes de juliol de 2013 pels governs estatal (de Racionalidad y Sostenibilidad de la Administración Local) i català (de governs locals de Catalunya) mostra que les propostes normatives contenen limitacions severes a la creació d"aquestes personificacions i d"altres ens vinculats a les entitats locals, així com un conjunt de mesures restrictives tendents al redimensionament del sector públic local, que, si s"aproven finalment, constituiran una manifestació més del declinar de l"auge de les PIL

Gravitational lensing by eigenvalue distributions of random matrix models

We propose to use eigenvalue densities of unitary random matrix ensembles as mass distributions in gravitational lensing. The corresponding lens equations reduce to algebraic equations in the complex plane which can be treated analytically. We prove that these models can be applied to describe lensing by systems of edge-on galaxies. We illustrate our analysis with the Gaussian and the quartic unitary matrix ensembles.Comment: 25 pages,11 figure

Multiple orthogonal polynomials, string equations and the large-n limit

The Riemann-Hilbert problems for multiple orthogonal polynomials of types I and II are used to derive string equations associated with pairs of Lax-Orlov operators. A method for determining the quasiclassical limit of string equations in the phase space of the Whitham hierarchy of dispersionless integrable systems is provided. Applications to the analysis of the large-n limit of multiple orthogonal polynomials and their associated random matrix ensembles and models of non-intersecting Brownian motions are given