The 1/N expansion of the weak coupling phase of two-dimensional QCD on a sphere is constructed. It is demonstrated that the phase transition from the weak to the strong coupling phase is induced by instantons. A double scaling limit of the theory at the point of the phase transition is constructed, the value of string susceptibility is determined to be γstr = −1. The possibility of instanton in...

We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two stable phases, as the intensity of the noise vanishes and the size of the interval diverges. In particular, we prove that, in a suitable scaling limit, the front ...

We show that B-model topological strings on local Calabi-Yau threefolds are large N duals of matrix models, which in the planar limit naturally give rise to special geometry. These matrix models directly compute F-terms in an associated N = 1 supersymmetric gauge theory, obtained by deforming N = 2 theories by a superpotential term that can be directly identified with the potential of the matri...

For a complex simple simply connected Lie group G, and a compact Riemann surface C, we consider two sorts of families of flat G-connections over C. Each family is determined by a point u of the base of Hitchin’s integrable system for (G, C). One family ∇h̄,u consists of G-opers, and depends on h̄ ∈ C×. The other family ∇R,ζ,u is built from solutions of Hitchin’s equations, and depends on ζ ∈ C×, ...

We complete the computations in [BSZ2] and give a supersymmetric formula for the scaling limit correlation functions for simultaneous zeros of generalized polynomials. We also give an explicit formula for the scaling limit pair correlation function for the point case in all dimensions.

Multidimensional scaling is widely used to handle data which consist of dissimilarity measures between pairs of objects or people. We deal with two major problems in metric multidimensional scaling configuration of objects and determination of the dimension of object configuration within a Bayesian framework. A Markov chain Monte Carlo algorithm is proposed for object configuration, along with ...

Multidimensional scaling as a technique for the presentation of high-dimensional data with standard visualization techniques is presented. The technique used is often known as Sammon mapping. We explain the mathematical foundations of multidimensional scaling and its robust calculation. We also demonstrate the use of this technique in the area of evolutionary algorithms. First, we present the v...

The dependency of the brightness dimension of timbre on fundamental frequency (FO) was examined experimentally. Subjects compared the timbres of 24 synthetic stimuli, produced by the combination of six values of spectral centroid to obtain different values of expected brightness, and four FO's, ranging over 18 semitones. Subjects were instructed to ignore pitch differences. Dissimilarity scores...

It has been reported that long-term memory function, including the semantic structure of category, is impaired in patients with schizophrenia. The present study was performed to determine: (1) whether the deficit in semantic structure in schizophrenia is independent of cultural backgrounds, and (2) the effect of age of onset and verbal intelligence on the degradation of semantic structure in th...

We consider the scaling limit of linear statistics for eigenphases of a matrix taken from one of the classical compact groups. We compute their moments and find that the first few moments are Gaussian, whereas the limiting distribution is not. The precise number of Gaussian moments depends upon the particular statistic considered.