A geometric proof of the Matsuki orbit duality for flag manifolds is established in [2] by analyzing the gradient flow of the normsquared of a moment map. In the present paper, we investigate explicit formulas for integral curves associated with this flow, leading to a correspondence between certain integral curves and Cayley transforms. In addition, an exhaustive collection of curves is presen...

A novel method for pattern recognition using Discrete Fourier Transforms on the global pulse signal of a pulse-coupled neural network (PCNN) is presented in this paper. We describe the mathematical model of the PCNN and an original way of analyzing the pulse of the network in order to achieve scaleand translation-independent recognition for isolated objects. We also analyze the error as a resul...

I. Background material 1 A. Mumford-Tate groups and domains B. The structure theorem for global variations of Hodge structure C. Hodge groups and domains II. General context A. Algebro-geometric B. Representation theoretic C. Arithmetic III. Cyclic spaces and their enlargements A. General definitions and some properties B. Two examples C. Enlargements of cycle spaces IV. Penrose-Radon transform...

An asymptotic expression for the expected area of the union of n random rectangles is derived by Mellin transforms, where their two diagonal corners are independently and uniformly distributed over (0, 1). The general result for d-dimensional hyper-rectangles is also stated. COMPUTATIONAL GEOMETRY, CONVEX HULL, GEOMETRIC PROBABILITY, GEOMETRY OF RECTANGLES, MELLIN TRANSFORM, CALCULUS OF FINITE ...

We develop a new and general approach to prove multiplier theorems in various geometric settings. The main idea is use martingale transforms Gundy-Varopoulos representation for multipliers defined via suitable extension procedure. Along the way, we provide probabilistic proof of generalization result by Stinga Torrea, which independent interest. Our methods here also recover sharp Lp bounds sec...

The simplicity of this equation makes these hyperelliptic curves particularly well suited for explicit computer calculations requiring higher genus curves. On the other hand, the special form of the equation raises the question of how generic or random, if at all, these curves are. For instance, all of these curves have 2-rank 0. The question of genericity can be restated more precisely as the ...

Pose variation is one of the challenging factors for face recognition. In this paper, we propose a novel cross-pose face recognition method named as Regularized Latent Least Square Regression (RLLSR). The basic assumption is that the images captured under different poses of one person can be viewed as pose-specific transforms of a single ideal object. We treat the observed images as regressor, ...

We express the generalized Cauchy-Stieltjes transforms (GCST) of some particular Beta distributions depending on a positive parameter λ as λ-powered Cauchy-Stieltjes transforms (CST) of some probability measures. The CST of the latter measures are shown to be the geometric mean of the CST of the Wigner law together with another one. Moreover, they are absolutely continuous and we derive their d...