The aim of this paper is to develop a theory of finite transformation monoids and in particular to study primitive transformation monoids. We introduce the notion of orbitals and orbital digraphs for transformation monoids and prove a monoid version of D. Higman’s celebrated theorem characterizing primitivity in terms of connectedness of orbital digraphs. A thorough study of the module (or repr...

The numerical computation of a multivariate normal probability is often a diicult problem. This article describes a transformation that simpliies the problem and places it into a form that allows eecient calculation using standard numerical multiple integration algorithms. Test results are presented that compare implementations of two algorithms that use the transformation, with currently avail...

The Fisher information and the Rao measure are obtained in closed form for a family of probability density functions parametrized by the manifold PSL(2,R) of projective transformations of the real projective line. In addition, the Fisher information and the Rao measure are obtained for the sub-manifold of affine transformations. An application of these results to computer vision is described. T...

In this paper, a proposed technique for the inverse of the transformation method is presented. The direct transformation technique, recently developed by the authors [9], evaluateSeptember 16, 2007s the probability density function (p.d.f) -in closed formof the response (i.e. displacement) of stochastic mechanical system; where the probability density function of the input (i.e. Young's modulus...

A quasi-maximum likelihood approach is used for separating the instantaneous mixtures of temporally correlated, independent sources without either any preliminary transformation or a priori assumption about the probability distribution of the sources. A first order Markov model is used to represent the joint probability density of successive samples of each source. The joint probability density...

A technique is presented in order to evaluate the probability of failure in analytical form instead of approximation methods like FORM/SORM and no series expansion is involved in this expression. This technique is based on the Finite Element Method to obtain the expression of the response of stochastic systems, and the transformation of random variables to obtain the probability density functio...