Abstract We obtain a canonical representation for block matrices. The facilitates simple computation of the determinant, matrix inverse, and other powers matrix, as well logarithm exponential. These results are particularly useful covariance correlation matrices, where evaluation Gaussian log-likelihood estimation greatly simplified. illustrate this with an empirical application using large pan...

In this paper, a matrix form analoguous to the companion matrix which is often encountered in the theory of one dimensional (1-D) linear control systems is suggested for a class of polynomials in two indeterminates and real coefficients, here referred to as two dimensional (2-D) polynomials. These polynomials arise in the context of the theory of 2-D linear discrete control systems. Necessary a...

Digital images are widely used in computer applications. To store or transmit the uncompressed images requires considerable storage capacity and transmission bandwidth. Image compression is a means to perform transmission or storage of visual data in the most economical way. This paper explains about how images can be encoded to be transmitted in a multiplexing time-frequency domain channel. Mu...

This paper is a critical evaluation of an approach to control in natural language processing systems which makes use of canonical structures as a way of collapsing multiple analyses in individual components. We give an overview here of how the Lucy natural language interface system currently realizes this control model and then evaluate what we take to be the strengths and weaknesses of such an...

This paper describes a way of recognizing equivalent knowledgebased diagnosis applications at knowledge level, based on the notion of Conceptual Equivalence, that is formally developed. This notion of Conceptual Equivalence induces the definition of a generic inference structure for knowledge-based diagnosis applications named COPE, acronym for Compare, Observe, Predict and Evaluate.

Matrix-geometric distributions (MG) and discrete (time) rational arrival processes (DRAP) are natural extensions of discrete phasetype distributions (DPH) and discrete Markov arrival processes (DMAP) respectively. However, the exact relation of the Markovian classes and their non-Markovian counterparts and the boundaries of these classes are not known yet. It has been shown that for the order t...

We study a novel representation of semiautomata, which is motivated by the method of trace-assertion specifications of software modules. Each state of the semiautomaton is represented by an arbitrary word, the canonical word leading to that state. The transitions of the semiautomaton give rise to a right congruence, the state-equivalence, on the set of input words of the semiautomaton: two word...

A complete 3-D Canonical Piecewise-Linear (CPWL) representation is developed constructively in this paper. The key to the representation is the establishment of the explicit functional formulation of basis function. It is proved that basis function is the most elementary generating function from which a fully general 3-D PWL function can be formulated. This CPWL representation laid a solid theo...