Parikh matrix is a numerical property of a word on an ordered alphabet. It is used for studying word in terms of its sub words. It was introduced by Mateescu et al. in 2000. Since then it has been being studied for various ordered alphabets. In this paper Parikh Matrices over tertiary alphabet are investigated. Algorithm is developed to display Parikh Matrices of words over tertiary alphabet. T...

Given a controllable pair of matrices (A; B), the distance to the set of uncontrollable pairs is obtained as the minimum singular value of the set of augmented matrices A ? I; B] as varies over the complex plane. This study develops one dimensional and two dimensional algorithms to calculate or estimate the distance. The algorithms give guaranteed upper and lower bounds.

Lapointe and Kirsch (1995) have recently explored the possibility of reconstructing phylogenetic trees from lacunose distance matrices. They have shown that missing cells can be estimated using the ultrametric property of distances, and that reliable trees can be derived from such filled matrices. Here, we extend their work by introducing a novel way to estimate distances based on the four-poin...

We consider problems of estimation of structured covariance matrices, and in particular of matrices with a Toeplitz structure. We follow a geometric viewpoint that is based on some suitable notion of distance. To this end, we overview and compare several alternatives metrics and divergence measures. We advocate a specific one which represents the Wasserstein distance between the corresponding G...

A formula for the distance of a Toeplitz matrix to the subspace of {e}-circulant matrices is presented, and applications of {e}-circulant matrices to preconditioning of linear systems of equations with a Toeplitz matrix are discussed. Copyright c © 2006 John Wiley & Sons, Ltd. key words: Toeplitz matrix, circulant matrix, {e}-circulant, matrix nearness problem, distance to normality, preconditi...

In their 1978 paper \Distance Matrix Polynomials of Trees", [4], Graham and Lov asz proved that the coeÆcients of the characteristic polynomial of the distance matrix of a tree (CPD(T )) can be expressed in terms of the numbers of certain subforests of the tree. This result was generalized to trees with weighted edges by Collins, [1], in 1986. Graham and Lov asz computed these coeÆcients for al...

Short proofs are given to various characterizations of the (circum-)Euclidean squared distance matrices. Linear preserver problems related to these matrices are discussed.

We introduce the concept of distance mean-regular graph, which can be seen as a generalization of both vertex-transitive and distance-regular graphs. A graph Γ = (V,E) with diameter D is distance meanregular when, for given u ∈ V , the averages of the intersection numbers ai(u, v), bi(u, v), and ci(u, v) (defined as usual), computed over all vertices v at distance i = 0, 1, . . . , D from u, do...

Non-deterministic matrices, a natural generalization of many-valued matrices, are semantic structures in which the value assigned to a complex formula may be chosen non-deterministically from a given set of options. We show that by combining non-deterministic matrices and distance-based considerations, one obtains a family of logics that are useful for reasoning with uncertainty. These logics a...

Short proofs are given to various characterizations of the (circum-)Euclidean squared distance matrices. Linear preserver problems related to these matrices are discussed.