Markov random fields provide a compact representation of joint probability distributions by representing its independence properties in an undirected graph. The well-known Hammersley-Clifford theorem uses these conditional independences to factorize a Gibbs distribution into a set of factors. However, an important issue of using a graph to represent independences is that it cannot encode some t...

The purpose of this research is to establish the variety of expanded narratives generated by children aged 6 based on a series of pictures, which is determined by his or her individual neuropsychological characteristics, as well as by the maturity of perception and of processing visual-spatial information. The material of the research is a number of stories produced by Russian children based on...

By a 'representation' we shall mean throughout a representation by n x n matrices with entries from an arbitrary (commutative) field. Clifford has constructed all representations of completely simple semigroups [1; 4]. Munn has determined the representations of finite semigroups for which the corresponding semigroup algebra is semi-simple [6]. It is noted by Clifford and Preston [4] that if S i...

The class of normal subshifts includes irreducible nontrivial topological Markov shifts, sofic synchronized systems, Dyck β-shifts, substitution minimal and so on. We will characterize one-sided conjugacy classes in terms the associated C∗-algebras its gauge actions with potentials. In particular, shifts are characterized simple purely infinite Cuntz-Krieger algebras matrices left Fischer cover...

The present thesis introduces Clifford Algebra as a framework for neural computation. Clifford Algebra subsumes, for example, the reals, complex numbers and quaternions. Neural computation with Clifford algebras is model–based. This principle is established by constructing Clifford algebras from quadratic spaces. Then the subspace grading inherent to any Clifford algebra is introduced, which al...

In the present paper we give a partially negative answer to a conjecture of Ghahramani, Runde and Willis. We also discuss the derivation problem for both foundation semigroup algebras and Clifford semigroup algebras. In particular, we prove that if S is a topological Clifford semigroup for which Es is finite, then H1(M(S),M(S))={0}.

Clifford algebras are used for definition of spinors. Because of using spin-1/2 systems as an adequate model of quantum bit, a relation of the algebras with quantum information science has physical reasons. But there are simple mathematical properties of the algebras those also justifies such applications. First, any complex Clifford algebra with 2n generators, Cll(2n, C), has representation as...

is a homomorphism of classical matrix Lie groups. The lefthand group consists of 2 × 2 complex matrices with determinant 1. The righthand group consists of 4× 4 real matrices with determinant 1 which preserve some fixed real quadratic form Q of signature (1, 3). This map is alternately called the spinor map and variations. The image of this map is the identity component of SO1,3(R), denoted SO1...

In this paper, the Fischer matrices of maximal subgroup G = 21+8+ : (U4(2):2) U6(2):2 will be derived from quotient group Q G/Z(21+8+) 28 (U4(2):2), where Z(21+8+) denotes center extra-special 2-group 21+8+. Using approach, and associated ordinary character table are computed in an elegantly simple manner. This approach can used to compute any split extension form 21+2n+ :G, n ∈ N, provided irr...