The main thrust of my research is the use of techniques from information theory, probability and combinatorics to study structural, enumerative and algorithmic aspects of graph homomorphisms and related models, both in particular instances (independent sets and colorings, for example) and in general. Graph homomorphisms are important objects in graph theory, where they generalize a number of ce...

In this paper we introduce the idea of probability in the definition of Sequential Dynamical Systems, thus obtaining a new concept, Probabilistic Sequential System. The introduction of a probabilistic structure on Sequential Dynamical Systems is an important and interesting problem. The notion of homomorphism of our new model, is a natural extension of homomorphism of sequential dynamical syste...

Regular homomorphisms of oriented maps essentially arise from a factorization by a subgroup of automorphisms. This kind of map homomorphism is studied in detail, and generalized to the case when the induced homomorphism of the underlying graphs is not valency preserving. Reconstruction is treated by means of voltage assignments on angles, a natural extension of the common assignments on darts. ...

In this paper, some properties of the dual B-homomorphism are provided, along with natural and fundamental theorem B-homomorphisms for B-algebras. The first third isomorphism theorems B algebra also presented in paper.

The minimum cost homomorphism problem has arisen as a natural and useful optimization problem in the study of graph (and digraph) coloring and homomorphisms: it unifies a number of other well studied optimization problems. It was shown by Gutin, Rafiey, and Yeo that the minimum cost problem for homomorphisms to a digraph H that admits a so-called extended MinMax ordering is polynomial time solv...

We study this and associated theorems in the context of a logmodular function algebra and, in particular, in the Banach algebra, H, of bounded analytic functions on D. Those multiplicative linear functionals (homomorphisms) on if which are in the weak* closure of some Stolz angle at 1 are called Stolz homomorphisms. We call a homomorphism h a Lindelof homomorphism provided h(f) = 0 whenever ess...

Understanding how the brain stores and processes information is central to mathematical neuroscience. Neural data is often represented as a neural code: a set of binary firing patterns C ⊂ {0, 1}n. We have previously introduced the neural ring, an algebraic object which encodes combinatorial information, in order to analyze the structure of neural codes. We now relate maps between neural codes ...

1. Introduction. When studying ideal theory in semirings, it is natural to consider the quotient structure of a semiring modulo an ideal. If 7 is an ideal in a semiring R, the collection {x+l}xeit oí sets x + I={x+i\iEl} need not be a partition of R. Faced with this problem, [2] used equivalence relations to determine cosets relative to an ideal. La Torre successfully established analogues of s...

A fundamental fact for the algebraic theory of constraint satisfaction problems (CSPs) over a fixed template is that pp-interpretations between at most countable ω-categorical relational structures have two algebraic counterparts for their polymorphism clones: a semantic one via the standard algebraic operators H, S, P, and a syntactic one via clone homomorphisms (capturing identities). We prov...

Abstract. Let L and M be two finite lattices. The ideal J(L,M) is a monomial ideal in a specific polynomial ring and whose minimal monomial generators correspond to lattice homomorphisms ϕ: L→M. This ideal is called the ideal of lattice homomorphism. In this paper, we study J(L,M) in the case that L is the product of two lattices L_1 and L_2 and M is the chain [2]. We first characterize the set...