Fermat's Equation in Matrices

The Fermat equation is solved in integral two by two matrices of determinant one as well as in finite order integral three by three matrices.

Approaches to Sequence Similarity Representation

We discuss several approaches to similarity preserving coding of symbol sequences and possible connections of their distributed versions to metric embeddings. Interpreting sequence representation methods with embeddings can help develop an approach to their analysis and may lead to discovering useful properties.

High Level Color Similarity Retrieval

In this paper a new method for image retrieval using high level color semantic features is proposed. It is based on extraction of low level color characteristics and their conversion into high level semantic features using Johannes Itten theory of color, Dempster-Shafer theory of evidence and fuzzy production rules.

Web-based Simultaneous Equation Solver

* This work has been supported by NIMP, University of Plovdiv under contract No MU-1.

Simultaneous Control of Chaotic Systems Using RBF Networks

Chaos control is a concept that recently acquiring more attention among the research community, concerning the fields of engineering, physics, chemistry, biology and mathematic. This paper presents a method to simultaneous control of deterministic chaos in several nonlinear dynamical systems. A radial basis function networks (RBFNs) has been used to control chaotic trajectories in the equilibrium points. Such neural network improves results, avoiding those problems that appear in other control methods, being also efficient dealing with a relatively small random dynamical noise.

Solving Maximum Clique Problem for Protein Structure Similarity

Computing the similarity between two protein structures is a crucial task in molecular biology, and has been extensively investigated. Many protein structure comparison methods can be modeled as maximum weighted clique problems in specific k-partite graphs, referred here as alignment graphs. In this paper we present both a new integer programming formulation for solving such clique problems and a dedicated branch and bound algorithm for solving the maximum cardinality clique problem. Both approaches have been integrated in VAST, a software for aligning protein 3D structures largely used in the National Center for Biotechnology Information, an original clique solver which uses the well known Bron and Kerbosch algorithm (BK). Our computational results on real protein alignment instances show that our branch and bound algorithm is up to 116 times faster than BK.

Using Covariance as a Similarity Measure for Document Language Identification in Hard Contexts

2000 Mathematics Subject Classification: C2P99.