Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type

MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32

Methods of Color Images Procession for Further Identification of the Object

The offered paper deals with the problems of color images preliminary procession. Among these are: interference control (local ones and noise) and extraction of the object from the background on the stage preceding the process of contours extraction. It was considered for a long time that execution of smoothing in segmentation through the boundary extraction is inadmissible, but the described methods and the obtained results evidence about expedience of using the noise control methods.

Hausdorff Distances for Searching in Binary Text Images

This work has been partially supported by Grant No. DO 02-275, 16.12.2008, Bulgarian NSF, Ministry of Education and Science.

On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems

We deal with a class of elliptic eigenvalue problems (EVPs) on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions (BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational formulation which is shown to fit into the general framework of abstract EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs) without and with numerical quadrature. The aim of the paper is to show that well–known error estimates, established for the finite element approximation of elliptic EVPs with classical BCs, hold for the present types of EVPs too. Some attention is also paid to the computational aspects of the resulting algebraic EVP. Finally, the analysis is illustrated by two non-trivial numerical examples, the exact eigenpairs of which can be determined.

Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem

We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].

Application of Artificial Intelligence Methods to Computer Design of Inorganic Compounds

In this paper the main problems for computer design of materials, which would have predefined properties, with the use of artificial intelligence methods are presented. The DB on inorganic compound properties and the system of DBs on materials for electronics with completely assessed information: phase diagram DB of material systems with semiconducting phases and DB on acousto-optical, electro-optical, and nonlinear optical properties are considered. These DBs are a source of information for data analysis. Using the DBs and artificial intelligence methods we have predicted thousands of new compounds in ternary, quaternary and more complicated chemical systems and estimated some of their properties (crystal structure type, melting point, homogeneity region etc.). The comparison of our predictions with experimental data, obtained later, showed that the average reliability of predicted inorganic compounds exceeds 80%. The perspectives of computational material design with the use of artificial intelligence methods are considered.

Neural-Like Growing Networks in Intelligent System of Recognition of Images

The neural-like growing networks used in the intelligent system of recognition of images are under consideration in this paper. All operations made over the image on a pre-design stage and also classification and storage of the information about the images and their further identification are made extremely by mechanisms of neural-like networks without usage of complex algorithms requiring considerable volumes of calculus. At the conforming hardware support the neural network methods allow considerably to increase the effectiveness of the solution of the given class of problems, saving a high accuracy of result and high level of response, both in a mode of training, and in a mode of identification.

Application of the Artificial Intelligence Algorithms with a Cognitive Graphic as a Tool for a System Analysis of Electrophysiological Processes

Summarizing the accumulated experience for a long time in the polyparametric cognitive modeling of different physiological processes (electrocardiogram, electroencephalogram, electroreovasogram and others) and the development on this basis some diagnostics methods give ground for formulating a new methodology of the system analysis in biology. The gist of the methodology consists of parametrization of fractals of electrophysiological processes, matrix description of functional state of an object with a unified set of parameters, construction of the polyparametric cognitive geometric model with artificial intelligence algorithms. The geometry model enables to display the parameter relationships are adequate to requirements of the system approach. The objective character of the elements of the models and high degree of formalization which facilitate the use of the mathematical methods are advantages of these models. At the same time the geometric images are easily interpreted in physiological and clinical terms. The polyparametric modeling is an object oriented tool possessed advances functional facilities and some principal features.

The Computational Analysis of Bulgarian Dialect Pronunciation

The paper presents a computational analysis of Bulgarian dialect variation, concentrating on pronunciation differences. It describes the phonetic data set compiled during the project* ‘Measuring Linguistic Unity and Diversity in Europe’ that consists of the pronunciations of 157 words collected at 197 sites from all over Bulgaria. We also present the results of analyzing this data set using various quantitative methods and compare them to the traditional scholarship on Bulgarian dialects. The results have shown that various dialectometrical techniques clearly identify east-west division of the country along the ‘jat’ border, as well as the third group of varieties in the Rodopi area. The rest of the groups specified in the traditional atlases either were not confirmed or were confirmed with a low confidence.

Data Extraction from Carte Du Ciel Triple Images

Carte du Ciel (from French, map of the sky) is a part of a 19th century extensive international astronomical project whose goal was to map the entire visible sky. The results of this vast effort were collected in the form of astrographic plates and their paper representatives that are called astrographic maps and are widely distributed among many observatories and astronomical institutes over the world. Our goal is to design methods and algorithms to automatically extract data from digitized Carte du Ciel astrographic maps. This paper examines the image processing and pattern recognition techniques that can be adopted for automatic extraction of astronomical data from stars’ triple expositions that can aid variable stars detection in Carte du Ciel maps.

Content-Based Image Retrieval for Computer Tomography Images Using Wavelet Descriptors

An approach to building a CBIR-system for searching computer tomography images using the methods of wavelet-analysis is presented in this work. The index vectors are constructed on the basis of the local features of the image and on their positions. The purpose of the proposed system is to extract visually similar data from the individual personal records and from analogous analysis of other patients.