For the purpose of protein-DNA recognition analysis, amino acids are classified on the basis of protein-DNA contacts geometry and statistics. However, the methods of crisp classification do not allow describing the diversity of properties of amino acids. Amino acid residues have a variety of properties and can simultaneously belong to different classes. So, the classification of amino acids with different types of fuzzing was used. Voronoi–Delaunay tessellation was used to determine the spatial relationship between the amino acids of proteins and DNA nucleotides. Classification of amino acids was carried out on the statistics of contacts and the statistics of area of contact between amino acids and nucleotides. Classic hierarchical and nonhierarchical methods were used for crisp classification of amino acids with different types of distance measures. General variation approach was used for fuzzy classification of amino acids. Using the proposed mathematical model, it was shown that about 30% of all contacts between amino acids and nucleotides in protein-DNA complexes are not random. Crisp classification methods showed the existence of clustering invariants of amino acids. By fuzzy classification methods, it was shown that 6 classes are optimal for protein-DNA recognition task. The fuzzy classification of amino acids data is supposed to be used to construct the substitution matrix for DNA-binding protein sequences

Intellectual processing of qualitative data problem was investigated. Two examples of the states of the problems and algorithms for qualitative data processing, presented in the form of the equity-type characteristics and the large dimension empirical graphs was considered. The methodology of data mining (group) characteristics of equity-type (equivalent blurred classifications) was developed, this method was tested on real data. The possibilities of the exact and approximate representation of the large dimension graph through its description were studied. The optimization approach to the construction of the fuzzy classification was distributed to the problem of aggregation. In the framework of the structural-classification mining methodology of complex data the original information processing algorithms by large dimension graphs aggregation methods were developed. The ordered fuzzy classification and aggregate graphs descriptions problems relationship was considered. The developed algorithms computer simulation was held.

The modification of the collective multivariate expertise method (CMVE) was developed, adequate to the interdepartmental type problems, called as the method of an independent collective multivariate expertise (IMVE). The main and very significant difference between the developed IMVE method from the CMVE one is that in the process of examination are developed not solutions of the original problem in General, but identify and develop solutions to relatively independent of the problems associated with the initial objective, comprehensive solution which ensures the solution of the original problem. Implementation of the method of IMVE is divided into 5 main stages: creating the list of candidates; the relatively independent list of the expertise problems; the assessment of the potential experts competence; establishment of expert commission, including issues on which there are differences of opinion; the work of expert commissions. In conclusion, consulting group, which conducted the IMVE, forms the final draft of the problem solution. The independent collective multivariate expertise method was used for solving 2 large scale applied problems - organization and management of the inter-regional bus services market problem, and the task of creating intelligent control systems medical-diagnostic processes in the large scale medical clinic.

A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be regarded as methodologically incomplete.

Modern financial and economic system extremely complex, and the creation of accurate adequate models from first principles is very difficult. In recent times, in financial mathematics for the analysis of these time series are increasingly using methods of statistical physics, nonlinear dynamics and chaos theory. One of the most effective tools - this a symbolic dynamics, which allows you to explore a variety of complex phenomena in dynamical systems: chaos, strange attractors, hyperbolic, structural stability, controllability, etc. This report illustrates the basic features of the symbolic CTQ-analysis applied to the study of the dynamics of financial indicators. As an example, we study the structure and parameters of the synchronization rates of world currencies (the U.S. Dollar [USD], Euro [EUR], Japanese Yen [JPH], Swiss Franc [CHF], and the British Pound [GBP]) against the ruble of the Russian Federation [RUB] for period from 01.01.1999 on 31.03.2013.