Vagis A. Methods analysis and recognition of complex discrete objects

The thesis is devoted to research on the theory of complexity of problems of recognition of discrete objects on the dfsis of a Bayesian approach. Effective (polynomial) methods of recognition of discrete objects on such structures as Bayesian networks, models of Markov chains of certain orders and independent attributes are developed. Numerical results of application of these methods the solution of important applied problems in biology and medicine are described. Fundamental symmetry relations on two DNA threads are established and proved. Symmetry relations unlike ones in foreign works are for the first described in the form of mathematical formulas, that considerably simplifies perception of these results and is a basis of creation of mathematical apparatus for receiving new results. On the basis of the mathematical formulas, defining symmetry of the DNA threads, rules of decrease and increase of symmetry are deduced. On the basis of Markov property, it is shown that symmetry for the tree, the fours and short sequences of the bases follows from the symmetry of pairs of bases. Properties of the symmetry for adentical polarity of DNA threads are investigated: the number of the connecting restrictions in a data recording information in the Watson-Crick model is less, than at model from adentical polarity of DNA threads. Therefore, in the nature more effective is realized, from the point of view of the theory information, Watson-Crick model. Symmetry on amino acids for the proteins synthesized on DNA threads follows from reduction the symmetry in DNA. For a prediction of secondary structure of proteins, Bayesian procedures on the basis of non-stationary Markov models of various orders were constructed. New effective Bayesian procedures of recognition of inflammatory processes of a progression of gliomas are developed for a network in the form of a tree on the basis of the analysis of erythrocyte sedimentation rate. Modern computer approach to recognition of hematologic diseases with application of effective Bayesian procedures is reasonable. Owing the fast work of Bayesian procedure, short combinations of indicators with the highest quality of recognition of the studied diseases are received. This approach can form a basis for development of diagnostic criteria for different types of the medical diseases demanding a large number of laboratory and other types of researches.