A. M. Gupal

• National Academy of Sciences of Ukraine

This book is devoted to finite-dimensional problems of non-convex non-smooth optimization and numerical methods for their solution. The problem of nonconvexity is studied in the book on two main models of nonconvex dependencies: these are the so-called generalized differentiable functions and locally Lipschitz functions. Non-smooth functions natura...

An analysis of the undecidability of Diophantine equations showed that problems of recognition of the properties of the NP class are decidable, i.e., a non-deterministic algorithm or exhaustive search at the problem input gives a positive or negative answer. For polynomial Diophantine equations, such a non-deterministic algorithm does not exist. A...

The authors consider the application of Bayesian recognition procedures on Markov chain models to inflammatory processes in gliomas. Parameters of protein structures of blood plasma in gliomas, metastases, and brain concussion obtained with the help of a laser spectrograph are analyzed. A comparative analysis of the results of recognition on the ba...

Application of Bayesian recognition procedures to the analysis of inflammatory processes in gliomas is considered. Parameters of protein structures of blood plasma in gliomas, metastases, and concussion, obtained by a laser spectrograph, are analyzed. A comparative analysis is carried out for the results of recognition, on the basis of protein stru...

Introduction. The article discusses the application of Bayesian recognition procedures with one independent feature in relation to the erythrocyte sedimentation rate data taken from patients with gliomas, metastases, meningiomas, traumatic brain injury and from a group of healthy people. Purpose of the article. Analysis of erythrocyte sedimentation...

For every disease, there is a certain set of genes whose mutations increase the risk of illness development. DNA sequencing of sick and healthy individuals results in the determination of genes related to certain diseases. Efficient procedures are described in order to determine point mutations in gene sequences of the examined patients. The optima...

The use of Bayesian recognition procedure for surface plasmon resonance with the addition of verapamil hydrochloride and ketamine to the blood in the analysis of neurosurgical tumor pathologies significantly improved recognition compared to pure blood samples. An analysis of the difference in such pathologies due to the method of surface plasmon re...

DNA symmetry is used to generate optimal genetic codes whose noise immunity with respect to polarity of amino acids in case of mutations in nucleotides is much greater than immunity of standard codes. Noise immunity of optimal symmetric and non-symmetric genetic codes is analyzed. Databases of genetic diseases are used to show that optimal symmetri...

A promising computer approach to recognition of hematologic diseases is substantiated. Due to highly efficient Bayesian procedures, computer search is used to find combinations of indicators that have the highest recognition quality. Such method allows conducting fast diagnostics without performing it completely.

The code symmetric with respect to polarity of amino acids for the case of mutations in nucleotides is constructed using DNA symmetry. Standard code is compared with randomly generated codes. The noise immunity of genetic code against amino acid polarity is analyzed. Databases of genetic diseases are used to show that symmetric code corrects violat...

The authors consider the problem of reconstruction of hidden state sequences for mixture distributions with constituents described by the generalization of high-order Markov chains and hidden Markov models. A new algorithm to solve the problem using dynamic programming is proposed, as well as its modifications to eliminate recursion and reduce sear...

The EM algorithm is considered for the problem of separation of distribution mixtures described by Markov chains, together with the related weighted likelihood maximization problem. Auxiliary algorithms are proposed to select the initial approximation and optimal number of mixture components, as well as a method to approximate the distribution mixt...

The noise immunity of genetic codes with nucleotide mutations is analyzed. The universal code is compared with randomly generated codes. The noise immunity of genetic code against polarity, hydrophobicity, and helix propensity is analyzed. A genetic algorithm for the optimization of noise immunity of a code is described.

Algorithmic compositions in the form of expert mixtures with exclusive competence zones are considered in order to increase the quality of classification of gene fragments with the help of models based on Markov chains.

A number of similarities between living cells and universal computers are considered. Intracellular life processes are compared to computation processes inside a computer. Proteins coordinating intracellular processes are associated with computer programs during runtime. The possibility of the existence of a genetic programming language that allows...

A new method to model intracellular reactions coordinated by proteins is discussed. Proteins are described using locally interacting charged particles. The interaction is defined algorithmically, which allows disregarding the physical nature of protein activity in the analysis of the processes. Based on the proposed approach, a modeling software en...

A model of the recognition of functional sites of genes in DNA on the basis of hidden Markov models is considered. It is shown how algorithms based on Markov chain models of various orders can be used to detect fragments of genes of three genomes of higher organisms.

Symmetry and properties of recording information in DNA is derived. It is proved that the symmetry of base sequences of a DNA implies that of short sequences, including separate bases. On the basis of the Markov chain model, it is shown that the symmetry of base sequences follows from that of pairs of bases. For the second complementary strand in t...

It is shown that two types of symmetry are possible for pairs of bases; however, only one, more efficient method of encoding and decoding information is implemented in nature. It is proved that the symmetry of short sequences including separate bases follows from the symmetry of sequences of bases. A model of Markov chains is used to show that the...

Torsion angles formed by C α atoms of four neighboring residues are predicted using a Bayesian classification procedure on nonstationary Markov chains. The predicted sequence of torsion angles is used to construct a three-dimensional protein structure on Z 3 lattice. Keywordstorsion angle-Bayesian procedure-Markov chain-protein secondary structur...

Modern methods of predicting protein spatial structure are reviewed. Numerical results of predicting the secondary structure of protein on the basis of Bayesian recognition procedures on nonstationary Markov chains are discussed. Complementary principles of encoding genetic information in DNA and proteins are presented. Keywordsrecognition-biophys...

Error estimates of empirical-risk minimization methods for an infinite number of decision rules are analyzed. Optimal deterministic estimates of the error of the Bayesian classification procedure for independent features are obtained based on averaging over a great number of training samples as a control. For the Boolean case, the Bayesian procedur...

The paper discusses numerical results of predicting protein secondary structure using Bayesian classification procedures based on nonstationary Markovian chains. A new approach is used, based on the classification of pairs of states for pairs of neighboring amino acids. It improves the prediction accuracy as compared with that of the classification...

Results on Bayesian classification procedures, optimal on structures such as Markov chain and independent features, are reviewed. Numerical results of predicting protein secondary structure based on Bayesian classification procedures on non-stationary Markov chains are discussed. Complementarity relations for encoding bases in one DNA strand are pr...

The behavior of inductive inference procedures depending on the content of a learning sample is analyzed. It is shown that if a learning sample contains no information on some class of objects or statistical information on a priori probabilities of classes, then any procedure performs unpredictably badly and its error is strictly positive.

We have determined the new complementary principles in encoding bases on DNA chain in chromosomes of human genome and some other investigated genomes. The obtained results show that regularity analogues to Chargaff rule (or complementary principle of Watson-Crick) holds not only for two-chain DNA spiral but even for each separate chain. Moreover, w...

The chemical structure of DNA is characterized by sequences of four basic nitrogens occurring in one of two nucleic acid chains and in a complementary fashion in the other. Markov chain is the aspect of probability theory that analyzes discrete states in which transition is a fixed probability not affected by the history of the system. It is shown...

Proceeding from a probabilistic approach, the authors conclude that Bayesian approach is the basis for creation of inductive inference procedures. These procedures are analyzed on Markovian chains and Bayesian networks.

It is shown, that Bayesian approach is the basis of constructing inductive inference procedures. Issues of application of this approach in inductive logic, Bayesian networks and information theory are discussed.

Learning procedures on Bayesian networks are studied on the basis of beta and Dirichlet distributions.

An upper-bound estimate of the error of the Bayesian procedure of solution of classification problems depending on the volume of training samples is given. The suboptimality of the Bayesian approach is proved and the complexity of the class of problems considered is determined.

The upper bound of the error of the Bayesian procedure for solving classification and recognition problems is obtained, depending on the number of attributes and the training-sample size. It is proved that the Bayesian method is suboptimal.

Bayesian pattern recognition procedure has been proven suboptimal for the case of independent features and distribution of a Markov chain. The error estimation of the recognition procedure is obtained dependently on the number of attributes and on the size of a learning sample.

The estimation of the error for the Bayes recognition procedure based on the Markov chain is made. It is proved that the Bayes method is suboptimal. Complexity of the class of problems is obtained.

It is shown that the Bayes pattern recognition procedure is suboptimal for independent attributes and distribution of Markov chain. The error of pattern recognition procedure is obtained depending on a number of attributes and learning sample size. It is found that the search of new Bayesian recognition procedures is connected with studying the spe...

Without Abstract

Without Abstract

The subject of this paper can be classified as machine learning. In general, the problem considered in this paper can be stated as follows. Suppose that the application domain is represented by some empirical data (a learning sample). Given the sample values of certain parameters at the input, it is required to infer from the empirical data the val...

A stochastic finite-difference method for the minimization of discontinuous functions is investigated. The basic idea of the algorithm consists of approximating the discontinuous function by a sequence of continuous smoothed functions that, except for the points of discontinuity, converge to the original function.