Sergey Petoukhov | Mechanical Engineering Research Institute, Russian Academy of Sciences (original) (raw)

Papers by Sergey Petoukhov

Метафизика, Dec 15, 2021

Аннотация. Статья посвящена универсальным алгебраическим закономерностям нуклеотидных последовате... more Аннотация. Статья посвящена универсальным алгебраическим закономерностям нуклеотидных последовательностей в ДНК геномов высших и низших организмов. Выявленные автором закономерности связаны с известным бинарным характером генетических структур и выражаются в геномных гештальт-феноменах, которые аналогичны генетически наследуемым феноменам гештальтпсихологии. Это позволяет автору развивать идеи гештальтгенетики и алгебраической биологии. Множество генетических феноменов тетраструктуризации вызывает ассоциации с концепцией тетраэйдосов Ю.И. Кулакова.

The article continues the author's publications about the matrix-tensor study of universal rules ... more The article continues the author's publications about the matrix-tensor study of universal rules of stochastic (probabilistic) organization of long singlestranded DNA sequences in eukaryotic and prokaryotic genomes. The author reveals that corresponding matrices of probabilities of n-plets in n-textual representations of each genomic DNA are numerically interrelated each with other in such algebraic form, which has analogies with formalisms of the known tensor-matrix theory of digital antenna arrays. These arrays combine many separate antennas into a single coordinated ensemble with unique emergent properties, due to which antenna arrays are widely used in devices of medicine, astrophysics, avionics, etc. The noted analogies allow putting forward the author's hypothesis that stochastic organization of genomic DNAs is connected with bio-antenna arrays. From the point of view of this hypothesis, many known facts about using principles of antenna arrays in inherited physiological phenomena are collected in a single grouping with genomic DNA: echolocation of dolphins and other animals; complex faceted eyes of insects; images on butterfly wings, consisting of many photonic crystals as nanoantenna arrays, etc. This new topic about the biological meaning of profitable properties of antenna arrays includes problems of biological evolution, the origin of the genetic code, regenerative medicine, development of algebraic biology, which are discussed.

BioSystems, Nov 1, 2018

Biological symmetries, theories of the morphogenetic field, resonant interactions and the role of... more Biological symmetries, theories of the morphogenetic field, resonant interactions and the role of photons in morphogenetic processes represented the main fields of interest of Lev Beloussov and his followers. This review article includes some results of our study on the important role of resonances and photonic crystals in genetic informatics. Mathematical formalisms of differential Riemannian geometry and tensor analysis are used for modeling inherited curved surfaces in biomorphology and for understanding conformal bio-symmetries connected with the networks of curvature lines of surfaces. Notions of a morpho-resonance field as one of variants of morphogenetic fields are discussed. The connection of the golden section with the Fibonacci matrix of growth used in morphogenetic models of phyllotaxis is shown. Photonic crystals are considered as important participants of organisation of molecular-genetic informatics.

Springer eBooks, 2021

The paper discusses and develops the proposed by the authors new approaches to modeling strong ar... more The paper discusses and develops the proposed by the authors new approaches to modeling strong artificial intelligence, the transition from traditional artificial neural networks to categorical neural networks with more complex topology and hierarchy, functional systems integrated with a universal agent of artificial intelligence, genome analysis by methods of algebraic biology and categorical physico-chemical systems. Methods of categorical systems theory, which formalized an essential part of the theory of functional systems, are proposed for describing the indicated categorical neural networks, a G-graph network hierarchy (G is a given graph), a hybrid functional system equipped with a universal AI agent that implements a version of strong AI, physicochemical molecular systems, including DNA and RNA, as the basis of algebraic biological research.

BioSystems, Jun 1, 2019

The revelation of compositional principles of the organization of long DNA sequences is one of th... more The revelation of compositional principles of the organization of long DNA sequences is one of the crucial tasks in the study of biosystems. This paper is devoted to the analysis of compositional differences between real DNA sequences and Markov-like randomly generated similar sequences. We formulate, among other things, a generalization of Chargaff's second rule and verify it empirically on DNA sequences of five model organisms taken from Genbank. Moreover, we apply the same frequency analysis to simulated sequences. When comparing the afore mentioned - real and random - sequences, significant similarities, on the one hand, as well as essential differences between them, on the other hand, are revealed and described. The significance and possible origin of these differences, including those from the viewpoint of maximum informativeness of genetic texts, is discussed. Besides, the paper discusses the question of what is a "long" DNA sequence and quantifies the choice of length. More precisely, the standard deviations of relative frequencies of bases stabilize from the length of approximately 100 000 bases, whereas the deviations are about three times as large at the length of approximately 25 000 bases.

IOP conference series, Apr 1, 2021

The article is devoted to the study of new approaches to the development of mathematical models i... more The article is devoted to the study of new approaches to the development of mathematical models in genetic biomechanics, which studies the structural relationships of the genetic coding system with genetically inherited biological forms. More specifically, we are talking about models based on the recurrent harmonic progression known in science, the universal connection of which with the information sequences of DNA heredity molecules in the genomes of higher and lower organisms was revealed in the laboratory of biomechanical systems research at the IMASH RAS. This progression is associated with fundamental hyperbolic rules for organizing DNA nucleotide sequences of genomes and is represented on a two-dimensional Cartesian plane by a hyperbolic sequence associated with natural logarithms. The latter have long been used in science to adequately model many inherited biological phenomena. The article describes previously unknown connections of natural logarithms with the structure of the molecular genetic system. The problems of modeling biological phenomena in connection with the revealed structural properties of the molecular genetic system are discussed.

Advances in intelligent systems and computing, 2020

Fibonacci numbers and their applications are actively used in various fields of mathematics, comp... more Fibonacci numbers and their applications are actively used in various fields of mathematics, computer technologies and informatics, economics and biology. The article describes author’s results of studying extended versions of the Fibonacci sequence in form of additive sequences of 2n-dimensional hyperbolic numbers having Fibonacci coordinates. Special attention is paid to matrix representation of hyperbolic numbers. Some applications of new additive sequences are shown including phyllotaxis laws of morphogenesis and the main psychophysical Weber-Fechner law. An important role of hyperbolic numbers in modelling natural phenomena is noted.

Advances in intelligent systems and computing, 2020

The Kronecker tensor product of matrices is one of the most important operations in quantum mecha... more The Kronecker tensor product of matrices is one of the most important operations in quantum mechanics and quantum informatics. The article is devoted to various applications of this mathematical operation for revealing hidden interrelations among molecular-genetic structures and for developing quantum biology and algebraic biology. Special attention is paid to matrix representations of the set of DNA nucleobases and their hydrogen bonds. These representations reveal, in particular, hidden symmetries in alphabets of DNA n-plets and also possibilities of applications of hyperbolic numbers and their extensions for modeling some hidden regularities in long DNA sequences.

Advances in intelligent systems and computing, 2020

Algebraic biology is engaged in mathematical modeling of the structural features of the molecular... more Algebraic biology is engaged in mathematical modeling of the structural features of the molecular genetic system and the inherited properties of organisms (phyllotaxis, inheritance of traits in Mendelian genetics, Weber-Fechner law, etc.) without a detailed analysis of genome reading processes. At the same time algebraic biology is a deeply systemic science. The consideration of human person as a system, including the subsystem of his intellect, modeled in some degree by artificial intelligence, leads to the necessity of using the methods of categorical theory of systems in addition to classical algebraic methods. Examples that are not reducible to the set-theoretic approach are given; generalizations of U-numbers of matrix genetics to the categorical case are outlined.

Advances in intelligent systems and computing, 2020

The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic ex... more The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic extensions in the form of 2n-dimensional hyperbolic numbers in bioinformatics, algebraic biology and musicology. These applications reveal hidden interconnections between structures of different biological phenomena. It helps to understand living bodies as holistic essences, structural organisation of which has relations with musical harmony, first of all, with Pythagorean musical scales on the basis of the quint ratio 3/2. Presented results are connected with a problem of genetic fundamentals of aesthetics and inborn feeling of harmony. On the basis of these and some other results, the author believes that 2n-dimensional hyperbolic numbers and their matrix representations are a key element for effective algebraic modeling many aspects of inherited structural organisation of biological bodies and for developing algebraic biology. The received results lead to new approaches in bioinformatics, musicological analysis, acoustic biotechnologies and artificial intelligence.

Advances in intelligent systems and computing, May 3, 2019

This paper’s aim is to show the possibilities of modelling the information content carried by qua... more This paper’s aim is to show the possibilities of modelling the information content carried by quantum mechanical DNA molecules by means of the formalism used in quantum informatics. Such modelling would open new options to reveal nature’s information patents and to use them, for instance, in quantum computing and artificial intelligence (A.I.). Moreover, it would give an opportunity of understanding the ways of managing information in living organisms. As an empirical base, the open accessible data from GenBank which contains hundreds of millions of long DNA texts collected from thousands of organisms can be used.

Advances in intelligent systems and computing, May 3, 2019

The article is devoted to parallelisms between the structural organization of the molecular genet... more The article is devoted to parallelisms between the structural organization of the molecular genetic system and mathematics of quantum computers. This mathematics is perspective for developing systems of artificial intelligence. Using this mathematics to study, the genetic system can reveal bioinformational patents of the living nature for scientific and technologic progress. Unitary matrices are the basis of all calculations in quantum computers. Our described results show that structured systems of molecular genetic alphabets in their matrix forms of representations can be considered as sets of sparse unitary matrices related with phenomenologic features of the degeneracy of the genetic code. These sparse unitary matrices have orthogonal systems of functions in their rows and columns. A complementarity exists among some unitary genetic matrices in relation to each other. Tensor (or Kronecker) families of unitary genetic matrices with their fractal-like properties are also considered. These new results are interesting for development of quantum-algorithmic genetics and for revealing fundamental principles of bioinformatics.

Advances in intelligent systems and computing, 2020

The article discusses new methods of studying and using Hadamard matrices. This class of matrices... more The article discusses new methods of studying and using Hadamard matrices. This class of matrices is commonly used in developing AI systems, noise-immune coding of data and simulation of bioinformational entities. The relations between Hadamard matrices and hyper-complex numbers are discussed. A special attention is given to the new method of pre-orthogonal sequences for building multi-block Hadamard matrices of large orders. This method, due to its mathematical characteristics, should also be useful in modeling the noise-immunity features of genetic coding.

Advances in intelligent systems and computing, 2020

The analysis of algebraic biology in its current state, as a separate independent science with it... more The analysis of algebraic biology in its current state, as a separate independent science with its subject of study, tasks and methods for their solution, is carried out. The necessity of applying the systems approach in algebraic biology in its modern version using the categorical theory of systems and the categorical language for algebraic methods for studying DNA and its properties is shown. On this way, authors hope, in particular, to find new approaches to the creation of artificial intelligence systems and effective biotechnologies of regenerative medicine. Examples of everyday structures that are not reducible to sets are considered.

Structural Chemistry, Dec 9, 2016

The article is written for the special journal issue dedicated to Alan L. Mackay on his 90th birt... more The article is written for the special journal issue dedicated to Alan L. Mackay on his 90th birthday. The remarkable ideas of Alan L. Mackay about generalized crystallography, its connections with encoding of information, and also the interrelationship between art and science generate many ideas and their consequences. Mackay paid a special attention to the theme of five-fold symmetry, Fibonacci numbers and the golden section, which are essential in the structures of quasicrystals and living bodies. The present article considers a continuation of this theme in relation to the genetic coding system and to ratios of musical harmony. Hidden connections between the matrix representations the genetic code system and the golden section and the Pythagoras's theory of esthetics of proportions are described. Such connections testify the validity of the molecular-genetic foundation of many known facts about inborn feeling of harmony in our perceptions, which becomes a part of the scientific field of Bbiochemical esthetics" (the term first introduced by Russian biophysicist S. Shnoll, 7). Data from theory of resonances and mathematics of noise-immunity coding of information are used in the article.

Progress in Biophysics & Molecular Biology, Dec 1, 2017

The ancient Chinese book I-Ching was written a few thousand years ago. It introduces the system o... more The ancient Chinese book I-Ching was written a few thousand years ago. It introduces the system of symbols Yin and Yang (equivalents of 0 and 1). It had a powerful impact on culture, medicine and science of ancient China and several other countries. From the modern standpoint, I-Ching declares the importance of dyadic groups of binary numbers for the Nature. The system of I-Ching is represented by the tables with dyadic groups of 4 bigrams, 8 trigrams and 64 hexagrams, which were declared as fundamental archetypes of the Nature. The ancient Chinese did not know about the genetic code of protein sequences of amino acids but this code is organized in accordance with the I-Ching: in particularly, the genetic code is constructed on DNA molecules using 4 nitrogenous bases, 16 doublets, and 64 triplets. The article also describes the usage of dyadic groups as a foundation of the bio-mathematical doctrine of the geno-logic code, which exists in parallel with the known genetic code of amino acids but serves for a different goal: to code the inherited algorithmic processes using the logical holography and the spectral logic of systems of genetic Boolean functions. Some relations of this doctrine with the I-Ching are discussed. In addition, the ratios of musical harmony that can be revealed in the parameters of DNA structure are also represented in the I-Ching book.

Nucleation and Atmospheric Aerosols, 2023

To reveal the hidden regularities of the stochastic organization of nucleotide sequences in infor... more To reveal the hidden regularities of the stochastic organization of nucleotide sequences in informational singlestranded DNA molecules of genomes of higher and lower biological species, the following author's method was applied: each such sequence is represented as a set of parallel n-texts, each of which is written in its own n-plets alphabet of DNA (among these alphabets include alphabets of 4 nucleotides, 16 duplets, 64 triplets, etc.). A comparative analysis of the percentage compositions of n-plets in these n-texts is carried out and the universal regularities of the multilevel blockstochastic organization of genomic DNA information sequences are revealed. The analogies of the phenomena of blockstochastic organization of these DNAs with genetically inherited physiological phenomena of similar types are discussed, including the Bernstein problem in the field of biomechanics of movements and also the ability of the brain, studied by Gestalt psychology.

The article is devoted to algebraic modeling of universal rules of stochastic organization of gen... more The article is devoted to algebraic modeling of universal rules of stochastic organization of genomic DNA of higher and lower organisms, previously published by the author. The proposed algebraic apparatus, which uses formalisms of quantum mechanics and quantum informatics and which is based on the so-called tensor-unitary transformations of vectors that generate families of interrelated stochastic-deterministic vectors of increased dimensions. The features of the vectors' interconnections in these families model the stochastic-deterministic properties of the named phenomenological rules. There are new approaches to modeling of developing multi-parameter biosystems, whose number of parameters increases in the course of step-by-step development. In the light of the presented materials, the issues of fractal-like organization in genetically inherited biosystems are considered. The development of the theory of stochastic determinism as an antipode of deterministic chaos is discussed.

Метафизика, Dec 15, 2021

Аннотация. Статья посвящена универсальным алгебраическим закономерностям нуклеотидных последовате... more Аннотация. Статья посвящена универсальным алгебраическим закономерностям нуклеотидных последовательностей в ДНК геномов высших и низших организмов. Выявленные автором закономерности связаны с известным бинарным характером генетических структур и выражаются в геномных гештальт-феноменах, которые аналогичны генетически наследуемым феноменам гештальтпсихологии. Это позволяет автору развивать идеи гештальтгенетики и алгебраической биологии. Множество генетических феноменов тетраструктуризации вызывает ассоциации с концепцией тетраэйдосов Ю.И. Кулакова.

The article continues the author's publications about the matrix-tensor study of universal rules ... more The article continues the author's publications about the matrix-tensor study of universal rules of stochastic (probabilistic) organization of long singlestranded DNA sequences in eukaryotic and prokaryotic genomes. The author reveals that corresponding matrices of probabilities of n-plets in n-textual representations of each genomic DNA are numerically interrelated each with other in such algebraic form, which has analogies with formalisms of the known tensor-matrix theory of digital antenna arrays. These arrays combine many separate antennas into a single coordinated ensemble with unique emergent properties, due to which antenna arrays are widely used in devices of medicine, astrophysics, avionics, etc. The noted analogies allow putting forward the author's hypothesis that stochastic organization of genomic DNAs is connected with bio-antenna arrays. From the point of view of this hypothesis, many known facts about using principles of antenna arrays in inherited physiological phenomena are collected in a single grouping with genomic DNA: echolocation of dolphins and other animals; complex faceted eyes of insects; images on butterfly wings, consisting of many photonic crystals as nanoantenna arrays, etc. This new topic about the biological meaning of profitable properties of antenna arrays includes problems of biological evolution, the origin of the genetic code, regenerative medicine, development of algebraic biology, which are discussed.

BioSystems, Nov 1, 2018

Biological symmetries, theories of the morphogenetic field, resonant interactions and the role of... more Biological symmetries, theories of the morphogenetic field, resonant interactions and the role of photons in morphogenetic processes represented the main fields of interest of Lev Beloussov and his followers. This review article includes some results of our study on the important role of resonances and photonic crystals in genetic informatics. Mathematical formalisms of differential Riemannian geometry and tensor analysis are used for modeling inherited curved surfaces in biomorphology and for understanding conformal bio-symmetries connected with the networks of curvature lines of surfaces. Notions of a morpho-resonance field as one of variants of morphogenetic fields are discussed. The connection of the golden section with the Fibonacci matrix of growth used in morphogenetic models of phyllotaxis is shown. Photonic crystals are considered as important participants of organisation of molecular-genetic informatics.

Springer eBooks, 2021

The paper discusses and develops the proposed by the authors new approaches to modeling strong ar... more The paper discusses and develops the proposed by the authors new approaches to modeling strong artificial intelligence, the transition from traditional artificial neural networks to categorical neural networks with more complex topology and hierarchy, functional systems integrated with a universal agent of artificial intelligence, genome analysis by methods of algebraic biology and categorical physico-chemical systems. Methods of categorical systems theory, which formalized an essential part of the theory of functional systems, are proposed for describing the indicated categorical neural networks, a G-graph network hierarchy (G is a given graph), a hybrid functional system equipped with a universal AI agent that implements a version of strong AI, physicochemical molecular systems, including DNA and RNA, as the basis of algebraic biological research.

BioSystems, Jun 1, 2019

The revelation of compositional principles of the organization of long DNA sequences is one of th... more The revelation of compositional principles of the organization of long DNA sequences is one of the crucial tasks in the study of biosystems. This paper is devoted to the analysis of compositional differences between real DNA sequences and Markov-like randomly generated similar sequences. We formulate, among other things, a generalization of Chargaff's second rule and verify it empirically on DNA sequences of five model organisms taken from Genbank. Moreover, we apply the same frequency analysis to simulated sequences. When comparing the afore mentioned - real and random - sequences, significant similarities, on the one hand, as well as essential differences between them, on the other hand, are revealed and described. The significance and possible origin of these differences, including those from the viewpoint of maximum informativeness of genetic texts, is discussed. Besides, the paper discusses the question of what is a "long" DNA sequence and quantifies the choice of length. More precisely, the standard deviations of relative frequencies of bases stabilize from the length of approximately 100 000 bases, whereas the deviations are about three times as large at the length of approximately 25 000 bases.

IOP conference series, Apr 1, 2021

The article is devoted to the study of new approaches to the development of mathematical models i... more The article is devoted to the study of new approaches to the development of mathematical models in genetic biomechanics, which studies the structural relationships of the genetic coding system with genetically inherited biological forms. More specifically, we are talking about models based on the recurrent harmonic progression known in science, the universal connection of which with the information sequences of DNA heredity molecules in the genomes of higher and lower organisms was revealed in the laboratory of biomechanical systems research at the IMASH RAS. This progression is associated with fundamental hyperbolic rules for organizing DNA nucleotide sequences of genomes and is represented on a two-dimensional Cartesian plane by a hyperbolic sequence associated with natural logarithms. The latter have long been used in science to adequately model many inherited biological phenomena. The article describes previously unknown connections of natural logarithms with the structure of the molecular genetic system. The problems of modeling biological phenomena in connection with the revealed structural properties of the molecular genetic system are discussed.

Advances in intelligent systems and computing, 2020

Fibonacci numbers and their applications are actively used in various fields of mathematics, comp... more Fibonacci numbers and their applications are actively used in various fields of mathematics, computer technologies and informatics, economics and biology. The article describes author’s results of studying extended versions of the Fibonacci sequence in form of additive sequences of 2n-dimensional hyperbolic numbers having Fibonacci coordinates. Special attention is paid to matrix representation of hyperbolic numbers. Some applications of new additive sequences are shown including phyllotaxis laws of morphogenesis and the main psychophysical Weber-Fechner law. An important role of hyperbolic numbers in modelling natural phenomena is noted.

Advances in intelligent systems and computing, 2020

The Kronecker tensor product of matrices is one of the most important operations in quantum mecha... more The Kronecker tensor product of matrices is one of the most important operations in quantum mechanics and quantum informatics. The article is devoted to various applications of this mathematical operation for revealing hidden interrelations among molecular-genetic structures and for developing quantum biology and algebraic biology. Special attention is paid to matrix representations of the set of DNA nucleobases and their hydrogen bonds. These representations reveal, in particular, hidden symmetries in alphabets of DNA n-plets and also possibilities of applications of hyperbolic numbers and their extensions for modeling some hidden regularities in long DNA sequences.

Advances in intelligent systems and computing, 2020

Algebraic biology is engaged in mathematical modeling of the structural features of the molecular... more Algebraic biology is engaged in mathematical modeling of the structural features of the molecular genetic system and the inherited properties of organisms (phyllotaxis, inheritance of traits in Mendelian genetics, Weber-Fechner law, etc.) without a detailed analysis of genome reading processes. At the same time algebraic biology is a deeply systemic science. The consideration of human person as a system, including the subsystem of his intellect, modeled in some degree by artificial intelligence, leads to the necessity of using the methods of categorical theory of systems in addition to classical algebraic methods. Examples that are not reducible to the set-theoretic approach are given; generalizations of U-numbers of matrix genetics to the categorical case are outlined.

Advances in intelligent systems and computing, 2020

The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic ex... more The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic extensions in the form of 2n-dimensional hyperbolic numbers in bioinformatics, algebraic biology and musicology. These applications reveal hidden interconnections between structures of different biological phenomena. It helps to understand living bodies as holistic essences, structural organisation of which has relations with musical harmony, first of all, with Pythagorean musical scales on the basis of the quint ratio 3/2. Presented results are connected with a problem of genetic fundamentals of aesthetics and inborn feeling of harmony. On the basis of these and some other results, the author believes that 2n-dimensional hyperbolic numbers and their matrix representations are a key element for effective algebraic modeling many aspects of inherited structural organisation of biological bodies and for developing algebraic biology. The received results lead to new approaches in bioinformatics, musicological analysis, acoustic biotechnologies and artificial intelligence.

Advances in intelligent systems and computing, May 3, 2019

This paper’s aim is to show the possibilities of modelling the information content carried by qua... more This paper’s aim is to show the possibilities of modelling the information content carried by quantum mechanical DNA molecules by means of the formalism used in quantum informatics. Such modelling would open new options to reveal nature’s information patents and to use them, for instance, in quantum computing and artificial intelligence (A.I.). Moreover, it would give an opportunity of understanding the ways of managing information in living organisms. As an empirical base, the open accessible data from GenBank which contains hundreds of millions of long DNA texts collected from thousands of organisms can be used.

Advances in intelligent systems and computing, May 3, 2019

The article is devoted to parallelisms between the structural organization of the molecular genet... more The article is devoted to parallelisms between the structural organization of the molecular genetic system and mathematics of quantum computers. This mathematics is perspective for developing systems of artificial intelligence. Using this mathematics to study, the genetic system can reveal bioinformational patents of the living nature for scientific and technologic progress. Unitary matrices are the basis of all calculations in quantum computers. Our described results show that structured systems of molecular genetic alphabets in their matrix forms of representations can be considered as sets of sparse unitary matrices related with phenomenologic features of the degeneracy of the genetic code. These sparse unitary matrices have orthogonal systems of functions in their rows and columns. A complementarity exists among some unitary genetic matrices in relation to each other. Tensor (or Kronecker) families of unitary genetic matrices with their fractal-like properties are also considered. These new results are interesting for development of quantum-algorithmic genetics and for revealing fundamental principles of bioinformatics.

Advances in intelligent systems and computing, 2020

The article discusses new methods of studying and using Hadamard matrices. This class of matrices... more The article discusses new methods of studying and using Hadamard matrices. This class of matrices is commonly used in developing AI systems, noise-immune coding of data and simulation of bioinformational entities. The relations between Hadamard matrices and hyper-complex numbers are discussed. A special attention is given to the new method of pre-orthogonal sequences for building multi-block Hadamard matrices of large orders. This method, due to its mathematical characteristics, should also be useful in modeling the noise-immunity features of genetic coding.

Advances in intelligent systems and computing, 2020

The analysis of algebraic biology in its current state, as a separate independent science with it... more The analysis of algebraic biology in its current state, as a separate independent science with its subject of study, tasks and methods for their solution, is carried out. The necessity of applying the systems approach in algebraic biology in its modern version using the categorical theory of systems and the categorical language for algebraic methods for studying DNA and its properties is shown. On this way, authors hope, in particular, to find new approaches to the creation of artificial intelligence systems and effective biotechnologies of regenerative medicine. Examples of everyday structures that are not reducible to sets are considered.

Structural Chemistry, Dec 9, 2016

The article is written for the special journal issue dedicated to Alan L. Mackay on his 90th birt... more The article is written for the special journal issue dedicated to Alan L. Mackay on his 90th birthday. The remarkable ideas of Alan L. Mackay about generalized crystallography, its connections with encoding of information, and also the interrelationship between art and science generate many ideas and their consequences. Mackay paid a special attention to the theme of five-fold symmetry, Fibonacci numbers and the golden section, which are essential in the structures of quasicrystals and living bodies. The present article considers a continuation of this theme in relation to the genetic coding system and to ratios of musical harmony. Hidden connections between the matrix representations the genetic code system and the golden section and the Pythagoras's theory of esthetics of proportions are described. Such connections testify the validity of the molecular-genetic foundation of many known facts about inborn feeling of harmony in our perceptions, which becomes a part of the scientific field of Bbiochemical esthetics" (the term first introduced by Russian biophysicist S. Shnoll, 7). Data from theory of resonances and mathematics of noise-immunity coding of information are used in the article.

Progress in Biophysics & Molecular Biology, Dec 1, 2017

The ancient Chinese book I-Ching was written a few thousand years ago. It introduces the system o... more The ancient Chinese book I-Ching was written a few thousand years ago. It introduces the system of symbols Yin and Yang (equivalents of 0 and 1). It had a powerful impact on culture, medicine and science of ancient China and several other countries. From the modern standpoint, I-Ching declares the importance of dyadic groups of binary numbers for the Nature. The system of I-Ching is represented by the tables with dyadic groups of 4 bigrams, 8 trigrams and 64 hexagrams, which were declared as fundamental archetypes of the Nature. The ancient Chinese did not know about the genetic code of protein sequences of amino acids but this code is organized in accordance with the I-Ching: in particularly, the genetic code is constructed on DNA molecules using 4 nitrogenous bases, 16 doublets, and 64 triplets. The article also describes the usage of dyadic groups as a foundation of the bio-mathematical doctrine of the geno-logic code, which exists in parallel with the known genetic code of amino acids but serves for a different goal: to code the inherited algorithmic processes using the logical holography and the spectral logic of systems of genetic Boolean functions. Some relations of this doctrine with the I-Ching are discussed. In addition, the ratios of musical harmony that can be revealed in the parameters of DNA structure are also represented in the I-Ching book.

Nucleation and Atmospheric Aerosols, 2023

To reveal the hidden regularities of the stochastic organization of nucleotide sequences in infor... more To reveal the hidden regularities of the stochastic organization of nucleotide sequences in informational singlestranded DNA molecules of genomes of higher and lower biological species, the following author's method was applied: each such sequence is represented as a set of parallel n-texts, each of which is written in its own n-plets alphabet of DNA (among these alphabets include alphabets of 4 nucleotides, 16 duplets, 64 triplets, etc.). A comparative analysis of the percentage compositions of n-plets in these n-texts is carried out and the universal regularities of the multilevel blockstochastic organization of genomic DNA information sequences are revealed. The analogies of the phenomena of blockstochastic organization of these DNAs with genetically inherited physiological phenomena of similar types are discussed, including the Bernstein problem in the field of biomechanics of movements and also the ability of the brain, studied by Gestalt psychology.

The article is devoted to algebraic modeling of universal rules of stochastic organization of gen... more The article is devoted to algebraic modeling of universal rules of stochastic organization of genomic DNA of higher and lower organisms, previously published by the author. The proposed algebraic apparatus, which uses formalisms of quantum mechanics and quantum informatics and which is based on the so-called tensor-unitary transformations of vectors that generate families of interrelated stochastic-deterministic vectors of increased dimensions. The features of the vectors' interconnections in these families model the stochastic-deterministic properties of the named phenomenological rules. There are new approaches to modeling of developing multi-parameter biosystems, whose number of parameters increases in the course of step-by-step development. In the light of the presented materials, the issues of fractal-like organization in genetically inherited biosystems are considered. The development of the theory of stochastic determinism as an antipode of deterministic chaos is discussed.