Curriculum Vitae of Dr. Sergey Petoukhov
Laureate of the State Prize of the USSR
Member of the Academy of Quality Problems
Head, Laboratory of Studying Biomechanical Systems, Mechanical Engineering Research Institute, Russian Academy of Sciences,
d.4, Malyi Kharitonievskiy pereulok, Moscow, 101990, Russia

Biography

Dr. Sergey Petoukhov is Full Professor and Grand Ph.D. from the World Information Distributed University since 2004.
Dr. Sergey Petoukhov has been elected as a member of the European Academy of Informatization in 2004.
He is a laureate of the State Prize of the USSR (1986).
He is the Head of the Laboratory of Studying Biomechanical Systems, Mechanical Engineering Research Institute, Russian Academy of Sciences, Moscow, Russia.

Sergey V. PETOUKHOV
Dr. Phys.-Math. Sci, Grand Ph.D., Full Professor,
Laureate of the State prize of the USSR, academician, spetoukhov@gmail.com

S.Petoukhov is a member of editorial boards of the international journals
"Journal of Biological Systems" (World Scientific, New Jersey/London/Singapore/Beijing/...) and "Symmetry: Culture and Science" (SYMMETRION, published in Hungary).
He is a guest editor of "Symmetry in Genetic Information", ISBN 963216 242 0, special double issue of the journal "Symmetry: Culture and Science", 2001, v.12, #3-4.
He is an editor (together with M.He and G.Narasimhan) of the book "Advances in Bioinformatics and its Applications", Series in Mathematical Biology and Medicine, v. 8, 2005, World Scientific.

S.Petoukhov was one of the main organizers of a few International conferences:
the conferences on symmetries in science and culture (1989, Budapest, Hungary; 1992, Hiroshima, Japan; 1995, Washington, USA; 1998, Haifa, Israel; 2003 and 2006, Budapest, Hungary), the conference "Bioinformatics and its Applications" (2004, Fort Lauderdale, USA), etc.

Main publications

He is author of 200 scientific works approximately, including seven books. Examples of his publications are:

  1. Petoukhov S.V. "Biomechanics, Bionics and Symmetry", Moscow, 1981, 239 p. (in Russian);
  2. Petoukhov S.V "Geometries of Living Nature and Algorithms of Self-Organization", Moscow, 1988 (in Russian);
  3. Petoukhov S.V. Non-Euclidean geometries and algorithms of living bodies. - Computers & Mathematics with Applications, v.17, Num. 4-6, 1989, p.505-534.
  4. Petoukhov S.V. "Biosolitons. The Bases of Soliton Biology", Moscow, 1999, 288 p., (http://members.tripod.com/vismath/sg/pet.htm);
  5. Petoukhov S.V "The Biperiodic Table of Genetic Code and Number of Protons", Moscow, 2001, 258 p. (http://members.tripod.com/vismath/sg/petoukhov.htm);
  6. Petoukhov S.V., Genetic codes I: Binary sub-alphabets, bi-symmetric matrices and golden section In: Symmetry in Genetic Information, ed. by Petoukhov S.V. (special double issue of the Journal "Symmetry: Culture and Science", International Symmetry Foundation, Budapest, 2001), pp.255-274;
  7. Petoukhov S.V., Genetic codes II: Numeric rules of degeneracy and a chronocyclic theory. In: Symmetry in Genetic Information, ed. by Petoukhov S.V. (special double issue of the Journal "Symmetry: Culture and Science", International Symmetry Foundation, Budapest, 2001), pp. 275-306
  8. S.V.Petoukhov "Attributive conception of genetic code, its bi-periodic tables and problem of unification bases of biological languages" - Symmetry: Culture and Science", vol. 14-15, part 1, 2003-2004, pp.281-307;
  9. Petoukhov S.V. "The rules of degeneracy and segregations in genetic codes. The chronocyclic conception and parallels with Mendel's law's" - In: "Advances in Bioinformatics and its Applications" (editors - M.He, G.Narasimhan, S.Petoukhov), Proceedings of the International Conference (Florida, USA, 16-19 December 2004), Series in Mathematical Biology and Medicine, v.8, 2005, pp.512-532, New Jersey-London-Singapore-Beijing, World Scientific.
  10. Petoukhov S.V., Symmetries in biology. In Supplement to the book: Shubnikov A. V. and Koptsik V.A., Symmetries in Science and Art (3-d edition, Regular and Chaotic Dynamics, Moscow, 2004) pp. 482-523 (in Russian).
  11. Petoukhov S.V. (together with M.He). Harmony of living nature, symmetries of genetic systems and matrix genetics. - International Journal of Integrative Medicine, 2007, v.1, Num.1, p.41-43.
  12. Petoukhov S.V. Matrix Genetics, Algebras of the Genetic Code, Noise Immunity”, Moscow: Publishing company  “Regular and chaotic dynamics”, 2008, 316 p.
  13. Petoukhov S.V. & He M. Symmetrical Analysis Techniques for Genetic Systems and Bioinformatics: Advanced Patterns and Applications. 2010, Hershey, USA: IGI Global. 271 p. (See contents below)
  14. He M., Petoukhov S.V. Mathematics of Bioinformatics: Theory, Practice, and Applications. USA: John Wiley & Sons, Inc., 2010, 295 p. (See contents below)

He is a specialist in theoretical and mathematical biology (in particular, in problems of genetic codes and bioinformatics), biomechanics, crystallography, theories of symmetry and self-organization.

Contact: spetoukhov@gmail.com

Sergey

Symmetrical Analysis Techniques for Genetic Systems and Bioinformatics: Advanced Patterns and Applications
Sergey Petoukhov
Russian Academy of Sciences, Moscow, Russia
Matthew He
Nova Southeastern University, Fort Lauderdale, USA

IGI Global
Hershey • London • Melbourne • Singapore


TABLE OF CONTENTS

PREFACE
AUTHORS
ACKNOWLEDGMENTS

SECTION I SYMMETRICAL ANALYSIS TECHNIQUES AND SYMBOLIC MATRICES OF MATRIX GENETICS

CHAPTER 1 GENETIC CODE: EMERGENCE OF SYMMETRICAL PATTERN, BEGINNINGS OF MATRIX GENETICS
1.1 Introduction and background
1.2 Significance of symmetrical patterns for biology, molecular genetics and bioinformatics
1.3 Information science, noise immunity and the matrix approach to the genetic code
1.4 The basic structures of the genetic code
1.5 The binary sub-alphabets of the genetic alphabet for numbering the multiplets in genetic matrices
1.6 The natural system of numbering the genetic multiplets
1.7 The matrix numbering the genetic multiplets and matrices of diadic shifts
1.8 Future trends and conclusion
REFERENCES

CHAPTER 2 SYMMETRIES OF DEGENERACY OF THE VERTEBRATE MITOCHONDRIAL CODE IN THE MATRIX FORM
Introduction and background
2.1 Peculiarities of degeneracy of the genetic code
2.2 Symmetrical properties of genetic matrices of triplets under permutations of positions inside triplets
2.3 Genomatrices with the property of the tetra-self-reproducing
2.4 Symmetrical properties of genetic matrices under alphabetic permutations in the set of 64 triplets
2.5 Future trends and conclusion
REFERENCES

CHAPTER 3 BIOLOGICAL EVOLUTION OF DIALECTS OF THE GENETIC CODE
3.1 Introduction and background
3.2 Phenomenological rules of evolution of known dialects of genetic codes
3.3 The chronocyclic conception and the degeneracy in the dialects of the genetic code
3.4 Why 20 amino-acids?
3.5 Future trends and conclusion
REFERENCES

SECTION II SYMMETRICAL ANALYSIS TECHNIQUES AND NUMERIC MATRICES OF THE GENETIC CODE

CHAPTER 4 NUMERIC GENOMATRICES OF HYDROGEN BONDS, THE GOLDEN SECTION, MUSICAL HARMONY AND AESTHETIC FEELINGS
4.1 Introduction and background
4.2 Numeric genomatrices of hydrogen bonds
4.3 The numeric genomatrices and the golden section
4.4 The genomatrices, musical harmony and Pythagorean musical scale
4.5 A scale of the golden wurf, music and Fibonacci numbers
4.6 On harmony of a scale of protons in the set of amino-acids
4.7 Future trends and conclusion
REFERENCES

CHAPTER 5 GENETIC CODE AND STOCHASTIC MATRICES

5.1 Introduction and background
5.2 Genetic code, Hamming distance, and stochastic matrices
5.3 Genetic code, attributive mapping, and stochastic matrices
5.4 Genetic code, power of matrices, and stochastic matrices
5.5 Future trends and conclusion
REFERENCES

CHAPTER 6 THE GENETIC CODE, HADAMARD MATRICES, NOISE IMMUNITY AND QUANTUM COMPUTERS

6.1 Introduction and background
6.2 The genetic code and Hadamard matrices
6.3 About importance of amino-groups NH2
6.4 Genetic informatics, Hadamard matrices and quantum computers
6.5 Why does the genetic alphabet consist of four letters?
6.6 Cyclic shifts, cyclic codes and the principle of molecular economy in genetic informatics
6.7 Future trends and conclusion
REFERENCES

SECTION III ALGEBRAS OF GENETIC CODES

CHAPTER 7 GENOMATRICES AND THE GENETIC OCTET YIN-YANG-ALGEBRAS
7.1 Introduction and background
7.2 The genetic octet matrix as the matrix form of presentation of the octet algebra
7.3 The alphabetic algorithm of the Yin-Yang-digitization of 64 triplets
7.4 The genomatrix YY8 as the element of the octet Yin-Yang-algebra
7.5 The structural analogies between the genomatrix [C A; G U](3) and the matrix YY8
7.6 The six kinds of the genetic octet Yin-Yang-algebras connected with permutations of positions in triplets
7.7 The genetic Yin-Yang octets as “double genoquaternions”
7.8 The comparison between the classical vector calculation and the genovector calculation
7.9 The parametric reduction of the genetic octet Yin-Yang-algebra to the 4-dimensional algebra of tetrions
7.10 About genetic mechanics and the idea by Pythagoras
7.11 What is life from the viewpoint of algebra? The problem of algebraization of
bioinformatics and biology
7.12 Solutions and recommendations
7.13 Future trends and conclusion
REFERENCES


CHAPTER 8 THE EVOLUTION OF THE GENETIC CODE FROM THE VIEWPOINT OF THE GENETIC 8-DIMENSIONAL YIN-YANG-ALGEBRA
8.1 Introduction and background
8.2 The comparison analysis and phenomenological rules of dialects of the genetic code
8.3 The molecular-sexual approach in molecular genetics
8.4 The example of the pairs of histones
8.5 Whether an unknown quantum mechanical factor of a “sexual attraction” among genetic molecules exists?
8.6 The analysis of the insulin structure as the simplest example
8.7 Some applications of results of matrix genetics in bioinformatics and algebraic biology.
8.8 Solutions and recommendations
8.9 Future trends and conclusion
REFERENCES

CHAPTER 9 MULTIDIMENSIONAL NUMBERS AND THE GENOMATRICES OF HYDROGEN BONDS
Introduction and background
9.1 The hyperbolic matrions as a special kind of hypercomplex numbers
9.2 The circular matrions
9.3 The rules of eigenvalues of matrices of circular matrions
9.4 Circular matrions and the series of natural numbers
9.5 Solutions and recommendations
9.6 Future trends and conclusion
REFERENCES

SECTION IV CONNECTIONS OF MATRIX GENETICS WITH OTHER FIELDS OF SCIENCE AND CULTURE

CHAPTER 10 GENETIC SYSTEM, FIBONACCI NUMBERS AND PHYLLOTAXIS
LAWS
10.1 Introduction and background
10.2 Fibonacci’s matrices and biological laws of phyllotaxis
10.3 Additional facts about the golden section and matrices
10.4 Hadamard matrices, projective geometry and the golden wurf
10.5 Future trends and conclusion
REFERENCES

CHAPTER 11 PHYSIOLOGICAL CYCLES AND THEIR ALGEBRAIC MODELS IN MATRIX GENETICS

11.1 Introduction and background
11.2 Revealing new genetic algebras as a result of cyclic permutations of genetic
elements
11.3 The oppositional category of genetic Yin-Yang-matrices
11.4 Generative and suppressive properties of yin-yang-matrices of the two categories
11.5 Joining of the idea by Pythagoras and the idea of cyclic changes: about cellular
automata, neurocomputers and a notion of biological time
11.6 Solutions and recommendations
11.7 Future trends and conclusion
REFERENCES

CHAPTER 12 MATRIX GENETICS AND CULTURE
12.1 Introduction and background
12.2 Genetic code and linguistics
12.3 The genetic code, a color perception and a color communication
12.4 Parallels between patterns of the genetic code and patterns of "I Ching"
12.5 Musical harmony in the matrices of the genetic code and of “I Ching”
12.6 Future trends and conclusion
REFERENCES
INDEX

 

MATHEMATICS OF BIOINFORMATICS
-THEORY, PRACTICE, AND APPLICATIONS

Matthew He and Sergey Petoukhov

Wiley Book Series on Bioinformatics, 2010


TABLE OF CONTENTS
Preface
Acknowledgement

Chapter 1 Bioinformatics and Mathematics
§ 1.1 Introduction
§ 1.2 Genetic Code and Mathematics
§ 1.3 Mathematical Background
§ 1.4 Converting Data to Knowledge
§ 1.5 Big Picture: Informatics
§ 1.6 Challenges and Perspectives
References

Chapter 2 Genetic Codes, Matrices, and Symmetrical Techniques
§ 2.1 Introduction
§ 2.2 Matrix Theory and Symmetry Preliminaries
§ 2.3 Genetic Codes and Matrices
§ 2.4 Genetic Matrices, Hydrogen Bonds and the Golden Section
§ 2.5 Symmetrical Patterns, Molecular Genetics and Bioinformatics
§ 2.6 Challenges and Perspectives
References

Chapter 3 Biological Sequences, Sequence Alignment, and Statistics
§ 3.1 Introduction
§ 3.2 Mathematical Sequences
§ 3.3 Sequence Alignment
§ 3.4 Sequence Analysis and Further Discussions
§ 3.5 Challenges and Perspectives
References

Chapter 4 Structures of DNA and Knot Theory
§ 4.1 Introduction
§ 4.2 Knot Theory Preliminaries
§ 4.3 DNA Knots and Links
§ 4.4 Challenges and Perspectives
References

Chapter 5 Protein Structures, Geometry, and Topology
§ 5.1 Introduction
§ 5.2 Computational Geometry and Topology Preliminaries
§ 5.3 Protein Structures and Prediction
§ 5.4 Statistical Approach and Discussions
§ 5.5 Challenges and Perspectives
References

Chapter 6 Biological Networks and Graph Theory
§ 6.1 Introduction
§ 6.2 Graph Theory Preliminaries and Network Topology
§ 6.3 Models of Biological Networks
§ 6.4 Challenges and Perspectives
References

Chapter 7 Biological Systems, Fractals, and Systems Biology
§ 7.1 Introduction
§ 7.2 Fractal Geometry Preliminaries
§ 7.3 Fractal Geometry in Biological Systems
§ 7.4 Systems Biology and Perspectives
§ 7.5 Challenges and Perspectives
References

Chapter 8 Matrix Genetics, Hadamard Matrix, and Algebraic Biology
§ 8.1 Introduction
§ 8.2 Genetic Matrices and the Degeneracy of the Genetic Code
§ 8.3 The Genetic Code and Hadamard Matrices
§ 8.4 Genetic Matrices and Matrices of Hypercomplex Numbers
§ 8.5 Some Rules of Evolution of Variants of the Genetic Code
§ 8.6 Challenges and Perspectives
References

Chapter 9 Bioinformatics, Living Systems and Cognitive Informatics
§ 9.1 Introduction
§ 9.2 Emerging Pattern, Dissipative Structure, and Evolving Cognition
§ 9.3 Denotational Mathematics and Cognitive Computing
§ 9.4 Challenges and Perspectives
References

Chapter 10 The Evolutionary Trends and Central Dogma of Informatics
§ 10.1 Introduction
§ 10.2 Evolutionary Trends of Informatics
§ 10.3 Central Dogma of Informatics
§ 10.4 Challenges and Perspectives
References

Appendix A Bioinformatics Notation and Databases
Appendix B Bioinformatics/Genetics/Timeline
Appendix C Bioinformatics Glossary
About Authors
Index