The Genetic Coding, United-Hypercomplex Numbers and Artificial Intelligence

  • Sergey PetoukhovEmail author
  • Elena Petukhova
  • Ludmila Hazina
  • Ivan Stepanyan
  • Vitaliy Svirin
  • Tamara Silova
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 658)


Scientists try to reproduce in devices of artificial intelligence intellectual properties of living organisms, which are connected with the genetic code system. This article is devoted to the study and modeling of the genetic system on the basis of mathematical formalisms, which are used in digital devices of artificial intelligence and technology of noise-immunity coding of information. The genetic code of amino acid sequences in proteins does not allow understanding and modeling of inherited processes such as inborn coordinated motions of living bodies, innate principles of sensory information processing, quasi-holographic properties, etc. To be able to model these phenomena, the concept of geno-logical coding, which is connected with logical functions and Boolean algebra, is put forward. Structured alphabets of DNA in their matrix form of representations are connected with dyadic groups of binary numbers and a new type of systems of multidimensional numbers. This type generalizes systems of complex numbers and hypercomplex numbers, which serve as the basis of mathematical natural sciences and many technologies. The new systems are called in a general case as “systems of united-hypercomplex numbers”. They can be widely used in models of multi-parametrical systems in the field of algebraic biology, artificial life, devices of biological inspired artificial intelligence, etc.


Genetic Code Boolean Algebra Hypercomplex Numbers 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Petoukhov S. V.: Matrix Genetics, Algebras of the Genetic Code, Noise Immunity. RCD, Moscow, Russia (2008) (in Russian).Google Scholar
  2. 2.
    Petoukhov, S.V., He M.: Symmetrical Analysis Techniques for Genetic Systems and Bioinformatics: Advanced Patterns and Applications. IGI Global, Hershey, USA (2010).Google Scholar
  3. 3.
    Petoukhov S.V., Petukhova E.S.: Symmetries in genetic systems and the concept of geno- logical coding. - Information, 8(1), 2; doi: 10.3390/info8010002 (2017).
  4. 4.
    Petoukhov S.V.: Genetic coding and united-hypercomplex systems in the models of algebraic biology. Biosystems, v. 158, August, pp. 31–46 (2017).Google Scholar
  5. 5.
    Mohammed Abo-Zahhad,Sabah M. Ahmed,Shimaa A. Abd-Elrahman,”Genomic Analysis and Classification of Exon and Intron Sequences Using DNA Numerical Mapping Techniques”, IJITCS, vol.4, no.8, pp.22-36, 2012.
  6. 6.
    Prakash Chandra Srivastava, Anupam Agrawal, Kamta Nath Mishra, P. K. Ojha, R. Garg,”Fingerprints, Iris and DNA Features based Multimodal Systems: A Review”, IJITCS, vol.5, no.2, pp.88-111, 2013.DOI:  10.5815/ijitcs.2013.02.10.
  7. 7.
    Hamdy M. Mousa,”DNA-Genetic Encryption Technique”, International Journal of Computer Network and Information Security (IJCNIS), Vol.8, No.7, pp.1-9, 2016.DOI:  10.5815/ijcnis.2016.07.01.
  8. 8.
    Stewart I.: Life’s other secret: the new mathematics of the living world. Penguin, New York, USA (1999).Google Scholar
  9. 9.
    Seberry J., Wysocki B.J., Wysocki T.A.: On some applications of Hadamard matrices. Metrica, 62, pp. 221-239 (2005).Google Scholar
  10. 10.
    Harmuth, H. F.: Sequency theory. Academic Press, N.-Y., USA (1977).Google Scholar
  11. 11.
    Morita Y., Sakurai Y.: Holography by Walsh Waves. In: Proceedings of the Symposium (4th) Held at the Catholic University of America, Washington, D. C. on 16-18 April, pp. 122-126 (1973).Google Scholar
  12. 12.
    Karpovsky M.G., Stankovic R.S., Astola J.T.: Spectral Logic and its Applications for the Design of Digital Devices. John Wiley & Sons Inc., New Jersey, USA (2008).Google Scholar
  13. 13.
    Belousov L.: Morphomechanics of Development. Springer International Publishing AG, Switzerland, (2015).Google Scholar
  14. 14.
    Pribram K.: Languages of the Brain. Englewwod Cliffs, New Jersey, USA (1971).Google Scholar
  15. 15.
    Jenuwein Th., Allis C.D.: Translating the histone code. Science, v. 293, pp.1074-1080 (2001).Google Scholar
  16. 16.
    All-or-none law. (this page was last modified on 26 March 2017).
  17. 17.
    Penrose, R.: Shadows of the Mind. Oxford University Press, Oxford, England (1996).Google Scholar
  18. 18.
    Yaglom I.M.: The Boolean Structure and its Models. Sovetskoye Radio, Moscow, USSR, 1980 (in Russian).Google Scholar
  19. 19.
    Schrödinger E.: What is life? University Press, Cambridge, England (1955).Google Scholar
  20. 20.
    Varfolomeev S.D.: Chemical enzymology. Akademia, Moscow, Russia (2005).Google Scholar
  21. 21.
    Hamilton A. Invention of the year. The retail DNA test. Time, Oct. 29 (2008).Google Scholar
  22. 22.
    Petoukhov S.V.: The genetic code, algebra of projection operators and problems of inherited biological ensembles. –, 8th version of the article from 3 May 2017, pp. 1-93 (2017).
  23. 23.
    Davis P.J.: Arithmetics. – In: “Mathematics in the modern world”, Scientific American, N. Y., USA, p. 29-45 (1964).Google Scholar
  24. 24.
    Pavlov D. G.: Leading article. Hypercomplex numbers in geometry and in physics, 1(1), p. 4-7 (2004) (in Russian).Google Scholar
  25. 25.
    Russel B.: A History of Western Philosophy. - Book One, Part I, Chapter III. Simon & Schuster/Touchstone N.Y., USA (1967).Google Scholar
  26. 26.
    Heisenberg W.: Physics and Philosophy: The Revolution in Modern Science. Penguin Classics N.Y., USA (2000).Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Sergey Petoukhov
    • 1
    Email author
  • Elena Petukhova
    • 1
  • Ludmila Hazina
    • 1
  • Ivan Stepanyan
    • 1
  • Vitaliy Svirin
    • 1
  • Tamara Silova
    • 1
  1. 1.Mechanical Engineering Research InstituteRussian Academy of SciencesMoscowRussia

Personalised recommendations