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New Mathematical Approaches to the Problems of Algebraic Biology

  • Georgy K. TolokonnikovEmail author
  • Sergey V. Petoukhov
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1126)

Abstract

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.

Keywords

Hypercomplex numbers Genetic code DNA Tensor product System theory Categories Topos 

References

  1. 1.
    Petoukhov, S.V.: Matrix genetics, algebra of genetic code, noise immunity. RHD, Moscow (2008)Google Scholar
  2. 2.
    Petoukhov, S.V., He, M.: Symmetrical Analysis Techniques for Genetic Systems and Bioinformatics: Advanced Patterns and Applications. IGI Global, Hershey (2009)Google Scholar
  3. 3.
    Petoukhov, S.V.: Matrix genetics and algebraic properties of the multi-level system of genetic alphabets. Neuroquantology 9(4), 60–81 (2011)CrossRefGoogle Scholar
  4. 4.
    Petoukhov, S.V.: The system-resonance approach in modeling genetic structures. Biosystems 139, 1–11 (2016)CrossRefGoogle Scholar
  5. 5.
    Petoukhov, S., Petukhova, E., Hazina, L., Stepanyan, I., Svirin, V., Silova, T.: The genetic coding, united-hypercomplex numbers and artificial intelligence. In: Hu, Z.B., Petoukhov, S., He, M. (eds.) Advances in Artificial Systems for Medicine and Education. Advances in Intelligent Systems and Computing, vol. 658. Springer, Cham (2017)Google Scholar
  6. 6.
    Chernoivanov, V.I., Sudakov, S.K., Tolokonnikov, G.K.: Biomachsystems, functional systems, categorical theory of systems. Institute of Normal Physiology, Moscow (2018)Google Scholar
  7. 7.
    Anokhin, P.K.: The fundamental questions of the general theory of functional systems. In: Principles of System Organization of Functions, Moscow, Nauka, pp. 5–61 (1973)Google Scholar
  8. 8.
    von Bertalanffy, L.: General System Theory. A Critical Review, General Systems, vol. VII, pp. 1–20 (1962)Google Scholar
  9. 9.
    Wiener, N.: Cybernetics or Control and Communication in the Animal and the Machine. The Technology Press and Wiley, New York (1948)Google Scholar
  10. 10.
    Vasiliev S.N., Zherlov A.K., Fedosov E.A., Fedunov B.E. Intelligent control of dynamic systems. Moscow, Fizmatlit (2000)Google Scholar
  11. 11.
    Szabo, M.: Polycategories. Comm. Algebra 3(8), 663–689 (1975)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Tolokonnikov, G.K.: Manifest: neurographs, neurocategories and categorical gluing. Biomashsystems 1(1), 59–146 (2017)Google Scholar
  13. 13.
    Tolokonnikov, G.K.: Convolution polycategories and categorical splices for modeling neural networks. In: Advances in Intelligent Systems and Computing, Volume 938, Advances in Computer Science for Engineering and Education II, Proceedings ICCSEEA 2019, pp. 259–267 (2019). ISSN 2194-5357. ISSN 2194-5365Google Scholar
  14. 14.
    Goldblat, R.: Topoi: Categorical Analysis of Logic. Dover Publications, Mineola (2006). ISBN-10 0486450260Google Scholar
  15. 15.
    Johnston, P.T.: Theory of Topos. Dover Publications, Mineola (2014). ISBN-13 978-0486493367Google Scholar
  16. 16.
    Abramsky, S., Coecke, B.: Categorical quantum mechanics. In: Handbook of Quantum Logic and Quantum Structures: Quantum Logic, pp. 261–324. Elsevier, North-Holland (2009)CrossRefGoogle Scholar
  17. 17.
    Doring, A., Isham, C.J.: A topos foundation for theories of physics. J. Math. Phys. 49(5), 053515 (2008)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Karande, A.M., Kalbande, D.R.: Weight assignment algorithms for designing fully connected neural network. Int. J. Intell. Syst. Appl. (IJISA) 10(6), 68–76 (2018)Google Scholar
  19. 19.
    Dharmajee Rao, D.T.V., Ramana, V.: Winograd’s inequality: effectiveness for efficient training of deep neural networks. Int. J. Intell. Syst. Appl. (IJISA) 6, 49–58 (2018)Google Scholar
  20. 20.
    Hu, Z., Tereykovskiy, I.A., Tereykovska, L.O., Pogorelov, V.V.: Determination of structural parameters of multilayer perceptron designed to estimate parameters of technical systems. Int. J. Intell. Syst. Appl. (IJISA) 10, 57–62 (2017)Google Scholar
  21. 21.
    Awadalla, M.H.A.: Spiking neural network and bull genetic algorithm for active vibration control. Int. J. Intell. Syst. Appl. (IJISA) 10(2), 17–26 (2018)Google Scholar
  22. 22.
    Abuljadayel, A., Wedyan, F.: An approach for the generation of higher order mutants using genetic algorithms. IJISA 10(1), 34–35 (2018)CrossRefGoogle Scholar
  23. 23.
    Kumar, A., Sharma, R.: A genetic algorithm based fractional fuzzy PID controller for integer and fractional order systems. Int. J. Intell. Syst. Appl. (IJISA) 10(5), 23–32 (2018)Google Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Federal Scientific Agro-Engineering Center VIMRussian Academy of SciencesMoscowRussia
  2. 2.Mechanical Engineering Research InstituteRussian Academy of SciencesMoscowRussia

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