Skip to main content

A Self-Induced Metric on Groupoids and its Application to the Analysis of Cellular Interactions in Biology

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

The application of finite groupoids to the modeling of the interaction of living cells in biology is considered. For this application, special numerical characteristics for groupoid elements based on the general form of the Cayley table of groupoids were established. In particular, a self-induced metric on groupoids was constructed to analyze and describe small variations in the Cayley tables of groupoids.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    V. A. Artamonov, “Universal algebras,” Itogi Nauki Tekh. Ser. Algebra. Topol. Geom., 27, 45–124 (1989).

    MathSciNet  Google Scholar 

  2. 2.

    V. D. Belousov, Foundations of the Theory of Quasigroups and Loops [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  3. 3.

    M. I. Graev and A. V. Koganov, Geometrical and Topological Structures on Groupoids [in Russian], Moscow (2002).

  4. 4.

    M. A. Harrison, “The number of isomorphism types of finite algebras,” Proc. Am. Math. Soc., 17, 731–737 (1966).

    Article  MATH  Google Scholar 

  5. 5.

    A. A. Ivanov, “Complete theory of mono-unary algebras,” Algebra Logika, 23, No. 1, 48–73 (1984).

    Article  Google Scholar 

  6. 6.

    M. N. Nazarov, “Concentrated model of cell populations with emulation of signal exchange,” Vestn. MGADA, 5, 150–157 (2011).

    Google Scholar 

  7. 7.

    A. L. Rasstrigin, “Formations of finite monounary algebras,” Chebyshevskii Sb., 12, No. 2, 102–109 (2011).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to M. N. Nazarov.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 3, pp. 149–160, 2013.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Nazarov, M.N. A Self-Induced Metric on Groupoids and its Application to the Analysis of Cellular Interactions in Biology. J Math Sci 206, 561–569 (2015). https://doi.org/10.1007/s10958-015-2333-5

Download citation

Keywords

  • Main Diagonal
  • Relative Priority
  • Zero Multiplication
  • Iterative Search
  • Triangular Inequality