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TMF, 2015, Volume 185, Number 2, Pages 346–360 (Mi tmf8955)  

This article is cited in 5 scientific papers (total in 5 papers)

Ultrametricity in the theory of complex systems

S. V. Kozyrev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We review applications of $p$-adic and ultrametric methods in the theory of complex systems. We consider the following examples: the $p$-adic parameterization of the Parisi matrix in the replica method; the method of hierarchical (interbasin) kinetics, which allows describing macromolecular dynamics by models of ultrametric diffusion; the two-dimensional $2$-adic parameterization of the genetic code, which demonstrates that degenerations of the genetic code are described by local constancy domains of maps in the $2$-adic metric. We discuss clustering methods for a family of metrics and demonstrate that the multiclustering (ensemble clustering) approach is related to the Bruhat–Tits building theory.

Keywords: ultrametrics, complex system, clustering

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.4213/tmf8955

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English version:
Theoretical and Mathematical Physics, 2015, 185:2, 1665–1677

Bibliographic databases:

Document Type: Article
Received: 24.04.2015
Revised: 06.05.2015

Citation: S. V. Kozyrev, “Ultrametricity in the theory of complex systems”, TMF, 185:2 (2015), 346–360; Theoret. and Math. Phys., 185:2 (2015), 1665–1677

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Kozyrev, A. A. Mironov, A. E. Teretenkov, I. V. Volovich, “Flows in non-equilibrium quantum systems and quantum photosynthesis”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 20:4 (2017), 1750021  crossref  mathscinet  zmath  isi  scopus
    2. B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich, E. I. Zelenov, “$p$-Adic mathematical physics: the first 30 years”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121  crossref  mathscinet  zmath  isi  scopus
    3. S. V. Kozyrev, “Quantum transport in degenerate systems”, Proc. Steklov Inst. Math., 301 (2018), 134–143  mathnet  crossref  crossref  isi  elib  elib
    4. V. V. Zharinov, “Analysis in algebras and modules”, Proc. Steklov Inst. Math., 301 (2018), 98–108  mathnet  crossref  crossref  isi  elib  elib
    5. V S. Kozyrev, “Biology as a constructive physics”, P-Adic Numbers Ultrametric Anal. Appl., 10:4 (2018), 305–311  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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