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Ultrametricity in the theory of complex systems

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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.

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Authors and Affiliations

  1. Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

    S. V. Kozyrev

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Correspondence to S. V. Kozyrev.

Additional information

This research was funded by a grant from the Russian Science Foundation (Project No. 14-50-00005).

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 185, No. 2, pp. 346–360, November, 2015.

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Kozyrev, S.V. Ultrametricity in the theory of complex systems. Theor Math Phys 185, 1665–1677 (2015). https://doi.org/10.1007/s11232-015-0371-2

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  • DOI: https://doi.org/10.1007/s11232-015-0371-2

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