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
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
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
Theoretical and Mathematical Physics, 2015, 185:2, 1665–1677
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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http://mi.mathnet.ru/eng/tmf8955
https://doi.org/10.4213/tmf8955
http://mi.mathnet.ru/eng/tmf/v185/i2/p346
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
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
S. V. Kozyrev, "Quantum transport in degenerate systems", Proc. Steklov Inst. Math., 301 (2018), 134–143
V. V. Zharinov, "Analysis in algebras and modules", Proc. Steklov Inst. Math., 301 (2018), 98–108
V S. Kozyrev, "Biology as a constructive physics", P-Adic Numbers Ultrametric Anal. Appl., 10:4 (2018), 305–311
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