Geodesic
Ultrametricity in the theory of complex systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 2, pp. 346-360 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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S. V. Kozyrev. Ultrametricity in the theory of complex systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 2, pp. 346-360. http://geodesic.mathdoc.fr/item/TMF_2015_185_2_a6/

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