Ultrametricity in the~theory of complex systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 2, pp. 346-360
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{TMF_2015_185_2_a6,
author = {S. V. Kozyrev},
title = {Ultrametricity in the~theory of complex systems},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {346--360},
publisher = {mathdoc},
volume = {185},
number = {2},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2015_185_2_a6/}
}
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/