Ultrametricity in the theory of complex systems

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• 作者：S. V. Kozyrev
• 关键词：ultrametrics ; complex system ; clustering
• 刊名：Theoretical and Mathematical Physics
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：185
• 期：2
• 页码：1665-1677
• 全文大小：515 KB
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• 作者单位：S. V. Kozyrev (1)
  
  1. Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Applications of Mathematics
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-9333

文摘

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