Kei Tokita's Research Interests

Research Interests


Statistical and Computational Physics for Complex Systems

I am trying to clarify the problems in the so-called "complex systems" like ecological systems, proteins, neural networks and their learning processes, and combinatorial optimization problems in terms of nonlinear mechanics, statistical physics and computational physics. Although the subjects are quite different each other at first glance, they share the key concepts: their complex behaviors are emerged by large number of relatively simple elements with complex interactions. Studying them in the uniform view point, we can make each particular case clear all the more.

  1. Large-scale Ecological systems
    • Random interspecies interactions and the extinction threshold
      - The Extinction dynamics (KT&AY, 99; 00)
    • Origin of the biodiversity of ecosystems
      - Biotic fusion, extinction, invasion, neutral mutation...(KT&AY, 03)
    • Game dynamical equation w/antisymmetric random interactions
      - A mechanism of mainteining biodiversity (TC&KT, 02)
    • Lotka-Volterra equation w/hierarchically ordered random interactions (KT&TC, in prep.)
    • Species abundance patterns in replicator dynamics w/random interactions (KT, 04; 06; YY,TG&KT 07;08)
    • Species abundance distributions and the species area relationships (HI&KT 12)
    • Neutral models of ecology (TO&KT 13)

  2. Protein foldings and inverse foldings
    • Fast algorithm for the inverse folding problem = The Design equation (YI,KT&MK, 98; KT,MK&YI, 00)

  3. Neural networks and learning theories
    • Multivalley free energy landscape in the Hopfield model (KT, 93; 94)
    • Full replica-symmetry-breaking(RSB) formulation of the Hopfield model (KT, 94)

  4. Miscellaneous
    • Statistical mechanics of combinatorial optimization problems
    • Nonequiliburium dynamics for economical systems, game, cell, viruses and immune systems, etc.
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