Reinforced walk on graphs and neural networks

Volume 189 / 2008

Józef Myjak, Ryszard Rudnicki Studia Mathematica 189 (2008), 255-268 MSC: Primary 60K37; Secondary 60J10, 60J20, 60G50, 82C41. DOI: 10.4064/sm189-3-4

Abstract

A directed-edge-reinforced random walk on graphs is considered. Criteria for the walk to end up in a limit cycle are given. Asymptotic stability of some neural networks is shown.

Authors

  • Józef MyjakDipartimento di Matematica Pura ed Applicata
    Università di L'Aquila
    Via Vetoio, 67100 L'Aquila, Italy
    and
    WMS AGH
    al. Mickiewicza 30
    30-059 Kraków, Poland
    e-mail
  • Ryszard RudnickiInstitute of Mathematics
    Polish Academy of Sciences
    Bankowa 14
    40-007 Katowice, Poland
    and
    Institute of Mathematics
    Silesian University
    Bankowa 14
    40-007 Katowice, Poland
    e-mail

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