Geodesic
Reinforced walk on graphs and neural networks
Józef Myjak 1   ; Ryszard Rudnicki 2
1 Dipartimento 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
2 Institute of Mathematics Polish Academy of Sciences Bankowa 14 40-007 Katowice, Poland and Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland
Studia Mathematica, Tome 189 (2008) no. 3, pp. 255-268 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm189-3-4
Keywords: directed edge reinforced random walk graphs considered criteria walk end limit cycle given asymptotic stability neural networks shown

Józef Myjak  1   ; Ryszard Rudnicki  2

1 Dipartimento 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
2 Institute of Mathematics Polish Academy of Sciences Bankowa 14 40-007 Katowice, Poland and Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland 
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Józef Myjak; Ryszard Rudnicki. Reinforced walk on graphs and neural networks. Studia Mathematica, Tome 189 (2008) no. 3, pp. 255-268. doi: 10.4064/sm189-3-4

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