Abstract

Hierarchical networks are attracting a renewal interest for modeling the organization of a number of biological systems and for tackling the complexity of statistical mechanical models beyond mean-field limitations. Here we consider the Dyson hierarchical construction for ferromagnets, neural networks, and spin glasses, recently analyzed from a statistical-mechanics perspective, and we focus on the topological properties of the underlying structures. In particular, we find that such structures are weighted graphs that exhibit a high degree of clustering and of modularity, with a small spectral gap; the robustness of such features with respect to the presence of thermal noise is also studied. These outcomes are then discussed and related to the statistical-mechanics scenario in full consistency. Last, we look at these weighted graphs as Markov chains and we show that in the limit of infinite size, the emergence of ergodicity breakdown for the stochastic process mirrors the emergence of metastabilities in the corresponding statistical mechanical analysis.

Autore Pugliese

• Barra Adriano

Tutti gli autori

• Agliari E. , Barra A. , Galluzzi A. , Guerra F. , Tantari D. , Tavani F.

Titolo volume/Rivista

PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS

Anno di pubblicazione

2015

ISSN

1539-3755

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

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Numero di citazioni Scopus

Non Disponibile

Ultimo Aggiornamento Citazioni

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Settori ERC

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Codici ASJC

Non Disponibile