In this paper we show that a well-known model of genetic regulatory networks, namely that of Random Boolean Networks (RBNs), allows one to study in depth the relationship between two important properties of complex systems, i.e. dynamical criticality and power-law distributions. The study is based upon an analysis of the response of a RBN to permanent perturbations, that may lead to avalanches of changes in activation levels, whose statistical properties are determined by the same parameter that characterizes the dynamical state of the network (ordered, critical or disordered). Under suitable approximations, in the case of large sparse random networks an analytical expression for the probability density of avalanches of different sizes is proposed, and it is shown that for not-too-small avalanches of critical systems it may be approximated by a power law. In the case of small networks the above-mentioned formula does not maintain its validity, because of the phenomenon of self-interference of avalanches, which is also explored by numerical simulations.

Dynamically critical systems and power-law distributions: Avalanches revisited / Di Stefano, Marina L.; Villani, Marco; LA ROCCA, Luca; Kauffman, Stuart A.; Serra, Roberto. - STAMPA. - 587:(2016), pp. 29-39. (Intervento presentato al convegno 10th Italian Workshop on Artificial Life and Evolutionary Computation, WIVACE 2015 tenutosi a Bari nel 22-25 settembre 2015) [10.1007/978-3-319-32695-5_3].

Dynamically critical systems and power-law distributions: Avalanches revisited

VILLANI, Marco;LA ROCCA, Luca;SERRA, Roberto
2016

Abstract

In this paper we show that a well-known model of genetic regulatory networks, namely that of Random Boolean Networks (RBNs), allows one to study in depth the relationship between two important properties of complex systems, i.e. dynamical criticality and power-law distributions. The study is based upon an analysis of the response of a RBN to permanent perturbations, that may lead to avalanches of changes in activation levels, whose statistical properties are determined by the same parameter that characterizes the dynamical state of the network (ordered, critical or disordered). Under suitable approximations, in the case of large sparse random networks an analytical expression for the probability density of avalanches of different sizes is proposed, and it is shown that for not-too-small avalanches of critical systems it may be approximated by a power law. In the case of small networks the above-mentioned formula does not maintain its validity, because of the phenomenon of self-interference of avalanches, which is also explored by numerical simulations.
2016
10th Italian Workshop on Artificial Life and Evolutionary Computation, WIVACE 2015
Bari
22-25 settembre 2015
587
29
39
Di Stefano, Marina L.; Villani, Marco; LA ROCCA, Luca; Kauffman, Stuart A.; Serra, Roberto
Dynamically critical systems and power-law distributions: Avalanches revisited / Di Stefano, Marina L.; Villani, Marco; LA ROCCA, Luca; Kauffman, Stuart A.; Serra, Roberto. - STAMPA. - 587:(2016), pp. 29-39. (Intervento presentato al convegno 10th Italian Workshop on Artificial Life and Evolutionary Computation, WIVACE 2015 tenutosi a Bari nel 22-25 settembre 2015) [10.1007/978-3-319-32695-5_3].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1103843
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