Abstract
The identification of critical states is a major task in complex systems, and the availability of measures to detect such conditions is of utmost importance. In general, criticality refers to the existence of two qualitatively different behaviors that the same system can exhibit, depending on the values of some parameters. In this paper, we show that the relevance index may be effectively used to identify critical states in complex systems. The relevance index was originally developed to identify relevant sets of variables in dynamical systems, but in this paper, we show that it is also able to capture features of criticality. The index is applied to two prominent examples showing slightly different meanings of criticality, namely the Ising model and random Boolean networks. Results show that this index is maximized at critical states and is robust with respect to system size and sampling effort. It can therefore be used to detect criticality.
Highlights
In this paper, the relevance index (RI) is applied to the task of identifying critical states in complex systems
Since individual network realizations can show different behaviors, the study of the random Boolean networks (RBNs) dynamics is based on averages computed on ensembles of networks sharing the same values of connectivity and bias
The computation of the RI requires a collection of the states of each variable; these have been obtained by collecting in a single series all of the states encountered by a specific RBN starting from
Summary
The relevance index (RI) is applied to the task of identifying critical states in complex systems (more precisely, we identify regions near critical points; in order not to overload the writing, in the following, we use the expression “critical states”). This index had been originally introduced for a different purpose, i.e., as a way to identify key features of the organization of complex dynamical systems, and it has proven able to provide useful results in various kinds of models, including, e.g., those of gene regulatory networks and protein-protein interactions. Since the RI allows a variable to belong to more than one group, it can be applied to “tangled” organizations, which are widespread in complex biological and social systems and which do not have the clean tree-like topology of pure hierarchies
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