A Fast and Effective Method to Identify Relevant Sets of Variables in Complex Systems

Gianluca D’Addese, Martina Casari, Roberto Serra and Marco Villani
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Gianluca D’Addese: Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41121 Modena, Italy
Martina Casari: Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41121 Modena, Italy
Roberto Serra: Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41121 Modena, Italy
Marco Villani: Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41121 Modena, Italy

Mathematics, 2021, vol. 9, issue 9, 1-27

Abstract: In many complex systems one observes the formation of medium-level structures, whose detection could allow a high-level description of the dynamical organization of the system itself, and thus to its better understanding. We have developed in the past a powerful method to achieve this goal, which however requires a heavy computational cost in several real-world cases. In this work we introduce a modified version of our approach, which reduces the computational burden. The design of the new algorithm allowed the realization of an original suite of methods able to work simultaneously at the micro level (that of the binary relationships of the single variables) and at meso level (the identification of dynamically relevant groups). We apply this suite to a particularly relevant case, in which we look for the dynamic organization of a gene regulatory network when it is subject to knock-outs. The approach combines information theory, graph analysis, and an iterated sieving algorithm in order to describe rather complex situations. Its application allowed to derive some general observations on the dynamical organization of gene regulatory networks, and to observe interesting characteristics in an experimental case.

Keywords: information theory; complex systems; dynamical organization; gene regulatory networks; knock-out (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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