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

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.

Laplacian Spectra of Persistent Structures in Taiwan, Singapore, and US Stock Markets

“…One of the directions explored by complex systems scientists is to embed the variables onto a low-dimensional manifold, using information contained in their time series [ 4 , 5 ]. Recently, D’Addese et al [ 6 ] and Villani et al [ 7 ] used information-theoretic methods to identify the relevant sets of variables in random Boolean networks, gene-regulatory networks, MAPK signaling pathways in eukaryotes, and other systems, and the manifold they evolve on. Others have turned instead to topological data analysis (TDA) and persistent homology to achieve the same goal [ 8 , 9 ].…”