An Iterative Information-Theoretic Approach to the Detection of Structures in Complex Systems

Systems that exhibit complex behaviors often contain inherent dynamical structures which evolve over time in a coordinated way. In this paper, we present a methodology based on the Relevance Index method aimed at revealing the dynamical structures hidden in complex systems. The method iterates two basic steps: detection of relevant variable sets based on the computation of the Relevance Index, and application of a sieving algorithm, which refines the results. This approach is able to highlight the organization of a complex system into sets of variables, which interact with one another at different hierarchical levels, detected, in turn, in the different iterations of the sieve. The method can be applied directly to systems composed of a small number of variables, whereas it requires the help of a custom metaheuristic in case of systems with larger dimensions. We have evaluated the potential of the method by applying it to three case studies: synthetic data generated by a nonlinear stochastic dynamical system, a small-sized and well-known system modeling a catalytic reaction, and a larger one, which describes the interactions within a social community, that requires the use of the metaheuristic. The experiments we made to validate the method produced interesting results, effectively uncovering hidden details of the systems to which it was applied.