An Information Theoretic Approach to Detecting Relevant Subsets of Variables in Dynamical Systems.

Abstract

In this thesis we describe complex systems by means of dynamical models with the aim of studying the hierarchical self-organization of the systems. To achieve this goal we address the issue of identifying sets of variables, called "relevant subsets", which describe highly integrated modules that drive the system toward a sequence of meta-stable intermediate states. In order to find a measure for the interaction and the integration among variables, we exploit a fundamental property of the complex dynamical systems which was introduced by Kauffman. He stated that there is a continuous exchange of information among the system constituents and also between the environment and the system. On this basis, extending previous works on neural networks, an information-theoretic measure is introduced, i.e. the Dynamical Cluster Index, in order to identify good candidate relevant subsets. We show that the analysis of the different parts of the index is extremely useful to better characterize the nature of sub-systems which are identified by the detected relevant subsets. Several different application domains are investigate to test the effectiveness and the robustness of this measures. Finally, we study the influence that detected relevant subsets have on the system by focusing on the causal interactions among variables through the different dynamical states. For this purpose, we introduce the F-index which is an information theoretic measure based on the transfer entropy.