Title: Functional Dynamical Structures in Complex Systems: an Information-Theoretic Approach,
Abstract: Understanding the dynamical behavior of complex systems is of exceptional
relevance in everyday life, from biology to economy. In order to describe the
dynamical organization of complex systems, existing methods require the
knowledge of the network topology. By contrast, in this thesis we develop a new
method based on Information Theory which does not require any topological
knowledge. We introduce the Dynamical Cluster Index to detect those groups of
system elements which have strong mutual interactions, named as Relevant
Subsets. Among them, we identify those which exchange most information with the
rest of the system, thus being the most influential for its dynamics. In order
to detect such Functional Dynamical Structures, we introduce another
information theoretic measure, called D-index. The experimental results make us
confident that our method can be effectively used to study both artificial and
natural complex systems.