Reconstructing evolutionary modular networks from time series data

The behavior and dynamics of complex systems are in focus of many research fields. The complexity of such systems comes not only from the number of their elements but also from the unavoidable emergence of new properties of the system, which are not just a simple summation of the properties of its elements. The behavior of complex systems can be fitted with a number of well developed models, which, however, do not incorporate the modularity and the evolution of a system simultaneously. In this paper, we propose a generalized model that addresses this issue. In our model, the random cluster process in context of the finite set statistics is used to model the dynamics of the underlying process of the complex systems. In addition, we demonstrate how to reconstruct a sequence of Bayesian networks that reflect the evolution of probability dependencies between variables of the system.