Colloquium Mathematics - Dr. M.Jozsa

Title: Relationship between Granger non-causality and network graphs of state-space representations

Abstract:
In this seminar, we study the relationship between the network graph of complex stochastic dynamical systems and the statistical properties of their observed behavior. The systems in question are from the class of linear time invariant state-space (LTI-SS) representations and the class of general bilinear state-space (GB-SS) representations of stationary stochastic processes.

First, we show that LTI-SS and GB-SS representations with certain network graphs induce a series of causality properties in their output processes. Conversely, if a process has these causality properties, it guarantees the existence of the representations above. These results suggest methods to reconstruct certain connectivity structures of state-space systems, a problem that arises in several domains such as systems biology and neuroscience. We will cover the challenges and the advantages of the suggested methods in practice.