The title of my research project is Cointegration and Phase Synchronization, and adresses the challenge of mathematically describing interactions in dynamical systems, especially synchronization of cells in physiological processes. The phenomenon of synchronization in dynamical systems is ubiquitous in naturally occurring events, such as communicating braincells, blood flow in organs, circadian rhythms, pacemakers, etc. Hence, synchronization is a universal natural phenomenon. The idea of my research is to modify the theory of cointegration to analyze biological systems. Cointegration have been used almost exclusively by econometricians, and previous attempts on applying cointegration analysis to biological systems have been without success. My contribution is to develop, from scratch, the required theory, necessary for realistic biological models. My supervisors are professor of Statistics Susanne Ditlevsen and professor of Econometrics Anders Rahbek. I am affiliated with the Dynamical Systems Interdisciplinary Network.
Abstract: We present cointegration analysis as a method to infer the network struc- ture of a linearly phase coupled oscillating system. By defining a class of oscillating systems with interacting phases, we derive a data generating process where we can specify the coupling structure of a network that resembles biological processes. In particular we study a network of Winfree oscillators, for which we present a statistical analysis of various simulated networks, where we conclude on the coupling structure: the direction of feedback in the phase processes and proportional coupling strength between individual components of the system. We show that we can correctly classify the network structure for such a system by cointegration analysis, for various types of coupling, including uni-/bi-directional and all-to-all coupling. Finally, we analyze a set of EEG recordings and discuss the current applicability of cointegration analysis in the field of neuroscience.
Upcoming and past presentations (click on link to view slides/posters):