Dynamics of time series

The focus of this project is to develop and adapt computational and data driven methods from dynamical systems theory to time series analysis. Central research questions are:

  • How can we identify whether data has been produced by a chaotic but discrete or a random physical system or a combination of the two?
  • What are good observables for attractor reconstruction, model approximation and prediction? What knowledge of the dynamics and/or application allows the approximation method to increase approximation accuracy, computational speed?
  • Which computational methods can be applied to neurophysiological time series to reveal novel characteristics of the underlying dynamical system? Are these (easily) interpretable within the context of the application and?
  • What are their limitations and drawbacks? How can the computational method be adapted to overcome them?

I have addressed these questions within the framework of the competitive research grant Forschungspreis 2015 I was awarded. The project was interdisciplinary with the group of Neurologist Prof. C. Reinsberger, focusing on neurophysiological data in the context of Epilepsy, motor control and ageing.

The aim was to approximate functional connectivity networks of human subjects from neural time-series data (EEG). This goal I pursued by employing and adapting data driven and dimension reduction methods (dynamic mode decomposition based on the Koopman operator). Additionally attractor reconstruction, recurrence analysis, and clustering methods were also explored.
These methods (programmed in MATLAB and python3) I then utilised to extract computational markers (neural maps) which indicated brain network differences between patients with and without epilepsy [1]. Moreover, I expanded the collaboration with the Institute of Sports Medicine to detect age-related [2] and expertise-related differences [3] within the sensorimotor brain networks obtained from EEG data of patients performing visuo-motor tasks.

[1] K. Mora, M. Dellnitz, S. Vieluf, N. Tanaka, M. Hilbert, S. Stufflebeam, C. Reinsberger
Dynamic mode decomposition of normal resting state EEG: an approach to dynamical systems identifying characteristics of temporal lobe epilepsy
(in preparation)

[2] S. Vieluf, K. Mora, C. Gölz, E. Reuter, B. Godde, M. Dellnitz, C. Reinsberger, C. Voelcker-Rehage
Age- and expertise related differences of sensorimotor network dynamics during force control
(Journal, ResearchGate)

[3] C. Gölz, C. Voelcker-Rehage, K. Mora, E. Reuter, B. Godde, M. Dellnitz, C. Reinsberger, S. Vieluf
Improved neuromuscular control manifests in expertise-related differences in force output and brain network dynamics
(Journal, ReseachGate)

aperiodikDynamics of time series