NIC Series Volume 21:   Measuring Synchronization in Model Systems and Electroencephalographic Time Series from Epilepsy Patients Thomas Kreuz   ISBN 3-00-012373-3 February 2004, 138 pages   PDF

The main aim of this dissertation is the comparative investigation of different measures of synchronization derived from various approaches and concepts. These include both measures for estimating the degree of dependence between two time series as well as measures which quantify the directionality of this dependence. The first group comprises the linear cross correlation, mutual information, six different indices for phase synchronization (based either on the Hilbert or on the wavelet transform) as well as symmetrized variants of two nonlinear interdependence measures and of event synchronization. The anti-symmetrized variants of the last three measures form the group of measures of directionality.

In the first part of this dissertation the symmetric measures are tested in a controlled setting by means of various model systems. Using the coupling strength as a first control parameter it is investigated to which extent the different measures are able to distinguish between different degrees of dependence. Furthermore, the robustness of the measures against external noise is estimated by varying the signal-to-noise ratio as the second control parameter.

Subsequently, all measures are employed to analyze electroencephalographic recordings from epilepsy patients. This application part consists of two single studies. First a comprehensive comparison on the predictability of epileptic seizures is carried out. Object of investigation is the capability of the different measures to reliably distinguish between the intervals preceding epileptic seizures and the intervals far away from any seizure activity. Already in this study a great deal of attention is paid to the statistical validation of seizure predictions. This issue is particularly addressed in the last part of this dissertation in which the method of measure profile surrogates is introduced as an appropriate tool to distinguish between measures and algorithms unsuited for the prediction of epileptic seizures, and more promising approaches. Two of the measures of synchronization are used to illustrate this new approach.