Nonlinear Time Series Analysis: P. Grassberger, John von Neumann Institute for Computing, Juelich, Germany
This will be a general introduction, with emphasis on biomedical applications.

After an introduction where the two paradigms of stochasticity and deterministic chaos are opposed, and several physiological examples are sketched, I'll start the more technical part by dicsussing time delay embeddings and choices of parameters for them.

A first application will deal with noise reduction and signal separation based on the geometry of embeddings. Fetal heart beat extraction from a univariant ECG signal is discussed as a special case.

We then discuss classical invariants (metric entropy, attractor dimension, Lyapunov exponents) and argue why using them as indicators for chaotic determinism is not very useful. The same should be true also for alternatives like false nearest neighbors or forecasting errors. In contrast we shall argue that strict determinism is not needed for the arsenal of nonlinear time series analysis to be useful. In contrast, I shall present evidence that effective "attractor" dimensions can be useful for predicting epileptic seizures and localizing epileptic foci.

Finally we shall discuss various methods to study interdependencies between different time series. This includes cross correlation and coherence, mutual information, phase synchronization, and other interdependence measures. We shall discuss their usefulness in EEG analysis, in particular for epilepsy patients. Among these measures, of particular interest are asymmetric measures because they could, independent of time delays, indicate causal connections. Again this is illustrated with epileptic EEGs.