Teaching & Dissemination

Introduction to time series analysis

Univariate: Measures for individual time series

      - Linear time series analysis: Autocorrelation, Fourier Spectrum, Wavelet Analysis

      - Non-linear time series analysis: Lyapunov Exponent, Dimension, Entropy

Bivariate: Measures for two time series

       - Measures of synchronization for continuous data (e.g., EEG):

        Cross correlation, Coherence, Mutual Information, Phase Synchronization, Nonlinear Interdependence

- Measures of directionality: Granger Causality, Transfer Entropy

- Measures of synchronization for discrete data (e.g., spike trains):

         Victor-Purpura distance, van Rossum distance, Event Synchronization, ISI-Distance, SPIKE-Distance

- Measure of directionality for discrete data: SPIKE-Order

Applications to electrophysiological signals (in particular single-unit data and EEG from epilepsy patients)

Epilepsy – “Window to the human brain”

First lecture    [PDF]

Introduction to time series analysis

Introduction to epilepsy & epileptic seizure prediction

Data acquisition

Dynamical systems

Second lecture   [PDF]

Univariate measures I

Linear measures:

Autocorrelation, Fourier Spectrum, Wavelet Analysis

Non-linear measures:

Introduction to nonlinear dynamics

State space reconstruction

Lyapunov Exponent

Third lecture   [PDF]

Univariate measures I

Non-linear measures:

Dimensions

[Excursion: Fractals]

Entropy

Relationship among different measures

Fourth lecture [PDF]

Measures of synchronization for continuous data:

Cross Correlation, Coherence

Mutual Information

Phase Synchronization

Nonlinear Interdependence

Measures of directionality:

Granger Causality

Transfer Entropy

Fifth lecture    [PDF]

Measures of synchronization for discrete data:

Victor-Purpura Distance

van Rossum Distance

Event Synchronization

ISI-Distance

SPIKE-Distance

Sixth lecture      [PDF]

Directional measure SPIKE-order

Application to Epileptic seizure prediction:

Predictive performance of measures of continuous synchronization

The method of measure profile surrogates