Teaching & Dissemination
Lecture series: Time series analysis
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