Lectures
Time series analysis (including applications to electrophysiological signals)
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”
Updated slides of the lectures will be available soon (and potentially on request).
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
[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