Lectures


 

 

Time series analysis (including applications to electrophysiological signals)

 

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”

 

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