Coupling analysis of transient dynamics

ECGC – Ensemble Conditional Granger Causality

calculates time-resolved conditional Granger causality for ensemble data

ESCT – Ensemble Symbolic Coupling Traces

calculates time-resolved symbolic coupling traces for ensemble data

PESCT – Permutation Ensemble Symbolic Coupling Traces

calculates time-resolved symbolic coupling traces using a permutation approach for ensemble data

(for MATLAB^®)

General Notes

The ensemble approach provides a versatile method to extend coupling analysis tools for a time variant coupling analysis capable of dealing with nonstationary time series via significantly reducing the required window lenth for a windowed analysis. Here, three examples, the Ensemble Conditional Granger Causality (ECGC), the Ensemble Symbolic Coupling Traces (ESCT), and the Permutation Ensemble Symbolic Coupling Traces (PESCT), are presented. The EGCG-function returns a struct containing the results of the Granger causality (GC) test plus the results from the Granger-Sargent significance test. With activated graphic output the significant GC indices are shown via a colour-coded matrix (no ensemble) or via n*(n-1)/2 (n is the number of regarded variables) plots comparing the significant GC indices for two variables over time (activated ensemble approach). The ESCT and the PESCT return a plot showing the coupling strength and coupling effect (symmetric/diamteric) for each time-lag. Without the ensemble option a bar diagram is returned. With activated ensemble approach a colour-coded matrix shows the results for each time-lag and time point. For further information, please consider the references given further below and the MATLAB-functions themselves.

Usage

ecgc_res = ecgc(dat,maxlag,ensemble,silent,varargin)
esct_res = esct(dat,wlen,taurange,pval,ensemble,silent)
pesct_res = pesct(dat,wlen,tau,taurange,pval,ensemble,silent)

Example

% bivariate AR-model

len = 500; % # time points to be computed by the model 
N = 100; % # time points to be used in the analysis
M = 200; % ensemble size
dat = zeros(2,N,M); % data container
noise = randn(2,len,M); % white noise

for mm = 1:M % ensemble loop
    x = zeros(2,len);
    x(:,1:2) = randn(2,2);
    for ii = 3:len % time loop
        x(1,ii) = 0.3*x(1,ii-1) + 0.7*x(2,ii-1) + 0.01*noise(1,ii,mm);
        x(2,ii) = 0.3*x(2,ii-1) - 0.7*x(1,ii-2) + 0.01*noise(2,ii,mm);
    end
    dat(:,:,mm) = x(:,end-N+1:end);
end
 
ecgc_res = ecgc(dat,10,1,0,0.05);
esct_res = esct(dat,3,-10:10,0.05,1,0);
pesct_res = pesct(dat,4,1,-10:10,0.05,1,0);

References

• Mueller, A., Riedl, M., Penzel, T., Kurths, J., Wessel, N.: Kardiorespiratorische Koordination und Ensemble-Kopplungsspuren zur ereignisbasierten Charakterisierung kardiovaskulärer Interaktionen während des Schlafes, Somnologie, 18, 243–251, 2014.

• Mueller, A., Riedl, M., Penzel, T., Bonnemeier, H., Kurths, J., et al.: Coupling analysis of transient cardiovascular dynamics, Biomed. Tech., 58, 131–139, 2013.

• Seth, A. K.: A MATLAB toolbox for Granger causal connectivity analysis. J. Neurosci. Methods, 186, 262–273, 2010.

• Wessel, N., Suhrbier, A., Riedl, M., Marwan, N., Malberg, H., et al.: Detection of time-delayed interactions in biosignals using symbolic coupling traces, Europhys. Lett., 87, 10004, 2009.

Download

ecgc.m
esct.m
pesct.m

Author

Andreas Müller