Bootstrap ratio maps for two PLS analyses comparing eyes-closed and eyes-open conditions.

<p>Top row: the dependent variable in the first analysis is the shape parameter and bootstrap ratios indicate channels at which values are greater in the eyes-closed versus the eyes-open condition. Bottom row: the dependent variable in the second analysis is the scale parameter and bootstrap ratios indicate channels at which values are greater in the eyes-open versus the eyes-closed condition.</p

Scenario 2: causality and phase synchronization.

<p>Relations between the reconstructed causality and phase-related effects in the case where the phase shift between the driver and response is : (A) measure of spectral Granger causality as a function of frequency; (B) transfer entropy as a function of the time lag ; (C) phase-locking index and (D) phase shift as functions of frequency.</p

Empirical probability distributions.

<p>Empirical probability distributions for the inter-departure time for all subjects at one representative channel (Cz) and one representative frequency (15 Hz). Fitted Gamma density functions are displayed in blue.</p

Processing pipeline.

<p>The electroencephalogram (<b>A</b>) is transformed into the time-frequency domain (<b>B</b>) using complex wavelets. Local minima in the scalogram (<b>B</b>, red vertical lines) are identified and marked as message departures. The delay between successive departures is calculated in terms of digitization intervals (<b>C</b>). The empirical probability distribution of is fitted using the two-parameter Gamma distribution function (<b>D</b>).</p

An Erlang-type service facility.

<p>The server is comprised of stages/stations arranged in series, each with exponentially distributed service times with rate . The total time to traverse all stages has a Gamma distribution with shape parameter and scale parameter . In the context of brain function, the server may represent a population of neurons, while the service stages may represent the sequence of steps required to process a unit of information, such as the diffusion of vesicles at a group synapses.</p

Group means for the maximum likelihood estimates of the Gamma distribution scale parameter .

<p>Group means are displayed separately for eyes-closed (top row) and eyes-open (bottom row) conditions, and frequencies from 5 to 30 Hz.</p

Group means for the maximum likelihood estimates of the Gamma distribution shape parameter .

<p>Group means are displayed separately for eyes-closed (top row) and eyes-open (bottom row) conditions, and frequencies from 5 to 30 Hz.</p

Fits for the Gamma and Weibull distributions.

<p>Histograms for the inter-departure time are shown for three subjects (rows) and all frequencies (columns), at one representative channel. Fitted density functions for the Gamma (blue) and Weibull (red) distributions are overlayed.</p

Influence of time delay in coupling.

<p>(A) Standard Granger causality; (B) spectral causality; (C) transfer entropy as functions of the observed time diffrence at 10 Hz; and (D) phase difference at 10 Hz as a function of the time delay in coupling, given that the strength of coupling was unchanged.</p

ECoG data: causality and phase synchronization.

<p>(A) Estimated spectral causality; (B) transfer entropy; (C) phase-locking index; and (D) phase differences, computed using local field potentials recorded from a pair of ECoG electrodes. Solid lines represent the mean of statistics under investigation, averaged across trials. The shaded area represents the variability (- and -quantiles) of the corresponding statistics based on surrogate data.</p