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

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

Influence of coupling strength.

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

Scenario 2: time series and spectral power.

<p>Characteristics of the driver and response in the case of a negative phase difference () between them at Hz (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0053588#pone-0053588-g003" target="_blank">Fig. 3</a>): (A) simulated signals (two seconds of a randomly chosen realization); and (B) mean spectral density and cross power spectral density, averaged across realizations. The errorbars represent the standard error computed across realizations.</p

ECoG data: spectral power.

<p>Mean spectral density and cross power spectral density of two ECoG channels, averaged across trials. The errorbars represent the standard error computed across trials.</p

Scenario 1: causality and phase synchronization.

<p>Relations between the reconstructed causality and effects of phase-locking and phase differences in the case where there is no phase shift at the main frequency ( Hz): (A) measure of spectral Granger causality as a function of frequency; (B) transfer entropy as a function of the time lag between the past of one signal and the future of the other; (C) phase-locking index and (D) phase shift as functions of frequency.</p

Overlap of the MC and HC.

<p>A. Rendering of the MC and HC. B. Rendering of the overlap between the MC and HC. The two connectomes exhibit a statistically significant overlap (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003529#s3" target="_blank">Results</a>). The renderings were performed with BrainGL and a mean-shift edge bundling algorithm <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003529#pcbi.1003529-Bttger1" target="_blank">[52]</a>.</p

Rich club structure in the macaque and human brain.

<p>A. The normalized RCC suggests the presence of a rich club organization in both the human and macaque brains. For the unormalized curves see Fig. S3. The RCC obtained within the rich club regime (>1) were significantly higher than the ones obtained from random networks matched for node, edge and degree distribution (p<0.0001). B. Network and anatomical representation of the regions corresponding to the peak of the normalized RCC which is marked with a diamond in panel A (k = 56 for macaque and k = 55 for human). In the network representation, green and blue nodes represent rich club and non-rich club regions at level k respectively. Only connections involving at least one rich club region are depicted. The anatomical representation depicts the regions constituting the rich club on the inflated fiducials of both hemispheres of the brains of the two species. The spheres represent the centre of mass of the regions. Note the convergence of the rich club analysis to a highly overlapping set of regions in the two species. C. The observed overlap is significant within a range of the rich club regime. The significance was established by drawing randomly from a uniform distribution a number of regions from the MC and HC equal to the number of regions corresponding at each level k for the MC and HC separately. The procedure was repeated 10000 times and the overlap of these randomly drawn regions was computed forming a null distribution with which the original overlap values were compared.</p

Schematic depiction of the main points of the analysis.

<p>A. The RM was used in order to construct the connectivity matrices of the two species, i.e. the MC and HC (panel B). The resulting connectivity matrices have i = 82 rows and j = 82 columns. B. Example of the calculation of the HCS for region i = 1. The entries of row 1 from the MC and row 1 from HC were used, resulting in entry HCS_i = 1. The same procedure was used for all regions, resulting in a 1×82 vector HCS containing the HCS indexes of all the regions. C. Example of calculation of the HMIS for region i = 1. The MC and HC were used for the separate calculation of the matching index matrices MI_ij (one for each species separately). The HMIS index for region i = 1 is calculated from the entries of row 1 of the matching index matrices of the two species. The procedure is repeated for all regions, resulting in a 1×82 vector HMIS containing the HMIS indexes of all the regions. D. Toy networks demonstrating differences of the HCS and the HMIS. Given two hypothetical “brains” that form a network with 4 regions and 4 connections the HCS and HMIS indexes are calculated for brain region A. On the one hand, the HCS index is equal to 1 (perfect similarity), since region A in both networks is connected exactly to the same regions, i.e. nodes B, C and D. On the other hand, the HMIS index is −0.5, indicating a divergence of the connectivity similarity profiles of region A in networks/brains 1 and 2. These discrepancies arise from the “rewiring” of the connection marked with an arrow.</p