Density threshold in synthetic networks and in brain networks.

<p>(<b>a</b>–<b>b</b>) Blue curves show the trends of the connection density threshold <i>ρ</i> for one-hundred generated small-world <i>p</i>_<i>ws</i> = 0.1 and scale-free <i>m</i>_<i>ba</i> = 9 networks along different sizes <i>n</i>. Blue squares spot out the average <i>ρ</i> values returned by the maximization of <i>J</i>. The black line shows the fit <i>ρ</i> = <i>c</i>/(<i>n</i> − 1) to the data, with <i>c</i> = 3.258 for small-world networks and <i>c</i> = 3.215 for scale-free networks (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005305#pcbi.1005305.s009" target="_blank">S1 Table</a>). The background color codes for the average value of the quality function <i>J</i>. Insets indicate that the optimal average node degree, corresponding to the density that maximizes <i>J</i>, converges to <i>k</i> = 3 for large network sizes (<i>n</i> = 16834). (<b>c</b>) Optimal density values maximizing group-averaged <i>J</i> profiles for different brain networks. Imaging connectomes come from previously published studies (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005305#pcbi.1005305.t001" target="_blank">Table 1</a>). The fit <i>ρ</i> = <i>c</i>/(<i>n</i> − 1) to the pooled data gives <i>c</i> = 3.06 (adjusted <i>R</i>² = 0.994). The inset shows a sharp distribution for the corresponding average node degree, with a mode <i>k</i> = 3. (<b>d</b>–<b>e</b>) Average <i>J</i> profile (black curves) for simulated small-world and scale-free networks as a function of the network size (<i>n</i>) and of the density (<i>ρ</i>). <i>J</i> values are represented in normalized units (n.u.), having scaled them by the global maximum obtained for <i>n</i> = 1024. Blue and red curves show respectively the profiles of global- (<i>E</i>_<i>g</i>) and local-efficiency (<i>E</i>_<i>l</i>). (<b>f</b>) Group-averaged <i>J</i> profile for fMRI connectomes (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005305#pcbi.1005305.t001" target="_blank">Table 1</a>). The grey dashed line indicates the actual density maximizing <i>J</i>, i.e., <i>ρ</i> = 0.035, corresponding to an average node degree <i>k</i> = 3.115. The graph illustrates the brain network of a representative healthy subject (lateral view, frontal lobe on the left <i>L</i>_<i>x</i>).</p

Statistical comparison of brain network distances across filtering methods.

<p>Bar plots show the medians of distance between brain network properties of samples in the healthy and diseased group. Vertical bars denote lower and upper quartiles. Medians and quartiles are in normalized units (n.u.) for the sake of representation. Overall, the choice of the filtering method significantly affects distances between samples (Kruskalwallis tests, <i>P</i> < 0.01, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005305#pcbi.1005305.s011" target="_blank">S3 Table</a>). For all graph quantities, ECO tends to give significantly larger distances as compared to other methods (Tukey-Kramer post hoc tests, <i>P</i> < 0.05); in some isolated cases, no significant improvements are reported (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005305#pcbi.1005305.s012" target="_blank">S4 Table</a>). By construction, MST gives null distances for local-efficiency as there are no triangles in tree-like networks.</p

Size of the largest component in brain networks filtered with ECO and statistical comparison between groups.

<p>The size of the largest component is given as a percentage of total nodes. Blue lines stand for median values of the healthy group; red lines are median values of the diseased group. Vertical bars denote lower and upper quartiles. The dashed gray line shows the expected size for the giant component in a Erdos-Renyi random graph with <i>p</i> = 1/<i>n</i>). No statistical between-group differences for any threshold value were reported (Wilcoxon ranks-sum tests, <i>P</i> ≥ 0.01).</p

Statistical comparison of <i>J</i> values and distances across different thresholding methods.

<p>Panel a) White squares show the medians of the <i>J</i> values of all the subjects in the two groups. Vertical bars denote the 5<i>th</i> and 95<i>th</i> percentiles. Panel b) Grey bars show the medians of the distances between samples (individuals) of different brain states. Vertical bars denote lower and upper quartiles. The choice of the filtering method significantly affects the <i>J</i> values and the respective distances between samples (Kruskalwallis tests, <i>P</i> < 0.01 for both <i>J</i> values and related distances, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005305#pcbi.1005305.s011" target="_blank">S3 Table</a>). Overall, ECO gives significantly larger values as compared to the other methods (Tukey-Kramer post hoc tests, <i>P</i> < 0.05); in some isolated cases no significant improvements are reported (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005305#pcbi.1005305.s012" target="_blank">S4 Table</a>).</p

Experimental details and network characteristics of imaging connectomes.

<p>Experimental details and network characteristics of imaging connectomes.</p

Experimental and simulation setups.

<p>(A) Apparatus and experimental setting of the double video system and dual-EEG recording <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036414#pone.0036414-Dumas1" target="_blank">[27]</a>. (B) Right and Top views of the pair of virtual brains. Each weighted network represents the 90 brain regions and their average anatomical connectivity. Arrows indicate the directed coupling from the motor to visual.</p

Example of simulation with variation of the C_intra control parameter over time.

<p>(A) Timecourses of all ROIs instantaneous frequency. (B) Related timecourse of the C_intra parameter.</p

Influence of the global anatomical connectivity strength on intra-brain synchronization.

<p>Average PLV across all pairs of electrodes inside each simulated subject helmet for the gamma (A) and alpha (B) frequency bands. The decrease of PLV after C_intra = 0.7 for the alpha band seems caused by fluctuations of the mean low-frequency rhythm peak at strong anatomical coupling.</p

Procedure Flowchart illustrating the different steps of the simulations and their comparisons with the real EEG data.

<p>Procedure Flowchart illustrating the different steps of the simulations and their comparisons with the real EEG data.</p

Real and simulated functional data.

<p>PLV matrices for real (A) and simulated (B) data and related histogram (C). h-PLV matrix for real (D) and simulated (E) data and related histogram (F). PLV and h-PLV are computed for the gamma band and averaged across either the 9 pairs of real subjects during resting state condition or 9 pairs of simulated subjects with C_intra = 0.49 and C_inter = 0. It can be seen from this example that PLV and h-PLV exhibit different distributions. Notice that the difference of the dynamics between the partners gives an asymmetry in the h-PLV matrix.</p