27 research outputs found

### Spatial distributions of connectivity degree for the stable low-|Δθ| (left columns) and stable high-|Δθ| (middle columns) networks, and for the shifting-|Δθ| network that shifted its phase relations from low-|Δθ| in low-<i>q</i> (low-modularity) states to high-|Δθ| in high-<i>q</i> (high-modularity) states (right, highlighted columns), for representative frequencies (row pairs) and the five behavioral conditions (column triplets labeled A-E).

Left column for each condition. Spatial distributions of connectivity degree for the stable low-|Δθ| network that always maintained low-|Δθ| relations regardless of q. For each site (per frequency per condition per participant) its connectivity degree was computed as the number of sites with which it maintained stable low-|Δθ| relations minus the number expected by chance (assuming the site pairs constituting the stable low-|Δθ| network were randomly distributed); a large positive value indicates a “hub” status (substantially above-chance connectivity degree with the stable low-|Δθ| network) whereas a large negative value indicates an “out-of-network” status (substantially below-chance connectivity degree with the stable low-|Δθ| network). The topographic heatmaps show t-values (warmer colors for above-chance values and cooler colors for below-chance values) with the upper and lower limits corresponding to the Bonferroni-corrected two-tailed statistical significance at α = 0.05 (see the color bar at the upper-left corner). The same heatmaps with connectivity degrees indicated as proportions of deviations from the chance levels (rather than t-values) are shown in S1 Fig. As in Fig 5, the heatmaps are slightly different for high-q (upper rows) and low-q (lower rows) states because of the missing site pairs that dipped below median PCV in high-q or low-q states. Middle column for each condition. Spatial distributions of connectivity degree for the stable high-|Δθ| network that always maintained high-|Δθ| relations regardless of q. Right column for each condition. Spatial distributions of connectivity degree for the shifting-|Δθ| network that shifted their phase relations from low-|Δθ| in low-q (low-modularity) states to high-|Δθ| in high-q (high-modularity) states. Note that the shifting-|Δθ| network (high-|Δθ| in high-q states and low-|Δθ| in low-q states) exhibited a consistent spatial structure, characterized by bilateral anterior and posterior hubs regardless of frequency or condition (except at 10 Hz in the minimal-visual-input conditions, A-C).</p

### Representative connections in the stable low-|Δθ| (left columns), stable high-|Δθ| (middle columns), and shifting-|Δθ| (right, highlighted columns) networks, for representative frequencies (row pairs) and the five behavioral conditions (column triplets).

The lines represent site pairs with above median PCVs (per frequency per condition per participant) within each network (stable low-|Δθ|, stable high-|Δθ|, or shifting-|Δθ|), which we refer to as "connections," that were shared by at least half of the participants (N>12 for the three rest conditions and N>11 for the two nature video conditions). Short- (d = 0.5–1), medium- (d = 1–1.5), and long- (d = 1.5–2) distance connections are indicated with gray, black, and red lines, respectively. Left column for each condition. Representative connections in the stable low-|Δθ| network. As in Figs 5 and 7 the representative connections were slightly different for high-q (upper rows) and low-q (lower rows) states because of the missing site pairs that dipped below median PCV in high-q or low-q states. Middle column for each condition. Representative connections in the stable high-|Δθ| network. Right column for each condition (highlighted). Representative connections in the shifting-|Δθ| network, that shifted from low-|Δθ| in low-q states to high-|Δθ| in high-q states. Note the prevalence of anterior-posterior long-distance connections (red lines) in the shifting-|Δθ| network.</p

### Connectivity characteristics (distance, orientation, and region) of the stable low-|Δθ|, stable high-|Δθ|, and shifting-|Δθ| networks.

A. The prevalence of the short- (d = 0.5–1), medium- (d = 1–1.5), and long- (d = 1.5–2) distance connections (columns, also coded with line thickness) of the four types (within-anterior [red], within-posterior [blue], anterior-posterior [purple], and cross-hemisphere [green]) as a function of frequency for the stable low-|Δθ| network. The counts have been corrected to account for the differences in the available numbers of connections of different distances and types (see main text). With the correction, stochastic (e.g., phase-scrambled) data would generate overlapping curves within each panel. The row pairs correspond to the five behavioral conditions. As in Figs 5, 7 and 8, the patterns were slightly different for high-q (upper rows) and low-q (lower rows) states because of the missing site pairs that dipped below median PCV in high-q or low-q states. B. The prevalence of the short-, medium-, and long-distance connections (columns, also coded with line thickness) of the four types (color coded) as a function of frequency for the stable high-|Δθ| network. C. The prevalence of the short-, medium-, and long-distance connections (columns, also coded with line thickness) of the four types (color coded) as a function of frequency for the shifting-|Δθ| network. D. Average 2D orientations of short- (thin curves), medium- (medium-thick curves), and long- (thick curves) distance connections (relative to the anterior-posterior axis) with >45° indicating a horizontal bias, <45° indicating a vertical/longitudinal bias, and 45° indicating no orientation bias, for the stable low-|Δθ|, stable high-|Δθ|, and shifting-|Δθ| networks (columns). For all panels, the shadings around the lines represent the 95% confidence intervals. Note that the shifting-|Δθ| network was consistently dominated by anterior-posterior long-distance connections (the purple curves dominant in C, right column) that were longitudinally biased (the thick curves generally <45° in D, right column) for all frequencies and conditions, except in the alpha range in the minimal-visual-input conditions (the purple curves dip in C, right column, and the thick curves peak in D, right column, in the alpha range in the top three row pairs).</p

### Fig 3 -

Distributions of pairwise inter-site phase differences |Δθ| in high-q (top 5%) and low-q (bottom 5%) states for representative frequencies (color coded) for the five behavioral conditions (columns). Equivalent to the right panels in Fig 2, but the histograms (generated with 40 angular bins) have been averaged across participants, and are shown for representative frequencies (3–50 Hz, coded with cooler to warmer colors) and for the five behavioral conditions (columns). The shadings around the lines represent the 95% confidence intervals. Note that high-|Δθ| (>3π/4) relations were consistently elevated in high-q (high-modularity) states (upper row), whereas low-|Δθ| (q (low-modularity) states (lower row).</p

### Inter-site temporal power correlations (top row), average powers (middle row), and inter-site-pair correlations between inter-site power correlation and average power (bottom row) in high-<i>q</i> (red) and low-<i>q</i> (blue) states for long-distance connections (<i>d</i> = 1.5–2) in the stable low-|Δθ| (left columns), stable high-|Δθ| (middle columns), and shifting-|Δθ| (right columns) networks as a function of frequency for the five behavioral conditions (column triplets).

Top row. Inter-site temporal power correlations (in Fisher-z transformed Spearman’s r) in high-q (red) and low-q (blue) states, averaged separately for the three networks, plotted as a function of frequency. Higher temporal power correlations may suggest stronger long-distance neural interactions. Middle row. Powers averaged within each of the three networks in high-q and low-q states as a function of frequency. The unit is percentile rank (computed per frequency per site per condition per participant); although average powers tended to be higher in high-q states than in low-q states in all cases, the power elevations were modest as the maximum average power was only about 60th percentile. Bottom row. Inter-site-pair correlations between inter-site power correlation and average power in high-q and low-q states in the three networks as a function of frequency. The correlations were generally positive in high-q states indicating that the inter-site power correlations were higher for site pairs with higher average spectral powers in high-q states. The correlations hovered around zero in low-q states indicating that the inter-site power correlations were relatively independent of average power in low-q states. Only long-distance (d = 1.5–2) site pairs were included in this analysis as their interactions would unlikely reflect volume-conduction effects. We also did not impose the above-median PCV criterion for this analysis so that the site pairs included in the three networks were identical between low-q and high-q states. The shadings around the lines represent the 95% confidence intervals.</p

### Temporal distributions of <i>q</i> (maximized modularity in global phase relations) for representative frequencies (3–50 Hz) for the five behavioral conditions.

The y-axis is probability density (a.u.). Frequencies from 3 Hz to 50 Hz are coded with cooler to warmer colors. The shadings around the lines represent the 95% confidence intervals. Note that the q distributions are similar for all representative frequencies and across the five behavioral conditions.</p

### Spatial distributions of connectivity degree for the stable low-|Δθ| (left columns) and stable high-|Δθ| (middle columns) networks, and for the shifting-|Δθ| network that shifted its phase relations from low-|Δθ| in low-<i>q</i> (low-modularity) states to high-|Δθ| in high-<i>q</i> (high-modularity) states (right, highlighted columns), for representative frequencies (row pairs) and the five behavioral conditions (column triplets labeled A-E).

This is the same as Fig 7 except that connectivity degrees are indicated as proportions of deviations from the chance levels (rather than t-values). For instance, a value of 0.3 (or -0.3) would indicate that the corresponding connectivity degree was 30% more (or less) than expected by chance. See the color bar in the upper left corner. (TIF)</p

### Scatter plots showing the relationships between PCV (phase clustering value) and 3D inter-site distance for representative frequencies (rows) for the five behavioral conditions (columns).

Each point represents the PCV (computed across all time points, y-axis) for a pair of sites separated by a specific 3D distance (x-axis). Points are shown for all site pairs from all participants for the corresponding frequency (row) and behavioral condition (column). Although the distance is in an arbitrary unit, the distances between the majority of neighboring sites were less than d = 0.5 (M = 0.42, SD = 0.085) and d = 2 corresponded to the maximum distance (between two circumferential sites on opposite sides). In each panel, linear regression slopes are indicated for four equal intervals, d = 0–0.5, d = 0.5–1, d = 1–1.5, and d = 1.5–2. Note that PCV rapidly attenuated by the distance of d = 0.5 as the regression slopes were typically more than an order of magnitude steeper in the first interval than in any other intervals, suggesting that volume-conduction effects were largely confined within neighboring sites as previously reported for surface-Laplacian transformed EEG (see main text).</p

### The MATLAB code we used to run the standard community-detection algorithm [14, 21] to quantify phase modularity (at each time point per frequency per condition per participant) as the index <i>q</i> (maximized modularity; 0 ≤ <i>q</i> ≤ 1).

The MATLAB code we used to run the standard community-detection algorithm [14, 21] to quantify phase modularity (at each time point per frequency per condition per participant) as the index q (maximized modularity; 0 ≤ q ≤ 1).</p