Fig. 5: Regional entropy, or membership diversity.

a Left: equation for Shannon entropy (“Methods”). Values are normalized [0, 1]. h_i = 0 if a node i belongs to a single network (is disjoint); h_i = 1 if a node belongs to all networks with equal strength (is maximally overlapping). Right: distribution of entropies for all regions. The peak at h = 0 corresponds to disjoint regions. The second peak at \(h \propto \log (2)\) corresponds to regions with membership values of 0.5 for two networks and 0 elsewhere. Error bars are 95% confidence intervals based on hierarchical bootstrap (“Methods”). b Spatial patterns of regional entropies rank-ordered (total of 542 regions) to facilitate comparisons across conditions (BOLD, Ca²⁺_slow, and Ca²⁺_fast). The non-rank-ordered version is shown in Supplementary Fig. 8a. Unimodal areas such as visual and somatomotor areas have low entropy (cool colors), whereas transmodal regions have high entropy (hot colors). c Entropy was positively (Pearson) correlated across modalities (variability obtained based on hierarchical bootstrapping; “Methods”). d Differences in entropy between conditions are quantified by subtracting each pair of conditions. A statistical test (paired permutation test, two-sided, p < 0.05, Holm–Bonferroni corrected) revealed BOLD > Ca²⁺ in most regions, except for some frontal areas where BOLD = Ca²⁺, and higher visual areas where BOLD < Ca²⁺ (left and middle). Ca²⁺_slow exhibited a large territory of regions with entropy <Ca²⁺_fast (right). Source data are provided as a Source Data file.