Fig. 4: Topography and functional specialization of randomly sampled synergistic subsets in the brain.

Data in panels a and b was derived from a random sample of 100,000 synergistic 10-node subsets (HCP data). a Drawing random sub-samples of 500 subsets, we computed their Jaccard similarity, capturing the number of nodes in common between each subset pair. The similarity matrix was clustered using the kmeans algorithm, iterating between 2 and 30 clusters, with 10,000 repetitions. Optimal cluster quality was determined using the ‘silhouette’ criterion on the resulting cluster assignments. Random samples consistently yielded around 9–11 optimal clusters, with one example (10 clusters) shown in this panel. A Jaccard similarity of 0.25 corresponds to two subsets having 4 out of 10 nodes in common. b Frequency of individual node participation across 100,000 synergistic subsets, displayed on a surface rendering of the cerebral cortex indicating the boundaries of the 200 nodes used for constructing the FC matrix. c Each of the 200 nodes is affiliated with one of 7 canonical functional systems⁶⁰. Frequency of participation of individual nodes in synergistic subsets (negative O-information, subset size ranging from 3 to 15 nodes) is aggregated (averaged) for each functional system. The plot displays the ratio of empirical frequency over the expected frequency if nodes were selected by chance. A ratio > 1 or < 1 indicates that the system is over-represented or under-represented, respectively, in synergistic subsets. Sample sizes identical to those used in Fig. 4a.