Fig. 2: Schematic overview of the method.

a Regions of interest (ROIs). Functional MRI BOLD signals were extracted from spherical ROIs based on the previously defined parcellation²⁷. We only kept 247 ROIs that had usable data from all subjects. Each ROI can be assigned to one of 13 putative functional systems. The brain figure was visualized by the BrainNet Viewer⁴² under the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). b An example of Pearson correlation coefficients calculated between regional BOLD time series over the course of the experiment. Each BOLD time series was divided into 10-TR (25 s) time windows, and consecutive time windows were placed every 2 TRs leading to 80% overlap between consecutive time windows. Pairwise Pearson correlation coefficients were calculated between ROI time series in each time window. c An example of edge strength over time. In each time window, there were 247*(247 − 1)/2 edges. d Nonnegative matrix factorization (NMF). In each time window, the matrix of edge strengths was unfolded into one column. Then, edges from all time windows in all participants were concatenated into a single matrix. Each row in the full data matrix contained an edge (pairwise correlation coefficients between BOLD time series from two ROIs) and each column contained a time window (across all scans and participants). Correlation values in this matrix were strictly non-negative; the full data matrix was divided into two halves, with one half containing the positive pairwise correlation coefficients (zero if the correlation coefficient was negative) and one half containing the absolute values of negative pairwise correlation coefficients (zero if the correlation coefficient was positive). Thus, subgraphs were identified based on both the similarity of positive functional connectivity and the similarity of negative functional connectivity together. Then, NMF was applied to decompose the concatenated matrix into a matrix W, which encoded the strengths of edges for each subgraph, and a matrix H, which encoded the time-dependent expression of each subgraph. For example, the strength of edges of the fourth subgraph (the fourth column in the matrix W) can be folded into a squared matrix, reflecting the edge strength between every pair of ROIs.