## Learning functional subgraph architecture of cognitive control processes.

(*A*) We measure fMRI BOLD signals from 262 functional regions of interest (234 cortical and subcortical brain areas parcellated by ([31]; *top*) and 28 cerebellar brain areas parcellated by ([32]; *bottom*) as 28 healthy adult human subjects perform Stroop and Navon cognitive control tasks. (*B*) We concatenate BOLD signal from 6 task blocks (corresponding to 30 seconds of BOLD activity, and comprising several trials) in each of 3 task conditions (fixation, low demand, high demand) for each of 2 tasks (Stroop and Navon). (*C*) Next, we calculate the Pearson correlation coefficient between each pair of regional BOLD signals to create an adjacency matrix for every experimental block. We encode this information in dynamic functional networks with brain regions as graph nodes and block-varying correlation as weighted graph edges. To assess the relative role of correlated (positively weighted edges) and anticorrelated (negatively weighted edges) functional interactions during cognitive control, we threshold each adjacency matrix at the zero edge weight and group positive edges and negative edges into separate adjacency matrices (see Materials and methods). (*D*) We concatenate all pairwise edges over task blocks and subjects, and we generate a single network configuration matrix for the entire study cohort (*left*). We apply non-negative matrix factorization (NMF)—a parts-based decomposition of the dynamic network—to the configuration matrix and cluster graph edges with co-varying weights into a matrix of subgraphs (*middle*) and a matrix of time-varying coefficients (*right*) that quantify the level of expression of each subgraph in each task block. We use a cross-validation parameter optimization procedure and identify 12 subgraphs specific to the cognitive control tasks (S2 Fig). (*E*) For each subgraph, we reconstitute its vector of edge weights into a fully-weighted symmetric adjacency matrix (*left*) and track its associated positive and negative expression coefficients over task blocks (*right*). Briefly, the positive and negative expression coefficients signify the likelihood that the subgraph edges represent correlations or anticorrelations for each moment in time (see Materials and methods). (*F*) We rank functional subgraphs in decreasing order (A-L) of the difference between positive and negative expression weight, averaged over task blocks and subjects. Bar height represents the mean difference over subjects and error bars represent standard error of the mean. Red bars correspond to subgraphs that are, on average, more positively expressed and blue bars correspond to subgraphs that are, on average, more negatively expressed.