Resting-State Temporal Synchronization Networks Emerge from Connectivity Topology and Heterogeneity
Fig 3
Community structure of spatiotemporal synchronization patterns.
a) The temporal evolution of the synchronization matrix is represented in a n×n×T tensor T. The tensor can be factorized as a sum of K rank-one tensors, each one being an outer product of three vectors, ak, bk, ck, of dimension equal to n, n, and T, respectively (Equation 8). The network communities are contained in the vectors ak, the elements of which give the participation weight of each node (i.e., brain region) in the community k. The temporal activation sk(t) of each community k is related to ck and to the participation weights as: sk(t) = ck(t)Σjak(j). b) Detected community patterns (ak. akT) for the example session #1. c) Top: temporal activation strength of each community, for the scanning session #1 (same colors as in (b)). Bottom: temporal evolution of both the order parameter R(t) (left y-axis) and the total activation strength [S(t) = Σksk(t)] (right y-axis), for session #1. d-e) same as (b-c) but for session #7. f) Correlation matrix between all detected communities from all scanning sessions (top), re-arranged according to cluster membership. Bottom: corresponding dendrogram based on correlation coefficients.