Fig. 4
From: Symmetry breaking organizes the brain’s resting state manifold
Manifold subspaces and characteristic dynamics. (A) The edge-based dynamic functional connectivity \(dFC_e\) of a simulation of the model in the working point (top) shows the off-diagonal structure of similarity of the system’s activity across time. The edge time series (middle) shows the time evolution of the functional connectivity of the simulated BOLD signal between each of the node pairs and exhibits the characteristic co-activation events defined as time points with the root sum squared (RSS, bottom) crossing the threshold of 95th percentile. Dividing the edge-time series into 5 clusters (k-means, shown in the color bar under the dFC) has separated the event and non-event time points, and also differentiated the events based on their respective similarity. (B) The time intervals in \(\textbf{r}(t)\) corresponding to the 5 clusters were selected; in the first panel, the centroids of the time points of the individual clusters are marked with a cross in the projection to the first two principal components of the whole time series, following panels show the projection of the \(\textbf{r}(t)\) intervals of particular clusters. All time points are shown in aggregation as density plots. Cluster #2 captures the high-activity subspace, cluster #4 corresponds to the low-activity state, and the clusters #1, #3, and #5 capture the co-activation events. (C) Local trajectories in the manifold subspaces: the time series of the three example events (a, b, c, marked in panel A bottom) was projected to the first two components of PCA applied to each time segment individually. The red gradient denotes the dwell time of the system in the projected plane and shows a clear separation of the event subspace together with the rapid in- and out-transition. The smoothened trajectory marks the advance of the system through the event and out of it and is colored by the value of RSS (yellow at the peak of the event and blue at the beginning and the end). (D) The event trajectories on the manifold. The trajectory of the simulated BOLD signal is projected in the space defined by the first three PCA components with the events colored by the RSS value (yellow at the peak of the event).
