Individual variability in state-space relationships.
Subject-specific relationships between resting (), attention (), and memory () states shown for a single subject (upper row) and for the entire set of subjects (lower row). (a) Subject-specific brain networks can each be described by a state-space of network couplings, quantified by versus , that is analogous to the state space shown in Figure 2 for the representative brain network. Each subject can then be compactly described by a triad of points, one each for resting (circular marker), attention (square marker), and memory (triangular marker) states, that marks the distribution averages and for each cognitive state. (b) The separation between two states can be quantified by the angular separation between distribution averages, with . (c) To isolate the angular separation between states, we perform a remapping of the state space in which we represent each individual by a triangle whose vertices are defined by cyclical permutations of . Each vertex is visually indicated by the superposition of markers that denote the two cognitive states related by (e.g. is denoted by the superposition of a circular () and square () marker). This remapping reveals a high degree of inter-subject consistency in the relative separation between states, as noted by the clusters of markers of a given type and the highly overlapping triangles linking these clusters. (d) Subjects can be grouped according to the rank order of angular separations. This method naturally isolates one primary group of subjects who show the smallest separation between attention and memory states. The subject shown in the upper row falls into this primary group, as indicated by the proximity of (superposition of triangular and square markers) to the vertical dotted line marking . The remaining two secondary groups show the smallest separation between rest and memory ( closest to ) and between attention and memory ( closest to ).