Fig. 1
From: Symmetry breaking organizes the brain’s resting state manifold
Structured flows on manifolds as the focus of resting state characterization. For the structure of the connectivity of the dynamical system, we consider the spectrum defined by the two symmetrical limit cases: a fully disconnected network, and a network where the external input dominates the activity at each node. Driven by noise, the disconnected system exhibits fully statistical, high-dimensional dynamics - it explores the whole state space in an equidirectional manner. On the other hand, the dynamics of the strongly connected system are equally high-dimensional as the system is constrained by the high external input to a subspace which it explores again equidirectionally driven by the sum of the noisy network inputs. The dynamics of the sparsely connected system lead to an object in between—a low-dimensional attractive manifold with an associated flow (SFM). It is this object we wish to put in the center of interest and characterize. While the SFM object remains the same, connections are made to data of various modalities with the help of suitable data features.
