Section: New Results

Network symmetries and functional modules in the brain

Participants : Vincenzo Nicosia, Miguel Valencia, Mario Chavez [Correspondant] , Albert Diaz-Guilera, Vito Latora.

We study the classical Kuramoto model in which the oscillators are associated to the nodes of a network and the interactions include a phase frustration, thus preventing full synchronization. The system organizes into a regime of remote synchronization where pairs of nodes with the same network symmetry are fully synchronized, despite their distance on the graph. We provide analytical arguments to explain this result and we show how the frustration parameter affects the distribution of phases. An application to brain networks suggests that anatomical symmetry plays a role in neural synchronization by determining correlated functional modules across distant locations.

Figure 7. a) Brain areas with similar and dissimilar phases of the frustrated Kuramoto model are colored and superimposed onto an anatomical image. b) Examples of functional data from one subject recorded at the brain areas indicated in panel a). Colors are the same as those used in the anatomical image. c) Functional correlation (normalised values) $Z$ between pairs of nodes as a function of their phase differences $\Delta \theta$ according to the simulated Kuramoto dynamics. The black solid curve corresponds to the average value over all the subjects, while the gray area covers the 5^th and the 95^th percentiles of the distribution. The dashed horizontal line indicates the threshold for statistical significant correlations ($p<0.05$, corrected for multiple comparisons).

Related publication: [19]