Bosiljka Tadić1,2
1 Department of Theoretical Physics, Jozef Stefan Institute, Ljubljana, Slovenia
2 Complexity Science Hub, Vienna, Austria
bosiljka.tadic [at] ijs.si
Abstract
Recent advances in the physics of complex systems aim at understanding the emergence of new features at a larger scale—the central idea of physical notion of complexity, linking the features of collective dynamical behaviors with higher-order interactions. Mapping the brain imaging data onto brain networks and revealing their detailed structures enables the application of these approaches in the study of complex brain functioning. Increasing evidence shows that connections between many brain regions play a role in specific brain processes and help describe pathways of neurodegeneration. In this context, studies highlight the importance of synchronization processes and the role of central brain regions (hubs).
In this lecture, we describe some representative examples that motivated our research. We then present more details of our results obtained by mapping human connectome data onto brain networks (Figure) and their higher-order structures described by simplicial complexes.
Furthermore, we present a phenomenological model of the phase synchronization processes simulated on the core network consisting of simplexes of all orders around eight brain hubs. Our results reveal partial synchronization patterns explain how the brain avoids pathological states of full synchronization. Co-evolving phases at groups of nodes (brain regions) result in multifractal fluctuations of the order parameter, which measures the degree of synchrony.
Keywords: human connectome, higher-order networks, synchronization, multifractality
Acknowledgement: Supported by the Slovenian Research Agency the Program P1-0044.