Lecture
This lecture explores the concept of higher-order interactions in large-scale brain networks beyond pairwise interactions, using simplicial complexes to model social contagion and formalism. Examples include collaboration, gene-gene interactions, and neuronal interactions. The lecture delves into constructing simplicial complexes from data, distribution of k-simplices, and studying the human brain's structural connectome. It also covers information theory for higher-order interdependencies and the use of persistent homology in analyzing multivariate time series. The framework is tested on coupled map lattices, fMRI data, financial time-series, and infectious diseases data, showing the robustness of distinguishing different dynamical regimes.