Higher-Order Systems

Higher-order systems as a modelling framework.- Graphs, simplicial complexes and hypergraphs: Spectral theory and topology.- Random Simplicial Complexes: Models and Phenomena.- Topological Data Analysis.- Flow-based Community Detection in Hypergraphs.- Pattern formation on hypergraphs.- Non-pairwise interaction in oscillatory ensembles: From theory to data analysis.- From symmetric networks to heteroclinic dynamics and chaos in coupled phase oscillators with higher-order interactions.- Explosive synchronization and multistability in large systems of Kuramoto oscillators with higher-order interactions.- Multiorder Laplacian for Kuramoto dynamics with higher-order interactions.- The Master Stability Function for Synchronization in Simplicial Complexes.- Geometry, Topology and Simplicial Synchronization.- Signal processing on simplicial complexes.- Social contagion on higher order structures.- Consensus Dynamics and Opinion Formation on Hypergraphs.- Collective games on hypergraphs.- Topological Data Analysis of Spatial Systems.- Higher-order description of brain function.- Higher-Order Interactions in Biology: The Curious Case of Epistasis.