Higher-order interactions: what does it mean to be connected?
In a new perspective article out in «Nature Physics», an international team of scientists led by ISI Senior Research Scientist Giovanni Petri, and including Micah Murray, associate professor FBM, and Benedetta Franceschiello both of the Radiology Department CHUV-UNIL and CIBM Center for Biomedical Imaging, highlights modern evidence of collective behaviours depicted by higher-order interactions and outlines three key challenges for the physics of higher-order systems.
The first is understanding how rich and general is the phenomenology of dynamical processes. The second involves topological dynamical processes. By endowing groups with their own states, it becomes possible to define couplings between higher-order interactions of different dimensions and study how the states of groups of all sizes evolve in time. Finally, the third challenge refers to a crucial ingredient in modelling real systems: the reconstruction of higher-order interactions from incomplete and lower-order data, e.g. how can we reconstruct the group structure from observations of pairwise interactions.
"Network science helps us to better understand the evolution of the highly interconnected world in which we live, and complex networks have become the main paradigm for modelling the dynamics of interacting systems. Higher-order mathematical structures are therefore a better tool to map the real organization of many social, biological and man-made systems", says Micah Murray.
Read the article in Nature Physics