Collective dynamics behind success.

Understanding the collective dynamics behind the success of ideas, products, behaviors, and social actors is critical for decision-making across diverse contexts, including hiring, funding, career choices, and the design of interventions for social change. Methodological advances and the increasing availability of big data now allow for a broader and deeper understanding of the key facets of success. Recent studies unveil regularities beneath the collective dynamics of success, pinpoint underlying mechanisms, and even enable predictions of success across diverse domains, including science, technology, business, and the arts.

Higher-order connectomics of human brain function reveals local topological signatures of task decoding, individual identification, and behavior.

Traditional models of human brain activity often represent it as a network of pairwise interactions between brain regions. Going beyond this limitation, recent approaches have been proposed to infer higher-order interactions from temporal brain signals involving three or more regions. However, to this day it remains unclear whether methods based on inferred higher-order interactions outperform traditional pairwise ones for the analysis of fMRI data.

Deeper but smaller: Higher-order interactions increase linear stability but shrink basins.

A key challenge of nonlinear dynamics and network science is to understand how higher-order interactions influence collective dynamics. Although many studies have approached this question through linear stability analysis, less is known about how higher-order interactions shape the global organization of different states. Here, we shed light on this issue by analyzing the rich patterns supported by identical Kuramoto oscillators on hypergraphs.

Dynamical Fluctuations of Random Walks in Higher-Order Networks.

Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate how fluctuations of a dynamical quantity of a random walk exploring a higher-order network arise over time. In the quenched case, where the hypergraph structure is fixed, through large deviation theory we show that the appearance of rare events is hampered in nodes with many higher-order interactions, and promoted elsewhere.