Higher-order structure is more complex than current measures and models - Nicholas Landry скачать в хорошем качестве

Higher-order structure is more complex than current measures and models - Nicholas Landry

Modeling heterogeneous contact patterns between individuals as a pairwise network, where all interactions occur between two individuals, has yielded valuable insights into the structure and the dynamical behavior of complex systems. Higher-order networks relax this pairwise assumption and represent group interactions of arbitrary size, which can more closely represent the rich structure and dynamics of empirical systems. In contrast to pairwise networks, interactions in higher-order networks can overlap, differ in size, and include one another. We show that there are critical limitations in the measurement and modeling of higher-order networks. First, although researchers often assume that the structure of a higher-order system is consistent across all scales of interaction, connection patterns of individuals or entities in empirical systems are often stratified by interaction size. We address this limitation by introducing an approach for filtering higher-order datasets. Second, traditional modeling approaches to higher-order networks tend to either not consider inclusion at all (e.g., hypergraph models) or explicitly assume perfect and complete inclusion (e.g., simplicial complex models). We show that, contrary to current modeling practice, empirically observed systems rarely lie at either end of this spectrum and that generative models fitted to empirical datasets rarely capture their inclusion structure. Nicholas Landry is the TGIR Postdoctoral Research Fellow at the University of Vermont. His research expertise is broadly the study of dynamics on complex systems, especially the spread of contagion on interaction networks involving group (higher-order) interactions. This seminar is part of the Network Seminar series at LPI Paris (https://interactiondatalab.com/networ....