[01174] Hypernetworks and their dynamics in theory and applications
Session Time & Room : 5D (Aug.25, 15:30-17:10) @G704
Type : Proposal of Minisymposium
Abstract : Collective dynamics of interacting units are prevalent in nature and engineering, whether it is neurons in the brain or opinion building in social networks. Recently, there has been tremendous interest in simultaneous interactions between three or more units, so-called higher-order interactions. The drive comes from various disciplines, for example ecology, where simultaneous competition for resources of multiple species causes nonstationary fluctuations of species abundancies. Such advances suggest to model the underlying structures by hypernetworks represented by hypergraphs.
This minisymposium displays recent models in real-world applications and theoretical studies on hypernetwork dynamics to highlight development and connect experts from both communities.
Organizer(s) : Christian Bick, Sören von der Gracht
01174 (1/1) : 5D @G704 [Chair: Sören von der Gracht]
[04246] Bridging between higher-order mechanisms and phenomena
Format : Talk at Waseda University
Author(s) :
Giovanni Petri (CENTAI)
Abstract : Complex networks have become the main paradigm for modelling the dynamics of complex interacting systems.
However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by higher-order interactions involving groups of three or more units.
Higher-order structures, such as hypergraphs and simplicial complexes, are therefore a better tool to map the multilayered real organization of many social, biological and man-made systems. At the same time, higher-order observables, typically topological or information-theoretic in nature and often sharing the same simplicial language, have been gathering attention for their capacity to capture properties of complex systems that are invisible to standard statistical descriptions. This had led to a certain confusion between these two facets, mechanisms on one side, phenomena on the other.
Here, using recent examples from both dynamical models and neuroimaging analysis, I highlight collective behaviours induced by higher-order interactions, the difficulty in linking data and models through recent advances in topological data analysis and higher-order information theory, and finally outline key open questions for the physics of higher-order complex systems.
[03667] Emergent hypernetworks in weakly coupled oscillators
Format : Talk at Waseda University
Author(s) :
Eddie Nijholt (Imperial College London)
Jorge Luis Ocampo-Espindola (Saint Louis University)
Deniz Eroglu (Kadir Has University)
István Kiss (Saint Louis University)
Tiago Pereira (Universidade de São Paulo)
Abstract : Networks of weakly coupled oscillators play a profound role in our understanding of complex systems. Studies on model reconstruction from data show the emergence of hyper-connections corresponding to triplet and higher-order interactions among oscillators, even though such models were originally defined as networks with only pairwise interactions. We show that hypernetworks can spontaneously appear in the presence of pairwise, albeit nonlinear, coupling given certain frequency resonance conditions. The conceptual explanation is that model reconstruction finds the so-called normal form of the system instead, which allows us to predict the emergent hypernetwork in terms of appearing and forbidden motifs. These results are moreover demonstrated in experiments with electrochemical oscillators. This is joint work with Jorge Luis Ocampo-Espindola, Deniz Eroglu, István Z. Kiss and Tiago Pereira.
[04161] Do higher-order interactions promote coexistence in diverse ecological communities?
Format : Talk at Waseda University
Author(s) :
Theo L Gibbs (Princeton University)
Gabriel Gellner (University of Guelph)
Simon Levin (Princeton University)
Kevin McCann (University of Guelph)
Alan Hastings (UC Davis)
Jonathan Levine (Princeton University)
Abstract : Most ecological models assume that species interactions operate only between pairs of species. In a diverse community, however, higher-order interactions can emerge, in which two or more species jointly impact the growth of a focal species. In this talk, I will discuss two ways that higher-order interactions affect species coexistence. Randomly-sampled higher-order interactions do not promote coexistence, but additional constraints on the higher-order interactions can reverse exclusions caused by pairwise interactions.
[04389] Hypernetworks: cluster synchronization is a higher order effect
Format : Talk at Waseda University
Author(s) :
Bob Rink (Vrije Universiteit Amsterdam)
Eddie Nijholt (Imperial College London)
Sören von der Gracht (Paderborn University)
Abstract : Many networked systems are governed by non-pairwise interactions that can be encoded by means of a hypernetwork. Here, we define dynamical systems on hypernetworks, and we explain how to classify robust cluster synchronization patterns by finding balanced partitions. We show that synchronization is determined by polynomial systems of high order. Hence, unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order, nonlinear effect. We show how this generates remarkable synchrony breaking bifurcations.
