Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session Z09: HigherOrder Interactions: The Next Frontier of Complex SystemsFocus Recordings Available

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Sponsoring Units: GSNP DCOMP Chair: Yuanzhao Zhang, Santa Fe Institute Room: McCormick Place W180 
Friday, March 18, 2022 11:30AM  12:06PM 
Z09.00001: Consensus dynamics and opinion formation on hypergraphs Invited Speaker: Renaud Lambiotte We investigate consensus dynamics on temporal hypergraphs that encode network systems with timedependent, multiway interactions. 
Friday, March 18, 2022 12:06PM  12:18PM 
Z09.00002: Cluster synchronization on hypergraphs Anastasiya Salova, Raissa M D'Souza Cluster synchronization is a type of synchronization in which different groups of nodes follow distinct trajectories. It can manifest in behaviors such as chimera states and remote synchronization with wide areas of applicability from neuroscience to power grid analysis. In contrast to the broadly analyzed case of cluster synchronization on dyadic networks, we study cluster synchronization on hypergraphs, where hyperedges correspond to higher order interactions. Importantly, we show that our analysis can not be reduced to analyzing dynamics on hypergraph projections onto dyadic networks. 
Friday, March 18, 2022 12:18PM  12:30PM 
Z09.00003: Hypergraph assortativity: A dynamical systems perspective Nicholas Landry, Juan G Restrepo The largest eigenvalue of the matrix describing a network's contact structure is often important in predicting the behavior of dynamical processes. We extend this notion to hypergraphs and motivate the importance of an analogous eigenvalue, the expansion eigenvalue, for hypergraph dynamical processes. Using a meanfield approach, we derive an approximation to the expansion eigenvalue and its associated eigenvector in terms of the degree sequence for uncorrelated hypergraphs. We introduce a generative model for hypergraphs that includes degree assortativity, and use a perturbation approach to derive an approximation to the expansion eigenvalue and its corresponding eigenvector for assortative hypergraphs. We validate our results with both synthetic and empirical datasets. We define the dynamical assortativity, a dynamically sensible definition of assortativity for uniform hypergraphs, and describe how reducing the dynamical assortativity of hypergraphs through preferential rewiring can extinguish epidemics. 
Friday, March 18, 2022 12:30PM  12:42PM 
Z09.00004: Higherorder components in hypergraphs JungHo Kim, K. I. Goh Most hypergraph studies have been focused on the interaction within a hyperedge but not on the interaction between hyperedges. We introduce sconnectivity in hypergraphs as the connectivity between two hyperedges sharing s common nodes and scomponent as the connected component only through s or higherorder connectivities. Such higherorder components are observed ubiquitously in realworld hypergraphs but lack in their degreepreserved randomized counterparts. To this end, we propose a novel random hypergraph model in which higherorder components substantially exist. The concept of the group consisting of randomly preassigned nodes is introduced in the model. Our hypergraph model evolves by recruiting either a random node (with probability 1p) or a random group (with probability p) to a random hyperedge until the desired mean degree is reached. We analytically compute the properties of the model hypergraphs, such as the giantscomponent size, supported by numerical simulations. A series of scomponent percolation transitions is discovered. Implications of the sconnectivity to the structure and dynamics of hypergraph systems are also investigated. We anticipate that this model could provide a framework for exploring the higherorder architectures in hypergraphs. 
Friday, March 18, 2022 12:42PM  1:18PM 
Z09.00005: Geometry, topology and simplicial synchronization Invited Speaker: Ana Paula Millan

Friday, March 18, 2022 1:18PM  1:30PM 
Z09.00006: The power of complex systems' informationbased networks to make predictions: from finance to fashion industry Tiziana Di Matteo Data are everywhere and they carry information. Using, understanding and filtering such information has become a major activity across science, industry and society at large. It is therefore important to have tools that can analyse this information and that reduce complexity while keeping the integrity of the dataset and that can provide meaningful information that can be used for prediction. 
Friday, March 18, 2022 1:30PM  1:42PM 
Z09.00007: Higherorder Representations of Liner Shipping Data Timothy LaRock, Tina EliassiRad, Mengqiao Xu Global maritime cargo shipping handles about 80% of global trade volume and can be represented as a complex network. We examine a dataset of liner shipping service routes, where each route is a walk representing the path of a cargo ship through the porttoport network. These routes were scheduled by shipping companies during 2015 and aggregated by Alphaliner, a leading source of maritime trade data. Previous work on this data used an undirected cooccurrence representation, treating every route as a clique. We show that this representation cannot accurately model cargo moving through the network, since directionality of the edges is lost, and indirect connections are made direct. We compare 3 representations of service route data, discussing their strengths and weaknesses as well as their relation to existing higherorder network models. We present results from a new method for computing navigational paths for cargo through the network that respect the directionality inherent to the routes and balance factors important to industry practice, such as shipping distance and path length. We conclude by showing the importance of this representational choice in analyzing the structural core of the shipping network. 
Friday, March 18, 2022 1:42PM  1:54PM 
Z09.00008: Randomising hypergraphs by permuting their incidence matrix Tiziano Squartini, Fabio Saracco, Giovanni Petri, Renaud Lambiotte Network theory has emerged as a powerful paradigm to explain phenomena where units interact in a highly nontrivial way. So far, however, research in the field has mainly focused on pairwise interactions, disregarding the possibility that morethantwo constituent units could interact at a time. Hypergraphs represent a class of mathematical objects that could serve the scope of describing this novel kind of manybodies interactions. In this paper, we propose benchmark models for hypergraphs analysis that generalise the usual ErdosRenyi and Configuration Model in the simplest possible way, i.e. by randomising the hypergraph incidence matrix while preserving the corresponding connectivity/topological constraints  whose definition is, now, adapted to the novel framework. After exploring the mathematical properties of the proposed benchmark models, we consider two different applications: first, we define a novel quantity, the hyperedge assortativity, whose expected value we theoretically derive for all the introduced null models and which we, then, use to detect deviations in the corresponding realworld hypergraphs; second, we define a principled procedure for testing the statistical significance of the number of hyperedges connecting any two nodes. 
Friday, March 18, 2022 1:54PM  2:06PM 
Z09.00009: Unveiling the higherorder structure of multivariate time series Andrea Santoro, Federico Battiston, Giovanni Petri, Enrico Amico Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience, economics, and to understand some of their underlying dynamical features. Despite several methods currently exists for the analysis of multivariate time series, most of them do not investigate whether the signals stem from either independent, joint, or group interactions. Here, we propose a new framework to investigate the higherorder dependencies within a multivariate time series. We distinguish instantaneous cofluctuation patterns at different group levels (pairs, triplets, etc), and then characterize the additional coherence of higherorder cofluctuation patterns using TDA tools. We test our framework on coupled chaotic maps, demonstrating that it robustly differentiates various spatiotemporal regimes, including chaotic dynamical phases and various types of synchronization. By analysing fMRI signals, we find that, during rest, the human brain mainly oscillates between chaotic and partially intermittent states, with higherorder structures reflecting Default Mode Network and somatomotor regions, respectively. In financial time series, instead, the presence of higherorder structures can efficiently discriminate crises from periods of financial stability. 
Friday, March 18, 2022 2:06PM  2:18PM 
Z09.00010: Meanfield interactions in evolutionary spatial games Evgeni Burovski, Lev Shchur, Dmitriy Antonov We introduce a meanfield term to an evolutionary spatial game model. Namely, we consider the game of Nowak and May, based on the Prisoner's dilemma, and augment the game rules by a selfconsistent meanfield term. This way, an agent operates based on local information from its neighbors and nonlocal information via the meanfield coupling. We simulate the model and construct the steadystate phase diagram, which shows significant new features due to the meanfield term: while for the game of Nowak and May, steady states are characterized by a constant mean density of cooperators, the meanfield game contains steady states with a continuous dependence of the density on the payoff parameter. Moreover, the meanfield term changes the nature of transitions from discontinuous jumps in the steadystate density to jumps in the first derivative. The main effects are observed for stationary steady states, which are parametrically close to chaotic states: the meanfield coupling drives such stationary states into spatial chaos. Our approach can be readily generalized to a broad class of spatial evolutionary games with deterministic and stochastic decision rules. 
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