Physics Reports, Journal Year: 2024, Volume and Issue: 1056, P. 1 - 70
Published: Jan. 19, 2024
Language: Английский
Physics Reports, Journal Year: 2023, Volume and Issue: 1018, P. 1 - 64
Published: May 1, 2023
Language: Английский
Citations
147
Physical Review Research, Journal Year: 2020, Volume and Issue: 2(3)
Published: Sept. 14, 2020
Traditionally, interaction systems have been described as networks, where links encode information on the pairwise influences among nodes. Yet, in many systems, interactions take place larger groups. Recent work has shown that higher-order between oscillators can significantly affect synchronization. However, these early studies mostly considered up to 4 at time, and analytical treatments are limited all-to-all setting. Here, we propose a general framework allows us effectively study populations of all possible orders considered, for any complex topology by arbitrary hypergraphs, coupling functions. To this scope, introduce multi-order Laplacian whose spectrum determines stability synchronized solution. Our is validated three structures increasing complexity. First, population with orders, which derive full manner Lyapunov exponents system, investigate effect including attractive repulsive interactions. Second, apply synchronization synthetic model heterogeneous Finally, compare dynamics coupled couplings only, real dataset describing macaque brain connectome, highlighting importance faithfully representing complexity real-world systems. Taken together, our obtain complete characterization synchrony paving way towards treatment dynamical processes beyond
Language: Английский
Citations
145
SIAM Review, Journal Year: 2023, Volume and Issue: 65(3), P. 686 - 731
Published: Aug. 1, 2023
Network-based modeling of complex systems and data using the language graphs has become an essential topic across a range different disciplines. Arguably, this graph-based perspective derives its success from relative simplicity graphs: A graph consists nothing more than set vertices edges, describing relationships between pairs such vertices. This simple combinatorial structure makes interpretable flexible tools. The as system models, however, been scrutinized in literature recently. Specifically, it argued variety angles that there is need for higher-order networks, which go beyond paradigm pairwise relationships, encapsulated by graphs. In survey article we take stock these recent developments. Our goals are to clarify (i) what networks are, (ii) why interesting objects study, (iii) how they can be used applications.
Language: Английский
Citations
142
Published: Nov. 23, 2021
Higher-order networks describe the many-body interactions of a large variety complex systems, ranging from brain to collaboration networks. Simplicial complexes are generalized network structures which allow us capture combinatorial properties, topology and geometry higher-order Having been used extensively in quantum gravity discrete or discretized space-time, simplicial have only recently started becoming representation choice for capturing underlying systems. This Element provides an in-depth introduction very hot topic theory, covering wide range subjects emergent hyperbolic topological data analysis dynamics. Elements aims demonstrate that provide general mathematical framework reveal how dynamics depends on geometry.
Language: Английский
Citations
134
Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2022, Volume and Issue: 32(1)
Published: Jan. 1, 2022
Higher-order interactions might play a significant role in the collective dynamics of brain. With this motivation, we here consider simplicial complex neurons, particular, studying effects pairwise and three-body on emergence synchronization. We assume to be mediated through electrical synapses, while for second-order interactions, separately study diffusive coupling nonlinear chemical coupling. For all considered cases, derive necessary conditions synchronization by means linear stability analysis, compute errors numerically. Our research shows that even if weak strength, can lead under significantly lower first-order strengths. Moreover, overall cost is reduced due introduction compared interactions.
Language: Английский
Citations
115
Scientific Reports, Journal Year: 2021, Volume and Issue: 11(1)
Published: March 29, 2021
Abstract Human social interactions in local settings can be experimentally detected by recording the physical proximity and orientation of people. Such interactions, approximating face-to-face communications, effectively represented as time varying networks with links being unceasingly created destroyed over time. Traditional analyses temporal have addressed mostly pairwise where describe dyadic connections among individuals. However, many network dynamics are hardly ascribable to but often comprise larger groups, which better described higher-order interactions. Here we investigate organizations analyzing five publicly available datasets collected different settings. We find that ubiquitous and, similarly their counterparts, characterized heterogeneous dynamics, bursty trains rapidly recurring events separated long periods inactivity. evolution formation groups looking at transition rates between structures. more spontaneous settings, group slower disaggregation, while work these phenomena abrupt, possibly reflecting pre-organized dynamics. Finally, observe reinforcement suggesting longer a stays together higher probability same interaction pattern persist future. Our findings suggest importance considering structure when investigating human
Language: Английский
Citations
113
Science Advances, Journal Year: 2021, Volume and Issue: 7(28)
Published: July 7, 2021
Novel clustering techniques enable the detection of modules in large datasets with multiway interactions.
Language: Английский
Citations
113
Nature Communications, Journal Year: 2023, Volume and Issue: 14(1)
Published: March 23, 2023
Abstract Higher-order networks have emerged as a powerful framework to model complex systems and their collective behavior. Going beyond pairwise interactions, they encode structured relations among arbitrary numbers of units through representations such simplicial complexes hypergraphs. So far, the choice between hypergraphs has often been motivated by technical convenience. Here, using synchronization an example, we demonstrate that effects higher-order interactions are highly representation-dependent. In particular, typically enhance in but opposite effect complexes. We provide theoretical insight linking synchronizability different hypergraph structures (generalized) degree heterogeneity cross-order correlation, which turn influence wide range dynamical processes from contagion diffusion. Our findings reveal hidden impact on dynamics, highlighting importance choosing appropriate when studying with nonpairwise interactions.
Language: Английский
Citations
108
Information Sciences, Journal Year: 2022, Volume and Issue: 621, P. 672 - 690
Published: Nov. 25, 2022
Language: Английский
Citations
100
Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences, Journal Year: 2022, Volume and Issue: 478(2261)
Published: May 1, 2022
Simplicial complexes describe the simple fact that in social networks a link can connect more than two individuals. As we show here, this has far-reaching consequences for epidemic spreading, particular context of multilayer network model, where one layer is virtual and other physical contact network. The responsible transmission information via pairwise or higher order 2-simplex interactions among individuals, while spreading. We use microscopic Markov chain approach to derive probability transition equations determine outbreak thresholds. further support these results with Monte Carlo simulations, which are good agreement, thus confirming analytical tractability proposed model. find rates frequently low when actual disease medium, be mitigated effectively by introducing relative ease higher-order means could exploited inhibit outbreaks.
Language: Английский
Citations
98