1
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Zou Y, Peng X, Yang W, Zhang J, Lin W. Dynamics of simplicial SEIRS epidemic model: global asymptotic stability and neural Lyapunov functions. J Math Biol 2024; 89:12. [PMID: 38879853 DOI: 10.1007/s00285-024-02119-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2023] [Revised: 04/17/2024] [Accepted: 05/24/2024] [Indexed: 06/28/2024]
Abstract
The transmission of infectious diseases on a particular network is ubiquitous in the physical world. Here, we investigate the transmission mechanism of infectious diseases with an incubation period using a networked compartment model that contains simplicial interactions, a typical high-order structure. We establish a simplicial SEIRS model and find that the proportion of infected individuals in equilibrium increases due to the many-body connections, regardless of the type of connections used. We analyze the dynamics of the established model, including existence and local asymptotic stability, and highlight differences from existing models. Significantly, we demonstrate global asymptotic stability using the neural Lyapunov function, a machine learning technique, with both numerical simulations and rigorous analytical arguments. We believe that our model owns the potential to provide valuable insights into transmission mechanisms of infectious diseases on high-order network structures, and that our approach and theory of using neural Lyapunov functions to validate model asymptotic stability can significantly advance investigations on complex dynamics of infectious disease.
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Affiliation(s)
- Yukun Zou
- Research Institute of Intelligent Complex Systems, Fudan University, 220 Handan Road, Shanghai, 200433, China
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, 220 Handan Road, Shanghai, 200433, China
| | - Xiaoxiao Peng
- Research Institute of Intelligent Complex Systems, Fudan University, 220 Handan Road, Shanghai, 200433, China
- Shanghai Center for Mathematical Sciences and School of Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai, 200433, China
| | - Wei Yang
- Research Institute of Intelligent Complex Systems, Fudan University, 220 Handan Road, Shanghai, 200433, China.
- Shanghai Center for Mathematical Sciences and School of Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai, 200433, China.
- Shanghai Artificial Intelligence Laboratory, Shanghai, 200232, China.
| | - Jingdong Zhang
- Research Institute of Intelligent Complex Systems, Fudan University, 220 Handan Road, Shanghai, 200433, China
- Shanghai Center for Mathematical Sciences and School of Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai, 200433, China
| | - Wei Lin
- Research Institute of Intelligent Complex Systems, Fudan University, 220 Handan Road, Shanghai, 200433, China
- Shanghai Center for Mathematical Sciences and School of Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai, 200433, China
- Shanghai Artificial Intelligence Laboratory, Shanghai, 200232, China
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, 220 Handan Road, Shanghai, 200433, China
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2
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Gallo L, Lacasa L, Latora V, Battiston F. Higher-order correlations reveal complex memory in temporal hypergraphs. Nat Commun 2024; 15:4754. [PMID: 38834592 DOI: 10.1038/s41467-024-48578-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2023] [Accepted: 05/02/2024] [Indexed: 06/06/2024] Open
Abstract
Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we use time-varying hypergraphs to describe such systems, and we introduce a framework based on higher-order correlations to characterize their temporal organization. The analysis of human interaction data reveals the existence of coherent and interdependent mesoscopic structures, thus capturing aggregation, fragmentation and nucleation processes in social systems. We introduce a model of temporal hypergraphs with non-Markovian group interactions, which reveals complex memory as a fundamental mechanism underlying the emerging pattern in the data.
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Affiliation(s)
- Luca Gallo
- Department of Network and Data Science, Central European University, Vienna, Austria.
| | - Lucas Lacasa
- Institute for Cross-Disciplinary Physics and Complex Systems (IFISC), CSIC-UIB, Palma de Mallorca, Spain
| | - Vito Latora
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK
- Department of Physics and Astronomy, University of Catania, 95125, Catania, Italy
- INFN Sezione di Catania, Via S. Sofia, 64, 95125, Catania, Italy
- Complexity Science Hub Vienna, A-1080, Vienna, Austria
| | - Federico Battiston
- Department of Network and Data Science, Central European University, Vienna, Austria.
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3
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Murphy C, Thibeault V, Allard A, Desrosiers P. Duality between predictability and reconstructability in complex systems. Nat Commun 2024; 15:4478. [PMID: 38796449 PMCID: PMC11127975 DOI: 10.1038/s41467-024-48020-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2023] [Accepted: 04/15/2024] [Indexed: 05/28/2024] Open
Abstract
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here, we find an intricate relationship between predictability and reconstructability using an information-theoretical point of view. We use the mutual information between a random graph and a stochastic process evolving on this random graph to quantify their codependence. Then, we show how the uncertainty coefficients, which are intimately related to that mutual information, quantify our ability to reconstruct a graph from an observed time series, and our ability to predict the evolution of a process from the structure of its interactions. We provide analytical calculations of the uncertainty coefficients for many different systems, including continuous deterministic systems, and describe a numerical procedure when exact calculations are intractable. Interestingly, we find that predictability and reconstructability, even though closely connected by the mutual information, can behave differently, even in a dual manner. We prove how such duality universally emerges when changing the number of steps in the process. Finally, we provide evidence that predictability-reconstruction dualities may exist in dynamical processes on real networks close to criticality.
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Affiliation(s)
- Charles Murphy
- Département de physique, de génie physique et d'optique, Université Laval, Québec, QC, G1V 0A6, Canada.
- Centre interdisciplinaire en modélisation mathématique, Université Laval, Québec, QC, G1V 0A6, Canada.
| | - Vincent Thibeault
- Département de physique, de génie physique et d'optique, Université Laval, Québec, QC, G1V 0A6, Canada
- Centre interdisciplinaire en modélisation mathématique, Université Laval, Québec, QC, G1V 0A6, Canada
| | - Antoine Allard
- Département de physique, de génie physique et d'optique, Université Laval, Québec, QC, G1V 0A6, Canada
- Centre interdisciplinaire en modélisation mathématique, Université Laval, Québec, QC, G1V 0A6, Canada
| | - Patrick Desrosiers
- Département de physique, de génie physique et d'optique, Université Laval, Québec, QC, G1V 0A6, Canada.
- Centre interdisciplinaire en modélisation mathématique, Université Laval, Québec, QC, G1V 0A6, Canada.
- Centre de recherche CERVO, Québec, QC, G1J 2G3, Canada.
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4
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Kim JH, Goh KI. Higher-Order Components Dictate Higher-Order Contagion Dynamics in Hypergraphs. PHYSICAL REVIEW LETTERS 2024; 132:087401. [PMID: 38457718 DOI: 10.1103/physrevlett.132.087401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2022] [Revised: 11/13/2023] [Accepted: 01/25/2024] [Indexed: 03/10/2024]
Abstract
The presence of the giant component is a necessary condition for the emergence of collective behavior in complex networked systems. Unlike networks, hypergraphs have an important native feature that components of hypergraphs might be of higher order, which could be defined in terms of the number of common nodes shared between hyperedges. Although the extensive higher-order component (HOC) could be witnessed ubiquitously in real-world hypergraphs, the role of the giant HOC in collective behavior on hypergraphs has yet to be elucidated. In this Letter, we demonstrate that the presence of the giant HOC fundamentally alters the outbreak patterns of higher-order contagion dynamics on real-world hypergraphs. Most crucially, the giant HOC is required for the higher-order contagion to invade globally from a single seed. We confirm it by using synthetic random hypergraphs containing adjustable and analytically calculable giant HOC.
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Affiliation(s)
- Jung-Ho Kim
- Department of Physics, Korea University, Seoul 02841, Korea
| | - K-I Goh
- Department of Physics, Korea University, Seoul 02841, Korea
- Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095, USA
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5
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Rizi AK, Keating LA, Gleeson JP, O'Sullivan DJP, Kivelä M. Effectiveness of contact tracing on networks with cliques. Phys Rev E 2024; 109:024303. [PMID: 38491705 DOI: 10.1103/physreve.109.024303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2023] [Accepted: 01/08/2024] [Indexed: 03/18/2024]
Abstract
Contact tracing, the practice of isolating individuals who have been in contact with infected individuals, is an effective and practical way of containing disease spread. Here we show that this strategy is particularly effective in the presence of social groups: Once the disease enters a group, contact tracing not only cuts direct infection paths but can also pre-emptively quarantine group members such that it will cut indirect spreading routes. We show these results by using a deliberately stylized model that allows us to isolate the effect of contact tracing within the clique structure of the network where the contagion is spreading. This will enable us to derive mean-field approximations and epidemic thresholds to demonstrate the efficiency of contact tracing in social networks with small groups. This analysis shows that contact tracing in networks with groups is more efficient the larger the groups are. We show how these results can be understood by approximating the combination of disease spreading and contact tracing with a complex contagion process where every failed infection attempt will lead to a lower infection probability in the following attempts. Our results illustrate how contact tracing in real-world settings can be more efficient than predicted by models that treat the system as fully mixed or the network structure as locally treelike.
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Affiliation(s)
- Abbas K Rizi
- Department of Computer Science, School of Science, Aalto University, FI-00076 Aalto, Finland
| | - Leah A Keating
- MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick V94 T9PX, Ireland
- Department of Mathematics, University of California, Los Angeles, California 90095, USA
| | - James P Gleeson
- MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick V94 T9PX, Ireland
| | - David J P O'Sullivan
- MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick V94 T9PX, Ireland
| | - Mikko Kivelä
- Department of Computer Science, School of Science, Aalto University, FI-00076 Aalto, Finland
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6
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Muolo R, Njougouo T, Gambuzza LV, Carletti T, Frasca M. Phase chimera states on nonlocal hyperrings. Phys Rev E 2024; 109:L022201. [PMID: 38491593 DOI: 10.1103/physreve.109.l022201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 01/08/2024] [Indexed: 03/18/2024]
Abstract
Chimera states are dynamical states where regions of synchronous trajectories coexist with incoherent ones. A significant amount of research has been devoted to studying chimera states in systems of identical oscillators, nonlocally coupled through pairwise interactions. Nevertheless, there is increasing evidence, also supported by available data, that complex systems are composed of multiple units experiencing many-body interactions that can be modeled by using higher-order structures beyond the paradigm of classic pairwise networks. In this work we investigate whether phase chimera states appear in this framework, by focusing on a topology solely involving many-body, nonlocal, and nonregular interactions, hereby named nonlocal d-hyperring, (d+1) being the order of the interactions. We present the theory by using the paradigmatic Stuart-Landau oscillators as node dynamics, and we show that phase chimera states emerge in a variety of structures and with different coupling functions. For comparison, we show that, when higher-order interactions are "flattened" to pairwise ones, the chimera behavior is weaker and more elusive.
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Affiliation(s)
- Riccardo Muolo
- Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
- Department of Mathematics, University of Namur, B5000 Namur, Belgium
- naXys, Namur Institute for Complex Systems, University of Namur, B5000 Namur, Belgium
| | - Thierry Njougouo
- naXys, Namur Institute for Complex Systems, University of Namur, B5000 Namur, Belgium
- Faculty of Computer Science, University of Namur, B5000 Namur, Belgium
- Department of Electrical and Electronic Engineering, University of Buea, P.O. Box 63, Buea, Cameroon
| | - Lucia Valentina Gambuzza
- Department of Electrical, Electronics and Computer Science Engineering, University of Catania, 95125 Catania, Italy
| | - Timoteo Carletti
- Department of Mathematics, University of Namur, B5000 Namur, Belgium
- naXys, Namur Institute for Complex Systems, University of Namur, B5000 Namur, Belgium
| | - Mattia Frasca
- Department of Electrical, Electronics and Computer Science Engineering, University of Catania, 95125 Catania, Italy
- Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti", IASI-CNR, 00185 Roma, Italy
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7
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Di Gaetano L, Battiston F, Starnini M. Percolation and Topological Properties of Temporal Higher-Order Networks. PHYSICAL REVIEW LETTERS 2024; 132:037401. [PMID: 38307051 DOI: 10.1103/physrevlett.132.037401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2023] [Revised: 10/23/2023] [Accepted: 12/11/2023] [Indexed: 02/04/2024]
Abstract
Many complex systems that exhibit temporal nonpairwise interactions can be represented by means of generative higher-order network models. Here, we propose a hidden variable formalism to analytically characterize a general class of higher-order network models. We apply our framework to a temporal higher-order activity-driven model, providing analytical expressions for the main topological properties of the time-integrated hypergraphs, depending on the integration time and the activity distributions characterizing the model. Furthermore, we provide analytical estimates for the percolation times of general classes of uncorrelated and correlated hypergraphs. Finally, we quantify the extent to which the percolation time of empirical social interactions is underestimated when their higher-order nature is neglected.
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Affiliation(s)
- Leonardo Di Gaetano
- Department of Network and Data Science, Central European University, 1100 Vienna, Austria
| | - Federico Battiston
- Department of Network and Data Science, Central European University, 1100 Vienna, Austria
| | - Michele Starnini
- Departament de Fisica, Universitat Politecnica de Catalunya, Campus Nord, 08034 Barcelona, Spain
- CENTAI Institute, 10138 Turin, Italy
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8
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St-Onge G, Hébert-Dufresne L, Allard A. Nonlinear bias toward complex contagion in uncertain transmission settings. Proc Natl Acad Sci U S A 2024; 121:e2312202121. [PMID: 38154065 PMCID: PMC10769855 DOI: 10.1073/pnas.2312202121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Accepted: 11/24/2023] [Indexed: 12/30/2023] Open
Abstract
Current epidemics in the biological and social domains are challenging the standard assumptions of mathematical contagion models. Chief among them are the complex patterns of transmission caused by heterogeneous group sizes and infection risk varying by orders of magnitude in different settings, like indoor versus outdoor gatherings in the COVID-19 pandemic or different moderation practices in social media communities. However, quantifying these heterogeneous levels of risk is difficult, and most models typically ignore them. Here, we include these features in an epidemic model on weighted hypergraphs to capture group-specific transmission rates. We study analytically the consequences of ignoring the heterogeneous transmissibility and find an induced superlinear infection rate during the emergence of a new outbreak, even though the underlying mechanism is a simple, linear contagion. The dynamics produced at the individual and group levels are therefore more similar to complex, nonlinear contagions, thus blurring the line between simple and complex contagions in realistic settings. We support this claim by introducing a Bayesian inference framework to quantify the nonlinearity of contagion processes. We show that simple contagions on real weighted hypergraphs are systematically biased toward the superlinear regime if the heterogeneity of the weights is ignored, greatly increasing the risk of erroneous classification as complex contagions. Our results provide an important cautionary tale for the challenging task of inferring transmission mechanisms from incidence data. Yet, it also paves the way for effective models that capture complex features of epidemics through nonlinear infection rates.
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Affiliation(s)
- Guillaume St-Onge
- Laboratory for the Modeling of Biological and Socio-Technical Systems, Northeastern University, Boston, MA02115
| | - Laurent Hébert-Dufresne
- Vermont Complex Systems Center, University of Vermont, Burlington, VT05401
- Department of Computer Science, University of Vermont, Burlington, VT05401
- Département de physique, de génie physique et d’optique, Université Laval, Québec, QCG1V 0A6, Canada
| | - Antoine Allard
- Vermont Complex Systems Center, University of Vermont, Burlington, VT05401
- Département de physique, de génie physique et d’optique, Université Laval, Québec, QCG1V 0A6, Canada
- Centre interdisciplinaire en modélisation mathématique, Université Laval, Québec, QCG1V 0A6, Canada
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9
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Bianconi G, Dorogovtsev SN. Nature of hypergraph k-core percolation problems. Phys Rev E 2024; 109:014307. [PMID: 38366447 DOI: 10.1103/physreve.109.014307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Accepted: 12/11/2023] [Indexed: 02/18/2024]
Abstract
Hypergraphs are higher-order networks that capture the interactions between two or more nodes. Hypergraphs can always be represented by factor graphs, i.e., bipartite networks between nodes and factor nodes (representing groups of nodes). Despite this universal representation, here we reveal that k-core percolation on hypergraphs can be significantly distinct from k-core percolation on factor graphs. We formulate the theory of hypergraph k-core percolation based on the assumption that a hyperedge can be intact only if all its nodes are intact. This scenario applies, for instance, to supply chains where the production of a product requires all raw materials and all processing steps; in biology it applies to protein-interaction networks where protein complexes can function only if all the proteins are present; and it applies as well to chemical reaction networks where a chemical reaction can take place only when all the reactants are present. Formulating a message-passing theory for hypergraph k-core percolation, and combining it with the theory of critical phenomena on networks, we demonstrate sharp differences with previously studied factor graph k-core percolation processes where it is allowed for hyperedges to have one or more damaged nodes and still be intact. To solve the dichotomy between k-core percolation on hypegraphs and on factor graphs, we define a set of pruning processes that act either exclusively on nodes or exclusively on hyperedges and depend on their second-neighborhood connectivity. We show that the resulting second-neighbor k-core percolation problems are significantly distinct from each other. Moreover we reveal that although these processes remain distinct from factor graphs k-core processes, when the pruning process acts exclusively on hyperedges the phase diagram is reduced to the one of factor graph k-cores.
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Affiliation(s)
- Ginestra Bianconi
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, United Kingdom
- Alan Turing Institute, 96 Euston Road, London NW1 2DB, United Kingdom
| | - Sergey N Dorogovtsev
- Departamento de Física da Universidade de Aveiro & I3N, 3810-193 Aveiro, Portugal
- Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia
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10
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Hu Q, Zhang XD. Fundamental patterns of signal propagation in complex networks. CHAOS (WOODBURY, N.Y.) 2024; 34:013149. [PMID: 38285726 DOI: 10.1063/5.0180450] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2023] [Accepted: 12/28/2023] [Indexed: 01/31/2024]
Abstract
Various disasters stem from minor perturbations, such as the spread of infectious diseases and cascading failure in power grids. Analyzing perturbations is crucial for both theoretical and application fields. Previous researchers have proposed basic propagation patterns for perturbation and explored the impact of basic network motifs on the collective response to these perturbations. However, the current framework is limited in its ability to decouple interactions and, therefore, cannot analyze more complex structures. In this article, we establish an effective, robust, and powerful propagation framework under a general dynamic model. This framework reveals classical and dense network motifs that exert critical acceleration on signal propagation, often reducing orders of magnitude compared with conclusions generated by previous work. Moreover, our framework provides a new approach to understand the fundamental principles of complex systems and the negative feedback mechanism, which is of great significance for researching system controlling and network resilience.
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Affiliation(s)
- Qitong Hu
- School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
- Ministry of Education (MOE) Funded Key Lab of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240, China
- Shanghai Center for Applied Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Xiao-Dong Zhang
- School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
- Ministry of Education (MOE) Funded Key Lab of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240, China
- Shanghai Center for Applied Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
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11
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Mancastroppa M, Iacopini I, Petri G, Barrat A. Hyper-cores promote localization and efficient seeding in higher-order processes. Nat Commun 2023; 14:6223. [PMID: 37802994 PMCID: PMC10558485 DOI: 10.1038/s41467-023-41887-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 09/22/2023] [Indexed: 10/08/2023] Open
Abstract
Going beyond networks, to include higher-order interactions of arbitrary sizes, is a major step to better describe complex systems. In the resulting hypergraph representation, tools to identify structures and central nodes are scarce. We consider the decomposition of a hypergraph in hyper-cores, subsets of nodes connected by at least a certain number of hyperedges of at least a certain size. We show that this provides a fingerprint for data described by hypergraphs and suggests a novel notion of centrality, the hypercoreness. We assess the role of hyper-cores and nodes with large hypercoreness in higher-order dynamical processes: such nodes have large spreading power and spreading processes are localized in central hyper-cores. Additionally, in the emergence of social conventions very few committed individuals with high hypercoreness can rapidly overturn a majority convention. Our work opens multiple research avenues, from comparing empirical data to model validation and study of temporally varying hypergraphs.
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Affiliation(s)
- Marco Mancastroppa
- Aix Marseille Univ, Université de Toulon, CNRS, CPT, Turing Center for Living Systems, Marseille, France
| | - Iacopo Iacopini
- Network Science Institute, Northeastern University London, London, E1W 1LP, United Kingdom
- Department of Network and Data Science, Central European University, 1100, Vienna, Austria
| | - Giovanni Petri
- Network Science Institute, Northeastern University London, London, E1W 1LP, United Kingdom
- CENTAI, Corso Inghilterra 3, 10138, Turin, Italy
| | - Alain Barrat
- Aix Marseille Univ, Université de Toulon, CNRS, CPT, Turing Center for Living Systems, Marseille, France.
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12
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Kim J, Lee DS, Goh KI. Contagion dynamics on hypergraphs with nested hyperedges. Phys Rev E 2023; 108:034313. [PMID: 37849153 DOI: 10.1103/physreve.108.034313] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2023] [Accepted: 09/11/2023] [Indexed: 10/19/2023]
Abstract
In complex social systems encoded as hypergraphs, higher-order (i.e., group) interactions taking place among more than two individuals are represented by hyperedges. One of the higher-order correlation structures native to hypergraphs is the nestedness: Some hyperedges can be entirely contained (that is, nested) within another larger hyperedge, which itself can also be nested further in a hierarchical manner. Yet the effect of such hierarchical structure of hyperedges on the dynamics has remained unexplored. In this context, here we propose a random nested-hypergraph model with a tunable level of nestedness and investigate the effects of nestedness on a higher-order susceptible-infected-susceptible process. By developing an analytic framework called the facet approximation, we obtain the steady-state fraction of infected nodes on the random nested-hypergraph model more accurately than existing methods. Our results show that the hyperedge-nestedness affects the phase diagram significantly. Monte Carlo simulations support the analytical results.
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Affiliation(s)
- Jihye Kim
- Department of Physics, Korea University, Seoul 02841, Korea
| | - Deok-Sun Lee
- School of Computational Sciences and Center for AI and Natural Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - K-I Goh
- Department of Physics, Korea University, Seoul 02841, Korea
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13
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Zhang H, Cao L, Fu C, Cai S, Gao Y. Epidemic spreading on multi-layer networks with active nodes. CHAOS (WOODBURY, N.Y.) 2023; 33:073128. [PMID: 37459223 DOI: 10.1063/5.0151777] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2023] [Accepted: 06/09/2023] [Indexed: 07/20/2023]
Abstract
Investigations on spreading dynamics based on complex networks have received widespread attention these years due to the COVID-19 epidemic, which are conducive to corresponding prevention policies. As for the COVID-19 epidemic itself, the latent time and mobile crowds are two important and inescapable factors that contribute to the significant prevalence. Focusing on these two factors, this paper systematically investigates the epidemic spreading in multiple spaces with mobile crowds. Specifically, we propose a SEIS (Susceptible-Exposed-Infected-Susceptible) model that considers the latent time based on a multi-layer network with active nodes which indicate the mobile crowds. The steady-state equations and epidemic threshold of the SEIS model are deduced and discussed. And by comprehensively discussing the key model parameters, we find that (1) due to the latent time, there is a "cumulative effect" on the infected, leading to the "peaks" or "shoulders" of the curves of the infected individuals, and the system can switch among three states with the relative parameter combinations changing; (2) the minimal mobile crowds can also cause the significant prevalence of the epidemic at the steady state, which is suggested by the zero-point phase change in the proportional curves of infected individuals. These results can provide a theoretical basis for formulating epidemic prevention policies.
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Affiliation(s)
- Hu Zhang
- School of Physics, University of Electronic Science and Technology of China, Chengdu 610054, China
- Peking University Shenzhen Graduate School, Shenzhen 518055, China
| | - Lingling Cao
- School of Physics, University of Electronic Science and Technology of China, Chengdu 610054, China
| | - Chuanji Fu
- School of Physics, University of Electronic Science and Technology of China, Chengdu 610054, China
| | - Shimin Cai
- Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 610054, China
| | - Yachun Gao
- School of Physics, University of Electronic Science and Technology of China, Chengdu 610054, China
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14
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Burgio G, Gómez S, Arenas A. Spreading dynamics in networks under context-dependent behavior. Phys Rev E 2023; 107:064304. [PMID: 37464705 DOI: 10.1103/physreve.107.064304] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2022] [Accepted: 05/18/2023] [Indexed: 07/20/2023]
Abstract
In some systems, the behavior of the constituent units can create a "context" that modifies the direct interactions among them. This mechanism of indirect modification inspired us to develop a minimal model of context-dependent spreading. In our model, agents actively impede (favor) or not diffusion during an interaction, depending on the behavior they observe among all the peers in the group within which that interaction occurs. We divide the population into two behavioral types and provide a mean-field theory to parametrize mixing patterns of arbitrary type-assortativity within groups of any size. As an application, we examine an epidemic-spreading model with context-dependent adoption of prophylactic tools such as face masks. By analyzing the distributions of groups' size and type-composition, we uncover a rich phenomenology for the basic reproduction number and the endemic state. We analytically show how changing the group organization of contacts can either facilitate or hinder epidemic spreading, eventually moving the system from the subcritical to the supercritical phase and vice versa, depending mainly on sociological factors, such as whether the prophylactic behavior is hardly or easily induced. More generally, our work provides a theoretical foundation to model higher-order contexts and analyze their dynamical implications, envisioning a broad theory of context-dependent interactions that would allow for a new systematic investigation of a variety of complex systems.
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Affiliation(s)
- Giulio Burgio
- Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
| | - Sergio Gómez
- Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
| | - Alex Arenas
- Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
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15
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The dynamic nature of percolation on networks with triadic interactions. Nat Commun 2023; 14:1308. [PMID: 36894591 PMCID: PMC9998640 DOI: 10.1038/s41467-023-37019-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2022] [Accepted: 02/24/2023] [Indexed: 03/11/2023] Open
Abstract
Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex networks, the percolation transition can become discontinuous. However, little is known about percolation in networks with higher-order interactions. Here, we show that percolation can be turned into a fully fledged dynamical process when higher-order interactions are taken into account. By introducing signed triadic interactions, in which a node can regulate the interactions between two other nodes, we define triadic percolation. We uncover that in this paradigmatic model the connectivity of the network changes in time and that the order parameter undergoes a period doubling and a route to chaos. We provide a general theory for triadic percolation which accurately predicts the full phase diagram on random graphs as confirmed by extensive numerical simulations. We find that triadic percolation on real network topologies reveals a similar phenomenology. These results radically change our understanding of percolation and may be used to study complex systems in which the functional connectivity is changing in time dynamically and in a non-trivial way, such as in neural and climate networks.
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16
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Zhong S, Wu X, Li Y, Liu C. Indirect transmission and disinfection strategies on heterogeneous networks. Phys Rev E 2022; 106:054309. [PMID: 36559356 DOI: 10.1103/physreve.106.054309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2022] [Accepted: 11/01/2022] [Indexed: 06/17/2023]
Abstract
Besides direct contacts of individuals, indirect contacts with environments being the medium is another route of epidemic transmission, which most previous studies have ignored. Disinfection is one of the most effective and commonly used measures to prevent and control epidemic spreading. In this paper, we propose a metapopulationlike model incorporating direct and indirect transmissions for susceptible-infected-susceptible-like epidemics on heterogeneous networks. Furthermore, we explore the epidemic spreading process with heterogeneous disinfection on both spatial and time dimensions. Specifically, we put forward three types of disinfection strategies, namely, the static disinfection strategy, the random time disinfection strategy, and the event-triggered disinfection strategy. Comparative analysis of the three strategies suggests that managers should prioritize disinfection resource allocation to large-flow environments, especially when disinfection resources are limited. In addition, timely disinfection of environments with infected visitors is an effective and economical strategy. Our model sheds light on the interplay dynamics of indirect transmission and disinfection and the results provide theoretical support for governors to select proper disinfection strategies in practical scenarios.
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Affiliation(s)
- Su Zhong
- School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China
| | - Xiaoqun Wu
- School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China
| | - Yanting Li
- School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China
| | - Congying Liu
- School of Mathematics and Statistics, Jiangsu Normal University, Jiangsu 221116, China
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17
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Campi G, Perali A, Marcelli A, Bianconi A. Sars-Cov2 world pandemic recurrent waves controlled by variants evolution and vaccination campaign. Sci Rep 2022; 12:18108. [PMID: 36302922 PMCID: PMC9612611 DOI: 10.1038/s41598-022-22816-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2022] [Accepted: 10/19/2022] [Indexed: 12/30/2022] Open
Abstract
While understanding the time evolution of Covid-19 pandemic is needed to plan economics and tune sanitary policies, a quantitative information of the recurrent epidemic waves is elusive. This work describes a statistical physics study of the subsequent waves in the epidemic spreading of Covid-19 and disclose the frequency components of the epidemic waves pattern over two years in United States, United Kingdom and Japan. These countries have been taken as representative cases of different containment policies such as "Mitigation" (USA and UK) and "Zero Covid" (Japan) policies. The supercritical phases in spreading have been identified by intervals with RIC-index > 0. We have used the wavelet transform of infection and fatality waves to get the spectral analysis showing a dominant component around 130 days. Data of the world dynamic clearly indicates also the crossover to a different phase due to the enforcement of vaccination campaign. In Japan and United Kingdom, we observed the emergence in the infection waves of a long period component (~ 170 days) during vaccination campaign. These results indicate slowing down of the epidemic spreading dynamics due to the vaccination campaign. Finally, we find an intrinsic difference between infection and fatality waves pointing to a non-trivial variation of the lethality due to different gene variants.
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Affiliation(s)
- Gaetano Campi
- grid.5326.20000 0001 1940 4177Institute of Crystallography, Consiglio Nazionale delle Ricerche CNR, Via Salaria Km 29.300, Monterotondo Roma, 00015 Rome, Italy ,grid.499323.6Rome International Centre Materials Science, Superstripes RICMASS, Via dei Sabelli 119A, 00185 Rome, Italy
| | - Andrea Perali
- grid.5602.10000 0000 9745 6549Physics Unit, School of Pharmacy, University of Camerino, 62032 Camerino, MC Italy
| | - Augusto Marcelli
- grid.463190.90000 0004 0648 0236INFN-Laboratori Nazionali di Frascati, Via E. Fermi 54, 00044 Frascati, RM Italy
| | - Antonio Bianconi
- grid.5326.20000 0001 1940 4177Institute of Crystallography, Consiglio Nazionale delle Ricerche CNR, Via Salaria Km 29.300, Monterotondo Roma, 00015 Rome, Italy ,grid.499323.6Rome International Centre Materials Science, Superstripes RICMASS, Via dei Sabelli 119A, 00185 Rome, Italy ,grid.183446.c0000 0000 8868 5198National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow, Russian Federation 115409
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18
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Impact of basic network motifs on the collective response to perturbations. Nat Commun 2022; 13:5301. [PMID: 36075905 PMCID: PMC9458749 DOI: 10.1038/s41467-022-32913-w] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2022] [Accepted: 08/22/2022] [Indexed: 11/08/2022] Open
Abstract
Many collective phenomena such as epidemic spreading and cascading failures in socioeconomic systems on networks are caused by perturbations of the dynamics. How perturbations propagate through networks, impact and disrupt their functions may depend on the network, the type and location of the perturbation as well as the spreading dynamics. Previous work has analyzed the retardation effects of the nodes along the propagation paths, suggesting a few transient propagation "scaling” regimes as a function of the nodes’ degree, but regardless of motifs such as triangles. Yet, empirical networks consist of motifs enabling the proper functioning of the system. Here, we show that basic motifs along the propagation path jointly determine the previously proposed scaling regimes of distance-limited propagation and degree-limited propagation, or even cease their existence. Our results suggest a radical departure from these scaling regimes and provide a deeper understanding of the interplay of self-dynamics, interaction dynamics, and topological properties. Spreading processes and cascading failures on complex networks are often triggered by external perturbations. The authors uncover the impact of network motifs on the processes of perturbations propagation through networks, and networks’ response dynamics.
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19
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Mizutaka S, Mori K, Hasegawa T. Synergistic epidemic spreading in correlated networks. Phys Rev E 2022; 106:034305. [PMID: 36266882 DOI: 10.1103/physreve.106.034305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Accepted: 08/04/2022] [Indexed: 06/16/2023]
Abstract
We investigate the effect of degree correlation on a susceptible-infected-susceptible (SIS) model with a nonlinear cooperative effect (synergy) in infectious transmissions. In a mean-field treatment of the synergistic SIS model on a bimodal network with tunable degree correlation, we identify a discontinuous transition that is independent of the degree correlation strength unless the synergy is absent or extremely weak. Regardless of synergy (absent or present), a positive and negative degree correlation in the model reduces and raises the epidemic threshold, respectively. For networks with a strongly positive degree correlation, the mean-field treatment predicts the emergence of two discontinuous jumps in the steady-state infected density. To test the mean-field treatment, we provide approximate master equations of the present model. We quantitatively confirm that the approximate master equations agree with not only all qualitative predictions of the mean-field treatment but also corresponding Monte Carlo simulations.
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Affiliation(s)
- Shogo Mizutaka
- Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi 924-1292, Japan
| | - Kizashi Mori
- Graduate School of Science and Engineering, Ibaraki University, 2-1-1 Bunkyo, Mito 310-8512, Japan
| | - Takehisa Hasegawa
- Graduate School of Science and Engineering, Ibaraki University, 2-1-1 Bunkyo, Mito 310-8512, Japan
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20
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Silk MJ, Wilber MQ, Fefferman NH. Capturing complex interactions in disease ecology with simplicial sets. Ecol Lett 2022; 25:2217-2231. [PMID: 36001469 DOI: 10.1111/ele.14079] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Revised: 04/21/2022] [Accepted: 06/29/2022] [Indexed: 11/28/2022]
Abstract
Network approaches have revolutionized the study of ecological interactions. Social, movement and ecological networks have all been integral to studying infectious disease ecology. However, conventional (dyadic) network approaches are limited in their ability to capture higher-order interactions. We present simplicial sets as a tool that addresses this limitation. First, we explain what simplicial sets are. Second, we explain why their use would be beneficial in different subject areas. Third, we detail where these areas are: social, transmission, movement/spatial and ecological networks and when using them would help most in each context. To demonstrate their application, we develop a novel approach to identify how pathogens persist within a host population. Fourth, we provide an overview of how to use simplicial sets, highlighting specific metrics, generative models and software. Finally, we synthesize key research questions simplicial sets will help us answer and draw attention to methodological developments that will facilitate this.
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Affiliation(s)
- Matthew J Silk
- NIMBioS, University of Tennessee, Knoxville, Tennessee, USA.,CEFE, Univ Montpellier, CNRS, EPHE, IRD, Montpellier, France
| | - Mark Q Wilber
- Department of Forestry, Wildlife and Fisheries, University of Tennessee, Knoxville, Tennessee, USA
| | - Nina H Fefferman
- NIMBioS, University of Tennessee, Knoxville, Tennessee, USA.,Department of Ecology and Evolutionary Biology, University of Tennessee, Knoxville, Tennessee, USA.,Department of Mathematics, University of Tennessee, Knoxville, Tennessee, USA
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21
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Falcó C, Corral Á. Finite-time scaling for epidemic processes with power-law superspreading events. Phys Rev E 2022; 105:064122. [PMID: 35854596 DOI: 10.1103/physreve.105.064122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2021] [Accepted: 05/31/2022] [Indexed: 06/15/2023]
Abstract
Epidemics unfold by means of a spreading process from each infected individual to a variable number of secondary cases. It has been claimed that the so-called superspreading events of the COVID-19 pandemic are governed by a power-law-tailed distribution of secondary cases, with no finite variance. Using a continuous-time branching process, we demonstrate that for such power-law-tailed superspreading, the survival probability of an outbreak as a function of both time and the basic reproductive number fulfills a "finite-time scaling" law (analogous to finite-size scaling) with universal-like characteristics only dependent on the power-law exponent. This clearly shows how the phase transition separating a subcritical and a supercritical phase emerges in the infinite-time limit (analogous to the thermodynamic limit). We also quantify the counterintuitive hazards posed by this superspreading. When the expected number of infected individuals is computed removing extinct outbreaks, we find a constant value in the subcritical phase and a superlinear power-law growth in the critical phase.
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Affiliation(s)
- Carles Falcó
- Centre de Recerca Matemàtica, Edifici C, Campus Bellaterra, E-08193 Barcelona, Spain
- Departament de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, E-08193 Barcelona, Spain
| | - Álvaro Corral
- Centre de Recerca Matemàtica, Edifici C, Campus Bellaterra, E-08193 Barcelona, Spain
- Departament de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, E-08193 Barcelona, Spain
- Complexity Science Hub Vienna, Josefstädter Straße 39, 1080 Vienna, Austria
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22
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Cui K, KhudaBukhsh WR, Koeppl H. Motif-based mean-field approximation of interacting particles on clustered networks. Phys Rev E 2022; 105:L042301. [PMID: 35590665 DOI: 10.1103/physreve.105.l042301] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2022] [Accepted: 04/07/2022] [Indexed: 06/15/2023]
Abstract
Interacting particles on graphs are routinely used to study magnetic behavior in physics, disease spread in epidemiology, and opinion dynamics in social sciences. The literature on mean-field approximations of such systems for large graphs typically remains limited to specific dynamics, or assumes cluster-free graphs for which standard approximations based on degrees and pairs are often reasonably accurate. Here, we propose a motif-based mean-field approximation that considers higher-order subgraph structures in large clustered graphs. Numerically, our equations agree with stochastic simulations where existing methods fail.
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Affiliation(s)
- Kai Cui
- Department of Electrical Engineering and Information Technology, Technische Universität Darmstadt, 64287 Darmstadt, Germany
| | | | - Heinz Koeppl
- Department of Electrical Engineering and Information Technology, Technische Universität Darmstadt, 64287 Darmstadt, Germany
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23
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Majhi S, Perc M, Ghosh D. Dynamics on higher-order networks: a review. J R Soc Interface 2022; 19:20220043. [PMID: 35317647 PMCID: PMC8941407 DOI: 10.1098/rsif.2022.0043] [Citation(s) in RCA: 73] [Impact Index Per Article: 36.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2022] [Accepted: 02/18/2022] [Indexed: 12/25/2022] Open
Abstract
Network science has evolved into an indispensable platform for studying complex systems. But recent research has identified limits of classical networks, where links connect pairs of nodes, to comprehensively describe group interactions. Higher-order networks, where a link can connect more than two nodes, have therefore emerged as a new frontier in network science. Since group interactions are common in social, biological and technological systems, higher-order networks have recently led to important new discoveries across many fields of research. Here, we review these works, focusing in particular on the novel aspects of the dynamics that emerges on higher-order networks. We cover a variety of dynamical processes that have thus far been studied, including different synchronization phenomena, contagion processes, the evolution of cooperation and consensus formation. We also outline open challenges and promising directions for future research.
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Affiliation(s)
- Soumen Majhi
- Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
- Complexity Science Hub Vienna, Josefstödter Straße 39, 1080 Vienna, Austria
- Alma Mater Europaea, Slovenska ulica 17, 2000 Maribor, Slovenia
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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24
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Millán AP, Ghorbanchian R, Defenu N, Battiston F, Bianconi G. Local topological moves determine global diffusion properties of hyperbolic higher-order networks. Phys Rev E 2021; 104:054302. [PMID: 34942729 DOI: 10.1103/physreve.104.054302] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2021] [Accepted: 10/13/2021] [Indexed: 12/18/2022]
Abstract
From social interactions to the human brain, higher-order networks are key to describe the underlying network geometry and topology of many complex systems. While it is well known that network structure strongly affects its function, the role that network topology and geometry has on the emerging dynamical properties of higher-order networks is yet to be clarified. In this perspective, the spectral dimension plays a key role since it determines the effective dimension for diffusion processes on a network. Despite its relevance, a theoretical understanding of which mechanisms lead to a finite spectral dimension, and how this can be controlled, still represents a challenge and is the object of intense research. Here, we introduce two nonequilibrium models of hyperbolic higher-order networks and we characterize their network topology and geometry by investigating the intertwined appearance of small-world behavior, δ-hyperbolicity, and community structure. We show that different topological moves, determining the nonequilibrium growth of the higher-order hyperbolic network models, induce tuneable values of the spectral dimension, showing a rich phenomenology which is not displayed in random graph ensembles. In particular, we observe that, if the topological moves used to construct the higher-order network increase the area/volume ratio, then the spectral dimension continuously decreases, while the opposite effect is observed if the topological moves decrease the area/volume ratio. Our work reveals a new link between the geometry of a network and its diffusion properties, contributing to a better understanding of the complex interplay between network structure and dynamics.
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Affiliation(s)
- Ana P Millán
- Amsterdam UMC, Vrije Universiteit Amsterdam, Department of Clinical Neurophysiology and MEG Center, Amsterdam Neuroscience, De Boelelaan 1117, Amsterdam, The Netherlands
| | - Reza Ghorbanchian
- School of Mathematical Sciences, Queen Mary University of London, Mile End Road, E1 4NS, London, United Kingdom
| | - Nicolò Defenu
- Institute for Theoretical Physics, ETH Zürich Wolfgang-Pauli-Str. 27, 8093 Zurich, Switzerland
| | - Federico Battiston
- Department of Network and Data Science, Central European University, 1100 Vienna, Austria
| | - Ginestra Bianconi
- School of Mathematical Sciences, Queen Mary University of London, Mile End Road, E1 4NS, London, United Kingdom.,The Alan Turing Institute, British Library, 96 Euston Road, NW1 2DB, London, United Kingdom
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25
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Krishnagopal S, Bianconi G. Spectral detection of simplicial communities via Hodge Laplacians. Phys Rev E 2021; 104:064303. [PMID: 35030957 DOI: 10.1103/physreve.104.064303] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2021] [Accepted: 11/12/2021] [Indexed: 11/07/2022]
Abstract
While the study of graphs has been very popular, simplicial complexes are relatively new in the network science community. Despite being a source of rich information, graphs are limited to pairwise interactions. However, several real-world networks such as social networks, neuronal networks, etc., involve interactions between more than two nodes. Simplicial complexes provide a powerful mathematical framework to model such higher-order interactions. It is well known that the spectrum of the graph Laplacian is indicative of community structure, and this relation is exploited by spectral clustering algorithms. Here we propose that the spectrum of the Hodge Laplacian, a higher-order Laplacian defined on simplicial complexes, encodes simplicial communities. We formulate an algorithm to extract simplicial communities (of arbitrary dimension). We apply this algorithm to simplicial complex benchmarks and to real higher-order network data including social networks and networks extracted using language or text processing tools. However, datasets of simplicial complexes are scarce, and for the vast majority of datasets that may involve higher-order interactions, only the set of pairwise interactions are available. Hence, we use known properties of the data to infer the most likely higher-order interactions. In other words, we introduce an inference method to predict the most likely simplicial complex given the community structure of its network skeleton. This method identifies as most likely the higher-order interactions inducing simplicial communities that maximize the adjusted mutual information measured with respect to ground-truth community structure. Finally, we consider higher-order networks constructed through thresholding the edge weights of collaboration networks (encoding only pairwise interactions) and provide an example of persistent simplicial communities that are sustained over a wide range of the threshold.
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Affiliation(s)
- Sanjukta Krishnagopal
- Gatsby Computational Neuroscience Unit, University College London, London, WC1E 6BT, United Kingdom
| | - Ginestra Bianconi
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, United Kingdom and The Alan Turing Institute, London, NW1 2DB, United Kingdom
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