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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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2
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Han L, Lin Z, Tang M, Liu Y, Guan S. Impact of human contact patterns on epidemic spreading in time-varying networks. Phys Rev E 2023; 107:024312. [PMID: 36932475 DOI: 10.1103/physreve.107.024312] [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: 08/14/2022] [Accepted: 02/06/2023] [Indexed: 03/19/2023]
Abstract
Human contact behaviors involve both dormant and active processes. The dormant (active) process goes from the disappearance (creation) to the creation (disappearance) of an edge. The dormant (active) time is the elapsed time since the edge became dormant (active). Many empirical studies have revealed that dormant and active times in human contact behaviors tend to show a long-tailed distribution. Previous researches focused on the impact of the dormant process on spreading dynamics. However, the epidemic spreading happens on the active process. This raises the question of how the active process affects epidemic spreading in complex networks. Here, we propose a novel time-varying network model in which the distributions of both the dormant time and active time of edges are adjustable. We develop a pairwise approximation method to describe the spreading dynamical processes in the time-varying networks. Through extensive numerical simulations, we find that the epidemic threshold is proportional to the mean dormant time and inversely proportional to the mean active time. The attack rate decreases with the increase of mean dormant time and increases with the increase of mean active time. It is worth noting that the epidemic threshold and the attack rate (e.g., the infected density in the steady state) are independent of the heterogeneities of the dormant time distribution and the active time distribution. Increasing the heterogeneity of the dormant time distribution accelerates epidemic spreading while increasing the heterogeneity of the active time distribution slows it down.
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Affiliation(s)
- Lilei Han
- School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Zhaohua Lin
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China
| | - Ming Tang
- School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
- Shanghai Key Laboratory of Multidimensional Information Processing, East China Normal University, Shanghai 200241, China
| | - Ying Liu
- School of Computer Science, Southwest Petroleum University, Chengdu 610500, China
| | - Shuguang Guan
- School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
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3
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Bauzá Mingueza F, Floría M, Gómez-Gardeñes J, Arenas A, Cardillo A. Characterization of interactions' persistence in time-varying networks. Sci Rep 2023; 13:765. [PMID: 36641475 PMCID: PMC9840642 DOI: 10.1038/s41598-022-25907-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Accepted: 12/06/2022] [Indexed: 01/15/2023] Open
Abstract
Many complex networked systems exhibit volatile dynamic interactions among their vertices, whose order and persistence reverberate on the outcome of dynamical processes taking place on them. To quantify and characterize the similarity of the snapshots of a time-varying network-a proxy for the persistence,-we present a study on the persistence of the interactions based on a descriptor named temporality. We use the average value of the temporality, [Formula: see text], to assess how "special" is a given time-varying network within the configuration space of ordered sequences of snapshots. We analyse the temporality of several empirical networks and find that empirical sequences are much more similar than their randomized counterparts. We study also the effects on [Formula: see text] induced by the (time) resolution at which interactions take place.
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Affiliation(s)
- Francisco Bauzá Mingueza
- Department of Theoretical Physics, University of Zaragoza, 50006, Zaragoza, Spain
- GOTHAM Lab, Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018, Zaragoza, Spain
| | - Mario Floría
- GOTHAM Lab, Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018, Zaragoza, Spain
- Department of Condensed Matter Physics, University of Zaragoza, 50006, Zaragoza, Spain
| | - Jesús Gómez-Gardeñes
- GOTHAM Lab, Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018, Zaragoza, Spain
- Department of Condensed Matter Physics, University of Zaragoza, 50006, Zaragoza, Spain
| | - Alex Arenas
- Department of Computer Science and Mathematics, University Rovira i Virgili, 43007, Tarragona, Spain
| | - Alessio Cardillo
- Department of Computer Science and Mathematics, University Rovira i Virgili, 43007, Tarragona, Spain.
- GOTHAM Lab, Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018, Zaragoza, Spain.
- Internet Interdisciplinary Institute (IN3), Open University of Catalonia, 08018, Barcelona, Spain.
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Millán AP, van Straaten ECW, Stam CJ, Nissen IA, Idema S, Baayen JC, Van Mieghem P, Hillebrand A. Epidemic models characterize seizure propagation and the effects of epilepsy surgery in individualized brain networks based on MEG and invasive EEG recordings. Sci Rep 2022; 12:4086. [PMID: 35260657 PMCID: PMC8904850 DOI: 10.1038/s41598-022-07730-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2021] [Accepted: 02/24/2022] [Indexed: 11/08/2022] Open
Abstract
Epilepsy surgery is the treatment of choice for drug-resistant epilepsy patients. However, seizure-freedom is currently achieved in only 2/3 of the patients after surgery. In this study we have developed an individualized computational model based on MEG brain networks to explore seizure propagation and the efficacy of different virtual resections. Eventually, the goal is to obtain individualized models to optimize resection strategy and outcome. We have modelled seizure propagation as an epidemic process using the susceptible-infected (SI) model on individual brain networks derived from presurgical MEG. We included 10 patients who had received epilepsy surgery and for whom the surgery outcome at least one year after surgery was known. The model parameters were tuned in in order to reproduce the patient-specific seizure propagation patterns as recorded with invasive EEG. We defined a personalized search algorithm that combined structural and dynamical information to find resections that maximally decreased seizure propagation for a given resection size. The optimal resection for each patient was defined as the smallest resection leading to at least a 90% reduction in seizure propagation. The individualized model reproduced the basic aspects of seizure propagation for 9 out of 10 patients when using the resection area as the origin of epidemic spreading, and for 10 out of 10 patients with an alternative definition of the seed region. We found that, for 7 patients, the optimal resection was smaller than the resection area, and for 4 patients we also found that a resection smaller than the resection area could lead to a 100% decrease in propagation. Moreover, for two cases these alternative resections included nodes outside the resection area. Epidemic spreading models fitted with patient specific data can capture the fundamental aspects of clinically observed seizure propagation, and can be used to test virtual resections in silico. Combined with optimization algorithms, smaller or alternative resection strategies, that are individually targeted for each patient, can be determined with the ultimate goal to improve surgery outcome. MEG-based networks can provide a good approximation of structural connectivity for computational models of seizure propagation, and facilitate their clinical use.
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Affiliation(s)
- Ana P Millán
- Department of Clinical Neurophysiology and MEG Center, Amsterdam Neuroscience, Vrije Universiteit Amsterdam, Amsterdam UMC, Amsterdam, The Netherlands.
| | - Elisabeth C W van Straaten
- Department of Clinical Neurophysiology and MEG Center, Amsterdam Neuroscience, Vrije Universiteit Amsterdam, Amsterdam UMC, Amsterdam, The Netherlands
| | - Cornelis J Stam
- Department of Clinical Neurophysiology and MEG Center, Amsterdam Neuroscience, Vrije Universiteit Amsterdam, Amsterdam UMC, Amsterdam, The Netherlands
| | - Ida A Nissen
- Department of Clinical Neurophysiology and MEG Center, Amsterdam Neuroscience, Vrije Universiteit Amsterdam, Amsterdam UMC, Amsterdam, The Netherlands
| | - Sander Idema
- Department of Neurosurgery, Amsterdam Neuroscience, Vrije Universiteit Amsterdam, Amsterdam UMC, Amsterdam, The Netherlands
| | - Johannes C Baayen
- Department of Neurosurgery, Amsterdam Neuroscience, Vrije Universiteit Amsterdam, Amsterdam UMC, Amsterdam, The Netherlands
| | - Piet Van Mieghem
- Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands
| | - Arjan Hillebrand
- Department of Clinical Neurophysiology and MEG Center, Amsterdam Neuroscience, Vrije Universiteit Amsterdam, Amsterdam UMC, Amsterdam, The Netherlands
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5
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Williams OE, Mazzarisi P, Lillo F, Latora V. Non-Markovian temporal networks with auto- and cross-correlated link dynamics. Phys Rev E 2022; 105:034301. [PMID: 35428139 DOI: 10.1103/physreve.105.034301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2021] [Accepted: 02/03/2022] [Indexed: 06/14/2023]
Abstract
Many of the biological, social and man-made networks around us are inherently dynamic, with their links switching on and off over time. The evolution of these networks is often observed to be non-Markovian, and the dynamics of their links are often correlated. Hence, to accurately model these networks, predict their evolution, and understand how information and other relevant quantities propagate over them, the inclusion of both memory and dynamical dependencies between links is key. In this article we introduce a general class of models of temporal networks based on discrete autoregressive processes for link dynamics. As a concrete and useful case study, we then concentrate on a specific model within this class, which allows to generate temporal networks with a specified underlying structural backbone, and with precise control over the dynamical dependencies between links and the strength and length of their memories. In this network model the presence of each link is influenced not only by its past activity, but also by the past activities of other links, as specified by a coupling matrix, which directly controls the causal relations, and hence the correlations, among links. We propose a maximum likelihood method for estimating the model's parameters from data, showing how the model allows a more realistic description of real-world temporal networks and also to predict their evolution. Due to the flexibility of maximum likelihood inference, we illustrate how to deal with heterogeneity and time-varying patterns, possibly including also nonstationary network dynamics. We then use our network model to investigate the role that, both the features of memory and the type of correlations in the dynamics of links have on the properties of processes occurring over a temporal network. Namely, we study the speed of a spreading process, as measured by the time it takes for diffusion to reach equilibrium. Through both numerical simulations and analytical results, we are able to separate the roles of autocorrelations and neighborhood correlations in link dynamics, showing that not only is the speed of diffusion nonmonotonically dependent on the memory length, but also that correlations among neighboring links help to speed up the spreading process, while autocorrelations slow it back down. Our results have implications in the study of opinion formation, the modeling of social networks, and the spreading of epidemics through mobile populations.
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Affiliation(s)
- Oliver E Williams
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
| | - Piero Mazzarisi
- Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126 Pisa, Italy
| | - Fabrizio Lillo
- Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126 Pisa, Italy
- Department of Mathematics, University of Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy
| | - Vito Latora
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
- Dipartimento di Fisica ed Astronomia, Università di Catania and INFN, I-95123 Catania, Italy
- Complexity Science Hub Vienna (CSHV), A-1080 Vienna, Austria
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