Higher-order percolation processes on multiplex hypergraphs

Sun, Hanlin; Bianconi, Ginestra

doi:10.1103/physreve.104.034306

Cited by 66 publications

(32 citation statements)

References 65 publications

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“…Hence the constraint dλ/dR 2 =0 is satisfied at λ=λ b , which leads to R 2 (λ b ) = 1 2 (1 − aq bp ) from Eq. (17). Substituting the value of R 2 back into Eq.…”

Section: Solution Of Coherencementioning

confidence: 99%

“…An n-simplicial complex comprises the n-simplexes and the downward closure (n−1)simplexes. Recently, the call for simplicial complexes in encoding higher-order interaction in complex systems has put a spurt on in untangling the reciprocation between network geometry and dynamical processes [7][8][9][10][11][12][13][14][15][16][17]. One novel phenomena that naturally borns out of simplicial complex encoded higher-order interactions is the abrupt transition to synchronization and desynchronization [8,11,18].…”

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confidence: 99%

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First-order route to antiphase clustering in adaptive simplicial complexes

Kachhvah¹,

Jalan²

2022

Preprint

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This Letter investigates the transition to synchronization of oscillator ensembles encoded by simplicial complexes in which pairwise and higher-order coupling weights adapt with time through the Hebbian learning mechanism. These concurrently evolving disparate adaptive coupling weights lead to a novel phenomenon in that the in-phase synchronization is completely obliterated; instead, the anti-phase synchronization is originated. Besides this, the onsets of anti-phase synchronization and desynchronization are manageable through both dyadic and triadic Hebbian learning rates. The theoretical validation of these numerical assessments is delineated thoroughly by employing Ott-Antonsen dimensionality reduction. The framework and results of the Letter would help to understand the underlying synchronization behavior of a range of real-world systems, such as the brain functions and social systems where interactions evolve with time.

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“…Hence the constraint dλ/dR 2 =0 is satisfied at λ=λ b , which leads to R 2 (λ b ) = 1 2 (1 − aq bp ) from Eq. (17). Substituting the value of R 2 back into Eq.…”

Section: Solution Of Coherencementioning

confidence: 99%

mentioning

confidence: 99%

First-order route to antiphase clustering in adaptive simplicial complexes

Kachhvah¹,

Jalan²

2022

Preprint

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“…Concerning dynamical processes, frameworks for hypernetwork robustness and analysis of higher-order percolation processes [48][49][50] are put forward for multiplex hypernetworks. Analogous to the largest eigenvalue of the matrix representing the interaction structure of a network built upon dyadic connections, the concept of an 'expansion eigenvalue' for hypernetwork dynamical processes is proposed and approximated through a mean-field approach [51].…”

Section: Introductionmentioning

confidence: 99%

Dynamics on higher-order networks: a review

Majhi

Perc

Ghosh

2022

J. R. Soc. Interface.

247

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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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“…Over the past two decades, real-world systems are often modelled as complex networks [1][2][3][4], where nodes denote entities within the systems, and links represent the interactions among them. Most recently, many complex systems have been described by multiple interdependent networks or multilayer networks [5][6][7][8][9][10][11][12][13][14][15][16]. As a typical example, there exists an intricate interplay between the power system and communication network [6], where, on the one hand, the basic function of the communication system requires a proper power supply from the electrical system to keep its running; on the other hand, only when the communication system is working properly can the electricity generated by the power system be transferred continuously to the places where it is needed.…”

Section: Introductionmentioning

confidence: 99%

Epidemics on multilayer simplicial complexes

et al. 2022

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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, in particular in the context of a multilayer network model, where one layer is a virtual social network and the other one is a physical contact network. The social network layer is responsible for the transmission of information via pairwise or higher order 2-simplex interactions among individuals, while the physical layer is responsible for the epidemic spreading. We use the microscopic Markov chain approach to derive the probability transition equations and to determine epidemic outbreak thresholds. We further support these results with Monte Carlo simulations, which are in good agreement, thus confirming the analytical tractability of the proposed model. We find that information transmission rates are frequently low when actual disease transmission rates in the physical network are low or medium, and we show that this can be mitigated effectively by introducing 2-simplex interactions in the social network. The relative ease of introducing higher-order interactions in virtual social networks means that this could be exploited to inhibit epidemic outbreaks.

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Higher-order percolation processes on multiplex hypergraphs

Cited by 66 publications

References 65 publications

First-order route to antiphase clustering in adaptive simplicial complexes

First-order route to antiphase clustering in adaptive simplicial complexes

Dynamics on higher-order networks: a review

Epidemics on multilayer simplicial complexes

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