Bond percolation in coloured and multiplex networks

Kryven, Ivan

doi:10.1038/s41467-018-08009-9

Cited by 36 publications

(33 citation statements)

References 53 publications

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“…Percolation is among the most widely studied critical phenomena on networks [21][22][23][24][25][26][27][28][29] and for many years it has been argued that percolation could only lead to second-order phase transitions. However, in recent years, there has been an increasing interest in unveiling the basic mechanisms responsible for abrupt percolation transitions in complex networks.…”

Section: Introductionmentioning

confidence: 99%

Renormalization group for link percolation on planar hyperbolic manifolds

2019

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Network geometry is currently a topic of growing scientific interest, as it opens the possibility to explore and interpret the interplay between structure and dynamics of complex networks using geometrical arguments. However, the field is still in its infancy. In this work we investigate the role of network geometry in determining the nature of the percolation transition in planar hyperbolic manifolds. In Ref.[1], S. Boettcher, V. Singh, R. M. Ziff have shown that a special type of twodimensional hyperbolic manifolds, the Farey graphs, display a discontinuous transition for ordinary link percolation. Here we investigate using the renormalization group the critical properties of link percolation on a wider class of two-dimensional hyperbolic deterministic and random manifolds constituting the skeletons of two-dimensional cell complexes. These hyperbolic manifolds are built iteratively by subsequently gluing m-polygons to single edges. We show that when the size m of the polygons is drawn from a distribution qm with asymptotic power-law scaling qm Cm −γ for m 1, different universality classes can be observed depending on the value of the power-law exponent γ. Interestingly, the percolation transition is hybrid for γ ∈ (3, 4) and becomes continuous for γ ∈ (2, 3].

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Section: Introductionmentioning

confidence: 99%

Renormalization group for link percolation on planar hyperbolic manifolds

2019

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“…For instance, when an interdependent multilayer network is drawn from the configura-tion model, percolation may lead to multiple discontinuous and hybrid transitions due to a successive deactivation of different layers at different values of the percolation parameter [31]. Similar effect is also seen in classical percolation as it can display multiple phase transitions corresponding to deactivation of one or several layers at a time [32,35]. Nevertheless, these phase transitions are continuous and second order.…”

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confidence: 86%

Enhancing the robustness of a multiplex network leads to multiple discontinuous percolation transitions

Kryven

Bianconi

2019

Phys. Rev. E

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The Alan Turing Institute, the British Library, London NW1 2DB, United Kingdom Determining design principles that boost robustness of interdependent networks is a fundamental question of engineering, economics, and biology. It is known that maximizing the degree correlation between replicas of the same node leads to optimal robustness. Here we show that increased robustness might also come at the expense of introducing multiple phase transitions. These results reveal yet another possible source of fragility of multiplex networks that has to be taken into the account during network optimisation and design.Multilayer networks [1-3] formed by several interacting layers have emerged as a powerful framework to analyse a variety of complex systems, including such classical examples as global infrastructures, economic networks, temporal networks and the multi-level structure of the brain. Other disciplines, as material science and chemical synthesis, are on the way to adopt the network science toolbox, less for analysis purpose, but mainly for its potential for optimisation and rational design [4][5][6][7][8]. Therefore, predicting the robustness of multilayer networks [9-11], assessing the risk of large avalanches of failures [9][10][11][12][13][14][15], and designing robust multilayer architectures [16][17][18] are the key theoretical questions entailing implications for engineering, economics, and biology. Recent works on percolation in multilayer networks revealed that the correlation between intra-layer degrees of replica nodes [16,17] and link overlap [19][20][21] have profound consequences in determining the response of a multiplex network to random damage. The case of positive interlayer degree correlation [1,16], when a hub node in one layer is likely to be interdependent on a hub node in another layer, is known to increase robustness of interdependent multiplex networks. It is widely believed that maximizing the inter-layer degree correlation is a good design principle for building robust infrastructures. The network optimization is used not only for engineered networks and infrastructures [22][23][24][25][26][27] but also for economic [28] and biological networks [29,30]. Therefore, it is of fundamental importance to understand how maximizing the inter-layer degree correlation may affect the properties of multiplex networks.

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“…Although a detailed handling is beyond the scope of the present discussion, k-core decomposition and percolation methods may be useful for estimating subnetworks (e.g. giant components) that are particularly likely to have high integrated information (Cellai et al, 2016;Bianconi, 2017;Kryven, 2019). An intriguing recent study used these kinds of techniques to track the transition from conscious to unconscious subliminal perceptual states (Arese Lucini et al, 2019).…”

Section: Conscious and Unconscious Cores And Workpaces; Physical Submentioning

confidence: 99%

Integrated World Modeling Theory (IWMT) Revisited

Safron¹

2019

Preprint

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Here, I provide clarifications and discuss further issues relating to Safron (2020), “An Integrated World Modeling Theory (IWMT) of consciousness: Combining Integrated Information and Global Workspace Theories with the Free Energy Principle and Active Inference Framework; towards solving the Hard problem and characterizing agentic causation.” As a synthesis of major theories of complex systems and consciousness, with IWMT we may be able to address some of the most difficult problems in the sciences. This is a claim deserving of close scrutiny and much skepticism. What would it take to solve the Hard problem? One could answer the question of how it is possible that something like subjectivity could emerge from objective brain functioning (i.e., moving from a third person to a first person ontology), but a truly satisfying account might still require solving all the “easy” and “real” problems of consciousness. In this way, IWMT does not claim to definitively solve the Hard problem, as explaining all the particular ways that things feel across all relevant aspects of experience is likely an impossible task. Nonetheless, IWMT does claim to have made major inroads into our understanding of consciousness, and here I will attempt to justify this position by discussing challenging problems and outstanding questions with respect to philosophy, (neuro)phenomenology, computational principles, practical applications, and implications for existing theories of mind and life.

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Bond percolation in coloured and multiplex networks

Cited by 36 publications

References 53 publications

Renormalization group for link percolation on planar hyperbolic manifolds

Renormalization group for link percolation on planar hyperbolic manifolds

Enhancing the robustness of a multiplex network leads to multiple discontinuous percolation transitions

Integrated World Modeling Theory (IWMT) Revisited

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