Time Centrality in Dynamic Complex Networks

Costa, Eduardo Chinelate; Vieira, Alex Borges; Wehmuth, Klaus; Ziviani, Artur; Silva, Ana Paula Couto da

doi:10.1142/s021952591550023x

Cited by 33 publications

(35 citation statements)

References 22 publications

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“…Therefore, the diffusion power of a dynamic network has proven to be paramount with the purpose of optimizing the average fitness/payoff of an algorithmic network that plays the Busy Beaver Imitation Game. Besides, this diffusion power may come either from the cover time [Costa et al 2015] or from a small diameter compared to the network size.…”

Section: Resultsmentioning

confidence: 99%

Expected Emergence of Algorithmic Information from a Lower Bound for Stationary Prevalence

Abrahão¹,

Wehmuth²,

Ziviani³

2018

Anais Do Encontro De Teoria Da Computação (ETC)

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We study emergent information in populations of randomly generated networked computable systems that follow a Susceptible-Infected-Susceptible contagion (or infection) model of imitation of the fittest neighbor. These networks have a scale-free degree distribution in the form of a power-law following the Barabási-Albert model. We show that there is a lower bound for the stationary prevalence (or average density of infected nodes) that triggers an unlimited increase of the expected emergent algorithmic complexity (or information) of a node as the population size grows.

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Section: Resultsmentioning

confidence: 99%

Expected Emergence of Algorithmic Information from a Lower Bound for Stationary Prevalence

Abrahão¹,

Wehmuth²,

Ziviani³

2018

Anais Do Encontro De Teoria Da Computação (ETC)

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“…We define a central node o cen that can compute a function Now, we come back to node centralities in network science in order to rank the node that can be quickly accessible by an arbitrary diffusion from an arbitrary fraction of the nodes. From [19]: Definition 6.3. Let d t (G t , t i , u, τ ) be the minimum number of time intervals (nonspatial steps or, specially in the present article, node cycles) for a diffusion starting on any vertex v ∈ X of a fraction τ = X of vertices in the TVG G t at time instant t i to reach vertice u, where X ∈ P (V (G t )) is arbitrary.…”

Section: Solving the Halting Problem Through The Busy Beaver Imitatiomentioning

confidence: 99%

Learning the Undecidable from Networked Systems

Abrahão

D’Ottaviano

Wehmuth

et al. 2020

Unravelling Complexity

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This article presents a theoretical investigation of computation beyond the Turing barrier from emergent behavior in distributed systems. In particular, we present an algorithmic network that is a mathematical model of a networked population of randomly generated computable systems with a fixed communication protocol. Then, in order to solve an undecidable problem, we study how nodes (i.e., Turing machines or computable systems) can harness the power of the metabiological selection and the power of information sharing (i.e., communication) through the network. Formally, we show that there is a pervasive network topological condition, in particular, the small-diameter phenomenon, that ensures that every node becomes capable of solving the halting problem for every program with a length upper bounded by a logarithmic order of the population size. In addition, we show that this result implies the existence of a central node capable of emergently solving the halting problem in the minimum number of communication rounds. Furthermore, we introduce an algorithmic-informational measure of synergy for networked computable systems, which we call local algorithmic synergy. Then, we show that such algorithmic network can produce an arbitrarily large value of expected local algorithmic synergy.

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Section: Emergent Open-endedness From Contagion Of the Fittestmentioning

confidence: 99%

“…Inspired by the networks in [33][34][35], let G SIS (f, t) be 17 a family of Time-Varying Graphs in which every G t ∈ G SIS (f, t) achieves stationary prevalence ρ in a number of time intervals ∆ * t (after an arbitrary time instant t ∈ T(G t ) from which contagion may have been started in first place) following the SIS scheme. Thus, G SIS (f, t) defines a family of dynamic networks [18,21] that follows the SIS model. Since we have defined static networks as a special case of dynamic networks, family G SIS (f, t) can be seen as a generalization of the model presented in [33][34][35] to 11 See also [4,15] for a complete evolutionary formalization of this property.…”

Section: Modelmentioning

confidence: 99%

“…Thus, the diffusion power of a dynamic (or static) network has proved to be paramount with the purpose of optimizing the average fitness/payoff of an algorithmic network that plays the Busy Beaver Imitation Game in a randomly generated population of Turing machines. Furthermore, this diffusion power may come either from the cover time [18] or from a small diameter [6,12] compared to the network size.Open-endedness is commonly defined in evolutionary computation and evolutionary biology as the inherent potential of a evolutionary process to trigger an endless increase of complexity or irreducible information [4,5,22]. That means that in the long run eventually will appear an organism that is as complex as one may want.…”

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Emergent Open-Endedness from Contagion of the Fittest

Abrahão¹,

Wehmuth²,

Ziviani³

2018

ComplexSystems

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In this paper, we study emergent irreducible information in populations of randomly generated computable systems that are networked and follow a "Susceptible-Infected-Susceptible" contagion model of imitation of the fittest neighbor. We show that there is a lower bound for the stationary prevalence (or average density of "infected" nodes) that triggers an unlimited increase of the expected local emergent algorithmic complexity (or information) of a node as the population size grows. We call this phenomenon expected (local) emergent open-endedness. In addition, we show that static networks with a power-law degree distribution following the Barabási-Albert model satisfy this lower bound and, thus, display expected (local) emergent open-endedness. Emergent Open-Endedness from Contagion of the Fittest 3The population of our present model plays the Busy Beaver Imitation Game (BBIG), in which each node always imitates the fittest neighbor only. Nevertheless, differently from the model in [4], we present a variation on the information-sharing (or communication) protocol. The major difference in respect to this previous work comes from allowing nodes to become "cured" (with rate δ). Additionally, now nodes also get "infected" with rate ν-which may have a value different from 1. In [4], one has that ν = 1 always holds. Summarizing, although still playing a BBIG, susceptible nodes follow a rule of imitating the neighbor that had output the largest integer (which corresponds to the fittest individual outcome in the population). However, they follow this rule with probability ν, and "infected" nodes come back-become "cured"-to the initial stage with probability δ. Thus, the effective spreading rate λ = ν/δ defined in [33][34][35] assumes a direct interpretation of the rate in which the Imitation-of-the-Fittest Protocol [4] was applied on a node-and this is the reason why we are using the words "infection" and "cure" between quotation marks. Therefore, the diffusion or "infection" scheme of the best output returned by a randomly generated node is ruled by the Susceptible-Infected-Susceptible epidemic model (SIS) in which susceptible nodes have a constant probability ν of being "infected" by a previously "infected" neighbor and "infected" nodes have a constant probability δ of becoming "cured". We also assume, as in [33][34][35], that the prevalence of "infected" nodes (i.e., the average density of "infected" nodes) becomes stationary after sufficient time 1 .Our proofs follow mainly from information theory, computability theory, and graph theory applied on a variation on the information-sharing protocol of the model in [4]. In particular, we have proved results for general dynamic networks and for dynamic networks with a small diameter-O(log(N )) compared to the network size N -in [4]. Further, these results are also directly extended to static networks [4] with the small-diameter property. Therefore, we have shown that there are topological conditions that trigger a phase transition in which eventually the algorithmic networ...

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Time Centrality in Dynamic Complex Networks

Cited by 33 publications

References 22 publications

Expected Emergence of Algorithmic Information from a Lower Bound for Stationary Prevalence

Expected Emergence of Algorithmic Information from a Lower Bound for Stationary Prevalence

Learning the Undecidable from Networked Systems

Emergent Open-Endedness from Contagion of the Fittest

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