Method for estimating critical exponents in percolation processes with low sampling

Bastas, Nikolaos; Kosmidis, Kosmas; Giazitzidis, Paraskevas; Maragakis, Michael

doi:10.1103/physreve.90.062101

Cited by 16 publications

(16 citation statements)

References 34 publications

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“…Only one value of p is associated to the critical percolation transition for which the size distribution of clusters follows a power law and it is called the critical probability p c . To find p c , we perform multiple percolations for a uniformly distributed set of q * ∈ (0, 1) (with 0.01 spacing), to find the critical value q * c corresponding to the maximum size of the second largest cluster [5,12].…”

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confidence: 99%

On the stability of traffic breakup patterns in urban networks

Cogoni,

Busonera

2021

Preprint

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We investigate the behavior of extended urban traffic networks within the framework of percolation theory by using real and synthetic traffic data. Our main focus shifts from the statistical properties of the cluster size distribution studied recently, to the spatial analysis of the clusters at criticality and to the definition of a similarity measure between whole urban configurations. We discover that the breakup patterns of the complete network, formed by the connected functional road clusters at criticality, show remarkable stability from one hour to the next, and predictability for different days at the same time. We prove this by showing how the average spatial distributions of the highest-rank clusters evolve over time, and by building a taxonomy of traffic states via dimensionality-reduction of the distance matrix, obtained via a clustering similarity score. Finally, we show that a simple random percolation model can approximate the breakup patterns of heavy real traffic when longranged spatial correlations are imposed.

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confidence: 99%

On the stability of traffic breakup patterns in urban networks

Cogoni,

Busonera

2021

Preprint

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“…27. Namely, we combine Newman and Ziff [31], Bastas et al [32] algorithms with finite size corrections [1,33] to estimate p c :…”

Section: Methodsmentioning

confidence: 99%

Percolation thresholds on triangular lattice for neighbourhoods containing sites up-to the fifth coordination zone

Malarz

2021

Preprint

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We determine thresholds pc for random-site percolation on a triangular lattice for all available neighborhoods containing sites from the first to the fifth coordination zones, including their complex combinations. There are 31 distinct neighbourhoods. The dependence of the value of the percolation thresholds pc on the coordination number z are tested against various theoretical predictions. The newly proposed single scalar index ξ = i zir 2 i /ζi (depending on the coordination zone number ζ, the neighbourhood coordination number z and the square-distance r 2 to sites in ζ-th coordination zone from the central site) allows to differentiate among various neighbourhoods and relate pc to ξ. The thresholds roughly follow a power law pc ∝ ξ −γ with γ ≈ 0.705(23).

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“…According to Refs. [36][37][38] instead of searching common crossing point of L x X(p; L) curves for various L one may wish to minimise…”

Section: Methodsmentioning

confidence: 99%

“…(1) and Sec. II) combined with Bastas et al technique [36][37][38] allows for estimation of percolation thresholds for simple cubic lattice in d = 4 and for neighbourhoods ranging from NN to 3NN+2NN+NN with the accuracy u(p C ) = 23 × 10 −5 .…”

Section: B Percolation Thresholdsmentioning

confidence: 99%

Efficient space virtualization for the Hoshen–Kopelman algorithm

Kotwica

Gronek

Malarz

2019

Int. J. Mod. Phys. C

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In this paper the efficient space virtualisation for the Hoshen-Kopelman algorithm is presented. We observe minimal parallel overhead during computations, due to negligible communication costs. The proposed algorithm is applied for computation of random-site percolation thresholds for four dimensional simple cubic lattice with sites' neighbourhoods containing next-next-nearest neighbours (3NN). The obtained percolation thresholds are pC (NN) = 0.19680(23), pC (2NN) = 0.08410(23), pC (3NN) = 0.04540(23), pC (2NN+NN) = 0.06180(23), pC (3NN+NN) = 0.04000(23), pC (3NN+2NN) = 0.03310(23), pC (3NN+2NN+NN) = 0.03190(23), where 2NN and NN stand for next-nearest neighbours and nearest neighbours, respectively. 11 87 s t r _ b u f f e r = " " 88 c a l l get_command_argument ( 1 , s t r _ b u f f e r ) 89 read ( s t r _ b u f f e r , fmt=" ( I ) " ) L 90 s t r _ b u f f e r = " " 91 c a l l get_command_argument ( 2 , s t r _ b u f f e r ) 92 read ( s t r _ b u f f e r , fmt=" (F) " ) p_min 93 s t r _ b u f f e r = " " 94 c a l l get_command_argument ( 3 , s t r _ b u f f e r ) 95 read ( s t r _ b u f f e r , fmt=" (F) " ) p_max 96 s t r _ b u f f e r = " " 97 c a l l get_command_argument ( 4 , s t r _ b u f f e r ) 98 read ( s t r _ b u f f e r , fmt=" (F) " ) p_step 99 s t r _ b u f f e r = " " 100 c a l l get_command_argument ( 5 , s t r _ b u f f e r ) 101 read ( s t r _ b u f f e r , fmt=" ( I ) " ) N_run

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Method for estimating critical exponents in percolation processes with low sampling

Cited by 16 publications

References 34 publications

On the stability of traffic breakup patterns in urban networks

On the stability of traffic breakup patterns in urban networks

Percolation thresholds on triangular lattice for neighbourhoods containing sites up-to the fifth coordination zone

Efficient space virtualization for the Hoshen–Kopelman algorithm

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