Efficient space virtualization for the Hoshen–Kopelman algorithm

Kotwica, Michalina; Gronek, Piotr; Malarz, Krzysztof

doi:10.1142/s0129183119500554

Cited by 30 publications

(22 citation statements)

References 47 publications

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“…In Hoshen-Kopelman algorithm each actor is labelled in such way, that actors with the same opinions and in the same cluster have identical labels. The algorithm allows for cluster detection in multi-dimensional space and for complex neighbourhoods [71][72][73][74][75], here however, we assume the simplest case, i.e. square lattice with von Neumann neighbourhood.…”

Section: Clustering Of Opinionsmentioning

confidence: 99%

Noise induced unanimity and disorder in opinion formation

Kowalska-Styczeń

Malarz

2020

PLoS ONE

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We propose an opinion dynamics model based on Latané 's social impact theory. Actors in this model are heterogeneous and, in addition to opinions, are characterised by their varying levels of persuasion and support. The model is tested for two and three initial opinions randomly distributed among actors. We examine how the noise (randomness of behaviour) and the flow of information among actors affect the formation and spread of opinions. Our main research involves the process of opinion formation and finding phases of the system in terms of parameters describing noise and flow of the information for two and three opinions available in the system. The results show that opinion formation and spread are influenced by both (i) flow of information among actors (effective range of interactions among actors) and (ii) noise (randomness in adopting opinions). The noise not only leads to opinions disorder but also it promotes consensus under certain conditions. In disordered phase and when the exchange of information is spatially effectively limited, various faces of disorder are observed, including system states, where the signatures of self-organised criticality manifest themselves as scale-free probability distribution function of cluster sizes. Then increase of noise level leads system to disordered random state. The critical noise level above which histograms of opinion clusters' sizes loose their scale-free character increases with increase of the easy of information flow.

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Section: Clustering Of Opinionsmentioning

confidence: 99%

Noise induced unanimity and disorder in opinion formation

Kowalska-Styczeń

Malarz

2020

PLoS ONE

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“…With regards to the latter system, Malarz and coworkers [29][30][31][32][33] have carried out several studies on lattices with various complex neighborhoods, that is, lattices with combinations of two or more types of neighbor connections, in two, three and four dimensions. Their results have all concerned site percolation, and are generally given to only three significant digits.…”

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confidence: 99%

Precise bond percolation thresholds on several four-dimensional lattices

Xun

Ziff

2020

Phys. Rev. Research

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We study bond percolation on several four-dimensional (4D) lattices, including the simple (hyper) cubic (SC), the SC with combinations of nearest neighbors and second nearest neighbors (SC-NN+2NN), the body-centered cubic (BCC), and the face-centered cubic (FCC) lattices, using an efficient single-cluster growth algorithm. For the SC lattice, we find pc = 0.1601312(8), which confirms previous results (based on other methods), and find a new value pc = 0.035827(2) for the SC-NN+2NN lattice, which was not studied previously for bond percolation. For the 4D BCC and FCC lattices, we obtain pc = 0.074212(2) and 0.049517(2), which are substantially more precise than previous values. We also find critical exponents τ = 2.3135(5) and Ω = 0.40(3), consistent with previous results, including the recent four-loop series result of Gracey [Phys. Rev. D 92, 025012, (2015)], Ω = 0.4003.

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“…As a result, the network contains a number of subgraphs of s linked susceptible nodes, considered as clusters of size s. To extract clusters of different sizes numerically, we apply an algorithm developed by Hoshen and Kopelman [39]. This algorithm is successfully applied in studies of percolation phenomenon in disordered environments [40,41,42,43,44] . For cluster containing s nodes, let us introduce the number of such clusters per one node n s (p) [44] (the probability P s (p) to find a cluster containing s susceptible nodes is thus P s (p) = sn s (p)).…”

Section: Random Scenariomentioning

confidence: 99%

Spreading processes in "post-epidemic" environments. II. Safety patterns on scale-free networks

Blavatska,

Holovatch

2021

Preprint

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This paper continues our previous study on spreading processes in inhomogeneous populations consisting of susceptible and immune individuals [V. Blavatska, Yu. Holovatch, Physica A 573, 125980 (2021)]. A special role in such populations is played by "safety patterns" of susceptible nodes surrounded by the immune ones. Here, we analyze spreading on scale-free networks, where the distribution of node connectivity k obeys a power-law decay ∼ k −λ . We assume, that only a fraction p of individual nodes can be affected by spreading process, while remaining 1 − p are immune. We apply the synchronous cellular automaton algorithm and study the stationary states and spatial patterning in SI, SIS and SIR models in a range 2 < λ < 3. Two immunization scenarios, the random immunization and an intentional one, that targets the highest degrees nodes are considered. A distribution of safety patterns is obtained for the case of both scenarios. Estimates for the threshold values of the effective spreading rate β c as a function of active agents fraction p and parameter λ are obtained and efficiency of both vaccination techniques are analyzed quantitatively. The impact of the underlying network heterogeneous structure is manifest e.g. in decreasing the β c values within the random scenario as compared to corresponding values in the case of regular latticek. This result quantitatively confirms the compliency of scale-free networks for disease spreading. On contrary, the vaccination within the targeted scenario makes the complex networks much more resistant to epidemic spreading as compared with regular lattice structures.

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Efficient space virtualization for the Hoshen–Kopelman algorithm

Cited by 30 publications

References 47 publications

Noise induced unanimity and disorder in opinion formation

Noise induced unanimity and disorder in opinion formation

Precise bond percolation thresholds on several four-dimensional lattices

Spreading processes in "post-epidemic" environments. II. Safety patterns on scale-free networks

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