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Profile and scaling of the fractal exponent of percolations in complex networks

T. Hasegawa, T. Nogawa, K. Nemoto
2013 Europhysics letters  
Since the neighbor of the ordered phase is not a simple disordered phase but a critical phase, conventional finite size scaling technique does not work.  ...  We confirm the validity of our scaling hypothesis through Monte-Carlo simulations for bond percolations in some network models: the decorated (2,2)-flower and the random attachment growing network, where  ...  Acknowledgments The authors thank M. Sato, K. Konno, and N. Masuda for valuable comments.  ... 
doi:10.1209/0295-5075/104/16006 fatcat:3rryzmbbu5fwllb7pvzzn5jxqe

Randomized Robust matrix Completion for the Community Detection Problem

Adel Karimian, Mostafa Rahmani, Andre Beckus, George K. Atia
2018 2018 52nd Asilomar Conference on Signals, Systems, and Computers  
We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model.  ...  The clustering is first applied to a sub-matrix of the graph's adjacency matrix associated with a reduced graph sketch constructed using random sampling.  ...  compares the phase transition plots of the proposed randomized methods in the sample complexity and minimum cluster size plane.  ... 
doi:10.1109/acssc.2018.8645348 dblp:conf/acssc/KarimianRBA18 fatcat:3jfqkvruozh2jkzsv5eyepkuwe

Criticality-based analysis and design of unstructured peer-to-peer networks as "Complex systems"

F. Banaei-Kashani, C. Shahabi
2003 CCGrid 2003. 3rd IEEE/ACM International Symposium on Cluster Computing and the Grid, 2003. Proceedings.  
Due to enormous complexity of the unstructured peer-to-peer networks as large-scale, self-configure, and dynamic systems, the models used to characterize these systems are either inaccurate, because of  ...  We provide two examples of application of this modeling approach that demonstrate its power.  ...  Acknowledgments This research has been funded in part by NSF grants EEC-9529152 (IMSC ERC) and IIS-0082826, and unrestricted cash gifts from Microsoft, NCR, and Okawa Foundation.  ... 
doi:10.1109/ccgrid.2003.1199387 dblp:conf/ccgrid/Banaei-KashaniS03 fatcat:v5zbog2isbep5mqspsp5ayuzei

Infinite-disorder scaling of random quantum magnets in three and higher dimensions

István A. Kovács, Ferenc Iglói
2011 Physical Review B  
Using a very efficient numerical algorithm of the strong disorder renormalization group method we have extended the investigations about the critical behavior of the random transverse-field Ising model  ...  in three and four dimensions, as well as for Erd\H os-R\'enyi random graphs, which represent infinite dimensional lattices.  ...  In 3D and 4D the clusters have a hypercubic shape with a linear length, L, while for the ER model a graph consists of N sites and of kN/2 edges being in random positions.  ... 
doi:10.1103/physrevb.83.174207 fatcat:v46tltb7fjbtfkj65kj3vsz4zq

The work of Hugo Duminil-Copin [article]

Geoffrey R. Grimmett
2022 arXiv   pre-print
This article is an account of the scientific work of Hugo Duminil-Copin at the time of his award in 2022 of the Fields Medal "for solving longstanding problems in the probabilistic theory of phase transitions  ...  in statistical physics, especially in dimensions three and four".  ...  of the three-dimensional Ising model, (ii) the 'triviality' of the Ising model scaling limits in four dimensions, and (iii) the sharpness of the phase transition for a range of stochastic models in arbitrary  ... 
arXiv:2207.02022v1 fatcat:m4hfgvzm2bb6vjsquinlzxn7cm

Dense Percolation in Large-Scale Mean-Field Random Networks Is Provably "Explosive"

Alexander Veremyev, Vladimir Boginski, Pavlo A. Krokhmal, David E. Jeffcoat, Sergio Gómez
2012 PLoS ONE  
the previously derived formula for the size of the largest clique (a cluster with all possible links) in such a network.  ...  Moreover, the size of the largest dense (highly connected) cluster in a mean-field random network is explicitly characterized by rigorously proven tight asymptotic bounds, which turn out to naturally extend  ...  In other words, the size of the largest dense connected component in a large-scale Erdös-Rényi random network exhibits a first-order phase transition; moreover, the existence of this phase transition has  ... 
doi:10.1371/journal.pone.0051883 pmid:23272185 pmcid:PMC3525599 fatcat:zzyolmzbjbbofadmzfrdhntwfm

Clique percolation in random graphs

Ming Li, Youjin Deng, Bing-Hong Wang
2015 Physical Review E  
discontinuous phase transition in the thermodynamic limit and a continuous phase transition for l=1.  ...  As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two k-cliques means that they share at least l1 makes a step-function-like  ...  However, the fraction of vertices in the giant clique cluster φ takes an unnormal phase transition for l > 1, and a continuous phase transition for l = 1.  ... 
doi:10.1103/physreve.92.042116 pmid:26565177 fatcat:3jtmvcfn75ahhengcqk436zsry

Explosive percolation: Unusual transitions of a simple model

N. Bastas, P. Giazitzidis, M. Maragakis, K. Kosmidis
2014 Physica A: Statistical Mechanics and its Applications  
There a simple model was proposed, which changed slightly the classical percolation process so that the emergence of the spanning cluster is delayed.  ...  In this paper we review the recent advances on explosive percolation, a very sharp phase transition first observed by Achlioptas et al. (Science, 2009).  ...  On the other hand, Liang et al. [41] implemented the Achlioptas process in random graphs, scale-free networks, and in 2D lattices.  ... 
doi:10.1016/j.physa.2014.03.085 fatcat:ct3dchxk5fdaxk3g7soy4tmmpu

Finite-size scaling functions of the phase transition in the ferromagnetic Ising model on random regular graphs [article]

Suman Kulkarni, Deepak Dhar
2022 arXiv   pre-print
In the thermodynamic limit, the Ising model on these graphs show a phase transition. This transition is rounded off for finite graphs.  ...  We discuss the finite-size scaling of the ferromagnetic Ising model on random regular graphs.  ...  Acknowledgments The authors thank Prof. Kedar Damle for useful discussions. Suman acknowledges the National Supercomputing Mission (Param Bramha, IISER Pune) for the computational resources provided.  ... 
arXiv:2110.02928v3 fatcat:dvpzktozhffttjhsi7ffainq6i

Bipartite and directed scale-free complex networks arising from zeta functions

Piergiulio Tempesta
2014 Communications in nonlinear science & numerical simulation  
The bipartite L-graphs and the multiplicative zeta graphs are relevant examples of the proposed construction. Phase transitions and percolation thresholds for our models are determined.  ...  We construct a new class of directed and bipartite random graphs whose topology is governed by the analytic properties of L-functions.  ...  Acknowledgments The research of P. T. has been partly supported by the grant FIS2011-00260, Ministerio de Ciencia e Innovación, Spain.  ... 
doi:10.1016/j.cnsns.2013.08.037 fatcat:czpy2btafrhwbcqyhlmlqlc7gq

Recent advances in percolation theory and its applications

Abbas Ali Saberi
2015 Physics reports  
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component.  ...  In this review we will first outline the basic features of the ordinary model and take a glimpse at a number of selective variations and modifications of the original model.  ...  This random graph is shown to exhibit a percolation phase transition in the size of the maximal component, as well as in the connectivity of the arising random graph.  ... 
doi:10.1016/j.physrep.2015.03.003 fatcat:fwp76ca44vanfh2inf5a6tzjiq

The hard-core model on random graphs revisited

Jean Barbier, Florent Krzakala, Lenka Zdeborová, Pan Zhang
2013 Journal of Physics, Conference Series  
degree K>=20, and that for K>16 the nature of the phase transition is the same as for large K.  ...  We revisit the classical hard-core model, also known as independent set and dual to vertex cover problem, where one puts particles with a first-neighbor hard-core repulsion on the vertices of a random  ...  Acknowledgments This work has been supported in part by the ERC under the European Union's 7th Framework Programme Grant Agreement 307087-SPARCS, by the Grant DySpaN of "Triangle de la Physique" and by  ... 
doi:10.1088/1742-6596/473/1/012021 fatcat:aq2xhemaifhdhluh33h37r2bei

Structural properties of scale-free networks [chapter]

Reuven Cohen, Shlomo Havlin, Daniel ben-Avraham
2004 Handbook of Graphs and Networks  
In most random network models the structure is locally tree-like (since most loops occur 1.2 Small and Ultra-Small Worlds 7 Minimal graphs and lower bound We begin by showing that the radius of any scale-free  ...  We study percolation in scale-free networks and show that in the regime £ © the networks are resilient to random breakdown and the percolation transition occurs only in the limit of extreme dilution.  ...  DbA thanks the support of the National Science Foundation (USA).  ... 
doi:10.1002/3527602755.ch4 fatcat:q5vtarvswbhllk7xtkuqjht4xm

Explosive percolation in graphs

Santo Fortunato, Filippo Radicchi
2011 Journal of Physics, Conference Series  
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics.  ...  In this work we survey a numerical study of the explosive percolation transition on various types of graphs, from lattices to scale-free networks, and show the consistency of these results with recent  ...  [12] suggested that this is due to the non-random addition of links during the Achlioptas process, because of which the degree distribution of the system during the growth deviates from that imposed  ... 
doi:10.1088/1742-6596/297/1/012009 fatcat:qirisfsgyrgj3dbgva4uyl7are

Rounding of first-order phase transitions and optimal cooperation in scale-free networks

M. Karsai, J-Ch. Anglès d'Auriac, F. Iglói
2007 Physical Review E  
It is shown rigorously that the homogeneous model has a strongly first-order phase transition, which turns to second-order for random interactions (benefits), the properties of which are studied numerically  ...  The agents are found to be typically of two kinds: a fraction of m (being the magnetization of the Potts model) belongs to a large cooperating cluster, whereas the others are isolated one man's projects  ...  In several models the phase transition in regular lattices is of first order, such as for the q-state Potts model for sufficiently large values of q.  ... 
doi:10.1103/physreve.76.041107 pmid:17994936 fatcat:od5cv3rf7jci3d65gvrrh35sue
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