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Analytic Description of the Phase Transition of Inhomogeneous Multigraphs [article]

Élie de Panafieu, Vlady Ravelomanana
2014 arXiv   pre-print
We also obtain new results on the phase transition of the satisfiability of quantified 2-Xor-formulas, a problem introduced by Creignou, Daud\'e and Egly (2007).  ...  By means of analytic combinatorics, we then analyze the birth of "complex components", which are components with at least two cycles.  ...  Recently, different authors gave precise descriptions of the phase transitions associated to several tractable decision problems.  ... 
arXiv:1409.8424v1 fatcat:j27y5y5eg5bitf5rj4x3fkf5su

Analytic description of the phase transition of inhomogeneous multigraphs [chapter]

Élie de Panafieu, Vlady Ravelomanana
2013 The Seventh European Conference on Combinatorics, Graph Theory and Applications  
As applications, we derive new proofs of known results on the 2-colorability problem [16] and on the enumeration of properly q-colored multigraphs [18] , and new results on the phase transition of the  ...  By means of analytic combinatorics, we then analyze the birth of complex components, which are components with at least two cycles.  ...  Related Works Recently, different authors gave precise descriptions of the phase transitions associated to several tractable decision problems.  ... 
doi:10.1007/978-88-7642-475-5_72 fatcat:euucg23vqjbk7fvqtrhthppki4

Master equation analysis of mesoscopic localization in contagion dynamics on higher-order networks [article]

Guillaume St-Onge, Vincent Thibeault, Antoine Allard, Louis J. Dubé, Laurent Hébert-Dufresne
2020 arXiv   pre-print
In this regime, the phase transition is smeared, characterized by an inhomogeneous activation of the groups.  ...  When considering heterogeneous networks, both at the level of nodes and groups, we characterize analytically the region associated with mesoscopic localization in the structural parameter space.  ...  Another notable effect is the smearing of the phase transition, where the order parameter develops inhomogeneously beyond the critical point [27] [28] [29] [30] [31] .  ... 
arXiv:2004.10203v2 fatcat:5vg4jddedrgy5pvja4r6ildafm

The birth of the strong components [article]

Sergey Dovgal, Élie de Panafieu, Dimbinaina Ralaivaosaona, Vonjy Rasendrahasina, Stephan Wagner
2022 arXiv   pre-print
Random directed graphs D(n,p) undergo a phase transition around the point p = 1/n, and the width of the transition window has been known since the works of Luczak and Seierstad.  ...  By using techniques from analytic combinatorics, we establish the exact limiting value of this probability as a function of μ and provide more properties of the structure of a random digraph around, below  ...  This simple idea has grown into the discovery of the symbolic method for directed graphs (which, as discovered later, has been independently established around 50 years ago by Liskovets, Robinson and then  ... 
arXiv:2009.12127v2 fatcat:z2jdyr57wbfn7bmvtokl2rd6wm

Properties of random graphs with hidden color

Bo Söderberg
2003 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
The calculability of local and global structural properties of graphs from the resulting ensembles is demonstrated.  ...  We investigate in some detail a recently suggested general class of ensembles of sparse undirected random graphs based on a hidden stub-coloring, with or without the restriction to nondegenerate graphs  ...  Nowicki on the complications associated with subgraph distributions is gratefully acknowledged. This work was in part supported by the Swedish Foundation for Strategic Research.  ... 
doi:10.1103/physreve.68.026107 pmid:14525049 fatcat:ybht4tqslfgjhfvb4fmypia4ne

Enumeration and structure of inhomogeneous graphs [article]

Élie de Panafieu
2015 arXiv   pre-print
We analyze a general model of weighted graphs, introduced by de Panafieu and Ravelomanana (2014) and similar to the "inhomogeneous graph model" of Söderberg (2002).  ...  The weight of the graph is then the product of the weights of its vertices and edges.  ...  Inhomogeneous graphs have been used in de Panafieu and Ravelomanana (2014) to analyze the phase transition of satisfiability problems. We present two new applications.  ... 
arXiv:1501.07775v2 fatcat:h77ehaleg5hshdvq47zozpl5oe

Enumeration and structure of inhomogeneous graphs

Élie De Panafieu
2015 Discrete Mathematics & Theoretical Computer Science  
We analyze a general model of weighted graphs, introduced by de Panafieu and Ravelomanana (2014) and similar to the inhomogeneous graph model of Söderberg (2002).  ...  We investigate the sum of the weights of those graphs and their structure.  ...  Applications Inhomogeneous graphs have been used in [4] to analyze the phase transition of satisfiability problems.  ... 
doi:10.46298/dmtcs.2501 fatcat:eoprmzbhzjgblejdibortf4eiy

The theory of filtrations of subalgebras, standardness, and independence

A M Vershik
2017 Russian Mathematical Surveys  
One of the key notions, that of standardness, plays the role of a generalization of the notion of the independence of a sequence of random variables.  ...  The survey is devoted to the combinatorial and metric theory of filtrations, i. e., decreasing sequences of σ-algebras in measure spaces or decreasing sequences of subalgebras of certain algebras.  ...  also related to the theory of invariant measures, phase transitions, etc.  ... 
doi:10.1070/rm9763 fatcat:4zk76hvxqjca5m32deo3buj5eu

Dynamical collision network in granular gases

J. Ignacio Alvarez-Hamelin, Andrea Puglisi
2007 Physical Review E  
The clear transition between those two phases appears in the evolution of the k-shells structure in the collision network.  ...  Because of energy dissipation, the gas cools down: its initial spatially homogeneous dynamics, characterized by the Haff law, i.e. a t^-2 energy decay, is unstable towards a strongly inhomogeneous phase  ...  ACKNOWLEDGMENTS The authors wish to thank the Laboratoire de Physique Théorique d' Orsay  ... 
doi:10.1103/physreve.75.051302 pmid:17677049 fatcat:fczus2szffenlfzcmkc3trozae

Contrast integration over area is extensive: A three-stage model of spatial summation

Daniel H. Baker, Tim S. Meese
2011 Journal of Vision  
Unfortunately, (i) this approach is compromised by retinal inhomogeneity and (ii) it potentially confounds summation of signal with summation of internal noise. The Swiss cheese stimulus of T. S.  ...  of the contrast integrators by probability summation.  ...  We also thank an anonymous reviewer and Keith May for encouraging us to perform the scale-dependent modeling.  ... 
doi:10.1167/11.14.14 pmid:22178702 fatcat:6dno4goc7jfkzgbqmqcedr2ame

The attenuation surface for contrast sensitivity has the form of a witch's hat within the central visual field

A. S. Baldwin, T. S. Meese, D. H. Baker
2012 Journal of Vision  
However, many psychophysical studies of spatial visual function concentrate on the central 64.5 deg (or so) of the visual field.  ...  To reduce the potential effects of stimulus uncertainty, circular markers surrounded the targets.  ...  Part of this work has appeared in abstract form at the 2010 AVA Spring Meeting (Baldwin, Meese, & Baker, 2010  ... 
doi:10.1167/12.11.23 pmid:23104816 fatcat:tyugpr25xzahjllbyk7yeyvqnu

The absolute of finitely generated groups: II. The Laplacian and degenerate parts [article]

A.Vershik, A.Malyutin
2018 arXiv   pre-print
The article continues the series of papers on the absolute of finitely generated groups.  ...  The absolute of a group with a fixed system of generators is defined as the set of ergodic Markov measures for which the system of cotransition probabilities is the same as for the simple (right) random  ...  The value α = 1/2 corresponds to the critical point at which the Markov chain loses ergodicity (phase transition). At this point, eigenfunctions stop being minimal.  ... 
arXiv:1807.05129v1 fatcat:jru7zndjifdablhmr6py6ps6xq

Universality for the directed configuration model: metric space convergence of the strongly connected components at criticality [article]

Serte Donderwinkel, Zheneng Xie
2021 arXiv   pre-print
A phase transition for the emergence of a giant SCC is known to occur at the critical value 𝔼[D^-D^+] = μ.  ...  We use the product topology on the sequence of multigraphs.  ...  Acknowledgements The authors would like to thank Christina Goldschmidt and Robin Stephenson for many fruitful discussions, and for kindly allowing us to use some of their figures, and Igor Kortchemski  ... 
arXiv:2105.11434v2 fatcat:ssdnzthifzdbne2mmxncdaycpu

Dynamical Phenomena on Complex Networks [article]

Luca Dall'Asta
2006 arXiv   pre-print
A second part of the thesis is devoted to the study of the weighted representation of networks and their relations with the functional properties of infrastructure systems (e.g. the airports network).  ...  Our mean-field analysis of the traceroute model provides a better understanding of the Internet topology.  ...  Along the last century, statistical physicists have developed a suite of analytical and numerical techniques by means of which it has been possible to understand the origin of phase transitions and critical  ... 
arXiv:physics/0609124v1 fatcat:ezmd363mujf2bg3b3q4av4qyle

The phase transition in bounded-size Achlioptas processes [article]

Oliver Riordan, Lutz Warnke
2017 arXiv   pre-print
Perhaps the best understood phase transition is that in the component structure of the uniform random graph process introduced by Erdős and Rényi around 1960.  ...  Here, settling a number of conjectures and open problems, we show that all 'bounded-size' Achlioptas processes share (in a strong sense) all the key features of the Erdős--Rényi phase transition.  ...  of the phase transition phenomenon.  ... 
arXiv:1704.08714v1 fatcat:jjmhg4gmdvfgxj2di5lfebhewy
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