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Analytic Description of the Phase Transition of Inhomogeneous Multigraphs
[article]
2014
arXiv
pre-print
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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]
2013
The Seventh European Conference on Combinatorics, Graph Theory and Applications
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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]
2020
arXiv
pre-print
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2020 pre-print arXiv:2004.10203v1 fatcat:jy6akrsf6bdylprbzf6yriutpe
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]
2022
arXiv
pre-print
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2020 pre-print arXiv:2009.12127v1 fatcat:2cbjt7fwqfezheeyihu7t5w624
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
2003
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
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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]
2015
arXiv
pre-print
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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
2015
Discrete Mathematics & Theoretical Computer Science
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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
2017
Russian Mathematical Surveys
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2017 pre-print arXiv:1705.06619v1 fatcat:dmoprkmvlff2dod6n7hb344fei
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
2007
Physical Review E
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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
2011
Journal of Vision
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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
2012
Journal of Vision
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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]
2018
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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]
2006
arXiv
pre-print
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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]
2017
arXiv
pre-print
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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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