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General and exact approach to percolation on random graphs

Antoine Allard, Laurent Hébert-Dufresne, Jean-Gabriel Young, Louis J. Dubé
2015 Physical Review E  
(i) We introduce a set of iterative equations that solve the exact distribution of the size and composition of components in finite size quenched or random multitype graphs.  ...  We show how a graph can successively undergo a continuous then a discontinuous phase transition, and preliminary results suggest that clustering increases the amplitude of the discontinuity at the transition  ...  ACKNOWLEDGMENTS We acknowledge support from the Instituts de recherche en santé du Canada, the Conseil de recherches en sciences naturelles et en génie du Canada and the Fonds de recherche du Québec -Nature  ... 
doi:10.1103/physreve.92.062807 pmid:26764744 fatcat:s4ihklnntzacpgtb6dg3644lfq

Coexistence of phases and the observability of random graphs

Antoine Allard, Laurent Hébert-Dufresne, Jean-Gabriel Young, Louis J. Dubé
2014 Physical Review E  
Lett. 109, 258701 (2012)] introduced the concept of observability transitions: the percolation-like emergence of a macroscopic observable component in graphs in which the state of a fraction of the nodes  ...  We show how their concept of depth-L percolation---where the state of nodes up to a distance L of monitored nodes is known---can be mapped unto multitype random graphs, and use this mapping to exactly  ...  ACKNOWLEDGMENTS The authors would like to acknowledge the financial support of the Canadian Institutes of Health Research, the Natural Sciences and Engineering Research Council of Canada, and the Fonds  ... 
doi:10.1103/physreve.89.022801 pmid:25353528 fatcat:biinnpw2mfevnhztbyad7hcnxu

Two-scale multitype contact process: coexistence in spatially explicit metapopulations [article]

Nicolas Lanchier
2010 arXiv   pre-print
Similarly, we prove that the geometry of the graph can drastically affect the limiting behavior of multitype versions of the contact process.  ...  Namely, while it is strongly believed (and partly proved) that the coexistence region of the multitype contact process on the regular lattice reduces to a subset of the phase diagram with Lebesgue measure  ...  a phase of weak survival.  ... 
arXiv:1003.0117v1 fatcat:2wln6tw3p5go5fl7vchnfkwk5a

Transience and recurrence of rotor-router walks on directed covers of graphs

Wilfried Huss, Ecaterina Sava
2012 Electronic Communications in Probability  
The aim of this note is to extend the result of Angel and Holroyd concerning the transience and the recurrence of transfinite rotor-router walks, for random initial configuration of rotors on homogeneous  ...  We address the same question on directed covers of finite graphs, which are also called trees with finitely many cone types or periodic trees.  ...  For defining the critical point of this phase transition, we need to introduce some additional definitions.  ... 
doi:10.1214/ecp.v17-2096 fatcat:u2c6sr5whbdbzgwf6s72zqssry

Viral Evolution and Adaptation as a Multivariate Branching Process [article]

Fernando Antoneli, Francisco Bosco, Diogo Castro, Luiz Mario Janini
2011 arXiv   pre-print
In the present work we analyze the problem of adaptation and evolution of RNA virus populations, by defining the basic stochastic model as a multivariate branching process in close relation with the branching  ...  Biol. 46 (1985) 239-262), in their study of polynucleotide evolution. We show that in the absence of beneficial forces the model is exactly solvable.  ...  The result shows that, with respect to ω r , the model has a critical behavior in complete analogy to a second order phase transition (see FIG. 3) .  ... 
arXiv:1110.3368v4 fatcat:nzde4nuqcjg5vb62vjavb6kabq

Diffusion on the Scaling Limit of the Critical Percolation Cluster in the Diamond Hierarchical Lattice

B. M. Hambly, T. Kumagai
2010 Communications in Mathematical Physics  
We construct critical percolation clusters on the diamond hierarchical lattice and show that the scaling limit is a graph directed random recursive fractal.  ...  In the two dimensional case the incipient infinite cluster (IIC), the critical  ...  The system exhibits a phase transition in that at a critical probability p c ∈ (0, 1) there exists an (unique) infinite connected component C ∞ of the set of open edges.  ... 
doi:10.1007/s00220-009-0981-3 fatcat:eop4xvtdvzhmhki3gzcdkl4p24

Randomised Reproducing Graphs

Jonathan Jordan
2011 Electronic Journal of Probability  
We show that as the probabilities associated with the model vary there are a number of phase transitions, in particular concerning the degree sequence.  ...  We introduce a model for a growing random graph based on simultaneous reproduction of the vertices.  ...  The following result shows that our model exhibits a phase transition in this respect, with the transition occurring where 2γ + α = 1.  ... 
doi:10.1214/ejp.v16-921 fatcat:jgfhozdhhrbbjctsifhpvicroa

Boolean percolation on digraphs and random exchange processes [article]

Georg Braun
2022 arXiv   pre-print
For various underlying directed graphs, we discuss connections between this model and random exchange processes.  ...  We study, in a general graph-theoretic formulation, a long-range percolation model introduced by Lamperti.  ...  The author thanks Martin Zerner and Elmar Teufl for many helpful comments. The author is grateful for a PhD scholarship of the Landesgraduiertenförderung Baden-Württemberg.  ... 
arXiv:2111.04772v2 fatcat:zneu6n66szf6jc2dqsd5jefvm4

Some rigorous results for the stacked contact process [article]

Nicolas Lanchier, Yuan Zhang
2014 arXiv   pre-print
The main purpose of this work is to study the existence of a phase transition between extinction and persistence of the infection in the parameter region where the hosts survive.  ...  Regardless of whether they are healthy or infected, hosts give birth and die at the same rate and in accordance to the evolution rules of the neutral multitype contact process.  ...  The authors would like to thank Rick Durrett for suggesting the problem and for his comments on a preliminary version of this work.  ... 
arXiv:1410.3842v1 fatcat:vuzf5n4au5aaherm7awy3qquly

Simulating the Emergence and Survival of Mutations Using a Self Regulating Multitype Branching Processes

Charles J. Mode, Towfique Raj, Candace K. Sleeman
2011 Journal of Probability and Statistics  
In this paper all computer simulation experiments were carried out within a framework of self regulating multitype branching processes, which are part of a stochastic working paradigm.  ...  In his famous book,The Genetical Theory of Natural Selection, Sir R. A.  ...  binomial random variable with index Y t and probability S t | X t .  ... 
doi:10.1155/2011/867493 fatcat:hsmqsgsopfed5eevb2fvytywja

Some rigorous results for the stacked contact process

Nicolas Lanchier, Yuan Zhang
2016 Latin American Journal of Probability and Mathematical Statistics  
The main purpose of this work is to study the existence of a phase transition between extinction and persistence of the infection in the parameter region where the hosts survive.  ...  Regardless of whether they are healthy or infected, hosts give birth and die at the same rate and in accordance to the evolution rules of the neutral multitype contact process.  ...  The authors would like to thank Rick Durrett for suggesting the problem and for his comments on a preliminary version of this work. N. L. was partially supported by NSA Grant MPS-14-040958.  ... 
doi:10.30757/alea.v13-08 fatcat:qi4rlse445eo3gsixj533z2lnq

Recurrence and transience for the frog model on trees

Christopher Hoffman, Tobias Johnson, Matthew Junge
2017 Annals of Probability  
We prove the model undergoes a phase transition, finding it recurrent for d=2 and transient for d≥ 5. Simulations suggest strong recurrence for d=2, weak recurrence for d=3, and transience for d≥ 4.  ...  The frog model is a growing system of random walks where a particle is added whenever a new site is visited. A longstanding open question is how often the root is visited on the infinite d-ary tree.  ...  We also thank Nina Gantert who pointed out an inaccuracy in a previous version.  ... 
doi:10.1214/16-aop1125 fatcat:zmfi7fjxxrgzroloj5e75aafga

Multitype Bellman-Harris branching model provides biological predictors of early stages of adult hippocampal neurogenesis

Biao Li, Amanda Sierra, Juan Jose Deudero, Fatih Semerci, Andrew Laitman, Marek Kimmel, Mirjana Maletic-Savatic
2017 BMC Systems Biology  
Adult hippocampal neurogenesis, the process of formation of new neurons, occurs throughout life in the hippocampus.  ...  the overall efficiency of neurogenesis in both normal and diseased conditions.  ...  Availability of data and materials All data and materials will be shared in accordance with the NIH Grants Policy on Sharing of Unique Research Resources.  ... 
doi:10.1186/s12918-017-0468-3 pmid:28984196 pmcid:PMC5629620 fatcat:4yfzahjacff7necddhqpwuaeqi

Subject Index

2010 Advances in Applied Probability  
IP address: 207.241.231.83, on 16 Jul 2021 at 22:37:08, subject to the Cambridge Core terms of use, available APPLIED PROBABILITY phase transition B. N. B. De Lima and A.  ...  AAP 39 (2007) 898-921 conjugate duality in asset allocation C. Labbé and A. J. Heunis AAP 39 (2007) 77-104 connectivity in random geometric graph P. Balister et al.  ...  Britton AAP 39 (2007) 949-972 epidemic model random-graph P. Neal JAP 44 (2007) 41-57 equal-sized wagering D. Hartvigsen JAP 46 (2009) 35-54 equilibrium selection in evolutionary game H.-C.  ... 
doi:10.1017/s0001867800046917 fatcat:lw2dosl3qjcgnpl7scl2tealry

SIR epidemics and vaccination on random graphs with clustering [article]

Carolina Fransson, Pieter Trapman
2018 arXiv   pre-print
In this paper we consider SIR epidemics on random graphs with clustering.  ...  In addition, the impact of random vaccination with a perfect vaccine on the final outcome of the epidemic is investigated.  ...  Acknowledgements We thank the members of the journal club on infectious diseases at Stockholm University and Daniel Ahlberg for suggestions that lead to substantial improvements of the paper.  ... 
arXiv:1802.05011v1 fatcat:3rhf54dwzna6fccvoikuh2ouvm
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