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作者：Bruss, F. Thomas; Duerinckx, Mitia
作者单位：Universite Libre de Bruxelles
摘要：Since its early beginnings, mankind has put to test many different society forms, and this fact raises a complex of interesting questions. The objective of this paper is to present a general population model which takes essential features of any society into account and which gives interesting answers on the basis of only two natural hypotheses. One is that societies want to survive, the second, that individuals in a society would, in general, like to increase their standard of living. We star...
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作者：Durrett, Richard; Moseley, Stephen
作者单位：Duke University
摘要：We consider a multistage cancer model in which cells are arranged in a d-dimensional integer lattice. Starting with all wild-type cells, we prove results about the distribution of the first time when two neutral mutations have accumulated in some cell in dimensions d > 2, extending work done by Komarova [Genetics 166 (2004) 1571-1579] for d = 1.
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作者：Gravner, Janko; Hoffman, Christopher; Pfeiffer, James; Sivakoff, David
作者单位：University of California System; University of California Davis; University of Washington; University of Washington Seattle; Duke University
摘要：The Hamming torus of dimension d is the graph with vertices {1,...,n}(d) and an edge between any two vertices that differ in a single coordinate. Bootstrap percolation with threshold 9 starts with a random set of open vertices, to which every vertex belongs independently with probability p, and at each time step the open set grows by adjoining every vertex with at least 9 open neighbors. We assume that n is large and that p scales as n(-alpha) for some alpha> 1, and study the probability that ...
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作者：Bertoin, Jean; Uribe Bravo, Geronimo
作者单位：University of Zurich; Universidad Nacional Autonoma de Mexico
摘要：We consider Bernoulli bond percolation on a large scale-free tree in the supercritical regime, meaning informally that there exists a giant cluster with high probability. We obtain a weak limit theorem for the sizes of the next largest clusters, extending a recent result in Bertoin [Random Structures Algorithms 44 (2014) 29-44] for large random recursive trees. The approach relies on the analysis of the asymptotic behavior of branching processes subject to rare neutral mutations, which may be ...
