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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：Lang, Annika; Schwab, Christoph
作者单位：Chalmers University of Technology; University of Gothenburg; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Isotropic Gaussian random fields on the sphere are characterized by Karhunen-Loeve expansions with respect to the spherical harmonic functions and the angular power spectrum. The smoothness of the covariance is connected to the decay of the angular power spectrum and the relation to sample Holder continuity and sample differentiability of the random fields is discussed. Rates of convergence of their finitely truncated Karhunen-Loeve expansions in terms of the covariance spectrum are establishe...
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作者：Ibrahimi, Morteza; Kanoria, Yash; Kraning, Matt; Montanari, Andrea
作者单位：Columbia University; Stanford University; Stanford University
摘要：The XOR-satisfiability (XORSAT) problem requires finding an assignment of n Boolean variables that satisfy in exclusive OR (XOR) clauses, whereby each clause constrains a subset of the variables. We consider random XORSAT instances, drawn uniformly at random from the ensemble of formulae containing n variables and m clauses of size k. This model presents several structural similarities to other ensembles of constraint satisfaction problems, such as k-satisfiability (k-SAT), hypergraph bicolori...
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作者：Carmona, Rene; Lacker, Daniel
作者单位：Princeton University; Princeton University
摘要：Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to include rank and nearest-neighbor effects. Moreover, the data may depend discontinuously on the state variable, and more generally its entire history. Existence and uniqueness results are proven, along with a procedure for identifying and constructing distributed...
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作者：Jiang, Yunjiang
作者单位：Stanford University
摘要：We prove sharp rates of convergence to the Ewens equilibrium distribution for a family of Metropolis algorithms based on the random transposition shuffle on the symmetric group, with starting point at the identity. The proofs rely heavily on the theory of symmetric Jack polynomials, developed initially by Jack [Proc. Roy. Soc. Edinburgh Sect. A 69 (1970/1971) 1-18], Macdonald [Symmetric Functions and Hall Polynomials (1995) New York] and Stanley [Adv. Math. 77 (1989) 76-115]. This completes th...
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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：Lanchier, N.
作者单位：Arizona State University; Arizona State University-Tempe
摘要：This article investigates an evolutionary game based on the framework of interacting particle-systems. Each point of the square lattice is occupied by a player who is characterized by one of two possible strategies and is attributed a payoff based on her strategy, the strategy of her neighbors and a payoff matrix. Following the traditional approach of evolutionary game theory, this payoff is interpreted as a fitness: the dynamics of the system is derived by thinking of positive payoffs as birt...
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作者：Pfaffelhuber, Peter; Popovic, Lea
作者单位：University of Freiburg; Concordia University - Canada
摘要：We study the effects of fast spatial movement of molecules on the dynamics of chemical species in a spatially heterogeneous chemical reaction network using a compartment model. The reaction networks we consider are either single- or multi-scale. When reaction dynamics is on a single-scale, fast spatial movement has a simple effect of averaging reactions over the distribution of all the species. When reaction dynamics is on multiple scales, we show that spatial movement of molecules has differe...
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作者：Brummitt, Charles D.; Chatterjee, Shirshendu; Dey, Partha S.; Sivakoff, David
作者单位：University of California System; University of California Davis; New York University; University of Warwick; University System of Ohio; Ohio State University; University System of Ohio; Ohio State University
摘要：We introduce a new kind of percolation on finite graphs called jigsaw percolation. This model attempts to capture networks of people who innovate by merging ideas and who solve problems by piecing together solutions. Each person in a social network has a unique piece of a jigsaw puzzle. Acquainted people with compatible puzzle pieces merge their puzzle pieces. More generally, groups of people with merged puzzle pieces merge if the groups know one another and have a pair of compatible puzzle pi...
