**7 results** match your criteria *Annals Of Applied Probability[Journal] *

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Ann Appl Probab 2016 Aug 1;26(4):2540-2555. Epub 2016 Sep 1.

Department of Biostatistics, Columbia University.

From its beginning, there have been attempts by physicists to formulate quantum mechanics without requiring the use of wave functions. An interesting recent approach takes the point of view that quantum effects arise solely from the interaction of finitely many classical "worlds." The wave function is then recovered (as a secondary object) from observations of particles in these worlds, without knowing the world from which any particular observation originates. Read More

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http://dx.doi.org/10.1214/15-AAP1154 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5542025 | PMC |

Ann Appl Probab 2015 Feb;25(1):104-115

Department of Mathematics, Box 90320, Duke U., Durham NC 27708-0320.

We consider a multistage cancer model in which cells are arranged in a -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 ≥ 2, extending work done by Komarova [12] for = 1. Read More

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http://dx.doi.org/10.1214/13-AAP989 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4587779 | PMC |

Ann Appl Probab 2013 ;23(1):230-250

DEPARTMENT OF MATHEMATICS DUKE UNIVERSITY BOX 90320 DURHAM, NORTH CAROLINA 27708-0320 USA

In order to analyze data from cancer genome sequencing projects, we need to be able to distinguish causative, or "driver," mutations from "passenger" mutations that have no selective effect. Toward this end, we prove results concerning the frequency of neutural mutations in exponentially growing multitype branching processes that have been widely used in cancer modeling. Our results yield a simple new population genetics result for the site frequency spectrum of a sample from an exponentially growing population. Read More

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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3588108 | PMC |

http://dx.doi.org/10.1214/11-aap824 | DOI Listing |

Ann Appl Probab 2012 Apr;22(2):576-607

Computer Science Division, University of California, Berkeley, Berkeley, CA 94720, Berkeley USA.

For population genetics models with recombination, obtaining an exact, analytic sampling distribution has remained a challenging open problem for several decades. Recently, a new perspective based on asymptotic series has been introduced to make progress on this problem. Specifically, closed-form expressions have been derived for the first few terms in an asymptotic expansion of the two-locus sampling distribution when the recombination rate is moderate to large. Read More

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http://projecteuclid.org/euclid.aoap/1333372008 | Publisher Site |

http://dx.doi.org/10.1214/11-AAP780 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3685441 | PMC |

Ann Appl Probab 2012 ;22(5):1962-1988

Stanford University and University of Pennsylvania.

We study the rate of convergence for the largest eigenvalue distributions in the Gaussian unitary and orthogonal ensembles to their Tracy-Widom limits. We show that one can achieve an () rate with particular choices of the centering and scaling constants. The arguments here also shed light on more complicated cases of Laguerre and Jacobi ensembles, in both unitary and orthogonal versions. Read More

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http://dx.doi.org/10.1214/11-AAP819 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3647289 | PMC |

Ann Appl Probab 2010 Jun;20(3):1005-1028

Computer Science Division, University of California, Berkeley, Berkeley, CA 94720, USA.

Ewens sampling formula (ESF) is a one-parameter family of probability distributions with a number of intriguing combinatorial connections. This elegant closed-form formula first arose in biology as the stationary probability distribution of a sample configuration at one locus under the infinite-alleles model of mutation. Since its discovery in the early 1970s, the ESF has been used in various biological applications, and has sparked several interesting mathematical generalizations. Read More

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http://projecteuclid.org/euclid.aoap/1276867305 | Publisher Site |

http://dx.doi.org/10.1214/09-AAP646 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2910927 | PMC |

Ann Appl Probab 2009 ;19(1):467-476

College of Optical Sciences, Department of Radiology, University of Arizona, Tucson, Arizona 85721, USA,

For independent X and Y in the inequality P(X ≤ Y + μ), we give sharp lower bounds for unimodal distributions having finite variance, and sharp upper bounds assuming symmetric densities bounded by a finite constant. The lower bounds depend on a result of Dubins about extreme points and the upper bounds depend on a symmetric rearrangement theorem of F. Riesz. Read More

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http://dx.doi.org/10.1214/08-AAP536 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2828638 | PMC |

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