17,279 research outputs found

    Reconstructing perfect phylogenies via binary matrices, branchings in DAGs, and a generalization of Dilworth\u27s theorem

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    Curriculum Guidelines for Undergraduate Programs in Data Science

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    The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in Data Science. The group consisted of 25 undergraduate faculty from a variety of institutions in the U.S., primarily from the disciplines of mathematics, statistics and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in Data Science

    Zero-one law for directional transience of one-dimensional random walks in dynamic random environments

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    We prove the trichotomy between transience to the right, transience to the left and recurrence of one-dimensional nearest-neighbour random walks in dynamic random environments under fairly general assumptions, namely: stationarity under space-time translations, ergodicity under spatial translations, and a mild ellipticity condition. In particular, the result applies to general uniformly elliptic models and also to a large class of non-uniformly elliptic cases that are i.i.d. in space and Markovian in time. An immediate consequence is the recurrence of models that are symmetric with respect to reflection through the origin.Comment: 14 pages, 1 figure. Added Corollary 2.
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