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    On the Neutralome of Great Apes and Nearest Neighbor Search in Metric Spaces

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    Author
    Woerner, August Eric
    Issue Date
    2016
    Keywords
    Metric Space
    Nearest Neighbor
    Neutralome
    Null Model
    Genetics
    Linked Selection
    Advisor
    Hammer, Michael
    Kececioglu, John
    
    Metadata
    Show full item record
    Publisher
    The University of Arizona.
    Rights
    Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
    Abstract
    Problems of population genetics are magnified by problems of big data. My dissertation spans the disciplines of computer science and population genetics, leveraging computational approaches to biological problems to address issues in genomics research. In this dissertation I develop more efficient metric search algorithms. I also show that vast majority of the genomes of great apes are impacted by the forces of natural selection. Finally, I introduce a heuristic to identify neutralomes—regions that are evolving with minimal selective pressures—and use these neutralomes for inferences on effective population size in great apes. We begin with a formal and far-reaching problem that impacts a broad array of disciplines including biology and computer science; the 𝑘-nearest neighbors problem in generalized metric spaces. The 𝑘-nearest neighbors (𝑘-NN) problem is deceptively simple. The problem is as follows: given a query q and dataset D of size 𝑛, find the 𝑘-closest points to q. This problem can be easily solved by algorithms that compute 𝑘th order statistics in O(𝑛) time and space. It follows that if D can be ordered, then it is perhaps possible to solve 𝑘-NN queries in sublinear time. While this is not possible for an arbitrary distance function on the points in D, I show that if the points are constrained by the triangle inequality (such as with metric spaces), then the dataset can be properly organized into a dispersion tree (Appendix A). Dispersion trees are a hierarchical data structure that is built around a large dispersed set of points. Dispersion trees have construction times that are sub-quadratic (O(𝑛¹·⁵ log⁡ 𝑛)) and use O(𝑛) space, and they use a provably optimal search strategy that minimizes the number of times the distance function is invoked. While all metric data structures have worst-case O(𝑛) search times, dispersion trees have average-case search times that are substantially faster than a large sampling of comparable data structures in the vast majority of spaces sampled. Exceptions to this include extremely high dimensional space (d>20) which devolve into near-linear scans of the dataset, and unstructured low-dimensional (d<6) Euclidean spaces. Dispersion trees have empirical search times that appear to scale as O(𝑛ᶜ) for 0
    Type
    text
    Electronic Dissertation
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Graduate College
    Genetics
    Degree Grantor
    University of Arizona
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