Graduate Thesis Or Dissertation


Wasserstein β-Diversity Metrics over Graphs: Derivation, Efficient Computation and Applications Public Deposited

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  • Microbial ecology has been transformed by metagenomics, the study of the genetic in-formation in entire communities of organisms. In the following we develop metagenomic tools arising from the classic Wasserstein metric as applied to questions regarding the diversity between microbial communities. We provide a novel proof of the characteriza-tion of the successful UniFrac metric as the Wasserstein metric over a graph-theoretic tree, and use the proof to develop an extremely e°cient computational algorithm. The analytic framework we develop is then leveraged to provide formulations for the distri-bution of this Wasserstein based metric. We implement these ideas and demonstrate their utility on realworld datasets. We next turn to applying the Wasserstein metric as a reference-free diversity metric by utilizing de Bruijn graphs, mathematical structures at the heart of genome assembly techniques. We show how these techniques are related to established phylogenetically-aware diversity metrics. We then implement our results using newly developed approximation techniques for the computation of the Wasserstein metric and demonstrate this novel metric's utility in comparison to established metrics.
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