Event Type:

Ph.D.Defense

Date/Time:

Friday, September 7, 2018 - 11:00 to 12:00

Location:

Strand Agriculture Hall Room 160

Abstract:

Microbial ecology has been transformed by the study of the genetic information in entire communities of organisms. In the following we develop mathematical tools arising from the classic Wasserstein metric as applied to questions regarding the diversity between microbial communities. We provide a novel proof of the characterization of the successful UniFrac metric as the Wasserstein metric over a phylogenetic tree, and use the proof to develop an extremely efficient computational algorithm. The analytic framework we develop is then leveraged to provide formulations for the expectation of this Wasserstein based metric. We implement these ideas and demonstrate their utility on real world 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 their utility in comparison to established metrics.