We present the idea of using the "earth mover's distance" (aka the first Wasserstein metric) to measure the distance between samples of DNA. This reduces to finding the most efficient way to transform one kind of graph (known as de Bruijn graphs) into another.

We develop a pre-processing step that significantly improves k-mer based metagenomic profiling techniques.

We present a computational technique that answers the question "Which organisms are present in a given sample of of DNA from a microbial community, and at what relative amount" while simultaneously predicting the relatedness of novel (never-before seen organisms) in relation to known organisms. This relies on a mathematical technique referred to as sparsity-promoting optimization and relies on a technique similar to the Jaccard index.

In a network of interacting quantities (such as a food web), we examine how qualitative and quantitative predictions change when a quantity (such as the abundance of an organism or a set of organisms) is increased. This is quantified in terms of which model parameters cause the largest change in predictions.

Rapidly answers “why are these data sets different” by leveraging hierarchical/relatedness information. In short, we develop an algorithm to quickly compute the Unifrac distance by leveraging the earth mover's distance, prove its correctness, and derive time and space complexity characterizations.

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