I am a mathematical biologist interested in developing mathematically sound approaches to the analysis of high-throughput DNA sequencing data. To do this, I utilize and develop techniques from the fields of probability, compressed sensing, and optimization. I am particularly interested in developing methods to analyze genomic and metagenomic data.
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.
The Oregon State University Microbiome Initiative (OMBI) is a microbiome research and education program that centers on addressing pertinent problems in metagenomics.
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.
In a very reproducible fashion, we assess a wide variety of computational techniques in metagenomics, including assembly (putting together pieces of genomes, called contigs, from short reads), binning (figuring out where the contigs came from), and taxonomic profiling (determining which organisms are present in a sample and at what relative amount).
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.