• publication
    Tuesday, November 1, 2016
    After introducing the notion of a random substitution Markov chain, we relate it to other notions of a "random substitution" and give a complete description of the Martin boundary for a few interesting examples.
  • publication
    Thursday, February 27, 2014
    We prove that nonnegative least squares (typically prone to over-fitting) can be slightly modified to return sparse results.
  • publication
    Thursday, March 13, 2014
    Extending the results of Quikr to whole genome shotgun metagenomic samples, we develop a method to automatically select a parameter that balances sparsity (how succinct the result is) with accuracy.
  • publication
    Wednesday, January 1, 2014
    We review a variety of entropy/randomness-based techniques that are useful in a variety of data mining applications.
  • publication
    Tuesday, May 24, 2016
    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.

MTH 321: Introductory applications of mathematical software

This is a course that I created back in 2014 (that continues to run, typically in the Fall and Spring) to introduce students to Mathematica, Matlab, and LaTeX. In the future, I will be incorporating modules on Python and/or Julia. This hands-on course has been attended by over 80 undergradutes, as well as a handfull of graduate students and faculty as well!

I wrote a (~200 page) textbook to accompany this course which can be found here.

MetaPalette Summary video

Very brief explanation of how MetaPalette works.