Past Research

  • Santa Clara University, Santa Clara, CA.
    Department of Mathematics and Computer Science
    • Senior Honors Thesis with Professors Glenn Appleby and Nicholas Tran [2002]
      Genome Rearrangements and Sorting by Reversals
      Genetic comparison in molecular biology has undergone a major paradigm shift-- a shift from gene comparison based on local mutations (i.e. insertions, deletions, and substitutions of nucleotides) to chromosome comparison based on global rearrangements (i.e. inversions and transpositions of chromosomal segments). Analysis of genomes evolving by inversions leads to a combinatorial problem of sorting by reversals (i.e. sorting of an array using reversals of arbitrary fragments) studied in detail recently. We study sorting of signed permutations by reversals since it adequately models rearrangements in small genomes like chloroplast or mitochondrial DNA. Drawing from results found during the development of deterministic algorithms for the sorting by reversals problem, we take some steps in the direction of developing a randomized algorithm for the same.
    • Numerical PDEs with Professor Dan Ostrov [2001]
      Assisted research by computing numerical solutions of first-order nonlinear partial differential equations. These (Hamilton-Jacobi) equations were applied to photographic shape-from-shading (reconstructing a 3D surface based on a black+white photo of the surface) for discontinuous images.