- University of Texas at Austin
Dr. Oscar Gonzalez: Department
of Mathematics [2003-2004]
- Dynamics of DNA filament in a fluid
The goal of this work was to explore the correlation
between the shape of a closed (or cyclic) DNA filament
and its migration speed in a uid. The basic problem was to determine
how the average migration behavior of a filament
is in uenced by features of its shape. Given a shape, we would like to find bounds on the migration speed. Conversely,
given a speed, we would like to characterize the possible shapes.
Phylo Lab: Center for Computational Biology and Bioinformatics 
- Computational Phylogenetics
A phylogenetic network is a model used to describe the evolution
of a set of species with cross-species interaction. We studied
the theory of triangulated graphs to understand how they could be
applied to solve the Character Compatibility Problem on
Santa Clara University, Santa Clara, CA.
- NASA Ames Research Center, Moffett Field, CA
Computational Sciences Division: Smart Systems Research Lab [2000-2001]
- Breast Cancer Diagnostics
This project was for the development of a non-surgical system for detection of breast
(with specific application aboard the International Space Station).
I designed a non-invasive diagnostic system that performed real-time image processing on results
from an ultrasound monitor. Experiments were performed on tumored mice
for optimization of the system.
- Space Shuttle Docking
Performed research for application of an automated docking system for the US Space Shuttle by studying
shuttle systems and data provided by them; performed research on sensor fusion/data mining techniques (e.g. Kalman
filtering); assisted in development of a data mining/data visualization tool for application to the International
Aviation Systems Research & Technology Division: Center-TRACON Automation System Group [1999-2000]
- Optimized Trajectories ("EGADS")
I designed and developed an error analysis tool that assists in the optimization
of airplane trajectory predictions to be used for a suite of software tools (CTAS) for air traffic control (ATC) and
flight management (FMS).
Earth Science Division
- Geophysical research with Dr. Friedemann Freund 
We studied methods for characterizing the amount of H2O in olivine, which is a question of great interest for the upper mantle. We showed that to measure how much "water" is in olivine, it is not sufficient to measure the hydroxyl content through IR spectroscopy.
Department of Mathematics and Computer Science
- Senior Honors Thesis with Professors Glenn Appleby and Nicholas Tran 
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 
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.