Current projects

Graph theoretic analysis of brain imaging data. In this project, we analyze brain imaging data, such as magnetic resonance imaging data, by first, determining how the data can be interpreted as a graph and second, applying mathematical theory about graphs to try and differentiate healthy and diseased conditions in the data. Collaborators on this work include L. Jager, ENS A. McGlaughlin, CDR D. Ruth, and A. Soldan

Bent functions and graph theory. In this project, we are investigating properties of bent functions, an important class of functions used in cryptography. Collaborators on this work include D. Joyner, Caroline Melles, ENS Steven Walsh, and ENS Charles Celerier.

First-order methods for packing/covering semidefinite programs. In this project, we investigate the use of first-order methods to solve semidefinite programs. Collaborators on this work include R. Zhang, R. Michael Lewis, G. Iyengar, A. Mills and C. Stein. Papers for this project can be found here and here. Some slides from talks I've given on these methods can be found here and here. Code and data generators for the packing method extended to the Sparse PCA can be found here.

Resource planning in medical facilities. We investigate algorithms and patient data in order to help determine when resource allocation at medical facilities. This work has continued with work at Walter Reed Medical Center with MAJ Marcus Colyer, M.D. and MIDN Marissa Molkenbuhr. I recently gave two talks about that our work. Here are the slides from a talk I gave at MAPSP 2009. Here is the paper we submitted. This is joint work with L. Leemis, G. Phillips, A. Carpenter, and Alan Papir.

Determining airline routes with less delay. We use data analysis on several years of flight data combined with network optimization techniques to design algorithms that find flight routes with a low probability of delay. Here is our poster from Data Expo 2009 at JSM, which was awarded honorable distinction. Here is the conference version of the paper we wrote. The journal version has been accepted by the Journal of Computational Graphical Statistics. This is joint work with T. Dey and P. Steele.