Research Interests

• computational algebraic topology
  
  
  1. Optimal homologous cycles, total unimodularity, and linear programming  (SIAM J. Computing, 2011, 40(4), p26-40; preliminary version in STOC 2010;
     joint work with Tamal Dey @ Ohio State and Anil Hirani @ Illinois)
  Talk given at the Theory Seminar at Brown.
  2. Simplicial flat norm with scale (joint work with Kevin Vixie at WSU)     Talk
  
  
  
• integer programming (IP) and basis reduction
  
  
  3. Column basis reduction and decomposable knapsack problems (Discrete Optimization, 2009, Vol. 6, Is. 3, p242-270; DOI).    Instances
  4. Bounds on the size of branch-and-bound proofs for integer knapsacks (OR Letters, 2008, Vol 36, No. 1, p19-25; DOI).
  5. Is Thinner Better? - Cascade Knapsack Problems   (abstract and instances).
     Cascade Knapsack Problems:   Talk given at MIP 2008
  6. Lattice-based Algorithms for Number Partitioning in the Hard Phase (joint work with William Webb at WSU)
     Talk given at the AMS Spring Western Section Meeting at San Francisco (Apr 25-26, 2009)
     


• basis reduction and public key cryptosystems
  
  
  • Knapsack cryptosystems using recurrence sequences:   Talk given at INFORMS 09 at San Diego (Oct 12-15 2009)
  
  
• computational approaches to protein structure and function
  
  
  7. A topological characterization of protein structure (in Biocomputing,
  the proceedings of the Conference on Data Mining in Biomedicine held at the University of Florida).
  8. Development of a four-body statistical pseudo-potential to discriminate native from non-native
     protein conformations (Bioinformatics, 19, 2003; p1540-1548).
  9. Four-Body Scoring Function for Mutagenesis   (Bioinformatics 23, 2007; p3009-3015).
  10. Scoring Function to Predict Solubility Mutagenesis   (Algorithms for Molecular Biology, 5:33, 2010)
  11. Neighborhood properties are important determinants of Ts mutants   (PLoS ONE, 6(12): e28507)
  
  
• geometry of neck muscles
  
  
  12. Effect of curved muscle paths on neck biomechanics (in CMBBE, 2011)    (joint work with Anita Vasavada at WSU)
  
  
• integer programming in forestry
  
  
  • Talk on an IP model for optimal habitat reserve selection   given at INFORMS 09 at San Diego (Oct 12-15 2009)

IMA short course on Applied Algebraic Topology, June 15-26, 2009.
INFORMS 09
STOC 2010
Modern Trends in Optimization and Its Application at IPAM, Sep 13-Dec 17, 2010.
ASCR/BES Data Workshop, Bethesda, MD, Oct 24-25, 2011.

Professional Affiliations

INFORMS    Mathematical Programming Society (MPS)    AMS    ACM-SIGACT    IACR