Al Holder - Professional Rose-Hulman Mathematics


Rose-Hulman NSF-REU
Studies in Computational Biology

  • Possible Topics of Study
    • Haplotype Inference: Diploid organisms, such as humans, receive half of their genetic code from each parent. The locations on the genome in which diversity occurs are called single nucleotide polymorphisms (SNPs), and the strings of parental SNPs are called haplotypes. A paired collection of haplotypes is called a genotype, and the problem of haplotyping is to find a collection of haplotypes that can combine to create the known genotypes. Since solutions are non-unique, an inference rule is used to identify meaningful solutions.
    • Flux Balance Analysis (FBA): The metabolic networks of several single cell organisms is known, and FBA is a computational model that is used to investigate whole-cell metabolisms. The underlying optimization model linear, although several nonlinear extensions exists.
    • Protein Structure Alignment: Aligning and grouping proteins is one of the major problems in computational biology. A new spectral method was introduced in 2010, and we study this model. The alignment method maps the 3D atomic coordinates into a high dimensional, smooth contact space to make alignments.
    • Sequence Alignment: Many biological entities are described with finite sequences, and aligning these sequences to make relational inferences is important. In particular, multiple sequence alignment is an important problem across a wide range of applications. These problems have natural formulations as integer optimization problems, which we study.
  • Summer 2010
    • Pictures:
    • Final Papers:
    • Past REU Publications:
      • Diversity Graphs, 2009, co-authored with P. Blain, C. Davis, J. Silva, and C. Vinzant, in Clustering Challenges in Biological Networks, eds. S. Butenko, W. Chaovalitwongse and P. Pardalos, World Scientific, pages 129-150.
      • Asymptotic Sign-Solvability, Multiple Objective Linear Programming, and The Nonsubstitution Theorem, 2006, co-authored with L. Cayton, R. Herring, J. Holzer, C. Nightingale, and T. Stohs, Mathematical Methods in Operations Research, vol. 64, num. 3, pages 541-555.
      • An Extension of the Fundamental Theorem of Linear Programming, 2002, co-authored with A. Brown, A. Gedlaman, and S. Martinez, Operations Research Letters, vol. 30, num. 5, pages 281-288.