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Full-Text Articles in Life Sciences
Computational Biology, Harvey Greenberg, Allen Holder
Computational Biology, Harvey Greenberg, Allen Holder
Mathematical Sciences Technical Reports (MSTR)
Computational biology is an interdisciplinary field that applies the techniques of computer science, applied mathematics, and statistics to address biological questions. OR is also interdisciplinary and applies the same mathematical and computational sciences, but to decision-making problems. Both focus on developing mathematical models and designing algorithms to solve them. Models in computational biology vary in their biological domain and can range from the interactions of genes and proteins to the relationships among organisms and species.
G-Lattices For An Unrooted Perfect Phylogeny, Monica Grigg
G-Lattices For An Unrooted Perfect Phylogeny, Monica Grigg
Mathematical Sciences Technical Reports (MSTR)
We look at the Pure Parsimony problem and the Perfect Phylogeny Haplotyping problem. From the Pure Parsimony problem we consider structures of genotypes called g-lattices. These structures either provide solutions or give bounds to the pure parsimony problem. In particular, we investigate which of these structures supports an unrooted perfect phylogeny, a condition that adds biological interpretation. By understanding which g-lattices support an unrooted perfect phylogeny, we connect two of the standard biological inference rules used to recreate how genetic diversity propagates across generations.
A Decomposition Of The Pure Parsimony Problem, Allen Holder, Thomas M. Langley
A Decomposition Of The Pure Parsimony Problem, Allen Holder, Thomas M. Langley
Mathematical Sciences Technical Reports (MSTR)
We partially order a collection of genotypes so that we can represent the problem of inferring the least number of haplotypes in terms of substructures we call g-lattices. This representation allows us to prove that if the genotypes partition into chains with certain structure, then the NP-Hard problem can be solved efficiently. Even without the specified structure, the decomposition shows how to separate the underlying integer programming model into smaller models.
Approximation Methods For Singular Diffusions Arising In Genetics, Nacer E. Abrouk
Approximation Methods For Singular Diffusions Arising In Genetics, Nacer E. Abrouk
Mathematical Sciences Technical Reports (MSTR)
Stochastic models in population genetics leading to diffusion equations are considered. When the drift and the square of the diffusion coefficients are polynomials, an infinite system of ordinary differential equations for the moments of the diffusion process can be derived using the Martingale property. An example is provided to show how the classical Fokker-Planck Equation approach may not be appropriate for this derivation. A Gauss-Galerkin method for approximating the laws of the diffusion, originally proposed by Dawson (1980), is examined. In the few special cases for which exact solutions are known, comparison shows that the method is accurate and the …