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Full-Text Articles in Physical Sciences and Mathematics
Constructing Phylogenetic Trees Using Maximum Likelihood, Anna Cho
Constructing Phylogenetic Trees Using Maximum Likelihood, Anna Cho
Scripps Senior Theses
Maximum likelihood methods are used to estimate the phylogenetic trees for a set of species. The probabilities of DNA base substitutions are modeled by continuous-time Markov chains. We use these probabilities to estimate which DNA bases would produce the data that we observe. The topology of the tree is also determined using base substitution probabilities and conditional likelihoods. Felsenstein [2] introduced this method of finding an estimate for the maximum likelihood phylogenetic tree. We will explore this method in detail in this paper.
On The Hardness Of Counting And Sampling Center Strings, Christina Boucher, Mohamed Omar
On The Hardness Of Counting And Sampling Center Strings, Christina Boucher, Mohamed Omar
All HMC Faculty Publications and Research
Given a set S of n strings, each of length ℓ, and a nonnegative value d, we define a center string as a string of length ` that has Hamming distance at most d from each string in S. The #CLOSEST STRING problem aims to determine the number of center strings for a given set of strings S and input parameters n, ℓ, and d. We show #CLOSEST STRING is impossible to solve exactly or even approximately in polynomial time, and that restricting #CLOSEST STRING so that any one of the parameters n, ℓ, or d is fixed leads to …