Medicine and Health Sciences Commons^™

A Maximum Pseudo-Likelihood Approach For Estimating Species Trees Under The Coalescent Model, Liang Liu, Lili Yu, Scott V. Edwards

Biostatistics Faculty Publications

Background

Several phylogenetic approaches have been developed to estimate species trees from collections of gene trees. However, maximum likelihood approaches for estimating species trees under the coalescent model are limited. Although the likelihood of a species tree under the multispecies coalescent model has already been derived by Rannala and Yang, it can be shown that the maximum likelihood estimate (MLE) of the species tree (topology, branch lengths, and population sizes) from gene trees under this formula does not exist. In this paper, we develop a pseudo-likelihood function of the species tree to obtain maximum pseudo-likelihood estimates (MPE) of species trees, …

On The Eigenstructures Of Functional K-Potent Matrices And Their Integral Forms, Yan Wu, Daniel F. Linder

Biostatistics Faculty Publications

In this paper, a functional k-potent matrix satisfies the equation, where k and r are positive integers, and are real numbers. This class of matrices includes idempotent, Nilpotent, and involutary matrices, and more. It turns out that the matrices in this group are best distinguished by their associated eigen-structures. The spectral properties of the matrices are exploited to construct integral k-potent matrices, which have special roles in digital image encryption.