Tracing evolutionary links between species

The idea that all life on earth traces back to a common beginning dates back at least to Charles Darwin's {\em Origin of Species}. Ever since, biologists have tried to piece together parts of this `tree of life' based on what we can observe today: fossils, and the evolutionary signal that is present in the genomes and phenotypes of different organisms. Mathematics has played a key role in helping transform genetic data into phylogenetic (evolutionary) trees and networks. Here, I will explain some of the central concepts and basic results in phylogenetics, which benefit from several branches of mathematics, including combinatorics, probability and algebra.Comment: 18 pages, 6 figures (Invited review paper (draft version) for AMM

Majorisation ordering of measures invariant under transformations of the interval

PhDMajorisation is a partial ordering that can be applied to the set of probability measures on the unit interval I = [0, 1). Its defining property is that one measure μ majorises another measure , written μ , if R I fdμ R I fd for every convex real-valued function f : I ! R. This means that studying the majorisation of MT , the set of measures invariant under a transformation T : I ! I, can give us insight into finding the maximising and minimising T-invariant measures for convex and concave f. In this thesis I look at the majorisation ordering of MT for four categories of transformations T: concave unimodal maps, the doubling map T : x 7! 2x (mod 1), the family of shifted doubling maps T : x 7! 2x + (mod 1), and the family of orientation-reversing weakly-expanding maps

Dicumarol

Thesis (M.D.)--Boston Universit

A Bayesian analysis of simultaneous equation models by combining recursive analytical and numerical approaches

Economics