Algebraic Methods in Phylogenetics

Maximum Likelihood Methods in Molecular Phylogenetics

Algebraic Methods in Combinatorics

1. (A result of Bourbaki on finite geometries, from Răzvan) Let X be a finite set, and let F be a family of distinct proper subsets of X. Suppose that for every pair of distinct elements in X, there is a unique member of F which contains both elements. Prove that |F| ≥ |X|. Solution: Let X = [n] and F = {A1, . . . , Am}. We need to show that n ≤ m. Define the m × n incidence matrix A over R by ...

Algebraic Methods in Combinatorics

In the last fifty years, algebraic methods have been used with striking success in combinatorics. This course looks at some of the most important of these methods, and some of the most beautiful results obtained using them. We will also explore connections with combinatorial geometry, probability theory and theoretical computer science. Many questions in extremal combinatorics have the followin...

A classification of consensus methods for phylogenetics

A consensus tree method takes a collection of phylogenetic trees and outputs a single “representative” tree. The first consensus method was proposed by Adams in 1972. Since then a large variety of different methods have been developed, and there has been considerable debate over how they should be used. This paper has two goals. First, we survey the main consensus tree methods used in phylogene...

Deep Green Plant Phylogenetics: novel analytical methods

The tree of life is inherently fractal. Look closely at one lineage of a phylogeny and it dissolves into many separate lineages, and so on down to a very fine scale. There is now a great body of phylogenetic research that has provided numerous tools applicable at particular, usually fairly constrained, scales. These tools have left many phylogenetic questions unanswered. We think these question...