Fe b 20 06 WHY NEIGHBOR - JOINING WORKS

1 8 Fe b 20 07 THE NEIGHBOR - NET ALGORITHM

The neighbor-joining algorithm is a popular phylogenetics method for constructing trees from dissimilarity maps. The neighbor-net algorithm is an extension of the neighbor-joining algorithm and is used for constructing split networks. We begin by describing the output of neighbor-net in terms of the tessellation of M n 0 by associahedra. This highlights the fact that neighbor-net outputs a tree...

ar X iv : m at h / 06 02 37 1 v 1 [ m at h . A G ] 1 7 Fe b 20 06 Braid Monodromy of Hypersurface Singularities

Fe b 20 06 Invariant triple products

0 60 30 01 v 1 2 8 Fe b 20 06 Theoretical and computational aspects of 1 - vertex transfer matrices

We introduce the notion of 1-vertex transfer matrix for near neighbor Potts models with k kinds of particles. We show that the topological entropy (free energy) of this model can be expressed as the limit the logarithm of spectral radii of 1-vertex transfer matrices. Storage and computations using the 1-vertex transfer matrix are much smaller than storage and computations needed for the standar...

Neighbor joining with phylogenetic diversity estimates

The Neighbor-Joining algorithm is a recursive procedure for reconstructing trees that is based on a transformation of pairwise distances between leaves. We present a generalization of the neighborjoining transformation, which uses estimates of phylogenetic diversity rather than pairwise distances in the tree. This leads to an improved neighbor-joining algorithm whose total running time is still...