71 citations · 183 across the 34 of their papers we have counts for
6 papers · 1 filter
Lie geometry of 2x2 Markov matrices
Jeremy G. Sumner
In recent work discussing model choice for continuous-time Markov chains, we have argued that it is important that the Markov matrices that define the model are closed under matrix…
A tensorial approach to the inversion of group-based phylogenetic models
Jeremy G. Sumner, Peter D. Jarvis, Barbara R. Holland
Using a tensorial approach, we show how to construct a one-one correspondence between pattern probabilities and edge parameters for any group-based model. This is a generalisation…
Tensor Rank, Invariants, Inequalities, and Applications
Elizabeth S. Allman, Peter D. Jarvis, John A. Rhodes +1
Though algebraic geometry over is often used to describe the closure of the tensors of a given size and complex rank, this variety includes tensors of both smaller and…
Lie Markov models with purine/pyrimidine symmetry
Jesús Fernández-Sánchez, Jeremy G. Sumner, Peter D. Jarvis +1
Continuous-time Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying time-independent rates of substitution…
Adventures in Invariant Theory
P. D. Jarvis, J. G. Sumner
We provide an introduction to enumerating and constructing invariants of group representations via character methods. The problem is contextualised via two case studies arising fro…
Low-parameter phylogenetic estimation under the general Markov model
Barbara R. Holland, Peter D. Jarvis, Jeremy G. Sumner
In their 2008 and 2009 papers, Sumner and colleagues introduced the "squangles" - a small set of Markov invariants for phylogenetic quartets. The squangles are consistent with the…