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Lie-Markov models derived from finite semigroups


Sumner, JG and Woodhams, MD, Lie-Markov models derived from finite semigroups, Bulletin of Mathematical Biology, 81, (2) pp. 361-383. ISSN 0092-8240 (2018) [Refereed Article]

Copyright Statement

Copyright 2018 Society for Mathematical Biology

DOI: doi:10.1007/s11538-018-0455-x


We present and explore a general method for deriving a Lie-Markov model from a finite semigroup. If the degree of the semigroup is k, the resulting model is a continuous-time Markov chain on k-states and, as a consequence of the product rule in the semigroup, satisfies the property of multiplicative closure. This means that the product of any two probability substitution matrices taken from the model produces another substitution matrix also in the model. We show that our construction is a natural generalization of the concept of group-based models.

Item Details

Item Type:Refereed Article
Keywords:Lie algebras, continuous-time Markov chains, group-based models, phylogenetics
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Biological mathematics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the physical sciences
UTAS Author:Sumner, JG (Associate Professor Jeremy Sumner)
UTAS Author:Woodhams, MD (Dr Michael Woodhams)
ID Code:127748
Year Published:2018
Funding Support:Australian Research Council (DP150100088)
Web of Science® Times Cited:2
Deposited By:Mathematics and Physics
Deposited On:2018-08-13
Last Modified:2022-07-05

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