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Lie-Markov models derived from finite semigroups
Citation
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
Abstract
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 (Dr 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: | 7 |
| Deposited By: | Mathematics and Physics |
| Deposited On: | 2018-08-13 |
| Last Modified: | 2019-03-07 |
| Downloads: | 0 |
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