dorsal/arxiv
View SchemaEntanglement Invariants and Phylogenetic Branching
| Authors | J. G. Sumner, P. D. Jarvis |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0402007 |
| URL | https://arxiv.org/abs/q-bio/0402007 |
Abstract
It is possible to consider stochastic models of sequence evolution in phylogenetics in the context of a dynamical tensor description inspired from physics. Approaching the problem in this framework allows for the well developed methods of mathematical physics to be exploited in the biological arena. We present the tensor description of the homogeneous continuous time Markov chain model of phylogenetics with branching events generated by dynamical operations. Standard results from phylogenetics are shown to be derivable from the tensor framework. We summarize a powerful approach to entanglement measures in quantum physics and present its relevance to phylogenetic analysis. Entanglement measures are found to give distance measures that are equivalent to, and expand upon, those already known in phylogenetics. In particular we make the connection between the group invariant functions of phylogenetic data and phylogenetic distance functions. We introduce a new distance measure valid for three taxa based on the group invariant function known in physics as the "tangle". All work is presented for the homogeneous continuous time Markov chain model with arbitrary rate matrices.
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"abstract": "It is possible to consider stochastic models of sequence evolution in\nphylogenetics in the context of a dynamical tensor description inspired from\nphysics. Approaching the problem in this framework allows for the well\ndeveloped methods of mathematical physics to be exploited in the biological\narena. We present the tensor description of the homogeneous continuous time\nMarkov chain model of phylogenetics with branching events generated by\ndynamical operations. Standard results from phylogenetics are shown to be\nderivable from the tensor framework. We summarize a powerful approach to\nentanglement measures in quantum physics and present its relevance to\nphylogenetic analysis. Entanglement measures are found to give distance\nmeasures that are equivalent to, and expand upon, those already known in\nphylogenetics. In particular we make the connection between the group invariant\nfunctions of phylogenetic data and phylogenetic distance functions. We\nintroduce a new distance measure valid for three taxa based on the group\ninvariant function known in physics as the \"tangle\". All work is presented for\nthe homogeneous continuous time Markov chain model with arbitrary rate\nmatrices.",
"arxiv_id": "q-bio/0402007",
"authors": [
"J. G. Sumner",
"P. D. Jarvis"
],
"categories": [
"q-bio.PE"
],
"title": "Entanglement Invariants and Phylogenetic Branching",
"url": "https://arxiv.org/abs/q-bio/0402007"
},
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