dorsal/arxiv
View SchemaHadamard Conjugation for the Kimura 3ST Model: Combinatorial Proof using Pathsets
| Authors | Michael D. Hendy, Sagi Snir |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0505055 |
| URL | https://arxiv.org/abs/q-bio/0505055 |
Abstract
In most stochastic models of molecular sequence evolution the probability of each possible pattern of homologous characters at a site is estimated numerically. However in the case of Kimura's three-substitution-types (K3ST) model, these probabilities can be expressed analytically by Hadamard conjugation as a function of the phylogeny T and the substitution probabilities on each edge of T, together with an analytic inverse function. In this paper we produce a direct proof of these results, using pathset distances which generalise pairwise distances between sequences. This interpretation allows us to apply Hadamard conjugation to a number of topical problems in the mathematical analysis of sequence evolution.
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"abstract": "In most stochastic models of molecular sequence evolution the probability of\neach possible pattern of homologous characters at a site is estimated\nnumerically. However in the case of Kimura\u0027s three-substitution-types (K3ST)\nmodel, these probabilities can be expressed analytically by Hadamard\nconjugation as a function of the phylogeny T and the substitution probabilities\non each edge of T, together with an analytic inverse function. In this paper we\nproduce a direct proof of these results, using pathset distances which\ngeneralise pairwise distances between sequences. This interpretation allows us\nto apply Hadamard conjugation to a number of topical problems in the\nmathematical analysis of sequence evolution.",
"arxiv_id": "q-bio/0505055",
"authors": [
"Michael D. Hendy",
"Sagi Snir"
],
"categories": [
"q-bio.PE"
],
"title": "Hadamard Conjugation for the Kimura 3ST Model: Combinatorial Proof using Pathsets",
"url": "https://arxiv.org/abs/q-bio/0505055"
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