{
  "annotation_id": "2f73684b-b52d-4b6c-9efc-8264e410155d",
  "date_created": "2026-03-02T18:01:31.815000Z",
  "date_modified": "2026-03-02T18:01:31.815000Z",
  "file_hash": "fc20b542b8eb7da4ea1b547ceaa5a8af3a6a6711ecebe891c46a338d6a724da0",
  "private": false,
  "record": {
    "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"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a1070c62-1931-4373-bac4-cf0955def898",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}