{
  "annotation_id": "57d59b44-b65d-434a-a39c-aca58611506f",
  "date_created": "2026-03-02T18:01:28.815000Z",
  "date_modified": "2026-03-02T18:01:28.815000Z",
  "file_hash": "a68620925db9202303015eabb998f5b0ebded928e9191ec8b8cf26659da12fc5",
  "private": false,
  "record": {
    "abstract": "An analysis of the Kimura 3ST model of DNA sequence evolution is given on the\nbasis of its continuous Lie symmetries. The rate matrix commutes with a\nU(1)xU(1)xU(1) phase subgroup of the group GL(4) of 4x4x4 invertible complex\nmatrices acting on a linear space spanned by the 4 nucleic acid base letters.\nThe diagonal `branching operator\u0027 representing speciation is defined, and shown\nto intertwine the U(1)xU(1)xU(1) action. Using the intertwining property, a\ngeneral formula for the probability density on the leaves of a binary tree\nunder the Kimura model is derived, which is shown to be equivalent to\nestablished phylogenetic spectral transform methods.",
    "arxiv_id": "q-bio/0310037",
    "authors": [
      "J. D. Bashford",
      "P. D. Jarvis",
      "J. G. Sumner",
      "M. A. Steel"
    ],
    "categories": [
      "q-bio.PE",
      "math.ST",
      "q-bio.QM",
      "stat.TH"
    ],
    "doi": "10.1088/0305-4470/37/8/L01",
    "title": "U(1)xU(1)xU(1) symmetry of the Kimura 3ST model and phylogenetic   branching processes",
    "url": "https://arxiv.org/abs/q-bio/0310037"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "73007465-d5df-4696-811f-ae7650b479e0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}