{
  "annotation_id": "2e2953f2-420e-405d-9eab-6210de727a0a",
  "date_created": "2026-03-02T18:01:31.408000Z",
  "date_modified": "2026-03-02T18:01:31.408000Z",
  "file_hash": "76acd7c55645aa6df0c0d15732e3a49daf9e4cea192e022f5fd2157d56618512",
  "private": false,
  "record": {
    "abstract": "Statistical models of evolution are algebraic varieties in the space of joint\nprobability distributions on the leaf colorations of a phylogenetic tree. The\nphylogenetic invariants of a model are the polynomials which vanish on the\nvariety. Several widely used models for biological sequences have transition\nmatrices that can be diagonalized by means of the Fourier transform of an\nabelian group. Their phylogenetic invariants form a toric ideal in the Fourier\ncoordinates. We determine generators and Gr\\\"obner bases for these toric\nideals. For the Jukes-Cantor and Kimura models on a binary tree, our Gr\\\"obner\nbases consist of certain explicitly constructed polynomials of degree at most\nfour.",
    "arxiv_id": "q-bio/0402015",
    "authors": [
      "Bernd Sturmfels",
      "Seth Sullivant"
    ],
    "categories": [
      "q-bio.PE",
      "math.AC"
    ],
    "title": "Toric ideals of phylogenetic invariants",
    "url": "https://arxiv.org/abs/q-bio/0402015"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0de5765b-d560-4051-ac0f-9d2e053c5c06",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}