{
  "annotation_id": "cb701993-ec2b-46fb-befb-15836c4fadb8",
  "date_created": "2026-03-02T18:01:31.423000Z",
  "date_modified": "2026-03-02T18:01:31.423000Z",
  "file_hash": "a762074f151a1bd78c3774cd5eefce7545c0b5fc2906c6346d63ab71684dc8cd",
  "private": false,
  "record": {
    "abstract": "We discuss properties which must be satisfied by a genetic network in order\nfor it to allow differentiation.\n  These conditions are expressed as follows in mathematical terms. Let $F$ be a\ndifferentiable mapping from a finite dimensional real vector space to itself.\nThe signs of the entries of the Jacobian matrix of $F$ at a given point $a$\ndefine an interaction graph, i.e. a finite oriented finite graph $G(a)$ where\neach edge is equipped with a sign. Ren\\\u0027e Thomas conjectured twenty years ago\nthat, if $F$ has at least two non degenerate zeroes, there exists $a$ such that\n$G(a)$ contains a positive circuit. Different authors proved this in special\ncases, and we give here a general proof of the conjecture. In particular, we\nget this way a necessary condition for genetic networks to lead to\nmultistationarity, and therefore to differentiation.\n  We use for our proof the mathematical literature on global univalence, and we\nshow how to derive from it several variants of Thomas\u0027 rule, some of which had\nbeen anticipated by Kaufman and Thomas.",
    "arxiv_id": "q-bio/0403033",
    "authors": [
      "Christophe Soule"
    ],
    "categories": [
      "q-bio.MN"
    ],
    "journal_ref": "ComplexUs 1 (2003) 123-133",
    "title": "Graphic requirements for multistationarity",
    "url": "https://arxiv.org/abs/q-bio/0403033"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b0c23534-7e10-4559-a30f-ad638caa4ec5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}