{
  "annotation_id": "421df30b-aadc-45c1-8911-a6e44250856e",
  "date_created": "2026-03-02T18:01:34.941000Z",
  "date_modified": "2026-03-02T18:01:34.941000Z",
  "file_hash": "d9ff97cbd1076ebe30ababa569ff53134178a6aea745a72f90aaf2a0b522713f",
  "private": false,
  "record": {
    "abstract": "We describe here the new concept of $\\epsilon$-Homomorphisms of Probabilistic\nRegulatory Gene Networks(PRN). The $\\epsilon$-homomorphisms are special\nmappings between two probabilistic networks, that consider the algebraic action\nof the iteration of functions and the probabilistic dynamic of the two\nnetworks. It is proved here that the class of PRN, together with the\nhomomorphisms, form a category with products and coproducts. Projections are\nspecial homomorphisms, induced by invariant subnetworks. Here, it is proved\nthat an $\\epsilon$-homomorphism for 0 \u003c$\\epsilon$\u003c 1 produces simultaneous\nMarkov Chains in both networks, that permit to introduce the concepts of\n$\\epsilon$-isomorphism of Markov Chains, and similar networks.",
    "arxiv_id": "q-bio/0606032",
    "authors": [
      "Maria A. Avino-Diaz",
      "Oscar Moreno"
    ],
    "categories": [
      "q-bio.GN",
      "math.DS"
    ],
    "title": "Probabilistic Regulatory Networks: Modeling Genetic Networks",
    "url": "https://arxiv.org/abs/q-bio/0606032"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3f5e0426-efd9-462a-92da-2279c2b334b7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}