{
  "annotation_id": "65fe4409-3ef5-4c8a-9db2-acff9b4fe898",
  "date_created": "2026-03-02T18:01:32.234000Z",
  "date_modified": "2026-03-02T18:01:32.234000Z",
  "file_hash": "441d973b807fe82c8daeb785b500119a378c598885c47fe6db83eb8d27a24dbd",
  "private": false,
  "record": {
    "abstract": "An abstract DNA-type system is defined by a set of nonlinear kinetic\nequations with polynomial nonlinearities that admit soliton solutions\nassociated with helical geometry. The set of equations allows for two different\nLax representations: A von Neumann form and a Darboux-covariant Lax pair. We\nexplain why non-Kolmogorovian probability models occurring in soliton kinetics\nare naturally associated with chemical reactions. The most general known\ncharacterization of soliton kinetic equations is given and a class of explicit\nsoliton solutions is discussed. Switching between open and closed states is a\ngeneric behaviour of the helices. The effect does not crucially depend on the\norder of nonlinearity (i.e. types of reactions), a fact that may explain why\nsimplified models possess properties occuring in realistic systems. We explain\nalso why fluctuations based on Darboux transformations will not destroy the\ndynamics but only switch between a finite number of helical structures.",
    "arxiv_id": "q-bio/0411031",
    "authors": [
      "Diederik Aerts",
      "Marek Czachor"
    ],
    "categories": [
      "q-bio.PE",
      "nlin.PS",
      "q-bio.QM",
      "quant-ph"
    ],
    "doi": "10.1088/0951-7715/19/3/003",
    "journal_ref": "Nonlinearity 19, 575-589 (2006)",
    "title": "Abstract DNA-type systems",
    "url": "https://arxiv.org/abs/q-bio/0411031"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "93491920-c923-4810-9cca-b2af1574f221",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}