{
  "annotation_id": "68cfbfa9-3adc-4b63-9c69-29c3d8f43d97",
  "date_created": "2026-03-02T18:01:11.090000Z",
  "date_modified": "2026-03-02T18:01:11.090000Z",
  "file_hash": "16bb2695593244c48978e92beb33b23ee42a29b5bda501ead401705cc1adf260",
  "private": false,
  "record": {
    "abstract": "We apply generic order parameter equations for the emergence of retinotopy\nbetween manifolds of different geometry to one- and two-dimensional Euclidean\nand spherical manifolds. To this end we elaborate both a linear and a nonlinear\nsynergetic analysis which results in order parameter equations for the dynamics\nof connection weights between two cell sheets. Our results for strings are\nanalogous to those for discrete linear chains obtained previously by Haeussler\nand von der Malsburg. The case of planes turns out to be more involved as the\ntwo dimensions do not decouple in a trivial way. However, superimposing two\nmodes under suitable conditions provides a state with a pronounced retinotopic\ncharacter. In the case of spherical manifolds we show that the order parameter\nequations provide stable stationary solutions which correspond to retinotopic\nmodes. A further analysis of higher modes furnishes proof that our model\ndescribes the emergence of a perfect one-to-one retinotopy between two spheres.",
    "arxiv_id": "physics/0607259",
    "authors": [
      "Martin Guessmann",
      "Axel Pelster",
      "Guenter Wunner"
    ],
    "categories": [
      "physics.bio-ph"
    ],
    "doi": "10.1002/andp.200610244",
    "journal_ref": "Ann. Phys. (Leipzig) 16, 395 (2007)",
    "title": "Solutions of the Haeussler-von der Malsburg Equations in Manifolds with   Constant Curvatures",
    "url": "https://arxiv.org/abs/physics/0607259"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ee8e57b0-edb4-42f6-a0c5-1fd66713df75",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}