{
  "id": "2001.01704",
  "version": "v1",
  "published": "2020-01-06T18:36:09.000Z",
  "updated": "2020-01-06T18:36:09.000Z",
  "title": "Characterization of Multivaluedness in Networks",
  "authors": [
    "Michael Anton van Wyk"
  ],
  "comment": "3 pages, 1 figure",
  "categories": [
    "eess.SY",
    "cs.SY",
    "eess.SP",
    "math.DS"
  ],
  "abstract": "The motivation for this work stems from the observation that as few as two counter-cascaded systems, with a common input, can exhibit multivaluedness from output to output. Our main result is a theorem that provides a necessary and sufficient condition for multivaluedness to be exhibited by three interconnected systems based on the novel notions of immanence and its opposite, transcendence, introduced here. Subsequent corollaries provide simple conditions to test for multivaluedness under specific circumstances. This note presents the theoretical developments with applications in network science and other areas of signal processing to be presented in subsequent publications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-06T18:36:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C82"
    ],
    "keywords": [
      "multivaluedness",
      "characterization",
      "common input",
      "main result",
      "sufficient condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}