{
  "id": "2305.10074",
  "version": "v1",
  "published": "2023-05-17T09:20:47.000Z",
  "updated": "2023-05-17T09:20:47.000Z",
  "title": "Inverse problem for electrical networks via twist",
  "authors": [
    "Terrence George"
  ],
  "comment": "30 pages, 8 figures. Comments welcome",
  "categories": [
    "math.CO"
  ],
  "abstract": "We construct an electrical-network version of the twist map for the positive Grassmannian, and use it to solve the inverse problem of recovering conductances from the response matrix. Each conductance is expressed as a biratio of Pfaffians as in the inverse map of Kenyon and Wilson; however, our Pfaffians are the more canonical $B$ variables instead of their tripod variables, and are coordinates on the positive orthogonal Grassmannian studied by Henriques and Speyer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-17T09:20:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse problem",
      "electrical networks",
      "response matrix",
      "positive orthogonal grassmannian",
      "electrical-network version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}