{
  "id": "1707.02227",
  "version": "v1",
  "published": "2017-07-05T22:58:56.000Z",
  "updated": "2017-07-05T22:58:56.000Z",
  "title": "Coloring Fibonacci-Cayley tree: An application to neural networks",
  "authors": [
    "Jung-Chao Ban",
    "Chih-Hung Chang"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1706.09283",
  "categories": [
    "math.DS"
  ],
  "abstract": "This paper investigates the coloring problem on Fibonacci-Cayley tree, which is a Cayley graph whose vertex set is the Fibonacci sequence. More precisely, we elucidate the complexity of shifts of finite type defined on Fibonacci-Cayley tree via an invariant called entropy. It comes that computing the entropy of a Fibonacci tree-shift of finite type is equivalent to studying a nonlinear recursive system. After proposing an algorithm for the computation of entropy, we apply the result to neural networks defined on Fibonacci-Cayley tree, which reflect those neural systems with neuronal dysfunction. Aside from demonstrating a surprising phenomenon that there are only two possibilities of entropy for neural networks on Fibonacci-Cayley tree, we reveal the formula of the boundary in the parameter space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-05T22:58:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A35",
      "37B10",
      "92B20"
    ],
    "keywords": [
      "neural networks",
      "coloring fibonacci-cayley tree",
      "application",
      "finite type",
      "parameter space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}