{
  "id": "0902.1787",
  "version": "v2",
  "published": "2009-02-11T00:37:38.000Z",
  "updated": "2009-10-31T10:03:41.000Z",
  "title": "Generalized Fisher information matrix in nonextensive systems with spatial correlation",
  "authors": [
    "Hideo Hasegawa"
  ],
  "comment": "18 pages, 3 figures: revised version accepted in Phys. Rev. E",
  "journal": "Phys. Rev. E 80 (2009) 051125.",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "By using the $q$-Gaussian distribution derived by the maximum entropy method for spatially-correlated $N$-unit nonextensive systems, we have calculated the generalized Fisher information matrix of $g_{\\theta_n \\theta_m}$ for $(\\theta_1, \\theta_2, \\theta_3) = (\\mu_q, \\sigma_q^2$, $s$), where $\\mu_q$, $\\sigma_q^2$ and $s$ denote the mean, variance and degree of spatial correlation, respectively, for a given entropic index $q$. It has been shown from the Cram\\'{e}r-Rao theorem that (1) an accuracy of an unbiased estimate of $\\mu_q$ is improved (degraded) by a negative (positive) correlation $s$, (2) that of $\\sigma_q^2$ is worsen with increasing $s$, and (3) that of $s$ is much improved for $s \\simeq -1/(N-1)$ or $s \\simeq 1.0$ though it is worst at $s = (N-2)/2(N-1)$. Our calculation provides a clear insight to the long-standing controversy whether the spatial correlation is beneficial or detrimental to decoding in neuronal ensembles. We discuss also a calculation of the $q$-Gaussian distribution, applying the superstatistics to the Langevin model subjected to spatially-correlated inputs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-31T10:03:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.70.-a",
      "89.70.Cf",
      "05.10.Gg"
    ],
    "keywords": [
      "generalized fisher information matrix",
      "spatial correlation",
      "gaussian distribution",
      "maximum entropy method",
      "unit nonextensive systems"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "doi": "10.1103/PhysRevE.80.051125",
      "year": 2009,
      "month": "Nov",
      "volume": 80,
      "number": 5,
      "pages": "051125"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009PhRvE..80e1125H"
    }
  }
}