{
  "id": "1308.6661",
  "version": "v2",
  "published": "2013-08-30T07:10:53.000Z",
  "updated": "2014-11-12T18:57:54.000Z",
  "title": "Griffiths phases and the stretching of criticality in brain networks",
  "authors": [
    "Paolo Moretti",
    "Miguel A. Muñoz"
  ],
  "comment": "Final version. A misprint in Equation (2) was corrected. Supplementary Information included",
  "journal": "Nature Communications 4, 2521 (2013)",
  "doi": "10.1038/ncomms3521",
  "categories": [
    "cond-mat.dis-nn",
    "q-bio.NC"
  ],
  "abstract": "Hallmarks of criticality, such as power-laws and scale invariance, have been empirically found in cortical networks and it has been conjectured that operating at criticality entails functional advantages, such as optimal computational capabilities, memory, and large dynamical ranges. As critical behavior requires a high degree of fine tuning to emerge, some type of self-tuning mechanism needs to be invoked. Here we show that, taking into account the complex hierarchical-modular architecture of cortical networks, the singular critical point is replaced by an extended critical-like region which corresponds --in the jargon of statistical mechanics-- to a Griffiths phase. Using computational and analytical approaches, we find Griffiths phases in synthetic hierarchical networks and also in empirical brain networks such as the human connectome and the caenorhabditis elegans one. Stretched critical regions, stemming from structural disorder, yield enhanced functionality in a generic way, facilitating the task of self-organizing, adaptive, and evolutionary mechanisms selecting for criticality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-30T07:10:53.000Z",
      "title": "Brain architecture, Griffiths phases, and the stretching of criticality",
      "abstract": "Hallmarks of criticality, such as power-laws and scale invariance, have been empirically found in cortical networks and it has been claimed that operating at criticality entails functional advantages, such as optimal computational capabilities, memory, and large dynamical ranges. An apparent paradox is that criticality requires a high degree of fine tuning to emerge and hence, self-organizing mechanisms need to be invoked. Here we show that, taking explicitly into account the complex hierarchical-modular architecture of cortical networks, the standard critical point picture is replaced by an extended critical-like region which corresponds -- in the jargon of statistical mechanics -- to a Griffiths phase. Using computational and analytical approaches, we find Griffiths phases in synthetic hierarchical networks and also in empirical neural networks such as those of C. elegans and the human connectome. Stretched critical regions, stemming from structural disorder, yield optimal functionality in a generic way, facilitating the task of self-organizing, adaptive and evolutionary mechanisms selecting for criticality.",
      "comment": "Initial version. Supplementary Information included",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-12T18:57:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "griffiths phase",
      "brain architecture",
      "criticality entails functional advantages",
      "optimal computational capabilities",
      "cortical networks"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Nature Communications",
      "year": 2013,
      "month": "Oct",
      "volume": 4,
      "pages": 2521
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013NatCo...4E2521M"
    }
  }
}