{
  "id": "1505.02190",
  "version": "v1",
  "published": "2015-05-07T14:40:23.000Z",
  "updated": "2015-05-07T14:40:23.000Z",
  "title": "Moment Closure - A Brief Review",
  "authors": [
    "Christian Kuehn"
  ],
  "comment": "preprint, comments and suggestion welcome, intended as a short survey paper (max 20 pages) for a broad audience in mathematics, physics and quantitative biology",
  "categories": [
    "cond-mat.stat-mech",
    "math.DS",
    "nlin.AO",
    "q-bio.QM"
  ],
  "abstract": "Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one \"moment\", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing \"higher-order moments\" in terms of \"lower-order moments\". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-07T14:40:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brief review",
      "moment closure methods appear",
      "moment closure methods occur",
      "moment closure approximations",
      "full state space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150502190K"
    }
  }
}