Essec\Faculty\Model\Contribution {#2233
  #_index: "academ_contributions"
  #_id: "10190"
  #_source: array:26 [
    "id" => "10190"
    "slug" => "fixed-points-of-the-abe-formulation-of-stochastic-hopfield-networks"
    "yearMonth" => "2007-09"
    "year" => "2007"
    "title" => "Fixed points of the Abe formulation of Stochastic Hopfield Networks"
    "description" => "KRATZ, M., ATENCIA, M. et JOYA, G. (2007). Fixed points of the Abe formulation of Stochastic Hopfield Networks. Dans: 17th ICANN. Porto."
    "authors" => array:3 [
      0 => array:3 [
        "name" => "KRATZ Marie"
        "bid" => "B00072305"
        "slug" => "kratz-marie"
      ]
      1 => array:1 [
        "name" => "ATENCIA Miguel"
      ]
      2 => array:1 [
        "name" => "JOYA Gonzalo"
      ]
    ]
    "ouvrage" => "17th ICANN"
    "keywords" => array:1 [
      0 => "Hopfield network"
    ]
    "updatedAt" => "2021-07-13 14:31:29"
    "publicationUrl" => null
    "publicationInfo" => array:3 [
      "pages" => null
      "volume" => null
      "number" => null
    ]
    "type" => array:2 [
      "fr" => "Communications dans une conférence"
      "en" => "Presentations at an Academic or Professional conference"
    ]
    "support_type" => array:2 [
      "fr" => null
      "en" => null
    ]
    "countries" => array:2 [
      "fr" => null
      "en" => null
    ]
    "abstract" => array:2 [
      "fr" => """
        The stability of stochastic Hopfield neural networks, in the Abe formulation, is studied. The aim is to determine whether the ability of the deterministic system to solve combinatorial optimization problems is preserved after the addition of random noise. In particular, the stochastic stability of the attractor set is analyzed: vertices, which are feasible points of the problem, should be stable, whereas interior points, which are unfeasible, should be\n
        unstable. Conditions on the noise intensity are stated, so that these properties are guaranteed. This theoretical investigation establishes the foundations for practical application of stochastic networks to combinatorial optimization.
        """
      "en" => """
        The stability of stochastic Hopfield neural networks, in the Abe formulation, is studied. The aim is to determine whether the ability of the deterministic system to solve combinatorial optimization problems is preserved after the addition of random noise. In particular, the stochastic stability of the attractor set is analyzed: vertices, which are feasible points of the problem, should be stable, whereas interior points, which are unfeasible, should be\n
        unstable. Conditions on the noise intensity are stated, so that these properties are guaranteed. This theoretical investigation establishes the foundations for practical application of stochastic networks to combinatorial optimization.
        """
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2024-12-21T13:21:43.000Z"
    "docTitle" => "Fixed points of the Abe formulation of Stochastic Hopfield Networks"
    "docSurtitle" => "Communications dans une conférence"
    "authorNames" => "<a href="/cv/kratz-marie">KRATZ Marie</a>, ATENCIA Miguel, JOYA Gonzalo"
    "docDescription" => "<span class="document-property-authors">KRATZ Marie, ATENCIA Miguel, JOYA Gonzalo</span><br><span class="document-property-authors_fields">Systèmes d'Information, Data Analytics et Opérations</span> | <span class="document-property-year">2007</span>"
    "keywordList" => "<a href="#">Hopfield network</a>"
    "docPreview" => "<b>Fixed points of the Abe formulation of Stochastic Hopfield Networks</b><br><span>2007-09 | Communications dans une conférence </span>"
    "docType" => "research"
    "publicationLink" => "<a href="#" target="_blank">Fixed points of the Abe formulation of Stochastic Hopfield Networks</a>"
  ]
  +lang: "fr"
  +"_type": "_doc"
  +"_score": 8.565679
  +"parent": null
}