{"id":513,"date":"2014-12-01T14:57:45","date_gmt":"2014-12-01T14:57:45","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/aslangul\/?p=513"},"modified":"2015-04-17T20:24:54","modified_gmt":"2015-04-17T20:24:54","slug":"reseau-bethe","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/aslangul\/2014\/12\/01\/reseau-bethe\/","title":{"rendered":"R\u00e9seau de Bethe (arbre de Cayley)"},"content":{"rendered":"<p>Le r\u00e9seau de Bethe, ou encore arbre de Cayley, est une arborescence sans boucle dont chaque n\u0153ud poss\u00e8de un nombre fixe (coordinance) de premiers voisins ; la figure montre \u00e0 gauche un arbre de coordinance 3. Cet objet a priori purement g\u00e9om\u00e9trique est la base d&#8217;un grand nombre de mod\u00e8les allant de la biophysique (r\u00e9activit\u00e9 des prot\u00e9ines) aux sciences bibliom\u00e9triques (&#8220;rayonnement&#8221; (!) d&#8217;un chercheur selon la nature et le nombre de ses collaborations).<\/p>\n<p>Une question importante, valant d&#8217;ailleurs pour tout type de r\u00e9seau, est la pertinence du d\u00e9sordre : lorsque des liens sont bris\u00e9s al\u00e9atoirement, quelle est la concentration faisant perdre au syst\u00e8me sa connectivit\u00e9 \u00e0 grande \u00e9chelle ? Pour le chercheur, \u00e0 en croire les &#8220;experts&#8221;, ce serait sa mort intellectuelle et sociale.<\/p>\n<p><a href=\"https:\/\/blogs.futura-sciences.com\/aslangul\/wp-content\/uploads\/sites\/10\/2014\/12\/ArbreDeBetheAI.jpg\" rel=\"lightbox[513]\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-520\" src=\"https:\/\/blogs.futura-sciences.com\/aslangul\/wp-content\/uploads\/sites\/10\/2014\/12\/ArbreDeBetheAI-450x237.jpg\" alt=\"ArbreDeBetheAI\" width=\"450\" height=\"237\" srcset=\"https:\/\/blogs.futura-sciences.com\/aslangul\/wp-content\/uploads\/sites\/10\/2014\/12\/ArbreDeBetheAI-450x237.jpg 450w, https:\/\/blogs.futura-sciences.com\/aslangul\/wp-content\/uploads\/sites\/10\/2014\/12\/ArbreDeBetheAI.jpg 709w\" sizes=\"auto, (max-width: 450px) 100vw, 450px\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>Il est int\u00e9ressant de constater que cette structure g\u00e9om\u00e9trique se retrouve presque \u00e0 l&#8217;identique dans la nature, comme en t\u00e9moigne la photo ci-dessus \u00e0 droite d&#8217;une <em>euphorbia tirucalli<\/em>, prise \u00e0 l&#8217;exposition ELK qui s&#8217;est tenue en septembre \u00e0 Blankenberge (Belgique). Cette manifestation annuelle rassemble des centaines d&#8217;exposants proposant aux passionn\u00e9s de cactus, plantes \u00e0 caudex,&#8230; des exemplaires rares dont chacun est un \u00e9merveillement et donne raison \u00e0 Buffon s&#8217;extasiant devant l&#8217;infinie vari\u00e9t\u00e9 des spectacles de la Nature.<\/p>\n<!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"<p>Le r\u00e9seau de Bethe, ou encore arbre de Cayley, est une arborescence sans boucle dont chaque n\u0153ud poss\u00e8de un nombre fixe (coordinance) de premiers voisins ; la figure montre \u00e0 gauche un arbre de coordinance 3. Cet objet a priori purement g\u00e9om\u00e9trique est la base d&#8217;un grand nombre de mod\u00e8les allant de la biophysique (r\u00e9activit\u00e9 &hellip; <a href=\"https:\/\/blogs.futura-sciences.com\/aslangul\/2014\/12\/01\/reseau-bethe\/\" class=\"more-link\">Continuer la lecture de <span class=\"screen-reader-text\">R\u00e9seau de Bethe (arbre de Cayley)<\/span>  <span class=\"meta-nav\">&rarr;<\/span><\/a><!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt --><\/p>\n","protected":false},"author":9,"featured_media":531,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[99,6],"tags":[],"class_list":["post-513","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-loisirs","category-sciences"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>R\u00e9seau de Bethe (arbre de Cayley), par Claude Aslangul<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blogs.futura-sciences.com\/aslangul\/2014\/12\/01\/reseau-bethe\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"R\u00e9seau de Bethe (arbre de Cayley), par Claude Aslangul\" \/>\n<meta property=\"og:description\" content=\"Le r\u00e9seau de Bethe, ou encore arbre de Cayley, est une arborescence sans boucle dont chaque n\u0153ud poss\u00e8de un nombre fixe (coordinance) de premiers voisins ; la figure montre \u00e0 gauche un arbre de coordinance 3. Cet objet a priori purement g\u00e9om\u00e9trique est la base d&#8217;un grand nombre de mod\u00e8les allant de la biophysique (r\u00e9activit\u00e9 &hellip; Continuer la lecture de R\u00e9seau de Bethe (arbre de Cayley) &rarr;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/blogs.futura-sciences.com\/aslangul\/2014\/12\/01\/reseau-bethe\/\" \/>\n<meta property=\"og:site_name\" content=\"PHYSMATIQUES, le blog de Claude ASLANGUL, physicien th\u00e9oricien\" \/>\n<meta property=\"article:published_time\" content=\"2014-12-01T14:57:45+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2015-04-17T20:24:54+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/blogs.futura-sciences.com\/aslangul\/wp-content\/uploads\/sites\/10\/2014\/12\/CayleyBethe.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"429\" \/>\n\t<meta property=\"og:image:height\" content=\"322\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/aslangul\/2014\/12\/01\/reseau-bethe\/\",\"url\":\"https:\/\/blogs.futura-sciences.com\/aslangul\/2014\/12\/01\/reseau-bethe\/\",\"name\":\"R\u00e9seau de Bethe (arbre de Cayley), par Claude Aslangul\",\"isPartOf\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/aslangul\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/aslangul\/2014\/12\/01\/reseau-bethe\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/aslangul\/2014\/12\/01\/reseau-bethe\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/blogs.futura-sciences.com\/aslangul\/wp-content\/uploads\/sites\/10\/2014\/12\/CayleyBethe.jpg\",\"datePublished\":\"2014-12-01T14:57:45+00:00\",\"dateModified\":\"2015-04-17T20:24:54+00:00\",\"author\":{\"@id\":\"\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/blogs.futura-sciences.com\/aslangul\/2014\/12\/01\/reseau-bethe\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/aslangul\/2014\/12\/01\/reseau-bethe\/#primaryimage\",\"url\":\"https:\/\/blogs.futura-sciences.com\/aslangul\/wp-content\/uploads\/sites\/10\/2014\/12\/CayleyBethe.jpg\",\"contentUrl\":\"https:\/\/blogs.futura-sciences.com\/aslangul\/wp-content\/uploads\/sites\/10\/2014\/12\/CayleyBethe.jpg\",\"width\":429,\"height\":322},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/aslangul\/#website\",\"url\":\"https:\/\/blogs.futura-sciences.com\/aslangul\/\",\"name\":\"PHYSMATIQUES, le blog de Claude ASLANGUL, physicien th\u00e9oricien\",\"description\":\"&quot;Si la vie est complexe, c&#039;est parce qu&#039;elle a une partie r\u00e9elle et une partie imaginaire.&quot;  Sophus Lie\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/blogs.futura-sciences.com\/aslangul\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"fr-FR\"},{\"@type\":\"Person\",\"@id\":\"\",\"url\":\"https:\/\/blogs.futura-sciences.com\/aslangul\/author\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"R\u00e9seau de Bethe (arbre de Cayley), par Claude Aslangul","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/blogs.futura-sciences.com\/aslangul\/2014\/12\/01\/reseau-bethe\/","og_locale":"fr_FR","og_type":"article","og_title":"R\u00e9seau de Bethe (arbre de Cayley), par Claude Aslangul","og_description":"Le r\u00e9seau de Bethe, ou encore arbre de Cayley, est une arborescence sans boucle dont chaque n\u0153ud poss\u00e8de un nombre fixe (coordinance) de premiers voisins ; la figure montre \u00e0 gauche un arbre de coordinance 3. 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