{"id":1003,"date":"2020-10-23T12:04:05","date_gmt":"2020-10-23T03:04:05","guid":{"rendered":"http:\/\/mathematicians.korea.ac.kr\/sk23\/?p=1003"},"modified":"2020-10-23T12:09:39","modified_gmt":"2020-10-23T03:09:39","slug":"%ed%8a%b9%ea%b0%95-hodge-laplacians-and-simplicial-networks","status":"publish","type":"post","link":"https:\/\/mathematicians.korea.ac.kr\/sk23\/2020\/10\/23\/%ed%8a%b9%ea%b0%95-hodge-laplacians-and-simplicial-networks\/","title":{"rendered":"[\ud2b9\uac15] Hodge Laplacians and simplicial networks"},"content":{"rendered":"<p>\uc81c\ubaa9: Hodge Laplacians and simplicial networks<br \/>\n\uc5f0\uc0ac: \uc774\uac15\uc8fc \ubc15\uc0ac\ub2d8 (\uc11c\uc6b8\ub300\ud559\uad50)<br \/>\n\uc77c\uc2dc: 10\uc6d4 30\uc77c \uae08\uc694\uc77c \uc624\ud6c4 4\uc2dc 30\ubd84<\/p>\n<p>\uc90c\uc73c\ub85c \uc2e4\uc2dc\ud558\ub294 \uc2e4\uc2dc\uac04 \uc628\ub77c\uc778 \ud2b9\uac15\uc785\ub2c8\ub2e4.<br \/>\n\ucc38\uc5ec\ub97c \uc6d0\ud558\ub294 \ubd84\ub4e4\uc740 29\uc77c\uae4c\uc9c0 \uba54\uc77c\ub85c \uc54c\ub824\uc8fc\uc2dc\uae30 \ubc14\ub78d\ub2c8\ub2e4. <\/p>\n<p>Abstract: The Hodge Laplacian on a simplicial complex is a discrete analogue of the Laplace-Beltrami operator. Combinatorial Hodge theory says that the kernel of this operator is isomorphic to the homology group as a vector space, and an element of the space satisfies the energy-minimizing property. Based on the theory, we introduce the notion of effective resistance for simplicial networks. We present a formula for the simplicial effective resistance via high-dimensional tree-numbers, providing its combinatorial interpretation. Moreover, as a tool for analyzing simplicial networks, we suggest a definition of information centrality for simplicial networks.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\uc81c\ubaa9: Hodge Laplacians and simplicial networks \uc5f0\uc0ac: \uc774\uac15\uc8fc \ubc15\uc0ac\ub2d8 (\uc11c\uc6b8\ub300\ud559\uad50) \uc77c\uc2dc: 10\uc6d4 30\uc77c \uae08\uc694\uc77c \uc624\ud6c4 4\uc2dc 30\ubd84 \uc90c\uc73c\ub85c \uc2e4\uc2dc\ud558\ub294 \uc2e4\uc2dc\uac04 \uc628\ub77c\uc778 \ud2b9\uac15\uc785\ub2c8\ub2e4. \ucc38\uc5ec\ub97c \uc6d0\ud558\ub294 \ubd84\ub4e4\uc740 29\uc77c\uae4c\uc9c0 \uba54\uc77c\ub85c \uc54c\ub824\uc8fc\uc2dc\uae30 \ubc14\ub78d\ub2c8\ub2e4. Abstract: The Hodge Laplacian on a simplicial complex is a discrete analogue of the Laplace-Beltrami operator. Combinatorial Hodge theory says that the kernel of this operator &#8230; <a title=\"[\ud2b9\uac15] Hodge Laplacians and simplicial networks\" class=\"read-more\" href=\"https:\/\/mathematicians.korea.ac.kr\/sk23\/2020\/10\/23\/%ed%8a%b9%ea%b0%95-hodge-laplacians-and-simplicial-networks\/\" aria-label=\"[\ud2b9\uac15] Hodge Laplacians and simplicial networks\uc5d0 \ub300\ud574 \ub354 \uc790\uc138\ud788 \uc54c\uc544\ubcf4\uc138\uc694\">\ub354 \uc77d\uae30<\/a><\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1003","post","type-post","status-publish","format-standard","hentry","category-news-events"],"distributor_meta":false,"distributor_terms":false,"distributor_media":false,"distributor_original_site_name":"","distributor_original_site_url":"https:\/\/mathematicians.korea.ac.kr\/sk23","push-errors":false,"_links":{"self":[{"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/posts\/1003","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/comments?post=1003"}],"version-history":[{"count":2,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/posts\/1003\/revisions"}],"predecessor-version":[{"id":1005,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/posts\/1003\/revisions\/1005"}],"wp:attachment":[{"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/media?parent=1003"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/categories?post=1003"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/tags?post=1003"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}