{"id":23128,"date":"2021-01-05T21:27:04","date_gmt":"2021-01-05T13:27:04","guid":{"rendered":"https:\/\/swarma.org\/?p=23128"},"modified":"2021-01-05T21:27:04","modified_gmt":"2021-01-05T13:27:04","slug":"%e7%a7%91%e6%8a%80%e7%9f%a5%e8%af%86%e7%bd%91%e7%bb%9c%e4%b8%ad%e9%ab%98%e9%98%b6%e7%bb%93%e6%9e%84%e7%9a%84%e6%b6%8c%e7%8e%b0-arxiv%e8%ae%ba%e6%96%87%e9%80%9f%e9%80%92","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=23128","title":{"rendered":"\u79d1\u6280\u77e5\u8bc6\u7f51\u7edc\u4e2d\u9ad8\u9636\u7ed3\u6784\u7684\u6d8c\u73b0 | arXiv\u8bba\u6587\u901f\u9012"},"content":{"rendered":"
<\/p>\n

\u5bfc\u8bed<\/p>\n

\u79d1\u5b66\u7814\u7a76\u4e2d\uff0c\u4f4e\u5782\u7684\u679c\u5b9e\u8d8a\u6765\u8d8a\u5c11\uff0c\u8be5\u5982\u4f55\u5e94\u5bf9\uff1f\u4f5c\u4e3a\u7814\u7a76\u79d1\u5b66\u53d1\u5c55\u5185\u5728\u89c4\u5f8b\u7684\u79d1\u5b66\u5b66\uff0c\u660e\u5c3c\u82cf\u8fbe\u5927\u5b66\u7684Thomas Gebhart \u548c Russell J. Funk\uff0c\u4f7f\u7528\u7f51\u7edc\u79d1\u5b66\u4f5c\u4e3a\u5de5\u5177\uff0c\u5bf9\u4e0d\u540c\u5e74\u4ee3\u7684\u79d1\u7814\u6d3b\u52a8\u80cc\u540e\u7684\u7f51\u7edc\u7ed3\u6784\u8fdb\u884c\u4e86\u7814\u7a76\u3002\u533a\u522b\u4e86\u9ad8\u9636\u548c\u4f4e\u9636\u7f51\u7edc\u5bf9\u5e94\u7684\u7814\u7a76\uff0c\u5e76\u6307\u51fa\u4e24\u8005\u5b58\u5728\u663e\u8457\u4e0d\u540c\u3002\u626b\u63cf\u4e0b\u65b9\u4e8c\u7ef4\u7801\u5373\u53ef\u67e5\u770b\u4e0b\u8f7dPDF\u6587\u4ef6\u3002<\/p>\n


\u626b\u7801\u83b7\u53d6\u8bba\u6587PDF
\u90ed\u745e\u4e1c | \u4f5c\u8005
\u9093\u4e00\u96ea | \u7f16\u8f91<\/p>\n

\u8bba\u6587\u9898\u76ee\uff1a
The Emergence of Higher-Order Structure in Scientific and Technological Knowledge Networks
\u8bba\u6587\u5730\u5740\uff1a
https:\/\/arxiv.org\/abs\/2009.13620
 <\/p>\n


1.\u53d1\u73b0\uff1a\u79d1\u7814\u7f51\u7edc\u4e2d\u7684\u9ad8\u9636\u7ed3\u6784<\/p>\n



\u8fc7\u53bb\u4e00\u767e\u5e74\u95f4\uff0c\u79d1\u7814\u56e2\u961f\u89c4\u6a21\u8d8a\u6765\u8d8a\u5927\uff0c\u79d1\u7814\u4eba\u5458\u9700\u8981\u638c\u63e1\u7684\u77e5\u8bc6\u4e5f\u8d8a\u6765\u8d8a\u591a\u3002\u8fd9\u610f\u5473\u7740\u8981\u60f3\u505a\u597d\u79d1\u7814\uff0c\u9700\u8981\u66f4\u9ad8\u6548\u5730\u91cd\u7ec4\u5df2\u6709\u77e5\u8bc6\u3002\u800c\u5c06\u4e0a\u8ff0\u76f4\u89c9\u53cd\u6620\u5230\u79d1\u5b66\u5b66\u7684\u7814\u7a76\u4e2d\uff0c\u53ef\u4ee5\u5c06\u6bcf\u4e00\u9879\u65b0\u7814\u7a76\u770b\u6210\u7531\u5df2\u77e5\u6982\u5ff5\u3001\u53d1\u73b0\u6216\u53d1\u660e\u4e3a\u8282\u70b9\u6240\u7ec4\u6210\u7684\u7f51\u7edc\u3002\u7136\u800c\u4e4b\u524d\u7684\u7814\u7a76\uff0c\u5173\u6ce8\u7684\u662f\u8282\u70b9\u4e2d\u4e24\u4e24\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/p>\n

\u7814\u7a76\u8005\u4f7f\u7528\u4ece1970\u5e74\u81f3\u4eca\u7684\u79d1\u7814\u8bba\u6587\u5408\u4f5c\u8005\u7f51\u7edc\uff0c\u5206\u5b66\u79d1\u540e\uff0c\u8003\u5bdf\u4e0d\u540c\u62d3\u6251\u7ef4\u5ea6\u7684\u8d1d\u8482\u6570\uff08betti number\uff09\uff0c\u53ef\u4ee5\u53d1\u73b0\u5728\u8ba1\u7b97\u673a\u3001\u7269\u7406\u3001\u7535\u5b50\u5de5\u7a0b\u4e2d\uff0c\u4ee3\u8868\u9ad8\u9636\u7f51\u7edc\u7ed3\u6784\u7684\u66f2\u7ebf\u663e\u8457\u5347\u9ad8\uff0c\u540c\u65f6\u4f4e\u7ef4\u62d3\u6251\u7ed3\u6784\u964d\u4f4e\u3002\u8fd9\u610f\u5473\u7740\u8fd9\u4e9b\u9886\u57df\u8fd1\u5e74\u6765\u7684\u53d1\u5c55\uff0c\u4f9d\u8d56\u53c2\u4e0e\u8005\u4e4b\u95f4\u7d27\u5bc6\u7684\u5408\u4f5c\u548c\u4e92\u8865\u3002
\u56fe1. \u4e0d\u540c\u5b66\u79d1\u7684\u8bba\u6587\u5408\u4f5c\u8005\u7f51\u7edc\u5728\u4e0d\u540c\u62d3\u6251\u7ef4\u5ea6\u4e0b\u8d1d\u8482\u6570\u968f\u65f6\u95f4\u53d8\u5316\u7684\u66f2\u7ebf<\/p>\n

\u800c\u8003\u8651\u6bcf\u4e2a\u5b50\u5b66\u79d1\u5185\u90e8\u7684\u77e5\u8bc6\u7f51\u7edc\u548c\u5408\u4f5c\u8005\u7f51\u7edc\u4e4b\u95f4\u7684\u5dee\u5f02\uff0c\u53ef\u4ee5\u53d1\u73b0\u5b66\u79d1\u95f4\uff0c\u4e24\u79cd\u7f51\u7edc\u7684\u5dee\u5f02\u6ca1\u6709\u968f\u65f6\u95f4\u5448\u73b0\u660e\u663e\u7684\u8d8b\u52bf\uff0c\u4f46\u5728\u9886\u57df\u5185\uff0c\u5219\u51fa\u73b0\u4e86\u9ad8\u9636\u7ed3\u6784\u7684\u663e\u8457\u63d0\u5347\u3002\u8fd9\u6307\u51fa\u968f\u7740\u5f85\u89e3\u51b3\u95ee\u9898\u8d8a\u6765\u8d8a\u96be\uff0c\u9700\u8981\u66f4\u5927\u7684\u79d1\u7814\u56e2\u961f\uff0c\u5305\u542b\u4e00\u4e2a\u9886\u57df\u5185\u4f17\u591a\u5b50\u9886\u57df\u7684\u4e13\u4e1a\u6280\u80fd\uff0c\u800c\u77e5\u8bc6\u7f51\u7edc\u4e0e\u8bba\u6587\u5408\u4f5c\u8005\u7f51\u7edc\u7684\u62d3\u6251\u5dee\u5f02\uff0c\u610f\u5473\u7740\u540e\u8005\u662f\u524d\u8005\u7684\u539f\u56e0\uff08\u79d1\u7814\u4eba\u5458\u521b\u9020\u65b0\u77e5\uff0c\u6539\u53d8\u77e5\u8bc6\u7f51\u7edc\u7684\u7ed3\u6784\uff09\u3002
\u56fe2. \u8de8\u5b66\u79d1\u4e0e\u5b66\u79d1\u5185\u90e8\u7684\u7f51\u7edc\u5728\u4e0d\u540c\u62d3\u6251\u7ef4\u5ea6\u4e0a\u968f\u65f6\u95f4\u76f8\u4f3c\u5ea6\u7684\u53d8\u5316<\/p>\n

\u56fe3. \u7f51\u7edc\u4f20\u7edf\u7279\u5f81\u548c\u62d3\u6251\u7279\u5f81\u7684\u76f8\u5173\u6027\u70ed\u56fe\uff0c\u4e0d\u540c\u7684\u989c\u8272\u4ee3\u8868\u76ae\u5c14\u68ee\u76f8\u5173\u7cfb\u6570<\/p>\n

\u4e0a\u56fe\u6240\u793a\uff0c\u5404\u4e2a\u4f20\u7edf\u7279\u5f81\uff08\u7eb5\u8f74\uff09\u548c\u7f51\u7edc\u7684\u62d3\u6251\u7279\u5f81\uff08\u6a2a\u8f74\uff09\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u90fd\u4e0d\u660e\u663e\u3002\u8fd9\u610f\u5473\u7740\u81f3\u5c11\u5bf9\u4e8e\u7814\u7a76\u77e5\u8bc6\u63a2\u7d22\u53ca\u4fe1\u606f\u4f20\u64ad\uff0c\u7f51\u7edc\u7684\u62d3\u6251\u7ed3\u6784\u53d8\u5316\u4e5f\u662f\u503c\u5f97\u5173\u6ce8\u7684\u5206\u6790\u65b9\u6cd5\u3002
\u603b\u7ed3\u6765\u770b\uff0c\u8be5\u7814\u7a76\u9664\u4e86\u6307\u51fa\u8fd1\u5e74\u6765\u79d1\u7814\u5408\u4f5c\u8005\u7f51\u7edc\u4e2d\u5448\u73b0\u51fa\u7684\u9ad8\u9636\u7ed3\u6784\uff0c\u8fd9\u4e9b\u7ed3\u6784\u5bf9\u5e94\u7740\u66f4\u4e3a\u590d\u6742\u7684\u6982\u5ff5\uff0c\u66f4\u4e3a\u62bd\u8c61\u7684\u8bcd\u6c47\u3002\u8be5\u7814\u7a76\u8fd8\u8bc1\u660e\u4e86\u4f7f\u7528\u7f51\u7edc\u62d3\u6251\uff0c\u53ef\u4ee5\u63cf\u8ff0\u4f7f\u7528\u4f20\u7edf\u7684\u7f51\u7edc\u7279\u5f81\uff08\u5982\u805a\u7c7b\u7cfb\u6570\u3001\u8282\u70b9\u4e2d\u5fc3\u5ea6\u7b49\uff09\u65e0\u6cd5\u63cf\u8ff0\u7684\u7279\u5f81\u3002
 <\/p>\n

2. \u65b9\u6cd5\uff1a\u7f51\u7edc\u62d3\u6251\u7ed3\u6784<\/p>\n



\u4e0d\u540c\u4e8e\u8282\u70b9\u4e4b\u95f4\u7684\u4e24\u4e24\u5173\u7cfb\uff0c\u6216\u8005\u63cf\u8ff0\u8282\u70b9\u7279\u5f81\u7684\u6307\u6807\uff08\u4f8b\u5982\u4e2d\u5fc3\u5ea6\uff09\uff0c\u7f51\u7edc\u7684\u62d3\u6251\u6027\u8d28\u662f\u5bf9\u7f51\u7edc\u6574\u4f53\u7684\u5b8f\u89c2\u63cf\u8ff0\u3002\u8fd9\u9879\u7814\u7a76\u5229\u7528\u7684\u65b9\u6cd5\u662f Persistent homology\uff08\u6301\u7eed\u540c\u8c03\uff09\uff0c\u8fd9\u91cc\u53ea\u505a\u7b80\u5355\u4ecb\u7ecd\uff0c\u5177\u4f53\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n

\u56fe4. \u7f51\u7edc\u7684\u62d3\u6251\u7ed3\u6784\u793a\u610f\u56fe<\/p>\n

\u56fe4\u4e2dA\u4ee3\u8868\u7684\u7f51\u7edc\uff0c\u5982\u679c\u70b9\u4e0e\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u5206\u522b\u4e3ai\uff0cj\uff0ck\u65f6\uff0c\u5206\u522b\u80fd\u591f\u8fde\u63a5\u7684\u8fb9\u7ec4\u6210\u7684\u7f51\u7edc\u4f9d\u6b21\u5982\u56fe4C\u6240\u793a\u3002\u800c\u5982\u679cn\u4e2a\u70b9\u4e4b\u95f4\u4e24\u4e24\u90fd\u6709\u8fde\u63a5\uff0c\u90a3\u4e48\u8fd9\u6837\u7684\u7fa4\u4f53\u5728\u56fe4b\u4e2d\u7528\u4e0d\u540c\u989c\u8272\u8868\u793a\uff0c\u4e0d\u540c\u989c\u8272\u5bf9\u5e94\u7684\u6570\u5b57\u5bf9\u5e94\u8fd9\u4e9b\u8282\u70b9\u5728\u76f8\u5e94\u62d3\u6251\u7ef4\u5ea6\u4e0a\u7684 homological dimension\uff08\u540c\u8c03\u7ef4\u6570\uff09\u3002\u800c\u56fe\u4e2d\u7684\u5706\u5708\u88ab\u79f0\u4e3a\u7ed3\u6784\u6d1e\uff0c\u6307\u5728\u8fd9\u6837\u7684\u8ddd\u79bb\u4e0a\uff0c\u7ed3\u6784\u6d1e\u5468\u56f4\u7684\u8282\u70b9\u5728\u62d3\u6251\u4e0a\u662f\u7b49\u4ef7\u7684\u3002<\/p>\n

\u5bf9\u7f51\u7edc\u62d3\u6251\u53caPersistent homology\u611f\u5174\u8da3\u7684\u8bfb\u8005\uff0c\u53ef\u4ee5\u53c2\u8003\u4e0b\u9762\u7684\u8bba\u6587\uff1a<\/p>\n

Mehmet E Aktas, Esra Akbas, and Ahmed El Fatmaoui. Persistence homology of networks: methods and applications. Applied Network Science, 4(1):61, 2019.<\/p>\n

\u590d\u6742\u79d1\u5b66\u6700\u65b0\u8bba\u6587


\u96c6\u667a\u6591\u56fe\u9876\u520a\u8bba\u6587\u901f\u9012\u680f\u76ee\u4e0a\u7ebf\u4ee5\u6765\uff0c\u6301\u7eed\u6536\u5f55\u6765\u81eaNature\u3001Science\u7b49\u9876\u520a\u7684\u6700\u65b0\u8bba\u6587\uff0c\u8ffd\u8e2a\u590d\u6742\u7cfb\u7edf\u3001\u7f51\u7edc\u79d1\u5b66\u3001\u8ba1\u7b97\u793e\u4f1a\u79d1\u5b66\u7b49\u9886\u57df\u7684\u524d\u6cbf\u8fdb\u5c55\u3002\u73b0\u5728\u6b63\u5f0f\u63a8\u51fa\u8ba2\u9605\u529f\u80fd\uff0c\u6bcf\u5468\u901a\u8fc7\u5fae\u4fe1\u670d\u52a1\u53f7\u300c\u96c6\u667a\u6591\u56fe\u300d\u63a8\u9001\u8bba\u6587\u4fe1\u606f\u3002\u626b\u63cf\u4e0b\u65b9\u4e8c\u7ef4\u7801\u5373\u53ef\u4e00\u952e\u8ba2\u9605\uff1a<\/p>\n

<\/div>\n

\u63a8\u8350\u9605\u8bfb
Science\u7ecf\u5178\u7efc\u8ff0\u6587\u7ae0\uff1a\u4ec0\u4e48\u662f\u79d1\u5b66\u5b66<\/a>
\u770b\u61c2\u7f51\u7edc\u5206\u6790\uff0c\u6210\u4e3a\u9ad8\u9636\u7403\u8ff7<\/a><\/p>\n

2020\u5e74\u7f51\u7edc\u79d1\u5b66\u76844\u4e2a\u524d\u6cbf\u65b9\u5411\uff1a\u4ece\u65f6\u5e8f\u7f51\u7edc\u5230\u9ad8\u9636\u7f51\u7edc<\/a>
PRL\uff1a\u627e\u5bfb\u7f51\u7edc\u4e2d\u7684\u521b\u65b0\u201c\u5b88\u95e8\u5458\u201d<\/a><\/p>\n

\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/a><\/p>\n

\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u8ffd\u8e2a\u590d\u6742\u79d1\u5b66\u9876\u520a\u8bba\u6587 <\/div>\n","protected":false},"excerpt":{"rendered":"

\u5bfc\u8bed \u79d1\u5b66\u7814\u7a76\u4e2d\uff0c\u4f4e\u5782\u7684\u679c\u5b9e\u8d8a\u6765\u8d8a\u5c11\uff0c\u8be5\u5982\u4f55\u5e94\u5bf9\uff1f\u4f5c\u4e3a\u7814\u7a76\u79d1\u5b66\u53d1\u5c55\u5185\u5728\u89c4\u5f8b\u7684\u79d1\u5b66\u5b66\uff0c\u660e\u5c3c\u82cf\u8fbe\u5927\u5b66\u7684Thomas Gebhart \u548c Russell J. Funk\uff0c\u4f7f\u7528\u7f51\u7edc\u79d1\u5b66\u4f5c\u4e3a\u5de5\u5177\uff0c\u5bf9\u4e0d\u540c\u5e74\u4ee3\u7684\u79d1\u7814\u6d3b\u52a8\u80cc\u540e\u7684\u7f51\u7edc\u7ed3\u6784\u8fdb\u884c\u4e86\u7814\u7a76\u3002\u533a\u522b\u4e86\u9ad8\u9636\u548c\u4f4e\u9636\u7f51\u7edc\u5bf9\u5e94\u7684\u7814\u7a76\uff0c\u5e76\u6307\u51fa\u4e24\u8005\u5b58\u5728\u663e\u8457\u4e0d\u540c\u3002\u626b\u63cf\u4e0b\u65b9\u4e8c\u7ef4…<\/p>\n","protected":false},"author":1,"featured_media":23120,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/23128"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=23128"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/23128\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/23120"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23128"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23128"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23128"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=23128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}