{"id":28421,"date":"2021-08-29T15:52:20","date_gmt":"2021-08-29T07:52:20","guid":{"rendered":"https:\/\/swarma.org\/?p=28421"},"modified":"2021-08-29T15:52:20","modified_gmt":"2021-08-29T07:52:20","slug":"%e5%a6%82%e4%bd%95%e8%b6%85%e8%b6%8a%e5%9b%be%e8%ae%ba%ef%bc%8c%e6%8e%a2%e7%b4%a2%e5%a4%a7%e6%95%b0%e6%8d%ae%e4%b8%ad%e7%9a%84%e5%a4%8d%e6%9d%82%e8%81%94%e7%b3%bb%ef%bc%9f","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=28421","title":{"rendered":"\u5982\u4f55\u8d85\u8d8a\u56fe\u8bba\uff0c\u63a2\u7d22\u5927\u6570\u636e\u4e2d\u7684\u590d\u6742\u8054\u7cfb\uff1f"},"content":{"rendered":"
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\u7814\u7a76\u9886\u57df\uff1a\u7f51\u7edc\uff0c\u56fe\u8bba\uff0c\u8d85\u56fe\uff0c\u62d3\u6251\uff0c\u9a6c\u5c14\u53ef\u592b\u94fe\uff0c\u5f20\u91cf<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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Stephen Ornes<\/span> | \u4f5c\u8005<\/strong><\/span><\/p>\n

\u6881\u91d1<\/span> | \u8bd1\u8005<\/strong><\/span><\/strong><\/span><\/p>\n

\u5218\u57f9\u6e90<\/span> | \u5ba1\u6821<\/strong><\/span><\/strong><\/span>
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1. \u56fe\u8bba\u662f\u4e0d\u591f\u7684<\/strong><\/strong><\/p>\n<\/section>\n

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\u6570\u5b66\u4e2d\u901a\u5e38\u7528\u7f51\u7edc\u6765\u8ba8\u8bba\u8fde\u63a5\u95ee\u9898\uff0c\u7f51\u7edc\u7531\u9876\u70b9\u548c\u8fde\u63a5\u9876\u70b9\u7684\u8fb9\u7ec4\u6210\u3002\u81f3\u5c11\u4ece18\u4e16\u7eaa\u5f00\u59cb\uff0c\u7f51\u7edc\u5c31\u6210\u4e3a\u6a21\u62df\u73b0\u5b9e\u4e16\u754c\u7684\u6709\u6548\u65b9\u6cd5\u3002\u4f46\u51e0\u5341\u5e74\u524d\uff0c\u5de8\u5927\u6570\u636e\u96c6\u7684\u51fa\u73b0\u8feb\u4f7f\u7814\u7a76\u4eba\u5458\u6269\u5c55\u4ed6\u4eec\u7684\u5de5\u5177\u7bb1\uff0c\u540c\u65f6\u4e5f\u4e3a\u4ed6\u4eec\u63d0\u4f9b\u4e86\u5e9e\u5927\u7684\u6c99\u76d2\u6765\u5e94\u7528\u65b0\u7684\u6570\u5b66\u89c1\u89e3\u3002\u79d1\u7f57\u62c9\u591a\u5927\u5b66\u535a\u5c14\u5fb7\u5206\u6821\u7684\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6 Josh Grochow \u8bf4\uff0c\u4ece\u90a3\u4ee5\u540e\uff0c\u968f\u7740\u7814\u7a76\u4eba\u5458\u53d1\u5c55\u51fa\u65b0\u7684\u7f51\u7edc\u6a21\u578b\uff0c\u53ef\u4ee5\u5728\u5927\u6570\u636e\u7684\u566a\u97f3\u4e2d\u627e\u5230\u590d\u6742\u7684\u7ed3\u6784\u548c\u4fe1\u53f7\uff0c\u51fa\u73b0\u4e86\u4e00\u4e2a\u4ee4\u4eba\u5174\u594b\u7684\u5feb\u901f\u589e\u957f\u671f\u3002<\/span>
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\u4e0d\u8fc7\uff0cGrochow \u548c\u8d8a\u6765\u8d8a\u591a\u7684\u7814\u7a76\u4eba\u5458\u53d1\u73b0\uff0c\u5728\u5bfb\u627e\u5927\u6570\u636e\u4e4b\u95f4\u7684\u8054\u7cfb\u65f6\uff0c\u56fe\u8bba\u6709\u5176\u5c40\u9650\u6027<\/strong>\u3002\u56fe\u5c06\u6bcf\u4e00\u79cd\u5173\u7cfb\u8868\u793a\u4e3a\u4e8c\u5143\u7ec4<\/span>\uff08dyad\uff09<\/span>\u6216\u6210\u5bf9\u7684\u4ea4\u4e92\u3002\u7136\u800c\uff0c\u8bb8\u591a\u590d\u6742\u7cfb\u7edf\u4e0d\u80fd\u53ea\u7528\u6210\u5bf9\u7684\u8fde\u63a5\u6765\u8868\u793a<\/strong>\u3002\u4f8b\u5982\uff0c\u8981\u5efa\u7acb\u4e00\u4e2a\u5173\u4e8e\u517b\u80b2\u5173\u7cfb\u7684\u7f51\u7edc\u6a21\u578b\u65f6\uff0c\u663e\u7136\uff0c\u6bcf\u4e2a\u7236\u6bcd\u90fd\u4e0e\u5b69\u5b50\u6709\u8054\u7cfb\uff0c\u4f46\u517b\u80b2\u5173\u7cfb\u5e76\u4e0d\u50cf\u56fe\u8bba\u53ef\u80fd\u6a21\u62df\u7684\u90a3\u6837\uff0c\u4ec5\u4ec5\u662f\u8fd9\u4e24\u79cd\u8054\u7cfb\u7684\u603b\u548c\u3002\u6a21\u62df\u7c7b\u4f3c\u540c\u8f88\u538b\u529b\u7684\u73b0\u8c61\u65f6\uff0c\u4e5f\u4f1a\u9047\u5230\u540c\u6837\u7684\u95ee\u9898\u3002<\/span><\/section>\n
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\u201c\u6709\u5f88\u591a\u76f4\u89c2\u7684\u6a21\u578b\u3002\u53ea\u6709\u5728\u6570\u636e\u4e2d\u5df2\u7ecf\u6709\u4e86\u7fa4\u4f53<\/span>\uff08group\uff09<\/span>\u7684\u60c5\u51b5\u4e0b\uff0c\u540c\u8f88\u538b\u529b\u5bf9\u793e\u4f1a\u52a8\u529b\u5b66\u7684\u5f71\u54cd\u624d\u80fd\u88ab\u6355\u6349\u5230\u3002\u201d\u5fb7\u56fd\u4e9a\u741b\u5de5\u4e1a\u5927\u5b66\u7684Leonie Neuh\u00e4user\u8bf4\u9053\u3002\u4f46\u4e8c\u5143\u7f51\u7edc\u65e0\u6cd5\u6355\u6349\u5230\u7fa4\u4f53\u7684\u5f71\u54cd<\/strong>\u3002<\/span><\/section>\n
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\u6570\u5b66\u5bb6\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u4f7f\u7528\u201c\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u201d<\/span>\uff08higher-order interaction\uff09<\/span>\u8fd9\u4e2a\u672f\u8bed\uff0c\u6765\u63cf\u8ff0\u7fa4\u4f53\u52a8\u529b\u5b66<\/span>\uff08\u800c\u975e\u4e8c\u5143\u8fde\u63a5\uff09<\/span>\u5f71\u54cd\u4e2a\u4f53\u884c\u4e3a\u7684\u590d\u6742\u65b9\u5f0f\u3002\u4ece\u91cf\u5b50\u529b\u5b66\u4e2d\u7684\u7ea0\u7f20\uff0c\u5230\u75be\u75c5\u5728\u7fa4\u4f53\u4e2d\u7684\u4f20\u64ad\u8f68\u8ff9\uff0c\u8fd9\u7c7b\u6570\u5b66\u73b0\u8c61\u968f\u5904\u53ef\u89c1\u3002\u4f8b\u5982\uff0c\u5982\u679c\u4e00\u4e2a\u836f\u7406\u5b66\u5bb6\u60f3\u8981\u5efa\u7acb\u4e00\u4e2a\u5173\u4e8e\u836f\u7269\u95f4\u76f8\u4e92\u4f5c\u7528\u7684\u6a21\u578b [1]\uff0c\u56fe\u8bba\u53ef\u80fd\u4f1a\u663e\u793a\u4e24\u79cd\u836f\u7269\u5982\u4f55\u76f8\u4e92\u4f5c\u7528\u2014\u2014\u4f46\u5982\u679c\u662f3\u79cd\u30014\u79cd\u836f\u7269\u5462\uff1f<\/span><\/section>\n
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\u867d\u7136\u63a2\u7d22\u8fd9\u4e9b\u76f8\u4e92\u4f5c\u7528\u7684\u5de5\u5177\u5e76\u975e\u65b0\u9c9c\u4e8b\u7269\uff0c\u4f46\u76f4\u5230\u6700\u8fd1\u51e0\u5e74\uff0c\u9ad8\u7ef4\u6570\u636e\u96c6\u624d\u6210\u4e3a\u53d1\u73b0\u7684\u5f15\u64ce\uff0c\u7ed9\u6570\u5b66\u5bb6\u548c\u7f51\u7edc\u79d1\u5b66\u5bb6\u5e26\u6765\u65b0\u60f3\u6cd5\u3002\u8fd9\u4e9b\u52aa\u529b\u5df2\u7ecf\u4ea7\u751f\u4e86\u6709\u8da3\u7684\u7ed3\u679c\uff0c\u5173\u4e8e\u56fe\u7684\u6781\u9650\u548c\u6269\u5c55\u56fe\u8bba\u7684\u53ef\u80fd\u6027\u3002<\/span><\/section>\n
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Grochow\u8bf4\uff0c\u201c\u73b0\u5728\u6211\u4eec\u77e5\u9053\u7f51\u7edc\u53ea\u662f\u5b83\u7684\u5f71\u5b50\u3002\u201d\u5982\u679c\u4e00\u4e2a\u6570\u636e\u96c6\u6709\u590d\u6742\u7684\u5e95\u5c42\u7ed3\u6784\uff0c\u90a3\u4e48\u5c06\u5176\u5efa\u6a21\u4e3a\u4e00\u4e2a\u56fe\uff0c\u53ef\u80fd\u53ea\u4f1a\u63ed\u793a\u51fa\u6574\u4e2a\u56fe\u666f\u7684\u4e00\u4e2a\u6709\u9650\u6295\u5f71\u3002<\/strong><\/span><\/section>\n
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\u592a\u5e73\u6d0b\u897f\u5317\u56fd\u5bb6\u5b9e\u9a8c\u5ba4<\/span>\uff08Pacific Northwest National Laboratory\uff09<\/span>\u7684\u6570\u5b66\u5bb6 Emilie Purvine \u8bf4\uff1a\u201c\u6211\u4eec\u610f\u8bc6\u5230\uff0c\u4ece\u6570\u5b66\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u7528\u6765\u7814\u7a76\u4e8b\u7269\u7684\u6570\u636e\u7ed3\u6784\u4e0e\u4ece\u6570\u636e\u4e2d\u770b\u5230\u7684\u73b0\u8c61\u4e0d\u592a\u76f8\u7b26\u3002\u201d<\/span><\/section>\n
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\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u6570\u5b66\u5bb6\u3001\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u548c\u5176\u4ed6\u7814\u7a76\u4eba\u5458\u8d8a\u6765\u8d8a\u5173\u6ce8\u4ee5\u591a\u79cd\u5f62\u5f0f\u63a8\u5e7f\u56fe\u8bba\u7684\u65b9\u6cd5\uff0c\u4ee5\u63a2\u7d22\u9ad8\u9636\u73b0\u8c61\u3002\u5728\u8fc7\u53bb\u51e0\u5e74\u91cc\uff0c\u4eba\u4eec\u63d0\u51fa\u4e86\u5927\u91cf\u65b9\u6cd5\u6765\u63cf\u8ff0\u8fd9\u4e9b\u76f8\u4e92\u4f5c\u7528\uff0c\u5e76\u5728\u9ad8\u7ef4\u6570\u636e\u96c6\u4e2d\u5bf9\u5176\u8fdb\u884c\u6570\u5b66\u9a8c\u8bc1\u3002<\/span><\/section>\n
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\u5bf9Purvine\u6765\u8bf4\uff0c\u5bf9\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u7684\u6570\u5b66\u63a2\u7d22\u5c31\u50cf\u65b0\u7ef4\u5ea6\u7684\u6620\u5c04\u3002\u5979\u89e3\u91ca\u8bf4\uff0c\u53ef\u4ee5\u5c06\u56fe\u60f3\u8c61\u4e3a\u4e00\u5757\u4e8c\u7ef4\u571f\u5730\uff0c\u5728\u8fd9\u4e2a\u5e73\u9762\u4e0a\u53ef\u4ee5\u5efa\u9020\u7684\u4e09\u7ef4\u5efa\u7b51\u4f1a\u975e\u5e38\u4e0d\u540c\u3002\u5728\u5730\u9762\u4e0a\u770b\u6765\uff0c\u5b83\u4eec\u4f3c\u4e4e\u662f\u4e00\u6837\u7684\uff0c\u4f46\u5728\u4e0a\u9762\u5efa\u9020\u7684\u4e1c\u897f\u662f\u4e0d\u540c\u7684\u3002<\/span><\/section>\n
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\u56fe1. \u8d85\u56fe\u7b49\u5de5\u5177\u80fd\u591f\u7ed8\u5236\u6570\u636e\u70b9\u4e4b\u95f4\u7684\u5fae\u5999\u8054\u7cfb\uff0c\u8fd9\u4ee4\u592a\u5e73\u6d0b\u897f\u5317\u56fd\u5bb6\u5b9e\u9a8c\u5ba4\u7684 Emilie Purvine \u611f\u5230\u5174\u594b\u4e0d\u5df2\u3002| \u6765\u6e90\uff1aAndrea Starr\/\u592a\u5e73\u6d0b\u897f\u5317\u56fd\u5bb6\u5b9e\u9a8c\u5ba4<\/span><\/p>\n

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\u5728\u5bfb\u627e\u9ad8\u7ef4\u7ed3\u6784\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6570\u5b66\u53d8\u5f97\u7279\u522b\u6a21\u7cca\u548c\u6709\u8da3\u3002\u4f8b\u5982\uff0c\u56fe\u7684\u9ad8\u9636\u7c7b\u4f3c\u7269\u88ab\u79f0\u4e3a\u8d85\u56fe<\/span>\uff08hypergraph\uff09<\/span>\uff0c\u5b83\u6709\u201c\u8d85\u8fb9\u201d<\/span>\uff08hyperedge\uff09<\/span>\u800c\u4e0d\u662f\u8fb9\u3002\u8d85\u8fb9\u53ef\u4ee5\u8fde\u63a5\u591a\u4e2a\u8282\u70b9\uff0c\u8fd9\u610f\u5473\u7740\u5b83\u53ef\u4ee5\u8868\u793a\u591a\u8def<\/span>\uff08\u6216\u591a\u7ebf\u6027\uff09<\/span>\u5173\u7cfb\u3002\u8fb9\u53ef\u4ee5\u770b\u4f5c\u662f\u4e00\u6761\u7ebf\uff0c\u800c\u8d85\u8fb9\u53ef\u4ee5\u770b\u4f5c\u662f\u4e00\u4e2a\u9762\uff0c\u5c31\u50cf\u4e00\u5757\u9632\u6c34\u5e03\u9489\u5728\u4e09\u4e2a\u6216\u66f4\u591a\u5730\u65b9\u3002<\/span>
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\u4e0d\u8fc7\uff0c\u5173\u4e8e\u8d85\u56fe\u4e0e\u4f20\u7edf\u7684\u56fe\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u4ecd\u6709\u5f88\u591a\u672a\u77e5\u3002\u6570\u5b66\u5bb6\u4eec\u76ee\u524d\u6b63\u5728\u7814\u7a76\uff0c\u56fe\u8bba\u4e2d\u7684\u54ea\u4e9b\u89c4\u5219\u4e5f\u9002\u7528\u4e8e\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\uff0c\u8fd9\u4e3a\u63a2\u7d22\u65b0\u9886\u57df\u63d0\u4f9b\u4e86\u601d\u8def\u3002<\/span><\/section>\n
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\u8d85\u56fe\u53ef\u4ee5\u4ece\u5927\u6570\u636e\u96c6\u4e2d\u68b3\u7406\u51fa\u666e\u901a\u7684\u56fe\u65e0\u6cd5\u68b3\u7406\u51fa\u7684\u5173\u7cfb<\/span><\/strong>\uff0c\u4e3a\u4e86\u8bf4\u660e\u8fd9\u4e00\u70b9\uff0cPurvine \u4e3e\u4e86\u79d1\u5b66\u51fa\u7248\u9886\u57df\u7684\u4e00\u4e2a\u7b80\u5355\u4f8b\u5b50\u3002\u5047\u8bbe\u6709\u4e24\u4e2a\u6570\u636e\u96c6\uff0c\u6bcf\u4e2a\u6570\u636e\u96c6\u5305\u542b\u4e09\u540d\u6570\u5b66\u5bb6<\/span>\uff08\u4e0d\u59a8\u547d\u540d\u4e3aA\u3001B\u3001C\uff09<\/span>\u5408\u8457\u7684\u8bba\u6587\u3002\u5176\u4e2d\u4e00\u4e2a\u6570\u636e\u96c6\u5305\u542b6\u7bc7\u8bba\u6587\uff0c\u4e09\u5bf9<\/span>\uff08AB\u3001AC\u548cBC\uff09<\/span>\u4e2d\u7684\u6bcf\u4e00\u5bf9\u90fd\u6709\u4e24\u7bc7\u8bba\u6587\u3002\u53e6\u4e00\u4e2a\u6570\u636e\u96c6\u603b\u5171\u53ea\u6709\u4e24\u7bc7\u8bba\u6587\uff0c\u6bcf\u4e00\u7bc7\u90fd\u7531\u4e09\u4f4d\u6570\u5b66\u5bb6<\/span>\uff08ABC\uff09<\/span>\u5171\u540c\u64b0\u5199\u3002<\/span><\/section>\n
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\u4ece\u4efb\u610f\u4e00\u4e2a\u6570\u636e\u96c6\u4e2d\u63d0\u53d6\u7684\u8868\u793a\u5408\u4f5c\u5173\u7cfb\u7684\u56fe\uff0c\u770b\u8d77\u6765\u53ef\u80fd\u90fd\u50cf\u4e00\u4e2a\u4e09\u89d2\u5f62\uff0c\u8868\u660e\u6bcf\u4e2a\u6570\u5b66\u5bb6<\/span>\uff083\u4e2a\u8282\u70b9\uff09<\/span>\u90fd\u4e0e\u5176\u4ed6\u4e24\u4e2a\u5408\u4f5c\u8fc7<\/span>\uff083\u4e2a\u8fde\u63a5\uff09<\/span>\u3002Purvine\u8bf4\uff0c\u5982\u679c\u552f\u4e00\u7684\u95ee\u9898\u662f\u8c01\u4e0e\u8c01\u5408\u4f5c\uff0c\u90a3\u5c31\u4e0d\u9700\u8981\u8d85\u56fe\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u4f46\u5982\u679c\u6709\u4e86\u8d85\u56fe\uff0c\u5c31\u53ef\u4ee5\u770b\u5230\u4e00\u4e9b\u4e0d\u592a\u660e\u663e\u7684\u7ed3\u6784\u3002\u4f8b\u5982\uff0c\u7b2c\u4e00\u4e2a\u6570\u636e\u96c6<\/span>\uff08\u5305\u542b6\u7bc7\u8bba\u6587\uff09<\/span>\u7684\u8d85\u56fe\u53ef\u80fd\u6709\u4e00\u4e9b\u8d85\u8fb9\uff0c\u8868\u660e\u6bcf\u4e2a\u6570\u5b66\u5bb6\u8d21\u732e\u4e864\u7bc7\u8bba\u6587\u3002\u6bd4\u8f83\u4e24\u4e2a\u6570\u636e\u96c6\u7684\u8d85\u56fe\u53ef\u4ee5\u53d1\u73b0\uff0c\u7b2c\u4e00\u7ec4\u8bba\u6587\u7684\u4f5c\u8005\u4e0d\u540c\uff0c\u800c\u7b2c\u4e8c\u7ec4\u7684\u4f5c\u8005\u76f8\u540c\u3002<\/span><\/section>\n
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3. \u590d\u6742\u7684\u8d85\u56fe<\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

\u8fd9\u79cd\u9ad8\u9636\u65b9\u6cd5\u5728\u5e94\u7528\u7814\u7a76\u4e2d\u5df2\u7ecf\u88ab\u8bc1\u660e\u662f\u6709\u7528\u7684\u3002\u4f8b\u5982\u751f\u6001\u5b66\u5bb6\u5df2\u7ecf\u5c55\u793a\uff0c20\u4e16\u7eaa90\u5e74\u4ee3\u5411\u9ec4\u77f3\u56fd\u5bb6\u516c\u56ed\u4e2d\u91cd\u65b0\u5f15\u5165\u72fc\uff0c\u5982\u4f55\u5f15\u53d1\u4e86\u751f\u7269\u591a\u6837\u6027\u548c\u98df\u7269\u94fe\u7ed3\u6784\u7684\u53d8\u5316\u3002\u5728\u6700\u8fd1\u4e00\u7bc7\u8bba\u6587\u4e2d\uff0cPurvine \u548c\u540c\u4e8b\u5206\u6790\u4e86\u4e00\u4e2a\u5173\u4e8e\u75c5\u6bd2\u611f\u67d3\u7684\u751f\u7269\u53cd\u5e94\u7684\u6570\u636e\u5e93\uff0c\u4f7f\u7528\u8d85\u56fe\u6765\u8bc6\u522b\u6700\u5173\u952e\u7684\u57fa\u56e0[2]\u3002\u4ed6\u4eec\u8fd8\u8868\u660e\uff0c\u56fe\u8bba\u901a\u5e38\u63d0\u4f9b\u7684\u6210\u5bf9\u5206\u6790\u600e\u6837\u9057\u6f0f\u6389\u4e86\u8fd9\u4e9b\u76f8\u4e92\u4f5c\u7528\u3002Purvine\u8bf4\uff1a\u201c\u8fd9\u5c31\u662f\u6211\u4eec\u4ece\u8d85\u56fe\u4e2d\u770b\u5230\u7684\u529b\u91cf\uff0c\u8d85\u56fe\u8d85\u8d8a\u4e86\u56fe\u3002\u201d<\/span><\/section>\n
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\u7136\u800c\uff0c\u4ece\u56fe\u63a8\u5e7f\u5230\u8d85\u56fe\u5f88\u5feb\u5c31\u53d8\u5f97\u590d\u6742\u8d77\u6765<\/strong>\u3002\u8bf4\u660e\u8fd9\u4e00\u70b9\u7684\u4e00\u79cd\u65b9\u6cd5\u662f\uff0c\u8003\u8651\u56fe\u8bba\u4e2d\u7684\u6b63\u5219\u5207\u5272\u95ee\u9898<\/span>\uff08canonical cut problem\uff09<\/span>\uff0c\u5373\uff1a\u7ed9\u5b9a\u56fe\u4e0a\u4e24\u4e2a\u4e0d\u540c\u7684\u8282\u70b9\uff0c\u8981\u5b8c\u5168\u5207\u65ad\u8fd9\u4e24\u4e2a\u8282\u70b9\u4e4b\u95f4\u7684\u6240\u6709\u8fde\u63a5\uff0c\u53ef\u4ee5\u5207\u5272\u7684\u6700\u5c0f\u8fb9\u6570\u662f\u591a\u5c11\uff1f\u5bf9\u4e8e\u4e00\u4e2a\u7ed9\u5b9a\u7684\u56fe\uff0c\u8bb8\u591a\u7b97\u6cd5\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u627e\u5230\u6700\u4f73\u5207\u5272\u6570\u3002<\/span><\/section>\n
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\u4f46\u662f\u5982\u4f55\u5207\u5272\u8d85\u56fe\u5462\uff1f\u5eb7\u5948\u5c14\u5927\u5b66\u7684\u6570\u5b66\u5bb6Austin Benson\u8bf4\uff0c\u6709\u5f88\u591a\u65b9\u6cd5\u53ef\u4ee5\u5c06\u5207\u5272\u7684\u6982\u5ff5\u63a8\u5e7f\u5230\u8d85\u56fe\uff0c\u4f46\u76ee\u524d\u8fd8\u6ca1\u6709\u4e00\u4e2a\u660e\u786e\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u56e0\u4e3a\u8d85\u8fb9\u53ef\u4ee5\u901a\u8fc7\u591a\u79cd\u65b9\u5f0f\u88ab\u5207\u65ad\uff0c\u4ea7\u751f\u65b0\u7684\u8282\u70b9\u7fa4\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u6700\u8fd1\uff0cBenson\u548c\u4e24\u4f4d\u540c\u4e8b\u4e00\u8d77\uff0c\u8bd5\u56fe\u7ed9\u51fa\u5207\u5272\u8d85\u56fe\u7684\u6240\u6709\u4e0d\u540c\u65b9\u6cd5 [3]\u3002\u4ed6\u4eec\u7684\u53d1\u73b0\u6697\u793a\u5b58\u5728\u5404\u79cd\u5404\u6837\u7684\u8ba1\u7b97\u590d\u6742\u6027\uff1a\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u95ee\u9898\u5f88\u5bb9\u6613\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u89e3\u51b3\uff0c\u8fd9\u57fa\u672c\u4e0a\u610f\u5473\u7740\u8ba1\u7b97\u673a\u53ef\u4ee5\u5728\u5408\u7406\u7684\u65f6\u95f4\u5185\u7ed9\u51fa\u89e3\u51b3\u65b9\u6848\u3002\u4f46\u5728\u53e6\u4e00\u4e9b\u60c5\u51b5\u4e0b\uff0c\u95ee\u9898\u57fa\u672c\u4e0a\u662f\u65e0\u6cd5\u89e3\u51b3\u7684\uff0c\u751a\u81f3\u6839\u672c\u4e0d\u80fd\u786e\u5b9a\u662f\u5426\u5b58\u5728\u4e00\u4e2a\u89e3\u51b3\u65b9\u6848\u3002<\/span><\/section>\n
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Benson\u8bf4\uff1a\u201c\u4ecd\u7136\u6709\u8bb8\u591a\u60ac\u800c\u672a\u51b3\u7684\u95ee\u9898\u3002\u6709\u4e9b\u4e0d\u53ef\u80fd\u7684\u7ed3\u679c\u5f88\u6709\u8da3\uff0c\u56e0\u4e3a\u4f60\u4e0d\u53ef\u80fd\u5c06\u8d85\u56fe\u7b80\u5316\u6210\u56fe\u3002\u4ece\u7406\u8bba\u65b9\u9762\u6765\u8bf4\uff0c\u5982\u679c\u6ca1\u6709\u628a\u5b83\u7b80\u5316\u6210\u53ef\u4ee5\u7528\u56fe\u627e\u5230\u7684\u4e1c\u897f\uff0c\u5c31\u610f\u5473\u7740\u90a3\u91cc\u6709\u65b0\u4e1c\u897f\u3002\u201d<\/span><\/section>\n
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4. \u5c06\u62d3\u6251\u5b66\u4e0e\u56fe\u8bba\u8054\u7cfb\u8d77\u6765<\/strong><\/strong><\/p>\n<\/section>\n

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\u4f46\u8d85\u56fe\u5e76\u4e0d\u662f\u63a2\u7d22\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u7684\u552f\u4e00\u65b9\u6cd5\uff0c\u62d3\u6251\u5b66\u63d0\u4f9b\u4e86\u4e00\u79cd\u66f4\u76f4\u89c2\u7684\u65b9\u6cd5<\/strong>\u3002\u62d3\u6251\u5b66\u662f\u4e00\u4e2a\u6570\u5b66\u5206\u652f\uff0c\u7814\u7a76\u5f53\u62c9\u4f38\u3001\u538b\u7f29\u6216\u4f7f\u7269\u4f53\u53d8\u5f62\u65f6\u90a3\u4e9b\u4fdd\u6301\u4e0d\u53d8\u7684\u51e0\u4f55\u5c5e\u6027\u3002\u5f53\u62d3\u6251\u5b66\u5bb6\u7814\u7a76\u4e00\u4e2a\u7f51\u7edc\u65f6\uff0c\u4ed6\u4eec\u5bfb\u627e\u5f62\u72b6\u3001\u8868\u9762\u548c\u7ef4\u5ea6\u3002\u4ed6\u4eec\u53ef\u80fd\u4f1a\u6ce8\u610f\u5230\uff0c\u8fde\u63a5\u4e24\u4e2a\u8282\u70b9\u7684\u8fb9\u662f\u4e00\u7ef4\u7684\uff0c\u5e76\u8ffd\u95ee\u4e0d\u540c\u7f51\u7edc\u4e2d\u4e00\u7ef4\u7269\u4f53\u7684\u6027\u8d28\u3002\u6216\u8005\uff0c\u4ed6\u4eec\u53ef\u80fd\u4f1a\u770b\u5230\u7531\u4e09\u4e2a\u8282\u70b9\u8fde\u63a5\u800c\u6210\u7684\u4e8c\u7ef4\u4e09\u89d2\u5f62\u8868\u9762\uff0c\u5e76\u63d0\u51fa\u7c7b\u4f3c\u7684\u95ee\u9898\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u62d3\u6251\u5b66\u5bb6\u79f0\u8fd9\u4e9b\u7ed3\u6784\u4e3a\u5355\u7eaf\u590d\u5f62<\/span>\uff08simplicial complex\uff09<\/span>[4]\uff0c\u5b9e\u9645\u5c31\u662f\u901a\u8fc7\u62d3\u6251\u7684\u6846\u67b6\u6765\u89c2\u5bdf\u8d85\u56fe\u3002\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u795e\u7ecf\u7f51\u7edc\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5f88\u597d\u7684\u4f8b\u5b50\u3002\u795e\u7ecf\u7f51\u7edc\u7531\u6a21\u62df\u5927\u8111\u795e\u7ecf\u5143\u5904\u7406\u4fe1\u606f\u7684\u7b97\u6cd5\u9a71\u52a8\u3002\u56fe\u795e\u7ecf\u7f51\u7edc<\/strong><\/span>\uff08Graph neural networks, GNNs\uff09<\/span>\u5c06\u4e8b\u7269\u4e4b\u95f4\u7684\u8fde\u63a5\u5efa\u6a21\u4e3a\u6210\u5bf9\u8fde\u63a5\uff0c\u64c5\u957f\u63a8\u65ad\u5927\u6570\u636e\u96c6\u4e2d\u7f3a\u5931\u7684\u6570\u636e\uff0c\u4f46\u5c31\u50cf\u5728\u5176\u4ed6\u5e94\u7528\u4e2d\u4e00\u6837\uff0c\u5b83\u4eec\u53ef\u80fd\u9057\u6f0f\u6389\u7531\u4e09\u4e2a\u6216\u66f4\u591a\u8282\u70b9\u7ec4\u6210\u7684\u7fa4\u4f53\u624d\u4f1a\u4ea7\u751f\u7684\u76f8\u4e92\u4f5c\u7528\u3002\u8fd1\u5e74\u6765\uff0c\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u53d1\u5c55\u4e86\u5355\u7eaf\u578b\u795e\u7ecf\u7f51\u7edc<\/strong><\/span>\uff08Simplicial neural networks\uff09<\/span>[5]\uff0c\u4f7f\u7528\u9ad8\u9636\u590d\u5f62\u62d3\u5c55\u4e86\u56fe\u795e\u7ecf\u7f51\u7edc\u65b9\u6cd5\uff0c\u4ee5\u627e\u5230\u8fd9\u4e9b\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u5355\u7eaf\u590d\u5f62\u5c06\u62d3\u6251\u5b66\u4e0e\u56fe\u8bba\u8054\u7cfb\u8d77\u6765<\/span><\/strong>\uff0c\u800c\u4e14\u50cf\u8d85\u56fe\u4e00\u6837\uff0c\u5b83\u4eec\u63d0\u51fa\u4e86\u5f15\u4eba\u6ce8\u76ee\u7684\u6570\u5b66\u95ee\u9898\uff0c\u5c06\u63a8\u52a8\u672a\u6765\u7684\u7814\u7a76\u3002\u4f8b\u5982\uff0c\u5728\u62d3\u6251\u5b66\u4e2d\uff0c\u5355\u7eaf\u590d\u5f62\u7684\u7279\u6b8a\u7c7b\u578b\u7684\u5b50\u96c6\u672c\u8eab\u4e5f\u662f\u5355\u7eaf\u590d\u5f62\uff0c\u56e0\u6b64\u5177\u6709\u76f8\u540c\u7684\u6027\u8d28\u3002\u5982\u679c\u5bf9\u8d85\u56fe\u4e5f\u662f\u5982\u6b64\uff0c\u90a3\u4e48\u5b50\u96c6\u5c06\u5305\u62ec\u5176\u4e2d\u7684\u6240\u6709\u8d85\u8fb9\u2014\u2014\u5305\u62ec\u6240\u6709\u5d4c\u5165\u7684\u53cc\u5411\u8fb9\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u4f46\u60c5\u51b5\u5e76\u975e\u603b\u662f\u5982\u6b64\u3002Purvine\u8bf4\uff1a\u201c\u6211\u4eec\u73b0\u5728\u770b\u5230\u7684\u662f\uff0c\u6570\u636e\u5904\u4e8e\u4e2d\u95f4\u5730\u5e26\uff0c\u4e0d\u662f\u6bcf\u4e00\u4e2a\u8d85\u8fb9\uff0c\u4e0d\u662f\u6bcf\u4e00\u4e2a\u590d\u6742\u76f8\u4e92\u4f5c\u7528\u90fd\u662f\u76f8\u540c\u5927\u5c0f\u3002\u4f60\u53ef\u4ee5\u6709\u4e09\u65b9\u4e92\u52a8\uff0c\u5374\u4e0d\u80fd\u6709\u6210\u5bf9\u4e92\u52a8\u3002\u201d\u5927\u6570\u636e\u96c6\u6e05\u695a\u8868\u660e\uff0c\u65e0\u8bba\u662f\u5728\u751f\u7269\u4fe1\u53f7\u7f51\u7edc\uff0c\u8fd8\u662f\u540c\u8f88\u538b\u529b\u7b49\u793e\u4f1a\u884c\u4e3a\u4e2d\uff0c\u7fa4\u4f53\u7684\u5f71\u54cd\u5f80\u5f80\u8fdc\u8d85\u4e2a\u4eba\u7684\u5f71\u54cd\u3002<\/span><\/section>\n
 <\/span><\/section>\n
Purvine \u5c06\u6570\u636e\u63cf\u8ff0\u4e3a\u6570\u5b66\u4e09\u660e\u6cbb\u7684\u4e2d\u95f4\u90e8\u5206\uff0c\u4e0a\u9762\u662f\u62d3\u6251\u601d\u60f3\uff0c\u4e0b\u9762\u662f\u56fe\u8bba\u7684\u9650\u5236<\/strong>\u3002\u7f51\u7edc\u79d1\u5b66\u5bb6\u73b0\u5728\u9762\u4e34\u7740\u4e3a\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u5bfb\u627e\u65b0\u89c4\u5219\u7684\u6311\u6218\u3002Purvine\u8bf4\uff0c\u5bf9\u4e8e\u6570\u5b66\u5bb6\u6765\u8bf4\uff0c\u201c\u8fd8\u6709\u4e86\u53d1\u6325\u7684\u7a7a\u95f4\u3002\u201d<\/span><\/section>\n
 <\/span><\/section>\n
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5. \u968f\u673a\u6e38\u8d70\u548c\u77e9\u9635<\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

\u8fd9\u79cd\u53d1\u6325\u521b\u9020\u6027\u7684\u7a7a\u95f4\u4e5f\u53ef\u4ee5\u5ef6\u4f38\u5230\u5176\u4ed6\u5de5\u5177\u3002Benson\u8bf4\uff0c\u5728\u56fe\u548c\u5176\u4ed6\u63cf\u8ff0\u6570\u636e\u7684\u5de5\u5177\u4e4b\u95f4\u5b58\u5728\u5404\u79cd\u7f8e\u5999\u7684\u8054\u7cfb\uff0c\u201c\u4f46\u4e00\u65e6\u8fdb\u5165\u66f4\u9ad8\u9636\u7684\u73af\u5883\uff0c\u5c31\u5f88\u96be\u5efa\u7acb\u8d77\u8fd9\u79cd\u8054\u7cfb\u201d\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u5f53\u5c1d\u8bd5\u8003\u8651\u9ad8\u7ef4\u7248\u672c\u7684\u9a6c\u5c14\u53ef\u592b\u94fe\u65f6\uff0c\u8fd9\u4e00\u70b9\u5c24\u5176\u660e\u663e\u3002\u9a6c\u5c14\u53ef\u592b\u94fe<\/strong>\u63cf\u8ff0\u4e00\u79cd\u591a\u9636\u6bb5\u7684\u8fc7\u7a0b\uff0c\u5176\u4e2d\u4e0b\u4e00\u9636\u6bb5\u53ea\u53d6\u51b3\u4e8e\u5143\u7d20\u5f53\u524d\u7684\u4f4d\u7f6e\uff1b\u7814\u7a76\u4eba\u5458\u4f7f\u7528\u9a6c\u5c14\u53ef\u592b\u94fe\u6765\u63cf\u8ff0\u4fe1\u606f\u3001\u80fd\u91cf\u751a\u81f3\u91d1\u94b1\u5728\u7cfb\u7edf\u4e2d\u7684\u6d41\u52a8\u3002\u9a6c\u5c14\u53ef\u592b\u94fe\u6700\u8457\u540d\u7684\u4f8b\u5b50\u4e5f\u8bb8\u662f\u968f\u673a\u6e38\u8d70<\/strong><\/span>\uff08random walk\uff09<\/span>\u3002\u968f\u673a\u6e38\u8d70\u8fc7\u7a0b\u4e2d\uff0c\u6bcf\u4e00\u6b65\u7531\u524d\u4e00\u6b65\u968f\u673a\u51b3\u5b9a\u3002\u968f\u673a\u6e38\u8d70\u4e5f\u662f\u4e00\u79cd\u7279\u5b9a\u7684\u56fe\uff1a\u56fe\u4e0a\u7684\u4efb\u4f55\u6e38\u8d70\u90fd\u53ef\u4ee5\u8868\u793a\u4e3a\uff0c\u6cbf\u7740\u8fb9\u4ece\u4e00\u4e2a\u8282\u70b9\u79fb\u52a8\u5230\u53e6\u4e00\u4e2a\u8282\u70b9\u7684\u5e8f\u5217\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u4f46\u8981\u5982\u4f55\u4ece\u968f\u673a\u6e38\u8d70\u8fd9\u6837\u7b80\u5355\u7684\u4e8b\u60c5\u5ef6\u4f38\u51fa\u53bb\u5462\uff1f\u7814\u7a76\u4eba\u5458\u8f6c\u5411\u9ad8\u9636\u9a6c\u5c14\u53ef\u592b\u94fe\uff0c\u5b83\u4e0d\u662f\u4ec5\u4ec5\u4f9d\u8d56\u4e8e\u5f53\u524d\u7684\u4f4d\u7f6e\uff0c\u800c\u662f\u53ef\u4ee5\u8003\u8651\u8bb8\u591a\u4e4b\u524d\u7684\u72b6\u6001\u3002\u8fd9\u79cd\u65b9\u6cd5\u88ab\u8bc1\u660e\u5bf9\u7f51\u7edc\u6d4f\u89c8\u884c\u4e3a\u548c\u673a\u573a\u4ea4\u901a\u6d41\u7b49\u7cfb\u7edf\u5efa\u6a21\u6709\u7528\u3002<\/span><\/section>\n
 <\/span><\/section>\n
Benson\u8fd8\u6709\u5176\u4ed6\u6269\u5c55\u65b9\u6cd5\uff1a\u4ed6\u548c\u540c\u4e8b\u6700\u8fd1\u63cf\u8ff0\u4e86\u4e00\u79cd\u65b0\u7684\u968f\u673a\u8fc7\u7a0b\u6a21\u578b [6]\uff0c\u5c06\u9ad8\u9636\u9a6c\u5c14\u53ef\u592b\u94fe\u548c\u5f20\u91cf\uff08tensor\uff09\u8fd9\u79cd\u6570\u5b66\u5de5\u5177\u7ed3\u5408\u5728\u4e00\u8d77<\/strong>\u3002 \u4ed6\u4eec\u7528\u8fd9\u79cd\u65b9\u6cd5\u5bf9\u7ebd\u7ea6\u5e02\u51fa\u79df\u8f66\u884c\u9a76\u6570\u636e\u96c6\u8fdb\u884c\u4e86\u6d4b\u8bd5\uff0c\u770b\u80fd\u5426\u826f\u597d\u5730\u9884\u6d4b\u8f68\u8ff9\u3002\u7ed3\u679c\u597d\u574f\u53c2\u534a\uff1a\u65b0\u6a21\u578b\u6bd4\u4e00\u822c\u7684\u9a6c\u5c14\u53ef\u592b\u94fe\u66f4\u597d\u5730\u9884\u6d4b\u4e86\u51fa\u79df\u8f66\u7684\u8fd0\u52a8\uff0c\u4f46\u4e24\u79cd\u6a21\u578b\u90fd\u4e0d\u662f\u5f88\u53ef\u9760\u3002<\/span><\/section>\n
 <\/span><\/section>\n
<\/section>\n

\u56fe2. \u5eb7\u5948\u5c14\u5927\u5b66\u7684 Austin Benson \u6700\u8fd1\u5229\u7528\u9ad8\u9636\u9a6c\u5c14\u53ef\u592b\u94fe\u548c\u5f20\u91cf\uff0c\u5e2e\u52a9\u6a21\u62df\u4e86\u7ebd\u7ea6\u5e02\u7684\u51fa\u79df\u8f66\u51fa\u884c\u3002\u7ed3\u679c\u6bd4\u4f20\u7edf\u7684\u9a6c\u5c14\u53ef\u592b\u94fe\u8981\u597d\uff0c\u4f46\u4ecd\u9700\u6539\u8fdb\u3002| \u6765\u6e90\uff1aAustin Benson<\/span><\/p>\n

 <\/span><\/section>\n
\u5f20\u91cf\u672c\u8eab\u662f\u7814\u7a76\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u7684\u53e6\u4e00\u79cd\u5de5\u5177\uff0c\u8fd1\u5e74\u6765\u5f00\u59cb\u53d1\u6325\u91cd\u8981\u4f5c\u7528\u3002\u8981\u7406\u89e3\u5f20\u91cf<\/strong>\uff0c\u9996\u5148\u53ef\u4ee5\u601d\u8003\u77e9\u9635\uff0c\u77e9\u9635\u5c06\u6570\u636e\u6309\u7167\u884c\u548c\u5217\u6392\u5217\uff1b\u7136\u540e\u60f3\u8c61\u7531\u77e9\u9635\u7ec4\u6210\u7684\u77e9\u9635\uff0c\u6216\u8005\u77e9\u9635\u4e0d\u4ec5\u6709\u884c\u548c\u5217\uff0c\u8fd8\u6709\u6df1\u5ea6\u6216\u5176\u4ed6\u7ef4\u5ea6\u7684\u6570\u636e\u2014\u2014\u8fd9\u5c31\u662f\u5f20\u91cf\u3002\u5982\u679c\u8bf4\u77e9\u9635\u5bf9\u5e94\u97f3\u4e50\u4e2d\u7684\u4e8c\u91cd\u594f\uff0c\u90a3\u4e48\u5f20\u91cf\u5c06\u5305\u62ec\u4e50\u5668\u7684\u6240\u6709\u53ef\u80fd\u914d\u7f6e\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u5bf9\u7269\u7406\u5b66\u5bb6\u6765\u8bf4\uff0c\u5f20\u91cf\u5e76\u4e0d\u65b0\u9c9c\uff0c\u4ed6\u4eec\u4e00\u76f4\u7528\u5f20\u91cf\u6765\u63cf\u8ff0\u4e00\u4e2a\u7c92\u5b50\u7684\u4e0d\u540c\u53ef\u80fd\u91cf\u5b50\u6001\u4e4b\u7c7b\u7684\u73b0\u8c61\uff0c\u4f46\u7f51\u7edc\u79d1\u5b66\u5bb6\u7528\u8fd9\u4e2a\u5de5\u5177\u5c06\u77e9\u9635\u7684\u529b\u91cf\u6269\u5c55\u5230\u9ad8\u7ef4\u6570\u636e\u96c6\u4e2d<\/strong>\u3002\u6570\u5b66\u5bb6\u7528\u5b83\u4eec\u89e3\u51b3\u65b0\u7684\u95ee\u9898\u3002Grochow \u7528\u5f20\u91cf\u6765\u7814\u7a76\u540c\u6784\u95ee\u9898<\/span>\uff08isomorphism problem\uff09<\/span>\uff0c\u540c\u6784\u95ee\u9898\u672c\u8d28\u4e0a\u662f\u8ffd\u95ee\uff0c\u5982\u4f55\u77e5\u9053\u4e24\u4e2a\u7269\u4f53\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u662f\u5426\u76f8\u540c\u3002\u4ed6\u6700\u8fd1\u4e0e Youming Qiao \u7684\u5408\u4f5c\u63d0\u4f9b\u4e86\u4e00\u79cd\u65b0\u65b9\u6cd5 [7]\uff0c\u6765\u8bc6\u522b\u4e5f\u8bb8\u5f88\u96be\u6216\u4e0d\u53ef\u80fd\u89e3\u51b3\u7684\u590d\u6742\u95ee\u9898\u3002<\/span><\/section>\n
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6. \u4ec0\u4e48\u65f6\u5019\u4f7f\u7528\u8d85\u56fe\uff1f<\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n
<\/span>
<\/section>\n
Benson \u5173\u4e8e\u7ebd\u7ea6\u51fa\u79df\u8f66\u7684\u6a21\u578b\u63d0\u51fa\u4e86\u4e00\u4e2a\u666e\u904d\u95ee\u9898\uff1a\u7814\u7a76\u4eba\u5458\u4ec0\u4e48\u65f6\u5019\u771f\u6b63\u9700\u8981\u8d85\u56fe\u8fd9\u6837\u7684\u5de5\u5177\uff1f<\/strong>\u5728\u8bb8\u591a\u60c5\u51b5\u4e0b\uff0c\u5982\u679c\u6761\u4ef6\u5408\u9002\uff0c\u8d85\u56fe\u5c06\u7ed9\u51fa\u4e0e\u56fe\u5b8c\u5168\u540c\u6837\u7c7b\u578b\u7684\u9884\u6d4b\u548c\u5206\u6790\u3002\u201c\u5982\u679c\u67d0\u4e9b\u4e1c\u897f\u5df2\u7ecf\u5c01\u88c5\u5728\u7f51\u7edc\u4e2d\uff0c\u771f\u7684\u6709\u5fc5\u8981\u5bf9\u7cfb\u7edf\u8fdb\u884c<\/span>\uff08\u9ad8\u9636\uff09<\/span>\u5efa\u6a21\u5417\uff1f\u201d\u4e9a\u741b\u5de5\u4e1a\u5927\u5b66\u7684 Michael Schaub \u95ee\u9053\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u8fd9\u53d6\u51b3\u4e8e\u6570\u636e\u96c6\u3002Schaub \u8bf4\uff1a\u201c\u5bf9\u4e8e\u793e\u4ea4\u7f51\u7edc\uff0c\u56fe\u662f\u4e00\u4e2a\u5f88\u597d\u7684\u62bd\u8c61\u63cf\u8ff0\uff0c\u4f46\u793e\u4ea4\u7f51\u7edc\u8fdc\u4e0d\u6b62\u4e8e\u6b64\u3002\u5bf9\u4e8e\u9ad8\u9636\u7cfb\u7edf\uff0c\u6709\u66f4\u591a\u7684\u5efa\u6a21\u65b9\u6cd5\u3002\u201d\u4f8b\u5982\uff0c\u56fe\u8bba\u53ef\u4ee5\u663e\u793a\u4e2a\u4f53\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u4f46\u65e0\u6cd5\u6355\u6349\u793e\u4ea4\u5a92\u4f53\u4e0a\u7684\u670b\u53cb\u7fa4\u4f53\u5982\u4f55\u5f71\u54cd\u4e2a\u4f53\u7684\u884c\u4e3a\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u540c\u6837\u7684\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u4e0d\u4f1a\u51fa\u73b0\u5728\u6bcf\u4e2a\u6570\u636e\u96c6\u4e0a\uff0c\u6240\u4ee5\u5947\u7279\u7684\u662f\uff0c\u65b0\u7406\u8bba\u662f\u53d7\u6570\u636e\u9a71\u52a8\u7684<\/strong>\u2014\u2014\u8fd9\u6311\u6218\u4e86\u6700\u521d\u5438\u5f15 Purvine \u8fdb\u5165\u8fd9\u4e00\u9886\u57df\u7684\u5e95\u5c42\u903b\u8f91\u3002\u5979\u8bf4\uff1a\u201c\u6211\u559c\u6b22\u6570\u5b66\u662f\u56e0\u4e3a\u5b83\u662f\u57fa\u4e8e\u903b\u8f91\u7684\uff0c\u5982\u679c\u6cbf\u7740\u6b63\u786e\u7684\u65b9\u5411\uff0c\u5c31\u4f1a\u5f97\u5230\u6b63\u786e\u7684\u7b54\u6848\u3002\u4f46\u6709\u65f6\uff0c\u5f53\u4f60\u5b9a\u4e49\u4e00\u4e2a\u5168\u65b0\u7684\u6570\u5b66\u9886\u57df\u65f6\uff0c\u5173\u4e8e\u4ec0\u4e48\u662f\u6b63\u786e\u7684\u65b9\u6cd5\u4f1a\u5b58\u5728\u4e3b\u89c2\u6027\u3002\u5982\u679c\u6ca1\u6709\u8ba4\u8bc6\u5230\u6709\u591a\u79cd\u65b9\u5f0f\u53ef\u4ee5\u505a\u5230\u8fd9\u4e00\u70b9\uff0c\u5c31\u53ef\u80fd\u628a\u7814\u7a76\u5f15\u5411\u9519\u8bef\u7684\u65b9\u5411\u3002\u201d<\/span><\/section>\n
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Grochow \u8bf4\uff0c\u6700\u7ec8\uff0c\u8fd9\u4e9b\u5de5\u5177\u4ee3\u8868\u4e86\u4e00\u79cd\u81ea\u7531\uff0c\u4e0d\u4ec5\u5141\u8bb8\u7814\u7a76\u4eba\u5458\u66f4\u597d\u5730\u7406\u89e3\u4ed6\u4eec\u7684\u6570\u636e\uff0c\u800c\u4e14\u5141\u8bb8\u6570\u5b66\u5bb6\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u63a2\u7d22\u5145\u6ee1\u53ef\u80fd\u6027\u7684\u65b0\u4e16\u754c\u3002\u201c\u6709\u65e0\u5c3d\u7684\u4e1c\u897f\u53ef\u4ee5\u63a2\u7d22\uff0c\u8fd9\u65e2\u6709\u8da3\u53c8\u7f8e\u4e3d\uff0c\u5e76\u4e14\u662f\u8bb8\u591a\u4f1f\u5927\u95ee\u9898\u7684\u6765\u6e90\u3002\u201d<\/span><\/section>\n

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[1] Tekin, E., White, C., Kang, T.M. et al. Prevalence and patterns of higher-order drug interactions in Escherichia coli. npj Syst Biol Appl 4, 31 (2018). <\/span>https:\/\/doi.org\/10.1038\/s41540-018-0069-9<\/span><\/section>\n
[2] Hypergraph Models of Biological Networks to Identify Genes Critical to Pathogenic Viral Response. <\/span>https:\/\/arxiv.org\/abs\/2010.03068<\/span><\/section>\n
[3] Hypergraph Cuts with General Splitting Functions. <\/span>https:\/\/arxiv.org\/abs\/2001.02817<\/span><\/section>\n
[4] Simplicial complexes and complex systems. Vsevolod Salnikov et al 2019 Eur. J. Phys. 40 014001. <\/span>https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6404\/aae790\/meta<\/span><\/section>\n
[5] Simplicial Neural Networks. <\/span>https:\/\/arxiv.org\/pdf\/2010.03633.pdf<\/span><\/section>\n
[6] The Spacey Random Walk: A Stochastic Process for Higher-Order Data. <\/span>https:\/\/doi.org\/10.1137\/16M1074023<\/span><\/section>\n
[7] On the Complexity of Isomorphism Problems for Tensors, Groups, and Polynomials I: Tensor Isomorphism-Completeness. <\/span>https:\/\/drops.dagstuhl.de\/opus\/volltexte\/2021\/13570\/<\/span><\/section>\n


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https:\/\/www.quantamagazine.org\/how-big-data-carried-graph-theory-into-new-dimensions-20210819\/<\/span><\/section>\n

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