{"id":57676,"date":"2025-03-08T16:36:42","date_gmt":"2025-03-08T08:36:42","guid":{"rendered":"https:\/\/swarma.org\/?p=57676"},"modified":"2025-03-08T16:36:42","modified_gmt":"2025-03-08T08:36:42","slug":"nat-phys-%e9%80%9f%e9%80%92%ef%bc%9a%e9%ab%98%e9%98%b6%e6%8b%89%e6%99%ae%e6%8b%89%e6%96%af%e9%87%8d%e6%95%b4%e5%8c%96","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=57676","title":{"rendered":"Nat. Phys.\u901f\u9012\uff1a\u9ad8\u9636\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316"},"content":{"rendered":"
\n
\n
\n
\n
\n
\n
\n
\n

<\/p>\n<\/section>\n

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

\u6458\u8981<\/strong><\/p>\n<\/section>\n<\/section>\n

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

\u91cd\u6574\u5316\u7fa4\u662f\u7269\u7406\u5b66\u4e2d\u5173\u4e8e\u6807\u5ea6\u3001\u6807\u5ea6\u4e0d\u53d8\u6027\u548c\u666e\u9002\u6027\u7406\u8bba\u7684\u652f\u67f1\u3002\u6700\u8fd1\uff0c\u901a\u8fc7\u57fa\u4e8e\u6269\u6563\u52a8\u529b\u5b66\uff0c\u8fd9\u4e00\u5de5\u5177\u5df2\u88ab\u5e94\u7528\u4e8e\u5177\u6709\u6210\u5bf9\u76f8\u4e92\u4f5c\u7528\u7684\u590d\u6742\u7f51\u7edc\u3002\u7136\u800c\uff0c\u968f\u7740\u590d\u6742\u7cfb\u7edf\u4e2d\u591a\u4f53\u76f8\u4e92\u4f5c\u7528\u7684\u91cd\u8981\u6027\u6108\u53d1\u51f8\u663e\uff0c\u8feb\u5207\u9700\u8981\u5c06\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u6269\u5c55\u5230\u9ad8\u9636\u7f51\u7edc\u3002\u5728\u6b64\uff0c\u6211\u4eec\u586b\u8865\u4e86\u8fd9\u4e00\u7a7a\u767d\uff0c\u63d0\u51fa\u4e86\u4e00\u79cd\u9002\u7528\u4e8e\u4efb\u610f\u9ad8\u9636\u7f51\u7edc\u7684\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4\u65b9\u6848\u3002\u6211\u4eec\u65b9\u6cd5\u7684\u6838\u5fc3\u5728\u4e8e\u5f15\u5165\u8de8\u9636\u62c9\u666e\u62c9\u65af\u7b97\u5b50\uff08cross-order Laplacians\uff09\uff0c\u5b83\u5141\u8bb8\u63cf\u8ff0\u5728\u4efb\u610f\u9636\u8d85\u8fb9\u4e0a\u7684\u6269\u6563\u8fc7\u7a0b\uff0c\u53ef\u4ee5\u901a\u8fc7\u4efb\u610f\u5176\u4ed6\u9636\u7684\u8d85\u8fb9\u53d1\u751f\uff0c\u5bf9\u73b0\u6709\u7684\u9ad8\u9636\u62c9\u666e\u62c9\u65af\u7b97\u5b50\u8fdb\u884c\u4e86\u63a8\u5e7f\u3002\u8fd9\u79cd\u65b9\u6cd5\u4f7f\u6211\u4eec\u80fd\u591f\u63a2\u7a76\u9ad8\u9636\u7ed3\u6784\uff0c\u5b9a\u4e49\u4e0d\u540c\u9636\u7684\u6807\u5ea6\u4e0d\u53d8\u6027\uff0c\u5e76\u63d0\u51fa\u4e00\u79cd\u7c97\u7c92\u5316\u65b9\u6848\u3002\u6211\u4eec\u5728\u53d7\u63a7\u7684\u5408\u6210\u9ad8\u9636\u7cfb\u7edf\u4e0a\u9a8c\u8bc1\u4e86\u6211\u4eec\u7684\u65b9\u6cd5\uff0c\u7136\u540e\u5c06\u5176\u7528\u4e8e\u68c0\u6d4b\u6765\u81ea\u591a\u4e2a\u9886\u57df\u7684\u73b0\u5b9e\u4e16\u754c\u590d\u6742\u7cfb\u7edf\u4e2d\u7279\u5b9a\u4e8e\u9636\u7684\u6807\u5ea6\u4e0d\u53d8\u6027\u7279\u5f81\u7684\u5b58\u5728\u3002<\/span><\/span><\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n

\n

<\/p>\n<\/section>\n

\u7814\u7a76\u9886\u57df\uff1a\u9ad8\u9636\u7f51\u7edc\uff0c\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4\uff0c\u4ea4\u53c9\u9636\u62c9\u666e\u62c9\u65af\uff0c\u5c3a\u5ea6\u4e0d\u53d8\u6027\uff0c\u590d\u6742\u7cfb\u7edf<\/span><\/strong><\/strong><\/span><\/strong><\/strong><\/strong><\/section>\n<\/section>\n
\n
<\/strong><\/strong><\/strong><\/section>\n<\/section>\n
\n
<\/strong><\/strong><\/section>\n
<\/strong><\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
\n
\n
<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

 <\/span><\/p>\n

<\/section>\n
\n
\u8bba\u6587\u9898\u76ee\uff1aHigher-order Laplacian renormalization<\/span><\/section>\n
\u53d1\u8868\u65f6\u95f4\uff1a2025\u5e742\u670824\u65e5<\/span><\/section>\n
\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/doi.org\/10.1038\/s41567-025-02784-1<\/span><\/section>\n
\u671f\u520a\u540d\u79f0\uff1aNature Physics<\/em><\/span><\/section>\n<\/blockquote>\n
<\/section>\n
\u91cd\u6574\u5316\u7fa4<\/span>\uff08RG\uff09<\/span>\u662f\u7269\u7406\u5b66\u4e2d\u7814\u7a76\u76f8\u53d8\u4e0e\u666e\u9002\u6027\u7684\u6838\u5fc3\u5de5\u5177\u3002\u8fd1\u5e74\u6765\uff0c\u79d1\u5b66\u5bb6\u8bd5\u56fe\u5c06\u5176\u63a8\u5e7f\u5230\u590d\u6742\u7f51\u7edc\u9886\u57df\uff0c\u4f46\u4f20\u7edf\u65b9\u6cd5\u4f9d\u8d56\u51e0\u4f55\u5d4c\u5165\u5047\u8bbe\uff0c\u96be\u4ee5\u63cf\u8ff0\u7f51\u7edc\u5185\u5728\u7684\u62d3\u6251\u7ed3\u6784\u3002\u968f\u7740\u9ad8\u9636\u7f51\u7edc<\/span>\uff08\u5982\u8d85\u56fe\u3001\u5355\u7eaf\u590d\u5f62\uff09<\/span>\u7684\u5174\u8d77\uff0c\u53d1\u5c55\u9488\u5bf9\u9ad8\u9636\u7ed3\u6784\u7684\u91cd\u6574\u5316\u65b9\u6cd5\u53d8\u5f97\u8feb\u5207\uff0c\u8fd9\u7c7b\u7f51\u7edc\u80fd\u63cf\u8ff0\u591a\u8282\u70b9\u76f8\u4e92\u4f5c\u7528\uff0c\u5982\u793e\u4ea4\u7fa4\u7ec4\u3001\u86cb\u767d\u8d28\u590d\u5408\u4f53\u3002Nature Physics<\/em>\u6700\u65b0\u7814\u7a76\u586b\u8865\u4e86\u8fd9\u4e00\u7a7a\u767d\uff0c\u63d0\u51fa\u9ad8\u9636\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4<\/span>\uff08LRG\uff09<\/span>\uff0c\u4e3a\u5206\u6790\u591a\u5c3a\u5ea6\u590d\u6742\u7cfb\u7edf\u63d0\u4f9b\u4e86\u65b0\u6846\u67b6\u3002<\/span><\/section>\n

<\/span><\/section>\n


<\/span><\/h4>\n

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

\u4ea4\u53c9\u9636\u62c9\u666e\u62c9\u65af\u7b97\u5b50\uff1a\u9ad8\u9636\u6269\u6563\u7684\u201c\u5bfc\u822a\u4eea\u201d<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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

<\/p>\n

\u7814\u7a76\u56e2\u961f\u7684\u6838\u5fc3\u521b\u65b0\u5728\u4e8e\u8de8\u9636\u62c9\u666e\u62c9\u65af\u7b97\u5b50<\/span>\uff08cross-order Laplacians\uff09<\/span>\u3002\u5047\u8bbe\u5df2\u786e\u8ba4<\/span>\u8d85\u56fe\u0394\u5177<\/span>\u6709\u5c3a\u5ea6\u4e0d\u53d8\u6027\uff0c\u600e\u6837\u80fd\u591f\u5c06\u5176\u7b80\u5316\u4e3a\u4e00\u4e2a\u66f4\u5c0f\u4f46\u7b49\u6548\u7684\u8d85\u56fe\uff0c\u4f46\u4ecd\u80fd\u88ab\u8bc6\u522b\u5177\u6709\u5c3a\u5ea6\u4e0d\u53d8\u6027\u5462\uff1f\u6cbf\u7528\u7f51\u7edc\u91cd\u6574\u5316\u7684\u601d\u8def\uff0c\u7814\u7a76\u8005\u8bbe\u8ba1\u4e86\u4e00\u5957\u9ad8\u9636\u62c9\u666e\u62c9\u65af\u91cd\u6b63\u5316\u65b9\u6848\uff0c\u5305\u62ec\u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/span><\/section>\n

<\/span><\/section>\n
1\u3001\u8ba1\u7b97\u4ea4\u53c9\u9636\u62c9\u666e\u62c9\u65af\u77e9\u9635\"image.png\"<\/sub><\/strong><\/span>\uff0c\u8be5\u77e9\u9635\u63cf\u8ff0\u4e86\u5728k\u9636\u8d85\u8fb9\u4e0a\u901a\u8fc7m\u9636\u8d85\u8fb9\u8fdb\u884c\u7684\u6269\u6563\u8fc7\u7a0b\u3002<\/span>\u8be5\u77e9\u9635\u662f\u4f20\u7edf\u62c9\u666e\u62c9\u65af\u7684\u63a8\u5e7f\uff0c\u7528\u4e8e\u5904\u7406\u66f4\u590d\u6742\u7684\u591a\u5143\u5173\u7cfb\u3002<\/span><\/section>\n

<\/span><\/section>\n
2\u3001\u9009\u62e9\u4e00\u4e2a\u6269\u6563\u65f6\u95f4<\/strong><\/span>\u03a4*<\/span><\/sup>\uff0c<\/span>\u5b83\u5bf9\u5e94\u4e8e\u4f60\u60f3\u8981\u201c\u7f29\u653e\u201d\u5e76\u5728\u8be5\u7279\u5b9a\u5206\u8fa8\u7387\u4e0b\u5206\u6790\u7f51\u7edc\u7684\u5c3a\u5ea6\u3002<\/span><\/section>\n

<\/span><\/section>\n
3\u3001\u5212\u5206k\u9636\u8d85\u8fb9<\/strong>\uff1a\u901a\u8fc7\u5bc6\u5ea6\u77e9<\/span>\u9635 \u03c1(k,m)<\/span>(\u03a4<\/span>*<\/span><\/sup>) \uff0c\u8ba1\u7b97k\u9636\u8d85\u8fb9\u7684\u5212\u5206\uff0c\u4f7f\u5f97\u5728\u6269\u6563\u8fc7\u7a0b\u4e2d\u5f3a\u76f8\u5173\u7684\u8d85\u8fb9\u88ab\u5212\u5206\u5230\u540c\u4e00\u7ec4\u4e2d\u3002<\/span><\/section>\n

<\/span><\/section>\n
4\u3001\u8d85\u56fe\u7684\u7c97\u7c92\u5316<\/strong>\uff1a\u901a\u8fc7\u5408\u5e76\u8282\u70b9\u7c97\u7c92\u5316\u8d85\u56fe\u0394<\/span>\uff0c\u5f97\u5230\u4e00\u4e2a\u65b0\u7684\u8f83\u5c0f\u7684\u8d85\u56fe<\/span>\"image.png\"\u3002<\/span><\/section>\n

<\/span><\/section>\n
5\u3001\u91cd\u590d\u8be5\u8fc7\u7a0b<\/strong>\uff1a\u8be5\u8fc7\u7a0b\u88ab\u8fed\u4ee3\u8fdb\u884c\uff0c\u6bcf\u6b21\u8fed\u4ee3\u90fd\u4f1a\u5f97\u5230\u4e00\u4e2a\u9876\u70b9\u6570\u91cf\u51cf\u5c11\u6216\u4e0d\u53d8\u7684\u8d85\u56fe\u5e8f\u5217\uff0c\u6574\u4e2a\u8fc7\u7a0b\u88ab\u547d\u540d\u4e3a\u91cd\u6b63\u5316\u6d41<\/strong>\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5177\u4f53\u800c\u8a00\uff0c\u4f20\u7edf\u7f51\u7edc\u6269\u6563\u4ec5\u901a\u8fc7\u8fb9<\/span>\uff081-\u8d85\u8fb9\uff09<\/span>\u4f20\u9012\u4fe1\u606f\uff0c\u800c\u9ad8\u9636\u7f51\u7edc\u4e2d\uff0c\u4fe1\u606f\u53ef\u5728\u4e0d\u540c\u9636\u7684\u201c\u8d85\u8fb9\u9ad8\u901f\u516c\u8def\u201d\u4e0a\u8df3\u8f6c\u3002\u4f8b\u5982\uff0c\u4e09\u89d2\u5f62<\/span>\uff082-\u8d85\u8fb9\uff09<\/span>\u53ef\u901a\u8fc7\u5171\u4eab\u9876\u70b9<\/span>\uff080-\u8d85\u8fb9\uff09<\/span>\u6216\u5d4c\u5957\u4e8e\u56db\u9762\u4f53<\/span>\uff083-\u8d85\u8fb9\uff09<\/span>\u5b9e\u73b0\u8fde\u63a5<\/span>\uff08\u56fe1a\uff09<\/span>\u3002\u8be5\u7b97\u5b50\u901a\u8fc7\u6784\u5efa\u90bb\u63a5\u56fe<\/span>\uff08adjacency graph\uff09<\/span>\uff0c\u5c06k\u9636\u8d85\u8fb9\u7684\u8fde\u63a5\u5173\u7cfb\u6620\u5c04\u4e3a\u52a0\u6743\u56fe\u8282\u70b9\uff0c\u6743\u91cd\u7531m\u9636\u8d85\u8fb9\u7684\u5171\u4eab\u6570\u91cf\u51b3\u5b9a\u3002\u4f8b\u5982\uff0cG(1,2)<\/sub> \u63cf\u8ff0\u8fb9<\/span>\uff081-\u8d85\u8fb9\uff09<\/span>\u5982\u4f55\u901a\u8fc7\u4e09\u89d2\u5f62<\/span>\uff082-\u8d85\u8fb9\uff09<\/span>\u76f8\u8fde\u3002\u8fd9\u79cd\u8bbe\u8ba1\u7a81\u7834\u4e86\u51e0\u4f55\u9650\u5236\uff0c\u4f7f\u6269\u6563\u8fc7\u7a0b\u80fd\u81ea\u7531\u7a7f\u68ad\u4e8e\u4e0d\u540c\u9636\u7ed3\u6784\uff0c\u5f62\u6210\u52a8\u6001\u7684\u201c\u62d3\u6251\u671b\u8fdc\u955c\u201d\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

\u56fe 1. \u8de8\u9636\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u65b9\u6848\uff1a\u5212\u5206\u4e0e\u7c97\u7c92\u5316\u3002\uff08a\uff09\u8d85\u56fe\u7684\u90bb\u63a5\u56fe\u6784\u5efa\u793a\u610f\u56fe\u3002\u6ce8\u610f\u5b58\u5728\u50cf G(0,2)<\/sub>  \u8fd9\u6837\u7684\u60c5\u51b5\uff0c\u5176\u4e2d\u8fb9\u662f\u6709\u6743\u91cd\u7684\uff08\u6b64\u5904\u7528\u591a\u91cd\u8fb9\u8868\u793a\uff09\u3002\uff08b\uff09\u6211\u4eec\u66f4\u9ad8\u9636\u7c97\u7c92\u5316\u65b9\u6848\u7684\u56fe\u793a\u8868\u793a\uff0ck = 2\uff1a\uff08i\uff09\u4ece \u03c1(\u03c4) \u83b7\u5f97\u4e24\u4e2a\u8d85\u8fb9\u7684\u5212\u5206\uff0c\u6b64\u5904\u7528\u989c\u8272\u8868\u793a\uff1b\uff08ii\uff09\u6bcf\u4e2a\u9876\u70b9\u7ee7\u627f\u4e00\u4e2a\u5305\u542b\u5176\u6240\u5c5e\u4e24\u4e2a\u8d85\u8fb9\u6807\u7b7e\u7684\u7279\u5f81\uff1b\uff08iii\uff09\u5177\u6709\u76f8\u540c\u7279\u5f81\u7684\u9876\u70b9\u88ab\u7c98\u5408\u5728\u4e00\u8d77\uff0c\u8d85\u8fb9\u4ece\u8d77\u59cb\u8d85\u56fe\u4e2d\u8bf1\u5bfc\u5f97\u51fa\u3002<\/span><\/p>\n


<\/span><\/section>\n

<\/span><\/section>\n

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

\u71b5\u654f\u611f\u6027\u66f2\u7ebf\uff1a\u6355\u6349\u5c3a\u5ea6\u4e0d\u53d8\u6027<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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

<\/p>\n

\u7814\u7a76\u901a\u8fc7\u51af\u00b7\u8bfa\u4f9d\u66fc\u71b5<\/span>\uff08von Neumann entropy\uff09<\/span>\u91cf\u5316\u9ad8\u9636\u7f51\u7edc\u8282\u70b9\u6216\u8d85\u8fb9\u4e4b\u95f4\u8fde\u63a5\u6a21\u5f0f\u7684\u590d\u6742\u5ea6\uff0c\u8ba1\u7b97\u51af\u00b7\u8bfa\u4f9d\u66fc\u71b5\u5bf9\u6269\u6563\u65f6\u95f4\u03a4<\/span>*<\/span><\/sup>\u7684\u5bfc\u6570\u2014\u2014\u5bfc\u6570\u71b5\u654f\u611f\u6027<\/span>\uff08entropic susceptibility,  C<\/span>(\u03a4<\/span>)<\/sub><\/span>\uff09<\/span><\/span>\u91cf\u5316\u9ad8\u9636\u7ed3\u6784\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0a\u7684\u54cd\u5e94\u6027\u548c\u654f\u611f\u6027\u3002\u5f53C<\/span>(\u03a4<\/span>)<\/sub><\/span>\u5728\u65f6\u95f4\u03c4\u8303\u56f4\u5185\u5448\u73b0\u5e73\u5766\u533a<\/span>\uff08plateau\uff09<\/span>\uff0c\u8868\u660e\u7cfb\u7edf\u5728\u8be5\u5c3a\u5ea6\u4e0a\u65e0\u7279\u5f81\u957f\u5ea6\uff0c\u5373\u5c3a\u5ea6\u4e0d\u53d8\u6027\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4ece\u4e0b\u9762\u7684\u4f2a\u5206\u5f62\u5355\u7eaf\u590d\u5f62\u53ef\u4ee5\u770b\u5230\uff0cC(1,2)<\/sub>\u548cC(2,1)<\/sub>\u66f2\u7ebf\u5c55\u73b0\u51fa\u8de8\u8d8a\u591a\u4e2a\u6570\u91cf\u7ea7\u7684\u632f\u8361\u5e73\u5766\u533a\uff0c\u5370\u8bc1\u5176\u81ea\u76f8\u4f3c\u6027\uff1b\u800c\u4f20\u7edf\u8282\u70b9-\u8fb9\u89c6\u89d2C<\/span>(0,1)<\/sub>\u5374\u56e0\u5c0f\u4e16\u754c\u6548\u5e94\u63a9\u76d6\u4e86\u5c42\u6b21\u7ed3\u6784\u3002\u8fd9\u63d0\u793a\u6211\u4eec\uff0c\u9ad8\u9636\u7ed3\u6784\u7684\u5c3a\u5ea6\u7279\u6027\u53ef\u80fd\u9690\u85cf\u4e8e\u7279\u5b9a\u9636\u7684\u76f8\u4e92\u4f5c\u7528\u4e2d\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

\u56fe 2. \u4f2a\u5206\u5f62\u5355\u7eaf\u590d\u5f62\u4e2d\u7684\u6807\u5ea6\u4e0d\u53d8\u6027\u548c\u91cd\u6574\u5316\u3002(a) \u6784\u5efa\u5177\u6709\u4e8c\u7ef4\u7684\u4f2a\u5206\u5f62\u5355\u7eaf\u5f62\u590d\u5408\u4f53\u7684\u524d\u4e09\u4e2a\u6b65\u9aa4\u7684\u56fe\u793a\u3002(b). \u6240\u6709\u8de8\u9636\u62c9\u666e\u62c9\u65af\u77e9\u9635\u7684\u71b5\u654f\u611f\u6027\uff0c\u8ba1\u7b97\u5f97\u51fa\u7684\u662f\u901a\u8fc7\u516d\u4e2a\u6b65\u9aa4\u6784\u5efa\u7684\u4e8c\u7ef4\u4f2a\u5206\u5f62\u5355\u7eaf\u5f62\u590d\u5408\u4f53\uff081,095\u4e2a\u9876\u70b9\uff09\u3002(c) \u968f\u7740\u6784\u5efa\u5355\u7eaf\u5f62\u590d\u5408\u4f53\u6b65\u9aa4\u6570\u7684\u589e\u52a0\uff0cSIP\uff08\u71b5\u654f\u611f\u6027\u6307\u6570\uff09\u7684\u53d8\u5316\u3002(d) \u5de6\u4fa7\uff1a\u4f7f\u7528\u03c4* = 0.2\u7684\"image.png\"<\/sub>\u91cd\u6574\u5316\u65b9\u6848\u7684\u524d\u4e09\u4e2a\u6b65\u9aa4\uff1b\u53f3\u4fa7\uff1a\u4f7f\u7528\u03c4* = 2.6\u7684<\/span>\"image.png\" <\/sub>\u91cd\u6574\u5316\u65b9\u6848\u7684\u524d\u4e09\u4e2a\u6b65\u9aa4\u3002<\/span><\/span><\/p>\n

<\/span><\/section>\n


<\/span><\/h4>\n

<\/span><\/section>\n

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

\u91cd\u6574\u5316\u5b9e\u6218\uff1a\u4ece\u5408\u6210\u6570\u636e\u5230\u771f\u5b9e\u4e16\u754c<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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

<\/p>\n

\u7814\u7a76\u901a\u8fc7\u4e24\u7c7b\u5408\u6210\u6a21\u578b\u9a8c\u8bc1\u4e86\u8be5\u65b9\u6cd5\u7684\u6709\u6548\u6027\u3002\u5728\u4f2a\u5206\u5f62\u6a21\u578b\u4e2d\uff0c\u62c9\u666e\u62c9\u65af\u7b97\u5b50<\/strong>\u6210\u529f\u9006\u5411\u5176\u6784\u9020\u8fc7\u7a0b\uff0c\u5c06\u8fed\u4ee3\u751f\u6210\u7684\u590d\u5f62\u9010\u5c42\u574d\u7f29\u56de\u521d\u59cb\u5355\u5143<\/span>\uff08\u56fe2d\uff09<\/span>\u3002NGF\u6a21\u578b<\/strong>\uff1a\u76f8\u6bd4\u8282\u70b9\u89c6\u89d2\"image.png\"<\/sub>\u7684\u91cd\u6574\u5316\uff0c\u57fa\u4e8e\"image.png\"<\/sub>\u7684\u65b9\u6cd5\u66f4\u6e10\u8fdb\u5730\u4fdd\u7559\u7ed3\u6784\uff0c\u907f\u514d\u8fc7\u5ea6\u574d\u7f29<\/span>\uff08\u56fe3c\uff09<\/span>\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

\u56fe 3. \u5e94\u7528\u4e8e NGF \u5355\u7eaf\u590d\u5f62\u7684\u9ad8\u9636\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u65b9\u6848\u3002\uff08a\uff09NGF\u5355\u7eaf\u5f62\u590d\u5408\u4f53\u7684\u71b5\u654f\u611f\u6027\uff08SIP\uff09\u53ca\u5176\u5728\u5341\u6b21\u91cd\u590d\u5b9e\u9a8c\u4e2d\u768495%\u7f6e\u4fe1\u533a\u95f4\uff0c\u8003\u8651\u4e86\u5473\u9053s = 1\uff0c\u7ef4\u5ea6d \u2208 {1, 2, 3, 4}\uff0c\u03b2 = 5\uff0c\u4e14\u67093,000\u4e2a\u9876\u70b9\u3002\u6570\u5b57\u8868\u793aSIP\u503c\u3002\uff08b\uff09\u4e00\u4e2a\u5c0f\u578b\u4e8c\u7ef4NGF\u5355\u7eaf\u5f62\u590d\u5408\u4f53\u4f7f\u7528\"image.png\"<\/sub>\uff08\u4e0a\uff09\u548cL\u00d7(1,2)\uff08\u4e0b\uff09\u8fdb\u884c\u91cd\u6574\u5316\u3002\uff08c\uff09 \u5de6\u4fa7\uff1aC<\/span>(0,1)<\/sub>\u4e0e\u7ecf\u8fc7\u4e00\u6b65\"image.png\"<\/sub>\u91cd\u6574\u5316\u540e\u7684\u5355\u7eaf\u5f62\u590d\u5408\u4f53\u9876\u70b9\u6570\u91cf\u968f\u03c4\u7684\u53d8\u5316\u3002\u53f3\u4fa7\uff1aC<\/span>(1,2)<\/sub>\u4e0e\u7ecf\u8fc7\u4e00\u6b65\"image.png\"<\/sub>\u91cd\u6574\u5316\u540e\u7684\u5355\u7eaf\u5f62\u590d\u5408\u4f53\u9876\u70b9\u6570\u91cf\u968f\u03c4\u7684\u53d8\u5316\u3002\uff08d\uff09 \u5728\u8003\u8651\u7684\u4e24\u79cd\u91cd\u6574\u5316\u65b9\u6cd5\u540e\uff0c\u71b5\u654f\u611f\u6027C(1,2)<\/sub>\u7684\u6f14\u53d8\u3002\u8d77\u59cb\u7684NGF\u5355\u7eaf\u5f62\u590d\u5408\u4f53\u67092,000\u4e2a\u9876\u70b9\uff0c\u901a\u8fc7\"image.png\"<\/sub>\uff08\u03c4* = 0.06\uff09\u88ab\u51cf\u5c11\u5230854\u4e2a\u9876\u70b9\uff0c\u901a\u8fc7\"image.png\"<\/sub>\uff08\u03c4* = 0.6\uff09\u88ab\u51cf\u5c11\u52301,318\u4e2a\u9876\u70b9\u3002<\/span><\/p>\n


<\/span><\/section>\n
\u8fdb\u4e00\u6b65\u5c06\u8be5\u65b9\u6cd5\u5e94\u7528\u4e8e\u771f\u5b9e\u6570\u636e\u4e2d<\/span>\uff08\u56fe4\uff09<\/span>\uff0c\u9ad8\u4e2d\u793e\u4ea4\u8054\u7cfb\u7f51\u7edc<\/span>\uff08High-school contacts\uff09<\/span>\u7684\u71b5\u654f\u611f\u6027\u5448\u73b0\u82b1\u6735\u72b6\u6a21\u5f0f\uff0c\u5728\u7279\u5b9a\u9636\u6570\u5b58\u5728\u5c3a\u5ea6\u4e0d\u53d8\u6027\uff0c\u53ef\u80fd\u4e0e\u5b66\u751f\u95f4\u7684\u793e\u4ea4\u4e92\u52a8\u3001\u96c6\u7fa4\u6027\u6216\u5c0f\u7ec4\u5f62\u6210\u6709\u5173\u3002\u800c\u4e0b\u9762\u7684\u6069\u9686\u6570\u636e\u96c6<\/span>\uff08Enron email data\uff09<\/span>\u5219\u8868\u73b0\u51fa\u8f83\u4e3a\u5747\u5300\u7684\u71b5\u654f\u611f\u6027\u5206\u5e03\uff0c\u8282\u70b9\u95f4\u7684\u4ea4\u4e92\u867d\u7136\u5177\u6709\u590d\u6742\u6027\uff0c\u4f46\u6574\u4f53\u6765\u770b\uff0c\u7f51\u7edc\u5728\u4e0d\u540c\u9636\u6570\u4e0a\u7684\u5c3a\u5ea6\u7279\u5f81\u8868\u73b0\u8f83\u4e3a\u5e73\u8861\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

\u56fe 4. \u771f\u5b9e\u6570\u636e\u4e2d\u7684\u9ad8\u9636\u5c3a\u5ea6\u4e0d\u53d8\u6027\u3002(a) \u4ece\u771f\u5b9e\u4e16\u754c\u6570\u636e\u96c6\u4e2d\u83b7\u5f97\u7684\u516d\u4e2a\u8d85\u56fe\uff08\u622a\u65ad\u81f3 4 \u9636\uff09\u7684 P(k,m) <\/sub>\u503c\u3002\u8fd9\u7070\u8272\u7ebf\u6761\u53ca\u5173\u8054\u533a\u57df\u4ee3\u8868\u4e86\u96f6\u6a21\u578b\u5728\u5341\u6b21\u91cd\u590d\u4e2d P(k,m) <\/sub>\u503c\u7684\u5e73\u5747\u503c\u548c 95% \u7f6e\u4fe1\u533a\u95f4\u3002NDC\uff0c\u56fd\u5bb6\u836f\u54c1\u4ee3\u7801\u3002(b) \u4e0d\u540c\u7c7b\u578b\u7684 20 \u4e2a\u771f\u5b9e\u8d85\u56fe\u7684LDA\u6295\u5f71\uff0c\u7528\u4e0d\u540c\u989c\u8272\u8868\u793a\uff0c\u5176\u5927\u5c0f\u4e0e\u6700\u9ad8 SIP \u503c\u6210\u6bd4\u4f8b\u3002\u5f69\u8272\u533a\u57df\u7a81\u51fa\u663e\u793a\u4e86\u5c5e\u4e8e\u540c\u4e00\u7c7b\u8d85\u56fe\u7684\u90bb\u8fd1\u70b9\u7684\u7c07\u3002c\uff0c\u4ece\u771f\u5b9e\u4e16\u754c\u7f51\u7edc\u6570\u636e\u96c6\u4e2d\u83b7\u5f97\u7684\u516d\u4e2a\u4e8c\u9636\u56e2\u590d\u5408\u4f53\u7684 SIP \u503c P<\/span>(k,m) <\/sub>\u3002\u7070\u8272\u7ebf\u6761\u53ca\u5173\u8054\u533a\u57df\u4ee3\u8868\u4e86\u96f6\u6a21\u578b\u5728\u5341\u6b21\u91cd\u590d\u4e2d P<\/span>(k,m) <\/sub>\u503c\u7684\u5e73\u5747\u503c\u548c 95% \u7f6e\u4fe1\u533a\u95f4\u3002(d) 34 \u4e2a\u4e0d\u540c\u7c7b\u578b\u7684\u5b9e\u9645\u56e2\u590d\u5408\u4f53\u7684 LDA \u6295\u5f71\uff0c\u7528\u4e0d\u540c\u989c\u8272\u8868\u793a\uff0c\u5176\u5927\u5c0f\u4e0e\u7f51\u7edc\u7684\u6700\u9ad8 SIP \u503c\u6210\u6bd4\u4f8b\u3002\u5f69\u8272\u533a\u57df\u7a81\u51fa\u663e\u793a\u4e86\u5c5e\u4e8e\u540c\u4e00\u7c7b\u7684\u90bb\u8fd1\u70b9\u7c07\uff1a\u793e\u4f1a\u8d77\u6e90\uff08i\uff09\u3001\u57fa\u7840\u8bbe\u65bd\uff08ii\uff09\u548c\u751f\u7269\u8d77\u6e90\uff08iii\uff09\u3002<\/span><\/p>\n


<\/span><\/section>\n


<\/span><\/h4>\n

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

\u610f\u4e49\u4e0e\u5c55\u671b<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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

<\/p>\n

\u8fd9\u9879\u7814\u7a76\u9996\u6b21\u5c06\u91cd\u6574\u5316\u7fa4\u7cfb\u7edf\u63a8\u5e7f\u5230\u4efb\u610f\u9ad8\u9636\u7f51\u7edc\uff0c\u5176\u4ef7\u503c\u4f53\u73b0\u5728\uff1a\u5728\u7406\u8bba\u5c42\u9762\u7a81\u7834\uff0c<\/strong>\u63d0\u4f9b\u8de8\u9636\u7ed3\u6784\u7684\u7edf\u4e00\u5206\u6790\u6846\u67b6\uff0c\u8d85\u8d8a\u4f20\u7edfHodge\u62c9\u666e\u62c9\u65af\u7b97\u5b50\u7684\u5c40\u9650\u6027\u3002\u6709\u5f88\u5f3a\u7684\u5e94\u7528\u6f5c\u529b\uff0c<\/strong>\u4e3a\u793e\u4ea4\u4f20\u64ad\u3001\u8111\u7f51\u7edc\u5206\u6790\u7b49\u9886\u57df\u63ed\u793a\u591a\u5c3a\u5ea6\u673a\u5236\u7684\u9636\u7279\u5f02\u6027\uff0c\u4f8b\u5982\u75be\u75c5\u9632\u63a7\u53ef\u9488\u5bf9\u7279\u5b9a\u9636\u7ed3\u6784\u8bbe\u8ba1\u5e72\u9884\u7b56\u7565\u3002\u672a\u6765\uff0c\u7ed3\u5408\u591a\u9636\u7b97\u5b50\u7ec4\u5408\u4e0e\u673a\u5668\u5b66\u4e60\uff0c\u6216\u80fd\u8fdb\u4e00\u6b65\u89e3\u7801\u590d\u6742\u7cfb\u7edf\u4e2d\u201c\u4f4e\u79e9\u6f5c\u5728\u7ed3\u6784\u201d\uff0c\u63a8\u52a8\u7f51\u7edc\u79d1\u5b66\u8fc8\u5411\u66f4\u9ad8\u7ef4\u5ea6\u3002<\/span><\/section>\n
<\/section>\n
<\/section>\n

\u5f6d\u6668<\/span> <\/span>| \u7f16\u8bd1<\/span><\/strong><\/span><\/strong><\/p>\n

<\/p>\n

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

\u9ad8\u9636\u7f51\u7edc\u793e\u533a<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\n


<\/p>\n<\/section>\n

\u968f\u7740\u5bf9\u73b0\u5b9e\u4e16\u754c\u63a2\u7d22\u7684\u4e0d\u65ad\u6df1\u5165\uff0c\u4eba\u4eec\u53d1\u73b0\u5728\u8bb8\u591a\u771f\u5b9e\u7684\u590d\u6742\u7cfb\u7edf\u4e2d\uff0c\u7ec4\u6210\u7cfb\u7edf\u7684\u4e2a\u4f53\u4e4b\u95f4\u4e0d\u4ec5\u5b58\u5728\u4e8c\u5143\u4ea4\u4e92\u5173\u7cfb\uff0c\u4e5f\u5e7f\u6cdb\u5b58\u5728\u591a\u4e2a\u4f53\u540c\u65f6\uff08\u6216\u4ee5\u7279\u5b9a\u987a\u5e8f\uff09\u8fdb\u884c\u4ea4\u4e92\uff0c\u5373\u9ad8\u9636\u4ea4\u4e92\u73b0\u8c61\u3002\u4e3a\u6b64\uff0c\u7814\u7a76\u4eba\u5458\u5206\u522b\u53d1\u5c55\u51fa\u4e86\u57fa\u4e8e\u8d85\u56fe\u3001\u5355\u7eaf\u590d\u5f62\u3001\u4f9d\u8d56\u5173\u7cfb\u7b49\u7684\u7f51\u7edc\u9ad8\u9636\u8868\u793a\u6a21\u578b\uff0c\u4e3a\u590d\u6742\u7f51\u7edc\u5206\u6790\u548c\u7814\u7a76\u63d0\u4f9b\u4e86\u65b0\u7684\u601d\u8def\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u7531\u7535\u5b50\u79d1\u6280\u5927\u5b66\u5415\u7433\u5a9b\u8001\u5e08\u3001\u4efb\u6653\u9f99\u8001\u5e08\u53ca\u4e2d\u56fd\u5730\u8d28\u5927\u5b66\uff08\u5317\u4eac\uff09\u7ba1\u9752\u8001\u5e08\u5728\u96c6\u667a\u4ff1\u4e50\u90e8\u8054\u5408\u53d1\u8d77\u4e86\u3010\u9ad8\u9636\u7f51\u7edc\u8bfb\u4e66\u4f1a<\/a><\/span>\u3011\u3002\u8bfb\u4e66\u4f1a\u56f4\u7ed5\u9ad8\u9636\u4ea4\u4e92\u7f51\u7edc\u7684\u57fa\u672c\u6982\u5ff5\u3001\u6a21\u578b\u3001\u65b9\u6cd5\u4e0e\u5e94\u7528\u7b49\u7814\u7a76\u8fdb\u884c\u7814\u8ba8\uff0c\u6309\u7167\u300c\u57fa\u7840\u7406\u8bba\u300d+\u300c\u6df1\u5165\u7406\u8bba\u300d+\u300c\u6848\u4f8b\u7814\u8ba8\u300d\u7684\u6a21\u5f0f\u5c55\u5f00\u3002\u8bfb\u4e66\u4f1a\u7b2c\u4e00\u5b63\u5df2\u7ecf\u5706\u6ee1\u7ed3\u675f\uff0c\u7b2c\u4e8c\u5b63\u6b63\u5728\u7b79\u5907\u4e2d\u3002\u73b0\u5728\u62a5\u540d\u52a0\u5165\u53ef\u4ee5\u89e3\u9501\u7b2c\u4e00\u5b63\u5168\u90e8\u5f55\u64ad\u89c6\u9891\u5e76\u52a0\u5165\u793e\u7fa4\u4ea4\u6d41\u3002<\/span><\/section>\n

<\/p>\n

\"\u56fe\u7247\"<\/span><\/a><\/section>\n
\n

<\/p>\n

\u8be6\u60c5\u8bf7\u89c1\uff1a<\/span><\/p>\n

\u63a2\u7d22\u590d\u6742\u7cfb\u7edf\u9ad8\u9636\u4ea4\u4e92\u7684\u5965\u79d8 | \u9ad8\u9636\u7f51\u7edc\u8bfb\u4e66\u4f1a\u542f\u52a8<\/strong><\/a>
<\/span><\/strong><\/p>\n

<\/p>\n<\/section>\n

\n
<\/section>\n<\/section>\n
\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/strong><\/section>\n
1. <\/strong>Nat. Rev. Phys.\u901f\u9012\uff1a\u9ad8\u9636\u7f51\u7edc\u4e0a\u7684\u4f20\u67d3\u52a8\u529b\u5b66<\/a><\/strong><\/span><\/strong><\/section>\n
2. <\/strong>\u62d3\u6251\u6df1\u5ea6\u5b66\u4e60\u6355\u6349\u6570\u636e\u7684\u9ad8\u9636\u5173\u7cfb\uff1a\u4fe1\u606f\u4f20\u9012\u62d3\u6251\u795e\u7ecf\u7f51\u7edc\u6982\u8ff0<\/a><\/strong><\/span><\/strong><\/section>\n
3. <\/strong>Nat. Phys.\u901f\u9012\uff1a\u5f02\u6784\u7f51\u7edc\u7684\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4<\/a><\/strong><\/span><\/strong><\/section>\n
<\/strong><\/section>\n
<\/strong><\/section>\n
4. <\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
<\/strong>5. <\/strong>\u89e3\u9501\u96c6\u667a\u5168\u7ad9\u5185\u5bb9\uff0c\u5f00\u542f\u65b0\u5e74\u5b66\u4e60\u8ba1\u5212<\/a><\/strong><\/section>\n

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

<\/p>\n


<\/span><\/p>\n

\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/span><\/section>\n<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u6458\u8981 \u91cd\u6574\u5316\u7fa4\u662f\u7269\u7406\u5b66\u4e2d\u5173\u4e8e\u6807\u5ea6\u3001\u6807\u5ea6\u4e0d\u53d8\u6027\u548c\u666e\u9002\u6027\u7406\u8bba\u7684\u652f\u67f1\u3002\u6700\u8fd1\uff0c\u901a\u8fc7\u57fa\u4e8e\u6269\u6563\u52a8\u529b\u5b66\uff0c\u8fd9\u4e00\u5de5\u5177\u5df2\u88ab\u5e94\u7528\u4e8e\u5177\u6709\u6210\u5bf9\u76f8\u4e92\u4f5c\u7528\u7684\u590d\u6742\u7f51\u7edc\u3002\u7136\u800c\uff0c\u968f\u7740\u590d\u6742\u7cfb\u7edf\u4e2d\u591a\u4f53\u76f8\u4e92\u4f5c\u7528\u7684\u91cd\u8981\u6027\u6108\u53d1\u51f8\u663e\uff0c\u8feb\u5207\u9700\u8981\u5c06\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u6269\u5c55\u5230\u9ad8\u9636\u7f51\u7edc\u3002\u5728\u6b64\uff0c\u6211\u4eec\u586b\u8865\u4e86\u8fd9\u4e00\u7a7a\u767d\uff0c\u63d0\u51fa\u4e86\u4e00\u79cd\u9002\u7528\u4e8e\u4efb\u610f\u9ad8\u9636\u7f51\u7edc\u7684\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4\u65b9\u6848…<\/p>\n","protected":false},"author":1,"featured_media":57656,"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\/57676"}],"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=57676"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/57676\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/57656"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=57676"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=57676"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=57676"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=57676"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}