{"id":29795,"date":"2021-11-05T15:43:32","date_gmt":"2021-11-05T07:43:32","guid":{"rendered":"https:\/\/swarma.org\/?p=29795"},"modified":"2021-11-05T15:43:32","modified_gmt":"2021-11-05T07:43:32","slug":"nature-phycics%ef%bc%9a%e5%a4%8d%e6%9d%82%e7%bd%91%e7%bb%9c%e4%b8%ad%e9%ab%98%e9%98%b6%e7%9b%b8%e4%ba%92%e4%bd%9c%e7%94%a8%e7%9a%84%e7%89%a9%e7%90%86%e5%ad%a6","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=29795","title":{"rendered":"Nature Phycics\uff1a\u590d\u6742\u7f51\u7edc\u4e2d\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u7684\u7269\u7406\u5b66"},"content":{"rendered":"
\n
\n
\n
\n

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

\n
\n
\n
\n
\n
\n

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

\u5bfc\u8bed<\/strong><\/p>\n<\/section>\n<\/section>\n

\n

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

<\/strong>\u5bf9\u76f8\u4e92\u4f5c\u7528\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u8fdb\u884c\u5efa\u6a21\uff0c\u5982\u4eca\u7684\u5e38\u7528\u5de5\u5177\u662f\u590d\u6742\u7f51\u7edc\u3002\u4f46\u5b83\u53ea\u80fd\u5305\u542b\u8282\u70b9\u95f4\u7684\u4e24\u4e24\u4e92\u52a8\uff0c\u65e0\u6cd5\u53cd\u6620\u73b0\u5b9e\u4e2d\u591a\u4e2a\u8282\u70b9\u95f4\u7684\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u300210\u67084\u65e5\uff0cNature Physics<\/em> \u7684\u8bc4\u8bba\u6587\u7ae0\u201c\u590d\u6742\u7cfb\u7edf\u4e2d\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u7684\u7269\u7406\u5b66\u201d\uff0c\u5c55\u793a\u4e86\u5982\u4f55\u4f7f\u7528\u8d85\u56fe\uff08hypergraph\uff09\u548c\u5355\u7eaf\u590d\u5f62\uff08simplicial complexe\uff09\u7b49\u5de5\u5177\uff0c\u5bf9\u76f8\u4e92\u4f5c\u7528\u7cfb\u7edf\u7684\u7206\u53d1\u6027\u884c\u4e3a\u3001\u62d3\u6251\u52a8\u6001\u53d8\u5316\u8fdb\u884c\u5efa\u6a21\u3002<\/span><\/strong><\/p>\n


<\/p>\n

\u7814\u7a76\u9886\u57df\uff1a\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\uff0c\u9ad8\u9636\u7f51\u7edc\uff0c\u8d85\u56fe\uff0c\u5355\u7eaf\u590d\u5f62\uff0c\u7f51\u7edc\u52a8\u529b\u5b66<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\n
\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
<\/strong><\/section>\n<\/section>\n
\n

\u90ed\u745e\u4e1c<\/span> | \u4f5c\u8005<\/strong><\/span><\/strong><\/p>\n

\u9648\u5173\u8363\u3001\u6881\u91d1 <\/span>| \u5ba1\u6821<\/strong><\/span><\/p>\n

\u9093\u4e00\u96ea<\/span> | \u7f16\u8f91<\/strong><\/span><\/p>\n<\/section>\n

 <\/span><\/p>\n


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

<\/p>\n

\n
\n
\n

\u8bba\u6587\u9898\u76ee\uff1a<\/span><\/p>\n

The physics of higher-order interactions in complex systems<\/span><\/p>\n

\u8bba\u6587\u94fe\u63a5\uff1a<\/span><\/p>\n

https:\/\/www.nature.com\/articles\/s41567-021-01371-4<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


<\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

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

1. \u4f55\u4e3a\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\uff1f<\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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


<\/p>\n

\u751f\u6001\u7cfb\u7edf\u4e2d\u7684\u591a\u4e2a\u7269\u79cd\u5982\u4f55\u4ea7\u751f\u76f8\u4e92\u4f5c\u7528\uff0c\u793e\u4ea4\u7f51\u7edc\u4e2d\u8ff7\u56e0\u5982\u4f55\u4f20\u64ad\uff0c\u5927\u8111\u4e2d\u795e\u7ecf\u5143\u5982\u4f55\u8fde\u63a5\uff0c\u590d\u6742\u7f51\u7edc\u5bf9\u7406\u89e3\u6211\u4eec\u65e5\u5e38\u751f\u6d3b\u4e2d\u9047\u5230\u7684\u8fd9\u4e9b\u4e92\u52a8\u73b0\u8c61\u90fd\u6709\u5e2e\u52a9\u3002\u7136\u800c\uff0c\u7f51\u7edc\u4e2d\u7684\u8fb9\u53ea\u5305\u542b\u4e24\u4e2a\u8282\u70b9\uff0c\u4f46\u73b0\u5b9e\u4e2d\u7684\u4e92\u52a8\u5374\u5f80\u5f80\u6d89\u53ca\u591a\u4e2a\u53c2\u4e0e\u8005\u3002<\/span><\/section>\n

<\/section>\n
\u4f8b\u5982\u8c23\u8a00\u7684\u4f20\u64ad\uff0c\u4e00\u4e2a\u4eba\u8bf4\u7684\u65f6\u5019\u522b\u4eba\u662f\u4e0d\u4fe1\u7684\uff0c\u82e5\u662f\u4e24\u4e2a\u4eba\u5148\u540e\u4f20\u64ad\u540c\u4e00\u4e2a\u4fe1\u606f\uff0c\u5c31\u5f88\u5bb9\u6613\u8ba9\u522b\u4eba\u76f8\u4fe1\u2014\u2014\u8fd9\u5c31\u662f\u6240\u8c13\u7684\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u3002\u4e0b\u56fe\u4e2d\uff08a\uff09\u662f\u7b80\u5355\u7684\u7f51\u7edc\uff0c\u53ea\u5305\u542b\u4e24\u4e24\u76f8\u4e92\u4f5c\u7528\u7684\u8282\u70b9\u3002\uff08b\uff09\u4e2d\u7684\u8d85\u56fe\u53ef\u4ee5\u8868\u793a\u4efb\u610f\u6570\u91cf\u8282\u70b9\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u5176\u4e2d\u5305\u542b\u4e86\u4e00\u7ec4\u8282\u70b9\u7684\u9634\u5f71\u8868\u793a\u8d85\u8fb9\u3002\uff08c\uff09\u4e2d\u7684\u5355\u7eaf\u590d\u5f62\u662f\u8868\u793a\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u7684\u53e6\u4e00\u79cd\u65b9\u5f0f\u3002\u4f20\u7edf\u56fe\u4e2d\u7684\u8fb9\u79f0\u4e3a 1-simplex\uff0c\u4e09\u89d2\u5f62\u4e3a2-simplex\uff0c\u4ee3\u8868\u8fd9\u4e09\u4e2a\u8282\u70b9\u4e2d\u4e24\u4e24\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u3002<\/span><\/section>\n
               <\/span><\/section>\n
<\/section>\n
\u56fe1. \u7b80\u5355\u7f51\u7edc\u3001\u8d85\u56fe\u3001\u5355\u7eaf\u590d\u5f62\u5bf9\u6bd4\u56fe<\/span><\/section>\n

<\/section>\n
\u4e4b\u524d\u7684\u6587\u732e\u4ece\u6e17\u6d41[1,2]\u3001\u540c\u6b65[3,4]\u3001\u793e\u4ea4\u4f20\u67d3[5,6]\u3001\u8fdb\u5316\u8fc7\u7a0b[7]\u8fdb\u884c\u8fc7\u8bba\u8ff0\uff0c\u8bf4\u660e\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u4f1a\u5bf9\u7cfb\u7edf\u52a8\u529b\u5b66\u4f1a\u4ea7\u751f\u663e\u8457\u5f71\u54cd\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u5177\u4f53\u8ba8\u8bba\u5f15\u5165\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u5bf9\u590d\u6742\u7cfb\u7edf\u7684\u6f14\u5316\u5efa\u6a21\u5e26\u6765\u7684\u4e24\u4e2a\u52a9\u529b\uff1a\u4e00\u662f\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u5e26\u6765\u7684\u975e\u7ebf\u6027\u4f1a\u5bfc\u81f4\u7206\u53d1\u6027\u8f6c\u53d8<\/span>\uff08explosive transition\uff09<\/span>\uff0c\u4e8c\u662f\u53ef\u4ee5\u63a2\u7d22\u7cfb\u7edf\u62d3\u6251\u7ed3\u6784\u7684\u52a8\u6001\u53d8\u5316\u3002\u6b64\u5916\uff0c\u5982\u4f55\u4ece\u8282\u70b9\u95f4\u76f8\u4e92\u4f5c\u7528\u7684\u89c2\u5bdf\u6570\u636e\u63a8\u65ad\u51fa\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u7684\u5b58\u5728\uff0c\u76ee\u524d\u4ecd\u7136\u662f\u4e00\u4e2a\u5f00\u653e\u95ee\u9898\u3002<\/span><\/section>\n

<\/section>\n

<\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

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

2. \u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u5bfc\u81f4\u7206\u53d1\u6027\u8f6c\u53d8<\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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


<\/p>\n

\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u7206\u53d1\u73b0\u8c61<\/a><\/span>\u662f\u7cfb\u7edf\u6f14\u5316\u4e2d\u7684\u4e00\u4e2a\u7814\u7a76\u70ed\u70b9\uff0c\u5bf9\u5e94\u7684\u73b0\u8c61\u5305\u62ec\u6d41\u884c\u75c5\u7684\u4f20\u64ad\u3001\u8424\u706b\u866b\u7684\u540c\u6b65\u95ea\u70c1\u7b49\u3002\u7136\u800c\u5728\u7b80\u5355\u7f51\u7edc\u4e0a\u590d\u73b0\u7206\u53d1\u6027\u7684\u7a81\u53d8\u9700\u8981\u5f15\u5165\u989d\u5916\u7684\u89c4\u5219\uff0c\u4f8b\u5982\u8ba9\u5305\u542b\u5f02\u8d28\u6027\u7684\u7f51\u7edc\u4e2d\u8282\u70b9\u9707\u8361\u7684\u9891\u7387\u4e0e\u8282\u70b9\u7684\u5ea6\u6570\u76f8\u5173\uff0c\u5982\u6b64\u5c31\u80fd\u591f\u4f7f\u7f51\u7edc\u4e2d\u7684\u540c\u6b65\u73b0\u8c61\u5448\u73b0\u7206\u53d1\u6027\u8f6c\u53d8\u3002<\/span><\/section>\n

<\/section>\n
\u4e0a\u8ff0\u6a21\u578b\u63cf\u8ff0\u7684\u7206\u53d1\u73b0\u8c61\uff0c\u5176\u53d8\u5316\u662f\u8fde\u7eed\u7684\u3002\u4f46\u73b0\u5b9e\u4e2d\u7684\u7206\u53d1\u73b0\u8c61\uff0c\u5176\u7cfb\u7edf\u7684\u6f14\u53d8\u5374\u53ef\u4ee5\u8868\u73b0\u5f97\u975e\u8fde\u7eed\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8ba9\u4e00\u4e2a\u8282\u70b9\u53d7\u5230\u5176\u4ed6\u51e0\u4e2a\u8282\u70b9\u72b6\u6001\u7684\u975e\u7ebf\u6027\u7ec4\u5408\u7684\u5f71\u54cd\uff0c\u6765\u5f15\u5165\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u3002\u5982\u56fe2\u6240\u793a\uff0c\u5f53\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u7684\u5f3a\u5ea6\u7a81\u7834\u4e34\u754c\u503c\u540e\uff0c\u7cfb\u7edf\u7684\u5b8f\u89c2\u72b6\u6001<\/span>\uff08\u7eb5\u8f74\uff09<\/span>\u4f1a\u53d1\u751f\u975e\u8fde\u7eed\u7a81\u53d8\uff1b\u4f46\u5f53\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u8f83\u5f31\u65f6\uff0c\u5b8f\u89c2\u72b6\u6001\u4e0d\u4f1a\u51fa\u73b0\u975e\u8fde\u7eed\u7a81\u53d8\u3002<\/span><\/section>\n
               <\/span><\/section>\n
<\/span><\/section>\n
\u56fe2. \u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u5bf9\u7cfb\u7edf\u7206\u53d1\u6027\u884c\u4e3a\u7684\u5f71\u54cd<\/span><\/section>\n

<\/section>\n
\u5728\u4e0d\u540c\u95ee\u9898\u5efa\u6a21\u4e2d\u90fd\u53ef\u4ee5\u5f15\u5165\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u3002\u4f8b\u5982\u75be\u75c5\u4f20\u64ad\u6a21\u578b\uff0c\u5c06\u8282\u70b9\u5206\u4e3a\u611f\u67d3\u8005<\/span>\uff08Infectious node\uff09<\/span>\u548c\u6613\u611f\u8005<\/span>\uff08Susceptible node\uff09<\/span>\u3002\u6613\u611f\u4eba\u7fa4\u65e2\u53ef\u4ee5\u901a\u8fc7\u8fb9\u88ab\u611f\u67d3\u8005\u611f\u67d3\uff0c\u4e5f\u53ef\u4ee5\u53d7\u5230\u591a\u4e2a\u611f\u67d3\u8005\u7ec4\u6210\u7684\u7fa4\u4f53\u611f\u67d3<\/span>\uff08\u56fe3a\uff09<\/span>\u3002\u56fe3b\u63cf\u8ff0\u7684\u662f\u65e5\u672c\u7269\u7406\u5b66\u5bb6\u85cf\u672c\u7531\u7eaa<\/span>\uff08Yoshiki Kuramoto\uff09<\/span>\u63d0\u51fa\u7684\u8026\u5408\u632f\u5b50\u540c\u6b65\u95ee\u9898\u3002\u4e24\u79cd\u73b0\u8c61\u4e2d\uff0c\u5f15\u5165\u9ad8\u9636\u4e92\u52a8\u540e\uff0c\u80fd\u591f\u7528\u66f4\u7ec6\u7684\u7c92\u5ea6\u53bb\u63cf\u8ff0\u7cfb\u7edf\u4e2d\u7684\u975e\u7ebf\u6027\u53cd\u9988\u3002<\/strong><\/span><\/section>\n
               <\/span><\/section>\n
<\/span><\/section>\n
\u56fe3.\uff08a\uff09\u75be\u75c5\u4f20\u64ad\uff08b\uff09\u8026\u5408\u632f\u5b50\u540c\u6b65\u573a\u666f\u4e0b\u7684\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528<\/span><\/section>\n

<\/section>\n
\u5bf9\u75be\u75c5\u4f20\u64ad\u7684\u9ad8\u9636\u5efa\u6a21\uff0c\u53ea\u9700\u8981\u5f15\u5165\u4e09\u4e2a\u8282\u70b9\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u5c31\u53ef\u4ee5\u91cd\u73b0\u4e00\u4e2a\u5305\u542b\u75be\u75c5\u7206\u53d1\u4e0e\u5426\u8fd9\u79cd\u53cc\u7a33\u5b9a\u6001<\/span>\uff08bistability\uff09<\/span>\u7684\u7cfb\u7edf\uff0c\u4e0a\u8ff0\u7ed3\u8bba\u662f\u9c81\u68d2\u4e14\u666e\u9002\u7684\uff0c\u4e0d\u4ec5\u9002\u7528\u4e8e\u5bf9\u75be\u75c5\u4f20\u64ad\uff0c\u4e5f\u9002\u7528\u4e8e\u5bf9\u6e17\u6d41\u73b0\u8c61\u5efa\u6a21\u3002\u5728\u632f\u5b50\u540c\u6b65\u4e2d\uff0c\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u7684\u5f15\u5165\u53ef\u4ee5\u5728\u4e0d\u589e\u52a0\u989d\u5916\u89c4\u5219\u65f6\uff0c\u8ba9\u7cfb\u7edf\u7684\u6f14\u5316\u5448\u73b0\u51fa\u53cc\u7a33\u6001\u4ee5\u53ca\u6ede\u540e\u5faa\u73af<\/span>\uff08hysteresis cycle\uff09<\/span>\u3002<\/span><\/section>\n

<\/section>\n
\u5c3d\u7ba1\u7f3a\u5c11\u4e25\u683c\u7684\u8bc1\u660e\uff0c\u4f46\u5df2\u6709\u8bc1\u636e\u8868\u660e\uff0c\u5728\u8bf8\u591a\u622a\u7136\u4e0d\u540c\u7684\u7cfb\u7edf\u4e2d\uff0c\u5f15\u5165\u975e\u7ebf\u6027\u7684\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u5e76\u6539\u53d8\u5176\u5f3a\u5ea6\uff0c\u662f\u4fc3\u6210\u7206\u53d1\u6027\u8f6c\u53d8\u7684\u901a\u7528\u673a\u5236<\/strong>\u3002\u5728\u4e24\u4e24\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u4e2d\uff0c\u5f15\u5165\u5f02\u8d28\u6027<\/span>\uff08\u4f8b\u5982\u901a\u8fc7\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\uff09<\/span>\uff0c\u53ef\u4ee5\u4fc3\u6210\u4e34\u754c\u884c\u4e3a\u4ece\u8fde\u7eed\u8f6c\u4e3a\u975e\u8fde\u7eed\u3002<\/span><\/section>\n

<\/section>\n

<\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

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

3. \u63a2\u7d22\u7f51\u7edc\u62d3\u6251\u7ed3\u6784\u7684\u52a8\u6001\u6f14\u5316<\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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


<\/p>\n

\u5728\u5f15\u5165\u4e86\u8d85\u56fe\u548c\u5355\u7eaf\u590d\u5f62\u540e\uff0c\u7cfb\u7edf\u4e2d\u5404\u4e2a\u90e8\u5206\u7684\u76f8\u4e92\u4f5c\u7528\u5c06\u4e0d\u4ec5\u7531\u8fde\u8fb9\u63cf\u8ff0\uff0c\u8fd8\u80fd\u901a\u8fc7\u8d85\u8fb9\u6216 n-simplex \u6765\u63cf\u8ff0\u3002\u8fd9\u4f7f\u5f97\u67d0\u4e00\u6761\u8fb9\u7684\u72b6\u6001\u53ef\u4ee5\u53d7\u5230\u591a\u4e2a\u8282\u70b9\u7684\u96c6\u5408\u7684\u5f71\u54cd\uff0c\u5e76\u540c\u65f6\u5bf9\u591a\u6761\u8fb9\u4ea7\u751f\u5f71\u54cd\u3002\u5982\u6b64\uff0c\u5c31\u53ef\u4ee5\u5728\u6a21\u578b\u4e2d\u5f15\u5165\u76f8\u4e92\u4f9d\u8d56\u548c\u53cd\u9988\u3002<\/span><\/section>\n

<\/section>\n
\u4f8b\u5982\u4e0b\u56fe\u7684\u632f\u5b50\u540c\u6b65\u95ee\u9898\uff0c\u5728\u5f15\u5165\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u65f6\uff0c\u6a21\u578b\u9700\u8981\u63cf\u8ff0\u7684\u4e0d\u4ec5\u662f\u6bcf\u4e2a\u70b9\u7684\u72b6\u6001\uff0c\u8fd8\u6709\u9ad8\u9636\u8fde\u63a5\u7684\u6539\u53d8\u60c5\u51b5\u3002\u5728\u8be5\u573a\u666f\u4e2d\uff0c\u8282\u70b9\u95f4\u7684\u6210\u5bf9\u76f8\u4e92\u4f5c\u7528\uff0c\u4e0d\u4ec5\u4ec5\u4f53\u73b0\u5728\u5bf9\u5e94\u56fe\u4e2d\u7684\u8fb9\u7684\u72b6\u6001\uff0c\u8fd8\u5305\u62ec\u4e86 2-simplex \u4e0a\u7684\u5708\u7684\u72b6\u6001\uff0c\u8fb9\u4e0a\u7684\u7ea2\u8272\u5708\u70b9\u6307\u7684\u662f\u4e24\u8005\u4e4b\u95f4\u7684\u8fb9\u754c\u6761\u4ef6\u3002\u7cfb\u7edf\u5728\u6f14\u5316\u65f6\uff0c\u540c\u6b65\u73b0\u8c61\u4f1a\u7531\u9ad8\u9636\u8fde\u63a5\u7684\u90e8\u5206\u6269\u6563\u5230\u4f4e\u9636\u8fde\u63a5\u7684\u90e8\u5206<\/span>\uff08\u56feb\uff09<\/span>\uff1b\u6216\u8005\u76f8\u53cd\uff0c\u7531\u4f4e\u9636\u90e8\u5206\u6269\u6563\u5230\u9ad8\u9636\u90e8\u5206<\/span>\uff08\u56fec\uff09<\/span>\u3002<\/span><\/section>\n
        <\/span><\/section>\n

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

\u56fe4. \u632f\u5b50\u540c\u6b65\u5728\u5f15\u5165\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u540e\uff0c\u540c\u6b65\u73b0\u8c61\u81ea\u53d1\u7531\u9ad8\u9636\u5411\u4f4e\u9636\uff0c\u6216\u7531\u4f4e\u9636\u5411\u9ad8\u9636\u6295\u5f71\uff08projection\uff09<\/span><\/p>\n


<\/section>\n
\u4ee5\u4e0a\u5c55\u793a\u7684\uff0c\u542f\u793a\u4e86\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u5f15\u5165\u540e\u80fd\u591f\u63a2\u7d22\u7684\u53e6\u4e00\u95ee\u9898\uff0c\u5373\u7f51\u7edc\u7684\u62d3\u6251\u7ed3\u6784\u5982\u4f55\u968f\u65f6\u95f4\u6f14\u5316<\/strong>\u3002\u76ee\u524d\u5e38\u7528\u7684\u65b9\u6cd5\uff0c\u662f\u5c06\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u6295\u5c04\u6210\u4e24\u4e24\u4e4b\u95f4\u7684\u4e92\u52a8\uff0c\u4ee5\u53ca\u901a\u8fc7\u62c9\u666e\u62c9\u65af\u77e9\u9635\u53d8\u5316\u6765\u5bf9\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u8fdb\u884c\u5904\u7406\u3002<\/span><\/section>\n

<\/section>\n

<\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

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

4. \u4ece\u89c2\u6d4b\u6570\u636e\u4e2d\u91cd\u6784\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u7f51\u7edc<\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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


<\/p>\n

\u4e00\u4e2a\u66f4\u4e3a\u57fa\u7840\u7684\u95ee\u9898\uff0c\u662f\u5982\u4f55\u4ece\u89c2\u6d4b\u6570\u636e\u4e2d\u63a8\u65ad\u51fa\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u7684\u5b58\u5728\u3002\u5373\u4f7f\u7cfb\u7edf\u4e2d\u5b58\u5728\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\uff0c\u4f46\u89c2\u5bdf\u5230\u7684\u6570\u636e\u5374\u5f80\u5f80\u662f\u4e24\u4e24\u8282\u70b9\u4e4b\u95f4\u7684\u3002\u4f8b\u5982A\u4eceB\u5904\u542c\u5230\u4e86\u4e00\u5219\u8c23\u8a00\uff0c\u4f46\u5b83\u53ef\u80fd\u662f\u4eceB\u4e4b\u524d\u5176\u4ed6\u4eba\u90a3\u91cc\u4f20\u6765\u7684\u3002\u5982\u4f55\u6839\u636e\u65f6\u95f4\u5e8f\u5217\u63a8\u6d4b\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u7684\u5b58\u5728\u5462\uff1f<\/strong><\/span><\/section>\n

<\/section>\n
\u7b80\u5355\u5047\u8bbe\u4e09\u4e2a\u8282\u70b9\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u603b\u662f\u5b58\u5728\uff0c\u8fd9\u5e76\u4e0d\u662f\u4e00\u4e2a\u597d\u7684\u505a\u6cd5\u3002\u901a\u8fc7\u8d1d\u53f6\u65af\u63a8\u65ad<\/strong>\u6216\u8005\u7edf\u8ba1\u6a21\u578b\u4e2d\u7684\u96f6\u5047\u8bbe<\/strong>\uff0c\u7528\u8bc1\u636e\u8bf4\u660e\u5176\u5b58\u5728\uff0c\u662f\u91cd\u6784\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u7f51\u7edc\u7684\u4e24\u79cd\u5e38\u7528\u65b9\u6cd5\u3002<\/span><\/section>\n
               <\/span><\/section>\n
<\/span><\/section>\n
\u56fe5. \u4ece\u95f4\u63a5\u7684\u65f6\u95f4\u5e8f\u5217\u4e2d\u91cd\u6784\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u7f51\u7edc<\/span><\/section>\n

<\/section>\n
\u9664\u4e86\u76f4\u63a5\u89c2\u6d4b\u5230\u7684\u76f8\u4e92\u5f71\u54cd\u4e8b\u4ef6\uff0c\u8fd8\u53ef\u4ee5\u901a\u8fc7\u7cfb\u7edf\u7684\u72b6\u6001\u968f\u65f6\u95f4\u7684\u6539\u53d8\uff0c\u6765\u63a8\u65ad\u662f\u5426\u5b58\u5728\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528<\/strong>\uff0c\u4f8b\u5982\u8282\u70b9\u95f4\u662f\u5426\u5b58\u5728\u540c\u6b65\uff0c\u662f\u5426\u6709\u76f8\u5173\u6027\u7b49\u3002\u7136\u800c\uff0c\u8fd9\u7c7b\u65b9\u6cd5\u4e0d\u80fd\u533a\u5206\u76f8\u5173\u6027\u548c\u56e0\u679c\u6027\u3002\u8282\u70b9\u95f4\u7684\u72b6\u6001\u5171\u540c\u53d8\u5316\uff0c\u4e0d\u4e00\u5b9a\u610f\u5473\u7740\u4e24\u8005\u4e4b\u95f4\u5b58\u5728\u76f8\u4e92\u4f5c\u7528\uff0c\u800c\u8282\u70b9\u95f4\u6ca1\u6709\u8fde\u901a\u7684\u8fb9\uff0c\u4e5f\u4ecd\u7136\u53ef\u80fd\u5b58\u5728\u76f8\u4e92\u8fd0\u52a8\u3002\u57fa\u4e8e\u4fe1\u606f\u8bba\u7684\u65b9\u6cd5\uff0c\u4f8b\u5982 Granger \u56e0\u679c\u6027\u548c\u8f6c\u79fb\u71b5\u7b49\uff0c\u4e5f\u53ef\u7528\u6765\u5224\u5b9a\u8282\u70b9\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u76f8\u4e92\u4f5c\u7528\u3002<\/span><\/section>\n

<\/section>\n

<\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

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

5. \u672a\u6765\u7684\u7814\u7a76\u65b9\u5411\u5c55\u671b<\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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


<\/p>\n

\u5f53\u524d\u7684\u6a21\u578b\uff0c\u90fd\u5047\u8bbe\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u51fa\u73b0\u4e0e\u5426\u4e0d\u4f1a\u968f\u65f6\u95f4\u800c\u6539\u53d8\u3002\u5982\u4f55\u5728\u6a21\u578b\u4e2d\u52a0\u5165\u53d8\u5316\u7684\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528<\/strong>\uff0c\u662f\u672a\u6765\u7684\u4e00\u4e2a\u7814\u7a76\u65b9\u5411\u3002\u6b64\u5916\uff0c\u5bf9\u4e8e\u5df2\u6709\u95ee\u9898\uff0c\u4f8b\u5982\u632f\u5b50\u7f51\u7edc\u7684\u76f8\u53d8\uff0c\u5728\u5efa\u6a21\u4e2d\u52a0\u5165\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\uff0c\u53ef\u4ee5\u5bf9\u5176\u52a8\u529b\u5b66\u7684\u6f14\u5316\u7ed9\u51fa\u66f4\u6e05\u695a\u7684\u63cf\u8ff0\u3002<\/span><\/section>\n

<\/section>\n
\u603b\u7ed3\u6765\u770b\uff0c\u5bf9\u4e8e\u590d\u6742\u7cfb\u7edf\u7684\u5efa\u6a21\uff0c\u5f15\u5165\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\uff0c\u53ef\u4ee5\u5728\u4f17\u591a\u573a\u666f<\/span>\uff08\u5305\u62ec\u591a\u5c42\u7f51\u7edc\u3001\u975e\u9a6c\u5c14\u53ef\u592b\u65f6\u5e8f\u7f51\u7edc\uff09<\/span>\u4e2d\uff0c\u5bf9\u66f4\u4e3a\u8d34\u8fd1\u73b0\u5b9e\u7684\u76f8\u4e92\u4f5c\u7528\u8fdb\u884c\u63cf\u8ff0\uff0c\u4ece\u800c\u5728\u4eff\u771f\u5b9e\u9a8c\u4e2d\u590d\u73b0\u51fa\u4e4b\u524d\u6a21\u578b\u65e0\u6cd5\u91cd\u73b0\u7684\u73b0\u8c61\u3002\u5728\u514b\u670d\u4e86\u6570\u636e\u6536\u96c6\u548c\u7f51\u7edc\u91cd\u6784\u7684\u969c\u788d\u540e\uff0c\u53ef\u4ee5\u8ba9\u590d\u6742\u7f51\u7edc\u7684\u5e94\u7528\u8303\u56f4\u8fdb\u4e00\u6b65\u6269\u5927\u3002<\/span><\/section>\n

<\/section>\n

<\/section>\n
\u53c2\u8003\u6587\u732e<\/span><\/strong><\/span><\/section>\n
[1] Schaub, M. T., Benson, A. R., Horn, P., Lippner, G. & Jadbabaie, A. Random walks on simplicial complexes and the normalized Hodge Laplacian. SIAM Rev. 62, 353\u2013391 (2020).<\/span><\/section>\n
[2] Carletti, T., Battiston, F., Cencetti, G. & Fanelli, D. Random walks on hypergraphs. Phys. Rev. E 101, 022308 (2020)<\/span><\/section>\n
[3] Mill\u00e1n, A. P., Torres, J. J. & Bianconi, G. Synchronization in network geometries with fnite spectral dimension. Phys. Rev. E 99, 022307 (2019).<\/span><\/section>\n
[4] Skardal, P. S. & Arenas, A. Abrupt desynchronization and extensive multistability in globally coupled oscillator simplexes. Phys. Rev. Lett. 122, 248301 (2019).<\/span><\/section>\n
[5] Iacopini, I., Petri, G., Barrat, A. & Latora, V. Simplicial models of social contagion. Nat. Commun. 10, 2485 (2019)<\/span><\/section>\n
[6] de Arruda, G. F., Petri, G. & Moreno, Y. Social contagion models on hypergraphs. Phys. Rev. Res. 2, 023032 (2020)<\/span><\/section>\n
[7] Alvarez-Rodriguez, U. et al. Evolutionary dynamics of higher-order interactions in social networks. Nat. Hum. Behav. 5, 586\u2013595 (2021)<\/span><\/section>\n
\n
\n

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


<\/p>\n

\n
\n
\n
\n
\n

\u7f51\u7edc\u79d1\u5b66\u96c6\u667a\u8bfe\u5802\u7b2c\u4e09\u671f\u62a5\u540d\u4e2d<\/strong><\/span><\/p>\n

\u4ece\u6570\u5b66\u5efa\u6a21\u5230\u591a\u5b66\u79d1\u5e94\u7528
<\/strong><\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


<\/section>\n<\/h2>\n
\u4ece\u73b0\u5b9e\u793e\u4f1a\u7684\u5173\u7cfb\u7f51\u5230\u865a\u62df\u7684\u4e92\u8054\u7f51\uff0c\u4ece\u7ebf\u4e0b\u5230\u7ebf\u4e0a\uff0c\u6211\u4eec\u7684\u751f\u6d3b\u59cb\u7ec8\u6ca1\u6709\u8131\u79bb\u590d\u6742\u7f51\u7edc\u3002\u771f\u5b9e\u7684\u590d\u6742\u7f51\u7edc\u4ece\u5176\u8bde\u751f\u5f00\u59cb\u5c31\u4e0d\u65ad\u5730\u6f14\u5316\u7740\u3002\u7f51\u7edc\u8282\u70b9\u4e0d\u65ad\u5730\u589e\u52a0\uff0c\u8282\u70b9\u4e4b\u95f4\u7684\u8fde\u63a5\u4e0d\u65ad\u5730\u589e\u957f\u3002\u7136\u800c\uff0c\u590d\u6742\u7f51\u7edc\u7684\u5f62\u6210\u673a\u5236\u662f\u4ec0\u4e48\uff1f\u5177\u6709\u4ec0\u4e48\u6837\u7684\u6f14\u5316\u89c4\u5f8b\uff1f\u5b83\u4eec\u7684\u6f14\u5316\u673a\u5236\u5bf9\u7f51\u7edc\u7684\u529f\u80fd\u548c\u52a8\u529b\u5b66\u884c\u4e3a\u6709\u4ec0\u4e48\u5f71\u54cd\uff1f\u4e3a\u4e86\u56de\u7b54\u8fd9\u4e9b\u95ee\u9898\uff0c\u79d1\u5b66\u5bb6\u4eec\u5bf9\u590d\u6742\u7f51\u7edc\u7684\u63a2\u7d22\u4ece\u672a\u505c\u6b62\u3002<\/span><\/section>\n

<\/section>\n
\u7f51\u7edc\u79d1\u5b66\u662f\u4e00\u4e2a\u84ec\u52c3\u53d1\u5c55\u7684\u5d2d\u65b0\u4ea4\u53c9\u5b66\u79d1\uff0c\u53ef\u4ee5\u770b\u505a\u590d\u6742\u7cfb\u7edf\u7684\u9aa8\u67b6\uff0c\u6838\u5fc3\u662f\u7814\u7a76\u5404\u79cd\u5927\u578b\u590d\u6742\u7f51\u7edc\u4e4b\u95f4\u7684\u5171\u6027\u548c\u5904\u7406\u5b83\u4eec\u7684\u666e\u9002\u65b9\u6cd5\uff0c\u5176\u7814\u7a76\u5bf9\u4e8e\u53d1\u5c55\u590d\u6742\u7cfb\u7edf\u7684\u57fa\u672c\u7406\u8bba\u53ca\u6784\u5efa\u4ea7\u751f\u4e86\u6781\u5927\u7684\u63a8\u52a8\u4f5c\u7528\u3002<\/span><\/section>\n

<\/section>\n
\u7f51\u7edc\u79d1\u5b66\u7684\u7b2c\u4e09\u4e2a\u5341\u5e74\uff0c\u5df2\u7ecf\u8fc7\u53bb\u4e86\u51e0\u5e74\u3002\u4ece\u56fd\u5185\u5916\u7f51\u7edc\u79d1\u5b66\u7814\u7a76\u7684\u53d1\u5c55\u8d8b\u52bf\u6765\u770b\uff0c\u5404\u79cd\u5404\u6837\u7684\u66f4\u590d\u6742\u7684\u7f51\u7edc\u6a21\u578b\u548c\u7ed3\u6784\u4ee5\u53ca\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u52a8\u529b\u5b66\u5f15\u8d77\u4e86\u4eba\u4eec\u7684\u6781\u5927\u5174\u8da3\u3002\u4e3a\u4e86\u56de\u5e94\u8fd9\u79cd\u8feb\u5207\u9700\u6c42\uff0c \u6211\u4eec\u7f51\u7edc\u79d1\u5b66\u7b2c\u4e09\u671f\u8bfe\u7a0b\u5c06\u56f4\u7ed5\u590d\u6742\u7f51\u7edc\u7684\u6570\u5b66\u5efa\u6a21\u4e0e\u5e94\u7528\u8fdb\u884c\u591a\u89d2\u5ea6\u7684\u4ecb\u7ecd\u3002<\/span><\/section>\n

<\/section>\n
\u96c6\u667a\u5b66\u56ed\u7279\u9080\u9648\u5173\u8363\u3001\u6a0a\u745b\u3001\u5468\u8fdb\u3001\u674e\u7fd4\u3001\u5f20\u6c5f\u3001\u95eb\u5c0f\u52c7\u3001\u5218\u5b97\u534e\u3001\u77f3\u5ddd\u3001\u865e\u6587\u6b66\u3001\u8d75\u6d77\u5174\u3001\u53f2\u5b9a\u534e\u52a0\u5165\u6253\u9020\u7b2c\u4e09\u671f\u8bfe\u7a0b<\/a>\uff0c\u6b22\u8fce\u4f60\u7684\u52a0\u5165\u3002<\/span><\/section>\n

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

<\/section>\n

<\/section>\n
\u8be6\u60c5\u8bf7\u70b9\u51fb\uff1a<\/span><\/section>\n
\u4ece\u6570\u5b66\u5efa\u6a21\u5230\u591a\u5b66\u79d1\u5e94\u7528\u2014\u2014\u7f51\u7edc\u79d1\u5b66\u00b7\u96c6\u667a\u8bfe\u5802\u5168\u65b0\u5347\u7ea7<\/a><\/span><\/strong><\/span><\/section>\n

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

\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/p>\n