{"id":32058,"date":"2022-01-22T18:16:25","date_gmt":"2022-01-22T10:16:25","guid":{"rendered":"https:\/\/swarma.org\/?p=32058"},"modified":"2022-01-22T18:16:25","modified_gmt":"2022-01-22T10:16:25","slug":"%e9%87%8f%e5%8c%96%e6%b6%8c%e7%8e%b0%ef%bc%9a%e4%bf%a1%e6%81%af%e8%ae%ba%e6%96%b9%e6%b3%95%e8%af%86%e5%88%ab%e5%a4%9a%e5%8f%98%e9%87%8f%e6%95%b0%e6%8d%ae%e4%b8%ad%e7%9a%84%e5%9b%a0%e6%9e%9c%e6%b6%8c","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=32058","title":{"rendered":"\u91cf\u5316\u6d8c\u73b0\uff1a\u4fe1\u606f\u8bba\u65b9\u6cd5\u8bc6\u522b\u591a\u53d8\u91cf\u6570\u636e\u4e2d\u7684\u56e0\u679c\u6d8c\u73b0"},"content":{"rendered":"
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Fernando E. Rosas, Pedro A. M. Mediano, Henrik J. Jensen\u7b49<\/span> <\/span>| \u4f5c\u8005<\/strong><\/span><\/p>\n

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Reconciling emergences: An information-theoretic approach to identify causal emergence in multivariate data<\/span><\/span>
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\u6d8c\u73b0\u73b0\u8c61\u901a\u5e38\u88ab\u63cf\u8ff0\u4e3a\u5f3a\u6216\u5f31[1]\u3002\u5f3a\u6d8c\u73b0<\/strong><\/span>\uff08strong emergence\uff09<\/span>\u5bf9\u5e94\u4e8e\u5177\u6709\u4e0d\u53ef\u8fd8\u539f\u56e0\u679c\u6548\u5e94\u7684\u968f\u9644\u7279\u5f81\u8fd9\u4e00\u7565\u5fae\u77db\u76fe\u7684\u60c5\u51b5[2]\uff1b\u5373\u7279\u5f81\u5b8c\u5168\u7531\u5fae\u89c2\u6c34\u5e73\u51b3\u5b9a\uff0c\u4f46\u53ef\u4ee5\u65bd\u52a0\u4e0d\u5b8c\u5168\u7531\u5fae\u89c2\u56e0\u7d20\u89e3\u91ca\u7684\u56e0\u679c\u6548\u5e94<\/span>\uff08\u6587\u732e\u4e2d\u6700\u5e38\u8bba\u8bc1\u7684\u5f3a\u6d8c\u73b0\u60c5\u51b5\u662f\u610f\u8bc6\u7ecf\u9a8c\u76f8\u5bf9\u4e8e\u5176\u76f8\u5e94\u7269\u7406\u57fa\u7840\u7684\u60c5\u51b5[3, 4]\uff09<\/span>\u3002\u5f3a\u6d8c\u73b0\u65e2\u662f\u4e00\u4e2a\u5947\u8ff9\uff0c\u4e5f\u662f\u4e00\u4e2a\u957f\u671f\u4ee4\u4eba\u5934\u75bc\u7684\u54f2\u5b66\u95ee\u9898\uff0c\u5b83\u88ab\u63cf\u8ff0\u4e3a “\u50cf\u9b54\u672f\u4e00\u6837\u4ee4\u4eba\u4e0d\u8212\u670d”\uff0c\u540c\u65f6\u88ab\u6307\u8d23\u5728\u903b\u8f91\u4e0a\u4e0d\u4e00\u81f4[2]\uff0c\u5e76\u5f97\u5230\u4e0d\u5408\u6cd5\u7684\u5f62\u800c\u4e0a\u5b66\u7684\u652f\u6301[5]\u3002\u5f31\u6d8c\u73b0<\/strong><\/span>\uff08weak emergence\uff09<\/span>\u88ab\u63d0\u51fa\u6765\u4f5c\u4e3a\u5f3a\u6d8c\u73b0\u7684\u4e00\u4e2a\u66f4\u6e29\u548c\u7684\u66ff\u4ee3\u65b9\u6848\uff0c\u5373\u5b8f\u89c2\u7279\u5f81\u5728\u5b9e\u8df5\u4e2d\u5177\u6709\u4e0d\u53ef\u8fd8\u539f\u7684\u56e0\u679c\u6548\u5e94\uff0c\u4f46\u5728\u539f\u5219\u4e0a\u5374\u6ca1\u6709\u3002\u5f31\u6d8c\u73b0\u7684\u4e00\u4e2a\u6d41\u884c\u8868\u8ff0\u7531 Bedau \u63d0\u51fa[5]\uff0c\u5b83\u5bf9\u5e94\u7684\u7279\u5f81\u7531\u5fae\u89c2\u5c42\u9762\u7684\u5143\u7d20\u4ee5\u5982\u6b64\u590d\u6742\u7684\u65b9\u5f0f\u4ea7\u751f\uff0c\u4ee5\u81f3\u4e8e\u4e0d\u80fd\u901a\u8fc7\u89e3\u6790\u65b9\u6cd5\u5f97\u51fa\uff0c\u800c\u53ea\u80fd\u901a\u8fc7\u8be6\u5c3d\u7684\u6a21\u62df\u3002\u867d\u7136\u8fd9\u79cd\u8868\u8ff0\u901a\u5e38\u88ab\u79d1\u5b66\u754c\u6240\u63a5\u53d7\uff0c\u4f46\u5b83\u5e76\u4e0d\u9002\u5408\u4e8e\u89e3\u51b3\u5728\u90e8\u5206-\u6574\u4f53\u5173\u7cfb\u4e3a\u4e3b\u8981\u7814\u7a76\u5bf9\u8c61\u7684\u60c5\u51b5\u4e0b\u5173\u4e8e\u6d8c\u73b0\u7684\u5206\u4f53\u8bba<\/span>\uff08mereological\uff09<\/span>\u95ee\u9898\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u5728\u5efa\u7acb\u5bf9\u5f3a\u6d8c\u73b0\u7684\u6df1\u5165\u7406\u89e3\u65f6\uff0c\u90e8\u5206\u56f0\u96be\u5728\u4e8e\u7f3a\u4e4f\u7b80\u5355\u800c\u6e05\u6670\u7684\u5206\u6790\u6a21\u578b\uff0c\u4ee5\u6307\u5bfc\u793e\u533a\u4e2d\u7684\u8ba8\u8bba\u5e76\u4ea7\u751f\u6210\u719f\u7684\u7406\u8bba\u3002\u4eba\u4eec\u5df2\u7ecf\u81f4\u529b\u4e8e\u5f15\u5165\u5bf9\u5f31\u6d8c\u73b0\u7684\u91cf\u5316\u5ea6\u91cf[6]\uff0c\u8fd9\u4f7f\u5f97\u53ef\u4ee5\u7528\u7ec6\u7c92\u5ea6\u7684\u6570\u636e\u9a71\u52a8\u65b9\u6cd5\u66ff\u4ee3\u4f20\u7edf\u7684\u5168\u6216\u65e0\u5206\u7c7b\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4e00\u4e2a\u6709\u5438\u5f15\u529b\u7684\u66ff\u4ee3\u65b9\u6848\u6765\u81ea\u4e8e\u6587\u732e[7]\u4e2d\u4ecb\u7ecd\u3001\u4e4b\u540e\u5728\u6587\u732e [8, 9] \u4e2d\u5f97\u5230\u53d1\u5c55\u7684\u5173\u4e8e\u56e0\u679c\u6d8c\u73b0\u7684\u5de5\u4f5c\uff0c\u5b83\u8868\u660e\u5b8f\u89c2\u53ef\u89c2\u6d4b\u91cf\u6709\u65f6\u53ef\u4ee5\u6bd4\u5fae\u89c2\u53d8\u91cf\u8868\u73b0\u51fa\u66f4\u591a\u7684\u56e0\u679c\u6548\u5e94<\/span>\uff08\u5728 Pearl \u7684do-\u6f14\u7b97 [10] \u6846\u67b6\u5185\u7406\u89e3\uff09<\/span>\u3002\u7136\u800c\uff0c\u8fd9\u4e2a\u6846\u67b6\u4f9d\u8d56\u4e8e\u5728\u5b9e\u8df5\u4e2d\u5f88\u96be\u6ee1\u8db3\u7684\u5f3a\u5047\u8bbe\uff0c\u8fd9\u4e25\u91cd\u963b\u788d\u4e86\u5b83\u7684\u9002\u7528\u6027<\/span>\uff08\u8fd9\u4e00\u70b9\u5c06\u5728\u5b83\u4e0e\u5176\u4ed6\u5b9a\u91cf\u6d8c\u73b0\u7406\u8bba\u7684\u5173\u7cfb\u90e8\u5206\u8fdb\u4e00\u6b65\u9610\u8ff0\uff09<\/span>\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u53d7\u53c2\u8003\u6587\u732e[6, 7]\u7684\u542f\u53d1\uff0c\u5728\u6b64\u6211\u4eec\u5f15\u5165\u4e00\u4e2a\u5b9e\u7528\u4e14\u54f2\u5b66\u4e0a\u65e0\u7f2a\u8bef\u7684\u6846\u67b6\u6765\u7814\u7a76\u591a\u53d8\u91cf\u6570\u636e\u4e2d\u7684\u56e0\u679c\u6d8c\u73b0\u3002\u5728\u6b64\u524d\u5de5\u4f5c[11]\u7684\u57fa\u7840\u4e0a\uff0c\u6211\u4eec\u4ece\u4e00\u4e2a\u5b9e\u9a8c\u8005\u7684\u89d2\u5ea6\u51fa\u53d1\uff0c\u4ed6\u5bf9\u611f\u5174\u8da3\u7684\u5e95\u5c42\u73b0\u8c61\u6ca1\u6709\u9884\u5148\u7684\u77e5\u8bc6\uff0c\u4f46\u6709\u6240\u6709\u76f8\u5173\u53d8\u91cf\u7684\u5145\u8db3\u6570\u636e\uff0c\u53ef\u4ee5\u5bf9\u73b0\u8c61\u8fdb\u884c\u51c6\u786e\u7684\u7edf\u8ba1\u63cf\u8ff0\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u63d0\u51fa\u4e86\u4e00\u4e2a\u56e0\u679c\u6d8c\u73b0\u7684\u5f62\u5f0f\u5b9a\u4e49\uff0c\u5b83\u4e0d\u662f\u5982\u6587\u732e[7]\u4e2d\u90a3\u6837\u4f9d\u8d56\u4e8e\u7c97\u7c92\u5ea6\u7684\u51fd\u6570\uff0c\u800c\u662f\u57fa\u4e8e\u591a\u53d8\u91cf\u7cfb\u7edf\u4e2d\u7684\u4fe1\u606f\u6d41\u89c4\u5f8b\u6765\u89e3\u51b3\u5f3a\u6d8c\u73b0\u7684\u201c\u6096\u8bba\u201d\u7279\u6027<\/strong>\u3002<\/span><\/section>\n
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\u8fd9\u9879\u5de5\u4f5c\u7684\u4e3b\u8981\u8d21\u732e\u662f\u5bf9\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\u8fdb\u884c\u4e86\u4e25\u683c\u7684\u5b9a\u91cf\u5b9a\u4e49\uff0c\u5e76\u5f15\u5165\u56e0\u679c\u89e3\u8026\u7684\u65b0\u6982\u5ff5\u4f5c\u4e3a\u56e0\u679c\u6d8c\u73b0\u7684\u8865\u5145\u65b9\u5f0f\u3002\u53e6\u4e00\u4e2a\u8d21\u732e\u662f\u6269\u5927\u56e0\u679c\u6d8c\u73b0\u5206\u6790\u7684\u9002\u7528\u8303\u56f4\uff0c\u4ee5\u5305\u62ec\u89c2\u5bdf\u6027\u6570\u636e\u7684\u60c5\u51b5\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u56e0\u679c\u5e94\u8be5\u4ece Granger \u6240\u8bf4\u7684\u9884\u6d4b\u80fd\u529b\u7684\u610f\u4e49\u4e0a\u7406\u89e3[12]\u3002\u6b64\u5916\uff0c\u6211\u4eec\u7684\u6846\u67b6\u4ea7\u751f\u4e86\u5b9e\u7528\u7684\u6807\u51c6\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u5e94\u7528\u4e8e\u5927\u578b\u7cfb\u7edf\uff0c\u7ed5\u8fc7\u4e25\u91cd\u9650\u5236\u5148\u524d\u65b9\u6cd5\u7684\u9650\u5236\u6027\u4f30\u8ba1\u95ee\u9898\u3002<\/span><\/section>\n
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\u672c\u6587\u7684\u5176\u4f59\u90e8\u5206\u7ed3\u6784\u5982\u4e0b\u3002\u9996\u5148\uff0c\u201c\u57fa\u672c\u76f4\u89c9\u201d\u90e8\u5206\u8ba8\u8bba\u6d8c\u73b0\u7684\u6700\u5c0f\u793a\u4f8b\u3002\u7136\u540e\uff0c”\u56e0\u679c\u6d8c\u73b0\u7684\u5f62\u5f0f\u7406\u8bba”\u90e8\u5206\u4ecb\u7ecd\u7406\u8bba\u7684\u6838\u5fc3\uff0c”\u6d4b\u91cf\u6d8c\u73b0”\u90e8\u5206\u8ba8\u8bba\u4ece\u5b9e\u9a8c\u6570\u636e\u4e2d\u91cf\u5316\u6d8c\u73b0\u7684\u5b9e\u9645\u65b9\u6cd5\u3002\u6211\u4eec\u7684\u6846\u67b6\u5728\u4e00\u4e9b\u6848\u4f8b\u7814\u7a76\u4e2d\u5f97\u5230\u4e86\u8bf4\u660e\uff0c\u8fd9\u5728\u201c\u6848\u4f8b\u7814\u7a76\u201d\u90e8\u5206\u3002\u6700\u540e\uff0c\u5728\u201c\u8ba8\u8bba\u201d\u4e00\u8282\u4e2d\uff0c\u6211\u4eec\u8ba8\u8bba\u4e86\u6211\u4eec\u7684\u53d1\u73b0\u6240\u5e26\u6765\u7684\u4e00\u4e9b\u5f71\u54cd\u3002<\/span><\/section>\n
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2. \u57fa\u672c\u76f4\u89c9<\/strong><\/strong><\/p>\n<\/section>\n

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\u4e3a\u4e86\u7ed9\u6211\u4eec\u7684\u76f4\u89c9\u6253\u4e0b\u57fa\u7840\uff0c\u8ba9\u6211\u4eec\u9996\u5148\u4ecb\u7ecd\u4e00\u4e9b\u6700\u5c0f\u793a\u4f8b\uff0c\u8fd9\u4e9b\u4f8b\u5b50\u4f53\u73b0\u4e86\u56e0\u679c\u6d8c\u73b0\u884c\u4e3a\u7684\u51e0\u4e2a\u5173\u952e\u6982\u5ff5\u3002\u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u8003\u8651\u7531n\u4e2a\u90e8\u5206\u7ec4\u6210\u7684\u7cfb\u7edf\uff0c\u7531\u4e8c\u8fdb\u5236\u5411\u91cf<\/span>\u63cf\u8ff0\uff0c\u5b83\u4eec\u6309\u7167\u8f6c\u79fb\u6982\u7387<\/span>\u7ecf\u5386\u9a6c\u5c14\u53ef\u592b\u8fc7\u7a0b\u7684\u968f\u673a\u52a8\u529b\u5b66\u3002\u4e3a\u4e86\u7b80\u5355\u8d77\u89c1\uff0c\u6211\u4eec\u5047\u8bbe\u5728\u65f6\u95f4t\uff0c\u7cfb\u7edf\u5904\u4e8e\u4e00\u4e2a\u5b8c\u5168\u968f\u673a\u7684\u4f4d\u5f62\uff08\u5373<\/span>\uff09\u3002\u4ece\u8fd9\u91cc\u5f00\u59cb\uff0c\u6211\u4eec\u8003\u8651\u4e09\u79cd\u6f14\u5316\u89c4\u5219\u3002<\/span>
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\u4f8b1\uff1a<\/span><\/strong>\u8003\u8651\u4e00\u4e2a\u65f6\u95f4\u6f14\u5316\uff0c\u5176\u4e2d<\/span>\u7684\u5947\u5076\u6027\u4ee5\u6982\u7387<\/span>\u4fdd\u5b58\u3002\u6570\u5b66\u4e0a\uff0c<\/span><\/section>\n

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\u5bf9\u6240\u6709<\/span>\uff0c\u5f53<\/span>\u4e3a\u5076\u6570\u65f6\uff0c<\/span>\u4e3a1\uff1b\u5f53<\/span>\u4e3a\u5947\u6570\u65f6\uff0c<\/span>\u4e3a0\u3002\u7b80\u5355\u5730\u8bf4\uff1a<\/span>\u4e3a\u4ece\u6240\u6709\u4e0e<\/span>\u5947\u5076\u6027\u76f8\u540c\u7684\u5b57\u7b26\u4e32\u96c6\u5408\u4e2d\u968f\u673a\u62bd\u53d6\u7684\u6837\u672c\u7684\u6982\u7387\u4e3a \u03b3\uff0c\u6765\u81ea\u4e0e\u5947\u5076\u6027\u76f8\u53cd\u7684\u5b57\u7b26\u4e32\u7684\u6837\u672c\u7684\u6982\u7387\u4e3a 1-\u03b3\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u8fd9\u4e2a\u6f14\u5316\u89c4\u5219\u6709\u8bb8\u591a\u6709\u8da3\u7684\u6027\u8d28\u3002\u9996\u5148\uff0c\u8be5\u7cfb\u7edf\u6709\u4e00\u4e2a\u975e\u5e73\u5eb8\u7684\u56e0\u679c\u7ed3\u6784\uff0c\u56e0\u4e3a\u672a\u6765\u72b6\u6001\u7684\u4e00\u4e9b\u5c5e\u6027<\/span>\uff08\u5176\u5947\u5076\u6027\uff09<\/span>\u53ef\u4ee5\u4ece\u8fc7\u53bb\u72b6\u6001\u4e2d\u9884\u6d4b\u51fa\u6765\u3002\u7136\u800c\uff0c\u8fd9\u79cd\u7ed3\u6784\u53ea\u5728\u96c6\u4f53\u5c42\u9762\u4e0a\u662f\u660e\u663e\u7684\uff0c\u56e0\u4e3a\u6ca1\u6709\u4efb\u4f55\u4e00\u4e2a\u53d8\u91cf\u5bf9\u5176\u81ea\u8eab\u6216\u4efb\u4f55\u5176\u4ed6\u53d8\u91cf\u7684\u6f14\u5316\u6709\u9884\u6d4b\u80fd\u529b<\/span>\uff08\u89c1\u56fe1\uff09<\/span>\u3002\u6b64\u5916\uff0c\u5373\u4f7f\u662f\u7cfb\u7edf\u7684\u5b8c\u6574\u8fc7\u53bb<\/span>\u5bf9\u4efb\u4f55\u5355\u4e2a\u4e2a\u4f53\u7684\u672a\u6765<\/span>\u4e5f\u6ca1\u6709\u9884\u6d4b\u80fd\u529b\u3002\u8fd9\u79cd\u60c5\u51b5\u663e\u793a\u4e86\u4e00\u79cd\u6781\u7aef\u7684\u56e0\u679c\u7684\u51fa\u73b0\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u201c\u56e0\u679c\u89e3\u8026<\/strong>\u201d\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5947\u5076\u6027\u9884\u6d4b\u81ea\u5df1\u7684\u6f14\u5316\uff0c\u4f46\u6ca1\u6709\u4e00\u4e2a\u5143\u7d20<\/span>\uff08\u6216\u5143\u7d20\u7684\u5b50\u96c6\uff09<\/span>\u53ef\u4ee5\u9884\u6d4b\u4efb\u4f55\u5176\u4ed6\u5143\u7d20\u7684\u6f14\u5316\u3002<\/span><\/section>\n
 <\/span><\/section>\n
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\u56fe1. \u56e0\u679c\u6d8c\u73b0\u7684\u52a8\u529b\u5b66\u6f14\u5316\u7684\u6700\u5c0f\u793a\u4f8b\u3002\u5728\u5de6\u56fe\uff08\u4f8b1\uff09\u4e2d\uff0c\u7cfb\u7edf\u7684\u5947\u5076\u6027\u503e\u5411\u4e8e\u88ab\u4fdd\u7559\uff0c\u800c\u5e95\u5c42\u5143\u7d20\u4e4b\u95f4\u6ca1\u6709\u53d1\u751f\u76f8\u4e92\u4f5c\u7528\uff0c\u8fd9\u662f\u4e00\u4e2a\u56e0\u679c\u89e3\u8026\u7684\u4f8b\u5b50\u3002\u5728\u53f3\u56fe\uff08\u4f8b2\uff09\u4e2d\uff0c\u7cfb\u7edf\u7684\u5947\u5076\u6027\u53ea\u51b3\u5b9a\u4e00\u4e2a\u5143\u7d20\uff0c\u5bf9\u5e94\u4e8e\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\u3002<\/span><\/p>\n

 <\/span><\/section>\n
\u4f8b2\uff1a<\/span><\/strong>\u73b0\u5728\u8003\u8651\u4e00\u4e2a\u7cfb\u7edf\uff0c<\/span>\u7684\u5947\u5076\u6027\u51b3\u5b9a\u4e86<\/span>\uff08\u5373<\/span>\uff09\uff0c\u800c<\/span>\u65f6\u7684<\/span>\u662f\u4e00\u4e2a\u72ec\u7acb\u4e8e<\/span>\u7684\u968f\u673a\u629b\u786c\u5e01\u60c5\u5f62\uff08\u89c1\u56fe1\uff09\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c<\/span>\u5b8c\u5168\u51c6\u786e\u5730\u9884\u6d4b<\/span>\uff0c\u540c\u65f6\u53ef\u4ee5\u9a8c\u8bc1\uff0c\u5bf9\u4e8e\u6240\u6709\u7684<\/span>\uff0c<\/span>\u3002\u56e0\u6b64\uff0c\u5728\u8fd9\u4e2a\u6f14\u5316\u89c4\u5219\u4e0b\uff0c\u6574\u4e2a\u7cfb\u7edf\u5bf9\u4e00\u4e2a\u7279\u5b9a\u7684\u5143\u7d20\u5177\u6709\u56e0\u679c\u6548\u5e94\uff0c\u5c3d\u7ba1\u8fd9\u4e2a\u6548\u5e94\u4e0d\u80fd\u5f52\u56e0\u4e8e\u4efb\u4f55\u5355\u72ec\u7684\u5143\u7d20<\/span>\uff08\u76f8\u5173\u8ba8\u8bba\u89c1\u6587\u732e[13]\uff09<\/span>\u3002\u8fd9\u662f\u4e00\u4e2a\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c<\/strong>\u7684\u6700\u5c0f\u4f8b\u5b50\u3002 <\/span><\/section>\n
 <\/span><\/section>\n
\u4f8b3\uff1a<\/span><\/strong>\u73b0\u5728\u8ba9\u6211\u4eec\u6765\u7814\u7a76\u4e00\u4e2a\u5305\u542b\u4f8b1\u548c\u4f8b2\u4e24\u79cd\u673a\u5236\u7684\u6f14\u5316\u89c4\u5219\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u8003\u8651\uff1a<\/span><\/section>\n

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

<\/section>\n
\u4e0e\u4f8b1\u4e00\u6837\uff0c<\/span>\u7684\u5947\u5076\u6027\u88ab\u8f6c\u79fb\u5230<\/span>\u7684\u6982\u7387\u4e3a\u03b3\uff1b\u9664\u6b64\u4e4b\u5916\uff0c\u53ef\u4ee5\u4fdd\u8bc1<\/span>\u3002\u56e0\u6b64\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4e0d\u4ec5\u6709\u4e00\u4e2a\u65e0\u6cd5\u4ece\u90e8\u5206\u89e3\u91ca\u7684\u5b8f\u89c2\u6548\u5e94\uff0c\u540c\u65f6\u8fd8\u6709\u53e6\u4e00\u4e2a\u4ece\u6574\u4f53\u5230\u5176\u4e2d\u4e00\u4e2a\u90e8\u5206\u7684\u6548\u5e94\u3002\u91cd\u8981\u7684\u662f\uff0c\u8fd9\u4e24\u79cd\u6548\u5e94\u662f\u72ec\u7acb\u5b58\u5728\u7684\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u4ee5\u4e0a\u662f\u4e0d\u80fd\u4ece\u57fa\u672c\u7ec4\u6210\u90e8\u5206\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u51fa\u53d1\uff0c\u8ffd\u8e2a\u5230\u6574\u4f53\u52a8\u529b\u5b66\u6f14\u5316\u89c4\u5f8b\u7684\u6700\u5c0f\u793a\u4f8b\u3002\u4f8b1\u663e\u793a\u4e86\u4e00\u4e2a\u96c6\u4f53\u5c5e\u6027\u5982\u4f55\u5728\u4e0d\u4e0e\u5e95\u5c42\u5143\u7d20\u76f8\u4e92\u4f5c\u7528\u7684\u60c5\u51b5\u4e0b\u4f20\u64ad\uff1b\u4f8b2\u663e\u793a\u4e86\u4e00\u4e2a\u96c6\u4f53\u5c5e\u6027\u5982\u4f55\u5f71\u54cd\u7279\u5b9a\u90e8\u5206\u7684\u6f14\u5316\uff1b\u4f8b3\u663e\u793a\u4e86\u8fd9\u4e24\u79cd\u73b0\u8c61\u5982\u4f55\u5728\u540c\u4e00\u4e2a\u7cfb\u7edf\u4e2d\u53d1\u751f\u3002\u6240\u6709\u8fd9\u4e9b\u95ee\u9898\u90fd\u7531\u4e0b\u4e00\u8282\u4e2d\u63d0\u51fa\u7684\u7406\u8bba\u6765\u5f62\u5f0f\u5316\u63cf\u8ff0\u3002<\/span><\/section>\n
 <\/span><\/section>\n
 <\/span><\/section>\n

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<\/svg><\/section>\n<\/section>\n<\/section>\n
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3. \u56e0\u679c\u6d8c\u73b0\u7684\u5f62\u5f0f\u7406\u8bba<\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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


<\/p>\n

\u672c\u8282\u4ecb\u7ecd\u4e86\u6211\u4eec\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u7684\u4e3b\u8981\u5185\u5bb9\u3002\u4e3a\u4e86\u660e\u786e\u601d\u8def\uff0c\u6211\u4eec\u8bbe\u60f3\u4e00\u4e2a\u79d1\u5b66\u5bb6\u6d4b\u91cf\u4e00\u4e2a\u7531n\u4e2a\u90e8\u5206\u7ec4\u6210\u7684\u7cfb\u7edf\u3002\u5047\u8bbe\u79d1\u5b66\u5bb6\u5728\u4e00\u6bb5\u65f6\u95f4\u5185\u5b9a\u65f6\u6d4b\u91cf\u7cfb\u7edf\uff0c\u800c\u8fd9\u4e9b\u6d4b\u91cf\u7684\u7ed3\u679c\u7528<\/span>\u8868\u793a\uff0c\u5176\u4e2d<\/span>\u5bf9\u5e94\u4e8e\u7b2ci\u90e8\u5206\u5728\u65f6\u95f4<\/span>\u7684\u72b6\u6001\uff0c<\/span>\u4e3a\u76f8\u7a7a\u95f4\u3002\u5f53\u63d0\u5230\u4e00\u4e2a\u90e8\u5206\u7684\u96c6\u5408\u65f6\uff0c\u6211\u4eec\u4f7f\u7528\u7684\u7b26\u53f7\u662f<\/span>\uff0c\u5176\u4e2d<\/span>\u3002\u6211\u4eec\u8fd8\u4f7f\u7528\u4e86\u7b80\u77ed\u7684\u7b26\u53f7<\/span>\u3002<\/span>
<\/section>\n
 <\/span><\/section>\n

\n
3.1 \u968f\u9644\u6027<\/span><\/strong><\/span><\/section>\n<\/h2>\n
 <\/span><\/section>\n
\u6211\u4eec\u7684\u5206\u6790\u8003\u8651\u4e86\u7cfb\u7edf\u6f14\u5316\u7684\u4e24\u4e2a\u65f6\u95f4\u70b9\uff0c\u5206\u522b\u8868\u793a\u4e3a t \u548c t’\uff0c\u5176\u4e2d t<t’\u3002\u76f8\u5e94\u7684\u52a8\u529b\u5b66\u7f16\u7801\u4e3a\u8f6c\u79fb\u6982\u7387<\/span>\u3002\u6211\u4eec\u8003\u8651\u901a\u8fc7\u6761\u4ef6\u6982\u7387<\/span>\u4ea7\u751f\u7684\u7279\u5f81<\/span>\uff0c\u8fd9\u4e9b\u7279\u5f81\u4e0e\u5e95\u5c42\u7cfb\u7edf\u5177\u6709\u968f\u9644\u6027<\/span>\uff08supervenience\uff09<\/span>\uff1b\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u7cfb\u7edf\u5728 t \u65f6\u95f4\u7684\u5b8c\u6574\u72b6\u6001\u53ef\u4ee5\u5b8c\u5168\u51c6\u786e\u5730\u77e5\u9053\uff0c\u8f6c\u79fb\u6982\u7387\u5bf9 t’>t \u65f6\u95f4\u7684\u672a\u6765\u72b6\u6001\u4e0d\u63d0\u4f9b\u4efb\u4f55\u9884\u6d4b\u80fd\u529b\u3002\u6211\u4eec\u5728\u4e0b\u9762\u7684\u5b9a\u4e49\u4e2d\u5f62\u5f0f\u5316\u5730\u8bf4\u660e\u8fd9\u4e00\u70b9\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u5b9a\u4e491\uff1a<\/span><\/strong>\u8bbe<\/span>\u4e3a\u4e00\u968f\u673a\u8fc7\u7a0b\uff0c\u5982\u679c\u5bf9\u4e8e\u6240\u6709<\/span>\uff0c<\/span>\u5f62\u6210\u9a6c\u5c14\u53ef\u592b\u94fe\uff0c\u90a3\u4e48\u79f0<\/span>\u5bf9<\/span>\u5177\u6709\u968f\u9644\u6027\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4e0a\u9762\u7684\u6761\u4ef6\u76f8\u5f53\u4e8e\u8981\u6c42\u5f53<\/span>\u7ed9\u5b9a\u65f6\uff0c<\/span>\u5728\u7edf\u8ba1\u4e0a\u4e0e<\/span>\u65e0\u5173\u3002\u56fe2\u8bf4\u660e\u4e86\u968f\u9644\u7279\u5f81\u548c\u5e95\u5c42\u7cfb\u7edf\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/span><\/section>\n
 <\/span><\/section>\n
<\/section>\n

\u56fe2. \u56e0\u679c\u6d8c\u73b0\u5173\u7cfb\u56fe\u3002\u56e0\u679c\u6d8c\u73b0\u7684\u7279\u5f81\u5177\u6709\u8d85\u8d8a\u4e2a\u522b\u6210\u5206\u7684\u9884\u6d4b\u80fd\u529b\u3002\u5f53\u8fd9\u79cd\u9884\u6d4b\u80fd\u529b\u6307\u5411\u5355\u4e2a\u5143\u7d20\u65f6\uff0c\u5c31\u4f1a\u53d1\u751f\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\uff1b\u5f53\u5b83\u6307\u5411\u81ea\u8eab\u6216\u5176\u4ed6\u9ad8\u9636\u7279\u5f81\u65f6\uff0c\u5c31\u4f1a\u53d1\u751f\u56e0\u679c\u89e3\u8026\u3002<\/span><\/p>\n

 <\/span><\/section>\n
\u8fd9\u4e00\u5bf9\u968f\u9644\u6027\u7684\u5f62\u5f0f\u5316\u523b\u753b\u4e86\u7279\u5f81<\/span>\uff08\u5b83\u5b8c\u5168\u7531\u7cfb\u7edf\u5728\u7ed9\u5b9a\u65f6\u95f4t\u7684\u72b6\u6001\u51b3\u5b9a\uff09<\/span>\uff0c\u5e76\u4e14\u5141\u8bb8\u7279\u5f81\u662f\u6709\u566a\u58f0\u7684\u2014\u2014\u8fd9\u5bf9\u6211\u4eec\u7684\u7ed3\u679c\u5e76\u4e0d\u5173\u952e\uff0c\u4f46\u5bf9\u4e8e\u5c06\u5176\u9002\u7528\u9886\u57df\u6269\u5c55\u5230\u5b9e\u9645\u573a\u666f\u662f\u5f88\u6709\u7528\u7684\u3002\u5b9e\u9645\u4e0a\uff0c\u5b9a\u4e491\u5305\u62ec\u4f5c\u4e3a\u7279\u5b9a\u60c5\u51b5\u7684\u786e\u5b9a\u6027\u51fd\u6570F\uff1a<\/span>\uff0c\u4f7f\u5f97<\/span>\uff0c\u4ee5\u53ca\u5728\u89c2\u5bdf\u566a\u58f0\u4e0b\u8ba1\u7b97\u7684\u7279\u5f81\uff0c\u4f8b\u5982<\/span>\uff0c\u5176\u4e2d<\/span>\u5728\u6240\u6709t\u4e0b\u4e0e<\/span>\u65e0\u5173\u3002\u76f8\u53cd\uff0c\u5229\u7528<\/span>\u5728\u591a\u4e2a\u65f6\u95f4\u70b9\u7684\u503c\uff08\u5982<\/span>\u7684\u5085\u91cc\u53f6\u53d8\u6362\uff09\u8ba1\u7b97\u7684\u7279\u5f81\u901a\u5e38\u4e0d\u5177\u6709\u968f\u9644\u6027\u3002<\/span><\/section>\n
 <\/span><\/section>\n

\n
3.2 \u90e8\u5206\u4fe1\u606f\u5206\u89e3<\/span><\/strong><\/section>\n<\/h2>\n
 <\/span><\/section>\n
\u6211\u4eec\u7684\u7406\u8bba\u57fa\u4e8e\u90e8\u5206\u4fe1\u606f\u5206\u89e3<\/strong><\/span>\uff08Partial Information Decomposition\uff0cPID\uff09<\/span>\u6846\u67b6[14]\uff0c\u5b83\u4e3a\u63a8\u7406\u591a\u53d8\u91cf\u7cfb\u7edf\u4e2d\u7684\u4fe1\u606f\u63d0\u4f9b\u4e86\u5f3a\u5927\u7684\u5de5\u5177\u3002\u7b80\u800c\u8a00\u4e4b\uff0cPID \u5c06n\u4e2a\u6e90 <\/span>\u63d0\u4f9b\u7684\u5173\u4e8e\u76ee\u6807\u53d8\u91cfY\u7684\u4fe1\u606f\u4ee5\u4fe1\u606f\u539f\u5b50<\/span>\uff08information atoms\uff09<\/span>\u7684\u5f62\u5f0f\u5206\u89e3\uff1a<\/span><\/section>\n

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

<\/section>\n
\u5176\u4e2d<\/span>\u662f\u4e00\u5957\u53cd\u94fe\u96c6\u5408<\/span>\uff08antichain collections\uff09<\/span>[14]\u3002\u76f4\u89c2\u5730\u8bf4\uff0c\u5bf9<\/span>\uff0c<\/span>\u4ee3\u8868\u53d8\u91cf\u96c6\u5408<\/span>\u63d0\u4f9b\u3001\u4f46\u5176\u5b50\u96c6\u5408\u4e0d\u63d0\u4f9b\u7684\u5197\u4f59\u4fe1\u606f<\/strong>\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8en=2\u4e2a\u6e90\u53d8\u91cf\uff0c\u03b1 = {{1}{2}} \u5bf9\u5e94\u4e8e\u4e24\u4e2a\u6e90\u63d0\u4f9b\u7684\u5173\u4e8eY\u7684\u4fe1\u606f\uff0c\u03b1 = {{i}} \u5bf9\u5e94\u4e8e Xi<\/sub> \u5355\u72ec\u63d0\u4f9b\u7684\u4fe1\u606f\u3002\u6700\u6709\u8da3\u7684\u662f\uff0c\u03b1 = {{12}} \u5bf9\u5e94\u4e8e\u4e24\u4e2a\u6e90\u5171\u540c\u63d0\u4f9b\u4f46\u4e0d\u5355\u72ec\u63d0\u4f9b\u7684\u4fe1\u606f\uff0c\u8fd9\u901a\u5e38\u88ab\u79f0\u4e3a\u4fe1\u606f\u534f\u540c<\/span>\uff08informational synergy\uff09<\/span>\u3002<\/span><\/section>\n
 <\/span><\/section>\n
PID \u7684\u4e00\u4e2a\u7f3a\u70b9\u662f\u4fe1\u606f\u539f\u5b50\u7684\u6570\u91cf\uff08\u5373<\/span>\u7684\u52bf\uff09\u968f\u7740\u6e90\u7684\u6570\u91cf\u8d85\u6307\u6570\u589e\u957f\u3002\u56e0\u6b64\uff0c\u6839\u636e\u7279\u5b9a\u6807\u51c6\u5bf9\u5206\u89e3\u8fdb\u884c\u7c97\u7c92\u5316\u662f\u5f88\u6709\u7528\u7684\u3002\u8fd9\u91cc\u6211\u4eec\u5f15\u5165n\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684 k \u9636\u534f\u540c\u6548\u5e94<\/strong><\/span>\uff08k th-order synergy\uff09<\/span>\u7684\u6982\u5ff5\uff0c\u5176\u8ba1\u7b97\u65b9\u6cd5\u4e3a\uff1a<\/span><\/section>\n

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

<\/span><\/section>\n
\u5176\u4e2d<\/span>\u3002\u76f4\u89c2\u5730\u8bf4\uff0c<\/span>\u5bf9\u5e94\u7684\u662f\u5173\u4e8e\u76ee\u6807\u7684\u4fe1\u606f\uff0c\u8fd9\u4e9b\u4fe1\u606f\u7531\u6574\u4e2a<\/span>\u63d0\u4f9b\uff0c\u4f46\u4e0d\u5305\u542b\u5728\u4efb\u4f55\u7531k\u4e2a\u6216\u66f4\u5c11\u90e8\u5206\u7ec4\u6210\u7684\u96c6\u5408\u4e2d\uff0c\u5f53\u8fd9\u4e9b\u90e8\u5206\u4e0e\u5176\u4ed6\u90e8\u5206\u5206\u5f00\u8003\u8651\u65f6\u3002\u56e0\u6b64\uff0c<\/span>\u53ea\u5305\u542b\u6709k\u4e2a\u4ee5\u4e0a\u6e90\u7684\u7ec4\u7684\u96c6\u5408\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u540c\u6837\u5730\uff0c\u6211\u4eec\u5f15\u5165<\/span>\u7684\u72ec\u7279\u4fe1\u606f<\/strong><\/span>\uff08unique information\uff09<\/span>\uff0c\u5176\u4e2d<\/span>\u4e3a\u5173\u4e8e\u6700\u591ak\u4e2a\u5176\u4ed6\u53d8\u91cf\u7684\u96c6\u5408\uff0c\u5176\u8ba1\u7b97\u516c\u5f0f\u4e3a\uff1a<\/span><\/section>\n

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<\/section>\n

<\/span><\/section>\n
\u5176\u4e2d<\/span>\uff0c<\/span>\u4e3a<\/span>\u4e2d\u4e0d\u5305\u542b\u5728<\/span>\u4e2d\u7684\u6240\u6709\u53d8\u91cf\u3002\u7b80\u5355\u5730\u8bf4\uff0c<\/span>\u8868\u793a<\/span>\u643a\u5e26\u7684\u5173\u4e8e<\/span>\u7684\u4fe1\u606f\uff0c\u4f46\u662f<\/span>\u4e2d\u4efb\u4f55k\u4e2a\u6216\u66f4\u5c11\u7684\u53d8\u91cf\u7ec4\u90fd\u4e0d\u5177\u6709\u8fd9\u4e9b\u4fe1\u606f\u3002\u6ce8\u610f\u8fd9\u4e9b\u7c97\u7c92\u5316\u7684\u9879\u53ef\u4ee5\u7528\u6765\u5efa\u7acb\u9644\u5f55S1<\/span>\uff08\u7b2c1\u8282\uff09<\/span>\u4e2d\u63cf\u8ff0\u7684<\/span>\u7684\u4e00\u822c\u5206\u89e3\uff0c\u5176\u5c5e\u6027\u5728\u9644\u5f55S1<\/span>\uff08\u7b2c2\u8282\uff09<\/span>\u4e2d\u5f97\u5230\u8bc1\u660e\u3002<\/span><\/section>\n
 <\/span><\/section>\n
PID\u7684\u4e00\u4e2a\u7279\u70b9\u662f\uff0c\u5b83\u89c4\u5b9a\u4e86\u4fe1\u606f\u539f\u5b50\u7684\u7ed3\u6784\u548c\u5b83\u4eec\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u4f46\u5b83\u6ca1\u6709\u89c4\u5b9a\u4e00\u4e2a\u7279\u5b9a\u7684\u51fd\u6570\u5f62\u5f0f\u6765\u8ba1\u7b97<\/span>\u3002\u4e8b\u5b9e\u4e0a\uff0c\u53ea\u6709\u4e00\u4e2a\u4fe1\u606f\u539f\u5b50\u5fc5\u987b\u88ab\u6307\u5b9a\u6765\u786e\u5b9a\u6574\u4e2aPID\u2014\u2014\u901a\u5e38\u662f\u6240\u6709\u5355\u4e2a\u5143\u7d20\u4e4b\u95f4\u7684\u5197\u4f59[14]\u3002\u5728PID\u6587\u732e\u4e2d\uff0c\u6709\u591a\u4e2a\u5173\u4e8e<\/span>\u7684\u5177\u4f53\u51fd\u6570\u5f62\u5f0f\u7684\u5efa\u8bae\uff0c\u53ef\u4ee5\u89c1\u6587\u732e[15-18]\u3002\u4e00\u4e2a\u57fa\u4e8e\u6700\u8fd1\u7684PID[19]\u7684\u5b8c\u5168\u8ba1\u7b97\u4fe1\u606f\u539f\u5b50\u7684\u7279\u6b8a\u65b9\u6cd5\u5c06\u5728\u201c\u901a\u8fc7\u534f\u540c\u901a\u9053\u6d4b\u91cf\u6d8c\u73b0\u201d\u4e00\u8282\u4e2d\u8ba8\u8bba\u3002<\/span><\/section>\n
     <\/span><\/section>\n
\u65b9\u4fbf\u7684\u662f\uff0c\u6211\u4eec\u7684\u7406\u8bba\u5e76\u4e0d\u4f9d\u8d56\u4e8ePID\u7684\u5177\u4f53\u51fd\u6570\u5f62\u5f0f\uff0c\u800c\u53ea\u662f\u4f9d\u8d56\u4e8e\u9644\u5f55S1<\/span>\uff08\u7b2c2\u8282\uff09<\/span>\u4e2d\u7cbe\u786e\u8868\u8ff0\u7684\u51e0\u4e2a\u57fa\u672c\u5c5e\u6027\u3002\u56e0\u6b64\uff0c\u8be5\u7406\u8bba\u53ef\u4ee5\u4f7f\u7528\u4efb\u4f55PID\u8fdb\u884c\u5b9e\u4f8b\u5316\uff0c\u53ea\u8981\u8fd9\u4e9b\u5c5e\u6027\u5f97\u5230\u6ee1\u8db3\u3002\u91cd\u8981\u7684\u662f\uff0c\u5982\u201c\u5927\u578b\u7cfb\u7edf\u7684\u5b9e\u7528\u6807\u51c6\u201d\u4e00\u8282\u6240\u793a\uff0c\u8be5\u7406\u8bba\u5141\u8bb8\u63a8\u5bfc\u51fa\u72ec\u7acb\u4e8e\u6240\u9009PID\u7684\u5b9e\u7528\u5ea6\u91cf\u3002<\/span><\/section>\n
 <\/span><\/section>\n

\n
3.3 \u5b9a\u4e49\u56e0\u679c\u6d8c\u73b0<\/span><\/strong><\/section>\n

<\/span><\/section>\n<\/h2>\n
\u6709\u4e86PID\u7684\u5de5\u5177\uff0c\u73b0\u5728\u6211\u4eec\u4ecb\u7ecd\u5bf9\u56e0\u679c\u6d8c\u73b0\u7684\u5f62\u5f0f\u5b9a\u4e49\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u5b9a\u4e492\uff1a<\/span><\/strong>\u5bf9\u4e8e\u4e00\u4e2a\u7531<\/span>\u63cf\u8ff0\u7684\u7cfb\u7edf\uff0c\u4e00\u4e2a\u968f\u9644\u7279\u5f81<\/span>\u88ab\u8ba4\u4e3a\u8868\u73b0\u51fa k \u9636\u56e0\u679c\u6d8c\u73b0\uff0c\u5982\u679c<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n
 <\/span><\/section>\n
\u76f8\u5e94\u5730\uff0c\u5f53\u4e00\u4e2a\u968f\u9644\u7279\u5f81<\/span>\u5177\u6709\u4e0d\u53ef\u8fd8\u539f\u56e0\u679c\u6548\u5e94\u65f6\uff0c\u5373\u5f53\u5b83\u65bd\u52a0\u7684\u56e0\u679c\u6548\u5e94\u4e0d\u662f\u7531\u7cfb\u7edf\u7684\u4efb\u4f55\u90e8\u5206\u4f20\u9012\u65f6\uff0c\u56e0\u679c\u6d8c\u73b0\u5c31\u53d1\u751f\u4e86\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c<\/span>\u4ee3\u8868\u7cfb\u7edf\u4e2d\u6d8c\u73b0\u7684\u96c6\u4f53\u5c5e\u6027\uff0c\u5982\u679c\u5b83\uff1a1\uff09\u5305\u542b\u52a8\u6001\u76f8\u5173\u7684\u4fe1\u606f<\/span>\uff08\u8fd9\u610f\u5473\u7740\u5b83\u9884\u6d4b\u7cfb\u7edf\u7684\u672a\u6765\u6f14\u5316\uff09<\/span>\uff1b2\uff09\u8fd9\u4e2a\u4fe1\u606f\u8d85\u51fa\u4e86\u7cfb\u7edf\u4e2dk\u4e2a\u90e8\u5206\u7684\u7fa4\u4f53\u5355\u72ec\u8003\u8651\u65f6\u6240\u7ed9\u51fa\u7684\u4fe1\u606f\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u4e3a\u4e86\u66f4\u597d\u5730\u7406\u89e3\u8fd9\u4e2a\u5b9a\u4e49\u7684\u542b\u4e49\uff0c\u6211\u4eec\u7814\u7a76\u5b83\u7684\u4e00\u4e9b\u57fa\u672c\u5c5e\u6027\u3002<\/span><\/section>\n
 <\/span><\/section>\n

\u5f15\u74061\uff1a<\/span><\/strong>\u8003\u8651\u4e00\u4e2a\u7279\u5f81<\/span>\uff0c\u5b83\u5728<\/span>\u4e0a\u8868\u73b0\u51fa\u4e00\u9636\u56e0\u679c\u6d8c\u73b0\uff0c\u90a3\u4e48\uff1a<\/span><\/p>\n

\uff081\uff09\u7cfb\u7edf\u7684\u7ef4\u5ea6\u7b26\u5408<\/span>\u3002<\/span><\/p>\n

\uff082\uff09\u4e0d\u5b58\u5728\u4e00\u4e2a\u786e\u5b9a\u6027\u7684\u51fd\u6570<\/span>\uff0c\u4f7f<\/span>\uff0c\u5bf9\u4e8e\u4efb\u4f55 j = 1, …, n\u3002<\/span><\/section>\n

<\/section>\n
\u8bc1\u660e\u89c1S1\u9644\u5f55\u7b2c3\u8282\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u8fd9\u4e24\u4e2a\u5c5e\u6027\u5c06\u56e0\u679c\u6d8c\u73b0\u786e\u7acb\u4e3a\u4e00\u79cd\u57fa\u672c\u7684\u96c6\u4f53\u73b0\u8c61\u3002\u5b9e\u9645\u4e0a\uff0c\u5c5e\u6027\uff081\uff09\u6307\u51fa\uff0c\u56e0\u679c\u6d8c\u73b0\u662f\u591a\u53d8\u91cf\u7cfb\u7edf\u7684\u4e00\u4e2a\u5c5e\u6027\uff0c\u800c\u5c5e\u6027\uff082\uff09\u6307\u51fa\uff0c\u5982\u679c<\/span>\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e2a\u5355\u4e00\u53d8\u91cf\u5b8c\u7f8e\u9884\u6d4b\uff0c\u5b83\u5c31\u4e0d\u53ef\u80fd\u6709\u6d8c\u73b0\u884c\u4e3a\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u4e3a\u4e86\u4f7f\u7528\u5b9a\u4e492\uff0c\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u53ef\u4ee5\u6d4b\u8bd5\u7684\u5019\u9009\u7279\u5f81<\/span>\u3002\u7136\u800c\uff0c\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u5e76\u6ca1\u6709\u660e\u663e\u7684\u5019\u9009\u6d8c\u73b0\u7279\u5f81\uff0c\u5bf9\u4e8e\u8fd9\u79cd\u60c5\u51b5\uff0c\u5b9a\u4e492\u4f3c\u4e4e\u6709\u95ee\u9898\u3002\u6211\u4eec\u7684\u4e0b\u4e00\u4e2a\u7ed3\u679c\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5b8c\u5168\u57fa\u4e8e\u7cfb\u7edf\u52a8\u529b\u5b66\u7684\u6d8c\u73b0\u7279\u5f81\u7684\u5b58\u5728\u6807\u51c6\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u5b9a\u74061\uff1a<\/span><\/strong>\u4e00\u4e2a\u7cfb\u7edf<\/span>\u5177\u6709k\u9636\u56e0\u679c\u6d8c\u73b0\u7279\u5f81\uff0c\u5f53\u4e14\u4ec5\u5f53<\/span><\/section>\n
<\/section>\n
\u8bc1\u660e\u89c1S1\u9644\u5f55\u7b2c2\u8282\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u63a8\u8bba1\uff1a<\/span><\/strong>\u4e0b\u9762\u7684\u7ea6\u675f\u5bf9\u4e8e\u4efb\u4f55\u968f\u9644\u7279\u5f81<\/span>\u90fd\u6210\u7acb\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n
 <\/span><\/section>\n
\u8fd9\u4e00\u7ed3\u679c\u8868\u660e\uff0c\u8868\u73b0\u51fa\u6d8c\u73b0\u80fd\u529b\u4e0e\u7cfb\u7edf\u5404\u90e8\u5206\u5728\u672a\u6765\u6f14\u5316\u4e2d\u7684\u534f\u540c\u6027\u5bc6\u5207\u76f8\u5173\u3002\u91cd\u8981\u7684\u662f\uff0c\u8fd9\u4e00\u7ed3\u679c\u4f7f\u6211\u4eec\u80fd\u591f\u4ec5\u4ec5\u901a\u8fc7\u68c0\u67e5\u7cfb\u7edf\u5404\u90e8\u5206\u4e4b\u95f4\u7684\u534f\u540c\u6548\u5e94\u2014\u2014\u800c\u4e0d\u9700\u8981\u77e5\u9053\u8fd9\u4e9b\u7279\u5f81\u53ef\u80fd\u662f\u4ec0\u4e48\uff0c\u5c31\u80fd\u786e\u5b9a\u7cfb\u7edf\u662f\u5426\u5177\u6709\u4efb\u4f55\u6d8c\u73b0\u7279\u5f81<\/strong>\u3002\u76f8\u53cd\uff0c\u8fd9\u4e2a\u7ed3\u679c\u4e5f\u4f7f\u6211\u4eec\u80fd\u591f\u901a\u8fc7\u68c0\u67e5\u4e00\u4e2a\u7b80\u5355\u7684\u6761\u4ef6\uff0c\u5373\u52a8\u529b\u5b66\u534f\u540c\u6548\u5e94\u7684\u7f3a\u5931\uff0c\u6765\u6392\u9664\u56e0\u679c\u6d8c\u73b0\u7684\u5b58\u5728\u3002\u6b64\u5916\uff0c\u63a8\u8bba1\u610f\u5473\u7740<\/span>\u53ef\u4ee5\u4f5c\u4e3a\u7cfb\u7edf\u6d8c\u73b0\u80fd\u529b\u7684\u8861\u91cf\u6807\u51c6\uff0c\u56e0\u4e3a\u5b83\u4e3a\u6240\u6709\u53ef\u80fd\u7684\u968f\u9644\u7279\u5f81\u7684\u72ec\u7279\u4fe1\u606f\u63d0\u4f9b\u4e86\u4e0a\u754c\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u5b9a\u74061\u5728\u56e0\u679c\u6d8c\u73b0\u548c\u7cfb\u7edf\u7684\u7edf\u8ba1\u5b66\u4e4b\u95f4\u5efa\u7acb\u4e86\u76f4\u63a5\u8054\u7cfb\uff0c\u4ece\u800c\u65e0\u9700\u89c2\u5bdf\u8005\u63d0\u51fa\u611f\u5174\u8da3\u7684\u7279\u5b9a\u7279\u5f81\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u4e00\u4e2a\u7cfb\u7edf\u7684\u6d8c\u73b0\u80fd\u529b\u53d6\u51b3\u4e8e\u7cfb\u7edf\u7684\u5fae\u89c2\u5143\u7d20\u7684\u5212\u5206\u2014\u2014\u4e8b\u5b9e\u4e0a\uff0c\u7cfb\u7edf\u5728\u4e00\u79cd\u5fae\u89c2\u8868\u793a\u4e0b\u53ef\u80fd\u6709\u6d8c\u73b0\u80fd\u529b\uff0c\u4f46\u5728\u6539\u53d8\u53d8\u91cf\u540e\uff0c\u76f8\u5bf9\u4e8e\u53e6\u4e00\u79cd\u5fae\u89c2\u8868\u793a\u53ef\u80fd\u5c31\u6ca1\u6709\u6d8c\u73b0\u80fd\u529b\u3002\u56e0\u6b64\uff0c\u5728\u6211\u4eec\u7684\u7406\u8bba\u4e2d\uff0c\u6d8c\u73b0\u603b\u662f\u6307\u201c\u5173\u4e8e\u4e00\u79cd\u7ed9\u5b9a\u5fae\u89c2\u5212\u5206\u7684\u6d8c\u73b0\u201d\u3002<\/span><\/section>\n
 <\/span><\/section>\n

\n
3.4 \u6d8c\u73b0\u7684\u5206\u7c7b<\/span><\/strong><\/section>\n<\/h2>\n
 <\/span><\/section>\n
\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u7684\u7406\u8bba\u80fd\u591f\u68c0\u6d4b\u5230\u662f\u5426\u6709\u6d8c\u73b0\u53d1\u751f\uff1b\u4e0b\u4e00\u6b65\u5219\u9700\u8981\u786e\u5b9a\u662f\u54ea\u79cd\u6d8c\u73b0\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u5b9a\u74061\u4e2d\u63d0\u51fa\u7684\u6d8c\u73b0\u7684\u7279\u5f81\u5224\u65ad\u6807\u51c6\u4e0e\u6574\u5408\u4fe1\u606f\u5206\u89e3<\/strong><\/span>\uff08Integrated Information Decomposition, \u03a6ID\uff09<\/span>\u7ed3\u5408\uff0c\u03a6ID \u662f PID \u5728\u591a\u76ee\u6807\u73af\u5883\u4e0b\u7684\u6700\u65b0\u6269\u5c55[20]\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u4f7f\u7528 \u03a6ID\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u4e00\u4e2a PID \u539f\u5b50\u5206\u89e3\u4e3a\uff1a<\/span><\/section>\n

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

<\/section>\n
\u4f8b\u5982\uff0c\u5982\u679cn=2\uff0c\u90a3\u4e48<\/span>\u4ee3\u8868\u4e24\u4e2a\u65f6\u95f4\u5e8f\u5217\u5728\u4e24\u4e2a\u65f6\u95f4\u6bb5\u5171\u4eab\u7684\u4fe1\u606f\uff08\u4f8b\u5982<\/span>\u90fd\u662f\u5f7c\u6b64\u7684\u62f7\u8d1d\uff09\u3002\u5e76\u4e14<\/span>\u5bf9\u5e94\u4e8e<\/span>\u4e2d\u5bf9<\/span>\u6709\u72ec\u7279\u5f71\u54cd\u7684\u534f\u540c\u539f\u56e0\uff08\u4f8b\u5982<\/span>\uff09\u3002\u5173\u4e8e \u03a6ID \u7684\u66f4\u591a\u7ec6\u8282\u548c\u76f4\u89c9\u53ef\u4ee5\u5728\u6587\u732e[20]\u4e2d\u627e\u5230\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u901a\u8fc7 \u03a6ID \u63d0\u4f9b\u7684\u7ec6\u7c92\u5ea6\u5206\u89e3\uff0c\u6211\u4eec\u53ef\u4ee5\u5206\u8fa8\u51fa\u4e0d\u540c\u60c5\u5f62\u7684\u534f\u540c\u4f5c\u7528\u3002\u7279\u522b\u5730\uff0c\u6211\u4eec\u5f15\u5165k\u9636\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c <\/span> \u548c\u56e0\u679c\u89e3\u8026 <\/span>\uff1a<\/span><\/section>\n

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

<\/section>\n
\u4ece\u8fd9\u4e9b\u5b9a\u4e49\u548c\u516c\u5f0f\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u9a8c\u8bc1\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n
 <\/span><\/section>\n
\u56e0\u6b64\uff0c\u4e00\u4e2a\u7cfb\u7edf\u7684\u56e0\u679c\u6d8c\u73b0\u80fd\u529b\u81ea\u7136\u5206\u89e3\u4e3a\u4e24\u4e2a\u4e0d\u540c\u90e8\u5206\uff1a\u5173\u4e8e k-plets \u672a\u6765\u53d8\u91cf\u7684\u4fe1\u606f\uff0c\u4ee5\u53ca\u8d85\u51fak-plets\u4ee5\u5916\u7684\u672a\u6765\u96c6\u4f53\u5c5e\u6027\u7684\u4fe1\u606f\u3002\u5c5e\u4e8e\u8fd9\u4e24\u4e2a\u6982\u5ff5\u7684 \u03a6ID \u539f\u5b50\u5728\u56fe3\u4e2d\u4e24\u4e2a\u65f6\u95f4\u5e8f\u5217\u7684 \u03a6ID \u683c\u70b9\u4e2d\u5f97\u5230\u4e86\u8bf4\u660e\u3002\u672c\u8282\u7684\u5176\u4f59\u90e8\u5206\u5c06\u8868\u660e\uff0c<\/span>\u548c<\/span>\u5206\u522b\u662f\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\u548c\u56e0\u679c\u89e3\u8026\u7684\u81ea\u7136\u5ea6\u91cf\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\uff1a<\/span><\/strong>\u76f4\u89c2\u5730\u8bf4\uff0c\u5f53\u96c6\u4f53\u6027\u8d28\u5bf9\u4e2a\u4f53\u90e8\u5206\u5177\u6709\u4e0d\u53ef\u8fd8\u539f\u7684\u56e0\u679c\u6548\u5e94\u65f6\uff0c\u5c31\u4f1a\u51fa\u73b0\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\u3002\u5f62\u5f0f\u5316\u8868\u8ff0\u5c31\u662f\uff1a<\/span><\/section>\n

<\/span><\/section>\n
\u5b9a\u4e493\uff1a<\/span><\/strong>\u4e00\u4e2a\u968f\u9644\u7279\u5f81<\/span>\u8868\u73b0\u51fak\u9636\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\uff0c\u5982\u679c\u5bf9\u4e8e\u67d0\u4e2a\u03b1\uff0c|\u03b1|=k\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n
 <\/span><\/section>\n
\u8bf7\u6ce8\u610f\uff0c\u4e0e\u5b9a\u4e492\u4e0d\u540c\u7684\u662f\uff0c\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\u8981\u6c42\u7279\u5f81<\/span>\u5bf9\u6574\u4e2a\u7cfb\u7edf\u7684\u7279\u5b9a\u5b50\u96c6\u7684\u6f14\u5316\u6709\u72ec\u7279\u7684\u9884\u6d4b\u80fd\u529b\u3002\u7279\u522b\u662f\uff0c\u4e00\u4e2a\u5bf9\u6bd4\u5982\u8bf4<\/span>\u6709\u9884\u6d4b\u80fd\u529b\u7684\u7279\u5f81<\/span>\u88ab\u79f0\u4e3a\u53d1\u6325\u4e86\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\u6548\u5e94\uff0c\u56e0\u4e3a\u5b83\u9884\u6d4b\u4e86<\/span>\u7684\u4e00\u4e9b\u60c5\u51b5\uff0c\u800c\u8fd9\u4e9b\u60c5\u51b5\u5728<\/span>\u7684\u4efb\u4f55\u7279\u5b9a<\/span>\u4e2d\u65e0\u6cd5\u9884\u6d4b\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5728\u4e00\u4e2a\u5177\u6709\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\u7684\u7cfb\u7edf\u4e2d\uff0c\u6574\u4f53\u5bf9\u90e8\u5206\u7684\u5f71\u54cd\u4e0d\u80fd\u8fd8\u539f\u4e3a\u4f4e\u5c42\u6b21\u7684\u76f8\u4e92\u4f5c\u7528\u3002\u201c\u57fa\u672c\u76f4\u89c9\u201d\u4e00\u8282\u4e2d\u7684\u4f8b2\u63d0\u4f9b\u4e86\u4e00\u4e2a\u6700\u5c0f\u793a\u4f8b\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u6211\u4eec\u7684\u4e0b\u4e00\u4e2a\u7ed3\u679c\u662f\u5c06\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\u4e0e\u516c\u5f0f\u4e2d\u5f15\u5165\u7684\u6307\u6570<\/span>\u5f62\u5f0f\u5316\u5730\u8054\u7cfb\u8d77\u6765\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u5b9a\u74062\uff1a<\/span><\/strong>\u5982\u679c<\/span>\uff0c\u5219\u4e00\u4e2a\u7cfb\u7edf<\/span>\u5177\u6709\u65bd\u52a0 k \u9636\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\u7684\u7279\u5f81\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u8bc1\u660e\u89c1\u9644\u5f55S1\u7b2c3\u8282\u3002<\/span><\/section>\n
 <\/span><\/section>\n
<\/section>\n

\u56fe3. \u6574\u5408\u4fe1\u606f\u5206\u89e3\uff08\u03a6ID\uff09\uff1an=2 \u4e2a\u65f6\u95f4\u5e8f\u5217\u7684 \u03a6ID \u7f51\u683c[20]\uff0c\u5f3a\u8c03\u4e86\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\uff08D\uff09\u548c\u56e0\u679c\u89e3\u8026\uff08G\uff09\u9879\u3002<\/span><\/p>\n

 <\/span><\/section>\n
\u56e0\u679c\u89e3\u8026<\/span><\/strong>\u3002\u9664\u4e86\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\u5916\uff0c\u5f53\u96c6\u4f53\u5c5e\u6027\u5bf9\u5176\u4ed6\u96c6\u4f53\u5c5e\u6027\u5177\u6709\u4e0d\u53ef\u8fd8\u539f\u56e0\u679c\u6548\u5e94\u65f6\uff0c\u56e0\u679c\u89e3\u8026\u4e5f\u4f1a\u53d1\u751f\u3002\u7528\u672f\u8bed\u6765\u8868\u793a\uff1a<\/span><\/section>\n

<\/span><\/section>\n
\u5b9a\u4e494\uff1a<\/span><\/strong>\u4e00\u4e2a\u968f\u9644\u7279\u5f81<\/span>\u88ab\u79f0\u4e3a\u8868\u73b0\u51fak\u9636\u56e0\u679c\u89e3\u8026\uff0c\u5982\u679c<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n
 <\/span><\/section>\n
\u6b64\u5916\uff0c\u5982\u679c<\/span>\uff0c\u5e76\u4e14\u5bf9\u4e8e\u6240\u6709<\/span>\uff0c\u6709<\/span>\uff0c\u90a3\u4e48<\/span>\u5c31\u88ab\u8ba4\u4e3a\u5177\u6709\u7eaf\u56e0\u679c\u89e3\u8026<\/strong><\/span>\uff08pure causal decoupling\uff09<\/span>\u3002\u6700\u540e\uff0c\u5982\u679c\u6240\u6709\u6d8c\u73b0\u7279\u5f81\u90fd\u8868\u73b0\u51fa\u7eaf\u56e0\u679c\u89e3\u8026\uff0c\u90a3\u4e48\u7cfb\u7edf\u5c31\u88ab\u8ba4\u4e3a\u662f\u5b8c\u5168\u89e3\u8026\u7684\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u4ee5\u4e0a\uff0c<\/span>\u6307\u7684\u662f<\/span>\u548c<\/span>\u5171\u4eab\uff0c\u4e14\u5728\u4efb\u4f55\u5fae\u89c2\u5143\u7d20\u4e2d\u90fd\u627e\u4e0d\u5230\u7684\u4fe1\u606f\uff0c\u65e0\u8bba\u662f\u5728\u65f6\u95f4t\u8fd8\u662ft’\u3002\uff08\u6ce8\u610f<\/span>\u662f<\/span>\u548c<\/span>\u4e4b\u95f4\u5171\u4eab\uff0c\u800c<\/span>\u6216<\/span>\u7684k\u4e2a\u6216\u66f4\u5c11\u53d8\u91cf\u7ec4\u5408\u672c\u8eab\u6ca1\u6709\u7684\u4fe1\u606f\u3002\uff09<\/span><\/section>\n
 <\/span><\/section>\n
\u8868\u73b0\u51fa\u56e0\u679c\u89e3\u8026\u7684\u7279\u5f81\u4ecd\u7136\u53ef\u4ee5\u5bf9\u4e2a\u4f53\u5143\u7d20\u7684\u6f14\u5316\u65bd\u52a0\u5f71\u54cd\uff0c\u800c\u8868\u73b0\u51fa\u7eaf\u89e3\u8026\u7684\u7279\u5f81\u5219\u4e0d\u80fd\u3002\u5b9e\u9645\u4e0a\uff0c\u6761\u4ef6<\/span>\u610f\u5473\u7740\u9ad8\u9636\u56e0\u679c\u6548\u5e94\u4e0d\u5f71\u54cd\u4efb\u4f55\u7279\u5b9a\u90e8\u5206\uff0c\u53ea\u5f71\u54cd\u7cfb\u7edf\u6574\u4f53\u3002\u6709\u8da3\u7684\u662f\uff0c\u4e00\u4e2a\u8868\u73b0\u51fa\u7eaf\u56e0\u679c\u89e3\u8026\u7684\u7279\u5f81\u53ef\u4ee5\u88ab\u8ba4\u4e3a\u662f\u6709\u201c\u81ea\u5df1\u7684\u751f\u547d\u201d\uff1b\u4e00\u79cd\u7edf\u8ba1\u5b66\u4e0a\u7684\u5e7d\u7075\uff0c\u5b83\u968f\u7740\u65f6\u95f4\u63a8\u79fb\u800c\u5ef6\u7eed\uff0c\u7cfb\u7edf\u7684\u4efb\u4f55\u5355\u4e2a\u90e8\u5206\u90fd\u4e0d\u4f1a\u5f71\u54cd\u5b83\u6216\u88ab\u5b83\u5f71\u54cd\u3002\u5728\u201c\u57fa\u672c\u76f4\u89c9\u201d\u90e8\u5206\u7684\u7b2c\u4e00\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u7cfb\u7edf\u7684\u5947\u5076\u6027\u6784\u6210\u4e86\u5b8c\u7f8e\u56e0\u679c\u89e3\u8026\u7684\u4e00\u4e2a\u7b80\u5355\u4f8b\u5b50\u3002\u91cd\u8981\u7684\u662f\uff0c\u201c\u6848\u4f8b\u7814\u7a76\u201d\u4e00\u8282\u4e2d\u7684\u6848\u4f8b\u7814\u7a76\u8868\u660e\uff0c\u56e0\u679c\u89e3\u8026\u4e0d\u4ec5\u53ef\u4ee5\u53d1\u751f\u5728\u73a9\u5177\u6a21\u578b\u4e2d\uff0c\u4e5f\u53ef\u4ee5\u53d1\u751f\u5728\u5177\u6709\u5b9e\u9645\u610f\u4e49\u7684\u5404\u79cd\u60c5\u51b5\u4e0b\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u5728\u8fd9\u4e00\u8282\u7684\u6700\u540e\uff0c\u6211\u4eec\u6b63\u5f0f\u5efa\u7acb\u56e0\u679c\u89e3\u8026\u548c\u516c\u5f0f\u4e2d\u5f15\u5165\u7684\u6307\u6570<\/span>\u4e4b\u95f4\u7684\u8054\u7cfb\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5b9a\u74063\uff1a<\/span><\/strong>\u5f53\u4e14\u4ec5\u5f53<\/span>\u65f6\uff0c\u7cfb\u7edf\u62e5\u6709\u8868\u73b0\u51fa\u56e0\u679c\u89e3\u8026\u7684\u7279\u5f81\u3002\u6b64\u5916\uff0c\u5982\u679c<\/span>\u4e14<\/span>\uff0c\u7cfb\u7edf\u662f\u5b8c\u5168\u89e3\u8026\u7684\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u8bc1\u660e\u89c1\u9644\u5f55S1\u7b2c3\u8282\u3002<\/span><\/section>\n
 <\/span><\/section>\n
 <\/span><\/section>\n

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<\/svg><\/section>\n<\/section>\n<\/section>\n
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4. \u5ea6\u91cf\u56e0\u679c\u6d8c\u73b0<\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n

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


<\/p>\n

\u672c\u8282\u63a2\u8ba8\u5c06\u4e0a\u4e00\u8282\u4e2d\u63d0\u51fa\u7684\u6846\u67b6\u4ed8\u8bf8\u5b9e\u65bd\u7684\u65b9\u6cd5\u3002\u6211\u4eec\u8ba8\u8bba\u4e24\u79cd\u65b9\u6cd5\uff1a\u9996\u5148\uff0c4.1\u8282\u201c\u5927\u578b\u7cfb\u7edf\u7684\u5b9e\u7528\u6807\u51c6\u201d\u4ecb\u7ecd\u5728\u5927\u578b\u7cfb\u7edf\u4e2d\u5b9e\u7528\u7684\u5145\u5206\u6027\u6807\u51c6\uff1b\u7136\u540e\uff0c4.2\u8282\u201c\u901a\u8fc7\u4f7f\u7528\u534f\u540c\u901a\u9053\u6d4b\u91cf\u56e0\u679c\u6d8c\u73b0\u201d\uff0c\u8bf4\u660e\u5982\u679c\u91c7\u7528\u8ba1\u7b97 \u03a6ID \u539f\u5b50\u7684\u7279\u5b9a\u65b9\u6cd5\uff0c\u5e94\u5982\u4f55\u8fdb\u4e00\u6b65\u8003\u8651\u3002\u540e\u4e00\u79cd\u65b9\u6cd5\u63d0\u4f9b\u4e86\u51c6\u786e\u7684\u5224\u522b\uff0c\u4f46\u4ee3\u4ef7\u662f\u6570\u636e\u5bc6\u96c6\uff0c\u56e0\u6b64\u53ea\u9002\u7528\u4e8e\u5c0f\u7cfb\u7edf\uff1b\u524d\u4e00\u79cd\u65b9\u6cd5\u53ef\u4ee5\u5728\u5927\u7cfb\u7edf\u4e2d\u8ba1\u7b97\uff0c\u5176\u7ed3\u679c\u72ec\u7acb\u4e8e\u6240\u9009\u62e9\u7684 PID\uff0c\u4f46\u5bb9\u6613\u51fa\u73b0\u9519\u8bef\u68c0\u6d4b<\/span>\uff08\u5373\u5047\u9634\u6027\uff09<\/span>\u3002<\/span>
<\/section>\n
 <\/span><\/section>\n

\n
4.1 \u5927\u578b\u7cfb\u7edf\u7684\u5b9e\u7528\u6807\u51c6<\/span><\/strong><\/span><\/section>\n<\/h2>\n
 <\/span><\/section>\n
\u6211\u4eec\u63d0\u51fa\u7684\u6846\u67b6\u867d\u7136\u5728\u7406\u8bba\u4e0a\u5f88\u6709\u5438\u5f15\u529b\uff0c\u4f46\u5728\u4f30\u8ba1\u8bb8\u591a\u968f\u673a\u53d8\u91cf\u7684\u8054\u5408\u6982\u7387\u5206\u5e03\u4ee5\u53ca\u03a6ID\u539f\u5b50\u672c\u8eab\u7684\u8ba1\u7b97\u65b9\u9762\u5b58\u5728\u6311\u6218\u3002\u4f5c\u4e3a\u66ff\u4ee3\u65b9\u6848\uff0c\u6211\u4eec\u8003\u8651\u4e0d\u9700\u8981\u91c7\u7528\u4efb\u4f55\u7279\u5b9a \u03a6ID \u6216 PID \u51fd\u6570\u7684\u8fd1\u4f3c\u65b9\u6cd5\uff0c\u5e76\u4e14\u7531\u4e8e\u8fd9\u4e9b\u8fd1\u4f3c\u65b9\u6cd5\u53ea\u57fa\u4e8e\u6210\u5bf9\u5206\u5e03\uff0c\u56e0\u800c\u662f\u6570\u636e\u9ad8\u6548\u7684\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u4f5c\u4e3a\u8861\u91cfk\u9636\u56e0\u679c\u7684\u5b9e\u9645\u6807\u51c6\uff0c\u6211\u4eec\u5f15\u5165<\/span>\uff0c<\/span>\u548c<\/span>\u3002\u4e3a\u7b80\u5355\u8d77\u89c1\uff0c\u6211\u4eec\u5728\u6b64\u5199\u51fak=1\u7684\u7279\u6b8a\u60c5\u51b5\uff0c\u5e76\u63d0\u4f9b\u4efb\u610fk\u7684\u5b8c\u6574\u516c\u5f0f\u8bc1\u660e\u3002\u5728\u9644\u5f55S1\u7b2c4\u8282\u4e2d\u63d0\u4f9b\u4e86\u76f8\u5e94\u8bc1\u660e\u3002<\/span><\/section>\n
 <\/span><\/section>\n
<\/section>\n
 <\/span><\/section>\n
\u6211\u4eec\u7684\u4e0b\u4e00\u4e2a\u7ed3\u679c\u662f\u5c06\u8fd9\u4e9b\u91cf\u4e0e\u7b2c\u4e00\u8282\u201c\u56e0\u679c\u6d8c\u73b0\u7684\u5f62\u5f0f\u7406\u8bba\u201d\u4e2d\u7684\u5f62\u5f0f\u5b9a\u4e49\u8054\u7cfb\u8d77\u6765\uff0c\u663e\u793a\u5b83\u4eec\u4f5c\u4e3a\u68c0\u6d4b\u56e0\u679c\u6d8c\u73b0\u7684\u5b9e\u7528\u6807\u51c6\u7684\u4ef7\u503c\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u547d\u98981\uff1a<\/span><\/strong>\u662fVt<\/sub>\u5177\u6709\u56e0\u679c\u6d8c\u73b0\u7279\u6027\u7684\u5145\u5206\u6761\u4ef6\u3002\u540c\u6837\u5730, <\/span>\u662fVt <\/sub>\u8868\u73b0\u51fa\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\u7684\u5145\u5206\u6761\u4ef6\u3002\u6700\u540e\uff0c<\/span>\u548c<\/span>\u662f\u56e0\u679c\u89e3\u8026\u7684\u5145\u5206\u6761\u4ef6\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u8bc1\u660e\u89c1\u9644\u5f55S1\u7b2c4\u8282\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u867d\u7136\u901a\u8fc7\u547d\u98981\u8ba1\u7b97\u4e00\u4e2a\u7cfb\u7edf\u662f\u5426\u5177\u6709\u6d8c\u73b0\u7279\u5f81\u53ef\u80fd\u5728\u8ba1\u7b97\u4e0a\u5177\u6709\u6311\u6218\u6027\uff0c\u4f46\u662f\u5982\u679c\u6211\u4eec\u6709\u4e00\u4e2a\u53ef\u80fd\u662f\u6d8c\u73b0\u7684\u5019\u9009\u7279\u5f81V\uff0c\u5c31\u53ef\u4ee5\u8ba1\u7b97\u516c\u5f0f (10) \u4e2d\u53ea\u4f9d\u8d56\u4e8e\u6807\u51c6\u4e92\u4fe1\u606f\u548c\u53cc\u53d8\u91cf\u8fb9\u9645\u3001\u5e76\u4e14\u4e0e\u7cfb\u7edf\u5927\u5c0f\u5448\u7ebf\u6027\u6bd4\u4f8b<\/span>\uff08\u5bf9\u4e8e k=1\uff09<\/span>\u7684\u7b80\u5355\u91cf\u3002\u8fd9\u4e9b\u91cf\u5f88\u5bb9\u6613\u7528\u6807\u51c6\u7684\u4fe1\u606f\u8bba\u5de5\u5177\u8ba1\u7b97\u5e76\u6d4b\u8bd5\u5176\u663e\u8457\u6027[21, 22]\u3002\u6b64\u5916\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u7684\u7ed3\u679c\u5bf9\u4efb\u4f55\u4e0e\u9644\u5f55S1\u7b2c2\u8282\u4e2d\u89c4\u5b9a\u7684\u5c5e\u6027\u517c\u5bb9\u7684\u03a6ID\u548cPID\u7684\u9009\u62e9\u90fd\u662f\u6709\u6548\u7684\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5728\u66f4\u5e7f\u6cdb\u7684\u80cc\u666f\u4e0b\uff0c<\/span>\u548c<\/span>\u4e0e\u76f8\u4e92\u4f5c\u7528\u4fe1\u606f[14, 23]\u3001\u5197\u4f59-\u534f\u540c\u6307\u6570[24]\u4ee5\u53ca\u6700\u8fd1\u7684O-\u4fe1\u606f\u03a9[25]\u4e00\u6837\uff0c\u90fd\u5c5e\u4e8e\u201c\u6574\u4f53\u51cf\u53bb\u603b\u548c\u201d<\/span>\uff08whole-minus-sum\uff09<\/span>\u7cfb\u5217\u7684\u5ea6\u91cf\u2014\u2014\u5b83\u4eec\u4e0d\u80fd\u6d4b\u91cf\u534f\u540c\u672c\u8eab\uff0c\u53ea\u80fd\u6d4b\u91cf\u534f\u540c\u548c\u5197\u4f59\u7684\u5dee\u503c<\/strong>\u3002\u5728\u5b9e\u8df5\u4e2d\uff0c\u8fd9\u610f\u5473\u7740\u5982\u679c\u7cfb\u7edf\u4e2d\u5b58\u5728\u5197\u4f59\uff0c\u5c06\u66f4\u96be\u53d1\u73b0\u6d8c\u73b0\uff0c\u5b9e\u9645\u7684\u5197\u4f59\u5c06\u63a8\u52a8<\/span>\u548c<\/span>\u53d8\u5f97\u66f4\u8d1f\u3002\u6b64\u5916\uff0c\u901a\u8fc7\u5bf9\u6240\u6709\u8fb9\u9645\u4e92\u4fe1\u606f\uff08\u5982<\/span>\u5728<\/span>\u7684\u60c5\u51b5\u4e0b\uff09\u6c42\u548c\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u6709\u6548\u5730\u91cd\u590d\u8ba1\u7b97\u5197\u4f59\u5ea6\u8fben\u6b21\uff0c\u8fdb\u4e00\u6b65\u8ba9\u5ea6\u91cf\u6807\u51c6\u53d8\u5f97\u66f4\u7cdf\u7cd5\u3002\u5982\u679c\u6211\u4eec\u613f\u610f\u81f4\u529b\u4e8e\u4e00\u4e2a\u7279\u5b9a\u7684\u03a6ID\u6216PID\u51fd\u6570\uff0c\u8fd9\u79cd\u91cd\u590d\u8ba1\u7b97\u95ee\u9898\u662f\u53ef\u4ee5\u907f\u514d\u7684\uff0c\u6b63\u5982\u6211\u4eec\u63a5\u4e0b\u6765\u6240\u5c55\u793a\u7684\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u53ef\u4ee5\u8c03\u6574k\u7684\u503c\u4ee5\u63a2\u7d22\u4e0d\u540c\u201c\u5c3a\u5ea6\u201d\u7684\u6d8c\u73b0\u3002\u4f8b\u5982\uff0ck=1\u5bf9\u5e94\u4e8e\u5355\u4e2a\u5fae\u89c2\u5143\u7d20\u7684\u6d8c\u73b0\uff0c\u800ck=2\u6307\u7684\u662f\u6240\u6709\u8026\u5408\u7684\u6d8c\u73b0\u2014\u2014\u5373\u5355\u4e2a\u5143\u7d20\u53ca\u5176\u6210\u5bf9\u76f8\u4e92\u4f5c\u7528\u3002\u56e0\u6b64\uff0c\u4e00\u822c\u6765\u8bf4\uff0c\u547d\u98981\u4e2d\u7684\u6807\u51c6\u5bf9\u4e8e\u8f83\u5927\u7684k\u503c\u6765\u8bf4\u5f88\u96be\u6ee1\u8db3\u3002\u6b64\u5916\uff0c\u4ece\u5b9e\u9645\u89d2\u5ea6\u6765\u770b\uff0c\u8003\u8651\u8f83\u5927\u7684k\u503c\u9700\u8981\u5728\u9ad8\u7ef4\u5206\u5e03\u4e2d\u4f30\u8ba1\u4fe1\u606f\u91cf\uff0c\u8fd9\u901a\u5e38\u9700\u8981\u6307\u6570\u7ea7\u7684\u5927\u91cf\u6570\u636e\u3002<\/span><\/section>\n
 <\/span><\/section>\n

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4.2 \u901a\u8fc7\u534f\u540c\u901a\u9053\u5ea6\u91cf\u56e0\u679c\u6d8c\u73b0<\/span><\/strong><\/span><\/section>\n<\/h2>\n
 <\/span><\/section>\n
\u672c\u8282\u5229\u7528\u53c2\u8003\u6587\u732e[19]\u4e2d\u62a5\u544a\u7684\u5173\u4e8e\u4fe1\u606f\u5206\u89e3\u7684\u6700\u65b0\u5de5\u4f5c\uff0c\u63d0\u51fa\u4e00\u79cd\u76f4\u63a5\u6d4b\u91cf\u6d8c\u73b0\u80fd\u529b\u4ee5\u53ca\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\u548c\u56e0\u679c\u89e3\u8026\u6307\u6570\u7684\u65b9\u6cd5\u3002\u672c\u8282\u7684\u4e3b\u8981\u5185\u5bb9\u662f\uff0c\u5982\u679c\u91c7\u7528\u4e00\u4e2a\u7279\u5b9a\u7684\u03a6ID\uff0c\u90a3\u4e48\u5c31\u6709\u53ef\u80fd\u76f4\u63a5\u8bc4\u4f30<\/span>\u548c<\/span>\uff0c\u63d0\u4f9b\u4e00\u4e2a\u76f4\u63a5\u68c0\u6d4b\u6d8c\u73b0\u7684\u9014\u5f84\uff0c\u800c\u4e0d\u9700\u8981\u91cd\u590d\u8ba1\u7b97\u5197\u4f59\uff0c\u5c31\u50cf\u201c\u5927\u578b\u7cfb\u7edf\u7684\u5b9e\u7528\u6807\u51c6\u201d\u4e00\u8282\u4ecb\u7ecd\u7684\u65b9\u6cd5\u90a3\u6837\u3002\u6b64\u5916\uff0c\u7531\u4e8e\u6240\u9009\u62e9\u7684\u7279\u5b9a\u03a6ID\u7684\u7279\u6027\uff0c\u989d\u5916\u7684\u5c5e\u6027\u53ef\u80fd\u4f1a\u53d8\u5f97\u53ef\u7528\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u8ba9\u6211\u4eec\u9996\u5148\u4ecb\u7ecd\u4e00\u4e0bk-\u534f\u540c\u901a\u9053<\/strong><\/span>\uff08k-synergistic channel\uff09<\/span>\u7684\u6982\u5ff5\uff1a\u5728\u6240\u6709 |\u03b1|=k \u7684\u60c5\u51b5\u4e0b\uff0c\u4f20\u9012\u5173\u4e8eX\u7684\u4fe1\u606f\u4f46\u4e0d\u4f20\u9012\u5173\u4e8e\u4efb\u4f55\u90e8\u5206<\/span>\u4fe1\u606f\u7684\u6620\u5c04<\/span>\u3002\u6240\u6709k-\u534f\u540c\u901a\u9053\u7684\u96c6\u5408\u8868\u793a\u4e3a\uff1a<\/span><\/section>\n

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 <\/span><\/section>\n
\u901a\u8fc7k-\u534f\u540c\u901a\u9053\u4ea7\u751f\u7684\u53d8\u91cf V \u88ab\u79f0\u4e3ak-\u534f\u540c\u53ef\u89c2\u6d4b\u91cf\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u6709\u4e86\u8fd9\u4e2a\u5b9a\u4e49\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba4\u4e3ak\u9636\u534f\u540c\u6548\u5e94\u662f\u53ef\u4ee5\u4ece\u4e00\u4e2ak-\u534f\u540c\u901a\u9053\u4e2d\u63d0\u53d6\u7684\u6700\u5927\u4fe1\u606f\uff1a<\/span><\/section>\n
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 <\/span><\/section>\n
\u8fd9\u4e2a\u60f3\u6cd5\u53ef\u4ee5\u81ea\u7136\u6269\u5c55\u5230\u56e0\u679c\u89e3\u8026\u7684\u60c5\u51b5\uff0c\u8981\u6c42\u53cc\u65b9\u90fd\u6709\u534f\u540c\u901a\u9053\uff0c\u4e5f\u5c31\u662f<\/span><\/section>\n

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 <\/span><\/section>\n
\u6700\u540e\uff0c\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\u6307\u6570\u53ef\u4ee5\u4ece\u4e24\u8005\u7684\u5dee\u8ba1\u7b97\u51fa\u6765\uff1a<\/span><\/section>\n

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 <\/span><\/section>\n
\u8bf7\u6ce8\u610f\uff0c<\/span>\u662f\u5e94\u7528\u5728<\/span>\u4e0a\u7684\u6570\u636e\u5904\u7406\u4e0d\u7b49\u5f0f\u7684\u76f4\u63a5\u7ed3\u679c\uff0c\u56e0\u6b64 <\/span>\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u901a\u8fc7\u5229\u7528\u8fd9\u79cd\u6d4b\u91cf\u534f\u540c\u4f5c\u7528\u7684\u7279\u5b9a\u65b9\u5f0f\u7684\u7279\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u8bc1\u660e\u4ee5\u4e0b\u7ed3\u679c\u3002\u4e3a\u6b64\uff0c\u53ef\u4ee5\u8bf4\uff0c\u5982\u679c<\/span>\uff0c\u5219\u7279\u5f81<\/span>\u662f\u81ea\u5173\u8054\u7684\u3002<\/span><\/section>\n
 <\/span><\/strong><\/section>\n
\u547d\u98982\uff1a<\/span><\/strong>\u5982\u679cXt<\/sub>\u662f\u7a33\u5b9a\u7684\uff0c\u6240\u6709\u81ea\u5173\u8054k-\u534f\u540c\u53ef\u89c2\u6d4b\u91cf\u90fd\u662fk\u9636\u6d8c\u73b0\u7684\u3002<\/span><\/section>\n

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\u8bc1\u660e\u3002\u89c1S1\u9644\u5f55\u7b2c4\u8282\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u603b\u4e4b\uff0c<\/span>\u548c<\/span>\u63d0\u4f9b\u4e86\u6570\u636e\u9a71\u52a8\u7684\u5de5\u5177\u6765\u6d4b\u8bd5\u2014\u2014\u53ef\u80fd\u662f\u62d2\u7edd\u2014\u2014\u5173\u4e8e\u611f\u5174\u8da3\u7684\u573a\u666f\u4e2d\u51fa\u73b0\u7684\u5047\u8bbe\u3002\u53c2\u8003\u6587\u732e[26]\u4e2d\u8ba8\u8bba\u4e86\u8ba1\u7b97\u8fd9\u4e9b\u91cf\u7684\u6709\u6548\u7b97\u6cd5\u3002\u867d\u7136\u76ee\u524d\u7684\u5b9e\u73b0\u53ea\u80fd\u7528\u4e8e\u76f8\u5bf9\u8f83\u5c0f\u7684\u7cfb\u7edf\uff0c\u4f46\u8fd9\u4e00\u601d\u8def\u8868\u660e\uff0c\u672a\u6765PID\u7684\u53d1\u5c55\u53ef\u80fd\u4f1a\u4f7f\u6d8c\u73b0\u6307\u6570\u7684\u8ba1\u7b97\u66f4\u5177\u53ef\u6269\u5c55\u6027\uff0c\u907f\u514d\u516c\u5f0f\uff0810\uff09\u7684\u9650\u5236\u3002<\/span><\/section>\n
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5. \u6848\u4f8b\u7814\u7a76<\/strong><\/strong><\/p>\n<\/section>\n

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


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\u8ba9\u6211\u4eec\u603b\u7ed3\u4e00\u4e0b\u5230\u76ee\u524d\u4e3a\u6b62\u7684\u7ed3\u679c\u3002\u6211\u4eec\u9996\u5148\u57fa\u4e8ePID\u7ed9\u51fa\u4e86\u6d8c\u73b0\u7279\u5f81\u7684\u4e00\u4e2a\u4e25\u683c\u5b9a\u4e49<\/span>\uff083.3\u8282\u201c\u5b9a\u4e49\u56e0\u679c\u6d8c\u73b0\u201d\uff09<\/span>\uff0c\u7136\u540e\u7528\u03a6ID\u5c06\u6d8c\u73b0\u80fd\u529b\u5206\u89e3\u4e3a\u56e0\u679c\u89e3\u8026\u548c\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\u6307\u6570<\/span>\uff083.4\u8282\u201c\u6d8c\u73b0\u7684\u5206\u7c7b\u201d\uff09<\/span>\u3002\u5c3d\u7ba1\u8fd9\u4e9b\u6307\u6570\u4e0d\u662f\u76f4\u63a5\u8ba1\u7b97\u7684\uff0c\u4f46\u03a6ID\u6846\u67b6\u5141\u8bb8\u6211\u4eec\u5236\u5b9a\u5bb9\u6613\u8ba1\u7b97\u7684\u5145\u5206\u6761\u4ef6<\/span>\uff084.1\u8282\u201c\u5927\u578b\u7cfb\u7edf\u7684\u5b9e\u7528\u6807\u51c6\u201d\uff09<\/span>\u3002\u672c\u8282\u8bf4\u660e\u8fd9\u4e9b\u6761\u4ef6\u5728\u5404\u79cd\u6848\u4f8b\u7814\u7a76\u4e2d\u7684\u5e94\u7528\u3002\u516c\u5f0f\uff0810\uff09\u4e2d\u8ba1\u7b97\u6240\u6709\u6d8c\u73b0\u6761\u4ef6\u7684\u4ee3\u7801\u5728\u5728\u7ebf\u5f00\u653e\u6e90\u7801\u5e93\u4e2d\u63d0\u4f9b<\/span>\uff08https:\/\/github.com\/pmediano\/ReconcilingEmergences\uff09<\/span>\u3002<\/span>
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5.1 \u63a8\u5b9a\u7684\u56e0\u679c\u6d8c\u73b0\u7684\u5178\u578b\u4f8b\u5b50<\/span><\/strong><\/section>\n<\/h2>\n
 <\/span><\/section>\n
\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u63d0\u51fa\u7528\u4e24\u4e2a\u8457\u540d\u7cfb\u7edf\u5bf9\u6211\u4eec\u7684\u5b9e\u7528\u6d8c\u73b0\u6807\u51c6<\/span>\uff08\u547d\u98981\uff09<\/span>\u8fdb\u884c\u8bc4\u4f30\u3002\u5eb7\u5a01\u751f\u547d\u6e38\u620f<\/span>\uff08Conway\u2019s Game of Life\uff09<\/span>[27]\u548c\u96f7\u8bfa\u9e1f\u7fa4\u6a21\u578b<\/span>\uff08Reynolds\u2019 flocking model\uff09<\/span>[28]\u3002\u4e24\u8005\u90fd\u88ab\u5e7f\u6cdb\u8ba4\u4e3a\u662f\u6d8c\u73b0\u884c\u4e3a\u7684\u5178\u578b\u4f8b\u5b50\uff0c\u5e76\u5728\u590d\u6742\u6027\u548c\u4eba\u5de5\u751f\u547d\u6587\u732e\u4e2d\u5f97\u5230\u4e86\u6df1\u5165\u7814\u7a76[29]\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u4f7f\u7528\u8fd9\u4e9b\u6a21\u578b\u4f5c\u4e3a\u6211\u4eec\u65b9\u6cd5\u7684\u6d4b\u8bd5\u6848\u4f8b\u3002\u6a21\u62df\u7684\u6280\u672f\u7ec6\u8282\u5728\u9644\u5f55S1\u7b2c5\u8282\u4e2d\u63d0\u4f9b\u3002<\/span><\/section>\n
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\u5eb7\u5a01\u7684\u751f\u547d\u6e38\u620f<\/span><\/strong>\u3002\u751f\u547d\u6e38\u620f\u7684\u4e00\u4e2a\u4f17\u6240\u5468\u77e5\u7684\u7279\u5f81\u662f\u7c92\u5b50\u7684\u5b58\u5728\uff1a\u8fd9\u91cc\u7684\u7c92\u5b50\u662f\u6307\u8d1f\u8d23\u4f20\u9012\u548c\u4fee\u6539\u4fe1\u606f\u7684\u8fde\u8d2f\u3001\u81ea\u6211\u7ef4\u6301\u7684\u7ed3\u6784[30]\u3002\u8fd9\u4e9b\u7c92\u5b50\u4e00\u76f4\u662f\u5e7f\u6cdb\u7814\u7a76\u7684\u5bf9\u8c61\uff0c\u5e76\u6709\u8be6\u7ec6\u7684\u5206\u7c7b\u65b9\u6cd5\u548c\u5206\u7c7b[29, 31]\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u4e3a\u4e86\u6d4b\u8bd5\u7c92\u5b50\u7684\u6d8c\u73b0\u7279\u6027\uff0c\u6211\u4eec\u6a21\u62df15×15\u65b9\u5f62\u5143\u80de\u9635\u5217\u7684\u6f14\u5316\uff0c\u6211\u4eec\u5c06\u5176\u89c6\u4e3a\u4e8c\u8fdb\u5236\u5411\u91cf<\/span>\uff0cn = 225\u3002\u4f5c\u4e3a\u521d\u59cb\u6761\u4ef6\uff0c\u6211\u4eec\u8003\u8651\u5bf9\u5e94\u4e8e\u201c\u7c92\u5b50\u5bf9\u649e\u673a\u201d\u8bbe\u7f6e\u7684\u4f4d\u5f62\uff0c\u4e24\u4e2a\u5df2\u77e5\u7c7b\u578b\u7684\u7c92\u5b50\u9762\u5bf9\u9762<\/span>\uff08\u56fe4\uff09<\/span>\u3002\u5728\u6bcf\u6b21\u8bd5\u9a8c\u4e2d\uff0c\u901a\u8fc7\u6539\u53d8\u7c92\u5b50\u7684\u4f4d\u7f6e\u3001\u7c7b\u578b\u548c\u76f8\u5bf9\u4f4d\u79fb\uff0c\u7cfb\u7edf\u88ab\u968f\u673a\u5316\u3002\u5728\u9009\u62e9\u4e00\u4e2a\u521d\u59cb\u4f4d\u5f62\u540e\uff0c\u8457\u540d\u7684\u751f\u547d\u6e38\u620f\u6f14\u5316\u89c4\u5219[27]\u88ab\u5e94\u75281000\u6b21\uff0c\u5bfc\u81f4\u6700\u7ec8\u72b6\u6001<\/span>\u3002\u6a21\u62df\u8868\u660e\uff0c\u8fd9\u4e2a\u65f6\u95f4\u95f4\u9694\u8db3\u4ee5\u4f7f\u7cfb\u7edf\u5728\u78b0\u649e\u540e\u5904\u4e8e\u7a33\u5b9a\u72b6\u6001\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u4e3a\u4e86\u4f7f\u7528\u516c\u5f0f\uff0810\uff09\u7684\u6807\u51c6\uff0c\u6211\u4eec\u9700\u8981\u9009\u62e9\u4e00\u4e2a\u5019\u9009\u7684\u6d8c\u73b0\u7279\u5f81<\/span>\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u8003\u8651\u4e00\u4e2a\u7b26\u53f7\u5316\u7684\u3001\u79bb\u6563\u503c\u5411\u91cf\u6765\u7f16\u7801\u7f51\u683c\u4e0a\u7684\u7c92\u5b50\u7c7b\u578b\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u6211\u4eec\u8003\u8651<\/span>\uff0c\u5176\u4e2d<\/span>\uff0c\u5982\u679c\u5728\u65f6\u95f4t\u6709\u4e00\u4e2aj\u7c7b\u578b\u7684\u7c92\u5b50\uff0c\u65e0\u8bba\u5176\u4f4d\u7f6e\u6216\u65b9\u5411\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u6709\u4e86\u8fd9\u4e9b\u53d8\u91cf\uff0c\u6211\u4eec\u4f7f\u7528\u4e92\u4fe1\u606f\u7684\u8d1d\u53f6\u65af\u4f30\u8ba1\u5668\u6765\u8ba1\u7b97\u516c\u5f0f\uff0810\uff09\u4e2d\u7684\u91cf[32]\u3002\u7ed3\u679c\u662f\uff0c\u6b63\u5982\u9884\u671f\u90a3\u6837\uff0c\u56e0\u679c\u5173\u7cfb\u51fa\u73b0\u7684\u6807\u51c6\u662f<\/span>\u3002\u6b64\u5916\uff0c\u6211\u4eec\u53d1\u73b0<\/span>\uff0c\u8fd9\u6bd4<\/span>\u5c0f\u4e86\u51e0\u4e2a\u6570\u91cf\u7ea7\u3002\u8bef\u5dee\u4ee3\u8868\u4ee3\u7528\u6570\u636e\u7684\u6807\u51c6\u504f\u5dee\uff0c\u5982\u9644\u5f55S1\u7b2c5\u8282\u6240\u8ff0\u3002\u4f7f\u7528\u547d\u98981\uff0c\u8fd9\u4e24\u4e2a\u7ed3\u679c\u8868\u660e\uff0c\u751f\u547d\u6e38\u620f\u4e2d\u7684\u7c92\u5b50\u52a8\u529b\u5b66\u53ef\u80fd\u4e0d\u4ec5\u662f\u6d8c\u73b0\u7684\uff0c\u800c\u4e14\u4e0e\u5b83\u4eec\u7684\u5e95\u5c42\u662f\u56e0\u679c\u89e3\u8026\u7684\u3002<\/strong><\/span><\/section>\n
 <\/span><\/section>\n
<\/section>\n

\u56fe4. \u5eb7\u5a01\u751f\u547d\u6e38\u620f\u4e2d\u7684\u56e0\u679c\u6d8c\u73b0\u3002\u7cfb\u7edf\u88ab\u521d\u59cb\u5316\u4e3a “\u7c92\u5b50\u5bf9\u649e\u673a”\u8bbe\u7f6e\uff0c\u5e76\u8fd0\u884c\u5230\u78b0\u649e\u540e\u8fbe\u5230\u4e00\u4e2a\u7a33\u5b9a\u4f4d\u5f62\u3002\u4f7f\u7528\u7c92\u5b50\u7c7b\u578b\u4f5c\u4e3a\u968f\u9644\u7279\u5f81V\uff0c\u6211\u4eec\u53d1\u73b0\u8be5\u7cfb\u7edf\u7b26\u5408\u6211\u4eec\u5bf9\u56e0\u679c\u6d8c\u73b0\u7684\u5b9e\u7528\u6807\u51c6\u3002<\/span><\/p>\n

 <\/span><\/section>\n
\u96f7\u8bfa\u7684\u9e1f\u7fa4\u6a21\u578b<\/span><\/strong>\u3002\u4f5c\u4e3a\u7b2c\u4e8c\u4e2a\u6d4b\u8bd5\u6848\u4f8b\uff0c\u6211\u4eec\u8003\u8651\u96f7\u8bfa\u7684\u96c6\u7fa4\u884c\u4e3a\u6a21\u578b\u3002\u8fd9\u4e2a\u6a21\u578b\u7531 boids<\/span>\uff08\u7c7b\u4f3c\u9e1f\u7684\u7269\u4f53\uff09<\/span>\u7ec4\u6210\uff0c\u6bcf\u4e2aboid\u7531\u4e09\u4e2a\u6570\u5b57\u8868\u793a\uff1a\u5b83\u5728\u4e8c\u7ef4\u7a7a\u95f4\u7684\u4f4d\u7f6e\u548c\u884c\u8fdb\u65b9\u5411\u7684\u89d2\u5ea6\u3002\u4f5c\u4e3a\u6d8c\u73b0\u7684\u5019\u9009\u7279\u5f81\uff0c\u6211\u4eec\u6309\u7167Seth[6]\u7684\u505a\u6cd5\uff0c\u4f7f\u7528\u9e1f\u7fa4\u8d28\u5fc3\u7684\u4e8c\u7ef4\u5750\u6807\u3002<\/span><\/section>\n
 <\/span><\/section>\n

\u5728\u8fd9\u4e2a\u6a21\u578b\u4e2d\uff0cboid\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u9075\u5faa\u4e09\u4e2a\u89c4\u5219\uff0c\u6bcf\u4e2a\u89c4\u5219\u7531\u4e00\u4e2a\u6807\u91cf\u53c2\u6570\u8c03\u8282[6]\u3002<\/span><\/p>\n

\u00b7 \u805a\u96c6\uff08a1<\/sub>\uff09\uff1a\u5f53\u5b83\u4eec\u98de\u5411\u9e1f\u7fa4\u4e2d\u5fc3\u65f6\u3002<\/span><\/p>\n

\u00b7 \u56de\u907f\uff08a2<\/sub>\uff09\uff1a\u5f53\u5b83\u4eec\u98de\u79bb\u5176\u6700\u8fd1\u7684\u90bb\u5c45\u65f6\uff1b<\/span><\/p>\n

\u00b7 \u5bf9\u9f50\uff08a3<\/sub>\uff09\uff1a\u5f53\u5b83\u4eec\u7684\u98de\u884c\u65b9\u5411\u4e0e\u90bb\u5c45\u4e00\u81f4\u65f6\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u6839\u636e\u53c2\u8003\u6587\u732e[6]\uff0c\u6211\u4eec\u7814\u7a76\u4e86\u4e0d\u540c\u53c2\u6570\u8bbe\u7f6e\u4e0b N=10 \u4e2a boid \u7684\u5c0f\u9e1f\u7fa4\uff0c\u4ee5\u5c55\u793a\u6211\u4eec\u7684\u5b9e\u7528\u6d8c\u73b0\u6807\u51c6\u7684\u4e00\u4e9b\u7279\u6027\u3002\u8bf7\u6ce8\u610f\uff0c\u8fd9\u9879\u7814\u7a76\u662f\u4e3a\u4e86\u8bf4\u660e\u6240\u63d0\u51fa\u7684\u7406\u8bba\uff0c\u800c\u4e0d\u662f\u4f5c\u4e3a\u5bf9\u9e1f\u7fa4\u6a21\u578b\u7684\u8be6\u7ec6\u63a2\u7d22\uff0c\u5173\u4e8e\u8fd9\u4e2a\u6a21\u578b\u5df2\u6709\u5927\u91cf\u6587\u732e\u5b58\u5728<\/span>\uff08\u4f8b\u5982\uff0c\u89c1Vicsek\u7684\u5de5\u4f5c[33]\u548c\u5176\u4e2d\u7684\u53c2\u8003\u6587\u732e\uff09<\/span>\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u56fe5\u663e\u793a\u4e86\u5728\u4fdd\u6301 a1<\/sub> \u548c a3<\/sub> \u56fa\u5b9a\u7684\u60c5\u51b5\u4e0b\uff0c\u5bf9\u56de\u907f\u53c2\u6570a2<\/sub>\u8fdb\u884c\u53c2\u6570\u626b\u63cf\u7684\u7ed3\u679c\u3002\u5f53\u6ca1\u6709\u56de\u907f\u65f6\uff0cboid \u56f4\u7ed5\u7f13\u6162\u79fb\u52a8\u7684\u8d28\u5fc3\u65cb\u8f6c\uff0c\u53ef\u79f0\u4e3a\u6709\u5e8f\u7684\u5f62\u6001\u3002\u76f8\u53cd\uff0c\u5f53\u56de\u907f\u53c2\u6570 a2<\/sub> \u8f83\u5927\u65f6\uff0c\u8fd1\u90bb\u7684\u6392\u65a5\u529b\u592a\u5f3a\uff0c\u65e0\u6cd5\u5f62\u6210\u6301\u4e45\u7684\u9e1f\u7fa4\uff0c\u5b64\u7acb\u7684 boid \u5206\u6563\u5728\u7a7a\u95f4\u4e2d\uff0c\u76f8\u4e92\u56de\u907f\u3002\u5f53\u56de\u907f\u53c2\u6570\u5904\u4e8e\u4e2d\u95f4\u503c\u65f6\uff0c\u968f\u7740\u9e1f\u7fa4\u805a\u96c6\u548c\u89e3\u4f53\uff0c\u8d28\u5fc3\u5f62\u6210\u4e00\u4e2a\u5e73\u6ed1\u7684\u8f68\u8ff9\u3002\u4e0eSeth[6]\u7684\u7814\u7a76\u7ed3\u679c\u4e00\u81f4\uff0c\u6211\u4eec\u7684\u6807\u51c6\u8868\u660e\uff0c\u5728\u8fd9\u4e2a\u4e2d\u95f4\u8303\u56f4\u5185\uff0c\u7fa4\u4f53\u8868\u73b0\u51fa\u56e0\u679c\u6d8c\u73b0\u884c\u4e3a\u3002<\/span><\/section>\n
   <\/span><\/section>\n
\u901a\u8fc7\u5206\u522b\u7814\u7a76\u6784\u6210 \u0470 \u7684\u4e24\u4e2a\u9879\uff0c\u6211\u4eec\u53d1\u73b0\uff0c\u5bf9\u4e8e\u8f83\u5c0f\u548c\u8f83\u5927\u7684\u56de\u907f\u53c2\u6570 a2<\/sub>\uff0c\u90fd\u6ca1\u6709\u51fa\u73b0\u6d8c\u73b0\uff0c\u4f46\u672a\u51fa\u73b0\u7684\u539f\u56e0\u4e0d\u540c<\/span>\uff08\u89c1\u56fe5\uff09<\/span>\u3002\u5b9e\u9645\u4e0a\uff0c\u5bf9\u4e8e\u8f83\u5927\u7684 a2<\/sub> \u6765\u8bf4\uff0c\u8d28\u5fc3\u7684\u81ea\u6211\u53ef\u9884\u6d4b\u6027\uff08\u5373<\/span>\uff09\u8f83\u5c0f\uff1b\u800c\u5bf9\u4e8e\u8f83\u5c0f\u7684 a2<\/sub> \u6765\u8bf4\uff0c\u8d28\u5fc3\u7684\u81ea\u6211\u53ef\u9884\u6d4b\u6027\u8f83\u5927\uff0c\u4f46\u4ecd\u7136\u4f4e\u4e8e\u5355\u4e2aboid\u7684\u4e92\u4fe1\u606f\uff08\u5373<\/span>\uff09\u3002\u8fd9\u4e9b\u7ed3\u679c\u8868\u660e\uff0c\u4f4e\u56de\u907f\u60c5\u666f\u4e0d\u662f\u7531\u534f\u540c\u4f5c\u7528\u7684\u51cf\u5c11\uff0c\u800c\u662f\u7531\u5197\u4f59\u7684\u589e\u52a0\u6240\u4e3b\u5bfc\uff0c\u8fd9\u6709\u6548\u5730\u589e\u52a0\u4e86\u68c0\u6d4b\u6d8c\u73b0\u6240\u9700\u7684\u534f\u540c\u4f5c\u7528\u9608\u503c\u3002\u7136\u800c\uff0c\u8bf7\u6ce8\u610f\uff0c\u7531\u4e8e\u8be5\u6807\u51c6\u7684\u5c40\u9650\u6027\uff0c<\/span>\u8fd9\u4e00\u4e8b\u5b9e\u5e76\u4e0d\u662f\u7ed3\u8bba\u6027\u7684\uff0c\u4e0d\u80fd\u6392\u9664\u6d8c\u73b0\u7684\u53ef\u80fd\u6027\u3002\u8fd9\u662f\u5bf9\u50cf \u0470 \u8fd9\u6837\u7684\u201c\u6574\u4f53\u51cf\u53bb\u603b\u548c\u201d\u4f30\u8ba1\u5668\u7684\u5e38\u89c1\u9650\u5236\uff1b\u8fdb\u4e00\u6b65\u7684\u5b8c\u5584\u53ef\u80fd\u4f1a\u63d0\u4f9b\u4e0d\u90a3\u4e48\u5bb9\u6613\u53d7\u8fd9\u4e9b\u95ee\u9898\u5f71\u54cd\uff0c\u5e76\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\u51c6\u786e\u6267\u884c\u7684\u754c\u9650\u3002<\/span><\/section>\n
 <\/span><\/section>\n
<\/section>\n

\u56fe5. \u9e1f\u7fa4\u6a21\u578b\u4e2d\u7684\u56e0\u679c\u6d8c\u73b0\u3002\u968f\u7740\u56de\u907f\u53c2\u6570\u7684\u589e\u52a0\uff0c\u7fa4\u4f53\u4ece\u5438\u5f15\u7684\u5f62\u6001\uff08\u5176\u4e2d\u6240\u6709\u9e1f\u6709\u89c4\u5f8b\u5730\u56f4\u7ed5\u4e00\u4e2a\u7a33\u5b9a\u8d28\u5fc3\u65cb\u8f6c\uff09\u8f6c\u53d8\u4e3a\u6392\u65a5\u7684\u5f62\u6001\uff08\u5176\u4e2d\u9e1f\u5728\u7a7a\u95f4\u6269\u6563\uff0c\u770b\u4e0d\u5230\u7fa4\u4f53\uff09\u3002a\uff09\u6211\u4eec\u7684\u6807\u51c6 \u0470 \u5728\u56de\u907f\u53c2\u6570\u7684\u4e2d\u95f4\u8303\u56f4\u68c0\u6d4b\u5230\u56e0\u679c\u6d8c\u73b0\uff08\u8bef\u5dee\u6761\u4ee3\u8868\u5bf9\u4ee3\u7528\u6570\u636e\u4f30\u8ba1\u7684\u6807\u51c6\u504f\u5dee\uff09\u3002b) boid\uff08\u7070\u8272\uff09\u548c\u5176\u8d28\u5fc3\uff08\u7ea2\u8272\uff09\u7684\u6837\u672c\u8f68\u8ff9\u3002<\/span><\/p>\n

 <\/span><\/section>\n

\n
5.2 \u5fc3\u667a\u6765\u81ea\u7269\u8d28\uff1a\u6d8c\u73b0\u3001\u884c\u4e3a\u548c\u795e\u7ecf\u751f\u7406\u5b66<\/span><\/strong><\/span><\/section>\n<\/h2>\n
 <\/span><\/section>\n
\u62e5\u6709\u5f62\u5f0f\u5316\u7684\u6d8c\u73b0\u7406\u8bba\u7684\u4e00\u4e2a\u8bf1\u4eba\u7ed3\u679c\u662f\uff0c\u80fd\u591f\u4ece\u5b9a\u91cf\u89d2\u5ea6\u770b\u5f85\u4e00\u4e2a\u6d8c\u73b0\u7684\u539f\u578b\uff1a\u5fc3\u667a-\u7269\u8d28\u5173\u7cfb[35, 36]\u3002\u4f5c\u4e3a\u8fd9\u4e2a\u65b9\u5411\u7684\u7b2c\u4e00\u6b65\uff0c\u6211\u4eec\u5728\u672c\u8282\u7684\u6700\u540e\u5c06\u6211\u4eec\u7684\u6d8c\u73b0\u6807\u51c6\u5e94\u7528\u4e8e\u795e\u7ecf\u751f\u7406\u5b66\u6570\u636e\u3002<\/span><\/section>\n

<\/section>\n
\u6211\u4eec\u7814\u7a76\u4e86\u65e5\u672c\u7315\u7334\u8fdb\u884c\u4f38\u624b\u4efb\u52a1\u7684\u540c\u6b65\u76ae\u8d28\u8111\u7535\u56fe<\/span>\uff08electrocorticogram\uff0cECoG\uff09<\/span>\u548c\u52a8\u4f5c\u6355\u6349<\/span>\uff08motion capture\uff0cMoCap\uff09<\/span>\u6570\u636e[34]\uff0c\u8fd9\u4e9b\u6570\u636e\u4ece\u5728\u7ebfNeurotycho\u6570\u636e\u5e93\u83b7\u5f97\u3002\u8bf7\u6ce8\u610f\uff0cMoCap\u6570\u636e\u4e0d\u80fd\u88ab\u5047\u5b9a\u4e3a\u73b0\u6709ECoG\u6570\u636e\u7684\u968f\u9644\u7279\u5f81\uff0c\u56e0\u4e3a\u5b83\u4e0d\u6ee1\u8db3\u6211\u4eec\u7684\u968f\u9644\u5b9a\u4e49\u6240\u8981\u6c42\u7684\u6761\u4ef6\u72ec\u7acb\u6027\u6761\u4ef6<\/span>\uff08\u89c1\u201c\u56e0\u679c\u6d8c\u73b0\u7684\u5f62\u5f0f\u7406\u8bba\u201d\u4e00\u8282\uff09<\/span>\u3002\u8fd9\u79cd\u60c5\u51b5\u5f88\u53ef\u80fd\u53d1\u751f\uff0c\u56e0\u4e3a\u795e\u7ecf\u7cfb\u7edf\u53ea\u88ab\u90e8\u5206\u89c2\u5bdf\u5230\u2014\u2014\u5373ECoG\u5e76\u6ca1\u6709\u6355\u6349\u5230\u7315\u7334\u76ae\u5c42\u4e2d\u76f8\u5173\u6d3b\u52a8\u7684\u6bcf\u4e00\u4e2a\u6765\u6e90\u3002\u8bf7\u6ce8\u610f\uff0c\u6211\u4eec\u7684\u6846\u67b6\u5bf9\u975e\u968f\u9644\u7279\u5f81\u7684\u5174\u8da3\u6709\u9650\uff0c\u56e0\u4e3a\u5b83\u4eec\u53ef\u4ee5\u4ee5\u5e73\u5eb8\u7684\u65b9\u5f0f\u6ee1\u8db3\u547d\u98981<\/span>\uff08\u4f8b\u5982\uff0c\u5982\u679c\u72ec\u7acb\u4e8e\u5e95\u5c42\u7cfb\u7edf\u7684\u65f6\u95f4\u5e8f\u5217\u662f\u81ea\u5173\u8054\u7684\uff0c\u5b83\u4eec\u5c06\u6ee1\u8db3 \u0470>0\uff09<\/span>\u3002\u76f8\u53cd\uff0c\u6211\u4eec\u91cd\u70b9\u5173\u6ce8\u4e0e\u9884\u6d4b\u7315\u7334\u884c\u4e3a\u6709\u5173\u7684\u7f16\u7801\u5728ECoG\u4fe1\u53f7\u4e2d\u7684\u90a3\u90e8\u5206\u795e\u7ecf\u6d3b\u52a8\uff0c\u5e76\u63a8\u6d4b\u8fd9\u4e00\u4fe1\u606f\u662f\u5e95\u5c42\u795e\u7ecf\u6d3b\u52a8\u7684\u4e00\u4e2a\u6d8c\u73b0\u7279\u5f81<\/span>\uff08\u56fe6\uff09<\/span>\u3002<\/span><\/section>\n
 <\/span><\/section>\n
<\/section>\n

\u56fe6. \u6e05\u9192\u7315\u7334\u8fd0\u52a8\u884c\u4e3a\u4e2d\u7684\u56e0\u679c\u6d8c\u73b0\u3002a) \u5f55\u97f3\u4e2d\u4f7f\u7528\u7684\u76ae\u8d28\u8111\u7535\u56fe\uff08ECoG\uff09\u7535\u6781\u7684\u4f4d\u7f6e\uff08\u84dd\u8272\uff09\u53e0\u52a0\u5728\u7315\u7334\u5de6\u534a\u7403\u7684\u56fe\u50cf\u4e0a\uff08\u5927\u8111\u524d\u65b9\u671d\u5411\u9875\u9762\u9876\u90e8\uff09\u3002b) \u6240\u7528\u768464\u901a\u9053ECoG\u8bb0\u5f55\u7684\u65f6\u95f4\u5e8f\u5217\u6837\u672c\uff08\u84dd\u8272\uff09\uff0c\u5bf9\u5e94\u4e8e\u611f\u5174\u8da3\u7684\u7cfb\u7edf<\/span>\u3002c) \u7315\u7334\u624b\u8155\u7684\u4e09\u7ef4\u4f4d\u7f6e\u7531\u8fd0\u52a8\u6355\u6349\u6d4b\u91cf\uff08\u84dd\u8272\uff09\uff0c\u5e76\u7531\u56de\u5f52\u6a21\u578b\u9884\u6d4b\uff08\u6a59\u8272\uff09\uff0c\u53ef\u4ee5\u4f5c\u4e3a\u4e00\u4e2a\u968f\u9644\u7279\u5f81<\/span>\u3002d) \u6211\u4eec\u7684\u6d8c\u73b0\u6807\u51c6\u5f97\u5230<\/span>\uff0c\u68c0\u6d4b\u5230\u4e0eECoG\u6e90\u6709\u5173\u884c\u4e3a\u7684\u56e0\u679c\u6d8c\u73b0\u3002\u539f\u59cb\u6570\u636e\u548c\u56fe\u50cf\u6765\u81ea\u53c2\u8003\u6587\u732e[34]\u548cNeurotycho\u6570\u636e\u5e93\u3002<\/span><\/p>\n


<\/section>\n
\u4e3a\u4e86\u9a8c\u8bc1\u8fd9\u4e00\u5047\u8bbe\uff0c\u6211\u4eec\u628a\u795e\u7ecf\u6d3b\u52a8<\/span>\uff08\u7531\u5206\u5e03\u5728\u5de6\u534a\u7403\u768464\u4e2aECoG\u901a\u9053\u6d4b\u91cf\uff09<\/span>\u4f5c\u4e3a\u611f\u5174\u8da3\u7684\u7cfb\u7edf\uff0c\u5e76\u8003\u8651\u6839\u636eECoG\u4fe1\u53f7\u5bf9\u7315\u7334\u53f3\u624b\u8155\u7684\u4e09\u7ef4\u5750\u6807\u8fdb\u884c\u65e0\u8bb0\u5fc6\u9884\u6d4b\u3002\u56e0\u6b64\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c<\/span>\uff0c\u4e14<\/span>\u3002\u4e3a\u4e86\u5efa\u7acbVt<\/sub><\/span>\uff0c\u6211\u4eec\u4f7f\u7528\u4e86\u90e8\u5206\u6700\u5c0f\u4e8c\u4e58\u6cd5<\/span>\uff08Partial Least Squares\uff0cPLS\uff09<\/span>\u548c\u652f\u6301\u5411\u91cf\u673a<\/span>\uff08Support Vector Machine\uff0cSVM\uff09<\/span>\u56de\u5f52\u5668\uff0c\u5176\u7ec6\u8282\u53ef\u5728\u9644\u5f55S1\u7b2c6\u8282\u4e2d\u627e\u5230\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u5728\u5bf9\u89e3\u7801\u5668\u8fdb\u884c\u8bad\u7ec3\u5e76\u5728\u4e00\u4e2a\u4fdd\u6301\u4e0d\u53d8\u7684\u6d4b\u8bd5\u96c6\u4e0a\u8fdb\u884c\u8bc4\u4f30\u540e\uff0c\u7ed3\u679c\u663e\u793a \u0470>0\uff0c\u8bc1\u5b9e\u4e86\u6211\u4eec\u7684\u731c\u60f3\uff0c\u5373\u4e0e\u8fd0\u52a8\u6709\u5173\u7684\u4fe1\u606f\u662f\u7315\u7334\u76ae\u5c42\u6d3b\u52a8\u7684\u4e00\u4e2a\u6d8c\u73b0\u7279\u5f81\u3002\u5bf9\u4e8e\u77ed\u65f6\u95f4\u5c3a\u5ea6\uff08t’-t = 8 ms\uff09\uff0c\u6211\u4eec\u53d1\u73b0<\/span>\uff0c\u6bd4<\/span>\u5c0f\u51e0\u4e2a\u6570\u91cf\u7ea7\uff0c\u8868\u660e\u8be5\u884c\u4e3a\u53ef\u80fd\u6709\u4e00\u4e2a\u4e0e\u5355\u4e2aECoG\u901a\u9053\u89e3\u8026\u7684\u91cd\u8981\u7ec4\u6210\u90e8\u5206<\/span>\uff08\u8bef\u5dee\u662f\u6839\u636e\u65f6\u95f4\u6570\u636e\u4f30\u8ba1\u7684\u6807\u51c6\u504f\u5dee\uff09<\/span>\u3002\u6b64\u5916\uff0c\u5728\u591a\u4e2a\u4e0d\u8d85\u8fc7 ~0.2s \u7684\u65f6\u95f4\u5c3a\u5ea6 t’-t \u4e0a\uff0c\u6d8c\u73b0\u6807\u51c6\u90fd\u5f97\u5230\u6ee1\u8db3\uff0c\u8d85\u8fc7\u8fd9\u4e2a\u65f6\u95f4\u5c3a\u5ea6\uff0cVt<\/sub>\u548c\u5355\u4e2a\u7535\u6781\u7684\u9884\u6d4b\u80fd\u529b\u4e0b\u964d\uff0c\u53d8\u5f97\u51e0\u4e4e\u76f8\u540c\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u4f5c\u4e3a\u5bf9\u7167\uff0c\u6211\u4eec\u8fdb\u884c\u4e86\u4e00\u4e2a\u66ff\u4ee3\u6570\u636e\u6d4b\u8bd5\uff0c\u4ee5\u786e\u8ba4\u56fe6\u4e2d\u7684\u7ed3\u679c\u4e0d\u662f\u7531ECoG\u65f6\u95f4\u5e8f\u5217\u7684\u81ea\u5173\u8054\u9a71\u52a8\u7684\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u4f7f\u7528\u76f8\u540c\u7684ECoG\u6570\u636e\u91cd\u65b0\u8fdb\u884c\u5206\u6790<\/span>\uff08\u5305\u62ec\u8bad\u7ec3\u548c\u6d4b\u8bd5PLS-SVM\uff09<\/span>\uff0c\u4f46\u5bf9\u624b\u8155\u4f4d\u7f6e\u8fdb\u884c\u4e86\u65f6\u95f4\u8c03\u6574\uff0c\u7ed3\u679c\u662f Vt<\/sub>\u6ca1\u6709\u4eceECoG\u4e2d\u63d0\u53d6\u4efb\u4f55\u6709\u610f\u4e49\u7684\u4fe1\u606f\uff0c\u4f46\u5177\u6709\u7531\u81ea\u5173\u8054\u3001\u8fc7\u6ee4\u548c\u6b63\u5219\u5316\u5f15\u8d77\u7684\u76f8\u540c\u5c5e\u6027\u3002\u6b63\u5982\u9884\u671f\u7684\u90a3\u6837\uff0c\u66ff\u4ee3\u6570\u636e<\/span>\u660e\u663e\u4f4e\u4e8e\u4f7f\u7528\u672a\u8c03\u6574\u7684\u624b\u8155\u4f4d\u7f6e\u6570\u636e\uff0c\u8bc1\u5b9e\u6d4b\u91cf\u7684<\/span>\u662f\u6b63\u7684\uff0c\u9ad8\u4e8e\u5bf9ECoG\u7684\u7c7b\u4f3c\u968f\u673a\u6295\u5f71\u7684\u9884\u671f\u503c<\/span>\uff08\u8be6\u60c5\u89c1\u9644\u5f55S1\u7b2c6\u8282\uff09<\/span>\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u8fd9\u79cd\u5206\u6790\u867d\u7136\u53ea\u662f\u4e00\u4e2a\u6982\u5ff5\u7684\u8bc1\u660e\uff0c\u4f46\u6709\u52a9\u4e8e\u6211\u4eec\u91cf\u5316\u884c\u4e3a\u5982\u4f55\u4ee5\u53ca\u5728\u591a\u5927\u7a0b\u5ea6\u4e0a\u4ece\u96c6\u4f53\u795e\u7ecf\u6d3b\u52a8\u4e2d\u6d8c\u73b0\uff1b\u5e76\u4e3a\u8fdb\u4e00\u6b65\u6d4b\u8bd5\u548c\u91cf\u5316\u5fc3\u667a-\u7269\u8d28\u5173\u7cfb\u7684\u7ecf\u9a8c\u63a2\u7d22\u6253\u5f00\u4e86\u5927\u95e8\u3002<\/span><\/section>\n
 <\/span><\/section>\n

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 <\/span>
<\/section>\n<\/h1>\n

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<\/svg><\/section>\n<\/section>\n<\/section>\n
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6. \u8ba8\u8bba<\/strong><\/strong><\/p>\n<\/section>\n

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


<\/p>\n

\u5f88\u5927\u4e00\u90e8\u5206\u73b0\u4ee3\u79d1\u5b66\u6587\u732e\u8ba4\u4e3a\uff0c\u5f3a\u6d8c\u73b0\u662f\u4e0d\u53ef\u80fd\u7684\u6216\u5b9a\u4e49\u4e0d\u6e05\u7684\u3002\u8fd9\u79cd\u5224\u65ad\u5e76\u4e0d\u662f\u5b8c\u5168\u6ca1\u6709\u6839\u636e\u7684\uff1a\u4e00\u4e2a\u540c\u65f6\u5177\u6709\u968f\u9644\u6027<\/span>\uff08\u5373\u53ef\u4ee5\u4ece\u7cfb\u7edf\u7684\u72b6\u6001\u4e2d\u8ba1\u7b97\u51fa\u6765\uff09<\/span>\u548c\u4e0d\u53ef\u8fd8\u539f\u56e0\u679c\u6548\u5e94<\/span>\uff08\u5373\u544a\u8bc9\u6211\u4eec\u4e00\u4e9b\u90e8\u5206\u6240\u6ca1\u6709\u7684\u4e1c\u897f\uff09<\/span>\u7684\u5c5e\u6027\u786e\u5b9e\u53ef\u4ee5\u770b\u8d77\u6765\u9887\u4e3a\u77db\u76fe [5]\u3002\u5c3d\u7ba1\u5982\u6b64\uff0c\u901a\u8fc7\u5c06\u968f\u9644\u6027\u4e0e\u9759\u6001\u5173\u7cfb\u8054\u7cfb\u8d77\u6765\uff0c\u5c06\u56e0\u679c\u6548\u5e94\u4e0e\u52a8\u6001\u7279\u5f81\u8054\u7cfb\u8d77\u6765\uff0c\u6211\u4eec\u7684\u6846\u67b6\u663e\u793a\uff0c\u8fd9\u4e24\u79cd\u73b0\u8c61\u4e0e\u591a\u53d8\u91cf\u4fe1\u606f\u52a8\u529b\u5b66\u7684\u89c4\u5f8b[20]\u662f\u5b8c\u5168\u517c\u5bb9\u7684\u2014\u2014\u8fd9\u4e00\u70b9\u662f\u53cd\u76f4\u89c9\u7684\u2014\u2014\u4e3a\u8fd9\u4e2a\u6096\u8bba\u63d0\u4f9b\u4e86\u4e00\u4e2a\u521d\u6b65\u89e3\u51b3\u65b9\u6848\u3002<\/span>
<\/section>\n
 <\/span><\/section>\n
\u6211\u4eec\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u662f\u5173\u4e8e\u9884\u6d4b\u80fd\u529b\uff0c\u800c\u4e0d\u662f\u201c\u53ef\u89e3\u91ca\u6027\u201d[3]\uff0c\u56e0\u6b64\u4e0e\u5f3a\u6d8c\u73b0\u7684\u89c2\u70b9\u65e0\u5173\uff0c\u5982Chalmers\u7684\u89c2\u70b9[3]\u3002\u7136\u800c\uff0c\u6211\u4eec\u7684\u6846\u67b6\u5305\u542b\u901a\u5e38\u4e0e\u5f3a\u6d8c\u73b0\u76f8\u5173\u7684\u65b9\u9762\u2014\u2014\u6bd4\u5982\u81ea\u4e0a\u800c\u4e0b\u56e0\u679c\u2014\u2014\u5e76\u4e14\u4f7f\u5b83\u4eec\u53ef\u4ee5\u91cf\u5316\u3002\u6211\u4eec\u7684\u6846\u67b6\u4e5f\u4e0d\u7b26\u5408\u5f31\u6d8c\u73b0\u7684\u4f20\u7edf\u5b9a\u4e49<\/span>\uff08\u5728\u201c\u57fa\u672c\u76f4\u89c9\u201d\u4e00\u8282\u4e2d\u7814\u7a76\u7684\u7cfb\u7edf\u4e0d\u662fBedau[5]\u610f\u4e49\u4e0a\u7684\u5f31\u6d8c\u73b0\uff0c\u5b83\u4eec\u7b80\u5355\uff0c\u4e14\u5bb9\u6613\u88ab\u89e3\u91ca\u7684\u6377\u5f84\u6240\u5f71\u54cd\uff09<\/span>\uff0c\u4f46\u4e0e\u66f4\u666e\u904d\u7684\u5f31\u6d8c\u73b0\u6982\u5ff5\u517c\u5bb9\uff0c\u4f8b\u5982Seth\u63d0\u51fa\u7684\u6982\u5ff5<\/span>\uff08\u89c1\u201c\u4e0e\u5176\u4ed6\u6d8c\u73b0\u91cf\u5316\u7406\u8bba\u7684\u5173\u7cfb\u201d\u4e00\u8282\uff09<\/span>\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u7684\u7406\u8bba\u53ef\u4ee5\u88ab\u770b\u4f5c\u662f\u8c03\u548c\u8fd9\u4e9b\u65b9\u6cd5\u7684\u4e00\u79cd\u5c1d\u8bd5[36]\uff0c\u8868\u660e\u4e00\u4e2a\u201c\u5f31\u201d\u6846\u67b6\u53ef\u4ee5\u6709\u591a\u201c\u5f3a\u201d\u3002<\/span><\/section>\n
   <\/span><\/section>\n
\u6211\u4eec\u7406\u8bba\u7684\u4e00\u4e2a\u91cd\u8981\u7ed3\u679c\u662f\u5728\u56e0\u679c\u6d8c\u73b0\u548c\u7edf\u8ba1\u534f\u540c\u4e4b\u95f4\u5efa\u7acb\u57fa\u672c\u8054\u7cfb\uff1a\u7814\u7a76\u53d1\u73b0\uff0c\u7cfb\u7edf\u627f\u8f7d\u6d8c\u73b0\u7279\u5f81\u7684\u80fd\u529b\u7531\u5176\u5143\u7d20\u5728\u672a\u6765\u6f14\u5316\u4e2d\u7684\u534f\u540c\u7a0b\u5ea6\u51b3\u5b9a\u3002\u867d\u7136\u5728\u8fc7\u53bb\u5173\u4e8e\u534f\u540c\u7684\u60f3\u6cd5\u4e0e\u6d8c\u73b0\u6709\u677e\u6563\u7684\u8054\u7cfb[37]\uff0c\u4f46\u8fd9\u662f<\/span>\uff08\u5c31\u6211\u4eec\u6240\u77e5\uff09<\/span>\u7b2c\u4e00\u6b21\u5229\u7528\u591a\u53d8\u91cf\u4fe1\u606f\u8bba\u7684\u6700\u65b0\u8fdb\u5c55\uff0c\u5f62\u5f0f\u5316\u5730\u63d0\u51fa\u548c\u91cf\u5316\u8fd9\u79cd\u60f3\u6cd5\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u7814\u7a76\u4e00\u4e9b\u5173\u4e8e\u6240\u63d0\u51fa\u7406\u8bba\u7684\u9002\u7528\u6027\u7684\u6ce8\u610f\u4e8b\u9879\uff0c\u5b83\u4e0e\u5148\u524d\u5de5\u4f5c\u7684\u5173\u7cfb\uff0c\u4ee5\u53ca\u4e00\u4e9b\u5f00\u653e\u6027\u95ee\u9898\u3002<\/span><\/section>\n
   <\/span><\/section>\n

\n
6.1 \u7406\u8bba\u7684\u8303\u56f4<\/span><\/strong><\/span><\/section>\n<\/h2>\n
 <\/span><\/section>\n
\u6211\u4eec\u7684\u7406\u8bba\u4fa7\u91cd\u4e8e\u6d8c\u73b0\u7684\u540c\u6b65\u6027[38]\u65b9\u9762\uff0c\u5206\u6790\u52a8\u6001\u7cfb\u7edf\u5404\u8981\u7d20\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u4ee5\u53ca\u5b83\u4eec\u968f\u65f6\u95f4\u5171\u540c\u6f14\u53d8\u7684\u96c6\u4f53\u5c5e\u6027\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u7684\u7406\u8bba\u76f4\u63a5\u9002\u7528\u4e8e\u4efb\u4f55\u5177\u6709\u660e\u786e\u52a8\u529b\u5b66\u6f14\u5316\u7684\u7cfb\u7edf\uff0c\u5305\u62ec\u7531\u5177\u6709\u968f\u673a\u521d\u59cb\u6761\u4ef6\u7684\u786e\u5b9a\u6027\u52a8\u529b\u7cfb\u7edf\u63cf\u8ff0\u7684\u7cfb\u7edf[11]\uff0c\u548c\u7531 Fokker-Planck \u65b9\u7a0b\u63cf\u8ff0\u7684\u968f\u673a\u7cfb\u7edf[39]\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u6211\u4eec\u7684\u7406\u8bba\u5728\u70ed\u529b\u5b66\u5e73\u8861\u7cfb\u7edf\u4e2d\u7684\u5e94\u7528\u53ef\u80fd\u5e76\u4e0d\u76f4\u63a5\uff0c\u56e0\u4e3a\u5b83\u4eec\u7684\u52a8\u529b\u5b66\u5f80\u5f80\u4e0d\u662f\u7531\u76f8\u5e94\u7684\u5409\u5e03\u65af\u5206\u5e03\u552f\u4e00\u786e\u5b9a\u7684<\/span>\uff08\u4e3e\u4e00\u4e2a\u660e\u786e\u7684\u4f8b\u5b50\uff0c\u5f53\u8003\u8651 Ising \u6a21\u578b\u65f6\uff0c\u5373\u4f7f\u7cfb\u7edf\u5904\u4e8e\u5e73\u8861\u72b6\u6001\uff0cKawasaki \u548c Glauber \u52a8\u529b\u5b66\u7684\u884c\u4e3a\u5df2\u77e5\u662f\u4e0d\u540c\u7684[40]\uff1b\u56e0\u6b64\u53ef\u80fd\u63d0\u4f9b\u4e0e\u201c\u6d4b\u91cf\u6d8c\u73b0\u201d\u90e8\u5206\u63cf\u8ff0\u7684\u76f8\u5f53\u4e0d\u540c\u7684\u6d4b\u91cf\u503c\uff09<\/span>\u3002\u5bfb\u627e\u539f\u5219\u6027\u65b9\u6cd5\u6765\u6307\u5bfc\u6211\u4eec\u7684\u7406\u8bba\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\u7684\u5e94\u7528\u662f\u672a\u6765\u7814\u7a76\u7684\u4e00\u4e2a\u6709\u8da3\u6311\u6218\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u6b64\u5916\uff0c\u8003\u8651\u5230\u201c\u6d8c\u73b0\u201d\u8fd9\u4e2a\u6982\u5ff5\u7684\u5e7f\u5ea6\uff0c\u8fd8\u6709\u4e00\u4e9b\u66f4\u503e\u5411\u4e8e\u54f2\u5b66\u7684\u5176\u4ed6\u7406\u8bba\uff0c\u4e0e\u6211\u4eec\u7684\u6846\u67b6\u6b63\u4ea4\u3002\u8fd9\u5305\u62ec\uff0c\u4f8b\u5982\uff0c\u4f5c\u4e3a\u6839\u672c\u7684\u65b0\u9896\u6027<\/span>\uff08radical novelty\uff0c\u6307\u7cfb\u7edf\u4e2d\u6ca1\u6709\u9884\u5148\u89c2\u5bdf\u5230\u7684\u7279\u5f81\uff09<\/span>\u7684\u6d8c\u73b0\u7406\u8bba[41]\uff0c\u6700\u8457\u540d\u7684\u662f\u5b89\u5fb7\u68ee\u7684\u683c\u8a00\u201cmore is different\u201d [42, 43]\uff0c\u7279\u522b\u662f\u4ed6\u5bf9\u751f\u7269\u5b66\u4e2d\u6d8c\u73b0\u7684\u65b9\u6cd5<\/span>\uff08\u6ce8\u610f\uff0c\u5b89\u5fb7\u68ee\u7684\u4e00\u4e9b\u89c2\u70b9\uff0c\u7279\u522b\u662f\u4e0e\u521a\u5ea6\uff08rigidity\uff09\u6709\u5173\u7684\u89c2\u70b9\uff0c\u4e0e\u6211\u4eec\u7684\u6846\u67b6\u6240\u53d1\u5c55\u7684\u65b9\u6cd5\u5bc6\u5207\u76f8\u5173\uff09<\/span>\uff0c\u4e5f\u5728\u8003\u592b\u66fc\u7684\u5de5\u4f5c\u4e2d\u5f97\u5230\u9610\u8ff0[44, 45]\u3002\u53e6\u5916\uff0c\u4e0a\u4e0b\u6587\u6d8c\u73b0<\/span>\uff08contextual emergence\uff09\u5f3a<\/span>\u8c03\u4e86\u5b8f\u89c2\u5c42\u9762\u7684\u4e0a\u4e0b\u6587\u4f5c\u7528\uff0c\u5b83\u4eec\u65e0\u6cd5\u5728\u5fae\u89c2\u5c42\u9762\u4e0a\u63cf\u8ff0\uff0c\u4f46\u4e3a\u5b8f\u89c2\u6d8c\u73b0\u5728\u5fae\u89c2\u5c42\u9762\u65bd\u52a0\u4e86\u9650\u5236[46, 47]\u3002\u8fd9\u4e9b\u90fd\u662f\u6709\u4ef7\u503c\u7684\u54f2\u5b66\u7acb\u573a\uff0c\u5728\u6587\u732e[46, 48]\u4e2d\u5df2\u7ecf\u4ece\u7edf\u8ba1\u529b\u5b66\u89d2\u5ea6\u8fdb\u884c\u4e86\u7814\u7a76\u3002\u672a\u6765\u7684\u5de5\u4f5c\u5c06\u8bd5\u56fe\u628a\u8fd9\u4e9b\u5176\u4ed6\u65b9\u6cd5\u4e0e\u6211\u4eec\u63d0\u51fa\u7684\u6846\u67b6\u7edf\u4e00\u8d77\u6765\u3002<\/span><\/section>\n
 <\/span><\/section>\n

\n
6.2 \u56e0\u679c<\/span><\/strong><\/span><\/section>\n<\/h2>\n
 <\/span><\/section>\n
\u8bc4\u4f30\u4e00\u4e2a\u7cfb\u7edf\u7684\u56e0\u679c\u7ed3\u6784\u7684\u5b9e\u9645\u65b9\u6cd5\u662f\u5206\u6790\u5176\u5bf9\u5e72\u9884\u7684\u53cd\u5e94\uff0c\u6216\u57fa\u4e8e\u4e13\u4e1a\u77e5\u8bc6\u5efa\u7acb\u5e72\u9884\u6a21\u578b<\/span>\uff08\u56e0\u679c\u56fe\uff09<\/span>\uff0c\u8fd9\u5bfc\u81f4\u4e86\u7531Judea Pearl[10]\u7387\u5148\u63d0\u51fa\u7684\u8457\u540d\u7684 do-\u6f14\u7b97<\/strong> \u3002\u4e0d\u5e78\u7684\u662f\uff0c\u8fd9\u79cd\u65b9\u6cd5\u4e0d\u9002\u7528\u4e8e\u8bb8\u591a\u4eba\u4eec\u611f\u5174\u8da3\u7684\u573a\u666f\uff0c\u56e0\u4e3a\u5e72\u9884\u53ef\u80fd\u4f1a\u4ea7\u751f\u8fc7\u9ad8\u7684\u6210\u672c\uff0c\u751a\u81f3\u662f\u4e0d\u53ef\u80fd\u7684\uff0c\u800c\u4e14\u4e13\u4e1a\u77e5\u8bc6\u53ef\u80fd\u65e0\u6cd5\u83b7\u5f97\u3002\u8fd9\u4e9b\u60c5\u51b5\u4ecd\u7136\u53ef\u4ee5\u901a\u8fc7\u7edf\u8ba1\u56e0\u679c\u7684 Wiener-Granger \u7406\u8bba<\/strong>\u6765\u8bc4\u4f30\uff0c\u8be5\u7406\u8bba\u901a\u8fc7\u8003\u8651\u8fc7\u53bb\u548c\u672a\u6765\u4e8b\u4ef6\u4e4b\u95f4\u7684\u975e\u4e2d\u4ecb\u76f8\u5173\u6027\uff0c\u7814\u7a76\u6574\u4e2a\u611f\u5174\u8da3\u7cfb\u7edf\u7684\u9884\u6d4b\u80fd\u529b\u84dd\u56fe[12]\u3002\u5f53\u6240\u6709\u76f8\u5173\u53d8\u91cf\u90fd\u88ab\u6d4b\u91cf\u65f6\uff0c\u8fd9\u4e24\u4e2a\u6846\u67b6\u63d0\u4f9b\u76f8\u4f3c\u7684\u7ed3\u679c\uff0c\u4f46\u5f53\u5b58\u5728\u672a\u89c2\u5bdf\u5230\u7684\u76f8\u4e92\u4f5c\u7528\u53d8\u91cf\u65f6\uff0c\u8fd9\u4e24\u4e2a\u6846\u67b6\u4f1a\u6709\u6839\u672c\u4e0d\u540c[10]\u3002Wiener-Granger\u5b66\u6d3e\u548cPearl\u5b66\u6d3e\u4e4b\u95f4\u7684\u4e89\u8bba\u5df2\u7ecf\u5728\u5176\u4ed6\u76f8\u5173\u80cc\u666f\u4e0b\u8fdb\u884c\u4e86\u8ba8\u8bba\uff0c\u4f8b\u5982\u53c2\u8003\u6587\u732e[49, 50]\u5173\u4e8e\u6574\u5408\u4fe1\u606f\u7406\u8bba<\/span>\uff08Integrated Information Theory\uff0cIIT\uff09<\/span>\u7684\u8ba8\u8bba\uff0c\u4ee5\u53ca\u53c2\u8003\u6587\u732e[51]\u5bf9\u795e\u7ecf\u5f71\u50cf\u65f6\u95f4\u5e8f\u5217\u5206\u6790\u4e2d\u7684\u6709\u6548\u8fde\u63a5\u548c\u529f\u80fd\u8fde\u63a5\u7684\u8ba8\u8bba<\/span>\uff08\u7b80\u800c\u8a00\u4e4b\uff0c\u6709\u6548\u8fde\u63a5\u65e8\u5728\u63ed\u793a\u89c2\u5bdf\u6570\u636e\u80cc\u540e\u7684\u6700\u5c0f\u7269\u7406\u56e0\u679c\u673a\u5236\uff0c\u800c\u529f\u80fd\u8fde\u63a5\u5219\u63cf\u8ff0\u6709\u5411\u6216\u65e0\u5411\u7684\u7edf\u8ba1\u4f9d\u8d56[51]\uff09<\/span>\u3002<\/span><\/section>\n
   <\/span><\/section>\n
\u5728\u6211\u4eec\u7684\u7406\u8bba\u4e2d\uff0c\u4e3b\u8981\u5206\u6790\u5bf9\u8c61\u662f\u9999\u519c\u7684\u4e92\u4fe1\u606f<\/span>\uff0c\u5b83\u53d6\u51b3\u4e8e\u8054\u5408\u6982\u7387\u5206\u5e03<\/span>\u3002\u8fd9\u4e2a\u5206\u5e03\u7684\u6765\u6e90<\/span>\uff08\u65e0\u8bba\u662f\u901a\u8fc7\u88ab\u52a8\u89c2\u5bdf\u8fd8\u662f\u4e3b\u52a8\u5e72\u9884\u5f97\u5230\uff09<\/span>\u5c06\u6539\u53d8\u5bf9\u4e0a\u8ff0\u6570\u91cf\u7684\u89e3\u91ca\uff0c\u5e76\u5bf9 Pearl \u5b66\u6d3e\u548c Wiener-Granger \u5b66\u6d3e\u6709\u4e0d\u540c\u7684\u8bf4\u6cd5\uff1b\u8fd9\u4e9b\u5dee\u5f02\u7684\u4e00\u4e9b\u5f71\u54cd\u5c06\u5728\u4e0b\u9762\u8ba8\u8bba\u6587\u732e[7]\u65f6\u63a2\u8ba8\u3002\u5c3d\u7ba1\u5982\u6b64\uff0c\u7531\u4e8e\u83b7\u5f97<\/span>\u7684\u4e24\u79cd\u65b9\u6cd5\u90fd\u5141\u8bb8\u53d1\u751f\u534f\u540c\u4f5c\u7528\uff0c\u6211\u4eec\u7684\u7ed3\u679c\u539f\u5219\u4e0a\u9002\u7528\u4e8e\u8fd9\u4e24\u4e2a\u6846\u67b6\u2014\u2014\u8fd9\u4f7f\u6211\u4eec\u80fd\u591f\u5728\u4e0d\u5bf9\u5173\u4e8e\u56e0\u679c\u672c\u8eab\u7684\u7406\u8bba\u91c7\u53d6\u50f5\u786c\u7acb\u573a\u7684\u60c5\u51b5\u4e0b\uff0c\u5236\u5b9a\u6211\u4eec\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u3002<\/span><\/section>\n
 <\/span><\/section>\n

\n
6.3 \u4e0e\u5176\u4ed6\u91cf\u5316\u6d8c\u73b0\u7406\u8bba\u7684\u5173\u7cfb<\/span><\/strong><\/span><\/section>\n<\/h2>\n
 <\/span><\/section>\n
\u8fd9\u9879\u5de5\u4f5c\u662f\u901a\u8fc7\u4fe1\u606f\u8bba\u5c06\u590d\u6742\u6027\u7406\u8bba\u5f62\u5f0f\u5316\u8fd9\u4e00\u66f4\u5e7f\u6cdb\u8fd0\u52a8\u7684\u4e00\u90e8\u5206\u3002\u7279\u522b\u662f\uff0c\u6211\u4eec\u7684\u6846\u67b6\u6700\u76f4\u63a5\u5730\u53d7\u5230Seth[6]\u548cHoel\u7b49\u4eba[7]\u5de5\u4f5c\u7684\u542f\u53d1\uff0c\u540c\u65f6\u4e5f\u4e0eChang\u7b49\u4eba[52]\u7684\u6700\u65b0\u5de5\u4f5c\u6709\u5173\u3002\u672c\u8282\u5c06\u7b80\u8981\u4ecb\u7ecd\u8fd9\u4e9b\u7406\u8bba\uff0c\u5e76\u8ba8\u8bba\u5b83\u4eec\u4e0e\u6211\u4eec\u7684\u7406\u8bba\u6709\u4f55\u4e0d\u540c\u3002<\/span><\/section>\n
   <\/span><\/section>\n
Seth[6]\u63d0\u51fa\uff0c\u4e00\u4e2a\u8fc7\u7a0bVt<\/sub> \u76f8\u5bf9\u4e8eXt<\/sub> \u662f Granger-\u6d8c\u73b0\u7684<\/span>\uff08\u6216G-\u6d8c\u73b0\u7684\uff09<\/span>\uff0c\u5982\u679c\u6ee1\u8db3\u4e24\u4e2a\u6761\u4ef6\uff1a(i) Vt<\/sub>  \u76f8\u5bf9 Xt<\/sub>  \u662f\u81ea\u4e3b\u7684\uff08\u5373<\/span>\uff09\uff0c\u548c (ii) Vt<\/sub>  \u76f8\u5bf9 Xt<\/sub>  \u662f G-\u56e0\u679c\u7684\uff08\u5373<\/span>\uff09\u3002\u540e\u4e00\u4e2a\u6761\u4ef6\u88ab\u7528\u6765\u4fdd\u8bc1Xt<\/sub> \u548cVt<\/sub> \u4e4b\u95f4\u7684\u5173\u7cfb\uff1b\u5728\u6211\u4eec\u7684\u6846\u67b6\u4e2d\uff0c\u4e0e\u6b64\u7b49\u4ef7\u7684\u4f5c\u7528\u7531\u968f\u9644\u6027\u7684\u8981\u6c42\u6765\u627f\u62c5\u3002\u81ea\u4e3b\u6027\u7684\u6761\u4ef6\u5f53\u7136\u4e0e\u6211\u4eec\u7684\u56e0\u679c\u89e3\u8026\u6982\u5ff5\u6709\u5173\u3002\u7136\u800c\uff0c\u6b63\u5982\u53c2\u8003\u6587\u732e[14]\u6240\u663e\u793a\u7684\u90a3\u6837\uff0c\u6761\u4ef6\u4e92\u4fe1\u606f\u6df7\u6dc6\u4e86\u72ec\u7279\u4fe1\u606f\u548c\u534f\u540c\u4fe1\u606f\uff0c\u8fd9\u53ef\u80fd\u5bfc\u81f4\u4e0d\u7406\u60f3\u7684\u60c5\u51b5\uff1a\u4f8b\u5982\uff0c\u53ef\u80fd\u662f<\/span>\uff0c\u800c\u540c\u65f6<\/span>\uff0c\u8fd9\u610f\u5473\u7740\u7279\u5f81 Vt<\/sub>  \u7684\u52a8\u529b\u5b66\u53ea\u6709\u5728\u4e0e\u6574\u4e2a\u7cfb\u7edf Xt<\/sub>  \u4e00\u8d77\u8003\u8651\u65f6\u624d\u662f\u53ef\u89c1\u7684\uff0c\u800c\u4e0d\u80fd\u5355\u72ec\u8003\u8651\u3002\u6211\u4eec\u7684\u6846\u67b6\u901a\u8fc7PID\u7ec6\u5316\u8fd9\u4e2a\u6807\u51c6\u6765\u907f\u514d\u8fd9\u4e2a\u95ee\u9898\uff0c\u5e76\u4e14\u53ea\u4f7f\u7528\u72ec\u7279\u4fe1\u606f\u6765\u5b9a\u4e49\u6d8c\u73b0\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u6211\u4eec\u7684\u5de5\u4f5c\u4e5f\u53d7\u5230 Hoel \u53ca\u5176\u540c\u4e8b\u5728\u53c2\u8003\u6587\u732e[7]\u4e2d\u63d0\u51fa\u7684\u6846\u67b6\u7684\u5f3a\u70c8\u5f71\u54cd\u3002\u4ed6\u4eec\u7684\u65b9\u6cd5\u662f\u57fa\u4e8e\u4e00\u4e2a\u4e0e\u7cfb\u7edf\u7684\u4e00\u4e2a\u611f\u5174\u8da3\u7279\u5f81\u76f8\u5173\u7684\u7c97\u7c92\u5316\u51fd\u6570F(\u00b7)\uff0c\u5373 Vt<\/sub> = F(Xt<\/sub>)\uff0c\u8fd9\u662f\u6211\u4eec\u5bf9\u968f\u9644\u6027\u7684\u66f4\u666e\u904d\u5b9a\u4e49\u7684\u4e00\u4e2a\u7279\u6b8a\u60c5\u51b5\u3002\u5f53 Vt<\/sub> \u548c Vt’<\/sub> \u4e4b\u95f4\u7684\u4f9d\u8d56\u5173\u7cfb\u6bd4 Xt<\/sub>  \u548c Xt’<\/sub>  \u4e4b\u95f4\u7684\u4f9d\u8d56\u5173\u7cfb\u201c\u66f4\u5f3a\u201d\u65f6\uff0c\u5373\u8ba4\u4e3a\u53d1\u751f\u4e86\u6d8c\u73b0\u3002\u8bf7\u6ce8\u610f\uff0c<\/span>\u662f\u4e00\u4e2a\u9a6c\u5c14\u53ef\u592b\u94fe\uff0c\u7531\u4e8e\u6570\u636e\u5904\u7406\u4e0d\u7b49\u5f0f\uff0c\u4ece\u800c\u6709 I(Vt<\/sub>;Vt’<\/sub> )<= I(Xt<\/sub>;Xt’<\/sub> ) \uff1b\u56e0\u6b64\uff0c\u76f4\u63a5\u4f7f\u7528\u9999\u519c\u4e92\u4fe1\u606f\u65e0\u6cd5\u5b9e\u73b0\u4e0a\u8ff0\u6807\u51c6\u3002\u76f8\u53cd\uff0c\u8fd9\u4e2a\u6846\u67b6\u5de5\u4f5c\u7684\u91cd\u70b9\u662f\u8f6c\u79fb\u6982\u7387<\/span>\u548c<\/span>\uff0c\u56e0\u6b64\uff0c\u4e92\u4fe1\u606f\u9879\u662f\u7528\u6700\u5927\u71b5\u5206\u5e03\u800c\u4e0d\u662f\u9759\u6001\u8fb9\u9645\u6765\u8ba1\u7b97\u7684\u3002\u901a\u8fc7\u8fd9\u6837\u505a\uff0cHoel \u7b49\u4eba\u4e0d\u662f\u8003\u8651\u7cfb\u7edf\u5b9e\u9645\u505a\u4ec0\u4e48\uff0c\u800c\u662f\u8003\u8651\u7cfb\u7edf\u53ef\u80fd\u505a\u7684\u6240\u6709\u6f5c\u5728\u8f6c\u79fb\u3002\u7136\u800c\uff0c\u5728\u6211\u4eec\u770b\u6765\uff0c\u8fd9\u79cd\u65b9\u6cd5\u5e76\u4e0d\u9002\u5408\u8bc4\u4f30\u52a8\u529b\u5b66\u7cfb\u7edf\uff0c\u56e0\u4e3a\u5b83\u53ef\u80fd\u8003\u8651\u5230\u4ece\u672a\u5b9e\u9645\u63a2\u7d22\u8fc7\u7684\u8f6c\u79fb\u3002\u9759\u6001\u5206\u5e03\u548c\u6700\u5927\u71b5\u5206\u5e03\u4e4b\u95f4\u7684\u5dee\u5f02\u5728\u5177\u6709\u591a\u4e2a\u5438\u5f15\u5b50\u7684\u975e\u904d\u5386\u7cfb\u7edf\u4e2d\u53ef\u80fd\u7279\u522b\u660e\u663e\u2014\u2014\u89c1\u53c2\u8003\u6587\u732e[50]\uff0c\u6574\u5408\u4fe1\u606f\u8bba\u8bed\u5883\u4e0b\u7684\u76f8\u5173\u8ba8\u8bba\u3002\u6b64\u5916\uff0c\u8fd9\u4e2a\u6846\u67b6\u4f9d\u8d56\u4e8e\u5bf9<\/span>\u6240\u7f16\u7801\u7684\u5fae\u89c2\u8f6c\u79fb\u7684\u786e\u5207\u4e86\u89e3\uff0c\u8fd9\u5728\u5927\u591a\u6570\u5e94\u7528\u4e2d\u662f\u4e0d\u53ef\u80fd\u5f97\u5230\u7684\u3002     <\/span><\/section>\n
 <\/span><\/section>\n
\u6700\u540e\uff0cChang\u7b49\u4eba[4]\u8003\u8651\u7684\u968f\u9644\u53d8\u91cf\u5bf9\u76f8\u5e94\u7684\u5fae\u89c2\u5e95\u5c42\u662f “\u975e\u5e73\u5eb8\u4fe1\u606f\u5c01\u95ed\u7684”<\/span>\uff08non-trivially informationally closed\uff0cNTIC\uff09<\/span>\u3002NTIC\u7684\u57fa\u7840\u662f\u57fa\u4e8e\u5c06 X \u5212\u5206\u4e3a\u4e00\u4e2a\u611f\u5174\u8da3\u7684\u5b50\u7cfb\u7edf<\/span>\u53ca\u5176\u6240\u5904\u7684\u7531<\/span>\u7ed9\u51fa\u7684\u201c\u73af\u5883\u201d\u3002\u6709\u8da3\u7684\u662f\uff0c\u4f5c\u4e3a NTIC \u7684\u7cfb\u7edf\u8981\u6c42 Vt<\/sub> \u53ea\u5bf9<\/span>\u662f\u968f\u9644\u7684\uff08\u5373 <\/span>\uff09\uff0c\u5e76\u4e14\u4ece\u73af\u5883\u5230\u7279\u5f81\u7684\u4fe1\u606f\u6d41\uff08\u5373<\/span>\uff09\u7531\u7279\u5f81\u672c\u8eab\u4ecb\u5bfc\uff0c\u56e0\u6b64\uff0c<\/span>\u662f\u4e00\u4e2a\u9a6c\u5c14\u53ef\u592b\u94fe\u3002\u56e0\u6b64\uff0cNTIC \u8981\u6c42\u7279\u5f81\u5bf9\u5176\u81ea\u8eab\u7684\u52a8\u529b\u5b66\u6709\u8db3\u591f\u7684\u7edf\u8ba1\uff0c\u8fd9\u7c7b\u4f3c\u4e8e\u6211\u4eec\u7684\u56e0\u679c\u89e3\u8026\u6982\u5ff5\uff0c\u4f46\u4fa7\u91cd\u4e8e\u5b8f\u89c2\u7279\u5f81\u3001\u4e3b\u4f53\u548c\u5176\u73af\u5883\u4e4b\u95f4\u7684\u4e92\u52a8\u3002\u5c06\u6211\u4eec\u7684\u6846\u67b6\u6269\u5c55\u5230\u4e3b\u52a8\u63a8\u7406\u6240\u6d89\u53ca\u7684\u4e3b\u4f53-\u73af\u5883\u7cfb\u7edf\uff0c\u662f\u6211\u4eec\u672a\u6765\u5de5\u4f5c\u7684\u4e00\u90e8\u5206\u3002<\/span><\/section>\n
 <\/span><\/section>\n

\n
6.4 \u5c40\u9650\u6027\u548c\u5f00\u653e\u95ee\u9898<\/span><\/strong><\/span><\/section>\n<\/h2>\n
 <\/span><\/section>\n
\u672c\u6587\u63d0\u51fa\u7684\u6846\u67b6\u4e3b\u8981\u5173\u6ce8\u5177\u6709\u9a6c\u5c14\u53ef\u592b\u52a8\u529b\u5b66\u7684\u5b8c\u5168\u53ef\u89c2\u5bdf\u7cfb\u7edf\u7684\u7279\u5f81\u3002\u7136\u800c\uff0c\u8fd9\u4e9b\u5047\u8bbe\u5728\u5904\u7406\u5b9e\u9a8c\u6570\u636e\u2014\u2014\u7279\u522b\u662f\u751f\u7269\u548c\u793e\u4f1a\u7cfb\u7edf\u4e2d\u7684\u5b9e\u9a8c\u6570\u636e\u65f6\u5f80\u5f80\u4e0d\u6210\u7acb\u3002\u4f5c\u4e3a\u4e00\u4e2a\u91cd\u8981\u6269\u5c55\uff0c\u672a\u6765\u7684\u5de5\u4f5c\u5e94\u8be5\u7814\u7a76\u672a\u89c2\u6d4b\u53d8\u91cf\u5bf9\u6211\u4eec\u7684\u5ea6\u91cf\u7684\u5f71\u54cd\u3002\u4f8b\u5982\uff0c\u53ef\u4ee5\u5229\u7528 Takens \u7684\u5d4c\u5165\u5b9a\u7406<\/span>\uff08embedding theorem\uff09<\/span>[53-55]\u6216\u5176\u4ed6\u65b9\u6cd5[56]\u3002     <\/span><\/section>\n
 <\/span><\/section>\n
\u6211\u4eec\u7684\u6846\u67b6\u7684\u4e00\u4e2a\u6709\u8da3\u7279\u70b9\u662f\uff0c\u5c3d\u7ba1\u5b83\u53d6\u51b3\u4e8ePID\u548c\u03a6ID\u7684\u9009\u62e9\uff0c\u4f46\u5b83\u7684\u5b9e\u9645\u5e94\u7528\u901a\u8fc7\u201c\u5927\u578b\u7cfb\u7edf\u7684\u5b9e\u7528\u6807\u51c6\u201d\u4e00\u8282\u4e2d\u8ba8\u8bba\u7684\u6807\u51c6\u662f\u4e0e\u8fd9\u4e9b\u9009\u62e9\u65e0\u5173\u7684\u3002\u7136\u800c\uff0c\u7531\u4e8e\u5bf9\u5fae\u89c2\u5197\u4f59\u7684\u9ad8\u4f30\uff0c\u5b83\u4eec\u5bfc\u81f4\u7684\u4ee3\u4ef7\u662f\u68c0\u6d4b\u6d8c\u73b0\u7684\u7075\u654f\u5ea6\u6709\u9650\uff1b\u56e0\u6b64\uff0c\u5f53\u6d8c\u73b0\u5f88\u663e\u8457\u65f6\uff0c\u5b83\u4eec\u53ef\u4ee5\u68c0\u6d4b\u5230\uff0c\u4f46\u5728\u6d8c\u73b0\u66f4\u5fae\u5c0f\u7684\u60c5\u51b5\u4e0b\u53ef\u80fd\u4f1a\u9057\u6f0f\u3002\u6b64\u5916\uff0c\u8fd9\u4e9b\u6807\u51c6\u4e0d\u80fd\u6392\u9664\u6d8c\u73b0\uff0c\u56e0\u4e3a\u5b83\u4eec\u662f\u5145\u5206\u6761\u4ef6\u800c\u4e0d\u662f\u5fc5\u8981\u6761\u4ef6\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u56e0\u6b64\uff0c\u672a\u6765\u5de5\u4f5c\u7684\u53e6\u4e00\u4e2a\u9014\u5f84\u5e94\u8be5\u662f\u5bfb\u627e\u6539\u8fdb\u7684\u5b9e\u7528\u6807\u51c6\uff0c\u4ee5\u4fbf\u4ece\u6570\u636e\u4e2d\u68c0\u6d4b\u6d8c\u73b0\u3002\u4e00\u4e2a\u6709\u8da3\u7684\u7814\u7a76\u65b9\u5411\u662f\u4e3a<\/span>\u548c<\/span>\u63d0\u4f9b\u53ef\u6269\u5c55\u7684\u8fd1\u4f3c\uff0c\u5c31\u50cf\u5728\u201c\u901a\u8fc7\u534f\u540c\u901a\u9053\u6d4b\u91cf\u6d8c\u73b0\u201d\u4e00\u8282\u4e2d\u4ecb\u7ecd\u7684\uff0c\u8fd9\u53ef\u4ee5\u5728\u5927\u578b\u7cfb\u7edf\u4e2d\u8ba1\u7b97\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u53e6\u4e00\u4e2a\u6709\u5f85\u89e3\u51b3\u7684\u95ee\u9898\u662f\uff0c\u6d8c\u73b0\u80fd\u529b\u5982\u4f55\u53d7\u5230\u7cfb\u7edf\u7684\u5fae\u89c2\u5212\u5206\u7684\u53d8\u5316\u6240\u5f71\u54cd<\/span>\uff08\u53c2\u89c1\u201c\u5b9a\u4e49\u56e0\u679c\u6d8c\u73b0\u201d\u4e00\u8282\uff09<\/span>\u3002\u8fd9\u65b9\u9762\u6709\u8da3\u7684\u5e94\u7528\u5305\u62ec\u611f\u5174\u8da3\u7684\u5143\u7d20\u53d7\u5230\u6df7\u5408\u8fc7\u7a0b\u5f71\u54cd\u7684\u60c5\u666f\uff0c\u4f8b\u5982\u8111\u7535\u56fe\u7684\u60c5\u51b5\uff0c\u5176\u4e2d\u6bcf\u4e2a\u7535\u6781\u68c0\u6d4b\u6df7\u5408\u7684\u5927\u8111\u4fe1\u53f7\u6e90\u3002\u5176\u4ed6\u6709\u8da3\u7684\u95ee\u9898\u5305\u62ec\u7814\u7a76\u5bf9\u6240\u6709\u5408\u7406\u7684\u5fae\u89c2\u5212\u5206\u5177\u6709\u975e\u96f6\u6d8c\u73b0\u80fd\u529b\u7684\u7cfb\u7edf\uff0c\u8fd9\u53ef\u80fd\u5bf9\u5e94\u4e8e\u4e00\u79cd\u66f4\u5f3a\u7c7b\u578b\u7684\u6d8c\u73b0\u3002<\/span><\/section>\n
 <\/span><\/section>\n
 <\/span><\/section>\n

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7. \u7ed3\u8bba<\/strong><\/strong><\/p>\n<\/section>\n

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\uff08\u6211\u4eec\u4e5f\u4f1a\u5bf9\u6bcf\u6b21\u5206\u4eab\u7684\u5185\u5bb9\u8fdb\u884c\u5f55\u5236\uff0c\u526a\u8f91\u540e\u53d1\u5e03\u5728\u96c6\u667a\u5b66\u56ed\u5b98\u7f51\u4e0a\uff0c\u4f9b\u8bfb\u4e66\u4f1a\u6210\u5458\u56de\u770b\uff09<\/span><\/section>\n


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\u8bba\u6587\u9605\u8bfb\u6e05\u5355<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

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I. \u56e0\u679c\u6d8c\u73b0\u7406\u8bba<\/span><\/strong><\/span><\/h3>\n