{"id":29556,"date":"2021-10-27T20:52:58","date_gmt":"2021-10-27T12:52:58","guid":{"rendered":"https:\/\/swarma.org\/?p=29556"},"modified":"2021-10-27T20:52:58","modified_gmt":"2021-10-27T12:52:58","slug":"%e9%bd%90%e5%a4%ab%e5%ae%9a%e5%be%8b%e4%b8%ba%e4%bd%95%e6%99%ae%e9%81%8d%e5%ad%98%e5%9c%a8%ef%bc%9f%e4%bb%8e%e6%9c%80%e7%9c%81%e5%8a%9b%e5%8e%9f%e5%88%99%e5%88%b0%e6%9c%80%e5%a4%a7%e5%8c%96%e5%a4%9a","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=29556","title":{"rendered":"\u9f50\u592b\u5b9a\u5f8b\u4e3a\u4f55\u666e\u904d\u5b58\u5728\uff1f\u4ece\u6700\u7701\u529b\u539f\u5219\u5230\u6700\u5927\u5316\u591a\u6837\u6027"},"content":{"rendered":"
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<\/strong>\u9f50\u592b\u5b9a\u5f8b\uff08Zipf\u2019s law\uff09\u662f\u4e00\u79cd\u5178\u578b\u7684\u5e42\u5f8b\u5206\u5e03\uff0c\u4ece\u8bed\u8a00\u4e2d\u8bcd\u6c47\u7684\u51fa\u73b0\u9891\u7387\uff0c\u5230\u56fd\u5bb6\u4eba\u53e3\u5728\u4e0d\u540c\u89c4\u6a21\u57ce\u5e02\u95f4\u7684\u5206\u5e03\uff0c\u518d\u5230\u7f51\u9875\u8bbf\u95ee\u9891\u7387\u3001\u6536\u5165\u7684\u6392\u5e8f\uff0c\u90fd\u9075\u5faa\u9f50\u592b\u5b9a\u5f8b\u3002\u4e0d\u8fc7\uff0c\u9f50\u592b\u5b9a\u5f8b\u4e3a\u4ec0\u4e48\u666e\u904d\u5b58\u5728\uff1f\u9f50\u592b\u672c\u4eba\u8ba4\u4e3a\uff0c\u8fd9\u662f\u56e0\u4e3a\u7cfb\u7edf\u8981\u9075\u5faa\u6700\u7701\u529b\u539f\u5219\u30022021\u5e749\u6708 PRL \u53d1\u8868\u7684\u9898\u4e3a\u201c\u6700\u5927\u5316\u591a\u6837\u6027\u548c\u9f50\u592b\u5b9a\u5f8b\u201d\u7684\u8bba\u6587\uff0c\u901a\u8fc7\u6c42\u89e3\u7edf\u8ba1\u6a21\u578b\u6307\u51fa\uff0c\u9f50\u592b\u5b9a\u5f8b\u603b\u662f\u4e0e\u7ec4\u6210\u90e8\u5206\u89c4\u6a21\u7684\u591a\u6837\u6027\u6700\u5927\u5316\u540c\u65f6\u53d1\u751f\u3002\u800c\u6700\u5927\u5316\u591a\u6837\u6027\u80cc\u540e\u53cd\u6620\u7684\uff0c\u6216\u8bb8\u6b63\u662f\u66f4\u4e00\u822c\u7684\u6700\u7701\u529b\u539f\u5219\u548c\u7269\u7406\u5b66\u4e2d\u7684\u6700\u5c0f\u4f5c\u7528\u91cf\u539f\u7406\u3002<\/strong><\/span><\/p>\n


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\u7814\u7a76\u9886\u57df\uff1a\u9f50\u592b\u5b9a\u5f8b\uff0c\u5e42\u5f8b\u5206\u5e03\uff0c\u591a\u6837\u6027\uff0c\u4fe1\u606f\u71b5\uff0c\u6700\u7701\u529b\u539f\u5219<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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

Maximal Diversity and Zipf\u2019s Law<\/span><\/p>\n

\u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.127.128301<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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1. \u4ece\u9f50\u592b\u5b9a\u5f8b\u5230\u6700\u7701\u529b\u539f\u5219<\/strong><\/strong><\/p>\n<\/section>\n

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\u9f50\u592b\u5b9a\u5f8b\u662f\u54c8\u4f5b\u5927\u5b66\u8bed\u8a00\u5b66\u5bb6\u4e54\u6cbb\u00b7\u9f50\u592b<\/span>\uff08George Zipf\uff09<\/span>1949\u5e74\u53d1\u73b0\u7684\u4e00\u4e2a\u5b9e\u9a8c\u5b9a\u5f8b\uff0c\u5373\u5728\u81ea\u7136\u8bed\u8a00\u91cc\uff0c\u4e00\u4e2a\u5355\u8bcd\u51fa\u73b0\u7684\u9891\u7387\u4e0e\u5b83\u5728\u9891\u7387\u8868\u91cc\u7684\u6392\u5e8f\u6210\u53cd\u6bd4\u3002<\/strong><\/span><\/p>\n

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\u4f8b\u5982\uff0c\u5728\u82f1\u8bed\u7684 Brown \u8bed\u6599\u5e93\u4e2d\uff0c\u300cthe\u300d\u3001\u300cof\u300d\u3001\u300cand\u300d\u662f\u51fa\u73b0\u9891\u7387\u6700\u9ad8\uff0c\u6392\u5e8f 1\u30012\u30013 \u7684\u5355\u8bcd\uff0c\u5206\u522b\u5360\u6574\u4e2a\u8bed\u6599\u5e93100\u4e07\u4e2a\u5355\u8bcd\u6570\u7684 7%\u30013.6%\u30012.9%[1]\u3002\u53ef\u89c1\u6392\u5e8f\u7b2c2\u4f4d\u300cof\u300d\u7684\u9891\u7387\u5927\u7ea6\u662f\u7b2c1\u300cthe\u300d\u76841\/2\uff0c\u7b2c3\u7684\u300cand\u300d\u662f\u5176 1\/3\u3002\u4ee5\u6b64\u7c7b\u63a8\uff0c\u6392\u5e8f\u7b2cn\u5355\u8bcd\u7684\u9891\u7387\u662f\u6700\u5e38\u89c1\u9891\u7387\u76841\/n\u3002\u6700\u7b80\u5355\u7684\u9f50\u592b\u5b9a\u5f8b\u6392\u5e8f\u9075\u4ece\u4e00\u6b21\u53cd\u6bd4\u5373 1\/f \u5173\u7cfb\u3002\u7531\u6b64\u53ef\u4ee5\u5f97\u5230\u5b83\u7684\u7b49\u4ef7\u63cf\u8ff0\uff1a<\/span><\/p>\n

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\u5728\u7ed9\u5b9a\u8bed\u6599\u4e2d\uff0c\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a\u5355\u8bcd\uff0c\u5176\u9891\u7387\uff08Frequency\uff09\u4e0e\u9891\u7387\u6392\u5e8f\uff08Rank\uff09\u4e58\u79ef\u5927\u81f4\u662f\u4e00\u4e2a\u5e38\u6570\uff0c\u5373\uff1aRank * Frequency \u2248 Constant<\/span><\/p>\n<\/blockquote>\n

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\u56fe1\uff1a\u9f50\u592b\u5b9a\u5f8b\u3002\u6392\u5e8f\u548c\uff08\u7edd\u5bf9\uff09\u9891\u7387\u5448\u53cd\u6bd4\uff0c\u6216\u8005\u8bf4\u4e58\u79ef\u4e3a\u4e00\u4e2a\u5e38\u6570\u3002<\/span><\/section>\n

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\u5bf9\u6570\u5b66\u5bb6\u548c\u7edf\u8ba1\u5b66\u5bb6\u6765\u8bf4\uff0c\u9f50\u592b\u5b9a\u5f8b\u662f\u4e00\u79cd\u5178\u578b\u7684\u5e42\u5f8b\u5206\u5e03<\/strong>\uff0c\u66f4\u786e\u5207\u8bf4\u662f\u53e6\u4e00\u79cd\u7edf\u8ba1\u5206\u5e03\u5e15\u7d2f\u6258\u5206\u5e03<\/span>\uff08Pareto distribution\uff09<\/span>\u7684\u7279\u4f8b\u3002\u540e\u8005\u4ea6\u79f0\u5e15\u7d2f\u6258\u5b9a\u5f8b\uff0c\u6700\u5f62\u8c61\u7684\u63cf\u8ff0\u4e3a\u300c\u4e8c\u516b\u5b9a\u5f8b\u300d\uff1a\u4efb\u4f55\u56fd\u5bb6\u768420\uff05\u7684\u4eba\u53e3\u62e5\u670980\uff05\u7684\u56fd\u6c11\u8d22\u5bcc\uff0c\u5b8c\u621080\uff05\u7684\u5de5\u4f5c\u9700\u898120\uff05\u7684\u5de5\u4f5c\u91cf\u7b49\u3002\u8fd9\u4e9b\u5206\u5e03\u90fd\u53cd\u6620\u4e86\u4e00\u79cd\u666e\u904d\u7684\u300c\u7a77\u8005\u6108\u7a77\uff0c\u5bcc\u8005\u6108\u5bcc\u300d\u7684\u5e42\u5f8b\u73b0\u8c61\u3002\u5728\u9f50\u592b\u5b9a\u5f8b\u4e2d\uff0c\u5219\u662f\u7b2c1\u5bcc\u6709\u7684\u662f\u7b2cn\u5bcc\u6709\u7684n\u500d\u3002<\/span><\/p>\n

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\u9f50\u592b\u5b9a\u5f8b\u662f\u5b9a\u91cf\u8bed\u8a00\u5b66\u7814\u7a76\u4e2d\u57fa\u4e8e\u7ecf\u9a8c\u53d1\u73b0\u7684\u7b2c\u4e00\u4e2a\u6570\u5b66\u89c4\u5f8b\uff0c\u5374\u53ef\u4ee5\u5728\u5f88\u591a\u975e\u8bed\u8a00\u5b66\u9886\u57df\u7684\u6392\u5e8f\u4e2d\u88ab\u89c2\u5bdf\u5230\u3002\u4f8b\u5982\u4e0d\u540c\u56fd\u5bb6\u4e2d\u57ce\u5e02\u7684\u6570\u91cf\u3001\u516c\u53f8\u7684\u89c4\u6a21\u3001\u7f51\u9875\u8bbf\u95ee\u9891\u7387\u3001\u6536\u5165\u6392\u5e8f\u3001\u5730\u9707\u9707\u7ea7\u3001\u56fa\u4f53\u7834\u788e\u65f6\u7684\u788e\u7247\u5927\u5c0f\u7b49\u7b49\u3002<\/span><\/p>\n

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\u53ef\u662f\u9f50\u592b\u5b9a\u5f8b\u4e3a\u4ec0\u4e48\u666e\u904d\u5b58\u5728\uff1f<\/span><\/p>\n

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\u9f50\u592b\u5728\u81ea\u5df1\u4e00\u90e8\u8457\u4f5c\u300a\u6700\u7701\u529b\u539f\u5219\u2014\u2014\u4eba\u7c7b\u884c\u4e3a\u751f\u6001\u5b66\u5bfc\u8bba\u300b\u4e2d\u7ed9\u51fa\u4e86\u4e00\u4e2a\u57fa\u4e8e\u4eba\u7c7b\u884c\u4e3a\u548c\u7ecf\u6d4e\u5b66\u7684\u89e3\u91ca\u3002\u4ed6\u8ba4\u4e3a\uff0c\u4eba\u672c\u8eab\u4f5c\u4e3a\u4e00\u4e2a\u300c\u80fd\u91cf-\u7269\u8d28\u300d\u7cfb\u7edf\uff0c\u4e3a\u4e86\u89e3\u51b3\u67d0\u4e2a\u95ee\u9898\uff0c\u4e00\u5b9a\u4f1a\u9075\u5faa\u6240\u505a\u5168\u90e8\u529f\uff08work\uff09\u6700\u5c0f\u3001\u6216\u6210\u672c\uff08cost\uff09\u6700\u5c0f\u7684\u8def\u5f84\u79fb\u52a8<\/strong>\uff0c\u8fd9\u65e2\u5305\u62ec\u7cfb\u7edf\u672c\u8eab\u7684\u7269\u8d28-\u80fd\u91cf\u6d41\u52a8\uff0c\u4e5f\u5305\u62ec\u6574\u4f53\u5355\u4f4d\u5728\u73af\u5883\u4e2d\u7684\u79fb\u52a8\uff0c\u5e76\u79f0\u4e4b\u4e3a\u6700\u7701\u529b\u539f\u5219<\/strong><\/span>\uff08Principle of Least Effort\uff09<\/span>\u3002<\/span><\/p>\n

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\u4f8b\u5982\uff0c\u9f50\u592b\u8ba4\u4e3a\uff0c\u8bed\u8a00\u4f5c\u4e3a\u4e00\u4e2a\u4ea4\u6d41\u7cfb\u7edf\uff0c\u56e0\u4e3a\u8981\u9075\u5faa\u6700\u7701\u529b\u539f\u5219\uff0c\u4f1a\u51fa\u73b0\u4e24\u79cd\u7ecf\u6d4e\uff1a\u8a00\u8005\u7ecf\u6d4e<\/strong>\u548c\u542c\u8005\u7ecf\u6d4e<\/strong>\u3002\u524d\u8005\u8ffd\u6c42\u4e00\u62db\u6253\u904d\u5929\u4e0b\uff0c\u5c31\u50cf\u62e5\u6709\u4e00\u4e2a\u4e07\u80fd\u88c5\u5907\u6728\u5320\uff0c\u8981\u96c6\u6210\u952f\u5b50\u3001\u9524\u5b50\u7b49\u6240\u6709\u529f\u80fd\uff1b\u4f46\u5bf9\u542c\u8005\u6765\u8bf4\uff0c\u5982\u679c\u50cf\u5a74\u513f\u6216\u732b\u90a3\u6837\u53ea\u4f1a\u53d1\u4e00\u4e2a\u97f3\uff0c\u5c31\u9700\u8981\u82b1\u8d39\u5927\u91cf\u7cbe\u529b\u624d\u80fd\u89e3\u7801\u5b83\u7a76\u7adf\u5728\u8bf4\u4ec0\u4e48\u3002\u4e8e\u662f\u8bed\u8a00\u4e2d\u5c31\u51fa\u73b0\u4e86\u4e24\u79cd\u76f8\u4e92\u77db\u76fe\u7684\u7ecf\u6d4e\uff1a<\/span><\/p>\n

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\uff081\uff09\u8a00\u8005\u7ecf\u6d4e\uff1a\u8bcd\u6c47\u8868\u4ec5\u7531\u4e00\u4e2a\u8bcd\u8bed\u7ec4\u6210\uff0c\u5b83\u6307\u79f0\u6240\u6709 m \u4e2a\u4e0d\u540c\u7684\u610f\u4e49\u3002\u9f50\u592b\u79f0\u4e4b\u4e3a\u300c\u7edf\u4e00\u5316\u4e4b\u30ab\u300d<\/span>\uff08the Force of Unification\uff09<\/span>\uff1b<\/span><\/p>\n


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\uff082) \u542c\u8005\u7ecf\u6d4e\uff1a\u8bcd\u6c47\u8868\u7531 m \u4e2a\u8bcd\u8bed\u7ec4\u6210\uff0cm \u4e2a\u8bcd\u8bed\u6307\u79f0 m \u4e2a\u610f\u4e49\u3002\u79f0\u4e4b\u4e3a\u300c\u591a\u5143\u5316\u4e4b\u30ab\u300d<\/span>(the Force of Diversification\uff09<\/span>\u3002<\/span><\/p>\n

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\u4e8e\u662f\u5728\u6781\u7aef\u51b2\u7a81\u7684\u8fd9\u4e24\u79cd\u529b\u4f5c\u7528\u4e0b\uff0c\u4e3a\u9075\u5faa\u6700\u7701\u529b\u539f\u5219\uff0c\u7279\u5b9a\u8bed\u8a00\u7684\u8bcd\u6c47\u4e0d\u65ad\u4f18\u5316\uff0c\u6700\u7ec8\u51b3\u5b9a\u4e86\u8bcd\u8bed\u4e2d\u5b9e\u9645\u6570\u91cf\u7684\u8bcd\u6c47\u548c\u610f\u4e49\u3002<\/span><\/p>\n

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\u8fd9\u79cd\u8bf4\u6cd5\u6709\u9053\u7406\u5417\uff1f\u65f6\u8fc7\u5883\u8fc1\uff0c\u4ece\u8fc7\u53bb\u5230\u5f53\u4ee3\uff0c\u5bf9\u8fd9\u4e2a\u95ee\u9898\u7684\u63a2\u7a76\u4e5f\u4ece\u7ecf\u9a8c\u8f6c\u5411\u4e86\u7406\u8bba\u3002\u4eca\u5e745\u6708 PRL \u53d1\u8868\u7684\u4e00\u7bc7\u8bba\u6587 Maximal Diversity and Zipf\u2019s Law<\/em> \u4e2d\uff0c\u591a\u540d\u7814\u7a76\u8005\u8054\u5408\u901a\u8fc7\u6c42\u89e3\u4e00\u4e2a\u7edf\u8ba1\u6a21\u578b\uff0c\u5b9a\u4e49\u4e86\u4e00\u4e2a\u7cfb\u7edf\u591a\u6837\u6027\u6307\u6570 D<\/strong>\uff0c\u8ba1\u7b97\u53d1\u73b0\u7cfb\u7edf\u7ec4\u6210\u90e8\u5206\u5927\u5c0f\u7684\u591a\u6837\u6027\u6700\u5927\u5316\u603b\u662f\u4e0e\u9f50\u592b\u5b9a\u5f8b\u540c\u65f6\u53d1\u751f<\/strong>\uff0c\u5e76\u968f\u7cfb\u7edf\u603b\u7ef4\u6570\u589e\u52a0\u800c\u589e\u52a0\u3002\u968f\u540e\u7814\u7a76\u8005\u6d4b\u8bd5\u4e86\u8bed\u8a00\u5b66\u548c\u57ce\u5e02\u4eba\u53e3\u5206\u5e03\uff0c\u53d1\u73b0\u6570\u636e\u4e0e\u6a21\u578b\u975e\u5e38\u543b\u5408\u3002<\/span><\/p>\n


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\u7814\u7a76\u8005\u8ba4\u4e3a\uff0c\u5728\u9f50\u592b\u5b9a\u5f8b\u53d1\u751f\u7684\u60c5\u51b5\u4e0b\uff0c\u4f1a\u5c06\u591a\u6837\u6027\u63d0\u5347\u5230\u4e00\u79cd\u9a71\u52a8\u529b\u7684\u4f5c\u7528\uff0c\u8fd9\u5c31\u5bfc\u81f4\u4e86\u81ea\u7136\u3001\u793e\u4f1a\u548c\u4eba\u6587\u79d1\u5b66\u8bb8\u591a\u7cfb\u7edf\u7ec4\u6210\u90e8\u5206\u5171\u540c\u9075\u5b88\u7684\u7ecf\u9a8c\u5206\u5e03\uff0c\u5e76\u4e14\u5f88\u53ef\u80fd\u548c\u81ea\u7136\u6f14\u5316\u4f18\u5316\u8fc7\u7a0b\u9ad8\u5ea6\u76f8\u5173\u3002<\/span><\/p>\n


<\/p>\n

 <\/span>
<\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

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

2. \u7406\u8bba\u63a8\u5bfc\uff1a<\/strong><\/strong><\/p>\n

\u6700\u5927\u591a\u6837\u6027\u4e0e\u9f50\u592b\u5b9a\u5f8b\u5171\u540c\u51fa\u73b0<\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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


<\/p>\n

\u591a\u6837\u6027\u662f\u751f\u6001\u5b66\u3001\u7ecf\u6d4e\u5b66\u3001\u4fe1\u606f\u8bba\u7b49\u5b66\u79d1\u7684\u6838\u5fc3\u6982\u5ff5\uff0c\u53ef\u4ee5\u901a\u8fc7\u591a\u79cd\u591a\u6837\u6027\u6307\u6807[2,3]\u91cf\u5316\uff0c\u4f8b\u5982\u7269\u79cd\u4e30\u5ea6\u3001Gini-Simpson \u6307\u6570\u6216\u9999\u519c\u71b5\u3002\u9ad8\u5ea6\u591a\u6837\u6027\u5f80\u5f80\u53ef\u4ee5\u4ee3\u8868\u9002\u5e94\u6027\u548c\u6027\u80fd\u65b9\u9762\u7684\u4f18\u52bf<\/strong>\u3002\u4f8b\u5982\u5728\u751f\u6001\u5b66\u4e2d\uff0c\u5206\u5316\u826f\u597d\u7684\u751f\u6001\u7cfb\u7edf\u901a\u5e38\u88ab\u8ba4\u4e3a\u66f4\u7a33\u5b9a[4-7]\uff0c\u540c\u6837\u5728\u7ecf\u6d4e\u4e0a\u5f3a\u5927\u7684\u56fd\u5bb6\u4e5f\u5f80\u5f80\u6709\u66f4\u591a\u6837\u7684\u751f\u4ea7\u65b9\u5f0f [8]\u3002\u4f46\u591a\u6570\u60c5\u51b5\u4e0b\uff0c\u591a\u6837\u6027\u4f1a\u53d7\u5230\u5404\u79cd\u9650\u5236\u56e0\u7d20\u5f71\u54cd\u3002\u5982\u751f\u6001\u4e2d\u53ef\u7528\u7684\u80fd\u91cf\u548c\u7269\u8d28\u91cf\uff0c\u5c31\u4e0d\u4f1a\u5141\u8bb8\u4eba\u53e3\u65e0\u9650\u589e\u52a0\u3002\u540c\u6837\uff0c\u4e00\u4e2a\u7ecf\u6d4e\u4f53\u6240\u751f\u4ea7\u7684\u4e0d\u540c\u4ea7\u54c1\u7684\u6570\u91cf\u4e5f\u53d7\u5230\u5176\u5b9e\u529b\u9650\u5236\u3002\u56e0\u6b64\uff0c\u591a\u6837\u6027\u8f6c\u5316<\/span>\uff08diversity drift\uff09<\/span>\u662f\u4e00\u4e2a\u590d\u6742\u7684\u4f18\u5316\u8fc7\u7a0b\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u5728\u8003\u8651\u8bf8\u591a\u9650\u5236\u4e0b\uff0c\u672c\u7814\u7a76\u4e2d\u91c7\u7528\u4e86\u57fa\u4e8e\u4e30\u5bcc\u5ea6\u6307\u6570<\/strong><\/span>\uff08richness index\uff09<\/span>\u7684\u591a\u6837\u6027\u5ea6\u91cf\uff0c\u5b83\u4ee3\u8868\u67d0\u4e2a\u96c6\u5408\u4e2d\u7684\u4e0d\u540c\u79cd\u7c7b\u5bf9\u8c61\u7684\u6570\u91cf\uff0c\u9002\u5408\u5bf9\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u4f18\u5316\u8d8b\u52bf\u8fdb\u884c\u5b9a\u91cf\u63cf\u8ff0\u3002\u4f8b\u5982\u5bf9\u6574\u6570\u96c6\u800c\u8a00\uff0c {3, 7, 1, 9, 0, 1} \u5c31\u6bd4 {3, 2, 3, 7, 7, 2} \u4e30\u5bcc\uff0c\u524d\u8005\u6709\u4e94\u4e2a\u4e0d\u540c\u7684\u6570\u5b57\uff0c\u540e\u8005\u53ea\u6709\u4e09\u4e2a\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u7814\u7a76\u8005\u8003\u8651\u4e86\u53ef\u4ee5\u901a\u8fc7\u6807\u7b7e\u5b9a\u91cf\u8bc6\u522b\u7684\u4e00\u822c\u60c5\u51b5\uff0c\u5373\u5bf9\u5b9e\u4f53\u96c6\u5408<\/span>\u7684\u4e30\u5bcc\u5ea6\u3002\u5bf9\u4efb\u610f N\uff0c\u82e5sn<\/sub><\/span>\u4ee3\u8868\u603b\u8d44\u6e90 S \u5206\u914d\u7ed9\u7b2cn\u4e2a\u5b9e\u4f53\u7684\u90e8\u5206\uff0c\u5982\u5927\u5c0f\uff0c\u5219\u901a\u8fc7\u7d2f\u52a0\u6709 <\/span>\u3002<\/span><\/p>\n


<\/p>\n

\u5b9e\u4f53\u53ef\u4ee5\u662f\u603b\u4eba\u53e3\u4e3aS\u7684\u56fd\u5bb6\u7684\u57ce\u5e02[13]\uff0c\u957f\u5ea6\u4e3aS\u7684\u4e66\u4e2d\u4ee5\u7279\u5b9a\u7edd\u5bf9\u9891\u7387\u51fa\u73b0\u7684\u4e00\u4e2a\u8bcd[14]\uff0c\u6216\u4e00\u4e2a\u7531\u86cb\u767d\u8d28\u603b\u6570S\u5408\u6210\u7684\u7ec6\u80de\u4e2d\u4ee5\u4e30\u5ea6{sn<\/sub><\/span>}\u8868\u8fbe\u7684\u57fa\u56e0[15]\u7b49\u7b49\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u9f50\u592b\u5b9a\u5f8b\u662f\u9891\u7387\u548c\u6392\u5e8f\u5448\u4e00\u6b21\u53cd\u6bd4\u5173\u7cfb\u3002\u5206\u522b\u4ee5s(r)\u548c r\u8868\u793a\uff0c\u5219\u5f53<\/span>\u6210\u7acb\u65f6\uff0c\u5b9a\u5f8b\u6210\u7acb\u3002\u8bbe <\/span>\uff0c\u7528 p(s) \u5206\u5e03\u51fd\u6570\u6765\u8868\u793a[17,23]\u5373\u6709\uff1a<\/span>\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u8003\u8651N\u4e2a\u6574\u6570\u7684\u968f\u673a\u53d8\u91cf\u96c6\uff0c\u5219\u53ef\u4ee5\u7ed9\u51fa\u4e00\u4e2a\u7279\u5b9a\u4f4d\u5f62<\/span>\u548c\u76f8\u5e94\u914d\u5206\u51fd\u6570<\/span>\uff08partition function\uff09<\/span>\u4e0b\uff0cs\u5728\u603b\u5927\u5c0fS\u4e0b\u7684\u6982\u7387\u5206\u5e03\uff1a<\/span><\/p>\n


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

<\/p>\n


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

\u5728\u7ed9\u5b9a\u4f4d\u5f62C\u4e2d\uff0c\u5982\u679c\u5b9a\u4e49 ts<\/sub><\/span> \u4e3a\u90e8\u5206\u5927\u5c0f s\u2208[1,S] \u51fa\u73b0\u7684\u6b21\u6570\uff0c\u90a3\u4e48\u591a\u6837\u6027\u6307\u6570 D<\/span>\uff08diversity index D\uff09<\/span>\u88ab\u5b9a\u4e49\u4e3a\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u03b4\u4e3a\u514b\u7f57\u5185\u514b\u51fd\u6570\uff0c\u5bf9\u03b4ij<\/sub><\/span>\uff0c\u5f53 i=j \u65f6\u503c1\uff0c\u5426\u5219\u4e3a0\u3002<\/strong>\u56e0\u6b64D\u5c31\u662f\u88ab\u6307\u6d3e\u4e3a\u4e0d\u540c\u503c\u5927\u5c0f\u7684\u5b9e\u4f53\u6216\u7ec4\u4ef6\u79cd\u7c7b\u7684\u6570\u91cf\uff0c\u4e14 D  \u2264 N\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u7814\u7a76\u5bf9\u9ad8\u5ea6\u591a\u6837\u5316\u7684\u4f4d\u5f62\u66f4\u611f\u5174\u8da3\uff0c\u56e0\u6b64\u8003\u8651\u80fd\u83b7\u5f97\u5e7f\u6cdb\u5927\u5c0f\u8303\u56f4\u7684\u5e42\u5f8b\u5206\u5e03\uff1a<\/span><\/p>\n


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

<\/p>\n


<\/p>\n

\u5206\u6bcd\u662f\u4e00\u4e2a\u80fd\u7528\u9ece\u66fc Zeta \u51fd\u6570\u8868\u8fbe\u7684\u5e7f\u4e49\u7684\u8c03\u548c\u6570\u3002\u8fd9\u6837\u6211\u4eec\u5c31\u5f97\u5230\u4e86<\/span>\u7684\u7cbe\u786e\u8868\u8fbe\u3002<\/span><\/p>\n

<\/p>\n

\u56fe2\uff1a\u7ec4\u5757\u90e8\u5206\u5927\u5c0f\u5206\u5e03 p(s) \u968f s \u7684\u53d8\u5316\u56fe\uff0c\u53f3\u8fb9\u4ece\u4e0b\u5230\u4e0a\u5e42\u5f8b p(s) \uff5es-\u03c4<\/span><\/sup> \u968f\u6307\u6570 \u03c4 \u7684\u589e\u52a0\u3002\u76f8\u540c\u5927\u5c0f\u7684\u5b9e\u4f53\u88ab\u63cf\u8ff0\u4e3a\u76f8\u540c\u8272\u5757\uff0c\u6240\u6709\u5b9e\u4f53\u52a0\u8d77\u6765\u6761\u5f62\u603b\u957f\u5ea6\u4e3aS\u3002\u5bf9\u4e8e\u8f83\u5927\u7684 \u03c4 \uff0c\u5927\u591a\u6570\u5b9e\u4f53\u90fd\u6709\u8f83\u5c0f\u7684\u548c\u76f8\u4f3c\u7684\u5c3a\u5bf8\uff0c\u5bfc\u81f4\u591a\u6837\u6027\u8f83\u4f4e\uff1b\u5728\u53e6\u4e00\u7aef\u8f83\u5c0f\u7684 \u03c4\uff0c\u5927\u5c3a\u5bf8\u66f4\u5bb9\u6613\u51fa\u73b0\uff08\u672c\u5e94\u5bfc\u81f4\u66f4\u5927\u5c3a\u5bf8\u591a\u6837\u6027\uff09\uff0c\u4f46\u56e0\u4e3a\u4f1a\u5bfc\u81f4\u586b\u5145 S \u6240\u9700\u7684\u5b9e\u4f53\u603b\u6570 N \u53d8\u5c11\uff0c\u6545\u591a\u6837\u6027\u4e5f\u6bd4\u8f83\u4f4e\u3002\u5728 \u03c4 \u7684\u4e2d\u95f4\u503c\u4e0a\uff0c\u591a\u6837\u6027\u6709\u671b\u8fbe\u5230\u6700\u5927\u3002<\/span><\/section>\n

 <\/span><\/p>\n

\u7814\u7a76\u76ee\u6807\u662f\u8ba1\u7b97\u5e73\u5747\u591a\u6837\u6027 <D>s<\/sub><\/span> \u548c\u4f7f\u5176\u6700\u5927\u5316\u7684 \u03c4 \u503c\u3002\u7ecf\u5bf9<D>s<\/sub><\/span> \u62c6\u5206\u8ba1\u7b97\u53ef\u77e5\uff0c\u5176\u4f30\u8ba1\u53ea\u53d6\u51b3\u4e8e\u7cfb\u7edf\u7ec4\u4ef6\u5e73\u5747\u6570 <N>s<\/sub><\/span> \u548c ps<\/sub><\/span>(s)\u3002\u4e8c\u8005\u90fd\u53ef\u4ee5\u7528\u9012\u5f52\u65b9\u6cd5\u7cbe\u786e\u6c42\u5230[11]\uff0c\u4f46\u8fd9\u91cc\u53ea\u9700\u6839\u636e<\/span> \u5bf9\u8f83\u5927 S \u5373\u53ef\u5f97\u5230\u6709\u6548\u4f30\u8ba1\uff1a<\/span><\/p>\n

 <\/span><\/p>\n

<\/p>\n


<\/p>\n

\u5373\u4e0d\u540c\u7684\u5e42\u6307\u6570 \u03c4 \u4e0b\uff0c\u5927\u5c0f\u4e3a S \u7684\u7cfb\u7edf\u7ec4\u4ef6\u5e73\u5747\u6570\u91cf <N>s<\/sub><\/span>\u3002\u8fd9\u4e2a\u516c\u5f0f\u53ef\u4ee5\u770b\u505a\u662f\u4e0e\u9f50\u592b\u5b9a\u5f8b\u76f8\u5173\u7684 Heaps \u5b9a\u5f8b[37]<\/span>\uff08\u5373\u7ed9\u5b9a\u8bed\u6599\u5927\u5c0f n\uff0c\u72ec\u7acb\u5355\u8bcd\u6570 V(n) \u662f n \u7684\u6307\u6570\u51fd\u6570\uff09<\/span>\u7684\u63a8\u5e7f\uff0c\u5b83\u53cd\u6620\u4e86\u4e0d\u540c S \u4e0b\u7ec4\u4ef6\u5206\u5e03<\/span>\uff08\u672c\u7814\u7a76\u662fps<\/sub><\/span>(s)\uff09<\/span>\u7edf\u8ba1\u5177\u6709\u9c81\u68d2\u6027\u7684\u7cfb\u7edf[27,28]\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u7531\u6b64\u53ef\u4ee5\u5f97\u5230\u5e73\u5747\u591a\u6837\u6027 <D>s<\/sub><\/span> \u7684\u4f30\u8ba1\uff1a<\/span><\/p>\n

 <\/span><\/p>\n

<\/p>\n

 <\/span><\/p>\n

\u516c\u5f0f\uff0811\uff09\u88ab\u79f0\u4e3a\u591a\u6837\u6027\u5b9a\u5f8b<\/strong>\u3002\u4ece\u56fe3\u53ef\u4ee5\u770b\u51fa\u5bf9\u8d8a\u5927\u7684S\uff0c\u5e73\u5747\u591a\u6837\u6027 <D>s<\/sub><\/span> \u8d8a\u5927\uff0c\u4f46\u90fd\u5728 \u03c4 = 2 \u9644\u8fd1\u8fbe\u5230\u5cf0\u503c\u3002\u56fe2\u5219\u8868\u660e\uff0c\u8fd9\u79cd\u73b0\u8c61\u662f\u7531\u4e8e\u5b9e\u4f53\u6570<N>s<\/sub><\/span>\u7684\u4e30\u5bcc\u5ea6\uff0c\u4e0e\u5b9e\u4f53\u5927\u5c0f\u591a\u6837\u6027\u4e4b\u95f4\u7684\u7ade\u4e89\u6240\u81f4\uff0c\u5927\u7684 \u03c4 \u6709\u5229\u4e8e\u5b9e\u4f53\u6570\u7684\u4e30\u5ea6\uff0c\u800c\u5c0f\u7684 \u03c4 \u5219\u6709\u5229\u4e8e\u5b9e\u4f53\u7684\u591a\u6837\u6027\u3002<\/strong><\/span><\/p>\n

 <\/span><\/p>\n

<\/p>\n

\u56fe3\uff1a\u4ee5\u865a\u7ebf\u8868\u793a\u7684\u5e73\u5747\u591a\u6837\u6027 <D>s<\/sub>\uff0c\u7531\u516c\u5f0f\uff0811\uff09\u5bf9\u4e0d\u540c\u5927\u5c0f\u7684 S \u6a21\u62df\u5f97\u5230\u3002\u4e0d\u540c\u5b9e\u5757\u7edf\u8ba1\u9075\u4ece\u5168\u5c40\u7ea6\u675f\u4f4d\u5f62\u4e0b\u7684\u5206\u5e03\uff086\uff09\uff0c\u7ed3\u679c\u662f104<\/sup>~106<\/sup>\u79cd\u4f4d\u5f62\u7684\u5e73\u5747\u6570\u3002\u4ec5\u663e\u793a\u4e24\u7aef\u7684\u5b9e\u7ebf\u662f\u7531\u516c\u5f0f\uff0810\uff09\u7ed9\u51fa\u7684\u5206\u6790\u89e3\u3002<\/span><\/section>\n
\u63d2\u56fe\uff1a\u5728\u516c\u5f0f\uff0811\uff09\u4e0b\uff0c\u7531<\/span>\uff0c\u4ee5 \u03c4 \u4e3a\u53d8\u91cf\u7684\u6307\u6570 \u03b1(\u03c4\uff09\uff0c\u5b9e\u7ebf\u662f\u5206\u6790\u7ed3\u679c\uff0c\u5706\u70b9\u662f\u6a21\u62df\u6570\u636e\u62df\u5408\u3002<\/span><\/section>\n

 <\/span><\/p>\n

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 <\/span><\/p>\n

 <\/span><\/p>\n

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

<\/section>\n

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


<\/p>\n

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 <\/span><\/p>\n

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 <\/span><\/p>\n

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 <\/span><\/p>\n

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 <\/span><\/p>\n

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 <\/span><\/p>\n

\u603b\u5927\u5c0f\u4e3a S \u7684\u7cfb\u7edf\uff1a<\/span><\/p>\n

    \n
  • \n

    S \u8d8a\u5927\uff0c\u7ec4\u4ef6\u5e73\u5747\u79cd\u7c7b\u6570 <N> \u8d8a\u5927\u2014\u2014\u516c\u5f0f8\uff08Heaps \u5b9a\u5f8b\uff09\uff1b<\/span><\/p>\n<\/li>\n

  • \n

    S \u8d8a\u5927\uff0c\u7ec4\u4ef6\u5e73\u5747\u5c3a\u5bf8\u591a\u6837\u6027 <D> \u8d8a\u5927\u2014\u2014\u516c\u5f0f11\uff08\u591a\u6837\u6027\u5b9a\u5f8b\uff09\uff0c\u56fe3\uff1b<\/span><\/p>\n<\/li>\n<\/ul>\n


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

    \u5bf9\u56fa\u5b9a S \u7684\u7cfb\u7edf\uff1a<\/span><\/p>\n

      \n
    • \n

      \u03c4 \u2191\uff0c<N>\u2191\uff0c\u4f46<\/span>s\u5c3a\u5bf8\u90fd\u5f88\u5c0f\u4e14\u63a5\u8fd1\uff0c\u6545<D>\u2193\u2014\u2014\u516c\u5f0f8\uff0c11\uff0c\u56fe2\uff1b<\/span><\/p>\n<\/li>\n

    • \n

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       <\/span><\/section>\n
      \u5373\u5927\u7684 \u03c4 \u6709\u5229\u4e8e\u7ec4\u4ef6\u79cd\u7c7b\u6570 <N>\uff0c\u5c0f\u7684 \u03c4 \u5219\u6709\u5229\u4e8e\u7ec4\u4ef6\u5c3a\u5bf8\u7684\u591a\u6837\u6027 <D>\uff0c\u4e8c\u8005\u7ade\u4e89\u7ed3\u679c\uff0c\u5bfc\u81f4\u5f53 \u03c4\u22482  \u65f6\uff0c\u7cfb\u7edf\u5e73\u5747\u591a\u6837\u6027<D>\u53d6\u5f97\u6700\u5927\u503c\u3002<\/span><\/span><\/section>\n
       <\/span><\/section>\n

      <\/section>\n

      \n
      \n
      \n
      \n
      \n

      <\/section>\n

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

      4. \u591a\u6837\u6027\u3001\u6700\u5927\u6548\u7387\u4e0e\u6700\u5c0f\u4f5c\u7528\u91cf\u539f\u7406<\/strong><\/strong><\/p>\n<\/section>\n

      \n

      <\/section>\n

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

      <\/section>\n
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       <\/span><\/section>\n
      \u81f3\u4e8e\u4e3a\u4f55\u5982\u6b64\uff0c\u7814\u7a76\u8005\u4eec\u6700\u540e\u63a8\u60f3\uff0c\u5f53\u4ee5\u9002\u5f53\u7684\u6210\u672c\u51fd\u6570\u7684\u6781\u503c\u4e3a\u6846\u67b6\u65f6\uff0c\u8d4b\u4e88\u67d0\u4e9b\u95ee\u9898\u76f8\u5e94\u7684\u8865\u5145\u63cf\u8ff0\uff0c\u5c31\u53ef\u80fd\u5f62\u6210\u67d0\u79cd\u65b0\u7b56\u7565\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u591a\u6837\u6027\u5c06\u626e\u6f14\u4e00\u4e2a\u91cd\u8981\u7684\u9a71\u52a8\u529b\u89d2\u8272\u3002<\/span><\/section>\n
       <\/span><\/section>\n
      \u8fd9\u65f6\uff0c\u6211\u4eec\u518d\u56de\u987e\u6700\u5f00\u59cb\u9f50\u592b\u672c\u4eba\u5bf9\u9f50\u592b\u5b9a\u5f8b\u7684\u601d\u8003\u4f1a\u53d1\u73b0\uff0c\u6700\u5927\u591a\u6837\u6027\u5f88\u53ef\u80fd\u5c31\u662f\u66f4\u5927\u7684\u6700\u7701\u529b\u539f\u5219\u7684\u4e00\u90e8\u5206<\/strong>\u3002\u5728\u9f50\u592b\u4e4b\u540e\uff0c\u5f88\u591a\u7814\u7a76\u8005\u4ece\u4fe1\u606f\u901a\u8baf\u89d2\u5ea6\u8fdb\u884c\u4e86\u7814\u7a76\uff0c\u53d1\u73b0\u901a\u8baf\u7cfb\u7edf\u8981\u8fbe\u5230\u6700\u4f18\u4f20\u8f93\u5c31\u4f1a\u6d8c\u73b0\u51fa\u9f50\u592b\u5b9a\u5f8b\u884c\u4e3a[32][39]\u3002\u6b64\u5916\u8fd8\u6709\u4e00\u4e9b\u5176\u5b83\u7814\u7a76\uff0c\u8bc1\u660e\u9f50\u592b\u5b9a\u5f8b\u4e0e\u6700\u5927\u8f93\u51fa\u6548\u7387\u6709\u5173\u3002\u5982\u5728 arxiv \u4e00\u7bc7\u9884\u5370\u672c\u8bba\u6587 [33]\u4e0a\uff0c\u4f5c\u8005\u901a\u8fc7\u5f15\u5165\u6548\u7387\u7684\u6982\u7387\u6cdb\u51fd\uff0c\u8bc1\u660e\u751f\u547d\u4f53\u7c7b\u4f3c\u4e8e\u70ed\u673a\uff0c\u9075\u4ece\u9f50\u592b\u5b9a\u5f8b\u548c\u6700\u7701\u529b\u539f\u5219\u5c31\u4f1a\u4ea7\u751f\u6700\u5927\u6548\u7387\u8f93\u51fa\u3002<\/span><\/section>\n
       <\/span><\/section>\n
      \u4e3a\u4ec0\u4e48\u8fd9\u4e9b\u7cfb\u7edf\u90fd\u4f1a\u9075\u5faa\u6700\u7701\u529b\u539f\u5219\uff1f\u8ffd\u672c\u6eaf\u6e90\uff0c\u5176\u5b9e\u9f50\u592b\u4e00\u5f00\u59cb\u8003\u8651\u7684\u300c\u7269\u8d28-\u80fd\u91cf\u300d\u7cfb\u7edf\uff0c\u5c31\u6765\u81ea\u7269\u7406\u5b66\u7684\u6700\u5c0f\u4f5c\u7528\u91cf\u539f\u7406<\/strong><\/span>\uff08least action principle\uff09<\/span>\uff0c\u5b83\u53ef\u8868\u8ff0\u4e3a\u54c8\u5bc6\u987f\u539f\u7406<\/span>\uff08Hamilton\u2019s principle\uff09<\/span>\u3002\u5728\u6839\u672c\u4e0a\u5b83\u4eec\u90fd\u662f\u6570\u5b66\u4e0a\u4e00\u7c7b\u8ba8\u8bba\u6cdb\u51fd\u6781\u503c\u95ee\u9898\u7684\u53d8\u5206\u539f\u7406<\/span>\uff08Variational principle\uff09<\/span>\u3002<\/span><\/section>\n
       <\/span><\/section>\n
      <\/section>\n

      \u56fe5\uff1a\u54c8\u5bc6\u987f\u539f\u7406\uff1a\u4e8b\u7269\u771f\u5b9e\u8fd0\u52a8\u72b6\u6001\u603b\u662f\u529b\u56fe\u4f7f\u54c8\u5bc6\u987f\u4f5c\u7528\u91cf\uff08\u5373\u62c9\u683c\u6717\u65e5\u51fd\u6570L\u7684\u79ef\u5206S\uff09\u53d6\u6781\u503c\uff0c\u901a\u5e38\u662f\u6700\u5c0f\u503c\u3002\u8fd9\u6761\u6700\u77ed\u8def\u5f84\u79f0\u4e3a\u6b63\u8def\uff08\u771f\u5b9e\u8fd0\u52a8\uff0c\u7ea2\u8272\uff09\uff0c\u5176\u4f59\u8def\u5f84\u79f0\u4e3a\u65c1\u8def\uff08\u53ef\u80fd\u8fd0\u52a8\uff09\u3002<\/span><\/p>\n

       <\/span><\/section>\n

      \u6700\u5c0f\u4f5c\u7528\u91cf\u539f\u7406\u51e0\u4e4e\u4f53\u73b0\u5728\u4e00\u5207\u6570\u5b66\u548c\u7269\u7406\u7cfb\u7edf\u4e2d\uff1a<\/span><\/p>\n

        \n
      • \n

        \u8d39\u9a6c\u539f\u7406<\/span>\uff08Fermat principle\uff09<\/span>\uff1a\u5149\u7ebf\u4f20\u64ad\u7684\u8def\u5f84\u662f\u9700\u65f6\u6700\u5c11\u7684\u8def\u5f84<\/span>\uff08\u6700\u77ed\u65f6\u95f4\u539f\u7406\uff09<\/span>\uff1b<\/span><\/p>\n<\/li>\n

      • \n

        \u7ecf\u5178\u7269\u7406\u7cfb\u7edf\uff1a\u7269\u4f53\u4e24\u70b9\u95f4\u6240\u8d70\u7684\u8def\u5f84\uff0c\u603b\u4f1a\u4f7f\u5176\u5e73\u5747\u52a8\u80fdT\u51cf\u53bb\u5e73\u5747\u52bf\u80fdV\u5c3d\u53ef\u80fd\u5c0f<\/span>\uff08\u6b64\u65f6\u683c\u6717\u65e5\u51fd\u6570 L= T – V\uff09<\/span>\uff1b<\/span><\/p>\n<\/li>\n

      • \n
        \u7535\u78c1\u5b66\u3001\u91cf\u5b50\u573a\u8bba\u3001\u91cf\u5b50\u529b\u5b66<\/span>\uff08\u8d39\u66fc\u8def\u5f84\u79ef\u5206\u6cd5\uff09<\/span>\u3001\u5e7f\u4e49\u76f8\u5bf9\u8bba<\/span>\uff08\u7231\u56e0\u65af\u5766-\u5e0c\u5c14\u4f2f\u7279\u4f5c\u7528\u91cf\uff09<\/span>\u5bf9\u5e94\u7684\u6700\u5c0f\u4f5c\u7528\u91cf\u3002<\/span><\/section>\n<\/li>\n<\/ul>\n
         <\/span><\/section>\n
        \u5e76\u4e0d\u610f\u5916\uff0c\u6700\u5c0f\u4f5c\u7528\u91cf\u539f\u7406\u5176\u5b9e\u4e5f\u662f\u5e42\u5f8b\u5206\u5e03\u7684\u4e00\u79cd\u6210\u56e0\u3002\u5728\u6570\u5b66\u4e0a\uff0c\u5e42\u5f8b\u53ef\u7531\u5e7f\u4e49\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406[40]\u7ed9\u51fa\uff1an\u4e2a\u8d8b\u4e8e\u65e0\u7a77\u3001\u5177\u6709\u72ec\u7acb\u540c\u5206\u5e03\u3001\u65b9\u5dee\u53ef\u65e0\u9650\u7684\u968f\u673a\u53d8\u91cf\u7684\u548c\u4f1a\u8d8b\u5411 Levy\u7a33\u5b9a\u5206\u5e03<\/span>\uff08\u5c3e<\/span>\u7aef\u5373\u5e42\u5f8b\u5206\u5e03\uff1b\u65b9\u5dee\u6709\u9650\u5219\u7ed9\u51fa\u6b63\u6001\u5206\u5e03\uff09<\/span>\u3002\u800c\u4ece\u6700\u5c0f\u4f5c\u7528\u91cf\u539f\u7406\u770b\uff0c\u5176\u4e2d\u5e42\u5f8b\u662f\u968f\u673a\u53d8\u91cf\u6ee1\u8db3\u6761\u4ef6\u65e0\u9650\u65b9\u5dee\u6761\u4ef6\u4e0b\u80fd\u4f7f\u4fe1\u606f\u71b5\u5177\u6709\u6700\u5927\u503c\u7684\u552f\u4e00\u5206\u5e03\uff0c\u5373\u5728\u53ef\u80fd\u7a7a\u95f4\u4e2d\uff0c\u5c31\u50cf\u5149\u8d70\u6700\u77ed\u8def\u5f84\uff0c\u968f\u673a\u53d8\u91cf\u6574\u4f53\u4e5f\u53d6\u5f97\u300c\u6781\u503c\u300d\u5e76\u5448\u73b0\u51fa\u4e86\u6700\u4f18\u5206\u5e03\u66f2\u7ebf\u3002<\/span><\/section>\n
         <\/span><\/section>\n
        \u6b64\u5916\uff0c\u5177\u6709\u6700\u5927\u591a\u6837\u6027\u548c\u4fe1\u606f\u71b5\u7684\u7cfb\u7edf\uff0c\u4e5f\u4e0d\u4ec5\u4ec5\u5177\u5907\u7a33\u5b9a\u6027\u548c\u9c81\u68d2\u6027\u3002\u6839\u636e\u5b66\u8005\u65af\u79d1\u7279\u00b7\u4f69\u5947<\/span>\uff08Scott E. Page\uff09<\/span>\u7684\u8bf4\u6cd5\uff0c\u8fd8\u5177\u6709\u6240\u8c13\u300c\u591a\u6837\u6027\u7ea2\u5229<\/strong>\u300d\u3002\u4ed6\u8bc1\u660e\u4e86\u4e00\u4e2a\u5b9a\u7406[34]\uff1a\u5bf9\u4e8e\u7cfb\u7edf\u7684\u9700\u8981\u521b\u65b0\u548c\u63a2\u7d22\u7684\u96be\u9898\uff0c\u591a\u6837\u6027\u672c\u8eab\u4f1a\u5e26\u6765\u8d85\u51fa\u539f\u6709\u7cfb\u7edf\u5e73\u5747\u503c\u7684\u9884\u6d4b\u80fd\u529b\u3002<\/span><\/section>\n

        <\/span><\/section>\n
        \u591a\u6837\u6027\u9884\u6d4b\u5b9a\u7406\uff1a<\/span><\/section>\n
        \u7fa4\u4f53\u603b\u80fd\u529b = \u5e73\u5747\u4e2a\u4eba\u80fd\u529b + \u7fa4\u4f53\u591a\u6837\u6027\u3002<\/span><\/section>\n
         <\/span><\/section>\n
        \u8fd9\u79cd\u80fd\u529b\u8d85\u8fc7\u4e00\u4e2a\u4f53\u2014\u2014\u5982\u5929\u624d\u7684\u80fd\u529b\u3002\u663e\u7136\u8fd9\u662f\u4e00\u4e2a\u6d8c\u73b0\u7684\u8fc7\u7a0b\u3002\u6b64\u5916\u4ece\u7b97\u6cd5\u89d2\u5ea6\u770b\uff0c\u8fd9\u4e5f\u662f\u6a21\u62df\u81ea\u7136\u6f14\u5316\u7684\u8fdb\u5316\u8ba1\u7b97\uff0c\u5bf9\u591a\u76ee\u6807\u6216\u7ec4\u5408\u4f18\u5316\u95ee\u9898\u5177\u6709\u975e\u5e38\u4f18\u5f02\u7684\u6548\u679c[36-38]\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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        5. \u603b\u7ed3<\/strong><\/strong><\/p>\n<\/section>\n

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        <\/section>\n

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

        <\/section>\n
        \u9f50\u592b\u5b9a\u5f8b\u603b\u4e0e\u7ec4\u6210\u90e8\u5206\u89c4\u6a21\u7684\u591a\u6837\u6027\u6700\u5927\u5316\u540c\u65f6\u53d1\u751f\uff0c\u8fd9\u79cd\u81ea\u7136\u76f8\u5173\u6027\uff0c\u80cc\u540e\u53cd\u6620\u7684\u662f\u66f4\u4e00\u822c\u7684\u6700\u7701\u529b\u539f\u5219\u548c\u6700\u5c0f\u4f5c\u7528\u91cf\u539f\u7406<\/strong>\u3002\u5982\u679c\u628a\u81ea\u7136\u770b\u6210\u4e00\u79cd\u901a\u4fe1\u7cfb\u7edf\u548c\u52a8\u529b\u7cfb\u7edf\uff0c\u90a3\u4e48\u8981\u53d6\u5f97\u5305\u62ec\u672a\u6765\u5728\u5185\u53ef\u80fd\u5e73\u5747\u6548\u7387\u7684\u6700\u5927\u5316\uff0c\u4e0d\u4ec5\u8981\u5728\u8a00\u8005\u7ecf\u6d4e<\/span>\uff08\u53d1\u9001\u7aef\u3001\u8d77\u70b9\uff09<\/span>\u5185\u90e8\u4f18\u5316\uff0c\u5f62\u6210\u7edf\u4e00\u673a\u5236<\/span>\uff08\u7edf\u4e00\u5316\u4e4b\u30ab\uff09<\/span>\uff0c\u8fd8\u5fc5\u987b\u501f\u52a9\u300c\u591a\u5143\u5316\u4e4b\u529b\u300d\u5728\u542c\u8005\u7ecf\u6d4e\u4f18\u5316<\/span>\uff08\u63a5\u6536\u7aef\u3001\u8868\u8fbe\u65b9\u3001\u7ec8\u70b9\uff09<\/span>\uff0c\u4ee5\u6700\u5c0f\u6d88\u8017\u6210\u672c\u901a\u5f80\u672a\u6765\u65b0\u7684\u7cfb\u7edf\u81ea\u8eab\u548c\u5916\u90e8\u53ef\u80fd\u8def\u5f84\u3002<\/span><\/section>\n
         <\/span><\/section>\n
        \u6211\u4eec\u77e5\u9053\uff0c\u6839\u636e\u4e2a\u4f53\u4fe1\u606f\u7406\u8bba\uff0c\u751f\u547d\u672c\u8eab\u662f\u4e00\u79cd\u80fd\u5c06\u81ea\u8eab\u4fe1\u606f\u4ece\u8fc7\u53bb\u4f20\u64ad\u5230\u672a\u6765\u3001\u5e76\u4fdd\u6301\u4e00\u5b9a\u65f6\u95f4\u5b8c\u6574\u6027\u5ea6\u91cf\u7684\u96c6\u5408\u4f53[42]\u3002\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u5e7f\u4e49\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u4fdd\u8bc1\u4e86\u5e42\u5f8b\u5206\u5e03\u4f1a\u4ea7\u751f\u6700\u5927\u4fe1\u606f\u71b5\uff0c\u8ba9\u6700\u5927\u591a\u6837\u6027\u6210\u4e3a\u6700\u5c0f\u4f5c\u7528\u91cf\u539f\u7406\u65b0\u7684\u8d77\u70b9\uff0c\u4ee5\u6700\u5927\u6548\u7387\u300c\u89e3\u51b3\u300d\u67d0\u79cd\u5c1a\u672a\u660e\u786e\u3001\u672a\u77e5\u65b9\u5411\u7684\u300c\u96be\u9898\u300d\u3002<\/span><\/section>\n
         <\/span><\/section>\n
        \u53c2\u5dee\u591a\u6001\u4e43\u5e78\u798f\u7684\u672c\u6e90\u3002\u5c31\u73b0\u5b9e\u610f\u4e49\u800c\u8a00\uff0c\u591a\u5143\u5316\u4e4b\u529b\u7684\u5b9e\u8d28\u662f\u4ea7\u751f\u4e86\u591a\u6837\u6027\u89c6\u89d2<\/span>\uff08\u975e\u67d0\u79cd\u540d\u4e49\u4e0a\u7684\u6807\u7b7e\uff09<\/span>\uff0c\u901a\u8fc7\u8d85\u52a0\u6027\u4ea7\u751f\u8d85\u8fc7\u4e86\u4efb\u4f55\u5355\u4e00\u7ec4\u5757\u7684\u80fd\u529b\u7684\u300c\u7ea2\u5229\u300d\uff0c\u8fd9\u662f\u4e00\u4e2a\u81ea\u4e0b\u800c\u4e0a\u6d8c\u73b0\u7684\u8fc7\u7a0b\uff0c\u5bf9\u89e3\u51b3\u6ca1\u6709\u65e2\u5f80\u8def\u5f84\u501f\u9274\u3001\u9700\u8981\u521b\u65b0\u624d\u80fd\u89e3\u51b3\u7684\u96be\u9898\u81f3\u5173\u91cd\u8981\u3002<\/span><\/section>\n
         <\/span><\/section>\n
        \u9053\u6cd5\u81ea\u7136\uff0c\u672c\u6587\u7814\u7a76\u8ba9\u6211\u4eec\u770b\u5230\uff0c\u81ea\u7136\u4e0d\u4ec5\u4ec5\u4f1a\u8d70\u6211\u4eec\u770b\u5230\u7684\u6700\u77ed\u8def\u5f84\u3002\u4ee5\u540e\u5f53\u6211\u4eec\u6b23\u8d4f\u53c2\u5dee\u591a\u6001\u3001\u7f8e\u4e3d\u591a\u59ff\u7684\u4e16\u754c\u65f6\uff0c\u4e5f\u53ef\u4ee5\u50cf\u8bd7\u4eba\u4e00\u6837\u8bf4\uff0c\u54e6\uff0c\u539f\u6765\u90a3\u4e5f\u662f\u5927\u81ea\u7136\u5728\u6700\u5b8c\u7f8e\u9ad8\u6548\u5730\u8868\u8fbe\u81ea\u5df1\u3002<\/span><\/section>\n
         <\/span><\/section>\n
         <\/span><\/section>\n
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        \u53c2\u8003\u6587\u732e<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

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        <\/p>\n

        [1] Fagan, Stephen; Gen\u00e7ay, Ramazan (2010), “An introduction to textual econometrics”, in Ullah, Aman; Giles, David E. A. (eds.), Handbook of Empirical Economics and Finance, CRC Press, pp. 133\u2013153, ISBN 9781420070361. P. 139: “For example, in the Brown Corpus, consisting of over one million words, half of the word volume consists of repeated uses of only 135 words.”<\/span><\/section>\n
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        [34] https:\/\/www.thegreatcourses.com\/courses\/the-hidden-factor-why-thinking-differently-is-your-greatest-asset<\/span><\/section>\n
        [35] \u667a\u80fd\u4f18\u5316\u7b97\u6cd5\u53ca\u5176MATLAB\u5b9e\u4f8b\uff08\u7b2c2\u7248\uff09 <\/span><\/section>\n
        [36] \u6f14\u5316\u5b66\u4e60\uff1a\u7406\u8bba\u4e0e\u7b97\u6cd5\u8fdb\u5c55<\/span><\/section>\n
        [37] M. Joshi, M. Gyanchandani and D. Rajesh Wadhvani, “Analysis Of Genetic Algorithm, Particle Swarm Optimization and Simulated Annealing On Benchmark Functions,” 2021 5th International Conference on Computing Methodologies and Communication (ICCMC), 2021, pp. 1152-1157, doi: 10.1109\/ICCMC51019.2021.9418458.<\/span><\/section>\n
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        [41] \u7a33\u5b9a\u5206\u5e03\u4e0e\u5e7f\u4e49\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406 http:\/\/swarmagents.cn.13442.m8849.cn\/bs\/files\/jake2011616211724.pdf<\/span><\/section>\n
        [42] https:\/\/link.springer.com\/article\/10.1007\/s12064-020-00313-7#Sec10<\/span><\/section>\n


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        \uff08\u53c2\u8003\u6587\u732e\u53ef\u4e0a\u4e0b\u6ed1\u52a8<\/strong>\u67e5\u770b\uff09<\/p>\n<\/section>\n<\/section>\n


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        \u590d\u6742\u79d1\u5b66\u6700\u65b0\u8bba\u6587<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

        \n


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

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

        <\/p>\n


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

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