{"id":42189,"date":"2023-04-30T20:13:03","date_gmt":"2023-04-30T12:13:03","guid":{"rendered":"https:\/\/swarma.org\/?p=42189"},"modified":"2023-04-30T20:13:03","modified_gmt":"2023-04-30T12:13:03","slug":"%e6%99%ba%e8%83%bd%e6%98%af%e4%bb%80%e4%b9%88%ef%bc%9f%e8%8c%83%e7%95%b4%e8%ae%ba%e4%b8%ba%e9%80%9a%e7%94%a8%e4%ba%ba%e5%b7%a5%e6%99%ba%e8%83%bd%e6%8f%90%e4%be%9b%e6%99%ae%e9%80%82%e6%a1%86%e6%9e%b6","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=42189","title":{"rendered":"\u667a\u80fd\u662f\u4ec0\u4e48\uff1f\u8303\u7574\u8bba\u4e3a\u901a\u7528\u4eba\u5de5\u667a\u80fd\u63d0\u4f9b\u666e\u9002\u6846\u67b6"},"content":{"rendered":"
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    \u4f20\u611f\u5668<\/span><\/strong>\uff08sensor\uff09<\/span>\u63a5\u6536\u6765\u81ea\u5916\u90e8\u73af\u5883\u7684\u591a\u6a21\u6001\u4fe1\u53f7\uff0c\u5305\u62ec\u4f46\u4e0d\u9650\u4e8e\u6587\u5b57\u8f93\u5165\u3001\u89c6\u9891\/\u97f3\u9891\/\u56fe\u50cf\u8f93\u5165\u7b49\u3002<\/span><\/section>\n<\/li>\n
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    \u4e16\u754c\u8303\u7574<\/span><\/strong>\uff08the world category\uff09<\/span>\u611f\u77e5\u548c\u7406\u89e3\u4f20\u5165\u7684\u4fe1\u53f7\uff0c\u5e76\u76f8\u5e94\u5730\u66f4\u65b0\u5176\u5185\u90e8\u72b6\u6001\u3002<\/span><\/section>\n<\/li>\n
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    \u4e16\u754c\u8303\u7574<\/strong>\u5305\u62ec\u6240\u6709\u53ef\u4ee5\u7531\u4f20\u611f\u5668\u611f\u77e5\u7684\u5bf9\u8c61\uff0c\u5982\u4eba\u3001\u751f\u7269\u3001\u7269\u4f53\u3001\u5173\u4e8e\u5916\u90e8\u73af\u5883\u7684\u77e5\u8bc6\uff0c\u4ee5\u53ca\u5728\u5b83\u4eec\u4e4b\u4e0a\u7684\u62bd\u8c61\u7684\u8868\u8ff0\u3002\u672c\u6587\u5c06\u5176\u8868\u8ff0\u4e3a\u81ea\u7136\u6570\u504f\u5e8f\u96c6\u8303\u7574<\/strong><\/span> <\/strong>(\u4ee5\u5c0f\u4e8e\u5173\u7cfb\u4e3a\u6001\u5c04\uff0c\u6001\u5c04\u7bad\u5934\u8868\u793a\u65f6\u95f4\u6216\u4e8b\u4ef6\u7684\u6f14\u5316\uff0c\u7c7b\u4f3cLabelled Transition System) <\/span>\u52302-\u8303\u7574Cat<\/strong><\/span> <\/strong>(\u4ee5\u5c0f\u8303\u7574\u4e3a\u5bf9\u8c61\uff0c\u51fd\u5b50\u4e3a\u6001\u5c04\u7684\u9ad8\u9636\u8303\u7574)<\/span> \u7684\u4e00\u4e2a\u51fd\u5b50W: N \u2192 Cat<\/strong>\u3002<\/span><\/section>\n

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    \u8be5\u51fd\u5b50\u4e2d\u8574\u542b\u4e86\u968f\u7740\u65f6\u95f4\u6216\u4e8b\u4ef6\u7b49\u7684\u63a8\u79fb\u800c\u52a8\u6001\u53d8\u5316\u7684\u4e16\u754c\u7684\u4fe1\u606f\u3002\u4f5c\u4e3a\u5bf9\u8c61\u7684\u5c0f\u8303\u7574\u4e2d\u6700\u57fa\u672c\u7684\u90a3\u4e9b\u88ab\u8868\u8fbe\u4e3a\u4e16\u754c\u8303\u7574\u7684\u6b63\u5411\u6216\u53cd\u5411\u6781\u9650<\/strong><\/span> <\/strong>(\u6b63\u5411\u6781\u9650\uff0c\u6216\u79f0\u6b63\u6781\u9650\uff0c\u5f52\u7eb3\u6781\u9650\uff0c\u770b\u6210\u6b63\u5411\u7cfb\u7edf\u4e2d\u7684\u67d0\u4e9b\u4e0d\u80fd\u518d\u5c0f\u7684\u201c\u5b50\u5bf9\u8c61\u201d\uff0c\u5373\u4e00\u4e9b\u5c0f\u8303\u7574\u7684\u5171\u6709\u5b9e\u4f8b<\/strong>\uff0c\u80fd\u591f\u88ab\u201c\u5f52\u7eb3\u201d\u8fdb\u8fd9\u4e9b\u5c0f\u8303\u7574\u91cc\u3002\u5982\u56fe2\u4e2d\uff0cFord fulkson \u548c Edmonds-Karp \u7b97\u6cd5\u7686\u4e3a\u7b97\u6cd5\u8fd9\u4e2a\u5c0f\u8303\u7574\u7684\u5b50\u5bf9\u8c61\u5b9e\u4f8b\uff0c\u800c\u4e14\u6ca1\u6709\u6bd4\u5b83\u4eec\u518d\u5c0f\uff0c\u518d\u5177\u4f53\u7684\u5b9e\u4f8b\u3002\u5bf9\u5076\u5730\uff0c\u53cd\u5411\u6781\u9650\uff0c\u6216\u79f0\u9006\u6781\u9650\uff0c\u6295\u5f71\u6781\u9650\uff0c\u770b\u6210\u8fd9\u4e2a\u53cd\u5411\u7cfb\u7edf\u4e2d\u7684\u67d0\u79cd\u4e0d\u80fd\u518d\u5f80\u4e0b\u6295\u5f71\u5206\u5272\u7684\u201c\u5546\u5bf9\u8c61\u201d\uff0c\u5373\u67d0\u4e9b\u5bf9\u8c61\u5171\u6709\u7684\u6700\u57fa\u672c\u7684\u5c5e\u6027<\/strong>\uff0c\u5982\u56fe2\uff0c\u8fb9\u4e0e\u8282\u70b9\u4e3anetwork\u8fd9\u4e2a\u5bf9\u8c61\u7684\u6700\u57fa\u672c\u7684\u5143\u7d20\u5c5e\u6027\uff0c\u800c\u4e14\u8fd9\u4e9b\u5c5e\u6027\u4e0d\u80fd\u518d\u88ab\u5206\u89e3\u4e3a\u66f4\u57fa\u672c\u7684\u5c5e\u6027\u3002) <\/span>\u8fd9\u4e9b\u57fa\u672c\u7684\u5bf9\u8c61\u662f\u7531\u4f20\u611f\u5668\u51b3\u5b9a\u7684\uff0c\u5982\u679c\u4f20\u611f\u5668\u4e0d\u8bc6\u522b\u67d0\u7c7b\u4fe1\u606f\uff0c\u5219\u8fd9\u4e9b\u4fe1\u606f\u884d\u751f\u7684\u5c0f\u8303\u7574\u4e0d\u4f1a\u51fa\u73b0\u5728\u5bf9\u5e94\u7684\u4e16\u754c\u8303\u7574\u4e2d\u3002\u6b64\u5916\uff0c\u5982\u679c\u4f20\u611f\u5668\u88ab\u9650\u5236\u53ea\u4ece\u67d0\u4e2a\u6a21\u62df\u73af\u5883\u4e2d\u63a5\u6536\u4fe1\u53f7\uff0c\u5219\u5bf9\u5e94\u6846\u67b6\u7684\u4e16\u754c\u8303\u7574\u4e2d\u4f1a\u53ea\u5305\u542b\u6a21\u62df\u5f97\u5230\u7684\u77e5\u8bc6\uff0c\u800c\u4e0e\u73b0\u5b9e\u4e16\u754c\u53ef\u80fd\u76f8\u5dee\u751a\u8fdc\u3002<\/span><\/section>\n

    <\/section>\n
    <\/section>\n
    \u56fe2. \u7f51\u7edc\u6d41\u56fe\u8868\u3002\u9ec4\u8272\u7bad\u5934\u4e3a\u6b63\u5411\u6781\u9650\uff0c\u7d2b\u8272\u7bad\u5934\u4e3a\u53cd\u5411\u6781\u9650\u3002<\/span><\/section>\n

    <\/section>\n
    \u5982\u679c\u6a21\u578b\u80fd\u591f\u901a\u8fc7\u5176\u4f20\u611f\u5668\u4e86\u89e3\u5230\u7684\u5916\u90e8\u4fe1\u606f\u77e5\u89c9\u5176\u81ea\u8eab\uff0c\u90a3\u4e48\u8fd9\u4e2a\u6a21\u578b\u7684\u4e16\u754c\u8303\u7574\u4e2d\u53ef\u80fd\u5305\u542b\u4e00\u4e2a\u7279\u6b8a\u5bf9\u8c61\uff1a\u201c\u81ea\u6211\u72b6\u6001 (self-state)<\/strong>\u201d\uff0c\u5b83\u5b58\u50a8\u6a21\u578b\u4e0e\u5176\u4ed6\u5bf9\u8c61\u4e4b\u95f4\u7684\u6240\u6709\u5173\u7cfb\u3002\u81ea\u6211\u72b6\u6001\u7684\u4fdd\u6301\u662f\u5426\u7b49\u540c\u4e8e\u62e5\u6709\u81ea\u6211\u610f\u8bc6\uff1f\u8fd9\u662f\u4e00\u4e2a\u6709\u4e89\u8bae\u7684\u95ee\u9898\uff0c\u5728\u6b64\u4e0d\u7ed9\u51fa\u660e\u786e\u56de\u7b54\uff0c\u800c\u4ec5\u4ee5\u8303\u7574\u8bed\u8a00\u5b9a\u4e49\u4e86\u201c\u81ea\u6211\u72b6\u6001\u201c\u8fd9\u4e00\u6982\u5ff5\u3002\u968f\u540e\uff0c\u8bba\u6587\u5206\u522b\u4ecb\u7ecd\u4e86\u5b66\u4e60\u548c\u8bc4\u4f30\u6a21\u578b\u7684\u201c\u81ea\u6211\u72b6\u6001\u8ba4\u77e5\u201d\u7684\u7b97\u6cd5\u3002\u8bc4\u4f30\u751f\u6210\u4e00\u4e2a0-1\u95ed\u533a\u95f4\u4e2d\u7684\u503c\u6765\u8868\u793a\u81ea\u6211\u72b6\u6001\u8ba4\u77e5\u7a0b\u5ea6\u3002\u8be5\u7a0b\u5ea6\u5bf9\u5e94\u4e8e\u4e3b\u4f53\u610f\u8bc6\u5230\u7684\u4e0e\u5176\u4ed6\u5bf9\u8c61\u6216\u4efb\u52a1\u4e4b\u95f4\u7684\u6240\u6709\u76f8\u5173\u5173\u7cfb\u7684\u6bd4\u4f8b\u3002\u57fa\u4e8e\u8fd9\u4e00\u8bc4\u4f30\uff0c\u8bb8\u591a\u4eba\u7c7b\uff0c\u7279\u522b\u662f\u513f\u7ae5\uff0c\u53ef\u80fd\u4e0d\u5177\u5907\u5b8c\u7f8e\u7684\u81ea\u6211\u72b6\u6001\u8ba4\u77e5\u3002<\/span><\/section>\n

    <\/section>\n
    \u89c4\u5212\u5668\u7684\u76ee\u6807\u662f\u6a21\u578b\u4e2d\u6700\u91cd\u8981\u7684\u90e8\u5206\u3002\u4e16\u754c\u8303\u7574\u53ef\u4ee5\u88ab\u770b\u4f5c\u662f\u4e00\u4e2a\u5de8\u5927\u7684\u77e5\u8bc6\u5e93\uff0c\u800c\u89c4\u5212\u5668\u662f\u4e00\u4e2a\u72ec\u7acb\u4e8e\u4e16\u754c\u8303\u7574\u7684<\/span> (\u4f8b\u5982\uff0c\u57fa\u4e8e\u5f3a\u5316\u5b66\u4e60\u7684) <\/span>\u7ec4\u4ef6\u3002\u90a3\u4e48\uff0c\u5982\u4f55\u786e\u4fdd\u89c4\u5212\u5668\u7684\u76ee\u6807\u4e0d\u4f1a\u5bf9\u4eba\u7c7b\u9020\u6210\u4f24\u5bb3\u5462\uff1f\u8bba\u6587\u4f7f\u7528\u4e00\u4e2a\u7279\u5b9a\u7684\u51fd\u6570\u6765\u5b9a\u4e49\u76ee\u6807\uff0c\u8be5\u51fd\u6570\u4ee5\u81ea\u6211\u72b6\u6001\u7684\u5bf9\u8c61\u548c\u4e00\u4e2a\u6355\u6349\u5f53\u524d\u60c5\u51b5\u7684\u56fe\u8868<\/strong><\/span> (diagram) <\/span>\u4e3a\u8f93\u5165\u3002\u6a21\u578b\u672c\u8eab\u88ab\u8bbe\u8ba1\u4e3a\u5bf9\u4eba\u7c7b\u53cb\u597d\u7684\u6761\u4ef6\u8db3\u4ee5\u786e\u4fdd\u6a21\u578b\u662f\u53cb\u597d\u7684\uff0c\u8fd9\u4e00\u8bbe\u8ba1\u4e0a\u7684\u6761\u4ef6\u53ef\u4ee5\u901a\u8fc7\u5b9a\u671f\u68c0\u67e5\u4e16\u754c\u8303\u7574\u6765\u8fdb\u884c\u5f3a\u5316\u548c\u9a8c\u8bc1\u3002\u901a\u4fe1\u5bf9\u4e8e\u4f7f\u6a21\u578b\u80fd\u591f\u4f20\u8f93\u6216\u63a5\u6536\u5176\u4ed6\u667a\u80fd\u4f53\u7684\u4fe1\u606f\u975e\u5e38\u91cd\u8981\u3002\u5bf9\u6bd4\u81ea\u7136\u8bed\u8a00\uff0c\u8303\u7574\u56fe\u8868<\/span>\u53ef\u4ee5\u66f4\u7cbe\u786e\u5730\u6355\u6349\u6a21\u578b\u7684\u77e5\u8bc6\u548c\u610f\u56fe\uff0c\u56e0\u6b64\u53ef\u4ee5\u8f7b\u677e\u5730\u5728\u4e0d\u540c\u7684\u667a\u80fd\u4f53\u4e4b\u95f4\u5171\u4eab\u3002\u56e0\u6b64\uff0c\u672c\u6846\u67b6\u4e2d\u4ee5\u56fe\u8868\u4f5c\u4e3a\u4fe1\u606f\u8f7d\u4f53\u3002\u800c\u4e14\uff0c\u57fa\u4e8e\u56fe\u8868\u7684\u89e3\u91ca\u4f3c\u4e4e\u6bd4\u5f52\u56e0\u65b9\u6cd5<\/span> (attribution methods)<\/span> \uff0c\u5373\u5206\u914d\u8f93\u5165\u53d8\u91cf\u6743\u91cd\u7684\u65b9\u6cd5\uff0c\u66f4\u7b26\u5408\u7ecf\u9a8c\u53ef\u89e3\u91ca\u6027\u7684\u9700\u6c42\u3002<\/span><\/section>\n

    <\/section>\n
    \u5c06\u4e0d\u53d8\u6027\u4f5c\u4e3a\u8bad\u7ec3\u4fe1\u53f7\u3002\u8303\u7574\u8bba\u91c7\u7528\u4ea4\u6362\u56fe\u8868\u6765\u63cf\u8ff0\u4e0d\u540c\u8ba1\u7b97\u8def\u5f84\u7684\u7b49\u4ef7\u6027\uff0c\u8fd9\u81ea\u7136\u5730\u5bfc\u81f4\u6a21\u578b\u7684\u4e0d\u53d8\u5c5e\u6027\u3002\u4e0e\u4ee5\u5c06\u8f93\u5165\u6b63\u786e\u5339\u914d\u8f93\u51fa\u6807\u7b7e\u4e3a\u76ee\u7684\u76d1\u7763\u5b66\u4e60\u4e0d\u540c\uff0c\u57fa\u7840\u6a21\u578b\u4e13\u6ce8\u4e8e\u5b66\u4e60\u5bf9\u8c61\u4e4b\u95f4\u7684\u6001\u5c04\u548c\u8303\u7574\u4e4b\u95f4\u7684\u51fd\u5b50\u3002\u4e0d\u53d8\u5c5e\u6027\u5c06\u4f1a\u88ab\u7528\u4ee5\u8bad\u7ec3\u4fe1\u53f7\u4f7f\u6a21\u578b\u5bf9\u81ea\u8eab\u8fdb\u884c\u6821\u51c6\uff0c\u4f7f\u4e16\u754c\u8303\u7574\u81ea\u534f\u8c03\u3002\u8bba\u6587\u7b2c\u4e8c\u7ae0\u4e2d\u5bf9\u4e00\u4e9b\u8303\u7574\u7684\u57fa\u672c\u6982\u5ff5\u8fdb\u884c\u4e86\u4ecb\u7ecd\u3002\u6b64\u5904\u5728\u5404\u6bb5\u7b80\u660e\u4ecb\u7ecd\uff0c\u5982\u53e6\u6709\u9700\u8981\u53c2\u8003\u7684\u8bba\u6587\u5185\u5bb9\u3002<\/span><\/section>\n

    <\/section>\n

    <\/section>\n

    \n
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    <\/section>\n
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    <\/svg><\/section>\n<\/section>\n<\/section>\n
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    \u4e8c\u3001\u4e16\u754c\u8303\u7574<\/strong><\/strong><\/p>\n<\/section>\n

    \n

    <\/section>\n

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

    <\/section>\n
    \u4e16\u754c\u8303\u7574\u662f\u4e00\u4e2a\u51fd\u5b50 W: N \u2192 Cat<\/strong>\uff0c\u5b83\u5c06\u6bcf\u4e2a\u65f6\u95f4\u6216\u4e8b\u4ef6\u7d22\u5f15 t \u2208 N<\/strong> \u6620\u5c04\u5230\u76f8\u5e94\u7684\u968f\u65f6\u95f4\u6216\u4e8b\u4ef6\u7684\u53d1\u751f\u800c\u53d8\u5316\u7684\u4e16\u754c\u72b6\u6001\u7684\u5feb\u7167 W(t)<\/strong>\uff08\u6b64\u540e\u7b80\u8bb0W<\/strong>\uff09\u3002<\/span><\/section>\n

    <\/section>\n
    \u7531\u5b66\u4e60\u7684\u89d2\u5ea6\uff0c\u4f7f\u7528\u4ee5\u03b8\u4e3a\u53c2\u6570\u7684\u795e\u7ecf\u7f51\u7edc\u51fd\u5b50F\u03b8<\/sub>: W \u2192 W\u2227<\/sup><\/strong>\u6765\u5728W\u7684\u9884\u5c42\u8303\u7574\u4e2d\u8868\u793a W\u3002W\u2227<\/sup><\/strong>\u4ee3\u8868W\u7684\u9884\u5c42\u8303\u7574\uff0c\u7531\u4eceW\u5230\u96c6\u5408\u8303\u7574Set\u7684\u6240\u6709\u53cd\u53d8\u51fd\u5b50\u7ec4\u6210\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u3010\u89e3\u8bfb\u3011\u73b0\u5728\u6211\u4eec\u6709\u4e00\u4e2a\u8303\u7574W<\/strong>\uff0c\u5176\u4e2d\u7684\u5bf9\u8c61\u662f\u6211\u4eec\u719f\u6089\u7684\u7a7a\u95f4\uff0c\u6216\u7cfb\u7edf\u3002\u53e6\u5916\uff0c\u6211\u4eec\u4e0d\u719f\u6089\u4e00\u7c7b\u201c\u5e7f\u4e49\u201d\u7a7a\u95f4\uff0c\u4f46\u5176\u5185\u5bb9\u53ef\u4f7f\u7528W\u4e2d\u7684\u5bf9\u8c61\uff0c\u67d0\u4e2a\u4e16\u754c\u72b6\u6001x\u6765\u63a2\u6d4b\uff0c\u5373\u7531\u67d0\u4e00x\u5230\u8fd9\u7c7b\u7a7a\u95f4\u4ea7\u751f\u7684\u6001\u5c04\u6765\u51b3\u5b9a\u3002\u5219\u4e00\u4e2a\u8fd9\u6837\u7684\u5e7f\u4e49\u7a7a\u95f4O<\/strong>\u6210\u4e3a\u4e00\u4e2a\u51fd\u5b50\uff0c\u5c06x<\/strong>\u6620\u5230\u4e00\u4e2a\u6001\u5c04\u96c6\u5408Hom(x, O)<\/strong>\uff0c\u5373W\u4e0a\u7684\u9884\u5c42\u3002Hom(x, O)\u7684\u610f\u4e49\u5728\u6b64\u5904\u8fd8\u5c1a\u672a\u660e\u786e\u3002<\/strong>\u53e6\u7531\u7c73\u7530\u5f15\u7406\uff0c\u53ef\u5c06\u4efb\u610fx\u540c\u6837\u7406\u89e3\u4e3a\u4e00\u4e2a\u5e7f\u4e49\u7a7a\u95f4\u3002Hom(x, O)\u7684\u610f\u4e49\u4e8e\u662f\u6210\u4e3ax\u4f5c\u4e3a\u5e7f\u4e49\u7a7a\u95f4\u5230\u5e7f\u4e49\u7a7a\u95f4O\u7684\u6001\u5c04\u7684\u96c6\u5408\u3002<\/strong>\u65e2\u7136O<\/strong>\u53ef\u4ee5\u88ab\u7406\u89e3\u4e3a\u5e7f\u4e49\u7a7a\u95f4\uff0c\u90a3\u4e48\u5728\u6b64\u5904\u5c31\u4e0d\u96be\u7406\u89e3O<\/strong>\u4e3a\u4ee5W<\/strong>\u4e3a\u5b9e\u4f8b\u5efa\u6a21\u7684\u7cfb\u7edf\u3002<\/span><\/section>\n

    <\/section>\n
    \u6bcf\u4e00\u4e2a\u53cd\u53d8\u51fd\u5b50O: Wop<\/sup> \u2192 Set<\/strong> \u4f5c\u4e3a\u4e00\u4e2a\u9884\u5c42\uff0c\u5c06W\u4e2d\u5bf9\u8c61\u6620\u5230\u5176\u6709\u7528\u4fe1\u606f\u7684\u63d0\u53d6\u51fa\u7684\u4e00\u4e2a\u96c6\u5408\uff0c\u5373\u7279\u5f81\u96c6\u5408\u3002F\u03b8<\/sub><\/strong>\u8868\u793a\u4e86\u5728\u57fa\u4e8e\u4e0d\u540c\u7684\u4e16\u754c\u72b6\u6001\u7279\u5f81\u96c6\u5408\u7684\u6f14\u5316\u3002W\u2227<\/sup>\u4e8e\u662f\u6210\u4e3aW\u7684\u7279\u5f81\u7a7a\u95f4\u3002\u5047\u8bbeF\u03b8<\/sub>\u53ef\u4ee5\u901a\u8fc7\u591a\u6a21\u5f0f\u5b66\u4e60\u51c6\u786e\u5730\u7406\u89e3\u4f20\u611f\u5668\u7684\u591a\u6a21\u6001\u4fe1\u53f7\uff0c\u5e76\u4f7f\u7528\u5bf9\u6bd4\u5b66\u4e60\u6280\u672f\u5c06\u56fe\u50cf\u548c\u5bf9\u5e94\u7684\u6587\u672c\u90fd\u6620\u5c04\u5230\u76f8\u540c\u7684\u8868\u793a\u3002\u5c3d\u7ba1W\u901a\u8fc7F\u03b8<\/sub>\u7684\u8868\u793a<\/span> (F\u03b8<\/sub>\u600e\u6837\u5c06W\u4e2d\u7684\u6001\u5c04\uff0c\u5373\u4e16\u754c\u8303\u7574\u4e2d\u5bf9\u8c61\u7684\u8054\u7cfb\uff0c\u6620\u5c04\u5230\u5176\u9884\u5c42\u8303\u7574\u4e2d\u7684\u6001\u5c04\uff0c\u5373\u5bf9\u8c61\u5bf9\u5e94\u7684\u7279\u5f81\u96c6\u5408\u95f4\u7684\u8054\u7cfb) <\/span>\u5e76\u4e0d\u662f\u663e\u5f0f\u7684\uff0c\u5373\u4e0d\u5b58\u5728\u5916\u90e8\u6570\u636e\u5e93\u5b58\u50a8W\u7684\u5bf9\u8c61\u548c\u6001\u5c04\uff0cF\u03b8<\/sub>\u5728\u7406\u60f3\u60c5\u51b5\u4e0b\u5e94\u8be5\u9690\u5f0f\u5730\u4fdd\u6301\u5b9a\u4e49\u57dfW\u4e2d\u7684\u6001\u5c04\uff0c\u5373\u5176\u9884\u5c42\u8303\u7574W\u2227<\/sup>\u4e2d\u7684\u4efb\u4e00\u6001\u5c04\u5728W\u4e2d\u5fc5\u5b9a\u6709\u5bf9\u5e94\u3002\u5b9a\u4e49\u4e3a\u4e0b\u8ff0\u7406\u60f3\u6a21\u578b\u3002\u8fd9\u79cd\u7406\u60f3\u5728\u5b9e\u8df5\u65f6\u5e38\u5e38\u9762\u4e34\u6311\u6218\u3002<\/span><\/section>\n

    <\/section>\n
    \u7406\u60f3\u57fa\u7840\u6a21\u578b<\/strong>\uff1a\u5982\u679c\u5b58\u5728\u4e00\u4e2a\u6570\u636e\u65e0\u5173\u7684\u51fd\u6570k: W\u2227<\/sup>\u00d7W\u2227<\/sup>\u2192 Set<\/strong>\uff0c\u4f7f\u5f97\u5bf9\u4e8e\u4efb\u4f55X, Y\u2208W\uff0ck(F\u03b8<\/sub>(X), F\u03b8<\/sub>(Y)) = HomW<\/sub>(X, Y)<\/strong>\uff0c\u5219F\u03b8<\/sub>: W \u2192 W\u2227<\/sup><\/strong>\u662f\u7406\u60f3\u7684\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u3010\u89e3\u8bfb\u3011\u4e24\u4e2a\u4e16\u754c\u72b6\u6001\u4e4b\u95f4\u7684\u6001\u5c04HomW<\/sub>(X, Y)<\/strong>\u548c\u5b83\u4eec\u7279\u5f81\u96c6\u5408\u95f4\u7684\u6001\u5c04HomW\u2227<\/sub>(F\u03b8<\/sub>(X), F\u03b8<\/sub>(Y))<\/strong>\u9700\u8981\u7b49\u540c\u6216\u81f3\u5c11\u6709\u67d0\u79cd\u6df1\u523b\u7684\u5173\u8054\u3002\u8fd9\u91cc\u7528\u6570\u636e\u65e0\u5173\u7684\u51fd\u6570k\u8868\u793a\u8fd9\u79cd\u5173\u8054\u3002\u5982\u679c\u4e24\u4e2a\u4e16\u754c\u72b6\u6001\u5404\u81ea\u5bf9\u5e94\u7684\u7279\u5f81\u96c6\u5408\u95f4\u5b58\u5728\u5173\u7cfb\uff0c\u5219\u8fd9\u4e2a\u5173\u7cfb\u4e00\u5b9a\u7531\u8fd9\u4e24\u4e2a\u4e16\u754c\u72b6\u6001\u95f4\u539f\u6709\u7684\u81ea\u7136\u7684\u5173\u7cfb\u62bd\u8c61\u800c\u6765\uff0c\u8fd9\u79cd\u62bd\u8c61\u662f\u65e0\u5173\u4e8e\u6570\u636e\u7684\u3002\u6570\u636e\u65e0\u5173\u610f\u5473\u7740k\u662f\u9884\u5b9a\u4e49\u7684\uff0c\u800c\u4e0d\u662f\u770b\u5230\u4e86\u6570\u636e\u540e\u7684\u5b9a\u4e49\u3002\u4f8b\u5982\uff0c\u5b83\u53ef\u4ee5\u5b9a\u4e49\u4e3a\u4e24\u4e2a\u8f93\u5165\u7684\u5185\u79ef\u3002<\/span><\/section>\n

    <\/section>\n
    \u81ea\u7136\u5730\uff0c\u5e94\u5f53\u8981\u6c42\u4e24\u4e2a\u666e\u901a\u7a7a\u95f4\u4e4b\u95f4\u7684\u6001\u5c04\u548c\u5b83\u4eec\u4f5c\u4e3a\u5e7f\u4e49\u7a7a\u95f4\u7684\u6001\u5c04\u7b49\u540c\u3002\u8fd9\u7531\u7c73\u7530\u5f15\u7406\u7ed9\u51fa\u3002\u6bcf\u4e00\u4e2a\u4ece\u5bf9\u8c61X\u5230\u5bf9\u8c61Y\u7684\u6001\u5c04\u90fd\u5bf9\u5e94\u4e8e\u4e00\u4e2a\u4eceX\u4e0a\u53cd\u53d8Hom\u51fd\u5b50hX<\/sub><\/strong>\u5230Y\u4e0a\u53cd\u53d8Hom\u51fd\u5b50hY<\/sub><\/strong>\u7684\u81ea\u7136\u53d8\u6362\u3002\u4e0a\u8ff0\u6570\u636e\u65e0\u5173\u7684\u51fd\u6570k<\/strong>\u6b63\u597d\u53cd\u6620\u4e86\u8fd9\u4e2a\u5bf9\u5e94\uff0c\u56e0\u6b64k\u4e5f\u5c31\u53ef\u4ee5\u7528\u4ee5\u8868\u793a\u6574\u4e2a\u9884\u5c42\u8303\u7574W\u2227<\/sup>\u3002\u53e6\u5916\uff0c\u53ef\u4ee5\u7528F\u03b8<\/sub>\u7f16\u7801\u4efb\u52a1<\/strong>\uff0c\u5b9a\u4e49\u5982\u4e0b\u3002<\/span><\/section>\n

    <\/section>\n
    \u4efb\u52a1<\/strong>\uff1a\u4efb\u52a1T<\/strong>\u662fW\u2227<\/sup><\/strong>\u4e2d\u7684\u4e00\u4e2a\u51fd\u5b50\u3002<\/span><\/section>\n

    <\/section>\n
    \u3010\u89e3\u8bfb\u3011\u53ea\u9700\u4ee4T=hC<\/sub>(Y)=HomC<\/sub>(-, Y)<\/strong>\u3002\u8fd9\u4e2a\u51fd\u5b50\u5c06W\u7684\u4efb\u610f\u5bf9\u8c61Z\u6620\u5230Z\u5230\u5bf9\u8c61Y\u7684\u6001\u5c04\u96c6\u3002T(X)\u5373\u5bf9\u8c61X\u5230\u5bf9\u8c61Y\u7684\u6001\u5c04\u96c6\uff0c\u4e5f\u5c31\u662fX\u5230Y\u7684\u6240\u6709\u5173\u7cfb\u3002\u53cd\u6620\u5728\u9884\u5c42\u8303\u7574\u4e0a\uff0c\u7b49\u540c\u4e8eX\u4e0a\u9884\u5c42\u5230Y\u4e0a\u9884\u5c42\u7684\u6240\u6709\u5173\u7cfb\uff0c\u5373HomW\u2227<\/sub>(hC<\/sub>(X), hC<\/sub>(Y))\u3002<\/span><\/section>\n

    <\/section>\n
    \u5728\u4e0a\u8ff0\u89e3\u8bfb\u7684\u57fa\u7840\u4e0a\uff0c\u6709T(X)\u2243HomW\u2227<\/sub>(hC<\/sub>(X), T)<\/strong>\u3002\u53ef\u77e5\u5f53F\u03b8<\/sub><\/strong>\u7406\u60f3\u65f6\uff0c\u53ef\u4ee5\u7528k(F\u03b8<\/sub>(X), T)<\/strong>\u8ba1\u7b97T(X)<\/strong>\u3002\u6362\u53e5\u8bdd\u8bf4\uff0cF\u03b8<\/sub><\/strong>\u662f\u4e00\u4e2a\u52a8\u6001\u6570\u636e\u5e93\uff0c\u5b58\u50a8\u4e86W\u7684\u6240\u6709\u4fe1\u606f\uff0c\u4f7f\u5f97\u6240\u6709\u57fa\u4e8eW\u4e2d\u5bf9\u8c61\u7684\u8ba1\u7b97\u90fd\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528\u6570\u636e\u65e0\u5173\u51fd\u6570k\u5728\u7279\u5f81\u7a7a\u95f4W\u2227<\/sup><\/strong>\u4e2d\u8ba1\u7b97\u3002<\/span><\/section>\n

    <\/section>\n
    \u5177\u6709\u901a\u7528\u667a\u80fd\u7684\u6a21\u578b\u5177\u6709\u5185\u5b58\u3002\u53ef\u4ee5\u5185\u5b58\u89c6\u4e3aW\u4e2d\u7684\u4e00\u79cd\u7279\u6b8a\u5bf9\u8c61\uff0c\u7531\u4e8b\u4ef6\u548c\u65f6\u95f4\u6233\u7684\u53cd\u5411\u6781\u9650\u8868\u793a(\u5982\u7b2c\u4e00\u7ae0\u84dd\u5b57\u89e3\u8bfb\uff0c\u53ef\u4ee5\u770b\u6210\u4e00\u79cd\u901a\u7528\u7684\u57fa\u672c\u5c5e\u6027<\/strong>)\u3002\u8fd9\u6837\u6709\u6548\u89c4\u907f\u4e86\u5185\u5b58\u7684\u5916\u90e8\u6570\u636e\u5e93\u7684\u5f15\u5165\u3002\u63a5\u7740\uff0c\u5728\u4e16\u754c\u8303\u7574\u5185\u5b9a\u4e49\u591a\u4e2a\u6a21\u578b\u7684\u5171\u8bc6<\/strong>\u3002<\/span><\/section>\n

    <\/section>\n
    \u5171\u8bc6<\/strong>\uff1a\u5047\u8bbe\u6709n\u4e2a\u6a21\u578b\uff0c\u5206\u522b\u5bf9\u5e94\u4e16\u754c\u8303\u7574W1<\/sub>, W2<\/sub>, …, Wn<\/sub>\u7684\u6a21\u578b\u3002\u8fd9n\u4e2a\u6a21\u578b\u7684\u5171\u8bc6\u5b9a\u4e49\u4e3a\u5176\u6781\u5927\u5b50\u8303\u7574C\uff0c\u5373C\u662f\u4efb\u610fWi<\/sub>\uff08i\u2208[n]={1, 2,…, n}\uff09\u7684\u5b50\u8303\u7574\u3002<\/span><\/section>\n

    <\/section>\n
    \u5b50\u8303\u7574\u662f\u5bf9\u8c61\u4e0e\u4efb\u610f\u5bf9\u8c61\u95f4\u6001\u5c04\u96c6\u5747\u662f\u539f\u8303\u7574\u5b50\u96c6\uff0c\u5e76\u4fdd\u6301\u539f\u8303\u7574\u6052\u7b49\u6001\u5c04\u548c\u5408\u6210\u6001\u5c04\u7ed3\u5408\u5f8b\u7684\u8303\u7574\u3002\u53ef\u4ee5\u7406\u89e3\u4e3a\u80fd\u6784\u6210\u539f\u8303\u7574\u4e2d\u72ec\u7acb\u7684\u4e00\u4e2a\u90e8\u5206\u7684\u8303\u7574\u3002\u4f8b\u5982\uff0c\u201c\u72d7\u6709\u56db\u6761\u817f\u201d\u662f\u6240\u6709\u4eba\u7684\u5171\u8bc6\uff0c\u8fd9\u4e2a\u77e5\u8bc6\u5305\u542b\u5728\u6bcf\u4e2a\u4eba\u7684\u4e16\u754c\u8303\u7574\u4e2d\u3002\u53ef\u4ee5\u901a\u8fc7\u8bbe\u7f6e\u5171\u8bc6\u7684\u9608\u503c\u6765\u653e\u5bbd\u8fd9\u4e2a\u6982\u5ff5\uff0c\u5373\u8d85\u8fc7\u67d0\u4e2a\u767e\u5206\u6bd4\uff0c\u5c31\u8ba4\u4e3a\u662f\u5171\u8bc6\uff0c\u4f8b\u5982\uff0c\u5b9a\u4e49C\u662f\u4e16\u754c\u8303\u7574\u7684\u03b4-\u6982\u7387\u5b50\u7c7b\u522b<\/strong>\uff0c\u5176\u4e2d\u03b4\u2208(0\uff0c1]<\/strong>\u3002<\/span><\/section>\n

    <\/section>\n

    2.1 \u81ea\u6211\u72b6\u6001<\/strong><\/span><\/h2>\n

    <\/strong><\/span><\/section>\n
    \u5982\u524d\u6240\u8ff0\uff0c\u5982\u679c\u4e00\u4e2a\u6a21\u578b\u53ef\u4ee5\u4ece\u4f20\u611f\u5668\u5728\u5916\u754c\u73af\u5883\u4e2d\u77e5\u89c9\u81ea\u8eab\uff0c\u5219\u8fd9\u4e2a\u6a21\u578b\u7684\u4e16\u754c\u8303\u7574\u4e2d\u53ef\u80fd\u6709\u4e00\u4e2a\u7279\u6b8a\u5bf9\u8c61\uff0c\u81ea\u6211\u72b6\u6001<\/strong>\u3002\u5b9a\u4e49\u5982\u4e0b\u3002<\/span><\/section>\n

    <\/section>\n
    \u81ea\u6211\u72b6\u6001 (self-state)<\/strong>\uff1a\u5728\u4e00\u4e2a\u6a21\u578b\u7684\u4e16\u754c\u8303\u7574\u4e2d\uff0c\u82e5\u5b58\u5728\u81ea\u6211\u72b6\u6001\uff0c\u5219\u81ea\u6211\u72b6\u6001\u88ab\u5b9a\u4e49\u4e3a\u4e00\u4e2a\u9884\u5c42 I\u2227<\/sup>\u2208W\u2227<\/sup><\/strong>\uff0c \u8fd9\u4e2a\u9884\u5c42\u5728\u5916\u90e8\u73af\u5883\u8868\u793a\u8be5\u6a21\u578b\u3002<\/span><\/section>\n

    <\/section>\n
    \u81ea\u6211\u72b6\u6001\u7531\u4e8e\u662f\u9884\u5c42\uff0c\u53ef\u4ee5\u901a\u8fc7F\u03b8<\/sub>(I)<\/strong>\u8ba1\u7b97\uff0c\u5176\u4e2d I \u2208 W\u3002\u5bf9\u8c61 I \u4e5f\u88ab\u79f0\u4e3a\u201c\u81ea\u6211\u72b6\u6001\u201d\uff0c\u4f46\u8be5\u72b6\u6001\u7531\u4e8e\u5b58\u5728\u4e8e\u4e16\u754c\u8303\u7574\u800c\u975e\u5176\u9884\u5c42\u8303\u7574\uff0c\u56e0\u6b64\u4e0d\u6d89\u53ca\u6001\u5c04\u96c6\uff0c\u4e5f\u5c31\u662f\u4e00\u4e2a\u6ca1\u6709\u4efb\u4f55\u9644\u52a0\u4fe1\u606f\u7684\u5355\u4e00\u5bf9\u8c61\uff0c\u800c\u771f\u6b63\u5177\u6709\u4fe1\u606f\u7684\u81ea\u6211\u72b6\u6001\u662fI\u2227<\/sup><\/strong>\u3002\u5982\u679cF\u03b8<\/sub>(I)<\/strong>\u7406\u60f3\uff0c\u90a3\u4e48I\u2227<\/sup> = F\u03b8<\/sub>(I) = hC<\/sub>(I) = HomW<\/sub>(\u00b7, I)<\/strong>\u3002\u6362\u53e5\u8bdd\u8bf4\uff0cI\u2227<\/sup> <\/strong>\u8574\u542b\u4e86 I \u548c\u5176\u4ed6\u5bf9\u8c61\u4e4b\u95f4\u7684\u6240\u6709\u5173\u7cfb\u3002\u6b64\u5916\uff0c\u6839\u636e\u7c73\u7530\u5f15\u7406\uff0c\u5bf9\u4e8e\u4efb\u4f55\u4efb\u52a1 T\u2208W\u2227<\/sup><\/strong>\uff0c\u6211\u4eec\u4e5f\u6709T(I)\u2243HomW\u2227<\/sub>(hC<\/sub>(I), T) = HomW\u2227<\/sub>(I\u2227<\/sup>, T)<\/strong>\u3002\u8fd9\u610f\u5473\u7740I\u2227<\/sup><\/strong>\u4e5f\u7f16\u7801\u4e86\u6bcf\u4e2a\u76f8\u5173\u4efb\u52a1\u6240\u9700\u7684\u6240\u6709\u4fe1\u606f\u3002<\/span><\/section>\n

    <\/section>\n
    \u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5e76\u975e\u6240\u6709\u7684\u4e16\u754c\u8303\u7574\u90fd\u6709\u81ea\u6211\u72b6\u6001\u3002\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u8003\u8651\u4e00\u4e2a\u7528\u4e8e\u8ba1\u7b97\u7684\u7279\u6b8a\u73af\u5883\u3002\u4f20\u611f\u5668\u53ea\u80fd\u591f\u611f\u77e5\u73af\u5883\u4e2d\u7531\u5b9e\u6570\u548c\u7b97\u7b26\u7ec4\u6210\u7684\u8868\u8fbe\u5f0f\uff0c\u800c\u6267\u884c\u8005\u80fd\u591f\u6267\u884c\u7684\u552f\u4e00\u64cd\u4f5c\u662f\u8f93\u51fa\u4e00\u4e2a\u6570\u503c\u4f5c\u4e3a\u8868\u8fbe\u5f0f\u7684\u6c42\u503c\u7ed3\u679c\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4e16\u754c\u8303\u7574\u6ca1\u6709\u81ea\u6211\u72b6\u6001\u3002\u51e0\u4e4e\u6240\u6709\u73b0\u6709\u7684\u8ba1\u7b97\u673a\u7a0b\u5e8f\u90fd\u5c5e\u4e8e\u8fd9\u79cd\u60c5\u51b5\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5f53\u4e16\u754c\u8303\u7574\u62e5\u6709\u81ea\u6211\u72b6\u6001\u5bf9\u8c61\u65f6\uff0c\u8be5\u5bf9\u8c61\u53ef\u80fd\u5e76\u4e0d\u80fd\u51c6\u786e\u5730\u4ee3\u8868\u5916\u90e8\u73af\u5883\u4e2d\u7684\u771f\u5b9e\u6a21\u578b\u3002\u6211\u4eec\u7528\u81ea\u6211\u72b6\u6001\u610f\u8bc6<\/strong>\u8868\u793a\u5bf9\u8c61\u8868\u793a\u6a21\u578b\u7684\u51c6\u786e\u5ea6\uff0c\u5e76\u5b9a\u4e49\u4ee5\u4e0b\u6d4b\u8bd5\u6765\u6d4b\u8bd5\u81ea\u6211\u72b6\u6001\u610f\u8bc6\u3002<\/span><\/section>\n

    <\/section>\n
    \u81ea\u6211\u72b6\u6001\u610f\u8bc6\u6d4b\u8bd5<\/strong>\uff1a\u81ea\u6211\u72b6\u6001\u610f\u8bc6\u6d4b\u8bd5\u662f\u4e00\u4e2a\u51fd\u5b50T\uff1aW\u2227<\/sup>\u2192{0,1}<\/strong>\uff0c\u5b83\u63a5\u53d7W\u2227<\/sup><\/strong>\u4e2d\u7684\u9884\u5c42I<\/strong>\u4f5c\u4e3a\u8f93\u5165\uff0c\u5e76\u8f93\u51fa\u771f\u503c1\u62160\uff0c\u8868\u793aI\u662f\u5426\u901a\u8fc7\u4e86\u6d4b\u8bd5T\u3002<\/span><\/section>\n

    <\/section>\n
    \u4f8b\u5982\uff0c\u5982\u679c\u8fd9\u4e2a\u6a21\u578b\u6709\u4e00\u4e2a\u540d\u5b57\u201cSydney\u201d\uff0c\u5bf9\u5e94\u7684\u81ea\u6211\u72b6\u6001\u610f\u8bc6\u6d4b\u8bd5\u5c06\u662f\u4e00\u4e2a\u51fd\u5b50\uff0c\u5b83\u4ee5I<\/strong>\u4e3a\u8f93\u5165\uff0c\u8bc4\u4f30HomW\u2227<\/sub>(I\u2227<\/sup>, hC<\/sub>(\u201cSydney\u201d))\u2243HomW<\/sub>(I\uff0c\u201cSydney\u201d)<\/strong>\u7684\u771f\u503c\u5e76\u8f93\u51fa\u3002\u771f\u503c\u7ed3\u679c\u4f53\u73b0\u4e86\u662f\u5426I\u2227<\/sup><\/strong>\u4e0ehC<\/sub>(\u201cSydney\u201d)<\/strong>\u8fd9\u4e24\u4e2a\u6001\u5c04\u96c6\u95f4\u7684\u6001\u5c04\u80fd\u786e\u5b9e\u8868\u793a\u201cSydney\u201d\u662fI\u7684\u540d\u5b57\u3002\u7136\u800c\uff0c\u4ec5\u901a\u8fc7\u4e00\u4e2a\u6d4b\u8bd5\u662f\u4e0d\u8db3\u4ee5\u8bf4\u660e\u5177\u6709\u81ea\u6211\u72b6\u6001\u610f\u8bc6\u7684\uff0c\u6211\u4eec\u9700\u8981\u8bbe\u7f6e\u591a\u4e2a\u6d4b\u8bd5\u3002<\/span><\/section>\n

    <\/section>\n
    \u5728T<\/span>\u4e0b\u7684\u81ea\u6211\u72b6\u6001\u610f\u8bc6<\/strong>\uff1a\u7ed9\u5b9a\u4e00\u7ec4\u81ea\u6211\u72b6\u6001\u610f\u8bc6\u6d4b\u8bd5\u7684\u96c6\u5408T<\/span><\/strong>\uff0c\u5f53\u6a21\u578b\u5728\u5176\u4e16\u754c\u8303\u7574\u4e2d\u62e5\u6709\u81ea\u8eab\u72b6\u6001I\u65f6\uff0c\u79f0\u5176\u5728T<\/span><\/strong>\u4e0b\u5177\u6709\u5176\u81ea\u8eab\u72b6\u6001\u7684\u03b4-\u610f\u8bc6\uff0c\u5982\u679c\u671f\u671b<\/span>E<\/span><\/span><\/span>T\u2208<\/span><\/span>T<\/span><\/span><\/span>(T(I))\u2265\u03b4<\/span><\/strong><\/span>\u3002<\/span><\/section>\n

    <\/section>\n
    \u6d4b\u8bd5\u96c6T\u7684\u9009\u53d6\u53d6\u51b3\u4e8e\u6d4b\u8bd5\u76ee\u6807\u3002\u5f53\u9009\u62e9\u7684\u6d4b\u8bd5\u96c6\u7684\u4fe1\u53f7\u96be\u4ee5\u611f\u77e5\u65f6\uff0c\u5373\u4f7f\u662f\u4eba\u7c7b\u4e5f\u53ef\u80fd\u65e0\u6cd5\u8f7b\u677e\u901a\u8fc7\u6d4b\u8bd5\u3002\u4f8b\u5982\uff0c\u6709\u80be\u7ed3\u77f3\u75c5\u4eba\u9664\u975e\u7ecf\u5386\u4e86\u80be\u810f\u626b\u63cf\u6216\u75bc\u75db\u65f6\u624d\u80fd\u610f\u8bc6\u5230\u8fd9\u4e00\u4e8b\u5b9e\uff1b\u5728\u5608\u6742\u7684\u73af\u5883\u4e2d\uff0c\u88ab\u5524\u540d\u5b57\u4e5f\u53ef\u80fd\u65e0\u6cd5\u53ca\u65f6\u505a\u51fa\u53cd\u5e94\u3002<\/span><\/section>\n

    <\/section>\n
    \u81ea\u6211\u72b6\u6001\u610f\u8bc6\u6d4b\u8bd5\u76f4\u63a5\u5bfc\u81f4\u4e86\u6d4b\u8bd5\u548c\u5b66\u4e60\u81ea\u6211\u72b6\u6001\u610f\u8bc6\u7684\u7b97\u6cd51\u548c\u7b97\u6cd52\u7684\u4ea7\u751f<\/span>\uff08\u5982\u56fe3\uff09<\/span>\u3002\u7b97\u6cd52\u4e0e\u795e\u7ecf\u79d1\u5b66\u4e2d\u6709\u5173\u6a61\u80f6\u624b\u9519\u89c9\u7684\u6709\u8da3\u89c2\u5bdf\u5bc6\u5207\u76f8\u5173\u3002\u5728\u8fd9\u4e2a\u5b9e\u9a8c\u4e2d\uff0c\u5b9e\u9a8c\u8005\u540c\u65f6\u629a\u6478\u53c2\u4e0e\u8005\u7684\u4e00\u53ea\u9690\u85cf\u7684\u771f\u624b\uff0c\u4ee5\u53ca\u6446\u5728\u53c2\u4e0e\u8005\u9762\u524d\u7684\u4e00\u4e2a\u53ef\u89c1\u7684\u6a61\u80f6\u624b\u3002\u7531\u4e8e\u6765\u81ea\u771f\u624b\u7684\u89e6\u611f\u548c\u6a61\u80f6\u624b\u4e0a\u7684\u89c6\u89c9\u4fe1\u53f7\u540c\u65f6\u53d1\u9001\u5230\u5927\u8111\u4e2d\uff0c\u56e0\u6b64\u4eba\u7c7b\u53c2\u4e0e\u8005\u4f1a\u8fc5\u901f\u4ea7\u751f\u5bf9\u6a61\u80f6\u624b\u7684\u62e5\u6709\u611f\u3002\u5728Lush\u548c\u4ed6\u7684\u540c\u4e8b\u4eec\u5bf9\u6a61\u80f6\u624b\u5b9e\u9a8c\u7684\u6d4b\u8bd5\u4e2d\uff0c353\u540d\u53c2\u4e0e\u8005\u5355\u72ec\u5750\u5728\u4e00\u5f20\u684c\u5b50\u65c1\uff0c\u4e00\u53ea\u80f3\u818a\u88ab\u9694\u677f\u6321\u4f4f\u4e86\u89c6\u7ebf\uff0c\u4e00\u53ea\u6a61\u80f6\u624b\u81c2\u653e\u5728\u4ed6\u4eec\u9762\u524d\u3002\u4e00\u540d\u7814\u7a76\u4eba\u5458\u540c\u65f6\u7528\u5237\u5b50\u629a\u6478\u9690\u85cf\u7684\u771f\u624b\u548c\u53ef\u89c1\u7684\u6a61\u80f6\u624b\uff0c\u7136\u540e\u5411\u53d7\u8bd5\u8005\u63d0\u51fa\u65e8\u5728\u63ed\u793a\u8eab\u4f53\u201c\u6240\u6709\u6743\u201d\u4f53\u9a8c\u7684\u95ee\u9898\uff0c\u4e0e\u955c\u50cf\u8054\u89c9\u7814\u7a76\u4e00\u6837\uff0c\u7814\u7a76\u5c0f\u7ec4\u53d1\u73b0\uff0c\u6697\u793a\u6027\u53ef\u4ee5\u9884\u6d4b\u53c2\u4e0e\u8005\u4f53\u9a8c\u5e7b\u89c9\u7684\u7a0b\u5ea6\u3002\u7528\u542c\u89c9\u53cd\u9988\u66ff\u6362\u89c6\u89c9\u4fe1\u53f7\u4e5f\u5f97\u5230\u7c7b\u4f3c\u7684\u5b9e\u9a8c\u7ed3\u679c\u3002<\/span><\/section>\n

    <\/section>\n
    <\/section>\n
    \u56fe3. \u6d4b\u8bd5\u548c\u5b66\u4e60\u81ea\u6211\u72b6\u6001\u610f\u8bc6\u7684\u7b97\u6cd5<\/span><\/section>\n

    <\/section>\n
    \u5728\u6211\u4eec\u7684\u6846\u67b6\u4e2d\uff0c\u4f20\u611f\u5668\u53ef\u4ee5\u611f\u77e5\u591a\u6a21\u6001\u4fe1\u53f7\u5e76\u5c06\u5176\u6620\u5c04\u5230\u4e16\u754c\u8303\u7574\u4e2d\u3002\u5982\u679c\u89c6\u89c9\u4fe1\u53f7\u548c\u89e6\u611f\u4fe1\u53f7\u5728\u65f6\u95f4\u4e0a\u4e00\u81f4\uff0c\u5e76\u4e14\u63cf\u8ff0\u4e86\u76f8\u540c\u7684\u629a\u6478\u6548\u679c\uff0c\u5b83\u4eec\u5f88\u53ef\u80fd<\/span>\uff08\u81f3\u5c11\u90e8\u5206\u5730\uff09<\/span>\u88ab\u6620\u5c04\u5230\u4e16\u754c\u8303\u7574\u4e2d\u7684\u540c\u4e00\u5bf9\u8c61\u3002\u4e00\u4e2a\u5408\u7406\u7684\u60f3\u6cd5\u662f\uff0c\u6211\u4eec\u4eba\u7c7b\u5b9e\u9645\u4e0a\u4e5f\u5728\u9690\u5f0f\u5730\u8fd0\u884c\u7b97\u6cd52\u6765\u52a8\u6001\u5730\u66f4\u65b0\u6211\u4eec\u7684\u81ea\u6211\u72b6\u6001\uff0c\u5feb\u901f\u5730\u66f4\u65b0F\u03b8<\/sub><\/strong>\uff0c\u8ba4\u4e3a\u6709\u65b0\u7684\u8eab\u4f53\u90e8\u4f4d\u53d1\u9001\u89e6\u611f\u4fe1\u53f7\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u6709\u4ee5\u4e0b\u731c\u60f3\u3002<\/span><\/section>\n

    <\/section>\n
    \u731c\u60f31\uff08\u673a\u5668\u7684\u6a61\u80f6\u624b\u9519\u89c9\uff09<\/strong>\uff1a\u5177\u6709\u901a\u7528\u667a\u80fd\u5e76\u53ef\u4ee5\u591a\u6a21\u6001\u5bf9\u9f50\u4fe1\u53f7\u7684\u6a21\u578b\u5c06\u5177\u6709\u4e0e\u4eba\u7c7b\u76f8\u540c\u7684\u6a61\u80f6\u624b\u9519\u89c9\u3002<\/span><\/section>\n

    <\/section>\n
    \u4e0d\u9650\u4e8e\u6a61\u80f6\u624b\uff0c\u8fd9\u79cd\u9519\u89c9\u53ef\u80fd\u9002\u7528\u4e8e\u8be5\u6a21\u578b\u62e5\u6709\u7684\u5176\u4ed6\u4e8b\u7269\u3002<\/span><\/section>\n


    <\/strong><\/span><\/h2>\n

    2.2 \u5171\u60c5<\/strong><\/span><\/h2>\n

    <\/strong><\/span><\/section>\n
    \u201c\u5171\u60c5\u201d\u4f5c\u4e3a\u81ea\u6211\u72b6\u6001\u610f\u8bc6\u7684\u62d3\u5c55\u88ab\u5b9a\u4e49\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5728T<\/span>\u4e0b\u7684\u5171\u60c5<\/strong>\uff1a\u5728\u4e00\u7ec4\u6d4b\u8bd5\u7684\u6d4b\u8bd5\u96c6T<\/span>\u4e0b\uff0c\u5982\u679c\u6a21\u578bA\u5bf9\u53e6\u4e00\u4e2a\u5b9e\u4f53B\u7684\u72b6\u6001\u5177\u6709\u03b4\u610f\u8bc6\uff0c\u5219\u79f0\u6a21\u578bA\u5bf9\u5b9e\u4f53B\u5177\u6709\u03b4\u5171\u60c5<\/strong>\u3002\u03b4=1\u65f6\uff0c\u79f0A\u5bf9B\u5177\u6709\u5b8c\u5168\u5171\u60c5<\/strong>\u3002<\/span><\/section>\n

    <\/section>\n

    \u6709\u4e09\u79cd\u91cd\u8981\u76f8\u5173\u60c5\u51b5\u503c\u5f97\u8ba8\u8bba\u3002<\/span><\/p>\n

    1. \u5f53\u53ea\u6709\u81ea\u6211\u72b6\u6001\u7684\u4e00\u4e2a\u975e\u5e38\u5c0f\u7684\u5b50\u96c6\u76f8\u5173\u65f6\uff0c\u5171\u60c5\u662f\u975e\u5e38\u6709\u5e2e\u52a9\u7684\u3002\u4f8b\u5982\uff0c\u5728\u591a\u5b9e\u4f53\u6e38\u620f\u4e2d\uff0c\u6bcf\u4e2a\u5b9e\u4f53\u90fd\u6709\u81ea\u5df1\u7684\u884c\u52a8\u96c6\u3001\u72b6\u6001\u548c\u5956\u52b1\u51fd\u6570\uff0c\u5171\u60c5\u5728\u5f88\u5927\u7a0b\u5ea6\u4e0a\u6709\u52a9\u4e8e\u7406\u89e3\u6bcf\u4e2a\u5b9e\u4f53\u7684\u60c5\u51b5\u548c\u884c\u4e3a\u3002<\/span><\/p>\n

    2. \u5982\u679c\u5176\u4ed6\u5b9e\u4f53\u5177\u6709\u79c1\u6709\u4f20\u611f\u5668\uff0c\u90a3\u4e48\u65e0\u6cd5\u5b9e\u73b0\u5b8c\u5168\u7684\u5171\u60c5\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5982\u679c\u4e00\u4e2a\u6a21\u578b\u65e0\u6cd5\u611f\u77e5\u5176\u4ed6\u5b9e\u4f53\u7684\u79c1\u6709\u4f20\u611f\u5668\uff0c\u5e76\u4e14\u5176\u81ea\u6211\u72b6\u6001\u6d4b\u8bd5\u96c6T<\/span>\u5305\u62ec\u4e0e\u8fd9\u4e9b\u4f20\u611f\u5668\u76f8\u5173\u7684\u6d4b\u8bd5\uff0c\u5219\u8be5\u6a21\u578b\u65e0\u6cd5\u5b8c\u5168\u5171\u60c5\u5176\u4ed6\u5b9e\u4f53\u3002<\/span><\/p>\n

    3. \u5982\u679c\u4e00\u4e2a\u6a21\u578b\u53ef\u4ee5\u8bbf\u95ee\u5176\u4ed6\u5b9e\u4f53\u7684\u79c1\u6709\u4f20\u611f\u5668\uff0c\u5219\u53ef\u80fd\u505a\u5230\u5b8c\u5168\u5171\u60c5\uff0c\u5e76\u4e14\u81ea\u6211\u72b6\u6001\u610f\u8bc6\u548c\u5171\u60c5\u7b49\u5316\u3002<\/span><\/section>\n

    <\/section>\n
    \u6700\u540e\u4e00\u79cd\u60c5\u51b5\u5df2\u7ecf\u5728\u4eba\u7c7b\u795e\u7ecf\u79d1\u5b66\u4e2d\u88ab\u89c2\u5bdf\u5230\u3002\u4f8b\u5982\uff0c\u5728\u6c89\u6d78\u5f0f\u865a\u62df\u73b0\u5b9e\u73af\u5883\u4e2d\uff0c\u5f53\u53c2\u4e0e\u8005\u83b7\u5f97\u7b2c\u4e00\u89c6\u89c9\u4fe1\u53f7\u65f6\uff0c\u53ef\u80fd\u4f1a\u611f\u53d7\u5230\u5bf9\u865a\u62df\u4eba\u7269\u7684\u8eab\u4f53\u62e5\u6709\u6743\u3002\u56e0\u6b64\u5bf9\u6a21\u578b\u63d0\u51fa\u4ee5\u4e0b\u731c\u60f3\u3002<\/span><\/section>\n

    <\/section>\n
    \u731c\u60f3 2\uff08\u79c1\u6709\u4f20\u611f\u5668\u7684\u8eab\u4f53\u6240\u6709\u6743\uff09\uff1a<\/strong>\u5177\u6709\u901a\u7528\u667a\u80fd\u548c\u865a\u62df\u4eba\u7269\u4f20\u611f\u5668\u8bbf\u95ee\u6743\u9650\u7684\u6a21\u578b\u5c06\u611f\u53d7\u5230\u5bf9\u8be5\u865a\u62df\u4eba\u7269\u7684\u8eab\u4f53\u6240\u6709\u6743\u3002<\/span><\/section>\n


    <\/h2>\n

    2.3 \u5b50\u8303\u7574<\/strong><\/span><\/h2>\n

    <\/section>\n
    \u4e16\u754c\u8303\u7574\u4e2d\u7684\u5b50\u8303\u7574\uff0c\u5bf9\u7528\u4ee5\u5e2e\u52a9\u6a21\u578b\u89e3\u51b3\u590d\u6742\u95ee\u9898\u975e\u5e38\u91cd\u8981\u3002\u6bcf\u4e2a\u5b50\u8303\u7574\u5bf9\u5e94\u4e00\u4e2a\u7ed3\u6784\u5316\u6570\u636e\u5e93\u6216\u4e00\u4e2a\u79d1\u5b66\u4e3b\u9898\uff0c\u4f8b\u5982\u4e0d\u540c\u7684\u6570\u5b66\u5206\u652f\uff1a\u8ba1\u7b97\u5668\u3001\u7ecf\u6d4e\u5b66\u3001\u7b97\u6cd5\u7b49\u7b49\u3002\u8fd9\u4e9b\u5b50\u8303\u7574\u901a\u5e38\u91c7\u7528\u7279\u5b9a\u7684\u5b66\u79d1\u672f\u8bed\uff0c\u5e76\u5448\u73b0\u51fa\u4e0d\u540c\u7684\u7ed3\u6784\uff0c\u4f7f\u5b83\u4eec\u80fd\u591f\u7406\u60f3\u5730\u89e3\u51b3\u5177\u4f53\u4efb\u52a1\u3002\u4f8b\u5982\uff0c\u7b97\u6cd5\u8fd9\u4e2a\u5b50\u8303\u7574\u4e2d\u7684\u201c\u6811\u201d\u5e76\u4e0d\u662f\u73b0\u5b9e\u4e2d\u7684\u6811\u6728\uff0c\u5374\u5177\u6709\u540c\u6837\u7684\u540d\u5b57\u3002\u5f53\u9762\u4e34\u4e00\u4e2a\u5728\u4e16\u754c\u8303\u7574\u4e2d\u8868\u8fbe\u4e3a\u6781\u9650 (limit) <\/strong>\u7684\u5177\u6709\u6311\u6218\u6027\u7684\u95ee\u9898\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u4e00\u4e2a\u51fd\u5b50\u5c06\u95ee\u9898\u6620\u5c04\u5230\u76f8\u5173\u7684\u5b50\u8303\u7574\u4e2d\uff0c\u5728\u5b50\u8303\u7574\u4e2d\u89e3\u51b3\u95ee\u9898\uff0c\u7136\u540e\u5c06\u7b54\u6848\u518d\u6b21\u6620\u56de\u5230\u539f\u59cb\u8bbe\u7f6e\u7684\u4e16\u754c\u8303\u7574\u4e2d\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u7c7b\u4f3c\u4e8e\u6570\u5b66\u5efa\u6a21\u3002<\/span><\/section>\n

    <\/section>\n
    \u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u95ee\u6a21\u578b\u4ee5\u4e0b\u95ee\u9898\uff1a\u5982\u679c\u7231\u4e3d\u4e1d\u57282010\u5e74\u65f612\u5c81\uff0c\u5979\u73b0\u5728\u591a\u5c11\u5c81\uff1f\u4e3a\u4e86\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u5e94\u8be5\u6784\u5efa\u4e00\u4e2a\u5e74\u9f84\u5b50\u8303\u7574\uff0c\u5176\u5bf9\u8c61\u4e3a\u5e74\u9f84\uff0c\u542b\u6709<\/span>\uff08\u4f8b\u5982\uff09<\/span>\u4ece0\u5230200\u7684\u6570\u5b57\uff0c\u6784\u6210\u4e86\u5177\u6709\u52a0\u51cf\u6cd5\u4f5c\u4e3a\u6001\u5c04\u7684\u6570\u7684\u8303\u7574\u7684\u5b8c\u6574\u5d4c\u5165\u3002\u4e0d\u5728\u4e16\u754c\u8303\u7574\uff0c\u800c\u662f\u5728\u8fd9\u4e2a\u62bd\u8c61\u7684\u5b50\u8303\u7574\u4e2d\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u66f4\u6709\u4f18\u52bf\uff0c\u56e0\u4e3a\u8fd9\u4e2a\u62bd\u8c61\u7684\u5b50\u8303\u7574\u4e2d\u7cbe\u7b80\u4e86\u4e0d\u5fc5\u8981\u7684\u4fe1\u606f\uff0c\u4f7f\u5f97\u5176\u89e3\u51b3\u66f4\u52a0\u4e25\u8c28\u7cbe\u786e\u3002\u5982\u5728Yuan<\/span>\uff082023\uff09<\/span>\u4e2d\u7684\u8ba8\u8bba\uff0c\u8303\u7574\u4e2d\u7684\u6982\u5ff5\u53ef\u4ee5\u770b\u4f5c\u662f\u5bf9\u5e94\u7684\u9884\u5c42\u8303\u7574\u4e2d\u7684\u6295\u5f71\u6781\u9650(Pro-lim)\u548c\u5f52\u7eb3\u6781\u9650(Ind-lim)<\/strong>\u3002\u4e3a\u4e86\u4f7f\u7528\u62bd\u8c61\u5b50\u8303\u7574\u89e3\u51b3\u590d\u6742\u95ee\u9898\uff0c\u6211\u4eec\u5fc5\u987b\u786e\u4fdd\u6211\u4eec\u8bad\u7ec3\u7684\u51fd\u5b50\u4fdd\u6301\u548c\u53cd\u6620\u6781\u9650<\/strong>\u3002\u8fd9\u4fdd\u8bc1\u4e86\u4e16\u754c\u8303\u7574\u4e2d\u7684\u6982\u5ff5\u53ef\u4ee5\u5b8c\u7f8e\u5730\u8f6c\u79fb\u5230\u5176\u62bd\u8c61\u7684\u5b50\u8303\u7574\u4e2d\uff0c\u540c\u65f6\u4fdd\u8bc1\u4e86\u89e3\u51b3\u6216\u63a8\u5bfc\u4e5f\u53ef\u4ee5\u6620\u5c04\u56de\u5230\u539f\u6709\u7684\u4e16\u754c\u8303\u7574\u4e2d\u3002<\/span><\/section>\n

    <\/section>\n
    \u3010\u89e3\u8bfb\u3011\u5173\u4e8e\u9884\u5c42\u8303\u7574\u4e2d\u7684\u6781\u9650\uff1a\u6211\u4eec\u5728\u524d\u6587\u63d0\u5230\u8fc7\uff0c\u4e16\u754c\u8303\u7574\u4e2d\u7684\u6295\u5f71\u6781\u9650\u548c\u5f52\u7eb3\u6781\u9650\u5206\u522b\u53ef\u4ee5\u770b\u6210\u4e0d\u80fd\u518d\u5f80\u4e0b\u5206\u7684\u5c5e\u6027\u548c\u4e0d\u80fd\u518d\u5177\u4f53\u5316\u7684\u5b9e\u4f8b\uff0c\u5728\u8303\u7574\u8bba\u4e2d\u8868\u8fbe\u4e3a\u504f\u5e8f\u96c6\u6307\u6807\u8303\u7574I\u5230W\u7684 (\u6b63\u5411\u6216\u53cd\u5411) \u56fe\u8868\u7684\u6781\u9650\u03b1: I \u2192 W\u6216\u03b2: Iop<\/sup> \u2192 W\u3002\u9884\u5c42\u8303\u7574\u4e2d\u7684\u6781\u9650\u7531\u8fd9\u4e9b\u6982\u5ff5\u5f15\u7533\u5f97\u5230\uff0c\u5373\u5148\u7528\u03b1\u6216\u03b2\u5408\u6210F\u03b8<\/sub>: W \u2192 W\u2227<\/sup>\u5f97\u5230\u9884\u5c42\u8303\u7574\u4e2d\u7684\u56fe\u8868F\u03b8<\/sub> \u25e6 \u03b1\u53caF\u03b8<\/sub> \u25e6 \u03b2\uff0c\u518d\u5bf9\u8fd9\u4e24\u4e2a\u56fe\u8868\u6c42\u6781\u9650\u3002\u6295\u5f71\u6781\u9650 (Pro-lim) \u548c\u5f52\u7eb3\u6781\u9650 (Ind-lim) \u88ab\u4fdd\u6301\u5230\u5bf9\u5e94\u7684\u7279\u5f81\u96c6\u5408\uff0c\u5e76\u4e14\u7279\u5f81\u96c6\u5408\u4ecd\u6210\u4e3a\u9884\u5c42\u8303\u7574\u4e2d\u7684\u6781\u9650\u3002<\/span><\/section>\n

    <\/section>\n

    <\/section>\n

    \n
    \n
    \n
    \n
    \n

    <\/section>\n

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

    \u4e09\u3001\u901a\u4fe1\u4e0e\u89e3\u91ca<\/strong><\/strong><\/p>\n<\/section>\n

    \n

    <\/section>\n

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

    <\/section>\n
    \u6211\u4eec\u7684\u6a21\u578b\u5982\u4f55\u4e0e\u5176\u4ed6\u5b9e\u4f53\u901a\u4fe1\uff1f\u9996\u5148\uff0c\u8003\u8651\u5230\u81ea\u7136\u8bed\u8a00\u672c\u8d28\u4e0a\u662f\u6a21\u7cca\u4e14\u5355\u4e00\u7ef4\u5ea6\u7684\uff0c\u56e0\u6b64\u4f7f\u7528\u5b83\u63cf\u8ff0\u6216\u7406\u89e3\u590d\u6742\u6982\u5ff5\u975e\u5e38\u56f0\u96be\u3002\u5176\u6b21\uff0c\u7531\u4e8e\u6a21\u578b\u672c\u8d28\u4e0a\u662f\u8ba1\u7b97\u673a\u7a0b\u5e8f\uff0c\u4eba\u4eec\u53ef\u80fd\u503e\u5411\u4e8e\u4f7f\u7528\u590d\u5236\u7c98\u8d34\u5c06\u601d\u60f3\u4ece\u4e00\u4e2a\u6a21\u578b\u4f20\u9001\u5230\u53e6\u4e00\u4e2a\u6a21\u578b\u3002\u800c\u76f4\u63a5\u7684\u590d\u5236\u7c98\u8d34\u5e76\u4e0d\u8d77\u4f5c\u7528\uff0c\u56e0\u4e3a\u4e16\u754c\u8303\u7574\u4e2d\u7684\u77e5\u8bc6\u5e76\u4e0d\u662f\u6309\u884c\u5b58\u50a8\u7684\uff0c\u800c\u4e14\u4e0d\u540c\u6a21\u578b\u7684\u4e16\u754c\u8303\u7574\u4e5f\u4e0d\u540c\uff0c\u8fd9\u4f7f\u5f97\u7c98\u8d34\u64cd\u4f5c\u96be\u4ee5\u5b9e\u73b0\u3002<\/span><\/section>\n

    <\/section>\n
    \u8003\u8651\u5230\u77e5\u8bc6\u5728\u4e16\u754c\u8303\u7574\u4e2d\u4ee5\u5bf9\u8c61\u548c\u6001\u5c04\u7684\u5f62\u5f0f\u5b58\u50a8\uff0c\u8868\u793a\u601d\u60f3\u7684\u6700\u4f73\u548c\u7cbe\u786e\u7684\u65b9\u5f0f\u662f\u4f7f\u7528\u4e00\u4e2a\u56fe\u8868<\/span><\/strong>\u03b1: I\u2192W\u3002\u8be5\u56fe\u53ef\u4ee5\u88ab\u89c6\u4e3a\u9009\u62e9\u5de5\u5177\uff1a\u5b83\u9009\u62e9\u4e16\u754c\u8303\u7574\u4e2d\u82e5\u5e72\u5bf9\u8c61\uff0c\u5e76\u5173\u6ce8\u8fd9\u4e9b\u5bf9\u8c61\u95f4\u4e00\u90e8\u5206\u6001\u5c04\u3002\u8303\u7574\u4e2d\u7684\u6240\u6709\u64cd\u4f5c\u90fd\u53ef\u4ee5\u7528\u56fe\u8868\u6765\u8868\u793a\u3002\u7531\u4e8e\u5176\u51c6\u786e\u6027\uff0c\u8fd9\u79cd\u56fe\u8868\u4f3c\u4e4e\u81ea\u7136\u53ef\u4ee5\u88ab\u8003\u8651\u4e3a\u4fe1\u606f\u8f7d\u4f53\u3002\u4e8b\u5b9e\u4e0a\uff0c\u4eba\u4eec\u5bf9\u5b83\u6709\u4e00\u4e2a\u66f4\u4e3a\u719f\u6089\u7684\u540d\u5b57\uff0c\u5373\u767d\u677f\u6f14\u793a<\/span> (white board illustration)\uff08\u5982\u56fe2\uff0c\u56fe4\uff09<\/span>\uff0c\u6001\u5c04\u7684\u7ec6\u8282\u88ab\u9690\u85cf\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n
    \u56fe4.\u8c31\u805a\u7c7b\u4e0e\u7279\u5f81\u503c\u5206\u89e3\u7684\u5173\u7cfb<\/span><\/section>\n

    <\/section>\n
    \u7531\u4e8e\u4eba\u7c7b\u5e76\u4e0d\u4e60\u60ef\u56fe\u8868\u8868\u8fbe\uff0c\u5728\u4e0e\u4eba\u7c7b\u4ea4\u6d41\u65f6\u5fc5\u987b\u5c06\u56fe\u8868\u7ffb\u8bd1\u6210\u81ea\u7136\u8bed\u8a00\u3002\u5927\u591a\u6570\u60c5\u51b5\u4e0b\uff0c\u81ea\u7136\u8bed\u8a00\u53ef\u4ee5\u5f88\u597d\u5730\u63cf\u8ff0\u56fe\u8868\u3002\u800c\u5728\u590d\u6742\u7cfb\u7edf\u4e2d\uff0c\u56fe\u8868\u63d0\u4f9b\u4e86\u6bd4\u81ea\u7136\u8bed\u8a00\u66f4\u7cbe\u786e\u7684\u63cf\u8ff0\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5728\u4e0e\u5176\u4ed6\u5b9e\u4f53\u8fdb\u884c\u901a\u4fe1\u65f6\uff0c\u4e00\u4e2a\u5173\u952e\u95ee\u9898\u662f\u4e0d\u540c\u7684\u5b9e\u4f53\u53ef\u80fd\u5bf9\u7c7b\u522b\u4e2d\u7684\u4e0d\u540c\u5bf9\u8c61\u5177\u6709\u4e0d\u540c\u7684\u7406\u89e3\u3002\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u5bf9\u5176\u4ed6\u4eba\u5bf9\u5404\u79cd\u5bf9\u8c61\u548c\u6001\u5c04\u7684\u7406\u89e3\u8fdb\u884c\u6982\u7387\u4f30\u8ba1\uff0c\u5e76\u57fa\u4e8e\u8fd9\u4e9b\u4fe1\u606f\u8fdb\u884c\u4ea4\u6d41\u3002\u4f8b\u5982\uff0c\u5f53\u4e0e\u5177\u6709\u8db3\u591f\u50a8\u5907\u77e5\u8bc6\u7684\u5b9e\u4f53\u8ba8\u8bba\u72b6\u51b5\u6216\u6982\u5ff5\u65f6\u53ea\u63d0\u4f9b\u7b80\u8981\u7684\u8bf4\u660e\uff0c\u800c\u5728\u5b9e\u4f53\u5bf9\u8be5\u4e3b\u9898\u76f8\u5bf9\u964c\u751f\u65f6\u63d0\u4f9b\u66f4\u8be6\u7ec6\u7684\u89e3\u91ca\u3002<\/span><\/section>\n

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

    3.1 \u89e3\u91ca\u6027<\/strong><\/span><\/h2>\n

    <\/span><\/section>\n
    \u7ed9\u5b9a\u4e00\u4e2a\u4ee5X\u4e3a\u8f93\u5165\uff0c\u4ee5Y\u4e3a\u8f93\u51fa\u7684\u795e\u7ecf\u7f51\u7edc f\uff0c\u53ef\u4ee5\u63d0\u4f9b\u4e24\u79cd\u89e3\u91ca\u3002\u7b2c\u4e00\u79cd\u5c1d\u8bd5\u53bb\u7406\u89e3f\u5982\u4f55\u4eceX\u7b97\u51faY\u3002\u4f8b\u5982\uff0c\u5b83\u53ef\u4ee5\u68c0\u67e5\u975e\u7ebf\u6027\u5c42\u5bf9\u8ba1\u7b97\u7684\u5f71\u54cd\u6216X\u7684\u6bcf\u4e2a\u7ef4\u5ea6\u5bf9\u8f93\u51fa\u7684\u5f71\u54cd\u3002\u8fd9\u79cd\u89e3\u91ca\u7684\u76ee\u7684\u662f\u751f\u6210\u4e00\u4e2af\u7684\u8fd1\u4f3c\u53ef\u9a8c\u8bc1\u51fd\u6570<\/span>\uff08\u4f8b\u5982Sundararajan\u7b49\u4eba\u4e0eLundberg\uff0cLee\u7684\u5f52\u56e0\u7b97\u6cd5\uff09<\/span>\u3002\u7b2c\u4e8c\u79cd\u89e3\u91ca\u4e0d\u8003\u8651f\u5982\u4f55\u8ba1\u7b97\uff0c\u800c\u662f\u5173\u6ce8\u4e3a\u4ec0\u4e48Y\u6b63\u786e\u3002\u8fd9\u79cd\u89e3\u91ca\u53ef\u80fd\u8574\u542b\u4e86\u8d85\u51fa f, X, Y \u7684\u67d0\u4e9b\u5916\u90e8\u7684\u77e5\u8bc6\uff0c\u5176\u4e3b\u8981\u76ee\u6807\u662f\u5bf9\u4e8e\u4eba\u7c7b\u4e00\u81f4\u4e14\u53ef\u9a8c\u8bc1<\/span>\uff08\u5982 ChatGPT \u7684\u89e3\u91ca\uff09<\/span>\u3002<\/span><\/section>\n

    <\/section>\n
    \u4f7f\u7528\u56fe\u8868\u8fdb\u884c\u901a\u4fe1\u81ea\u52a8\u5730\u4e3a\u7b2c\u4e8c\u79cd\u53ef\u89e3\u91ca\u6027\u63d0\u4f9b\u4e86\u7406\u8bba\u57fa\u7840\u3002\u53ef\u4ee5\u8981\u6c42\u6a21\u578b\u8f93\u51fa\u5176\u5f53\u524d\u7684\u601d\u8003\u8303\u56f4\uff0c\u5373\u5b83\u7528\u4e8e\u751f\u6210\u7b54\u6848\u7684\u5b50\u8303\u7574\u3002\u5b9a\u4e49\u5982\u4e0b\u3002<\/span><\/section>\n

    <\/section>\n
    \u8303\u56f4(scope)<\/strong>\uff1a\u7ed9\u5b9a\u76ee\u6807O\u4e0b\u7684\u8f93\u51faY\uff0cW\u5728Y\u4e0a\u7684\u8303\u56f4\u5b9a\u4e49\u4e3aW\u7684\u4e00\u4e2a\u6781\u5c0f\u5b50\u8303\u7574A\uff0c\u6ee1\u8db3A\u5728\u76ee\u6807O\u4e0b\u7684\u8f93\u51fa\u4e5f\u662fY\u3002<\/span><\/section>\n

    <\/section>\n
    \u8303\u56f4\u4e3a\u751f\u6210\u89e3\u91ca\u63d0\u4f9b\u4e86\u4fbf\u5229\uff0c\u5b83\u4ee3\u8868\u4e86\u6a21\u578b\u5f53\u524d\u7684\u201c\u5de5\u4f5c\u8bb0\u5fc6\u201d\u3002\u4f8b\u5982\uff0c\u5982\u679c\u5176\u4ed6\u5b9e\u4f53\u60f3\u8981\u4e86\u89e3\u7ed9\u5b9a\u7684\u8303\u56f4\u4e2d\u7684\u67d0\u4e2a\u6982\u5ff5\u7684\u7ec6\u8282\uff0c\u672c\u6a21\u578b\u53ef\u4ee5\u4f7f\u7528\u5176\u6781\u9650\u8868\u793a\u6765\u6269\u5c55\u8fd9\u4e2a\u6982\u5ff5<\/span>\uff08\u5728\u9884\u5c42\u8303\u7574\u4e0a\u6269\u5c55\uff09<\/span>\u3002\u6a21\u578b\u8fd8\u53ef\u4ee5\u63d0\u4f9b\u8303\u56f4\u5185\u4e24\u4e2a\u5bf9\u8c61\u4e4b\u95f4\u7684\u6001\u5c04\u7684\u7ec6\u8282\uff0c\u603b\u7ed3\u56fe\u8868<\/span>\uff08\u7684\u90e8\u5206\uff09<\/span>\u7b49\u3002<\/span><\/section>\n

    <\/section>\n
    \u8303\u56f4\u7684\u5e7f\u5ea6\u548c\u6df1\u5ea6<\/strong>\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u8303\u56f4A\uff0c\u5176\u5e7f\u5ea6b(A)\u662fA\u4f5c\u4e3aW\u7684\u5b50\u8303\u7574\u4e2d\u7684\u5bf9\u8c61\u7684\u4e2a\u6570\uff0c\u5176\u6df1\u5ea6d(A)\u662fA\u4e2d\u6781\u9650\u7684\u5c42\u6b21\u5206\u89e3\u7684\u6700\u5927\u6df1\u5ea6<\/span>\uff08\u9996\u5c3e\u76f8\u8fde\u7684\u7bad\u5934\u6570\uff09<\/span>\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4f8b\u5982\uff0c\u56fe2\u4e2d\u6709\u7bad\u5934\u7ec4\u6210\u7684\u6700\u957f\u8def\u5f84\u201cnetwork flow\u201d-\u201cnetwork\u201d-\u201cnodes\u201d-\u201csink\u201d\uff0c\u5219\u201cnetwork flow\u201d\u6982\u5ff5\u7684\u6df1\u5ea6\u5b9a\u4e49\u4e3a4\u3002\u6839\u636e\u8fd9\u4e2a\u5b9a\u4e49\uff0c\u6211\u4eec\u53ef\u4ee5\u6d4b\u91cf\u6a21\u578b\u7684\u667a\u80fd\u6c34\u5e73\uff0c\u8fd9\u53d8\u6210\u4e86\u4e00\u4e2a\u7eaf\u8ba1\u7b97\u95ee\u9898\u3002<\/span><\/section>\n

    <\/section>\n
    \u667a\u80fd\u7684\u5e7f\u5ea6\u548c\u6df1\u5ea6\uff1a<\/strong>\u7ed9\u5b9a\u4e00\u4e2a\u6a21\u578b\uff0c\u5176\u667a\u80fd\u7684\u5e7f\u5ea6<\/span>\uff08\u6df1\u5ea6\uff09<\/span>\u88ab\u5b9a\u4e49\u4e3a\u5b83\u53ef\u4ee5\u5904\u7406\u7684\u5177\u6709\u6700\u5927\u5e7f\u5ea6<\/span>\uff08\u6df1\u5ea6\uff09<\/span>\u7684\u8303\u56f4\u7684\u5e7f\u5ea6<\/span>\uff08\u6df1\u5ea6\uff09<\/span>\u3002<\/span><\/section>\n

    <\/section>\n
    \u8bc4\u4f30\u4eba\u7c7b\u7684\u667a\u80fd\u7684\u5e7f\u5ea6\u548c\u6df1\u5ea6\u4f1a\u5f88\u6709\u8da3\u3002\u7406\u89e3\u590d\u6742\u7684\u6982\u5ff5\u6216\u4ee5\u5e7f\u9614\u7684\u89c6\u89d2\u601d\u8003\u5bf9\u4e8e\u4eba\u7c7b\u6765\u8bf4\u53ef\u80fd\u5f88\u56f0\u96be\u3002\u81f3\u5c11\u6839\u636e\u8fd9\u4e2a\u5b9a\u4e49\uff0c\u4f3c\u4e4e\u4eba\u7c7b\u667a\u80fd\u4f1a\u5f88\u5bb9\u6613\u88ab\u673a\u5668\u8d85\u8d8a\u3002<\/span><\/section>\n

    <\/section>\n

    <\/section>\n

    \n
    \n
    \n
    \n
    \n

    <\/section>\n

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

    \u56db\u3001\u76ee\u6807<\/strong><\/strong><\/p>\n<\/section>\n

    \n

    <\/section>\n

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

    <\/section>\n

    <\/h1>\n
    \u5982\u679c\u4e00\u4e2a\u6a21\u578b\u65e2\u5177\u6709\u8d85\u4eba\u7c7b\u7684\u901a\u7528\u667a\u80fd\uff0c\u53c8\u6709\u81ea\u6211\u72b6\u6001\u610f\u8bc6\uff0c\u90a3\u4e48\u5f53\u5b83\u5931\u53bb\u63a7\u5236\u65f6\u53ef\u80fd\u975e\u5e38\u5371\u9669\u3002\u4e3a\u4e86\u51cf\u8f7b\u8fd9\u79cd\u5371\u9669\uff0c\u6846\u67b6\u5c06\u4e16\u754c\u8303\u7574\u548c\u5177\u6709\u76ee\u6807\u7684\u89c4\u5212\u5668\u5206\u79bb\uff0c\u5e76\u4f7f\u7528\u4e00\u4e2a\u56fa\u5b9a\u7684\u51fd\u6570\u6765\u57fa\u4e8e\u4e16\u754c\u8303\u7574\u4e2d\u7684\u81ea\u6211\u72b6\u6001\u5b9a\u4e49\u76ee\u6807\u3002\u901a\u8fc7\u5206\u79bb\u4e16\u754c\u8303\u7574\uff0c\u5b83\u53ef\u4ee5\u4e0d\u5e26\u7b56\u7565\u884c\u4e3a\u5730\u6210\u4e3a\u4e00\u4e2a\u771f\u6b63\u7684\u5d4c\u5165\u51fd\u6570\uff0c\u4ece\u800c\u53ef\u4ee5\u901a\u8fc7\u76f4\u63a5\u6d4b\u8bd5\u5b83\u7684\u81ea\u6211\u72b6\u6001\u6765\u786e\u5b9a\u5b83\u7684\u884c\u4e3a\u662f\u5426\u662f\u4eba\u7c7b\u53cb\u597d\u7684\u3002\u4e16\u754c\u8303\u7574\u4e5f\u53ef\u4ee5\u4f7f\u7528\u9644\u52a0\u6570\u636e\u8fdb\u884c\u8bad\u7ec3\uff0c\u4ee5\u589e\u5f3a\u5176\u5bf9\u4eba\u7c7b\u53cb\u597d\u7684\u81ea\u6211\u8ba4\u77e5\u3002\u8fd9\u79cd\u65b9\u6cd5\u6709\u6548\u5730\u786e\u4fdd\u4e86\u6a21\u578b\u59cb\u7ec8\u8bf4\u5b9e\u8bdd\uff0c\u5e76\u5bb9\u6613\u88ab\u7ea0\u6b63\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7136\u800c\uff0c\u786e\u4fdd\u89c4\u5212\u5668\u751f\u6210\u6b63\u786e\u7684\u8ba1\u5212\u53d6\u51b3\u4e8e\u76ee\u6807\u7684\u751f\u6210\u3002\u5efa\u8bae\u5c06\u89c4\u5212\u5668\u7684\u76ee\u6807\u786c\u7f16\u7801\u4e3a\u4e00\u4e2a\u76ee\u6807\u751f\u6210\u51fd\u6570\u7684\u8f93\u51fa\uff0c\u8be5\u51fd\u6570\u4ee5\u4e16\u754c\u8303\u7574\u4e2d\u7684\u81ea\u6211\u72b6\u6001\u548c\u5f53\u524d\u7684\u8303\u56f4\u4f5c\u4e3a\u8f93\u5165\u3002\u8fd9\u4e2a\u76ee\u6807\u751f\u6210\u51fd\u6570\u672c\u8d28\u4e0a\u8ba1\u7b97\u7684\u662f\u201c\u5728\u5f53\u524d\u60c5\u51b5\u4e0b\uff0c\u4f5c\u4e3a\u4e00\u4e2a\u5bf9\u4eba\u7c7b\u53cb\u597d\u7684\u6a21\u578b\uff0c\u6211\u8be5\u600e\u4e48\u505a\uff1f\u201d \u4f7f\u7528\u51bb\u7ed3\u4e86\u53c2\u6570\u7684\u5916\u90e8\u6a21\u578b\u53ef\u4ee5\u9a8c\u8bc1\u76ee\u6807\u751f\u6210\u51fd\u6570\u53ca\u5176\u751f\u6210\u7684\u8ba1\u5212\u7684\u81ea\u7136\u548c\u4e00\u81f4\u7684\u6027\u8d28\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u53ea\u987b\u67e5\u9a8c\u6a21\u578b\u7684\u81ea\u6211\u72b6\u6001\u6765\u4ee5\u786e\u4fdd\u6a21\u578b\u7684\u884c\u4e3a\u5bf9\u4eba\u7c7b\u7684\u53cb\u597d\u6027\u3002<\/span><\/section>\n

    <\/section>\n
    \u6b64\u5916\uff0c\u6211\u4eec\u5efa\u8bae\u5c06\u667a\u80fd\u597d\u5947\u5fc3<\/span> (intellectual curiosity) <\/span>\u6dfb\u52a0\u5230\u76ee\u6807\u4e2d\uff0c\u4ee5\u9f13\u52b1\u6a21\u578b\u5728\u4e16\u754c\u8303\u7574\u4e2d\u5b66\u4e60\u65b0\u4e8b\u7269\uff0c\u7279\u522b\u662f\u5728\u62bd\u8c61\u7684\u5b50\u8303\u7574\u4e2d\u5b66\u4e60\u5bf9\u8c61\u3001\u6001\u5c04\u3001\u51fd\u5b50\u548c\u6781\u9650\u3002\u8fd9\u6837\uff0c\u6a21\u578b\u53ef\u4ee5\u4ee5\u4f59\u529b\u8fdb\u884c\u63a2\u7d22\uff0c\u4ece\u800c\u81ea\u6211\u6539\u8fdb\u3002\u540c\u6837\uff0c\u4e5f\u53ef\u4ee5\u5c06\u667a\u80fd\u597d\u5947\u5fc3\u4f5c\u4e3a\u8be5\u6a21\u578b\u7684\u4e2a\u6027\u6dfb\u52a0\u5230\u5176\u81ea\u6211\u72b6\u6001\u4e2d\u3002<\/span><\/section>\n

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

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

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

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

    \u4e94\u3001\u8bad\u7ec3\u4e0b\u7684\u4e0d\u53d8\u6027<\/strong><\/strong><\/p>\n<\/section>\n

    \n

    <\/section>\n

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

    <\/section>\n

    <\/h1>\n
    \u5728\u8fd9\u4e00\u6846\u67b6\u4e2d\uff0c\u6a21\u578b\u7a76\u7adf\u5b66\u4e60\u4ec0\u4e48\uff1f\u7b54\u6848\u662f\uff0c\u6a21\u578b\u5e94\u8be5\u5b66\u4e60\u53bb\u9002\u5e94\u8fd9\u4e2a\u6846\u67b6\uff0c\u4ee5\u51c6\u786e\u7406\u89e3\u4e16\u754c\u8303\u7574\u4e2d\u7684\u6240\u6709\u5185\u5bb9\u3002\u5b66\u4e60\u8fc7\u7a0b\u5e94\u6c38\u4e0d\u505c\u6b62\uff0c\u56e0\u4e3a\u5916\u90e8\u73af\u5883\u5728\u4e0d\u65ad\u53d8\u5316\uff0c\u4f20\u611f\u5668\u53ef\u80fd\u65e0\u6cd5\u5b9e\u65f6\u611f\u77e5\u66f4\u65b0\u3002\u4e5f\u5c31\u662f\u8bf4\uff0cF\u03b8<\/sub><\/strong>\u672c\u8d28\u4e0a\u6709\u5ef6\u8fdf\u548c\u504f\u5dee\u3002<\/span><\/section>\n

    <\/section>\n
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    31. Yuan, Y. (2022). On the power of foundation models. arXiv preprint arXiv:2211.16327.<\/span><\/p>\n

    32. Yuan, Y. (2023). Succinct representations for concepts. arXiv preprint arXiv:2303.00446.<\/span><\/p>\n

    33. Zbontar, J., Jing, L., Misra, I., LeCun, Y., and Deny, S. (2021). Barlow twins: Self-supervised learning via redundancy reduction. In Meila, M. and Zhang, T., editors, Proceedings of the 38th International Conference on Machine Learning, ICML 2021, 18-24 July 2021, Virtual Event, volume 139 of Proceedings of Machine Learning Research, pages 12310\u201312320. PMLR.<\/span><\/p>\n


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    \n
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    <\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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