{"id":35757,"date":"2022-07-10T20:53:21","date_gmt":"2022-07-10T12:53:21","guid":{"rendered":"https:\/\/swarma.org\/?p=35757"},"modified":"2022-07-10T20:53:21","modified_gmt":"2022-07-10T12:53:21","slug":"%e5%a4%9a%e5%b1%82%e7%bd%91%e7%bb%9c%e9%87%8d%e6%9e%84%ef%bc%9a%e7%bb%93%e6%9e%84%e5%8c%ba%e5%88%86%e5%ba%a6%e5%a6%82%e4%bd%95%e5%86%b3%e5%ae%9a%e5%8f%af%e9%87%8d%e6%9e%84%e6%80%a7%ef%bc%9f","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=35757","title":{"rendered":"\u591a\u5c42\u7f51\u7edc\u91cd\u6784\uff1a\u7ed3\u6784\u533a\u5206\u5ea6\u5982\u4f55\u51b3\u5b9a\u53ef\u91cd\u6784\u6027\uff1f"},"content":{"rendered":"
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\u4f46\u662f\uff0c\u591a\u5c42\u7f51\u7edc\u7684\u7ed3\u6784 M \u662f P(<\/span>\u03b8)<\/span> \u7684\u9690\u53d8\u91cf\uff0c\u7406\u8bba\u4e0a\u4e0d\u80fd\u6c42\u5f97\u5176\u663e\u5f0f\u89e3\u3002\u4e8e\u662f\uff0c\u672c\u6587\u901a\u8fc7\u671f\u671b\u6700\u5927\u5316\u7b97\u6cd5\u4ee5\u83b7\u5f97\u6570\u503c\u89e3\uff0c\u8fd9\u4e00\u8fc7\u7a0b\u4e5f\u5373\u4e3a\u7f51\u7edc\u53c2\u6570\u7a7a\u95f4\u4e0e\u7f51\u7edc\u7ed3\u6784\u7a7a\u95f4\u7684\u5750\u6807\u4e0a\u5347\u6cd5\uff0c\u5982\u56fe2b\u6240\u793a\u3002\u4ee5\u6bcf\u5c42\u90fd\u4e3a\u914d\u7f6e\u6a21\u578b\u7684\u4e24\u5c42\u7f51\u7edc\u4e3a\u4f8b\uff0c\u7f51\u7edc\u6a21\u578b\u53c2\u6570 \u03b8<\/span> \u5373\u4e3a\u7f51\u7edc\u7684\u5ea6\u5e8f\u5217<\/sub>\u3002\u5982\u56fe2c\u6240\u793a\uff0c\u7ed9\u5b9a\u4efb\u610f\u521d\u59cb\u53c2\u6570<\/sub><\/span>\u540e\uff0c\u53ef\u4ee5\u8ba1\u7b97\u83b7\u5f97<\/sub>\uff0c\u5176\u4e2d\u6bcf\u4e00\u6761\u8fb9\u7684\u7070\u5ea6\u4ee3\u8868\u4e86\u8be5\u65b9\u6cd5\u6240\u63a8\u65ad\u7684\u8fde\u63a5\u5b58\u5728\u6982\u7387\u3002\u7136\u540e\u6839\u636e\u8ba1\u7b97\u83b7\u5f97\u7684<\/sub>\uff0c\u5bf9\u53c2\u6570\u8fdb\u884c\u66f4\u65b0\u4ee5\u83b7\u5f97<\/sub>\uff0c\u56e0\u4e3a\u6b64\u65f6\u5047\u8bbe\u4e86\u591a\u5c42\u7f51\u7edc\u7ed3\u6784 M \u662f\u5e38\u6570\uff0c\u5df2\u4e0d\u518d\u662f\u9690\u53d8\u91cf\u3002\u4ee5\u6b64\u65b9\u5f0f\u8fdb\u884c\u8fed\u4ee3\u66f4\u65b0\uff0c\u76f4\u81f3\u6536\u655b\uff0c\u800c\u671f\u671b\u6700\u5927\u5316\u7b97\u6cd5\u5219\u4fdd\u8bc1\u4e86\u8be5\u8fed\u4ee3\u8fc7\u7a0b\u7684\u6536\u655b\u6027\u3002\u6b64\u5916\uff0c\u53ef\u4ee5\u8bc1\u660e\u8be5\u65b9\u6cd5\u5bf9\u7f51\u7edc\u6a21\u578b\u53c2\u6570\u7684\u4f30\u8ba1\u4e3a\u6e10\u8fdb\u6709\u6548\u4f30\u8ba1\uff0c\u5373\u5f53\u7f51\u7edc\u89c4\u6a21\u8d8b\u5411\u4e8e\u65e0\u7a77\u5927\u65f6\uff0c\u5bf9\u53c2\u6570\u7684\u4f30\u8ba1\u65b9\u5dee\u8d8b\u5411\u4e8e\u514b\u62c9\u7f8e\u7f57\u4e0b\u754c<\/span> (CRLB, Cramer-\u00adRao Lower Bound)<\/span>\u3002<\/span><\/sub><\/section>\n
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\u56fe2. \u57fa\u4e8e\u4e0d\u5b8c\u5168\u4fe1\u606f\u7684\u591a\u5c42\u7f51\u7edc\u91cd\u6784\u65b9\u6cd5\u3002a \u591a\u5c42\u7f51\u7edc M \u4e0e\u5176\u5355\u5c42\u805a\u5408\u7f51\u7edc A0<\/sup><\/span> \u548c\u5c40\u90e8\u89c2\u6d4b\u96c6<\/span> \u0393 \u793a<\/span>\u4f8b\u3002b \u671f\u671b\u6700\u5927\u5316\u7b97\u6cd5\u5728\u53c2\u6570\u7a7a\u95f4\u548c\u7ed3\u6784\u7a7a\u95f4\u6267\u884c\u5750\u6807\u4e0a\u5347\u6cd5\u7684\u8fed\u4ee3\u8fc7\u7a0b\u3002c\u4ee5\u914d\u7f6e\u6a21\u578b\u4e3a\u4f8b\u7684\u4e00\u5f20\u4e24\u5c42\u7f51\u7edc\u901a\u8fc7\u671f\u671b\u6700\u5927\u5316\u7b97\u6cd5\u7684\u8fed\u4ee3\u8fc7\u7a0b\u793a\u4f8b\u3002<\/span><\/p>\n


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3. \u591a\u5c42\u7f51\u7edc\u7684\u53ef\u91cd\u6784\u6027<\/span><\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n
\u4e3a\u4e86\u91cf\u5316\u591a\u5c42\u7f51\u7edc M \u7684\u4e0d\u786e\u5b9a\u6027\uff0c\u672c\u6587\u5c06\u4ee5\u4e24\u5c42\u7f51\u7edc\u4e3a\u4f8b\uff0c\u8ba1\u7b97\u5728\u5df2\u77e5\u5355\u5c42\u805a\u5408\u7f51\u7edc A0<\/sup><\/span> \u7684\u60c5\u51b5\u4e0b\uff0c\u591a\u5c42\u7f51\u7edc\u7684\u4fe1\u606f\u71b5 H(M\uff5cA0<\/sup><\/span>) \u3002\u7ecf\u8fc7\u5e73\u5747\u573a\u8fd1\u4f3c\uff0c\u53d1\u73b0\u4e86\u8be5\u4fe1\u606f\u71b5\u4e0e\u5c40\u90e8\u89c2\u6d4b\u6bd4\u4f8b c \uff0c\u4e24\u5c42\u7f51\u7edc\u5e73\u5747\u5ea6\u4e4b\u6bd4 r \uff0c\u4e24\u5c42\u8fb9\u91cd\u5408\u5ea6 v \u9ad8\u5ea6\u76f8\u5173\u3002\u56fe3a\u5c55\u793a\u4e86\u4fe1\u606f\u71b5 H \u4e0e c, r, v \u4e09\u8005\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u4e8e\u662f\uff0cH \u7684\u5927\u5c0f\u63cf\u8ff0\u4e86\u591a\u5c42\u7f51\u7edc\u5173\u4e8e\u5fae\u89c2\u7ed3\u6784\u7684\u533a\u5206\u5ea6\uff0c\u56e0\u4e3a\u8f83\u9ad8\u7684\u533a\u5206\u5ea6<\/span>\uff08\u4f8b\u5982 r \u63a5\u8fd10\uff09<\/span>\u4f1a\u5bfc\u81f4\u8f83\u5c0f\u7684\u4fe1\u606f\u71b5\u3002<\/span><\/section>\n

<\/section>\n
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Accurary\u22481-\u03c1\u00b7H\uff0c<\/span><\/span><\/section>\n

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\u5982\u56fe3b\u6240\u793a\u3002\u5176\u4e2d \u03c1<\/span> \u662f c, r, v<\/span> \u7684\u51fd\u6570\uff0c\u800c s \u662f\u5173\u4e8e\u5c40\u90e8\u89c2\u6d4b\u91cf\u51cf\u5c11\u4e0d\u786e\u5b9a\u6027\u7684\u5c3a\u5ea6\u56e0\u5b50\u3002\u5982\u56fe3c\u6240\u793a\uff0c\u7814\u7a76\u8fdb\u4e00\u6b65\u53d1\u73b0 s \u4e0e\u591a\u5c42\u7f51\u7edc\u7684\u5ea6\u5e8f\u5217\u7684\u4f59\u5f26\u76f8\u4f3c\u6027\u6210\u6b63\u6bd4\uff0c\u63cf\u8ff0\u4e86\u591a\u5c42\u7f51\u7edc\u7684\u4e2d\u89c2\u7ed3\u6784\u7279\u5f81\u3002\u56fe 3d\u5c55\u793a\u4e86\u4e0d\u540c\u7684\u5ea6\u5e8f\u5217\u4f59\u5f26\u76f8\u4f3c\u6027\u5728\u591a\u5c42\u7f51\u7edc\u4e2d\u7684\u793a\u4f8b\u3002\u56e0\u6b64\uff0c\u591a\u5c42\u7f51\u7edc\u7684\u53ef\u91cd\u6784\u6027\u88ab\u4e0e\u5fae\u89c2\u548c\u4e2d\u89c2\u7ed3\u6784\u6709\u5173\u7684\u533a\u5206\u5ea6\u6307\u6807 (1-\u03c1<\/span>\u00b7H<\/span>) \u6240\u786e\u5b9a\u3002\u4ee5\u4e0a\u7ed3\u8bba\u8868\u660e\uff0c\u53ef\u4ee5\u901a\u8fc7\u8be5\u533a\u5206\u5ea6\u6307\u6807\u9884\u6d4b\u91cd\u6784\u51c6\u786e\u7387\uff0c\u4ece\u800c\u5728 \u03c1<\/span> \u6216 H<\/span> \u8f83\u5c0f\u7684\u60c5\u51b5\u4e0b\u83b7\u5f97\u8f83\u9ad8\u7684\u91cd\u6784\u51c6\u786e\u7387\u3002<\/span><\/section>\n

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\u56fe3. \u591a\u5c42\u7f51\u7edc\u53ef\u91cd\u6784\u6027\u7684\u4e0e\u7f51\u7edc\u7ed3\u6784\u7684\u7406\u8bba\u7814\u7a76\u3002a\uff1a\u4fe1\u606f\u71b5 H \u4e0e c, r, v \u7684\u5173\u7cfb\u3002b\uff1a\u91cd\u6784\u51c6\u786e\u7387\u4e0e\u6307\u6807 <\/span>\u03c1<\/span>\u00b7H<\/span><\/span> \u7684\u7ebf\u6027\u5173\u7cfb\u3002c\uff1a\u5c3a\u5ea6\u56e0\u5b50 s \u4e0e\u5ea6\u5e8f\u5217\u4f59\u5f26\u76f8\u4f3c\u6027\u4e4b\u95f4\u7684\u6b63\u6bd4\u5173\u7cfb\u3002d\uff1a\u4e0d\u540c\u7684\u5ea6\u5e8f\u5217\u4f59\u5f26\u76f8\u4f3c\u6027\u5728\u591a\u5c42\u7f51\u7edc\u4e2d\u7684\u793a\u4f8b\u3002<\/span><\/p>\n


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4. \u591a\u5c42\u7f51\u7edc\u7684\u6700\u4f18\u91cd\u6784<\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u5728\u5b9e\u9645\u4e2d\uff0c\u83b7\u53d6\u591a\u5c42\u7f51\u7edc\u5c40\u90e8\u7ed3\u6784\u7684\u89c2\u6d4b\u8d44\u6e90\u901a\u5e38\u662f\u6709\u9650\u7684\u3002\u56e0\u6b64\uff0c\u5728\u4e00\u5b9a\u7684\u89c2\u6d4b\u603b\u91cf\u4e0b\uff0c\u7814\u7a76\u4e0d\u540c\u5c42\u4e2d\u7684\u8d44\u6e90\u5206\u914d\u6bd4\u4f8b\uff0c\u4ee5\u63d0\u9ad8\u91cd\u6784\u51c6\u786e\u7387\u5177\u6709\u91cd\u8981\u610f\u4e49\u3002\u540c\u6837\uff0c\u4ee5\u4e24\u5c42\u7f51\u7edc\u4e3a\u4f8b\uff0c\u8bb0c1<\/sub>\u4e3a\u7b2c\u4e00\u5c42\u7684\u5c40\u90e8\u89c2\u6d4b\u91cf\uff0c\u800cc2<\/sub>\u4e3a\u7b2c\u4e8c\u5c42\u7684\u5c40\u90e8\u89c2\u6d4b\u91cf\u3002\u5f53\u89c2\u6d4b\u603b\u91cf\u4e00\u5b9a\u65f6\uff0c\u4ee5\u6bcf\u4e00\u5c42\u7684\u5c40\u90e8\u89c2\u6d4b\u91cf\u4e4b\u6bd4c1<\/sub>\/c2<\/sub>\u4f5c\u4e3a\u53d8\u91cf\uff0c\u5efa\u7acb\u5bf9\u5e94\u7684\u89c2\u6d4b\u7b56\u7565\u7a7a\u95f4\uff0c\u5982\u56fe4c\u6240\u793a\uff0c\u5e76\u6839\u636e\u4e0d\u540c\u7b56\u7565\u8ba1\u7b97\u76f8\u5bf9\u5e94\u7684\u4fe1\u606f\u71b5\u51fd\u6570\uff0c\u4ee5\u8868\u5f81\u6574\u5f20\u7f51\u7edc\u7684\u4e0d\u786e\u5b9a\u6027\u3002<\/span><\/section>\n

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[1] Boccaletti S, Bianconi G, Criado R, et al. The structure and dynamics of multilayer networks[J]. Physics reports, 2014, 544(1): 1-122.<\/span><\/section>\n
[2] Moreno Y, Perc M. Focus on multilayer networks[J]. New Journal of Physics, 2019, 22(1): 010201.<\/span><\/section>\n
[3] Buldyrev S V, Parshani R, Paul G, et al. Catastrophic cascade of failures in interdependent networks[J]. Nature, 2010, 464(7291): 1025-1028.<\/span><\/section>\n

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