{"id":33330,"date":"2022-03-25T21:44:23","date_gmt":"2022-03-25T13:44:23","guid":{"rendered":"https:\/\/swarma.org\/?p=33330"},"modified":"2022-03-25T21:44:23","modified_gmt":"2022-03-25T13:44:23","slug":"%e7%a4%be%e4%ba%a4%e5%aa%92%e4%bd%93%e4%bf%a1%e6%81%af%e4%bc%a0%e6%92%ad%e7%9a%84%e6%99%ae%e9%80%82%e8%a7%84%e5%be%8b%ef%bc%9a%e4%b8%b4%e7%95%8c%e6%80%a7%e4%b8%8e%e5%a4%8d%e6%9d%82%e6%80%a7","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=33330","title":{"rendered":"\u793e\u4ea4\u5a92\u4f53\u4fe1\u606f\u4f20\u64ad\u7684\u666e\u9002\u89c4\u5f8b\uff1a\u4e34\u754c\u6027\u4e0e\u590d\u6742\u6027"},"content":{"rendered":"
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1. \u793e\u4ea4\u5e73\u53f0\u4e2d\u7684\u96ea\u5d29\u73b0\u8c61<\/strong><\/strong><\/p>\n<\/section>\n

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\u5bf9\u96ea\u5d29\u66f4\u7cbe\u786e\u7684\u5b9a\u4e49\u5982\u4e0b\u3002\u7ed9\u5b9a\u65f6\u95f4\u5e8f\u5217{t1<\/span><\/sub><\/span>, t2<\/span><\/sub><\/span>,…}\uff0c\u96ea\u5d29\u5b9a\u4e49\u5728\u4ecetb<\/sub><\/span>\u5f00\u59cb\u7684\u4e00\u7cfb\u5217\u4e8b\u4ef6{tb<\/span><\/sub><\/span>,tb+1<\/span><\/sub><\/span>,…,tb+s-1<\/span><\/sub><\/span>}\uff0c\u5176\u4e2d tb<\/span><\/sub><\/span>-tb-1<\/span><\/sub><\/span> >\u0394 \uff0ctb+s<\/span><\/sub><\/span>-tb+s-1<\/sub><\/span> >\u0394\uff0c\u5e76\u4e14\u5bf9\u4e8e\u6240\u6709\u7684i=1,…,S\uff0c\u90fd\u6709 tb+i<\/span><\/sub><\/span> – tb+i-1<\/sub><\/span> \u2266\u0394\u3002\u5176\u4e2d\u0394\u662f\u4e00\u4e2a\u65f6\u95f4\u5206\u8fa8\u7387\u8d85\u53c2\u6570\u3002\u6839\u636e\u0394\u53d6\u503c\u7684\u4e0d\u540c\uff0c\u540c\u6837\u7684\u65f6\u95f4\u5e8f\u5217\u4f1a\u88ab\u5206\u89e3\u6210\u4e0d\u540c\u7684\u96ea\u5d29\u3002S\u662f\u96ea\u5d29\u89c4\u6a21\u7684\u5927\u5c0f\uff0c\u5373\u5728\u7ed9\u5b9a\u65f6\u95f4\u5e8f\u5217\u5185\u7684\u4e8b\u4ef6\u6570\u91cf\uff0cT\u662f\u96ea\u5d29\u6301\u7eed\u65f6\u95f4\u3002<\/span><\/section>\n
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\u548c\u75be\u75c5\u4f20\u64ad\u7c7b\u4f3c\uff0c\u5f53\u524d\u88ab\u5e7f\u6cdb\u63a5\u53d7\u7684\u8bf4\u6cd5\u662f\uff0c\u4fe1\u606f\u662f\u4e00\u4e2a\u7b80\u5355\u4f20\u64ad<\/strong><\/span>\uff08simple contagion\uff09<\/span>\u8fc7\u7a0b\uff0c\u5373\u4e00\u6b21\u63a5\u89e6\u5c31\u4f7f\u8282\u70b9\u6fc0\u6d3b\u8fd9\u79cd\u673a\u5236\u5c31\u8db3\u4ee5\u63cf\u8ff0\u6574\u4e2a\u8fc7\u7a0b\u3002\u4e0d\u8fc7\u4e5f\u6709\u76f8\u5f53\u6570\u91cf\u7684\u7814\u7a76\u652f\u6301\u590d\u6742\u4f20\u64ad<\/strong><\/span>\uff08complex contagion\uff09<\/span>\u8303\u5f0f\u3002\u5982\u6700\u65e9\u7531Centola\u548cMacy\u63d0\u51fa\u7684\uff0c\u8ba4\u4e3a\u5728\u4e00\u4e2a\u590d\u6742\u4f20\u64ad\u8fc7\u7a0b\u4e2d\uff0c\u4e2a\u4f53\u53c2\u4e0e\u4fe1\u606f\u4f20\u64ad\u9700\u8981\u6765\u81ea\u548c\u591a\u4e2a\u719f\u4eba\u7684\u63a5\u89e6 [1]\u3002\u590d\u6742\u4f20\u64ad\u4e5f\u7531\u4e00\u4e9b\u6a21\u578b\u8fdb\u884c\u4e86\u8bc1\u660e\uff0c\u5982\u7ebf\u6027\u9608\u503c\u6a21\u578b\u548c\u968f\u673a\u573a\u4f0a\u8f9b\u6a21\u578b<\/span>\uff08Random Field Ising Model, \u4e0b\u7b80\u79f0 RFIM\uff09<\/span>[2]\u3002<\/span><\/section>\n
 <\/span><\/section>\n

 <\/span><\/p>\n

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<\/svg><\/section>\n<\/section>\n<\/section>\n
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3. \u4fe1\u606f\u4f20\u64ad\u7279\u70b9\u7684\u7814\u7a76<\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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


<\/p>\n

\n
3.1 \u666e\u9002\u6027<\/span><\/strong><\/span><\/section>\n<\/h3>\n
 \u200d<\/span><\/span><\/section>\n
\u672c\u6587\u5b9a\u4e49\u4e86\u200d<\/span>\u6700\u4f18\u5206\u8fa8\u7387\u0394*\u4f5c\u4e3a\u63cf\u8ff0\u65f6\u95f4\u5e8f\u5217\u7684\u4e00\u7ef4\u6e17\u6d41\u6a21\u578b\u7684\u76f8\u53d8\u70b9\uff0c\u6570\u636e\u96c6\u4e2d\u7684\u6bcf\u4e2a\u65f6\u95f4\u5e8f\u5217\u88ab\u89c6\u4e3a\u4e00\u7ef4\u6e17\u6d41\u6a21\u578b\u7684\u4e00\u4e2a\u5b9e\u4f8b\u3002\u7814\u7a76\u4e2d\u6d4b\u91cf\u4e86\u6bcf\u4e2a\u65f6\u95f4\u5e8f\u5217\u4e2d\u6700\u5927\u96ea\u5d29\u7684\u5927\u5c0f\uff0c\u5e76\u5b9a\u4e49\u4e86\u6e17\u6d41\u5f3a\u5ea6\u53ca\u76f8\u5e94\u7684\u78c1\u5316\u7387<\/span>\uff08susceptibility\uff09<\/span>\u3002\u6700\u4f18\u5206\u8fa8\u7387\u0394*\u901a\u8fc7\u6700\u5927\u5316\u78c1\u5316\u7387\u5f97\u5230\uff0c\u6700\u7ec8\u53ef\u4ee5\u5bf9\u6bcf\u4e00\u4e2a\u65f6\u95f4\u5e8f\u5217\u90fd\u8ba1\u7b97\u4e00\u4e2a\u6700\u4f18\u5206\u8fa8\u7387\u3002\u200d\u200d\u200d<\/span><\/span><\/section>\n
 <\/span><\/section>\n
\u5bf9\u4e8e\u4e0d\u540c\u5206\u8fa8\u7387\uff0c\u4f7f\u7528\u5bf9\u5e94\u7684\u6700\u4f18\u5206\u8fa8\u7387\u5f52\u4e00\u5316\u540e\u53ef\u5c55\u73b0\u51fa\u8fd1\u4e4e\u76f8\u540c\u7684\u5b9a\u91cf\u76f8\u53d8\u884c\u4e3a<\/span>\uff08\u5982\u56fe1\u6240\u793a\uff09<\/span>\u3002\u8fd9\u8868\u660e\u4fe1\u606f\u5728\u793e\u4ea4\u5a92\u4f53\u4e0a\u7684\u4f20\u64ad\u53ef\u4ee5\u770b\u6210\u662f\u4e00\u4e2a\u666e\u9002\u8fc7\u7a0b\u3002<\/span><\/section>\n
 <\/span><\/section>\n
<\/section>\n

\u56fe1. \u5206\u522b\u5c55\u793a\u4e86\u6e17\u6d41\u5f3a\u5ea6(a)\uff0c\u76f8\u5e94\u7684\u78c1\u5316\u7387(b) \u548c\u65f6\u95f4\u5206\u8fa8\u7387\u7684\u5173\u7cfb\u3002\u4e0d\u540c\u7684\u989c\u8272\u4ee3\u8868\u4e0d\u540c\u7684\u793e\u4ea4\u5a92\u4f53\u3002\u5b50\u56fe\u90fd\u4f7f\u7528\u6700\u4f18\u5206\u8fa8\u7387\u5bf9\u6a2a\u5750\u6807\u8fdb\u884c\u4e86\u5f52\u4e00\u5316\u3002<\/span><\/p>\n

 <\/span><\/section>\n
\u8fdb\u4e00\u6b65\uff0c\u4f7f\u7528\u6700\u4f18\u5206\u8fa8\u7387\u8ba1\u7b97\u96ea\u5d29\u7684\u89c4\u6a21S\u548c\u6301\u7eed\u65f6\u95f4T\uff0c\u5e76\u523b\u753b\u5b83\u4eec\u7684\u5206\u5e03<\/span>\uff08\u5982\u56fe2a\uff0c2b\uff09<\/span>\uff0c\u53d1\u73b0\u4e0d\u540c\u7684\u6570\u636e\u96c6\u90fd\u8868\u73b0\u51fa\u4e86\u4e00\u81f4\u7684\u884c\u4e3a\uff0c\u5e76\u4e14\u4e5f\u6210\u529f\u9a8c\u8bc1\u4e86\u65f6\u95f4T\u548c\u89c4\u6a21S\u4e4b\u95f4\u7684\u5173\u7cfb<\/span>\uff08\u5982\u56fe2c\uff09<\/span>\uff0c\u518d\u6b21\u9a8c\u8bc1\u8fd9\u79cd\u666e\u9002\u8fc7\u7a0b\u7684\u5b58\u5728\u3002<\/span><\/section>\n

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<\/section>\n

\u56fe2. (a) \u96ea\u5d29\u89c4\u6a21\u7684\u5206\u5e03\u3002(b) \u96ea\u5d29\u6301\u7eed\u65f6\u95f4\u7684\u5206\u5e03\u3002(c) \u96ea\u5d29\u6301\u7eed\u65f6\u95f4\u548c\u89c4\u6a21\u7684\u5173\u7cfb\u3002(d) \u4e0d\u540c\u5e73\u53f0\u7684\u62df\u5408\u53c2\u6570\u548c\u6a21\u578b\u6a21\u62df\u53c2\u6570\u5bf9\u6bd4<\/span><\/p>\n

\n

<\/section>\n
3.2 \u4e34\u754c\u6027<\/span><\/strong><\/span><\/section>\n<\/h3>\n
 <\/span><\/section>\n
\u56fe2\u7684\u5e42\u5f8b\u5206\u5e03\u7ed3\u679c\u8868\u660e\uff0c\u4fe1\u606f\u4f20\u64ad\u8fc7\u7a0b\u80cc\u540e\u5b58\u5728\u7740\u4e34\u754c\u73b0\u8c61\uff0c\u8fd9\u79cd\u4e34\u754c\u6027\u53ef\u4ee5\u901a\u8fc7\u5bf9\u4e34\u754c\u6307\u6570\u7684\u62df\u5408\u6765\u8fdb\u884c\u523b\u753b\u3002\u672c\u6587\u901a\u8fc7\u6570\u503c\u6a21\u62df\u7684\u65b9\u5f0f\uff0c\u4f7f\u7528\u5e73\u5747\u968f\u673a\u573a\u4f0a\u8f9b\u6a21\u578b<\/strong><\/span>\uff08mean-filed RFIM\uff09<\/span>\u548c\u5206\u652f\u8fc7\u7a0b<\/strong><\/span>\uff08Branching Process, \u4e0b\u7b80\u79f0BP\uff09<\/span>[3] \u5206\u522b\u5bf9\u4f20\u64ad\u8fc7\u7a0b\u8fdb\u884c\u4e86\u6a21\u62df\u3002\u5176\u4e2d\uff0c\u5e73\u5747\u968f\u673a\u573a\u4f0a\u8f9b\u6a21\u578b\u662f\u591a\u5bf9\u591a\u7684\u590d\u6742\u4f20\u64ad\u8fc7\u7a0b\uff0c\u5206\u652f\u8fc7\u7a0b\u662f\u4e00\u5bf9\u591a\u7684\u7b80\u5355\u4f20\u64ad\u8fc7\u7a0b\u3002\u62df\u5408\u7ed3\u679c\u5728\u5168\u6570\u636e\u96c6\u4e0a\u7684\u7ed3\u679c\u5982\u56fe2a-2c\u6240\u793a\uff0c\u5bf9\u6bcf\u4e2a\u5e73\u53f0\u5206\u522b\u8fdb\u884c\u62df\u5408\u7684\u7ed3\u679c\u5982\u56fe2d\u6240\u793a\u3002\u7ed3\u679c\u663e\u793a\uff0c\u4e0d\u540c\u5e73\u53f0\u7684\u4e34\u754c\u6307\u6570\u8868\u73b0\u51fa\u4e86\u4e00\u81f4\u6027<\/strong>\uff0c\u5e76\u4e14\u4f7f\u7528RFIM\u65b9\u6cd5\u62df\u5408\u7684\u4f20\u64ad\u7ed3\u679c\u4e0e\u5b9e\u9645\u6570\u636e\u66f4\u52a0\u543b\u5408\u3002<\/span><\/section>\n
 <\/span><\/section>\n

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3.3 \u590d\u6742\u6027<\/span><\/strong><\/span><\/section>\n<\/h3>\n
 <\/span><\/section>\n
\u4ece\u73b0\u8c61\u4e0a\u770b\uff0c\u6570\u636e\u7684\u8868\u73b0\u548cRFIM\u7684\u62df\u5408\u7ed3\u679c\u66f4\u52a0\u76f8\u7b26\uff0c\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u53ef\u4ee5\u8bf4\u660e\u5728\u6574\u4e2a\u6570\u636e\u4e0a\u7684\u5b8f\u89c2\u884c\u4e3a\u66f4\u504f\u5411\u590d\u6742\u4f20\u64ad\u8fc7\u7a0b\u3002\u53e6\u5916\uff0c\u672c\u6587\u4e3a\u8fdb\u4e00\u6b65\u9a8c\u8bc1\u7ed3\u8bba\uff0c\u63d0\u51fa\u4e86\u4e00\u4e2a\u6700\u5927\u4f3c\u7136\u65b9\u6cd5\u9a8c\u8bc1\u62df\u5408\u7ed3\u679c\u7684\u6709\u6548\u6027<\/span>\uff08\u8be5\u65b9\u6cd5\u542f\u53d1\u4e8e\u5de5\u4f5c[4]\uff09<\/span>\u3002\u8fd9\u4e2a\u65b9\u6cd5\u652f\u6301\u4e09\u79cd\u4e0d\u540c\u7684\u6d4b\u8bd5\u3002<\/span><\/section>\n

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

1. \u8bc4\u4ef7\u4e00\u6bb5\u65f6\u95f4\u5e8f\u5217\u6700\u4f73\u7684\u62df\u5408\u53c2\u6570\u2014\u2014\u5177\u4f53\u6765\u8bf4\u662fBP\u7684\u5206\u652f\u7387<\/span>\uff08branching ratio\uff09<\/span>\u548cRFIM\u7684\u65e0\u5e8f\u53c2\u91cf<\/span>\uff08disorder parameter\uff09<\/span>\u2014\u2014\u548c\u6a21\u578b\u7684\u4e34\u754c\u503c\u7684\u6bd4\u8f83\uff1b<\/span><\/p>\n

2. \u53ef\u4ee5\u7528p-value\u8bc4\u4ef7\u6bcf\u4e2a\u62df\u5408\u65b9\u6cd5\u7684\u6709\u6548\u6027\uff1b<\/span><\/p>\n

3. \u901a\u8fc7\u5bf9\u6bd4\u4e0d\u540c\u65b9\u6cd5\u7684\u4f3c\u7136\u6982\u7387\uff0c\u6765\u8bc4\u4ef7\u4e00\u4e2a\u5e8f\u5217\u7528BP\u8fd8\u662f\u7528RFIM\u5efa\u6a21\u66f4\u597d\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u56fe3\u5c55\u793a\u4e86\u4e24\u4e2a\u6a21\u578b\u62df\u5408\u7684\u6709\u6548\u6027\u68c0\u9a8c\u3002<\/span><\/section>\n
 <\/span><\/section>\n
<\/section>\n

\u56fe3. (a) \u662fRFIM\u7684\u7ed3\u679c\uff0c(b) \u662fBP\u7684\u7ed3\u679c\uff0c\u7ad6\u76f4\u7684\u865a\u7ebf\u4ee3\u8868\u6a21\u578b\u7684\u4e34\u754c\u503c\u6240\u5728\u3002<\/span>(c) \u662f\u5bf9\u6570\u4f3c\u7136\u7684\u5360\u6bd4\u6982\u7387\uff0c\u84dd\u7eff\u8272\u8868\u793aBP\u6bd4RFIM\u66f4\u597d\u7684\u65f6\u95f4\u5e8f\u5217\uff0c\u7ea2\u8272\u5219\u8868\u793a\u76f8\u5e94\u65f6\u95f4\u5e8f\u5217\u7528RFIM\u66f4\u597d\u3002<\/span>(d) \u6839\u636e (c) \u7684\u5206\u7c7b\u65b9\u5f0f\uff0c\u5c06\u65f6\u95f4\u5e8f\u5217\u660e\u663e\u533a\u5206\u6210\u4e24\u79cd\u4e0d\u540c\u7684\u884c\u4e3a\uff08\u8fd9\u91cc\u4ec5\u53d6\u9760\u8fd1\u4e34\u754c\u70b9\u9644\u8fd1\u7684\u65f6\u95f4\u5e8f\u5217\u4f5c\u4e3a\u5bf9\u5e94\u5206\u7c7b\u7684\u4ee3\u8868\uff09\uff0c\u5e76\u8ba1\u7b97\u5bf9\u5e94\u5e8f\u5217\u7684\u96ea\u5d29\u89c4\u6a21\u5206\u5e03\u3002<\/span>\u5b9e\u5fc3\u70b9\u4ee3\u8868\u4f7f\u7528\u7684\u6a21\u578b\u662fRFIM\uff0c\u7a7a\u5fc3\u70b9\u662fBP\u3002<\/span>\u865a\u7ebf\u5bf9\u5e94\u7684\u5206\u522b\u662f\u4e24\u79cd\u6a21\u578b\u7684\u6700\u4f73\u5e42\u6307\u6570\u62df\u5408\u3002<\/span><\/p>\n

 <\/span><\/section>\n
\u901a\u8fc7\u5206\u6790\uff0c\u4f5c\u8005\u53d1\u73b0\u6700\u4f73\u62df\u5408\u53c2\u6570\u7684\u8303\u56f4\u5f88\u5e7f<\/span>\uff08\u56fe3a, 3b\uff09<\/span>\uff0c\u5305\u542b\u4e86\u6a21\u578b\u7684\u4e34\u754c\u72b6\u6001\u548c\u5f88\u5927\u4e00\u90e8\u5206\u7684\u4e9a\u4e34\u754c\u72b6\u6001\uff0c\u5373\u5927\u591a\u6570\u4e8b\u4ef6\u90fd\u5c5e\u4e8e\u5f15\u53d1\u5927\u96ea\u5d29\u7684\u5c11\u6570\u65f6\u95f4\u5e8f\u5217\u3002\u56e0\u6b64\u5bf9\u4e8eBP\u548cRFIM\u6765\u8bf4\uff0c\u7cfb\u7edf\u7684\u5927\u5c3a\u5ea6\u884c\u4e3a\u4e3b\u8981\u90fd\u662f\u7531\u5c11\u6570\u7684\u65f6\u95f4\u5e8f\u5217\u51b3\u5b9a\uff0c\u5b83\u4eec\u7684\u53c2\u6570\u7a7a\u95f4\u90fd\u975e\u5e38\u72ed\u7a84\u4e14\u5728\u4e34\u754c\u70b9\u9644\u8fd1<\/span>\uff08\u56fe3a, b\u7684\u5b50\u56fe\uff09<\/span>\u3002<\/span><\/section>\n
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3.4 \u4e0d\u540c\u4f20\u64ad\u6a21\u5f0f\u7684\u8bed\u4e49\u4fe1\u606f<\/span><\/strong><\/span><\/section>\n<\/h3>\n
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\u6587\u7ae0\u6700\u540e\u4f5c\u8005\u63a8\u6d4b\uff0c\u672c\u6587\u7ed3\u8bba\u7684\u666e\u9002\u6027\u5f88\u53ef\u80fd\u8d85\u51fa\u4e86\u6587\u4e2d\u6240\u5c55\u793a\u7684\u8fd9\u4e9b\u6570\u636e\u96c6\u3002\u5982\u679c\u771f\u7684\u662f\u8fd9\u6837\uff0c\u90a3\u4e48\u80cc\u540e\u4e00\u5b9a\u5b58\u5728\u4e00\u79cd\u673a\u5236\u5f97\u4ee5\u89e3\u91ca\u8fd9\u79cd\u666e\u9002\u6027\u3002\u7406\u89e3\u8fd9\u4e2a\u80cc\u540e\u7684\u673a\u5236\uff0c\u4ee5\u53ca\u5982\u4f55\u5f00\u53d1\u51fa\u8fd9\u79cd\u53ef\u4ee5\u5bf9\u5728\u7ebf\u793e\u4ea4\u5a92\u4f53\u7684\u4fe1\u606f\u4f20\u64ad\u8fdb\u884c\u9884\u6d4b\u7684\u673a\u5236\uff0c\u4ecd\u65e7\u662f\u4e00\u4e2a\u6311\u6218\u3002<\/span><\/section>\n
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\u53c2\u8003\u6587\u732e<\/span><\/strong><\/span><\/section>\n
[1] Centola, D. & Macy, M. Complex contagions and the weakness of long ties. Am. J. Sociol. 113, 702\u2013734 (2007).<\/span><\/section>\n
[2] Dodds, P. S. & Watts, D. J. A generalized model of social and biological contagion. J. Theor. Biol. 232, 587\u2013604 (2005).<\/span><\/section>\n
[3] Watson, H. W. & Galton, F. On the probability of the extinction of families. J.R. Anthropol. Inst. G.B. Irel. 4, 138\u2013144 (1875)<\/span><\/section>\n
[4] Clauset, A., Shalizi, C. R. & Newman, M. E. Power-law distributions in empirical data. SIAM Rev. 51, 661\u2013703 (2009).<\/span><\/section>\n


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