{"id":39727,"date":"2023-01-09T23:10:56","date_gmt":"2023-01-09T15:10:56","guid":{"rendered":"https:\/\/swarma.org\/?p=39727"},"modified":"2023-01-09T23:10:56","modified_gmt":"2023-01-09T15:10:56","slug":"%e8%87%aa%e7%bb%84%e7%bb%87%e4%b8%b4%e7%95%8c%e6%80%a7%e7%9a%84%e5%85%b3%e9%94%ae%ef%bc%9a%e8%bf%91%e4%bc%bc%e5%b9%82%e5%be%8b%e4%b8%8e%e9%95%bf%e7%a8%8b%e5%85%b3%e8%81%94","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=39727","title":{"rendered":"\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u7684\u5173\u952e\uff1a\u8fd1\u4f3c\u5e42\u5f8b\u4e0e\u957f\u7a0b\u5173\u8054"},"content":{"rendered":"
\n
\n
\n
\n

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

\n
\n
\n
\n
\n
\n

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

\u6458\u8981<\/strong><\/p>\n<\/section>\n<\/section>\n

\n

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

\u672c\u6587\u7b80\u8981\u4ecb\u7ecd\u4e86\u5e42\u5f8b\u51fd\u6570 (power laws) \u548c\u5173\u8054\u51fd\u6570 (correlation functions) \u662f\u5982\u4f55\u5ea6\u91cf\u4e34\u754c\u6027 (criticality) \u7684\u53ca\u5b83\u4eec\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u901a\u8fc7\u6bd4\u8f83\u964d\u96e8\u3001\u5927\u8111\u548c\u68ee\u6797\u706b\u707e\u6a21\u578b\u7684\u73b0\u8c61\u5b66 (phenomenology)\uff0c\u6211\u4eec\u8ba8\u8bba\u4e86\u4e34\u754c\u72b6\u6001\u9644\u8fd1\u81ea\u7ec4\u7ec7\u7684\u76f8\u5173\u7279\u5f81\u3002\u5f97\u5230\u7ed3\u8bba\uff1a\u7cfb\u7edf\uff08\u81ea\uff09\u7ec4\u7ec7\u5230\u4e00\u4e2a\u5177\u6709\u5e7f\u4e49\u76f8\u5173\u6027\u548c\u8fd1\u4f3c\u5e42\u5f8b\u7684\u533a\u95f4\uff0c\u662f\u4e0a\u8ff0\u4e09\u79cd\u7cfb\u7edf\u53ef\u80fd\u5171\u6709\u7684\u6f14\u5316\u7279\u5f81\u3002<\/span><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n


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

\n

\u5173\u952e\u8bcd\uff1a\u81ea\u7ec4\u7ec7\u4e34\u754c\uff0c\u6df7\u6c8c\u8fb9\u7f18\uff0c\u5e42\u5f8b\uff0c\u5173\u8054\u51fd\u6570\uff0c\u957f\u7a0b\u76f8\u5173<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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

Henrik Jeldtoft Jensen<\/span> <\/span>| <\/strong><\/span>\u4f5c\u8005<\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/p>\n

\u6731\u6b23\u6021<\/span> <\/span>| <\/strong><\/span><\/strong>\u8bd1\u8005<\/span><\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/p>\n

\u5218\u57f9\u6e90<\/span> <\/span>| <\/strong><\/span>\u4f5c\u8005<\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n

\u9093\u4e00\u96ea<\/span> <\/span>| <\/strong><\/span>\u7f16\u8f91<\/strong><\/p>\n


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

 <\/span><\/p>\n

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

\u8bba\u6587\u6807\u9898\uff1a<\/span><\/p>\n

What is critical about criticality: in praise of the correlation function<\/span><\/p>\n

\u8bba\u6587\u5730\u5740\uff1a<\/span><\/section>\n
https:\/\/iopscience.iop.org\/article\/10.1088\/2632-072X\/ac24f2<\/span><\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n

<\/section>\n

<\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

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

1. \u5f15\u8a00<\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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

<\/section>\n
\u7814\u7a76\u4eba\u5458\u5bf9\u4e34\u754c\u70b9\u53ca\u5176\u9644\u8fd1\u72b6\u6001\u7684\u7814\u7a76\u5174\u8da3\u4ece20\u4e16\u7eaa\u7814\u7a76\u7269\u7406\u5b66\u4e2d\u7684\u4e8c\u9636\u76f8\u53d8\u5f00\u59cb\uff0c\u5728\u91cd\u6574\u5316\u7fa4\u8bba<\/span> (renormalisation group theory) <\/span>\u4e2d\u8fbe\u5230\u9876\u5cf0[1]\u300220\u4e16\u7eaa80\u5e74\u4ee3\u201c\u6df7\u6c8c\u8fb9\u7f18\u201d[2]\u548c\u201c\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u201d<\/span>\uff08SOC\uff09<\/span>[3]\u7b49\u6982\u5ff5\u5728\u4e0d\u540c\u7684\u9886\u57df\u4e2d\u88ab\u521b\u9020\uff0c\u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u548c\u9ad8\u7ef4\u975e\u5e73\u8861\u7edf\u8ba1\u529b\u5b66\u7684\u65b9\u6cd5\u53d7\u5230\u8d85\u654f\u611f\u4e34\u754c\u72b6\u6001\u7684\u7279\u6b8a\u6027\u8d28\u7684\u542f\u53d1\uff0c\u5e76\u88ab\u5bc4\u4e88\u5e0c\u671b\u80fd\u627e\u5230\u4e00\u79cd\u673a\u5236\u89e3\u91ca\u8fd9\u79cd\u4f3c\u4e4e\u65e0\u5904\u4e0d\u5728\u7684\u975e\u51e1\u73b0\u8c61\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u867d\u7136\u6df7\u6c8c\u8fb9\u7f18\u548c\u4e34\u754c\u6027\u6709\u65f6\u4ee5\u4e00\u79cd\u6709\u70b9\u677e\u6563\u7684\u63cf\u8ff0\u65b9\u5f0f\u540c\u4e49\u4f7f\u7528[4\uff0c5]\uff0c\u4f46\u8fd9\u4e24\u4e2a\u6982\u5ff5\u90fd\u6709\u7cbe\u786e\u7684\u6570\u5b66\u5b9a\u4e49\uff0c\u5e76\u4e14\u53ea\u6709\u5f53\u7cfb\u7edf\u7684\u63a7\u5236\u53c2\u6570\u88ab\u8c03\u6574\u5230\u4e00\u5b9a\u503c\u65f6\u624d\u53d1\u751f\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5982\u679c\u674e\u4e9a\u666e\u8bfa\u592b\u8f93\u51fa\u4e3a\u6b63\uff0c\u90a3\u4e48\u52a8\u529b\u7cfb\u7edf\u5c31\u662f\u6df7\u6c8c\u7684\u3002[6]\u3002\u5373\u4f7f\u53ea\u6d89\u53ca\u4e00\u4e9b\u53c2\u6570<\/span>\uff08\u901a\u5e38\u8868\u793a\u4e3a\u81ea\u7531\u5ea6\uff09<\/span>\u4e5f\u53ef\u80fd\u53d1\u751f\u6df7\u6c8c\u884c\u4e3a\u3002\u5982\u679c\u53ef\u4ee5\u901a\u8fc7\u8fed\u4ee3\u6620\u5c04\u6765\u8868\u793a\u65f6\u95f4\u6f14\u5316\uff0c\u4f8b\u5982\u5177\u6709\u975e\u91cd\u53e0\u4e16\u4ee3\u7684\u7269\u79cd<\/span>\uff08\u4f8b\u5982\u4e00\u5e74\u751f\u6606\u866b\uff09<\/span>\u7684\u79cd\u7fa4\u5927\u5c0f\uff0c\u5219\u5373\u4f7f\u5bf9\u4e8e\u4e00\u7ef4\u81ea\u7531\u5ea6xn<\/sub>\u4e5f\u53ef\u80fd\u51fa\u73b0\u6df7\u6c8c\u73b0\u8c61\u3002\u6700\u8457\u540d\u7684\u53ef\u80fd\u662f\u7531\u4e0b\u8ff0\u65b9\u7a0b\u7ed9\u51fa\u7684logistic\u6620\u5c04[7]<\/span><\/section>\n

<\/section>\n
  (1)<\/span><\/section>\n

<\/span><\/section>\n
\u5f53\u53c2\u6570r\u5927\u4e8er\u221e<\/sub>\u22483.57\u65f6\uff0c\u4e0a\u8ff0\u7cfb\u7edf\u51fa\u73b0\u6df7\u6c8c\u73b0\u8c61\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u4e25\u683c\u6765\u8bb2\uff0c\u5e73\u8861\u7edf\u8ba1\u529b\u5b66\u7684\u4e34\u754c\u72b6\u6001\u53ea\u80fd\u53d1\u751f\u5728\u65e0\u9650\u591a\u81ea\u7531\u5ea6\u7684\u6781\u9650\u4e2d\u3002\u4e34\u754c\u72b6\u6001\u7684\u6807\u5fd7\u662f\u957f\u7a0b\u76f8\u5173[1]\u3002Ising \u6a21\u578b\u662f\u652f\u6301\u4e34\u754c\u72b6\u6001\u7684\u539f\u578b\u7cfb\u7edf\u3002\u57fa\u7840\u7684\u6a21\u578b\u7531\u81ea\u65cb\u53d8\u91cfSi<\/sub>\u00b11\uff0ci=1, 2,\u2026,N\u7ec4\u6210\uff0ci \u6807\u8bb0\u7ebf\u6027\u6269\u5f20 L \u7684 d \u7ef4\u8d85\u7acb\u65b9\u4f53\u4e0a\u7684\u4f4d\u7f6e\uff0c\u56e0\u6b64N=Ld<\/sup>\u3002\u65b9\u5dee\u7cfb\u6570:<\/span><\/section>\n

<\/span><\/section>\n
<\/span><\/section>\n
  (2)\u3002<\/span><\/section>\n

<\/section>\n
\u5176\u4e2drij<\/sub>\u662f\u4f4d\u7f6e i \u548c\u4f4d\u7f6e j \u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u7528\u6765\u8861\u91cf\u4e0d\u540c\u4f4d\u7f6e\u4e4b\u95f4\u7684\u76f8\u4e92\u4f9d\u8d56\u6027\u3002C(rij<\/sub>)\u5728\u7edf\u8ba1\u5b66\u4e2d\u8868\u793a\u65b9\u5dee\uff0c\u4f46\u5728\u7edf\u8ba1\u529b\u5b66\u6587\u732e\u4e2d\uff0c\u5b83\u603b\u662f\u4f5c\u4e3a\u5173\u8054\u51fd\u6570\u51fa\u73b0\u3002\u6211\u4eec\u5c06\u575a\u6301\u8fd9\u4e00\u4f20\u7edf\u3002\u76f8\u5173\u6027C\u4e0e\u76f8\u4e92\u4f9d\u8d56\u6027r=rij<\/sub>\u7684\u4f9d\u8d56\u5173\u7cfb\u80fd\u7528\u5982\u4e0b\u6570\u5b66\u5f62\u5f0f\u8868\u793a\uff1a<\/span><\/section>\n

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

  (3)<\/span><\/p>\n


<\/section>\n
\u8fd9\u91cc\u03be\u88ab\u79f0\u4e3a\u5173\u8054\u957f\u5ea6\uff0c\u5728\u975e\u4e34\u754c\u72b6\u6001\u957f\u5ea6\u5c3a\u5ea6\u6709\u9650\u3002\u8c03\u6574\u6e29\u5ea6T\u5230\u4e34\u754c\u6e29\u5ea6Tc<\/sub>\u53ef\u4ee5\u8fbe\u5230\u4e34\u754c\u72b6\u6001\u3002\u5f53T\u63a5\u8fd1Tc<\/sub>\u65f6\uff0c\u5173\u8054\u957f\u5ea6\u03be\u8d8b\u4e8e\u65e0\u7a77\u5927\u3002\u03be(T)\u2192\u221e\u3002<\/span><\/section>\n

<\/span><\/section>\n
T\u2260Tc<\/sub>\u65f6\uff0c\u8ddd\u79bbr\u5c0f\u4e8e\u03be\uff0c\u5982r<<\u03be\u65f6\uff0c\u5173\u8054\u51fd\u6570\u5c06\u4ee3\u6570\u8870\u51cf\uff0c\u5448\u5e42\u5f8b\u5206\u5e03C(r)~r-a<\/sup>\u3002\u8ddd\u79bbr\u5927\u4e8e\u03be\uff0c\u5982r>>\u03be\u65f6\uff0c\u5173\u8054\u51fd\u6570\u6307\u6570\u8870\u51cf\uff0cC(r)~e-r\/<\/sup><\/span>\u03be<\/sup><\/span>\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u53ea\u6709\u5728\u4e34\u754c\u72b6\u6001T=Tc<\/sub>\u65f6\uff0c\u65e0\u8bba\u8ddd\u79bbr\u6709\u591a\u5927\uff0c\u76f8\u5173\u6027\u90fd\u5c06\u6309\u7167\u5e42\u5f8bC(r)\u221dr-a<\/sup>\u7f13\u6162\u8870\u51cf\uff0c\u800c\u4e14\u7531\u4e8e\u03be \u2192\u221e\uff0c\u6545\u4e0d\u5b58\u5728\u5355\u4e00\u7684\u7279\u5f81\u5c3a\u5ea6\u533a\u5206\u7a7a\u95f4\u548c\u65f6\u95f4\u3002\u6211\u4eec\u8bf4\u8fd9\u4e2a\u72b6\u6001\u5c31\u5177\u6709\u5c3a\u5ea6\u4e0d\u53d8\u6027\uff0c\u662f\u56e0\u4e3a\u4e0d\u8003\u8651\u653e\u5927\u56e0\u5b50\u65f6\uff0c\u5b83\u5728\u6240\u6709\u7684\u7a7a\u95f4\u548c\u65f6\u95f4\u5c3a\u5ea6\u4e0a\u7684\u8868\u73b0\u90fd\u4e00\u81f4\u3002\u56e0\u6b64\uff0c\u7a7a\u95f4\u7ed3\u6784\u5e94\u4e3a\u5206\u5f62\u7ed3\u6784\u3002\u6982\u7387\u5206\u5e03\uff0c\u6bd4\u5982\u90a3\u4e9b\u63cf\u8ff0\u5bf9\u5916\u90e8\u6270\u52a8\u7684\u54cd\u5e94\uff0c\u5e94\u9075\u5faa\u5e42\u5f8b\u5206\u5e03\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027[3\uff0c8\uff0c9]\u7ed9\u51fa\uff1a\u8bb8\u591a\u4e0d\u5e73\u8861\u7684\u7cfb\u7edf\uff0c\u5728\u52a8\u529b\u7684\u7f13\u6162\u9a71\u52a8\u4e0b\uff0c\u4f1a\u81ea\u7ec4\u7ec7\u5230\u521a\u521a\u63cf\u8ff0\u7684\u4e34\u754c\u72b6\u6001\u3002\u539f\u59cb\u8bba\u6587[3]\u7684\u57fa\u672c\u539f\u7406\u662f\uff0c\u7531\u4e8e\u4e34\u754c\u72b6\u6001\u662f\u6807\u5ea6\u4e0d\u53d8\u7684\uff0c\u56e0\u6b64\u53ef\u4ee5\u901a\u8fc7\u7814\u7a76\u81ea\u7ec4\u7ec7\u7cfb\u7edf\u53d1\u751f\u80fd\u91cf\u8017\u6563\u7206\u53d1<\/span>\uff08\u4f20\u7edf\u4e0a\u79f0\u4e3a\u96ea\u5d29\uff09<\/span>\u7684\u6982\u7387\u5206\u5e03\u6765\u7814\u7a76\u4e34\u754c\u6027\uff0c\u96ea\u5d29\u662f\u9010\u6e10\u589e\u52a0\u5e94\u529b\u7684\u7ed3\u679c\u3002\u5982\u679c\u8fd9\u6837\u7684\u5206\u5e03\u670d\u4ece\u5e42\u5f8b\u5206\u5e03\uff0c\u6211\u4eec\u5c31\u80fd\u7814\u7a76\u4e34\u754c\u72b6\u6001\uff0c\u5c3d\u7ba1\u4e0d\u80fd\u76f4\u63a5\u68c0\u9a8c\u65b9\u7a0b(2)\u4e2d\u7684\u5173\u8054\u51fd\u6570\u4ee3\u6570\u4e0a\u4f9d\u8d56\u5206\u79bb\u3002\u8fd9\u662f\u4e00\u4e2a\u660e\u667a\u7684\u7814\u7a76\u8d77\u70b9\uff0c\u4f46\u5b83\u5e76\u4e0d\u603b\u662f\u6b63\u786e\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4e8b\u4ef6\u5927\u5c0f\u7684\u5206\u5e03\u670d\u4ece\u5e42\u5f8b\u5206\u5e03\uff0c\u5373\u4f7f\u5404\u4e2a\u5f1b\u8c6b\u4e8b\u4ef6\u53d1\u751f\u96ea\u5d29\u5b8c\u5168\u72ec\u7acb\u3002\u5178\u578b\u7684\u4f8b\u5b50\u6709\u4e0d\u76f8\u5173\u5206\u652f\u8fc7\u7a0b\u548c\u72ec\u7acb\u968f\u673a\u6e38\u8d70\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u7b80\u5355\u56de\u987e\u4e00\u4e0b\uff0c\u4e0d\u76f8\u5173\u5206\u652f\u8fc7\u7a0b\u7531\u53ef\u4ee5\u4ea7\u751f\u5b50\u4ee3\u7684\u201c\u8282\u70b9\u201d\u7ec4\u6210\u3002\u628a\u6bcf\u4e2a\u8282\u70b9\u770b\u4f5c\u4e00\u4e2a\u795e\u7ecf\u5143\uff0c\u5b83\u7684\u5b50\u4ee3\u5c31\u662f\u4ece\u7b2c\u4e00\u4e2a\u8282\u70b9\u63a5\u6536\u7535\u4fe1\u53f7\u7684\u8282\u70b9\u3002\u56fe1\u663e\u793a\u4e86\u8be5\u8fc7\u7a0b\u3002\u6bcf\u4e2a\u8282\u70b9\u4ea7\u751fk\u4e2a\u5177\u6709\u76f8\u540c\u72ec\u7acb\u6982\u7387pk<\/sub>\u7684\u540e\u4ee3\uff0ck = 1\uff0c2\uff0c……\u3002\u751f\u6210\u6811\u7684\u5927\u5c0fS\uff0c\u5373\u6839\u8282\u70b9\u4ea7\u751f\u7684\u8282\u70b9\u603b\u6570\uff0c\u9075\u5faa\u4ee5\u4e0b\u5f62\u5f0f\u7684\u5206\u5e03[10]:<\/span><\/section>\n

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

  (4)<\/span><\/p>\n

\u5176\u4e2d\u5c3a\u5ea6S0<\/sub>\u7531\u5e73\u5747\u5206\u652f\u6bd4\u03bc\u786e\u5b9a\u3002<\/span><\/section>\n

<\/span><\/section>\n
 \uff08<\/span>5<\/span>\uff09<\/span><\/section>\n

<\/section>\n
\u5f53\u5206\u652f\u6bd4\u03bc\u7b49\u4e8e1\u65f6\uff0c\u8be5\u8fc7\u7a0b\u4e3a\u4e34\u754c\u8fc7\u7a0b\u3002\u56e0\u4e3a\u5f53\u03bc\u63a5\u8fd11\u65f6\uff0c\u5c3a\u5ea6S0<\/sub>\u6309\u7167S0<\/sub>~(1-\u03bc)-2<\/sup><\/span>\u53d1\u6563\u3002\u53c2\u89c1\u7b49\u5f0f\uff084\uff09\uff0c\u8fd9\u610f\u5473\u7740\u4e34\u754c\u5206\u652f\u8fc7\u7a0b\u53d1\u751f\u96ea\u5d29\u7684\u6982\u7387\u5206\u5e03\u75313\/2\u6307\u6570\u7684\u5e42\u5f8b\u63cf\u8ff0\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n
\u56fe\u8868 1<\/span><\/section>\n

<\/span><\/section>\n
\u4e00\u4e2a\u5206\u652f\u8fc7\u7a0b\u7684\u5b9e\u73b0\u3002\u6bcf\u4e2a\u8282\u70b9\u4ee5\u76f8\u540c\u7684\u72ec\u7acb\u6982\u7387pk<\/sub>\u4ea7\u751fk\u4e2a\u540e\u4ee3\uff08k = 0\uff0c1\uff0c2\uff0c…\uff09\u3002\u65f6\u95f4\u4ee5\u4e16\u4ee3t\u4e3a\u5355\u4f4d\u8ba1\u7b97\uff0c\u6811\u7684\u6f14\u5316\u6216\u96ea\u5d29\u7531n\uff08t\uff09\u8868\u793a\uff0cn\uff08t\uff09\u662f\u7b2ct\u4ee3\u7684\u8282\u70b9\u6570<\/span>\uff08\u89c1\u4e0a\u56fe\uff09<\/span>\u3002\u96ea\u5d29\u7684\u6301\u7eed\u65f6\u95f4T\u662f\u4ece\u7b2ct = 0\u4ee3\u5230n(t)\uff1e0\u7684\u6700\u540e\u4e00\u4ee3\uff0c\u5982\u56fe\u4e2dT= 6\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u96ea\u5d29\u7684\u6301\u7eed\u65f6\u95f4\u7531\u603b\u4ee3\u6570T<\/span>\uff08\u76f4\u5230\u6ca1\u6709\u6839\u8282\u70b9\u7684\u65b0\u540e\u4ee3\u4ea7\u751f\u4e3a\u6b62\uff09<\/span>\u7ed9\u51fa\uff0c\u53c2\u89c1\u56fe1\u3002\u5f53\u5206\u652f\u6bd4\u8fbe\u5230\u4e34\u754c\u503c\u03bc = 1\u65f6\uff0c\u6301\u7eed\u65f6\u95f4\u7684\u5206\u5e03\u4e5f\u53d8\u6210\u5e42\u5f8b\uff0cP(T)~T-2<\/sup><\/span>\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4e3a\u4ec0\u4e48\u4e0d\u76f8\u5173\u4e8b\u4ef6\u80fd\u4ea7\u751f\u65e0\u6807\u5ea6\u5e42\u5f8b\u5206\u5e03\u3002\u56e0\u4e3a\u6839\u521d\u59cb\u5316\u540e\uff0c\u4ee3\u9645t\u4e2d\u8282\u70b9\u6570\u7684\u53d8\u91cfn\uff08t\uff09\u662f\u76f8\u5173\u7684\u3002\u5c3d\u7ba1\u5404\u8282\u70b9\u4ea7\u751f\u540e\u4ee3\u72ec\u7acb\uff0c\u4f46\u7b2ct+ 1\u4ee3\u7684\u8282\u70b9\u6570\u663e\u7136\u4e0e\u4e0a\u4e00\u4ee3\u7684\u8282\u70b9\u6570n\uff08t\uff09\u76f8\u5173\u3002\u5982\u679c\u5728\u7b2ct\u4ee3\u4e2d\u6709\u8bb8\u591a\u8282\u70b9\uff0c\u5373n\uff08t\uff09\u8f83\u5927\uff0c\u5219\u4e0en\uff08t\uff09\u8f83\u5c0f\u7684\u60c5\u51b5\u76f8\u6bd4\uff0c\u7b2ct + 1\u4ee3\u4e2d\u7684\u8282\u70b9\u6570\u4e5f\u66f4\u53ef\u80fd\u8f83\u5927\u3002\u4f46\u8fd9\u79cd\u76f8\u5173\u6027\u5e76\u4e0d\u662f\u5f88\u6df1\u523b\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u968f\u673a\u6e38\u8d70\u4fe1\u53f7f(t)\u7684\u60c5\u51b5\u7c7b\u4f3c\u3002\u5982\u679cf(t+1)= f(t)+\u0394t\uff0c\u5176\u4e2d\u0394t\u662f\u76f8\u540c\u5206\u5e03\u91cc\u53d6\u5f97\u7684\u72ec\u7acb\u968f\u673a\u6570\uff0c\u5219f(t+1)-f(t)\u7684\u53d8\u5316\u662f\u72ec\u7acb\u7684\u968f\u673a\u6570\uff0c\u4f46\u4fe1\u53f7f(t)\u4ecd\u7136\u5177\u6709\u5e42\u5f8b\u7279\u5f81\u3002\u4f8b\u5982\uff0c\u8003\u8651\u7b2c\u4e00\u6b21\u8fd4\u56de\u4e58\u4ee5T\u7684\u5206\u5e03\u3002\u7b2c\u4e00\u6b21\u8fd4\u56de\u65f6\u95f4\u662ff(t+T)\u4e4b\u524d\u7684\u65f6\u95f4T\uff0c\u5047\u5b9a\u7b2c\u4e00\u6b21\u8fd4\u56de\u503cf(t)\u7684\u65f6\u95f4\u4e3at\u3002\u8fd9\u79cd\u5206\u5e03\u9075\u5faa\u5e42\u5f8bT-3\/2<\/sup><\/span>\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5728\u6982\u62ec\u4e86\u4e0d\u76f8\u5173\u7684\u968f\u673a\u8fc7\u7a0b\u53ef\u4ee5\u4ea7\u751f\u96ea\u5d29\u7684\u5e42\u5f8b\u5206\u5e03\u4e4b\u540e\uff0c\u66f4\u91cd\u8981\u7684\u95ee\u9898\u662f\u521a\u521a\u7684\u8ba8\u8bba\u4e0e\u5927\u8111\u662f\u5426\u8868\u73b0\u51fa\u4e34\u754c\u884c\u4e3a\u6709\u591a\u5927\u7684\u76f8\u5173\u6027\uff0c\u66f4\u5177\u4f53\u5730\u8bf4\uff0c\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u4e0e\u5927\u8111\u52a8\u529b\u5b66\u6709\u591a\u76f8\u5173\u6027\uff1f\u4ee5\u53ca\u5982\u4f55\u76f8\u5173\uff1f\u6211\u4eec\u5148\u56de\u987e\u4e00\u4e0b\uff0c\u5df2\u6709\u7814\u7a76\u53d1\u73b0\uff1a\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0a\u89c2\u5bdf\u5230\u7684\u5927\u8111\u795e\u7ecf\u5143\u6d3b\u52a8\u96ea\u5d29\u5448\u6307\u6570\u4e3a3\/2\u548c2\u7684\u5e42\u5f8b\u5206\u5e03\u3002\u4f17\u6240\u5468\u77e5\uff0c\u5728\u6570\u767e\u4e2a\u795e\u7ecf\u5143\u96c6\u4f53\u653e\u7535\u4ea7\u751f\u7684\u5c40\u90e8\u573a\u7535\u4f4d\u4e0a\uff0cBeggs\u548cPlenz [11]\u7528\u529f\u80fd\u6027\u78c1\u5171\u632f\u6210\u50cf<\/span>\uff08fMRI\uff09<\/span>\u68c0\u6d4b\u7684\u96ea\u5d29\u5206\u5e03\u5448\u6307\u6570\u4e3a3\/2\u548c2\u7684\u5e42\u5f8b\u5206\u5e03\uff0cChialvo\u53ca\u5176\u5408\u4f5c\u8005\u4e5f\u89c2\u5bdf\u5230\u4e86\u96ea\u5d29\u5e42\u5f8b\u5206\u5e03\u76843\/2\u6307\u6570\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u7136\u800c\uff0c\u6211\u4eec\u5e94\u8be5\u8bb0\u4f4f\uff0c\u7cbe\u786e\u786e\u5b9a\u6307\u6570\u5f88\u56f0\u96be\uff0c\u73b0\u5728\u6709\u7814\u7a76\u5458[13]\u5df2\u7ecf\u63d0\u51fa\u4e86\u7814\u7a76\u5e42\u5f8b\u5206\u5e03\u884c\u4e3a\u7684\u66ff\u4ee3\u65b9\u6848\u3002\u4e0d\u8fc7\u6211\u4eec\u5728\u8fd9\u91cc\u7684\u91cd\u70b9\u7565\u6709\u4e0d\u540c\uff0c\u6211\u4eec\u8981\u7814\u7a76\uff1a\u6362\u8a00\u4e4b\uff0c\u5728\u957f\u7a0b\u76f8\u5173\u6027\u65b9\u9762\uff0c\u5373\u4fbf\u662f\u4ec5\u4ec5\u662f\u8fd1\u4f3c\u5e42\u5f8b\u7684\u884c\u4e3a\u4e5f\u4ecd\u7136\u6709\u8da3\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5373\u4f7f\u5728\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u7684\u6846\u67b6\u5185\uff0c\u8fd9\u4e9b\u6307\u6570\u7684\u51c6\u786e\u503c\u4ee5\u53ca\u5b83\u4eec\u5982\u4f55\u4f9d\u8d56\u4e8e\u5927\u8111\u6d3b\u52a8\u7684\u7ec6\u8282\u4e5f\u4e00\u76f4\u662f\u8be6\u7ec6\u8ba8\u8bba\u7684\u7126\u70b9\uff0c\u53c2\u89c1[14]\u53ca\u5176\u53c2\u8003\u6587\u732e\u3002\u8fd9\u91cc\u6211\u4eec\u53ea\u60f3\u5f3a\u8c03\uff0c\u867d\u7136\u5355\u4e2a\u795e\u7ecf\u5143\u96ea\u5d29\u53ef\u80fd\u8868\u73b0\u51fa\u5206\u652f\u6bd4\u7b49\u4e8e1\u7684\u4e0d\u76f8\u5173\u5206\u652f\u8fc7\u7a0b\u7684\u6307\u6570\u7279\u5f81\uff0c\u4f46\u96ea\u5d29\u4e4b\u95f4\u7684\u7b49\u5f85\u65f6\u95f4\u5206\u5e03\u8868\u660e\u6bcf\u4e2a\u96ea\u5d29\u7684\u5f00\u59cb\u662f\u76f8\u5173\u7684\u3002\u4f17\u6240\u5468\u77e5\uff0c\u5982\u679c\u795e\u7ecf\u5143\u5728\u6bcf\u4e2a\u65f6\u95f4\u5355\u4f4d\u5185\u4ee5\u6052\u5b9a\u7684\u6982\u7387\u53d1\u751f\u96ea\u5d29\uff0c\u5373\u4e3a\u6cca\u677e\u8fc7\u7a0b\uff0c\u90a3\u4e48\u96ea\u5d29\u4e4b\u95f4\u7684\u65f6\u95f4\u5c06\u6210\u6307\u6570\u5206\u5e03\u3002\u5bf9\u6bd4\u5206\u6790\u8868\u660e\uff0c\u7b49\u5f85\u65f6\u95f4\u670d\u4ece\u5e42\u5f8b\u5206\u5e03[14\uff0c15]\u3002[16]\u4ece\u529f\u80fd\u6027\u78c1\u5171\u632f\u6210\u50cf\u4e2d\u63d0\u53d6\u7684\u7a7a\u95f4\u548c\u65f6\u95f4\u76f8\u5173\u6027\u8865\u5145\u4e86\u76f8\u5173\u8111\u6d3b\u52a8\u7684\u6307\u6807\uff0c\u5e76\u89c2\u5bdf\u5230\u7a7a\u95f4\u5206\u79bb\u51fd\u6570\u7684\u5e42\u5f8b\u8870\u51cf\u4ee5\u53ca1\/f\u65f6\u95f4\u529f\u7387\u8c31\uff0c\u8868\u660e\u65f6\u95f4\u76f8\u5173\u6027\u4e3a\u5bf9\u6570\u8870\u51cf\u3002\u56e0\u6b64\uff0c\u901a\u8fc7\u76f8\u5173\u4e34\u754c\u72b6\u6001\u4e4b\u95f4\u7684\u81ea\u7ec4\u7ec7\u8fc7\u7a0b\uff0c\u66f4\u597d\u5730\u7406\u89e3\u7cfb\u7edf\u7684\u5404\u4e2a\u65b9\u9762\uff0c\u786e\u5b9e\u4ecd\u5177\u4ef7\u503c\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5728\u4e0b\u4e00\u8282\u5f00\u59cb\u8ba8\u8bba\u4e4b\u524d\uff0c\u6211\u4eec\u8fd8\u8981\u8bf4\u660e\u53e6\u4e00\u4e2a\u5173\u4e8e\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u96ea\u5d29\u52a8\u529b\u5b66\u76f8\u5173\u6027\u7684\u8ff9\u8c61\u3002De Arcangelis\u53ca\u5176\u5408\u4f5c\u8005\u5728\u4e00\u7cfb\u5217\u5de5\u4f5c\u4e2d\u53d1\u5c55\u4e86\u53d7\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u542f\u53d1\u7684\u6a21\u578b[17]\uff0c\u5f00\u53d1\u8fd9\u4e9b\u6a21\u578b\u662f\u4e3a\u4e86\u5206\u6790\u6291\u5236[14\u300115]\u3001\u6a21\u5757\u5316\u7ed3\u6784[18]\u3001\u7a81\u89e6\u53ef\u5851\u6027\u7684\u7406\u8bba[19]\u7684\u91cd\u8981\u6027\uff0c\u751a\u81f3\u89e3\u51b3\u4e86\u96ea\u5d29\u52a8\u529b\u5b66\u5982\u4f55\u80fd\u591f\u652f\u6301\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u6a21\u5f0f\u8bc6\u522b[20]\u3002\u5927\u91cf\u5de5\u4f5c\u8868\u660e\uff0c\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u542f\u53d1\u7684\u5efa\u6a21\u548c\u5206\u6790\u65b9\u6cd5\u5728\u8ba8\u8bba\u975e\u4e34\u754c\u6027\u95ee\u9898\u65f6\u4e5f\u5f88\u6709\u610f\u4e49\u3002<\/span><\/section>\n

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

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

\n
\n
\n
\n
\n

<\/section>\n

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

2. \u7206\u53d1\u52a8\u529b\u5b66\u53ca\u5176\u76f8\u5173\u6027<\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n
 <\/span><\/section>\n
\u73b0\u5728\u6211\u4eec\u8f6c\u800c\u8ba8\u8bba\u65b0\u95ee\u9898\uff1a\u4e34\u754c\u6001\u7684\u81ea\u7ec4\u7ec7\u662f\u600e\u6837\u53d1\u751f\u7684\uff0c\u4ee5\u53ca\u4e0d\u540c\u7cfb\u7edf\u548c\u6a21\u578b\u4e0a\u7684\u4e34\u754c\u6001\u81ea\u7ec4\u7ec7\u6709\u4f55\u76f8\u540c\u70b9\u3002\u7406\u89e3\u4e0a\u8ff0\u95ee\u9898\uff0c\u4f1a\u8ba9\u6211\u4eec\u53d1\u73b0\uff0c\u5373\u4f7f\u6ca1\u6709\u5b8c\u7f8e\u8c03\u6574\u5230\u5e73\u8861\u7684\u4e34\u754c\u72b6\u6001\uff0c\u4f46\u4ece\u4e8b\u4ef6\u5206\u5e03\u7684\u5c3a\u5ea6\u6765\u5224\u65ad\uff0c\u7edf\u8ba1\u529b\u5b66\u4ecd\u7136\u6709\u6548\uff0c\u6709\u8da3\u7684\u957f\u7a0b\u76f8\u5173\u6027\u4ecd\u7136\u91cd\u8981\u3001\u5e76\u4e14\u5728\u64cd\u4f5c\u4e0a\u662f\u53ef\u5f97\u7684\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u6211\u4eec\u5c06\u8be6\u7ec6\u4ecb\u7ecdChialvo\u53ca\u5176\u5408\u4f5c\u8005\u7684\u89c2\u5bdf\u7ed3\u679c\uff1a\u901a\u8fc7\u529f\u80fd\u78c1\u5171\u632f\u6210\u50cf[12\uff0c21]\u76d1\u6d4b\u7684\u5927\u8111\u6d3b\u52a8\u7206\u53d1\u7684\u65f6\u7a7a\u7edf\u8ba1\u4e0e\u5927\u6c14\u964d\u6c34\u6d3b\u52a8[22]\u5177\u6709\u663e\u8457\u7684\u5171\u540c\u6027\u3002\u800c\u4e14\uff0c\u5927\u8111\u6d3b\u52a8\u548c\u964d\u6c34\u91cf\u7684\u7edf\u8ba1\u6570\u636e\u4e0e\u68ee\u6797\u706b\u707e\u6a21\u578b<\/span>\uff08FFM\uff09<\/span>[24]\u7684\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u975e\u5e38\u76f8\u4f3c[23]\u3002<\/span><\/section>\n

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

\u7b80\u5355\u4ecb\u7ecd\u4e00\u4e0b\u68ee\u6797\u706b\u707e\u6a21\u578b\u3002\u6a21\u578b\u7684\u52a8\u529b\u5b66\u53ef\u4ee5\u5f62\u8c61\u5730\u8868\u793a\u4e3a\u67d0\u79cd\u6d3b\u52a8\u5728\u4eba\u7fa4\u4e2d\u7684\u4f20\u64ad\u3002\u8be5\u6a21\u578b\u8003\u8651\u4e86d\u7ef4\u7684\u8d85\u7acb\u65b9\u6676\u683c\uff0c\u8fd9\u91cc\u6211\u4eec\u53ea\u8ba8\u8bbad = 2\u7684\u7ed3\u679c\uff0c\u5e76\u4e14\u4f7f\u7528\u542b\u6709N=L2<\/sup><\/span>\u4e2a\u683c\u70b9\u7684\u5c3a\u5bf8\u4e3aL\u7684\u6b63\u65b9\u4f53\u6676\u683c\u3002\u6bcf\u4e2a\u4f4d\u7f6e\u53ef\u4ee5\u6709\u4e09\u79cd\u72b6\u6001\uff1a\u6ca1\u6709\u6811E\u3001\u5305\u542b\u6811T\u6216\u5305\u542b\u7740\u706b\u7684\u6811F\u3002\u57fa\u672c\u7684\u6f14\u5316\u8fc7\u7a0b\u4e3a\uff1a<\/span><\/p>\n

1.\u9009\u62e9\u4e00\u5757\u7a7a\u5730\uff1b<\/span><\/p>\n

2.\u4ee5p\u7684\u6982\u7387\u79cd\u4e00\u68f5\u6811\uff1aE\u2192T\uff1b<\/span><\/p>\n

3.\u968f\u673a\u9009\u62e9\u4e00\u68f5\u6811\u5e76\u70b9\u71c3\u5b83\uff0c\u6bd4\u5982\u4ee5f\u7684\u6982\u7387\uff1aT\u2192F\uff1b<\/span><\/p>\n

4.\u4e0b\u4e00\u65f6\u523b\uff0c\u6b63\u5728\u71c3\u70e7\u7684\u6811\u7684\u90bb\u6811\u4e5f\u70e7\u8d77\u6765\uff1aT\u2192F\uff1b<\/span><\/p>\n

5.\u4e0b\u4e00\u65f6\u523b\uff0c\u706b\u707e\u73b0\u573a\u5316\u4e3a\u7070\u70ec\uff1aF\u2192E\u3002<\/span><\/section>\n

<\/section>\n
\u8be5\u6a21\u578b\u5df2\u88ab\u5e7f\u6cdb\u7814\u7a76\uff0c\u8fd1\u671f\u7684\u6a21\u62df\u7814\u7a76\u53ef\u4ee5\u53c2\u89c1[25]\u53ca\u5176\u53c2\u8003\u6587\u732e\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5f53f\u53d6\u6781\u9650f<<p\u65f6\uff0c\u5373\u5916\u90e8\u70b9\u706b\u975e\u5e38\u7f55\u89c1\u65f6\u3002\u5728\u8fd9\u4e2a\u6781\u9650\u4e2d\uff0c\u52a8\u529b\u5b66\u7684\u663e\u8457\u7279\u5f81\u5728\u4e8e\u5f62\u6210\u8fde\u63a5\u7c07\u3002\u7531\u4e8e\u51e0\u4e4e\u6ca1\u6709\u5916\u754c\u70b9\u706b\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u8ba4\u4e3a\uff0c\u5728\u5916\u90e8\u70b9\u706b\u6240\u4ee3\u8868\u7684\u5916\u90e8\u80fd\u91cf\u8f93\u5165\u7684\u65f6\u95f4\u5c3a\u5ea6\u4e0a\uff0c\u8fde\u63a5\u7c07\u662f\u88ab\u77ac\u95f4\u70e7\u6bc1\u7684\u3002\u6a21\u62df\u7ed3\u679c\u8868\u660e\uff0c\u88ab\u70e7\u6bc1\u7684\u56e2\u7c07\u7684\u5c3a\u5bf8\u5206\u5e03\u8fd1\u4f3c\u670d\u4ece\u5e42\u5f8b\u5206\u5e03\u3002\u4f46\u662f\uff0c\u6a21\u578b\u4e2d\u7684\u4e34\u754c\u6027\u548c\u89c4\u6a21\u4e0d\u53d8\u6027\u4e5f\u5e76\u4e0d\u5bfb\u5e38[26\uff0c27]\u3002\u4f8b\u5982\uff0cGrassberger [26]\u63d0\u51fa\uff0c\u6bd4\u503c\u03b8 = p\/f\u8db3\u591f\u5927\u65f6\uff0c\u53ea\u8981\u7cfb\u7edf\u5927\u5c0f\u8db3\u591f\u5927\uff0c\u5927\u5230\u53ef\u4ee5\u5bb9\u7eb3\u751f\u6210\u7684\u5de8\u5927\u6811\u7c07\uff0c\u5c31\u53ef\u80fd\u4f1a\u8868\u73b0\u51fa\u6e17\u6d41\u4e2d\u7684\u7f29\u653e\u3002\u8fd9\u53ef\u80fd\u662f\u771f\u7684\uff0c\u4f46[28]\u7684\u5206\u6790\u8868\u660e\uff0c\u53ea\u6709\u5f53\u03b8\uff1e10<\/span>40<\/sup><\/span><\/span>\u65f6\u624d\u80fd\u89c2\u5bdf\u5230\u8fd9\u79cd\u7f29\u653e\uff0c\u800c\u4e14\u4e3a\u4e86\u907f\u514d\u6a21\u62df\u53d7\u5230\u7cfb\u7edf\u5927\u5c0f\u7684\u5f71\u54cd\uff0c\u8fd8\u9700\u8981\u8fbe\u5230\u96be\u4ee5\u8fbe\u5230\u7684\u7cfb\u7edf\u5927\u5c0f\uff0c\u5373\u7ebf\u6027\u5927\u5c0f\u4e3aL~1040<\/sup><\/span> [25]\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u6211\u4eec\u7531\u6b64\u5f97\u51fa\u7ed3\u8bba\uff0c\u867d\u7136\u771f\u6b63\u7684\u6e10\u8fd1<\/span>\uff08\u7cfb\u7edf\u89c4\u6a21\u8d8b\u4e8e\u65e0\u7a77\u5927\uff09<\/span>\u884c\u4e3a\u76ee\u524d\u8fd8\u65e0\u6cd5\u5b9e\u73b0\uff0c\u4f46\u5fc5\u987b\u6307\u51fa\uff0c\u901a\u8fc7\u4eff\u771f\u7814\u7a76\u7cfb\u7edf\u89c4\u6a21\u7684\u6a21\u578b\u8868\u73b0\u786e\u5b9e\u6709\u6548\uff0c\u53ef\u4ee5\u6df1\u5165\u4e86\u89e3\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u4e0e\u771f\u5b9e\u7684\u7cfb\u7edf\u7684\u76f8\u5173\u6027\u3002<\/span><\/section>\n

<\/span><\/section>\n
Peters\u548cNeelin [22]\u66fe\u89c2\u5bdf\u5230\uff0c\u5f53\u7ed8\u5236\u964d\u6c34\u91cf\u4e0e\u5927\u6c14\u6e7f\u5ea6\u56fe\u65f6\uff0c\u5728\u72ed\u7a84\u7684\u6e7f\u5ea6\u8303\u56f4\u5185\u53ef\u4ee5\u770b\u5230\u4e00\u4e2a\u6025\u5267\u7684\u5f00\u59cb\u3002\u56fe2\u663e\u793a\u4e86\u964d\u96e8\u3001\u5927\u8111\u6d3b\u52a8\u548c\u68ee\u6797\u706b\u707e\u6a21\u578b\u7684\u8868\u73b0\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n
\u56fe\u8868 2<\/span><\/section>\n

(a) \u4e00\u822c\u6027\u8349\u56fe\uff0c\u7c7b\u4f3c\u4e8e\u5e73\u8861\u76f8\u53d8\u7684\u4e34\u754c\u72b6\u6001\u3002\u8fd9\u4e09\u6761\u66f2\u7ebf\uff1a\u5b9e\u7ebf\u8868\u793a\u5e8f\u53c2\u91cf\uff0c\u957f\u865a\u7ebf\u8868\u793a\u9a7b\u7559\u65f6\u95f4\uff0c\u865a\u7ebf\u8868\u793a\u65b9\u5dee\uff08\u5728\u5e73\u8861\u7cfb\u7edf\u4e2d\u76f8\u5f53\u4e8e\u78c1\u5316\u7387\uff09\u3002\u5728\u4e00\u4e2a\u4e34\u754c\u5e73\u8861\u76f8\u53d8\uff08\u5982\u63d2\u56fe\u6240\u793a\uff09\u4e2d\uff0c\u5982\u4f0a\u8f9b\u6a21\u578b\u548c\u78c1\u6027\u7cfb\u7edf\uff0c\u5e8f\u53c2\u6570\u5728\u76f8\u53d8\u7684\u4e00\u4fa7\u4e25\u683c\u4e3a\u96f6\uff0c\u7136\u540e\u5728\u4e00\u4e2a\u5c16\u9510\u7684\u503c\u5904\u53d8\u4e3a\u975e\u96f6\uff0c\u4e34\u754c\u503c\u4e3apc<\/sub>\uff0c\u78c1\u5316\u7387\u5728p<\/span>c<\/sub>\u5904\u53d1\u6563\u3002\u56e0\u4e3a\u63a7\u5236\u53c2\u6570\u03c1\u662f\u5916\u751f\u7684\uff0c\u6240\u4ee5\u65e0\u9700\u8003\u8651\u5e73\u8861\u7cfb\u7edf\u4e2d\u7684\u9a7b\u7559\u65f6\u95f4\u3002<\/span><\/p>\n

(b)\u964d\u6c34\u91cf\uff0c\u53c2\u8003[22]\u4e2d\u56fe1\u548c\u56fe3\u7ed8\u5236\u3002x\u8f74\u8868\u793a\u5927\u6c14\u4e2d\u7684\u84b8\u6c7d\u542b\u91cf\u3002\u5b9e\u7ebf\u8868\u793a\u5e8f\u53c2\u91cf\uff0c\u5982\u964d\u6c34\u91cf\u3002\u865a\u7ebf\u662f\u65b9\u5dee\uff0c\u957f\u865a\u7ebf\u662f\u89c2\u5bdf\u5230\u7279\u5b9a\u503cw\u7684\u6b21\u6570\uff0c\u5373\u9a7b\u7559\u65f6\u95f4\u3002<\/span><\/p>\n

(c)\u5927\u8111\u6d3b\u52a8\uff0c\u53c2\u8003[12]\u4e2d\u56fe3\uff08E\uff09\u7ed8\u5236\u3002x\u8f74\u8868\u793a\u6d3b\u8dc3\u4f53\u7d20\u7684\u6570\u91cf\u3002\u5b9e\u7ebf\u8868\u793a\u5e8f\u53c2\u91cf\uff0c\u5373\u5f52\u4e00\u5316\u4e3a\u6d3b\u8dc3\u4f53\u7d20\u6570\u91cf\u7684\u6700\u5927\u805a\u7c7b\u7684\u5e73\u5747\u503c\u3002\u865a\u7ebf\u8868\u793a\u65b9\u5dee\uff0c\u957f\u865a\u7ebf\u8868\u793a\u5f52\u4e00\u5316\u7684\u9a7b\u7559\u65f6\u95f4\u3002<\/span><\/p>\n

(d)\u68ee\u6797\u706b\u707e\u6a21\u578b\uff0c\u53c2\u8003[23]\u4e2d\u7684\u56fe1\u7ed8\u5236\u3002x\u8f74\u8868\u793a\u6811\u6240\u5360\u636e\u7684\u4f4d\u7f6e\u6570\u3002\u5b9e\u7ebf\u8868\u793a\u6709\u5e8f\u53c2\u6570\uff0c\u5373\u5f52\u4e00\u5316\u4e3a\u6811\u4f4d\u70b9\u7684\u6570\u76ee\u7684\u6700\u5927\u7c07\u7684\u5e73\u5747\u503c\u3002\u865a\u7ebf\u8868\u793a\u65b9\u5dee\uff0c\u957f\u865a\u7ebf\u8868\u793a\u5f52\u4e00\u5316\u7684\u9a7b\u7559\u65f6\u95f4\u3002<\/span><\/p>\n


<\/span><\/section>\n
\u8be5\u56fe\u7efc\u5408\u4e86\u6587\u732e\u4e2d\u7684\u56db\u5e45\u56fe\u3002\u9996\u5148\uff0c\u53c2\u8003\u6587\u732e[22]\u4e2d\u7684\u56fe1\uff0c\u8be5\u56fe\u7ed8\u5236\u4e86\u964d\u6c34\u91cf\u53ca\u5176\u65b9\u5dee\u4e0e\u5927\u6c14\u4e2d\u84b8\u6c7d\u91cf\u7684\u51fd\u6570\u5173\u7cfb\u3002\u5927\u6c14\u5728\u67d0\u4e00\u84b8\u6c7d\u6c34\u5e73\u4e0a\u6240\u82b1\u8d39\u7684\u65f6\u95f4\u5982[22]\u4e2d\u7684\u56fe3\u6240\u793a\uff0c\u8fd9\u4e2a\u65f6\u95f4\u79f0\u4e3a\u9a7b\u7559\u65f6\u95f4\u3002\u5176\u6b21\uff0c[12]\u4e2d\u7684\u56fe3\uff08E\uff09\u663e\u793a\u4e86\u6d3b\u6027\u529f\u80fd\u6027\u78c1\u5171\u632f\u6210\u50cf\u4f53\u7d20\u7c07\u7684\u6700\u5927\u5c3a\u5bf8<\/span>\uff08\u9ad8\u4e8e\u7279\u5b9a\u9608\u503c\uff09<\/span>\u7684\u5f52\u4e00\u5316\u5927\u5c0f\uff0c\u4e0e\u6d3b\u6027\u4f53\u7d20\u603b\u6570\u3001\u53ca\u5176\u65b9\u5dee\u548c\u9a7b\u7559\u65f6\u95f4\u7684\u51fd\u6570\u3002\u6700\u540e\uff0c[23]\u7684\u56fe1\u4e2d\u7ed9\u51fa\u4e86\u7c7b\u4f3c\u7684\u5206\u6790\uff0c\u5305\u542b\u6700\u5927\u6811\u7c07\u3001\u5176\u65b9\u5dee\u548c\u9a7b\u7559\u65f6\u95f4\u4e0e\u6811\u7684\u6570\u91cf<\/span>\uff08\u88ab\u8ba4\u4e3a\u662f\u80fd\u591f\u4ea7\u751f\u6d3b\u6027\u7684\u573a\u5730\uff09<\/span>\u7684\u51fd\u6570\u5173\u7cfb\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5728\u8fd9\u4e09\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u90fd\u89c2\u5bdf\u5230\u6240\u8c13\u7684\u5e8f\u53c2\u91cf\uff0c\u5373\u533a\u522b\u7cfb\u7edf\u76f8\u5bf9\u4e8e\u4e34\u754c\u72b6\u6001\u7684\u53c2\u91cf\uff0c\u5728\u63a7\u5236\u53c2\u91cf\u7684\u4e00\u4e2a\u76f8\u5bf9\u72ed\u7a84\u7684\u53d6\u503c\u8303\u56f4\u5185\uff0c\u4ece\u5f88\u4f4e\u7684\u503c\u5f00\u59cb\u4e0a\u5347\u3002\u4e0a\u8ff0\u4e09\u79cd\u60c5\u51b5\u7684\u5e8f\u53c2\u6570\u5206\u522b\u4e3a\uff1a\u964d\u6c34\u91cf\u3001\u6d3b\u6027\u4f53\u7d20\u8fde\u901a\u7c07\u7684\u5927\u5c0f\u548c\u70e7\u6bc1\u7c07\u7684\u5927\u5c0f\u3002\u4e09\u79cd\u60c5\u51b5\u7684\u63a7\u5236\u53c2\u6570\u5206\u522b\u4e3a\uff1a\u5927\u6c14\u4e2d\u7684\u84b8\u6c7d\u91cf\u3001\u6d3b\u6027\u4f53\u7d20\u7684\u6570\u91cf\u548c\u6811\u6728\u7684\u6570\u91cf\u3002\u5728\u8fd9\u4e09\u79cd\u60c5\u51b5\u4e0b\uff0c\u5f53\u63a7\u5236\u53c2\u6570\u5728\u5e8f\u53c2\u91cf\u51fa\u73b0\u548c\u65b9\u5dee\u8fbe\u5cf0\u7684\u533a\u57df\u7684\u4e2d\u90e8\u9644\u8fd1\u53d6\u67d0\u4e2a\u503c\u65f6\uff0c\u89c2\u5bdf\u5230\u4e8b\u4ef6\u5206\u5e03<\/span>\uff08\u5206\u522b\u4e3a\u964d\u6c34\u4e8b\u4ef6\u7684\u6570\u76ee\u3001\u6700\u5927\u6d3b\u8dc3\u4f53\u7d20\u7c07\u7684\u5927\u5c0f\u3001\u6700\u5927\u70e7\u6bc1\u6811\u7c07\u7684\u5927\u5c0f\uff09<\/span>\u8fd1\u4f3c\u5e42\u5f8b\u5206\u5e03\u3002\u8fd9\u610f\u5473\u7740\uff0c\u5728\u8fd9\u4e09\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u90fd\u89c2\u5bdf\u5230\u4e86\u4e34\u754c\u5e73\u8861\u76f8\u53d8\u4e2d\u7684\u4e00\u4e2a\u6025\u5267\u8f6c\u53d8\u7684\u6269\u5c55\u7248\u672c\uff0c\u53c2\u89c1\u56fe2\u4e2d\u7684\u63d2\u56fe\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u6211\u4eec\u8981\u5f3a\u8c03\u4e24\u70b9\u3002\u7b2c\u4e00\uff0c\u8fd9\u4e09\u4e2a\u5b8c\u5168\u4e0d\u540c\u7684\u7cfb\u7edf\u5728\u5982\u4f55\u81ea\u7ec4\u7ec7\u7684\u65b9\u9762\u60ca\u4eba\u7684\u76f8\u4f3c\uff0c\u5b83\u4eec\u662f\u5982\u4f55\u7ec4\u7ec7\u81ea\u5df1\u7684\uff0c\u6240\u4ee5\u5b83\u4eec\u9891\u7e41\u51fa\u73b0\u5728\u8868\u73b0\u51fa\u6f5c\u5728\u7684\u8fd1\u4e34\u754c\u8f6c\u53d8\u7684\u533a\u57df\u4e2d\u3002\u7b2c\u4e8c\uff0c\u5c3d\u7ba1\u5927\u8111\u548c\u5927\u6c14\u90fd\u662f\u975e\u5e38\u5927\u7684\u7cfb\u7edf\uff0c\u4f46\u5b83\u4eec\u90fd\u5177\u6709\u68ee\u6797\u706b\u707e\u6a21\u578b\u7684\u6709\u9650\u5927\u5c0f\u5c5e\u6027\u3002\u8fd9\u8868\u660e\uff0c\u4e0e\u5e73\u8861\u4e34\u754c\u73b0\u8c61\u76f8\u53cd\uff0c\u6211\u4eec\u77e5\u9053\u5728\u53d1\u6563\u7cfb\u7edf\u5c3a\u5bf8\u7684\u9650\u5236\u4e0b\u7406\u89e3\u6e10\u8fd1\u884c\u4e3a\u81f3\u5173\u91cd\u8981\uff0c\u7ed3\u5408\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u7684\u96ea\u5d29\u52a8\u529b\u5b66\u8003\u8651\uff0c\u6709\u9650\u7cfb\u7edf\u7684\u5c3a\u5ea6\u8868\u73b0\u7279\u522b\u6709\u8da3\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u8fd9\u610f\u5473\u7740\uff0c\u5e94\u7528\u81ea\u7ec4\u7ec7\u5e76\u4e0d\u662f\u81ea\u7ec4\u7ec7\u5230\u4e00\u4e2a\u660e\u786e\u5b9a\u4e49\u7684\u4e34\u754c\u70b9\uff0c\u800c\u7531\u52a8\u529b\u5b66\u5c06\u81ea\u8eab\u5e26\u5230\u67d0\u4e2a\u63a5\u8fd1\u4e34\u754c\u884c\u4e3a\u7684\u533a\u57df\u7684\u8d8b\u52bf\u7ec4\u6210\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u90a3\u4e48\u95ee\u9898\u4ecd\u7136\u662f\u4ec0\u4e48\u4f7f\u8fd9\u4e2a\u533a\u57df\u8d8b\u8fd1\u67d0\u79cd\u4e34\u754c\u72b6\u6001\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u56de\u5230\u5173\u8054\u5e76\u56de\u60f3\u8d77\u5e73\u8861\u4e34\u754c\u6001\u7684\u5e42\u5f8b\u548c\u53d1\u6563\u7075\u654f\u5ea6<\/span>\uff08\u78c1\u5316\u7387\uff09<\/span>\u90fd\u662f\u957f\u7a0b\u4ee3\u6570\u5173\u8054\u7684\u7ed3\u679c\u3002\u662f\u5426\u6709\u8bc1\u636e\u8868\u660e\uff0c\u8fd9\u4e09\u4e2a\u7cfb\u7edf\u9a7b\u7559\u65f6\u95f4\u7684\u5cf0\u503c\u51fa\u73b0\u7684\u533a\u57df\u4e0e\u65b9\u7a0b\uff083\uff09\u6240\u63cf\u8ff0\u7684\u76f8\u5173\u6027\u6709\u5173\uff1f\u5173\u8054\u957f\u5ea6\u03be\u8db3\u591f\u5927\u4f7f\u5f97\u7f13\u6162\u7684\u5e42\u5f8b\u8870\u51cfr-a<\/sup><\/span>\u80fd\u591f\u57fa\u672c\u4e0a\u51b3\u5b9a\u7cfb\u7edf\u884c\u4e3a\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5927\u6c14\u7cfb\u7edf\u7684\u7ed3\u8bba\u8fd8\u672a\u53ef\u77e5\u3002[16]\u4e2d\u7528\u529f\u80fd\u78c1\u5171\u632f\u6210\u50cf\u7814\u7a76\u8840\u6c27\u4fe1\u53f7\u76f8\u5173\u6027\u8868\u660e\uff0c\u5927\u8111\u5c31\u662f\u8fd9\u79cd\u60c5\u51b5\u3002\u6700\u8fd1\u7684\u68ee\u6797\u706b\u707e\u6a21\u578b\u7814\u7a76\u8bc1\u5b9e\uff0c\u5c3d\u7ba1\u4e8b\u4ef6\u5206\u5e03\u7684\u6807\u5ea6\u4ee4\u4eba\u56f0\u60d1\uff0c\u4f46\u7a7a\u95f4\u76f8\u5173\u6027\u603b\u662f\u957f\u7a0b\u7684[28]\u3002\u5728\u8fd9\u79cd\u65b9\u6cd5\u4e2d\uff0c\u53ef\u4ee5\u8ba4\u4e3a\u5173\u8054\u957f\u5ea6\u662f\u4e00\u4e2a\u968f\u673a\u53d8\u91cf\u3002\u5bf9\u4e8e\u4e0a\u8ff0\u7cfb\u7edf\u7684\u6bcf\u4e2a\u77ac\u65f6\u6784\u578b\uff0c\u5c06\u65b9\u7a0b\uff082\uff09\u4e2d\u7684\u5173\u8054\u51fd\u6570\u62df\u5408\u4e3a\u65b9\u7a0b\uff083\uff09\u4e2d\u7684\u51fd\u6570\u5f62\u5f0f\uff0c\u4ee5\u786e\u5b9a\u63cf\u8ff0\u8be5\u7279\u5b9a\u6784\u578b\u7684\u5173\u8054\u957f\u5ea6\u03be\u3002\u8fd9\u4e00\u65b9\u6cd5\u4e0d\u540c\u4e8e\u5e73\u8861\u7cfb\u7edf\u7814\u7a76\u4e2d\u786e\u5b9a\u5173\u8054\u957f\u5ea6\u7684\u5e38\u89c1\u65b9\u6cd5\u3002\u4eff\u771f\u6cd5\u901a\u5e38\u9996\u5148\u5728\u6240\u6709\u751f\u6210\u7684\u6784\u578b\u4e0a\u5bf9\u65b9\u7a0b\uff082\uff09\u4e2d\u7684\u5173\u8054\u51fd\u6570\u6c42\u5e73\u5747\uff0c\u7136\u540e\u4ece\u5bf9\u8be5\u5e73\u5747\u51fd\u6570\u7684\u62df\u5408\u4e2d\u63d0\u53d6\u5173\u8054\u957f\u5ea6\u3002[28]\u4e2d\u53d1\u5c55\u4e86\u65b0\u65b9\u6cd5\uff0c\u8be5\u65b9\u6cd5\u5c06\u5173\u8054\u957f\u5ea6\u4f5c\u4e3a\u6bcf\u4e2a\u5355\u72ec\u6784\u578b\u7684\u7279\u5f81\uff0c\u4ee5\u91cd\u73b0\u4e24\u4e2a\u539f\u578b\u6a21\u578b\u7684\u5df2\u77e5\u5e73\u8861\u884c\u4e3a\uff0c\u5982\u4f0a\u8f9b\u6a21\u578b\u548c\u4e8c\u7ef4XY\u6a21\u578b\u3002\u66f4\u6709\u8da3\u7684\u662f\uff0c\u8be5\u65b9\u6cd5\u4e3a\u68ee\u6797\u706b\u707e\u6a21\u578b\u4e2d\u7684\u76f8\u5173\u6027\u63d0\u4f9b\u4e86\u65b0\u7684\u7406\u89e3\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5bf9\u4e8e\u68ee\u6797\u706b\u707e\u6a21\u578b\uff0c\u5f53\u53d8\u91cfSi<\/sub>=1\u65f6\u8868\u793a\u6709\u6811\uff0cS<\/span>i<\/sub>=<\/span>0\u65f6\u8868\u793a\u8be5\u4f4d\u7f6e\u4e3a\u7a7a\u3002\u5ffd\u7565\u706b\u707e\u71c3\u70e7\u70b9\uff0c\u56e0\u4e3a\u706b\u707e\u5728\u5355\u4e2a\u65f6\u95f4\u6b65\u957f\u4ee5p\u4e3a\u751f\u957f\u6982\u7387\u79fb\u9664\u8fde\u63a5\u7c07\u3002\u5f53\u6a21\u62df\u6811\u751f\u957f\u548c\u706b\u707e\u52a8\u529b\u5b66\u65f6\uff0c\u5bf9\u77ac\u65f6\u6784\u578b\u7684\u5173\u8054\u957f\u5ea6\u7684\u5206\u5e03P\uff08\u03be\uff09\u8fdb\u884c\u91c7\u6837\u3002\u6a21\u62df\u53d1\u73b0\uff0c\u5bf9\u4e8eL = 3000\u7684\u7cfb\u7edf\uff0c\u5206\u5e03P\uff08\u03be\uff09\u7528\u6709\u9650\u7cfb\u7edf\u7684\u5c3a\u5ea6\u53ef\u4ee5\u5f88\u597d\u5730\u63cf\u8ff0\uff0c\u8fd9\u610f\u5473\u7740\u5f53L\u53d8\u5316\u65f6\uff0c\u5f53\u03b8<\/span>\/L2<\/sup><\/span>\u7ed9\u51fa\u7684\u6bcf\u4e2a\u4f4d\u70b9\u7684\u6d3b\u6027\u4fdd\u6301\u4e0d\u53d8\u65f6\uff0c\u4e0d\u540cL\u503c\u7684P\uff08\u03be\uff09\u53ef\u4ee5\u574d\u7f29\u4e3a\u4e00\u4e2a\u201c\u901a\u7528\u201d\u51fd\u6570\u3002\u5bf9\u7cfb\u7edf\u5927\u5c0f\u7684\u4f9d\u8d56\u6027\u8868\u660e\uff1a\u4ece\u5206\u5e03P\uff08\u03be\uff09\u63d0\u53d6\u7684\u5e73\u5747\u5173\u8054\u957f\u5ea6\u4f9d\u8d56\u4e8e\u7cfb\u7edf\u5927\u5c0f\uff0c\u5982<\u03be<\/span>>\u221dL<\/span>1.1<\/sup><\/span>\u3002\u8fd9\u8868\u660e\uff0c\u968f\u7740L\u7684\u589e\u52a0\uff0c\u5f53\u7531\u706b\u707e\u6982\u7387f\u7ed9\u51fa\u7684\u52a8\u529b\u4e0e\u751f\u957f\u6982\u7387p\u8d8b\u4e8e\u65e0\u5173\u65f6\uff0c\u6bd4\u5982\u5f53\u5916\u751f\u52a8\u529b\u5f88\u6162\u65f6\uff0c\u7cfb\u7edf\u7684\u76f8\u5173\u6027\u4f1a\u8d8b\u4e8e\u957f\u7a0b\u3002<\/span><\/section>\n

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

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

\n
\n
\n
\n
\n

<\/section>\n

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

3. \u8ba8\u8bba\u4e0e\u603b\u7ed3<\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n
 <\/span><\/section>\n
\u6211\u4eec\u6ce8\u610f\u5230\uff0c\u9996\u6b21\u7528\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u7cbe\u786e\u8c03\u6574\u5230\u9884\u671f\u4e34\u754c\u70b9\u4f3c\u4e4e\u6ca1\u6709\u5728\u964d\u96e8\u3001\u5927\u8111\u548c\u68ee\u6797\u706b\u707e\u6a21\u578b\u4e2d\u53d1\u751f\u3002\u8fd9\u5e76\u6ca1\u6709\u8ba9\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u6846\u67b6\u53d8\u5f97\u65e0\u5173\u7d27\u8981\u3002\u76f8\u53cd\uff0c\u81ea\u7ec4\u7ec7\u73b0\u8c61\u786e\u5b9e\u53d1\u751f\u5728\u5e8f\u53c2\u91cf\u4e0a\u5347\u7684\u533a\u57df\u9644\u8fd1\u3002\u6b64\u5916\uff0c\u5bf9\u68ee\u6797\u706b\u707e\u6a21\u578b\u7684\u7814\u7a76\u8868\u660e\uff1a\u867d\u7136\u4e8b\u4ef6\u5206\u5e03\u7684\u5e42\u5f8b\u53ef\u80fd\u53ea\u662f\u8fd1\u4f3c\u7684\uff0c\u4f46\u8fd9\u4e09\u4e2a\u7cfb\u7edf\u8017\u65f6\u6700\u591a\u7684\u533a\u57df\u5374\u4e0e\u975e\u5e38\u5e7f\u5927\u7684\u7a7a\u95f4\u76f8\u5173\u6027\u4e4b\u95f4\uff0c\u76f8\u4e92\u5173\u8054\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4e0d\u540c\u7cfb\u7edf\u7684\u5171\u6709\u89c4\u5f8b\u8868\u660e\uff1a\u7531\u8d1f\u8f7d\u3001\u4f20\u64ad\u548c\u5f1b\u8c6b\u9a71\u52a8\u7684\u52a8\u529b\u5b66\u7684\u57fa\u672c\u6210\u5206\u503e\u5411\u4e8e\u7ec4\u7ec7\u6210\u63a5\u8fd1\u67d0\u79cd<\/span>\uff08\u76f8\u5173\uff09<\/span>\u6e17\u6d41\u5f00\u59cb\u7684\u6784\u578b\u3002\u7a7a\u95f4\u6269\u5c55\u7ed3\u6784\u7684\u5efa\u7acb\uff0c\u7136\u540e\u901a\u8fc7\u964d\u6c34\uff0c\u795e\u7ecf\u5143\u653e\u7535\u6216\u706b\u707e\u5728\u4e0a\u8ff0\u4e09\u79cd\u60c5\u51b5\u4e0b\u5206\u522b\u7a81\u7136\u5d29\u6e83\uff0c\u4e0d\u65ad\u5730\u5c06\u201c\u8d85\u8fc7\u4e34\u754c\u201d\u7684\u6784\u578b\u8f6c\u53d8\u4e3a\u201c\u4f4e\u4e8e\u4e34\u754c\u201d\u7684\u6784\u578b\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u68ee\u6797\u706b\u707e\u6a21\u578b\u7684\u6a21\u62df\u8868\u660e\uff1a\u5bf9\u4e8e\u53ef\u7ba1\u7406\u7684\u53c2\u6570\u72b6\u6001\uff0c\u53ef\u4f18\u5148\u8bbf\u95ee\u6784\u578b\u7684\u533a\u57df\uff0c\u6bd4\u5982\u9a7b\u7559\u65f6\u95f4\u5206\u5e03\u4e2d\u5cf0\u503c\u5468\u56f4\u7684\u533a\u57df\uff0c\u968f\u7740\u7531\u8d1f\u8f7d<\/span>\uff08\u6811\u6728\u751f\u957f\uff09<\/span>\u548c\u80fd\u91cf\u91ca\u653e\u89e6\u53d1<\/span>\uff08\u5916\u90e8\u8bf1\u5bfc\u706b\u707e\uff09<\/span>\u7ed9\u51fa\u7684\u4e24\u4e2a\u65f6\u95f4\u5c3a\u5ea6\u4e4b\u95f4\u7684\u95f4\u9694<\/span>\uff08\u5373\u03b8<\/span>=p\/f\uff09<\/span>\u7684\u589e\u52a0\u800c\u52a0\u5bbd\u3002\u68ee\u6797\u706b\u707e\u6a21\u578b\u4e2d\u9a7b\u7559\u65f6\u95f4\u7684\u5cf0\u5bbd\u8fd1\u4f3c<\/span>\u4e3a\u03c3~\u03b80.1<\/sup><\/span><\/span>\uff0c\u89c1[25]\u3002\u56e0\u6b64\uff0c\u5c06\u6a21\u578b\u63a8\u5411\u66f4\u6269\u5c55\u7684\u5e42\u5f8b\u548c\u66f4\u957f\u7684\u5173\u8054\u957f\u5ea6\u4e5f\u6269\u5927\u4e86\u8bbf\u95ee\u4e34\u754c\u6784\u578b\u548c\u4e34\u754c\u6784\u578b\u7684\u8303\u56f4\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u7ed3\u8bba\u662f\uff0c\u6d41\u5165-\u6d41\u51fa\u52a8\u529b\u5b66\u5e76\u4e0d\u80fd\u5fae\u8c03\u5230\u4e34\u754c\u70b9\uff0c\u4f46\u662f\u53ef\u4ee5\u5fae\u8c03\u5230\u6269\u5c55\u76f8\u5173\u6027\u7684\u533a\u57df\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u8fd9\u4e00\u70b9\u5728\u4e4b\u524d\u5c31\u5df2\u7ecf\u6709\u4eba\u63d0\u51fa\u8fc7\uff0c\u4f8b\u5982[13\uff0c29\uff0c30]\uff0c\u4f46\u5728\u8fd9\u91cc\u6211\u4eec\u8981\u5f3a\u8c03\u7684\u662f\uff0c\u5c3d\u7ba1\u6ca1\u6709\u8fbe\u5230\u4e25\u683c\u7684\u4e34\u754c\u6027\uff0c\u4f46\u76f8\u5173\u6027\u8db3\u591f\u5e7f\u6cdb\uff0c\u8db3\u4ee5\u4f7f\u4e09\u4e2a\u5b8c\u5168\u4e0d\u540c\u7684\u7cfb\u7edf<\/span>\uff08\u964d\u6c34\uff0c\u5927\u8111\u548c\u68ee\u6797\u706b\u707e\u6a21\u578b\uff09<\/span>\u4e2d\u7684\u6d41\u5165-\u6d41\u51fa\u52a8\u529b\u5b66\u5177\u6709\u663e\u8457\u7684\u76f8\u4f3c\u6027\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4eba\u4eec\u5e38\u5e38\u8ba4\u4e3a\uff0c\u5927\u8111\u5728\u4e34\u754c\u70b9\u6216\u5176\u9644\u8fd1\u5de5\u4f5c\u7684\u539f\u56e0\u662f\u8fd9\u79cd\u72b6\u6001\u5177\u6709\u8d85\u654f\u6027<\/span>\uff08\u8868\u73b0\u4e3a\u78c1\u5316\u7387\u7684\u53d1\u6563\uff09<\/span>\u3002\u770b\u8d77\u6765\u5f88\u5408\u7406\uff0c\u4f46\u4e3a\u4ec0\u4e48\u5927\u8111\u6ca1\u6709\u5904\u4e8e\u4e34\u754c\u72b6\u6001\u5462\uff1f\u5982Lizier\u53ca\u5176\u5408\u4f5c\u8005[31]\u6240\u8bf4\uff0c\u5927\u8111\u53ef\u80fd\u5728\u4e34\u754c\u70b9\u533a\u57df\u5185\u64cd\u4f5c\u66f4\u6709\u8ba1\u7b97\u4f18\u52bf\uff0c\u56e0\u4e3a\u5b83\u5c06\u4e9a\u4e34\u754c\u533a\u57df\u7684\u9ad8\u6570\u636e\u5b58\u50a8\u80fd\u529b\u4e0e\u8d85\u4e34\u754c\u533a\u57df\u5185\u66f4\u5feb\u7684\u4fe1\u606f\u4f20\u9012\u7ed3\u5408\u8d77\u6765\u3002\u6240\u4ee5\uff0c\u65e0\u6cd5\u7cbe\u786e\u8c03\u6574\u5230\u4e34\u754c\u72b6\u6001\u53ef\u80fd\u4e5f\u4e0d\u5931\u4e3a\u4e00\u4ef6\u597d\u4e8b\u3002<\/span><\/section>\n

<\/section>\n

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

\u53c2\u8003\u6587\u732e<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

\n
\n
\n
\n


<\/p>\n

[1] Goldenfeld N 1992 Lectures on Phase Transitions and the Renormalization Group (Boca Raton, FL: CRC Press)<\/span><\/section>\n
[2] Packard N H 1988 Adaptation Toward the Edge of Chaos (Champaign, IL: University of Illinois) Urbana-Champaign, Center for<\/span><\/section>\n
Complex Systems Research<\/span><\/section>\n
[3] Bak P, Tang C andWiesenfeld K 1987 Self-organized criticality: an explanation of the 1\/f noise Phys. Rev. Lett. 59 381\u20134<\/span><\/section>\n
[4] Barras C 2013Mind Maths; your brain teeters on the edge of chaos. NewScientist https:\/\/institutions.newscientist.com\/article\/<\/span><\/section>\n
mg21729032-100-mind-maths-your-brain-teeters-on-the-edge-of-chaos\/<\/span><\/section>\n
[5] Washington University in St 2019 Brain tunes itself to criticality, maximizing information processing: criticality is a hallmark<\/span><\/section>\n
of normally functioning neural networks in the intact brain. ScienceDaily www.sciencedaily.com\/releases\/2019\/10\/<\/span>191007113314.htm<\/span><\/section>\n
[6] Ott E 1993 Chaos in Dynamical Systems (Cambridge: Cambridge University Press)<\/span><\/section>\n
[7] May RM 1976 Simple mathematical models with very complicated dynamics Nature 261 459<\/span><\/section>\n
[8] Jensen H J 1998 Self-Organized Criticality: Emergent Complex Behaviour in Physical and Biological Systems (Cambridge: Cambridge <\/span>University Press)<\/span><\/section>\n
[9] Pruessner G 2012 Self-Organized Criticality: Theory, Models and Charaterisation (Cambridge: Cambridge University Press)<\/span><\/section>\n
[10] Harris T E 1963 The Theory of Branching Processes (Berlin: Springer)<\/span><\/section>\n
[11] Beggs J M and Plenz D 2003 Neuronal avalanches in neocortical circuits J. Neurosci. 23 11167\u201377<\/span><\/section>\n
[12] Tagliazucchi E, Balenzuela P, Fraiman D and Chialvo D R 2012 Criticality in large-scale brain fMRI dynamics unveiled by a novel<\/span><\/section>\n
point process analysis Front. Physiol. 3 1\u201312<\/span><\/section>\n
[13] Wilting J and Priesemann V 2019 25 years of criticality in neuroscience\u2014established results, open controversies, novel concepts <\/span>Curr. Opin. Neurobiol. 58 105\u201311<\/span><\/section>\n
[14] Lombardi F, Herrmann H J and De Arcangelis L 2017 Balance of excitation and inhibition determines 1\/f power spectrum in <\/span>neuronal networks Chaos 27 047402<\/span><\/section>\n
[15] Lombardi F, Herrmann H J, Perrone-Capano C, Plenz D and De Arcangelis L 2012 Balance between excitation and inhibition <\/span>controls the temporal organization of neuronal avalanches Phys. Rev. Lett. 108 228703<\/span><\/section>\n
[16] Paul E, Lambiotte R, Chialvo D R, Christensen K, Jensen H J, Sharp D J and Turkheimer F 2011 Self-similar correlation function <\/span>in brain resting-state functional magnetic resonance imaging J. R. Soc. Interface 8 472\u20139<\/span><\/section>\n
[17] De Arcangelis L, Perrone-Capano C and Herrmann H J 2006 Self-organized criticalitymodel for brain plasticity Phys. Rev. Lett. 96<\/span>028107<\/span><\/section>\n
[18] Russo R, Herrmann H J and De Arcangelis L 2014 Brain modularity controls the critical behavior of spontaneous activity Sci. Rep. <\/span>4 1\u20135<\/span><\/section>\n
[19] Michiels Van Kessenich L, De Arcangelis L and Herrmann H J 2016 Synaptic plasticity and neuronal refractory time cause scaling <\/span>behaviour of neuronal avalanches Sci. Rep. 6 1\u20137<\/span><\/section>\n
[20] Michiels Van Kessenich L, Berger D, De Arcangelis L and Herrmann H J 2019 Pattern recognition with neuronal avalanche <\/span>dynamics Phys. Rev. E 99 010302<\/span><\/section>\n
[21] Chialvo D R 2010 Emergent complex neural dynamics Nat. Phys. 6 744\u201350<\/span><\/section>\n
[22] Peters O and Neelin J D 2006 Critical phenomena in atmospheric precipitation Nat. Phys. 2 393\u20136<\/span><\/section>\n
[23] Palmieri L and Jensen H J 2018 The emergence of weak criticality in SOC systems Europhys. Lett. 123 20002<\/span><\/section>\n
[24] Drossel B and Schwabl F 1992 Self-organized critical forest-fire model Phys. Rev. Lett. 69 1629\u201332<\/span><\/section>\n
[25] Palmieri L and Jensen H J 2020 The forest fire model: the subtleties of criticality and scale invariance Front. Phys. 8 1\u20138<\/span><\/section>\n
[26] Grassberger P 2002 Critical behaviour of the Drossel\u2013Schwabl forest fire model New J. Phys. 4 17.1\u201317.15<\/span><\/section>\n
[27] Pruessner G and Jensen H J 2002 Broken scaling in the forest-fire model Phys. Rev. E 65 056707<\/span><\/section>\n
[28] Palmieri L and Jensen H J 2020 Investigating critical systems via the distribution of correlation lengths Phys. Rev. Res. 2 013199<\/span><\/section>\n
[29] Bonachela J A and Mu\u00f1oz M A 2009 Self-organization without conservation: true or just apparent scale-invariance? J. Stat. Mech. P09009<\/span><\/section>\n
[30] Bonachela J A, De Franciscis S, Torres J and Mu\u00f1oz M A 2010 Self-organization without conservation: are neuronal avalanches generically critical? J. Stat. Mech. P02015<\/span><\/section>\n
[31] Li M, Han Y, Aburn M J, BreakspearM, Poldrack R A, Shine J M and Lizier J T 2019 Transitions in information processing dynamics at the whole-brain network level are driven by alterations in neural gain PLoS Comput. Biol. 15 e1006957<\/span><\/span><\/section>\n


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

\n
\n

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


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

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

\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\u6211\u7684\u96c6\u667a\u300d\u63a8\u9001\u8bba\u6587\u4fe1\u606f\u3002\u626b\u63cf\u4e0b\u65b9\u4e8c\u7ef4\u7801\u5373\u53ef\u4e00\u952e\u8ba2\u9605\uff1a<\/span>
<\/section>\n


<\/p>\n

<\/p>\n


<\/section>\n

<\/section>\n
\n

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