{"id":32182,"date":"2022-01-29T21:03:55","date_gmt":"2022-01-29T13:03:55","guid":{"rendered":"https:\/\/swarma.org\/?p=32182"},"modified":"2022-01-29T21:03:55","modified_gmt":"2022-01-29T13:03:55","slug":"%e8%af%86%e5%88%ab%e6%97%b6%e5%8f%98%e5%9b%a0%e6%9e%9c%e5%85%b3%e7%b3%bb%ef%bc%9a%e6%96%b0%e5%b7%a5%e5%85%b7%e5%ba%94%e5%af%b9%e5%9b%a0%e6%9e%9c%e5%ba%a6%e9%87%8f%e7%9a%84%e7%bb%b4%e6%95%b0%e7%81%be","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=32182","title":{"rendered":"\u8bc6\u522b\u65f6\u53d8\u56e0\u679c\u5173\u7cfb\uff1a\u65b0\u5de5\u5177\u5e94\u5bf9\u56e0\u679c\u5ea6\u91cf\u7684\u7ef4\u6570\u707e\u96be\u548c\u975e\u5e73\u7a33\u6027\u6311\u6218"},"content":{"rendered":"
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\u7814\u7a76\u9886\u57df\uff1a<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong>\u56e0\u679c\u5206\u6790\uff0c\u4fe1\u606f\u8bba\uff0c\u590d\u6742\u7cfb\u7edf<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u7530\u6d0b<\/span> <\/span>| \u4f5c\u8005<\/strong><\/span><\/p>\n

\u6881\u91d1<\/span> | \u5ba1\u6821<\/strong><\/span><\/strong><\/span>
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\u9093\u4e00\u96ea<\/span> | \u7f16\u8f91<\/strong><\/span>
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Fourier-domain transfer entropy spectrum<\/span><\/p>\n

\u8bba\u6587\u94fe\u63a5\uff1a<\/span>https:\/\/journals.aps.org\/prresearch\/abstract\/10.1103\/PhysRevResearch.3.L042040<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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1. \u56e0\u679c\u5206\u6790\uff1a\u524d\u6cbf\u4e0e\u6311\u6218<\/strong><\/strong><\/p>\n<\/section>\n

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\u7406\u89e3\u7cfb\u7edf\u95f4\u7684\u56e0\u679c\u5173\u7cfb\u662f\u7269\u7406\u5b66[1]\u548c\u795e\u7ecf\u79d1\u5b66[2]\u7b49\u591a\u4e2a\u5b66\u79d1\u7684\u5171\u540c\u6311\u6218\u3002\u5ea6\u91cf\u56e0\u679c\u5173\u7cfb\u7684\u6311\u6218\u5f80\u5f80\u5728\u4e8e\u7cfb\u7edf\u7684\u89c2\u6d4b\u503c<\/span>\uff08\u4f8b\u5982\u65f6\u95f4\u5e8f\u5217\uff09<\/span>\u5341\u5206\u7a00\u7f3a\uff0c\u4e14\u7814\u7a76\u8005\u7f3a\u4e4f\u5bf9\u4e8e\u7cfb\u7edf\u95f4\u7684\u8026\u5408\u5173\u7cfb\u7684\u5148\u9a8c\u77e5\u8bc6\u3002\u5728\u8fc7\u53bb\u51e0\u5341\u5e74\uff0c\u57fa\u4e8e\u4e0d\u5145\u8db3\u7684\u4fe1\u606f\u548c\u6570\u636e\u8fdb\u884c\u56e0\u679c\u5173\u7cfb\u5206\u6790\u6210\u4e3a\u4e86\u7269\u7406\u5b66\u3001\u6570\u5b66\u548c\u7edf\u8ba1\u5b66\u6700\u91cd\u8981\u7684\u95ee\u9898\u4e4b\u4e00[3]\u3002\u5728\u7edf\u8ba1\u7406\u8bba\u89d2\u5ea6<\/strong><\/span>\uff08\u4f8b\u5982Granger\u56e0\u679c[4]\u53ca\u5176\u63a8\u5e7f[5\u201310]\uff09<\/span>\u548c\u4fe1\u606f\u8bba\u89d2\u5ea6<\/strong><\/span>\uff08\u4f8b\u5982\u8f6c\u79fb\u71b5[11]\u53ca\u5176\u63a8\u5e7f[12\u201320]\uff09<\/span>\uff0c\u7814\u7a76\u8005\u5df2\u7ecf\u53d6\u5f97\u4e86\u4e30\u5bcc\u7684\u8fdb\u5c55\u3002\u5c3d\u7ba1\u56e0\u679c\u7684\u672c\u8d28\u4f9d\u7136\u5b58\u5728\u4e89\u8bba[21]\uff0c\u4e0a\u8ff0\u4e24\u4e2a\u89d2\u5ea6\u5df2\u88ab\u8bc1\u5b9e\u5177\u6709\u6df1\u523b\u7684\u6570\u5b66\u8054\u7cfb[22,23]\u3002<\/span>
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\u5982\u679c\u6211\u4eec\u7528<\/sub>\u8868\u793a<\/span>X<\/span><\/math-formula>\u7684\u5386\u53f2\u4fe1\u606f\uff0c\u5219\u201c\u7cfb\u7edf<\/span>X<\/span><\/math-formula>\u662f\u7cfb\u7edf<\/span>Y<\/span><\/math-formula>\u7684\u539f\u56e0\u201c\u53ef\u4ee5\u88ab\u7406\u89e3\u4e3a\u2014\u2014\u5728\u65f6\u523b<\/span>t<\/span><\/math-formula>\uff0c\u5982\u679c\u201c\u57fa\u4e8e\u7cfb\u7edf<\/span>Y<\/span><\/math-formula>\u7684\u5386\u53f2\u4fe1\u606f<\/sub>\u9884\u6d4b\u7cfb\u7edf<\/span>Y<\/span><\/math-formula>\u5f53\u524d\u72b6\u6001\u7684\u4e0d\u786e\u5b9a\u6027\u201d\u4e0d\u7b49\u4e8e\u201c\u57fa\u4e8e\u7cfb\u7edf<\/span>Y<\/span><\/math-formula>\u201d\u7684\u5386\u53f2\u4fe1\u606f<\/sub>\u548c\u7cfb\u7edf<\/span>X<\/span><\/math-formula>\u7684\u5386\u53f2\u4fe1\u606f<\/sub>\u4e00\u540c\u9884\u6d4b\u7cfb\u7edf<\/span>Y<\/span><\/math-formula>\u5f53\u524d\u72b6\u6001\u7684\u4e0d\u786e\u5b9a\u6027\u201c\uff0c\u5219\u7cfb\u7edf<\/span>X<\/span><\/math-formula>\u7684\u5386\u53f2\u4fe1\u606f\u5bf9\u7cfb\u7edf<\/span>Y<\/span><\/math-formula>\u5f53\u524d\u72b6\u6001\u6709\u56e0\u679c\u6027\u7684\u5f71\u54cd\u3002\u4e00\u8a00\u853d\u4e4b\uff0c\u56e0\u679c\u6548\u5e94\u5728\u4e8e\u5386\u53f2\u4fe1\u606f\u5bf9\u5f53\u524d\uff08\u6216\u672a\u6765\uff09\u72b6\u6001\u7684\u4e0d\u786e\u5b9a\u6027\u7684\u63a7\u5236<\/strong>\u3002\u96c6\u667a\u4ff1\u4e50\u90e8\u7684\u5f80\u671f\u6587\u7ae0\u300a\u4f5c\u4e3a\u56e0\u679c\u79d1\u5b66\u5bb6\u7684\u795e\u7ecf\u7cfb\u7edf\uff1a\u56e0\u679c\u7f16\u7801<\/a>\u300b\u4e2d\u66fe\u4ecb\u7ecd\u4e86\u5927\u8111\u80fd\u57fa\u4e8e\u795e\u7ecf\u52a8\u529b\u5b66\u5bf9\u4e8e\u56e0\u679c\u5173\u7cfb\u8fdb\u884c\u7c7b\u4f3c\u7684\u8868\u5f81[65]\u3002<\/span><\/section>\n

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\u57fa\u4e8e\u4e0a\u8ff0\u601d\u60f3\u884d\u751f\u51fa\u7684\u6240\u6709\u56e0\u679c\u5ea6\u91cf\u5de5\u5177\u4e2d\uff0c\u8f6c\u79fb\u71b5<\/strong><\/span>\uff08Transfer entropy\uff09<\/span>[11]\u5728\u795e\u7ecf\u79d1\u5b66[24\u201328]\u548c\u7ecf\u6d4e\u5b66[29\u201333]\u4e2d\u6709\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u8f6c\u79fb\u71b5\u5bf9\u975e\u7ebf\u6027\u56e0\u679c\u5173\u7cfb\u5177\u6709\u9c81\u68d2\u7684\u53d1\u73b0\u80fd\u529b\uff0c\u5e76\u4e14\u548c\u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u548c\u4fe1\u606f\u8bba\u6709\u7740\u672c\u8d28\u7684\u8054\u7cfb[3,11]\u3002\u4f8b\u5982\uff0c\u8f6c\u79fb\u71b5\u7b49\u4ef7\u4e8e\u6761\u4ef6\u4e92\u4fe1\u606f [3,34]\u3002\u5728\u8f6c\u79fb\u71b5\u7684\u6700\u521d\u5b9a\u4e49\u4e2d\uff0c\u7cfb\u7edf<\/span>X<\/span><\/math-formula>\u7684\u5386\u53f2\u4fe1\u606f<\/sub>\u5bf9\u4e8e\u7cfb\u7edf<\/span>Y<\/span><\/math-formula>\u5f53\u524d\u72b6\u6001\u7684\u4e0d\u786e\u5b9a\u6027\u7684\u63a7\u5236\u6548\u5e94\u7b49\u4ef7\u4e8e\u7ed9\u5b9a<\/sub>\u540e\uff0c<\/sub>\u548cY(t)\u95f4\u4e92\u4fe1\u606f\u7684\u671f\u671b\u503c\u3002\u867d\u7136\u8f6c\u79fb\u71b5\u5177\u6709\u4e0d\u4f9d\u8d56\u5148\u9a8c\u6a21\u578b\u7684\u7279\u70b9\uff0c\u4f46\u5176\u5728\u771f\u5b9e\u573a\u666f\u4e0b\u7684\u4f7f\u7528\u4f9d\u7136\u4f1a\u53d7\u5230\u8bb8\u591a\u9650\u5236<\/strong>\u3002\u4f8b\u5982\uff0c\u8f6c\u79fb\u71b5\u7684\u5ea6\u91cf\u5b58\u5728\u7ef4\u6570\u707e\u96be[15]\u548c\u566a\u58f0\u654f\u611f\u6027[35]\u3002\u867d\u7136\u5927\u91cf\u7684\u7814\u7a76\u5df2\u7ecf\u63a2\u7d22\u4e86\u8f6c\u79fb\u71b5\u7684\u6700\u4f18\u4f30\u8ba1\u65b9\u6848<\/span>\uff08\u4f8b\u5982\uff0c\u7b26\u53f7\u5316[12]\u3001\u76f8\u65f6\u95f4\u5e8f\u5217[13]\u3001\u96c6\u6210\u4f30\u8ba1[16]\u3001Lempel-Ziv\u590d\u6742\u5ea6[18]\u3001\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc[19]\u548ck\u8fd1\u90bb[36]\uff09<\/span>\uff0c\u4ecd\u7136\u6709\u8bb8\u591a\u56f0\u96be\u672a\u88ab\u514b\u670d\uff1a<\/span><\/p>\n

1. \u5df2\u6709\u7814\u7a76\u5c06\u7cfb\u7edf\u89c6\u4e3a\u4e00\u4e2a\u6574\u4f53\uff0c\u7136\u800c\uff0c\u66f4\u666e\u904d\u7684\u60c5\u51b5\u662f\u56e0\u679c\u5173\u7cfb\u53ea\u5b58\u5728\u4e8e\u7279\u5b9a\u7684\u5b50\u7cfb\u7edf\u95f4<\/span>\uff08\u4f8b\u5982\uff0c\u53ea\u5b58\u5728\u4e8e<\/span>X<\/span><\/math-formula>\u548c<\/span>Y<\/span><\/math-formula>\u7684\u9ad8\u9891\u5206\u91cf\u95f4\uff09<\/span>\u3002\u4e0d\u533a\u5206\u7cfb\u7edf\u7ec4\u4ef6\u5219\u4f1a\u63a9\u76d6\u8fd9\u4e9b\u56e0\u679c\u5173\u7cfb\u3002<\/span><\/section>\n
2. \u56e0\u679c\u5173\u7cfb\u662f\u968f\u65f6\u95f4\u53d8\u5316\u7684\u3002\u867d\u7136\u8f6c\u79fb\u71b5\u7684\u521d\u59cb\u7248\u672c\u80fd\u591f\u88ab\u7d2f\u79ef\u5730\u8ba1\u7b97\u6216\u7ed3\u5408\u6ed1\u52a8\u65f6\u95f4\u7a97\u8fdb\u884c\u52a8\u6001\u8ba1\u7b97\uff0c\u4e00\u4e2a\u66f4\u7cbe\u786e\u4e14\u66f4\u81ea\u7136\u7684\u65f6\u53d8\u56e0\u679c\u5173\u7cfb\u5ea6\u91cf\u5de5\u5177\u4f9d\u7136\u7f3a\u5931\u3002<\/span><\/section>\n

3. \u6982\u7387\u5bc6\u5ea6\u4f30\u8ba1\u2014\u2014\u4e00\u4e2a\u8ba1\u7b97\u8f6c\u79fb\u71b5\u7684\u5148\u51b3\u6761\u4ef6\u2014\u2014\u5728\u73b0\u5b9e\u573a\u666f\u4e2d\u5f80\u5f80\u662f\u6210\u672c\u9ad8\u6602\u7684<\/span>\uff08\u9700\u6c42\u5927\u6837\u672c\u91cf\uff09<\/span>\u6216\u4e0d\u51c6\u786e\u7684<\/span>\uff08\u975e\u5e73\u7a33\u8fc7\u7a0b\u548c\u9ad8\u7ef4\u7a7a\u95f4\uff09<\/span>\u3002\u4e00\u4e2a\u9002\u7528\u4e8e\u975e\u5e73\u7a33<\/span>\uff08nonstationary\uff09<\/span>\u548c\u9ad8\u7ef4<\/span>\uff08high-dimensional\uff09<\/span>\u8fc7\u7a0b\u7684\u9ad8\u6548\u8f6c\u79fb\u71b5\u4f30\u8ba1\u65b9\u6848\u4f9d\u7136\u7f3a\u5931\u3002<\/span><\/p>\n

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2. \u56e0\u679c\u5ea6\u91cf\u65b0\u5de5\u5177\uff1a\u5085\u91cc\u53f6\u57df\u8f6c\u79fb\u71b5\u589e<\/strong><\/strong><\/p>\n<\/section>\n

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\u5728\u8be5\u7814\u7a76\u8bba\u6587\u4e2d\uff0c\u4f5c\u8005\u63d0\u51fa\u4e86\u5085\u91cc\u53f6\u57df\u8f6c\u79fb\u71b5\u8c31<\/strong><\/span>\uff08Fourier-domain transfer entropy spectrum\uff09<\/span>\u4f5c\u4e3a\u8f6c\u79fb\u71b5\u7684\u63a8\u5e7f\u3002\u7406\u89e3\u5085\u91cc\u53f6\u57df\u8f6c\u79fb\u71b5\u8c31\uff0c\u53ea\u9700\u8981\u6293\u4f4f\u4ee5\u4e0b\u4e09\u4e2a\u65b9\u9762\uff1a<\/span><\/p>\n

1. \u5085\u91cc\u53f6\u57df<\/strong><\/span>\uff08Fourier-domain\uff09<\/span>\uff0c\u5373\u4f7f\u7528\u7c7b\u4f3c\u5085\u91cc\u53f6\u53d8\u6362\u7684\u65b9\u6cd5\u5c06\u539f\u59cb\u7cfb\u7edf\u8fdb\u884c\u518d\u8868\u5f81\u540e\u5f97\u5230\u7684\u7a7a\u95f4\u3002\u901a\u8fc7\u518d\u8868\u5f81\uff0c\u4f5c\u8005\u63a2\u7d22\u4e86\u5982\u4f55\u4e3a\u8bc6\u522b\u65f6\u53d8\u7684\u56e0\u679c\u5173\u7cfb\u521b\u9020\u57fa\u7840\u3002<\/span><\/section>\n
2. \u8f6c\u79fb\u71b5<\/strong><\/span>\uff08Transfer entropy\uff09<\/span>\u5ea6\u91cf\uff0c\u5373\u57fa\u4e8e\u518d\u8868\u5f81\u540e\u7684\u7cfb\u7edf\u8fdb\u884c\u56e0\u679c\u5ea6\u91cf\u3002\u5728\u5ea6\u91cf\u8fc7\u7a0b\u4e2d\uff0c\u4f5c\u8005\u63a2\u7d22\u4e86\u5982\u4f55\u964d\u4f4e\u6982\u7387\u5bc6\u5ea6\u4f30\u8ba1\u7684\u4ee3\u4ef7\uff0c\u5e76\u63d0\u5347\u5bf9\u975e\u5e73\u7a33\u3001\u9ad8\u7ef4\u968f\u673a\u8fc7\u7a0b\u91c7\u6837\u7684\u7cbe\u5ea6\u3002<\/span><\/section>\n

3. \u8c31<\/strong><\/span>\uff08Spectrum\uff09<\/span>\u3002\u4f5c\u8005\u63a2\u7d22\u4e86\u5982\u4f55\u5c06\u4efb\u610f\u65f6\u523b\u7684\u56e0\u679c\u5173\u7cfb\u8fdb\u884c\u5c55\u5f00\uff0c\u4ece\u800c\u80fd\u5206\u6790\u4e0d\u540c\u7cfb\u7edf\u5206\u91cf\u95f4\u7684\u56e0\u679c\u5173\u7cfb\uff0c\u5e76\u6cbf\u7740\u65f6\u95f4\u548c\u7cfb\u7edf\u5206\u91cf\u4e24\u4e2a\u7ef4\u5ea6\u5c55\u5f00\u5f62\u6210\u56e0\u679c\u8c31\u3002<\/span><\/p>\n

     <\/span><\/section>\n
\u4ece\u4e0a\u8ff0\u601d\u8def\u51fa\u53d1\uff0c\u4f5c\u8005\u5bf9\u4e8e\u6bcf\u4e2a\u65b9\u9762\u8fdb\u884c\u4e86\u7cfb\u7edf\u7684\u63a2\u7d22\u3002<\/span><\/section>\n

<\/section>\n
\u9996\u5148\uff0c\u4f5c\u8005\u5206\u6790\u4e86\u5982\u4f55\u57fa\u4e8e\u5085\u91cc\u53f6\u57df\u5bf9\u7cfb\u7edf\u8fdb\u884c\u8868\u5f81\u3002\u4e00\u4e2a\u5408\u7406\u7684\u8868\u5f81\u5e94\u8be5\u81ea\u7136\u5730\u5c06\u7cfb\u7edf\u533a\u5206\u4e3a\u591a\u4e2a\u7cfb\u7edf\u5206\u91cf\uff0c\u5e76\u4e14\u80fd\u53cd\u6620\u7cfb\u7edf\u53ef\u80fd\u5b58\u5728\u7684\u975e\u5e73\u7a33\u7279\u6027\u3002\u4e3a\u4e86\u83b7\u53d6\u4e00\u4e2a\u4e0d\u4f9d\u8d56\u5148\u9a8c\u6a21\u578b\u7684\u7cfb\u7edf\u5212\u5206\uff0c\u4f5c\u8005\u8003\u8651\u4e86\u5c06\u7cfb\u7edf\u5212\u5206\u4e3a\u4e0d\u540c\u9891\u7387\u5206\u91cf\uff0c\u8fd9\u4e00\u601d\u8def\u5728\u7269\u7406[38]\u3001\u6570\u5b66[39]\u3001\u795e\u7ecf\u79d1\u5b66[40]\u548c\u5de5\u7a0b[41]\u9886\u57df\u90fd\u6709\u5e7f\u6cdb\u7684\u5e94\u7528\uff0c\u4fdd\u8bc1\u4e86\u7406\u8bba\u7684\u6613\u7528\u6027\u3002\u4e3a\u4e86\u907f\u514d\u5bf9\u7cfb\u7edf\u5e73\u7a33\u6027\u7684\u5047\u8bbe\uff0c\u901a\u5e38\u53ef\u4ee5\u91c7\u7528\u5c0f\u6ce2\u53d8\u6362[42]\u6216\u5e0c\u5c14\u4f2f\u7279-\u9ec4\u53d8\u6362[43]\u800c\u975e\u5085\u91cc\u53f6\u53d8\u6362<\/span>\uff08\u5085\u91cc\u53f6\u53d8\u6362\u5e26\u6709\u5e73\u7a33\u6027\u5047\u8bbe[44]\uff09<\/span>\u3002\u5c0f\u6ce2\u53d8\u6362\u548c\u5e0c\u5c14\u4f2f\u7279-\u9ec4\u53d8\u6362\u90fd\u80fd\u8fdb\u884c\u65f6\u9891\u8868\u5f81\uff0c\u5373\u5f97\u5230\u4e00\u4e2a\u65f6\u53d8\u7684\u9891\u7387\u8c31\u3002\u4e24\u7c7b\u65b9\u6cd5\u5404\u6709\u4f18\u7f3a\u70b9\uff0c\u9700\u8981\u57fa\u4e8e\u73b0\u5b9e\u573a\u666f\u8fdb\u884c\u9009\u62e9[43,45]\u3002\u4f5c\u8005\u9009\u62e9\u4e86\u6709\u5b8c\u5907\u7406\u8bba\u57fa\u7840\u7684\u5c0f\u6ce2\u53d8\u6362\u8fdb\u884c\u7406\u8bba\u63a8\u5bfc\u3002\u5bf9\u4e8e\u7cfb\u7edfX\uff0c\u4f5c\u8005\u4f7f\u7528\u5c0f\u6ce2\u53d8\u6362\u540e\u7684\u65f6\u53d8\u529f\u7387\u8c31\u4f5c\u4e3a\u5176\u5085\u91cc\u53f6\u57df\u8868\u5f81F(X, t, \u03c9)\uff0c\u5176\u4e2dt\u8868\u793a\u65f6\u95f4\u8f74\u800c\u03c9\u8868\u793a\u9891\u7387\u8f74 <\/span>[\u56fe1(a)]<\/span>\u3002\u4e3a\u4e86\u4fdd\u8bc1\u7814\u7a76\u7684\u6613\u91cd\u590d\u6027\uff0c\u4f5c\u8005\u4f7f\u7528\u4e86\u4e00\u4e2a\u5f00\u6e90\u7684\u795e\u7ecf\u4fe1\u53f7\u6570\u636e\u96c6\u3002\u8be5\u6570\u636e\u96c6\u5305\u542b\u4e86\u4f7f\u7528\u8fd1\u7ea2\u5916\u5149\u8c31\u5b66<\/span>\uff08NIRS\uff09<\/span>\u8bb0\u5f55\u7684\u989d\u4e0a\u56de<\/span>\uff08superior frontal cortex\uff09<\/span>\u7684\u795e\u7ecf\u6d3b\u52a8[50,51]\uff0c\u53ef\u4f5c\u4e3aX\u548cY\u7684\u89c2\u6d4b\u503c\u3002<\/span><\/section>\n

<\/section>\n
\u5728\u5f97\u5230\u4e86F(X, t, \u03c9)\u548cF(Y, t, \u03c9)\u540e\uff0c\u4f5c\u8005\u9700\u8981\u63a2\u7d22\u5982\u4f55\u5ea6\u91cf\u4e24\u8005\u95f4\u7684\u8f6c\u79fb\u71b5\u3002\u9996\u8981\u7684\u6311\u6218\u5728\u4e8eF(X, t, \u03c9)\u548cF(Y<\/span>, t, \u03c9)\u90fd\u662f\u5b9e\u503c\u7684\u8c31\uff0c\u968f\u7740\u7cfb\u7edf\u7684\u89c2\u6d4b\u65f6\u95f4<\/span>t<\/span><\/math-formula>\u589e\u957f\u6216\u8003\u8651\u7684\u9891\u7387\u03c9\u7684\u7c92\u5ea6\u53d8\u7ec6\uff0cF(X, t, \u03c9)\u548cF(Y, t, \u03c9)\u7684\u6982\u7387\u5bc6\u5ea6\u5206\u5e03\u5c06\u4e0d\u53ef\u907f\u514d\u5730\u5904\u4e8e\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u3002\u82e5<\/span>X<\/span><\/math-formula>\u548c<\/span>Y<\/span><\/math-formula>\u5bf9\u5e94\u975e\u5e73\u7a33\u968f\u673a\u8fc7\u7a0b\uff0c\u5219\u60c5\u51b5\u4f1a\u66f4\u52a0\u4e25\u5cfb\uff0c\u56e0\u4e3aF(X, t, \u03c9)\u548cF(Y, t, \u03c9)\u7684\u9ad8\u7ef4\u6982\u7387\u5bc6\u5ea6\u5206\u5e03\u4e0d\u80fd\u5728\u6709\u9650\u7684\u89c2\u6d4b\u6837\u672c\u96c6\u4e2d\u8fdb\u884c\u8db3\u591f\u7684\u91c7\u6837\u3002\u5728\u6b64\u57fa\u7840\u4e0a\uff0c\u4efb\u4f55\u5bf9F(X, t, \u03c9)\u548c<\/span>F(Y, t, \u03c9)<\/span><\/math-formula>\u7684\u6982\u7387\u5bc6\u5ea6\u5206\u5e03\u7684\u76f4\u63a5\u4f30\u8ba1\u65b9\u6848\u90fd\u4e0d\u53ef\u907f\u514d\u5730\u9677\u5165\u9ad8\u7ef4\u7a7a\u95f4\u548c\u975e\u5e73\u7a33\u8fc7\u7a0b\u7684\u53cc\u91cd\u56f0\u5883\u4e2d\uff0c\u51e0\u4e4e\u4e0d\u53ef\u80fd\u5f97\u5230\u51c6\u786e\u7684\u7b54\u6848\u3002\u4e3a\u4e86\u514b\u670d\u8fd9\u4e00\u56f0\u96be\uff0c\u4f5c\u8005\u63a8\u5e7f\u4e86\u7ecf\u5178\u7684\u7b26\u53f7\u5316\u65b9\u6cd5[52]\uff0c\u63d0\u51fa\u4e86\u4e8c\u7ef4\u7b26\u53f7\u5316<\/strong><\/span>\uff08two-dimensional symbolization\uff09<\/span>\u7f16\u7801<\/strong>\u3002\u8be5\u7f16\u7801\u662f\u4e00\u79cd\u7c97\u7c92\u5316\u65b9\u6848\uff0c\u5728\u9009\u62e9<\/span>F(X, t, \u03c9)<\/span><\/math-formula>\u4e0a\u4efb\u610f\u4e00\u4e2a\u70b9\u540e\uff0c\u8be5\u7f16\u7801\u80fd\u591f\u6cbf\u7740\u65f6\u95f4\u8f74\u548c\u9891\u7387\u8f74\u83b7\u53d6\u8be5\u70b9\u4e0e\u76f8\u90bb\u70b9\u7684\u6570\u503c\u5927\u5c0f\u5173\u7cfb\u5e76\u8fdb\u884c\u6392\u5e8f\uff0c\u57fa\u4e8e\u6392\u5e8f\u7ed3\u679c\u5bf9\u539f\u59cb\u6570\u503c\u8d77\u4f0f\u89c4\u5f8b\u8fdb\u884c\u4fdd\u5e8f\u8868\u5f81\u7684\u540c\u65f6\uff0c\u53c8\u7565\u53bb\u4e86\u5177\u4f53\u7684\u6570\u503c\u5927\u5c0f\u4ece\u800c\u5bf9\u80cc\u666f\u566a\u97f3\u5f62\u6210\u62b5\u6297\u3002\u901a\u8fc7\u5c06\u6cbf\u7740\u65f6\u95f4\u8f74\u548c\u9891\u7387\u8f74\u7684\u6392\u5e8f\u7ed3\u679c\u8f6c\u6362\u4e3a\u7279\u5b9a<\/span>p<\/span><\/math-formula>\u8fdb\u5236\u7a7a\u95f4\u4e2d\u7684\u5143\u7d20<\/span> [\u56fe1(b)]<\/span>\uff0c\u518d\u7edf\u4e00\u6620\u5c04\u5230<\/span>10<\/span><\/math-formula>\u8fdb\u5236\u7a7a\u95f4\u4e2d\u4ee5\u66ff\u6362F(X, t, \u03c9)\u4e2d\u7684\u539f\u59cb\u503c\u5f97\u5230<\/sub>\uff0c\u4ece\u800c\u5c06<\/span>F(X, t, \u03c9)<\/span><\/math-formula>\u7684\u6982\u7387\u5bc6\u5ea6\u7a7a\u95f4\u4ece\u9ad8\u7ef4\u5b9e\u6570\u7a7a\u95f4\u5d4c\u5165\u5230\u4e00\u4e2a<\/span>1<\/span><\/math-formula>\u7ef4\u7684\u6574\u6570\u7a7a\u95f4\uff0c\u4e14\u8be5\u6574\u6570\u7a7a\u95f4\u53ea\u5305\u542b\u5c11\u6570\u5143\u7d20<\/span>\uff08\u5177\u4f53\u6570\u91cf\u7531\u7c97\u7c92\u5316\u7c92\u5ea6\u63a7\u5236\uff09<\/span>\u3002\u5728\u5d4c\u5165\u540e\u7684<\/span>1<\/span><\/math-formula>\u7ef4\u6574\u6570\u7a7a\u95f4\u4e2d\uff0c<\/span>X<\/span><\/math-formula>\u548c<\/span>Y<\/span><\/math-formula>\u7cfb\u7edf\u7684\u80cc\u666f\u566a\u97f3\u5df2\u88ab\u8fc7\u6ee4\uff0c\u4e14\u5176\u6982\u7387\u5bc6\u5ea6\u5206\u5e03\u80fd\u5728\u6781\u5c0f\u7684\u89c2\u6d4b\u6570\u636e\u96c6\u4e2d\u8fdb\u884c\u5145\u5206\u91c7\u6837\u3002<\/span><\/section>\n

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

\u56fe1. \u5085\u91cc\u53f6\u8f6c\u79fb\u71b5\u8c31\u5206\u6790\u3002(a)\u57fa\u4e8eNIRS\u6570\u636e\u7684\u5085\u91cc\u53f6\u57df\u8868\u5f81F(X, t, \u03c9)\u548cF(, t, \u03c9)Y\u3002(b)\u5bf9F(X, t, \u03c9)\u548cF(Y, t, \u03c9)\u7684\u7c97\u7c92\u5ea6\u7c97\u7c92\u5316\u7ed3\u679c\uff08\u4e0a\u6392\uff09\u548c\u7ec6\u7c92\u5ea6\u7c97\u7c92\u5316\u7ed3\u679c\uff08\u4e0b\u6392\uff09\u3002(c)\u5085\u91cc\u53f6\u8f6c\u79fb\u71b5\u8c31<\/span>T(X, Y, t, \u03c9)<\/span><\/math-formula>\u53ca\u5176\u4e0e\u5c0f\u6ce2\u534f\u540c\uff08wavelet coherence\uff09\u7684\u5bf9\u6bd4\u5206\u6790\u3002(d)\u65f6\u53d8\u548c\u9891\u53d8\u7684\u56e0\u679c\u5173\u7cfb\u5206\u6790\u8868\u660e\u5b58\u5728<\/span>X\u2192Y<\/span><\/math-formula>\u7684\u56e0\u679c\u5173\u7cfb\u3002<\/span><\/p>\n

 <\/span><\/section>\n
\u5728\u5f97\u5230<\/sub>\u548c<\/sub>\u540e\uff0c\u5ea6\u91cf\u8f6c\u79fb\u71b5\u7684\u5148\u51b3\u6761\u4ef6\u5df2\u5f97\u5230\u4e86\u8f83\u597d\u7684\u4fdd\u8bc1\u3002\u4f5c\u8005\u76f4\u63a5\u57fa\u4e8e\u539f\u59cb\u7684\u8f6c\u79fb\u71b5\u7ed9\u51fa\u4e86\u5ea6\u91cf\uff0c\u5f97\u5230\u4e86\u5085\u91cc\u53f6\u57df\u8f6c\u79fb\u71b5\u8c31<\/strong>T(X, Y, t, \u03c9)<\/span>[\u89c1\u56fe1(c)]<\/span>\u3002\u5728T(X, Y, t, \u03c9)\u4e2d\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u65f6\u523bt\u548c\u9891\u7387\u03c9\uff0c\u5c31\u80fd\u5f97\u5230\u7cfb\u7edfX\u548cY\u7684\u03c9\u9891\u7387\u5206\u91cf\u5728\u65f6\u523bt\u7684\u8f6c\u79fb\u71b5\uff0c\u4ece\u800c\u53cd\u6620\u56e0\u679c\u5173\u7cfb\u3002\u5728T(X, Y, t, \u03c9)\u4e2d\uff0c\u56e0\u679c\u5173\u7cfb\u4e0d\u4ec5\u662f\u65f6\u53d8\u7684<\/span>\uff08\u6cbf\u7740t\u8f74\u53d8\u5316\uff09<\/span>\uff0c\u8fd8\u662f\u9891\u53d8\u7684<\/span>\uff08\u6cbf\u7740\u03c9\u8f74\u53d8\u5316\uff09<\/span>\u3002\u81ea\u7136\uff0c\u5c06T(X, Y, t, \u03c9)\u6cbf\u7740t\u8f74\u76f8\u52a0\u53ef\u5f97\u5230\u9891\u53d8\u7684\u56e0\u679c\u5173\u7cfbT(X, Y, \u03c9)\uff0c\u5c06T(X, Y, t, \u03c9)\u6cbf\u7740\u03c9\u8f74\u76f8\u52a0\u53ef\u5f97\u5230\u9891\u53d8\u7684\u56e0\u679c\u5173\u7cfbT(X, Y, t)\uff0c\u5c06T(X, Y, t, \u03c9)\u7684\u6240\u6709\u6570\u503c\u8fdb\u884c\u52a0\u548c\u53ef\u5f97\u5230\u7ecf\u5178\u7684\u8f6c\u79fb\u71b5T(X, Y)<\/span>[\u56fe1(d)]<\/span>\u3002\u7531\u6b64\uff0c\u8be5\u65b9\u6cd5\u80fd\u591f\u63d0\u4f9bT(X, Y)\u5c55\u5f00\u540e\u7684\u7ed3\u679c\uff0c\u4ece\u800c\u80fd\u63d0\u4f9b\u66f4\u4e30\u5bcc\u7684\u56e0\u679c\u5173\u7cfb\u7684\u4fe1\u606f<\/strong>\u3002\u540c\u65f6\uff0c\u901a\u8fc7\u5bf9T(X, Y, t, \u03c9)\u4e2d\u7684\u6570\u503c\u8fdb\u884c\u52a0\u6743\uff0c\u4f7f\u7528\u8005\u53ef\u5bf9\u56e0\u679c\u5173\u7cfb\u8fdb\u884c\u7b5b\u9009\uff0c\u4ece\u800c\u9002\u7528\u4e8e\u5404\u7c7b\u79d1\u5b66\u548c\u5de5\u7a0b\u573a\u666f\u4e2d\u7684\u964d\u566a\u3002<\/strong><\/span><\/section>\n
 <\/span><\/section>\n
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\u56fe2. \u5085\u91cc\u53f6\u8f6c\u79fb\u71b5\u8c31\u7684\u4fe1\u6548\u5ea6\u5206\u6790\u3002(a)T(X, Y, t, \u03c9)\u5bf9\u7c97\u7c92\u5316\u53c2\u6570\u7684\u4f9d\u8d56\u6027\u5206\u6790\u3002(b)\u57fa\u4e8etimeshifting surrogates \u548c\u7f6e\u6362\u68c0\u9a8c\uff0c\u8bc1\u660eT(X, Y, t, \u03c9)\u5177\u6709\u7edf\u8ba1\u663e\u8457\u6027p<10-3<\/sup>\u548c\u9ad8\u7edf\u8ba1\u6548\u529b\u03be\u3002(c)\u901a\u8fc7\u6539\u53d8\u6269\u6563\u8026\u5408logistic\u632f\u5b50X\u548cY\u7684\u8026\u5408\u5173\u7cfb\uff0c\u80fd\u591f\u654f\u611f\u5730\u8c03\u8282T(X, Y, t, \u03c9)\u7684\u6570\u503c\u3002(d)\u901a\u8fc7\u6539\u53d8\u6269\u6563\u8026\u5408logistic\u632f\u5b50X\u548cY\u7684\u8026\u5408\u5173\u7cfb\uff0c\u80fd\u591f\u654f\u611f\u5730\u8c03\u8282T(X, Y, t, \u03c9)\u7684\u7edf\u8ba1\u663e\u8457\u6027\u3002<\/span> <\/span><\/p>\n


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\u4f5c\u8005\u5bf9T(X, Y, t, \u03c9)\u7684\u4fe1\u6548\u5ea6\u8fdb\u884c\u4e86\u7cfb\u7edf\u7684\u68c0\u9a8c\u3002\u4e00\u65b9\u9762\uff0c\u4f5c\u8005\u5206\u6790\u4e86T(X, Y, t, \u03c9)\u5bf9\u7c97\u7c92\u5316\u5c3a\u5ea6\u7684\u4f9d\u8d56\u6027\uff0c\u8bc1\u660e\u4e86\u57fa\u4e8eT(X, Y, t, \u03c9)\u7684\u56e0\u679c\u5206\u6790\u5bf9\u53c2\u6570\u5e76\u4e0d\u4f9d\u8d56<\/span> [\u56fe2(a)]<\/span>\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u4f5c\u8005\u7ed3\u5408 timeshifting surrogates [56\u201358] \u548c\u7f6e\u6362\u68c0\u9a8c [59,60]\u63d0\u51fa\u4e86\u9488\u5bf9T(X, Y, t, \u03c9)\u7684\u7edf\u8ba1\u68c0\u9a8c\uff0c\u4ee5\u68c0\u9a8c\u4fe1\u606f\u5ea6\u91cf\u5728\u6709\u9650\u6570\u636e\u96c6\u4e0b\u5e38\u51fa\u73b0\u7684\u504f\u5dee[55]\uff0c\u8bc1\u660e\u4e86T(X, Y, t, \u03c9)\u7684\u9ad8\u7edf\u8ba1\u6548\u529b <\/span>[\u56fe2(b)]<\/span>\u3002\u6b64\u5916\uff0c\u4f5c\u8005\u4f7f\u7528\u4e86\u5206\u53c9\u6307\u6570\u4e3a4\u7684\u6269\u6563\u8026\u5408 logistic \u632f\u5b50<\/span>\uff08diffusively coupled logistic oscillators\uff09<\/span>[62,63]\u68c0\u9a8c\u4e86T(X, Y, t, \u03c9)\u662f\u5426\u80fd\u968f\u7740\u771f\u5b9e\u56e0\u679c\u5173\u7cfb\u7684\u5f3a\u5f31\u8d77\u4f0f\u800c\u654f\u611f\u5730\u53d8\u5316\uff0c\u8bc1\u660e\u4e86T(X, Y, t, \u03c9)\u5728\u56e0\u679c\u53d1\u73b0\u65b9\u9762\u7684\u654f\u611f\u6027<\/span> [\u56fe2(c-d)]<\/span>\u3002<\/span><\/section>\n

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