{"id":60623,"date":"2025-06-12T22:06:46","date_gmt":"2025-06-12T14:06:46","guid":{"rendered":"https:\/\/swarma.org\/?p=60623"},"modified":"2025-06-12T22:06:46","modified_gmt":"2025-06-12T14:06:46","slug":"nat-rev-phys-%e9%87%8d%e7%a3%85%e7%bb%bc%e8%bf%b0%ef%bc%9a%e5%a4%8d%e6%9d%82%e7%bd%91%e7%bb%9c%e9%87%8d%e6%95%b4%e5%8c%96%e7%a0%94%e7%a9%b6%e8%bf%9b%e5%b1%95","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=60623","title":{"rendered":"Nat.Rev.Phys.\u91cd\u78c5\u7efc\u8ff0\uff1a\u590d\u6742\u7f51\u7edc\u91cd\u6574\u5316\u7814\u7a76\u8fdb\u5c55"},"content":{"rendered":"
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\u91cd\u6574\u5316\u7fa4 (renormalization group, RG)\u7406\u8bba\u662f\u4e00\u5957\u5f3a\u6709\u529b\u7684\u7406\u8bba\u6846\u67b6\uff0c\u4e3b\u8981\u5e94\u7528\u4e8e\u591a\u81ea\u7531\u5ea6\u7cfb\u7edf\u7684\u7814\u7a76\u3002\u8be5\u7406\u8bba\u901a\u8fc7\u5bf9\u7cfb\u7edf\u72b6\u6001\u3001\u6a21\u578b\u53c2\u6570\u548c\u8026\u5408\u5e38\u6570\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0b\u7684\u63cf\u8ff0\uff0c\u5b9e\u73b0\u7cfb\u7edf\u5728\u4e0d\u540c\u5206\u8fa8\u7387\u5c42\u6b21\u95f4\u7684\u8f6c\u6362\u3002\u8be5\u7406\u8bba\u4e0d\u4ec5\u80fd\u8bc6\u522b\u76f8\u53d8\u4e34\u754c\u70b9\uff0c\u8fd8\u80fd\u6709\u6548\u5206\u6790\u7cfb\u7edf\u5728\u4e34\u754c\u70b9\u9644\u8fd1\u7684\u884c\u4e3a\u7279\u5f81\u3002\u5728\u4f20\u7edf\u7269\u7406\u5e94\u7528\u4e2d\uff0c\u91cd\u6574\u5316\u7fa4\u7406\u8bba\u901a\u5e38\u57fa\u4e8e\u540c\u8d28\u6027 (homogeneity)\u3001\u5bf9\u79f0\u6027\u3001\u51e0\u4f55\u7ed3\u6784\u548c\u5c40\u90e8\u6027 (locality) \u7b49\u57fa\u7840\u6982\u5ff5\uff0c\u6784\u5efa\u5ea6\u91cf\u8ddd\u79bb\u3001\u5c3a\u5ea6\u53d8\u6362\u548c\u81ea\u76f8\u4f3c\u7c97\u7c92\u5316\u65b9\u6848\u3002\u8fd1\u5e74\u6765\uff0c\u7814\u7a76\u8005\u4eec\u81f4\u529b\u4e8e\u5c06\u8be5\u7406\u8bba\u62d3\u5c55\u81f3\u590d\u6742\u7f51\u7edc\u7814\u7a76\u3002\u7136\u800c\uff0c\u590d\u6742\u7f51\u7edc\u7cfb\u7edf\u666e\u904d\u5b58\u5728\u4e09\u4e2a\u663e\u8457\u7279\u5f81\uff1a\u663e\u5f0f\u51e0\u4f55\u5750\u6807\u7684\u7f3a\u5931\u3001\u8282\u70b9\u4e0e\u5b50\u56fe\u7edf\u8ba1\u6027\u8d28\u7684\u5f02\u8d28\u6027\uff0c\u4ee5\u53ca\u7c7b\u5747\u5300\u683c\u70b9\u7684\u5bf9\u79f0\u6027\u7684\u7f3a\u4e4f\uff0c\u8fd9\u4e9b\u7279\u6027\u5bfc\u81f4\u5efa\u7acb\u7edf\u4e00\u7684\u91cd\u6574\u5316\u6d41\u7a0b\u9762\u4e34\u4e25\u5cfb\u6311\u6218\u3002\u672c\u6587\u7cfb\u7edf\u68b3\u7406\u7f51\u7edc\u91cd\u6574\u5316\u9886\u57df\u7684\u4e3b\u6d41\u7814\u7a76\u65b9\u6cd5\uff0c\u8bc4\u8ff0\u91cd\u8981\u7406\u8bba\u7a81\u7834\uff0c\u5e76\u7740\u91cd\u63a2\u8ba8\u5f53\u524d\u5c1a\u672a\u89e3\u51b3\u7684\u5173\u952e\u79d1\u5b66\u95ee\u9898\u3002<\/span><\/span><\/strong><\/p>\n


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\u5173\u952e\u8bcd\uff1a\u91cd\u6574\u5316\u7fa4\uff0c\u590d\u6742\u7f51\u7edc\uff0c\u7f51\u7edc\u7c97\u7c92\u5316\uff0c\u51e0\u4f55\u91cd\u6574\u5316\uff0c\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\uff0c\u591a\u5c3a\u5ea6\u7f51\u7edc<\/span>
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Andrea Gabrielli, Diego Garlaschelli, Subodh P. Patil, M. \u00c1ngeles Serrano\u4e28\u4f5c\u8005<\/span><\/span><\/p>\n

\u8bf8\u845b\u660c\u9756\u4e28\u8bd1\u8005<\/span><\/span><\/p>\n

\u9676\u5982\u610f\u4e28\u5ba1\u6821<\/span><\/span><\/p>\n


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\u5173\u4e8e\u91cd\u6574\u5316\u7fa4\uff0c\u4f60\u7edd\u5bf9\u4e0d\u80fd\u9519\u8fc7\u7684\u4e00\u6b21\u5206\u4eab\ud83d\udc47<\/span><\/span><\/p>\n

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\u8bba\u6587\u9898\u76ee\uff1aNetwork renormalization<\/span><\/p>\n

\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/www.nature.com\/articles\/s42254-025-00817-5<\/span><\/p>\n

\u8bba\u6587\u6765\u6e90\uff1aNature review physics<\/span><\/p>\n<\/blockquote>\n


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            k-\u7a7a\u95f4\u4e0a\u7684\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4<\/span><\/p>\n<\/li>\n

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                \u4fe1\u606f\u51e0\u4f55\u4e0e\u53c2\u6570\u6d41<\/span><\/p>\n<\/li>\n<\/ul>\n<\/ul>\n

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

                \u91cd\u6574\u5316\u548c\u53ef\u91cd\u6574\u5316\u662f\u73b0\u4ee3\u7269\u7406\u5b66\u7406\u89e3\u5b87\u5b99\u4e2d\u7269\u8d28\u73b0\u8c61\u7684\u57fa\u7840\u6982\u5ff5\uff0c\u8be5\u7406\u8bba\u5047\u5b9a\u5728\u8db3\u591f\u5927\u7684\u65f6\u7a7a\u5c3a\u5ea6\u4e0a\uff0c\u5c0f\u5c3a\u5ea6\u7ec6\u8282\u662f\u53ef\u4ee5\u88ab\u5e73\u5747\u6389\u7684\uff0c\u4ece\u800c\u89e3\u91ca\u4e86\u4e3a\u4ec0\u4e48\u6211\u4eec\u5728\u65e5\u5e38\u751f\u6d3b\u4e2d\u65e0\u9700\u4e86\u89e3\u4e9a\u539f\u5b50\u7c92\u5b50\u6c34\u5e73\u7684\u7cbe\u786e\u884c\u4e3a\u3002\u91cd\u6574\u5316\u65b9\u6cd5\u7684\u5f62\u5f0f\u5316\u82b1\u8d39\u4e86\u7269\u7406\u5b66\u5bb6\u6570\u5341\u5e74\u65f6\u95f4\uff0c\u5e76\u6700\u7ec8\u4fc3\u6210\u4e86\u5bf9\u67d0\u4e9b\u7269\u7406\u73b0\u8c61\u666e\u904d\u6027\u7684\u60ca\u4eba\u6d1e\u5bdf\u3002\u77e5\u8bc6\u68461 \u603b\u7ed3\u4e86\u4f20\u7edf\u5e94\u7528\u4e8e\u7269\u7406\u7cfb\u7edf\u7684\u91cd\u6574\u5316\u548c\u91cd\u6574\u5316\u7fa4\u53d8\u6362\u7684\u57fa\u672c\u6982\u5ff5\u3002<\/span><\/p>\n

                \u9664\u4e86\u201c\u4f20\u7edf\u201d\u7269\u7406\u7cfb\u7edf\uff0c\u81ea\u7136\u754c\u548c\u793e\u4f1a\u4e2d\u7684\u5927\u578b\u590d\u6742\u7cfb\u7edf\u4e5f\u5305\u542b\u591a\u4e2a\u76f8\u4e92\u4f5c\u7528\u7684\u5c3a\u5ea6\uff0c\u4e14\u6ca1\u6709\u5148\u9a8c\u7684\u6700\u4f73\u5206\u8fa8\u7387\u5c3a\u5ea6\u3002\u56e0\u800c\u81ea\u7136\u4f1a\u95ee\uff0c\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\uff0c\u91cd\u6574\u5316\u662f\u5426\u540c\u6837\u9002\u7528\uff1f\u4f8b\u5982\uff0c\u5728\u5efa\u6a21\u4f01\u4e1a\u95f4\u5546\u54c1\u548c\u670d\u52a1\u6d41\u52a8\u65f6\uff0c\u5f53\u5c06\u4f01\u4e1a\u805a\u96c6\u6210\u66f4\u5e7f\u6cdb\u7684\u7c7b\u522b\uff08\u5982\u7ecf\u6d4e\u90e8\u95e8\uff09\u65f6\uff0c\u5176\u5173\u7cfb\u662f\u5426\u80fd\u88ab\u4e00\u81f4\u5730\u8868\u793a\uff1f\u540c\u6837\uff0c\u5728\u8003\u8651\u7f51\u7edc\u4e0a\u7684\u6d41\u884c\u75c5\u4f20\u64ad\u65f6\uff0c\u4eba\u4eec\u5e0c\u671b\u63a2\u7d22\u5f53\u6a21\u578b\u548c\u53c2\u6570\u5177\u6709\u4e0d\u786e\u5b9a\u6027\u65f6\uff0c\u57fa\u4e8e\u805a\u5408\u7684\u5206\u6790\u7ed3\u679c\u5728\u957f\u671f\u884c\u4e3a\u4e0a\u662f\u5426\u4e0e\u4ed3\u5ba4\u6a21\u578b\u7684\u7ed3\u679c\u6709\u6240\u4e0d\u540c\u3002<\/span><\/p>\n

                \u5c3d\u7ba1\u5c06\u7269\u7406\u7cfb\u7edf\u7684\u7814\u7a76\u7ecf\u9a8c\u76f4\u63a5\u79fb\u690d\u5230\u590d\u6742\u7f51\u7edc\u4e0a\u53ef\u80fd\u5f88\u8bf1\u4eba\uff0c\u4f46\u5fc5\u987b\u6279\u5224\u6027\u5730\u91cd\u65b0\u5ba1\u89c6\u5176\u4e2d\u7684\u5173\u952e\u5047\u8bbe\uff0c\u5305\u62ec\u5728\u7269\u8d28\u901a\u5e38\u5177\u5907\u7684\u76f8\u4e92\u4f5c\u7528\u7684\u5c40\u90e8\u6027\u548c\u7a7a\u95f4\u89c4\u5219\u6027\u2014\u2014\u5176\u4e2d\u65e0\u5e8f\u6027\u901a\u5e38\u53ef\u89c6\u4e3a\u5c0f\u6270\u52a8\u3002\u6b64\u5916\uff0c\u5728\u8003\u8651\u7f51\u7edc\u4e0a\u7684\u52a8\u6001\u8fc7\u7a0b\u65f6\uff0c\u5fc5\u987b\u786e\u4fdd\u65e0\u8bba\u662f\u5bf9\u4e8e\u7279\u5b9a\u4e2a\u4f53\u8fd8\u662f\u5bf9\u7edf\u8ba1\u7cfb\u7efc\uff0c\u4efb\u4f55\u7c97\u7c92\u5316\u65b9\u6cd5\u80fd\u591f\u90fd\u80fd\u641e\u4fdd\u6301\u539f\u5148\u7684\u52a8\u529b\u5b66\u6027\u8d28\u3002\u56e0\u6b64\uff0c\u6709\u5fc5\u8981\u91cd\u65b0\u5ba1\u89c6\u91cd\u6574\u5316\u7684\u57fa\u672c\u524d\u63d0\uff0c\u5373\u901a\u8fc7\u5bf9\u5c0f\u5c3a\u5ea6\u7684\u5e73\u5747\u6765\u7406\u89e3\u6574\u4f53\u7684\u884c\u4e3a\uff0c\u5e76\u4e14\u5728\u590d\u6742\u7cfb\u7edf\u7684\u610f\u4e49\u4e0b\u91cd\u65b0\u8868\u8ff0\u91cd\u6574\u5316\u65b9\u6cd5\u4e5f\u5341\u5206\u91cd\u8981\u3002<\/span><\/p>\n

                \u672c\u6587\u5c06\u7cfb\u7edf\u7efc\u8ff0\u91cd\u6574\u5316\u65b9\u6cd5\u5728\u590d\u6742\u7f51\u7edc\u4e2d\u7684\u5e94\u7528\uff0c\u5206\u6790\u771f\u5b9e\u4e16\u754c\u7684\u7f51\u7edc\u7684\u5178\u578b\u7279\u5f81\uff1a\u666e\u904d\u7f3a\u4e4f\u663e\u5f0f\u51e0\u4f55\u7ed3\u6784\u5d4c\u5165\u3001\u591a\u5c3a\u5ea6\u5f02\u8d28\u6027\u548c\u4e0d\u540c\u5c3a\u5ea6\u95f4\u7684\u4ea4\u4e92\u8fde\u63a5\uff0c\u5e76\u63ed\u793a\u5728\u8fd9\u4e9b\u7279\u6027\u8981\u6c42\u4e0b\uff0c\u9700\u8981\u5982\u4f55\u5bf9\u4f20\u7edf\u91cd\u6574\u5316\u65b9\u6cd5\u8fdb\u884c\u6839\u672c\u6027\u6539\u9020\u3002\u672c\u6587\u9996\u5148\u56de\u987e\u4e86\u57fa\u4e8e\u591a\u79cd\u7c97\u7c92\u5316\u65b9\u6848\u5b9e\u73b0\u7684\u7f51\u7edc\u91cd\u6574\u5316\u65b9\u6cd5\uff0c\u7ee7\u800c\u8003\u67e5\u4ece\u4e0d\u540c\u7406\u8bba\u57fa\u7840\u51fa\u53d1\u3001\u65e8\u5728\u5c06\u91cd\u6574\u5316\u7fa4\u6838\u5fc3\u539f\u7406\u63a8\u5e7f\u81f3\u542b\u5f02\u8d28\u6027\u4e0e\u65e0\u5e8f\u6027\u7f51\u7edc\u7684\u7814\u7a76\u8def\u5f84\uff0c\u6700\u7ec8\u5398\u6e05\u8be5\u9886\u57df\u4e2d\u5c1a\u672a\u89e3\u51b3\u7684\u5f00\u653e\u95ee\u9898\u548c\u5f85\u63a2\u7d22\u65b9\u5411\u3002<\/span><\/p>\n


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

                \n
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                \n
                \n
                \n
                \n

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

                \u77e5\u8bc6\u68461 | \u7edf\u8ba1\u7269\u7406\u548c\u573a\u8bba\u4e2d\u7684\u91cd\u6574\u5316<\/span><\/span><\/span><\/p>\n


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

                \u7269\u7406\u7cfb\u7edf\u4e2d\u76f8\u4e92\u4f5c\u7528\u7684\u5c40\u90e8\u6027\u4e0e\u56e0\u679c\u6027\u534f\u540c\u4f5c\u7528\u4f1a\u9650\u5236\u5c0f\u5c3a\u5ea6\u6da8\u843d\u7684\u5f71\u54cd\uff0c\u4f7f\u5f97\u5b8f\u89c2\u5c3a\u5ea6\u4e0b\u4ec5\u9700\u5c11\u91cf\u53c2\u6570\u5373\u53ef\u523b\u753b\u8be5\u7cfb\u7edf\u3002\u8be5\u601d\u60f3\u7684\u89c4\u8303\u5316\u59cb\u4e8e20\u4e16\u7eaa60\u5e74\u4ee3\uff0cLeo Kadanoff\u5c06\u7c97\u7c92\u5316\u6982\u5ff5\uff08\u65e9\u671f\u7531Paul\u4e0eTatiana Ehrenfest[167]\u7814\u7a76\uff09\u5e94\u7528\u4e8e\u7edf\u8ba1\u529b\u5b66\u7cfb\u7edf\uff0c\u4ee5\u7406\u89e3\u5176\u4e8c\u9636\u76f8\u53d8\u4e34\u754c\u70b9\u90bb\u57df\u7684\u884c\u4e3a[118]\u3002<\/span><\/span><\/p>\n


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

                Ising\u6a21\u578b\u662f\u7ecf\u5178\u8303\u4f8b\uff0c\u5176\u6676\u683c\u81ea\u65cb\u7ecf\u5386\u65e0\u5e8f\u6001\u4e0e\u6709\u5e8f\u6001\uff08\u78c1\u5316\u6001\uff09\u4e4b\u95f4\u7684\u76f8\u53d8\u3002\u901a\u8fc7\u5f15\u5165\u201c\u5757\u81ea\u65cb\u201d\u81ea\u7531\u5ea6\u53ef\u5b9e\u73b0\u6a21\u578b\u7684\u7c97\u7c92\u5316\u3002\u5757\u81ea\u65cb\u53d8\u91cf\u95f4\u76f8\u4e92\u4f5c\u7528\u7684\u6807\u5ea6\u884c\u4e3a\u901a\u8fc7\u91cd\u6574\u5316\u7fa4\u7406\u8bba[111]\u5f97\u4ee5\u5f62\u5f0f\u5316\u3002\u65e9\u671f\u57fa\u4e8e\u6676\u683c\u7684\u6570\u503c\u8ba1\u7b97[168]\u4e4b\u540e\u53d1\u5c55\u4e3a\u66f4\u666e\u9002\u7684\u53d8\u5206\u65b9\u6cd5[169\u2013172]\u3002<\/span><\/span><\/p>\n


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

                \u91cd\u6574\u5316\u7fa4\u7406\u8bba\u901a\u8fc7\u5728\u5b9e\u7a7a\u95f4\u53ef\u7528\u7684\u65b9\u6cd5\u5bf9\u5fae\u89c2\u7ec6\u8282\u8fdb\u884c\u5f62\u5f0f\u5316\u5e73\u5747\uff0c\u4ece\u800c\u5b9a\u4e49\u4e86\u4efb\u610f\u5c3a\u5ea6\u4e0b\u7684\u6709\u6548\u81ea\u7531\u5ea6\u4e0e\u76f8\u4e92\u4f5c\u7528\uff0c\u6210\u4e3a\u7edf\u8ba1\u529b\u5b66\u7684\u91cd\u5927\u7a81\u7834\u3002Kenneth Wilson\u540e\u7eed\u5c06\u5176\u53d1\u5c55\u4e3a\u8fde\u7eed\u573a\u8bba\u4e2d\u7684\u91cd\u6574\u5316\u65b9\u6cd5[113,173]\u3002Wilson\u7684\u5de5\u4f5c\u4e0d\u4ec5\u4e3a\u7406\u89e3\u4e34\u754c\u73b0\u8c61\u7684\u6807\u5ea6\u884c\u4e3a\u5960\u5b9a\u7406\u8bba\u57fa\u7840\uff0c\u66f4\u5c06\u573a\u8bba\u4e2d\u5904\u7406\u540d\u4e49\u53d1\u6563\u91cf\u7684\u96f6\u6563\u65b9\u6cd5\u7cfb\u7edf\u5316\u3002\u8fd9\u4e9b\u53d1\u6563\u6027\u6e90\u4e8e\u6570\u5b66\u4e0a\u4e3a\u89e3\u51b3\u4efb\u610f\u5c0f\u5c3a\u5ea6\u95ee\u9898\u7684\u7406\u60f3\u5316\u64cd\u4f5c\uff0c\u867d\u7136\u7814\u7a76\u8005\u4eec\u5bf9\u6b64\u66fe\u63d0\u51fa\u51cf\u9664\u65b9\u6848[174]\uff0c\u4f46\u8be5\u65b9\u6848\u5728\u91cd\u6574\u5316\u7fa4\u7406\u8bba\u5efa\u7acb\u524d\u7f3a\u4e4f\u6982\u5ff5\u57fa\u7840\u3002\u6b64\u540e\uff0c\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u50ac\u751f\u4e86\u201c\u7406\u8bba\u4e4b\u7406\u8bba\u201d\uff0c\u63ed\u793a\u5fae\u89c2\u7ec6\u8282\u8fe5\u5f02\u7684\u7269\u7406\u7cfb\u7edf\u5728\u4e34\u754c\u70b9\u9644\u8fd1\u5982\u4f55\u51fa\u73b0\u666e\u9002\u884c\u4e3a[175\u2013179]\u3002<\/span><\/span><\/p>\n


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

                \u8fc7\u53bb\u4e94\u5341\u5e74\u95f4\uff0c\u91cd\u6574\u5316\u7fa4\u6280\u672f\u5df2\u6269\u5c55\u81f3\u4ece\u6700\u5927\u5c3a\u5ea6\u7684\u5b87\u5b99\u5b66\u5230\u6700\u5c0f\u5c3a\u5ea6\u7684\u7c92\u5b50\u7269\u7406\u7b49\u5e7f\u6cdb\u9886\u57df\u3002\u5728\u7edf\u8ba1\u529b\u5b66\u8303\u7574\u5185\uff0c\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u5df2\u63a8\u5e7f\u81f3\u540c\u8d28\u5747\u5300\u7684\u5206\u5f62\u683c\u70b9\u4e0a\u7684\u975e\u5e73\u8861\u7cfb\u7edf[180\u2013186]\uff0c\u5176\u5c40\u90e8\u5e73\u79fb\u4e0d\u53d8\u6027\u80fd\u591f\u7b80\u5316\u8ba1\u7b97\u3002\u8d85\u8d8a\u521d\u59cb\u5e94\u7528\u7684\u91cd\u8981\u8303\u4f8b\u5305\u62ec\uff1a\u6d41\u884c\u75c5\u52a8\u529b\u5b66\u6a21\u578b[187]\u3001\u751f\u7269\u7fa4\u4f53\u884c\u4e3a\u52a8\u529b\u5b66[188\u2013190]\u3001\u795e\u7ecf\u7f51\u7edc[191\u2013194]\u3001\u52a8\u6001\u4e0e\u6709\u5411\u903e\u6e17[195,196]\u3001\u89c2\u70b9\u52a8\u529b\u5b66\u7684\u9009\u6c11\u6a21\u578b[197]\uff0c\u4ee5\u53ca\u4e00\u7ef4\u94fe[198]\u3001\u683c\u70b9[199]\u548c\u5c42\u7ea7\u6811[200]\u4e0a\u975e\u7ebf\u6027\u632f\u5b50\u6a21\u578b\uff08\u5982Kuramoto\u6a21\u578b[120,121]\uff09\u7684\u540c\u6b65\u6a21\u578b\u3002\u6b64\u5916\uff0c\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u5728\u5f20\u91cf\u7f51\u7edc[192,201\u2013203]\u53ca\u4fe1\u606f\u8bba\u6846\u67b6[204\u2013208]\u4e2d\u4ea6\u83b7\u6210\u529f\u5e94\u7528\u3002<\/span><\/span><\/p>\n


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

                \u4e0e\u5e73\u8861\u6001\u4e0d\u540c\uff0c\u975e\u5e73\u8861\u7cfb\u7edf\u4e2d\u51b3\u5b9a\u666e\u9002\u7c7b\u7684\u8981\u7d20\u5f80\u5f80\u672a\u77e5\uff0c\u4e14\u5fae\u6270\u5904\u7406\u4e2d\u9ad8\u9636\u91cd\u6574\u5316\u7fa4\u8ba1\u7b97\u901a\u5e38\u4e0d\u53ef\u884c\u3002\u975e\u5fae\u6270\u91cd\u6574\u5316\u7fa4\u4f5c\u4e3a\u6709\u6f5c\u529b\u7684\u66ff\u4ee3\u65b9\u6848[209\u2013212]\uff0c\u5df2\u5e94\u7528\u4e8e\u683c\u70b9\u4e0a\u7684\u6d41\u884c\u75c5\u6269\u6563\u52a8\u529b\u5b66\u6a21\u578b\u7b49\u7814\u7a76[213]\u3002<\/span><\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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


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

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

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

                <\/span><\/section>\n
                \n
                <\/section>\n<\/section>\n<\/section>\n
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                \u590d\u6742\u7f51\u7edc\u91cd\u6574\u5316\u7684\u6311\u6218<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

                \n

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

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


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

                \u5e94\u7528\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\uff0c\u7814\u7a76\u8005\u4eec\u5df2\u6210\u529f\u53d1\u73b0\u4e86\u4e00\u5927\u7c7b\u7cfb\u7edf\u7684\u666e\u9002\u6027\u7279\u5f81\uff0c\u5bf9\u6784\u5efa\u81ea\u7136\u73b0\u8c61\u7684\u81ea\u4e0b\u800c\u4e0a\u7684\u6a21\u578b\u5177\u6709\u91cd\u8981\u4ef7\u503c\u3002\u7136\u800c\u5728\u66f4\u591a\u771f\u5b9e\u4e16\u754c\u95ee\u9898\u4e2d\uff0c\u76f8\u4e92\u4f5c\u7528\u6781\u5c11\u5448\u73b0\u7c7b\u683c\u70b9\u4f3c\u7684\u540c\u8d28\u89c4\u5219\u6027\u3002\u7ed3\u6784\u65e0\u5e8f\u6027\u4e0e\u7a7a\u95f4\u975e\u5747\u5300\u76f8\u4e92\u4f5c\u7528\u5bfc\u81f4\u4e86\u5177\u6709\u62d3\u6251\u51e0\u4f55\u5f02\u8d28\u6027\u7684\u7f51\u7edc\u6a21\u5f0f\uff08pattern\uff09\u3002\u771f\u5b9e\u4e16\u754c\u7f51\u7edc\u7684\u7279\u5f81\u5305\u62ec\uff1a\u7b2c\u4e00\uff0c\u5ea6\u5206\u5e03\uff08\u8282\u70b9\u8fde\u63a5\u6570\u7684\u5206\u5e03\uff09\u5177\u6709\u591a\u6837\u6027\uff1b\u7b2c\u4e8c\uff0c\u5373\u4f7f\u662f\u5927\u89c4\u6a21\u7f51\u7edc\uff0c\u5176\u4efb\u610f\u4e24\u70b9\u95f4\u7684\u5e73\u5747\u8def\u5f84\u957f\u5ea6\u5f80\u5f80\u4e5f\u5f88\u77ed\uff08\u5373\u5c0f\u4e16\u754c\u7f51\u7edc\u7279\u6027\uff09\uff1b\u7b2c\u4e09\uff0c\u5373\u4f7f\u662f\u7a00\u758f\u7f51\u7edc\uff0c\u5176\u5c40\u90e8\u4e09\u89d2\u5bc6\u5ea6\uff08\u96c6\u805a\u7cfb\u6570\uff09\u4e5f\u662f\u975e\u96f6\u7684\u6709\u9650\u503c\uff1b\u7b2c\u56db\uff0c\u6a21\u5757\u5316\u7684\u793e\u533a\u7ed3\u6784\u6216\u5c42\u7ea7\u578b\u7ed3\u6784\u7b49[1-4]\u3002\u8fd9\u4e9b\u4e0d\u89c4\u5219\u7279\u5f81\u5bf9\u63a8\u5e7f\u6807\u51c6\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u6784\u6210\u6311\u6218\uff0c\u540c\u65f6\u7cfb\u7edf\u6709\u9650\u6027\u5f15\u8d77\u7684\u8fb9\u754c\u6548\u5e94\u4e0e\u6709\u9650\u5c3a\u5ea6\u7684\u6548\u5e94[5-9]\u4f1a\u5bfc\u81f4\u95ee\u9898\u66f4\u52a0\u590d\u6742\u3002<\/span><\/p>\n

                \u5229\u7528\u91cd\u6574\u5316\u7fa4\u5bf9\u7cfb\u7edf\u8fdb\u884c\u5206\u6790\uff0c\u901a\u5e38\u7531\u4ee5\u4e0b\u4e09\u4e2a\u57fa\u672c\u6b65\u9aa4\u7ec4\u6210\u3002\u7b2c\u4e00\uff0c\u5b9a\u4e49\u7c97\u7c92\u5316\u53d8\u91cf\u3002\u53ef\u4ee5\u662f\u5728\u5b9e\u7a7a\u95f4\u4e2d\u5c06\u7c97\u7c92\u5316\u53d8\u91cf\u5b9a\u4e49\u4e3a\u5305\u542b\u591a\u4e2a\u5fae\u89c2\u5355\u5143\u7684\u76f8\u540c\u4ecb\u89c2\u5355\u5143\u6216\u8005\u5b9a\u4e49\u4e3a\u80fd\u591f\u5e73\u94fa\u5b9e\u7a7a\u95f4\u201c\u6a21\u5757\u201d\uff1b\u4e5f\u53ef\u4ee5\u5c06\u5176\u5b9a\u4e49\u4e3a\u5728\u5bf9\u5076\u7684 k-\u7a7a\u95f4\u4e2d\u5c06\u53d8\u91cf\u5206\u89e3\u4e3a\u4ece\u6700\u77ed\u5230\u6700\u957f\u7684\u4e0d\u540c\u6ce2\u957f\u7684\u5206\u91cf\uff1b\u7b2c\u4e8c\uff0c\u5229\u7528\u6c42\u5e73\u5747\u6216\u8fb9\u7f18\u5206\u5e03\uff0c\u7ea6\u5316\u6389\u7cfb\u7edf\u4e2d\u7531\u5c40\u90e8\u6da8\u843d\u4e3a\u4ee3\u8868\u7684\u5fae\u5c0f\u7ec6\u8282\uff0c\u5373\u5c06\u5c0f\u5c3a\u5ea6\u5355\u5143\u6216\u77ed\u6ce2\u957f\uff08\u5feb\u901f\uff09\u6a21\u6001\u7b49\u5c5e\u6027\u8fdb\u884c\u5e73\u5747\u5316\uff0c\u4ece\u800c\u5f97\u5230\u66f4\u4e0a\u4e00\u5c42\u7ea7\u7684\u6027\u8d28\uff1b\u7b2c\u4e09\uff0c\u5bf9\u7c97\u7c92\u5316\u7cfb\u7edf\u7684\u8026\u5408\u6a21\u5f0f\u548c\u53c2\u6570\u6570\u503c\u8fdb\u884c\u91cd\u6574\u5316\u3002\uff08\u5728\u5177\u6709\u8fde\u7eed\u81ea\u7531\u5ea6\u7684\u7406\u8bba\u4e2d\uff0c\u91cd\u6574\u5316\u8fd8\u9700\u8981\u4e00\u4e9b\u6280\u5de7\u6765\u5904\u7406\u4e0d\u53ef\u907f\u514d\u51fa\u73b0\u7684\u65e0\u7a77\u5927\u3002\u8fd9\u79cd\u65b9\u6cd5\u5728\u7c92\u5b50\u7269\u7406\u5b66\u548c\u7edf\u8ba1\u573a\u8bba\u4e2d\u662f\u719f\u77e5\u7684[10,11]\uff0c\u4f46\u5728\u5f53\u524d\u590d\u6742\u7f51\u7edc\u7684\u80cc\u666f\u4e0b\uff0c\u7531\u4e8e\u79bb\u6563\u548c\u6709\u9650\u6027\u8d28\uff0c\u4e0d\u9700\u8981\u8fd9\u79cd\u989d\u5916\u7684\u5904\u7406\u624b\u6bb5\uff09\u3002\u8fd9\u4e9b\u64cd\u4f5c\u7684\u91cd\u590d\u6267\u884c\uff0c\u53ef\u4ee5\u4ea7\u751f\u91cd\u6574\u5316\u6d41\uff08RG flow\uff09\uff0c\u5176\u8f68\u8ff9\u548c\u4e0d\u52a8\u70b9\u4e5f\u662f\u7814\u7a76\u5bf9\u8c61\u4e4b\u4e00\u3002<\/span><\/p>\n

                \u7b2c\u4e00\u6b65\u662f\u5b9a\u4e49\u7c97\u7c92\u5316\u53d8\u91cf\u3002\u8fd9\u5bf9\u4e8e\u5d4c\u5165\u5728\u5e73\u79fb\u4e0d\u53d8\u7684\u5ea6\u91cf\u7a7a\u95f4\uff08\u5982\u89c4\u5219\u683c\u70b9\u6216\u6b27\u51e0\u91cc\u5f97\u51e0\u4f55\uff09\u4e2d\u7684\u5177\u6709\u5c40\u90e8\u76f8\u4e92\u4f5c\u7528\u7684\u5747\u5300\u7269\u7406\u7cfb\u7edf\u6765\u8bf4\u662f\u76f4\u63a5\u7684\uff0c\u56e0\u4e3a\u8ddd\u79bb\u548c\u90bb\u57df\u7684\u6982\u5ff5\u4f7f\u5f97\u201c\u76f8\u540c\u7684\u4ecb\u89c2\u5355\u5143\u201d\u6216\u201c\u6ce2\u957f\u201d\u6613\u4e8e\u5b9a\u4e49\uff08\u4f8b\u5982\uff0c\u4e8c\u7ef4\u683c\u5b50\u53ef\u4ee5\u5bb9\u6613\u5730\u7c97\u7c92\u5316\u5230\u4e00\u4e2a\u5177\u6709\u76f8\u540c\u5bf9\u79f0\u6027\u548c\u7ef4\u5ea6\u7684\u7f29\u5c0f\u683c\u5b50\u4e0a\uff09\u3002\u5728\u5177\u6709\u5168\u5c40\u5747\u5300\u540c\u8d28\u76f8\u4e92\u4f5c\u7528\u7684\u7cfb\u7edf\u4e2d\uff0c\u5982\u5728\u5e73\u5747\u573a\u6a21\u578b\u4e2d\u7406\u60f3\u5316\u7684\u90a3\u6837\uff0c\u7cfb\u7edf\u7684\u7ed3\u6784\u662f\u53ef\u4ee5\u7b80\u5355\u5730\u6620\u5c04\u5230\u4e00\u4e2a\u5168\u8fde\u63a5\u7684\u56fe\u4e0a\u3002\u7136\u800c\uff0c\u5728\u9ad8\u5ea6\u975e\u5747\u5300\u548c\u5c0f\u4e16\u754c\u7f51\u7edc\u4e2d\u5b9a\u4e49\u7c97\u7c92\u5316\u53d8\u91cf\u53d8\u5f97\u4e0d\u90a3\u4e48\u7b80\u5355\uff0c\u8fd9\u63d0\u51fa\u4e86\u4e00\u4e2a\u95ee\u9898\uff1a\u5728\u8fd9\u4e2a\u80cc\u666f\u4e0b\uff0c\u5982\u4f55\u9002\u5f53\u5730\u5b9a\u4e49\u5757\u8282\u70b9\u6216\u6162\u6a21\u6001\uff1f \u6b64\u5916\uff0c\u8fd9\u7c7b\u7f51\u7edc\u901a\u5e38\u662f\u4f7f\u7528\u7ecf\u9a8c\u4fe1\u606f\u7684\u5206\u8fa8\u7387\u6c34\u5e73\u6784\u5efa\u7684\uff0c\u8fd9\u4e9b\u6c34\u5e73\u901a\u5e38\u53d7\u5230\u6570\u636e\u9650\u5236\u7684\u7ea6\u675f\u3002\u4f8b\u5982\uff0c\u6d41\u884c\u75c5\u4f20\u64ad\u548c\u7ecf\u6d4e\u51b2\u51fb\u901a\u5e38\u662f\u5728\u805a\u5408\u6c34\u5e73\u4e0a\u89c2\u5bdf\u5230\u7684\uff08\u6bd4\u5982\u4e9a\u7fa4\u4f53\u7684\u63a5\u89e6\u6216\u7ecf\u6d4e\u90e8\u95e8\u6d41\u52a8\uff09\uff0c\u800c\u4e0d\u662f\u5728\u5b9e\u9645\u52a8\u6001\u53d1\u751f\u7684\u66f4\u7ec6\u5c3a\u5ea6\u4e0a\uff08\u4e2a\u4f53\u611f\u67d3\u6216\u516c\u53f8\u5c42\u9762\u7684\u4f20\u64ad\u51b2\u51fb\uff09\u3002\u76f4\u63a5\u5728\u8fd9\u4e9b\u805a\u5408\u6c34\u5e73\u4e0a\u5efa\u6a21\u8fc7\u7a0b\u901a\u5e38\u65e0\u6cd5\u6355\u6349\u5230\u7cfb\u7edf\u5728\u66f4\u7ec6\u5c3a\u5ea6\u4e0a\u7684\u52a8\u6001\uff0c\u8fd9\u4e00\u70b9\u57282008\u5e74\u91d1\u878d\u5371\u673a\u671f\u95f4\u7684\u51b2\u51fb\u4f20\u64ad\u7814\u7a76\u548cCOVID-19\u7206\u53d1\u671f\u95f4\u7684\u6d41\u884c\u75c5\u4f20\u64ad\u7814\u7a76\u4e2d\u6709\u6240\u4f53\u73b0[12,13]\u3002<\/span><\/p>\n

                \u7b2c\u4e8c\u6b65\u662f\u5e73\u5747\u6389\u5c40\u90e8\u6ce2\u52a8\u3002\u4e0e\u7b2c\u4e00\u6b65\u7c7b\u4f3c\u7c7b\u4f3c\uff0c\u5728\u540c\u8d28\u683c\u70b9\u6216\u5ea6\u91cf\u7a7a\u95f4\u4e2d\uff0c\u5229\u7528\u5185\u90e8\u5bf9\u79f0\u6027\uff0c\u53ef\u4ee5\u901a\u8fc7\u5750\u6807\u5316\u5b9a\u4e49\u7684\u90bb\u8fd1\u6027\u523b\u753b\u8fde\u901a\u6027\u6982\u5ff5\uff0c\u5373\u7a7a\u95f4\u4e0a\u66f4\u63a5\u8fd1\u7684\u8282\u70b9\u66f4\u6709\u53ef\u80fd\u8fde\u63a5\u3002\u5728\u8fd9\u4e9b\u7a7a\u95f4\u4e0a\u7684\u7269\u7406\u7406\u8bba\u662f\u5c40\u90e8\u7684\uff0c\u7c97\u7c92\u5316\u7406\u8bba\u53ea\u6d89\u53ca\u5c40\u90e8\u573a\u53ca\u5176\u6709\u9650\u9636\u5bfc\u6570\u3002\u7136\u800c\uff0c\u5c40\u90e8\u6027\u6982\u5ff5\u5e76\u4e0d\u80fd\u76f4\u63a5\u63a8\u5e7f\u5230\u4e0d\u89c4\u5219\u7684\u7f51\u7edc\u5316\u7a7a\u95f4\u7684\u60c5\u5f62\u3002\u5728\u5bf9\u79f0\u7684\u5e03\u5c14\u7f51\u7edc\u4e2d\uff0c\u53ef\u4ee5\u901a\u8fc7\u90bb\u63a5\u77e9\u9635\uff08\u523b\u753b\u76f8\u90bb\u76f4\u63a5\u76f8\u4e92\u4f5c\u7528\uff09\u6216\u5176\u5e42\uff08\u523b\u753b\u76f4\u5230\u7b2cn\u7ea7\u8fd1\u90bb\u7684\u76f8\u4e92\u4f5c\u7528\uff09\u6765\u5b9a\u4e49\u76f8\u4e92\u4f5c\u7528\uff0c\u4e5f\u53ef\u4ee5\u4f7f\u7528\u6700\u77ed\u8def\u8bf1\u5bfc\u7684\u79bb\u6563\u5ea6\u91cf[14]\u3002\u7f51\u7edc\u7684\u7a00\u758f\u6027\u3001\u4e0d\u540c\u8def\u5f84\u8ddd\u79bb\u5904\u5ea6\u5206\u5e03\u7684\u5f02\u8d28\u5206\u5e03\u4ee5\u53ca\u65e0\u5e8f\u957f\u7a0b\u76f8\u4e92\u4f5c\u7528\uff08\u5c0f\u4e16\u754c\u7279\u6027\uff09\u7b49\u8bf8\u591a\u56e0\u7d20\u4f7f\u5f97\u5728\u590d\u6742\u7f51\u7edc\u4e2d\u660e\u786e\u5b9a\u4e49\u5c40\u90e8\u6027\u53d8\u5f97\u590d\u6742\u3002<\/span><\/p>\n

                \u6700\u540e\uff0c\u7b2c\u4e09\u6b65\u662f\u91cd\u6574\u5316\u8026\u5408\u548c\u53c2\u6570\u3002\u8fd9\u4e00\u6b65\u7684\u590d\u6742\u6027\u4e0e\u524d\u4e24\u6b65\u5bc6\u5207\u76f8\u5173\u3002\u5728\u65e0\u5e8f\u7684\u683c\u70b9\u7cfb\u7edf\uff08\u5982\u81ea\u65cb\u73bb\u7483[15]\uff09\u4e2d\uff0c\u76f8\u4e92\u4f5c\u7528\u62d3\u6251\u53ef\u80fd\u662f\u89c4\u5219\u7684\uff0c\u4f46\u8026\u5408\u5e38\u6570\u7684\u5f02\u8d28\u53ef\u80fd\u975e\u5e38\u9ad8\u3002\u8fd9\u79cd\u5f02\u8d28\u6027\u53ef\u4ee5\u7528\u968f\u673a\u53d8\u91cf\u5efa\u6a21\uff0c\u5176\u4e2d\u81ea\u5e73\u5747\u80fd\u786e\u4fdd\u7a7a\u95f4\u5e73\u5747\u5bf9\u5e94\u4e8e\u5206\u5e03\u5e73\u5747\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u91cd\u6574\u5316\u8026\u5408\u9700\u8981\u5c06\u7ec6\u5c3a\u5ea6\u8026\u5408\u5e38\u6570\u7684\u6982\u7387\u5206\u5e03\u5bf9\u5e94\u5230\u7c97\u7c92\u5316\u540e\u7684\u5e38\u6570\u7684\u8bf1\u5bfc\u5206\u5e03\u4e0a[16]\u3002\u5728\u5f02\u8d28\u7f51\u7edc\u4e2d\uff0c\u6311\u6218\u66f4\u52a0\u4e25\u5cfb\uff0c\u56e0\u4e3a\u76f8\u4e92\u4f5c\u7528\u7684\u62d3\u6251\u672c\u8eab\u662f\u65e0\u89c4\u5219\u7684\u3002\u7531\u4e8e\u8bb8\u591a\u590d\u6742\u7f51\u7edc\u662f\u57fa\u4e8e\u7279\u5b9a\u6027\u8d28\u4ece\u7cfb\u7efc\u4e2d\u62bd\u6837\u800c\u5f97\u5230\u7684\u968f\u673a\u56fe\uff0c\u56e0\u6b64\uff0c\u91cd\u6574\u5316\u8026\u5408\u6a21\u5f0f\u548c\u53c2\u6570\u6570\u503c\u9700\u8981\u5c06\u7ec6\u7c92\u5ea6\u56fe\u4e0a\u7684\u521d\u59cb\u6982\u7387\u5206\u5e03\u53d8\u6362\u5230\u7c97\u7c92\u5ea6\u56fe\u4e0a\u7684\u65b0\u5206\u5e03\u3002\u4ece\u7406\u8bba\u4e0a\u6765\u8bf4\uff0c\u8be5\u53d8\u6362\u5b9a\u4e49\u4e86\u4e00\u4e2a\u91cd\u6574\u5316\u6d41\uff0c\u5177\u6709\u5176\u81ea\u8eab\u72ec\u7279\u7684\u6cdb\u51fd\u8f68\u8ff9\u548c\u4e0d\u52a8\u70b9\u3002<\/span><\/p>\n

                \u53d7\u8fd9\u4e9b\u8003\u8651\u7684\u542f\u53d1\uff0c\u8fd1\u5e74\u6765\u7814\u7a76\u4eba\u5458\u81f4\u529b\u4e8e\u4e3a\u590d\u6742\u7f51\u7edc\u91cd\u6574\u5316\u5efa\u7acb\u901a\u7528\u6846\u67b6\u3002\u4e0b\u6587\u5c06\u603b\u7ed3\u5404\u4e0d\u540c\u4f46\u76f8\u4e92\u5173\u8054\u7684\u4e00\u7cfb\u5217\u7b56\u7565\u6765\u5b9e\u73b0\u8fd9\u4e00\u76ee\u6807\u7684\u65b9\u6cd5\u3002\u6211\u4eec\u9996\u5148\u5bf9\u7c97\u7c92\u5316\u590d\u6742\u7f51\u7edc\u7684\u65b9\u6cd5\u8fdb\u884c\u5bbd\u6cdb\uff08\u4f46\u4f9d\u7136\u65e0\u6cd5\u5168\u9762\u7684\uff09\u6982\u8ff0\uff0c\u7136\u540e\u6df1\u5165\u63a2\u8ba8\u5728\u5f02\u8d28\u7f51\u7edc\u4e0a\u8ff0\u5bf9\u91cd\u6574\u5316\u7a0b\u5e8f\u7684\u4e09\u4e2a\u6b65\u9aa4\u4e2d\u7684\u82e5\u5e72\u6b65\u9aa4\u8fdb\u884c\u63a8\u5e7f\u7684\u65b9\u6cd5\u3002<\/span><\/p>\n

                <\/span>
                <\/span><\/span><\/span><\/h1>\n

                \n
                \n
                \n
                \n
                \n

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

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

                \u7f51\u7edc\u7c97\u7c92\u5316\u65b9\u6cd5<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

                \n

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

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


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

                \u7531\u4e8e\u771f\u5b9e\u4e16\u754c\u4e2d\u7684\u590d\u6742\u7f51\u7edc\u666e\u904d\u7f3a\u4e4f\u57fa\u672c\u683c\u70b9\u7ed3\u6784\uff0c\u56e0\u6b64\u5efa\u7acb\u7edf\u4e00\u7684\u7c97\u7c92\u5316\u65b9\u6848\u53d8\u5f97\u5341\u5206\u590d\u6742\uff0c\u8fd9\u540c\u65f6\u4e5f\u50ac\u751f\u4e86\u82e5\u5e72\u5927\u7c7b\u7684\u591a\u6837\u5316\u65b9\u6cd5\u3002<\/span><\/p>\n

                <\/span>\u57fa\u4e8e\u6700\u77ed\u8def\u7684\u65b9\u6cd5<\/span><\/span><\/span><\/h2>\n

                \u91c7\u7528\u6700\u77ed\u8def\u7684\u957f\u5ea6\u5b9a\u4e49\u8282\u70b9\u95f4\u8ddd\u662f\u7f51\u7edc\u7c97\u7c92\u5316\u65b9\u6cd5\u4e4b\u4e00\uff0c\u8be5\u65b9\u6cd5\u501f\u52a9\u5206\u5f62\u51e0\u4f55\u4e2d\u7684\u76d2\u8986\u76d6\u601d\u60f3\uff08box-covering\uff09[17,18]\u5b9e\u73b0\u8fed\u4ee3\u91cd\u6574\u5316\u7fa4\u53d8\u6362\u3002\u8be5\u65b9\u6cd5\u4ee5\u6700\u77ed\u8def\u8ddd\u79bb\u4e3a\u5ea6\u89c4\uff08\u6ce8\uff1a\u6570\u5b66\u4e0a\u901a\u5e38\u79f0\u4e3a\u5ea6\u91cf\uff09\uff0c\u5c06\u6307\u5b9a\u8ddd\u79bb\u5185\u7684\u8282\u70b9\u805a\u5408\u6210\u7c97\u7c92\u5316\u8282\u70b9\u5f62\u6210\u66f4\u7c97\u7684\u7a7a\u95f4\u5206\u8fa8\u7387\uff0c\u4ece\u800c\u751f\u6210\u91cd\u6574\u5316\u7fa4\u5e8f\u5217[14]\u3002\u6b64\u65b9\u6cd5\u80fd\u591f\u63ed\u793a\u7f51\u7edc\u7684\u81ea\u76f8\u4f3c\u6027\u4e0e\u5206\u5f62\u7279\u5f81[14,19\u201321]\uff0c\u5e76\u80fd\u7ed9\u51fa\u65b0\u751f\u957f\u673a\u5236[22]\u548c\u7f51\u7edc\u666e\u9002\u7c7b\u5206\u7c7b[5,23]\u3002\u7136\u800c\u53d7\u9650\u4e8e\u5c0f\u4e16\u754c\u7279\u6027\uff0c\u4ee5\u6700\u77ed\u8def\u4e3a\u8ddd\u79bb\u51c6\u5219\u7684\u91cd\u6574\u5316\u7fa4\u53d8\u6362\u96be\u4ee5\u6709\u6548\u89e3\u8026\u548c\u63ed\u793a\u6807\u5ea6\u884c\u4e3a\u3002\u56e0\u6b64\uff0c\u8fd9\u7c7b\u53d8\u6362\u4e0b\u5ea6\u5206\u5e03\u7684\u81ea\u76f8\u4f3c\u6027\u5e76\u4e0d\u4f34\u968f\u5173\u8054\u51fd\u6570\u7684\u6807\u5ea6\u5f8b\u800c\u51fa\u73b0\uff0c\u7279\u522b\u662f\u5728\u7f51\u7edc\u96c6\u805a\u65b9\u9762\uff0c\u8fd9\u4e2a\u7279\u5f81\u8868\u73b0\u5f97\u66f4\u52a0\u660e\u663e\u3002<\/span><\/p>\n

                \u53e6\u4e00\u65b9\u9762\uff0c\u7814\u7a76\u8005\u63d0\u51fa\uff0c\u53ef\u4ee5\u5728\u5177\u6709\u77ed\u7a0b\u8fde\u63a5\u6027\u8d28\u7684\u89c4\u5219\u683c\u70b9\u7f51\u7edc\u4e2d\u6dfb\u52a0\u957f\u7a0b\u8fde\u63a5\uff0c\u8fdb\u800c\u5b9e\u73b0\u5b9e\u7a7a\u95f4\u91cd\u6574\u5316\u7fa4\u53d8\u6362\u3002\u8fd9\u7c7b\u53d8\u6362\u5df2\u7528\u4e8e\u7814\u7a76\u82e5\u5e72\u95ee\u9898\uff0c\u5305\u62ecWatts-Strogatz\u6a21\u578b\u5728\u4e34\u754c\u70b9\u9644\u8fd1\u7684\u884c\u4e3a\uff08\u5728\u6700\u77ed\u8def\u5bc6\u5ea6\u8d8b\u4e8e\u96f6\u7684\u6781\u9650\u60c5\u5f62[24]\uff09\u4ee5\u53ca\u7ecf\u53d8\u6362\u5176\u62d3\u6251\u6027\u8d28\u4fdd\u6301\u4e0d\u53d8\u7684\u683c\u70b9\u4e0a\u7684\u65e0\u6807\u5ea6\u7f51\u7edc\u6a21\u578b[25]\u3002\u7136\u800c\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u9700\u9884\u77e5\u8282\u70b9\u5750\u6807\uff0c\u6216\u9700\u660e\u786e\u533a\u5206\u77ed\u7a0b\u8fde\u63a5\uff08\u5b9a\u4e49\u5b9e\u9645\u53c2\u4e0e\u7c97\u7c92\u5316\u7684\u8def\u5f84\u957f\u5ea6\uff09\u4e0e\u957f\u7a0b\u8fde\u63a5\u3002\u5bf9\u4e8e\u771f\u5b9e\u7f51\u7edc\uff0c\u8fd9\u7c7b\u4fe1\u606f\u901a\u5e38\u672a\u77e5\u751a\u81f3\u65e0\u6cd5\u660e\u786e\u5b9a\u4e49\u3002<\/span><\/p>\n

                <\/span>\u8c31\u65b9\u6cd5<\/span><\/span><\/span><\/h2>\n

                \u53e6\u4e00\u79cd\u65b9\u6cd5\u57fa\u4e8e\u7f51\u7edc\u7684\u8c31\u6027\u8d28\uff0c\u8be5\u7c7b\u65b9\u6cd5\u901a\u8fc7\u4fdd\u6301\u7279\u5b9a\u8fc7\u7a0b\u7684\u52a8\u529b\u5b66\u884c\u4e3a\u7684\u65b9\u5f0f\u8fdb\u884c\u7c97\u7c92\u5316\u5904\u7406\u3002\u8c31\u7c97\u7c92\u5316\u65b9\u6cd5\u6700\u521d\u662f\u4e3a\u7814\u7a76\u7f51\u7edc\u4e0a\u7684\u968f\u673a\u6e38\u8d70\u800c\u8bbe\u8ba1\u7684\uff0c\u5176\u901a\u8fc7\u4fdd\u7559\u968f\u673a\u77e9\u9635\u7684\u6700\u5927\u7279\u5f81\u503c\u53ca\u5bf9\u5e94\u7279\u5f81\u5411\u91cf\u6765\u786e\u4fdd\u5927\u5c3a\u5ea6\u884c\u4e3a\u7684\u4fdd\u6301\uff0c\u5728\u6709\u6548\u5254\u9664\u5feb\u6a21\u6001\u7684\u540c\u65f6\u4fdd\u6301\u6162\u6a21\u6001\u4e0d\u53d8[26]\u3002\u8be5\u65b9\u6cd5\u5df2\u63a8\u5e7f\u81f3\u4e8c\u90e8\u7f51\u7edc\uff08bipartite networks\uff09[27]\uff0c\u5e76\u5df2\u7528\u4e8e\u8026\u5408\u632f\u5b50\u7684\u540c\u6b65\u52a8\u529b\u5b66\u7814\u7a76\u4e2d\uff0c\u6b64\u65f6\u7f51\u7edc\u7684\u62c9\u666e\u62c9\u65af\u77e9\u9635\u6210\u4e3a\u8fd9\u4e00\u65b9\u6cd5\u7684\u6838\u5fc3\u7b97\u7b26\uff08\u6ce8\uff1a\u201c\u7b97\u7b26\u201d\u5728\u6570\u5b66\u4e0a\u901a\u5e38\u79f0\u4e3a\u201c\u7b97\u5b50\u201d\uff09[28\u201330]\u3002\u7c7b\u4f3c\u7684\u8c31\u7c97\u7c92\u5316\u601d\u60f3\u4e5f\u53ef\u4ee5\u7528\u4e8e\u6709\u5411\u7f51\u7edc\u7684\u540c\u6b65[31]\u548c\u53ef\u63a7\u6027\u5206\u6790[32]\u7b49\u7814\u7a76\u3002\u4f7f\u7528\u56fe\u7684\u62c9\u666e\u62c9\u65af\u77e9\u9635\u7684\u7279\u5f81\u5411\u91cf\u4e0e\u7279\u5f81\u503c\uff0c\u7814\u7a76\u8005\u8fdb\u4e00\u6b65\u5229\u7528\u786e\u5b9a\u6027\u591a\u5c42\u7f51\u7edc\uff08\u5982\u9ad8\u65af\u6a21\u578b\u7684Cayley\u6811\u548c\u94bb\u77f3\u6676\u683c[33,34]\uff09\u63a2\u7d22\u4e86\u573a\u8bba\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u5bf9\u5904\u7406\u6709\u5e8f-\u65e0\u5e8f\u73b0\u8c61\u7684\u53ef\u80fd\u6027[33]\u3002\u8fd9\u4e9b\u7814\u7a76\u4e3a\u5efa\u7acb\u57fa\u4e8e\u62c9\u666e\u62c9\u65af\u8c31\u7684\u56fe\u91cd\u6574\u5316\u7406\u8bba\u6846\u67b6[35]\u5960\u5b9a\u4e86\u57fa\u7840\uff0c\u672c\u6587\u540e\u7eed\u5c06\u5bf9\u6b64\u8bbe\u7acb\u72ec\u7acb\u7ae0\u8282\u8fdb\u884c\u8be6\u7ec6\u8ba8\u8bba\u3002<\/span><\/p>\n

                <\/span>\u62d3\u6251\u65b9\u6cd5<\/span><\/span><\/span><\/h2>\n

                \u4e0e\u4e0a\u8ff0\u65b9\u6cd5\u5e76\u884c\u53d1\u5c55\u7684\uff0c\u662f\u57fa\u4e8e\u62d3\u6251\u6027\u8d28\u7684\u7c97\u7c92\u5316\u65b9\u6cd5\u3002\u8fd9\u7c7b\u6280\u672f\u5305\u62ec\uff1a\u8282\u70b9\u4e2d\u5fc3\u6027\u5ea6\u91cf\uff08\u5982\u5ea6[36]\u548c\u5e7f\u4e49\u5ea6[37]\uff09\u3001\u57fa\u4e8e\u90bb\u5c45\u91cd\u53e0\u7684\u8282\u70b9\u76f8\u4f3c\u6027\u5ea6\u91cf[38]\uff0c\u8fd9\u5305\u62ec\u4f20\u7edf\u7684\u793e\u4ea4\u7f51\u7edc\u4e2d\u7684\u7ed3\u6784\u7b49\u6548\u8282\u70b9[39]\u3001\u98df\u7269\u7f51\u4e2d\u7684\u8425\u517b\u7b49\u6548\u7269\u79cd[40]\u7684\u6982\u5ff5\u7b49\uff09\u3001\u4ee5\u53ca\u4f5c\u4e3a\u53cd\u590d\u91cd\u73b0\u7684\u6a21\u5f0f\u7684\u7f51\u7edc\u6a21\u4f53\u5206\u6790[41]\u7b49\u3002<\/span><\/p>\n

                \u7279\u522b\u503c\u5f97\u5173\u6ce8\u7684\u65b9\u6cd5\u8fd8\u5305\u62ec\u8bf8\u5982\u57fa\u4e8e\u5ea6\u9608\u503c\u7684\u91cd\u6574\u5316[42]\u548ck\u6838\u5206\u89e3[43]\u7b49\u8282\u70b9\u5254\u9664\u65b9\u6cd5\u3002\u524d\u8005\u901a\u8fc7\u79fb\u9664\u5ea6\u4f4e\u4e8e\u7279\u5b9a\u9608\u503c\u7684\u8282\u70b9\u6765\u5b9a\u4e49\u5d4c\u5957\u5b50\u56fe\u7684\u5c42\u7ea7\u7ed3\u6784\uff1b\u540e\u8005\u5c06\u7f51\u7edc\u5206\u89e3\u4e3a\u4e00\u7cfb\u5217\u6781\u5927\u5b50\u56fe\uff0c\u5e76\u786e\u4fdd\u5b50\u56fe\u7684\u6bcf\u4e2a\u9876\u70b9\u5747\u6ee1\u8db3\u6700\u5c0f\u5ea6\u7ea6\u675f\u3002\u8fd9\u4e9b\u65b9\u6cd5\u5728\u771f\u5b9e\u7cfb\u7edf\u4e2d\u6709\u6548\u63ed\u793a\u4e86\u8d85\u8d8a\u5ea6\u5206\u5e03\u6807\u5ea6\u4e0d\u53d8\u6027\u7684\u5c42\u7ea7\u81ea\u76f8\u4f3c\u6027\uff0c\u4f8b\u5982\u805a\u7c7b\u8c31\uff08clustering spectrum\uff09\u7684\u6807\u5ea6\u5f8b\u3002<\/span><\/p>\n

                \u6b64\u5916\uff0c\u7814\u7a76\u8005\u8fd8\u63d0\u51fa\u4e86\u57fa\u4e8e\u591a\u5c3a\u5ea6\u793e\u533a\u68c0\u6d4b\u4e2d\u6a21\u5757\u5316\u6982\u5ff5\u7684\u7b56\u7565[44]\uff0c\u5176\u601d\u8def\u7c7b\u4f3c\u4e8e\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u7684\u591a\u5c42\u56fe\u5212\u5206\u7b97\u6cd5\u3002\u8fd9\u7c7b\u7b97\u6cd5\u5305\u542b\u57fa\u4e8e\u8282\u70b9\u6216\u8fb9\u5c5e\u6027\u7684\u7c97\u7c92\u5316\u542f\u53d1\u5f0f\u65b9\u6cd5\uff0c\u4f8b\u5982\u9488\u5bf9\u8fde\u63a5\u5747\u5300\u5206\u5e03\u7684\u56fe\u7684\u91cd\u8fb9\u542f\u53d1\u5f0f\u7b97\u6cd5\uff0c\u901a\u8fc7\u5408\u5e76\u5177\u6709\u5927\u6743\u503c\u8fde\u63a5\u7684\u8282\u70b9\u5b9e\u73b0\u7c97\u7c92\u5316[45]\u3002\u5bf9\u4e8e\u5177\u6709\u5ea6\u5206\u5e03\u5448\u5e42\u5f8b\u7684\u56fe\uff0c\u4e5f\u53ef\u4ee5\u4f7f\u7528\u57fa\u4e8e\u793e\u533a\u7684\u7c97\u7c92\u5316\u65b9\u6848\uff0c\u5c06\u9ad8\u5ea6\u4e92\u8fde\u7684\u9876\u70b9\u96c6\u5408\u5e76[46]\u3002<\/span><\/p>\n

                \u62d3\u6251\u65b9\u6cd5\u4f9d\u8d56\u4e8e\u7279\u5b9a\u7ed3\u6784\u6a21\u5f0f\uff0c\u4f8b\u5982\u5c42\u7ea7\u793e\u533a\u7ed3\u6784\u6216\u7ed3\u6784\u7b49\u4ef7\u8282\u70b9\u7684\u5b58\u5728\uff0c\u56e0\u800c\u5f53\u8fd9\u4e9b\u7279\u5f81\u7f3a\u5931\u65f6\uff0c\u8be5\u65b9\u6cd5\u4f1a\u5931\u6548\u3002\u8fd9\u4e2a\u5c40\u9650\u6027\u5177\u6709\u7269\u7406\u5b66\u4e2d\u5178\u578b\u7684\u91cd\u6574\u5316\u76f8\u77db\u76fe\u7684\u98ce\u9669\uff0c\u8fd9\u662f\u56e0\u4e3a\u540e\u8005\u8981\u6c42\u5373\u4f7f\u7f3a\u4e4f\u4ecb\u89c2\u7279\u5f81\uff0c\u4ecd\u80fd\u5bf9\u7b80\u5355\u6676\u683c\u7cfb\u7edf\u8fdb\u884c\u4e00\u81f4\u4e14\u53ef\u8fed\u4ee3\u7684\u7c97\u7c92\u5316\u64cd\u4f5c\u3002<\/span><\/p>\n

                <\/span>\u5bf9\u79f0\u65b9\u6cd5<\/span><\/span><\/span><\/h2>\n

                \u53e6\u4e00\u79cd\u9488\u5bf9\u8fc7\u7a0b\u7684\u65b9\u6cd5\u5229\u7528\u5bf9\u79f0\u6027\u5b9a\u4e49\u7684\u7b49\u4ef7\u7c7b\u6765\u6784\u9020\u7c97\u7c92\u5316\u65b9\u6848\u3002\u5728\u4ece\u751f\u7269\u79d1\u5b66\u5230\u8ba1\u7b97\u673a\u79d1\u5b66\u7684\u7814\u7a76\u4e2d\uff0c\u80fd\u591f\u8868\u5f81\u7f51\u7edc\u4e0a\u52a8\u6001\u8fc7\u7a0b\u5c40\u90e8\u5bf9\u79f0\u6027\u7684\u65b9\u6cd5\u4e3a\u523b\u753b\u7cfb\u7edf\u57fa\u672c\u6a21\u5757\u63d0\u4f9b\u4e86\u666e\u9002\u6027\u539f\u5219[47]\u3002\u5177\u4f53\u800c\u8a00\uff0c\u5f53\u7f51\u7edc\u5728\u8282\u70b9\u53d8\u6362\u4e0b\u80fd\u591f\u4fdd\u6301\u8f93\u5165\u6811\u4e0d\u53d8\uff08input trees invariant\uff09\u65f6\uff0c\u7f51\u7edc\u4f1a\u6d8c\u73b0\u5747\u8861\u5212\u5206\uff08equitable partitions\uff09[48]\uff0c\u8be5\u6027\u8d28\u5df2\u88ab\u7528\u4e8e\u5b9a\u4e49\u5e38\u5fae\u5206\u65b9\u7a0b\u7684\u6210\u5757\u6027\uff08lumpability\uff09[49,50]\u3001\u5e03\u5c14\u540e\u5411\u7b49\u4ef7\uff08Boolean backward equivalence\uff09[51]\u4ee5\u53ca\u7ea4\u7ef4\u67d3\u8272\u6027\u8d28\uff08fibration colouring\uff09[52]\u7b49\u6982\u5ff5\u3002<\/span><\/p>\n

                \u5bf9\u79f0\u6027\u8bf1\u5bfc\u7684\u5747\u8861\u5212\u5206\u53ef\u5c06\u7cfb\u7edf\u7ea6\u5316\u4e3a\u4fdd\u7559\u6574\u4f53\u52a8\u529b\u5b66\u4e0e\u540c\u6b65\u7279\u6027\u7684\u52a8\u529b\u5b66\u53d8\u91cf\u7684\u96c6\u5408\uff0c\u6b64\u7279\u6027\u5145\u5206\u8bc1\u660e\u4e86\u8be5\u65b9\u6cd5\u7684\u5b9e\u7528\u6027[53]\u3002\u5c3d\u7ba1\u57fa\u4e8e\u5bf9\u79f0\u6027\u7684\u65b9\u6cd5\u8bc6\u522b\u9488\u5bf9\u8fc7\u7a0b\u7684\u7b49\u4ef7\u7c7b\u8282\u70b9\u8fd9\u4e00\u91cd\u8981\u7f51\u7edc\u7ea6\u5316\u6280\u672f\u6781\u4e3a\u6709\u6548\uff0c\u4f46\u5176\u901a\u5e38\u4ec5\u80fd\u786e\u5b9a\u5355\u4e00\u5212\u5206\uff08\u901a\u5e38\u5bf9\u5e94\u6700\u5927\u7f51\u7edc\u7ea6\u5316\uff09\u3002\u4e0e\u7eaf\u62d3\u6251\u5b66\u65b9\u6cd5\u7c7b\u4f3c\uff0c\u8fd9\u7c7b\u65b9\u6cd5\u65e0\u6cd5\u8fed\u4ee3\u5e94\u7528\uff08\u6ce8\uff1a\u65e0\u6cd5\u8fed\u4ee3\u662f\u56e0\u4e3a\u7ecf\u8fc7\u4e00\u6b65\u7ea6\u5316\u540e\uff0c\u5bf9\u79f0\u6027\u6216\u62d3\u6251\u6027\u8d28\u5c31\u53d1\u751f\u4e86\u6539\u53d8\u3002\uff09\uff0c\u4e14\u5728\u5bf9\u79f0\u6027\u7f3a\u5931\u7684\u4f53\u7cfb\u4e2d\u7f3a\u4e4f\u666e\u9002\u6027\u3002<\/span><\/p>\n

                <\/span>\u5de5\u7a0b\u6280\u672f\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u7684\u7c97\u7c92\u5316<\/span><\/span><\/span><\/h2>\n

                \u5f00\u53d1\u4e92\u8054\u7f51\u53ca\u5176\u4ed6\u901a\u4fe1\u4e0e\u4ea4\u901a\u7f51\u7edc\u7684\u7f29\u5c3a\u5de5\u7a0b\u6a21\u578b\u65b9\u6cd5\uff0c\u4e00\u76f4\u662f\u901a\u4fe1\u6280\u672f\u9886\u57df\u7814\u7a76\u7684\u957f\u671f\u76ee\u6807[54\u201356]\u3002\u8fd1\u5e74\u6765\uff0c\u5982\u4f55\u5728\u4fdd\u6301\u56fe\u7ed3\u6784\u5173\u952e\u5c5e\u6027\u57fa\u672c\u4e0d\u53d8\u7684\u524d\u63d0\u4e0b\u7f29\u51cf\u5176\u89c4\u6a21\uff0c\u4e5f\u6210\u4e3a\u673a\u5668\u5b66\u4e60\u9886\u57df\u7684\u91cd\u8981\u8bfe\u9898\u2014\u2014\u56fe\u5d4c\u5165\u6280\u672f\u548c\u56fe\u795e\u7ecf\u7f51\u7edc\u7b49\u6df1\u5ea6\u5b66\u4e60\u5de5\u5177\u6b63\u65e5\u76ca\u5e7f\u6cdb\u5e94\u7528\u4e8e\u56fe\u7ed3\u6784\u6570\u636e\u5206\u6790\u3002\u7c97\u7c92\u5316\u65b9\u6848\u65e8\u5728\u901a\u8fc7\u538b\u7f29\u56fe\u7ed3\u6784\u964d\u4f4e\u5b9e\u9645\u5e94\u7528\u4e2d\u7684\u8ba1\u7b97\u6210\u672c\u4e0e\u590d\u6742\u5ea6[57\u201363]\uff0c\u5176\u5728\u8bbe\u8ba1\u9ad8\u6548\u901a\u4fe1\u4e0e\u6570\u636e\u5b58\u50a8\u7ea0\u9519\u7f16\u7801\u65b9\u9762\u5177\u6709\u91cd\u8981\u4ef7\u503c\u3002\u7814\u7a76\u8005\u5df2\u8fd0\u7528\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u751f\u6210\u5c0f\u578b\u7f51\u7edc\u7f16\u7801\uff0c\u53ef\u6709\u6548\u8ba1\u7b97\u6811\u72b6\u7f51\u7edc\u4e2d\u7f6e\u4fe1\u4f20\u64ad\u7684\u6027\u80fd[64]\u3002\u5c3d\u7ba1\u8fd9\u4e9b\u65b9\u6cd5\u53d7\u7f51\u7edc\u91cd\u6574\u5316\u601d\u60f3\u9a71\u52a8\uff0c\u4f46\u5176\u901a\u5e38\u805a\u7126\u4e8e\u7279\u5b9a\u8fc7\u7a0b\uff0c\u5bf9\u56fe\u7ed3\u6784\u6570\u636e\u4e0e\u590d\u6742\u7cfb\u7edf\u591a\u5c3a\u5ea6\u672c\u8d28\u7684\u5e95\u5c42\u539f\u7406\u63ed\u793a\u6709\u9650\u3002<\/span><\/p>\n

                \n

                \u5173\u4e8e\u5173\u4e8e\u6587\u732e63\u7684\u8bba\u6587\u89e3\u8bfb<\/span><\/span><\/p>\n

                \"\u6d77\u62a5\u9884\u89c8\"<\/span><\/span><\/p>\n<\/blockquote>\n

                <\/span>\u4fe1\u606f\u8bba\u65b9\u6cd5<\/span><\/span><\/span><\/h2>\n

                \u4fe1\u606f\u8bba\u65b9\u6cd5\u4e5f\u80fd\u591f\u63a2\u7d22\u7f51\u7edc\u4e0d\u540c\u5c3a\u5ea6\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u3002\u5728\u590d\u6742\u7f51\u7edc\u4e2d\uff0c\u66f4\u5927\u5c3a\u5ea6\u901a\u5e38\u80fd\u63d0\u4f9b\u5173\u4e8e\u7f51\u7edc\u8fde\u63a5\u7ed3\u6784\u7684\u66f4\u4e30\u5bcc\u7684\u4fe1\u606f\u91cf\uff0c\u8fd9\u4e00\u73b0\u8c61\u79f0\u4e3a\u56e0\u679c\u6d8c\u73b0\u73b0\u8c61[65]\uff0c\u56e0\u679c\u6d8c\u73b0\u53ef\u6709\u6548\u964d\u4f4e\u8282\u70b9\u95f4\u5173\u7cfb\u89c2\u6d4b\u7684\u4e0d\u786e\u5b9a\u6027\u3002\u6b64\u5916\uff0c\u9488\u5bf9\u5177\u6709\u7279\u5b9a\u7684\u56fe\u4e0a\u7684\u52a8\u529b\u5b66\u8fc7\u7a0b\uff0c\u53ef\u80fd\u5b58\u5728\u591a\u79cd\u6355\u6349\u539f\u59cb\u8fc7\u7a0b\u4e0d\u540c\u7279\u5f81\u7684\u7c97\u7c92\u5316\u63cf\u8ff0\u3002\u4fe1\u606f\u8bba\u65b9\u6cd5\u6709\u52a9\u4e8e\u8bc4\u4f30\u7f51\u7edc\u52a8\u529b\u5b66\u8fc7\u7a0b\u72b6\u6001\u7a7a\u95f4\u7684\u5212\u5206\u5982\u4f55\u5f71\u54cd\u5176\u7ea6\u5316\u540e\u7684\u52a8\u529b\u5b66\u884c\u4e3a[66]\u3002<\/span><\/p>\n

                <\/span>\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u7684\u57fa\u672c\u539f\u7406<\/span><\/span><\/span><\/h2>\n

                \u771f\u5b9e\u4e16\u754c\u7f51\u7edc\u7684\u5f02\u8d28\u6027\u53ef\u80fd\u4f7f\u5f97\u4e0d\u540c\u65b9\u6cd5\u5f97\u5230\u7684\u7ed3\u679c\u51fa\u73b0\u76f8\u4e92\u77db\u76fe\uff0c\u89e3\u51b3\u8fd9\u79cd\u65b9\u6cd5\u4e0a\u7684\u4e0d\u7b49\u4ef7\u6027\u9700\u8981\u57fa\u4e8e\u7b2c\u4e00\u6027\u539f\u7406\u5efa\u7acb\u9002\u7528\u8303\u56f4\u66f4\u5e7f\u6cdb\u7684\u590d\u6742\u7f51\u7edc\u91cd\u6574\u5316\u6846\u67b6\u3002\u6784\u5efa\u8fd9\u6837\u7684\u6846\u67b6\u9700\u8981\u91cd\u65b0\u5ba1\u89c6\u91cd\u6574\u5316\u65b9\u6848\u7684\u6839\u57fa\uff0c\u4e5f\u5c31\u662f\uff0c\u90a3\u4e9b\u76f8\u5bf9\u6210\u719f\u7684\uff0c\u5b9a\u4e49\u5728\u5177\u5907\u89c4\u5219\u683c\u70b9\u548c\u5747\u5300\u540c\u8d28\u5ea6\u91cf\u7684\u7cfb\u7edf\u4e0a\u7684\u91cd\u6574\u5316\u65b9\u6cd5\uff0c\u540c\u65f6\u4e5f\u9700\u6ce8\u610f\u524d\u8ff0\u7ae0\u8282\u8ba8\u8bba\u7684\u6311\u6218\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u56de\u987e\u5e94\u5bf9\u8fd9\u4e9b\u6311\u6218\u800c\u5c1d\u8bd5\u7684\u4e0d\u540c\u65b9\u6cd5\u3002\u4e3a\u4e86\u4fbf\u4e8e\u8ba8\u8bba\uff0c\u6211\u4eec\u9996\u5148\u4e3a\u8bfb\u8005\u4eec\u8bb2\u89e3\u5176\u4e2d\u7684\u4e00\u4e9b\u5171\u540c\u57fa\u7840\u3002<\/span><\/p>\n

                \u6211\u4eec\u9996\u5148\u8ba8\u8bba\u7c97\u7c92\u5316\u53d8\u91cf\u7684\u5b9a\u4e49\u3002\u4e3a\u4e86\u56fa\u5b9a\u7b26\u53f7\uff0c\u5f15\u5165 <\/span><\/span><\/span> \u7684\u90bb\u63a5\u77e9\u9635 <\/span><\/span><\/span> \u6765\u8868\u793a\u5728\u7ed9\u5b9a\u5206\u8fa8\u7387\u5c3a\u5ea6\u4e0b\u7684\u7f51\u7edc\uff0c\u5373\u5bf9\u7ed9\u5b9a\u7684\u5c42\u7ea7\uff08\u5c3a\u5ea6\uff09 <\/span><\/span><\/span> \uff0c <\/span><\/span><\/span> \u4ee3\u8868\u8be5\u5728\u5c42\u7ea7\u80fd\u591f\u89c2\u5bdf\u5230\u7684\u8282\u70b9\u6570\u3002 <\/span><\/span><\/span> \u8868\u793a\u201c\u6700\u7cbe\u7ec6\u201d\u5c42\u7ea7\uff08\u5373\u7f51\u7edc\u6570\u636e\u53ef\u7528\u7684\u539f\u59cb\u5c42\u7ea7\uff09\uff0c\u800c <\/span><\/span><\/span> \u8868\u793a\u7c97\u7c92\u5316\u8fc7\u7a0b\u7684\u7b2c <\/span><\/span><\/span> \u6b21\u8fed\u4ee3\uff08\u5728\u8003\u8651\u201c\u7ec6\u7c92\u5316\u201d\u65b9\u6cd5\u65f6\uff0c\u4e5f\u5141\u8bb8\u201c\u8d1f\u5c42\u7ea7\u201d <\/span><\/span><\/span> \u7684\u51fa\u73b0\uff0c\u7a0d\u540e\u4f1a\u8fdb\u4e00\u6b65\u89e3\u91ca\uff09\u3002\u5bf9\u4e8e\u52a0\u6743\u7f51\u7edc\uff0c\u8fd8\u9700\u8981\u7528\u4e8e\u8868\u793a\u94fe\u63a5\u5f3a\u5ea6\u7684\u6743\u91cd\u77e9\u9635 <\/span><\/span><\/span> \u3002<\/span><\/p>\n

                \u5bf9\u53d8\u91cf\u7684\u7c97\u7c92\u5316\u53ef\u4ee5\u901a\u8fc7\u4e0d\u540c\u65b9\u5f0f\u5b9e\u73b0\u3002\u63a8\u5e7f\u201c\u5b9e\u7a7a\u95f4\u201d\u91cd\u6574\u5316\u7a0b\u5e8f\u7684\u65b9\u6cd5\u901a\u8fc7\u201c\u5757\u8282\u70b9\u201d\u6765\u5b9a\u4e49\u7c97\u7c92\u5316\u53d8\u91cf\uff0c\u8fd9\u4e9b\u5757\u8282\u70b9\u51b3\u5b9a\u4e86\u4e0b\u4e00\u5c42\u7ea7\u90bb\u63a5\u77e9\u9635\u7684\u884c\u548c\u5217\u3002\u5bf9\u4e8e\u8fd9\u4e9b\u65b9\u6cd5\uff0c\u5b9a\u4e49\u201c\u7a7a\u95f4\u5e73\u94fa\u201d\uff08tiling\uff09\u7684\u7b49\u4ef7\u64cd\u4f5c\u662f\u5b9a\u4e49\u7279\u5b9a\u7684\u5212\u5206 <\/span><\/span><\/span> \uff0c\u6ee1\u8db3\u5c06\u7b2c <\/span><\/span><\/span> \u5c42\u7ea7\u7684 <\/span><\/span><\/span> \u4e2a\u8282\u70b9 <\/span><\/span><\/span> \u6620\u5c04\u5230\u4e0b\u4e00\u5c42\u7ea7 <\/span><\/span><\/span> \u7684\u6570\u91cf\u66f4\u5c11\u7684 <\/span><\/span><\/span> \u4e2a\u7c97\u7c92\u5316\u8282\u70b9\uff08\u201c\u5757\u201d\uff09 <\/span><\/span><\/span> \u3002\u800c\u90a3\u4e9b\u8bd5\u56fe\u63a8\u5e7f k \u7a7a\u95f4\u91cd\u6574\u5316\u7a0b\u5e8f\u7684\u65b9\u6cd5\u5219\u662f\u9700\u8981\u53bb\u7ed9\u51fa\u63a8\u5e7f\u7684\u201c\u5bf9\u5076\u7a7a\u95f4\u201d\u7684\u5b9a\u4e49\uff0c\u8fd9\u53ef\u4ee5\u901a\u8fc7\u5c06\u683c\u70b9\u5206\u89e3\u4e3a\u57fa\u672c\u6a21\u6001\u7684\u90bb\u63a5\u77e9\u9635\u7684\u663e\u5f0f\u7b97\u7b26\u8868\u793a\u6765\u5b9e\u73b0\u3002\uff08\u6ce8\uff1a\u4e00\u4e2a\u7ebf\u6027\u7a7a\u95f4\u7684\u5bf9\u5076\u7a7a\u95f4\u5728\u6570\u5b66\u4e0a\u7c97\u7565\u5730\u662f\u6307\u8fd9\u4e2a\u7ebf\u6027\u7a7a\u95f4\u4e0a\u7684\u6240\u6709\u7ebf\u6027\u6cdb\u51fd\u6240\u6784\u6210\u7684\u7ebf\u6027\u7a7a\u95f4\u3002\uff09<\/span><\/p>\n

                \u5bf9\u5b9e\u7a7a\u95f4\u4e2d\u7cbe\u7ec6\u7ec6\u8282\u7684\u79ef\u5206\u6d88\u53bb\u64cd\u4f5c\uff08\u201c\u79ef\u6389\u201d\uff09\uff0c\u5176\u672c\u8d28\u662f\u5b9a\u4e49\u4e86\u4e00\u4e2a <\/span><\/span><\/span> \u5230 <\/span><\/span><\/span> \u7684\u6ee1\u5c04\uff08\u5373\u591a\u5bf9\u4e00\u6620\u5c04\uff0c\u56e0\u800c\u662f\u4e0d\u53ef\u9006\u7684\uff09\uff0c\u540c\u65f6\u5982\u679c\u9700\u8981\uff0c\u8fd8\u9700\u5b9a\u4e49\u4ece <\/span><\/span><\/span> \u5230 <\/span><\/span><\/span> \u7684\u6ee1\u5c04\uff0c\u800c\u5728k\u7a7a\u95f4\u4e2d\u5219\u9700\u8981\u5b9a\u4e49\u5bf9\u5076\u7b97\u5b50\u5728\u76f8\u90bb\u5c42\u7ea7\u95f4\u7684\u7c7b\u4f3c\u6620\u5c04\u3002\u5bf9\u6b64\u7684\u81ea\u7136\u9009\u62e9\u662f\u91c7\u7528\u5c40\u90e8\u6620\u5c04\uff0c\u5373\u7c97\u7c92\u5316\u77e9\u9635 <\/span><\/span><\/span> \u7684\u5143\u7d20 <\/span><\/span><\/span> \u548c <\/span><\/span><\/span> \u4ec5\u4f9d\u8d56\u4e8e\u7ec6\u7c92\u5ea6\u77e9\u9635\u4e2d\u5305\u542b\u4e8e\u8be5\u7c97\u7c92\u5316\u8282\u70b9\u7684\u5fae\u89c2\u8282\u70b9\u7684\u5143 <\/span><\/span><\/span> \uff0c\u5373<\/span><\/p>\n

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

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

                \u5176\u4e2d <\/span><\/span><\/span> \u8868\u793a\u67d0\u4e2a\u51fd\u6570\u3002\u4f8b\u5982\uff0c\u5728\u7eaf\u4e8c\u503c\u5c42\u7ea7\u4e0a\uff0c\u5f53\u4e14\u4ec5\u5f53\u5728 <\/span><\/span><\/span> \u5c42\u7ea7\u4e0a\u5b58\u5728\u4ece\u5757 <\/span><\/span><\/span> \u201c\u5185\u90e8\u201d\u4efb\u610f\u8282\u70b9\uff08\u8bb0\u4e3a <\/span><\/span><\/span> \uff09\u5230\u5757 <\/span><\/span><\/span> \u201c\u5185\u90e8\u201d\u4efb\u610f\u8282\u70b9\uff08\u7c7b\u4f3c\u5730\u8bb0\u4e3a <\/span><\/span><\/span> \uff09\u7684\u81f3\u5c11\u4e00\u6761\u8fde\u8fb9\u65f6\uff0c\u5757 <\/span><\/span><\/span> \u5230\u5757 <\/span><\/span><\/span> \u7684\u8fde\u8fb9\u624d\u5b58\u5728\u3002\u6b64\u7c97\u7c92\u5316\u6b65\u9aa4\u751f\u6210\u7684\u90bb\u63a5\u77e9\u9635 <\/span><\/span><\/span> \u7684\u5143\u7d20\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/span><\/p>\n

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

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

                \u7c7b\u4f3c\u5730\uff0c\u53ef\u4ee5\u5f15\u5165\u4e00\u4e2a\u5c40\u90e8\u65b9\u6848\uff0c\u4ece <\/span><\/span><\/span> \u83b7\u5f97\u7c97\u7c92\u5316\u77e9\u9635 <\/span><\/span><\/span> \uff1a<\/span><\/p>\n

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

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

                \u5176\u4e2d <\/span><\/span><\/span> \u8868\u793a\u4e00\u4e2a\u51fd\u6570\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c <\/span><\/span><\/span> \u548c <\/span><\/span><\/span> \u7684\u9009\u62e9\u7684\u81ea\u7531\u5ea6\u5bfc\u81f4\u4e86\u7ed3\u679c\u5bf9\u65b9\u6848\u7684\u4f9d\u8d56\u6027\uff0c\u8fd9\u662f\u4efb\u4f55\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u4e2d\u90fd\u666e\u904d\u5b58\u5728\u7684\u9700\u8981\u6ce8\u610f\u7684\u4e8b\u9879\u3002\u66f4\u91cd\u8981\u7684\u662f\uff0c\u5982\u4e0a\u6240\u8ff0\uff0c <\/span><\/span><\/span> \u548c <\/span><\/span><\/span> \u662f\u6ee1\u5c04\uff0c\u56e0\u6b64\u4e00\u822c\u4e0d\u53ef\u9006\uff1a\u8fd9\u4e9b\u6027\u8d28\u5bf9\u5e94\u4e8e\u5c0f\u5c3a\u5ea6\u4fe1\u606f\u4e22\u5931\uff0c\u4f7f\u5f97\u91cd\u6574\u5316\u7fa4\u4ec5\u80fd\u6210\u4e3a\u534a\u7fa4\u3002\u7c7b\u4f3c\u5730\uff0c\u5bf9\u5076\u7a7a\u95f4\u65b9\u6cd5\u4e2d\u5bf9\u5feb\u6a21\u6001\u6709\u635f\u79ef\u5206\u4e5f\u5177\u6709\u76f8\u540c\u7684\u6027\u8d28\u3002<\/span><\/p>\n

                \u6700\u540e\uff0c\u9700\u8981\u5c06\u91cd\u6574\u5316\u63a8\u5e7f\u5230\u8026\u5408\u7cfb\u6570\u548c\u6a21\u578b\u53c2\u6570\u4e0a\u3002\u5982\u679c\u7f51\u7edc\u662f\u4e00\u4e2a\u5355\u4e00\u7684\u786e\u5b9a\u6027\u56fe\uff08\u4f8b\u5982\u7ecf\u9a8c\u7f51\u7edc\uff09\uff0c\u5177\u6709\u67d0\u4e9b\u7279\u5b9a\u7684\u4e92\u4f5c\u6a21\u5f0f\u6216\u8fc7\u7a0b\u7279\u5f81\uff0c\u90a3\u4e48\u8fd9\u6700\u540e\u4e00\u6b65\u53d6\u51b3\u4e8e\u8026\u5408\u7cfb\u6570\u548c\u6a21\u578b\u53c2\u6570\u672c\u8eab\u7684\u6027\u8d28\u3002\u5bf9\u4e8e\u8fc7\u7a0b\u4e0e\u8be5\u7f51\u7edc\u5728\u5176\u5bf9\u5076\u7a7a\u95f4\u4e2d\u7684\u8868\u793a\u80fd\u591f\u4e00\u4e00\u5bf9\u5e94\uff0c\u90a3\u4e48\u8fd9\u4e00\u6b65\u9aa4\u53ef\u4ee5\u76f4\u63a5\u4ece\u79ef\u5206\u6389\u5c0f\u5c3a\u5ea6\u7ec6\u8282\u7684\u6b65\u9aa4\u7684\u7ed3\u679c\u4e2d\u5f97\u51fa\uff0c\u4f8b\u5982\uff0c\u5728\u62c9\u666e\u62c9\u65af\u7f51\u7edc\u91cd\u6574\u5316\u90e8\u5206\u4e2d\u8be6\u7ec6\u8ba8\u8bba\u7684\u6269\u6563\u8fc7\u7a0b\u3002\u76f8\u53cd\uff0c\u5982\u679c\u201c\u7f51\u7edc\u201d\u4e0d\u662f\u786e\u5b9a\u6027\u7684\uff0c\u800c\u662f\u7531\u968f\u673a\u56fe\u6a21\u578b\uff08\u5e26\u6709\u5176\u81ea\u8eab\u53c2\u6570\uff09\u8868\u793a\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u7f51\u7edc\u5728\u539f\u59cb\u5206\u8fa8\u7387 <\/span><\/span><\/span> \u65f6\u5df2\u7ecf\u5177\u6709\u591a\u6b21\u7edf\u8ba1\u62bd\u6837\uff0c\u90a3\u4e48\u91cd\u6574\u5316\u8026\u5408\u8fd8\u9700\u8981\u5305\u62ec\u968f\u673a\u56fe\u53c2\u6570\u7684\u91cd\u6574\u5316\uff0c\u4f8b\u5982\u51e0\u4f55\u7f51\u7edc\u91cd\u6574\u5316\u548c\u591a\u5c3a\u5ea6\u7f51\u7edc\u91cd\u6574\u5316\u90e8\u5206\u6240\u8ba8\u8bba\u7684\u5185\u5bb9\u3002\u8fd9\u6837\u505a\u9700\u8981\u5bf9\u56fe\u548c\u968f\u673a\u56fe\u6a21\u578b\u53c2\u6570\u4e0a\u8bf1\u5bfc\u6982\u7387\u5206\u5e03\u7684\u51fd\u6570\u6d41\u8fdb\u884c\u5355\u72ec\u5206\u6790\u3002\u9700\u8981\u5f3a\u8c03\u7684\u662f\uff0c\u5728\u5176\u4e0d\u52a8\u70b9\u5904\uff08\u6982\u7387\u5206\u5e03\u4e0d\u518d\u6539\u53d8\u5176\u5f62\u72b6\uff0c\u800c\u4ec5\u6539\u53d8\u5176\u53c2\u6570\uff09\uff0c\u91cd\u6574\u5316\u6d41\u53ef\u80fd\u4f1a\u5728\u7edf\u8ba1\u4e0a\u201c\u53ef\u9006\u201d\uff0c\u5373\u53ef\u4ee5\u901a\u8fc7\u53c2\u6570\u53d8\u5316\u5c06\u6982\u7387\u5206\u5e03\u7684\u6d41\u4ece\u8f83\u9ad8\u5c42\u7ea7\u9006\u5411\u5230\u8f83\u4f4e\u5c42\u7ea7\u3002\u5982\u679c\u5c06\u5176\u5e94\u7528\u5728\u539f\u59cb\u5c42\u7ea7 <\/span><\/span><\/span> \u4e0a\uff0c\u8fd9\u79cd\u9006\u5411\u7684\u6d41\u5b9e\u9645\u4e0a\u53ef\u80fd\u4ea7\u751f\u7f51\u7edc\u7684\u7ec6\u7c92\u5316\u7248\u672c\uff08 <\/span><\/span><\/span> \uff09\uff0c\u4f1a\u5177\u6709\u66f4\u591a\u7684\u8282\u70b9\uff0c\u5e76\u4e14\u901a\u5e38\u5177\u6709\u66f4\u7a00\u758f\u7684\u62d3\u6251\u7ed3\u6784\u3002<\/span><\/p>\n

                \u5b8c\u6210\u4e86\u4e0a\u8ff0\u7684\u68b3\u7406\u4e4b\u540e\uff0c\u672c\u6587\u5c06\u4ecb\u7ecd\u4e09\u79cd\u4e0d\u540c\u7684\u65b9\u6cd5\uff0c\u4ee5\u4e92\u8865\u7684\u65b9\u5f0f\u89e3\u51b3\u5f15\u8a00\u4e2d\u8ba8\u8bba\u7684\u4e09\u4e2a\u6b65\u9aa4\u3002<\/span><\/p>\n

                <\/span>
                <\/span><\/span><\/h1>\n

                \n
                \n
                \n
                \n
                \n

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

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

                \u51e0\u4f55\u7f51\u7edc\u91cd\u6574\u5316<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

                \n

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

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


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

                \u590d\u6742\u7f51\u7edc\u4e2d\u7684\u7a7a\u95f4\u5c40\u90e8\u6027\u53ef\u901a\u8fc7\u51e0\u4f55\u6846\u67b6\u6062\u590d[67]\uff0c\u8be5\u6846\u67b6\u901a\u8fc7\u5c06\u771f\u5b9e\u7f51\u7edc\u5d4c\u5165\u53cc\u66f2\u7a7a\u95f4\uff0c\u5c06\u7ed3\u6784\u5f02\u8d28\u6027\u4e0e\u975e\u5c40\u90e8\u6027\u8f6c\u5316\u4e3a\u5c40\u90e8\u6027\u7279\u5f81\uff0c\u4ece\u800c\u6062\u590d\u51e0\u4f55\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5[68\u201371]\u7684\u9002\u7528\u6027\u3002<\/span><\/p>\n

                <\/span>\u51e0\u4f55\u6a21\u578b<\/span><\/span><\/span><\/h2>\n

                \u51e0\u4f55\u8f6f\u914d\u7f6e\u6a21\u578b[42,72]\u57fa\u4e8e\u8282\u70b9\u95f4\u7684\u6d41\u884c\u5ea6\uff08popularity\uff09\u4e0e\u76f8\u4f3c\u6027\uff08similarity\uff09\u6765\u5b9a\u4e49\u8282\u70b9\u95f4\u7684\u5ea6\u91cf\u8ddd\u79bb\u3002\u8fd9\u4e9b\u62bd\u8c61\u7ef4\u5ea6\u7684\u7ed3\u5408\u4f7f\u5f97\u53cc\u66f2\u51e0\u4f55\u6210\u4e3a\u53ef\u5d4c\u5165\u5c42\u7ea7\u7ed3\u6784\u4e0e\u5c0f\u4e16\u754c\u7ed3\u6784\u7684\u6700\u81ea\u7136\u7684\u7a7a\u95f4\u3002\u6b64\u7a7a\u95f4\u4e2d\u7684\u8ddd\u79bb\u7f16\u7801\u4e86\u8282\u70b9\u95f4\u5f62\u6210\u8fde\u63a5\u7684\u6982\u7387\uff0c\u90bb\u8fd1\u8282\u70b9\u66f4\u503e\u5411\u4e8e\u8fde\u63a5\u3002\u8be5\u65b9\u6cd5\u4e0e\u968f\u673a\u51e0\u4f55\u56fe[73,74]\u53ca\u793e\u4ea4\u7f51\u7edc\u9690\u7a7a\u95f4\u6a21\u578b[75]\u7684\u601d\u8def\u76f8\u4f3c\u3002<\/span><\/p>\n

                \u5728\u8be5\u6a21\u578b\u7684\u725b\u987f\u7248\u672c[42]\uff08\u79f0\u4e3a <\/span><\/span><\/span> \u6a21\u578b\uff09\u4e2d\uff0c\u7b2c <\/span><\/span><\/span> \u5c42\u7684\u6bcf\u4e2a\u8282\u70b9 <\/span><\/span><\/span> \uff08 <\/span><\/span><\/span> \uff09\u88ab\u8d4b\u4e88\u4e00\u4e2a\u6d41\u884c\u5ea6\u53d8\u91cf\u53ca\u76f8\u4f3c\u6027\u7a7a\u95f4\u4e2d\u7684\u5750\u6807\u3002\u6d41\u884c\u5ea6\u7531\u9690\u85cf\u5ea6 <\/span><\/span><\/span> \u7f16\u7801\uff0c\u8be5\u9690\u85cf\u5ea6\u4ece\u4efb\u610f\u5206\u5e03 <\/span><\/span><\/span> \u4e2d\u62bd\u53d6\uff0c\u901a\u5e38\u4e3a\u6307\u6570 <\/span><\/span><\/span> \u7684\u5e42\u5f8b\u5206\u5e03\uff08 <\/span><\/span><\/span> \uff09\u3002\u5f53\u7ef4\u5ea6 <\/span><\/span><\/span> \u65f6\uff0c\u76f8\u4f3c\u6027\u7a7a\u95f4\u4e3a\u534a\u5f84\u4e3a <\/span><\/span><\/span> \u7684\u4e00\u7ef4\u7403\u9762\uff0c\u5176\u8bbe\u8ba1\u9700\u6ee1\u8db3 <\/span><\/span><\/span> \u4e2a\u8282\u70b9\u4ee5\u6052\u5b9a\u5bc6\u5ea6\u5206\u5e03\uff0c\u5176\u4e2d\u6bcf\u4e2a\u8282\u70b9 <\/span><\/span><\/span> \u88ab\u8d4b\u4e88\u89d2\u5750\u6807 <\/span><\/span><\/span> \uff0c\u7531\u6b64\u5b9a\u4e49\u8282\u70b9\u5bf9 <\/span><\/span><\/span> \u4e0e <\/span><\/span><\/span> \u4e4b\u95f4\u7684\u89d2\u8ddd\u79bb <\/span><\/span><\/span> \u3002\u8282\u70b9 <\/span><\/span><\/span> \u4e0e <\/span><\/span><\/span> \u7684\u8fde\u63a5\u6982\u7387 <\/span><\/span><\/span> \u9075\u5faa\u5f15\u529b\u5b9a\u5f8b\u5f62\u5f0f[76]\uff0c\u5e76\u5b9a\u4e49\u4e86\u6700\u5927\u71b5[2]\u7cfb\u7efc<\/span><\/p>\n

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

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

                \u5176\u4e2d<\/span><\/p>\n

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

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

                \u53c2\u6570 <\/span><\/span><\/span> \u51b3\u5b9a\u4e86\u5e73\u5747\u5ea6 <\/span><\/span><\/span> \uff0c\u4e14\u5404\u8282\u70b9\u7684\u671f\u671b\u5ea6\u4e0e\u5176 <\/span><\/span><\/span> \u503c\u6210\u6b63\u6bd4\u3002 <\/span><\/span><\/span> \u8c03\u63a7\u7f51\u7edc\u62d3\u6251\u7684\u96c6\u805a\u6027\uff0c\u53cd\u6620\u9690\u7a7a\u95f4\u4e2d\u7684\u4e09\u89d2\u4e0d\u7b49\u5f0f\u7ea6\u675f\uff0c\u5e76\u4f5c\u4e3a\u9006\u6e29\u5ea6\u53c2\u6570[76,77]\u3002<\/span><\/p>\n

                \u8be5\u6a21\u578b\u5728 <\/span><\/span><\/span> \u5904\u5448\u73b0\u53cd\u5e38\u62d3\u6251\u76f8\u53d8\uff08\u53c2\u8003\u6587\u732e77\uff09\u3002\u5728\u51e0\u4f55\u76f8\uff08 <\/span><\/span><\/span> \uff09\u4e2d\uff0c\u96c6\u805a\u7cfb\u6570\u4fdd\u6301\u6709\u9650\u503c[42]\uff1b\u800c\u5728\u975e\u51e0\u4f55\u76f8\uff08 <\/span><\/span><\/span> \uff09\u7684\u70ed\u529b\u5b66\u6781\u9650\u4e0b\uff0c\u96c6\u805a\u7cfb\u6570\u8d8b\u4e8e\u96f6\u3002\u7136\u800c\uff0c\u5728\u51c6\u51e0\u4f55\u533a\u57df <\/span><\/span><\/span> \u5185\uff0c\u96c6\u805a\u7cfb\u6570\u8870\u51cf\u81f3\u96f6\u7684\u901f\u5ea6\u6781\u6162[78]\uff0c\u8868\u660e\u6709\u9650\u89c4\u6a21\u7f51\u7edc\u4ecd\u4fdd\u7559\u663e\u8457\u6c34\u5e73\u7684\u96c6\u805a\u6027\uff0c\u80fd\u591f\u4e0e\u67d0\u4e9b\u771f\u5b9e\u590d\u6742\u7f51\u7edc\u5177\u6709\u76f8\u5f53\u6027\u8d28\u3002\u56e0\u6b64\uff0c\u8f83\u4f4e\u201c\u6e29\u5ea6\u201d\uff08\u4f4e <\/span><\/span><\/span> \uff09\u5bf9\u5e94\u77ed\u7a0b\u8fde\u63a5\u5360\u4f18\uff0c\u800c\u8f83\u9ad8\u201c\u6e29\u5ea6\u201d\uff08\u9ad8 <\/span><\/span><\/span> \uff09\u5219\u662f\u5bf9\u4e0d\u540c\u957f\u5ea6\u8fde\u63a5\u7684\u751f\u6210\u6982\u7387\u7684\u5e73\u8861\u3002<\/span><\/p>\n

                <\/span><\/span> \u6a21\u578b\u5177\u6709\u7eaf\u51e0\u4f55\u5f62\u5f0f\u2014\u2014 <\/span><\/span><\/span> \u6a21\u578b[72]\uff0c\u5176\u4e2d\u9690\u85cf\u5ea6 <\/span><\/span><\/span> \u5bf9\u5e94\u4e8e\u5f84\u5411\u5750\u6807 <\/span><\/span><\/span> \uff0c\u4ece\u800c\u5c06\u8fde\u63a5\u6982\u7387\uff08\u65b9\u7a0b(4)\uff09\u8f6c\u6362\u4e3a\u4ec5\u4f9d\u8d56\u4e8e\u53cc\u66f2\u7a7a\u95f4\u4e2d\u8282\u70b9\u95f4\u8ddd\u7684\u8d39\u7c73-\u72c4\u62c9\u514b\u51fd\u6570\u3002Mercator\u5de5\u5177[79,80]\u901a\u8fc7\u7edf\u8ba1\u63a8\u65ad\u4e0e\u673a\u5668\u5b66\u4e60\u6280\u672f\uff0c\u6700\u5927\u5316\u89c2\u6d4b\u7f51\u7edc\u7ed3\u6784\u4e0e <\/span><\/span><\/span> \uff08\u7b49\u4ef7\u4e8e <\/span><\/span><\/span> \uff09\u6a21\u578b[81]\u7684\u5951\u5408\u5ea6\uff0c\u5c06\u771f\u5b9e\u7f51\u7edc\u5d4c\u5165\u6b64\u7a7a\u95f4\u3002\u751f\u6210\u7684\u7a7a\u95f4\u6620\u5c04\u53ef\u8fdb\u4e00\u6b65\u7528\u4e8e\u53ef\u89c6\u5316\u3001\u5206\u6790\u3001\u5bfc\u822a\u53ca\u91cd\u6574\u5316\u7b49\u4e0b\u6e38\u4efb\u52a1\u3002<\/span><\/p>\n

                \u8be5\u6a21\u578b\u65cf\u80fd\u6709\u6548\u89e3\u91ca\u771f\u5b9e\u7f51\u7edc\u8fde\u63a5\u6027\u7684\u5173\u952e\u7279\u5f81\uff0c\u5305\u62ec\u5f02\u8d28\u5ea6\u5206\u5e03[42,72,82]\u3001\u663e\u8457\u96c6\u805a\u6027[42,72,82\u201384]\u3001\u5c0f\u4e16\u754c\u73b0\u8c61[42,85\u201387]\u3001\u6e17\u6d41\u6027\u8d28[88\u201390]\u3001\u8c31\u7279\u5f81[91]\u53ca\u81ea\u76f8\u4f3c\u6027[42]\u3002\u8be5\u6846\u67b6\u8fd8\u53ef\u4ee5\u8fdb\u4e00\u6b65\u6269\u5c55\u81f3\u751f\u957f\u7f51\u7edc\u7684\u4f18\u5148\u8fde\u63a5\u673a\u5236[92]\u3001\u52a0\u6743\u7f51\u7edc[93]\u3001\u4e8c\u90e8\u7f51\u7edc[94,95]\u3001\u4e92\u8865\u6027\u9a71\u52a8\u7f51\u7edc[96]\u3001\u591a\u5c42\u7f51\u7edc[97,98]\u3001\u5177\u6709\u793e\u533a\u7ed3\u6784\u7684\u7f51\u7edc[99\u2013101]\u3001\u6709\u5411\u7f51\u7edc[102]\u4ee5\u53ca\u8282\u70b9\u542b\u5173\u8054\u7279\u5f81\u7684\u7f51\u7edc[103]\u3002<\/span><\/p>\n


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

                <\/section>\n

                \u56fe1  \u771f\u5b9e\u7f51\u7edc\u4e0a\u51e0\u4f55\u91cd\u6574\u5316\u7684\u76f4\u63a5\u4e0e\u9006\u5411\u65b9\u6cd5\u53ca\u5176\u7ed3\u679c\u3002 a. \u51e0\u4f55\u91cd\u6574\u5316\uff08GR\uff09\u53d8\u6362\u793a\u610f\u56fe\u3002\u5728\u5c42\u7ea7 <\/span><\/span><\/span> \u4e2d\uff0c\u6cbf\u76f8\u4f3c\u6027\u5706\u5b9a\u4e49 <\/span><\/span><\/span> \u4e2a\u8fde\u7eed\u8282\u70b9\u7ec4\u6210\u7684\u975e\u91cd\u53e0\u84dd\u8272\u5757\uff0c\u4ece\u800c\u5c06\u539f <\/span><\/span><\/span> \u4e2a\u8282\u70b9\u5212\u5206\u4e3a <\/span><\/span><\/span> \u4e2a\u5757\uff0c\u5f62\u6210\u5206\u533a <\/span><\/span><\/span> \u3002\u8fd9\u4e9b\u5757\u88ab\u7c97\u7c92\u5316\u4e3a\u5c42\u7ea7 <\/span><\/span><\/span> \u4e2d\u7684\u8d85\u8282\u70b9\uff0c\u6bcf\u4e2a\u8d85\u8282\u70b9\u7684\u89d2\u5750\u6807\u7531\u5176 <\/span><\/span><\/span> \u5c42\u6784\u6210\u8282\u70b9\u6240\u5728\u533a\u57df\u786e\u5b9a\u3002\u5982\u65b9\u7a0b(2)\u6240\u8ff0\u8fde\u63a5 <\/span><\/span><\/span> \u5c42\u7684\u8d85\u8282\u70b9\uff0c\u8be5\u8fc7\u7a0b\u53ef\u8fed\u4ee3\u751f\u6210 <\/span><\/span><\/span> \u5c42\u3002\u7531\u4e8e\u534a\u7fa4\u6027\u8d28\uff0c <\/span><\/span><\/span> \u5c42\u4ea6\u53ef\u76f4\u63a5\u901a\u8fc7 <\/span><\/span><\/span> \u7684\u5757\u4ece <\/span><\/span><\/span> \u5c42\u751f\u6210\u3002b. GR \u590d\u73b0\u4eba\u8111\u8fde\u63a5\u7ec4\u7684\u591a\u5c3a\u5ea6\u8fde\u901a\u7ed3\u6784\u3002\u57fa\u4e8e\u89e3\u5256\u6570\u636e\u91cd\u5efa\u4e94\u7ea7\u957f\u5ea6\u5c3a\u5ea6\u7684\u591a\u5c3a\u5ea6\u5c42\u7ea7\u8868\u793a\uff08\u4e0a\u56fe\uff09\u3002\u5404\u5c3a\u5ea6 <\/span><\/span><\/span> \u4e0b\u8fde\u63a5\u7ec4\u7684\u62d3\u6251\u7279\u6027\uff08\u7b26\u53f7\uff09\u4e0e\u57fa\u4e8e\u6700\u9ad8\u5206\u8fa8\u7387\u51e0\u4f55\u6620\u5c04\u7684 GR \u9884\u6d4b\uff08\u66f2\u7ebf\uff09\u9ad8\u5ea6\u543b\u5408\uff08\u4e0b\u56fe\uff09\u3002\u4ece\u5de6\u81f3\u53f3\u4f9d\u6b21\u4e3a\uff1a\u4e92\u8865\u7d2f\u79ef\u5ea6\u5206\u5e03 <\/span><\/span><\/span> \u3001\u805a\u7c7b\u7cfb\u6570 <\/span><\/span><\/span> \u3001\u5f52\u4e00\u5316\u6700\u8fd1\u90bb\u5e73\u5747\u5ea6 <\/span><\/span><\/span> \u53ca\u5bcc\u4ff1\u4e50\u90e8\u7cfb\u6570 <\/span><\/span><\/span> \u3002\u8ba1\u7b97\u4e2d\u91c7\u7528\u91cd\u6574\u5316\u5ea6 <\/span><\/span><\/span> \u4ee5\u6d88\u9664\u5404\u5c42\u7ea7\u5e73\u5747\u5ea6\u5dee\u5f02\u7684\u5f71\u54cd\u3002 c. \u51e0\u4f55\u5206\u652f\u751f\u957f\u8fc7\u7a0b\uff08GBG\uff09\u4ee5\u81ea\u76f8\u4f3c\u65b9\u5f0f\u6f14\u5316\u7f51\u7edc\u3002d. GBG \u662f GR \u7684\u7edf\u8ba1\u9006\u8fc7\u7a0b\uff1a\u5bf9\u4e92\u8054\u7f51\u91cd\u6574\u5316\u5c42\u7ea7\u5e94\u7528 GBG \u53ef\u6062\u590d\u539f\u59cb\u7f51\u7edc\u7684\u7edf\u8ba1\u7b49\u6548\u7ed3\u6784\uff1b\u53cd\u4e4b\uff0c\u5bf9 GBG \u751f\u6210\u7684\u4eba\u4f53\u4ee3\u8c22\u7f51\u7edc\u66ff\u4ee3\u4f53\u5e94\u7528 GR \u53ef\u590d\u539f\u539f\u59cb\u67b6\u6784\u3002e. GR \u4e0e GBG \u7684\u7ed3\u5408\u4e3a\u5355\u5b9e\u4f8b\u771f\u5b9e\u7f51\u7edc\u7684\u6709\u9650\u5c3a\u5bf8\u6807\u5ea6\u7814\u7a76\u63d0\u4f9b\u65b9\u6cd5\uff0c\u53ef\u6570\u503c\u4f30\u7b97\u4e34\u754c\u6307\u6570\u3002\u4ee5\u4e92\u8054\u7f51\u94fe\u8def\u968f\u673a\u5931\u6548\u7684\u952e\u903e\u6e17\u6a21\u62df\u4e3a\u4f8b\uff0c\u7f51\u7edc\u5c3a\u5bf8 <\/span><\/span><\/span> \u3001\u4e34\u754c\u952e\u5360\u636e\u6982\u7387 <\/span><\/span><\/span> \u53ca\u78c1\u5316\u7387\u6700\u5927\u503c <\/span><\/span><\/span> \u5747\u7b26\u5408\u5e42\u5f8b\u5173\u7cfb\uff08\u9ed1\u8272\u7b26\u53f7\u4e3a\u539f\u59cb\u7f51\u7edc\u6570\u636e\uff09\u3002GBG \u4e0e GR \u58f3\u5c42\u53c2\u6570\u4e3a\u5206\u652f\u7387 <\/span><\/span><\/span> \u3001\u5757\u5c3a\u5bf8 <\/span><\/span><\/span> \uff0c\u7ed3\u679c\u8868\u660e\u4e92\u8054\u7f51\u56fe\u5b58\u5728\u903e\u6e17\u9608\u503c\u6d88\u5931\u73b0\u8c61\uff0c\u7b26\u5408\u65e0\u6807\u5ea6\u7f51\u7edc\u9884\u671f\u3002\u56fea\u6539\u7f16\u81ea\u6587\u732e[70]\uff08Springer Nature Limited\uff09\uff1b\u56feb\u8f6c\u8f7d\u81ea\u6587\u732e[104]\uff08PNAS\uff09\uff1b\u56fec\u3001d\u3001e\u6539\u7f16\u81ea\u6587\u732e[69]\uff08PNAS\uff09\u3002<\/span><\/p>\n

                <\/span>\u51e0\u4f55\u91cd\u6574\u5316\u6280\u672f<\/span><\/span><\/span><\/h2>\n

                <\/span><\/span> \u6216 <\/span><\/span><\/span> \u6a21\u578b\u901a\u8fc7\u5bf9\u7f51\u7edc\u7684\u53cc\u66f2\u6620\u5c04\u8fdb\u884c\u8fed\u4ee3\u64cd\u4f5c\uff0c\u4ece\u800c\u4e3a\u590d\u6742\u7f51\u7edc\u7684\u51e0\u4f55\u91cd\u6574\u5316\u7fa4\u5960\u5b9a\u4e86\u57fa\u7840[68-71]\u3002\u5728 <\/span><\/span><\/span> \u5c42\u4e2d\u914d\u7f6e\u597d\u5d4c\u5165\u7a7a\u95f4\u4e2d\u7684\u5750\u6807\u540e\uff0c\u901a\u8fc7\u7c97\u7c92\u5316\u548c\u91cd\u6807\u5ea6\u5f97\u5230\u65b0\u7684\u4e00\u5c42 <\/span><\/span><\/span> \u3002\u8fd9\u6d89\u53ca\u901a\u8fc7\u5206\u533a <\/span><\/span><\/span> \u5c06\u76f8\u4f3c\u6027\u5b50\u7a7a\u95f4\u5212\u5206\u4e3a <\/span><\/span><\/span> \u4e2a\u6247\u533a\uff08\u5373\u91cd\u6574\u5316\u4e09\u6b65\u66f2\u4e2d\u7684\u7b2c\u4e00\u6b65\uff09\uff0c\u4f7f\u540c\u4e00\u6247\u533a <\/span><\/span><\/span> \uff08 <\/span><\/span><\/span> \uff09\u5185\u7684\u8282\u70b9 <\/span><\/span><\/span> \u6210\u4e3a\u8d85\u8282\u70b9\u3002\u5982\u679c\u539f\u59cb\u8282\u70b9\u4e4b\u95f4\u81f3\u5c11\u5b58\u5728\u4e00\u4e2a\u8fde\u63a5\uff0c\u5982\u516c\u5f0f (2) \u6240\u793a\uff08\u56fe1a\uff09\uff0c\u5219\u8d85\u8282\u70b9\u4e4b\u95f4\u5efa\u7acb\u8fde\u8fb9\uff0c\u4ece\u800c\u5e73\u5747\u6389\u66f4\u5c3a\u5ea6\u66f4\u5c0f\u7684\u7ec6\u8282\u3002\u8fed\u4ee3\u6b64\u8fc7\u7a0b\uff0c\u901a\u8fc7\u9010\u6b65\u9009\u62e9\u66f4\u957f\u7a0b\u7684\u8fde\u63a5\uff0c\u751f\u6210\u8de8\u5c3a\u5ea6 <\/span><\/span><\/span> \u7684\u91cd\u6574\u5316\u6d41\u3002<\/span><\/p>\n

                \u51e0\u4f55\u91cd\u6574\u5316\u8868\u660e\uff0c\u591a\u5c3a\u5ea6\u81ea\u76f8\u4f3c\u6027\u53ef\u4ee5\u4f5c\u4e3a\u771f\u5b9e\u4e16\u754c\u7684\u7f51\u7edc\u4e2d\u8de8\u9886\u57df\u666e\u904d\u5b58\u5728\u7684\u5bf9\u79f0\u6027[68,71]\uff0c\u5e76\u4e14\u8fd8\u80fd\u51c6\u786e\u9884\u6d4b\u4eba\u7c7b\u5927\u8111\u8fde\u63a5\u7ec4\u7684\u591a\u5c3a\u5ea6\u91cd\u6784\u4e2d\u89c2\u5bdf\u5230\u7684\u81ea\u76f8\u4f3c\u6027\uff0c\u8fd9\u4e9b\u53d1\u73b0\u8868\u660e\u51e0\u4f55\u91cd\u6574\u5316\u975e\u5e38\u63a5\u8fd1\u4e8e\u5c0f\u4e16\u754c\u548c\u975e\u5c0f\u4e16\u754c\u673a\u5236\u4e4b\u95f4\u7684\u4e34\u754c\u7ed3\u6784\u8f6c\u53d8[104]\uff08\u56fe1b\uff09\u3002\u8fd9\u4e9b\u53d1\u73b0\u53ef\u7531 <\/span><\/span><\/span> \u6216 <\/span><\/span><\/span> \u6a21\u578b\u5728\u51e0\u4f55\uff08 <\/span><\/span><\/span> \uff09[68] \u548c\u975e\u51e0\u4f55\uff08 <\/span><\/span><\/span> \uff09[71] \u673a\u5236\u4e0b\u7684\u53ef\u91cd\u6574\u5316\u6027\u6240\u89e3\u91ca\u3002\u5bf9\u9690\u85cf\u5ea6\u7684\u5c3a\u5ea6\u53d8\u6362\u662f\u901a\u8fc7\u8981\u6c42\u8fde\u63a5\u6982\u7387\u4e0d\u53d8\u6027\uff08\u516c\u5f0f (4)\uff09\u7684\u6761\u4ef6\u4e0b\u83b7\u5f97\u7684\u3002\u89d2\u5ea6\u5750\u6807\u6d41\u5f0f\u53ef\u7531\u4efb\u4f55\u4fdd\u6301\u539f\u59cb\u6a21\u578b\u65cb\u8f6c\u4e0d\u53d8\u6027\u7684\u53d8\u6362\u6765\u5b9a\u4e49\u3002\u8bb0 <\/span><\/span><\/span> \uff0c\u5219\u4fdd\u6301\u8fde\u63a5\u6982\u7387\u5e76\u56e0\u800c\u5728\u91cd\u6574\u5316\u6d41\u4e2d\u80fd\u591f\u4fdd\u6301\u7f51\u7edc\u62d3\u6251\u6027\u8d28\u7684\u53d8\u6362\u53ef\u5199\u4e3a<\/span><\/p>\n

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

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

                \u5176\u4e2d\uff0c\u7ea6\u5b9a <\/span><\/span><\/span> \u8868\u793a\u5c5e\u4e8e\u8d85\u8282\u70b9 <\/span><\/span><\/span> \u7684\u8282\u70b9\u3002\u4e0a\u8ff0\u53d8\u6362\u91cd\u6574\u5316\u4e86\u8026\u5408\u7cfb\u6570\u548c\u53c2\u6570\u503c\u3002<\/span><\/p>\n

                \u5168\u5c40\u53c2\u6570\u7684\u6f14\u5316\u5982\u4e0b\uff1a <\/span><\/span><\/span> \uff0c <\/span><\/span><\/span> \uff0c\u5176\u4e2d <\/span><\/span><\/span> \u662f\u7b49\u5927\u5c0f\u8d85\u8282\u70b9\u4e2d\u7684\u8282\u70b9\u6570\uff0c <\/span><\/span><\/span> \u662f\u5c3a\u5ea6\u4e0d\u53d8\u7684\u3002\u8fd9\u4e9b\u53d8\u6362\u6ee1\u8db3\u534a\u7fa4\u6027\u8d28\uff1a\u7528 <\/span><\/span><\/span> \u4e2a\u8282\u70b9\u7684\u7ec4\u91cd\u6574\u5316\u4e24\u6b21\u7b49\u540c\u4e8e\u7528 <\/span><\/span><\/span> \u4e2a\u8282\u70b9\u7684\u7ec4\u91cd\u6574\u5316\u4e00\u6b21\u3002\u6982\u7387 <\/span><\/span><\/span> \u4fdd\u6301 <\/span><\/span><\/span> \u7684\u539f\u59cb\u5f62\u5f0f\uff0c\u5f53 <\/span><\/span><\/span> \u65f6\uff08\u53c2\u8003\u6587\u732e 68\uff09\uff0c\u5e73\u5747\u5ea6 <\/span><\/span><\/span> \u662f\u5177\u6709\u6d41 <\/span><\/span><\/span> \u7684\u89c2\u6d4b\u91cf\u3002\u53ea\u8981\u5177\u5907\u826f\u597d\u7684\u5d4c\u5165\uff0c\u4e0a\u8ff0\u884c\u4e3a\u6027\u8d28\u4e5f\u9002\u7528\u4e8e\u771f\u5b9e\u7f51\u7edc\u3002\u771f\u5b9e\u7f51\u7edc\u901a\u7545\u5177\u5907\u5178\u578b\u7279\u5f81 <\/span><\/span><\/span> \uff0c \u8868\u660e\u6d41\u4f1a\u8d8b\u5411\u4e8e\u9ad8\u8fde\u63a5\u5ea6\u7684\u56fe\uff1b\u800c\u5982\u679c <\/span><\/span><\/span> \uff0c\u7f51\u7edc\u7684\u6d41\u4f1a\u8d8b\u5411\u4e8e\u4e00\u7ef4\u73af\uff1b\u5728\u5c0f\u4e16\u754c\u548c\u975e\u5c0f\u4e16\u754c\u9636\u6bb5\u4e4b\u95f4\u7684\u8f6c\u53d8\u5904\uff0c <\/span><\/span><\/span> \uff0c\u5e73\u5747\u5ea6\u4fdd\u6301\u4e0d\u53d8\uff08\u66f4\u591a\u7ec6\u8282\u89c1\u539f\u6587\u9644\u5f55\uff09\u3002\u6700\u540e\uff0c\u5bf9\u4e8e <\/span><\/span><\/span> \uff0c\u94fe\u63a5\u6570\u5728\u91cd\u6574\u5316\u4e0b\u4fdd\u6301\u4e0d\u53d8[71]\u3002<\/span><\/p>\n

                <\/span>\u63a8\u5e7f\u5230\u5e26\u6743\u7f51\u7edc<\/span><\/span><\/span><\/h2>\n

                \u901a\u8fc7\u4fdd\u6301\u6743\u91cd\u4e0e\u5ea6\u5173\u7cfb\u7684\u53d8\u6362\uff0c\u7f51\u7edc\u7684\u6743\u91cd\u7ed3\u6784\u5728\u91cd\u6574\u5316\u7fa4\u6d41\u4e2d\u53ef\u4ee5\u5f97\u4ee5\u4fdd\u7559\u3002\u51e0\u4f55\u6743\u91cd\u91cd\u6574\u5316\uff08geometric renormalization of weights\uff0cGRW\uff09\u6280\u672f[70]\u7531\u6b64\u4ea7\u751f\uff0c\u5b83\u53ef\u4ee5\u5bf9\u52a0\u6743\u7f51\u7edc\u7ed3\u6784\u8fdb\u884c\u591a\u5c3a\u5ea6\u5c55\u5f00[105,106]\uff0c\u4ece\u800c\u5f62\u6210\u81ea\u76f8\u4f3c\u5c42\u7ea7\u3002\u8be5\u6280\u672f\u7684\u6570\u5b66\u57fa\u7840\u5728\u4e8e\u52a0\u6743 <\/span><\/span><\/span> \u6a21\u578b\u7684\u53ef\u91cd\u6574\u5316\u6027[93]\u3002\u5728\u5b9e\u9645\u64cd\u4f5c\u4e2d\uff0c\u901a\u5e38\u9009\u62e9\u91cd\u6574\u5316\u94fe\u63a5\u7684\u6700\u5927\u6743\u91cd\u4f5c\u4e3a\u8fd1\u4f3c\u65b9\u6cd5\u3002\u5728\u5305\u62ec\u7ec6\u80de\u4e2d\u7684\u4ee3\u8c22\u7f51\u7edc\u3001\u5546\u4e1a\u673a\u573a\u4e4b\u95f4\u7684\u822a\u73ed\u7f51\u7edc\u3001\u79d1\u5b66\u5408\u4f5c\u7f51\u7edc\u7b49\u6765\u81ea\u4e0d\u540c\u9886\u57df\u7684\u5f02\u8d28\u5ea6\u5206\u5e03\u52a0\u6743\u7f51\u7edc\u4e2d\uff0c\u4f7f\u7528\u8fd9\u79cd\u79f0\u4e3asup-GRW\u7684\u7b56\u7565\u6216\u57fa\u4e8e\u5176\u7406\u8bba\u7684\u53d8\u6362[70]\u8fdb\u884c\u7c97\u7c92\u5316\u548c\u91cd\u6807\u5ea6\u65f6\uff0c\u5747\u53ef\u4ee5\u89c2\u5bdf\u5230\u51e0\u4f55\u6807\u5ea6\u884c\u4e3a\uff08\u8be6\u89c1\u9644\u5f55\uff09\u3002<\/span><\/p>\n

                <\/span>\u81ea\u76f8\u4f3c\u7ec6\u7c92\u5316<\/span><\/span><\/span><\/h2>\n

                \u51e0\u4f55\u5206\u652f\u751f\u957f\uff08geometric branching growth\uff0cGBG\uff09\u6a21\u578b[69]\u4f5c\u4e3a\u51e0\u4f55\u91cd\u6574\u5316\u7684\u9006\u5411\u6280\u672f\uff0c\u80fd\u51c6\u786e\u9884\u6d4b\u771f\u5b9e\u4e16\u754c\u7684\u589e\u957f\u7f51\u7edc\u7684\u81ea\u76f8\u4f3c\u884c\u4e3a\uff0c\u4f8b\u5982\u4e16\u754c\u8d38\u6613\u7f51\u548c\u671f\u520a\u5f15\u6587\u7f51\u7edc\u7684\u957f\u671f\u6f14\u5316\u884c\u4e3a\u3002\u8be5\u6a21\u578b\u901a\u8fc7\u751f\u6210\u81ea\u76f8\u4f3c\u5ea6\u91cf\u63a8\u5e7f\u6765\u590d\u5236\u7f51\u7edc\u539f\u59cb\u7ed3\u6784\uff0c\u53ef\u63a8\u5e7f\u81f3\u4efb\u610f\u5927\u7f51\u7edc\u89c4\u6a21\u3002<\/span><\/p>\n

                \u4e3a\u4e86\u4ece\u5c42\u7ea7 <\/span><\/span><\/span> \u5f00\u59cb\u751f\u6210\u51e0\u4f55\u5206\u652f\u751f\u957f\u6a21\u578b\u7ec6\u7c92\u5ea6\u5c42\u7ea7 <\/span><\/span><\/span> \uff08\u76f8\u5bf9\u4e8e\u7c97\u7c92\u5316\u65b9\u5411\u7684\u201c\u53cd\u5411\u201d\uff09\uff0c\u5c06\u539f\u59cb\u5c42\u7ea7\u4e2d\u7684\u8282\u70b9\u4ee5\u6982\u7387 <\/span><\/span><\/span> \u5212\u5206\u4e3a <\/span><\/span><\/span> \u4e2a\u540e\u4ee3\uff08\u56fe1c\uff09\uff0c\u4ece\u800c\u4f7f\u8282\u70b9\u6570\u91cf\u589e\u52a0\u4e3a <\/span><\/span><\/span> \uff0c\u5176\u4e2d <\/span><\/span><\/span> \u4e3a\u5206\u652f\u7387\u3002\u4e0d\u5206\u88c2\u7684\u8282\u70b9\u4fdd\u7559\u5176\u5750\u6807\uff0c\u6bcf\u4e2a\u540e\u4ee3\u8282\u70b9\u8d4b\u4e88\u65b0\u7684\u5750\u6807\u3002\u540e\u4ee3\u7684\u9690\u85cf\u5ea6\u5fc5\u987b\u901a\u8fc7\u6ee1\u8db3\u516c\u5f0f (6) \u6765\u9075\u5faa\u51e0\u4f55\u91cd\u6574\u5316\u89c4\u5219\uff0c\u5e76\u4e14\u5b83\u4eec\u7684\u5206\u5e03 <\/span><\/span><\/span> \u4e5f\u5e94\u4fdd\u6301\u4e0e\u7956\u5148\u5c42\u7ea7\u7684\u5206\u5e03\u76f8\u540c\uff0c\u8fd9\u5c31\u8981\u6c42\u5ea6\u5206\u5e03\u5fc5\u987b\u662f\u4e00\u4e2a\u7a33\u5b9a\u5206\u5e03[107]\u3002\u6b64\u5916\uff0c\u5b83\u4eec\u7684\u89d2\u5750\u6807\u56fa\u5b9a\u5728\u7956\u5148\u7684\u5de6\u53f3\u4e24\u4fa7\uff0c\u53ef\u4ee5\u7565\u6709\u89d2\u504f\u79fb\uff0c\u4ee5\u4fdd\u6301\u5176\u65cb\u8f6c\u987a\u5e8f\u3002\u66f4\u591a\u7ec6\u8282\u89c1\u9644\u5f55\u3002\u4e00\u65e6\u4e3a\u540e\u4ee3\u5206\u914d\u4e86\u5750\u6807\uff0c\u5c31\u9700\u8981\u786e\u5b9a\u65b0\u5c42\u7ea7\u4e2d\u7684\u8fde\u63a5\uff0c\u4ee5\u786e\u4fdd\u751f\u6210\u7684\u7f51\u7edc\u5c5e\u4e8e <\/span><\/span><\/span> \u7cfb\u7efc\u3002<\/span><\/p>\n

                \u8bbe <\/span><\/span><\/span> \uff0c\u8fed\u4ee3\u5e94\u7528\u51e0\u4f55\u5206\u652f\u751f\u957f\u6a21\u578b\u5c06\u751f\u6210\u4e00\u7cfb\u5217\u9010\u6e10\u7ec6\u7c92\u5316\u7684\u81ea\u76f8\u4f3c\u5c42\u7ea7\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u539f\u59cb\u7684\u7ecf\u9a8c\u8fde\u63a5\u6982\u7387\u3001\u5ea6\u5206\u5e03\u3001\u96c6\u805a\u7cfb\u6570\u548c\u793e\u533a\u7ed3\u6784\u5728\u6d41\u4e2d\u5f97\u4ee5\u4fdd\u7559\uff0c\u800c\u5e73\u5747\u5ea6\u5219\u4f1a\u51cf\u5c0f\u3002\u901a\u8fc7\u6dfb\u52a0\u989d\u5916\u7684\u94fe\u63a5\u5e76\u8bbe\u7f6e <\/span><\/span><\/span> \uff08\u5176\u4e2d <\/span><\/span><\/span> \uff09\u5f97\u5230\u51e0\u4f55\u5206\u652f\u751f\u957f\u6a21\u578b\u7684\u81a8\u80c0\u7248\u672c\uff0c\u8fd9\u79cd\u6539\u8fdb\u53ef\u4ee5\u589e\u52a0\u5e73\u5747\u5ea6\u6216\u8005\u81f3\u5c11\u53ef\u4ee5\u907f\u514d\u5e73\u5747\u5ea6\u7684\u5feb\u901f\u51cf\u5c0f\u3002\u51e0\u4f55\u5206\u652f\u751f\u957f\u6a21\u578b\u662f\u79ef\u5206\u91cd\u6574\u5316\u7684\u7edf\u8ba1\u9006\u8fc7\u7a0b\uff08\u56fe1d\uff09\uff0c\u800c\u81a8\u80c0\u51e0\u4f55\u5206\u652f\u751f\u957f\u6a21\u578b\u5219\u662f\u6536\u7f29\u51e0\u4f55\u91cd\u6574\u5316\uff08deflationary GR\uff09\u7684\u7edf\u8ba1\u9006\u8fc7\u7a0b\uff0c\u5176\u4e2d\u526a\u6389\u94fe\u63a5\u7684\u64cd\u4f5c\u4f1a\u51cf\u5c0f\u5e73\u5747\u5ea6\u3002\u52a0\u6743\u548c\u975e\u52a0\u6743\u7684 <\/span><\/span><\/span> \u6a21\u578b\u7684\u91cd\u6574\u5316\u80fd\u591f\u51c6\u786e\u590d\u73b0\u771f\u5b9e\u7f51\u7edc\u4e2d\u89c2\u5bdf\u5230\u7684\u591a\u5c3a\u5ea6\u81ea\u76f8\u4f3c\u6027\uff0c\u8fd9\u8868\u660e\u76f8\u540c\u7684\u539f\u5219\u80fd\u591f\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0a\u51b3\u5b9a\u7f51\u7edc\u7684\u957f\u7a0b\u548c\u77ed\u7a0b\u8fde\u63a5\u7684\u8fde\u901a\u6027\u3002<\/span><\/p>\n

                <\/span>\u5e94\u7528<\/span><\/span><\/span><\/h2>\n

                \u51e0\u4f55\u91cd\u6574\u5316\u4e0e\u51e0\u4f55\u5206\u652f\u751f\u957f\u6a21\u578b\u7684\u7ed3\u5408\u80fd\u591f\u5b9e\u73b0\u5168\u5c3a\u5ea6\u7684\u7f51\u7edc\u81ea\u4e0a\u800c\u4e0b\u7684\u591a\u5c3a\u5ea6\u5c55\u5f00\u3002\u5176\u5e94\u7528\u5305\u62ec\u591a\u5c3a\u5ea6\u65b9\u6cd5\u7684\u8bbe\u8ba1\uff0c\u5982\u63d0\u5347\u5355\u5c3a\u5ea6\u65b9\u6cd5\u6027\u80fd\u7684\u591a\u5c3a\u5ea6\u5bfc\u822a[68]\u3002\u901a\u8fc7\u51e0\u4f55\u91cd\u6574\u5316\u65b9\u6cd5\u53ef\u5f88\u65b9\u4fbf\u5730\u751f\u6210\u4fdd\u6301\u8fde\u63a5\u5bc6\u5ea6\u7b49\u7edf\u8ba1\u7279\u6027\u7684\u771f\u5b9e\u7f51\u7edc\u7f29\u653e\u526f\u672c[68,69]\u3002\u8fd9\u4e9b\u526f\u672c\u80fd\u4e3a\u7814\u7a76\u771f\u5b9e\u7f51\u7edc\u4e2d\u7684\u5c3a\u5bf8\u4f9d\u8d56\u73b0\u8c61\u63d0\u4f9b\u652f\u6301\uff0c\u5728\u4ee5\u4e0b\u65b9\u9762\u5177\u6709\u91cd\u8981\u5e94\u7528\u524d\u666f\uff1a\u63a2\u7a76\u5c3a\u5bf8\u8bf1\u5bfc\u7684\u968f\u673a\u5171\u632f\u6548\u5e94\u3001\u901a\u8fc7\u6709\u9650\u5c3a\u5ea6\u6807\u5ea6\u6280\u672f\u5206\u6790\u4e34\u754c\u884c\u4e3a69\uff0c\u4ee5\u53ca\u5bf9\u8ba1\u7b97\u5bc6\u96c6\u578b\u8fc7\u7a0b\u8fdb\u884c\u9ad8\u4fdd\u771f\u6a21\u62df\u7684\u6a21\u578b\u964d\u9636\u3002<\/span><\/p>\n

                <\/span>
                <\/span><\/span><\/h1>\n

                \n
                \n
                \n
                \n
                \n

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

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

                \u62c9\u666e\u62c9\u65af\u7f51\u7edc\u91cd\u6574\u5316<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

                \n

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

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


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

                \u590d\u6742\u7f51\u7edc\u91cd\u6574\u5316\u7684\u53e6\u4e00\u65b9\u6cd5[35,108]\u662f\u5229\u7528\u8282\u70b9\u95f4\u7684\u62c9\u666e\u62c9\u65af\u6269\u6563\u6982\u5ff5[109,110]\u901a\u8fc7\u5b9e\u65f6\u68c0\u6d4b\u591a\u5c3a\u5ea6\u7ed3\u6784\u800c\u5b9e\u73b0\u9876\u70b9\u548c\u8fb9\u7684\u7c97\u7c92\u5316\uff0c\u5e76\u6700\u7ec8\u91cd\u6574\u5316\u7f51\u7edc\u4e0a\u7684\u52a8\u529b\u5b66\u6a21\u578b\u3002\u4e0e\u524d\u8ff0\u51e0\u4f55\u65b9\u6cd5\u7c7b\u4f3c\uff0c\u8be5\u6846\u67b6\u53ef\u57fa\u4e8e\u76f4\u89c2\u4e14\u7269\u7406\u53ef\u5b9e\u73b0\u7684\u5b9e\u7a7a\u95f4\u7248\u672c\u800c\u5efa\u7acb\uff0c\u8fd9\u7c7b\u4f3c\u4e8e\u7edf\u8ba1\u7269\u7406\u4e2d\u7684Migdal-Kadanoff\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5[111,112]\uff0c\u4f46\u5176\u72ec\u7279\u4e4b\u5904\u5728\u4e8e\u9075\u5faa\u4e86Wilson\u91cd\u6574\u5316\u7fa4\u601d\u60f3[113]\u800c\u5efa\u7acb\u5728\u4e25\u683c\u5bf9\u5076\u7a7a\u95f4\u6216\u8005 <\/span><\/span><\/span> \u7a7a\u95f4\u8868\u8ff0\u4e4b\u4e0a\u3002\u8fd9\u4e24\u79cd\u8868\u8ff0\u5747\u901a\u8fc7\u8fed\u4ee3\u65b9\u5f0f\u7c97\u7c92\u5316\u7f51\u7edc\uff0c\u540c\u65f6\u5728\u76f8\u5f53\u5927\u7684\u5c3a\u5ea6\u8303\u56f4\u5185\u80fd\u591f\u4fdd\u6301\u6269\u6563\u52a8\u529b\u5b66\u6027\u8d28\u3002<\/span><\/p>\n

                <\/span>\u5c06\u62c9\u666e\u62c9\u65af\u6269\u6563\u89c6\u4e3a\u8fd1\u90bb\u68c0\u6d4b<\/span><\/span><\/span><\/h2>\n

                \u6784\u5efa\u5f02\u6784\u65e0\u5411\u7f51\u7edc(\u4e8c\u503c\u6216\u52a0\u6743)\u7684\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4\uff08Laplacian renormalization group\uff0cLRG\uff09\u65b9\u6cd5\u7684\u7b2c\u4e00\u6b65\u9aa4\u662f\u5229\u7528\u5bf9\u79f0\u56fe\u62c9\u666e\u62c9\u65af\u7b97\u5b50[110,114] <\/span><\/span><\/span> \u5b9a\u4e49\u8282\u70b9\u5728\u56fa\u5b9a\u5c3a\u5ea6\u4e0b\u7684\u201c\u7b49\u6548\u201d\u90bb\u57df\u3002\u8be5\u7b97\u5b50\u5728\u521d\u59cb\u5c42\u7ea7 <\/span><\/span><\/span> \u7531\u90bb\u63a5\u77e9\u9635 <\/span><\/span><\/span> \u6784\u9020\uff0c\u5176\u77e9\u9635\u5143\u7d20\u4e3a <\/span><\/span><\/span> \uff0c\u5176\u4e2d <\/span><\/span><\/span> \u4e3aKronecker <\/span><\/span><\/span> \u7b26\u53f7\uff0c <\/span><\/span><\/span> \u8868\u793a\u8282\u70b9 <\/span><\/span><\/span> \u7684\u5ea6( <\/span><\/span><\/span> )\u3002<\/span><\/p>\n

                \u8bbe <\/span><\/span><\/span> \u4ee3\u8868\u5b9a\u4e49\u5728\u7f51\u7edc\u4e0a\u7684\u6269\u6563\u573a\u5728\u65f6\u523b <\/span><\/span><\/span> \u7684\u503c\uff0c\u5e76\u8bb0 <\/span><\/span><\/span> \u4e3a\u8282\u70b9 <\/span><\/span><\/span> \u7684\u5206\u91cf\uff0c\u5047\u8bbe\u5176\u9075\u5faa\u70ed\u6269\u6563\u65b9\u7a0b <\/span><\/span><\/span> \uff0c\u5219\u53ef\u5f62\u5f0f\u5316\u8868\u793a\u4e3a<\/span><\/p>\n

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

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

                \u5176\u4e2d\u6269\u6563\u6f14\u5316\u7b97\u5b50 <\/span><\/span><\/span> \u3002\u77e9\u9635\u5143\u7d20 <\/span><\/span><\/span> \u7ed9\u51fa\u4e86\u8be5\u573a\u5728\u65f6\u95f4 <\/span><\/span><\/span> \u5185\u4ece\u8282\u70b9 <\/span><\/span><\/span> \u5230 <\/span><\/span><\/span> (\u53ca\u53cd\u5411)\u901a\u8fc7\u6240\u6709\u53ef\u80fd\u8def\u5f84\u53d1\u751f\u7684\u6269\u6563\u7684\u6bd4\u4f8b[115,116]\u3002<\/span><\/p>\n

                \u8bbe <\/span><\/span><\/span> \u7684\u7279\u5f81\u503c\u4e3a <\/span><\/span><\/span> (\u6ee1\u8db3 <\/span><\/span><\/span> )\uff0c\u5bf9\u5e94\u7279\u5f81\u5411\u91cf\u4e3a <\/span><\/span><\/span> \u3002\u5bf9\u4e8e\u8fde\u901a\u65e0\u5411\u7f51\u7edc\uff0c\u6240\u6709\u7279\u5f81\u503c\u975e\u8d1f\u4e14\u4ec5\u542b\u4e00\u4e2a\u96f6\u7279\u5f81\u503c\uff0c\u4e14\u53ef\u5c06\u7279\u5f81\u5411\u91cf\u6b63\u4ea4\u5f52\u4e00\u5316\u3002 <\/span><\/span><\/span> \u5171\u4eab\u4e86\u7279\u5f81\u503c\u4e3a <\/span><\/span><\/span> \u7684\u7279\u5f81\u5411\u91cf\u3002\u53c2\u6570 <\/span><\/span><\/span> \u53ef\u89c6\u4e3a\u7f51\u7edc\u5c3a\u5ea6\u5ea6\u91cf\uff1a\u8f83\u5927 <\/span><\/span><\/span> \u5bf9\u5e94\u6269\u6563\u8fde\u63a5\u7684\u66f4\u5927\u90bb\u57df\u3002\u4f8b\u5982\u5bf9\u683c\u70b9\u6765\u8bf4\uff0c\u6bcf\u4e2a <\/span><\/span><\/span> \u5bf9\u5e94\u7a7a\u95f4\u5c3a\u5ea6 <\/span><\/span><\/span> ( <\/span><\/span><\/span> \u4e3a\u6269\u6563\u5e38\u6570)\uff0c\u6b64\u65f6 <\/span><\/span><\/span> \u5728\u6bcf\u4e2a\u65f6\u95f4 <\/span><\/span><\/span> \u90fd\u8bf1\u5bfc\u4e86\u7f51\u7edc\u7684\u4e00\u4e2a\u6700\u4f18\u5212\u5206[117]\u3002<\/span><\/p>\n

                <\/span>\u5b9e\u7a7a\u95f4\u4e2d\u7684\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4<\/span><\/span><\/span><\/h2>\n

                \u57fa\u4e8e\u7269\u7406\u8be0\u91ca\uff0c\u53ef\u5229\u7528 <\/span><\/span><\/span> \u5c06\u539f\u59cb\u7f51\u7edc( <\/span><\/span><\/span> )\u7684 <\/span><\/span><\/span> \u4e2a\u8282\u70b9\u5728\u4efb\u610f\u65f6\u523b <\/span><\/span><\/span> \u4e0b\u5212\u5206\u4e3a <\/span><\/span><\/span> \u4e2a\u201c\u6269\u6563\u7b49\u6548\u201d\u7684\u5b50\u56fe\uff0c\u7ee7\u800c\u7c97\u7c92\u5316\u4e3a\u8d85\u8282\u70b9\u4ee5\u5b9a\u4e49\u4e0b\u4e00\u5c42\u7ea7( <\/span><\/span><\/span> )\u7f51\u7edc\u3002\u901a\u8fc7\u5bf9\u5fae\u89c2\u5c0f\u5c3a\u5ea6\u8fde\u8fb9\u5173\u7cfb\u7684\u526a\u88c1\u6765\u786e\u5b9a\u8d85\u8282\u70b9\u95f4\u91cd\u6574\u5316\u540e\u7684\u8fb9(\u5982\u516c\u5f0f(1)(3))\u3002\u5bf9\u4e8e\u89c4\u5219\u683c\u70b9\uff0c\u56fa\u5b9a <\/span><\/span><\/span> \u5c31\u7b49\u4ef7\u4e8e\u56fa\u5b9a\u7a7a\u95f4\u5c3a\u5ea6 <\/span><\/span><\/span> \uff0c\u6b64\u8fc7\u7a0b\u5b8c\u5168\u53ef\u4ee5\u7c7b\u6bd4\u4e8eIsing\u6a21\u578b\u4e2d\u7684Kadanoff\u5757\u81ea\u65cb\u65b9\u6cd5[118]\u3002<\/span><\/p>\n

                \u7f51\u7edc\u7684\u62c9\u666e\u62c9\u65af\u7c97\u7c92\u5316\u65b9\u6cd5\u53ef\u6982\u62ec\u5982\u4e0b\u3002\u9996\u5148\u5b9a\u4e49\u4e8c\u503c\u5316\u62c9\u666e\u62c9\u65af\u77e9\u9635 <\/span><\/span><\/span> \uff0c\u5176\u5143\u7d20\u4e3a\uff1a<\/span><\/p>\n

                <\/p>\n
                \u82e5\u5176\u4ed6\u60c5\u51b5<\/section>\n

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

                \u9700\u6ce8\u610f <\/span><\/span><\/span> \u662f <\/span><\/span><\/span> \u7684\u5355\u4f4d\u77e9\u9635\uff0c\u4e14\u5bf9\u6240\u6709 <\/span><\/span><\/span> \u6709 <\/span><\/span><\/span> \u3002\u5bf9\u56fa\u5b9a\u7684 <\/span><\/span><\/span> \uff0c\u77e9\u9635 <\/span><\/span><\/span> \u53ef\u89c6\u4e3a\u539f\u7f51\u7edc\u7684\u8d85\u56fe\u7684\u90bb\u63a5\u77e9\u9635\uff0c\u5176\u5305\u542b <\/span><\/span><\/span> \u4e2a\u5728\u5c3a\u5ea6 <\/span><\/span><\/span> \u4e0a\u901a\u8fc7\u6269\u6563\u8fde\u63a5\u7684\u8fde\u901a\u5206\u652f\u3002\u6b64\u8fc7\u7a0b\u5c06\u539f\u6765\u7684 <\/span><\/span><\/span> \u4e2a\u8282\u70b9\u5212\u5206\u4e3a <\/span><\/span><\/span> \u4e2a\u8d85\u8282\u70b9\uff08\u56fe2a\uff09\u3002 <\/span><\/span><\/span> \u8d8a\u5927\uff0c\u8fde\u901a\u5206\u652f\u6570\u91cf\u8d8a\u5c11\u4e14\u6bcf\u4e2a\u8fde\u901a\u5206\u652f\u7684\u89c4\u6a21\u8d8a\u5927\u3002 <\/span><\/span><\/span> \u610f\u5473\u7740\u4ec5\u5b58\u5728\u5355\u4e00\u5206\u652f\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u56e0\u5747\u5300\u6269\u6563\u573a\u6700\u7ec8\u6240\u6709\u7f51\u7edc\u8282\u70b9\u5747\u8fde\u63a5\u5728\u4e00\u8d77\u3002\u57fa\u4e8e\u65b9\u7a0b(3)\u7684\u7c97\u7c92\u5316\u52a0\u6743\u90bb\u63a5\u77e9\u9635 <\/span><\/span><\/span> \u53ef\u901a\u8fc7\u5b9a\u4e49\u8d85\u8282\u70b9\u95f4\u7684\u52a0\u6743\u8d85\u8fb9\u6765\u6784\u9020\uff0c\u5176\u6743\u91cd\u7b49\u4e8e\u8fde\u63a5\u4e24\u5bf9\u5e94\u7ec6\u5c3a\u5ea6\u7c07\u7684\u5fae\u8fb9\u6743\u91cd\u7ecf\u9002\u5f53\u5f52\u4e00\u5316\u540e\u7684\u603b\u548c\uff08\u56fe2b\uff09\u3002\u4ea6\u53ef\u91c7\u7528\u7edf\u8ba1\u7269\u7406\u7c97\u7c92\u5316\u4e2d\u7684\u4e00\u81f4\u6027\u88c1\u526a\u65b9\u6cd5\u83b7\u53d6\u4e8c\u503c\u90bb\u63a5\u77e9\u9635 <\/span><\/span><\/span> \uff08\u4f8b\u5982\u901a\u8fc7\u65b9\u7a0b(1)\uff09\u3002\u6574\u4e2a\u8fc7\u7a0b\u53ef\u8fed\u4ee3\u6267\u884c\u4ee5\u5b9a\u4e49\u66f4\u9ad8\u5c42\u7ea7 <\/span><\/span><\/span> \uff08\u56fe2c,d\uff09\u3002<\/span><\/p>\n


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

                <\/section>\n

                \u56fe2  \u5b9e\u7a7a\u95f4\u4e2d\u7684\u62c9\u666e\u62c9\u65af\u7f51\u7edc\u91cd\u6574\u5316\u65b9\u6cd5\u7684\u6784\u9020\u3002 a. \u5e95\u5c42 ( <\/span><\/span><\/span> ) \u8868\u793a\u539f\u59cb\u7f51\u7edc <\/span><\/span><\/span> \uff08\u6b64\u5904\u4e3a Barab\u00e1si-Albert \u7f51\u7edc\uff0c\u901a\u8fc7\u6bcf\u6b21\u6dfb\u52a0\u4e00\u4e2a\u5e26 <\/span><\/span><\/span> \u6761\u8fde\u63a5\u7684\u8282\u70b9\u6f14\u5316\u800c\u6210\uff0c\u6700\u7ec8\u89c4\u6a21\u4e3a <\/span><\/span><\/span> \u4e2a\u8282\u70b9\uff09\uff0c\u4e0a\u5c42\u5c55\u793a\u6269\u6563\u65f6\u95f4\u5c3a\u5ea6 <\/span><\/span><\/span> \u5bf9\u5e94\u7684\u5212\u5206 <\/span><\/span><\/span> \u3002\u4e0d\u540c\u989c\u8272\u6807\u8bc6 <\/span><\/span><\/span> \u4e2a Kadanoff \u8d85\u8282\u70b9\u3002 b. \u57fa\u4e8e <\/span><\/span><\/span> \uff0c\u6bcf\u4e2a\u5757\u88ab\u805a\u5408\u4e3a\u5355\u4e2a\u8d85\u8282\u70b9 <\/span><\/span><\/span> \uff08 <\/span><\/span><\/span> \uff09\uff0c\u4fdd\u7559\u4e0e\u539f\u8282\u70b9\u8fde\u63a5\u7684\u8fb9\uff0c\u4ece\u800c\u5728\u4e0b\u4e00\u5c42\u7ea7 <\/span><\/span><\/span> \u6784\u5efa\u7c97\u7c92\u5316\u7f51\u7edc <\/span><\/span><\/span> \u3002 c. \u5b9e\u7a7a\u95f4\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4\uff08LRG\uff09\u8fc7\u7a0b\u7684\u4e09\u4e2a\u6b65\u9aa4\u3002 d. \u968f\u673a\u6811\u7684 LRG \u7c97\u7c92\u5316\u3002\u56fe\u8f6c\u8f7d\u81ea\u6587\u732e[108]\uff0c\u9075\u5faa CCBY 4.0 \u534f\u8bae\u3002<\/span><\/p>\n

                k-\u7a7a\u95f4\u4e0a\u7684\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4<\/span><\/span><\/p>\n

                \u8be5\u516c\u5f0f\u5316\u8fc7\u7a0b\u80fd\u591f\u4e0eWilson\u5728\u8fde\u7eed\u573a\u8bba\u4e2d\u7684\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u76f4\u63a5\u7c7b\u6bd4[119]\uff0c\u53ef\u4ee5\u663e\u5f0f\u5730\u4f53\u73b0\u51fa\u5176\u534a\u7fa4\u6027\u8d28\u3002\u5b83\u53ef\u89c6\u4e3a\u5b9e\u7a7a\u95f4\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4\u5728\u5085\u91cc\u53f6\u7a7a\u95f4\u7684\u5bf9\u5e94\uff0c\u5176\u4e2d\u5085\u91cc\u53f6\u57fa\u7531\u62c9\u666e\u62c9\u65af\u7279\u5f81\u5411\u91cf\u7ed9\u51fa\uff0c\u6ce2\u6a21\u6001\u7531\u62c9\u666e\u62c9\u65af\u7279\u5f81\u503c\u66ff\u4ee3\u3002\u5728\u89c4\u5219\u683c\u70b9\u4e0a\uff0c\u8fd9\u4e9b\u7279\u5f81\u5411\u91cf\u786e\u5b9e\u4e0e\u5e73\u9762\u6ce2\u5085\u91cc\u53f6\u57fa\u4e00\u81f4\uff0c\u5176\u7279\u5f81\u503c\u7b80\u5316\u4e3a <\/span><\/span><\/span> \u3002<\/span><\/p>\n

                \u8be5\u65b9\u6cd5\u4e3a\u91cd\u6574\u5316\u8fc7\u7a0b\u63d0\u4f9b\u66f4\u6df1\u523b\u7684\u6d1e\u89c1\uff0c\u4e0d\u4ec5\u5141\u8bb8\u7f51\u7edc\u7c97\u7c92\u5316\uff0c\u8fd8\u80fd\u6070\u5f53\u7684\u91cd\u6807\u5ea6\u5d4c\u5165\u5176\u4e2d\u7684\u7edf\u8ba1\u52a8\u529b\u5b66\u6a21\u578b\uff08\u5982Ising\u6a21\u578b\u6216\u5207\u89e6\u8fc7\u7a0b\uff09\u4ee5\u63a2\u6d4b\u548c\u7814\u7a76\u7279\u5f81\uff08\u5173\u8054\uff09\u5c3a\u5ea6\u53ca\u53ef\u80fd\u7684\u76f8\u53d8\u3002\u7531\u4e8e <\/span><\/span><\/span> \u4e0e <\/span><\/span><\/span> \u662f\u5384\u7c73\u7b97\u5b50\uff08\u6ce8\uff1a\u6570\u5b66\u4e0a\u901a\u5e38\u79f0\u4e3a\u81ea\u4f34\u7b97\u5b50\uff09\uff0c\u6211\u4eec\u91c7\u7528\u91cf\u5b50\u529b\u5b66\u201cbra-ket\u201d\u7b26\u53f7\u4e66\u5199\uff1a<\/span><\/p>\n

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

                \u7279\u5f81\u5411\u91cf\u7684\u5b8c\u5907\u6027\u4fdd\u8bc1\u4e86\u7c97\u7c92\u5316\u53d8\u91cf\u5b9a\u4e49\u7684\u5408\u7406\u6027\u3002\u540e\u7eed\u6b65\u9aa4\u6309Wilson\u8303\u5f0f[113]\u5b9e\u73b0\u91cd\u6574\u5316\u7a0b\u5e8f\uff1a<\/span><\/p>\n

                  \n
                • \n
                  \n

                  \u8bbe\u5b9a\u65f6\u95f4 <\/span><\/span><\/span> \u4ee5\u786e\u5b9a\u65b0\u5206\u8fa8\u7387\u5c3a\u5ea6\uff08\u6216\u4f4e\u80fd\u622a\u65ad\uff09<\/span><\/p>\n<\/section>\n<\/li>\n

                • \n
                  \n

                  \u5c06\u62c9\u666e\u62c9\u65af\u8c31\u5212\u5206\u4e3a\u4e24\u7c7b\uff1a <\/span><\/span><\/span> \u4e2a\u201c\u5feb\u201d\u7279\u5f81\u503c <\/span><\/span><\/span> \uff0c\u4ee5\u53ca <\/span><\/span><\/span> \u4e2a\u201c\u6162\u201d\u7279\u5f81\u503c <\/span><\/span><\/span><\/p>\n<\/section>\n<\/li>\n

                • \n
                  \n

                  \u79ef\u6389\u8c31\u7684\u201c\u5feb\u201d( <\/span><\/span><\/span> )\u533a\u57df\uff0c\u91cd\u5b9a\u4e49\u6162\u7279\u5f81\u5411\u91cf\u8d21\u732e\u7684\u622a\u65ad\u62c9\u666e\u62c9\u65af\u7b97\u5b50 <\/span><\/span><\/span> \u3002\u8fd9\u5bf9\u82f1\u8bed\u91cd\u6574\u5316\u65b9\u6cd5\u7684\u7b2c\u4e8c\u6b65\u3002<\/span><\/p>\n<\/section>\n<\/li>\n

                • \n
                  \n

                  \u91cd\u65b0\u8ba1\u7b97\u65f6\u95f4\u6807\u5ea6 <\/span><\/span><\/span> \uff0c\u4f7f <\/span><\/span><\/span> \uff0c\u4f5c\u4e3a\u65b0\u7684\u65f6\u95f4\u5355\u4f4d\uff0c\u5bf9\u5e94\u7c97\u7c92\u5316\u62c9\u666e\u62c9\u65af\u7b97\u5b50\u91cd\u6574\u5316\u81f3\u5c42\u7ea7 <\/span><\/span><\/span> \uff0c <\/span><\/span><\/span> \u3002\u8fd9\u5bf9\u5e94\u4e8e\u91cd\u6574\u5316\u65b9\u6cd5\u7684\u7b2c\u4e09\u6b65\u3002<\/span><\/p>\n<\/section>\n<\/li>\n<\/ul>\n

                  \u8fed\u4ee3\u8fd9\u4e9b\u6b65\u9aa4\u53ef\u751f\u6210\u805a\u5408\u6240\u6709\u5c42\u7ea7 <\/span><\/span><\/span> \u7684\u91cd\u6574\u5316\u62c9\u666e\u62c9\u65af\u7b97\u5b50 <\/span><\/span><\/span> \u3002\u8be5\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4\u7684 <\/span><\/span><\/span> \u7a7a\u95f4\u516c\u5f0f\u53ef\u4e0e\u5b9e\u7a7a\u95f4\u89e3\u91ca\u4e92\u4e3a\u8865\u5145\uff08\u89c1\u9644\u5f55\uff09\u3002<\/span><\/p>\n

                  Ising \u6a21\u578b\u3001\u63a5\u89e6\u8fc7\u7a0b\u4ee5\u53ca\u5927\u591a\u6570\u4ee5\u89c4\u5219\u683c\u70b9\u4e0a\u5c40\u90e8\u5e73\u79fb\u4e0d\u53d8\u76f8\u4e92\u4f5c\u7528\u4e3a\u7279\u5f81\u7684\u7edf\u8ba1\u6a21\u578b\u7684\u7edf\u8ba1\u573a\u8868\u8ff0\uff0c\u90fd\u5141\u8bb8\u9ad8\u65af\u8fd1\u4f3c\uff0c\u5176\u6838\u5b8c\u5168\u7531\u62c9\u666e\u62c9\u65af\u7b97\u5b50\u51b3\u5b9a\uff0c\u8be5\u7b97\u5b50\u5728\u683c\u70b9\u4e0a\u7684\u62c9\u666e\u62c9\u65af\u5e73\u9762\u6ce2\u57fa\u4e0b\u7684\u77e9\u9635\u662f\u5bf9\u89d2\u7684[120,121]\u3002\u5bf9\u4e8e\u4e0d\u89c4\u5219\u7f51\u7edc\u4e0a\u7684\u76f8\u540c\u6a21\u578b[34,122,123]\u8fd9\u4e00\u70b9\u4ecd\u7136\u6210\u7acb\uff0c\u552f\u4e00\u7684\u533a\u522b\u662f\u62c9\u666e\u62c9\u65af\u7b97\u5b50\u4e0d\u518d\u5177\u6709\u5e73\u79fb\u4e0d\u53d8\u6027\u3002\u8fd9\u79cd\u9ad8\u65af\u8fd1\u4f3c\u5728\u6240\u6709\u60c5\u51b5\u4e0b\u90fd\u662f\u552f\u4e00\u7cbe\u786e\u53ef\u89e3\u7684\u573a\u8bba\uff0c\u975e\u9ad8\u65af\u76f8\u4e92\u4f5c\u7528\u901a\u5e38\u9700\u8981\u901a\u8fc7\u56f4\u7ed5\u5b83\u7684\u5fae\u6270\u6cd5\u6765\u7814\u7a76\u3002\u8fd9\u662f Wilson \u91cd\u6574\u5316\u7fa4\u7684\u5173\u952e\u70b9\u4e4b\u4e00\uff1a\u5085\u91cc\u53f6\u57fa\u662f\u5728\u7cbe\u786e\u53ef\u89e3\u7684\u9ad8\u65af\u8fd1\u4f3c\u4e0b\u80fd\u4f7f\u77e9\u9635\u4e3a\u5bf9\u89d2\u77e9\u9635\u7684\u57fa\uff0c\u5373\u8fd9\u4e9b\u72b6\u6001\u662f\u7531\u7ebf\u6027\u65e0\u5173\u4e14\u6b63\u4ea4\u7684\u53d8\u91cf\u7684\u53e0\u52a0\u51b3\u5b9a\u3002\u56e0\u6b64\uff0c\u5f53\u7814\u7a76\u975e\u9ad8\u65af\u9879\u7684\u53d8\u6362\u7684\u7ec6\u8282\u65f6\uff0c\u5c3a\u5ea6\u53d8\u6362\uff08\u7f29\u653e\uff09\u5728\u5229\u7528\u9ad8\u65af\u8fd1\u4f3c\u7684\u57fa\u5750\u6807\u4e2d\u4ee5\u76f4\u63a5\u91cd\u53c2\u6570\u5316\u8fdb\u884c\u7684\u3002\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4\u80fd\u591f\u5c06\u5176\u89c6\u4e3a\u7edf\u8ba1\u6a21\u578b\u7684\u975e\u5c40\u90e8\u548c\u5f02\u8d28\u5d4c\u5165\u7a7a\u95f4\uff0c\u4ece\u800c\u5c06\u8fd9\u79cd\u65b9\u6cd5\u63a8\u5e7f\u5230\u4e0d\u89c4\u5219\u7f51\u7edc\u7684\u60c5\u5f62\u3002<\/span><\/p>\n

                  \u6700\u540e\uff0c\u7f51\u7edc\u5355\u7eaf\u590d\u5f62\u4e0a\u7684\u62c9\u666e\u62c9\u65af\u7b97\u5b50\u7684\u8c31\u7ef4\u6570\u4e5f\u6709\u6240\u7814\u7a76[124,125]\uff0c\u5e76\u4e14\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4\u4e5f\u53ef\u4ee5\u63a8\u5e7f\u5230\u7531\u5355\u7eaf\u590d\u5f62\u548c\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u6784\u5efa\u7684\u7f51\u7edc\u4e2d[126,127]\uff08\u89c1\u9644\u5f55\uff09\u3002<\/span><\/p>\n

                  <\/span>\u6269\u6563\u6f14\u5316\u7b97\u5b50\u7684\u7edf\u8ba1\u7269\u7406\u5b66\u89e3\u91ca<\/span><\/span><\/span><\/h2>\n

                  \u7b97\u5b50 <\/span><\/span><\/span> \u53ef\u7528\u4e8e\u6784\u5efa\u7f51\u7edc\u7684\u201c\u672c\u5f81\u5c3a\u5ea6\u626b\u63cf\u4eea\u201d\u3002\u8be5\u201c\u626b\u63cf\u4eea\u201d\u5177\u5907\u5e73\u8861\u6001\u7edf\u8ba1\u7269\u7406\u4e2d\u71b5\u654f\u611f\u6027\u6216\u70ed\u5bb9\u7684\u5168\u90e8\u6570\u5b66\u7279\u6027\uff0c\u5176\u663e\u8457\u6781\u5927\u503c\uff08\u5728\u65e0\u9650\u5c3a\u5bf8\u6781\u9650\u4e0b\u53d1\u6563\uff09\u80fd\u591f\u8868\u660e\u7f51\u7edc\u7ed3\u6784\u7ec4\u7ec7\u4e2d\u7684\u4e00\u7c7b\u76f8\u53d8\u3002\u5177\u4f53\u800c\u8a00\uff0c <\/span><\/span><\/span> \u7684\u7279\u5f81\u503c <\/span><\/span><\/span> \u53ef\u7528\u6765\u5b9a\u4e49\u5b9e\u65f6\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570 <\/span><\/span><\/span> \uff0c\u5176\u4e2d\u914d\u5206\u51fd\u6570 <\/span><\/span><\/span> \uff0c <\/span><\/span><\/span> \u4e3a\u72c4\u62c9\u514b\u03b4\u51fd\u6570\u3002\u8be5\u6d4b\u5ea6\u5bf9\u5e94\u7684\u9999\u519c\u71b5\u4e3a <\/span><\/span><\/span> \u3002\u7531\u4e8e\u65e0\u5411\u7f51\u7edc\u7684 <\/span><\/span><\/span> \u4e3a\u5384\u7c73\u4e14\u534a\u6b63\u5b9a\uff0c <\/span><\/span><\/span> \u53ef\u5f62\u5f0f\u5316\u89c6\u4e3a\u51af\u00b7\u8bfa\u4f9d\u66fc\u71b5 <\/span><\/span><\/span> \uff0c\u4e0e\u91cf\u5b50\u6b63\u5219\u5bc6\u5ea6\u7b97\u5b50 <\/span><\/span><\/span> \u76f8\u5173\u8054\uff08\u53c2\u8003\u6587\u732e109,128,129\uff09\uff0c\u6b64\u5904 <\/span><\/span><\/span> \u626e\u6f14\u54c8\u5bc6\u987f\u91cf\u89d2\u8272\uff0c <\/span><\/span><\/span> \u5219\u5bf9\u5e94\u9006\u6e29\u5ea6[130,131]\u3002\u7b49\u4ef7\u5730\uff0c\u914d\u5206\u51fd\u6570 <\/span><\/span><\/span> \u901a\u8fc7 <\/span><\/span><\/span> \u4e0e\u81ea\u7531\u80fd\u76f8\u5173\u8054\u3002<\/span><\/p>\n

                  \u8be5\u5f62\u5f0f\u7c7b\u6bd4\u7684\u76f4\u63a5\u63a8\u8bba\u662f\u4e0b\u8ff0\u91cf<\/span><\/p>\n

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

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

                  \u5177\u6709\u71b5\u654f\u611f\u6027\u7684\u6570\u5b66\u7279\u6027\uff0c\u56e0\u800c\u662f\u4e2a\u70ed\u5bb9[15,129]\u3002\u5728\u8282\u70b9\u6570\u65e0\u7a77\u5927\u7684\u6781\u9650\u4e0b\uff0c\u76f8\u53d8\u70b9\u53ef\u89e3\u91ca\u4e3a <\/span><\/span><\/span> \u5728\u5455\u8840\u5c3a\u5ea6 <\/span><\/span><\/span> \u5904\u7684\u5947\u5f02\u6027\u6216\u867d\u6709\u9650\u4f46 <\/span><\/span><\/span> \u503c\u975e\u5e38\u5927\u7684\u60c5\u5f62\u3002\u6362\u8a00\u4e4b\uff0c <\/span><\/span><\/span> \u662f\u7f51\u7edc\u62d3\u6251\u53d1\u751f\u7a81\u53d8\u7684\u5185\u8574\u5c3a\u5ea6\uff0c\u7c7b\u4f3c\u4e8eIsing\u6a21\u578b\u4e2d\u5173\u8054\u957f\u5ea6\u5c3a\u5ea6\u7684\u4f5c\u7528\u3002\u4f8b\u5982\uff0c\u5728\u5177\u6709\u76f8\u540c\u5c3a\u5bf8\u7684\u5757\u6784\u6210\u7684\u7f51\u7edc\u6a21\u578b\uff0c\u8981\u6c42\u5757\u5185\u90e8\u7a20\u5bc6\u8fde\u63a5\u4f46\u662f\u5757\u4e4b\u95f4\u76f8\u4e92\u8fde\u63a5\u8f83\u5f31[132]\uff0c\u5728\u8fd9\u4e2a\u6a21\u578b\u4e2d <\/span><\/span><\/span> \u5448\u73b0\u53cc\u5cf0\uff1a\u4e00\u4e2a\u5bf9\u5e94\u4e8e\u5355\u5757\u7684\u6269\u6563\u5c3a\u5ea6\uff0c\u53e6\u4e00\u4e2a\u5bf9\u5e94\u4e8e\u5757\u95f4\u5178\u578b\u8def\u5f84\u7684\u66f4\u5927\u5c3a\u5ea6\u3002\u5728\u6b64\u610f\u4e49\u4e0a\uff0c <\/span><\/span><\/span> \u53ef\u4f5c\u4e3a\u672c\u5f81\u5c3a\u5ea6\u63a2\u6d4b\u5668\uff0c\u901a\u8fc7\u8bc6\u522b\u7f51\u7edc\u7ed3\u6784\u53d1\u751f\u62d3\u6251\u8f6c\u53d8\u7684\u7279\u5f81\u5c3a\u5ea6\u6765\u8bf1\u5bfc\u7f51\u7edc\u7684\u7c97\u7c92\u5316\u8fc7\u7a0b[132]\u3002<\/span><\/p>\n

                  <\/span>\u62d3\u6251\u6807\u5ea6\u4e0d\u53d8\u7f51\u7edc<\/span><\/span><\/span><\/h2>\n

                  \u5f53 <\/span><\/span><\/span> \u65f6\u7f51\u7edc\u5177\u6709\u62d3\u6251\u6807\u5ea6\u4e0d\u53d8\u6027\uff0c\u5176\u4e2d <\/span><\/span><\/span> \u662f\u62c9\u666e\u62c9\u65af\u7279\u5f81\u503c\u5bc6\u5ea6\uff0c <\/span><\/span><\/span> \u548c <\/span><\/span><\/span> \u4e3a\u62c9\u666e\u62c9\u65af\u8c31\u7ef4\u5ea6[133]\uff08\u89c1\u9644\u5f55\uff09\u3002\u6b64\u65f6\u71b5\u654f\u611f\u6027\u4e0e <\/span><\/span><\/span> \u65e0\u5173\uff0c\u4fdd\u6301\u6052\u5b9a\u503c <\/span><\/span><\/span> [35]\u3002\u8fd9\u79cd <\/span><\/span><\/span> \u65e0\u5173\u6027\u4f1a\u5728\u89c4\u5219\u683c\u70b9\u6216\u968f\u673a\u6811\u4e2d\u51fa\u73b0\uff0c\u4e5f\u5b58\u5728\u4e8e\u66f4\u590d\u6742\u7f51\u7edc\u5982\u5206\u5c42\u6a21\u5757\u5316\u7f51\u7edc[134]\u4e2d\u3002\u6839\u636e\u672c\u8282\u8ba8\u8bba\u7684\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4\u7684\u989d\u5b9a\u4e49\uff0c\u6240\u6709\u62d3\u6251\u5c3a\u5ea6\u4e0d\u53d8\u7f51\u7edc\u5728\u62c9\u666e\u62c9\u65af\u5c3a\u5ea6\u53d8\u6362\u548c\u7c97\u7c92\u5316\u4e0b\u4fdd\u6301\u76f8\u540c\u62d3\u6251\u7ed3\u6784[135]\uff08\u53e6\u89c1[136]\uff09\u3002\u56e0\u6b64\uff0c <\/span><\/span><\/span> \u53ef\u4f5c\u4e3a\u5b9e\u9645\u7f51\u7edc\u5c3a\u5ea6\u4e0d\u53d8\u6027\u7684\u63a2\u6d4b\u5668\uff0c\u82e5\u5176\u4e3a\u5e38\u6570\u503c\u5219\u53ef\u76f4\u63a5\u7528\u4e8e\u5ea6\u91cf\u8c31\u7ef4\u5ea6\u3002<\/span><\/p>\n

                  <\/span>
                  <\/span><\/span><\/h1>\n

                  \n
                  \n
                  \n
                  \n
                  \n

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

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

                  \u591a\u5c3a\u5ea6\u7f51\u7edc\u7684\u91cd\u6574\u5316<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

                  \n

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

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


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

                  \u591a\u5c3a\u5ea6\u7f51\u7edc\u91cd\u6574\u5316\u65b9\u6cd5[137\u2013139] \u65e8\u5728\u5f15\u5165\u5728\u4efb\u610f\u8282\u70b9\u805a\u5408\u4e0b\u4fdd\u6301\u4e00\u81f4\u7684\u968f\u673a\u56fe\u6a21\u578b\u3002\u5176\u52a8\u673a\u6e90\u4e8e\u4e24\u4e2a\u76f8\u5173\u7684\u8003\u8651\u3002\u4e00\u65b9\u9762\uff0c\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u7f51\u7edc\uff0c\u4e0d\u540c\u7684\u8282\u70b9\u5212\u5206\u53ef\u80fd\u56e0\u4e0d\u540c\u539f\u56e0\u800c\u5177\u6709\u76f8\u5173\u6027\uff0c\u4f8b\u5982\uff0c\u672c\u6587\u4e2d\u8ba8\u8bba\u7684\u591a\u79cd\u65b9\u6cd5\u53ef\u80fd\u4f1a\u4ea7\u751f\u4e0d\u540c\u7684\u8282\u70b9\u7c97\u7c92\u5316\u65b9\u5f0f\uff0c\u56e0\u6b64\uff0c\u9700\u8981\u5728\u591a\u79cd\u53ef\u80fd\u7684\u8282\u70b9\u805a\u5408\u65b9\u5f0f\u4e0b\u5bf9\u540c\u4e00\u7cfb\u7edf\u8fdb\u884c\u4e00\u81f4\u5efa\u6a21\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5728\u771f\u5b9e\u4e16\u754c\u7684\u7f51\u7edc\u6570\u636e\u4e2d\uff0c\u201c\u8282\u70b9\u201d\u7684\u542b\u4e49\u5e76\u975e\u603b\u662f\u540c\u8d28\u7684\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u6709\u65f6\u5c3d\u7ba1\u5927\u591a\u6570\u8282\u70b9\u4ee3\u8868\u67d0\u4e2a\u5c42\u7ea7\u4e0a\u89c2\u5bdf\u5230\u7684\u7cfb\u7edf\u5355\u5143\uff08\u4f8b\u5982\u5236\u9020\u751f\u4ea7\u7f51\u7edc\u4e2d\u7684\u5355\u4e2a\u516c\u53f8\uff09\uff0c\u4f46\u5176\u4ed6\u8282\u70b9\u5374\u53ef\u80fd\u4ee3\u8868\u66f4\u7c97\u5c42\u7ea7\u7684\u805a\u5408\uff08\u4f8b\u5982\u6574\u4e2a\u884c\u4e1a\u6216\u56fd\u5bb6\uff0c\u6bcf\u4e2a\u90fd\u805a\u5408\u4f53\u4e86\u591a\u5bb6\u516c\u53f8\uff09\u3002\u8fd9\u4e24\u79cd\u573a\u666f\u63d0\u793a\uff0c\u6240\u7814\u7a76\u7684\u7cfb\u7edf\u5e94\u62e5\u6709\u4e00\u4e2a\u552f\u4e00\u7684\u968f\u673a\u56fe\u6a21\u578b\uff0c\u8be5\u6a21\u578b\u5728\u4efb\u610f\u8282\u70b9\u805a\u5408\uff08\u6216\u8282\u70b9\u62c6\u89e3\uff09\u540e\u4ecd\u80fd\u591f\u5177\u5907\u4e00\u81f4\u6027\uff08\u5373\u751f\u6210\u4e00\u81f4\u7684\u56fe\u6982\u7387\u5206\u5e03\uff09\u3002<\/span><\/p>\n

                  \u8fd9\u4e00\u8981\u6c42\u610f\u5473\u7740\uff0c\u591a\u5c3a\u5ea6\u91cd\u6574\u5316\u65b9\u6cd5\u5e94\u5f53\u5bf9\u7c97\u7c92\u5316\u53d8\u91cf\u7684\u5b9a\u4e49\u4fdd\u6301\u5b8c\u5168\u4e0d\u53ef\u77e5\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u4eba\u4eec\u53ef\u4ee5\u4efb\u610f\u201c\u5e73\u94fa\u201d\u8282\u70b9\u96c6\uff0c\u5f15\u5165\u4efb\u4f55\u6240\u9700\u7684\u5212\u5206 <\/span><\/span><\/span> \uff0c\u800c\u4e0d\u4f9d\u8d56\u4e8e\u5ea6\u91cf\u6216\u6269\u6563\u90bb\u8fd1\u6027\u7684\u6982\u5ff5\u3002\u5bf9\u4e8e\u5e73\u5747\u6389\u7ec6\u5fae\u7ec6\u8282\u7684\u8fc7\u7a0b\uff0c\u539f\u5219\u4e0a\u8be5\u65b9\u6cd5\u5e94\u5141\u8bb8\u4e0d\u540c\u7684\u9009\u62e9\uff0c\u4f46\u5177\u4f53\u800c\u8a00\uff0c\u8003\u8651\u5230\u67d0\u4e9b\u5e94\u7528\u4e2d\u6784\u6210\u8282\u70b9\uff08\u5982\u5355\u4e2a\u516c\u53f8\uff09\u4e4b\u95f4\u7684\u4efb\u4f55\u8fde\u63a5\u5bf9\u5b9a\u4e49\u8d85\u8282\u70b9\uff08\u5982\u56fd\u5bb6\u6216\u7ecf\u6d4e\u90e8\u95e8\uff09\u4e4b\u95f4\u7684\u8054\u7cfb\u5177\u6709\u91cd\u8981\u6027\uff0c\u56e0\u6b64\u9009\u62e9\u4e86\u65b9\u7a0b (2) \u4e2d\u7684\u65b9\u6848[137]\u3002\u65e0\u8bba\u5982\u4f55\uff0c\u591a\u5c3a\u5ea6\u65b9\u6cd5\u7684\u72ec\u7279\u4e4b\u5904\u5728\u4e8e\u8bc6\u522b\u51fa\u91cd\u6574\u5316\u7fa4\u6d41\u7684\u4e0d\u52a8\u70b9\uff0c\u5728\u8be5\u4e0d\u52a8\u70b9\u4e0a\u53ef\u4ee5\u5bf9\u4efb\u610f\u8282\u70b9\u805a\u5408\u65b9\u5f0f\u8fdb\u884c\u8026\u5408\u7cfb\u6570\u548c\u53c2\u6570\u503c\u7684\u7cbe\u786e\u91cd\u6574\u5316\uff0c\u672c\u8282\u5c06\u5bf9\u6b64\u8fdb\u884c\u9610\u91ca\u3002<\/span><\/p>\n

                  <\/span>\u8282\u70b9\u805a\u5408\u4e0b\u7684\u4e0d\u53d8\u6027<\/span><\/span><\/span><\/h2>\n

                  \u6240\u6c42\u7684\u805a\u5408\u4e0d\u53d8\u968f\u673a\u56fe\u6982\u5ff5\u5728\u601d\u60f3\u4e0a\u7c7b\u4f3c\u4e8e\u7a33\u5b9a\u968f\u673a\u53d8\u91cf[140-142]\uff0c\u5373\u7ec4\u5408\u540e\u4ecd\u670d\u4ece\u76f8\u540c\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\uff08\u4f8b\u5982\u6c42\u548c[141,142]\u6216\u53d6\u6781\u5927\u503c\u540e[143,144]\uff09\u3002\u6b64\u5904\u4f7f\u7528\u5728\u7c97\u7c92\u5316\u65b9\u6cd5\u5c0f\u8282\u672b\u5c3e\u6240\u5f15\u5165\u7684\u7b26\u53f7\uff1a\u8003\u8651\u4ee5\u6982\u7387 <\/span><\/span><\/span> \u751f\u6210\u5177\u4f53\u5b9e\u73b0 <\/span><\/span><\/span> \u7684\u968f\u673a\u56fe\u7cfb\u7efc\uff0c\u5176\u4e2d <\/span><\/span><\/span> \u662f\u6a21\u578b\u6240\u6709\u53c2\u6570\u7684\u96c6\u5408\u3002\u7ed9\u5b9a\u6982\u7387\u5206\u5e03 <\/span><\/span><\/span> \u548c\u4efb\u610f\u5212\u5206 <\/span><\/span><\/span> \uff0c\u53ef\u5728\u9ad8\u4e00\u5c42\u7ea7 <\/span><\/span><\/span> \u5bfc\u51fa\u7ed3\u679c\u4e00\u4e2a\u56fe\u7cfb\u7efc\u7531\u7279\u5b9a\u6982\u7387\u5206\u5e03 <\/span><\/span><\/span> \u63cf\u8ff0\uff08\u56fe3a\uff09\u3002\u591a\u5c3a\u5ea6\u91cd\u6574\u5316\u65b9\u6cd5[147]\u7684\u6838\u5fc3\u601d\u60f3\u662f\uff1a\u8bc6\u522b\u5728\u6240\u6709\u5c42\u6b21\u548c\u6240\u6709\u53ef\u80fd\u7684\u5212\u5206\u4e0b\u4fdd\u6301\u4e0d\u53d8\u7684\u56fe\u6982\u7387\u5206\u5e03\u51fd\u6570\u7684\u5f62\u5f0f\uff08\u56e0\u6b64\u53ef\u4ece <\/span><\/span><\/span> \u4e2d\u7701\u7565\u4e0b\u6807 <\/span><\/span><\/span> \uff09\u3002\u53ea\u6709\uff08\u91cd\u6574\u5316\uff09\u53c2\u6570 <\/span><\/span><\/span> \u5141\u8bb8\u4f9d\u8d56\u5c42\u7ea7 <\/span><\/span><\/span> \uff0c\u4e14\u901a\u5e38\u662f\u901a\u8fc7 <\/span><\/span><\/span> \u4e0e <\/span><\/span><\/span> \u5173\u8054\u3002\u8be5\u6761\u4ef6\u5bf9\u5e94\u4e8e\u901a\u8fc7\u5728\u56fe\u6982\u7387\u7a7a\u95f4\u4e2d\u8bc6\u522b\u91cd\u6574\u5316\u7fa4\u6d41\u4e0d\u52a8\u70b9\u6765\u5b9e\u73b0\u53c2\u6570\u7684\u7cbe\u786e\u91cd\u6574\u5316\u3002<\/span><\/p>\n


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

                  <\/section>\n

                  \u56fe3  \u591a\u5c3a\u5ea6\u7f51\u7edc\u91cd\u6574\u5316\u65b9\u6cd5\u3002 a. \u7ed9\u5b9a\u90bb\u63a5\u77e9\u9635\u4e3a <\/span><\/span><\/span> \u3001\u53c2\u6570\u96c6\u4e3a <\/span><\/span><\/span> \u7684\u56fe\u6982\u7387\u5206\u5e03 <\/span><\/span><\/span> \uff0c\u8282\u70b9\u5212\u5206 <\/span><\/span><\/span> \u5c06\u8282\u70b9\u96c6\u6620\u5c04\u5230\u7c97\u7c92\u5316\u90bb\u63a5\u77e9\u9635 <\/span><\/span><\/span> \u7684\u201c\u5757\u8282\u70b9\u201d\u4e0a\u3002\u82e5\u5b58\u5728\u4ece <\/span><\/span><\/span> \u5230 <\/span><\/span><\/span> \u7684\u8fde\u63a5\uff08\u5176\u4e2d <\/span><\/span><\/span> \uff09\uff0c\u5219\u7ed8\u5236\u8be5\u8fde\u63a5\u3002\u9700\u6ce8\u610f\uff0c\u5c42\u7ea7 <\/span><\/span><\/span> \u7684\u591a\u4e2a\u56fe\u53ef\u80fd\u5728\u5c42\u7ea7 <\/span><\/span><\/span> \u5408\u5e76\u4e3a\u540c\u4e00\u56fe\uff0c\u56e0\u6b64\u7c97\u7c92\u5316\u5c06\u8bf1\u5bfc\u4e0b\u4e00\u5c42\u7ea7\u56fe\u7684\u65b0\u6982\u7387\u5206\u5e03 <\/span><\/span><\/span> \u3002\u591a\u5c3a\u5ea6\u65b9\u6cd5\u65e8\u5728\u5bfb\u627e\u8be5\u6982\u7387\u7684\u5c3a\u5ea6\u4e0d\u53d8\u5f62\u5f0f\u3002 b. \u57fa\u4e8e\u591a\u5c3a\u5ea6\u6a21\u578b\u9884\u6d4b\u91cd\u6574\u5316\u56fd\u9645\u8d38\u6613\u7f51\u7edc\u5728\u4e0d\u540c\u5730\u7406\u805a\u5408\u5c42\u7ea7\u7684\u5c40\u57df\u62d3\u6251\u6027\u8d28\u3002\u9996\u884c\u5c55\u793a\u4e09\u4e2a\u4ee3\u8868\u6027\u5c42\u7ea7\uff08 <\/span><\/span><\/span> \uff0c\u5bf9\u5e94 <\/span><\/span><\/span> \uff08\u5de6\uff09\u3001 <\/span><\/span><\/span> \uff08\u4e2d\uff09\u3001 <\/span><\/span><\/span> \uff08\u53f3\uff09\uff09\u4e2d\u6240\u6709 <\/span><\/span><\/span> \u4e2a\u8282\u70b9\u7684\u89c2\u6d4b\u4e0e\u9884\u6d4b\u5ea6\u503c <\/span><\/span><\/span> \u968f <\/span><\/span><\/span> \u7684\u53d8\u5316\u3002\u4e2d\u95f4\u884c\u5bf9\u5e94\u76f8\u540c\u5c42\u7ea7\u4e0b\u6240\u6709\u8282\u70b9\u7684\u89c2\u6d4b\u4e0e\u9884\u6d4b\u6700\u8fd1\u90bb\u5e73\u5747\u5ea6 <\/span><\/span><\/span> \u3002\u672b\u884c\u5c55\u793a\u76f8\u540c\u6761\u4ef6\u4e0b\u5c40\u57df\u805a\u7c7b\u7cfb\u6570 <\/span><\/span><\/span> \u7684\u89c2\u6d4b\u4e0e\u9884\u6d4b\u503c\u3002GDP \u8868\u793a\u56fd\u5185\u751f\u4ea7\u603b\u503c\u3002\u56fe\u8f6c\u8f7d\u81ea\u6587\u732e[137]\uff0c\u9075\u5faa CC BY 4.0 \u534f\u8bae\u3002<\/span><\/p>\n

                  <\/span>\u5e26\u72ec\u7acb\u8fb9\u7684\u591a\u5c3a\u5ea6\u6a21\u578b<\/span><\/span><\/span><\/h2>\n

                  \u5bf9\u4e8e\u5e26\u72ec\u7acb\u8fb9\u7684\u56fe\u6a21\u578b\uff0c\u53ef\u4ee5\u627e\u5230\u663e\u5f0f\u4e0d\u52a8\u70b9 <\/span><\/span><\/span> \u3002\u8fd9\u7c7b\u6a21\u578b\u7684\u6982\u7387\u5206\u5e03\u53ef\u5206\u89e3\u4e3a\u8282\u70b9\u5bf9 <\/span><\/span><\/span> \u7684\u8fde\u63a5\u6982\u7387 <\/span><\/span><\/span> \uff1a<\/span><\/p>\n

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

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

                  \u591a\u5c3a\u5ea6\u6a21\u578b\uff08multiscale model\uff0cMSM\uff09[137]\u53ef\u5b9a\u4e49\u4e3a\u8fde\u63a5\u6982\u7387\u7a7a\u95f4\u4e2d\u91cd\u6574\u5316\u7fa4\u6d41\u7684\u552f\u4e00\u975e\u5e73\u51e1\u4e0d\u52a8\u70b9\uff0c\u5373\u5728\u65b9\u7a0b(2)\u4e0b\u6ee1\u8db3\u5c3a\u5ea6\u4e0d\u53d8\u6027\u8981\u6c42\u7684\u89e3\uff1a<\/span><\/p>\n

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

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

                  \u5176\u4e2d\u53c2\u6570 <\/span><\/span><\/span> \u88ab\u5206\u89e3\u4e3a\u5982\u4e0b\u53c2\u6570\uff1a\u5168\u5c40\u53c2\u6570 <\/span><\/span><\/span> \u8c03\u8282\u7f51\u7edc\u6574\u4f53\u8fde\u63a5\u5bc6\u5ea6\uff0c <\/span><\/span><\/span> \u4e2a\u6b63\u5b9a\u8282\u70b9\u7279\u5f02\u6027\u52a0\u6027\u53c2\u6570 <\/span><\/span><\/span> \uff08\u79f0\u4e3a\u201c\u9002\u5e94\u5ea6\u201d\u503c\uff09\u51b3\u5b9a\u8282\u70b9\u5efa\u7acb\u8fde\u63a5\u7684\u4e2a\u4f53\u503e\u5411\uff0c\u4ee5\u53ca\uff08\u53ef\u9009\uff09 <\/span><\/span><\/span> \u4e2a\u4e8c\u5143\u53c2\u6570 <\/span><\/span><\/span> \u8868\u793a\u8282\u70b9\u5bf9\u6548\u5e94\uff08\u5982\u8282\u70b9\u76f8\u4f3c\u6027\u3001\u8ddd\u79bb\u6216\u5171\u540c\u793e\u533a\u6210\u5458\u8d44\u683c\uff09\u3002\u51fd\u6570 <\/span><\/span><\/span> \u662f\u4efb\u610f\u5355\u8c03\u6b63\u503c\u51fd\u6570\u3002<\/span><\/p>\n

                  <\/span>\u53c2\u6570\u91cd\u6574\u5316\u4e0e\u805a\u5408\u4e0d\u53d8\u6027<\/span><\/span><\/span><\/h2>\n

                  \u5f53\u4f7f\u7528\u5212\u5206 <\/span><\/span><\/span> \u5c06\u7f51\u7edc\u7c97\u7c92\u5316\u81f3 <\/span><\/span><\/span> \u5c42\u7ea7\u65f6\uff0c\u6784\u578b <\/span><\/span><\/span> \u7684\u6982\u7387\u4ecd\u7cbe\u786e\u7531\u65b9\u7a0b(10)\u548c(11)\u63cf\u8ff0\uff0c\u5176\u4e2d <\/span><\/span><\/span> \u66ff\u6362\u4e3a <\/span><\/span><\/span> \u4e14\u53c2\u6570\u91cd\u6574\u5316\u4e3a\uff1a<\/span><\/p>\n

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

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

                  \u5176\u4e2d <\/span><\/span><\/span> \u5177\u6709\u5c3a\u5ea6\u4e0d\u53d8\u6027\uff0c\u5373\u91cd\u6574\u5316\u8fc7\u7a0b\u4e2d\u4fdd\u6301\u4e0d\u53d8\u3002\uff08\u6ce8\uff1a\u6b64\u5904\u539f\u6587\u53ef\u80fd\u6709\u7b14\u8bef\uff0c\u8fd9\u91cc\u6dfb\u52a0\u4e86\u4e00\u4e2a <\/span><\/span><\/span> \u3002\uff09<\/span><\/p>\n

                  \u5f53 <\/span><\/span><\/span> \u4e3a\u8d85\u5ea6\u91cf\u65f6\uff08\u5373 <\/span><\/span><\/span> \u53ef\u8868\u793a\u4e3a\u6811\u56fe\u4e2d\u8282\u70b9 <\/span><\/span><\/span> \u548c <\/span><\/span><\/span> \u5230\u5176\u5171\u540c\u5206\u652f\u70b9\u7684\u8ddd\u79bb\uff0c\u5176\u4e2d\u8282\u70b9\u4e3a\u53f6\u8282\u70b9\uff09\uff0c\u91cd\u6574\u5316\u540e\u4ecd\u4fdd\u6301\u8d85\u5ea6\u91cf\u6027\uff1a\u5bf9\u4efb\u610f <\/span><\/span><\/span> \u548c <\/span><\/span><\/span> \uff0c\u6709 <\/span><\/span><\/span> \uff08\u53c2\u8003\u6587\u732e137\uff09\u3002\u53e6\u4e00\u7279\u4f8b\u662f\uff0c\u4ee4 <\/span><\/span><\/span> \u53ef\u6d88\u53bb\u6240\u6709\u4e8c\u5143\u6548\u5e94\uff08dyadic effects\uff09\uff0c\u4f7f\u6a21\u578b\u5b8c\u5168\u7531\u9002\u5e94\u5ea6\u9a71\u52a8\u3002\u5173\u952e\u7684\u662f\uff0c\u9002\u5e94\u5ea6\u53c2\u6570\u672c\u8eab\u4e0d\u53ef\u6d88\u53bb\uff0c\u4ee3\u8868\u6a21\u578b\u4e2d\u4e0d\u53ef\u7ea6\u7b80\u7684\u7279\u5f81\u3002<\/span><\/p>\n

                  \u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u65b9\u7a0b(11)\u5bf9\u5e94\u7684\u914d\u5206\u51fd\u6570 <\/span><\/span><\/span> \u662f\u53ef\u4ee5\u7cbe\u786e\u8ba1\u7b97\u7684\uff0c\u5e76\u53ef\u4ee5\u8bc1\u660e\u5176\u5728\u4efb\u610f\u8ba1\u7b97\u5c42\u7ea7\u53d6\u503c\u76f8\u540c[137]\uff0c\u8fd9\u8bc1\u5b9e\u4e86\u591a\u5c3a\u5ea6\u6a21\u578b\u4f4d\u4e8e\u91cd\u6574\u5316\u6d41\u7684\u4e0d\u52a8\u70b9\u4e0a\uff08\u89c1\u9644\u5f55\uff09\u3002\u4e0e\u4e4b\u524d\u8ba8\u8bba\u7684\u51e0\u4f55\u6216\u62c9\u666e\u62c9\u65af\u65b9\u6cd5\u4e0d\u540c\uff0c\u591a\u5c3a\u5ea6\u6a21\u578b\u65e2\u4e0d\u9700\u8981\u5e26\u8282\u70b9\u5750\u6807\u7684\u5ea6\u91cf\u7a7a\u95f4\u5d4c\u5165\uff0c\u4e5f\u4e0d\u9700\u8981\u6269\u6563\u90bb\u8fd1\u6027\u6982\u5ff5\u6765\u8fdb\u884c\u91cd\u6574\u5316\u3002\u5b9e\u9645\u4e0a\uff0c\u8be5\u6a21\u578b\u5141\u8bb8\u4efb\u610f\u5212\u5206\uff0c\u5176\u805a\u5408\u4e0d\u53d8\u6027\u76f8\u5bf9\u4e8e\u90bb\u8fd1\u9a71\u52a8\u7684\u5c3a\u5ea6\u4e0d\u53d8\u6027\u4e5f\u66f4\u52a0\u663e\u8457\u3002<\/span><\/p>\n

                  \u591a\u5c3a\u5ea6\u6a21\u578b\u53ef\u4ee5\u63a8\u5e7f\u81f3\u52a0\u6743[145]\u548c\u5b9a\u5411[139]\u7f51\u7edc\u3002\u5b9a\u5411\u7f51\u7edc\u7684\u63a8\u5e7f\u662f\u76f4\u63a5\u7684\uff1a\u7531\u4e8e\u6a21\u578b\u4e0d\u4f9d\u8d56\u51e0\u4f55\u8ddd\u79bb\uff08\u4f46\u662f\u5fc5\u987b\u8981\u6c42\u5bf9\u79f0\uff0c\u5c3d\u7ba1\u5b9a\u5411\u7f51\u7edc\u5177\u6709\u901a\u5e38\u4e0d\u5bf9\u79f0\u6027\uff09\uff0c\u53ef\u901a\u8fc7\u4e3a\u6bcf\u4e2a\u8282\u70b9\u6dfb\u52a0\u53e6\u4e00\u4e2a\u9002\u5e94\u5ea6\u53d8\u91cf\u5904\u7406\u5b9a\u5411\u7f51\u7edc\u3002\u4e3a\u6bcf\u4e2a\u8282\u70b9\u589e\u52a0\u7b2c\u4e09\u4e2a\u9002\u5e94\u5ea6\u53c2\u6570\u540e\uff0c\u6a21\u578b\u8fd8\u80fd\u63cf\u8ff0\u975e\u5e73\u51e1\u7684\u4e92\u5229\u5ea6\uff08reciprocity\uff09[109]\uff0c\u4ece\u800c\u80fd\u5efa\u6a21\u771f\u5b9e\u4e16\u754c\u7684\u6709\u5411\u7f51\u7edc[100-109]\u3002\u66f4\u4e00\u822c\u5730\uff0c\u9002\u5e94\u5ea6\u53d8\u91cf <\/span><\/span><\/span> \u53ef\u4ee5\u662f\u4efb\u610f\u7ef4\u5411\u91cf\uff0c\u4e0a\u8ff0\u8868\u8fbe\u5f0f\u4e2d\u7684\u4e58\u79ef <\/span><\/span><\/span> \u53ef\u89e3\u91ca\u4e3a\u5185\u79ef[100,101]\u3002<\/span><\/p>\n

                  \u771f\u5b9e\u4e16\u754c\u7f51\u7edc\u91cd\u6574\u5316\u7684\u6dec\u706b\u53d8\u4f53<\/span><\/span><\/p>\n

                  \u5728\u591a\u5c3a\u5ea6\u6a21\u578b\u7684\u201c\u6dec\u706b\u201d\u53d8\u4f53\u4e2d\uff0c\u53ef\u4ee5\u5c06\u8282\u70b9\u9002\u5e94\u5ea6\u89e3\u91ca\u4e3a\u67d0\u79cd\u786e\u5b9a\u6027\u7684\u5c5e\u6027\uff0c\u4f8b\u5982\u89c2\u6d4b\u91cf\u6216\u6f5c\u5728\u7684\u8282\u70b9\u7279\u5f81\u7b49[137,139,150,151]\u3002\u56e0\u6b64\u8be5\u53d8\u4f53\u53ef\u7528\u4e8e\u5bf9\u771f\u5b9e\u4e16\u754c\u7684\u7f51\u7edc\u8fdb\u884c\u57fa\u4e8e\u7ecf\u9a8c\u91cf\u7684\u663e\u5f0f\u5efa\u6a21\uff08\u5982\u9002\u5e94\u5ea6\u6a21\u578b\u65cf[152]\uff09\uff0c\u6216\u57fa\u4e8e\u6f5c\u5728\u53d8\u91cf\u7684\u5efa\u6a21\uff08\u5982\u8282\u70b9\u5d4c\u5165\u7b97\u6cd5\u65cf[153]\uff09\u3002\u7136\u800c\uff0c\u8fd9\u4e9b\u7b97\u6cd5\u65cf\u7684\u901a\u7528\u6a21\u578b\u662f\u5728\u56fa\u5b9a\u5206\u8fa8\u7387\u5c42\u7ea7\u6784\u5efa\u7684\uff0c\u800c\u591a\u5c3a\u5ea6\u6a21\u578b\u8981\u6c42\u901a\u8fc7\u91cd\u6574\u5316\u53c2\u6570\u5728\u6240\u6709\u805a\u5408\u5c42\u7ea7\u4e00\u81f4\u63cf\u8ff0\u540c\u4e00\u7cfb\u7edf\uff0c\u5373\u4fdd\u6301\u76f8\u540c\u8fde\u63a5\u6982\u7387\u3002\u56e0\u6b64\uff0c\u8fd9\u662f\u552f\u4e00\u5728\u805a\u5408\u540e\u4ecd\u4fdd\u6301\u9002\u5e94\u5ea6\u6a21\u578b\u7279\u5f81\u7684\u9002\u5e94\u5ea6\u53ef\u52a0\u6027\u6a21\u578b[137,150]\uff0c\u540c\u65f6\u4e5f\u662f\u5728\u4efb\u610f\u7c97\u7c92\u5316\u4e0b\u751f\u6210\u4e00\u81f4\u8282\u70b9\u5d4c\u5165\u7684\u65b9\u6cd5[151]\u3002<\/span><\/p>\n

                  \u8be5\u6a21\u578b\u5728\u591a\u4e2a\u5c42\u7ea7\u6210\u529f\u590d\u73b0\u4e86\u56fd\u9645\u8d38\u6613\u7f51\u7edc[137,139]\uff08\u9002\u5e94\u5ea6\u5bf9\u5e94\u4e8e\u5404\u56fd\u7ecf\u9a8cGDP\uff0c\u4e8c\u5143\u56e0\u5b50\u5bf9\u5e94\u4e8e <\/span><\/span><\/span> \u63cf\u8ff0\u7684\u5730\u7406\u8ddd\u79bb\uff09\u3001\u4f01\u4e1a\u95f4\u7f51\u7edc[150]\u548c\u6295\u5165\u4ea7\u51fa\u7f51\u7edc[151]\uff08\u5916\u5411\/\u5185\u5411\u9002\u5e94\u5ea6\u5206\u522b\u5b9a\u4e49\u4e3a\u516c\u53f8\/\u884c\u4e1a\u603b\u4ea7\u51fa\/\u603b\u6295\u5165\uff0c <\/span><\/span><\/span> \uff09\u7684\u7279\u6027\u3002\u5f53\u4e8c\u5143\u548c\/\u6216\u9002\u5e94\u5ea6\u91cf\u4ece\u6570\u636e\u8f93\u5165\u65f6\uff0c\u4ec5\u5269\u5168\u5c40\u53c2\u6570\u4f5c\u4e3a\u81ea\u7531\u53c2\u6570\u3002\u8be5\u53c2\u6570\u53ef\u5728\u7279\u5b9a\u5206\u8fa8\u7387\u5c42\u7ea7\u62df\u5408\uff0c\u540c\u65f6\u63d0\u4f9b\u6240\u6709\u5176\u4ed6\u5c42\u7ea7\u7684\u9884\u6d4b\u3002\u8fd9\u4e9b\u591a\u5c3a\u5ea6\u9884\u6d4b\u4e0e\u591a\u5c42\u7ea7\u7ecf\u9a8c\u7f51\u7edc\u7279\u6027\u9ad8\u5ea6\u543b\u5408[137,139,150]\uff08\u56fe3b\uff09\u3002<\/span><\/p>\n

                  \u9700\u6ce8\u610f\u8be5\u6a21\u578b\u80fd\u5728\u6781\u7aef\u975e\u5747\u5300\u7684\u60c5\u51b5\u4e0b\u89e3\u51b3\u805a\u5408\u65b9\u6848\uff08\u5176\u4ed6\u65b9\u6cd5\u5728\u6b64\u7c7b\u60c5\u5f62\u4e0b\u5931\u6548\uff09\uff1a\u4f8b\u5982\u5728\u751f\u4ea7\u7f51\u7edc\u4e2d\uff0c\u90e8\u5206\u8282\u70b9\u53ef\u4ee3\u8868\u67d0\u4e00\u6b27\u76df\u56fd\u5bb6\u7684\u72ec\u7acb\u4f01\u4e1a\uff0c\u5176\u4ed6\u8282\u70b9\u53ef\u4ee3\u8868\u5269\u4f59\u6b27\u76df\u56fd\u5bb6\u6574\u4f53\uff08\u5404\u56fd\u4f01\u4e1a\u88ab\u805a\u5408\u4e3a\u5355\u4e00\u8282\u70b9\uff09\uff0c\u800c\u201c\u4e16\u754c\u5176\u4ed6\u5730\u533a\u201d\u8282\u70b9\u5219\u53ef\u4ee3\u8868\u6240\u6709\u975e\u6b27\u76df\u56fd\u5bb6\u7684\u805a\u5408\u4f53[150]\u3002<\/span><\/p>\n

                  \u5f53\u7136\uff0c\u5bf9\u4e8e\u4e00\u822c\u771f\u5b9e\u7f51\u7edc\uff0c\u5e76\u4e0d\u80fd\u4fdd\u8bc1\u5b58\u5728\u53ef\u4e0e\u591a\u5c3a\u5ea6\u6a21\u578b\u4e2d\u52a0\u6027\u9002\u5e94\u5ea6\u53d8\u91cf\u5bf9\u5e94\u7684\u7ecf\u9a8c\u8282\u70b9\u7279\u5f81\u3002\u5728\u6b64\u60c5\u5f62\u4e0b\uff0c\u9002\u5e94\u5ea6\u53d8\u91cf\u53ef\u89c6\u4e3a\u9700\u4f18\u5316\u62df\u5408\u7684\u81ea\u7531\u53c2\u6570\uff08\u901a\u5e38\u4e3a\u7ed9\u5b9a\u7ef4\u5ea6\u7684\u5411\u91cf\uff09\uff0c\u5176\u62df\u5408\u4ec5\u4f9d\u8d56\u4e8e\u7ecf\u9a8c\u7f51\u7edc\u7684\u7ed3\u6784\u4fe1\u606f[151]\u3002\u6b64\u8fc7\u7a0b\u751f\u6210\u62bd\u8c61\u5411\u91cf\u7a7a\u95f4\u4e2d\u7684\u8282\u70b9\u5d4c\u5165\u8868\u793a\uff0c\u5176\u5411\u91cf\u548c\u5bf9\u5e94\u8282\u70b9\u7684\u5408\u5e76\u64cd\u4f5c[151]\u3002\u8be5\u65b9\u5411\u7684\u5f00\u653e\u6027\u6311\u6218\u4ecd\u5728\u4e8e\u786e\u5b9a\u5d4c\u5165\u5411\u91cf\u7684\u6700\u4f18\u7ef4\u5ea6\u53ca\u5176\u552f\u4e00\u6027\u95ee\u9898\u3002<\/span><\/p>\n

                  \u96c6\u7fa4\u65e0\u6807\u5ea6\u7f51\u7edc\u4e0e\u7ec6\u7c92\u5ea6\u5316\u7684\u9000\u706b\u53d8\u4f53<\/span><\/span><\/p>\n

                  \u5728\u9000\u706b\u53d8\u4f53[137,138]\u4e2d\uff0c\u5c06\u8282\u70b9\u9002\u5e94\u5ea6\u89c6\u4e3a\u968f\u673a\u53d8\u91cf\uff0c\u7c7b\u4f3c\u4e8e\u975e\u5747\u5300\u968f\u673a\u56fe\u5bb6\u65cf\u7684\u60c5\u51b5[154]\u3002\u56e0\u6b64\uff0c\u5b83\u4f5c\u4e3a\u4e00\u4e2a\u201c\u9690\u201d\u53d8\u91cf\uff0c\u4e0d\u4e0e\u4efb\u4f55\u7279\u5b9a\u7684\u771f\u5b9e\u4e16\u754c\u7279\u5f81\u76f8\u5173\u8054\u3002\u5728\u8fd9\u79cd\u65b9\u6cd5\u4e2d\uff0c\u805a\u5408\u4e0d\u53d8\u6027\u7684\u8981\u6c42\u4e5f\u9002\u7528\u4e8e\u9002\u5e94\u5ea6\uff1a\u5728\u4efb\u4f55\u5c42\u6b21\u7ea7\u522b <\/span><\/span><\/span> \uff0c\u4eba\u4eec\u5e94\u5f53\u80fd\u4ece\u76f8\u540c\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u4e2d\u62bd\u53d6\u8282\u70b9\u9002\u5e94\u5ea6\uff0c\u800c\u65e0\u9700\u201c\u77e5\u9053\u201d\u5b83\u4eec\u5728\u66f4\u7ec6\u5c42\u6b21\u4e0a\u7684\u503c\uff08\u6216\u5bc6\u5ea6\u51fd\u6570\uff09\u3002\u7531\u4e8e\u9002\u5e94\u5ea6\u5177\u6709\u52a0\u6027\uff0c\u8fd9\u4e00\u8981\u6c42\u7acb\u5373\u8868\u660e\u5b83\u5e94\u4e3a <\/span><\/span><\/span> -\u7a33\u5b9a\u968f\u673a\u53d8\u91cf[141]\uff0c\u610f\u5473\u7740\u5176\u5bc6\u5ea6\u51fd\u6570\u5728\u5927 <\/span><\/span><\/span> \u65f6\u8870\u51cf\u4e3a <\/span><\/span><\/span> \u3002\u4e3a\u786e\u4fdd\u9002\u5e94\u5ea6\u7684\u5fc5\u8981\u6b63\u6027\uff0c\u6307\u6570\u9700\u5728 <\/span><\/span><\/span> \u8303\u56f4\u5185\uff0c\u8fd9\u5bfc\u81f4\u9002\u5e94\u5ea6\u7684\u5747\u503c\uff08\u53ca\u6240\u6709\u66f4\u9ad8\u9636\u77e9\uff09\u53d1\u6563\u3002\u5728\u6b64\u8303\u56f4\u5185\uff0c\u552f\u4e00\u5df2\u77e5\u7684 <\/span><\/span><\/span> -\u7a33\u5b9a\u5206\u5e03\u4e3aL\u00e9vy\u5206\u5e03\uff08 <\/span><\/span><\/span> \uff09\uff0c\u4f46\u5bf9\u4e8e\u4efb\u610f <\/span><\/span><\/span> \u503c\uff0c\u4eba\u4eec\u90fd\u80fd\u63a8\u5bfc\u51fa\u4e25\u683c\u7ed3\u679c\uff0c\u4e14\u8fd9\u4e9b\u7ed3\u679c\u57fa\u672c\u4e0e <\/span><\/span><\/span> \u65e0\u5173[138]\u3002\u82e5\u5c06\u8282\u70b9\u805a\u96c6\u6210\u5927\u5c0f\u76f8\u7b49\u7684\u5757\uff0c\u9002\u5e94\u5ea6\u5c06\u4fdd\u6301\u76f8\u540c\u7684\u5bc6\u5ea6\uff0c\u4ec5\u9700\u5bf9\u5168\u5c40\u53c2\u6570\u8fdb\u884c\u91cd\u65b0\u7f29\u653e\u3002\u5728\u9000\u706b\u53d8\u4f53\u4e2d\uff0c\u591a\u5c3a\u5ea6\u6a21\u578b\u80fd\u751f\u6210\u4efb\u610f\u5927\u7684\u7f51\u7edc\uff0c\u5176\u6027\u8d28\u786e\u5b9e\u53ef\u5728\u8282\u70b9\u6570\u91cf\u53d1\u6563\u7684\u6e10\u8fd1\u6781\u9650\u4e0b\u7814\u7a76[138]\u3002<\/span><\/p>\n

                  \u9002\u5e94\u5ea6\u7684\u65e0\u7a77\u5747\u503c\u7684\u7279\u6027\u4f7f\u5f97\u9000\u706b\u591a\u5c3a\u5ea6\u6a21\u578b\u7684\u671f\u671b\u62d3\u6251\u6027\u8d28\u4e0e\u5177\u6709\u6709\u9650\u5747\u503c\u9002\u5e94\u5ea6\u7684\u7c7b\u4f3c\u6a21\u578b\u4ea7\u751f\u7684\u6027\u8d28\u5927\u4e0d\u76f8\u540c\u3002\u7279\u522b\u5730\uff0c\u4eba\u4eec\u80fd\u4e25\u683c\u8bc1\u660e[137,138]\uff0c\u671f\u671b\u5ea6\u5206\u5e03 <\/span><\/span><\/span> \u5177\u6709\u666e\u9002\u7684\u5e42\u5f8b\u5c3e\u8870\u51cf <\/span><\/span><\/span> \uff0c\u4e0e <\/span><\/span><\/span> \u503c\u65e0\u5173\u3002\u5bf9\u4e8e\u805a\u5408\u5230 <\/span><\/span><\/span> \u4e2a\u8282\u70b9\u7684\u5c42\u6b21 <\/span><\/span><\/span> \uff0c\u82e5 <\/span><\/span><\/span> \uff0c\u8870\u51cf\u8868\u73b0\u4e3a\u7eaf\u5e42\u5f8b[138]\uff1b\u5bf9\u4e8e\u66f4\u7c97\u7c92\u5316\u7684\u805a\u5408\uff0c\u5206\u5e03\u5c3e\u90e8\u4f1a\u51fa\u73b0\u4f9d\u8d56\u5bc6\u5ea6\u7684\u622a\u65ad[137]\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u9000\u706b\u6a21\u578b\u5c55\u793a\u4e86\u8bb8\u591a\u73b0\u5b9e\u7f51\u7edc\u7279\u6027\uff0c\u5305\u62ec\u8870\u51cf\u7684\u540c\u914d\u6027\u8f6e\u5ed3\u3001\u5728\u7a00\u758f\uff08\u5bc6\u5ea6\u6d88\u5931\uff09\u72b6\u6001\u4e0b\u6d88\u5931\u7684\u5168\u5c40\u805a\u7c7b\u7cfb\u6570\uff0c\u4ee5\u53ca\u4e0d\u6d88\u5931\u7684\u5c40\u90e8\u805a\u7c7b\u7cfb\u6570\u3002\u5728\u5176\u4ed6\u7a00\u758f\u8fb9\u72ec\u7acb\u6a21\u578b\u4e2d\uff0c\u9664\u975e\u5047\u8bbe\u5b83\u4eec\u4f9d\u8d56\u5ea6\u91cf\u8ddd\u79bb\uff0c\u5426\u5219\u4e0d\u4f1a\u51fa\u73b0\u4e0d\u6d88\u5931\u7684\u5c40\u90e8\u805a\u7c7b\u7cfb\u6570\u3002\u56e0\u6b64\uff0c\u65e0\u7a77\u5747\u503c\u9002\u5e94\u5ea6\u5373\u4f7f\u65e0\u51e0\u4f55\u7ed3\u6784\u4e5f\u80fd\u751f\u6210\u6b63\u5c40\u90e8\u805a\u7c7b\u7cfb\u6570\u7684\u53d1\u73b0\uff0c\u6210\u4e3a\u9000\u706b\u591a\u5c3a\u5ea6\u6a21\u578b\u7684\u91cd\u8981\u6d1e\u89c1\u3002<\/span><\/p>\n

                  \u6700\u540e\uff0c\u7531\u4e8e <\/span><\/span><\/span> -\u7a33\u5b9a\u968f\u673a\u53d8\u91cf\u5177\u6709\u65e0\u9650\u53ef\u5206\u6027\uff08\u5373\u5b83\u4eec\u53ef\u8868\u793a\u4e3a\u6765\u81ea\u540c\u4e00\u5bb6\u65cf\u7684\u4efb\u610f\u6570\u91cf\u72ec\u7acb\u540c\u5206\u5e03\uff08i.i.d.\uff09\u968f\u673a\u53d8\u91cf\u4e4b\u548c\uff09\uff0c\u5728\u9000\u706b\u65b9\u6cd5\u4e2d\uff0c\u4eba\u4eec\u80fd\u5c06\u8282\u70b9\u65e0\u9650\u7ec6\u5206\u4e3a\u5b50\u8282\u70b9\uff0c\u6bcf\u4e2a\u5b50\u8282\u70b9\u62e5\u6709\u5404\u81ea\u7684i.i.d.\u9002\u5e94\u5ea6\u3002\u8fd9\u610f\u5473\u7740\u5728\u6b64\u60c5\u51b5\u4e0b\uff0c\u91cd\u6574\u5316\u6d41\u4e0d\u4ec5\u5b9a\u4e49\u4e86\u4e00\u4e2a\u81ea\u5e95\u5411\u4e0a\u7684\u534a\u7fa4\uff0c\u8fd8\u5b9a\u4e49\u4e86\u4e00\u4e2a\u53cc\u5411\u8fdb\u884c\u7684\u7fa4[137]\u3002\u4e00\u4e2a\u516c\u5f00\u6311\u6218\u5728\u4e8e\uff0c\u5982\u4f55\u5c06\u6a21\u578b\u8fd9\u4e00\u5f15\u4eba\u6ce8\u76ee\u7684\u7406\u8bba\u7279\u6027\u8f6c\u5316\u4e3a\u5b9e\u7528\u5de5\u5177\uff0c\u4ee5\u7ec6\u5316\u53ea\u80fd\u5728\u7c97\u7c92\u5316\u6c34\u5e73\u89c2\u5bdf\u7684\u73b0\u5b9e\u7f51\u7edc\uff0c\u56e0\u4e3a\u73b0\u5b9e\u7f51\u7edc\u4e2d\u7684\u8282\u70b9\u672a\u5fc5\u5177\u6709 <\/span><\/span><\/span> -\u7a33\u5b9a\u53d8\u91cf\u7684\u7279\u6027\u3002<\/span><\/p>\n

                  <\/span>
                  <\/span><\/span><\/span><\/h1>\n

                  \n
                  \n
                  \n
                  \n
                  \n

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

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

                  \u5c55\u671b<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

                  \n

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

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


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

                  \u5c3d\u7ba1\u76ee\u524d\u7f51\u7edc\u91cd\u6574\u5316\u7684\u67d0\u4e9b\u65b9\u6cd5\u5728\u6784\u5efa\u51e0\u4f55\u4e0e\u7cfb\u7efc\u5f02\u8d28\u6027\u7684\u901a\u7528\u6846\u67b6\u65b9\u9762\u53d6\u5f97\u663e\u8457\u8fdb\u5c55\uff0c\u4f46\u4ecd\u5b58\u5728\u82e5\u5e72\u6311\u6218\u4e0e\u5f00\u653e\u6027\u95ee\u9898\uff0c\u6211\u4eec\u5c06\u5728\u6b64\u8ba8\u8bba\u3002<\/span><\/p>\n

                  <\/span>\u5206\u8fa8\u7387\u6c34\u5e73<\/span><\/span><\/span><\/h2>\n

                  \u771f\u5b9e\u4e16\u754c\u7684\u7f51\u7edc\u5b9e\u73b0\u4e2d\uff0c\u7531\u4e8e\u62d3\u6251\u7ed3\u6784\u7684\u5f02\u8d28\u6027\uff0c\u56e0\u800c\u5c06\u51e0\u4f55\u548c\u62d3\u6251\u7684\u7ec4\u7ec7\u5f52\u4e8e\u201c\u529f\u80fd\u5355\u5143\u201d\u7684\u64cd\u4f5c\u5177\u6709\u76f8\u5f53\u6311\u6218\u6027\u3002\u8fd9\u6bd4\u540c\u8d28\u7684\u683c\u70b9\u6216\u89c4\u5219\u6811\u7684\u60c5\u51b5\u66f4\u4e3a\u590d\u6742\u3002\u6b64\u5916\uff0c\u5728\u771f\u5b9e\u4e16\u754c\u7f51\u7edc\u7f51\u7edc\u7684\u4e0d\u540c\u8868\u793a\u5f62\u5f0f\u4e2d\uff0c\u5b9a\u4e49\u8282\u70b9\u7684\u5408\u7406\u5206\u8fa8\u7387\u5c3a\u5ea6\u901a\u5e38\u5e76\u975e\u662f\u7cfb\u7edf\u5185\u8574\u7684\u56fa\u6709\u6027\u8d28\uff0c\u800c\u662f\u6e90\u4e8e\u89c2\u6d4b\u9650\u5236\u6216\u6570\u636e\u805a\u5408\u7684\u7c97\u7cd9\u7a0b\u5ea6\u3002\u4f8b\u5982\uff0c\u4fdd\u5bc6\u6027\u95ee\u9898\u5bfc\u81f4\u91d1\u878d\u5173\u7cfb\u7f51\u7edc\uff08\u5982\u94f6\u884c\u95f4\u501f\u8d37\u4e0e\u98ce\u9669\u655e\u53e3\uff09\u548c\u7ecf\u6d4e\u5173\u7cfb\u7f51\u7edc\uff08\u5982\u4f9b\u5e94\u94fe\uff09\u4e2d\u7684\u4e2a\u4f53\u8fde\u63a5\u7684\u4fe1\u606f\u65e0\u6cd5\u83b7\u53d6\uff0c\u800c\u4eba\u9645\u63a5\u89e6\u6570\u91cf\u5bf9\u6d41\u884c\u75c5\u7f51\u7edc\u7684\u5f71\u54cd\u4ec5\u80fd\u90e8\u5206\u53ef\u89c1\u3002\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u4eba\u4eec\u5e0c\u671b\u786e\u5b9a\u5e76\u533a\u5206\u7f51\u7edc\u5c5e\u6027\u56fa\u6709\u7684\u7279\u5f81\u5c3a\u5ea6\u4e0e\u6570\u636e\u5206\u8fa8\u7387\u76f8\u5173\u7684\u5c3a\u5ea6\u3002<\/span><\/p>\n

                  \u4e0e\u52a8\u529b\u5b66\u8fc7\u7a0b\u76f8\u5bb9\u7684\u91cd\u6574\u5316<\/span><\/span><\/p>\n

                  \u5bf9\u4efb\u610f\u7f51\u7edc\u4e0a\u7684\u52a8\u529b\u5b66\u7ed3\u6784\u548c\u8fc7\u7a0b\u7684\u91cd\u6574\u5316\u7684\u4e3b\u8981\u6311\u6218\u5728\u4e8e\uff0c\u5982\u4f55\u4f7f\u7528\u4e0e\u5e95\u5c42\u56fe\u7ed3\u6784\u548c\u7cfb\u7efc\u968f\u673a\u6027\u7684\u91cd\u6574\u5316\u76f8\u517c\u5bb9\u7684\u65b9\u5f0f\uff0c\u6765\u8fdb\u884c\u5bf9\u52a8\u529b\u5b66\u7ed3\u6784\u548c\u8fc7\u7a0b\u8fdb\u884c\u91cd\u6574\u5316\u3002\u6b64\u524d\u7814\u7a76\u8fd9\u4e00\u95ee\u9898\u7684\u5b66\u8005\u4eec\u4ec5\u9650\u4e8e\u63a2\u8ba8\u89c4\u5219\u6216\u5206\u5f62\u683c\u70b9\u4e0a\u7684\u52a8\u6001\u8fc7\u7a0b\uff0c\u5728\u8fd9\u4e9b\u89c4\u5219\u683c\u70b9\u4e2d\uff0c\u7c97\u7c92\u5316\u7684\u7ed3\u6784\u90e8\u5206\u80fd\u591f\u76f8\u5f53\u81ea\u7136\u5730\u52a0\u4ee5\u5b9a\u4e49\u3002<\/span><\/p>\n

                  \u5177\u4f53\u800c\u8a00\uff0c\u7cbe\u786e\u7684\u91cd\u6574\u5316\u7fa4\u8ba1\u7b97\u5df2\u5e94\u7528\u4e8e\u5206\u5f62\u7f51\u7edc\u4e0a\u7684\u9ad8\u65af\u573a[155]\u548c\u968f\u673a\u6e38\u8d70[156]\uff0c\u5e76\u6269\u5c55\u81f3\u7814\u7a76Hanoi\u7f51\u7edc\u4e0aIsing\u6a21\u578b\u7684\u4e0d\u52a8\u70b9[157]\uff0c\u63ed\u793a\u51fa\u4e0d\u540c\u533a\u57df\u5185\u72ec\u7279\u7684\u4e34\u754c\u975e\u666e\u9002\u884c\u4e3a\u3002\u7814\u7a76\u8005\u5229\u7528\u88c1\u526a\u6280\u672f\u63a2\u7d22\u4e86\u7f51\u7edc\u589e\u957f\u6a21\u578b\u4e0a\u6e17\u6d41\u4e34\u754c\u884c\u4e3a\uff0c\u53d1\u73b0\u5176\u4e0e\u65e0\u5173\u8054\u7f51\u7edc\u4e2d\u89c2\u5bdf\u5230\u7684\u884c\u4e3a\u5b58\u5728\u504f\u5dee[158]\u3002\u8fd9\u4e9b\u65b9\u6cd5\u4e5f\u7528\u4e8e\u5206\u6790\u771f\u5b9e\u4e16\u754c\u7684\u7cfb\u7edf\u3002\u4f8b\u5982\uff0c\u5b66\u8005\u4eec\u4e3a\u795e\u7ecf\u5143\u7f51\u7edc\u4e2d\u7684\u6d3b\u52a8\u5f00\u53d1\u4e86\u552f\u8c61\u7684\u7c97\u7c92\u5316\u7a0b\u5e8f\uff0c\u5728\u5c06\u5176\u5e94\u7528\u4e8e\u6d77\u9a6c\u4f53\u7ec6\u80de\u65f6\uff0c\u80fd\u591f\u53d1\u73b0\u9759\u6001\u548c\u52a8\u6001\u7684\u53d8\u91cf\u5747\u5448\u73b0\u6807\u5ea6\u7279\u5f81\uff0c\u8868\u660e\u7f51\u7edc\u7fa4\u4f53\u884c\u4e3a\u4e2d\u5b58\u5728\u975e\u5e73\u51e1\u7684\u4e0d\u52a8\u70b9[159]\u3002<\/span><\/p>\n

                  \u4e00\u822c\u800c\u8a00\uff0c\u6211\u4eec\u53ef\u4ee5\u9884\u671f\u771f\u5b9e\u4e16\u754c\u7f51\u7edc\u53ca\u5176\u7c97\u7c92\u5316\u7248\u672c\u4e2d\u7684\u7ed3\u6784\u5f02\u8d28\u6027\u4f1a\u5bfc\u81f4\u52a8\u529b\u5b66\u8fc7\u7a0b\u7684\u91cd\u6574\u5316\u4e0e\u62d3\u6251\u7ed3\u6784\u7684\u91cd\u6574\u5316\u4e4b\u95f4\u5b58\u5728\u8026\u5408\u3002\u7136\u800c\u5f00\u53d1\u72ec\u7acb\u4e8e\u5177\u4f53\u65b9\u6848\u7684\u6846\u67b6\uff0c\u4ee5\u517c\u5bb9\u7684\u65b9\u5f0f\u540c\u65f6\u91cd\u6574\u5316\u7f51\u7edc\u52a8\u6001\u53ca\u5e95\u5c42\u51e0\u4f55\u6216\u7cfb\u7efc\u7ed3\u6784\uff0c\u4ecd\u662f\u4e00\u9879\u6311\u6218\u3002<\/span><\/p>\n

                  <\/span>\u5e7f\u4e49\u4e34\u754c\u6027\uff1f<\/span><\/span><\/span><\/h2>\n

                  \u771f\u5b9e\u4e16\u754c\u7f51\u7edc\u4e2d\u8fde\u63a5\u7684\u5f3a\u5f02\u8d28\u6027\u4e0e\u975e\u5c40\u90e8\u6027\u53ef\u80fd\u5f71\u54cd\u52a8\u529b\u5b66\u6a21\u578b\u5728\u4e34\u754c\u70b9\u9644\u8fd1\u7684\u5c40\u90e8\u6fc0\u53d1\u4e0e\u96c6\u4f53\u6fc0\u53d1\u4e4b\u95f4\u7684\u8f6c\u53d8\u6027\u8d28\u3002\u8fd9\u4e9b\u6027\u8d28\u4e5f\u53ef\u80fd\u5f15\u53d1\u66f4\u590d\u6742\u7684\u884c\u4e3a\uff0c\u4ece\u800c\u9700\u8981\u66f4\u5e7f\u4e49\u7684\u4e34\u754c\u6027\u5b9a\u4e49\u3002\u4f8b\u5982\u5728\u771f\u5b9e\u63a5\u89e6\u7f51\u7edc\u4e0a\u7684\u75ab\u60c5\u4f20\u64ad\u52a8\u529b\u5b66\u4e2d\uff0c\u96c6\u4f53\u5927\u6d41\u884c\u6001\u4e0e\u5c40\u90e8\u5730\u65b9\u75c5\u6d41\u884c\u6001\u95f4\u7684\u8f6c\u53d8\u53ef\u80fd\u6bd4\u8fd1\u4f3c\u683c\u70b9\u7684\u7406\u60f3\u5316\u63a5\u89e6\u7f51\u7edc\u66f4\u4e3a\u590d\u6742\u3002\u76f8\u4e92\u4f5c\u7528\u53c2\u6570\u53ef\u80fd\u5b58\u5728\u5b8c\u6574\u533a\u57df\uff0c\u4f7f\u5f97\u5176\u4e2d\u4e34\u754c\u884c\u4e3a\u5728\u5b8f\u89c2\u4f46\u5c40\u90e8\u7684\u96c6\u4f53\u5b50\u7f51\u7edc\u4e2d\u9010\u6b65\u663e\u73b0\uff0c\u6b64\u7c7b\u53c2\u6570\u533a\u57df\u7684\u5f62\u6210\u7531\u5f3a\u62d3\u6251\u5f02\u8d28\u6027\u53ca\u6f5c\u5728\u5c42\u7ea7\u7ed3\u6784\u51b3\u5b9a\u3002\u8be5\u73b0\u8c61\u8868\u660e\uff0c\u62d3\u6251\u590d\u6742\u6027\u53ef\u80fd\u8981\u6c42\u5c06\u4e34\u754c\u70b9\u6982\u5ff5\u6269\u5c55\u81f3\u7c7b\u4f3c\u4e8eGriffith\u76f8\u7684\u8303\u7574[160,161]<\/span><\/p>\n

                  <\/span>\u4fe1\u606f\u8bba\u89c6\u89d2\u4e0b\u7684\u53c2\u6570\u76f8\u5173\u6027\u4e0e\u65e0\u5173\u6027<\/span><\/span><\/span><\/h2>\n

                  \u7c97\u7c92\u5316\u610f\u5473\u7740\u4fe1\u606f\u4e22\u5931\u3002\u8fd9\u79cd\u4e22\u5931\u975e\u4f46\u4e0d\u662f\u7f3a\u9677\uff0c\u53cd\u800c\u662f\u91cd\u6574\u5316\u7fa4\u6280\u672f\u7684\u6838\u5fc3\u5de5\u5177\uff0c\u56e0\u4e3a\u5b83\u80fd\u8bc6\u522b\u5728\u6700\u6709\u4ef7\u503c\u7684\u65f6\u7a7a\u5c3a\u5ea6\u53c2\u6570\uff0c\u5e76\u5728\u8fd9\u4e2a\u5c3a\u5ea6\u4e0a\u63cf\u8ff0\u7cfb\u7edf\u884c\u4e3a\u3002\u91cd\u6574\u5316\u65b9\u6cd5\u6700\u521d\u7684\u8bbe\u8ba1\u76ee\u6807\u5c31\u662f\u7528\u4e8e\u7814\u7a76\u5177\u6709\u5927\u81ea\u7531\u5ea6\u7684\u7269\u7406\u7cfb\u7edf\uff0c\u5e76\u8bc6\u522b\u7cfb\u7edf\u53c2\u6570\u5982\u4f55\u4ece\u5fae\u89c2\u6d41\u5411\u5b8f\u89c2\u5c3a\u5ea6\u3002\u8be5\u8de8\u5c3a\u5ea6\u4fe1\u606f\u6d41\u7684\u5173\u952e\u5728\u4e8e\uff1a\u968f\u7740\u5c3a\u5ea6\u589e\u5927\uff0c\u67d0\u4e9b\u53c2\u6570\u5bf9\u7cfb\u7edf\u884c\u4e3a\u7684\u76f8\u5173\u6027\u589e\u5f3a\uff0c\u800c\u5176\u4ed6\u53c2\u6570\u9010\u6e10\u65e0\u5173\u3002\u5728\u590d\u6742\u7f51\u7edc\u80cc\u666f\u4e0b\uff0c\u63a2\u7d22\u81ea\u4e0b\u800c\u4e0a\u7814\u7a76\u8fd9\u79cd\u4fe1\u606f\u968f\u53c2\u6570\u7684\u6d41\u52a8\uff0c\u53ef\u4e3a\u57fa\u4e8e\u7b2c\u4e00\u6027\u539f\u7406\u7406\u89e3\u54ea\u4e9b\u91cf\u548c\u63a7\u5236\u53c2\u6570\u5728\u6700\u5927\u65f6\u7a7a\u5c3a\u5ea6\u6700\u91cd\u8981\u63d0\u4f9b\u91cd\u8981\u4ef7\u503c\u3002\u901a\u8fc7\u4fe1\u606f\u8bba\uff08 Fisher \u4fe1\u606f\u4e0e\u5e94\u7528\u4e8e\u590d\u6742\u7cfb\u7edf\u7684\u4fe1\u606f\u51e0\u4f55\u5f62\u5f0f\u4f53\u7cfb\u5728\uff09\uff0c\u4e5f\u53ef\u4ece\u7eaf\u7ecf\u9a8c\u89c6\u89d2\u83b7\u5f97\u4e92\u8865\u7684\u81ea\u4e0a\u800c\u4e0b\u7684\u65b9\u6cd5\u3002<\/span><\/p>\n

                  \u7269\u7406\u7cfb\u7edf\u4e2d\u7684\u53c2\u6570\u76f8\u5173\u6027\u6982\u5ff5\u5728\u573a\u8bba\u53ca\u5176\u6d41\u4f53\u52a8\u529b\u5b66\u6781\u9650\u4e0b\u662f\u901a\u8fc7\u5e42\u6b21\u8ba1\u7b97\u53ef\u91cd\u6574\u5316\u6982\u5ff5\u4f53\u73b0\u7684\uff0c\u8be5\u6982\u5ff5\u5927\u81f4\u8ffd\u8e2a\u4e86\u63cf\u8ff0\u7cfb\u7edf\u52a8\u529b\u5b66\u6240\u6709\u53ef\u80fd\u9879\u7684\u5bfc\u6570\u5c55\u5f00\u3002\u5373\uff0c\u5728\u7406\u8bba\u7a7a\u95f4\u4e2d\u8fdb\u884c\u6709\u6548\u7684\u6cf0\u52d2\u5c55\u5f00\uff0c\u4f7f\u5f97\u5373\u65f6\u7279\u5f81\u663e\u73b0\u3002\u5728\u8db3\u591f\u5927\u5c3a\u5ea6\u4e0b\uff0c\u542b\u9ad8\u9636\u5bfc\u6570\u7684\u9879\u5bf9\u7269\u7406\u89c2\u6d4b\u91cf\u7684\u8d21\u732e\u9012\u51cf\u3002\u4ece\u4fe1\u606f\u8bba\u89c6\u89d2\u770b\uff0c\u8fd9\u610f\u5473\u89c2\u6d4b\u7cfb\u7efc\u7684\u7ed3\u679c\u66f4\u654f\u611f\u5730\u4f9d\u8d56\u4e8e\u5bfc\u6570\u5c55\u5f00\u4e2d\u4e3b\u5bfc\u9636\u9879\u7684\u7cfb\u6570\u3002\u56e0\u6b64\uff0c\u53c2\u6570\u76f8\u5173\u6027\u6982\u5ff5\u53ef\u76f4\u63a5\u8f6c\u8bd1\u4e3a\u4fe1\u606f\u8bba\u91cf\uff0c\u4e14\u80fd\u63a8\u5e7f\u81f3\u7269\u7406\u7cfb\u7edf\u4e4b\u5916\u3002\u8fd9\u79cd\u8f6c\u8bd1\u4e0d\u4ec5\u5177\u6709\u76f4\u63a5\u6982\u5ff5\u7528\u9014\uff0c\u66f4\u4e3a\u8bc6\u522b\u548c\u7406\u89e3\u51b3\u5b9a\u4efb\u610f\u7cfb\u7edf\u5728\u5927\u5c3a\u5ea6\u884c\u4e3a\u7684\u53c2\u6570\u5f00\u8f9f\u901a\u9053\u2014\u2014\u5373\u4f7f\u7f3a\u4e4f\u5fae\u89c2\u6a21\u578b\u63cf\u8ff0\uff0c\u6216\u5904\u7406\u4efb\u610f\u51e0\u4f55\u4e0e\u7cfb\u7efc\u968f\u673a\u6027\u65f6\u4ea6\u7136\u3002<\/span><\/p>\n


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

                  <\/section>\n

                  \u56fe4  \u4fe1\u606f\u8bba\u53c2\u6570\u6d41\u3002 a. MNIST\uff08Modified National Institute of Standards and Technology\uff09\u6570\u636e\u96c6\u4e2d\u7684\u624b\u5199\u6570\u5b57\u201c7\u201d\u5b9e\u4f8b\u3002 b. \u6210\u529f\u5206\u7c7b MNIST \u6570\u636e\u96c6\u4e2d\u5de6\u4fa7\u56fe\u50cf\u768430\u4e2a\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\u7684 Fisher \u4fe1\u606f\u77e9\u9635\u7279\u5f81\u503c\uff08\u5de6\u56fe\uff09\u53ca\u5176\u5206\u7bb1\u5bc6\u5ea6\u76f4\u65b9\u56fe\uff08\u53f3\u56fe\uff09\u3002\u7279\u5f81\u503c\u5448\u73b0\u6307\u6570\u578b\u5c42\u7ea7\u7ed3\u6784\uff0c\u8868\u660e\u4ec5\u5c11\u91cf\u96c6\u4f53\u6743\u91cd\u5bf9\u8bad\u7ec3\u7f51\u7edc\u7cbe\u5ea6\u8d77\u5173\u952e\u4f5c\u7528\u3002\u56fe\u7531 Leone Luzzatto \u63d0\u4f9b\u3002<\/span><\/p>\n

                  <\/span>\u4fe1\u606f\u51e0\u4f55\u4e0e\u53c2\u6570\u6d41<\/span><\/span><\/span><\/h2>\n

                  \u7ed9\u5b9a\u4efb\u610f\u6570\u636e\u96c6\uff0c\u53ef\u6784\u5efa\u7531\u5047\u8bbe\u6a21\u578b\u751f\u6210\u7684\u4f3c\u7136\u51fd\u6570\u6765\u63cf\u8ff0\u8be5\u6570\u636e\u96c6\u3002\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\u5373\u4e3a\u8bc6\u522b\u4f7f\u8be5\u4f3c\u7136\u51fd\u6570\u6700\u5927\u5316\u7684\u53c2\u6570\u96c6\uff0c\u5e76\u5c06\u5176\u4f5c\u4e3a\u5bf9\u5e95\u5c42\u6a21\u578b\u7684\u6700\u4f73\u63a8\u65ad\u3002\u5bf9\u6570\u4f3c\u7136\u76f8\u5bf9\u4e8e\u53c2\u6570\u7684\u4e8c\u9636\u5bfc\u6570\u81ea\u7136\u5f62\u6210\u5ea6\u91cf\u53c2\u6570\u7a7a\u95f4\u8ddd\u79bb\u7684\u5ea6\u91cf\u7ed3\u6784\uff0c\u80fd\u591f\u6355\u6349\u4f3c\u7136\u504f\u79bb\u6700\u5927\u503c\u7684\u53d8\u5316\u65b9\u5f0f\u3002\u8fd9\u79cd\u63a8\u65ad\u7684\u51e0\u4f55\u5316\uff08\u79f0\u4e3a\u4fe1\u606f\u51e0\u4f55[162]\uff09\u4f7f\u5f97\u5728\u53c2\u6570\u6d41\u7684\u7edf\u4e00\u6846\u67b6\u4e0b\u91cd\u6784\u7edf\u8ba1\uff08\u8d1d\u53f6\u65af\uff09\u63a8\u65ad\u4e0e\u91cd\u6574\u5316\u6210\u4e3a\u53ef\u80fd[163]\u3002<\/span><\/p>\n

                  \u57fa\u4e8e\u7ed9\u5b9a\u6570\u636e\u96c6\u6784\u5efa\u7684\u4f3c\u7136\u5bf9\u5e94\u7684 Fisher \u4fe1\u606f\u5ea6\u91cf\u5177\u6709\u663e\u8457\u7684\u7279\u5f81\u503c\u5c42\u7ea7\u7ed3\u6784\u3002\u8be5\u5c42\u7ea7\u610f\u5473\u7740\uff1a\u6700\u5927\u7279\u5f81\u503c\u5bf9\u5e94\u53c2\u6570\u7684\u5fae\u5c0f\u53d8\u5316\u5bf9\u89c2\u6d4b\u7ed3\u679c\u5f71\u54cd\u6700\u5927\uff08\u56fe4\uff09\uff0c\u5176\u610f\u4e49\u76f4\u63a5\u6620\u5c04\u81f3\u91cd\u6574\u5316\u7fa4\u610f\u4e49\u4e0a\u7684\u53c2\u6570\u76f8\u5173\u6027\u6982\u5ff5\u2014\u2014\u6700\u76f8\u5173\u53c2\u6570\u5bf9\u5e94\u6700\u5927\u7279\u5f81\u503c[164]\u3002\u8fd9\u89e3\u91ca\u4e86\u4e3a\u4f55\u5728\u7cfb\u7edf\u4fe1\u606f\u6709\u9650\u65f6\uff0c\u7b80\u5355\u6a21\u578b\u5e38\u80fd\u5f02\u5e38\u6709\u6548\u5730\u6355\u6349\u5927\u90e8\u5206\u76f8\u5173\u7279\u5f81\u3002\u5728\u8bad\u7ec3\u7528\u4e8e\u624b\u5199\u6570\u5b57\u8bc6\u522b\u7684\u795e\u7ecf\u7f51\u7edc\u4e2d\uff08\u56fe4\uff09\uff0c Fisher \u4fe1\u606f\u7684\u6700\u5927\u7279\u5f81\u503c\u5bf9\u5e94\u7684\u96c6\u4f53\u6743\u91cd\u51e0\u4e4e\u5b8c\u5168\u51b3\u5b9a\u8bad\u7ec3\u7f51\u7edc\u7684\u6d4b\u8bd5\u7cbe\u5ea6\uff0c\u5176\u4f59\u53c2\u6570\u4e0e\u6743\u91cd\u7ec4\u5408\u57fa\u672c\u65e0\u5173\u3002\u8f7b\u91cf\u5316\u7684\u6a21\u578b\u6846\u67b6[165]\u4e5f\u80fd\u591f\u901a\u8fc7 Fisher \u4fe1\u606f\u7279\u5f81\u503c\u7684\u5c42\u7ea7\u7ed3\u6784\u8bc6\u522b\u8fd9\u4e9b\u53c2\u6570\u3002<\/span><\/p>\n

                  \u5f53\u5bf9\u7f51\u7edc\u6570\u636e\u96c6\u6216\u6a21\u578b\u5d4c\u5165\u7684\u6a21\u62df\u7684\u5b9e\u73b0\u8fdb\u884c\u4e0d\u65ad\u7684\u7c97\u7c92\u5316\u540e\uff0c\u7c97\u7c92\u5316\u7684\u4f3c\u7136\u51fd\u6570\u4ea7\u751f\u7684\u90e8\u5206\u7279\u5f81\u503c\u76f8\u5173\u6027\u589e\u5f3a\u800c\u53e6\u4e00\u90e8\u5206\u7684\u76f8\u5173\u6027\u51cf\u5f31\uff0c\u6b64\u8fc7\u7a0b\u4e0e\u91cd\u6574\u5316\u7fa4\u76f8\u5173\u6027\u7cbe\u786e\u5bf9\u5e94\u3002\u57fa\u4e8e\u6b64\uff0c\u4ec5\u901a\u8fc7\u7814\u7a76\u6570\u636e\u4e0d\u65ad\u7c97\u7c92\u5316\u4e0b\u7684\u53c2\u6570\u6d41\uff0c\u5373\u53ef\u7cfb\u7edf\u63a8\u65ad\u4e0d\u540c\u76f8\u4e0e\u63a7\u5236\u53c2\u6570\u7684\u5b58\u5728\uff0c\u6b64\u5904\u552f\u4e00\u7684\u5047\u8bbe\u662f\u7c97\u7c92\u5316\u65b9\u6848\u9009\u62e9\u3001\u5e95\u5c42\u7684\u51e0\u4f55\/\u7cfb\u7efc\u968f\u673a\u6027\u7684\u53c2\u6570\u5316\u65b9\u5f0f\u53ca\u5176\u5148\u9a8c\u5206\u5e03\u7684\u8bbe\u5b9a\u3002\u8be5\u65b9\u6cd5\u5df2\u7528\u4e8e\u8bc6\u522b\u5f02\u8d28\u6027\u5316\u5b66\u7cfb\u7edf\u7684\u4e0d\u540c\u76f8[166]\uff0c\u5728\u590d\u6742\u7f51\u7edc\u80cc\u666f\u4e0b\u4ea6\u5177\u7814\u7a76\u524d\u666f\u3002<\/span><\/p>\n


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

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

                  \n
                  \n
                  \n
                  \n


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

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


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

                    \n
                    \n

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


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

                    \u590d\u6742\u7f51\u7edc\u52a8\u529b\u5b66\u8bfb\u4e66\u4f1a<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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

                    \u96c6\u667a\u4ff1\u4e50\u90e8\u8054\u5408\u5408\u80a5\u5de5\u4e1a\u5927\u5b66\u7269\u7406\u7cfb\u6559\u6388\u674e\u660e\u3001\u540c\u6d4e\u5927\u5b66\u526f\u6559\u6388\u5f20\u6bc5\u8d85\u3001\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7279\u8058\u526f\u7814\u7a76\u5458\u53f2\u8d35\u5143\u4e0e\u5728\u8bfb\u535a\u58eb\u751f\u90b1\u4ef2\u666e\u3001\u5f20\u7ae0\u5171\u540c\u53d1\u8d77<\/span><\/span><\/span>\u300c\u590d\u6742\u7f51\u7edc\u52a8\u529b\u5b66\u300d\u8bfb\u4e66\u4f1a<\/a><\/span>\u3002\u672c\u6b21\u8bfb\u4e66\u4f1a\u5c06\u63a2\u8ba8\uff1a\u540c\u6b65\u76f8\u53d8\u7684\u4e34\u754c\u6027\u3001\u5982\u4f55\u666e\u9002\u5730\u523b\u753b\u591a\u7a33\u6001\u4e0e\u4e34\u754c\u70b9\u3001\u5982\u4f55\u8bc6\u522b\u5e76\u9884\u6d4b\u4e34\u754c\u8f6c\u53d8\u3001\u5982\u4f55\u901a\u8fc7\u5c40\u90e8\u5e72\u9884\u6765\u8c03\u63a7\u7cfb\u7edf\u4fdd\u6301\u6216\u56de\u5230\u671f\u671b\u7a33\u6001\u3001\u7206\u70b8\u903e\u6e17\u4e34\u754c\u884c\u4e3a\u7684\u5173\u952e\u7279\u5f81\u3001\u4e0d\u540c\u7c7b\u578b\u7684\u7ea7\u8054\u8fc7\u7a0b\u5bf9\u903e\u6e17\u76f8\u53d8\u7684\u5f71\u54cd\u6709\u4f55\u5f02\u540c\u3001\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u7684\u5f71\u54cd\u80fd\u5426\u7b49\u6548\u4e3a\u82e5\u5e72\u7b80\u5355\u673a\u5236\u7684\u53e0\u52a0\u3001\u5982\u4f55\u6709\u6548\u5730\u4fc3\u8fdb\u4eba\u7c7b\u4e2a\u4f53\u95f4\u7684\u5408\u4f5c\u7b49\u95ee\u9898\u3002<\/span><\/span>\u8bfb\u4e66\u4f1a\u5df2\u5b8c\u7ed3\uff0c\u73b0\u5728\u62a5\u540d\u53ef\u52a0\u5165\u793e\u7fa4\u5e76\u89e3\u9501\u56de\u653e\u89c6\u9891\u6743\u9650\u3002<\/span><\/span><\/span><\/span><\/section>\n
                    <\/span><\/a><\/p>\n

                    \u8be6\u60c5\u8bf7\u89c1\uff1a\u590d\u6742\u7f51\u7edc\u4e0a\u7684\u81ea\u7ec4\u7ec7\u4e0e\u96c6\u4f53\u884c\u4e3a\uff1a\u4ece\u6269\u6563\u3001\u76f8\u53d8\u5230\u535a\u5f08 | \u8bfb\u4e66\u4f1a\u542f\u52a8<\/a><\/span><\/span><\/p>\n


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

                    \u63a8\u8350\u9605\u8bfb<\/span><\/span><\/strong><\/strong><\/strong><\/section>\n
                    <\/strong><\/section>\n
                    1. Nature Physics\u8bc4\u8bba\uff1a\u91cd\u6574\u5316\u7fa450\u5e74\uff0c\u5e94\u7528\u4e8e\u975e\u5e73\u8861\u7cfb\u7edf\u524d\u666f\u5e7f\u9614<\/span><\/a><\/span><\/strong>
                    <\/span><\/strong><\/span><\/section>\n
                    2. \u91cd\u6574\u5316\u9047\u89c1\u673a\u5668\u5b66\u4e60\uff1a\u591a\u5c3a\u5ea6\u89c6\u89d2\u63a2\u7d22\u590d\u6742\u7cfb\u7edf\u5185\u5728\u7684\u7edf\u4e00\u6027<\/span><\/a><\/span>
                    <\/span><\/strong><\/strong><\/section>\n
                    3. Nature Physics\uff1a\u91cd\u6574\u5316\u7fa4\u2014\u2014\u7406\u89e3\u5f02\u6784\u7f51\u7edc\u7684\u663e\u5fae\u955c<\/span><\/a><\/span>
                    <\/span><\/strong><\/strong><\/section>\n
                    <\/strong><\/section>\n
                    4. <\/span><\/strong><\/span>\u6e38\u620f\u5316\u79d1\u7814\u2014\u2014\u8ba9\u6211\u4eec\u7a81\u7834\u5185\u5377\u3001\u5171\u7814\u6d8c\u73b0<\/a><\/span><\/strong><\/strong><\/span><\/section>\n
                    <\/strong>5.  <\/span><\/strong>\u63a2\u7d22\u8005\u8ba1\u5212 | \u96c6\u667a\u4ff1\u4e50\u90e82025\u5185\u5bb9\u56e2\u961f\u62db\u52df\uff08\u5168\u804c&\u517c\u804c\uff09<\/a><\/span><\/strong><\/span><\/section>\n

                    6. \u52a0\u5165\u96c6\u667a\uff0c\u73a9\u8f6c\u590d\u6742\uff0c\u5171\u521b\u6591\u56fe\uff01\u96c6\u667a\u4ff1\u4e50\u90e8\u7ebf\u4e0b\u5fd7\u613f\u8005\u62db\u52df<\/span><\/a><\/span><\/strong>
                    <\/span><\/strong><\/span><\/p>\n


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


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

                    \u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/span><\/span><\/section>\n<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

                    \u6458\u8981 \u91cd\u6574\u5316\u7fa4 (renormalization group, RG)\u7406\u8bba\u662f\u4e00\u5957\u5f3a\u6709\u529b\u7684\u7406\u8bba\u6846\u67b6\uff0c\u4e3b\u8981\u5e94\u7528\u4e8e\u591a\u81ea\u7531\u5ea6\u7cfb\u7edf\u7684\u7814\u7a76\u3002\u8be5\u7406\u8bba\u901a\u8fc7\u5bf9\u7cfb\u7edf\u72b6\u6001\u3001\u6a21\u578b\u53c2\u6570\u548c\u8026\u5408\u5e38\u6570\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0b\u7684\u63cf\u8ff0\uff0c\u5b9e\u73b0\u7cfb\u7edf\u5728\u4e0d\u540c\u5206\u8fa8\u7387\u5c42\u6b21\u95f4\u7684\u8f6c\u6362\u3002\u8be5\u7406\u8bba\u4e0d\u4ec5\u80fd\u8bc6\u522b\u76f8\u53d8\u4e34\u754c\u70b9\uff0c\u8fd8\u80fd\u6709\u6548\u5206\u6790\u7cfb\u7edf\u5728\u4e34\u754c\u70b9\u9644\u8fd1\u7684\u884c\u4e3a\u7279\u5f81\u3002\u5728\u4f20\u7edf\u7269\u7406…<\/p>\n","protected":false},"author":1,"featured_media":60610,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/60623"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=60623"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/60623\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/60610"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=60623"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=60623"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=60623"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=60623"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}