{"id":57171,"date":"2025-03-29T17:01:37","date_gmt":"2025-03-29T09:01:37","guid":{"rendered":"https:\/\/swarma.org\/?p=57171"},"modified":"2025-03-29T17:01:37","modified_gmt":"2025-03-29T09:01:37","slug":"%e9%87%8d%e6%95%b4%e5%8c%96%e7%be%a4%e6%96%b9%e6%b3%95%e5%a6%82%e4%bd%95%e5%ba%94%e7%94%a8%e5%9c%a8%e7%bd%91%e7%bb%9c%e7%a7%91%e5%ad%a6%e4%b8%ad%ef%bc%9fnat-rev-phys-%e7%bb%bc%e8%bf%b0","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=57171","title":{"rendered":"\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u5982\u4f55\u5e94\u7528\u5728\u7f51\u7edc\u79d1\u5b66\u4e2d\uff1fNat. Rev. Phys. \u7efc\u8ff0"},"content":{"rendered":"
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\u91cd\u6574\u5316\u7fa4\uff08RG\uff09\u662f\u4e00\u79cd\u5f3a\u5927\u7684\u7406\u8bba\u6846\u67b6\u3002\u5b83\u88ab\u7528\u4e8e\u5177\u6709\u591a\u81ea\u7531\u5ea6\u7684\u7cfb\u7edf\uff0c\u4ee5\u5728\u4e0d\u540c\u5206\u8fa8\u7387\u6c34\u5e73\u4e0a\u8f6c\u6362\u5176\u914d\u7f6e\u63cf\u8ff0\uff0c\u4ee5\u53ca\u76f8\u5173\u7684\u6a21\u578b\u53c2\u6570\u548c\u8026\u5408\u5e38\u6570\u3002\u91cd\u6574\u5316\u7fa4\u8fd8\u63d0\u4f9b\u4e86\u4e00\u79cd\u8bc6\u522b\u76f8\u53d8\u4e34\u754c\u70b9\u5e76\u7814\u7a76\u5176\u5468\u56f4\u7cfb\u7edf\u884c\u4e3a\u7684\u65b9\u6cd5\u3002\u5728\u4f20\u7edf\u7684\u7269\u7406\u5e94\u7528\u4e2d\uff0c\u91cd\u6574\u5316\u7fa4\u4e3b\u8981\u57fa\u4e8e\u540c\u8d28\u6027\u3001\u5bf9\u79f0\u6027\u3001\u51e0\u4f55\u548c\u5c40\u90e8\u6027\u7684\u6982\u5ff5\u6765\u5b9a\u4e49\u5ea6\u91cf\u8ddd\u79bb\u3001\u5c3a\u5ea6\u53d8\u6362\u548c\u81ea\u76f8\u4f3c\u7684\u7c97\u7c92\u5316\u65b9\u6848\u3002\u6700\u8fd1\uff0c\u4eba\u4eec\u52aa\u529b\u5c06\u91cd\u6574\u5316\u7fa4\u7684\u6982\u5ff5\u6269\u5c55\u5230\u590d\u6742\u7f51\u7edc\u3002\u7136\u800c\uff0c\u5728\u8fd9\u7c7b\u7cfb\u7edf\u4e2d\uff0c\u660e\u786e\u7684\u51e0\u4f55\u5750\u6807\u4e0d\u4e00\u5b9a\u5b58\u5728\uff0c\u4e0d\u540c\u7684\u8282\u70b9\u548c\u5b50\u56fe\u53ef\u80fd\u5177\u6709\u4e0d\u540c\u7684\u7edf\u8ba1\u7279\u6027\uff0c\u800c\u4e14\u4e0d\u5b58\u5728\u5747\u5300\u7684\u6676\u683c\u5bf9\u79f0\u6027\u2014\u2014\u6240\u6709\u8fd9\u4e9b\u7279\u5f81\u90fd\u4f7f\u5f97\u5b9a\u4e49\u4e00\u81f4\u7684\u91cd\u6574\u5316\u7a0b\u5e8f\u53d8\u5f97\u590d\u6742\u3002\u5728\u8fd9\u7bc7\u6280\u672f\u7efc\u8ff0\u4e2d\uff0c\u6211\u4eec\u8ba8\u8bba\u4e86\u7f51\u7edc\u91cd\u6574\u5316\u7684\u4e3b\u8981\u65b9\u6cd5\u3001\u91cd\u8981\u8fdb\u5c55\u4ee5\u53ca\u4ecd\u7136\u5b58\u5728\u7684\u5f00\u653e\u6027\u6311\u6218\u3002<\/span><\/span><\/strong><\/span><\/strong><\/p>\n


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

\u53d1\u8868\u65f6\u95f4\uff1a2025\u5e743\u670826\u65e5<\/span><\/span><\/p>\n

\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/doi.org\/10.1038\/s42254-025-00817-5<\/span><\/span><\/p>\n

\u671f\u520a\u540d\u79f0\uff1a<\/span><\/span>Nature Reviews Physics<\/span><\/span><\/em><\/p>\n<\/blockquote>\n


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\u96c6\u667a\u793e\u533a\u5bf9\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u7684\u5bfc\u8bfb\uff0c\u4ee5\u53ca\u91cd\u6574\u5316\u7fa4\u4e0e\u673a\u5668\u5b66\u4e60\u7684\u78b0\u649e\uff1a<\/span>\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<\/a><\/span><\/p>\n<\/blockquote>\n


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\u91cd\u6574\u5316\u7fa4<\/span>\uff08Renormalization Group\uff0cRG\uff09<\/span>\u662f\u7269\u7406\u5b66\u4e2d\u7814\u7a76\u591a\u4f53\u7cfb\u7edf\u76f8\u53d8\u548c\u666e\u9002\u6027\u73b0\u8c61\u7684\u6838\u5fc3\u5de5\u5177\u3002\u5b83\u901a\u8fc7\u9010\u5c42\u201c\u7c97\u7c92\u5316\u201d\u5fae\u89c2\u81ea\u7531\u5ea6\uff0c\u63ed\u793a\u7cfb\u7edf\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0b\u7684\u6709\u6548\u884c\u4e3a\u3002\u7136\u800c\uff0c\u4f20\u7edfRG\u4f9d\u8d56\u5747\u5300\u6027\u3001\u5bf9\u79f0\u6027\u548c\u51e0\u4f55\u5c40\u57df\u6027\u7b49\u5047\u8bbe\uff0c\u96be\u4ee5\u76f4\u63a5\u5e94\u7528\u4e8e\u590d\u6742\u7f51\u7edc\u2014\u2014\u8fd9\u7c7b\u7cfb\u7edf\u901a\u5e38\u7f3a\u4e4f\u663e\u5f0f\u51e0\u4f55\u5d4c\u5165\u3001\u8282\u70b9\u5f02\u8d28\u6027\u5f3a\uff0c\u4e14\u5177\u6709\u5c0f\u4e16\u754c\u6027<\/span>\uff08Small-World Property\uff09<\/span>\u548c\u6a21\u5757\u5316\u7ed3\u6784\u3002\u8fd1\u5e74\u6765\uff0c\u7814\u7a76\u8005\u8bd5\u56fe\u5c06RG\u601d\u60f3\u62d3\u5c55\u81f3\u590d\u6742\u7f51\u7edc\uff0c\u4ee5\u89e3\u6790\u5176\u8de8\u5c3a\u5ea6\u7684\u7edf\u8ba1\u89c4\u5f8b\u548c\u52a8\u529b\u5b66\u884c\u4e3a\u3002<\/span><\/span>Nature Reviews Physics<\/span><\/span><\/em>\u6700\u65b0\u6280\u672f\u7efc\u8ff0\u7cfb\u7edf\u68b3\u7406\u4e86\u8fd9\u4e00\u9886\u57df\u7684\u65b9\u6cd5\u8fdb\u5c55\u3001\u5173\u952e\u6311\u6218\u4e0e\u672a\u6765\u65b9\u5411\u3002<\/span><\/span><\/p>\n


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\u590d\u6742\u7f51\u7edc<\/span>\uff08\u5982\u793e\u4ea4\u7f51\u7edc\u3001\u751f\u7269\u7f51\u7edc\u3001\u7ecf\u6d4e\u7f51\u7edc\uff09<\/span>\u7684\u62d3\u6251\u5f02\u8d28\u6027\u548c\u7ed3\u6784\u4e0d\u89c4\u5219\u6027\uff0c\u4f7f\u5f97\u4f20\u7edfRG\u7684\u4e09\u5927\u6b65\u9aa4\uff1a\u5b9a\u4e49\u7c97\u7c92\u53d8\u91cf\u3001\u5e73\u5747\u5fae\u89c2\u6da8\u843d\u3001\u91cd\u6574\u5316\u8026\u5408\u53c2\u6570\uff0c\u9762\u4e34\u6839\u672c\u4e0a\u7684\u56f0\u96be\u3002\u4f8b\u5982\uff0c\u5728\u5747\u5300\u6676\u683c\u4e2d\uff0c\u901a\u8fc7\u5212\u5206\u76f8\u540c\u5c3a\u5bf8\u7684\u201c\u5757\u8282\u70b9\u201d\u5373\u53ef\u5b9e\u73b0\u7c97\u7c92\u5316\uff0c\u4f46\u590d\u6742\u7f51\u7edc\u7684\u8282\u70b9\u5ea6\u5206\u5e03\u5bbd\u6cdb\u3001\u8def\u5f84\u957f\u5ea6\u77ed\u4e14\u805a\u7c7b\u7cfb\u6570\u9ad8\uff0c\u65e0\u6cd5\u76f4\u63a5\u5b9a\u4e49\u4e00\u81f4\u7684\u7c97\u7c92\u5316\u5355\u5143\u3002\u6b64\u5916\uff0c\u7f51\u7edc\u52a8\u529b\u5b66<\/span>\uff08\u5982\u6d41\u884c\u75c5\u4f20\u64ad\u3001\u91d1\u878d\u51b2\u51fb\u4f20\u5bfc\uff09<\/span>\u4e0e\u62d3\u6251\u7ed3\u6784\u7684\u8026\u5408\uff0c\u8981\u6c42\u7c97\u7c92\u5316\u8fc7\u7a0b\u5fc5\u987b\u4fdd\u6301\u52a8\u529b\u5b66\u7684\u4e00\u81f4\u6027\uff0c\u800c\u975e\u4ec5\u5173\u6ce8\u9759\u6001\u7ed3\u6784\u3002<\/span><\/span><\/p>\n


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\u4f5c\u8005\u6307\u51fa\uff0c\u590d\u6742\u7f51\u7edc\u7684\u91cd\u6574\u5316\u9700\u89e3\u51b3\u4f20\u7edfRG\u63d0\u51fa\u7684\u4e09\u5927\u95ee\u9898\uff1a<\/span><\/span><\/p>\n

1. \u5982\u4f55\u5b9a\u4e49\u7c97\u7c92\u53d8\u91cf<\/span><\/span>\uff1a<\/span>\u5728\u65e0\u51e0\u4f55\u5750\u6807\u7684\u7f51\u7edc\u4e2d\uff0c\u9700\u4f9d\u8d56\u62d3\u6251\u7279\u5f81<\/span>\uff08\u5982\u6700\u77ed\u8def\u5f84\u3001\u6a21\u5757\u5316\u793e\u533a\uff09<\/span>\u6216\u52a8\u529b\u5b66\u7b49\u6548\u6027<\/span>\uff08\u5982\u6269\u6563\u8fc7\u7a0b\uff09<\/span>\u5212\u5206\u5757\u8282\u70b9\u3002<\/span><\/span><\/p>\n

2. \u5982\u4f55\u4fdd\u7559\u8de8\u5c3a\u5ea6\u76f8\u5173\u6027<\/span><\/span>\uff1a<\/span>\u5c0f\u4e16\u754c\u6027\u4f7f\u5f97\u957f\u7a0b\u8fde\u63a5\u666e\u904d\u5b58\u5728\uff0c\u5c40\u57df\u6da8\u843d\u7684\u5e73\u5747\u5316\u53ef\u80fd\u7834\u574f\u5173\u952e\u7684\u957f\u7a0b\u5173\u8054\u3002<\/span><\/span><\/p>\n

3. \u5982\u4f55\u91cd\u6574\u5316\u53c2\u6570<\/span><\/span>\uff1a<\/span>\u82e5\u7f51\u7edc\u672c\u8eab\u662f\u968f\u673a\u56fe\u6a21\u578b<\/span>\uff08Random Graph\uff09<\/span>\uff0c\u9700\u5c06\u5fae\u89c2\u53c2\u6570\u5206\u5e03\u6620\u5c04\u5230\u7c97\u7c92\u5c3a\u5ea6\uff0c\u5e76\u8ffd\u8e2a\u5176\u6d41\u65b9\u7a0b<\/span>\uff08Flow Equation\uff09<\/span>\u3002<\/span><\/span><\/p>\n


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1. \u57fa\u4e8e\u6700\u77ed\u8def\u5f84\u7684\u51e0\u4f55\u65b9\u6cd5<\/span><\/span><\/p>\n

\u65e9\u671f\u5c1d\u8bd5\u501f\u9274\u5206\u5f62\u51e0\u4f55\u7684\u201c\u76d2\u5b50\u8986\u76d6\u6cd5\u201d<\/span>\uff08Box-Covering Method\uff09<\/span>\uff0c\u5c06\u7f51\u7edc\u8282\u70b9\u6309\u6700\u77ed\u8def\u5f84\u8ddd\u79bb\u5206\u7ec4\uff0c\u751f\u6210\u81ea\u76f8\u4f3c\u7684\u91cd\u6574\u5316\u5e8f\u5217\u3002\u5c3d\u7ba1\u8be5\u65b9\u6cd5\u80fd\u63ed\u793a\u67d0\u4e9b\u7f51\u7edc<\/span>\uff08\u5982\u5206\u5f62\u7f51\u7edc\uff09<\/span>\u7684\u6807\u5ea6\u884c\u4e3a\uff0c\u4f46\u5c0f\u4e16\u754c\u6027\u5bfc\u81f4\u8def\u5f84\u8ddd\u79bb\u65e0\u6cd5\u6709\u6548\u533a\u5206\u4e0d\u540c\u5c3a\u5ea6\uff0c\u805a\u7c7b\u7cfb\u6570<\/span>\uff08Clustering Coefficient\uff09<\/span>\u7b49\u5173\u952e\u6027\u8d28\u5728\u7c97\u7c92\u5316\u540e\u53ef\u80fd\u4e22\u5931\u3002<\/span><\/span><\/p>\n


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2. \u8c31\u65b9\u6cd5\uff08Spectral Methods\uff09<\/span><\/span><\/p>\n

\u4ee5\u7f51\u7edc\u62c9\u666e\u62c9\u65af\u77e9\u9635<\/span>\uff08Laplacian Matrix\uff09<\/span>\u7684\u8c31\u5206\u89e3\u4e3a\u57fa\u7840\uff0c\u4fdd\u7559\u4e3b\u5bfc\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u4ee5\u7c97\u7c92\u5316\u7f51\u7edc\u3002\u4f8b\u5982\uff0c\u968f\u673a\u6e38\u8d70<\/span>\uff08Random Walk\uff09<\/span>\u7684\u6269\u6563\u8fc7\u7a0b\u53ef\u901a\u8fc7\u622a\u65ad\u9ad8\u9891\u6a21\u6001<\/span>\uff08Fast Modes\uff09<\/span>\u5b9e\u73b0\u52a8\u529b\u5b66\u7b49\u6548\u7684\u7c97\u7c92\u5316\u3002\u8c31\u65b9\u6cd5\u5728\u540c\u6b65<\/span>\uff08Synchronization\uff09<\/span>\u548c\u53ef\u63a7\u6027<\/span>\uff08Controllability\uff09<\/span>\u7814\u7a76\u4e2d\u8868\u73b0\u7a81\u51fa\uff0c\u4f46\u5176\u8ba1\u7b97\u590d\u6742\u5ea6\u9ad8\uff0c\u4e14\u4f9d\u8d56\u7279\u5b9a\u52a8\u529b\u5b66\u5047\u8bbe\u3002<\/span><\/span><\/p>\n


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3. \u62d3\u6251\u65b9\u6cd5\uff08Topological Methods\uff09<\/span><\/span><\/p>\n

\u57fa\u4e8e\u8282\u70b9\u4e2d\u5fc3\u6027<\/span>\uff08\u5982\u5ea6\u503c\uff09<\/span>\u3001\u7ed3\u6784\u7b49\u4ef7\u6027<\/span>\uff08Structurally Equivalent Nodes\uff09<\/span>\u6216\u793e\u533a\u7ed3\u6784\u5212\u5206\u5757\u8282\u70b9\u3002\u5178\u578b\u65b9\u6cd5\u5305\u62ec\u5ea6\u9608\u503c\u5316<\/span>\uff08\u79fb\u9664\u4f4e\u5ea6\u8282\u70b9\uff09<\/span>\u548ck\u6838\u5206\u89e3<\/span>\uff08\u4fdd\u7559\u9ad8\u5ea6\u4e92\u8fde\u7684\u5b50\u56fe\uff09<\/span>\u3002\u6b64\u7c7b\u65b9\u6cd5\u80fd\u63ed\u793a\u7f51\u7edc\u7684\u5c42\u6b21\u81ea\u76f8\u4f3c\u6027\uff0c\u4f46\u4f9d\u8d56\u4e8e\u9884\u8bbe\u7684\u62d3\u6251\u6a21\u5f0f\uff0c\u65e0\u6cd5\u666e\u9002\u5e94\u7528\u4e8e\u65e0\u663e\u8457\u793e\u533a\u7ed3\u6784\u7684\u7f51\u7edc\u3002<\/span><\/span><\/p>\n


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4. \u5bf9\u79f0\u6027\u65b9\u6cd5\uff08Symmetry-Based Methods\uff09<\/span><\/span><\/p>\n

\u5229\u7528\u7f51\u7edc\u7684\u52a8\u529b\u5b66\u5bf9\u79f0\u6027<\/span>\uff08\u5982\u8f93\u5165\u6811\u7b49\u4ef7\u6027\uff09<\/span>\u5b9a\u4e49\u7c97\u7c92\u5206\u533a\u3002\u4f8b\u5982\uff0c\u7ea4\u7ef4\u7740\u8272<\/span>\uff08Fibration Coloring\uff09<\/span>\u901a\u8fc7\u8282\u70b9\u8f93\u5165\u6811\u7684\u540c\u6784\u6027\u5408\u5e76\u7b49\u6548\u8282\u70b9\uff0c\u4fdd\u7559\u52a8\u529b\u5b66\u540c\u6b65\u6027\u3002\u7136\u800c\uff0c\u5bf9\u79f0\u6027\u65b9\u6cd5\u901a\u5e38\u4ec5\u80fd\u8bc6\u522b\u5355\u4e00\u5206\u533a\uff0c\u4e14\u65e0\u6cd5\u8fed\u4ee3\u5e94\u7528\u4e8e\u975e\u5bf9\u79f0\u7f51\u7edc\u3002<\/span><\/span><\/p>\n


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5. \u5de5\u7a0b\u4e0e\u673a\u5668\u5b66\u4e60\u9a71\u52a8\u7684\u65b9\u6cd5<\/span><\/span><\/p>\n

\u4e3a\u964d\u4f4e\u8ba1\u7b97\u6210\u672c\uff0c\u56fe\u795e\u7ecf\u7f51\u7edc<\/span>\uff08Graph Neural Networks\uff09<\/span>\u91c7\u7528\u542f\u53d1\u5f0f\u7c97\u7c92\u5316\u7b56\u7565<\/span>\uff08\u5982\u8fb9\u6743\u91cd\u805a\u5408\u3001\u8282\u70b9\u5d4c\u5165\u6c42\u548c\uff09<\/span>\u3002\u5c3d\u7ba1\u5b9e\u7528\u6027\u5f3a\uff0c\u8fd9\u7c7b\u65b9\u6cd5\u7f3a\u4e4f\u5bf9\u7f51\u7edc\u591a\u5c3a\u5ea6\u672c\u8d28\u7684\u7406\u8bba\u89e3\u91ca\uff0c\u5c5e\u4e8e\u201c\u4efb\u52a1\u5bfc\u5411\u201d\u800c\u975e\u201c\u539f\u7406\u5bfc\u5411\u201d\u3002<\/span><\/span><\/p>\n


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\u51e0\u4f55\u91cd\u6574\u5316\uff08Geometric Renormalization\uff09<\/span><\/span><\/strong><\/h4>\n

\u590d\u6742\u7f51\u7edc\u4e2d\u7684\u7a7a\u95f4\u5c40\u57df\u6027\u53ef\u4ee5\u5728\u51e0\u4f55\u6846\u67b6\u4e0b\u5f97\u5230\u6062\u590d\u3002\u901a\u8fc7\u5c06\u73b0\u5b9e\u4e16\u754c\u4e2d\u7ed3\u6784\u5f02\u8d28\u6027\u548c\u975e\u5c40\u57df\u6027\u7684\u7f51\u7edc\u5d4c\u5165\u5230\u53cc\u66f2\u7a7a\u95f4\u4e2d\uff0c\u6062\u590d\u7ed3\u6784\u7684\u51e0\u4f55\u5c40\u57df\u6027\uff0c\u8fdb\u800c\u5b9e\u73b0\u5c3a\u5ea6\u53d8\u6362\u3002\u6bcf\u4e2a\u8282\u70b9\u88ab\u8d4b\u4e88\u201c\u6d41\u884c\u5ea6\u201d<\/span>\uff08Popularity\uff0c\u5bf9\u5e94\u5f84\u5411\u5750\u6807\uff09<\/span>\u548c\u201c\u76f8\u4f3c\u5ea6\u201d<\/span>\uff08Similarity\uff0c\u5bf9\u5e94\u89d2\u5750\u6807\uff09<\/span>\u552f\u72ec\uff0c\u8fde\u63a5\u6982\u7387\u7531\u53cc\u66f2\u8ddd\u79bb\u51b3\u5b9a\u3002\u7c97\u7c92\u5316\u65f6\uff0c\u5c06\u76f8\u90bb\u8282\u70b9\u5408\u5e76\u4e3a\u8d85\u8282\u70b9\uff0c\u5e76\u91cd\u65b0\u8ba1\u7b97\u5750\u6807\u4e0e\u8026\u5408\u53c2\u6570\u3002\u8be5\u65b9\u6cd5\u6210\u529f\u9884\u6d4b\u4e86\u4eba\u8111\u8fde\u63a5\u7ec4<\/span>\uff08Connectome\uff09<\/span>\u7684\u591a\u5c3a\u5ea6\u81ea\u76f8\u4f3c\u6027\uff0c\u5e76\u53ef\u901a\u8fc7\u9006\u5411\u7684\u201c\u51e0\u4f55\u5206\u652f\u751f\u957f\u201d<\/span>\uff08Geometric Branching Growth\uff09<\/span>\u751f\u6210\u7edf\u8ba1\u7b49\u6548\u7684\u7ec6\u7c92\u5ea6\u7f51\u7edc\u3002<\/span><\/span><\/p>\n


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\u56fe 1. \u771f\u5b9e\u7f51\u7edc\u4e0a\u51e0\u4f55\u7f51\u7edc\u91cd\u6574\u5316\u7684\u76f4\u63a5\u65b9\u6cd5\uff08Directed\uff09\u548c\u9006\u65b9\u6cd5\uff08inverse\uff09\u4e0e\u7ed3\u679c\u3002<\/span><\/span><\/p>\n


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\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\uff08Laplacian Renormalization\uff09<\/span><\/span><\/strong><\/h4>\n

\u53e6\u4e00\u79cd\u7528\u4e8e\u590d\u6742\u7f51\u7edc\u91cd\u6574\u5316\u7684\u901a\u7528\u65b9\u6cd5\uff0c\u91c7\u7528\u8282\u70b9\u95f4\u7684Laplacian\u6269\u6563\u6982\u5ff5\u68c0\u6d4b\u591a\u5c3a\u5ea6\u7ed3\u6784\uff0c\u4ece\u800c\u5bf9\u4e00\u822c\u7f51\u7edc\u7684\u9876\u70b9\u548c\u8fb9\u8fdb\u884c\u7c97\u7c92\u5316\uff0c\u6700\u7ec8\u5b9e\u73b0\u5bf9\u7f51\u7edc\u52a8\u529b\u5b66\u8fdb\u884c\u91cd\u6574\u5316\u3002\u8fd9\u4e00\u65b9\u6cd5\u7c7b\u4f3c\u4e8e\u524d\u4e00\u8282\u4e2d\u63cf\u8ff0\u7684\u51e0\u4f55\u65b9\u6cd5\uff0c\u4e5f\u53ef\u4ee5\u5728\u76f4\u89c2\u4e14\u5177\u6709\u7269\u7406\u610f\u4e49\u7684\u5b9e\u7a7a\u95f4\u4e2d\u52a0\u4ee5\u8868\u8ff0\uff0c\u4e0e\u7edf\u8ba1\u7269\u7406\u4e2d\u7684Migdal\u2013Kadanoff\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u9ad8\u5ea6\u76f8\u4f3c\u3002\u8fd9\u79cd\u91cd\u6574\u5316\u65b9\u6cd5\u7684\u72ec\u7279\u4e4b\u5904\u5728\u4e8e\uff0c\u5b83\u4ee5\u5bf9\u5076\u6216k\u7a7a\u95f4\u8868\u793a\u7684\u5f62\u5f0f\u8fdb\u884c\u4e86\u4e25\u683c\u8868\u8ff0\uff0c\u5728\u8fd9\u4e24\u79cd\u60c5\u5f62\u4e0b\uff0c\u8be5\u65b9\u6cd5\u90fd\u5f15\u5165\u4e86\u4e00\u79cd\u8fed\u4ee3\u7684\u7f51\u7edc\u7c97\u7c92\u5316\u65b9\u6848\uff0c\u80fd\u591f\u5728\u4e0d\u65ad\u6269\u5927\u7684\u65f6\u7a7a\u5c3a\u5ea6\u4e0a\u4fdd\u7559\u5176\u6269\u6563\u52a8\u529b\u5b66\u7279\u5f81\u3002\u8be5\u65b9\u6cd5\u7684\u5b9e\u7a7a\u95f4\u7248\u672c\u7c7b\u4f3cKadanoff\u7684\u5757\u81ea\u65cb\u91cd\u6574\u5316\uff0c\u800ck\u7a7a\u95f4\u7248\u672c\u5219\u7c7b\u6bd4Wilson\u7684\u8fde\u7eed\u573a\u8bbaRG\uff0c\u80fd\u89e3\u6790\u7f51\u7edc\u7684\u8c31\u7ef4\u5ea6<\/span>\uff08Spectral Dimension\uff09<\/span>\u548c\u62d3\u6251\u76f8\u53d8\u3002\u4f8b\u5982\uff0c\u968f\u673a\u5757\u6a21\u578b<\/span>\uff08Stochastic Block Model\uff09<\/span>\u7684\u793e\u533a\u7ed3\u6784\u53ef\u901a\u8fc7\u6269\u6563\u5bb9\u91cf<\/span>\uff08Diffusive Capacity\uff09<\/span>\u7684\u5cf0\u503c\u68c0\u6d4b\u3002<\/span><\/span><\/p>\n

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\u5ef6\u5c55\u9605\u8bfb\uff1a<\/span>Nat. Phys.\u901f\u9012\uff1a\u5f02\u6784\u7f51\u7edc\u7684\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4<\/a><\/span><\/p>\n<\/blockquote>\n


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\u56fe 2. \u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u4e2d\u7684\u5b9e\u7a7a\u95f4\u6784\u9020\u3002<\/span><\/span><\/p>\n


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\u591a\u5c3a\u5ea6\u91cd\u6574\u5316\uff08Multiscale Renormalization\uff09<\/span><\/span><\/strong><\/h4>\n


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\u63d0\u51fa\u4e86\u4e00\u79cd\u201c\u805a\u5408\u4e0d\u53d8\u201d\u7684\u968f\u673a\u56fe\u6a21\u578b\uff0c\u5176\u968f\u673a\u53d8\u91cf\u5728\u8282\u70b9\u5212\u5206\u540e\u4ecd\u7136\u5728\u7edf\u8ba1\u5206\u5e03\u4e0a\u4fdd\u6301\u4e00\u81f4\u3002\u6a21\u578b\u5047\u8bbe\u8fde\u63a5\u6982\u7387\u7531\u8282\u70b9\u7684<\/span><\/span>\u9002\u5e94\u5ea6\uff08Fitness\uff09\u548c\u5bf9\u5076\u6548\u5e94\uff08Dyadic Effects\uff09<\/span><\/span><\/strong>\u5171\u540c\u51b3\u5b9a\uff0c\u7c97\u7c92\u5316\u540e\u53c2\u6570\u6309\u52a0\u548c\u6216\u6700\u5927\u4f3c\u7136\u89c4\u5219\u91cd\u6574\u5316\u3002\u8be5\u65b9\u6cd5\u6210\u529f\u590d\u73b0\u4e86\u56fd\u9645\u8d38\u6613\u7f51\u7edc\u7684\u591a\u5c3a\u5ea6\u7279\u6027\uff0c\u4e14\u80fd\u901a\u8fc7\u9006\u5411\u7ec6\u7c92\u5316<\/span>\uff08Fine-Graining\uff09<\/span>\u751f\u6210\u65e0\u9650\u53ef\u5206<\/span>\uff08Infinitely Divisible\uff09<\/span>\u7684\u5fae\u89c2\u7f51\u7edc\u3002\u5176\u201c\u6dec\u706b\u201d\u7248\u672c<\/span>\uff08Quenched Variant\uff09<\/span>\u5229\u7528\u5b9e\u9645\u7ecf\u6d4e\u6570\u636e<\/span>\uff08\u5982GDP\uff09<\/span>\u4f5c\u4e3a\u9002\u5e94\u5ea6\uff0c\u800c\u201c\u9000\u706b\u201d\u7248\u672c<\/span>\uff08Annealed Variant\uff09<\/span>\u5219\u901a\u8fc7\u7a33\u5b9a\u5206\u5e03<\/span>\uff08Stable Distribution\uff09<\/span>\u751f\u6210\u65e0\u6807\u5ea6<\/span>\uff08Scale-Free\uff09<\/span>\u7f51\u7edc\u3002<\/span><\/span><\/p>\n


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\u56fe 3. \u591a\u5c3a\u5ea6\u7f51\u7edc\u91cd\u6574\u5316\u65b9\u6cd5\u3002<\/span><\/span><\/p>\n


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1. \u5206\u8fa8\u7387\u7684\u672c\u8d28\u6027<\/span><\/span>\uff1a<\/span>\u9700\u533a\u5206\u7f51\u7edc\u5185\u5728\u5c3a\u5ea6\u4e0e\u6570\u636e\u89c2\u6d4b\u9650\u5236\u3002\u4f8b\u5982\uff0c\u91d1\u878d\u7f51\u7edc\u7684\u5fae\u89c2\u94fe\u63a5\u56e0\u9690\u79c1\u95ee\u9898\u4e0d\u53ef\u89c1\uff0c\u800c\u6d41\u884c\u75c5\u63a5\u89e6\u7f51\u7edc\u4ec5\u90e8\u5206\u5df2\u77e5\u3002<\/span><\/span><\/span><\/p>\n


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2. \u52a8\u529b\u5b66\u4e0e\u7ed3\u6784\u7684\u534f\u540c\u91cd\u6574\u5316<\/span><\/span><\/span>\uff1a<\/span>\u73b0\u6709\u65b9\u6cd5\u591a\u5173\u6ce8\u9759\u6001\u62d3\u6251\uff0c\u800c\u5b9e\u9645\u7f51\u7edc<\/span>\uff08\u5982\u795e\u7ecf\u6d3b\u52a8\u3001\u8206\u8bba\u4f20\u64ad\uff09<\/span>\u7684\u52a8\u529b\u5b66\u7c97\u7c92\u5316\u9700\u4e0e\u7ed3\u6784\u53d8\u6362\u8026\u5408\u3002<\/span><\/span><\/p>\n


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3. \u5e7f\u4e49\u4e34\u754c\u6027\uff08Generalized Criticality\uff09<\/span><\/span>\uff1a<\/span>\u5f02\u8d28\u6027\u548c\u957f\u7a0b\u8fde\u63a5\u53ef\u80fd\u5bfc\u81f4\u591a\u91cd\u76f8\u53d8\u6216\u6269\u5c55\u7684Griffiths\u76f8<\/span>\uff08Griffiths Phase\uff09<\/span>\uff0c\u9700\u91cd\u65b0\u5b9a\u4e49\u4e34\u754c\u6307\u6570<\/span>\uff08Critical Exponents\uff09<\/span>\u3002<\/span><\/span><\/p>\n


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4. \u4fe1\u606f\u51e0\u4f55\u4e0e\u53c2\u6570\u6d41<\/span><\/span>\uff1a<\/span>\u901a\u8fc7Fisher\u4fe1\u606f\u77e9\u9635<\/span>\uff08Fisher Information Matrix\uff09<\/span>\u8bc6\u522b\u201c\u76f8\u5173\u53c2\u6570\u201d\uff0c\u6784\u5efa\u6570\u636e\u9a71\u52a8\u7684\u91cd\u6574\u5316\u6846\u67b6\uff0c\u5df2\u5728\u5316\u5b66\u7f51\u7edc\u548c\u795e\u7ecf\u7f51\u7edc\u4e2d\u521d\u89c1\u6210\u6548\u3002<\/span><\/span><\/p>\n


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\u590d\u6742\u7f51\u7edc\u7684\u91cd\u6574\u5316\u6807\u5fd7\u7740\u7edf\u8ba1\u7269\u7406\u4e0e\u6570\u636e\u79d1\u5b66\u7684\u6df1\u5ea6\u4ea4\u53c9\u3002\u4ece\u53cc\u66f2\u5d4c\u5165\u7684\u51e0\u4f55\u76f4\u89c2\uff0c\u5230\u62c9\u666e\u62c9\u65af\u8c31\u7684\u52a8\u529b\u5b66\u672c\u8d28\uff0c\u518d\u5230\u591a\u5c3a\u5ea6\u968f\u673a\u56fe\u7684\u805a\u5408\u4e0d\u53d8\u6027\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u4e3a\u89e3\u6790\u793e\u4ea4\u3001\u751f\u7269\u3001\u6280\u672f\u7f51\u7edc\u7684\u666e\u9002\u89c4\u5f8b\u63d0\u4f9b\u4e86\u65b0\u8303\u5f0f\u3002\u672a\u6765\uff0c\u7ed3\u5408\u4fe1\u606f\u8bba\u3001\u673a\u5668\u5b66\u4e60\u4e0e\u975e\u5e73\u8861\u7269\u7406\u7684\u8de8\u5b66\u79d1\u5de5\u5177\uff0c\u6216\u5c06\u50ac\u751f\u4e00\u5957\u201c\u7f51\u7edc\u573a\u8bba\u201d\uff0c\u7edf\u4e00\u63cf\u8ff0\u4ece\u5fae\u89c2\u4e92\u52a8\u5230\u5b8f\u89c2\u6d8c\u73b0\u7684\u8de8\u5c3a\u5ea6\u89c4\u5f8b\u3002<\/span><\/span><\/p>\n


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\u5f6d\u6668<\/span><\/span> <\/span><\/span>| \u7f16\u8bd1<\/span><\/span><\/strong><\/span><\/strong><\/p>\n


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


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

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\u8bfb\u4e66\u4f1a\u8ba1\u5212\u4ece3\u67087\u65e5\u5f00\u59cb\uff0c\u6bcf\u5468\u4e94\u665a19:30-21:30\u8fdb\u884c\uff0c\u6301\u7eed8-10\u5468\u3002\u8bda\u631a\u9080\u8bf7\u9886\u57df\u5185\u7814\u7a76\u8005\u3001\u5bfb\u6c42\u8de8\u9886\u57df\u878d\u5408\u7684\u7814\u7a76\u8005\u52a0\u5165\uff0c\u5171\u540c\u63a2\u8ba8\u3002<\/span><\/span><\/section>\n


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\"\u56fe\u7247\"<\/span><\/a><\/section>\n
\n


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\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<\/section>\n


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\u63a8\u8350\u9605\u8bfb<\/span><\/span><\/strong><\/strong><\/strong><\/section>\n
<\/strong><\/section>\n
1. <\/span><\/strong>\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<\/a><\/span><\/strong><\/strong><\/span><\/section>\n
2. <\/span><\/strong>Nat. Phys.\u901f\u9012\uff1a\u5f02\u6784\u7f51\u7edc\u7684\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4<\/a><\/span><\/strong><\/span><\/section>\n
3. 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>
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4. <\/span><\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/span><\/strong><\/strong><\/span><\/section>\n
<\/strong>5. <\/span><\/strong>\u89e3\u9501\u96c6\u667a\u5168\u7ad9\u5185\u5bb9\uff0c\u5f00\u542f\u65b0\u5e74\u5b66\u4e60\u8ba1\u5212<\/a><\/span><\/strong><\/section>\n

6. <\/span><\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/a><\/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\uff08RG\uff09\u662f\u4e00\u79cd\u5f3a\u5927\u7684\u7406\u8bba\u6846\u67b6\u3002\u5b83\u88ab\u7528\u4e8e\u5177\u6709\u591a\u81ea\u7531\u5ea6\u7684\u7cfb\u7edf\uff0c\u4ee5\u5728\u4e0d\u540c\u5206\u8fa8\u7387\u6c34\u5e73\u4e0a\u8f6c\u6362\u5176\u914d\u7f6e\u63cf\u8ff0\uff0c\u4ee5\u53ca\u76f8\u5173\u7684\u6a21\u578b\u53c2\u6570\u548c\u8026\u5408\u5e38\u6570\u3002\u91cd\u6574\u5316\u7fa4\u8fd8\u63d0\u4f9b\u4e86\u4e00\u79cd\u8bc6\u522b\u76f8\u53d8\u4e34\u754c\u70b9\u5e76\u7814\u7a76\u5176\u5468\u56f4\u7cfb\u7edf\u884c\u4e3a\u7684\u65b9\u6cd5\u3002\u5728\u4f20\u7edf\u7684\u7269\u7406\u5e94\u7528\u4e2d\uff0c\u91cd\u6574\u5316\u7fa4\u4e3b\u8981\u57fa\u4e8e\u540c\u8d28\u6027\u3001\u5bf9\u79f0\u6027\u3001\u51e0\u4f55\u548c\u5c40\u90e8\u6027\u7684\u6982\u5ff5\u6765\u5b9a\u4e49\u5ea6\u91cf\u8ddd\u79bb\u3001\u5c3a\u5ea6\u53d8\u6362\u548c\u81ea\u76f8…<\/p>\n","protected":false},"author":1,"featured_media":57163,"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\/57171"}],"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=57171"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/57171\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/57163"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=57171"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=57171"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=57171"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=57171"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}