{"id":40493,"date":"2023-02-08T22:49:53","date_gmt":"2023-02-08T14:49:53","guid":{"rendered":"https:\/\/swarma.org\/?p=40493"},"modified":"2023-02-08T22:49:53","modified_gmt":"2023-02-08T14:49:53","slug":"nature-physics%ef%bc%9a%e9%87%8d%e6%95%b4%e5%8c%96%e7%be%a4-%e7%90%86%e8%a7%a3%e5%bc%82%e6%9e%84%e7%bd%91%e7%bb%9c%e7%9a%84%e6%98%be%e5%be%ae%e9%95%9c","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=40493","title":{"rendered":"Nature Physics\uff1a\u91cd\u6574\u5316\u7fa4\u2014\u2014\u7406\u89e3\u5f02\u6784\u7f51\u7edc\u7684\u663e\u5fae\u955c"},"content":{"rendered":"
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\u91cd\u6574\u5316\u7fa4\u662f\u666e\u9002\u6027\u548c\u76f8\u53d8\u7406\u8bba\u7684\u57fa\u77f3\uff0c\u662f\u68c0\u9a8c\u52a8\u529b\u7cfb\u7edf\u5bf9\u79f0\u6027\u548c\u7ec4\u7ec7\u5c3a\u5ea6\u7684\u6709\u529b\u5de5\u5177\u3002\u7136\u800c\uff0c\u7531\u4e8e\u4e0d\u540c\u5c3a\u5ea6\u4e4b\u95f4\u7684\u76f8\u5173\u6027\uff0c\u5b83\u5728\u590d\u6742\u7f51\u7edc\u4e2d\u7684\u5e94\u7528\u7279\u522b\u5177\u6709\u6311\u6218\u6027\u3002<\/strong>\u8fd1\u65e5\u53d1\u8868\u4e8e Nature Physics<\/em> \u7684\u4e00\u9879\u7814\u7a76\u63d0\u51fa\u4e00\u4e2a\u57fa\u4e8e\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4\u6269\u6563\u7684\u590d\u6742\u7f51\u7edc\u65b9\u6cd5\uff0c\u80fd\u591f\u5728\u5f02\u8d28\u7f51\u7edc\u4e2d\u8bc6\u522b\u51fa\u5408\u9002\u7684\u65f6\u7a7a\u5c3a\u5ea6\u3002<\/strong><\/p>\n

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Konstantin Klemm<\/span> <\/span>| \u4f5c\u8005<\/strong><\/span><\/span><\/p>\n

\u90ed\u745e\u4e1c<\/span> <\/span>| \u8bd1\u8005<\/span><\/strong><\/span><\/p>\n

\u6731\u6b23\u6021<\/span> <\/span>| \u5ba1\u6821<\/span><\/span><\/strong><\/span><\/p>\n

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


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Laplacian renormalization group for heterogeneous networks<\/span><\/section>\n
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\u91cd\u6574\u5316<\/span>\uff08Renormalization\uff09<\/span>\u662f\u4e00\u79cd\u57fa\u4e8e\u91cd\u590d\u7c97\u7c92\u5316\u8fc7\u7a0b\u7684\u6280\u672f\uff0c\u7528\u4e8e\u7814\u7a76\u7edf\u8ba1\u7269\u7406\u5b66\u4e2d\u7684\u5c3a\u5ea6\u4e0d\u53d8\u6027\u548c\u4e34\u754c\u6027\u3002\u6700\u8fd1 Nature Physics<\/em> \u7684\u7814\u7a76[1]\uff0c\u201c\u9488\u5bf9\u5f02\u6784\u7f51\u7edc\u7684\u62c9\u666e\u62c9\u65af\u91cd\u6574\u5316\u7fa4\u201d\uff0c\u6269\u5c55\u4e86\u91cd\u6574\u5316\u5de5\u5177\u7bb1\uff0c\u5141\u8bb8\u63a2\u7d22\u73b0\u5b9e\u4e16\u754c\u7f51\u7edc\u7684\u5c3a\u5ea6\u4e0d\u53d8\u6027\u3002<\/span><\/section>\n
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Villegas \u53ca\u5176\u540c\u4e8b\u6269\u5927\u4e86\u91cd\u6574\u5316\u7fa4\u7684\u5e94\u7528\u8303\u56f4\uff0c\u5c06\u5176\u6269\u5c55\u5230\u8d85\u8d8a\u7f51\u683c\u7ed3\u6784\u7684\u4efb\u610f\u7f51\u7edc\u7cfb\u7edf\u3002\u5404\u79cd\u751f\u7269\u548c\u6280\u672f\u7f51\u7edc\uff0c\u5982\u751f\u7269\u4f53\u7684\u65b0\u9648\u4ee3\u8c22\u901a\u8def\u53ca\u4e92\u8054\u7f51\uff0c\u5728\u9002\u5f53\u7684\u5757\u5f62\u6210\u65b9\u6848\u4e0b\u5177\u6709\u5c3a\u5ea6\u4e0d\u53d8\u6027\u3002\u7136\u800c\uff0c\u5e76\u975e\u6240\u6709\u7684\u7f51\u7edc\u7ed3\u6784\u90fd\u5177\u6709\u8fd9\u79cd\u6027\u8d28\u3002\u4eba\u5de5\u7f51\u7edc\uff0c\u5982\u968f\u673a\u56fe\u548c\u968f\u673a\u5757\u6a21\u578b<\/span>\uff08stochastic block models\uff09<\/span>\u5c31\u672a\u80fd\u901a\u8fc7\u5c3a\u5ea6\u4e0d\u53d8\u6027\u6d4b\u8bd5\u3002<\/span><\/section>\n
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\u56fe1.\u51e0\u4f55\u548c\u7f51\u7edc\u7cfb\u7edf\u4e2d\u7684\u8fed\u4ee3\u7c97\u7c92\u5316\u3002\uff08a\uff09\u79d1\u8d6b\u66f2\u7ebf\uff0c\u4e00\u4e2a\u9012\u5f52\u6784\u9020\u7684\u5206\u5f62\uff0c\u901a\u8fc7\u53cd\u8f6c\u5c40\u90e8\u6784\u9020\u89c4\u5219\u8fdb\u884c\u7c97\u7c92\u5316\u3002\uff08b\uff09\u6b63\u65b9\u5f62\u7f51\u683c\u4e0a\u7684\u4f0a\u8f9b\u6a21\u578b\uff0c\u7528 Kadanoff \u7684\u5757\u65b9\u6cd5\u8fdb\u884c\u7c97\u7c92\u5316\uff08\u6bcf\u4e2a 3\u00d73 \u5757\u4e2d\u7684\u4e0a\/\u4e0b\u81ea\u65cb\u88ab\u5927\u591a\u6570\u81ea\u65cb\u65b9\u5411\u6240\u53d6\u4ee3\uff09\u3002\uff08c\uff09\u6811\u72b6\u7f51\u7edc\uff08\u5de6\u56fe\uff09\u88ab\u5212\u5206\u6210\u4e0d\u540c\u989c\u8272\u7684\u65b9\u5757\u3002\u7c97\u7c92\u5ea6\u7f51\u7edc\uff08\u4e2d\u56fe\uff09\u4e2d\u7684\u8d85\u7ea7\u8282\u70b9\u96c6\u4e2d\u4e86\u6bcf\u4e2a\u533a\u5757\u7684\u8282\u70b9\uff0c\u8be5\u8fc7\u7a0b\u901a\u8fc7\u91cd\u590d\u5bfb\u627e\u5757\uff08\u6761\u7eb9\u6c14\u6ce1\uff09\u8fdb\u884c\u7c97\u7c92\u5316\u3002\u8fd9\u5c31\u5f15\u51fa\u4e86\u4e24\u8282\u70b9\u7684\u7f51\u7edc\uff08\u53f3\u56fe\uff09\u3002<\/span><\/p>\n

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\u56fe2. Kadanoff \u65b9\u6cd5\u7684\u793a\u610f\u56fe\u3002\uff08a\uff09\u4e0b\u5c42\u4e3a BA \u7f51\u7edc\uff0c\u4e0d\u540c\u7684\u989c\u8272\u8bc6\u522b Kadanoff \u8d85\u8282\u70b9\u3002\uff08b\uff09\u6bcf\u4e2a\u5757\u6210\u4e3a\u5355\u4e2a\u4e0e\u539f\u5757\u4e2d\u6bcf\u6761\u8fde\u8fb9\u76f8\u5173\u8054\u7684\u8282\u70b9\u3002<\/span><\/p>\n

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\u8fd9\u4e9b\u957f\u7a0b\u8fde\u8fb9\u7684\u4e00\u5c0f\u90e8\u5206\u8db3\u4ee5\u8d4b\u4e88\u7f51\u7edc\u5c0f\u4e16\u754c\u5c5e\u6027[3]\u2014\u2014\u5728\u793e\u4ea4\u7f51\u7edc\u4e2d\u88ab\u901a\u4fd7\u5730\u79f0\u4e3a\u201c\u516d\u5ea6\u5206\u9694\u201d\u3002\u4efb\u4f55\u4e24\u4e2a\u4eba\u90fd\u7531\u719f\u4eba\u7ec4\u6210\u7684\u8f83\u77ed\u7684\u8fde\u8fb9\u88ab\u8fde\u63a5\u8d77\u6765\u2014\u2014\u5982\u679c\u719f\u4eba\u7f51\u7edc\u662f\u4e8c\u7ef4\u7f51\u7edc\uff0c\u90a3\u4e48\u8ddd\u79bb\u8981\u6bd4\u9884\u671f\u77ed\u5f97\u591a\u3002\u5728\u4e00\u4e2a\u5c0f\u4e16\u754c\u7f51\u7edc\u4e2d\uff0c\u7f51\u7edc\u7684\u76f4\u5f84<\/span>\uff08\u4efb\u610f\u4e24\u4e2a\u8282\u70b9\u4e4b\u95f4\u7684\u5e73\u5747\u8ddd\u79bb\uff09<\/span>\u968f\u7740\u8282\u70b9\u7684\u6570\u91cf\u5bf9\u6570\u7f29\u653e\u3002\u5bf9\u4efb\u610f\u7ef4\u5ea6\u7684\u7f51\u683c\uff0c\u8fd9\u53ef\u4ee5\u770b\u4f5c\u76f4\u5f84\u6807\u5ea6\u6240\u5177\u6709\u7684\u65e0\u7a77\u7ef4\u5ea6\u6781\u9650<\/span>\uff08infinite dimension limit\uff09<\/span>\u3002\u56e0\u6b64\uff0c\u5927\u591a\u6570\u771f\u5b9e\u4e16\u754c\u7f51\u7edc\u8868\u73b0\u51fa\u7684\u5c0f\u4e16\u754c\u7f51\u7edc\u7279\u6027\uff0c\u5b9e\u9645\u4e0a\u63cf\u8ff0\u4e86\u6709\u9650\u7ef4\u5ea6\u7684\u7f3a\u5931\uff0c\u4ece\u800c\u963b\u788d\u4e86\u7f51\u7edc\u5728\u4f4e\u7ef4\u6b27\u6c0f\u7a7a\u95f4\u4e2d\u7684\u5d4c\u5165<\/strong>\u3002<\/span><\/section>\n
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\u4e4b\u524d\u7684\u7f51\u7edc\u91cd\u6574\u5316\u65b9\u6cd5[5]\u5c1d\u8bd5\u901a\u8fc7\u5c06\u7f51\u7edc\u5d4c\u5165\u5230\u4e00\u4e2a\u4e8c\u7ef4\u53cc\u66f2\u7a7a\u95f4\uff0c\u6a21\u62df\u4e3a\u5e9e\u52a0\u83b1\u5706\u76d8<\/span>\uff08Poincar\u00e9 disk\uff09<\/span>\u89e3\u51b3\u4e86\u8fd9\u4e2a\u95ee\u9898\u3002\u5c06\u6240\u9700\u7684\u5757\u6295\u5f71\u5230\u5706\u76d8\u7684\u8fb9\u754c\uff0c\u5448\u73b0\u4e3a\u8fd9\u4e2a\u4e00\u7ef4\u6d41\u5f62\u4e2d\u7684\u7c07\u3002\u8fd9\u79cd\u65b9\u6cd5\u63ed\u793a\u4e86\u6765\u6e90\u4e8e\u751f\u7269\u3001\u6280\u672f\u548c\u793e\u4f1a\u7684\u51e0\u4e2a\u771f\u5b9e\u7f51\u7edc\u4e2d\u660e\u786e\u7684\u5c3a\u5ea6\u4e0d\u53d8\u6027\u3002\u6b64\u5916\uff0c\u5b83\u4e0e\u6765\u81ea\u9690\u85cf\u5ea6\u91cf\u7a7a\u95f4\u7684\u73b0\u6709\u7f51\u7edc\u7406\u8bba\u6709\u7740\u5f88\u5f3a\u7684\u8054\u7cfb\u3002\u8fd9\u4e2a\u7814\u7a76\u7684\u4e0d\u8db3\u4e4b\u5904\u5728\u4e8e\uff0c\u8be5\u65b9\u6cd5\u662f\u4e3a\u53ef\u5d4c\u5165\u5230\u53cc\u66f2\u51e0\u4f55\u7684\u7f51\u7edc\u91cf\u8eab\u5b9a\u5236\u7684\uff0c\u4e0d\u9002\u7528\u4e8e\u5176\u4ed6\u7f51\u7edc\u7ed3\u6784\uff0c\u5982\u7f51\u683c\u3002<\/span><\/section>\n
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Villegas \u7b49\u4eba\u5b8c\u5168\u6452\u5f03\u51e0\u4f55\u5b66\u7684\u5047\u8bbe\uff0c\u8003\u8651\u7f51\u7edc\u4e0a\u7684\u6269\u6563\u8fc7\u7a0b\u3002\u4ed6\u4eec\u8ba4\u4e3a\u5757\u662f\u6269\u6563\u8fc7\u7a0b\u4e2d\u5177\u6709\u663e\u8457\u6982\u7387\u6d41\u7684\u8282\u70b9\u96c6\u5408<\/span>\uff08\u56fe1c\uff09<\/span>\u3002\u6982\u7387\u5411\u91cf\u6309\u7167\u70ed\u65b9\u7a0b<\/span>\uff08heat equation\uff0c\u5373\u70ed\u4f20\u5bfc\u65b9\u7a0b\uff09<\/span>\u7684\u7f51\u7edc\u7248\u672c\u6f14\u5316\uff0c\u7531\u62c9\u666e\u62c9\u65af\u77e9\u9635<\/span>\uff08Laplacian Matrix\uff09<\/span>\u63a7\u5236\u3002\u8be5\u77e9\u9635\u662f\u8457\u540d\u7684\u7528\u4e8e\u5411\u91cf\u8ba1\u7b97\u7684\u62c9\u666e\u62c9\u65af\u7b97\u5b50\u7684\u79bb\u6563\u5bf9\u5e94\u7269\u3002<\/span><\/section>\n
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\u5c31\u50cf\u4f20\u7edf\u7684\u62c9\u666e\u62c9\u65af\u7b97\u5b50\uff0c\u7f51\u7edc\u62c9\u666e\u62c9\u65af\u7b97\u5b50\u5728\u65f6\u95f4\u548c\u7a7a\u95f4\u5c3a\u5ea6\u7d27\u5bc6\u8026\u5408\u3002\u5c24\u5176\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u7f51\u7edc\u62c9\u666e\u62c9\u65af\u7b97\u5b50\u7684\u7279\u5f81\u5411\u91cf\u5c31\u50cf\u5728\u5f39\u6027\u4ecb\u8d28\u4e2d\u632f\u8361\u7684\u9a7b\u6ce2\u3002\u6ce2\u6570\u968f\u7740\u76f8\u5173\u7279\u5f81\u503c\u53d8\u5316[6]\u30fc\u30fc\u6ce2\u8d8a\u77ed\uff0c\u632f\u52a8\u8d8a\u5feb\u3002<\/span><\/section>\n
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Villegas \u548c\u540c\u4e8b\u4eec\u5229\u7528\u7a7a\u95f4\u4e0e\u65f6\u95f4\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u7528\u52a8\u91cf\u7a7a\u95f4\u65b9\u6cd5\u8865\u5145\u4ed6\u4eec\u7684\u5757\u91cd\u6574\u5316\u6280\u672f\u3002\u8fd9\u91cc\u7c97\u7c92\u5316\u6295\u5c04\u6700\u5927\u7279\u5f81\u503c\u7684\u7279\u5f81\u5411\u91cf\uff0c\u4ece\u800c\u6d88\u9664\u4e86\u7f51\u7edc\u62c9\u666e\u62c9\u65af\u7b97\u5b50\u4e2d\u7684\u6700\u5c0f\u7a7a\u95f4\u5c3a\u5ea6\u3002\u6b64\u5916\uff0c\u7c97\u7c92\u5316\u4e0d\u4ec5\u5728\u7a7a\u95f4\u4e0a\u5c55\u5f00\uff0c\u800c\u4e14\u5728\u65f6\u95f4\u5c3a\u5ea6\u4e0a\u5c55\u5f00\uff0c\u4f7f\u5f97\u8be5\u65b9\u6cd5\u53ef\u4ee5\u7528\u4e8e\u52a8\u529b\u7cfb\u7edf\u7684\u91cd\u6574\u5316[7]\u3002<\/span><\/section>\n
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\u8fd9\u79cd\u57fa\u4e8e\u62c9\u666e\u62c9\u65af\u7b97\u5b50\u7684\u7c97\u7c92\u5316\u65b9\u6cd5\u53ca\u65e9\u671f\u7684\u53cc\u66f2\u5d4c\u5165\u6cd5\uff0c\u5e76\u4e0d\u662f\u7269\u7406\u5b66\u5728\u7f51\u7edc\u5206\u5272<\/span>\uff08network partition\uff09<\/span>\u65b9\u9762\u7684\u9996\u6b21\u5c1d\u8bd5\u3002\u66f4\u591a\u4f8b\u5b50\u6709\uff1a\u57fa\u4e8e\u76d2\u8ba1\u6570<\/span>\uff08Box-counting\uff09<\/span>\u7684\u7f51\u7edc\u7ef4\u5ea6\u4f30\u8ba1[8]\u548c\u793e\u56e2\u7ed3\u6784\u68c0\u6d4b[9]\uff0c\u8fd9\u662f\u8fc7\u53bb20\u5e74\u5f00\u53d1\u7684\u4e00\u7cfb\u5217\u5206\u5272\u65b9\u6cd5\u3002\u8fd9\u4e9b\u65b9\u6cd5\u5927\u90e8\u5206\u662f\u5728\u6ca1\u6709\u8003\u8651\u91cd\u6574\u5316\u7406\u8bba\u7684\u524d\u63d0\u4e0b\u7814\u53d1\u7684\u3002\u7136\u800c\uff0c\u901a\u8fc7\u6bd4\u8f83\u65b0\u7684\u7c97\u7c92\u5316\u65b9\u6cd5\u548c\u5df2\u6709\u7684\u7c97\u7c92\u5316\u65b9\u6cd5\uff0c\u53ef\u4ee5\u83b7\u5f97\u6709\u4ef7\u503c\u7684\u89c1\u89e3\u3002\u4eba\u4eec\u53ef\u80fd\u5e0c\u671b\uff0c\u57fa\u4e8e\u7f51\u7edc\u7684\u5c3a\u5ea6\u4e0d\u53d8\u6027\u7684\u9c81\u68d2\u8868\u5f81\uff0c\u53ef\u4ee5\u63ed\u793a\u4e0d\u53ea\u4e00\u4e2a\uff0c\u800c\u662f\u4e00\u7ec4\u7f51\u7edc\u5206\u5272\u65b9\u6848\u3002<\/span><\/section>\n
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\u4f46\u662f\u8fd9\u4e00\u5207\u90fd\u662f\u4e3a\u4e86\u4ec0\u4e48\u5462\uff1f\u73b0\u5b9e\u4e16\u754c\u7f51\u7edc\u662f\u6709\u9650\u5c3a\u5bf8\u7684\u3002\u5b83\u4eec\u5728\u6bcf\u4e2a\u7c97\u7c92\u5316\u6b65\u9aa4\u4e2d\u90fd\u4f1a\u6536\u7f29\uff0c\u56e0\u6b64\u91cd\u6574\u5316\u603b\u662f\u6d41\u5411\u5e73\u51e1\u89e3\u2014\u2014\u5355\u4e2a\u5b64\u7acb\u7684\u8282\u70b9\u3002\u90a3\u4e48\uff0c\u6211\u4eec\u5982\u4f55\u8bc1\u660e\u7f51\u7edc\u7684\u5c3a\u5ea6\u4e0d\u53d8\u6027<\/strong>\u5462\uff1f\u4e00\u4e2a\u542f\u53d1\u5f0f\u65b9\u6cd5\u662f\uff0c\u901a\u8fc7\u6bd4\u8f83\u7c97\u7c92\u5316\u524d\u540e\u7f51\u7edc\u7684\u8282\u70b9\u5ea6\u6570\u5206\u5e03\u548c\u5176\u4ed6\u7f51\u7edc\u6307\u6807\u6765\u8bc1\u660e\u3002<\/span><\/section>\n
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Villegas \u548c\u540c\u4e8b\u4eec\u4e5f\u53d1\u73b0\u4e86\u6269\u6563\u8fc7\u7a0b\u672c\u8eab\u7684\u7a7a\u95f4\u5c3a\u5ea6\u4e0d\u53d8\u6027\uff0c\u6b63\u5982\u65f6\u95f4\u65e0\u5173\u7684\u71b5\u4ea7\u751f\u901f\u7387\u6240\u8868\u660e\u7684\u90a3\u6837\u3002\u8fd9\u4e9b\u7814\u7a76\u7ed3\u679c\u4ee4\u4eba\u5174\u594b\uff0c\u540c\u65f6\u8fd8\u6709\u4e00\u4e2a\u4e2a\u57fa\u4e8e\u6848\u4f8b\u7684\u4ee4\u4eba\u4fe1\u670d\u7684\u542f\u53d1\u5f0f\u8bba\u70b9\u3002\u8fd9\u4e9b\u53d1\u73b0\u8ba9\u6211\u4eec\u8d8a\u6765\u8d8a\u63a5\u8fd1\u7f51\u7edc\u5c3a\u5ea6\u4e0d\u53d8\u6027\u8fd9\u4e00\u6982\u5ff5\uff0c\u4ee5\u53ca\u4e0e\u91cd\u6574\u5316\u7fa4\u53d6\u5f97\u4e00\u81f4\u3002<\/span><\/section>\n
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\u672c\u6587\u7ffb\u8bd1\u81ea\uff1a<\/span>https:\/\/www.nature.com\/articles\/s41567-022-01842-2<\/span><\/section>\n
\u539f\u6587\u9898\u76ee\u201cA zoom lens for networks\u201d\u3002<\/span><\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n

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\u53c2\u8003\u8d44\u6599<\/span><\/strong><\/span><\/section>\n
1. Villegas, P., Gili, T., Caldarelli, G. & Gabrielli, A. Nat. Phys. https:\/\/doi.org\/10.1038\/<\/span><\/section>\n
s41567-022-01866-8 (2023).<\/span><\/section>\n
2. Kadanof, L. P. Phys. Phys. Fiz. 2, 263 (1966).<\/span><\/section>\n
3. Watts, D. J. & Strogatz, S. H. Nature 393, 440 (1998).<\/span><\/section>\n
4. Egu\u00edluz, V. M., Hern\u00e1ndez-Garc\u00eda, E., Piro, O. & Klemm, K.<\/span><\/section>\n
Phys. Rev. E 68, 055102 (2003).<\/span><\/section>\n
5. Garc\u00eda-P\u00e9rez, G., Bogu\u00f1\u00e1, M. & Serrano, M. \u00c1. Nat. Phys. 14, 583\u2013589 (2018).<\/span><\/section>\n
6. Biyiko\u011fu, T., Leydold, J. & Stadler, P. F. Laplacian Eigenvectors of Graphs: Perron\u2013Frobenius  and Faber\u2013Krahn Type Theorems (Springer, 2007).<\/span><\/section>\n
7. Lesne, A. A comparative introduction to the renormalization methods used in statistical  mechanics and for dynamical systems. In Workshop on Renormalization in Mathematics and  Physics (IHP, 1996); <\/span>https:\/\/www.lptmc.jussieu.fr\/user\/lesne\/rg-IHP-2.pdf<\/span><\/section>\n
8. Song, C., Havlin, S. & Makse, H. A. Nature 433, 392\u2013395 (2005).<\/span><\/section>\n
9. Fortunato, S. & Newman, M. E. J. Nat. Phys. 18, 848\u2013850 (2022).<\/span><\/section>\n

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