{"id":36874,"date":"2022-08-29T21:22:14","date_gmt":"2022-08-29T13:22:14","guid":{"rendered":"https:\/\/swarma.org\/?p=36874"},"modified":"2022-08-29T21:22:14","modified_gmt":"2022-08-29T13:22:14","slug":"%e7%bb%9f%e8%ae%a1%e7%89%a9%e7%90%86%e3%80%81%e6%97%a0%e5%ba%8f%e7%b3%bb%e7%bb%9f%e5%92%8c%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=36874","title":{"rendered":"\u7edf\u8ba1\u7269\u7406\u3001\u65e0\u5e8f\u7cfb\u7edf\u548c\u795e\u7ecf\u7f51\u7edc"},"content":{"rendered":"
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2021\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u5f97\u4e3b\u5e15\u91cc\u897f\u5728\u65e0\u5e8f\u7cfb\u7edf\u65b9\u9762\u4f5c\u51fa\u5f00\u521b\u4e4b\u4e3e\uff0c\u4ed6\u63d0\u51fa\u590d\u672c\u5bf9\u79f0\u7834\u7f3a\u65b9\u6cd5\u89e3\u51b3\u81ea\u65cb\u73bb\u7483\u95ee\u9898\uff0c\u8fd9\u4e00\u65b9\u6cd5\u4e5f\u5bf9\u795e\u7ecf\u7f51\u7edc\u7b49\u4ea4\u53c9\u5b66\u79d1\u4ea7\u751f\u6df1\u539a\u5f71\u54cd\uff0c\u6fc0\u53d1\u672a\u6765\u5bf9\u4eba\u5de5\u667a\u80fd\u548c\u4eba\u8111\u7b49\u590d\u6742\u7cfb\u7edf\u7684\u8fdb\u4e00\u6b65\u7814\u7a76\u3002<\/span><\/strong><\/span><\/p>\n


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\u4e2d\u5c71\u5927\u5b66\u6559\u6388\u3001PMI Lab \u7684\u9ec4\u6d77\u5e73\u8fd1\u65e5\u51fa\u7248\u300a\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u300b\uff08\u82f1\u6587\u7248\uff09\u65b0\u4e66\uff0c\u5e76\u7ec4\u7ec7\u540c\u4e3b\u9898\u7684\u5728\u7ebf\u8bfe\u7a0b<\/a>\uff0c\u5e2e\u52a9\u5b66\u751f\u5b66\u4e60\u7edf\u8ba1\u529b\u5b66\u7684\u57fa\u672c\u539f\u7406\u53ca\u5176\u5728\u7406\u89e3\u795e\u7ecf\u7f51\u7edc\u5185\u90e8\u5de5\u4f5c\u539f\u7406\u7684\u5e94\u7528\u3002\u8bfe\u7a0b\u81ea9\u670817\u65e5\u5f00\u59cb\uff0c\u7279\u522b\u5f00\u653e50\u4f4d\u514d\u8d39\u540d\u989d\uff0c8\u670831\u65e5\u524d\u53ef\u7533\u8bf7\uff0c\u8be6\u60c5\u89c1\u6587\u672b\u3002<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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2021\u5e74\uff0c\u8bfa\u8d1d\u5c13\u5956\u59d4\u5458\u4f1a\u51b3\u5b9a\u5c06\u7269\u7406\u5956\u9881\u53d1\u7ed9\u7814\u7a76\u590d\u6742\u7cfb\u7edf\u7684\u4e09\u4f4d\u79d1\u5b66\u5bb6\uff0c\u4e00\u65f6\u5f15\u8d77\u65e0\u6570\u8be7\u5f02\u548c\u54d7\u7136\uff0c\u8fd9\u662f\u8bfa\u8d1d\u5c14\u5956\u9996\u6b21\u9881\u53d1\u7ed9\u590d\u6742\u7cfb\u7edf\u7814\u7a76\u9886\u57df\u3002<\/span>
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2013\u5e74\u5e15\u91cc\u897f\u83b7\u5f97\u300a\u81ea\u7136\u300b<\/span>\uff08Nature\uff09<\/span>\u5468\u520a\u9881\u53d1\u7684\u6770\u51fa\u5bfc\u5e08\u5956\u65f6\uff0c\u63d0\u5230\u4ed6\u7684\u5bfc\u5e08\uff0c\u8bf4\u4ed6\u5bfc\u5e08\u66fe\u7ecf\u8bf4\u8fc7\uff0c\u79d1\u5b66\u7814\u7a76\u7684\u76ee\u7684\u5c31\u662f\u4eab\u53d7\u89e3\u51b3\u95ee\u9898\u7684\u4e50\u8da3\uff0c\u8fd9\u53ef\u80fd\u662f\u5361\u6bd4\u535a\u7559\u7ed9\u5e15\u91cc\u897f\u6700\u5b9d\u8d35\u7684\u8d22\u5bcc\u3002\u5e15\u91cc\u897f\u5728\u4ed6\u7684\u79d1\u5b66\u751f\u6daf\u4e2d\u5c06\u8fd9\u53e5\u8bdd\u4f53\u9a8c\u5f97\u6dcb\u6f13\u5c3d\u81f4\uff01<\/span><\/section>\n

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1970\u5e74\u4ee3\u672b\u671f\uff0c\u5e15\u91cc\u897f\u7684\u7814\u7a76\u5174\u8da3\u8f6c\u5411\u65e0\u5e8f\u7cfb\u7edf\u7684\u7406\u8bba\u7814\u7a76\uff0c\u56e0\u4e3a\u8fd9\u7c7b\u7cfb\u7edf\u7684\u590d\u6742\u6027\u6df1\u6df1\u5438\u5f15\u4e86\u5e15\u91cc\u897f\u3002<\/span>\u65e0\u5e8f\u7cfb\u7edf\u7406\u8bba\u7814\u7a76\u59cb\u4e8e1980\u5e74\u4ee3\uff0c\u5e15\u91cc\u897f\u662f\u5148\u884c\u8005\u4e4b\u4e00\u3002<\/span><\/span><\/section>\n

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\u200d2.2 <\/span><\/strong><\/strong>\u81ea\u65cb\u73bb\u7483<\/span><\/strong><\/span><\/strong><\/strong><\/span><\/section>\n

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\u6211\u4eec\u53ef\u4ee5\u628a\u8fd9\u4e9b\u5c0f\u7403\u5f62\u6210\u7684\u56fe\u6848\u770b\u4f5c\u662f\u73bb\u7483\u6216\u9897\u7c92\u6750\u6599<\/span>\uff08\u5982\u6c99\u5b50\u6216\u8005\u783e\u77f3\uff09<\/span>\u7684\u7b80\u5316\u6a21\u578b\u3002\u5e15\u91cc\u897f\u6700\u521d\u7814\u7a76\u7684\u662f\u53e6\u4e00\u79cd\u7c7b\u4f3c\u7cfb\u7edf\u2014\u2014\u81ea\u65cb\u73bb\u7483\uff0c\u8fd9\u662f\u78c1\u6027\u5408\u91d1\u6750\u6599\u7684\u4e00\u79cd\u4e9a\u7a33\u5b9a\u72b6\u6001\u3002\u81ea\u65cb\u73bb\u7483\u662f\u5178\u578b\u7684\u65e0\u5e8f\u7cfb\u7edf\uff0c\u5728\u7ecf\u5178\u7edf\u8ba1\u7269\u7406\u91cc\uff0c\u81ea\u65cb\u53ef\u4ee5\u6807\u8bb0\u7c92\u5b50\u7684\u79bb\u6563\u72b6\u6001\uff0c\u6bd4\u5982\u5411\u4e0a\u6216\u5411\u4e0b\u3002\u4e00\u822c\u7684\u78c1\u4f53\u4e2d\uff0c\u6240\u6709\u78c1\u77e9\u7684\u81ea\u65cb\u90fd\u6307\u5411\u540c\u4e00\u4e2a\u65b9\u5411\uff0c\u5176\u5206\u5e03\u662f\u957f\u7a0b\u6709\u5e8f\u7684\u3002\u800c\u81ea\u65cb\u73bb\u7483\u4e2d\u5904\u4e8e\u683c\u70b9\u4e0a\u7684\u81ea\u65cb\u7684\u76f8\u4e92\u4f5c\u7528\u662f\u5b8c\u5168\u968f\u673a\u7684\uff0c\u8fd9\u79cd\u968f\u673a\u6027\u5bfc\u81f4\u81ea\u65cb\u53d6\u5411\u51fa\u73b0\u963b\u632b\u6548\u5e94<\/span>\uff08frustration effect\uff09<\/span>\uff0c\u5373\u81ea\u65cb\u7684\u53d6\u5411\u96be\u4ee5\u6ee1\u8db3\u5c40\u90e8\u80fd\u91cf\u6700\u4f4e\u7684\u8981\u6c42\u3002\u81ea\u65cb\u73bb\u7483\u7684\u4e00\u4e2a\u663e\u8457\u7279\u5f81\u662f\u5b8f\u89c2\u5e73\u5747\u78c1\u77e9\u6d88\u5931\uff0c\u4f46\u5b58\u5728\u81ea\u65cb\u73bb\u7483\u5e8f\u3002\u8fd9\u91cc\u7684\u201c\u73bb\u7483\u201d\u4e00\u8bcd\u5b9e\u9645\u4e0a\u662f\u957f\u7a0b\u65e0\u5e8f\u72b6\u6001\u7684\u4ee3\u540d\u8bcd\uff0c\u8868\u793a\u8fd9\u79cd\u65e0\u5e8f\u72b6\u6001\u7c7b\u4f3c\u4e8e\u4e00\u822c\u7684\u73bb\u7483\u3002<\/span><\/section>\n

<\/section>\n
\u5728\u5e15\u91cc\u897f\u5173\u4e8e\u81ea\u65cb\u73bb\u7483\u7684\u4e66\u4e2d\u7684\u4ecb\u7ecd\uff0c\u4ed6\u5199\u9053\uff1a\u7814\u7a76\u81ea\u65cb\u73bb\u7483\u5c31\u50cf\u770b\u838e\u58eb\u6bd4\u4e9a\u7684\u56db\u5927\u60b2\u5267\u3002\u5982\u679c\u4f60\u60f3\u8ddf\u4e24\u4e2a\u4eba\u540c\u65f6\u505a\u670b\u53cb\uff0c\u4f46\u662f\u8fd9\u4e24\u4e2a\u670b\u53cb\u4e4b\u95f4\u4e92\u76f8\u654c\u89c6\uff0c\u8fd9\u4f1a\u8ba9\u4eba\u6cae\u4e27\u3002\u8fd9\u7c7b\u573a\u666f\u5728\u53e4\u5178\u60b2\u5267\u4e2d\u66f4\u662f\u7a81\u51fa\uff0c\u5982\u679c\u611f\u60c5\u6700\u8981\u597d\u7684\u670b\u53cb\u6210\u4e3a\u4e86\u654c\u4eba\u5728\u540c\u4e00\u4e2a\u821e\u53f0\u4e0a\u76f8\u9047\uff0c\u600e\u6837\u624d\u80fd\u628a\u623f\u95f4\u91cc\u7684\u7d27\u5f20\u6c1b\u56f4\u964d\u5230\u6700\u4f4e\uff1f<\/span><\/section>\n

<\/section>\n
2.3 \u81ea\u65cb\u73bb\u7483\u7684\u7814\u7a76\u80cc\u666f<\/span><\/strong><\/span><\/strong><\/strong><\/span><\/section>\n

<\/section>\n
\u73bb\u7483\u6001\u7684\u7269\u7406\u672c\u8d28\u76f4\u5230\u4eca\u5929\u4f9d\u7136\u60ac\u800c\u672a\u51b3\u300250\u591a\u5e74\u524d\uff0c\u7269\u7406\u5b66\u5bb6\u4e3a\u4e86\u7814\u7a76\u73bb\u7483\u6001\u63d0\u51fa\u4e86\u81ea\u65cb\u73bb\u7483\u7684\u6982\u5ff5\u3002\u7231\u5fb7\u534e\u5179<\/span>\uff08S. Edwards\uff09<\/span>\u548c\u5b89\u5fb7\u68ee<\/span>\uff08P. Anderson\uff09<\/span>\u4e8e1975\u5e74\u63d0\u51fa\u77ed\u7a0b\u76f8\u4e92\u4f5c\u7528\u7684\u81ea\u65cb\u73bb\u7483\u6a21\u578b [1]\u3002\u540c\u4e00\u5e74\uff0c\u8c22\u7075\u987f<\/span>\uff08D. Sherrington\uff09<\/span>\u548c\u67ef\u514b\u5e15\u7279\u91cc\u514b<\/span>\uff08S. Kirkpatrick\uff09<\/span>\u63d0\u51fa\u81ea\u65cb\u73bb\u7483\u7684\u5e73\u5747\u573a\u6a21\u578b<\/span>\uff08\u7b80\u79f0S-K\u6a21\u578b\uff09<\/span>[2]\uff0c\u4ed6\u4eec\u7684\u5de5\u4f5c\u6807\u5fd7\u7740\u7269\u7406\u5b66\u5bb6\u5bf9\u81ea\u65cb\u73bb\u7483\u7cfb\u7edf\u7684\u7814\u7a76\u62c9\u5f00\u4e86\u5e8f\u5e55\u3002S-K\u6a21\u578b\u5c06\u77ed\u7a0b\u6a21\u578b\u63a8\u5e7f\u5230\u5168\u8fde\u63a5\u7684\u60c5\u5f62\uff0c\u5373\u6bcf\u4e2a\u81ea\u65cb\u90fd\u540c\u5176\u4ed6\u81ea\u65cb\u4e24\u4e24\u8fde\u63a5\u3002\u73b0\u5728\u77e5\u9053S-K\u6a21\u578b\u7684\u5e73\u5747\u573a\u6027\u8d28<\/span>\uff08\u5305\u62ec\u52a8\u529b\u5b66\u884c\u4e3a\uff09<\/span>\u5b58\u5728\u6570\u5b66\u89e3\u6790\u5f62\u5f0f\uff0c\u8fd9\u53ef\u80fd\u662f\u5e15\u91cc\u897f\u975e\u5e38\u7740\u8ff7\u4e8e\u6b64\u7c7b\u6a21\u578b\u7684\u539f\u56e0\u4e4b\u4e00\u3002<\/span>
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\u77ed\u7a0b\u76f8\u4e92\u4f5c\u7528<\/span><\/strong>  \u6682\u4e14\u5ffd\u7565\u865a\u7ebf\u7684\u8d21\u732e\uff0c\u7c97\u7ebf\u4ee3\u8868\u94c1\u78c1\u76f8\u4e92\u4f5c\u7528<\/span>\uff08\u8981\u6c42\u76f8\u90bb\u81ea\u65cb\u671d\u5411\u4e00\u81f4\uff09<\/span>\uff0c\u7ec6\u7ebf\u4ee3\u8868\u53cd\u94c1\u78c1\u76f8\u4e92\u4f5c\u7528<\/span>\uff08\u8981\u6c42\u76f8\u90bb\u81ea\u65cb\u671d\u5411\u76f8\u53cd\uff09<\/span>\uff0c\u8fd9\u6837\u5de6\u4e0a\u683c\u70b9\u7684\u81ea\u65cb\u96be\u4ee5\u53d6\u5408\u9002\u7684\u671d\u5411\uff0c\u4ece\u800c\u4f7f\u5f97\u4f53\u7cfb\u7684\u80fd\u91cf\u6700\u4f4e\u3002<\/span><\/section>\n

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\u5168\u8fde\u63a5\u5e73\u5747\u573a\u6a21\u578b<\/span><\/strong>  \u6bcf\u4e2a\u81ea\u65cb<\/span>\uff08\u5706\u5f62\u683c\u70b9\uff09<\/span>\u90fd\u4e0e\u5176\u4ed6\u81ea\u65cb\u4e24\u4e24\u8fde\u63a5\u3002<\/span><\/section>\n

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\u5f53\u65f6\u56f0\u6270\u7269\u7406\u5b66\u5bb6\u7684\u4e00\u6735\u4e4c\u4e91\u662f\uff0cS-K\u6a21\u578b\u7684\u4f4e\u6e29\u71b5\u4e3a\u8d1f\u503c\uff0c\u8fd9\u5f3a\u70c8\u8fdd\u80cc\u4e86\u7269\u7406\u76f4\u89c2\uff0c\u56e0\u4e3a\u81ea\u65cb\u53d6\u5411\u53ea\u6709\u4e24\u4e2a\u65b9\u5411<\/span>\uff08\u79bb\u6563\u53d6\u503c\uff09<\/span>\u7684\u7cfb\u7edf\u7684\u71b5\u4e0d\u53ef\u80fd\u4e3a\u8d1f<\/span>\uff08\u7cfb\u7edf\u7684\u6784\u578b\u6570\u662f\u53ef\u6570\u7684\uff09<\/span>\u30021978\u5e74\uff0c\u5bf9S-K\u6a21\u578b\u7684\u7a33\u5b9a\u6027\u5206\u6790\u8bc1\u660e\uff0cS-K\u6a21\u578b\u7684\u4f4e\u6e29\u89e3\u662f\u4e0d\u7a33\u5b9a\u7684 [3]\u3002\u90a3\u4e48\uff0c\u4e00\u4e2a\u91cd\u8981\u7684\u95ee\u9898\u968f\u4e4b\u800c\u6765\uff0cS-K\u6a21\u578b\u7684\u8d1f\u71b5\u5371\u673a\u6839\u6e90\u5728\u54ea\uff1f\u6b21\u5e74\uff0c\u8fd9\u4e2a\u95ee\u9898\u88ab\u5e74\u8f7b\u7684\u5e15\u91cc\u897f\u89e3\u51b3 [4]\uff0c\u5f53\u65f6\u4ed6\u5e74\u4ec531\u5c81\u3002\u8fd9\u4f3c\u4e4e\u518d\u6b21\u5370\u8bc1\u4e86\u201c\u81ea\u53e4\u5929\u624d\u51fa<\/span>\uff08\u9752\uff09<\/span>\u5c11\u5e74\u201d\uff01<\/span><\/section>\n

<\/section>\n
2.4 \u5e15\u91cc\u897f\u7684\u9b54\u6cd5<\/span><\/strong><\/strong><\/span>
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\u9488\u5bf9\u81ea\u65cb\u73bb\u7483\u7cfb\u7edf\uff0c\u5e15\u91cc\u897f\u63d0\u51fa\u4e86\u590d\u672c\u5bf9\u79f0\u7834\u7f3a<\/span>\uff08replica symmetry breaking, RSB\uff09<\/span>\u7684\u6982\u5ff5\uff0c\u53d1\u5c55\u4e86\u4e00\u5957\u6709\u6548\u7684\u6570\u5b66\u65b9\u6cd5\uff0c\u5e76\u7ed9\u51fa\u4e86\u4e00\u4e2a\u7cbe\u786e\u7684\u7406\u8bba\u89e3\u3002<\/span><\/section>\n

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\u5176\u7269\u7406\u672c\u8d28\u5c31\u662f\u5c06\u539f\u6709\u6a21\u578b\u81ea\u65cb\u4e4b\u95f4\u7684\u590d\u6742\u76f8\u4e92\u4f5c\u7528\uff0c\u8f6c\u6362\u4e3a\u540c\u4e00\u6a21\u578b\u7684\u591a\u4e2a\u62f7\u8d1d<\/span>\uff08\u5373\u591a\u4e2a\u590d\u672c\uff09<\/span>\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u3002\u8fd9\u6837\uff0c\u590d\u672c\u4e4b\u95f4\u5c31\u5b58\u5728\u4e00\u8026\u5408\u77e9\u9635\uff0c\u5982\u679c\u8fd9\u4e00\u77e9\u9635\u7684\u975e\u5bf9\u89d2\u5143\u7d20\u5747\u540c<\/span>\uff08\u5bf9\u89d2\u5143\u7d20\u663e\u7136\u4e00\u6837\uff09<\/span>\uff0c\u90a3\u4e48\u8fd9\u4e2a\u5747\u540c\u7684\u5143\u7d20\u5c31\u662f\u7edf\u8ba1\u7269\u7406\u7684\u5e8f\u53c2\u91cf\uff0c\u4ece\u800c\u523b\u753b\u4e86\u524d\u9762\u63d0\u5230\u7684\u81ea\u65cb\u73bb\u7483\u5e8f\u3002\u5e15\u91cc\u897f\u4ee5\u5929\u624d\u7684\u60f3\u8c61\u529b\u5f15\u5165\u4e86\u7834\u7f3a\uff0c\u5373\u6b63\u786e\u7684\u590d\u672c\u77e9\u9635\u5e94\u8be5\u5728\u5bf9\u89d2\u7ebf\u4e0a\u51fa\u73b0\u4e0d\u65ad\u5206\u5757\u7ed3\u6784\uff0c\u6bcf\u4e00\u6b21\u5206\u5757\u5c06\u5f15\u5165\u65b0\u7684\u5e8f\u53c2\u91cf\uff1b\u800c\u4e14\uff0c\u5bf9\u4e8eS-K\u6a21\u578b\uff0c\u8fd9\u79cd\u5206\u5757\u662f\u65e0\u7a77\u591a\u6b21\u7684\u3002\u8fd9\u6837\uff0c\u5e8f\u53c2\u91cf\u5c06\u53d8\u6210\u8fde\u7eed\u7684\u51fd\u6570\u3002\u5e15\u91cc\u897f\u53d1\u73b0\uff0c\u53ea\u6709\u8fd9\u6837\uff0cS-K\u6a21\u578b\u7684\u4f4e\u6e29\u71b5\u624d\u80fd\u5728\u590d\u672c\u5bf9\u79f0\u7834\u7f3a\u65e0\u7a77\u591a\u6b21\u4e4b\u540e\u8d8b\u4e8e\u96f6\uff0c\u8d1f\u71b5\u5371\u673a\u624d\u5f97\u4ee5\u89e3\u51b3\uff0c\u4e5f\u4e0d\u8fdd\u53cd\u70ed\u529b\u5b66\u7b2c\u4e09\u5b9a\u5f8b\u3002<\/span><\/section>\n

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\u590d\u672c\u5bf9\u79f0\u7834\u7f3a\u7684\u6570\u5b66\u8868\u8ff0<\/span><\/strong>  3\u4e2a\u5927\u65b9\u5757\u5206\u522b\u8868\u793a\u4e0d\u540c\u5c42\u6b21\u7269\u7406\u8fd1\u4f3c\u7684\u590d\u672c\u77e9\u9635\u3002(a)\u6700\u4f4e\u9636\u7684\u590d\u672c\u5bf9\u79f0\u8fd1\u4f3c\uff0c\u5373\u6240\u6709\u975e\u5bf9\u89d2\u77e9\u9635\u5143\u4e00\u6837\uff1b(b)\u4e00\u9636\u590d\u672c\u5bf9\u79f0\u7834\u7f3a\uff0c\u5373\u5728\u5bf9\u89d2\u7ebf\u4e0a\u5206\u51fan\/m1\u4e2a<\/span>\uff08\u56fe\u4e2d\u662f3\u4e2a\uff09<\/span>m1\u00d7m1\u5757\u77e9\u9635\uff0c\u56e0\u6b64\u6bd4(a)\u60c5\u5f62\u591a\u51fa\u4e00\u4e2a\u989d\u5916\u7684\u81ea\u65cb\u73bb\u7483\u5e8f<\/span>\uff08\u5757\u77e9\u9635\u7684\u975e\u5bf9\u89d2\u5143\u7d20\uff09<\/span>\uff1b(c)\u4e8c\u9636\u590d\u672c\u5bf9\u79f0\u7834\u7f3a\uff0c\u6bcf\u4e2a\u5757\u77e9\u9635\u53c8\u4ee5\u540c\u6837\u65b9\u5f0f\u88ab\u7ec6\u5206\u4e3am2\u00d7m2\u7684\u5757\u77e9\u9635 [5]\u3002<\/span><\/section>\n

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\u968f\u7740\u5e15\u91cc\u897f\u4e0e\u5408\u4f5c\u8005\u51e0\u5341\u5e74\u5982\u4e00\u65e5\u7684\u6df1\u5165\u7814\u7a76\uff0c\u590d\u672c\u5bf9\u79f0\u7834\u7f3a\u7684\u7269\u7406\u610f\u4e49\u9010\u6e10\u660e\u6717\u3002\u8fd9\u4e00\u731c\u60f3\u572820\u591a\u5e74\u540e\u88ab\u6cd5\u56fd\u6570\u5b66\u5bb6\u5854\u62c9\u683c\u5170<\/span>\uff08M. Talagrand\uff09<\/span>\u8bc1\u660e [6]\uff0c\u6210\u4e3a\u7269\u7406\u5b66\u53f2\u4e0a\u4e3a\u6570\u4e0d\u591a\u7684\u7ecf\u5178\u6848\u4f8b\uff01\u5e15\u91cc\u897f\u540e\u6765\u603b\u7ed3\u9053\uff1a\u5f53\u7269\u7406\u5b66\u5bb6\u4f7f\u7528\u6570\u5b66\u65f6\uff0c\u4ed6\u4eec\u4ee5\u66f4\u5bbd\u677e\u7684\u65b9\u5f0f\u4f7f\u7528\u5b83<\/span>\uff08when physicists use mathematics, they use it in a looser way\uff09<\/span>\u3002\u8fd9\u5341\u5206\u8d34\u5207\u5730\u5f62\u5bb9\u4e86\u7269\u7406\u5b66\u5bb6\u773c\u4e2d\u6570\u5b66\u4e0e\u7269\u7406\u7684\u5173\u7cfb\uff1a\u7269\u7406\u662f\u6570\u5b66\u7684\u5b9e\u5728\u3002\u4f8b\u5982\uff0c2015\u5e74\uff0c\u968f\u673a\u6fc0\u5149\u7269\u7406\u7cfb\u7edf\u4e2d\u7684\u5b9e\u9a8c\u4e5f\u8bc1\u5b9e\u4e86\u590d\u672c\u5bf9\u79f0\u7834\u7f3a\u7684\u6982\u5ff5 [7]\u3002\u7269\u7406\u5b66\u5bb6\u5728\u89e3\u51b3\u7269\u7406\u95ee\u9898\u7684\u8fc7\u7a0b\u4e2d\uff0c\u64c5\u957f\u5728\u7269\u7406\u76f4\u89c9\u6307\u5f15\u4e0b\u505a\u8fd1\u4f3c\uff1b\u800c\u6700\u4e0d\u53ef\u601d\u8bae\u7684\u5730\u65b9\u662f\uff0c\u8fd9\u79cd\u8fd1\u4f3c\u6700\u540e\u5374\u662f\u7cbe\u786e\u7684\u3002\u8fd9\u6837\u7684\u601d\u7ef4\uff0c\u4e5f\u8bb8\u53ef\u4ee5\u603b\u7ed3\u4e3a\u4e0d\u6c42\u4e25\u683c\uff0c\u53ea\u6c42\u7cbe\u786e\u3002\u572821\u4e16\u7eaa\u590d\u6742\u7cfb\u7edf\u7814\u7a76\u4e2d\uff0c\u8fd9\u6837\u7684\u7814\u7a76\u98ce\u683c\u53ef\u4ee5\u8bf4\u662f\u5fc5\u9700\u7684\u3002<\/span><\/section>\n

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\u7b14\u8005\u5728\u4e2d\u56fd\u79d1\u5b66\u9662\u7406\u8bba\u7269\u7406\u7814\u7a76\u6240\u8bfb\u7814\u7a76\u751f\u65f6\uff0c\u6709\u5e78\u53c2\u52a0\u4e862008\u5e74\u5728\u5317\u4eac\u4e3e\u529e\u7684\u81ea\u65cb\u73bb\u7483\u53ca\u5176\u4ea4\u53c9\u5b66\u79d1\u7684\u56fd\u9645\u7814\u8ba8\u4f1a\uff0c\u7b14\u8005\u81f3\u4eca\u4ecd\u8bb0\u5fc6\u72b9\u65b0\u3002\u5728\u5e15\u91cc\u897f\u62a5\u544a\u7ed3\u675f\u65f6\uff0c\u6709\u4eba\u5411\u4ed6\u8ba8\u6559\u4ed6\u662f\u5982\u4f55\u5f00\u521b\u590d\u672c\u5bf9\u79f0\u7834\u7f3a\u7684\u601d\u60f3\u65f6\uff0c\u5e15\u91cc\u897f\u7b11\u7740\u56de\u7b54\u9053\uff1a\u201c\u56e0\u4e3a\u90a3\u65f6\u5019\u4e0d\u7528\u5230\u5904\u5f00\u4f1a\uff0c\u6211\u80fd\u4e13\u6ce8\u4e8e\u4e00\u4ef6\u4e8b\u60c5\u201d<\/span>\uff08\u5927\u610f\uff09<\/span>\u3002\u8fd9\u8bf4\u660e\uff0c\u8981\u5b8c\u6210\u4e00\u4ef6\u6709\u6df1\u523b\u5f71\u54cd\u529b\u7684\u4e8b\u60c5\uff0c\u9700\u8981\u7684\u4e13\u6ce8\u4e0e\u5927\u91cf\u7684\u65f6\u95f4\u548c\u7cbe\u529b\u4e0a\u7684\u6295\u5165\u7b49\u540c\u3002\u5f53\u7136\uff0c\u524d\u63d0\u662f\u79d1\u5b66\u5bb6\u5173\u6ce8\u91cd\u8981\u7684\u79d1\u5b66\u95ee\u9898\uff0c\u5e76\u4e14\u4e0e\u67d0\u4e2a\u7814\u7a76\u9886\u57df\u4e00\u8d77\u6210\u957f<\/span>\uff08\u4e0d\u662f\u8001\u5316\uff09<\/span>\u3002\u53ef\u89c1\u79d1\u5b66\u5bb6\u4e00\u751f\u80fd\u505a\u6210\u4e00\u4ef6\u91cd\u8981\u7684\u4e8b\u60c5\uff0c\u5c31\u5df2\u7ecf\u975e\u5e38\u4e86\u4e0d\u8d77\u4e86\uff01\u5e15\u91cc\u897f\u5f00\u521b\u7684\u9886\u57df\u957f\u671f\u6765\u770b\u662f\u5c0f\u4f17\u65b9\u5411\uff0c\u4f46\u4ed6\u51e0\u5341\u5e74\u5982\u4e00\u65e5\u5730\u575a\u6301\uff0c\u8ba9\u81ea\u65cb\u73bb\u7483\u7814\u7a76\u7684\u6d93\u6d93\u7ec6\u6d41\u7ec8\u6210\u5927\u6cb3\uff0c\u8fd9\u79cd\u7cbe\u795e\u5c24\u5176\u503c\u5f97\u6709\u5fd7\u4e8e\u79d1\u5b66\u63a2\u7d22\u7684\u5e74\u8f7b\u4eba\u5b66\u4e60\uff01<\/span><\/section>\n

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2. \u200d\u590d\u672c\u5bf9\u79f0\u7834\u7f3a\u5bf9\u4ea4\u53c9\u5b66\u79d1\u7684\u5f71\u54cd<\/span><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u590d\u672c\u5bf9\u79f0\u7834\u7f3a\u672c\u5c5e\u4e8e\u975e\u5e38\u62bd\u8c61\u7684\u6570\u5b66\u7269\u7406\u6982\u5ff5\uff0c\u4f4640\u5e74\u6765\uff0c\u6211\u4eec\u96be\u4ee5\u7f6e\u4fe1\u5730\u770b\u5230\u5b83\u5e7f\u6cdb\u5730\u5b58\u5728\u4e8e\u5404\u4ea4\u53c9\u5b66\u79d1\u9886\u57df\uff0c\u751a\u81f3\u5f71\u54cd\u4e86\u6982\u7387\u8bba\u7684\u7814\u7a76\u5206\u652f\u3002\u63a5\u4e0b\u6765\u7b80\u8ff0\u4e00\u4e0b\u590d\u672c\u5bf9\u79f0\u7834\u7f3a\u5728\u795e\u7ecf\u7f51\u7edc\u53ca\u4f18\u5316\u95ee\u9898\u7814\u7a76\u65b9\u9762\u7684\u5f71\u54cd\u3002\u795e\u7ecf\u7f51\u7edc\u662f\u5f53\u524d\u79d1\u5b66\u7814\u7a76\u8303\u5f0f<\/span>\uff08AI for Science\uff09<\/span>\u7684\u57fa\u672c\u5de5\u5177\uff0c\u800c\u4f18\u5316\u95ee\u9898\u66f4\u662f\u975e\u5e38\u53e4\u8001\u7684\u5b66\u79d1\u65b9\u5411\u3002<\/span>
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3.1 \u795e\u7ecf\u7f51\u7edc\u7684\u7406\u8bba\u7814\u7a76<\/span><\/strong><\/span><\/strong><\/strong><\/span><\/section>\n

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\u5e15<\/span>\u91cc\u897f\u5f00\u521b\u7684\u590d\u672c\u5bf9\u79f0\u7834\u7f3a\u7684\u7814\u7a76\u8303\u5f0f\uff0c\u662f\u5176\u83b7\u5f97\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u7684\u91cd\u8981\u539f\u56e0\u3002<\/span>\u8be5\u8303\u5f0f\u57281980\u5e74\u4ee3\u4e2d\u671f\u5c31\u5df2\u5ef6\u4f38\u5230\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7684\u7406\u8bba\u7814\u7a76\u3002<\/span>\u8fd9\u5bf9\u4e8e\u5f53\u524d\u4eba\u5de5\u667a\u80fd\u7684\u57fa\u7840\u7406\u8bba\u7814\u7a76\u4e0d\u4e4f\u5177\u6709\u53c2\u8003\u4ef7\u503c\u3002<\/span><\/span><\/section>\n

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\u65e9\u671f\u7684\u7814\u7a76\u96c6\u4e2d\u4e8e\u5206\u6790\u8054\u60f3\u8bb0\u5fc6\u7f51\u7edc\u3002\u8fd9\u7c7b\u7f51\u7edc\u662f\u6839\u636e\u795e\u7ecf\u79d1\u5b66\u7684\u8d6b\u5e03\u5f8b\u6765\u8bbe\u8ba1\u7684\u7b80\u5355\u5faa\u73af\u795e\u7ecf\u7f51\u7edc\uff0c\u5b83\u80fd\u591f\u63d0\u53d6\u90e8\u5206\u88ab\u7834\u574f\u7684\u8bb0\u5fc6\u6a21\u5f0f\uff0c\u4ece\u800c\u6a21\u62df\u5927\u8111\u7684\u8054\u60f3\u8bb0\u5fc6\u529f\u80fd\u3002\u590d\u672c\u65b9\u6cd5\u7684\u4e3b\u8981\u8d21\u732e\u5728\u4e8e\u89e3\u6790\u4e86\u8054\u60f3\u8bb0\u5fc6\u7684\u76f8\u56fe\uff0c\u53d1\u73b0\u4e86\u8bb0\u5fc6\u76f8\u3001\u987a\u78c1\u76f8\u548c\u81ea\u65cb\u73bb\u7483\u76f8\uff0c\u5e76\u4e14\u53d1\u73b0\u901a\u8fc7\u8bb0\u5fc6\u76f8\u7684\u8f6c\u53d8\u90fd\u662f\u4e00\u7ea7\u76f8\u53d8 [8]\u3002\u8fd9\u4e2a\u5de5\u4f5c\u4f7f\u5f97\u7edf\u8ba1\u7269\u7406\u7b2c\u4e00\u6b21\u80fd\u591f\u6df1\u523b\u7406\u89e3\u590d\u6742\u7684\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u4e0e\u529f\u80fd\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u5e76\u7531\u6b64\u5f00\u542f\u8ba1\u7b97\u795e\u7ecf\u79d1\u5b66\u8fd9\u4e00\u5b66\u79d1\u3002\u505a\u51fa\u8fd9\u4e00\u5f00\u521b\u6027\u5de5\u4f5c\u7684\u79d1\u5b66\u5bb6\u4e4b\u4e00\uff0c\u610f\u5927\u5229\u7406\u8bba\u7269\u7406\u5b66\u5bb6\u963f\u7c73\u7279<\/span>\uff08D. Amit\uff09<\/span>\u66f4\u662f\u57281989\u5e74\u5c31\u51fa\u7248\u4e86\u76f8\u5173\u5b66\u672f\u4e13\u8457\uff0c\u5c06\u5176\u4e00\u751f\u90fd\u8d21\u732e\u7ed9\u4e86\u8ba1\u7b97\u795e\u7ecf\u79d1\u5b66\u7684\u65e9\u671f\u53d1\u5c55\uff0c\u57f9\u517b\u4e86\u5f88\u591a\u8fd9\u4e00\u9886\u57df\u7684\u9886\u5bfc\u8005\u3002\u53e6\u4e00\u79d1\u5b66\u5bb6\u4f50\u59c6\u6ce2\u6797\u65af\u57fa<\/span>\uff08H. Sompolinsky\uff09<\/span>\u5728\u4ee5\u8272\u5217\u521b\u5efa\u4e86\u57c3\u5fb7\u8499\u548c\u8389\u8389\u00b7\u8428\u592b\u62c9\u8111\u79d1\u5b66\u4e2d\u5fc3\uff0c\u5e76\u5927\u529b\u53d1\u5c55\u795e\u7ecf\u7269\u7406\u5b66\uff0c\u6210\u4e3a\u4e86\u6a2a\u8d2f\u7edf\u8ba1\u7269\u7406\u3001\u795e\u7ecf\u7f51\u7edc\u548c\u8111\u79d1\u5b66\u9886\u57df\u7684\u5927\u5e08\u7ea7\u4eba\u7269\u3002 <\/span><\/section>\n

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\u540c\u4e00\u65f6\u671f\uff0c\u53d7\u963f\u7c73\u7279\u5f71\u54cd\u7684\u7c92\u5b50\u7269\u7406\u5b66\u5bb6\u963f\u535a\u7279<\/span>\uff08L. Abbott\uff09<\/span>\u4e5f\u57281990\u5e74\u4ee3\u8f6c\u5411\u795e\u7ecf\u7f51\u7edc\u548c\u8111\u79d1\u5b66\u7814\u7a76\uff0c\u968f\u540e\u5728\u54e5\u4f26\u6bd4\u4e9a\u5927\u5b66\u521b\u5efa\u4e86\u4eab\u8a89\u4e16\u754c\u7684\u624e\u514b\u66fc\u5927\u8111\u884c\u4e3a\u7814\u7a76\u6240\uff0c\u57f9\u517b\u4e86\u8fd9\u4e00\u9886\u57df\u76f8\u5f53\u6d3b\u8dc3\u7684\u5f88\u591a\u5e74\u8f7b\u5b66\u8005\u3002\u540c\u57281980\u5e74\u4ee3\u4e2d\u671f\uff0c\u52a0\u5fb7\u7eb3<\/span>\uff08E. Gardner\uff09<\/span>\u4e5f\u4ee5\u4e00\u5df1\u4e4b\u529b\u521b\u5efa\u4e86\u5728\u611f\u77e5\u673a<\/span>\uff08\u76d1\u7763\u5b66\u4e60\u7684\u5178\u578b\u7f51\u7edc\uff09<\/span>\u4e2d\u7684\u52a0\u5fb7\u7eb3\u7406\u8bba [9]\uff0c\u8be5\u7406\u8bba\u4e5f\u662f\u57fa\u4e8e\u590d\u672c\u5206\u6790\u7684\u7814\u7a76\u8303\u5f0f\uff0c\u5176\u5f3a\u5927\u4e4b\u5904\u5728\u4e8e\u80fd\u591f\u5b9a\u91cf\u8ba1\u7b97\u795e\u7ecf\u7f51\u7edc\u8ba1\u7b97\u7684\u7269\u7406\u6781\u9650\uff0c\u6bd4\u5982\u5b58\u50a8\u5bb9\u91cf\u3001\u6700\u5c0f\u6570\u636e\u91cf\u3001\u7b97\u6cd5\u5b66\u4e60\u6781\u9650\u7b49 [5]\u3002<\/span><\/section>\n

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1995\u5e74\uff0c\u5f17\u6717\u5179<\/span>\uff08S. Franz\uff09<\/span>\u548c\u5e15\u91cc\u897f\u4e3a\u7814\u7a76\u81ea\u65cb\u73bb\u7483\u63d0\u51fa\u4e86Franz-Parisi\u52bf [10]\uff0c\u5de7\u5999\u5730\u5c06\u7edf\u8ba1\u7269\u7406\u6784\u578b\u7a7a\u95f4\u7684\u51e0\u4f55\u7ed3\u6784\u7eb3\u5165\u70ed\u529b\u5b66\u52bf\u51fd\u6570\u7684\u8ba1\u7b97\u30022014\u5e74\uff0c\u7b14\u8005\u5c06Franz-Parisi\u52bf\u7528\u4e8e\u5206\u6790\u611f\u77e5\u673a\u5b66\u4e60\u7684\u8ba1\u7b97\u590d\u6742\u6027\u8d77\u6e90\uff0c\u63ed\u5f00\u4e86\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u6001\u7a7a\u95f4\u7684\u51e0\u4f55\u5206\u6790\u5e8f\u5e55 [11]\u3002\u968f\u540e\u5b66\u754c\u63d0\u51fa\u5c40\u57df\u71b5\u7684\u6982\u5ff5 [12]\uff0c\u62d3\u5c55\u4e86\u4eba\u4eec\u5bf9\u795e\u7ecf\u8ba1\u7b97\u7684\u8ba4\u77e5\u8fb9\u754c\u3002\u4f20\u7edf\u7684\u5e73\u8861\u6001\u5206\u6790\u663e\u793a\uff0c\u8fd9\u4e9b\u51e0\u4f55\u5b64\u7acb\u7684\u6001\u57fa\u672c\u662f\u96f6\u71b5\u7684\uff1b\u7136\u800c\uff0c\u7ecf\u9a8c\u8bbe\u8ba1\u7684\u5b66\u4e60\u7b97\u6cd5\u52a8\u529b\u5b66\u5f80\u5f80\u88ab\u6001\u7a7a\u95f4\u7684\u5c11\u6570\u7a20\u5bc6\u533a\u57df\u6240\u5438\u5f15\uff0c\u800c\u8fd9\u4e9b\u533a\u57df\u5bf9\u795e\u7ecf\u7f51\u7edc\u7684\u6cdb\u5316<\/span>\uff08\u5373\u4e3e\u4e00\u53cd\u4e09\u80fd\u529b\uff09<\/span>\u6027\u80fd\u6709\u5173\u952e\u6027\u7684\u5f71\u54cd [12]\u3002<\/span><\/section>\n

<\/section>\n
\u9664\u6b64\u4e4b\u5916\uff0c\u590d\u672c\u65b9\u6cd5\u8fd8\u53ef\u7528\u4e8e\u5bf9\u65e0\u76d1\u7763\u5b66\u4e60<\/span>\uff08\u5373\u65e0\u5e08\u81ea\u901a\uff09<\/span>\u7684\u7814\u7a76\u3002\u7b14\u8005\u4ece2015\u5e74\u5f00\u59cb\u7740\u529b\u4e8e\u8fd9\u65b9\u9762\u7684\u7406\u8bba\u7814\u7a76\uff0c\u7528\u7b80\u660e\u7684\u6570\u5b66\u548c\u6e05\u6670\u7684\u7269\u7406\u56fe\u50cf\u52fe\u52d2\u51fa\u5b66\u4e60\u8fc7\u7a0b\u7684\u672c\u8d28\u662f\u81ea\u53d1\u5bf9\u79f0\u6027\u7834\u7f3a [13]\u3002\u8fd9\u79cd\u7c7b\u578b\u7684\u7814\u7a76\u8fd8\u6709\u5f88\u591a\uff0c\u90fd\u4e0e\u5e15\u91cc\u897f\u5728\u81ea\u65cb\u73bb\u7483\u7406\u8bba\u7684\u5f00\u521b\u6027\u7814\u7a76\u606f\u606f\u76f8\u5173\u3002<\/span><\/section>\n

<\/section>\n
\u5728\u8fd140\u5e74\u6765\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7684\u7406\u8bba\u7814\u7a76\u4e2d\uff0c\u590d\u672c\u65b9\u6cd5\u53ca\u590d\u672c\u5bf9\u79f0\u7834\u7f3a\u7684\u6982\u5ff5\u626e\u6f14\u7740\u4e0d\u53ef\u6216\u7f3a\u7684\u89d2\u8272\u3002\u5982\u4eca\uff0c\u65e0\u8bba\u5728\u673a\u5668\u5b66\u4e60\u6216\u795e\u7ecf\u79d1\u5b66\u6709\u5efa\u6811\u7684\u79d1\u5b66\u5bb6\u4e2d\uff0c\u6709\u76f8\u5f53\u4e00\u90e8\u5206\u5728\u804c\u4e1a\u751f\u6daf\u65e9\u671f\u66fe\u63a5\u53d7\u8fc7\u7edf\u8ba1\u7269\u7406\u6216\u7269\u7406\u5b66\u7684\u4e25\u683c\u8bad\u7ec3\u3002\u5728\u5e15\u91cc\u897f\u83b7\u5f97\u8bfa\u8d1d\u5c14\u5956\u4e4b\u9645\uff0c\u8bb8\u591a\u8ba1\u7b97\u795e\u7ecf\u79d1\u5b66\u5bb6\u6216\u7406\u8bba\u673a\u5668\u5b66\u4e60\u5b66\u8005\u8868\u8fbe\u4e86\u5bf9\u4ed6\u7684\u795d\u8d3a\u548c\u611f\u6fc0\uff0c\u56e0\u4e3a\u5e15\u91cc\u897f\u7684\u601d\u60f3\u4fc3\u6210\u4e86\u5982\u4eca\u795e\u7ecf\u7f51\u7edc\u7684\u7406\u8bba\u7814\u7a76\u8fd9\u4e00\u4ea4\u53c9\u5b66\u79d1\u7684\u7e41\u8363\uff01<\/span><\/section>\n

<\/section>\n
3.2 \u7ec4\u5408\u4f18\u5316\u7b97\u6cd5\u7684\u7269\u7406\u5206\u6790<\/span><\/strong><\/span><\/strong><\/strong><\/span><\/section>\n

<\/section>\n
21\u4e16\u7eaa\u521d\uff0c\u5e15\u91cc\u897f\u4e0e\u5408\u4f5c\u8005\u7cfb\u7edf\u5730\u63d0\u51fa\u7a7a\u8154\u65b9\u6cd5 [14]\uff0c\u8fd9\u662f\u4e0e\u590d\u672c\u65b9\u6cd5\u76f8\u8f85\u76f8\u6210\u7684\u7269\u7406\u5b66\u57fa\u672c\u65b9\u6cd5\u3002\u7a7a\u8154\u65b9\u6cd5\u7684\u672c\u8d28\u5728\u4e8e\u5206\u6790\u7a00\u758f\u56e0\u5b50\u56fe<\/span>\uff08\u8fd9\u7c7b\u56fe\u4e00\u822c\u6709\u4e24\u79cd\u8282\u70b9\uff0c\u4e00\u79cd\u4ee3\u8868\u53d8\u91cf\u6216\u81ea\u65cb\uff0c\u53e6\u4e00\u79cd\u4ee3\u8868\u7ea6\u675f\u6216\u76f8\u4e92\u4f5c\u7528\uff1b\u5178\u578b\u7684\u8ba1\u7b97\u673a\u79d1\u5b66\u95ee\u9898\uff0c\u6bd4\u5982\u7ec4\u5408\u4f18\u5316\u7684\u968f\u673ak-SAT\u95ee\u9898\u5c31\u53ef\u6620\u5c04\u6210\u8fd9\u6837\u7684\u7269\u7406\u95ee\u9898\uff09<\/span>\u65f6\uff0c\u901a\u8fc7\u5f15\u5165\u56fe\u4e0a\u8282\u70b9\u7684\u865a\u62df\u7f3a\u5931\uff0c\u6784\u9020\u7a7a\u8154\u6982\u7387\u7684\u8fed\u4ee3\u65b9\u7a0b\uff0c\u4ece\u800c\u6c42\u89e3\u4f53\u7cfb\u7684\u81ea\u7531\u80fd\u7b49\u7269\u7406\u91cf\u3002\u8fd9\u7c7b\u7ec4\u5408\u4f18\u5316\u95ee\u9898\u7684\u590d\u6742\u6027\u4e5f\u6df1\u6df1\u5438\u5f15\u5e15\u91cc\u897f\u5bf9\u5176\u8fdb\u884c\u6df1\u5165\u7cfb\u7edf\u7684\u7814\u7a76\u3002\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u4ed6\u4e0e\u5408\u4f5c\u8005\u53d1\u73b0\uff0c\u5904\u4e8eNP-\u5b8c\u5907\u7c7b\u7684\u968f\u673ak-SAT\u95ee\u9898<\/span>\uff08k\u53ef\u4ee5\u7406\u89e3\u4e3a\u81ea\u65cb\u7684\u591a\u4f53\u76f8\u4e92\u4f5c\u7528\uff0cSAT\u53ef\u4ee5\u7406\u89e3\u4e3a\u6c42\u89e3\u80fd\u91cf\u57fa\u6001\uff09<\/span>\u4e5f\u5b58\u5728\u590d\u672c\u5bf9\u79f0\u7834\u7f3a\u76f8\uff0c\u5e76\u4e14\u5728\u590d\u672c\u5bf9\u79f0\u7834\u7f3a\u601d\u60f3\u7684\u6307\u5bfc\u4e0b\uff0c\u5e15\u91cc\u897f\u4e0e\u5408\u4f5c\u8005\u63d0\u51fa\u5168\u65b0\u7684\u7b97\u6cd5\u2014\u2014\u8c03\u67e5\u4f20\u64ad\u6cd5<\/span>\uff08survey propagation\uff09<\/span>\uff0c\u6c42\u89e3\u7ec4\u5408\u4f18\u5316SAT\u95ee\u9898\u57fa\u6001\u7684\u6781\u9650\u903c\u8fd1\u7406\u8bba\u9608\u503c [15]\u3002<\/span><\/section>\n

<\/section>\n
\u4e3a\u4e86\u8868\u5f70\u4ed6\u4eec\u7684\u8d21\u732e\uff0c\u7f8e\u56fd\u7269\u7406\u5b66\u4f1a\u57282016\u5e74\u5c06\u7edf\u8ba1\u7269\u7406\u5b66\u754c\u7684\u91cd\u8981\u5956\u9879\u201c\u6602\u8428\u683c\u5956\u201d\u6388\u4e88\u5e15\u91cc\u897f\u4e0e\u5176\u5408\u4f5c\u8005\u3002\u8fd9\u663e\u793a\u4e86\u7edf\u8ba1\u7269\u7406\u4e0e\u8ba1\u7b97\u673a\u79d1\u5b66\u751a\u81f3\u4fe1\u606f\u79d1\u5b66\u7684\u57fa\u672c\u95ee\u9898\u5b58\u5728\u7740\u6df1\u523b\u7684\u8054\u7cfb\u3002<\/span><\/section>\n

<\/section>\n
3.3 \u590d\u6742\u7cfb\u7edf\u7684\u7814\u7a76\u8def\u5728\u4f55\u65b9\uff1a\u667a\u80fd\u8d77\u6e90<\/span><\/strong><\/span><\/strong><\/strong><\/span><\/section>\n

<\/section>\n
\u5f53\u4eca, \u975e\u5e38\u590d\u6742\u7684\u4e24\u7c7b\u7cfb\u7edf\u2014\u2014\u4ee5\u8fde\u63a5\u4e3b\u4e49\u4e3a\u4ee3\u8868\u7684\u4eba\u5de5\u667a\u80fd\u548c\u4eba\u8111\uff0c\u4ecd\u7136\u7f3a\u4e4f\u4ece\u539f\u7406\u5c42\u9762\u4e0a\u53bb\u7406\u89e3\u7684\u7a81\u7834\u3002<\/span>\u5176\u4e2d\u4eba\u5de5\u667a\u80fd\u6beb\u65e0\u7591\u95ee\u5df2\u7ecf\u5728\u91cd\u5851\u4eba\u7c7b\u793e\u4f1a\u7ecf\u6d4e\u7684\u65b9\u65b9\u9762\u9762\uff0c\u800c\u4eba\u7c7b\u5bf9\u4e8e\u5927\u8111\u7684\u7406\u89e3\u4e5f\u5fc5\u5c06\u5bf9\u793e\u4f1a\u6587\u660e\u4ea7\u751f\u4e0d\u53ef\u4f30\u91cf\u7684\u5f71\u54cd\u3002<\/span>\u6700\u8fd1\uff0c\u79d1\u5b66\u63a2\u7d22\u5956\u5386\u5c4a\u5f97\u4e3b\u8bc4\u9009\u51fa\u7684\u5341\u5927\u79d1\u5b66\u6280\u672f\u95ee\u9898\u7684\u524d3\u4e2a\u5206\u522b\u4e3a\uff1a<\/span>\u2460\u4eba\u7c7b\u7684\u610f\u8bc6\uff0c\u4ee5\u53ca\u5b66\u4e60\u548c\u8bb0\u5fc6\u7684\u751f\u7269\u57fa\u7840\u4ece\u4f55\u800c\u6765\uff1b<\/span>\u2461\u4eba\u8111\u548c\u673a\u5668\u662f\u5426\u80fd\u5b9e\u73b0\u76f4\u63a5\u901a\u8baf\uff1b<\/span>\u2462\u901a\u7528\u4eba\u5de5\u667a\u80fd\u662f\u5426\u80fd\u5b9e\u73b0\u3002<\/span>\u5bfb\u627e\u8fd9\u4e9b\u95ee\u9898\u7684\u7b54\u6848\u5e76\u975e\u6613\u4e8b\uff0c\u5c3d\u7ba1\u6700\u540e\u7b54\u6848\u53ef\u80fd\u5f88\u7b80\u5355\u3002<\/span> <\/span><\/span><\/section>\n

<\/section>\n
\u7edf\u8ba1\u7269\u7406\u65b9\u6cd5\u662f\u4e00\u5ea7\u67b6\u8d77\u5fae\u89c2\u4f5c\u7528\u5230\u5b8f\u89c2\u6d8c\u73b0\u7684\u6865\u6881\uff0c\u800c\u5e15\u91cc\u897f\u5728\u65e0\u5e8f\u7cfb\u7edf\u7814\u7a76\u7684\u5960\u57fa\u6027\u8d21\u732e\uff0c\u5c06\u6307\u5f15\u7269\u7406\u3001\u6570\u5b66\u3001\u673a\u5668\u5b66\u4e60\u4e0e\u7406\u8bba\u8111\u79d1\u5b66\u4ea4\u53c9\u65b9\u5411\u7684\u79d1\u5b66\u5bb6\u7834\u89e3\u4eba\u5de5\u667a\u80fd\u548c\u4eba\u8111\u7684\u5965\u79d8\u3002\u673a\u5668\u667a\u80fd\u548c\u751f\u7269\u667a\u80fd\u662f\u7531\u975e\u5e38\u590d\u6742\u7684\u7ec4\u5143<\/span>\uff08\u6bd4\u5982\u795e\u7ecf\u7ec6\u80de\u3001\u795e\u7ecf\u7a81\u89e6\u7b49\uff09<\/span>\uff0c\u901a\u8fc7\u65f6\u7a7a\u591a\u5c42\u7ea7\u7684\u76f8\u4e92\u4f5c\u7528\u6240\u5f62\u6210\u7684\u96c6\u4f53\u884c\u4e3a\uff0c\u5176\u4e2d\u7cbe\u786e\u7684\u6570\u5b66\u673a\u5236\u5f88\u96be\u4e00\u76ee\u4e86\u7136\u3002\u5728\u8fd9\u6761\u8270\u8f9b\u7684\u6c42\u7d22\u9053\u8def\u4e0a\uff0c\u517c\u5177\u7269\u7406\u6df1\u523b\u6027\u548c\u6570\u5b66\u7f8e\u7684\u7406\u8bba\u65e0\u7591\u5c06\u5f00\u542f\u672c\u4e16\u7eaa\u5728\u8ba4\u77e5\u79d1\u5b66\u65b9\u9762\u7684\u79d1\u5b66\u9769\u547d\uff0c\u8ba9\u4ece\u7b2c\u4e00\u6027\u539f\u7406\u51fa\u53d1\u8bbe\u8ba1\u667a\u80fd\u4e16\u754c\u53d8\u6210\u4e86\u53ef\u80fd\u3002\u4e5f\u53ea\u6709\u5230\u4e86\u90a3\u4e2a\u65f6\u523b\uff0c\u5c31\u50cf\u9ea6\u514b\u65af\u97e6\u4ece\u5176\u65b9\u7a0b\u7ec4\u5bfc\u51fa\u5149\u662f\u7535\u78c1\u6ce2\u90a3\u6837\uff0c\u4eba\u7c7b\u6587\u660e\u4e5f\u5fc5\u5c06\u6b65\u5165\u4e00\u4e2a\u5d2d\u65b0\u7684\u65f6\u4ee3\uff01<\/span><\/section>\n

<\/section>\n

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\u9ec4\u6d77\u5e73\uff1a\u526f\u6559\u6388\uff0c\u4e2d\u5c71\u5927\u5b66\u7269\u7406\u5b66\u9662\uff0c\u5e7f\u5dde 510275\u3002huanghp7@mail.sysu.edu.cn<\/span><\/section>\n
Huang Haiping: Associate Professor, School of Physics, Sun Yat-sen University, Guangzhou 510275.<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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<\/p>\n

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

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<\/p>\n

    \n
  1. \n

    Edwards S F, Anderson P W. Theory of spin glasses. Journal of Physics F, 1975, 5(5): 965-974. <\/span><\/p>\n<\/li>\n

  2. \n

    Sherrington D, Kirkpatrick S. Solvable model of a spin-glass. Physical Review Letters, 1975, 35(26): 1792-1976.<\/span><\/p>\n<\/li>\n

  3. \n

    Almeida J, Thouless D J. Stability of the Sherrington-Kirkpatrick solution of a spin glass model. Journal of Physics A General Physics, 2001, 11(5): 983.<\/span><\/p>\n<\/li>\n

  4. \n

    Parisi G. Infinite number of order parameters for spin-glasses. Physical Review Letters, 1979, 43(23): 1754-1756.<\/span><\/p>\n<\/li>\n

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    M\u00e9zard M, Parisi G, Zecchina R. Analytic and algorithmic solution of random satisfiability problems. Science, 2002, 297: 812-815.<\/span><\/p>\n<\/li>\n<\/ol>\n


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