{"id":1089,"date":"2014-03-04T14:52:43","date_gmt":"2014-03-04T06:52:43","guid":{"rendered":"http:\/\/systemsci.org\/jinshanw\/?p=1089"},"modified":"2017-11-04T16:19:11","modified_gmt":"2017-11-04T08:19:11","slug":"%e5%b9%bf%e4%b9%89%e6%8a%95%e5%85%a5%e4%ba%a7%e5%87%ba%e5%88%86%e6%9e%90%e5%92%8c%e7%bb%86%e8%8a%82%e6%8a%95%e5%85%a5%e4%ba%a7%e5%87%ba%e5%88%86%e6%9e%90","status":"publish","type":"post","link":"https:\/\/www.systemsci.org\/jinshanw\/2014\/03\/04\/%e5%b9%bf%e4%b9%89%e6%8a%95%e5%85%a5%e4%ba%a7%e5%87%ba%e5%88%86%e6%9e%90%e5%92%8c%e7%bb%86%e8%8a%82%e6%8a%95%e5%85%a5%e4%ba%a7%e5%87%ba%e5%88%86%e6%9e%90\/","title":{"rendered":"\u5e7f\u4e49\u6295\u5165\u4ea7\u51fa\u5206\u6790\u548c\u7ec6\u8282\u6295\u5165\u4ea7\u51fa\u5206\u6790"},"content":{"rendered":"

\u5e0c\u671b\u89e3\u51b3\u7684\u6839\u672c\u95ee\u9898\uff1a<\/p>\n

    \n
  1. \u4ea7\u4e1a\u90e8\u95e8\u4e4b\u95f4\u7684\u76f8\u4e92\u5173\u7cfb1\u3002\u5982\u679c\u6211\u4eec\u5e0c\u671b\u67d0\u4e2a\u4ea7\u4e1a\u90e8\u95e8\u7684\u603b\u4ea7\u51fa\uff08\u5305\u542b\u4e2d\u95f4\u6d88\u8017\uff09\u6216\u8005\u662f\u51c0\u4ea7\u51fa\uff08\u4e0d\u5305\u542b\u4e2d\u95f4\u6d88\u8017\uff0c\u53ea\u8ba1\u7b97\u76f4\u63a5\u6d88\u8d39\uff09\u6709\u4e00\u4e2a\u5355\u4f4d\u7684\u589e\u52a0\uff0c\u6211\u4eec\u9700\u8981\u589e\u52a0\u7684\u5404\u4e2a\u5176\u4ed6\u4ea7\u4e1a\u90e8\u95e8\u7684\u603b\u6295\u5165\u6216\u8005\u51c0\u6295\u5165\uff08\u4e0d\u5305\u542b\u901a\u8fc7\u4e2d\u95f4\u751f\u4ea7\u8fc7\u7a0b\u5f97\u5230\u7684\u6295\u5165\uff09\u662f\u591a\u5c11\u3002\u4f8b\u5982\uff0c\u5728\u5305\u542b\u6700\u7ec8\u6d88\u8d39\u548c\u52b3\u52a8\u529b\u7684\u5f00\u653e\u7cfb\u7edf\u7684\u6295\u5165\u4ea7\u51fa\u4e2d\uff0c\u8fd9\u4e2a\u95ee\u9898\u5c31\u662f\uff1a\u4e3a\u4e86\u5f97\u5230\u6700\u7ec8\u6d88\u8d39\u7684\u67d0\u4e00\u4e2a\u4ea7\u54c1\u7684\u4e00\u4e2a\u5355\u4f4d\u7684\u589e\u52a0\uff0c\u9700\u8981\u52b3\u52a8\u529b\u90e8\u95e8\u5728\u5404\u4e2a\u4ea7\u4e1a\u4e0a\u589e\u52a0\u591a\u5c11\u6295\u5165\u3002\u5728\u5c01\u95ed\u7cfb\u7edf\u4e2d\uff0c\u8fd9\u4e2a\u95ee\u9898\u5982\u4f55\u56de\u7b54\u8fd8\u4e0d\u77e5\u9053\u3002<\/li>\n
  2. \u4ea7\u4e1a\u90e8\u95e8\u4e4b\u95f4\u7684\u76f8\u4e92\u5173\u7cfb2\u3002\u5982\u679c\u6211\u4eec\u51cf\u5c11\u67d0\u4e2a\u4ea7\u4e1a\u90e8\u95e8\u7684\u603b\u6295\u5165\uff08\u5305\u542b\u4e2d\u95f4\u6295\u5165\uff09\u6216\u8005\u662f\u51c0\u6295\u5165\uff08\u4e0d\u5305\u542b\u4e2d\u95f4\u6295\u5165\uff0c\u53ea\u8ba1\u7b97\u76f4\u63a5\u6295\u5165\uff09\u4e00\u4e2a\u5355\u4f4d\uff0c\u5404\u4e2a\u5176\u4ed6\u4ea7\u4e1a\u90e8\u95e8\u7684\u51c0\u4ea7\u51fa\uff08\u4e0d\u5305\u542b\u901a\u8fc7\u6295\u5165\u7ed9\u4e2d\u95f4\u751f\u4ea7\u8fc7\u7a0b\u7684\u90e8\u5206\uff09\u548c\u603b\u4ea7\u51fa\u662f\u591a\u5c11\u3002\u4f8b\u5982\uff0c\u5728\u5305\u542b\u6700\u7ec8\u6d88\u8d39\u548c\u52b3\u52a8\u529b\u7684\u5f00\u653e\u7cfb\u7edf\u7684\u6295\u5165\u4ea7\u51fa\u4e2d\uff0c\u8fd9\u4e2a\u95ee\u9898\u5c31\u662f\uff1a\u51cf\u5c11\u52b3\u52a8\u529b\u90e8\u95e8\u5728\u67d0\u4e2a\u4ea7\u4e1a\u4e0a\u7684\u6295\u5165\u4e00\u4e2a\u5355\u4f4d\uff0c\u6240\u6709\u4ea7\u54c1\u7684\u603b\u4ea7\u91cf\u548c\u51c0\u4ea7\u91cf\u5982\u4f55\u53d8\u5316\u3002<\/li>\n
  3. \u4ea7\u4e1a\u90e8\u95e8\u4e4b\u95f4\u7684\u76f8\u4e92\u5173\u7cfb3\u3002\u5982\u679c\u6211\u4eec\u5e0c\u671b\u5728\u6574\u4e2a\u7cfb\u7edf\u4e2d\u53bb\u6389\u67d0\u4e2a\u4ea7\u4e1a\u90e8\u95e8\uff0c\u6574\u4e2a\u7cfb\u7edf\u4e2d\u53d7\u5f71\u54cd\u6700\u5927\u7684\u90e8\u95e8\u662f\u54ea\u4e00\u4e2a\uff1f<\/li>\n
  4. \u4ea7\u4e1a\u90e8\u95e8\u7684\u5f71\u54cd\u529b\u5ea6\u91cf\u3002\u54ea\u4e00\u4e2a\u4ea7\u4e1a\u90e8\u95e8\u5bf9\u6574\u4e2a\u7cfb\u7edf\u6700\u91cd\u8981\uff1f<\/li>\n<\/ol>\n

    \u8fd9\u4e9b\u95ee\u9898\u53ef\u4ee5\u901a\u8fc7\u6295\u5165\u4ea7\u51fa\u77e9\u9635\uff08\u603b\u6295\u5165\u4e0e\u603b\u6295\u5165\u4e4b\u95f4\u7684\u5173\u7cfb\u6216\u8005\u603b\u4ea7\u51fa\u4e0e\u603b\u4ea7\u51fa\u4e4b\u95f4\u7684\u5173\u7cfb\uff09\uff0c\u4e5f\u53ef\u4ee5\u901a\u8fc7\u6982\u7387\u8f6c\u79fb\u77e9\u9635\uff08\u603b\u6295\u5165\u4e0e\u603b\u4ea7\u51fa\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u6216\u8005\u603b\u4ea7\u51fa\u4e0e\u603b\u6295\u5165\u4e4b\u95f4\u7684\u5173\u7cfb\uff09\u6765\u8ba8\u8bba\u3002\u6570\u5b66\u624b\u6bb5\u4e0d\u4e00\u6837\uff0c\u5305\u542b\u7684\u4fe1\u606f\u5e94\u8be5\u662f\u4e00\u6837\u7684\u3002<\/p>\n

    \u6240\u6709\u7684\u6295\u5165\u4ea7\u51fa\u5206\u6790\u4ece\u8fd9\u91cc\u5f00\u59cb\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u4ea7\u4e1a\u90e8\u95e8\u7684\u96c6\u5408\\(\\left\\{j=1,\\cdots,N\\right\\}\\)\uff0c\u6bcf\u4e00\u4e2a\u90e8\u95e8\u4e4b\u95f4\u7684\u6295\u5165\u4ea7\u51fa\u7edd\u5bf9\u91cf\\(\\left\\{x^{i}_{j}\\right\\}\\)\uff0c\u8868\u793a\u90e8\u95e8\\(i\\)\u6295\u5165\u5230\u90e8\u95e8\\(j\\)\u7684\u4ea7\u54c1\\(i\\)\u7684\u6570\u91cf\u3002\u8fd9\u91cc\u4ea7\u54c1\u548c\u90e8\u95e8\u76f8\u4e92\u8ba4\u540c\u3002\u6211\u4eec\u4f1a\u8ba8\u8bba\u90e8\u95e8\u548c\u4ea7\u54c1\u6709\u533a\u522b\u7684\u66f4\u52a0\u7ec6\u8282\u7684\u6295\u5165\u4ea7\u51fa\u5206\u6790\u3002<\/p>\n

    \u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\uff1a<\/p>\n

      \n
    1. \u53cd\u5411\u6295\u5165\u4ea7\u51fa\u77e9\u9635
      \n\\[B^{i}_{j}=\\frac{x^{i}_{j}}{X^{j}},\\hspace{2cm} (1)\\]
      \n\u5176\u4e2d\\(X^{i}=\\sum_{j=1}^{N}x^{i}_{j}\\)\u3002\u4e8e\u662f\uff0c\u6211\u4eec\u6709
      \n\\[\\sum_{j=1}^{N}B^{i}_{j}X^{j}=X^{i}\\Longrightarrow B^{a}_{b}X^{b}=X^{a},\\hspace{2cm} (2)\\]
      \n\u4ece\u8fd9\u91cc\u6211\u4eec\u770b\u51fa\u6765\uff0c\\(B\\)\u7684\u53f3\u672c\u5f81\u5411\u91cf\u662f\u5e73\u5eb8\u7684\uff0c\u5c31\u662f\\(X^{a}\\)\u3002<\/p>\n

      \u5982\u679c\u6211\u4eec\u5728\u53d6\u548c\u4e2d\u53bb\u6389\u5176\u4e2d\u7684\u67d0\u4e00\u4e2a\u90e8\u95e8\\(k\\)\uff0c\u5219
      \n\\[\\sum_{j\\neq k}B^{i}_{j}X^{j}+x^{i}_{k}=X^{i}\\Longrightarrow B^{\\left(-k\\right)}X^{\\left(-k\\right)}+Y_{\\left(k\\right)} = X^{\\left(-k\\right)}. \\]
      \n\u4e8e\u662f\uff0c
      \n\\[X^{\\left(-k\\right)} = \\left(1-B^{\\left(-k\\right)}\\right)^{-1}Y_{\\left(k\\right)}, \\hspace{2cm} (12)\\]
      \n\u5e76\u4e14
      \n\\[X^{k} = \\sum_{j\\neq k}B^{k}_{j}X^{\\left(-k\\right),j}+x^{k}_{k}. \\]
      \n\u8fd9\u91cc\u7684\u65b9\u7a0b\uff0812\uff09\u5c31\u662fLoentief\u6295\u5165\u4ea7\u51fa\u7684\u6838\u5fc3\u516c\u5f0f\u3002\u5728\u90a3\u91cc\uff0c\u901a\u5e38\u628a\u90e8\u95e8\\(k\\)\u53d6\u4f5c\u6700\u7ec8\u9700\u6c42\u90e8\u95e8\\(N\\)\u3002\u8fd9\u4e2a\u8868\u8fbe\u5f0f\u53ef\u4ee5\u7528\u6765\u56de\u7b54\u9884\u671f\\(k\\)\u90e8\u95e8\u7684\u4ea7\u80fd\u6709\u4e00\u4e2a\u5355\u4f4d\u7684\u589e\u52a0\u7684\u60c5\u51b5\u4e0b\uff0c\u7cfb\u7edf\u7684\u5176\u4ed6\u90e8\u95e8\u7684\u4ea7\u80fd\u5982\u4f55\u53d8\u5316\u3002\u5728\u8fd9\u4e2a\u6761\u4ef6\u4e0b\uff0c\u6211\u4eec\u80fd\u591f\u8ba1\u7b97\u51fa\u6765\u6240\u6709\u7684\\(\\Delta x^{i}_{j}\\)\u4e8e\u662f\u4e5f\u5c31\u5f97\u5230\u4e86\u6240\u6709\u7684\\(\\Delta X_{j}\\)\uff0c\u6240\u6709\u90e8\u95e8\u7684\u9700\u8981\u7684\u6295\u5165\u7684\u589e\u91cf\u3002\u8fd9\u6837\uff0c\u6211\u4eec\u5c31\u76f8\u5f53\u4e8e\u56de\u7b54\u4e86\uff1a\u5982\u679c\u9700\u8981\u589e\u52a0\\(k\\)\u90e8\u95e8\u7684\u4e00\u4e2a\u5355\u4f4d\u51c0\u4ea7\u51fa\uff0c\u9700\u8981\u7684\u5404\u90e8\u95e8\u7684\u603b\u6295\u5165\u662f\u591a\u5c11\u3002\u5982\u679c\u6211\u4eec\u8fd8\u80fd\u591f\u77e5\u9053\u521d\u671f\u989d\u5916\u6295\u5165\u7684\u591a\u5c11\u5c31\u66f4\u597d\u4e86\uff0c\u4e5f\u5c31\u662f\u53bb\u6389\u4e2d\u95f4\u751f\u4ea7\u8fc7\u7a0b\u4ea7\u751f\u7684\u6295\u5165\u3002\u6709\u53ef\u80fd\u628a\\(F\\)\u548c\\(B\\)\u5408\u8d77\u6765\u53ef\u4ee5\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002\n<\/li>\n

    2. \u6b63\u5411\u6295\u5165\u4ea7\u51fa\u77e9\u9635
      \n\\[F^{i}_{j}=\\frac{x^{i}_{j}}{X_{i}},\\hspace{2cm} (3)\\]
      \n\u5176\u4e2d\\(X_{i}=\\sum_{j=1}^{N}x^{j}_{i}\\)\u3002\u76f8\u5e94\u5730\uff0c\u6211\u4eec\u6709
      \n\\[\\sum_{j=1}^{N}X_{i}F^{i}_{j}=X_{j}\\Longrightarrow X_{a}F^{a}_{b}=X_{b},\\hspace{2cm} (4)\\]
      \n\u4ece\u8fd9\u91cc\u6211\u4eec\u770b\u51fa\u6765\uff0c\\(F\\)\u7684\u5de6\u672c\u5f81\u5411\u91cf\u662f\u5e73\u5eb8\u7684\uff0c\u5c31\u662f\\(X_{a}\\)\u3002\n<\/li>\n
    3. \u6b63\u5411\u6982\u7387\u8f6c\u79fb\u77e9\u9635
      \n\\[MF^{i}_{j}=\\frac{x^{i}_{j}}{X_{j}}.\\hspace{2cm} (5)\\]
      \n\u5982\u679c\u6211\u4eec\u8fd8\u662f\u7167\u7740\u4e0a\u9762\u7684\u65b9\u5f0f\u4f01\u56fe\u5199\u51fa\u672c\u5f81\u5411\u91cf\u7684\u5f62\u5f0f\uff0c\u6211\u4eec\u6709
      \n\\[\\sum_{j=1}^{N}MF^{i}_{j}X_{j}=X^{i}.\\hspace{2cm} (6)\\]
      \n\u8fd9\u4e2a\u662f\u77e2\u91cf\u548c\u5bf9\u5076\u77e2\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u800c\u4e0d\u662f\u540c\u7c7b\u578b\u7684\u77e2\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u628a\u4e00\u4e2a\u6295\u5165\u5411\u91cf\u53d8\u6210\u4e00\u4e2a\u4ea7\u51fa\u5411\u91cf\u3002\u540c\u65f6\uff0c\u6211\u4eec\u53d1\u73b0\u8fd9\u4e2a\u77e9\u9635\u7684\u5de6\u53f3\u672c\u5f81\u77e2\u91cf\u53ef\u80fd\u90fd\u4e0d\u662f\u5e73\u5eb8\u7684\u3002\n<\/li>\n
    4. \u53cd\u5411\u6982\u7387\u8f6c\u79fb\u77e9\u9635
      \n\\[MB^{i}_{j}=\\frac{x^{i}_{j}}{X^{i}}.\\hspace{2cm} (7)\\]
      \n\u5982\u679c\u6211\u4eec\u8fd8\u662f\u7167\u7740\u4e0a\u9762\u7684\u65b9\u5f0f\u4f01\u56fe\u5199\u51fa\u672c\u5f81\u5411\u91cf\u7684\u5f62\u5f0f\uff0c\u6211\u4eec\u6709
      \n\\[\\sum_{i=1}^{N}X^{i}MB^{i}_{j}=X_{j}.\\hspace{2cm} (8)\\]
      \n\u5b83\u628a\u4e00\u4e2a\u4ea7\u51fa\u5411\u91cf\u53d8\u6210\u4e00\u4e2a\u6295\u5165\u5411\u91cf\u3002\u540c\u65f6\uff0c\u6211\u4eec\u53d1\u73b0\u8fd9\u4e2a\u77e9\u9635\u7684\u5de6\u53f3\u672c\u5f81\u77e2\u91cf\u53ef\u80fd\u90fd\u4e0d\u662f\u5e73\u5eb8\u7684\u3002\n<\/li>\n<\/ol>\n

      \u6709\u4e86\u8fd9\u56db\u4e2a\u5b9a\u4e49\uff0c\u6211\u4eec\u53ef\u4ee5\u95ee\\(B\\)\u7684\u5de6\u672c\u5f81\u77e2\u91cf\u3001\\(F\\)\u7684\u53f3\u672c\u5f81\u77e2\u91cf\u3001\\(MF\\)\u548c\\(MB\\)\u7684\u5de6\u53f3\u672c\u5f81\u77e2\u91cf\u6709\u4ec0\u4e48\u542b\u4e49\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u8ba8\u8bba\u5982\u4f55\u628a\u5e73\u5eb8\u7684\u5173\u7cfb\uff082\uff09\u548c\uff084\uff09\u53d8\u5f97\u6709\u7528\u3002\u7531\u4e8e\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u7684\u7279\u70b9\uff0c\u5728\u8fd9\u91cc\u6211\u4eec\u4ec5\u4ec5\u8ba8\u8bba\u6700\u5927\u672c\u5f81\u503c\uff0c\u4e5f\u5c31\u662f\\(1\\)\u6240\u5bf9\u5e94\u7684\u672c\u5f81\u5411\u91cf\u3002
      \n\\[\\tilde{P}B=\\tilde{P}\\Longrightarrow \\sum_{i}\\tilde{P}_{i}\\frac{x^{i}_{j}}{X^{j}} = \\tilde{P}_{j} \\Longrightarrow \\sum_{i}X^{i}\\tilde{P}_{i}\\frac{x^{i}_{j}}{X^{i}} = X^{j}\\tilde{P}_{j} \\Longrightarrow P_{a} MB^{a}_{b} = P_{b}. (9)\\]
      \n\u4e8e\u662f\\(B\\)\u7684\u5de6\u672c\u5f81\u77e2\u91cf\u4e0e\\(MB\\)\u7684\u5de6\u672c\u5f81\u77e2\u91cf\u662f\u4e00\u6837\u7684\uff08\u5dee\u4e00\u4e2a\u5e38\u6570\uff09\u3002\u540c\u7406\u53ef\u4ee5\u628a\\(F\\)\u7684\u53f3\u672c\u5f81\u77e2\u91cf\u4e0e\\(MF\\)\u7684\u53f3\u672c\u5f81\u77e2\u91cf\u8054\u7cfb\u8d77\u6765\u3002<\/p>\n

      \u73b0\u5728\u6211\u4eec\u6765\u770b\\(MB\\)\u7684\u53f3\u672c\u5f81\u77e2\uff0c\u5047\u8bbe\u4e3a\\(W\\)\uff0c\u5219
      \n\\[\\sum_{j}\\frac{x^{i}_{j}}{X^{i}}W^{j} = W^{i} \\Longrightarrow \\sum_{j}x^{i}_{j}W^{j} = X^{i}W^{i} \\Longrightarrow W^{j} = 1. \\]
      \n\u4e8e\u662f\uff0c\u6211\u4eec\u53d1\u73b0\\(MB\\)\u7684\u53f3\u672c\u5f81\u77e2\u662f\u5e73\u5eb8\u7684\u3002\u540c\u7406\uff0c\\(MF\\)\u7684\u5de6\u672c\u5f81\u77e2\u4e5f\u662f\u5e73\u5eb8\u7684\u3002<\/p>\n

      \u603b\u7ed3\u4e00\u4e0b\uff1a\u56db\u79cd\u5f52\u4e00\u5316\u65b9\u6cd5\u5b9a\u4e49\u4e86\u77e9\u9635\\(B,F,MB,MF\\)\uff0c\u5176\u4e2d\\(B\\)\u7684\u53f3\u672c\u5f81\u77e2\u548c\\(MB\\)\u7684\u53f3\u672c\u5f81\u77e2\u662f\u5e73\u5eb8\u7684\u3001\\(F\\)\u7684\u5de6\u672c\u5f81\u77e2\u548c\\(MF\\)\u7684\u5de6\u672c\u5f81\u77e2\u662f\u5e73\u5eb8\u7684\uff0c\\(B\\)\u7684\u5de6\u672c\u5f81\u77e2\u548c\\(MB\\)\u7684\u5de6\u672c\u5f81\u77e2\u8ba4\u540c\uff0c\\(F\\)\u7684\u53f3\u672c\u5f81\u77e2\u548c\\(MF\\)\u7684\u53f3\u672c\u5f81\u77e2\u8ba4\u540c\u3002<\/p>\n

      \u4e5f\u5c31\u662f\u8bf4\uff0c\u5bf9\u4e8e\u901a\u5e38\u7684\u6295\u5165\u4ea7\u51fa\u5206\u6790\u77e9\u9635\uff0c\u5982\u679c\u6211\u4eec\u8ba1\u7b97\u672c\u5f81\u77e2\u91cf\u800c\u4e0d\u662f\u7ebf\u6027\u65b9\u7a0b\uff08\u53c2\u8003\u6295\u5165\u4ea7\u51fa\u77e9\u9635\u5206\u6790\u7684\u4e3b\u8981\u601d\u60f3\u5c0f\u7ed3<\/a>\uff09\uff0c\u90a3\u4e48\u8fd9\u4e2a\u672c\u5f81\u77e2\u91cf\u548c\u7a33\u5b9a\u6982\u7387\u5206\u5e03\u662f\u4e00\u4e2a\u4e1c\u897f\uff08\u5dee\u4e00\u4e2a\u5e38\u6570\uff09\uff0c\u800c\u540e\u8005\u662fPageRank\u7b97\u6cd5\u7684\u57fa\u7840\u3002<\/p>\n

      \u8fd9\u4e2a\u65f6\u5019\uff0c\u6211\u4eec\u518d\u6765\u8003\u8651\u53bb\u6389\u4e00\u884c\u4e00\u5217\u7684\u672c\u5f81\u5411\u91cf\u7684\u542b\u4e49\u5c31\u6bd4\u8f83\u6e05\u695a\u4e86\u3002\u4ee5\u8fd9\u4e2a\u4e3a\u57fa\u7840\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba8\u8bba\u4e24\u4e2a\u4ea7\u4e1a\u90e8\u95e8\u7684\u5173\u7cfb\uff0c\u4ee5\u53ca\u6bcf\u4e00\u4e2a\u4ea7\u4e1a\u90e8\u95e8\u7684\u91cd\u8981\u6027\u8861\u91cf\u3002<\/p>\n

      \u7ec6\u8282\u7684\u6295\u5165\u4ea7\u51fa\u5206\u6790\uff0c\u4e5f\u5c31\u662f\u8003\u8651\u5230\u4ea7\u54c1\u4e4b\u95f4\u7684\u914d\u6bd4\u7684\u6295\u5165\u4ea7\u51fa\u5206\u6790\uff08\u4e3e\u4f8b\u6765\u8bf4\uff0c\u4e00\u65a4\u9762\u7c89\u548c\u534a\u65a4\u6c34\u751f\u4ea7\u4e00\u65a4\u9762\u5305\u548c\u534a\u65a4\u810f\u6c34\uff0c\u5982\u679c\u9700\u8981\u589e\u52a0\u9762\u5305\u4ea7\u91cf\u4e00\u65a4\uff0c\u5b9e\u9645\u4e0a\u5c31\u610f\u5473\u7740\u589e\u52a0\u810f\u6c34\u534a\u65a4\u3002\u8fd9\u4e2a\u9762\u5305\u548c\u810f\u6c34\u4e4b\u95f4\u4e0d\u662f\u7b80\u5355\u7684\u6295\u5165\u4ea7\u51fa\u5173\u7cfb\uff0c\u800c\u662f\u5171\u540c\u751f\u4ea7\u5173\u7cfb\u3002\u8fd9\u4e2a\u5173\u7cfb\u6ca1\u6709\u88ab\u901a\u5e38\u7684\u6295\u5165\u4ea7\u51fa\u8003\u8651\u8fdb\u6765\uff09\uff0c\u9700\u8981\u8003\u8651\u4e24\u4e2a\u77e9\u9635\\({L_{\\alpha}}^{j}\\)\u548c\\(R_{\\alpha,j}\\)\uff0c\u5206\u522b\u8868\u793a\u53d1\u751f\u4e00\u6b21\u5de5\u827a\\(\\alpha\\)\u7684\u751f\u4ea7\u9700\u8981\u548c\u4ea7\u751f\\(j\\)\u4ea7\u54c1\u7684\u6570\u91cf\u3002\u5982\u679c\u6211\u4eec\u77e5\u9053\u8fd9\u4e2a\u65f6\u95f4\u5185\u6bcf\u4e00\u4e2a\u751f\u4ea7\u90e8\u95e8\u7684\u751f\u4ea7\u7684\u6b21\u6570\\(V^{\\alpha}\\)\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u53ef\u4ee5\u8ba1\u7b97\u603b\u9700\u6c42\u548c\u603b\u4ea7\u51fa\u5206\u522b\u4e3a\uff0c
      \n\\[X^{j}=\\sum_{\\alpha}L_{\\alpha}^{j}V^{\\alpha}, \\hspace{2cm} (10)\\]
      \n\u4e3a\u4ea7\u54c1\\(j\\)\u6295\u5165\u5230\u6240\u6709\u4ea7\u4e1a\u7684\u603b\u548c\u3002
      \n\\[X_{j}=\\sum_{\\alpha}R_{\\alpha,j}V^{\\alpha}, \\hspace{2cm} (11)\\]
      \n\u4e3a\u6240\u6709\u4ea7\u4e1a\u751f\u4ea7\u51fa\u6765\u7684\u4ea7\u54c1\\(j\\)\u603b\u548c\u3002<\/p>\n

      \u5f53\u5047\u8bbe\u4e00\u4e2a\u4ea7\u4e1a\u90e8\u95e8\u53ea\u751f\u4ea7\u4e00\u6837\u4ea7\u54c1\u7684\u65f6\u5019\uff0c\\(R_{\\alpha,j}=\\delta_{\\alpha,j}\\)\uff0c\u4e8e\u662f\\(X_{j}=V^{\\alpha}\\)\uff0c\u4e8e\u662f\uff0c\u516c\u5f0f\uff0810\uff09\u6210\u4e3a
      \n\\[X^{j}=\\sum_{i}L_{i}^{j}X_{i}. \\hspace{2cm} (13)\\]
      \n\u8fd9\u4e2a\u65f6\u5019\uff0c\u53ef\u4ee5\u770b\u51fa\u6765\uff0c\\(L\\)\u4e0e\\(MF\\)\u76f8\u5f53\u3002\u5bf9\u4e8e\u8fd9\u4e2a\u751f\u4ea7\u8fc7\u7a0b\uff0c\u53ef\u4ee5\u5b58\u5728\u591a\u79cd\u7406\u89e3\u3002\u4f8b\u5982\uff0c\u7ed9\u5b9a\u6295\u5165\u5411\u91cf\\(X^{a}\\)\uff0c\u6211\u4eec\u5e0c\u671b\u5f97\u5230\u6700\u4f18\u7684\u4ea7\u51fa\u5411\u91cf\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u8981\u6c42\u6295\u5165\u5411\u91cf\u5b9e\u9645\u4e0a\u6765\u81ea\u4e8e\u4ea7\u51fa\u5411\u91cf\u3002\u4f8b\u5982\uff0c\u7ed9\u5b9a\u603b\u4ef7\u683c\u548c\u6295\u5165\u8d44\u91d1\uff0c\u6211\u4eec\u5e0c\u671b\u5f97\u5230\u6700\u4f18\u7684\u4ea7\u51fa\u503c\u3002\u6240\u6709\u7684\u8fd9\u4e9b\u95ee\u9898\u90fd\u53ef\u4ee5\u7528\u8fd9\u4e2a\\(L\\)\u548c\\(R\\)\u7684\u6570\u5b66\u6a21\u578b\u6765\u63cf\u8ff0\u3002<\/p>\n

      \u5bf9\u4e8e\u4e00\u4e2a\u5c01\u95ed\u7cfb\u7edf\uff08\u603b\u6295\u5165\u7b49\u4e8e\u603b\u4ea7\u51fa\uff09\uff0c\u5219
      \n\\[\\sum_{\\alpha}L_{\\alpha}^{j}V^{\\alpha} = \\sum_{\\alpha}R_{\\alpha,j}V^{\\alpha} \\Longrightarrow \\sum_{\\alpha}\\left(L_{\\alpha}^{j}-R_{\\alpha,j}\\right)V^{\\alpha}=0 , \\hspace{2cm} (14)\\]
      \n\u5bf9\u4e8e\u4e00\u4e2a\u5f00\u653e\u7cfb\u7edf\u7cfb\u7edf\uff08\u603b\u6295\u5165\u4e0d\u7b49\u4e8e\u603b\u4ea7\u51fa\uff0c\u4f46\u662f\u5916\u754c\u8f93\u51fa\u5df2\u77e5\uff09\uff0c\u5219
      \n\\[\\sum_{\\alpha}\\left(L_{\\alpha}^{j} – R_{\\alpha,j}\\right)V^{\\alpha} = b^{j}. \\hspace{2cm} (15)\\]
      \n\u8fd9\u4e24\u4e2a\u65b9\u7a0b\u610f\u5473\u7740\uff0c\u4e3a\u4e86\u6ee1\u8db3\u5916\u754c\u7684\u9700\u6c42\uff0c\u5404\u4e2a\u90e8\u95e8\u7684\u751f\u4ea7\u9891\u7387\u662f\u53d7\u7ea6\u675f\u7684\uff08\u5982\u679c\u80fd\u591f\u5b8c\u5168\u786e\u5b9a\u4e0b\u6765\u5c31\u66f4\u597d\u4e86\u3002\u901a\u5e38\u505a\u4e0d\u5230\uff0c\u56e0\u4e3a\u65b9\u7a0b\u4e0d\u662f\u65b9\u7684\uff09\u3002<\/p>\n

      \u56de\u5230\u5316\u5b66\u53cd\u5e94\u7f51\u7edc\u7684\u5c42\u6b21\uff0c\\(L\\)\u548c\\(R\\)\u88ab\u5408\u8d77\u6765\u79f0\u4e3a\u5316\u5b66\u53cd\u5e94\u7cfb\u6570\u77e9\u9635\\(S\\)\uff0c\u76f8\u5f53\u4e8e\u628a\\(L\\)\u5f53\u4f5c\u8d1f\u7684\\(R\\)\u5f53\u4f5c\u6b63\u7684\uff0c\u4e00\u8d77\u53eb\u505a\\(S\\)\u3002\u8fd9\u4e2a\u65f6\u5019\u7cfb\u7edf\u7684\u884c\u4e3a\u5b8c\u5168\u7531\u5982\u4e0b\u5fae\u5206\u65b9\u7a0b\u63cf\u8ff0\uff0c
      \n\\[\\frac{d}{dt} X_{i} = \\sum_{r=1}^{M} \\kappa^{r}\\Pi_{j=1}^{N} \\left(X_{j}\\right)^{\\frac{\\left|S_{r}^{j}\\right| – S_{r}^{j}}{2}}S_{r}^{i}, \\hspace{2cm} (16)\\]
      \n\u5176\u4e2d\\(\\kappa^{r}\\)\u662f\u5316\u5b66\u53cd\u5e94\u901f\u7387\u5e38\u6570\uff08\u5916\u751f\u53d8\u91cf\uff09\u3002\u8054\u7cfb\u4e24\u4e2a\u516c\u5f0f\uff0c\u6211\u4eec\u53d1\u73b0\uff0c\u5b9e\u9645\u4e0a\uff0c\u76f8\u5f53\u4e8e
      \n\\[ \\kappa^{r}\\Pi_{j=1}^{N} \\left(X_{j}\\right)^{\\frac{\\left|S_{r}^{j}\\right| – S_{r}^{j}}{2}} = V^{r}.\\hspace{2cm} (17)\\]<\/p>\n

      \u8fd9\u4e5f\u5c31\u662f\u8bf4\uff0c\u5c3d\u7ba1\u6574\u4e2a\u5316\u5b66\u53cd\u5e94\u662f\u7531\u5916\u751f\u53d8\u91cf\u7cfb\u6570\u77e9\u9635\\(S\\)\u548c\u5916\u751f\u53d8\u91cf\u53cd\u5e94\u901f\u7387\u77e2\u91cf\\(\\kappa\\)\u6240\u51b3\u5b9a\u7684\u4e00\u4e2a\u7cfb\u7edf\uff0c\u4f46\u662f\uff0c\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u8bf4\uff0c\u4f8b\u5982\u4f18\u5316\u8fdb\u5316\u7684\u7ed3\u679c\u4f7f\u5f97\u7cfb\u7edf\u51fa\u4e8e\u5e73\u8861\u7684\u5c01\u95ed\u7cfb\u7edf\u72b6\u6001\u6216\u8005\u5916\u754c\u8f93\u51fa\u4e00\u5b9a\u7684\u5f00\u653e\u7cfb\u7edf\u7684\u72b6\u6001\uff08\u8fd8\u53ef\u4ee5\u6709\u5176\u4ed6\u7684\u7ea6\u675f\u548c\u4f18\u5316\u76ee\u6807\uff0c\u4f8b\u5982\u7ecf\u6d4e\u5b66\u7684\u6700\u5927\u5229\u6da6\u76ee\u6807\uff09\uff0c\u901f\u7387\u77e2\u91cf\\(\\kappa\\)\u4e5f\u662f\uff0c\u4e00\u4e2a\u7531\\(S\\)\uff08\u52a0\u4e0a\\(b\\)\u5728\u5f00\u653e\u7cfb\u7edf\u4e2d\uff09\u51b3\u5b9a\u7684\uff0c\u9002\u5408\u8fd9\u4e2a\\(S\\)\u7684\u6ee1\u8db3\u4e00\u4e9b\u989d\u5916\u7ea6\u675f\u548c\u6700\u5927\u5316\u67d0\u4e9b\u989d\u5916\u76ee\u6807\u7684\uff0c\u53c2\u6570\u3002<\/p>\n

      \u4e8e\u662f\uff0c\u6574\u4e2a\u95ee\u9898\u7684\u7814\u7a76\u53ef\u4ee5\u8d70\u4e24\u6761\u8def\uff1a\u7b2c\u4e00\uff0c\u5728\u5916\u751f\u53d8\u91cf\\(\\kappa\\)\u5b8c\u5168\u5df2\u77e5\u7684\u60c5\u51b5\u4e0b\uff0c\u7528\u516c\u5f0f\uff0816\uff09\u8ba8\u8bba\u65f6\u95f4\u6f14\u5316\u7684\u8fc7\u7a0b\u548c\u6f14\u5316\u7684\u7ed3\u679c\uff1b\u7b2c\u4e8c\uff0c\u901a\u8fc7\\(S\\)\uff08\u6309\u7167\u516c\u5f0f\uff0814\uff09\u52a0\u4e0a\u5176\u4ed6\u7ea6\u675f\uff09\u6765\u786e\u5b9a\\(V\\)\u4ece\u800c\u4e5f\u786e\u5b9a\\(\\kappa\\)\uff0c\u63a5\u7740\u5f97\u5230\\(X\\)\u3002\u524d\u8005\u5c31\u662f\u5316\u5b66\u53cd\u5e94\u7f51\u7edc\u548c\u5fae\u5206\u65b9\u7a0b\u7684\u65b9\u5f0f\u3002\u540e\u8005\u88ab\u79f0\u4e3a\u5316\u5b66\u53cd\u5e94\u7f51\u7edc\u548c\u6d41\u5e73\u8861\u5206\u6790\uff08Flux Balanced Analysis\uff09\u3002<\/p>\n

      \u5728\u7b2c\u4e00\u4e2a\u6570\u5b66\u6a21\u578b\u4e2d\uff08\u6682\u65f6\u5ffd\u7565\\(b\\)\u7684\u95ee\u9898\uff0c\u5f53\u4f5c\u5c01\u95ed\u7cfb\u7edf\uff09\uff0c\u7814\u7a76\u67d0\u4e2a\u7269\u79cd\u591a\u4e86\u5c11\u4e86\u5bf9\u5176\u4ed6\u7684\u5f71\u54cd\u975e\u5e38\u7b80\u5355\uff0c\u53ea\u8981\u653e\u5230\u5fae\u5206\u65b9\u7a0b\u4e2d\u53bb\u6f14\u5316\u4e00\u4e0b\u5f97\u5230\u4e00\u4e2a\u5b9a\u6001\u672b\u72b6\u6001\u5c31\u884c\u4e86\u3002\u4f46\u662f\uff0c\u8fd9\u6837\u5c31\u9700\u8981\\(\\kappa\\)\u8fd9\u4e00\u5916\u751f\u53d8\u91cf\u3002<\/p>\n

      \u5728\u7b2c\u4e8c\u4e2a\u6570\u5b66\u6a21\u578b\u4e2d\uff0c\u5bf9\u4e8e\u67d0\u4e2a\u5316\u5b66\u53cd\u5e94\uff08\u4ea7\u4e1a\u90e8\u95e8\uff09\u7684\u91cd\u8981\u6027\u5c31\u6bd4\u8f83\u5bb9\u6613\u8ba8\u8bba\uff0c\u4f8b\u5982\\(S\\)\u4e2d\u53bb\u6389\u67d0\u4e00\u4e2a\u5217\uff08\u53cd\u5e94\u89d2\u6807\\(r\\)\uff09\uff0c\u7136\u540e\u5c31\u53ef\u4ee5\u8ba8\u8bba\u8fd9\u4e2a\u65f6\u5019\u7684\\(V\\)\uff0c\u5e76\u4e14\u8fdb\u800c\u5f97\u5230\u8fd9\u4e2a\u65f6\u5019\u7684\\(X\\)\u3002\u4f46\u662f\uff0c\u5982\u4f55\u8ba8\u8bba\u67d0\u4e00\u4e2a\\(X_j\\)\u5bf9\u4e00\u4e2a\\(X_k\\)\u7684\u5f71\u54cd\u5462\uff1f<\/p>\n

      \u53ef\u4ee5\u8003\u8651\u8fd9\u6837\uff1a\u5728\u6ee1\u8db3\u7ea6\u675f\uff08\u4f8b\u5982\\(X_j\\)\u6700\u5927\u503c\u7ea6\u675f\uff09\u7684\u60c5\u51b5\u4e0b\uff0c\u5728\u540c\u6837\u7684\\(S\\)\u7684\u60c5\u51b5\u4e0b\uff0c\u4f7f\u5f97\u67d0\u4e2a\u7c7b\u4f3c\u7684\u76ee\u6807\u6700\u5927\u7684\u8fd9\u6837\u7684\\(V\\)\uff0c\u7136\u540e\u4ece\\(V\\)\u5f97\u5230\\(X\\)\uff0c\u6765\u5f97\u5230\\(X_j\\)\u5bf9\\(X_k\\)\u7684\u5f71\u54cd\u3002<\/p>\n

      \u53ef\u4ee5\u5c1d\u8bd5\u3002\u7531\u4e8e\u8fd9\u4e2a\u6d41\u5e73\u8861\u5206\u6790\u4e0e\u5316\u5b66\u53cd\u5e94\u3001\u57fa\u56e0\u7f51\u7edc\u8054\u7cfb\u66f4\u7d27\u5bc6\uff0c\u53ef\u4ee5\u8003\u8651\uff0c\u5148\u7528\u8fd9\u6837\u7684\u4f53\u7cfb\u505a\u4f8b\u5b50\uff0c\u6765\u53d1\u5c55\u65b9\u6cd5\uff0c\u7136\u540e\uff0c\u56de\u5230\u7ecf\u6d4e\u5b66\u548c\u79d1\u5b66\u8ba1\u91cf\u5b66\u3002<\/p>\n

      2014\u5e74\u590d\u6742\u7cfb\u7edf\u6691\u671f\u5b66\u6821\u62a5\u544a<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

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