{"id":42997,"date":"2023-06-08T18:46:14","date_gmt":"2023-06-08T10:46:14","guid":{"rendered":"https:\/\/swarma.org\/?p=42997"},"modified":"2023-06-08T18:46:14","modified_gmt":"2023-06-08T10:46:14","slug":"%e9%9a%8f%e6%9c%ba%e7%9f%a9%e9%98%b5%e4%b9%8b%e5%8e%84%e7%b1%b3%e7%af%87%ef%bc%9a%e7%88%b1%e5%be%b7%e5%8d%8e%e5%85%b9%e9%81%87%e8%a7%81%e4%bc%8a%e8%be%9b-%e5%91%a8%e5%85%ad%e7%9b%b4%e6%92%ad%c2%b7","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=42997","title":{"rendered":"\u968f\u673a\u77e9\u9635\u4e4b\u5384\u7c73\u7bc7\uff1a\u7231\u5fb7\u534e\u5179\u9047\u89c1\u4f0a\u8f9b | \u5468\u516d\u76f4\u64ad\u00b7\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b\u7b2c27\u8bb2"},"content":{"rendered":"<div class='wxsyncmain'>\n<section powered-by=\"xiumi.us\" style=\"margin-bottom: 0px;outline: 0px;letter-spacing: 0.544px;white-space: normal;color: rgb(63, 63, 63);font-family: PingFangSC-light;font-size: 15px;background-color: rgb(255, 255, 255);visibility: 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&quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;caret-color: rgb(89, 89, 89);visibility: visible;\">\u8bfe\u7a0b\u7b80\u4ecb<\/span><\/strong><\/strong><\/p>\n<\/section>\n<section style=\"margin-top: -2px;outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;visibility: visible;\">\n<section style=\"outline: 0px;float: left;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;float: right;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;outline: 0px;white-space: normal;line-height: 1.75em;\"><br  \/><\/section>\n<p style=\"margin-right: 8px;margin-left: 8px;letter-spacing: 0.578px;white-space: normal;line-height: 1.75em;\"><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;\">\u968f\u673a\u77e9\u9635\u5728\u795e\u7ecf\u7f51\u7edc\u7684\u7814\u7a76\u4e2d\u8d77\u5230\u975e\u5e38\u91cd\u8981\u7684\u4f5c\u7528\uff0c\u7279\u522b\u662f\u523b\u753b\u795e\u7ecf\u7f51\u7edc\uff08\u6bd4\u5982Hopfield\u7f51\u7edc\u3001\u7387\u6a21\u578b\uff09\u5728\u4e0d\u52a8\u70b9\u5904\u7684\u7a33\u5b9a\u6027\uff0c\u800c\u7f51\u7edc\u7684\u5931\u7a33\u5bf9\u5e94\u7740\u795e\u7ecf\u5143\u96c6\u4f53\u884c\u4e3a\u7684\u76f8\u53d8\u3002\u4e0a\u8ff0\u63d0\u5230\u7684\u5e94\u7528\u53ef\u4ee5\u62bd\u8c61\u6210\u4e00\u4e2a\u7684\u968f\u673a\u77e9\u9635\u95ee\u9898\uff1a\u7ed9\u5b9a\u77e9\u9635\u4e2d\u77e9\u9635\u5143\u7684\u65e0\u5e8f\u5206\u5e03\uff0c\u8ba1\u7b97\u77e9\u9635\u7279\u5f81\u8c31\u5206\u5e03\u7684\u6e10\u8fdb\u89e3\u6790\u89e3\u3002\u8fd9\u4e2a\u95ee\u9898\u4ece\u7edf\u8ba1\u7269\u7406\u7684\u89c6\u89d2\u6765\u770b\u53ef\u4ee5\u8f6c\u6362\u4e3a\u6c42\u89e3\u4e00\u4e2a\u4e24\u4f53\u76f8\u4e92\u4f5c\u7528\u7684\u81ea\u7531\u80fd\u3002\u4e8e\u662f\uff0c\u6211\u4eec\u5728\u524d\u9762\u4ecb\u7ecd\u7684\u590d\u672c\u65b9\u6cd5\u3001\u7a7a\u8154\u65b9\u6cd5\u5c31\u80fd\u81ea\u7136\u5730\u5f15\u5165\u4ee5\u8ba1\u7b97\u8c31\u5206\u5e03\u3002\u5728\u672c\u6b21\u8bfe\u7a0b\u4e2d\uff0c\u5c06\u9996\u5148\u4ecb\u7ecd\u968f\u673a\u77e9\u9635\u7279\u5f81\u8c31\u7684\u7edf\u8ba1\u7269\u7406\u63cf\u8ff0\uff0c\u5206\u522b\u8003\u8651\u5384\u7c73\u77e9\u9635\u548c\u975e\u5384\u7c73\u77e9\u9635\u3002\u968f\u540e\u5c06\u4f7f\u7528\u7edf\u8ba1\u7269\u7406\u65b9\u6cd5\u5305\u62ec\u590d\u672c\u65b9\u6cd5\u3001\u7a7a\u8154\u65b9\u6cd5\u3001\u8d39\u66fc\u56fe\u65b9\u6cd5\u5f97\u5230\u7ecf\u5178\u7684\u534a\u5706\u5f8b\u3001Marcenko-Pastur\u5f8b\u4ee5\u53ca\u692d\u5706\u5f8b\u3002<\/span><\/p>\n<section style=\"letter-spacing: 0.578px;white-space: normal;line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"letter-spacing: 0.578px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;font-size: 15px;color: rgb(63, 63, 63);\">\u672c\u4e3b\u9898\u5bf9\u5e94<\/span><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247634469&amp;idx=3&amp;sn=36d67d75c21f6ce172cc03704f40f34a&amp;scene=21#wechat_redirect\" data-linktype=\"2\" style=\"letter-spacing: 0.578px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;font-size: 15px;color: rgb(0, 122, 170);\">SMNN\u4e66\u7c4d<\/a><span style=\"letter-spacing: 0.578px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;font-size: 15px;color: rgb(63, 63, 63);\">\u7684<\/span><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;text-indent: 0em;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;\">\u7b2c17\u7ae0\uff08\u4e0a\u534a\u90e8\u5206\u5185\u5bb9\uff09\uff0c\u5177\u4f53\u4e3a\uff1a<\/span><\/section>\n<section style=\"line-height: 1.75em;text-align: justify;margin: 0px 8px 8px;text-indent: 0em;\"><strong><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;text-decoration: none solid rgb(63, 63, 63);\">Chapter 17:&nbsp; Statistical Mechanics of Random Matrices<\/span><\/strong><\/section>\n<ul class=\"list-paddingleft-1\" style=\"list-style-type: disc;\">\n<li style=\"font-weight: bold;\">\n<section style=\"line-height: 1.75em;text-align: left;margin: 0px 8px 8px;text-indent: 0em;\"><strong><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;text-decoration: none solid rgb(63, 63, 63);\">17.1 Spectral Density<\/span><\/strong><\/section>\n<\/li>\n<li style=\"font-weight: bold;\">\n<section style=\"line-height: 1.75em;text-align: left;margin: 0px 8px 8px;text-indent: 0em;\"><strong><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;text-decoration: none solid rgb(63, 63, 63);\">17.2 Replica Method and Semi-circle Law<\/span><\/strong><\/section>\n<\/li>\n<li style=\"font-weight: bold;\">\n<section style=\"line-height: 1.75em;text-align: left;margin: 0px 8px 8px;text-indent: 0em;\"><strong><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;text-decoration: none solid rgb(63, 63, 63);\">17.3 Cavity Approach and Marchenko<\/span><\/strong><\/section>\n<\/li>\n<li style=\"font-weight: bold;\">\n<section style=\"line-height: 1.75em;text-align: left;margin: 0px 8px;text-indent: 0em;\"><strong><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;text-decoration: none solid rgb(63, 63, 63);\">17.4 Spectral Densities of Random Asymmetric Matrices<\/span><\/strong><\/section>\n<\/li>\n<\/ul>\n<p><br  \/><\/p>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 0px;\"><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;\"><br  \/><\/span><\/p>\n<h3 style=\"margin-bottom: 0em;white-space: normal;outline: 0px;font-family: mp-quote, -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;letter-spacing: 0.544px;background-color: rgb(255, 255, 255);visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"outline: 0px;letter-spacing: 0.544px;text-align: right;font-size: 13px;visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"margin-top: 10px;margin-bottom: 10px;outline: 0px;letter-spacing: 0.544px;text-align: center;visibility: visible;\">\n<section style=\"outline: 0px;display: inline-block;vertical-align: middle;visibility: visible;\">\n<section style=\"margin-bottom: -2px;outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;visibility: visible;\">\n<section style=\"outline: 0px;float: left;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;float: right;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;clear: both;line-height: 0;visibility: visible;\">\n<section style=\"outline: 0px;line-height: 0;width: 0px;visibility: visible;\"><svg viewbox=\"0 0 1 1\" style=\"vertical-align: top;visibility: visible;\"><\/svg><\/section>\n<\/section>\n<\/section>\n<section style=\"padding-right: 10px;padding-left: 10px;outline: 0px;border-left: 3px solid rgb(33, 166, 210);border-right: 3px solid rgb(33, 166, 210);border-top-color: rgb(33, 166, 210);border-bottom-color: rgb(33, 166, 210);font-size: 16px;color: rgb(0, 0, 0);line-height: 1.4;visibility: visible;\">\n<p style=\"outline: 0px;visibility: visible;\"><strong style=\"outline: 0px;visibility: visible;\"><strong style=\"outline: 0px;text-align: left;color: rgb(33, 166, 210);letter-spacing: 0.544px;visibility: visible;\"><span style=\"outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;caret-color: rgb(89, 89, 89);visibility: visible;\">\u672c\u8282\u8bfe\u7a0b\u5927\u7eb2<\/span><\/strong><\/strong><\/p>\n<\/section>\n<section style=\"margin-top: -2px;outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;visibility: visible;\">\n<section style=\"outline: 0px;float: left;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;float: right;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n<section style=\"margin-bottom: 0px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">&nbsp;<\/span><\/section>\n<p style=\"margin-bottom: 8px;margin-left: 8px;margin-right: 8px;\"><span style=\"color: rgb(63, 63, 63);font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;font-size: 15px;letter-spacing: 0.578px;\">1. \u968f\u673a\u77e9\u9635\u8c31\u5bc6\u5ea6<\/span><\/p>\n<p style=\"margin-bottom: 8px;margin-left: 8px;margin-right: 8px;\"><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;\">2. \u590d\u672c\u65b9\u6cd5\u53ca\u534a\u5706\u5f8b<\/span><\/p>\n<p style=\"margin-bottom: 8px;margin-left: 8px;margin-right: 8px;\"><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;\">3. \u7a7a\u8154\u65b9\u6cd5\u53caMP\u5f8b<\/span><\/p>\n<p style=\"margin-bottom: 8px;margin-left: 8px;margin-right: 8px;\"><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;\">4. \u975e\u5384\u7c73\u77e9\u9635\u7684\u8c31\u5206\u5e03<\/span><\/p>\n<p style=\"margin-bottom: 8px;margin-left: 8px;margin-right: 8px;\"><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;\">\u5173\u952e\u8bcd\uff1a\u7279\u5f81\u8c31\u5206\u5e03\u3001\u683c\u6797\u51fd\u6570\u3001\u534a\u5706\u5f8b\u3001MP\u5f8b\u3001\u692d\u5706\u5f8b<\/span><\/p>\n<p style=\"margin-bottom: 8px;margin-left: 8px;margin-right: 8px;\"><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;\"><\/span><\/p>\n<section style=\"margin-bottom: 8px;margin-left: 8px;margin-right: 8px;\"><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;\"><\/span><\/section>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 0px;\"><br  \/><\/p>\n<h3 style=\"margin-bottom: 0em;outline: 0px;white-space: normal;font-family: mp-quote, -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;letter-spacing: 0.544px;background-color: rgb(255, 255, 255);visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"outline: 0px;letter-spacing: 0.544px;text-align: right;font-size: 13px;visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"margin-top: 10px;margin-bottom: 10px;outline: 0px;letter-spacing: 0.544px;text-align: center;visibility: visible;\">\n<section style=\"outline: 0px;display: inline-block;vertical-align: middle;visibility: visible;\">\n<section style=\"margin-bottom: -2px;outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;visibility: visible;\">\n<section style=\"outline: 0px;float: left;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;float: right;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;clear: both;line-height: 0;visibility: visible;\">\n<section style=\"outline: 0px;line-height: 0;width: 0px;visibility: visible;\"><svg viewbox=\"0 0 1 1\" style=\"vertical-align: top;visibility: visible;\"><\/svg><\/section>\n<\/section>\n<\/section>\n<section style=\"padding-right: 10px;padding-left: 10px;outline: 0px;border-left: 3px solid rgb(33, 166, 210);border-right: 3px solid rgb(33, 166, 210);border-top-color: rgb(33, 166, 210);border-bottom-color: rgb(33, 166, 210);font-size: 16px;color: rgb(0, 0, 0);line-height: 1.4;visibility: visible;\">\n<p style=\"outline: 0px;visibility: visible;\"><strong style=\"outline: 0px;visibility: visible;\"><strong style=\"outline: 0px;text-align: left;color: rgb(33, 166, 210);letter-spacing: 0.544px;visibility: visible;\"><span style=\"outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;caret-color: rgb(89, 89, 89);visibility: visible;\">\u8d1f\u8d23\u4eba\u4ecb\u7ecd<\/span><\/strong><\/strong><\/p>\n<\/section>\n<section style=\"margin-top: -2px;outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;visibility: visible;\">\n<section style=\"outline: 0px;float: left;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;float: right;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n<section style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;line-height: 1.75em;text-align: center;\"><br  \/><\/section>\n<section style=\"text-align: center;margin-bottom: 0px;\"><img class=\"rich_pages wxw-img js_insertlocalimg\" data-ratio=\"1.292929292929293\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"990\" style=\"width: 174px;height: 225px;\" src=\"\/wp-content\/uploads\/2023\/06\/wxsync-2023-06-c208b5d42c96c91e5a09519a54f7ac47.jpeg\"  \/><\/section>\n<p style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;margin-bottom: 8px;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u9ec4\u6d77\u5e73<\/span><\/strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\uff0c\u4e2d\u5c71\u5927\u5b66\u7269\u7406\u5b66\u9662\u6559\u6388\u3002\u672c\u79d1\u6bd5\u4e1a\u4e8e\u4e2d\u5c71\u5927\u5b66\u7406\u5de5\u5b66\u9662\uff0c\u535a\u58eb\u6bd5\u4e1a\u4e8e\u4e2d\u56fd\u79d1\u5b66\u9662\u7406\u8bba\u7269\u7406\u7814\u7a76\u6240\uff0c\u968f\u540e\u5728\u9999\u6e2f\u79d1\u6280\u5927\u5b66\u7269\u7406\u7cfb\u3001\u4e1c\u4eac\u5de5\u4e1a\u5927\u5b66\u8ba1\u7b97\u667a\u80fd\u7cfb&nbsp; (2012\u5e74\u83b7\u65e5\u672c\u5b66\u672f\u632f\u5174\u4f1a\u8d44\u52a9) \u4ee5\u53ca\u65e5\u672c\u7406\u5316\u5b66\u7814\u7a76\u6240 (RIKEN) \u8111\u79d1\u5b66\u4e2d\u5fc3\u4ece\u4e8b\u7edf\u8ba1\u7269\u7406\u4e0e\u673a\u5668\u5b66\u4e60\u3001&nbsp; \u795e\u7ecf\u8ba1\u7b97\u4ea4\u53c9\u7684\u57fa\u7840\u7406\u8bba\u7814\u7a76\uff0c2017\u5e74\u56e0\u5728\u65e0\u76d1\u7763\u5b66\u4e60\u65b9\u9762\u7684\u7814\u7a76\u83b7\u5f97 RIKEN &nbsp;\u6770\u51fa\u7814\u7a76\u5956\u3002\u4e8e2018\u5e74\u5165\u9009\u4e2d\u5c71\u5927\u5b66\u767e\u4eba\u8ba1\u5212\uff0c\u5728\u7269\u7406\u5b66\u9662\u7ec4\u5efa\u4e86\u201c\u7269\u7406\u3001\u673a\u5668\u4e0e\u667a\u80fd\u201d&nbsp; \uff08PMI\uff09\u7814\u7a76\u5c0f\u7ec4\uff0c\u4e13\u6ce8\u4e8e\u5404\u79cd\u795e\u7ecf\u8ba1\u7b97\u7684\u7406\u8bba\u57fa\u7840\uff0c\u957f\u671f\u76ee\u6807\u662f\u4f7f\u7528\u57fa\u4e8e\u7269\u7406\u7684\u8fd1\u4f3c\u6765\u63ed\u793a\u673a\u5668\u53ca\u5927\u8111\u667a\u80fd\u7684\u57fa\u672c\u539f\u7406\u3002\u66fe\u4e3b\u6301\u56fd\u5bb6\u81ea\u7136\u79d1\u5b66\u57fa\u91d1\u9752\u5e74\u57fa\u91d1\u3001\u4f18\u79c0\u9752\u5e74\u57fa\u91d1\u7b49\u56fd\u5bb6\u7ea7\u9879\u76ee\u3002<\/span><\/p>\n<section style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">PMI Lab\uff1ahttps:\/\/www.labxing.com\/hphuang2018<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><br  \/><\/span><\/section>\n<p style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><br  \/><\/p>\n<h3 style=\"margin-bottom: 0em;outline: 0px;white-space: normal;font-family: mp-quote, -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;letter-spacing: 0.544px;background-color: rgb(255, 255, 255);visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"outline: 0px;letter-spacing: 0.544px;text-align: right;font-size: 13px;visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"margin-top: 10px;margin-bottom: 10px;outline: 0px;letter-spacing: 0.544px;text-align: center;visibility: visible;\">\n<section style=\"outline: 0px;display: inline-block;vertical-align: middle;visibility: visible;\">\n<section style=\"margin-bottom: -2px;outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;visibility: visible;\">\n<section style=\"outline: 0px;float: left;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;float: right;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;clear: both;line-height: 0;visibility: visible;\">\n<section style=\"outline: 0px;line-height: 0;width: 0px;visibility: visible;\"><svg viewbox=\"0 0 1 1\" style=\"vertical-align: top;visibility: visible;\"><\/svg><\/section>\n<\/section>\n<\/section>\n<section style=\"padding-right: 10px;padding-left: 10px;outline: 0px;border-left: 3px solid rgb(33, 166, 210);border-right: 3px solid rgb(33, 166, 210);border-top-color: rgb(33, 166, 210);border-bottom-color: rgb(33, 166, 210);font-size: 16px;color: rgb(0, 0, 0);line-height: 1.4;visibility: visible;\">\n<p style=\"outline: 0px;visibility: visible;\"><strong style=\"outline: 0px;visibility: visible;\"><strong style=\"outline: 0px;text-align: left;color: rgb(33, 166, 210);letter-spacing: 0.544px;visibility: visible;\"><span style=\"outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;caret-color: rgb(89, 89, 89);visibility: visible;\">\u76f4\u64ad\u4fe1\u606f<\/span><\/strong><\/strong><\/p>\n<\/section>\n<section style=\"margin-top: -2px;outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;visibility: visible;\">\n<section style=\"outline: 0px;float: left;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;float: right;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;outline: 0px;white-space: normal;line-height: 1.75em;\"><br  \/><\/section>\n<h2 style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><\/h2>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u76f4\u64ad\u65f6\u95f4<\/span><\/strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\uff1a<\/span><\/section>\n<p style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">2023\u5e746\u670810\u65e5\uff08\u5468\u516d\uff0910:00-12:00<\/span><\/p>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><br  \/><\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u53c2\u4e0e\u65b9\u5f0f\u4e00\uff1a\u89c6\u9891\u53f7\u9884\u7ea6\u76f4\u64ad<\/span><\/strong><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;\">\u96c6\u667a\u5b66\u56ed\u89c6\u9891\u53f7\u9884\u7ea6<\/section>\n<section style=\"line-height: 1.75em;\"><br  \/><\/section>\n<\/li>\n<\/ul>\n<section class=\"channels_iframe_wrp\"><mp-common-videosnap class=\"js_uneditable custom_select_card channels_live_iframe\" data-pluginname=\"mpvideosnap\" data-headimgurl=\"https:\/\/wx.qlogo.cn\/finderhead\/PdibpV1sFDHdC5AR6SqCNbOfwAEdPtWSb2Y5v1iaq3YTCocFBPFM1xzQ\/0\" data-username=\"v2_060000231003b20faec8c4e78d10c3d6cd04ef30b077c6436f3ed47f70be822497426f6452dd@finder\" data-nickname=\"\u96c6\u667a\u4ff1\u4e50\u90e8\" data-desc=\"\u5c06\u572806\u670811\u65e5 20:00 \u76f4\u64ad\" data-livewording=\"\u9884\u7ea6\" data-intro=\"\u601d\u8003\u673a\u5668\uff1a\u4eba\u5de5\u667a\u80fd\u827a\u672f\u4e0e\u4eba\u5de5\u751f\u547d | \u590d\u6742\u79d1\u5b66\u00d7\u827a\u672f\u6d3b\u52a8\u7b2c\u4e5d\u671f\" data-type=\"live\" data-status=\"0\" data-noticeid=\"finderlivenotice-v2_060000231003b20faec8c4e78d10c3d6cd04ef30b077c6436f3ed47f70be822497426f6452dd@finder-1686103256046861-1907180787\" data-isdisabled=\"0\" data-errortips=\"\"><\/mp-common-videosnap><\/section>\n<ul class=\"list-paddingleft-1\" style=\"list-style-type: disc;\">\n<li style=\"color: rgb(63, 63, 63);\">\n<p style=\"line-height: 1.75em;text-align: left;margin-top: 16px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u96c6\u667a\u5b66\u56ed B \u7ad9\u514d\u8d39\u76f4\u64ad\uff0c\u623f\u95f4\u53f7 https:\/\/live.bilibili.com\/6782735<\/span><\/p>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><br  \/><\/section>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u53c2\u4e0e\u65b9\u5f0f\u4e8c\uff1a\u4ed8\u8d39\u52a0\u5165\u8bfe\u7a0b\uff0c\u67e5\u770b\u8bfe\u7a0b\u56de\u653e<\/span><\/strong><\/p>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u4ed8\u8d39\u540e\uff0c\u53ef\u53c2\u4e0e\u96c6\u667a\u5b66\u56ed\u5e73\u53f0\u76f4\u64ad\u5e76\u52a0\u5165\u4ea4\u6d41\u7fa4\u83b7\u5f97\u89c6\u9891\u56de\u653e\u6743\u9650\u3002\u6b22\u8fce\u5bf9\u7edf\u8ba1\u529b\u5b66\u7684\u57fa\u672c\u539f\u7406\u611f\u5174\u8da3\u7684\u4f60\uff0c\u52a0\u5165\u3010<a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247628086&amp;idx=2&amp;sn=32c39ccfc209a0ac02d8995e0a64f54b&amp;chksm=e899afbbdfee26ad74fe0809f477e061095857882da0dde32640c94906424e20818d3404dd6a&amp;scene=21#wechat_redirect\" textvalue=\"\u9ec4\u6d77\u5e73\uff1a\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b | 50\u4eba\u514d\u8d39\u540d\u989d\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" data-linktype=\"2\" rel=\"noopener noreferrer\">\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66<\/a>\u3011\u8bfe\u7a0b\uff01<\/span><\/p>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u8bfe\u7a0b\u5b9a\u4ef7\uff1a499\u5143<\/span><\/p>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u8bfe\u7a0b\u65f6\u95f4\uff1a\u4ece2023\u5e742\u670818\u65e5\u8d77\uff0c\u6bcf\u5468\u516d 10:00-12:00\uff08\u8282\u5047\u65e5\u9664\u5916\uff09<\/span><\/p>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: center;\"><img class=\"rich_pages wxw-img\" data-height=\"260\" data-ratio=\"1\"  data-type=\"png\" data-w=\"260\" data-width=\"260\" style=\"width: 151px;height: 151px;\" src=\"\/wp-content\/uploads\/2023\/06\/wxsync-2023-06-ca25249416ecddfbbcd128074d57f740.png\"  \/><\/section>\n<p style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;text-align: center;line-height: 1.5em;\"><span style=\"color: rgb(136, 136, 136);font-size: 13px;\">\u626b\u7801\u4ed8\u8d39\u62a5\u540d\u8bfe\u7a0b<\/span><\/p>\n<p style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;text-align: center;line-height: 1.5em;\"><span style=\"color: rgb(136, 136, 136);font-size: 13px;\">https:\/\/campus.swarma.org\/course\/4543<\/span><\/p>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><br  \/><\/section>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u4ed8\u8d39\u6d41\u7a0b\uff1a<\/span><\/strong><\/p>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u7b2c\u4e00\u6b65\uff1a\u626b\u7801\u4ed8\u8d39<\/span><\/p>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u7b2c\u4e8c\u6b65\uff1a\u5728\u8bfe\u7a0b\u8be6\u60c5\u9875\u9762\uff0c\u586b\u5199\u201c\u5b66\u5458\u4fe1\u606f\u767b\u8bb0\u8868\u201d<\/span><\/p>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u7b2c\u4e09\u6b65\uff1a\u626b\u7801\u6dfb\u52a0\u52a9\u6559\u5fae\u4fe1\uff0c\u5165\u7fa4<\/span><\/p>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u672c\u8bfe\u7a0b\u53ef\u5f00\u53d1\u7968\u3002<\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><br  \/><\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><br  \/><\/span><\/section>\n<section powered-by=\"xiumi.us\" style=\"margin-top: 10px;margin-bottom: 0px;outline: 0px;letter-spacing: 0.544px;white-space: normal;color: rgb(136, 136, 136);font-size: 14px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;background-color: rgb(255, 255, 255);text-align: center;justify-content: center;\">\n<section style=\"outline: 0px;display: inline-block;width: auto;vertical-align: top;min-width: 10%;height: auto;box-shadow: rgb(0, 0, 0) 0px 0px 0px;border-bottom: 9px solid rgb(169, 215, 227);border-bottom-right-radius: 0px;\">\n<section powered-by=\"xiumi.us\" style=\"margin-bottom: -15px;outline: 0px;\">\n<section style=\"padding-right: 10px;padding-left: 10px;outline: 0px;color: rgb(12, 130, 169);font-size: 16px;line-height: 2;letter-spacing: 3px;\">\n<p style=\"outline: 0px;\"><strong style=\"outline: 0px;\">\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66<\/strong><\/p>\n<p style=\"outline: 0px;\"><strong style=\"outline: 0px;\">\u6bcf\u5468\u66f4\u65b0\uff0c\u6301\u7eed\u62a5\u540d\u4e2d<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;outline: 0px;letter-spacing: 0.544px;white-space: normal;clear: both;min-height: 1em;color: rgb(136, 136, 136);font-size: 14px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;background-color: rgb(255, 255, 255);line-height: 2em;\"><br  \/><\/section>\n<h2 style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><\/h2>\n<h3 style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"color: rgb(33, 166, 210);\"><strong><span style=\"font-size: 15px;\">\u672c\u5b66\u671f\u5185\u5bb9\u4ecb\u7ecd<\/span><\/strong><\/span><\/h3>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u672c\u5b63\u5185\u5bb9\u4ece2023\u5e742\u6708\u5e95\uff5e6\u6708\u5e95\uff0c\u5c06\u56f4\u7ed5\u4e66\u7c4d\u7b2c9\u7ae0-17\u7ae0\u8fdb\u884c\u4ecb\u7ecd\uff0c\u6211\u4eec\u5c06\u8bb2\u6388\u73b0\u4ee3\u795e\u7ecf\u7f51\u7edc\u7684\u524d\u6cbf\u7406\u8bba\uff0c\u8986\u76d6\u76d1\u7763\u5b66\u4e60\uff0c\u65e0\u76d1\u7763\u5b66\u4e60\uff0c\u6df1\u5ea6\u7f51\u7edc\u964d\u7ef4\u7406\u8bba\uff0c\u5faa\u73af\u795e\u7ecf\u7f51\u7edc\u7684\u52a8\u529b\u5b66\u5e73\u5747\u573a\u7406\u8bba\uff0c\u968f\u673a\u77e9\u9635\u7406\u8bba\u7b49\u3002\u6211\u4eec\u5c06\u5728\u5b66\u4e60\u7406\u8bba\u7684\u540c\u65f6\u7a7f\u63d2\u5404\u79cd\u5c0f\u9879\u76ee\u548c\u6587\u732e\u9605\u8bfb\uff0c\u5e2e\u52a9\u5b66\u751f\u5168\u65b9\u4f4d\u7684\u9e1f\u77b0\u795e\u7ecf\u7f51\u7edc\u7406\u8bba\u7814\u7a76\u7684\u5168\u8c8c\u3002<\/span><\/section>\n<h3 style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><br  \/><\/h3>\n<h3 style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"color: rgb(33, 166, 210);\"><strong><span style=\"font-size: 15px;\">\u7cfb\u5217\u8bfe\u7a0b\u5927\u7eb2<\/span><\/strong><\/span><\/h3>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u8bfe\u7a0b\u4e3b\u8981\u76ee\u7684\u662f\u57f9\u517b\u4e00\u6279\u6709\u671b\u5728\u795e\u7ecf\u7f51\u7edc\u7406\u8bba\u6df1\u8015\u7684\u9752\u5e74\u5b66\u8005\uff08\u4fa7\u91cd\u5b66\u751f\uff09\uff0c\u8bfe\u7a0b\u6d89\u53ca\u9ec4\u6d77\u5e73\u8001\u5e08\u6700\u65b0\u51fa\u7248\u7684\u4e66\u7c4d\u300aStatistical Mechanics of Neural Networks\u300b\u7684\u5927\u90e8\u5206\u5185\u5bb9\uff0c\u76ee\u6807\u662f\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\u4e66\u7c4d\u6db5\u76d6\u4e86\u7528\u4e8e\u7406\u89e3\u795e\u7ecf\u7f51\u7edc\u539f\u7406\u7684\u5fc5\u8981\u7edf\u8ba1\u529b\u5b66\u77e5\u8bc6\uff0c\u5305\u62ec\u590d\u672c\u65b9\u6cd5\u3001\u7a7a\u8154\u65b9\u6cd5\u3001\u5e73\u5747\u573a\u8fd1\u4f3c\u3001\u53d8\u5206\u6cd5\u3001\u968f\u673a\u80fd\u91cf\u6a21\u578b\u3001Nishimori\u6761\u4ef6\u3001\u52a8\u529b\u5b66\u5e73\u5747\u573a\u7406\u8bba\u3001\u5bf9\u79f0\u6027\u7834\u7f3a\u3001\u968f\u673a\u77e9\u9635\u7406\u8bba\u7b49\uff0c\u540c\u65f6\u8be6\u7ec6\u63cf\u8ff0\u4e86\u76d1\u7763\u5b66\u4e60\u3001\u65e0\u76d1\u7763\u5b66\u4e60\u3001\u8054\u60f3\u8bb0\u5fc6\u7f51\u7edc\u3001\u611f\u77e5\u5668\u7f51\u7edc\u3001\u968f\u673a\u5faa\u73af\u7f51\u7edc\u7b49\u795e\u7ecf\u7f51\u7edc\u53ca\u5176\u529f\u80fd\u7684\u7269\u7406\u6a21\u578b\u4ee5\u53ca\u89e3\u6790\u7406\u8bba\u3002\u672c\u4e66\u901a\u8fc7\u7b80\u6d01\u7684\u6a21\u578b\u5c55\u793a\u4e86\u795e\u7ecf\u7f51\u7edc\u539f\u7406\u7684\u6570\u5b66\u7f8e\u548c\u7269\u7406\u6df1\u5ea6\uff0c\u5e76\u4ecb\u7ecd\u4e86\u76f8\u5173\u5386\u53f2\u548c\u5c55\u671b\u672a\u6765\u7814\u7a76\u7684\u91cd\u8981\u8bfe\u9898\uff0c\u53ef\u4f9b\u5bf9\u795e\u7ecf\u7f51\u7edc\u539f\u7406\u611f\u5174\u8da3\u7684\u5b66\u751f\u3001\u7814\u7a76\u4eba\u5458\u4ee5\u53ca\u5de5\u7a0b\u5e08\u9605\u8bfb\u53c2\u8003\u3002<\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><br  \/><\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: center;\"><img class=\"rich_pages wxw-img\" data-height=\"865\" data-ratio=\"1.476109215017065\"  data-type=\"png\" data-w=\"586\" data-width=\"586\" style=\"height: 300px;width: 203px;\" src=\"\/wp-content\/uploads\/2023\/06\/wxsync-2023-06-c2db1e9bdae4de393cb2b9837d0bcb00.png\"  \/><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><br  \/><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"color: rgb(33, 166, 210);\"><strong><span style=\"font-size: 15px;\">\u4e66\u7c4d\u76ee\u5f55\uff08\u8be6\u7248\uff09\uff1a<\/span><\/strong><\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 1: &nbsp;Introduction<\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 2: &nbsp;Spin Glass Models and Cavity Method<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">2.1 Multi-spin Interaction Models<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">2.2 Cavity Method<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">2.3 From Cavity Method to Message Passing Algorithms<\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 3: &nbsp;Variational Mean-Field Theory and Belief Propagation<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">3.1 Variational Method<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">3.2 Variational Free Energy<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">3.3 Mean-Field Inverse Ising Problem<\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 4: &nbsp;Monte Carlo Simulation Methods<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">4.1 Monte Carlo Method<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">4.2 Importance Sampling<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">4.3 Markov Chain Sampling<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">4.4 Monte Carlo Simulations in Statistical Physics<\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 5: &nbsp;High-Temperature Expansion<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">5.1 Statistical Physics Setting<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">5.2 High-Temperature Expansion<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">5.3 Properties of the TAP Equation<\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 6: &nbsp;Nishimori Line<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">6.1 Model Setting<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">6.2 Exact Result for Internal Energy<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">6.3 Proof of No RSB Effects on the Nishimori Line<\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 7: &nbsp;Random Energy Model<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">7.1 Model Setting<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">7.2 Phase Diagram<\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 8: &nbsp;Statistical Mechanical Theory of Hopfield Model<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">8.1 Hopfield Model<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">8.2 Replica Method<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">8.3 Phase Diagram<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">8.4 Hopfield Model with Arbitrary Hebbian Length<\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 9: &nbsp;Replica Symmetry and Replica Symmetry Breaking<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">9.1 Generalized Free Energy and Complexity of States<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">9.2 Applications to Constraint Satisfaction Problems<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">9.3 More Steps of Replica Symmetry Breaking<\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 10: &nbsp;Statistical Mechanics of Restricted Boltzmann Machine<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">10.1 Boltzmann Machine<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">10.2 Restricted Boltzmann Machine<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">10.3 Free Energy Calculation<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">10.4 Thermodynamic Quantities Related to Learning<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">10.5 Stability Analysis<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">10.6 Variational Mean-Field Theory for Training Binary RBMs<\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 11: &nbsp;Simplest Model of Unsupervised Learning with Binary<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">11.1 Model Setting<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">11.2 Derivation of sMP and AMP Equations<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">11.3 Replica Computation<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">11.4 Phase Transitions<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">11.5 Measuring the Temperature of Dataset<\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 12: &nbsp;Inherent-Symmetry Breaking in Unsupervised Learning<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">12.1 Model Setting<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">12.2 Phase Diagram<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">12.3 Hyper-Parameters Inference<\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 13: &nbsp;Mean-Field Theory of Ising Perceptron<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">13.1 Ising Perceptron model<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">13.2 Message-Passing-Based Learning<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">13.3 Replica Analysis<\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 14: &nbsp;Mean-Field Model of Multi-layered Perceptron<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">14.1 Random Active Path Model<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">14.2 Mean-Field Training Algorithms<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">14.3 Spike and Slab Model<\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 15: &nbsp;Mean-Field Theory of Dimension Reduction in Neural Networks<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">15.1 Mean-Field Model<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">15.2 Linear Dimensionality and Correlation Strength<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">15.3 Dimension Reduction with Correlated Synapses<\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 16: &nbsp;Chaos Theory of Random Recurrent Neural Networks<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">16.1 Spiking and Rate Models<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">16.2 Dynamical Mean-Field Theory<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">16.3 Lyapunov Exponent and Chaos<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">16.4 Excitation-Inhibition Balance Theory<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">16.5 Training Recurrent Neural Networks<\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 17: &nbsp;Statistical Mechanics of Random Matrices<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">17.1 Spectral Density<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">17.2 Replica Method and Semi-circle Law<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">17.3 Cavity Approach and Marchenko<\/section>\n<\/li>\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"line-height: 1.75em;text-align: left;\">17.4 Spectral Densities of Random Asymmetric Matrices<\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 18: &nbsp;Perspectives<\/span><\/section>\n<h3 style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><br  \/><\/h3>\n<h3 style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"color: rgb(33, 166, 210);\"><strong><span style=\"font-size: 15px;\">\u62a5\u540d\u52a0\u5165\u8bfe\u7a0b<\/span><\/strong><\/span><\/h3>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u6b22\u8fce\u5bf9\u7edf\u8ba1\u529b\u5b66\u7684\u57fa\u672c\u539f\u7406\u611f\u5174\u8da3\u7684\u4f60\uff0c\u52a0\u5165\u3010\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u3011\u8bfe\u7a0b\uff01<\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u8bfe\u7a0b\u4ef7\u683c 499\u5143<\/span><\/strong><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: center;\"><img class=\"rich_pages wxw-img\" data-height=\"260\" data-ratio=\"1\"  data-type=\"png\" data-w=\"260\" data-width=\"260\" style=\"width: 152px;height: 152px;\" src=\"\/wp-content\/uploads\/2023\/06\/wxsync-2023-06-b953a1e5abd9de17a86135b07f66da94.png\"  \/><\/section>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;text-align: center;margin-bottom: 8px;\"><span style=\"color: rgb(136, 136, 136);font-size: 13px;\">\u626b\u7801\u4ed8\u8d39\u62a5\u540d\u8bfe\u7a0b<\/span><\/p>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u7b2c\u4e00\u6b65\uff1a\u626b\u7801\u4ed8\u8d39<\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u7b2c\u4e8c\u6b65\uff1a\u5728\u8bfe\u7a0b\u8be6\u60c5\u9875\u9762\uff0c\u586b\u5199\u201c\u5b66\u5458\u4fe1\u606f\u767b\u8bb0\u8868\u201d<\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u7b2c\u4e09\u6b65\uff1a\u626b\u7801\u6dfb\u52a0\u52a9\u6559\u5fae\u4fe1\uff0c\u5165\u7fa4<\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u672c\u8bfe\u7a0b\u53ef\u5f00\u53d1\u7968\u3002<\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><br  \/><\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u8bfe\u7a0b\u8d1f\u8d23\u4eba\u9ec4\u6d77\u5e73\u7684\u8bc4\u8bba\u6587\u7ae0\uff1a<a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247634468&amp;idx=1&amp;sn=3cba5dbd1ba494176182eaf6fc13ec00&amp;chksm=e89994a9dfee1dbf1cfa3d7a2fc35c66ef2980cdcdc14977e81fad5c52dd00c4af39266abd8f&amp;scene=21#wechat_redirect\" textvalue=\"\u7edf\u8ba1\u7269\u7406\u3001\u65e0\u5e8f\u7cfb\u7edf\u548c\u795e\u7ecf\u7f51\u7edc\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"11\" tab=\"innerlink\" data-linktype=\"2\" rel=\"noopener noreferrer\">\u7edf\u8ba1\u7269\u7406\u3001\u65e0\u5e8f\u7cfb\u7edf\u548c\u795e\u7ecf\u7f51\u7edc<\/a><\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u70b9\u51fb\u4e86\u89e3\u7cfb\u5217\u8bfe\u7a0b\u8be6\u60c5\uff1a<a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247628086&amp;idx=2&amp;sn=32c39ccfc209a0ac02d8995e0a64f54b&amp;chksm=e899afbbdfee26ad74fe0809f477e061095857882da0dde32640c94906424e20818d3404dd6a&amp;scene=21#wechat_redirect\" textvalue=\"\u9ec4\u6d77\u5e73\uff1a\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b | 50\u4eba\u514d\u8d39\u540d\u989d\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" data-linktype=\"2\" rel=\"noopener noreferrer\">\u9ec4\u6d77\u5e73\uff1a\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b | 50\u4eba\u514d\u8d39\u540d\u989d<\/a><\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><br  \/><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"color: rgb(33, 166, 210);\"><strong><span style=\"color: rgb(33, 166, 210);font-size: 15px;\">\u5f80\u671f\u56de\u987e\uff1a<\/span><\/strong><\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247653177&amp;idx=2&amp;sn=76298aabed72158b13dbc74218d4a120&amp;chksm=e899cdb4dfee44a29c2f200c077276413da177c65f42ca1ea1512904c5e0860ebd37e21e184e&amp;scene=21#wechat_redirect\" textvalue=\"\u9ec4\u6d77\u5e73\uff1a\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u7cfb\u5217\u8bfe\u7a0b\u4e0a\u5b66\u671f\u7ed3\u8bfe\u603b\u7ed3\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" data-linktype=\"2\" rel=\"noopener noreferrer\"><span style=\"font-size: 15px;\">\u9ec4\u6d77\u5e73\uff1a\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u7cfb\u5217\u8bfe\u7a0b\u4e0a\u5b66\u671f\u7ed3\u8bfe\u603b\u7ed3<\/span><\/a><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247656430&amp;idx=3&amp;sn=65f262b6d3252130572ac5cd21429f92&amp;chksm=e8993963dfeeb07521fb31b5d4f9fa4fe7045f2183db904b512eca17598ae4b835ea53e15ae2&amp;scene=21#wechat_redirect\" textvalue=\"\u590d\u672c\u5bf9\u79f0\u4e0e\u7834\u7f3a | \u5468\u516d\u76f4\u64ad\u00b7\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b\u7b2c13\u8bb2\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" style=\"font-size: 15px;\" data-linktype=\"2\" rel=\"noopener noreferrer\"><span style=\"font-size: 15px;\">\u7b2c13-15\u8bb2\uff1a\u590d\u672c\u5bf9\u79f0\u4e0e\u7834\u7f3a<\/span><\/a><br  \/><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247659530&amp;idx=2&amp;sn=b6c21b9037a8c48e6c2db8cf4df4bc4c&amp;chksm=e8992a87dfeea3912ac65a562c4923674d456c17b5a8b9f989d6286d73c2f8c99e7e22572727&amp;scene=21#wechat_redirect\" textvalue=\"\u53d7\u9650\u5236\u73bb\u5c14\u5179\u66fc\u673a\u7684\u7edf\u8ba1\u529b\u5b66\uff08\u4e8c\uff09 | \u5468\u516d\u76f4\u64ad\u00b7\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b\u7b2c17\u8bb2\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" style=\"font-size: 15px;\" data-linktype=\"2\" rel=\"noopener noreferrer\"><span style=\"font-size: 15px;\">\u7b2c16-17\u8bb2\uff1a\u53d7\u9650\u5236\u73bb\u5c14\u5179\u66fc\u673a\u7684\u7edf\u8ba1\u529b\u5b66<\/span><\/a><br  \/><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247660383&amp;idx=3&amp;sn=b1c54d13d956d6891ae2908fdc8661dc&amp;chksm=e89929d2dfeea0c4ce7f541d22bb1c936e886626144ab243dd07fd02e67815a35f537a370a2f&amp;scene=21#wechat_redirect\" textvalue=\"\u65e0\u76d1\u7763\u5b66\u4e60\u7684\u6700\u7b80\u6a21\u578b\uff1a\u5e8f\u5982\u4f55\u4ece\u5b66\u4e60\u6570\u636e\u81ea\u53d1\u6d8c\u73b0 | \u5468\u516d\u76f4\u64ad\u00b7\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b\u7b2c18\u8bb2\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" style=\"font-size: 15px;\" data-linktype=\"2\" rel=\"noopener noreferrer\"><span style=\"font-size: 15px;\">\u7b2c18\u8bb2\uff1a\u65e0\u76d1\u7763\u5b66\u4e60\u7684\u6700\u7b80\u6a21\u578b\uff1a\u5e8f\u5982\u4f55\u4ece\u5b66\u4e60\u6570\u636e\u81ea\u53d1\u6d8c\u73b0<\/span><\/a><br  \/><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247661711&amp;idx=3&amp;sn=f402fe070bd3df9e027acc446a705d83&amp;chksm=e8992202dfeeab1462ec6f7f3d1696dc4272f55422f8306e2ce333af4f516cf1f84f78d2f09c&amp;scene=21#wechat_redirect\" textvalue=\"\u65e0\u76d1\u7763\u5b66\u4e60\u7684\u5185\u7980\u5bf9\u79f0\u6027\u7834\u7f3a | \u5468\u516d\u76f4\u64ad\u00b7\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b\u7b2c19\u8bb2\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" style=\"font-size: 15px;\" data-linktype=\"2\" rel=\"noopener noreferrer\"><span style=\"font-size: 15px;\">\u7b2c19-20\u8bb2\uff1a\u65e0\u76d1\u7763\u5b66\u4e60\u7684\u5185\u7980\u5bf9\u79f0\u6027\u7834\u7f3a<\/span><\/a><br  \/><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247662962&amp;idx=3&amp;sn=c473bdc80224f75b817ea4d6df3497b1&amp;chksm=e89927ffdfeeaee96d15693d066f600d66977cdd5946f58981ad2e64169efe2dfbc1c4b1ae97&amp;scene=21#wechat_redirect\" textvalue=\"\u76d1\u7763\u5b66\u4e60\u7684\u7edf\u8ba1\u7269\u7406\u201c\u6807\u51c6\u6a21\u578b\u201d\uff1a\u7b97\u6cd5\u3001\u5b58\u50a8\u3001\u5206\u7c7b\u4e0e\u51e0\u4f55 | \u5468\u516d\u76f4\u64ad\u00b7\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b\u7b2c21\u8bb2\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" style=\"font-size: 15px;\" data-linktype=\"2\" rel=\"noopener noreferrer\"><span style=\"font-size: 15px;\">\u7b2c21\u8bb2\uff1a\u76d1\u7763\u5b66\u4e60\u7684\u7edf\u8ba1\u7269\u7406\u201c\u6807\u51c6\u6a21\u578b\u201d\uff1a\u7b97\u6cd5\u3001\u5b58\u50a8\u3001\u5206\u7c7b\u4e0e\u51e0\u4f55<\/span><\/a><br  \/><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247663464&amp;idx=2&amp;sn=3d71cfc22c92aff5595008bc0df38cf7&amp;chksm=e89925e5dfeeacf3162ca5e037ee7754b8043559c36020fd4175063fb17b44643fe1a03d8b48&amp;scene=21#wechat_redirect\" textvalue=\"\u76d1\u7763\u5b66\u4e60\u7684\u6700\u4f18\u8d1d\u53f6\u65af\u6846\u67b6\uff1a\u7b97\u6cd5\u4e0e\u76f8\u53d8 | \u5468\u516d\u76f4\u64ad\u00b7\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b\u7b2c22\u8bb2\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" style=\"font-size: 15px;\" data-linktype=\"2\" rel=\"noopener noreferrer\"><span style=\"font-size: 15px;\">\u7b2c22\u8bb2\uff1a\u76d1\u7763\u5b66\u4e60\u7684\u6700\u4f18\u8d1d\u53f6\u65af\u6846\u67b6\uff1a\u7b97\u6cd5\u4e0e\u76f8\u53d8<\/span><\/a><br  \/><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247664395&amp;idx=2&amp;sn=60ecbe77d19c58fb52a97b14da845804&amp;chksm=e8991986dfee909063bd178b2d35d1e24149f6ec9bc904dc61f4494b5b2623e98c531c6531e3&amp;scene=21#wechat_redirect\" textvalue=\"\u7269\u7406\u542f\u53d1\u7684\u6df1\u5ea6\u5b66\u4e60\u7b97\u6cd5\uff1a\u968f\u673a\u8def\u5f84\u6fc0\u53d1\u3001\u7cfb\u7efc\u5143\u5b66\u4e60\u4e0e\u6a21\u5f0f\u5206\u89e3 | \u5468\u516d\u76f4\u64ad\u00b7\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b\u7b2c23\u8bb2\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" style=\"font-size: 15px;\" data-linktype=\"2\" rel=\"noopener noreferrer\"><span style=\"font-size: 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tab=\"innerlink\" data-linktype=\"2\" rel=\"noopener noreferrer\"><span style=\"font-size: 15px;\">\u7b2c25\u8bb2\uff1a\u8109\u51b2\u795e\u7ecf\u7f51\u7edc\u4e0e\u5174\u594b\u6291\u5236\u5e73\u8861\u7406\u8bba\uff1a\u5e73\u5747\u573a\u7406\u8bba\u5bf9\u8111\u79d1\u5b66\u7684\u4e00\u6b21\u4f1f\u5927\u80dc\u5229<\/span><\/a><br  \/><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247665539&amp;idx=3&amp;sn=3482c0c00a276590d0edbce299002c95&amp;chksm=e8991d0edfee94180a777e91d3c47c1b8099ea48d6586fb04deff0961a280f0136c277a8aeb6&amp;scene=21#wechat_redirect\" textvalue=\"\u52a8\u529b\u5b66\u5e73\u5747\u573a\u7406\u8bba\u4e0e\u6df7\u6c8c\u76f8\u53d8\uff1a\u7d22\u666e\u6797\u65af\u57fa\u9047\u89c1\u859b\u5b9a\u8c14 | \u5468\u516d\u76f4\u64ad\u00b7\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b\u7b2c26\u8bb2\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" style=\"font-size: 15px;\" data-linktype=\"2\" rel=\"noopener noreferrer\"><span style=\"font-size: 15px;\">\u7b2c26\u8bb2\uff1a\u52a8\u529b\u5b66\u5e73\u5747\u573a\u7406\u8bba\u4e0e\u6df7\u6c8c\u76f8\u53d8\uff1a\u7d22\u666e\u6797\u65af\u57fa\u9047\u89c1\u859b\u5b9a\u8c14<\/span><\/a><br  \/><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;\"><br  \/><\/section>\n<section style=\"outline: 0px;margin-bottom: 0px;\"><strong style=\"outline: 0px;letter-spacing: 0.544px;font-size: 15px;text-align: left;color: rgb(255, 255, 255);font-family: PingFangSC-light;\"><span style=\"outline: 0px;background-color: rgb(12, 130, 169);\">\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfe\u7a0b<\/span><\/strong><\/section>\n<p style=\"display: none;\"><mp-style-type data-value=\"3\"><\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5bfc\u8bed 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