{"id":3786,"date":"2023-12-23T23:55:17","date_gmt":"2023-12-23T14:55:17","guid":{"rendered":"https:\/\/hayashiyus.jp\/?p=3786"},"modified":"2024-07-01T14:57:13","modified_gmt":"2024-07-01T05:57:13","slug":"%e8%87%aa%e7%94%b1%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e5%8e%9f%e7%90%86%e3%81%a8%e7%b5%b1%e5%90%88%e6%83%85%e5%a0%b1%e9%87%8f","status":"publish","type":"post","link":"https:\/\/hayashiyus.jp\/?p=3786","title":{"rendered":"\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\u539f\u7406\u3068\u7d71\u5408\u60c5\u5831\u7406\u8ad6\u306e\u67b6\u6a4b"},"content":{"rendered":"\r\n

\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\u539f\u7406\u306b\u5f93\u3046\u30b7\u30b9\u30c6\u30e0\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\uff0c\u3059\u306a\u308f\u3061\u80fd\u52d5\u7684\u63a8\u8ad6\u3092\u884c\u3046\u30a8\u30fc\u30b8\u30a7\u30f3\u30c8\u306e\u5185\u90e8\u72b6\u614b\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f\uff0c\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f\u3092\u7528\u3044\u3066\u8a18\u8ff0\u3067\u304d\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u308b\uff0e\u7b46\u8005\u306f\u3053\u306e\u30d6\u30ed\u30b0\u6295\u7a3f\u3092\u901a\u3058\u3066\uff0c\u2460\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f\u306b\u306f\u30b2\u30fc\u30b8\u5bfe\u79f0\u6027\u304c\u96a0\u308c\u3066\u3044\u308b<\/font>\u3053\u3068\u3092\u660e\u3089\u304b\u306b\u3057\uff0c\u2461\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f\u3092\u305d\u308c\u81ea\u8eab\u306b\u5bfe\u3059\u308b\u5171\u5f79\u306a\u8868\u73fe\u306b\u79fb\u3057\u63db\u3048\u308b\u30b2\u30fc\u30b8\u5909\u63db\u304c\u5b58\u5728\u3059\u308b<\/font>\u3053\u3068\u3092\u793a\u3059\uff0e\u305d\u3057\u3066\u6700\u5f8c\u306b\uff0c\u30b2\u30fc\u30b8\u5909\u63db\u3092\u901a\u3058\u3066\u5f97\u3089\u308c\u305f\u5171\u5f79\u306a\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f\u3092\u8abf\u3079\u308b\u3053\u3068\u3092\u901a\u3058\u3066\uff0c\u2462\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\u539f\u7406\u3068\u7d71\u5408\u60c5\u5831\u7406\u8ad6\u3092\u67b6\u6a4b\u3059\u308b\u9053\u7b4b<\/font>\u3092\u660e\u3089\u304b\u306b\u3059\u308b\uff0e<\/p>\r\n

  <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\"\"<\/center>\r\n\r\n\r\n\r\n

1. \u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f\u306b\u6f5c\u3080\u5bfe\u79f0\u6027<\/h4>\r\n\r\n\r\n
\r\n

1\u22121. \u78ba\u7387\u7684\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u304b\u3089\u306e\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f\u306e\u5c0e\u51fa<\/h4>\r\n

<\/p>\r\n

<\/p>\r\n

\u89e3\u6790\u529b\u5b66\u306e\u6a19\u6e96\u7684\u306a\u624b\u7d9a\u304d\u306b\u5f93\u3063\u3066\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f\u3092\u5c0e\u51fa\u3059\u308b\uff0e\u3053\u306e\u624b\u7d9a\u304d\u3092\u7d4c\u7531\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\uff0c\u78ba\u7387\u7684\u30e9\u30b0\u30e9\u30f3\u30b8\u30a2\u30f3\uff0c\u78ba\u7387\u7684\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306b\u6f5c\u3080\u62d8\u675f\u6761\u4ef6\uff0c\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f\u306e\u96a0\u308c\u305f\u5bfe\u79f0\u6027\u3092\u7099\u308a\u51fa\u3059\uff0e\u306f\u3058\u3081\u306b\u78ba\u7387\u7684\u30e9\u30b0\u30e9\u30f3\u30b8\u30a2\u30f3<\/p>\r\n

(1) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u3092\u5c0e\u5165\u3059\u308b\uff0e\u305f\u3060\u3057\uff0c\u6dfb\u5b57\"j, k, l\"\u306f\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f\u306e\u89e3\"x\"\u304c\u6301\u3064\u81ea\u7531\u5ea6\"j, k, l\left(=1,\cdots,n\right)\"\u3092\u8868\u3057\u3066\u3044\u308b\uff0e\u672c\u7a3f\u3067\u306f\"x\"\u3092\u30cb\u30e5\u30fc\u30ed\u30f3\u96c6\u56e3\u306e\u72b6\u614b\u3092\u8868\u3059\u72b6\u614b\u30d9\u30af\u30c8\u30eb\uff0c\"x_{j}\"\u306e\u305d\u308c\u305e\u308c\u3092\u5404\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u72b6\u614b\u3068\u307f\u306a\u3059\uff0e\u307e\u305f\uff0c\u8cea\u91cf\u884c\u5217\u306e\u6210\u5206\"m_{jk}\"\uff0c\u6469\u64e6\u884c\u5217\u306e\u6210\u5206\"\gamma_{jk}\"\uff0c\"L^{jk}=\left(\gamma^{-1}\right)^{jk}\"\u306f\uff0c\u305d\u308c\u305e\u308c\u30cb\u30e5\u30fc\u30ed\u30f3\u9593\u306e\u76f8\u4e92\u4f5c\u7528\u306e\u5f37\u3055\u3092\u8868\u3059\u5b9a\u6570\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\uff0c\u5404\u884c\u5217\u304c\u975e\u5bfe\u89d2\u6210\u5206\u3092\u6301\u3064\u5834\u5408\uff0c\u30cb\u30e5\u30fc\u30ed\u30f3\u9593\u306b\u306f\u76f8\u4e92\u4f5c\u7528\u304c\u50cd\u3044\u3066\u3044\u308b\uff0e\"f_{j}(t)\"\u306f\u975e\u4fdd\u5b58\u529b\uff0c\"\xi_{j}(t)\"\u306f\u767d\u8272\u30ac\u30a6\u30b9\u30ce\u30a4\u30ba\u3092\u8868\u3057\uff0c\u5f8c\u8005\u306e\u78ba\u7387\u5e73\u5747\u306b\u3064\u3044\u3066<\/p>\r\n

(2) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u304c\u6210\u308a\u7acb\u3064\u3068\u3057\u3088\u3046\uff0e\u305f\u3060\u3057\uff0c\"\beta\"\u306f\u30b7\u30b9\u30c6\u30e0\u306e\u9006\u6e29\u5ea6\u3092\u8868\u3059\uff0e\u3053\u306e\u3068\u304d\u30b7\u30b9\u30c6\u30e0\u306e\u904b\u52d5\u91cf\"p\"\u306f<\/p>\r\n

(3) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u3067\u5b9a\u7fa9\u3055\u308c\u308b\uff0e\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u5909\u63db\u3092\u7528\u3044\u3066\uff0c\u3053\u306e\u30b7\u30b9\u30c6\u30e0\u306e\u78ba\u7387\u7684\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u3092\u6c42\u3081\u308b\u3068<\/p>\r\n

(4) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u3068\u306a\u308b\u306e\u3067\uff0c\u6b63\u6e96\u65b9\u7a0b\u5f0f\u3088\u308a\u3053\u306e\u30b7\u30b9\u30c6\u30e0\u304c\u5f93\u3046\u904b\u52d5\u65b9\u7a0b\u5f0f\u304c\u5b9a\u307e\u308b\uff0e<\/p>\r\n

(5) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

(4)\u5f0f\u306e\u4e0a\u6bb5\u306e\u5f0f\u3092\u6642\u9593\u30d1\u30e9\u30e1\u30fc\u30bf\"t\"\u306b\u3064\u3044\u3066\u5fae\u5206\u3059\u308b\u3068<\/p>\r\n

(6) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u3068\u306a\u308b\u306e\u3067\uff0c\u3053\u306e(5)\u5f0f\u3068(4)\u5f0f\u306e\u4e0b\u6bb5\u306e\u5f0f\u3092\u7a81\u304d\u5408\u308f\u305b\u308b\u3068\uff0c\u3053\u306e\u30b7\u30b9\u30c6\u30e0\u304c\u5f93\u3046\u904b\u52d5\u65b9\u7a0b\u5f0f\u304c\u4ee5\u4e0b\u306b\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308b\uff0e
\r\n\u30a2\u30f3\u30c0\u30fc\u30c0\u30f3\u30d7\u7cfb\u306e\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f\uff1a<\/p>\r\n

(7) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u66f4\u306b\u3053\u3053\u3067\"\ddot{x}^{k} - L^{kl} \dot{f}_{l}=0\"\u3092\u8981\u8acb\u3059\u308b\u3068\uff0c\u30aa\u30fc\u30d0\u30fc\u30c0\u30f3\u30d7\u7cfb\u306e\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f\uff1a<\/p>\r\n

(8) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u304c\u5c0e\u304b\u308c\u308b\uff0e\u3053\u3046\u3057\u3066(1)\uff0c(4)\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u78ba\u7387\u7684\u30e9\u30b0\u30e9\u30f3\u30b8\u30a2\u30f3\"\widetilde{L}(x, \dot{x})\"\uff0c\u78ba\u7387\u7684\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\"\widetilde{H}(x, p)\"\u304c\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f(7)\uff0c(8)\u5f0f\u3092\u4e0e\u3048\u308b\u3053\u3068\u304c\u78ba\u304b\u3081\u3089\u308c\u305f\uff0e<\/p>\r\n<\/div>\r\n\r\n

\r\n

1\u22122. \u78ba\u7387\u7684\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306b\u6f5c\u3080\u62d8\u675f\u6761\u4ef6<\/h4>\r\n

<\/p>\r\n

<\/p>\r\n

(8)\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f\u304b\u3089\u6b21\u306e\u30d5\u30a9\u30c3\u30ab\u30fc\u30fb\u30d7\u30e9\u30f3\u30af\u65b9\u7a0b\u5f0f\u304c\u5c0e\u304b\u308c\u308b\uff0e<\/p>\r\n

(9) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u3053\u306e\u30d5\u30a9\u30c3\u30ab\u30fc\u30fb\u30d7\u30e9\u30f3\u30af\u65b9\u7a0b\u5f0f\u306e\u89e3\"P(x, t)\"\u306f\uff0c\u6642\u523b\"t\"\u306b\u304a\u3051\u308b\u30cb\u30e5\u30fc\u30ed\u30f3\u96c6\u56e3\u306e\u72b6\u614b\u5206\u5e03\u3092\u8868\u3057\u3066\u3044\u308b\uff0e\u72b6\u614b\u5206\u5e03\"P(x, t)\"\u306f\uff0c\u6b21\u306e\u6027\u8cea\u3092\u6e80\u305f\u3059\u305f\u3081\uff0c\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f\u306e\u89e3\"x\"\u304c\u5f93\u3046\u3079\u304d\u78ba\u7387\u5206\u5e03\u3068\u898b\u505a\u3059\u3053\u3068\u304c\u3067\u304d\u308b\uff0e<\/p>\r\n

(10) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u307e\u305f\u78ba\u7387\u5206\u5e03\u304c\u6e80\u305f\u3059\u3079\u304d\u6027\u8cea(10)\u5f0f\u304b\u3089\u72b6\u614b\u5206\u5e03\"P(x, t)\"\u306b\u5bfe\u3057\u3066\u6b21\u306e\u6027\u8cea\u304c\u8981\u8acb\u3055\u308c\u308b\uff0e<\/p>\r\n

(11) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u3053\u3053\u3067\u78ba\u7387\u7684\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\"S(x)\"\uff0c\uff08\u78ba\u7387\u7684\uff09\u975e\u5e73\u8861\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\"F(x)\"\u3092\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u308b\u3068<\/p>\r\n

(12) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u6b21\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3064\uff0e<\/p>\r\n

(13) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u3053\u3053\u304b\u3089\u6b21\u306e\u7b49\u5f0f\u304c\u5c0e\u304b\u308c\u308b\uff0e<\/p>\r\n

(14) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u3057\u305f\u304c\u3063\u3066\uff0c\u30aa\u30fc\u30d0\u30fc\u30c0\u30f3\u30d7\u7cfb\u306e\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f(8)\u5f0f\u306e\u4e21\u8fba\u306b\u5bfe\u3057\u3066\u78ba\u7387\u5e73\u5747\u3092\u3068\u308b\u3068<\/p>\r\n

(15) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u304c\u6210\u308a\u7acb\u3064\uff0e(15)\u5f0f\u3092\u307f\u308b\u3068\u30aa\u30fc\u30d0\u30fc\u30c0\u30f3\u30d7\u7cfb\u306e\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f(8)\u5f0f\u3092<\/p>\r\n

(16) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u3068\u66f8\u304d\u76f4\u3057\u3066\u3082\u826f\u3055\u305d\u3046\u3060\u304c\uff0c\u5f53\u521d(8)\u5f0f\u306b\u306f\u5b58\u5728\u3057\u306a\u304b\u3063\u305f\"\frac{1}{\beta}\frac{\partial S}{\partial x^{k}}\"\u306f\u4e00\u4f53\u3069\u3053\u304b\u3089\u73fe\u308c\u305f\u306e\u3060\u308d\u3046\u304b\uff1f\u30d5\u30a9\u30c3\u30ab\u30fc\u30fb\u30d7\u30e9\u30f3\u30af\u65b9\u7a0b\u5f0f(9)\u5f0f\u306f\uff08\u78ba\u7387\u7684\uff09\u975e\u5e73\u8861\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\"F(x)\"\u3092\u4f7f\u3063\u3066\u6b21\u306e\u3088\u3046\u306b\u66f8\u304d\u76f4\u305b\u308b\uff0e<\/p>\r\n

(17) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u9006\u306b\uff0c\u3053\u306e\u65b0\u3057\u3044\u30d5\u30a9\u30c3\u30ab\u30fc\u30fb\u30d7\u30e9\u30f3\u30af\u65b9\u7a0b\u5f0f(17)\u5f0f\u3092\u51fa\u767a\u70b9\u306b\u3059\u308b\u3068\uff0c\u3053\u306e\u3088\u3046\u306a\u65b9\u7a0b\u5f0f\u3092\u5c0e\u304f\u904b\u52d5\u65b9\u7a0b\u5f0f\u3068\u3057\u3066\u4ee5\u4e0b\u304c\u5c0e\u304b\u308c\u308b [Nelson 67]\uff0e<\/p>\r\n

(18) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u3053\u3053\u3067\"\xi^{\ast}_{j}(t)\"\u306f\u65b0\u3057\u3044\u767d\u8272\u30ac\u30a6\u30b9\u30ce\u30a4\u30ba\u3092\u8868\u3057\uff0c\u305d\u306e\u78ba\u7387\u5e73\u5747\u306b\u3064\u3044\u3066\u4ee5\u4e0b\u304c\u6210\u308a\u7acb\u3064<\/p>\r\n

(19) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u5b9f\u306f\uff0c\u3053\u306e\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\"U(x)\"\uff0c\u975e\u4fdd\u5b58\u529b\"f_{j}(x)\"\uff0c\u767d\u8272\u30ac\u30a6\u30b9\u30ce\u30a4\u30ba\"\xi_{j}(t)\"\u306b\u5bfe\u3059\u308b\u5909\u63db<\/p>\r\n

(20) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u306f\uff0c\u78ba\u7387\u7684\u30e9\u30b0\u30e9\u30f3\u30b8\u30a2\u30f3\"\widetilde{L}(x, \dot{x})\"\u306e\u30d8\u30c3\u30bb\u884c\u5217<\/p>\r\n

(21) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u304c\u6301\u3064\u7279\u7570\u6027<\/p>\r\n

(22) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u304b\u3089\u5c0e\u304b\u308c\u308b\uff0e\u78ba\u7387\u7684\u30e9\u30b0\u30e9\u30f3\u30b8\u30a2\u30f3\u306e\u5024\u306f\u6642\u3005\u523b\u3005\u3068\u78ba\u7387\u7684\u306b\u63fa\u3089\u3050\u305f\u3081\uff0c\u305d\u306e\u30d8\u30c3\u30bb\u884c\u5217\u306e\u5024\u3082\u78ba\u7387\u7684\u306b\u63fa\u3089\u3044\u3067\u3044\u308b\uff0e\u3053\u306e\u30d8\u30c3\u30bb\u884c\u5217\"W_{jk}\"\u304c\u7279\u7570\u6027\uff08(22)\u5f0f\u306e\u6027\u8cea\uff09\u3092\u6301\u3064\u3068\u304d\uff0c\u901f\u5ea6\"\dot{x}\"\u304b\u3089\u904b\u52d5\u91cf\"p\"\u3078\u306e\u5909\u63db\u306f1\u5bfe1\u306b\u5b9a\u307e\u3089\u305a\uff0c\u78ba\u7387\u7684\u30e9\u30b0\u30e9\u30f3\u30b8\u30a2\u30f3\u304b\u3089\u78ba\u7387\u7684\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u3078\u306e\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u5909\u63db\u306f\u6b63\u5e38\u306b\u6a5f\u80fd\u3057\u306a\u304f\u306a\u308b\uff0e<\/p>\r\n

(23) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u3053\u306e\u3088\u3046\u306a\u72b6\u6cc1\u3067\u306f\uff0c\u78ba\u7387\u7684\u30e9\u30b0\u30e9\u30f3\u30b8\u30a2\u30f3\uff0c\u78ba\u7387\u7684\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u304b\u3089\u4f59\u5206\u306a\u81ea\u7531\u5ea6\u3092\u53d6\u308a\u9664\u304f\u5fc5\u8981\u304c\u3042\u308b\uff0e\u3053\u306e\u3068\u304d\u91cd\u8981\u306b\u306a\u308b\u306e\u304c\uff0c\u7279\u7570\u30e9\u30b0\u30e9\u30f3\u30b8\u30a2\u30f3\u306e\u6761\u4ef6\uff08(22)\u5f0f\u306e\u6027\u8cea\uff09\u304b\u3089\u8981\u8acb\u3055\u308c\u308b\u62d8\u675f\u6761\u4ef6\"\phi^{l}(x, p)\"\u3060\uff0e\u3053\u306e\u62d8\u675f\u6761\u4ef6\"\phi^{l}(x, p)\"\u3092\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u306e\u672a\u5b9a\u4e57\u6570\u6cd5\u306b\u5f93\u3063\u3066\u78ba\u7387\u7684\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306b\u4ed8\u52a0\u3059\u308b\u3053\u3068\u3067\uff0c\u78ba\u7387\u7684\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u304b\u3089\u4f59\u5206\u306a\u81ea\u7531\u5ea6\u3092\u53d6\u308a\u9664\u304f\u3053\u3068\u304c\u3067\u304d\u308b\uff0e<\/p>\r\n

(24) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u3053\u306e\u65b0\u3057\u3044\u78ba\u7387\u7684\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\"\widetilde{H}^{\prime}(x, p)\"\u304b\u3089\u306f\u4f59\u5206\u306a\u81ea\u7531\u5ea6\u304c\u53d6\u308a\u9664\u304b\u308c\u3066\u3044\u308b\u305f\u3081\uff0c\u3044\u3064\u3067\u3082\u554f\u984c\u306a\u304f\u6b63\u6e96\u65b9\u7a0b\u5f0f\u3092\u5c0e\u304f\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u5929\u4e0b\u308a\u7684\u3060\u304c\uff0c\u3053\u3053\u3067\u88dc\u6b63\u9805\"\lambda_{l}\phi^{l}(x, p)\"\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3068\u3063\u3066\u307f\u3088\u3046\uff0e<\/p>\r\n

(25) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u5b9f\u306f\uff0c\u3053\u306e\u3088\u3046\u306a\u88dc\u6b63\u9805\"\lambda_{l}\phi^{l}(x, p)\"\u306e\u56fa\u5b9a\u306f\u30b2\u30fc\u30b8\u56fa\u5b9a\u306b\u5bfe\u5fdc\u3057\uff0c\u65b0\u3057\u3044\"\widetilde{H}^{\prime}(x, p)\"\u306b\u57fa\u3065\u304d\u6b21\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u5c0e\u304f\uff0e<\/p>\r\n

(26) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u7d50\u5c40\uff0c\u4e0a\u8a18\u306e\u3088\u3046\u306a\u7279\u5225\u306a\u30b2\u30fc\u30b8\u3092\u9078\u629e\u3057\u305f\u89b3\u6e2c\u8005\u306b\u3068\u3063\u3066\u306f\uff0c\u30aa\u30fc\u30d0\u30fc\u30c0\u30f3\u30d7\u7cfb\u306e\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f\uff08\"\ddot{x}^{k} - L^{kl} \dot{f}_{l}=0\"\uff09\u304c<\/p>\r\n

(27) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u3068\u306a\u308b\u3053\u3068\u304c\u78ba\u304b\u3081\u3089\u308c\u305f\uff0e\u3053\u306e\u3088\u3046\u306a\u89b3\u6e2c\u8005\u306b\u3068\u3063\u3066\uff0c\u30cb\u30e5\u30fc\u30ed\u30f3\u96c6\u56e3\u306f\uff08\u78ba\u7387\u7684\uff09\u975e\u5e73\u8861\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u6e1b\u5c11\u3055\u305b\u308b\u65b9\u5411\u306b\u6642\u9593\u767a\u5c55\u3057\u3066\u3044\u304f\u3088\u3046\u306b\u89b3\u5bdf\u3055\u308c\u308b\uff0e<\/p>\r\n<\/div>\r\n\r\n\r\n

2. \u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\u539f\u7406\u3068\u7d71\u5408\u60c5\u5831\u7406\u8ad6\u306e\u67b6\u6a4b<\/h4>\r\n\r\n\r\n
\r\n

2\u22121. \u975e\u5e73\u8861\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\u3068\u7d71\u5408\u60c5\u5831\u91cf\u306e\u95a2\u4fc2<\/h4>\r\n

<\/p>\r\n

<\/p>\r\n

\u30b7\u30b9\u30c6\u30e0\u304c\u5e73\u8861\u72b6\u614b\u306b\u3042\u308b\u3068\u304d\uff0c\u3059\u306a\u308f\u3061\"\frac{\partial P(x, t)}{\partial t}=0\"\u3068\u306a\u308b\u3068\u304d\uff0c\u5e73\u8861\u72b6\u614b\u306b\u304a\u3051\u308b\u30b7\u30b9\u30c6\u30e0\u306e\u72b6\u614b\u5206\u5e03\"P_{\mathrm{eq}}(x, t)\"\u306b\u3064\u3044\u3066\u6b21\u304c\u6210\u308a\u7acb\u3064\uff0e<\/p>\r\n

(28) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u3053\u306e\u3068\u304d\u975e\u5e73\u8861\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\"F(t)\"\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u305b\u308b\uff0e<\/p>\r\n

(29) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u305f\u3060\u3057\uff0c\"D_{\mathrm{KL}}(\cdots)\"\u306fKL-\u30c0\u30a4\u30d0\u30fc\u30b8\u30a7\u30f3\u30b9\u3092\u8868\u3057\u3066\u3044\u308b\uff0e\u3053\u306e\u3068\u304d\u30b7\u30b9\u30c6\u30e0\u5168\u4f53\u304c\u5358\u4f4d\u6642\u9593\u3042\u305f\u308a\u306b\u751f\u307f\u51fa\u3059\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u751f\u6210\u7387\u306f<\/p>\r\n

(30) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3068\u306a\u308b\uff0e\u307e\u305f\u5bfe\u6570Sobolev\u4e0d\u7b49\u5f0f\u304b\u3089\u4ee5\u4e0b\u306e\u4e0d\u7b49\u5f0f\u304c\u5c0e\u304b\u308c\u308b\uff08\u5e73\u8861\u72b6\u614b\u3078\u306e\u7dda\u5f62\u53ce\u675f\uff09\uff0e<\/p>\r\n

(31) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

(32) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3053\u3053\u3067\u30b7\u30b9\u30c6\u30e0\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u62e1\u5f35\u3059\u308b\uff0e<\/p>\r\n

  <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u3092\u30b5\u30d6\u30b7\u30b9\u30c6\u30e0\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306e\u548c\u3068\u3057\u3066\u66f8\u304f\u3068<\/p>\r\n

(33) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3053\u3053\u3067\u30b7\u30b9\u30c6\u30e0\u5168\u4f53\u306e\u60c5\u5831\u306e\u7d71\u5408\u5ea6\u5408\u3044\u3092\u8868\u3059\u7d71\u5408\u60c5\u5831\u91cf\u306e\u751f\u6210\u7387<\/p>\r\n

(34) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3092\u5c0e\u5165\u3057\u3088\u3046\uff0e<\/p>\r\n\r\n

\u3057\u305f\u304c\u3063\u3066\uff0c\u30b7\u30b9\u30c6\u30e0\u5168\u4f53\u306e\u60c5\u5831\u306e\u7d71\u5408\u5ea6\u5408\u3044\u3092\u8868\u3059\u7d71\u5408\u60c5\u5831\u91cf\u306f<\/p>\r\n

(35) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n\r\n

\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\u539f\u7406\u3068\u7d71\u5408\u60c5\u5831\u7406\u8ad6\u3092\u67b6\u6a4b\u3067\u304d\u308b\u3053\u3068\u304c\u660e\u3089\u304b\u306b\u306a\u3063\u305f\uff0e<\/p>\r\n<\/div>\r\n\r\n\r\n

\u53c2\u8003\u6587\u732e<\/h4>\r\n

<\/p>\r\n

<\/p>\r\n

    \r\n\t
  1. \u6797 \u7950\u8f14; \u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\u539f\u7406\u3068\u7269\u7406\u5b66<\/a>. \u4eba\u5de5\u77e5\u80fd 2023; 38 \u5dfb 6 \u53f7 p. 847-852.<\/li>\r\n\t
  2. Takuya Isomura, Karl Friston; Reverse-Engineering Neural Networks to Characterize Their Cost Functions<\/a>.\u00a0Neural Comput 2020; 32 (11): 2085\u20132121.<\/li>\r\n\t
  3. Takuya Isomura, Hideaki Shimazaki and Karl Friston; Canonical neural networks perform active inference<\/a>.\u00a0Commun Biol 2022; 5, 55.<\/li>\r\n\t
  4. Maxwell J. D. Ramstead, Dalton A. R. Sakthivadivel, Conor Heins, Magnus Koudahl, Beren Millidge, Lancelot Da Costa, Brennan Klein and Karl Friston; On Bayesian mechanics – a physics of and by beliefs<\/a>.\u00a0Interface Focus 2023; Volume 13, Issue 3.<\/li>\r\n\t
  5. Edward Nelson; Dynamical Theories of Brownian Motion<\/a>.\u00a0Princeton University Press 1967.<\/li>\r\n
  6. Kunio Yasue; Quantum mechanics and stochastic control theory<\/a>. Journal of Mathematical Physics 1981, 22, 1010\u20131020<\/li>\r\n\t
  7. Adam B. Barrett and Anil K. Seth; Practical Measures of Integrated Information for Time-Series Data<\/a>.\u00a0PLOS Computational Biology 2011; 7(1): e1001052.<\/li>\r\n\t
  8. Max Tegmark; Improved Measures of Integrated Information<\/a>.\u00a0PLOS Computational Biology 2016; 12(11): e1005123.<\/li>\r\n\t
  9. Nadine Spychala and Miguel Aguilera; Exploring the relation of variational inference and integrated information in a minimal model<\/a>.\u00a0Proceedings of the ALIFE 2023: Ghost in the Machine; pp. 52.<\/li>\r\n
  10. Miguel Aguilera and Ezequiel A. Di Paolo; Integrated information in the thermodynamic limit<\/a>. Neural Networks 2019; Volume 114: Pages 136-146.<\/li>\r\n<\/ol>","protected":false},"excerpt":{"rendered":"

    \u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\u539f\u7406\u306b\u5f93\u3046\u30b7\u30b9\u30c6\u30e0\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\uff0c\u3059\u306a\u308f\u3061\u80fd\u52d5\u7684\u63a8\u8ad6\u3092\u884c\u3046\u30a8\u30fc\u30b8\u30a7\u30f3\u30c8\u306e\u5185\u90e8\u72b6\u614b\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f\uff0c\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f\u3092\u7528\u3044\u3066\u8a18\u8ff0\u3067\u304d\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u308b\uff0e\u7b46\u8005\u306f\u3053\u306e\u30d6\u30ed\u30b0\u6295\u7a3f\u3092\u901a\u3058\u3066\uff0c\u2460\u30e9\u30f3\u30b8\u30e5\u30d0\u30f3\u65b9\u7a0b\u5f0f\u306b\u306f\u30b2 […]<\/p>\n","protected":false},"author":135576855,"featured_media":3800,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"jetpack_seo_schema_type":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_hide_featured_image":false,"_jetpack_featured_image_duplicate_dismissed":0,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"{title}\n\n{excerpt}\n\n{url}","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":true},"categories":[1],"tags":[],"class_list":["post-3786","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/pcnxx5-Z4","jetpack_featured_media_url":"https:\/\/i0.wp.com\/hayashiyus.jp\/wp-content\/uploads\/2023\/12\/langevin_dynamics_eyecatch-e1703123182817.png?fit=944%2C689&ssl=1","_links":{"self":[{"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/posts\/3786","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/users\/135576855"}],"replies":[{"embeddable":true,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3786"}],"version-history":[{"count":100,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/posts\/3786\/revisions"}],"predecessor-version":[{"id":4703,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/posts\/3786\/revisions\/4703"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/media\/3800"}],"wp:attachment":[{"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3786"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3786"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3786"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}