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[Video of Lecture](https://youtu.be/SuxK68tj-V8)\n", + "\n", + "6. [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek37.pdf)" ] }, { "cell_type": "markdown", - "id": "21f2937f", + "id": "dd264b1c", "metadata": { "editable": true }, @@ -69,7 +71,7 @@ }, { "cell_type": "markdown", - "id": "da32a24e", + "id": "608927bc", "metadata": { "editable": true }, @@ -79,7 +81,7 @@ }, { "cell_type": "markdown", - "id": "2b7f8433", + "id": "60640670", "metadata": { "editable": true }, @@ -103,7 +105,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "2a8c5baa", + "id": "947b67ee", "metadata": { "collapsed": false, "editable": true @@ -117,7 +119,7 @@ }, { "cell_type": "markdown", - "id": "47d8423d", + "id": "0a787eca", "metadata": { "editable": true }, @@ -128,7 +130,7 @@ }, { "cell_type": "markdown", - "id": "08d37b91", + "id": "d7e84ac7", "metadata": { "editable": true }, @@ -140,7 +142,7 @@ }, { "cell_type": "markdown", - "id": "a3c412ef", + "id": "f34c217e", "metadata": { "editable": true }, @@ -150,7 +152,7 @@ }, { "cell_type": "markdown", - "id": "3f1b2071", + "id": "b145d4eb", "metadata": { "editable": true }, @@ -162,7 +164,7 @@ }, { "cell_type": "markdown", - "id": "07536cbd", + "id": "2df6d60d", "metadata": { "editable": true }, @@ -176,7 +178,7 @@ }, { "cell_type": "markdown", - "id": "34287135", + "id": "1deafba0", "metadata": { "editable": true }, @@ -192,7 +194,7 @@ }, { "cell_type": "markdown", - "id": "c1063bfb", + "id": "520ac423", "metadata": { "editable": true }, @@ -202,7 +204,7 @@ }, { "cell_type": "markdown", - "id": "d327d2e3", + "id": "48e7232b", "metadata": { "editable": true }, @@ -214,7 +216,7 @@ }, { "cell_type": "markdown", - "id": "b2c9a9cd", + "id": "0194af20", "metadata": { "editable": true }, @@ -224,7 +226,7 @@ }, { "cell_type": "markdown", - "id": "062a7534", + "id": "9f58d823", "metadata": { "editable": true }, @@ -236,7 +238,7 @@ }, { "cell_type": "markdown", - "id": "b1b15536", + "id": "10129d02", "metadata": { "editable": true }, @@ -250,7 +252,7 @@ }, { "cell_type": "markdown", - "id": "a259e250", + "id": "4cd07523", "metadata": { "editable": true }, @@ -260,7 +262,7 @@ }, { "cell_type": "markdown", - "id": "002197c1", + "id": "1bda7e01", "metadata": { "editable": true }, @@ -271,7 +273,7 @@ }, { "cell_type": "markdown", - "id": "55e8dca9", + "id": "aa64bdd1", "metadata": { "editable": true }, @@ -286,7 +288,7 @@ }, { "cell_type": "markdown", - "id": "a97ffaec", + "id": "3e7f4c5d", "metadata": { "editable": true }, @@ -296,7 +298,7 @@ }, { "cell_type": "markdown", - "id": "b59a4220", + "id": "79ed73a8", "metadata": { "editable": true }, @@ -308,7 +310,7 @@ }, { "cell_type": "markdown", - "id": "ba5dcc08", + "id": "1b70ad9b", "metadata": { "editable": true }, @@ -320,7 +322,7 @@ }, { "cell_type": "markdown", - "id": "d8907fed", + "id": "2fbef92d", "metadata": { "editable": true }, @@ -335,7 +337,7 @@ }, { "cell_type": "markdown", - "id": "728d5b78", + "id": "0728a369", "metadata": { "editable": true }, @@ -348,7 +350,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "02d7e401", + "id": "a48d43f0", "metadata": { "collapsed": false, "editable": true @@ -407,7 +409,7 @@ }, { "cell_type": "markdown", - "id": "4dd147c2", + "id": "6c1c6ed1", "metadata": { "editable": true }, @@ -419,7 +421,7 @@ }, { "cell_type": "markdown", - "id": "75ca7f80", + "id": "a82ce6e3", "metadata": { "editable": true }, @@ -431,7 +433,7 @@ }, { "cell_type": "markdown", - "id": "5b897c75", + "id": "cb0de7c2", "metadata": { "editable": true }, @@ -441,7 +443,7 @@ }, { "cell_type": "markdown", - "id": "46aa12f6", + "id": "b76c0dea", "metadata": { "editable": true }, @@ -455,7 +457,7 @@ }, { "cell_type": "markdown", - "id": "8ac05816", + "id": "4eeb07f6", "metadata": { "editable": true }, @@ -465,7 +467,7 @@ }, { "cell_type": "markdown", - "id": "cee76d94", + "id": "cc7d6c64", "metadata": { "editable": true }, @@ -477,7 +479,7 @@ }, { "cell_type": "markdown", - "id": "88cf9577", + "id": "08bd65db", "metadata": { "editable": true }, @@ -488,7 +490,7 @@ }, { "cell_type": "markdown", - "id": "0108d67e", + "id": "a1c5a4d1", "metadata": { "editable": true }, @@ -503,7 +505,7 @@ }, { "cell_type": "markdown", - "id": "1e307469", + "id": "f178c97e", "metadata": { "editable": true }, @@ -517,7 +519,7 @@ }, { "cell_type": "markdown", - "id": "c8dc7485", + "id": "3853aec7", "metadata": { "editable": true }, @@ -528,7 +530,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "2909407a", + "id": "81740e7b", "metadata": { "collapsed": false, "editable": true @@ -589,7 +591,7 @@ }, { "cell_type": "markdown", - "id": "d25693ff", + "id": "aa1b6e08", "metadata": { "editable": true }, @@ -611,7 +613,7 @@ }, { "cell_type": "markdown", - "id": "78b0bf65", + "id": "d1b9be1a", "metadata": { "editable": true }, @@ -626,7 +628,7 @@ }, { "cell_type": "markdown", - "id": "9ee803d8", + "id": "2e1267e6", "metadata": { "editable": true }, @@ -637,7 +639,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "ac420f7a", + "id": "494e82a7", "metadata": { "collapsed": false, "editable": true @@ -703,7 +705,7 @@ }, { "cell_type": "markdown", - "id": "c548d574", + "id": "46858c7c", "metadata": { "editable": true }, @@ -714,7 +716,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "687e9d89", + "id": "6a917123", "metadata": { "collapsed": false, "editable": true @@ -788,7 +790,7 @@ }, { "cell_type": "markdown", - "id": "27a27a67", + "id": "361b2aa8", "metadata": { "editable": true }, @@ -807,7 +809,7 @@ }, { "cell_type": "markdown", - "id": "a12c19b2", + "id": "2dacb8ef", "metadata": { "editable": true }, @@ -828,7 +830,7 @@ }, { "cell_type": "markdown", - "id": "b8436434", + "id": "59c9add4", "metadata": { "editable": true }, @@ -844,7 +846,7 @@ }, { "cell_type": "markdown", - "id": "f00e1864", + "id": "a5168cc9", "metadata": { "editable": true }, @@ -858,7 +860,7 @@ }, { "cell_type": "markdown", - "id": "ea91af30", + "id": "47321307", "metadata": { "editable": true }, @@ -886,7 +888,7 @@ }, { "cell_type": "markdown", - "id": "bc9502a0", + "id": "96f44d6b", "metadata": { "editable": true }, @@ -918,7 +920,7 @@ }, { "cell_type": "markdown", - "id": "6a236a2a", + "id": "898ef421", "metadata": { "editable": true }, @@ -935,7 +937,7 @@ }, { "cell_type": "markdown", - "id": "29dc562b", + "id": "4e827950", "metadata": { "editable": true }, @@ -948,7 +950,7 @@ }, { "cell_type": "markdown", - "id": "6a34f155", + "id": "05e99546", "metadata": { "editable": true }, @@ -961,7 +963,7 @@ }, { "cell_type": "markdown", - "id": "0afd8cd8", + "id": "b92afe6c", "metadata": { "editable": true }, @@ -974,7 +976,7 @@ }, { "cell_type": "markdown", - "id": "f0b27e71", + "id": "b20a4aca", "metadata": { "editable": true }, @@ -988,7 +990,7 @@ }, { "cell_type": "markdown", - "id": "3b04b9c6", + "id": "7884cc0d", "metadata": { "editable": true }, @@ -1010,7 +1012,7 @@ }, { "cell_type": "markdown", - "id": "05eca708", + "id": "392aeed0", "metadata": { "editable": true }, @@ -1025,7 +1027,7 @@ }, { "cell_type": "markdown", - "id": "473025f4", + "id": "04581249", "metadata": { "editable": true }, @@ -1037,7 +1039,7 @@ }, { "cell_type": "markdown", - "id": "26e0b288", + "id": "d21077a4", "metadata": { "editable": true }, @@ -1050,7 +1052,7 @@ }, { "cell_type": "markdown", - "id": "091efee5", + "id": "b4bed668", "metadata": { "editable": true }, @@ -1064,7 +1066,7 @@ }, { "cell_type": "markdown", - "id": "22c5f80e", + "id": "9c15b282", "metadata": { "editable": true }, @@ -1075,7 +1077,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "102b1658", + "id": "602bda4c", "metadata": { "collapsed": false, "editable": true @@ -1100,7 +1102,7 @@ }, { "cell_type": "markdown", - "id": "79448e46", + "id": "332831a7", "metadata": { "editable": true }, @@ -1116,7 +1118,7 @@ }, { "cell_type": "markdown", - "id": "dbc8b940", + "id": "187eb27c", "metadata": { "editable": true }, @@ -1137,7 +1139,7 @@ }, { "cell_type": "markdown", - "id": "b63ae18d", + "id": "8ddbdbb5", "metadata": { "editable": true }, @@ -1157,7 +1159,7 @@ }, { "cell_type": "markdown", - "id": "c5ee074e", + "id": "35ea8e21", "metadata": { "editable": true }, @@ -1176,7 +1178,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "cfc48413", + "id": "77a60fcd", "metadata": { "collapsed": false, "editable": true @@ -1211,7 +1213,7 @@ }, { "cell_type": "markdown", - "id": "fbb8c0eb", + "id": "b030b80c", "metadata": { "editable": true }, @@ -1224,7 +1226,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "cc1e51cd", + "id": "9bdf875b", "metadata": { "collapsed": false, "editable": true @@ -1301,7 +1303,7 @@ }, { "cell_type": "markdown", - "id": "22a23ea0", + "id": "365cebd9", "metadata": { "editable": true }, @@ -1316,7 +1318,7 @@ }, { "cell_type": "markdown", - "id": "f0258497", + "id": "e7c9011a", "metadata": { "editable": true }, @@ -1326,7 +1328,7 @@ }, { "cell_type": "markdown", - "id": "69f1d941", + "id": "f1c85da0", "metadata": { "editable": true }, @@ -1338,7 +1340,7 @@ }, { "cell_type": "markdown", - "id": "876e1d2b", + "id": "66df0f80", "metadata": { "editable": true }, @@ -1350,7 +1352,7 @@ }, { "cell_type": "markdown", - "id": "67381fd3", + "id": "9f02b845", "metadata": { "editable": true }, @@ -1364,7 +1366,7 @@ }, { "cell_type": "markdown", - "id": "f08ec530", + "id": "21997f1a", "metadata": { "editable": true }, @@ -1376,7 +1378,7 @@ }, { "cell_type": "markdown", - "id": "3d99c5ee", + "id": "cdefe165", "metadata": { "editable": true }, @@ -1386,7 +1388,7 @@ }, { "cell_type": "markdown", - "id": "03ecb7f9", + "id": "ac200d56", "metadata": { "editable": true }, @@ -1398,7 +1400,7 @@ }, { "cell_type": "markdown", - "id": "a6db0c6c", + "id": "eb3edfb3", "metadata": { "editable": true }, @@ -1418,7 +1420,7 @@ }, { "cell_type": "markdown", - "id": "167f76aa", + "id": "7fe05c0d", "metadata": { "editable": true }, @@ -1431,7 +1433,7 @@ }, { "cell_type": "markdown", - "id": "d8d5cb23", + "id": "2ae403f1", "metadata": { "editable": true }, @@ -1443,7 +1445,7 @@ }, { "cell_type": "markdown", - "id": "e127c141", + "id": "44272171", "metadata": { "editable": true }, @@ -1460,7 +1462,7 @@ }, { "cell_type": "markdown", - "id": "7ea2c03c", + "id": "9cde29ef", "metadata": { "editable": true }, @@ -1472,7 +1474,7 @@ }, { "cell_type": "markdown", - "id": "e2e33c54", + "id": "9b77f20e", "metadata": { "editable": true }, @@ -1501,7 +1503,7 @@ }, { "cell_type": "markdown", - "id": "88f943e6", + "id": "4479bd97", "metadata": { "editable": true }, @@ -1534,7 +1536,7 @@ }, { "cell_type": "markdown", - "id": "aa4a8927", + "id": "31ea65c9", "metadata": { "editable": true }, @@ -1592,7 +1594,7 @@ }, { "cell_type": "markdown", - "id": "72d0192b", + "id": "3f3fe4c4", "metadata": { "editable": true }, @@ -1617,7 +1619,7 @@ }, { "cell_type": "markdown", - "id": "44fcd423", + "id": "69d08c69", "metadata": { "editable": true }, @@ -1643,7 +1645,7 @@ }, { "cell_type": "markdown", - "id": "8de0942f", + "id": "4e2b549d", "metadata": { "editable": true }, @@ -1686,7 +1688,7 @@ }, { "cell_type": "markdown", - "id": "f08a4bbe", + "id": "48c2661e", "metadata": { "editable": true }, @@ -1717,7 +1719,7 @@ }, { "cell_type": "markdown", - "id": "dc1fa30f", + "id": "a2106298", "metadata": { "editable": true }, @@ -1739,7 +1741,7 @@ }, { "cell_type": "markdown", - "id": "1fbfcb5e", + "id": "477a053c", "metadata": { "editable": true }, @@ -1759,7 +1761,7 @@ }, { "cell_type": "markdown", - "id": "83d5dfc2", + "id": "f0924df8", "metadata": { "editable": true }, @@ -1775,7 +1777,7 @@ }, { "cell_type": "markdown", - "id": "4cf425f2", + "id": "7743f26d", "metadata": { "editable": true }, @@ -1795,7 +1797,7 @@ }, { "cell_type": "markdown", - "id": "a8de083c", + "id": "ef4b5d6a", "metadata": { "editable": true }, @@ -1807,7 +1809,7 @@ }, { "cell_type": "markdown", - "id": "f8b98ecd", + "id": "927e2738", "metadata": { "editable": true }, @@ -1819,7 +1821,7 @@ }, { "cell_type": "markdown", - "id": "c41121c9", + "id": "1753de13", "metadata": { "editable": true }, @@ -1831,7 +1833,7 @@ }, { "cell_type": "markdown", - "id": "0c9cde87", + "id": "0db67ba3", "metadata": { "editable": true }, @@ -1843,7 +1845,7 @@ }, { "cell_type": "markdown", - "id": "9079853e", + "id": "7831e978", "metadata": { "editable": true }, @@ -1854,7 +1856,7 @@ }, { "cell_type": "markdown", - "id": "1b2340aa", + "id": "92a7758a", "metadata": { "editable": true }, @@ -1866,7 +1868,7 @@ }, { "cell_type": "markdown", - "id": "1c63eff7", + "id": "df62a4ff", "metadata": { "editable": true }, @@ -1876,7 +1878,7 @@ }, { "cell_type": "markdown", - "id": "e05e89e4", + "id": "c8a2b948", "metadata": { "editable": true }, @@ -1888,7 +1890,7 @@ }, { "cell_type": "markdown", - "id": "b3cbe567", + "id": "3f269e80", "metadata": { "editable": true }, @@ -1898,7 +1900,7 @@ }, { "cell_type": "markdown", - "id": "5d2f1096", + "id": "f4ec584c", "metadata": { "editable": true }, @@ -1919,7 +1921,7 @@ }, { "cell_type": "markdown", - "id": "4c4f3846", + "id": "4b741016", "metadata": { "editable": true }, @@ -1932,7 +1934,7 @@ }, { "cell_type": "markdown", - "id": "57d24251", + "id": "76108e75", "metadata": { "editable": true }, @@ -1944,7 +1946,7 @@ }, { "cell_type": "markdown", - "id": "caff3ad3", + "id": "4c6a3353", "metadata": { "editable": true }, @@ -1961,7 +1963,7 @@ }, { "cell_type": "markdown", - "id": "67133da8", + "id": "3e0a76ae", "metadata": { "editable": true }, @@ -1977,7 +1979,7 @@ }, { "cell_type": "markdown", - "id": "d2d2d644", + "id": "fa5fd82e", "metadata": { "editable": true }, @@ -1999,7 +2001,7 @@ }, { "cell_type": "markdown", - "id": "897d1ca3", + "id": "89cda2f6", "metadata": { "editable": true }, @@ -2017,7 +2019,7 @@ }, { "cell_type": "markdown", - "id": "549532b3", + "id": "69310c2b", "metadata": { "editable": true }, @@ -2037,7 +2039,7 @@ }, { "cell_type": "markdown", - "id": "f014a3a2", + "id": "7d6b8734", "metadata": { "editable": true }, @@ -2051,7 +2053,7 @@ }, { "cell_type": "markdown", - "id": "67bed63f", + "id": "106ce6bf", "metadata": { "editable": true }, @@ -2063,7 +2065,7 @@ }, { "cell_type": "markdown", - "id": "3014fe59", + "id": "3ba64fd6", "metadata": { "editable": true }, @@ -2075,7 +2077,7 @@ }, { "cell_type": "markdown", - "id": "a99d9c1c", + "id": "d2e1a9ee", "metadata": { "editable": true }, @@ -2087,7 +2089,7 @@ }, { "cell_type": "markdown", - "id": "907f9915", + "id": "00aae51f", "metadata": { "editable": true }, @@ -2099,7 +2101,7 @@ }, { "cell_type": "markdown", - "id": "551eb7db", + "id": "38adfadd", "metadata": { "editable": true }, @@ -2110,7 +2112,7 @@ }, { "cell_type": "markdown", - "id": "ea8ae470", + "id": "484156fb", "metadata": { "editable": true }, @@ -2122,7 +2124,7 @@ }, { "cell_type": "markdown", - "id": "9f5d78fd", + "id": "45d1d0c2", "metadata": { "editable": true }, @@ -2136,7 +2138,7 @@ }, { "cell_type": "markdown", - "id": "8291642f", + "id": "e62d5568", "metadata": { "editable": true }, @@ -2147,7 +2149,7 @@ }, { "cell_type": "markdown", - "id": "ee0e74ec", + "id": "3eb873c1", "metadata": { "editable": true }, @@ -2159,7 +2161,7 @@ }, { "cell_type": "markdown", - "id": "3699f7e5", + "id": "fc1129f6", "metadata": { "editable": true }, @@ -2181,7 +2183,7 @@ }, { "cell_type": "markdown", - "id": "16cdd781", + "id": "6f15ce48", "metadata": { "editable": true }, @@ -2205,7 +2207,7 @@ }, { "cell_type": "markdown", - "id": "779881a9", + "id": "44cb65e2", "metadata": { "editable": true }, @@ -2221,7 +2223,7 @@ }, { "cell_type": "markdown", - "id": "0724c747", + "id": "e3862c40", "metadata": { "editable": true }, @@ -2237,7 +2239,7 @@ }, { "cell_type": "markdown", - "id": "02a113cb", + "id": "c4aa2b35", "metadata": { "editable": true }, @@ -2251,7 +2253,7 @@ }, { "cell_type": "markdown", - "id": "e013ce1a", + "id": "01de27d3", "metadata": { "editable": true }, @@ -2269,7 +2271,7 @@ }, { "cell_type": "markdown", - "id": "1baa5b4e", + "id": "78a1a601", "metadata": { "editable": true }, @@ -2290,7 +2292,7 @@ { "cell_type": "code", "execution_count": 9, - "id": "8aab54bd", + "id": "c721352d", "metadata": { "collapsed": false, "editable": true @@ -2350,7 +2352,7 @@ }, { "cell_type": "markdown", - "id": "26c6e4f1", + "id": "e36cec47", "metadata": { "editable": true }, @@ -2361,7 +2363,7 @@ { "cell_type": "code", "execution_count": 10, - "id": "226c13ec", + "id": "fc5df7eb", "metadata": { "collapsed": false, "editable": true @@ -2425,7 +2427,7 @@ }, { "cell_type": "markdown", - "id": "6895dbfe", + "id": "0b27af70", "metadata": { "editable": true }, @@ -2440,7 +2442,7 @@ { "cell_type": "code", "execution_count": 11, - "id": "f8d01982", + "id": "adef9763", "metadata": { "collapsed": false, "editable": true @@ -2524,7 +2526,7 @@ }, { "cell_type": "markdown", - "id": "cffe8367", + "id": "310fe5b2", "metadata": { "editable": true }, @@ -2535,7 +2537,7 @@ { "cell_type": "code", "execution_count": 12, - "id": "b57871a9", + "id": "bcf65acf", "metadata": { "collapsed": false, "editable": true @@ -2613,7 +2615,7 @@ }, { "cell_type": "markdown", - "id": "37b273c1", + "id": "f5e2c550", "metadata": { "editable": true }, @@ -2626,7 +2628,7 @@ { "cell_type": "code", "execution_count": 13, - "id": "9ff0eb69", + "id": "300a02a4", "metadata": { "collapsed": false, "editable": true @@ -2670,7 +2672,7 @@ }, { "cell_type": "markdown", - "id": "e7d143b6", + "id": "5cb5fd26", "metadata": { "editable": true }, @@ -2681,7 +2683,7 @@ { "cell_type": "code", "execution_count": 14, - "id": "9b5e2d1d", + "id": "030efc5d", "metadata": { "collapsed": false, "editable": true @@ -2740,7 +2742,7 @@ }, { "cell_type": "markdown", - "id": "8b6fb13f", + "id": "66850bb7", "metadata": { "editable": true }, @@ -2750,7 +2752,7 @@ }, { "cell_type": "markdown", - "id": "06c3f4bb", + "id": "e1608bcf", "metadata": { "editable": true }, @@ -2761,7 +2763,7 @@ { "cell_type": "code", "execution_count": 15, - "id": "4abf9ccd", + "id": "0ba7d8f7", "metadata": { "collapsed": false, "editable": true @@ -2826,7 +2828,7 @@ }, { "cell_type": "markdown", - "id": "18d42e29", + "id": "0503f74b", "metadata": { "editable": true }, @@ -2837,7 +2839,7 @@ { "cell_type": "code", "execution_count": 16, - "id": "03415114", + "id": "c2a2732a", "metadata": { "collapsed": false, "editable": true @@ -2907,7 +2909,7 @@ }, { "cell_type": "markdown", - "id": "41120d8f", + "id": "b8475863", "metadata": { "editable": true }, @@ -2924,7 +2926,7 @@ }, { "cell_type": "markdown", - "id": "16eb2a88", + "id": "4d4d0717", "metadata": { "editable": true }, @@ -2952,7 +2954,7 @@ { "cell_type": "code", "execution_count": 17, - "id": "a6df3a5c", + "id": "46375144", "metadata": { "collapsed": false, "editable": true @@ -2972,7 +2974,7 @@ }, { "cell_type": "markdown", - "id": "fc15d89b", + "id": "39426ccf", "metadata": { "editable": true }, @@ -2988,7 +2990,7 @@ }, { "cell_type": "markdown", - "id": "4e4b5ee0", + "id": "df7fe27f", "metadata": { "editable": true }, @@ -3008,7 +3010,7 @@ }, { "cell_type": "markdown", - "id": "4455b9a0", + "id": "8fd48e39", "metadata": { "editable": true }, @@ -3035,7 +3037,7 @@ }, { "cell_type": "markdown", - "id": "9592eb20", + "id": "d6c60a0a", "metadata": { "editable": true }, @@ -3048,7 +3050,7 @@ }, { "cell_type": "markdown", - "id": "e3022ea8", + "id": "1bb6eaa0", "metadata": { "editable": true }, @@ -3060,7 +3062,7 @@ }, { "cell_type": "markdown", - "id": "246a28bf", + "id": "25135896", "metadata": { "editable": true }, @@ -3075,7 +3077,7 @@ { "cell_type": "code", "execution_count": 18, - "id": "d132a060", + "id": "469ca11e", "metadata": { "collapsed": false, "editable": true @@ -3102,7 +3104,7 @@ }, { "cell_type": "markdown", - "id": "9e70a01f", + "id": "33722029", "metadata": { "editable": true }, @@ -3116,7 +3118,7 @@ }, { "cell_type": "markdown", - "id": "2c0ad6b4", + "id": "fe27291e", "metadata": { "editable": true }, @@ -3128,7 +3130,7 @@ }, { "cell_type": "markdown", - "id": "3c6081b8", + "id": "ead1167d", "metadata": { "editable": true }, @@ -3145,7 +3147,7 @@ }, { "cell_type": "markdown", - "id": "845af933", + "id": "b2efb706", "metadata": { "editable": true }, @@ -3157,7 +3159,7 @@ }, { "cell_type": "markdown", - "id": "564afbbd", + "id": "65333100", "metadata": { "editable": true }, @@ -3167,7 +3169,7 @@ }, { "cell_type": "markdown", - "id": "c4088263", + "id": "1fde497c", "metadata": { "editable": true }, @@ -3179,7 +3181,7 @@ }, { "cell_type": "markdown", - "id": "96983e3d", + "id": "264ce562", "metadata": { "editable": true }, @@ -3189,7 +3191,7 @@ }, { "cell_type": "markdown", - "id": "91d029d7", + "id": "0f63a6f8", "metadata": { "editable": true }, @@ -3201,7 +3203,7 @@ }, { "cell_type": "markdown", - "id": "20d351f6", + "id": "2ba0a6e4", "metadata": { "editable": true }, @@ -3212,7 +3214,7 @@ }, { "cell_type": "markdown", - "id": "7a8e79fd", + "id": "3b377f93", "metadata": { "editable": true }, @@ -3224,7 +3226,7 @@ }, { "cell_type": "markdown", - "id": "4ec7ad68", + "id": "f05e9d08", "metadata": { "editable": true }, @@ -3234,7 +3236,7 @@ }, { "cell_type": "markdown", - "id": "df09c13b", + "id": "84784b8e", "metadata": { "editable": true }, @@ -3246,7 +3248,7 @@ }, { "cell_type": "markdown", - "id": "bb2a9c1f", + "id": "b62c6e5a", "metadata": { "editable": true }, @@ -3256,7 +3258,7 @@ }, { "cell_type": "markdown", - "id": "b3507e2d", + "id": "ecce9763", "metadata": { "editable": true }, @@ -3268,7 +3270,7 @@ }, { "cell_type": "markdown", - "id": "2010542f", + "id": "c9e1842a", "metadata": { "editable": true }, @@ -3278,7 +3280,7 @@ }, { "cell_type": "markdown", - "id": "e03a1590", + "id": "be12163e", "metadata": { "editable": true }, @@ -3290,7 +3292,7 @@ }, { "cell_type": "markdown", - "id": "71872755", + "id": "a097e9ab", "metadata": { "editable": true }, @@ -3300,7 +3302,7 @@ }, { "cell_type": "markdown", - "id": "167238dc", + "id": "239422b0", "metadata": { "editable": true }, @@ -3312,7 +3314,7 @@ }, { "cell_type": "markdown", - "id": "38d0cc0f", + "id": "ed9778bb", "metadata": { "editable": true }, @@ -3322,7 +3324,7 @@ }, { "cell_type": "markdown", - "id": "e9e1beb9", + "id": "7179b77b", "metadata": { "editable": true }, @@ -3334,7 +3336,7 @@ }, { "cell_type": "markdown", - "id": "9a8576e4", + "id": "aad2f56e", "metadata": { "editable": true }, @@ -3344,7 +3346,7 @@ }, { "cell_type": "markdown", - "id": "937d703f", + "id": "26aa9739", "metadata": { "editable": true }, @@ -3356,7 +3358,7 @@ }, { "cell_type": "markdown", - "id": "e4723b95", + "id": "d270cb13", "metadata": { "editable": true }, @@ -3366,7 +3368,7 @@ }, { "cell_type": "markdown", - "id": "6df6f6d8", + "id": "5a52457b", "metadata": { "editable": true }, @@ -3378,7 +3380,7 @@ }, { "cell_type": "markdown", - "id": "39bdaf00", + "id": "8c98105d", "metadata": { "editable": true }, @@ -3390,7 +3392,7 @@ }, { "cell_type": "markdown", - "id": "e4584236", + "id": "4d82302f", "metadata": { "editable": true }, @@ -3402,7 +3404,7 @@ }, { "cell_type": "markdown", - "id": "d0c5d728", + "id": "a3a07a10", "metadata": { "editable": true }, @@ -3412,7 +3414,7 @@ }, { "cell_type": "markdown", - "id": "9b637fd2", + "id": "ea19374e", "metadata": { "editable": true }, @@ -3424,7 +3426,7 @@ }, { "cell_type": "markdown", - "id": "9627e6fb", + "id": "11dd1361", "metadata": { "editable": true }, @@ -3437,7 +3439,7 @@ }, { "cell_type": "markdown", - "id": "662fe97e", + "id": "f6a52f34", "metadata": { "editable": true }, @@ -3449,7 +3451,7 @@ }, { "cell_type": "markdown", - "id": "fa2d5cb5", + "id": "9d6807dc", "metadata": { "editable": true }, @@ -3463,7 +3465,7 @@ { "cell_type": "code", "execution_count": 19, - "id": "a530b3ba", + "id": "2ed0cafc", "metadata": { "collapsed": false, "editable": true @@ -3560,7 +3562,7 @@ }, { "cell_type": "markdown", - "id": "58cc6d9d", + "id": "f72dbb49", "metadata": { "editable": true }, @@ -3581,7 +3583,7 @@ }, { "cell_type": "markdown", - "id": "6a2d3f87", + "id": "b7759b1f", "metadata": { "editable": true }, @@ -3593,7 +3595,7 @@ }, { "cell_type": "markdown", - "id": "9eab78a9", + "id": "ba0ecd6e", "metadata": { "editable": true }, @@ -3603,7 +3605,7 @@ }, { "cell_type": "markdown", - "id": "50d7f5c3", + "id": "ae897f1e", "metadata": { "editable": true }, @@ -3615,7 +3617,7 @@ }, { "cell_type": "markdown", - "id": "4c96e589", + "id": "f9c41f7f", "metadata": { "editable": true }, @@ -3625,7 +3627,7 @@ }, { "cell_type": "markdown", - "id": "b57830ea", + "id": "fa013cc4", "metadata": { "editable": true }, @@ -3637,7 +3639,7 @@ }, { "cell_type": "markdown", - "id": "05325bc6", + "id": "0c9b24be", "metadata": { "editable": true }, @@ -3655,7 +3657,7 @@ { "cell_type": "code", "execution_count": 20, - "id": "d95b15bc", + "id": "4f9b1fa0", "metadata": { "collapsed": false, "editable": true @@ -3731,7 +3733,7 @@ }, { "cell_type": "markdown", - "id": "b88ebede", + "id": "1aa5ca37", "metadata": { "editable": true }, @@ -3745,7 +3747,7 @@ { "cell_type": "code", "execution_count": 21, - "id": "47036b16", + "id": "a731e32c", "metadata": { "collapsed": false, "editable": true @@ -3834,7 +3836,7 @@ }, { "cell_type": "markdown", - "id": "52faee2f", + "id": "6ea197d8", "metadata": { "editable": true }, diff --git a/doc/LectureNotes/_build/html/_static/pygments.css b/doc/LectureNotes/_build/html/_static/pygments.css index d7dd57783..012e6a00a 100644 --- a/doc/LectureNotes/_build/html/_static/pygments.css +++ b/doc/LectureNotes/_build/html/_static/pygments.css @@ -6,11 +6,11 @@ html[data-theme="light"] .highlight span.linenos.special { color: #000000; backg html[data-theme="light"] .highlight .hll { background-color: #fae4c2 } html[data-theme="light"] .highlight { background: #fefefe; color: #080808 } html[data-theme="light"] .highlight .c { color: #515151 } /* Comment */ -html[data-theme="light"] .highlight .err { color: #A12236 } /* Error */ -html[data-theme="light"] .highlight .k { color: #6730C5 } /* Keyword */ -html[data-theme="light"] .highlight .l { color: #7F4707 } /* Literal */ +html[data-theme="light"] .highlight .err { color: #a12236 } /* Error */ +html[data-theme="light"] .highlight .k { color: #6730c5 } /* 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a/doc/LectureNotes/_build/html/chapter1.html +++ b/doc/LectureNotes/_build/html/chapter1.html @@ -28,7 +28,7 @@ - + diff --git a/doc/LectureNotes/_build/html/chapter10.html b/doc/LectureNotes/_build/html/chapter10.html index 288d09ee9..6ec417b1f 100644 --- a/doc/LectureNotes/_build/html/chapter10.html +++ b/doc/LectureNotes/_build/html/chapter10.html @@ -28,7 +28,7 @@ - + diff --git a/doc/LectureNotes/_build/html/chapter11.html b/doc/LectureNotes/_build/html/chapter11.html index ae7f7eb73..88738e241 100644 --- a/doc/LectureNotes/_build/html/chapter11.html +++ b/doc/LectureNotes/_build/html/chapter11.html @@ -28,7 +28,7 @@ - + diff --git a/doc/LectureNotes/_build/html/chapter12.html b/doc/LectureNotes/_build/html/chapter12.html index 8d18565ef..d39624f88 100644 --- a/doc/LectureNotes/_build/html/chapter12.html +++ b/doc/LectureNotes/_build/html/chapter12.html @@ -28,7 +28,7 @@ - + diff --git a/doc/LectureNotes/_build/html/chapter13.html b/doc/LectureNotes/_build/html/chapter13.html index 55b2f892f..e5581a940 100644 --- a/doc/LectureNotes/_build/html/chapter13.html +++ b/doc/LectureNotes/_build/html/chapter13.html @@ -28,7 +28,7 @@ - + diff --git a/doc/LectureNotes/_build/html/chapter2.html b/doc/LectureNotes/_build/html/chapter2.html index bd3b80769..5e1e5205e 100644 --- a/doc/LectureNotes/_build/html/chapter2.html +++ b/doc/LectureNotes/_build/html/chapter2.html @@ -28,7 +28,7 @@ - + diff --git a/doc/LectureNotes/_build/html/chapter3.html b/doc/LectureNotes/_build/html/chapter3.html index 6e0056b22..0ad5ef3cd 100644 --- a/doc/LectureNotes/_build/html/chapter3.html +++ b/doc/LectureNotes/_build/html/chapter3.html @@ -28,7 +28,7 @@ - + diff --git a/doc/LectureNotes/_build/html/chapter4.html b/doc/LectureNotes/_build/html/chapter4.html index fd9a23a22..08b3066d0 100644 --- a/doc/LectureNotes/_build/html/chapter4.html +++ b/doc/LectureNotes/_build/html/chapter4.html @@ -28,7 +28,7 @@ - + diff --git a/doc/LectureNotes/_build/html/chapter5.html b/doc/LectureNotes/_build/html/chapter5.html index a5f08388f..5bb6c31ed 100644 --- a/doc/LectureNotes/_build/html/chapter5.html +++ b/doc/LectureNotes/_build/html/chapter5.html @@ -28,7 +28,7 @@ - + diff --git a/doc/LectureNotes/_build/html/chapter6.html b/doc/LectureNotes/_build/html/chapter6.html index 105ec70f3..d83af1cd3 100644 --- a/doc/LectureNotes/_build/html/chapter6.html +++ b/doc/LectureNotes/_build/html/chapter6.html @@ -28,7 +28,7 @@ - + diff --git a/doc/LectureNotes/_build/html/chapter7.html b/doc/LectureNotes/_build/html/chapter7.html index 4975f05be..ee67eddbf 100644 --- a/doc/LectureNotes/_build/html/chapter7.html +++ b/doc/LectureNotes/_build/html/chapter7.html @@ -28,7 +28,7 @@ - + diff --git a/doc/LectureNotes/_build/html/chapter8.html b/doc/LectureNotes/_build/html/chapter8.html index c3607b538..6121f71b7 100644 --- a/doc/LectureNotes/_build/html/chapter8.html +++ b/doc/LectureNotes/_build/html/chapter8.html @@ -28,7 +28,7 @@ - + diff --git a/doc/LectureNotes/_build/html/chapter9.html b/doc/LectureNotes/_build/html/chapter9.html index 0865f4e0d..6394a7849 100644 --- a/doc/LectureNotes/_build/html/chapter9.html +++ b/doc/LectureNotes/_build/html/chapter9.html @@ -28,7 +28,7 @@ - + diff --git a/doc/LectureNotes/_build/html/chapteroptimization.html b/doc/LectureNotes/_build/html/chapteroptimization.html index 9f2680360..2afbdae59 100644 --- a/doc/LectureNotes/_build/html/chapteroptimization.html +++ b/doc/LectureNotes/_build/html/chapteroptimization.html @@ -28,7 +28,7 @@ - + diff --git a/doc/LectureNotes/_build/html/clustering.html b/doc/LectureNotes/_build/html/clustering.html index 1292b0fc9..deef36280 100644 --- a/doc/LectureNotes/_build/html/clustering.html +++ b/doc/LectureNotes/_build/html/clustering.html @@ -28,7 +28,7 @@ - + diff --git a/doc/LectureNotes/_build/html/exercisesweek34.html b/doc/LectureNotes/_build/html/exercisesweek34.html index 6b949390f..b7a9613b3 100644 --- a/doc/LectureNotes/_build/html/exercisesweek34.html +++ b/doc/LectureNotes/_build/html/exercisesweek34.html @@ -28,7 +28,7 @@ - + @@ -477,11 +477,11 @@ document.write(`

b) Compute the mean square error for the line model and for the second degree polynomial model.

-
import numpy as np
-import matplotlib.pyplot as plt
-from sklearn.preprocessing import PolynomialFeatures # use the fit_transform method of the created object!
-from sklearn.linear_model import LinearRegression
-from sklearn.metrics import mean_squared_error
+
import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.preprocessing import PolynomialFeatures # use the fit_transform method of the created object!
+from sklearn.linear_model import LinearRegression
+from sklearn.metrics import mean_squared_error
@@ -518,7 +518,7 @@ document.write(`

Hopefully your model fit the data quite well, but to know how well the model actually generalizes to unseen data, which is most often what we care about, we need to split our data into training and testing data.

-
from sklearn.model_selection import train_test_split
+
from sklearn.model_selection import train_test_split
diff --git a/doc/LectureNotes/_build/html/exercisesweek35.html b/doc/LectureNotes/_build/html/exercisesweek35.html index ab328b4de..b66673519 100644 --- a/doc/LectureNotes/_build/html/exercisesweek35.html +++ b/doc/LectureNotes/_build/html/exercisesweek35.html @@ -28,7 +28,7 @@ - + @@ -513,7 +513,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,

We calculate the optimal intercept by including a feature with the constant value of 1 in our model, which is then multplied by some parameter \(\theta_0\) from the OLS method into the optimal intercept value (which will be \(\theta_0\)). In practice, we include the intercept in our model by adding a column of ones to the start of our feature matrix.

-
import numpy as np
+
import numpy as np
@@ -542,7 +542,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,

b) Use the expression from 3d) to find the optimal parameters \(\boldsymbol{\hat{\beta}_{OLS}}\) for predicting spending based on these features. Create a function for this operation, as you are going to need to use it a lot.

-
def OLS_parameters(X, y):
+
def OLS_parameters(X, y):
     return ...
 
 #beta = OLS_parameters(X, y)
@@ -567,7 +567,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
 
a) Create a feature matrix \(\boldsymbol{X}\) for the features \(x, x^2, x^3, x^4, x^5\), including an intercept column of ones at the start. Make this into a function, as you will do this a lot over the next weeks.

 

 

-
def polynomial_features(x, p):
+
def polynomial_features(x, p):
     n = len(x)
     X = np.zeros((n, p + 1))
     #X[:, 0] = ...
@@ -591,7 +591,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
 
c) Like in exercise 4 last week, split your feature matrix and target data into a training split and test split.

 

 

-
from sklearn.model_selection import train_test_split
+
from sklearn.model_selection import train_test_split
 
 #X_train, X_test, y_train, y_test = ...
 

diff --git a/doc/LectureNotes/_build/html/exercisesweek36.html b/doc/LectureNotes/_build/html/exercisesweek36.html
index 533249336..751e6cabd 100644
--- a/doc/LectureNotes/_build/html/exercisesweek36.html
+++ b/doc/LectureNotes/_build/html/exercisesweek36.html
@@ -28,7 +28,7 @@
 
 
 
-    
+    
     
     
     
@@ -465,10 +465,10 @@ defining a new cost function to be optimized, that is

 
Exercise 3 - Scaling data#

 

 

-
import numpy as np
-import matplotlib.pyplot as plt
-from sklearn.model_selection import train_test_split
-from sklearn.preprocessing import StandardScaler
+
import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.model_selection import train_test_split
+from sklearn.preprocessing import StandardScaler
 

 

 

@@ -485,7 +485,7 @@ defining a new cost function to be optimized, that is

 
a) Adapt your function from last week to only include the intercept column if the boolean argument intercept is set to true.

 

 

-
def polynomial_features(x, p, intercept=False):
+
def polynomial_features(x, p, intercept=False):
     n = len(x)
     X = np.zeros((n, p + 1))
     #X[:, 0] = ...
@@ -498,7 +498,7 @@ defining a new cost function to be optimized, that is

 

 

 

-
def polynomial_features(x, p, intercept=False):
+
def polynomial_features(x, p, intercept=False):
     n = len(x)
     X = np.zeros((n, p))
     X[:, 0] = x[:]
@@ -544,7 +544,7 @@ defining a new cost function to be optimized, that is

 
a) Implement a function for computing the optimal Ridge parameters using the expression from 2a).

 

 

-
def Ridge_parameters(X, y):
+
def Ridge_parameters(X, y):
     # Assumes X is scaled and has no intercept column
     return np.linalg.inv(X.T @ X) @ X.T @ y
 
diff --git a/doc/LectureNotes/_build/html/exercisesweek37.html b/doc/LectureNotes/_build/html/exercisesweek37.html
index 57fd8df99..541dd9132 100644
--- a/doc/LectureNotes/_build/html/exercisesweek37.html
+++ b/doc/LectureNotes/_build/html/exercisesweek37.html
@@ -28,7 +28,7 @@
 
 
 
-    
+    
     
     
     
diff --git a/doc/LectureNotes/_build/html/exercisesweek38.html b/doc/LectureNotes/_build/html/exercisesweek38.html
index 4afe575f5..6f8bc1037 100644
--- a/doc/LectureNotes/_build/html/exercisesweek38.html
+++ b/doc/LectureNotes/_build/html/exercisesweek38.html
@@ -28,7 +28,7 @@
 
 
 
-    
+    
     
     
     
@@ -519,7 +519,7 @@ show that

 
a) Using the expression above, compute the mean squared error, bias and variance of the given data. Check that the sum of the bias and variance correctly gives (approximately) the mean squared error.

 

 

-
import numpy as np
+
import numpy as np
 
 n = 100
 bootstraps = 1000
@@ -539,15 +539,15 @@ show that

 
d) Perform a bias-variance analysis of a polynomial OLS model fit to a one-dimensional function by computing and plotting the bias and variances values as a function of the polynomial degree of your model.

 

 

-
import numpy as np
-import matplotlib.pyplot as plt
-from sklearn.preprocessing import (
+
import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.preprocessing import (
     PolynomialFeatures,
 )  # use the fit_transform method of the created object!
-from sklearn.linear_model import LinearRegression
-from sklearn.metrics import mean_squared_error
-from sklearn.model_selection import train_test_split
-from sklearn.utils import resample
+from sklearn.linear_model import LinearRegression
+from sklearn.metrics import mean_squared_error
+from sklearn.model_selection import train_test_split
+from sklearn.utils import resample
 

 

 

diff --git a/doc/LectureNotes/_build/html/genindex.html b/doc/LectureNotes/_build/html/genindex.html
index fd1ca2ca1..39273ec36 100644
--- a/doc/LectureNotes/_build/html/genindex.html
+++ b/doc/LectureNotes/_build/html/genindex.html
@@ -27,7 +27,7 @@
 
 
 
-    
+    
     
     
     
diff --git a/doc/LectureNotes/_build/html/intro.html b/doc/LectureNotes/_build/html/intro.html
index 478abf33e..2a7d32f8e 100644
--- a/doc/LectureNotes/_build/html/intro.html
+++ b/doc/LectureNotes/_build/html/intro.html
@@ -28,7 +28,7 @@
 
 
 
-    
+    
     
     
     
diff --git a/doc/LectureNotes/_build/html/linalg.html b/doc/LectureNotes/_build/html/linalg.html
index 974945b13..8ef0ee04f 100644
--- a/doc/LectureNotes/_build/html/linalg.html
+++ b/doc/LectureNotes/_build/html/linalg.html
@@ -28,7 +28,7 @@
 
 
 
-    
+    
     
     
     
diff --git a/doc/LectureNotes/_build/html/objects.inv b/doc/LectureNotes/_build/html/objects.inv
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-    
+    
     
     
     
diff --git a/doc/LectureNotes/_build/html/schedule.html b/doc/LectureNotes/_build/html/schedule.html
index 320e1fb5a..05766026d 100644
--- a/doc/LectureNotes/_build/html/schedule.html
+++ b/doc/LectureNotes/_build/html/schedule.html
@@ -28,7 +28,7 @@
 
 
 
-    
+    
     
     
     
diff --git a/doc/LectureNotes/_build/html/search.html b/doc/LectureNotes/_build/html/search.html
index 15768ee6a..3dc8c9e24 100644
--- a/doc/LectureNotes/_build/html/search.html
+++ b/doc/LectureNotes/_build/html/search.html
@@ -26,7 +26,7 @@
 
 
 
-    
+    
     
     
     
diff --git a/doc/LectureNotes/_build/html/searchindex.js b/doc/LectureNotes/_build/html/searchindex.js
index a683db16a..e481099dc 100644
--- a/doc/LectureNotes/_build/html/searchindex.js
+++ b/doc/LectureNotes/_build/html/searchindex.js
@@ -1 +1 @@
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and training set up": [[69, "adding-error-analysis-and-training-set-up"], [70, "adding-error-analysis-and-training-set-up"]], "Adjust hyperparameters": [[43, "adjust-hyperparameters"]], "Algorithms and codes for Adagrad, RMSprop and Adam": [[72, "algorithms-and-codes-for-adagrad-rmsprop-and-adam"]], "Algorithms for Setting up Decision Trees": [[51, "algorithms-for-setting-up-decision-trees"]], "An Overview of Ensemble Methods": [[52, "an-overview-of-ensemble-methods"]], "An example cell": [[23, "an-example-cell"]], "An extrapolation example": [[46, "an-extrapolation-example"]], "An optimization/minimization problem": [[69, "an-optimization-minimization-problem"]], "And finally  \\boldsymbol{X}\\boldsymbol{X}^T": [[70, "and-finally-boldsymbol-x-boldsymbol-x-t"]], "And finally ADAM": [[72, "and-finally-adam"]], "And what about using neural networks?": [[69, "and-what-about-using-neural-networks"]], "Another Example, now with a polynomial fit": [[71, "another-example-now-with-a-polynomial-fit"]], "Another example, the moons again": [[51, "another-example-the-moons-again"]], "Applied Data Analysis and Machine Learning": [[62, null]], "Authors": [[31, null]], "Autocorrelation function": [[66, "autocorrelation-function"]], "Automatic differentiation": [[55, "automatic-differentiation"]], "Back to Ridge and LASSO Regression": [[70, "back-to-ridge-and-lasso-regression"], [71, "back-to-ridge-and-lasso-regression"]], "Back to the Cancer Data": [[53, "back-to-the-cancer-data"]], "Background literature": [[64, "background-literature"]], "Bagging": [[52, "bagging"]], "Bagging Examples": [[52, "bagging-examples"]], "Basic Matrix Features": [[63, "basic-matrix-features"]], "Basic ideas of the Principal Component Analysis (PCA)": [[53, null]], "Basic math of the SVD": [[47, "basic-math-of-the-svd"], [70, "basic-math-of-the-svd"], [71, "basic-math-of-the-svd"]], "Basics": [[49, "basics"]], "Basics of a tree": [[51, "basics-of-a-tree"]], "Batch Normalization": [[43, "batch-normalization"]], "Batches and mini-batches": [[72, "batches-and-mini-batches"]], "Bayes\u2019 Theorem and Ridge and Lasso Regression": [[47, "bayes-theorem-and-ridge-and-lasso-regression"]], "Blinds Dark": [[4, null]], "Blinds Light": [[5, null]], "Boosting, a Bird\u2019s Eye View": [[52, "boosting-a-bird-s-eye-view"]], "Bootstrap": [[48, "bootstrap"]], "Bringing it together, first back propagation equation": [[54, "bringing-it-together-first-back-propagation-equation"]], "Building a Feed Forward Neural Network": [[43, null]], "Building a tree, regression": [[51, "building-a-tree-regression"]], "Building neural networks in Tensorflow and Keras": [[43, "building-neural-networks-in-tensorflow-and-keras"]], "But none of these can compete with Newton\u2019s method": [[72, "but-none-of-these-can-compete-with-newton-s-method"]], "CDN": [[29, "cdn"]], "CHANGELOG": [[29, "changelog"]], "CNNs in more detail, building convolutional neural networks in Tensorflow and Keras": [[45, "cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras"]], "Cancer Data again now with Decision Trees and other Methods": [[51, "cancer-data-again-now-with-decision-trees-and-other-methods"]], "Challenge: Choosing a Fixed Learning Rate": [[72, "challenge-choosing-a-fixed-learning-rate"]], "Choose cost function and optimizer": [[43, "choose-cost-function-and-optimizer"]], "Citations": [[22, "citations"]], "Classical PCA Theorem": [[53, "classical-pca-theorem"]], "Clustering and Unsupervised Learning": [[56, null]], "Code blocks and outputs": [[24, "code-blocks-and-outputs"]], "Code for SVD and Inversion of Matrices": [[47, "code-for-svd-and-inversion-of-matrices"]], "Code with a Number of Minibatches which varies": [[72, "code-with-a-number-of-minibatches-which-varies"]], "Codes and Approaches": [[56, "codes-and-approaches"]], "Codes for the SVD": [[47, "codes-for-the-svd"], [70, "codes-for-the-svd"], [71, "codes-for-the-svd"]], "Coding Setup and Linear Regression": [[57, "coding-setup-and-linear-regression"]], "Collect and pre-process data": [[43, "collect-and-pre-process-data"]], "Colors": [[0, "colors"], [1, "colors"], [2, "colors"], [3, "colors"], [4, "colors"], [5, "colors"], [6, "colors"], [7, "colors"], [8, "colors"], [9, "colors"], [10, "colors"], [11, "colors"], [12, "colors"], [13, "colors"], [14, "colors"], [15, "colors"]], "Communication channels": [[69, "communication-channels"]], "Compare  Bagging on Trees with Random Forests": [[52, "compare-bagging-on-trees-with-random-forests"]], "Comparing with a numerical scheme": [[44, "comparing-with-a-numerical-scheme"]], "Comparison with OLS": [[71, "comparison-with-ols"]], "Compiled translation files": [[39, "compiled-translation-files"]], "Computation of gradients": [[72, "computation-of-gradients"]], "Computing the Gini index": [[51, "computing-the-gini-index"]], "Conditions on convex functions": [[71, "conditions-on-convex-functions"]], "Conjugate gradient method": [[55, "conjugate-gradient-method"]], "Content with notebooks": [[24, null]], "Contributors": [[31, "contributors"]], "Convergence rates": [[72, "convergence-rates"]], "Convex function": [[71, "convex-function"]], "Convex functions": [[55, "convex-functions"], [71, "convex-functions"]], "Convolution Examples: Polynomial multiplication": [[45, "convolution-examples-polynomial-multiplication"]], "Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)": [[45, "convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms"]], "Convolutional Neural Network": [[54, "convolutional-neural-network"]], "Convolutional Neural Networks": [[45, null]], "Correlation Function and Design/Feature Matrix": [[70, "correlation-function-and-design-feature-matrix"]], "Correlation Matrix": [[53, "correlation-matrix"], [70, "correlation-matrix"]], "Correlation Matrix with Pandas": [[70, "correlation-matrix-with-pandas"]], "Course Format": [[69, "course-format"]], "Course setting": [[65, null]], "Covariance Matrix Examples": [[70, "covariance-matrix-examples"]], "Covariance and Correlation Matrix": [[70, "covariance-and-correlation-matrix"]], "Create a notebook with MyST Markdown": [[23, "create-a-notebook-with-myst-markdown"]], "Creator": [[31, "creator"]], "Cross-validation": [[48, "cross-validation"]], "Deadlines for projects (tentative)": [[69, "deadlines-for-projects-tentative"]], "Decision trees, overarching aims": [[51, null]], "Deep Neural Networks": [[72, "deep-neural-networks"]], "Deep learning methods": [[69, "deep-learning-methods"]], "Define model and architecture": [[43, "define-model-and-architecture"]], "Defining the cost function": [[43, "defining-the-cost-function"]], "Definitions": [[61, "definitions"]], "Deliverables": [[57, "deliverables"], [58, "deliverables"], [61, "deliverables"]], "Dependencies": [[29, "dependencies"]], "Derivation of the AdaGrad Algorithm": [[72, "derivation-of-the-adagrad-algorithm"]], "Derivatives and the chain rule": [[54, "derivatives-and-the-chain-rule"]], "Derivatives, example 1": [[70, "derivatives-example-1"]], "Deriving OLS from a probability distribution": [[47, "deriving-ols-from-a-probability-distribution"]], "Deriving and Implementing Ordinary Least Squares": [[58, "deriving-and-implementing-ordinary-least-squares"]], "Deriving and Implementing Ridge Regression": [[59, "deriving-and-implementing-ridge-regression"]], "Deriving the  Lasso Regression Equations": [[70, "deriving-the-lasso-regression-equations"], [71, "deriving-the-lasso-regression-equations"], [71, "id6"]], "Deriving the  Ridge Regression Equations": [[70, "deriving-the-ridge-regression-equations"], [71, "deriving-the-ridge-regression-equations"], [71, "id3"]], "Deriving the back propagation code for a multilayer perceptron model": [[54, "deriving-the-back-propagation-code-for-a-multilayer-perceptron-model"]], "Developing a code for doing neural networks with back propagation": [[43, "developing-a-code-for-doing-neural-networks-with-back-propagation"]], "Diagonalize the sample covariance matrix to obtain the principal components": [[53, "diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components"]], "Different kernels and Mercer\u2019s theorem": [[50, "different-kernels-and-mercer-s-theorem"]], "Disadvantages": [[51, "disadvantages"]], "Discriminative Modeling": [[69, "discriminative-modeling"]], "Domains and probabilities": [[66, "domains-and-probabilities"]], "Dropout": [[43, "dropout"]], "Economy-size SVD": [[70, "economy-size-svd"], [71, "economy-size-svd"]], "Elements of Probability Theory and Statistical Data Analysis": [[66, null]], "Empirical Evidence: Convergence Time and Memory in Practice": [[72, "empirical-evidence-convergence-time-and-memory-in-practice"]], "Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods": [[52, null]], "Entropy and the ID3 algorithm": [[51, "entropy-and-the-id3-algorithm"]], "Essential elements of ML": [[69, "essential-elements-of-ml"]], "Evaluate model performance on test data": [[43, "evaluate-model-performance-on-test-data"]], "Example": [[27, "example"]], "Example 2": [[70, "example-2"]], "Example 3": [[70, "example-3"]], "Example 4": [[70, "example-4"]], "Example Matrix": [[70, "example-matrix"], [71, "example-matrix"]], "Example of discriminative modeling, taken from Generative Deep Learning by David Foster": [[69, "example-of-discriminative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of generative modeling, taken from Generative Deep Learning by David Foster": [[69, "example-of-generative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of own Standard scaling": [[70, "example-of-own-standard-scaling"]], "Example relevant for the exercises": [[70, "example-relevant-for-the-exercises"]], "Example: Exponential decay": [[44, "example-exponential-decay"]], "Example: Population growth": [[44, "example-population-growth"]], "Example: The diffusion equation": [[44, "example-the-diffusion-equation"]], "Example: binary classification problem": [[43, "example-binary-classification-problem"]], "Examples": [[69, "examples"]], "Examples of likelihood functions used in logistic regression and neural networks": [[49, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Exercise 1 - Choice of model and degrees of freedom": [[59, "exercise-1-choice-of-model-and-degrees-of-freedom"]], "Exercise 1 - Finding the derivative of Matrix-Vector expressions": [[58, "exercise-1-finding-the-derivative-of-matrix-vector-expressions"]], "Exercise 1 - Github Setup": [[57, "exercise-1-github-setup"]], "Exercise 1, scale your data": [[60, "exercise-1-scale-your-data"]], "Exercise 1: Expectation values for ordinary least squares expressions": [[61, "exercise-1-expectation-values-for-ordinary-least-squares-expressions"]], "Exercise 1: Setting up various Python environments": [[42, "exercise-1-setting-up-various-python-environments"]], "Exercise 2 - Deriving the expression for OLS": [[58, "exercise-2-deriving-the-expression-for-ols"]], "Exercise 2 - Deriving the expression for Ridge Regression": [[59, "exercise-2-deriving-the-expression-for-ridge-regression"]], "Exercise 2 - Setting up a Github repository": [[57, "exercise-2-setting-up-a-github-repository"]], "Exercise 2, calculate the gradients": [[60, "exercise-2-calculate-the-gradients"]], "Exercise 2: Expectation values for Ridge regression": [[61, "exercise-2-expectation-values-for-ridge-regression"]], "Exercise 2: making your own data and exploring scikit-learn": [[42, "exercise-2-making-your-own-data-and-exploring-scikit-learn"]], "Exercise 3 - Creating feature matrix and implementing OLS using the analytical expression": [[58, "exercise-3-creating-feature-matrix-and-implementing-ols-using-the-analytical-expression"]], "Exercise 3 - Fitting an OLS model to data": [[57, "exercise-3-fitting-an-ols-model-to-data"]], "Exercise 3 - Scaling data": [[59, "exercise-3-scaling-data"]], "Exercise 3 - Setting up a Python virtual environment": [[57, "exercise-3-setting-up-a-python-virtual-environment"]], "Exercise 3, using the analytical formulae for OLS and Ridge regression to find the optimal paramters \\boldsymbol{\\theta}": [[60, "exercise-3-using-the-analytical-formulae-for-ols-and-ridge-regression-to-find-the-optimal-paramters-boldsymbol-theta"]], "Exercise 3: Deriving the expression for the Bias-Variance Trade-off": [[61, "exercise-3-deriving-the-expression-for-the-bias-variance-trade-off"]], "Exercise 3: Normalizing our data": [[42, "exercise-3-normalizing-our-data"]], "Exercise 4 - Fitting a polynomial": [[58, "exercise-4-fitting-a-polynomial"]], "Exercise 4 - Implementing Ridge Regression": [[59, "exercise-4-implementing-ridge-regression"]], "Exercise 4 - Testing multiple hyperparameters": [[59, "exercise-4-testing-multiple-hyperparameters"]], "Exercise 4 - The train-test split": [[57, "exercise-4-the-train-test-split"]], "Exercise 4, Implementing the simplest form for gradient descent": [[60, "exercise-4-implementing-the-simplest-form-for-gradient-descent"]], "Exercise 4: Adding Ridge Regression": [[42, "exercise-4-adding-ridge-regression"]], "Exercise 4: Computing the Bias and Variance": [[61, "exercise-4-computing-the-bias-and-variance"]], "Exercise 5 - Comparing your code with sklearn": [[58, "exercise-5-comparing-your-code-with-sklearn"]], "Exercise 5, Ridge regression and a new Synthetic Dataset": [[60, "exercise-5-ridge-regression-and-a-new-synthetic-dataset"]], "Exercise 5: Analytical exercises": [[42, "exercise-5-analytical-exercises"]], "Exercise 5: Interpretation of scaling and metrics": [[61, "exercise-5-interpretation-of-scaling-and-metrics"]], "Exercise:  Cross-validation as resampling techniques, adding more complexity": [[48, "exercise-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Exercise: Analysis of real data": [[48, "exercise-analysis-of-real-data"]], "Exercise: Bias-variance trade-off and resampling techniques": [[48, "exercise-bias-variance-trade-off-and-resampling-techniques"]], "Exercise: Lasso Regression on the Franke function  with resampling": [[48, "exercise-lasso-regression-on-the-franke-function-with-resampling"]], "Exercise: Ordinary Least Square (OLS) on the Franke function": [[48, "exercise-ordinary-least-square-ols-on-the-franke-function"]], "Exercise: Ridge Regression on the Franke function  with resampling": [[48, "exercise-ridge-regression-on-the-franke-function-with-resampling"]], "Exercises": [[42, "exercises"]], "Exercises and Projects": [[48, "exercises-and-projects"]], "Exercises week 34": [[57, null]], "Exercises week 35": [[58, null]], "Exercises week 36": [[59, null]], "Exercises week 37": [[60, null]], "Exercises week 38": [[61, null]], "Expectation values": [[66, "expectation-values"]], "Extending to more than one variable": [[71, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[69, "extremely-useful-tools-strongly-recommended"]], "FAQ": [[29, "faq"]], "Features": [[29, "features"]], "Feed-forward neural networks": [[54, "feed-forward-neural-networks"]], "Feed-forward pass": [[43, "feed-forward-pass"]], "Final back propagating equation": [[54, "final-back-propagating-equation"]], "Fine-tuning neural network hyperparameters": [[43, "fine-tuning-neural-network-hyperparameters"]], "Fitting an Equation of State for Dense Nuclear Matter": [[42, "fitting-an-equation-of-state-for-dense-nuclear-matter"]], "Fixing the singularity": [[70, "fixing-the-singularity"], [71, "fixing-the-singularity"]], "Format for electronic delivery of report and programs": [[64, "format-for-electronic-delivery-of-report-and-programs"]], "Frequently used scaling functions": [[70, "frequently-used-scaling-functions"], [72, "frequently-used-scaling-functions"]], "From OLS to Ridge and Lasso": [[71, "from-ols-to-ridge-and-lasso"]], "From one to many layers, the universal approximation theorem": [[54, "from-one-to-many-layers-the-universal-approximation-theorem"]], "Functionality in Scikit-Learn": [[70, "functionality-in-scikit-learn"], [72, "functionality-in-scikit-learn"]], "Further Dimensionality Remarks": [[45, "further-dimensionality-remarks"]], "Further properties (important for our analyses later)": [[47, "further-properties-important-for-our-analyses-later"], [70, "further-properties-important-for-our-analyses-later"], [71, "further-properties-important-for-our-analyses-later"]], "Gaussian Elimination": [[63, "gaussian-elimination"]], "General Features": [[51, "general-features"]], "General linear models and linear algebra": [[69, "general-linear-models-and-linear-algebra"]], "Generalizing the fitting procedure as a linear algebra problem": [[69, "generalizing-the-fitting-procedure-as-a-linear-algebra-problem"], [69, "id1"]], "Generative Adversarial Networks": [[46, "generative-adversarial-networks"]], "Generative Models": [[46, "generative-models"]], "Generative Versus Discriminative Modeling": [[69, "generative-versus-discriminative-modeling"]], "Geometric Interpretation and link with Singular Value Decomposition": [[53, "geometric-interpretation-and-link-with-singular-value-decomposition"]], "Github Dark": [[6, null]], "Github Dark Colorblind": [[7, null]], "Github Dark High Contrast": [[8, null]], "Github Light": [[9, null]], "Github Light Colorblind": [[10, null]], "Github Light High Contrast": [[11, null]], "Gotthard Dark": [[12, null]], "Gotthard Light": [[13, null]], "Gradient Boosting, Classification Example": [[52, "gradient-boosting-classification-example"]], "Gradient Boosting, Examples of Regression": [[52, "gradient-boosting-examples-of-regression"]], "Gradient Clipping": [[43, "gradient-clipping"]], "Gradient Descent Example": [[71, "id1"], [72, "id1"]], "Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent": [[52, "gradient-boosting-basics-with-steepest-descent-functional-gradient-descent"]], "Gradient descent": [[44, "gradient-descent"]], "Gradient descent and Ridge": [[71, "gradient-descent-and-ridge"], [72, "gradient-descent-and-ridge"]], "Gradient descent and revisiting Ordinary Least Squares from last week": [[72, "gradient-descent-and-revisiting-ordinary-least-squares-from-last-week"]], "Gradient descent example": [[71, "gradient-descent-example"], [72, "gradient-descent-example"]], "Grading": [[67, "grading"], [67, "id2"], [69, "grading"]], "Greative": [[14, null]], "How to take derivatives of Matrix-Vector expressions": [[58, "how-to-take-derivatives-of-matrix-vector-expressions"]], "Hyperplanes and all that": [[50, "hyperplanes-and-all-that"]], "Important Matrix and vector handling packages": [[63, "important-matrix-and-vector-handling-packages"]], "Important technicalities: More on Rescaling data": [[70, "important-technicalities-more-on-rescaling-data"]], "Improving gradient descent with momentum": [[72, "improving-gradient-descent-with-momentum"]], "Improving performance": [[43, "improving-performance"]], "In summary": [[67, "in-summary"]], "Including Stochastic Gradient Descent with Autograd": [[55, "including-stochastic-gradient-descent-with-autograd"], [72, "including-stochastic-gradient-descent-with-autograd"]], "Incremental PCA": [[53, "incremental-pca"]], "Install": [[28, "install"]], "Installation": [[27, "installation"]], "Installing R, C++, cython or Julia": [[69, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[69, "installing-r-c-cython-numba-etc"]], "Instructor information": [[67, "instructor-information"]], "Interpretations and optimizing our parameters": [[69, "interpretations-and-optimizing-our-parameters"], [69, "id2"], [69, "id3"], [70, "interpretations-and-optimizing-our-parameters"], [70, "id1"], [70, "id2"]], "Interpreting the Ridge results": [[70, "interpreting-the-ridge-results"], [71, "interpreting-the-ridge-results"], [71, "id4"]], "Introducing JAX": [[55, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[53, "introducing-the-covariance-and-correlation-functions"], [70, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[42, "introduction"], [48, "introduction"], [62, "introduction"], [63, "introduction"]], "Introduction to numerical projects": [[64, "introduction-to-numerical-projects"]], "Iterative Fitting, Classification and AdaBoost": [[52, "iterative-fitting-classification-and-adaboost"]], "Iterative Fitting, Regression and Squared-error Cost Function": [[52, "iterative-fitting-regression-and-squared-error-cost-function"]], "Kernel PCA": [[53, "kernel-pca"]], "Kernels and non-linearity": [[50, "kernels-and-non-linearity"]], "LU Decomposition, the inverse of a matrix": [[63, "lu-decomposition-the-inverse-of-a-matrix"]], "Lasso Regression": [[71, "lasso-regression"]], "Lasso case": [[71, "lasso-case"]], "Layers": [[43, "layers"]], "Layers used to build CNNs": [[45, "layers-used-to-build-cnns"]], "Learn more": [[22, "learn-more"]], "Learning goals": [[57, "learning-goals"], [58, "learning-goals"], [59, "learning-goals"], [60, "learning-goals"], [61, "learning-goals"]], "Learning outcomes": [[62, "learning-outcomes"], [69, "learning-outcomes"]], "Lectures and ComputerLab": [[69, "lectures-and-computerlab"]], "License": [[27, "license"], [28, "license"], [29, "license"]], "License for Sphinx": [[35, null]], "Licenses for incorporated software": [[35, "licenses-for-incorporated-software"]], "Limitations of supervised learning with deep networks": [[43, "limitations-of-supervised-learning-with-deep-networks"]], "Linear Algebra, Handling of Arrays and more Python Features": [[63, null]], "Linear Regression": [[42, null]], "Linear Regression Problems": [[70, "linear-regression-problems"], [71, "linear-regression-problems"]], "Linear Regression and  the SVD": [[71, "linear-regression-and-the-svd"]], "Linear Regression, basic elements": [[42, "linear-regression-basic-elements"]], "Linking Bayes\u2019 Theorem with Ridge and Lasso Regression": [[47, "linking-bayes-theorem-with-ridge-and-lasso-regression"]], "Linking the regression analysis with a statistical interpretation": [[47, "linking-the-regression-analysis-with-a-statistical-interpretation"]], "Linking with the SVD": [[47, "linking-with-the-svd"], [70, "linking-with-the-svd"]], "Links to relevant courses at the University of Oslo": [[68, "links-to-relevant-courses-at-the-university-of-oslo"]], "Logistic Regression": [[49, null], [49, "id1"]], "MNIST and GANs": [[46, "mnist-and-gans"]], "Machine Learning": [[69, "machine-learning"]], "Machine learning": [[62, "machine-learning"]], "Main textbooks": [[69, "main-textbooks"]], "Making a tree": [[51, "making-a-tree"]], "Making your own Bootstrap: Changing the Level of the Decision Tree": [[52, "making-your-own-bootstrap-changing-the-level-of-the-decision-tree"]], "Making your own test-train splitting": [[70, "making-your-own-test-train-splitting"]], "Markdown + notebooks": [[24, "markdown-notebooks"]], "Markdown Files": [[22, null]], "Material for exercises week 35": [[70, "material-for-exercises-week-35"]], "Material for lab sessions  sessions Tuesday and Wednesday": [[71, "material-for-lab-sessions-sessions-tuesday-and-wednesday"]], "Material for lecture Monday September 2": [[71, "material-for-lecture-monday-september-2"]], "Material for lecture Monday September 8": [[72, "material-for-lecture-monday-september-8"]], "Material for the lab sessions": [[72, "material-for-the-lab-sessions"]], "Mathematical Interpretation of Ordinary Least Squares": [[47, "mathematical-interpretation-of-ordinary-least-squares"], [70, "mathematical-interpretation-of-ordinary-least-squares"], [71, "mathematical-interpretation-of-ordinary-least-squares"]], "Mathematical optimization of convex functions": [[50, "mathematical-optimization-of-convex-functions"]], "Mathematics of CNNs": [[45, "mathematics-of-cnns"]], "Mathematics of the SVD and implications": [[47, "mathematics-of-the-svd-and-implications"], [70, "mathematics-of-the-svd-and-implications"], [71, "mathematics-of-the-svd-and-implications"]], "Matrices in Python": [[69, "matrices-in-python"]], "Matrix  multiplication": [[43, "matrix-multiplication"]], "Matrix-vector notation  and activation": [[54, "matrix-vector-notation-and-activation"]], "Meet the  covariance!": [[66, "meet-the-covariance"]], "Meet the Covariance Matrix": [[47, "meet-the-covariance-matrix"], [70, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[70, "meet-the-hessian-matrix"]], "Meet the Pandas": [[69, "meet-the-pandas"]], "Memory Usage and Scalability": [[72, "memory-usage-and-scalability"]], "Memory constraints": [[72, "memory-constraints"]], "Min-Max Scaling": [[70, "min-max-scaling"]], "Momentum based GD": [[55, "momentum-based-gd"], [72, "momentum-based-gd"]], "More complicated Example: The Ising model": [[48, "more-complicated-example-the-ising-model"]], "More interpretations": [[70, "more-interpretations"], [71, "more-interpretations"], [71, "id5"]], "More on Dimensionalities": [[45, "more-on-dimensionalities"]], "More on Rescaling data": [[48, "more-on-rescaling-data"]], "More on Steepest descent": [[71, "more-on-steepest-descent"]], "More on convex functions": [[71, "more-on-convex-functions"]], "More preprocessing": [[70, "more-preprocessing"], [72, "more-preprocessing"]], "Motivation for Adaptive Step Sizes": [[72, "motivation-for-adaptive-step-sizes"]], "Multilayer perceptrons": [[54, "multilayer-perceptrons"]], "MyST markdown": [[24, "myst-markdown"]], "Network requirements": [[44, "network-requirements"]], "Neural Networks vs CNNs": [[45, "neural-networks-vs-cnns"]], "Neural networks": [[54, null]], "Non-Convex Problems": [[72, "non-convex-problems"]], "Note about SVD Calculations": [[70, "note-about-svd-calculations"], [71, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[71, "note-on-scikit-learn"]], "Notebooks with MyST Markdown": [[23, null]], "Numerical experiments and the covariance, central limit theorem": [[66, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[63, "numpy-and-arrays"], [69, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[69, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and gradient descent, the central part of any Machine Learning algortithm": [[71, "optimization-and-gradient-descent-the-central-part-of-any-machine-learning-algortithm"]], "Optimization, the central part of any Machine Learning algortithm": [[55, null]], "Optimizing our parameters": [[69, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[69, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[43, "optimizing-the-cost-function"]], "Organizing our data": [[42, "organizing-our-data"], [69, "organizing-our-data"]], "Other Matrix and Vector Operations": [[63, "other-matrix-and-vector-operations"]], "Other Types of Recurrent Neural Networks": [[46, "other-types-of-recurrent-neural-networks"]], "Other courses on Data science and Machine Learning  at UiO": [[69, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning  at UiO, contn": [[69, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other popular texts": [[69, "other-popular-texts"]], "Other techniques": [[53, "other-techniques"]], "Other types of networks": [[54, "other-types-of-networks"]], "Other ways of visualizing the trees": [[51, "other-ways-of-visualizing-the-trees"]], "Our Copyright Policy": [[20, "our-copyright-policy"]], "Our model for the nuclear binding energies": [[69, "our-model-for-the-nuclear-binding-energies"]], "Overview of first week": [[69, "overview-of-first-week"]], "Overview video on Stochastic Gradient Descent (SGD)": [[72, "overview-video-on-stochastic-gradient-descent-sgd"]], "Own code for Ordinary Least Squares": [[69, "own-code-for-ordinary-least-squares"], [70, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[53, "pca-and-scikit-learn"]], "Pandas AI": [[69, "pandas-ai"]], "Part a : Ordinary Least Square (OLS) for the Runge function": [[64, "part-a-ordinary-least-square-ols-for-the-runge-function"]], "Part b: Adding Ridge regression for  the Runge  function": [[64, "part-b-adding-ridge-regression-for-the-runge-function"]], "Part c: Writing your own gradient descent code": [[64, "part-c-writing-your-own-gradient-descent-code"]], "Part d: Including momentum and more advanced ways to update the learning the rate": [[64, "part-d-including-momentum-and-more-advanced-ways-to-update-the-learning-the-rate"]], "Part e: Writing our own code for Lasso regression": [[64, "part-e-writing-our-own-code-for-lasso-regression"]], "Part f: Stochastic gradient descent": [[64, "part-f-stochastic-gradient-descent"]], "Part g: Bias-variance trade-off and resampling techniques": [[64, "part-g-bias-variance-trade-off-and-resampling-techniques"]], "Part h):  Cross-validation as resampling techniques, adding more complexity": [[64, "part-h-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Partial Differential Equations": [[44, "partial-differential-equations"]], "Pitaya Smoothie": [[15, null]], "Plans for week 35": [[70, "plans-for-week-35"]], "Plans for week 36": [[71, "plans-for-week-36"]], "Plans for week 37, lecture Monday": [[72, "plans-for-week-37-lecture-monday"]], "Practical tips": [[55, "practical-tips"], [72, "practical-tips"]], "Practicalities": [[67, "practicalities"], [67, "id1"]], "Preamble: Note on writing reports, using reference material, AI and other tools": [[64, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"]], "Predicting New Points With A Trained Recurrent Neural Network": [[46, "predicting-new-points-with-a-trained-recurrent-neural-network"]], "Preprocessing our data": [[70, "preprocessing-our-data"]], "Prerequisites": [[69, "prerequisites"]], "Prerequisites and background": [[62, "prerequisites-and-background"]], "Prerequisites: Collect and pre-process data": [[45, "prerequisites-collect-and-pre-process-data"]], "Probability Distribution Functions": [[66, "probability-distribution-functions"]], "Program example for gradient descent with Ridge Regression": [[71, "program-example-for-gradient-descent-with-ridge-regression"], [72, "program-example-for-gradient-descent-with-ridge-regression"]], "Program for stochastic gradient": [[55, "program-for-stochastic-gradient"]], "Project 1 on Machine Learning, deadline October 6 (midnight), 2025": [[64, null]], "Properties of PDFs": [[66, "properties-of-pdfs"]], "Pros and cons": [[72, "pros-and-cons"]], "Pros and cons of trees, pros": [[51, "pros-and-cons-of-trees-pros"]], "Python installers": [[62, "python-installers"], [69, "python-installers"]], "Quickly add YAML metadata for MyST Notebooks": [[23, "quickly-add-yaml-metadata-for-myst-notebooks"]], "RMS prop": [[55, "rms-prop"]], "RMSProp algorithm, taken from Goodfellow et al": [[72, "rmsprop-algorithm-taken-from-goodfellow-et-al"]], "RMSProp: Adaptive Learning Rates": [[72, "rmsprop-adaptive-learning-rates"]], "RMSprop for adaptive learning rate with Stochastic Gradient Descent": [[72, "rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent"]], "Random Numbers": [[66, "random-numbers"]], "Random forests": [[52, "random-forests"]], "Randomized PCA": [[53, "randomized-pca"]], "Reading material": [[69, "reading-material"]], "Reading recommendations:": [[70, "reading-recommendations"]], "Reading suggestions 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"reminder-on-newton-raphson-s-method"]], "Reminder on Statistics": [[48, "reminder-on-statistics"]], "Reminder on different scaling methods": [[72, "reminder-on-different-scaling-methods"]], "Replace or not": [[55, "replace-or-not"], [72, "replace-or-not"]], "Required Technologies": [[62, "required-technologies"]], "Resampling Methods": [[48, null]], "Resampling and the Bias-Variance Trade-off": [[61, "resampling-and-the-bias-variance-trade-off"]], "Resampling methods": [[48, "id1"]], "Residual Error": [[70, "residual-error"], [71, "residual-error"]], "Resources on differential equations and deep learning": [[44, "resources-on-differential-equations-and-deep-learning"]], "Revisiting Ordinary Least Squares": [[71, "revisiting-ordinary-least-squares"]], "Revisiting our Linear Regression Solvers": [[55, "revisiting-our-linear-regression-solvers"]], "Rewriting the Covariance and/or Correlation Matrix": [[70, "rewriting-the-covariance-and-or-correlation-matrix"]], "Rewriting the fitting procedure as a linear algebra problem": [[69, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem"]], "Rewriting the fitting procedure as a linear algebra problem, more details": [[69, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details"]], "Ridge Regression": [[71, "ridge-regression"]], "Ridge and LASSO Regression": [[70, "ridge-and-lasso-regression"], [71, "ridge-and-lasso-regression"], [71, "id2"]], "Ridge and Lasso Regression": [[47, null], [47, "id1"]], "SGD example": [[72, "sgd-example"]], "SGD vs Full-Batch GD: Convergence Speed and Memory Comparison": [[72, "sgd-vs-full-batch-gd-convergence-speed-and-memory-comparison"]], "SVD analysis": [[71, "svd-analysis"]], "Same code but now with momentum gradient descent": [[55, "same-code-but-now-with-momentum-gradient-descent"], [72, "same-code-but-now-with-momentum-gradient-descent"], [72, "id3"], [72, "id4"]], "Sample Roles and Directives": [[22, "sample-roles-and-directives"]], "Schedule first week": 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installations": [[64, "software-and-needed-installations"], [69, "software-and-needed-installations"]], "Solving Differential Equations  with Deep Learning": [[44, null]], "Solving the one dimensional Poisson equation": [[44, "solving-the-one-dimensional-poisson-equation"]], "Solving the wave equation with Neural Networks": [[44, "solving-the-wave-equation-with-neural-networks"]], "Some famous Matrices": [[63, "some-famous-matrices"]], "Some simple problems": [[55, "some-simple-problems"], [71, "some-simple-problems"]], "Some useful matrix and vector expressions": [[70, "some-useful-matrix-and-vector-expressions"]], "Splitting our Data in Training and Test data": [[42, "splitting-our-data-in-training-and-test-data"], [70, "splitting-our-data-in-training-and-test-data"]], "Standard steepest descent": [[55, "standard-steepest-descent"]], "Statistical analysis and optimization of data": [[62, "statistical-analysis-and-optimization-of-data"], [69, 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OLS from a probability distribution": [[5, "deriving-ols-from-a-probability-distribution"]], "Deriving and Implementing Ordinary Least Squares": [[16, "deriving-and-implementing-ordinary-least-squares"]], "Deriving and Implementing Ridge Regression": [[17, "deriving-and-implementing-ridge-regression"]], "Deriving the  Lasso Regression Equations": [[28, "deriving-the-lasso-regression-equations"], [29, "deriving-the-lasso-regression-equations"], [29, "id6"]], "Deriving the  Ridge Regression Equations": [[28, "deriving-the-ridge-regression-equations"], [29, "deriving-the-ridge-regression-equations"], [29, "id3"]], "Deriving the back propagation code for a multilayer perceptron model": [[12, "deriving-the-back-propagation-code-for-a-multilayer-perceptron-model"]], "Developing a code for doing neural networks with back propagation": [[1, "developing-a-code-for-doing-neural-networks-with-back-propagation"]], "Diagonalize the sample covariance matrix to obtain the principal components": [[11, "diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components"]], "Different kernels and Mercer\u2019s theorem": [[8, "different-kernels-and-mercer-s-theorem"]], "Disadvantages": [[9, "disadvantages"]], "Discriminative Modeling": [[27, "discriminative-modeling"]], "Domains and probabilities": [[24, "domains-and-probabilities"]], "Dropout": [[1, "dropout"]], "Economy-size SVD": [[28, "economy-size-svd"], [29, "economy-size-svd"]], "Elements of Probability Theory and Statistical Data Analysis": [[24, null]], "Empirical Evidence: Convergence Time and Memory in Practice": [[30, "empirical-evidence-convergence-time-and-memory-in-practice"]], "Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods": [[10, null]], "Entropy and the ID3 algorithm": [[9, "entropy-and-the-id3-algorithm"]], "Essential elements of ML": [[27, "essential-elements-of-ml"]], "Evaluate model performance on test data": [[1, "evaluate-model-performance-on-test-data"]], "Example 2": [[28, "example-2"]], "Example 3": [[28, "example-3"]], "Example 4": [[28, "example-4"]], "Example Matrix": [[28, "example-matrix"], [29, "example-matrix"]], "Example of discriminative modeling, taken from Generative Deep Learning by David Foster": [[27, "example-of-discriminative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of generative modeling, taken from Generative Deep Learning by David Foster": [[27, "example-of-generative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of own Standard scaling": [[28, "example-of-own-standard-scaling"]], "Example relevant for the exercises": [[28, "example-relevant-for-the-exercises"]], "Example: Exponential decay": [[2, "example-exponential-decay"]], "Example: Population growth": [[2, "example-population-growth"]], "Example: The diffusion equation": [[2, "example-the-diffusion-equation"]], "Example: binary classification problem": [[1, "example-binary-classification-problem"]], "Examples": [[27, "examples"]], "Examples of likelihood functions used in logistic regression and neural networks": [[7, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Exercise 1 - Choice of model and degrees of freedom": [[17, "exercise-1-choice-of-model-and-degrees-of-freedom"]], "Exercise 1 - Finding the derivative of Matrix-Vector expressions": [[16, "exercise-1-finding-the-derivative-of-matrix-vector-expressions"]], "Exercise 1 - Github Setup": [[15, "exercise-1-github-setup"]], "Exercise 1, scale your data": [[18, "exercise-1-scale-your-data"]], "Exercise 1: Expectation values for ordinary least squares expressions": [[19, "exercise-1-expectation-values-for-ordinary-least-squares-expressions"]], "Exercise 1: Setting up various Python environments": [[0, "exercise-1-setting-up-various-python-environments"]], "Exercise 2 - Deriving the expression for OLS": [[16, "exercise-2-deriving-the-expression-for-ols"]], "Exercise 2 - Deriving the expression for Ridge Regression": [[17, "exercise-2-deriving-the-expression-for-ridge-regression"]], "Exercise 2 - Setting up a Github repository": [[15, "exercise-2-setting-up-a-github-repository"]], "Exercise 2, calculate the gradients": [[18, "exercise-2-calculate-the-gradients"]], "Exercise 2: Expectation values for Ridge regression": [[19, "exercise-2-expectation-values-for-ridge-regression"]], "Exercise 2: making your own data and exploring scikit-learn": [[0, "exercise-2-making-your-own-data-and-exploring-scikit-learn"]], "Exercise 3 - Creating feature matrix and implementing OLS using the analytical expression": [[16, "exercise-3-creating-feature-matrix-and-implementing-ols-using-the-analytical-expression"]], "Exercise 3 - Fitting an OLS model to data": [[15, "exercise-3-fitting-an-ols-model-to-data"]], "Exercise 3 - Scaling data": [[17, "exercise-3-scaling-data"]], "Exercise 3 - Setting up a Python virtual environment": [[15, "exercise-3-setting-up-a-python-virtual-environment"]], "Exercise 3, using the analytical formulae for OLS and Ridge regression to find the optimal paramters \\boldsymbol{\\theta}": [[18, "exercise-3-using-the-analytical-formulae-for-ols-and-ridge-regression-to-find-the-optimal-paramters-boldsymbol-theta"]], "Exercise 3: Deriving the expression for the Bias-Variance Trade-off": [[19, "exercise-3-deriving-the-expression-for-the-bias-variance-trade-off"]], "Exercise 3: Normalizing our data": [[0, "exercise-3-normalizing-our-data"]], "Exercise 4 - Fitting a polynomial": [[16, "exercise-4-fitting-a-polynomial"]], "Exercise 4 - Implementing Ridge Regression": [[17, "exercise-4-implementing-ridge-regression"]], "Exercise 4 - Testing multiple hyperparameters": [[17, "exercise-4-testing-multiple-hyperparameters"]], "Exercise 4 - The train-test split": [[15, "exercise-4-the-train-test-split"]], "Exercise 4, Implementing the simplest form for gradient descent": [[18, "exercise-4-implementing-the-simplest-form-for-gradient-descent"]], "Exercise 4: Adding Ridge Regression": [[0, "exercise-4-adding-ridge-regression"]], "Exercise 4: Computing the Bias and Variance": [[19, "exercise-4-computing-the-bias-and-variance"]], "Exercise 5 - Comparing your code with sklearn": [[16, "exercise-5-comparing-your-code-with-sklearn"]], "Exercise 5, Ridge regression and a new Synthetic Dataset": [[18, "exercise-5-ridge-regression-and-a-new-synthetic-dataset"]], "Exercise 5: Analytical exercises": [[0, "exercise-5-analytical-exercises"]], "Exercise 5: Interpretation of scaling and metrics": [[19, "exercise-5-interpretation-of-scaling-and-metrics"]], "Exercise:  Cross-validation as resampling techniques, adding more complexity": [[6, "exercise-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Exercise: Analysis of real data": [[6, "exercise-analysis-of-real-data"]], "Exercise: Bias-variance trade-off and resampling techniques": [[6, "exercise-bias-variance-trade-off-and-resampling-techniques"]], "Exercise: Lasso Regression on the Franke function  with resampling": [[6, "exercise-lasso-regression-on-the-franke-function-with-resampling"]], "Exercise: Ordinary Least Square (OLS) on the Franke function": [[6, "exercise-ordinary-least-square-ols-on-the-franke-function"]], "Exercise: Ridge Regression on the Franke function  with resampling": [[6, "exercise-ridge-regression-on-the-franke-function-with-resampling"]], "Exercises": [[0, "exercises"]], "Exercises and Projects": [[6, "exercises-and-projects"]], "Exercises week 34": [[15, null]], "Exercises week 35": [[16, null]], "Exercises week 36": [[17, null]], "Exercises week 37": [[18, null]], "Exercises week 38": [[19, null]], "Expectation values": [[24, "expectation-values"]], "Extending to more than one variable": [[29, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[27, "extremely-useful-tools-strongly-recommended"]], "Feed-forward neural networks": [[12, "feed-forward-neural-networks"]], "Feed-forward pass": [[1, "feed-forward-pass"]], "Final back propagating equation": [[12, "final-back-propagating-equation"]], "Fine-tuning neural network hyperparameters": [[1, "fine-tuning-neural-network-hyperparameters"]], "Fitting an Equation of State for Dense Nuclear Matter": [[0, "fitting-an-equation-of-state-for-dense-nuclear-matter"]], "Fixing the singularity": [[28, "fixing-the-singularity"], [29, "fixing-the-singularity"]], "Format for electronic delivery of report and programs": [[22, "format-for-electronic-delivery-of-report-and-programs"]], "Frequently used scaling functions": [[28, "frequently-used-scaling-functions"], [30, "frequently-used-scaling-functions"]], "From OLS to Ridge and Lasso": [[29, "from-ols-to-ridge-and-lasso"]], "From one to many layers, the universal approximation theorem": [[12, "from-one-to-many-layers-the-universal-approximation-theorem"]], "Functionality in Scikit-Learn": [[28, "functionality-in-scikit-learn"], [30, "functionality-in-scikit-learn"]], "Further Dimensionality Remarks": [[3, "further-dimensionality-remarks"]], "Further properties (important for our analyses later)": [[5, "further-properties-important-for-our-analyses-later"], [28, "further-properties-important-for-our-analyses-later"], [29, "further-properties-important-for-our-analyses-later"]], "Gaussian Elimination": [[21, "gaussian-elimination"]], "General Features": [[9, "general-features"]], "General linear models and linear algebra": [[27, "general-linear-models-and-linear-algebra"]], "Generalizing the fitting procedure as a linear algebra problem": [[27, "generalizing-the-fitting-procedure-as-a-linear-algebra-problem"], [27, "id1"]], "Generative Adversarial Networks": [[4, "generative-adversarial-networks"]], "Generative Models": [[4, "generative-models"]], "Generative Versus Discriminative Modeling": [[27, "generative-versus-discriminative-modeling"]], "Geometric Interpretation and link with Singular Value Decomposition": [[11, "geometric-interpretation-and-link-with-singular-value-decomposition"]], "Gradient Boosting, Classification Example": [[10, "gradient-boosting-classification-example"]], "Gradient Boosting, Examples of Regression": [[10, "gradient-boosting-examples-of-regression"]], "Gradient Clipping": [[1, "gradient-clipping"]], "Gradient Descent Example": [[29, "id1"], [30, "id1"]], "Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent": [[10, "gradient-boosting-basics-with-steepest-descent-functional-gradient-descent"]], "Gradient descent": [[2, "gradient-descent"]], "Gradient descent and Ridge": [[29, "gradient-descent-and-ridge"], [30, "gradient-descent-and-ridge"]], "Gradient descent and revisiting Ordinary Least Squares from last week": [[30, "gradient-descent-and-revisiting-ordinary-least-squares-from-last-week"]], "Gradient descent example": [[29, "gradient-descent-example"], [30, "gradient-descent-example"]], "Grading": [[25, "grading"], [25, "id2"], [27, "grading"]], "How to take derivatives of Matrix-Vector expressions": [[16, "how-to-take-derivatives-of-matrix-vector-expressions"]], "Hyperplanes and all that": [[8, "hyperplanes-and-all-that"]], "Important Matrix and vector handling packages": [[21, "important-matrix-and-vector-handling-packages"]], "Important technicalities: More on Rescaling data": [[28, "important-technicalities-more-on-rescaling-data"]], "Improving gradient descent with momentum": [[30, "improving-gradient-descent-with-momentum"]], "Improving performance": [[1, "improving-performance"]], "In summary": [[25, "in-summary"]], "Including Stochastic Gradient Descent with Autograd": [[13, "including-stochastic-gradient-descent-with-autograd"], [30, "including-stochastic-gradient-descent-with-autograd"]], "Incremental PCA": [[11, "incremental-pca"]], "Installing R, C++, cython or Julia": [[27, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[27, "installing-r-c-cython-numba-etc"]], "Instructor information": [[25, "instructor-information"]], "Interpretations and optimizing our parameters": [[27, "interpretations-and-optimizing-our-parameters"], [27, "id2"], [27, "id3"], [28, "interpretations-and-optimizing-our-parameters"], [28, "id1"], [28, "id2"]], "Interpreting the Ridge results": [[28, "interpreting-the-ridge-results"], [29, "interpreting-the-ridge-results"], [29, "id4"]], "Introducing JAX": [[13, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[11, "introducing-the-covariance-and-correlation-functions"], [28, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[0, "introduction"], [6, "introduction"], [20, "introduction"], [21, "introduction"]], "Introduction to numerical projects": [[22, "introduction-to-numerical-projects"]], "Iterative Fitting, Classification and AdaBoost": [[10, "iterative-fitting-classification-and-adaboost"]], "Iterative Fitting, Regression and Squared-error Cost Function": [[10, "iterative-fitting-regression-and-squared-error-cost-function"]], "Kernel PCA": [[11, "kernel-pca"]], "Kernels and non-linearity": [[8, "kernels-and-non-linearity"]], "LU Decomposition, the inverse of a matrix": [[21, "lu-decomposition-the-inverse-of-a-matrix"]], "Lasso Regression": [[29, "lasso-regression"]], "Lasso case": [[29, "lasso-case"]], "Layers": [[1, "layers"]], "Layers used to build CNNs": [[3, "layers-used-to-build-cnns"]], "Learning goals": [[15, "learning-goals"], [16, "learning-goals"], [17, "learning-goals"], [18, "learning-goals"], [19, "learning-goals"]], "Learning outcomes": [[20, "learning-outcomes"], [27, "learning-outcomes"]], "Lectures and ComputerLab": [[27, "lectures-and-computerlab"]], "Limitations of supervised learning with deep networks": [[1, "limitations-of-supervised-learning-with-deep-networks"]], "Linear Algebra, Handling of Arrays and more Python Features": [[21, null]], "Linear Regression": [[0, null]], "Linear Regression Problems": [[28, "linear-regression-problems"], [29, "linear-regression-problems"]], "Linear Regression and  the SVD": [[29, "linear-regression-and-the-svd"]], "Linear Regression, basic elements": [[0, "linear-regression-basic-elements"]], "Linking Bayes\u2019 Theorem with Ridge and Lasso Regression": [[5, "linking-bayes-theorem-with-ridge-and-lasso-regression"]], "Linking the regression analysis with a statistical interpretation": [[5, "linking-the-regression-analysis-with-a-statistical-interpretation"]], "Linking with the SVD": [[5, "linking-with-the-svd"], [28, "linking-with-the-svd"]], "Links to relevant courses at the University of Oslo": [[26, "links-to-relevant-courses-at-the-university-of-oslo"]], "Logistic Regression": [[7, null], [7, "id1"]], "MNIST and GANs": [[4, "mnist-and-gans"]], "Machine Learning": [[27, "machine-learning"]], "Machine learning": [[20, "machine-learning"]], "Main textbooks": [[27, "main-textbooks"]], "Making a tree": [[9, "making-a-tree"]], "Making your own Bootstrap: Changing the Level of the Decision Tree": [[10, "making-your-own-bootstrap-changing-the-level-of-the-decision-tree"]], "Making your own test-train splitting": [[28, "making-your-own-test-train-splitting"]], "Material for exercises week 35": [[28, "material-for-exercises-week-35"]], "Material for lab sessions  sessions Tuesday and Wednesday": [[29, "material-for-lab-sessions-sessions-tuesday-and-wednesday"]], "Material for lecture Monday September 2": [[29, "material-for-lecture-monday-september-2"]], "Material for lecture Monday September 8": [[30, "material-for-lecture-monday-september-8"]], "Material for the lab sessions": [[30, "material-for-the-lab-sessions"]], "Mathematical Interpretation of Ordinary Least Squares": [[5, "mathematical-interpretation-of-ordinary-least-squares"], [28, "mathematical-interpretation-of-ordinary-least-squares"], [29, "mathematical-interpretation-of-ordinary-least-squares"]], "Mathematical optimization of convex functions": [[8, "mathematical-optimization-of-convex-functions"]], "Mathematics of CNNs": [[3, "mathematics-of-cnns"]], "Mathematics of the SVD and implications": [[5, "mathematics-of-the-svd-and-implications"], [28, "mathematics-of-the-svd-and-implications"], [29, "mathematics-of-the-svd-and-implications"]], "Matrices in Python": [[27, "matrices-in-python"]], "Matrix  multiplication": [[1, "matrix-multiplication"]], "Matrix-vector notation  and activation": [[12, "matrix-vector-notation-and-activation"]], "Meet the  covariance!": [[24, "meet-the-covariance"]], "Meet the Covariance Matrix": [[5, "meet-the-covariance-matrix"], [28, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[28, "meet-the-hessian-matrix"]], "Meet the Pandas": [[27, "meet-the-pandas"]], "Memory Usage and Scalability": [[30, "memory-usage-and-scalability"]], "Memory constraints": [[30, "memory-constraints"]], "Min-Max Scaling": [[28, "min-max-scaling"]], "Momentum based GD": [[13, "momentum-based-gd"], [30, "momentum-based-gd"]], "More complicated Example: The Ising model": [[6, "more-complicated-example-the-ising-model"]], "More interpretations": [[28, "more-interpretations"], [29, "more-interpretations"], [29, "id5"]], "More on Dimensionalities": [[3, "more-on-dimensionalities"]], "More on Rescaling data": [[6, "more-on-rescaling-data"]], "More on Steepest descent": [[29, "more-on-steepest-descent"]], "More on convex functions": [[29, "more-on-convex-functions"]], "More preprocessing": [[28, "more-preprocessing"], [30, "more-preprocessing"]], "Motivation for Adaptive Step Sizes": [[30, "motivation-for-adaptive-step-sizes"]], "Multilayer perceptrons": [[12, "multilayer-perceptrons"]], "Network requirements": [[2, "network-requirements"]], "Neural Networks vs CNNs": [[3, "neural-networks-vs-cnns"]], "Neural networks": [[12, null]], "Non-Convex Problems": [[30, "non-convex-problems"]], "Note about SVD Calculations": [[28, "note-about-svd-calculations"], [29, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[29, "note-on-scikit-learn"]], "Numerical experiments and the covariance, central limit theorem": [[24, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[21, "numpy-and-arrays"], [27, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[27, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and gradient descent, the central part of any Machine Learning algortithm": [[29, "optimization-and-gradient-descent-the-central-part-of-any-machine-learning-algortithm"]], "Optimization, the central part of any Machine Learning algortithm": [[13, null]], "Optimizing our parameters": [[27, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[27, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[1, "optimizing-the-cost-function"]], "Organizing our data": [[0, "organizing-our-data"], [27, "organizing-our-data"]], "Other Matrix and Vector Operations": [[21, "other-matrix-and-vector-operations"]], "Other Types of Recurrent Neural Networks": [[4, "other-types-of-recurrent-neural-networks"]], "Other courses on Data science and Machine Learning  at UiO": [[27, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning  at UiO, contn": [[27, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other popular texts": [[27, "other-popular-texts"]], "Other techniques": [[11, "other-techniques"]], "Other types of networks": [[12, "other-types-of-networks"]], "Other ways of visualizing the trees": [[9, "other-ways-of-visualizing-the-trees"]], "Our model for the nuclear binding energies": [[27, "our-model-for-the-nuclear-binding-energies"]], "Overview of first week": [[27, "overview-of-first-week"]], "Overview video on Stochastic Gradient Descent (SGD)": [[30, "overview-video-on-stochastic-gradient-descent-sgd"]], "Own code for Ordinary Least Squares": [[27, "own-code-for-ordinary-least-squares"], [28, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[11, "pca-and-scikit-learn"]], "Pandas AI": [[27, "pandas-ai"]], "Part a : Ordinary Least Square (OLS) for the Runge function": [[22, "part-a-ordinary-least-square-ols-for-the-runge-function"]], "Part b: Adding Ridge regression for  the Runge  function": [[22, "part-b-adding-ridge-regression-for-the-runge-function"]], "Part c: Writing your own gradient descent code": [[22, "part-c-writing-your-own-gradient-descent-code"]], "Part d: Including momentum and more advanced ways to update the learning the rate": [[22, "part-d-including-momentum-and-more-advanced-ways-to-update-the-learning-the-rate"]], "Part e: Writing our own code for Lasso regression": [[22, "part-e-writing-our-own-code-for-lasso-regression"]], "Part f: Stochastic gradient descent": [[22, "part-f-stochastic-gradient-descent"]], "Part g: Bias-variance trade-off and resampling techniques": [[22, "part-g-bias-variance-trade-off-and-resampling-techniques"]], "Part h):  Cross-validation as resampling techniques, adding more complexity": [[22, "part-h-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Partial Differential Equations": [[2, "partial-differential-equations"]], "Plans for week 35": [[28, "plans-for-week-35"]], "Plans for week 36": [[29, "plans-for-week-36"]], "Plans for week 37, lecture Monday": [[30, "plans-for-week-37-lecture-monday"]], "Practical tips": [[13, "practical-tips"], [30, "practical-tips"]], "Practicalities": [[25, "practicalities"], [25, "id1"]], "Preamble: Note on writing reports, using reference material, AI and other tools": [[22, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"]], "Predicting New Points With A Trained Recurrent Neural Network": [[4, "predicting-new-points-with-a-trained-recurrent-neural-network"]], "Preprocessing our data": [[28, "preprocessing-our-data"]], "Prerequisites": [[27, "prerequisites"]], "Prerequisites and background": [[20, "prerequisites-and-background"]], "Prerequisites: Collect and pre-process data": [[3, "prerequisites-collect-and-pre-process-data"]], "Probability Distribution Functions": [[24, "probability-distribution-functions"]], "Program example for gradient descent with Ridge Regression": [[29, "program-example-for-gradient-descent-with-ridge-regression"], [30, "program-example-for-gradient-descent-with-ridge-regression"]], "Program for stochastic gradient": [[13, "program-for-stochastic-gradient"]], "Project 1 on Machine Learning, deadline October 6 (midnight), 2025": [[22, null]], "Properties of PDFs": [[24, "properties-of-pdfs"]], "Pros and cons": [[30, "pros-and-cons"]], "Pros and cons of trees, pros": [[9, "pros-and-cons-of-trees-pros"]], "Python installers": [[20, "python-installers"], [27, "python-installers"]], "RMS prop": [[13, "rms-prop"]], "RMSProp algorithm, taken from Goodfellow et al": [[30, "rmsprop-algorithm-taken-from-goodfellow-et-al"]], "RMSProp: Adaptive Learning Rates": [[30, "rmsprop-adaptive-learning-rates"]], "RMSprop for adaptive learning rate with Stochastic Gradient Descent": [[30, "rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent"]], "Random Numbers": [[24, "random-numbers"]], "Random forests": [[10, "random-forests"]], "Randomized PCA": [[11, "randomized-pca"]], "Reading material": [[27, "reading-material"]], "Reading recommendations:": [[28, "reading-recommendations"]], "Reading suggestions week 34": [[27, "reading-suggestions-week-34"]], "Readings and Videos:": [[30, "readings-and-videos"]], "Recurrent neural networks": [[12, "recurrent-neural-networks"]], "Recurrent neural networks: Overarching view": [[4, null]], "Reducing the number of degrees of freedom, overarching view": [[0, 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\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/statistics.html b/doc/LectureNotes/_build/html/statistics.html
index ab3c1a8a3..cd2f12154 100644
--- a/doc/LectureNotes/_build/html/statistics.html
+++ b/doc/LectureNotes/_build/html/statistics.html
@@ -28,7 +28,7 @@
 
 
 
-    
+    
     
     
     
diff --git a/doc/LectureNotes/_build/html/teachers.html b/doc/LectureNotes/_build/html/teachers.html
index 000257eb8..1091bcdd8 100644
--- a/doc/LectureNotes/_build/html/teachers.html
+++ b/doc/LectureNotes/_build/html/teachers.html
@@ -28,7 +28,7 @@
 
 
 
-    
+    
     
     
     
diff --git a/doc/LectureNotes/_build/html/textbooks.html b/doc/LectureNotes/_build/html/textbooks.html
index 8b5aad202..922abafd1 100644
--- a/doc/LectureNotes/_build/html/textbooks.html
+++ b/doc/LectureNotes/_build/html/textbooks.html
@@ -28,7 +28,7 @@
 
 
 
-    
+    
     
     
     
diff --git a/doc/LectureNotes/_build/html/week34.html b/doc/LectureNotes/_build/html/week34.html
index 641d906b8..ddf4a94dd 100644
--- a/doc/LectureNotes/_build/html/week34.html
+++ b/doc/LectureNotes/_build/html/week34.html
@@ -28,7 +28,7 @@
 
 
 
-    
+    
     
     
     
diff --git a/doc/LectureNotes/_build/html/week35.html b/doc/LectureNotes/_build/html/week35.html
index 61ea30c34..3045d5fe5 100644
--- a/doc/LectureNotes/_build/html/week35.html
+++ b/doc/LectureNotes/_build/html/week35.html
@@ -28,7 +28,7 @@
 
 
 
-    
+    
     
     
     
@@ -893,7 +893,7 @@ We assume our data can represented by a fourth-order polynomial. For the 
 
# matrix inversion to find theta
 # First we set up the data
-import numpy as np
+import numpy as np
 x = np.random.rand(100)
 y = 2.0+5*x*x+0.1*np.random.randn(100)
 # and then the design matrix X including the intercept
@@ -927,7 +927,7 @@ We assume our data can represented by a fourth-order polynomial. For the Scikit-Learn here we can define our own \(R2\) function as

 

 

-
def R2(y_data, y_model):
+
def R2(y_data, y_model):
     return 1 - np.sum((y_data - y_model) ** 2) / np.sum((y_data - np.mean(y_data)) ** 2)
 

 

@@ -944,7 +944,7 @@ Since we are not using Scikit-Learn here we can define our own
 
We can easily add our MSE score as

 

 

-
def MSE(y_data,y_model):
+
def MSE(y_data,y_model):
     n = np.size(y_model)
     return np.sum((y_data-y_model)**2)/n
 
@@ -956,7 +956,7 @@ Since we are not using Scikit-Learn here we can define our own
 
and finally the relative error as

 

 

-
def RelativeError(y_data,y_model):
+
def RelativeError(y_data,y_model):
     return abs((y_data-y_model)/y_data)
 print(RelativeError(y, ytilde))
 

@@ -983,16 +983,16 @@ but now splitting the data into a training set and a test set.

 

 
%matplotlib inline
 
-import os
-import numpy as np
-import pandas as pd
-import matplotlib.pyplot as plt
-from sklearn.model_selection import train_test_split
+import os
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+from sklearn.model_selection import train_test_split
 
 
-def R2(y_data, y_model):
+def R2(y_data, y_model):
     return 1 - np.sum((y_data - y_model) ** 2) / np.sum((y_data - np.mean(y_data)) ** 2)
-def MSE(y_data,y_model):
+def MSE(y_data,y_model):
     n = np.size(y_model)
     return np.sum((y_data-y_model)**2)/n
 
@@ -1033,7 +1033,7 @@ but now splitting the data into a training set and a test set.

 

 

 
# equivalently in numpy
-def train_test_split_numpy(inputs, labels, train_size, test_size):
+def train_test_split_numpy(inputs, labels, train_size, test_size):
     n_inputs = len(inputs)
     inputs_shuffled = inputs.copy()
     labels_shuffled = labels.copy()
@@ -1138,13 +1138,13 @@ simple test design matrix with random numbers. Each column could then
 represent a specific feature whose mean value is subracted.

 

 

-
import sklearn.linear_model as skl
-from sklearn.metrics import mean_squared_error
-from sklearn.model_selection import  train_test_split
-from sklearn.preprocessing import MinMaxScaler, StandardScaler, Normalizer
-import numpy as np
-import pandas as pd
-from IPython.display import display
+
import sklearn.linear_model as skl
+from sklearn.metrics import mean_squared_error
+from sklearn.model_selection import  train_test_split
+from sklearn.preprocessing import MinMaxScaler, StandardScaler, Normalizer
+import numpy as np
+import pandas as pd
+from IPython.display import display
 np.random.seed(100)
 # setting up a 10 x 5 matrix
 rows = 10
@@ -1200,12 +1200,12 @@ the aims is to reproduce Figure 2.11 of \(X\) defined by a fourth-order polynomial.  Scale your data and split it in training and test data.

 

 

-
import matplotlib.pyplot as plt
-import numpy as np
-from sklearn.linear_model import LinearRegression
-from sklearn.preprocessing import PolynomialFeatures
-from sklearn.model_selection import train_test_split
-from sklearn.pipeline import make_pipeline
+
import matplotlib.pyplot as plt
+import numpy as np
+from sklearn.linear_model import LinearRegression
+from sklearn.preprocessing import PolynomialFeatures
+from sklearn.model_selection import train_test_split
+from sklearn.pipeline import make_pipeline
 
 
 np.random.seed(2018)
@@ -1485,13 +1485,13 @@ discussion of Ridge regression.

 
The code here is a simple demonstration of how to implement Ridge regression with our own code and compare this with scikit-learn.

 

 

-
import numpy as np
-import pandas as pd
-import matplotlib.pyplot as plt
-from sklearn.model_selection import train_test_split
-from sklearn import linear_model
+
import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+from sklearn.model_selection import train_test_split
+from sklearn import linear_model
 
-def MSE(y_data,y_model):
+def MSE(y_data,y_model):
     n = np.size(y_model)
     return np.sum((y_data-y_model)**2)/n
 
@@ -1649,9 +1649,9 @@ In general the economy-size SVD leads to less FLOPS and still conserving the des
 
Codes for the SVD#

 

 

-
import numpy as np
+
import numpy as np
 # SVD inversion
-def SVD(A):
+def SVD(A):
     ''' Takes as input a numpy matrix A and returns inv(A) based on singular value decomposition (SVD).
     SVD is numerically more stable than the inversion algorithms provided by
     numpy and scipy.linalg at the cost of being slower.
@@ -2024,7 +2024,7 @@ covariance matrix through the np.linalg.eig() function.

 

 

 
# Importing various packages
-import numpy as np
+import numpy as np
 n = 100
 x = np.random.normal(size=n)
 print(np.mean(x))
@@ -2047,7 +2047,7 @@ code which sets up the correlations matrix for the previous example in
 a more brute force way. Here we scale the mean values for each column of the design matrix, calculate the relevant mean values and variances and then finally set up the \(2\times 2\) correlation matrix (since we have only two vectors).

 

 

-
import numpy as np
+
import numpy as np
 n = 100
 # define two vectors                                                                                           
 x = np.random.random(size=n)
@@ -2082,8 +2082,8 @@ this matrix we easily see that it is a positive definite matrix.

 
We whow here how we can set up the correlation matrix using pandas, as done in this simple code

 

 

-
import numpy as np
-import pandas as pd
+
import numpy as np
+import pandas as pd
 n = 10
 x = np.random.normal(size=n)
 x = x - np.mean(x)
@@ -2521,20 +2521,20 @@ and \(\tilde{X}_{ij} = X_{ij} - \frac
 Note also that we do not split the data into training and test.

 

 

-
import numpy as np
-import matplotlib.pyplot as plt
+
import numpy as np
+import matplotlib.pyplot as plt
 
-from sklearn.linear_model import LinearRegression
+from sklearn.linear_model import LinearRegression
 
 
 np.random.seed(2021)
 
-def MSE(y_data,y_model):
+def MSE(y_data,y_model):
     n = np.size(y_model)
     return np.sum((y_data-y_model)**2)/n
 
 
-def fit_beta(X, y):
+def fit_beta(X, y):
     return np.linalg.pinv(X.T @ X) @ X.T @ y
 
 
@@ -2664,13 +2664,13 @@ intercept.

 
Armed with this wisdom, we attempt first to simply set the intercept equal to False in our implementation of Ridge regression for our well-known  vanilla data set.

 

 

-
import numpy as np
-import pandas as pd
-import matplotlib.pyplot as plt
-from sklearn.model_selection import train_test_split
-from sklearn import linear_model
+
import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+from sklearn.model_selection import train_test_split
+from sklearn import linear_model
 
-def MSE(y_data,y_model):
+def MSE(y_data,y_model):
     n = np.size(y_model)
     return np.sum((y_data-y_model)**2)/n
 
@@ -2739,14 +2739,14 @@ What happens if we do not include the intercept in our fit?
 Let us see how we can change this code by zero centering.

 

 

-
import numpy as np
-import pandas as pd
-import matplotlib.pyplot as plt
-from sklearn.model_selection import train_test_split
-from sklearn import linear_model
-from sklearn.preprocessing import StandardScaler
+
import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+from sklearn.model_selection import train_test_split
+from sklearn import linear_model
+from sklearn.preprocessing import StandardScaler
 
-def MSE(y_data,y_model):
+def MSE(y_data,y_model):
     n = np.size(y_model)
     return np.sum((y_data-y_model)**2)/n
 # A seed just to ensure that the random numbers are the same for every run.
diff --git a/doc/LectureNotes/_build/html/week36.html b/doc/LectureNotes/_build/html/week36.html
index 63f2674f5..3294e83c4 100644
--- a/doc/LectureNotes/_build/html/week36.html
+++ b/doc/LectureNotes/_build/html/week36.html
@@ -28,7 +28,7 @@
 
 
 
-    
+    
     
     
     
diff --git a/doc/LectureNotes/_build/html/week37.html b/doc/LectureNotes/_build/html/week37.html
index 3379e57d3..3fbcb0ab1 100644
--- a/doc/LectureNotes/_build/html/week37.html
+++ b/doc/LectureNotes/_build/html/week37.html
@@ -28,7 +28,7 @@
 
 
 
-    
+    
     
     
     
@@ -487,9 +487,10 @@ doconce format html week37.do.txt --no_mako -->
 
  • Improving gradient descent with momentum
    • 
 
  • Introducing stochastic gradient descent
    • 
 
  • More advanced updates of the learning rate: ADAgrad, RMSprop and ADAM
    • 
+
  • Video of Lecture
    • 
+
  • Whiteboard notes
    • 
 
-
-
+
 
    
 
    Readings and Videos:#
    
 
      
diff --git a/doc/LectureNotes/_build/jupyter_execute/week37.ipynb b/doc/LectureNotes/_build/jupyter_execute/week37.ipynb
index 6bd1dea13..b072ac35a 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week37.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week37.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "53d0b4e7",
+   "id": "d842e7e1",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0c919844",
+   "id": "0cd52479",
    "metadata": {
     "editable": true
    },
@@ -29,7 +29,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a5769b3d",
+   "id": "699b6141",
    "metadata": {
     "editable": true
    },
@@ -46,13 +46,15 @@
     "3. Introducing stochastic gradient descent\n",
     "\n",
     "4. More advanced updates of the learning rate: ADAgrad, RMSprop and ADAM\n",
-    "\n",
-    ""
+    "\n",
+    "5. [Video of Lecture](https://youtu.be/SuxK68tj-V8)\n",
+    "\n",
+    "6. [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek37.pdf)"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "21f2937f",
+   "id": "dd264b1c",
    "metadata": {
     "editable": true
    },
@@ -69,7 +71,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da32a24e",
+   "id": "608927bc",
    "metadata": {
     "editable": true
    },
@@ -79,7 +81,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b7f8433",
+   "id": "60640670",
    "metadata": {
     "editable": true
    },
@@ -103,7 +105,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "2a8c5baa",
+   "id": "947b67ee",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -117,7 +119,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47d8423d",
+   "id": "0a787eca",
    "metadata": {
     "editable": true
    },
@@ -128,7 +130,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08d37b91",
+   "id": "d7e84ac7",
    "metadata": {
     "editable": true
    },
@@ -140,7 +142,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3c412ef",
+   "id": "f34c217e",
    "metadata": {
     "editable": true
    },
@@ -150,7 +152,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f1b2071",
+   "id": "b145d4eb",
    "metadata": {
     "editable": true
    },
@@ -162,7 +164,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "07536cbd",
+   "id": "2df6d60d",
    "metadata": {
     "editable": true
    },
@@ -176,7 +178,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "34287135",
+   "id": "1deafba0",
    "metadata": {
     "editable": true
    },
@@ -192,7 +194,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c1063bfb",
+   "id": "520ac423",
    "metadata": {
     "editable": true
    },
@@ -202,7 +204,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d327d2e3",
+   "id": "48e7232b",
    "metadata": {
     "editable": true
    },
@@ -214,7 +216,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2c9a9cd",
+   "id": "0194af20",
    "metadata": {
     "editable": true
    },
@@ -224,7 +226,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "062a7534",
+   "id": "9f58d823",
    "metadata": {
     "editable": true
    },
@@ -236,7 +238,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b1b15536",
+   "id": "10129d02",
    "metadata": {
     "editable": true
    },
@@ -250,7 +252,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a259e250",
+   "id": "4cd07523",
    "metadata": {
     "editable": true
    },
@@ -260,7 +262,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "002197c1",
+   "id": "1bda7e01",
    "metadata": {
     "editable": true
    },
@@ -271,7 +273,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "55e8dca9",
+   "id": "aa64bdd1",
    "metadata": {
     "editable": true
    },
@@ -286,7 +288,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a97ffaec",
+   "id": "3e7f4c5d",
    "metadata": {
     "editable": true
    },
@@ -296,7 +298,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b59a4220",
+   "id": "79ed73a8",
    "metadata": {
     "editable": true
    },
@@ -308,7 +310,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ba5dcc08",
+   "id": "1b70ad9b",
    "metadata": {
     "editable": true
    },
@@ -320,7 +322,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d8907fed",
+   "id": "2fbef92d",
    "metadata": {
     "editable": true
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@@ -335,7 +337,7 @@
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@@ -348,7 +350,7 @@
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@@ -407,7 +409,7 @@
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@@ -419,7 +421,7 @@
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@@ -431,7 +433,7 @@
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@@ -441,7 +443,7 @@
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@@ -455,7 +457,7 @@
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@@ -465,7 +467,7 @@
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@@ -477,7 +479,7 @@
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@@ -488,7 +490,7 @@
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@@ -503,7 +505,7 @@
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@@ -517,7 +519,7 @@
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@@ -528,7 +530,7 @@
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@@ -589,7 +591,7 @@
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@@ -611,7 +613,7 @@
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@@ -626,7 +628,7 @@
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@@ -637,7 +639,7 @@
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@@ -703,7 +705,7 @@
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@@ -714,7 +716,7 @@
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@@ -788,7 +790,7 @@
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@@ -807,7 +809,7 @@
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@@ -828,7 +830,7 @@
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@@ -844,7 +846,7 @@
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@@ -858,7 +860,7 @@
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@@ -886,7 +888,7 @@
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@@ -918,7 +920,7 @@
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@@ -935,7 +937,7 @@
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@@ -948,7 +950,7 @@
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@@ -961,7 +963,7 @@
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@@ -974,7 +976,7 @@
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@@ -988,7 +990,7 @@
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@@ -1010,7 +1012,7 @@
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@@ -1025,7 +1027,7 @@
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@@ -1037,7 +1039,7 @@
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@@ -1050,7 +1052,7 @@
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@@ -1064,7 +1066,7 @@
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@@ -1075,7 +1077,7 @@
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@@ -1100,7 +1102,7 @@
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@@ -1116,7 +1118,7 @@
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@@ -1137,7 +1139,7 @@
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@@ -1157,7 +1159,7 @@
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@@ -1176,7 +1178,7 @@
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@@ -1211,7 +1213,7 @@
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@@ -1224,7 +1226,7 @@
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@@ -1301,7 +1303,7 @@
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@@ -1316,7 +1318,7 @@
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@@ -1326,7 +1328,7 @@
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@@ -1338,7 +1340,7 @@
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@@ -1350,7 +1352,7 @@
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@@ -1364,7 +1366,7 @@
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@@ -1376,7 +1378,7 @@
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@@ -1386,7 +1388,7 @@
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@@ -1398,7 +1400,7 @@
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@@ -1418,7 +1420,7 @@
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@@ -1431,7 +1433,7 @@
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@@ -1443,7 +1445,7 @@
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@@ -1460,7 +1462,7 @@
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@@ -1472,7 +1474,7 @@
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@@ -1501,7 +1503,7 @@
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@@ -1534,7 +1536,7 @@
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@@ -1592,7 +1594,7 @@
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@@ -1617,7 +1619,7 @@
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@@ -1643,7 +1645,7 @@
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@@ -1686,7 +1688,7 @@
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@@ -1717,7 +1719,7 @@
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@@ -1739,7 +1741,7 @@
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@@ -1759,7 +1761,7 @@
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@@ -1775,7 +1777,7 @@
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@@ -1795,7 +1797,7 @@
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@@ -1807,7 +1809,7 @@
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@@ -1819,7 +1821,7 @@
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@@ -1831,7 +1833,7 @@
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@@ -1843,7 +1845,7 @@
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@@ -1854,7 +1856,7 @@
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@@ -1866,7 +1868,7 @@
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@@ -1876,7 +1878,7 @@
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@@ -1888,7 +1890,7 @@
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@@ -1898,7 +1900,7 @@
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@@ -1919,7 +1921,7 @@
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@@ -1932,7 +1934,7 @@
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@@ -1944,7 +1946,7 @@
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@@ -1961,7 +1963,7 @@
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@@ -1977,7 +1979,7 @@
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@@ -1999,7 +2001,7 @@
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@@ -2017,7 +2019,7 @@
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@@ -2037,7 +2039,7 @@
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@@ -2051,7 +2053,7 @@
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@@ -2063,7 +2065,7 @@
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@@ -2075,7 +2077,7 @@
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@@ -2087,7 +2089,7 @@
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@@ -2099,7 +2101,7 @@
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@@ -2110,7 +2112,7 @@
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@@ -2122,7 +2124,7 @@
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@@ -2136,7 +2138,7 @@
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@@ -2147,7 +2149,7 @@
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@@ -2159,7 +2161,7 @@
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@@ -2181,7 +2183,7 @@
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@@ -2205,7 +2207,7 @@
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@@ -2221,7 +2223,7 @@
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@@ -2237,7 +2239,7 @@
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@@ -2251,7 +2253,7 @@
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@@ -2269,7 +2271,7 @@
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+   "id": "78a1a601",
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     "editable": true
    },
@@ -2290,7 +2292,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "8aab54bd",
+   "id": "c721352d",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2350,7 +2352,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "26c6e4f1",
+   "id": "e36cec47",
    "metadata": {
     "editable": true
    },
@@ -2361,7 +2363,7 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "226c13ec",
+   "id": "fc5df7eb",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2425,7 +2427,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6895dbfe",
+   "id": "0b27af70",
    "metadata": {
     "editable": true
    },
@@ -2440,7 +2442,7 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "f8d01982",
+   "id": "adef9763",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2524,7 +2526,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cffe8367",
+   "id": "310fe5b2",
    "metadata": {
     "editable": true
    },
@@ -2535,7 +2537,7 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "b57871a9",
+   "id": "bcf65acf",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2613,7 +2615,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37b273c1",
+   "id": "f5e2c550",
    "metadata": {
     "editable": true
    },
@@ -2626,7 +2628,7 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "9ff0eb69",
+   "id": "300a02a4",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2670,7 +2672,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e7d143b6",
+   "id": "5cb5fd26",
    "metadata": {
     "editable": true
    },
@@ -2681,7 +2683,7 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "id": "9b5e2d1d",
+   "id": "030efc5d",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2740,7 +2742,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8b6fb13f",
+   "id": "66850bb7",
    "metadata": {
     "editable": true
    },
@@ -2750,7 +2752,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "06c3f4bb",
+   "id": "e1608bcf",
    "metadata": {
     "editable": true
    },
@@ -2761,7 +2763,7 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "4abf9ccd",
+   "id": "0ba7d8f7",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2826,7 +2828,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "18d42e29",
+   "id": "0503f74b",
    "metadata": {
     "editable": true
    },
@@ -2837,7 +2839,7 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "03415114",
+   "id": "c2a2732a",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2907,7 +2909,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "41120d8f",
+   "id": "b8475863",
    "metadata": {
     "editable": true
    },
@@ -2924,7 +2926,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "16eb2a88",
+   "id": "4d4d0717",
    "metadata": {
     "editable": true
    },
@@ -2952,7 +2954,7 @@
   {
    "cell_type": "code",
    "execution_count": 17,
-   "id": "a6df3a5c",
+   "id": "46375144",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2972,7 +2974,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fc15d89b",
+   "id": "39426ccf",
    "metadata": {
     "editable": true
    },
@@ -2988,7 +2990,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4e4b5ee0",
+   "id": "df7fe27f",
    "metadata": {
     "editable": true
    },
@@ -3008,7 +3010,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4455b9a0",
+   "id": "8fd48e39",
    "metadata": {
     "editable": true
    },
@@ -3035,7 +3037,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9592eb20",
+   "id": "d6c60a0a",
    "metadata": {
     "editable": true
    },
@@ -3048,7 +3050,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e3022ea8",
+   "id": "1bb6eaa0",
    "metadata": {
     "editable": true
    },
@@ -3060,7 +3062,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "246a28bf",
+   "id": "25135896",
    "metadata": {
     "editable": true
    },
@@ -3075,7 +3077,7 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "id": "d132a060",
+   "id": "469ca11e",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3102,7 +3104,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9e70a01f",
+   "id": "33722029",
    "metadata": {
     "editable": true
    },
@@ -3116,7 +3118,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2c0ad6b4",
+   "id": "fe27291e",
    "metadata": {
     "editable": true
    },
@@ -3128,7 +3130,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3c6081b8",
+   "id": "ead1167d",
    "metadata": {
     "editable": true
    },
@@ -3145,7 +3147,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "845af933",
+   "id": "b2efb706",
    "metadata": {
     "editable": true
    },
@@ -3157,7 +3159,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "564afbbd",
+   "id": "65333100",
    "metadata": {
     "editable": true
    },
@@ -3167,7 +3169,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c4088263",
+   "id": "1fde497c",
    "metadata": {
     "editable": true
    },
@@ -3179,7 +3181,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "96983e3d",
+   "id": "264ce562",
    "metadata": {
     "editable": true
    },
@@ -3189,7 +3191,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "91d029d7",
+   "id": "0f63a6f8",
    "metadata": {
     "editable": true
    },
@@ -3201,7 +3203,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20d351f6",
+   "id": "2ba0a6e4",
    "metadata": {
     "editable": true
    },
@@ -3212,7 +3214,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a8e79fd",
+   "id": "3b377f93",
    "metadata": {
     "editable": true
    },
@@ -3224,7 +3226,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4ec7ad68",
+   "id": "f05e9d08",
    "metadata": {
     "editable": true
    },
@@ -3234,7 +3236,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "df09c13b",
+   "id": "84784b8e",
    "metadata": {
     "editable": true
    },
@@ -3246,7 +3248,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bb2a9c1f",
+   "id": "b62c6e5a",
    "metadata": {
     "editable": true
    },
@@ -3256,7 +3258,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b3507e2d",
+   "id": "ecce9763",
    "metadata": {
     "editable": true
    },
@@ -3268,7 +3270,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2010542f",
+   "id": "c9e1842a",
    "metadata": {
     "editable": true
    },
@@ -3278,7 +3280,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e03a1590",
+   "id": "be12163e",
    "metadata": {
     "editable": true
    },
@@ -3290,7 +3292,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71872755",
+   "id": "a097e9ab",
    "metadata": {
     "editable": true
    },
@@ -3300,7 +3302,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "167238dc",
+   "id": "239422b0",
    "metadata": {
     "editable": true
    },
@@ -3312,7 +3314,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38d0cc0f",
+   "id": "ed9778bb",
    "metadata": {
     "editable": true
    },
@@ -3322,7 +3324,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e9e1beb9",
+   "id": "7179b77b",
    "metadata": {
     "editable": true
    },
@@ -3334,7 +3336,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a8576e4",
+   "id": "aad2f56e",
    "metadata": {
     "editable": true
    },
@@ -3344,7 +3346,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "937d703f",
+   "id": "26aa9739",
    "metadata": {
     "editable": true
    },
@@ -3356,7 +3358,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e4723b95",
+   "id": "d270cb13",
    "metadata": {
     "editable": true
    },
@@ -3366,7 +3368,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6df6f6d8",
+   "id": "5a52457b",
    "metadata": {
     "editable": true
    },
@@ -3378,7 +3380,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39bdaf00",
+   "id": "8c98105d",
    "metadata": {
     "editable": true
    },
@@ -3390,7 +3392,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e4584236",
+   "id": "4d82302f",
    "metadata": {
     "editable": true
    },
@@ -3402,7 +3404,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d0c5d728",
+   "id": "a3a07a10",
    "metadata": {
     "editable": true
    },
@@ -3412,7 +3414,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b637fd2",
+   "id": "ea19374e",
    "metadata": {
     "editable": true
    },
@@ -3424,7 +3426,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9627e6fb",
+   "id": "11dd1361",
    "metadata": {
     "editable": true
    },
@@ -3437,7 +3439,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "662fe97e",
+   "id": "f6a52f34",
    "metadata": {
     "editable": true
    },
@@ -3449,7 +3451,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fa2d5cb5",
+   "id": "9d6807dc",
    "metadata": {
     "editable": true
    },
@@ -3463,7 +3465,7 @@
   {
    "cell_type": "code",
    "execution_count": 19,
-   "id": "a530b3ba",
+   "id": "2ed0cafc",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3560,7 +3562,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58cc6d9d",
+   "id": "f72dbb49",
    "metadata": {
     "editable": true
    },
@@ -3581,7 +3583,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a2d3f87",
+   "id": "b7759b1f",
    "metadata": {
     "editable": true
    },
@@ -3593,7 +3595,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9eab78a9",
+   "id": "ba0ecd6e",
    "metadata": {
     "editable": true
    },
@@ -3603,7 +3605,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50d7f5c3",
+   "id": "ae897f1e",
    "metadata": {
     "editable": true
    },
@@ -3615,7 +3617,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4c96e589",
+   "id": "f9c41f7f",
    "metadata": {
     "editable": true
    },
@@ -3625,7 +3627,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b57830ea",
+   "id": "fa013cc4",
    "metadata": {
     "editable": true
    },
@@ -3637,7 +3639,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "05325bc6",
+   "id": "0c9b24be",
    "metadata": {
     "editable": true
    },
@@ -3655,7 +3657,7 @@
   {
    "cell_type": "code",
    "execution_count": 20,
-   "id": "d95b15bc",
+   "id": "4f9b1fa0",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3731,7 +3733,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b88ebede",
+   "id": "1aa5ca37",
    "metadata": {
     "editable": true
    },
@@ -3745,7 +3747,7 @@
   {
    "cell_type": "code",
    "execution_count": 21,
-   "id": "47036b16",
+   "id": "a731e32c",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3834,7 +3836,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52faee2f",
+   "id": "6ea197d8",
    "metadata": {
     "editable": true
    },
diff --git a/doc/LectureNotes/week37.ipynb b/doc/LectureNotes/week37.ipynb
index 8e275c56f..fe89adb05 100644
--- a/doc/LectureNotes/week37.ipynb
+++ b/doc/LectureNotes/week37.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "53d0b4e7",
+   "id": "d842e7e1",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0c919844",
+   "id": "0cd52479",
    "metadata": {
     "editable": true
    },
@@ -29,7 +29,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a5769b3d",
+   "id": "699b6141",
    "metadata": {
     "editable": true
    },
@@ -46,13 +46,15 @@
     "3. Introducing stochastic gradient descent\n",
     "\n",
     "4. More advanced updates of the learning rate: ADAgrad, RMSprop and ADAM\n",
-    "\n",
-    ""
+    "\n",
+    "5. [Video of Lecture](https://youtu.be/SuxK68tj-V8)\n",
+    "\n",
+    "6. [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek37.pdf)"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "21f2937f",
+   "id": "dd264b1c",
    "metadata": {
     "editable": true
    },
@@ -69,7 +71,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da32a24e",
+   "id": "608927bc",
    "metadata": {
     "editable": true
    },
@@ -79,7 +81,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b7f8433",
+   "id": "60640670",
    "metadata": {
     "editable": true
    },
@@ -103,7 +105,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "2a8c5baa",
+   "id": "947b67ee",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -117,7 +119,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47d8423d",
+   "id": "0a787eca",
    "metadata": {
     "editable": true
    },
@@ -128,7 +130,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08d37b91",
+   "id": "d7e84ac7",
    "metadata": {
     "editable": true
    },
@@ -140,7 +142,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3c412ef",
+   "id": "f34c217e",
    "metadata": {
     "editable": true
    },
@@ -150,7 +152,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f1b2071",
+   "id": "b145d4eb",
    "metadata": {
     "editable": true
    },
@@ -162,7 +164,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "07536cbd",
+   "id": "2df6d60d",
    "metadata": {
     "editable": true
    },
@@ -176,7 +178,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "34287135",
+   "id": "1deafba0",
    "metadata": {
     "editable": true
    },
@@ -192,7 +194,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c1063bfb",
+   "id": "520ac423",
    "metadata": {
     "editable": true
    },
@@ -202,7 +204,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d327d2e3",
+   "id": "48e7232b",
    "metadata": {
     "editable": true
    },
@@ -214,7 +216,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2c9a9cd",
+   "id": "0194af20",
    "metadata": {
     "editable": true
    },
@@ -224,7 +226,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "062a7534",
+   "id": "9f58d823",
    "metadata": {
     "editable": true
    },
@@ -236,7 +238,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b1b15536",
+   "id": "10129d02",
    "metadata": {
     "editable": true
    },
@@ -250,7 +252,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a259e250",
+   "id": "4cd07523",
    "metadata": {
     "editable": true
    },
@@ -260,7 +262,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "002197c1",
+   "id": "1bda7e01",
    "metadata": {
     "editable": true
    },
@@ -271,7 +273,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "55e8dca9",
+   "id": "aa64bdd1",
    "metadata": {
     "editable": true
    },
@@ -286,7 +288,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a97ffaec",
+   "id": "3e7f4c5d",
    "metadata": {
     "editable": true
    },
@@ -296,7 +298,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b59a4220",
+   "id": "79ed73a8",
    "metadata": {
     "editable": true
    },
@@ -308,7 +310,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ba5dcc08",
+   "id": "1b70ad9b",
    "metadata": {
     "editable": true
    },
@@ -320,7 +322,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d8907fed",
+   "id": "2fbef92d",
    "metadata": {
     "editable": true
    },
@@ -335,7 +337,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "728d5b78",
+   "id": "0728a369",
    "metadata": {
     "editable": true
    },
@@ -348,7 +350,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "02d7e401",
+   "id": "a48d43f0",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -407,7 +409,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4dd147c2",
+   "id": "6c1c6ed1",
    "metadata": {
     "editable": true
    },
@@ -419,7 +421,7 @@
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@@ -431,7 +433,7 @@
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@@ -441,7 +443,7 @@
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@@ -477,7 +479,7 @@
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@@ -528,7 +530,7 @@
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@@ -589,7 +591,7 @@
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@@ -611,7 +613,7 @@
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@@ -626,7 +628,7 @@
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@@ -637,7 +639,7 @@
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@@ -703,7 +705,7 @@
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@@ -714,7 +716,7 @@
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@@ -788,7 +790,7 @@
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@@ -828,7 +830,7 @@
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@@ -844,7 +846,7 @@
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@@ -858,7 +860,7 @@
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@@ -886,7 +888,7 @@
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@@ -918,7 +920,7 @@
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@@ -935,7 +937,7 @@
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@@ -948,7 +950,7 @@
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@@ -961,7 +963,7 @@
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@@ -974,7 +976,7 @@
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@@ -988,7 +990,7 @@
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@@ -1010,7 +1012,7 @@
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@@ -1025,7 +1027,7 @@
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@@ -1037,7 +1039,7 @@
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@@ -1050,7 +1052,7 @@
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@@ -1064,7 +1066,7 @@
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@@ -1075,7 +1077,7 @@
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@@ -1100,7 +1102,7 @@
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@@ -1116,7 +1118,7 @@
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@@ -1137,7 +1139,7 @@
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@@ -1157,7 +1159,7 @@
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@@ -1176,7 +1178,7 @@
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@@ -1211,7 +1213,7 @@
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@@ -1224,7 +1226,7 @@
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@@ -1301,7 +1303,7 @@
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@@ -1316,7 +1318,7 @@
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@@ -1326,7 +1328,7 @@
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@@ -1338,7 +1340,7 @@
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@@ -1350,7 +1352,7 @@
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@@ -1364,7 +1366,7 @@
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@@ -1376,7 +1378,7 @@
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@@ -1386,7 +1388,7 @@
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@@ -1398,7 +1400,7 @@
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@@ -1418,7 +1420,7 @@
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@@ -1431,7 +1433,7 @@
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@@ -1443,7 +1445,7 @@
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@@ -1460,7 +1462,7 @@
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@@ -1472,7 +1474,7 @@
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@@ -1501,7 +1503,7 @@
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@@ -1534,7 +1536,7 @@
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@@ -1592,7 +1594,7 @@
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@@ -1617,7 +1619,7 @@
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@@ -1643,7 +1645,7 @@
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@@ -1686,7 +1688,7 @@
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@@ -1717,7 +1719,7 @@
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@@ -1739,7 +1741,7 @@
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@@ -1759,7 +1761,7 @@
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@@ -1775,7 +1777,7 @@
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@@ -1795,7 +1797,7 @@
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@@ -1807,7 +1809,7 @@
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@@ -1819,7 +1821,7 @@
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@@ -1831,7 +1833,7 @@
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@@ -1843,7 +1845,7 @@
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@@ -1854,7 +1856,7 @@
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@@ -1866,7 +1868,7 @@
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@@ -1876,7 +1878,7 @@
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@@ -1888,7 +1890,7 @@
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@@ -1898,7 +1900,7 @@
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@@ -1919,7 +1921,7 @@
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@@ -1932,7 +1934,7 @@
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@@ -1944,7 +1946,7 @@
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@@ -1961,7 +1963,7 @@
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@@ -1977,7 +1979,7 @@
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@@ -1999,7 +2001,7 @@
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@@ -2017,7 +2019,7 @@
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@@ -2037,7 +2039,7 @@
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@@ -2051,7 +2053,7 @@
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@@ -2063,7 +2065,7 @@
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@@ -2075,7 +2077,7 @@
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@@ -2087,7 +2089,7 @@
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@@ -2099,7 +2101,7 @@
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@@ -2110,7 +2112,7 @@
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@@ -2122,7 +2124,7 @@
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@@ -2136,7 +2138,7 @@
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@@ -2147,7 +2149,7 @@
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@@ -2159,7 +2161,7 @@
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@@ -2181,7 +2183,7 @@
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@@ -2205,7 +2207,7 @@
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@@ -2221,7 +2223,7 @@
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@@ -2237,7 +2239,7 @@
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@@ -2251,7 +2253,7 @@
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@@ -2269,7 +2271,7 @@
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@@ -2290,7 +2292,7 @@
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@@ -2350,7 +2352,7 @@
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@@ -2361,7 +2363,7 @@
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@@ -2613,7 +2615,7 @@
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@@ -2907,7 +2909,7 @@
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@@ -2952,7 +2954,7 @@
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@@ -2972,7 +2974,7 @@
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@@ -2988,7 +2990,7 @@
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@@ -3008,7 +3010,7 @@
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@@ -3035,7 +3037,7 @@
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@@ -3048,7 +3050,7 @@
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@@ -3060,7 +3062,7 @@
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@@ -3075,7 +3077,7 @@
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@@ -3102,7 +3104,7 @@
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@@ -3116,7 +3118,7 @@
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@@ -3128,7 +3130,7 @@
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@@ -3145,7 +3147,7 @@
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@@ -3157,7 +3159,7 @@
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@@ -3167,7 +3169,7 @@
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@@ -3179,7 +3181,7 @@
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@@ -3189,7 +3191,7 @@
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@@ -3201,7 +3203,7 @@
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@@ -3212,7 +3214,7 @@
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@@ -3224,7 +3226,7 @@
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@@ -3234,7 +3236,7 @@
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@@ -3246,7 +3248,7 @@
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   {
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@@ -3256,7 +3258,7 @@
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   {
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@@ -3268,7 +3270,7 @@
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   {
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@@ -3278,7 +3280,7 @@
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   {
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@@ -3290,7 +3292,7 @@
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@@ -3300,7 +3302,7 @@
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@@ -3312,7 +3314,7 @@
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@@ -3322,7 +3324,7 @@
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@@ -3334,7 +3336,7 @@
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@@ -3344,7 +3346,7 @@
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@@ -3356,7 +3358,7 @@
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@@ -3366,7 +3368,7 @@
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@@ -3378,7 +3380,7 @@
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@@ -3390,7 +3392,7 @@
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@@ -3402,7 +3404,7 @@
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@@ -3437,7 +3439,7 @@
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@@ -3449,7 +3451,7 @@
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@@ -3463,7 +3465,7 @@
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@@ -3560,7 +3562,7 @@
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@@ -3581,7 +3583,7 @@
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@@ -3593,7 +3595,7 @@
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@@ -3603,7 +3605,7 @@
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@@ -3615,7 +3617,7 @@
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@@ -3625,7 +3627,7 @@
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@@ -3637,7 +3639,7 @@
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@@ -3655,7 +3657,7 @@
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-   "id": "d95b15bc",
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@@ -3731,7 +3733,7 @@
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@@ -3745,7 +3747,7 @@
   {
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-   "id": "47036b16",
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@@ -3834,7 +3836,7 @@
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diff --git a/doc/pub/week37/html/._week37-bs001.html b/doc/pub/week37/html/._week37-bs001.html
index d3d5205cb..fec983a52 100644
--- a/doc/pub/week37/html/._week37-bs001.html
+++ b/doc/pub/week37/html/._week37-bs001.html
@@ -384,13 +384,14 @@ MathJax.Hub.Config({
 
    1.  Plain gradient descent (constant learning rate), reminder from last week with examples using OLS and Ridge
      2. 
 
    2.  Improving gradient descent with momentum
      3. 
 
    3.  Introducing stochastic gradient descent
      4. 
-
    4.  More advanced updates of the learning rate: ADAgrad, RMSprop and ADAM
-
-
      5. 
+
    5.  More advanced updates of the learning rate: ADAgrad, RMSprop and ADAM
      6. 
+
    6.  Video of Lecture
      7. 
+
    7.  Whiteboard notes
      8. 
 
    
 
    
 
    
 
+
 
    
 
 
      
diff --git a/doc/pub/week37/html/week37-reveal.html b/doc/pub/week37/html/week37-reveal.html
index 239b77715..e4cf90870 100644
--- a/doc/pub/week37/html/week37-reveal.html
+++ b/doc/pub/week37/html/week37-reveal.html
@@ -204,9 +204,9 @@ MathJax.Hub.Config({
 
    •  Plain gradient descent (constant learning rate), reminder from last week with examples using OLS and Ridge
      • 
 
    •  Improving gradient descent with momentum
      • 
 
    •  Introducing stochastic gradient descent
      • 
-
    •  More advanced updates of the learning rate: ADAgrad, RMSprop and ADAM
-
-
      • 
+
    •  More advanced updates of the learning rate: ADAgrad, RMSprop and ADAM
      • 
+
    •  Video of Lecture
      • 
+
    •  Whiteboard notes
      • 
 
 
    
 
diff --git a/doc/pub/week37/html/week37-solarized.html b/doc/pub/week37/html/week37-solarized.html
index 1e222348d..093e60695 100644
--- a/doc/pub/week37/html/week37-solarized.html
+++ b/doc/pub/week37/html/week37-solarized.html
@@ -334,12 +334,13 @@ MathJax.Hub.Config({
 
  •  Plain gradient descent (constant learning rate), reminder from last week with examples using OLS and Ridge
    • 
 
  •  Improving gradient descent with momentum
    • 
 
  •  Introducing stochastic gradient descent
    • 
-
  •  More advanced updates of the learning rate: ADAgrad, RMSprop and ADAM
-
-
    • 
+
  •  More advanced updates of the learning rate: ADAgrad, RMSprop and ADAM
    • 
+
  •  Video of Lecture
    • 
+
  •  Whiteboard notes
    • 
 
 
    
 
+
 









    
 
    Readings and Videos: 
    
 
    
diff --git a/doc/pub/week37/html/week37.html b/doc/pub/week37/html/week37.html
index ab0cae504..4d7dbab99 100644
--- a/doc/pub/week37/html/week37.html
+++ b/doc/pub/week37/html/week37.html
@@ -411,12 +411,13 @@ MathJax.Hub.Config({
 
  •  Plain gradient descent (constant learning rate), reminder from last week with examples using OLS and Ridge
    • 
 
  •  Improving gradient descent with momentum
    • 
 
  •  Introducing stochastic gradient descent
    • 
-
  •  More advanced updates of the learning rate: ADAgrad, RMSprop and ADAM
-
-
    • 
+
  •  More advanced updates of the learning rate: ADAgrad, RMSprop and ADAM
    • 
+
  •  Video of Lecture
    • 
+
  •  Whiteboard notes
    • 
 
 
    
 
+
 









    
 
    Readings and Videos: 
    
 
    
diff --git a/doc/pub/week37/ipynb/ipynb-week37-src.tar.gz b/doc/pub/week37/ipynb/ipynb-week37-src.tar.gz
index 3b29921efd3bec48e44352780778e7e1ffbdd5a3..db3ca308bc9483db48fa6edc80207feba5daf942 100644
GIT binary patch
delta 38
tcmdncF1Mjwj!nLsgMsBmBU>vQV=Eg|D;skw8%rx2YbzVuRyOuk%>dJc3LF3c

delta 38
tcmdncF1Mjwj!nLsgCQrsk*$@Dv6YRfm5sTTjir^1wUv!+D;xW&W&qMM3JU-L

diff --git a/doc/pub/week37/ipynb/week37.ipynb b/doc/pub/week37/ipynb/week37.ipynb
index ff7fc79f0..fe89adb05 100644
--- a/doc/pub/week37/ipynb/week37.ipynb
+++ b/doc/pub/week37/ipynb/week37.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "53d0b4e7",
+   "id": "d842e7e1",
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@@ -14,7 +14,7 @@
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   {
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@@ -29,7 +29,7 @@
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+   "id": "699b6141",
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@@ -46,13 +46,15 @@
     "3. Introducing stochastic gradient descent\n",
     "\n",
     "4. More advanced updates of the learning rate: ADAgrad, RMSprop and ADAM\n",
-    "\n",
-    ""
+    "\n",
+    "5. [Video of Lecture](https://youtu.be/SuxK68tj-V8)\n",
+    "\n",
+    "6. [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek37.pdf)"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "21f2937f",
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@@ -69,7 +71,7 @@
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@@ -79,7 +81,7 @@
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@@ -103,13 +105,10 @@
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+    "editable": true
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@@ -120,7 +119,7 @@
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@@ -131,7 +130,7 @@
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@@ -143,7 +142,7 @@
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@@ -153,7 +152,7 @@
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@@ -165,7 +164,7 @@
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@@ -179,7 +178,7 @@
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    "metadata": {
     "editable": true
    },
@@ -195,7 +194,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c1063bfb",
+   "id": "520ac423",
    "metadata": {
     "editable": true
    },
@@ -205,7 +204,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d327d2e3",
+   "id": "48e7232b",
    "metadata": {
     "editable": true
    },
@@ -217,7 +216,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2c9a9cd",
+   "id": "0194af20",
    "metadata": {
     "editable": true
    },
@@ -227,7 +226,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "062a7534",
+   "id": "9f58d823",
    "metadata": {
     "editable": true
    },
@@ -239,7 +238,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b1b15536",
+   "id": "10129d02",
    "metadata": {
     "editable": true
    },
@@ -253,7 +252,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a259e250",
+   "id": "4cd07523",
    "metadata": {
     "editable": true
    },
@@ -263,7 +262,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "002197c1",
+   "id": "1bda7e01",
    "metadata": {
     "editable": true
    },
@@ -274,7 +273,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "55e8dca9",
+   "id": "aa64bdd1",
    "metadata": {
     "editable": true
    },
@@ -289,7 +288,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a97ffaec",
+   "id": "3e7f4c5d",
    "metadata": {
     "editable": true
    },
@@ -299,7 +298,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b59a4220",
+   "id": "79ed73a8",
    "metadata": {
     "editable": true
    },
@@ -311,7 +310,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ba5dcc08",
+   "id": "1b70ad9b",
    "metadata": {
     "editable": true
    },
@@ -323,7 +322,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d8907fed",
+   "id": "2fbef92d",
    "metadata": {
     "editable": true
    },
@@ -338,7 +337,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "728d5b78",
+   "id": "0728a369",
    "metadata": {
     "editable": true
    },
@@ -350,38 +349,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
-   "id": "02d7e401",
+   "execution_count": 2,
+   "id": "a48d43f0",
    "metadata": {
     "collapsed": false,
-    "editable": true,
-    "jupyter": {
-     "outputs_hidden": false
-    }
+    "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Eigenvalues of Hessian Matrix:[0.29918563 4.58469793]\n",
-      "[[4.04503963]\n",
-      " [2.96930082]]\n",
-      "[[-3.92478381e+176]\n",
-      " [-4.83829315e+176]]\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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Hjh3RoEEDJCYmWgV91f3lL39BXl4ebr75Zjz88MPo0KEDrly5giNHjmD9+vVYsmQJkpKSkJeXh6ysLDzzzDPmoRmysrLw+OOPY8iQIZg8eTIAJbhavnw5UlJS0LVrV3z++ed44YUX7AYmnoqPj8fQoUPxzDPPoH79+li8eDH279/vsLz+1VdfxZgxYzBq1ChMmzYNLVq0wM8//4zvvvsOe/bswapVq3zSXiK3BDiBm0iV9u3bJ9OnT5c2bdpIZGSkREVFSbt27eSee+6RTz75xGrbjIwMqV+/vs39fPvttzJixAhp2LChNG7cWG699VY5duyYAJBnn33Watu1a9dK165dJSIiQlq2bCnPPfecPPvssw6ryURELly4IH/+85+lQ4cOEhERITExMXLjjTfKo48+alUJBEBmzpxZq5229jlnzhxJTEyUkJCQWpVCtrzxxhvSvn17iYiIkBtuuEGWLl0qGRkZVtVkIkpJ/IsvvijdunWTqKgoadCggaSkpMiMGTPk4MGDIqJUgU2ePFlatWolkZGREhcXJ4MHD5a1a9da7evy5cvy//7f/zO/b1xcnAwdOlS2b99utd3SpUulX79+Ur9+fYmOjpa2bdvKPffcI7t37zZvM3jwYOncuXOt47J1DNnZ2ZKSkiLh4eE2z2VNp0+flocffljatGkj4eHhEhsbK7169ZKnn35aLly4IMePH5emTZvK0KFDraqsqqqqZMKECXLdddeZK/vOnTsn9957rzRt2lTq1asnAwcOlMLCQhk8eLAMHjzY/FpThVf1EngRyzAINasPTd+106dPm5eZvi+LFy+Wtm3bSnh4uKSkpMiKFSusXmurmkxE5IsvvpDbbrtNmjZtKuHh4dK8eXMZOnSoLFmypM7Pi8jfDCIigQrEiIhIvQwGA2bOnImXX3450E0h8ilWkxEREZGuMRgiIiIiXWMCNRER2cQsCtIL3hkiIiIiXWMwRERERLrGYIiIiIh0TRc5Q1VVVTh+/DgaNmxoc9oEIiIiUh8Rwfnz5x3OQ+gpXQRDx48fR3JycqCbQURERG4oLi722SjrgE6CIdMUAsXFxU5No0BERESBV15ejuTkZJtTAXmTLoIhU9dYo0aNGAwRERFpjK9TXJhATURERLrGYIiIiIh0jcEQERER6RqDISIiItI1BkNERESkawyGiIiISNcYDBEREZGuMRgiIiIiXWMwRERERLrGYIiIiIh0jcEQERER6RqDISIiItI1BkNERESkawyGiIiISNcYDBEREZGuMRgiIiIiXWMwRERERLoW8GBo69atmDBhAhITE2EwGPD+++/b3XbGjBkwGAxYuHCh39pHREREwS3gwdDFixfRrVs3vPzyy3Vu9/7772PXrl1ITEz0U8uIiIhID8IC3YAxY8ZgzJgxdW5TUlKCBx98EB9//DHGjRvnp5YRERGRHgT8zpAjVVVVmDp1Kp544gl07tw50M0hIiKiIBPwO0OOPP/88wgLC8PDDz/s9GsqKipQUVFhfl5eXu6LphEREVEQUPWdoc8//xyLFi3C8uXLYTAYnH5dVlYWYmJizI/k5GQftpKIiIi0TNXBUGFhIU6dOoWWLVsiLCwMYWFhOHr0KB577DG0bt3a7uvmzJmDsrIy86O4uNh/jSYiIiJNUXU32dSpUzF8+HCrZaNGjcLUqVMxffp0u6+LjIxEZGSkr5tHREREQSDgwdCFCxdw6NAh8/PDhw9j3759iI2NRcuWLREXF2e1fXh4OJo3b44OHTr4u6lEREQUhAIeDO3evRtpaWnm57NmzQIAZGRkYPny5QFqFREREelFwIOhIUOGQESc3v7IkSO+awwRERHpjqoTqImIiIh8jcEQERER6RqDISIiItI1BkNERESkawyGiIiISNcYDBEREZGuMRgiIiIiXWMwRERERLrGYIiIiIh0jcEQERER6RqDISIiItI1BkNERESkawyGiIiISNcYDBEREZGuMRgiIiIiXWMwRERERLrGYIiIiIh0jcEQERER6RqDISIiItI1BkNERESkawyGiIiISNcYDBEREZGuMRgiIiIiXWMwRERERLrGYIiIiIh0jcEQERER6RqDISIiItI1BkNERESkawyGiIiISNcYDBEREZGuMRgiIiIiXWMwRERERLrGYIiIiIh0jcEQERER6RqDISIiItI1BkNERESkawyGiIiISNcYDBEREZGuMRgiIiIiXQt4MLR161ZMmDABiYmJMBgMeP/9983rrl27hqeeego33ngj6tevj8TERNxzzz04fvx44BpMREREQSXgwdDFixfRrVs3vPzyy7XWXbp0CXv27MEzzzyDPXv2IDc3F99//z1+85vfBKClREREFIwMIiKBboSJwWDAmjVrMGnSJLvbFBUVoW/fvjh69Chatmzp1H7Ly8sRExODsrIyNGrUyEutJSIiIl/y1/U7zGd79pGysjIYDAZcd911drepqKhARUWF+Xl5ebkfWkZERERaFPBuMldcuXIFs2fPxl133VVnhJiVlYWYmBjzIzk52Y+tJCIiIi3RTDB07do13HHHHaiqqsLixYvr3HbOnDkoKyszP4qLi/3USiIiItIaTXSTXbt2DbfddhsOHz6MTz/91GG/YWRkJCIjI/3UOiIiIg0wGoHCQqC0FEhIAFJTgdDQQLdKFVQfDJkCoYMHDyI/Px9xcXGBbhIREZG25OYCjzwC/PSTZVlSErBoEZCeHrh2qUTAg6ELFy7g0KFD5ueHDx/Gvn37EBsbi8TEREyZMgV79uzBunXrYDQaceLECQBAbGwsIiIiAtVsIiIibcjNBaZMAWoWj5eUKMtXr9Z9QBTw0vqCggKkpaXVWp6RkYG5c+eiTZs2Nl+Xn5+PIUOGOPUeLK0nIiJdMhqB1q2t7whVZzAod4gOH1Zll5luSuuHDBmCuuIxFQ2DREREpC2FhfYDIUC5W1RcrGzn5A2GYKSZajIiIiJyUWmpd7cLUgyGiIiIglVCgne3C1IMhoiIiIJVaqqSE2Qw2F5vMADJycp2OsZgiIiIKFiFhirl80DtgMj0fOFCVSZP+xODISIiomCWnq6Uz7doYb08KYll9b8KeDUZERER+Vh6OjBxIkegtoPBEBERkR6Ehuq6fL4u7CYjIiIiXWMwRERERLrGYIiIiIh0jTlDRERE5D1Go+YStRkMERERkXfk5gKPPGI9H1pSkjLWkYpL+NlNRkRERM4xGoGCAiA7W/nXaLSsy80FpkypPTFsSYmyPDfXny11CYMhIiIiciw3F2jdGkhLA+66S/m3dWtludGo3BESqf0607LMTOvgSUUYDBEREVHdHN31mT+/9rrqRIDiYiWXSIUYDBEREZF9ztz1+ec/ndtXaan32uVFDIaIiIjIvsJCx3d9zp51bl8JCd5pk5cxGCIiIiL7nL2bExsLGAy21xkMQHKyUmavQgyGiIiIyD5n7+Y88ojyb82AyPR84ULVjjfEYIiIiIjsS01VxgpydNfn6aeB1auBFi2s1yclKctVPM4QB10kIiIi+0JDlUETp0xRAp/qidQ17/qkpwMTJ3IEaiIiIgoy6enK3R1bo0svXGh91yc0FBgyxN8t9AiDISIiInJMo3d9nMFgiIiIiJyjwbs+zmACNREREekagyEiIiLSNQZDREREpGsMhoiIiEjXGAwRERGRrrGajIiIKJgYjUFZ/u5LDIaIiIiCxapVwAMPAGfOWJYlJSkjSKt4OoxAYzcZERFRMHjySeC226wDIUAZMXrKFCA3NzDt0gAGQ0RERFq3ejXwwgv214sAmZlKFxrVwmCIiIhIy4xGpWvMkeJiJZeo5msLCoDsbOVfnQZLzBkiIiLSssJC4PRp57YtLbX8d26u7YlX3ckvcjZpW6XJ3bwzREREpGXVAxxHEhKUf3NzlTyi6oEQAJSUuJ5flJsLtG4NpKUBd92l/Nu6de19OLtdADAYIiIi0jJTgONIkybKnRijUbkjJFJ7G9MyZ/OLnA2qvBl8+QCDISIiIi1LTVW6txx55RWlS6qwsHZQUp2I7fyimpwNqq5e9V7w5SMBD4a2bt2KCRMmIDExEQaDAe+//77VehHB3LlzkZiYiOjoaAwZMgTffPNNYBpLRESkNqGhSp6PwWB/myeeAG69VflvZ7vVHG3nbFC1eLF3gi8fCngwdPHiRXTr1g0vv/yyzfX/93//h7///e94+eWXUVRUhObNm2PEiBE4f/68n1tKRESkUunpSnl9zTtEMTHAO+8A//d/lmXOdqs52s7ZoOqHH5zbzpXcJy8LeDXZmDFjMGbMGJvrRAQLFy7E008/jfRfM9vfeustNGvWDCtXrsSMGTP82VQiIiL1Sk8HqqqUMntTdVlZGfD440B4uKVCzNStVlJiu+vKYFDWp6ZaL69ZCda0qXPtatvWue2cDdJ8IOB3hupy+PBhnDhxAiNHjjQvi4yMxODBg7F9+3a7r6uoqEB5ebnVg4iIKKjl5iojUNcss6+ZpGzqVgNqd62Zni9caF3ybqsSLCMDiIuz3z1nMADJyUpwlpTkeLsawVdVFfD55w6P2itUHQydOHECANCsWTOr5c2aNTOvsyUrKwsxMTHmR3Jysk/bSUREFFCuVoiZutVatLDeNilJWV59nCF7lWDHjwNnzyr7ryuoiohwOvg6f155u9/9DkhMBIYOdeLYvUDVwZCJocaHJyK1llU3Z84clJWVmR/FxcW+biIREVHdfDnaszsVYunpwJEjQH4+sHKl8u/hw9aBkKMgy2BQ7g45CqrqCL5K/7UaC4+lY8QIZVe33AIsWwacPAk0aODSp+C2gOcM1aV58+YAlDtECdX6Ek+dOlXrblF1kZGRiIyM9Hn7iIiInOLN0Z5tcbdCLDQUGDLE/vbOBFlnzwKbNyv7qmtk6fR0YOJEXPu0EN9vKcWW7xPwr32p2P+g9Xbt2wPjxwPjxgHduinDI/maqoOhNm3aoHnz5sjLy0OPHj0AAFevXsWWLVvw/PPPB7h1RERETjB1M9W8u2LK5anZLeUOb1WI1eRskHXqFHDnnXWu3rABWLcuFJs2DUH1VN6wMGDQIEsAdMMNlnX+SvkNeDB04cIFHDp0yPz88OHD2LdvH2JjY9GyZUtkZmZiwYIFaN++Pdq3b48FCxagXr16uOuuuwLYaiIiIic4082UmQlMnKgsc3feLncrxBxxM8gSAfbtA9atAz76CPjf/6yb1bQpMHasEvyMGKGMABBIAQ+Gdu/ejbS0NPPzWbNmAQAyMjKwfPlyPPnkk7h8+TIeeOABnDt3Dv369cOmTZvQsGHDQDWZiIjIOc7m8syfD7z+uvvdaKYKsSlTlMCneuRhr0KsLqYy+pISpZ/qzBmHQdbFi0pv2UcfKY/jx6037dlTCX7Gjwd69wZCVJS1bBCxdXTBpby8HDExMSgrK0OjRo0C3RwiItKL7GylFN0dpiDGlW40W7lJyclKIOTJPuy0TwBs+N1q/POndBQUABUVltX16wPDhyvBz9ixSnWYq/x1/WYwRERE6lBzUD9XuonUqqBAGZPHXaY7L4cPu35Xx53P0V5+kw2lYcmYWbkQa2AJstq0seT+DB4MREU597b2MBjyIgZDREQq5+tqq0AxGpXBCu3l8jgrP7/uqi9vMLXVzh2hKgBn0QSZ+AdK0AKFSIUhNBQDB1q6v1JS6p4izVX+un4HPGeIiIh0zh/VVoHiKJfH2QDJH/N2OchvCgHQBKdxvmELJE8cgpXjgZEjgcaNfd80X1NR+hIREemOqyMna1Fdoz3Pm+fcPpydB8xNly8De9c7F3C9/+9S/Pe/wO23B0cgBDAYIiKiQHJn5GQtsjfa89NP1z1vl0lGhmVuMS8pLgaWLFG6t+LigEdfcK6MPqRF4CZU9RV2kxER6ZFakpXdHTlZi+yN9mzqRqvL8eOedRkajTAWFOKHbcrIz4u/SsW+r6zP95GkVJw7l4TrLpZAqROrwd2xijSAd4aIiPTG1gzkrVt7/c6DU3w1crLWxMbWvd7NLsNz54Bts3JxtlFrhA5Pww1z78IfVqZh7VetcYshFwMGAAsWAF9+CRw+ForG/1mk3KRydjb7IMFqMiIib1DLnRZH7CUruzOmjTc4qrZyp7RcS1woZTfLz1e+Xza+byLA/v2WkZ/jC3PxXtUUAGJ190NgAAyAwdb59sZYRV7C0novYjBERD6llbJwB6XTAQs8TAEBYHvkZC1Xk9XF0fmwJzNT+Uyqve5KfBLe7rMIC/an4/BhZVkIjDiC1miBn2x3A9V1vp0J7v3wB4Dfrt+iA2VlZQJAysrKAt0UIgo2OTkiBoOIchm3PAwG5ZGTE+gWWuTn126nrUd+vv/blpMjkpRk3Y7kZHV9ft7m7Pmw8aiq8dwIgxhhkMnIkYgIkdGjRXIfdnL/7pxvW+crKcnr58tf12/mDBERuUtrZeFqTla2V20VjHeETFz8nAUGVBlCUQWgZu1ZiNLxhbfjM3H2lBEbNgCTb/LR+Tbdyat5R8s0LlQgcs88xGCIiMhdWisL9zRZ2WhUppfIzlb+9XaQZ6q2uvNO5d9gzBGqzoWk8CoYAAhCxGj3wm2AoN6ZYjTYW+ja/l1JTtfaHwBOYjBERPrizQu6mu+02JKaWveYNgaDkihrq3RaTRVowcLR+ajmJyThlYhM5/Zr+r55cr7t0dofAE5iMERE+uHtC7rWysJNU0MArpVOB2G3iCqEhuLaS4uUhJsaHV9Vvz6WXZeJxbfm49Cmw5ixbqJz+zV939w933XR2h8AzvJpRpJKMIGaiHyS6FxZqSSN2tqvad/Jycp2auJKsrLpGO0l36r1GFXsxAmRpUtFbrlFpGFDkcnIkWOw/ozLr0uWkn/VOB8VFSLx8a6fC28mp/s5Cd9f12+W1hNR8PNlSblWy8KdLYsuKFDuoDnij1nVNUoE2LvXMvbP//5nvb5pU2D8GCPuaVOIPsmlqHe9jfNha/iG6hx937xVBu/ncaE4az0Rkbe4kufg6gXdNAmnrXGGAjBIndPsTQ1RU7B2i/jYhQvA5s1K8PPRR7U/nl69gHHjlHnBevUCQkJCAQyxvTNnBmZ09H1z9nw7Yup6mzJFCXxs/QGgwVGqGQwRUfDz9QU9PR2YOFEbI1C7yt95UVoZyduGH39UAp9165QbalevWtbVrw+MGKEEP2PHuvBx1VW9ZdKkCXDoEBAR4UnznefoD4CJE5UPQEPnkMEQEQU/f1zQvfWXt9qYKpIcdYt4Y/JOrYzk/atr14Dt2y3dX999Z73++uuV4GfcOGDwYCAy0o03cXRXEwBOn1YaYuv756vg0t4fAB98ULtLWsXn0ITBEBEFP39e0IONv7pF7HUFmSrWPMm98mJAcOYMsGGDEvxs3AiUlVnWhYYquzZ1f3Xo4FTVfN08uavp6+Cy5h8AvjyHvubT9GyVYDUZEZmryWpWfqlx2gw18uV0Gb6sWPNw2oiqKpEvvhCZP1/k5ptrf33i40WmThV5912Rc+dcb55D7lZvrVpl/7P0xffdR+eQ1WRexGoyIgKgqtm4NclXXS6+qlizd6fCQeXVpUvAp59a8n9q9lJ162bp/urb18fpMFevKndzTp+2vd5W9daqVcoo3vYGFPXFhLw+OoesJiMi8rZgTnT2B1/lRfkiwd3RtBEGgzJtxMSJQGgojh2zBD+ffgpcuWLZPDoaGDbMkvycnOx8MzxiCt7rCoQA627K3Fzgttvq3q8n1ZP2aLzqkMEQEelLsCY6a5kvEtydHE7htamFePnrIfjqK+vVLVta7v6kpSkBkV+5U05vCgCd5c3ARGujsdfAYIiIyFUaLv9WJV8kuDt5oc/PLsVXAEJCgJtvtiQ/d+7sheRnd7lbTu9M5Vl13gxMNF6kwLnJiIhcobcJS309Uz3gmzm0nLzQdxqagBUrgFOnlFhi9mygS5cABkKAa+X01blyp8fVCVod8cU59CMGQ0REztLbhKX+DPxMA/m1aGG9PCnJpZLsK1eUkveH3kvF8dAkVMF2VCMwQJKS8cymVNx1FxAX5+kBeJG7+Teu3OnxRWDipXMYCKwmIyJyhi/nN1MjNyuxPOZGF2RJiWXai82blWowAJiMXKyGMm9cCDQ0b5y7lVmO5g0DlM/ynXcs8+n5ghe7kf11/WYwRETkDD1NWKrywK+qCigqUiq/1q0D9u2zXp+YaEl+HnkhF1FPaWw4BU8mQ7U3cbDJe+8Bt97q9Sb7CkvriYjUROOlwy7x5cS2biorAzZtUu7+rF9vXW1uMAD9+lmSn7t1q562kg7crrHhFDwZ9dvevGFqDwADjMEQEZEzNF467BIVBH4iwPffW8b+KSwEKist6xs1AkaNUoKfMWOU4iq7tDicgqPJUOsKajielssYDBEROUMNpcP+KukPUOB39Sqwdatl4tNDh6zXd+hg6f4aOBAID/fq23vGF+fGk6BGiwFgADEYIiJyhr8mLLXHnzO6+zHwO3FC6fb66COlG+zCBcu68HDlej5unPJo187jt/MNX54bBjV+wQRqIiJXBGJ+s0BUdtlLxPXwPauqgL17LXd/ioqs1zdvrkx5MX48MHw40LChm+33l0BV3ekEq8m8iMEQEXmVP0egDmRll5cCv/PnlZJ3U/n7iRPW63v3tiQ/9+ypjAatCSqvugsGDIa8iMEQEWlWoEv63Qz8fvjBkvy8ZYuSD2TSoAEwYoQl+VmzOeeBPjc6wNJ6IiLyf2WXreDHiQv5tWvAZ59Zur/277de37atJfl50CAgMtI7zQ0oFVTdkXcwGCIiUjN/Vna5mAh8+jSwYYMS/Hz8sTIWkElYmBJHmbq/brghwPN9+YKehlsIcqrvJqusrMTcuXOxYsUKnDhxAgkJCZg2bRr+/Oc/I8TJjmV2kxEFKT3MHu/JaMSucCIRWCan44svLN1fu3ZZbx4fb0l+HjkSiIlxvzma4K9zo2PsJvvV888/jyVLluCtt95C586dsXv3bkyfPh0xMTF45JFHAt08IgoUf5aaB5I/SvqNRuWztHVBF4HAgHP3ZKLHdRNxrMT6fbp3t9z96dNHZ9f8QA+3QF6j+pz9HTt2YOLEiRg3bhxat26NKVOmYOTIkdi9e3egm0ZEgaK32eN9PRu4g+k3DBDEXixGm5JCREcDEyYAr76qzMixdy/wt78BN92k02u+vXPTogUwdy5QUaEkWhuNgWgdOUn1d4YGDhyIJUuW4Pvvv8cNN9yAL774Atu2bcPChQsD3TQiCgQHdzFgMACZmcrIvcF0dfbhFAvGn0rhzF4WPlmKDnOB6GiP3zK41Dw3Bw8Cr70GPPusZZtgvGsZRFQfDD311FMoKytDSkoKQkNDYTQaMX/+fNx55512X1NRUYGKigrz8/Lycn80lYj8QYWTiPqNF0cj/vlnYONGJf+nfG0CPnTiNd3HJAAMhGwznZvcXOWOUM1g3XTXcu5coH374M1x0yjVB0Pvvvsu3n77baxcuRKdO3fGvn37kJmZicTERGRkZNh8TVZWFubNm+fnlhKRX7Cc2S0iwDffWJKft29XRoMGgBCkosSQhAQpQQgCNO9aMHB01xLg3SKVUn01WXJyMmbPno2ZM2eal/3tb3/D22+/jf01B7L4la07Q8nJyawmIwoGHOjOaZcvKx+Xaeyfo0et13fpYhn7p39pLkJv9/70G7ri7HfThJ+tQ6wm+9WlS5dqldCHhoaiyvQnjQ2RkZGIDIoRvYgc0ENpeU1qmD1exX76yTLtxebNSkBkEhkJDBtmmfi0Vavqr0wHQlfbrtDz5bxrnlLTb8DVu5HBnOOmMaoPhiZMmID58+ejZcuW6Ny5M/bu3Yu///3v+N3vfhfophEFVrCWlju6uLGc2YrRqEx2arr7s2+f9foWLZS7P+PHA0OHAvXq1bEzHyZpmxvrzX2r7TfgzuCKwZzjpiWicuXl5fLII49Iy5YtJSoqSq6//np5+umnpaKiwul9lJWVCQApKyvzYUuJ/CgnR8RgEFH+V2p5GAzKIycn0C10T06OSFKS9TElJdk+HlvbJidr99hdcO6cyLvvitxzj0h8fO2vQP/+In/7m8i+fSJVVYFu7a9cObfO7s/T30BlpUh+vsjKlcq/lZXutaX6/pKSbLfL0WPlSs/eO0j56/qt+pwhb+AI1BRUgnWmbCdGQK71176aukh8SAQ4cMCS/LxtG1BZaVkfEwOMGqXc/Rk9GmjSJHBttcmdc1sXb/wGfHVXyXSsgO1uXHuY42YTZ633IgZDFFSCMYE4WAM8D1RUAFu3Wrq/fvjBen1KiiX5ecAAIDw8MO10yBfn1tPfgLeDM1v7rxlo2aPD77YrmEBNRLYFY2m5nscOqqa0FFi/Xgl+Nm0CLl60rIuIUA7dlPzctm3AmukaX5xbT34D/hi009YgjM8+yxw3FXMpGCouLkZycrKv2kJEzgjGmbKDMcBzQlUV8Pnnlu6vzz+3Xt+8uSX4GT4caNgwMO30iC/OrSe/AX8F3jUHyOzSRXuVejriUjCUkpKCWbNmYfbs2ahfv76v2kQUeGrORQnG0vJgC/Dq+P6cPw/k5SnBz/r1wMmT1i/t08cy8WmPHkCI6meQdMAX59aT30CgAm9fV+qRZ1zJtv7ss8+kb9++kpCQIEuXLvVFQrdPsJqMXOLtqhdfMFXS1Kxa0Wo1maMqHINBqRTztNrHH2x8f642T5K103Nk+HCR8HDrQ2vQQCQ9XWTpUpHS0kA33gd8dW7d/Q3k5ztX3ZWf7+mRkxf46/rtVmn9W2+9JUlJSdK9e3fJ18AXhsEQOU1LJevBVloeDAHer8dQVeP7Y4RBjDDIZOQIINKunUhmpkhenogLo4Rol6/OrTu/gWAKvHVA9aX1ly9fRlZWFl566SWMHDkSL7zwAtq1a+fNm1Zew2oycooWK5rU3J3nDltVOMnJmsirOFVqRP3OrVHv3E8w2FhfBQMuXJeEE9sP44aOGj5H7vLVuXXnN2Cv/J3TY6iO6kvrL126hD179iAnJwf//Oc/ER4ejpkzZ2Lu3LloqLIsPwZD5JRgLFkPNHcuVBoJ8ESU0Z5Nyc/RuwqQD35/6qSmc6vhwFtPVFlav2TJEhQVFaGoqAjfffcdQkND0bVrV8ycORPdu3fHihUr0KlTJ6xZswa9e/f2VZuJfEOnFU0+4+6gdjWrcFTk4kXgk08syc8lJZZ1d4DfH4fUdG6Z0EzVuBQMzZ8/HzfddBMyMjJw0003oXfv3lYTov7ud7/DggULMG3aNHz99ddebyyRTwVbRVMg2RvUrqREWa6hbojDhy0Tn+bnK4MhmtSrp5S8jx8PTLouAbjNiR068/1R0x2UYKam4IwCyusjUJ88eRKJiYkwGo3e3K1H2E1GTjHlDDkq11VTzpAauZp7pbILf2UlsH27pfvr22+t17dubRn5ecgQICrq1xWufH8A+8estslHbTEalW7lggLl+ZAhyoO/C/Iy1ecM2SMi2Lp1KwYPHuzN3XqEwRA5jYmVnnMl9+rnn1Vx4T97Fti4UQmANm4Ezp2zrAsNVaa7MI3907Gj5etQizPfH8D+MQO+nSbCG3JzgfvuUz606uLigNdeC3z7KKhoNhhSIwZD5BImVnomOxu46y7H22VmKgFAAC78IsDXX1vu/uzYoYwGbRIbC4wZowQ/o0YBjRu7sPO6vj+A/WBHRAkoagYZ1bcJ9J3J3Fzgllvq3iYnh78T8hoGQ17EYIhcprKuG01x9s5QfDxw5oztdT648F++rNyMMk18euyY9fobb7R0f910k4dva+v7A9TdfeisQFWjGY1Aq1bWWeO2JCUBR47w90JeocpqMiLdYGKl+5yZKiE+Hjh92v4+vDQ/VHGxJfn5k0+UgMgkKgoYOtQSALVs6fbb1Gbr+1NQ4HkgBLhWjebNoL6w0HEgBCjHGOQT6lLwYTBE5E96uOMUGqp0f02ZYn+W7rvvtnQb1cXFMnSjEdi1y9L99eWX1uuTkizBz9ChSjWY33irpN7ZakZvJ2K70n49Dx9AmsRgiMhdrgY2WqgS8pb0dCXnx94s3bGxzgVDTlz4f/kF+PhjJfjZsME65cZgAPr3tyQ/33hjHcnPvubpkAyuTMDri6ENXGk/h58gjWHOEJE7XA1s7F2c1FQl5Av2AkYPhjEQAfbvt+T+bNum7M4kJgYYPVoJfkaPVnrkVMGZY46NVSrsAPerGX01rQxzhigAmEDtRQyGyKtcDWw0Pu6Oz7gwjEFFBbBlixIArVtnGarHpGNHS/fXzTcD4eF+aL873C29d6Wa0ZfTyrCajPzMb9dvn04DqxKctZ68xjTjta3Zru3NeJ2fb3/76o/8fNuzcCcluTard2Wlsq+VK5V/1Tz7dh2zjpeUiLz+usikSSL161tvEhEhMmqUyD//KfLDD4E+CBc5M9O6J+dw5Urnvm8rV7rf/ri42vuLi3N/9nkiO1Q/a72W8M4QeY07f3X7c9wdLeYl/XonrKqkFAfKE/Du8VR8uD4Ue/ZYb5aQYMn9GTYMaNAgMM31Cl/e/fPHhMMcgZr8hN1kXsRgiLzG2cBm5UrgzjuV//bXuDsazEsqLwfy8iwTn546Zb2+b19L91ePHgFMftYSTitDQYTjDBGpkTuTufpj3B2jUbkjZGv/Isp7ZGYqs3QH+AJ48KAl+XnrVuDaNcu6hg2BkSOVAGjMGKBZs8C1U7OcGdpg4cKAfw+I1CQk0A0g0hRTYGPvFoXBoCS7Vi9/Nl2cTOtrbg8o4+44w974LYWFdQ/oVz2Y8rOrV5UBD2fNAm64QXnMmqUsu3YNaN8eePRRYPNm5cbY6tXAtGkMhDxiGtqgRQvr5UlJqrxDSBRovDNEwc3buRnu/tXt63F3nB3kzk+D4Z08qYz5s24dsGkTcP68ZV1YGDB4sNL1NW6cEhyRD6SnK3cC9VCZSOQhBkMUvHyVTOwosLG377ouTkaj4660ugbcc6f7zotEgL17Ld1fRUXWh9G0KTB2rNL9NWIEwNQ9P+G0MkROYQI1aZ+tuz8ffOD7ZGJv33VyYdwdm23xc9LshQtKV5cp+fn4cev1PXtaqr969wZC1Nopr5dxnYg0iNVkXsRgKIjZuvvTogVw5Yr1vAzVqbmaxtbxODvgnifBlJN+/NEy8Wl+vpIPZFK/PjB8uBL8jB0LJCZ69Fb+ocWhCIh0hMGQFzEYClL2Ssmd5ck4K77kyZ0KT4IpG65dA7Zvt0x8+t131uvbtLGUvg8erMwErxkaHIqASG8YDHkRg6Eg5GiKC2dUHwsomHjY7XPmDLBxoxL8fPyxMhGqSWgoMHCgpfsrJUWjY//4av4uIvIqjjNEVBdHpeTO8EUysRryT1xMmhUBvvrKkvy8cydQVWVZHxenjPkzfrwyBlDjxt5vst+5MhSBGu8eEpFXMRgibfKkRNxRZZa7NJR/cumS0ktoCoCKi63Xd+1q6f7q1y8Ib46obCgCIgosBkOkTe7e1fHVCLz28k9KSpTlKsg/OXbMkvz8ySdKjrlJVJSS/DxunJL83LJl4NrpFwEeioCI1IU5Q4Gkhi4VrXJUSm6PB8nEDtuisvwTo1Hp8jIlP3/1lfX65GTl7s/48crUadHRfmta4HH+LiJNYM5QsNNQl4pL/BXg1TUStD3z5gFPP+399qgo/+TcOWDTBiMOLSvE0Z2l+P5CAgqRiiqEIiQE6N/fkvzcpYuKk599/T3i/F1EVJ3oQFlZmQCQsrKyQDdFkZMjYjCIKP8LtjwMBuWRkxPoFronJ0ckKcn6mJKSfHs8tt7T1sNgEElOFqms9H4bVq50/P6Asp2XVVWJfPONyPPPiwwaJHJLSI4cg/XncSY6SbY8kiNnzjjYWWWlSH6+0s78fN98Vs7w5/fI1nslJ2v3N0gUZPx1/WYw5G+VlXVfvH150falQAZ4lZUi//iHcwFJfr7333/zZr++9+XLIhs2iDz4oEjr1pbdT0aOGGEQozvnIBCBrL12+Pt7pJYgkIhq8df1mzlD/lZQoCRoOKLWAQFtUUPOTHY2cNddjrdzd2whe902tro7a/LC8ZeUKFNerFunzO5+6ZJlXUQEMDzNiHd2tUaDX36CzZ6vutqglsEH1fA9IiJVYc5QsArGkl415Mw4W/WTl2fZ3tk8FHv5XXfeCbz4Yt35StXzTwAlGHYiD6aqSpns1FT6vnev9frEREvuz7BhQP2iQiDNjXNgNCrHZusYRJT2Z2YqE8z6OgBRw/eIiHRJE8FQSUkJnnrqKWzYsAGXL1/GDTfcgDfffBO9evUKdNNcF4wlvWoI8FJTlTnJSkrq3m7ZMuUBOJewXlfJ/AsvOG5XixbKewC173rUeP+yMmDTJiX4Wb8eOH3asqnBAPTtawmAunevkfzs7jnwRwDibDK0Gr5HRKRLqg+Gzp07hwEDBiAtLQ0bNmxA06ZN8cMPP+C6664LdNPck5qqXAQdlfR6e0BAX1JDgBcaCtx3H/Dss86/xtEYQI7umjhj+XIlyrETUMmUKfjwntVYVJyOrVuBykrL6kaNlBGfx49XRoBu2rSO93H3HPg6AHGlalIN3yMi0iefZiR5wVNPPSUDBw70aB+qSqAWsSSJ1kwU1Wo1mSkp3Fbiqz+Twp2t6nK2bfn5ru+v5uPtt+tMmDfCIEeRLCGoFEDkhhtEZs0S+eQTkYoKF47d3XPg7DG6k/ztajK0Wr5HRKQa/rp+hwQ6GHNk7dq16N27N2699VY0bdoUPXr0wOuvv17nayoqKlBeXm71UJX0dOVuRIsW1suTklQxUrHLTGO2ALUHrvHnmC3u3DGo3g1Ukze6Y06frrMbKgSClijGuzML8f33wIEDwEsvAUOHKonRTnP3HJjuVNobcMhgUEZndPVOpTN31TIzle08PQYiIk/5NNTygsjISImMjJQ5c+bInj17ZMmSJRIVFSVvvfWW3dc8++yzAqDWQzV3hkyCraQ30GO2OLqzUNfD1hhAHtwZqoJBfmmULH9u87b77+8Od86BL+5UenLHKdDfIyJSDZbW/yoiIgK9e/fG9u3bzcsefvhhFBUVYceOHTZfU1FRgYqKCvPz8vJyJCcnq6O0PtgFeooRU8IzYPuuhD22hjJwc8qPql+L26dgNX5GLArg56EU3DkHtnJ7PJm6xNOhDgL9PSIiVWBp/a8SEhLQqVMnq2UdO3ZETk6O3ddERkYiMjLS100jW0JDA1v2bOqCdDT2j0ldCesOpmwQAHvSHkfLz7LRpMLyXj8hCbMjF0LGpOOesUYYn01C6AkfJMzbCxjcOQfp6Ur5vLcCEE+ToQP9PSIiXVF9MDRgwAAcOHDAatn333+PVq1aBahFXsS/fn2j5oX94EGlysydOajsBFeloUmYWbkQaz5NRwiykIpCdG9airYDE9Dh96lYNjQUSjweCsT5YA4sX8xt580AJBirJokoePm0E84L/ve//0lYWJjMnz9fDh48KCtWrJB69erJ22+/7fQ+VFdNJqKe6Q/0ws08lNOnRf7zH5Hbp1TKuPr5cgdWymDkSwgqJTRUZMgQkRdeEPnuO2WeMG+/v919aWFuu2CrmiQiv2POUDXr1q3DnDlzcPDgQbRp0wazZs3CH/7wB6dfr6rpOAD1TH+gN07ciRMBvvzSMvLzzp3Wpyk+XhnzZ/x4ZQwgl4a78sadQK1NWeHtXCQi0hV/Xb81EQx5SlXBkNYuZjpw6RLwySdK8PPRR7VPTbduSvAzbpwyCnRAT4sW57ZjdzARuYkJ1MGK8y+pwtGjSuCzbp0SN1y5YlkXHQ0MH64EP2PHKjcyVEOLU1YwGZqIVI7BkD9U/8v422+de42aLmZBoLJS6fIydX99/bX1+pYtlbs/48cr1+3o6IA007GDB53bjlNWEBE5jcGQr9nKmXAGL2Ye+/lnYONGJfjZsAE4d86yLiQEuPlmS/dX5872B2FWDaMReO01x9tprUpL691oWm8/ETEY8il7idJ1Ycmx20SUG2+muz+ffQZUVVnWN24MjB6tBECjRgFxcYFrq1sKC5VSdUf+8AftXIx9MUSAP2m9/UQEgMGQ79Q1N5M9nH/JZVeuKDk/pvyfo0et13fubLn7078/EKblb7yzXaft2/u2Hd5i74+FkhJludqrKrXefiIy0/KlQd0cJUrbkpTEkmMnlJRYgp9PPlGqwUwiI5VJTseNUx6tWwesmd7n6ajOauJoIleDQZnIdeJEdf5hoPX2E5EVBkO+4uxf8X/+M9Cpk3dyDYI0d8FoBIqKLN1f+/ZZr09MtCQ/Dx0K1K8fkGb6nrdGdVbD90TrVZVabz8RWWEw5CvO/nU+bJh3/mcZZLkLZWXAxx8rwc/69cCZM5Z1BgPQr59y52f8eGUcINUnP3uDg7nSADjuYlXL90SLQwRU56v2qyFQJdIhBkO+4s+5mezlLvz0k2ZyF0SA779X7v6sWwds26aUw5s0aqQkPY8fr4wA3aRJ4NoaUPYmonWmi1VNOS5a7/LzRfvVEqgS6RBHoPYl08UHsP1XvDcuPo5GtAaUUQNVOKJ1RQWwdasl/+eHH6zXd+hgSX4eOBAIDw9MO1XJ1TsIahv53NQeR38sqPB7C8D77ecUPUQ2cToOLwrodBy+nptJY9MznDihdHutWwfk5QEXLljWhYcrTTQlP7drF7BmBh81fk/88ceCL3mr/WoLVIlUhNNxBIv0dKWixFd5AM6MO+PKdl5WVQXs2WNJft6923p98+bKlBfjxytTYDRsGJBmBj815uh40uWnBt5qP5OxiQKOwZA/+HJuptOnvbudF5w/r9z1MU18evKk9frevS3dXz17KqNBk4+pNUfH138s+Jo32q/GQJVIZxgMaZ2zmcQ+zjg+dMiS+7NlC3DtmmVdgwbAyJFK8DNmjAfXW08rbfRcqZOaCrRoYf8OYSBHPtf6RK6etl+tgSqRjjAY0roWLby7nZOuXVMqvkzdXwcOWK9v29Zy92fQIGUwRI94Wmmj90qdDz5Qhuu2hSOfKwIVLPuz8pSIbBMdKCsrEwBSVlYW6KZ4X2WlSFKSiPK/UduP5GRlOw+dPCmyfLnIrbeKNGpk/RZhYSJpaSIvviiyf79IVZUXjs0kJ0fEYKh9XAaD8sjJ8e3rtc7e8ZsecXHB/xk4kpNT+3eUlOS/z8V0jmqeJ718R4ns8Nf1m9VkwcBHVTkiwBdfWO7+7Nplvfv4eEvy88iRQEyMB8dgj6eVNnqv1HFm6IWkJODIkeA8fmeopazd15WnRBrE0novCvpgCPDa/0gvXlTm+zIlP9dMMene3dL91aePH66fnpaEq7Gk3J/0fvyOqC1Y1nNeG5ENLK0nRV3/c6y57ocfgO3bXf4f6ZEjluTn/HxlMEST6GhgxAgl+Bk7Vrku+JWnlTZ6r9TR+/E7oraydq0nkxNpFIMhNasr6Rewv+7OO+vcbWUlsGOHpfvrm2+s17dqZbn7M2SIEhAFjKeVNsFYqePK3YNgPH5vYrBIRGAwpF51zSN1yy22X1PHHFNnzwIbNyrBz8aNwLlzlnUhIcCAAZaJTzt1UtHEp55W2gRbpY6rVXHOHH98vLK+oEB/3TIMFokIzBlSJ2eSXu359eIuPx7GN/tDzROf7tihjAZtEhsLjB6tBD+jRinPVcvTBHGtT/tg4m6ir73jt0VPww0A2p8jjSjI+e367dNaNZXQXGl9fn7dpfJOPG5rml9rcZcuIrNnixQWily7FuiDdJGt0ufkZOdLjj19faA5GkLBYKh7CAVbx29vP3or5WZZO5FqsbTeizR3Zyg7G7jrLo92cSdWYk3knRg2zDLxaatWXmpfoOh5BGpvVIWZjr+kBMjMBM6csb2dHu+GsKydSJVYTaZnXshPeHhBAt58BKhXzwvtUQtPK220XKnjjURf0/EXFNgPhAB9Tgyq9TnSiMgjDIbUyEHSq2mJrRxnMRhgSEpC/ydTAf5/PHh4M9GXFVS2aTlYJiKP6Gu+8MJCpQuqoEDpMlApCQnFT08sgghQVSPkqf5caoZDBoOyxFtzTBmNymelgc8s6JkCZHtlfgaD0q3jTFUcK6iIiKzoKxgaP17JxUlLUypIcnMD3SKzigpg0ybg4YeBdu2A5EfScQtWowTWE6xWxsTDmP0eDDk5MCTVmHw1Kcl7lVG5ucpnlJam2s9MV0JDLeNL1QyIXJ1o1ZuBFRFRENBXMFSdaUyeAF7cjx8H3ngDmDwZiItTStz/9S/gxx+BiAjg4sh0fDX9H6iMbWJ+TUTZaYQ9MUt5cuSIkjC7cqXy7+HD3guEpkypXdqvgs9M19LTlWC3hYdBsDcDKyKiIKCvajIAVrnofq6aqaoCdu+2TH2xZ4/1+ubNLQMfDh8ONNgUgAkk1TZXE9Xmrao4VlARkcpxolYvshsMmfhwksryciAvTwmA1q8HTp60Xt+nj2Xqix49lNGgAQQuKOHEnvqi5eEGiCjosbTen7xcNXPwoOXuz9atwLVrlnUNGgAjRyoB0Jgxyt0gmwI1gSQrjfSFFVRERAyGAFhXzbjxl/LVq8C2bZaJT7//3np9u3aWuz+DBin5QA4FKihxtoLo5Emlyox3E4iISOP0HQzVnKTThUkwT51Sur0++gj4+GPg/HnLurAwJegx5f/ccIMbbQtU+bOjiT0BJfB59FHLc73NZ6VW7PIiInKLfnOGaiYhO5gEU1atxr7r080TnxYVWW/apAkwdqwS/IwYAcTEeNhodyaQ9GZirbMTe5raAmhnwtNg5Ops9kREGsAEai+yGQxVr5pxkKwsMOB4SBJaVh1GVbVhnXv0sHR/9elTLfnZW1yZbd3bF0Nb+wsNtT/wIqvMAsfd2eyJiFSOwZAXmT/MdevQqLy89l0TJyuoRkfmI2r0EIwbp9wFqjnci084U/7sq4th9TtNJ09ad43Zwyoz/+JQCEQUxFhN5gupqUCND7OyEjj4aSk6OvHyta+WIiLDN02zy9EEkkajEizZimlFlIthZqayD1cvhtUrjbKznXsNq8z8K1BVh0REQURzI1BnZWXBYDAgMzPT7X2cPQu8/TZw551Krs8f/+pcEnJEqwDN1WQKSu68U/m3elDjysXQE5zPSp04FAIRkcc0dWeoqKgIr732Grp27erW6196Cdi8Gdi5UxkN2uSbxqk4W5GE2EslMKCOZGU1ztXkr4uhoyozNX9GwYxBKhGRxzRzZ+jChQu4++678frrr6Nx48Zu7eMvfwG2b1cCoRtvBObMUcYHOnE6FHH/XaSk2GhtriZ/XQw5n5U6cdJVIiKPaSYYmjlzJsaNG4fhw4c73LaiogLl5eVWD0AZ+XnxYuDoUeDLL4EFC4ABA369fntrEkx/8+fFUKufUTBjkEpE5DFNdJO988472LNnD4qKipzaPisrC/Pmzau1fNWqWvnT1hwlK6uR6WI4ZYpy8bNVgu/Ni6EWP6NgZwpSbQ2twElXiYgcUn1pfXFxMXr37o1NmzahW7duAIAhQ4age/fuWLhwoc3XVFRUoKKiwvy8vLwcycnJPi/NCyjOQE4cgZqIggzHGfrV+++/j8mTJyO02v/UjUYjDAYDQkJCUFFRYbXOFn99mAHHiyEREQURjjP0q2HDhuGrr76yWjZ9+nSkpKTgqaeechgI6QpnICciInKZ6oOhhg0bokuXLlbL6tevj7i4uFrLiYiIiFylmWoyIiIiIl9Q/Z0hWwoKCgLdBM8wt4eIiEg1NBkMaZq3Z5cnIiIij7CbzJ9Ms8vXnEuspERZnpsbmHYRERHpGIMhf3E0uzygzC5vNPq1WURERHrHYMhf/DW7PBEREbmEwZC/+Gt2eSIiInIJgyF/cXbW+IMHfdsOIiIissJgyF8czS5vMncuE6mJiIj8iMGQv5hml3dmKjgmUhMREfkNg6GajEagoADIzlb+9WZQkp4OzJtX9zZMpCYiIvIrDrpYnT8GRGzf3rntmEhNRETkF7wzZOKvARGdTaR2djsiIiLyCIMhwL8DIjpKpDYYgORkZTsiIiLyOQZDgH8HRDQlUgO1AyLT84ULOXErERGRnzAYAvw/IGJ6OrB6NdCihfXypCRlOSdsJSIi8hsmUAOByeNJTwcmTlTuNpWWKvtOTeUdISIiIj9jMARY8nhKSmznDRkMynpv5/GEhgJDhnh3n0REROQSdpMBzOMhIiLSMQZDJszjISIi0iV2k1XHPB4iIiLdYTBUE/N4iIiIdIXdZERERKRrDIaIiIhI1xgMERERka4xGCIiIiJdYzBEREREusZgiIiIiHSNwRARERHpGoMhIiIi0jUGQ0RERKRrDIaIiIhI1xgMERERka4xGCIiIiJdYzBEREREusZgiIiIiHSNwRARERHpGoMhIiIi0jUGQ0RERKRrDIaIiIhI11QfDGVlZaFPnz5o2LAhmjZtikmTJuHAgQOBbhYREREFCdUHQ1u2bMHMmTOxc+dO5OXlobKyEiNHjsTFixcD3TQiIiIKAgYRkUA3whWnT59G06ZNsWXLFgwaNMip15SXlyMmJgZlZWVo1KiRj1tIRERE3uCv63eYz/bsI2VlZQCA2NhYu9tUVFSgoqLC/Ly8vNzn7SIiIiJtUn03WXUiglmzZmHgwIHo0qWL3e2ysrIQExNjfiQnJ/uxlURERKQlmuommzlzJj766CNs27YNSUlJdrezdWcoOTmZ3WREREQawm6yGh566CGsXbsWW7durTMQAoDIyEhERkb6qWVERESkZaoPhkQEDz30ENasWYOCggK0adMm0E0iIiKiIKL6YGjmzJlYuXIlPvjgAzRs2BAnTpwAAMTExCA6OjrArSMiIiKtU33OkMFgsLl82bJlmDZtmlP7YGk9ERGR9jBn6Fcqj9WIiIhI4zRVWk9ERETkbQyGiIiISNcYDBEREZGuMRgiIiIiXWMwRERERLrGYIiIiIh0jcEQERER6RqDISIiItI1BkNERESkawyGiIiISNcYDBEREZGuMRgiIiIiXWMwRERERLrGYIiIiIh0jcEQERER6RqDISIiItI1BkNERESkawyGiIiISNcYDBEREZGuMRgiIiIiXWMwRERERLrGYIiIiIh0jcEQERER6RqDISIiItI1BkNERESkawyGiIiISNcYDBEREZGuMRgiIiIiXWMwRERERLrGYIiIiIh0jcEQERER6RqDISIiItI1BkNERESkawyGiIiISNcYDBEREZGuMRgiIiIiXWMwRERERLrGYIiIiIh0TTPB0OLFi9GmTRtERUWhV69eKCwsDHSTiIiIKAhoIhh69913kZmZiaeffhp79+5FamoqxowZg2PHjgW6aURERKRxBhGRQDfCkX79+qFnz57497//bV7WsWNHTJo0CVlZWQ5fX15ejpiYGJSVlaFRo0a+bCoRERF5ib+u36q/M3T16lV8/vnnGDlypNXykSNHYvv27QFqFREREQWLsEA3wJEzZ87AaDSiWbNmVsubNWuGEydO2HxNRUUFKioqzM/LysoAKBEmERERaYPpuu3rTizVB0MmBoPB6rmI1FpmkpWVhXnz5tVanpyc7JO2ERERke+cPXsWMTExPtu/6oOh+Ph4hIaG1roLdOrUqVp3i0zmzJmDWbNmmZ//8ssvaNWqFY4dO+bTD1NtysvLkZycjOLiYl3lSvG4edx6wOPmcetBWVkZWrZsidjYWJ++j+qDoYiICPTq1Qt5eXmYPHmyeXleXh4mTpxo8zWRkZGIjIystTwmJkZXXyKTRo0a8bh1hMetLzxufdHrcYeE+DbFWfXBEADMmjULU6dORe/evdG/f3+89tprOHbsGO6///5AN42IiIg0ThPB0O23346zZ8/iL3/5C0pLS9GlSxesX78erVq1CnTTiIiISOM0EQwBwAMPPIAHHnjArddGRkbi2Weftdl1Fsx43DxuPeBx87j1gMft2+PWxKCLRERERL6i+kEXiYiIiHyJwRARERHpGoMhIiIi0jUGQ0RERKRrmgyGFi9ejDZt2iAqKgq9evVCYWFhndtv2bIFvXr1QlRUFK6//nosWbKk1jY5OTno1KkTIiMj0alTJ6xZs8ZXzXebK8edm5uLESNGoEmTJmjUqBH69++Pjz/+2Gqb5cuXw2Aw1HpcuXLF14fiEleOu6CgwOYx7d+/32q7YDvf06ZNs3ncnTt3Nm+jhfO9detWTJgwAYmJiTAYDHj//fcdviYYft+uHnew/L5dPe5g+X27etzB8vvOyspCnz590LBhQzRt2hSTJk3CgQMHHL7OH79xzQVD7777LjIzM/H0009j7969SE1NxZgxY3Ds2DGb2x8+fBhjx45Famoq9u7diz/96U94+OGHkZOTY95mx44duP322zF16lR88cUXmDp1Km677Tbs2rXLX4flkKvHvXXrVowYMQLr16/H559/jrS0NEyYMAF79+612q5Ro0YoLS21ekRFRfnjkJzi6nGbHDhwwOqY2rdvb14XjOd70aJFVsdbXFyM2NhY3HrrrVbbqf18X7x4Ed26dcPLL7/s1PbB8vt29biD5fft6nGbaP337epxB8vve8uWLZg5cyZ27tyJvLw8VFZWYuTIkbh48aLd1/jtNy4a07dvX7n//vutlqWkpMjs2bNtbv/kk09KSkqK1bIZM2bITTfdZH5+2223yejRo622GTVqlNxxxx1earXnXD1uWzp16iTz5s0zP1+2bJnExMR4q4k+4epx5+fnCwA5d+6c3X3q4XyvWbNGDAaDHDlyxLxMC+e7OgCyZs2aOrcJlt93dc4cty1a/H1X58xxB8vvuzp3zncw/L5FRE6dOiUAZMuWLXa38ddvXFN3hq5evYrPP/8cI0eOtFo+cuRIbN++3eZrduzYUWv7UaNGYffu3bh27Vqd29jbp7+5c9w1VVVV4fz587Umu7tw4QJatWqFpKQkjB8/vtZfloHkyXH36NEDCQkJGDZsGPLz863W6eF8v/nmmxg+fHitUdrVfL7dEQy/b2/Q4u/bE1r+fXtDsPy+y8rKAKDOSVj99RvXVDB05swZGI3GWrPVN2vWrNas9iYnTpywuX1lZSXOnDlT5zb29ulv7hx3TS+99BIuXryI2267zbwsJSUFy5cvx9q1a5GdnY2oqCgMGDAABw8e9Gr73eXOcSckJOC1115DTk4OcnNz0aFDBwwbNgxbt241bxPs57u0tBQbNmzA73//e6vlaj/f7giG37c3aPH37Y5g+H17Klh+3yKCWbNmYeDAgejSpYvd7fz1G9fMdBzVGQwGq+ciUmuZo+1rLnd1n4Hgbhuzs7Mxd+5cfPDBB2jatKl5+U033YSbbrrJ/HzAgAHo2bMn/vWvf+Gf//yn9xruIVeOu0OHDujQoYP5ef/+/VFcXIwXX3wRgwYNcmufgeJuG5cvX47rrrsOkyZNslqulfPtqmD5fbtL679vVwTT79tdwfL7fvDBB/Hll19i27ZtDrf1x29cU3eG4uPjERoaWivaO3XqVK2o0KR58+Y2tw8LC0NcXFyd29jbp7+5c9wm7777Lu6991689957GD58eJ3bhoSEoE+fPqr5S8KT467upptusjqmYD7fIoKlS5di6tSpiIiIqHNbtZ1vdwTD79sTWv59e4vWft+eCJbf90MPPYS1a9ciPz8fSUlJdW7rr9+4poKhiIgI9OrVC3l5eVbL8/LycPPNN9t8Tf/+/Wttv2nTJvTu3Rvh4eF1bmNvn/7mznEDyl+M06ZNw8qVKzFu3DiH7yMi2LdvHxISEjxusze4e9w17d271+qYgvV8A0q1xqFDh3Dvvfc6fB+1nW93BMPv211a/317i9Z+357Q+u9bRPDggw8iNzcXn376Kdq0aePwNX77jTudaq0S77zzjoSHh8ubb74p3377rWRmZkr9+vXNWfWzZ8+WqVOnmrf/8ccfpV69evLoo4/Kt99+K2+++aaEh4fL6tWrzdt89tlnEhoaKs8995x899138txzz0lYWJjs3LnT78dnj6vHvXLlSgkLC5NXXnlFSktLzY9ffvnFvM3cuXNl48aN8sMPP8jevXtl+vTpEhYWJrt27fL78dnj6nH/4x//kDVr1sj3338vX3/9tcyePVsASE5OjnmbYDzfJr/97W+lX79+NvephfN9/vx52bt3r+zdu1cAyN///nfZu3evHD16VESC9/ft6nEHy+/b1eMOlt+3q8dtovXf9x//+EeJiYmRgoICq+/tpUuXzNsE6jeuuWBIROSVV16RVq1aSUREhPTs2dOqLC8jI0MGDx5stX1BQYH06NFDIiIipHXr1vLvf/+71j5XrVolHTp0kPDwcElJSbH6camFK8c9ePBgAVDrkZGRYd4mMzNTWrZsKREREdKkSRMZOXKkbN++3Y9H5BxXjvv555+Xtm3bSlRUlDRu3FgGDhwoH330Ua19Btv5FhH55ZdfJDo6Wl577TWb+9PC+TaVTtv73gbr79vV4w6W37erxx0sv293vufB8Pu2dcwAZNmyZeZtAvUbN/zaQCIiIiJd0lTOEBEREZG3MRgiIiIiXWMwRERERLrGYIiIiIh0jcEQERER6RqDISIiItI1BkNERESkawyGiIiISNcYDBEREZGuMRgiIiIiXWMwRESalJ2djaioKJSUlJiX/f73v0fXrl1RVlYWwJYRkdZwbjIi0iQRQffu3ZGamoqXX34Z8+bNwxtvvIGdO3eiRYsWgW4eEWlIWKAbQETkDoPBgPnz52PKlClITEzEokWLUFhYyECIiFzGO0NEpGk9e/bEN998g02bNmHw4MGBbg4RaRBzhohIsz7++GPs378fRqMRzZo1C3RziEijeGeIiDRpz549GDJkCF555RW88847qFevHlatWhXoZhGRBjFniIg058iRIxg3bhxmz56NqVOnolOnTujTpw8+//xz9OrVK9DNIyKN4Z0hItKUn3/+GQMGDMCgQYPw6quvmpdPnDgRFRUV2LhxYwBbR0RaxGCIiIiIdI0J1ERERKRrDIaIiIhI1xgMERERka4xGCIiIiJdYzBEREREusZgiIiIiHSNwRARERHpGoMhIiIi0jUGQ0RERKRrDIaIiIhI1xgMERERka4xGCIiIiJd+/9Z4+2/f0AIuwAAAABJRU5ErkJggg==",
-      "text/plain": [
-       "
    "
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "%matplotlib inline\n",
     "\n",
@@ -411,7 +385,7 @@
     "print(theta_linreg)\n",
     "theta = np.random.randn(2,1)\n",
     "\n",
-    "eta = 2.5/np.max(EigValues)\n",
+    "eta = 1.0/np.max(EigValues)\n",
     "Niterations = 1000\n",
     "\n",
     "for iter in range(Niterations):\n",
@@ -435,7 +409,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4dd147c2",
+   "id": "6c1c6ed1",
    "metadata": {
     "editable": true
    },
@@ -447,7 +421,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "75ca7f80",
+   "id": "a82ce6e3",
    "metadata": {
     "editable": true
    },
@@ -459,7 +433,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5b897c75",
+   "id": "cb0de7c2",
    "metadata": {
     "editable": true
    },
@@ -469,7 +443,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46aa12f6",
+   "id": "b76c0dea",
    "metadata": {
     "editable": true
    },
@@ -483,7 +457,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8ac05816",
+   "id": "4eeb07f6",
    "metadata": {
     "editable": true
    },
@@ -493,7 +467,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cee76d94",
+   "id": "cc7d6c64",
    "metadata": {
     "editable": true
    },
@@ -505,7 +479,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "88cf9577",
+   "id": "08bd65db",
    "metadata": {
     "editable": true
    },
@@ -516,7 +490,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0108d67e",
+   "id": "a1c5a4d1",
    "metadata": {
     "editable": true
    },
@@ -531,7 +505,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1e307469",
+   "id": "f178c97e",
    "metadata": {
     "editable": true
    },
@@ -545,7 +519,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c8dc7485",
+   "id": "3853aec7",
    "metadata": {
     "editable": true
    },
@@ -555,38 +529,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
-   "id": "2909407a",
+   "execution_count": 3,
+   "id": "81740e7b",
    "metadata": {
     "collapsed": false,
-    "editable": true,
-    "jupyter": {
-     "outputs_hidden": false
-    }
+    "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Eigenvalues of Hessian Matrix:[0.28267705 4.52578812]\n",
-      "[[4.39166208]\n",
-      " [2.57978284]]\n",
-      "[[4.38905562]\n",
-      " [2.58193415]]\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "
    "
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from random import random, seed\n",
     "import numpy as np\n",
@@ -642,7 +591,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d25693ff",
+   "id": "aa1b6e08",
    "metadata": {
     "editable": true
    },
@@ -664,7 +613,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "78b0bf65",
+   "id": "d1b9be1a",
    "metadata": {
     "editable": true
    },
@@ -679,7 +628,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9ee803d8",
+   "id": "2e1267e6",
    "metadata": {
     "editable": true
    },
@@ -689,63 +638,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
-   "id": "ac420f7a",
+   "execution_count": 4,
+   "id": "494e82a7",
    "metadata": {
     "collapsed": false,
-    "editable": true,
-    "jupyter": {
-     "outputs_hidden": false
-    }
+    "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      ">0 f([0.74724774]) = 0.55838\n",
-      ">1 f([0.59779819]) = 0.35736\n",
-      ">2 f([0.47823856]) = 0.22871\n",
-      ">3 f([0.38259084]) = 0.14638\n",
-      ">4 f([0.30607268]) = 0.09368\n",
-      ">5 f([0.24485814]) = 0.05996\n",
-      ">6 f([0.19588651]) = 0.03837\n",
-      ">7 f([0.15670921]) = 0.02456\n",
-      ">8 f([0.12536737]) = 0.01572\n",
-      ">9 f([0.10029389]) = 0.01006\n",
-      ">10 f([0.08023512]) = 0.00644\n",
-      ">11 f([0.06418809]) = 0.00412\n",
-      ">12 f([0.05135047]) = 0.00264\n",
-      ">13 f([0.04108038]) = 0.00169\n",
-      ">14 f([0.0328643]) = 0.00108\n",
-      ">15 f([0.02629144]) = 0.00069\n",
-      ">16 f([0.02103315]) = 0.00044\n",
-      ">17 f([0.01682652]) = 0.00028\n",
-      ">18 f([0.01346122]) = 0.00018\n",
-      ">19 f([0.01076897]) = 0.00012\n",
-      ">20 f([0.00861518]) = 0.00007\n",
-      ">21 f([0.00689214]) = 0.00005\n",
-      ">22 f([0.00551372]) = 0.00003\n",
-      ">23 f([0.00441097]) = 0.00002\n",
-      ">24 f([0.00352878]) = 0.00001\n",
-      ">25 f([0.00282302]) = 0.00001\n",
-      ">26 f([0.00225842]) = 0.00001\n",
-      ">27 f([0.00180673]) = 0.00000\n",
-      ">28 f([0.00144539]) = 0.00000\n",
-      ">29 f([0.00115631]) = 0.00000\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "
    "
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from numpy import asarray\n",
     "from numpy import arange\n",
@@ -806,7 +705,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c548d574",
+   "id": "46858c7c",
    "metadata": {
     "editable": true
    },
@@ -816,63 +715,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
-   "id": "687e9d89",
+   "execution_count": 5,
+   "id": "6a917123",
    "metadata": {
     "collapsed": false,
-    "editable": true,
-    "jupyter": {
-     "outputs_hidden": false
-    }
+    "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      ">0 f([0.74724774]) = 0.55838\n",
-      ">1 f([0.54175461]) = 0.29350\n",
-      ">2 f([0.37175575]) = 0.13820\n",
-      ">3 f([0.24640494]) = 0.06072\n",
-      ">4 f([0.15951871]) = 0.02545\n",
-      ">5 f([0.1015491]) = 0.01031\n",
-      ">6 f([0.0638484]) = 0.00408\n",
-      ">7 f([0.03976851]) = 0.00158\n",
-      ">8 f([0.02459084]) = 0.00060\n",
-      ">9 f([0.01511937]) = 0.00023\n",
-      ">10 f([0.00925406]) = 0.00009\n",
-      ">11 f([0.00564365]) = 0.00003\n",
-      ">12 f([0.0034318]) = 0.00001\n",
-      ">13 f([0.00208188]) = 0.00000\n",
-      ">14 f([0.00126053]) = 0.00000\n",
-      ">15 f([0.00076202]) = 0.00000\n",
-      ">16 f([0.00046006]) = 0.00000\n",
-      ">17 f([0.00027746]) = 0.00000\n",
-      ">18 f([0.00016719]) = 0.00000\n",
-      ">19 f([0.00010067]) = 0.00000\n",
-      ">20 f([6.05804744e-05]) = 0.00000\n",
-      ">21 f([3.64373635e-05]) = 0.00000\n",
-      ">22 f([2.19069576e-05]) = 0.00000\n",
-      ">23 f([1.31664443e-05]) = 0.00000\n",
-      ">24 f([7.91100141e-06]) = 0.00000\n",
-      ">25 f([4.75216828e-06]) = 0.00000\n",
-      ">26 f([2.85408468e-06]) = 0.00000\n",
-      ">27 f([1.71384267e-06]) = 0.00000\n",
-      ">28 f([1.02900153e-06]) = 0.00000\n",
-      ">29 f([6.17748881e-07]) = 0.00000\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "
    "
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from numpy import asarray\n",
     "from numpy import arange\n",
@@ -941,7 +790,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "27a27a67",
+   "id": "361b2aa8",
    "metadata": {
     "editable": true
    },
@@ -960,7 +809,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a12c19b2",
+   "id": "2dacb8ef",
    "metadata": {
     "editable": true
    },
@@ -981,7 +830,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b8436434",
+   "id": "59c9add4",
    "metadata": {
     "editable": true
    },
@@ -997,7 +846,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f00e1864",
+   "id": "a5168cc9",
    "metadata": {
     "editable": true
    },
@@ -1011,7 +860,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea91af30",
+   "id": "47321307",
    "metadata": {
     "editable": true
    },
@@ -1039,7 +888,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc9502a0",
+   "id": "96f44d6b",
    "metadata": {
     "editable": true
    },
@@ -1071,7 +920,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a236a2a",
+   "id": "898ef421",
    "metadata": {
     "editable": true
    },
@@ -1088,7 +937,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "29dc562b",
+   "id": "4e827950",
    "metadata": {
     "editable": true
    },
@@ -1101,7 +950,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a34f155",
+   "id": "05e99546",
    "metadata": {
     "editable": true
    },
@@ -1114,7 +963,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0afd8cd8",
+   "id": "b92afe6c",
    "metadata": {
     "editable": true
    },
@@ -1127,7 +976,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0b27e71",
+   "id": "b20a4aca",
    "metadata": {
     "editable": true
    },
@@ -1141,7 +990,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3b04b9c6",
+   "id": "7884cc0d",
    "metadata": {
     "editable": true
    },
@@ -1163,7 +1012,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "05eca708",
+   "id": "392aeed0",
    "metadata": {
     "editable": true
    },
@@ -1178,7 +1027,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "473025f4",
+   "id": "04581249",
    "metadata": {
     "editable": true
    },
@@ -1190,7 +1039,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "26e0b288",
+   "id": "d21077a4",
    "metadata": {
     "editable": true
    },
@@ -1203,7 +1052,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "091efee5",
+   "id": "b4bed668",
    "metadata": {
     "editable": true
    },
@@ -1217,7 +1066,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22c5f80e",
+   "id": "9c15b282",
    "metadata": {
     "editable": true
    },
@@ -1228,13 +1077,10 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "102b1658",
+   "id": "602bda4c",
    "metadata": {
     "collapsed": false,
-    "editable": true,
-    "jupyter": {
-     "outputs_hidden": false
-    }
+    "editable": true
    },
    "outputs": [],
    "source": [
@@ -1256,7 +1102,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "79448e46",
+   "id": "332831a7",
    "metadata": {
     "editable": true
    },
@@ -1272,7 +1118,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbc8b940",
+   "id": "187eb27c",
    "metadata": {
     "editable": true
    },
@@ -1293,7 +1139,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b63ae18d",
+   "id": "8ddbdbb5",
    "metadata": {
     "editable": true
    },
@@ -1313,7 +1159,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c5ee074e",
+   "id": "35ea8e21",
    "metadata": {
     "editable": true
    },
@@ -1332,13 +1178,10 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "cfc48413",
+   "id": "77a60fcd",
    "metadata": {
     "collapsed": false,
-    "editable": true,
-    "jupyter": {
-     "outputs_hidden": false
-    }
+    "editable": true
    },
    "outputs": [],
    "source": [
@@ -1370,7 +1213,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fbb8c0eb",
+   "id": "b030b80c",
    "metadata": {
     "editable": true
    },
@@ -1382,43 +1225,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
-   "id": "cc1e51cd",
+   "execution_count": 8,
+   "id": "9bdf875b",
    "metadata": {
     "collapsed": false,
-    "editable": true,
-    "jupyter": {
-     "outputs_hidden": false
-    }
+    "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[4.08805934]\n",
-      " [2.86802426]]\n",
-      "Eigenvalues of Hessian Matrix:[0.26504701 4.42519896]\n",
-      "theta from own gd\n",
-      "[[4.08805934]\n",
-      " [2.86802426]]\n",
-      "theta from own sdg\n",
-      "[[4.10653666]\n",
-      " [2.86499207]]\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "
    "
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Importing various packages\n",
     "from math import exp, sqrt\n",
@@ -1490,7 +1303,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22a23ea0",
+   "id": "365cebd9",
    "metadata": {
     "editable": true
    },
@@ -1505,7 +1318,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0258497",
+   "id": "e7c9011a",
    "metadata": {
     "editable": true
    },
@@ -1515,7 +1328,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69f1d941",
+   "id": "f1c85da0",
    "metadata": {
     "editable": true
    },
@@ -1527,7 +1340,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "876e1d2b",
+   "id": "66df0f80",
    "metadata": {
     "editable": true
    },
@@ -1539,7 +1352,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "67381fd3",
+   "id": "9f02b845",
    "metadata": {
     "editable": true
    },
@@ -1553,7 +1366,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f08ec530",
+   "id": "21997f1a",
    "metadata": {
     "editable": true
    },
@@ -1565,7 +1378,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3d99c5ee",
+   "id": "cdefe165",
    "metadata": {
     "editable": true
    },
@@ -1575,7 +1388,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "03ecb7f9",
+   "id": "ac200d56",
    "metadata": {
     "editable": true
    },
@@ -1587,7 +1400,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a6db0c6c",
+   "id": "eb3edfb3",
    "metadata": {
     "editable": true
    },
@@ -1607,7 +1420,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "167f76aa",
+   "id": "7fe05c0d",
    "metadata": {
     "editable": true
    },
@@ -1620,7 +1433,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d8d5cb23",
+   "id": "2ae403f1",
    "metadata": {
     "editable": true
    },
@@ -1632,7 +1445,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e127c141",
+   "id": "44272171",
    "metadata": {
     "editable": true
    },
@@ -1649,7 +1462,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7ea2c03c",
+   "id": "9cde29ef",
    "metadata": {
     "editable": true
    },
@@ -1661,7 +1474,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e2e33c54",
+   "id": "9b77f20e",
    "metadata": {
     "editable": true
    },
@@ -1690,7 +1503,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "88f943e6",
+   "id": "4479bd97",
    "metadata": {
     "editable": true
    },
@@ -1723,7 +1536,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aa4a8927",
+   "id": "31ea65c9",
    "metadata": {
     "editable": true
    },
@@ -1781,7 +1594,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "72d0192b",
+   "id": "3f3fe4c4",
    "metadata": {
     "editable": true
    },
@@ -1806,7 +1619,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "44fcd423",
+   "id": "69d08c69",
    "metadata": {
     "editable": true
    },
@@ -1832,7 +1645,7 @@
   },
   {
    "cell_type": "markdown",
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@@ -2008,7 +1821,7 @@
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@@ -2020,7 +1833,7 @@
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@@ -2032,7 +1845,7 @@
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@@ -2065,7 +1878,7 @@
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@@ -2077,7 +1890,7 @@
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@@ -2121,7 +1934,7 @@
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@@ -2133,7 +1946,7 @@
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@@ -2150,7 +1963,7 @@
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@@ -2166,7 +1979,7 @@
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@@ -2206,7 +2019,7 @@
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@@ -2226,7 +2039,7 @@
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@@ -2240,7 +2053,7 @@
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@@ -2252,7 +2065,7 @@
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@@ -2264,7 +2077,7 @@
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@@ -2276,7 +2089,7 @@
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@@ -2288,7 +2101,7 @@
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@@ -2299,7 +2112,7 @@
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@@ -2311,7 +2124,7 @@
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@@ -2325,7 +2138,7 @@
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@@ -2336,7 +2149,7 @@
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@@ -2348,7 +2161,7 @@
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@@ -2370,7 +2183,7 @@
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@@ -2394,7 +2207,7 @@
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@@ -2410,7 +2223,7 @@
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@@ -2426,7 +2239,7 @@
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@@ -2440,7 +2253,7 @@
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@@ -2458,7 +2271,7 @@
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@@ -2479,13 +2292,10 @@
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@@ -2542,7 +2352,7 @@
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@@ -2553,13 +2363,10 @@
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@@ -2620,7 +2427,7 @@
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@@ -2635,13 +2442,10 @@
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@@ -2733,13 +2537,10 @@
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@@ -2827,13 +2628,10 @@
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@@ -3553,7 +3336,7 @@
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@@ -3563,7 +3346,7 @@
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@@ -3575,7 +3358,7 @@
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@@ -3585,7 +3368,7 @@
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@@ -3597,7 +3380,7 @@
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@@ -3609,7 +3392,7 @@
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@@ -3621,7 +3404,7 @@
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@@ -3631,7 +3414,7 @@
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@@ -3643,7 +3426,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9627e6fb",
+   "id": "11dd1361",
    "metadata": {
     "editable": true
    },
@@ -3656,7 +3439,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "662fe97e",
+   "id": "f6a52f34",
    "metadata": {
     "editable": true
    },
@@ -3668,7 +3451,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fa2d5cb5",
+   "id": "9d6807dc",
    "metadata": {
     "editable": true
    },
@@ -3682,13 +3465,10 @@
   {
    "cell_type": "code",
    "execution_count": 19,
-   "id": "a530b3ba",
+   "id": "2ed0cafc",
    "metadata": {
     "collapsed": false,
-    "editable": true,
-    "jupyter": {
-     "outputs_hidden": false
-    }
+    "editable": true
    },
    "outputs": [],
    "source": [
@@ -3782,7 +3562,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58cc6d9d",
+   "id": "f72dbb49",
    "metadata": {
     "editable": true
    },
@@ -3803,7 +3583,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a2d3f87",
+   "id": "b7759b1f",
    "metadata": {
     "editable": true
    },
@@ -3815,7 +3595,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9eab78a9",
+   "id": "ba0ecd6e",
    "metadata": {
     "editable": true
    },
@@ -3825,7 +3605,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50d7f5c3",
+   "id": "ae897f1e",
    "metadata": {
     "editable": true
    },
@@ -3837,7 +3617,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4c96e589",
+   "id": "f9c41f7f",
    "metadata": {
     "editable": true
    },
@@ -3847,7 +3627,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b57830ea",
+   "id": "fa013cc4",
    "metadata": {
     "editable": true
    },
@@ -3859,7 +3639,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "05325bc6",
+   "id": "0c9b24be",
    "metadata": {
     "editable": true
    },
@@ -3877,13 +3657,10 @@
   {
    "cell_type": "code",
    "execution_count": 20,
-   "id": "d95b15bc",
+   "id": "4f9b1fa0",
    "metadata": {
     "collapsed": false,
-    "editable": true,
-    "jupyter": {
-     "outputs_hidden": false
-    }
+    "editable": true
    },
    "outputs": [],
    "source": [
@@ -3956,7 +3733,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b88ebede",
+   "id": "1aa5ca37",
    "metadata": {
     "editable": true
    },
@@ -3970,13 +3747,10 @@
   {
    "cell_type": "code",
    "execution_count": 21,
-   "id": "47036b16",
+   "id": "a731e32c",
    "metadata": {
     "collapsed": false,
-    "editable": true,
-    "jupyter": {
-     "outputs_hidden": false
-    }
+    "editable": true
    },
    "outputs": [],
    "source": [
@@ -4062,7 +3836,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52faee2f",
+   "id": "6ea197d8",
    "metadata": {
     "editable": true
    },
@@ -4076,25 +3850,7 @@
    ]
   }
  ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.9.15"
-  }
- },
+ "metadata": {},
  "nbformat": 4,
  "nbformat_minor": 5
 }
diff --git a/doc/src/week37/week37.do.txt b/doc/src/week37/week37.do.txt
index 4b2a9c628..fec74292d 100644
--- a/doc/src/week37/week37.do.txt
+++ b/doc/src/week37/week37.do.txt
@@ -15,9 +15,11 @@ o Plain gradient descent (constant learning rate), reminder from last week with
 o Improving gradient descent with momentum
 o Introducing stochastic gradient descent
 o More advanced updates of the learning rate: ADAgrad, RMSprop and ADAM
-#   * "Video of Lecture":"https://youtu.be/omLmp_kkie0"
-#   * "Whiteboard notes":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesSeptember9.pdf"
+o "Video of Lecture":"https://youtu.be/SuxK68tj-V8"
+o "Whiteboard notes":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek37.pdf"
 !eblock
+
+
 !split
 ===== Readings and Videos: ===== 
 !bblock