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Oslo, Norway\n", "\n", - "Date: **October 28-November 1 **" + "Date: **October 28**" ] }, { "cell_type": "markdown", - "id": "cc149251", + "id": "3d29f8f9", "metadata": { "editable": true }, @@ -44,18 +44,22 @@ "\n", " * For a more in depth discussion on neural networks we recommend Goodfellow et al chapter 9. See also chapter 11 and 12 on practicalities and applications\n", "\n", - " * Reading suggestions for implementation of CNNs see :\"https://github.com/rasbt/machine-learning-book/tree/main/ch14\". \n", + " * Reading suggestions for implementation of CNNs see Rashcka et al.'s chapter 14 at . \n", "\n", " * Video on Deep Learning at \n", "\n", " * Video on Convolutional Neural Networks from MIT at \n", "\n", - " * Video on CNNs from Stanford at " + " * Video on CNNs from Stanford at \n", + "\n", + " * Video of lecture October 28 at \n", + "\n", + " * Whiteboard notes at " ] }, { "cell_type": "markdown", - "id": "cb91fe3f", + "id": "34fc94b3", "metadata": { "editable": true }, @@ -64,14 +68,12 @@ "\n", "* Main focus is discussion of and work on project 2\n", "\n", - "* If you did not get time to finish the exercises from week 43, you can also keep working on them and hand in this coming Friday\n", - "\n", - "" + "* If you did not get time to finish the exercises from week 43, you can also keep working on them and hand in this coming Friday" ] }, { "cell_type": "markdown", - "id": "a4b9ec87", + "id": "3239c466", "metadata": { "editable": true }, @@ -81,7 +83,7 @@ }, { "cell_type": "markdown", - "id": "be0fb3b3", + "id": "79352c78", "metadata": { "editable": true }, @@ -108,7 +110,7 @@ }, { "cell_type": "markdown", - "id": "dca41cde", + "id": "bd4b7c7a", "metadata": { "editable": true }, @@ -124,7 +126,7 @@ }, { "cell_type": "markdown", - "id": "7105a270", + "id": "cc1736b4", "metadata": { "editable": true }, @@ -142,7 +144,7 @@ }, { "cell_type": "markdown", - "id": "4ace549e", + "id": "70bf2bf1", "metadata": { "editable": true }, @@ -172,7 +174,7 @@ }, { "cell_type": "markdown", - "id": "da0cb6c8", + "id": "3a7dca56", "metadata": { "editable": true }, @@ -202,7 +204,7 @@ }, { "cell_type": "markdown", - "id": "5b622758", + "id": "de304dc3", "metadata": { "editable": true }, @@ -242,7 +244,7 @@ }, { "cell_type": "markdown", - "id": "29c5c182", + "id": "91bb5b86", "metadata": { "editable": true }, @@ -269,7 +271,7 @@ }, { "cell_type": "markdown", - "id": "fceb2409", + "id": "413cf44d", "metadata": { "editable": true }, @@ -281,7 +283,7 @@ }, { "cell_type": "markdown", - "id": "36313c49", + "id": "adda54b9", "metadata": { "editable": true }, @@ -291,7 +293,7 @@ }, { "cell_type": "markdown", - "id": "81b9cf02", + "id": "4507a4f9", "metadata": { "editable": true }, @@ -309,7 +311,7 @@ }, { "cell_type": "markdown", - "id": "7d7c1544", + "id": "148bc604", "metadata": { "editable": true }, @@ -338,7 +340,7 @@ }, { "cell_type": "markdown", - "id": "28fa62d6", + "id": "2cc27405", "metadata": { "editable": true }, @@ -360,7 +362,7 @@ }, { "cell_type": "markdown", - "id": "efa30734", + "id": "f76305aa", "metadata": { "editable": true }, @@ -382,7 +384,7 @@ }, { "cell_type": "markdown", - "id": "9a435714", + "id": "4411a90d", "metadata": { "editable": true }, @@ -398,7 +400,7 @@ }, { "cell_type": "markdown", - "id": "aed2d756", + "id": "b3d0dbca", "metadata": { "editable": true }, @@ -415,7 +417,7 @@ }, { "cell_type": "markdown", - "id": "68e1ac1b", + "id": "a09c0720", "metadata": { "editable": true }, @@ -439,7 +441,7 @@ }, { "cell_type": "markdown", - "id": "866c9fc7", + "id": "48da38d8", "metadata": { "editable": true }, @@ -450,7 +452,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "3809b7f8", + "id": "762be0c3", "metadata": { "collapsed": false, "editable": true @@ -521,7 +523,7 @@ }, { "cell_type": "markdown", - "id": "2d46cd2c", + "id": "9e557414", "metadata": { "editable": true }, @@ -544,7 +546,7 @@ }, { "cell_type": "markdown", - "id": "b2b7cf91", + "id": "2fa21082", "metadata": { "editable": true }, @@ -556,7 +558,7 @@ }, { "cell_type": "markdown", - "id": "d7e0ed27", + "id": "78091a35", "metadata": { "editable": true }, @@ -568,7 +570,7 @@ }, { "cell_type": "markdown", - "id": "f5780c89", + "id": "ba4e1957", "metadata": { "editable": true }, @@ -580,7 +582,7 @@ }, { "cell_type": "markdown", - "id": "e7a0f90c", + "id": "1a7d9e0f", "metadata": { "editable": true }, @@ -590,7 +592,7 @@ }, { "cell_type": "markdown", - "id": "1819294d", + "id": "d2be6986", "metadata": { "editable": true }, @@ -602,7 +604,7 @@ }, { "cell_type": "markdown", - "id": "b1140da6", + "id": "c89576c7", "metadata": { "editable": true }, @@ -614,100 +616,7 @@ }, { "cell_type": "markdown", - "id": "a6e6e69a", - "metadata": { - "editable": true - }, - "source": [ - "## Mathematics of CNNs\n", - "\n", - "The mathematics of CNNs is based on the mathematical operation of\n", - "**convolution**. In mathematics (in particular in functional analysis),\n", - "convolution is represented by mathematical operations (integration,\n", - "summation etc) on two functions in order to produce a third function\n", - "that expresses how the shape of one gets modified by the other.\n", - "Convolution has a plethora of applications in a variety of\n", - "disciplines, spanning from statistics to signal processing, computer\n", - "vision, solutions of differential equations,linear algebra,\n", - "engineering, and yes, machine learning.\n", - "\n", - "Mathematically, convolution is defined as follows (one-dimensional example):\n", - "Let us define a continuous function $y(t)$ given by" - ] - }, - { - "cell_type": "markdown", - "id": "b6566857", - "metadata": { - "editable": true - }, - "source": [ - "$$\n", - "y(t) = \\int x(a) w(t-a) da,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "id": "d287ce8e", - "metadata": { - "editable": true - }, - "source": [ - "where $x(a)$ represents a so-called input and $w(t-a)$ is normally called the weight function or kernel.\n", - "\n", - "The above integral is written in a more compact form as" - ] - }, - { - "cell_type": "markdown", - "id": "688b3c77", - "metadata": { - "editable": true - }, - "source": [ - "$$\n", - "y(t) = \\left(x * w\\right)(t).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "id": "839e96f3", - "metadata": { - "editable": true - }, - "source": [ - "The discretized version reads" - ] - }, - { - "cell_type": "markdown", - "id": "71855a8f", - "metadata": { - "editable": true - }, - "source": [ - "$$\n", - "y(t) = \\sum_{a=-\\infty}^{a=\\infty}x(a)w(t-a).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "id": "b4949f55", - "metadata": { - "editable": true - }, - "source": [ - "Computing the inverse of the above convolution operations is known as deconvolution and the process is commutative.\n", - "\n", - "How can we use this? And what does it mean? Let us study some familiar examples first." - ] - }, - { - "cell_type": "markdown", - "id": "3390b6b3", + "id": "982931d8", "metadata": { "editable": true }, @@ -726,7 +635,7 @@ }, { "cell_type": "markdown", - "id": "8b13b77d", + "id": "cead60e0", "metadata": { "editable": true }, @@ -738,7 +647,7 @@ }, { "cell_type": "markdown", - "id": "0a8f0215", + "id": "d1986b13", "metadata": { "editable": true }, @@ -748,7 +657,7 @@ }, { "cell_type": "markdown", - "id": "f71bd497", + "id": "1a2d79b8", "metadata": { "editable": true }, @@ -760,7 +669,7 @@ }, { "cell_type": "markdown", - "id": "347bcaf2", + "id": "46e743d4", "metadata": { "editable": true }, @@ -770,7 +679,7 @@ }, { "cell_type": "markdown", - "id": "e381d21e", + "id": "7342bf69", "metadata": { "editable": true }, @@ -782,7 +691,7 @@ }, { "cell_type": "markdown", - "id": "9c6b7be9", + "id": "d1efa756", "metadata": { "editable": true }, @@ -795,7 +704,7 @@ }, { "cell_type": "markdown", - "id": "5e776582", + "id": "2ca3e8f6", "metadata": { "editable": true }, @@ -814,7 +723,7 @@ }, { "cell_type": "markdown", - "id": "0f4ccfff", + "id": "3b52d4e1", "metadata": { "editable": true }, @@ -826,7 +735,7 @@ }, { "cell_type": "markdown", - "id": "4e37b9b5", + "id": "30a7affc", "metadata": { "editable": true }, @@ -838,7 +747,7 @@ }, { "cell_type": "markdown", - "id": "4bc06433", + "id": "58b6c025", "metadata": { "editable": true }, @@ -848,7 +757,7 @@ }, { "cell_type": "markdown", - "id": "23989fd4", + "id": "3212b62b", "metadata": { "editable": true }, @@ -860,7 +769,7 @@ }, { "cell_type": "markdown", - "id": "724837cb", + "id": "9b4093fe", "metadata": { "editable": true }, @@ -872,7 +781,7 @@ }, { "cell_type": "markdown", - "id": "b6cb72c3", + "id": "f887571e", "metadata": { "editable": true }, @@ -884,7 +793,7 @@ }, { "cell_type": "markdown", - "id": "33e4a7dc", + "id": "3c52aecb", "metadata": { "editable": true }, @@ -895,7 +804,7 @@ }, { "cell_type": "markdown", - "id": "85138b80", + "id": "c2ca7d94", "metadata": { "editable": true }, @@ -909,7 +818,7 @@ }, { "cell_type": "markdown", - "id": "a13e9010", + "id": "d0814379", "metadata": { "editable": true }, @@ -927,7 +836,7 @@ }, { "cell_type": "markdown", - "id": "fa3caefc", + "id": "37aa2860", "metadata": { "editable": true }, @@ -940,7 +849,7 @@ }, { "cell_type": "markdown", - "id": "172a8a08", + "id": "9634d093", "metadata": { "editable": true }, @@ -958,7 +867,7 @@ }, { "cell_type": "markdown", - "id": "4ac06a92", + "id": "29991f53", "metadata": { "editable": true }, @@ -972,7 +881,7 @@ }, { "cell_type": "markdown", - "id": "0616100a", + "id": "a4c5c132", "metadata": { "editable": true }, @@ -988,7 +897,7 @@ }, { "cell_type": "markdown", - "id": "cecd64c6", + "id": "23bbc731", "metadata": { "editable": true }, @@ -1006,7 +915,7 @@ }, { "cell_type": "markdown", - "id": "31eecb48", + "id": "a8be6a8f", "metadata": { "editable": true }, @@ -1022,7 +931,7 @@ }, { "cell_type": "markdown", - "id": "216deb07", + "id": "b1f6dde3", "metadata": { "editable": true }, @@ -1037,7 +946,7 @@ }, { "cell_type": "markdown", - "id": "7c493c62", + "id": "52d1e6d0", "metadata": { "editable": true }, @@ -1056,7 +965,7 @@ }, { "cell_type": "markdown", - "id": "00c500fa", + "id": "5dd784d6", "metadata": { "editable": true }, @@ -1068,7 +977,7 @@ }, { "cell_type": "markdown", - "id": "9e6ef884", + "id": "50cd21e3", "metadata": { "editable": true }, @@ -1079,7 +988,7 @@ }, { "cell_type": "markdown", - "id": "ae753e43", + "id": "5631b73a", "metadata": { "editable": true }, @@ -1100,7 +1009,7 @@ }, { "cell_type": "markdown", - "id": "338765ee", + "id": "4cbbda23", "metadata": { "editable": true }, @@ -1116,7 +1025,7 @@ }, { "cell_type": "markdown", - "id": "134b1339", + "id": "1d55097f", "metadata": { "editable": true }, @@ -1134,7 +1043,7 @@ }, { "cell_type": "markdown", - "id": "88a54d0b", + "id": "21812778", "metadata": { "editable": true }, @@ -1146,7 +1055,7 @@ }, { "cell_type": "markdown", - "id": "c08db532", + "id": "ab3720f7", "metadata": { "editable": true }, @@ -1156,7 +1065,7 @@ }, { "cell_type": "markdown", - "id": "5abec963", + "id": "1e1dd46d", "metadata": { "editable": true }, @@ -1168,7 +1077,7 @@ }, { "cell_type": "markdown", - "id": "8443ca56", + "id": "1f73e566", "metadata": { "editable": true }, @@ -1180,7 +1089,7 @@ }, { "cell_type": "markdown", - "id": "fb5ccd85", + "id": "00b9b1d2", "metadata": { "editable": true }, @@ -1192,7 +1101,7 @@ }, { "cell_type": "markdown", - "id": "b6672462", + "id": "b27a9b22", "metadata": { "editable": true }, @@ -1202,7 +1111,7 @@ }, { "cell_type": "markdown", - "id": "f32a4c6c", + "id": "f5e818df", "metadata": { "editable": true }, @@ -1214,7 +1123,7 @@ }, { "cell_type": "markdown", - "id": "8c6e4830", + "id": "5d40e9b7", "metadata": { "editable": true }, @@ -1226,7 +1135,7 @@ }, { "cell_type": "markdown", - "id": "050ee2b1", + "id": "a2488003", "metadata": { "editable": true }, @@ -1238,7 +1147,7 @@ }, { "cell_type": "markdown", - "id": "66b7b033", + "id": "f3424a4a", "metadata": { "editable": true }, @@ -1254,7 +1163,7 @@ }, { "cell_type": "markdown", - "id": "ed3176b2", + "id": "b8ec7a35", "metadata": { "editable": true }, @@ -1267,7 +1176,7 @@ }, { "cell_type": "markdown", - "id": "88a97f5d", + "id": "0e2c28ae", "metadata": { "editable": true }, @@ -1279,7 +1188,7 @@ }, { "cell_type": "markdown", - "id": "4a509c92", + "id": "9eb2d76b", "metadata": { "editable": true }, @@ -1289,7 +1198,7 @@ }, { "cell_type": "markdown", - "id": "4ba88953", + "id": "f17d4c03", "metadata": { "editable": true }, @@ -1301,7 +1210,7 @@ }, { "cell_type": "markdown", - "id": "4dc3fee8", + "id": "027e2d72", "metadata": { "editable": true }, @@ -1316,7 +1225,7 @@ }, { "cell_type": "markdown", - "id": "5cc81f97", + "id": "88be64cf", "metadata": { "editable": true }, @@ -1331,7 +1240,7 @@ }, { "cell_type": "markdown", - "id": "851d4c45", + "id": "d297ed25", "metadata": { "editable": true }, @@ -1343,7 +1252,7 @@ }, { "cell_type": "markdown", - "id": "b261ea99", + "id": "de288b76", "metadata": { "editable": true }, @@ -1353,7 +1262,7 @@ }, { "cell_type": "markdown", - "id": "ea27a3c6", + "id": "2aaea6bf", "metadata": { "editable": true }, @@ -1365,7 +1274,7 @@ }, { "cell_type": "markdown", - "id": "83c0c6a0", + "id": "00d4208e", "metadata": { "editable": true }, @@ -1381,7 +1290,7 @@ }, { "cell_type": "markdown", - "id": "dc0b2072", + "id": "96af754f", "metadata": { "editable": true }, @@ -1393,7 +1302,7 @@ }, { "cell_type": "markdown", - "id": "fde836e1", + "id": "21b0c1e8", "metadata": { "editable": true }, @@ -1406,7 +1315,7 @@ }, { "cell_type": "markdown", - "id": "a070285d", + "id": "be785720", "metadata": { "editable": true }, @@ -1420,7 +1329,7 @@ }, { "cell_type": "markdown", - "id": "bf6e590b", + "id": "b7058d94", "metadata": { "editable": true }, @@ -1430,7 +1339,7 @@ }, { "cell_type": "markdown", - "id": "3d3965b6", + "id": "b88a0094", "metadata": { "editable": true }, @@ -1443,7 +1352,7 @@ }, { "cell_type": "markdown", - "id": "cd0d4353", + "id": "5e4e20bc", "metadata": { "editable": true }, @@ -1458,7 +1367,7 @@ }, { "cell_type": "markdown", - "id": "eb62911e", + "id": "d75708bf", "metadata": { "editable": true }, @@ -1470,7 +1379,7 @@ }, { "cell_type": "markdown", - "id": "fdb87605", + "id": "a905172f", "metadata": { "editable": true }, @@ -1480,7 +1389,7 @@ }, { "cell_type": "markdown", - "id": "702d1de3", + "id": "1cae567c", "metadata": { "editable": true }, @@ -1493,7 +1402,7 @@ }, { "cell_type": "markdown", - "id": "46f9ffd9", + "id": "8fd08506", "metadata": { "editable": true }, @@ -1504,7 +1413,7 @@ }, { "cell_type": "markdown", - "id": "54240b13", + "id": "5eb78b07", "metadata": { "editable": true }, @@ -1516,7 +1425,7 @@ }, { "cell_type": "markdown", - "id": "c3cc19f1", + "id": "96796312", "metadata": { "editable": true }, @@ -1526,7 +1435,7 @@ }, { "cell_type": "markdown", - "id": "8fd26ae6", + "id": "10c03ac1", "metadata": { "editable": true }, @@ -1541,7 +1450,7 @@ }, { "cell_type": "markdown", - "id": "907b64ed", + "id": "fcd5c905", "metadata": { "editable": true }, @@ -1551,7 +1460,7 @@ }, { "cell_type": "markdown", - "id": "ea24309a", + "id": "04f7219c", "metadata": { "editable": true }, @@ -1563,7 +1472,7 @@ }, { "cell_type": "markdown", - "id": "9d331112", + "id": "9ee70da3", "metadata": { "editable": true }, @@ -1573,7 +1482,7 @@ }, { "cell_type": "markdown", - "id": "da875dab", + "id": "32bf0b36", "metadata": { "editable": true }, @@ -1589,7 +1498,7 @@ }, { "cell_type": "markdown", - "id": "628f45dd", + "id": "bd9f1937", "metadata": { "editable": true }, @@ -1617,7 +1526,7 @@ }, { "cell_type": "markdown", - "id": "9cd55f79", + "id": "47cafbf5", "metadata": { "editable": true }, @@ -1633,7 +1542,7 @@ }, { "cell_type": "markdown", - "id": "5f94b9d4", + "id": "cf5c61df", "metadata": { "editable": true }, @@ -1645,7 +1554,7 @@ }, { "cell_type": "markdown", - "id": "0a3b9e01", + "id": "c22d0618", "metadata": { "editable": true }, @@ -1657,7 +1566,7 @@ }, { "cell_type": "markdown", - "id": "8764ddc0", + "id": "910ce75f", "metadata": { "editable": true }, @@ -1667,7 +1576,7 @@ }, { "cell_type": "markdown", - "id": "d30b4ff0", + "id": "0615df08", "metadata": { "editable": true }, @@ -1681,7 +1590,7 @@ }, { "cell_type": "markdown", - "id": "7e5eafdb", + "id": "452f4413", "metadata": { "editable": true }, @@ -1693,7 +1602,7 @@ }, { "cell_type": "markdown", - "id": "390faa33", + "id": "cb97c13e", "metadata": { "editable": true }, @@ -1715,7 +1624,7 @@ }, { "cell_type": "markdown", - "id": "11f478e0", + "id": "3425f9b9", "metadata": { "editable": true }, @@ -1747,7 +1656,7 @@ }, { "cell_type": "markdown", - "id": "68226a92", + "id": "9659e588", "metadata": { "editable": true }, @@ -1763,7 +1672,7 @@ }, { "cell_type": "markdown", - "id": "ba4397fc", + "id": "696da180", "metadata": { "editable": true }, @@ -1783,7 +1692,7 @@ }, { "cell_type": "markdown", - "id": "c04e04d6", + "id": "f62d8385", "metadata": { "editable": true }, @@ -1800,7 +1709,7 @@ }, { "cell_type": "markdown", - "id": "cf546e23", + "id": "da48ec69", "metadata": { "editable": true }, @@ -1816,7 +1725,7 @@ }, { "cell_type": "markdown", - "id": "b65107c4", + "id": "82697e96", "metadata": { "editable": true }, @@ -1835,7 +1744,7 @@ }, { "cell_type": "markdown", - "id": "41864fb7", + "id": "603caa07", "metadata": { "editable": true }, @@ -1848,7 +1757,7 @@ }, { "cell_type": "markdown", - "id": "4eebcdb7", + "id": "a15c5a6f", "metadata": { "editable": true }, @@ -1860,7 +1769,7 @@ }, { "cell_type": "markdown", - "id": "7a5e62e4", + "id": "dbffa234", "metadata": { "editable": true }, @@ -1881,7 +1790,7 @@ }, { "cell_type": "markdown", - "id": "c7238366", + "id": "c08597db", "metadata": { "editable": true }, @@ -1902,7 +1811,7 @@ }, { "cell_type": "markdown", - "id": "0b97aeeb", + "id": "36ead32a", "metadata": { "editable": true }, @@ -1928,7 +1837,7 @@ }, { "cell_type": "markdown", - "id": "3fd6f59e", + "id": "76a692c3", "metadata": { "editable": true }, @@ -1947,7 +1856,7 @@ }, { "cell_type": "markdown", - "id": "0172461a", + "id": "177759f2", "metadata": { "editable": true }, @@ -1958,7 +1867,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "327406f1", + "id": "f4f578f8", "metadata": { "collapsed": false, "editable": true @@ -2009,7 +1918,7 @@ }, { "cell_type": "markdown", - "id": "21cd0cbc", + "id": "6fd14013", "metadata": { "editable": true }, @@ -2020,7 +1929,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "0acee68a", + "id": "bea60977", "metadata": { "collapsed": false, "editable": true @@ -2053,7 +1962,7 @@ }, { "cell_type": "markdown", - "id": "e02f61a7", + "id": "849c5abf", "metadata": { "editable": true }, @@ -2064,7 +1973,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "91574522", + "id": "f6cf91b0", "metadata": { "collapsed": false, "editable": true @@ -2101,7 +2010,7 @@ }, { "cell_type": "markdown", - "id": "4176bd54", + "id": "1762e77d", "metadata": { "editable": true }, @@ -2112,7 +2021,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "ec107763", + "id": "85cb8818", "metadata": { "collapsed": false, "editable": true @@ -2139,7 +2048,7 @@ }, { "cell_type": "markdown", - "id": "72b0127c", + "id": "7cad90f7", "metadata": { "editable": true }, @@ -2150,7 +2059,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "99644dc7", + "id": "526e2167", "metadata": { "collapsed": false, "editable": true @@ -2191,7 +2100,7 @@ }, { "cell_type": "markdown", - "id": "1c309dbb", + "id": "3676714e", "metadata": { "editable": true }, @@ -2207,7 +2116,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "6a35ed0c", + "id": "ddec0620", "metadata": { "collapsed": false, "editable": true @@ -2228,7 +2137,7 @@ }, { "cell_type": "markdown", - "id": "b150d131", + "id": "68c162f4", "metadata": { "editable": true }, @@ -2241,7 +2150,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "96a7b1f0", + "id": "af8654a4", "metadata": { "collapsed": false, "editable": true @@ -2265,7 +2174,7 @@ }, { "cell_type": "markdown", - "id": "b6ad06dc", + "id": "1038efea", "metadata": { "editable": true }, @@ -2280,7 +2189,7 @@ { "cell_type": "code", "execution_count": 9, - "id": "0d9a9552", + "id": "6a377cfd", "metadata": { "collapsed": false, "editable": true @@ -2301,7 +2210,7 @@ }, { "cell_type": "markdown", - "id": "c4304aa4", + "id": "22897193", "metadata": { "editable": true }, @@ -2311,7 +2220,7 @@ }, { "cell_type": "markdown", - "id": "180db190", + "id": "30ef3e7c", "metadata": { "editable": true }, @@ -2330,7 +2239,7 @@ { "cell_type": "code", "execution_count": 10, - "id": "8f52da8c", + "id": "349e7619", "metadata": { "collapsed": false, "editable": true @@ -2347,7 +2256,7 @@ }, { "cell_type": "markdown", - "id": "c5497eff", + "id": "3d8d954b", "metadata": { "editable": true }, @@ -2357,7 +2266,7 @@ }, { "cell_type": "markdown", - "id": "4ba34f8d", + "id": "7f0847a8", "metadata": { "editable": true }, @@ -2368,7 +2277,7 @@ { "cell_type": "code", "execution_count": 11, - "id": "d2e64017", + "id": "783f6194", "metadata": { "collapsed": false, "editable": true @@ -2385,7 +2294,7 @@ }, { "cell_type": "markdown", - "id": "00059fe8", + "id": "0e1cce97", "metadata": { "editable": true }, @@ -2396,7 +2305,7 @@ { "cell_type": "code", "execution_count": 12, - "id": "4a1f365f", + "id": "7d87be54", "metadata": { "collapsed": false, "editable": true @@ -2417,7 +2326,7 @@ }, { "cell_type": "markdown", - "id": "aaba024a", + "id": "5287a9fb", "metadata": { "editable": true }, @@ -2450,7 +2359,7 @@ }, { "cell_type": "markdown", - "id": "764fc43e", + "id": "5376c8cd", "metadata": { "editable": true }, @@ -2474,7 +2383,7 @@ }, { "cell_type": "markdown", - "id": "a16e632d", + "id": "8cf0b8dc", "metadata": { "editable": true }, @@ -2497,7 +2406,7 @@ { "cell_type": "code", "execution_count": 13, - "id": "1deab9eb", + "id": "f2619dd7", "metadata": { "collapsed": false, "editable": true @@ -2638,7 +2547,7 @@ }, { "cell_type": "markdown", - "id": "1bf4b5e1", + "id": "04f25816", "metadata": { "editable": true }, @@ -2651,7 +2560,7 @@ { "cell_type": "code", "execution_count": 14, - "id": "4ccdf2fd", + "id": "9afe39a2", "metadata": { "collapsed": false, "editable": true @@ -2664,7 +2573,7 @@ }, { "cell_type": "markdown", - "id": "318c8ba3", + "id": "3e912906", "metadata": { "editable": true }, @@ -2675,7 +2584,7 @@ { "cell_type": "code", "execution_count": 15, - "id": "3e05068e", + "id": "aa146e1b", "metadata": { "collapsed": false, "editable": true @@ -2697,7 +2606,7 @@ }, { "cell_type": "markdown", - "id": "0fdd8790", + "id": "fba31aff", "metadata": { "editable": true }, @@ -2713,7 +2622,7 @@ { "cell_type": "code", "execution_count": 16, - "id": "4d30014d", + "id": "abdcad5a", "metadata": { "collapsed": false, "editable": true @@ -2760,7 +2669,7 @@ }, { "cell_type": "markdown", - "id": "3303262d", + "id": "894970b1", "metadata": { "editable": true }, @@ -2775,7 +2684,7 @@ { "cell_type": "code", "execution_count": 17, - "id": "4328896b", + "id": "6a778d9d", "metadata": { "collapsed": false, "editable": true @@ -2796,7 +2705,7 @@ }, { "cell_type": "markdown", - "id": "9ff7fd7a", + "id": "4fd0dfdb", "metadata": { "editable": true }, @@ -2813,7 +2722,7 @@ { "cell_type": "code", "execution_count": 18, - "id": "f44c1e1d", + "id": "53d2e40d", "metadata": { "collapsed": false, "editable": true @@ -2872,7 +2781,7 @@ }, { "cell_type": "markdown", - "id": "2f6650d0", + "id": "09771b87", "metadata": { "editable": true }, @@ -2889,7 +2798,7 @@ { "cell_type": "code", "execution_count": 19, - "id": "d50993c9", + "id": "08f622fa", "metadata": { "collapsed": false, "editable": true @@ -2910,7 +2819,7 @@ }, { "cell_type": "markdown", - "id": "a712dc3c", + "id": "81c7eaef", "metadata": { "editable": true }, @@ -2927,7 +2836,7 @@ }, { "cell_type": "markdown", - "id": "632866a9", + "id": "0998392d", "metadata": { "editable": true }, @@ -2939,7 +2848,7 @@ }, { "cell_type": "markdown", - "id": "fb33615f", + "id": "147961a0", "metadata": { "editable": true }, @@ -2955,7 +2864,7 @@ }, { "cell_type": "markdown", - "id": "c150b10d", + "id": "f67f1f6d", "metadata": { "editable": true }, @@ -2967,7 +2876,7 @@ }, { "cell_type": "markdown", - "id": "29b9caee", + "id": "dec83f81", "metadata": { "editable": true }, @@ -2982,7 +2891,7 @@ }, { "cell_type": "markdown", - "id": "8b512529", + "id": "5a5b1e07", "metadata": { "editable": true }, @@ -2994,7 +2903,7 @@ }, { "cell_type": "markdown", - "id": "3c6f0bc9", + "id": "7c27a0fe", "metadata": { "editable": true }, @@ -3012,7 +2921,7 @@ }, { "cell_type": "markdown", - "id": "6be766c2", + "id": "4c81a107", "metadata": { "editable": true }, @@ -3031,7 +2940,7 @@ }, { "cell_type": "markdown", - "id": "30872978", + "id": "24228635", "metadata": { "editable": true }, @@ -3043,7 +2952,7 @@ }, { "cell_type": "markdown", - "id": "dab55864", + "id": "89692cf6", "metadata": { "editable": true }, @@ -3060,7 +2969,7 @@ }, { "cell_type": "markdown", - "id": "59009d4e", + "id": "0ecfdafa", "metadata": { "editable": true }, @@ -3073,7 +2982,7 @@ }, { "cell_type": "markdown", - "id": "cfd71d57", + "id": "33c6332e", "metadata": { "editable": true }, @@ -3102,7 +3011,7 @@ }, { "cell_type": "markdown", - "id": "254de1f6", + "id": "a573879c", "metadata": { "editable": true }, @@ -3112,7 +3021,7 @@ }, { "cell_type": "markdown", - "id": "277ad313", + "id": "e515a3e4", "metadata": { "editable": true }, @@ -3124,7 +3033,7 @@ }, { "cell_type": "markdown", - "id": "4408da81", + "id": "e53c0a21", "metadata": { "editable": true }, @@ -3145,7 +3054,7 @@ }, { "cell_type": "markdown", - "id": "97f368a4", + "id": "aee15740", "metadata": { "editable": true }, @@ -3163,7 +3072,7 @@ }, { "cell_type": "markdown", - "id": "2157445c", + "id": "2ed1f60a", "metadata": { "editable": true }, @@ -3179,7 +3088,7 @@ }, { "cell_type": "markdown", - "id": "1b823cf8", + "id": "9859970d", "metadata": { "editable": true }, @@ -3192,7 +3101,7 @@ }, { "cell_type": "markdown", - "id": "fcd68006", + "id": "128b4dc2", "metadata": { "editable": true }, @@ -3216,7 +3125,7 @@ }, { "cell_type": "markdown", - "id": "57d7a347", + "id": "c6fb6517", "metadata": { "editable": true }, @@ -3237,7 +3146,7 @@ }, { "cell_type": "markdown", - "id": "b76fc717", + "id": "b01d3014", "metadata": { "editable": true }, @@ -3250,7 +3159,7 @@ { "cell_type": "code", "execution_count": 20, - "id": "47bc5ad3", + "id": "67babc7b", "metadata": { "collapsed": false, "editable": true @@ -3332,7 +3241,7 @@ }, { "cell_type": "markdown", - "id": "435a988d", + "id": "406e9884", "metadata": { "editable": true }, @@ -3346,7 +3255,7 @@ { "cell_type": "code", "execution_count": 21, - "id": "2c04ebbf", + "id": "c9887d3f", "metadata": { "collapsed": false, "editable": true @@ -3373,7 +3282,7 @@ }, { "cell_type": "markdown", - "id": "66b71a9c", + "id": "239d497a", "metadata": { "editable": true }, @@ -3394,7 +3303,7 @@ { "cell_type": "code", "execution_count": 22, - "id": "d56d781d", + "id": "bf4ab84e", "metadata": { "collapsed": false, "editable": true @@ -3444,7 +3353,7 @@ }, { "cell_type": "markdown", - "id": "611f44ba", + "id": "4bf788aa", "metadata": { "editable": true }, @@ -3459,7 +3368,7 @@ { "cell_type": "code", "execution_count": 23, - "id": "2ab1f7fd", + "id": "6d3dca2d", "metadata": { "collapsed": false, "editable": true @@ -3500,7 +3409,7 @@ }, { "cell_type": "markdown", - "id": "edc50ddb", + "id": "0dacddbe", "metadata": { "editable": true }, @@ -3542,7 +3451,7 @@ { "cell_type": "code", "execution_count": 24, - "id": "154bca97", + "id": "17f9a3e4", "metadata": { "collapsed": false, "editable": true @@ -3828,7 +3737,7 @@ }, { "cell_type": "markdown", - "id": "fd97e246", + "id": "2ebd51a9", "metadata": { "editable": true }, @@ -3851,7 +3760,7 @@ }, { "cell_type": "markdown", - "id": "483ec09a", + "id": "6e37ad83", "metadata": { "editable": true }, @@ -3864,7 +3773,7 @@ { "cell_type": "code", "execution_count": 25, - "id": "34cc7cfe", + "id": "09290632", "metadata": { "collapsed": false, "editable": true @@ -3912,7 +3821,7 @@ }, { "cell_type": "markdown", - "id": "c7222d94", + "id": "111f84ed", "metadata": { "editable": true }, @@ -3934,7 +3843,7 @@ }, { "cell_type": "markdown", - "id": "379d2b61", + "id": "589e5822", "metadata": { "editable": true }, @@ -3956,7 +3865,7 @@ { "cell_type": "code", "execution_count": 26, - "id": "bbba88c5", + "id": "c9c28b65", "metadata": { "collapsed": false, "editable": true @@ -4118,7 +4027,7 @@ }, { "cell_type": "markdown", - "id": "5eb1543d", + "id": "1fcb9ea1", "metadata": { "editable": true }, @@ -4139,7 +4048,7 @@ { "cell_type": "code", "execution_count": 27, - "id": "16e0cbb4", + "id": "d8651caa", "metadata": { "collapsed": false, "editable": true @@ -4202,7 +4111,7 @@ }, { "cell_type": "markdown", - "id": "64614807", + "id": "e6b69672", "metadata": { "editable": true }, @@ -4226,7 +4135,7 @@ { "cell_type": "code", "execution_count": 28, - "id": "a51bc72b", + "id": "a37def90", "metadata": { "collapsed": false, "editable": true @@ -4454,7 +4363,7 @@ }, { "cell_type": "markdown", - "id": "06920905", + "id": "c8b1cfa7", "metadata": { "editable": true }, @@ -4475,7 +4384,7 @@ { "cell_type": "code", "execution_count": 29, - "id": "5e83fa76", + "id": "27960893", "metadata": { "collapsed": false, "editable": true @@ -4779,7 +4688,7 @@ }, { "cell_type": "markdown", - "id": "ca41cb1a", + "id": "a0cd956f", "metadata": { "editable": true }, @@ -4792,7 +4701,7 @@ { "cell_type": "code", "execution_count": 30, - "id": "286cc674", + "id": "87e14f3b", "metadata": { "collapsed": false, "editable": true @@ -5327,7 +5236,7 @@ }, { "cell_type": "markdown", - "id": "6ef4db14", + "id": "bfc23ff8", "metadata": { "editable": true }, @@ -5346,7 +5255,7 @@ { "cell_type": "code", "execution_count": 31, - "id": "945f7d8f", + "id": "1d20960c", "metadata": { "collapsed": false, "editable": true @@ -5359,7 +5268,7 @@ }, { "cell_type": "markdown", - "id": "d408af9d", + "id": "6752a03f", "metadata": { "editable": true }, @@ -5375,7 +5284,7 @@ { "cell_type": "code", "execution_count": 32, - "id": "30f3c371", + "id": "c21b80e7", "metadata": { "collapsed": false, "editable": true @@ -5401,7 +5310,7 @@ }, { "cell_type": "markdown", - "id": "c573fd8e", + "id": "10e46b6b", "metadata": { "editable": true }, @@ -5425,7 +5334,7 @@ { "cell_type": "code", "execution_count": 33, - "id": "048be09a", + "id": "29d4f033", "metadata": { "collapsed": false, "editable": true @@ -5460,7 +5369,7 @@ }, { "cell_type": "markdown", - "id": "28786469", + "id": "96a37378", "metadata": { "editable": true }, @@ -5479,7 +5388,7 @@ { "cell_type": "code", "execution_count": 34, - "id": "4802753a", + "id": "79096135", "metadata": { "collapsed": false, "editable": true @@ -5507,7 +5416,7 @@ }, { "cell_type": "markdown", - "id": "f56208e1", + "id": "7601ba4d", "metadata": { "editable": true }, @@ -5536,7 +5445,7 @@ { "cell_type": "code", "execution_count": 35, - "id": "980e32cb", + "id": "30431eab", "metadata": { "collapsed": false, "editable": true @@ 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Week 42: Logistic Regression and Optimization, reminders from week 38 and week 40","3. Linear Regression","14. Building a Feed Forward Neural Network","15. Solving Differential Equations with Deep Learning","16. Convolutional Neural Networks","17. Recurrent neural networks: Overarching view","4. Ridge and Lasso Regression","5. Resampling Methods","6. Logistic Regression","8. Support Vector Machines, overarching aims","9. Decision trees, overarching aims","10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","11. Basic ideas of the Principal Component Analysis (PCA)","13. Neural networks","7. Optimization, the central part of any Machine Learning algortithm","12. Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Exercises week 39","Exercises week 41","Exercises week 42","Exercises week 43","Applied Data Analysis and Machine Learning","2. Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 7 (midnight), 2024","Project 2 on Machine Learning, deadline November 4 (Midnight)","Teaching schedule with links to material","1. Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Linear Regression and Statistical interpretations","Week 37: Statistical interpretations and Resampling Methods","Week 38: Logistic Regression and Optimization","Week 39: Optimization and Gradient Methods","Week 40: Gradient descent methods (continued) and start Neural networks","Week 41 Neural networks and constructing a neural network code","Week 42 Constructing a Neural Network code with examples","Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations","Week 44, Convolutional Neural Networks 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Week 42: Logistic Regression and Optimization, reminders from week 38 and week 40","3. Linear Regression","14. Building a Feed Forward Neural Network","15. Solving Differential Equations with Deep Learning","16. Convolutional Neural Networks","17. Recurrent neural networks: Overarching view","4. Ridge and Lasso Regression","5. Resampling Methods","6. Logistic Regression","8. Support Vector Machines, overarching aims","9. Decision trees, overarching aims","10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","11. Basic ideas of the Principal Component Analysis (PCA)","13. Neural networks","7. Optimization, the central part of any Machine Learning algortithm","12. Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Exercises week 39","Exercises week 41","Exercises week 42","Exercises week 43","Applied Data Analysis and Machine Learning","2. Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 7 (midnight), 2024","Project 2 on Machine Learning, deadline November 4 (Midnight)","Teaching schedule with links to material","1. Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Linear Regression and Statistical interpretations","Week 37: Statistical interpretations and Resampling Methods","Week 38: Logistic Regression and Optimization","Week 39: Optimization and Gradient Methods","Week 40: Gradient descent methods (continued) and start Neural networks","Week 41 Neural networks and constructing a neural network code","Week 42 Constructing a Neural Network code with examples","Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations","Week 44, Convolutional Neural Networks 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\ No newline at end of file diff --git a/doc/LectureNotes/_build/html/week44.html b/doc/LectureNotes/_build/html/week44.html index bb4c6a3a5..872f24161 100644 --- a/doc/LectureNotes/_build/html/week44.html +++ b/doc/LectureNotes/_build/html/week44.html @@ -536,11 +536,6 @@ const thebe_selector_output = ".output, .cell_output" Mathematics of CNNs -

  • - - Mathematics of CNNs - -
  • Convolution Examples: Polynomial multiplication @@ -978,11 +973,6 @@ const thebe_selector_output = ".output, .cell_output" Mathematics of CNNs
  • -
  • - - Mathematics of CNNs - -
  • Convolution Examples: Polynomial multiplication @@ -1319,7 +1309,7 @@ doconce format html week44.do.txt --no_mako -->

    Week 44, Convolutional Neural Networks (CNN)

    Morten Hjorth-Jensen, Department of Physics, University of Oslo, Norway

    -

    Date: **October 28-November 1 **

    +

    Date: October 28

    Plan for week 44

    Material for the lecture Monday October 28, 2024.

    @@ -1330,10 +1320,12 @@ doconce format html week44.do.txt --no_mako -->
    @@ -1342,8 +1334,7 @@ doconce format html week44.do.txt --no_mako -->
  • Main focus is discussion of and work on project 2

  • If you did not get time to finish the exercises from week 43, you can also keep working on them and hand in this coming Friday

  • - - +

    Material for Lecture Monday October 28

    @@ -1723,37 +1714,6 @@ y(t) = \sum_{a=-\infty}^{a=\infty}x(a)w(t-a).

    Computing the inverse of the above convolution operations is known as deconvolution and the process is commutative.

    How can we use this? And what does it mean? Let us study some familiar examples first.

    -
    -

    Mathematics of CNNs

    -

    The mathematics of CNNs is based on the mathematical operation of -convolution. In mathematics (in particular in functional analysis), -convolution is represented by mathematical operations (integration, -summation etc) on two functions in order to produce a third function -that expresses how the shape of one gets modified by the other. -Convolution has a plethora of applications in a variety of -disciplines, spanning from statistics to signal processing, computer -vision, solutions of differential equations,linear algebra, -engineering, and yes, machine learning.

    -

    Mathematically, convolution is defined as follows (one-dimensional example): -Let us define a continuous function \(y(t)\) given by

    -
    -\[ -y(t) = \int x(a) w(t-a) da, -\]
    -

    where \(x(a)\) represents a so-called input and \(w(t-a)\) is normally called the weight function or kernel.

    -

    The above integral is written in a more compact form as

    -
    -\[ -y(t) = \left(x * w\right)(t). -\]
    -

    The discretized version reads

    -
    -\[ -y(t) = \sum_{a=-\infty}^{a=\infty}x(a)w(t-a). -\]
    -

    Computing the inverse of the above convolution operations is known as deconvolution and the process is commutative.

    -

    How can we use this? And what does it mean? Let us study some familiar examples first.

    -

    Convolution Examples: Polynomial multiplication

    Our first example is that of a multiplication between two polynomials, @@ -2289,7 +2249,7 @@ classification.

    labels = (n_inputs) = (1797,)
    -_images/week44_125_1.png +_images/week44_118_1.png diff --git a/doc/LectureNotes/_build/jupyter_execute/week44.ipynb b/doc/LectureNotes/_build/jupyter_execute/week44.ipynb index 074810ddf..9cf963aad 100644 --- a/doc/LectureNotes/_build/jupyter_execute/week44.ipynb +++ b/doc/LectureNotes/_build/jupyter_execute/week44.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "dc01b8a4", + "id": "8ca0d33d", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "96f11533", + "id": "bddb3681", "metadata": { "editable": true }, @@ -22,12 +22,12 @@ "# Week 44, Convolutional Neural Networks (CNN)\n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo, Norway\n", "\n", - "Date: **October 28-November 1 **" + "Date: **October 28**" ] }, { "cell_type": "markdown", - "id": "cc149251", + "id": "3d29f8f9", "metadata": { "editable": true }, @@ -44,18 +44,22 @@ "\n", " * For a more in depth discussion on neural networks we recommend Goodfellow et al chapter 9. See also chapter 11 and 12 on practicalities and applications\n", "\n", - " * Reading suggestions for implementation of CNNs see :\"https://github.com/rasbt/machine-learning-book/tree/main/ch14\". \n", + " * Reading suggestions for implementation of CNNs see Rashcka et al.'s chapter 14 at . \n", "\n", " * Video on Deep Learning at \n", "\n", " * Video on Convolutional Neural Networks from MIT at \n", "\n", - " * Video on CNNs from Stanford at " + " * Video on CNNs from Stanford at \n", + "\n", + " * Video of lecture October 28 at \n", + "\n", + " * Whiteboard notes at " ] }, { "cell_type": "markdown", - "id": "cb91fe3f", + "id": "34fc94b3", "metadata": { "editable": true }, @@ -64,14 +68,12 @@ "\n", "* Main focus is discussion of and work on project 2\n", "\n", - "* If you did not get time to finish the exercises from week 43, you can also keep working on them and hand in this coming Friday\n", - "\n", - "" + "* If you did not get time to finish the exercises from week 43, you can also keep working on them and hand in this coming Friday" ] }, { "cell_type": "markdown", - "id": "a4b9ec87", + "id": "3239c466", "metadata": { "editable": true }, @@ -81,7 +83,7 @@ }, { "cell_type": "markdown", - "id": "be0fb3b3", + "id": "79352c78", "metadata": { "editable": true }, @@ -108,7 +110,7 @@ }, { "cell_type": "markdown", - "id": "dca41cde", + "id": "bd4b7c7a", "metadata": { "editable": true }, @@ -124,7 +126,7 @@ }, { "cell_type": "markdown", - "id": "7105a270", + "id": "cc1736b4", "metadata": { "editable": true }, @@ -142,7 +144,7 @@ }, { "cell_type": "markdown", - "id": "4ace549e", + "id": "70bf2bf1", "metadata": { "editable": true }, @@ -172,7 +174,7 @@ }, { "cell_type": "markdown", - "id": "da0cb6c8", + "id": "3a7dca56", "metadata": { "editable": true }, @@ -202,7 +204,7 @@ }, { "cell_type": "markdown", - "id": "5b622758", + "id": "de304dc3", "metadata": { "editable": true }, @@ -242,7 +244,7 @@ }, { "cell_type": "markdown", - "id": "29c5c182", + "id": "91bb5b86", "metadata": { "editable": true }, @@ -269,7 +271,7 @@ }, { "cell_type": "markdown", - "id": "fceb2409", + "id": "413cf44d", "metadata": { "editable": true }, @@ -281,7 +283,7 @@ }, { "cell_type": "markdown", - "id": "36313c49", + "id": "adda54b9", "metadata": { "editable": true }, @@ -291,7 +293,7 @@ }, { "cell_type": "markdown", - "id": "81b9cf02", + "id": "4507a4f9", "metadata": { "editable": true }, @@ -309,7 +311,7 @@ }, { "cell_type": "markdown", - "id": "7d7c1544", + "id": "148bc604", "metadata": { "editable": true }, @@ -338,7 +340,7 @@ }, { "cell_type": "markdown", - "id": "28fa62d6", + "id": "2cc27405", "metadata": { "editable": true }, @@ -360,7 +362,7 @@ }, { "cell_type": "markdown", - "id": "efa30734", + "id": "f76305aa", "metadata": { "editable": true }, @@ -382,7 +384,7 @@ }, { "cell_type": "markdown", - "id": "9a435714", + "id": "4411a90d", "metadata": { "editable": true }, @@ -398,7 +400,7 @@ }, { "cell_type": "markdown", - "id": "aed2d756", + "id": "b3d0dbca", "metadata": { "editable": true }, @@ -415,7 +417,7 @@ }, { "cell_type": "markdown", - "id": "68e1ac1b", + "id": "a09c0720", "metadata": { "editable": true }, @@ -439,7 +441,7 @@ }, { "cell_type": "markdown", - "id": "866c9fc7", + "id": "48da38d8", "metadata": { "editable": true }, @@ -450,7 +452,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "3809b7f8", + "id": "762be0c3", "metadata": { "collapsed": false, "editable": true @@ -732,7 +734,7 @@ }, { "cell_type": "markdown", - "id": "2d46cd2c", + "id": "9e557414", "metadata": { "editable": true }, @@ -755,7 +757,7 @@ }, { "cell_type": "markdown", - "id": "b2b7cf91", + "id": "2fa21082", "metadata": { "editable": true }, @@ -767,7 +769,7 @@ }, { "cell_type": "markdown", - "id": "d7e0ed27", + "id": "78091a35", "metadata": { "editable": true }, @@ -779,7 +781,7 @@ }, { "cell_type": "markdown", - "id": "f5780c89", + "id": "ba4e1957", "metadata": { "editable": true }, @@ -791,7 +793,7 @@ }, { "cell_type": "markdown", - "id": "e7a0f90c", + "id": "1a7d9e0f", "metadata": { "editable": true }, @@ -801,7 +803,7 @@ }, { "cell_type": "markdown", - "id": "1819294d", + "id": "d2be6986", "metadata": { "editable": true }, @@ -813,7 +815,7 @@ }, { "cell_type": "markdown", - "id": "b1140da6", + "id": "c89576c7", "metadata": { "editable": true }, @@ -825,100 +827,7 @@ }, { "cell_type": "markdown", - "id": "a6e6e69a", - "metadata": { - "editable": true - }, - "source": [ - "## Mathematics of CNNs\n", - "\n", - "The mathematics of CNNs is based on the mathematical operation of\n", - "**convolution**. In mathematics (in particular in functional analysis),\n", - "convolution is represented by mathematical operations (integration,\n", - "summation etc) on two functions in order to produce a third function\n", - "that expresses how the shape of one gets modified by the other.\n", - "Convolution has a plethora of applications in a variety of\n", - "disciplines, spanning from statistics to signal processing, computer\n", - "vision, solutions of differential equations,linear algebra,\n", - "engineering, and yes, machine learning.\n", - "\n", - "Mathematically, convolution is defined as follows (one-dimensional example):\n", - "Let us define a continuous function $y(t)$ given by" - ] - }, - { - "cell_type": "markdown", - "id": "b6566857", - "metadata": { - "editable": true - }, - "source": [ - "$$\n", - "y(t) = \\int x(a) w(t-a) da,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "id": "d287ce8e", - "metadata": { - "editable": true - }, - "source": [ - "where $x(a)$ represents a so-called input and $w(t-a)$ is normally called the weight function or kernel.\n", - "\n", - "The above integral is written in a more compact form as" - ] - }, - { - "cell_type": "markdown", - "id": "688b3c77", - "metadata": { - "editable": true - }, - "source": [ - "$$\n", - "y(t) = \\left(x * w\\right)(t).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "id": "839e96f3", - "metadata": { - "editable": true - }, - "source": [ - "The discretized version reads" - ] - }, - { - "cell_type": "markdown", - "id": "71855a8f", - "metadata": { - "editable": true - }, - "source": [ - "$$\n", - "y(t) = \\sum_{a=-\\infty}^{a=\\infty}x(a)w(t-a).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "id": "b4949f55", - "metadata": { - "editable": true - }, - "source": [ - "Computing the inverse of the above convolution operations is known as deconvolution and the process is commutative.\n", - "\n", - "How can we use this? And what does it mean? Let us study some familiar examples first." - ] - }, - { - "cell_type": "markdown", - "id": "3390b6b3", + "id": "982931d8", "metadata": { "editable": true }, @@ -937,7 +846,7 @@ }, { "cell_type": "markdown", - "id": "8b13b77d", + "id": "cead60e0", "metadata": { "editable": true }, @@ -949,7 +858,7 @@ }, { "cell_type": "markdown", - "id": "0a8f0215", + "id": "d1986b13", "metadata": { "editable": true }, @@ -959,7 +868,7 @@ }, { "cell_type": "markdown", - "id": "f71bd497", + "id": "1a2d79b8", "metadata": { "editable": true }, @@ -971,7 +880,7 @@ }, { "cell_type": "markdown", - "id": "347bcaf2", + "id": "46e743d4", "metadata": { "editable": true }, @@ -981,7 +890,7 @@ }, { "cell_type": "markdown", - "id": "e381d21e", + "id": "7342bf69", "metadata": { "editable": true }, @@ -993,7 +902,7 @@ }, { "cell_type": "markdown", - "id": "9c6b7be9", + "id": "d1efa756", "metadata": { "editable": true }, @@ -1006,7 +915,7 @@ }, { "cell_type": "markdown", - "id": "5e776582", + "id": "2ca3e8f6", "metadata": { "editable": true }, @@ -1025,7 +934,7 @@ }, { "cell_type": "markdown", - "id": "0f4ccfff", + "id": "3b52d4e1", "metadata": { "editable": true }, @@ -1037,7 +946,7 @@ }, { "cell_type": "markdown", - "id": "4e37b9b5", + "id": "30a7affc", "metadata": { "editable": true }, @@ -1049,7 +958,7 @@ }, { "cell_type": "markdown", - "id": "4bc06433", + "id": "58b6c025", "metadata": { "editable": true }, @@ -1059,7 +968,7 @@ }, { "cell_type": "markdown", - "id": "23989fd4", + "id": "3212b62b", "metadata": { "editable": true }, @@ -1071,7 +980,7 @@ }, { "cell_type": "markdown", - "id": "724837cb", + "id": "9b4093fe", "metadata": { "editable": true }, @@ -1083,7 +992,7 @@ }, { "cell_type": "markdown", - "id": "b6cb72c3", + "id": "f887571e", "metadata": { "editable": true }, @@ -1095,7 +1004,7 @@ }, { "cell_type": "markdown", - "id": "33e4a7dc", + "id": "3c52aecb", "metadata": { "editable": true }, @@ -1106,7 +1015,7 @@ }, { "cell_type": "markdown", - "id": "85138b80", + "id": "c2ca7d94", "metadata": { "editable": true }, @@ -1120,7 +1029,7 @@ }, { "cell_type": "markdown", - "id": "a13e9010", + "id": "d0814379", "metadata": { "editable": true }, @@ -1138,7 +1047,7 @@ }, { "cell_type": "markdown", - "id": "fa3caefc", + "id": "37aa2860", "metadata": { "editable": true }, @@ -1151,7 +1060,7 @@ }, { "cell_type": "markdown", - "id": "172a8a08", + "id": "9634d093", "metadata": { "editable": true }, @@ -1169,7 +1078,7 @@ }, { "cell_type": "markdown", - "id": "4ac06a92", + "id": "29991f53", "metadata": { "editable": true }, @@ -1183,7 +1092,7 @@ }, { "cell_type": "markdown", - "id": "0616100a", + "id": "a4c5c132", "metadata": { "editable": true }, @@ -1199,7 +1108,7 @@ }, { "cell_type": "markdown", - "id": "cecd64c6", + "id": "23bbc731", "metadata": { "editable": true }, @@ -1217,7 +1126,7 @@ }, { "cell_type": "markdown", - "id": "31eecb48", + "id": "a8be6a8f", "metadata": { "editable": true }, @@ -1233,7 +1142,7 @@ }, { "cell_type": "markdown", - "id": "216deb07", + "id": "b1f6dde3", "metadata": { "editable": true }, @@ -1248,7 +1157,7 @@ }, { "cell_type": "markdown", - "id": "7c493c62", + "id": "52d1e6d0", "metadata": { "editable": true }, @@ -1267,7 +1176,7 @@ }, { "cell_type": "markdown", - "id": "00c500fa", + "id": "5dd784d6", "metadata": { "editable": true }, @@ -1279,7 +1188,7 @@ }, { "cell_type": "markdown", - "id": "9e6ef884", + "id": "50cd21e3", "metadata": { "editable": true }, @@ -1290,7 +1199,7 @@ }, { "cell_type": "markdown", - "id": "ae753e43", + "id": "5631b73a", "metadata": { "editable": true }, @@ -1311,7 +1220,7 @@ }, { "cell_type": "markdown", - "id": "338765ee", + "id": "4cbbda23", "metadata": { "editable": true }, @@ -1327,7 +1236,7 @@ }, { "cell_type": "markdown", - "id": "134b1339", + "id": "1d55097f", "metadata": { "editable": true }, @@ -1345,7 +1254,7 @@ }, { "cell_type": "markdown", - "id": "88a54d0b", + "id": "21812778", "metadata": { "editable": true }, @@ -1357,7 +1266,7 @@ }, { "cell_type": "markdown", - "id": "c08db532", + "id": "ab3720f7", "metadata": { "editable": true }, @@ -1367,7 +1276,7 @@ }, { "cell_type": "markdown", - "id": "5abec963", + "id": "1e1dd46d", "metadata": { "editable": true }, @@ -1379,7 +1288,7 @@ }, { "cell_type": "markdown", - "id": "8443ca56", + "id": "1f73e566", "metadata": { "editable": true }, @@ -1391,7 +1300,7 @@ }, { "cell_type": "markdown", - "id": "fb5ccd85", + "id": "00b9b1d2", "metadata": { "editable": true }, @@ -1403,7 +1312,7 @@ }, { "cell_type": "markdown", - "id": "b6672462", + "id": "b27a9b22", "metadata": { "editable": true }, @@ -1413,7 +1322,7 @@ }, { "cell_type": "markdown", - "id": "f32a4c6c", + "id": "f5e818df", "metadata": { "editable": true }, @@ -1425,7 +1334,7 @@ }, { "cell_type": "markdown", - "id": "8c6e4830", + "id": "5d40e9b7", "metadata": { "editable": true }, @@ -1437,7 +1346,7 @@ }, { "cell_type": "markdown", - "id": "050ee2b1", + "id": "a2488003", "metadata": { "editable": true }, @@ -1449,7 +1358,7 @@ }, { "cell_type": "markdown", - "id": "66b7b033", + "id": "f3424a4a", "metadata": { "editable": true }, @@ -1465,7 +1374,7 @@ }, { "cell_type": "markdown", - "id": "ed3176b2", + "id": "b8ec7a35", "metadata": { "editable": true }, @@ -1478,7 +1387,7 @@ }, { "cell_type": "markdown", - "id": "88a97f5d", + "id": "0e2c28ae", "metadata": { "editable": true }, @@ -1490,7 +1399,7 @@ }, { "cell_type": "markdown", - "id": "4a509c92", + "id": "9eb2d76b", "metadata": { "editable": true }, @@ -1500,7 +1409,7 @@ }, { "cell_type": "markdown", - "id": "4ba88953", + "id": "f17d4c03", "metadata": { "editable": true }, @@ -1512,7 +1421,7 @@ }, { "cell_type": "markdown", - "id": "4dc3fee8", + "id": "027e2d72", "metadata": { "editable": true }, @@ -1527,7 +1436,7 @@ }, { "cell_type": "markdown", - "id": "5cc81f97", + "id": "88be64cf", "metadata": { "editable": true }, @@ -1542,7 +1451,7 @@ }, { "cell_type": "markdown", - "id": "851d4c45", + "id": "d297ed25", "metadata": { "editable": true }, @@ -1554,7 +1463,7 @@ }, { "cell_type": "markdown", - "id": "b261ea99", + "id": "de288b76", "metadata": { "editable": true }, @@ -1564,7 +1473,7 @@ }, { "cell_type": "markdown", - "id": "ea27a3c6", + "id": "2aaea6bf", "metadata": { "editable": true }, @@ -1576,7 +1485,7 @@ }, { "cell_type": "markdown", - "id": "83c0c6a0", + "id": "00d4208e", "metadata": { "editable": true }, @@ -1592,7 +1501,7 @@ }, { "cell_type": "markdown", - "id": "dc0b2072", + "id": "96af754f", "metadata": { "editable": true }, @@ -1604,7 +1513,7 @@ }, { "cell_type": "markdown", - "id": "fde836e1", + "id": "21b0c1e8", "metadata": { "editable": true }, @@ -1617,7 +1526,7 @@ }, { "cell_type": "markdown", - "id": "a070285d", + "id": "be785720", "metadata": { "editable": true }, @@ -1631,7 +1540,7 @@ }, { "cell_type": "markdown", - "id": "bf6e590b", + "id": "b7058d94", "metadata": { "editable": true }, @@ -1641,7 +1550,7 @@ }, { "cell_type": "markdown", - "id": "3d3965b6", + "id": "b88a0094", "metadata": { "editable": true }, @@ -1654,7 +1563,7 @@ }, { "cell_type": "markdown", - "id": "cd0d4353", + "id": "5e4e20bc", "metadata": { "editable": true }, @@ -1669,7 +1578,7 @@ }, { "cell_type": "markdown", - "id": "eb62911e", + "id": "d75708bf", "metadata": { "editable": true }, @@ -1681,7 +1590,7 @@ }, { "cell_type": "markdown", - "id": "fdb87605", + "id": "a905172f", "metadata": { "editable": true }, @@ -1691,7 +1600,7 @@ }, { "cell_type": "markdown", - "id": "702d1de3", + "id": "1cae567c", "metadata": { "editable": true }, @@ -1704,7 +1613,7 @@ }, { "cell_type": "markdown", - "id": "46f9ffd9", + "id": "8fd08506", "metadata": { "editable": true }, @@ -1715,7 +1624,7 @@ }, { "cell_type": "markdown", - "id": "54240b13", + "id": "5eb78b07", "metadata": { "editable": true }, @@ -1727,7 +1636,7 @@ }, { "cell_type": "markdown", - "id": "c3cc19f1", + "id": "96796312", "metadata": { "editable": true }, @@ -1737,7 +1646,7 @@ }, { "cell_type": "markdown", - "id": "8fd26ae6", + "id": "10c03ac1", "metadata": { "editable": true }, @@ -1752,7 +1661,7 @@ }, { "cell_type": "markdown", - "id": "907b64ed", + "id": "fcd5c905", "metadata": { "editable": true }, @@ -1762,7 +1671,7 @@ }, { "cell_type": "markdown", - "id": "ea24309a", + "id": "04f7219c", "metadata": { "editable": true }, @@ -1774,7 +1683,7 @@ }, { "cell_type": "markdown", - "id": "9d331112", + "id": "9ee70da3", "metadata": { "editable": true }, @@ -1784,7 +1693,7 @@ }, { "cell_type": "markdown", - "id": "da875dab", + "id": "32bf0b36", "metadata": { "editable": true }, @@ -1800,7 +1709,7 @@ }, { "cell_type": "markdown", - "id": "628f45dd", + "id": "bd9f1937", "metadata": { "editable": true }, @@ -1828,7 +1737,7 @@ }, { "cell_type": "markdown", - "id": "9cd55f79", + "id": "47cafbf5", "metadata": { "editable": true }, @@ -1844,7 +1753,7 @@ }, { "cell_type": "markdown", - "id": "5f94b9d4", + "id": "cf5c61df", "metadata": { "editable": true }, @@ -1856,7 +1765,7 @@ }, { "cell_type": "markdown", - "id": "0a3b9e01", + "id": "c22d0618", "metadata": { "editable": true }, @@ -1868,7 +1777,7 @@ }, { "cell_type": "markdown", - "id": "8764ddc0", + "id": "910ce75f", "metadata": { "editable": true }, @@ -1878,7 +1787,7 @@ }, { "cell_type": "markdown", - "id": "d30b4ff0", + "id": "0615df08", "metadata": { "editable": true }, @@ -1892,7 +1801,7 @@ }, { "cell_type": "markdown", - "id": "7e5eafdb", + "id": "452f4413", "metadata": { "editable": true }, @@ -1904,7 +1813,7 @@ }, { "cell_type": "markdown", - "id": "390faa33", + "id": "cb97c13e", "metadata": { "editable": true }, @@ -1926,7 +1835,7 @@ }, { "cell_type": "markdown", - "id": "11f478e0", + "id": "3425f9b9", "metadata": { "editable": true }, @@ -1958,7 +1867,7 @@ }, { "cell_type": "markdown", - "id": "68226a92", + "id": "9659e588", "metadata": { "editable": true }, @@ -1974,7 +1883,7 @@ }, { "cell_type": "markdown", - "id": "ba4397fc", + "id": "696da180", "metadata": { "editable": true }, @@ -1994,7 +1903,7 @@ }, { "cell_type": "markdown", - "id": "c04e04d6", + "id": "f62d8385", "metadata": { "editable": true }, @@ -2011,7 +1920,7 @@ }, { "cell_type": "markdown", - "id": "cf546e23", + "id": "da48ec69", "metadata": { "editable": true }, @@ -2027,7 +1936,7 @@ }, { "cell_type": "markdown", - "id": "b65107c4", + "id": "82697e96", "metadata": { "editable": true }, @@ -2046,7 +1955,7 @@ }, { "cell_type": "markdown", - "id": "41864fb7", + "id": "603caa07", "metadata": { "editable": true }, @@ -2059,7 +1968,7 @@ }, { "cell_type": "markdown", - "id": "4eebcdb7", + "id": "a15c5a6f", "metadata": { "editable": true }, @@ -2071,7 +1980,7 @@ }, { "cell_type": "markdown", - "id": "7a5e62e4", + "id": "dbffa234", "metadata": { "editable": true }, @@ -2092,7 +2001,7 @@ }, { "cell_type": "markdown", - "id": "c7238366", + "id": "c08597db", "metadata": { "editable": true }, @@ -2113,7 +2022,7 @@ }, { "cell_type": "markdown", - "id": "0b97aeeb", + "id": "36ead32a", "metadata": { "editable": true }, @@ -2139,7 +2048,7 @@ }, { "cell_type": "markdown", - "id": "3fd6f59e", + "id": "76a692c3", "metadata": { "editable": true }, @@ -2158,7 +2067,7 @@ }, { "cell_type": "markdown", - "id": "0172461a", + "id": "177759f2", "metadata": { "editable": true }, @@ -2169,7 +2078,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "327406f1", + "id": "f4f578f8", "metadata": { "collapsed": false, "editable": true @@ -2192,7 +2101,7 @@ }, "metadata": { "filenames": { - "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week44_125_1.png" + "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week44_118_1.png" } }, "output_type": "display_data" @@ -2243,7 +2152,7 @@ }, { "cell_type": "markdown", - "id": "21cd0cbc", + "id": "6fd14013", "metadata": { "editable": true }, @@ -2254,7 +2163,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "0acee68a", + "id": "bea60977", "metadata": { "collapsed": false, "editable": true @@ -2301,7 +2210,7 @@ }, { "cell_type": "markdown", - "id": "e02f61a7", + "id": "849c5abf", "metadata": { "editable": true }, @@ -2312,7 +2221,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "91574522", + "id": "f6cf91b0", "metadata": { "collapsed": false, "editable": true @@ -2349,7 +2258,7 @@ }, { "cell_type": "markdown", - "id": "4176bd54", + "id": "1762e77d", "metadata": { "editable": true }, @@ -2360,7 +2269,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "ec107763", + "id": "85cb8818", "metadata": { "collapsed": false, "editable": true @@ -2387,7 +2296,7 @@ }, { "cell_type": "markdown", - "id": "72b0127c", + "id": "7cad90f7", "metadata": { "editable": true }, @@ -2398,7 +2307,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "99644dc7", + "id": "526e2167", "metadata": { "collapsed": false, "editable": true @@ -2439,7 +2348,7 @@ }, { "cell_type": "markdown", - "id": "1c309dbb", + "id": "3676714e", "metadata": { "editable": true }, @@ -2455,7 +2364,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "6a35ed0c", + "id": "ddec0620", "metadata": { "collapsed": false, "editable": true @@ -2476,7 +2385,7 @@ }, { "cell_type": "markdown", - "id": "b150d131", + "id": "68c162f4", "metadata": { "editable": true }, @@ -2489,7 +2398,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "96a7b1f0", + "id": "af8654a4", "metadata": { "collapsed": false, "editable": true @@ -2513,7 +2422,7 @@ }, { "cell_type": "markdown", - "id": "b6ad06dc", + "id": "1038efea", "metadata": { "editable": true }, @@ -2528,7 +2437,7 @@ { "cell_type": "code", "execution_count": 9, - "id": "0d9a9552", + "id": "6a377cfd", "metadata": { "collapsed": false, "editable": true @@ -2549,7 +2458,7 @@ }, { "cell_type": "markdown", - "id": "c4304aa4", + "id": "22897193", "metadata": { "editable": true }, @@ -2559,7 +2468,7 @@ }, { "cell_type": "markdown", - "id": "180db190", + "id": "30ef3e7c", "metadata": { "editable": true }, @@ -2578,7 +2487,7 @@ { "cell_type": "code", "execution_count": 10, - "id": "8f52da8c", + "id": "349e7619", "metadata": { "collapsed": false, "editable": true @@ -2595,7 +2504,7 @@ }, { "cell_type": "markdown", - "id": "c5497eff", + "id": "3d8d954b", "metadata": { "editable": true }, @@ -2605,7 +2514,7 @@ }, { "cell_type": "markdown", - "id": "4ba34f8d", + "id": "7f0847a8", "metadata": { "editable": true }, @@ -2616,7 +2525,7 @@ { "cell_type": "code", "execution_count": 11, - "id": "d2e64017", + "id": "783f6194", "metadata": { "collapsed": false, "editable": true @@ -2633,7 +2542,7 @@ }, { "cell_type": "markdown", - "id": "00059fe8", + "id": "0e1cce97", "metadata": { "editable": true }, @@ -2644,7 +2553,7 @@ { "cell_type": "code", "execution_count": 12, - "id": "4a1f365f", + "id": "7d87be54", "metadata": { "collapsed": false, "editable": true @@ -2665,7 +2574,7 @@ }, { "cell_type": "markdown", - "id": "aaba024a", + "id": "5287a9fb", "metadata": { "editable": true }, @@ -2698,7 +2607,7 @@ }, { "cell_type": "markdown", - "id": "764fc43e", + "id": "5376c8cd", "metadata": { "editable": true }, @@ -2722,7 +2631,7 @@ }, { "cell_type": "markdown", - "id": "a16e632d", + "id": "8cf0b8dc", "metadata": { "editable": true }, @@ -2745,7 +2654,7 @@ { "cell_type": "code", "execution_count": 13, - "id": "1deab9eb", + "id": "f2619dd7", "metadata": { "collapsed": false, "editable": true @@ -2886,7 +2795,7 @@ }, { "cell_type": "markdown", - "id": "1bf4b5e1", + "id": "04f25816", "metadata": { "editable": true }, @@ -2899,7 +2808,7 @@ { "cell_type": "code", "execution_count": 14, - "id": "4ccdf2fd", + "id": "9afe39a2", "metadata": { "collapsed": false, "editable": true @@ -2912,7 +2821,7 @@ }, { "cell_type": "markdown", - "id": "318c8ba3", + "id": "3e912906", "metadata": { "editable": true }, @@ -2923,7 +2832,7 @@ { "cell_type": "code", "execution_count": 15, - "id": "3e05068e", + "id": "aa146e1b", "metadata": { "collapsed": false, "editable": true @@ -2945,7 +2854,7 @@ }, { "cell_type": "markdown", - "id": "0fdd8790", + "id": "fba31aff", "metadata": { "editable": true }, @@ -2961,7 +2870,7 @@ { "cell_type": "code", "execution_count": 16, - "id": "4d30014d", + "id": "abdcad5a", "metadata": { "collapsed": false, "editable": true @@ -3008,7 +2917,7 @@ }, { "cell_type": "markdown", - "id": "3303262d", + "id": "894970b1", "metadata": { "editable": true }, @@ -3023,7 +2932,7 @@ { "cell_type": "code", "execution_count": 17, - "id": "4328896b", + "id": "6a778d9d", "metadata": { "collapsed": false, "editable": true @@ -3044,7 +2953,7 @@ }, { "cell_type": "markdown", - "id": "9ff7fd7a", + "id": "4fd0dfdb", "metadata": { "editable": true }, @@ -3061,7 +2970,7 @@ { "cell_type": "code", "execution_count": 18, - "id": "f44c1e1d", + "id": "53d2e40d", "metadata": { "collapsed": false, "editable": true @@ -3120,7 +3029,7 @@ }, { "cell_type": "markdown", - "id": "2f6650d0", + "id": "09771b87", "metadata": { "editable": true }, @@ -3137,7 +3046,7 @@ { "cell_type": "code", "execution_count": 19, - "id": "d50993c9", + "id": "08f622fa", "metadata": { "collapsed": false, "editable": true @@ -3158,7 +3067,7 @@ }, { "cell_type": "markdown", - "id": "a712dc3c", + "id": "81c7eaef", "metadata": { "editable": true }, @@ -3175,7 +3084,7 @@ }, { "cell_type": "markdown", - "id": "632866a9", + "id": "0998392d", "metadata": { "editable": true }, @@ -3187,7 +3096,7 @@ }, { "cell_type": "markdown", - "id": "fb33615f", + "id": "147961a0", "metadata": { "editable": true }, @@ -3203,7 +3112,7 @@ }, { "cell_type": "markdown", - "id": "c150b10d", + "id": "f67f1f6d", "metadata": { "editable": true }, @@ -3215,7 +3124,7 @@ }, { "cell_type": "markdown", - "id": "29b9caee", + "id": "dec83f81", "metadata": { "editable": true }, @@ -3230,7 +3139,7 @@ }, { "cell_type": "markdown", - "id": "8b512529", + "id": "5a5b1e07", "metadata": { "editable": true }, @@ -3242,7 +3151,7 @@ }, { "cell_type": "markdown", - "id": "3c6f0bc9", + "id": "7c27a0fe", "metadata": { "editable": true }, @@ -3260,7 +3169,7 @@ }, { "cell_type": "markdown", - "id": "6be766c2", + "id": "4c81a107", "metadata": { "editable": true }, @@ -3279,7 +3188,7 @@ }, { "cell_type": "markdown", - "id": "30872978", + "id": "24228635", "metadata": { "editable": true }, @@ -3291,7 +3200,7 @@ }, { "cell_type": "markdown", - "id": "dab55864", + "id": "89692cf6", "metadata": { "editable": true }, @@ -3308,7 +3217,7 @@ }, { "cell_type": "markdown", - "id": "59009d4e", + "id": "0ecfdafa", "metadata": { "editable": true }, @@ -3321,7 +3230,7 @@ }, { "cell_type": "markdown", - "id": "cfd71d57", + "id": "33c6332e", "metadata": { "editable": true }, @@ -3350,7 +3259,7 @@ }, { "cell_type": "markdown", - "id": "254de1f6", + "id": "a573879c", "metadata": { "editable": true }, @@ -3360,7 +3269,7 @@ }, { "cell_type": "markdown", - "id": "277ad313", + "id": "e515a3e4", "metadata": { "editable": true }, @@ -3372,7 +3281,7 @@ }, { "cell_type": "markdown", - "id": "4408da81", + "id": "e53c0a21", "metadata": { "editable": true }, @@ -3393,7 +3302,7 @@ }, { "cell_type": "markdown", - "id": "97f368a4", + "id": "aee15740", "metadata": { "editable": true }, @@ -3411,7 +3320,7 @@ }, { "cell_type": "markdown", - "id": "2157445c", + "id": "2ed1f60a", "metadata": { "editable": true }, @@ -3427,7 +3336,7 @@ }, { "cell_type": "markdown", - "id": "1b823cf8", + "id": "9859970d", "metadata": { "editable": true }, @@ -3440,7 +3349,7 @@ }, { "cell_type": "markdown", - "id": "fcd68006", + "id": "128b4dc2", "metadata": { "editable": true }, @@ -3464,7 +3373,7 @@ }, { "cell_type": "markdown", - "id": "57d7a347", + "id": "c6fb6517", "metadata": { "editable": true }, @@ -3485,7 +3394,7 @@ }, { "cell_type": "markdown", - "id": "b76fc717", + "id": "b01d3014", "metadata": { "editable": true }, @@ -3498,7 +3407,7 @@ { "cell_type": "code", "execution_count": 20, - "id": "47bc5ad3", + "id": "67babc7b", "metadata": { "collapsed": false, "editable": true @@ -3580,7 +3489,7 @@ }, { "cell_type": "markdown", - "id": "435a988d", + "id": "406e9884", "metadata": { "editable": true }, @@ -3594,7 +3503,7 @@ { "cell_type": "code", "execution_count": 21, - "id": "2c04ebbf", + "id": "c9887d3f", "metadata": { "collapsed": false, "editable": true @@ -3621,7 +3530,7 @@ }, { "cell_type": "markdown", - "id": "66b71a9c", + "id": "239d497a", "metadata": { "editable": true }, @@ -3642,7 +3551,7 @@ { "cell_type": "code", "execution_count": 22, - "id": "d56d781d", + "id": "bf4ab84e", "metadata": { "collapsed": false, "editable": true @@ -3692,7 +3601,7 @@ }, { "cell_type": "markdown", - "id": "611f44ba", + "id": "4bf788aa", "metadata": { "editable": true }, @@ -3707,7 +3616,7 @@ { "cell_type": "code", "execution_count": 23, - "id": "2ab1f7fd", + "id": "6d3dca2d", "metadata": { "collapsed": false, "editable": true @@ -3748,7 +3657,7 @@ }, { "cell_type": "markdown", - "id": "edc50ddb", + "id": "0dacddbe", "metadata": { "editable": true }, @@ -3790,7 +3699,7 @@ { "cell_type": "code", "execution_count": 24, - "id": "154bca97", + "id": "17f9a3e4", "metadata": { "collapsed": false, "editable": true @@ -4076,7 +3985,7 @@ }, { "cell_type": "markdown", - "id": "fd97e246", + "id": "2ebd51a9", "metadata": { "editable": true }, @@ -4099,7 +4008,7 @@ }, { "cell_type": "markdown", - "id": "483ec09a", + "id": "6e37ad83", "metadata": { "editable": true }, @@ -4112,7 +4021,7 @@ { "cell_type": "code", "execution_count": 25, - "id": "34cc7cfe", + "id": "09290632", "metadata": { "collapsed": false, "editable": true @@ -4160,7 +4069,7 @@ }, { "cell_type": "markdown", - "id": "c7222d94", + "id": "111f84ed", "metadata": { "editable": true }, @@ -4182,7 +4091,7 @@ }, { "cell_type": "markdown", - "id": "379d2b61", + "id": "589e5822", "metadata": { "editable": true }, @@ -4204,7 +4113,7 @@ { "cell_type": "code", "execution_count": 26, - "id": "bbba88c5", + "id": "c9c28b65", "metadata": { "collapsed": false, "editable": true @@ -4366,7 +4275,7 @@ }, { "cell_type": "markdown", - "id": "5eb1543d", + "id": "1fcb9ea1", "metadata": { "editable": true }, @@ -4387,7 +4296,7 @@ { "cell_type": "code", "execution_count": 27, - "id": "16e0cbb4", + "id": "d8651caa", "metadata": { "collapsed": false, "editable": true @@ -4450,7 +4359,7 @@ }, { "cell_type": "markdown", - "id": "64614807", + "id": "e6b69672", "metadata": { "editable": true }, @@ -4474,7 +4383,7 @@ { "cell_type": "code", "execution_count": 28, - "id": "a51bc72b", + "id": "a37def90", "metadata": { "collapsed": false, "editable": true @@ -4702,7 +4611,7 @@ }, { "cell_type": "markdown", - "id": "06920905", + "id": "c8b1cfa7", "metadata": { "editable": true }, @@ -4723,7 +4632,7 @@ { "cell_type": "code", "execution_count": 29, - "id": "5e83fa76", + "id": "27960893", "metadata": { "collapsed": false, "editable": true @@ -5027,7 +4936,7 @@ }, { "cell_type": "markdown", - "id": "ca41cb1a", + "id": "a0cd956f", "metadata": { "editable": true }, @@ -5040,7 +4949,7 @@ { "cell_type": "code", "execution_count": 30, - "id": "286cc674", + "id": "87e14f3b", "metadata": { "collapsed": false, "editable": true @@ -5575,7 +5484,7 @@ }, { "cell_type": "markdown", - "id": "6ef4db14", + "id": "bfc23ff8", "metadata": { "editable": true }, @@ -5594,7 +5503,7 @@ { "cell_type": "code", "execution_count": 31, - "id": "945f7d8f", + "id": "1d20960c", "metadata": { "collapsed": false, "editable": true @@ -5607,7 +5516,7 @@ }, { "cell_type": "markdown", - "id": "d408af9d", + "id": "6752a03f", "metadata": { "editable": true }, @@ -5623,7 +5532,7 @@ { "cell_type": "code", "execution_count": 32, - "id": "30f3c371", + "id": "c21b80e7", "metadata": { "collapsed": false, "editable": true @@ -5649,7 +5558,7 @@ }, { "cell_type": "markdown", - "id": "c573fd8e", + "id": "10e46b6b", "metadata": { "editable": true }, @@ -5673,7 +5582,7 @@ { "cell_type": "code", "execution_count": 33, - "id": "048be09a", + "id": "29d4f033", "metadata": { "collapsed": false, "editable": true @@ -5708,7 +5617,7 @@ }, { "cell_type": "markdown", - "id": "28786469", + "id": "96a37378", "metadata": { "editable": true }, @@ -5727,7 +5636,7 @@ { "cell_type": "code", "execution_count": 34, - "id": "4802753a", + "id": "79096135", "metadata": { "collapsed": false, "editable": true @@ -5755,7 +5664,7 @@ }, { "cell_type": "markdown", - "id": "f56208e1", + "id": "7601ba4d", "metadata": { "editable": true }, @@ -5784,7 +5693,7 @@ { "cell_type": "code", "execution_count": 35, - "id": "980e32cb", + "id": "30431eab", "metadata": { "collapsed": false, "editable": true @@ -5853,7 +5762,7 @@ }, { "cell_type": "markdown", - "id": "f685c435", + "id": "c0f7ead9", "metadata": { "editable": true }, @@ -5871,7 +5780,7 @@ }, { "cell_type": "markdown", - "id": "24fe6c43", + "id": "8eba3502", "metadata": { "editable": true }, @@ -5895,7 +5804,7 @@ { "cell_type": "code", "execution_count": 36, - "id": "308cc1ff", + "id": "d15712bc", "metadata": { "collapsed": false, "editable": true @@ -5926,7 +5835,7 @@ }, { "cell_type": "markdown", - "id": "ec8c5476", + "id": "65c59f0c", "metadata": { "editable": true }, @@ -5956,7 +5865,7 @@ }, { "cell_type": "markdown", - "id": "1980bd23", + "id": "20545917", "metadata": { "editable": true }, @@ -5967,7 +5876,7 @@ { "cell_type": "code", "execution_count": 37, - "id": "da7442ee", + "id": "8613dd26", "metadata": { "collapsed": false, "editable": true @@ -6017,7 +5926,7 @@ }, { "cell_type": "markdown", - "id": "84438582", + "id": "1d4fbbf9", "metadata": { "editable": true }, @@ -6038,7 +5947,7 @@ }, { "cell_type": "markdown", - "id": "f8973e64", + "id": "6d31f7ab", "metadata": { "editable": true }, @@ -6049,7 +5958,7 @@ { "cell_type": "code", "execution_count": 38, - "id": "f57676b2", + "id": "15082cf9", "metadata": { "collapsed": false, "editable": true @@ -6070,7 +5979,7 @@ }, { "cell_type": "markdown", - "id": "fca3cae7", + "id": "5211e804", "metadata": { "editable": true }, diff --git a/doc/LectureNotes/_build/jupyter_execute/week44.py b/doc/LectureNotes/_build/jupyter_execute/week44.py index 2bdeb9030..5881aca8a 100644 --- a/doc/LectureNotes/_build/jupyter_execute/week44.py +++ b/doc/LectureNotes/_build/jupyter_execute/week44.py @@ -8,7 +8,7 @@ # # Week 44, Convolutional Neural Networks (CNN) # **Morten Hjorth-Jensen**, Department of Physics, University of Oslo, Norway # -# Date: **October 28-November 1 ** +# Date: **October 28** # ## Plan for week 44 # @@ -22,21 +22,23 @@ # # * For a more in depth discussion on neural networks we recommend Goodfellow et al chapter 9. See also chapter 11 and 12 on practicalities and applications # -# * Reading suggestions for implementation of CNNs see :"https://github.com/rasbt/machine-learning-book/tree/main/ch14". +# * Reading suggestions for implementation of CNNs see Rashcka et al.'s chapter 14 at . # # * Video on Deep Learning at # # * Video on Convolutional Neural Networks from MIT at # # * Video on CNNs from Stanford at +# +# * Video of lecture October 28 at +# +# * Whiteboard notes at # ## Lab sessions on Tuesday and Wednesday # # * Main focus is discussion of and work on project 2 # # * If you did not get time to finish the exercises from week 43, you can also keep working on them and hand in this coming Friday -# -# # ## Material for Lecture Monday October 28 @@ -337,43 +339,6 @@ for k in (5,10, 20, 100,200,400,500): print('Signa to noise ratio '+ str(round(srv)) +'dB') -# ## Mathematics of CNNs -# -# The mathematics of CNNs is based on the mathematical operation of -# **convolution**. In mathematics (in particular in functional analysis), -# convolution is represented by mathematical operations (integration, -# summation etc) on two functions in order to produce a third function -# that expresses how the shape of one gets modified by the other. -# Convolution has a plethora of applications in a variety of -# disciplines, spanning from statistics to signal processing, computer -# vision, solutions of differential equations,linear algebra, -# engineering, and yes, machine learning. -# -# Mathematically, convolution is defined as follows (one-dimensional example): -# Let us define a continuous function $y(t)$ given by - -# $$ -# y(t) = \int x(a) w(t-a) da, -# $$ - -# where $x(a)$ represents a so-called input and $w(t-a)$ is normally called the weight function or kernel. -# -# The above integral is written in a more compact form as - -# $$ -# y(t) = \left(x * w\right)(t). -# $$ - -# The discretized version reads - -# $$ -# y(t) = \sum_{a=-\infty}^{a=\infty}x(a)w(t-a). -# $$ - -# Computing the inverse of the above convolution operations is known as deconvolution and the process is commutative. -# -# How can we use this? And what does it mean? Let us study some familiar examples first. - # ## Mathematics of CNNs # # The mathematics of CNNs is based on the mathematical operation of diff --git a/doc/LectureNotes/_build/jupyter_execute/week44_118_1.png b/doc/LectureNotes/_build/jupyter_execute/week44_118_1.png new file mode 100644 index 0000000000000000000000000000000000000000..0fb3d71eb45a86b49806ff42e5c09080aab777c3 GIT binary patch literal 4604 zcmc(jc~p~E`p46uqgIPCW$U1TrHU01T-YImsi3mSKwLl+6hwp&!yZC_)Xu3OOCnGN zBTHow8H9+Mumz&k5H%!700CKoAc=-Gh7bZ-emAt|ch2uj&zWC)=FI$&?alk%_dd__ z{eJFq-)nz6c0_xl;YJ7qqU~|i%^w2MqJi%(H>?Bic^^j@;KL!oJs<&zxtM@G9~Tbs zIiC;{jY)`(4Beg-9v2^pxqQ&l!SaB`_Dcx~G4YO8R_Omd!4eY}VfEE9tsyYTXE8?u z;~@~}dClvSyNH@d2m}`C;r7?#$tAO+gy^&3%JmDrL-#-TPO4+~T?q_?+`M@E*+s>M z3)rsaEgngQ;ZID4vYvcd=@IBw@#3(TwJOt6_n@8*E9-L9hWnef-$JWrL&6GNcWuuO zyWI)TnycHQyaIN2kat)9Ezr(kXuL?x%8 z;1e>oiK!2Pe0OiRCI=UM8vhJ|Y)5771wR6j(Vsvd&&i>iAQ0ErxPm#&B)&pmM>W=uxRO$?uCK4}>FZ1A zA`}IuMAm1p0v{Xxl-Iwi;6I8)S_ISWFLKCw91bV8$K8O*tM-~~5th|SU)g&FXyu-d zs$cJFNOD=ZblkkKSwKcrw6!^r$>fPA>rHZ|*hQ?dc6`{>%R;KLsdsT%S=k_ipmw4u zCr#9uC+bcz!Nfio=5912*|>g)kX6y1XkMvB(*BJ(82ZM?GDd{$r48_Oyv$H3nYf*)sQ+Lt) z)iIf==|pyjVqynromn}!QQLGw8}UujFuIB9Zg5tYvCOoZ=vbYrdvf>O#{ex%WO0bQ zi{5&uaZcM@>mC>R3*XMg551G$Z?epsrZ8MqR#!>*F1Tz&=V3%QF|zj#^ZP$RcnIq-P)*zOC~eX{#00)#3O04!e1m zI@(<9Du(sm@p1YfzAjN9Ztzu0O|fF80gE~ij6clkO}_VuVPHE)ee+;Mr(9TW(jO(w zA=ZckwB*QW)=(2BL?JrG$ck&(hFIw#X|lgGGo+JkU`4!r`*!7$T1p`pfh7A*PKT&d zQiV?ZYr-ltLSCgj-PjxQgRC3{@sE$H32u}X0Lph6Kk!?^DnqWPvzqnn?+fXC8KUqMJtbSC?k9-Lv&eKZ>nw zQ9o_g)ecpzNZs9Z337G_v90^<(~NAb^_%Ho!&@1ao)?QImB|cX zev2}h3AMhiZn~-)qgE-I55n15z%!<%U`#GTt*D?-=Brr#YEhbsF>J?>bHG0gke`|~ z3+W5s51W??^&rc|Hc5L?C1WrGs8J_k-#yPmx|FSiYg@0wMzd}n2=}DVr_E<)X7=>- zBrBx@lM8R3_Kb}g`y!N!eygW|V-|ki#8MGd3VCe*iBrrl5?mh!qcBt{&f;e}jX?Fw z-2{~mUN)E8j+b?U5cD;bEp@_nvaJ}YBjO*~Q{QBnwzjqTIxYzWg65eA?9dOqYH=H1 zX=xihxCMYfTy2%MyDatNi{8|om)sn>)nbs1NubEIGq|b3{n)vYUdJ1q7qwqK7oAs8 zLKrT_1ci86-c2yp)ZC7rdXTuyA?_uscktd7g?!;I7B_xneJF=)(-_7g+9$k!HMo>* z)v})Fs6A)s45ulr!uKRu(dir&JV>tUp*c^XgKt|-}@@eQGkZBuD zpqa_jVKnwsoZ@2A7 z8Y`bFT77A9%v@6^jd1&;`ejLRhc&q3O4Oj*@TlR1g%}0M7IA55slXTtd+iFp)a*o) z@d*TH)$-&K^!&_B&aKO>yNz-0@|I^J5L?UTT@e%2MZsCCb8S{GDlv(rQm&F51^Hf< z*8sLHJC>*v<`u2=6*V=xT$Z0eJ0_dToxp$gs-q5ik3g}410io{z6ftPS&J(q_ z+LnxEyN&*X1>)<>-CEhw;&8b`En!?88Ql>kJPe z{c_s)n?ZkaQ*8G;+8Amr)!5a%y}jK-0*F;0DDaw?AJY}Wnwu`7?> zH(g7iSVacAJp;4k(N!u{74CKKyEk-PJde)ha;tDUUrAdrXtWQRCDw*QcX7PZ;MZ5S zU0+c;nue|{e(;c7y?QlY5a_$>Wc|qkLFp`NyHt|9FM`B0`afOOA85pW_az|cl<_N9 zu2kWg#!^r``cAJKJ2-m^Jv}6*rsjp7JbDzBY)yI*zdG9l;(!}CIy&YH+}%d-^B_%T zp}BFXPoF;ZkoYr91V621MI?g}=c5VrCduPqP^D4{M&gxgoze1X=%ZjovZsB*ANwY= zGeHyNLmn6%Ew!fTkNiK|%-A zyf9x-ozC?x>ysd)BZk|yd4r>kzy(#f{wSMBQ0tnCx_oQ`4r+avkSw)~&(f<#Fl1FQoDW@Hoy z60z7_oUOlvB?j%#j_w`4n!tiZ(!T!wLTf8i;LV*JFJ%dm!HNwvGBN^{F4r>qRwVHh z2}_=$p1-?t$IXE_zV-F>t` z5dhFbLc{ROtTBLK8fmBC@dXhF9BeUTpyd9wJ2)sefR|=Q8}u4b>mL z#0Ko=`ck&+enh4Ar)<~-Ha+AXii2tvZ z7Kws?cigkupGS{t0VM?c3IOC4VM$6(E$fsoC=qBis&H#CU&Gi2$sTO&fGcR=cyz!n zyU4NnrZKWLv~ze3+d~f{fD;T2J;`>kn>w+jonr0Ho6R`WB9SKCmmqPplTjIibbkFL1>-o91c@3@_FTBXF!d3h424E8A+KnA0 z+Z{NN|BEt>y&vsqXf_4TmZ83!FT>AyknQa4i>)zh%Mk$dsgfGA0kBid7ZkFmfCvVT zQ&0PVL3@UVZdy}}Q@(Se{hkK`e^kG}@z?=no>g&Ix*gno+`Huu+e-yq(i=Vd_D`;@ QU?7Nx`!TnMZ_j=IKd0k?r~m)} literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/week44.ipynb b/doc/LectureNotes/week44.ipynb index 5a26ea0b7..86616fad5 100644 --- a/doc/LectureNotes/week44.ipynb +++ b/doc/LectureNotes/week44.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "33cfff3f", + "id": "8ca0d33d", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "a44fb58f", + "id": "bddb3681", "metadata": { "editable": true }, @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "57d251e2", + "id": "3d29f8f9", "metadata": { "editable": true }, @@ -50,12 +50,16 @@ "\n", " * Video on Convolutional Neural Networks from MIT at \n", "\n", - " * Video on CNNs from Stanford at " + " * Video on CNNs from Stanford at \n", + "\n", + " * Video of lecture October 28 at \n", + "\n", + " * Whiteboard notes at " ] }, { "cell_type": "markdown", - "id": "4a18fe31", + "id": "34fc94b3", "metadata": { "editable": true }, @@ -64,14 +68,12 @@ "\n", "* Main focus is discussion of and work on project 2\n", "\n", - "* If you did not get time to finish the exercises from week 43, you can also keep working on them and hand in this coming Friday\n", - "\n", - "" + "* If you did not get time to finish the exercises from week 43, you can also keep working on them and hand in this coming Friday" ] }, { "cell_type": "markdown", - "id": "3ae00447", + "id": "3239c466", "metadata": { "editable": true }, @@ -81,7 +83,7 @@ }, { "cell_type": "markdown", - "id": "0ed6a703", + "id": "79352c78", "metadata": { "editable": true }, @@ -108,7 +110,7 @@ }, { "cell_type": "markdown", - "id": "a7c8edbb", + "id": "bd4b7c7a", "metadata": { "editable": true }, @@ -124,7 +126,7 @@ }, { "cell_type": "markdown", - "id": "c74d37fd", + "id": "cc1736b4", "metadata": { "editable": true }, @@ -142,7 +144,7 @@ }, { "cell_type": "markdown", - "id": "a6aecf45", + "id": "70bf2bf1", "metadata": { "editable": true }, @@ -172,7 +174,7 @@ }, { "cell_type": "markdown", - "id": "7dabb368", + "id": "3a7dca56", "metadata": { "editable": true }, @@ -202,7 +204,7 @@ }, { "cell_type": "markdown", - "id": "58985aa5", + "id": "de304dc3", "metadata": { "editable": true }, @@ -242,7 +244,7 @@ }, { "cell_type": "markdown", - "id": "1bab74a3", + "id": "91bb5b86", "metadata": { "editable": true }, @@ -269,7 +271,7 @@ }, { "cell_type": "markdown", - "id": "2f33f8a1", + "id": "413cf44d", "metadata": { "editable": true }, @@ -281,7 +283,7 @@ }, { "cell_type": "markdown", - "id": "eaf3f45e", + "id": "adda54b9", "metadata": { "editable": true }, @@ -291,7 +293,7 @@ }, { "cell_type": "markdown", - "id": "0e84c466", + "id": "4507a4f9", "metadata": { "editable": true }, @@ -309,7 +311,7 @@ }, { "cell_type": "markdown", - "id": "10d45a95", + "id": "148bc604", "metadata": { "editable": true }, @@ -338,7 +340,7 @@ }, { "cell_type": "markdown", - "id": "d80f26a1", + "id": "2cc27405", "metadata": { "editable": true }, @@ -360,7 +362,7 @@ }, { "cell_type": "markdown", - "id": "68d919a2", + "id": "f76305aa", "metadata": { "editable": true }, @@ -382,7 +384,7 @@ }, { "cell_type": "markdown", - "id": "a01f5449", + "id": "4411a90d", "metadata": { "editable": true }, @@ -398,7 +400,7 @@ }, { "cell_type": "markdown", - "id": "641f70ad", + "id": "b3d0dbca", "metadata": { "editable": true }, @@ -415,7 +417,7 @@ }, { "cell_type": "markdown", - "id": "b547814e", + "id": "a09c0720", "metadata": { "editable": true }, @@ -439,7 +441,7 @@ }, { "cell_type": "markdown", - "id": "959b7c24", + "id": "48da38d8", "metadata": { "editable": true }, @@ -450,7 +452,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "2d761bb6", + "id": "762be0c3", "metadata": { "collapsed": false, "editable": true @@ -521,7 +523,7 @@ }, { "cell_type": "markdown", - "id": "c8dfa74c", + "id": "9e557414", "metadata": { "editable": true }, @@ -544,7 +546,7 @@ }, { "cell_type": "markdown", - "id": "304b1167", + "id": "2fa21082", "metadata": { "editable": true }, @@ -556,7 +558,7 @@ }, { "cell_type": "markdown", - "id": "82dac147", + "id": "78091a35", "metadata": { "editable": true }, @@ -568,7 +570,7 @@ }, { "cell_type": "markdown", - "id": "471c9322", + "id": "ba4e1957", "metadata": { "editable": true }, @@ -580,7 +582,7 @@ }, { "cell_type": "markdown", - "id": "09155a02", + "id": "1a7d9e0f", "metadata": { "editable": true }, @@ -590,7 +592,7 @@ }, { "cell_type": "markdown", - "id": "b7a3d486", + "id": "d2be6986", "metadata": { "editable": true }, @@ -602,7 +604,7 @@ }, { "cell_type": "markdown", - "id": "44ee5981", + "id": "c89576c7", "metadata": { "editable": true }, @@ -614,7 +616,7 @@ }, { "cell_type": "markdown", - "id": "73c72e3d", + "id": "982931d8", "metadata": { "editable": true }, @@ -633,7 +635,7 @@ }, { "cell_type": "markdown", - "id": "380fd888", + "id": "cead60e0", "metadata": { "editable": true }, @@ -645,7 +647,7 @@ }, { "cell_type": "markdown", - "id": "a6770e0d", + "id": "d1986b13", "metadata": { "editable": true }, @@ -655,7 +657,7 @@ }, { "cell_type": "markdown", - "id": "302f8f6e", + "id": "1a2d79b8", "metadata": { "editable": true }, @@ -667,7 +669,7 @@ }, { "cell_type": "markdown", - "id": "9bcd41c9", + "id": "46e743d4", "metadata": { "editable": true }, @@ -677,7 +679,7 @@ }, { "cell_type": "markdown", - "id": "432e59c5", + "id": "7342bf69", "metadata": { "editable": true }, @@ -689,7 +691,7 @@ }, { "cell_type": "markdown", - "id": "5fda8842", + "id": "d1efa756", "metadata": { "editable": true }, @@ -702,7 +704,7 @@ }, { "cell_type": "markdown", - "id": "d7ee3cc3", + "id": "2ca3e8f6", "metadata": { "editable": true }, @@ -721,7 +723,7 @@ }, { "cell_type": "markdown", - "id": "2e7cefe9", + "id": "3b52d4e1", "metadata": { "editable": true }, @@ -733,7 +735,7 @@ }, { "cell_type": "markdown", - "id": "3a57ee54", + "id": "30a7affc", "metadata": { "editable": true }, @@ -745,7 +747,7 @@ }, { "cell_type": "markdown", - "id": "0c8b6913", + "id": "58b6c025", "metadata": { "editable": true }, @@ -755,7 +757,7 @@ }, { "cell_type": "markdown", - "id": "7d4f78af", + "id": "3212b62b", "metadata": { "editable": true }, @@ -767,7 +769,7 @@ }, { "cell_type": "markdown", - "id": "2491c3b2", + "id": "9b4093fe", "metadata": { "editable": true }, @@ -779,7 +781,7 @@ }, { "cell_type": "markdown", - "id": "fad8fc64", + "id": "f887571e", "metadata": { "editable": true }, @@ -791,7 +793,7 @@ }, { "cell_type": "markdown", - "id": "730ff956", + "id": "3c52aecb", "metadata": { "editable": true }, @@ -802,7 +804,7 @@ }, { "cell_type": "markdown", - "id": "68037259", + "id": "c2ca7d94", "metadata": { "editable": true }, @@ -816,7 +818,7 @@ }, { "cell_type": "markdown", - "id": "b2f68357", + "id": "d0814379", "metadata": { "editable": true }, @@ -834,7 +836,7 @@ }, { "cell_type": "markdown", - "id": "62b20822", + "id": "37aa2860", "metadata": { "editable": true }, @@ -847,7 +849,7 @@ }, { "cell_type": "markdown", - "id": "28b60646", + "id": "9634d093", "metadata": { "editable": true }, @@ -865,7 +867,7 @@ }, { "cell_type": "markdown", - "id": "7d85c5c5", + "id": "29991f53", "metadata": { "editable": true }, @@ -879,7 +881,7 @@ }, { "cell_type": "markdown", - "id": "cc333147", + "id": "a4c5c132", "metadata": { "editable": true }, @@ -895,7 +897,7 @@ }, { "cell_type": "markdown", - "id": "e813afad", + "id": "23bbc731", "metadata": { "editable": true }, @@ -913,7 +915,7 @@ }, { "cell_type": "markdown", - "id": "b86ebc62", + "id": "a8be6a8f", "metadata": { "editable": true }, @@ -929,7 +931,7 @@ }, { "cell_type": "markdown", - "id": "243141b7", + "id": "b1f6dde3", "metadata": { "editable": true }, @@ -944,7 +946,7 @@ }, { "cell_type": "markdown", - "id": "dfa56e2f", + "id": "52d1e6d0", "metadata": { "editable": true }, @@ -963,7 +965,7 @@ }, { "cell_type": "markdown", - "id": "f4edc25f", + "id": "5dd784d6", "metadata": { "editable": true }, @@ -975,7 +977,7 @@ }, { "cell_type": "markdown", - "id": "a86fd159", + "id": "50cd21e3", "metadata": { "editable": true }, @@ -986,7 +988,7 @@ }, { "cell_type": "markdown", - "id": "ef87dca2", + "id": "5631b73a", "metadata": { "editable": true }, @@ -1007,7 +1009,7 @@ }, { "cell_type": "markdown", - "id": "e32a63e2", + "id": "4cbbda23", "metadata": { "editable": true }, @@ -1023,7 +1025,7 @@ }, { "cell_type": "markdown", - "id": "6000ff06", + "id": "1d55097f", "metadata": { "editable": true }, @@ -1041,7 +1043,7 @@ }, { "cell_type": "markdown", - "id": "47f80db7", + "id": "21812778", "metadata": { "editable": true }, @@ -1053,7 +1055,7 @@ }, { "cell_type": "markdown", - "id": "2800a950", + "id": "ab3720f7", "metadata": { "editable": true }, @@ -1063,7 +1065,7 @@ }, { "cell_type": "markdown", - "id": "7cab0f9d", + "id": "1e1dd46d", "metadata": { "editable": true }, @@ -1075,7 +1077,7 @@ }, { "cell_type": "markdown", - "id": "07645ed0", + "id": "1f73e566", "metadata": { "editable": true }, @@ -1087,7 +1089,7 @@ }, { "cell_type": "markdown", - "id": "a2974555", + "id": "00b9b1d2", "metadata": { "editable": true }, @@ -1099,7 +1101,7 @@ }, { "cell_type": "markdown", - "id": "ebbfd407", + "id": "b27a9b22", "metadata": { "editable": true }, @@ -1109,7 +1111,7 @@ }, { "cell_type": "markdown", - "id": "fdb38437", + "id": "f5e818df", "metadata": { "editable": true }, @@ -1121,7 +1123,7 @@ }, { "cell_type": "markdown", - "id": "60d32f97", + "id": "5d40e9b7", "metadata": { "editable": true }, @@ -1133,7 +1135,7 @@ }, { "cell_type": "markdown", - "id": "289c5d5a", + "id": "a2488003", "metadata": { "editable": true }, @@ -1145,7 +1147,7 @@ }, { "cell_type": "markdown", - "id": "0f99bfab", + "id": "f3424a4a", "metadata": { "editable": true }, @@ -1161,7 +1163,7 @@ }, { "cell_type": "markdown", - "id": "ea711e56", + "id": "b8ec7a35", "metadata": { "editable": true }, @@ -1174,7 +1176,7 @@ }, { "cell_type": "markdown", - "id": "e3b78574", + "id": "0e2c28ae", "metadata": { "editable": true }, @@ -1186,7 +1188,7 @@ }, { "cell_type": "markdown", - "id": "6022493c", + "id": "9eb2d76b", "metadata": { "editable": true }, @@ -1196,7 +1198,7 @@ }, { "cell_type": "markdown", - "id": "09654ff5", + "id": "f17d4c03", "metadata": { "editable": true }, @@ -1208,7 +1210,7 @@ }, { "cell_type": "markdown", - "id": "b2ec11d7", + "id": "027e2d72", "metadata": { "editable": true }, @@ -1223,7 +1225,7 @@ }, { "cell_type": "markdown", - "id": "40b30836", + "id": "88be64cf", "metadata": { "editable": true }, @@ -1238,7 +1240,7 @@ }, { "cell_type": "markdown", - "id": "f930208c", + "id": "d297ed25", "metadata": { "editable": true }, @@ -1250,7 +1252,7 @@ }, { "cell_type": "markdown", - "id": "80b4893d", + "id": "de288b76", "metadata": { "editable": true }, @@ -1260,7 +1262,7 @@ }, { "cell_type": "markdown", - "id": "dc9dd0b8", + "id": "2aaea6bf", "metadata": { "editable": true }, @@ -1272,7 +1274,7 @@ }, { "cell_type": "markdown", - "id": "58a3357b", + "id": "00d4208e", "metadata": { "editable": true }, @@ -1288,7 +1290,7 @@ }, { "cell_type": "markdown", - "id": "529f7cdc", + "id": "96af754f", "metadata": { "editable": true }, @@ -1300,7 +1302,7 @@ }, { "cell_type": "markdown", - "id": "66dec35a", + "id": "21b0c1e8", "metadata": { "editable": true }, @@ -1313,7 +1315,7 @@ }, { "cell_type": "markdown", - "id": "0c422088", + "id": "be785720", "metadata": { "editable": true }, @@ -1327,7 +1329,7 @@ }, { "cell_type": "markdown", - "id": "099f31ca", + "id": "b7058d94", "metadata": { "editable": true }, @@ -1337,7 +1339,7 @@ }, { "cell_type": "markdown", - "id": "4a433685", + "id": "b88a0094", "metadata": { "editable": true }, @@ -1350,7 +1352,7 @@ }, { "cell_type": "markdown", - "id": "b4761147", + "id": "5e4e20bc", "metadata": { "editable": true }, @@ -1365,7 +1367,7 @@ }, { "cell_type": "markdown", - "id": "3fbfc908", + "id": "d75708bf", "metadata": { "editable": true }, @@ -1377,7 +1379,7 @@ }, { "cell_type": "markdown", - "id": "818858c4", + "id": "a905172f", "metadata": { "editable": true }, @@ -1387,7 +1389,7 @@ }, { "cell_type": "markdown", - "id": "fd530fe5", + "id": "1cae567c", "metadata": { "editable": true }, @@ -1400,7 +1402,7 @@ }, { "cell_type": "markdown", - "id": "9354b7d5", + "id": "8fd08506", "metadata": { "editable": true }, @@ -1411,7 +1413,7 @@ }, { "cell_type": "markdown", - "id": "00fa313a", + "id": "5eb78b07", "metadata": { "editable": true }, @@ -1423,7 +1425,7 @@ }, { "cell_type": "markdown", - "id": "270e4865", + "id": "96796312", "metadata": { "editable": true }, @@ -1433,7 +1435,7 @@ }, { "cell_type": "markdown", - "id": "edbcab84", + "id": "10c03ac1", "metadata": { "editable": true }, @@ -1448,7 +1450,7 @@ }, { "cell_type": "markdown", - "id": "36b795e3", + "id": "fcd5c905", "metadata": { "editable": true }, @@ -1458,7 +1460,7 @@ }, { "cell_type": "markdown", - "id": "7ede6ae6", + "id": "04f7219c", "metadata": { "editable": true }, @@ -1470,7 +1472,7 @@ }, { "cell_type": "markdown", - "id": "6ddb6ed0", + "id": "9ee70da3", "metadata": { "editable": true }, @@ -1480,7 +1482,7 @@ }, { "cell_type": "markdown", - "id": "21e963dd", + "id": "32bf0b36", "metadata": { "editable": true }, @@ -1496,7 +1498,7 @@ }, { "cell_type": "markdown", - "id": "d475664d", + "id": "bd9f1937", "metadata": { "editable": true }, @@ -1524,7 +1526,7 @@ }, { "cell_type": "markdown", - "id": "f4c3af28", + "id": "47cafbf5", "metadata": { "editable": true }, @@ -1540,7 +1542,7 @@ }, { "cell_type": "markdown", - "id": "50275b5c", + "id": "cf5c61df", "metadata": { "editable": true }, @@ -1552,7 +1554,7 @@ }, { "cell_type": "markdown", - "id": "9b57dc67", + "id": "c22d0618", "metadata": { "editable": true }, @@ -1564,7 +1566,7 @@ }, { "cell_type": "markdown", - "id": "94ff2ab0", + "id": "910ce75f", "metadata": { "editable": true }, @@ -1574,7 +1576,7 @@ }, { "cell_type": "markdown", - "id": "a2a3dd25", + "id": "0615df08", "metadata": { "editable": true }, @@ -1588,7 +1590,7 @@ }, { "cell_type": "markdown", - "id": "d15a0013", + "id": "452f4413", "metadata": { "editable": true }, @@ -1600,7 +1602,7 @@ }, { "cell_type": "markdown", - "id": "5836e519", + "id": "cb97c13e", "metadata": { "editable": true }, @@ -1622,7 +1624,7 @@ }, { "cell_type": "markdown", - "id": "cfb92cbf", + "id": "3425f9b9", "metadata": { "editable": true }, @@ -1654,7 +1656,7 @@ }, { "cell_type": "markdown", - "id": "190d6c8b", + "id": "9659e588", "metadata": { "editable": true }, @@ -1670,7 +1672,7 @@ }, { "cell_type": "markdown", - "id": "882258b7", + "id": "696da180", "metadata": { "editable": true }, @@ -1690,7 +1692,7 @@ }, { "cell_type": "markdown", - "id": "bed7823c", + "id": "f62d8385", "metadata": { "editable": true }, @@ -1707,7 +1709,7 @@ }, { "cell_type": "markdown", - "id": "22f5d684", + "id": "da48ec69", "metadata": { "editable": true }, @@ -1723,7 +1725,7 @@ }, { "cell_type": "markdown", - "id": "b2649f3e", + "id": "82697e96", "metadata": { "editable": true }, @@ -1742,7 +1744,7 @@ }, { "cell_type": "markdown", - "id": "1834e420", + "id": "603caa07", "metadata": { "editable": true }, @@ -1755,7 +1757,7 @@ }, { "cell_type": "markdown", - "id": "dd440897", + "id": "a15c5a6f", "metadata": { "editable": true }, @@ -1767,7 +1769,7 @@ }, { "cell_type": "markdown", - "id": "642fb412", + "id": "dbffa234", "metadata": { "editable": true }, @@ -1788,7 +1790,7 @@ }, { "cell_type": "markdown", - "id": "8cb95015", + "id": "c08597db", "metadata": { "editable": true }, @@ -1809,7 +1811,7 @@ }, { "cell_type": "markdown", - "id": "ec129aa9", + "id": "36ead32a", "metadata": { "editable": true }, @@ -1835,7 +1837,7 @@ }, { "cell_type": "markdown", - "id": "1784ef4f", + "id": "76a692c3", "metadata": { "editable": true }, @@ -1854,7 +1856,7 @@ }, { "cell_type": "markdown", - "id": "1f4a8fa4", + "id": "177759f2", "metadata": { "editable": true }, @@ -1865,7 +1867,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "27ce77a4", + "id": "f4f578f8", "metadata": { "collapsed": false, "editable": true @@ -1916,7 +1918,7 @@ }, { "cell_type": "markdown", - "id": "96465954", + "id": "6fd14013", "metadata": { "editable": true }, @@ -1927,7 +1929,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "e8ef9f8b", + "id": "bea60977", "metadata": { "collapsed": false, "editable": true @@ -1960,7 +1962,7 @@ }, { "cell_type": "markdown", - "id": "1ba8c4a7", + "id": "849c5abf", "metadata": { "editable": true }, @@ -1971,7 +1973,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "e951d8a7", + "id": "f6cf91b0", "metadata": { "collapsed": false, "editable": true @@ -2008,7 +2010,7 @@ }, { "cell_type": "markdown", - "id": "b65d95c6", + "id": "1762e77d", "metadata": { "editable": true }, @@ -2019,7 +2021,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "4854ee21", + "id": "85cb8818", "metadata": { "collapsed": false, "editable": true @@ -2046,7 +2048,7 @@ }, { "cell_type": "markdown", - "id": "f0be310d", + "id": "7cad90f7", "metadata": { "editable": true }, @@ -2057,7 +2059,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "d437f3ee", + "id": "526e2167", "metadata": { "collapsed": false, "editable": true @@ -2098,7 +2100,7 @@ }, { "cell_type": "markdown", - "id": "5a3d47b9", + "id": "3676714e", "metadata": { "editable": true }, @@ -2114,7 +2116,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "2ff3e78a", + "id": "ddec0620", "metadata": { "collapsed": false, "editable": true @@ -2135,7 +2137,7 @@ }, { "cell_type": "markdown", - "id": "bf052d5b", + "id": "68c162f4", "metadata": { "editable": true }, @@ -2148,7 +2150,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "c271073c", + "id": "af8654a4", "metadata": { "collapsed": false, "editable": true @@ -2172,7 +2174,7 @@ }, { "cell_type": "markdown", - "id": "19173173", + "id": "1038efea", "metadata": { "editable": true }, @@ -2187,7 +2189,7 @@ { "cell_type": "code", "execution_count": 9, - "id": "f25a2b00", + "id": "6a377cfd", "metadata": { "collapsed": false, "editable": true @@ -2208,7 +2210,7 @@ }, { "cell_type": "markdown", - "id": "b6bb4493", + "id": "22897193", "metadata": { "editable": true }, @@ -2218,7 +2220,7 @@ }, { "cell_type": "markdown", - "id": "0904c3ae", + "id": "30ef3e7c", "metadata": { "editable": true }, @@ -2237,7 +2239,7 @@ { "cell_type": "code", "execution_count": 10, - "id": "fe15cab4", + "id": "349e7619", "metadata": { "collapsed": false, "editable": true @@ -2254,7 +2256,7 @@ }, { "cell_type": "markdown", - "id": "5bb3e108", + "id": "3d8d954b", "metadata": { "editable": true }, @@ -2264,7 +2266,7 @@ }, { "cell_type": "markdown", - "id": "d1ee0550", + "id": "7f0847a8", "metadata": { "editable": true }, @@ -2275,7 +2277,7 @@ { "cell_type": "code", "execution_count": 11, - "id": "12a863db", + "id": "783f6194", "metadata": { "collapsed": false, "editable": true @@ -2292,7 +2294,7 @@ }, { "cell_type": "markdown", - "id": "0c92f59f", + "id": "0e1cce97", "metadata": { "editable": true }, @@ -2303,7 +2305,7 @@ { "cell_type": "code", "execution_count": 12, - "id": "ad5de6ba", + "id": "7d87be54", "metadata": { "collapsed": false, "editable": true @@ -2324,7 +2326,7 @@ }, { "cell_type": "markdown", - "id": "268e4681", + "id": "5287a9fb", "metadata": { "editable": true }, @@ -2357,7 +2359,7 @@ }, { "cell_type": "markdown", - "id": "63a3c676", + "id": "5376c8cd", "metadata": { "editable": true }, @@ -2381,7 +2383,7 @@ }, { "cell_type": "markdown", - "id": "23f5d36c", + "id": "8cf0b8dc", "metadata": { "editable": true }, @@ -2404,7 +2406,7 @@ { "cell_type": "code", "execution_count": 13, - "id": "8781066d", + "id": "f2619dd7", "metadata": { "collapsed": false, "editable": true @@ -2545,7 +2547,7 @@ }, { "cell_type": "markdown", - "id": "ffc048f1", + "id": "04f25816", "metadata": { "editable": true }, @@ -2558,7 +2560,7 @@ { "cell_type": "code", "execution_count": 14, - "id": "ad1eebc2", + "id": "9afe39a2", "metadata": { "collapsed": false, "editable": true @@ -2571,7 +2573,7 @@ }, { "cell_type": "markdown", - "id": "8ede1233", + "id": "3e912906", "metadata": { "editable": true }, @@ -2582,7 +2584,7 @@ { "cell_type": "code", "execution_count": 15, - "id": "2a0ff87f", + "id": "aa146e1b", "metadata": { "collapsed": false, "editable": true @@ -2604,7 +2606,7 @@ }, { "cell_type": "markdown", - "id": "b012d951", + "id": "fba31aff", "metadata": { "editable": true }, @@ -2620,7 +2622,7 @@ { "cell_type": "code", "execution_count": 16, - "id": "5e99cc1a", + "id": "abdcad5a", "metadata": { "collapsed": false, "editable": true @@ -2667,7 +2669,7 @@ }, { "cell_type": "markdown", - "id": "5a633ec6", + "id": "894970b1", "metadata": { "editable": true }, @@ -2682,7 +2684,7 @@ { "cell_type": "code", "execution_count": 17, - "id": "7263c6aa", + "id": "6a778d9d", "metadata": { "collapsed": false, "editable": true @@ -2703,7 +2705,7 @@ }, { "cell_type": "markdown", - "id": "51292641", + "id": "4fd0dfdb", "metadata": { "editable": true }, @@ -2720,7 +2722,7 @@ { "cell_type": "code", "execution_count": 18, - "id": "e4126eff", + "id": "53d2e40d", "metadata": { "collapsed": false, "editable": true @@ -2779,7 +2781,7 @@ }, { "cell_type": "markdown", - "id": "0de2275f", + "id": "09771b87", "metadata": { "editable": true }, @@ -2796,7 +2798,7 @@ { "cell_type": "code", "execution_count": 19, - "id": "65747114", + "id": "08f622fa", "metadata": { "collapsed": false, "editable": true @@ -2817,7 +2819,7 @@ }, { "cell_type": "markdown", - "id": "1a00b6b5", + "id": "81c7eaef", "metadata": { "editable": true }, @@ -2834,7 +2836,7 @@ }, { "cell_type": "markdown", - "id": "fac7ab1e", + "id": "0998392d", "metadata": { "editable": true }, @@ -2846,7 +2848,7 @@ }, { "cell_type": "markdown", - "id": "b00005e0", + "id": "147961a0", "metadata": { "editable": true }, @@ -2862,7 +2864,7 @@ }, { "cell_type": "markdown", - "id": "30e6b25a", + "id": "f67f1f6d", "metadata": { "editable": true }, @@ -2874,7 +2876,7 @@ }, { "cell_type": "markdown", - "id": "46ee3e18", + "id": "dec83f81", "metadata": { "editable": true }, @@ -2889,7 +2891,7 @@ }, { "cell_type": "markdown", - "id": "83eeff5c", + "id": "5a5b1e07", "metadata": { "editable": true }, @@ -2901,7 +2903,7 @@ }, { "cell_type": "markdown", - "id": "e9431c97", + "id": "7c27a0fe", "metadata": { "editable": true }, @@ -2919,7 +2921,7 @@ }, { "cell_type": "markdown", - "id": "45db87af", + "id": "4c81a107", "metadata": { "editable": true }, @@ -2938,7 +2940,7 @@ }, { "cell_type": "markdown", - "id": "b8306772", + "id": "24228635", "metadata": { "editable": true }, @@ -2950,7 +2952,7 @@ }, { "cell_type": "markdown", - "id": "dbd3cbde", + "id": "89692cf6", "metadata": { "editable": true }, @@ -2967,7 +2969,7 @@ }, { "cell_type": "markdown", - "id": "d210e12e", + "id": "0ecfdafa", "metadata": { "editable": true }, @@ -2980,7 +2982,7 @@ }, { "cell_type": "markdown", - "id": "599e20b0", + "id": "33c6332e", "metadata": { "editable": true }, @@ -3009,7 +3011,7 @@ }, { "cell_type": "markdown", - "id": "cb695360", + "id": "a573879c", "metadata": { "editable": true }, @@ -3019,7 +3021,7 @@ }, { "cell_type": "markdown", - "id": "8d46bb8e", + "id": "e515a3e4", "metadata": { "editable": true }, @@ -3031,7 +3033,7 @@ }, { "cell_type": "markdown", - "id": "eb890b89", + "id": "e53c0a21", "metadata": { "editable": true }, @@ -3052,7 +3054,7 @@ }, { "cell_type": "markdown", - "id": "b4bbb381", + "id": "aee15740", "metadata": { "editable": true }, @@ -3070,7 +3072,7 @@ }, { "cell_type": "markdown", - "id": "01687a74", + "id": "2ed1f60a", "metadata": { "editable": true }, @@ -3086,7 +3088,7 @@ }, { "cell_type": "markdown", - "id": "615c3a40", + "id": "9859970d", "metadata": { "editable": true }, @@ -3099,7 +3101,7 @@ }, { "cell_type": "markdown", - "id": "72955cc1", + "id": "128b4dc2", "metadata": { "editable": true }, @@ -3123,7 +3125,7 @@ }, { "cell_type": "markdown", - "id": "f12ceb05", + "id": "c6fb6517", "metadata": { "editable": true }, @@ -3144,7 +3146,7 @@ }, { "cell_type": "markdown", - "id": "ea780463", + "id": "b01d3014", "metadata": { "editable": true }, @@ -3157,7 +3159,7 @@ { "cell_type": "code", "execution_count": 20, - "id": "a90afd15", + "id": "67babc7b", "metadata": { "collapsed": false, "editable": true @@ -3239,7 +3241,7 @@ }, { "cell_type": "markdown", - "id": "54721472", + "id": "406e9884", "metadata": { "editable": true }, @@ -3253,7 +3255,7 @@ { "cell_type": "code", "execution_count": 21, - "id": "e468e682", + "id": "c9887d3f", "metadata": { "collapsed": false, "editable": true @@ -3280,7 +3282,7 @@ }, { "cell_type": "markdown", - "id": "f594d7ff", + "id": "239d497a", "metadata": { "editable": true }, @@ -3301,7 +3303,7 @@ { "cell_type": "code", "execution_count": 22, - "id": "4d8a800e", + "id": "bf4ab84e", "metadata": { "collapsed": false, "editable": true @@ -3351,7 +3353,7 @@ }, { "cell_type": "markdown", - "id": "34754ffe", + "id": "4bf788aa", "metadata": { "editable": true }, @@ -3366,7 +3368,7 @@ { "cell_type": "code", "execution_count": 23, - "id": "5de68401", + "id": "6d3dca2d", "metadata": { "collapsed": false, "editable": true @@ -3407,7 +3409,7 @@ }, { "cell_type": "markdown", - "id": "d966b48f", + "id": "0dacddbe", "metadata": { "editable": true }, @@ -3449,7 +3451,7 @@ { "cell_type": "code", "execution_count": 24, - "id": "614f7d11", + "id": "17f9a3e4", "metadata": { "collapsed": false, "editable": true @@ -3735,7 +3737,7 @@ }, { "cell_type": "markdown", - "id": "91fe208e", + "id": "2ebd51a9", "metadata": { "editable": true }, @@ -3758,7 +3760,7 @@ }, { "cell_type": "markdown", - "id": "54732a57", + "id": "6e37ad83", "metadata": { "editable": true }, @@ -3771,7 +3773,7 @@ { "cell_type": "code", "execution_count": 25, - "id": "3def1d1b", + "id": "09290632", "metadata": { "collapsed": false, "editable": true @@ -3819,7 +3821,7 @@ }, { "cell_type": "markdown", - "id": "82c734a0", + "id": "111f84ed", "metadata": { "editable": true }, @@ -3841,7 +3843,7 @@ }, { "cell_type": "markdown", - "id": "46b99df3", + "id": "589e5822", "metadata": { "editable": true }, @@ -3863,7 +3865,7 @@ { "cell_type": "code", "execution_count": 26, - "id": "c2acf854", + "id": "c9c28b65", "metadata": { "collapsed": false, "editable": true @@ -4025,7 +4027,7 @@ }, { "cell_type": "markdown", - "id": "ccfb1123", + "id": "1fcb9ea1", "metadata": { "editable": true }, @@ -4046,7 +4048,7 @@ { "cell_type": "code", "execution_count": 27, - "id": "af9bb6f5", + "id": "d8651caa", "metadata": { "collapsed": false, "editable": true @@ -4109,7 +4111,7 @@ }, { "cell_type": "markdown", - "id": "677b815c", + "id": "e6b69672", "metadata": { "editable": true }, @@ -4133,7 +4135,7 @@ { "cell_type": "code", "execution_count": 28, - "id": "6d819597", + "id": "a37def90", "metadata": { "collapsed": false, "editable": true @@ -4361,7 +4363,7 @@ }, { "cell_type": "markdown", - "id": "80e7a053", + "id": "c8b1cfa7", "metadata": { "editable": true }, @@ -4382,7 +4384,7 @@ { "cell_type": "code", "execution_count": 29, - "id": "c5ff412e", + "id": "27960893", "metadata": { "collapsed": false, "editable": true @@ -4686,7 +4688,7 @@ }, { "cell_type": "markdown", - "id": "55f90495", + "id": "a0cd956f", "metadata": { "editable": true }, @@ -4699,7 +4701,7 @@ { "cell_type": "code", "execution_count": 30, - "id": "b1b5c407", + "id": "87e14f3b", "metadata": { "collapsed": false, "editable": true @@ -5234,7 +5236,7 @@ }, { "cell_type": "markdown", - "id": "d865fd5b", + "id": "bfc23ff8", "metadata": { "editable": true }, @@ -5253,7 +5255,7 @@ { "cell_type": "code", "execution_count": 31, - "id": "c9ca06bf", + "id": "1d20960c", "metadata": { "collapsed": false, "editable": true @@ -5266,7 +5268,7 @@ }, { "cell_type": "markdown", - "id": "f27c441a", + "id": "6752a03f", "metadata": { "editable": true }, @@ -5282,7 +5284,7 @@ { "cell_type": "code", "execution_count": 32, - "id": "5b16f84e", + "id": "c21b80e7", "metadata": { "collapsed": false, "editable": true @@ -5308,7 +5310,7 @@ }, { "cell_type": "markdown", - "id": "8a9bbaf9", + "id": "10e46b6b", "metadata": { "editable": true }, @@ -5332,7 +5334,7 @@ { "cell_type": "code", "execution_count": 33, - "id": "cb05b690", + "id": "29d4f033", "metadata": { "collapsed": false, "editable": true @@ -5367,7 +5369,7 @@ }, { "cell_type": "markdown", - "id": "7a156970", + "id": "96a37378", "metadata": { "editable": true }, @@ -5386,7 +5388,7 @@ { "cell_type": "code", "execution_count": 34, - "id": "9c0fc11c", + "id": "79096135", "metadata": { "collapsed": false, "editable": true @@ -5414,7 +5416,7 @@ }, { "cell_type": "markdown", - "id": "6549339a", + "id": "7601ba4d", "metadata": { "editable": true }, @@ -5443,7 +5445,7 @@ { "cell_type": "code", "execution_count": 35, - "id": "036596e7", + "id": "30431eab", "metadata": { "collapsed": false, "editable": true @@ -5512,7 +5514,7 @@ }, { "cell_type": "markdown", - "id": "3e34540f", + "id": "c0f7ead9", "metadata": { "editable": true }, @@ -5530,7 +5532,7 @@ }, { "cell_type": "markdown", - "id": "e592802c", + "id": "8eba3502", "metadata": { "editable": true }, @@ -5554,7 +5556,7 @@ { "cell_type": "code", "execution_count": 36, - "id": "13593040", + "id": "d15712bc", "metadata": { "collapsed": false, "editable": true @@ -5585,7 +5587,7 @@ }, { "cell_type": "markdown", - "id": "e12c7c55", + "id": "65c59f0c", "metadata": { "editable": true }, @@ -5615,7 +5617,7 @@ }, { "cell_type": "markdown", - "id": "863ae79c", + "id": "20545917", "metadata": { "editable": true }, @@ -5626,7 +5628,7 @@ { "cell_type": "code", "execution_count": 37, - "id": "69a1b463", + "id": "8613dd26", "metadata": { "collapsed": false, "editable": true @@ -5676,7 +5678,7 @@ }, { "cell_type": "markdown", - "id": "9903fa36", + "id": "1d4fbbf9", "metadata": { "editable": true }, @@ -5697,7 +5699,7 @@ }, { "cell_type": "markdown", - "id": "6b21aaad", + "id": "6d31f7ab", "metadata": { "editable": true }, @@ -5708,7 +5710,7 @@ { "cell_type": "code", "execution_count": 38, - "id": "b8697733", + "id": "15082cf9", "metadata": { "collapsed": false, "editable": true @@ -5729,7 +5731,7 @@ }, { "cell_type": "markdown", - "id": "c1bd80e7", + "id": "5211e804", "metadata": { "editable": true },

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