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[37 <./lectures/../img/lez5-img7.JPG> <./lectures/../img/lez5-img8.JPG> <./lec tures/../img/lez5-img9.JPG>] LaTeX Warning: Command \textquoteright invalid in math mode on input line 236. LaTeX Warning: Command \textquoteright invalid in math mode on input line 236. File: lectures/../img/lez5-img10.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez5-img10.JPG used on input line 240 . (pdftex.def) Requested size: 272.99881pt x 178.77272pt. Underfull \hbox (badness 10000) in paragraph at lines 229--245 [] Underfull \hbox (badness 10000) in paragraph at lines 229--245 [] Underfull \hbox (badness 10000) in paragraph at lines 255--265 [] Underfull \hbox (badness 10000) in paragraph at lines 255--265 [] [38 <./lectures/../img/lez5-img10.JPG>] Underfull \hbox (badness 10000) in paragraph at lines 267--273 [] Underfull \hbox (badness 10000) in paragraph at lines 267--273 [] ) [39] [40] (lectures/lecture6.tex Chapter 6. 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Underfull \hbox (badness 10000) in paragraph at lines 188--192 [] Overfull \hbox (55.32307pt too wide) detected at line 194 \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 argmin \OT1/cmr/m/n/12 ( \OML/cmm/m/it/12 I\ OMS/cmsy/m/n/12 f[] \OT1/cmr/m/n/12 = 1\OMS/cmsy/m/n/12 g  \U/msb/m/n/12 E [] \OT1/cmr/m/n/12 + \OML/cmm/m/it/12 I\OMS/cmsy/m/n/12 f[] \OT1/cmr/m/n/12 = \OMS /cmsy/m/n/12 \OT1/cmr/m/n/12 1\OMS/cmsy/m/n/12 g  \U/msb/m/n/12 E [] \OT1/cmr /m/n/12 ) = [][] [] Underfull \hbox (badness 10000) in paragraph at lines 199--200 [] Underfull \hbox (badness 10000) in paragraph at lines 202--208 [] [45 <./lectures/../img/lez6-img3.JPG>] Underfull \hbox (badness 10000) in paragraph at lines 229--233 [] File: lectures/../img/lez6-img4.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez6-img4.JPG used on input line 246. (pdftex.def) Requested size: 272.99881pt x 132.1502pt. ) [46 <./lectures/../img/lez6-img4.JPG>] [47] (lectures/lecture7.tex Chapter 7. 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Underfull \hbox (badness 10000) in paragraph at lines 127--145 [] [50 <./lectures/../img/lez7-img2.JPG> <./lectures/../img/lez7-img3.JPG>] Underfull \hbox (badness 10000) in paragraph at lines 147--159 [] Underfull \hbox (badness 10000) in paragraph at lines 147--159 [] Overfull \hbox (76.34352pt too wide) detected at line 161 \OML/cmm/m/it/12 `[] [] \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 min `[] [] [] [] [] `[] [] [][]\OMS/cmsy/m/n/12 ! [] [] File: lectures/../img/lez7-img4.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez7-img4.JPG used on input line 165. (pdftex.def) Requested size: 117.00119pt x 36.9666pt. File: lectures/../img/lez7-img5.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez7-img5.JPG used on input line 172. (pdftex.def) Requested size: 117.00119pt x 54.55045pt. LaTeX Warning: Command \textquoteright invalid in math mode on input line 176. 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Underfull \hbox (badness 10000) in paragraph at lines 8--10 [] Overfull \hbox (27.40504pt too wide) detected at line 12 \OML/cmm/m/it/12 S \OT1/cmr/m/n/12 = \OMS/cmsy/m/n/12 f\OT1/cmr/m/n/12 (\OML/cm m/m/it/12 x[]; y[]\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 :::\OT1/cmr/m/n/12 (\OML/cm m/m/it/12 x[]; y[]\OT1/cmr/m/n/12 )\OMS/cmsy/m/n/12 g \OML/cmm/m/it/12 x[] \OMS /cmsy/m/n/12 2 \U/msb/m/n/12 R[] \OML/cmm/m/it/12 y[] \OMS/cmsy/m/n/12 2 f\OT1 /cmr/m/n/12 1\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 +1\OMS/cmsy/m/n/12 g \OML/cmm/m /it/12 `[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 w\OT1/cmr/m/n/12 ) = \OML/cmm/m/it/ 12 I\OMS/cmsy/m/n/12 f\OML/cmm/m/it/12 y[]w[]x[] \OMS/cmsy/m/n/12  \OT1/cmr/m/ n/12 0\OMS/cmsy/m/n/12 g [] Underfull \hbox (badness 10000) in paragraph at lines 16--22 [] Underfull \hbox (badness 10000) in paragraph at lines 29--37 [] Underfull \hbox (badness 10000) in paragraph at lines 29--37 [] Underfull \hbox (badness 10000) in paragraph at lines 29--37 [] Overfull \hbox (17.38333pt too wide) detected at line 38 \OMS/cmsy/m/n/12 8\OML/cmm/m/it/12 A [] and \OMS/cmsy/m/n/12 8\OML/cmm/m/it/1 2 C \OMS/cmsy/m/n/12 9\OML/cmm/m/it/12 S [] [] \OMS/cmsy/m/n/12  \OML/cmm/m/it /12 c \OMS/cmsy/m/n/12  [] [] [] [] File: lectures/../img/lez13-img1.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez13-img1.JPG used on input line 51. 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Underfull \hbox (badness 10000) in paragraph at lines 202--211 [] Overfull \hbox (10.59775pt too wide) detected at line 224 \OML/cmm/m/it/12 h\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 ) = \OML/c mm/m/it/12 w[] x `[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 w\OT1/cmr/m/n/12 ) = \OML /cmm/m/it/12 `\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 w[] x[]; y[]\OT1/cmr/m/n/12 ) [ ] \OML/cmm/m/it/12 `\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 w[] x[]; y[]\OT1/cmr/m/n/ 12 ) = (\OML/cmm/m/it/12 w[] x[] \OMS/cmsy/m/n/12 \OML/cmm/m/it/12 y[]\OT1/cm r/m/n/12 )[] [] ) [97 <./lectures/../img/lez14-img4.JPG>] (lectures/lecture15.tex Chapter 15. Underfull \hbox (badness 10000) in paragraph at lines 7--9 [] Underfull \hbox (badness 10000) in paragraph at lines 14--20 [] [98 ] File: lectures/../img/lez15-img1.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez15-img1.JPG used on input line 45. (pdftex.def) Requested size: 117.00119pt x 54.50513pt. 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Underfull \hbox (badness 10000) in paragraph at lines 96--101 [] Overfull \hbox (43.52298pt too wide) detected at line 109 \OT1/cmr/m/n/12 = \OMS/cmsy/m/n/12 [] \OT1/cmr/m/n/12 (\OML/cmm/m/it/12 w[] \O MS/cmsy/m/n/12 \OML/cmm/m/it/12 w[]\OT1/cmr/m/n/12 )[] (\OML/cmm/m/it/12 w[] \OMS/cmsy/m/n/12 \OML/cmm/m/it/12 u\OT1/cmr/m/n/12 ) = [] [] \OMS/cmsy/m/n /12  [] File: lectures/../img/lez15-img4.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez15-img4.JPG used on input line 117 . (pdftex.def) Requested size: 117.00119pt x 78.18626pt. Underfull \hbox (badness 10000) in paragraph at lines 113--125 [] [100 <./lectures/../img/lez15-img3.JPG>] Overfull \hbox (88.26935pt too wide) detected at line 137 \OT1/cmr/m/n/12 = [][] \OMS/cmsy/m/n/12 [][] \OT1/cmr/m/n/12 + []\OMS/cmsy/m/ n/12 k\OML/cmm/m/it/12 w[] \OMS/cmsy/m/n/12 \OML/cmm/m/it/12 w[]\OMS/cmsy/m/n /12 k[] [] Underfull \hbox (badness 10000) in paragraph at lines 137--139 [] Underfull \hbox (badness 10000) in paragraph at lines 142--145 [] Overfull \hbox (52.34819pt too wide) detected at line 147 \OMS/cmsy/m/n/12  []k\OML/cmm/m/it/12 w[] \OMS/cmsy/m/n/12 \OML/cmm/m/it/12 u\OMS/cmsy/m/n/12 k[] []k\OML/cmm/m/it/12 w[] \OMS/cmsy/m/n/12 \OML/cmm/m/i t/12 u\OMS/cmsy/m/n/12 k[] \OT1/cmr/m/n/12 + [] [] \OMS/cmsy/m/n/12 k\OML/cmm/m /it/12 w[] \OMS/cmsy/m/n/12 \OML/cmm/m/it/12 u\OMS/cmsy/m/n/12 k[] [] \OT1/cm r/m/n/12 + [] [] [] [] Overfull \hbox (10.22507pt too wide) in paragraph at lines 147--153 \T1/cmr/m/n/12 where $\OML/cmm/m/it/12 w[] \OT1/cmr/m/n/12 = 0$ \T1/cmr/m/n/12 and $\OMS/cmsy/m/n/12 k\OML/cmm/m/it/12 w[] \OMS/cmsy/m/n/12 \OML/cmm/m/it/ 12 u\OMS/cmsy/m/n/12 k[]  \OT1/cmr/m/n/12 4 \OML/cmm/m/it/12 U[]$ \T1/cmr/m/n /12 and $\OMS/cmsy/m/n/12 k\OML/cmm/m/it/12 w[] \OMS/cmsy/m/n/12 \OML/cmm/m/ it/12 w[]\OMS/cmsy/m/n/12 k[] \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 []\OMS/cmsy/m /n/12 kr\OML/cmm/m/it/12 `[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 w[]\OT1/cmr/m/n/1 2 )\OMS/cmsy/m/n/12 k[]$ [] Underfull \hbox (badness 10000) in paragraph at lines 164--171 [] [101 <./lectures/../img/lez15-img4.JPG>]) Underfull \hbox (badness 10000) in paragraph at lines 196--137 [] Underfull \hbox (badness 10000) in paragraph at lines 196--137 [] [102] (lectures/lecture16.tex Chapter 16. 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Underfull \hbox (badness 10000) in paragraph at lines 56--70 [] Underfull \hbox (badness 10000) in paragraph at lines 56--70 [] Underfull \hbox (badness 10000) in paragraph at lines 75--78 [] Overfull \hbox (37.19511pt too wide) detected at line 94 \OMS/cmsy/m/n/12  [] k\OML/cmm/m/it/12 U\OMS/cmsy/m/n/12 k[] \OT1/cmr/m/n/12 + [][] + [] [] \OML/cmm/m/it/12 I\OMS/cmsy/m/n/12 f\OML/cmm/m/it/12 y[] w[]x[] \OMS/cmsy/m/n/12  \OT1/cmr/m/n/12 0\OMS/cmsy/m/n/12 g [] [104 <./lectures/../img/lez16-img2.JPG>] File: lectures/../img/lez16-img3.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez16-img3.JPG used on input line 106 . (pdftex.def) Requested size: 155.99762pt x 86.88896pt. 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Underfull \hbox (badness 10000) in paragraph at lines 7--12 [] Underfull \hbox (badness 10000) in paragraph at lines 12--14 [] Underfull \hbox (badness 10000) in paragraph at lines 16--21 [] Overfull \hbox (17.19559pt too wide) detected at line 41 \OT1/cmr/m/n/12 +[][] + [][] + [] [] \OML/cmm/m/it/12 [] [] [109 ] Overfull \hbox (62.05049pt too wide) detected at line 59 [] [] [] \OML/cmm/m/it/12 << [] []max[]\OMS/cmsy/m/n/12 kr\OML/cmm/m/it/12 `[ ]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 w[]\OT1/cmr/m/n/12 )\OMS/cmsy/m/n/12 k [] [] Underfull \hbox (badness 10000) in paragraph at lines 59--68 [] Underfull \hbox (badness 10000) in paragraph at lines 59--68 [] Underfull \hbox (badness 10000) in paragraph at lines 69--76 [] Underfull \hbox (badness 10000) in paragraph at lines 78--87 [] [110] Underfull \hbox (badness 10000) in paragraph at lines 108--111 [] Overfull \hbox (2.33182pt too wide) detected at line 113 \OML/cmm/m/it/12 `[]\OT1/cmr/m/n/12 ([]) \OMS/cmsy/m/n/12  [] [] \OML/cmm/m/it /12 `[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 w[]\OT1/cmr/m/n/12 ) [](\OML/cmm/m/it/ 12 x[]; y[]\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 :::\OT1/cmr/m/n/12 (\OML/cmm/m/it/ 12 x[]; y[]\OT1/cmr/m/n/12 ) [] Overfull \hbox (24.90033pt too wide) detected at line 136 [] [] \OML/cmm/m/it/12 `[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 w[]\OT1/cmr/m/n/12 ) \OMS/cmsy/m/n/12  [][] \OT1/cmr/m/n/12 + [] [] [] [111] Underfull \hbox (badness 10000) in paragraph at lines 143--146 [] ) [112] (lectures/lecture18.tex Chapter 18. 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Underfull \hbox (badness 10000) in paragraph at lines 13--16 [] Underfull \hbox (badness 10000) in paragraph at lines 18--23 [] Underfull \hbox (badness 10000) in paragraph at lines 25--53 [] Underfull \hbox (badness 10000) in paragraph at lines 59--67 [] [118 ] Overfull \hbox (23.0944pt too wide) detected at line 72 \OT1/cmr/m/n/12 = [] \OML/cmm/m/it/12 [] < k\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x[]; \OMS/cmsy/m/n/12 \OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; k\OT1/cmr/m/n/12 (\ OML/cmm/m/it/12 x; \OMS/cmsy/m/n/12 \OT1/cmr/m/n/12 ) \OML/cmm/m/it/12 >[] \OT 1/cmr/m/n/12 = [] \OML/cmm/m/it/12 [] < \OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x[ ]\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; []\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1 /cmr/m/n/12 ) \OML/cmm/m/it/12 >[] \OT1/cmr/m/n/12 = [] \OML/cmm/m/it/12 []k\ OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x[]; x\OT1/cmr/m/n/12 ) = \OML/cmm/m/it/12 g\O T1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 ) [] Underfull \hbox (badness 10000) in paragraph at lines 76--79 [] Overfull \hbox (32.28714pt too wide) detected at line 85 \OML/cmm/m/it/12 < f; g >[]\OT1/cmr/m/n/12 =\OML/cmm/m/it/12 < [] [] k\OT1/cmr /m/n/12 (\OML/cmm/m/it/12 x[]; \OMS/cmsy/m/n/12 \OT1/cmr/m/n/12 )\OML/cmm/m/it /12 ; [] [] k\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x[]; \OMS/cmsy/m/n/12 \OT1/cmr /m/n/12 ) \OML/cmm/m/it/12 >[] \OT1/cmr/m/n/12 = [] [] \OML/cmm/m/it/12 [] [ ] < k\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x[]; \OMS/cmsy/m/n/12 \OT1/cmr/m/n/12 ) \OML/cmm/m/it/12 ; k\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x[]; \OMS/cmsy/m/n/12  \ OML/cmm/m/it/12 >[] \OT1/cmr/m/n/12 = [] Underfull \hbox (badness 10000) in paragraph at lines 99--105 [] [119] Underfull \hbox (badness 10000) in paragraph at lines 124--130 [] [120] Underfull \hbox (badness 10000) in paragraph at lines 140--147 [] File: lectures/../img/lez19-img1.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez19-img1.JPG used on input line 157 . (pdftex.def) Requested size: 155.99762pt x 75.78299pt. ) Underfull \hbox (badness 10000) in paragraph at lines 164--148 [] [121 <./lectures/../img/lez19-img1.JPG>] (lectures/lecture20.tex Chapter 20. Underfull \hbox (badness 10000) in paragraph at lines 23--26 [] Underfull \hbox (badness 10000) in paragraph at lines 29--32 [] Underfull \hbox (badness 10000) in paragraph at lines 45--48 [] [122 ] Overfull \hbox (33.66243pt too wide) detected at line 66 \OML/cmm/m/it/12 [] \OT1/cmr/m/n/12 = [] \OML/cmm/m/it/12 [] \OT1/cmr/m/n/12 = [] = \OML/cmm/m/it/12 h[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 w\OT1/cmr/m/n/12 ) [] [] Underfull \hbox (badness 10000) in paragraph at lines 70--76 [] File: lectures/../img/lez20-img1.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez20-img1.JPG used on input line 88. (pdftex.def) Requested size: 117.00119pt x 70.84105pt. 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Overfull \hbox (20.70583pt too wide) detected at line 11 \OML/cmm/m/it/12 w[] \OT1/cmr/m/n/12 = [] [] \OML/cmm/m/it/12 y[] x[] I\OMS/cms y/m/n/12 f\OML/cmm/m/it/12 h[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 w[]\OT1/cmr/m/n /12 ) \OML/cmm/m/it/12 > \OT1/cmr/m/n/12 0\OMS/cmsy/m/n/12 g \OML/cmm/m/it/12 s []; :::; s[] \OT1/cmr/m/n/12 (\OML/cmm/m/it/12 realised draws in training\OT1/c mr/m/n/12 ) [] Underfull \hbox (badness 10000) in paragraph at lines 23--31 [] Underfull \hbox (badness 10000) in paragraph at lines 23--31 [] [127 ] Underfull \hbox (badness 10000) in paragraph at lines 55--60 [] Overfull \hbox (0.64156pt too wide) detected at line 72 \U/msb/m/n/12 E [] \OT1/cmr/m/n/12 = \U/msb/m/n/12 E [] \OT1/cmr/m/n/12 = [] [] \U/msb/m/n/12 E [] \OT1/cmr/m/n/12 = [] [] \U/msb/m/n/12 E [] [] Underfull \hbox (badness 10000) in paragraph at lines 82--89 [] [128] Underfull \hbox (badness 10000) in paragraph at lines 95--98 [] Underfull \hbox (badness 10000) in paragraph at lines 106--117 [] Underfull \hbox (badness 10000) in paragraph at lines 119--128 [] Underfull \hbox (badness 10000) in paragraph at lines 119--128 [] Underfull \hbox (badness 10000) in paragraph at lines 130--137 [] [129] Overfull \hbox (42.9944pt too wide) detected at line 154 \OT1/cmr/m/n/12 = [](\OML/cmm/m/it/12 w[]\OT1/cmr/m/n/12 ) \OMS/cmsy/m/n/12 [] \OT1/cmr/m/n/12 + [] [] \OMS/cmsy/m/n/12 [] [] \OT1/cmr/m/n/12 + [](\OMS/ cmsy/m/n/12 k\OML/cmm/m/it/12 w[]\OMS/cmsy/m/n/12 k[] k\OML/cmm/m/it/12 w\OMS /cmsy/m/n/12 k[]\OT1/cmr/m/n/12 ) = [] File: lectures/../img/lez21-img1.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez21-img1.JPG used on input line 181 . 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