class19

Class19 - 6 $ 2 4 AB A A%9 8 ¢7 5 $#3 12 ¢0 && $"    ¥ ¥ £  §¦  ¦   £ ¨¦ §¦ ¤£ ¢ © ©   £ £ A ¢

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Unformatted text preview: 6 $ 2 4 AB A A %9@ 8 ¢7 5 $ ! ' ! ! #3 12 ¢0 ) (  & & $ %# "    ¥ ¥ £  §¦  ¦   £ ¨¦ ¡ §¦ ¡ ¤£ ¡ ¢ © ©   £ £ A ¢ § ¦  6 6 © 6 @ # ¢ & A3  $ A 29 2 6 8¢ 8¢ 6 ¢A A $ ! # " ¢ © 2  6 6 2 ¢ $ $ 6A 2 1  A # # §@ §  3 3 $ #  & ¢  ¥ 6 ¢ $ $ £ ¤& 2 A $ ¦3 # §3 § © 3 ¢ 12 1 $ ¦ A 3 62 A A £ £ 6 ¢A A $ A 8 § 6 © b & A $ & ¢ &$ A $ § § ¦  # 3 3 © § 3 & A # A §@ 8¢ ¥ 5 ¨@  • ¥ • A • 2 • A & ¢ ¥ 6 ¢ $ $ £ ¤& 2 §3 ¦3 # " • §£ ¡ £ £ 6 ¢A A $ A ¢ & & $ 2 2 2 ¢ A 8¢ ¥ 5 6 $ & A  $ & ¢ § § ¨ # # 3 ! • £ £ 6 ¢A A 2 6 & ¢ 8¢ 8¢ ¥ $ 7 3 ¢4 ¦  §@ § ! 6 8¢ 6 ¦  14 $ • 2 • A £ £ 6 ¢A A A ¢ § ¦  b @ # & A3  $ A ! §@ 3 ¡" 6 © 6 29 2 6 8¢ 8¢ ¥ $ A # • b §£ ¡  2 2 2 ¢ A  6 6 2 6 2 2 2 § §  A ¢ A $ ¦ §@ § $ § A %§ @ & $ ¢ A A § 3 3 3 © § 3 & A 1A 2 A A ! £ £ 6 ¢A A $ A 5 $ ¢ & ¢ A 6 6  $ & 6 2 2 2 # §# § § # A §@ & & 8¢ ¥ 5 6 $ $ 3 3 3 3 §  6 6 2 6 6 2 1 52 8 & A  $ & ¢ $ ¢ A & A¢  A ¢  & & ¢  # § 3 §3 ¨ §3 # ! 8 2 6 2 ¦ # # 3 3 7 ¢4 A §@ ¢ A §@ & & ¢ & A $ & & $ A ¢ £§ 2 6 ¢ &@ & & §@ ! !  5 8 8 2 6 6 1 &   A A $ ¢ $  ¢ & A A $ $ ¢ ©¢ 2 2 2 2 ¦ § ¥ # 3 3 §3 § § §@ ¤ ! £ £ £ &$ ¢ $ 6 ¢A A $ A 2 A 3 ¦  ¦ §3 § # A §@ ¢ & 8¢ ¥ 6 6 8¢ 6 6 © ¢ 12 1 $ ¢ !  6 6 © § § ¨ ¦  # &@ A §@ A & A $ & ¢ &$ A $ & A 2& A $ ¢ 8 § 3 3 3 © § 3 & A 8¢  £ £ © 2 © 2 ¥ 6 § § § ¨ § ¢A A $ A # A %§ @ $ §@ &@ A ¢ A A & A ¢  6 8¢ 3 3 ! ( 2 £ £ ¥ ¥ 6 6 § ¨ 3 & ¢  ¢ $ ¢A A $ A ¢ $ $ # §3 ¦3 # A ¦3 A §@  A ¢¦ £ ¤& 8 62 A !   £ £  ¨¦ © © ¡ ¢ ¡   fS 5 8 1¢A ¨ # # !  2 2 2 3 §3 # ! 8 1 A § " " xi , y i . # # ' 3 3 1 © & A & $ #  −p ¢ ¢ 6A ¢ $ $ ©¢ −p A  ¦ V fS 62 6 &$ A ¢ $ A A §@ 8 6 6 6 1 © § ¦ # ¢  §3 A §@ ¢ & A ! § 2 2 2 2 7 $ ¢ A § A §@ A 8 2& $ A fS A ! £ Ni § ' © §3 £ 6 6 © 2 6 ¢ & $  & ¢ ¥ 12 1 6 6 & A & ¢ ¢  ¢ $ $ ¢A & ¢ $ $ £ ¤& 2 ¦ ¤ §@ § @ 3 3 §3 ¦3 # " −p A  2 2 ¢ A  A ©¢ 2 ¨ ! £ ¢ ¥ 6  A3 " ¦ # 6 ¢ $ # §3  3 $ A A 62 § 9 A §@ A $ A ¢ 8 2& © # A3 8¢  £ # 6 1 1 © © 2  $ $& ¢ 6$ §@ # 0 3 3 3 # " , ..., x , y } ¢ A 8 2& ¢ e ¦ ¦ p i∈S p N $ A A  ¢A 3 e ¢¦ ¢ 82 12 & §@ § ¥ p ©  $ & 3 e ¦ $ 1A A 2 S { x ,y S → fS N ei . ¥¤ £ £   ¦ §¦  © ¡ ¡   &' " LS ¢ " ! ( 8 6 © 2 I fS . & A $ & ¢ &$ ¢ $ § § ¦ 3 # 3 5 ¥ & ¢ $# #3 9 § £ ¢ " # 2 " § 6  i # £ § ©§ 3 & A £ 8 © ¢ V f S i xi , y i . # # " ¢ I fS ' ' 6 ¢A 8¢ ¥ # ¢¡ LS % £ £ A $ A A $@ " " ! V fS x , y dP x, y x,y # " # # " 8 6 6 2 ¢  $ ¢ §3 ¥ ! fS ¦¥ ©   ¢ ¥ ©      © ¥  ¤   ¢ © §¢  ¢¤ § ¨¢  ¢ £¡ ¨ i  £ ( § ¤¥ ¦ § V f S i xi , y i   © § ¨ § ¨ ¨ I fS . , yi § © § ...dP x ¨ ,y § © ¦ ¦ © © ¦ © © ¦ ¨ §  ¨ £ ( ¨ § ¨ § ¨ ¨ § ,y ¨ ¨ £ ¤¥ ¦ ¦ © © ¦ © ¦ © © ¦ V fS i xi , yi dP x , y ...dP x ¦  £ ( V fS i xi , yi dP xi , yi ¨ ¦ © ¦ © dP x , y ...dP xi− , yi− dP xi ¨ i © ¨ ¨ ¦ i ¦ £ § £ ( LS ¨ § £ £ ¨ § ¦¥   ¡  © © ¢ ¥ ©      ©  ¢ £¤ ¥ ¤   ¢ © § ¨¢ © §¢  ¢¡ ¢ £  8 1 © 6 6 2 6 6 § §3 & A & $ $ ¢ # # ¦ # A3 $ ¢  $ ! £ £ £ 2 1A 1 $ ¢ 6 8 6 2 2 2 § ¢A A $ A & ¢ A § # A %§ @ A $ 8¢ ¥ ¦  3 © 3 ¢ 12 1 2 6 8¢ 8  # # 3 @ &@ & A ¦3 &# ¢ 6 ¢ ¢ A $@ A § # ©§ 3 ¢ ¢ $ ! ! ¢ & & A $ ¢ $§ § § § 3 3 3  &A 3 6 6 2 6 6 2 ¢ ! 2 6 6 A §@ A  $ ¢A ¢ 3  6 A $  $ & § 9 $@ ' 3 − £ £ 6 ¢A A $ A A ¢A ¢ A & 6A 6 2 2 2 § § & # § ¦ # A %§ @ A 8¢ ¥ 8 1  ¢ $ A ©¢ 62 A 6  ¡  ¢ ¢ ¦ ¢ ¢ ¡   ©   ¡ ¥ ¢ ¢ ¤     ¢ §¢ © §¢ ¢ £¤ ¢ £¡    ¡ ¦¥  © IS f S i ' " i ¢ y i − f S xi − Qii 8¢ ¥ A $ A . 2 2 2 & ¢ A 8¢ § # A §@ 3 " % # K £§ £ 6 A %§ @ λI− £ ¢ £ A § £ i # # c £ % 2 A@ ¢ fx § ' " " # " c i K x, x i , # © 2 6 ¨ 9 & @ ¢ A §@ & $ ¢ §3 # A §@ ¢ 8 6 ¢ 6 A ! § £ i ¢ ¢ K " # # ! Q !  $ A & f ∈H 6 © 3 " " % # # f xi − y i λ||f ||K . λ I − y. ¢ ¢ ' 6 © 12 6 ¥2 ¥ A ¢ $ ¢ $ $ 3 # # §3 A §@  A3 © ¡ ¦ © ¥ ¥ §  © §¢ © §¢ ¦¥ ¢   ¤   £ ¢    ¤  © ©  ¡ © ¥ ¥ 6 ¢ # £ § j ¢ " ∗ Qij yj . ¢ &@ f S i xi ∗ Qij yj − yi £ § j # # " Qii fS i xi − yi " Qij yj − yi # " QiifS i xi − yi % i ¢ j § ¢ Qij yj % § j £ ¢ # " f S i xi − y i ¢ ∗ yi ¦ i $ 3 j ¢ ¢ yj ! ¦ © § # 2 A ¡ A@ § ¢  ¥ 2 A A %§ @ ∗ yj  6  $ A ¨ " f S i xi  © © §¢ ¦¥ §¢ ¢ A 6 A A ¨ ¦ § y∗ £ ¢    ¤  ' ¢ # " # " y i − f S xi . − Qii © ©  # # " " % ¢ y i − f S i xi ¡ © ¥ ¥ ¦ © § ¡  © # Qii fS i xi − yi . 4 ¢ " © §¢ ¦¥ §¢ ¢ f S xi − y i i £ Q ¢ £ % 8  2 2 1 § ¨ ¢  A $ § A §@ A ©¢ 6  $ A ! λI µ− . i ( ( $ & 8A ¥ 6 A # 3 2 § # " £ § £ ' " ¢ # # " y i − f S xi −− Q A A §@ ©¢ Q ! ' " ! IS f S i ≈ i § § ! ¢ $ ¥ 2 2 2 § §3 & ¢ ¢ $ $ & & ¢  3 §3 ¦3 A §@ ¢ ¢ 6A 2 6 $ © 3 ¢ 12 1 6 0  2 © $ § A §@ 3 %  8 ¥  A A 1  @ 3 A  ¢ § § A3 & ©¢ 6 1A 6  $  @ λI 2 ¢ K K . µi 2 1 & ¢  2 2 2 ¢ 6A ¢ $ $ ¥2 6A ¢ 6A A A ¥ § $ § § ¦ 3 §3 ¦3 # A §@ A £ ¤& 8 ©¢  ¢ ¥ ¢ ¤  © ¡ ¦ © ¥ ¥  ¢ ¥ ¤    © § ¢  ¡ ¡ ¥ ¢ ¡ ¢   ¢ τ≤ ( ¢ R ρ A $ %# @ §3 ¥ 6 2 $ & ¢  A $ § § ¦ 3 3 A %§ @ ρ 6 1 2 5 1A $ 6 6 2 !  1 2 © 86 6 § & & A ¢ A §  A3 $ 3 ! § ( ¥2 ¢A ¢ 27 A 3 ! τ 6 2 $ & ! A §@ ¢ ¢ A §@ 6 § & R 3 5  2 1 2 6 2 1 6 6 2 1 2 § § # 0 # # ! ¢ ' , ..., . # " ©  2 6 § §@ & A A § A §@ $ & $ A & $@ 3 3 6 ( ¢ ¥ & $  8& § §@ @ $ ¥ & ¦ '  ' @ @ 3 ¢ " ¢ # " # A ¥ 6  2 0 & A $ $ $ § § ¦ A3 A $ A © 8& & ¡ ¢  3 ¢ ¥  £ ¥ ¦¤ §  § ©¨ $ £  ©  ¦£ §¨    ¡   ©  ¡  ¢ & ¨ A §@ 3 ©  $ & A $ A3 $ A $ $ & A  $ ¢  A 1A  ¢ © ¢¡ i n 1 3 © 62 6 ¢ ¦ & A § ¦ w xi y i > , A § § # ! 6 8¢  $ $ {− , } w∈ $ ©¢ 2 6 1 & & A¢  A §@ ¢  6A § 3 A §@ yi  @ &$ ¦ n  ¥ A $ A xi ∈ { x , y , ..., x , y },  2 & A3 A §@ ¢ 6 1 ¢ § A %§ @ 3 3 ! § w ¢ t 2 w ¢ ¢ t ¤ w £ ¡ £ ¡ t % £ ¡ £ 6 2 $ §@ 3 §3 § ( ¢ 6 6 2 6 § ¢ $ A # # # A %§ @  A ¢¦ ¢ 8 26 A ! 3 3 3 ! ¢ £ ¡ ! ¦ ¢ ' i £ ¡ ¤ ¡ # 4 y i w xi ≥ ρ > , ( ¢ w  ¦ A3 & ¢ t & $ %# 3 w & & A w &$ $ ¥ A $ A  § @ ¦ # A §@ 6A © 6 © 6 ¢ 3 3 3  & ¢ A A $ %# @ 6 @ ¥ ¢  $ § § A §@ ¢ ¢ A §@ 2& 6 2 6  2  8¢ 2 §@  6 1 2 5 1A & §@ 3 3 3 3  8 ¦ 6 1 ¢ $ & A ¢ & & A¢  § § § # # 3 3 1  © $ A 8& & $ A 5 ¢ ¥ § §@ § # 3 3 ©& 3 2 ρ 5 © xi 3  8 2 6 2 2 2 6 &$ ¢ ¢ A § §@ @ ¦ §@ § ¦ § A §@ ¢  6A &$ ¦ A %§ @ $  8& $ $ A §@ 3 3 ! A § ¦ 2 © 62 6 $ ¢ ¢  A $ ¢ 6 2 1 6 1 2 § § @ # $ $ & A A 3 §3 $ %# 5 1A ¥ 8  A §@ A ! w , ..., . y i xi t  ¦ ¦ §@ 3 τ 6 6 ¢  $ §3  ! ¦ ¦  3 ( ¢ 6 9 § A  § A ¦  ¢¦ ¢ ¦ A §@ § A § 8 12 6 $ ' 3 ¢ A §@ ¢ ! ¢ ¥ 5 A $ A 8 2& A 8 2 A A 8¢  § @ #   ¦ #  5 § & $ $ A $ & ¢ § # ¦ ¦ A §@ $ ©¢ 6 62 2 2 6 1 6 6 2 ¥2 A¢ ¦ 3 3 3 ! § 2 A ¦ A@ § 6  & A ¢ A  A §@ & ¢A @ @ 3 3 © § 3 2 © 86 6 A ! £ © & & $ 3 xi 8 5 ¢ #  i A | 6 8¢ 6 # # ¦ di ©¢ ! ¢ w| 2 ¢ ! § 3 A3 & & $ %# ¢ τ ¦ ¦ τ ¦ ¦ A §@ ¢ 6  6A & A ©¢ & w 6A ≥ |w £ ¡ £ ¡ A £ ¡ ( ¢ w 8¢  τ & τ 3 £ ¡ ¦ di  w # ! w 5 2 ¢ A 6 τ $ ( 2 A A $@ w A3 # 3 2 $ di 6 6 ¢ 2 £ ¡ 2 A § 0 ! 1 2 6 § § ¦ A3  $ & A $ A 8 τ d i y i xi i τ. w diyixi w| ≥ τ ρ. £ ¦ ¦ ¡ ¢ §¦  © £ 6 $ §@ R   8 © ! w 2 © ¢ A  ( 1 6 § 9 §3  A $ %# & A $ ¢  3 $  © 6 §  @ 3 ¦ A3 & & $ %# & A A & $ § # 8 12 2 6 &  § ¢¦ & & ¢  A §@ ¦ 3 ¢  ¢ ¤ % %   τ 5 3 6 ¢ ' y i xi w & A $  A § 1 §@ ¢ xi 62 ¢ ¢A 2 & 2 $ @ £ A §@ & A   xi ≤ R i ¢ A  3 3 8 " £ ¡ £ ¡ £ ¡ 8  2 ¦ 6 6 1 ¦ ¢ A $ & A §@ $ ' 3 ! 6 A ¦ § ¢ ¤ τ 6 τ ¦ @ @ $ A # # ! τ £ ¡ § § ¥ $ § 2 A3 & ¢ ( ¢ 3 ¢ § , ..., 6 1 & A  $ A $ ¢ A ! 1 ¢ w ¢ ! ( 2 A 6 i ¢ A §@ ¢ A $ & 2 A $@ τ 62 2 ¦ A §@ w w . £ ¡ £ ¦ ¦ © ¡ ¢ §¦  £  ¢  $ ¦ τρ ≤ w &   τ 6 ¦ ¦ 3 §   £ ¡ ( 2 6 6 ¢  5 2 6 6 # 3 §3 $ §@ # 3 A3 ¢ 8 ! R τ≤ ρ ¢ τ 2 ( 2 2 2 A $ ¢ A A § A $@ ! ! 1 & & A § ≤ τR . ≤ τR , 5 ¥ A¢ $ ©¢ 2 6A 8¢ &   ¦ ¦  3 !  τ   £ ¡ & A 6 8¢ ¢  A §@ § 6 6 3 " τ & 3 3 3 §3 § @ ©¢ w A 6# 6 26 ¢  &$  @ $ w  8 τ £ ¡ £ ¦ ¦ © ¡ ¢ §¦  £ 6 ¢ & $ @  © 2 § b A 1 1 & 6 2 $ A $ $ & A § ¦ # §@ 7 3 ¢4 § £ ¢ " " ! # # "  ≤ & $ ¢$ § ¦ 3 i θ −yifS i xi 1 6  §@ # ¡ IS f S i 8¢ 5  $ 6$ 6 A ' '  © 6 2 1 2 ¢ & & A $ ¢  A 1A § 9 A %§ @ τ R . ρ A ¢ & $ A 6 #  §@ & ¢  ¢A ¢ A §3  A §@ A %§ @ $ 2 2 2 © 86 6 2 § @ ¦ A# $ ©& 82 ! £ £ £ 6 12  ¢A A $ A  ¢A § # A §@ & ¢ ¢A A 8¢ ¥ 6 2 2 2 2 © 86 § §@ § A §@ $ A¢ 3 !   © ¢ © §¢ ©  ¢ £¤ §¢   ¢¡ ¦¥ ¡   ©  © 2 2 2 A $ & ¢ A ¦ 3 $ ¢A A 2 ¢  A ¢ © & $ 6 $ $ A 8& 5 1 § §@ #  ¢ 6 6  $ ¢  A A¢ 5  $ 8 2 ¥ A $ 8¢ 6 1 $ § § § @ ¦ # §@ § 3 3 6 6 ¢ $ A¢ A ¥ $  ¢ ¢  A ¢ ¢ & & 6A 6 6 2 2 1 1 6 8& ¥ © 2 @ §@ § § A@ A 3 § £ ¢ " # " c i K x, x i , # © 2 6 @ §3 # ¢ A %§ @ & $ ¢ ¢ 8 & 7 ¢4 A %§ @  6A 3 4 ! " ! N © 3 6 8¢ ¥ # IS f S i ≤ & § § ! $ i A ¥ 2 1 1 8& ¥ © 2 A & A fx ¢ A ¥ 2 2 1 1 & ¢  A ¢ 8& 2 © 86 § §  ! N . N £ £ 6 ¢A A A  $ $ ¢ ¢ A 5 6 § 7  ¦   ¢4 # A §@ 8¢ 6 2 2 2 8¢ ¥ $ A A $@ ! ¦    ¢ ¥  © ¡ ¢ ©  ©   ¢   ¡ ¡    © ¡  © ¢ 8 6 ¢ # ¢ & A %§ @ § & 6 1 6 ¢ ¢ 6 2 © 2 §3  3 ¥ ¦ A3 § $ § £ © ¢ " c i K x, x i . # " fx §@ # 2 § i cj K x i , x j § j i # ≤ θ −y i # i " j # " cj K x i , x j § ≥ # " ¢ j " # # " θ −yifS i xi # " f S i xi " cj K x i , x j # " # " f S xi − c i K x i , x i . # # # " # " " # " θ −yi fS xi − ciK xi , xi " £ i § § ≤ ¢ i £ " θ −yifS i xi # ' © ¢ 2  $ 6 $  8& ' 2 ¢ ¥ @ 3 § £ i # 2 ¢ A §@ & $ @ ! $ 8¢ A § §@ $ ¢ 2 ¢  © ¢   ¡  ¡  ¢ ©  © 3 7 ¢4 ¥ b b , −i  ¦ § −i J −i −i αj yj K xi , xj . j i © ¦ − α ∗ yi i 4  ©  § ¢ 0 ¢ £¡  ¢    ' 3 ¤ ¨ ∗ −i  ¢ £¡ ¢ "¨ ¥  ¢ £¨  1¢ ©    ¢ £¡    !  ( ) § © § 0 © ¦  ¢ ¦ αi − ¥ 3  ¨  i © © §  α∗ i ¢¨  ©   ¢ £¡  j © ¦   1 2 ! −i 0 ©   § J 0 ©  ( ) § © © § ¢ 1¢ ¤ −i −i  4  1 ¨ ¨ ! J yj yk αj αk K xi , xj . © £ © ¨  ¥ & %$ '  # ¢ # ¢  ¢ £¨ ¢ £¡  ! ¢ £¨  "§  ©      § ©   § § ¥ ¦¤ ¢ £¡  © ¥ © £   © ¢ ¡   ¡  ¢  ¡  © © ¢ ¢ b j,k i £ ©  ¡  © ¢ £ ¢ ¥ ' © ¦ © ¤ §     ¡ ¢ '  i i j i © cj K x i , xj . © ¦ j ¦ ≥ α∗ yj K xi , xj j  ≥ α ∗ yi i  fS i xi © i ¦ j  ¦ αi yj K xi , xj j © α∗ yi i J 0 −i i © ¦ © xi , xj . $ j ( i ∗ −i α∗ yj K j © ¦ i ©  j ¦ j −i ≥ α ∗ yi i αi yj K xi , xj j α∗ yj K xi , xj j ¦ −J − α ∗ yi i © i © ¦ 0 ≥ α ∗ yi i  j  ¦ αi yj K xi , xj j ¦ α∗ yi i −i  i −i 0 j ≥J © α∗ yj K xi , xj j © − α ∗ yi i 1 4 ¨   ¢ £¡ 4 §  2  ¨  '  −i ¨ ' ¨ § 4 §  ¨  2  ' ¨ ¨ ¢  § −i  0 ¦ 0 −i − © § ©  § ¢ § ≥J ≤J  §  © 0 ¦ 0 ¨ £ © § ¨    ¢ £¡ ! § © ¢ −i ©¢ ¦ ∗ −i ∗ −i ¦ ∗ −i  −i © ¦ 0 J 3 §  1 4 1  ¨     § ' − 1   § 3 ¢ −  ¢ £¡  ¢ §   ¢ § ¢ £¡ 0 1  ¢ 0 ¢¡ J −i  £ !  ¨ ¨ 1 J ∗ −i © ¢  ¡  ©  !   ¢ ¢ £¡ 2 ©  ¡  ¢ b −i B j 6 $ § j ¢ # " i © αi − & A ¢ # 3 "  2 $ ¢ # # ! # " # R ≥ K x, x − K x, z 12 6 ¢ §3 A § £ " # # "  ≤ |{i ' % αi R y j y k αj αk K x i , x j , j,k i ≤α≤C # 3 2 A@ θ −yifS i xi " $ $ # ¢ ' ¢ © 2  6 ¢ $ $  8& 2 # @ §@ ¥ 3 § £ i § ' © © $ ¦  3  8 A §@ A ¨ ¢ " # " % # c i K x, x i   $ 2 A fx ! ¦ i y j αj ! −i ¢ 0 © J −i § § §  −i ¢  A 8& i © 2 @ ¢ A §@ & $ ! 2 $ $ ¢ A §@ 7 3 ¢4 ¥ 8 6 6 1 6 6 2 © 2 ¢ § b. ξi ≥ }|, x, z ¢ ¢ & ¦ 3 §3 # A §@ & ¢ § A3 $ § b £   ¥  © © ¢ ¡  ¡  ¢  ¢ b £ i § " £ i § " # ¢ j § ¢ ' λj i θ αi S i − # § # " xj , ' ¢ ' ¢ ¡ λj ¢ θ −yifS i xi # j i,αi> 6  &@ A 3 i ¢ 6  $ § 3 i " ' §@ ¥ & A § ¡ 2 A A@ § 6 1 6  ¢ § A %§ @ A A § A  6A &$ ¦ A %§ @ & 3 3 3 Si & ©¢ 2 " . . 6 ¦ A §@ $ xi # ¢ # # " # " " y i f S xi − f S i xi αi S i , ¢ £ £ 6 ¢A 6 82 12 § ¦ # A §@ A  ¢A 8¢ ¥ A $ A 8 8 ¥ $  $ 2 § § § ¦ ¦ @ A §@ 6A 6A 6 6 © A ¢  A ¢ 2& 2 2 1 1 8& ¢ & A A §@ & 3 ! !  © ¥ ¡  © § ¨ ¤ ¤ ¥ ¤  ¦ §¨ §  § ¨§  © © © ©  ¤ ¤  § ¥ © § ¨ £  ¤ ¤ ¨¥ © § § ¥ © © © § § § ¤ £ ¥ © ¤ ¨ ¤  § § § ¤ ¤ ¤  ¤   £ ¥ ¥  ¨ © ¤  ¤ © ¨ ¤ ¤  § © §§ §  ¥© § ¤ £  ¢ $ ¢ ¦ & & A& 3 3 § ¢  " §3 # # $ %# 8¢ 6 & 8A ¦ 6 § A %§ @ A ¢ 1 ©¢ 12 & $@ !   A 2 2 2 ¢ A A  A 1A 6 $ § ¦ ¦ ¢  $ ¢A A 2 2 2 2 1 © 6 ¦  A ¢ §  ¢ A#  $ ¢ A A ¦ 3 3 3 §3 A § 6 § A §@ ¥$ 6 8¢ 6 6 6 £ ¢A  § 2 2 2 § ¦ A & ¢ A  A § ¦ A §@ $ ¢ 1A 6 2 $ 3 © § 3 & A 8¢ 6 8 §  O n £ ( £ ¥ 6 ( £ § A A ¢ A $ A  & ¢  # £ 2 2  ¢A & ¢ A & A $ §3 A §@ A 2 © 2  $ ¢ & A ¦ A §@ $ §@ &@ 5 1A 3 $ 2 & A § 6 3 A ¢ 6 ¥$ 6 § # 2 $ A ¢ 1 © $ # §  @ 9 §@ § § ¥ 3 3 3 ! !   © ¥     ¢ © §¢ © §¢  ¢ £¤ ¦¥  ©    ¥ ¡ ¢¤ ¥ ¢ ¥ ¡  © ¢ S ni ¦ V fS i , zi − I f S ¦   © ≤ ≤ n § d n  ¨ ¨  £ ¨ ( © ¨ δ n δ (   % ¤ ¡ ¨  ¢    ' ©¢ ' §' 3 M δ, M δ. ¨   § '   ¨   !   § 3 ¤   ©  § ¤¥       ¦  ¨ ¦ §  £ ¨ ( ( © ¨ § ¡ 1 ' §' 3  % ¤ ¡  ¢   '  ¨   3 ©¢   ¥!  ¡     (   ¢  ¢ ¢ 3 ¤ ¢ £¡  ¢ § ' ¢ § §'  ¢ § ¢ ©     4  ¡ ¢¡ §     δ ( 1     3 n ( © n d ( n d £ §  ¡  d ( ¨ d  ¦ ¦ n ¨ §  ¥! § ¡ d n d  ¨ ' '  ¦ £ ¥ ' ¢ ≤ ¦ ¨ V f S i , z i − I S fS   ©  ni ¨ £ S  ¤¥ ¤¥  S I f S − I S fS d M δ. !    ¢   ¢ § 3    ¢ ¢ ¤ ¥¨   £ 4 '  '  ¢ §  © ' ¢ # ¢  ¢¨ # ¥  ¨ ¢¡ ' ¢ ' §' 3 % ¡ "§  ¥ ¢   ¢ ¢  ¤  ¦ ¡  ...
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This note was uploaded on 11/11/2011 for the course BIO 9.07 taught by Professor Ruthrosenholtz during the Spring '04 term at MIT.

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