From 0a00e83e7f2ae7c73260e2e1255cd527a540292c Mon Sep 17 00:00:00 2001 From: Francois Pelletier Date: Wed, 17 Apr 2019 09:13:14 -0400 Subject: [PATCH] ajout chapitre 16 --- chapitre15.tex | 9 +++- chapitre16.tex | 114 +++++++++++++++++++++++++++++++++++++++++++++ notes_de_cours.tex | 1 + umbrella.png | Bin 0 -> 26570 bytes 4 files changed, 123 insertions(+), 1 deletion(-) create mode 100644 chapitre16.tex create mode 100644 umbrella.png diff --git a/chapitre15.tex b/chapitre15.tex index a2e8eb6..c7a6804 100644 --- a/chapitre15.tex +++ b/chapitre15.tex @@ -98,7 +98,14 @@ $m_{1:t}(i)$ est la probabilité du chemin le plus probable jusqu'à l'état $i$ \subsection{Modèles de Markov cachés} \label{sec:ch15hiddenmarkov} -Représentation des probabilités sous la forme de matrice de transition. +Représentation des probabilités du modèle d'observation sous la forme de matrice de transition. On ne considère que le cas observé, donc la matrice est diagonale et les valeurs prennent $P(e_t|X_t=i)$ ou $0$. LLes calculs de filtrage et d'information a posteriori deviennent de simples opérations de base sur des matrices et des vecteurs. + +\begin{itemize} +\item Forward: $f_{1:t+1}=\alpha O_{t+1}T^Tf_{1:t}$ +\item Backward: $b_{k+1:1}=T O_{k+1}b_{k+2:t}$ +\end{itemize} + + diff --git a/chapitre16.tex b/chapitre16.tex new file mode 100644 index 0000000..c24c289 --- /dev/null +++ b/chapitre16.tex @@ -0,0 +1,114 @@ +\section{Chapitre 16: } +\label{sec:ch15} + +\subsection{Théorie de la décision} +\label{sec:ch16theoriedecision} + +\begin{itemize} +\item Utilité et probabilités +\item Décision selon croyance et objectif +\item Présence d'incertain et de buts conflictuels +\end{itemize} + +Combiner l'objectif et l'incertitude: + +\begin{itemize} +\item Chaque état a une utilisé. +\item Chaque action a une utilité espérée: + \begin{align} + E[U(a|e)] = \sum_{i}P(R(a)=s^{\prime}|a,e)U(s^{\prime}) + \end{align} +\end{itemize} + +L'agent rationnel choisit l'action qui maximise l'utilité espérée $\argmax_{a}E[U(a|e)]$. + +\subsection{Théorie de l'utilité} +\label{sec:ch16theorieutilite} + +Relations de préférence: + +\begin{itemize} +\item A est préféré à B: $A \succ B$ +\item A est indifférent de B: $A \sim B$ +\item A est préféré ou indifférent de B: $A \succeq B$ +\end{itemize} + +Contraintes sur les préférences: + +\begin{itemize} +\item Ordonnabilité: $ (A \succ B) \vee (B \succ A) \implies (A \sim B)$ +\item Transitivité: $(A \succ B) \vee (B \succ C) \implies (A \sim C)$ +\item Continuité: $A \succ B \succ C \implies \exists p, [p,A; 1-p,C] \sim B$ +\item Substituabilité: $A \sim B \implies [p,A; 1-p,C] \sim [p,B; 1-p,C]$ +\item Monotonie: $A \succ B \implies (p \geq q \iff [p,A; 1-p,B] \succeq [q,A; 1-q,B])$ +\item Décomposabilité: $[p,A; 1-p,[q,B; 1-q,C]] \sim [p,A; (1-p)q,B;(1-p)(1-q),C]$ +\end{itemize} + +Principe d'utilité: + +\begin{align} + &\exists U t.q. \\ + U(A) &> U(B) \iff A \succ B\\ + U(a) &= U(B) \iff A \sim B +\end{align} + +\begin{mydef} + Une loterie $L$ se définit par $L(A,B)=[p,A;(1-p),B]$. +\end{mydef} + +Utilité maximale espérée d'une loterie: + +\begin{align} + U([p_1,S_1;\ldots;p_n,S_n]) = \sum_{i=1}^n p_iU(S_i) +\end{align} + +Utilité de l'argent: + +\begin{itemize} +\item Courbe linéaire: neutre au risque +\item Courbe logarithmique: aversion au risque +\end{itemize} + + +\subsection{Réseau de décision} +\label{sec:ch16reseaudecision} + +On ajoute des noeuds d'actions et d'utilité aux réseaux bayesiens. + +Un réseau de décision représente: +\begin{itemize} +\item L'état courant de l'agent +\item Les actions possibles +\item L'état résultant de son action +\item L'utilité de l'état résultant +\end{itemize} + + +\subsection{Recherche d'information} +\label{sec:ch16rechinfo} + +Valeur de l'information: Différence entre la valeur espérée après l'information, moins la valeur avant l'information. + +Valeur de la meilleure action $\alpha$ avant la nouvelle information: + +\begin{align} + E[U(\alpha|e)]\max_{a}\sum_{i}U(R(a))P(R(a)|a,e) +\end{align} + +Valeur de la meilleure action $\alpha_{e_j}$ après la nouvelle information: + +\begin{align} + E[U(\alpha_{e_j}|e)]\max_{a}\sum_{i}U(R(a))P(R(a)|a,e,e_j) +\end{align} + +On ne connait pas $e_j$, alors on somme sur les valeurs possibles: + +\begin{align} + VPI_e(E_j)=\left(\sum_kP(E_j=e_{jk}|e)E[U(\alpha_{e_{jk}}|e,E_j=e_{jk})] \right)-E[U(\alpha|e)] +\end{align} + + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "notes_de_cours" +%%% End: \ No newline at end of file diff --git a/notes_de_cours.tex b/notes_de_cours.tex index 467b945..19f9041 100644 --- a/notes_de_cours.tex +++ b/notes_de_cours.tex @@ -104,6 +104,7 @@ \include{chapitre13} \include{chapitre14} \include{chapitre15} +\include{chapitre16} % Ajouter les autres chapitres au besoin \bibliography{bibliographie} diff --git a/umbrella.png b/umbrella.png new file mode 100644 index 0000000000000000000000000000000000000000..9744abca6048b4a4d64896006db6788992ab8cc9 GIT binary patch literal 26570 zcmdqJc{JDS+cx~wB$QG@GE-D4ijp~mN*OB|lLnHZGS8JUQyNfaGL^BADMF@HNQR6_ zGG)p<_8!;X_wRnzyPo@9>;3Op>)E^2ZinyZ`dq_#9_Mi!=jE$*Mrk80D=mdW*?2-( zL4!hBEr>s7tY3%UIpuV0@t<{ftBvKm+TU$xr_7FRD!J|IAH#Ey&b}nwZ2#29qy4v|4}JX9FWs)Bps=Qr#n@lC zlBH3`cU?iCJN`uechrN9>EAzvb^W;O`S0H*zVWwam$l;!tyMpJ*7L=SJzrZ|;$OTt zX`hjpxbF1n(|Ettt6N)J*N*a$_>!VF04Jk1N1+1SweWFl;mDglx3l=4PkU4z#a9Qp9_X@-9?>P4BWiCZ8EI2+- zO5#0mVAK5kynvvf!m(piw6wHpT3Q}>y4KmV$5OOxPdIsbd2RNqAWwV!`cP3((f41! z)@|Cf$==@nT~!rzX=!O@X6C@d85ZM(WBWsSMMbwgefqTe)2HKS&d}ewbxTc6&Hc+4 z4XyL%W$G99?c3KgFt8p!J-4t>*3!Z(EiFAhJF8@GpQlrGPq_K@*RNl>4jtOM#di&U z?cBLjKtMqD=1pNTstXrS_U(H~N&Fq1ojrINCnu+# z-#*%cUig)gviru38y7EH4Sx{7efxILK%z#9hu(hXwzSk#1!H607cX9Tc#ws~3^6h@ z%ku=w?s+1&=Skf2=WAXBRn*qf9XobxJw3gmwl>Q;dNv=|<%QC(U$ttT0)=f$7-`q8 ztSnka9KF4+rlv;u%o#;n+rt>s#Y>k~Sz21g#*9x*dHDI!{T> zt)k+wn#IP(COIR6x$Qx1pTOR|TR(q%91$W?Lo^sq%*RaLfUdF|((nw)Ee*E}@ zlL-R*_n#YX6cZEU5)#^s?XZ5s28C#8m--SnH+u&MQ`5REi#=IY%z_RM4q~>yS^k*; z88;4$#>B+LJt1MIoV+~4mMwQ5JlMR3nwpo7Z_Uceig?NMxU4LO{QUep*X05=HT@D- z_VXDAo+`WUWn~GMm6dH~V7N0dVB*gryz0)KJK_QP63H)K42?HLK76=^O~#cCn^3#h zIsc5YQKu5tEs$NpOWvEl=V#5MJgc5nk5BF_diz$`>bq>L8ksR?XJ?Ol>}?OCqk|ql zW__g)~zdRZ`bX2*}g47gT_~Zhwb(49YjUf=ukloC&}cfP~qF7xi<$X}nrl`s)&+&_N&XfjYAn{Cx2 zx6tFwIWW}p6368Eu-cgJsZ(@UE?=(y94RsQ=}7l;242Mnm`^G$9I$7iW=t-BmuLB& zoU~!TzN64?EOEDH;%3S!S*0M3x4lLDs!@!;oc`4C4^{{BMq0c{PY*noVQ@M~^3VG1 zEG+9A|IXLBX*fGe)?9vdxb}HMLc`ysy1$z#wDk0&*6r*83H(0y@5deKc79#^YxvCN zgWJv9a|5DW7ffH}=I){}GBGJ0D4ydPY0bKavun-%gZ;_l$MvI~g@aA!4HNFHrha(m z4%O4}@W%JPTL;4}i(|u&SPqFRd}g=vP2jf=yImFe7~hXY8>nD5e4d#pw8dB9^2Lj? zMn*;=w|}WD%=HEhj`x&n85pDwt8s>@?20d0S@2t#jQ(5Sk$>A1lY9B{Wd(|WkkErD zmzfJ~MGlAh`um5)wGwq{q~b2teEO7-QM_>fM{jRUYik&mc{dNw-4MYGa^CdpaRmk9 z`rgUHh}G6BOAb1Pw)+A&q@H0J)>AyayuQ3R`*L7uezJgGJw{Ey8S4a!4?X&*z-uLh_tBj0{PM#GvySTN_Pl#~V=dvVS4=am*`$C4Z-e+55!w3RBR>#b8GK0YNgQ>~?k zfx>$5@_Ov|57pHsldeWa+yUDUdELEtukh!l*C(BZ%}h;WElZX|cAb9qb#%;smpHrK z{XW+#*RE-*sHiX>|2jP-Rs0z-HqK_aIT#U|DyH-vbtAK(^RaE)wiVE))zwTNLKQQXoj|#tRlLnq!c6R)fpTB-7PWIO&Njc3t z(A(c)WA7M`eZDf+yUDTd$@%KKx**Dfd-qnq9WSG^{`2$1byL#@8y}U)0>jcWmB}GL=5u>s-ZLhCw5+T)i zkfL?cvS?x*;J~At9MQKEl{>7L7i{#s6GRa*r#?%JkuhQ*Unc8hR4-h(pc8QCpI42^ z%zPldG%im|N5@NH+`L(KtZ0&6KhNrpL>IgD^w8Ob@$yZ(B_$&$4>B?ir0L~r3?KD1 zJv%F){VY7(bgb(wWy$ za$D-F7`7?Wj zM1kgLUZ*D=vq|aQwU@77KY1xD?CPgy#}RFQ@bpn7BqoxmQe9Q$jZJMrPPE;aL05)U zkSnv`$%Kc+OMg!NnV8_lad!Om^x6QXv4H+%du?^~<}FD8Wof!^&X~>4C$F@+PBkd4 zac@r3Kzxu-@-nY)Q&STo3ybp0b7@-=5sB3FZZDSy>9uBm;vwlJ2+GRyE+Dob2oe3Ow9&babm^U!KoM z?C8*IE3ny16_cDS5c~GsJK0w`Iooo32a}?i_HX=9TWj_@qfMgBdC_@xL2~b&J>qPJ z=Skf7yWIVECqF;`7QYIe!-~H2Sa9NdPm&8-n)Buy=*vtRjOf0l)XR1afZGKMvHgVS9Eh7`n;q+UWZ0!~Ur!*x= zUnR|-w~nUi1G6D1QjC1saw`{O+gtGKlQg7`B@hlA`gu6n)ZuXOk8 z<;fnp_L)y!UVfiFlT0GzcxErd-FM3Sl2*p8byI0B1`Bni%ocK%bN@5aw*i`BND?X!n%)2?@S zR%h7^p98*p*WJyzb(hLJfSBNrki_Bo*46bd?_R-s4PbU(y?SLeHK2|Zb71}Y_4PK| zQc);yivO-SMM&7upG?@YnwtK7Wxx*4U{ld6J!PJoeHG?@K2puR*{fLe=fhsRNW^XFy%?T6Me@7H^mX;hwxAVGcqC2w?6?q-HAhkkaINbzll zu6}%1;m15t%^PHrwmiCDM1(O(HM$ZZY67G0^<*}1*GT!Qje(2VQ5J$Fw0zb_yR95u zm>RtI@uLdgu3bMc1;CPD90h-e)Yq$#cNV+-Ys1j+FoEZ(25)uZ^L14TGaGxYT^5Xl_`{Xr65IRW#z)jY$g;Uz<;TTsOFA3I;@8+ zI$9HIO?a4|G%JaZU7h*;O>NH;mLnEyl$eBswX%zgb7#m*%q=eRa&uEj*#4G9csZA< zJs~@R^Y_&&F>x1}rQznZ^7Do+o~OePPbiN?Uc7wSZg{#+wP zXavB2jr+`K=gY$xL-|uk$z>v*a>p=1KSxK?ZAbo;dD59yKj8k_+NvD7U!Mmj|JCc) z@%N}VJ(P=$k@>syC^a>8J%xZbeSLPMlP#2I5_bDZArNxFkbr=)oTe9dhEQnv`iN(L z94XinGJ}bFl%IdJudk1$5nrH@4Zq2)6`#S+$5)?g-d^3%5KO86_WBxvmZ5g~^ztbS z3yU?fc}nlFSL~l@Ag2H&(H%)YcmDiV3L^hoGv_yTEx~oKr)@j;6@Mmq`&yKP7r^tV z_+9Zrna~44mBG0D954QInOop^-q&bfQ+h>ZNjk6peU@% zX-q07DIMi%gx7}cav>ohKZl1;kyYKe0`6()8wF1>s(m{1NIIHlPLKJIc|G}reo*A6}Ex+GQ^$nHl% z$;*u5yGX9-@|R}s_>d5os$a+?VK@3-Q&lQq_(5yu&Y|ZQO-)TppPzX2;PGP*^1Qk_ z)pqX8MYVJ1yinb}Yi?$$3S{pcUcB%oG&uNMY3EQ4YVh>%Dc%(Hss43?#8og8jUr;yP*6 zJ7@OoeR6W5)2_P*1F@K-E=ftDITa!ZuIgBlaUnA`HTBZU;+V3kY85r7b4->kOJm5J zE=M{lDk}Yj#SZq{L5KfTAsh(b`l&3am#5aN%5hnx5xk_3api^$tRm}m-&l9D+&M)c7J}1FQ#bl5$Wf|WTF!@^ z)6|sLOgghuUcUUyMjjEHAuXM(OUILb9Ce%$ked8>=xcpFmr7yxj&JQd7_<|LiXx)y zf6x>l*(LoLPF9s!eheriA}+>e{LB^wJE(%G#jz5*`GP{@(FVm88HIta13M}RgAE4rAhWkGtTx&@MT)(&LuJ_si=H($rwIkcmsz&&&$)()Vky_4(;ES zWm9ZuRuwk;cT+@u05)Dw_VC+{e2$3CY8%D`U(q>at)> zLep%wTQmkLUZjUQdi#zYjn|@G5=#dx1_K=w`am66;|J)|3|p32pP<0qOmY1ZzVc;M zc@||)YyNG1M2YScs$`DG*R?v**>rze05=MOJoy+Y!8|iFLvg=*cNOwtFNh}nwsSbk z-^a%O$|gCFRn*sSK2WlB&~(hks`f$eZl!?C)3@?aYf*Z0zh47+kM6r>nc( z{`29p86_)s5wXA)WwRRFRZBhl%!w2^(Dag-OkY51bk<@5Ys?=6ZhJhWXLK|W`@?x* zFlofL8ugg}(?i$dz<{>VZ@Q>1)di(?16XQ=a6G zyREj1JbK%UytCtIet$KHE=)w@Rj$|W?vy{1le}@dt9Ab^(Za@Ehld4qb##<@f**K# zuBD1;dU;;c!eYO9XTcN7`qh^hIt!-OjBHTzER0z7w&ifAc|KCv7Rti+dz(g`I%j(u zlsFTB4o$N+R*qI660>Ob%!J0qa)U~I;Ok4X+{+2!#%Y!$a2M44KY#yDZOAJyBb$Xq z#ANfn3$GN6hp(mbUb=K?^qB-|(3r2R)0Uod#|9)&~*zoUN4C6~< zW6$t#`_*C)N(|}g=@bk7nakJ!C`Ec)K;QOs^8~NQ-mtQ>1Fy3VD2ARg{^w5_HvJvs zFrzLK_W`C++&^nm5dHl5GsS%?|Cx*5UR_}|qHf&+jn4R z*&8^q%DodQ)}fLQf%I}!cd)WjC@mR==fe;1@jZ_Z-(P>OWL;j<8wOtm)PE|gwD;`Y%gyAM(;O8a&r86Dy^~XKet%Rs3ZzV@Sqm1HWJ8)aAj^9 zRWH;?lFL(#tmfWXg@XewRxie0VW*=ifY_5G0|zT zv(V1_m*%zuU`CPND3q{g&#numx7&nD{=w0CxlMV`o3U#{?~Om@G-Xgxzih6Se@2!9 z^qLbdYIhsw<8a1elYzz;4=_h0cPYF-;5zvGiiL%1UH4h29X<*?+S=L|aaKr>Ik)MV zwf8^6R|n8YigG;JUm~&Om}mH6NA*}GBIUYu>x2#;uIvqx*}p;PrC*l#lvEH=o6P^N zqo!Uh8@}ANy=|z4f*_!TLKL-acJr=bu{0(@kZD9FJ9WxWu|0p;j~mH+zCW551r%tS zvX$kYDdb{{1Gc=< zZX=LlQ;0y16nOIcZxz~(pj6;}crt<2FRiejAudpAr%LpKsDc8m=UwOn%ZuHAn@uEA z8@DJZY_k76F72{7^2Q$gN^nHPl3IkV)6zs014tp1G$uu9G+TGQtEgDp?K~Nv*leh$ z=MVXy7o=_lQvA!{!z{zeqGrwSpo$| z#IDp|?WE3m z=sDo;aI&5^*plT1faZHtBhrj5f2g{)*6-)7{K~eADvcjLe5gi|)ts*Xa#&4d$n{oG z;$#(uCW~`qJ<=wMd@pQ1kL9PKjC^~o)DmmrnY$n~(x6B(8ZZE0~uD7G7I;yX6H zmX4ueezG4~QF-rbs=<2zH&7>@Rf;cYq&$X-Me1eVVg3ReRvo@A4X6`H3Tk_WO6FBo zR_yQJH}t*Z)Y)qY=s@WWy7CxMR;priU0Cj?h@+1HR(4BC>61|;F8PWqjvuv9gQ9PW=(kARH7uGVylW;QYz?7e=K5iq;@B zHq-V-d+x>{sTmehQjV4UjgqiVRYHP0l55!=2*ryD3Xd0R(VNW~hCy~+4%9o2Sp2-? zIW1;uYb%B#pN)-e92DC3e>fXon|ct|0U#y?7-<1`ANxJAC>z&jmmWRAx5WqtAu}th z6!l$jc(|W>ykab1VF9f#6>|5xS66DsQC;+1(xsSV-YvxgQ&8}LDuK>gP2OvXABQ;n*<(4Wg(_CX9s`Q7>X z$=>rq)&pvMe0*df><1Gr9r>9pHkorK_vU$Je*C$YGKzSlODrSw15*b%P(% zzA`{Aq;IQxe zV~*Xs2dzsi(_$o?XahhYW;t$m06mO}*QgnEnyJK)ea=+h>Xjj@3=_U?Xj3K=~JSM7J*c-i-*% zJP0tzp1Tpg2E|h?UOs>BfdefM3{F0eNQ76eTp1*z3e?&|ax`%mY-APj0h+d9f7mq# zN`S<&HSUC$fIMAqqwGJpGhgpawClp|wQJTORm6df`2yf|B1LORJewmvKmTbUhtx?` zscA^1+k-*Dr(JmM1%=9nopo4z!7wu!_5T-Sa#(Wagl9C158`$e!@Gc?UJr6lEsVDS9?#(8l%x5<4K_5Z&*7K)_Cli2e9Qafd(8 z)5|ZV>Z-Z85rq_S7iY@^d_T+)&xh*^(lCW&P9PIAP>70$<2O53>dvWAz%KUc5RfB1 zo0$7p@ghBBEf1_L;Y|>Cw}bEY!ud;=|4Ik&RTacph3fP^@XK198hdDnM3j*Pi&+%S zQmEQr7hR>q>EZ#nUf$Wsj?5tlVYIV%Yr{aM@P6v(oiLqVhJ5 zU0WL~Fj9H#fs&6$(hfFzLOAw@ILrVSgp#A9I5=5Ps&K5Y(-Kv%({4e*e>gt)?8p!> zo#Qhzm2(rlBv-tD|9*UH2?u>=;YHK5%*@T?mC3{-Va6lC;vX{i6NJ(OwIgLA(ij)V zL)>B{uLbieJqQU|hdO2hyEx;cU8l=%emNH|SA`{th>G?gUbVs)K^DBSQc*!k$rvUN zdtk2y2qPBL-ct+H!z4O@bPa-6h7Of3=!dXF*XVbhiCC|xsj2T>tsNBdK zD=~*Zd|>##_w?Ms6k+HWF{S~8V*h{u8}=89P`{8|Rs#`N5Kv4~n&^OoS%fZ9fIi&eqkfY8g3A0Iq?xXM$G z3Zyq?p3buktC4S5?s&EImV~F=9dIQtY-aGqV+vsNk0TGm5yODc4k9M6u#g-oaEUsL z55G1w9pedxuVXXpkC5r$eG^AUd=M2yk58wJPfV1OncBX6H=_Zl1RdXCVOvYkeGpD7 z@j@P-E5TZk$-)Ou4YzDUu`7?KIlH)k_n^ZR1-$2ZRP*4`qk9n%Y~&4g?pzDbf;wB|B}f{$6VW(_g>0sLY}cZdh`%SwXD3{=+dRQCi|yd zPGYnnGniD=&Fn4d`tmqdcx@}VV1EAmnY@wdnz8X}u#T;5ZE}K4bTSo}grV?UguAoj zodt?N$numow40mULy@bJ)6$MZkAjS$2Ak%G4<|uk#=@@%(hw+bbK7q)Zcv_xMD&0MWHk|H{%$4!G?nX49aj5v1V#( z6E299{~{tDFz&ePMpD7-M**{_fB_&)5FhWWR|o&~X(sn=1H}Xth1z9t<~R-*aTa=b zcv$-#`sklE)A#Ea51g;C_gr6l%)lV3Ev6kY4onpB_!3Jhra)I$x2GG1BY1_k&}(Op zwkIzLy-Qnt@ZeLGIs72aQ!wdWeUp#!R2%wD;0{ya7IDFO#&==jOuAIG1phc&?SQj!f7EL8t-`+oYg5$RUE z-L^8!7Wo{Mu&UT+0(I;p8A1#R8;2wxUq5GT?09y?aN&b``?=-Dktp ziHVD2@mB-uknIC=Qun>GR{2CM5;)=iW%>1x_E*`pl|JSi77$`9!m^qT4a{{w=@be$ zmve<}3W7}Xd|POiSr6bGd z1OCG1J{Rj8$*Z$YuZS3gxKRUYeE*cT{_y2w0Iv9&{A}(o(xM(}l z=84*SK$4uqSNrdK2sdvND-o*9_MF_fI`3kG4~(^v(_b~=HNY=8d0W~0rEG>C3w6t^ zOl(4xlHEAc+|pwF>6s{tq`eS4%$|cNgrs+=gt^1@c(_)t(01eBrG6Qb32$^3ZNs`92G=lFan?^Insm zI!#2oHxFw}{`wRTIp%>}EEi>sJDy`zHJ@}kToLDHjXU5FN8U2%6au@NIn4nd0$7Ca z5}g%hDD#k%moH(OV`E!-H`2W?1XlQiLP9ZcCgf|@+9^TfHBUSpDgFdXe(XIHZM&-Z zzRy`!uKAvmbi;chEJxYs`ondz!z{PVZSeC73lCpS!3W<(=Hxwe==CQ_Y-7Y4_s~#g z3N~clop#YfhwcGgw2551c8y4w#4QB_*xG!(^qJz6l)=?++Jm*><4XCt#9>r9(j#vPw=5YM>|W2Bfs z-IV-9Oo4}icwcXPd$krRLdW#ARBUW4v6Ea_Y}0@%e{RmcqsT$CB{q}8f6`AJC&QG! ze}_$kWi}4MMyDUX{NI7au!I}{Qe{&J4nRW}%RFf8^v>;i)RXq6s|-X%7U*N*5kaY; zp{oi99Me7>kF|767vXEw&b_gnk=C=#5$m66(J3xD+i{yk^g1I!WP16x`qFQ{F}PYE zbBsmGaY`z5P+1V{<3p=8&w1OE9)jj0ToGhdB%&14(PHANNd?dos`k7_+&7N=N3O1kk8E9Je{4a~% z$N#qI`3Q)K<$baV`2SrskSyAMhnF`xBuPm*UCPda-BUb zsoP8jJlX%3^Do&}W>fQ_o31@ew~}05=ur1FH=h;jwkpnVls=m#?>E2e4qeFp<}T)< zSFautFLZhNJ=PsNdlXC}_P=GUr%*@9*C% zax!4r;fgz)ffHccKKk(>yKkTCn+#Fp%ARgipX(?v@KaHW=YG(^+w~)-#Xw$5ixD0` z@YE97>?j2&ZO%-)cI~pCZaSZZ>WOfz1UJJE;7+yL!-1S>oW_f&gS1~?-H5WF9(=;+ z%!}l9DB65tia_T+(h959$^7+&zAZX}{ij z;1f7Z)_?+gzc-`kR?GZZLx0eIIfFz|qoB}NPSBvpIylU;w`c-FK{GkrVzBB>`mx_H zu840rWyb!kSVH|%yd!H3Wb+3R5&p;m-(gQ6=lHN?S4YZ-38*Fq^d-Fm)X#ziSmo)# z<0H!;OHh%JnZ@#YBqa1nwKx<~f7|4rV&$ri5YP1afXY^}?&MzQ+kT0YB(%mYtkqbC zCszTT5Dy>(=^_8JN_3AT1wmgN3&Q12K)(F5(%vwwB$e4rK;qFN82K-TV5I|?;$x; zWbJiM4A)H>C<$;}mdW&H?hh^OUAjf4c$-*v2RrhSNR;KMZ7EBk+Y2*k052NKi3E+F zx1fSHQ`!pcGTIJ~j*hNzziwvcX$tBdJv7ywo%$n=@8C=R@_<`DIV&r8zkY!N7;0i{ z2W7wqJDA(bJU_4{1Lec#&xvrx{h6KyI{|v2E!TXZ9r*ObXJDYxpeoCk|>0OroLWLlhsMXD4)8l64%$gmG0BLhGcEJ64iA0L00csl&zwQJts z>*0H3J#pd$T#SeeAVSK~Uox7f;v~Ms@6DSxRv$8X+o>sNwjwqL*u9A(kWJc|1$9g% z*cZN3Go)W-6%_?Iyh+9rlaT1etKWkT{7>tJEh%r&S5grrQOQ=K{37-sq`Mg z4Q)#TSO!k)=E7mu)@;+QARK8Zgc(4@9PbM?{Lvrnw$5re_#sMl&#bJQ=a*;?NmY`R z+0UG~k3_}+_2PVPp6mTf?8Dj6J$O+~($LTp(0d9ums`0S`J2-9??_bIGSBfp^nm0+y3pF>0ZG~?M?6IJ%!2KgcbLmD&ufRQ3%OtHE(=jiwlk! zS}I#KwEVN8+$ZUbRdmI=gls}cBq2WHIN|xc#|NdrUUuUmAstXXt!7HKovY3og=99a8 zna?eMyKyA&&cCCR?!B8pN4Cnzgjb)eVY?zCD>Z{~B|)zLReEhR+|s-jQv%IHOC;ZT(tT2!{K?pZ2hAplFo z@Mh_k z_cK?9J^&>m=4~Pl;f>w3L1Q z^*T4#3r-nu-$qxju0x(TVm1EV!xvi1jSgZ2jG>|H0#8oDq0zGpHwl_gUiO8;gZrYB z#mvZv3i}Buy$l_}5Nu$iYOeStR5^u`NEU<^+VXHJ0h@@fg;FSI9za~p&@dy!k{D9J zU?hLKcKtdnVlw(Y=^Uz{yJDBNbqLNpuumQ}LKE2?1)e)vd&rdiS5q>y_*i(z;Yd=r zaA7+PHiTtqYipAToNH?$^M*lXX>T}n>QrlcdwD|x1KMqYkC_eN`y)XHBsv(=oGm+y zf3F~XB33i6UAs09O^-m`>fmF6!AUbMTDp?c(-lvj-UvoRl+_P##OmUE(1oDdt!~}A zi%1p`8A)O`dM6RH-!(L-$7cyua_FJW2OUw|PfmKesvJM=*{0f5(swIg?YW62hz&ue z^3qZ&(0J%{-MVn-gLC@n@tSv30c z1SdN_FmlbHFkc|Qe21;-9A7dmP17;jrc?h=BgX`pUgp>> zQqewD@d^oH>iLTjqwHx|^R*jVN00A%6q}u`m1e&O9lW)E5ZC{uV=~5H+l_Utr=htM z6tqc!C)jIdm+=M)wh_@A0on-93$+9+5~C{nD_#A zJQ-n7kZO1+dKgh~*%Ym{JC6u}y#zju5N84fXe}by9}GX`&Hblnex4fb+yNXaNDdt#CujRjtgd-qDF>yp7=W zz^$Vs2_UK)^Ed!k-4zLE7z+t--&660W7zay-1eUmJj)h?jcB&f76- zc~ETA_3{a!4ThhzHb6>5rFfnFHmQJKb8ZU9i^TfWe*DPzSsV?>vLNyiIxu*mw-A~a zA{s9bPuwSlZIv8{QKIMBPw@QH_>EeH^zJx17L140q0tKNPBOE=Es7WwGJ-XGt|HC^ zjb|HNGB?r1h~UkQ^iSE0rNG&PlFtJz7o-4SR>RG&{)66#t0`9V-+*zG(J z3?P~ltqYlUGZRzd@PqA*c|do7YTEW^&z++^%Fn|iXFoA}O#kfJZ4gU6_0m4<#N7^L z6A&&QWySl-%3D$R}-H@j=q}VeXmiTN`PGHU%PXqw~B1O`Pi5+9Ym5w`L_W7Q`{9rR}?CtnwYF z_YfFO(6AWVpb_{RUYi2)#HWGR4_Hx{WrFlCuv86MX8*EnB8c{U$e2#z0bs7|GndOxm!hhgT!4QbnCwo z$cxR3xf|p8;_S__?9bY1X^l@a&UxoHp3|*L_|kmt+KsAn`*M8_-skd5+svqbOqStT zunTo5UuyrXl3_>mdL6aujpIdz8AU$a`Tcy)dT)=qjJjBjb{y5qv!cRzqEJwf00->= zHm*b+-O4Q)h0+XrwigC6ax^e|D5yP1GXNS&h+>GswlyK_sdPMYEn1D~&Onty=LihO z7hx$MpPsG&=_YjbBTIA4)ZNrnLF^Lju~pb^CKeWzPzHPY`@Nw8A;*tL@|0VjLbArr ztP$Kg@ol9XhFRSJCFT~t+A+g1koqmPvNzyTjaJRrSu*fgaO z$e=Y5I#I$qP+gncB;m3kLJk!t=Ozl^Kp7}HVR+kB!Vd>5bGA}T9c33olmPr9+#I@H zN!0)S`=j0ckAGX7Hr7HYC&z$9AH){$EZ{|DL1jVSapdLW5yFqeMsIJhaf~S7 z74Qb<(sVpw1(}TeA=~nL<0*JaUFZ9l*~G2aLxa4FIt_N^K&&{HEHSA}i1sIzrlaAt zzyF53yu9zKZVOw{v-4q{x4)h~R5sFshcz_1e*He;ECRd_`;YThAT8!_pl=S;b9cOT zVusnU3dJQM?29#x*M*^(ZE4KyFOi~&YCkYE^n+OU5R;HmYXajoY(~l?RVP|A&qRpb zf&U-M{3USu+UR(KE;N7UCfEH{)9$c5wxL4-iAh6UJr)U61BC?Igs0yBdMf<`%q=lW z1S77~c*>D>|8307laWk~bqUX(*JG=#rv$J|gy41vMZgE=qzY?I>?nAQ8nN$bD5oRD zf}uappYhvHfkD9p`Gy!K(c?&XK61Z8&EDg!EU*bAgLF%JWW0a_CkHzM zKTy^eTnz%jV2m$VdG3tgU@yo>6TlKAsN-lzjYkO50O8whD*ToU4pqewx4)13eg)UWt8)L0}`MaA+R@+5#hMLRp4md?NCkTg$T7 z&fU9xVIw>N!woyxEGoKyd#Ju_q8-A92NgX->F1 zMcAbpOheDlpB~t@STK9m&=O(jM>ryAnE<9VYz?D;Fkivj;{` zKO8H& z;mTd0o=dpZfow4be3aGAo5vtSKYaA)CR!kHR{!7xshXIY_8@L6Kw+Pno`%8U4$LQ$ zk>^S#z5j`dxDUw-JBc*2VrKqSpRxd7=yau!Lp=B2pvB*hWDZw_}lxSNrAZmaH4!4iW_mfyFtg$xYI-tQAd^)|o~q%Gu15=>@`Vfe{9i2j z4;^|$TIVSy@P*YmrxpTW51?<|DYgY=O+BInATA{^3yFPD^Eau8Je^oc!6s~ zaA%OR0HemqllS$E54p&LA;zH~zV7;$H?^1Njq6^@IDdVB=naMI-T;>GmS4@(K6t&j zP}{b>v5eOHktP18%HS$n-1ViUB?;blhh0-02jqY>sA7O{IebNL{j4@vjN59nVqoyoFDf|r z7%EULb@fuIknnI~ni~y{XoEue2ovzr)u9R}kM;14uns79-I?f3B>@Gp6vi~26hHcv z)1l=7UI-PjQ>;$)lp&hAc(H1Z=sL6ats7ESI&d)XgtGF$p9P(N#wu?0o%HJjYYT=r z{dP^9eCg5m^CuU)Ac*ai(7g}@U+bMp#7wJgW!>ntoR6bfXT@4dbE zKtFQ?;HNw=#l}DfQU#qdaY;$uh+`4rHng~};8wsVfkgB!|8s=^Qm%&_clRLW;&js9 zX{9bv1weMgqRZmgyd z-2_>l_a$Uk@{c96E!FqQs5yAp$4o1 z>?c$+xCEPmNR%YFkWEfibrWbZG@8p3gx1@eqVM4wC{m?M4`*^$Tr@ zQjZW*iWqtmuWnJ|jd|lijY+!va1Kd3UUng07a$>l|FCu44nibn1UVuAn;u%K8kRSW z9wn`L#2yW^ESbH75EfLzgs3npo_f6p?+?PY=?&u|@X`F4zNgyDgGDRVg-aPyfdhwS;z{Cl+1S6w@f&w7N8h4atD0O!3ym_9=VZjzPOMh`_5@$OK z!DV>w(SLi*(%k$s&{xM8rdHx-=aag@3o8RQ|6D%s>vLrLh>`Xs;v z^d)XR@Svmj)xzYTY40G`TTs*Kqjw$>dP~}HfiKPIQv-{%*|C(d?Qbk^A3+JZs(v)< zn*K%kf8K8IxzreB@X0NO(Rnd{rWlz2rMw0P2CN+w65pgGCreHiG=YpzQ#XzNg9rxS z3oeLZkBZO82tp<~^Jeen^?8fnNIG8pR89bexQp}DZTw)AA7Z`^usbZ$j9`sNC!3!>_0EODyNjAm`GfLY4^ zf~99uG;@ZG`CKwLcvFgNw87-h{+bPv=)hqwzW1kcsM@b77|oP63oCH_HjUOPd>vt% zXKSYb*8S}3o7hrVGGImT2R1J|CkIVwWlGX8ggO4=QAX%xIe1w)qw>hXgR9*84Q|8$ zVc-fq0GylN-N4t@d%NJO6h_&ot*hG$kLy^y0G86uAsof=pw)2tXWFD9+!nZ+f)-4N z+B@nS78VwyT-ANkFHZMY46E*tzOHO)x*PW6wvE+ccWQvHAmA1KdiT$m@#5}2dF{vx zR56{#2fn0ImIBQw#Lb9?$)aENEjEr{-r^z()P6rB=_usNK>({f=*`~U6;)NnA0F?1 zOD-kjd^h$oOU5rUlHKlA+aq8#0GLvX3OZU^IUqai9y&^g!PDFW325mAr7G?+^2kZZ z@g#67x-~06BbWOy@V3U>D+NPpg*$QbtFBD<_YH626y*bD0PYtgY^bh^qA)InBKK8- z8Y${~H?+QlM2w@krZ;Z9M@U*{XJ?mRHF{n=Twn%OPB4!40lIk%nA9b($ls=;6%`R7 zmsOBn)pWy>uF-j&+lwRNK6n{K!cCLWfAen5kdkmS66!rOSJA zqTOKj=X7C$#%^-m1En4W(jbs3xsQn4-ghKuYNEHQZ2e*E zp^AZ)?Kn5i4MTcjxf3@JtF*HifUb>MWJK;9ymocYXTTU9;7PnIGa8F*renG~AeEHV$sp1mUs63?SeX zVCL|+HuyDmw5qIGMFpw&p|)TmXtUt-^!?RT82A&~jx$kI1%Ca8R@bL63t*gs8rDPV?B@9jl$^&sfzvZaKRjL^E946RF z>fDYjZGY3o#2(V6BQaLQ`zFu-5(&-3KHu%SxDnCFIqA?vn>Q=fue}Hph=WL4PC*zr zNpUnDfvyX^Se|P$7bfNOHZ95@wkm6{psdp<#*m0_g6!@nu<_IVf0{b?xSsDlj(^>% z(|%HOOVQ1xQWELdj(&=$bbeCPb{wtL*oGdZrbI-#ibyJlwdEv=MdVV{IP^p1GP#VV zs5RC)PKu#SZRh#6J9?1 zXNN2&?@ni|Q%eran78K~sb2icPEM8WJWh!#6NK8PTK&xAf0uJOuyW^=DO2i=D?W{y zKK9UD&IfRK=C*AHRGL~l+rq(YiW3rKa^y%yPW$j-!*&3mrZ#vh3!* zptXxMO{`ZB+EVf!d|2dfp3i=HK3G;IdM)4Arpwk$)5JJqj)h?z^xWzZHcss?Uefxm zOAiAi)smKnCsH1XucWa%WL;Qc^GjdC~h*y^zp<*YNYV zyVkSUMpD$y<4la_h#1Yj>Uvz@w0R<@FdiKVEP#}B1c!n)S4TX)GvRC0hN5ux_a6dz za4p7LV@^2n7MvTSA>2?`IIzqvU8y>u`3*rwl1L(%e7I<)q(F805bW<9aTX67T zTE_|FcP*{{bH8#pgAhagWM*)O{vJ}Hu^D0owSj^aCA1O|+{MDQN!N#xl8AI=3{*!fnvjOTxAHzj(IVh5jtCiu}U8i8GvGQ!2RqH1={9qG73bGo|k7v z4$0;Xy^j~w-MI1nH0Qz$6VepKF(pcRgggWaU%>3opy^u7a?Kz++$mHU;qpb!iFty? z4*B+v{MA8DlP6b+`UuU6J3X&Rk0{p2gzAk`+IE0XWctQX#b)BfYWgfA!qGysDZ*vk zX;0a|m9i&F5%e+)eiuJ&xfl@=_(Ykl0Xt08|&rmT?Mo3 z7~c5K*;|W$Nds_OadTofqVJx>?1LCCgYp$kT;7jk)vG&2pLvP)!pPh_LmW5&EFg&7 zxB1h~PB)e$k3*kYhCkulg9m2v_G!Xi`DFM>iV_pe^WwxoxB~>S95+q}M zj@<+RWp3ZDu-1fd5$p)!Zfcv<&zEyo;#^joeWkHhjaIs2i0)Sh%vLPO%SNvUxNl*w#t2SYH70usZ67rC z(bF|?DkDo)J`}p#4PsohE21&B$L>47P!lrHw!jch>nS|6skP4+B6AQ7$xjJJ@+Zpk zrnZ4gi6?*p6Jaoe&iq4%(uKb#3veUzSZ+yWjqE_w&|wXr9>8%^-caY5}<*$aO_E&sS-0rfd=cBDXDwpUFTxo024QN2q2- zKDq6E-uI>Tk>M4~6I6)AK_BMWe&GojsqUKmv3_=TP`AHLO56Kfv>2ph57HosCHaqW z_lpctvGp!-!?3)`EC-xP zBFB~?793jhlP3nqtINvsbiwYB{z(h$FHr?D@hY*`2tZ5=b-=fF<=60C(~I`*O)#CZ zh;bPAh=4=%+3>%Ui1#Vm_2D42wdYvyhKxO!ad9kRT9q_%nWEF$A(QF$$qEVbg3gqh zfKgnmUTXCy5Nt$r^hIWBlK04v`}n9*{k;ct{60COD7pdi8370M#25VDdv7z*PC)kQ zHZJQt{cq?yYPA}D-?^Btt{#7S>!`~?40yPMJv15>(>NLEQ~7^-{8-Fc9D2sC>s=TQ z)z5TMAEIWWj1l?8-F@Qi;jl!zgjJ{Y<;c=Cm6{D!Io^?s(%L(i;G+mOG z#YJifKwwPy{j_hV=c53DgraC|%E<6!?=rs!iaL@21!JOZXfW-&F}}lpL}4|aTPx;r zB0fimDwP=QsjaU!rtIx<4CyPrb4d5aZ^m>DN2peoJRq*~!|)lo6`Y7L1s!Yv47OamTA8t&bb};i6%QI%x%LHSiqnzl z^o2AbTjjpdoKbM%sY1DV_vT`9!kFv<%Z*q6VlR)hzkgII8UaE-G`1dFk= zu~Cd>051TR5m8Y|2$OghZ+Uupu4=K+y6nf*1Ojn~NQkkswe6!|NI-2DOlDi-bvi$x z?LZDLpFVI}7!ZIXJ{@abM2D0$DXbOr^!nX7;-%C7y)D76G-7+0%|6UD&j$oT6XF zMF)=04hcd*V8lYWH}C<9G(KcufWq&Hj)?b1%lao6AMw7@*YJ}?W$QJjC9YY-ZKT(* z6ZbML1ygdXp8QBNm(}sm&J0itX|@$*qg!3cyQ1GkJDI!Zx}#c{2?o85!9BHm!V*7I z>h9i6r9(xpgD+7`g_ulEnpVU3N&)LK`Pp9Vh4j9>Y;MnwPo$8ao1HB|+@ZdrUkeKQ z<_zQQ;=sXO59dL+uJUO=R~KWtvo*7J2}H+q&S%sQ^&t_92onPJy7b;bXRRW)mg7hy z7zEYIOL4P^hi~A$S`N|AM-4Z0XpX`B8&T2G4RMiB9``On=}elchi)pxe|)n4_}QF6 z_~7_5Q^zL3JD}0~qT%OfW8&iCN*0`S4v{y<$A_R3<5||f8mAiV$;%;s=#kEAs#f!p z*4EbYhTTd}(5Hy_EDZJjSzNpY!0qnonOf`|=Ik+l{_*>_HNf2PRM_FaR-V@oYc;$G zF(bTH<6+_(itRXLM*Vv;7tY(g=e#hioc^#h>xU63*1Q#bea)99&olT59!GrF{AY0F z*3FwOCdN>Nl&TpvLzqbSgA+5<>t9z_*IcsvWz^w5idubU)rOM8haau#->*G%8-hg5 zIB8HhD(Tp1jx4ikk*u8haUTj+_mYZ=3RxQRBIPQU%=`1wtMPYTO?Q^S;)lgN+}plB zpa2o%ptM<4y{Qv(ys=9nLmk-MRp>Q7r>r4}@2WHgn}<)GjgRxoO8rbAG6TIDb{umq=~?Y9OG87;bCX3lneVHo@bqN;Fc$ht#WcJ h@qMaWX(xWuP25p)YA2GuvlY$;{w{{{mtDw7&oV literal 0 HcmV?d00001