HAL Id: inria-00072173
https://hal.inria.fr/inria-00072173
Submitted on 23 May 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,
A Local Approach for Inter-individual Functional Registration
Isabelle Corouge, Pierre Hellier, Bernard Gibaud, Christian Barillot
To cite this version:
Isabelle Corouge, Pierre Hellier, Bernard Gibaud, Christian Barillot. A Local Approach for Inter- individual Functional Registration. [Research Report] RR-4415, INRIA. 2002. �inria-00072173�
ISRN INRIA/RR--4415--FR+ENG
a p p o r t
d e r e c h e r c h e
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
A Local Approach for Inter-individual Functional Registration
Isabelle Corouge , Pierre Hellier , Bernard Gibaud , Christian Barillot
N˚4415
Mars 2002
THÈME 3
. 0/ !'12 3!'
4&57698;:=<><?:A@CB9DEBFG9:IH,JK>:=DEDL:AM:N<?<?K>:=DEOPH,QC:=DLRS69DETVUWK?8S69F3TYXH;@CZDLK?5L[EK\69RYQC69DEK><?<?B][_^
`a"b#c_d e-fhgji=kldLmonNp&koqsrNi+a"rNcCc_d#t?cnupvawqsi"dNx
qycn{zNdL|Lx~}"rui"i"LdL|Lx"p'rNi"iwn{q|o|lnuiwp'dE|
,mor{d#k0 q|kvn
nu"]rNmk}dmodLpvawd#mvpva"di-{Nw7fAn{mv|0{NNfN-wn{zNdL|
+3L#"uu ¢¡£= ¥¤¡£N¦§j¨v©Eª¦0©#«¡£N¬¦o¦o>®N ¥¯¦v¤=§j ¥©L¤~°L±"²u¬°L ¥¤C ¥¯ °L³L ¥¤=³N´uµ¦0ªu¬©Eª©L§j¦0°L¤_ ¥¤¡¦o¬j¶ ¥¤~®u ¸·{ ¸®N¹=°L±
«¹=§j ¥©L¤§j¨l£N¦v¯¦C¡©¬¦o³E ¥§\¡¦o¬-«¹=¤N¨o¡ ¥©E¤=°L±°L¨o¡ ¥·L°#¡ ¥©E¤N§C°#¨v¨v©L¬®u ¥¤=³¡©W°#¤~°'¡©E¯ ¥¨&°L±¨v©L¬j¡ ¥¨&°#±º§\¡j¬¹N¨o¡¹N¬¦v§v´3¡£=¦
§j¹=±¥¨v ¼»½£N ¸§Cª~°Lª¦l¬_ ¥§_²~°#§j¦&®©E¤¡£=¦°L§j§j¹N¯ªN¡ ¥©E¤¡£=°#¡_°L¤¾ ¥¯ª©L¬j¡°L¤¡ª~°'¬j¡_©L« ¡£=¦¿«¹N¤=¨o¡ ¥©L¤~°L±º ¸¤¡¦o¬j
§j¹=²{À\¦v¨o¡ ·L°#¬ ¸°#²= ¥±¥ ¥¡>ÁA ¥§¦v¤=¨v©{®u¦&®Â ¥¤A¡£=¦C°L¤~°'¡©E¯ ¥¨&°#±·L°#¬ ¸°L²N ¥±¸ ¢¡>Á»½£N¦o¬¦o«©#¬¦E´µ3¦°L ¥¯Ã ¥¤Â¡£N ¥§Äª~°#ª¦o¬-°#¡
ªN¬©Eª©L§j ¥¤=³_°-³E¦v¤N¦o¬ ¥¨Å«y¬°#¯¦oµ©#¬Æ¡©-¬¦v³L ¥§\¡¦o¬«¹=¤N¨o¡ ¥©E¤=°L± °L¨o¡ ¥·L°#¡ ¥©E¤N§°L¨v¨o©L¬®N ¥¤N³¡©¬¦o±¸¦o·E°#¤{¡0°L¤~°'¡©E¯ ¥¨&°#±
±s°#¤~®u¯ °#¬Æ{§v» Ç3©E¯ª=°#¬¦&®Ä¡©0È>¨v±¸°L§j§j ¥¨&°L±¢Éº ¸¤¡¦o¬j¶ ¥¤~®u ¥·u ¸®u¹~°L±~«y¹=§j ¥©E¤-§j¨£=¦v¯¦v§v´¡£N ¥§S°LªNªN¬©7°#¨l£- ¥§S±¥©¨&°L±¼» Ê>¡¬¦o±¸ ¥¦v§
©E¤Â°§\¡°#¡ ¥§\¡ ¥¨&°#±§j¹N±¸¨o ;§j£=°Lª¦¯©{®N¦v±,°#¨v¨v©E¹N¤¡ ¸¤N³«y©L¬¡£=¦ ¥¤{¡¦l¬j> ¥¤=®N ¥·{ s®u¹~°#±·E°'¬ ¸°L²= ¥±¥ ¢¡?Á©L«°+ª©Lª=¹N±s°'¡ ¥©E¤
©L« §j¹=²{À\¦v¨l¡§v´0°L¤=®ªN¬©'·{ s®u ¥¤=³A®N¦l«©L¬¯ °'¡ ¥©E¤I¯©{®N¦v§ ¬¦v±¸°#¡ ¥·7¦v±¢Á¡©°W¬¦o«¦l¬¦v¤=¨v¦+§j£~°#ª¦ÂËÌ°W¯¦&°#¤§j¹=±¥¨v¹N§Íl»
½£=¦ ®N¦l«©L¬¯ °'¡ ¥©E¤PÎ~¦o±s®©E²N¡°# ¥¤=¦&®²¦l¡?µ¦o¦v¤W°C³L ¸·E¦v¤W§j¹=±¥¨v¹N§Ï°#¤~®¡£N¦Ä¬¦o«¦l¬¦v¤=¨v¦ §j¹N±¸¨o¹=§ ¥§Ï¦oÐ{¡¦v¤=®N¦&®¿¡©°
¤=¦v ¥³E£{²©#¬£=©©{®C©#«Ñ¡£=¦0³E ¥·7¦o¤_§j¹=±¥¨v¹N§;²Á-¹=§j ¥¤N³Ä¡£=¦º¡£N ¸¤u¶ª=±¸°#¡¦0§jªN±¸ ¥¤N¦0 ¸¤¡¦o¬ª©L±¸°#¡ ¥©E¤w»Ê>¡, ¥§,¡£=¦v¤C°LªNª=±¥ ¥¦&®C¡©
«¹=¤N¨o¡ ¥©E¤=°L±2°L¨l¡ ¸·L°#¡ ¥©L¤=§±¥©¨&°'¡¦&®+ ¥¤¡£=¦ ·{ ¥¨v ¥¤= ¢¡?Á©#«¡£N ¥§º§j¹=±¥¨v¹N§v»0½£N ¸§°Lª=ªu¬©7°#¨l£¿ ¥§¨v©L¯ª~°#¬¦v®µ, ¢¡£¬ ¥³E ¸®
°L¤~®-¤=©L¤C¬ ¥³E ¸®C¬¦v³E ¥§\¡j¬°'¡ ¸©L¤¯¦o¡£=©{®u§v»2P¦ªu¬¦v§j¦v¤¡; ¸¤¡£= ¥§,ª~°Lª¦l¬;¬¦o§j¹=±¢¡§,©E¤¿Ò_ÓÔY§j©L¯ °#¡©L§j¦v¤=§j©#¬jÁ®=°'¡°
°L¨&Õ¹= ¢¬¦&®-©E¤Öv×ħj¹=²{À\¦v¨l¡§v» ¦§j£=©&µI¡£~°'¡S¡£=¦0¤=©L¤N¶±¥ ¥¤=¦&°'¬±¥©¨&°#±]«y¹=§j ¥©E¤_§j¨£=¦o¯¦§j ¥³E¤= ¢Î=¨&°L¤¡±¢Á¬¦v®N¹=¨o¦v§S¡£=¦
«¹=¤N¨o¡ ¥©E¤=°L±w·E°'¬ s°#²= ¥±¥ ¢¡?ÁC°#«y¡¦l¬¬¦v³L ¥§\¡j¬°#¡ ¥©E¤w»
ØWÙ=ÚÛoÜ-Ý
Þ3u ß#àá¨v¦o¬¦v²u¬°L±, ¥¯ °L³L ¸¤N³N´Sªu¬©E²=°L²= ¥±¥ ¥§\¡ ¥¨¤=¦v¹u¬©E ¥¯ °L³L ¸¤N³P°'¡±s°#§v´S§\¡°#¡ ¥§\¡ ¥¨&°#±º§j£~°#ª¦_¯©{®N¦o±Ì´
¡£= ¥¤N¶ª=±¸°'¡¦§jª=±¥ ¥¤=¦E´N¤=©L¤N¶±¥ ¥¤=¦&°'¬;¬¦o³E ¥§\¡j¬°#¡ ¥©E¤w´¨v©#¬j¡ ¸¨v°L±9§j¹N±¥¨v ¼´N«y¹=¤=¨l¡ ¸©L¤~°#±°L¨l¡ ¸·L°#¡ ¥©L¤=§v´~Ò_Ó3ÔY®N ¥ª©E±¥¦v§v»
âãÑälå\æLçä0è3éyå\ê?ë'ì
í,îÌï î¶ðLñ ò¼îÌó3ï2î¼ñôõlö¢÷ø&ù¶ø&ú7û&ü&ôý7þ7üÿ¢ÿ¢ö¢üù3ö¢ù¶ö sù
{ø&ù>ø&ö¢ù>ü;îCô7ö'üù?öEü,ï ü7ü! &ô"{üù"vù#û&ö"vú $3ú7ö#ò¼ù¶ü% 7ü'&(sù
)
îÌï î¶ðLñ ò*Ñó3ïðuô÷"vù¶ö¢ÿ¢ÿ¢ø+3ö¢ù>ö yù
Unité de recherche INRIA Rennes
$ 001 ,3!' 0'#01
à°L¤=§±¥¦¨&°L®u¬¦º®N¦;± ¥¯ °L³L¦o¬ ¥¦º¨l¬v²N¬°#±¸¦;¡j¬ ¸®N ¥¯¦v¤=§j ¥©L¤=¤=¦o±¸±¥¦E´{¤N©E¹N§3ªN¬©Lª©E§j©L¤=§¹N¤-§j¨£o¯ °0®N¦
«¹=§j ¥©L¤ ¸¤¡¦o¬j¶ ¥¤~®u ¥·u ¸®u¹=¦v±¥±¥¦ª©E¹u¬2¬¦v¨&°L±¥¦o¬®N¦v§ °#¨o¡ ¥·E°'¡ ¸©L¤=§2«©L¤=¨o¡ ¥©E¤N¤=¦v±¥±¥¦v§§j¦v±¥©E¤ ®N¦o§ §\¡j¬¹N¨o¡¹N¬¦o§°#¤~°'¡©E¯ ¸Õ¹=¦v§
¨v©L¬j¡ ¥¨&°#±¸¦o§v´]±¥¦v§º§j ¸±¥±¥©E¤N§v»Ç3¦Ï§j¨l£v¯ °Ä¦v§\¡²=°L§ §j¹N¬º±£Áuª©L¡£v§j¦ Õ{¹¹=¤=¦ª=°#¬j¡ ¥¯ª©#¬j¡°L¤¡¦ ®N¦±¸°-·L°#¬ ¸°L²N ¥±¸ ¢¡
¸¤¡¦o¬j¶§j¹#À\¦o¡§,«©L¤=¨o¡ ¥©E¤N¤=¦v±¥±¥¦Å¦o§\¡¦v¤N¨v©{®v¦ §j¹N¬º±¸° ·L°#¬ ¸°#²= ¥±¥ ¥¡Å°L¤=°#¡©E¯ ¸Õ¹=¦L»º©L¡j¬¦ ©E²{À\¦o¨o¡ ¢«3¦v§\¡®N¦ªN¬©Lª©E§j¦o¬
¹=¤¿¨&°E®{¬¦Å³ v¤o¬ ¸Õ¹=¦Ïª©E¹u¬¬¦v¨&°#±¸¦l¬ ®N¦v§0°#¨o¡ ¥·E°'¡ ¥©E¤=§«y©E¤N¨o¡ ¥©E¤=¤N¦v±¥±¥¦v§0§j¦v±¥©E¤®N¦v§0°#¯¦o¬§0°#¤~°#¡©L¯ ¸Õ{¹N¦v§ºª¦l¬j¡ ¥
¤=¦v¤¡§v»2Ç3©L¯ª~°'¬v¦®N¦o§°#ª=ªu¬©¨l£N¦v§2È>¨v±¸°#§j§j sÕ¹N¦v§\É,®N¦«¹=§j ¥©L¤ ¸¤¡¦o¬j¶ ¥¤~®u ¥·u ¸®u¹=¦v±¥±¥¦E´7¤N©L¡j¬¦,°#ª=ªN¬©¨£=¦S¦o§\¡±¥©¨&°#±¥¦E»
Ó ±¥±¥¦§°LªNª=¹= ¥¦§j¹u¬,¹=¤ ¯©{®o±¸¦º§\¡°#¡ ¥§\¡ ¸Õ{¹N¦0®N¦;«©#¬¯¦v§,®N¦v§3§j ¸±¥±¥©E¤N§S¬¦v¤~®N°L¤¡S¨v©L¯ªN¡¦®N¦±¸°Ï·L°#¬ ¸°#²= ¥±¥ ¥¡º ¸¤¡¦o¬j
¸¤=®N ¥·{ ¸®N¹=¦o±¸±¥¦º®¹=¤N¦ª©Lª=¹=±¸°'¡ ¸©L¤C®u¦º§j¹#À\¦o¡§v´u¦o¡«y©L¬¹N¤= ¥§j§°L¤¡;®N¦o§¯©{®N¦v§3®N¦º®o«y©L¬¯ °#¡ ¥©L¤ª=°#¬¬°#ª=ª©L¬j¡ ¹N¤=¦
«©L¬¯¦®u¦¬o«l¬¦v¤=¨v¦ ˼¹N¤C§j ¥±¥±¸©L¤¯©&Á¦v¤Íl»w¦0¨l£=°L¯ª_®u¦0®l«©L¬¯ °'¡ ¥©E¤©E²u¡¦v¤{¹C¦v¤¡j¬¦0¹N¤C§j ¥±¥±¸©L¤+®N©E¤N¤¦l¡±¥¦
§j ¸±¥±¥©E¤¿®u¦¬o«l¬¦v¤=¨v¦0¦o§\¡o¡¦o¤~®N¹Å¹=¤·7©E ¥§j ¥¤~°#³E¦±¥©¨&°L±®N¹C§j ¥±¥±¥©E¤¿®u©E¤=¤0¦v¤C¹u¡ ¥±¸ ¥§°#¤{¡± ¸¤¡¦o¬ª©L±¸°#¡ ¥©E¤²=°L§v¦
§j¹N¬,±¥¦v§¡£= ¥¤u>ªN±¸°#¡¦§jªN±¸ ¥¤N¦v§v» Ê?±"¦v§\¡;°L±¥©#¬§°#ª=ªN±¸ ¸Õ¹°L¹NÐ-°#¨o¡ ¥·E°'¡ ¥©E¤=§S«y©E¤=¨l¡ ¸©L¤=¤N¦v±¥±¸¦o§±¥©¨&°#±¸ ¥§v¦o§°L¹·7©E ¥§j ¥¤~°#³E¦
®N¦ ¨v¦Ï§j ¥±¥±¥©E¤w»ÏÇ3¦o¡j¡¦Å°#ª=ªu¬©¨l£N¦Ï¦v§\¡¨v©E¯ª=°#¬v¦ ®N¦v§¯!l¡£=©{®N¦o§º®u¦ ¬¦v¨v°L±¸°L³L¦Å¬ ¥³E ¸®N¦Ï¦o¡¤N©E¤N̬ ¥³E ¸®u¦v§v»"º©L¹=§
ªN¬v§j¦v¤¡©L¤=§®N¦v§;¬v§j¹=±¢¡°#¡§º©E²N¡¦o¤u¹N§§j¹u¬®u¦v§®u©E¤N¤v¦v§§j©E¯¦v§\¡£v§j ¸Õ¹=¦v§°L¨&Õ¹N ¸§j¦o§ª~°'¬0Ò_°#³E¤l¡©7Ó2¤=¨vªN£~°#±¸©#
Ô¬°Lª=£N ¥¦Ë¶Ò_Ó3Ô0Í9§j¹u¬SÖ&׺§j¹#À\¦o¡§v»#º©E¹N§Ñ¯©E¤¡j¬©E¤N§ÑÕ¹=¦±¸¦3§j¨l£v¯ °º®u¦«¹N§j ¥©E¤Ä ¥¤¡¦o¬j¶ ¥¤~®N ¥·{ ¸®N¹N¦v±¥±¸¦¤=©L¤N¶±¥ ¸¤&°L ¢¬¦
±¸©¨v°L±]¬v®N¹= ¢¡;®u¦«¼° $o©E¤_§j ¥³E¤N ¢Î~¨&°'¡ ¸·E¦ ±¸°Å·L°#¬ ¸°#²= ¥±¥ ¥¡0«y©E¤=¨l¡ ¸©L¤=¤N¦v±¥±¸¦ °#ªN¬v§S¬¦v¨&°#±¸°L³E¦L»
% Ý E Û '& Ê>¯ °L³E¦l¬ ¸¦¨(o¬v²N¬°#±¥¦ ßLàÅ´]°#¡±¸°#§Ïªu¬©E²~°#²= ¥±¥ ¥§\¡¦E´Ñ¯©{®o±¸¦Å§\¡°#¡ ¥§\¡ ¸Õ{¹N¦®N¦Ï«©L¬¯¦o§v´9¡£= ¥¤u>ªN±¸°#¡¦
§jª=±¥ ¥¤=¦E´u¬¦v¨&°#±s°#³E¦ ¤=©L¤N¶±¥ ¸¤&°L ¢¬¦E´N§j ¥±¥±¸©L¤=§;¨v©L¬j¡ ¥¨&°#¹NÐ"´°#¨o¡ ¥·E°'¡ ¥©E¤=§S«y©E¤=¨l¡ ¸©L¤=¤N¦v±¥±¸¦o§v´"®N ¥ª*)E±¥¦v§Ò_ÓÔÏ»
4
9 $(;!'
gji koa"d¿p'rNiNkod5~k r'6qyiNkod#mlt?qyiw}q87~qy}:9wn';Si"rNmlcn;sq8<Ln{klqyrui2x)=ºd¿nu}w}mldE|l|Åqyikla"q|wnu]dLmklawdmldLzuq|komon{klqyrui
r6e>nuiwnkoruc_qypLn';,nuiw}?6@9"iwp'klqyruiwn;}"n{kon"x %A!A }"nkvnB6ÌmlrNcC7n{moqyr9w| |39:DdEp&kv| n{iw}nNp+EF9"qymldE}G=0qskla
7numlqyr9w|-c_r~}wn';yq¸koqsdE|IH¶dJzJcn{zuiwd'klqp¿modL|lrui]n{iwp#dqscn{zNqsiwzKH¶0gMLN6ÌrNmCnuiwnkoruc_qp#n';º}"nkvn"xScn{zNi"d't
kor~d#iwp#d#"awn;srNzumvn{"aPOQH¶SRTNLrum6@9"iwp'klqyruiwn;2cn{zNi"d'koqypÏmldE|rNiwn{i]p'dÅqscn{zNqsiwzBH@6¶A0gMLU6ÌrumV6@9wiwp&koqsrNiwn';
}wnkonwx +/BWW+W LJYX awqZ;ydWn{iwn{klruc_qp#n;qycn{zuqyi"z[7=q|39wn';yqZ<LdL|\D"mvn{qyiIc_rumo"a"r;srNzONxkoqy|o|39"dL|Lx +/IWW+W x
6@9wiwp&koqsrNiwn';3qscnuzuqyi"z¿d#i]n'D:;ydL| klrI;srp#n;sq8<#dp'd#mod+Dwmon;nup'klq87~q¸k]OJÏ`a"dOkoaP9w| wmlr7~q}d-p'rNc_:;sdLc_d#i=konum3O
qyi*6ÌrNmlcnkoqsrNiQ=0a"qypvaApLn{iSD9d d5:;yruqskldE}klr¿zNqZ7Nd n\6@9"iwp'klqyruiwn;p#numkoruzNmonu"aPOr'6SaP9"cn{iSD"mvn{qyi2xwrNm0klr
p#ruiw|klm9wp'kCn{i]nklrNc_qypLn';nuiw}^6@9wiwp&koqsrNiwn';0nk;ynN|dE|`_¥a\xb_ycda\xb_¢ua/e0|M9wpva nk3;nu|ldL|D9d#qyi"zwnumkoqyp+9:;n{m;ZO
d+5]dEp&kldE}Cklr-nNp#p#r9"i=kf6ÌrNmSkla"dÏqsi=kod#mlt?qyiw}q87~qy}*9]n';:7n{moqn'D"q8;sqsk]OJhg |o|39"c_qsi"z klawn{kºn{i_qyc_]rNmkvn{i=k;wnumk;r6
koa"dU6@9"iwp&koqsrNiwn';~qyi=kld#mltj|M9:D"dLp&kh7n{moqynD"q8;sqsk]OÄqy|d#iwp#r}dL}-rui koa"d0n{iwn{klrNcCqp#n;7n{moqn'D"q8;sqsk]Oux7koa"dº"mlrN]r=|dE}
c_d#kla"r}qsi=kldLiw}"|ºkord+5~wmldE|l|U6@9"iwp'klqyruiwn;Ñci9:;sklqst\wnkoqsdLiNkv|}"nkvn-qyinC|lqsi"z;sdÄmod6ÌdLmldLiNkoqyn;j;yqyi:kudE}¿korCnui
nuiwnkoruc_qp#n';c_r}d+;2J
gji=kldLmtj|39:DdLp'kmldLzuq|komon{klqyruiWkodLpva"i"q1EF9"dL|nD]r9"iw}Âqsi?;yq¸kod#mvnk39wmldB_slda/JmTn;yrD]n';Sc_d'koa"r}"|n{qyc nk
o iw}qyi"znkomonuiw|]6ÌrNmlcn{klqyruiAmod#zNqy|kldLmlqyi"z¿rNi"d7Nr;89"c_d-kor=ºnumo}n{i"rukla"dLmÅrNi"duxÑc_r=|kr'6;kla"dLcpDPOArut
koqsc_q8<#qyi"z nI|qyc_qZ;n{moq¸k]O*c_dLnN|M9"modSD9d'k]=ºd#d#iYkla"dk]=rq7Nr;89"c_dL|JrX a"d#isDwnu|ldL} rNit;Z9"c_qyiwn{i]p'dqyit
6ÌrNmlcn{klqyrui2xkoa"qy|_|lqsc_q8;ynumlqsk]Op'moq¸kod#moqsrNi¾r'ud#mv| koa"dPnu}*7n{i=kvn{zud¿klrÂkon'kNd+qyi=klrÂnNp#p#r9"i=kCn;Z;nd7n{q8;ynD:;yd
qyi*6ÌrNmlcnkoqsrNi2x)D:9"k-dLnN|q8;ZOv6¶n{q8;y|qyimldLzuqyruiw|w;yq8kudp'rNmkoqypLn';,n{modLnN|n=0a"d#mod_kla"dqyi=kldLmt\qsi]}qZ7~q}*9wn;x77numlqnt
DwqZ;yq¸k]Oq| a"qyzua^_yua2J `a]nky|b=0aPOc_d'klawr~}w|=0a"qpvaWd5:;yqp'qsk3;8Od+5:;srNq¸kÅn{iwn{klruc_qp#n; qyi*6ÌrumocnklqyruiQDPO
mod#zNqy|kldLmlqyi"zCwn{mlklqp9;ynumn{iwn{klruc_qp#n;2|kom39wp'k39"modL|0numldn{kklmvnup'klq87udJ{zr=ºd+7Nd#mºkla"dOr6¼kldLiB;nupkn|M9*|_t
p#qsdLi=k,iF9wciD9d#mSr'6#;n{iw}cnum3k|klrawnuiw}*;ydºkla"d0a"qyzua_qyi=kld#mlt\qsiw}"qZ7~q}*9wn';*7numlqn'D"q8;yq¸k]Oq|l|39"dJ}g0pLp'rumv}qyi"z;8Oux
n-]r=ºd#m36@9:;wklr~r;]klrqscn{zNd n{i]n';8O~|lq|f;yqZkNdÏnup'klq87ud |lawnu]dÏcCr}d;y|nH¶nuc_rui"z=0a"qypva`=db=0q8;8;9mod'kvn{qyirui:;8O
koa"rN|ld~;ydLnu}"qsi"zÄkor nÄc_r~}wn';wnuiwn';8O|q|L3q|,nui_nu"9dLn';yqyi"z n';skldLmliwn{klq87udw_yda\x=|lqyiwp'd|39wpva_c_r~}"d+;|,n{mod0i"r{k
rNi:;8O+n'D:;ydÅklr_mod#"modL|ld#i=kkla"d |lawnu]dÄr'6n{iPrD"dLp&k~D:9"k n';|rCklawdn=ndO¿qsk p#nuiI7n{mOJhR,qsklawd#m0koa"d+Omld;ZO
rNiWn_"aPO~|lqp#n';{_ueda?x_sa\xwrum ruiAn|konkoqy|klqp#n;f_yLeda\x_¢da\x]nu""morNnupva x~kla"dOmodEF9"qymldn;ydLnumli"qyi"z¿|konuzudux
nNpva"qyd+7udE}¿koawn{ik~|ºkor¿nCklmvn{qyi"qyi"z|d#kLxkor]dLmM6ÌrNmlc koa"d-nN}dEF9wn{klqyruiBD]d#k]=dLd#iPc_r~}"d+; nuiw}}wnkonwxwn{i]}
DPOklawqy|Åc_dLnuin{modnD:;sd-klrp#n{"k39"mod koa"d7numlqn'D"q8;yq¸k]OQ=0qskla"qyiÂnp;nu|o| r6,rDdEp&ko|JNgb;skla"r9"zuaÂ|awnu]d
c_r}d;y|,numldzNd#i"dLmon;Z;8O9w|ldL}6Ìrum,|ld#zNc_d#i=kon{klqyruiC:9"mo]r=|dNx=ºd0awnd7udqyiF7NdL|klqyzNn{kldL}-qsi_koa"q|Swn{9d#m,kla"dLqsm
9]|d_qyikoa"dp'rui=kod5~kr'6ºnuiwnkoruc_r{t26@9"iwp'klqyruiwn;iwrumoc_n;sq8<Ln{klqyrui2xkorPmldLzuq|kod#mÄ|wnumo|ld_}"nkvnnN|l|lrp'qnkldE}
=0qsklakoa"dc_r~}"d+;ydL}|kom39wp'k39"modL|r63qyi=kldLmldE|kJ
X qsklakoa"q|-zNrNn';?x}=d"moru9rN|ld¿nWmod#zNqy|klmvnkoqsrNiÂc_d'koa"r}^=0a"qpvaqy|iD]ruklaq;yrp#n;n{i]}Dwnu|ldL} rui¾n
p#rumlklqp#n;,|M9:;p'qº|a]n{9dcCr}d;,JPg\k-mod+;yqydL|rNiÂkoa"d+nN|l|39"c_klqyrui koawnk|39:;p'qºn{modCmod+;yd+7nuiNk-nuiwnkoruc_qp#n';
;n{i]}cn{mk~|6Ìrumh6@9wiwp&koqsrNiwn';"nuiwn';8O|q|_=a2J`a"dmod#zuq|klmvnklqyrui-r'66@9wiwp&koqsrNiwn';"}"n{konwx=0a"qypva_n{mod;srp#n{kldE}
qyin|lwn{klqn';i"d#qyzuaPD9rumoa"r~r}Ar'6ºp'rumlklqp#n;S|M9:;p'q?x2q| o iwn;Z;8Onupvawqsd7udL}Aklawnui:k|ÏklrWnkldLpvawi"q8EF9"dDwnN|dE}
rNi+koa"dÄklawqsit\:;nkod |:;yqyi"dÄqsi=kldLml9r;nkoqsrNi[_ya\x_¢da/J
gji dLp&kJE"x=ºd;}dE|lp#mlq8D9dSkla"dp'rui]|kom39wp'klqyruiÄr'6koa"d;|kon{klq|koqypLn';uc_r}d;ur'6wp#rumlklqp#n;u|M9;yp#q>x79d#m36ÌrumocCdE}
DPOv;ydLnumliwqsi"z`6ÌmlrNc nP|d#kr'6º|lawnu]dE|+J_`a"dCklmvn{qyi"qyi"z|konuzudCqy| o mo|k }d'kvn{q8;sdE}ÑxÑklawd#i=dC"modL|ld#i=kÄkla"d
|kon{klq|koqypLn';unuiwn';8O|q|Ñc_d'koa"r}Ñx %A!
nwmlqyiwp'qywn;Np'rNc_]rNi"d#i=k n{i]n';8O~|lq|fHÌgnLJEgjii ~dLp'kJEe~=dSqyi=klmor}*9wp'd
koa"dÄqsi=kod#mo]r;yn{klqyrui|opva"dLcCdnuiw}¿koa"dw=ºndOqskp#nuiID9dp'rucD"qyi"dL}+klrCklawdÄ|kon{klq|koqypLn';2|lawn{9dÅcCr}d;#6Ìrum
koa"dv;yrp#n';Ïn{iw} i"rNit/;sqyi"dLnummldLzuq|komon{klqyrui*r'6w6@9"iwp'klqyruiwn;ÏnNp&klq87nkoqsrNiw|+JV`a"d#i koa"dA9d#m36Ìrumocn{iwp#dWqy|
q8;8;Z9w|klmvnkodL} ruid+5~9d#moqycCdLi=kon';,vRUT|rNc_n{klr=|dLiw|rNm3OA}wnkonJX d+p'rNcC]n{modkoa"q| n{"wmlr=nupva?=0q¸koan
;yrp#n;wmoqszNqy}mod#zNqy|klmvnkoqsrNin{""morNnNpvan{iw}m=0qskla+z;yrDwn;wmod#zuq|klmvnklqyrui_c_d'koa"r}"|nHÌmoqszNqy}¿nuiw}i"rNit\mlqyzuq}LJ
3Ä!'12!'º $0 3!'-
('º!
rNmkoqypLn';|M9;yp#qnumldÅn{iwn{klrNcCqp#n;9|klm9wp'k39"modL|U=0a"rN|ldÄ|awnu]dn7n{moqyn{klqyruiw|n{c_ruiwz-qyiw}q87=q}*9wn;y|numldÄp'rNct
;sd+5#J}X dºwmlrN]r=|dklrwD:9"q8;}nÅc_r}d+;r6wklawdL|ld|klm9wp'k39"modL|}6Ìmoruc nÄ|konkoqy|klqp#n;n{iwn;ZO|lqy|3r'6nÏklmvn{qyi"qsiwz
|ld'kSqyi_rumv}d#m3klrÄmodL|39:;skqyi_nÅp#ruc_wnNp&k,n{iw}c_dLnui"qsiwz'6@9:;"mod#wmldE|dLiNkvnkoqsrNi r'6]kla"dLqsm;|lawnu]dE|Sn{iw}r'6]kla"dLqsm
7numlqnkoqsrNiw|+Jzr=ºd+7udLmLx9w|lqsiwzPn|konkoqy|klqp#n;Sn{iwn;ZO|lqy|ÅqycC;sqydL||lruc_d_p'rui]|komonuqsi=ko|J g\kmodEF9"qymldE| wnumt
koqyp+9:;n{m;ZO_kordE|kvn'D:;yqy|la¿koa"dÅ]rNqsi=kklrC]rNqsi=kp'rNmlmodL|l9ruiw}dLiwp'dE|,r62kla"d|lawn{9dL|kor;ydLnumli2x~qyi+koa"dÄ|dLiw|d
koawnk0koa"d wnumonuc_d'kldLmt/7udEp&korumv|;mod#"modL|ld#i=koqsi"zCkoa"d-}"n{kon_awnd7NdÏkor¿p'rNmlmodL|l]rNiw}J;`awd#mod6Ìrumodux~koa"dkomonuqsit
qyi"zC|kvn{zudÏi"d#dE}"|klr_p'rNiw|q}dLm;koa"d6Ìr;Z;yr=0qyi"z-9ruqyi=ko|koa"dÅd5~klmvnup'klqyrui¿r62kla"dÄ|klm9wp&k9"mldE|;r6 qyiNkod#modL|kLx
koa"d#qym0mod#"modL|ld#i=kon{klqyruin{iw}+kla"dLqsm c_n{kopva"qyi"zjJ
! #"%$'&($&()
`awdd+5=komonNp&koqsrNi n{iw}-mldL"mldE|dLi=konkoqsrNir'6koa"dºp#rumlklqp#n;=|39:;p'qP9w|ldL}qyi koa"qy|3wnu]dLmmodL|39:;sk6Ìmoruc "mod+7~qyr9w|
=ºrumkq_yEa\xV_'a?x}=0a"qpva^=d`D"mlqyd+*jOmodLp#n;Z;;i"r=NJv P9:;p'qnumld¿}"d o i"dE}nu|Äkoa"d#qym-c_dE}qynui¾|M9wmM6¶nNp'd¿n{i]}
d+5~klmvnup&kodL}6Ìmoruc A0gf7Nr;89"c_dL|DPO¿n-c_d'koa"r}+iwr= k~i"r=0i+nu|koa"d,nNp&klq87udÏmlq8D:D9rui.-ÅcCd#kla"r}I=0a"qpva
;ydLnN}"|-klrÂnÂwnumonucCd#klmoqyp¿cCr}d;sqyi"zÂr'6koa"d|39:;p'qw_yEa/J0/qymv|kEx;n|ld#moqsdE|-r6"mod#"morp'dL|o|lqsi"zÂn{qyc_|Cnk
}"d o i"qyi"zPn¿mod#zNqsrNiAr'6;qyi=kldLmldE|kH¶1ÏgML p#ruiw|lq|koqsi"zr'6,koa"d\9"i"qyruir6;zO~moq3nuiw}|39:;p'q2J0r9"zNa:;8Ouxklawqy|
1Ïg,q|rD"kon{qyi"dE}`DPO o mv|k|ld#zNcCdLi=klqyi"z-koa"dwD"mvn{qyin{i]}|ldLp#ruiw}IDPO¿p;nu|o|qZ6@O~qsi"zklawdÏkoqy|o|39"dL|qyi=klrCkla"d
koa"mod#d¿p;nu|o|ldL|w=0a"qskld¿cn{kkldLmLx3zumod+Oc_n{kkod#mnuiw}p'dLmldD"mlrut\|l"qyiwn';*9wqy} _y#a2J2/"moruc kla"q|wnumkoq¸koqsrNi
nuiw}qyi¾rumv}dLm klr }q|koqsi"z9"q|aKD]d#k]=dLd#iI|39:;p'qn{iw}zO~mlq?xSq¸kCqy|modL|lrumlkldL} korÂ}qZud#mod#i=klqn';ºzudLruc_d'kom3O
nuiw}Âwn{mlklqp9:;n{m;8Okorkla"d436575¿ru9d#mvnkorum\_ca?x=0a"qypva q|np+9"m77n{k39"modCd5~klmvnup'klrumw=ºd+;8;,nu}"nukldE}WkorPn
|39"m36¶nup#d|M9wpvanu|koa"dÏp#rumlkld5Ñx=|qyiwp'dÏ]r=|qsklq87udÏp9"m7nk39wmldpvawnumonNp&kod#moqZ<LdL|3klawdklrN¿r'62nzO~m39w|Lx=0awd#modLnu|
iwd#zNn{klq87udp9wm37nk9"mod_pva]n{mvnup&kod#moqZ<LdL| kla"d`D]rukklrNc r6nW|39:;p9w|J+`a"q| |39:;yp#q98zO~moqSwn{mlklqsklqyrui mldE|M9;¸kv|#x
n'6¼kldLmÅ|3kud;sd#klruiwqZ<Enklqyrui xwqyiAklawd|39"]dLm
o
p'qn';klru9ruzNmonu"aPO+r6,kla"dCp'rNmkod5ÑxwkoawnkÄq|kor|ondOqyid+5=kod#moiwn';
komonNp'dE|;r62kla"dÄ|39:;yp#q,JS`a"dLi2x~klawdL|ldÏd+5=kod#moiwn';]klmvnup#dL|º|dLm37Nd0klrCqyi"q¸koqyn;sq8<#dÄn{inup'klq87ud c_r}d;9d+5~klmvnup&koqsiwz
koa"d|M9wmM6¶nNp'dÅr'6qyi=kldLmldE|kJ,`a"dÄ]rNqsi=k0qy|ºkoawnkkoa"dÄklrN]r;srNzOr'6kla"dnNp&klq87udÅc_r}d+; pva]n{i"zNdL|{6ÌmlrNc >
H>nup'klq87udp+9"m7udL0klrW'> H¶nNp&klq87udC|M9wmM6¶nNp'dLJÄgjiv6¶nup'kLx2n|d#kÅr6,]rukld#i=koqyn;y|Än{mod-}d o i"dE}|39wpvaAkoawnkÅkla"d
qyi"qsklqn';Sp9wm37Ndux;yr~pLnkodL}n{kÏkoa"d|M9wmM6¶nNp'dCr'6,koa"dD"monuqsi xÑd+7ur;Z7NdL| klr=n{mv}kla"dD9r{klklruc r'6,koa"d|M9:;p9]|#x
koaP9w|qyi"qsklqn';yqZ<Lqsi"z¿nuiAnup'klq87ud |39"mM6¶nNp'dÄkor¿rukoqsc_q8<#dqyiArumv}dLmklr¿d+5=komonNp&k0koa"d c_dL}qn{iA|39"m36¶nup#dr'6kla"d
|39:;p9w|J:/3qyiwn';8;8Ouxkoa"d0pva"ruqp'dr'6wkoa"dwn{mvn{c_d#kld#moq8<LnkoqsrNiawnu|}D9d#dLi o 5dE} ruiCnÏp+9:D"qp<;;tj|l:;sqyi"d|M9wmM6¶nNp'dux
=0awqypvaqy|b=d;Z;2nN}"n{kodL}+klrc_r}d+;#6Ìmod#dw6ÌrNmlcrDdEp&ko|J
X dklaP9w|}q|9rN|ldr'6ÏnÂwn{mvn{c_d#klmoqyp+mldL"mldE|dLi=konkoqsrNi¾r'6 kla"dW|lawn{9dL|Cr'6Åqsi=kod#modL|kkoa"mlr9"zuaIkla"d
;tj|;sqyi"dc_r}d+;yqsiwzJP`a"d+|l:;sqyi"dNxwnumonuc_d'kldLmlq8<#dE}GDPO>=In{i]}@?]x3qy|}dL|op'moq8D]dE}[DPO>ACBED^k~i"r{kv| n{i]}
ACB+FHGIACB+FKJ<=4LACB7FKJ<?Ap#rui=klmor;3]rNqsi=kv|w=0a"d#modMACB+FKJ<= H¶mldE|JHACB7FKJ<?*LÏqy|ÏklawdCiP9"cD]dLmr'6p#rui=klmor;
9ruqyi=ko|ÏqsiÂklawdC}qymodLp&koqsrNinu|o|lr~p#qyn{kldE}Q=0q¸koaÂwnumonuc_d'kldLm(= HÌmodL|l)J?*LJ `a"dCwn{mvn{c_d#klmoqyp }"qsmodLp'klqyrui=
mod#wmldE|dLiNkv|kla"d;yd#iwz{klaPr63koa"d |39:;yp+9w|nuiw}kla"d-}"qsmodLp'klqyruiN?¿qsko| }"d#koa)JTÅq87~qsi"zOACB+FÅp#rui=klmor;Ñ9ruqyi=ko|
p#ruc_:;yd'kod+;8O_}"d
o
i"dE|,koa"dÄ|M9:;p#n;9|39"m36¶nup#dJfruiw|ldEF9"dLiNk;ZONx=ºdÏpLn{i¿mod#wmldE|dLiNkºn-|39:;yp+9w|UDFO_koa"d7NdLp'klrum
r6wqsko|hk~i"r{kv|3rumq¸kv|p'rui=komlr;N9ruqyi=ko|J3`a"dmvnkoqsrPACB7FQRACBSD}d
o
i"dL|koa"d0|c_r~r{koa"qsiwz6¶nNp&klrNm2kla"d0|lc_n;Z;yd#m
koa"q|mvnklqyr_qy|Lx"koa"d-|lc_r=rukla"dLm0klawd-|M9wmM6¶nNp'dN=0q8;Z;D]d`H%=da]nd7ud pva"r=|dLiACB7FTQRACBEDGVUKQXWKYPLJ;`awd cn{qyi
nN}*7n{i=konuzud;klrw9w|ldºp#rui=klmor;~9ruqyiNkv|qy|3koa"d#qymSp'rNcC]nup&kxD:9"kSp#ruc_:;yd'kodºmod#wmldE|dLiNkvnkoqsrNi r'69dLnupvaC|M9wmM6¶nNp'dJ
~qyiwp#d-koa"dC|kon{klq|koqypLn';n{iwn;ZO|lqy|9w|ldL}Wa"dLmldi"d#dE}"| klrdL|kon'D;sq|aAkla"dC]rNqsi=kÏklr]rNqsi=kÅp#rumomldE|9rui"t
}"d#iwp#dL|)D9d'k]=ºd#dLi-n';8;N|lawnu]dE|2r'6koa"d,komonuqsiwqsi"zÏ|d#kLxnmod#zNqy|klmvnkoqsrNiÅnuiw}modL|on{c_:;yqsi"z|konuzud,q|i"dLp#dL|o|lnum3OJ
`aP9w|kla"dC|M9;yp#q=0q8;Z;}D]dd5"modL|o|dE}qsiWkoa"d|on{c_d-|3O|kod#cr'6,p'r~rNmo}qyiwn{kldL| n{iw}S=0q8;8; awnd7Ndkla"dC|lnuc_d
iP9"cD]dLm0r'63]rNqsi=ko|Jg\kci9w|k~D]diwr{kldE}¿koawnkkoa"d;t\|l:;yqsi"dÄc_r}d+;yqyi"z_c_nkudE|qsk0]r=|l|lq8D:;sdÅkor_pva]n{i"zNd
num3Dwq¸komonumlq8;ZOklawdwnumonuc_d'klmoq8<LnkoqsrNiS=0q¸koa"r9"kÄn'u9dEp&klqyi"zkla"d|39:;p9w|Å|a]n{9dJgji"qsklqn';8;ZONxÑdLnNpva|M9;yp+9w|Åqy|
d+5"mldE|l|ldL} qyikla"d+qscn{zNd+p'r~rNmo}qyiwn{kld¿|3O~|kldLcC=0a"qpvaq|-}qZu9dLmldLi=k6ÌmlrNc rNi"d+|39:DdEp&k korn{i"rukla"dLmJ
`awdq}dLnq| korWnu|o|rp'qnkod qsko|Är=0iÂ|3O|kod#cr6p'r~rumv}qyiwnkodL| =0q¸koadEnupvaÂ|39:;p9w|LxD:9"q8;sk|lrklawn{kÅqskqy|
p#ruc_c_rui+klr_n';8;|39:;p'q2JhXÂdp#n;Z;qsk ,];yrp#n';p'r~rNmo}qyiwn{kldÏ|3O|kod#cM-J3g\kq|V9w|d+6@9:;9klr}d#kld#moc_qsiwd koa"dÄmlqyzuq}
komonuiw|M6Ìrumoc_n{klqyruiqH¶mlrukonkoqsrNi
klmvn{i]|M;nkoqsrNijL0n';yqyzui"qyi"zn;Z;h;yrp#n';S|3O|kod#c| r6n5dE|Ånuiw}Wkornu":;8OPq¸kÄklr
koa"d nu|o|lr~p#qyn{kldE}+|lawn{9dL|J
d'k ~D9dkla"d\;srpLn';p#r~rumv}qsi]nkldC|MO|kldLcr6;n+|39:;p9w|JÅ`awd-rumoqyzuqyi Äq|Ïkla"d
p#d#i=kldLm r6"c_nN|l| r'6koa"d|39:;p9w|Jgb5~dE|7xnuiw}n{mod;}d o i"dL} nN|Ñkoa"dºn'5dL|Ñr6"qsi"dLmkoqyn r'6~klawdº|39:;p#n';
|39"m36¶nup#duxwnuiw}Wn{mod}dLp#qy}dE}klrD9d-|lr_klawn{k6Ìr;Z;yr=|klawd;sdLi"z{koaWr'6klawd-|M9;yp+9w|#xÏqsko|Ï}d#"klaAn{i]}
ºq¸kv|,i"rNmlcn;,J`a"q|;}q|lp#mlqyc_qsi]nklqyruiD9d'k]=ºd#dLi_kla"d0koa"mod#d n'5~dE|Sq| o mv|kºp#n{momoqsdE}r9k{DPOp#ruiw|lq}d#moqsiwz
koawnkHÌmodL|l)JLqy|kla"dCn5qy| r'6Sqyi"d#mlklqn_klawd ,cCr=|kÅp'r;8;yqsi"dEn{m-w=0qsklaAkla"dMACB7FKJ<=KH¶mldE|)JACB+FKJ<?PL
]|d9w}r{t\wnumon;Z;yd+;S}qymldEp&koqsrNiw|+eSdEnupva r'6klawd#c D]dLqsi"zÂ}d
o
iwdL}DPOkoa"dk]=ºrWd5~klmod#c_qsklqydL|r6nW|M9:;p9]|+y
;yqyi"dqsiP}qymldEp&koqsrNi=YH¶mldE|J?*LJ`a"d#i q|rDkvn{qyi"dL}BDPOklawdN7udLp'klrNmºwmlr}*9wp'k <G!"$#J
`a"dP|39:;yp#qawnd7udi"r=áklr?D]dd5"modL|o|ldL}qyi¾koa"d#qym;srp#n;ºp#r~rumv}qsi]nkld|MO|kldLc_|Jg\k_nuc_r9"i=ko|-klr
}"d'kldLmlc_qyi"qyi"zwxV6ÌrNm+dLnNpvaY|M9;yp+9w|#xkoa"dcn{klmoq5&% }d o i"qsiwzkla"d pvawn{iwzudWr'6D]nu|lqy|6ÌmlrNc koa"dG;yrp#n';
p#r~rumv}qsi]nkld|3O|kod#c'
kor=ºnumo}"|koa"dqscnuzud p'r~rNmo}qyiwn{kldÄ|MO|kld#cPxj;sd#kq¸kD9d ()*+,J-2d'k/.
nuiw}0ND]dÄkoa"dÄmlrukonkoqsrNicn{klmoq5+nuiw}kla"dÅklmvn{i]|M;nkoqsrNiI7NdLp&korumr'6kla"dqyiP7udLmo|ldÅpva]n{i"zNdÏr6DwnN|q|-%213
H %A!A 6Ìmoruc4klr=n{mv}"|* LJ,`awd#iPqsiPa"rNc_ruzudLi"d#r9w|p'r~rumv}qyiwnkodL|
%
153
G76
. 0
8898 U;:
=0a"d#mod. G=< >nuiw},0PG!?@?BA
qsiwp#d.Ãqy|rNmkoa"ruzNruiwn; % G 6
.,C
?
.,C50
888
U :
`awqy| klmvn{iw|M6ÌrumocnkoqsrNiA}d o iwdL| kla"d\;srpLn';3mlqyzuq}Wmod#zuq|klmvnklqyruiP"morp'dE|l|Lxj=0awqypva[=0qZ;8;D9d_p#n';8;ydL}D qyi
koa"dN6Ìr;Z;yr=0qsiwzJ{g ":;8O=qyi"z_koa"qy| mlqyzuq}klmvn{iw|M6ÌrumocnkoqsrNi¿klrn';8;Ñkla"d-]rNqsi=ko|r'6dLnupvaW|39:;p9w|n;sqyzui]|kla"d
komonuqsiwqsi"zÂ|d#kCnu|-qZ;8;89w|komon{kldE}rui/3qyz9"modAJFEr{kod¿koawnkCi"ra"rNc_r{klawd'k]O qy|-]dLmM6ÌrNmlc_dL}¾qsikoa"q|G
c_d#kla"r}JfgÏ|nCc_n{kkod#m0r'66¶nup'kLxkoa"dqscnuzudÄ}"nkvnD9d#qyi"z¿nNp+EF9"qymldE}klrCkoa"d |lnuc_dÄ|op#n;sdNx~kla"q|0dLiwn'D:;ydL|
korp#n{"k39"modÅkla"dqyi=kld#mlt\qsiw}"qZ7~q}*9wn';2|lq8<#dw7n{moqyn{klqyruiqsikla"d |lawnu]dc_r}d+;2J
`a"dPi"d+5~k_|konuzudp#ruiw|lq|kv|qyiImodL|on{c_:;yqyi"zAkoa"dW|M9:;p'qr6 klawd+komonuqsi"qyi"z|d#kJqX dmldE|lnucC;sdkla"d
d;sdLc_d#i=ko|-r'60klawd¿klmvn{qyi"qyi"zW9ru:9:;nkoqsrNi¾ruikoa"d+rNi"d=0a"qpvaawnN|klawd+c_rN|kC|on{c_:;yd¿9ruqyiNkv|#xS|l:;yqsi"d
wmlrN]dLmkoqsdE|d#iw|39"moqsi"zÅkoawnkSkoa"drumoqyzuqyiwn';|lawn{9dL|,numld"modL|ld#m7udE}J 1Ïi]p'dºkla"dÏ|M9:;p'q]n{modºmodL|on{c_:;ydL}Cn{i]}
n;sqyzuiwdL}Ñxkoa"d0cnkvpva"qsiwzÅq|S9d#m36Ìrumoc_dL}DFO]9w|kºnu|o|qyzui"qyi"zÄp'rNiNkomlr;~]rNqsi=kSklr p#rui=klmor;~9ruqyi=k;nup#p#rumv}qyi"z
korCkla"dLqsm p+9"m7=q8;yqsi"dEn{m0n'D]|lp#qy|o|lnJ
HJI "I#$KLI#$M "$NGO &" NQPK.$KSR*TU&V5TWR XV"YI#$ZR6&/K
`awd-|kvnkoqy|klqp#n; n{iwn;ZO|lqy|r'6kla"d klmvn{qyi"qsiwz¿|d#k;sdEnu}"|klr¿nc_r}d;sqyi"z¿r6Sp#rumlklqp#n;2|M9:;p'q3n{iw}Pr6kla"dLqsm
7numlqnkoqsrNiw|J-`a"d_c_r}d+;SpLn{k9"mldE|koa"d|a]n{9d7n{moqn'D"q8;sqsk]OPrDw|ld#m7udE}S=0qskla"qyikoa"dklmvn{qyi"qsiwz|ld'kJig |
nPcn{kkldLm r'66¶nup'kLxkla"d|kvnklq|klqp#n';n{iwn;ZO|lqy|Ämod+7NdLn';|Åklawd¿cn{qyi c_r}dE|r'6~7n{moqyn{klqyrui mld;yn{klq87udCklrAn
/3qyz9"mod g |lqy}d7~qyd+= r6n}wnkonDwnu|ld-r6Ïc;yd6¼k p'dLiNkomon;S|M9:;p'qSn;sqyzui"dE}Aqyikoa"d\;srp#n;Sp'r~rumv}qyiwnkod
|3O|kod#cQJ`a"d0|M9:;p'q"p#ruc_d6ÌmlrNc nÄ}"nkvn'DwnN|dcnu}dV9"_r'63cÅa"dEn';sklaPOux{moqyzua=kt\awn{i]}dL}Ñx{e=
87toE~OudEn{mv|
r;y}+cn';ydL|Jh>ÏqymldEp&klqyrui]|r6 koa"dn5dL|n{mod 6Ìrum5+n5q| }6Ìr~r{klt?a"dEnu}ÑxF6ÌrNmOn5qy|klr=n{mv}_kla"dr9ko|lq}dÏr6
koa"dND"mvn{qyi2xP6Ìrum~<n'5~q|nui=kld#mor{t\9rN|kld#moqyrumJ
mod6ÌdLmldLiwp'd |lawnu]dNx=0a"qpvaAp#nuiSD]dkoa"d-c_dEn{iA|lawn{9dr7udLm0kla"d klmvn{qyi"qsiwz¿|d#kb6ÌrumÏqsiw|konuiwp'dJVXÂd9]|d-n
wmlqyiwp'qywn;=p#ruc_]rNi"d#i=kn{iwn;ZO|lqy|=0a"qypvad#iwnD:;ydL| klr mod#wmldE|dLiNk3}"nkvn qyi-nÏi"d+=^DwnN|q|LxErNmkoa"ruzNruiwn;>x7n{i]}
=0awqypva |M9"w"mldE|l|ldL| klawdCmodL}:9"iw}"nuiwpOWr6;qsi:6Ìrumoc_n{klqyrui)JWrumod#r7Nd#mExwkoa"qy|Änuiwn';8O|q| dLiwn'D;sdE|Ånc_r}"n';
nu""mord5qscnkoqsrNi2x=]dLmM6ÌrNmlc_dL}IDPO+mod'kvn{qyi"qsiwz-koa"dc_rN|k |qyzui"q
o
pLn{i=kºc_r}dE|+J
& Ý Ý Ù 3 &Ú >
d'krD9dkla"d0komonuqsiwqsi"z9ru9:;yn{klqyrui_cnu}d~9wr'6d+;yd#c_d#i=ko|Lxn|lawn{9duxkoa"dc_dLnui|awnu]d
rNi¿x koa"dp#r7n{moqynuiwp'dcnkomlqZ5J g |awnu]d !#"
3%$&$&$'
xq| mod#wmldE|dLiNkodL}QDPOkla"d\7udEp&klrNmr'6;p#rui=klmor;
9ruqyi=ko|r6koa"d |;sqyi"dÅklawn{kc_r~}"d+;|kla"dc_dE}qynui|39"m36¶nup#dÅr6 koa"d |M9;yp+9w|
G!( *) ,+ ) ,- ) WW+W .( #/ .+ 0/ ,- 0/ C
=0q¸koa2AG ACB+F
`awdÅc_dEn{iW|a]n{9dux*9w|ldL}Pnu|ºkoa"dÄmld+6Ìd#mod#iwp#d|awnu]dNx"n{iw}koa"d p'r7n{moqn{iwp#d cnkomlqZ5n{modÄzuq87udLiIDPO
1
G 3
'32
'
0"
3
4 G 3
' 2 '
#"
35 5
5C
=0q¸koa
5 G6 ?
>Ïqn{zurNiwn';yq8<#qyi"z-koa"d p'r7numlqn{iwp#d cnkomlqZ5 4 "mlr7~q}dL|koa"di"d+= c_r~}wn';)DwnN|q|7P
4 G87:9:7 C =0awd#mod;9 G
5<>=?
@
3 W+WW !@BA,C s=0qsklaD@
3FE
@BG
E
WW+W
E
@HA!C
`awd#in{iPO|lawn{9dI*pLn{i?D]d=0moq¸klkld#iCJ GKLM7ONt=0a"d#modIN G B 3 W+WW B A!C ZC q|Åklawdm7udLp'klrNmÅr6
c_r}"n;"n{c_:;yq¸k9w}dL|,r'69}"d6ÌrumocnkoqsrNiCnuiw}
?
7ON$p#rumomldE|9rui]}"|klrÅkla"d}"d6ÌrumocnkoqsrNi7NdLp&korumv|3qsi_dLnNpva
9ruqyi=k-r'6P*klr=n{mv}"|Åkoa"d¿c_dLnui¾|awnu]dJv ~qsi]p'dkoa"d¿d#qyzudLiP77n;Z9wd@H qy| kla"d7numlqn{iwp#dd5:;n{qyi"dL}?DPO
koa"d
<RQS
cCr}dNxÑnm;ynumlzNdwn{mlkÏr6kla"d77numlqn'DwqZ;yq¸k]OPp#nuiSD]dd5:;n{qyi"dL}vDFOmod'konuqsiwqsi"z+rui:;8O+koa"d o mo|kUT
c_r}dE|+J`a"db7n';89"dPT qy|pva"rN|ld#i_|rÄkoawnk
2WV 0"
3
@BxNklawdb7n{moqynuiwp'dd5:;n{qyi"dE}DFO-kla"d o mo|kTc_r}dE|#x
mod#wmldE|dLiNkv| n}dL|lqsmodL}A"mlrN]rNmkoqsrNi2x D xÑr'6Skoa"d\=0a"r;ydi7n{moqn{iwp#d @ C
ekoawnkÄqy| klrP|ondOT q|Ï|39wpvaAkoawnk
)
D[=0a"d#mod @ C G 2 A!C
0"
3
@B3J 0d'kvn{qyi"qsiwz+rui;ZOT c_r~}"dL|Ïd#iwnD:;sdE|9]| kornNpva"qyd+7udn¿c_r}"n';
nu""mord5qscnkoqsrNi
G L 7 N
N G87
C
?
=0awd#mod 7 q|n|39:D"cn{klmoq5r6P7 p'rNiNkvn{qyi"qyi"z+koa"d o mv|kJT dLqszNd#iP7udEp&klrNmo| r'6 xklaP9w|}d o i"qyi"zPkla"d
c_r}"n;nu""mord5qscnkoqsrNivDwnN|q|+J`a"d7udLp'klrNm N G B 3 W+W+W
B V
ZC*mldL"modL|ld#i=ko|ÅnP|awnu]dCqyikoa"dIT+t
}"qsc_d#i]|qyruiwn;|lwnup#d+}d
o
i"dL}YDPOkoa"dwmlqyiwp'qywn;p'rNc_]rNi"d#i=ko|JÂ`awdn{i]n';8O~|lq|qy|Cp'rNiP7ud#iwqsdLiNkC|qyiwp'd
koa"q|U=ºrumk~qsiwz |wnNp'dÏqy|r'6;yr=ºd#m}"qsc_d#i]|qyruiGHTQLJfzr=ºd+7Nd#mEx N ci9]|kD]dÄp'rNiw|komonuqsiwdL}_qyi+rumv}dLm,klr
mod#wmldE|dLiNkÅn{i,ln';8;sr=n'D;sd+-|lawn{9dIH %A!A
n+|lawnu]dCp'rui]|q|kod#i=k =0qsklakla"d\;ydLn{moi=kÅ|lawn{9dL|LJNTÅq87ud#ikla"d
nN|l|39"c_koqsrNiPklawn{k klawd}q|komlq8D:9koqsrNiWr'6f7NdLp&korumv|P
qy| zNn'9]|l|lqynuix]koa"d-mvn{iwzudr'6f7numlqn'D"q8;yq¸k]Or'6,dLnNpva
B .0"
3%$&$&$
V
x"q|k]O~"qp#n';8;8O+|M9]pvanN|
?
@B B%WL
@B HL
gji6¶nNp&kEx}9wiw}d#m-kla"dnu|o|M9wcC"klqyrui ,* 4 &xSqskp'rNc_dL|koawnk B 8 !@ n{iw}|lr9 B
@ G W"!$# J0`aP9w|#xhHdL0p#nuiSD]dCp'rNiw|q}dLmldE}nN|n¿p#ruiw}qsklqyruiWr6,mldL"modL|ld#i=kon{klq87=qsk]O¿r63koa"dp+;ynN|l|
r6rDdLp'ko|r'6qyiNkod#modL|kJ
+Ù &ÌE
d+7udLmon;kldE|kv|awnd7NdND]dLd#iAp#numlmoqydL}r9k DFOcn'k~qsiwzkla"dp#n{mv}qyiwn'; r'6kla"d klmvn{qyi"qsiwz]rN:9:;nklqyruiS7num3O
H%9"CklrNcNÅ|39:;p'q!Lnuiw}_n';|rnDPO-pvawnui"zuqyi"zÏkla"dk]O~9d0r'69|39:;p'q)H>p'd#i=komon;"|M9:;p9]|#x;yn{kld#mvn';|39:;p9w|Lxu|39"]dLmlqyrum
6Ìmorui=kvn'; |39:;p9w|Lx WW+W r6xD]ruklaAa"dLc_qy|l"a"dLmldE|LJ~XÂd"mldE|dLi=kkla"dmldE|M9;¸kv|rD"kon{qyi"dE}PruiAn_komonuqsi"qyi"z+|ld'k
cnN}d~9"r'6koa"dcw;yd6¼kp#d#i=klmvn';]|M9:;p'q]mldLzuq|kod#modL}qsiCkoa"d"mod+7~qyr9w|,|konuzudJ`a"dE|d |39:;p'qwp#ruc_dV6Ìmoruc n
}wnkonDwnu|ldp'rNiw|lqy|kldE}_r'6,c7ur;89"i=kldLd#mv|#x=n';8;wcn';ydL|Lx~eN
87toEONdLnumo|Sr;y}2xNa"dEn';sklaPOn{iw}_moqyzua=kt\awn{i]}dL}Ñx
=0awrS9"iw}dLm3=ºd#i=k-nW`Ä'tjA ~UTÄ e>|k39w}:OJN/qyz9wmld¿eW|la"r=|Åklawd¿"modL}rNcCqyiwnuiwp'dr6koa"d o mv|k
c_r}dE|+J_gjiw}dLdL}Ñx kla"d o mo|k-+c_r}dE|Äd5:;n{qyi nB;n{mozudCwn{mlkr'6ºkla"dCklrukon;f7n{moqyn{klqyruiKH>n'D9r9k{%\LJ
`awd o mo|kÅc_r}d_d5:;n{qyiw|Årui qsko|Är=0iÂn;sc_r=|keu% r'6;koa"dCklrukon';x7numlqnkoqsrNiYH@=0a"dLmldEnu|ÄnP|M9;yp+9w|Åqy|
}"dL|op'moqZD9dL}iDFOE{Åp'rui=komlr;N9ruqyi=ko|Lxklawn{kSqy|klrÄ|ondO e"Eb7n{moqynD:;sdE|#xnuiw}DPO c_rumod,koawn{icuNu~7numlqn'D:;ydL|
qZ6bk~i"r{kv| n{mod+p#ruiw|lqy}"d#modL}LJN/3qyz9"mod¿=nW|a"r=|kla"dI77numlqnkoqsrNiw| numlr9"iw}Âkla"d+cCdEn{iI|lawnu]dGH/3qszjJ3L
}:9"d+korkoa"d
o
mv|k_c_r~}"dJI`a"dO¾n{mod+cn{qyi:;8Omld;yn{klq87ud+klr kla"dB;yd#i"zukla nuiw}IklrÂkla"dklrNmo|lqsrNi¾r'6Ïkla"d
|39:;p9w|J>1Ïikoa"dp#rui=klmvn{mOux /3qsz9"mld+Dq8;Z;89w|klmvnkldE|koa"d+c_qyi"rumqsi *j9"d#iwp#d+r60kla"d U'&
QS
cCr}d _kla"d
}"d6ÌrumocnkoqsrNiw|0n{modawn{mv}*;8O}q|klqyiwp&kEx9n;Z; kla"d-|39:;p'q3n{mod n';ycCr=|k |39"9d#moqsc_9rN|ldL}kor_kla"dcCdEn{iW|lawn{9dJ
g0pLp'rNmo}qyi"z;ZO-kla"q|;|kon{klq|koqypLn';wc_r}d;sqyi"z q|;nu""moru"moqyn{kldkor d5"modL|o|klawdÏ|lawn{9dL|n{iw}Ckoa"db7n{moqyn{klqyruiw|
qyiWn_p'ruc_wnNp&kn{i]}+c_dLnui"qyi"z'6@9:;=ºndOJ
( )
0* Ä!'- ) !#0'$1 $,+ -w'!'0 . 0/ !#1Ñ Ä!'-
`awd }d6ÌrNmlcnkoqsrNi
o
d;y}H
?
7JNLºrDkvn{qyi"dL}BD9d'k]=ºd#dLin_zNqZ7Nd#i|39:;p9w| n{iw}+kla"dc_dEn{iW|M9;yp+9w|0p#nui
D9d-d+5~kld#i]}dL}kor¿klawdi7~qyp#qsiwq¸k]Or'6Skoa"dp#ruiw|lqy}"d#modL}P|M9;yp+9w|bDPOQ9w|lqsi"zn{iAn{w"mlrN"moqyn{kldqyiNkod#mo]r;yn{klqyrui2x
koa"d_klawqsit\:;nkod¿|:;yqyi"dqsi=kod#mo]r;yn{klqyruiqsir9"m p#nN|dQ_la\x{_ya\xU_¢{da/J¿g\k-pLn{i kla"dLiD]d+nu":;yqsdE}ÂklrAn{iPO
/3qyz9"mod {g |q}dN7~qsd= r'63kla"d c_dEn{iQ;sd+6¼kÏp'dLi=klmvn';2|39:;yp+9w|0r6koa"dklmvn{qyi"qyi"z¿|ld'k p'rNiw|lqy|kldE}r6koa"d¿c
;yd6¼k p#d#i=klmvn';2|39:;p'q2J
0 2 4 6 8 10 12 14 16 18
0 10 20 30 40 50 60 70 80 90 100
principal components
cumulative variance (%)
/3qyz9"mode U9"ci9;yn{klq87udi7numlqn{iwp#dnNp#p'rNmo}"qsi"z¿klr¿koa"dCiF9wciD9d#mÄr'6,"moqyiwp'qywn';p'rNc_]rNi"d#i=ko|Ïmod'konuqsiwdL}J
`awdÏkomonuqsiwqsi"z|ld'k p#ruiw|lqy|ko|ºr6ºc;yd6¼k p#d#i=klmvn';2|39:;p'q2J
nD
/3qyz9"mod- ÏnFL7numlqnkoqsrNiw| r6,klawd o mo|kÅc_r}d_n{mor9"i]}Pkla"d_c_dLnuiÂ|39:;p9w|Lx
? @ 3
IB
3 L @ 3 J
DL77numlqnkoqsrNiw|ºr'6kla"dOU&
QS
c_r}d n{mor9"i]}klawdcCdEn{iW|39:;yp+9w|Lx
? @
3
B
3 6L
@
3
J
rDdLp'k nu|o|rp#qyn{kldL}B=0qsklaPkoa"qy|Å|39:;yp+9w|JUX d kvn'kud nN}*7n{i=konuzudÄr'6koa"qy| d5~kldLiw|lqsrNiWr'6kla"d}d6ÌrNmlcnkoqsrNi
o
d+;}?H
? 7 N LºkormldLzuq|kod#m0|]n{mv|dn6@9"iwp'klqyruiwn; }"n{konSH¶vRUT }qs9r;ydL|qsiPr9wm p#nN|ddL{;yrp#n{kldL}qyiPkla"d
;yd6¼k p#d#i=klmvn';2|39:;p9w|0numldEn kor=ºnumo}w|ºnCmod6ÌdLmldLiNkoqyn;mld;yn{klq87udÅklrCklawdcCdEn{iB;sd+6¼kÏp'dLi=klmvn';Ñ|M9;yp+9w|+J
& I VC R*N "YI#$ZR6&K $'&) I V P$&FN"I V!HN'$&/V V5I /R
`awdf9w|ldSr'6~kla"qyit\:;nkld|:;yqyi"d,qyiNkod#mo]r;yn{klqyruin6Ìrum mldLzuq|komon{klqyruiÅ:9"mo]r=|dSqyic_dL}qp#n;uqyc_nuzuqyi"zV=ºnN| o mv|k
wmlrN]r=|dE}`DPO;ºr~rk|kldLqsi)Jgji_s+a?x"awd "moru9rN|ldL|0n{iWn;szNd+D"mvn{qpÏnu""morNnNpva+kor¿}dL|op'moqZD9d }d+6Ìrumoc_n{klqyruiw|
|l9dLp'qo dE}wDFOÏk]=ºr|d#ko|Ñr6p#rumomldE|9rui]}qsiwzº9ruqyi=ko|J`a"q|2c_d#kla"r}Ä"mor7~qy}dE|2n{iÄqyi=kld#mo9r;nklqyruin6@9"i]p&klqyrui
=0a"qpvac_nuw|rNi"dr'6klawdk]=rW|ld'kv|r'6p'rNmlmodL|l9ruiw}qyi"z]rNqsi=kv|#xkla"d|r9"mop#d|d#kLx3rui=klrPkoa"d¿r{koa"d#m
rNi"dux"kla"dkvn{mozud#k |d#kJWrumod#r7Nd#mExNkoa"dN6@9"i]p&klqyrui q|}d o i"dL}PqyiA|lruc_di"d#qyzuaPD9rumoa"r~r}r6koa"d-|ld'k r6
|lr9wmop#d 9ruqyiNkv||lrklawn{kºqskpLn{iID]dÄn{";sqydL}¿klr_n-9ruqyi=kºqyi¿koa"d|r9"mop#d |lwnup#d kor
o
i]}¿qsko|ºa"ruc_r;srNzur9]|
qyikla"dÄkvn{mozud#k|lwnup#dJ
d'kU G ( ,+ !- <
GVUL W+W+W
'AiD9dkla"dC|d#k r'6,|lr9"mvp'd9ruqyi=ko| qsiWkoa"dRf9]p;yqy}dEn{i|lwnNp'dux
nuiw} G
G!( .+ ,-
<
GIUL W+WW
Akla"dÏ|d#k,r'6konumlzNd'kS]rNqsi=kv|+J`a"d|ld'k}dL|op'moq8D]dE|Sn|awnu]d
Sx d5"modL|o|dE}SDPO L67JN nup#p#rumv}qyi"zklrPr9"mÄcCr}d;,JG2d'k"!
$#
G&% ? #
%D]dCkoa"dRf9wp;yq}dLnui
}"qy|konuiwp'dSD9d'k]=ºd#dLi k]=ºr¾|lr9"mvp'dP9ruqyiNkv| n{i]} '#J `a"d#i*koa"dS6@9"iwp'klqyrui qy|¿kla"dÂ|M9"c r'6Äk]=ºr
kod#moc| Än{i n|i"d_wn{mlkw=0a"qypva mod#"modL|ld#i=ko|Ïqsko|wD9d#awnd7~qyrumÄnkqsi o i"qsk]Oux nuiw}Ân|ldLp'rNiw}A]n{mlkn=0a"qpva qy|
nN|MO~c_kor{klqp#n;Z;8O *]n{k
(.+ ,- G = 3 L
= (L
= +;L
= -UL
C
#,"
3
# % # ?
(,+ ,- % H>L
=0awd#mod
klawd{DwnN|q|#6@9"iwp'klqyrui qy|2kla"d{6@9"iw}"nucCdLi=kon';~|lr;89klqyruir6kla"dfDwqsawnumlc_rNi"qyp,dEF9wnkoqsrNi G G
8 8
'x D]dLqsiwzklawdÄmorui"dEpkudLmy|6@9"iwp'klqyrui)Jg\kpLn{iD9d|la"r=0im_¢da=klawn{kkoa"d;dE9]nklqyrui-r'6wnkoa"qsi
9"i"qZ6Ìrumoc c_d#kon';:;nkld-rumoqszNqsiwn;Z;8OO*]n{k n{iw}Piwr= D9d#i=kDPOB7ud#mlklqp#n;2}q|:;nup#d#c_d#i=kv|q|}qymldEp&k3;8O
mld;yn{kldE}Ikor kla"dvDwqsawnumlc_rNi"qypdE9]nklqyruiJ gji e>ÃklawdQ6@9"iwp&koqsrNi q| !@2G %!%bH@=0awd#modLnu|
!@ G !
G
!-qyiA'> nuiw} !@ G %!%
A
qsi>nLe
klawd_p#r~d|¿p'qyd#i=ko|@G = 3
=
=
=
C nuiw}F G 3
G@ W+WW C C numldCrD"kon{qyi"dE}GDPO
|r;Z7~qyi"zCkla"dN;yqyi"dLnum|MO|kld#cN
L G
C G 8
=0a"d#modIG
U ( 3 + 3 - 3
JJJ JJJ JJJ JJJ
U ( C + C - C
"!
# x
qy|_nA%$>A cnklmoqZ5xx=0awrN|ld¿zudLi"d#mvn';;kld#moc qy|
! #
3'&
# &
C2x,nuiw} qy|klawd`7udEp&korum-r6
rui"dÄp'r~rNmo}qyiwn{kld r62klawdÏkvn{mozud#kº|ld'kNH A.A
G!(
3 WW+W
.( C &x*=0a]nkqsc_:;yqsdE|klawn{kNH?L;ci9w|k~D]d
d5"modL|o|dE}6ÌrNm
(.+ !- 'x
(.+ ,- n{iw}
(.+ ,- MLJ
0dLzNnumo}qyi"zkoa"d kvn{mozud#kÏ|d#kÅnN|0klawd-c_dLnui|a]n{9d,x]kla"dC}d6ÌrNmlcnkoqsrNi o d+;}YH
?
7;NLq|0koa"d#i
mod#wmldE|dLiNkodL}\DPO-koa"d d;sdLc_d#i=ko|;r'6+ %(&xn{iw}_qskq|d5~kldLiw}dL}_r9ko|lq}d0klawdÏ|lr9"mvp'd|lawn{9dPkoawn{i:k|
korCkla"dw6@9"i]p&klqyrui J
) VX " +*
`awdV6@9"iwp&koqsrNi
qy|,}"d
o
i"dE}_rui-,
A
xD:9kºawnu|korND]dÏn{":;yqydL}_rui;ZOqsi_koa"db7~qyp#qsiwq¸k]OCr'69kla"dÏp'rui]|komonuqsi=kJ
gÏ|-nWcn{kkldLm-r66¶nNp&kEx}=ºd+numld¿qyi=kldLmldE|kodL} qsiI"mlrNwn{z=nkoqsi"zkoa"d}d+6Ìrumocnklqyruin;Z;r7ud#mÄkoa"d!,qyi *9t
dLiwp'dmvn{iwzud7-Är'63kla"d|M9:;p9]|0r'6qsi=kod#modL|kLx:D:9"k i"r{kÅn';8;2r7udLmkoa"dD"mvn{qyi)Jº`a"d#mod6ÌrNmldÄqskqy|Ï}dL|lqsmvn'D;sdÅklr
d+5:;sqp'qsk3;8O;sqyc_q¸kºklawd qyi *9"dLiwp'dÏr'6Ñklawd koa"qsi"t?:;nkodÏ|l:;yqsi"dÏqsi=kod#mo]r;yn{klqyrui_klrCn "mod'tj}d o i"dL}_iwd#qyzuaPD]rNmt
awr=r}+r'6ÑklawdÅp#ruiwp#d#moi"dL}¿|39:;p9w|JS`a"q|ºpLn{iD9dnupva"qyd+7NdL}DPO¿}d o i"qyi"zCn-wn{mvn';8;yd+;yd#"qy]dE}qpbD9r9"iw}"qsi"z
7Nr;89"c_dux xS|l]dEp'qZ6@O=qyi"zkla"d¿iwd#qyzuaPD]rNmlawr=r}JSz r=d7ud#mEx qyi¾rNmo}dLmklr"mldE|dLm37Nd_kla"dp'rui=koqsiP9"qsk]OÂr6
koa"dklmvn{iw|M6Ìrumocnklqyrui x=ºd}"d o i"dn!,6@9:<<+OS7Nr;89"c_d7- klawmlr9"zua[=0a"qypvakla"d_}d+6Ìrumoc_n{klqyruiv=0q8;8;,p#n{i]p'd+;
qsko|ld+;Z6r9k0qyiPn_p#rui=klqyiP9"r9w|V=ndOJS`a"q|6@9:<<+O`7Nr;89"c_dp#n{iBD9d }dL|op'moqZD9dL}+klawmlr9"zuaPn6@9"iwp&koqsrNi2x/.10;x
}"d o i"dE}Pnu|
. 032 , A
?A
,
4G (.+ ,- 65
?A
. 087 ( W. 0:9 + W. 08; -
=0awd#mod 6@9wiwp&koqsrNiw|<. 0>= awnd7udÅklawd 6Ìr;Z;yr=0qyi"z_"mlrN]dLmkoqsdE|
}d
o
i"dL}rNi ,ºx
G x %A!A k]=0qyp#d }qZu9dLmldLiNkoqynD:;ydÄnuiw}+kla"d |ldLp#ruiw}rumv}d#m0}dLmlq87nkoqZ7NdÅq|p#rui=klqyiP9"r9w|Lx
}dEp'modLnu|lqyi"zrNi ,x
d+7Nd#iH¼koa"qy|b;ynN|k0"moru9d#mlk]O¿q|0|M9*|¿p#qsdLiNkb=0awd#iB=rNm3k~qyi"zqyikla"dN;yrp#n;2|wnNp'ddL&x
, ¿|M9]pva+koawnk .
0>=
G 8 x . $
0>=
D]dLqsi"z_koa"d |ldLp'rNiw}¿rNmo}"d#m}dLmlq87nklq87udÅr'6 .10 =e
=0awd#mod x
n{iw}
|l9dLp'qZ6@OAkoa"d`;yqycCqsko|-r'6ºkla"d`D]r9"iw}qyi"zvD9rd5Âqyi( x +Ânuiw}-A}qymodLp&koqsrNi)JN/"rum
d+5"n{c_:;yduxqZ6 G
?
koa"d#i . 0 7 =0q8;8;)D]d pvawrN|ld#iP|M9wpvakla]nk .
087
G 8
TÅq87udLi|39wpvan . 0 6@9"iwp'klqyrui2x;sd#k-n]rNqsi=k4 G (,+ !- , A
nuiw} 4G (.+ ,- nD]dqsko|
qycn{zNdÅ9ruqyi=k~DFO+kla"dÄkoa"qyit?;yn{kld|;sqyi"dqyiNkod#mo]r;yn{klqyruiB;sqyc_q¸kodL}klr_rNi"dÄi"d#qyzuaPD9rumoa"r~r~} mJ,`awd#i2x
4 G 4F W. 0 4; L34 W.
0 4;
=0awd#mod . 0 G U ? . 0 J
`a"dpvawruqp'dºr'6. 0 nu|}=ºd+;8;"nu|3klawdk39"i"dr6]koa"dV;sqyc_q¸kv|Sr'6]kla"d~D9rd5-q|qsiwp+9"ciD9d#i=kf9"9rui_n{iCd59d#mlkLx
nuiw}\=0qZ;8;w;yndO-nÄmor;yd0qZ6Ñ}"d6ÌrumocnkoqsrNi
o
d;y}w|x6Ìmoruc }"qud#mod#i=k;|39:;yp#qwn{mod}dE|qymldE}klrND9db9w|ldL}ÑxNrum,qZ6}wnkon
r9k;r69koa"d7~qp'qyi"qsk]Or6Ñkla"d |39:;p9w|;awnd7udklrD9d0klmodLn{kldE}\6Ìrum;d+5"n{c_:;ydJhzr=ºd+7udLmLxNn |qyi"z;sdm9:;yd p'r9:;}
D9dN6ÌrNm qyiw|kvn{iwp#dklr}d
o
iwd
nN|klawd ,cCq}~t?kla"qpk~i"dL|o| -År'6;n_zO~m39w|Lx=0awd#modÄkla"dcCq}~t?kla"qpk~i"dL|o|0r6Sn
zO~m39w|0p#r9:;}BD]d-awn';Z6kla"d-}"qy|konuiwp'dND9d'k]=ºd#dLikoa"d zNmond7~qsk]O+p'dLiNkod#mv|r'6Sqsko|k]=ºrmD]r9"iw}qyi"z+|39:;p'q{H%;sq8kud
p#d#i=klmvn';"nuiw}C]r=|kvp'dLiNkomon;"|M9;yp#q:6Ìrumkoa"d9rN|kop#d#i=klmvn';zO=m9w|}6ÌrNm,d5"n{c_:;ydLJ/3qyz9"mod Åzuq87udE|d5"n{c_:;ydL|
r69rN|o|q8D:;ydn6@9"iwp&koqsrNiw|<.
0 =
U W
, x+.
3
0>=
G 3
3
Q x
8
W W
, :. G
0"=
G !" U qZ6 8 %
%
=
3
G ? 3 G#
<
A$&%
'
1)(
% % ? ( '
G
qZ6
= %
% B
8 qZ6 B % %
=0qskla
=
n{iw}NB , |M9]pva+koawnk
=*
B
W
, x+.
A
0>=
G,+ 1 Q
x- 8
X da]nd7ud+|lqsc9:;nkldE}¾n|ld'k_r'6 |lr9wmop#d+n{iw}¾konumlzNd'k-9ruqyi=ko|BH¶|ld#dN/qyzJhl"xkorujL'x;n{i]}¾p'rNcC9kldE}
koa"d 6@9"iwp&koqsrNi p#rumomldE|9ruiw}"qsi"zkorIkoa"dL|ldAk]=ºr |ld'kv|+J /3qsz9"mod[l"x D]rukkorucPxÏ|la"r=|koa"d mldE|M9:;skr6
koa"dPn{":;yqp#nkoqsrNi¾r'6 ruiIkla"dB=0a"r;ydzumoqy}J^g;¸koa"r9"zNa¾koa"d}"d6ÌrumocnkoqsrNiq=dEn'kNd#iw|i6¶n{m6ÌmlrNc kla"d
p#ruiw|klmvn{qyi=kLxNq¸kºmldLc_nuqsi]|Sqsi#*9"d#i=kJfrNiP7ud#mv|ld+;8OM/3qszjJ~Åq8;8;Z9w|klmvnkodL|,kla"dÏdudLp&kºr'6klawdÏn{w:;sqp#n{klqyruir6Ñn
modL|klmoqp&klqyruir'6 kor¿n|9dLp#qo dL}i"d#qyzuaPD9rumoa"r~r}e#/3qszjJ9 klru x:7~qynn}r~rNmV6@9"iwp&koqsrNi2x /3qyzJ9D9r{klklrucPx
7~qn_rui"d. 0 6@9"iwp'klqyrui)J`a"dN;yqsc_qskon{klqyruiWr'63klawd-}d6ÌrNmlcn{klqyruiQ7~qynn}r~rNmV6@9"iwp&koqsrNiWqy| d|¿p'qyd#i=kEx:D:9k
}"r=dE|i"r{k0"modL|ld#m7ud kla"d p#rui=klqyiP9"qsk]OJ 1Ïi+koa"dr{koa"d#mawnuiw}Ñxkoa"dÄmldE|komlqp&koqsrNi+r6koa"dÄd5~klmvn{9r;nkoqsrNi¿klr
koa"di7~qp'qyi"qsk]OWr'6SklawdCp#ruiw|klmvn{qyi=k7~qyn+rui"d . 0
6@9wiwp&koqsrNiq| d+u9dEp&klq87udCn{iw}Âp'rNiNkoqsiP9"qsk]O"mldE|dLm37~qyi"zwxnu|
pLn{iBD]d |ld#dLirNi2/3qyzJ9x*D]rukkorucQJ