Nonlinear autoassociation is not equivalent to PCA. Neural

! "$#&%!
' )(+*,
-/.021.436567/89.:';=<>?56@BA
]=^`_Qabdc&ePf`gMhfBi?jaclkQmonE_qprkQs_qk
t^ubr{fBaz„prk…sp‡†Bkqmz„p‡c&e
ˆ^`brp‡g6^\IŽ‹f2†u^vn_Qf`clpr^
h^us4^`‘4^
‹^ucl{^`brpdk`œ•B^`j”`f™’xpd_qž™Ÿt^`b[œ h^
9C 0D7E:F17GH8I<KJMNPL O .4GFJQ<IG
tkqj4^umclivkqswcxf`gyzeE_|{fBbdfB}`e
nivpdcl{‰ˆ^`brb
acl}BkQm„z…sp‡†BkQm„z„p‡c&e
‹k“’^`m”=ŽI‹o•?–w—E˜™–wš
¡fBz„kDŸ”EmkqpdžqbrkQmqœ¢m„ac„}Bkqmzqœ¢kq‘a
R.S2;UTWVXY3[Z'@\;
hkQswclkqmxg~fBm€f`brkq_Qab^umƒ‚
Škq{4^D†EprfBm„^`bŒ‹kqamfBz„_Qprkqs_qk
xac„}Bkqmz…spd†`kqmz„pdc&e
‹kQ’^`m„”=ŽK‹•›–w—˜D–wš
}`bra_|”Ÿj4^D†Ebrf™†Kœ£macl}BkQm„zQœ£kQ‘a
¦¤ ¥9§|¨“©qª¬«™¨
­ _qfBivivfBs®ivprzjIkQm„_Qkqjc„prfBs¯’xpdc„{prs°cl{k?‹kQaml^`b‹k“c&’f`m„”°_qfBivi±asp‡c&e
pdzYcl{4^uc€kQ†`kqs²’xp‡cl{³sfBsbrpdskD^um„pdc„prkQzYprs´c„{kqpdm‰{pr‘‘kqs²br^™e`kqmQ޵^uaclfw^uz„z„fE_qpr^\¶
c„fBm„z±c„ml^`pdskq‘,’xp‡cl{·Š^`_|”¬jmfBj4^`}B^uclpdfBs¸^`m„kYkQ¹¬apd†u^`bdkqswcºclf¯brpdskD^um¦ivkQcl{f‘z
za_|{»^`z?ym„pds_qpdj4^`bhfBivjIf`skqswc ­ s4^`b‡eEz„prz$¼[yh ­½ œ!¾ƒ{k$jam„jKfBz„k€f`goc„{prz
j^`jIkQm›prz±clf°‘kQi?fBszclm„^uclkYc„{4^ucvsfBsbdprskq^`m›^`ac„fw^`zz„fE_qp^\clfBmz›^`_Qc„a4^`brb‡eÀ¿Kk“¶
{^™†`k€‘pdÁIkqm„kQswclbde+g~mfBiÂbdprskq^`mºi?k“cl{fE‘z?^`s‘¸cl{4^\c?c„{kQe¸_q^`s fBacljKkqmg~f`m„i
c„{kqzk¦ivkQc„{f‘zx’x{kqsWazkq‘$g~f`mbr^uclkQswckÍEclml^u_QclpdfBsĎ=jmf\¡kq_“clprf`sW^`s‘/_qbr^`z„zp‡¶
Å _D^uc„prfBsĜÆÇ{prbdkµbdprskq^`m^`aclfB^`z„zf_Qp^uc„fBm„zkqi±abr^uclkµyh ­ ^`s‘$c„{¬azk“{pd¿pdc
^YÈ=^ucÉfBmÊasprivf‘4^ubMm„kQ_qfBszclma_Qc„prfBs®kqm„mfBmÊz„amg6^`_qkuŽM^`aclfw^`zz„fE_qpr^uclfBmz’xpdcl{
sfBsbrpdskD^um„pdc„prkQz±prs·cl{kQprm›{pr‘‘kqsHbr^DeBkqmvbrkq^`m„s·‘fBi?^`pdsz›¿¬e·¿aprbr‘prs}¯kqmm„fBm
mkq_QfBszc„m„a_“clpdfBsHz„amg6^`_QkqzËcl{^ucDŽƒ‘kQjIkQs‘pds},fBs c„{k$cl^`z„”=Žƒ_qf`s¬cl^`prs³ÌºÍÎÐÏ6ÑÓÒ
Ô ÎrÕÉbdf_q^`b!†`^ubrbrk“eEzqœÖ¾ƒ{pdz±j4^`mclpr_Qab^umµpds¬c„kqmjIfBbr^uclpdfBs°¿p^`z±^`brbdf2’xzµsfBsbdprskq^`m
^uaclfw^uz„z„fE_qpr^uclf`m„zËclfUm„kQjm„kQz„kqswcW^`jjmfBjm„pr^uclk¯_Qb^`zz„p Å _D^uc„prfBszYfugºsfBsbdprskq^`m
˜
i¦abdc„p‡¶&ivfE‘4^`b9‘fBiP^uprszQŽIpds$_qf`s¬c„ml^`zcclfPbrprskD^`m^`ac„fw^`zz„fE_qp^\clfBmz’x{pd_|{¯^`m„k
pds4^`jjm„fBjmp^uc„kg~fBmza_|{?cl^`z„”¬zQœ &svg6^`_“cDެ^`aclfw^`zz„fE_qpr^uclfBmzM’xpdc„{v{pr‘‘kQs?aspdc
sfBsbrpdskD^um„pdc„prkQzv_q^`s»¿KkWz„{f™’xs»clf+jKkqmg~fBm„i sf`sbrpdskD^`m?_qbr^`z„zp Å _q^uclpdfBsH^`s‘
sfBsbrpdskD^umm„kQ_qfB}BspdclpdfBsĜ
š
­ Ös ^`ac„fw^`z„zf_Qp^uc„fBmxprz^vg~kQkq‘g~fBm’^um„‘W_QfBsskQ_QclpdfBspdzc‘kQ†Epr_Qkµ’x{f`z„k±}BfB^`bŒprzxclf?m„k“¶
_QfBszclm„a_Qcƒcl{kprsjacx^ucc„{kfBacljacb^DeBkQmqœMÆÇ{kQs/az„kq‘Y’xp‡cl{‰^¦{pd‘‘kQs/br^DeBkqmz„i?^`brbdkqm
c„{4^`s$c„{k¦pdsjac ufBac„jacob^DeBkQm^`s‘$brprskD^`m^`_“clpd†u^uc„prfBszf`sbde`ŽKc„{k±^`aclfw^`zz„fE_qpr^uclfBmpriº¶
jbrkqivkqswc„z^Ë_qf`i?jmkqzz„prf`sWz„_|{kQi?k±’x{pr_|{W’^`zz„{f2’xsÖc„fË¿Ikµkq¹¬ap‡†`^ubrkqswcc„fYym„pds_qpdj4^`b
hf`i?jKfBskQs¬c ­ s4^`b‡eEz„prz¼[yh ­½ ^`bdz„f±”¬sf™’xs€^`z =Ñ `ÍEÎ `ÎÐÍ=Õ ±Õ \Ì Ô “ÑÓÏ6Ñ ¿we
А^`bd‘pŒ^`s‘€ˆfBm„spr”=˜ œ ­ sf`c„{kqmpdswclkqmkqzclprs}›^`s‘Ym„kQb^uc„kq‘Ëmkqzabdc’^`zƒfB¿c|^`pdskq‘Ë¿we
ŠfBam„br^`m„‘‰^us‘ Ê^`ivjY’x{fv_qb^upri/Žpds‰c„{kqpdm˜ ±j^`jIkQm
¼œ‡œdœ ½ g~fBmƒ^`aclfw^`zz„fE_qpr^uclpdfBs?’xp‡cl{Ëbdprskq^`mfBacljacaspdc„zqŽEcl{kfBjclpri?^`b4’kqpr}`{¬c
†u^`bdakqz_D^`s›¿Kkƒ‘kqmpd†BkQ‘›¿¬e±zc|^us‘4^`m‘vbdprskq^`mM^ubr}BkQ¿ml^Ž`_qfBszprzclprs}kqz„zkqswclpr^`brb‡e
pds›z„prs}Bab^um†u^`brakx‘kQ_qfBivjKfBz„p‡clprf`s/¼ n t ½ ^`s‘Pi?^`”¬prs}cl{¬az!cl{ksfBsbdprskq^`m
g~as_Qc„prfBszx^\cƒcl{kÊ{pd‘‘kqs/b^De`kqmx_qfBivjbdkQclkQbde?asskQ_qkQz„zl^ume Ž
ŠfBam„b^um„‘‰^`s‘ Ê^`ivjĘ [œ
ŠfBam„b^um„‘/^`s‘ Ê^`ivjĘ Ê¿4^`_|”ukq‘cl{kQprmY_qbr^`pri az„pds}+cl{kQfBm„k“clpd_D^`b_QfBszpr‘kQml^uc„prfBsz
’x{prbrk hf`cclmkqbrb^us‘€€asmf˜ !^`m„mpd†`kq‘®^uccl{k›z„^`i?kº_QfBs_QbrazprfBsόpds‘kQjIkQs‘kqswc„bdeBŽ
az„prs}?^us€kÍjKkqmprivkqswc|^ubÄi?k“cl{fE‘fBbdfB}`e`œ
yF^`ml^`‘f™pd_D^`bdbdeBŽwsfBsbrpdskD^um^`ac„fw^`z„zf_Qp^uc„fBm„z!^um„k^`brzfg6^`i?f`azMg~fBmcl{kQprm_q^`j4^`_Qpdc&e±c„f
zfBbd†`kcl{kkQs_qfE‘kQmƒjm„fB¿brkqi ¼ ai?kQbr{4^`mc¦Õ“Ï `Î r˜ ½ Ž4^±jmfB¿brkQi ’x{pd_|{‰_D^`ssf`cx¿Ik
zfBbd†`kq‘Ö¿weÖyh ­ ¿Kkq_q^`az„kºfugcl{k±zprs}`ab^`mpdc&e/f`gc„{k±jmprs_Qprj4^`b'_qf`i?jKfBskQs¬c„zqœ °€f`m„k“¶
f™†`kqmqŽIm„kQ_qkqswcmkqzkD^`m_|{Öz„a}B}`kqzc„zocl{^ucosfBsbrpdskD^um^uaclfw^uz„z„fE_qpr^uclf`m„z^`m„kɒkQbrb‡¶ z„ap‡clkQ‘/g~fBm
­ zƒ^±i?^uc„c„kqmf`gŒg6^`_“cDŽ m„a}`bdew^u”K˜ B– Ä^`s‘ y{4^ucl^`”®Õ“Ï `Î r˜ đkQi?fBszclm„^uclk
g~amcl{kqmcl{4^\cg~f`m^us¬ev‹ÉŽBcl{k‹x¶ prsjacDެ‹ƒ¶&fBac„jackqs_qfE‘kqmjm„f`¿brkQi _D^`s?¿Ik lÕ Ô lՓÒ
™Õ 4Ï&Õ ¿we±^usº^`ac„fw^`z„zf_Qp^uc„fBm'f`g=fBsb‡eÉc&’fsfBsbrprskD^`m'{pr‘‘kqsºaspdclzQœF¾ƒ{kg6^`_QcFcl{4^uc
br^`m„}`kºkqs_Qf‘pds}Bz_q^`sÀ^u_Qcla^`brb‡eW¿Kk/ÎrÕ 9Õ º¿weWc&’f\¶&{pd‘‘kqsE¶&asp‡cµ^`aclfB^`z„zf_Qp^uc„fBm„z
’^`zµ‘kqivfBszclml^\clkq‘®¿we pdjz„kQmq˜ !’x{f$z{f™’kQ‘,cl{4^\cµza_|{,‘k“†Epr_qkQz±^`mk?_q^`j4^\¶
¿brkÊf`gFbrkD^um„spds}º{f™’²clfvkqs_qfE‘kÉc„{kÊjIf`z„pdc„prfBsYfug^›z„jKf`c¦¼6fBmƒ_Qbrazclkqm ½ fugsf`m„i?^`brb‡e
‘przc„m„pd¿aclkQ‘YjIf`prswclzƒ^ujjIkq^`m„pds}º^ucml^`s‘fBi bdf_q^uclpdfBszfBs/^˘™– ¦˜™–¦z„¹¬a4^um„kq‘€^`mml^DeBœ
!
"
#
$
%
&
'
( )
+*
,
- '
( .
/
0
21
2
3 21
54
.
76
“Î “Ñ `Ï6Ñ vf`g_qkQmcl^`prs‰c&eEjIkQzf`g 4ÎÐÑ 9Õ ÃÎ ™Õ Ô qÎrÕx^`s‘®ÌºÍÎÐÏ6ÑÓÒ&Ì `ΑfBiP^uprsz
¼ •B^uj”`f™’xpr_Qž‰Õ“Ï `Î r˜ [Ž yFk“clz„_|{k/Õ“Ï `Î r˜ ½ ŽM^`sfucl{kQmÉcl^`z„”Wg~fBm’x{pd_|{+yh ­ ^`s‘
bdprskq^`mƒ^`aclfw^`zz„fE_qpr^uclpdfBs‰^`m„ksf`c^`jjmfBjm„pr^uclko¿IkQ_D^`azkµfugFc„{kqpdm³brpdskD^umm„kQzclmpr_“clprf`sĜ
&sYzjpdc„kof`gÄc„{kfB¿w†Eprf`az_QfBswclml^u‘pr_“clprf`sPk“{pd¿pdc„kq‘Ë¿wevcl{kQz„kg6^`_“clzQŽcl{kqm„k{4^`z¿KkqkQs
bdpdcclbrk¦kQÁIfBmcµ^ucÉk“jbr^`prsprs}Ycl{k?zfBam„_Qk?fugcl{przÊprs_QfBszprzc„kqs_“eBœË¾ƒ{k?jam„jKfBz„kvf`gc„{prz
j^`jIkQmprzoc„f‰‘kqivfBszclml^\clkºk“jKkqmprivkqswc|^`bdbde‰cl{^uc ŠfBam„br^`m„‘/^`s‘ Ê^`ivjĘ £z_Qb^`pdi
‘fkQzƒsf`cxskQ_qkqzzl^`mprb‡eË{fBbd‘/^`s‘Yclf›^`s^`bdeEžqkc„{k‘p‡Á9kQm„kqs_qkqzx¿KkQc&’kqkQsWyh ­ ^`s‘‰sfBs¶
bdprskq^`m^`ac„fw^`z„zf_Qp^uc„fBm„zƒ’x{kQsÖpdc‘fEkqzsf`cDœ &sWj^`mc„pr_qab^`mQŽ=’kµc„kqzcocl{k¦jKkqmg~f`m„i?^`s_qk
fugÊsfBsbdprskq^`mP^uaclfw^uz„z„fE_qpr^uclf`m„zvm„kqbr^uclp‡†Bk‰clf+yh ­ ^`s‘HbrpdskD^`m?^`ac„fw^`zz„fE_qp^\clprf`sUfBsH^
sfBsbrpdskD^umi±abdclp ¶&ivf‘^`b_qbr^`z„zp Å _q^uclpdfBsËjmfB¿bdkqi prszjprmkq‘Ë¿we?cl{kjm„f\¡kQ_QclkQ‘YclfBjKfBbrf`}`e
fug!^Pm„kq^`b‡¶ ’f`m„br‘€‘fBi?^`prs9œ ­ gÓclkQmoz„{f2’xpds}Pc„{4^ucoc„{kqmk¦pdzqŽ9pds‘kQkq‘ÄŽ9^?‘p‡Á9kQm„kqs_qk±pds€cl{k
_Qb^`zz„p Å _D^uc„prfBs€^`_Q_qam„^`_Qe€fB¿cl^`prskQ‘W¿we€c„{k¦bdprskq^`m^`s‘WsfBsbrpdskD^um‘k“†Epr_qkQzfBs$c„{prz‘fu¶
i?^`pdsϒkµk“jbr^`prs‰cl{pdz‘pdÁIkqm„kQs_qkÉ¿we/_qfBivj4^`mprs}›cl{kÉm„kQ_qfBszclma_Qc„prfBs$kqm„mfBmxz„amg6^`_qkQz
_QfBszclm„a_QclkQ‘$¿we‰kD^u_|{€zezclkQi f™†`kqmƒcl{kc„kqzc‘fBi?^`pdsĜ
€f`m„kz„jKkq_Qp Å _q^`brb‡eBŽ™fBamŒk“jIkQm„pdi?kQs¬c„zŒ‘kqivfBszclm„^uclkMc„{4^ucsfBsbrprskD^`mIz„pr}`i?fBpd‘4^`b2z„pds}Bbdk“¶
{pr‘‘kQs›b^DeBkQm!^`aclfB^`z„zf_Qp^uc„fBm„zMi?^De¦zfBivkQclpdi?kQzMprswc„kqm„jKfBbr^uclkz„kQc„z!f`g9jKfBpds¬c„zM‘p‡Á9kQm„kqswc„bde
g~mfBi yh ­ œ &s+j^`mc„pr_qab^`mQŽ'’kYz„{f™’ cl{^ucDŽMf`sÀcl{k?clkqzcº‘fBi?^`pds®_QfBsz„pd‘kqmkq‘ÄŽ’x{pdbrk
yh ­ ¼~fBm±kq¹¬ap‡†u^`brkQs¬c„bde`ŽbrprskD^`m¦^`aclfB^`z„zf_Qp^uc„prfBs ½ k“{pd¿pdc„z±È=^ucºf`m±aspdi?fE‘4^`bm„kQ_qfBs¶
zclma_Qc„prfBs®kqm„mfBmÊz„amg6^`_qkQzqŽMsfBsbrpdskD^umz„pr}`i?fBpd‘4^`b^uaclfw^uz„z„fE_qpr^uclf`m„zÊ¿apdbr‘¯kqmm„fBmÉm„kQ_qfBs¶
zclma_Qc„prfBs°z„amg6^`_qkQzÉc„{4^ucÉ_qf`s¬cl^`prs¯i±abdclpdjbrk¦brfE_D^`b'†`^ubrbrk“eEzqœ ­ zµ^/i?^ucclkqmfugg6^`_“cDŽŒcl{k
mkq_QfBszc„m„a_“clpdfBs®kQm„mfBmÊz„amg6^`_qkQzµ¿aprbdcÊ¿weWc„{kvz„pr}`i?fBpd‘4^`bF^`ac„fw^`z„zf_Qp^uc„fBm„zÊ^um„k›_qbdfBz„kQbde
mkqbr^uclkQ‘¦clfoc„{kmkq_QfBszc„m„a_“clpdfBsºkqmm„fBmFz„amg6^`_qk¿aprb‡c¿we¦^oml^`‘p^`b¬¿4^`zprz'g~as_Qc„prfBs¦^`ac„fw^`z¶
zf_Qp^uc„fBmqެcl{¬azƒza}B}BkQzc„prs}±c„{4^uc’x{kqsYcl{koz„pr}`i?fBpd‘4^`bK^`ac„fw^`zz„fE_qp^\clfBm‘fEkqzƒsf`cfBjKkqm¶
^\clkÉbrpr”ukÉyh ­ _QfBi?jaclpds}P^v}Bbrf`¿4^`brpdžqkQ‘/zfBbraclprf`s‰c„f?c„{kµpdswclkqmjIf`b^uc„prfBsYjmfB¿bdkqi Ž
c„{kqs$pdcfBjIkQml^uc„kqzbrpr”ukÉ^Pml^`‘p^`bŒ¿4^uz„przg~as_“clprf`sW^`ac„fw^`zz„fE_qp^\clfBm _qf`i?jaclprs}›^?brfE_D^ub‡¶
pdžqkQ‘/zfBbraclprf`s‰c„fºcl{kÊprswc„kqm„jKfBbr^uclpdfBsËjmfB¿brkQi€œ
­ bdc„{fBa}`{/¿Kf`c„{‰c„{kz„pd}BivfBpr‘4^ub9^`s‘€Š]¸^`ac„fw^`zz„fE_qp^\clfBmzƒ^`m„ksfBsbrpdskD^umqŽ^ubrb
2
'
( 2
!1 '
( )
%
®Æ k¿IkQ}Bprsf`amŒzc„a‘e¿we‘pdz„_Qaz„zprs}ƒcl{kbrprivpdcl^uclpdfBsz4f`g ŠfBamb^`m‘/^`s‘ É^ui?jĘ ¢z
_Qb^`pdi€œvÆÀkvcl{kQs,‘kQi?fBszclm„^uclk?k“jKkqm„pdi?kQswc|^`bdbdeWc„{4^ucÉcl{kQz„kËbdprivpdc|^\clprf`szo_q^`sÀpds‘kqkQ‘
¿KkPkÍ_qkqkQ‘kq‘·¿we,zc|^`s‘^`m„‘,jm„fB¿bdkqivzµ’xp‡cl{pds®cl{kË_qfBswc„k“Ec›f`gƒ_Qb^`zz„p Å _D^uc„prfBsÀ^`s‘,’k
^us4^`bdeEžQkËcl{kQz„k/m„kqzabdc„zqŽ_qfBs_qbra‘prs}W’xp‡cl{¸z„f`i?kYzjIkQ_qabr^uclpdfBsz›^`zºclf֒x{we+zpr}BivfBpr‘^`b
^uaclfw^uz„z„fE_qpr^uclf`m„zƒz„f`i?k“clprivkqz‘fP^us‘‰z„fBivkQc„privkqzƒ‘fvsf`cxfBjKkqm„^uclkbdpr”ukÊyh ­ œ
%
-
! "
#
ÆÇ{kqsÉ_qfBszpr‘kQm„pds}cl{kmkqzabdc„zŒf`g А^ubr‘pŒ^us‘$ˆfBm„spr”=˜ Ž ŠfBamb^`m‘‰^`s‘ Ê^`i?j9˜
^us‘ hf`cclm„kQbrbŒ^us‘W/asm„f˜ ^us‘°c„{kvkQ†Epr‘kQs_qkvcl{4^\cµsfBsbrpdskD^umÊ^`aclfB^`z„zf_Qp^uc„fBm„z
_q^`s/z„fBb‡†BkÊjm„f`¿brkQi?zc„{4^ucx_D^ussf`c¿Kkz„fBb‡†Bkq‘€¿we‰yh ­ ¼ xaivkqbr{^`mc¦Õ“Ï `Î r˜ [Ž
•B^`j”uf™’xpr_qžYÕ“Ï `Î r˜ Ž y'kQclz_|{k/Õ“Ï `Î r˜ ½ ޱ^usprivjIfBmc|^`swc€¹¬akqzclprf`s _QfBivkqz$c„f
ivprs‘
tfEkqzcl{k Šf`am„br^`m„‘/^`s‘ Ê^`ivjĘ M_Qb^`pdi {fBbd‘WprsÖ^ubrb'_D^`zkqzfBm‘fkQzpdc
‘kqjKkqs‘¯fBsÖ_Qkqmcl^`prs¯^uz„z„ai?jc„prfBsz_qfBs_Qkqmsprs}Ëc„{kºas‘kqm„b‡eEprs}Y‘f`iP^`pds$fBm
c„{kÉ^`ac„fw^`z„zf_Qp^uc„fBm%$
­ _D^`mkQg~ab4bdff`”±^uc!cl{k‘pdz„_Qaz„zprfBsvb^`pd‘›fBacprs ŠfBamb^`m‘€^us‘ Ê^`ivjĘ =mkQ†`kD^`bdz
c„{4^uc!cl{k_Qb^`pdi ^`_“cla4^ubrbde¦‘fEkqz!‘kqjKkqs‘PfBs?^Éj^`mc„pr_qab^`m_QfBs‘p‡clprf`sĜM/fBm„kz„jKkq_Qp Å _q^`brb‡eBŽ
bdkQc &)¿Kkºcl{k›sf`sbrpdskD^`mg~as_Qc„prfBs¯jmkqz„kQswc±^ucÊc„{k›fBacljacÉf`gc„{k›{pr‘‘kqs°asp‡clzÊf`g^
sfBsbrpdskD^um^`ac„fw^`z„zf_Qp^uc„fBmv¼6p[œ£kuœd'Ž &)pdzcl{k›g~as_“clpdfBsÖcl{4^ucÊi?^`”ukqzÊcl{kv^`ac„fw^`zz„fE_qp^\clfBm
sfBsbrpdskD^um ½ œ¾ƒ{k^`zz„aivjclpdfBsÉiP^`‘k¿we ŠfBamb^`m‘‰^`s‘ Ê^`i?j9˜ ¬prsÉfBm„‘kqmŒclf_D^`mme
f`acc„{kqpdm‘kQi?f`szc„ml^uc„prfBs?przc„{4^ucg~fBmziP^ubrb4†u^`brakQzf`)g (*Ž &P+¼ ( ½ _q^`sË¿Kk^`jjm„fDpri?^uclkQ‘
^uz_qbdfBz„kQbde€^`z‘kQz„pdm„kq‘¯¿we/cl{k±bdprskq^`moj^`mcof`g!pdc„zjIf™’kqmzkqmprkqzkÍj4^`szprfBsĜʈf™’k“†BkqmQŽ
c„{przoi?kq^`szoc„{4^uc (-,/.ŒŽIcl{k±†`kq_Qc„fBmf`g!jmk“¶ zeEs4^`jc„pr_º{pd‘‘kQsÖaspdc^`_Qc„pd†u^uclpdfBsz¦¼6p[œ£kuœdŽ
c„{kÉ{pr‘‘kqs$aspdc^`_“clpd†u^uc„prfBszƒjm„pdfBmƒclf›cl{kQprmƒclm„^`szg~f`m„i?^uclpdfBs‰¿¬0e & ½ Ž=i±azc¿IkÊprs‰cl{k
mkQg~kQm„kqs_qkqzƒc„f sfBsbdprskq^`m^`aclfB^`z„zf_Qp^uc„fBm„z ±prsPc„{kmkqi?^`prs‘kqmfug'c„{przj4^`jKkqm_QfBm¶
mkqzjIfBs‘/c„f?mkQg~kqmkqs_Qkqzxclf›z„pd}BivfBpr‘4^ub9^`aclfw^`zz„fE_qpr^uclfBmzqœ
%
7
'
( '
( )
'
( )
%
"
%
$
bdprskq^`mvml^`s}`kWf`gÊcl{k$z„¹¬a4^`z{prs},g~as_Qc„prfBsĜ¾ƒ{przYm„kQiP^um„”¸z„a}`}BkqzclzËcl{^ucYsfBsbrprskD^`m
^uaclfw^uz„z„fE_qpr^uclf`m„z‘fÉsf`c!skQ_qkQz„zl^um„prb‡eºkqi¦ab^uc„kxyh ­ ’x{kQs?c„{kxskQcprsjaclz^`mkxfBaclzpr‘k
c„{kÊbrpdskD^`mml^`s}`kf`gc„{kÊz„¹¬a4^`z{prs}›g~as_“clpdfBsĜ
¾ƒ{kºmkqi?^`prs‘kqmf`gcl{k¦j4^`jKkqm‘kQi?f`szc„ml^uc„kqzk“jKkqmprivkqswc|^`bdbdeYc„{4^ucc„{kqmkº^`m„k¦prs¶
‘kqkq‘Y‘pdÁIkqm„kQs_qkQzƒ¿Ik“c&’kQkqs‰cl{kobrprskD^`m^`s‘YsfBsbrpdskD^umz_|{kqivkqzx^`s‘Ëcl{4^uccl{kQz„k‘p‡Á9kQm¶
kQs_qkQz{^™†`kµjml^`_“clpr_q^`bÄ_QfBsz„kQ¹¬akqs_Qkqzog~f`mcl{kc|^uz„”Ëf`g_qbr^`z„zp Å _q^uclpdfBsĜ
"
Æ®k±sf™’ ‘kQz„_qmpr¿Kk¦cl{k¦c&’fYzkQc„zf`g!k“jKkqm„pdi?kQswclzo’kº_qfBs‘a_Qc„kq‘Ög~fBmcl{pdzoj4^`jKkqmQœoÆ®k
Å m„zcÉjmkqzkqswc¦c„{kºg~fBamʑkQ†Epd_qkqzÉ_qf`sz„pd‘kqmkq‘,^us‘®_QfBivj4^`m„kQ‘®pds¯fBamÊzc„a‘e°^`z’kqbrb^`z
c„{kc|^`z”YfBs‰’x{pr_|{/cl{k“e˒kQm„kµ_qfBivj4^`mkq‘ĜƮkÉc„{kqs€‘kqz_qm„pd¿Ikc„{kÉc„kqzc‘fBiP^uprs‰az„kQ‘
g~f`mc„{prz_qfBivj4^`mprz„f`svg~fBbdbrf™’kq‘P¿we?fBamk“jIkQm„pdi?kQs¬c„z^`s‘Pcl{kQprmm„kqzabdc„zqœ¾ƒ{kQz„kmkqzabdc„z
^um„kÊz„a¿z„kq¹¬akQswclbde/‘pdz„_Qaz„zkq‘$pds€nkq_“clprf`s œ
ʌ4 ·
´
%Œ
! ³
Œ= 4 ·
Y756@B7EJ ¾ƒ{kW‘kQ†Epd_qkqz?’kWaz„kq‘»pds fBam?kÍjKkqmprivkqswclzË^`m„k$y!mprs_Qprj4^ubohf`i?jKfBskQs¬c
­ s4^`b‡ezprz˼[yh ­½ ^us‘,cl{mkqkY^uaclfw^uz„z„fE_qpr^uclf`m„zqœW]=mfBi ^`s+^`s^`bde¬clpd_D^`bjKfBprswcµf`gƒ†EprkQ’ÊŽ
c„{kg~fBamƒ‘k“†Epr_qkQzx‘pdÁIkqmƒpds‰c„{4^ucƒc&’f?fugFc„{kqi ^um„kÊjamkqbdePbrpdskD^`m’x{prbdkcl{kÊf`c„{kqmc&’f
{^™†`ksfBsbrprskD^`m_D^uj4^`¿pdbrpdc„prkQzqœŒ¾ƒ{kcl{mkqkƒ^`aclfw^`zz„fE_qpr^uclfBmz'^`m„k_qfBsskq_Qc„prfBsprzcFivkQcl{f‘z
’x{pr_|{›‘pdÁIkqmFg~m„fBi fBskx^`sf`cl{kQm’xpdc„{ºm„kQ}w^`m„‘ºc„fcl{kc&eEjKkƒf`gI^`aclfB^`z„zf_Qp^uc„fBmFc„{kQeºaz„k`œ
&s?i?f`m„k‘kQcl^`prb[ŽB’k_qfBivj4^`mko^ÉfBsk“¶ {pr‘‘kqs¶ b^DeBkQm^uaclfw^uz„z„fE_qpr^uclf`m!’x{fBz„k{pr‘‘kqsY^`s‘
f`acljacb^DeBkQm„z^um„k±¿Kf`cl{$brprskD^`m±¼!9¶" ½$# ^PfBsk“¶&{pr‘‘kQs¶&br^DeBkqmkq‘¯^`aclfw^`zz„fE_qpr^uclfBm’x{fBzk
{pr‘‘kQs+b^DeBkQm¦pdz¦sfBsbrprskD^`mÉ¿ac±’x{fBz„kËf`acljacºb^DeBkQm±przµbrpdskD^`m?¼6‹%9¶" ½$# ^`s‘¸^€fBsk“¶
{pr‘‘kQs¶&br^DeBkqmkq‘³^`aclfB^`z„zf_Qp^uc„fBm˒x{fBzkÀ{pd‘‘kqsb^De`kqm€^`s‘fBacljac$br^DeBkqm€^`mk°¿Kf`c„{
sfBsbrpdskD^umɼ[‹%9¶&‹% ½ œ &s€kD^`_|{€f`gc„{kqzkµ‘k“†Epr_qkQzqŽ=cl{kÊg~as_“clpdfBs€az„kq‘$prsYcl{kÉsfBsbrprskD^`m
aspdc„zƒprzcl{kÉaz„a4^`bbdfB}Bprzclpd_g~as_“clpdfBsĜ
%.
)
4. Jq; ¾ƒ{k›fBjIkQml^uc„prfBsÖfugc„{kºg~fBam‘k“†pd_qkQzƒ¡azcɑkqz_qm„pd¿IkQ‘°’^`zÊ_qf`s¬c„ml^`zclkQ‘ÀfBsÖcl{k
cl^`z„”‰f`gM_qb^uz„z„p Å _D^\clprf`sĜ ­ g~fBm„i?^`bŒ‘k Å spdc„prfBs/f`gMc„{kÉ_qb^uz„z„p Å _D^\clprf`s€jmfB¿bdkqi c&eEjpr_q^`brb‡e
pdsw†BfBb‡†Bkqzx^usYprsjac†BkQ_Qc„fBm (Ž4^`s‘‰^±‘prz„_Qm„k“clkmkqz„jKfBszk†Bkq_“clfBm›’x{pd_|{€^um„kza_|{Ycl{4^uc
c„{k¦j^`prm¦¼ ( ½ ¿IkQbrfBs}`zc„fËz„fBivkÉas”¬sf™’xsP¡fBprswcjm„fB¿^`¿prbdpdc&eY‘przc„m„pd¿aclpdfBsĎ ›œ¾ƒ{k
}`fw^`b'f`g!_qbr^`z„zp Å _q^uclpdfBs$pdzc„fËprs‘a_qkº^vg~as_Qc„prfBs M¼ ( ½ g~m„fBi ^Pz„k“cv¼ ( ½ 2¼ ( ½ ŽMœ‡œdœ
+¼ ( ½ f`gc„ml^`pdsprs}Wk“^`ivjbrkQzqŽz„fÖcl{^uc M¼ ( ½ jmkq‘pd_Qc„z Kœ &s¸cl{przºj4^`jKkqmQŽ’k/^`z¶
zaivk›c„{4^uc ÖprzÉ^Y¿pds4^`me$†Bkq_“clfBmQœ ­ b‡cl{f`a}B{¯_qbr^`z„zp Å _q^uclpdfBs¯¿¬e°‹kqam„^`b‹k“c&’fBm”¬z¦prz
c&eEjpd_D^`bdbde¯jKkqmg~fBm„ivkq‘,az„prs}Ö^€‘pdz„_Qm„privprs^uclpdfBs¶&skQc&’fBm„” qŽpdcµ_D^`s¸^`bdz„f€¿Ik?jIkQmg~fBmi?kQ‘
az„prs}P^vm„kq_QfB}Bsp‡clpdfBs/^`jjmfw^`_|{$pdi?jbrkqivkqswc„kq‘‰¿we$yh ­ fBmxcl{kµ^`ac„fw^`z„zf_Qp^uc„fBmqœ¾ƒ{prz
^ujjm„fB^`_|{,przʑpdz„_Qaz„zkq‘¸prs ¡„^˜ !g~fBmµyh ­ ^`s‘Àprs ˆ^`szfBs$^us‘ kQ}Bb ˜ w— !g~fBm
^uaclfw^uz„z„fE_qpr^uclf`m„zƒ^`s‘YfBjIkQml^uc„kqzx^`zg~f`brbrf™’xz ‘amprs}±c„{koc„ml^`pdsprs}¦j{4^`zk`Žc„{kÊ^`ac„fw^`z¶
zf_Qp^uc„fBmÉprzµcl^`a}B{wc¦{f™’ c„f$mkq_qf`szc„m„a_“c›k“^`ivjbrkQz¦f`gƒc„{kP_QfBs_qkQjcDœ s_QkPclm„^`prsprs}
pdzƒ_qfBivjbdkQclkQ‘ÄŽ4_qbr^`z„zp Å _q^uclpdfBsYprzƒjKkqmg~fBm„ivkq‘/fBs/^›skQ’²†`kq_“clfBm (¿we‰_qf`i?j4^um„prs}ºpdclz
…z„pds}±za_|{/^¦z„_|{kQi?kuŽ "![Žc„{komkqzjIfBsz„k†u^`m„pr^`¿bdk^uz„z„fE_qpr^uclkQ‘P’xpdc„{Ëprsjac†`kq_ö
c„fBm (#!&Ž™c|^u”`kqz'fBs?¼6pdscl{k!z„pdi?jbrkqzcŒ_D^uz„k ½ ^ƒ†u^`brakf`g ˜ xfBm – ƒ’x{pd_|{µpdzŒprswclkQm„jmkQclkQ‘
^uzclfºivkD^`sËc„{4^uc (#!¿Kkqbrf`s}BzfBmƒ‘fkQzƒsf`cƒ¿KkqbdfBs}±clf±c„{k_qf`s_qkQjcla4^ubŒ_qb^uz„zƒf`gcl{k
jm„fB¿bdkqi/œ ­ gÓc„kqmxclml^uprspds}¦cl{kµsk“c&’f`m„”Ëclf?^`jjm„fDpri?^uclkc„{kÉg~as_Qc„prfB$s M+¼ ( ½ g~mfBi
’x{pr_|{,cl{k?clm„^`prsprs}/k“^`ivjbrkQzº^`mkP¿KkqbrpdkQ†`kq‘Àc„fW{4^D†BkY¿KkqkQs,}Bkqskqml^\clkq‘9Žp‡c¦pdzµkͬ¶
jKkq_“clkQ‘€cl{^ucDŽ4p‡g'c„{kÊclml^uprspds}ºz„k“c’^`z^`jjmfBjmp^uc„kqbdeP‘kqzpr}Bskq‘ÄŽc„{kµskQc&’fBm„”Ë’xpdbrb
¿Kkº^`¿brk¦c„fY_qfBivjac„k¦cl{k›^ujjm„f`jm„pr^uclk±br^`¿Kkqb¼ ˜ Yf`m – ½ g~fBm^`swe$prsjac†BkQ_Qclf`m
fugŒz„pdžq&k %4Žwcl{koz„pdžqkf`gÄcl{koprsjacb^DeBkQmqŽEkQ†BkQsYpdgIcl{4^uc†BkQ_Qclf`m‘pd‘Psf`c^`jjKkD^umprs›cl{k
c„ml^`pdsprs}±z„k“cDœ
' ÆÀk€‘kqz_qm„pd¿Ik€cl{k€i?k“cl{fE‘Ug~fBm?^`ac„fw^`zz„fE_qp^\clfBmzqŽcl^`”¬prs}®prswclf®_qfBszpr‘kQml^uc„prfBs
c„{4^ucxp‡cxprzƒz„pdi?pdb^`m!g~fBmxyh ­ œ
*
-.
-
" -$
—
" -$
" $
" $
*
lÕ “Ï ÃÍ “Ï6Ñ ÇÕ ºclf¯^ cl{mkqz{fBbr‘9Ž!^`s‘·^`z„zpr}Bsprs}Wp‡c¦c„fWcl{kË_QfBs_Qkqjc„a4^`bƒ_qbr^`z„z
p‡gcl{k¦m„kq_QfBszclm„a_QclpdfBsÖkqmm„fBmoprzoziP^ubrbrkQmc„{4^`sWc„{przoc„{m„kQz„{f`br‘¯^`s‘Wc„fPcl{kºf`cl{kQm_qbr^`z„z
fucl{kQm’xprzk`œÉ¾ƒ{kºpr‘kD^Ë¿Kkq{pds‘Wcl{pdzm„kQ_qfB}`spdc„prfBs¶ ¿4^`zkq‘W_Qb^`zz„p Å _D^uc„prfBsWz_|{kqivkºprzcl{4^uc
zprs_Qkcl{kÉ^`aclfw^`zz„fE_qpr^uclfBmprzc„ml^`pdskq‘Ëc„fv_QfBivjm„kQz„z^`s‘‰‘kQ_qfBivjm„kQz„zxk“^`ivjbdkqzƒf`gcl{k
_QfBs_Qkqjc„a4^`b!_qbr^`z„zfBsbdeBŽÄ’x{kqs®c„kqzclkq‘°fBs®^Ysf™†Bkqb!‘4^\c|^YjIf`prswcDŽŒp‡c’xprbdb_qf`i?jmkqzz¦^`s‘
‘kq_qf`i?jmkqzzƒpdcƒ^ujjm„f`jm„pr^uclkQbde›pdg9cl{pdzk“^`ivjbrk¿IkQbrfBs}Bzc„f¦cl{ko_qfBs_Qkqjc„a4^`b ¶&_qbr^`z„zQŽ¿ac
p‡c’xpdbrb9sf`cƒ‘f›z„f›^ujjm„f`jm„pr^uclkQbde?pdgŒcl{kk“^`ivjbrk‘fkQzƒsf`cx¿Kkqbrf`s}¦clfºc„{k_qfBs_qkqjcla4^`b
_Qb^`zzqœ
ʌ4 Ë '¬ ´ !
&sµfBm„‘kqmclf_qfBivj4^`mk^us‘¦kÍjb^`pdsÉc„{k_Qb^`zz„p Å _D^uc„prfBsÊjKkqmg~fBm„i?^`s_Qkf`gcl{k!g~fBam‘k“†Epr_qkQz
_QfBszpr‘kQm„kq‘¯pds€cl{przzcla‘e`ŽÄc&’fYkÍjIkQm„privkqswc„zo’kQm„kº_QfBs‘a_“clkQ‘°g~fBmkD^`_|{Ö_Qb^`zz„p Å kqmf`s
^±c&’fu¶&‘privkqszprfBs4^ubŒ^`mc„p Å _Qp^`bI‘fBi?^`prs9œM¾ƒ{przxjmfB¿bdkqi ’^`zprszjprmkq‘Yg~m„f`i)m„kq^`b‡¶ ’f`m„br‘
‘^uc|^°^`z›z„{f™’xsHpds ]Fpr}Bamk֘/’x{pr_|{ pdbrbdazc„ml^uc„kqz±cl{k/c„ml^`szpdc„prfBs,g~mfBiÂm„kq^`b‡¶ ’f`m„br‘+c„f
^umclp Å _qpr^`bŒ‘4^ucl^œnEjIkQ_qp Å _D^`bdbdeBŽI]pd}Bam„kv˜¬¼6^ ½ ‘pdz„jbr^Dezo^Yš2¶ ‘privkqszprfBs^`bŒm„kQjm„kQz„kqswcl^uclpdfBs
fugƒz„fBs^`mµcl^`m„}Bk“c±mkq_qf`}Bspdc„prfBs°‘4^ucl^$^D†u^`prbr^`¿bdk›g~mfBi cl{k˅µœhoœ &m†EprskPkQjIfBzpdc„fBmeÖg~fBm
€^`_|{prsk ŒkD^um„spds}œ¾ƒ{kQz„k±‘^uc|^º’kQm„k±_QfBivjm„kQz„z„kQ‘$g~m„f`i z„p‡Ec&eYg~kq^uclamkqzclf?c&’fŽKaz¶
pds}Êym„pds_qpdj4^`b4hf`i?jKfBskQs¬c ­ s4^`bdeEzprzqœ &svc„{przjbrf`cqŽw¿b^u_|”µclmp^`s}BbrkQz^`s‘º’x{p‡clkƒ_qpdm„_Qbrkqz
_QfBm„mkqzjIfBs‘®clf ^`_“cla4^ubjKfBpds¬c„z?¼6ivprskQzµ^us‘®mf_|”¬zQŽMm„kQz„jKkq_Qc„pd†`kqbde ½ ^`s‘®‘4^uc|^‰_qbdazc„kqmz
^um„k±pds‘pr_q^uclkQ‘W¿weWjKfBbdeE}Bf`szqœÊ]pd}BamkP˜¬¼~¿ ½ z{f™’xzÊc„{k±z„^`i?kµc&’fu¶ ‘privkqsz„prf`s4^`b'm„kqjm„k“¶
zkqswc|^\clprf`s®f`gz„f`s4^`mc|^`m}BkQcÊmkq_QfB}Bsp‡clprf`s֑4^uc|^Ž'¿acÊcl{pdzÊc„privk¦’xpdc„{¯i?kq^`szÊm„kQjb^`_Qprs}
c„{kP_QbrazclkQm„z ™œ ­ b‡cl{f`a}B{®c„{prz Å }BamkPpdzƒ¡azcº^€c&’fu¶ ‘privkqszprfBs^`bjm„f2¡kq_Qc„prfBsÀf`gcl{k
f`m„pr}`prs4^`bE‘4^ucl^z„kQcqެpdc_QbrkD^um„bdeµprs‘pr_q^uclkQzMcl{kc&eEjpd_D^`b4”¬prs‘vfug9jmfB¿bdkqi c„{4^ucc„{kx^`ac„fw^`z¶
¾ƒ{k±m„kQ_qfBszclma_Qc„prfBsÖkQm„mfBmo_QfBm„mkqz„jKfBs‘zclf ( ¼ ( ½ DŽK’x{kqmk
pdzµc„{kPg~as_“clpdfBs,privjbdkqivkqswclkQ‘À¿weÀc„{kY^`ac„fw^`zz„fE_qp^\clfBmµ^`s!‘ ( ^`s‘ +¼ ( ½
mkqjmkqzkqswcopdsjacaspdc P^us‘€f`acljacxaspdc ?f`gFc„{kÊskQc&’fBm”KŽ=mkqz„jKkq_“clp‡†Bkqb‡eBœ
hbrazclkqmzfugFg~k“’kQmc„{4^`sYcl{mkqkÉjIf`prswclzQŽ{f™’k“†BkQmqŽ=’kQm„kÉpr}Bsf`m„kq‘9œ
03 *
zf_Qp^uc„fBm{4^`zÊclf€‘kD^ub!’xp‡cl{ v̺ÍEÎÐÏ[ÑÓÒ&Ì `ÎÐÑÓÏ uœvÆÀkv_|{fBzkY^‰z„privjbdk±c&’fu¶ ‘privkqsz„prf`s4^`b
^u¿zc„ml^`_“clprf`s®f`gcl{k?i±abdclp ¶&ivf‘^`brp‡c&eYjm„f`¿brkQi g~fBmÊ¿IkQs_|{i?^`m„”¬pds}€jam„jKfBz„kQz¦^us‘®kͬ¶
jb^`pdsprs}ºc„{kµ_q^`j4^`¿prbrp‡clpdkqzƒf`g!^uaclfw^uz„z„fE_qpr^uclf`m„zqœ¾ƒ{przo^`mc„p Å _Qp^`bđfBiP^uprs/przprbrbdazc„ml^uc„kq‘
pdsÀ]Fpr}BamkY˜¬¼6_ ½ ^`s‘À_QfBszprzc„zµfugg~fBamÊ_QfBs_qkQjcla^`b!‘4^uc|^‰_qbdazc„kqmzɒxp‡cl{°i?kq^`szÉm„kqjm„k“¶
zkqswclkQ‘$¿weY¿br^`_|”Pc„m„p^us}BbrkQzƒ^`s‘‰spdsk_qf`aswclkqm¶&_QfBs_qkQjcla^`bF‘^uc|^º_qbdazc„kqmzx’xp‡cl{‰ivkD^`sz
mkqjmkqzkqswclkQ‘²¿weH’x{pdc„kÖ_qpdm„_qbdkqzQœ &sÇi?fBmk֑kQcl^`prb[Žƒcl{k¯_qf`s_qkQjcla4^ub_qbrazclkQm„z/^`mkÖbrfu¶
_q^uclkQ‘›^ucMjKfBpds¬c„zƒ¼ š š ½ 2¼ š ½ 2¼ š ½ ^`s‘/¼ ½ Ž`mkqzjIkQ_Qclp‡†BkQbdeBŽB’x{prbrk!cl{k_qfBas¬c„kqm¶
_QfBs_Qkqjc„a4^`b'_qbrazclkQm„z^`m„kÉbrfE_D^\clkq‘/^ucjKfBprswclzµ¼ d˜ d˜ ½ Ž'¼ ‡˜ ½ Ž'¼ š ½ Ž'¼ š ½ Ž'¼ ½ Ž
¼ ½ ŽF¼ ½ ޼ ‡˜ ½ ^`s‘¸¼ ½ Ž=m„kQz„jKkq_Qc„pd†`kqbde`œ !^`_|{W_QbrazclkQmoprz_qf`i?jKfBz„kQ‘Wf`g u–
jKfBpds¬c„zFsfBm„i?^`brb‡eo‘przc„m„pd¿aclkQ‘±^`mfBas‘Écl{kQz„ki?kq^`szF^`s‘¦’xp‡cl{ʆ`^um„p^us_qk , –˜BœF¾ƒ{k
_QfBaswclkQm¶ _qfBs_Qkqjc„a4^`b!_qbdazc„kqmzµ^um„k±g~amcl{kQmɑpd†Epr‘kQ‘¯prswclfYpds¬c„kqms4^`b^`s‘®kÍc„kqms4^`b_qbdaz¶
c„kqmzqœ &swclkQm„s4^`b'_qf`aswclkqm¶&_QfBs_qkQjcla^`b_Qbrazclkqmz_QfBm„mkqzjIfBs‘$clfvcl{kÉ_qfBas¬c„kqm¶&_qf`s_qkQjcla4^ub
‘^uc|^oc„{4^uc^`mkƒbrfE_D^uc„kq‘±pdsz„pd‘kcl{kƒ_QfBsw†BkÍv{Eabrb‘k Å skQ‘?¿we±c„{kƒ_qf`s_qkQjcla4^ub4‘4^uc|^’x{pdbrk
kÍEclkqms4^`b'_qfBas¬c„kqm¶&_qf`s_qkQjcla4^ub_qbdazc„kqmz_QfBm„mkqz„jKfBs‘€clf?c„{kÉ_qfBaswc„kqm¶ _qfBs_qkqjcla4^`bF‘4^ucl^
bdf_q^uclkQ‘‰fBaclzpr‘kc„{przƒ_QfBsw†BkÍ${¬abdb œ
!1 5
5 5 5 5
1.0
0.0
0.2
Feature # 2
0.8
Principal Component # 2
Principal Component # 2
.
@
]Fpr}Bamk˘ ¾'ml^usz„p‡clprf`s$g~m„fBi cl{kºzfBs4^`m‘kQclkQ_Qc„prfBs¯‘fBi?^`pds$clfYcl{k›^`mc„p Å _Qp^`b'sfBs¶
bdprskq^`m‘f`iP^`pdsĜ
0.0
Principal Component # 1
Principal Component # 1
0.2
0.4
0.6
0.8
Feature # 1
1.0
" '= F Œ ¾ƒ{k Å mzck“jKkqmprivkqswcƒ’kÉ_qf`s‘a_“clkq‘€_qfBsz„przclkQ‘$f`gF_qfBivj4^`mprs}±c„{kÊ_qbr^`z„zp Å _q^uclpdfBs‰^`_“¶
_Qaml^u_Qe?f`gŒcl{kg~fBamzeEzc„kqivzƒfBsPcl{kclkQzcƒ‘fBiP^uprsvf`g']pr}`am„kɘ¬¼6_ ½ œ ­ gÓclkqm{4^D†Eprs}±¿KkqkQs
c„askQ‘vc„fÊc„{kqpdmfBjc„pri?^`bzkQcclprs}BzqŽBc„{kƒg~fBam‘k“†pd_qkQz!’kqmkc„ml^`pdskq‘›fBs›_QfBs_qkQjcla^`b4‘4^ucl^
^us‘Ö^vc„{m„kQz„{f`br‘$’^`zokQzcl^`¿brpdz„{kQ‘W¿we Å c„c„prs}vcl{kµm„kq_QfBszclm„a_QclpdfBsWkQm„m„f`mofB¿cl^`prskq‘$f`s
^u‘‘pdc„prfBs^`b4_qfBs_qkqjcla4^`bI‘4^ucl^µclf¦^ É^uaz„zp^`sP^`s‘ËzkQc„c„prs}±^¦¿If`as‘4^`mev_qfBmm„kqzjIf`s‘prs}
c„fP^ºjmk“¶ z„jKkq_qp Å kq‘€_qfBs Å ‘kqs_qk¦pdswclkqm†u^`b œna¿z„kq¹¬akQswclbde`ŽKc„{kÉzeEzc„kqivz’kqmkµclkQzc„kq‘$f`s
^±c„kqzc„prs}vz„k“c_qfBswc|^uprspds}º¿Ifucl{‰prszc|^`s_qkqz^`s‘‰_QfBaswclkQm¶&pdszcl^`s_Qkqzf`gFc„{kÊ_qfBs_qkqjcDœ
FZ G'5[G Ö0217Y756@B7EJ ¾ƒ{ksEai±¿IkQmf`g{pd‘‘kQsYaspdc„zazkq‘‰¿we?c„{ksfBsbdprskq^`m_qfBs¶
skq_Qc„prfBsprzcPzeEzc„kqivzY’^`zY‘kQclkQm„ivprskQ‘»¿weHm„assprs},kD^`_|{Çsk“c&’f`m„” ’xp‡cl{²˜BŽošŽ Ž Ž
˜ Ž BšŽ^us‘ {pr‘‘kQsUaspdc„zºfBs Å †Bk/_qm„f`z„z¶ †u^`brpd‘4^uclpdfBs,zkQclzv_qf`s¬cl^`prsprs}®š WjKfBprswclz
jKkqm_qbrazclkQmqœ c’^`zƒ_qf`s_qbda‘kq‘Yc„{4^ucƒpdsËfBm„‘kqmc„fºm„kD^u_|{€^±}`ffE‘Ë_qbr^`z„zp Å _q^uclpdfBsËjKkqmg~fBm¶
i?^`s_Qk`Ž\cl{kc&’fsf`sbrpdskD^`m'^`aclfw^`zz„fE_qpr^uclfBmzF{^`‘µc„f¿Ikclm„^`prskQ‘µ’xp‡cl{P˜ {pd‘‘kqs¦aspdc„zqœ
cʒ^`zµ^`brzf/z{f™’xsÀcl{^ucÊcl{k›sk“c&’fBm”¬z±{4^`‘°_qfBsw†`kqm„}`kq‘,¿we jIfE_|{+šu–B–B–Ë’x{pr_|{°’^uz
c„{¬az±z„kQbrkQ_QclkQ‘¸^`z±^€zclf`jjprs}WjIf`prswcDœ jclpdi?pdžD^uc„prfBsόpds®c„{przµk“jIkQm„pdi?kQs¬cqŽ’^`z±jKkqm¶
g~f`m„ivkq‘+azprs}Öcl{k/¿^`_|”¬jm„fBj^`}w^uc„prfBs+jmf_Qkq‘am„k‰’xpdcl{+zc|^`s‘4^`m„‘·brkq^`m„sprs}Öm„^uclk‰^`s‘
ivfBivkqswclai f`gʖœ£– ®^us‘H–œ ސmkqzjIkQ_Qclp‡†BkQbdeBœ³]4fBmvyh ­ Žzprs_Qk€cl{k/c„kqzcP‘fBi?^`prs·prz
c&’fu¶ ‘privkqszprfBs^`b ŽŒfBsbde¯fBskvfBmÊc&’f$jm„pds_qpdj4^`bM_QfBi?jKfBskQswclz¦_QfBabd‘À¿Kk?azkq‘Äœ cɒ^uz
‘kQclkQm„ivprskQ‘Pcl{^ucf`skojmprs_Qprj4^ubK_QfBivjIfBskqswceEprkQbr‘z^¦¿KkQcclkqm_qbr^`z„zp Å _q^uclpdfBs?m„^uclkcl{4^us
c&’fŽ^`s‘ÄŽEcl{kQm„kQg~f`m„k`ŽEcl{koyh ­ k“jKkqmprivkqswc’^`z_QfBs‘a_“clkQ‘Yaz„pds}º^µzprs}`brkjm„pds_qpdj4^`b
_QfBivjIfBskqswcDœ pdskD^umF^uaclfw^uz„z„fE_qpr^uclpdfBsÉjIkQmg~fBmi?kQ‘¦¿KkQc„c„kqm^`z'’kqbdbE’xp‡cl{¦^z„pds}Bbdk{pd‘‘kQs
aspdcÊcl{^`s®’xp‡cl{¯c&’fWf`mÉivfBmk # c„{kqmkQg~fBmk`ŽFpdcʒ^uz¦^`bdz„f‰clkQzclkQ‘À’xpdc„{À^/z„pds}Bbrk›{pd‘‘kQs
aspdcqœY¾ƒ{kPzclfBjjprs}€_qm„p‡clkQm„prf`sĎFbdkD^`msprs}/m„^uclkP^`s‘®i?fBivkqswc„ai az„kQ‘,¿we®c„{kvbrprskD^`m
^uaclfw^uz„z„fE_qpr^uclf`mM’kQm„kxcl{kzl^`ivk^`zcl{f`z„kaz„kQ‘P¿weºcl{ksfBsbrprskD^`m‘k“†Epr_qkQzqœ &svcl{kƒg~fBam
zeEzclkQi?zQŽ4cl{kcl{m„kqz{fBbd‘/’^`zxz„k“cozf?^uzxc„fv^`brbdf2’Çg~fBmx^ w— _qfBs Å ‘kqs_qkÉprswclkQm†u^`b œ
-) '.
)
-)
5
˜D–
30
10
20
Pos Misclass
Neg Misclass
0
Average Percent Error
40
Average Percent Error
Over Five Trials
PCA
L-L
NL-L NL-NL
F] pr}Bamkš Fhb^`zz„p Å _D^uc„prfBs m„mfBmF^uc„k!f`gc„{kg~f`am_qb^uz„z„p Å _D^\clprf`sÉz_|{kqivkqzQœ!yFfBzpdc„pd†Bk
ivprz_qbr^`z„zp Å _q^uclpdfBsºml^uc„kqz^`mkpds‘pd_D^uc„kq‘vprs›}Bml^Deº’x{pdbrkƒskQ}w^uc„pd†BkxfBskqz^`m„kprs‘pr_D^\clkq‘
pds‰¿b^`_|”=œ
TY@[email protected]@ P.0™7EJ ¾ƒ{km„kQz„ab‡clz’kfB¿c|^`pdskq‘?prsPc„{przk“jKkqm„pdi?kQswcƒ^`mkojmkqz„kQswclkq‘/prs
]Fpr}Bamk›šœÉ¾ƒ{prz Å }Bam„kºjbrf`c„zcl{k›^D†BkQml^`}`kv_Qb^`zz„p Å _D^uc„prfBs$kqm„mfBmm„^uclkQzÉf™†`kqm Å †`k›c„m„pr^`brz
f`¿c|^`pdskq‘U¿we·c„{k€g~f`am?zeEzclkQi?z?fBs c„{k/c„kqzcˑfBi?^`pdsUf`g]pr}Bam„k¯˜¬¼6_ ½ œÇ¾ƒ{k€}Bml^`j{
z{f™’xzcl{4^ucyh ­ ^us‘ 9¶"¸fB¿c|^uprskQ‘$†BkQmeÖbr^`m„}Bkµ_qbr^`z„zp Å _q^uclpdfBsWkqmm„fBmoml^uc„kqzo’x{kQm„kq^`z
c„{k±c&’f€sf`sbrpdskD^`mo^`ac„fw^`z„zf_Qp^uc„fBm„zofB¿c|^uprskQ‘Öbrf™’ kqm„mfBmml^\clkqzQœ¦¾ƒ{pdz‘kqivfBszclm„^uclkQz
c„{4^ucY’x{pdbrk¯yh ­ ^`s‘9¶" _q^`sÇclkq_|{spr_q^`brb‡eH¿Kk°az„kq‘g~fBmY_qbr^`z„zp Å _q^uclpdfBsĎxcl{k“e^`m„k
sf`c‰cl{4^uc/azkQg~abÉfBsÇcl{k°jmfB¿brkQi f`g±]pr}Bam„k+˜¬¼~_ ½ ’x{kqmkD^`z€¿If`c„{³‹9¶" ^`s‘³‹Ä¶
‹ eEpdkqbr‘H^`_q_Qkqjcl^`¿brkÖ_Qb^`zz„p Å _D^uc„prfBsUml^uc„kqzYfBsHc„{4^ucYjm„fB¿bdkqi/œ ¾ƒ{pdzËm„kQz„ab‡cDŽxcl{¬azqŽ
­ zY^°iP^ucclkQm?f`gg6^u_QcDŽƒsfBsbrpdskD^um?^uaclfw^uz„z„fE_qpr^uclpdfBs¶ ¿4^`z„kQ‘U_Qb^`zz„p Å _D^uc„prfBs·’^uz
jm„kQ†EpdfBaz„b‡evaz„kQ‘/pdsPjm„^`_Qc„pr_q^`bIzkQcclprs}Bzpds¬†`fBbd†Epds}ºhˆƒ¶ ¦{kqbrpd_qfBjclkqm}Bkq^`m„¿KfDY^`s‘
ivf`c„fBmµivfBsp‡clfBmprs}À¼ •B^`j”uf™’xpr_qžYÕ“Ï `Î r˜ Ž yFk“clz_|{k€Õ“Ï `Î r˜ ½ ^`s‘,eEprkQbr‘kQ‘
^u_q_qaml^uc„kÉmkqzabdc„zqœ
'
( ˜`˜
)
'
( )
_QfBs Å mi?zƒc„{4^ucxcl{kQm„kÉ_D^`s/¿Kk¦^º‘p‡Á9kQm„kqs_qkÉprs‰cl{kÊ_qf`i?jac|^uc„prfBszƒjKkqmg~fBm„ivkq‘/¿we/yh ­
¼~fBmŒbrpdskD^umÄ^`ac„fw^`zz„fE_qp^\clprf`s ½ ^`s‘µsf`sbrpdskD^`mÄ^`aclfB^`z„zf_Qp^uc„prfBsĎD^`s‘cl{4^\cŒcl{pdzŒ‘pdÁIkqmkqs_Qk
{^`zjm„^`_Qc„pr_D^ubI_QfBsz„kQ¹¬akqs_Qkqzƒg~fBmcl{kocl^`z„”vf`g_Qb^`zz„p Å _D^uc„prfBsĜ &sYfBm„‘kqmc„fº^`s4^`b‡eEžqkc„{prz
‘pdÁIkqm„kQs_qkvprs¯ivfBm„kº‘kqjc„{ĎF’k?_QfBs‘a_QclkQ‘®c„{k?kÍjIkQm„privkqswc„zµjmkqzkqswclkQ‘,prsÖcl{k?skÍEc
zkq_“clprf`sĜ
" '= F Œ ¾ƒ{kPk“jKkqmprivkqswclzɑkqz_qmpr¿Kkq‘Àpds°c„{przÉz„kQ_Qc„prfBs®z„kqkQ”Öclf/k“jb^uprs¯cl{kvm„kQz„ab‡clzÉfB¿c|^uprskQ‘
pdsvc„{kjm„k“†pdfBazz„k“cf`g9k“jIkQm„pdi?kQs¬c„z¿wev_qf`i?jaclprs}¦^`s‘?jbdf`c„c„prs}c„{kmkq_QfBszc„m„a_“clpdfBs
kQm„mfBm?zamg6^u_qkqzP_qfBszclma_Qc„kq‘Ç¿we yh ­ ^us‘Uc„{k€c„{m„kQkW_qfBsskq_“clprf`sprzcPzezclkQi?zY^\gÓclkqm
¿Kkqpds}±clm„^`prskq‘YfBsYcl{kÉ_QfBs_Qkqjc„a4^`bŒ‘4^ucl^‰¼6p[œ£kuœdŽc„{k‘4^ucl^ºz„aiviP^um„pržQkq‘Ë¿weY¿b^`_|”vclm„pr^`s¶
}`brkqzÉprsÀ]pr}`am„k‰˜¬¼~_ ½„½ œ &s,f`cl{kqmʒfBm‘zqŽM’kË^um„kPpdswclkqmkqzclkq‘Àprs Å s‘prs}$fBacµ{f™’ cl{k
pdswclkqmjIf`b^uc„prfBs›zc„ml^uc„kq}`evazkq‘Y¿we›cl{k†u^`m„pdfBaz‘kQ†Epr_Qkqz_QfBszpr‘kQm„kq‘Pprs?c„{przzc„a‘e?‘pdÁIkqm
g~mfBi)f`skÉ^`sf`c„{kqmQœ
FZ G'5[G Ë0217 ‰756@B7EJ ÆÇpdcl{prs¦c„{kƒ_qfBswc„k“Ec!f`g jKkqmprivkqswcnk“c šEŽ`c&’fʑp‡Á9kQm„kQs¬c
{pr‘‘kQs€aspdcxzkQc„c„prs}`zx’kqmkÉc„kqzclkq‘ ÊÕ Ô “Ñ v^`s‘ \Ì Ô lÕ “Ñ 4œM¾ƒ{pdzx’^`zx‘fBskµzf
^uzclf Å s‘/f`ac’x{k“cl{kQmf`msf`cc„{kzeEzclkqivzxfBjKkqml^\clk¹¬a4^`bdpdcl^uclp‡†Bkqb‡e›‘pdÁIkqmkqswclb‡eP’x{kQs
az„kq‘vprz!^sf`s¶&¿Kf`c„c„brkQskq_|”±f`mprs›^¿Ifuc„clbdkqskQ_|”¦g6^`z{prfBs9œ &s›cl{kƒkÍj^`sz„pdfBsvz„kQcclpds}ŽBcl{k
z„^`ivk€˜ ‰{pd‘‘kqsÀaspdcÉzkQc„c„prs}/’^uz¦azkq‘Àg~fBmÊcl{k?sf`sbrpdskD^`mÊzezclkQi?zº^uzÉc„{fBz„k?az„kQ‘
pds cl{k Å m„zcYk“jKkqm„pdi?kQswcY’x{prbdkWyh ­ ^`s‘Hc„{kÖbrpdskD^`m?^`ac„fw^`zz„fE_qp^\clfBmv’kQm„kÖclkQzclkQ‘
’xp‡cl{¸c&’f®jm„pds_qpdj4^`b_QfBivjIfBskqswclz›fBm›{pd‘‘kqs·asp‡clzQœ &sUf`cl{kQmº’fBm‘zqŽcl{k/fBjc„pri?^`b
sfBs¶&¿Kf`cclbrkQskq_|”»zkQcclprs}·g~fBmYc„{k®sfBsbrpdskD^umËzeEzc„kqivz€’kqmkÀ_qf`i?j4^um„kq‘Çclf¸cl{k®fBsbde
sfBs¶&¿Kf`cclbrkQskq_|”¦z„kQcclpds}ÊjIfBzz„pd¿brkg~fBmc„{kxbrprskD^`mMzeEzclkQi?zQœ ­ bdbcl{kxf`c„{kqm!j4^uml^`ivkQc„kqm„z
mkqi?^`prskq‘ºcl{kzl^ui?k^`zprs jIkQm„privkqswcnk“c )˜BެkÍ_Qkqjcg~fBmcl{kbdkD^`msprs}m„^uclkf`g 9¶"
‹f`c„kPcl{4^\c¦g~fBmÉcl{k?brprskD^`mµ^`ac„fw^`z„zf_Qp^uc„fBmqŽF{pr‘‘kqs,br^DeBkqmz±}BmkD^uc„kqm¦c„{4^`sÀc&’f
^um„kÉ^`_Qc„a4^`bdbde?jIfBzz„pd¿brkuŽ¿acxcl{kQe‰^`mkÊkq¹¬apd†u^`bdkqswcƒclf›{pd‘‘kQs€br^™e`kqmzfugzpržqkc&’fœ
)
˜™š
’x{pr_|{Y{4^`‘?clf±¿Kkopds_qmkD^`zkq‘Ëg~m„f`i –œ– clfº–œd˜og~f`mg~abdbI_QfBsw†BkQm„}BkQs_qkc„f¦c|^`”ukjbr^`_qkuœ &s
c„{k¦_QfBivjm„kQz„z„pdfBsWzkQc„c„prs}ŽIcl{k¦s¬ai±¿Kkqmfugjm„pds_qpdj4^`b_qf`i?jKfBskQs¬c„z^`s‘${pr‘‘kqsWaspdclz
’kqmkºm„kQzclmpr_“clkq‘€clfËfBsk¦g~fBm^`brbcl{kµzeEzc„kqivzz„pds_qk±p‡copdzc„{k¦fBsbde/¿Ifuc„clbdkqskQ_|”€zkQcclprs}
^D†u^`pdb^`¿bdkM}Bp‡†BkqsÊcl{^uccl{k!clkQzcF‘fBi?^`prspdzc&’fu¶ ‘privkqszprfBs^`b œ ­ brbBcl{kfucl{kQmFj4^uml^`ivkQc„kqm„z
mkqi?^`prskq‘Ycl{kÊz„^`i?kÊ^uzpds MjKkqmprivkqswc ˜Bœ
Œ:F.GFJD5~<KG P7JqZF3Ó02J ¾ƒ{kvm„kqzabdc„zµ’k?f`¿c|^`pdskq‘®az„pds}‰cl{kvk“j4^`sz„prf`s,z„k“c„clpds}/f`g
jKkqm„pdi?kQswc±nEkQc šY^`m„k›jmkqzkqswclkQ‘Àprs°]pd}Bamk Y’x{pr_|{°‘przjb^DeEz \¶t jbdf`clzf`gcl{k
kQm„mfBmml^\clprf?z„amg6^`_qkQz_qfBszclma_Qc„kq‘¯¿we֋͏^`s‘¯‹%9¶&‹%Ž9mkqz„jKkq_“clp‡†Bkqb‡eBœÊ¾ƒ{k±mkqzabdc„z
g~f`m¦yh ­ ^us‘Àbdprskq^`mÊ^`ac„fw^`z„zf_Qp^uc„prfBs°^`mkPsfuc¦‘pdz„jbr^DeBkq‘®z„pds_qkvcl{k“e®kÍ{pr¿p‡cµ^/È=^uc
mkq_QfBszc„m„a_“clpdfBs€kQm„mfBmƒz„amg6^`_qkuœ &s/c„{kÊ}Bml^`j{zƒf`g]pr}Bam„k 4¼6^ ½ ^`s‘À¼6¿ ½ Žc„{kÊjbrf`c„zx^`m„k
.
.
/.
.
]Fpr}Bamk »xkq_qf`szc„m„a_“clprf`s²kqmm„fBmz€f`gº‹%9¶" ¼6]pr}Bam„kU¼[^ ½½ ŽÊ^`s‘‹%9¶‹ [¼ ]pd}u¶
a m„k$¼6¿ ½½ ’xp‡cl{·˜ ‰{pr‘‘kqsÀaspdc„zÉf`s®cl{kP^`mclp Å _qpr^`b‘f`iP^`pds¯}BkqskQml^uc„kq‘Àg~mfBi ] pd}u¶
am„k›˜¬¼6_ ½ œ
‘ml^D’xsP^ubrfBs}cl{k¬¶|ŽBew¶|ެ^us‘?žÃ¶^\kQz!’x{kqm„k±_qfBmm„kqzjIf`s‘z!clfcl{k¬¶&^\przf`gKcl{kƒpdsjac
‘fBiP^uprsĎe`Ž4clfvpdclzew¶&^\prz^`s‘€žµpdzcl{kÉkqmm„fBmxml^\clprfv^uck“†Bkqme/jIfBpdswc_QfBszpr‘kQm„kq‘€prsYcl{k
zj4^`_Qkµza_|{€c„{4^uc
˜
¼˜ ½
¼ ( ½ , ¼„¼º¼+( ½ ( ½ ³¼
±¼ ½ ½ ½
&s‰cl{kµ^u¿If™†Bkg~fBmi±abr^Ž (W^`s‘ Ëm„kQjm„kQz„kqswccl{kc&’fP‘pdi?kQsz„pdfBszƒf`gFkD^u_|{€‘4^\c|^›jIfBpdswcDŽ
±¼ ½ przµc„{kPg~as_QclpdfBs,mkD^`bdpržqkQ‘,¿we®c„{kPc„ml^`pdskq‘+^uaclfw^uz„z„fE_qpr^uclf`m„zqŽM^`s‘ prz¦^$i?fE‘kQb‡¶
˜
.
)
-
-.
‘kqjKkqs‘kQswcYz„_q^`brk‰g6^`_Qc„fBmvaz„kQ‘ g~fBmvjbrf`cclpds}¯jam„jKfBzkqzqœÇ¾ƒ{k$jbrf`c„z›f`gÊ]pd}Bam„kQz 4¼[^ ½
^us‘´¼6¿ ½ ^`mkYj4^`mclpr_Qab^um„bde¯{kqbrjg~abg~fBm±as‘kqmzcl^`s‘pds}°c„{kYs4^uc„am„kYfugc„{k‰z„fBbdaclpdfBsz
_QfBivjaclkQ‘?¿weºc„{ksfBsbrpdskD^um^`ac„fw^`z„zf_Qp^uc„fBm„z!^us‘P_QfBswclml^uzclpds}cl{kQi clfÊcl{kxzfBbrac„prfBs
f`¿c|^`pdskq‘°¿we¯cl{kvbrpdskD^`mÉ^`aclfw^`zz„fE_qpr^uclfBmÊ^us‘,yh ­ œ &sÀj^`mc„pr_qab^`mQŽc„{kQe°z{f™’ cl{4^uc
c„{kqzk¦kQm„m„f`mzamg6^u_qkqzo^`m„kɹ¬a4^`bdpdc|^\clpd†`kqb‡eP‘p‡Á9kQm„kQs¬cg~m„f`i)cl{kÉfBskQzo_QfBi?jaclkQ‘€¿we€yh ­
^us‘·c„{k/brprskD^`m›^`aclfw^`zz„fE_qpr^uclfBmºzprs_Qk`Ž’x{prbrkYc„{k‰sfBsbdprskq^`m›^`ac„fw^`z„zf_Qp^uc„fBm„z›¿aprbr‘
i¦abdc„prjbdk“¶&bdf_q^`b‡¶ †u^`bdb‡kQem„kqjm„kqzkqswc|^\clprf`szf`gIcl{kxas‘kqmbdeEprs}ɑfBi?^`pds/¼[]pd}Bam„kQz 4¼[^ ½ ^`s‘
¼~¿ ½„½ Žyh ­ ^`s‘,c„{kËbdprskq^`mÉ^`aclfB^`z„zf_Qp^uc„fBmµbdkD^`ms,{f™’ clfWmkq_QfBszc„m„a_“cºcl{k?‘fBi?^`prs
jKkqmg~kq_“clbde/^us‘$kÍ{pr¿p‡co^›È=^ucm„kQ_qfBszclma_Qc„prfBs$kqm„mfBmxz„amg6^`_qkuœƒ¾ƒ{przz„a}B}Bkqzclzoc„{4^ucxcl{k
zfBbraclprf`sz_QfBivjaclkQ‘W¿we€^`aclfB^`z„zf_Qp^uc„fBm„zx’xpdc„{$sfBsbrprskD^`mpdclpdkqzxprs/cl{kQprm{pr‘‘kqsWbr^DeBkqm
az„kv^Ö̺ÍÎÐÏ6ÑÓÒ&Ì `ÎÑ 4Ï&Õ Ô \Î `Ï[Ñ qÑ o’x{pd_|{¯przsf`cÊaz„kq‘°¿weWcl{kvbdprskq^`moivkQc„{fE‘zqœ
amvm„kQz„ab‡clz?f`g]pd}Bamk °_D^`sU¿Ik€az„kQ‘ clf®k“jb^uprs¸cl{k€sfBsbdprskq^`mv^`aclfB^`z„zf_Qp^uc„fBm„z
¼6‹%9¶"·^`s‘¯‹9¶‹% ½ mkqzabdc„zf`g]pr}`am„k±š?’x{pr_|{¯z„{f2’ cl{^ucsfBsbrprskD^`mo^`aclfB^`z„zf_Qp^\¶
­ zkÍjIkQ_QclkQ‘Ëg~m„fBi А^`bd‘pŒ^`s‘$ˆfBm„spd”=˜ ŽEfBamm„kQz„ab‡clzc„{¬azz{f™’»cl{4^uccl{k
bdprskq^`m^`aclfw^`zz„fE_qpr^uclfBmoprz_q^`j4^`¿bdkºf`gkqi±abr^uclpds}Yyh ­ œ'‹f`clkuŽŒ{f™’k“†BkqmQŽFc„{4^ucDŽ'^`z
ivkqswc„prfBskQ‘$pds$cl{kÉclkÍcqŽ9pds$fBm‘kqmg~fBmc„{kµc&’fYj4^`m„^`‘pr}`i?zƒclfP¿Ikµkq¹¬apd†u^`bdkqswcDŽ=cl{k
bdprskq^`m!^`ac„fw^`zz„fE_qp^\clfBm{4^u‘?clfÉ¿Kkxc„ml^`pdskq‘›’xpdc„{P^Ébrkq^`m„spds}ml^\clkf`gŒ–œ‡˜¦¼6prszclkq^`‘vf`g
c„{k±bdkD^`msprs}vml^\clk¦fug–œ– ?az„kQ‘Ö¿we$cl{k¦sfBsbrprskD^`mzeEzc„kqivz ½ œ &sWcl{kµ_D^`zk±’x{kqmk
^°brkq^`m„spds}°ml^uc„k$f`gʖœ– ֒^uzËaz„kQ‘ÄŽcl{k$brpdskD^um?^uaclfw^uz„z„fE_qpr^uclf`m?}BfucPzcla_|”·prs ^
z„^`‘‘bdk‰jIfBpdswc/¼6zkqk А^ubr‘pŒ^us‘$ˆfBm„spr”=˜ ½ ^us‘UmkQc„am„skQ‘H^Ö_qf`szcl^`swcPfBacljac
_QfBm„mkqzjIfBs‘prs}Öc„f¯c„{kYivkD^`s¸f`gxcl{k‰g~f`am¦clm„^`prsprs}W_QbrazclkQm„zqœ+¾ƒ{przºfB¿zkqm†`^\clprf`s
pdz±prswc„kqm„kQzc„prs}Öpds+pdclzµf™’xs·mpr}B{wcº¿Kkq_q^`azk/p‡c±as‘kqmbrprskqz±cl{kY‘pdÁIkqmkqs_QkY¿Ik“c&’kQkqs
bdprskq^`m^`s‘?sfBsbdprskq^`m^`aclfB^`z„zf_Qp^uc„fBm„zkQ†`kqsYjmprfBm!clfÉcl{kbrprskD^`m!^`aclfw^`zz„fE_qpr^uclfBm £z
g~abrb!_qfBsw†`kqm„}`kqs_Qk`œ &s‘kQkq‘ÄŽ!pdcµz„a}B}Bkqzclz±c„{4^uc¦c„{kPbdprskq^`mµ^`aclfB^`z„zf_Qp^uc„fBmÉcl^`_|”¬brkQz
c„{kmkq_qf`szc„m„a_“clprf`sºjm„fB¿brkqi `Î `ÎÓÎ \Ž`azprs}Ê^¦Í 4ÑÓÒ&Ì `Ι¿pr^`zqŽ`’x{kqm„kq^`zMcl{ksfBs¶
bdprskq^`mƒ^`aclfw^`zz„fE_qpr^uclfBmzƒaz„k›Î `ÎEzc„ml^uc„kq}Bpdkqzx_|{4^`m„^`_Qc„kqm„pdžqkQ‘€¿weYcl{kqprm̺ÍEÎÐÏ6ÑÓÒ&Ì `Î
pdswclkqmjIf`b^uc„prfBsË¿p^`zkqzqœ
˜
.
.
!1 0
.
2
!1 !1 c„fBm„zM^`m„kƒ_q^`j4^`¿bdkf`gK_qbr^`z„zpdgÓeEprs}ocl{kƒsfBsbrpdskD^um„bdeÉzkqj4^`m„^`¿bdkƒ^`s‘›i±ab‡clp ¶&ivf‘4^ubB‘fBi?^`prs
fug]pd}Bamk˘¬¼6_ ½ œ &s‘kqkQ‘ÄŽz„prs_qkºcl{kºmkq_QfBszc„m„a_“clpdfBs®kQm„mfBmz„amg6^`_qkQzÊf`gc„{kºsfBsbrprskD^`m
^uaclfw^uz„z„fE_qpr^uclf`m„zMpds_qbda‘kƒz„k“†BkQml^`b=brfE_D^ub†u^`brbdkQeEz_qkQswclkqmkq‘P^uc!kD^`_|{?f`gKcl{kƒjKfBz„p‡clp‡†Bkƒ_qbdaz¶
c„kqmzº¼[]Fpr}Bamkqz 4¼[^ ½ ^`s‘+¼6¿ ½½ Ž=cl{kµkqm„mfBmom„^uclpdfBzf`gMcl{k¦_qf`aswclkqm¶&_QfBs_qkQjcla^`bM‘4^ucl^?_q^`s
^ubrbK¿Ik^ujjm„f`jm„pr^uclkQbdev{pr}`{Ëm„kQb^uc„pd†Bkclf±c„{kqpdm_qf`s_qkQjcla4^ubÄ_qfBas¬c„kqmj4^`mc„z’x{kQc„{kqmƒc„{kQe
^um„kbrfE_D^uc„kq‘vprs›cl{kprswclkQm„pdfBmqŽwcl{kzpr‘kQzqŽEfBmc„{kk“EclkQm„prf`mf`gIcl{kz„¹¬a4^`mkoas‘kqmbdeEprs}Êcl{k
_QfBs_Qkqjc„a4^`b9_QfBivjIfBskqswclzQœ¾ƒ{Eazx^`brb4cl{ko_qf`aswclkqm¶&_QfBs_qkQjcla^`bđ4^ucl^µ}Bk“cƒ^`jjm„fBjm„p^\clkqb‡e
‘pdÁIkqm„kQswclp^\clkq‘?’xpdcl{YmkqzjIkQ_Qcƒclf±c„{k_QfBs_qkQjcla^`bđ4^ucl^œ¾ƒ{k_Qb^`zz„p Å _D^uc„prfBs?m„kqzabdc„zfB¿¶
cl^`prskq‘¯¿we¯yh ­ ^us‘¯brprskD^`mo^`aclfB^`z„zf_Qp^uc„prfBsÖpds¯]pr}Bam„k›šP’xprbdb¿Kkºk“jbr^`prskQ‘¯prsWcl{k
sk“Ecj4^`ml^u}Bml^`j{/zprs_Qkcl{k“eY’kQm„kÉfB¿c|^uprskQ‘‰’xp‡cl{‰¿Kf`c„c„brkqskq_|”Ë‘k“†Epr_qkQzqœ
.
< À:'S27JqJD56<KG Ë7EJDZ'3Ó02J ¾ƒ{k¯m„kQz„ab‡clzYfB¿cl^`prskq‘»prsHc„{kÖjmkQ†EprfBazYz„kQc‰fugµkÍjIkQm„p‡¶
ivkqswc„z¦‘kQi?fBszclm„^uclkvcl{4^\c±sfBsbrprskD^`mÉ^`ac„fw^`zz„fE_qp^\clfBmz±^`mk?sfuc±kq¹¬ap‡†u^`brkQs¬cµclf€brprskD^`m
^uaclfw^uz„z„fE_qpr^uclf`m„zfBmÊyh ­ prsÖcl{kv_q^`z„kº’x{kQm„k›cl{kºs¬ai¦¿IkQmÉfug{pd‘‘kQs®aspdclzkÍ_qkqkQ‘z
c„{ksEai±¿IkQmfugÄprsjacasp‡clzqެfBm’x{kQsPcl{ks¬ai±¿Kkqmf`g9jm„pds_qpdj4^`b_QfBi?jKfBskQswclzprz!kq¹¬a4^`b
c„fcl{k‘fBi?^`prs±‘privkqszprfBs4^ubrpdc&e`œ ­ ac„fw^`zz„fE_qp^\clfBmzqŽB{f™’kQ†`kqmqŽ^`mki?f`zcMc&eEjpd_D^`bdbdeÉaz„kQ‘
^uzƒ_qfBivjm„kQz„zprfBs/‘kQ†Epd_qkqzƒ’xp‡cl{/^ºsEai±¿IkQmxf`g{pr‘‘kQs€aspdc„zƒz„i?^`brbdkqmc„{4^`s‰cl{ks¬ai¦¿IkQm
fugMprsjacaspdc„zqœÆ®kµsf2’ ‘prz„_Qaz„z’x{kQc„{kqmcl{kÉzl^ui?kÉm„kQz„ab‡c^`bdz„fv{fBbd‘zpds/c„{prz_D^uz„k`œ
]Fpr}Bamkqz ¼6^ ½ ޼~¿ ½ ^`s‘ ¼6_ ½ ‘przjb^De$c„{k›m„kQ_qfBszclma_Qc„prfBs°kqmm„fBmÊz„amg6^`_QkqzÉfB¿c|^uprskQ‘°¿we
yh ­ fBm%9¶"¼[]pd}Bamk ¼6^ ½„½ Ž9‹Ä¶³¼6]pr}`am„k ¼6¿ ½„½ ^`s‘¯‹%9¶‹´¼6]pr}`am„k ¼6_ ½„½ az„prs}
^Yzprs}Bbdk±jmprs_Qprj4^`bF_qfBivjKfBskqswcÊfBm{pr‘‘kQs¯aspdcqœ±¾ƒ{kQz„kvm„kq_QfBszclm„a_QclpdfBs°kqm„mfBm„z’kqmk
^ubrz„fºf`¿c|^`pdskq‘Yaz„prs}ºkq¹¬a4^uc„prfBs®¼˜ ½ œ¾ƒ{kÊm„kQ_qfBszclma_Qc„prfBs‰kQm„m„f`mz„amg6^`_qkQzf`¿c|^`pdskq‘Y¿we
c„{kqzk›‘kQ†Epr_QkqzÊz„{f2’ cl{^ucDŽ Å mzcÊf`g^`bdb ŽKsfBskºfugc„{kqi ^`m„kº^ujjm„f`jm„pr^uclk¦g~f`mog~abrbF_qbr^`z¶
zp Å _q^uclpdfBs°f`gcl{kvc„kqzc¦‘fBi?^`prs¯f`gƒ]pr}Bam„k‰˜¬¼6_ ½ zprs_Qkvc„{kQe®_D^usÀfBsb‡e¯_qbr^`z„zpdgÓe¯^`bdb¼6fBm
ivfBzcµfug ½ cl{kv‘^uc|^®¼~’x{k“cl{kQm¦_QfBs_qkQjcla^`bf`mÉ_QfBaswclkQm¶ _qfBs_Qkqjc„a4^`b ½ pds°f`sk?‘p^`}Bf`s4^`b
fugcl{kvpdsjacÉzj4^`_qk?^`zÉ_qfBs_qkqjcla4^`b^`s‘À^`bdb¼6fBmivfBzcµfug ½ cl{kvfucl{kQmµ‘4^\c|^°¼~’x{k“cl{kQm
_QfBs_Qkqjc„a4^`bKfBm!_qfBaswc„kqm¶ _qfBs_qkqjcla4^`b[Ž^`}B^`prs ½ ^uz_QfBaswclkQm¶&_QfBs_Qkqjc„a4^`b œ &s?f`cl{kqm!’fBm‘zqŽ
˜
.
@
]Fpr}Bamk xkq_QfBszc„m„a_“clpdfBsÊkqm„mfBm„zf`gyh ­ fBm 9¶"€¼~’xp‡cl{ÊfBskjmprs_Qprj4^ub`_qf`i?jKfBskQs¬c
f`m'f`sk!{pr‘‘kqs¦aspdc ½ Ž\‹%9¶"Ž2^`s‘±‹%9¶&‹%W¼Ó’xpdc„{µfBsk{pd‘‘kQsµaspdc ½ fBsÊcl{k^`mclp Å _qpr^`b
‘fBiP^uprsY}BkQskqm„^uclkQ‘/g~mfBi ]pd}Bam„k¦˜¬¼6_ ½ œ
¿Kkq_q^`azkÊc„{kQeP‘f›sf`cƒpdswclkqmjIf`b^uc„kcl{kclml^uprspds}±z„k“cƒg~abrb‡eBŽEcl{kQz„k‘k“†pd_qkQz^um„ksf`caz„kö
g~abÄg~fBmx_qb^uz„z„p Å _D^\clprf`s‰^`s‘‰cl{pdzkÍjb^`pdszƒcl{kÊ{pd}B{/_qb^uz„z„p Å _D^\clprf`sYkqm„mfBmxml^uc„kÊfB¿c|^uprskQ‘
¿weÖc„{k?bdprskq^`mzeEzclkqivz¦pds°]pr}Bam„k?šœ NjkQ†`kqmcl{kQbrkqzzqŽc„{kqzkPmkqz„abdclzµ^`mkvpdswclkqmkqzclprs}
zprs_Qk`ŽŒbdpr”`k¦prsWcl{kºsfBs¶ ¿If`cclbdkqskQ_|”$_D^uz„k`ŽŒc„{kQe֑fYprbrbdazc„ml^uc„kµc„{kº‘pdÁIkqmkqs_Qk›¿Ik“c&’kQkqs
c„{kbdprskq^`m'^`s‘±cl{ksfBsbrprskD^`m'z„_|{kQi?kQzqœ &s‘kqkq‘9ŽB’x{prbdkcl{kbrpdskD^`mzezclkQi?z‘pdz„jbr^De¦^us
as‘przclfBmclkQ‘Ëz„amg6^`_qk’xpdc„{Psf±z„^`‘‘bdkjKfBpds¬c„z¼6]pr}`am„k ¼[^ ½„½ Žwc„{kosf`sbrpdskD^`m!fBskqz{^™†`k
z„^`‘‘bdkxjIfBpdswclz¼[]Fpr}Bamkqz ¼~¿ ½ ^`s‘$¼6_ ½„½ œ¾ƒ{Eazqެcl{k_qfBivjmkqz„zprfBs›mkqz„abdclz‘kQi?fBszclm„^uclk
c„{4^ucFsfBsbdprskq^`mF^`aclfB^`z„zf_Qp^uc„prfBsÊprz'sf`ckq¹¬ap‡†`^ubrkqswc'clfbdprskq^`m'^`ac„fw^`z„zf_Qp^uc„prfBsÉfBmFyh ­
k“†BkQsÀprs¯cl{kv_q^`z„k›’x{kQm„k›cl{k›s¬ai±¿KkqmÊf`g{pr‘‘kqs°aspdc„zÊfBmjm„pds_qpdj4^`bM_QfBivjIfBskqswclzÊprz
„‹f`c„kÊc„{4^ucx’x{pdbrkg~fBmc„{kclkqzc‘fBi?^`prsYazkq‘€prsYcl{pdzƒzc„a‘eBŽ=_Qb^`zz„p Å _D^uc„prfBsY_q^`s
¿KkÊ^`_|{pdkQ†`kq‘$f`sbde?pdg'azprs}v^ºs¬ai±¿Kkqmƒf`gF{pr‘‘kqs‰asp‡clzƒ}BmkD^uc„kqmc„{4^`sYcl{ks¬ai¦¿IkQm
fugÄprsjacasp‡clzqެpdsvc„{k’fBm”ºf`g •B^`j”uf2’xpd_qžYÕ“Ï `Î r˜ K^us‘ yFk“clz„_|{k/Õ“Ï `Î r˜ Ž
c„{kÉsEai±¿IkQmxf`gM{pd‘‘kQs$asp‡clzxprzƒziP^ubrbrkQmcl{4^us/c„{kµs¬ai¦¿IkQmfugMprsjacasp‡clzqœ¾ƒ{prz
za}B}BkQzc„z±cl{4^ucµcl{k?{pr‘‘kqs¶ clfu¶ prsjac¦aspdc¦ml^uc„prf/‘fkQz±sf`c¦{4^D†Bk‰^`swe®¿Ikq^`m„pds}$f`s
c„{kº¿Kkq{4^D†EprfBmfugsf`sbrpdskD^`mo^`ac„fw^`z„zf_Qp^uc„fBm„zpdsÖ_qbr^`z„zp Å _q^uclpdfBsWc|^`z”¬zqŽz„pds_qk±’x{4^\c
mkD^`bdbde$iP^ucclkQm„zÊprzcl{kqprmÊ_q^`j4^`_Qpdc&eÖclf/prswc„kqm„jKfBbr^uclk±c„{kvc„ml^`pdsprs}Yz„kQcµm„kQ}w^`m‘brkQz„zÉf`g
{f2’³iP^us¬eË{pr‘‘kqs‰asp‡clzƒcl{4^\cxiP^DeËcl^`”`kuœ
˜
+*
,
( -
-)
'
( )
ziP^ubrbrkQmc„{4^`s‰cl{kÊs¬ai±¿Kkqmxf`gFprsjacxasp‡clzqœ
" "
" Æ®kP’xpdbrbsf™’ ^`s^`bdeEžqkP_D^`mkQg~abdbde¯cl{kPm„kqzabdc„z±’kYf`¿c|^`pdskq‘Àprs,cl{kËjm„k“†EprfBazºzkq_“clprf`s
^us‘?kÍjb^`pds±’x{we›fBam!fB¿zkqm†u^uc„prfBsz‘kqj4^umc!g~m„fBi cl{kxkÍjKkq_“c|^uc„prfBsz‘kQm„p‡†Bkq‘›g~m„f`i cl{k
j^`zcbrpdc„kqm„^uclamk`œ &sË^`‘‘pdclpdfBsĎB’ko’xprbdb4_qfBivj4^`mkc„{km„kqzabdc„zf`g9cl{ksfBsbdprskq^`m!^`ac„fw^`z¶
zf_Qp^uc„fBm„zc„f/c„{kPmkqz„abdcÉf`gƒ^usf`cl{kqmʒkQbrb‡¶ ”¬sf™’xsÀj4^`m„^`‘pd}Bi€Žm„^`‘p^ub‡¶&¿^`z„pdzog~as_“clprf`szqŽ
^us‘€zjIkQ_qabr^uclkÊfBsY’x{4^\csfBsbrpdskD^umƒ^`ac„fw^`z„zf_Qp^uc„fBm„zƒ_QfBivjaclkÊ^us‘/’x{weYc„{kQe‰‘f›zfœ
x %
4 (+*+ ! v
x
¾ƒ{k‘pdÁIkqm„kQs_qkx¿KkQc&’kqkQsPcl{kƒbdprskq^`m^`s‘vsfBsbrpdskD^umMzeEzc„kqivz_q^`sv¿IkƒkÍjb^`pdskq‘›¿we±cl{k
g6^u_QcÄc„{4^ucDŽ™g~fBmIcl{k!j4^`mclpd_qabr^`mIc„kqzc‘fBiP^uprs_QfBsz„pd‘kqmkq‘ QŽ ŠfBamb^`m‘‰^`s‘ É^ui?jĘ ¢z
^uz„z„ai?jc„prfBs‰{4^uz¿KkqkQs/†EpdfBb^uc„kq‘Äœ &s‘kqkQ‘ÄŽK^`zxi?kQswclprf`skq‘‰prs‰zkq_Qc„prfBs°˜BŽ
ŠfBam„b^um„‘/^`s‘ Ê^`ivjĘ £z‘prz_qazz„pdfBsv’^`zz„{f™’xsvclfÊ{fBbd‘vf`sbdeºpdsºcl{kx_D^uz„kx’x{kqmk
c„{k‰prsjaclzºclfÖc„{k‰sfBsbdprskq^`m›^`_Qc„pd†u^uc„prfBsÀg~as_Qc„prfBs¸f`gcl{k‰{pd‘‘kqs·asp‡clzºmkqi?^`prs¸prs
c„{kºbrpdskD^umoml^us}Bkºf`gcl{kºz¹¬a4^`z„{prs}Yg~as_“clpdfBsĜ ­ s¯fB¿z„kQm†u^uc„prfBs¯f`g!cl{kºjm„kö&zeEs4^ujclpd_
^u_Qclp‡†u^uclpdfBszf`gFcl{k›˜ º{pd‘‘kQs€aspdclzxf`g‹%9¶&‹%ÀmkQ†Bkq^`brzxcl{^ucDŽf`s$^D†BkQml^`}`k`Ž4cl{kQz„kʆu^`b‡¶
akqz^um„kÉkq¹¬a4^`bclf ,– º’xpdcl{/†u^`m„pr^`s_qk ,– ‡˜ ˜ œxnpdi?pdb^`mbdeBެg~fBm‹%9¶"Ž4’k
g~f`as‘®c„{4^uc , BšBšBš‰^`s‘ , £– œ ­ b‡cl{f`a}B{¯g~fBmÊprsjacµ†u^`bdakqzÊprs¯cl{k ¶|˜Bއ˜
pdswclkqm†u^`b ŽEcl{kzpr}BivfBpr‘vg~as_“clprf`sYprz_QbrfBzkclfºbrpdskD^umqŽEfBamƒm„kQz„ab‡clzƒzkqkqi clfºz„a}B}Bkqzcxcl{4^uc
^/z„i?^`brbM†EpdfBb^uc„prfBsÖfugcl{k ŠfBamb^`m‘€^us‘ É^ui?jĘ ^`zz„aivjc„prfBs°_D^`sÀiP^`”ukP^/¿pr}
‘pdÁIkqm„kQs_qkµprs/_qkQmc|^uprs$_QfBswclkÍc„z ’x{pdbrkcl{prz‘pdÁIkqmkqs_Qk¦ivpr}B{wcx¿Kk¦i?^`m„}Bpds4^`bŒ^us‘€c„{Eaz
f™†`kqm„bdff`”`kq‘º’x{kQs?_QfBszpr‘kQm„prs}ocl{kƒ{pr‘‘kQs›b^DeBkQm^`brf`sk`ŽBp‡cMpdzMiP^u}Bsp Å kq‘±pds±cl{kƒfBacljac
br^DeBkqmQŽÄ^`zz„a}`}Bkqzclkq‘¯¿we/cl{k±jbrf`c„zf`g]Fpr}Bamkqz 4¼[^ ½ ^`s‘+¼6¿ ½ ’x{pr_|{W‘fPsf`c‘prz„jb^De€^
]=f`mƒf`cl{kQmx_qb^uz„z„kQzxf`g‘fBiP^uprszQŽcl{pdzƒi?pd}B{wcƒsf`c¿Kkcl{kÊ_q^`z„kuœ
* *
&
%
-
)
).
.
-
&
-
!
.
,,
˜™—
!
È4^ucozamg6^u_qk¦fugcl{k¦z„f`mc_qfBivjac„kq‘$¿we€yh ­ fBm^`ac„fw^`zz„fE_qp^\clprf`sĜ¾ƒ{pdzmkqi?^`m„”‰^ubrz„f
{fBbr‘zg~fBmcl{kÉkQs_qfE‘kQmƒjm„fB¿brkqi f`g xaivkqbd{4^`mcµÕ“Ï `Î r˜ I’x{pr_|{/_D^`s‰¿Kkz„fBb‡†BkQ‘/¿we
^us®^uaclfw^uz„z„fE_qpr^uclf`mo’xpdc„{°sfBsbrpdskD^um{pr‘‘kqs¯asp‡clzÊ¿acÊsf`cÊ¿we°^‰bdprskq^`mof`sk ÊprsWc„{prz
jm„fB¿bdkqi/Žsf`sbrpdskD^`mpdc„prkqzprsYcl{kÉ{pr‘‘kQs€br^DeBkqm^`mkÊ^`brzf›z„{f™’xs€c„f›{4^D†Bkµ^`s€pdi?j^`_Qcqœ
4³*À x4 *À =
Æ®kƒ’xprbdbsf™’Ç^ucclkqivjc!clfÊkQzc|^u¿brpdz„{›cl{ks4^uc„am„kxf`gIcl{kx_qf`i?jac|^uc„prfBszMcl^`”¬prs}Éjbr^`_qkxprs
c„{kvsfBsbdprskq^`mÉ^`aclfB^`z„zf_Qp^uc„fBm„zÊ¿we°_qfBivj4^`mprs}‰cl{kQprmÊm„kQ_qfBszclma_Qc„prfBsÀkqm„mfBmÊz„amg6^`_qkQz
c„fWcl{kYmkq_QfBszc„m„a_“clpdfBs¸kqm„mfBm±zamg6^`_QkYfB¿cl^`prskQ‘+¿we¸^Wml^`‘p^`b¿4^`zprz¦g~as_QclpdfBs¼[Š] ½
^uaclfw^uz„z„fE_qpr^uclf`mx’xp‡cl{ É^`az„z„pr^`sW^u_Qclp‡†u^uclpdfBszxprs/cl{kÉ{pr‘‘kqsWaspdc„zo^`s‘WbrpdskD^`mxfBacljac
^u_Qclp‡†u^uclpdfBszqœ¾ƒ{kºm„kq_QfBszclm„a_QclpdfBs¯kqmm„fBmzamg6^u_qkºfB¿cl^`prskq‘W¿weÖza_|{°^ˑkQ†Epr_QkºfBsWcl{k
‘fBiP^uprsËf`gF]pd}Bamk±˜¬¼6_ ½ przjbrf`cclkq‘‰pds‰]pr}Bam„k Eœ¾ƒ{kÊj4^`mc„pr_Qab^`mŠ]·‹kQc&’fBm„”?cl{4^uc
eEpdkqbr‘kq‘ºcl{pdz Å }Bamk{^`z^Ê_q^`j4^`_Qpdc&eºfug {pr‘‘kqsvasp‡clz^`s‘ºcl{k†u^`mp^`s_Qkƒf`gKcl{k Ê^`az¶
zp^`s±g~as_Qc„prfBszM^`m„k Å kQ‘P^\c!^`s‘ºzkQcclfɚEœ œF¾ƒ{kƒm„kQ_qfBszclma_Qc„prfBs›kQm„m„f`mMz„amg6^`_qkƒfugKc„{prz
( )
F] pr}Bamk okQ_qfBszclma_Qc„prfBs¯kqmm„fBmzf`g!cl{k›Š]»^`aclfw^`zz„fE_qpr^uclfBmofBsWcl{kv^`mclp Å _qpr^`b
‘fBiP^uprsP}`kqskQml^uc„kq‘Ëg~m„f`i)]pd}Bamk¦˜¬¼~_ ½ œ¾ƒ{kskQc&’fBm”P{4^`zx^µ_D^`j4^u_qpdc&e?f`g {pd‘‘kQs
aspdc„zx^`s‘‰cl{k†u^`m„pr^`s_Qkf`gp‡clz Ê^`azz„p^us‰g~as_Qc„prfBszxpdz Å kq‘W^us‘‰z„kQco^ucšœ œ
^uaclfw^uz„z„fE_qpr^uclf`m’^`zƒ_qfBivjac„kq‘‰prsËc„{kz„^`i?kg6^uz„{pdfBsY^`zc„{4^ucƒf`gc„{kf`cl{kqmƒ^`aclfw^`zz„fu¶
_Qp^uc„fBm„zQŽ4az„pds}vkq¹¬a4^uc„prfBsÀ¼˜ ½ œ¾ƒ{kÉz„pdi?pdb^`mpdc&ev¿KkQc&’kqkqsWc„{kÊm„kQ_qfBszclma_Qc„prfBs€fB¿c|^uprskQ‘
¿we,c„{kYsfBsE¶&¿Kf`c„c„brkqskq_|”=ŽsfBsbrpdskD^um±^`ac„fw^`zz„fE_qp^\clfBmz‰¼6kQz„jKkq_qpr^`brb‡e,‹9¶"ŽF’x{pd_|{ ^ubrz„f
˜
5
-
{ ^`zºbrpdskD^`mµfBac„jac›^`_“clp‡†`^\clprf`sz ½ ^`s‘,cl{k‰Š]^uaclfw^uz„z„fE_qpr^uclf`m¦z„a}B}Bkqzclzºcl{^ucDŽbdpr”`k
c„{kŠ]°sk“c&’f`m„”=ŽEc„{ksfBsbdprskq^`m^`ac„fw^`zz„fE_qp^\clfBmzaz„kxcl{kQprmx˜ {pd‘‘kqsvasp‡clzclfÊjac
_QkqswclkQm„z‘f™’xs€f™†`kqmƒcl{kg~f`am_qbdazc„kqmzmkqjmkqzkqswclpds}vc„{kclm„^`prspds}¦‘^uc|^Ž^`s‘‰kQ†u^`bda4^uclk
c„{kʑprzc|^`s_qkÊf`g'cl{kclkQzc„prs}›‘4^ucl^±clf›cl{kQz„kÊ_qkQs¬c„kqmzqœ
¾ƒ{pdz±m„kQz„ab‡c¦c„fB}BkQc„{kqmɒxpdc„{Àcl{k?m„kQz„ab‡clz±f`g ŠfBam„b^um„‘‰^`s‘ Ê^`ivjĘ z„a}B}`kqzc„z
c„{4^uc/sfBsbrprskD^`m‰^`aclfw^`zz„fE_qpr^uclfBmz‰_D^`sm„kQz„fBmc€c„fUfBsk®f`gµc&’fUi?fE‘kQz/fug±fBjKkqm„^uclpdfBs
kQpdc„{kqmcl{kQevfBjKkqml^\clkxbrpd”`kyh ­ ެz„kQkq”¬prs}¦^É}`brfB¿4^ubrpržQkq‘ºzfBbrac„prfBsºc„fÉc„{kmkq_QfBszc„m„a_“clpdfBs
jm„fB¿bdkqicl{k“e+^`mkPclmeEprs}$c„fÖz„fBb‡†BkËf`m¦cl{k“eÀf`jIkQml^uc„kËbrpd”`kY^`s,Š]^uaclfw^uz„z„fE_qpr^uclf`mqŽ
zkqkQ”Epds}?^›bdf_q^`brpdžqkQ‘Yz„fBbdaclpdfBsĜ
³! €
´x4 '
¾ƒ{k$¹¬akqzclpdfBsU’k$sf™’ ^`z”¸prz ‰’x{kQsH‘fEkqzË^°z„pd}Bi?f`pr‘4^`b^`ac„fw^`z„zf_Qp^uc„fBm›m„kQz„fBmc?c„f
f`skYfBm›^`sfucl{kQmºf`gc„{kËc&’f®ivf‘kqzºf`g^`_“clprf`s+‘kqz_qm„pd¿IkQ‘Upds+cl{kYjmkQ†Eprf`az›z„kq_“clpdfBs $
Škq_D^uaz„kWfugocl{k$_qam„m„kQswcËb^u_|”+f`gclkQ_|{sfBbdfB}`e·^D†u^`prbr^`¿bdkËg~fBmv^`s4^`b‡ežQprs}¯g~kqkQ‘g~fBm’^`m‘
skqam„^`bsk“c&’f`m„”¬zÉg~abrbde`ŽK’kº_D^us°f`sbde/z„jKkq_Qab^\clkº^`zc„fP’x{kQs®kq^`_|{¯j{kqsfBi?kQsfBsW’xpdbrb
cl^`”`kÊjbr^`_qkuœ
&s€j4^`mc„pr_Qab^`mQŽ’kµz„a}`}Bkqzcc„{4^uccl{kÉz„pd}Bi?f`pr‘4^`bÄ^`aclfB^`z„zf_Qp^uc„fBm’xprbdbŒiP^`”ukÊaz„kµf`g
p‡clz'sfBsbdprskq^`m„p‡clpdkqzĒx{kQs±cl{k‘4^uc|^z„kQcpdc^uc„c„kqivjclzclfm„kQ_qfBszclma_Qc!pdzFi±abdclp ¶&ivf‘^`bB^`s‘
c„{kɑpdÁIkqmkqswco_QbrazclkQm„zxcl{4^uc_qf`i?jKfBz„kÊp‡co^um„k†BkQme/z„jmkD^`‘$fBacDœ &s‘kQkq‘ÄŽIpdg'cl{kɑ4^ucl^
zkQcpdzaspdi?fE‘4^`bfBmpdg!p‡copdzoi±ab‡clp ¶&ivf‘4^ubÄ¿ac_q^`sÖkD^uz„prb‡e/¿Ik±_QfBsg~azkq‘Ög~fBmasprivfE‘4^`b
‘^uc|^Žcl{kqsÀk“†BkQme®jIfBpdswcµpdsÖcl{kvclml^uprspds}Yz„k“cº^`_“clpd†u^uc„kqzÊ{pd‘‘kqs®asp‡cɆu^`bdakqzÉbrfE_D^\clkq‘
pds°c„{kPz„^`ivk›†Epd_qprspdc&e¯^`s‘®’x{pd_|{,prs_Qm„kq^`z„kvfBmɑkq_Qm„kD^uz„kËivfBsf`c„fBspd_D^`bdbdeBœ?na_|{,‘4^ucl^
ÆÀk’fBabr‘/brpd”`kc„f›c„{4^`s” É^`me‰hf`cclmkqbrbIg~fBmƒz„a}`}Bkqzclprs}vc„{przƒ_QfBi?j^`m„pdz„fBsĜ
najjKfBmcFg~fBmcl{pdzFzjIkQ_qabr^uclpdfBs¦_q^`s±¿Kkg~fBas‘¦prs •B^uj”`f™’xpr_Qž`˜ E’x{pr_|{±z{f™’xz
^ƒ_QbrkD^umđkq_Qm„kq^`z„kprsÊ_qbr^`z„zp Å _q^uclpdfBs^`_Q_qam„^`_QeÊ¿weʋ9¶‹%?^`zÄcl{k_QfBs_Qkqjc„a4^`bw_qbdazc„kqmz
fugFc„{kʑfBi?^`prsYpds€]Fpr}Bamk±˜¬¼~_ ½ ^`m„kivf™†BkQ‘$_qbdfBz„kQmclf›fBskÉ^`sf`cl{kQmqœ
)
+*
%
!
,
+*
,
˜
-
7
_q^`sĎc„{¬azqŽ¿KkË^`jjm„fDpri?^uclkQ‘Àbdprskq^`m„b‡eBŽ'prs®c„{kËz„^`i?kvg6^`z„{prfBsÀ^`zµc„{kQe°’f`abr‘,¿KkP¿we
^Ëbdprskq^`m^uaclfw^uz„z„fE_qpr^uclf`mqœ sÖcl{kºf`c„{kqmo{4^`s‘ÄŽŒp‡gcl{kº‘^uc|^ËzkQcÊprzoi±abdc„p‡¶ i?fE‘4^`b^`s‘
p‡gMcl{k¦‘p‡Á9kQm„kqswco_qbrazclkQm„z_QfBszclpdc„aclpds}vpdco^`m„kɆBkqme$zjm„kq^`‘ÖfBacqŽIc„{kqsÖ^ujjm„fDpri?^uc„prfBs
fugc„{kqpdm±{pd‘‘kqs¸aspdcº^u_Qclp‡†u^uclpdfBsÀ†u^`brakqz±¿we¸^Wbdprskq^`mµg~as_QclpdfBs,’xprbdbg6^uprb¿IkQ_D^`azk‰f`g
c„{k֑pdz„_qf`s¬c„prs¬ap‡clprkQzËprswc„m„fE‘a_qkQ‘´¿weUcl{k¯i±ab‡clp ¶&ivf‘4^ubƒs4^uclam„kÖf`gÉcl{k֑fBiP^uprsĜ &s
za_|{À_q^`z„kQzqŽ'cl{kvz„pd}Bi?f`pr‘4^`b'j4^`mcÉf`gc„{kv^`_Qc„pd†u^uclpdfBsWg~as_“clpdfBs®pdz†Bkqme¯az„k“g~ab!z„pds_qkvpdc
jKkqmi?p‡clz±c„{k€bdf_q^`bjmf_Qkqzz„prs}Àf`goz„kqj^`ml^uc„k€_QbrazclkQm„zvprs¸cl{k/zl^`ivkYg6^`z„{prfBsU^`zvŠ]
^uaclfw^uz„z„fE_qpr^uclf`m„zqœ &s‘kQkq‘ÄŽŒ¿we€az„pds}Y^Ëz„pd}BivfBpr‘4^ubÄg~as_Qc„prfBs9Ž9^P{pr‘‘kQsÖasp‡c_D^usÖiP^`j
^ubrb!cl{kY‘4^\c|^Ö_qfBswcl^`prskQ‘+prs+‘p‡Á9kQm„kQs¬c›_QbrazclkQm„z±clf°^`jjm„fDpri?^uclkQbde¯cl{kYzl^`ivkˑk“g6^`abdc
^u_Qclp‡†u^uclpdfBs/†u^`bdakY¼~f`g–PfBmµ˜ ½ ’x{pdbrkµpdc_q^`sWi?^`j$c„{k±‘4^ucl^Pprs$z„fBivk±f`c„{kqm_qbrazclkQm„z
’x{pr_|{¸g6^`brbprs+cl{k‰bdprskq^`m±j4^`mcvf`gc„{k‰z„pd}Bi?f`pr‘4^`b!g~as_“clpdfBs c„f¯i?fBmk prswc„kqm„kQzc„prs}
†u^`bdakqzQœ !^`_|{®{pr‘‘kqs°asp‡cµ_q^`s¯cl{kQsÀazkvc„{k›zl^`ivk›zclm„^uclkQ}`eÖg~fBmʑp‡Á9kQm„kqswcÉ_qbdazc„kqmz
^us‘ÄŽ`c„{Eazqެ^}BbdfB¿4^`b¬z„f`brac„prfBsµ_D^`sº¿Kkg~fBas‘º¿¬eÉcl{kf™†Bkqm„^`brbskQc&’fBm”¦¿we±_QfBi?jKfBas‘prs}
c„{kÊbrfE_D^`bdpržQkq‘ËzfBbrac„prfBsY_QfBivjaclkQ‘€¿we‰kq^`_|{€{pr‘‘kQs€aspdcqœ
npds_qkuŽ4prsYcl{kkqs_Qf‘kQmjm„fB¿bdkqi/Žc„{kÉ^`aclfB^`z„zf_Qp^uc„fBmprzƒkÍjIkQ_QclkQ‘€c„fvmkq_QfBszc„m„a_“c
‘^uc|^ÊjIf`prswclzbrfE_D^uc„kq‘ºg6^`m^D’^De›g~m„fBi kD^`_|{Ëfucl{kQm zprs_Qkc„{kQev^um„kbrfE_D^uc„kq‘?^uck“Eclmkqivk
_qfBmskqmz ‰f`gcl{kºpdsjacÊzj4^`_qk c„{przzjIkQ_qabr^uclpdfBs¯^`brzfYk“jbr^`prsz’x{weWc„{kºsfBsbrprskD^`m
^uaclfw^uz„z„fE_qpr^uclf`mm„kQz„fBmclzƒclf?^ºbrfE_D^`bdpržqkQ‘Ëz„f`brac„prfBsYsfuc^™†u^`pdb^`¿brkc„fvyh ­ prsËc„{4^uc_D^uz„k`œ
¾ƒ{kYjam„jKfBzk/fugc„{prz¦j4^`jKkqm¦’^`zºclf¯^`‘‘m„kQz„zºcl{kYj^`ml^`‘f™,ml^`pdz„kQ‘+¿¬e®cl{kY_Qb^`pdif`g
ŠfBam„b^um„‘/^`s‘ Ê^`ivjĘ cl{4^\cDŽ=prs€^`ac„fw^`z„zf_Qp^uc„prfBs9ŽsfBsbdprskq^`m„p‡clpdkqzpds/c„{k¦{pd‘‘kQs
aspdc„zF^um„k!_qfBivjbdkQclkQbdeoasskQ_qkqzzl^`meBŽB}`pd†BkQsµc„{4^ucsfBsbrprskD^`m^`aclfw^`zz„fE_qpr^uclfBmz^`m„k!”¬sf™’xs
c„fËjKkqmg~f`m„i c|^`z”¬zocl{4^\c_D^ussf`co¿Ikµz„fBb‡†Bkq‘Ö¿we$yh ­ fBmbrprskD^`m^`ac„fw^`z„zf_Qp^uc„prfBs9œ¾ƒ{k
j^`jIkQm±¿Kkq}Bpdsz±¿we+‘kQi?fBszclm„^uclpds}$c„{4^ucDŽ!^ubdcl{fBa}B{,¿Kf`c„{¸yh ­ ¼~fBm¦bdprskq^`m±^`aclfw^`zz„fu¶
_Qp^uc„prfBs ½ ^`s‘°sfBsbrprskD^`mzpr}BivfBpd‘4^`bF^`aclfB^`z„zf_Qp^uc„prfBsW_q^`s°¿Ik›azkq‘¯g~fBm_qbr^`z„zp Å _q^uclpdfBsĎ
"
2$
&
šu–
"
$
c„{kbrprskD^`mzezclkQi?z^`m„ksf`c^`jjm„fBjm„p^\clkƒg~fBm_qkQmcl^`prs›c&eEjIkQzf`g9i±abdc„p‡¶ i?fE‘4^`b^`s‘vsfBs¶
bdprskq^`m›‘fBi?^`prszv’x{kQm„kq^`zPcl{kWsfBsbdprskq^`m›zeEzc„kqivz‰^`m„k€_D^`j^`¿brk/f`gÊ_Qb^`zz„pdgÓeEpds}®za_|{
‘fBiP^uprsz!^`_Q_qam„^uclkQbde`œ ­ svk“jbr^`s4^uc„prfBs›f`gIcl{pdzmkqzabdcprz!jmf™†pd‘kq‘v¿we›cl{kxfB¿zkqm†`^\clprf`s
fugocl{k$prswc„kqm„jKfBbr^uclpdfBs+z„amg6^`_qkQzP_QfBszc„m„a_“clkQ‘»¿¬e¸c„{k€bdprskq^`mv^`s‘UsfBsbdprskq^`mºzeEzc„kqivz
’x{kqs€c„ml^`pdskq‘‰fBsYc„{kÊ_qfBs_Qkqjc„a4^`bk“^`ivjbdkqzƒf`gfBamƒ_qbr^`z„zp Å _q^uclpdfBsËclkQzc‘fBi?^`pdsĜ
¾ƒ{k+‘pdÁIkqm„kQs_qkÀprs³c„{k,prswc„kqm„jKfBbr^uclpdfBs³^us‘ÄŽµ^`zÖ^ mkqz„abdcDŽÉprs´cl{k,_Qb^`zz„p Å _D^uc„prfBs
z_|{kqivkvaz„kQ‘®¿weWc„{k›brprskD^`m^us‘¯sfBsbdprskq^`m‘k“†pd_qkQzÉc„{EazÉ_QfBswclm„^`‘pr_“clzcl{kv_Qb^`pdi ¿we
ŠfBam„b^um„‘/^`s‘ Ê^`ivjĘ Iprsp‡clp^ubrbdeÉ_QfBsz„pd‘kqmkq‘Äœ¾ƒ{prz_qfBswclm„^`‘pd_QclpdfBsvprzm„kqzfBbd†`kq‘Ë¿we
kÍEclml^u_Qclpds}$c„{k‰^`z„zaivjclpdfBs,fBsÀ’x{pr_|{+cl{kP_qb^upri przµ¿4^`zkq‘·^`s‘+z{f™’xprs}Wc„{4^uc¦c„{prz
^uz„z„ai?jc„prfBs‰pdzƒsf`cxskQ_qkqzzl^`mprb‡e/^`bd’^Dezƒ†`kqm„p Å kq‘9œ
&s³^·br^`zc/zc„kqjϒk°sf`clk¯cl{^uc‰’x{kqscl{k°sfBsbdprskq^`m‰^`ac„fw^`zz„fE_qp^\clfBmY‘fEkqz/sf`c
f`jIkQml^uc„k/pds ^Öbdprskq^`m±g6^`z„{prfBsĎpdc›kQi±abr^uclkQz?^¯ml^u‘p^`b¿4^`z„pdzºg~as_Qc„prfBsU^`ac„fw^`zz„fE_qp^\clfBm
^us‘»cl{¬az‰_qfBivjac„kqz‰^+brfE_D^ubrpržQkq‘Uz„fBbdaclpdfBsHclf,c„{k¯jm„fB¿brkqi pdcY^uc„c„kqivjclzËc„f+z„fBb‡†Bk`œ
nEjIkQ_qabr^uclpdfBsz^`zc„fʒx{kqsvsfBsbdprskq^`m^`ac„fw^`zz„fE_qp^\clfBmzM‘fÊm„kQz„fBmcc„fÊ^brprskD^`mMf`jIkQml^uc„pd†Bk
ivfE‘k^`s‘Y’x{kQs/c„{kQeˑf›sf`cx‘f›z„fv^`mkcl{kQs/g~f`m„i±abr^uclkQ‘‰^`s‘‰_qf`s_qbda‘kcl{kÉj^`jIkQmqœ
&
# "
Æ®kW’fBabr‘Çbdpr”`k€clf+k“jmkqzz€fBamË}Bml^\clpdc„a‘k$c„f É^umeÇhfuc„clmkqbdb^`s‘^`sÇ^usfBsweEi?fBaz
mkQ†Eprk“’kQmPg~fBm›cl{kQprm?k“Eclmkqivkqbde·{kQbrjg~ab_QfBivi?kQs¬c„zqœÆÀk/’fBabr‘»^`bdz„f®brpr”uk/c„f®c„{4^`s”
&ss4^Àn¬c|^`pds¬†u^`z±g~f`mvaz„kQg~abƒ‘prz_qazz„prf`szP^u¿IfBacv^`aclfB^`z„zf_Qp^uc„fBm„z›^`s‘·g~fBmº{kqm›_D^`mkQg~ab
mkD^`‘prs}‰f`g^‰jm„kQ†EpdfBazʆBkqmz„pdfBs®fugcl{przi?^`s¬az„_Qm„prjcDœ›¾ƒ{przÊmkqz„kq^`m„_|{®’^`zÉz„ajjIf`mclkQ‘
¿we·cl{k _QkWf`gɋo^D†u^`bkQz„kq^`m„_|{»cl{m„fBa}`{H}Bml^us¬cˋo–B–˜ ¶ \¶ o¶–˜B˜2š$clf¸€^`m„” ­ œ
bra_|”KœxÆ®k±^`mk±^`bdz„fP}`ml^uc„kQg~abclfPc„{kºnE_|{ff`bFf`g!$^ucl{kqi?^uclpd_D^`bFn_Qprkqs_qk±f`gM¾FkQb‡¶ ­ †Epd†
…spd†`kqmz„pdc&e»g~f`mYpdclz Å s^`s_qpr^`bzajjKfBmc$^`s‘Çcl{kÀhfB}Bspdclp‡†Bk°n_QprkQs_qk ^`¿If`ml^uc„fBme f`g
ymprs_QkQclf`s$…spd†`kqm„zpdc&eËg~f`mcl{kÊazkµf`g'cl{kqprmƒ_QfBivjaclpds}±g6^`_Qprbrp‡clpdkqzqœ
šE˜
"
А^`bd‘pŒ^`s‘€ˆfBm„spr”=˜ Éy!pdkqmm„k¯Š^`bd‘p^us‘ amc/ˆfBm„spd”=œ ‹kqam„^`bsk“c&’fBm”¬z$^`s‘
jm„pds_qpdj4^`b4_QfBi?jKfBskQswcƒ^`s4^ubdeEz„pdz Œkq^`m„spds}Êg~m„fBi k“^`ivjbdkqz!’xpdcl{fBacbrfE_D^`b4ivprspdiP^œ
µÕ“Í `Î µÕ“Ï “ŽKš Ž9˜ œ
ŠfBam„b^um„‘/^`s‘ Ê^`ivjĘ ʈµœ¬Šf`am„br^`m„‘v^`s
‘ ±œ É^ui?jĜ ­ aclfu¶&^`z„zf_Qp^uc„prfBsº¿weºi¦ab‡¶
clpdb^DeBkQmƒjIkQm„_qkQjclmfBszo^`s‘/z„prs}Bab^um†`^ubrak‘kQ_qfBivjKfBz„p‡clprf`sĜ xÑ \Î `Ñ `Î “Õ 9ՓÏ[Ñ “Ž
š ˜ š ŽI˜ œ
hf`cclm„kQbrbŒ^us‘W/asm„f˜ Ê^`mm„przfBsÊÆ œ`hfuc„clmkqbdb¬^`s‘µy^`ab€asm„fœEym„pds_qpdj4^`bw_qf`i›¶
jIf`skqswclz^`s4^`b‡eEz„prz!f`g9pri?^`}BkQz!†Epr^É¿4^u_|”vjm„fBj4^u}w^uclpdfBsĜ &s ™ÑÓÏ&Õ Ô Õ Ñ |Õ|Õ `Ò
Ñ vÏ 4Õ “Ñ Õ“Ï \Ï \Ò Ô Ï6Ñ `Î “Ï ÃÍEÌPÕ 4Ï `Ï6Ñ `Ñ 9Õ|Õ “ŽFh^`i±¿m„pr‘}Bk`Ž
 ­ ŽŒ˜ œ
ˆo^usz„fBs€^`s‘ kq}Bb[˜ w— ÉnEclkQj{kQs³•œˆo^`sz„fBsÇ^`s‘•`a‘e ÊkQ}Bb œ²y^`mz„spdj ­ _qfBs¶
skq_“clpdfBsprzcºsk“c&’fBm”,cl{4^\c›brkD^um„szºs4^\clam„^`bb^us}Ba4^`}`kË}Bml^ui?i?^`mµg~mfBi kÍjIfBzam„kYc„f
s4^uc„aml^`b!br^`s}Ba4^u}Bk›z„kqswc„kqs_Qkqzqœ &s! |Õ|Õ `Ñ vÏ 4"Õ oÑ 4Ï $# 4Í `%Î &DÕ lÕ |Õ
' 4ÑÓÏ6(Ñ `Õ “Ñ Õ |ՓŽÄ˜ B—œ
•B^`j”uf™’xpr_qžYÕ“Ï `Î r˜ ‹o^uc„{4^`brpdk›•B^`j”uf™’xpr_qžuŽFh^ucl{kQm„pdsk?/eBkQm„zqŽF^`s‘®$^um„” bra_|”=œ
­ sf™†Bkqb‡c&eʑkQc„kq_“clprf`s¦^`jjm„fw^u_|{Éc„f_Qb^`zz„p Å _D^uc„prfBs9œ &s |Õ|Õ `Ñ (Ï 4*Õ ) \Í ÃÏÕ|Õ 4(Ï + \Ñ 4,
Ï &DÕ lÕ |Õ -# ÃÏ6Ñ “Ñ `.Î 4Ï&ՓÎÓÎÐÑ EÕ |ՓŽj^`}Bkqz ˜ Bš Ž9˜ œ
•B^`j”uf™’xpr_qžu˜ ¦‹^ucl{^`brpdk •B^uj”`f™’xpr_Qž`œ |Õ Ô Ï[0Ò /Õ 4Ñ Ñ Ï 41Õ # ™Õ |Õ \Í 4Ï&Õ Ã0Ò `Ì Ô ÎrÕ 324# 5#oÍEÏ
“Ñ `Ï[Ñ 40Ò ™Õ 6# ÔwÔ 7 Ï 8MÎ “Ñ `Ï6Ñ 4œ
y{4t c„{kqzprzQŽIxac„}Bkqmz…spd†`kqmz„pdc&e`Ž _Qclf`¿IkQmɘ œ
m„a}`bdew^u”K˜ B– Œkqf`spr‘ m„a}`bdew^u”KœMˆf™’³c„fvzfBbd†`kcl{ks/¿pdckqs_Qf‘kQmxjm„fB¿brkqi ’xpdc„{
¡azcxc&’f?{pr‘‘kQs€aspdc„zq9œ ÉÕ“Í `Î \Ì Ô ÍEÏ `Ï6Ñ 4Ž=š –˜BŽI˜ B–œ
¡„^˜
m„”¬”¬p ¡„^œ =Í Ô |;Õ :°Õ“Ï ; `Ï6Ï&Õ =<xÕ 4ÑÓÏ[Ñ 4œ•`fB{s$ÆÇprbdkQe/‚
nfBszQŽŒ˜ œ
š`š
!
' .
&
2 2
03
7 0
2
3 0
21
' 0 21
0 -
%
2
0 21 '
( ' 0 0 0
0 0
!
-
21 .
2
3 21
- 7
!
.7 .
0
!1
5.
00
2
0
0 0 &
-
0 0 2
yFk“clz_|{k/Õ“Ï `Î r˜ ʾFfBi y'kQc„z„_|{kuŽ ­ s}BkqbdfÂ$^um„_D^us¬c„fBspdfŽ h{m„pdzc„p^`s t^`m„”ukqsĎ
nEclk“†Bk‰•œFˆo^usz„fBs9Ž É^`me®®œ a{sĎ^`s‘ ’^`s·n^`swclfBzfœ ­ skqaml^`bskQc&’fBm„”®^`a¶
clfw^uz„z„fE_qpr^uclf`m›g~f`m?pds‘a_“clprf`sUivf`clf`m›g6^uprbram„k‰jm„kQ‘pr_“clpdfBsĜ &s # |Õ /Ñ ÉÕ“Í `Î
& ÃÌ `Ï6Ñ - |Õ “Ñ
“Ï&Õ“Ì rŽ= &¾ŽIh^`i¦¿m„pd‘}Bk`Ž4 ­ ŽŒ˜ œ4 &¾ym„kqzzqœ
y{4^ucl^`”®Õ“Ï `Î r˜ Ét±œnIœKy{4^ucl^`”=ŽÄˆµœ9h{fBp[ŽK^`s‘ |œ fBm„kQsĜhf`szc„m„a_“clprf`s$f`g!ivprsp ¶
iP^ubÄs¶š™¶&sYkqs_qfE‘kqmzg~fBmx^us¬eËsĜ µÕ“Í `Î \Ì Ô ÍÏ `Ï[Ñ 4Ž — — Ž9˜ œ
xai?kQbr{4^umc¦Õ“Ï `Î r˜ Ét^™†Epd‘ ƒœ,xaivkqbr{^`mcqŽ kqfuÁ ƒœ®ˆprswc„fBsĎ´^`s‘ Êœ+•œ
ÆÇprbdbrp^ui?zQœŒkD^um„spds}prswc„kqm„s^`bm„kQjm„kQz„kQs¬cl^uclpdfBsz!¿we±kQm„m„f`mjm„fBj^`}w^uc„prfBsĜ &s›t^™†Epd‘ xœ
ai?kQbr{4^`mcW^us‘ •œœ€_DhbrkQbrb^us‘ÄŽÊkq‘p‡clfBmzq"Ž `ÎÓÎrՓΠÊÑ “Ï ÃÑ qÍÏ&Õ |Õ “Ñ `Ž
j4^`}BkQz ˜ œ4 &¾ym„kqzzqŽIh^`i±¿m„pr‘}Bk`Ž= ­ ŽŒ˜ œ
prjz„kqmQ˜ Ét^™†Epd‘ prjz„kqmQœ³ymfB}Bml^ui?ivprs}¯skQaml^ubsk“clzPc„f,‘f,zj4^uc„p^`bx_qf`i?jac|^\¶
clpdfBszqœ &sˋfEkqb ƒœn{4^`m”`k“eBŽkQ‘pdc„fBmqŽ : EՓΠ4ÑÓÏ6Ñ 2 # <Õ ™Ñ Õ 4ÑÓÏ6(Ñ `Õ
“Ñ Õ |ՓŽ_|{4^ujclkQmµ˜™–œ ­ ¿bdk“IŽ=‹f`m’ffE‘ĎĘ œ
'
( )
1 0 -
(
)
'
( .7
'
( )
7.
.
. 4
.)
21
)
4
!1
0 š
7.
2
2