Working Paper 03-29 Economics Series 08
Departamento de Economía Universidad Carlos III de Madrid
May 2003
Calle Madrid, 126 28903 Getafe (Spain) Fax (34) 91 624 98 75
A HERDING PERSPECTIVE ON GLOBAL GAMES AND MULTIPLICITY * James S. Costain1 Abstract Recently, it has been claimed that full-information multiple equilibria in games with strategic complementarities are not robust, because generalizing to allow slightly heterogeneous information implies uniqueness. This paper argues that this "global games" uniqueness result is itself not robust. If we generalize by allowing most agents to observe a few previous actions before choosing, instead of forcing players to move exactly simultaneously, then multiplicity of outcomes is restored.
Only a small sample of observations is needed to make our herding
equilibrium behave like a full-information sunspot equilibrium instead of a global games equilibrium.
Keywords: Herding, information cascades, multiplicity, uniqueness, heterogeneity, strategic complementarities, global games, adaptive learning, stochastic recursive algorithms
JEL Classification: C62, C72, C73, E00
1
Departamento de Economía, Universidad Carlos III de Madrid. E.mail:
[email protected]
* Thanks to Antonio Ciccone for encouraging me to study some related questions. Thanks also for helpful comments to Fabrizio Germano, Joel Shapiro, Stephen Morris, Hyun Song Shin, Frank Heinemann, Dan Friedman, Berthold Herrendorf, Marcel Jansen, Juan Ruiz, and Antonio Cabrales. This paper was first presented under the title "On Multiplicity and Heterogeneity in a Herding Model", at CEMFI, where I thank Guillermo Caruana and other seminar participants. Financial support from the Spanish Ministry of Science and Technology (MCyT grant SEC2002-01601) is gratefully acknowledged. Errors are the responsibility of the author.
/¼ }vj jD ehg5qiqzrye5vRfrjs jms@evmtKze4t K
e tjme/|~}i{utKzehikjmtKlyvGe¦´7e5
rehig5e'jse vmtKzet q
e tjme q}´jmghKzGesrv}ehvjmryKi>rviKjiepw}´jrj
2ehzGtKryivg5qikjm
2 ¢qe5
vrytKlV|zRtgh
ehg5qiqzrygq}@jghqzehvt
eúijtKlDtJn´v}@iry}e5ln {e5jeh
zryi@eh{xwkn |~}i{utzGe5ijmtKlyv5pjseh
2e¤zGtXnweªrzGq
2jmtKikj±ryzlyrgJtjryqivÔ|~q
Dqlyrg5nzGtK©ryi ¯qiRqie sutKi{p¤ve5lyehgjmri jmse'
2e5|~eh
2
e5{ q}´jmghKzGezr skj we'utK
jK|,jse'
qleK|7Klyrygn w}@j Ki4jmse%jmse5
ªsutKi@{Hp;tKgjmr¢rv2j¤qlryg5nrvªrojmve5l|¨v2qzGejmrzGe5v¡g5rjme5{'tKv tRv2q}
2gheK| iqi}ir}ehie5vv%ÁQeK ôg#s@zGrojj2×À
2qse ti{ »
rw7e³K·K·@½Â º¤r e5
e5ij¤tK
ehtKv¤K|¨lrjeh
mtUjm}
2e,sutJ¢Ke%|~q
zGtKlyrhe5{Bjse%}ehvjmrqiK|¨}ir}ehie5vvK| t q
2e tUjme(K}@jmg5qzGe5vªri {r e5
ehikj¡-tJnvh§¤ie-tJn/ryi fsrg#s jms@e(q}@jghqze%tvvghr tjme5{frjs\t r¢qe5i|~}i{tKzGe5ikj#tKl¨zr skj|QtKrylZj weR}ir}eRrvjsutj(jseRvjm
2}g5j}
e K|ªjseBehghKiqz(n zr skjeh
2zGrojz%}lojmry@lyeúe5}@rylyrw
ryt@ D}@jGe5¢Kehi frojmsri)tv2ryi le eh}rlyryw@
ry}@z/pvqzefghltvve5v¨K|Hz´{@ehlyvÔfrjmsGt ie5jq
2©vjm
2}g5j}
e¡tKlylX)jryiknv2s´g#©v tjªjse(zryg5
lye¢qehlÐjmúv2iXfwutKllÔrijR{r e5
e5ij¤t q
2e tUjmeq}@jmg5qzehvhptKvªghg5}
vªryi jmselrjme5
mtj}
eªqi seh
2{ryi Kjmsúz(}ljrylee5}rylryw
2ry}z z{ehlvDtKi@{ seh
2{ryi zG{ehlvstX¢Ke¤wehehig5
rjryg5ryhe5{
e5ghehikjlnqpfqi)jmse
K}i{vjmsutjRe¦´ryvjmri e3¦tzGlehvK| z%}@ljmrlyrghrojnzGtJn>i@KjRwe
qw@}v2jhs@ryvutKeh
e5¢tKly}tjme5vGv2qzGeBK|¤jsehv2e
2ehghe5ikj gh
2rjmrghrvzvwn)g5qzGtK
ri jms
2ehe tzGe5v,fsrg#sxsutJ¢qeújms@eúvmtKzeúutJnK |~}i@g5jmrqiv%w@}@j{r e5
ehikj(ryi@|~q
2zRtUjmryKi vejmvh¯¡tG|~}lloryi@|~q
2zRtUjmryKi tKzeKp7t lqwutKl tKzGepti{tRse5
{ri ú tzGe¡se(zRtKri ®ui{ri rvjsutj¤z(}ljrylryghrojnúK|t q
2e tje(q}´jmghKzGe5vªryv¡ryi{@eheh{
qw}@v2jJp7ehv27e5ghrtlyln r|Ôv2j
mtje rg ghqzlye5zGe5ikj#tK
2rjmrehvDtK
ev2j
qi
!#"%$'&)(+*),%- (.&- /0$12( 3546$78-948:%78$
Z¬ ¢qeh
vrigheG°Dqeh
tKi{«Kqsi>Á×½X¿q¾q¾kÂ3p;rjsutv w7e5ehi fr{ehlon4©iXfi jsutjz%}@ljmrlye eh}rlyryw@
rtzGtJntK
rve¨ryi,zG{ehlv;frjms,v2j
mtje rg±g5qzlye5zGe5ijmtK
rojmrehvh;D}´jz%}@ljmrlyrg rjn,sutKvK| jehiwehe5ivjm}{@ryeh{ri%jmseg5qikjme¦j¨K|v2ryz%}loj#tKi@ehq}v×zX¢qeKpK
eh@
ehv2ehikj#tUjmr¢Ke t e5ij tKzGe5vh jms@e/|QtKg5e K| s@e5jme5
ehie5q}v t ehikjmv5a¹¡e5
2ehi{K
2|×p ghrehikj¤utJnK se5jeh
ehie5rjnBe5¢Kehikjm}tKlylon ½
he lryzryiutjehv;z%}@ljmrlyrghrojnªwkn,{
ro¢´ri tKlylt e5ikjmvÔjX-tK
2{vZg5q
ie5
v2qly}@jryqi@vhptKvv2}zGri jmsutUjjseg#sqrghevej¡rvw7K}i{e5{H zq
e{
mtzRtjrygv2q
2j(K|D|~
t rylrjn4tK
rvehvryia lqwutKl tzGe5vpÔtKv({@e5®uie5{\wkn °-tK
lvv2qi(ti{ ¢Kti(º tKzzefÁ½X¿K¿q¶kÂi jms@ryv;ghKije¦jJpUjmsK} s,tfv2ryz%}@lj#tiehq}@vzX¢qep
e5
e5vehikjmtjmro¢qet e5ij tKze¨zRtJntKllyX z%}ljryleZeh}rlyrw
ryt@pJjmse¨rij
{}gjmryKi|utKi ryi@®irjehvrzRtlÔtzGq}@ij¤K|±se5jeh
ehie5rjn ryi't e5ikjmv ryi@|~q
2zRtUjmryKi tKwq}@j t q
2e tje |~}i{utzGe5ijmtKlyvK| jehi'v} >Gg5ehvjmBehlyrzGriutje,jms@ez(}ljrylryghrojnqp7lyeJt{ryi jBtB}i@ry}e t q
2e tUjmeq}@jghqzeB|~K
ehtKg#s t K
e tjmevj#tje\ÁN¼/q
2ryvGtKi{ ôsryi½X¿q¿K¾@p³K·K·k³q sutjryv5pueh}rlyryw@
ry}@z rvf}iry}etKve(t
qtKg#sBjselyrzGrojDK|Ð|~}llHryi@|~K
zGtjmrqiHpryi vrojmeK|Ðjmse |QtKgjjmsutUjjse |~}lyl7ryi@|~K
zGtjmrqi tKze¤rojmve5l|Ôe¦´srwrjvz%}ljrylryg5rjnq s@ryv¨jmse5q
ejmryghtKl¥
e5v}lojJp}v}utlyln@
X¢qe5{ú¢´rytrikjmeh
tjme5{R{KzGriutKig5eªtK
}zehikjmv5p sql{v%|~q
t4v2}
2ryv2ryi lonlytK
eúghlytKvvK| tzGe5vÁ u
mti©Ke5lVp¼/q
2
ryv5p±tKi{ tK}@hie5
hp ³K·q·q¶qÂpHti{4ryvªtKlyv2úv}@7K
2jme5{wkn e3¦@eh
2ryzehikj#tle5¢r{ehig5eK°-tKw@
mtKlehvhp ªt e5lVp7tKi{
2zGe5ijeh
/ÁV³·q·k³qÂ(ti{)¹¡ehriehzGtKiip ¡t e5lVp±tKi{>§¤g#©Ke5i@|~ehlv4ÁN³K·q·k³qÂ,tKv©\v2}w£2e5g5jmv jmú@ltJnBqievsjJpv2ryz%}@lj#tiehq}@vzX¢qepw@ryiutK
nkg#sqrghe tKzehv¡jsutj¡sutJ¢qez%}@ljmrlye eh}rlyryw@
rt,}i{e5
|~}llHryi´|~q
zGtjmrqiH vjmse lqwutKl tKzehvlyrojme5
mtj}
e¤q}l{/g5ltKrz/p jmse5ry
¡
ehv2}ljv¤vs@ tú}ir}e%zGtKri |~
2qz.t q
2e tje(|~}i{tKzGe5ikj#tKlv¡jmGjmset
e tje@
qq
2jryqi@v-zRt©ri eJtg#s g#sqrghe =s@rylye,jmsrv e5¢ry{e5igheryv g5qiv2ryv2jehikjfrjs'jse lyKwutKl tKzGe5v lyrojmeh
tjm}@
eKp;rojtKlv
mtKrve5vGti)Kw¢rq}v}ehvjmryKiH¯úDK}ly{)
e5v}lojmv{r 7eh
(r|¡ltJnqe5
vg#sqv2e/ri veh}e5ighe
mtjseh
fjmstKi/zX¢ryi vrz%}ljmtKie5q}vlo6n | jme5
ªtKllVpro|Ôe(
2e t
{BeJtKg#s j
ehtjmzehikj¡tKv t
tKi{Kz {
mtJ |~
qz jmsevmtKze q}lytjmrqi K|Ô7KjehikjmrytKlHlytJnqeh
2vhp¥rjfrve¦jm
2ehzehlon sutK
2{j,v2ehesX {r 7eh
2ehikj¨jm
2eJtjzGe5ijvg5q}l{GleJtK{jmvr iro®ugJtKikjln%{@r 7eh
e5ikjDt q
e3 tje,q}´jmghKzGe5vªr|ZtKikn r¢Kehi tKzGeryvlytXnKeh{4Kiln KigheúÁQvGjmsutjjms@eh
e,ryviGDtJn jmlyehtK
i¥ÂZti{Gro|@ltJnqe5
v±zGX¢qefv2ryz%}loj#tKi@ehq}v2ln ÁQvjmstj¨jmsengJtKii@Kj±ghqi{@rjmrqiqi Kjms@eh
ltJnKeh
v w7e5sutJ¢´rq
#Â3 lylXfryi v2eh}e5ijrtKl¡Á~q
eheJtUjmeh{u @ltJnzr skjtKllyX t q
2e tUjmew7e5sutJ¢ryq
jmBe5¢Kql¢KeRX¢qe5
,jmrzGep7qv2vrwln
2eJtKg#s@ryi {r 7eh
2ehikj,q}@jmg5qzehv e5¢Kehi ri jmsevmtzGev2jmtjmeK|t q
e tjme¤|~}i@{utKzehikj#tKlvh Æ ëJØ2رÓ7ÑÒÕ2Õ×ÎÊUØZÉÊUÞÓ7Î5ÌQÍVÉÑäÊ%ùûüüýmÿuÙÎ5ÚÞXÑÖÌNÕÛUÌNÌNÑÒÎÊâ môÐÙ ÍVØÊéXÍVÈÎÛUÜÈéXÑÒÊUÕ×ÚVØ2É5ÌQÑÒÊÜDÈØ×ÍVØÚVÎÜ5ØÊØ2ÑÅÍ~ß-ÙÛÚNÍNÈUØÚæÚVÑÒÊÜ5ÌHæUÉ5ÕËݱÛàäÍNÑÒãàÒÑÒÕÑÅÍ~ß5â
³
!#"%$ "%$;7 3%& ( 3 4 $78-94 :%78$
se%r{eJtGjsutj¡ve5}@ehikjmrytKlZlytXnzr sj ro¢qe(
2ryv2e,jmGz%}lojmry@lyet q
2e tUjmeq}@jmg5qzehv }i{e5
jmse'vmtzGe't K
e tjme4|~}@i{utKzehikj#tlyv zKjmro¢KtUjmehvGjmselrjme5
mtj}
e qi2seh
2{´ ryi K
2ryi@|~K
zGtjmrqi(ghtKvghtK{ehv2 Á -tKie5
~£2ehe½X¿q¿q³ Dry©sg#stKi{utKi@rVp¹¡r
vs@lyehro|~eh
5pktKi{ =e5lyg#sHp(½X¿q¿k³´p½X¿q¿K²@p,½J¿q¿q¾kÂ3 i jmse5vezG{ehlvhp¡t e5ijv -tKikjjm g#sqv2e ti tKg3 jmrqixghqi@vryvjme5ijfrojms tKi)t q
e tjmeR|~}@i{utKzehikj#tlVpw}@jjsryv,|~}i{utKzehikjmtKl-ryv(}i´ ©iXfiH¬¨tKg#s Kwve5
2¢qe5v(tú@
r¢tjevr iutKlÔghq
2
ehlytjme5{4frjs'jse%|~}i{tKzGe5ikj#tKlNp;tKi{ jmseng#s´KveRri v2eh}e5ighepZj#tK©ryi rij tghghK}ikj(jms@eRtKgjmrqivK|Djsqvefs g#s@qve w7e|~q
ejms@ehzB ¼/}lojmrlyeq}´jmghKzGe5v(tK
2e7qv2vrwlyewehgJt}veGltJnqe5
v,zRtJn
tjmrqiutKlln |~qlylXajmse%tKg5jryqiv¡K|¨Kjseh
2vhpHr iq
2ryi jmse5ry
¡fi'v2r iutlyvhpr|jmse%ri@|~q
2zRtjryqiri´ |~eh
2
eh{G|~
qz
2e5¢ryK}v-tKgjmrqiv±q}@jehr svjsutj{eh
2r¢qe5{R|~
Kz jmse5ry
±fiRvr iutKlyv5i Kjms@eh
q
2{vhp´z%}ljryle-q}@jghqzehvgJtKiG´g5gh}
w7e5gJtK}@ve¤t q
e tjryqiK|jseªri@|~q
2zRtU jmrqiryi jmsev2r iutlyvD|QtKrlyv5 ¹XDe¢qeh
5pjseh
2e±rvtKlyv2ghqikj
X¢qe5
v2n,tKwq}@jjmse¨
Kw}v2jiehv2vÔ|@se5
{ri wehsutJ¢ryq
5 irjrtKl¥e3¦tzGlehv5p´ri¢Kql¢ri t(v2r itKlufrjmsRqilnj%qvv2rywle¡¢tKly}@ehvhpvs@eh{ jsutj tKiryi´®uirjeDv2eh}ehi@gheK|ltJnqe5
vZg5q}l{g#s´Kve-jms@ef
Ki tKgjmryKiÁ~jseqieDjsutjrv tK
2e5j{@qzGriutjeh{(}@i{eh
Zjse-jm
2}et K
e tjmeDv2j#tUjmeXÂ3 D}´jltjeh
q
2©,v2sXDe5{jsutj tJ¢qeh
t elytJn%tKlo-tJnvZg5qik¢qeh
ehvj¤jmse
r sj tKgjmryKi%r|ujse-vr iutKlsutKvg5qikjmri}@q}v v}@7q
j'Á =riBtg5q}ikj#tKw@ln ri@®uirojme ve5}ehig5e%?A@CB½ED3³FDm¶GDIHIHIHKJ,eJtg#s g#sqve,tKi tKg5jryqMi LN.OPBUG· Dh½ J4sen\g#sqveRryi\q
2{eh
5¯Geh
2vqQi =R ½ ehv®u
vjJpeh
2vqi>³ ve5ghqi{p7ti{/v2|~K
2jmsseiKj#tUjmryKSi ?TNU@VB½ D3F³ DIHWHXHY=ZJ
2e5|~eh
2vjjmse ®u
2v2[j =±t ehikjvh lylH@ltJnqe5
vsutJ¢qe,jsevmtKze}@jmrlyrjn|~}igjmrq]i \ÔÁ L^D _D D ;±¹¡e5
e POa`rvfjse
mtKi@{qzt q
2e tje¤v2jmtjmeÁ~jms@eª|~}i{utzGe5ijmtKl ¨K|jmseªehghKiqz(n @e gJtKllt%s@r se5
´{@Gti{Btleh
.2wutK{@¨se,g5}z%}lytjmro¢qe
2qwutKw@rylyrojnR{@ryv2j
rw}@jmrqi K| ^rv b Á ¤Â3 )ryv-jse |~
mtKgjmrqi K|Ðjmseq}lytjmrqi g#sqvri jmltJn)v2jmg#© jmstjfryv5p c Á׽ @ lyrz g ½ h LNkO l G· DJn½ m c6dfe Nji s@eDutKr
Á _D ¨Â;K|ue3¦@ ehiK}vtKi{,ehi{@ ehi@q}vt K
e tjme¨¢tK
rytKwlehv;jmsutUje5ijeh
jmsef}@jrylrjn|~}igjmryKifrlylw7efghtKlyleh{%jms@eft q
2e tj+e F;)*ops@ev2utKg5e|qvv2rywle
q
q }@jghqzehvfryv @ `7l ·GDJ½(mNi{ro¢ry{}utlyvgJtiiKj{r
ehgjmlonúqwv2eh
¢qe,jse jm
2}ev2j#tUjme K|¨jmsee5ghqi@qz(n K
¤jmset K
e tjme,g#sqrghe -,i@v2jmehtK{Hp;jms@e5n4z(}v2j j
2n j ryi@|~e5
jmseft q
e tje-vrojm}utjryqi,qijmseDwutKvrvK|t¤lyrzGrojme5{(ryi´|~q
zGtjmrqive5jhptKi{zGtU¦´ryzryhe e¦´ehg5jeh{x}@jrylrjntghghK
{ri lnKR¬tKg#s7e5
vKiqwv2eh
¢qehv%t/vr iutKl N_Ofsryg#s\rv ghq
2
e5ltjeh{Gfrojmsjmse¡t q
e tjmefv2jmtjme±°Dqi{rojmrqiutKlKi ,prj¨rvri{ehehi@{ehikjmlontKi{ ry{e5ikjmryghtKlylon{ryvjm
rw}@jeh{)tKgh
2qvvri{r¢r{}utKlvhpZfrjs ) , GÁ ¤Â| p jmse5i jms@e/{rv2j
ryw@}@jmrqi>| g5qi{rojmrqiutKlqi R ®
v2jq
2{eh
v2j´g#stKv2jrygJtlyln {qzryiutUjmehv¡jmse{rv2j
ryw@}@jmrqi fse5i CR p;vújsutjtúsr s N¨ryi{@rygJtUjmehv¤t ´{ t q
2e tUjmefv2jmtjme9 =e¡tKv2v}zejsutj aryv¨g5qikjmryi}K}vDti{GstKv}@iwq}i@{eh{úv2}q
2j DegJtlylHrojmv{e5ivrojn ZÁ ¤Â3 = eghqiv2ry{e5
t }@jrylyrojn |~}i@g5jmrqijmsutjBie5v2jv/jms@
ehe vehg5rtKl ghtKve5v
e5ltjeh{jm ryz7K
2j#tij|QtKgjmq
2vÐ|~
2qzajms@eDlyrojme5
mtj}
e5vÐKi(se5
{ri tKi@{%z%}lojmry@lyryg5rjn¯ryi@|~q
2zRtUjmryKi
e¢qehlytjmrqiHpvjm
mtUjme ryg4g5qzG@lyehzehikjmtK
rojmrye5vhpDtKi{ utJnq ]se5jeh
2 ehi@ehrjnK]se4®u
2v2j vehg5rtKl;ghtKveryv-jsutjK|Ô}
2eri@|~q
2zRtjryqiG
e¢qehlytjmrqiH¯ \ N Á L^D ¤Â R L Á½ L7Â5Á½ ¤Â ÁN³q =rjs4jmse5ve
e|~eh
2ehig5ehvhpÐjmse@ltJnqe5
e|~eh
vvjmg#© r|tKi@{Kiln/r| ½ q³´se gJtKv2e,|vjm
mtUjme ryg ghKzGlehzehikj#t
rjrye5vDqilonúrv r¢KehiBwn¯ \"!$##Á L^D ¨Â R L % Á½ L7ÂhÁ×½ ±Â ÁQ¶k fsryg#sryzlryehvjmstj¨v2j´g#©,ryv
2e5|~eh
2
e5{fse5ie5¢Keh
&]½ q³se-jsry
2{vehghrytKlghtKve ryvutJnK se5jeh
ehie5rjn Kiln¯ \('*)$+Á L^D  R L Á½ L7 Á vjmsutj¡v2j´g#© rvf
e|~eh
2eh{ fs@ehie¢qeh
ryvfqvrojmro¢qeK-§¤}
ehie5
mtKl}@jrylyrojnR|~}i@g5jmrqi ryvftDe5r skjeh{/tX¢Keh
t eK|Ztlyl7js
e5eK¯ \ÔÁ L^D _D D ; R ,-'*).+\('/).+×Á L^D %  0,-!$# \"!$#mÁ L^D ¨1 2, N* \ N3 Á L^D ¤Â Á q  fseh
2efrojmsK}@jflyqv2vK| ehie5
mtKlrjnDeve4j , N3 R ½ 5, !$# 6, '*).+ iRq
{e5
Djm ehie5
mtje¤se5
{ri w7e5sutJ¢ryq
5pe z%}vj r¢KeªlytJnqeh
2vvqzeªri@|~q
2zRtU jmrqitKwq}@jZjmse5
v Kg#sqryg5ehv5pwe5nKqi{jmstj¨ryi@|~e5
2eh{%|~
Kz jse
ro¢tjmevr iutKlyv5¹eh
2eKp ²
Dev2}qvejmsutj7e5qleDqwv2eh
¢qetª
mti{qz^i}z%weh
Z|¥
e¢´rq}vÔg#sqryg5ehv5 uq
v2ryz lyrghrojnqpKeªtvv}@zGejmstj¨7e5
v2qpi = äv¨qwv2eh
¢KtUjmryKiv±tK
e{
tJf$i '&( *( ÁQw}´jfrjms@q}@j¨
e5ltghehzehikj#ÂÔ|~
qz seh
v2e5j±K|
e5{ehg5ehv2vq
24v ?TN @VBE½ D3F³ D(HIHIHD = ½ Jp v%jsutj =ryv£2}@v2jftKvlyr©Kehlonjm%qw@veh
¢qe¤jse¤g#sqrghe¤|Ðt ehikjª½tKvjsutj-|Ðt ehik>j =( ½ q
ftKiknKjseh
2ehg5eh{ri @ltJnqe5
h =etKv2v}ze jmsutU_j =ghtKiBqwve5
2¢Ke(}jm 0 N 23-5 @ zryi!Á 0 23-5 D =1 ½Â ÁQ²kÂ
e5{ehg5ehv2vq
2vhpeJtKg#s frjs ryi{@ehehi{e5ikjf
qwtKwrylrjn s}vjmse¤i}z(w7e5
K|Ð
e¢´r q}vtKgjmryKi>v /'qwve5
2¢Keh{4wkn =¨sutKvjse |~qlylfri wriqzrtKl{rv2jm
2ryw}´jmryKiH¯ 0 NÁ /;Â @
U Á /NR / = R 0 N 24/ 365 Á½ K ÁNµq uq>
= 0 243-5 p´jmsrv{@ryv2j
rw}@jmrqiú{ehvfij¡{@ehehi{Bq#i =puveghtKif
rje rjtKv 0\Á /; @ 0 2/ 3-5 Á×½ q ÁQ¾k sei}@z%w7e5
fK|Kwve5
2¢qe5{
2eh{e5ghe5vvK
vªfslytXnx2v2j´g#©ryv{e5iKjeh${ 8 NV ÔryiutKllnKpe¡zGtK©Kejse¡g5
}g5rtKltKvv2}zG´jmryKijsutj±ryi{@r¢ry{}tKlyv +UQ !"ri4jmseve5}ehig5eKsutjrvhp;lytJnqeh
={@´e5vi@Kj ©iX jmstj vs@erv¤jms e =Qjms 7e5
v2qiRjm,g#sqve±Ã´seª©iXfvqilnjsutjseh
±qvrojmryKiGghtKiiKjwe¡lehvv±jmsutpi / N3\½qp vrighevs@e,sutvKwve5
2¢qe5${ /NÔ@
e5¢rq}vfg#sqrghehv5s}v5p¥seh
fryi´|~q
zGtjmrqiRv2e5j¡ryv5¯ Á / N"D 8 N D NQ ÁQ¿k N @ sevejK|qvv2rywleDryi@{r¢ry{@}utKlv2jmtjme5vryv @VBUG· DJE½ DIHWHWH0 23-5 J +BUG· DhE½ DIHWHXH 0 24365 J - Àro¢qe5i se5
Rryi´|~q
zGtjmrqi O pDjms@e/lytJnqeh
Gz%}vjGj
2nxjm {eh{@}gheBjmse t q
2e tje vrojm}utjryqiÁ _D ¨Â O %e,{@ehiKjeseh
fghKi{rjryqitKl
2qwutKw@rylyrojnGtKvv2ehvv2zGe5ikj tKv5¯ !(#Á "GD%$ /D 8 D Â @ @
qwÁ '&("FD )&*$ /4D 8 D  Á½J·k i ehie5
mtKlNpjmseri{ro¢´r{}utKlghtKi'g#s´Kvetú
2qwutKwrlyrojnK|±ltJnryi LN R½g5qi´ {rjryqitKluqi tKiknGry{rqv2nig5
mtjrygv2jmtjme =eª{ehijme¡jsryv
KwutKwrlyrjntK,v + Á /4D 8 D Â3p fsryg#s rvt |~}igjmryKixzRtK@ryi aryikj7 lÅF· DJ(½ mNs}v5pjseúe¦´ehgjmeh{>}@jmrlyrojn'zRtU¦´r zGrJtjryqiR
qw@lyehz gJtKiwe{@e5®uie5{ qryikjfrvery-i tvh¯ µ
G ( o
Á /D'8 D Â
tK
zGtU¦ l +F\ÔÁ½D _D D ; Á½ +Â-\ÔÁN·GD [D D Â;m !(Á _D - /D 8 D ; + O7l G · DJ½(m Á½K½Â g5j}utKlylonqptKllyXfryi |~q
/zGr¦@e5{av2j
mtje rehv/ryv zq
2e e5ieh
tKl,jsutKi]ie5ghehv2vmtK
nq Àe5ieh
2ryghtKlylon\Á~ryi4jeh
zv¤K|±qvv2rywle%{rv2jm
2ryw}´jmryKiv !ªÂ¤túltJnqe5
¤fryllÔvjm
rg5jln/
e|~eh
·BK
½|~q
tlyzqv2j e¢qe5
2n s}@v,qlyrg5n gJtKiiq
2zRtKllnBwe{@ehvg5
rw7e5{wkn7 ** W, ) "G Á /4D 8BÂ
2eh
2ehv2ehikjmri jmse(vr iutKlyv¡tj¡fsryg#slytJnqeh
2v tK
2e(ryi@{r 7eh
2ehikj w7ejDe5ehi v2j´g#©tKi@{wqi{H/ôrigheRt/sr seh
ri{rgJtjehvsr seh
,pZti{xt/s@r se5
utJnq jGvjmg#©¥pDefryllvehtK
g#sB|~q
-jms@
ehv2sql{/vjm
mtUjme ryehv|jms@e|~KlylyXfri |~q
2z/¯ + Á /4D 8 D Â R ½ r Á /D 8BÂ + Á /4D 8 D Â R · r @ Á /D'8BÂ w}@jfefrlylHtlyvg#se5g#©úfse5jseh
fjms@ryvfryvriú|QtKg5jq@jryzGtKlri q}
fvrz%}lytjmrqivh
+
O
: 3 ( 3 ,%7 3 : /
ki núqlryg5n|~}i@g5jmrqi +Á /D'8 D ±ri{}g5ehvft(vjmg#sutKvjmryg @
ghehv2v LN;|~q
= Op? u
qz jmsrvv2j´g#sutv2jmrg
ghe5vvfDefryllHtKlv{e5®ie N h Á½X³q 9N@ LNtKi{ N@ ½= 9N O N@VBU·GD ½= D ³ = D(HXHWH½ J i vªjsutjÔDe-stX¢Ke R lry+z N d[e NV ¡jmejsutj NgJtitKlyv2ªweDgJtlygh}@ltjeh{(
2ehg5}
v2r¢qe5ln¯ N R N ½= Á LN( N  Á½J¶k sryv(
eh@
ehv2ehikj#tUjmryKi)rv(}v2e5|~}lDw7e5gJtK}v2e rj(vsXfvjmsutUj%eJtg#s)s@ryv2jq
2n B N"J Ne i sutKv jmsevjm
}@g5jm}@
eK|-$t ;)*G!")**) opHfs@ryg#s'v} K ehvjmvjmsutjegJtKi }ve
e5v}lojmv-|~
2qz jms@etK{utK@jr¢KeleJtK
2iryi lyrjeh
tjm}
2eªjmtKitKlnhe g5qik¢qe5
e5ighe,K| NV Ð\v27e5lylq}@jRjse vjmg#sutKvjmryg
ghe5vve5vú|~q
LN tKi{ NVp
ehghtKlylf®u
2v2jújsutjRjse ) , ZK|jseªt q
e tjef|~}@i{utKzehikj#tluryv b Á ¤Â3 ¡e3¦jJp´|~K
±ehtKg#p s = Op?p´tv2r itKl Nrv {
mtJfifrjms{rv2j
ryw@}@jmrqi RÁ ªÂs@ei}z(w7e5
±|qw@veh
¢tjmrqiv / Nryv{@
mtJfiGfrojms {ryvjm
2ryw}@jryqi 0 N Á /HÂse5i r|jse¡|~
tKg5jryqiK|
2eh{e5ghe5vvK
v-fs%stX¢Ke¤lytXnKeh{úvjmg#© ¾
"!
yr v NR $qp@ÁQvjmsutUjÐjse¨i}z%weh
fsªsutJ¢KelytJnqeh{,v2j´g#© rv 9NR = $Â;jse¨
qwtKwrylrjn jmsutUj¡e3¦@tKg5jln 8.
e5{ehg5ehv2vq
2v¤ltJnKeh{Bv2jmg#©¥p¥q}@jfK|4/ NR /'qwv2eh
¢KtUjmryKivhprv aNÁ 86 /4D $Â @ @
qwÁ 8 NR 86 =ZD /D $ @ 8 / = ½ Á $I=1Á $IQ= 8B Á = $IÁ = = 7$I8= Q/H Á½  fsryg#s/tK@
ktKg#s@ehvfjmse |~qllyXfryi wryiKzGrytKl7lryzrjryi {ryvjm
2ryw}@jryqi ro| =±rvltK
eK¯ Á 86 /4D $ @ 8 / $ 2 Á×½ $U 2 Á½ q  À r¢Kehijmseryi@{r¢ry{@}utKlvj#tje N^R Á / N;D 8 N"D N~Â3p¥ltJnqe5f
= Åvªg#sqrghery>v LNUR ½frojms
KwutKwrlyrj-n +HÁ / N!D 8 N;D N Âp7tKi{45eh
RKjmse5
2frveK¡sryv¡ryzlyrehvftKi e¦´lyrghroj|~K
z%}lyt |~q
(jseú
2qwutKwrlyrojnjmsut+j LN R ½qp ro¢qehi\jseR|~
tKg5jryqi N K|
e5{ehg5ehvv2q
vfs ltJnKeh{Bv2jmg#©¥pujmseryi@{e¦ =2pjmsevj#tje putKi{jmseqlyrg5n +HÁN¯ NÁ N D _D +HÁN @
2qwÁ LNUR^½ =ZD N D [D +HÁN R Á½J²k h 0.N Á /H h aN× Á 86 /4D N  + Á /D'8 D  GÁ ¤Â i i2 ¡Kjryg5e jmsutUjú|~q
úlytK
]e =_p 0 N 24365 R 0 24365 p N× Á /HÂ R RÁ /;Âp¡tKi{ N Á 86 /D $Â Á 86 /D $Â3puvjmseve5}ehig5e(K|Ô|~}igjmryKiv NÔtK@
ktg#sehv¡tlyryzrj ¯ (#Á $ D "GD +ÁV @ N ld[ryz e N×Á $ED%"FD +HÁN Á½Xµq uq
eJtKg#as / tKia{ 8pHjms@elryzrjryi {ryvjm
2ryw}@jryqi Á 86 /D ¨Â¤ryv t v2zGKjms|~}i@g5jmrqi K| -p´tKi{Gjseªlryzrjryi |~}ig5jryqi ryvH£2}v2jDtehr skjme5{úv}z X¢qe5
Djms@e|~}i@g5jmrqiv seh
2e5|~q
2e ryvft e |~}igjmrqiK| - s@ryv|~}@ig5jryqi se5lyv-}@vghqivjm
2}g5j-jse
2qwutKwrlyrojn{ryvjm
2ryw}@jryqiGX¢qeh
ft q
e3 tje¤q}@jghqzehvÁ D ¤Â3±°Dqivr{eh
jmse¤g5qi{rojmrqiutKl
KwutKwrlyrjn GN×Á $ "GD +ÁVÂÂZjmstj N j#tK©ehvvqze utK
jmrgh}lytK
D¢tKly}@e $,ryi NN¯ N×#Á $ED "GD +HÁNÂÂ @
2qw,Á NR $ =ZD R("GD +ÁVÂ2 Á½J¾k sei}z%weh
Zfs @ltJn(vjmg#©%}%jtKi{ryi@ghly}@{ryi t ehikj =2p 9Npqe5}tKlyve5rjms@eh
9N q
9N a½qp;{e57e5i{ri qifse5jseh
q
ij =ltJnvv2j´g#©¥%srv zGehtKiv¤egJtKi gJtKlgh}lytjme GN×Á $ _D +ÁV¨
e5gh}
2vr¢Kehlon |~
qz N #Á $ _D +ÁVÂ2Â uq
ftin $1O NVp@e,sutJ¢KeK¯ ¿
Á HÁNÂÂ
GN $ [ D +
R
N
= $ [D +HÁNÂ ½ N = $ D_D +ÁVÂ = ½ 1= ½ GN = =1$ ½ ½ _D +ÁVÂ N == $
Á½J¿kÂ
½ D _D +HÁNÂ ½ À r¢Kehijmse5ve
KwutKwrlyrjrye5vhpegJtKiGie¦j{e5®ui@ejse¡g5q
2ehv27qi@{ryi gh}@z%}ltUjmr¢Ke {ryvjm
2ryw}@jryqi X¢Keh
>tKi{ ,¯ ^N×#Á $ D " +ÁVÂ2 @ e h NÁ - _D +ÁVÂ2 b Á ¤Â ÁV³·k ! =e frlyl{@ehiKje,wk n jmselyrzGrojJptKfv = pu|Ôjsry+v ) , y¯ GÁ D +HÁN @ N ld[ryz e NÁ D +ÁV ÁV³½Â =stj{ehvjselyrzGrojmri {ryvjm
rw}@jryq i lyq©lyr©Ke s@eftKiv2eh
¨rvZzRt{eDehtKvreh
wknjmse|QtKgjjsutj N±ryvt vjmg#sutKv2jryg
e5gh}
2vr¢KeRtl q
2rjsz/p7ryijms@ev2ehiv2eG|-¬Z¢tKiv tKi{¹qi©UtKqsU£t ÁV³K·q·´½Âsen v2sX^jmsutj¡}i{@eh
¤g5eh
2jmtKryi/
e }lt
rjnúghqi{@rjmrqiv5p t(v2j´g#stKv2jrygª
2ehg5}
v2r¢qe¤tKl K
rjsz g5qik¢qeh
ehv-frojmsú@
qwutwrylrjnqi@e¡jm(vqze¡vj#tKw@lye ®@¦´eh{ 7qrikjK|tKitKv2vghrytjme5{\§ º ¬pt
qeh
jnjmsen'gJtKll¬vj#tKw@rylyrojn%iq}
gJtKv2eKpfjmse4¬Zv2jmtKwrylrjn g5
rjeh
2ryqi> vryzlon zGehtKivGjsutjújse4lryzrjqryikjvúK| N t
e 7Kryikjmv-fse5
e ag5
qv2vehvjmse q lyryi@eª|~
qz tKw7X¢KeK Ãryig5e stKvú}iwq}i{e5{v}q
jJp rvútKwX¢qe jse q lyrieBfs@ehi R*·@p tKi{xweh l roj(fse5i PR ½Ki\jmse ehie5
rygRgJtKv2eúfseh
2e rv(ie¢qeh
%jmtKi e5ikjjm jmse q lyrieKpDe ghtKi{e5®ui@e Á ¤Â @CB ! Á ¤Â D Á ¤Â D ! Á ¤Â DI H(HIH(D ! Á ¤Â Jjmwe jmse(³ Á ¤Â ½,qryikjvri\ÁQG· DJ½Â-tUjfs@ryg#s ^g5
qv2ve5v¡jms@e q lryiepghKi{rjryqitKlHqi t r¢Kehi ,º¤e5®uietlyv4jse vejK|R2v2jmtKwlehgh
2qvv2ryi vhp¨jmsutj%ryvhpg5
qv2vri v%|~
Kz tKw¢KeK¯ ! Á ¤Â @CB ! Á ¤Â D ! Á ¤Â DIH(HIH(D ! Á ¤Â J atKljsq} s q}
fzG{e5lH{ehv iKjvtjmrv2| n%tKlyljmse
2e }@ltK
2rjnghqi@{rjryqivÔK|7¬Z¢Ktiv±tKi{¹¡Ki©UtK7KsU£t@pKegJtKiv2sX jmse |~qllyXfryi
e5v}lojJpu}v2ryi tK
}zehikjmv|~
Kz u}{e5iweh
ti{ ;e¢´rieGÁ½X¿K¿q¾k ù" #&2%(ÇH')%(È' ب+ÿ *,ÙÛÊU#ÕÍVÑÒʤÑäÎ5ÊÎÛ´ÚHù Ê5ÎÿÔÍVÞXÉ3Ø×ÍNòÑÒÎÊÊØ2â Þ Î5Ê ãUÉ3Ü5Ø Î3Ù¥ö #É3ÊÌÐÉ3ÊÞ íÎÊUËmÉãÎ5!È QÉùyû3ü5üýÿHÕÎÚVÚNØÌQãKÎÊÞÌHÍNÎ $
½X·
ô}@7Kve jse4qlyrg5nx|~}igjmrqi ryv +útKi{ jse4t j#tK
ei tehjike j-v2jj#%tUjmjmsee ryv q , p±lrytKii@e{jsuste5ijjfsroe jmsú|~}@i
qg5jwurytqwi ryl(rjnÁ qD i_eD p´+jsÂ(e¤rlyvrzGie5roj¨¢KehK
| NÐe¦´ryvjmvhptKi@{Bvtjmrv2®ue5v O ! Á ¤Â ÁV³q³K N ldfryz e N @ fôe5etKehi{r¦7 s}v5pughqi@{rjryqiutl7qi jset q
2e tUjme¤vj#tje ,p NghKi¢Keh
ehvfjmqie |t%v2e5jK| ryv2q ltjeh{qryikjmv5¯jmse7Kryikjmv ! Á ¤ÂDfse5
ejmse a|~}igjmrqi |~q
jmsutj ]gh
2qvv2ehv¡jse e ) , GÁ D ªÂryvªtRv2jeh4|~}i@g5jmrqiHpfsryg#s q lyryi@e|~
2qz tw7X¢qe uq
ªehtKg#s ,pjms] ryig5
ehtKve5v¡qi@ln tUjjmseqryikjmv ! Á ªÂ À r¢Kehi pDe ghtKi iXghtKlyg5}ltje jmse/{ryvjm
rw}@jryq)i !jsutjRtlytXnKeh
vsK}ly{ tjj
rw}@jmejm tKi{ ghKi{rjryqitKlqiseh
ZKwve5
2¢tjmrqivfÁ /D 8 D Â KjmejmsutjZvryi@ghe t e5ijvZ©iX)iKjms@ryi tKwq}@jjsehr
Ôqv2rjmrqivryijmseve5}@ehig5e(Á~e¦´ghe5@jZjsut4j = / N~Â3p jmsef
2qwutKw@rylyrojn(|wehri tzehz%weh
|HtKikn®ui@rjmerirjrtKlve5}ehig5e ? R BE½ D3F³ D(HXHWH J ryvfie lyr rywle¤ghKzGut
eh{jmjms@e,
2qwutKw@rylyrojnR|Zwehryi riBjse,v2e5j B ½ D ³ DIHXHWHjJ s}v¤lytXnKeh
2vªvs@q}ly{/r i@q
e jms@e(
2qwutKwrlyrojmrye5v NtKi{ aNZtvvghrytjme5{/frojms wehri qie/K|ªjse/®u
2v2jGjmg#s´KveKptKi@{ ghKivr{eh
qilonxjmse5ry
lyryzrj,v tKi{ »¡vri -tJnqe5v -lytXpfro|t e5ijvúlytX7 n LVR ½ frojms
2qwutKw@rylyrojn + Á /D'8 D Âp-jsehi
tjmrqiutKl e¦´ehg5jmtjmrqivf
e5}ry
2ehvfjmse |~qllyXfryi
qwtKwrylrjnGtKv2vehv2vzehikjJ¯ ! Á 86 /D ±Â ZÁ ¤Â GÁ D +ÁVÂ2 ÁV³¶k !%Á#"FD $ /D'8 D  R e e Á 86 /D ±Â ZÁ ¤Â GÁ D +ÁVÂ2 e s@ryv¤
2qwutKw@rylyrojnBryi@|~q
2zRtUjmryKi/rv tKlyljmstjtKi'ryi@{r¢ry{@}utKliehe5{v jmg#sqveK´ jmrzRtKlln ¥tKi{/jmse%ri{ro¢´r{}utKl ävqlryg5n |~}@ig5jryqiHp7tKvDe%stX¢Ke£2}vj ve5ehiHpHv26} >ghe5v¤jm ghqi@v2jm
2}g5jjms@ryvghKi{rjryqitKl{rv2j
ryw@}@jmrqiHZs}vfDeghtKi/i@a{e5®ui@ee5}rylryw
2ry}zB !#"$% & ' ( ' '&( F ( orv,t ") , F) " +HÁ /D 8 D ;Â tKtij{ryvt]| nú)*jmse5ve "jD EghK*i{*rj( ryqi@vh ¯ ( " !(Á _D /D 8 D Âfs@ryg#s m v Àro¢qe5i !pu7Klyrygn +Rvqlo¢qehvjseryi{ro¢ry{}utl Åv-
Kwlye5z Á½K½Â ) ,Àro¢qehi +7p¥{rv2jm
2ryw}´jmryKi ! vmtjryv2®ehvªjse(
tjmrqiutKl;e3¦@ehgj#tjryqi@v¤ghqi {rjryqiÁN³K¶kÂ3$* ÙùQÛý Ê+ÿ×ÕíÐéXÍNÑÒÙÎØÛÚV0Ê ÊUØÐÕ×.ÍVÍNÈÑÒ1NÎéuØÊÉÙÎ̱78ÚVÞݱ1QØ×éÛòUÉ5àÖÊɨÌ;ØÞXÙÞÎ5Ø×-Ú òUÑÒÊÊU,/Ø2ùÞ¤ÑÒû3ʪühÑÒÿÊ%Ø2é@áhùQÛUÙý:ÛÉ#9JÊUÍVÿÕ×ÑäéXÎ5ÍNÊ,ÙÑÒÎÛ3ÊÊùyû Õ245ÍNÑÒÿ1~ÎéuÉÊ ÉàÒÌNÌ" ÎDÞXéUÞØ×ÉØòÌ;ãKÊÞXØØ2ÊUØÞòUÞÊÌHÑÒÊØÎ5Þ¤Êfù~6ý ÑäÙÊ55Ûÿ×Êù~é´ý{r e5
ehikjR
e ryzehvK| wehsutJ¢ryq
5 |ªjmse/seh
2{ryi ryig5ehikjmro¢qe ghqzehvzqv2jln |~
2qz ri@|~q
zG tjryqi4
2e5¢KehltUjmryKi Á~gJtKv2ehv , !$# R G· HÒ¶BtKi{ ·@ q Âpjms@ehi w}l ehvq}@jt
q}i@{ jse q lryiepZfrjms)tvri le v2j#twlye g5
qv2vryi |~K
eJtKg#s ,ptj ]·|~K
R ·tKi{/tj ½ |~q
R ½K u}igjmrqi ]w7e5i{vwutKg#©újDtK
2{vjse q lyryi@e¡tUjDjms@eªqqv2rjmeehi@{Hp@w}´j-{ehv-i@KjDg5
qv2vt tryiHpv(ltJnvsK}ly{Gghqik¢qe5
e jmGtGv2ryi le q}@jghqze fÁ ¤ÂD|~q
feJtKg#s ,f§¤iBjseKjmse5
¡stKi{Hpu|~q
sr seh
fv2j
mtje rg ghqzlehzehikj#tK
2rjryehv5p , !$# R F· HÖµRq
·´Ò¿@p7jmse |~}igjmryKig#sutKi e5v{
mtKzGtjrygJtlylnK¤j ½X¶
ryvfiX ÃvsutKeh{p¥frojmsjDRv2j#twlyegh
2qvv2ryi vhpghlyKve jmGheh
2útKi@{/qi@eKp¥|~q
feJtKg#s , sryvzeJtKivse5
{ri ghtKi f
2qi frjs qv2rjmro¢qe
2qwutKwrlyrojnqpghqik¢Keh
ryi jm zGK
e¤jmstKi/Kieq}@jmg5qze ryieJtKg#sBv2jmtjme , = e¨qwv2eh
2¢Kejse@
ghehv2vÔ|ghKi¢Keh
ehig5eDri r }
2ehvгftKi{,¶@ Ôr }
2e±³f@lyKjvjse vrz%}ltUjmeh{/gh}z(}ltjr¢Ke({rv2jm
2ryw}´jmryKi
2qwÁ & $ _D + ÂtKv tG|~}@ig5jryqi4| $kp7|~q
eJtKg#s tKi{R|~q
±eJtg#sú¢Ktly}eK| , !.# g5qivr{eh
2eh{H¨sutUj-ryv5pe¤lKj±jmse¡{ryvjm
rw}@jryqiHp tKgh
2qvvsrv2jmK
rye5vhpÐK|Djse|~
mtKgjmrqi |-ryi@{r¢ry{@}utKlyv¡fs sutJ¢KeRg#sqv2ehi LQR.½qpÐ}jm tKi{righl}{ryi jms@e¶q·q·js4ryi@{r¢ry{@}utKlV s#e ) , K| g5qi{rojmryKiutKlqi PR · lyrehv¤jm jselye5| j|ÁQK
tKw7X¢KeXªjmse ) , g5qi{rojmrqiutKlÔqi R ½q¯tKve¦´ehgjmeh{pZt lyX >ryvzq
e lry©ehlnfse5i R ·@ | , !$# R G· Hä¶q
R·@ q pjmse5itKvúK.| = R ¶K·q·@p
K} slon ²K· |sryvjmq
2ryehvGsutJ¢qe ghqik¢Keh
eh{,jjmse,2
2r skjmft q
e tjeq}@jmg5qzeK =rjms @
qwutwrylrjnª·@Ò¶´pjse¨q}@jghqze ryv R·%tKi{ a6· ti{Rfrjsú
2qwutKwrlyrojn·@ä¶@p@rojDrv R ½ tKi@{ ½q D}@j ryijms@eG
2ehzGtKryiri srv2jq
rehvhp ryvv@
eJt{tKlzGKv2j }i@r|~q
2zGlon we5jehe5ix·/ti{ ½q r }
e¶vsXfv tvmtKzle|±³K·q·sryvjmq
2rye5v|Zlye5i js q ·K·|~q
fjms@e,ghtKve , !.# R]G· H q p ghqi@{rjryqiutl¤qi R ½K ¹¡e5
e'De ve5e jmstj Nv2qzGejmrzGe5vBg5qik¢qe5
e5vtKlyzqvj ryzzGe5{rtUjmehlon j Kie\Á jmse5
eBryvt'ghq
2
ehv27Ki{ryi v@ry©KeBryi jms@e/{e5ivrojn |~}ig5jryqip lyjjme5{w7e5lyX¡Â }@j Kjseh
¤s@ryv2jq
rehv¡v2j#t
2j iehtK
¤5eh
ti{4jme5i{'vlyXflon/}@DtK
2{vhp tKi{/tK
e vjmrlylfr{ehlonúv@
eJt{/q}´jªtv| =4R q ·q·@ i ghqikjm
tKv2jhp7|~q
, !.# ]G· HÒµ´p Ôr }
2e%³vsXfv¤jsutj ryv¡tKlyzqv2jªtKlo-tJnvªiehtK
·q
ú½qseq}@jghqze R ·tKi{ ·4ghg5}
vtK
2q}i{)¶ q K|fjse jmryzeKp fsryleGjse q}@jghqze R · tKi{ "½ú´g5gh}
2v ½ q K|jms@eújmryze |~q
R ½ jmseª
qwtKwrylrjryehv±tK
2eª
2e5¢qe5
v2eh{H±s}vhpuvjm
Ki v2j
mtje rgªg5qzG@lyehzehikjmtK
rojmrye5v¨ryzln tJ¢qeh
t eltJn ghqik¢qe5
e5v(}rg#©lonqpw}@jzGtJn4ghKi¢Keh
ej jmsef
Ki tg5jmrqiH%s@ryv }ryg#© g5qik¢qeh
ehi@ghe(rvftKlyv2vehe5i ri Ôr }
2e¶@p@fse5
eryiBtvmtKzlye |³K·K·s@ryv2jq
rehv5p tKlylw}@jqietK
2eghlyehtK
lonRj
ehi@{ryi }Bq
{XfiBwknv2jme5] =4R ½J·@ i4tKlyl;jms@ehve(vryz(}ltjryqi@vhp;½X¾R@
eh{@ehghe5vv2q
vtK
2e(qw@veh
¢qe5{KitJ¢qeh
t ep;tKi{ jse lyrzGrojmryi xrvDg5lyqv2e¡jm%·(q
ª½Kp@vzqvjDlytJnqeh
2vgJtKiReJtKv2rylnri@|~eh
¨jmse¡jm
}@e -9 =sehi ÛÊÕ×Î÷ ÊÊ,ÞXÍNÑÅÍVÈÑäØ-Î5ÊUÜ5É3ÚVàkÉãUãÚNÈÎ5éqæUÍNÉ3ÈUæØDÑÒàÒÝÑÅÍ~ßfÉ JÎÑÒÙݱ¨ÛUÝâ ãÚVÎæUÉæÑäàÒÑäÍ~ßÌQÈÎ#ñ;Ê,ÑÒÌ ü ékæKØ2ÕÉÛUÌNØDñØDÈUÉ Ø-ÌNÕ2É3àÒØ2ÞæhßÍNÈØ ÎÍNÈØ2ÚVÌ2Ø2â ÌVÌDÍNÈUÉÊBû3üü(àÒÑäÊUØ2ÌfÉÚNØ JÑÖÌQÑÒæàÒØéHÌQÑÒÊUÕ×Ø,ÌQÎ5ÝDؤÈÑÖÌQÍNÎÚVÑÒØ2ÌfÌNÎÝ-Ø×ÍVÑäÝ-ØÌàäÑÒØ Ø É5ÕÍNàÒßÎ5ÊRÍNÎãúÎÙ ½
yr vvzGtKlylNp ryv±}ir}@ehlnlryi©eh{Gj ,pv ryv±ryi´|~eh
2eh{Rj´@Z¹¡Xe5¢Keh
hpjsryvtKlv zGehtKivjmstj|~q
lyX, !$# pt |~et e5ikjmv±tK
efv2qzGejmrzGe5vjmKjmtKlylon({@ehghe5r¢Keh{Hpehv27e5ghrtlyln ieJt
ªjmse(w7e ryii@ryi K|jmse(veh}e5ighe(|jse(®u
2v2j |~e5 lytJnqeh
2vªj#t©Ke%jms@e'f
Ki tKg5jryqipqjmse5ry
v}@ghghe5vv2q
vDtK
elry©Ke5lnjmlytKghesr s
KwutKwrlyrjnqijms@e- f
qi tKi{ jmG
eheJtUj¡jsehr
e5
2q
h-s@ryvryvfskn ^g5}
2¢Kehv¡wutKg#© jmXDtK
{vjmse q lyrietjwKjms ehi{@vhptKi{f
Ki q}@jmg5qzehv N¥tK
2e7e5
v2ryv2jehikjJptKv Ôr }
2ehv-½×¶¤vs@§ ijseKjms@eh
sutKi{pfrojmsv2j
qi eh
±v2jm
tjme rygfg5qzG@lyehzehikjmtK
rojmrye5vhpq@ltJnqe5
v±©i@ jmsutj¨jse jmsen qwv2eh
2¢KeúryvK| jehi\righqi@vryvjme5ijfrjs jseGj
}e ,BÀro¢qe5i\sr s , !$# pÐjmseGryig5ehikjmro¢qe jm%zryzrygjmse5
v-q}´jDe5r svjmse¡ryig5ehikjmro¢qeªj(g#sqveªryi tKg5ghq
2{utKig5eªfrjsGjseªjm
2}e v2jmtjmepuvjmse/f
2qi q}@jghqze ryvfv2ehl|V|~}l®lylyri e5¢qe5i rijseryi@®irje¤lyrzGrojJ , !.#
#* 4 3 :%*:%1
3+1 467 3 , : 483+* *
sryle4q}
g5qighl}vrqivújs}@v|Qt
zRtK©e'vehi@veKp¡DevsK}ly{g#se5g#©fs@e5jms@eh
jmsen g#sutKi eGro|DeRtKlojme5
¤jmse{ryvjm
2ryw}@jryqi'K| ,iutK
jmrgh}lytK
hpHeRv2sq}l{ g5qivr{eh
,t ghqikjryi}q}vÐv}@7K
2jÐ|~q
,pUvryi@ghe¨jmsrv;ryv;jmse±}v2}utKltKv2v}z@jmrqiryi jmse lqwutKl tKzGe5v lyrojmeh
tjm}@
eKpqtKi{zRtJn(ryzln(t v}wvj#tKikjrtKlln,{r 7eh
2ehikj¨ryi@|~e5
e5ighef
2qwlye5z/Ðs}v¨De ie¦jªtKvv2}zejsutj ]ryv{rv2jm
2ryw}´jmeh]{ 0\Á D Â ÁQv2RtKvwe5|~q
2eKp ]ryv}v2}utKlylonúwe5jehe5i ·/ti{>½XÂ =etK@
J¦´ryzGtjme%jsryvghtKvewkn'zRt©ri jmsev2}q
21j ` t
2ry{'K|¡½ q ½ 7Kryikjmv|~
qz #½,jm³´pfrjs4v2jehv¤|±·@Ò·q³´ = etKv2v}ze \rvªghKi{rjryqitKlylonúiq
2zRtl frjsRzeJtKi /G· H q tKi{Gv2j#ti{utK
2{R{e¢´rytjmrqi 9R G· Ho½qptKi{De¡ve5j 0 24365 R ½X·tKi{ R G · Hä¿@ = eghqzutK
2ejsegJtKv2ehv , !.# RG· Hä¶GtKi@{ , !$# R G· Hä²@ Ôr }
2e vsXfvDjseª
2ehv2}ljvhp´fs@ryg#s e5ieh
tKlyrheq}
e¢´rq}vghqig5ly}v2ryqi@vriútKi ryikjm}@rjmro¢qeªDtJnq±se
mtsviXav2sX ½ q ½ {r 7eh
2ehikj |~}igjmrqivvrz%}loj#tKie5q}v2lnqp qie(|~K
¤eJtKg#s
ry{ 7qrikj¤K| `úi4jms@e%ghe5ijeh
K|±ehtKg#s
mts4Dev2ehe%jseÃvsutKe K| jmstjf´g5gh}
2vfieJtK
R G· H q p@frojmsz%}lojmrlye¡gh
Kvvri v-|~q
wKjs , !$# R G· Hä¶tKi{ , !.# RG· HÒ²´úôrighejms@evjme5vrheG|~K
ryv·@ä·k³´p;eGghtKig5qig5ly}{e|~
Kz jmse
tKs jmsutUjÐfrojmslyXv2jm
tjme rygg5qzlye5zGe5ijmtK
rojmrehv¨Á , !$# RG· HÒ¶qÂpUz%}ljryleq}´jmghKzGe5vÐghg5}
|~
qz
2q} s@ln R G· Hä¶ jm R F· HÒ²q²RÁNtK
2q}i{Gqie¡v2j#ti{utK
2{R{e¢´rytjmrqiK| ¤Â3 uq
, !.# RG· HÒ²´p@jmse5
e,tK
e z(}ljryleªq}@jghqzehv|~
2qz R ¡G· HÒ²%j R E½ Hä²@ iBwKjms
mtK@svhptKvfDez¢Ke(tJDtJnB|~
2qz RaF· H q pu|~}i@g5jmrqi ^tK
g5v¡K}@j-t
{v |~
qzjmse q lryieputKlzGqvjw}@jij¡}rojmegh
2qvv2ryi jfrgheK vfwe5|~q
2eKpjsryvfryzlryehv ½q =
7 e5
v2ryv2jehikjfryi@rjmrytKl2eh
2
q
2vp´w}@jfe¢qehikj}utKl;ghKi¢Keh
ehig5e jmt%}ir}e q}@jghqzeªg5qi´ vrv2jme5ikj- frjs , uq
±zq
ee¦jm
2ehze¡¢tKl}ehvK| ,p w7e5ghqzehvDtKlyzqvjutjJpgh
2qvv2ryi jmse q lryieZ£2}v2j-qighe¤tKi{ ryzlon´ri }ryg#©Gghqik¢qe5
e5ighe j(jmse 2
r skjm%q}´jmghKzGe s}vfse5i sutKvghqikjryi}q}vv2}q
2jhpÐjseve5jK|-t q
2e tUjmev2jmtjme5v{r¢ry{@ehv ryikjmújs
e5e
e ryqi@vh¯f|~q
¤lyX ,pjseh
2eryv±£2}@v2jqie(q}@jmg5qzeKpfrojms 6· tK
2q}i{ RaG· H q jmse5
e,tK
ez%}lojmry@lye¤q}´jmghKzGe5v tKi{|~q
fsr s ajmseq}@jghqzeryvf}ir}ehlon ½qÃjm
2qi e5
vjm
tjme rygghqzlehzehikj#tK
2rjryehvDzRtK©ejseryikjme5
2¢tKlK|Zz(}ljrylryghrojn fry{e5
hp´w}@jroj-ryviqie5zG´jnRe¢qehifrjsú
e5ltjr¢KehlnlX , !$# sryv×jm
rutK
jmrje¡g5ltKv2vr ®ugJtUjmryKiB|Ô|~}i@{utKzehikj#tKlv/ÁV¼Bq
2ryvftKi{ ôsri'½X¿q¿q¾k±ryv-|QtKzrylrtK
¨|~
qz jmseg5qikjme¦j K|gh}
2
ehi@g5n'gh
2ryv2ehv }i{@eh
|~}lylÔryi@|~K
zGtjmrqiH lvp r }
2e sehlv }v
e5ryikjme5
2e5j jmse,gJtKv2e%K|¨wriutK
n v2j}{rye5{4ryi4ôehgjmrqi¶@o½q¯-wKjms R ·Rti{ R ½(lyryerivr{e jmse5qieK|Zz(}ljryleªq}@jghqzehvro| , !$# R G· Hä²@pw@}@jq}@jmv2ry{e rojfr| , !.# RG· Hä¶@
.
.
¤§ }
,@}
qveGseh
2eRrvj ghKzGut
ejmseryzlyrgJtjryqi@v¤K|-s@eh
{@ryi jm/jsqv2eRK|-|~}@lylo ryi@|~K
zGtjmrqi tKzehvtKi@{ lqwutKl tKzehvhGs}vhpÔv}qv2eRie3¦´jjmstj tKi@{ t
e 7e5
2|~e5g5jmlon qwv2eh
¢qeh{D¬}rylryw
2ry}z jms@ehiB
eh}r
e5v¡q´jmryzGtKlg#sqrgheKp r¢qe5i ]tKi@{ -¯ tK
zRtU¦ +\ÔÁE½ D _D D  Á×½ +- \ÁQG· D _D D  ÁV³ q  +Á D D ¤Â O +pO7l G · DJn½ m tKi{Brjftlyv
2eh}ry
2ehvjmstj )
e5v}lojmv|~
Kz t q
e tjmri g#sqrghehv +¯ R +Á D D ¤Â GÁ ¤Â ÁV³²k ¬}utjryqi@vÁV³ q ÂGtKi{ ÁV³K²qÂR{e5®ui@e txwehvj/
2ehv27qi@ve|~}igjmryKi $AR N Á D ¤Â fsryg#svj#tjehvjseD|~
tKg5jryqi $|t ehikjvfsªq}l{%ltJn 2vjmg#© g5qi{rojmrqiutKlqi(jse ryi@|~K
zGtjm rqN iGjsutjjms@e|~
tKg5 jryqi |Zt ehikjmvlytJn´ri v2j´g#©úeh
2e s}vfjms@eqrijv fseh
2e g5
qv2ve5vjse q lyryi@e,|~q
r¢Kehi tK
e,jmseq}´jmghKzGe5v fÁ ¤Âjsutj ghg5}
ryiú|~}lloryi@|~q
2zRtUjmryKie5}ryl ryN w
2ry}zB¬ N }ro¢Ktlyehikjlnqp´DegJtiB{@e5®uiet , ;I,Io " '&( F ( o tv¡tutry
Á + Á D ªÂp Á ªÂÂjmstjvqlo¢qeGÁV³ q Â-tKi{ ÁV³K²qÂ
½X²
Kjmrghe jmstjª}@i{eh
f|~}llÐri@|~q
2zRtjryqip´jms@e,r{ryqvnigh
tjmrgv2sg#© tK{{vsejmeh
2 ehi@ehrjnjutJnq7v(qi@lnqpij jmBryi@|~q
2zRtUjmryKiH%srvzeJtiv jmsutjfrojms'|~}lylZri@|~q
× zRtUjmryKiHpkv2j
qi eh
Dvjm
tjme rygghqzlehzehikj#tK
2rjryehvZ|QtJ¢Kq
Dz%}@ljmrlyrghrojn,|;eh}rlyryw@
ry}@z/p fsryle
ehtjme5
fse5jeh
ehie5rjn | '|QtJ¢qq
2v}@iry}e5iehv2vhÃ7e5ghr®gJtKlln¯
) ¹¡ql{ryi ®@¦´eh{jse{ryvjm
2ryw}@jryq% i
tKi@{4jmseut
m, tK!.z# e5rv jehv
}6,>'*g5)$ry+ ehpÐikjjsln4eh
2g5eGlyqrv2v(e%tjm}ihre5
}ept|~}@ily{ lryz(i´|~}ql
jzGrytlryjmghrroqji4n e5r| }@, ry!$ly#rwry
v r}v2z}6>ro| ghrehikjmlon ghlqve¤jGqi@eK ]ô}@7qv2e rvi@q
zGtKlVp¨frjs>g5qi{rojmrqiutKl-vj#tKi@{utK
{>{e5¢rytjmrqi g#
mtKtKsuiztK{i e5g5 jqe ehi
2{svhpHroryjmv,jmrys@Kg#ehius
tKqelryg5zGrpe v ehL)tútKi%}r|fiv2}rtg#lyl¨}@seKjmjmsu|~s@}@tehlyjZl
vt¤ri@{@|~lryqtJ{
2nKzRehv24
tjfjmryqrojmiBs( ehjs}e-rr¦´lyzryriweJ
tKr}i KzjmGs@ehDr|
%q4}@ulytr{ v v}6>g5ryehikjlnlt
eptKi{Bz%}lojmrlyrghrjnro| ryvv} >Gg5rye5ijln v2zRtlylV fôe5etKehi{r¦7 ijmse¡tKehi@{ro¦eªghtKlyg5}ltjew7K}i{vqijsehv2eªe5}@rylyrw
ryt@pq}v2ryi jmseryi@{r 7eh
× ehig5e(g5qi{rojmryKiÁ ³qÂtKi{jms@e|QtKgjfjmsutj½ |jms@e,iK
zGtKlH{rv2jm
2ryw}´jmryKiBlrye5vzGq
2e jmsuti³´Ò¶K¶ªv2jmtKi{utK
2{{e5¢rtUjmryKivZtKwX¢qerojmvzeJtiH = eD®ui{jsutjjseh
2eryvtKieh}rlyryw
r}z frojms & G· Hä¿q¿¤r|tKi@{Kilnr| -" Jpti{tKieh}rlyryw@
ry}@zaN 3f rjms G· Hä·@½ r|ti{ qilonr| " p´fse5
e " ÁNG· H ¿ , !$# F³ Hä¶q¶ , '*)$+ @ @.Á , , '/).+ Â3 v ryi'jmse
2q7Kvrjryqip
ehtjme5
, '*)$+ q
vs
2ryi©v,jse
e ryqiK|Dz%}ljrylryg5rjnqpfsryle
ehtjme5
, !$# e3¦´utKi{vrojJ uq
Ôe3¦@tKzG@lyeKpr| R G· Ho½qp , '*)$+ R G· Ho½qpqti{ , !.# R G· Hä¶@pjsehi " G · H½J¾@p7zGtjg#sryi tKlyzqvjªeh
|~ehg5jlnjms@e%
mtKi e(K|¨z(}ljryle seh
2{ryi q}@jmg5qzehv De|~q}@i{|~q
Zjmse5vefutK
tKze5jme5
vÁ~vehe¡Ã´e5g5jryqi¶@Ò³ tKi{ r }
e  }@j±r"| , !.# R G· HÒ²´p jmse5i " aF· HÒ²q¾´pv2(|~q
±jmse5ve¤ut
mtKze5jeh
v±jmse¡ryikjme5
2¢tKl O7l ¡G· HäG² DJE½ Hä² mK|z%}@ljmrlye seh
2{ryi K}@jmg5qzGe5vryvv}@wv2jmtKikjmrtlylAn W ,jsutKi jmseryikjeh
2¢tKl O l ¡G· Ho½XG¾ DJ½ H½X¾ m K||~}lylri@|~q
zGtjryqiz%}lojmrlyeeh}rlyryw@
rt´Ôise5
{ri eh}rylryw
2ry}zBpqieª|~KlylyXfvDjse gh
2f{i@Kj¤qi@lnBw7e5gJtK}@ve%K|¨vjm
tjme rygghqzlehzehikj#tK
2rjryehv5p¥w}@j tlyvGw7e5gJtK}@veKjs´ eh
2v tKgjmrqiv%
2e5¢qehtKl-ri@|~q
zGtjryqi tKwq}@j(jset q
e tjmeGv2j#tUjmeKsrv%sehlv(fr{ehi jmse
tKi eK|Ôz%}lojmry@lyryg5rjnriBs@eh
{@ryi eh}rlyrw
r}z/ Ãryig5ejmse5
exzGtJn e3¦´ryv2j'z(}ljryle'|~}@lyl(ri@|~q
2zRtjryqieh}rlyrw
ryt@p¤DexghtKi^tKlv {e5®ie>v2}iv27Kje5}@rylyrw
ryt ryi]fsrg#s e ur t g5qryi j{@ehghr{exfsryg#s eh}r lyrw
r}z"rvGlytJnqeh{ sutUjRrvhp-v2}qve jseh
2e4tK
2e |~}lylfryi´|~q
zGtjmrqixeh}rlyrw
ryt ÇHÈØÌQØZÚVØ2ÌNÛàäÍVÌ;É3ÚVØÉ3ÊUÉàäÎ5ÜÎ5ÛUÌ¥ÍVÎDÍNÈÎhÌQØÑÒÊ Ó7ÑÖÕÕÎÊبÉÊUÞ Ó7Î5ÌQÍVÉ3ÑÒÊ%ùû3ü5üýmÿâ ½µ
!
N *N Á ¤Â2¤ryi{e3¦´eh{wknQO B½ED3³DIHXHWH! JR°DsqveGtKikn'
mtKi@{qz ¢tK
rytKwle Á + Á D ¤Â D frjs4v}@7K
2j-p;ti{'tR|~}igjmryKiHÁ ¡zGtK*N ri ryikj$B½ED3³FD(HXHWH! JN ¤se5iDe {e5®ieft1 FG;'&( ( Fotv + !$! Á D  @ + Á ÂÐtKi{ ! ! Á [D  @ Á ¤ÂÐfse5i´ e5¢Keh
HÁ Â R7ZsSe ) , ZX¢qe5
q}´jmghKzGe5vÁ D ¤ÂZri%jmsrv±v2}iv27Kj±e5}@rylyrw
r}z^frylyl w7eghtKlyleh { ! ! Á D ªÂ s@e lyqwtKl tKzGe5v¤|~
mtKze5q
2© e5ieh
tKlyrhe5v q}
ª|~}llri@|~q
zGtjryqi tKze(wkn'tKl lyXfryi ryi@|~q
2zRtUjmryKiutKlsejmeh
2 e5iehrojn tKgh
2qvvt ehikjmv5x¹¡e5
eKp±r| tKi@{ tK
eRiKj qwv2eh
2¢Keh{Hpuw@}@j-z%}@v2j-riv2jeJtK{Rw7e¡ryi@|~e5
e5{úqilon|~
qz jse¤vr iutKl Zpjms@ehi q}
zG{e5l ryv(t lyKwutKl tKzeK * op* '&( ( o ryv(t/utry
RÁ + Á  D UÁ ¤ÂÂv}g#s jmsutUj¡g#s@qryg5ervq@jryzGtKlV¯ tK
zGtU¦ l +F\ÔÁ½ D _D Á ¤Â D  Á×½ +- \ÁQG· D _D Á ¤Â D ; m ZÁ Á ¤  b Á ªb  Á  + Á  O +pO7lÅF · DJ(½ m ÁV³Kµq tKi{
e5v}lojmv|~
Kz t q
2e tUjmryi g#sqrghehv + ¯ Á ¤Â R + Á  GÁ ¤Â ÁV³¾k j¤rvªghleJtK
|~
qzÁN³qµqÂftKi{)ÁV³¾kÂjsutjªq}
ªs@eh
{@ryi e5}rylryw
2ry}zBpuryi j}
ipryvªt e5i´ eh
tKlyrJtjryqiK|t lqwutKl tKzehveh}rylryw
2ry}zBpHrifsrg#slytJnqeh
2v(qw@veh
¢qe tvmtzGle Kjms@eh
fltJnKeh
v ¥tKg5jryqi@vritK{{rojmrqiújmjms@ev2r itKlV s@e lyqwtKl tKzehv-lrjme5
mtj}
eghlytKryzv¨jmsutj-e5¢qe5i/ri@®uirojme5vryzGtKl¥sejmeh
2 e5iehrojnúK| ryi@|~K
zGtjmrqiúK| jehilyehtK{vjm}ir}ehie5vv5iBq}
|~
mtzGeDq
2©¥p@DegJti/v2sX¯
D;e5j-}´jmrylrj+ ¢KtK|
rytKw7ieªghe iq
¨zGtKslNehpif¯ rojms g5qn i\ {row7jmrye Kiu tKr¢KlehzGiúehwktKn i Á q Â;G· e5H qjjmtKsie{ {g5rqv2jmi
2{rywrojm}´rqjmryiuKtKi l | jmtK©Ke5v¢tKl}ehvB·xq
'½frjs@
qwutwrylrjn ·@ q ehtKg#sHp¤jms@ehi tKv ·@p´jmse5
e,tK
N e3z% }lojmrlye lyqwtKl tzGe5ve5}rylryw
2rt(ro|ti{/Kiln ro| , !.# , '/).+ , R| ryv iq
2zRtlyln{@ryv2j
rw}@jme5{HpHjms@ehi'r| 4rv¤v6} >g5ryehikjlnv2zRtKllÔw@}@j fv2js
ryrygg#jms lon/+ UqÁ v2rÂjmroR¢qep7½jmrs@|ehtK
ie({ryv¤qi@tGlnú}irory| '}e rv 7lyqqwv2tKrjl r¢q etK zehvªe5}rylryw
2ry}z ri
!
!
½X¾
fôe5etKehi{r¦7
s@ryvZ
2qqvrojmryKi(
e5zGri{vÔ}vZjmsutUj lyKwutKl tKzehvZ{@ iKj¨tKlo-tJnvZrzGlon}ir}@e iehv2vh =rojms'túwriutK
2n/v2jmtjmev2utKghe9`úp;K}
zG{e5l ÅvªwehsutJ¢ryq
rv¤}utKlrj#tUjmr¢KehlonBjse vmtKzef
e tK
{@lyehv2v|fsejmse5
±ej
ehtjDroj±tKv±ts@eh
{@ryi tKzeKptKvt |~}lylryi´|~q
zGtjmrqi tKzeKpÔq
(tv%t lyqwutl tKzGe D}@j,fsehi ryv(i@q
zGtKlylon4{rv2j
ryw@}@jme5{ ÁQv2 jmstSj ` ryvftghKijryi}}zRÂDwKjmsújseseh
2{ryi tzGe ti{ jmse |~}llori@|~q
2zRtjryqi tzGe¤e3¦´srywroj tKi ryikjeh
2¢tKl7K|z%}lojmrlyefq}@jghqzehv5p@fsrlye¡jseª|~}lloryi@|~q
2zRtUjmryKilyryzrj¨|;jmse lqwutKl tKze sutKv¡t}@iry}eeh}rlyrw
r}z ti{ se5ighe,t}iry}eq}´jmghKzGe Á ¤Â3iBKjms@eh
DK
{v5pZrj,ryv
2ehghrve5ln'fsehi jmse|QtKzGK}v lyqwutl tKzehv}iry}e5iehv2vtK
}zehikj(rv tKlryghtKwlye¡jmsutjfjseseh
2{ryi z´{@ehl Åv
2eh{rg5jmrqivtK
2e {r 7eh
2ehikjJD«K}v2j¡tKvjse|~}@lylo ryi@|~K
zGtjmrqi g5qighl}vrqivtK@7ehtK
ú|~
mt rylyeBjm ryzeh
2|~e5g5j ri@|~q
2zRtjryqipDjmse lqwutKl tKze ghqi@ghly}@vryKivftKeJtK
|~
t ryle¡jKwve5
2¢tjmrqivfK|ÔKjms@eh
fltJnKeh
v ug#sqrghehv5
.
sryleroj iXtKeJt
v jsutj jse\se5
{ri z´{@ehlw7e5sutJ¢qehvzq
2elyr©Kejmse|~}@lylo ryi@|~K
zGtjmrqi tKzejsutKi\jms@e lqwutKl tKzeKpÐDeRz%}v2j(
e5zGe5z%w7e5
,jsutj(jse lqwutKl tKzehv}ir}@ehie5vv
e5v}loj(
2ehlryehvqiw7e5ryi v}6>g5ryehikjlnghlqvejm/|~}@lylryi´|~q
zGtjmrqiH s}vjm¡ghlytK
ro| nªjms@eD
e5ltjryqiwe5jehe5ijse¨jms
2ehe tKzGe5vhpUDevsq}@ly{%tlyvryik¢Kehv2jr tUjme fsutjghgh}@
vfryiq}
fse5
{ri zG{e5l;tKvDetK@
ktg#sB|~}llHryi´|~q
zGtjmrqiH i t lqwutKl tzGepKie%tK@
ktg#sehv|~}lylryi´|~q
zGtjmrqi wkn {@ehgh
2eJtKv2ryi jmsev2jmtKi´ {utK
2{{e5¢rtUjmryKi ,|ujmsev2r iutlV; D}@jri%q}
zG{ehlNpUjseh
2eryvtKlyv2 t¤ve5ghqi{
2q}@jmejm |~}lylryi@|~q
2zRtUjmryKiHpfs@ryg#s/tK
rvehvfie5rjseh
rijse lyKwutKl tzGe5vve5j} i@q
ryiBtv2jmtKi´ {utK
2{)s@eh
{@ryi z´{@ehlV¯eBtKlyv2'tK
2ktKg#s\|~}llDryi´|~q
zGtjmrqir|fDe righ
2eJtKv2e 0 24365 frjsq}@jw7K}i{Hp´
e5¢KeJtKlryi e5¢Keh
-zq
e¡tKg5gh}
tjme¡ryi@|~q
2zRtUjmryKi%jm%e¢qeh
DzGq
2et ehikjvh ¹¡e5
eDev2j}{@n jseryzlyrgJtjryqiv±K|Ôw7jms |~}lylryi@|~q
2zRtUjmryKiRlyrzGrojmv5 =
!#"%$
$7 $ 4 1 3+& %- (+12( 3 / 3 4
r }
e q v2sXfvfsutjfsutK@7e5ivftKv-jms@e vr iutKl Åv-
2ehg5ryvrqiÁ~jse¤ri¢Keh
2veK|Ðrjv-v2jmtKi´ {utK
2{{e5¢rtUjmryKi@Âf¢tK
rehv|~
qz.·GHä·q¶Gj4½X·@Á =e(ve5j , !$# R ·FHÖµ´p7ryzlnri v2jm
2qi ½X¿
v2j
mtje rg ghqzlye5zGe5ikj#tK
2rjmrehv5pZfrjms Kjseh
ut
mtKze5jeh
vtvri>ôehgjmryKi>¶´½qÒ ;
e5ghrvryKiÁ~sr s¢tK
2rtKi@gheXÂDzeJtiv-jmse5
eryvlrj2jmlye¡ryi@|~K
zGtjmrqiúryiújsevr iutKlN¹¡X- e5¢Keh
hpÐvrighe ehikjeh
v{r
ehgjmlon4ryi4jse}@jmrlyrojnB|~}@ig5jryqiHp;s@r s¢tK
rytKig5etKlyv2 zGehtKiv ¢qe5
2nv2j
qi @
e5|~e5
e5ighe5v¡X¢qe5[
L¯Z|~K
zRtKiknút ehikjvhp 'ryvv2lytK
e¤q
vvzGtKlljsutj jmse}@jrylyrojnghqz7Kiehik[j \ '/).+ Á L^D Â-{qzryiutjehv5putKi{jmsensutK
2{lnRgJtK
2efstjªjmse5
v {>¹¡e5ighe|~q
2ehghrvrqi R G· Hä·q¶@p¨jmse|~}igjmrqi ryvtKlzGKv2j ¥tUjJp-ti{)jse q}@jghqze {ehehi@{vª}i@ry}ehlonúqi , À
mt{}utKllnqp¥tv¡e(ryi@gh
ehtKve(
e5ghryv2ryqi pri{ro¢´r{}utKlvf
ehv27Ki{4zq
ejmRjsehr
¡Kw´ ve5
2¢tjmrqiv¨K|Kjmse5
v59 =rjsG
2ehg5ryvrqi R F· HÒ¶@pkjsefq}@jmg5qzervv2jrylyl@}iry}epw}@j jmse5
eBtK
2eBeh
2vrv2jme5ikjGe5
2q
v5 =rjms sr se5
%
e5ghrvryKiHpz(}ljryleRq}@jghqzehvghg5}
frjs47Kvrjr¢Ke(
2qwutKwrlyrojnq¬Z¢qehijsq} sehtKg#sryi@{r¢ry{@}utKl Åvfvr iutKlÐryv¡}@rjme(tKghg5}´
mtjeKpÐ7e5qleg5qi{rojmrqi4jmse5ry
g#sqrghe5v,qiKjseh
2v ltJnKpÔwKjms'wehghtK}vejmsen'©iX jmsutUjKjmse5
v Ðv2r itKlyv t
eryz
2¢ri jmptKi{tKlvwehgJt}veK|v2jm
tjme rygg5qzlye3 zGe5ikj#tK
2rjmrehv5Ôs}v5pqDe-stX¢Kez%}lojmry@lyeq}@jghqzehvtKvetK@
ktKg#s,|~}lylryi´|~q
zGtjmrqiHp tKi{Bryiújsryvv2ehiv2e,jms@e v2j#ti{utK
2{ lqwutKl tKzehvlryzrjmri
ehv2}lj|QtrylyvDryiq}
z´{@ehlV §¤ixjms@e Kjmse5
sutKi{Hp r }
eú²'v2sXfvjsutj f
2qi K}@jmg5qzGe5vw7e5ghqze lye5vv tKi{xlehvv,lyr©KehlontKv,etK@
ktKg#s |~}lyl±ryi@|~K
zGtjmrqiH sq} s\eh
2
qi@ehq}v(w7e5sutJ¢´rq
ryveh
v2ryvjmehikjhpDsr s vr iutKltKg5gh}
tKg5n)rzGlrye5v,jmstjjmselytXnKeh
2vfsg#sqve®u
2v2j }v}tKlylon zGtK©Ke%jse
r skj {e5ghryv2ryqiptKi{jmse@
qwutwrylrjnBK|±seh
2{ryi jújmse%f
2qi q}@jghqzet
qtKg#sehv/he5
s@eh
e|~q
ep De zGr skj
eJtvqiutwlntK
}ejmstj/jse e¦´ryvjme5ighe K|fz(}ljrylryghrojn4rijmsrv(lryzrjryv,iKjhpwn rjve5l|×pÔ¢Keh
n\
e5lye¢Ktijhi\jmsrv ve5ivepjse lyqwtKl tzGe5vlyryzrjryi
e5v}lojryvutK
jmrytKlylonGg5qi@®u
2zGe5{/wkn K}
zG{e5lV
!#"%$ ( -78& $
: / , $781 ( 3 / 354
r }
e5v-µ(ti{ ¾(tiutKln5e¡jms@eªe7ehgjmv-|;g#sutKi ryi 0#24365 |~
2qz³jm(¾q·@9= eªv2e5j-jse v2jmtKi{utK
2{{e¢rtjryqiK| jm aR.½KpÔleJtJ¢ryi Kjms@eh
utK
tKzGejme5
v,tKv,we5|~K
eKúôryi@ghe R G · Hä¿@pkjms@e¡tJ¢Keh
mt e¡i}z(w7e5
K|qwv2eh
2¢tjryqi@v ´e5v¨|~
2qz ½q侤jm(µq³´pkfsrg#sGv26} >ghehv jmvs@a}vjmsee 7ehgjmvK|tKi/e3¦jm
e5zGe5lntghgh}@
mtjee5v2jryzGtjme K| - uqp
0 24365 R ³´pjms@eh
erv tKlo-tJnv t\}ir}e4q}@jghqze4g5lyqv2e jm ·@ q pfwehgJt}ve frjs v2B|~e qwv2eh
¢KtUjmryKiv jmse5
eryv lyrojjlye(righe5ikjmr¢Kejseh
2{HRi{@r¢ry{}tKlyv¤zGtKriln |~qlylX)jsehr
¨fivr iutKlvhpkv2,wknjms@e¡lytX>K|ltK
e-i}z%weh
2v±jse¡K}@jmg5qzGerv¨}iry}ep ³K·
Kt i{ Deqw@veh
¢qe/tiutK
2X {rv2j
ryw@}@jmrqixK| Rri r }@
e ¾@igh
2eJtKv2ryi 0 24365 jm q p7jmse%K}@jmg5qzGe(ryv¤vjmryll}iry}ep;w}@jBeh
2q
v2tK
e(7e5
vrv2jehikj iX^jms@eh
et
e v}6>g5ryehikjqwv2eh
¢KtUjmryKiv-jm¡£2}vjmro| nG|~qllyXfryi Kjseh
2vh r }
e ¾%v2sXfvjmsutj|~K
Djmsrv gJtKv2eKp7
q} sln/µK· K|Zsrv2jq
rehvghqik¢qe5
e(}@ryg#©lnjmjmse
r skjªK}@jmg5qzGep¥w}@jªjse
e5zRtKri{e5
ftK
e vjmryllfry{@ehlnR{ryv27e5
v2eh{/tKvfK| =4R ¶K·q·@ jªtKll;sr s@eh
lye5¢Kehlv¡K| 0 p¥jmse5
e%t
ez%}ljryle q}@jghqzehvf|~q
feJtKg#s , lyzqvj tKlylsryvjmq
2ryehv stX¢KeRtlyzqv2jg5qik¢qeh
eh{jm N ·q
N ½wn =[R ¶q·q·´pÔti{jse ghqik¢Keh
ehig5e e5jmvG|QtKv2jeh
Rfrojms lytK
e5p
0 23-5^Ãj
qi v2j
mtje rg ghKzGlehzehikj#t
ro jmrehvzGehtKi7e5qlyeg5lyqv2ehlon4|~qlylX jsegh
2f{pvjms@eh
eryv z(}ljrylryghrojnBryi'vrojmeK| jmseRe¦´ghe5lylye5ikj%ryi´|~q
zGtjmrqiHB¼/K
ehX¢Keh
hp Ôr }
2eR¾/vsXfv(jsutj(jseú
2qwutKw@rylyrojnK| jmsef
2qi q}@jghqzeryvtKlzGKv2j e3¦tg5jmlon4jms@evtKzeKp;ryi@{ehehi{@ehikj(| 0 23-5 p;|~q
tKll 0#24365 ½X·´¡srvªv2} q e5v2jmv¡jmsutj¡jmse,
KwutKwrlyrjnúK|¢tK
rq}vq}@jmg5qzehvªrv¡zqvjmln {e5jeh
2zGrieh{wkn%jms@e{@ryv2j
rw}@jmrqi%K|7e5¢Kehikjmv¨jmstj¨gJtKighg5}
¨ryi%jms@ef®
v2j|~e vjmeh@vh s@ehvei}zeh
rgJtKlÔ
e5v}lojmv{ehzqivjm
tjme%jsutjr|±lytXnKeh
2vstX¢KetlytK
eKp;q
e¢qehi zG{e5
mtjeÁQlry©Ke,½X·k¨vmtKzlyeªK|qwv2eh
2¢tjryqi@vhpz%}@ljmrlyefq}´jmghKzGe5v´g5gh}
Dfrojms iKi´ jm
2r¢rtKlf
2qwutKw@rylyrojnqi jmsrvúve5ivep¡K}
úse5
{ri z´{e5l¡g5qikjm
tK{rygjmvRjse lqwutKl tKzehvf}ir}ehie5vv¤
2ehv2}ljªtKi{BryivjmehtK{ wehsutJ¢Kehv¤zq
elry©Ketv}i@vKjªe5}rylryw
2ry}z K|¥jmse-|~}@lyl@ri@|~q
2zRtjryqi tKzeKÔÔ¤|~}@
2jms@eh
ryik¢Kehv2jr tUjmeDjse
e5ltjryqi(frojmsv2}ivKjvhp lyej +wejmseGeh}rylryw
2ry}z v2j
mtje n tKi{ ghqi@vry{@eh
sX jmse|~}igjmryKi (Á D [D + 2Â g#sutKi ehvtK]v 0 243-5
XfvBltK
eK ej e Á D ¤Âúw7e rjvBlryzrjútKv 0 23-5 ôryzrylytK
lonqp±lye j e Á D ¤Âw7e4jse4lryzrjK|jms@e4eh}rlyryw@
ry}@z ) , RÁ D + ÂRtKv 0 24365 =rjs jms@ryviKj#tUjmryKiHp;DeGgJtKi\v2sX jmsutUj(q}@
,se5
{ri e5}rylryw
2ry}z ghqik¢Keh
ehvªri{ryvjm
rw}@jryqiRjRt%|~}lloryi@|~q
2zRtUjmryKiv2}iv27Kj¡eh}rlyrw
r}z/ ÎÉ5Ù¥ÌNÌNÆ ÎÛæU(Ý-ÌNØÑäØfÊUÚ #Ü¡ÞXÉ#ÚÌVÍNÉmÉ3ÑÒñ'ÎÝ-ÊÍ~ãÌ ñàÒÑäΪÊÜ¡ÙÑÒÎ5Êhñ;ÚÐÍNØ2ÑÅØ ÍVÚNXÈØÉÌ~Ý-ÍVÚVÑäØÊããÜ àäàÖØ5ÉÕéÕÎØÑÒÝ-ÊUÝ-ÕãØàäÛUÊhÎhÍÌNÌQÑÒÑÒéÎÊÑÒÊUÜÊUÌ2ÌQÉ¡âÍNØ2ÞXå´É5ÑÞ ÑÒKÚÌ~Ø2Î3ÍÚNÙ7éØ2Ê5ñ;ÝÍÔÑÅÉ3ÍVÙÈËJÛÎÑÒÊUÊÛXÕ×Ü ÍZÍNÑÒÌQÚVÎÝØÊ ãÉ3àÖ=ÉàÒàÕù ØÕÝ-ÈUÿ;ÉØñ;ÊÊhÜÑäÍ ÍNØÈ ÌÍVÑäÌQÊ(ÈÈUØÎÍNÈUÛÌVÉ3ØfàÖÞÝ-ÞXÕبÑÒÈUÌQÍNÝ-ÉÚVÊÑÒØæÜÉ3ÛXبÊÍNéKÍNÑÒÎÈÎÊ ØÚ ãÞXÚVÑ qÎØæÚÉ3ÌZæÙÑÒÚNàäÑ Î5Í~ÝߨÞXÜ5ÑÖÌ~àäÎ5ÍVÚNæUÑÒÉ3æàuÛXÍVÜhÑäÉ3Î5Ý-ʱØ2!Î Ì25éØñ;ÚÉ3ÈÜØ2Ü5ÚNØÚNØ2ÉúÜ5É3óQÍNÊUØuÎÎÑÖÛÌQØÍVÕ×øyÑÒÎ5ÊUÝ-ÞXØ2Ø2ãÌ2â´Ø2ÊUÇHÞXÈØÑÖÊhÌuͨÉ3ãÌNØãKàÒØ2Ø2ÉÕÍVÚVÑäÌÎ5ÍNÊUÎõªæKÚNØHØÌQÉÛUÊàÅÎ3ͱÍVÈÌNÎØÝ-Ú@ñHØ×ÍVÉmÑäßÝ-ÎØŲ̂Ú@É3Ý-ããUÎJàäÞÑÒØ2ØÌ à ùÓëJÉ3Ø2ÚVÕàÒÌVÎÌQÊUÎ5ÞÊ¡éUÉñÊUØ¨Þ Õ×mÎÉÊʪÕ×àÒîÛUÞXÉ3ØÝ-ÍVÝ-ÈUØÉ#ÍÔý ÉàäÒÎ#ñ;JåUÑÒÊÚVÉÜ-ÊãËàÒØ2Émàß5éØìÚÌÎÍNÚVÎfÚNÑÖÌÎ5éXæUÉÌNÊUØÚÞ ØZuÉØ2ÛÉ5ÕçÈ¡ÊUØãÚÚVéX(Ø ûJüÑÒüÎ5ÛUÿÌÐâ ÕÈÎÑÖÕ×Øñ;ÑäÍNÈÕÎÊUÌQÍVÉÊ5Í ãÕÈUÚVÎÉæÊÉ3ÜæرÑÒÎàäÑ ÛÍ~ß ÚÚNØÌQÑÒÛUÊUàÅÌ~ÍÍVÌØ2âZÉ5Þúì Î5Î3ÌQÙÍæÉÎ5ÜÛØ2ÊUÊ5ÞXÍÌÑÒÊñÜÎÍVÛÈàÖÞ ØÈUÊJÉÛ5ÝبæÝØ2ÚÉ3ÊJÎ3ߤÙÎÎ5æUæUÌNÌQØØ2ÚÚ ##É#É3ÍVÍNÑäÑÒÎ5ÎÊUÊUÌÌ éæÛXñ7ÍÎ5ÍNÛÈàÖØ2ÞGÑäÚZÊUãKÎ3ÎÍ¡àÒÑÒáhÕÛUߪÉÙàäÛÑ ÍVÊUÉ3ÕÍNÍV)Ñ ÑäÎ5ØÊUàÒß Ì ñÎÛàÖÞ¡æبÌNÑäÝ-ÑÒàÒÉÚHÍNÎ-ÍVÈÎ5ÌNØÕÉ3àÖÕ×ÛUàÒÉ3ÍNØ2Þ¡ÈØ2ÚNØ5â
³´½
ly rzGghroKj¤iKjm|tKryjmi@sv eis e5
7r{¦KrirytKiklyj l@ue5zGtK}tK
mtvrylv2zGryehwvhe
2pjmry}ehw
2z }´v¨j etK¦´jmv sughe5t0 @j>j24`.360 5 r2v¤3-{5 ryp@ v2tghi
2 e5{Gjmeg5%vqvi}@v2zGrys{e5ee5i
±jmsujjsstUeej ly)rzGro, jm ryi ! ! )Á D , ¤ Â e ehi@Á eh
mD tUªjmÂ(eh{ K|¡wkn'jsve qzse5e
{vr}i i v27zGj({e5ehl}@ryryv%lyrwe5
r}u}tKz.l-jmK|Djjssee |~}lylri@|~q
zGtjryqi zG{e5lV fôe5etKehi{r¦7 g5q
Klylt
2n)K|jmsrv
qqv2rjmrqi rvújmsutjro|jmse4|~}ll¤ryi´|~q
zGtjmrqi tKzGe sutKv z%}lojmry@lye(e5}rylryw
2rt@p¥jmse5i|~K
¤vqz9e 0 J^p 0 23-5 P0 ryzlyrehvfjmsee3¦@rv2jehig5eGK|Dt seh
2{ryi e5}rylryw
2ry}z fsryg#sBe¦´srwrjvz%}lojmry@lye¤q}´jmghKzGe5vh s@eRryikj}rjryqi'wehsri{ jsryv
K7qv2rjryqiryv-£2}v2j,jmsutUj(lytK
e 0 23-5
e¢qeJtlyv,jse jm
2}e,vj#tjetKlyzqv2jfeh
|~ehgjmlnKs}v5ptUjjseeh}rlyryw@
ry}@zq}´jmghKzGe5v|jms@e,se5
{ri zG{e5lVpzGKv2jÔltJnqe5
v js
e5vsKly{vtK
e±ghlqve¨jmfjmsKveD|@jms@e±|~}lloryi@|~q
2zRtUjmryKiªqlyrg5nq sryvªzG ehtKiv¤qryikjvªfseh
2e%jmselryzrjryi e Á D ¤ÂK|¨jse%se5
{ri N zG{e5lÔg5
qv2vehv jmse q lryie¡z%}v2jtKlyv2%w7eª7qrikjmvDfse5
e¤jseª|~}llori@|~q
2zRtjryqi Á D ¤ÂrvDqiújse i e Á D ¤Âplyr©Ketv2}iv27KjDeh}rlyryw@
ry}@z/p q lyrieK¹¡ehi@ghe¡jselyryzrjryi {ryvjm
2ryw}@jryq
mtKi@{qzryhe5v¢Keh
,q}@jmg5qzehv fsryg#s\tK
eeh}rlyrw
rytúK|Djse|~}@lylryi´|~q
zGtjmrqi tzGe D}@j}i@lyry©ev}i@vKjeh}rlyryw@
rtryi e5ieh
tKlVpHjsev}@ivKjeh}rlyryw@
ry}@z vehlehgjmeh{wkn e Á D ¤ÂryiBq}
vrz%}lytjmrqiv-rvfehllow7e5sutJ¢qeh{p7e3¦@s@rywrojmryi t7Kvrjr¢Keg5q
2ehlytjmrqi w7ejDe5ehi |~}@i{utKzehikj#tlyv ]tKi{Bq}@jghqzehv -
. .
se lyKwutKl tKzehv%lrjme5
mtj}
eGsutKvv2sXfi jsutjz(}ljryleGe5}@rylyrw
ryt/K| jehix¢tKirvs r|ri@|~q
2zRtjryqi'rv(vlr skjln'sejmeh
2 e5iehq}@v jsryv,v} K ehvjmv(jsutj(e vs@q}ly{e¦´7e5g5j }ir}@ehie5vv%ri
tKg5jryg5eKpv2ryig5e|~}@lyl¨ryi@|~K
zGtjmrqi4ryvghleJtK
2ln'ti}i
2eJtKlryvjmrygv27e5ghrytKl gJtKv2eK D}´j lyqwutl tKzehvfsutJ¢qejmse5zGv2ehl¢Kehv}v}tKlylon w7e5ehi4g5qivjm
}@g5jme5{4ryi/tKiB}i
2e tKlyrv2jryg%v27e5ghrtl±ghtKve¯,jsutjK|-e3¦@tKg5jln'vrz%}loj#tKie5q}v {e5ghrvryKiHúÀ r¢KehitBv2rjm}tjmrqi lyr©Keft¤wutKi@©%
}iprojve5ehzv±tKwv}@
{jmv}@7KvefjmsutjZzGqvj¨7e5qleg#s´Kvefw7e|~q
eKw´ ve5
2¢ryi tKiknKjms@eh
g#sqryg5ehv5iv2jeJtK{Hpzqv2jehqle frylylqwve5
2¢Ket
tKi{Kz v}wv2e5j K|
2eh{e5ghe5vvK
vh¯¡e¦@tKgjmln jse(vjm
2}g5j}
e(jsryvutKeh
¡zG{e5lyvhi v}g#s'tKi/ehik¢ry
2qi´ zGe5ikjJpHjms@e×jm
rutK
jmrje(g5ltKv2vr®gJtjryqiRK|-t q
e tje%v2jmtjme5vhpryig5ly}{@ryi tKi'rijeh
¢Ktl K|-z(}ljryle%q}@jghqzehv5pÔrvtB
2qw}vj(s@ehiqzehi@qiHRs@eG
2e rqi'K|-z%}@ljmrlyrghrojn/rv ³q³
ltK
eh
r|Zv2jm
tjme ryg,ghqzlehzehikj#tK
2rjryehvtK
2e%v2j
qi eh
5pHtKi{/jmehi@{v¤jmúwe%tUj¤lyehtKv2j¤tKv ltK
etKv-jse
e ryqiK|Ôz%}lojmry@lye¡|~}@lyloryi@|~K
zGtjmrqieh}rylryw
2rt@ = e-sutJ¢Kevehe5ijmsutjZtK
2ktKg#sri |~}ll´ri@|~q
zGtjryqiwkn%righ
2eJtKv2ryi v2r itKl´}utlyrjn {
ro¢qe5v±jsef
qwtKwrylrjnK|jmsef
2qi seh
2{ryi q}´jmghKzGejm5eh
@ptK
2jrtKllnghqi´®u
z ryi jmse lyKwutKl tKzehv±}ir}@ehie5vv
e5v}lojJ D}´j-rj±v2ehehzv-}i@lyry©ehlonqpryiGjseªe5ghqi@qzGrg ghqikje¦jmv(eRstX¢Keúzehikjmrqieh{pÐjsutj,e5¢qe5
2nKqie sutKv,tKlzGqvj7e5
2|~ehgj%
2r¢tjeri@|~q
× zRtUjmryKitKw7K}@jjmsejm
2}ev2jmtjme i@v2jmehtK{HprjzGtK©ehvvehi@ve,jv}qv2ejsutjg#sqrghe ryviKj¡e¦@tKgjmlnBv2ryz%}loj#tKi@ehq}v5ptKi{/jseh
2e5|~q
2e,jsutj¡vqze(
2e5¢ryK}v¡g#s@qryg5ehv¤t
e(Kw´ ve5
2¢qe5{H =sehiDetK@
ktg#s|~}@lylri@|~q
2zRtjryqiwkn ryi@gh
ehtKvri jms@etX¢Keh
t ei}z%weh
K|-Kwve5
2¢tjmrqiv5ptsr s
2qwutKw@rylyrojn |-
ehtKg#sri jsef
qi t q
2e tUjmeq}@jghqze
e5zRtKrivhi|QtKgjJpi}zeh
2rygJtlylnKp´jse
qwtKwrylrjnG{ryvjm
2ryw}@jryqiR¢Keh
¡t q
2e tUjme q}@j ghqzehv(sutK
{@ln'¢tK
rehv(frojmQs 0 23-5|~qS
0 23-5 ½X·@§¤ieúK|jseúzGtKikn DtJnvq}
seh
2{ryi z´{@ehlH
2ehve5z%wlehvfjmse |~}llori@|~q
2zRtjryqi tKze ryvjsutjfrjs t{rvgh
2e5je,t
e tjeGvj#tjeGv2utKghepÔjsryv
KwutKwrlyrjn {ryvjm
2ryw}@jryqie5}utKlyvjmstj%tvvghrytjme5{ frojms qieK|Ðjmse ehllowehstX¢Keh{|~}lylri@|~q
zGtjryqiv}@ivKj¡eh}rylryw
2rt@ Ãe5¢qe5
mtKlrzGq
j#tKikj¡w}@jqvv2rywlon {r >gh}loj e¦jme5ivrqivghKzGe(j zGri{H u}@jm}@
e
e5veJt
g#svs@q}ly{,
e5ltU¦jseDtvv}@zG@jryqi,K|¥tfwryitK
2ng#sKryghevejJpqti{tKllyX |~K
Ô
2ryg5ehv ÁQe5i{ e5iq}v}@wlyrg%vr iutKlv#Âj q}ly{tKlv weryikjme5
e5v2jmri jm vjm}{@n4{@niutKzryghv5p 7e5
sutv £2}@v2jwkn
eheJtUjmryi jse tKzetKiutKlonheh{)se5
eK ljme5
iutUjmr¢Kehlonqp¨DeBghq}@ly{
e5ryikjme5
2e5j±jmsefjmrzGri K|jseveh}e5ighep¥tKvv2}zryi jmstjDg#s@qryg5ehv¨j#tK©eªlytKghefX¢qe5
-t lyqi sq
2ry5qiHjÔDK}ly{(jsehiwe-zq
e±iutj}
mtlj¤lyri© qwv2eh
2¢tjryqi@vtKi{%tXnK 7vZjm ieJt
wknltJnKeh
v¨rijsefve5}@ehig5e utKi@{eq}l{e¦´7e5g5j±jmqwv2eh
2¢Ke¡{´n´itKzGrghvZjsutj }v}tKlylon%sX¢qe5
e5{úieJt
±v2qzev2j#twlyefq}@jghqzeKpqfrojms´g5gJtKv2ryqitKl
mti{qz jm
mtivrojmryKiv |~
qz qie v2jmtKwleK}@jmg5qzGe¤jtKiKjseh
5 s}vDeRsutJ¢qeRvjmrlyliKj,
e5vqlo¢qe5{jmseG{ehwtjmeG¢Keh
jmseG}iry}e5iehv2v%q
z%}lojmro lyrghrojn\K|jmsezGtKri w7ejDe5ehi |~}@i{utKzehikj#tlyvtKi{)q}@jghqzehv5 ¹XDe¢qeh
5p-jmsrv utKeh
v2j
qi lnv2} q e5v2jvjsutj lyKwutKl tKzGe5vsutJ¢qeiKjms@ryi jmg5qikjm
rw}@jejBjse {ehwtjme se ghqzlyrgJtjeh{)rjeh
mtUjmeh{>{qzryiutigheB
ehtKvqi@ryi tKw7K}@jútJ¢Keh
mt e lytJn jmsutUj,}@i{eh
2lyrehv¤jms@e lyqwutl tKzehv }i@ry}ehi@ehvv,
e5v}lojryv eJtvrylon4v2sq
2jg5ry
g5}rjeh{'wkn æKØ ÆVÆ×íÐØ àÒ àäñ; ;ÑÒÜÑÒÊXùÙû3Îü5ÚVÝü5û5É#ÿÍVÌNÑäÎ5ÈÊÎ#ñXÈÌ@ØÑÅÊÍ¥Õ×ÑÖØÌ@Ø2 (ÌVÌQÕØ2É3Ê5ÊUÍVÊÑÒÉÎ3àJÍ;ÙÎæKÚ@ØÍNÑäÈUÊhØÍNØ2Ü5ÚNàäãUÎ5ÚNæUØÉ3ÍNàJØ2ÜhÞªÉ3ÉÝ-Ì;Ø2ÉDÌ@ÛãÊÚVÑÖÑÖÕ×áhØÛâ ØÊUØ2ÌVÌÚNØÌQÛàäÍÍNÈUÉ3ÍÍNÈØ;ÌNÑäÜ5ÊUÉ3à ³K¶
Rt |~e5 qwv2eh
2¢tjryqi@v¤K|±Kjms@eh
v5 Ðeh
2sutKv jms@e lyqwtKl tKzGe5vª
2ehv}@ljv2jryllÔsutv tú
qle tKv tjmehg#s@iryghtKlÔj
ryg#© fse5ijmse,7qv2vrwrylrjn K|¨z(}ljrylryghrojnúrv¡ijªjms@e%}ehvjmryKi'tj sutKi{ D}´j¤Dev2sq}l{iKj v2}qvejsutjªjse lqwutKl tKzehv¤}@iry}e5iehv2v
2ehv2}lj rv tKixehzr
ryghtKl±
e5{rygjmryKiH ¡q
%v2sq}l{\DeBtj2jme5zG@j,jm{
tJ qlyrg5nghKighl}vrqiv tKwq}@jfsXaj@
e5¢Kehikj¡z%}ljrylryg5rjnwknv2j}{@nryi lqwutKl tKzehvh
-tKie5H
~£2e5µKeK¿qp µ×¾@w½Js@¾@r £2rjfÁ½X¿q¿q³qÂp ôryzlye-¼/{ehl|H¹eh
{.De5sutJ¢ryq
5ä u½J·kµÁN¶kÂ3p Dry©sg#stKi{utKi@rVpô}vs@ryl º tJ¢ry{/¹¡r
vs@lyrye|~eh
5p¥tKi{ ¢K = ehlyg#s\Á½X¿K¿k³qÂp se5q
2nBK| ¥ tK {vh p ½Xt·qvs·BrqÁ q iHÂ3pp°D}Hv2¥j¿Kq¿kz/³#pH½JtK·ki³K{²@ °D}lojm}
tKlZ°DstKi etv¤i@|~q
2zRtjryqitKlÔ°-tKvghtK{ehv5ä Dry©sg#stKi{utKi@rVpô}v2sryl º tJ¢´r{¹¡r
vs@lyrye|~eh
5pktKi{¢q = ehlg#s4Á×½X¿q¿q²kÂ3p2i@|~K
zGtjmrqiutKl t°-jJtK¯ vghtK { e5 v tK i{x )*d WtjmroqiutKEl± ¹ eh'
{@ ryUi )' ¯ )' i* i@iKj#tUjmeh{ rywlry
tKsknqÅ ¢tKrylytKwlye Dry©sg#stKi{utKi@rVpkÃ}vsrl kº tJ¢ry{,¹¡r
v2slyre5|~eh
5pKti{(¢K =e5lyg#sÁ×½X¿q¿q¾qÂp;eJtK
2iryi |~
Kz jm s e ehsu½tJ³¢ryÁNq¶k
(ÂDK|ª;§¤½ jq s½5eh×
2µKvh·@¯ú °Dqi@|~q
2zGrojnqp ¥tK{v5p¨tKi{ i@|~q
2zRtjryqitKl°-tKvghtK{ehv5ä °-tKwô
ehtKlehlye5gjmvhryp Ki/ijmjs@q
iqr} @s dfqiv2ehg5zGqzGtK
@rlye e5jªe(t i@eh|~lNKp
tKzGit{jmrdfqig ryi
2°DzGe5qik
2jm{ehry
iutUÁVjm³Kry·qK·qi ³qÂÀptKz¬ehv5}¯ryltKrywi4
2ry¬}¦z 7e5
rzGe5ijmtKlÃj}{@ nK仡iro¢7 Ðqz7e5} ¥tKw@
mt¬ghqiKzGrghv = q
©ryi tK7e5
²K·@½q °-tK
ôlehvlv2ehqgiHjmpuryK¹¡iHtKäivftK)*i@{¬¨op
2ryg! ¢K")t' i²@º ½tKzGHz¥¿Ke(¾qÁ¿U½X#¿q½J¿K·@¶k½X¾@p mÀ lyqwutlÀtKzehvDtKi{¬}rylryw
2ry}z °Dsu|~tKqz
2jlysenqghKp¨zG°Drsi
2ryvjm³Kq·q·qs@¶´eKp¥p °- tKz%!w"
2ry{ e »¡i'ro¢q e5
v[roj)*n
oehv2")vh a( -,T) ^' Kp °DsughtK
2ze5jmlye(enq°Dp°Dsqsr
2ghrye5vvjmqrv s@eh
2v2ehjmiktjJjme5,vh sÔryvªxzGtJeh¢KtKqiry{ v gjmhsuqztUj %lrygJÁN·ktUÂjmryRKi·v¨ tKt
ir{/vri v2}g#|~s/
2qjz sutjmj srvD{rvg5qikjmryi}rojnqp{e5®ie t,vjme5ú|~}ig5jryqi Á ±Â¨v}g#s ªÁ ±Â @ Á ¨1 Á ¨Â ÁN¶K·k ryvGtg5qikjmri}@q}vG|~}@ig5jryqiH ¡KjeBjsutj rvG}@iry}e5ln {e®uieh{pftKi{ rvghqivj#tKikj ryKix|tehjtKjg#
ms tKgKjm|frqjmiHsp7e fwurojmts4vryi@zvryi@Kry|zGttGjjt
mj¤tKgeJjmtKrqg#s'iH'v2jmtKwsulte(jv2rjvheJp tK{´nrv%v2jmt}ujme tK{
!tjmO rgú X! ¢qÁ e5¤
Â3eJpHtKtKg#is){wuftKrov2jmrysi ry7ikehjmtKe5©´
g5Âeht@jfjeJjtKehg#
s/zv}itKv{j#£2tK}wv2ljeeh{Bv2jmveh%tK{@jmn stvj j#t>je rv-gh+KiO jry i´}Á qª}@Âv ÁQw}@jDfrjmst%i@qi{r e5
ehikjrtKwle ;ej tKi{ w7e jsee¦´7e5g5jeh{ g#stKi e5v¡ri tKi{ ¯ GÁ N~ @ RÁ Á N 3 N Á NQ tKi@{ GÁ N~ @ RÁ ¡Á N  N  Á N~ ÁN¶´½Â v2jeJtK{@Xn\vj#itKjje e±jNsu tgJj;tji setKloe3-¦´tJ7ne5vfg5jmw7e5e {%ghvtKly}ug5t}
ltUeh{,jmeh{{ryve3j#¦@tK@i@lyghryg5e±rjKl| n¯ N |~
Kz jmse ) *kvj#tKw@lye = N ½ Á ="½Â N Á½ NÁ N"D ¤Â = N"Á = ½Â N (Á N  N / Á N"D N  R N×Á N"D ¤Â ="½ = ½ Á N D ªÂ N >³ N Á N( N×Á N D ¤Â2 R ³ =#Á N" N ÂhÁ N×Á N D ªÂ N~ Á = N× ½X ³ =#Á N" N Â5Á N×Á N"D ¤Â N 1 >¶ & ÁN¶q³q Á ="½X ³K²
N D
RÁ Á
N N Â
jm sustUefj|QjmtKsg5eújjjsueht
zj Á g5
N q v2ve5vN jmÂhs@Á e NÁ q N D ly¤ri eD |~
Kz N Â(tKryv%wXi@¢qqe¡itj±qvt rojmv2rj#¢KteKwp¨lyetKi@vjm{)eJtv{@jm
2nryg5v2jjmltn jmefirye ztjmlrory¢qehe v tJ-tJn |~
Kz v2jeJtK{´nv2j#tUjmehv5 X K t ( v l q i t v N R N frjs
2qwutKw@rylyrojnqiepjms@ehixwKjms tKi@{ t
e eh{ryv}uj#tKtKli@ghjme¡ |~R
2qÁ z Á NN j(D jmsN e¡3Â i eJN tÂ
eh vj}ÁivN"j#D tKw@N lyeªÂpvjmtKehv tK{@ nGr¢qe5v2j#i tUjmwkeªn]rv ÁQ¶k³q
2eJÂ3t]jeh¼/
±qjmsu
2ehtKXi ¢qe5½
hpÁ½1r|¤aj=sÂ3e p jms
Ke5iwutKwN rlyrjnKR pXghqi@N {frjrryjqsiutlK
qKi wutKwNrpXlyjmrjsnBtj qi@eKN §¤firlyl#jm£2s}ezGKjsriehj
stftKi@i e5{Hxprwu|¨tjvsryieh
2Ke|rytv jj
mqtKvgrojmjmrrq¢Ki e ÁQv2ªjmsutUj N R N ÂpUjmse5i%vrighe 'stKvZtvsutK
27ehtK©tjjseD}@iv2jmtKwlyev2jeJtK{@n,v2jmtjmep fryllwevjm
2ryg5jlnRlyehv2v-jmsutiBjsee¦´
e5vv2ryqi/ryi ÁN¶k³KÂs}vhpu|~q
ftlyl Np@DesutJ¢qe RÁ N~ & úÁ Á N D N  N  4Á N D N  & ³ =#Á N" N Â5Á Á = N×Á ½N"D ¤Â N  >¶ ÁN¶K¶k ¡Kje jmsutjjse7Kvrjr¢Ke utK
2jK| rvv}zzRtwlyeªfrojmsB
e5vehg5jfj =2sutjryv5p ¶ h e .N & h e zRtU¦ B N Dm·FJ & h e
ÁN¶  Ni Ni Nji Á½ 7= Xa{e®uie N SN @ Á NQ h zGtU¦ B RÁ N~ D#F· J ÁN¶ q  i ¡jmsuKtUjj erjRjmsrytvúj w q }irv{@eht {vw7}e5lyXeh
2zR t
2¹¡jmre5i i ghtKelpªe'wkwn n jghsqe4i@v2zGjm
2tK}
2g5jryji ryqitp%lyeBtKghiq{aik¢q|~e5
2q
z e5ighÁN¶ ej sDehqex
2ehv2zBehe p jmsNe lyryzrjlry+z N dfe S N e¦´rv2jmvútKi{ ryvRw7q}@i{eh{ wehlX^ r©Kefryvep Á NQ4Â S NR i zRtU¦ B Á Â DmF· Jªrv±tv2}wzGtK
2jryi tlyeDfsrg#sRrvw7q}@i{eh{RtKw¢KeKp´tKi{jmse5
e5|~K
e ghghqqikik¢K¢Keheh
ehehvhv¡jô´r@i ghefwKjms S N7tKi{ ªÁ N~ S N7ghqik¢Keh
eKpDegJtKighKighl}{ejmsutUj Á N~Â iKjmeGjmsutj(r| Á N~Âg5qik¢qe5
e5vhp¨jmse5i ¡Á N~ÂtKi{ Nz(}v2j(ghqik¢qe5
eúj´@ X =e frlyl-iX vsX jsutjr| Nghqik¢qe5
e5vhp-rojz%}vjGg5qik¢qe5
eBjmtvjmehtK{@n v2jmtjme jm}sie5v
j#ehtKtw| ljmee5
úv2jmDehtKe{@ne3¦´vjj#ehtij{ eK jse'tK
}zGe5ikjújm\v2sX jsutj NghtKiij ghqik¢Keh
e'jxtKi iKsj,ehÃi t}v2jme4ehqtKvgJ{@e¤tni jsuv2g#jmttsj jm´e KNvejmghs@tKg)ehii lghtKqj
sikeh¢qeB
2e5eG
eh ire vqf} 7qrojms v2s rjvr\¢qqevjrosu@jm
tr¢KqjRe¤wu|~tKw
2
pryql=%wurjtKn wjrlysug¥rojtp njjlyN¤r+z
2t%ehN dfzG7e KtKryryiki@j-vRÁ fryNQis rg#qsBil·@rn v qv2jmitKewlywueªtKv2v2jmryehi tK{@nR|v2tj#j2tUjmjm
me tg5jmNr qtKiHip¤{úKij se¤qi
2ehelyev¢r {tKikejK}| ivj#N tK wle¤;ev2jj/eJtKjs{´enúv2{jmrtv2jmjmeªtKiw7ghe ewe5jse5ehiehiazGjqs
2ee veh^g5r®u½ ghtKÁ×ly ½ lonqp g4g@ÂgJvtK}@i g#s w7ejmsug#tUsj qv2ehixlytK
N"e e5iNq } s\ v Bjmsu tj¡X]eRv2ghrytKiig5e g#s]qrv¡v2eRv2zGvKzGKjesHvp¥zGtKitK{lyl v righe'Á N N ÂhÁ NÁ NQ Â N Âryvv2j
rg5jmlonie tUjmr¢K eútJDtXn |~
qz vjmehtK{@n\vj#tjehv5pZ|~q
³qµ
= gjseh
2e¤e¦´rv2jmv = ¥g pÁN¶k³KÂDw7e5ghqzehv
·%v2}g#s jmsutUjÁ
N (N Â5Á N×Á N~Â1
NÂ
seh
2e5|~q
2e¤|~q
GÁ N  R RÁ N~ ªÁ ³="= ½> ¶ ÁN¶K²k |~qs
eeroi| e > tghjmqro¢qike ¢qe5u
tK
e5jv¡Kj|ÐGjmtsrv-qev¦´rojmro
2¢qehe v2viryK}i/z%wrv-ehi
fKlye5jfvv2v}jmzGstKzGi tKwple¡ferosujms tJ¢q
e e5vehgjj9= @jseh
2e h e GÁ Â R
ÁN¶qµq i Xa{e®uiejmsezGtK
2jryi tlye N SN R Á N  h RÁ  ÁN¶K¾k i ¡Kjryg5e,jmstj¡|~
2qzq}
¡
e¢´rq}v¡gJtKlgh}lytjmrqiHp SN S N -½ Nje i G N ôryi@ghe ryv¡tGzGtK
2jryi tlyeKp¥ti{4wq}i{e5{w7e5lyXprj¡ghqik¢qe5
e5v¤jmRtRlyrzGroj-fsryg#srv w77KK}vrijr{¢Ke5e-{xiw7}z%e5lyXweh
¨ lye5v}@vZ j%jmsro|DtKi jms@×ehpq
jeRsehryiv,t |~
K7z KvrÁQj¶ r¢KÂÐeGef
2qghwuqtKiw@g5lyry}lyro{@jn ef jjsusuttjZj j]sehg5
2qefikry¢qveht
ehqv%vrojjmr¢Kte
KwutKwrlyrjnjmstj ÁN¶K¿k N ldfryz e SN R
sryvrzGlrye5v7jmstj úÁ~lyry1z N dfe SN Â R pXfsryg#sryv;righqi@vryvjme5ij;frojms jms@e±zGtK
jmryi tKlye
K7e5e
2¦jnjJpKD| e i@±Kjm¹¡eªe5jisughte jjmsNrz%v-}tKv
j}ghzqikeh¢qike5j
gJeti jmw7e¡tKiBe¦ehjmle5ehiz{ehehik{jfjmK(|
ª} leªq}@j-ghqik¢qe5
e5ighe jmK|qtK
2ik{n eh
}i@½ v2 j#=twflyesehv2i jeJtK{´NDnrv,v2j#g5tUlyqjmv2eKeG¨ jmBsrjmvsryev}wiehvghj#tKtK}w@vlye eRvjmehvtKjmry{@llng5v2qjmiktj#jmtKerBivts@ryi@v,e jeht
2jz r¢Ker vjehi
2Kz j v}
mtzzGsBtKjwlye
}pfle s@qryg#}@sjfghtKKllyiX¢KfehvD
}ehvijmg5%eK }v2e¤jmseªvmtKze tK
}zehikjtKvDryiRjse¤
2e5¢ryq}@v-utK
tU Ðve5e jmsrvhp@v2}qve j sutj-etK
e¤g5}
2ehikjmlon tjtKi}iv2jmtKwle¤v2jeJtK{@núv2j#tUjme @vmtJn tv2KjwNeJtKR ¢K{@eRnt vij#O { tjwe eh@lrÁ XzG¤ zÂ3ªjmehs@{ryryvste5jmv2ie5jleJn tK{@N tKn'wvf¢Kj#teryljlÐeGwre(iprjmtKi4si@eeh{ rojmislee5e5¦j
ªj,K7|! e5j
wsr´e'e,{ jjmsle e5j wuv2jmtKtKv2! wryilye'vªw7Kvejm|±eJjmtts@j{@jen
mtKvj#gv2tKj#jmtUrw@qjmlyi ee ryzzGe5{rtUjmehlon wehlyX ¤i4jse(wutvryi'tw7X¢qe p stKv¤vlqe³Á !  ]· Á~j®|
v2LjNqR
2{eh½q
mp-Â ¥ftKsi@r{/g#s risujtKseehwuitKvGv2ryifrw7jme5s lyX
qw tKp w>rylrjsun tKvfvN×lÁ q7N D e¤³@Â3Á p-jm s e5i !  N ·@
r ve5vRwkn ½4Á½ NNÁ  N"ÁD = ¤ Â3p¥½j¨sjehBi Á = N N >|QtK½l lyvf Á =wkn>½Â3N Á = ^| LNT½RÂ-jm·@ p´=fs@N.@ryg#Á s= sutK½Âeh°Di@v-Kz%fwrjmrysRi@eh{
qfwrotKjms/wryljrsjne
³K¾
vlq7eryi´|~q
zGtjmrqiHpKjsryvzGehtKiv¨jmsutUj-v2jmtK
2jryi |~
Kz jseª}@iv2jmtKwlye¡v2jeJtK{@nvj#tje p ryve3¦´7e5g5jme5{ jm|QtKllwkn jms@e,tzGq}@ij RÁ  ³ NÁ N D ¤Â ½ =" ½ N Á !  Á½ NÁ N"D ¤Â ="N ½ Á !  fltsjryryqg#si gJryvªtKiie w7 etUjme3r¦¢KeKjmehpi@tK{i@eh{'{fjms@ryKg#sjms@ryehv¤
i7Kjryikvjm}v¤zi@zReJtKt
wlyehei@qf} rjms's
2jmeh veh gjvjm jmsu=(tj sN ryv ghR tK Á lyg5}´·kN Â f}irjvsj#tK7wqle v2rjv2rj¢qeJeDtK{@nú
qv2wj#tKtUwjme¤rylrfjnKrjZs ô}@7zGKvzrjrry¢Ki e¤ jms
Ke5wuvetKwjme5rly
rzjnvhpqrzGeflvrye5ehv±e-jjsusuttj-j¨jg5sqehik
2¢qe eh
ryvf eht%i@ghefqvjmrojmrtK¢Ki e
KwutKwrlyrjnjmstj Á ½Â N ldfryz e SN R
fsryg#sBgh Ki j
mtK{@ryg5jvjmsezGtK
2jryi tlyeª@
qeh
jn K|
78* * *
78*
* 1 3 4 3 *
\ re±v®@zG¦ q,i@pKw7jmqe5i@gJtKe }ryv2i eZfpurojms,qly|~r}@g5lynlkryj#i´tK|~©qeh
vfzGjmtsjme rq|~i q
2eJz tg#s K|t%ghjmtKsi%
2ehwve±s@qj
ly{ehtjme5Á {(D v¤e5uÂ-tK{
e5t®jme5ilehnq{/Zôwryn i@ghe \ÔÁE½ D _D D K R \ÔÁNG· D [D D q Á ³q sryvjs
e5vsql{/rzG@lyrye5vjsutjjms@e|~
tKg5jryqilytJn´ri v2j´g#©Rryv R ½ 2 RÁ Á D ¤Â ¤Â Á ¶k uq
ro¢qehi ,pe5}tjmrqiv±Á ³qÂtKi{GÁ ¶kÂ7{e®uie±tKiryi@gh
ehtKvri |~}i@g5jmrqi R N Á D ¤Â jmtKsvv2e´v2g5e5rj¨tjKeh|¥{®@f¦´e5r{Gjsjqsryike jv r¢KehiR , K|¥jms@ryvzGtKri tK
2eDjmse-|~}@lyl@ri@|~q
2zRtjryqieh}rlyrw
ryt ª v m j @ s % e D 5 e r k s j , !$# ½qpjse%}@jrylyrojn|~}ig5jryqi4tK
2k tKN g#se5v \ !.# ijmsrv¤lyrzGrojJp tKtKlyil;{ri|~{q
ro¢´eJr{tg#}us tKl,v-p lyMtXn R L ·@R p ½R r|G· tKH iq {/p¥tKqii{ lon r| R^½( t
·Ge H q ehpuv2} rlyrw
ryt@rvf¢Keh
jmryghtKlÐtj QR]·GH q p B i m j s e y l r G z o r f j K t v , !.# ·@pujmse,}@jmrlyrojnR|~}igjmrqi rvri{e57e5i{ehikjªK| -p¥v N rv sq
2ryh|ÐKie,jmtKrlVip@ghtK
2ieJ{tKv2jme,sse5
eejme5ry
vf te5}iiehrorjn }eryiehv2}}g#rylsrywt%
2ry}-z tJn |~qjsu
tehjftKg#jmsse{ e5ivrojn ( 4 ·tj tqKly
4l L ZRp@js·@ehpqi ri{e5e,7te5i{
ehqiktKjg#ln,sBKt%| ly-ryzrj±sriú}v fs ryg#N sryvÔe5s¢Kqeh
rnhqryikijm{tKro¢l@ryt{i}u{%tehl7e5}rjmrs@lyrehw
-
r}
2z]e5|~e5ryvÔ
>v }LiryR^}½qep qi}@ghj
2gheJqtKzv2ryeKi jmse¢tK
rytKig5e,K|ZtGiK
zGtK1l ryvfv} >Gg5rye5ijhp7w@}@jªi@Kjªi@ehghe5vvtK
2nKp7|~q
fjmsrv jmsÁ e z|D eJ¤teú9Â iBg5Rv2qr ik ijm
mtKtl g5 j%|¡jp@sjjeússryv{ehirv2jmjm
2s@ryewO }´jmÁNryF·KN iDJ|~½}Âji@pZg5jjmt srqehlyi irzGryjmvros@j ¢qehryeh
i
ejmrftgJ
tKseúl;ryg#tUjms js@
tKjmehslel¨e rye5i{}@ro¢ryflyryr{ws@}u
ryg#rytt@sBlypvvm
te5jghryR v2eh®ro¢qeh·@ev p R putKi{ R ½q =
³K¿
jmsutUjÐ frowjmqs}qi}{%
j}´sjmeryl
mrtKjni |~e-}iKg|¥jm|~ry}KliHlopri@Á |~q³q
2ÂDzRw7te5jghryqqziªehehv}rylryw
2rt@ptKvZe{ ryi,jmse-je¦jJpkijme , N3 ÁN³ ½1 2, !$# ÁV³ ½Â1 ³ , '*)$+ R · Á  eJzGutKqehg#
tKsitBvvryijm{@KsueG
tUzGKjÔ|tKro|´ljmjs{serye±vryjmvik
2r jrywehiu
2}@tK¢jlktKryryqlv;ig5p|qtKi³´{ä¶qrojm¶B
2rXqv¦´iuj#rtKtKzRi@llt{un¡jtKehi
loq{nx
zG{½ e5tK¢lKryfKt|jmrojmrjmqssizGevehtKtK
2
iqKwu}tKiw{ rly·GjroHjsq n4etzGzGi{(tKehvtKvvj#iHtKlyRrieh{v tKs@q
ryi{ v {ehe5}u¢rytKtl;jmjrqGi ·´7Ò·@p½jsghtKehii/jmwse egJstrlygh}@slehtvjj eh^{ |~t
vqvz ghjmrytsjmee5{Bri{fr ro7jms/eh
2ehtKiiBg5eehgh}qryilry{@wr
2jmryr}qz i )lehv2vjsutKiBq
, N 3 ÁN³ ½Â G· Hä¿q¾ ,-!$#" ³ ,-'*)$+Á G· H q >F³ Hä¶q¶ @ R · Á q d)ehltKeh
v
vtKjmi s tKri(i qpJ
je5sry}vHtKzleJjtªiF· vHH qjmsu tU" jH jmpUsfe5
s@e¨eh
e,e ¦´r" v2 jmv tiÁQG· e5H }¿ ry, lry!.w#
2,ry}F³ z Hä¶q¶f, rj'*s )$+ )@ &Á , G· HäN·@½¨ t j;, e¢q'*e5)$+
2Â3n
78* * *
78*
* 1 3 4 3 *
fsefehgh
2e,tKijs®e(i{Grie5{r¢}rry{lry}uwtK
2rlHtªrv¡K|rijm{s@re e5ly
qehwuiktjl w e5tKjzeheehwkinvvjmehtKg#
©Bg#s@tKryii { w|~qq
Zijm{s@
ehôv2}sg#qsl{Gtv2jmr siu
2ehtvlyvs@qly { ryvft (jmsutUj¡v2ql¢Kehv5¯ Á ²k l \ÔÁE½ D [D fÁ ¤Â D q%  \ÔÁNG· D [D fÁ ¤Â D q; m ZÁ Z( Á ¤( b Ö Á ¤b  Á Ö R · fvrisghehe
2e rjff{@Á ´¤e5. vR i@Kj½ t 7eh Gg5Ájf(j ¤seÂ3úvql}@sjmeGrqryiúikjm|~eq
mtK l¨ r ijseR{e5iqzryiutUjmq
ghtKi\weGr iq
2eh{ À r K ¢ h e B i q }
@ } m j r y l o r j R n ~ | } i g m j r q H i ¥ p K t i B { m j s e Q | K t g ¡ j j u s t j r ¡ v { r 2 v j
y r @ w @ } m j 5 e $0Á D Â3p { fsehi aryvf·q
½ frjmse5}tKl
qwtKwrylrjnjms@ryvfeh}utjryqiwehg5qzGe5vh¯ ½ q³ R · , !.# ½ )³ 2 3½ q³ 2, N ÁV³ ½X ³ , '*)$+ Á µq fseh
2e s@ryvehtKi}u{ tUjmryKtKi/
e ghtKjisew7v2ej#t
ehitK{u
tK
2tK{/i ie5K{B
zGj tKl{r¢Krev2j
ryw@}@jmrqitKi{{e5ivrojnq ³ , '*)$+ R , N Á½)³ RÁ qÂ2 , !$# ~³ 2½ q³ ½ Á ¾k =
h
{i4rjryehqi}utKtUljmqryKi ixÁ pf¾kÂsp¥ryg#jmsse,Dee¦´gJtehlyg5l jmtÁ jmrqi R ½ | qÂ3¯ eh}utlyvfjmse,lyry©ehlrys´{ jsutj R q½ p¥g5qi´ úÁ K R Á R ½ q R Á2Á ½ q³qÁ Á  ½ q³qÁ2 Á -@  3½ q³q  Á ¿k ¶q·
~|qi
jms@e(lyr·zGtKroijf{BtKv eh }utKlv·@½p¥jm|~Ks
rv¡lry ©eh·@lyr±sô´rzG{rwltKeh
2ghlKnqzGpkje5sv¤etGe¦´v7jme5e54g5jm|~t}jmirqg5i/jryqiB| fsryv ryg#s eh}utKlv¤· 2½ q³ ½ q³ Á R ·" qÂ1 ½3q³ 2Á R^½ KÂ R fhe5s
úeh
2e,wehrli jmselyR rzGroj½ tKqv³ tKi{4K·@ip e( tÁÁw7X¢qe(½ rKj ³q  Á @ÂDR^weh· ghK qzGÂ-e5ryv¡v¡tRtv2v2jjeheh |~|~}@}iig5gjjmryryqKiBiffss@ryryg#g#Á s4s q ·krrvv qhe5i
ew7w7e5e5lylyXX .RaR ·½3qtK³i{BtKih{e5
qúitew7tKXw¢qXe¢qrej rj @ÁtKÁ i{ Á½ q³qR  ½ ÂD qrÂDvfrytvtKvjmve5w/e5|~|~}Ki
eKgjmrqiBfs@ryg#s rv @ s h e
e ~ | q
e f p } v r i Á k ¿ Â K t i ^ { Á @ · p j s e q ·kÂp-e4v2ehe/jsutjRryi>jse lryzNrj* tKv
, r skj2s, tKNi{ v|~rq{
e,K|½3qÁ ³ ¾kÂDrvftv·@jmp"eh4, |~}ig jmr, qi/Ne5 }u|~qtK
DlH·jm , a!.# ½2q³´, p´tKi{%|~K4
, ,, ½ N K3³´ p |~qqi!.
lo# núra| , ½ q³¨¬¨, N}u*tU jmry2Ki, Á ¾k Â-sutKvfz%}@!$# ljmrlye¡vql}@jmrqiv-ri jmselyrzGroj-tv !$# ·r|ÔtKi{ !.# '*)$+
|~w7}e5ighgqjmzryeK¦ehi j v5¯ v2tK}i@{ qjmvs@e%e jvsutKtzGj e'b Á g5¤qÂfi{rv¤rojmtRryKiui@qtKl¤
zG{tKrv2lÐj{
ryryw@vjm}@
jmrrwq}@i jryKq| i 7tKv2tKvv}zw7ee(|~qjm
s@ee% vmtKzse(e5i }´jmryÁ lr²kjn  e ,-!$# ½ ³ * ½ q³ , N3 ÁV³ ½1 >³ ,-'*)$+ ½ 2½ q³ b Á ¤Â R · e = ezRt©Ke¤jms@eg#stKi eK|ТKt
rtwlye5 v P@ ^tKi{B
ehtK
tKi e¤jf
2rjme¤jsryvfÁ tq vh½¯  e Á.,-!$#15, N3 ³ ,-'*)$+ q )³ , N3 )³ , !$# ( 4½ q³ ½ ½ q³ b Á % R · e w}@sje ryq|~i#}i0\gjmÁ ry Kiv ½ tKi³F{ D @ iXa
e|~eh
-jGt(¢tK
2rtKw@lye fsrg#ssutKvjmse i@q
zGtKl{@ryv2Á jq
³qr {jmse5e(¢ry¹{tehjmeh
2riqe%v2i rDjn eq|i@rylv¡ n/ghryq iki@´jmghe5e5ehiv(ik{4jjm
mjmt j5ehehe{
2¢KttK ly
}uKt}jv%ie({ Djms@ejrysv¤te%rizj
eeJqtKtK
i6g#tKsxl rjmi srjmv%s@½ lyerqzGly³ryzrojJKpÐ|rj¡tKRlytKl±v¡jm=jmsseGes@Dryvlyej#e5tKr ] isk{jtKtKi
K{{ | jm³ s, e,tKN 3
2ryeik jm¢ e tK
mtKntvrylÔi tt
g5e%
mqtKtilyv2rz{jmtKlqnikv2jjtUghj,ryi\Kjisjmv2s@ryjmv,e tKik7ryjJikq jmrike ÃjJRpÔ
mtKjrylNiBspeRjmehse,}ujmstKlye5rl-zG
,jro2|~jJ}p@i¤g³ jme(,rqghNitK3v(i Ájm|
2eJ. t j¡½ jjmqsus³qte,Â3j(\etK¦´;ry
2©eheJe5vtKfv2
,ryrqvryii e b Á %Â b Á ½ K³qÂ-ieJtK
fjms@e,zeJtK iBK | Gp¥vGrjgJtKi/w7ejm
2eJtjeh{ tKvfghqivj#tKikjªryi jmserije
tKlVs}@v¡rijselyrzGroj-tKv ·@pe5}tjmrqi Á q ³qÂDwehg5qzehvh¯ e , !.# >³.Á , N3 2,-'*)$+~Â )³ ,-!$# * 3½ q³ ½ 3½ q³ R · e Á q ¶kÂ
¶@½
¹ h e 2
K e p 2 v y r i 5 g e r ( v B t i q
G z K t %) , yp e e Á½3  R e e CR ½qBr©Kefryvep l e ³ Á½ @ Ra³ e AR ½q se5
e|~q
epe5}utjmrq i Á q ¶qÂDw7e5ghqzehv , !.# ³Á , N* 2,-'*)$+  5,-!$#kR · Áq  fsryg#sBryvv2ql¢Keh {/q i
lnR wkn R ·@
e e
7lyrwKn ry
ikr}jm
v5z q%=¢Kqtv2e%lyrjm}rg5e5qqv¤iiKv2½q| ryp{jme5s
¤etKqv2¢ivtKlolnBgh}ryehtjvsjme5Ke {'| Bfe5ijmrojmsehs
2tryjÐg%´ghg5tKR ghv}e(·
ryryi tKi
2fee5s{}@rryg#ryvlys4jmrwrijm
sg5r}j¡e,z |~|~
}qtKlyz.
le¨ryi´{jm|~srqv2qjm
v2rzGeig5ttKjhjmvprv2qr´vi qg5rlyehttjjm}ehe5r{{ frjs X R v2ry½qi g5etKi ryi{ro¢ry{}utl Å1v / qw@veh
¢tjmrqivtK
2e t
mtKi{@qz"vtKzG@lyeG|~
2qzjse fjmsseq@leª
qwuqtw}ryllyrtjjmnrqKiH|@p t-8ltK
/4e rvD/ptv2iúf}|~Ki
;wrtKtikvn ve5{ D ehvjmry zG·@tjpq0
2436| 5 -gJ¨tKi¹¡wr esg#ehs
q0 v2eh24i(36v25 }6r>ighgh
2reJehtKikv2jmehlon v ltK
K wue'tKwvrlyrjjmn/sutU½ j4 tjBljmeJtKvjmjB se |~
tKj
g5}jryeqi^q}@j½ ghq z eÁ K|,D ¤jmsÂe q}lytjmrqitjj
rw}@jme5vBtj leJtKvj K m j Z e j u s t j m j @ s ± e jmryisutUjmjÐs@ejsreªi@|~ÁQeh
2q
e5vv2{ryw@lo
n¤q}´z%wujmtry}lwrlojjmrynlrrjm|~}lyreJehiÂvÔgjmKjms|ryK
2{@ehi,r v27srv;ehq
ghlye5{@qikikv jjmrKi}@Á }/4jmqg5D }q8Bv;zGÂfe5¢Krvtjs,
2Á n
2D ehghªv2K7iÂe5¨jg5ry¼/ijÐ}jmKq
}@ehtKvXlyllq¢KnªehtKf
h
p r}@jmszGeªg#e5tKsuiv2tKvji}vhpUzvehev jmg#susutUtKji ]e,ryrv±iúghjmKsie jry|~i}}iqg}@jmrvhqpi v(j sutjDtv2zRtKllug#sutKi eªryijms
2ehv2sqly{@vrzGlrye5vqilntvzGtKlyl s}vryitK
2jrygh}@ltK
5pHfsehi'jmse5
eryv v26} >ghrye5ikjmln ´{ryi´|~q
zGtjmrqitKwq}@j jse jm|~}
2}lyleGryi@vj#|~tKj
eKzGptt jmqrq iH
2e tôjev2w7}e5sutJq¢´vreq
Drye vtK{@
e5w@®urijm
e tK
rl n/Á ghlDq¤veÂ9jm@ f(suÁ tj,D [rjD + qÂ}jmly'{wweReGjm}s@i@e {eh
|~q}}@ijgghjmqryzKi eúrÁ i e5D }@ªryÂ-lyrwjsu
rt}j¡z ´g5fghs@}eh
2v¡i f0 rojm2sB3-5 7qR v2rj0 r¢qúe
2sqe5wuitKw@|~qryly
rojnútKikrn i s e5
{ri·@pÔtKe5i{}ryl|~ryqw
2rytK}ikz n fsehi$0 24365 R 0p¥egJtKiBg#sqve 0 23-5 lytK
e e5iq} s/v2jsutj ¡Á fD ¤Â N Á fD ¤3 Á qq  tKtKÁ g5ijK}uryjmitKe{llrojmnG¢sury´tU{j,g5}ughtj}l@s
-iryvrei ¢qryiehs
e5eht
2}u{j2jmtKryi
lyrro jwn4}@e5jrehv,}v¨ryil7rywKj(
2vryrv}jtrzB¢KjmreÔv2®ue5
s@{ qrywv|~tKqryw
vDrylw7rje5 n gJtK-jm},pÐv2qt eiiryli qni´s|~e5Keh
{}jriryslqrywv2eh
2e ry}}z r lyryw@-f
prys}@tKryiz/g#s{ p jmse5
e|~sq}
ve ro]| re viRKjflryghz lqve j NtKi@t{ jfv}@e g#s4R tKilyrz -Ö pXjsehiDestX¢Ke e Á e D ¤Â R *N Á e D ¤Â3se¤|QtKgj dfjmsue tj Á D ¤Ârvqi jmdfse e q lyryi@e¡|~q
ftKllT0 rzGlrye5v±jsutj rjvlyryzs}rj vjse eÁ ehe }D rylªrywÂD
2ryrvfttKKl|Ôvjsqe i lyrjmzGserojmri q s@lryehi
e{@ ryi z´{e5lHtK
2etKlyv2eh}rylryw
2rtK|Ôjse |~lyr}wly
lÔryryti@K|~K|;
jzGseªtjm|~r}qli/l7rzi@|~q{
2ehzRlNtjôryqúijmsze(´ly{@ryehzlVprjfryi s rg#ss e5ry
vD{ e3ri ¦@ tKg5zjl´n{fe5lsut
tKji{ghqg5z}
ryv-5ehrv¡i t(¢Kv2eh}
iehv}Krj jmeh
sr}e}z rslyryehw@w
2
{}@ryry}@ji z/r j±ztK§ªly´v2¡|Z{@ehg5lqehzR}
2zG
2tJvneKrojmp¥vÐjmly7s@tKqryghvfv2e±r{jtKrl¢qlkehe±v
iK
2KqwujwutKwtK
w}rlyrlrlyejronªjqn q}@i%qjfi(tjmszverqi
2 e±qlyevjv2su|~ry}tKwli%rlklyrryqji@i@n|~eKjm
|~szG}tltjflkjmryjmri@sq|~i eq
2ehlyzRrzG}tUrorjmj-lyryryKwKi | eh}rlyryw@
ry}@ z fse5i/zq
2e¤jmsutKiBqiee3¦@rv2jvhp¥tKvfghgh}@
vfryiq}
fv2ryz%}lytjmrqiv5 78* * *
78*
* 1 3 4 3 *
¶k³
'
&
'
T mapping: Z=0 dash, Z=1 solid. weightSTC=0.5 1
0.8
0.8
probability of choosing x=1
T mapping: Z=0 dash, Z=1 solid. weightSTC=0.3 1
0.6
0.4
0.2
0
probability of choosing x=1
0
0.6
0.4
0.2
0
0.2 0.4 0.6 0.8 1 fraction of predecessors choosing x=1
0
0.2 0.4 0.6 0.8 1 fraction of predecessors choosing x=1
T mapping: Z=0 dash, Z=1 solid. weightSTC=0.7 1
T mapping: Z=0 dash, Z=1 solid. weightSTC=0.9 1
0.8
0.8
probability of choosing x=1
probability of choosing x=1
0.6
0.4
0.2
0
0
0.6
0.4
0.2
0
0.2 0.4 0.6 0.8 1 fraction of predecessors choosing x=1
¶q¶
0
0.2 0.4 0.6 0.8 1 fraction of predecessors choosing x=1
)
'
&
'
CDF over S , i=300; weightSTC = 0.3
CDF over S , i=300; weightSTC = 0.5 probability of S (Z=0 dash, Z=1 solid)
0.5 0.4
0.5 0.4 0.3
i
0.3 0.2 0.1 0
0
0.2
0.4
0.6
0.8
0.2 0.1 0
1
0
0.2
0.4
0.6
0.8
Si
Si
CDF over Si, i=300; weightSTC = 0.7
CDF over Si, i=300; weightSTC = 0.9
0.5 0.4 0.3
1
0.5 0.4 0.3
i
probability of Si (Z=0 dash, Z=1 solid)
i
probability of S (Z=0 dash, Z=1 solid)
probability of Si (Z=0 dash, Z=1 solid)
i
0.2 0.1 0
0
0.2
0.4
0.6
0.8
0.2 0.1 0
1
S
0
0.2
0.4
0.6 S
i
¶
i
0.8
1
' & '
&
Sample of 200 HISTORIES of Si: Agg state Z=1, weightSTC = 0.5 fraction playing x=1 so far
1 0.8 0.6 0.4 0.2 0
0
50
100
150
200
250 300 350 400 count i Sample of 200 HISTORIES of S : Agg state Z=1, weightSTC = 0.7
450
500
100
450
500
i
fraction playing x=1 so far
1 0.8 0.6 0.4 0.2 0
0
50
150
200
250 count i
300
120
140
100
120
80 60 40 20 0
400
Frequency of Si: weightSTC=0.7
Number of histories
Number of histories
Frequency of Si: weightSTC=0.5
350
100 80 60 40 20
0
0.2
0.4
0.6
0.8
0
1
Si
0
0.2
0.4
0.6 Si
¶q
0.8
1
& % & 0
T mappings: Z by steps of 0.02. weightSTC=0.3 1 0.9
probability of choosing x=1
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1
0.2
0.3 0.4 0.5 0.6 0.7 0.8 fraction of predecessors choosing x=1
0.9
1
0.9
1
T mappings: Z by steps of 0.02. weightSTC=0.6 1 0.9
probability of choosing x=1
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1
0.2
0.3 0.4 0.5 0.6 0.7 0.8 fraction of predecessors choosing x=1
¶q²
% # '
T mapping: Z=0 dash, Z=1 solid. precision=0.1 1 probability of choosing x=1
probability of choosing x=1
T mapping: Z=0 dash, Z=1 solid. precision=0.03 1
0.8
0.6
0.4
0.2
0
0
probability of choosing x=1
probability of choosing x=1
0.6
0.4
0.2
probability of choosing x=1
probability of choosing x=1
0.2
0
0.2 0.4 0.6 0.8 1 fraction of predecessors choosing x=1
0.8
0.6
0.4
0.2
0
0.2 0.4 0.6 0.8 1 fraction of predecessors choosing x=1
T mapping: Z=0 dash, Z=1 solid. precision=10 1
0.8
0.6
0.4
0.2
0
0.4
0
0.2 0.4 0.6 0.8 1 fraction of predecessors choosing x=1
T mapping: Z=0 dash, Z=1 solid. precision=3 1
0
0.6
T mapping: Z=0 dash, Z=1 solid. precision=1 1
0.8
0
0.8
0
0.2 0.4 0.6 0.8 1 fraction of predecessors choosing x=1
T mapping: Z=0 dash, Z=1 solid. precision=0.3 1
0
0.8
0.6
0.4
0.2
0
0.2 0.4 0.6 0.8 1 fraction of predecessors choosing x=1
¶kµ
0
0.2 0.4 0.6 0.8 1 fraction of predecessors choosing x=1
% # '
probability of Si (Z=0 dash, Z=1 solid)
0.5 0.4 0.3 0.2 0.1 0
probability of Si (Z=0 dash, Z=1 solid)
CDF over Si, i=300; precision = 0.1
0
0.2
0.4
0.6
0.8
0.3 0.2 0.1
0
0.2
0.4
CDF over Si, i=300; precision = 1
0.2 0.1
0.2
0.4
0.6
0.8
0.4 0.3 0.2 0.1 0
1
1
0.5
0
0.2
0.4
Si
0.6
0.8
1
Si
CDF over Si, i=300; precision = 3
CDF over Si, i=300; precision = 10 0.6 probability of Si (Z=0 dash, Z=1 solid)
0.6 probability of Si (Z=0 dash, Z=1 solid)
0.8
CDF over Si, i=300; precision = 0.3
0.3
0.5 0.4 0.3 0.2 0.1 0
0.6 Si
0.4
0
0.4
Si
0.5
0
0.5
0
1
probability of Si (Z=0 dash, Z=1 solid)
probability of Si (Z=0 dash, Z=1 solid)
CDF over Si, i=300; precision = 0.03
0
0.2
0.4
0.6 Si
0.8
0.5 0.4 0.3 0.2 0.1 0
1
¶q¾
0
0.2
0.4
0.6 Si
0.8
1
T mapping: Z=0 dash, Z=1 solid. N=2
probability of choosing x=1
probability of choosing x=1
1
0.8
0.6
0.4
0.2
0
0.8
0.6
0.4
0.2
0
0.2 0.4 0.6 0.8 1 fraction of predecessors choosing x=1
0
T mapping: Z=0 dash, Z=1 solid. N=10
probability of choosing x=1
probability of choosing x=1
1
0.8
0.6
0.4
0.2
0
0.8
0.6
0.4
0.2
0
0.2 0.4 0.6 0.8 1 fraction of predecessors choosing x=1
0
T mapping: Z=0 dash, Z=1 solid. N=40 1 probability of choosing x=1
probability of choosing x=1
0.2 0.4 0.6 0.8 1 fraction of predecessors choosing x=1 T mapping: Z=0 dash, Z=1 solid. N=80
1
0.8
0.6
0.4
0.2
0
0.2 0.4 0.6 0.8 1 fraction of predecessors choosing x=1 T mapping: Z=0 dash, Z=1 solid. N=20
1
0
T mapping: Z=0 dash, Z=1 solid. N=5
1
0
0
0.8
0.6
0.4
0.2
0
0.2 0.4 0.6 0.8 1 fraction of predecessors choosing x=1
¶q¿
0
0.2 0.4 0.6 0.8 1 fraction of predecessors choosing x=1
probability of Si (Z=0 dash, Z=1 solid)
probability of Si (Z=0 dash, Z=1 solid)
0.5 0.4 0.3 0.2 0.1 0
0
0.2
0.4
0.6
0.8
0.4 0.3 0.2 0.1
0
0.2
0.4
CDF over Si, i=300; N = 10
CDF over Si, i=300; N = 20
0.2 0.1
0.2
0.4
0.6
0.8
0.4 0.3 0.2 0.1 0
1
1
0.5
0
0.2
0.4
Si
0.6
0.8
1
Si
CDF over Si, i=300; N = 40
CDF over Si, i=300; N = 80 0.6 probability of Si (Z=0 dash, Z=1 solid)
0.6 probability of Si (Z=0 dash, Z=1 solid)
0.8
Si
0.3
0.5 0.4 0.3 0.2 0.1 0
0.6
Si
0.4
0
0.5
0
1
0.5
0
CDF over Si, i=300; N = 5
probability of Si (Z=0 dash, Z=1 solid)
probability of Si (Z=0 dash, Z=1 solid)
CDF over Si, i=300; N = 2
0
0.2
0.4
0.6
0.8
0.5 0.4 0.3 0.2 0.1 0
1
Si
·
0
0.2
0.4
0.6 Si
0.8
1