About optimal use of color points of interest for
content-based image retrieval
Valérie Gouet, Nozha Boujemaa
To cite this version:
Valérie Gouet, Nozha Boujemaa. About optimal use of color points of interest for content-based
image retrieval. [Research Report] RR-4439, INRIA. 2002. <inria-00072149>
HAL Id: inria-00072149
https://hal.inria.fr/inria-00072149
Submitted on 23 May 2006
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
About optimal use of color points of interest
for content-based image retrieval
Valérie Gouet — Nozha Boujemaa
N° 4439
Avril 2002
ISSN 0249-6399
ISRN INRIA/RR--4439--FR+ENG
THÈME 3
apport
de recherche
!"#!"$%&'
()*!*%&!*'+,-&./0*122$34
*5 687:9<;>=@?BADCFE2?HGBIKJCFLNMO6QP"CFESR>?<TQ6F6
U$VXWY[Z\*]_^a`<bcZ>dfeNghbfikjN`VXjNYlY[Zm@YneHgoVSik`XZNp
iqYnesrNZ>t>pvuXjH`X`Xw>Z>t>pXgjN`X`SesixtftceH`SgZyt
zKdcjH{|Zb}^aY[Z>uXiqe
~esX8jHdcb}u,ZdcZygoVXZdogoVXZ`82HN\N
]vdfikHH<]H\"esrHZyt
%>(XHH ^a`gjH`<bcZ>`<bmSeHtcZ>u
ikYnesrNZ[dcZbcdfikZ>eHOt,tbcZYnt>pbcVSZnY[eHik`eHXXdfjNeHgoVSZ>t4SeHtcZ>u
jH`bcVXZ
< Z>iqdfdcZ><t£mveNmrNZkjNXSeHYles2Su,kZZ>tfgdfesiqdo,eHbcu,iqjHiqrH`Y js¤¥iq`vikHb>¦jHq§¨HZlVSesZ`¡`¡esgXjHS`dctjixu,,ZiqY[dfiq`Xesr©bcZlboteHZytcesªvdot4goV
qikªNjHZ"`
jNbc,VX{|ZnZ>g¢&b£VSdfZ>jHgqZ"jHrHiq`SYni«bfesikrHjNZN`Bp'jH¢&d£VXSixgoesVdcbcdfixZesm
< Z>dciqZ>tljN`QSeHdbfiqg xesdnesdfZ>eSpObcVXZytZ-Y[ZbfVXj,uXtn8Z>gjHY[Z-ik`SeNu,Z esbcZ-es`SuQY[jHdfZ-kj,geH&goVSesdoeHgbcZdfikm
<
<
¬eHe(Xbf8ikjNZ>es`Sd%t8Y Z>t bOt|b*eNuX8esZXbcZ>Z>Y[u'X¦kU$j(NVXZ>Zu¦jN^aik`<`¡bKbcgoVSVSiqeHt"dfgeNjHgh`<bcZ>bfdcZi vb>esp2bciqiqjHY[`eH¢&rHZ©VXixu,goV*ZytcXgdfdcj(iq,HbfZyikujN`dfZqiqeHeHtcXZ>ku¡ZixjHt`¡eH8tcjHZ>iqu`<bfjNt`*jHiq¤&`<(ik`<eHdcbcixZ>esdc`<Zybft|bt
bfjBdfjsbfesbciqjH`es`uik`esdcbcixg xesdjN`gjNY*Xiq`Se(bf¬ ikjN`StjH¤$bcVXZ®}iqk8Zdcb>¯ t"uXi«°FZdfZ`<bcixes)ik`v(esdfixes`<bft>¦D±XjHd
rNdfe"(es ZiqYnesrHZytp<t goVeu,Zytcgdciq,bciqjH` tZyu[bcj"Z£gjH`tixu,ZdfZ>u nbcj*bcVXiqdfu©jHdou,Zde(b¥qZ>eNt|by¦2²BjHdfZ
df´ Z>gZ`<bcqHpvrNZ`XZ>dfeHki ¬ esbciqjH`St¥bcjngjNkjNd)iqYnesrNZ>t¢)Z>dcZXdfjH8jNtcZ>un¤³jHd}tbcZdfZj(vixtiqjH`es`SuikYneHrHZ£dcZbcdfikZ>eH:¦
jHY[Z&js¤FbcVSZYµXdcjNj<tZbfj*gjN`Stixu,Z>d2bcVXZ}iq`v(esdfiqeH`NbotOjH`Skle(bO¶Sdot|b)jHdou,ZdKeH`SulbcjZ>`XdcixgoVlbcVXZ4goVSesdoeHgm
bfZdfi ¬ e(bfikjN`n¢&i«bfV©rHZ>jHY[ZbfdcixgeHSgjN`St|bfdfeHik`<bot2¤³jHdu,Z>tfgdfikSik`Xr"tSesbcixesdcZ>qesbciqjH`StO8Zb|¢ZZ>`©8jHiq`Nbotp<¢&VXiqkZ
jHbcVXZ>dft&gjH`Stcixu,Zd$VXiqrHVXZ>d&jHdou,Zd&iq`v(esdfiqeH`Nbot$es`SugjNYl bcZtcjHY[ZgjNY*Xiq`Se(bfikjN`St$js¤bcVXZ>Y#bfjneHgoVXiqZNZ
iqq Y[iq`Se(bfikjN`goVSeH`XrHZytOik`v(esdfixes`SgZH¦%^a`nbcVXixt)dcZ>jNdbypH¢Z4u,ixtcg tftObcVSZ4eHuXeH`<bfesrNZ>tKeH`Su©u,doe¢&SeNgoªvt2jH¤
bf¤³jNVXd} Z>tcgZ*jN`Nu,bfikZ°F`<ZbdfmZS`<eNb4tZygoVXu©jNiqiqY[gZ>eHt>rHpXZ¢&iqi«`SbfV-u,Zbc,VXiq`XZ"rnesiqesY `SujH¤2dfZSbcdcdfjNiqZ(j<est@iq¦ `Xrnes`DjN, bciqYnes tZjH¤OgjHqjHd}8jHiq`<bftjs¤2ik`<bcZ>dcZyt|b
·D¸<¹Fºf»*¼ (½%H ^aYnesrHZOiq`Su,Z,ik`Xr£es`SudfZbfdciqZ(eH:pyzOesdcbcixes < Z>dciqZ>t>ps¾)jHqjHdiqYnesrNZ>t>py¿jvg>esHuXZ>tfgdfik,bfjHdotp
À4ik°8Z>dcZ>`NbfiqeHik`v(esdfixes`<bft>¦
Unité de recherche INRIA Rocquencourt
Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex (France)
Téléphone : +33 1 39 63 55 11 — Télécopie : +33 1 39 63 53 30
% ! .& !".|!"$#&
*%&$% .0& -)!"&![ 3n&
`iq`Su,ZXe(bciqjH`Du¯ iqY[eHrHZyt$Sesd}qZgjN`<bcZ` viqt Z@pXqZ>t&Sdciq`SgiqSeHkZyt&esXXdfj,goVXZ>t$eHtcwZ>t
t d&qZSesdoeHu,iqrHY[Zu,Zxe"dfZ>goVSZdogoVXZ4esd&@¯ ZvZ>Y[XkZiqY[X qi < Z> `Nb `XZdcZygoVXZdogoVXZesXXdfj,ikYnesbciqHZ4t d
xebcjHbfesqikbcwBu,Z-@¯ iqYnesrHZN¦ ¾)Z-b|<8ZBu,Z-dfZ < bfZ-SeHtftZ-SeHd `XZBu,Zytcgdciq,bfikjN`QrNkjNSesqZuXZD:¯ ikYneHrHZH¦
¿jHdot Z4:¯ jH`-t>¯ iq`<bcwdfZ>tftcZ"qeldfZ>gjH`X`SeHiqtftfes`SgZu¯ jH,{|Zbft$j e dcZ bcZytSesdcbciqZqkZyt$t d `SZ jH`XZ
esdcbcix<g qikW>dcZNpgZ>tbcZ>goVS`Xi < Zyt4uXZvikZ>`X`XZ>`Nb£ik`eHu,w N e(bcZyt}Zb£ u,Zy t4u,ZytcNgdciq ,bfZ dot&X t4kj,ge B u,jHiq¬ HZ>`<b
dfwbcdfNZ)wqZ>w`vZ}<xixetfesSrH wytt¦eHÀ4uSeHes`S,tObfwgZHZ&¦Og¿jNe*`<bcu,ZZyvtcbfgZHdcpsiq,xe4bciqg>jHes`doeHu,gZbcw8dfjHixtciq`<esbcbfiqtjHes`qjHu,doZ$t @¯ iqtYnesZrHqqZ ZY[4ZS`<eHb&tcZ$eHtfu,tZ$j,giqjNwikZ`<Z>bftOtb)u'S¯ iqeN`<tbcw>wZ4d t bKt>d ¯ Zyt|` b
Z>uX`Si«°FtcZwY*dfZS`<kbcZliqZuxt*¯ iq `vuX(Zes®}dfiqiqeHk`N8boZt dcb>©¦-xe©z2j dfjsd*boe(qbfZ>iktjN`DiqYnZesb4rHSZy t t4Z` Xdf`Xw>ikgNiqZ>tcwe Y[ZuX`<Z©b rHt dfiqd t>p `X`XZ[Z©gjNbfZY*qkXZiq`SuXesZ>ixtftcgjHdf`Dik,u,bfikZ>jNt4`iq`<u,(jHeHikdcb ixes`<bf dcbfZt
gjH`Stcixu,wdfwZe Y[jNik`StK{ t N ¯ n @¯ jHdou,dcZ\S¦&~&w>gZY[Y[Z`<b> pFu,Z>trHw>`Xwdo esqiqtfe(bfikjN`St nxe©gj kZ d}jN`Nb4 wbcw
SdcjNj<tw>Z>t8j dxeBtbcw>dcw>j(<ixtcikjN`
Zb"qeDdfZ>goVSZdogoVXZnu¯ iqYnesrNZ>t>¦-¾)ZdcbfeHik`SZ>tu¯ Z`<bfdcZ©Z>kqZ>tXdcjNj<tZ>`<b
uXZ[gjH`Stcixu,wdfZdqZ>tiq`veHdcixes`<bot `Xi < Z>Y[Z`<b :¯ jHdou,dfZ nZbu'¯ Z>`XdcixgoVXiqdqe-g>esdoeHghbfwdfiqtfe(bfikjN`BSeHdu,Z>t
gjH`<bcdoesiq`<bcZytrHw>jHY[wbfdci < Z>t"u,w>gdciq(es`<b"qZ>t"dfZxe(bciqjH`t"tcSe(bfiqeHkZytZ>`NbfdcZ8jHiq`Nbot"u'¯ iq`<bcwd byp¥esqjHdot < Z
u'¯ e bcdfZ>t£iqYlSki Z`<bqZ>tiq`<(eHdcixes`<bft -u,ZytjHdou,dcZyt4t 8wdfikZ dot4ZbZ`¡geHqg kZ>`<b `XZngjHY"Xiq`SesixtjN`
vixtceH `<b njH,bfZ`X<iqd xendfjH t|bfZ>tftZe -goVes`XrNZY[Z`<bftu ¯ iqq Y[ iq`Se(bfikjN`'¦À£es`St4 gZdoes SjNdbypS`Xj t}wb m
uXikjN`StlkZytle(eH`NboesrNZ>tZbnik`SgjH`vHw>`XiqZ`<bftlu,Z-gZ>t[u,ik°FwdfZ`<bft[goVXjNi«p¥uXeH`StlkZ- bnuXZXdfjH8jNtcZd `XZ
bcesiqd&kixtcqZesbcgiqjHjH`<`bcZ>jH` ,bfik¦ YnesqZ"uXZ>t£jNik`<bot£u'¯ iq`<bcwd bgj qZ d£j d£:¯ ik`u,ZXe(bfikjN`
Zb£xedfZ>goVSZdogoVXZ*u¯ ikYneHrHZ>t
¼ y º ^a`SuXZXe(bfikjN`Zb£~&ZygoVXZdogoVXZu¯ ikYneHrHZ>t>pS~&Z < bfZ>t}esdcbciqZqkZytpX^aYneHrHZ>tgj kZ d>pÀZyt|m
gdciq,bfZ dot$kj,g>e pv^a`veHdcixes`<botuXi«°FwdfZ`<bciqZxt>¦
\
!"#$%&"!'())#("!'"!+*%,-/.01)$2
*!*%&!*%
465(7 > ¼ ½ %s98 ¼ 7
;<5 > = ¸ 8 7 ½ @¸ ? 8 7 = 7 ½¨ ¸ 8 ¸0A %/8 7 =CB ¼ 8 7 y ¼#D 8 7 ¸ ¸
X¦ ^aYneHrHZgoVSesdoeHgbcZ>dci ¬ esbciqjH` tciq`Xr[jNik`<bft$jH¤%iq`<bcZ>dcZyt|b$¦¦¦¦£¦¦¦¦¦¦¦¦¦¦¦¦£¦¦
X¦ N¦ ®esdfdfiqt$gjNkjNd$jNik`<bft}js¤iq`<bcZ>dcZyt|b ¦¦¦¦¦¦¦¦¦£¦¦¦¦¦¦¦¦¦¦¦¦£¦¦
X¦ N¦ ¾)VSesdoeHgbcZdfi ¬ e(bfikjN` tcik`Sr[gjHqjHd&u,ik°8Z>dcZ>`<bcixes'iq`veHdcixes`<bot ¦¦¦¦¦¦¦¦¦£¦¦
X¦ N¦ \ ´¾)jH`StciquXZdfik`XrljsbfVXZd&iqYnesrNZ4bfdfeH`St¤³jHdfY[esbciqjH`St¥¦¦¦£¦¦¦¦¦¦¦¦¦¦¦¦£¦¦
X¦ N¦ ikY[iqqeHdcikb|©Y[Z>eNt dcZµ¦¦¦¦£¦¦¦¦¦¦¦¦¦¦¦£¦¦¦¦¦¦¦¦¦¦¦¦£¦¦
X¦ ^a`u,Z,iq`Xrnes`Su-tcZ>esdogoVXiq`Xr" tbcdoe(bfZrN¦£¦¦¦¦¦¦¦¦¦¦¦£¦¦¦¦¦¦¦¦¦¦¦¦£¦¦
B ¼ 8 > K¼ D 8 ¸ ¸ >
I ¼ ¼ B%/ 8 % ¸B#¼ D ¼ ¼ J
\S¦ §¨VSiqgoV-jHdou,Z>d)¤³jNd$bcVXZgjHqjHd&u,ik°8Z>7 dcZ>`<bcixes'iq7`veHdcixes`<boMt L¦¦£¦¦¦¦¦¦¦¦¦¦¦¦£¦¦
\S¦ ¿j,ges'uXZ>tfgdfik,bfjHdotdcjN tbc`XZytct$es`Ou NN8Zrngj,u,iq`Xr¦¦¦¦£¦¦¦¦¦¦¦¦¦¦¦¦£¦¦
\S\S¦¦ \ vSj k jNbi«bfgik`XjNrnkjNd}rNZgjNjNYl`St|Zbobcesdf`Siqg>gesg¦jN`S¦t¦bcdo¦esiq¦`Nbo¦£t¦jHd$¦`X¦js¦bP¦L ¦¦¦¦¦¦¦¦¦¦£¦£¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦£¦£¦¦¦¦
: Q ¼ 7 %/ 8 ¼ 7
3
SSUTV>W)W(X)Y
:
E
F
F
G
H
4#4
>
9G
H
4R
! "! 2n.¥!
^a`¡gjN`<bcZ`<bcm@SeNtZyuDiqY[eHrHZldcZbcdfikZ>(es@¾^|~£tcvtbcZ>YntpbfVXZ < Zdf<m@v<m@ZXesY[XqZSesdoeHuXikrNY t eHkq
iq`vHjNkNZ>tbfVXZZ>`<bciqdcZikYneHrHZH¦¡²Dj<t|bljs¤ bcZ>`'pKrNkjNSes)XdcjNZ>dbfikZyt*jH¤}ikYneHrHZvixt es$gjH`<bfZ`<bftlesdfZ©Zvm
bfdfeNghbfZ>u¦ 4`lbcVXZ}jHbcVXZ>dKVSeH`Sup tZ>d¥gj qul8Z&ik`<bfZdfZ>tbcZ>u"bfjdcZbcdfikZ>HZ$jH`SkltiqY[ ikxesdOSeHdbotOjHdOjN,{|Z>gbft
jH¤%iqYnesrNZ>t>¦O^a`bfVXixtgjN`<bcZvbyp,rHqjHSeHikYnesrNZu,Z>tfgdfiq,bcjNdft$esdfZ ` tfesXqZH¦¥±SjHd$bfVXiqt dfj<tZNpXe[Y[jHdfZ
qj,geHStjN bciqjH`[Y tb¥8ZgjN`Stciqu,Z>dcZyupH¢&VSZdfZ&Z>eHgoV[dfZrNikjN`"jH¤8bfVXZtcikrN`SesSiqt)es`SeHk,tcZ>u"ik`SuXZ8Z`Su,Z>`<bcqH¦
²BjHdfZSdcZygixtZ>kNp¥bfVXZBgjN`SgZ>,bgjN`Stixtbft[¶Sdotb[iq`¨qjvg>esqi ¬ ik`SrdfZqZ(eH`NbndfZrNikjN`St[ik` bfVXZBiqY[eHrH´ ZDes`u
tcZ>gjH`Su¡iq`goVSeHdfeNghbcZ>dci iq`XrbcVSZXdfikY[ikbciqHZytjHXbfesiq`XZyup2<¡gjN`Stciqu,Z>dciq`XrDqj,gesu,Z>tfgdfiq,bcjNdft>¦ ZZ>ik`Xr
bf¤³jNVSd[e(bbcZy`SgojDVX`Xik`,i ¤³jNdcZ>Ynt[es¢&bcVXiqjHix`¡goV ¬ eseH8dcj ZD btbfbfeHVXXZ©kZ-iqY[¢&eHikbcrHVZndfuXZ>estcbfesZygheHb[tcZ[bcj¡gjH8`<jNbctfZ>t`<iqXbftqZixtiqYnªv`XesrNj(Z¢&`¡8Ze-dcb XdcdciqSjHesdfbci@p'iqjH¢)`SZ©t[eHqiqdcªHZ[Z-qjvSjHesªvdcbcik`Sixesr
j,g>g kbfesbciqjHN`' p,viqZ¢&8jHiq`Nb&jNd&ikq Yliq`SesbciqjH`DgoVSes`SrHZ>t>¦
^a`*bcVXixt2gjH`<bfZvb>pYnesiq`Xqb|¢)jgqeNtctcZ>tjs¤SSdciqY[i«bfikNZ>t%esdfZKdcZ>kZ>(es`<bbfj4goVSeHdfeNghbcZ>dci Z¥SesdcbjNdjHX{|Z>ghb
iq`eH`©iqY[eHrHZ %dfZrHiqjH` Xp,Xp F'es`Sun8jHiq`<bftjs¤'iq`<bcZ>dcZyt|by¦%^a`bcVXixtSes8Zdyp<¢)Z£esdfZ}¤³j,¬ g tcZ>ujH`©8jHiq`<bft
jH¤iq`<bcZdfZ>tb$¤³jHd}tcjHY[ZdcZyeHtcjH`StqiqtbcZyuZ>kj(¢ ±%iqdftb>pjNik`<bftjs¤Oiq`NbfZdfZ>tb}ZvbcdoeHgbciqjH`-8Zdc¤³jHdfY[t}¢)Z>k¢&VSe(bfZHZ>d$bcVXZ"ikYneHrHZgjN`<bcZ`<bot&iqt>p `XkiqªHZ
dfZrNikjN`,mSeHtcZ>u©eHXXdfjNeNgoVXZ>t¥ik`-¢&VXixgoVbfVXZ < esqikb|njs¤bfVXZtcZrHY[Z>`Nboe(bfikjN`tbcZixt&tZ>`StikbciqHZ£bfjliqYnesrNZ
rNZjNYlZbcdfiqg>es$gjN`NbfZ`<bft>¦²DjHdfZj(NZdyp%8jHiq`<bftneHdcZ-Y[jHdfZdfjH t|blbcj¡rNZjHY[Zbcdfiqgbcdoes`St¤³jHdfYne(bfikjN`St*jH¤
bfVXZikYneHrHZqiqªHZ£<iqZ¢&8jHiq`<b}goVSes`XrNZ>t>p<tciq`SgZ4bcVXZu,Zytcgdciq,bfikjN` ixtgjHY[ bfZ>ukj,g>esqkNpveH`SueHqtcjldcjN tb
bfjBSeHdbfiqeH¥j,gg «boe(bfikjN`'p `XkiqªHZjsbfVXZdrNZjNYlZbcdfiqg©XdciqY[i«bfikNZ>t*js¤&VXiqrHVXZ>d*qZHZ>:¦B±%iq`SesqqHpOgjN`NbfZ`<bm
eHtcZ>uDiqYnesrHZ"dcZbcdfikZ>(es'bfZ>goVX`Si < Zyt4Z,XkjNi«b£XVXjHbcjHY[Zbcdfiqg*ik`,¤³jNdcYnesbciqjH`
gjH`<bfeHik`XZyuDiq`BbcVSZ"iqYnesrHZyt¦
u,Z¶S`Si«bfikjN`'pen8jHiq`<b}js¤Oiq`NbfZdfZ>tb}iqtkj,g>e(bcZyu¢&VXZdfZbcVXixt}SVXjsbfjHY[Zbfdcixgik`X¤³jHdfY[esbciqjH`-ixt$bcVXZ*Ylj<t|b
dftcixiqrHgoV`XikeH¶`SgeHu`<gb>jH¦"Y[U$SVSeNZgh` b}e( b}tiqjN`X`Sr-g8ZN¦jHiq`Nbotp¢)Z[VSeNZ*bfVXZ[dciqrHV<b£bcj-Z,8Z>ghbeqjvg>es2iqY[eHrHZngoVSeHdfeNghbcZ>dci ¬ esbciqjH`
²BesbfgoVXiq`Xr-8jHiq`Nbotjs¤$ik`<bfZdfZ>tbixte-gxeHtftixgeH%bfeHtcªBiq` ¾)jHY[ bfZd ixtcikjN`
¤³jNdesXXqixge(bfikjN`St£kiqªHZ
tbcZ>dcZ>j
dfikr´ geHkiqXdoe(bciqjH` jHdn\HÀdfZ>gjN`Stbcd ghbfikjN`'pKtZ>Z¤³jNd[ZXesY[X qZ >Xp2 @¦ ´ ik`gZ >H0 GB¢&ikbcVQbcVXZ
¢jHdfª,t[js¤ goVXY[ixujH`¨8jHiq`Nb©ZvbcdoeHghbfikjN`¨es`SugoVSeHdfeNghbcZ>dci ¬ esbciqjH`'p¥bcVXZytZ
XdciqY[i«bfikNZ>tnSdcj(NZ>u bcVXZ>ikd
bciqkikb|¤³jHdgjH`<bfZ`<bmSeHtcZ>uiqYnesrHZ*dcZbcdfikZ>eHeHXXqiqg>e(bciqjH`t¦£®}j(¢ZHZ>d>pSi«biqt4iqYl8jHdcbfeH`<b}bcjgjH`tixu,Zd
bf VSe(bbfVXZiqdgjN`Su,ikbciqjH`St£js¤ tcZ[eHdcZ[u,ik°8Z>dcZ>`<bjH¤¥bfVXZ©t|bfZdfZj(vixtiqjH`BjN`XZ>t>p'es`u
ikbiqt£`XjHbj<tctcikSkZlbcj
uXikdfZ>gbcq©bcdoes`t8jNtcZbcjniqYnesrHZdfZbfdciqZ(eHFbcVXZ*tcjH bfikjN`St}u,Z>HZqjH8Z>u¤³jNdt|bfZdfZj(vixtiqjH`'¦)±XjHdZXesY[XqZHp
bfVXZ-rHdfj(¢&ik`Sr
HjN YlZ-jH¤bcVSZDikYnesrNZuSe(bfeHSeHtcZ> t[u,j¡`XjHb©esqkj(¢ bfjgjH`tixu,ZdneHk$bfVXZDrHZ>jHY[ZbfdcixgeH
gjH`Stbcdoesiq`<bft&e(esiqxesXqZjHd}¢&VSiqgoVBg>es`D8ZZ>tbciqYne(bcZyu-Zb|¢)Z>Z`-b|¢jnikYneHrHZ>t>pSqiqªHZbcVSZ*ZSik8jHxesdgjH`,m
tbcdoesiq`<b>¦^bikY[XqiqZ>t4bcjvjbcVXZl`XZZyuBjH¤)gjNYl bciq`XrbcVXZlY[jNtbgjHY[SeHgb£8jNtftcikXqZ*iq`Su,Z,Z>t4¤³dcjNY bcVXZ
SVXjsbfjHY[Zbfdcixg*iq`,¤³jNdcYne(bfikjN`'¦n}`XjHbcVXZ>desdfr Y[ Z>`NbgjN`SgZ>dc`tbfVXZ < esqi«b|
js¤¥bfVXZ©gjNkqZ>gbcZyu
iqYnesrHZytp
¢&VSiqgoVDY[jNtbcqDgeH`X`Xjsb4ZlgjH`<bfdcjNkqZ>u¦}U$VSZ*iqY[eHrHZ*goVesdoeHghbfZdfi ¬ e(bfikjN`tcVXj quD8Z*dfjH t|bbcjiqYnesrNZ
geHj,«bfu,Zikdf`S`Sr[e(bfeHik`SNZ>ut&u,j<ZytctctcgiqdcXiqkXZiq`XuXr[Z>tbcbcVSd Z*gh¢$bfikeNnZbcgjjHY[goVXesdfdoZ>eHtfghtbfiqjHZ`dfi ¦%Z^a`ikYnbfVXesiqrNt4Z>gt$jN¤³`NdfjHbfZYvb>8p,jH¢iq`NZbott&b js¤Ou,iqiqZ>`<ubcZiqdf`-Z>tkb>ikbc¦Z>dfesb b df`SZjHt`XjNZY[jHZ ¤
bfVXZ[tjN bfikjN`St£XdfZ>tcZ`<bcZyuD¢eNt4gjHY[SeHdcZyu-bcjbcVXZl¬ jsbfVXZdot£ik`XdoeHghbfiqg>es2geNtZyt¦À4Z>esqiq`Xr¢& ikbcV8jHiq`Nb
goVesdoeHghbfZdfi e(bfikjN` tiq`Xr-u,i«°FZdfZ`<bfiqeH%iq`v(esdfiqeH`Nbotp8¢Z"Z>`Sgj `<bcZdfZ>utZ>HZ>dfeHeskbcZ>dc`e(bciqHZyt}iq`vHjHqvik`Sr
¤³Zye(b dcZ&NZ>g¬ bcjHdot2js¤ NZdf*u,ik°8Z>dcZ>`Nbti ¬ Zyt¦2U$VXZ} dc8jNtcZ&js¤8bc VXixtKes8Zd¥ixt2bfj*u,ixtcg tctObcVXZeNu,(es`<bfeHrHZyt
eH`Suu,dfe¢&eHgoª,tjs¤bfVXZ>tcZu,ik°8Z>dcZ>`<bgoVXjHixgZytpv¢&ikbcV-bcVSZesiqYjs¤2XdfjH8jNtcik`Xr[es`-jN,bciqYnes tcZjs¤2gjHqjHd
8jHiq`<bft$jH¤%iq`<bcZdfZ>tb$¤³jHd&iqYnesrHZdfZbfdciqZ(es@¦
!#" S !%$
!"#$%&"!'())#("!'"!+*%,-/.01)$2
F
U$VXZ&es8ZdOixtOt|bfd gb dfZ>uleHt¤³jNkqj(¢}t¦ ´ Z>gbciqjH`©£gjN`Stixtbft%ik`ne£XdfikZ¤8tbfesbcZ$js¤esdcb%jH¤bfVXZ$Z,ixt|bfik`Xr
qi YnesrNZgoVesdoeHghbfZdfi ¬ e(bf ikjN`n bcZygoVX`Xi N Z>t&SeNtZyujN`DgjHqjHd&iq`<bcZ>dcZyt|b&8jHiq`Nbot}es`uuXi«°FZdfZ`<bcixesiq`v(esdfiqeH`Nbotp
¤³UjNjkqj(g¢jHY[Z>uSveHdcZ*e4bcXVXdcZ[Zytu,Z>ik`<°8bfZ>e(dcbfZ>ik`NjNb`tcjsjH¤S bcVXbciqZ$jH8`St>jNptft¢iqXZ*qZXdftbcZ>dotce(Zbf`<Zb4rHiqiq`¡Z>tt¤³ZyjHghd%bciqiq`SjH`u,Z\,iqe`Xrt|b es`Su,u"Bu,jNjH`Diq`Xbcr£VXdcZ[ZbcjNdf,ikZ>bciqYneHNesjN%`¢bfeVXZY-bcj ¦
eH`StZubcrHVSZZ}jNgY[jHqZjHbcd2dfix8g*jH¤³iqZy`<e(bb mSdceHZytctZ>uljH`goVSbcesVXdoZneHgiqbc`SZ>u,dcZi ¬ ,esik`XbciqrBjH`'eHp`SvudcZZ(bceHdfikZ>eseHbciqO`XXr£dfbcjvVXgZ&Z>u iqY[dcSZNeH¦[gbOU$jsVS¤Znu,dci«°FZyt ZdfkZbf`<tbKjNX,VSbfjseHbcikjN`SY[Z>uZbcesdfdfixZg
uXiqtfg tftcZ>uik`bcVSZgjH` g tiqjH`¦
©!0 !./%%$3£!0
*!"!"$2&
*0 !.
^aYneHrHZniq`Su,Z,iq`XrDSeNtZyujN`¡jNik`<bft*js¤$ik`<bfZdfZ>tb*gjH`tixt|bot¶Sdot|b"ik`¡8Ziq`Xr
esSkZ[bfjD¶S`Su¡iq`,¤³jHdfYne(bfikNZ
8jHiq`<bftiq`ZyeHgoVikYnesrNZ"jH¤¥bfVXZnuXe(boesSeNtZN¦*^a`¡tZyghbciqjH`,¦ l¢)ZldcZ>viqtci«b8jHiq`<bZvbcdoeHghbfikjN`eH`Su
goVSeHdm
eNghbfZdfi e(bciqjH` tciq`Xr
u,ik°8Z>dcZ>`<bcixesKiq`veHdcixes`<botSesdcbcixg qeHdcqHp%Z¤³jHdfZgjN`Stciqu,Z>dciq`XrDiq`tZyghbfikjN` ,¦ bcVXZ
iqYnesrNZ£¬ dfZbfdciqZ( eHFtbcdoe(bfZrN[bcj©esSXkjH`-uXe(boesSeNtZyt)iq`Su,Z,Z>uv©jNik`<bot&js¤%ik`<bcZ>dcZyt|by¦
!"!#%$'&)(
*$+,#$%(-#/.0$%1(2
¨§ VSZ`eHXXqikZyuD1bf'j
!iqYn es0rH(Zl df4Z3 bcdfiqZ(es@pFikYnesrNZ*Yne(bogoVXiq`XrSeNtZyuBjN`
8jHiq`Nbot£js¤¥iq`<bcZdfZ>tb4`SZZ>uSt48jHiq`<bft
¢&ikbcVZXgZqkZ>`Nb
pikZN¦OjNik`<bftbfVSe(bg>es`ZZ<bfdfeNghbfZ>un¤³dfjHY es`ikYnesrNZbfjnes`XjHbcVXZ>d¢&ikbcV
bfVXZtfesY[Z
eNgg dfeNg eH`Su `u,ZdeHdciqj t©gjN`Su,ikbciqjH`StkiqªHZ<iqZ¢&8jHiq`<bjHdikq Y[ik`SesbciqjH` goVSeH`XrHZyt¦
²
es`v8jHiq`NbKZvbcdoeHghbfjHdot%Z,iqtbO¤³jHdOrNdfe*eH ZiqYnesrNZ>t>ps b¥ikbKixtKegjNkjNd%jNZ>dfesbcjNd%¢&VSiqgoVl¶XbotK8ZbbfZd
bfVSe(bdcZ N ikdfZ>uQdcZ>Zye(boesXiqkikb| BbcVSZ
®eHdcdfiqtngjHqjHd©u,ZbcZygh bcjNd /GXp ¦ §ZBdfZviqtcikbi«bik`bfVXZB`XZ<b
tcZ>gbciqjH`'¦
;5$45$4 6 , 8:n ¼ ¼ B ¼ 8 7 y ¼KD 8 7 ¸ ¸ >
U$VSZ®eHdcdfiqt¥gjHqjHd¥ZvbcdoeHgbcjHd)gjHY[ bfe(bfikjN`[jH`Xq"iqY[XqikZytKbfVXZ}¶Sdotb¥jHdou,Zd)u,Zdfik(esbciqHZ>tKjs¤FbcVXZ4ikYneHrHZH¦
^bot¤³jHdfY xe(bfikjN`uXZ8Z`SuXt}jH`bcVXZ¤³ jNkqj(¢&ik`SrlYnesbcdfi«8 7 EGHJ
F I ; ; ; H)
F ILK H F
E H EGM I ; ; H ; M ILK H K M
E H E M I H M ILK H K M
ENMF I FM ILK MF
O
J@? 8=PR H S R M A
TRVUXW E S ; S KZY
7:9<;>=4?@ABDC
¢&VSZdfJZ ;>=P?@QA2tbfeH`SuXt2¤³jNd¥erNe tftixes`[tY[jvjsbfVXiq`Xrjs¤ti ¬ Z DeH`Su %dcZ>XdfZ>tcZ`<bft%bfVXZ&¶Sdot|b¥uXZdfik(e(m
bfikNZ>t$jH¤bcVSZgoVSes`X`SZ"Rn¢&ikbcV
` Y[Zdfiqg>esqkniqY[XkZ>Y[Z`<bcZyu tiq`XrnelrNe tctciqeH`gjH`vHjHm
bfikjN`js¤%ti ¬ GZ @2¦KU$VXZ£gjHqjHdjNik`<bot¥jH¤ik`<bfZdfZ>tb$ eHdcZ£u,Z¶S`SZ>u©v[bfVXZ48jNtcikbciqHZqj,geH8Zv bcdfZYnejH¤'bcVXZ
¤³jNkqj(¢&iq`Xr"jNZ>dfesbcjNd ÀZ[b =\7]A^-_)UdoeHgZ F =`7]A ¢&i«bfV _Z9bac aed
}¤ bcZd}bcVXixt$bcVSdcZytVXjNquXik`XrpvbcVXZ8jHiq`<bft&eNtctcj,gixe(bcZyunbfj[bcVX,Z fZyt|b}qj,gesZvbcdfZYne[esdfZ£ªNZ,by¦
`BeHuXeH,bfesbciqjH`dcjN tb&bcj©tfgesqZgoVSes`SrHZ>t$ixt&8jNtftiqXqZes`SuVSeNt&8ZZ`DSdcjNj<tZyuiq` F ¤³jNd&bcVXZ
rNdfen(eH Z*HZdotcikjN`js¤2bf VXZ*®eHdcdfixt$ZvbcdoeHgbcjHdy¦¥U$VXZY[ZbcVXj,u-ixt&dcjN tb -bcj©entfgeHkZ¤ eNghbfjHd&js¤Oh g
ikb£gjH`Stcixt|bot}iq`gjNY[ bciq`XreY kbcikmatcg>esqZdcZ>XdfZ>tcZ`<bfesbciqjH`-¤³jHdbcVXZlu,ZbfZ>gbcjHdes`u-bcVXZ>`Biq`
tZ>kZyghbfik`Xr
8jHiq`<bft&esb}¢&VXiqgoV-elkj,g>esY[Z>eNt dfZ bfVXZ¿eHXqeNgixes` )ixt$Yne(,ikYneHj(HZd&tfgeHkZyt¦
SSUTV>W)W(X)Y
G
! ^a`bcVSZ`XZvbtcZ>ghbfikjN`'p,¢Z£dfZvixtikb$bcVXZeHXXdfjNeNgoVXZ>t)SeHtcZ>ujH`-u,ik°8Z>dcZ>`<bcixes'iq`veHdcixes`<bot¥bfjngoVSesdoeHgm
bfZdfi ¬ Z£bcVXZ®4esdfdcixt$gjHqjHd$8jHiq`<bft>¦
;5$45 ; Q ,(XH ¸ 8HX/ 8 ¼ 7 %9 8 7 = ¼ ¼ ½ 8 ¸ ¸ 7 / 8: 8 7 A , 8 7 >
^a` Hp ´ goVXY[iqu
XdcjNj<tZyu-bcju,Z>tfgdfiqZ[es`BiqYnesrNZ*v tiq`XrbcVXZ[®eHdcdfixt}8jHiq`Nbot£js¤Kiq`NbfZdfZ>t´ b£goVSeHdm
eNghbfZdfi ¬ Z>u¢&ikbcV XVSjsbcjNY[ZbcdfixgDkj,g>esu,Z>tfgdfikXbcjHdot©gjHY[ bfZ>u¤³dfjHY rHdoe (es ZikYnesrNZ>t>¦ goV e
uXZ>tfgdfik,bfikjN`iq`vHjNkNZ>t4bcVXZ©®ikq8Zdcb>¯ tiq`<(eHdcixes`<bft es`SuY[jHdfZ[XdcZygixtZ>ktjNYlZngjHY*Sik`SesbciqjH`StjH¤
bfVXZY ik` jHdou,Zd"bcjrHZb[bcdoes`StcqesbciqjH`SeHeNtldcjHbfe(bfikjN`Sesiq`<(eHdcixes`SgZHpKeH`SubfjZ>`St dcZ` Y[Zdfiqg>es&tbfe(m
Sikqi«b|N¦lU$VSZ>tcZ <´ eH`Nbfi«bfikZytgeH`
8Z[gjHY[ bfZ>ue(bjHdou,Z>d NpjHd\ VXiqrHVXZ>d£jNdfuXZdesdfZ"iq`SgdcZyeHtcik`XrNk
gjHY[Xqiqg>e(bfZ>u ¦ Z>ZZ N e(bciqjH`Z>kj(¢¤³jNdKbcVSZiqdK¤³jHdfY qesbciqjH` nbfjbcVSikdounjHdou,Z>d¥e(b$erHiqHZ>`njNik`<b R
R HF I R F
M R R R
RHHRG
F
H
I
R H H I R M M
H M H M I
R H F HJI
R H F M I R M F M
R H H[H R R R R
R H H[H R MH R I F I RH H[M MH M H F=PRM
R H H M = R H M R M F ^XR H A I M
R H H[H R H I R H[H M R H F R M
R M M R MF
^ R R R ^
^ R H H[F HR MM A H I M F R H M
R H M M =4R M ^ R H F R
I R H M M R H R M F I
:
R M M M RH M A=PR ^X
H R^
M R R M
MMM M
R R H R R MF A
M M H MF
I R R M M M RR H F
I H[H[H H
RM
RHRM
Z>`XZdoesqi e(bfikjN`bcjgjNkjNdiqYnesrNZ>t¢eNtiq`<bcdfj,u gZyu tciq`Xr¶dftb%jNdfuXZd%ik`v(esdfiqeH`<bft¤³jHdOt|bfZdfZj<tcgjHXixg
iqYnesrNZ>tOYne(bogo¬ VXiq`Xrik` /G@pN¤³jHd¥t ,miqY[eHrHZ&dfZbfdciqZ( esSik` GFes`Su [bfjbcVSikdou[jHdou,ZdOiq` > ¤³jHd¥iqYnesrNZ
YnesbfgoVXiq`Xr `SuXZd¥iqq Y[iq`Se(bfikjN`©goVSes`SrHZ>t>¦U$VSZgjNkjNdKu,Z>tfgdfikXbciqjH`[XdfZ>tcZ`<bcZyulesbK¶Sdot|bKjNdfuXZdKixtKSeNtZyu
jN`XqjN`bcVSZ¶Sdotb"jHdou,Z>d*iq`<(eHdcixes`<bft*js¤}ZyeHgoVgoVSeH`X`XZ$es`uZ`XdfixgoVXZ>t*bcVXZ>Y ¢&i«bfVb|¢jD¶Sdot|bljHdou,Zd
< eH`<bcikbciqZ>t&tcZygik¶g£bcjngjNkjNd>p<bfj[bfesªNZik`bcVXZ¤³jNkqj(¢&iq`XrntZb E c ;
E c K
;>c K
\ ´ goV-e[u,Zytcgdciq,bfikjN`gjH`<bfeHik`St liq`veHdcixes`<bot)jH¤¶Sdotb}jHdou,Zdypvkixt|bfZ>u-e(b&Z N e(bciqjH`[Z>kj(¢ !#""
EE F
;
; F
= S @1A/9 K
K F
E cc >; $
E K
""
""
""
""
³
^bixteHkY[j<t|b©Z ik(esqZ`<b©bfj¡bcVXZ
rHdoe(es ZBiqYlSkZ>YlZ>`<bfe(bfikjN`¨ik`bfZdfYntnjs¤tbcjHdoesrNZDgjNtb iq`v(esdfiqeH`Nbot$ik`t|bfZ>eHuNjH ¤2 h¦¥^b}VeHt&8ZZ>`DXdcj(NZ>u bcjn8ZY[jHdfZdcjN tb$8Z>g>e tcZjs¤2bfVXZtZ>`Stci«bfikvikb|©bcj
`SgjHjHY[ixtZ[XqjsZ,¤)ikbcb|VXQZ©jHtc¤£Z>gbfjHVX`SZugjHesdf`dcu
Zytbf8VXjHiq`dfuu,ikjH`Sdoru,Zik`vd(uXesZdfdfiqeHik(`<e(bfbft©ikNgZ>jHt>Y[p¢& VXboixgoe(VbciqjHYn`ep}BeHt©8ZnZyt|¢boesjHXdotqixZ>t`XVXZ>Zyu
u<ikB` bc VXZn@¦` Y[4`¨ZdfixbcgVXesZ
!#" S !%$
!"#$%&"!'())#("!'"!+*%,-/.01)$2
H
g jH`<bcdoesdfHpFbfVXZ©gjNkjNdu,Z>tfgdfikXbciqjH`ikY[XqikZyt¶Sdot|bjNdfuXZdYnesrH`Si«b u,Z>tesdcbcixg xesdfkBtbfeHXqZ©e(b®eHdcdfiqt
gjHqjHd}8jHiq`<bft4kj,g>e(bciqjH`p8tcik`gZvDu,Z¶`Xi«bfikjN`DbcVSZ>tcZ*8jHiq`Nbot4eHdcZ*ZvbcdoeHgbcZ>uDesbqjvg>es%ZvbcdfZYnenjH¤ObcVXZ
¶dftb&jHdou,Zd&u,Z>dciq(e(bciqHZyt$js¤bcVXZtcikrN`Ses:gh¤|¦KtcZ>gbciqjH`D,¦ H¦ h¦
8 > = ¸ > 7 D¼ ,9 8 ¼ 7
;5$45 I Q ¼ 7 / 8:½ ¸ 8 7 = ¼ ¸ J
U$VSiqtKtcZ>gbciqjH`lYnesiq`Xklu,Z>eHqtK¢&i«bfVliq`v(esdfiqeH`SgZbcjiqq Y[iq`Se(bfikjN`ngoVSes`XrNZ>t>p(bcVe(bKixt2bcVXZ}tcjsmageHkqZ>u"XdfjH,m
qZY js¤ ">)'" 3 ik`DgjH`<bcZ>`Nbcm@eHtcZ>uikYnesrNZ ik`SuXZ,ik`Sr©es`SudcZbcdfikZ>(es'esSXkixgesbciqjH`St>¦O^a`DeHuXuXi«m
bfikjN`'pF¢)ZlXdfikZ S-dcZ>viqtci«b£bcVSZ"Y «bfi«matfgesqZ*iqY[XqZY[Z`<bfesbciqjH`BjH¤KbcVSZ*¤³Zye(b dcZlHZyghbcjNdft}¤³jHd£ik`v(esdfixes`SgZ
bfjntcg>esqZeH`SudcjN tbc`XZytctbfj[goVes`XrNZ>tjs¤2vikZ>¢&jNik`<b&vgjN`Stciqu,Z>dciq`Xr[e n`XZiq`<(eHdcixes`<bft>¦
Q ¼ ¼ © ¼ 7 >> 7 ¹
^aYneHrHZ4bcdoes`St¤³jHdfYne(bciqjH`tKY t|b&iq`Sg u,Z£bcVSZ£iqq Y[iq`Se(bfikjN`goVSeH`XrHZytpv¢&VXixgoVdfZSdcZytZ>`Nbot)elNZdf[gqeNt|m
tcixges$XdfjHSkZ>Y ik` iqY[eHrHZ-iq`Su,Z,iq`XrbfeHtcª,tnes`SuQVSeNt"rNZ`XZ>dfesbcZyuYnes`v¢jHdfª,tpKYneHik`Xq¤³jNdlrNkjNSes
iqYnesrNZ4u,Zytcgdciq,bciqjH`¦2U$VSZ£g>eHtcZ4jH¤ik`v(esdfixes`SgZ}bcj"bcVSiqt&gqeNtct)js¤goVes`XrNZ>t)dcZ N ikdfZ>t¥¶Sdot|bbcj[goVXjvjNtcZ4eH`
iqq Y[iq`Se(bfikjN`Y[j,u,Z>:¦l~&Z>gZ`<bcqHpqj,gesOu,Zytcgdciq,bfikjN`eHtc8Z>ghbot£VSeHt£8ZZ`¡gjN`Stciqu,Z>dcZyuBiq` > @p'¢&VSZdfZ
Z>ikrNV<b%Y[j,u,Zxt2esdfZ)Z>(es e(bfZ>u¤³jNdOgjHqjHd%iqY[eHrHZyt¦ ,Z>dciqY[Z`<bftOtcVXj(¢¡bcVe(b2bcVXZ&u,ixesrNjH`SeHNY[j,u,Z><¢&ikbcV
bf¤³jNdfeHd`Sqj,tcqgesesbc2iqjHg` jN`<:À4bcZU vbyp8pHVS¢&eVv e(iqb4`X&r ixtG£bcSVXesZ[dogeseNY[tZZbf¢&Zdoiktbcp(VixtKu,goik°8VSZ>eHdcdfZ>eN`NghbfbfiqZeHdfi ¬ iqZ>`vu(esvdfiqeHbf`NVXboZ&t¦8Z>^bfttbK¤³dfjHesdfbcY iqj <xe( bfeHikkjNikb|`D (iqt£gjHXY[dfZ>XtcqZZ`<,bci«Zyb|u
esb&Z < e(bfikjN` F"8Zqj(¢ R= A9 hc R= A I F ¢&VXZ>dcZ ixt&Te = A)u,ixesrHjN`SesFYne(bfdcikeH`Su elbcdoes`txe(bfikjN`SesFHZyghbfjHd$js¤2u,ikY[Z>`StiqjH`D\S¦
4`lbcVSZ&SeHtciqt2jH¤bfVXZ}À£UQY[j,u,Z>:pHb|¢)jeskbcZ>dc`e(bciqHZyt2ges`l8ZgjN`Stixu,Z>dcZyubcjeNgoVXiqZHZ$XVSjsbcjNY[Zbcdfixg
iq`v(esdfiqeH`SgZ )- 9+$"O% > 9>, (() K' ¾)jH`StciquXZdfik`XrdfesbciqjNtjH¤Xkj(¢jNdfu,Z>diq`veHdcixes`<bot'esqkj(¢}t
bcjZqikY[iq`Se(bfZleHkbcVSZlesdoesY[ZbfZdot&js¤)e n`XZ"iqq Y[iq`Se(bfikjN`
Y[j,u,Zxt>¦±SjHd£ik`t|boes`SgZHpv-ik`<bcdfjsm
u gik`Xrdoe(bfikj<t2js¤8bcVXZ&rNdfeNu,iqZ`<bOY[eHrH`Xikb u,ZHpHbcVXZ&`XjNdcYneHki esbciqjH`*jH¤bfVXZ}rNdfe(es Z$iq`<(eHdcixes`<bft
js¤2 Z < esbciqjH`D*Sdcj(vixu,ZbfVXZtcZb}js¤%ik`v(es dfixes`<bftjs¤2Z < esbciqjH¬ ` G
SSUTV>W)W(X)Y
F
! # "$
%
! "&
% F $ % #' ' % $
! " ! $ ' " ! $ ' ( " % ( F ! "
F
! ) ' $ " ! $ ' " ' % ( (
F
! ( F " $ %() %% $
! " $G ! U$VXixteHXXdfjNeHgoVixt©dfZ>eNtjN`SesXq 8jNtftcikXqZBjN`XkQ¤³jHdik`v(esdfixes`<bftnjH¤VXiqrHV¨jHdou,Z>dft1giq`Su,ZZyu e(b
¶Sdot|b©jNdfu,Z>d>p)`Xj¡ik`v(esdfixes`<bn¢)j quQdfZYnesiq` ¤³jNd©rHdoe¡(es ZDikYneHrHZ>tneH`Su bcVXZBtcZb©¢j xu Z
iku,` does Yn> e(bf¤³iqjHg>d}esqgk[jNkdfjNZ>d$u ik YngesZ>rNu[ZbfjY[J^esbfgoVX iq`X9 r[
v ik`v (tcesikdf`SiqeHr `<
bft¥¤³^jHd$ g9 jHqjH
d iqiqY[`<(eHeHrHdcZyixtes¦2`<bfU$t VX ixttcbfjHj" bfbfVXikjNiqdf`©uiqjHt$doeHu,XZ>Xd>q¦ ikZyu
.@ "K) /$" ^a`¡XdoeHghbfiqgZHpik`<bcdfj,u gik`Xr-doe(bfikj<tjs¤uXZdfik(e(bfikNZ>tiq`bcVXZ©goVSeHdfeNghbfZdcm
i ¬ e(bfikjN` eHt"ZNjHªHZyu8Zqj(¢ Y[e¡¢jHdotZ>`¡bcVXZ `StbfeHXiqkikb|¡js¤}bfVXZiq`v(esdfiqeH`Nbot*eHrNesiq`Stb"`XjNiqtcZHp
vYnesªviq`Xr[bcVXZ¤³jNdcY xeHt$ZNZ`Y[jHdfZtjNXVXixt|bfiqg>e(bcZyu¦K^a`bcVSiqt}gjH`<bcZvb>pSeH`XjsbfVXZd}eH«bfZdf`Se(bfikNZ
gjN`Stixtbftik``XjHdfYnesqi ik`SrbcVSZ£iqYnesrNZ¢&ikbcVdcZyt8Z>gb)bfj*bfVXZikq Yliq`SesbciqjH`Y[j,u,Z>:p,8Z¤³jNdcZgjNY"m
bfik`XrbfVXZ[ik`v(esdfiqeH`<¬ bft>¦U$VXiqteHXXdfjNeNgoVDVSeHt£8ZZ`¡tb u,iqZ>u iq` H 2¤³jHd£bfVXZngjHqjHd£iq`<(eHdcixes`<bft
js¤$¶Sdot|b"jHdou,Zdy¦D kj,g>es)e n`XZ©`XjNdcYnesqi ¬ e(bfikjN`jH¤$bcVXZikYnesrNZnrHdoe
(es Zytiqt*XdfjH8jNtcZ>u¤³jHd
esXSdcj,iqY[esbcZiq`<bcZdf`SeH%eH`Su-ZvbcZ>dc`esiqq Y[iq`Se(bfikjN`
goVSeH`XrHZytp8eHggjHdou,iq`Xr[bcjbcVXZlÀ4UY[j,u,Z>:¦
U$VXZZv8ZdfiqYlZ>`<bft}tcVXj(¢ bfVSe(bbcVXZ [iq`v(esdfiqeH`Nbot$rNeHik`-iq`DdcjN tbc`XZytct>p,¢&VXZ`BgjHY[ bfZ>u-e(¤ bfZd
ikYneHrHZ`XjHdfYnesqi ¬ e(bfikjN`'¦
U$VXZlboesXqZ "dcZygeHXi«b xe(bcZyt}bfVXZ[` Y*8Zdjs¤u,i«°FZdfZ`<bfiqeH%iq`v(esdfiqeH`Nbot}¤³jNd4rNdfe(es Z[es`SugjHqjHd
iqYnesrNZ>t ©bfj"jNdfu,Z>d\S¦OU$ VXZ£tcZ>gjH`Su©dc j(¢¨XdfZ>tcZ`<bot¥bfVXZ£` Y*8Zd$js¤ < eH`<bcikbciqZ>tjH,boesiq`X Z>u©¢&VXZ`bcVXZ
rNdfe(es Zlik`v(esdfiqeH`<bft£esdfZ*`XjNdcYnesqi Z>u
eHggjHdou,iq`Xrnbcj-es`e n`XZlikq Y[ik`SesbciqjH`Ylj,u,Z> :SesdoesY[Zm
bfZdot "gHbfVX ZxeHtb)jN`XZ}XdfZ>tcZ`<bftKbcVXZ4` ¬ Y*8Zd)js¤gjNkjNdKiq`<(eHdcixes`<bftK¢&VXZ`n bfVXZ4À£U¨Y[j,u,ZiqtgjN`Stciqu,Z>dcZyu
¤³jNd&ikq Y[ik`SesbciqjH`DgoVSeH`XrHZyt)`SjHdfY[eHki ¬ esbciqjH`'¦
4dfuXZ
d 4dfu,Z>d} 4dou,Zd&\
dfen(es Zu,ik°8Z>dcZ>`<bcixes'iq`veHdcixes`<bot
F
^a`<(eHdcixes`SgZbfjne n`XZiqk Y[ik`e(bciqjH`-goVSeH`XrHZyt @[uXu,@¦
\
H
Àik°8Z>dcZ>`<bcixesiq`<(eHdcixes`<bft$tcZygik¶g£bcjngjHqjHd
UjHbfesF¤³jNd}gjNkjNdiqYnesrNZ>t
H
s
^a`<(eHdcixes`SgZbfj[ikq Yliq`SesbciqjH`DgoVSes`SrHZ>t :À4U m G[uXu,@¦
s\
U%esXqZ doen(es Z sgjHqjHd$u,ik°8Z>dcZ>`<bcixes'iq`veHdcixes`<bot)Z>` Y[Zdoe(bciqjH`¦
#
/8 º >N ¸ B B% ¼
X
±SjHd}iqY[jNdboes`<b4g>esY[ZdoentVSi«¤ bfik`XrjHd}¤³j,g>esgoVes`XrNZ>t>pSenY «bfi«matcg>esqZesXSdcj<eHgoViqtdcZ ikdfZ>ubfjgjNY"m
bcZDbfVXZ
iq`v(esdfiqeH`Nbot¦ }` esXXdfjNeNgoVQdfjH t|b bcj tfgeHkZB¤ eHghbfjHd©jH¤iqtXdfjH8jNNtc Z>u ik` F 4v
gjHY[ bfik`SrDbcVXZu,Z>tfgdfiq,bcjNdft¤³jHd*ZyeHgoV8jHiq`<b"js¤&iq`<bcZdfZ>tblesb*ikbftlgoVSesdoeHgbcZdfixt|bfiqgntfgeHkZ ¢&VXixgoVVSeHt
8ZZ>` uXZbcZ>dcY[iq`Se(bfZ>uu dfik`SrbfVXZ[jNik`<bZvbcdoeHgbciqjH`t|bfZ ¦l®ZdfZ*bfVXZnu,Z>tfgdfikXbcjHdot tZyueHdcZ[tbcZZ>dm
eHXqZ*¶SkbcZ>dftgjHY[ bfZ>u
bfj-jHdou,Zd£Sp' bbcVXZntfesY[ZleHXXdfjNeNgoV
geH`
8ZlZ,XkjNi«bfZ>uB¤³jHd®}iqqZ>dby¯ t
uXi«°FZdfZ`<bcixesiq`v(esdfiqeH`Nbot¦
!#" S !%$
!"#$%&"!'())#("!'"!+*%,-/.01)$2
" 7 = ¸
&uSu,ik`Sr4bfVXZ&iq`<(eHdcixes`SgZ)SdcjNZ>db|${ tbKXdfZ>tcZ`<bcZyubfjbcdoes`Stcxe(bciqjH`esves`SuldfjsbfesbciqjH`SeHNiq`v(esdfiqeH`SgZNp(bcVXZ
goVesdoeHghbfZdfi e(bfikjN`l8Z>gjHY[Z>t)iq`<(eHdcixes`<bKbfj*bfVXZ£tciqYliqqi«b u,Z£rHdfj 'pNbcVSZ` eHtci«mik`v(esdfixes`<bObcj"Z>dftcZyghm
bfikNZ£bcdoes`St¤³¬ jHdfYne(bciqjH`t \ pSes`ugjH`StcZ < Z>`NbfkdcjN tbbfjntYnes q'viqZ¢&8jHNiq `Nb}goVSeH`XrHZyt¦
±SjHd `SgjH`Stbcdoesiq`XZyu"goVSeH`XrHZyt%js¤viqZ¢&8jHiq`<b>pNetcYnesq,XqeH`SesdKt dc¤ eHgZ)SesbfgoV `SuXZdfrHjvZ>t2es`[e n`XZ
bfdfeH`St¤³jHdf Y[esbciqjH`Diq`BbfVXZ"iqYnesrNZ>t>¦¾)jN`StZ < Z`<bcqHp8dfZ>gZ>`<b4¢jHdfªvt4u, Z>eH2¢&i«bfVe n `XZ"ik`v(esdfixes`<bft£gjNY"m
bfesbciqjH`'¦"^b£ixtj<tctciqXkZ"bc jZvbfZ`Su
bcVXZ[ixu,Z>ejs¤$tZyesdogoVXiq`Xr©8jHiq`Nbotik`bcVSZ e tctcixes`tfgeHkZ[tcSeHgZ
dfZSdcZytZ>`Nboe(bfikjN`¡bcj¡e n`XZ e tftixes`Qtcg>esqZtcSeHgZH¦U$VXZ-esXSdcj<eHgoVVSeNt*8ZZ>`Qiq`<bcdfjvu gZyuik` >\ ¢&VSZdfZes`De n`XZiq`v(esdfiqeH`Nb&`XZ>ikrNVvjNdcVXjvj,uiqtZ>tbciqY[esbcZyu-i«bfZdoe(bciqHZ>kN¦)±SjHd}j d& dfj<tZNpXbfVXZ8jHiq`Nb
ZvbcdoeHghbfikjN`gjN`Stixtbft'iq`*gjHY[ bfik`Xr}bcVXZ$(`SuY[jNYlZ>`<bYne(bfdcik£iq`vHjNkNZ>u£ik`*bcVXZ)jH8Zdoe(bfjHd'jH¤XZ < e(bfikjN`
niq`es`¡ZqqikStcZniq`St|bfZ>eNujH¤}egikdog qeHd¢&ik`SuXj(¢¦U$VXZ>`¤³jNdZ>eNgoV8jHiq`<b*js¤$iq`NbfZdfZ>tb>pbcVXZuXZ>tfgdfik,m
bfVjHedoHtZlesdfZ>Z©Z`¡gjNY[dcZ>Y[ j(bcHZyZ>uu'¤³¦[dcjNU$Y VSiqte-eH`XXjNXdcdfYnjN eHeNkgoi V
¬ Zyixut e(tZybfgouVik` eHdcj O`S¤³ujHd bcVSZ©`SgeHjNkiqikX`<dobe(bf¤³jNZ>du¢&¢&VXiqu,ixgoZ[VSt|eNbftdcZ>Zkbfiqgo`XVZ©estbc`Z>udcZ>tjªNZv¢
gjH`Stcixu,Zdfik`Srl±Sj dfikZ>dma²DZ>kqik`u,Z>tfgdfiq,bcjNdftjH `DgjHqjHd$ikYneHrHZ>t>¦
;5$45: 8 8 :, 8³ ¹ ¸ X ¸
¿Zb Z"bcVXZl¤³Zye(b dcZ[teHgZ"js¤KbfVXZngjNkjNd8jHiq`Nbot£js¤¥iq`<bcZdfZ>tbeHggjHdou,iq`XrnbcjbcVSZlqj,geH%goVSeHdfeNghbfZdcm
i ¬ esbciqjH`n{ t|biq`Nbfdcj,u gZ>u'¦ Z>ge tcZ*Z>eNgoVBiq`<(eHdcixes`<b4VeHtu,ik°8Z>dcZ>`NbYnesrN`Xi«b u,Zytp ixt£eH`
VvvZ>dcZ>«m
qiqStjNiquXZH¦OU$VXZY[jNtb$t ikbfesSkZ£Y[Zbcdfixgt$dfZxe(bcZyu[bcjnt goV©¤³Zye(b dcZtcSeHgZ>tdcZ>Ynesiq`St)bcVXZ²BeHVSesxes`XjNXixt
uXiqtbfeH`SgZ pFZyge tZ*i«b tcZ>t&bfVXZ[gj((esdfiqeH`SgZYnesbcdfi«-js¤ObfVXZ*8jHiq`<bgjHY[jN`XZ`<botes`u-bcV tbfeHªHZ>t
iq`<bcjleHggj F`<bKbfVXZu, i«°FZdfZ` gZjH¤bcVXZ>ikdYnesrN`Xi«b u,ZNp< bZyt8Z>giqeHkqlZyge tZbcVXixtY[esbcdfi«[iq`NbfZrNdfesbcZ>t
e"Y[j,u,ZjH¤`XjNiqtcZ4jH¤'bcVSZgjHY[8jH`XZ>`Nbot g,ikb&dcZ>XdcZytZ>`<bfte"gd giqeHeHtcZyghb&Z>tcZygixesqk[¤³jNd&tZygjH`ues`u
bfVXiqdfujNdfuXZdot'iq`<(eHdcixes`<bft>p¢&VXixgoV*esdfZ)gjH`StciquXZdfZ>u£bcj£8Z)Y[jHdfZK `XjNiqtcH¦%UdoeHuXi«bfikjN`X`SesqqHpybcVXZ$gj((eHdcixes`SgZ
Ynesbcdfi«Bixt£Z>tbciqY[esbcZyu
tbfe(bfiqtbcixgeHkqDj(HZ>d}bfVXZ[¢&VXjHqZ"8jHiq`<bftuXesbfeseHtcZHpFjHd8ZbbfZdj(NZd4exesdfrHZ"tcZb
jH¤'dcZ>XdfZ>tcZ`<bfesbciqHZ&8jHiq`Nbot)tfesY[XqZ>t>¦2}`XjHbcVXZ>d)iq`<bcZdfZ>tbciq`XrleHu,(es`<boesrHZ&ixt¥bcVSesb F iqt F u,ixt|bfdciq bfZ>up
tc²
j©esbfVSVSeHe(qbeH`XYnjHe(Xboixt£goVXu,Z>iqt£tbfeHeHtf`Stgj,Z[giqixestbcZ>Y[ujHbfdfjZ[bfgVXjHZlY[¢)XqjNZdfBtb4iq`u,ixbct|ZbodfesY `SgZ>jHt¤¥gbciqeHY[`BZ©8gZ"jNZ>Ylkiq Y[ikbf`SesesbcbciqZyjHuB`vbcVS-eHbc`VXdfjHZ>bctcVXVXZ>jNdqu,uXiqiq`XtrbfeH¦£`SU$gZyVXtZ p
b}e"tcik`Sr xesd$u,Z>gjHY[8jNtci«bfikjN`©js¤'bfVXZgj((esdfixes`SgZ}Yne(bcdfikesqkj(¢}t¥bc j[esXSknjN`©bcVSZgjHY[8jH`XZ>`Nbot)e
goVes`XrNZjs¤2SeHtciqtik`DjNdfuXZd$bcj©bcdoes`St¤³jHdfYbfVXZVvvZ>dcZ>kqiktjNiqu,ZZ =
S F A$ik`<bcje[V<v8ZdotSVXZdfZHpX8Z¤³jNdcZ
tiq`XrlbcVXZ YlZbcdfiqg>t¦
8 ¸<» B ¼ 8 7
4
$J$$ (
J*$ ( ^¤)¢)ZlgjH`tixu,Zd4bcVSZ"qj,ges2u,Zytcgdciq,bcjNdftXdfZ>tcZ`<bcZyuBes8j(HZNp8eH`BikYneHrHZ*ixt£dcZ>XdfZ>tcZ`<bcZyu-<DetZb4jH¤f
8jHiq`<bf>t W Y goVSeHdfeNghbfZdfi ¬ Z>uBiq`e¤³Z>e(b dfZ[tcSeNgTZ = S F A4¢&VXjNtcZnti ¬ Znu,Z>Z>`SuXtjN`
bfVXZnjHdou,Zdot Hp
jNd\DgjN`Stixu,Z>dcZyu
¤³jNdbcVSZnik`v(esdfiqeH`<bftgjNY[ bfesbciqjH`'p2es`u¢&VSZdfZ F dcZ>XdfZ>tcZ`<bft£bfVXZ²BeHVSesxes`XjNXixt
uXiqtbfeH`SgZN¦^a` bcVXixt"gjH`<bcZvb>pO iqxu,ik`SreH`ik`u,Z¤³jNdleuXe(´ boesSeNthZ W[R Y jH¤ iqYnesrHZyt*gjH`Stciqtbft"iq`
gjHY[ bfik`SrBetcZbjH¤ f ¤³Z>esb dfZnjNik`<botik` =
Ao¦ Z>eHdfgoVSik`Xr¤³jHd"es`¡ikYneHrHZ[jHdSeHdbjH¤$eH`
iqYnesrNZ ik`-bfVXZ*iq`Su,ZvZyu-ikYneHrHZuXesbf eseHtcZgjH`tixt|bot&iq` S 1F ".0*!()$( p¢&VXixgoVBgjNY[Z>t$bfjn¶S`Su-iq`DbcVSiqt
tcSeNgZ£bcVXZgkj<tZyt|b$8jHiq`Nbot$bcjlbfVXZ < Zdf©8jHiq`Nbot¦
SSUTV>W)W(X)Y
y
! ¿Zb W 8ZlbcVXZ©tcZbjH¤ ZdfD8jHiq`Nbot¦ltiqq tbcdoe(bfZ>u
ik`¶Sr dcZ [<gjH`tixu,Zdfiq`Xr©bfVXZngjHqjHd
Xu Z>tfgdfik,bfikjN`Y jH¤'bcVXZ8jHiq`<bft$js¤<ik `<bc Z>dcZyt|b$iq`Nbfdcj,u gZ>u e(b&Z < esbc iqjH`Sp< bcVXZdfZbfdciqZ(estbcdoe(bfZrHngjH`Stciqtbft
iqtf`-gjNe*dcZyNtjs¢&bciq`XVSrliqgoV¡esqrHesjHdfZ*dfikbc¤ VXY-`Sgh¦2bfikU$jN`VXZ>jHW¤¥bfVXY Zngku,j<iqttZybfeHt|b$`SgZ[jNik8`<Zbob|t¥¢bfZj*Z>bf` VXZ>&W eH`SY u < Z>¦[dcn 8HjHjHiqbc`<Zlbft&iqtesdfgZ4jHY[goV esdobfeHZ>ghu
bfZ¤³dfjHi ¬ dZ>Z>u[eNvgoV
iqYnesrNZHpvgjH`tixu,Zdfiq`XreDgjHY"Xik`e(bciqjH`js¤$bfVXZ©tcgjHdfZ>tdfZxe(bfZ>u
bcj-bcVSZ©Yne(bfgoVSZ>t = S \A4iq`vHjHqHZyu
iq`¡bcVSZiqY[eHrHZN¦-U$VSZ©ikYneHrHZ>tYlj<t|bltiqY[ikxesd*bcjDbfVXZ < Zdf¡esdfZ©goVSesdoeHgbcZdfi ¬ Z>uv
bfVXZ©8Z>tb"NjsbcZyt¦
U$VSZ*gjNYlSkZvikb|js¤ObcVSZ Zdf-ges`D8Z*Z ©giqZ`<bcq-dcZyu gZyu-veHdcdoes`XrNik`Sr"bfVXZ*iq`Su,Z,Z>t£eHggjHdou,iq`Xr
bfj[Y kbcixu,iqYlZ>`StcikjN`Sestbcd < gb dfZ>t>¦
The image database
The image query
Vectors comparison
! %# " &($ ') *%+,-./10 23*
# " &($ ') 4 56 4+*%70 23*
#" &(8 ') 4 56 4+*%70 23*
# " &($ ') 45 6 9 -:, ./10 23*
#" &(8 ') *%+ ,-./10 23*
#" &(; ') *%+ ,-./10 23*
00
#" &(< ') *%+,- ./10 23*
#%" &($ ') =7>>7 -0 23*
The query result
garden.jpg
%± ikr dcZ KU$VXZik`SuXZ,ik`Sr©es`SutZyesdogoVXiq`Xrltbcdoe(bfZrNH¦
´ goVBe©goVSesdoeHgbcZ>dci esbciqjH`g>es`-8ZZ`XdfixgoVXZ>u-vgjH`Stcixu,Zdfik`Sr©tSesbcixes'dfZxe(bfikjN`St$8Zb|¢ZZ`D8jHiq`<bft
jH¤'bcVSZtceHYlZ£iqY[eHrHZN¦%U$¬ VXixt&gxeHtftjs¤%rHZjNY[ZbcdfixgesFgjN`Stbcdoesiq`Nbot)eHdcZtcZY[i«mqjvg>esFtiq`SgZ4bfVXZesdfZ4SeNtZyu
jN`©bfVXZ4`SZiqrHVvjNdcVSj<j,unjH¤bfVXZ48jHiq`<bftbfj"Yne(bogoV'¦2§ZXdfZ>tcZ`<bik`bcVXZ£`XZ<b}tcZ>gbciqjH`©bfVXZgjH`t|bfdfeHik`<bft
Z>`Sgj `<bcZ>dcZyu©iq`qikbcZdoe(b dfZH¦
D¸ 8= ¼ ¼¼ ½ ¼ 7 >(> 8 7 y
U$VSZ"SeNtixgixu,Zye t eHkq-Z`Sgj `<bcZ>dcZyuBgjN`Stciqtbft4ik`gjN`Stixu,Z>dciq`Xregj XqZ"jH¤)sÀµjNik`<bot = S F A
eNte-jHbcZ>`NbfiqeHKYne(bogoVik¤$ik`¡bfVXZn`XZiqrHVv8jHdfVXjvj,u
jH¤ *bcVXZ>dcZ©eHdcZ[Z>`Xj rNV¡jNik`<bftY[esbfgoVXZyu
¢&ikbcV
`SZiqrH´ VvjNdftjH¤ F ¦
jNY[ZVSZ dfiqtbcixgtlSeNtZyu jN` rNZjHY[Zbcdfiqg>es&gjN`St|bfdfeHik`<bot"g>es` 8ZBeHuSu,Z>ubcj¡XdfZ>gixtcZbfVXZBte(bcixes
gjH`,¶r doe(bfikjN`Q jH¤£bfVXZ
`SZiqrHVvjNdft>¦ ^bu,Z8Z`uXtjN` bcVXZ
bcdoes`St¤³jHdfYne(bciqjH`t[Z,iqtbciq`Xr8Zb|¢ZZ>`bcVXZ
iqYnesrNZ>t%bcjYnesbfgoV'¦2U$VXZ}goVSeHdfeNghbcZ>dci esbciqjH`lesXXdfjNeNgoV*SeNtZyu*jN`nu,i«°FZdfZ`<bfiqeHXik`v(esdfixes`<bft2¢$eHtOu,Z¶S`XZyu
bfj8Zik`v(esdfiqeH`<b*bcj¡tcikY[iqkikb uXZrNdcj ¬ '¦U$VXZ>`Q¢Z`SZZ>ubcj¡u,Z¶`XZgjH`Stbcdoesiq`<bft"¢&VXixgoVbfeHªHZik`<bcj
eNggj `<bbcVXZytZu,Z>rHdfZZyt)jH¤¤³dfZZyu,jHY-¦
tcjH bciqjH`lgjH`tixt|bot%ik`[gjN`Stixu,Z>dciq`Xr}bfVXZ$XdfjH8Zdcb|£jH¤8eH`XrHqZ>t%gjN`StZ>dc(esbciqjH`8Zb|¢ZZ>`*`XZ>ikrNV<8jHdot g
ikb4t X8jNtc Z>t$bfVSe(bbcVXZdfiqrHixu,i«b|gjN`St|bfdfeHik`<b}ixt&dfZ>tcZyghbcZyu¦ ´ jHY[Z*e bcVXjNdft H<p > XdfjH8jNtcZ£bcjgjH`,m
tcixu,ZdObfVXZ4eH`XrHqZ}u,Z¶S`XZ>u©Zb|¢)Z>Z`[b|¢j`XZiqrHVv8jHdotOjs¤FbcVSZ8jHiq`Nb¥bcj*YnesbfgoV'pN¢&VXiqgoVnY tb)8Z}dcj rHVSk
Y[gjHiq`S`XtjHbfd"eH`<ikY[b}¤³8dcjHjNdcYbfeHeH`S`DgZikYniqtleHu,rHZZ¶bf`XjZ>ues`SjsZbcVSb|¢)ZdyZ>¦&Z`^a` bfVX G Z@pF8esjH`
iq`<eHb[`Xgr jH `SqeHtciqduXZgdfjNZ>`Sut|bfesdfeH`iku`<b}jHiq`XY[q¡XkjHv`Xiq`XZrjse¤}ikgbfjHt"Y[`XXZqiqZrH,Vvik8b|jHdojHt¤ ¦
?
C@DA
@BA @
E@
!#" S !%$
!"#$%&"!'())#("!'"!+*%,-/.01)$2
U$VSZ*es`XrNkZ8Zb|¢ZZ>`bcVXZ>ikd4dcZyt8Z>gbciqHZrHdoeHuXikZ>`Nbot$Y tb8ZXdfZ>tcZdfHZyu©¤³dfjHY es`-iqY[eHrHZbfjes`XjHbcVXZ>d>p
eNt$ikq t|bfdfesbcZyuiq`¶Sr dfZ,¦
G m2
Gm1
α
Gm’1
α
G m’2
%± iqr dfZ ¥¾)jH`StcZdf(e(bfikjN`js¤bcVXZeH`XrHqZ>t$8Zb|¢ZZ>``SZiqrHVvjNdft$rNdfeNu,iqZ`<bft>¦
®ZdfZbfVXZ-rHdoeHu,iqZ`<b tZyu¤³jHd"bcVSZrNZjNYlZbcdfiqg>es$gjN`St|bfdfeHik`<b*ixtlbcVSZY «bfiqtc8Z>ghbfdfeH$rHdoeHu,iqZ`<b"jH¤
À4ikm 8Z>` ¬ j &gjNY[ bcZyu u,iqdcZyghbfk¤³dfjHY bcVXZ tcSeNgZH¦D^b[ixt*eHtft Y[Z>u bcjZY[jHdfZ©dcjN tbbcj
`SjHixtZNpXtiq`SgZikb}ikY[XqiqZ>t}eHkFbfVXZgoVSes`S`XZxt$js¤bcVXZiqYnesrHZtcikY kbfes`SZj tqH¦
§ZDdcZ>viqtci«bfZ>uQik` bfVXiqttZyghbciqjH`QbcVSZD¢e¡bfjik`SuXZQeH`Su dcZbcdfikZ>HZikYnesrNZ>tlv tcik`SrjNik`<bft[jH¤
iq8`<jNbctfZ>tcdcikZyXt|qb-ZHpXgogVSjHes`SdogesZdodfeH`Xgiqbc`XZr"dfi ¬iq`-Z>u Ses¢&dcikbcbcixVg qu,eHikd)°8Z>bfdcVXZ>Z`NgobfiqVXeHjNiqgikZ£`v(jHes¤dfbfiqeHVX`<ZbfjHt>¦µdou,Z§d$Z¡¤³jNd&tceik¢ `v(esbfdfVSixe(esbD`<bftct$jHgY[jNZY[eH «bfbfZesdfbc`Siqe(jHbf`'ikNp,Z>jNtd$bcesVXdfZZ
tZ4bjs`X¤'j(¢&rHZ>VXjHZ>Y[dcZOZbfikbdcix¢$geHeHt'gY[jH`SeNu,tbcZKdoese}iqg`<jHbfY[t>¦SU$esVXdfixZyttjNZ£`u,¤³i«jN°FdZesdf`Z`<jNb$,esbckiqbcYnZdfes`S esbctiqZKHZ>jHt)¤vbcesVXdfZKZ}8Z`jHiqg`<j b m`NSbfeHZtcdfZ>Z>uungoiqV`nesbfdoVXeHghZ4bfqZikdfbciZdoe(e(bfb ik jNdf`'Z ¦
¬
´ goVentb u,©ixt$bcVXZt ,{|Zyghb&js¤%bcVSZ¤³jHqkj(¢&iq`Xr[tZyghbciqjH`¦
#
)*
!"#Q!*%$%&'
^a`QjHdou,ZdlbfjrNZb[jH,bfikYnes&iq`Su,Z,Z>t"¤³jHd[iqY[eHrHZdcZbcdfikZ>eH&esXXqixge(bfikjN`'pK¢Zbfdciq`QbcVXixtntZyghbfikjN`bcj
eH`Stc¢)Z>dKYnes`v Z>tbciqjH`St)t|bfikq`SjsbtcjHqHZyunes8j b)bcVXZ£gjN`SgdfZbfZ tcZjs¤gjHqjHdu,i«°FZdfZ`<bfiqeHSiq`<(eHdcixes`<bft
¤³jNd[ikYnesrNZYnesbfNgo VXiq`XrS¦ ´ ZZ>ik`XrbfVSe(b©e bcVXjNdftl tZ>ZY bfjiqY[XqZY[ Z`<b[bcVXZ>Y esb[u,ik°FZdfZ`<bnjHdou,ZdotpKe
¶dftb*Z,8ZdfikY[Z>`Nb[gjN`Stix tbcZ>u¡iq` tcZ>gbciqjH`\X¦ ©iq` u,ZbcZdfY[ik`Sik`Xri«¤}VSikrNVjHdou,ZdotVSeNZeDdfZ>eH¥iqYleHghb
¤³jNdgjHqjHdu,Z>tfgdfikXbciqjH`'¦ iqHZ`©bcVSesbiq`XdoeHgbcixgZbcVXZ£ikYneHrHZ4eNg < ixtikbciqjH`nSdcj,gZytctgeH`X`XjHb)8Z£eHk¢$e,t
gjH`<bcdfjHqqZ>uptZyghbciqjH`¨\S¦ ixt©u,Z>HjsbfZ>uQbcj¡bfZ>tbnbcVXZ>ikddcjN tbc`XZytct©eHrNeHik`StbnikYneHrHZDgj,u,iq`XrSp$qikªNZ-bcVXZ
gqeNtctcixges jN`XZH¦&U$VXZ>ikd4eHuXeH,bfesbciqjH`bcj©iqq Y[iq`Se(bfikjN`BgoVSes`SrHZ>t}iqt4t|b u,iqZ>u-iq`B\X¦ \X¦$±iq`SeHkqHpbcVXZ
gjH`<bcdfiq bciqjH`"js¤XbfVXZ&rHjNY[ZbcdfixgesvgjN`Stbcdoesiq`NbotjN`*`XZ>ikrNVvjNdcVXjvj,uixt2gjN`SgdfZbfZqZ(es e(bfZ>u*ik`[tZyghbfikjN`
\S¦ ¦
l¸ 7 , 8 > = ¸
U$VSZiqYnesrHZ-uXesbfeseHtcZ tcZ>u¤³jHd[Y[jNtb[jH¤}bcVSZZ,Z>dciqY[Z`<bftlixtlet StcZbnjs¤}bfVXZ
¾)jH Y*SiqegjHqjHd
iqYnesrNZ)uXesbfeseHtcZ * ¦O§Z&gjN`Stciqu,Z>dcZyuVXZ>dcZ >NH}iqYnesrNZ>tdcZ>XdcZytZ>`<bciq`Xr FH}dfikrNiqu*jH,{|ZyghbftboesªHZ>`
bf j
`Su,VXZiqdrHVSsZ©d"eHjN`XikrH`<qbfZ>t4t*js¢)¤KZ>vdciqZZ¢ `XjsgbljHdfªHdcZZyXtb"8jHiq``SuXjHik`Xdou,r©Z>bcdjbcje\HZ`SÀµt dcdfjHZbfesgbcjNiqjHdc`dfZ>g bDYnbfj e(bfygo0 VSFnik`Xu,rZ>rHdfesdfZbcZyZytt¦4¤³jH^aY[d"eHZ>eNrHgoZyVt}dfikZYnxe(eHbcrHZyZHu ¦
SSUTV>W)W(X)Y
! U$VSiqt£uXe(boesSeNtZ"u,jvZ>t4`Xjsbu,Z>eH¢&ikbcVtfgeHkZ"goVSes`XrNZ>t>¦^a`SuXZZ>uBVXZdfZbcVSZleHikY ixt`XjHbbfjZ,8ZdfikY[Z>`Nb
gjH`NY[bfikSeH¢&dcVXZixgoikbfVDt£dfjNZqikZ`<(besbf`VXgZ*Z*g¢&jHVSqjHikdqZ"goY[VSeHj,dfu,eNikgh¤³bfvZikdf`Xi r¬ e(SbciqeHjHd`bfiqg ixt}qdfeHjHd iq `<tbcb&dfikbc`Sjtcixtcg"g>eseHq`SZuDjHZd}vvbfiqdcZiq¢&`Stc8iqg*jHiqS`<b4esdogoesVSY[es`SZbfrHZZ>dot>tpX¦ ´ jNbYlbcjZ
jH¤KbcVSZ"iqYnesrHZyt tcZ>uesdfZ*XdfZ>tcZ`<bfZ>uDiq`B¶Sr dfZ"\X¦ ±SjHd4bcVXZ[Z,8ZdfikY[Z>`NbotjN`Biqk Y[ik`e(bciqjH`goVSes`SrHZ>t
jH¤%tcZ>gbciqjH`-\X¦ \XpXelSesdcbcixg qeHd}uXe(boesSeNtZ£¢&ikq'8ZgjN`Stixu,Z>dcZyu¦
%± iqr dfZ\ ´ esY[XqZ>t}js¤bfVXZ"¾)jH Y"Xiqe[gjHqjHd$jH,{|Zyghbot&uXe(boesSeNtZN¦
U$VXixtO8Z`SgoVSY[eHdcª"uXe(boesSeNtZ$¢$eHt%ik`u,Z,Z>u tciq`XrbcVXZ}®4esdfdcixt2gjNkjNdOjNik`<bftKjs¤iq`<bcZ>dcZyt|bKZ<bfdfeNghbfjHdy¦
eHgoVn8jHiq`Nb¢eNt¥goVSeHdfeNghbfZdfi ¬ Z>ul¢&i«bfVnbcVSZ£gqeNtc tOjH¤gjNkjNd)u,ik°8Z>dcZ>`<bcixesSiq`v(esdfiqeH`NbotKjH¤FZ < e(bfikjN`©*es`u
gjHY[ bfZ>uliq`h= A2esbKjHdou,Zd Np<4jHd¥\eNggjHdou,ik`SrbfjbcVXZ&Z,Z>dciqY[Z`<bft>¦%À Z&bfjbcVXZSesdcbcixg xesdKtcZb
jH¤Kaik8YnjHeHiq`NrHboZ>tKt ¢ ZtcdfZ>Z}upFZS vbfVXbfdfZ"eNghe bc[Zyu[`SZ"Z>Y d¥ iq«Ynbfi«esmatfrHgZNespNqqZ*Z>eNeHu,XiqX`XdfrjNeHbcjlgoVDe¢$uXeHestbfes`XjseHb£tcZ&ikY[ik`SXuXqZZY[nZ>js`N¤ bfZ>a u
a a2VXa4Zdf¤³ZHZ>¦e(b }dfXZ}SdcjjN,ik`<iq Y[botes¦ bcZ>}jk
rN ZjNYlZbcdfiqg>esgjN`Stbcdoesiq`Nbot¢)Z>dcZ tcZ>upXZXgZXb¤³jNd&bcVSZtc8Z>gik¶g>es'Zv8ZdfiqYl Z>`<bft$js¤bcVX ZxeHtbtcZ>ghbfikjN`'¦
¸ 8:/ 8 ¼ 7 ¸ N )½ 8:> =S( ²BjNtb)js¤bcVXZ£dcZyt «bot¥iq`©bfVXiqt$tcZ>gbciqjH`eHdcZ4XdfZ>tcZ`<bcZyu©eHt)XdfZ>gixtcikjN` dfZ>g>esqSu,ixesrHdoesYnt>¦^¤%¢)Z£gjH`tixu,Zd
gqeNtctcZ>t}js¤ Z>kZ>Y[Z`<bft ³VXZ>dc
Z 9eaneH`Su L9 a hpSbcVXZ"XdcZygixtiqjH`-¤³jNd}Z>eNgoVDikYneHrHZ Z>dc
ixt&bfVXZXdfjH8jHdcbciqjH`-jH¤2dfZbfdciqZNZ>uiqY[eHrHZyt&Z>kjN`XrHiq`Xr[bfjnbcVX
Z N ZdfgqeNtct1gXi«b£iqt4gjNYl bcZyu-jH`-<bc VSZ
¶dftb£dfZbfdciqZNZ>u
ikYnesrNZ>t>p¢&VXZdfZ ©ixt£bcVXZndfZ>g>esq%esdoesY[ZbfZd h¦[U$VXZ[rHdoesSVSt£XdcZytZ>`<b
bfVXZeHZdoesrNZ}XdfZ>giqtcikjN`©jHXbfesiq`XZyun¤³jHd&eHk8bcVSZ < Z>dciqZ>t>pvi:¦ ZH¦2¤³jNdeHk8bcVSZ£iqYnesrNZ>t)js¤'bfVXZrHdfj `Su,m:bfd bfV
uSe(bfeHSeHtcZH¦
j(¢ kZb t[gjH`StciquXZd"tcjHY[ZeHtcZyghbft"js¤&bfVXZjNik`<b[js¤}iq`NbfZdfZ>tb[goVesdoeHghbfZdfi ¬ e(bfikjN`¢&VXixgoV qjvjHª
iq`<bcZ>dcZyt|bfik`Xrlbfjl ZXesY[ik`SZH¦
J # . #/ #!#/ J 1$%!>$$(
v8ZdfiqYlZ>`<bft)ik` /G 8VeHt¥tcVXj(¢&`nbfVSe(b)bcVXZ tcZjH¤gjHqjHd)ik`X¤³jHdfY[esbciqjH`nqZ>eNuXtKbfj"e8jHiq`<b$uXZ>tfgdfik,bfikjN`
dfixgoVXZd$bfVSes` tciq`XrnrHdoe©(es Ziq`<(eHdcixes`<bft>pX Z>HZ`-ik¤OjH`XqiqY[XkZ>Y[Z`<bcZyuBe(b&¶SdotbjHdou,Zd :tZ>ZtZyghbfikjN`
X¦ N¦ h¦%^a`bcVXixt&gjN`NbfZvb>p,ikb&¢)j xu8Z`Xj(¢ iq`<bcZdfZ>tbciq`Xr"bcjngjN`Stciqu,Z>d$VXikrNVXZd$jNdfu,Z>dft)¤³jNd$gjHqjHd$8jHiq`Nb
uXeH`SZ>tfu¡gdfiqik`S,u,bfZikjN,`'Zyu¦[U$bcVXVXZZ`¡Z>¢`SZlgoVXVYneHesZldfªik Y[uSXe(bfqZeHY[SeHZtc`<ZnbfZ>vubcgVXjHZ©`SgtcjHixu,qjHZdfdik`Su,r-ik°8bcZ>VXdcZ>Z>`<Y bcixesesOb*iqbc`<VS(Z>eHtcdcZixesu,`<ikbf°8t Z> dcZ>`Nb"bfjjHdobfVXu,Ziqdfdout¦DjHdoU$u,VXZZd
SdcZygixtiqjH` (dcZygeHkFu,ixesrHdoesYnt)jH,boesiq`XZ>u-eHdcZ£XdfZ>tcZ`<bcZyuiq`¶Sr dfZS¦
~&j rHVSktcZyesªviq`XrSpO¢ZtcZZbcVe(blbcVXZDeHZ>dfeHrHZnXdfZ>giqtciqjH`(esdfiqZ>t*¤³dcjNY X¦ sDbfj ¤³jHdnesqbcVXZ
Y[Z>dcrNZ>un jNdfu,Z>dft>pHi@¦ ZH¦%bcVSesb$esbqZ>eNt|b)bcVXZ4¤³j dm@¶X¤ bcVjs¤'bfVXZ ¶SdotbiqYnesrHZytKdfZbfdciqZNZ>un8ZqjH`Xr*bcj"bcVXZ
<tcjH Y[Z>dcZ[gesxeHdctfbcixt>g ¦ xes¤d4gjHj , {|doZytcghZbftesqbcSVbfe(VXb£Z bcNVX Z"ZdfikYnlesiqYnrNZ>est4rNZ>tKZ>k¢jNZ`XdfrHZiq`XdfrnZb bf j©df`XbfZ>VXu[Z ¤³jNd Z> dcD9gNqeN¦2tc§t4esZ4`S`XuDjsbfdfiqZgbfZ>dcu©iqZNvZ>ixt uD esesqbk"¶S¤³dojHt|bd
<
!#" S !%$
!"#$%&"!'())#("!'"!+*%,-/.01)$2
y\
%± iqr dfZ OzKdfZ>giqtcikjN` dfZ>g>esq8uXiqeHrHdoesYeHg>gjNdfu,iq`Xr"bcjnu,ik°8Z>dcZ>`<b}ik`v(esdfiqeH`<bftjHdou,Zdot>¦
gjHdfdcZyt8jH`ulbcj"bcVXZtYneHkqZ>tbgoVSeH`XrHZyt¥jH¤vikZ>¢&jNik`<byp<¢&VSZdfZ>eHtKbcVXZXdfZ>giqtciqjH`nSeHdfeHYlZbcZ>du,ZygdfZ>eNtZyt
iq`vHZ>dftcZqn¢&i«bfVbcVXZ*eH`XrHqZjs¤%<iqZ¢¦)U$VXZ>tcZgjN`Stixu,Z>dfesbciqjH`St$esdfZ£`Xjsbt dfXdcixtcik`Xrntcik`gZi«b4ikq t|bfdfesbcZ>t
bfVXZ©¤ eNghbbfVSe(b"bcVXZu,ik°8Z>dcZ>`NbfiqeH¥iq`veHdcixes`<botesdfZ < eHtcikm@iq`veHdcixes`<botes`SubfVXZ`dfjH t|b*bcjBviqZ¢&8jHiq`Nb
goVes`X§¨rNikZ>bct V¡ dfZrNbceHjndfe[uDgbcZ>jdbobcesVXiqZn`df8ZjHqZiq`<(eHb>¦`SgZljs¤)bcVXZ[iq`<(eHdcixes`<bft tcZ>ue(bjNdfu,Z>deH`Su\iq`gjHY[SeHdcixtjN`Dbcj
jNdfuXZd HpXbcVXZrNdfeHXVSt&tcVXj(¢ bfVSe(bZ>Y[Xkj(viq`Xr[jHdou,Zd[tcqik rNVNbfkikY[Xdfj(HZytbcVXZdfZ>tcjN`StcZ>t¤³jHd4esqbcVXZ
viqZ¢&8jHiq`<bft>¦%±SjHd 9 XpNbcVXZ4dcZyt kbft)esdfZ 8ZbbfZdypN¢&VSiqgoV©Y[Zyes`StKbcVSesb)jHdou,Z>d)esqqj(¢}tObcj¶S`Su©eH`
eNZdoesrNZ4jH¤¥X¦ [iqY[eHrHZyt&Y[jHdfZik`BbcVXZ n¶Sdftb4iqYnesrNZ>t&dfZb dc`SZ>u¦&^b£iqtZ>tcZygixesqkdcZ>kZ>(es`<b}¤³jHdbcVXZ
¶dftbSesdcbjs¤bcVXZniqYnesrNZ>tdfZbcdfiqZHZyu hp%¢&VXikqZn8Z> gjNY[ik`XrDVesdou,k
Z>dfgZ,bfikXqZ[¤³jHd*VXikrNVXZd
viqZ¢&8jHiq`<bft>¦Kb}jHdou,Zd&\XpXbcVXZdfZ>t kbft&esdfZelXi«b}8ZbcbcZ>d}bcVes`¤³jHdtcZ>gjH`SujHdou,Zd$jN`Xk©¤³jHd&bfVXZbcVXiqdou
¶dftb"iqYnesrHZyt*dfZb df`XZ>u b[uXZ>gdfZ> eNtZ©¤³jHdlYlF jNdcZu,ik°8Z>dcZ>`Nb[8jHiq`Nbot*jH¤vikZ>¢p `<bciqbcjZygjHY[ZbcVXZ
¢jHdotb¤³jHdbfVXZntZygjN`SuBSeHdbjs¤)bcVXZ[dfZbfdciqZNZ>uBiqYnesrNZ>t ³¢&ikbcV¡e-u,i«°FZdfZ`gZ[js¤ h¦[U$VXZ>tcZ[dcZyt kbft
gkZyesdfk[tcVXj(¢ bcVSesb)bfVXZ£gjHqjHdgoVSesdoeHgbcZdfi e(bfikjN`St2SeNtZyunjH`nbfVXiqdfujHdou,Zd :es`SujH`tcZ>gjH`Su©jHdou,Zd)ik`e
qZ>tftcZd%ZvbcZ>`NbeHdcZ`XjHb2tbfeHXkZ)¤ eHgZ>u*¢&i«bfV"¬ goVSeH`XrHZytjH¤SvikZ>¢&jNik`<b>¦2U$VXixt%Y[eeHXZyesdOu,ixtceHX8jHiq`Nbfik`Sr
tciq`SgZ es`<bfi«bfikZyt}iq`St|bfZ>eNuDjs¤ ©VeHZ8ZZ`
ZY[Xqj(HZ>uDesbjHdou,Z>d4\Xp bi«bgeH`DZ"Z,Xxesiq`XZ>u-v
bfVXZ©¤³jN
kq j(¢&<iq`Xr
gjN`Stciqu,Z>dfesbciqjH`St l±%iqdftb*bfVXZiq`StbfeHXikqikb|jH¤&bcVXZu,Zdfiqesbciq HZytiq`SgdfZ>eNtZyt¢&ikbcVjNdfu,Z>d>p
eN´ ggjHdou,ik`SrDbcjbcVXZ-¢Zq«mªv`Xj(¢&`ixu,Z>e
bcVe(b©es`v¡Y[Z>eHt dfZY[Z`<bljs¤4(eHdcixe(bfikjN` esY[Xqi«¶Z>t"bcVXZ-`XjNiqtcZH¦
Z>gjN`Sup8bcVSZ*¤³jNdcY qesbciqjH`DjH¤KbcVXZliq`<(eHdcixes`<bft}¤³dcjNY Sesdcbcixes2u,ZdfiqesbciqHZyt}8Z>gjNY[Z>t£Y[jHdfZ*es`Su
Y[jHdfZ
gjHY[XqZ©¢&ikbcVjHdou, Zd tcZZ£Z < esbciqjH`- )es`SugjH`tZ N Z`<bcqnesY[Xqi«¶SZyt)bcVXZ`XjNiqtcZ4Sdcj,u gZ>u<nVSikrNV
jNdfuXZd&u,ZdfiqesbciqHZyt)Z>HZ>`Y[jHdfZH¦
U$VXZytZdfZYnesdfª,t)tcVXj qu`XjHb$8ZikrN`XjHdfZ>u'p<8Z>g>e tcZ£bcVXZ>dcZeHdcZ£Ynes`vnj<tctciqXkZ`XjNiqtcZtj dfgZ>t¥¤³jHd
qj,geH'u,Z>tfgdfikXbcjHdo
t OjN`XZ tVSj xu-gjH`tixu,Zd$¤³jNd}iq`St|boes `SgZ`XjHixtcZ£dfZxe(bfZ>ubcjniqYnesrNZeNg < ixtikbciqjH `pX`XjHixtcZ
SSUTV>W)W(X)Y
>
! Sdcj,u gZ>uvBikYneHrHZngj,u,iq`XrDes`Su8jNtftiqXqZnu,Z>tbcd ghbfikNZngjHY[XdfZ>tftcikjN`'¦"§¨ikbcVSj b¤³jNdcrNZbbfik`SrbfVSe(b
8jHiq`<bft&ZvbcdoeHghbfjHdot&t °8Z>d}¤³dfjHY uXZqjvg>esqi ¬ e(bfikjN`'pXiq`BtXikbcZ*js¤%bcVXZ¤ eNghb}bfVSe(bbcVXZ*®4esdfdcixt}gjHqjHd&jH`SZiqt
jHgoV¤¥esVXdoiqeHrHghVBbfZjNdfdfi ¬uXZ>Zud£ikv`vD(ese©dfiqrHeHjv`<j,bftu-gdfjHZY[8Z> e( bobfesZ>Xuiqqi«e(b|b£N¦4bcVXU$ZyVXtZlixtSjNdcikjN`<XboktZ>gY iq`
gjHS`<eHbfdfdceHiqk qZ @bfpSZ>bftVXbcZ"j¶Siqdf`StgbdcZyjHeHdotcu,ZZd4bcVXjHZ"`XZyik`t£t|eHboesdcZ*XiqkkZyikb|tc t
uXiqtb df8Z>uvbcVXixtiq`SeHg>g doeHgHp2tiq`SgZnbcVXZ>ikd[gjNY[ bfesbciqjH`eHdcZnSeNtZyu¡jH`¡¶Sdotb*jHdou,Zd"u,Zdfik(esbciqHZ>t
gjHdfdcZyt8jH`u,ik`Srbcjnqj,geHY[es,ikYne[e(b$bcVSZ>tcZjNik`<bft>p,vu,Z¶S`XikbciqjH`-js¤%bcVXZ®4esdfdcixt$gjNkjNdjNZ>dfesbcjNd>¦
^a`
bcVXZ[`XZ<btcZ>ghbfikjN`'pF¢)Zlqj<jNª¤ dbfVXZd£iq`NbfjbfVXZ[gjH`gZXb£jH¤)tZ>`StcikXiqqi«b|bcj`XjNiqtcZ*jH¤KbcVXZ[qj,ges
uXZ>tfgdfik,bfjHdot<gjH`tixu,Zdfiq`Xr*bfVXZ gj,u,iq`XrngeNtZN¦
4
# J1( !+J #(-#G&J(2$1( (L$ %+,1 # )$
U$VSZ}ikYneHrHZ>t tZyu"¤³jHdKbfVXZ}XdfZviqj tKZ,Z>dciqY[Z`<bft¥esdfZ&`XjsbK¤³dfZZjs¤'gj,u,iq`Xr`XjNiqtcZHp<tiq`SgZ}bcVXZ}rNdcj `Suvm
bfd bcVuXe(boesSeN tZ¢eNtlgjH`vHZ>dbfZ>u¡ ¤³dfjHY ik`<bcj
¤³jHdfY[esb>p)¢&VXiqgoVQiqtnegj,u,iq`XrY[jvuXZbfVSe(b
rNZ`XZ>dfesbcZyt*qjNtftZyt¦Q®}j(¢ZHZ>d>pO¢ZY[eNu,Z-t dfZbcj¡Y[ik`XiqY[i ¬ ZbcVXixt[`XjHixtcZv tcik`Sre¡gjNY[XdcZytctciqjH`
iq<Yn eHeskrNikZ>b|t¢&js¤ VXixgoa2VageH¦
`}`,Z©¤³jNjHd¤}b es`S`ves
bcZªvqiq`Siku`B¦S^adf`¡eNghbcbcVXixgixt*ZNpgjNjH`X`<bcZ*Zg><esby`Xp`Xikb"jHbixtdfZiqY[qjNjN`-dbobcesVX`<Z bNbcjB esgqi«jHb|`Stcixjsu,¤2ZbcdVSbfZ"VXgZjNgkqjvZ>uXgbcik`XZyur
`SjHixtZiq`bfVXZZ(eH esbciqjH`js¤%bcVXZqj,ges'gjHqjHd&u,Zytcgdciq,bcjNdft)¤³jNd&ikYnesrNZik`SuXZ,ik`Sr[eH`SudcZbcdfikZ>eH:¦
^a` y p NNjHqikjN`
YneHuXZlZ,Z>dciqY[Z`<bftjN`
bfVXZnik` Z`gZnjs¤ gj,u,iq`Xr-jH`rHdoe(eH ZniqYnesrNZ
uXZ>tfgdfik,bfjHdot*eH`SuSeHdbfiqg qeHdcqjH`qj,gesu,Z>tfgdfiq,bcjNdft* <¡jNStZ>dcviq`XrDbfVXZtbfeHXiqkikb|¡js¤u,Z>dciq(e(bciqHZytp
8jHiq`<bft¥js¤Fik`<bcZ>dcZyt|bes`Sunu,ik°FZdfZ`<bcixesXiq`v(esdfiqeH`Nbot2¤³jHd)u,i«°FZdfZ`<b)gjHY[XdfZ>tftiqjH`ldoe(bcZyt¦2®}ZZ>tbciqY[esbcZyt2¤³jHd
ZyeHgoVjH¤XbcVSZtb uXikZyu*u,Zytcgdciq,bcjNdftbcVSZ)Y[iq`XikYneHNbfVXdfZ>tcVXjHxujs¤8gjHY[XdfZ>tftcikjN`dcZ ikdfZ>u¤³jNd%gjH`Stcixu,Zdfik`Sr
bfVXZ*u,Zytcgdciq,bfjHd}t ©giqZ`<bcqdfjH t|b&bfj©gj,u,iq`Xrn`XjHixtcZH¦)U$VSZY[ik`XiqYnes N esqi«b|N Z,ZyghbfZ>uiqt ¤³jHd
¶dftbnjHdou,Zdyp 2a1¤³jHd©tcZ>gjH`SuQjHdou,Z>d[eH`Su 1¤³jHd[bcVSikdou jH`XZN¦U$VSZ>tcZdfZ>t kbftnu,j¡`XjHbnbfeHªHZbcVXZ
uXZbcZyghbfjHdu,Z>kj,g>esqi e(bciqjH`XVXZ>`XjHY[Z>`XjH`-iq`Nbfj©eHg>gj `NbypStcik`SgZbcVXZ*ik`v(esdfiqeH`<bft$VSeNZ£8ZZ>`BgjNYl bcZyu
jN`
8jHiq`<bftZvbfdfeNghbc¬ ZyuB8Z¤³jNdcZ[iqY[eHrHZ[gjNYlSdcZytctcikjN`' ¦*À4Z>eHkiq`Xr-¢&i«bfVrNdfe-(es Z[8jHiq`NbotZvbcdoeHgbc iqjH`'p
bfVXZ}Y[iq`XikYneH < esqikb|*dfZ>gjNY[YlZ>`Su,Zyu*bfjZvbfdfeNghbK8jHiq`NbotO¢&ikbcV < ikbcZtbfeHXqZ&kj,gesbciqjH`[ixt¥es8j b a©¦
&g>gjHdou,iq`XrbfjbfVXZ>tcZgjH`Stcixu,Zdoe(bfikjN`Stp&¢Z
VeHZBZv8ZdfiqYlZ>`<bcZ>u bcVXZXdfjHXqZYntu Z
bcj
guSj,e(u,bfeHik`SSrDeHtcjHZH`p%tgZjNbkbfjNik`Xdr
iqY[dcZyeHtrH8ZyZ>tgbcik`iqHu,ZZq, iq`XrS¦DU$VXdfZeHZkikb|uS
e(bfdoeHe(SbfZ>eHttcZ>bftj ¢)Z>adc©Znp rNZe`XaZ> dfeseHbcZ>`Suu ¤³dfajHY ¦-bcVXU$ZVXZrHdf j ¢ `SZdfu,Z"m:bfbfd VX Zbf`V
iq`Su,Z,Z>u tiq`Xr"bcVXZgjNkjNdu,ik°FZdfZ`<bcixes8ik`v<( esdfixes`<bft ©bfj*bfVXiqdfujHdou,Zdy¦2U$VXZ4
SdcZygixtiqjH` (dcZygeHkSg dfHZ>t
jN,bfeHik`SZ>u¤³jHd£tZygjN`SuDes`SuDbcVXiqdfuBjHdou,Zdot}esdfZXdfZ>tcZ`<bcZyu-ik`B¶Sr dfZ F©¢&i«bfVDbcVXZ"jH`XZyt}dfZxe(bfZ>ubcjbcVXZ
`Sjsb}gjNYlSdcZytctcZ>uikYnesrNZ>t&eH`SugjHY[ bfZ>u-e(b&XdfZviqj t$tcZ>gbciqjH`'¦OU$VXZg dcNZ>tdfZxe(bcZyu©bfjl¶Sdftb&jHdou,Zd
jN`XqesdfZ`Xjsb}SdcjNj<tZyuVSZdfZZyge tZ£bcVSZdcZ>Y[eHik`-NZdftiqY[ikxesd$bfj©Z>eNgoVjHbcVXZ>dft>pXiq`BtSi«bfZjs¤2bcVXZ
gjHY[XdfZ>tftiqjH`dfesbcZesSXkiqZ>u'¦
§Z"tcZZ*gkZyesdfkbcVSZ*iq` Z>`SgZ"js¤OikYneHrHZ*gjHY[XdfZ>tftiqjH`¤³jHd£tZygjN`SuDes`SubfVXiqdfuDjNdfuXZdotpX¢&VSZdfZ>eHt
bfVXZXdcZygixtiqjH`dfZYneHik`Stdfj rN VXk£ixu,Z`<bcixgeH<esb¶dftbjNdfu,Z>d¢&VSesbcZ>HZdbcVXZdoe(bcZesXSkiqZ>u¦%U$VXZ>tcZdcZyt kbft
eHdcZ&iq`eHrHdfZZY[Z>`Nb)¢&i«bfVnbcVXZ£gjN`Sg tcikjN`StOjs¤ NNjHqiqjH`©gjN`SgZ>dc`Sik`XrbfVXZ4tcZ`tiqXiqkikb|lbcj`XjNiqtcZeH`Sun8jHiq`Nb
uXZqjvg>esqi ¬ e(bfikjN`js¤2VXiqrHVjHdou,Zdot$u,ik°8Z>dcZ>`NbfiqeH < es`<bcikbciqZ>t>¦
±%iqr dfZ Gr<e(bcVSZdot}bfVXZ[XdcZygixtiqjH` dfZ>geHk%u,ixesrHdoesYnt4jH,boesiq`XZ>uB¤³jHdjHdou,Z>dft Hpes`u
\e(¤ bcZ>dbcVXZ
gj,u,iq`XrªNZZ>Xik`Sre eHkikb|Djs¤ a¦U$VXixt£eNZdoesrNZgjHY[XdfZ>tftcikjN`DdfesbcZ*ixt£`Xjsb `XdfZ>eHkixtbcixgiq`
SdfeNghbcixgZ¢&VXZ>dcZiqYnesrHZytY[<e ZgjHY[XdfZ>tftZyutcZHZ>dfeH8bciqYlZyt¦
tcZ>gjHU$`SVXu-ZjNg df uXdcZNd}Z>Z>t)`XjHdc,ixgoboV-esiq`XbcVSZ>u©Z"gobcVSdoeHeHu dfeNghgbcZ4Z>bcdcVSi ¬ esesb$bciqiqjH``XgdfqeNZ>ghesbfdfiqqg>HespFtcgiq`SeHgtcZ>Z"t>Y[pvi«esb&bfixgotVXikiqY[`Xr©8jNdfZ>tftt iq XkqbfZtbfj[Zyge jHnY[dcYZ¢bfjHVSdoe(tcb Z bctcVSik`XeH`r
!#" S !%$
!"#$%&"!'())#("!'"!+*%,-/.01)$2
4dou,ZdotHp
4dfuXZdot Np Xp \
±iqr dcZ F O^a` Z`gZjs¤ gj,u,iq`Xr[jH`ikYnesrNZik`SuXZ,ik`Sr t iq`Xr[bcVSZgjHqjHd$iq`veHdcixes`<bot¦
SSUTV>W)W(X)Y
F
9G
! ±%iqr dfZG z¥dcZygixtiqjH` (dcZygeHkuXiqeHrHdoesYjH,boesiq`XZ>uDes¤ bcZde gjHY[XdfZ>tftcikjN`ªNZZ>Xik`Sre < eHkikb|jH¤
a¦
tiq`XrDjH`SkjHdou,Zd [¤³jNdikY[8jHdcbfeH`NbviqZ¢&8jHiq`<bft>¦ 4`¡bcVXZnjHbcVXZ>dVSeH`Sup%jH`XZ©g>es`¡dcZyeHtcjH`SeHXqBtce
bf VSe(b&bfVXiqdfujHdou,Zd}goVesdoeHghbfZdfi ¬ e(bfikjN`niqt$bfj[ZXdfjNtfgdfiqZyu©¤³jNd$bcVXZgqeNtctjs¤2iqY[eHrHZyt tZyu¦
±SdcjNY bfVXZ>tcZgjN`Stciqu,Z>dfesbciqjH`St>pH¢ZtcVXj qu[8ZgeHdcZ¤ gjH`SgZdf`Xiq`XrbcVXZ tcZ}js¤VXiqrHVnjNdfu,Z>dftKik`v(esdfi«m
eH`<bft>pX¢&VXixgoVSdcj,u gZu,iqtfesSjNik`<bciq`XrndfZ>t kbft&eHt}dcZ>rNes douXt)bcVSZ` Y*8Zd}jH¤%iq`veHdcixes`<bot$ik`vHjNkNZ>u¦Kb
bfVXixtKt|boesrNZ&js¤8bcVXZtb u,HpNj dKjNXiq`XikjN`[iqt2bfVSe(bypH¢&VXZ>`[bcVXZikYnesrNZ&eHg < ixtci«bfikjN`[g>es`X`SjsbOZ4gjH`<bfdcjNkqZ>up
ikb4ixt}dfZ>eNtjN`SesSkZbfjgjN`Stixu,Z>diq`<(eHdcixes`<bft DbcjtZygjN`Su-jHdou,ZdjH`XqH¦U$VSZbcVXiqdouDjHdou,Zd4goVSesdoeHgbcZdfikm
¬VSe(ikrNbfikV jN`< tceHVXkj ikb| ©quiqY[`XeHjsrHb&Zy8t&Zu,Xi«°FdfjNZdftfiqg`Xdfrlik8¤³Z>dcujNp,Yiq`SHu,Z>Z>dcZ>utcikYnb$esYnqeHªHvZ>ikZ>t&¢&tcZ`jNikt`<Z£bf¤³t>jHp,d&qikªNZesdctbcbcixZ>g dc Z>xjNesd&tfgesjNSXXiqg£kixgtfese(bcbciqZ>jHkq`SikbctZiq`vikYnHjHeHqrHvZ>ik`St>¦r
,#%& ##/ #%$J(2$) bDtcZ>ghbfikjN` ,¦ H¦ \Xp}¢Z
SdcZytZ>`NbfZ>ub|¢j¢$e,tn¤³jHdrNeHik`Sik`Xr ik`v(esdfiqeH`SgZBbcj ikq Yliq`SesbciqjH` goVSeH`XrHZytp
eHtcZ>u¨¤³jNdbfVXZ¶Sdot|b-jH` bcVXZ¡`XjNdcYnesqi ¬ e(bfikjN` js¤*bcVXZ¡iq`<(eHdcixes`<bft>peH`Su jN` bfVX Z`SjHdfY[eHki ¬ esbciqjH` jH¤
bfVXZ-ikYneHrHZ¤³jHdlbcVXZDtcZ>gjH`Su jH`XZN¦Q&ggjHdou,iq`XrBbfj
bfVXZDgjH`g tiqjH`t"jH¤bfVXZ-XdcZ>vikj t"tcZ>gbciqjH`'p¥bcVXZ
goVesdoeHghbfZdfi e(bfikjN`StbcVSesb£¢Z"eHdcZ*rHjHiq`XrbcjZ,Z>dciqY[Z`<b¤³jNdbfVXZlgjHqjHd£gjH`t|boes`SgXdfjHSkZ>Y eHdcZ*bcVXZ
jN`XZ>t}ik`vHjNk¬viq`Xr[¶Sdot|b£es`SuBtcZ>gjH`SujNdfu,Z>dft>¦&U$VXZbfVXikdouDjNdfu,Z>d}iq`<(eHdcixes`<bft$¢ZdfZXdfj(HZyubcj©8Z*`XjNiqtcHp
eH`SubcVXixt£u,iqtfeHuXeH`<bfesrNZ¢)j qu8Z"u,doesYnesbcixgesqqeHg>gZ`<b e(bfZ>uvY[ikviq`Xr[bfVXZYbcjZqikY[iq`Se(bfZbcVXZ
esdoesY[ZbfZdot)jH¤bfVXZikq Y[ik`Ses bciqjH`-Y[j,u,Z@¦
!#" S !%$
H
!"#$%&"!'())#("!'"!+*%,-/.01)$2
§ZgjH`StciquXZd¤³jNdbcVSiqt*Z,Z>dciqY[Z`<b"eH`ikYnesrNZ©rHdfj `Suvm@bcd bcVuXesbfeseHtcZnjs¤s-bfdcixu,iqY[Z`StcikjN`Ses
jN,{|Z>gbftdcZ>XdcZytZ>`<bcZ>u `u,Zd *u,ik°FZdfZ`<biqk Y[ik`es`<bft£ es`SuDtcjH Y[Z*tcYnesqviqZ¢&8jHiq`Nb£goVSes`XrNZ>t y¦}}`
ZXesY[XqZ£ixt$XdfZ>tcZ`<bcZyuiq`¶Sr dcZHv¦
± iqr dcZH 4`SZ£jH¤bfVXZ\HÀjN,{|Z>gbft `u,Zd}tcjHY[Zikq Y[ik`SesbciqjH`DgoVSeH`XrHZyt¦
±Sj d&iq`Su,ZvZyt&VSeNZ48ZZ>`rNZ`XZ>dfesbcZyun¤³jHd$bfVXixt}uXe(boeHtcZbypXgjH`tixu,Zdfiq`XrleNggjHdou,ik`Sr*bfj©geHtcZ
H¦&U$VXZ "¶Sdot|b&jHdou,Z>d}gjHqjHd$iq`veHdcixes`<botuXikdfZ>gbcqgjNYl bcZyujN`bfVXZiqY[eHrHZyt g
,¦&U$VXZ ¶dftb¥jHdou,Z>d¥gjNkjNdOik`v(esdfiqeH`<bftKgjHY[ bfZ>u[jH`niqYnesrNZ>tOqj,gesqq*`XjNdcYnesqi ¬ Z>u'pNeHg>gjNdfu,iq`Xr£bcj
bcVXZbfZ>goVX`Si < ZXdfjH8jNtcZ>uik` H "`XjHdfYnesqi ¬ e(bciqjH` g
\X¦&U$VXZ B`XjNdcYnesqi ¬ Z>utcZ>gjH`SujNdfu,Z>d©iq`<(eHdcixes`<bftu,ikdfZ>gbcq gjHY[ bfZ>u¨jN`bcVXZikYneHrHZ>t `XjHdfYnesqi ¬ e(bfikjN` g
S¦&U$VX
Z `SjHdfY[eHki ¬ Zyu[tZygjH`u*jNdfu,Z>dOik`v(esdfixes`<bftOgjHY[ bfZ>u[jH`lbfVXZ}iqY[eHrHZyt2kj,geHkq*`SjHdfY[eHki ¬ Zyu
©`SjHdfY[eHki ¬ esbciqjH` ¦
U$VXZlXdfZ>giqtcikjN` dfZ>g>esqu,ixesrNdfeHY[tjH,boesiq`XZ>uB¤³jHd4bcVXZytZliq`Su,Z,Zyt4eHdcZ"XdcZytZ>`<bcZ>uBik`
¶Sr dfZ S¦§Z
jNStcZdfHZbfVSe(bbcVSZlSdcZygixtiqjH`
uXZ>gdfZ>eNtZyt}doesXixu,qD¢&VXZ`
bcVXZ[SeNtixg"ik`v(esdfiqeH`<bft£esdfZ"esSXkiqZ> uu,iqdcZyghbcq
jN`iqYnesrNZ>t>¦%kbfVXZ`XjHdfYnesqi ¬ e(bfikjN`esSXdcj<eHgoVXZyt¥iqY[Xdfj(HZ}bfVXZdfZbcdfiqZ(esFXdfj,gZ>tft`XjsboesXqHp, b&bcVXZ
8Z>tb}dfZ>t «bot&esdfZ4jN,bfeHik`SZ>u¤³jHd$bfVXZ ©`XjHdfYnesqi ¬ e(bfikjN`'¦
§¨VXZ>dcZyeHtbfVXZgjH`<bfdciq bfikjN`jH¤%tcZ>gjN`SujHdou,Zd$iq`<(eHdcixes`<bft$u,ixu`XjsbeHXZyesd$jHvviqj t$e(b&XdfZviqj t
trNcZ>ZgbObce}iqjH8`SjHtiq\X`<¦b2¥goesVS`SeHudfeN\Sgh¦ bfXZpdfbfi VXe(Z>bctc iqZ¥jHx`eHtdfbjHdfZ>t t| b%kbfbctj£tcikVXq j(¢Y[bcik`SVSesesbcb%iqjHtcZ>`"gjHeH`Sdcu£ixe(jHbfdoiku,jN`SZ>dt>¦tVSU$j VX ZxuikYnesZrNgZ¥jN`Sqj,tgixu,esZ>vdc`XZyjNu4dcYniq`eHjNkidfu,esZ>bcdiqjHbc`j
*gkZyesdfkndfZ>u gZ>t)bfVX¬ Zikq Yliq`Ses bciqjH`-u,i«°F ZdfZ`gZ>t>p, b}ikb}tZ>ZYntbcj[iq`<bcdfjvu gZtjNY[Z£`SjHixtZ£¬ ¢&VXixgoV
g>es`X`Sjsb&ZZ>kiqY[ik`e(bcZyuZHZ>`ik¤%bcVXZiq`veHdcixes`<bot)`SjHdfY[eHki ¬ esbciqjH`iqt&eNuXu,Z>u ¦
+ # *$]/1#" #$)(2 *$%( #/ $J# ^¤f &iqtKbcVXZ4` Y*8Zdjs¤jNik`<botKjs¤bfVXZiqYnesrNZ < Zdf"eH`SuZfbcVXZ4` Y*8Zdjs¤8jHiq`NbotKiq`nbcVSZ4uXesbfeseHtcZ
iq`Su,ZpbfVXZ"eHkrNjHdfi«bfVXYjs¤K`XZyesdfZ>tb4`XZ>ikrNV<8jHd£tZyesdogoV-VSeHt£egjHY[XqZ,i«b|iq` >=Pf fQAo¦£§¨VXZ`
bcVXZ
`SZiqrHVvjNdcVSj<j,ungjH`Stbcdoesiq`<bft)XdcZytZ>`<bcZ>ue(btcZ>gbciqjH`-,¦ H¦ *esdfZZ>YlSkj(NZ>upNbcVXixt$gjNYlSkZvikb|niq`SgdfZ>eNtZyt
`SjsbfeHXqH¦¿'ZGb f BZlbcVSZleNZdoesrHZ*` Y*8Zd£js¤¥`XZ>ikrNVvjNdft4Z>dsÀµZvbcdoeHgbcZyuB8jHiq`Nby¦"¾)jH`Stcixu,Zdfik`Sr
¤³jNdZ,eHY[XkZ
bcVXZes`Xr xesdgjH`Stbcdoesiq `<b©jH` rNdfeNu,iqZ`<bft>p&¢&VXixgoV VSeHtrHjHbkj(¢ZdgjNYl bfesbciqjH` gj<t|b
gjHY[SeHdciq`XrnbfjjHbcVXZ>d£eHXj<eHgoVXZytp8bfVSe(bgjNYlSkZvikb|-ZygjNYlZyt N eHu,doe(bfiqg*<D8Ziq`XrY kbciqXqikZyuBv
f F ¦
)T
)T
)T
T
! "!$#&%('*),+$ +.-0/21 %3$#4 &/2%56478:96%:!$384;4),% $<>="),),% @?A-B%#;4%#/DC6E0),:% @FG# #H $) 'D #&) 4/DCAHIE$JC
704&4!LK MM(NNNO 1 (O &53PO 1QDM*R 1 %<,%3$#M;+G;4DM*O
SSUTV>W)W(X)Y
! ±%ikr dfZ 2zKdcZygixtiqjH` dfZ>geHku,ixesrNdfeHYnt)eNggjNdfuXik`Xr"bcjniqq Y[iq`Se(bfikjN`goVes`XrNZ>t`XjHdfYnesqi ¬ e(bfikjN`'¦
^a`¡bfVXiqt"gjN`NbfZvb>p%jH`SZ©ges`eNtª
i«¤&bfVXiqt"eHuXuXi«bfikjN`SesKiq`,¤³jNdcYne(bfikjN`¡iqtdfZ>eHkq
ZytctcZ`<bfiqeHO¤³jHdiqYnesrNZ
iq`Su,Z,ik`Xr}eH`SudfZbcdfiqZ(esHeHXXqiqg>e(bfikjN`St¦Uj}rNZbeH`es`Stc¢)Z>d>p>¢)Z¥dcZm@iq`Su,ZvZyu4bcVXZK8Z`goVXYnesdfª4uXesbfeseHtcZ
vgjH`tixu,Zdfiq`Xrl¶Sdftb}jHdou,Z>d}ik`v(esdfixes`<bft&eH`Su-eHuXu,iq`Xrn`XZ>ikrNVvjNdcVXjvj,u-gjN`St|bfdfeHik`<bot¦¥U$VSZgjH`t|bfdfeHik`<bft
bf VXtZZyu8jH¢iqZ`Ndfb}Z©Sbc VSt$ZikSbfteNttixSgesgbcjHixes`t|dfbfZdfxeHe(ikbf`<ikb*jN`SjNt$`vbc VSZ tc` ik`X rlY"bfVXZ>ZdlesjH`X¤r 8 jHxesiq`Nd&bogtljN`SY[t|esbfbfdfgoeHVXik`<Zyb&ujHiq``rHbfdoVXeHZuXik`SZ>Z`NiqborHtVv¦2§jNdcZVSj<u,j,j[u`XjsjHb ¤
SdcZytZ>`Nb}iq`-bcVSiqtSes8Zd&bfVXZXdfZ>giqtciqjH` (dcZygesqu,ixesrHdoesY#jH,boesiq`XZ>u-8Z>g>e tcZi«b4iqtdcj rHVXqtcikY[iqqeHd&bcj
bfVXZ£jH`XZ£jH,boesiq`XZ>u¢&i«bfVSVXjsbfjHY[Zbfdcixg4gjH`Stbcdoesiq`<bft¥jH`XqH¦ d$Z,Xxes`e( bciqjH`©¤³jHdbcVXixt&u,ixtceHX8jHiq`Nbfik`Sr
dfZ>t kb}iqt&¶Sdftb&bcVe(b}bfVXZZ>`SgoVXYnesdfªuSe(bfeHSeHtcZiqt}`Xjsb}¢Zqt i«bfZ>u¤³jNd}ZY[XVSeNti ¬ iq`XrlbcVSZdcZ>kZ>(es`SgZ
jH¤ObcVXZl`XZ>ikrNV<8jHdfVXjvj,uDgjN`NbfdfeHik`<botp8ik`tjH¤ esd4eNt}bfVXZ[tZbft4js¤¥8jHiq`<bft4rHqjHSeHkqVeHZixu,Z`<bfiqg>esOte(bcixes
uXiqtbcdfik bciqjH` ik` Z>eHgoV ikYnesrNZHpeH`Su tcZ>gjH`Su¨bcVSesbbfVXZ¡` Y*8Zdjs¤*8jHiq`<bftZ>d-ikYnesrNZ a u,jvZ>t
`Sjsbnesqk j(¢ bfj ikxuQdcixgoV Z>`Xj rNV 8jHiq`<bl`XZ>ikrNVvjNdcVXjvj,uXt> ¦®}j(¢ZNZdl¢)Z-geH`QgjN`Sg u,Z bcVe(b[bcVXZ
SVXjsbfjHY[Zbfdcixg£ik`,¤³jNdcYnesbciqjH`iqt&gkZyesdfk©Y[jNdcZdfZqZ(es`<b>¦ Z>jHY[ZbfdcixggjH`t|bfdfeHik`<bftYneeHkqj(¢ bfjldoesixtcZ
eHY*Xiqr i«bfikZyt¥iq`©SeHdbfiqg qeHdgjH`,¶r doe(bfikjN`StOjs¤jNik`<bft>pN¤³jHdZXesY[XqZ¤³jNd)iq`St xe(bcZyun8jHiq`Nbot¥jNd)8jHiq`<bft
r<e(bfVXZdf Z>uliq`eSeHdb¥jH¤ bcVXZ4ikYneHrHZH¦2 Uj*gjN`,¶SdfY bfVXiqteHtft Y[,bciqjH`'p<es`©Z,Z>dciqZ`SgZ}¢$eHtKu,jN`XZ}jN`nbcVXZ
esdcbcixg xesd&geNtZjH¤jHX{|Z>ghb&dfZbfdciqZ(es'eH`Suiqt}uXZ>tfgdfik8Z>uZ>kj(¢ §Z"gjH`StciquXZdfZ>u-iqY[eHrHZyt}js¤ FHntv`<bcVSZbcixg*\NÀ jN,{|Z>gbft>p¢&ikbcVSj b£SeHgoªvrHdfj `Su-es`Su-¢&VXixgoV
tcVXj(¢
bfVXZU$jHVXXZD{|Z>ghtcboZtb `Stcu,Z>uZ>d&¤³YnjHd[es`vj ©d[vikZZ>v¢&8ZjNdfiqikYl`<boZ>t `<gbfXtltcjHY[Z>kjNZ`Xjsr¤%bcbcVSjZYeg>eHesdcY[ZZXdodfeBZ>tcdf Zjs`<bobfe(Z>bfuikjNes`Qb&es¶Sdfr j dc`SZuX¦eHZdcbcixgeH&e(,iqt
eHtftiq`XrDbfVXdcj rHV¡bfVXZjN, {|Z>gbleH`Su¢&ikbcV HBes`XrNkZyt bfj a ¦
§Zgj xu¡`X jsb tcZ©bcVSZuXesbfeNtZb
!
T T
T
!$#&%('*),+$ +@-0/ 1 %3$#4 &/@%5@),1 7G <$O
##6#&%(N H $) 'D #) 4/DC>#&%('*),+$ $1 C
S ! CBHIE$ O
!#" S !%$
y
!"#$%&"!'())#("!'"!+*%,-/.01)$2
%± ikr dfZ ´ StcZb}jH¤bfVXZ\HÀ jN,{|Z>gbft tcZ>u¤³jHd$bfVXZe bcjHYnesbcixg4Z>(es e(bfikjN`'¦
* js¤8bcVSZ4¾)jH Y*Xixe }`XiqHZ>dftcikb|HpHeNt2¤³jHdOXdfZviqj t2Z,Z>dciqY[Z`<bft>ps8Z>ge tcZ&i«bK¢$eHt2`XjHbKj<tctciqXkZ
bfj[ik`St xe(bfZbcVXZjN,{| Z>gbft¤³dfjHYSeNgoªvrHdfj `Su©XdcjNZ>dcqH ¦
U$VXZniqYnesrNZljH¤)ZyeHgoVjs¤bcVXZnjN,{|Z>gbft tcZ>u¢&VXixgoVgjHdfdcZyt8jH`uXt4bcjDe¶X,Z>ujNik`<bjH¤viqZ¢ ¢$eHt
t 8Zdfj<tZyujH`bcVXZ*jH`XZyt&js¤2bcVSZrHZ>`XZdfiqg uXesbfeHSeHtcZ tcZ>u-e(bSdcZ><iqj t&tZyghbciqjH`¦ je(bcbcZ`<bfikjN`¢$eHt
esixulbcjbfVXZiqYnesrHZytKtci ¬ ZHpvtjbfVSe(b$tjNYlZjH,{|ZyghbftKY[elVSeNZ&Z>Z`©iq`StcZdcbcZ>u[esdcbcixesqkN¦§Z}jHXbfesiq`XZyu
euXesbfeseHtcZjs¤FHHikYnesrNZ>t4¢&i«bfV FH©jH¤KbcVXZ>Y1gjN`<bfesiq`Xiq`Xr©bfVXZn\HÀµjHX{|Z>ghbot4tcZZ>` `u,Zdet8Z>gi«¶g
viqZ¢&8jHiq`<b>¦OU$VXZiqYnesrNZ>tOdfZxe(bfZ>u[bfjbcVXZ£jsbfVXZd)vikZ>¢&jNik`<bft¥¢)Z>dcZ`Xjsbik`Sg u,Z>uniq`© bfVXZ4uSe(bfeNtZb)es`u
¢ZdfZ£ik`SuXZ,Z>u-tcZSeHdfesbcZqH¦
U$VXZiq`Su,Z,ik`XrnSdcj,gZytct$Sdcj,u gZ>ues8j b H\NHH*jNik`<bot&js¤2ik`<bfZdfZ>tb&goVesdoeHghbfZdfi Z>u tiq`Xrl¶Sdot|b
jNtbcdfZ>uXDZd&bcVSgjNZ`
kjNd}gjHu,`Si«°FtciqZtdfbcZZy`<u-bfiqikeH`tik`vZyes(doesgodfVXiqeHiq`X`< r[bft$ik`
X bcVXt&ixt4`X Z>uSikrNe(VvbfeHSjNeHdctcVXZjvj,bcVSuZ"giqjHYn`t|esbfrHdfZyeHt}ik`<gbfjNt>`<¦ObfU$esiqVX`XZiq`Xe rn bfbcVXjHYnZ"es\N¬ bcÀ ixgjNZ,({|esZ> g bfe(t>bfpikvjN`
gjH`Stcixu,Zdfik`SrleNt N ZdfikZyteHk'bcVXZviqZ¢&8jHiq`Nbot&e(esiqqeHXkZ4¤³jHd$bfVXZ>tcZjHX{|Z>ghbot¦
^a`¶Sr dcZ >SpN¢Z4SdcZytZ>`NbbcVSZ£doe(bfikj"js¤¶Sdftb$j<tikbciqHZ£dcZbcdfikZ>(es8dcZyt kbft)¤³jNd)bfVX
Z ea*jH,{|Zyghbft$tcZZ>`
` Su,Zd "u, ik°8Z>dcZ>`<b$viqZ¢&8jHiq`<bft>pNbfVSe(b&dfZXdfZ>tcZ`<bot ea N ZdfikZytesb$eHk@¦OU$ VXZdcZbcdfikZ>(esF¢eNt$u,jH`XZ4¶Sdot|b
jN`Xq"vlZ,XqjHikbciq`XrbcVSZXVXjHbcjNYlZbcdfiqg}ik`,¤³jNdcYnesbciqjH`©gjN`<bfesiq`XZyu[ik`nbfVXZ4gjHqjHdKiq`v(esdfiqeH`NbotKes`u©tZygjN`Su
veNuXu,iq`Xr[`XZiqrHVv8jHdfVXjvj,ugjN`Stbcdoesiq`NbotSeHtcZ>ujH`bcVSZes`XrNkZ£Zb|¢)Z>Z`-rHdoeHuXikZ>`Nbot¦
U$VXZnrNdfeHXVStjN,bfeHik`XZyu¡esdfZ"¤ `SghbfikjN`jH¤)bfVXZ©dfjsboe(bciqjH`¡es`SrHqZ"bfdfeNu gik`XrbfVXZndcZ>qesbciqHZ[8jNtci«bfikjN`
8Zb|¢ZZ>`-bcVXZ"jH,{|Zyghb4t 8ZdfikY[8jN tcZ>u-iq`-bcVXZluXe(boesSeNtZeH`SubcVSZ"tcZ>esdogoVX ZyujN,{|Z>gb>¦}U$VXZ ¬ Zdfj©es`SrHqZ
bfdfeNu gZ>t&enu,ik°8Z>dcZ>`SgZ*Zb|¢)Z>Z`bcVXZ*SeHgoªvrHdfj `Su©jH¤%bfVXZgjNY[SesdfZ>ujHX{|Z>ghbot$jH`XqH¦§Z`XjsbfiqgZbcVXZ
8jNtcikbciqHZ-ikY[SeNghbnjs¤4bcVXZ tZ-js¤£bcVSZD`XZiqrHVv8jHdfVXjvjvuQgjN`St|bfdfeHik`<bot"jN` bfVXZ-dcZbcdfikZ>(es@¦U$VSZ>tcZjN`XZ>t
eHkqj(¢QbcjboesªHZik`<bcj"eHggj `<bKbfVXZ}rNkjNSes8tSesbcixesSuXiqtbcdfik bciqjH`©jH¤FbcVXZ Zdf*8jHiq`Nbot¥iq`[bcVSZdfZbcdfiqZHZyu
iqYnesrNZ>t>pXik`BeNuXu,ikbciqjH`D¢&ikbc VDbfVXZXVSjsbcjNY[ZbcdfixgtiqY[ikxesdfi«b| ik`X¤³jHdfY[esbciqjH`'N¦ ^b4ixtgkZyesd&bfVSe(bbcVXZ8jHiq`<bft
jH¢&¤Vbfe(VXb[Z*bct VX Z-,mjNik`XYnkeHrHSZ VX<js bfZjHdfY[ZY bfdc ixg-t|b4gjH`Zt|¤³bfj df eH`Sik`<ubftldfZu,xe(j¡bciq`XHjHZ>b[kr `XZ>eseHdod$es`<bcbfj©ZZZyeHesgob©Vesjsqbf:VX¦ Zd}¿'iqZ`-b bcVSt[Z`SXjsdfbcj(Z¢}¶StZy`uesqiqkYnesbfrHVSZye(tb p
bfVXixt[ikY[Xdfj(HZ>YlZ>`<b"ixt[dcZ>qesbciqHZq¡¢)ZyesªeNggjNdfuXik`Xr
bcj bcVSZ-gjHY[XqZ,ikb|ikY[Xq ikZyu <¡bfVXixtngxeHtft"jH¤
gjH`Stbcdoesiq`<bft tcZZgjH`StciquXZdoe(bciqjH`t)jH¤2tcZ>gbciqjH`-\X¦ ¦
3 !)!
U$VSZ df8jNtcZ}js¤bfVXiqtSeHZ>d¥¢$eHt¥bcjlt|b u,lbcVXZ4Z>VSevikjNd¥jH¤bcVXZu,ik°8Z>dcZ>`NbikY[XqZY[Z>`Nboe(bfikjN`St¥jH¤bcVXZ
gjHqjHd8jHiq`<bftjH¤&ik`<bcZ>dcZyt|b*eNtdfZr<esdouXt£XdfeNghbfiqg>es¥g>eHtcZ>tqikªNZgoVSeH`XrHZytjs¤&vikZ>¢&jNik`<b>p%iqY[eHrHZ©gjvuXik`Xr
`SjHixtZ*eH`SuDiqk Y[iq`Se(bfikjN`
goVSes`SrHZ>t>¦}§ZbfdciqZ>u-bfjtb uXbfVXZldcZ>kZ>eH`SgZ*js¤ObcVSZ*(esdfikj t}esdoesY[ZbfZdot
eNggjHdou,ik`SrnbcjbcVXZytZ[gjN`,¶Sr dfesbciqjH`St>¦ ,Z>dciqY[Z`<bftjN`BZ>`SgoVXYnesdfªBuXesbfeseHtcZ>t}qZ>eNu,Z>uBbcj-tZ>HZ>dfeH
jNStcZdfesbciqjH`St>¦±%iqdftb>p(bfVXZ&HZ> dcVSikrNV[tcZ`tiqXiqkikb|bcj`XjNiqtcZ$js¤bcVXZ$bfVXikdou"jHdou,ZdOu,ik°8Z>dcZ>`<bcixes,iq`<(eHdcixes`<bft
¢$eHtOgjH`,¶dcY[Z>ule(b¥tcZ>gbciqjH`St¥\X¦ $eH`Su[\X¦ 4<lgjN`Stixu,Z>dciq`Xr£<iqZ¢&8jHiq`<b¥goVSes`SrHZ>tOeH`Su"bcVXZ DgjvuXik`Xr
SSUTV>W)W(X)Y
H
! %± ikr dfZ y O~&Z>t kbft&jH¤%jN,{|Z>gbmSeHtcZ>udcZbcdfikZ>(esF¢&i«bfV ¢&ikbcVSj b}`XZ>ikrNVvjNdcVXjvj,ugjH`t|bfdfeHik`<bft>¦
¤³jNdcYnesb>¦2U$VXZ tZ£js¤'bfVXixt)NZdf[XdcZygixtZ£tZbjH¤iq`<(eHdcixes`<bft¥Xdfj(HZ>u[dfZqZ(eH`Nb$jH`Sk[iq`SeHdbfiqg qeHdgjH`,m
uXi«bfikjN`St}iq`vHjHqvik`SrnikYnesrNZ>tjs¤OVXiqrHV eHkikb|eH`SuDu,ik°8Z>dciq`Xrn¤³dfjHY tcYnesqvikZ>¢&jNik`<bot¦&^b£¢eNttcVXj(¢&`
bfjvj"bfVSe(b}tcZ>gjH`SujHdou,Zd$YnesrN`Xi«b u,Zy<t& tqikrNV<bcqnXdcj,u gZZbbfZd&dfZ>t «botbcVSeH`bfVXZSeHtcixg£uXZ>tfgdfik,bfikjN`
iqY[`vHjNjNdcZ©kveNiq`Xu,r©Z jH`SeskbcZn¶SbfdoVSt|esb£`¡jHdobfu,VXZZd4jHjHbc`XVXZyZ>tdf¦ t* ¢& VXb4Z`bfVXgZ"jHtc`SZ>tcgiqjHuX`SZdfuBik`Xik`<rDbcZ>iqqdc Zyt|Y[bfikiq`S`Sre(bfjHikjN`tZ>dcgo(VSe(esbf`SikjNrH`DZ>t>iq¦-t^abc`SVu,e(Z>bZ>bfuVXZiq`BteHZyXgh8bfZ>ikjNes` d
\S¦ \SpNegjHY[<S eHdcixtjN`"8Zb|¢ZZ>`nikYneHrHZeH`Su[ik`v(esdfixes`<bftO`SjHdfY[ eHki ¬ esbciqjH`St2¢$eHt¥u,jH`XZN¦%U$VSiqttVSj(¢)Zyu*bfVSe(b
Y[ik,ik`XrbcVXZliq`<(eHdcixes`<bft4esqkj(¢ bfj`XjHbfeHXk-dfZ>u gZbfVXZlZ°FZ>ghbotjH¤¥iqk Y[ik`e(bciqjH`goVSes`XrNZ>t4jH`BiqYnesrNZ
dfZbfdciqZ(eH:¦K¾)jH`StcZ < Z>`<bcqHpNbcVXixt$gjH`g tiqjH`niqY[j<tZytKbfVXZgoVXjHixgZ}jH¤iq`<(eHdcixes`<bft nbfjltcZ>gjH`Su[jNdfu,Z>d>p
tcZZ>ik`SrbfVSe(b¶SdotbjNdfuXZd < es`<bcikbciqZ>tYneB`Sjsb8Z tZyu`SjHdfY[eHki ¬ Zyu¦[U$VXZlbcVXiqdfujNStZ>dc(esbciqjH`
¢$eHt
eHj b}bfVXZ*`XZ>ikrNVvjNdcVXjvj,u-gjN`St|bfdfeHik`<botp¢&VXiqgoVBeHdcZ t esqk tcZ¤ ¤³jHd4tbcZ>dcZ>jNtfgjNXiqgeHXXqiqg>e(bfikjN`St¦
§Z- tce¢ VXZ>dcZbcVe(b[bcVXZdfiqgoVX`SZ>tft*jH¤}bcVXZ-XVSjsbcjNY[Zbcdfix g©iq`,¤³jH dfYne( bciqjH` gjN`Nboesiq`XZ>uik`QbcVXZ-gjNkjNd"iq`,m
(eHdcixes`<bft£YnesªNZ>t£bfVXZY `XjsbdfZ>eHkqBdfZqZ(es`<b¤³jHdrNkjNSesOiqYnesrNZliq`Su,Z,ik`Xr¦®}j(¢ZNZdypbcVSiqtgqeNtctjH¤
gjH`Stbcdoesiq`<bft2rNjsb)e8jNtci«bfikNZ}iqYleHghb¥¤³jHd¥jN,{|Z>gbKdcZbcdfikZ>(es :tZ>Z}tZyghbfikjN`©\X¦ h¦ 4`XZtcVXj qulboesªNZ$bcVXZ>ikd
dfZxe(bfikNZ£gjHY[XqZ,ikb|©ik`<bfj[eNggj `<b$¤³jHd&iqY[XkZ>Y[Z`<bciq`Xr©es`Z ©gikZ>`Nb}iq`Su,Z,ik`Xrntc,t|bfZY- ¦
&g>gjHdou,iq`XrBbfjBbfVXZ>tcZgjH`Stcixu,Zdoe(bfikjN`Stp2¢ZeHdcZu,ZNZqjHXiq`Xr
eH` iqYnesrHZik`u,Z,iq`XreH`SudfZbfdciqZ(es
Sqesb¤³jHdfYµSeHtcZ>u[jN`©gjHqjHd)jNik`<b¥jH¤'ik`<bfZdfZ>tb)u,Z>tfgdfiq,bciqjH`'p<iq`<NjHqvik`XrbfVXZ`SjHdfY[eHki ¬ Zyulik`v(esdfiqeH`<bft
bf`SjZiqtcrHZ>VvgjHjN`SdcuBVSj<jHj,douu,Z¦Kd±%esiqr `SudfZ t e(bcixXesdf2Z>dftcZZx`<e(bobft&ikjNel`Stb|<SeHiqtcg>Z>esuBZjNX`BeHYlbfVXSZ"kZ` jH¤2Y"t Z>,dmikjsYn¤)eH8rHjHZiq`<dcbfZt£bcdfYnikZ>(e(esbogo VXZ>tcu
ik`Sikr©`
t bcVXgoZ[V-8qj,jHgiq`Nesb
uXZ>tfgdfik,bfjHdot¦
^a`[SeHdfeHkqZ@p(j d2dfZ>tcZ>eHdfgoV¢jHdfª,tuXZ>es,¢&ikbcVlbfVXZ$jH,bfikY[i e(bfikjN`"jH¤8tbcjNdfeHrHZ)eH`Su"dcZbcdfikZ>eHXgj<t|botjH¤
j dO¤³Zye(b dcZ&NZ>ghbfjH dot2vlgjH`StciquXZdfik`XrY «bfiquXikY[Z`tiqjH`SeHSiq`S¬u,Z[tbcd ghb dfZ>t>pH¢&ikbcV[bcVSZesiqY jH¤F¶Xbbfik`Xr
bfj
tfgesqZH¦U$VXZYnesiq`ixtct Z©jH¤&bcVXixt*es8Zdm£bcVSZdfZqZ(es`SgZ©js¤}e
Sesdcbcixg xesd"gxeHtftjs¤}u,ik°FZdfZ`<bcixes
!#" S !%$
!"#$%&"!'())#("!'"!+*%,-/.01)$2
iq`v(esdfiqeH`Nbotpvixt&gd gixesFVXZ>dcZNpXtiq`SgZ£ikb}ixt$¢)Z>kkm@ªv`Xj(¢&`©bcVSesb&bcVXZgoVXjNiqgZ£jH¤bfVXZik`u,Ztbcd gb dfZ>t$es`u
jH¤bfVXZtZyesdogoVeHkrNjHdfi«bfVXYnt¥bfj©gjN`Stixu,Z>dxesdfrHZ>k©uXZ8Z`SuXt}jH`bcVXZtci ¬ Zjs¤bcVXZ¤³Zye(b dcZtcSeHgZH¦
zOesdcbcixes < Z>dc©jN`De"dfZ>gbfeH`Xr xesd$esdfZ>elu,Z¶S`XZ>uvnbfVXZ ct Zdy¦
~&Z>t kb}js¤bfVXZ < ZdfH¦OU$VXZdfZb df`XZ>uikYneHrHZ>t$eHdcZXdfZ>tcZ`<bcZyuvuXZ>gdfZ>eNtiq`XrljHdou,Zd$jH¤2tcikY[iqqeHdcikb|H¦
±iqr dcZ iqq tbcdoe(bfikjN`jH¤%dfZbfdciqZ(eH8jN`Dt Xm@iqYnesrHZ tcik`Sr[gjHqjHd&8jHiq`<bft$js¤%ik`<bfZdfZ>tb>¦
SSUTV>W)W(X)Y
N
! &($2&!&
&uSesY $e Y"Z>dcr¦~&Z>kixesSkZn¤³Zye(b dcZY[esbfgoVXiq`Xr
eNgdfjNtft¢&iquXZq¡tcZesdoe(bcZyu<iqZ¢}t>¦-^a`
"/(1(" " K' )$" "K, +'()" 1. "!+$" p,SesrNZ>t H H(!HNp<HHHS¦
´ ¦ )Z>kjN`XrHiqZHp'¾4¦¾esdotjN`'pF®¦ dfZZ`tSeH`'pes`Su NS¦²BeHkiqªF¦¾)jNkjNdm$es`SuBbcZ<b dfZmSeHtcZ>uDiqYnesrNZ
tc ZrN"/Y[ Z`<bf" esbc iqjH` Ktiq`X'(r[ZY )es$`S"u ikbft&
es SXkixgesbciqjH`bcjngjN`<bcZ`<bcm@SeNtZyu©iqYnesrHZdfZbfdciqZ(es@¦ 19 "! p >N X¦
\ U¦ "¦ iq`,¤³jHdou£es`SuU¦ ´ ¦¿Z¢&ikbb>¦ eHtci«miq`<(eHdcixes`<bft bfVXZjNdceH`Su£Z,XqjHikbfesbciqjH`'¦(^a` 19,"@.
% .@ "K,0()'"K,"@. >
p8SesrNZ>t y NsSp yHH\S¦
´ ¦<À4i FZ` ¬ jS¦' `SjsbcZjH`[bcVSZrHdoeHuXikZ>`Nb)js¤'eY «bfi«mikYneHrHZH¦ $" 1
$( "K,
-/.0 /()". pS\N\ 9G FXp > GX¦
F&N¦±e S< Z des`Su ¦ j {|ZYneHeS¦"^aYneHrHZldcZbcdfikZ>eHOvBdcZ>rHiqjH`St ¾)j<esdotZ[tcZrHY[Z>`Nboe(bfikjN`es`u
¶!$`X Z&%gjNkjNd$uXZ>tfgdfik,bfikjN`'¦2^a` "!')"K+$" "/(1("" )! "9()+$""!3 ) # *
' '(p8®tcik`Xm|¾)V pSU%esiq¢$es`'p,²BeHdfgoVDsNN,¦
G "¦ j Zb%es`
u ¦j {|Z>YneHeX¦ 4,{|Z>gbmSeHtcZ>u < Z>dciqZ>t tcik`Xr4gjHqjHdjNik`<botjH¤Xik`<bcZ>dcZyt|by¦N^a` )*)*)
- >
" "# "!+* , P( % .@ "K, $,0+% $(1)$), % ' (p
esrHZyt&\H v\ GS.p -e esi@p,®e¢$esiqi:p ´ p8sH H¦
H "¦ j Zbes`Suz%¦²DjN`NbfZ>tcik`SjNt>¦ }jNdcYnesqixtcesbciqjH`u,Z>tiqY[eHrHZyt'Z`"gj kZ d¤ eHgZ)e goVes`XrNZY[Z`<bft
u'3¯iqk) Y[( iq`Se( bfikjN"!`''¦- ^a .0` "K0/21P) 5("@$. 1)3 1"K
>" 34 3 *&3 ,0P"!" "KO, (
pSNjH Y[Z£^c^hpXSeHrHZ>t 9F6v<sSpN`XrHZ>dft>pX±Xdoes`gZHpSHH<,¦
"¦ j ZbypSz2¦²DjN`<bcZ>tciq`XjNt>pX~¦À4ZdfixgoVXZHpSeH`Su-À*¦z2ZqwH¦ eH e(bciqjH`Du,Z"u,wbfZ>ghbfZ dot}u,Z8jHiq`<bft
u'¯ iq`<bcwd b©8j d©qegj qZ d>¦^a` "#"K "K ,0)73 )-( ( "# .@(" P)+ 5 $( p
NjH Y[Z ^^hpXS eHrHZyt} F0H6 , G GXpNzOesdfiqt>pX±Xdoes`SgZHpSHHHS¦
"¦ j ZbypSz2¦²DjN`<bcZ>tciq`XjNt>pXes`Su-À"¦Sz2ZqwH¦ ¤ eHtbYne(bogoVXik`SrlY[ZbcVXj,u¤³jHd4gjHqjHd `SgeHkiqXdoe(bcZyu
iqYnesrNZ>t tiq`Xrlu,i«°FZdfZ`<bfiqeHiq`veHdcixes`<bot¦^a` 19,".& > ) 98 0 "K )$" "#*
(1"K pXHjN Y[Z^hpXSeHrHZyt\0G@H6v\@HGXp ´ j bcVSeHYlXbcjH`p-[p ´ Z>,bcZ>Y*8Zd yH S¦
> £z2¦ dfjNt>¦"¾)jHqjHd£iqk Y[ik`e(bciqjH`Y[j,u,Zxt4¤³jHdikYneHrHZlY[esbfgoVXiq`Xr-es`Su
ik`u,Z,iq`XrS¦^a` 19,"@.
%
"# )"K$"K "9((("C"= + )" ."#$" pSesrNZ>
t F N F H\Sp $eHdfgZqjH`SeSp
´ Ses iq0`':<p ; ´ Z>,bcZ>Y*8Zd4HHNX¦
À"¦O®}iqk8Zdcb>?
¦ > ! 3C% P .@9(1$ "#2 )$"#$ ¦¾eHY*XdfiquXrHZ©²BesbcVXZ>Y[esbcixgeB¿ikSdfeHdcNpO¾eHY"m
Sdcixu,rHZ `XikNZdotikb|©zKdfZ>tft>p HNX¦ y NNZ>eH`,ma²DiqgoVSZ NHjNkiqjH`
eH`Su ´ bfwXVes`XZ dcZyt¦^a` Z`SgZlu gj,uXeHrHZ}{|8Zr-t d£uXZ>tu,Z>tfgdfiq,bcZ dft
u'¯ iqYnesrHZyt@¦ > 1'-"! ,O) ." p 9F ³ \NH v\NHXp yHNX¦
>\ U¦s¿ik`u,Z8Zdfres`Su NS¦ eHdfu,iq`Xr¦ ´ VSes8ZmaeHuSes,bfZ>u*tcY[jvjsbcVSik`Xr£iq`lZyt|bfikYnesbciqjH`*jH¤8\smultVes8Zg Z>t
¤³ dfF jHYG e [ F6`SvZ)Nu,\sZ¤³jHp0dfN Y[`XesZ bciqjH>`SN@t'H,js¦¤Xqjvg>es,mauXdfikrNVNbf`XZ>tfttbcd gb dfZH¦ -/.0P", )$" K+"@. p
!#" S !%$
H\
!"#$%&"!'())#("!'"!+*%,-/.01)$2
¦ ²¦N²BeHdciqZm'N 1 k
!iqZ}es" `un ®"/¦ ( 1tc(tf"e(¶¦ 4" tiq`X rik¤ t¥
KeH`S'(u[Y[jH )Y[$Z" `<bftObcj ikxu©e < eNtiXiq`v(esdfiqeH`NbKiqYnesrNZ
iq`Su,Z¦O^a` )
p>N X¦
9F -df,t|bfiqeH`²BikªNjHxe({g ¬ vª©es`SuD¾)jHdou,Zqixe ´ goVXY[iqu¦¥^a`Su,Z,iq`Xr[SeHtcZ>ujH`DtfgeHkZiq`<(eHdcixes`<b$ik`<bcZ>dcZyt|b
8jHiq`<bft>¦¨^a` "!'()"+$" "9((1"KC" )$" pKeH`Sgj HZ>d>p$¾es`SeNuXeXpN q
HH H¦
/G £z2¦F²DjH`<bfZ>tcik`Xj<tp *¦ j Zb>pFes`SuD~¦8ÀZ>dcixgoVXZN¦$À4ik°8Z>dcZ>`NbfiqeH^a`v(esdfiqeH`<bft¤³jHd¾)jHqjHd}^aYneHrHZ>t>¦^a`
M1/,".O% d2:<; "!'()"+$" "9(((" " ')"+ ."#$" p dcixtes`XZNp t|m
bfdfeHkixeXp yH X¦
H ¾4¦ ´ goVXY[iqu-es`u~¦X²DjNVXdy¦%¿jvg>esFrHdoev(es Ziq`veHdcixes`<bot¥¤³jNd$ikYnesrNZ4dfZbfdciqZ(eH:¦
> 1"> *
+$"!" + )"OP"K 3 ) ", 8 " "!'( .0"K p > F Fs\H FH\sSpN²Be >N@ H,¦
N¦ ~¦ ´ Y[i«bfVeH`Su ´ ¦ ±¦S¾)VSes`Xr¦ 4iqt esxtcZZª 2 ¤ kqe bcjHYnesbcZ>ugjH`<bfZ`<bmSeHtcZ>u©ikYnesrNZ < Z>dc
tc,t|bfZY-¦O^a` 8 8 +,$ pSesrNZ>t @H6v Sp yH0 GX¦
> FVXZ`XrNHj 8VSeH`XrSpv~}eHgoVSiqu©À4ZdfixgoVXZHp 4qikviqZd)±e rNZdoeHt>pNeH`Su eH`XrsmaU es`©¿ jH`Xr¦ dcjN tb
bfZ>goVX`Si < Z¤³jNdYne(bogoVXPiq`X)r[+ 5 b|¢)$j `S"!g'eH(kiq X .0doe("KbcZyu ikYnesrNZ>t$bfVXdfj rNV-bcVXZdfZ>gj(HZ>dcnjH¤%bfVXZ `Sª<`Sj(¢&`
Z>XiqjNqeHd&rHZjNY[ZbcdfH¦
Kp H H >SpNÀ4Z>gZ>Y*8Zd yH0 FX¦
N
)
SSUTV>W)W(X)Y
Unité de recherche INRIA Rocquencourt
Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France)
Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique
615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France)
Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France)
Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38330 Montbonnot-St-Martin (France)
Unité de recherche INRIA Sophia Antipolis : 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France)
Éditeur
INRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France)
ISSN 0249-6399
© Copyright 2025 Paperzz