A Gaussian Prior for Smoothing Maximum Entropy Models stanley F

!"#
$ %&'(*)
",+-/.
0214357698;:=<?>@A78B5
CED5F3G6IH=CEDKJL8B5NMO8;6PH
<78BQ7RSF3GR:TBUU'U
VEWYX?Z[V]\2Z_^2^Za`Gb2c
d'e4f'ggGhFgBikjlg'mon2p'qsratd'e4uvraw'e4r
jxGtsw'r4yuvr{z|r4hvhvgw~}?w'uvrat
suvq

uvqsqL2p2t
yf7 Na2
4a/B
we4rat
qxuwe4gwqLr4qsmoxB'ump2mrawGqt
gnG9z=,&mg 2r4hvuw'yeaxw¡2r'uvr4¢r4 xBlmoxB'ump2m£h¤u¥Br4hvuf'g'g ¦qtsxBuwG§
uw'y¡iIg'tr42n2gw'rawGqsuxBhmg' 2r4hvaFxw' |hvu¥Brogqf'rat?moxB'ump2m¨h¤u¥Br4hvuf'g'g mr4qf'g' 2©uv{n2t
gw'rqsgogBrat«ª/qLqsuw'y¬gBi
qtsxuw'uw'y| /xBqx®~d'r4ratsxBh,mg'gqf'uw'y=mr4qf'g' 2]iIgt]moxB'um¯p2m°rawGqt
gnG=mg' 2r4h¤of2xr2r4rawn2t
g'n2gsr4 qsg
xB 2 /t
r4Lqf'uvn2t
g'hvram22p'qn2t
r4'u¤g'p'±t²r4p'hvqs 2gow'gqlmox¥Brluvqle4h¤raxGtf'gB¢!qf'r4srmggq_f'uw'yomr4q_f'g 2,e4gm]§
n2xt
r]¢uvqf_mggGqf'uw'ymr4q_f'g 2iIg'tgq_f'ratlq
Kn®r4³gBit²r4hxqsr4 ´mg' 2r4hva w¦qf'uv³¢lgts¥N2¢lr©p2t
Gr4~n2t
r4uvgp'
¢lgts¥uw¦moxB'ump2mrawGqt
g'no_mggGqf'uw'yxw' e4g'mon2xt
r©qf'r{n®rat«iPgtsmoxw'e4r©giksr4GratsxBh7gBi&qf'r4sr{xBhvygt²u¤q_f2m
¢uvqf¡e4gwGrawGqsuvgw2xBh7qsr4e4f2w'uvµKp'r4liPgt,mg'gqf'uw'y¬¶®§OytLxm·hxGw'yp2xByr©mg' 2r4h¤¸,r4eaxp'sr©giqf'r©moxBqp2t
r©2g' 2
gBit
r4sraxt
e4f¦uw=¶®§Oytsxm¨mg' 2r4h&mg'gqf'uw'y~xw' =qf're4hvgsre4gw2w'r4e4qsuvgw=®r4q¹¢lr4raw|moxB'ump2m¨rawqt²gn|xw' e4gwGrawGqsuvgw2xBh³¶®§OytsxGmºmg' 2r4hvalqf'uv 2gmoxuw»uv¬¢lr4hvh¼§Op'uvqsr4 ½qsg=y'xp'yr~q_f'r´n2rat¹iIgtLmoxw'e4r~giEmoxump2m
rawGqt
gnG|mg'gqf'uw'y=mr4qf'g' 2a=¾?ratx¦hxGt
yrwp2m2rat]gBi? /xBqxLr4qsa&¢lrª¿w' qf2xq¯xwÀz=mg'gqf'uw'y
mr4qf'g' n2t
gn2gGsr4 oqsgp'G¬ÁFxÂFrat
q
¬Ã sÄ n2rat«iPgtsmxB,¢r4hvh7xBgt,2r4qsqLratq_f2xwoxBhvh/gGqf'ratxBhvyg't
uvqf2mp2w' 2rat
e4gw'suv 2ratsxqsuvgw7¬Åf'uv]yraw'ratsxBhxw' Àr_Æ¬e4uvrawqmr4qf'g' =uwgGh¤Gr4¯p'suw'y´xÇ]xp'ssuxwÀn2t
uvgt?gw|qf'ron2xtLxmr_§
qsrat
©gi±q_f'r¬mg' 2r4hxw' =sr4hvr4e4qsuw'y=moxB'um¯p2mÉÈÊKËBÌ4ÍPÎaÏ_ÐÑËGÏÐ?uw'sqsraxB ÀgBi±moxump2mÒhvu¥Br4hvuf'gg' Ón2xtLxmr4qsrat
;xhp'r4lÔ=r©e4gwGqtsxBsqlqf'uv©mr4qf'g' ~¢uvqf¦n2t
r4'u¤g'p'Õ¶®§OytsxGmmg'gqf'uw'y¬mr4q_f'g 2?qsgr4Kn'hxBuw|uvqsp2n2rat
uvgt
n2rat¹iIgtLmoxw'e4r
¿
hxw'yp2xyr{mg' 2r4h¤¿moxump2mrawGqt
gnG2mg'gqf'uw'y
z=xB'ump2m rawqt²gn9z=©mg' 2r4hvuw'y f2x¯2r4rawÀp'e4e4r4s²i p'hvhv xGn2n'h¤uvr4 qsg~x ¢uv 2r¬tsxw'yGrogBi 2g'moxBuw'auwG§
e4hp' 2uw'y hxw'yp2xyr~mg' 2r4h¤uw'y x¯¢lr4hvhxBomoxwG=gqf'ratw2xBq_p2tsxBhhxw'y'p2xByrqxB_¥¡Ã N Ä Ngt{mxw
n2t
g'hvram2qf'uvq
Kn®r©gBikmg' 2r4hvuw'yeaxw2r©'uvr4¢r4 ~x³moxB'um¯p2m·hvu¥Br4hvuf'gg' Ó9z=ÁF,qtsxuw'uw'yiIg'tr42n2g'w'rawG§
qsuxBhlmg 2r4hva&xw' Àh¤u¥Br¡gqf'rat]moxB'um¯p2m hvu¥r4h¤uf'g'g Ymr4qf'g 2]uvn2t²gw'roqsggBrat«ª/qLqsuw'y~gBilqtsxBuw'uw'y| /xBqx2
Ô½f'uvh¤r?sr4ratLxBh2mg'gqf'uw'y{mr4qf'g' 2&iPgt&moxump2mrawGqt
gnG¯mg 2r4hvf2xr®r4raw¬n2t
g'n2gsr4 qsg{xB 2 /t
r4s,qf'uv
n2t
g'hvram Ã ® 2 ;Ä ¿n2t²r4uvgp'{t
r4_p'h¤qL© 2g~w'gqÕmx¥Br{uvq?e4hvraxt©f'gB¢ qf'r4Lr¯_mggGqf'uw'y~mr4qf'g' 2³e4gmn2xt
r
¢uvqf mg'gqf'uw'y¬mr4qf'g' 2liPgtlgq_f'ratq
2n2r4?gBikt
r4hxBqLr4 ´mg' 2r4hva
gB¢lr4rat47qf'rat
r¡f2xB¯x®r4raw=yt²raxBq© 2raxBhgit²r4sraxt
e4f¦uwÀmg'gqf'uw'y|¶2§Oy'tsxmÒhxw'y'p2xByr¬mg' 2r4hva&xw' uvqeaxw¦2r©f'gB¢³w¡qf2xq³moxB'um¯p2m rawqt²gn¡¶2§Oy'tsxmmg' 2r4hvÕxGt
r³e4hvgLr4h¤|t
r4hxBqsr4 qsge4gwGrawqsuvgw2xh ¶®§OytLxm
mg' 2r4hvajlgw'Lr4µKp'rawGqshv2qf'uv 2gmxBuwouv¢lr4hvh¼§Op'uvqsr4 ~qsgyxGp'yuw'y¯q_f'rÕn®rat«iIg'tsmoxw'e4r©gBi&moxB'ump2m·rawGqt
gnG
mg'gqf'uw'y¬mr4qf'g 2©t
r4hxBqsuvr©qLgogqf'ratl_mggGqf'uw'yoqsr4e4f2w'u¤µ2p'r4a
wqf'uvl¢lgts¥NB¢rp2t
r4¬n2t²r4uvgp'l¢lgts¥Euw¡moxB'ump2mrawGqt
gnGmg'gqf'uw'y¯xw' ¡e4gmon2xGt
rqf'r³n®rat«iPgt«§
moxw'e4r]gBisr4GratsxBhFgBi&qf'r4sr{xh¤yGgt
uvqf2m?¢uvqf¡e4gwGrawGqsuvgw2xBhFqsr4e4f2w'uvµKp'r4?iPgtl_mggGqf'uw'y¬¶®§Oytsxmhxw'y'p2xByr
mg' 2r4hva{&BxBhp2xBqsuw'y~q_f'rn®ratsn'hvr4uvq
|gBiraxBe4f|mr4qf'g' ´gBrat?xhxGt
yrowp2m®rat?gBi /xBqxsr4qsa7¢lrEª¿w' =qf2xBq
qf'roz= mg'gqf'uw'y=mr4qf'g' n2t
gn®gsr4 qsg´p'ÁFxÂFrat
q
Ã LÄ n2rat«iPgtsmxB{¢lr4hvhxB{g't©2r4qsqsrat]qf2xGw=xBhvh
gqf'rat]xBhvygt
uvqf2m¯p2w' 2rate4gw'Lu¤ 2ratLxBqsuvgw7 w=qf'uvomr4qf'g' F&x~Ç]xp'ssuxwn2t
uvgt©g'w mg' 2r4hn2xGtsxmr4qsrat²©u¤
xn2n'hvuvr4 xGw' mxBump2m ÈÊ2ËBÌ4ÍPÎaÏ_ÐÑËÏ_Ðluw'sqsraxB ÀgBimoxB'um¯p2m¨hvu¥Br4hvuf'gg' n2xtsxmr4qLrat?;xBhp'r4¯xGt
r{sr4hvr4e4qsr4 F
Ô½f'uvh¤r¡sumon'hvrxw' =r_Æ¬e4uvrawGqaqf'uv¯mr4qf'g' =r42f'u'u¤qL¬xBhvh&gBiqf'r¬®raf2xa'uvgt
]qf2xBq{f2xro2r4rawÀg'srat
Gr4
jf'raw¦xw' ~Ç©g'g /mxw¡qsg¬®r{2raw'r_ª/e4uxBhiPgt¶®§Oytsxm·mggq_f'uw'y|Ã Ä
wqf'r~t
ramoxuw' 2ratgBi³q_f'u¤¡sr4e4qsuvgw7,¢lrn2t²r4srawq¡xwuwqt²g /p'e4qsuvgw»qsg=moxB'um¯p2m rawqt²gnmg 2r4hvuw'y
xw' | 2uvseap's©¢³fG~_mggGqf'uw'y¬z=$mg' 2r4h¤]uv{w'r4e4r4sxt
w´d'r4e4qLu¤g'w N¢r]uwqt²g /p'e4r¬¶®§OytLxmhxw'y'p2xByr
mg' 2r4hvÕxw' _p2momoxt
u 4r{n2t
r4'uvgp'?¢g'ts¥gw¡mggq_f'uw'yqf'r4Lr¯mg' 2r4hva&Ô=r©hvuvsq?qf'r© 2r4sutsx'hvr¯n2t²gn2rat
qLu¤r4
gBilmg'gqf'uw'y~xBhvygt
uvqf2m{g'srat²r4 ==jf'raw=xGw' ÇEgg' /moxw7 w=d'r4e4qsuvgw 7¢ruwGqt
g' /p'e4r¬moxump2m
rawGqt
gnG=¶2§Oy'tsxmÒmg' 2r4hvxGw' 2uvseap'sqf'r4utt
r4hxBqsuvgw'_f'un¢u¤q_f|e4gwGrawqLu¤g'w2xBh¶®§OytsxGm mg' 2r4hva wd'r4e_§
qsuvg
w /l¢lr~_p2t
r4Yn2t
r4'uvgp'¢lgts¥uw!mg'gqf'uw'yYmoxB'um¯p2mÉrawGqt
gnGYmg' 2r4h¤~xGw' Yuw½d'r4e4qsuvgw l¢lr
n2t
r4srawGqÁFxÂFrat
q
Ç]xp'ssuxw¡n2t
uvgtlmr4qf'g' F&Ô=r?e4gwGqtsxBsq,qf'uv³mr4qf'g' ¡¢uvqfo_mggGqf'uw'y¬xBhvygt
uvqf2miPgt
e4gwGrawGqsuvgw2xBh¶®§OytLxm mg 2r4hv¬xGw' f'gB¢·qf2xBq{uvqxBqLu¤²ª/r4¬xBhvhgBi?eat
uvqsrat
ux|gBi³jf'rawxw' YÇ©g'g' /moxw7 w
d'r4e4qsuvg!w 2F¢lron2t
r4srawGq¯t²r4p'hvqs{gBir42n2rat
umrawGqs]e4gmon2xt
uw'y=xw'p2m¯®rat©gBi³moxump2m¨rawq_t
gnG xGw' =e4gwG§
rawGqsuvgw2xBh7mg'gqf'uw'yqsr4e4f2w'uvµKp'r4g'w¬¶®§OytsxGm hxw'y'p2xByr©mg 2r4hvuw'y/" &uw2xBhvh¤Nuwd'r4e4qsuvg#w ]¢lr³ 2uvseap'sgp2t
e4gw'e4hp'suvgw'a
$%&$
')(*,+&-/.,-
02135456879:')6<;,=>?+&1<@
lj gw'Lu¤ 2rat?q_f'r¯q_xB¥¡gBir4sqLumxBqsuw'yxn2t²g2x'uvhvu¤q
¦ 2u¤Lqt
u2p'qsuvgw!AKCB/lgBrat?xª¿w'uvqsrsr4qDBFEHG½yGu¤Graw~Lgmr
qtsxuw'uw'y¦ /xBqx¡sr4qJILKNMOBPRQTSUSTSQVBXWJY' wqp'uvqsuvr4hv&g'p2t?qxB¥ u¤©qLg¡ª¿w' x¡ 2uvsqt
u2p'qsuvgw!A2ZB/?sumuvhxt]qsg
qf'r©ramon'ut
uveaxBh 2uvsqt
u2p'qsuvgw\] [ CB/lyuvrawG¡qf'r{qtLxBuw'uw'y¡ /xBqx
K)^V_ ` Z BN
] [ Z BN<
¢³f'rat
r ^V_ Z BNl 2raw'gqsr4q_f'r¯w'p2m¯®ratgikqsumr4a B~g'e4eap2t
?u#w I xGw' ~¢³f'rat
r ` u¤?qf'r©su 4r]gBikq_f'
r I w qf'r
r4'qt
ramr©eaxBLr2¢lr©eaxw¡qx¥BJr A2Z B/±qsgo2r{uv 2rawGqsuveaxBhqsbg ] [ Z B/ K2p'q?qf'uv¢uvhvhq¹2n'uveaxBhvhv~hvraxB ~qLg¯gBrat¹ª/qsqsuw'yoqsg
qf'r]qtsxBuw'uw'y /xBqx2 w'sqsraxB F7uvq?¢lgp'hv ®ro2r4qsqsratqsg¬t²r4µKp'ut
rqf2xBJq A2Z B/moxBqse4fgw'hv¦qf'gsrn2t
gn2rat²qsuvr4³gBi
] [ Z BN,qf2xBq¢lr© 2r4ramqsg¡2r{Lu¤y'w'u ª/eaxGwq©xw' qf2xBqeaxw2rt
r4hvuxG'h¤¦r4sqsumoxBqLr4 ¡i t
g'mqf'r©qtsxuw'uw'y¡ /xBqx2

Ngt?r42xmon'hvrFe4gw'Lu¤ 2rat2BKÒ P Q _?¢³f'rat
r P xw' ]xt
r¬,w'yhvu¤_f=¢lgt
2Fxw' =hvr4q{qf'rqtLxBuw'uw'y
/xBqxI ®r³q_f'r³hvuvsqlgBiFe4gw'sr4eap'qsuvr?¢lgt
¬n2xut²agt 4Ð Ï
È ]Ì4qf2xBq,ge4eap2t,uwsgmrhxt²yre4gtsn2p'lgBi,w'yhvu¤_f
qsr4'qalÅfp'2qf'r{q_xB¥u¤?r4sqsumoxqsuw'y¬qf'rEi t²r4µKp'raw'e4¦gBi*,w'yhvuvf|'u¤y'tsxmaljlgw'Lu¤ 2rat©x'u¤y'tsxm qf2xBq 2g'r4
w'gq]ge4eap2tEuwÀqf'roq_tsxBuw'uw'y~ /xBqx®Fx
,oÔÀr¬f2xr [
JK 22p'q{uwq_p'u¤qLu¤Gr4h¤À¢r¢±xGwq
A2
suw'e4r]qf'uv³'uvytsxm¨f2xB©Ì4Ë Î{e4f2xw'e4r]gBikg'e4]eap2tst
uw'y/,Åf'uv³uv©xw¡r4KxGmon'hvr{gBikxn2t
gn2rat²q¹
gBi ] [ Z B/*qf2xBq&¢lr 2g{w'gq, 2r4ramsuvyw'u¼ª/eaxwGqxw' ¡qfp'& 2gw'gq¢xwGq&qsg{moxqse[f]r42xBe4qshvo¢uvqf AKC B/4 gB¢lr4rat4
hvr4qÕp'©xBs_p2mr©qf2xBq¢lr©g'Lrat
r{q_f2xBqqf'r©¢lgt
ge4eap2t²³¢uvqfi t²r4µKp'raw'e4 2 uwqf'r]qtsxBuw'uw'y¡ /xBqx2
Ð Î
K ] [ aP 2< K XS S
<
][
¸,r4eaxp'sr¡gBiqf'rx2p2w' /xw'e4rgBiqf'r¡¢lgt
7qf'uvuvn2t²r4p2mox'hv xwxBe4eap2tsxqsror4sqsumoxqsr¬gi±q_f'u¤]iOt
r_§
µ2p'raw'e4¬xw' ouvqLr4ramt
raxBsg'w2x'hvr³qsg{t²r4µKp'ut
rq_f2xBq&gp2t&Lr4h¤r4e4qLr4 ¬ 2uvsqt²u2p'qLu¤g'w A2Z BNxBqsuv
ª/r4,qf'r³xw2xBhvgyGgp'
e4gw'sq_tsxBuwq
A2
K A2 aP 2< K XS S
<

z|gt²r´yGraw'ratsxBhvhv¢rÀeaxw½Lr4h¤r4e4q=x$w'p2m¯®rat¦gBi¬w'gw2w'r4yxBqsuvrtsxw' 2g'm ;xGt
ux'hvr4=gt 4Î_ÈÍ Ï
Î Ì K
M P Z BNR QTSUSTS Q Z B/V Y=xw' t²r4µKp'ut
r=q_f2xBq¬q_f'r=r4Kn®r4e4qsr4 ½BxBhp'r gBiraxBe4fiPraxBqp2t²r=gBratoq_f'r mg' 2r4
h AKC B/u¤
r4µ2p2xBhFqsgoq_f2xBqlgBikq_f'r©ramon'ut
uveaxBh 2uvsq_t
u2p'qsuvgw ] [ Z B/
A2Z BN ¹Z B/<
K ] [ Z B/ sZ B/ Q K QUSTSTS Q S

Åf'r©e4gw'LqtsxBuwGqr4Kn2t²r4ssr4 ~uw r4µKp2xBqLu¤g'w ,eaxw®r{r42n2t
r4ssr4 ¦¢uvqfq
¢lg{_p'e[fiIraxBq_p2t
r4a
aPRQ < K u¼gi q_f'rat
¢K uvsr
iPgt 2K Q
Åf'r¯e4g'w'sqtsxBuwGqs?yuvraw¦uw r4µKp2xBqLu¤g'w 2g~w'gGq©yraw'ratsxBhvhv|n2r4e4u¼iP x¡p2w'uvµKp'rmg' 2r4,h A2Z B/472p'q{xsr4q
gBimg' 2r4hv ?Åf'r È ;Ð ÒÎ /ÍPÏ
Ë_Ê ~n2t²uw'e4un'hvr¡sqxBqsr4qf2xBq?¢r]f'gp'hv =sr4hvr4e4q©qf'rmg' 2r4,h AKC B/ E
¢uvqf¦qf'rhxt
yr4Lq©rawqt²gn Z AB K
A2Z BN2hvg,
y A2Z B/Ã Ä wGqp'uvqsuvr4hv&mg 2r4hv]¢uvqf|f'u¤y'f|rawq_t
gnG~xt
r
mgt²rÕp2w'u¼iPgtsmxw' ¡e4gtst
r4n®gw' ¡qsgoxBsp2muw'yhvr4sx2g'p'qq_f'r³¢lgt
hv FÅf'rÕmoxump2m·rawqt²gnomg' 2r4h7eaxw
2ruwGqsratsn2t²r4qsr4 xB©qf'romg' 2r4h&qf2xBq{xsp2mr4©gw'hv|qf'ro¥'w'g;¢h¤r4 2yGroqf2xBq?uv¯t
ran2t
r4Lrawqsr4 ¦qf'r]iIraxBq_p2t
r4
2rat
uvr4 i t
g'mqf'r©qtsxuw'uw'y¡ /xBqx22xw' ~w'gGqf'uw'y¬r4hvsr
Åf'r¬moxB'um¯p2m°rawGqt
gnG´n2xGtsxB 2uvym f2xB¯mxw|r4hvr4yxwGq¯n2t²gn2rat
qLu¤r4Ã Ä Åf'r¡moxB'ump2m°rawGqt
gnG
mg' 2r4hFuvÕp2w'uvµ2p'roxw' eaxw2r]f'gB¢³w¡qsg¬®r{xwr42n2g'w'rawqsuxBhmg 2r4hgBikq_f'r?iIgtLm
r42nF
sZB/s

A *CB/K
!"
# $ %$
&
&
!")
'(
!"
, -
/!"
0 -
'+*
.!"
&
!")
&
'(
'+*
21
76
3
56 4
698
;:
&
&
=69>
<
=69>
.?
@
<
6;A D
CB
A
E!"
GF
IHKJ
L
%M 23N
#S
9O
QP
UT#V
)HRJ
L
W
<
8
YX[Z
&
\G]
8P
>a69>
>_^ +`
¢³f'rat
r K r42nF 8P sZB/s±u¤©xow'gtLmoxBhvuaxBqsuvgw i xe4qsgtlxw' /K· P QUSTSTS Q xt²r{qf'r{n2xtLxmr_§
qsrat
gBi7qf'rmg 2r4hP<7p2t
qf'ratsmgt
rqf'rmoxB'ump2mrawGqt
gnG{mP g' 2r4h2uvxBhvsg?qf'rmoxB'um¯p2mhvu¥Br4hvuf'gg' ~mg' 2r4h
uwoq_f'r³e4hxBslgBiFr42n2gw'rawGqsuxBhFmg' 2r4hvyGu¤Grawr4µ2p2xBqsuvgw| 4 &uw2xh¤hv2q_f'r³hvgyB§Ohvu¥Br4hvuf'gg' |gBiFqf'rqtLxBuw'uw'y
\G]
,V
<
V
8
>_^
>a69>
#b
`
8
`
`
*c+d7egfehjilkmhneoilpq-egf+d%k=r-st+d7eouvgk=u%fpilw=qxu9qxu7y[z_egwYp{jilee}|Yhegvgpwpq-kmu7fpk~eegY{%w=rpkDpd%kfez_k={9u7skmuwDpilwmqxujqxu%yfegpgd7eou
vgk=u%fpilw=qxu9qxu7y[eg|Yhe}vgpwYpq-k=u%fpkw=r-peoiu%wpemw=rx{%e}fgpd%eQ[wY|Yq-G{%.eoujpilk=hjks9eorjt+qxrxr%u7kYp~ne+pd%e[w|Yq-{7)rxqxeorxqxdkks/[ksjeor_
wmu7sIpd7eGI[ksjeort+qxrxru7kYpeg|Yq-fpqxzpd%eGvgk=u%fpilw=qxujpfGwmileqxu7vgkmu7fq-fpeoujpg

/xBqxu¤?e4gw'eaxr]uw qf'r¯mg 2r4h&n2xtsxmr4qsrat
©/xw' ~q_fp'?uvq³uv©t
r4hxBqsuvr4hv~raxBL¬qsgª¿w' ´q_f'r{p2w'u¤µ2p'r¬moxu¼§
mp2mrawq_t
gnG mxBump2mhvu¥Br4hvuf'g'g' ~mg 2r4h7p'suw'y¯xBhvyg't
uvqf2m_p'e[fxB,yraw'ratsxBhvu4r4 ¬uvqsratLxBqsuvrseaxh¤uw'y¡Ã Ä
gtlumon2t²g;Gr4 u¤qLratsxBqsuvr©seaxh¤uw'y=Ã Ä
Ô½f'uvhvr³mg' 2r4hv&¢uvqff'u¤y'frawq_t
gnG©qsraw' qsgÕ®rtsxBqf'ratp2w'u¼iIgtLmgtF_mggGqf{xw' ¢lrmox©gw'hv{e4gw'LqtsxBuw
n2t
gn®rat
qsuvr4gB<i AKC B/,¢lr³e4gw'Lu¤ 2rat±suvyw'u¼ª/eaxwq¿xmoxB'ump2m rawGqt
g'n¬mg 2r4h7eaxw¡sqLu¤hvhFgBrat¹ª/qqtsxuw'uw'y¡ /xBqx
r4raw¡¢uvqf¡_moxBhvhw'p2m¯®rat
gBi&e4gw'sq_tsxBuwqLa /gt,r42xmon'hvr/e4g'w'suv 2rate4gw'LqtsxBuwGqslgw¡qf'r?iOt
r4µKp'raw'e4¡gBi&qf'r
¢lgt
W $xw' |qf'r¬'uvytsxmÉ\ W xw' xBLp2mrqf2xBq©qf'r¢g't
W »gw'hv=g'e4eap2t
¯xiPqsrat
qf'r©¢lgt
=\ ¦uw qf'r{q_tsxBuw'uw'y¬ /xBq_x2&Åf'raw72¢lr©¢uvhvhkf2xr
A2 DP{
W " K ] [ aP]W < K ] [
\ !W F
[b
"
"
&
&
"
'+*
xw' "
"
"
'+*
2
\ !W
\ W
¢³f'uve4foumon'hvuvr4DA2 DP{W <K ?iPgtxBhvh \ wqp'uvqsuvr4hvN¢lr¢xwq A2ZB/ EiIg'txBhvhB E#G!suw'e4r
xBhvh'uvytsxGmkf2xr&Lgmr&e4f2xw'e4rgBi2g'e4eap2tst
uw'y/7rat
g³n2t²g2x'uvhvu¤qLu¤r4&hvraxB ]qsguwGª¿w'uvqsrlhvgsuwEhvgyB§Ohvgsg
r4e4qsuvr
iOp2w'e4qsuvgw'xGw' eaxwhvraxB Yqsgn2g'gton2rat¹iIgtLmoxw'e4ruwYmoxGw xGn2n'h¤uveaxBqLu¤g'w'a{Î &¢?f'raw/A2ZB/t
ran2t²r4srawqL¬x
hxw'yp2xByGr³mg' 2r4h/qsg2r©p'sr4 ouwo_n2r4r4e4f¬t
r4e4gGyw'uvqsuvgw7Åf'p'a'uvquvl 2r4sutsx'hvr³qLgoÌ ¯ËËÍ ¬moxB'ump2mrawGqt
gnG
mg' 2r4hva/g'tx ²p'sq?n2xtsxmr4qLratl;xBhp'r4©x¢±xiOt
gm·qf'r4ut?moxB'um¯p2m h¤u¥Br4hvuf'g'g =r4LqsumoxBqsr4a
"
0
A " <K ] [ "
aPK
%$x$

V: !"D#$ %'&
(%*),+
Ô½f'uvh¤rqf'rat
r=f2xB~®r4raw t²r4hxqsuvr4hvÓhvuvqsqshvr¢lgts¥uw$_mggGqf'uw'yYmoxB'ump2m rawGqt
gnGÓmg 2r4hva©q_f'rat
r=f2xB
2r4raw¡x©y't
raxBq& 2raxBh2gBiF¢lgts¥Euwomggq_f'uw'y¶®§Oytsxmhxw'yp2xyr³mg' 2r4hva .- È È 'Î Ë0/Î - u¤lx{n2t
g'2x'uvh¤uvq

2uvsqt
u2p'qsuvgw A22 1agBrat¢lgt² {sr4µ2p'raw'e4r4$1lqf2xBqmg' 2r4hvf'gB¢gBiPqsraw]raxBe4fsr4µ2p'raw'e4r31g'e4eap2t
lxBx?srawGqsraw'e4r
ÁFxw'y'p2xByromg' 2r4h¤{f2xrmoxwG~xn2n'hvuveaxBqsuvgw'auw'e4hp' 2uw2y|n®r4r4e[f|t
r4e4gGyw'uvqsuvgw7moxe[f'uw'rqtsxw'Lhxqsuvgw7Fxw' n®r4h¤hvuw'y~e4g'tst
r4e4qsuvgw|Ã G a aÄ
Ngtlx¢lgt
sr4µ2p'raw'e44
r 1aK aP56505 $7 2¢lr³eaxw r4Kn2t²r4suvqs©n2t
g2x'uvhvuvq¹ ta2 1xB
ta2 1a K t4 aPs9 8 t4 : aPs9 850565;8 ta <7 : aP=56505 $7?>P@ 8 ta : aP=56505 $7v
7BA8P
C ta : aP50565 >P
K
P
O3 I
,
l
[>
g
" g
l[>
>_^
¢³f'rat
r¦qf'r~qLg¥Braw $7DAP K suvyw2xh¤¡qf'r¦raw' ÓgiÕqf'r¦srawGqsraw'e4r Åf'r|mgsq¢uv 2r4h¤G§¹p'sr4 ½hxw'y'p2xByr
mg' 2r4hva2]iOxt4xt
r¶®§OytsxGmhxw'yp2xByGr³mg' 2r4h¤ woxGwo¶®§Oytsxmmg' 2r4hP'¢r?mox¥Brlqf'r³xGn2n2t
gBumoxBqLu¤g'wqf2xBq
qf'rouv 2rawGqsuvq
=gBi±x ¢lgt
| 2ran2raw' 2og'w'h¤|gwÀn2xBsq{¢lgt² 2©qf2t
gp'yf qf'rouv 2rawqLu¤q
|gBiqf'rohxBLq¯¶ ¢lgt
2a
yuv'uw'yp'
7BA8P
7DA8P
C
t42 1a" K 8P ta : aP50565 >P E C 8P t : F>H>G?P I;>PKJ
¢³f'rat
r©q_f'r{w'gqxBqsuvgw 2raw'gqLr4qf'r©sr4µ2p'raw'e4r L56505 ©xw' ~¢³f'rat²r >IMA QTSUSTSQ 9NÕxGt
rÕxh¤hqx¥Braw¡qsgo®r
sgmr© 2u¤Lqsuw'yp'uvf'r4 2r4yGuw2w'uw'yB§OgiÑ§OsrawGqsraw'e4roqLg¥Braw7 >P
Åf'r¬moxB'um¯p2m°hvu¥Br4hvuf'gg' $r4sqsumoxBqsr A PO : >HG?I;>PKJ EgBiqf'rn2t
g2x'uvhvuvqsuvr4 ta : >=>G?P I;>PKJ ©gBrat
sgmr¬qtLxBuw'uw'yÀ /xBq#x I eaxw2reaxBhveap'hxBqsr4 $=Lumn'h¤e4gp2wGqsuw'y f'gB¢gBiIqLraw=qf'r¡qsg¥raw iIghvhvgB¢qf'r
" T
>
l[>
[>
>_^
>_^
A
[>
>
YX
[>
lA
>
>
>
>
Y
[>

>
>
>
Ð Ì[ÍPËGÏ ¡gt,e4gwGqsr4'q
xw' 2uv'u¤ 2uw'y|¡qf'r©qsgq_xBhFwp2m2rat±gBikqLumr4³qf'r{f'uvsqLgt
¡ge4eap2t
FÐ Î
>HG?I;>PKJ K ^ _ F>HG?I;>PKJ S
A 9O : F>H>G?P I;>PKJ "K ^ _
>HG I >P J
>H>G?P I;>PKJ
^ _
^_
g;¢lr4rat qf'r©moxB'um¯p2m·hvu¥Br4hvuf'gg' |r4sqsumoxBqsr4lgBiFqf'r4Lr{n2t
g2x'uvhvuvqsuvr4³q
2n'u¤eaxh¤hv¡hvraxB qsggBrat«ª/qsqsuw'y/'xw' uw'sqsraxB uvq&uv& 2r4sutsx'hvrqsg©p'srlmg'gqf'r4 ]r4sqsumoxBqLr4gBi/q_f'r4srl;xBhp'r4a< Ngtr4Kxmn'h¤rBg'w'rLumn'h¤rmg'gqf'uw'y
qsr4e4f2w'uvµKp'r|>uv¬P qLg=hvuw'raxGt
hvÓuwGqsratsn®ghxBqsr~q_f'r´moxB'ump2m hvu¥r4h¤uf'g'g r4sqsumoxqsr~gBi©qf'>r|P ¶2§Oy'tsxm n2t
g'2x'uvh¤uvq

A 9O : >=G?I;>PKJ ,¢uvqf~xw¡r4LqsumoxBqsr©gBi&qf'r¬P¶
«§OytsxGm n2t²g2x'uvhvu¤q
ta : >=G?I;> J ©Ã 2 aÄ
F>P
A[ : >HG I >PKJ <
K A 9O : >=>G?P I;>PKJ ½ < A : F>H>GP I > J R Q S
Åf'rohvgB¢lrat«§Ogt
2ratEr4sqsumoxBqLroeaxw2r¡ 2r_ª¿w'r4 xw2xh¤gGygp'shv&xw' qf'r¬t
r4eap2t
Lu¤g'w=eaxw raw' ¢uvqfx~p2w'uvytLxm
gt]p2w'u iPgtsm° 2uvsqt²u2p'qLu¤g'w7´d'uw'e4rqf'r¡hvg;¢lrat«§Og't
2rat© 2uvsqt²u2p'qLu¤g'w'¬xt
rohvr4sn2xt
sr4hv|r4sqsumoxqsr4 =iOt
gm qf'r
qtsxuw'uw'yo /xqx2q_f'r4ut±uwGqsratsn®ghxBqsuvgw¡yraw'ratLxBhvh¤~t²r4 /p'e4r4gBrat¹ª/qsqsuw'y/ hxt²yrÕw'p2m2rat,gBigGqf'rat,mg'gqf'uw'y
mr4qf'g' 2liPgt¶®§OytsxGmmg' 2r4h¤©f2xr©2r4raw|n2t
gn®gsr4 FFÎ 7Ã ® ® 2 ' ® Ä
ÔÀrÕn2t
r4Lrawqx2t
uvr_igBrat
'uvr4¢Ógikn2xBsq,¢g'ts¥uw¬¶®§OytLxmmg 2r4h7mggq_f'uw'yNk¾©w'r{2xsuve©g'srat
BxBqsuvgwu¤
qf2xBqqf'romoxB'ump2m hvu¥r4h¤uf'g'g r4sqsumoxqsr{gBiq_f'r¯n2t
g2xG'u¤hvuvq
~gBixGw~¶®§Oytsxm qf2xBq 2gr4{w'gqge4eap2t?uw¦qf'r
qtsxuw'uw'y /xBq_x¡u¤J 4rat²g~xw' |u¤©q_fp'©qsg'g¡h¤gB¢{7xw' |e4gw'sr4µ2p'rawGqshv´q_f'r¯z=Án2t
g'2x'uvh¤uvqsuvr4gBi¶®§OytsxGm©¢uvqf
w'gw 4rat
g¡e4gp2wGqs©xt
r{yGraw'ratsxBhvhv´qLggf'uvyf7©Åf'uv³ 2uve4f'gqsgm]´mgqsuv;xBqLr4³qf'rEiIgGh¤hvgB¢uw'y¡iOtsxmr4¢lgts¥iPgtr4G§
n2t
r4sLuw'y]mg'gqf'uw'y{mr4qf'g' 2aB¢³f'uve4feaxw2rp'sr4 qsg³r42n2t
r4smgsq&r4'u¤Lqsuw'y©mg'gqf'uw'y©qsr4e4f2w'u¤µ2p'r4©Ã Ä
>P

: >=G?I;>PKJ
>P
AÕ : >HG?I;>PKJ <
K >H>G?P I;>PKJ A{ : F>H>GP I > J Éu¼u¼ii ^ _ >H>HGG II >>PKPKJJ <K
S

P
/
> >P
>HG I >P J
YX
YX
[>
>
a$ 7$
>
[>
>
>
>
>
>
>
>
V
>
>
'
>
>
T
>
>
>
YX
[>
>
`
[>
>
T
[>
>
`
>
>
[>
>
[>
>
>
B
>
`
W
>
>
>
:
%$x$
>
>
>
>
^_
>
>
[
>
,
Å f2xBq]uva&u¼iExGw=¶®§Oytsxm >HG I >PKJ ge4eap2t²¯uwqf'r¡qtsxuw'uw'y| /xBqx®q_f'r¬r4sqLumxBqsr : F>H>GP I >PKJ Eu¤¡p'sr4 qf'uvor4sqLumxBqsr¡u¤yraw'ratsxBhvhvYx¦ 2u¤Le4gp2wqLr4 Yrat
Lu¤g'w=gBi?qf'r~moxB'um¯p2m°hvu¥Br4hvuf'gg'> ½P r4sqsumoxqsr=¾?qf'rat
¢uvsr
¢lr{2xBe4¥ogBÂ|qsgoxseaxBhvr4 rat²suvgwgBiqf'r¬P¶ «§OytLxm 2uvsqt²u2p'qLu¤g'w A{ : >=G?I;> J 4'¢³f'rat
r©qf'r©hvgB¢lrat«§
gt
2rat 2u¤Lqt
Fu>2P p'qsuvgw!uvoq
Kn'uveaxBhvhvY 2r_ª¿w'r4 $xw2xBhvgygp'Lh¤qLg´q_f'r~f'u¤y'f'rat«§Ogt
2rat 2uvsqt
u2p'qsuvgw7½Åf'rLeaxBhvuw'y
iOxBe4qsgt >HG I >PKJ ,u¤?e4f'gsraw¡qsgoxBs_p2t
r©qf2xBqraxe[f¡e4gw' 2uvqsuvgw2xhF 2uvsqt
u2p'qsuvgw¦p2mqsg Åf'r{xBhvyg't
uvqf2m
2r4seat
u®r4 G¡r4µKp2xBqLu¤g'w ,eaxw®r¯n'hxBe4r4 |uwqf'uvliOtsxmr4¢g'ts¥¢uvqf qf'r?iIgGh¤hvgB¢uw'yt
r4hxBqsuvgw'
: F>H>G?P I;>PKJ K A : F>H>G?P I;>PKJ
>P
K

>HG I >P J
A{ : F>H>G?P I;> J K A : F>H>G?P I;> J L
S
Åf'rat
roxt
rqf2t
r4ron2t
umoxt²´ 2uvsqLuw'e4qLu¤g'w'®r4q
¢r4raw¦mggq_f'uw'y|xBhvygt
uvqf2m ?¢³f'r4qf'rat©xw|xBhvygt²u¤q_f2mü¤
Ð /ÍPÎaÏ ÊKË - ÈG>ÍPP Î /g't sÈ ;Î /
Ë ³l¢³f2xBqq¹2n2r¦gBi© 2u¤Le4gp2wqLuw'yuvxn2n'hvuvr4 ½qsg=qf'rz=Á r4sqsumoxBqLr~qsg=eaxh¤eap'hxBqLr
: >HG I >P J 4/xw' ~f'gB¢½hvgB¢lrat«§Ogt
2rat, 2uvsqt
u2p'qsuvgw'{xGt
r©e4gmon2p'qs>r4 FP
wuwqsratLn2ghxBqsr4 ½mg' 2r4hvalqf'r~n2t
g'2x'uvh¤uvq
r4sqsumoxqsr : >=G?I;>PKJ gBiÕxGwY¶®§Oytsxm >HG?I;>PKJ ¢uvqf
w'gw 4rat
ge4gp2wql 2ran®raw' 2³gw¡q_f'r{n2t
g2x'uvhvuvq¹~xssuvyw'r4 qsgqf'r©e4gtLt
r4n2g'w' 2uw'y|P¶ ¹§Oytsxm >=G?I;> J 2xB
uw¡r4µKp2xqsuvgw= 4 w2xBe[¥r4 '§OgBÂ´mg' 2r4h¤2qf'r{n2t
g2xG'u¤hvuvq
r4sqsumoxBqLr³gBi&xw¬¶®§OytLxm·¢uvqfw'gw 4rat
ge4gp2wGqlu¤
2r4qsratsmuw'r4 ¢?f'u¤hvr©uvyw'gt²uw'yuwGiPgtsmxBqsuvgwi t
g'mhvgB¢rat¹§Ogt
2rat& 2uvsq_t
u2p'qsuvgw'a wGqsratsn2gGhxqsr4 ~mg' 2r4h¤uw'e4hp' 2r
r ©xBq r4hvuw'ra¥B§Oz|rat
e4rat mg'gqf'uw'y$Ã Ä xGw' YÔ$uvqsqsrawG§¹¸,r4hvh©mg'gqf'uw'yÓÃ Ä ³2xBe4¥Br4 '§OgBÂ mg' 2r4hvuw'e4hp' 2
mg'gqf'uw'y~Ã Ä /x'sgGhp'qLr© 2u¤Le4gp2wqLuw'y=Ã Ä 2xw' ©w'r4srat¹§ r4mggq_f'uw'y¦Ã Ä
>
>
T
>
>
[>
>
>
>
>
>
j:
>
>
>
[>
>
>
>
`
[>
>
>
>
>
>
T
>
j:
O
[>
>
>
#
[>
>
>
T
>
W
>
C
>
>
:
Åg 2r4seat
u2rqf'r] 2u¼Â rat²rawqq
2n2r4gik 2uvse4gp2wGqsuw'y/N¢lr©¢³t
uvqsr : >H>GP I >P J xB
: >H>GP I >P J <K ^ _ >=G?I;> PKJ F>H>G?P I;7>PKJ >HG I >P J >=G?I;>PKJ
^V_
¢³f'rat
r¿ >=G?I;>PKJ eaxw¦2r{'uvr4¢lr4 xqf'r{ 2uvse4g'p2wq©uwe4g'p2wq?n2xBe4rEi t
g'mqf'r{z=ÁÀr4sqsumoxBqLr¯xw' ¦¢³f'rat
r
F>HG?I;>PKJ ?u¤qf're4gwq_t
u2p'qsuvgw¦iOt
gmÒhvgB¢lrat«§Ogt
2rat? 2uvsq_t
u2p'qsuvgw'a~Åf'r;xBhp'r >HG I >PKJ ?uv2 4rat
giPgt
2xBe4¥Br4 '§OgBÂ mg 2r4hv´xGw' Yq
Kn'uveaxBhvhv >H>G?P I;>PKJ A{ : F>H>GP I > J iIg'touwGqsratsn2gGhxqsr4 mg' 2r4hva w - Ð /Î_ÈÏ
/Ð Ì _Ë /ÍPÐ 'aqf'rl 2uvse4gp2wGq7 >HG I >P J u¤,qx¥BrawEqsg©2r³n2t
g'n2gt
qLu¤g'w2xBhqLg³qf'rlgt²u¤yGuw2xh2e4gp2wq
>HG I >P J 4
^V_
xBuwr4µKp2xqsuvgw ¢³f'rat
rq_f'r 2uvse4g'p2wq&uvÕ ; 5 >HG I >P J 4 w¡È _Ì4Ë - 'ÍP3Î /Ð Ì Ë /ÍPÐ '7 >HG?I;>PKJ u¤
qx¥raw{qLg{2r³x?e4gw'LqxwGq woÇEgg' '§¹Åp2t
^ u_ w'y{ 2uvse4gp2wGqsuw'y/'qf'rl 2uvse4gp2wGquv,eaxBhveap'hxqsr4 p'Luw'y]qf'r
Ç©g'g' '§¹Åp2t
uw'yor4LqsumoxBqsroÃ Ä Kxqf'r4gt
r4qsuveaxBhvhvG§¹mgqsuv;xqsr4 ~ 2uvse4gp2wGq?qf2xBqf2xB2r4raw f'gB¢³w¡qsgo2r{xBe4eap2tLxBqsr
uw|w'gwG§On2xt
Lr{ /xBqxsuvqp2xBqsuvgw'Ã ' 2[Ä 2t²u¤r_il 2r4seat
un'qsuvgw¦gBi&qf'r¯ÇEgg' '§¹Åp2t
uw'yr4sqsumoxBqsr©uv©yuvraw uw
d'r4e4qsuvgw / r4h¤uw'ra¥§Oz|rat
e4rat©mggq_f'uw'y¡xw' ~Ô$uvqsqsrawG§¹¸,r4hvh&mg'gqf'uw'y¬p'sr]hvuw'raxGt? 2u¤Le4gp2wqLuw'y ©w'r4srat¹§
r4=mg'gqf'uw'y=p'sr4¯xG'sghp'qsr¡ 2u¤Le4gp2wqLuw'yNxw' ©xBq mg'gqf'uw'y=xw' jfp2t
e4fG§¹Ç{xh¤r¡mg'gqf'uw'yÃ 2LÄ
p'srÇ©g'g '§¹Åp2t
uw'yo 2uvse4gp2wGqsuw'y/
Åf'rª¿w2xh/mox gt 2u¤Lqsuw'e4qsuvgwo2r4q
¢lr4rawmggq_f'uw'y{xh¤yGgt
uvqf2m&uvf'gB¢qf'rhvgB¢lrat«§Ogt
2ratn2t
g2x'uvhvuv>q
oP r4
§
qsumoxBqLr4xt
r&eaxBhveap'hxBqsr4 FÔ½f'uvhvr±mgsq7mg'gqf'uw'y³mr4Fq_>f'P g 2 2r_ª¿w'rqf'r&hvgB¢lrat«§Ogt
2ratmg 2r4h A{ : >HG I > J
xw2xBhvgyGgp'shv~qsgq_f'rf'uvyf'rat¹§Ogt
2rat{mg 2r4<h A{ : >HG I >PKJ 47uw ©w'r4Lrat«§ r4|mggq_f'uw'y~x¡ 2u¼ÂFrat
rawGq{xnG§
n2t
gxe[f u¤?qx¥raw7Åf'rP¶ «§OytsxGmmg' 2r4huv?e[f'gLrawqsgo_xBqsuv
iPe4rat
qxBuwe4g'w'sqtsxBuwGqs? 2rat
uvr4 ¦i t
g'mqf'r
qtsxuw'uw'y¡ /xBqx22w2xmr4h¤
F>H>G?P I;>PKJ A© : F>H>GP I >PKJ , K ^ _ >HG I > J
Z
^_
iPgtxBhvhP¶ «§OytsxGm >HG?I;> J &Åf'uve4g'w'sqtsxBuwGqeaxw¡2r©t
ran2f2tsxsr4 ~F>xBP Åf'r³r42n2r4e4qLr4 ~wp2m2rat,gBiqsumr4
h A{ : >HG I >PKJ xGw' ~qf'rf'u¤Lqsgt
i t²r4µKp'raw'e4uvr4
>HG I > J ge4eap2t
?uwqf'r]qtsxBuw'uw'y¡ /xBqxyuvraw¦qf'r{mg 2r4<
>P
F>HG?I;>PKJ {_f'gp'hv r4µKp2xBhlqf'rxBe4qp2xh±w'p2m2rat]gBi³qLumr4ouvq¯g'e4eap2t
a ©w'r4Lrat«§ r4_mggGqf'uw'yéaxGw ®r
^V_
xn2n'hvuvr4 t
r4eap2t
Lu¤Gr4h¤|qsgh¤gB¢lrat«§Ogt² 2rat 2uvsqt²u2p'qLu¤g'w'aFuw¦¢³f'uve[f¦eaxBLr{qf're4gw'sq_tsxBuwqL¯Z ?xt
rw'gqxBqLu¤²ª/r4 r42xBe4qshv w'LqsraxB FNqf'r{t
uvyfGq
§¹f2xw' ~Lu¤ 2r]gBi&qf'r©e4gw'sqtLxBuwqsxt²r© 2u¤Le4gp2wqLr4 ´¢u¤q_fx'sghp'qsr] 2u¤Le4gp2wqLuw'yN
jf'raw=xw' Ç©g'g /moxGwÃ Ä n2t
gB'uv 2rxw r4qsraw'Lu¤Gr¬e4gmn2xt
uvsgwÀgBi³xBhvhgBiqf'r¢uv 2r4h¤G§¹p'sr4 !mg'gqf'uw'y
qsr4e4f2w'uvµKp'r4a,Åf'r4or4;xhp2xqsr³raxe[foxh¤yGgt
uvqf2mg'wox©¢uv 2r©tsxw'yrgBi¿qtLxBuw'uw'ysr4qLqf2t
g'p'yfuvqs&Ê2ÎaÏ Ê - Î BÐÑÍ ]gw
qsr4sq /xBqx2&Åf'rn2ratsn'hvr4'u¤q
I lgBixomg' 2r4h A]gw¦xqsr4sqlsr4aq I/uv³q_f'r{t
r4e4un2t
geaxhgBi&qf'r©yr4g'mr4qt
uve
xratsxByGrn2t
g2xG'u¤hvuvq
oqf2xBqqf'r³mg 2r4h/xBLsuvyw'&qsg©raxBe4f]¢g't
uwqf'rlqsr4sq&sr4qa&Åf'r4xBhvsg¯p'Lrq_f'r 2rat
uv;xBqLu¤Gr
mraxB_p2t
r aÏ
ËBÌ_Ì Î NÍPÏ¹Ë[Ê I < K$hvgy , I 4'¢³f'uve4feaxw®r©uwGqsratsn2t²r4qsr4 ~xBqf'r{xratLxByr³w'p2m2ratlgBi
'uvqs³w'r4r4 2r4 ¦qsgoe4g' 2r©raxBe[f¡¢lgt² ¬uwq_f'r³qsr4Lqsr4qp'suw'y¬q_f'r{mg 2r4h A'jf'raw|ÎÍÈ - Ã ' Ä xBhvsgoe4gw' /p'e4qLr4 r42n2rat
umrawGqs?uwGr4sqLu¤y'xBqsuw'yf'gB¢½q_f'r{eat
gL
§Orawq_t
gnGogBixohxw'yp2xyr{mg' 2r4huv³t
r4hxBqLr4 ~qsgouvqs©n2rat¹iIgtLmoxw'e4r
¢³f'rawp'sr4 uwx]n®r4r4e[f¦t
r4e4gyw'uvqsuvgw¡s'sqsram kÅf'r4oiPgp2w' x{Lqt
gw'yhvuw'raxtle4gtst²r4hxqsuvgw2r4q
¢lr4raw¡qf'r?q¹¢lg
mr4qt²u¤e4¢³f'rawe4gmn2xt
uw'ymg 2r4hv?qf2xBqlgw'hv 2u¼Â rat±uw mg'gqf'uw'y/
w|qsratsm©gBi±n®ratsn'hvr4uvq
jf'raw=xGw' ÇEgg' /moxwíIgp2w' Àqf2xBq ©w'r4srat«§ r4=mg'gqf'uw'y´xGw' ´Bxt
uxBqsuvgw'
e4gw'suvsqLrawqshvog'p'qn2rat«iPgtsmxh¤hNgqf'rat,xBhvygt
uvqf2mz|gt²rn2r4e4u¼ª/eaxBhvhvNqf'r4on2t
r4srawGq&iPgp2tmoxuwe4gw'e4hp'suvgw'
Åf'r,i xBe4qLgtFq_f2xBqxÂFr4e4qs&n2rat«iPgtsmoxGw'e4rq_f'r³mgsquvqf'rp'srlgBiFx©mg' 2u ª/r4 ¡hvgB¢rat¹§Ogt
2rat 2u¤Lqt
u2p'qsuvgw'
xBuw ©w'r4srat«§ r4omggq_f'uw'yNÅf'uvlu¤lqf'r©n2t
umoxt²¬t
raxBsg'w]iIg't&qf'r?r4e4r4hvhvrawGq³n2rat«iPgtsmxw'e4r³giqf'uv
xBhvygt
uvqf2m

>
[>
>
>
>
>
>
>
>
GT
>
>
>
>
>
>
>
>
>
3O
O
>
>
>
>
>
>
>
>
>
O
T
`
D
>
>
N
3
3O
O
>
>
>
>
[>
>
>
>
>
>
T
&
'
>
T
>
>
>

>
>
>
[>
>
>
>
>
*
>
j:
>
>
>
M
jO
QP
S
P
$
j:
2
1.8
trigram, 1MW training
ideal average discount
1.6
1.4
bigram, 1MW training
trigram, 200MW training
1.2
1
0.8
bigram, 200MW training
0.6
0.4
0.2
0
1
3
5
7
original count
9
11
13
&uvyp2t
r 2raxBh&xratsxByGr© 2u¤Le4gp2wq?iPgt?¶®§Oytsxm¢uvqf¦yuvrawe4gp2wGq?uw¦qtLxBuw'uw'y /xqxiPgt muvhvhvu¤g'w=¢lgt
qtsxuw'uw'y¡sr4q³xw' omuvhvhvu¤g'w~¢lgt² qtsxBuw'uw'yosr4qaN'u¤y'tsxmxw' ¦qt
uvytsxGm mg 2r4hv
:
' sgGhp'qLr¯ 2uvse4g'p2wqsuw'y¦u¤©_p2n2rat
uvgt?qsg¡hvuw'raxt© 2uvse4gp2wGqsuw'y/ /gt?¶®§Oytsxm³¢uvqf|xyuvraw¦e4gp2wGquw
qf'roqtsxuw'uw'y| /xBqx®q_f'r4éaxh¤eap'hxBqLrqf'rxratLxByr 2uvse4gp2wGq¯uwÀe4gp2wGq¯_n2xBe4r 7 >HG?I;>PKJ ?iOt
gm qf'r
z Á r4sqsumoxBqLrqf2xBq&¢lgp'hv ¡eaxp'srqf'r?r42n2r4e4qsr4 wp2m®ratgi¿qf'r4sr©¶®§Oytsxm&uw¡x©qLr4sqsr4q,qsg{2r?r4µ2p2xBh
qsgqf'r4ut³xBe4q_p2xBhw'p2m¯®rat¯ xBsp2muw'y l >HG I >P J , K 4Åf'uv?uv 2raxBhkxratLxByr© 2uvse4gp2wGq³uv? 2uvn'hxaGr4 uw &uvyp2t²r iPgt,e4gp2wGqs a iPgt,q¹¢lg]qtsxBuw'uw'yosr4qs,iPgtl'uvytsxmxGw' ¬qt²u¤y'tsxmmg' 2r4h¤, 7t
gm·qf'uv
ytsxn2f7¢rsr4r¢³f=xª/r4 = 2uvse4g'p2wq¢lgts¥G©¢lr4h¤hP¡Ô½f'uvh¤rÇ©g'g' '§¹Åp2t
uw'y| 2uvse4gp2wGqsuw'y|u¤xBe4qp2xBhvhv
2r4qsqsrat±qf2xw~xG'sghp'qsr© 2uvse4gp2wGqsuw'y~xBq³n2t
r4 2uve4qsuw'yqf'r¡È aÎÏ
È Î 2uvse4gp2wGqaNuvq³f2xB?r4qqsg¬®r¯p'sr4 ¦uw
p'e[fx¢±x¬xqsg¬n2t
r4 2uve4q?qf'r©e4gtst²r4e4q 2uvse4gp2wGqs³uw uw' 2uv'uv /p2xBh& 2uvsqt
u2p'qsuvgw'©¢lr4hvhP
wGqsratsn2gGhxqsr4 ´mg' 2r4hv©gp'qn®rat«iIg'tsm2xBe4¥Br4 '§OgBÂ mg 2r4hv?¢³f'raw¦e4gw'suv 2rat
uw'y~n2rat«iPgtsmxw'e4r{gw ²p'LqÕ¶®§
ytsxm¢uvqf!h¤gB¢ë4gp2wGqsuwYq_f'r~qtsxuw'uw'y! /xBqx2Åf'uvu¤~®r4eaxp'sr|hvgB¢rat¹§Ogt
2rat¡mg 2r4hv~n2t
gB'uv 2r
;xBhp2x'hvruwGiIgtLmoxBqsuvgwiPgtlr4sqLumxBqsuw'yoqf'r{n2t
g'2x'uvh¤uvqsuvr4]gBi*¶®§OytLxml¢uvqfhvgB¢½e4gp2wGqsa
2 2uw'y¦i t²r4r¬n2xtsxmr4qsrat
©qsg~xwÀxBhvygt
uvqf2mÒxw' Àgn'qsumu 4uw'y=qf'r4sr¬n2xGtsxmr4qsrat²©gw=f'r4hv '§Ogp'q /xBqx
eaxw¡umon2t
gBr©qf'r{n®rat«iIg'tsmoxw'e4r]gBikxw¦xBhvygt
uvqf2m
¸lxBsr4 =g'w~q_f'r4srog'srat²;xBqsuvgw'jf'raw=xGw' ÇEgg' /moxwÀn2t
gn2gGsroxw|xBhvygt
uvqf2m°w2xmr4 0Ë /GÐ lÎ / /Î4Ì4ÎaÏ Î ¦Ì ËËÍ Ð ~q_f2xBqu¤iIgp2w' !qsg|gp'qn®rat«iIg'tsm xBhvhgqf'ratmr4qf'g' 2oe4gw'Lu¤ 2rat²r4 F qouv¬xwuwqLratsn2ghxBqLr4 ;xGt
uxBqsuvgwgi ©w'r4srat¹§ r4mggq_f'uw'y¢uvqf~xwxGp'ymrawGqsr4 rat
suvgw gBix'sghp'qsr© 2uvse4gp2wGqsuw'y/ w'sqsraxB gBi
p'suw'y~xsuw'yhvro 2uvse4gp2wGq ïPgtxBhvh¶®§Oytsxma/q_f2t
r4r{sran2xGtsxBqsr] 2u¤Le4gp2wqL P[ Fxw' Axt²rp'Lr4 ~iPgt
¶®§Oytsxm¢uvqfg'w'r©e4gp2wq2q
¢ge4gp2wqLa2xw' ~qf2t²r4r{gtmgt
r©e4gp2wGqsa/t²r4n2r4e4qsuvr4hvÅf'uv?uvÕmgGqsuv;xBqsr4 |
qf'r]g'srat
BxBqsuvgwq_f2xBqlqf'r{uv 2raxBh 2uvse4gp2wGqiPgtlgw'r_§Oe4g'p2wqs©xw' q
¢lgB§Oe4gp2wGqsuv?suvyw'u¼ª/eaxwqLh¤¦moxBhvhvratqf2xw
qf'r©uv 2raxBh 2uvse4gp2wGq³gBihxGt
yratle4gp2wGqsaNxBf'gB¢³w¡u#w &uvyp2t²r
>
>
>
>
0

jP
O
O
&
(
: 4%@),+
&
Ô=r,eaxw]e4gw'sqtsp'e4qhxw'yp2xByGr±mg 2r4hv&rat
©Lumu¤hxtqLg³e4gwGrawGqsuvgw2xBh2¶®§Oytsxmmg' 2r4h¤&¢u¤q_f'uwqf'rmoxump2m
rawGqt
gnGiOtsxmr4¢lgtL¥/oÅf'rmoxB'ump2mÒrawGqt
gnG´mg' 2r4hv 2r4seat
u2r4 uwd'r4e4qsuvgw xt
r guwGq¯mg' 2r4hv &qsg
eat
raxBqLr~qf'r|e4gw' 2uvqsuvgw2xBh? 2uvsqt
u2p'qsuvgw'|p'sr4 $uwYe4g'wrawGqsuvgw2xBh©¶®§Oytsxm mg' 2r4hv¢r|p'sr|qf'riOtsxmr4¢g'ts¥
uwq_t
g /p'e4r4 |¸lt
gB¢³w|ÎaÍ,È - FÃ Ä w'sqsrax ~gBir4LqsumoxBqsuw'y¬x guwGq 2uvsqt
u2p'qsuvgw A2Z B/,gBrat,xmn'h¤r4J BF'¢lr
$
r4sqsumoxqsr¬x¡e4gw' 2uvqsuvgw2xBhl 2uvsqt²u2p'qLu¤g'wbA2 : B/?gBrat?_xmon'hvr4~ZBQ 4 w'LqsraxB =gBie4gw'LqtsxBuwGqs{xB{yGu¤Graw=
r4µ2p2xBqsuvgw 4¢lr{f2xr©e4gw'LqtsxBuwGqsgBi&qf'r?iPgtsm
Z
] [ Z B/ A2 : BN ¹Z BQ K
] [ ZB8Q ' ¹ZB8Q ' S
&
=69>
&
< =69>
< Åf'uveaxw!2r|uwqsratLn2t
r4qsr4 Óxt
ran'hxBe4uw'y AKCBQ ']uwYq_f'r guwqiIg'tsmp'hxqsuvgw¢uvqfN[ CB/A2 : B/ YÅf2xBq¡uva
¢lr¬xBs_p2mroqf2xBqf'uvsqsgt
¦iOt
r4µ2p'raw'e4u¤r4 ] [ ZB/©xGt
roqx¥raw¦i t²gm¨qf'r¡qtsxBuw'uw'y| /xBqx2x] w' =¢lrogw'hv=r4sqLumxBqsr
e4gw' 2uvqsuvgw2xBhn2t
g2x'uvhvuvqsuvr4aÒjlgw' 2uvqsuvgw2xBh]z=mg' 2r4h¤¦f2xt
r=moxGw!gBi¯qf'rÀxmr=n2t
gn®rat
qsuvr4´x(¹guwGq
mg' 2r4hvaluw'e4hp' 2uw'y$2r4uw'y mxBump2mÉh¤u¥Br4hvuf'g'g mg 2r4hvaxw' Yf2xre4g'mon2p'qxBqsuvgw2xh±xGw' Ón2rat¹iIgtLmoxw'e4r
xB 2Bxwq_xByr4lgBraHt guwqmg' 2r4hvuw¡hxw'yp2xByr©mg' 2r4hvuw'y|Ã 2 Ä e4g'w' 2u¤qLu¤g'w2xBhFmoxB'ump2mrawGqt
g'nomg' 2r4h
f2xBq_f'r?iIgtLm
Z
A & : B/<
K Z BN r4Kn 8P C BQ 's S
Åg¡e4gw'sqtsp'e4q{xmxBump2m¨rawGqt
gnG~¶®§OytsxmÒmg' 2r4hPF¢lrqx¥B2r BK F>H>GP I >PKJ qsg~®roqf'rof'uvsqsgt
|xw' 2K
qsgo®r¯q_f'r?iIghvhvgB¢uw'y¬¢lgt² F< /gt±raxBe[f §Oytsxm K >HG $>PKJ ¢u¤q_f )K QTSTSUSQ¶¦qf2xqg'e4eap2t
?uw
qf'r©qtLxBuw'uw'y /xBqx2G¢r©uw'e4hp' 2r¯xe4gw'sqtsxuwGqlqf2xBq*iIgt²e4r4qf'r?e4gw' 2uvqsuvgw2xBhFr42n2r4e4qxqsuvgwgBi ¯xe4e4gt
2uw'yoqsg
A]qsg¬®r©qf'r{xGmr{xBluvqsiOt
r4µ2p'raw'e4uwqf'r©qtLxBuw'uw'y¡ /xBqx®kÅf'r{e4gtst²r4n2gw' 2uw'yiIraxqp2t
r4 BZ BQ lxt
r
Z BQ K u¼gGiÕqf'Z B8rat
Q ¢'uvsK r >=G?I;>PKJ raw' 2³uw
S
d2p2'sqsuvqp'qLuw'y¡qf'r4srEiIraxqp2t
r4uwGqsgor4µ2p2xBqsuvgw=Z xw' sumon'hvu¼iI'uw'y/7¢lr{xtst
uvr{xBqe4gw'sqtsxuwGqslgBi&qf'r?iPgtsm
F>P
F>P
KN] [ B S

] [ >HG I >PKJ A2 : >HG I >PKJ ,
G
J
w´i xBe4q7qf'rgw'hv´Lghp'qsuvgw|qsgqf'r4Lr¯e4g'w'sqtsxBuwGqs©uv A2 : B/ K A 9O : B/4]jlgw'sr4µ2p'rawqLh¤qf'romoxump2m
rawGqt
gnG=mg 2r4h,uvouv 2rawqsuveaxBhlqsg¦qf'rmoxB'ump2m h¤u¥Br4hvuf'g'g ½¶®§Oytsxm°mg' 2r4hxw' uvq¯¢u¤hvh2r2raw'r_ª/e4uxBh?qsg
mg'gqf¡q_f'r©r4sqsumoxBqsr4gBikq_f'r{mg 2r4hn2xtsxmr4qLrat
/K M VY
ramoxts¥x'hvq_f'r³sr4q,gBimg' 2r4h¤lyuvraw¡G¯r4µ2p2xBqsuvgw|Z ¢u¤q_f¬¶®§OytsxGmiPraxBqp2t
r4,u¤luv 2rawGqsuveaxBh7qsg{qf'rsr4q
gBikmg 2r4hvl 2r4seat
u2r4 |r4µKp2xBqLu¤g'w= 4G¢³f'uve[f¡¢lr³p'sr4 qLg{r42n2t
r4s³mgGsqr4'uvsqsuw'yomg'gqf'uw'yoxBhvygt²u¤q_f2m
iPgtFe4g'wrawGqsuvgw2xBh/¶®§OytLxm mg 2r4hvaÅg©sr4rlqf'uvaGh¤r4qp', 2r_ª¿w'r³xsr4q&gBi §Oy'tsxmmg 2r4hv A : F>H>GP <>PKJ
iPgt )K QUSTSUS Q_¶¬x&uwr4µ2p2xBqsuvgw~Z G4B¢³f'rat
rraxe[f §OytsxGmmg 2r4hNgw'hve4gwq_xBuw'&iPraxBqp2t
r4&e4gtLt
r4n2g'w' 2uw'y
qsg¡¢lgt
~Lr4µKp'raw'e4r4p2n|qsg¡h¤raw'yGqf |Fxw' |¢³f'rat
roxBhvhmg' 2r4h¤]f2xt
r]qf'rxmron2xtLxmr4qsratsr4q ©©Åf'raw7
qsgo 2r4Leat
u2r{q_f'r¯moxB'ump2mrawq_t
gnG¬mg' 2r4h7iIg'tsmuwqsratLmgBir4µ2p2xBqsuvgw 4'¢lr©qx¥r
: >=>G?P I;>PKJ K A k : >=>G?P I;>PKJ
>P

>HG I > J
>P
8 A k : >=G?I;> J
K r42nF
9
8
>P
>HG I >P J
>P

>HG?I;> J
>P
: >=G?I;>PKJ K

>H>G?P I;>PKJ
A{ : >=>G?P I;> J K A k : >=>G?P I;> J S
8
YX[Z
,
&
\]
>
>6j>
`
>_^
>
>
>
>
/6
6
B
'
* >
>
&
0
'
*
>
>
>
>
>
W
^
X
[b
`
YXZ
>
>
[>
>
>
Ib
YX[Z
>
[>
>
\]
` '
[>
>
>
>
\] >
>
] \
>
YX[Z
>
>
\]
*
>
[>
>
>
>
>
>
>
YX[Z
[>
>
>
>
/g't©xw|mg' 2r4hgBilqf'riPgtsm 7¢reaxw e[f'g'gsr p'suw'y~q_f'r¬x2gBrr4µ2p2xBqsuvgw']sqxt
qLuw'y¡iOt
gm¨hvgB¢lrat«§
gt
2rat,mg' 2r4h¤,qsg{f'uvyf'rat«§Ogt² 2ratqLg©e4gw'sqtsp'e4qxGwr4µKp'uvBxBhvrawqr42n2g'w'rawqsuxBh7mg' 2r4hI ¸r4eaxGp'srmg'gqf'uw'y
r4sqsumoxqsr4{uwmoxB'ump2m rawqt²gn|¶®§Oytsxm°mg 2r4hvoxw' =_mggGqf'uw'y~e4gwGrawGqsuvgw2xBh¶®§Oytsxm°mg' 2r4h¤o®gqf
e4gw'suv 2ratqf'r©xmr©e4hxs³gi*mg' 2r4hva2qf'r4Lr{q
¢lg¯q_xB¥G±xGt
r©e4hvgsr4hv~t
r4hxBqsr4 F
`
`
V&
(
(%*),+
&
w»qf'uvosr4e4qsuvgw!xw' Yd'r4e4qsuvgw &¢lrp2t
r4n2t
r4'uvgp'o¢lgts¥|uw!moxB'ump2m rawGqt
g'n mg 2r4h_mggGqf'uw'y/
/GÐÌË NÍPÐ ¯È ;Ð
Î NÍPÏ
Ë_Ê Bxw' [ÈGÍ _Ë ®Ì[ÍPÏ
ÈÐ /Í9Ìuw!qf'r
rat
r¢lr~ 2uvseap'LËaË0/ 'ÏÐ
iPghvh¤gB¢uw'y¡sr4e4qsuvgw7N¢lr{n2t
r4srawGqqf'r¯Ç]xp'ssuxwn2t²u¤g't³mr4q_f'g |n2t
gn2gGsr4 ~~ÁxÂFrat
q
w 2r4seat²u'uw'y¦qf'r4sr
mr4qf'g' 2a&¢lr¡sgmr4qLumr4¬p'sr¡qf'(r ¹gGuwGqomoxB'um¯p2m°rawGqt
gnG|iPgtsmp'hxBqsuvgw iIg't{Lumn'h¤uve4uvq
hvhgBi?qf'r4sr
qsr4e4f2w'uvµKp'r4{xn2n'hv¦r4µKp2xBhvhv|¢lr4h¤hqsgoe4g'w' 2u¤qLu¤g'w2xBh&z=Ymg' 2r4hv 7qf'roxw2xBhvgyg'p'e4gw' 2uvqsuvgw2xBh&z=!r4µKp2xqsuvgw'
eaxw®r{ 2rat
uvr4 |~t
ran'hxBe4uw'#y B¢uvqfZ BQ ,xw' A2Z BN,¢uvqf ] [ C B/ A2 : B/
%&$ H 6<6<;
."45+?1 @H +X 6."135+&1<@
<
Ç©g'g' '§¹Åp2t
uw'y= 2uvse4g'p2wqsuw'y f2x¯2r4raw!n2t
gn®gsr4 ÁxpYÃ Ä xw' gLrawGiIr4hv ½Ã Ä xw' eaxw ®ruvr4¢lr4 xB
qf'r¬mxBump2mÒrawGqt
g'n|xw2xBhvgyqsg ©xBq omg'gqf'uw'yiPgt?e4gwGrawGqsuvgw2xBh¶®§OytsxGm mg' 2r4hva¬Åf'r4|g'Lrat
r
qf2xBqlqf'r©moxt²yuw2xBhvgiqf'r{mg' 2r4h AK : BN&f'g'p'h¤ ~w'gGq±®r©e4gw'sqtLxBuw'r4 qsg¯®r©r4KxBe4qLh¤¡qf'gLr³gBiqf'r³ramn'ut¹§
uveaxBh 2u¤Lqt
u2p'qsuvgw ] [ : BN4/2p'q?uw'sqsraxB |qxt²yr4q;xhp'r4]f'gp'hv =2r 2uvse4gp2wGqsr4 =xB?uw¦e4gwGrawGqsuvgw2xBh¶®§OytLxm
mg'gqf'uw'y/ w'sqsrax gBike4g'w'sqtsxBuwGqs³xByuvrawr4µ2p2xBqsuvgw= 4'qf'r4n2t
gn2gGsr{qf'r?iPghvhvgB¢uw'y¬e4gw'LqtsxBuwGqs
>P
>P
K ][ ;
] [ >HG?I;>PKJ A2 : >HG I >P J <
G J
¢³f'rat
r ][ Bluvqf'rÇ©g'g '§¹Åp2t
uw'y¡r4sqsumoxBqsr©giqf'r©iOt
r4µ2p'raw'e4gBi '
Åf'r{Ç©g'g '§¹Åp2t
uw'yr4sqsumoxBqLroÃ Ä uvÕxqf'r4gt
r4qsuveaxBhvhv´mgqsuv;xBqLr4 ´mr4qf'g' iPgtlr4LqsumoxBqsuw'y¡qf'r{xratsxByr
2uvse4gp2wGqiPgt?xwr4Grawq³2xsr4 ~gw uvqs³e4g'p2wq?uw~q_f'r{qtsxuw'uw'y¡ /xBqx2" /g't³xw¡r4Grawq?qf2xBqg'e4eap2t
qsumr4?uw
` xmn'h¤r42uwoe4gwGqtsxsq¢uvqfqf'r©moxB'um¯p2m·hvu¥Br4hvuf'gg' |r4sqsumoxBqsrW 'qf'r©Ç©g'g' '§¹Åp2t
uw'yor4LqsumoxBqsrgiqf'r
r4rawGTq q_tsp'r?i t²r4µKp'raw'e4uv W ¢³f'rat²r
K ¶ ¶ A8P
xw' o¢?f'rat
r³¶ u¤,qf'r³w'p2m2rat&gi mram2rat²gBi7qf'r³n2g' n2p'hxqsuvgwo¢u¤q_fr4Kxe4qshv ?e4g'p2wqs ©xq©Ã Ä p'yGyr4sqs
xn2n'hv'uw'y¦qf'uv{r4sqLumxBqsr{qLgraxBe[f guwq §Oy'tsxm 2u¤Lqt
u2p'qsuvgw7 K QUSTSUS Q_¶7sran2xtsxBqLr4h¤ ¿p2t
qf'ratLmgt
r
xBl¶ eaxw¬®r©rat
hvgB¢Óg'<t 4rat
gEiIgt*hxt
yr ' ©xq ³n2t
gn®gsr4x{mr4qf'g ¡¢³f'rat
r©¶®§Oytsxm¢uvqfhxt
yr?e4gp2wGqs
xt
row'gq© 2uvse4g'p2wqsr4 xw' | 2uvse4gp2wGqs©iPgt?hvgB¢e4gp2wGqs{xt
roxB sp'sqsr4 =qLg¬e4gmn2raw'xBqLroÁFxp=xw' gGsrawGiIr4hv p'sr]qf'r ©xBq ©Bxt
uxBqsuvgw gBikÇ©g'g' '§¹Åp2t
uw'y¡ 2uvse4gp2wGqsuw'y/
gB¢lr4rat4¢?f'rawe4gw'sq_tsxBuw'uw'ymoxGt
yuw2xBhvgBixmg 2r4hqsg¬Ç©g'g' '§¹Åp2t
uw'y¡ 2uvse4gp2wGqsr4 ´moxGt
yuw2xBhvgBi&qf'r
qtsxuw'uw'y= /xqx2qf're4gw'sq_tsxBuwqL¯mox w'g|hvgw'yrato®re4gw'suvsqsrawGqoxw' Yx|moxB'um¯p2m°rawGqt
gnG=mg' 2r4h³mox
w'gqr4'uvsqa /gtlr42xmon'hvrNuw´xqt
uvytLxmmg' 2r4he4g'w'suv 2ratliPraxBqp2t
r4?qf2xBqe4gw'sqtsxuw qf'r©iOt
r4µ2p'raw'e4uvr4©gBiqf'r
¶®§Oytsxm |xw' L! |xw' =xBsp2mrqf2xq³qf'r¢lgt
L!|g'w'h¤¦iPghvhvg;¢©qf'r¢g't
|uw
qf'r©qtLxBuw'uw'y¡ /xBqx®kÅf'raw7/¢lr©¢uvhvhf2xr©qf'r]e4gw'sqtsxuwGqs
K ] [ ! 2
: " L!7<
] [ " !7 A2
#
%$
'&"()
+3
O
3NO
O 1 3
P
nM 3
jO
QP
1
O
O
W
&
'
*
'
*
>
>
[>
>
>
^
/
"
)
)
"
"
.
#
)"
(gc+d7eegY{9q-=w=r-eou%v}eq-f u7kYpeg|wvgp+wYfeg|Yhk=u%elujpq-wmrks9eor-fvgw=u9u7kYpQeg|Yh9ile}ff h9ilk=~%w=~9qxrxq-pq egfegY{%w=rpk
z_k=iGpd7eegY{jq-=wmr-eou7vge/pk
u7kYpkvgvo{jiiqxu%yqxu
d7kmr-s
pd7e{9ujq-ymilwR[ksjeorQymq-Yelu
~j/egY{%wpq-kmu
pd%eGpilw=qxu9qxu7ysjwYpwj+c+djq-f q-fyYeou7eoilw=rxr-Ipd%eGvgwfet+q-pd
G{%fpGwffq-ymu
geoilkDkmiQkmu7eY
u
wYsjs;q-pq-k=u
pd%eDfwYeh9ilk=~%w=~9qxrxq-p 2pkwmrxrQt+kmilsjf
eg|Yq-fpqxu%y/f[kkYpdjqxu7ywmr-ykmiq-pd7[fg
xw' 7<K ][ L! 2 S
w]yraw'ratLxBhPB¢r&¢u¤hvh/f2xr ][ " L! 2 K ][ L! 2suw'e4r 2uvse4g'p2wqsiPgt¶®§OytLxmFgBi/ 2u¼ÂFrat
rawGq
hvraw'yqf|xt
r]eaxBhveap'hxBqsr4 =uw' 2ran2raw' 2rawGqshv e4g'w'sr4µKp'rawGqshvFq_f'r4sr{e4gw'LqtsxBuwGqs³¢u¤hvh®r¯uw'e4gw'Lu¤Lqsrawq w|n2tsxBe_§
qsuve4r7qf'rat
rxt
rw'g¬ 2ut
roe4g'w'sr4µKp'raw'e4r4©qLgf2x'uw'y¡uw'e4gw'suvsqsrawGq{e4g'w'sqtsxBuwGqsalÔ½f'uvhvroqtsxBuw'uw'y~xBhvygt²u¤q_f2m
p'e4f~xBu¤qLratsxBqsuvr]seaxBhvuw'ymoxw'gqe4gwGrat
yGr/xot
raxBLgw2x'hvr¯n2t
g'e4r4 /p2t
r]u¤?qsgoLqsgn¡qtsxuw'uw'y¡gw'e4r¯n®rat«iPgt«§
moxw'e4rgwsgmr±f'r4hv '§Ogp'qlsr4q,sqsgn'&umon2t²g;'uw'y/ gB¢r4Grat4Buw'e4gw'suvsqsraw'e4ouvls2mon'qsgmxBqsuvelgBi¿e4gw'LqtsxBuwGqs
qf2xBql¢uvhvhh¤rax ~qsg¬n®gg'tn2xtsxmr4qsrat,r4sqsumoxBqsr4
ÁxpoÃ Ä e4g'mon2xt
r4qf'rn2rat¹iIgtLmoxw'e4rgi¿Ç©g'g '§¹Åp2t
uw'y³ 2uvse4g'p2wqsuw'y?iPgt7mggq_f'uw'y?z=~¶®§OytsxGm½mg' 2r4h¤
¢uvqf| 2r4hvr4qsr4 ÀuwGqsratsn®ghxBqsuvgw!Ã Ä Fx¡Bxt
uxBqsuvgw|gi r4hvuw'ra¥B§Oz|rat
e4rat]mggq_f'uw'yN7iPgt?e4gwGrawqLu¤g'w2xBhk¶®§OytLxm
mg' 2r4hva</g'tx mu¤hvhvuvgw¢g't
{qtLxBuw'uw'y©Lr4q&gBi/Ô xBhvh/d'qt
r4r4q gp2tLw2xBhqLr4qaB 2r4hvr4qsr4 uwGqsratsn®ghxBqsuvgw'uvr4hv 2r4 ¬x
n2ratLn'h¤r4'uvq
{gBi gw]x 5 2 &¢lgt² ©qsr4sq7sr4qaÅf'rmoxump2m$rawGqt
gnGÕmg 2r4h'uvr4hv 2r4 ¬xlshvuvyfGqshv©p2n2rat
uvgt
n2ratLn'h¤r4'uvq
gBi 2 ¢³f'rat
r¬xh¤hl¶®§Oytsxm]qf2xBq©g'e4eap2tst
r4 gw'hv=gw'e4rouwÀqf'roqtLxBuw'uw'y| /xBq_x¡¢rat²ror4e4hp' 2r4 iOt
gmq_f'r³z=mg' 2r4hP gB¢r4Grat4BhxBqsratt
r4_p'h¤qL±G¬jf'rawxGw' ÇEgg' /moxw¦Ã Ä sqt
gw'yGh¤uw' 2uveaxBqsr]qf2xBqgGqf'rat
mg'gqf'uw'y³mr4qf'g 2iPgtNe4gwGrawqsuvgw2xh¶®§Oytsxm½mg 2r4hvaBp'e4f{x mg 2u¼ª/r4 ©w'r4srat«§ r4{mggq_f'uw'yNa¢lgp'hv gp'qn®rat«iPgtsm 2r4hvr4qsr4 ¦uwGqsratsn®ghxBqsuvgw|Gxomp'e4f¡hxt
yratmxt
yuw7
<% <. 9 ')(*,+?-.,- 02135456879
w¡q_f'rli p R4moxB'ump2m rawGqt
g'n]iOtsxmr4¢lgts¥E 2r4r4hvgn2r4 | ©r4h¤hx uvr4qtLx¯xGw' ©r4hvhx uvr4qtLx¬Ã Ä uw'sqsrax gBit
r4µKp'ut
uw'y=q_f2xBq©e4gw'sqtLxBuwqs{xGt
roxBqLu¤²ª/r4 =r4Kxe4qshvkx¦n2raw2xBhvq
|uvxssg'e4uxqsr4 =¢uvqf|uw'r42xBe4q{e4g'w'sqtsxBuwGq
xBqLu¤²i xBe4qLu¤g'w7 &uw' 2uw'yqf'rmoxB'um¯p2m£rawq_t
gnG{mg 2r4hNuvr4µ2p'u¤BxBhvrawqlqsgª¿w' 2uw'yqf'r³mg' 2r4h A2Z B/xqsuv
iI'uw'y
qf'ryuvraw|e4g'w'sqtsxBuwGqs?qf2xBq©muw'umu 4r4qf'r ©p'h¤h2xBe4¥§¹Á7r4u'hrat 2uvsqxw'e4r |Z A ] ±iOt
gm qf'r¬p2w'u¼iIg'tsm
mg' 2r4h ] ¹Z BN4 w¡iOp R4moxB'ump2m rawq_t
gnGq_f'r©g r4e4qsuvr?i p2w'e4qLu¤g'wuv³q_x¥Braw¡qsgo2r
´Z A ] oZ AB

¢³f'rat
r 5 uvlx{n2raw2xh¤q
]iOp2w'e4qsuvgw¬muw'umu 4r4 ¢³f'rawe4gw'sqtsxuwGqslxt
rlxBqsuv
ª/r4 r4KxBe4qLh¤¡xw' ]uv±x?¢lr4uvyfGq
§
uw'yn2xGtsxmr4qsrat ©r4hvhx uvr4qtsxoxGw' ©r4h¤hx uvr4qtsxp'yyGr4sqxon2raw2xBhvq
¡iOp2w'e4qsuvgwgBi&qf'r?iPgtsm
A2ZB/ sZBN
S
ZAB<K P
] [ ZB/ sZBN
Åf'uv³n®raw2xBhvq¹i p2w'e4qsuvgw¡eaxGw¬®r³uwGqsratsn2t
r4qsr4 ~xq_f'r³hvgyxGt
uvqf2mgBi&x¯Ç]xp'ssuxw 2uvsqt
u2p'qsuvgw¡¢u¤q_fo 2uxByg'w2xBh
e4gB;xt²uxGw'e4roe4rawqLrat
r4 =xt
gp2w' |qf'rqxt²yr4q³e4g'w'sqtsxBuwGq³BxBhp'r4aÅf'ro;xGt
uxw'e4r xBssg'e4uxBqsr4 |¢uvqf iIraxqp2t
r
²C B/eaxw|2rr4sqsumoxBqLr4 ~iOt
gm qf'rramon'ut
uveaxBh& 2uvsqt²u2p'qLu¤g'w=gBi sZ B/uw|qf'rqtsxuw'uw'y /xBq_x2 ©r4h¤hx u¤r4q_tsx
xw' ©r4hvhx uvr4qtLx~ 2r4Leat
u2r´x¦Bxt
uxwGq¯gi³yraw'ratsxBhvu 4r4 YuvqsratLxBqsuvrseaxBhvuw'y=qf2xq¯eaxGw ®r~p'sr4 qsg¦ª¿w' qf'r
gn'qsumoxhmg' 2r4hp2w' 2ratq_f'u¤g r4e4qsuvr©iOp2w'e4qsuvgw=Ã Ä
ÔÀreaxw]uwqLratsn2t
r4qqf'uvxBhvygt
uvqf2m i t²gm½q_f'r'uvr4¢³n2gGuwGq&gBi¿moxump2m È±ÊKËBÌ4ÍPÎaÏ_Ð9ËÏÐl9z Õ 7r4sqsumoxqsuvgw7
w z © r4sqLumxBqsuvgw7F¢lroxBqsqLramon'q³qLg¡ª¿w' =qf'romg' 2r4,h A¡¢uvqf¦qf'r¬f'uvyf'r4sqn2gsqLrat
uvgt©n2t
g2x'uvhvuvq
´yGu¤Graw
qf'r©qtLxBuw'uw'y¡ /xBqx I
xt
ylmoxB taZ A : I= K½xt
ymox tZ AB t4 I : AB K½xt
ymox Ã hvgy taZ AB hvgy ta I : A; Ä S
][
&
'

>
[>
!/ AK
L
a "
: [>>
!7<K ] [ L!7A2
)
"
: )
"
(
"
a
"
8
&
>_^
>
&
m6j>
<
T
&
m6j>
<
>
69>
69>
:
W
Åf'r,z © g
r4e4qsuvriOp2w'e4qsuvgwf2xBq
¢lglqsratsm;xn2t²u¤g'tFqsratLm - Ë taCA;xw' ¯xlhvu¥Br4hvuf'gg' ¡qsratsm - Ë t[ I : A;
Åf'r,iOp R4{z=¦g
r4e4qsuvr,i p2w'e4qsuvgw]yuvraw]uw]r4µKp2xqsuvgw uvxw2xBhvgygp'qsg?qf'rlz Õ g
r4e4qsuvr*i p2w'e4qsuvgw7
Åf'rlª¿t²sqqsratLmuwor4µ2p2xBqsuvgw¦ raw'e4gp2tLxByr4q_f'r³mg' 2r4hA?qsgf2xaGr±f'uvyfrawGqt
gnGxw' eaxwo2r?qf'gp'y'fq&gBi
xBqx¥Guw'y³qf'rt
gGh¤r,gBi¿x?n2t
uvgt 2uvsqt
u2p'qsuvgw]iOxgt
uw'y³mgt
rp2w'u¼iPgtsmmg' 2r4hvaÅf'r,sr4e4gw' qsratsm raw'e4gp2tsxyr4
A?qsg©xqsuv
iIqf'ryuvrawoe4g'w'sqtsxBuwGqsa2Ð Î Gqsg?ª/qq_f'rqtsxBuw'uw'y /xBqxE¢r4hvhPÅf'uv,qsratsm n'hx'x©Lumu¤hxtlt
gGh¤r?xB
qf'r]h¤u¥Br4hvuf'g'g qsratsm uw~z © r4sqsumoxBqsuvgw7 gB¢r4Grat4/2gGqfqsratLm³uw¦qf'rEi p R4¦z !g ¹r4e4qsuvrEi p2w'e4qLu¤g'w
xt
r,rat
© 2u¼ÂFrat
rawGqqf2xGw©qf'r4utz Õ e4gp2wGqsratsn2xt
qLa w¯ÁxÂFrat
q
FÇ]xp'ssuxwn2t
uvgtmr4qf'g' {qsg©2r, 2uvseap'ssr4 uw~d'r4e4qsuvgw /xq_tsxB 2uvqsuvgw2xBhFz © g ¹r4e4qsuvr?iOp2w'e4qsuvgw¦uv³p'sr4 F7xw' ~¢lr©e4gwGqtsxsqlqf'r©q
¢goxn2n2t²gxBe4f'r4uw
qf2xBqlsr4e4qLu¤g'w7
ÁxpÃ Ä e4gw'Lqtsp'e4qsr4 =xiOp R4´moxB'ump2m¨rawqt²gn~¶®§OytLxm"mg 2r4h&r4'e4hp' 2uw'y|xBhvh¶®§Oytsxm?¢uvqf¦gw'hv
gw'r?e4gp2wGq±p'Luw'yqf'r³ /xqx]sr4qsl 2r4seat
u2r4 ¦uwd'r4e4qsuvgw / Guvr4hv 2uw'yxn®ratsn'hvr4uvq
gBi 2Åf'uvuvLh¤uvyfGqshv
¢lgt
srqf2xwqf'rÕn®ratsn'hvr4uvqsuvr4{xBe4f'uvr4r4 ~Goqf'r? 2r4h¤r4qLr4 ~uwqLratsn2ghxBqLu¤g'wxw' ÇEgg' '§¹Åp2t
uw'yo 2uvse4gp2wGqsr4 z=
mg' 2r4hva
% <(3 681 U 3545(+?183 <
¾?qf'rat,mr4qf'g' 2iIgt&t²r4hxuw'ye4gw'sqtLxBuwqs&uw'e4hp' 2r©¢lgts¥©G r4¢³mxw¡Ã Ä xw' ©f'p' /xw2n2p2t?Ã Ä wqf'r4sr
xBhvygt²u¤q_f2ma'uw'sqsraxB ¦gBisr4hvr4e4qsuw'y¡qf'r{moxB'um¯p2m rawqt²gn¡mg 2r4h7gBratlmg' 2r4hvD A2Z BNq_f2xBqlxBqsuv
iP¬xsr4qlgBi
e4gw'sq_tsxBuwqL©r4KxBe4qLh¤qf'r4¦gw'hv t
r4µ2p'ut
roqf2xBq©q_f'royuvraw=moxGt
yuw2xBhv{gBi A2Z B/iOxBhvhuw|sg'mr¬tsxw'yGrxGt
gp2w' qf'r©qxGt
yr4ql;xBhp'r4a r4¢³moxw¡p'yGyr4sqs³xe4gw'sqtsxuwGqgBiqf'r©iPgtsm
=
=
$ %$
8
&
8P
2 N ZBN
A ZB
&
>
>_^
=6 >
N ZBN
] [ ZB
&
T
<
=6 >
<
¢uvqfiPraxBqp2t
r©¢lr4uvyfGqs iIgt,qf'r©q_xB¥gBir4sqsumoxqsuw'y¬n2gB¢lratln®r4e4qtsx2 ©f'p' /xw2n2p2t_p'yyr4sqsle4gw'LqtsxBuwGqs
gBi&qf'r?iPgtsm
AKC B/ sZ B/ Q 8K QTSUSTSQ
S
¸,gqf|gi±q_f'r4sr¬xn2n2t
g'xBe[f'r4]eaxw2ro'uvr4¢r4 xB]uw'Lqxw'e4r4gBiqf'riOp R4 moxB'ump2mÒrawGqt
gnG¦i tsxGmr4¢lgts¥N
w'LqsraxB {gi®xl_mggGqfi p2w'e4qLu¤g'w7Bqf'rn®raw2xBhvq¹ oZ AB7uvq_x¥Braw?qsg³®,r 4rat
gu i A±xBqsuv
ª/r4qf'rt
r4hxB'r4 {e4gw'LqtsxBuwGqs
xw' uwGª¿w'uvqsrgqf'rat
¢u¤LrÅf'r4Lr©q¹2n2r4gBi*mr4qf'g 2?f2xaGr©r4qqsgo2rxn2n'hvuvr4 ´qLgohxw'yp2xByr{mg 2r4hvuw'y/
>
&
>
=69>
> .?
Y@
<
a+H+ a FÁ xÂFrat
q
~Ã sÄ n2t
gn2gGsr4³xn2n'hv'uw'yxoÇ]xp'ssuxwn2t
uvgt±gw¡qf'r{n2xtsxGmr4qsrat
$qsgmg'gqfmoxump2mrawGqt
gnG
mg' 2r4hvaÅf'u¤?qsr4e4f2w'uvµKp'rf2xB³2r4raw|xn2n'hvuvr4 =n2t
r4'u¤g'p'shv~uw=Ã Ä r4eaxBhvhq_f2xBqxomoxB'um¯p2m rawqt²gnmg' 2r4h
uvoqf'rmoxB'um¯p2m°hvu¥Br4hvuf'gg' mg' 2r4hxmgw'y¦qf'rsr4qgBiÕmg' 2r4hvoyuvrawr4µ2p2xBqsuvgw$ 4=¸, n®rat«iIg'tsm]§
uw'y moxB'ump2m È¡ÊKËÌ[ÍPÎÏÐ9ËÏ_Ð{uw'sqsrax gBiÕmoxB'ump2m hvu¥r4h¤uf'g'g $r4sqLumxBqsuvgw7,¢r¡eaxwxn2n'hvYx|Ç{xGp'ssuxw
n2t
uvgt?e4rawGqsrat
r4 =xt
g'p2w' K ¡qsg¡mg'gqf qf'rz=Ámg 2r4hqsgB¢xt
¦qf'r¯p2w'u¼iPgtsm mg 2r4hP7qf'p'{f'gn2r_iOp'hvhv
xmr4hvuvgtsxqsuw'y¬gBrat«ª/qLqsuw'y/
z|gt²r{n2t
r4e4uvsr4hv7¢r]eaxw¡r4µ2p2xBqsr©ª¿w' 2uw'yqf'rmoxB'um¯p2m rawGqt
gnGmg 2r4hF¢u¤q_f¡ª¿w' 2uw'y´n2xtLxmr4qsrat

qf2xBqmoxumu 4rqf'r©hvgyB§Ohvu¥Br4hvuf'gg' _ ,gBi&qf'r©qtsxBuw'uw'y¡ /xBqx I
±< K ] [ Z B/®h¤gGy A C B/L
S
_
[b
b
4
[b
b
ab
&
]
<

Ô$uvqfoq_f'rÕÇ]xp'ssuxw¡n2t
uvgt4'¢³f'uve4fo¢lr?qx¥BrqLg¯f2xr? 2uxygw2xBhNe4g;Bxt
uxw'e4r'gp2t,g
r4e4qsuvri p2w'e4qLu¤g'w _
qf'raw qx¥Br4lqf'r?iPgtsmyGu¤Graw¡uw r4µKp2xqsuvgw G 4
_ ± K _ ± hvgy r4KnF
a
8P
a
K
± 8P e4g'w'sq; Q
_
8
ab
&
ab
>_^
>
8
ab
&
T
`
>_^
>
gT
`
>
b
>
>
b
¢³f'rat
r©q_f'r xt
r©qf'r©Bxt
uxw'e4r4?gBi&qf'r{Ç{xp'Lsuxw7
ÔÀr³e4gwGqtsxsqqf'uvg'¹r4e4qLu¤Gr?i p2w'e4qsuvgw¡¢u¤q_f¡qf'r³g'¹r4e4qLu¤Gr?i p2w'e4qsuvgw¡uw¡r4µ2p2xBqsuvgw= iPgt*i p R4moxBG§
ump2mÒrawGqt
gnG¬¸,gqf´i p2w'e4qsuvgw'of2xroq
¢lg¡qsratsmagw'ro¢³f'uve4f n2t²r_iIrat
mg' 2r4h¤qf2xq{xt
r¬mg't
r¬p2w'u¼iIg'tsm
xw' gw'ro¢³f'uve4fn2t
r_iPrat
¯mg' 2r4hvsumuvhxGtqsg~q_f'roqtsxBuw'uw'y| /xBqx2 w=qf'rÁFxÂFrat
q
i tsxGmr4¢lgts¥NFqf'roqLratsm
qf2xBqn2t
r_iPrat
³mg 2r4hv?sumuvhxGtqsgqf'r©qtsxBuw'uw'y¡ /xBqx]uv³xhvgyB§Ohvu¥Br4hvuf'gg' =;xhp'rN¢³f'uvhvrqf'r{xw2xBhvgyg'p'qLratsm
uwÀi p R4Àz uvox~_p2mÒgBi³LµKp2xt²r4 =e4gw'sqtLxBuwqratst
g't
aÅf'r¡p'uvqx'uvhvu¤q
gBir4uvqf'ratEiOp2w'e4qsuvgwp'hvqsumoxBqsr4hv
2ran2raw' 2©g'wqf'rxn2n'hvu¤eaxqsuvgw7 gB¢r4Grat4'iPgtlhxw'yp2xByGr¯mg' 2r4hvuw'yuvq©f2xB©2r4raw iIg'p2w' ~qf2xBqh¤u¥Br4hvuf'g'g Fgt
qf'r© 2rat
uvBxBqsuvromraxBp2t²r{n2ratsn'hvr4'u¤q
7uv³xop'Lr_i p'hn®rat«iPgtsmoxw'e4rmr4qt
uve
qsg¡qf'rÇ{xp'sLuxGw~n2t
uvgt?mr4qf'g' ´p'sr4 ¦uw~q_f'r¯ÁFxÂFrat
q
i tLxmr4¢lgts¥N'qf'r¯xw2xh¤gGygp'qsratLmuw¡iOp R4
z=$qf2xBq?iOxgt
©mgt²rp2w'u¼iPgtsmÒmg' 2r4hvu¤ |Z A ] 4Åf'riPgtsmratiOp2w'e4qsuvgw=n®raw2xBhvu 4r4mg 2r4hvqf2xBq
f2xr{moxwG¡hxGt
yr BxBhp'r4aN¢³f'uvh¤r]qf'r{hxBqLqsrat*i p2w'e4qsuvgw¦n2raw2xBhvu 4r4¯mg 2r4hvi xti t
g'm p2w'u¼iPgtsm*Ô f'uvhvrqf'r
e4gtst²r4e4q©iOp2w'e4qsuvgwqsg´p'Lr¢uvh¤hxBy'xBuw= 2ran®raw' YgwÀqf'rxn2n'hvu¤eaxqsuvgw7¢lr¬xGt
yp'r¡qf2xBq{q_f'roiPgtsmratÕi p2w'e4qLu¤g'w
uv¬yGraw'ratsxBhvhvÓmgt²r~xn2n2raxBhvuw'y/\
/gtr42xmon'hvr?x=mg' 2r4h³¢uvqf!x|suw'yhvr=w'gw 4rat
g n2xtLxmr4qsrat_f'gp'hv uwq_p'u¤qLu¤Gr4h¤$t
r4e4r4uvr´x moxBhvhn2raw2xBhvq
t
r4yxGt
2hvr4sogBi{f'gB¢ iOxt]iOt
gm p2w'u¼iPgtsm qf'uvmg' 2r4huvaÅfp'¢lr
fGKn®gqf'r4su 4r{q_f2xBqqf'r{Ç]xp'ssuxwn2t
uvgt?mr4qf'g' uvÕn2t²r_iIratsxG'h¤r]qsgiOp R4mxBump2mrawGqt
gnG
Åf'r Ç]xp'ssuxw$n2t
uvgtmr4qf'g xB 2 2hvu¤qLqshvr=e4gmon2p'qxqsuvgw!qsgr4uvsqLuw'y$moxB'um¯p2m rawGqt
g'nqtLxBuw'uw'y
xBhvygt²u¤q_f2ma d'uw'e4r¦qf'rhvgyxt
uvqf2m°gBi?qf'r~Ç{xp'Lsuxwn2t
uvgtuvoe4gw'eaxr*qf'r¬g' ¹r4e4qLu¤Gr¡i p2w'e4qsuvgwuv¡sqsuvhvh
e4gw'eaxr,uw xw' ]u¤quvt
raxBsg'w2x'hv©raxBs©qsglª¿w' ]qf'rg'n'qsumoxBh2mg 2r4hPÔ=r,eaxw{moxG¥BrxlLumn'h¤r?mg 2u¼ª/eaxBqLu¤g'w
qsg¦umn2t
gBr4 =uvqsratsxBqLu¤Gr¬seaxh¤uw'yÃ Ä qLgª¿w' qf'roz Õ mg' 2r4hP~Åf'rogt²u¤yGuw2xh±p2n® /xBqsrogi±raxe[f uwqf'uv
xBhvygt²u¤q_f2muv³qsgqxG¥Br
GFA8PKJ
GFJ
GFJ
>
>
`
>
`
b
>
`
¢³f'rat
r
GFJ _xBqsuv
ª/r4qf'r©r4µ2p2xBqsuvgw
`
>
`
>
>
>
xw' ¢³f'rat²r
6
/ sZB/<K
GFJ
N ²C B/2r42n7 ©Z BNs
sZB/ Ô$uvqf qf'r{Ç{xp'Lsuxwn2t
uvgt42r4µ2p2xBqsuvgw ,uv©t
ran'hxBe4r4 ~¢uvqf
] [ CB
&
=69>
<
N
ZB <K
V
/ sZB/<K
<
=69>
6
>

<
> 69>
] [ ZB
&
A ] ZB
&
=69>
/ sZB/®r4Kn7
A ] CB
&
<
=69>
>
GJ
6
Ns
ZB
`
>
GFJ
>
>
GFJ
S
a
³ qf'rt
uvyfGq
§¹f2xw' ~Lu¤ 2rgBi&qf'uv?r4µKp2xBqLu¤g'wuv©sqt
uve4qshv~mg'w'gqsgw'uve{uw GFJ 2uvq³uv{t
r4hxBqsuvr4hv¦raxBs¡qsgª¿w' |uvqs
sghp'qsuvgw¦p'suw'yxsraxt
e4fxBhvygt
uvqf2m &Ô=r© 2rat
uvr]qf'uvÕmg' 2u¼ª/r4 ´p2n® /xBqsr¯tLp'h¤r]uwqf'r{xn2n®raw' 2uv¿
>

,= (. +&(145+?64')= 3,6<; (1"; 61= 1835+?61"(> 45(- - 6<63"+?1<@
w|d'r4e4qsuvgw 7¢lr{hvuvsqsr4 |iPgp2t±i xBe4qLgt
?qf2xBq?¢rat²r{iPgp2w' =G~jf'raw=xw' =Ç©g'g' /moxwqLg¬suvyw'u¼ª/eaxwGqshv xÂFr4e4q
¶®§Oytsxm¨_mggGqf'uw'y~n2rat«iPgtsmoxGw'e4r q©uv{uwGiPgtsmoxBqLu¤GroqsgxBssr4s©q_f'r¬Ç{xp'Lsuxw|n2t
uvgt{mr4q_f'g =xBe4e4gt² 2uw'y
qsgoq_f'r4sr?iIg'p2tleat
uvqsrat
ux2
&ut
LqaBqf'r4¯n®guwq,gp'qqf2xBq&qf'rmg' 2u¼ª/r4 ¬hvgB¢lrat«§Ogt
2rat 2uvsqt
u2p'qsuvgw'lgB
i ©w'r4srat«§ r4¯_mggGqf'uw'y©u¤,qf'r
n2t
umoxt²´t
raxBLgw¡iPgtu¤qL©p2n2rat
uvgt²u¤q
=xmg'w'y¬e4gwGrawGqsuvgw2xBh&¶®§Oytsxm¨mggq_f'uw'yxBhvygt²u¤q_f2ma r4eaxh¤h,qf2xBq
qf'r4sr 2u¤Lqt
u2p'qsuvgw'¬xt²roe[f'gGsraw|qsgxqsuv
iI=moxGt
yuw2xBhe4g'w'sqtsxBuwGqs{xB]yuvraw|uw=r4µ2p2xBqsuvgw$Z gB¢lr4rat4
qf'uv©sr4q?gBi&e4gw'sqtsxuwGqs?uvoFÐ /Î /ÍPÐ È - qLgoqf're4gtst
r4_n2gw' 2uw'y~moxB'ump2mrawGqt
gnG¡e4gw'sqtsxuwGqsiIg't¯P¶ «§
ytsxGmax{yuvraw=G|r4µKp2xqsuvgwÓ 4¬Åfp'a&moxump2mÒrawGqt
gnG´¶®§OytLxm mg' 2r4hvof2xaGrosumuvhxtomg' 2u¼ª/r4 hvgB¢rat¹§Ogt
2ratl 2uvsqt²u2p'qLu¤g'w'{xBluw ©w'r4srat«§ r4~mggq_f'uw'yN
gB¢lr4rat4'z Õ mg 2r4hv{p2w' 2ratqf'r¯Ç]xp'ssuxwn2t²u¤g't³w'g¡hvgw'yratlxqsuv
iIq_f'r©z !e4gw'LqtsxBuwGqsr42xBe4qshv
w'LqsraxB F2qf'r]e4gw'sqtLxBuwqslqf2xq³xt
r©xqsuv
ª/r4 ~f2xr©qf'r?iPgtsm
K
A Z B/ sZ B/ S

] [ Z B/ sZ BN
%&$
9O
T
W
&
m6j>
>
T
&
<
` >
=69>
]
<
Å f2xBq?uva7qf'r]ramon'ut
uveaxBh&r4Kn®r4e4qxBqsuvgw' ] [ ZB/ ZBN³xt²r¯w'gB¢L 2u¤Le4gp2wqLr4 G~qf'rxmgp2wGq w
z=Y¶®§OytsxGmmg' 2r4h¤¿mgGsq kxGt
r{n2gLu¤qLu¤Gr ©p2xh¤uvqxqsuvr4hv7qf'uv³uv?r4raw~mg't
r© 2r4sutsx'hvrqf2xwmr4r4qLuw'y
qf'r¦qxt
yr4qLor4Kxe4qshvxB¬ramn'ut²u¤eaxh?i t
r4µ2p'raw'e4uvr4qsraw' YqLg ®r´f'uvyf'rat¡qf2xw»qtsp'r i t
r4µ2p'raw'e4uvr4¡iIg'tr4rawGqs
¢uvqf=w'g'w 4rat
g~e4gp2wGqsa w2xBhvgyg'p'¯2raf2x'uvgt©uv¯n2t²g /p'e4r4 ¢uvqf ©w'r4srat¹§ r4=_mggGqf'uw'y~¢³f'raw=xGn2n'h¤uvr4 t
r4eap2t
Lu¤Gr4h¤qsg{hvgB¢lrat«§Ogt
2rat* 2u¤Lqt
u2p'qsuvgw'a woq_f'u¤leaxBLrqxt²yr4q&e4gp2wGqsxt²r 2uvse4gp2wGqsr4 ¬q_f2t
gp'yfoxG'sghp'qsr
2uvse4gp2wGqsuw'y/ 2rat
uvBxBqsuvgw¦gBi&r4µKp2xBqLu¤g'w= ,uv³yGu¤Grawuwqf'r{xGn2n2raw' 2uv¿
d'r4e4g'w' F/jf'raw~xGw' ~Ç©g'g /moxGwn2guwGqgp'qqf2xq±xG'sghp'qsr© 2uvse4gp2wGqsuw'yuvp2n2rat²u¤g'tqsgqf'r©gGqf'ratlq
Kn®r4
gBil 2u¤Le4gp2wqLuw'y|e4gw'Lu¤ 2rat²r4 FkxGw' =qf2xBq{p'suw'y|x¡ 2u ÂFrat
rawGq{ 2uvse4g'p2wqEiIgt?g'w'r_§Oe4gp2wqL¯xw' =q
¢lgB§Oe4gp2wGqs©xw' x ¿xq¯ 2uvse4g'p2wqqf'rat
rax;iIqsrat]xBuwmg 2u¼ª/r4 ©w'r4srat¹§ r4mg'gqf'uw'y´n®rat«iPgtsmr4raw2r4qsqLrat4~Ô$uvqfÀqf'r
Ç{xGp'ssuxwn2t
uvgt4&qf'r¡ 2uvse4gp2wGqiPgt{xw¶®§Oytsxm u¤h¤uw'raxtuw ox{eaxw®r¬sr4rawÀiOt
gm r4µKp2xqsuvgw½
¯q_f'rn2t
g'2x'uvh¤uvq
xBssuvyw'r4 qsg |Gb A yt
gB¢]r4Kn®gw'rawGqsuxBhvh¤uw y't
gB¢©hvgyxt
uvqf2mu¤eaxh¤hvYxBx
iOp2w'e4qsuvgw|gBilqf'roqxt²yr4qÕn2t²g2x'uvhvu¤q
=g'te4gp2wGqa w|gqf'rat?¢lgt
2Ft
gp'yf'hv~_n2rax¥Guw'y´q_f'rÇ]xp'ssuxwÀn2t
uvgt
mr4qf'g' ~q_tsxw'shxBqsr4qsg - Ë ÈÏ_ÐÑÍ ¯Ð ] 2u¤Le4gp2wqLuw'yN³Åf'uv©uvÕxµ2p2xBhvu¤q_xBqsuvr4hv´xn2n®raxBhvuw'y~mg 2r4hgBiqf'r]uv 2raxBh
xratsxByGr³ 2uvse4gp2wGq? 2u¤_n'hxr4 ¦u#w &uvyp2t
r xw' uvÕmgt
r?r4h¤r4y'xwq?qf2xwp'Luw'ymp'hvqsun'h¤r ¿xBq 2u¤Le4gp2wqLa
Åf'ut² Fjf'raw|xw' ÇEgg' /moxw|t
ran®gt
q©qf2xq³uwGqsratsn2gGhxqsr4 mg' 2r4hv¯g'p'qn2rat«iPgtsm¨2xBe4¥Br4 '§OgBÂYmg' 2r4h¤]gw
¶®§Oytsxm¢uvqfhvgB¢e4gp2wqLa/xBhvgB¢lrat«§Ogt
2rat?mg' 2r4hvÕn2t
gB'uv 2r{;xhp2xG'h¤ruwGiPgtsmxBqsuvgw¡iPgtlr4LqsumoxBqsuw'y¡qf'r4sr
n2t
g2xG'u¤hvuvqsuvr4a xGn2n'u¤hv'qf'r³Ç]xp'ssuxwn2t
uvgt,2raf2xr4&hvu¥Br©xw]uwGqsratsn®ghxBqsr4 mg' 2r4h/xB¶®§Oytsxmn2t
g'2x'uvh¤uvq

r4sqsumoxqsr4³ 2ran®raw' =gw h¤gB¢lrat«§Ogt² 2ratuwGiPgtsmoxBqLu¤g'w7Åf'uv?iIghvhvgB¢?qt
uvuxBhvhv¦i t²gmq_f'r{g'srat²;xBqsuvgw qf2xBq?qf'r
n2t
g2xG'u¤hvuvq
A xBsLu¤y'w'qsg¬xw¶®§OytLxm 2ran®raw' 2©gwqf'r{n2xGtsxmr4qsrat±;xBhp'r4 iIg'txBhvh¶®§Oytsxm qf2xBq
xt
rlpGÆ¡r4&gBi ' gB¢lr4rat4qf'rÇ{xp'sLuxGw¯n2t²u¤g't&mr4qf'g' ¬p'sr4&qf'rluwGiIg'tsmoxBqsuvgwEiOt
gmhvgB¢lrat«§Ogt
2ratmg' 2r4h¤
uw x|mraxGw'uw'yi p'hl¢x Ngt{xGw=¶®§Oytsxm '&qf'rÇ{xp'sLuxGw=n2t
uvgtmr4qf'g' qLraw' 2¯qLg´xB sp'sq qLg;¢xt² 2
4rat
g ¢³f'raw ]uv
4rat
g/qf'roe4gtLt
r4n2g'w' 2uw'y iIraxqp2t
r¬f2xB{w'g¦r_ÂFr4e4q©gw¦qf'r¬mg' 2r4hPkxGw' =qf'rhvg;¢lrat«§Og't
2rat
¶®§Oytsxmn2t²g2x'uvhvu¤q
¡r4sqsumoxBqLruvp'sr4 F wgqf'rat¢lgt² 2aqf'rn2t
uvgtlxB sp'sqs¶®§OytLxmn2t
g2x'uvhvuvqsuvr4³qLg;¢xt² 2
qf'r©hvgB¢lrat«§Ogt
2ratn2t²g2x'uvhvu¤q
r4sqLumxBqsr/xBu¤? 2r4sutsx'hvr
&uw2xBhvhvjf'raw½xw' ÇEgg' /moxw w'gqsr|qf2xBq~xB 2 2uvqsuvgw2xh¯q_p2w2x'hvr n2xtsxmr4qsrat
eaxw$umon2t²g;Gr=eap2tst
rawGq
mg'gqf'uw'ymr4qf'g' 2a /g'tqf'r´Ç]xp'ssuxw!n2t
uvgt4lqf'r|w2xBqp2tsxhiOt
r4r|n2xtsxmr4qLrat
¬xt
r¦qf'r~Bxt
uxw'e4r4
m6 >
V
<
>
`
>
>
`
`
]
`
m
`

]
`
`
`

eDvgwmu
~egelu2w=h9hjrxq-egs
vgkmujpilwfpw
s;qxile}vgpr-
wm{7ffq-wmu
qxu
h9iq-k=iDkmu
h%w=ilwY[egpelilfGt q-pdIhjilegYq-k={%fDt+kmi/qxu
! #"%$'&)(
h9ilk=~%w=~9qxrxq-p 2fh%wvgeYDIwYv GwmIw=u%s
egpk
hjiq-kmi=%~kpdilegf{jr-pqxu%yqxu/rxqxu%e}wmiDsq-fvgkm{jujpqxu%yIt+djq-v dId7wYf+~e}eou
fd%k=t+u
a
+*
{7fe[w
>
ymilw
fkkYpdjqxu%yIt+d7eoilehjiq-kmilfd7w=Ye
-,. /" 021)(
qxiq-v djr-egpGh9iq-k=i[w=u%s
pkGheoiz_k=il
f{j~kmh7pq-[w=rxr-Y
ws9wf
+3
{7fegfGw
+e}pw
w¡q_f'r{2xBsuve{rat²suvgwogikqf'r{Ç]xp'ssuxw¡n2t
uvgtmr4qf'g q_f2xBql¢r©umon'hvramrawGqsr4 FN¢lrÕf2xB ~¶ iOt
r4r{n2xtsxGmr4qsrat

] K QUSTSTS Q¶a¢?f'rat
r³xBhvh §OytsxGmgi/qf'rlxmrlhvraw'yqf¢lrat
rle4gw'LqtsxBuw'r4 qsg{f2xrq_f'r_xmrl;xt²uxGw'e4r

©qf'r¬Ç]xp'ssuxwÀn2t
uvgt{mr4q_f'g =_xBqsuv
ª/r4¯xh¤h,gBiq_f'ro 2r4suv 2ratsxBqx hvu¤Lqsr4 G=jf'raw=xw' Ç©g'g /moxGw7Fuvq
mox~n2rat¹iIgtLme4gmn2r4qsuvqsuvr4hv|uw´¶®§OytLxm_mggGqf'uw'y/³Åf'rr42n2rat
umrawGqs©uw|d'r4e4qsuvgw o_f'g;¢qf2xBq?qf'uv?u¤
uw' 2r4r4 |qf'r©eaxBsr
%< % =+
Å g{e4gmon2xGt
r³q_f'r³n2rat«iPgtsmxw'e4r³gimxBump2m·rawq_t
gnGxGw' oe4gwGrawqLu¤g'w2xBh¿¶®§OytsxGmmg'gqf'uw'yqsr4e4f2w'uvµKp'r4a
¢lrtsxw]r4Kn®rat
umrawGqsgBrat&moxGw©qtLxBuw'uw'y]sr4q&su4r4p'suw'y{sr4GratsxBh' 2u ÂFrat
rawGq&qsr4'q&e4gtsn®gtsxiPgt&2gq_f¯'uvytLxm
xw' qt²u¤y'tsxmmg' 2r4hva
<%&$
')= 3,6<;,68>?6@9
¾iqf'r©e4gwGrawGqsuvgw2xBh¶®§OytLxmmg'gqf'uw'yoqLr4e[f2w'uvµ2p'r4a7¢lr©umn'h¤ramrawqsr4 ©xBq ©mg'gqf'uw'y~Ã Ä '¢³f'uve[f u¤
n2ratLf2xn'qf'rmgsq¯n®gn2p'hxtoxBhvyg't
uvqf2m°uwn2tLxBe4qsuve4rxw' mg' 2u ª/r4 ©w'r4Lrat«§ r4mg'gqf'uw'yÃ Ä ¢³f'uve4f
f2xB©2r4raw¦f'gB¢³w qsg¬g'p'qn2rat«iPgtsm xBhvhgq_f'rat¢uv 2r4hvG§¹p'sr4 =qsr4e4f2w'uvµKp'r4a w´x 2 2u¤qLu¤g'w77¢r]umon'hvramrawqLr4 =qf'r
;xGt
uxBqsuvgw¡gBi r4h¤uw'ra¥§Oz|rat
e4rat?mg'gqf'uw'yoyuvrawGor4µ2p2xBqsuvgw= '¢?f'rat
r³uw'sqLraxB ~gBi&x{Luw'yGh¤r n2xtLxmr4qsrat
x¡ 2u¼ÂFrat
rawq uv{p'sr4 |iPgtraxBe4f|hvr4r4h&gBiq_f'r¶®§OytLxm"mg 2r4hPoÅf'uv{mr4qf'g' = 2g'r4{w'gq{n2rat¹iIgtLmÒn2xt
qsuve_§
p'hxt
hv=¢lr4hvhP2p'q{uvop'sr4 xB¯x¦2xBsr4hvuw'r~xBhvygt
uvqf2m iIgt?r42n2gGsuvqsgt
n2p2tLn2gsr4¬ÔÀrt
r_iPrat©qLgqf'r4sr¡qf2t
r4r
umon'hvramrawGqxBqsuvgw'?¢uvqfq_f'r{mow'ramgw'uve4 7
Nxw' 22t
r4n®r4e4qsuvr4hv
ÔÀr{xBhvsg¬umon'hvramrawGqsr4 |sr4ratLxBhFmoxB'ump2m rawq_t
gnG¬mggq_f'uw'yqsr4e[f2w'uvµ2p'r4a /g'tlraxBe4fqsr4e4f2w'uvµKp'r7xBhvh
©n2xtsxmr4qsrat
©xt
r{uw'uvqsuxBhvu 4r4 qsg 4rat
gxGw' ´umon2t²g;Gr4 ~uvqsratsxBqLu¤Gr¯LeaxBhvuw'yuv{xn2n'hvuvr4 qsgoqtsxuw¦qf'rmg' 2r4hI
qLratsxBqsuvr,seaxBhvuw'y©u¤&qLratsmuw2xBqsr4 ¢³f'rawEqf'rn2ratsn'hvr4'u¤q
]gBi¿x³f'r4hv '§Ogp'q&Lr4qkw'g?hvgw'yrat 2r4eat
raxBLr4&suvyw'u¼ª/eaxwqLh¤
jlhp'sqsratr42n2xw'suvgwÃ 2LÄ uv?ramon'hvg;Gr4 ~qsg¬t²r4 /p'e4r¯e4g'mon2p'qxBqsuvgw7 w qf'r{umon'hvramrawGqxBqLu¤g'!w "
#$%F
w'g¡mg'gqf'uw'yuv{n2rat«iPgtsmr4 FoPd'uw'e4rqtsxuw'uw'yuv©qsratsmuw2xqsr4 |¢³f'raw|n2rat«iPgtsmoxGw'e4r¯g'w~x¡f'r4h¤ '§Og'p'q{sr4q©w'g
hvgw'yratEumn2t
gBr4aw'g|n2t
g2x'uvhvuvqsuvr4o¢uvhvhe4gwGrat
yGr¯qL#g 4rat
g´xB©uwÀqf'roeaxBLr¯¢?f'rat
roqtsxuw'uw'y|uv{e4gwGqsuw'p'r4 qsg¡e4gwGrat
yraw'e4r Åf'roxBhvygt²u¤q_f2&
m "
'($$
¡uv¯xw¦umon'hvramrawGqxBqsuvgw|gi±Ç©g'g' '§¹Åp2t
uw'y¦ 2u¤Le4gp2wqLuw'y
xB? 2r4seat
u2r4 Àuw|d'r4e4qsuvgw / ³Åf'rxBhvygt
uvqf2)
m "*+ouv©xw¦umn'h¤ramrawqxqsuvgw¦gBiÁFxÂFrat
q
³Ç{xGp'ssuxw
n2t
uvgt©mr4q_f'g =xB? 2r4seat
u2r4 ÀuwÀd'r4e4qsuvgw ©mrawGqsuvgw'r4 =raxt
hvuvrat47qf'uv{mr4q_f'g =f2xB©¶|iOt
r4ron2xtsxGmr4qsrat

]2gw'r?iPgtlraxBe4f¡hvr4r4hgikqf'r{¶®§OytLxmmg' 2r4hP
ÔÀrÕp'sr4 /xqxEi t
g'miPgp2t,sgp2t
e4r4 *qf'rÕ¸lt
gB¢³we4gtsn2p'¢?f'u¤e4fe4g'wqxuw'lqsr4'q,i t²gmx¯w'p2m2rat,gBikmu¤²§
e4r4hvhxw'r4gp'©sgp2t²e4r4{Ã Ä 'Ô xBhvhd'q_t
r4r4q gp2tLw2xBh9Ô½d w'r4¢n2xGn2ratlqsr4'q{Ã G4Ä q_f'r{¸t²gxB 2eaxBsq r4¢¯P¸ ?
e4gtsn2p'¢?f'u¤e4f¡e4gwGqxBuw'lqtsxw'Leat
un'qsuvgw'lgBiqsr4hvr4'u¤Lu¤g'w~xw' tsxB 2uvgow'r4¢lf'gB¢©Ã Ä 'xw' qf'r©d'¢uvqse[f'2g'xt
Pd'Ô½¸lle4gtsn2p'/¢³f'uve4f¦e4gwq_xBuw'³qtLxw'seat
un'qsuvgw'?gBiqsr4hvran2f'gw're4gwGrat
xqsuvgw'{Ã Ä wraxBe4fr42n2rat²umrawqa
¢lr{sr4hvr4e4qsr4 =xqtsxBuw'uw'ysr4qgixoyuvraw hvraw'yqf i t²gmg'w'r{sgp2t²e4r¿xw' ¦q
¢g¡f'r4h¤ '§Og'p'q©sr4qsi t
g'mqf'r{_xmr
sgp2t²e4r¯Åf'r]ª¿t
Lq{f'r4h¤ '§Og'p'q{sr4q©¢xB©p'sr4 =qsg¡gn'qsumu 4r¡qf'ron2xtsxmr4qsrat
?gBiraxBe4f¦mg'gqf'uw'y~xBhvygt²u¤q_f2m
Î 2qf'r n2xtLxmr4qsrat
gB,i "
$*
+¯gtqf'r] 2u¤Le4gp2wqL gimg 2u¼ª/r4 ©w'r4srat«§ r4~_mggGqf'uw'y/ x§
tsxmr4qsrat
&¢lrat
rlsr4hvr4e4qsr4 ¡qsgÕmuw'umu 4r©qf'r?n2ratsn'hvr4'u¤q
ogi¿qf'rf'r4hv '§Ogp'qlsr4q gB¢lr4hvh sraxt²e[fxBhvygt²u¤q_f2mÃ Ä
¢xBp'sr4 qsgon2rat¹iIgtLmqf'uvsraxt²e[f7&Åf'uv³f'r4hv '§Ogp'q?sr4q¢xBlxBhvsg¬p'sr4 qsg 2r4e4uv 2r¢³f'raw¡qsgqsratsmuw2xqsr©uvqsrat«§
xBqsuvr?seaxBhvuw'yiIgt,qf'r?z=mg' 2r4h¤Åf'r©Lr4e4gw' ~f'r4hv '§Ogp'qsr4q¢xBlp'sr4 qsgr4;xhp2xqsr©qf'r?ª¿w2xBhFn2ratLn'h¤r4'uvq

gBi&raxBe4f¡mg'gqf'uw'y¬xBhvygt²u¤q_f2m
NgtlraxBe4f¦ /xBqxsgp2t
e4rN¢lr¯tsxGwr42n2rat
umrawGqs¯p'Luw'yq_tsxBuw'uw'ysr4qsi t
g'm osrawGqsraw'e4r4oPx®gp'q
¢lgt
2qsg~xt²gp2w' 2 srawGqsraw'e4r4 x2gp'q muvhvhvu¤g'w¢g't
24 r4h¤ '§Og'p'q{sr4qs©¢lrat
r srawqLraw'e4r4a
`
`
`
j:
7$ $
- -
a
cross-entropy of test data (bits/token)
11
10
9
WSJ 2-gram
Brown 2-,3-gram
8
WSJ 3-gram
SWB 2-gram
7
SWB 3-gram
100
1000
10000
training set size (sentences)
100000
&uvyp2t
r &jt
gL
§Orawq_t
gnG{gBi2xBsr4hvuw'r{_mggGqf'uw'y¯xBhvygt²u¤q_f2m g'woqsr4Lqsr4q,g;Gratmp'hvqsun'h¤r©q_tsxBuw'uw'yosr4qLu 4r4
gw¸lt
gB¢³w72d'¢uvqse4f®gxt
F7xw' Ô xh¤hd'qt
r4r4q g'p2tsw2xBhFe4gtLn2gtsx
:
Ô½f'uvh¤rqtsxuw'uw'y!sr4qsiPgt¡hxw'yp2xyr mg' 2r4hv´moxÓt²raxBe[f$f'p2w' /t
r4 2|gBimu¤hvhvuvgw'=gBi¢lgt
2uw n2tLxBe4qsuve4r
¢lr~¢lrat
r=p2w2x'hvr=qsge4gw'suv 2rat hxGt
yratqtsxBuw'uw'ysr4qsqf2xGw¢lr| 2u¤ /p'r´qLg e4gmn2p'qxBqsuvgw2xBh?hvumuvqxBqsuvgw'a
ÅtsxBuw'uw'y~moxB'ump2m¨rawGqt
gnG~¶®§Oytsxm mg 2r4hvt
r4µKp'ut
r4{xyt
raxq 2raxBhmgt²r{e4gmon2p'q_xBqsuvgwq_f2xwqtLxBuw'uw'y
e4gwGrawGqsuvgw2xBh³¶®§OytsxGmºmg' 2r4hva w!xB 2 2uvqsuvgw7¢?f'rawYe4g'w'suv 2rat
uw'yYm¯p'hvqsun'hvr=n2xtsxmr4qsratsr4qsqLuw'yG¬uw!qf'r
gB¢lr4h¤hsraxt
e4f½PxBiPgt]qf'r Òn2xtsxmr4qLrat
uw "
*+4&qf'r¦u¤qLratsxBqsuvrseaxh¤uw'yYxBhvyg't
uvqf2m mp'sq¬®r
xn2n'hvuvr4 |sran2xtsxBqLr4h¤iPgt,raxBe[fn2xGtsxmr4qsrat,sr4qLqsuw'y/ÅgoqtsxBuwx]suw'yhvr¯mg 2r4hp'Luw'ymr4qf'g' "*+©iPgt
x muvhvh¤uvgw ¢g't
~qtLxBuw'uw'y¡sr4q©t
r4µ2p'ut²r4 xGt
gp2w' ~Lu¤~f'g'p2t
³gie4gmon2p'qxBqLu¤g'w¡gw~x z rawGqsup2m

e4gmon2p'qLrat4d2p2'sqxGwqsuxBhvhvhxt
yrat±qtsxBuw'uw'y¬Lr4qs³xt
r?iPraxBsu'hvru¼i*n2xtLxmr4qsratlg'n'qsumu axBqsuvgwuv©w'gqp'sr4 F
¾©p2t /xqxLr4qskxGt
rlu¤ 2rawGqsuveaxBh2qsg?qf'gLr±p'Lr4 G¯jf'raw¯xGw' ÇEgg' /moxw¡Ã Ä xw' e4gw'sr4µ2p'rawqLh¤gp2t&t²r4p'hvqs
xt
r 2ut
r4e4qshv|e4gmon2xGtsx'hvroqsg¡qf'r¬xw2xh¤gGygp'{t
r4p'hvqs{n2t²r4srawqLr4 |jf'raw=xw' =ÇEgg' /moxw7©z|gt²r¯ 2r4q_xBuvh¤
gBi&gp2tmr4q_f'g 2ghvgyG¬eaxw®r©iPgp2w' ~uw qf2xBql¢lgts¥N
<%
= .">Z3 w &uvyp2t
r 2¢lr© 2u¤_n'hxqf'r]eat
gs²§Orawqt²gngBikq_f'r¯2xBsr4hvuw'r r4hvuw'ra¥B§Oz|rat
e4ratEmg'gqf'uw'y¬xBhvygt²u¤q_f2mgBrat
x{tLxw'yrgBi7qtsxBuw'uw'ysr4qLu 4r4lgwsr4ratsxBhNe4gtsn®gtsx2 wqf'r³y'tsxn2f'&qsgEiIghvhvgB¢{¢lr 2uvn'hx¡qf'r³n2rat¹iIgtLmoxw'e4r
gBiraxBe4f xh¤yGgt
uvqf2m xBqf'r¡ 2u ÂFrat
raw'e4rgi±uvqseat
gGs
§OrawGqt
gnG|gw=q_f'r¬qsr4Lq{sr4qEi t
g'm q_f'roeat
gs²§Orawqt²gn|gBi
qf'r2xBsr4hvuw'r´mr4q_f'g ½Pp'suw'y|qf'r¡xmroq_tsxBuw'uw'y=sr4q4qsg i xe4u¤hvuvqxBqLruvp2xBhvu axBqsuvgw7=,xBe4f n®guwquwqf'r
ytsxGn2f'±n2t²r4srawqLr4 ~f'rat
rÕt²ran2t
r4srawGqsx{Luw'yGh¤r]r4Kn®rat
umrawGq 'iPgtxwxGw2xBhvsuvgi q_f'r©sqxw' /xt² oratst
gt,gBiqf'r4sr
g'srat²;xBqsuvgw't
r_iPrat,qsgojf'rawxw' Ç©g'g /mxw~Ã Ä kÅgyuvr{xt
gp'yfuv 2rax]gBiqf'r?sqxBqLu¤LqsuveaxBh7ratst
gt*uwGghvr4 F
u#w &uvyp2t
r4a ¬xw' 'qf'r{ 2u¼ÂFrat
raw'e4r2r4q
¢lr4raw $ oxw' "*
+omox¬w'gq?2r{Lu¤y'w'u ª/eaxGwqa
¢³f'uvhvrqf'rl 2u¼ÂFrat
raw'e4r³2r4q
¢lr4rawqf'r4Lrq
¢lg³xBhvyg't
uvqf2mxw' oxBhvh2gBi/qf'rlgq_f'rat
xBhmgsqe4rat
qxuw'hvuviIg'txBhmgGsq
r4rat
¡ /xBqxn2guwGqa
Jw &uvyp2t
r B¢lr&e4gmon2xt²rqf'rln2rat«iPgtsmoxGw'e4rgBi/qf'r,;xt²u¤g'p'moxB'ump2m rawq_t
gnG³mggq_f'uw'y©xBhvygt²u¤q_f2m
gBratmp'hvqsun'hvr©qtsxBuw'uw'ysr4qLu 4r4?p'suw'y¯ÔxBhvh¿d'qt
r4r4q gp2tsw2xh¿ /xqx2Åf'r³hvr_iPqy'tsxn2fuv,iIg't'uvytsxm·mg' 2r4h¤
xw' oq_f'rÕt
uvyfGq&ytsxGn2fuviPgtqt²u¤y'tsxm mg 2r4hva&ÔÀrsr4rqf2xq " %{u¤lgp'q_n2rat«iPgtsmr4 ¡qf'rgGqf'rat
xBhvygt²u¤q_f2mGYxÀhxGt
yr´mxt
yuw7l 2ramgw'LqtsxBqsuw'yqf'r´w'r4e4r4Lsuvq¹!gBi©mg'gqf'uw'y=iPgt¡moxB'um¯p2mÉrawGqt
gnG
mg' 2r4hva¾iFqf'r³t
ramxBuw'uw'yoxBhvyg't
uvqf2maGqf'r³Ç{xGp'ssuxwon2t
uvgt,mr4qf'g' osuvyw'u¼ª/eaxwGqshvogp'qn®rat«iPgtsmr4 ¬ÇEgg' '§
Åp2t
uw'y 2u¤Le4gp2wqLuw'yNÕÅf'gp'yf~w'gGq³f'gB¢³w¦f'rat
rN¢r]sr4rsumuvhxt©2raf2x'u¤g't?uw¦r42n2rat
umrawGqs©gw qf'r{gGqf'rat
N

diff in test cross-entropy from baseline (bits/token)
diff in test cross-entropy from baseline (bits/token)
relative performance of algorithms on WSJ corpus, 2-gram
0.8
ME-no-smooth
0.6
0.4
0.2
baseline
0
ME-disc-katz
-0.2
ME-gauss
100
1000
10000
training set size (sentences)
100000
relative performance of algorithms on WSJ corpus, 3-gram
ME-no-smooth
1.2
1
0.8
0.6
0.4
0.2
ME-disc-katz
0
baseline
-0.2
ME-gauss
-0.4
100
1000
10000
training set size (sentences)
100000
&uvyp2t
r rat«iPgtsmoxw'e4r?t
r4hxBqsuvr©qsg2xBsr4hvuw'r©gBi;xGt
uvgp'moxB'ump2m·rawGqt
gnGmg'gqf'uw'yoxBhvygt
uvqf2mlgBrat
mp'hvqsun'h¤rqtLxBuw'uw'y¡sr4qLu 4r4?gw¡qf'r©ÔxBhvhd'qt
r4r4q gp2tsw2xBhFe4g'tsn2p'a/'uvytsxGmxw' ~q_t
uvytsxmmg' 2r4hv
:
qf2t
r4r©e4g'tsn2gtLx2
Jw &uvyp2t
r48 ³xw' 4¢lr&e4gmon2xt
r&q_f'rn2rat¹iIgtLmoxw'e4r&gBi/moxB'um¯p2m rawqt²gn?mg'gqf'uw'y³xh¤yGgt
uvqf2m¢uvqf
e4gwGrawGqsuvgw2xBh&¶2§Oy'tsxm¨mg'gqf'uw'y~xBhvyg't
uvqf2m©gBratsr4ratsxBhe4gtsn®gtsx2 ¾ilqf'roe4gwGrawGqsuvgw2xBhmg'gqf'uw'y
mr4qf'g' 2aB¢lrlsr4rlqf2xBq ©xBq _mggGqf'uw'y©yraw'ratsxBhvhvgp'qn2rat¹iIgtLmq_f'r±2xsr4hvuw'r©xw' qf2xBqmg 2u¼ª/r4 ©w'r4srat¹§
r4©mg'gqf'uw'yuvLu¤y'w'u ª/eaxGwqshv2r4qsqsrat ¾i/qf'rlmoxB'ump2m$rawGqt
g'n©mr4qf'g' 2a¢r&Lr4rqf2xBq "
'($$
n2rat¹iIgtLme4gmon2xtLx'hvÓqLg ©xBq =mggq_f'uw'yiPgt¦'u¤y'tsxm mg' 2r4hva{xw' ½Lgmr4¢³f2xBq¢lgt²sr¦iIgt¡q_t
uvytsxm
mg' 2r4hvaFqf'g'p'yfuvq© 2g'r4{2r4qsqsrat?g'w~hxt²yrat /xqx¡sr4qsa©Åf'romr4q_f'g "*+¬n®rat«iIg'tsm©x2gp'q{x³¢lr4hvh
xBmg' 2u¼ª/r4 ©w'r4Lrat«§ r4_mggGqf'uw'y/2xw' uv³shvuvyfGqshv~2r4qsqLratlgBratlmgsql /xBqx]sr4qLa&Åfp'2qf'r{Ç{xGp'ssuxw
n2t
uvgtmr4qf'g' n2rat«iPgtsmoxB¢lr4hvhxB{gt®r4qsqsrat]qf2xwxBhvhlgqf'rat©¢u¤ 2r4hvG§¹p'sr4 ½xBhvygt
uvqf2m{iPgtEmg'gqf'uw'y
¶®§Oytsxm mg 2r4hva
Åguwr4LqsuvyxBqsrf'g;¢$qf'r©hvgy'xt
uvqf2muve{ 2uvse4g'p2wqsuw'ygBiqf'r{Ç{xp'Lsuxwn2t
uvgte4gmon2xt
r4qsgqf'r{mp'h¤qLun'hvr
x'sgGhp'qLr 2uvse4gp2wGqsgBiFmg' 2u ª/r4 ©w'r4srat«§ r4omggq_f'uw'yNB¢re4gmon2p'qsr4 ¬f'gB¢e4hvgsr4hvqf'rr42n2r4e4qLr4 w'p2m]§
2rat?gie4rat
qxBuw|¶®§Oytsxm?uw=xqsr4sq?sr4qÕxe4e4gt
2uw'yqsg¡raxBe[f|mg' 2r4h&moxBqse4f'r4 |qf'r¯xBe4q_p2xBhkw'p2m2rat?gBiq_f'gsr
¶®§Oytsxmuw qf'r©qsr4sqlsr4qa w~n2xt
qLu¤eap'hxt 'iIg'txh¤hF¶®§OytsxGmg'e4eap2tst
uw'y ]qsumr4uwx 2 ?¢lgt² ¬qtLxBuw'uw'y
sr4q I°iPgtlsg'mr '2¢lr©e4gmon2p'qsr4 ¦qf'r{tsxBqsuvgogikqf'r]r4Kn®r4e4qsr4 ´w'p2m2ratgBi&qsumr4³q_f'r4sr{¶®§Oytsxmge4eap2tst²r4 uw~x 2 ® ?¢lgt
qLr4sqlsr4q I qsgqf'r{xBe4qp2xBhFw'p2m2ratgBikqLumr4qf'r4¡ge4eap2tst²r4 >P

A2 : F>H>GP I >PKJ
G J
F
H
>
?
G
;
I
>
K
P
J
^ _
S
G J ^ >HG?I;>PKJ
_
Åf'r4sr¡tsxBqsuvg{xt²r¯ 2uvn'hxr4 ÀiIg't ¡uw &uvyp2t
r ¡iPgt©'uvytsxmÒxw' Àqt
uvytsxmÒmg 2r4hva¡Åf'r¬Ç{xGp'ssuxw
n2t
uvgt&xBe4f'uvr4r4tsxBqLu¤gGe4hvgsratqLg³qf'r,uv 2raxBh2;xBhp'rgi/gw'rlqf2xw{mg 2u¼ª/r4 ©w'r4srat¹§ r4]mg'gqf'uw'y?iIg'tmgGsq '
¢³f'uve4fuv&r4uv 2raw'e4r?qf2xBq&qf'rÇ{xGp'ssuxwn2t
uvgt&mr4qf'g' uvp2n®rat
uvgt&qsg©mp'hvqsun'h¤r ¿xBq 2uvse4gp2wGqsxBq&n2t
r4 2uve4qsuw'y
e4gtst²r4e4q³xratsxByr? 2uvse4gp2wGqsa
ÔÀrÕxBhvsguwGr4sqLu¤y'xBqsr4 ~f'gB¢½qf'r©wp2m®ratgBiuw' 2ran®raw' 2rawq©Bxt
uxw'e4rn2xtsxmr4qLrat
p'sr4 ¢uvqf¡qf'r{Ç]xp'
§
suxwn2t
uvgtoxÂFr4e4qsn2rat«iPgtsmxw'e4r wqf'r¡gt
uvyuw2xBhlumon'hvramrawq_xBqsuvgw "*+2&x 2u¼ÂFrat
rawq uvp'Lr4 "( (
#
#
-
- -
:
V
'
* V
'
*
'
*
^
'
>
>
^
*
>
>
>
>
>
N

e[w=r-fkilwmu
r-kmu7yYeli
ymilwY
eg|Yheliq-[eoujpf{7fqxu%y
u
z egwYp{jileq-f+u7kmu geoilkj+c+d9q-filegf{jr-pegsqxu
c+d7er-w=ilyYeIfhjqxegf[qxu
pd%e"!;t+q-pvd~kYw=ils
s{9hjrxq-vgwYpe}s2fegyYeoujpkmzpeg|p+qxu
ymilw[f
fq-ymujq%v}wmujpr
Nt+d%elileegwv d
ymilw=h9d7fwmilesq-fvo{7ffegs~j# d7eou
pd7eGvgkmiilegfhnkmu7s;qxu7yIpilwmqxujqxu%y/fegpg
a
ymilwYz_egwYp{jileq-fu7kmu geoilkIk=u9r-
qxujz_eoiq-k=iheoiz kmil[w=u%vge
wmu7s
kksj[w=u
" )(
$
t+d%eouIu7k
2c+d%e}2wmile/vgwm{7fegs~j
w
diff in test cross-entropy from baseline (bits/token)
diff in test cross-entropy from baseline (bits/token)
relative performance of algorithms on Broadcast News corpus, 2-gram
0.1
ME-disc-katz
0.05
baseline
0
-0.05
-0.1
katz
-0.15
kneser-ney-mod
ME-gauss
-0.2
100
1000
10000
training set size (sentences)
100000
diff in test cross-entropy from baseline (bits/token)
diff in test cross-entropy from baseline (bits/token)
relative performance of algorithms on Brown corpus, 2-gram
0.1
ME-disc-katz
0.05
baseline
0
-0.05
-0.1
-0.15
katz
-0.2
-0.25
-0.3
kneser-ney-mod
ME-gauss
-0.35
100
1000
10000
training set size (sentences)
relative performance of algorithms on Broadcast News corpus, 3-gram
0.1
ME-disc-katz
0.05
baseline
0
-0.05
katz
-0.1
kneser-ney-mod
-0.15
-0.2
ME-gauss
-0.25
100
1000
10000
training set size (sentences)
100000
relative performance of algorithms on Brown corpus, 3-gram
0.1
ME-disc-katz
0.05
0
baseline
-0.05
-0.1
katz
-0.15
-0.2
-0.25
kneser-ney-mod
-0.3
-0.35
100
ME-gauss
1000
10000
training set size (sentences)
&uvyp2t
r rat«iPgtsmoxw'e4r{t²r4hxqsuvrqsg2xsr4hvuw'rgBiBxt
uvgp'©mggq_f'uw'yxBhvygt²u¤q_f2m³gBratm¯p'hvqsun'hvroqtLxBuw'uw'y
sr4qLu 4r4?gw¡qf'r{¸lt
g'xB 2eaxBsq r4¢³xGw' ~¸t²g;¢?w¡e4gtsn2g'tsx22'uvytsxm¨xw' qt
uvytLxmmg 2r4hv
:

diff in test cross-entropy from baseline (bits/token)
diff in test cross-entropy from baseline (bits/token)
relative performance of algorithms on Switchboard corpus, 2-gram
0.1
0.05
baseline
0
-0.05
katz
-0.1
ME-disc-katz
-0.15
kneser-ney-mod
-0.2
ME-gauss
100
1000
10000
training set size (sentences)
100000
diff in test cross-entropy from baseline (bits/token)
diff in test cross-entropy from baseline (bits/token)
relative performance of algorithms on WSJ corpus, 2-gram
0.1
0.05
baseline
0
-0.05
ME-disc-katz
-0.1
katz
-0.15
kneser-ney-mod
-0.2
ME-gauss
-0.25
100
1000
10000
training set size (sentences)
100000
relative performance of algorithms on Switchboard corpus, 3-gram
0.1
ME-disc-katz
0.05
baseline
0
-0.05
katz
-0.1
-0.15
kneser-ney-mod
-0.2
ME-gauss
-0.25
100
1000
10000
training set size (sentences)
100000
relative performance of algorithms on WSJ corpus, 3-gram
0.1
ME-disc-katz
0.05
baseline
0
-0.05
ME-gauss
katz
-0.1
-0.15
-0.2
kneser-ney-mod
-0.25
-0.3
100
1000
10000
training set size (sentences)
100000
&uvyp2t
r rat«iPgtsmoxw'e4r{t²r4hxqsuvrqsg2xsr4hvuw'rgBiBxt
uvgp'©mggq_f'uw'yxBhvygt²u¤q_f2m³gBratm¯p'hvqsun'hvroqtLxBuw'uw'y
sr4qLu 4r4?gw¡qf'r{d'¢u¤qLe[f'2gxGt
´xw' ÔxBhvhd'qt
r4r4q gp2tsw2xBhFe4g'tsn2gtLx22'u¤y'tsxm¨xw' qt
uvytsxGm mg 2r4hv
:
ratio of expected to actual counts, 2-gram, 750k words training
ratio of expected to actual counts, 3-gram, 750k words training
kneser-ney-mod
kneser-ney-mod
1.15
expected count / actual count
expected count / actual count
1.1
1.05
1
0.95
ME-gauss
1.1
1.05
1
0.95
ME-gauss
0.9
0.9
0.85
0
5
10
15
20
count
25
30
35
0
5
10
15
20
count
25
30
35
&uvyp2t
r
xBqsuvgogBi&r42n2r4e4qsr4 |wp2m2ratqsgoxBe4qp2xh w'p2m2ratuwqsr4sqlsr4qgBi*¶®§OytLxml¢uvqf~xyuvraw¡e4gp2wGquw
qtsxuw'uw'y¡ /xBqx2X 2 E¢lgt
Ô xBhvhd'q_t
r4r4q gp2tLw2xBhFqtsxuw'uw'yoLr4qa/'uvytsxm xw' ~qt²u¤y'tsxmmg' 2r4h¤
:
-

diff in test cross-entropy from baseline (bits/token)
diff in test cross-entropy from baseline (bits/token)
relative performance of algorithms on WSJ corpus, 2-gram
0.1
0.05
baseline
0
-0.05
ME-gauss
-0.1
-0.15
ME-gauss-1
-0.2
ME-gauss-3n
100
1000
10000
training set size (sentences)
100000
relative performance of algorithms on WSJ corpus, 3-gram
0.1
0.05
baseline
0
-0.05
-0.1
-0.15
ME-gauss
-0.2
ME-gauss-1
-0.25
ME-gauss-3n
100
1000
10000
training set size (sentences)
100000
&uvyp2t
r rat«iPgtsmoxw'e4rt
r4hxBqsuvrqLg 2xsr4hvuw'r|gBi? 2u ÂFrat
rawGq¬n2xtLxmr4qsrat
uaxBqLu¤g'w'¯giÕÇ{xp'Lsuxwn2t
uvgtgBrat
mp'hvqsun'h¤rqtLxBuw'uw'y¡sr4qLu 4r4?gw¡qf'r©ÔxBhvhd'qt
r4r4q gp2tsw2xBhFe4g'tsn2p'a/'uvytsxGmxw' ~q_t
uvytsxmmg' 2r4hv
:
iPgt©raxBe4fÀh¤r4Gr4hgBiqf'r¶2§Oy'tsxm mg' 2r4hI Ô=rxBhvsg|e4gw'suv 2rat
r4 Yp'suw'y x¦suw'yhvr g;Grat{q_f'r¬¢³f'gGh¤rmg' 2r4h
"*
+$ a4xw' ¯p'suw'y]qf2t
r4rn2xGtsxmr4qsrat² P4 xGw' A¡iPgtraxBe4f©hvr4r4h2gBi/qf'rl¶®§Oytsxmmg' 2r4hI
qsg~®r¬xn2n'hvuvr4 qsg §Oy'tsxm©¢uvqf Fg't gt©mgt
re4gp2wGqs©uwÀqf'rqtsxBuw'uw'y| /xBqx2Ft
r4_n2r4e4qsuvr4hv¬Åf'u¤
hxBqsqsrat]n2xtsxmr4qsrat
u axBqsuvgw$ "*+$ /uvoxw2xBhvgyg'p'{qsgqf'rn2xtsxGmr4qsrat
uaxBqsuvgw gBi³mg 2u¼ª/r4 ©w'r4srat¹§
r4=mg'gqf'uw'y/Åf'r¬n®rat«iPgtsmoxw'e4r¡gBiqf'r4srqf2t
r4roBxt
uxBqsuvgw'gw|q_f'r¬Ô xh¤hld'qt
r4r4q gp2tsw2xBh,e4gtsn2p']u¤
2uvn'hxr4 u!w &u¤y'p2t
r ®´Åf'r¡;xGt
uxBqsuvgw' "
*+~xw' "
$*
+ ´'u¤r4hv $xBhmgsq]u¤ 2rawGqsuveaxBh³n®rat«iPgt«§
moxw'e4rxw' |qf'r;xt²uxqsuvgw "*+$ n®rat«iPgtsm©shvuvyfGqshv|¢g't
sr {f2xuw'y~Lran2xtsxBqsr];xt²uxGw'e4r4{iPgt
raxBe4f ¶®§OytLxm°h¤r4Gr4hhvraxB 2oqsg|umon2t
gBr4 n2rat«iPgtsmxw'e4r&qf'uvouv¬x|p'sr_iOp'hl 2u¤Lqsuw'e4qsuvgwqsg=moxG¥Br|Ô=rxBhvsg
uwGr4sqsuvyxBqsr4 ~mxwgqf'ratln2xtsxmr4qsrat«§Oq
uw'yse4f'ramr4a22p'q³w'gw'r©Lu¤y'w'u ª/eaxGwqshvgp'q_n2rat«iPgtsmr4 q_f'u¤lsumon'hvr
qsr4e4f2w'uvµKp'r
,+"+H+J
qf2xB2r4raw½xGt
yp'r4 Yq_f2xBq¬moxB'ump2m rawqt²gnmg' 2r4hv 2gYw'gq¬t
r4µ2p'ut
r|mg'gqf'uw'yY2r4eaxp'Lr´q_f'r4Yxt
r
xBht
raxB 2xBp2w'u¼iIg'tsmgtmg'gqfxB&n2gGssu'hvr³yuvrawqf'rle4gw'sqtsxuwGqsa gB¢lr4rat4mxBump2mrawGqt
gnG{mg' 2r4h¤
eaxw®ruvr4¢lr4 YxBomoxB'um¯p2m°hvu¥Br4hvuf'gg' $r4Kn®gw'rawqLuxh³mg' 2r4h¤xw' Yf2xr¡sumuvhxton2t
g'n2rat
qsuvr4¬x¯gGqf'rat
moxB'ump2m hvu¥Br4hvuf'gg' ½mr4qf'g' 2a /gtEr4Kxmn'h¤rlxB]eaxw2r¡sr4rawu!w &uvyp2t
r ¢³f'raw= /xqx¦u¤on'hvrawGqsu¼i p'hP
mg'gqf'uw'y¬f2x³xmoxh¤hvratr_ÂFr4e4qa/xw' ¢³f'raw /xBqx]uv³_n2xt
sr2_mggGqf'uw'youv³r4sLrawqsuxBhP
w|moxwG~qxB_¥?uw'e4hp' 2uw'y=hxw'y'p2xByromg' 2r4h¤uw'y/uvq{f2xB{®r4raw¦iIg'p2w' ´q_f2xBq©p2n2rat²u¤g't{n2rat¹iIgtLmoxw'e4reaxw
2r~xe[f'uvr4r4 $=e4g'w'sqtsp'e4qsuw'y=Grat
=hxt
yr~mg 2r4hv´9Lg n2xGtsxmr4qsrat²xGt
r¬_n2xt
sr4hvr4sqsumoxBqsr4 /xw' qf'raw
mg'gqf'uw'yqf'ram ³Åf'p'aNiPgt³mxBump2m rawqt²gn~mg 2r4hv{qLg¬2roe4g'mon2r4qsuvqsuvr¢uvqf¦gq_f'ratqsr4e4f2w'uvµKp'r4]uw
qf'r4sr© 2g'moxBuw'aN¢r{w'r4r4 ¦r_ÂFr4e4qsuvr{moxB'um¯p2m rawqt²gn¡mg'gqf'uw'y¬xh¤yGgt
uvqf2ma
w$qf'uv~¢lgtL¥/?¢lr|f'gB¢r4 $qf2xq´xÇ{xGp'ssuxw½n2t
uvgt eaxw½®r p'sr4 qsgmg'gqf$moxB'ump2m rawGqt
gnG
¶®§Oytsxm mg' 2r4hvqsg xe[f'uvr4r=n2rat¹iIgtLmoxw'e4r~r4µ2p2xBh©qsgÀgto_p2n2rat
uvgt¡qsgqf2xBq¡gBi¯xBhvh?gqf'ratqsr4e4f2w'u¤µ2p'r4iPgt
!
(
(
#
#
#
#
c+d7e[kmh7pq-[w=r+=wmiq-w=u%v}egf (
%(
z kmiGpd7e
w={%ffq-w=uhjiq-kmiGz km{ju%sI~jIpd%e
kmtQeorxrfegwmilvd
t+eoileD[kYfpr-Iqxu2pd7eilw=u%ye
t+d7eoileRq-fGpd%efq ge[kmzQpd7e[pilwmqxujqxu%y fegpgG{jr-pqxhjr-Yq
u7y ~j,vgkmujeoilpfGpd7e[=wmiq-wmu7vgegfGz ilk
hjilkm~7wm~jqxrxq p 2fh7wYvge
pkvg km{jujpGfh7wYvgeYNwmu7s s;q-fvgk={9ujpfwmileGileor-wYpq-eor-2vgk=u%fpw=ujpqxu2vgk={9ujpGfh7wYv}e[k=YeoiDsqeoileoujpDpilwmqxujqxu7yIfegpGfq gegfgDc+d%eDsq-fvgkm{jujpf
peou7s9e}sIpk[ymilk=t#t q-pd
s9wpwfegpfq geGwmu7sIfd9iqxuj
t+q-pdI
c+d7eilegwYfk=uIpd7wYpwDmw=iq-wYpq-k=u2t+q-pdIkmileh7wmilwYegpeoilf[w=[u%kpk={%phneoiz_kmil
pk[fegw=ilv d
eliilkmilf+qxuIh%w=ilwY[e}peoikmh7pq-q gwYpq-k=u

wmw=iq-wYpq-k=u2t+q-pdz egt+eoi+h7wmilw[egpeoilf+q-fs{%e
mg'gqf'uw'y¶®§Oytsxm mg 2r4hvax¦ª/r4hv $¢³f'uve4fYf2xBxwr4'qsraw'suvr=2g' 2gBi{xBssg'e4uxBqsr4 Ót²r4sraxt
e4f7YÅf'uv¡u¤
qf'rª¿t
sq]e4h¤raxGt 2ramgw'sq_tsxBqsuvgw|q_f2xBq¯x|moxB'ump2mÒrawGqt
gnG=mg'gqf'uw'y|mr4qf'g' eaxw2r~x{r_ÂFr4e4qsuvrxB
mg'gqf'uw'yqsr4e4f2w'uvµKp'r4 iIg'togq_f'ratoq
2n2r4gBi¯mg' 2r4hva©xw' ½mox¥Br4¡uvq~n2gLsu'h¤rqsge4gw'sqtLp'e4qmoxump2m
rawGqt
gnGÕmg 2r4hv&uw]n2xt
sr& /xqxLu¤q_p2xBqsuvgw'¢uvqf'gp'qh¤gGsgi®n®rat«iIg'tsmoxw'e4r ¿p2t²qf'ratsmgt²rauvq&xB 2 2'ut
qp2xBhvhv
w'ge4gmon2p'qxqsuvgw2xBh7e4gsqlqsgqf'r©moxB'um¯p2m rawqt²gnqtLxBuw'uw'y¡n2t
ge4r4 /p2t²r gB¢r4Grat4®r4eaxp'sr©gBiq_f'r©hxGt
yr
p2w' 2rat
hv'uw'ye4gmn2p'qxBqsuvgw2xBh2e4gGsqgi moxB'ump2mrawqt²gnxBhvygt
uvqf2ma2p'uvh¤ 2uw'y¬mxBump2mrawGqt
gnG{mg' 2r4h¤
iPgtlrat
hxGt
yr{ /xqx]sr4qsuv?sqsuvhvhxe4f2xBhvh¤raw'yGuw'y~n2t²g'hvram
Ô½f'uvhvr¬q_f'u¤mggq_f'uw'y=mr4q_f'g eaxw=®rr4Kn2t
r4Lsr4 Grat
|sumon'hv&¢lr¬f'gB¢·qf2xBq©uvqon2gsLr4ssr4oxBhvhgBi
qf'r© 2r4sutsxG'h¤r]µKp2xh¤uvqsuvr4?gBik¶®§OytsxGm _mggGqf'uw'yw'gGqsr4 Gjf'rawxw' Ç©g'g /moxGwi t
g'mramon'ut
uveaxBh&xw2xBhv'suva
w$xB 2 2uvqsuvgw7Eu¤q~xe[f'uvr4r4uvqsr4'e4r4hvh¤rawGq´n®rat«iPgtsmoxw'e4r=p'suw'y»iIr4¢lrat¡n2xtsxmr4qLrat
¬q_f2xw!qf'r|e4gmon2xtsxG'h¤
n2rat¹iIgtLmuw'ymg' 2u¼ª/r4 ©w'r4srat¹§ r4¦mg'gqf'uw'y/
Åf'rÇ{xGp'ssuxwn2t
uvgt&xw' qf'r ©w'r4srat«§ r4¯mr4qf'g 2&e4g'w'suvsqsrawGqshv¯g'p'qn2rat«iPgtsm gqf'ratmg'gqf'uw'y©qsr4e4fG§
w'uvµKp'r4Åf'r 2uvsqsuw'e4qsuvgw¡2r4q
¢lr4raw]qf'r4srxBhvygt²u¤q_f2mxw' qf'rlgq_f'rat
&uvqf'r4ut&p'srgi mg' 2u¼ª/r4 ohvg;¢lrat«§Og't
2rat
2uvsqt
u2p'qsuvgw'xB© 2r4seat
u®r4 uw=d'r4e4qsuvgw' xGw' ©Åf'r4sr 2uvsqt
u2p'qsuvgw'oxt²r{e4f'gsraw|qsg¡xBqLu¤²iI¦e4rat
qxBuw
moxt²yuw2xBhe4g'w'sqtsxBuwGqs 2rat
uvr4 iOt
gm qf'rlqtsxBuw'uw'y© /xBqx2Åf'p'aBqf'rp'srlgBi¿moxt²yuw2xBhe4g'w'sqtsxBuwGqs&mox{2rx
n2gB¢lrat«iOp'h2qsr4e4f2w'u¤µ2p'r?iPgt& 2r4suvyw'uw'yow'gBr4h/_mggGqf'uw'y¯xBhvygt²u¤q_f2ma¢?f'r4qf'ratiPgt&hxw'y'p2xByr³mg' 2r4hvuw'yogtiPgt
gqf'rat* 2gmoxBuw'a&,wGiIgt²e4uw'yomoxGt
yuw2xBh2e4gw'sq_tsxBuwqL&¢g'p'h¤ moxtL¥{x©Lu¤y'w'u ª/eaxGwql 2ran2xt
q_p2t
rliOt
gmqtsx 2u¤qLu¤g'w2xBh
qsr4e4f2w'uvµKp'r4©p'sr4 ~uw mg'gqf'uw'y/
w~xB 2 2uvqsuvgw77q_f'r{Ç{xp'sLuxGw~n2t
uvgtuv{xµKp2xh¤uvqxqsuvr4hv~ 2u¼ÂFrat
rawq©n2t
uvgtqf2xw¦f2xB³2r4raw|p'sr4 =n2t
r4'uvgp'shv
uw|¶2§Oy'tsxm mg'gqf'uw'y/ ?qsgp'e4f'r4 ´g'wuw|d'r4e4qsuvgw Nhvuw'raxGt? 2u¤Le4gp2wqLuw'yeaxGw´®romgqsuv;xqsr4 ~qf2t²gp'yf
x ©ut
uve4f'h¤r4q?gt¸,r4qxn2t
uvgtlgwn2t
g'2x'uvh¤uvqsuvr4oÃ Ä 22p'q³uvq³f2xB?2r4raw_f'g;¢?w¡qsgon2rat«iPgtsmn®gg't
hvÔ½f'uvhvr
x'sgGhp'qLr 2uvse4gp2wGqsuw'y{'u¤r4hv 22r4qLqsratn®rat«iIg'tsmoxw'e4rBuvquvlp2w'e4h¤raxGtf'gB¢qsg©r4hvr4yxwGqshvr4Kn2t
r4Lqf'uvqLr4e[f2w'uvµ2p'r
qf2t
g'p'yf¬xn2t
uvgt, 2uvsqt²u2p'qLu¤g'w7 w¡e4gwq_tsxBsqaGqf'r©Ç{xp'sLuxGw¬n2t
uvgt,uv³xn2n'hvuvr4 ~qLg n2xGtsxmr4qsrat²¢³f'uve4fxt
r
hvuw'raxtluw¡hvgyB§¹n2t
g2xG'u¤hvuvq
¿xGw' ¬hvraxB 2qLg¯hvgy'xt
uvqf2muve© 2uvse4gp2wGqsuw'y/Åf'uvLumn'h¤rn2t
uvgt,uvr4hv 2? 2u¤Le4gp2wqLuw'y
qf2xBqluv?µKp2xBhvuvqxBqLu¤Gr4h¤|xw' µ2p2xwqLu¤q_xBqsuvr4hvsumuvhxtqLgoqf'r©ramon'ut
uveaxBhuv 2raxBhP
gqFg'w'h¤]eaxw©q_f'rÇ{xGp'ssuxw{n2t²u¤g't&2rxGn2n'h¤uvr4 oqLgÕmoxump2m½rawGqt
g'n©mg' 2r4h¤uw'y/'2p'quvq&eaxw]xBhvsg©2rxnG§
n'hvuvr4 uwqf'r³mgt
rlyraw'ratsxBh Ð /Ð /Ð aÎÏ 'Î Î?n2xtsxB 2uvym Ã ' Ä z=xBumu 4uw'yorawGqt
gnG{uv,r4µKp'uv;xh¤rawGq
qsgª¿w' 2uw'yqf'rmg' 2r4hF¢uvqfq_f'r{moxh¤hvr4sq ©p'hvh2xBe[¥§¹Á7r4u'hratE 2u¤Grat
yraw'e4r]i t²gmqf'rp2w'u iPgtsm 2uvsqt
u2p'qsuvgw7
w¦muw'um¯p2m¨ 2uvrat²yraw'e4r¯mg' 2r4hvuw'y/7gw'r{Lr4h¤r4e4qL³qf'rmg' 2r4hFxBqsuv
iP'uw'y¡qf'r]yuvrawe4gw'LqtsxBuwGqse4hvgsr4sq?qsg
sgmro 2r_i xGp'h¤q 2uvsqt²u2p'qLu¤g'bw A NZ BN4¬Åf'rmg' 2r4h A NC B/?eaxw2r¬p'Lr4 qsg¦r4Kn2t²r4s¯n2t
uvgt]¥w'gB¢hvr4 2yrx®gp'q
qf'r© 2gmxBuw7z|uw'um¯p2m 2uvrat
yraw'e4rmg' 2r4h¤©f2xr©qf'r?iPgtsm
A ±ZBN<
K A NC B/]r4Kn 8P Z B/s S
Åf'r{xw2xh¤'suv?uw¦d'r4e4qsuvgw xn2n'hvu¤r4©qLgoqf'r4sr{mg' 2r4hv³¢u¤q_f'gp'q³mg' 2u¼ª/eaxBqsuvgw7
z=xB'ump2m¨rawqt²gn|mg' 2r4h¤uw'y=f2xBxB 2;xwGqxByGr4©g;Grat?e4gmon2r4qLuw'y=xn2n2t²gxBe4f'r4©uwÀqsratsm©gBir4hvr4yxw'e4r
yraw'ratsxh¤uvq
Fxw' =n2rat¹iIgtLmoxw'e4r7xw' ~qf'roÇ]xp'ssuxw¦n2t
uvgt?uv{x¬n®g;¢lrat«iOp'hFqsg'ghiIg'tlmg'gqf'uw'yyraw'ratsxhFz=
mg' 2r4hva&Ô½f'r4qf'ratlqf'r{Ç]xp'ssuxw¡n2t
uvgtn2t²g;Gr4p2n®rat
uvgtqLg¯gGqf'ratlxBhvygt
uvqf2mluw¡ 2gmoxuw'gqf'rat,qf2xw¶®§
ytsxGm mg 2r4hvuw'y¬uvLqsuvh¤hxw¡gn2raw ramon'ut
uveaxBhFµ2p'r4sqsuvgw7 w¶®§OytsxGm mg 2r4hva/w'giIraxBq_p2t
r4n2xt
qsuxBhvhvgBrat
hxn
raxBe4fgqf'rat4lxw' qf'uv¡uvw'gqqf'r¦eaxBsruwyGraw'ratsxBhP w!xB 2 2uvqsuvgw7f'gB¢"n2xtsxGmr4qsrat
f'gp'hv $2r~qLu¤r4 !uw
gqf'rat, 2gmxBuw'±f2xGr4qqsgo2r?r42n'h¤g't
r4 F gw'r4qf'r4hvr4sg'p2tt²r4p'hvqs³xw' xw2xBhv'suv ²p'Lqsu¼iIoq_f'r³e4f'guve4r©gBix
Ç{xGp'ssuxw¡n2t
uvgt,iPgtp'sr©uw¶®§OytsxGm mg 2r4hvuw'y//xw' Lqt
gw'yhvp'yyGr4sqlu¤qL±p'Lr©uw¡gGqf'rat,suvqp2xBqsuvgw'³x¢lr4hvhI
W
`
O 23N
jO
8
YX

q-pd
feoh7wmilwpe
qxu
yYelu%eoilw=r_
y=ilwY,[ksjeor-fg+t+eDz_km{ju%s
z_kmi egwYvdIr-egeor+k=z+pd7e
&
\G]
> 69>
>_^
pd%wpwIfqxu7ymr-eI=wmiq-w=u%v}e
z kmipd%et+d%k=r-e[ks9elrt+kmi egs2Y{jq-pet+elrxr_ pd7km{7ymd
y=ilwY[ks9elr+t+k=iegsIfrxq-y=djpr-

W
`
~egppeli= kmtQegYeoi=pdjq-fh7wmilpq-pq-kmujqxu7y
{7fqxu%y
q-fu7kYpwmhjh9rxq-vgw=~9r e
%<9 J) &
2
%, J
+ =+a
'&
a+=+,D VT %
2 %") =% 3% D<) w qf'uv³Lr4e4qsuvgw72¢lr© 2rat
uvr{q_f'r{mg 2u¼ª/r4 |e4gw'sq_tsxBuwqLyuvraw¡uwr4µ2p2xBqsuvgw lxw' qf'rmg' 2u ª/r4 |p2n2 /xBqLr
iPgt?umon2t
gBr4 |uvqsratsxBqsuvrseaxh¤uw'y¦yuvraw|uw|r4µ2p2xBqsuvgwY ,iPgt?qf'roÇ{xp'Lsuxw|n2t
uvgt{mr4q_f'g |p'yyGr4sqsr4 =
ÁFxÂFrat
q
ÀÔ=r~p'srqf're4gw' 2uvqsuvgw2xhz= iIgtLm¯p'hxBqLu¤g'w7bNgtEi p2t²qf'rat] 2r4qxBuvhvx®gp'qoumon2t
gBr4 uvqsratLxBqsuvr
seaxBhvuw'y¡p'e[f¦xB³n2t
g'gBigike4gwGrat
yGraw'e4r/t
r_iPratlqsg~Ã Ä
Åg= 2rat
uvr¦qf'r~mg' 2u¼ª/r4 Óe4g'w'sqtsxBuwGqsa&¢lrqxG¥Brqf'r~n2xt
qLuxh 2rat
uv;xBqLu¤Gr4gBi³qf'r¦g r4e4qsuvr¡i p2w'e4qLu¤g'w
yuvraw uw r4µKp2xqsuvgw= a ,¢uvqf¦t
r4n®r4e4q³qsgqf'r{n2xGtsxmr4qsrat² xw' ~Lr4qqf'ramqsg 4rat
g/
>
_ LK
&
K
&
_
e4gw'sqB
sZB8Q '
r42n
sZB8Q s
] [ ZB8Q '
] [ Z BQ ®hvgy
r42n
²CBQ s sZBQ
] [ Z B8Q ' ¹ZB8Q '
] [ CBQ '

Z
/
B

A : B/ Z BQ
] [ Z B8Q ' ¹ZB8Q '
] [ CBQ '
< K
>
< K
>6j>
`
>
8P
> ^
>
b
&
T
< &
T
=69>
< T
< =69>
&
&
=69>
< m6j>
69>
&
]
m6j>
]
=69>
T
P
>_^
e4gw'sqa
»
`
>
b
>
T
` >
` >
: B/
][
&
T
>
>
T
>
T
` >
&
T
]
`
/ A : B/ sZB8Q
] [ CB/ A : B/ ¹ZB8Q '
] [ CB
<
' ¹ZB8Q '
] [ ZB8Q
&
>69>
>
\G]
8
&
`
&
T
>6j>
>
< &
V
&
' ¹ZB8Q '
] [ ZB8Q
&
&
< &
K
&
T
`
=69>
`
K
&
>
&
]
< b
8
'2hvgy<A : B/
] [ ZB8Q
b
`
>
` >
< & µ2p2xBqsuvgw= *iIgGh¤hvgB¢?sumon'hv¡i t²gm·qf'r{hxBsqh¤uw'r
Åf'r 2rat
uv;xBqsuvgw!gBi?qf'r´mg' 2u¼ª/r4 Yumon2t
gBr4 !uvqsratsxBqsuvrLeaxBhvuw'yp2n2 /xqsr~uv¡u¤ 2rawGqsuveaxBh?qsg=qf'rg't
uvyuw2xBh
2rat
uv;xqsuvgwr4e4ran'q]iPgt?qf'rn2t
r4sraw'e4r¡gBir4q_tsxqsratLm©iPgt©q_f'r¬n2t
uvgt4 w=raxe[f|uvqsratLxBqsuvgw7&¢lroqt²~qsg ª¿w' K\M Y©qf2xq³moxB'umu 4r4³qf'r©uw'eat
raxsr{uwq_f'r{g r4e4qsuvr?iOp2w'e4qsuvgw
_ o _ K ] [ Z B8Q ' sZ BQ
L
A : BN2r42n¿
²Z B8Q 's
S
] [ Z BN2hvgy

Y>
+:
b
GT
&
b
&
&
&
<
]
Y>a69>
T
>
< &
Y>69>
T
>
>
&
> Y>
>
`
>
³ uvq?u¤©w'gq?e4hvraxt³f'gB¢½qLg¬moxB'umu4r¯q_f'u¤?iOp2w'e4qsuvgw 2ut²r4e4qshv7¢rEª¿w' ´xw¦xp''u¤hvuxt
i p2w'e4qLu¤g'w ¡ oqf2xBq
¢lr _È =moxB'umu4rqf2xBq³®gp2w' 2©qf'uviOp2w'e4qsuvgw iOt
gm®r4h¤gB¢{Ô=r{¢lgp'hv |hvu¥Brqf'r¯moxump2mgi ¬ oqsg
2r]hxt
yrat,qf2xw 4rat²go¢³f'raw'r4rat $uv³w'gqlgn'qLumxBhPFÐ Î 2¢³f'raw'r4Grat Y 2g'r4Õw'gGq_xBqsuv
iP¬qf'r©e4g'w'sqtsxBuwGqsluw
r4µ2p2xBqsuvgw 4
}suw'yoqf'r]uw'r4µKp2xBhvuvq
hvgy B /B '¢lr©yr4q
_ _ ±
C BQ '
] [ Z B8Q '
H K o S
A : BN2r42n¿
Z BQ s
] [ Z BN

O
[b
a$ 7$
[b
T
ab
T
ab
&
&
Y>6j>
< &
<
&
]
T
>
&
> 6 >
>

T
>
&
>
>
`
>
>
d2p2'sqsuvqp'qLuw'y¡uw
o
ZB8Q 'xw' |xn2n'hvuw'y raw'sraw ?uw'r4µKp2xBhvuvq
7¢lr{xtst
uvr{xBq
Z B8Q '
Z B8Q '
HK ¬
A : B/
4
r
K

n
ZBQ s

] [ CB/

C BQ '
Åx¥uw'y¡qf'r{n2xt
qLuxh¿ 2rat²u¤BxBqsuvrgBi ¬ l¢uvqft
r4n®r4e4q³qLg ¹®¢r©yGr4q
¬ o K ] [ ZB8Q ' ¹ZBQ
[ Z BN
A : BN ¹Z B8Q '2r42n¿ ©Z BQ s
]

] [ Z BQ
ZBQ K,V
#6
&
&
&
<
Y>a69>
&
>
=69>
6
>
T
6 >
&
]
>
< &
> 6 >
Y>a6
T
< T
>
&
> Y>
>
S
`
>
Y>
&
&
=69>
<
]
Y>6
T
>
`
Y>
>
S
&µ2p2xBqsuvgw¡ a ¿iIghvhvgB¢G©sr4qsqsuw'y?qf'r4sr 2rat²u¤BxBqsuvr4,qsg4rat
g/ gqsuve4rq_f2xBq ¡ <K ?xw' ]qf2xBq ¬ G<K
gw'hv|u¼i xBqsuv
ª/r4]qf're4gw'sqtsxuwGqsa q?iPghvhvgB¢©qf2xBq©qf'romoxump2m¨gBi ¡ o?¢uvhvh®rohxt
yrat?q_f2xw 4rat
g
¢³f'raw YuvÕw'gGqgn'qsumoxBhP/x 2r4sut
r4 F
% 6%<% %@+
Ã [Ä 7ÁFxÂFrat
q
&n2rat²sgw2xBhFe4g'momp2w'u¤eaxqsuvgw7 2
Ã ;ÄÕ ¸,rat
yrat d7 ©r4hvhx uvr4qtsx®xw' ¯ ©r4hvhx uvr4qtsx® mxBump2mÒrawGqt
g'n|xn2n2t
gxBe4f|qsg~w2xqp2tsxBh
hxw'yp2xyr¯n2t
g'e4r4ssuw'y/ Ë Ê 'ÍPÈÍPÐ9Ë /È - Ð 'ÐÌ4ÍPÐ Ì[GghP Kw'gN /n2n7 5®
Ã ;Ä d7 ©r4hvhx uvr4qtsx2¯ ©r4h¤hx u¤r4q_tsx27xw' 7ÁFxÂFrat
q
w' /p'e4uw'y iIraxBq_p2t
r4³gi*tsxGw' 2gmª/r4hv 2a 7Ï
È ®Ì Ë ÈÍPÍPÎÏ NÈ - Ì[Ð ÌÕÈ /´È Ð NÎ /ÍPÎ -F- Ð Î ÎBghP ®Kw'gN 5®
Ã ÄÕ xBqw2xn2xtL¥f'uP|È ;Ð /ÍPÏ
Ë_Ê |0Ë /Î - Ì [ËGÏ ÈÍ 'Ï
È - È È 'Î 4Ð 'Ð9Í Î4Ì4Ë - 'ÍPÐÑË N f7 o
qf'r4Lu¤¿}?w'uvrat
suvq
gBi raw2w's'hv;xw'ux2 f'uvhx 2r4hn2f'ux2 N 52
Ã ;Ä gsrawGiPr4h¤ F moxB'um¯p2mÉrawGqt
gnGYxn2n2t
gxe[fqsgxB /xn'qLu¤Gr~sqxqsuvsqsuveaxBh?hxGw'yp2xByr|mg 2r4hvuw'y/% Ë Ê ÍPÎÏ GÊKÎ_Î !¯È / È 'È 'Îa,ghP 2n2n7 5" 2 52$hvgw'yGrat¡rat
suvgw!n2p2'h¤uvf'r4 xB
/xn'qsuvr=d'qxqsuvsqsuveaxBh©ÁFxw'yp2xByGr~z|g 2r4hvuw'y z xump2mº,wq_t
gnG n2n2t
gxBe4f7% f7 oq_f'r4suva
jlg'mon2p'qsratd'e4uvraw'e4r ©ran2xt
qmrawqa2jxGtsw'r4yuvr{z|r4hvhvgw~}?w'uvrat
suvq
¿Å jlz=}l§¹jdG§ B§ a ® n2t4 /
Ã ÄÕ ¸,rat
yratxGw' Bzúvhvhvrat4 p'sq
§OuwG§Oqsumrhxw'y'p2xByr³mg' 2r4hvuw'y/% uw#$%&' (*)Bd'raxBqsqshvrÔ 52
Ã Ä lÁFxp7 /xn'qsuvr¦sqxBqLu¤LqsuveaxBhhxw'yp2xByGr´mg' 2r4hvh¤uw'y/ z d7&qf'r4suva ©ran2xGt
qmrawGqogBi{&hvr4e4qt
uveaxBh
,w'yuw'r4rat
uw'y xGw' j±gmon2p'qsrat?d'e4uvraw'e4rz=xBLxBe4fp'sr4qLqs w'Lqsuvqp'qsrogBiÅr4e4f2w'ghvgyjxm2t
uv 2yr7z
/
Ã Ä d7 ljf'raw½xw' lÇ©g'g' /moxw7 wramon'ut
uveaxBh]sqp' 2!gBi¯mggq_f'uw'yqsr4e4f2w'uvµKp'r4¦iPgtohxw'y'p2xByr
mg' 2r4hvuw'y/% ÅFr4e4f7 ran7/Å § ;§ 52 xt
Bxt
~}?w'u¤Grat
suvq
5®
Ã Ä xKw'r4 wGiPgtsmoxBqLu¤g'w=qf'r4g't
xGw' sqxBqsuvsqLu¤eaxh±mr4e[f2xw'uve4a +* Ì4Ð Ì Î aÐ9Î$,Ì4&ghP 5®n2n7
® 2
Ã Ä {xtst²ge4fxw' o xBqse4hvu¼Â Ç©raw'ratsxh¤u 4r4 |uvqsratsxBqLu¤Gr{seaxBhvuw'yiIgthvgyB§Ohvuw'raxt©mg' 2r4hva% Î- /È - Ì
Ë ´ÈÍ 'Î ÈÍPÐ È - ¿ÍPÈÍPÐ Ì[ÍPÐ 4Ì4'ghPX Kn2n7 2 5
b
,
4
4
4
b
WW
Q3
O
O N3
W
WW
O ;$ O
O
IO
P
O
%M 23N
O
O
O
+P
jO
1
W
3
O3
WW
I
N3
P
3
O
WW
+3
O
ON3
WW
:
}W
WW
WW
W W
}W
WW
-W
NP
g1
W
j
IO O
2
W
Ã [Ä &Á &¸lxf'hP" r4hvuw'ra¥/xGw' &Á&z|rat
e4rat4 moxB'um¯p2m°hvu¥Br4hvuf'gg' ½xn2n2t
gxBe4f|qsg|e4gwGqsuw'p'gp'
n®r4r4e[f|t
r4e4gGyw'uvqsuvgw7% 7Ï
È 2Ì FË ÈÍPÍPÎÏ NÈ - Ì[Ð ÌÕÈ /#´È Ð /Î NÍPÎ -- Ð Î _ÎaGghP N z §
Nw'g/ 2n2n7 ®z=xt4 5
Ã a;ÄE K¸lt
gB¢³w7 ¿j±ge4¥Br2d7 ©r4hvhx uvr4qtsx2 ©r4hvhx u¤r4q_tsx2 r4h¤uw'ra¥N o/ÁFxÂFrat
q
7Á&
z|rat
e4rat4xw' Fd7 g'gssuw7 sqxBqsuvsqLu¤eaxhxn2n2t
gxBe4f¦qsg~moxBe4f'uw'roqtsxGw'shxBqsuvgw7% Ë Ê ÍPÈÍPÐ9Ë NÈ Ð 'ÐÌ4ÍPÐ 4Ì4GghP 2/w'g/ /n2n7 p2w7 ®
Ã a;Ä z ?ratsw'uvyf2xw7 &jfp2t²e[f7xGw' Ô Ç{xBhvr n®r4h¤hvuw'ye4gtst²r4e4qsuvgwn2t
gytLxm 2xBLr4 gwx¦w'guvs
e4f2xw2w'r4hmg' 2r4hP% |uwÏ
Ë FË ©Í Î'
Ð9Ï_ÍPÎÎ /Í /ÍPÎÏ NÈÍPÐ9Ë /È - Ë Ë ,Ë Ê ÍPÈGÍPÐÑË NÈ - Ð 'ÐÌ4ÍPÐ 4Ì4
22n2n7 2 2
Ã Ä r4hvuw'ra¥ÓxGw' lÁ&,z´rat²e4rat4 wqLratsn2ghxBqLr4 Yr4sqsumoxqsuvgwgBi{z=xtL¥BgB=sgp2t
e4r|n2xtsxmr4qsrat
iOt
gm
n2xGt
sr{ /xqx2% =uw Ï
Ë Ë ¯Í Î ËÏ Ì 'Ë_Ê Ë ÈÍPÍPÎÏ Î Ë /Ð9ÍPÐ9Ë ~Ð Ï
È aÍPÐ _Îa msqsrat
/xm /Åf'r
r4qf'rat
hxw' 2 gt
qfG§ ghvhxw' F/z=x 2
Ã a;ÄE 2¸t²g;¢?w7d7 ©r4hvhx uvr4qtLx2¯ ©r4h¤hx uvr4qtsx2 2j©2ÁFxBuP2xw' 2Á&'z|rat
e4rat4 wor4sqLumxBqsr
gBixw¦p2n2n2rat?2gp2w' ¦iPgtlqf'r©rawGqt
gnG¡gBi*,w'yhvuvf7% Ë Ê 'ÍPÈÍPÐ9Ë /È - Ð 'ÐÌ4ÍPÐ 4Ì4ghP 2/w'g/ /n2n7
2 2'z=xt4
Ã Ä Å©'j©¸,r4hvhP 2Çojlhvraxt
2xw' Ô$uvqsqsraw7 7Î ;Í ,Ë Ê¿Ï
Î4Ì_Ì[Ð9Ë / t²rawqsuve4r xh¤hP2w'yGh¤r4¢lg'g jlhvu¼ÂFa
]
2
Ã Ä d7Bz ©xBq &LqsumoxBqsuvgw]gBi¿n2t
g'2x'uvh¤uvqsuvr4,iOt
gm$n2xGt
srl /xBqx±iIg'tFqf'r,hxw'yp2xByrmg' 2r4h2e4gmon®gw'rawGqgBi
x_n2r4r4e4ft
r4e4gyw'u 4rat4% 7Ï¹È 2Ì 7Ë _Ë GÌ[ÍPÐ 4Ì %GÊKÎ_Î oÈ /¿Ð NÈ - lÏ¹Ë Î ÌÌ4Ð BGghP d2d § G
w'g/ /n2n7X z=xt4 5 2
Ã Ä ©w'r4sratxw' r4 mn2t
gBr4 2xBe4¥uw'yB§OgÂYiPgt©m]§OytsxGmÒhxw'yp2xByGrmg' 2r4hvuw'y/% üw Ï
Ë lË
Í Î /ÍPÎÏ NÈÍPÐ9Ë /È - Ë lË Ë Ì4ÍPÐ Ì ÊKÎ_Î =È / ¿Ð /È - Ï
Ë Î ÌÌ4Ð ghP n2n7
N
Ã Ä r4}]&&ssraw7lxw' ©w'r4srat4
¾©wLqtsp'e4qp2t
uw'y n2t²g2x'uvhvu¤Lqsuve´ 2ran®raw' 2raw'e4r4uwsqsg'e4f2xBsqsuve
hxw'yp2xyr¯mg' 2r4hvuw'y/% Ë Ê 'ÍPÎaÏ Ê2ÎÎ kÈ / È 'È Î'ghP 2/n2n7 2 /
Ã ÄE Ç©g'g' F Åf'r±n®gn2p'hxBqsuvgwi t²r4µKp'raw'e4uvr4lgBi¿_n2r4e4uvr4xw' qf'rr4sqsumoxqsuvgwgBiFn2gn2p'hxBqsuvgwn2xtsxmr4qLrat
a% Ð9Ë ÎaÍPÏ_Ð BÈ/GghPX 22w'g/ xw'# /2n2n7 G /
Ã 2[Ä Ô&jfp2t²e[fxw' Ô &Ç{xBhvr e4g'mon2xt
uvsgwÀgBi³q_f'r¬raw2f2xw'e4r4 $Ç©g'g '§¹Åp2t
uw'y xGw' 2r4h¤r4qLr4 r4sqLumxBqsuvgw|mr4qf'g' 2?iIg'tr4sqLumxBqsuw'yn2t²g2x'uvhvu¤qLu¤r4gBi,w'yhvuvf='uvytsxma% ,Ë Ê ÍPÎÏ ÊKÎ_Î !È /
È 'È Î2ghP /n2n7 /
Ã ;Ä d78 ¿jf'raw7 oF¸,r4r_iIratsmxw7xw' gsrawGiPr4hv F *;xBhp2xBqLu¤g'w=mr4qt
uve4EiIgthxw'yp2xByGr¬mg' 2r4h¤% uw
& Ï
ËaÈ / ÈÌ[Í Î
,Ì 7Ï¹È 2Ì aÏ_Ð Ê¿ÍPÐ9Ë È / /ÎaÏLÌ4ÍPÈ /Ð ËÏ aÌ Ë_Ê¿ 52
Ã ;ÄE ¸lt
gB¢³w7'd7 ©r4hvhx uvr4qtsx2 ¯ ©r4hvhx uvr4qtsx® Gz´rat²e4rat4 ?xB /xBa'xw' ¬d7 gp2¥Bg moxump2m
n®raw2xBhvu 4r4 ¦rawq_t
gnG{e4gw'sq_tsp'e4qsuvgwgBi¿e4gw' 2uvqsuvgw2xh¿hvgy§Oh¤uw'raxt±hxGw'yp2xByr³xGw' oqtsxw'Lhxqsuvgwomg' 2r4hv±p'Luw'y
hvraxtsw'r4 ¦iPraxBqp2t
r4xw' |xyraw'ratsxh¤u 4r4 |e4suv axtxBhvygt
uvqf2m wGqsratsw2xBh ¸,z ran2gt²qa
Ã Ä Áxp7 gsrawGiPr4h¤ F©xw' ½d7 gp2¥BgGa /xn'qsuvr|hxw'yp2xByGr mg 2r4hvuw'yÓp'suw'yqf'r=moxump2m
rawGqt
gnGń2t²uw'e4un'hvr% uw lÏ
Ë *Ë ¬Í Î & ËÏ aÌ Ë_ÊYË È È 'È Î 7Î NË - Ë B
n2n7 5
a

O j$
W
W
O
O
IO
P
O
O
O
9O
W
O N3
W
O
WW
%$ g1
W W
+3
9O
O
O
O
O;1;$ O
Q3
O
O N3
%$ g1
O
j:
O
mNO
O
O
W N
Q3
O
O N3
WW
;M
O
WW
O j$ O
N N
O
O
3
O
NO
O
W
7$
O
W
O;1;$
O
3
O
NO
O W W
Q3
O
O N3
W W
N
W
O N3
W
O
O
O
O
O
O
WW
WW
7$
O
Q3
W W
g1
O
3
O
O N3
NO
=NP
WW
g1
Ã ;Ä d7 ©r4h¤hx uvr4qtsx{xGw' ¯ ©r4hvhx u¤r4q_tsx2/d'qxqsuvsqsuveaxBh¿mg 2r4hvuw'yoomoxB'ump2m rawGqt
g'n%p2w2n2p2'hvuvf'r4 t
ran®gt
qa
Ã Ä 7ÁFxp7 gGsrawGiIr4hv FFxw' |d7 gp2¥Bga _Åt
uvyyGrat«§¹2xBsr4 ¦hxGw'yp2xByrmg 2r4hv moxB'um¯p2m rawGqt
gnG
xn2n2t²gxBe4f7%=uw lÏ¹Ë Ë -
% ' ( n2t Kn2n7 ¹ ¹ 2
Ã Ä Ô r4¢³moxGw7 *qLraw'suvgw=qLg~qf'rmoxB'um¯p2m rawq_t
gnG mr4qf'g F 7Ï
È ®Ì *Ë 4ËÏ ÈÍPÐÑË
'ÎËÏ B2ghP Å,§ Nw'g/ /n2n7 " xw7 552
Ã Ä d7 ©fp' /xGw2n2p2t4 mr4qf'g !gBi{moxB'ump2m rawGqt
g'nr4sqsumoxBqLu¤g'w¢uvqf!t
r4hxBr4 $e4gw'LqtsxBuwGqsa% uw
( 2Ë ®Ì ©Ë_Ê BÐ ®Ì /Ð aÎaÏLÌ4ÐÑÍ È 'È 'Î´0Ë /GÎ - Ð ËÏ aÌ Ë_Ê Ï
Ë 'jlrawqLratiPgtÁFxGw'yp2xByr©xw' ( d2n®r4r4e[f t²ge4r4sLuw'yN gf2w' g'n2¥uw'©}³w'uvrat
Lu¤q
7¸lxBhvqsumgt
r
Ã Ä o jEBz xe ©xa{xGw' ¬Á&j© r4qsg/ f'uvratsxt
e4f'uveaxBh ©ut
uve4f'hvr4qhxw'yp2xByGr³mg' 2r4hI ÈÍ 'Ï¹È - È È Î
Ð /Î_ÎaÏ_Ð GghP 2w'g/ /n2n7 2
Ã ÄÕ ?xB /xB *sqsumoxBqsuvgw gBin2t
g2xG'u¤hvuvqsuvr4{uw|q_f'r{hxw'yp2xByGr¯mg' 2r4hgiqf'r ¸z n®r4r4e[f|t
r4e4gy'w'u¤qLu¤g'w
s'sqsram % 7Ï
È 2Ì Ë Ë GÌ4ÍPÐ Ì Ê2ÎÎ ~È /7Ð /È - Ï
Ë Î ÌÌ4Ð 2GghP d2d § w'gN /Fn2n7
5 p'y/ 5 /
Ã 2[Ä lÁFxÂFrat
q
xw' Ó¸?d2p2f2m _jlhp'sqsratr42n2xw'suvgw'~xw' !uvqsratsxBqsuvr¦seaxBhvuw'yiIg'tomoxB'um¯p2mÉrawGqt
gnG
hxw'yp2xyr~mg' 2r4h¤% uw |È ;Ð /ÍPÏ
Ë_Ê ´È / È BÎ4Ì4Ð9È |ÎaÍ 6Ë /BÌ[ xw'sg'w xw' kd'uvhvrat4
* 2a ?hp¢lrat eax 2ramuve p2'hvuvf'rat

Ã ;Ä ©p'e4ratsxxw' oÔ5 7tsxw'e4uva,Ë Ê ÍPÈGÍPÐÑË NÈ - /È - Ì4ÐÌË Ï
Î Ì[Î /Í È ÎaÏ_Ð _È # - Ð Ì 7¸lt
gB¢³w
}?w'uvrat
suvq
t
r4La t²g;'uv 2raw'e4r 552
Ã ;Ä Nz/d'qsratsw7 _d2n2r4e4u¼ª/eaxBqsuvgw¦gBi&qf'r N fp2 r4BxBhp2xBqsuvgw }?w'hvumu¤qLr4 =g'eax2p'hxt
¸
w'r4¢©2xBsr4hvuw'r% uw Ï
Ë Ë {Í Î GÊKÎ_Î Î _Ë NÐÑÍPÐ9Ë ËÏ Ì 'Ë_Ê¿ 52'n2n7 ®
Ã ÄÕ p' /w'uve[¥G- p2 &¸lp'suw'r4s³¸lt
g'xB 2eaxBsq r4¢a% ¦uw Ï
Ë 7Ë {Í Î & Ê2ÎÎ lÎ _Ë /Ð9ÍPÐÑË
ËÏ aÌ Ë_Ê7 522n2n7 G
Ã ;Ä FÇEg 'iOt
r4F ghvhvumoxw7&xw' 7z|e {xw'uvr4hP d'Ô Åj ¸l¾ FÅr4hvran2f'gw'ron®r4r4e[f e4gtsn2p'©iPgt
t
r4Lraxt
e4fxw' ~ 2r4r4hvgn2mrawqa =uw Ï
Ë Ë $ ' ( gGhI /n2n7 2 2
Ã Ä Ô t
r4sa/¸?X &hxw2w'rat²¿d7/Årap2¥Bghv¥G7xw' Ô &r4qsqsrat
hvuw'y/ ÎaÏ_Ð _È - lÎ Ð Ê2Î4Ì©Ð ,jxm2t
uv 2yr
}?w'uvrat
suvq
t
r4La/jxm2t
uv 2yr 552
Ã Ä d7 ©p'hvh2xBe4¥/ 4ËÏ ÈÍPÐ9Ë Î_ËÏ oÈ / 7ÍPÈÍPÐÌ4ÍPÐ 4Ì4Ô$uvhvr4 r4
¢ &gts¥N 2
Ã Ä oF¸,r4r_iPratsmoxw7 7¸,rat
yrat4xw' FÁFxÂFrat
q
mg' 2r4h&gBilh¤r4'uveaxBhxqsqtsxBe4qLu¤g'w~xw' =t
ran2p'hvsuvgw7% ·uw
lÏ¹Ë Ë Í Î 'z x /t
uv F/d2n2xBuw7 52
WW
j:
7$ g1
WW
O ;$
YP
W
NO
O
O
W
O
O1
Y
O
P
W
ON3
O %$
WW
W
[O O
O
W
3
O3 ;
WW
O j$ O
W
3
O
-O
O W
%M 23N
O
+P
O
P
O
WW
Q3
O
IO
P
g1
9O
WW
I
O
O +:
7$ g1
=NO
O
:
P
W
WW
%$ g1
=O
W W
7$ g1
:
WW
3
O
W
YO1
O
YP
O
W
7$ g1
WW

W
O

Download Report

A Gaussian Prior for Smoothing Maximum Entropy Models stanley F

Paperzz.com

Your Paperzz