34658769:<;=7>:?:A@?BC76D/:<EGFIH>9KJMLNBO7>LN5
PQSR6TVUXWZYQS[W]\V^/_`[a^b\cUZYTWZdfeSgSh6ij[6dfkNQlUZgXdmWon\c^%pqQlUZrcQS[sh6tju`vcwyxcw*p+QlUZryQS[zh>tj\cUX{]TSn
|=}M~SS>yyK
\cg Wj\V^AWZ6QjUZQSeSQS[WelUXnaRWTV[>TVfnagXdfg\y[g naYYQlWXUZdfeNQln,eSdfR6QlUZg]>TkNQj^b\eSgXQK\y[TcfryQlu
UTVde1TWXWTcegS86QeldR6QlU QSdf[rTVWXWTceNQ,dfgUZQSRaUZQSgXQS[WZQTVgT[6\y[audf[QTVUQ>TWZdf\y[g nag WZQSYh6Tc[6
kyTUZdf\y6g]WZQSe6[dQSg1pq6e
QlUZryQGUh>ANc/vh>%h6aA qeTV[
QWXUZdQSKdf[\cUaQlUjWZ\¡gX\yfkNQWZ6Qg nag WZQSYh
WZ6g UZQSTcdf[6rjWZQeSdfR6QlUy6Q]gX6eleSQSgXg/\c^8WZQSgXQ]TVWXWTVeGg/>TVg QSQS[¡fdfYdmWZQgX\j^¢TVUy_`[£WZ6dfg?R>TVR8QlU/{Q
WTcNQTadm¤IQlUZQS[WTcRRUZ\yTce=WZ\1WZ6QRaUZ\
QlY¥\c^MgX\yfkd[r¡[\y[ufdf[6QTU]Q>TWZdf\y[Kg nag WZQSYgShaTV[>RUZ\cR8\ygXQ
T£[Ql{<YQlWZ\¡^b\VUgX\yfkd[r£WZQSYa¦aUYQlWZ\dm¤IQlUZgq^§UZ\yY¨WZQ\VWZ6QlUZgdf[WZ>TWWZ6QQ>TWZdf\y[6gTVUZQ
[6\VW?UZQSRUZQSgXQl[WZQS*Tcg/Y¡mWZdkcTVUZdTWZQR8\ymna[6\cYd§TVfgShNTV[>£WZ6TVW/WZ6QqeS\cUZQ]\V^8WZ6Q]TVrc\cUZdmWZ6Y©^ª\cU%«>[>adf[6rjWZQ
gX\yfWZdf\c[=eTV[ QgXQSQS[=TcgqYQSgXgZTcrcQluR>TcgXgXdf[r¡\y[,T1rcUTVR6sap+\y6[6g+\y[WZ6QeS\yYRQG¬dmWZdfQSgq^ª\cUWZQjYTVdf[
Tcfry\VUZdmWZ6YgjTVUZQ1RUZQSgXQl[WZQSTc[6=WZ6Qln=eS\cYR>TVUZQ^bTkN\cUT mnK{dmWZWZ6Q[\{[ \y6[6gS66Q1YQlWZ\g
>TkNQ¡TcfgX\
QSQS[WZQSg WZQ®\y[UZQeSQuUZ\c6[6kyQlUZgXdf\y[6g1\V^P¯+{dmWZry\\UZQSgXmWZgSMdfg£R6TcR8QlU{]Tcg
R8\yg WZQ,\y[¯+°q±?²³%´gaµ{qQ gXdmWZQ\c[¶NTc[6TVUXn·¸WZxcwcwy¸a
¹<ºI»]¼½%¾6¿jÀIÁÀaÂjÃ?¾6ÀºÄÃ/Å`Æ+ºzǾÃ/È`ÉʺsËÌÃAÍaÈ`½+ÎjÀ8ÏÇÅ`½]É6ÐÑÉzÈ`ÂÒjºz¾6À8ÏÃ/ÅoÆ+ºzǾÃ/È`ÉÓÃAÍÍÃ?ÉÐ]À8Ï1Ô<Õ®Ö×
Ø ÙÚjÛ8ÜIÝޣߣàMÛIáÝÚ
âÓH8ãäåH6æ=äç/LéèN9êMë?äV76D%76ì¢êMãíãî:?H>D/LïH>DÑãêMBîBðLNä9íèïñILNêòèNí¢ë?ç/LN9ãåí¢D¥äç/Lïì7>ã䮿XLNóôêIL769ãåç%7>ãõLLND
æ HMèN@/ãL:öH>D(76ì¢FILNõ?9V76íèð76ääV7>èñAã÷âÄ@/èVç©H6æ£äç?íãí¢DzäLN9LãäèH>BðLãKæ 9H>Bøäç/L®æZ7>èNääç%76ääç/LùKúJÓè76D
õqLO:?LãèN9í¢õqL:¨7>ã®7<ãêAãäLNBûH6æüz@%7>:A9V76äíèðLüs@%76äíH>D/ãý76D/:(äç%76ä®ãH>ì¢5Mí¢D?FÊäç?íã®ãêAãäLNBþõ?9L76ñAãäç/L
èNí¢ë?ç/LN9ÿ÷
D/Lîí¢BîëH>9äV76DzäæXL76ä@?9Lé76ì¢FILNõ?9V76íè76ääV7>èñAã®ç%75ILðíãäç/LðæX7>èNä®äç%76ä®êIH>@¨H>D?ì¢êöD/LL:ò5ILN9êöæ LNó
ñsD/HaóD¥ë?ì76í¢DzäLAäãí¢D¥H>9:?LN9äHÄãLNä@?ë¥76D Lüz@%76äíH>DÑãêAãäLNB :?LãèN9í¢õ?í¢D?Föäç/LïèNí¢ë?ç/LN9å76D/: :?LNäLN9
Bîí¢D?í¢D?FÑäç/LÄñILNê @?D?íüz@/LNì¢êI÷ *ç?íãïBO76ñILãäç/LãLö76ääV7>èñAãBðH>9LÄ9L76ì¢íãäíè©76D/: äç?9L76äLND?í¢D?FÑäç%76D
:AíLN9LNDsäí76ìH>9ì¢í¢D/L76976ääV7>èVñMã®äç%76ääêMë?íè76ì¢ì¢êö9Lüz@?í¢9LðLND/H>9BðH>@/ã76BðH>@?DzäãH6æñMD/HóDòH>9èVç/H8ãLND
ë?ì76í¢DzäLAäã÷
Jsä9V76äLNF8íLãæXH>9ãH>ì¢5sí¢D?FD/H>DZì¢í¢D/L769®Lüs@%76äíH>D©ãêAãäLNBðãKç%75ILåõLLNDö:?LãVèN9í¢õqL:¥ÿ76D/:öãH>BðL
ç%75IL¡õLLND:?LN5ILNìH>ëL:í¢DsäH=èN9êMë?äV76D%76ì¢êMäíè*76ääV7>èVñMã*ÿ8ýAý÷
äç/LN9óH>9ñç%7>ã:?LãèN9í¢õL:®í¢DsäLN9Lãäí¢D?F
76ì¢FILNõ?9V76íèÄë?9H>ëLN9äíLãOæ H>@?D/:Ñí¢D äç/LÄùKúJqý1õ?@?äðóí¢äç/H>@?ä76Dzê 7>èNä@%76ì76ääV7>èñAãÓÿMý÷*ç/LN9LÊç%7>ã
õqLLNDÊãVH>BðL:?LNõ%76äLH5ILN9äç/LLOèNíLND/èNê<H6æjäç/LJ !G76ääV7>èñ<H>D<äç/LùKúJqý/76D/:ãH>BðLë%76ëqLN9ã*ç%75IL
76ë?ëqL769L:¨ÿ"Aý#%$í¢D/:Aíè76äí¢D?FOí¢äíãD/H>ä=7>ãFIHMHs:Ê7>ãèNì76í¢BðL:Êõzêäç/L76@?äç/H>9ã÷
D/LH6æäç/Lë?9H>õ?ìLNBðãäç?íã &%LNì:<H6æ9LãL769èçÄç%7>ãLND/èH>@?DzäLN9L:Êíãäç/L:AíOèN@?ì¢äê<H6æjë?9HM:A@/èNí¢D?F
FIHsHM:ÄL/76Bîë?ìLãKH6æ76ì¢FILNõ?9V76íè76ääV7>èVñMãKè7699íL:ÓH>@?ä=í¢DÄë?9V7>èNäíèL8÷'*ç/L®äí¢BðL76D/:ÊBðLNBðH>9êÊ9Lüs@?í¢9L
BðLNDzäãH6æ9@?D?D?í¢D?FÄãH>BðLðH6æäç/Lîë?9H>ëH8ãL:ò76ääV7>èVñMã®9V76ë?í:Aì¢ê©F89Hóã®H>@?äH6æ*äç/LðõqH>@?D/:?ããLNäõzê(7
76ë?ë?9HI7>èçð:Aí]LN9ã7ìH>äjæ`9H>B L769ì¢íLN9óH>9ñ®í¢Däç%76äLüz@%76äíH>D/ã769L¡D/H>äj9LNë?9LãVLNDzäL:î7>ãëqH>ì¢êMD/H>Bîí76ìã÷
ú1üs@%76äíH>D/ãK769L9LNë?9LãVLNDzäL:ö7>ãì¢íãäãH6æõ?í¢äãä9í¢D?FIãý/óç/LN9L®L7>èç ãä9í¢D?Fðíã,7î5>76ì¢@/L®7>ãVãí¢F8D?BðLNDzäKH6æ
5>769í76õ?ìLã,äç%76ä,ãV76äíã&%Lãäç/LLüz@%76äíH>D÷
(L¡ç%75IL@/ãL:9L:A@/èL: Z9H>@?D/:ð5ILN9ãíH>D/ãH6æKú¡JäH=äLãä1H>@?9BðLNäç/HM:?ã÷(*ç/L*9Lã@?ì¢äããç/HóÑäç%76ä
H>@?9äLèVç?D?íüz@/Lã*L7>ãí¢ì¢êîãH>ì¢5ILãäç/L,ãêMãäLNBèH>Bîí¢D?F®æ 9H>BæXH>@?9£9H>@?D/:?ã¡H6æKú¡JqýM76D/:Oäç%76ä£õH>äç &/5IL
76D/:Ñãí¨9H>@?D/:?ãOH6æúJ è76DÑõqLïõ?9H>ñILND¥æZ7>ãäLN9åäç%76D LMç%76@/ãäí¢5IL<ãL769èç÷ ç?í¢ìLõ?9L76ñsí¢D?F(ãí
9H>@?D/:?ã®H6æKú¡JÓíãD/H>ä5ILN9êÓí¢DsäLN9Lãäí¢D?FÊí¢D©í¢äãLNìbæýqäç?íãóH>9ñ F8í¢5ILã®76D(L/76Bîë?ìLîH6æ*7ã@/èèLããæ`@?ì
76ì¢FILNõ?9V76íè76ääV7>èVñ<76Fz76í¢D/ãä,ãH>BðLNäç?í¢D?FOäç%76ä,ìHsH>ñAã*ì¢í¢ñIL®79L76ìZóH>9ì: èNí¢ë?ç/LN9÷
EGäóí¢ì¢ì76ìãH õLèH>BðL<76ë?ë%769LNDzäîäç%76äýH>D 7ÊD/H>9BO76ìó¡H>9ñMãäV76äíH>Dýäç/LéD/LNó'BðLNäç/HM:¥óL<769L
ë?9H>ëqH8ãí¢D?F<íã76õ?ìLäHãH>ì¢5ILîãêMãäLNBðãKäç%76ä769Låë?9H>õ%76õ?ì¢êöH>@?äH6æ¡9L7>èç©õsêÄñMD/HóD©BðLNäç/HM:?ã÷/H>9
L?76Bîë?ìL8ýq7åãêAãäLNBèH>D/ãíãäí¢D?FéH6æLüs@%76äíH>D/ã,H6æ:?LNF89LL &/5IL®76D/:
1080
5>769í76õ?ìLã=:?LãèN9í¢õ?í¢D?FîæXH>@?9 9H>@?D/:?ãH6æ úJOóí¢äç %ñsD/HaóDë?ì76í¢DzäLAä6èNí¢ë?ç/LN9äLMä=õ?ìHsèVñMã*íã*ãH>ì¢5IL:ïí¢D (Bîí¢Dz@?äLãH>DÊ7K÷£Ü%ÚjÛIáÚß+ÛIáÝÚÚÞ ÜzߣÚÚ£áGÚ Û! #"$Ü%%áGÚ&'(ÝÜzáZÛ )
*ç?9H>@?F8ç/H>@?ääç/Lðë%76ëqLN9ó¡Lîóí¢ì¢ì£H>D?ì¢ê©èH>D/ãí:?LN9®Lüs@%76äíH>D/ãóç/LN9Lîäç/Lð5>769í76õ?ìLãç%75ILð5876ì¢@/Lãí¢D
GF
(2)
÷ LNäX
õL7åãLNä,H6æ+*¡HMH>ìL76D<58769í76õ?ìLã,H6æãí-,Ln
÷?ù ãêAãäLNB H6æm
**HsH>ìL76DÊLüs@%76äíH>D/ãf
1
(X
1
) = 0, . . . , f
m
(X
m
) = 0
. 0/íã=èH>D/ãí:?LN9L:]ý+óç/LN9L
f
i
=
f
i
(X
i
)
íã=71**HMH>ìL76DÄæ @?D/èNäíH>D í¢DÄ58769í76õ?ìLã
X
i
óç?íèçöíãK7Oã@?õ/ãLNäKH6æ
X
H6æãí-,Lk
i
÷2(L7>ãã@?BðL
k
i
≤
k
æXH>9ãH>BðL
k
÷Ô<º3ÎjÈoÍaÈ`½+Î54%×76 ÉI½qÎ3Æ+Ìj¾6ÃAÍaÈo½qÎ$8:9<;7=<>@?BA:C2=!DFEG9<>
f
i
(X
i
) = 0
EIH=<>J=HHE-K<>%LM?N>D9O8QP=<RSC%?HTDU9
DWV2?QPX=<;NEF=ZYNR-?NH
X
i
DWV[=!DH\=!DFEIHI]?H
f
i
= 0
^ *ç/L¡58769í76õ?ìLãí¢DX
i
769L& AL:í¢DîãH>BðL*H>9:?LN9ý876D/:ð7,èH>D&/F8@?9V76äíH>DîæXH>9
f
i
óí¢ì¢ìAõqL¡9LNë?9LãLNDsäL:
7>ã7,õ?í¢äãä9í¢D?FH6æ/ìLND?F8äç
k
i
÷*ç/L£õ?í¢äí¢D7,ãëLèNí&%è£ëH8ãí¢äíH>D®í¢Däç/L£èH>D&/F8@?9V76äíH>Dåç%7>ãäç/L15876ì¢@/L£æ H>9
äç/L58769í76õ?ìLí¢Dðäç/Lãc76BðLëqH8ãí¢äíH>Dðí¢D
Xi
÷<(Lóí¢ì¢ì%D/H>ä£óH>9ñåóí¢äçOäç/LLüs@%76äíH>D/ã7>ã1B®@?ì¢äí¢58769í76äL ëqH>ì¢êMD/H>Bîí76ìãý+õ?@?ä=í¢D/ãäL7>:Äí:?LNDsäíbæ`êÓ76DöLüs@%76äíH>Df
i
(X
i
) = 0
óí¢äç äç/L®H>9:?LN9L:öãLNäKH6æ15>769í76õ?ìLã
X
i
ý%76D/:Ä7åì¢íãä
L
i
H6æ76ì¢ìjèH>D&/F8@?9V76äíH>D/ã,æXH>9
f
i
÷ *ç?íã,H>õ2_LèNäíãäç/Lõ%7>ãíèõ?@?í¢ì:Aí¢D?FOõ?ìHMèñïæXH>9,H>@?9
BðLNäç/Hs:?ãaý/ãHåóLF8í¢5ILí¢ä=7D%76BðL8÷
Ô<º3ÎjÈoÍaÈ`½+Îa`×76 À»cb Ç1½qÅ
S
= (X, L)
d9!>eHEIHNDWH9O8f=<>g9<;OhZ?N;B?ihH:?\D+9O8jP=<;EG=kYNRl?H
X
=
X
(S)
=<>mh =nRSEIHNDL
=
L(S)
9O8d
9<>0] K<C[;O=!DFEG9<>eH8:9<;
X
^(LîLAëqLèNäL7>èVç
f
i
äH<ç%75ILO76ë?ë?9H%Mí¢BO76äLNì¢ê
2
k
i
−1
èH>D&/F8@?9V76äíH>D/ã÷ 9Hs:A@/èNí¢D?F 76D/:(ãäH>9í¢D?F
äç/Lì¢íãä
Li
äçz@/ã9Lüs@?í¢9Lãk
äHåõqLK9LNì76äí¢5ILNì¢ê<ãBO76ì¢ìZýMæXH>9L7>èçi
ó¡LB®@/ãäõL76õ?ìLäH9@?D<äç?9H>@?F8ç 76ì¢ì2
k
i
õ?í¢äãä9í¢D?FIãéH6æ=ìLND?F8äç
k
i
äH©:?LNäLN9Bîí¢D/L<óç?íèVç 769L<èH>D&/F8@?9V76äíH>D/ãé76D/:¥óç?íèVç 769LD/H>ä÷
ç/LNDÄóLãV7êïH>@?9=ãêMãäLNB ãç/H>@?ì:<õLHUo2=<;H:?óLBðL76DÄäç%76ä
ú5ILN9êãH>ì¢@?äíH>DÊH6æäç/LãêAãäLNB è76DïõLK9LNë?9LãLNDzäL:Ê7>ã76D
n
Zõ?í¢äãä9í¢D?F/ýMóç/LN9LL7>èç<õ?í¢äèH>DzäV76í¢D/ã äç/L,5876ì¢@/LæXH>9H>D/L=H6æ]äç/L,58769í76õ?ìLã£í¢DX
÷zú7>èç<Lüz@%76äíH>Déí¢DOäç/LKãêAãäLNBç%7>ãäHõL,ãV76äíã&%L:Oóí¢äç äç/LãH>ì¢@?äíH>DýAãHæXH>976DzêOãêsBõqH>ìS
ýMèH>D/è76äLND%76äí¢D?Fðõ?í¢äãæ`9H>B'äç/LKãH>ì¢@?äíH>Dí¢DzäHð7ãä9í¢D?Fæ H>9¡äç/L 5>769í76õ?ìLãX
(S)
óí¢ì¢ìë?9HM:A@/èL®7îèH>D&/F8@?9V76äíH>DÄæ H>@?D/:ÄH>DL(S)
÷ @?9*í:?L7íã*äHå:?LNìLNäLKèH>D&/F8@?9V76äíH>D/ã,äç%76äè76DïD/H>äõL=ë%769ä*H6æ7ãH>ì¢@?äíH>Dïæ`9H>B'äç/LèH>D&/F8@ 9V76äíH>D<ì¢íãäã¡í¢Däç/LKãêsBõqH>ìã÷AEæóL769L76õ?ìLäH9LNBðH5IL®76ì¢ìó9H>D?FîèH>D&/F8@?9V76äíH>D/ãó¡LKè76D<ãí¢Bîë?ì¢ê 9L7>:ïäç/L=5876ì¢@/Lã*H6æäç/LK9LNBO76í¢D?í¢D?FðèH>D&/F8@?9V76äíH>D/ãí¢Dïäç/L=58769íH>@/ãL(Si)
äH®FILNä7ãH>ì¢@?äíH>D<H6æäç/L ãêAãäLNBÊý/76äìL7>ãäóç/LNDÊí¢ä,íã@?D?íüz@/L8÷ Ô<º3ÎjÈoÍaÈ`½+Î]× ?\DY
⊆
X
^6
d
9<> ] K!CZ;B=!DFEG9<>T8\9<;
X
EIHH:=<EGhMDU9®ÉI½+ºz¾g=d
9<>0] K<C[;O=!DFEG9<>T8:9<;
Y
E8 DWV2?7D9 =<;B?T?BA:C2=<RZ8\9!;Q=<RIRP=<;EG=kYNRl?HQEW>Y
^ LNääGóHðãêsBõqH>ìãS
i
76D/:S
j
õLKF8í¢5ILND÷ LNäX
ij
=
X
(S
i
)
∩
X
(S
j
)
76D/:
L
ij
õL=äç/LãVLNäH6æ76ì¢ì
èH>D&/F8@?9V76äíH>D/ãæXH>9
X
ij
èH5ILN9L: õzê 76ä=ìL7>ãäH>D/LèH>D&/F8@?9V76äíH>D(H>D
L(S
i
)
÷]Jsí¢Bîí¢ì769ì¢êIýìLNä
L
ji
õqL äç/LîãLNäH6æ*76ì¢ìèH>D&/F8@?9V76äíH>D/ã®æ H>9X
ij
èHa5ILN9L:©õzêöãH>BðLåèH>D&/F8@?9V76äíH>D¨H>DL(S
j
)
÷(LîãV7êÓäç%76ä
S
i
76D/:
S
j
76F89LLíbæ
L
ij
=
L
ji
÷EGD è7>ãLóç/LNDöäç/LNêÄ:?HïD/H>ä76F89LLó¡Lå76ë?ë?ì¢êö7ðë?9HMèL:A@?9Lîè76ì¢ìL:
76F89LLNí¢D?F/÷ *ç%76ä,íãý?óL®:?LNìLNäLæ 9H>B
L(Si)
76D/:L(Sj
)
76ì¢ìjèH>D&/F8@?9V76äíH>D/ã,äç%76äK:?HîD/H>ä,èH5ILN976Dzê èH>D&/F8@?9V76äíH>D H>DL
ij
∩
L
ji
76D/:<FILNäì¢íãäã
L
0
i
76D/:L
0
j
÷ KH>D/LH6æäç/L®èH>D&/F8@?9V76äíH>D/ã=:?LNìLNäL:æ 9H>BL(S
i
)
76D/:
L(S
j
)
èH>@?ì:îõqLë%769ä£H6æ7Kæ`@?ì¢ì+ãH>ì¢@?äíH>DýIãí¢D/èLí¢ä£óH>@?ì:éõqL*í¢BîëH8ããí¢õ?ìLäH®ãV76äíãSæ êõH>äç
S
i
76D/:S
j
óí¢äç äç/LNBÊ÷'*ç/L®ãêMB®õH>ìãS
0
i
= (X
(S
i
), L
0
i
)
76D/:
S
0
j
= (X
(S
j
), L
0
j
)
76F89LLD/Hóý76D/: óL®9LNë?ì7>èL
S
i
óí¢äçS
0
i
76D/:S
j
óí¢äçS
0
j
÷*ç/Lðù=F89LLNí¢D?FÓ76ì¢FIH>9í¢äç?B óH>9ñAãõsê 9LNëL76äL:Aì¢ê &/D/:Aí¢D?FÄäGóHÊí¢D/:AíèLã
i
76D/:j
ã@/èVç(äç%76äS
i
76D/:Sj
:AíãV76F89LL8ýq76D/:Ó76ë?ë?ì¢ê<äç/L76F89LLNí¢D?Fïë?9HMèL:A@?9LäHL(Si)
76D/:L(Sj
)
÷% ç/LNDÊ9@?D?D?í¢D?Fïäç/L ù,F89LLNí¢D?FÑ76ì¢FIH>9í¢äç?B óLÄH6æ äLND 9@?D í¢DzäH ãí¢ä@%76äíH>D/ãéóç/LN9LS
i
76D/:S
j
76F89LL8ý£õ?@?äS
j
76D/:S
k
:AíãV76F89LL8÷qùæ äLN9,:?LNìLNäí¢D?FéãVH>BðLèH>D&/F8@?9V76äíH>D/ã=æ`9H>BS
j
äHOBO76ñILí¢ä=76F89LL®óí¢äçS
k
ý?í¢ä,BO7êïó¡LNì¢ì õqLäç%76äSi
76D/:Sj
:AíãV76F89LL8÷%EGDÄH>äç/LN9ó¡H>9:?ãý+76ë?ë?ì¢êMí¢D?FOäç/L®76F89LLNí¢D?Féë?9HsèL:A@?9L®äHðH>D/Lë%76í¢9KH6æ ãêMB®õH>ìãjBO7êè76@/ãL*:AíãV76F89LLNBðLNDsäí¢DîH>äç/LN9ë%76í¢9ãa÷Eæ/äç/LN9L¡íãLND/H>@?F8çðHa5ILN9ì76ëð76BðH>D?Fäç/L£58769íH>@/ãX
i
ó¡Låóí¢ì¢ìFILNä7ïèVç%76í¢DZ9L7>èNäíH>D¨H6æ¡:?LNìLNäíH>D/ã®H6æèH>D&/F8@?9V76äíH>D/ãäç%76äóí¢ì¢ì£7>èNä@%76ì¢ì¢ê 9LNBðH5ILð76ì¢ì èH>D&/F8@?9V76äíH>D/ãLAèLNë?ä*æXH>9äç/H8ãLäç%76ä=769Lë%769äH6æ7æ @?ì¢ìãH>ì¢@?äíH>D÷DÑäç/LÊH>äç/LN9Oç%76D/:]ý£76ì¢ìë%76í¢9ãðH6æãêMB®õH>ìãîBO7ê 76F89LL<õLyæ H>9LÓ7öãH>ì¢@?äíH>D è76D õL<ãLLND÷Eæ
äç/L76BðH>@?DsäH6æ9L7>:Aí¢ì¢ê 75876í¢ì76õ?ìL®í¢DAæXH>9BO76äíH>Döí¢DÄäç/LãêMãäLNB íã,õLNìHó ãH>BðLèN9í¢äíè76ìjBO7>ããaý/äç/L
èç%76í¢DZ9L7>èNäíH>DîH6æ?ë%76í¢9óíãL£76F89LLNí¢D?FIãjóí¢ì¢ìz:AíL1H>@?äõLyæXH>9L1LND/H>@?F8ç:?LNìLNäíH>D/ãjç%75IL1HMèèN@?99L:]÷ ç%76ä
äêMë?íè76ì¢ì¢ê(ç%76ë?ëLND/ãæXH>9®äç/Lð9L:A@/èL: Z9H>@?D/: úJ©ãêMãäLNBðã
. äç%76ä®í¢D¥76ì¢ì1ì¢í¢ñILNì¢í¢ç/HsHM:(ç%75ILO@?D?íüs@/L ãH>ì¢@?äíH>D/ã/íã,äç%76äK:?LNìLNäíH>D/ãHsèèN@?9=í¢DÄäç/LõqLNF8í¢D?D?í¢D?FH6æäç/Lù=F89LLNí¢D?F76ì¢FIH>9í¢äç?BÊý+õ?@?äKäç%76ä,äç/L ãêMB®õH>ìã*769L=ë?@?ä£í¢DsäHî76D76F89LLNí¢D?FîãäV76äL,óç?í¢ìL,äç/LN9Lãäí¢ì¢ì769LK7®ìH>äH6æjèH>D&/F8@?9V76äíH>D/ã*ìLyæ ä£í¢Dïäç/L ãêMB®õH>ìãýAãLLJMLèNäíH>D æXH>9*7:?LNäV76í¢ìL:<:?LãèN9í¢ë?äíH>DÊH6æjäç/LKù=F89LLNí¢D?FO76ì¢FIH>9í¢äç?BmãH>@?äë?@?ä,76D/:ïí¢äã èH>Bîë?ìLMí¢äGêI÷ *ç/LD/LAä,ãLèNäíH>DÓ:?L76ìãóí¢äçÄãä9V76äLNF8íLãæ H>9Ha5ILN9èH>Bîí¢D?Féäç?íãë?9H>õ?ìLNBÊ÷ ;,@?D?D?í¢D?Fäç/Lù=F89LLNí¢D?F76ì¢FIH>9í¢äç?B BO7êîõqLãVLLNDé7>ã1BðLããc76FILZë%7>ããí¢D?F®H>D7KF89V76ë?ç÷*ç/LD/HM:?Lã í¢DÊäç/LF89V76ë?çÊóí¢ì¢ìõqL76ì¢ì]äç/LãêsBõqH>ìã
S
1
, . . . , S
m
äH>FILNäç/LN9,óí¢äçÊäç/LãêMB®õH>ìã
S
ij
= (X
ij
, L
ij
∩
L
ji
)
76D/:
S
j
÷AEæ7èH>D&/F8@?9V76äíH>D
c
H>DL
i
:?HMLãD/H>äèHa5ILN9,76DzêïèH>D&/F8@?9V76äíH>DÄH>D
L(S
ij
)
ýMóLè76Däç?í¢D?ñ
H6æ
S
ij
ãLND/:Aí¢D?FÊ7éBðLããV76FILåHa5ILN9äç/LL:AFILåäH
S
i
äLNì¢ì¢í¢D?Fäç/LîãêsBõqH>ìäH:?LNìLNäL
c
÷!*ç/Lîù=F89LLNí¢D?F 76ì¢FIH>9í¢äç?Bóí¢ì¢ìèH>Dsäí¢Dz@/Lå7>ãìH>D?Fé7>ãäç/LN9L769LBðLããV76FILãäHîõLãLNDsäí¢D<äç/LF89V76ë?ç÷=ÜáGÚ Û>ÝSÝÜzà2¨Û Ý 'ßÛIáÝÚ Û8Ýa)a/Ü
ç/LND äç/LÊãêMB®õH>ìãO769LÊ76ì¢9L7>:Aê¥í¢D 76D 76F89LLNí¢D?F¨ãäV76äL8ýäç/LÄù,F89LLNí¢D?F¨76ì¢FIH>9í¢äç?B óí¢ì¢ìD/H>äð:?H
76DzêMäç?í¢D?F/÷?EDïäç?íã*è7>ãLKí¢äíã¡D/LèLããc769êðäHå:?HãH>BðLNäç?í¢D?FåäHBO76ñILKäç/L=ù=F89LLNí¢D?Fð76ì¢FIH>9í¢äç?B ãäV769ä
76Fz76í¢D÷%(Lç%75IL®L/76Bîí¢D/L:<äó¡HO:Aí]LN9LNDzä,ãä9V76äLNF8íLãæ H>9FILNääí¢D?FïH>@?äH6æ76D 76F89LLNí¢D?FéãäV76äL8÷
]×F4 Ö]ÂÅ ÈoÍÍaÈ ÎÆ
*ç/L &/9ãä£H6æäç/LBðLNäç/HM:?ãæXH>99LãäV769äí¢D?F®äç/L,ù,F89LLNí¢D?F76ì¢FIH>9í¢äç?BóLç%75IL,è76ì¢ìL:o RSEFDGDFEW>ZK8ýI76D/:
íãüz@?í¢äLãí¢Bîë?ìL8÷2 ç/LNDäç/LKF89V76ë?ç<9L7>èç/Lã,76DÊ76F89LLNí¢D?FOãäV76äLKóí¢äçD/H5síãí¢õ?ìLKãVH>ì¢@?äíH>D<óç%76äóL
:?HÄíãäç/LOæ H>ì¢ìHaóí¢D?F (LîæXHsèN@/ãH>D H>D/LïãêMB®õH>ì
S
ý76D/:¨ãë?ì¢í¢äL(S)
í¢D äóH ë%769äãýL
1
76D/:
L
2
÷
(Läç/LND 9LNë?ì7>èL
L(S)
óí¢äçL
1
H>9
L
2
76D/:öãäV769ääç/Låù,F89LLNí¢D?FÊ76ì¢FIH>9í¢äç?B 76Fz76í¢D÷!*ç/LåèH>99LèNä
èH>D&/F8@?9V76äíH>DÊæXH>9
S
.7>ãã@?Bîí¢D?Fð@?D?íüs@/LãH>ì¢@?äíH>D /íã*æXH>@?D/:<H>DÊLNí¢äç/LN9
L
1
H>9
L
2
ý?ãVHóç%76ä,óL769L
õ%7>ãíè76ì¢ì¢êå:?H>í¢D?FíãjF8@/LãVãí¢D?FH>Dîóç?íèçîë%769ääç%76ä1èH>DzäV76í¢D/ãäç?íãèH>D&/F8@?9V76äíH>D÷zEZæ%í¢äõLèH>BðLãèNìL769
äç%76ääç/LF8@/Lããó¡7>ãó9H>D?F/ý/óLóí¢ì¢ì9@?DÄäç/Lù,F89LLNí¢D?F76ì¢FIH>9í¢äç?B óí¢äçÊäç/LH>äç/LN9ì¢íãäí¢D/ãäL7>:]÷
/H>9*äç/L úJéãêAãäLNBðãýsF8@/Lããí¢D?FîH>D?ì¢êOH>D/èLKíã*D/H>ä¡LND/H>@?F8ç<ç/LNì¢ëïæXH>9*äç/LKù=F89LLNí¢D?Fð76ì¢FIH>9í¢äç?B
äH¨ãVH>ì¢5ILÄäç/L ãêAãäLNBÊ÷EGD FILND/LN9V76ìZý¡äç/L ãêMB®õH>ìãOóí¢ì¢ì76Fz76í¢D èH>BðLÄäH¥76D 76F89LLNí¢D?FÑãäV76äLÓóí¢äç
D/HÊ76ë?ë%769LNDzäãH>ì¢@?äíH>Dò7æ äLN9äç/L &/9ãäF8@/Lãã÷'*ç/LND©óLåD/LL: äHïF8@/Lãã76Fz76í¢Dý9@?D äç/Lîù=F89LLNí¢D?F
76ì¢FIH>9í¢äç?BH>D/èL*BðH>9L8ýz76D/:îãVHH>D÷8ú£7>èçéäí¢BðL*óLF8@/Lããaý>óL769LF8@/Lããí¢D?FH>D/L*õ?í¢ä1H6æqí¢DAæXH>9BO76äíH>Dý
ãí¢D/èLîäç/LðèH>99LèNäèH>D&/F8@?9V76äíH>DòíãæXH>@?D/:(H>D(LNí¢äç/LN9
L
1
H>9
L
2
÷
D/Lðè76DòãLLåäç%76ä®F8@/Lããí¢D?FÊH>D
äç/L5876ì¢@/Lã,H6æ£7îãLNä=H6æ58769í76õ?ìLã,æ H>99LãäV769äí¢D?FOäç/L®ù=F89LLNí¢D?Fï76ì¢FIH>9í¢äç?Bøíã,7ðë%769äíèN@?ì769=è7>ãLH6æ
ãë?ì¢í¢ääí¢D?F/÷
ç/LND óí¢ì¢ìí¢äïõqLèH>BðLöèNìL769äç%76ä<7òF8@/LãVãéó*7>ãïó9H>D?F$ ç/LND ó¡LÄBO76ñIL©7¨ó9H>D?F¥F8@/Lãã
ãH>BðLNóç/LN9L8ýóLÄ769LÓ:?LNìLNäí¢D?Fòäç/LÊèH>99LèNäïèH>D&/F8@?9V76äíH>D æ 9H>B 7©ãêMB®õH>ìmãðèH>D&/F8@?9V76äíH>D ì¢íãäý
BO76ñsí¢D?Fí¢ä1í¢BîëH8ããí¢õ?ìL,äH &/D/:é7ãH>ì¢@?äíH>D÷ ç%76ä£ç%76ë?ëLND/ãýIëH8ããí¢õ?ì¢êð7æ äLN91BO76ñMí¢D?FBðH>9L,F8@/LããLãý
íãäç%76ääç/Lù=F89LLNí¢D?Fé76ì¢FIH>9í¢äç?BC:?LNìLNäLã=76ì¢ìèH>D&/F8@?9V76äíH>D/ã,í¢DÊãVH>BðL
L(S)
÷e ç/LND<äç?íãç%76ë?ëqLND/ã óL=óí¢ì¢ì+õ%7>èVñsä9V7>èVñOäH®äç/Lì7>ãä¡F8@/Lãã1BO7>:?L8ýA76D/:éä9êîäç/L,H>äç/LN9¡ëqH8ããí¢õ?í¢ì¢í¢äêI÷MEZæ]äç?íã76ìãHä@?9D/ã¡H>@?ääHOõL7O:?L7>:ÓLND/:]ý+óLóí¢ì¢ìõ%7>èñMä9V7>èñÄäHOäç/L®F8@/LãVã,õLyæ H>9L®äç%76äýq76D/:Ää9êÊäç/L®H>äç/LN9KëH8ããí¢õ?í¢ì¢í¢äê
æ`9H>Bäç%76äëqH>í¢Dsäý/LNäè8÷
ç%76äó¡L769L=:?H>í¢D?FåíãFIH>í¢D?Fäç?9H>@?F8çÊ7®õ?í¢D%769êéãL769èVçä9LL8ýzìHMH>ñsí¢D?FæXH>9äç/LãH>ì¢@?äíH>DH6æäç/L
ãêAãäLNBÊ÷k ç/LNDïóL,æ H>ì¢ìHaó äç/L=õ?9V76D/èçÊH6æäç/L=ä9LL=èH>99LãëqH>D/:Aí¢D?FåäHäç/L=èH>99LèNä¡F8@/LããLã¡óL &/D/:
7OãVH>ì¢@?äíH>D÷ *ç/LìL75ILãH6æ£äç?íã=ä9LL®óí¢ì¢ìõLäç/LëqH>í¢Dsä=óç/LN9LóLLNí¢äç/LN9&/D/: 7OãH>ì¢@?äíH>Dý+H>9Käç/L
ëqH>í¢Dsäãóç/LN9LðãVH>BðL
*ç/LéH>äç/LN9BO76í¢D¥ãä9V76äLNF8êöæ H>9BO76ñsí¢D?F äç/Lïù,F89LLNí¢D?F©76ì¢FIH>9í¢äç?B ãäV769äå76Fz76í¢D íã®è76ì¢ìL:RSC[EW>ZK8÷ í¢äçÑäç?íãðBðLNäç/Hs:¥ó¡LÊ:?HöD/H>äð:?H(76Dzê F8@/Lããí¢D?F/ýõ?@?äîí¢D/ãäL7>:¥BðLN9FILÊäóHòãêsBõqH>ìãåí¢DsäH(H>D/L8ý äç/LN9LNõzê<õ?9í¢D?F8í¢D?Féäç/LNí¢9_SH>í¢Dsäí¢DAæ H>9BO76äíH>Dö76õqH>@?ä,äç/LãH>ì¢@?äíH>DÊí¢DzäHOäç/LH>ëLND÷ LNäãêsBõqH>ìã
S
i
76D/:S
j
õqLKF8í¢5ILND÷e(Lë?@?äZ
=
X(S
i
)
∪
X
(S
j
)
76D/:
X
ij
=
X(S
i
)
∩
X
(S
j
)
76D/:Ê:?L&/D/L7ì¢íãä
L
H6æèH>D&/F8@?9V76äíH>D/ã,æXH>9Z
÷ *ç/Lì¢íãäL
èH>D/ãíãäãH6æ76ì¢ìèH>D&/F8@?9V76äíH>D/ã(a, b, c)
ý óç/LN9Lb
íãî7öèH>D&/F8@?9V76äíH>DÑæXH>9X
ij
ý
(a, b)
∈
L(S
i
)
ý176D/:
(b, c)
∈
L(S
j
)
÷EDÑH>äç/LN9îóH>9:?ãaý
L
èH>D/ãíãäãH6æ76ì¢ì£èH>D&/F8@?9V76äíH>D/ãäç%76ä®èHa5ILN9H>D/LðèH>D&/F8@?9V76äíH>D¥H>D
L(S
i
)
76D/:(H>D/LðèH>D&/F8@?9V76äíH>D
H>D
L(S
j
)
÷'*ç/LåãêMB®õH>ì
S
= (Z, L) =
S
i
◦
S
j
íã=äç/L9Lã@?ì¢äH6æ£F8ì¢@?í¢D?Fäç/LåãêMB®õH>ìã
S
i
76D/:
S
j
ý
76D/:<äç/LèH>D&/F8@?9V76äíH>D èH>99LãëqH>D/:Aí¢D?FéäHåäç/LãH>ì¢@?äíH>DÄH6æäç/LãêAãäLNB íã*æXH>@?D/:<H>D
L
÷ ç/LND<H>@?9*ãêsBõqH>ìã*9L7>èVçÄ76D<76F89LLNí¢D?FðãäV76äL8ýsó¡Lè76DF8ì¢@/L=äH>FILNäç/LN9=ãêsBõqH>ìã¡äHåèN9L76äLD/LNó Lüz@%76äíH>D/ãa÷! ç/LNDOF8ì¢@?í¢D?FS
76D/:T
äH>FILNäç/LN9óL:Aíãè769:S
76D/:T
ý8ãí¢D/èL,76ì¢ì?í¢DAæXH>9BO76äíH>DOí¢DOäç/LNB 769L,èH>DsäV76í¢D/L:éí¢DS
◦
T
÷ ç/LNDOóL,ç%75IL=F8ì¢@/L:ðäH>FILNäç/LN9*ãLN5ILN9V76ì%ë%76í¢9ãH6æãêsBõqH>ìãäç/LD/LNó ãLNäH6æ ãêMB®õH>ìãóí¢ì¢ì]í¢DFILND/LN9V76ìD/H>äõqLKí¢DÄ76DÄ76F89LLNí¢D?FOãäV76äL8ýMãVHåóLè76DÊãäV769ääç/Lù=F89LLNí¢D?FO76ì¢FIH>9í¢äç?B76Fz76í¢D÷
*ç/L<ë?9íèLÄäH©ë%7ê¥óç/LND F8ì¢@?í¢D?F(äH>FILNäç/LN9éãêMB®õH>ìãðíãOìH>D?FILN9OèH>D&/F8@?9V76äíH>D ì¢íãäã÷1ùKãã@?B*
í¢D?F
S
76D/:T
76F89LL8ýKäç/L¨Ds@?B®õLN9©H6æéèH>D&/F8@?9V76äíH>D/ã©í¢DS
◦
T
óí¢ì¢ìõL 76äöìL7>ãä©7>ã õ?í¢F 7>ãmax
{|
L(S)
|
,
|
L(T
)
|}
ý*76D/: BO7ê¥õLÊ7>ãîõ?í¢F¨7>ã|
L(S)
| · |
L(T)
|
÷EDÑë?9V7>èNäíèLÄóL<ç%75ILÊäH(ãVLNäO7 äç?9Lãç/H>ì:(76D/:öH>D?ì¢êÄF8ì¢@/LäH>FILNäç/LN9ãêMB®õH>ìãKäç%76äKë?9HM:A@/èLîèH>D&/F8@?9V76äíH>D(ì¢íãäãKóí¢äç©ãí-,LõLNìHóäç?íã,äç?9Lãç/H>ì:]÷ *ç?íã,BðL76D/ã,ó¡LBO7ê<9@?DÓí¢DzäHïè7>ãLãóç/LN9L®óLè76DÄD/H>äK7]H>9:Ó76DsêÊãêMB®õH>ìãäH
õqLF8ì¢@/L:]÷
ç/LNDòèH>Bîë?@?äLN9èH>D/ãä9V76í¢DzäãBO76ñILîí¢ääHMHÊèH8ãäì¢êöäH<ëLN9Sæ H>9B F8ì¢@?í¢D?F/ýóLOç%75ILéèH>D/ãí:?LN9L:
ë%769äí76ì/F8ì¢@?í¢D?F/÷/H>9£äóH®ãêsBõqH>ìã
(X
i
, L
i
)
76D/:
(X
j
, L
j
)
ý>ó¡Lèç/HMH8ãL
Y
i
⊆
X
i
76D/:
Y
j
⊆
X
j
÷ KLMä óLBO76ñIL
L
0
i
76D/:L
0
j
õzêïë?9H_SLèNäí¢D?FO76ì¢ìèH>D&/F8@?9V76äíH>D/ã=H>DL
i
H>DsäHY
i
76D/:Ê76ì¢ì]èH>D&/F8@?9V76äíH>D/ã,H>DL
j
H>DzäHY
j
÷/EDÄFILND/LN9V76ìZý|
L
0
i
|
<
|
L
i
|
76D/:
|
L
0
j
|
<
|
L
j
|
ãí¢D/èL:AíLN9LNDsä=èH>D&/F8@?9V76äíH>D/ã=æXH>9
X
i
76D/:X
j
BO7êðõL,Lüs@%76ìqóç/LNDïë?9H_LèNäL:ïH>DzäHY
i
76D/:Y
j
÷zEæY
i
76D/:Y
j
óLN9Lèç/H8ãLND<è769Lyæ @?ì¢ì¢êîóLKBO7ê F8ì¢@/Läç/LãêMB®õH>ìã(Y
i
, L
0
i
)
76D/:
(Y
j
, L
0
j
)
76D/:Äè76@/ãL:AíãV76F89LLNBðLNDzäKóí¢äçÄãH>BðLH>äç/LN9=ãêsBõqH>ìãa÷ óHï:AíOèN@?ì¢äKíãVã@/Lã=èH>D/èLN9D?í¢D?Fë%769äí76ìF8ì¢@?í¢D?Féíã=ç/Hó äHéèç/HMH8ãL
Y
i
76D/:Y
j
í¢Dö76D H>ë?äí¢BO76ìó¡7êIýM76D/:îç/Haó äHLND/ã@?9Läç%76ä1äç/LD/LNó ãêMB®õH>ì/èH>Bîí¢D?Fæ 9H>Bë%769äí76ì/F8ì¢@?í¢D?Fíã£7>èNä@%76ì¢ì¢êåõ?9í¢D?F8í¢D?F
@/ãåèNìH8ãLN9äH ãH>ì¢5Mí¢D?FÓäç/LïãêAãäLNBÊ÷
D/Léãä9V76äLNF8ê(æ H>9åèç/HMH8ãí¢D?F
Y
ã@?õ/ãLNäãç%7>ãõqLLND ä9íL:]ýõ?@?ä ãHéæX769KóLå:?HïD/H>äç%75ILð76DsêÄ9Lã@?ì¢äãKäHï9LNëqH>9ä76õH>@?äë%769äí76ìF8ì¢@?í¢D?F/÷(LåH>D?ì¢êÊBðLNDsäíH>D©ë%769äí76ìF8ì¢@?í¢D?Fï7>ã,7äH>ë?íèæ H>9*æ @?ä@?9L9LãL769èVç÷
éÝc)a'(1áXÛ ÙX<>ß
EDÓäç?íãJMLèNäíH>DÓóLóí¢ì¢ììHMH>ñÊ76ä,óç%76äKäç/L®H>@?äë?@?ä=H6æ1äç/Lù,F89LLNí¢D?F76ì¢FIH>9í¢äç?B2íãý%76D/:Êóç%76äKí¢äã
9@?D?D?í¢D?F<äí¢BðL®íãa÷(Läç/LND©èH>Bîë%769Läç/Lù=F89LLNí¢D?FKì¢@?í¢D?FÄ76ì¢FIH>9í¢äç?B2óí¢äç ñMD/HóD(76ë?ë?9HI7>èVç/Lã
æ H>9=ãH>ì¢5sí¢D?Fðãë%769ãL **HsH>ìL76DÄãêMãäLNBðãH6æLüs@%76äíH>D/ã÷
Kí¢5ILND äç/LÄãLNäOH6æãêMB®õH>ìã
S
i
= (X
i
, L
i
)
ý
1
≤
i
≤
m
9LNì76äL: äH(äç/L<í¢D?í¢äí76ìKãêAãäLNB H6æ Lüz@%76äíH>D/ã.
0/yýsóLKèH>D/ãí:?LN97ãLNä¡H6æ]ã@?õ/ãêsBõqH>ìã
(X
i
, U
i
)
⊆
(X
i
, L
i
)
BðL76D?í¢D?Fäç%76ä
U
i
⊆
L
i
76ì¢ì
1
≤
i
≤
m
÷ *ç/Lì76ääLN9ãLNäH6æã@?õ/ãêMB®õH>ìã*íãè76ì¢ìL:Ä7BO7Mí¢BO76ì76F89LL:ÊãVLNä*H6æã@?õ/ãêMB®õH>ìã*íbæ äç/LãêMB®õH>ìã(X
i
, U
i
)
ë%76í¢9óíãL®76F89LL®76D/:<æ H>9,76DsêãVLNäã
U
0
i
U
i
⊆
U
i
0
⊆
L
i
,
óí¢äç
Ui
⊂
U
0
i
æXH>9,76äìL7>ãäH>D/L
i
ý?äç/LãLNä,H6æã@?õ/ãêMB®õH>ìã(Xi, U
0
i
)
ý
1
≤
i
≤
m
:?HMLãD/H>ä=76F89LL8÷ ¾6½%Â1½+ÀaÈoÍaÈo½qÎ 4+×^
V2? L1=!EIL1=<R =0K<;B? ?Bh H:?:D9O8 HNCeYH<L1Yi9<RH7EH C[>%EFA:Ce?
^
^
V2? 9!C[DSo C2D 9O8 DWV2?16K!;B?i?\EI>ZK =<RK9<;NEWDWVZL EIHnDWV2? L1=!EIL1=<R= K<;i?i?BhJH:?\D 9O8MHC%YH<LMYB9<RSH8:9<; DWV2?
EW>%EFDFEF=<RmH ?\D9O8 H<L1Yi9<RH
^
^
V2?n;NC[>%>%EW>ZK$DFEILM? 9B8nDWV2?16K<;i?i?NEW>ZK@=!RK9!;EFDWVkL EH Yi9<CZ>mhk?Bh Y
O(k
2
m
3
2
2
k
)
YNEFD 9oe?\;O=!DFEG9<>eH +EFDWV LM?NL19<;1;i?BA\C[EI;i?NLM?N>DWHO(m2
k
)
YNEFDWH^
;B9 9O8MùKãã@?BðL1äç/LN9L*769LäóHKBO7Aí¢BO76ìA76F89LL:ãLNäãH6æ%ã@?õ/ãêMB®õH>ìã
(X
i
, U
i
)
ý
1
≤
i
≤
m
76D/:(X
i
, U
i
0
)
ý
1
≤
i
≤
m
÷)*ç/LNDH>D/L=èH>D/ãä9@/èNäã*7®D/LNó ãLNä¡H6æã@?õ/ãêsBõqH>ìã(X
i
, U
i
∪
U
i
0
)
ý
1
≤
i
≤
m
÷ *ç/Lì76ääLN9ã@?õ/ãêMB®õH>ìã*ë%76í¢9óíãL®76F89LL8÷ *ç%76ä,íãH>D?ì¢êOëH8ããí¢õ?ìLóç/LNDUi
=
U
0
i
ý
1
≤
i
≤
m
÷ *ç/L &/9ãä,ãäV76äLNBðLNDsä,íãë?9Ha5IL:]÷jHéë?9Ha5ILåäç/LåãLèH>D/:©ãäV76äLNBðLNDzäýìLNä
(X
i
, U
i
)
ý
1
≤
i
≤
m
õqLäç/LåH>@?äë?@?äH6æ£äç/Lîù,F89LLNí¢D?F 76ì¢FIH>9í¢äç?Bø76D/:(X
i
, U
i
)
⊆
(X
i
, U
i
0
)
⊆
(X
i
, L
i
)
æ H>9ãH>BðL,ãLNäH6æ]ãêsBõqH>ìã
(X
i
, U
i
0
)
ý
1
≤
i
≤
m
óç?íèVçOë%76í¢9óíãLK76F89LL8÷*ç/Lí¢DsäLN9BðL:Aí76äL=ãäV76FIL,H6æ äç/L=ù=F89LLNí¢D?Fð76ì¢FIH>9í¢äç?B'íã¡7®ãLNäH6æjã@?õ/ãêsBõqH>ìã(X
i
, L
0
i
)
⊆
(X
i
, L
i
)
÷)LNääç?íãõqL,äç/L=ãäV76FIL_S@/ãä
õqLyæXH>9Lå:?LNìLNäí¢D?FÄ76Dzê H6æäç/LåèH>D&/F8@?9V76äíH>D/ãí¢D
U
0
i
\
U
i
ý
1
≤
i
≤
m
÷!*ç/LND(X
i
, U
i
0
)
⊆
(X
i
, L
0
i
)
ý
1
≤
i
≤
m
÷!*ç/Lðù=F89LLNí¢D?FÄ76ì¢FIH>9í¢äç?BûD/Hó :?LNìLNäLã®ãH>BðLa
∈
U
0
i
\
U
i
÷ *ç?íãBðL76D/ãäç/LN9Låíã7
ãêMB®õH>ì
(X
j
, L
0
j
)
ã@/èVç®äç%76ä
L
0
j
:?HMLãD/H>äèH>DsäV76í¢D76DsêèH>D&/F8@?9V76äíH>Däç%76äèHa5ILN9ãäç/L1ë?9H_SLèNäíH>DH6æ
a
H>DX
ij
=
X
i
∩
X
j
÷)*ç/LND
U
0
j
:?HMLãD/H>ä*èH>DsäV76í¢DÊ76DzêéèH>D&/F8@?9V76äíH>D<äç%76äèHa5ILN9ã*äç/L,ë?9H_LèNäíH>D H6æa
H>DX
ij
LNí¢äç/LN9ý¡ãH(X
i
, U
i
0
)
76D/:
(X
j
, U
j
0
)
:?HòD/H>äï76F89LL8÷*ç?íãOí¢Bîë?ì¢íLã
U
0
i
=
U
i
æXH>9é76ì¢ì
1
≤
i
≤
m
76D/:ë?9Ha5ILã,äç/LãäV76äLNBðLNDsä÷jHîë?9H5ILäç/Lì7>ãäãäV76äLNBðLNDzäKH>D/LãLLãäç%76ä
m
X
i
=1
|
L
i
| ≤
m2
k
.
H &/D/:Ó7åë%76í¢9KH6æ1ãêsBõqH>ìã
S
i
= (X
i
, L
0
i
)
76D/:
S
j
= (X
j
, L
0
j
)
ý?óç?íèçö:?HðD/H>ä76F89LL8ý%H>D/Lãç/H>@?ì:
ä9êÊ76äBðH8ãä
m(m
−
1)/2
ë%76í¢9ãK76ä=76DzêÊãäV76FIL®H6æäç/Lù=F89LLNí¢D?Fï76ì¢FIH>9í¢äç?BÊ÷qEæã@/èVç 7åë%76í¢9,LAíãäãP
i
|
L
i
|
ãç/H>@?ì:<õL:?LèN9L7>ãL:<õsê<76ä,ìL7>ãä
1
ý/H>äç/LN9óíãL®äç/L®76ì¢FIH>9í¢äç?BäLN9Bîí¢D%76äLã÷ í¢D/:Aí¢D?Fðäç/L èH>D&/F8@?9V76äíH>D/ã1äHK9LNBðH5IL¡æ 9H>BL
0
i
76D/:L
0
j
äV76ñILãO(k2
k
)
ãäLNë/ãõqLè76@/ãVL¡èH>BîBðH>DðèH>D&/F8@?9V76äíH>D/ã í¢DL
0
ij
, L
0
ji
.ãVLLîäç/Lð:?L&/D?í¢äíH>D¥H6æ¡äç/Lï76F89LLNí¢D?FÄë?9HMèL:A@?9L0/BO7ê©õLåæXH>@?D/:©õzê(7<ãVH>9äí¢D?F 76ì¢FIH
9í¢äç?BÊ÷+JMHåH>D<äç/Lóç/H>ìLäç/LèH>Bîë?ìLMí¢äGêïíã
O(km
3
2
2
k
)
H>ëLN9V76äíH>D/ãóí¢äç<õ?í¢D%769êk
ãä9í¢D?FIã÷ *ç/L ãäV76äLNBðLNDzäH>Däç/L1BðLNBðH>9ê9Lüs@?í¢9LNBðLNDzäãíãH>õz5MíH>@/ã÷ *ç?íã &/D?íãç/Lãäç/Lë?9HsH6æ%H6æ/äç/L9H>ëH8ãí¢äíH>D÷9H>ëH8ãí¢äíH>D ðí¢Bîë?ì¢íLãäç%76䮿XH>97 & ?L:
ãH>BðLH>äç/LN9äLèVç?D?íüz@/LãK7>ããë?ì¢í¢ääí¢D?FïH>9F8ì¢@?í¢D?F/÷
*ç/L=F8ì¢@?í¢D?FåíãõsêOí¢äãLNìbæj76õ?ìLKäHåãH>ì¢5IL76DzêïãêMãäLNBH6æjãë%769ãVL**HMH>ìL76DLüs@%76äíH>D/ã÷A;,L76ì¢ì¢êIýMH>D/L
76ë?ë?ì¢íLãF8ì¢@?í¢D?FéäHîèH>D/ãä9@/èNääç/LãLNäH6æ176ì¢ìãH>ì¢@?äíH>D/ãæ H>9äç/Lã@?õ/ãêMãäLNB H6æLüs@%76äíH>D/ã
f
1
(X
1
) = 0, . . . , f
t
(X
t
) = 0,
. /í¢D(58769í76õ?ìLã
X
(t) =
X
1
∪
. . .
∪
X
t
ã@?õ/ãLüs@/LNDzäì¢ê æXH>9
t
= 1, . . . , m
÷(Lðè76ì¢ì1äç?íã®äç/L Kì¢@?í¢D?F 76ì¢FIH>9í¢äç?BÊ÷%EGDÄ76D/H>äç/LN9,ë%76ëLN9óL®ë?9H5ILÒjºz½+¾º[b 4%× ?\D> =!DFC[;O=!R >%C[LMYi?N;H
m
=<> hk
1
, . . . , k
m
≤
k
Yi?QK<EWP?N>@=<>mh DWV2?7HC%YH ?\DWHT9O87PX=<;NE
=kYNRl?H
X
1
, . . . , X
m
⊂
X
=<>mh9 9<Rl?B=<> 8NC[>
d
DFEG9<>eH
f
1
, . . . , f
m
Yi?
d
V29H:?N>$C[>%E8\9<;NLTR =<> hnEI>mhk?(oe?N>
hk?N>DFR@9O8 ?i=
d
V9!DWV2?N;
^
V2?\>&DWV2?L1=!DWV2?NL1=!DFE
d
=<R? oe?
d
DU=DFEF9<> 9B8gDWV2?
d
9<Lo R-? <EWD #9O8 DWV2? RCZEW>ZK
=<RK9<;NEWDWVkL EH
O((2e
γ
0
+
)
n
+
poly(n)m)
./
YNEFD 9o%?N;O=DFEF9<>%H7=H
k
EIH] k?Bh =<> hn
D(?N>mhHQDU91EW> ]>EWD ^?N;i?
γ
0
=
−
ln 2
k
−
(2
1
k
−
1) ln(
1
−
2
−1
1
−
2
−
1
k
),
EH =<> ] k?BhQo29HNEWDFEWP?Q;i?B=<Rc>CZLMYi?N;=<> hpoly(n)
EHQ= o29<R<> 9<LTEG=<REI>n
^(Lå:?HéD/H>äë?9Ha5IL *ç/LH>9LNB ç/LN9LæXH>9ì7>èñÓH6æ¡ãë%7>èL8÷m(Lóí¢ì¢ìF8í¢5ILî7éç/LN@?9íãäíèåLãäí¢BO76äíH>D(H>D
äç/LèH>Bîë?ìLAí¢äêÊH6æäç/L Kì¢@?í¢D?Fé76ì¢FIH>9í¢äç?Bí¢D/ãäL7>:]÷e(LèH>D/ãí:?LN9äç/L®ãêsBõqH>ìã
(X
(t), U
t
),
(X
t
+1
, L
t
+1
), . . . ,
(X
m
, L
m
)
7æ`äLN9
t
−
1
76ë?ë?ì¢íè76äíH>D/ãKH6æF8ì¢@?í¢D?F/÷%3=LN9LU
t
íã,7îãVLNäH6æ
èH>D&/F8@?9V76äíH>D/ãæXH>9
X(t)
ý>ãH>ì¢@?äíH>D/ãäHKäç/L*ã@?õ/ãêAãäLNB H6æqLüs@%76äíH>D/ã.
/jH6æ%äç/L*í¢D?í¢äí76ì?ãêMãäLNBÊ÷ LNä
rt
õLäç/Lãí-,LH6æX(t)
÷
D/L®ãVLLãäç%76ä,äç/L®ãí-,L®H6æäç/L®ãVLNä
Ut
íã=76õH>@?ä2
r
t
−
t
õLè76@/ãL7>:?:Aí¢D?Fï7 D/LNó í¢D/:?LNëqLND/:?LNDsäLüz@%76äíH>Dï9L:A@/èLã*äç/L,Ds@?B®õLN9H6æãH>ì¢@?äíH>D/ã*õzêéH>D/L,ç%76ìbæjH>Dïäç/L75ILN9V76FIL8÷ D/LèH>D/ãí:?LN9ã1äç/LDz@?B®õLN9
r
t
7>ãäç/LDz@?BõqLN9¡H6æ &/ì¢ìL:OõqH%ALã1óç/LNDðë%769äíèNìLã769L9V76D/:?H>Bîì¢êO76ì¢ìHMè76äL:
í¢D
n
õH#?Lã=õzêÊèH>Bîë?ìL?LãKH6æk
ë%769äíèNìLã÷m?9H>B ÿ ý+ë?ë÷ (
óLñMD/Hó äç%76ä=äç/LLMëLèNäL:
Dz@?BõqLN9£H6æLNBîë?äêåõH#?Lãíã
n(1
−
k/n)
t
ý8ãHr
t
íã176ë?ë?9H#Aí¢BO76äLNì¢ê
n
−
n(1
−
k/n)
t
≈
n(1
−
e
−
tk/n
)
æ H>9K7õqH>@?D/:?L:
k
76D/:n
äLND/:Aí¢D?FOäHîí¢D&/D?í¢äêI÷+Eäí¢Bîë?ì¢íLã,äç%76äU
t
íãH6æãí-,L®76ë?ë?9H%Mí¢BO76äLNì¢ê
2
δ
(
t/n
)
n
,
óç/LN9L
δ(h) = 1
−
e
−
hk
−
h
÷ D/L &/D/:?ã¡äç%76äh
= ln
k/k
íãäç/LH>D?ì¢êOLAä9LNB®@?B H6æäç?íã¡æ @?D/èNäíH>D í¢DÑäç/Lí¢DzäLN95876ì0
< h
76D/:δ(ln
k/k) = 1
−
ln
k/k
−
1/k
íãîäç/LBO7Aí¢B®@?B H6æδ(h)
í¢D¥äç?íã í¢DzäLN95876ìZ÷qJMHîäç/L9@?D?D?í¢D?Féäí¢BðLH6æäç/L76ì¢FIH>9í¢äç?BíãLãäí¢BO76äL:Ó76äO((2
1
−
ln
k/k
−
1
/k
+
)
n
+
poly(n)m)
H>DÊäç/L75ILN9V76FIL8÷ D/Lè76DÓèç/Lèñ<äç%76ä=äç?íãç/LN@?9íãäíè®õqH>@?D/:<íã=LN5ILNDÊìLããLN9äç%76D
.
/76äìL7>ãäæ H>9
k
@?ë(äH20
ýõ?@?ä®äH<õqLð76ä®äç/Lî9í¢F8çzäãí:?LðH>D/Lðãç/H>@?ì:(ë?9Lyæ LN9 ./y÷ LNä
k
1
=
. . . k
m
=
k
õqH>@?D/:?L:Óõzê
O(c
n
)
ý/óç/LN9Lc <
2e
γ
0
ý%íãäLND/:Aí¢D?FïäH
0
7>ãn
äLND/:?ãKäHðí¢D&/D?í¢äGêI÷EDÊäç?íãKãLND/ãL®äç/L õqH>@?D/:.
/¡íãH>ë?äí¢BO76ìZ÷
EGDéäç/L76õH5ILKæXH>9B®@?ì76äíH>D<äç/L Kì¢@?í¢D?FO76ì¢FIH>9í¢äç?B 9Lüs@?í¢9Lã7>ã¡B®@/èçÄBðLNBðH>9êï7>ã*í¢äã¡9@?D?D?í¢D?F
äí¢BðL8ýMõ?@?ääç/LN9L=íã758769í76DzäýMè76ì¢ìL: Kì¢@?í¢D?F 8ýMäV76ñsí¢D?Fäç/L=ãc76BðL,9@?D?D?í¢D?Fåäí¢BðL=äH®äLN9Bîí¢D%76äL76D/:
H>D?ì¢êå@/ãí¢D?F
O(m2
k
)
õ?í¢äã1H6æqBðLNBðH>9êI÷zú5ILNDé7ãì¢í¢F8çsäì¢ê®æZ7>ãäLN9ó¡7êîH6æqF8ì¢@?í¢D?F.
Kì¢@?í¢D?F/íãëH8ããí¢õ?ìL8÷
Häç?íã£LND/:ðH>D/L,76ë?ë?ì¢íLãäç/L ì¢@?í¢D?F®76ì¢FIH>9í¢äç?B äH&/D/:O76ì¢ì/ãH>ì¢@?äíH>D/ã1æ H>9äç/L &/9ãä
t
0
Lüs@%76äíH>D/ãí¢D
.
0/yýs76D/:Oäç/LNDéH>D/L,ãVLNë%769V76äLNì¢ê*&/D/:?ã¡76ì¢ìqãH>ì¢@?äíH>D/ã1æXH>91äç/L,D/LMä
t
0
Lüs@%76äíH>D/ã1æXH>9£ãH>BðL,ë%769V76BðLNäLN9
t
0
÷ùæ äLN9äç%76äH>D/LîF8ì¢@/Lã®äç/LãLîäGóH ãêsBõqH>ìãäH<FILNä76ì¢ì£ãVH>ì¢@?äíH>D/ãæXH>9äç/L*&/9ãä
2t
0
Lüs@%76äíH>D/ã÷
*ç/LNDÄH>D/Lë?9HMèLL:?ã7>ã*í¢D<äç/Lõ%7>ãíè Kì¢@?í¢D?FO76ì¢FIH>9í¢äç?BÊ÷e í¢äçäç/L76õqHa5ILç/LN@?9íãäíè769F8@?BðLNDzä
t
0
ãç/H>@?ì:ïõqL
h
0
n
ýsóç/LN9L
h
0
íã¡äç/L=H>D?ì¢êïãH>ì¢@?äíH>DäH®äç/LLüs@%76äíH>D
δ(h) =
δ(2h)
÷e(L76ì¢ó¡7êAãFILNä7 õqLNääLN9¡õH>@?D/:ðäç%76DOäç%76ä¡H6æ]äç/Lõ%7>ãíè Kì¢@?í¢D?F76ì¢FIH>9í¢äç?B 76D/:Oãí¢Bîí¢ì769ì¢êîäç/Lç/LN@?9íãäíè=Lãäí¢BO76äíH>DíãîìLããLN9åäç%76äîäç/LBO76äç/LNBO76äíè76ì¢ì¢êÑë?9Ha5ILND H>D/L8÷(Lóí¢ì¢ìD/H>äîFIHÓæ`@?9äç/LN9ðí¢DsäH©:?LNäV76í¢ìãðH>DÑäç/L
Kì¢@?í¢D?FO76ì¢FIH>9í¢äç?Bç/LN9L8÷
*ç/LLãäí¢BO76äíH>D
.
/íã76ìãVHð7õqH>@?D/:<H>Däç/LèH>Bîë?ìLAí¢äê<H6æjäç/LèH>Bõ?í¢D/L:Äù=F89LLNí¢D?FKì¢@?í¢D?F
76ì¢FIH>9í¢äç?BÊý>óç/LN9L£ó¡L£9@?Däç/L¡ù,F89LLNí¢D?F76ì¢FIH>9í¢äç?B õqLNäGóLLNDîãH>BðL¡H6æ/äç/L£F8ì¢@?í¢D?FIã÷ *ç?íãíã76äjìL7>ãä
7>ãLOèNíLNDsäå7>ãäç/Lðë?ì76í¢D Kì¢@?í¢D?F 76ì¢FIH>9í¢äç?BÊ÷ *ç/LïLMëLN9í¢BðLNDzäã:?LãèN9í¢õL:(í¢Dòäç/LOD/LMäãLèNäíH>D
ãç/Hó äç%76ä*í¢ä¡íã¡B®@/èç<BðH>9LLOèNíLNDsäýAõ?@?ä*í¢äã*7>ãêsBîë?äH>äíèK9@?D?D?í¢D?Fîäí¢BðLK9LNBO76í¢D/ã*@?D?ñsD/HaóD÷e/H>9
äç?íãå9L7>ãH>DÑóLïóí¢ì¢ì@/ãL
.
/å7>ãî76D¥@?ë?ëqLN9åõH>@?D/:¥í¢D¥H>9:?LN9åäHöèH>Bîë%769Läç/L<ù=F89LLNí¢D?FKì¢@?í¢D?F
76ì¢FIH>9í¢äç?Bóí¢äçÊñMD/HóD 76ë?ë?9HI7>èç/Lã=äHðãH>ì¢5ILãêAãäLNBðãH6æãë%769ãL **HMH>ìL76DÄLüz@%76äíH>D/ãa÷
(H>9ãäÊè7>ãVL(Lãäí¢BO76äíH>D/ã<æXH>9
.
0/ïèH>BðLöæ 9H>B äç/L
k
lJMù þë?9H>õ?ìLNB 76D%76ì¢êAãíã÷k
lJMù ûíãÄ7 ë?9H>õ?ìLNBûäH:?LNäLN9Bîí¢D/L8ýF8í¢5ILNDò7ïèH>D<_l@?D/èNäí¢5ILåD/H>9BO76ìæXH>9BF
óí¢äçn
5>769í76õ?ìLã76D/:öã@/èVç©äç%76ä L7>èçÊèNì76@/ãLKH6æF
èH>DzäV76í¢D/ã76ä*BðH8ãäk
ì¢í¢äLN9V76ìãaýsóç/LNäç/LN9H>9¡D/H>ä*äç/LN9L=íã*7ãV76äíãSæ êsí¢D?Få7>ããí¢F8D?BðLNDsä æ H>9F
÷ *ç/LãLäó¡Hîë?9H>õ?ìLNBðã769LëqH>ì¢êMD/H>Bîí76ìZäí¢BðL®Lüs@?í¢5>76ìLNDsä÷ LNäf
(x
1
, . . . , x
k
) = 0
.Z/
õqLð76Dsê **HMH>ìL76D(Lüz@%76äíH>D©í¢D
k
**HsH>ìL76D©58769í76õ?ìLã÷ LNä(a
11
, . . . , a
1
k
), . . . ,
76D/:
(a
s
1
, . . . , a
sk
)
õqLî76ì¢ìõ?í¢D%769ê 5ILèNäH>9ãã@/èçöäç%76ä
f
(a
i
1
, . . . , a
ik
) = 1
÷ *ç/L5ILèNäH>9
(b
1
, . . . , b
k
)
íã7ïãH>ì¢@?äíH>DöäH
.
Z/¡íbæ176D/:ÊH>D?ì¢êéíbæí¢äíã7îãc76äíãSæ`êMí¢D?FO7>ããí¢F8D?BðLNDsäæXH>9äç/LèH>D<_l@?D/èNäí¢5IL®D/H>9BO76ì]æXH>9B
F
f
= (x
a
1
11
∨
. . .
∨
x
a
1
k
k
)
∧
. . .
∧
(x
a
s
1
1
∨
. . .
∨
x
a
sk
k
),
óç/LN9Ló¡L:?LND/H>äL
x
a
=
(
x,
íbæa
= 0,
¯
x,
íbæa
= 1,
äç%76äåíã
x
a
= 0
íbæK76D/: H>D?ì¢ê(íbæx
=
a
÷ í¢5ILND¨äç/LãêAãäLNB H6æKLüz@%76äíH>D/ã.
0/H>D/LéèH>D/ãä9@/èNäãå7
èH>D<_l@?D/èNäí¢5IL®D/H>9BO76ì]æXH>9B
F
óç?íèçÓíã,7åèH>D<_l@?D/èNäíH>D H6æF
f
i
÷
D/LD/Haó ãLLãäç%76ä
(b
1
, . . . , bn)
íã
7OãVH>ì¢@?äíH>DÓäH
.
0/íbæ76D/: H>D?ì¢êÊíbæ1äç?íã=5ILèNäH>9íãK7éãV76äíãSæ êsí¢D?F7>ããí¢F8D?BðLNDsä,æXH>9
F
÷ õz5MíH>@/ãì¢êIý]76Dzêk
lJMù ë?9H>õ?ìLNB BO7êïõL9LNë?9LãLNDsäL:ÊõzêÊ7åãêAãäLNB H6æk
lJMù.
æXH>9
k
≥
3
/íãOH>D/L<H6æäç/LÊèNì7>ããíè76ì èH>Bîë?ìLNäLÄë?9H>õ?ìLNBðãé76D/:Ñäç/LN9LÊíãO7ö587>ãä 9Lyæ LN9LND/èLKì¢íãä¡H>Déäç?íãë?9H>õ?ìLNBÊ÷A;,LèLNDsäì¢êðäç/LN9L,ç%7>ãõLLNDï7®ì769FIL=L]H>9ä£äH:?Lãí¢F8D:?LNäLN9Bîí¢D?íãäíè76D/:ð9V76D/:?H>Bîí-,L:éL?7>èNä76ì¢FIH>9í¢äç?Bðã£æXH>9
k
lJMù ÷ *ç/LãLL]H>9äã19Lã@?ì¢äL:ðí¢Dé7Dz@?BõqLN9¡H6æ:?LLNëé76D/: ëqHaóLN9Sæ @?ì*äLèç?D?íüs@/Lã®æXH>9ãVH>ì¢5sí¢D?F©JMù LOèNíLNDzäì¢êI÷ =íèLOL/76Bîë?ìLãH6æ,ã@/èç¨äLèç?D?íüs@/Lãð769Lðäç/L75Míã(@?äD%76B 76ì¢FIH>9í¢äç?BÊý1Jsç>D?í¢D?F HMè76ì*JML769èVç 76D/:ò;=76D/:?H>B ò76ì¢ñMãa÷JMù ôH>D
n
58769í76õ?ìLã è76D(õLåä9í¢5sí76ì¢ì¢êöãH>ì¢5IL:©í¢D©äí¢BðLO(2
n
)
õsêÓä9êMí¢D?FÓ76ì¢ìëH8ããí¢õ?ìLð7>ããí¢F8D?BðLNDsäãý]õ?@?ä®èH>D/ãä9@/èNäí¢D?F 76DO(c
n
)
76ì¢FIH>9í¢äç?B æXH>9c <
2
íã7ìH>D?FðãäV76D/:Aí¢D?FðH>ëLNDë?9H>õ?ìLNBÊ÷?3=HaóLN5ILN9ýAæXH>9ãBO76ì¢ì5>76ì¢@/LãH6æk
äç/LN9Lî769LB®@/èVçöæX7>ãäLN976ì¢FIH>9í¢äç?BðãKæXH>9k
lJMù óí¢äçc
=
c
k
<
2
ýqãLLäç/Låã@?95ILNêÓ769äíèNìLÿ
÷
Js@/èçÓõqH>@?D/:?ã,769LóH>9ãä,è7>ãVLLãäí¢BO76äíH>D/ã,äHåäç/Lë?9H>õ?ìLNBH6æãVH>ì¢5sí¢D?FOLüs@%76äíH>D/ã
.
0/y÷
*ç/LÓLãäí¢BO76äíH>D/ãéH6æäç/L Kì¢@?í¢D?F Ó76D/: Kì¢@?í¢D?Fò76ì¢FIH>9í¢äç?BðãèH>Bîë%769LÄæX75IH>9V76õ?ì¢êÑóí¢äç äç/L
76õqHa5ILó¡H>9ãä,è7>ãLõH>@?D/:?ã,76äìL7>ãä*æXH>9,ãBO76ì¢ì
k
7>ãH>D/L®ãLLã*æ 9H>B äç/L:/76äV7åäV76õ?@?ì76äL:ÊõLNìHóäç/Ló¡H>9ãä,è7>ãL Kì¢@?í¢D?F 8ý Kì¢@?í¢D?FAý
äç/L75ILN9V76FIL äç/L®75ILN9V76FIL
c
3
8÷
8÷(( 8÷
c
4
8÷) 8÷
( 8÷
(
c
5
8÷((" 8÷( 8÷
"
c
6
8÷
8÷)" 8÷(
. . .
. . .
. . .
. . .
*ç/LèH>D/ãäV76Dsä
c
k
íãF8í¢5ILNDÄã@/èçÄäç%76ääç/L®76ì¢FIH>9í¢äç?B 9@?D/ã,í¢D<äí¢BðL
O(c
n
k
)
÷ EGD(äç/LOè7>ãVLOH6æn
**HsH>ìL76D Lüz@%76äíH>D/ãH6æ=76ì¢FILNõ?9V76íèï:?LNF89LLd
í¢Dn
58769í76õ?ìLã:?L&/D?í¢D?Fö7ÄãH è76ì¢ìL: ãLNBîíZ9LNF8@?ì769ãêAãäLNBÊýäç/L<ëH>ë?@?ì769 9>õ?D/LN9n*7>ãíãO76ì¢FIH>9í¢äç?B FILNäãðäç/LÊèH>Bîë?ìLAí¢äê H6æO(
α
n
d
n
2
)
∼
2
2
H
(
α
d)
n
õ?í¢äðH>ëLN9V76äíH>D/ãýóç/LN9LH(α
d
)
:?LND/H>äLãðäç/L<õ?í¢D%769ê LNDsä9H>ëzê¥æ @?D/èNäíH>D÷
*ç/LåDz@?BõqLN9ã
α
d
769LåLMë?ì¢íèNí¢äì¢ê F8í¢5ILND©í¢DÑÿ%ý]L8÷F/÷
α
2
≈
0.09
ý
α
3
≈
0.15
ý76D/:
α
4
≈
0.2
÷%H>9
d
= 2
ýH>D/LåFILNäãäç/LõqH>@?D/:O(1.7
n
)
õzê F8@/Lããí¢D?FÊ7ïDz@?BõqLN9®H6æ¡5>769í76õ?ìLãõqLyæXH>9Läç/L K9>õ?D/LN9 *7>ãíã=76ì¢FIH>9í¢äç?B.
H>9 /76ë?ë?ì¢íè76äíH>Dý%ãLLOÿ%÷%*¡@?äæ H>9
d
≥
3
äç/L5876ì¢@/L2
2
H
(
α
d)
n
L?èLL:?ãäç/L èH8ãäåH6æ*äç/Léõ?9@?äLîæXH>9èL76ì¢FIH>9í¢äç?B!76D/:¨F8@/Lããí¢D?Fö76Dzê©Dz@?BõqLN9îH6æ58769í76õ?ìLã:?HMLãD/H>ä®ç/LNì¢ë÷Eäíã,èNìL769=äç%76äý+76ì¢äç/H>@?F8çÄäç/L76ì¢FILNõ?9V76íè:?LNF89LLãKH6æ9V76D/:?H>B2Lüs@%76äíH>D/ãí¢D
.
0/,769LõqH>@?D/:?L:Äõzê
k
ý äç/L®ë?9H>õ%76õ?í¢ì¢í¢äGêÓäç%76ä7éèH>D/ãí:?LN9V76õ?ìLë%769äKH6æ1äç/LNBþ769LH6æ*76ì¢FILNõ?9V76íè:?LNF89LL*éH>9=ì¢í¢D/L769Kíã,5ILN9êìHó÷ ç/LND
k
≤
4
óLð769Låç/Hó¡LN5ILN976õ?ìLåäH9LNë?ì7>èLåäç/LîLüs@%76äíH>Df
i
(X
i
) = 0
õzê©76D(Lüs@%76äíH>D
H6æ¡76ì¢FILNõ?9V76íè:?LNF89LL
≤
2
ý+äç/H>@?F8çÓóí¢äç ìHsH8ãí¢D?FïãH>BðL®í¢DAæ H>9BO76äíH>D©H>D äç/L &/D%76ìãH>ì¢@?äíH>D÷!*ç/LND óL76ë?ë?ì¢êîäç/L K9>õ?D/LN9*7>ãíã*76ì¢FIH>9í¢äç?BÊ÷Z*¡@?ä£äç/LK76õqHa5IL=Lãäí¢BO76äíH>D/ãí¢Bîë?ì¢êîäç%76ä¡H>@?9ù=F89LLNí¢D?FKì¢@?í¢D?Fð76ì¢FIH>9í¢äç?B ãäí¢ì¢ì+F8í¢5ILã7®õqLNääLN9*õH>@?D/:Oí¢Dïäç?íã*è7>ãL8÷?JMH®í¢ä¡ìHsH>ñAãë?ì76@/ãí¢õ?ìLKäç%76ääç/LKì76ääLN9
ç%7>ãFILND/LN9V76ì¢ì¢êÊ7õLNääLN9õqLNç%75síH>9,äç%76DÊäç/LæXH>9BðLN9÷
+j/Üsá()a%ÚjÛ
*ç/Lí:?L7>ã:?LãèN9í¢õL:ç%75ILõLLND<äLãäL:<H>D<Lüs@%76äíH>DÄãêAãäLNBðã*9LNë?9LãLNDzäí¢D?FO9L:A@/èL: Z9H>@?D/:Ê5ILN9
ãíH>D/ã£H6æúJq÷ *ç/L=Lüz@%76äíH>DéãêMãäLNBðãç%75IL,õqLLNDOèN9L76äL:O@/ãí¢D?F®äGóH®ë%769V76BðLNäLN9ã
r
ý8äç/LDs@?B®õLN9 H6æ£9H>@?D/:?ã76D/:Lüz@%76äíH>D/ãK76D/:<58769í76õ?ìLãí¢DÄ7îãêAãäLNBÊý
m
76D/:n
ýAíãäç/LNDÊF8í¢5ILNDÄõzên
= 56 + 32
·
ntxt
·
(r
−
2)
m
= 32
·
r
·
ntxt.
*ç/LL/7>èNä,èH>D/ãä9@/èNäíH>DÓH6æäç/LãêAãäLNBðãíãF8í¢5ILNDÄí¢DÊù,ë?ëLND/:AíÊù÷
JMH>BðLèVç/H>íèLã,9LNFz769:Aí¢D?Fïäç/Lí¢Bîë?ìLNBðLNDsäV76äíH>DöH6æäç/Lãë?ì¢í¢ääí¢D?Fï76D/:ÊF8ì¢@?í¢D?FéBðLNäç/Hs:?ã,ç%7>:<äH
õqLBO7>:?L8÷ *ç/Lãä9V76äLNF8íLãí¢Bîë?ìLNBðLNDsäL:Äó¡LN9L7>ã*æXH>ì¢ìHóãa÷
!omRSEFDGDFEI>[K Aú£7>èVç<äí¢BðLóLD/LL:ïäHîãë?ì¢í¢äýMóLD/LL:äHåãLNìLèNäH>D/LãêMB®õH>ìóç/H8ãLèH>D&/F8@?9V76äíH>D
ì¢íãäãç/H>@?ì: õqLèN@?äKí¢D ç%76ìbæ÷]JMH>BðLîLMëLN9í¢BðLNDzäí¢D?F<ó*7>ã:?H>D/L8ý76D/: ó¡L®æXH>@?D/:Óäç%76ä76ì¢ó*7êAã:?H>í¢D?F
äç/Lãë?ì¢í¢ääí¢D?Fí¢Däç/LKãêMB®õH>ì+äç%76ä76ì¢9L7>:AêOç%7>ãäç/LãBO76ì¢ìLãä¡Dz@?B®õLN9H6æëH8ããí¢õ?ìLKèH>D&/F8@?9V76äíH>D/ãý
ó¡7>ã,BðH8ãäLOèNíLNDzä÷%(LèH>@?ì:ÊD/H>äãLLKäç%76äí¢äBO76ääLN9L:<B®@/èVçÄç/Hó äç/L®ãë?ì¢í¢ääí¢D?FðH6æjäç/LèVç/H8ãLND
èH>D&/F8@?9V76äíH>D©ì¢íãäó*7>ãK:?H>D/L8ý+ãHðí¢ä=ó¡7>ããí¢Bîë?ì¢ê<:?H>D/Lõzê<ë?@?ääí¢D?FLN5ILN9êÊH>äç/LN9KèH>D&/F8@?9V76äíH>D©H>D
L
1
76D/:<äç/L9Lãä,H>D
L
2
÷
RCZEW>ZK ùäç?9Lãç/H>ì:
t
íãí¢D?í¢äí76ì¢í-,L:(äH64
.èVç/H8ãLNDòõLè76@/ãLîH6æ*äç/LðãëLèNí&%èîD%76ä@?9LðH6æ*äç/L
úJãêAãäLNBðã/y÷2(Läç/LNDÄ9@?D<äç/Læ H>ì¢ìHaóí¢D?FOë/ãLN@/:?H èHM:?L
óç?í¢ìL®ãêAãäLNB'D/H>ä,ãH>ì¢5IL:
óç?í¢ìLë?9H>F89LãVãíãBO7>:?L
19@?DÓù,F89LLNí¢D?Fé76ì¢FIH>9í¢äç?BÊ÷
1F8ì¢@/L76ì¢ì]ë%76í¢9ã,H6æãêsBõqH>ìãF8í¢5sí¢D?F
D/LNó ãêsBõqH>ìãóí¢äç
#
èH>D&/F8@?9V76äíH>D/ã≤
t
÷t
:= 2t
÷EGD/èN9L7>ãí¢D?F<äç/Låäç?9Lãç/H>ì:
t
H>D?ì¢êÓóç/LND(D/LèLãVãV769êÄíã®7ï:AêMD%76Bîíèîó¡7ê©H6æ &/D/:Aí¢D?FÊç/Haóì769FIL èH>D&/F8@?9V76äíH>DÓì¢íãäãóLB@/ãä=7>èèLNë?äæXH>9äç/Lù=F89LLNí¢D?FKì¢@?í¢D?Fï76ì¢FIH>9í¢äç?BCäHåóH>9ñ÷×F4 Ò¾6ºzºÓ¾½qÌjÎj¿jÀ
=H>äîã@?9ë?9íãí¢D?F8ì¢êIýjäç?9LLï9H>@?D/:?ãîH6æúJòíã5ILN9êòL7>ãêòäHÓãH>ì¢5ILïóí¢äç¥äç/LéBðLNäç/Hs:?ãî:?LãèN9í¢õL:]÷
í¢äç
ntxt
≥
2
ýqäç/Låù=F89LLNí¢D?F<76ì¢FIH>9í¢äç?Bþíã76õ?ìLäHï:?Héäç/L_H>õö76ìH>D/L.
í¢D(76õH>@?äH>D/LåãLèH>D/:/yý
D/Hðãë?ì¢í¢ääí¢D?FOH>9,F8ì¢@?í¢D?FðíãD/LèLããV769êI÷
í¢äç
ntxt
= 1
ý/7®ì¢í¢ääìLç/LNì¢ëïæ 9H>B äç/Lãë?ì¢í¢ääí¢D?FðH>9*F8ì¢@?í¢D?FîBðLNäç/Hs:?ã,769LKD/LL:?L:]÷e(LKäLãäL: äç/LöBðLNäç/Hs:?ãïæXH>@?9äí¢BðLã<L7>èçý*óí¢äç 7 :AíLN9LNDsä<ë?ì76í¢DzäLAä6èNí¢ë?ç/LN9äLMäÓë%76í¢9<L7>èç äí¢BðL8÷ *ç/L75ILN9V76FIL:?LNë?äçH6æäç/L=ãVL769èçïä9LL,@/ãí¢D?Fäç/LKãë?ì¢í¢ääí¢D?FBðLNäç/HM:éó¡7>ã
8.2
÷ *ç/L75ILN9V76FILãí-,LKH6æäç/L ì769FILãä,èH>D&/F8@?9V76äíH>D ì¢íãä@/ãí¢D?Fðäç/LF8ì¢@?í¢D?FOBðLNäç/Hs:<ó*7>ã647
÷×` ]½q̾龽qÌjÎj¿À
j76õ?ìL Äã@?BîBO769í-,Lãéäç/LÊ9Lã@?ì¢äãðæ 9H>B äLãäí¢D?F H>@?9OBðLNäç/HM:?ãéH>D ãêMãäLNBðãOèH>Bîí¢D?F¨æ`9H>B æXH>@?9
(LãLLäç%76äí¢D/èN9L7>ãí¢D?F
ntxt
9L:A@/èLãäç/LèH>Bîë?ìLAí¢äíLãæXH>9äç/Lãë?ì¢í¢ääí¢D?Fé76D/:<F8ì¢@?í¢D?FOBðLNäç Hs:?ãa÷%3KLN9L®ó¡L76ìãH &/D/:Ääç/LãêAãäLNB9LyæXLN99L:ÄäHOí¢DÓäç/L®í¢Dzä9HM:A@/èNäíH>D +æ H>9ntxt
= 16
76D/:r
= 4
óL®FILNä,76DÄLüz@%76äíH>DÓãêMãäLNB óí¢äç
1080
5>769í76õ?ìLã=76D/:2048
D/H>DZì¢í¢D/L769=Lüs@%76äíH>D/ã÷[WX¬aW · x ·¸
gXRdmWXWZdf[6ruaQSRWZ,\c^?WXUZQSQ ·ax ·S¸a ·xx a
rcdf[6r¡u%TVUZrcQSg Wel\y[^o>fdfg W
2
22
.
8
2
20
.
9
2
18
2
15
.
3
2
15
6} > °q\yYRfQl¬adfWZdfQSg]^ª\cUgX\yfkdf[6rg nag WZQSYgq^§UZ\yYÑ^b\cUUZ\y[>g]\V^/P¯+I
× È+ºÓÃ/ο ÀaÈѾ½qÌjÎj¿À
/H>9 &/5IL76D/:îãí9H>@?D/:?ãý>óL9V76DðH>@?ä1H6æ+BðLNBðH>9ê
.
* /jõqLyæXH>9L¡äç/Lù,F89LLNí¢D?FKì¢@?í¢D?Få76ì¢FIH>9í¢äç?B
ç%7>:öæXH>@?D/:(7ãH>ì¢@?äíH>Dý]ãHóLO:?HD/H>äç%75ILO76DsêÓ9Lã@?ì¢äã@/ãí¢D?F<äç?íãBðLNäç/HM:]÷ù,ì¢ìó¡Lðè76D(ãV7ê íã
äç%76äóç/LND
ntxt
= 8
ýAäç/L®ãí-,LH6æäç/Lì769FILãä,èH>D&/F8@?9V76äíH>DÄì¢íãäõqLèH>BðLãì769FILN9äç%76D2
24
÷ *ç/L<ãë?ì¢í¢ääí¢D?F©BðLNäç/HM:¥íãð76ìãHö5ILN9ê èH8ãäì¢ê¨äHö:?Höí¢DÑë?9V7>èNäíèL8ýõ?@?äîç/LN9Ló¡LÊè76D Lãäí¢BO76äLäç/L®:?LNë?äç H6æäç/LãL769èçÓä9LLóí¢äç/H>@?ä,ç%75sí¢D?FéäHðó¡76í¢ä=@?Dzäí¢ìjäç/L®7>èNä@%76ìjãH>ì¢@?äíH>DÓíã*æXH>@?D/:]÷ @?9
í¢Bîë?ìLNBðLNDzäV76äíH>DÄH6æäç/LKãë?ì¢í¢ääí¢D?FåBðLNäç/HM:O9V76Dï@?Dzäí¢ì
1024
ìL75ILã¡ç%7>:OõLLNDé5Míãí¢äL:éí¢Déäç/LKãL769èVç ä9LL8ý176D/:¥èH>Bîë?@?äL:¥äç/L75ILN9V76FIL<:?LNë?äçÑH6æ,äç/Lïä9LLéõ%7>ãVL: H>D¥äç?íã÷ (LïõqLNì¢íLN5ILïäç?íãåF8í¢5ILãî7üz@?í¢äL7>èèN@?9V76äLK9Lã@?ì¢ä÷ *ç/L=:?LNë?äçH6æäç/L,ìL75ILã*:?HsLãD/H>ä58769êO7ìH>äýA76D/:éóç/LNDéBðH>D?í¢äH>9í¢D?Fåäç/L
ë?9H>F89V76Bä9V75ILN9ãí¢D?FOäç/Lä9LL8ý%äç/L:AíLN9LNDsä=:?LNë?äç/ã=H6æìL75ILã=76ë?ëL769äHîõLLN5ILND?ì¢ê<:Aíãä9í¢õ?@?äL:]÷
j76õ?ìL ÊèH>DsäV76í¢D/ãäç/Lð9Lã@?ì¢äã÷jù,Fz76í¢DýL7>èç¥LNDzä9ê©íãå76D 75ILN9V76FILH6æ¡æXH>@?9:Aí]LN9LNDzäåäLãäã®@/ãí¢D?F
:AíLN9LNDsäîë?ì76í¢DzäLAä6èNí¢ë?ç/LN9äLMäéë%76í¢9ã÷ /H>9
r
= 6
76D/:ntxt
≥
4
H>@?9ë?9H>F89V76B èH>D/ã@?BðL:¥äHsH B®@/èVçÓBðLNBðH>9êäHå9@?D÷[WX¬W · x
«>kNQUZ\c6[6g x¸ xc¸a xyv xa
gXdm¬=UZ\c6[6g x x u u
6} z PQlRWZ,\c^/gXQTUZeGKWXUZQlQSg6gXdf[6r*gXRfdfWXWZdf[r*YQlWZ6\I
éÝÚ£àe'Gß>áZÝjÚ
EDÓäç?íãë%76ëLN9,ó¡L®ç%75ILë?9LãLNDsäL:ÓãH>BðL®D/LNó äLèVç?D?íüz@/Lã=æXH>9=76ääV7>èñMí¢D?Féäç/L®ë?9H>õ?ìLNBøH6æ1ãH>ì¢5Mí¢D?F
9LNë?9LãLNDzäí¢D?Fïäç/LLüs@%76äíH>D/ã÷
*ç/L<äLèVç?D?íüz@/Lãéë?9LãLNDsäL: ç/LN9LÄ769LÊD/LNóý£ãHöäç/LN9LÄíãOãäí¢ì¢ì=7©ìH>äOH6æKó¡H>9ñÑäH©õLÊ:?H>D/L<í¢D
äç?íã<:Aí¢9LèNäíH>D÷ D/L äH>ë?íè æ H>9éæ`@?ä@?9L 9LãL769èVç íãïäH &/D/: H>@?äóç/LNäç/LN9<ë%769äí76ìF8ì¢@?í¢D?F¥F8í¢5ILã
ã@?õ/ãäV76Dsäí76ì+í¢Bîë?9Ha5ILNBðLNDzäã*èH>Bîë%769L:OäH9LNF8@?ì769£F8ì¢@?í¢D?F/÷zù=D/H>äç/LN91íã£äH &/D/:ðH>@?ä1íbæH>@?91BðLNäç/HM:?ã
è76DõL¡èH>B®õ?í¢D/L:óí¢äçH>äç/LN9äLèç?D?íüs@/LãäHBO76ñIL*ãä9H>D?FILN976ì¢FIH>9í¢äç?Bðã÷
æ%èH>@?9ãL8ýäç/Lù=F89LLNí¢D?F
76ì¢FIH>9í¢äç?B óí¢äçÑí¢äãîè76äV76ì¢êAãäãîãç/H>@?ì: 76ìãHöõLïä9íL:ÑH>D ãêAãäLNBðãæ`9H>B H>äç/LN9îõ?ìHMèñ¥H>9ðãä9L76B
èNí¢ë?ç/LN9ãý/LãëLèNí76ì¢ì¢êäç/LùKúJq÷
(L,ç/H>ëqL,äç/L,D/LNó BðLNäç/Hs:?ã£æXH>9ãH>ì¢5Mí¢D?Fãë%769ãVL,ãêAãäLNBðã¡H6æLüz@%76äíH>D/ãóí¢ì¢ì+õLäV76ñILNDïí¢DzäHäç/L
äHsH>ì¢õH#<äH>FILNäç/LN9=óí¢äç<äç/LH>äç/LN9ã=76D/:Ê:?LN5ILNìH>ëL:æ @?9äç/LN9÷
$ O/Ü%Úà2
·c¡t£I°q\cUXWZ\ydfgShI¶a8³/dQlRUlna8 !"$#$% '&()#+*-,% /.0%123%/.54$6% 78:9<;=>@?a_u
?°q±?²³%ÊxcwcwNxh8st°]xyvVwa·ch>R6Rz6xc¸BA,xhIxVwywNx
xC?1sa6TcYdmUhI¶s³?TVWTUZdf[shzts°q\cUXWZ\ydfgShD?£3EfdfY\kIB83FG<% -HIJ0)#K7-L4, KJM*-,% .N%12%/."4$6% 7
OPQ;$=), =6%SR:7>T8U9<;$=>Zh¯/i±¦°q±?²³+<xVwywcwahIzt°]·ywh>RRs yxVANwh8xcwywcwa
*¶au`°jc>TV6rWGUZQyHX% &Y%FG<% DJ0)#K7ZL:7;[=)KJC\-L]^<3% ^<% S_)`bacha¶y\yaUZ[>TV\c^8³/UZQqTc[6B?R6RdfQ
?fryQ UTahµ+\cYQ¡· ah6_`gXgX6Qlg1·u h6RRs¸a·SA ah>¶y6[Q¡·
a*¶au`°jz>TV6rcQlUZQySHd% &e%Ff<% $J0)#K7gL7T;K=NJM\-<]0^<3% C^L% B&()#$;K:/%.;<==h@ij% /k_`-l ch
³?UZ\eSQSQSdf[6rcgj\V^/_X6[?°Ä´wNxh6R6Rz cvBA hT?° ³?UZQSgXgSh8¶ymnxVwywNx
v¡t£%°q\yaUXWZ\ydfgSh(mö QSdfQlUfHIJN%L^<>nH=0!of4$=%/7p[#% q&()#+r3%/C`b%%/.0^0!Vhé¯%ij±¦°q±?²³%
xVwywahIzt°]KxV¸NvV¸ah>RRs cNvBA Nv ah8xcwywa
¸¡t£?°q\cUXWZ\cdgSZst#%@43%/<;K )=kuS>..N% M`v%<.w8U9<;$==o_uU`(8chK°qu±[?¥xVwywa·ch?zt°]åxVwNxcwhARRsMxc¸c¸wA
x a·chIxcwcwa·c
¡t£c6QlUZrygX\y[zhN±1NeGaUZ\QSR6R8QlhcP¡jm<dfWZdf[rHx47Iy%zHIJN%L^<>U{U%6T/% L% $=>Qv{U|<T.0N%<h>aQSfQSelWZQS?UZQSTcg
df[°+UXnaRaWZ\yrcUTVR6nKxcwcwa·yh>st°]Kxyxcvh8R6Rzz·SwA·c·y·chIxcwcwa·c
6±j\
gX6T{h>I
UZRn:8z<% =>HIJN%L^</=4=;$<=;[/% &()#N")#%'H8-4h°q±?²³+¦(xcwcwNxhIst°]xVcxh
RRsI·A·S¸ah8xcwywyx
°j/°qd§Ih47q%@HIJN%L^<>qH>$%<=w@)#%@HU.,T %/."8z<T=>G4T.0/.VhcWZ}?¯+î°q\y[a^bQlUZQl[6eSQyh?st°]
ah8RRs6vBA¸y¸ah8xcwcwNv
·Swa°j6PdfQSYst#%~r2HIJ0)#K7.w"2<|j%/<=;K%- 7277;[=,%'HIJN%L^</Vh:?_?°q±?²³%Êxcwcwch8st°]
Nx ah8RRs Nx A hzxVwywV
·c·y°jI°qd§IhzI UZRnh 8±\ gX>TS{V47@t4Ty%k$ ==')#%VHI8z46h/a¯ÊxcwcwNvhzzt°] yvyvhIR6RzM·SNvA
·S¸NxhIxcwcwNv
·x
pTUQlWhy¶u`°j>TcrlUZQyhNTc[6¡pjTVfknh27y%/=BO'\z/]0^<% ^:7T;K=>SL-<% 7=>%>J;[I,% /.0%<
6% 7)3%/.q<%/9<;% % ,%
F
2
&2))#o ;K=>$S
F
2
±jQSgXQSTVUZeKUZQSR8\cUXW±±u vVwcah_`t±_?1hxcwcwa
·aCE*_o{TcYTh>2L%M[0$% SI;KT.(L!4[Hs
6Q1pqfQGWZd[K\c^AWZQ1¯v?%°]IhsNxc Gh8xVwywcah8R6Rz¸a·A ·y
·lqEj\yfeGdf[sh?£aQlkyTVg W´nTc[6\k8h6Tc[>,µ°q6dfg WonTcN\k8hT{U.07) =>
¶y\c6[5mdfQlnwòa\c[6gShz· a
·vpu²8²TV[6rh8¶cu s°q6QS[zhzTc[>t£°q\cUXWZ\cdgSh*-h7IT=>C<%/<;[=k% =7C6% )"~reT.+\-/]0^<% q^<%
/%<6%/.5JN%L^<>< TT
df[K_X°q_ °]xcwcwcah8st°] NxV¸hIaRaUZdf[6ryQGUh6RRsaNw·SA·ahIxVwywV
"$j%ÚÞ£á " ïÝÚÛ8ÜzߣàMÛIáGÚ ßqÛ8áÝÚ +Û!) SÜIÝ ) G
3=LN9LðóLð:?LãèN9í¢õLîç/HaóóLîBO7>:?LOäç/LîLüz@%76äíH>D ãêAãäLNB29LNë?9LãLNDzäí¢D?F äç/L1úJ©76ì¢FIH>9í¢äç?BÊ÷jù,ì¢ì
õ?í¢äãFIH>í¢D?F í¢DsäH äç/LO9H>@?D/:¨æ @?D/èNäíH>D¨í¢D 9H>@?D/: