Peter Ce an June 9% `(((

Transkript

!#"%$&"('"()+*-,/.0)1*-2&*-35476897:<;=)1>?4*-,/@9A$B)1/97)1!C*-,D"%E)GFIH<)197EKJC)1L'M52&$B9A6JC*-H<NO*QPR*-NO:
S<TU/V<61FIWXSY<UZ[\]:3O')16_^97)]PR`+9A)]PR97E/:Ca 352&$ba 97:<!a 97H<c6_,%:<dfeg<Z<h%<h%<Zi<Y<jZ
k)145lm*-\;=!noL:2&)1*-M5$&*-2&*-354A6<L:<2B)1*-)19A*-2&*-35476_$&/;=$&\p)19A"O35\]:;=$&)1/":<:<2&45!#$&!#6_97*-)1/*-972&$&)16
9A*-"%$B/''>q97*-/97)1L"%635\]:;r$B)1/"O\)197*-/!#"(\'97"($&*-/6, *-!#!#$&25:!#!#)1>?M52&:35)1!#6s=:45)1!#$&:<
$&/,%)1\)19A)161L*-L'2B:<"($&*-t;=)1/!#$&"(476:M5'/;=:/97)16!#L)197$&)1!uL)1\],%*-\]>:<9A)161v':;=\]:"%$&9
8!#!#$&35/>)1/"D[\p*-M52&)1>wa
FI*-L45x y=z )1,%"5<ZZ<ZGM54{[)1"%)1\|FI)]PR97E/:Ca182&2-\]$&35E"%!u\p)1!#)1\]NO)1;aQ}=E)\]$&35E/"/"%*~>?:5)
;=$&!#"%\$&M5'"%)GNO)1\]M5:"%$&>9A*-L$B)1!*-,"%E$&!;r*-97'>?)1"/$&!u35\]:/"()1;E/)1\p)1M54A6_L\p*-N$&;=)1;t"(E/:"
"%E$&!u9A*-L452&)1,%"/!#"(:<"()1>?)1"/$&!u$&9A2B';r)1;a
= p5=r7 %5
SDa S }=E)+L\p*-M52&)1>a+a+afafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
SDa }\]:;r$B"%$&*-:<2:<LL\p*-:<97Ea+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
S/a Da S \p;=$&/:"%$B*-afafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
S/a Da @)1\$&:"%$&*-afafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
S/a Da T )1"(E/*-;=!afafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
S/a Da g m)1)1;,%*-\:m$&>?L\p*-NO)1;>)1"%E*-;afa+afafafa+a0a+a+afafafa+afa
SDa T 8!#!#'>L"%$B*-/!ta+a+afafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
S7S
S
S 7=f =t¡A¢=5=¡A
Da S K$&9AE)qa+afa+a0a+a+afafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
Da @JC¤a0a+afa+a0a+a+afafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
Da T ¥*-;r)12B!C*-,D@JC¤¦a+afafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
/a TDa S .f:<'!#!#$&:m>*-;r)12Ia0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
/a TDa §=2&2&)1M5)1\35h 8'!#"($&¨>?*-;=)12a+a+afafafa+afafafa+a0a+a+afafafa+afa
/a TDa T s=)1"(:+>*-;=)12©afafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
/a TDa g $B/97E/$&m>*-;=)12-x FI[8@zªafafafa+afafafa+a0a+a+afafafa+afa
/a TDa U «m¤{>?*-;=)12¬afa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
/a TDa Y ®JC*-*-,]¯>*-;r)12°a+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
£
SU
SU
Sj
Sj
S
Si
S
U
±² 5=<³% =´ =+A5r57³ %r
TDa S ¥'2&"%$B!#L)19A$&)1!u\p)1!#L*-/!#)µa0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
TDa @:<>L2&$&/3{"(E/)G35\]:;r$B)1/"¶a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
TDa T [\p*-97)1!#!#)1!C9A*-"%\$&M5'"%$&3K"(*¨:M5'/;=:/97)afafa+afafafa+a0a+a+afafafa+afa
T/a TDa S [*-L'2&:"($&*-m;=)1/!#$&"(4¶afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
T/a TDa ·=*-2&'>)+!#:>?L2B$&/3¸a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
T/a TDa T @)1;=$&>)1/"(:<"($&*-¨\]:"%)¹afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
T/a TDa g ¤5*-!#!#$&2&$BH<:"%$B*-¸afa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
T/a TDa U FI*-"%:>?$B/:"%$&*-t:/;\p)1lm*-\]5$&3afa+afafafa+a0a+a+afafafa+afa
T/a TDa Y .f)1/)1\]:"($&*-m2&)13O"(E afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa

j

TS
T
T
TT
º
±£
TU
TY
² 5=<³% =´ <»==== <=7
gDa S ¼0)1"%)1\>?$&$&!#"%$B9I>?*-;=)12½a+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
gDa [\p*-M5:<M5$&2B$&!#"%$B9>?*-;=)12afa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
T

j
j
j

g
¾I¿ÀXÁÂ=ÀXÁÃ
£ÅÄ=¡A% ÆÇ %=´r=¡A% È
U/a S ÊËE4K;=)1/!#$&"(45ÌÍafafa+a+a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
U/a ÊËE4KM5:<45)1!#$&:/$B!#>?ÌÎa+a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
U/a T y=$&5)12&$&E/*-*-;, '9A"($&*-¸a+a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
U/a g [\]$&*-\;r$B!#"%\$&M5'"%$&*-!ma+a+a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
UDa g/a S yr*-97:"%$&*-KL:<\:<>)1"%)1\{a+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
UDa g/a @9A:2&)L:\]:>?)1"()1\Xa+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
U/a U ¼)1\]$BN:"%$B*-Ía+afafafa+a+a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
U/a Y >L2&)1>?)1"%:"%$B*-½afa+a+a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
±<É
T?*-;=:2&$&"(4 afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
Y/a T [\*-M52&)1>Ò, *-\]>:<2B$&H<:"($&*-Óa+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
Y/a g }=E/)Gv8[!#*-2&N$B/3K:2&35*-\]$B"%E>?!¨a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
YDa g/a S v8[,%*-\]>'2&:<"($&*-ªafa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
YDa g/a §rd<:<97"O:<2&35*-\$&"%E>?!Ôafa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
YDa g/a T yr*-lK)1\©M5*-'/;)1!#"%$&>:<"($&*-Ëafafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
YDa g/a g «m)1'\]$&!#"($&97!Õa+a+a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
Y/a U §=,%Ö97$&)1/974Ëafa+afafafa+a+a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
YDa U/a S m'>?M5)1\©*-,E/$&"(!½a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
YDa U/a @L)1:<\>?:¨\:<¨97*-\]\p)12&:"%$B*- afa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
YDa U/a T k)1/;=:<2B2-\]:/~9A*-\\)12B:<"($&*-afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
YDa U/a g ¤O\$&)1;=>?:m"()1!#"×a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
YDa U/a U ÊØ*-\;*-,/97:<'"($&*-Ùa+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
º<£
g?:/97)*-,D;=$&,(, )1\p)1/"5;=)1"%)1\>?$&$&!#"($&9!#)1\$&:<"($&*-!a+afa+a0a+a+a0a+a
jDa S/a S sr)1"(:+>?*-;=)12©a+a+a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
jDa S/a BJC*-*-,]¯>?*-;=)12°a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
j/a v8[2&$&>?$B"%!×a+afafafa+a+a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
jDa /a S .0:'!#!#$&:<K>?*-;=)12Ga+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
jDa /a sr)1"(:+>?*-;=)12©a+a+a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
jDa /a T JC)1!#'2&"%!×afafa+a+a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
£<£
U<U
U<U
U<j
U<
U<
Y<S
Y<U
ÜÅÝ ¡7 <´5
/a S Þ!#:<35)*-t;=)1/!#$B"%$&)1!ßa+a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
/a Þ!#:<35)*-t:M5'/;=:<9A)1!a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
Ï
Y<j
Y<j
ÉÅà ¡A+¡A%=r%<¡
i/a S 8\]"($&Ö97$&:<2-)1d<:<>L2&)áSâa0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
iDa S/a S ¼:<"(:ãafafafa+a+a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
iDa S/a 8MO';=:<9A)!#)1\$&:<"($&*-¹a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
iDa S/a T ¼)1/!#$&"(4K!#)1\$&:"%$&*-äafa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
i/a 8\]"($&Ö97$&:<2-)1d<:<>L2&)áâa0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
iDa /a S ¼:<"(:ãafafafa+a+a0a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
iDa /a @)1\]$&:"($&*-K*-t:M5'/;=:<9A)1!Çafafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
iDa /a T @)1\]$&:"($&*-K*-t;=)1/!#$B"%$&)1!a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
i/a T !#"%\:<97*-;=:f,%\*->Òm*-\]lm:4åafa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
iDa T/a S .0)1/)1\:<2!#)1"%"($&/35!a+afa+a0a+afafafa+a+a0a+afa+a0a+afa+a0a+a+a0a+a
Ï<É
Y<i
Y<i
j<Z
j<Z
j<T
j<T
j<U
j<j
<g
<g
iDa g
iDa U
U
i/a TDa ¼:"(:µa+a+afafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa g
i/a TDa T 8M5'/;=:/97)I!#)1\]$B:<"($&*-a+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa
i/a TDa g ¼)1!#$&"(4¨!#)1\$&:<"($&*-©n_:<\\*-l2B$&>?$&"(!æa+afafafa+a0a+a+afafafa+afa iZ
i/a TDa U ¼)1!#$&"(4¨!#)1\$&:<"($&*-©n_M5\p*-:<;2&$&>$&"(!âafa+afafafa+a0a+a+afafafa+afa iT
i/a TDa Y JC)1!#'2&"(!×a+afafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa i
«K*-2&*-9A)1)G2&:<;!#:<$B2&!u*-,Ds=*-E/)1>?$B:ça+afafafa+afafafa+a0a+a+afafafa+afa i
i/a gDa S FI)1\"%*-NO:+!#"%\p*-'E/:+@)197"%$&*-âa+a+afafafa+afafafa+a0a+a+afafafa+afa i
i/a gDa k*-M5452&:0ÊØ)1!#"@)197"%$&*-Îa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<Z
i/a gDa T @5:2&5:G/:;FI$BE/*-NO*-'@)19A"($&*-Ëafafafa+afafafa+a0a+a+afafafa+afa¦S<ZY
i/a gDa g WC:+5\]$&H)1>¬FI:N)a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<Zi
¼0$&!#9A'!#!#$B*-ça0a+a+afafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afaèSAST
<é à O=7³ =¡7 5=¡
o£
S<Z/a S×¥:<$&¨\)1!#'2B"%!êa+a+afafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afaèSASU
S<Z/a ×¼0$&\)197"($&*-/!u, *-\, '"('\)I\p)1!#)1:\97EÓa0a+a+afafafa+afafafa+a0a+a+afafafa+afaèSASY
S<Z/a T×8975/*-lm2B)1;r35)1>)1/"(!afa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afaèSASj
oìë¢r¢==r%í
o É
S7S/a Z/a Såy=$&!#"($&/3{*-,DL\p*-35\]:>?!fafa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afaèSASi
S7S/a Z/a å:M5'<;=)1îafafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afaèSASi
S7S/a Z/a Tå:;=Nh%!#)1)1;r!ïafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<
S7S/a Z/a gå:E/$&!#"(*wa+a+afafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<
S7S/a Z/a Uå:>?;="ça+afafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<g
S7S/a Z/a Yå97*-)1/*-972&$&)¬afafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<i
S7S/a Z/a jå97*-/!#"ða+a+afafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<TU
S7S/a Z/a å97*-'/"(h E$&"%!ïafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<TY
S7S/a Z/a iå;=)1/:MO'çafafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<Tj
S7S/a Z/a S<ZG;="(<;=> a+afafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<Ti
S7S/a Z/a SAS~35ñ5:<L;=h%LÎafafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<gS
S7S/a Z/a S<GE$&!#"%*-35\:<> afafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<Ug
S7S/a Z/a S<TG$&"(\]:/!#Lîa+afafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<UU
S7S/a Z/a S<gG>:<"(<35\$Îafafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<UY
S7S/a Z/a S<UG>*-/*-"(*-/$&97h !#L)1:\òa+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<Uj
S7S/a Z/a S<YG*-\p;=<!#97*-\)ãafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S?h H)1\p*-h \p*-lm!#h 97*-2&!afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<YS
S7S/a Z/a <ZG!#:>?L2&)1\äafafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<Yg
S7S/a Z/a <SG!#97*-\)1\]:/Ùafafa+a0a+afa+a0a+a+afafafa+afafafa+a0a+a+afafafa+afa¦S<YY
Y
B}=E)1\)I:\p)"%E\)1)5$&;r!u*-,D2B$&)1!n_2B$&)1!#6_;r:>?)1;2&$&)1!#6:<;!#"(:<"($&!#"($&97!a ¯
:\]}lK:<$&6_S<i<g
óôõó
öw÷?øúùûüIýwþ1øÿ
}rE)"(:!#f*-,-"(E/)uL\p)1!#)1/"!#"(';=40$&!="(*f;=)1!#$&35:/*-NO)12lK:<4+"%*+\p)19A*-!#"%\p'9A"<"%E)¯®!#L)19A$B)1!
\)1!#L*-!#)f,%'/97"%$&*-x%@JC¤5!#z*-,'/$&"(:<\4m*-\p3O:/$B!#>?!*-:t'/$B;r$B>?)1/!#$B*-/:2/)1/NO$&\p*-/h
>?)1/"(:23O\:<;=$&)1"!#*-2&)12B4,%\*->ª:M5'/;=:/97);=:<"(:¨*-?!#L)19A$&)1!G97*->?>'/$&"($&)1!a}=E$&!G$&
! lmE/:"/)197*-2&*-35$&!#"(!'!#':2&2&4{9A:2&2"(E/)G®$&/;=$&\p)19A"O35\]:;=$&)1/"O:<:<2B4O!#$B!#$¯ # S& % ao}rE)lm*-\p;¯®$&/h ! "!
;r$B\)197"%¯1>)1:<!"(E/:""(E/)35\:<;=$&)1"$&"(!#)12&,5$&!2&:"()1/"(6o/*-"-:9A97)1!#!#$&M52&)16o*-\=)1NO)1L\)1!#'>)1;a
}rE)m!#"(';r4ØlK$&2&2©97)1/"()1\G*-¥"(E/)m"(*-L*-2&*-354X*-,"(E/)mL\p*-M52&)1>?6="(E/'!;=$&!#\p)135:<\p;=$&/3?"%E)
ñO':/"($&"(:<"($&NO)K>)1:<!#'\$&/3Ç*-,C¯®!#:<>L2&)K!#97*-\p)1!#¯õa¤O*-\>?:2&2&476"%E$&!0"(:!#Ç9A:ØM5)¨"()1\]>)1;
¯B!#)1\]$B:<"($&*-t*-,/,%*-!#!#$&259A*->>?'$&"%$B)1!x%:<!#!#)1>MO2B:<35)1!#z ¯a
sr:45)1!#$&:0$&, )1\p)1/97)C$&!|'!#)1;{E/)1\p)C"(*f®!#ñO')1)1H)1¯Q"(E/)L*-L'2&:"%$B*-;=)1/!#$&"(40;=$&!#"(\]$&M5'h
"%$&*-!G*-'"|*-,|*-MO!#)1\N)1;Ø!#L)197$&)1!#¯O:<M5';r:/97)1!a}rE)1/6O"%E):!#!#'>?L"($&*-Ç*-,r;r)1!#$&"($&)1!
, *-\]>$&/3K:f®9A*->L:<97"D!#"(\'97"%'\p)1¯*-t:m)1/NO$&\p*-/>)1/"(:<2-35\]:;=$&)1/"$&!'"%$&2B$&H<)1;$&t97*-/h
!#"%\p'9A"($&*-*-,:35)1/)1\:<"(*-\C*-,E/45L*-"(E/)1!#)1!I:M5*-'"D"%E)0;=$&!#"(\]$&M5'"($&*-/!*-,=!#:<>L2&)f\:<5!
x "(*-L*-2&*-35$&9A:2&2&4B97*-2&2&:L!#)1;=¯/!#97*-\)1!#z%65:<; !#L)197$&)1!!#97*-\)1!x%\]:/35)1!#zr*-?"(E/)35\]:;=$&)1/"]a
}rE)¨>*-;=)12|$&"%\p*-;='9A)1; E/)1\p)~$&!+"%E'!0E/:2&,%h L\p*-MO:M5$&2&$&!#"($&9nr"(E/){;=)1/!#$&"($&)1!#6D*-XlmE$&9AE
"%E)t;r)1"()1\]>$&/$B!#"%$&9¨E/45L*-"(E/)1!#$&!~35)1/)1\:<"(*-\fM5'$&2B;r!$B"%!~E/45L*-"(E/)1!#)1!#6©:\p)K;=)1\]$&NO)1;wM54
9A*-E)1\)1"/:LL2&$&97:<"($&*-m*-,"%E)+M5:!#$&9\p'2&)1!u*-,/"(E/)GL\p*-M5:<M5$&2&$B"%4{"%E)1*-\]4a
óô$'
ö¨û(*),+.-.+1ü0/1(þ2(ù?ùûü0(*3÷
465 765 4 8:9;=<>@?
A<.BC>
\;=$&:<"($&*-*-\]$&35$&:<2&2B4>)1:<!¯®L'"%"($&/3"(E/$&35!I$&/"(*t*-\p;r)1\Q¯Ox%JC:<>)1/!#54tSi<TZ# SASiD%FE
.0*-*-;=:<2B2Si<Ug# Y<UD%G# YY.%E|ÊËE$&"%"(:O)1\GSi<YjC# ST<U% z#aG§=9A*-2&*-35$&!#"(!:;r*-L"()1;¥"(E/)¨lm*-\p;, *-\
:<\\]:/35$&/3Ø"(E/)t!#:>?L2B)1!:<;w!#L)19A$B)1!$& \)12&:"($&*- "(*Ø*-/)K*-\0>?*-\p)K)1N$B\*->?)1/"(:2
3O\:<;=$&)1"%!x ÊËE$&"("%:5)1\rSij<T:# S<TjD%F1E 8'!#"%$B¨Si<jYC# H%% z#aQ\p;r$B/:"%$&*-{"(E/'!©!#)1)15!©"(E/)I\p)1h
2&:<"($&*-!#E/$&L!MO)1"(lm)1)1mM5$&*-"($&9I97*->?>'/$&"($&)1!:<;)1N$&\p*-/>)1/"(:<2-x%$&/972&';=$&3K!#'979A)1!#h
!#$&*-/:2&z 35\:<;=$&)1"%!ux 8'!#"($&¨S<ij<YC# D%G# T%% z#aQ\]2B*-9A$-x%S<ij<TzG# SASTD% !#"%:"()1!C"%E:<"O*-\;=$&:<"($&*-¨$&!
B"(E/)G$&;=)1/"($&Ö97:<"($&*-t*-,D"(\)1;=!C:<;L:"("%)1\/!C*-,D97*->?L*-!#$&"($&*-:<2ON:\]$B:<"($&*-/¯a
j

465 765 7 Y[Z
9H<.?
A<.BC>
] F_^WF&`C ¾JI2K L ÁÂNMPOQSR ÀXÁTMC¿
UWV¾ÁXR%¿À
@)1\]$B:<"($&*-K$B!:+"()1\]>Ò$B/NO)1/"()1;L\p*-M5:<M52&4~M54~"%E)G:<\p9AE:<)1*-2B*-3O$B!#"%!ClmE*~'!#)+$B""(*~/:>?)
"%E)uL\*-97)1;='\)©*-,<L'"%"($&30"(E/)u!#:<>L2&)1!=*-,:\]"($&, :97"%!$&"%*+"(E/)C97*-\]\p)19A"x \p)12&:"%$&NO)1z9AE\*-*-h
2&*-35$&97:<2C*-\p;=)1\ aK"(E/)*-"(E/)1\E:<;=6©"%E))19A*-2&*-35$&!#"(!{'!#)"(E/)"()1\]>¶*-\;=$&:<"($&*-,%*-\
\ L'"%"($&/3"(E/$&3O!+$&"%**-\p;r)1\ \ 6$ba )Oa 6O:<\\]:/35$&/3!#:>?L2&)1!#6'!#':<2B2&4$&Ø!#)1N)1\:<2;=$&>?)1h
!#$&*-/!#6u!#* "%E:<""%E)L:<"("%)1\$&9A2&';=)1; lm$&"(E/$&w"(E/);=:<"(:MO)197*->?)1!~NO$&!#$&M52&)Oa)*-,
"%E)1!#);r$B>?)1/!#$B*-/!K>:<476CM5'"I/)1)1; /*-"MO)16"%$&>)Oa8/4 *-"%E)1\N:\]$B:<M52&)t$&!{:LL\*-h
L\]$&:"()Oa|©'!#)"(E/)~"%)1\> \ !#)1\]$B:<"($&*- \ E)1\)!#$&>L2&4, *-\"(*-L*-2&*-35$&97:<2=x%L\)1!#)1\N$&3t*-/2&4
*-\;=)1\(61/*-"D;=$&!#"(:/97)1!#z/*-\p;r$B/:"%$&*-K$&m*-/)G;=$&>)1/!#$&*-6/*-"/)197)1!#!#:<\$&2&4{"%E)G"%$&>)Oa
}=E/)'/;=)1\]2B4O$B/3 $&;=)1:?'L*-lmE$&97Ew!#)1\]$&:"%$B*-w$&!~MO:!#)1; E/:!{M5)1)1,%*-\]>'2&:<"()1;
L)1\E:<L!G:!f)1:\]2B4?:!f$&XS<iiKM54¤O2B$&/;=)1\]!#h%[)1"%\$&)OaI X:\97E/:)1*-2&*-354A6/$&"C$&!+3O)1)1\]:2&2&4
!#'LL*-!#)1;Ø"%E:<":/4t"(45L)0*-,r:<:\]"($&, :97"%6:, "()1\CM5)1$&/3t$B/NO)1/"()1;r6-!#L\p)1:;r!:<;Ç35:<$B/!
L*-L'2&:\]$&"(4A6O"(E/'!GM5)1$&/3L\*-;='97)1;Øx :/;X;=$&!#97:<\p;=)1;rz=$&?3O\p)1:"%)1\:<;X3O\p)1:"%)1\/'>h
M5)1\]!a©}=E/)1/6$&"(!fL*-L'2&:\]$B"%4;=)19A2&$B/)1!#6O:<!G/)1lq"(45L)1!G:<\p)$&N)1"%)1; :<; 97*->?$B/3?"(*
'!#)Oao}rE'!#61"%E)I/'>M5)1\|*-,5L\p*-;r'97)1;m:\]"($&, :97"%!r*-,97)1\]"(:$&~"%45L)L)1\r"($&>?)I'$&"5, *-\>?!
:¨'$&>?*-;=:2, '9A"($&*-Ø:2&*-/3"%E)~"%$&>)Oa©}rE$&!GL\*-97)1!#!GE/:!9A2B)1:<\:<:<2&*-35$&)1!G$&?MO$B*-!#h
"%\:<"($&35\]:LE/4¨x :t$&/NO:;r$B/3XV\]:;=$&:<"($&3K!#L)197$&)1!*-979A'\!$B2B*-lÒ/'>M5)1\]!Ö\!#"%6"%E)1
)1!#"%:M52&$&!#E)1!$&"(!#)12&,\p)1:<97E/$B/3Ç"(E/)t>:<d<$&>?'>¶L*-L'2&:<"($&*- ;r)1!#$&"(4O6r:/;w;=)19A2B$&/)1!:!
lm)12&2&6QMO)1$B/3*-'"(h 97*->?L)1"()1;mM540:Ö"("%)1\!#L)197$&)1!#z-:!lm)12B2<:!|$B{x%L:<2B)1*-z )197*-2&*-354x "(E/)1\p)16
:Ç!#L)197$&)1!KE:<!¨$&"%!K\)1:2&$&H)1; $&97E/)?*- :Ç35\]:;=$&)1/"*-,G:w)1/NO$&\p*-/>?)1"%:2NO:\]$&:M52&)16
\)1:97E/$&3"(E/)~>?:d$B>?'>L*-L'2&:"%$B*-Ø;r)1!#$&"(4:""(E/){L\*-L)1\*-L"%$B>?'>?6;=)1972&$&$&/3
*-mM5*-"%Et;=$&\p)197"%$&*-!C"%*-lK:<\p;=!C"%E)+$&97E/)+>?:\35$&!a
a !" F0bc" &d
kNl&m"!F&N! m
!!nD
@)1\$&:<"($&*-m$B!,%*-'/;=)1;'L*-t"(E/$B!:!#!#'>?L"($&*-*-,DE/'>L)1;'$&>?*-;=:25B\p)1!#L*-/!#)
, '9A"($&*-/!#¯au}=E$&!f:!#!#'>?L"($&*-Ç$B!f97)1/"(\]:2D"(*!#)1\$&:"%$&*-©au}=E)"%:!#>$&35E/"©!#)1)1>¹"%\$&Nh
$&:2/:"Ö\]!#"r3O2B:<9A)On5"%:5)0:~!#L)19A$B)1!#¯:M5'/;=:<9A)f>?:"%\$&d6-lKE/)1\p)!#:<>L2&)1!I:\)+\p)1L\)1h
!#)1/"()1;~MO4+\p*-lm!=:<;¨!#L)197$&)1!M54f97*-2&'>/!#6o:/;~L)1\]>'"%)u$&"(!=\*-lK!r'"%$B21"%E)E'>?L)1;
L:<"("()1\] :<LL)1:\]!f$&97*-2&'>?!aKÞ/, *-\"%':<"()12&476|"(E/)t'>?M5)1\0*-,L)1\]>'"%:"%$B*-/!$&h
9A\p)1:!#)1!Ilm$&"(f
E egihjQ65lmE)1\_
) e?$&!"(E/)~'>?M5)1\I*-,©!#:>?L2&)1!a©}=E/'!#6E/:N$B/3"%*!#)1\]$B:<"()
<Z~!#:>?L2&)1!MO4)1d<E/:'!#"%$&NO)!#)1:\97E>?)1:/!I"(*t)1N:2&':"%)0S<S<YgU<SZ<ZgZ<_T<_ZZZZ;=$&, h
, )1\p)1/"5L)1\]>'"%:"($&*-/!a
ÊËE:<"-!#)1\$&:"%$&*-{;=*-)1!$&!|$&2&2&'!#"(\]:"()1;m$&~"%E)I, *-2B2&*-lm$&3!#)1\]$&)1!|*-,OÖ35'\p)1!aQ@'LL*-!#)
"%E:<""%E)G!#L)19A$&)1!u:!#!#)1>?M52&:35)1!,%*-\]>)1;';r)1\L\)1NO:<$B2&$&/3{$&po')1/97)f*-,D:+!#$&3O2B)f)1h
N$B\*->?)1/"(:21N:\]$&:M52&)167!#:<476A"()1>?L)1\:<"('\p)Oa7}=E/)"%)1>L)1\]:"%'\p)©NO:<\$&)1;~$&"($&>?)16AMO'"<lm)
9A:/*-"=:<979A)1!#!$&"(!I;=$&\)197"D\p)19A*-\p;a !#"%)1:;=6lm)lK:<"r"(*m;=)1;='9A)+L:!#"r"()1>?L)1\:<"('\p)1!
, \p*->:!#!#)1>?M52&:3O)1!r:2&*-/)16A)1N)1lK$&"%E*-'"-:5/*-lK2&)1;=3O)*-,"(E/)!#L)19A$&)1!#¯1"()1>?L)1\:<"('\p)
*-L"%$B>?:0:/;"(*-2&)1\]:/97)1!a
OQiq&Q?ÁTMK UrR ÁTR ¿À2K stK LuLuMC¿ K¾JI
i
count of individuals
Randomly sampled coenocline
100
50
0
0
19
samples
}lK)1/"(4f\:<;r*->Ùx x~'/$B/, *-\>?)1;=z:!#!#)1>?M52&:35)1!x "(*-"%:21U<Z!#L)197$&)1!#z#aA¼0)1/h
!#$&"($&)1!*-,$B/;=$&NO$&;=':<25!#L)197$&)1!L*-L'2B:<"($&*-/!N:\]4¨lm$&"(E/*-'")1d<E/$&M5$&"($&/3K:<4mL:<"(h
"()1\]Ca
v %´5rp&w&w
¾JI2K L ÁÂNMPOQSR ÀXÁTMC¿
S<Z
UWV¾ÁXR%¿À
Seriated coenocline
100
50
0
0
19
v ´5=+w w
8!#!#)1>?M52&:3O)1!K, \p*->ïÖ3|aDSDa SØ:, "()1\~!#)1\]$&:"%$B*-Ca @L)19A$&)1!KL)1\], *-\>?:/97)1!
,%*-\]>¬'$&>?*-;=:259A'\N)1!a
8, "()1\=!#'9A97)1!#!#, '2!#)1\$&:"%$&*-6_:+E'>?L)1;L:"%"()1\]{)1>?)1\p35)1!aQm*-"%)"(E/:"O"%E)I9A'\N)1!C:\p)
/*-"D!#"(\]$B9A"(2&4K'$&>?*-;=:2bn<"(E/) \ /*-$&!#) \ $&!$&/E)1\)1"/"(*¨"(E/)+9A*-2B*-/$&H:<"($&*- V, *-!#!#$&2B$&H<:"($&*-
V{!#:>?L2&$B/3tL\p*-9A)1!#!a-}=E/$&!/*-$&!#)$B!$&)1N$&"(:MO2B)16:<;Ç:35*-*-;Ç*-\p;=$&/:"%$B*->)1"%E*-;Ø$&!
!#'LL*-!#)1;Ç"(*K97*-/97)1\]$&" a5 "%E$&!!#"()1L6-!#)1\]$B:<"($&*-\)1NO)1:2&!"(E/)f!#L)19A$B)1!#¯O"()1>?L)1\:<"('\p)
*-L"%$B>?:0:/;"(*-2&)1\]:/97)1!a
Scores along the time
30
score
y mC!F_&!
gradient
20
10
0
0
v ´5=+w ± w
19
time
@:<>L2&)!#97*-\)1!u, \p*->ÒÖ3|a#SDa GL2&*-"("%)1;NO)1\]!#'!u"%$B>?)Oa
m*-lG6=!#'LL*-!#)m"%E:<"C"(E/)¨!#:<>L2&)1!0lK)1\){*-\]$&35$&:<2B2&4Ø/'>MO)1\p)1;¥:979A*-\p;=$&/3Ç"(*?"(E/)1$B\
!#"%\:<"($&35\]:LE/$B9+L*-!#$B"%$&*-6$õa )Oa"(E/)1$&\*-\;=)1\\)1L\p)1!#)1/"(!"($&>)Oa=s=4tL2&*-"("%$B/3"%E)!#:<>L2&)
!#9A*-\p)1!ux \p.) o)19A"($&3¨"(E/)1$&\L*-!#$&"%$B*-*-t"(E/)G\p)19A*-!#"%\p'97"%)1;35\]:;r$B)1/"(z/:3O:$&!#"D"%$B>?)Glm)
35)1"/\p)19A*-!#"%\p'9A"()1;\)12B:<"($&NO)I"%)1>L)1\]:"%'\p)1!©$&t"(E/)GL:!#" a
O Qiq&Q?ÁTMK UrR ÁTR ¿À2K stK LuLuMC¿ K¾JI
465 765 z {|Z
A~}_B;[
S7S
}\]:;=$&"%$B*-/:2o>?)1"(E/*-;=!r*-,$&/;=$&\p)197"<35\]:;=$&)1/":/:2&45!#$&!=$&/972&';=)uL*-2&:<\*-\;=$&:<"($&*-x%[z 6
L\]$&9A$&L:2r9A*->L*-/)1/"(!:/:2&45!#$&!x%[FI8z 6O, :9A"(*-\:/:2&45!#$&!0x%¤18z 6/>'2&"($&;=$&>?)1!#$&*-/:2
!#9A:2&$&3x%¼@z%697*-\]\p)1!#L*-/;=)1/97):/:2&45!#$&!Ix F8z 6:/;Ø;=)1"(\)1;r)1;9A*-\\)1!#L*-;=)1/97)
:<:<2&45!#$&!ux%¼FI86_¼§=FIJC8m8z a
[*-2&:<\0*-\;=$&:<"($&*-/6C:2&!#* 5/*-lm :!{s=\:<45h F'\]"($&!#6*-\Ê $&!#9A*-!#$& *-\;=$&:<"($&*-6C$&!
*-/)*-,="(E/)0)1:\]2B$&)1!#">?)1"(E/*-;=!a}=E/)f"%lK*K!#:>?L2&)1!I"(E/:":\)G, '\"%E)1!#"$&!#L:<97)f;=)1Ö)
"%E)m)1/;=L*-$&"%!*-,u:tL\p*QPR)197"%$&*- :d$&!#6"(E/)1 L*-!#$&"($&*-/!*-,u*-"(E/)1\+!#:<>L2&)1!0:\){97:<2&97'h
2&:<"()1;lm$&"(Et\)1!#L)197"O"%*~"(E/$&!u:d$&!a
[\]$&9A$&L:297*->?L*-)1/"(!t:<:<2B4O!#$B!t\*-"(:<"()1!K"(E/)?;r:"(:ØL*-$&/"(!t!#*"(E/:"+>:<d<$&>?'>
N:\]$&:M5$&2&$&"(4~$&!uN$B!#$&M52&)Oao}rE)GÖ\]!#"OL\]$&9A$&L:297*->?L*-)1/"D:d$&!C35*-)1!C"(E/\p*-'35Em"%E)>?:dh
$&>?'>NO:<\$&:MO$B2&$&"(4A6O:<;X>?$&$&>?$&H)1!+"%E)!#'>*-,!#ñ5':<\p)1!*-,©;=$&!#"(:<9A)1!G,%\*-> L*-$&/"(!
"%*t"(E/):d$B! # j %J# SAS7S %c# S<.Z %# g.U %#aD[\]$B/97$&L:<29A*->L*-/)1"%!:\)f'!#)1, '2OlmE/)1!#L)19A$B)1!
\)1!#L*-!#)1!:\)2B$&/)1:\]2&4¨9A*-\\)12B:<"()1;"%*{"%E)f)1N$B\*->?)1/"]a<Þ, *-\]"('/:"()12&4A6lm)+\]:\)12B4
)1/97*-'/"()1\|!#'97E¨:!#$B"%':"%$B*-¨$&{"(E/)I:<"('\)OaQÊ E/)1~:LL2&$&)1;m"(*/*-2&$&)1:<\r\)1!#L*-!#)1!#6
L\]$&9A$&L:2-97*->?L*-/)1"D:/:2&45!#$&!CL\*-;='97)1!C:<¨:<\"%$B, :9A"(61"%E)G!#*-h 97:<2&2B)1;®E/*-\!#)1!#E/*-)+)1, h
, )197"%¯n"%E)"%\: P )19A"(*-\]4*-,r:¨35\]:;=$&)1/"=$&!*-"|:{!#"(\]:$&35E/"r2&$&/)16O:!I)1dL)197"%)1;?lm$&"(EÇ2&$&)1:<\
;r)1L)1;=)1/97)16M5'":f97'\]NO)Oa
¤O:97"%*-\+:<:<2B4O!#$B!$&!!#'L)1\Ö9A$&:2&2&4Ø!#$B>?$&2&:\+"%*Ç"(E/)KL\]$&9A$&L:297*->?L*-)1/"(G! ECE/*-lmh
)1N)1$6_$&"%!*-MoPR)197"%$&NO)G$&!u/*-"D:K*-L"($&>:<25L\p*QPR)19A"($&*-m*-,/"%E)+;=:"%:61M5'"/\:<"(E/)1\|"%E)+>*-;=)12
Ö"%"($&/
3 # T& %*# T.U %# g.Z %[# Ug %[# YU %[# Yi %[# T %#a}=E){>*-;=)12r$B!f"(E/:"©"(E/)~*-M5!#)1\]NO)1; NO:<2B')1!
*-,©N:\]$B:<M52&)1!I:\p)2&$&)1:<\9A*->MO$B/:"%$&*-!G*-,2&:"%)1",%:<97"%*-\!#65L2&'!G\]:/;=*->¹)1\\*-\]a|¤5:<97h
"%*-\f:<:<2&45!#$&!0'!#':<2&2B4Ø!#"%:\]"(!, \p*->èL\]$&9A$&L:297*->?L*-)1/"(!#6lmE$&97E¥$&"u\p*-"%:"%)1!f$&""%E)
!#*-h 97:<2&2B)1; ®!#$&>?L2&)~!#"(\'97"('$1¯aCÞ2&$&5)~L\]$&9A$BL:<297*->?L*-)1/"(!#6D"%E)~, :9A"(*-\:d)1!:\)
/*2&*-3O)1\|*-\]$&)1"%)1;$&{"(E/);=$&\p)19A"($&*-/!*-,/>?:d$B>?'>¸N:\]$&:/97)161M5'"5:<\p)\p*-"%:"()1;m"%E'!
, :9A"(*-\f2B*-:<;=$&3O!:\p)K972&*-!#)m)1$&"(E/)1\+"%*Ø*-)16*-\+H<)1\p*raÞ!#)1;w$& 3O\:<;=$&)1"u:<:<2&45!#$&!#6r$&"
!#',%,%)1\]!,%\*->è"%E)m!#:>?)tNO$&*-2&:"%$&*- *-,2B$&/)1:\]$&"(476:!L\]$&9A$BL:<2|9A*->L*-/)1/":<:<2B4O!#$B!
;r*-)1!a
'2&"($&;=$&>?)1!#$&*-/:2!#97:2&$&/3 $&!{:?>?)1"(E/*-; "%* \p)1N)1:2©"(E/)!#"%\p'9A"('\p)*-,\)12&:"($&*-/h
!#E/$&L!G, \p*->¹:{;=$&!#"(:<9A)>:<"(\]$Bda|%,>?)1"(\]$B9f:<"('\)0$&!G9A*-!#)1\]NO)1;r65$&"|$&!97:<2&2B)1;Ø:¨>)1"%h
\]$&9+>?'2&"($&;=$&>)1/!#$&*-:<2!#97:<2B$&/356O:<;Ø$&/972&';=)1!"%E)L\]$B/97$&L:<2/9A*->L*-/)1/"(!G:<:<2B4O!#$B!
>?)1/"($&*-)1;w:<M5*-NO)OaG%,"(E/)¨>?)1"(\]$&9:<"('\p){*-,u"(\]:/!#,%*-\]>?:"($&*-X$&!:MO:/;=*-)1;r6//*-/h
>?)1"(\]$&9>'2&"%$B;r$B>?)1/!#$B*-/:2D!#9A:2&$&3m$&!"%E)1;=)1Ö)1;?:!:>:<LL$&3mlmE$&9AE*-/2B4tE/:!
"%* *-M5)14 "(E/)>?*-*-"%*-$&97$&"%4¥9A*-!#"%\:<$&" a:/4XL*-L'2&:\>?)1"(E/*-;=!{*-,I;=*-$&/3 !#'9AE
"%\:<!#, *-\]>:<"($&*-Ø)1d<$&!#"%6$&/972&';=$&3?k\p'!#O:2&¯®!f:LL\*-:97
E # T % 6.0'"("%>:<¯B!+:<LL\p*-:<97E
# T&j %%6_:<;@:>?>*-/¯®!>:<LL$B/,3 # &S % a
FI*-\]\p)1!#L*-/;=)1/97):<:<2&45!#$&!|\)1L\p)1!#)1/"(!=M5*-"%E{!#L)19A$B)1!|:/;m!#:>?L2B)1!$&~:I97*->?>*-
*-\;=$&:<"($&*-~!#L:<97)OaQ}=E/)1\p))1d<$&!#"-!#)1NO)1\]:2;=$&,(, )1\p)1/":2&35*-\]$&"(E/>!©, *-\=;=*-$&/30FI*-\]\p)1!#L*-/h
;r)19A)u:/:2&45!#$&G! EQ"(E/)u>*-!#"lm$&;=)12&4+;=)1!#9A\$&M5)1;{$B!r"(E/)u\p)19A$BL\*-97:<2A:<NO)1\]:35$&/3G:2&35*-\]$&"(E/>
# g&U % aG897"(':<2&2B4A697*-\]\p)1!#L*-/;=)1/97)~:<:<2B4O!#$B!0>?:4ÇM5){;r*-)KM54Ç)1$&35)1:<:<2&45!#$&!f*-,u"%E)
N:\]$&:/97){V9A*-NO:\]$&:/97)>?:"%\$&daoÞ!#)1;$&t35\]:;=$&)1/"O:/:2&45!#$&!#6<97*-\]\p)1!#L*-/;=)19A):/:2&h
4O!#$B!!#',%,%)1\]!G, \p*->"(E/)K!#*-h%9A:2&2&)1; B:\97EØ)1,(, )197"%¯®6/: :\]"($&,%:<97":\]$&!#$B/3Ç,%\*->*-/2&$&)1:<\
\)1!#L*-!#)1!*-,/!#L)19A$&)1!a
¼)1"%\p)1/;=)1;97*-\]\p)1!#L*-/;=)1/97)G:<:<2&45!#$&!ulm:!u;=)1N)12&*-L)1;"(*{®9A'\p)1¯"(E/)G:\97EK)1,(, )197"
*-,"(E/)¨9A*-\\)1!#L*-;=)1/97)¨:/:2&45!#$&G! EE*-lm)1NO)1\%6$&!#"%)1:;¥*-,u"(:<5$&3Ç/*-2&$&)1:<\+!#L)19A$B)1!
$&/"(*~:<979A*-'"5, \p*->"(E/)NO)1\]4M5)135$&/$&/356_$&"O!#"%:\]"(!©,%\*->¸, :2&!#)I2&$B/)1:\]$&"(4:<!#!#'>L"%$B*-/!
:<;t"%\$&)1!C"%*\p)1>?*-NO)I"(E/)I)1,(, )197"-*-,O/*-/2B$&/)1:\]$&"(4{MO4®;=)1"%\p)1/;=$&3O¯®61$ba )Oao\)1>*-N$&3~"%E)
B"(\)1;r¯a/ "=$&!I;=*-)N$B:;r$BN$&;=$&3"%E)0Ö\]!#"r:d$&!"%*m!#)135>)1/"(!#6O:/;Ø!#'M5!#)1ñ5')1/"=97)1/h
"%)1\$&/3"(E/)!#)197*-/;K:d$B!r*-~H)1\_
* # j<.Z %# j.Y %G# S7S& %# S7S<.U % aQ}=E/$&!rL\*-97)1!#!r$&!|*-,%"%)197\]$B"%$&97$&H)1;n
S<
$&"/$B!$B/)12&)135:/"(6<:/;;=)1L)1/;*-m:f/'>?M5)1\©*-,!#)135>?)1/"(!'!#)1;# S<TS.%#a
UWV¾ÁXR%¿À
465 765 ZuZu;XBC9W?
><~[9BCZu;Z
A}_B;
"-:LL)1:<\!|"(E/:"-"(E/)1\p)$&!'LK"(*/*-lÙ/*>)1"%E*-;m$&{'!#)161lmE/$&97E{lm*-'2&;m"(:<5)"%E)I/*-h
2&$&)1:<\$&"%4*-,u!#L)19A$&)1!+\p)1!#L*-/!#){, '/97"($&*-/!f$&/"(*?:9A97*-'/"C,%\*->"(E/){NO)1\]4?M5)135$&/$&3a
!#"%)1:;=6r>)1"%E*-;=!;=)1N)12&*-L)1;¥, *-\+"%E)m2&$&)1:<\G>?*-;=)12|:<\p)K'!#)1;=6="%E)1$&\+>?$&!#:LL2&$&97:<h
"%$B*-?M5)1$&/3®9A'\p)1;=¯OM54t!#'M5!#)1ñ5')1/"rB;=)1"(\)1;r$B/35¯B65$&"%E)M5)1!#"r97:!#)Oa=8Ù/)1)1;Ø, *-\:
$&>?L\p*-NO)1;>)1"%E*-;$B!"(E/'!*-M5N$B*-'!a
dbC! !
N ^W!d
] .C&HC&
&&&F
óô$
ÿ 1ù -.+1ü0/,
¤5\*->ò*-l¶*-6lm)lm$&2B297*-/!#$&;=)1\*-2&4w'/$&"(:\]4¥*-\p35:<$&!#>?!¨lmE/$B9AE ;=* *-", *-\>
9A2B'!#"%)1\!#6!#L\)1:;?"(E/)fL\*-35)14K'!#$&3tx :9A"($&NO)12&4K*-\uL:!#!#$&N)12B4Oz=>*-N$&3tL\*-L:35'2&)1!#6
:<;E/:N$&3¨;=)1Ö)1;r6_'9AE:<3O$B/3K;=)1>*-3O\:<LE$&9,%'/97"%$B*-/!a
~"(E/), *-2&2B*-lm$&/356_lm)lm$&2&2:;r*-L""%E)L*-L'2&:"($&*-~;r)1!#$&"(4:<!r:I,%)1:<!#$&M52&)u>)1:<!#'\p)
*-,D!#L)197$&)1!#¯L)1\, *-\]>:<9A)Oa
FI*-!#$&;=)1\]$&3"(E/)~)1/NO$&\p*-/>)1/"(6lm)~\p)1ñ5'$&\)0"%E:<"r:~;r)1Ö)1;XL\*-L*-\"%$&*-?*-,"(E/)
L*-L'2&:"%$&*-X35)1"(!f$&"%*"%E)¨!#)1;=$&>)1/"(6lmE/)1\p)~$&"C, *-!#!#$B2&$&H)1!a89A"(':<2B2&4A6/lm)¨lK$&2&2rE/$&;=)
!#)1N)1\:<21L\p*-97)1!#!#)1!|';r)1\="(E/)"%)1\
> <,%*-!#!#$&2&$&H:<"($&*-97E/:/97.) DaQ}=E)1!#):\)u:2&2L\*-97)1!#!#)1!
\)1>*-N$B/3{"%E)+*-\p35:<$&!#>?:2\p)1>?:$&/!u,%\*->"%E)+,%*-!#!#$&25\)197*-\p;r6Q/:>?)12&4|n
L\p)1;=:<"($&*-¨x \p)1>?*-NO)1!C2&$&NO$&/3¨*-\35:/$&!#>!#z
;=)197:<476_lm:!#E/h :lm:4~x ;=*-)1!C/*-"D2B)1""(E/)G\p)1>?:$&m"(*{)1"%)1\|"%E)G!#)1;r$B>?)1/"(z
)1\p*-!#$&*-6<;=$&!#!#*-2&'"($&*-x \p)1>?*-NO)1!C"(E/)G\)1>:<$B/!Clm$&"(Et"(E/)!#)1;=$&>?)1"%z
*-/h%, *-!#!#$&2&$BH<:"%$B*-x%\)1>*-N)1!C"(E/)\p)1>?:$&!M5'\$&)1;$&m"(E/)G!#)1;=$&>?)1"%z a
ÊØ)u!#'LL*-!#)"(E/)u97*->?M5$&)1;¨)1,(, )197"_*-,"%E)1!#)uL\*-97)1!#!#)1!"%*GM5)uB'L\)1;=$&97"%:M52&)1¯7)1/*-'35E
"%*~,%*-\]>¬:+!#"%*-97E/:!#"($&9NO:<\$&:"%)"(E/:"/$&!u97E/:\]:9A"()1\]$B!#"%$&9u,%*-\©:f35$&NO)1m)1N$&\p*-/>)1/"]a
ÊØ)lm$&2&2_!#'LL*-!#)"%E:<"<!#:<>L2&$&/30$&!=;r*-)M54f"%:5$&/3+:97*-/!#"(:<"x 'L{"(*+:>?)1:!#'\h
$&/3{)1\]\p*-\]zONO*-2&'>?)G*-,D"(E/)!#)1;=$&>)1/"(6<)1d<"%\:<97"%$B/3~"%E)G, *-!#!#$&2&!u*-'"*-,/$&"(6<:/;97*-'/"($&/3
$&/;=$&NO$&;=':2&!uMO)12B*-/35$&/3¨"%*~;=$&,(, )1\p)1/"5!#L)197$&)1!a
¼'){"%*"(E/){9A*->L2&)1d$&"(4?*-,C"(E/){L\p*-MO2B)1>?6D'$&;=$&>?)1!#$&*-/:2|:/:2&45!#$&!+$&!+9A*-!#$&;=h
)1\)1;"%E\*-'35E*-'"|"(E/$&!lK*-\]|a=82B"%E*-'3OE*-, "()1'\)1:2&$&!#"($&9G*-NO)1\]!#$&>L2&$&Ö97:<"($&*-/65)1h
N$B\*->?)1/"(!u35*-N)1\/)1;MO4{:m'/$&NO:\]$&:"%)35\:<;=$&)1">:<4{*-9A97'\©$&K"%E)+K:<"('\)ñ5'$&"()
, \p)1ñ5')1/"(2&4Øx 97,#a"%45L$&97:2©H<*-:<2|9A*->>?'$&"%$B)1!{*-,"%E)t>?*-'"%:$&¥NO)135)1"%:"($&*-/6|$&/"()1\h
"%$B;r:2MO$B*-"%:6NO)135)1"%:"%$B*- *- >?*-$&!#"('\p)Ç35\]:;r$B)1/"(6!#"(\]:"%$BÖ)1;*-9A)1:/$B997*->?>'/$&"($&)1!
;=)1L)1/;=$&/3K*-M5:"%E45>?)1"(\]476-)1"%9a a a z a5§=/NO$&\p*-/>)1/"(!35*-N)1\/)1;ÇM54m!#)1NO)1\]:25!#"%\p*-/352&4
9A*-\\)12B:<"()1;,%:<97"(*-\]!>?$&35E/"M5)f'"%$&2B$&H<)1;, *-\C"(E/)f:<:<2&45!#$&!:<!lm)12&2B6:<!2&*-3t:<!"%E)097*-\h
\)12B:<"($&*-{$&!u!#"%\p*-/3~)1/*-'35E©a_%m"%E:<"O97:<!#)161;=')"(*"%E)>?'"(':<297*-\]\p)12&:"%$B*-K*-,/,%:<97"(*-\]!#6
"%E)G3O\:<;=$&)1"97:mM5)+97*-/!#$B;r)1\p)1;:<!C35*-NO)1\])1;M54{:<4¨*-,D"(E/)1>6<*-\MO4{:+2&:<"()1/"*-/)16
E/$&35E2&4K97*-\]\p)12&:"%)1;t"(*~:<2&2-*-,"%E)1>wa
8!lK$&2&2OMO)+;=$&!#97'!#!#)1;Ç2&:"%)1$6"(E/)+"%45L$&97:2®!#L)19A$&)1!\p)1!#L*-/!#)+, '/97"($&*-/¯O*-:<t)1h
N$B\*->?)1/"(:23O\:<;=$&)1"$&!G:¨'/$&>*-;r:2=, '9A"($&*-Øx lK$&"%E?!#$&/352&){>?:d$&>'>?z aÞ/,%*-\h
"%':<"()12&476_$&"/$&!u)1$&"%E)1\©)1:!#4A6_/*-\!#"%\:<$&35E"%,%*-\]lm:\;"(*~ñO':/"($&,%4¨®'/$&>*-;r:2&$&"(45¯-'!#$&/3
!#*->?)>?)1:!#'$C$B9A:!#)u"%E:<"<'/$&>*-;r:2&$&"(40$B!|*-"L)1\],%)19A"]aA@'97E:>)1:<!#'\p)C$&!r/)1)1;=)1;
, *-\©:m*-L"($&>?$BH<:"%$B*-t:<2&35*-\$&"%E>q"%*~!#)1)1{, *-\©:f, )1:!#$&M52&)!#*-2&'"($&*-CaÊØ)+lK$&2&25"%\4¨"(*{;r)1h
N)12B*-L:+'/$B>?*-;=:<2B$&"%4¨>?)1:!#'\)2&:<"()1\]a
OQi&QSKÃÃNVLÁTR ¿ÀmÃ
ST
82&"%E*-'35EMO)1$B/3+*-, "()1\)1L*-\"%)1;,%\*-> 9A:!#)C!#"%';=$&)1!#67'/$B>?*-;=:<2_\p)1!#L*-/!#)1!97*-'2&;
*-/2&4XM5)KL\p)1;=$&9A"()1; , *-\G"%E)m.02B)1:<!#*-$&:<X"(45L)m*-,u9A*->>?'/$B"%$&)1!#6rlmE)1\)¨$&/;=$&NO$&;=':<2
!#L)19A$&)1!r:\)C\p)12&:"%$&NO)12&4G$&;r)1L)1;=)1/"*-,)1:97E*-"%E)1\%6A:<;K,%*-\D"%E)u9A*->L\*->$&!#)>*-;=)12
*-,rÊ E/$&"("(:<5)1\Cx SiY<ZGz # S<TDg %%6lmE$&9AE$&!9A2&*-!#)f"%*{.02B)1:<!#*-¯B!I$&;=)1:!#6"(E/:""%E)f!#L)197$&)1!$&/h
"%)1\:<97"2&*-*-!#)12B4?M5'"!#"($&2&2=E/:NO){;=$&!#"($&9A"|)19A*-2&*-35$&97:2r"(*-2&)1\:<9A)1!GlmE$&9AEØ,%*-\97)"(E/)1>ª"(*
, *-2&2&*-lq"(E/))197*-2&*-35$&97:<2/3O\:<;=$&)1"%&! # S<T.g %#arm)1N)1\"%E)12&)1!#!#65)1N)1:~!#"%\p*-/397*->?L)1"($&"%$B*-
/)1)1;Ø/*-"rM5\)1:m"(E/)'$&>?*-;=:2D\)1!#L*-!#)L:"%"()1\]©nO"(E/)"(lm*t97*->?L)1"($&"%*-\!G9A*-'2&;Ø\p)1h
!#"%\$&9A"G"(E/)1$&\~\p)1:<2B$&H<)1; /$B9AE)1!m$& *-LL*-!#$&"()Ç;=$&\)197"($&*-/!#6>?*-;=$&,%4O$B/3w"(E/'!m"(E/)!#E/:L)
:<; V*-\!#5)1lÒ*-,="(E/)\p)1!#L*-/!#)0, '/97"($&*-/65L\p)1!#)1\]NO$&/3¨$&"%!'$&>?*-;=:2&$&"(4tx :2&:/!#*-
S<ii<Cj # iHU %%z#ar@L)19A$&:2/"(45L)1!*-,97*->?L)1"($&"($&*-/62&$&5)"%E)*-/)M5)1"(lm)1)1?:~!#"(\*-3!#"()1/*-)1h
9A*-'!G97*->?L)1"($&"%*-\6:/;X:~lm)1:)1'\]45)19A*-'!*-)9A*-'2B; L)1\pE/:L!I\p)1:<2B2&4t\)1!#E:<L)0"%E)
\)1!#L*-!#), '9A"($&*-?"(*m>'2&"%$B>?*-;=:<2B$&"%4 EE/*-lm)1NO)1\%65!#'97E!#L2B$&"%"($&3*-,r:~/$&97E/)0lm*-'2&;
2&)1:<; !#*-*-)1\m*-\K2B:<"()1\¨$B!#*-2&:<"($&*-*-,+L*-L'2&:"%$B*-/!, *-2&2B*-lm)1;ìMO4 !#L)197$&:"%$&*-6IlmE$&9AE
lm*-'2&;?\p)1!#"(*-\)I"(E/)G'$&>?*-;=:2-\)1!#L*-!#)+,%'/97"%$B*-/!:<35:$&Ca
}*M5):<M52&)"(*;r*t"(E/)~35\]:;=$&)1/"r:/:2&45!#$&!#6lK){>'!#":!#!#'>?)"(E/:""(E/)1\p))1d$&!#"(!:
!#',%Ö97$&)1/"/'>?M5)1\*-,C*-NO)1\]2&:LL$&3?/$B9AE)1!#6!#'9AEØ"(E/:"©"(E/)1\p){:\p){*"(lm*;r$B,%,%)1\)1"
L*-$&/"(!©*-"(E/)3O\:<;=$&)1"E/:NO$&/3f"%E)!#:>?)N:2&')1!=*-,-:<2B2!#L)197$&)1!r\)1!#L*-!#),%'/97"%$B*-/!a
m¡&
S<g
UWV¾ÁXR%¿À
'ôõó ¢£+.3÷ø
m$&97E/)+$&!:m$&>L*-\]"(:<"%6<"%E*-'35Et9A*-"%\p*-N)1\!#$&:2Ox%8\]"(E/'\|S<i<j&E_y=)1$&M5*-2&;Sii<U&E_ÊËE/$B"%h
"%:5)1\|)1"5:2baoS<ij<T6QÊØ:/35)1\!#O4~Si<jS
# ST.Z % z 6Q9A*-9A)1L"O$&K)197*-2&*-354a1«K'"%97E/$&!#*-mx SiU<jz
;r$B!#"%$&35'$&!#E/)1!M5)1"(lm)1)1Ø"(E/){B, ';=:<>)1/"(:<2$&9AE)1¯B6:/; "%E)¨®\)1:2&$&H)1;X/$&97E/)1¯a}=E¥
) ¤"&
, '/;=:>?)1"%:25/$&97E/)f$&!"(E/)f!#'>q*-,"%E)0\p)1!#*-'\97)1!uL*-"%)1"%$B:<2&2B4m'!#)1;?M54K"(E/)+!#L)197$&)1!#6 m&
lmE/)1\p)1:<!0"%E)t\)1:2&$&H)1;/$B9AE)t$&!~"%E:<"uL*-\]"($&*-*-,"%E)t, ';r:>?)1"%:2$&97E/)t:9A"(':<2B2&4
'!#)1;?'/;=)1\C97*->?L)1"($&"($&*-:<;?L\p)1;r:"($&*-mL\p)1!#!#'\)Gx «K'"%97E/$&!#*-S<iU<Cj # jHU %FE[$&:/5:
S<ij<CY # S7SHY % z nC"(E/)¨!#L)19A$B)1!>?:4ÇM5)K)1d<9A2&';=)1; , \p*->èL:\]"(!0*-,u$&"(!,%'/;=:<>)1/"(:<2=$&9AE)
MO)197:'!#){*-,C97*->?L)1"($&"($&*-X:<;¥*-"(E/)1\M5$&*-"($&9$&"%)1\:<97"($&*-/!aI}=E/){;=$&,%,%)1\)19A)0MO)1"(lm)1)1
"%E)I"%lK*$&!©97*-/!#$&;=)1\p)1;K:G\)1!#'2B"-*-,$&"%)1\:<97"($&*-¨lK$&"%E{*-"(E/)1\r!#L)19A$&)1!|x ÊØ)12&;=*-{@2&:'h
!#*-wS<i<CY # STD % z%6©*-\*-,I;=$&!#)1ñ5'$&2B$&M5\]$&'>òM5)1"(lm)1)1¥)1N$&\p*-/>)1/"(:<2C97E/:/35):/; "%E)
!#L)19A$&)1!\p)1!#L*-/!#)0x :2&:/!#*-)1"r:2baS<ii # i<HY %%z#a}=E/)\p)1:<2B$&H<)1;?/$&97E/)*-,r:~!#L)19A$&)1!$&!
'!#':<2&2B4t9A*-!#$&;=)1\)1;"%*¨MO)f"%E:<"L:\]"/*-,r"(E/)f, ';r:>?)1"%:25/$&97E/)flmE/)1\p)0"(E/)f!#L)19A$B)1!
E/:!:¨97*->?L)1"($&"($&N):;=N:/"(:3O)fx 8'!#"($&/6Om$&97E/*-2B2&!G:\35'2&)1!ISii<CZ # SDT %%z#ar8!L)1\ph
9A)1L"()1;¥M54Ç>:<4Ç:<'"(E/*-\!#6/$&97E/)¨$&!0:KñO':2&$&"(:"%$&NO)K"()1\]>n:mE/45L)1\!#L:<97)¨;=)12&$B>?$&"()1;
MO4"%E)¨"(*-2&)1\:<9A)~$&"%)1\N:2&!+*-Ø\)1!#*-'\p9A)1!Gx%)1/NO$&\*->?)1"%:2N:\]$B:<M52&)1!#6$&,C45*-' 2&$BO)1z a
«m*-lm)1NO)1\%6O:~!#L)19A$&)1!;r*-)1!*-"|®L)1\],%*-\]>?¯O)1ñ5':<2B2&4lm)12&2D$&)1N)1\4tL*-$&/"|*-,|"(E/),%'/h
;r:>?)1"%:2$&97E/.) E$B/!#"()1:<;=6r$&"%¯®!L)1\],%*-\]>:<9A)16>)1:<!#'\p)1;=6)Oa 3|a 6=M54Ø"%E)mL*-L'2&:"%$&*-
;r)1!#$&"(4A6=NO:<\$&)1!0,%\*->êL*-$&""(*?L*-$B/"(6|'!#':2&2&4Ç$B :t>:</)1\G"%E:<"C"(E/)¨M5)1!#"CL)1\], *-\ph
>?:/97)m$&!0:97E/$&)1NO)1;!#*->?)1lKE/)1\p)K$& "%E)K®9A)1"%)1\G*-,u"%E)m/$B9AE)16r"(:L)1\]$&3Ç*-'"%lK:<\p;=!
x z#ao}=E/)Gñ5':/"($&"%:"($&N)GL)1\, *-\]>:<9A)*-,D:f!#L)197$&)1!u*-m:+x L*-!#!#$&M52&4{>?'2B"%$&;=$&>)1/!#$&*-:<2Bz
)1/NO$&\*->?)1"%:25x \p)1!#*-'\97)1z97*-/"($&''>¦x%35\]:;r$B)1/"(z 6_$&!9A:2&2&)1;"(E/)+B!#L)197$&)1!u\)1!#L*-!#)
, '/97"($&*-/¯-x%8'!#"%$&KS<ij<CY # D %E_$&9AE$&tS<ii # S<ZD %%z#a
'ô$' ¨,©ª
ÊËE/$B"%"(:<5)1\©x%S<iUY<zO*-M5!#)1\]NO)1;"(E/:"/!#L)197$&)1!u\p)1!#L*-/!#)G, '9A"($&*-tx @JC¤O!#z%6<$õa )Oa 6_"(E/)G, '9Ah
"%$&*-!;=)1!#9A\$&M5$&/3t"(E/)L)1\, *-\>?:/97)f*-,r;=$&,%,%)1\)1"/!#L)197$&)1!I;=)1L)1/;=$&3m*-?:NO:2&')0*-,
!#*->?)t)1/NO$&\p*-/>)1/"(:<2©NO:\]$&:M52&)16=:<\p)K"(45L$&9A:2&2&4ØM5)12&2Bh !#E/:L)1;=6='/$&>*-;r:2ba~}rE'!#6E)
L\*-L*-!#)1;Ç"(E/:"!#L)197$&)1!\p)1!#L*-/!#)+, '9A"($&*->?$&35E/"=M5)0:LL\p*-d$&>:<"()1;lK$&"%E:.f:<'!#h
!#$&:<¥, '/97"($&*-Cat@$&9A)16|"%E).f:<'!#!#$B:<@JC¤ !#L\p)1:;w"%E\*-'35E"(E/))197*-2&*-35$&9A:2C2&$&"()1\]:h
"%'\p)16\)135:\;=2&)1!#!GlmE)1"%E)1\G, '/;=:>?)1"%:2&6*-\G\)1:2&$&H)1; /$&97E/)1!flm)1\){97*-/97)1\]/)1;aG8
9A*->>?*-/6'"%)1!#"()1; :<!#!#'>L"%$&*-X*-,©.f:<'!#!#$B:<Ç@JC¤lm:!+9A*->>?*-/2B4ÇE/)12&; x 8'!#"($&
SU
&!¦`§
N H@m&
C S<Y
¾JI2K L ÁÂNM:q&Q{À2R ¾JIKÂtKÀ@U«MCÂrÃ
L¿ÀmÃÂ
S<iU# YH% 6ISi<jC# jH%FEf8'!#"($& ª@>?$B"%ESi<iC# SgD%%z#a }=E)Ø!#4O>>?)1"(\]$&97$&"(4 *-,0"(E/)ØÊËE$&"(h
"%:5)1\o¯B!>?*-;=)12Olm:!E/)1:NO$&2&4m97\]$&"($&97$&H)1;M54m8'!#"($& @>$&"(Ex%S<ii# S<g% z#n:"D2&)1:!#"D,%*-\
L2&:/"(!#6"(E/)1497*-/!#$B;r)1\{:Ç!#45>?>)1"%\$&9>?*-;=)12*-,+M5*-"(E ,%'/;=:>?)1/"(:2:/; \)1:2&$&H)1;
/$&97E/)1!f'/\p)1:<2B$&!#"%$B9aFI'\\)1"©"(E/)1*-\]$B)1!f*-,CM5$&*-"($&997*->?>?'$&"($&)1!#¯|97*->?L*-!#$B"%$&*- lm)1\p)
\)1NO$&)1lm)1;KMO48'!#"($&¨@>?$B"%E¨x Si?:mSi<C # S<Hi %FE<.f\]$&>)fSij<Ci # YD %FE<.f:<'97EtìÊËE/$B"%"(:<5)1\©Sij<C # UH % z
lm)1\p)$&/97*->?L2&)1"()O
a ¬O)1)fì$&"(97E/)12&2-x%S<ii<SGz # S<gDS %/>?:;r)G'!#)G*-,35)1/)1\:<2&$BH<)1;:;r;=$&"($&NO)
>?*-;=)12&!fx .08¥!#z©"%*"()1!#"C, *-\!#45>?>)1"%\4aI.08¥!f:\)~:m*-/h%L:<\:<>)1"%\$&90)1d<"%)1!#$&*-
*-,=3O)1)1\]:2&$&H)1;?2&$B/)1:\>*-;=)12&!Ix .fy=!#z EE*-lm)1NO)1\%6-.f8!2&:97m:<:L\$&*-\]$O>?*-;=)12&6
"%E)14¨:\p)IL'\)12B4{;=:"%:h ;=\$&N)161Ö"%"($&3KL\p*-9A)1;='\p)Oa
Nm&d!$C &!¦ $ ] ¤
] ¤S!¦ k¡ 8 \)1,%*-\]>'2&:<"($&*-f*-,"%E)u9A*-"%$&''>ú9A*-9A)1L"<lm:!rL\p)1!#)1/"()1;M54f8'!#"($& @>$&"(E
x Si<izG# SgD% nQ"%E)14~*-'"%2&$B/)1;!#)1N)1\:<2E/45L*-"(E/)1!#)1!u:MO*-'"5"(E/)I@JC¤O!C:2&*-3{:G'$&;=$&>?)1h
!#$&*-/:2)1/NO$&\*->?)1"%:235\]:;=$&)1/"]aQ82&"(E/*-'35E{/*-"-!#"(:<"()1;K)1d<L2&$&97$&"%2B4A61"(E/)!#"%';=$&)1!|;r)1:2&"
lm$&"(E\)1:2&$&H)1;~/$&97E/)1G! EQ$&"lm:!=!#E/*-lm~"(E/:">?:/4f!#L)19A$&)1!=;=$&!#L2&:4+:<:!#45>?>?)1"(\]$B9A6A*-\
9A*->L2&)1d~@JC¤mx%8'!#"%$&Si<Cj # Hj %FE8'!#"%$B)1"D:2ba5S<ii<CZ # SDT %FE-8'!#"%$B/6m$B9AE*-2&!#6-¼*-E/)1\"%4
)145)1\]!#6_Si<ig # S<D % z#a
y=$&"("%2&):"("%)1"%$&*-¨lm:!©L:<$B;t"%*ñ5':2&$&"(:<"($&NO);=$&,%,%)1\)19A)1!r$&¨@JC¤5!©"%E:<"O>?:4)1>?)1\p35)
;='\]$&3"%E)"(\]:/!#$B"%$&*- , \p*->ò, ';=:<>)1/"(:<2u"(*¥\p)1:<2&$BH<)1; /$B9AE)OaX@JC¤¥9A*-\\)1!#L*-;rh
$&/3K"%*{"%E)0,%'/;=:<>)1/"(:<2-$&97E/)0$B!:2&!#*K97:2&2&)1;BLE/45!#$&*-2B*-3O$B9A:2&¯B6-lKE/)1\p)1:<!u"(E/:"D9A*-\\)1h
!#L*-/;=$&3t"%*m"(E/)f\)1:2&$&H)1;/$&97E/)$B!I:<2B!#*K97:<2&2B)1;?¯B)197*-2&*-35$&97:<2B¯õa/8 NO:\]$&)1"(4K*-,rL*-!#!#$&M52&)
\)1:2&$&H)1;@JC¤+!#E/:L)1!lm:!r;=)1!#97\]$&M5)1;~M54G')12&2&)1\ph ¼*->M5*-$&!=w§r2B2&)1/M5)1\p3fx%S<ij<gGz # S<Zg % 6
!#)1)m:2&!#*Ç"(E/)t!#)197"%$&*- *-¥§=2&2&)1M5)1\3Ç>*-;=)12&6L:35)mS</a:2&:<!#*- x%S<iij<z # iDU %9A*->h
L:<\p)1;t"(E/)"(lm*¨>*-;=)12&!u*-,/x L2B:<"%z9A*->L)1"%$&"($&*-6/:>?)12B4¨"(E/)G97*-)1N*-2&'"($&*-tx%FI*-/)12&2
S<iZ # T<Hg %%6Dk)1;=;=4ÇS<ii # <Z % z 6:/; "%E)KE$&)1\]:\97E/$B9A:2>?*-;=)12rx k)1;=;=4?Si)1/"(:<21;=:"%:*-\)1:2&$&H)1;~@JC¤5!|';=)1\>?'2&"($&!#L)197$&)1!|97*->?L)1"($&"($&*-~:<\p)Cñ5'$&"()\]:\p)
x §=2&2&)1M5)1\3+S<iUT # g<HT %%6QSi<UCg # gDg %EQ8'!#"%$&Si<C # .U %%6QSi<iZ # H % z%6QL\p)1;=$&9A"($&NO)u>?*-;=)12&!rMO:!#)1;
*-K,%'/;=:<>)1/"(:<2@JC¤5!C:<\p):2&>?*-!#">?$&!#!#$B/3{x 8'!#"($&KSi<iC # Hi %%z#ao§=d$&!#"($&/3~>*-;r)12B!:\p)
>?'"(':<2B2&4¨$B/97*->?L:"%$&M52&)16:/;$&/97*->?L2B)1"%)+x 8'!#"($&m .f:<45lm*-*-;=6S<ii<Cg # S7HS %%z#a
*-!#"<"%E)1*-\)1"($&97:<2o!#"(';=$&)1!=:<!#!#'>)u"%E)!#E:<L)u*-,<"%E)@JC¤f"(*GMO)u.f:<'!#!#$&:x%[$&:<5:<Si<SC# S7S<j%E
m)1lm>:<tSi<C# SZ<YH%FE.f$&2&2&)1\uSi<g# U<UD% 6.f:<'97EÙÊ E/$&"("(:<5)1\CSi<j# U<D% z#a\p;=$&/:"%$B*-
!#"%';=$&)1!, \p)1ñ5')1/"(2&4K;=*{"%E)0!#:>?)+x .0:'97EtS<i<C # UHg %FE.0\p)1$&35h @>$&"(EtS<i<TC# YjH%FE8'!#"%$B
S<iU # HY % 65"(E/*-'35EÇ!#)1)$B/97E/$&S<i<Cj # SZDS % Fz E«K*-lm)1N)1$65"%E)1$0$&!*-/2&42&$B"%"(2&)*-M5!#)1\]NO:<h
"%$B*-/:2/)1NO$&;=)1/97)f97*-/97)1\]$&/3t"(E/)!#E:<L)f*-,=@JC¤mx 8'!#"($&S<iU # HY %E-8'!#"($&/6-K$&9AE*-2&2&!
¬:\35'2&)1!fS<iiZ # S<HT %FE©M5'"!#)1)KÊËE/$B"%"(:<5)1\+S<iUY # S<THT % 6rSi<YZ # S<TDg %FE©ÊËE$&"("%:5)1\0:/;
m$&)1\$&/3~Si<YU # S<TDi %FE_[)1)1"OSij<C # S7S<Dg %E18'!#"($&/6_m$&97E/*-2B2&!u :<\p35'2&)1!Sii<CZ # SHT % z aQ@$&>h
$&2&:\]2&476Q)1d<L)1\]$&>)1/"(:<2Q)1N$&;=)19A)u*-,-;=$&,(, )1\p)1/"_@JC¤+, *-\]>!|$B!|:2&>?*-!#"2&:<975$&/3fx E*-lm)1N)1$6
!#)1)§=2&2B)1/M5)1\3fS<iUT # g<T % 6oSi<UCg # gHg %Eo8'!#"($& 8'!#"%$B{Si<CZ # SHZ % z aQ@5)1lm)1;{@JC¤5!lm)1\p)
$1L*-\"%)1;t!#)1NO)1\]:2"($&>?)1!ux%8'!#"%$&6<K$&9AE*-2&2&!uì:\35'2&)1!©Sii<CZ # SHT %E_8'!#"($&mSi<CZ # Hg %%z#a
}=E/)1\p)$&!¨2&$&"("%2B)?)1dL)1\$&>?)1"%:2)1N$&;=)19A), *-\~"(E/)?@JC¤!#E/:L)';=)1\{>'2&"($&h !#L)197$&)1!
9A*->L)1"%$B"%$&*-tx%§=2&2&)1/M5)1\p3~S<iU<CT # gDT %%6_S<iU<Cg # gHg %FE8'!#"($&mSi<C # .U %%6Sii<CZ # H %%z#a
v':2&$&"(:<"($&NO))1N$B\*->?)1/"(:21\)1:2&$&H)1;/$B9AE)x%v§rJCKz$&!=!#*->?)1"($&>)1!|'!#)1;{$&L2&:97)
*-,|@JC¤E-:2&"(E/*-'35E?!#'L)1\Ö9A$B:<2&2B4t!#$&>?$&2B:<$65"%E)14t!#E/*-'2&;X/*-"rM5)0>$&d)1;nOv§=JC¬>)1:<h
!#'$1!L\p*-M5:<M5$&2B$&"%4"(E/:""(E/)~!#L)197$&)1!lm$&2&2*-9797'\Ix $&?"%E)!#:<>L2&)1z 6OlmE/$B9AEØ$&!G:{ñ5':<h
"%$B"%4m\p)12&:"%)1;"%*¨L)1\],%*-\]>?:/97)16lmE)1\)1:!@JC¤m:"%"()1>?L"(!"(*m>?)1:!#'\p)f!#L)197$&)1!#¯5L)1\],%*-\h
>?:/97);=$&\)197"(2&4a
qQi&QS¥¿ UÂNsrÃ0¿ ®KÃTM®
'ô$ ¯Ñü0)?øþ.Ëü0°:¨,©ª
Sj
}rE)G!#L)19A$&)1!#¯\)1:2&$&H)1;m/$B9AE)f>*-;r)12B!:;=*-L"%)1;E)1\)I:"("%)1>L"/"(*{>*-;=)12-"%E)+!#L)197$&)1!#¯
)19A*-2&*-35$&97:2\)1!#L*-!#)I, '9A"($&*-!C:<2&*-3~"%E)I35\]:;r$B)1/"5x 97*-)1/*-972&$&)1z#ao}=E/)IM5:!#$&9u$&;=)1:$&!
"%E:<"lmE/)1 "%E)1\)¨$&!*-/2B4 )1352&$&35$&M52&)t:>?*-'/"*-,$&/"()1\h%!#L)19A$BÖ9{$B/"()1\]:9A"($&*-¥x%.02&)1:«
h ±*! "d
!#*-/$&:97*-/97)1L"f*-,+9A*->>?'$&"%476«Xa ya/.02&)1:!#*-x%S<iS<Cj # UD %%6Si<CY # UHj % z%zf6I"(E/)?\)1:2&h &
$&H<)1; /$&97E/)1!{lm$&2B2M5))1ñO':2u"%* , ';=:<>)1/"(:<2C*-)1!#6:/; $&,"(E/)1\p)$B!¨*-2&4:Ç!#$&352&)
;r*->$&/:/", :9A"(*-\"(E/:"35*-NO)1\]!+"(E/)!#'$B"%)16$&/;=$&NO$&;=':<2/!#L)19A$&)1!G\p)1!#L*-/!#),%'/97"%$&*-!
:<2&*-3K"(E/)+35\]:;r$B)1/"/*-,"(E/$B!,%:<97"%*-\lm$&2&25M5)G3O)1)1\]:2&2&4{'/$&>*-;=:<2ba§=NO)1m'/;=)1\©!#*->)
"%45L)1!*-,$&/"()1\h%!#L)19A$BÖ997*->?L)1"($&"%$B*-/6:<>)12&4A6"(E/)+9A*-)1NO*-2&'"($&*-/6:/;"(E/)+E/$&)1\:<\p9AE$&h
9A:2>?*-;=)12=x FI*-/)12&2=Si<CZ # THg % 6k)1;r;=4S<ii # <HZ %%6/!#)1)~:MO*-NO)1z 6$&"©lm:!G!#E/*-lmX6D"(E/:"
:<2&"(E/*-'35E "%E)Ç*-L"($&>?'> !#E/$&,%"%!#6"(E/)Ç)197*-2&*-35$&97:<2\)1!#L*-!#)?,%'/97"%$&*- \p)1>?:$&/!¨'/$&h
>?*-;=:<2x :2&:/!#*- Si<ij # i<DU % z#a¥¼0$&,%,%)1\)1"I, '9A"($&*-!#6'!#':2&2&4w/*-"+;=$&!#"($&/35'$&!#E$&/3
MO)1"(lm)1)1 "(E/)LE/45!#$&*-2&*-35$&97:<2:<;Ë)197*-2&*-35$&97:<2u@JC¤x%lm$&"(Ew:<w)1d<9A)1L"($&*- *-,:2&:/h
!#*-/6GS<iij # i:<"()?"(E/)Ø\p)1!#L*-/!#)Ø,%'/97"%$B*-/!#6
)Oa 3|am"(E/)t.0:'!#!#$&:, '9A"($&*-6©*-\"(E/)M5)1"%:, '9A"($&*-= ² Cj ³ aKÞ/,%*-\]"('/:"%)12B4A6©"(E/)tL'M5
h ´ ~µ c ¶FnD! ] ¤!
2&$&!#E/)1;@JC¤5!C:\)'!#':<2B2&4~;r)1!#97\]$BL"%$&NO)Ix%;r:"(:<h%*-\]$&)1"%)1;=z 6A$ba )Oa 61Ö"%!C>:<;=)"(*\p)1:<2&h%lm*-\]2B;
*-MO!#)1\N:"($&*-/6|\]:"%E)1\f"(E/: M5:!#)1;w*-¥:L\p*-L)1\+"(E/)1*-\p)1"($&9A:2>*-;=)12ba~K)1N)1\"%E)12&)1!#!#6
lm)¨E:<NO){/*-"(E/$&3Ç>?'97EØM5)1"%"()1\I"(E/:Ø"%E)1!#)¨:;=h E/*-975)1\]$&)1!G"(*-;=:<4aJC)1!#L*-/!#)¨, '9Ah
"%$&*-!f:\p)035)1/)1\:<2&2B4:!#!#'>?)1;X"(*!#E/*-lq!#$&3O2B)16>*-\)*-\2&)1!#!G;r$B!#"%$&9A"|*-L"%$B>?'>ª*-,
L)1\], *-\>?:/97)*-"%E)35\]:;r$B)1/·" EOL)1\, *-\>?:/97)!#E/*-'2&;Ø"(:L)1\*-,(,r"%*mM5*-"(E?;=$&\p)19A"($&*-!
:<lm:4X, \p*->¶"(E/)t*-L"($&>'>waK:/4Ø:!#!#'>?L"($&*-/!{lm)1\p)K>:<;=)t:MO*-'"uM5*-"(E, ';r:h
>?)1/"(:2:<; \p)1:2&$&H)1;Ç/$&97E/)1!#6:<;X:<!#!#*-97$&:"%)1;ØLE4O!#$B*-2&*-35$&9A:2=:<;X)19A*-2&*-35$&97:2D@JC¤5!
x 8'!#"($&t @>?$B"%EtSi<Ci # SDg %E[$&975)1"%"×s=:H<H:HS<ij<C # S7SH %E_8'!#"($&mSi>?'$&"%4t97*->?L*-!#$B"%$&*-lm)1\p)G\)1NO$&)1lm)1;M54m8'!#"%$Bt
@>?$&"(E?x%S<ii<z # SDg %#a/}=E)0:'"%E*-\]!I97*-/972&';=)165"%E:<":2&2/lK)1\)f$&/97*->?L2&)1"()x%)Oa 3|a/}5$&2&>:<
S<i<C # SHi %EI.f\]$&>)?Si<jCi # YH %EI.f:<'97E Ê E/$&"("%:5)1\~S<ij<C # UH %%z#aØ}rE)14L\p*-L*-!#)1;Ë:
\)1,%*-\]>?'2B:<"($&*-Ø*-,u"%E)¨97*-/"($&''>¶x%.02&)1:!#*-/$&:/zC97*-/97)1L"©:/; *-'"%2&$B/)1;!#*->)KE/45h
L*-"%E)1!#)1!C:<M5*-'"O"%E)I!#E/:L)I*-,O"%E)@JC¤-a )152&:/;tSi?>?)1"%)1;"(E/):<"('\)
*-,)1N$&\p*-/>)1/"(:<235\]:;=$&)1/"(!#61@JC¤!#E:<L)1!#61:/;m:/;¨@JC¤>?*-;=)12&!ao%¨"(E/), *-2&2&*-lK$&/3
lm)GL\)1!#)1":fMO\$&)1,/*-NO)1\]NO$&)1l*-,/"%E)+>*-;=)12&!uL'MO2B$&!#E/)1;!#*~, :\ a
765 z65 4 ¸¹?
º_T<H?
>B;[Z
»
}rE$&!$&!:{972&:!#!#$&97:<2O;=)1!#9A\$&L"%$BN)f>?*-;=)12!#$B/97)ÊËE$&"%"(:O)1\Q¯B!I35\]:;=$&)1/"!#"(';=$&)1!Ix%ÊËE/$B"%h
"%:5)1\DS<iUY # S<TDT %FEQ@lm:0Sij<CZ # S<g %EA.0:'9AEwÊ E/$&"("(:<5)1\DSi<jC # UH %E7ÊËE$&"%"(:O)1\/S<ij<C # STD%E
8'!#"%$&Si<Z # Hg %E-"()1\Cs=\]::<¨ y=*-*->?:S<iY # S<Dj %%z#aO%"L\*-NO$&;=)1!:0!#4O>>?)1"(\]$&976-M5)12&2&h
!#E/:L)1;@JC¤A6<;=)1Ö)1;:!n
±*"!!_
¼2½«¼¾¡¿ÀXÁÃÂÄ·ÅWjÉ ÂÆ¡Ç`È
È
x%Da Sz
lmE/)1\p) ¼ $&!C"(E/)!#L)197$&)1!#¯<L)1\], *-\>?:/97)x%L*-L'2&:<"($&*-m;=)1!#$&"%45z%6 $&!C"(E/))1N$&\p*-/>)1/h
"%:2/NO:<\$&:MO2B)fx%L*-!#$&"%$B*-*-"%E)35\]:;=$&)1/"(z 6 $&!I"(E/)L*-!#$B"%$&*-*-,=Å "%E)*-L"%$B>?'>?6Ém$&!I:
"%*-2&)1\:<9A)GL:\]:>?)1"()1\%61:/; ¼¾ $B!"(E/)G>:<d<$&Æ>?'>¬L)1\, *-\>?:/97):<97E/$&)1NO)1;a
L¿ÀmÃÂ
S<
Gaussian model tmax= 0.10
1000
1000
800
800
600
600
400
400
200
200
0
0
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
0.8
1
1000
1000
800
800
600
600
400
400
200
200
0
0
0
0.2
v ´5= w &w
0.4
0.6
0.8
1
0
0.2
0.4
0.6
§rd<:<>L2&)1!©*-,O9A*-)1*-9A2B$&/)1!C35)1/)1\:<"()1;mM54"(E/)I.f:<'!#!#$&:K35)1)1\]:"%*-\]aQ}=E/)
L:\]:>?)1"()1\"(*"%E)I>?*-;=)12&6Ê`ËJÌÍlK:<!|!#)1"O"(*0x%, \p*->ð'LL)1\r2B)1, "-"(*M5*-"%"(*->\$&35E/"(z#n
Z/a S<6_Z/a <61Z/a U<61:/;Da Z/a
82&"(E/*-'35E"(E/)0.0:'!#!#$&:<>*-;r)12M5)19A:>?)fN)1\4mL*-L'2&:\%6*m"(E/)1*-\p)1"%$&97:2O>*-;=)12/E/:!
M5)1)1¥L'M52&$&!#E)1; 45)1"(6©lmE/$B9AElK*-'2&; L\p*-;='9A)t.f:<'!#!#$B:<,%'/97"%$B*-:<!~LE4O!#$B*-2&*-35$&h
9A:25@JC¤-a7 /!#"()1:;r6<LE/45!#$&*-2&*-35$&97:2/*-M5!#)1\]NO:<"($&*-!35$&NO)0!#*->?)uPR'!#"($&Ö9A:"($&*-,%*-\C)1dL)197"%h
$&/3?!#O)1lK)1;@JC¤Çx%8'!#"%$&6=S<ii<CZ # D %Er8'!#"%$&X)1"C:2ba+Sii<Cg # SD %FE|$B/97E/$& S<ii # S<ZD %%z#a
«m*-lm)1NO)1\%6=:!L*-$&"%)1;w*-'"uM54Ø8'!#"%$B¥)1"C:2bax Si<ig<z # SD %%6r"()1!#"($&/3X*-,"%E)m.0:'!#!#$&:
@JC¤Ç!#E:<L)¨E/45L*-"%E)1!#$&!E/:!0M5)1)1Xñ5'$&"()m'/!#:"%$B!#, :9A"(*-\]4Çx%8'!#"%$B Si<CU # HY %%6=S<i<Cj # Dj %E
8'!#"%$B¨ @>?$&"(E{S<i<Ci # SHg %%z#aQs=\*-lK/¯B!x Si<g<z # DU %OL\*-L*-!#)1;K"%E)1*-\)1"($&97:<2#PR'!#"($&Ö9A:"($&*-
*-,.f:<'!#!#$&:?@JC¤!#)1)1>!"%*M5)M5:<!#)1;Ø*-Ç,%:<2B!#):<:<2B*-3O4lm$B"%EÇ!#"(:"%$&!#"($&97:<2/!#:<>L2&$&/3
"%E)1*-\]4{L2&'!C:K$&N:2&$&;:!#!#'>?L"($&*-t"%E:<"O"(E/))1/NO$&\p*-/>)1/"(:<2-35\]:;=$&)1/"(!C:\)I)19A)1!#h
!#:<\$&2&4{9A*-"%$B/'*-'!$&mx 35)1*-35\]:LE/$B9A:2&z/!#L:97)x 8'!#"($&mSi<j # Hj % z a
}=E/)f9A*-)1*-9A2&$B/)035)1)1\]:"%*-
\ Î DÏox !#)1)+8LL)1/;=$&dz/'!#)1!:!#$&352&)0L:\]:>?)1h
"%)1$&6 Ê`Ë*ÌGÍA61lm$&"(E{"%E).0:'!#!#$&:~>?*-;=)12&61lmE$&9AE{$&!|"%E)I>?:d$&>'>ð"%*-2&)1\:<9A)"%E:<"-97*-'2&;
M5):9AE$&)1N)1;aA}=E)"(*-2&)1\]:/97)1!E:<NO):I'$&, *-\>;=$&!#"(\]$BMO'"($&*-{lm$&"(E¨"(E/)2&$&>$&"%!Z<&6 Ê`ËJÌÍa
765 z65 7 Ð=»~»HZ
>Ñ_Z
9HÒÓÔº_A<~>«B;[Z
»
')12&2&)1\ph ¼0*->?M5*-$&!u §=2&2&)1/M5)1\p3¨x%S<ijg<z# SZ<g%DL\p)1!#)1/"()1;:+35\]:LE/$&97:2->?*-;=)12&6lmE/)1\p)
9A*->L)1"%$B"%$&*- ;=$&!#L2&:9A)1!+"(E/){!#L)19A$&)1!#¯=)197*-2&*-35$&97:<2=*-L"($&>?:t,%\*->"(E/)1$&\GLE4O!#$B*-2&*-35$&9A:2
*-L"%$B>?:/a1}=E)I>?*-;=)12lm:<!)1d"()1/;=)1;mM548'!#"($&¨x%S<ijY<:zG# D%1E E)I:!#!#'>?)1!©:ñ5':;r\:<"($&9
LE/45!#$&*-2&*-35$&97:2$1!#L*-!#)97'\]NO),%*-\=)1:<97E~!#L)19A$&)1!#6Q:<;m>?*-;=)12&!©97*->?L)1"($&"($&*-{MO4:!#)1h
\]$&)1!u*-,D2B$&/)1:\©$&"%)1\:<97"%$B*-m9A*-)1,(Ö97$&)1/"(!uMO)1"(lm)1)1m:2&2!#L)197$&)1!a_}*-"(:<2-!#"(:<;=$&/3{9A\p*-L$&!
;=)1"%)1\>?$&)1;?M54m:L*-!#$&"($&*-*-"%E)0)1/NO$&\p*-/>)1/"(:<2O35\]:;r$B)1/"]a-}=E)0\p)12&:<"($&*-!#E/$&LMO)1h
"%lK)1)1K:+"%*-"(:<2!#"%:/;=$&3{97\p*-Lt:<;t:<¨)1/NO$&\*->?)1"%:2-, :9A"(*-\r$&!C:<!#!#'>)1;L:<\:<M5*-2&$&9a
Si
}rE)97:<\\]45$&39A:L:9A$&"(40$B!"(E/)1~L:<\"%$B"%$&*-)1;m:>?*-/35!#"-"(E/)!#L)19A$&)1!|L\*-L*-\"%$B*-/:2&2&4"(*
"%E)1$&\L)1\],%*-\]>?:/97):, "()1\97*-/!#$&;=)1\]$B/3?"(E/)1$B\ILE/45!#$&*-2&*-35$&97:2r\p)1!#L*-/!#)~>*-;r$BÖ)1;¥M54
9A*->L)1"%$&"($&*-tlm$B"%Et*-"(E/)1\©!#L)197$&)1!a
8'!#"%$& x Sij<Y:<6 M5Gz # %# T %u9A\p)1:"%)1; :<X®)19A*-2&*-35$&97:2\p)1!#L*-/!#)K>*-;=)12&¯B6=:!0:t!#$&>L2&)
>?:"%E)1>?:"%$&97:21, *-\]>'2&:"%$&*-0*-,§=2&2&)1/M5)1\p35¯B!97*-/97)1L"%!aQFI*->L:<\p)C:2&!#*G¤O\p)1!#97*+x%S<i<z # giD%#a
}rE)GLE/45!#$&*-2&*-35$&97:<25@JC¤{*-,D)1:9AE¨!#L)19A$B)1!$B!:!#!#'>?)1;"(*{"(:O)"(E/)G,%*-\]>
kNnDbÕ¶
x%Da z
¼C× Ö ½ÙØrÚ × ¾ Â Ú ×ÜÛ _Å Ý Ú × Þ Å
È
lmE/)1\p) ¼p× Ö $B!"(E/)+L)1\], *-\>?:/97)Gx 8'!#"($&/6<S<ij<Y:@# % 6<9A:2&2&!$&"D®LE/45!#$&*-2&*-35$&97:<245$&)12&;=¯Bz*-,
!#L)19A$&)1!Jß:"/:0L*-$B/"*-t:m)1/NO$&\p*-/>?)1"%:2535\]:;r$B)1/"(6<lmE)1\)G"(E/)+35\]:;r$B)1/"(h , *-\>?$&3
N:\]$&:M52&)m:9AE$&)1NO)1!0"(E/)tNO:<2&')K*-, 6:/; Ú × ¾ 6 Ú ×bÛ 6|:<; Ú × :<\p)K"(E/)t>*-;=)12L:\]:>?)1h
"%)1\!a¨}=E/)t\p)1!#L*-/!#)m,%'/97"%$&*-¥$&!Å :<!#45>>?)1"(\]$&9{x !#5)1lm)1;=z È 6r\]:"(E/)1\+"%E:< !#4O>>?)1"(\]$&976
9A*-!#$&;=)1\)1; $&X"%E)¨*-\$&35$&/:2|35\:<LE$&9A:2>?*-;=)12r*-,C§=2&2&)1/M5)1\p3x%')12&2&)1\ph ¼0*->?M5*-$&!+
§r2B2&)1/M5)1\p3O6S<ij<gC# SZgD% z aOFI*->L)1"%$B"%$&*-$&!\p)1L\p)1!#)1/"()1;M54m:!#)1\$&)1!*-,=2&$&)1:<\u$&"%)1\:<97h
"%$&*-t97*-)1,(Ö9A$&)1"%!Jà ×iá M5)1"(lm)1)1K:2&2-!#L)197$&)1!C$&/NO*-2&NO)1;n
x%Da Tz
¼C× Ö ½ÙØrÚ × ¾ Â Ú ×bÛ Å_Ý Ú × Þ ÅWÂâ à ×iá[æ ¼ ×
È ×äå ã á
897*-/!#"(\]:$&/"C"(*"%E)K>?*-;=)12=$&!f"%E)¨:!#!#'>?L"($&*-X"%E:<""%E)¨"(*-"%:2rL)1\], *-\>?:/97)~*-,C:<2&2
!#L)19A$&)1!$B!:<2&!#*t;=)1"()1\]>$&/)1;ØM54t"(E/)L*-!#$&"($&*-Ç*-:<)1/NO$&\*->?)1"%:2/35\]:;=$&)1/"(65:<;
"%E:<"r"%E$&!"(*-"%:2/L)1\, *-\]>:<9A)0$&!IL:\]"($&"%$B*-/)1;Ø:>?*-/35!#"|"%E)L:<\"%$B9A$&L:"($&/3t!#L)197$&)1!I$&
L\*-L*-\"%$&*-X"(*"(E/)1$B\IL)1\],%*-\]>?:/97)~9A*->L*-!#)1;¥*-,CLE4O!#$B*-2&*-35$&9A:2r@JC¤?>*-;r$BÖ)1;¥M54
9A*->L)1"%$&"($&*-t,%\*->¬*-"(E/)1\!#L)19A$&)1!n
ç ¼ ½èÚGé Ú ê ØPÚGë
â ×äå ã á × ÅtÂ Å È
x%Da gz
lmE/)1\p)¨Ø$B!0"(E/){"%*-"(:<2='>?M5)1\G*-,C!#L)19A$&)1!+$&N*-2&NO)1;=6 ÚGé 6 Úê 6D:/; ÚGë :\p)>?*-;=)12|L:h
\]:>?)1"()1\]!a+}=E$&!97*-/!#"(\]:$&/"C:!#!#'>?)1!"(E/:"C"(E/)K\p)12&:"%$B*- M5)1"(lm)1)1X:<X)1N$&\p*-/>)1/h
"%:2, :9A"(*-$6O:/;XL)1\, *-\]>:<9A)0x :!!#"%:/;=$&397\*-Lzr$&!Gñ5':<;=\:<"($&9Gx 8'!#"($&ÇSi<jY:t# % z a
8'!#"%$&Ëx Si<jY<:0
z # %+!#E/*-lm!"(E/:"fM54 !#'$&"(:<M52&)Ø97E/*-$B9A)Ø*-, Ú :<Ù
; àKL:\]:>?)1"()1\]!K"%E)
, '2&2|\]:/35)K*-,u§=2&2&)1MO)1\p35¯B!f$1!#L*-!#)K97:<"()135*-\]$&)1!+9A:XM5)K:9AE$&)1N)1;aG}rE)1\)¨$&!0!#*->)
)1dL)1\]$B>?)1/"(:2r)1NO$&;=)1/97){!#'LL*-\]"($&/3Ø§=2&2&)1M5)1\35¯B!+97:<"()135*-\]$&)1!+x §=2&2&)1M5)1\3S<iU<Cg # gDg %FE
')12&2&)1\ph ¼*->M5*-$&!u @$&>?!uSi<YCY # SZ<HU %FE_')12&2&)1\ph ¼*->M5*-$&!Cì§r2B2&)1/M5)1\p3{Sij<Cg # SZ<g % z a
765 z65 z ì0Z
A.?@B;[Z
»
8!L*-$&"%)1;?*-'"DM54K.0\p)1$&35h @>?$&"(Etx Si<Tz=# Y<j% 6<"%E)1\)G$&!/*{"%E)1*-\)1"($&97:<25\p)1:<!#*-K"%*{)1dh
L)19A""%E)f@JC¤5!u"(*¨M5)G!#45>?>?)1"(\]$B9a_[E/45!#$&*-2&*-35$&97:<2O@JC¤5!:<\p)35)1/)1\]:2&2&4{x L\p)1NO:<$&2B$&/352&45z
!#O)1lK)1;Çx 8'!#"($&tSi<Z # Hg %E8'!#"%$&6m$&97E/*-2B2&!×:\35'2&)1!uSi<iZ # S<DT % z#a8'!#"($&tx Sij<Yz
# & %/!#'3535)1!#"%)1;"%Eî) íDh%, '9A"($&*-
x%Da Uz
¼Õ½èï æ FÄ ÅWÂðTÇñ æ Ä Ú ÂfÅÇ$ò
*-$6
óNFc &
ôõö Ä ¼ Ç ½ ôõö Ä ï Ç¡Ýø÷ ôõö ÄùÅtÂðXÇ¡Ýú ôõ&ö Ä Ú ÂfÅÇ
x%Da Yz
lmE/)1\p) ¼ $&!©"(E/)L*-L'2&:<"($&*-{;=)1/!#$&"(4A6 ï $&!:97*-/!#"(:<"%6 $&!©"(E/)2&*-lm)1\(61:<; Ú $B!©"%E)'Lh
L)1\2&$B>?$&"r*-,|"(*-2&)1\:<9A)f"%*t"(E/))1N$B\*->?)1/"(:2/NO:<\$&:<M5ð 2&)16 65:/; )1/;fí:$f!#E/:L)
Å ÷
a "!_ &
L¿ÀmÃÂ
<Z
$&Co')19A$B/3?L:\]:>?)1"()1\]!#65"(*9A*-N)1$&)1/"(2&4>?*-;=)12:¨@JC¤ao%"E/:!M5)1)1?!#E*-lmØ"%E:<"
lm$&"(E/$&~"(E/)2&$&>?$B"%! :/; Ú 6olmE/)1\p)u"%E[
) í/h ,%'/97"%$B*-{$B!|;=)1Ö/)1;=6o$B"9A:;=$&!#L2&:40NO:<\$&*-'!
!#E/:L)1!,%\*-> M5)12&2&h%ð !#E/:L)1;r6"%*¨)1d"(\)1>)12&4m!#5)1lm)1;=6:/;Ç)1NO)1Þh !#E/:L)1;?x%8'!#"%$B)1"
:<2õa-Sii<Cg # SH %Eyr*-)1"(!#97Et)1":<2baSi<jCT # Hi %E<8'!#"%$&Si<jY2
: # & %FE$&9AE$&S<iÕ
j # SZ.S % z#a82&h
"%E*-'35E"(E/r
) í/h , '9A"($&*->?$B3OE"=MO)+:97*-/NO)1/$&)1"lm:4K"(*K;=)1!#9A\$&M5)f;=$&,(, )1\p)1/"O!#E/:L)1!
*-M5!#)1\]NO)1;?$&t\p)1:<2B$&H<)1;@JC¤5!#6$&"/E/:!"(*¨M5)+!#"%\p)1!#!#)1;?E)1\)+"%E:<"/$&"$&!/*-";=)1\]$&NO)1;?,%\*->
:< '/;=)1\2&45$&/3w"(E/)1*-\p)1"%$B9A:2>*-;=)12&6"(E/'!tM5)1$&3?PR'!#"f:/*-"(E/)1\{:;rh%E/*-975)1\]4$& "(E/)
!#'$&"()Oa
Beta model alphamax= 0.50 gammamax= 0.50
100
100
90
80
80
70
60
60
50
40
40
30
20
20
10
0
0
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
0.8
1
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
-10
v ´5= w w
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
FI*-)1/*-972&$&)1!35)1/)1\:<"()1;¨M54"(E/)M5)1"%:>?*-;=)12:<";=$&,(, )1\p)1/"!#)1"("%$&35!*-,-"(E/)
"(lm*¨>?*-;=)125L:<\:<>)1"%)1\!a ËJÌÍ$&/97\)1:!#)1!ulmE/$B2&) Ë*ÌGÍG$&!9A*-!#"%:/"]a¤5\*->q"(*-L
2B)1, "5"%*M5*-"("%*->\]$&35E""(E/)I!#5÷ )1lm)1!#!u$&/97\)1:!#)1!nAx%:<z ú ËJÌÍDxtZ/a UZ&Eox M5z Ë*ÌGÍDxtSDa Z&E
÷
÷
x%9Az Ë*ÌGÍDxDa &Z Ex%;=z Ë*ÌGÍHxU/a Z/a
÷
÷
8'!#"%$BÇ)1"|:2ba©x Sii<gcz # S. %©\)1NO$&)1lm)1;Ø"(E/)~$&>L*-\]"(:<9A)*-,"%E)@JC¤5¯B!+!#E/:L)16:/;X)1dh
:<>$&/)1;K!#*->?)$&>L2&$&97:<"($&*-/!, *-\rN)135)1"(:<"($&*-~"%E)1*-\]4761*-\;=$&:<"($&*-{>?)1"(E/*-;=!#6_:<;m!#$&>h
'2&:"%$&*-!0*-,u972&$&>?:"($&99AE:<35)¨$&>L:<97"C*-XN)135)1"(:<"($&*-©aG}=E/)14?'!#)1;¥"(E/W
) í/h%, '/97"($&*-/!
x 8'!#"($& S<ijY # H %E$B/97E/$& S<ii # S<ZD %%6Si<Cj # SZ<S % zG"%*¥>?*-;=)12!#5)1lm)1;ËñO':2&$&"(:"%$&NO)
)1/NO$&\p*-/>?)1"%:2O\)1:2&$&H)1;$&97E/)0\p)1!#L*-/!#)1!*-u, kN" d&"!©"(*K>)1:<://':25"%)1>L)1\h
:<"('\p)Oa8 !#L)197'2&:"%$&*-)1d$&!#"(!Ix%8'!#"%$&Si<iZ6z # g %="%E:<"="(E/)@JC¤5¯®!I!#5)1l¬;=$&\)197"($&*-;r)1h
L)1/;=!C*-K:+L*-!#$&"($&*-m*-,"%E)!#L)19A$&)1!#¯<*-L"%$B>?'>¬*-m"(E/)35\:<;=$&)1" ao}=E/)2&*-35)1\"(:<$&2*-,
"%E)@JC¤!#E/*-'2B; M5)*-\$&)1/"()1;Ø"%*-lK:<\p;=!I"%E)97)1/"()1\*-,|"%E)35\]:;r$B)1/"]ar}=E/$&!E45L*-"%E)1h
!#$&!lm:!I"()1!#"%)1;ÇM548'!#"($&/65m$&97E/*-2B2&!:\35'2&)1!x Si<iZûz # ST % 6-8'!#"($&/.f:<45lm*-*-;
x Si<ig6z # S7&S %%65:<;Ø8'!#"%$&)1"|:2ba=x Si<ig<6z # S<. %|'!#$&/3"(E/).f)1/)1\]:2&$&H)1;Çy=$&)1:<\*-;=)12&!
x .fyr¥z-MO:!#)1;m*-{L*-2&45/*->$&:<2, '/97"($&*-Cao$&9AE$&/x%S<i0
i # SZ<. %%6oSi<0
j # SZ.S % z5'!#)1;m"(E/)
í/h , '9A"($&*-!¨"(*X"%)1!#""%E)L)1\, *-\>?:/97)t*-,I*-\;=$&:<"($&*->)1"%E*-;=G! E:!#$&>?$&2B:<\35*-:2C$&!
9AE:<2B2&)1/35)1;M54¨"(E/$&!!#"(';r4a
}=E/)97*-)1/*-972&$&)35)1/)1\]:"(*-r
\ Î DÏ_x%!#)1)08LL)1;r$Bdz='!#)1!I"(lm*tL:<\:<>)1"%)1\!#6
Ë*ÌGÍ :<; Ë*ÌGÍ lm$&"(Et"%E)MO)1"(:+>? *-;=)12& 6lmE/$&97Em:\)"%E)+'LL)1\|2&$&>$&"%!u*-,D"(E/)G'$&, *-\>
÷
ú
S
;r$B!#"%\$&M5'"%$&*-!*-,
÷ :<; ú L:<\:<>)1"%)1\!#61\)1!#L)197"($&N)12B4a
765 z65 {£<~>[üT}[<~>B;[Z
»rý~þt8:{|ÿpÔ Y $&/97E/$Bx%S<i<jzû# S<ZS.=% L\*-L*-!#)1;Ç:/*-"(E/)1\u>*-;r)12OM5:<!#)1;?*-Ãí/h%, '/97"($&*-/!a/}=E/)f!#$&>?h
L2&)/í h , '9A"($&*-mlK:<!C35)1/)1\:<2B$&H<)1;K, *-\'!#)$BK!#$&>'2&:<"($&3¨@JC¤5!a1}=E/)IL)1\, *-\]>:<9A)$&!
;r)1Ö)1;:!
ÍCË ÍCË Ú
¼2½ ñ ÊÂ [ ß"! Ý ò #%$ Â Ú'& Å & $ Ý Ä Â Ú Ç x%Da jz
lmE/)1\p) ¼ $&!~"%E)L)1\], *-\>?:/97)16 ¼¾ $B!{"(E/)>:<d<$&>?'>ÕL)1\, *-\>?:/97)t:<97E/$&)1NO)1;=6 $&!)(« m_ &
"%E))1/NO$&\p*-/>?)1"%:2/NO:\]$&:M52&)fx%L*-!#$&"($&*-?*-"%E)35\]:;=$&)1/"(z 6 $ $&!I"(E/)0L*-!#$&"%$B*-?*-,rÅ "%E)
*-L"%$&>'>?6*0
$&!+"%E)~\]:/35)16/:/; :<; :<\p)"(E/){!#E/:L){L:\]:>?)1"()1\]!a©}=E/) Ú :<;,+
L:<\:<>)1"%)1\!+lK)1\)~$&"%\p*-;='9A)1; *-÷ /2&4?"%*ú !#$&>?L2B$&, 4Ç"(E/){, *-\>?'2&:/nr"(E/)14?;r)1L)1; *-
÷
:<; :<!u, *-2B2&*-lm!n
ú
x%Da z
Ú*½ ÷
÷,Ýú
+ ½Ú ñ Ä Â Ú Ç ò
x%Da iz
}rE)!#E/:L)L:<\:<>)1"%)1\! :<; E:<NO)"%E), *-2B2&*-lm$&3?>?)1:/$B/3|arÊ E/)1 ½ 65"%E)
÷ $&"(E;=)1ú 9A\p)1:<!#$B/3+N:2&')1!=*-, :<; "%E)\p)1!#L*-/!#÷ )M5)19Aú *->)1!
, '/97"($&*-~$&!|!#45>>?)1"(\]$&9aoÊ¥
>?*-\p)L2B:<"(45O'\"%$B9A6A$ba )Oa 67E/:!=:o :"%"()1/)1;{"(*-LaQ·|:2&')1!=M5÷ )12&*-l SDú a Z35$&N)u\p)1!#L*-/!#)1!=lm$&"(E/h
*-'"D$&Co )197"($&*-L*-$&/"(!#6 lmE/)1\p)1:<!uNO:<2B')1!35\p)1:<"()1\r"%E:<mS/a Zf35$&NO)+"%:L)1\]$&3~"%:$&2&!a_ÊËE/)1
6O"(E/), '9A"($&*-Ç$B!ñO'$B"%)~!#$&>$&2&:\"(*t"%E){.f:<'!#!#$B:<, '/97"($&*-CDE E*-lm)1NO)1\%65$&"
½
E/÷ :!2&)1ú.!#!-0)1d/ "()1/;=)1;Ø"(:<$&2B!arÊËE)1
65"%E), '9A"($&*-Ç$B!!#O)1lK)1;Ø"%*t"(E/)2&)1,%"%65$ba )Oa 6-$&"
E/:!I$&"(!2&)1!#!!#"%)1)1Llm$&/3t*-"(E/)02B)1÷
, "·-E1"%Eú )0*-LL*-!#$&"()$&!"%\p')0lmE)1
a5}rE)02&$B>?$&"(!
*-,D!#L)19A$B)1!C*-9A97'\]\p)1/97)I:2&*-/3~"(E/)G35\]:;r$B)1/"5:<\p) $ Ú :/; $ ÷.2ú Ú a1¥$&/97E/$&
, '\]"(E/)1\35)1/)1\]:2&$&H)1!I"(E/)>*-;r)12/, *-\>'2&"($&L2&)35\]:;=Â $&)1/"(!GE/E*-lmÝ )1N)1$Ä 6O"%Â E$&!Ç $&!GM5)14O*-;
"%E)+!#97*-L)G*-,D"(E/)GL$1!#)1"!#"(';=4a
$&/97E/$Bm>?*-;=)12:2&2&*-lm!C,%*-\$&"%)1\ph !#L)197$&Ö9u$&"%)1\:<97"%$B*-Ca1 "O$&>?L2&)1>)1/"(!u"%E)1!#)$&/h
"%)1\:<97"%$B*-/!I$&:!#$&>$&2&:\ulm:<4K8'!#"%$&x Sij<Y:<=z # %;=*-)1!Ix !#)1)+§=2&2&)1MO)1\p3K>*-;=)12&z#a}=E)
$&>?L2&)1>)1/"(:<"($&*-$&!IM5:<!#)1;?*-::<!#!#'>L"%$&*-"%E:<""(E/)09AE:<3O)f$&:<M5'/;=:/97)0*-,=:
!#L)19A$&)1!|;=')"(*0"(E/)$&C o')19A)*-,O:/*-"(E/)1\=*-)1!#6o$&!L\p*-L*-\]"($&*-:<2"%*f"%E)L)1\, *-\]>:<9A)
*-,|"(E/*-!#)f!#L)19A$&)1!aOE/)0,%'\]"(E/)1\u:!#!#'>?)1!"(E/:""(E/)L\p*-L*-\]"($&*-/:2&$&"(4m97*-/!#"(:<"%6-"()1\]>)1;
:f®2&$&/)1:\$B/"()1\]:9A"($&*-m97*-)1,%Ö97$&)1"%¯®61;r*-)1!C*-"/NO:<\4~lm$&"/2B*-9A:"%$B*-K*-m)197*-2&*-35$&97:<2-35\]:;=$&h
)1/"]a_}=E/)G$&"%)1\:<97"($&*-m$&p o')1/97)1;L)1\, *-\]>:<9A)*-,/:f!#L)197$&)1!C$&!"%E)1Cn
x /a S<Zz
¼4×3 ½«¼ × Âøâ à × á[æ ¼ á
áHå ã ×
lmE/)1\p) ¼ × :/; ¼ á :<\p)u"%E):M5'/;=:<9A)1!=*-,!#L)197$&)1!=<ß :<;6516A\)1!#L)197"($&N)12B4fx%!#L)19A$&Ö)1;{M54
"%E)1$&\|LE45!#$&*-2&*-35$&97:<2-@JC¤5!#z%61:<;1à ×iá $&!©"(E/)2&$&/)1:\=$&/"()1\]:97"%$&*-¨9A*-)1,(Ö97$&)1/"-)1d<L\)1!#!#$&3
"%E)!#"%\p)1/35"(E¨*-,O"%E)I)1,(, )197"-"%E:<"5!#L)197$&)1!%5IE:<!*-KL)1\],%*-\]>:<9A)*-,"(E/)I!#L)197$&)1!6ßa1}=E)
!#'>?>?:"($&*-K)1d<"%)1;r!r*-NO)1\r:2&2!#L)19A$B)1!)1d97)1L"*-,5$&"(!#)12&, 6Q:<2&"(E/*-'35E{>?:/4_à × á ¯B!|9A:~M5)
)1ñO':2"(*H)1\p*raC}=E)$&/"()1\h%!#L)19A$BÖ9f$&"%)1\:<97"($&*-Ç$&!GL*-"()1/"($&:<2B2&4?:!#45>?>?)1"(\]$B9A6!#*"(E/:"
à × á )1)1;/*-"/M5)G)1ñ5':<2-"(*2à á× a
"%E)1\C:<!#L)197"%!u*-,D¥$&/97E/$&>*-;r)12-:\p)+"(E/)G$&9A*-\L*-\]:"%$B*-*-,/3O'$B2&;=!x%ÊËE/$B"%"(:<5)1\
S<ij<Zî# STY.%oE 8'!#"($&Si<U# YH%QE $&/97E/$BS<i<jC# SZSD% z%6Q*-,:2&LE:;=$&NO)1\]!#$&"(40L:"%"()1\]!=x [)1)1"
L¿ÀmÃÂ
<
S<ij# SASgH% 61¥$&/97E/$&KS<i<iC# SZD% 6_:\p3O'2B)1!©)1":2baoSi<j# i<D% z 61!#:>?L2B$&/3{L:<"("()1\]/!Cx%!#)1)
M5)12&*-lmz 6Q:<;mlmE/:"-E/)9A:2&2&!|Bñ5':2&$&"(:<"($&NO)/*-$B!#)1¯B61:/;m®ñO':/"($&"(:<"($&NO)*-$&!#)1¯<x%$&9AE$&/6
S<ij # S<ZDS %%z#a
Þ/,%*-\]"('/:"%)12B4A6_"(E/$&!C;=)1"(:<$&2B)1;t>?*-;=)12$&!u45)1":/*-"(E/)1\|L'\)12B4;r)1!#97\]$BL"%$&NO)I*-)On1:!
$&9AE$&tE/$&>!#)12&,D!#"(:<"()1!uB$&"/>?*-;=)12&!u"%E)fL:"("%)1\/!u*-,DNO:<\$&:<"($&*-m$Bm9A*->>?'$&"%4K9A*->h
L*-!#$&"($&*- :<2&*-3¥)197*-2&*-35$&97:<2u35\]:;=$&)1/"(!#6CM5'"I;=*-)1!¨*-"IL\)1"()1/; "(* >*-;r)12u"(E/)L\*-h
9A)1!#!#)1!lmE$&9AE35$&NO)f\$&!#)f"(*K!#'97EL:<"("()1\]/!a%/;=)1)1;?"(E/)+/:"%'\p)+*-,!#'9AEL\p*-9A)1!#!#)1!$&!
!#"%$B2&2-L*-*-\]2&4¨'/;=)1!#"(*-*-;r¯x $&9AE$&mSi<Cj # SZ<S % z#a
765 z657 88:9B;[Z
»
«m'$&!#>:<6o2&,(,- ¤5\p)1!#9A*+x Si<iTzu# jg% L\p)1!#)1/"()1;¨:/*-"(E/)1\;=)1!#97\]$&L"($&NO)>*-;=)12<*-,-@JC¤|a
}=E/)1$&\>?*-;=)12$&!G*-\35:/$&H)1;ØE/$B)1\]:\97E/$&97:2&2&4565lm$&"(EØ$&/97\)1:!#$&397*->?L2B)1d$&"(4a©}=E/)ÖNO)
E/$&)1\:<\p97E/$&97:<2<2&)1NO)12&!u*-,D"%E)G>?*-;=)12->?$&35E"DM5)!#'>?>?:\]$BH<)1;:!,%*-2&2&*-lm!n

= "! 0¶?> 6¶¤`! &
2B)1N)12-S/no/*~!#$&35/$&Ö97:/"D"(\)1;NE
2B)1N)12C/n$&/97\p)1:<!#$&3Xx ;=)19A\p)1:!#$&/35z"%\p)1/;=6rlmE/)1\p)t>?:d$&>'>Õ$&!~)1ñ5':<2"%*X"(E/)
'LL)1\MO*-'<
; ;E
2B)1N)12-T/no!#:<>):<!u2&)1NO)126M5'">?:d$&>'>q$&!uMO)12B*-lú"%E)+'LL)1\|M5*-'/:
; ;E
2B)1N)12-g/no!#4O>>?)1"(\]$&976$&/97\)1:!#):/;;=)19A\p)1:<!#)MO4{"(E/)!#:>?)G\]:"%.) E
2B)1N)12-U/no!#O)1lK)1;r6_$&9A\p)1:!#):<;;=)197\)1:!#)IM54{;r$B,%,%)1\)1"-\]:"%)1!a
}=E/)14tL\p*-L*-!#)1;Ç"%E), *-2B2&*-lm$&397*-/!#$B!#"%)1"|!#)1"=*-,=2&*-35$&!#"($&9f)1ñ5':"%$B*-/!"(*mM5)0:LL2&$&)1;
"%*~L*-!#$&"($&NO)G;r:"(:flm$B"%Em:m'LL)1\|MO*-'<
; ;n
x%Da S7S<z
2¼ ½ ; Ì
Ý
x /a S<z
¼Õ½ ; Ì@BAÍ
Ý
x /a S<Tz
¼@½ ; ÌC@BAÍ ED
Ý
Ý
x /a S<gz
¼2½ ; ÌC@BAÍ D ?AÍ
Ý
Ý
x /a S<Uz
¼2½ ; Ì@BAÍ D Í
lmE)1\) ¼ $&!C"(E/)I\p)1!#L*-/!#)16 $&!C"(E/)Ý )1dL2B:<:<"(*-Ý \]4)1N$B\*->?)1/"(:2N:\]$B:<M52&)16 6 Ú 6
à6
:<;F+~:\)f"%E)L:<\:<>)1"%)1\!I"%*tÅ M5))1!#"($&>?:"()1;r65*-$6lKE/)1?>*-;=)12&$&/3563O)1)1\]:"%)1;=ð 65:/;
;Ô$&!:9A*-!#"%:/"=lmE$&9AE)1ñ5':<2B!I"%E)>?:d$B>?'>¦L)1\], *-\>?:/97)f"(E/:"=9A:M5)0:"%"(:<$B/)1;
M54¨"(E/)+!#L)19A$B)1!';=)1\©9A*-!#$&;=)1\]:"%$B*-Ca}=E/)G)1ñ5':<"($&*-!/a SAS+"%*{/a Sg+9A:mM5)G*-MO"(:$&/)1;
, \p*->Õ§=ñ|aØ/a S<UM54¥Öd<$&/3 !#*->?)?*-,"(E/)L:\]:>?)1"()1\]!n$& "%E$&!¨!#)1!#)?"(E/)>?*-;=)12u$&!
E/$&)1\:<\p97E/$&97:<2õa
}=E/):'"(E/*-\]!lm)1$+:LL:<\p)1/"(2&4K$B/!#L$&\p)1;ÇM54t"%E)02&*-35$&!#"($&9+)1ñ5':<"($&*-/6-lKE/$&97E?"(E/)14
:<LL2B4Ø$&¥:t97*-/!#$&!#"()1/"lm:4a}=E/)m;=$&,(, )1\p)1/"©2B)1N)12&!*-,"(E/)m>*-;r)12x "(E/)m:'"%E*-\f97:2&2
"%E)1>ªB>*-;=)12&!#¯Bz|:<\p):9AE$&)1N)1;Ø"(E/\p*-'35EÇ:LL2&$&97:<"($&*-?*-,|;=$&,%,%)1\)1"9A*->M5$&/:"%$B*-/!+*-,
L:<\:<>)1"%)1\!©:!,%*-2&2&*-lm!n
T
ð Z Ú Z à Z+
ð Ú Z Z
ð Ú à Z
ð Ú à Ú
ð Ú à +
ð
2B)1N)12=VL:\]:>?)1"()1\
S
T
g
U
«m*-lm)1NO)1\%6_"(E/)1\p)$&!:+>?:#PR*-\©,%:<2B2&h M5:9A~lm$&"(Em"(E/)G«m¤¨>?*-;=)12bn1"%E)+L:\]:>?)1"()1\]! 6
Ú"%)16\à]!6;=:<)1!#;G9A\+f$&M5E/$&:/N3¨)+9A/'*¨\N)1)+9A*-!#2&E/*-:35L$&97)1:62/>?*-"%)1E:$&//3t$B/>3E-*-"%\E)O)1a4m}=:E/\)+)G>?>?*-)1;=\p)1)12&254m$&"(;=!#)1)12&!#,=97lm\]$&L:"(!$&*-*-:<"25;rL)1:!#\]$B3O:>?)1)1ð ; h
lm$&"(E?:!#!#)1>?M52&:3O)+!#$&>'2&:<"($&*-$&>$&/;a%/!#"()1:<;=6-$&"lK:<!9A*-!#"%\p'9A"()1;Ø"(*mM5)0:MO2B)f"(*
Ö""(E/)~!#E/:L)L:<\:<>)1"%)1\!"%*"(E/)*-M5!#)1\]NO)1;X:<M5';r:/97)NO:<2&')1!a©Þ, *-\]"('/:"()12&4A6O$&,
"%E)¨«m¤>?*-;=)12$&!+'!#)1;Xlm$&"(EØ"%E)~9A*-)1*-9A2&$B/){3O)1)1\]:"%*-\lm$&"(EÇ'/$&,%*-\]>;=$&!#"(\]$&M5'h
"%$&*-t*-,/«m¤KL:\]:>?)1"()1\]!#61"(E/)G\p)1!#'2&"%$B/3{9A*-)1*-9A2&$B/)+$&!u'//:"('\]:2bn_"(E/)1\p)$&!u)1NO$&;=)1/"
9A2&'!#"()1\]$B/3{*-,*-L"($&>?:+:\*-';t"%E)BH)1\*-¯L*-$&/"O*-,/"(E/)3O\:<;=$&)1" ao@45>>?)1"(\]$&97:<2<@JC¤5!
"%)1; "(*E/:N)0:{L)1::<"=H)1\*-65lmE$&2&!#"|:<!#45>?>)1"%\$&97:<2*-/)1!G"%)1;X"%*tE:<NO):{B, *-*-"(¯/:"
H<)1\p*rao¼$&!#"(:<"/x ,%\*->H<)1\p*-zOL)1:<5!u:<\p)INO)1\]4~\]:\p)Oa
HOF model amax= 5.00 bmax= 5.00 cmax= 5.00 dmax= 5.00 mmax= 100.00
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
-10
0
-5
0
5
10
-40
-20
0
20
40
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
-100
-50
0
50
100
0
-100
-50
0
50
100
v %´5rp w ± w
}=E/)G*-\$&35$&/:2-«m¤K>*-;=)12ba_K*-"%$&97)G"%E)G9A2&'!#"()1\]$B/3K*-,/@JC¤5!:\p*-'/;"%E)
H)1\*L*-$&" a
}rE)1\)+:\)+"%lK*Klm:45!I*-'"*-,=E/)1\p)Oa5}=E/)fÖ\]!#"$&!"%*K"%\4m"%*¨\)1h%L:<\:<>)1"%\$&!#)"(E/)0>*-;=)12
!#*"%E:<"5"(E/)/)1l L:\]:>?)1"()1\]!rE/:NO)'/$B, *-\]>¸;=$&!#"(\]$&M5'"($&*-Kx%O!#:/)16oL)1\]!ao97*->?>a z a
}rE'!#65, *-\"%E)0!#$&>L2&)1!#"|2B)1N)12OS«m¤>?*-;=)12/lK$&"%E!#$&3O2B)L:<\:<>)1"%)1$6 6-lKE/$&97E?;=)1h
Ö/)1!:097*-/!#"(:<"D;=)1/!#$&"(4KNO:<2B')16lK)+lK$&2&25$&/"(\p*-;r'97)G:0)1l¸L:\]:>?)1"()1\(6ð $ 6!#:<476<"(E/:"
lm*-'2&;?!#:"($&!#, 4~"(E/)G)1ñ5':<"($&*-Cn
L¿ÀmÃÂ
<g
x /a S<Yz
½ ôIH Ä $ ÂfÅÇ=Â ôJH ÄFÅCÇ
ð
}=E/){*-"%E)1\+2B)1N)12&!+:$~>?*-\p){9A*->L2&$&97:<"()1;=6MO'""%E)KL\]$B/97$&L2&){lm*-'2&;M5){"%E)K!#:>?)Oa
§a 3|a 6=, *-\G2&)1NO)12gt!#*->)m*-,"(E/)KO)14ØL:\]:>?)1"()1\]!+:\){"%E)m2&*-97:<"($&*- *-,"(E/)K*-L"%$&>'>
:<;"%E)+E)1$&35E/"D:"O"%E)+*-L"($&>'>wa1}rE)G*-L"%$&>'>q$&!u2&*-97:<"()1;:<"
j Ä à ÂðXÇ
½
Ú
ÅLKNMO
}=E/)GE/)1$&35E"/:""(E/:"/L*-$&"D$&!
x /a S<jz
$
x /a S<z
Ý ¿ ÀTÁ Ì Ý D È
@*~$&"/$B!"(E/)1!#)Gñ5'*-"%$B)1/"(!"(E/:"/!#E*-'2&;?M5)G!#$&>?'2BÈ:<"()1;È $B/!#"()1:<;*-,D"(E/)G*-\]$&35$&:<2-L:\]:>?h
¼ KNMO ½
)1"%)1\!a}rE)1¥"(E/)m>*-;=)12©lm*-'2&; 45$&)12&;w*-L"($&>?:;=$&!#"(\]$&M5'"()1;w'/$&,%*-\]>2&4A6|$&/!#"()1:;w*-,
9A2B'!#"%)1\p)1;*-/)1!a
82&"(E/*-'35E "%E$&!{lm:<4 $&!~9A2B)1:<6C"%E)1\))1d$B!#"%!~:/*-"(E/)1$6CB;=$&\]"(45¯B6CM5\p'"%), *-\p9A)tlK:<4
*-'" ao%"O$B!©:<97E/$B)1N)1;¨N$&:$B/"(\*-;='97$&/3*-,O45)1"-:<*-"%E)1\|L:\]:>?)1"()1\%6A"%E)IL*-!#$&"($&*-K*-{"(E/)
35\]:;r$B)1/"(P6 <a©82&"(E/*-'35EÇ"(E/)~>)1:<$&/3*-,©"(E/)L:\]:>?)1"()1\]! "(Q
* +~$1>:<$B/!*-M5!#9A'\p)16
"%E)G>?*-;=)12-9A:K*-lðMO)'!#)1;"(*{35)1)1\]:"%)®\)1:2&$&!#"($&97¯97*-)1/*-ð 972&$&/)1!n
¼Õ½ ¿ ÀXÁ Ú Í ?R $ æ ¿ ÀTÁ à + SÍ TR
Ä Ý Ä ðîÝ Ç Ç Ä Ý Ä Â Ç Ç
Extended HOF model amax= 5.00 bmax= 5.00 cmax= 5.00 dmax= 5.00 emax= 12.00 mmax= 100.00
x /a S<iz
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
-10
0
-5
0
5
10
-40
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
-40
-20
0
20
40
0
20
40
100
0
-20
0
-100
-50
0
50
100
v ´5= w º&w }rE)B)1d<"%)1;=)1;r¯-«K¤t>?*-;=)12ba/8, "()1\C:;r;=$&3m:BL*-!#$B"%$&*-:<2/L:<\:<>)1"%)1$6
# 6<"(E/)G97*-)1/*-972&$&/)1!u2&*-*-¨*-'"/>*-$GB\p)1:2&$&!#"($&9A¯a
q Qi&QS¥¿ UÂNsrÃ0¿ ®KÃTM®
765 z65U VCWtBBCYXB;[Z
»
U
}rE$&!$&!+:m>*-;r)12r$&"%\p*-;='9A)1; $&X"%E)KL\p)1!#)1/"©!#"(';=4aI8!08'!#"($&Xx Sij<Y:<z# %%L*-$&/"(!
*-'"%6_B"(E/)1\p)$B!©/**-M5NO$&*-'!C\p)1:<!#*-~lmE4!#L)19A$&)1!\)1!#L*-!#)1!©"%*0)1/NO$&\*->?)1"%:235\]:;=$&h
)1/"(!!#E/*-'2B;Ç"%:5)G"%E)0, *-\>q*-,!#45>?>?)1"(\]$B9A:25.0:'!#!#$&:<97'\]NO)1!#¯x LaTYz#a<«m)+\p)1L*-\]"(!
"%E:<"GLE/45!#$&*-2B*-3O$B9A:2)1dL)1\$&>?)1"%!mM5\$&/3w!#*->)Ø)1N$&;=)19A), *-\{:ØB\p*-*-, h 2B$&5)1¯B6:!#45>?h
>?)1"(\]$&976L$&)197)1lm$&!#)1h%2&$&)1:<\©6'/$B>?*-;=:<2O\p)1!#L*-/!#)G, '9A"($&*-tlm$&"(E:0!#$&352&)f>:<d<$&>?'>
x 8'!#"($&mSi<jY<:6QÖ3|a1<:z # %#ao@L)197$&)1!C:\)I\p)197*-3O$&H)1;t:<!CE:<NO$&/3~97:<\p;=$&/:2NO:2&')1!C, *-\
>?$&$&>?'>6*-L"($&>?'>6r:/;¥>?:d$&>'>è"(*-2&)1\:<9A)OaG}rE$&!>*-;r)12B6:<!f, :\:<!f5*-l
/*-"O"%E*-\*-'35E/2B4;r$B!#9A'!#!#)1;t$&{"(E/)2B$&"%)1\:<"('\p)16olm:!$&!#L$&\)1;KMO4"(E/)\)1L*-\"-*-,58'!#"%$&
x Si<jY<:Gz # D % a
¤O*-\lK):\)C;=)1:2&$&30lm$&"(E~L:<2B)1*-)19A*-2&*-35456o*-")19A*-2B*-3O476o"(E/):<'"(E/*-\E:<!r*-\]$B3O$B/:2&2&4
$&/97*-\]L*-\:<"()1;w:t, )1:"%'\p){9A:2&2&)1;L\p*-NO$&!#$&*-/:2&2&4Ø"(E/)KB97*-/"(:<>$&/:"%$B*-¥$&"%)1!#$&"%45¯|$&/"(*
"%E)+>*-;=)12bn_:97"%':2&2&4~"(E/)G\)1!#'2B"*-,:0/*-H<)1\p*L\p*-MO:M5$&2&$&"(4~"%E:<":f97*-/"(:>?$&:<"($&*-tM54
:f!#L)197$&)1!©®:<2&$B)1/¯"(*"(E/)I!#:>?L2&)x%)Oa 3aQ97*->?$B/3{, \p*->:/*-"(E/)1\|2&:<45)1\r*-,!#)1;=$&>)1/"O:<;
!#:<>L2&)1;w;=')m"%*Ø;=$&!#"('\]M5:"%$B*-¥*-,"%E)t!#)1;r$B>?)1/"(6*-\+:!#L)19A$B)1!/*-"\)197*-35/$&H)1;:!
$&/97*-\]L*-\:<"()1; "(*"%E)~"%E:<:<"(*-9A*-)1*-!#$&!+, \p*->ª:¨,%*-\)1$B3O?9A*->>?'/$B"%45z#au«m*-lm)1NO)1\%6O$&"
lm:<!u2&:"()1\!#L2&$&"(h *-,(,/"(*~:0!#"(:<;=h :2&*-/)L\p*-9A)1!#!a
}rE$&!>?*-;=)12D:"("%)1>L"%!I"(*t!#$&>'2&:<"()"(E/)!#L)197$&)1!I\p)1!#L*-/!#), '9A"($&*-lm$&"(E?:{'/$&h
>?*-;=:<2/L$&)19A)1lK$&!#)2&$&)1:<\B\p*-*-,]¯O, '9A"($&*-/6O97*-/!#$&!#"($&/335)1/)1\]:2&2&4t*-,|, *-'\!#)135>?)1/"(!aÎ CÏ"
¤O\p*->2&*-l )1/; "(*E$&35EØ)1/; *-,©"%E)¨35\:<;=$&)1""(E/)14:<\p)OnDx $&z©H)1\p*-h ;=)1/!#$&"(4!#)135>?)1/"(6
x $&$&zO$&9A\p)1:<!#$B/3;=)1/!#$B"%4!#)135>?)1"%61x%$&$&$&z5;=)197\)1:!#$&/30!#)13O>)1/"561:/;=6ox $BNz5H)1\*-h%;r)1!#$&"(4
!#)13O>)1/":35:<$&©a}lm*{2&$&/)1:\C!#)135>?)1"%!\)1L\p)1!#)1/""%E)f!#L)197$&)1!/$&97E/)flm$&;="%E6:2&2&*-lmh
$&/3t,%*-\"(E/)f:<!#45>>?)1"(\]$&9L*-!#$&"($&*-x !#5)1lmz*-,="%E)0*-L"($&>?'> lm$&"(E/$&"(E/)0$&97E/)Oa}lK*
9A*-!#"%:/"r!#)135>?)1/"(!Glm)1\p)0*-\]$B3O$B/:2&2&4$&/"(\p*-;r'97)1;Ø"(*m:<2B2&*-l¬, *-\"(E/)97*-/"(:<>$&/:"%$B*-Cn
:<979A$B;r)1"%:2_*-9A97'\]\p)1/97)1G! EQ2B:<"()1\%6A9A*-"%:>?$B/:"%$&*-{lm:!>*-;r)12B)1;K:!|:I!#)1L:\]:"()L\p*-97)1!#!
$&/;=)1L)1/;=)1"/*-,D"(E/)G\p)1!#L*-/!#)>?*-;=)12ba
}rE)G)1ñO':"($&*-m$&!n
¼ ¾ ÛR Û Ý Â`R _ # a Â E 2¹Åb2 a
Å
]
x /a <Zz
¼2½[Z\ Å ¼ ¾dc ?R Ý Ý T_ R fe #à & Å:2 a Ý Â ÊgßN!
^
\
lmE/)1\p) ¼ $&!I"(E/)0!#L)197$&)1!#¯OL)1\],%*-\]>?:/97)+:<"=35\]:;=$&)1/"NO:<2B')0*-, 6L$&!I!#L)197$&)1!#¯5\]:/35)16
$&!0L*-!#$&"%$B*-*-,u"%E)m*-L"%$B>?'>å*- "%E)m35\]:;=$&)1/"(6h
$&!®)19A97)1/Å "(\]$B9A$&"(476|:t>)1:<!#'\p)K*-,
:<a !#45>?>)1"%\4A6:<; ¼ ¾ $&!"%E)f>:<d<$&>?'> L)1\, *-\]>:<9A)G:9AE$&)1NO)1;M54K"(E/)f!#L)19A$B)1!97*-/h
!#$&;=)1\)1;a
<Y
L¿ÀmÃÂ
}rE)>*-;r)12B$&/3*-,-"(E/)9A*-)1*-9A2&$B/)I97*-/!#$&!#"(!©*-,-"(E/\p)1)>: P *-\r!#"()1L!x%!#)1)¥$&/97E/$&61S<ij
# SZ<S % z n
SDaC¼)1Ö$&"%$B*-t*-,D:f\p)1!#L*-/!#)G,%'/97"%$&*-K, *-\©)1NO)1\]4~!#L)197$&)1!u$&/NO*-2&NO)1;a
DaC@L)197$&Ö97:<"($&*-t*-,=:!#)1"*-,!#:>?L2&)f2&*-9A:"($&*-/!:<2&*-3m"(E/)0)1N$B\*->?)1/"(:235\]:;=$&h
)1/"]a
TDaC§=N:2&':"%$B*-m*-,/)1:9AE¨@JC¤{:<")1:<97EK!#:>?L2&$B/3{L*-$&/"]a
ôõó ¯ ?þ.-.+.|ù?ø*3+1ø* ûOø*ù?ü0/1ø
8!\p)19A*-35$&H<)1;M54K.f:<'97E×Ê E/$&"("(:<5)1\Cx Sij<z# U<.%%6"(E/)+>?$&*-\!#L)197$&)1!E/:N)+"(E/)1$&\
*-L"%$&>:!#9A:"("%)1\p)1;ñ5'$&"()+\]:/;=*->?2&4K:<2&*-3m"(E/)+3O\:<;=$&)1"%6<"%E)f>: P *-\!#L)197$&)1!"%)1;?"(*
E/:N)t:>?*-\p)t\)135'2&:\0;=$&!#"(\]$BMO'"($&*-*-,*-L"%$B>?:/at}=E)14 $&"%)1\L\)1"u"(E/$&!~*-M5!#)1\]NO:"%$&*-
:<!I:\p)1!#'2&"=*-,r.0:'!#)1¯B!97*->?L)1"($&"($&NO))1d972&'!#$&*-L\]$&9A$&L2B)OnO"(E/)!#L)197$&)1!$&97E/)L:9A5h
$&/3Ç:2&*-3"(E/){)1/NO$&\p*-/>?)1"%:2=35\]:;r$B)1/"rx :4Sij<gGz # iè:/;¥\p)135'2&:\]zC*-,u"%E)KL2&:97)1>?)1/"C*-,u*-L"($&>?:t97: *-9797'\%6:/;"(E/'!0"%E)14Ç>?'!#"
MO)0$&/97*-\]L*-\:<"()1;Ç$&"%*t"(E/)>*-;=)12ba/}=E/)!#)197*-/;ØL\p*-L*-!#$&"($&*-?$&!"%E:<""(E/)>:<d<$&>?'>
L)1\], *-\>?:/97)1!#6C"%*-2B)1\]:/97)1!#6C:<;r6C*-L"($&>:Ç2&*-97:<"($&*-/!#6u:\)t'9A*-\\)12B:<"()1; x%.0:'9AE¥
ÊËE/$B"%"(:<5)1$6<Sij<C # UD %%z#a
.0:'9AEwÊ E/$&"("(:<5)1\Dx%S<ij<C # UD %%6ASij<CY # UHT % z<'!#)1;¨*-2&4+2&*-35h \]:/;=*->6Q*-\D2&*-35h%/*-\]>:<2
;r$B!#"%\$&M5'"%$&*-!I, *-\uL)1\, *-\]>:<9A)G*-L"($&>?::/;B\:<3O)1!#¯5x%!#"%:/;=:\;;=)1N$&:"($&*-/!$&"%E)
.0:'!#!#$&:<~>*-;r)12Bz#aQy=:<35*-)13O\p*+x Si<g<z # Dg %'!#)1;¨'/$&,%*-\]>ð\]:/;=*->ú;=$&!#"(\]$&M5'"($&*-/!|, *-\
:<2&2=L:\]:>?)1"()1\]!a©}=E/$&!+$&!G:2&!#*"(E/)~lm:4$&ØlmE/$B9AEØL:\]:>?)1"()1\]!lm)1\p);=$&!#"(\]$&M5'"()1; $&
"%E$&!!#"(';=4a
@*G, :\%67*-/2&4f, )1l !#"(';=$&)1!="%)1!#"()1;Ë45L*-"%E)1!#)1!|:M5*-'""(E/);r$B!#"%\$&M5'"%$&*-*-,$1!#L*-!#)
, '/97"($&*-~L:<\:<>)1"%)1\!aA$&9AE$&~x Si<i<z # SZ<. %-L)1\, *-\>?)1;{:I;=$&\)197"35\:<;=$&)1":<:<2B4O!#$B!
*-Ç"%E)>?*-'"%:$&ÇNO)135)1"%:"%$B*-?*-,}<:<!#>:<$&:/n"%E);=$&!#"%\$&M5'"%$B*-Ç*-,:M5'/;=:<9A)f>?:dh
$&>?:+lm:!C/*-"/!#$B3O$&Ö97:<"%2&4¨;=$&,%,%)1\)1", \p*->Ò"(E/)2B*-3Oh%\]:/;=*->¬E4OL*-"(E/)1!#$B!a_«m*-lK)1N)1$6
"%E)t;r$B!#"%\$&M5'"%$&*- *-,:lK*-*-;r4X!#'M5!#)1"ulm:!/)1$&"(E/)1\+2&*-35h \:<;=*->?6r/*-\+2&*-35h /*-\>?:2ba
8'!#"%$&Xx%S<i<j*z # j %C:<:<2&45H)1; v§=JCm!0*-, k¡" d&&"!!#L)197$&)1!0:2&*-3?:m"()1>?L)1\:<"('$
3O\:<;=$&)1" nrMO*-"(EØ>?$B/*-\G:<;¥>: PR*-\!#L)197$&)1!+/*-"©97*-/"(\]:;=$&97"%$&3?"(E/){'/$&,%*-\]>ê;=$&!#"(\]$&h
MO'"($&*-tE4OL*-"(E/)1!#$B!a
j
<
¾JI2K L ÁÂNM:&QS¿ U ÂNsNR ÀjiÁXIKÂ¾I¿Â=Àm¿¾s¡R%ÀmÂ
ô$' ¨,(ÿ½ùþ.+./lk-1÷?ø0k~û(*),+1ø*/,-
!C&
«&!¦`ùC"
! H
8Ç$&>L*-\]"(:<":!#L)19A"r*-,>*-;r)12B$&/3$&!G:¨L*-!#$&"($&*-X*-,"(E/)~!#:>?L2&)~*-Ç"(E/)~35\]:;=$&)1/"]a
89A97*-\p;r$B/3K"(*m*-'\u:!#!#'>?L"($&*-/!Ix%L:<35)+S<z 6<"%E)035\]:;=$&)1/"$B!:LL\*-d<$&>?:"%)12B4K'/$B;r$Bh
>?)1!#$&*-/:b2 E1"(E/'!#61:I\p)1:<21'>?M5)1\x !#:>?L2B)!#97*-\)1z9A:~MO):!#!#$&35/)1;K"(*0)1NO)1\]4f!#:<>L2&)16
"%E:<"\)1L\p)1!#)1/"(!G$&"%!fL*-!#$&"($&*- *-X"(E/)¨3O\:<;=$&)1" aI%Ø$&/;=$&\p)19A"3O\:<;=$&)1"©:/:2&45!#$&!#6lm)
E/:N)f'!#':<2B2&4/*mL\$&*-\$B/, *-\>?:"%$B*-?:MO*-'"="(E/)35\:<;=$&)1"'/;=)1\]2&45$&3"%E)!#L:<97)0"(*
M5){!#:>?L2B)1¡; E/"%E'!#6/"(E/){L\*-L)1\!#:<>L2&$&/3>?*-;=)12=$&!G:Ç'/$&, *-\>?:"%$&NO){*-/)16/>*-;=h
)12&)1; N$B::'/$B, *-\]>å;r$B!#"%\$&M5'"%$&*-¥*-,!#:>?L2&)t!#97*-\)1!x%\]:/;=*->å!#:>?L2B$&/35z#aK%"(E/)
\)1:2lm*-\2&;!#$&"%':"($&*-/6<*-/2&4¨'/;=)1\©:0NO)1\]4~!#L)197$&:2-9A:!#)*-,;=$&\)197"O3O\:<;=$&)1":/:2&45!#$&!#6
lmE/)1{"(E/)IL'\L*-!#)I*-,35\:<;=$&)1"-\)197*-/!#"(\'97"($&*-K$&!9A*-Ö\]>?:"(*-\]476\p)135'2&:\!#:<>L2&$&/3
*-,/"(E/)G)1/NO$&\p*-/>)1/"(:<235\:<;=$&)1"97*-'2&;MO):LL\p*-L\]$&:"%)Oa78!¥$&/97E/$&Kx Si<j<6QLa1SUS<z
!#"%:"()1!#6Q¯B:\)135'2&:\D:\]\]:/35)1>)1/"*-,-!#:>?L2&)1!|$&)197*-2&*-35$&9A:2!#L:<97)$B!|>*-!#"-'/2&$&5)12&4"(*
:<\$&!#)I$&{L\]:97"%$&97)1¯õaQ«K*-lm)1N)1$61, *-\|"%E)IL'\]L*-!#)*-,!#)1)1$&3~E/*-l"(E/);=)1"()1\]>?$B/$&!#"($&9u$1h
9A*-!#"%\p'97"%$&*-X:2&35*-\]$&"(E/>;=)1"()1\]$&*-\:<"()1!G$&"(!fL)1\, *-\]>:<9A)lK$&"%EX35\]:;=':<2/:<LL2&$B9A:"%$B*-
*-,IL\p*-9A)1!#!#)1!"(E/:":9A"(':2&2&4X>?:Lw"%E)x $&:<979A)1!#!#$BMO2B)1zL*-L'2&:"%$B*-;=)1/!#$&"(4¥*-"%*X:
x :9A97)1!#!#$&M52&)1z5:MO';=:<9A)x !#)1)IL:35)TU<z%6oM5*-"%E¨\)135'2&:\%6Q:<;t\]:/;=*->!#:>?L2B$&/3~lm)1\p)
$&/972&';=)1;lm$&"(Et"%E)G>?*-;=)12ba
*-!#"O!#$&>?'2B:<"($&*-m!#"(';=$&)1!©97:<\\]$&)1;m*-'"O!#*-h ,%:<\=E:<NO)I)1>?L2B*-4O)1;>*-;r)12B!©$&KlKE/$&97E
!#:<>L2&$&3L*-$&/"(!lK)1\)u;=$&!#"(\]$&M5'"()1;K\p)13O'2B:<\2&4aQ«K*-lm)1N)1$6Q"(E/)L)1\],%*-\]>:<9A)*-,-*-\;=$&h
/:"%$B*-:<2B3O*-\$&"(E/>?!rlm)1\p)C!#E/*-lm"(*GN:\]4Glm$B"%E;=$&,(, )1\p)1/"_!#:>?L2&$&3f!#97E/)1>)1!=x $&9AE$&
S<iT<6oSi<&j E1*-E/2B)1\©S<iS<z a
ô$ ?
m ûOü03ø*ø*¹3|ü0/,-1û+]ý,-.+./nk -1ü (ý,/1),(*/,3|ø
z65 z65 4 [ÿ BC[º»H?
A~<HBC>;[Z
>_<Apo
@L)197$&)1!L)1\, *-\]>:<9A)16-:!I;=)1"()1\]>?$B/)1;ÇM54t"(E/))1N$&\p*-/>)1/"(:<2/, :9A"(*-\]x%!#z:<;Ø$&/"()1\h
!#L)19A$BÖ9+97*->?L)1"($&"($&*-/6O>?:L!I*-"%*t"(E/)L*-L'2B:<"($&*-?;=)1!#$&"%4765lmE/$B9AE$&!"%E))1!#!#)1/"($&:2
9A*->L*-/)1"*-,I"%E):M5'/;=:/97)>*-;=)12ba}=E/)1\p):<\p)t:<2B!#* *-"(E/)1\>)1:<!#'\p)1!~*-,L)1\h
, *-\>?:/97)16r2B$&5)mM5$&*->?:!#!L\*-;='97"%$B*- x%!#"%:/;=$&3Ø9A\p*-Lz 6=:/;w*-"(E/)1\]a«K*-lm)1N)1\+"(E/)
L$1!#)1"I!#"(';r4 ;=)1:<2&!{lm$&"(E '/$&"(:\]4*-\p35:<$&!#>?!¨:<;Ë"(E/)1$&\~97*-'/"(!K*-/2B4 E"(E/'!¨lm)
9A*-Ö/)~"(*;=)1!#$&"%4:!:¨L)1\, *-\]>:<9A)>)1:<!#'\p)Oa|}=E/)~L*-L'2&:"($&*-Ç;=)1/!#$&"(4$&!G"%E)1
'!#)1;:<!u"(E/)G;=)1L)1/;=)1/"ON:\]$B:<M52&)I*-,/"%E)+@JC¤-a
z65 z65 7 q,BC»~º[ZÃT?
Ù»<~>[Ò
t" !¦ 8/*-"(E/)1\~L:\]"*-,+"%E)?>?*-;=)12\)1L\p)1!#)1/"(!¨"(E/)!#:<>L2&$&3w!#9AE)1>?)Oa¥[:2&)1*-)19A*-2B*-3O$B!#"
;=)1:<2&!+L\p)1N:2&)1/"(2&4lm$&"(E NO*-2&'>)m\*-97?!#:>?L2B)1!0lm$&"(E )1/972&*-!#)1;, *-!#!#$B2&!0E)K'!#)1!0:!
:K!#*-'\p9A){*-,C$&, *-\]>:<"($&*-©a%;=)1:<2&2B4A6E/){lm*-'2&;2&$BO){"(*"(:<5){!#:<>L2&)1!#6D\p)1L\)1!#)1"%$B/3
9A*-!#"%:/" Ê$ß $ aQÞ/, *-\"%':<"()12&476o"(E/$&!©$B!'!#':2&2&4*-"OL*-!#!#$BMO2B)161:<!|lm)>$&!#!©"(E/)
L\)197$&!#);r:ð "($&/ðs3~r *-,OMO*-"(Em¯®2&*-lm)1\o¯<:<;t¯B'LL)1\o¯M5*-'/;=:<\4~*-,"(E/)!#:>?L2&)1;tNO*-2&'>)*-,
"%E)!#)1;=$&>?)1" a= !#)19A"($&*-?g6-x L:35)0TU<z%6-lm):!#!#'>?)lm)0:<\p)0:M52&)"(*m"%:5)!#:>?L2&)1!#6
*-\GB!#/:L!#E/*-"(!#¯B6=*-,u"(E/){9A*->>?'/$B"%$&)1!0"%E:<"C\p)1L\)1!#)1"97*-/!#"(:<" " I*-,u"(E/)¨!#)1;rh
$&>?)1"%6=lm$B"%E$& "(E/){!#:>?L2&$&3Ø)1\]\p*-'
\ u
É a+§=ñ5':<"($&*-Xg/a U!#E/*-lK!0"(E/)K\p)12&:"%$B*-Ø*-,
"%E)~!#:<>L2&)~N*-2&'>)¨"(*"%$B>?)16D'!#$&3?!#)1Ä·;=Æ $&# >)1Ç /"(:<"($&*-Ø\]:"()16:/; !#:<>L2&)~M5:<!#:2D:\)1:/a
§=ñO':"($&*-?g/a S<Y$&9A*-\L*-\]:"%)1!"%E)!#:<>L2&)NO*-2&'>?)$&"%*:~L\p*-MO:M5$&2&$&!#"($&9G)1!#"($&>?:"%)0*-,
:<M5';r:/97)16 ¼ a
Qi&QSLuMC¿¾ÂrÃÃÂ=Ã¾I¿ÀXÁTMRwvcVÁTR ÀxiðÁ¿«KvcVÀ2UrKÀm¾IÂ
i
¤O\p)1ñ5')1/"(2&4,%*-'/;Ë$B "(E/)2&$&"()1\]:"('\)16C>*-;r)12B$&/3*-,97*-)1/*-972&$&)1!K;=*-)1!K*-":<97h
9A*-'", *-\f"%E), :9A"u"(E/:""(E/)t"(\')t\p)1!#L*-/!#)t$B!{$B/:9A97)1!#!#$&M52&)On:2&2©lmE:<"lm)E/:N)K$&!
$&"%!~!#:>?L2&)1; NO:<2&')OaK%">$&35E/"I!#)1)1>å'/$&>L*-\]"(:<";=$&,(, )1\p)1/97.) E©E/*-lm)1NO)1$6lm)lm$&2B2
!#)1)¨2&:"()1\I"%E:<""%E$&!f$B!f"(E/){L\]$&>)¨!#*-'\p97){*-,C)1\\*-)1*-'!#2&4?\p)197*-/!#"(\'97"%)1; 35\]:;=$&)1/"(!a
ÊËE/)1)1N)1\u:M5'/;=:<9A)fx :/;E/)1/97)16-;=)1/!#$&"(45z|$B!)1!#"($&>?:"%)1;?MO4t>)1:<!*-,=97*-'/"($&/3
$&/;=$&NO$&;=':<2B!x :~;=$&!#9A\p)1"()N:\]$B:<M52&)16-*-LL*-!#)1;X"(*t"%E)>?)1:!#'$1!I2B$&5)"%E)MO$B*->?:!#!#6*-\
!#O)12B)1"%:2/>:<!#!#6-lmE$&97E:\)+97*-/"($&/'*-'!#z%6OlK)0:\)+"%*K;r)1:2Olm$&"(E:!#*-h%9A:2&2&)1; \ [*-$B!#!#*-
L*-$&/"L\*-97)1!#! \ $B !#L:9AÃ
) # S<.S %# S<. %# j&S %# S<.U %# T& %%6=lmE/)1\p)¨"(E/)K/'>?M5)1\G*-,$&/;=$&h
N$&;=':2&!u$&t97*-/!#"(:<"D:<>*-'/"D*-,/!#:<>L2&)1; E
Ê$ß E:<!u:f[*-$&!#!#*-;r$B!#"%\$&M5'"%$&*-
# S< %#aCÞ/,%*-\]"('/:"%)12B4A6O:<!Glm$B2&2=MO)~!#E*-lmØ2&ð :"%)1ðn$6r "(E/$B!f$ [*-$&!#!#*-X!#:>?L2&$B/3?L\p*-97)1!#!$&!
:m!#*-'\97)~*-,C:K!#'M5!#"(:<"%$&:2r)1\]\p*-\$&X:MO';=:<9A)~)1!#"($&>?:"%)16/'/2&)1!#!+"%E)¨!#:>?L2B)1!f:$
N)1\4t2&:<\p35)Oa \ ·=)1\]4m2&:\p3O) \ >?)1:/!IE)1\)+"%*t$B/972&';=)0"(E/*-'!#:/;=!*-,|$B/;=$&NO$&;=':<2&!a/}=E$&!
$&!65!#'\)165/*-"r97*->?>?*-?$&?L\:<97"%$B9A)f"%*t*-M5"(:<$&!#'97E?2&:\35)!#:>?L2B)1!a=«m*-lK)1N)1$65"%E$&!
'/97)1\]"(:<$&"%456*-$1\\*-\61$&!u$&/"(\]$&!#$&9I"(*"%E)GL\*-97)1!#!C*-,/:M5'/;=:<9A))1!#"%$&>:<"($&*-tNO$&:+$&/h
;r$BN$&;=':297*-'/"(!#6<:/;97:</*-"/M5)97$&\p9A'>N)1"%)1;M54~:<4{>)1:<!u'/2&)1!#!ulm)35$&NO)G'L
9A*-'"%$&3¨$B/;=$&NO$&;=':<2&!C$B¨,%:<NO*-\|*-,O!#*->?)97*-/"($&'*-'!NO:\]$&:M52&)16o2&$&5)"(E/)IM5$&*->:<!#!#6_"(*
MO:!#)G"%E)G:<M5'/;=:/97)I)1!#"($&>?:"%)G*-©a
T<Z
Constant density process
1000
500
0
0
29
sample
v ´5= ± w &w
FI*-/!#"(:<"/;=)1/!#$B"%4{L\*-97)1!#!#6_T<Z+!#:>?L2&)1!a1m*-"(E/$&3Ë:<LL)1!lK$&"%EKL*-Lh
'2B:<"($&*-Ë;=)1!#$&"%$B)1!mlm$&"(E/$& "%E)1!#)ÇTZØ!#:<>L2&)1!#6M5'"G*-M5!#)1\]NO)ÇE/*-lÕ!#"(*-97E/:!#"%$&9
97*->?L*-)1/"(!m:;r; /*-$&!#)OaX¤5\*->½M5*-"%"(*->½"%* "%*-Lnx%:<zI;=)1!#$&"%$B)1!Kx *¥97E/:/35)
"(E/\p*-'35Et"%$B>?)1z E_x%MOz[*-$&!#!#*-t!#:>?L2&)1;:MO';=:<9A)1!Clm$B"%Em)1d<:<97"ON*-2&'>)Gx x
Z/a Z<ZSN6 É x Z/a Z<ZZZ<ZZ<ZS6 {zxXZ/a ZST6 |.x ZDa ZS<6 àCzx S/a Z<2
Z à}|Hx SDa ZZ<6 zx Z/a Z<Z6 ÆP y |Hx
y
Z/a Z<Z6 xwSDa Z,
Z É x Z/a Z<Fz E©x 97z[*-$&!#!#*-w!#:<>L2&)1;w:MO';=:<9A)1!lm$B"%E:LL\p*-d$&h
>:<"(){ÆTN~ *-2&'>)¨!#'~ MoPR)197"©"(*)1\]\p*-\Ix x ZDa ZZ<S6 É x ZDa ZZ<ZS?6 z x Z/a Z<S?6 | x Z/a Z<S6
à z x{SDa ZZ à | x¨SDa ZZ<6 z xKZ/a Z<Z6 | xKZ/Æ a Z<y Z6 Æ ~ x¨S/a Z<[Z É y ~ x¨ZDa Zz E7x ;=z-[*-$&!#!#*-{!#:<>L2&)1;
:M5'/;=:/97)1!mlm$&"(E:LL\*-d<$&>?:"%)N*-2B'>?)X!#'MoPR)19A"+"(*w)1\]\p*-\%6:<;×!#"(*-97E/:!#"%$&9
!#)1;=$&>)1/"(:<"($&*-~\]:"()x x{Z/a ZZS<.6 É x{Z/a ZZZ<S6 z x{ZDa ZZ<iE6 | x¨ZDa ZS<.6 à z x¨S/a Z<[
Z à|x
S/a Z<Z6 z x{Z/a ZZ6 | x¨Z/a Z<Æ Zy 6 x¨S/a Z<*Z É y x¨Z/a Z<Fz EAx%)1z[*-$&!#!#*-{!#:<>L2&)1;{:<M5'/;=:/97)1!
lK$&"%E:LL\*-d<$&>?:"()N*-2&'Æ >~ )0!#'MoPR)197~ "D"(*¨)1\\*-\(6_!#"%*-97E/:!#"%$B9!#)1;r$B>?)1/"(:"%$&*-t\:<"()16
TS
:/;Ë!#"(*-97E/:!#"%$&9K, *-!#!#$&2&$BH<:"%$B*- \:<"()x Ë
x Z/a Z<ZS66É x Z/a Z<ZZ<S6}zxËZ/a Z<Zi<6 |Dx
Z/a ZS66àCzx Z/a U à}|Hx Z/a UU6 zx Z/a Z<Z6 |HÆPx y Z/a Z<Z6 x S/y a Z<Z É x Z/a Z<zFEx%, zI[*-$B!#!#*-
!#:>?L2&)1;:<M5';r:/97)1!Clm$&"(Et:LL\*-d<$&>?:"%)N*-ÆT2&'~ >)f!#'MoPR)1~ 97"/"(*{)1\]\p*-\%6_!#"(*-9AE:<!#h
"($&9m!#)1;=$&>?)1"%:"($&*- \]:"%)16C!#"(*-9AE:<!#"($&9t,%*-!#!#$&2&$&H:<"($&*-w\:<"()16C:<;Ë!#"(*-9AE:<!#"($&9t97*-/h
"(:<>$&/:"%$B*- $&"%)1!#$&"(4Øx ¥
x Z/a ZZS<6NÉ x ZDa ZZ<ZS<6T z x ZDa ZZ<i6P | ¥x Z/a Z<S6¡à z ¥x Z/a U
à | x ZDa UU<6 z ?x Z/a Z<S6 | ?x Æ Z/y a Z<U6 Æ ~ x S/a Z<Z0y É ~ x ZDa ZzE x 35z[*-$&!#!#*-!#:<>L2&)1;?:M5'/h
;=:<9A)1!lm$&"(EÇ:<LL\p*-d$B>?:"%)NO*-2&'>)!#'M1P )19A"|"%*t)1\\*-\(65!#"%*-97E/:!#"%$B9f!#)1;=$&>)1/"(:<h
"($&*-\:<"()16-!#"(*-9AE:<!#"($&9G, *-!#!#$&2B$&H<:"($&*-\:<"()16!#"(*-9AE:<!#"($&9G97*-/"(:<>$&/:"%$B*-?$&"%)1!#$&"%476
:/;¥!#"(*-97E/:!#"%$&902&)1/35"(E *-,C!#L)197$&)1!#¯35)1/)1\:<"($&*-Øx x ZDa ZZ<S6uÉ x ZDa ZZ<ZS6? z x
Z/a ZZi<6|.
x Z/a ZS6
àzx Z/a U0à}|Hx Z/a U<U6 zx ZDa ZS<6 |Dx Z/Æ a Z<y U6 ÆT~ x S/a ZZryÉ ~ x Z/a S<z a
140000
80000
70000
120000
60000
100000
50000
80000
40000
60000
30000
40000
20000
20000
0
200
10000
400
600
800
1000
1200
1400
1600
1800
2000
0
200
2200
400
600
800
1000
1200
1400
1600
1800
2000
2200
·=*-2&'>)!#:<>L2&)1;Ç97*-/!#"(:<"=;r)1!#$&"(4tL\*-97)1!#!a/y=)1, "]n-97*-/!#"(:/"=N*-2B'>?.) E
\]$B3OE" nQ97*-/!#"(:/"-NO*-2&'>?)lm$&"(E{!#"(*-97E/:!#"%$&9C)1\\*-\97*->?L*-)1/"-x%'!#':<2_!#$&"(':<"($&*-z#a
[:\]:>?)1"()1\r!#)1"("($&/3~lm:! xtZ/a Z<S&6 É xtZDa ZZ<ZSE6 }zxtZDa ZS<6 |HxtZ/a Z<S&6 àCzxmS/a î
y Z/a ZZZ<S6_:<; x?Z/a Z<ST6 É xZDa ZZ<Zg<Z f6 à{}|Dzxx
S/a Z6 zbxZ/a ZZ6 |Dx?Z/a ZZ6 ÆPy xS/a Z<0
Z É x
~ SDa Z6 zbx~ Z/a Z<Z6 |HxZ/a ZZ6 ÆPy xSDa ZZ É xy Z/a ZZZ<S/a
Z/a ZSf6 |DxZ/a Z<S
6 àCzxS/a r
Z à{ÆT|Dx
v %´5rp ± w w
ÆT~
~
z65 z65 z Y[Zu;<Z
>[A.?
A<.BC>9?
A.Z
@)1;=$&>?)1"%:"%$B*-{\:<"()u$&Co ')19A)1!|"%E):M5'/;=:/97)1!rNO$&:I>:<LL$B/30*-,-"($&>)"(*f!#)1;=$&>)1/"
"%E$&9A5)1!#!#6-$ba )Oa 6:<2&!#*{"(E/)0!#:>?L2B)0NO*-2&'>?)Oa-}=E/'!#6$&"$B!97\]$&"($&97:<25/*-"=*-2&4m"(*K"(:<5)+9A:\)
*-,|"(E/)fN*-2&'>)*-,=:<2B2!#:>?L2&)1!M5)0x :!>?'97E:!L*-!#!#$&M52&)1z=)1ñ5':2&6M5'"=:<2&!#*¨"%E)0!#)1;=$&h
>?)1/"(:"%$&*-\]:"%)f"%*tM5)fO*-lm/6O"(*-3O)1"(E/)1\lm$&"(E$B"%!NO:<\$&:/97)Oa/Ö3a?T/a T!#E/*-lm!E*-l¬:
!#2&$&35E/"DNO:\]$&:/97)$&m"(E/)G!#)1;=$&>?)1"%:"($&*-m\]:"()MO\p*-:;r)1!C"%E)G;r$B!#"%\$&M5'"%$&*-t97'\]NO)Oa
30000
25000
20000
15000
10000
5000
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
T<
v ´5= ± w ± w
·r*-2B'>?){!#:<>L2&)1; 97*-/!#"(:/"C;=)1/!#$&"(4?L\p*-97)1!#!+lK$&"%EXNO:<\45$&/3!#)1;=$&>?)1h
"(:"%$&*-?\]:"%)Oa[:\]:>?)1"()1\!#)1"("($&/3lm:<! xXZ/a Z<ZS<6CÉ xXZDa ZZ<Zg6{zxXZ/a ZZ<6g|.x
Z/a Z<S
6 àzxS/a 0
Z à}|HxS/a Z<6 zxZDa ZZ<6 |DxZDÆPa Zy Z<6 xS/a Z<Z y É xZDa ZZ<ZSDa
ÆT~
~
z65 z65 9BT<»~<6?
A~<.BC>
@)1NO)1\]:2L\*-97)1!#!#)1!f$BCo ')1/97)m"(E/)¨9AE:<9A){"%*, *-!#!#$&2B$&H<)OaG[\)1;=:"%$B*-Ø\)1>*-N)1!+2&$&NO$&/3
*-\35:/$&!#>!,%\*->Ò"%E)f)1N$&\p*-/>)1/"(6:/;, \p*->q"%E)G\)1L\p*-;='9A"($&*-mL\p*-9A)1!#!#6>?*-;=$&,%45h
$&/3¨"%E)f)197*-2&*-35$&97:<2O@JC¤¨*-,"%E)f!#L)197$&)1!u$&:0>:</)1\C!#$&>$&2&:\C"%*{9A*->L)1"%$B"%$&*-©a ,"(E/)
$&/;=$&NO$&;=':2D:<NO*-$&;=!L\p)1;r:"($&*-/6-$&"(!G\)1>:<$B/!I>'!#"ñ5'$&97O2B435)1"rMO'\$&)1;ØM54"%E){!#)1;=$&h
>?)1"%65$&*-\;=)1\"%*tE:<NO):~/*-H<)1\p*m97E/:/97)"%*t,%*-!#!#$&2&$&H)Oar}=E)*-\35:/$&!#>:<2/\)1>:<$&!
/*-"CM5'\]$B)1;¥ñ5'$&97O2B4Ç:<\p)~!#'MoPR)19A"C"(*?;=)197:<4:/;¥lK:<!#Eh :lm:<476D"(E/:"©;=*-)1!0*-"C2&)1"©"(E/)
\)1>:<$B{"(*)1"%)1\="(E/)I!#)1;=$&>)1/"]a1§=NO)1¨$B,OM5'\$&)1;=61)1\*-!#$&*-61*-\|;=$&!#!#*-2B'"%$&*-¨*-,"(E/)!#)1;rh
$&>?)1"/\p)1>?*-NO)1!C"%E)G\)1>:<$&!C"%*-35)1"(E/)1\©lK$&"%EK"%E)!#)1;r$B>?)1/"]a18, "()1\!#'\]NO$&NO$&/3{:2&2"(E/)
L\)1NO$&*-'!L\*-97)1!#!#)1!#6"(E/)f*-\35:/$&!#>:<2O\)1>:<$B/!>'!#"9A*-L)flm$&"(EM5$&*-"('\]M5:"%$B*-/6-:/;
;=$&!#!#*-2&'"($&*-/6<$&m*-\p;r)1\|/*-""%*{M5)\)1>*-N)1;, \p*->Ò"(E/)G,%*-!#!#$&25\)197*-\;a
60000
50000
40000
30000
20000
10000
0
200
300
400
500
600
700
800
900
1000
1100
v ´5= ± w º&w ·r*-2B'>?)!#:<>L2&)1;K97*-/!#"(:<";=)1/!#$&"(4L\p*-9A)1!#!=lm$B"%E~NO:<\4O$B/30!#)1;=$&>)1/"(:<h
"($&*-t\:<"()16<:/;,%*-!#!#$&2&$&H:<"($&*-©a<[:<\:<>)1"%)1\|!#)1"%"($&3Klm:! xZ/a Z<ZS<6
É xZDa ZZ<Zg6
}zx ZDa ZZ<6|.x Z/a ZS<6àCzx Z/a g<UÃà}|Hx Z/a U<U6 zx Z/a ZZ6 ÆP|.yx Z/a Z<Z6 ÆT~ x y S/a Z<ZÃÉ ~ x
Z/a Z<ZZSDa
z65 z657 þtBC>AH?
<~>_?
A<.BC> ?
>_;9ZYBC9 [<>Ò
0!d
* µ H
¤5*-\]>?:2C>?*-;=)12&!~*-,!#L)19A$&)1!~\p)1!#L*-/!#)t,%'/97"%$&*-!~'!#':<2&2B4 ;=*X/*-":<979A*-'",%*-\0"(E/)
L\)1!#)19A)*-,$B/;=$&NO$&;=':<2&!"%E:<"5>?:4~, \p*->ð"%$&>)"%*0"%$&>):<\$&!#)*-'"(!#$&;=)*-,O"%E)I!#L)19A$B)1!#¯
\)1:2&$&H)1; /$&97E/)On©*-\p3O:/$B!#>?!"(\]:/!#L*-\"%)1; "%*Ç;=)1:;=2&4?)1N$&\p*-/>)1/"(!afm*-\G;=*?"(E/)14
"%:5)$&/"(*~9A*-!#$&;=)1\]:"%$B*-m:f*-/H)1\*L\p*-M5:<M5$&2B$&"%4~*-,\)1lm*-\5$&/3{*-,/,%*-!#!#$&2&!$&/"(*~*-"%E)1\
!#)1;=$&>?)1"%!+M54Ç"%:LE/*-*->?$&9L\p*-97)1!#!#)1!a82&"%E*-'35E L)1\pE/:L!G, :\I"(*-*?97*-/!#)1\]NO:"%$&NO)16
"%E)1!#))1,(, )197"(!{:\p)>*-;=)12&)1;ËE)1\):!¨:Ç97*-/!#"(:/"¯B97*-/"(:>?$&:<"($&*- $&/"()1/!#$&"(45¯u"%* :<2&h
2&*-l¦, *-\/*-H<)1\p*:<M5'/;=:/97)1!G"%*MO){!#:>?L2&)1; $&Ø:<\M5$&"%\:<\$&2&42&:<\p35)~;r$B!#"%:/97)¨,%\*->
"%E)m!#L)197$&)1!#¯=*-L"%$&>'>wa}=E/$&!¯®9A*-"%:>?$B/:"%$&*- $&/"()1/!#$B"%45¯$B!>?*-;=)12&)1;wE)1\)¨:<!f;r)1h
L)1/;=)1/"=*-Ç"(E/)!#L)197$&)1!#¯O>?)1:?L)1\, *-\]>:<9A.) E5"(E/'!#6O, *-\)1'\]45)19A*-'!:<; 97*->?>*-
!#L)19A$B)1!$B"D$&!E/$&35E/6<lmE/)1\p)1:!,%*-\©!#"()1/*-)197*-'!:/;\]:\)!#L)197$&)1!u$&"D$&!97*-/!#$&;=)1\p)1;2B*-lKa
82&"(E/*-'35E"(E/$B!>?*-;=)12O$&!\p*-'35E/6$B"%!:<M5$&2&$B"%4m"(*K:2&2&*-l¸, *-\C!#'M5!#"(:<"%$B:<2O/*-H<)1\p*K;=)1/h
!#$&"($&)1!0,%:<\I,%\*->"(E/){*-L"($&>?'>è>?:5)¨$&":m!#'$&"(:<M52&){*-/)¨, *-\"(E/){L'\]L*-!#){*-,C"%)1!#"($&/3
"%E)G3O\:<;=$&)1"%¯®!C\)197*-/!#"(\p'9A"(:<M5$&2B$&"%4{'/;=)1\©:+lm$&;=)!#L)197"%\p'>q*-,/97*-/;=$&"($&*-!a
TT
JC)1lm*-\]5$&3 *-,, *-!#!#$&2&!~,%\*->è*-2&;=)1\0!#"(\]:"%:>:<4XL\p*-;r'97)16=$&,*-"\p)197*-3O$&H)1;r6r:
!#$&>?$&2B:<\)1,(, )197"|:!G9A*-"%:>?$B/:"%$&*-X;=*-)1!a«m*-lK)1N)1$6/"(E/){$1!#$B!#"%:/97)*-,C, *-!#!#$&2B!f"(*\p)1h
lm*-\]5$&3?LE/)1*->?)1:<6D*-";=$&\p)19A"(2&4"(E/)~!#L)19A$B)1!9A*->>?*-/)1!#!tVm!#97:<\p9A$B"%476L2B:<45!:
O)14t\p*-2&)fE/)1\p)Oa§=N)1:L\p*-2&$&Ö9G!#L)19A$B)1!>?:4t)1:!#$&2&4mM5);=)1!#"(\*-45)1;?;='\$&/3t"(E/)L\p*-h
9A)1!#!#x%)1!#z*-,-\)1lK*-\]5$&/3 Eo"(E/'!#6A:\p)1lm*-\]5)1;{!#9A:\p9A)C!#L)197$&)1!=>?:40Ö:<2&2B40M5)19A*->)u>?*-\p)
:<M5'/;=:/""(E/:$B!I:\)1lK*-\]5)1;Ç97*->?>?*-!#L)19A$B)1!a/ C o')19A)0*-,r97*-/"(:>?$&:<"($&*-?*-
:<M5'/;=:/97)$&!u;=)1>?*-/!#"(\]:"()1;$&KÖ3a#T/a U/a
450000
400000
350000
300000
250000
200000
150000
100000
50000
0
200
v %´5rp ± w £w
300
400
500
600
700
800
900
1000
1100
·=*-2&'>)¨!#:>?L2&)1; 97*-/!#"(:<"©;=)1/!#$&"(4?L\p*-9A)1!#!+lm$&"(EØNO:<\4O$B/3?!#)1;=$&>)1/h
"(:<"($&*-\]:"%)16<, *-!#!#$&2B$&H<:"($&*-/6:/;9A*-"%:>?$B/:"%$&*-©aO[:\]:>?)1"()1\C!#)1"%"($&3mlm:! x
Z/a ZZS<T6 É xZ/a Z<ZZ<gY6 {zxZDa ZZ<Y6 |HxZ/a Z<S<T6 àCzx?Z/a g_Z
9?
A<.BC>».Z
>[ÒA~}
.0)1/)1\:<"($&*- 2&)1/35"(E >:<L!f;=)1/!#$&"(4Ø:<;¥"($&>?)K*-/"(*Ç:<M5';r:/97)Oa+}=E)K2&*-lm)1\G$&!0"%E)
3O)1)1\]:"%$B*-K2&)13O"(E{*-,35$&NO)1¨!#L)197$&)1!#61"(E/)IE$&35E/)1\r$&!C"(E/)I:M5'/;=:<9A)97*->?L:\)1;mlK$&"%E
:<*-"%E)1\!#L)19A$&)1!=lm$B"%E"(E/)u!#:>?)L*-L'2&:<"($&*-;=)1/!#$B"%476QM5'"2B*-/35)1\2&)1/35"(E*-,*-/)35)1/h
)1\]:"%$&*-©a}rE)G$&C o')19A)f*-,3O)1)1\]:"%$B*-t2&)1/35"(ENO:\]$&:M5$&2&$&"(4¨*-:M5'/;=:<9A)G$&!!#E/*-lK
$&tÖ3|a T/a YDa
40000
35000
30000
25000
20000
15000
10000
5000
0
200
300
400
500
600
700
v %´5rp ± w Ï w
800
900
1000
1100
·=*-2&'>)!#:>?L2&)1;{97*-/!#"(:<"-;r)1!#$&"(40L\p*-9A)1!#!rlm$&"(EN:\]45$&30!#)1;=$&>)1/"(:<h
"($&*-\:<"()16,%*-!#!#$&2&$&H:"%$&*-659A*-"%:>?$&:<"($&*-6-:<;ÇN:\]45$&3m2&)13O"(E*-,r35)1)1\]:"%$&*-©a
[:\]:>?)1"()1\!#)1"%"($&/30lm:<! x¨ZDa ZZ<S.6 É xmZ/a Z<ZZg<6 }zbx¨ZDa ZZ<6 |.x¨ZDa ZS<.6 àzx¨ZDa gU
à | xZ/a UU6 z xZ/a Z<S6 | xZ/ÆPa Sy 6 xS/a ZrZ y É xZ/a S<U/a
Æ~
~
T<g
B}=E)*-/2&4¨2&*-35$&9I*-,/:fL\]:9A"($&97:<2<>?:m$&!u"(E/)GL\*-M5:M5$&2&$&"(4~"%E)1*-\]4a ¯
:>?)1!CF2&)1\]~:dlm)12B2&6_S<T<Sh Sj?)1"%$&*-)1; :<M5*-NO)16r:2&2|"%E:<"uL:2&)1*-)19A*-2B*-3O$B!#"E:<!:"CE/:/;w:\p)¨"(E/)t:M5'/;=:<9A)1!
*-,,%*-!#!#$&2!#L)197$&)1!+$& E/$&!f!#:<>L2&)1!a+}=E/'!#6';=)1\]!#"(:<;r$B/3ÇlmE:<"C:M5'/;=:/97)¨>)1:<
$& "%)1\>?!{*-,I)19A*-2B*-3O$B9A:2&2&4\p)12&)1NO:<""()1\]>!#6u$&!¨)1!#!#)1"%$B:<2ba?%w"%E$&!{!#)19A"($&*-/6ulm)lm$&2B2
!#"%:\]",%\*->q"(E/)f;r)1"()1\]>$&/$B!#"%$&9G>*-;r)12O*-,=:<M5';r:/97)Oa-ÊËE/)1:2&2O\)12&)1NO:/"/L\p*-97)1!#!#)1!
lm$&2&25M5)G$&/972&';=)1;=6<:/;"%E)G;r)1"()1\]>$&/$B!#"%$&9)1ñ5':<"($&*-t!#)1"/'L6lm)Glm$&2B2OL\p*-97)1)1;"(*{"%E)
L\*-M5:MO$B2&$&!#"($&9>*-;r)12õa
[*-L'2&:<"($&*-{;=)1/!#$&"($&)1!:\p)>)1:<!#'\p)1;¨*-{"(E/)'$&"-:\)1:/aA¼)1!#$&"%4$B!E/)1\p)N:35')12&4
;r)1Ö)1;?:!:0/'>?M5)1\u*-,$&;r$BN$&;=':2&!)1/97*-'/"()1\)1;$&: \ "%$&>)f97'" \ *-:'/$B":<\p)1:Da
}*-"(:<2</'>?M5)1\=*-,5$&/;=$&NO$&;=':2&!x%*-,O"(E/)!#L)19A$B)1!'/;=)1\=97*-/!#$&;=)1\]:"($&*-/z5"(E/:"-$&/E:<M5$&"()1;
!#*->?)+:<\p)1:G;r'\$&/3{:+"%$&>)G$&/"()1\]NO:<2B6$B!
½ + Ê ð
x%gDa Sz
6
lmE/)1\p)
$&!"(E/)K"%*-"(:<2|/'>MO)1\G*-,$&/;=$&NO$&;=':2&!)1/97*-'/"()1\p)1;$&¥:t"($&>)m$&/"()1\]NO:2|*- :<
:<\p)1:<6
+G$&!u:f®\)1:2&$&H)1;=¯<;=)1!#$&"%476
Ê$B!r"($&>)$B/"()1\]NO:<2olK$&"%E$&lmE$&9AE"(E/)u!#:>?L2&)1;~NO*-2&'>?)*-,!#)1;=$&>)1/"lK:<!,%*-\]>?)1;
$&!u"%E)+M5:!#:<2:<\p)1:G*-,/"(E/)G!#:<>L2&)16:<;
ð $B!0;='\]:"%$B*- *-,u*-)m35)1/)1\]:"($&*-X, *-\G"%E)K35$&NO)1

9A*-!#"%:/"D,%*-\"(E/)G35$&NO)1m!#L)19A$B)1!a
!#L)197$&)1!aGÊØ)K)1dL)197"C"(E/:"

$&!
}rE)0>*-;r)125!#E*-'2&;Ø:<9797*-'/"D:2&!#*K,%*-\C:L:\]"D*-,=;=)1/!#$&"(4m97:<'!#)1;M54m¯B:2&$&)1¯5$&/;=$&h
N$&;=':2&!#6$ba )Oa 6D"(E/*-!#)K*-/h%>?)1>?M5)1\!0*-,u9A*->>?'$&"%4Ø$B/972&';=)1;¥lm$&"(EX"%E)¨!#:>?L2B)KM54
:<979A$B;r)1"x !#)1)+M5)12&*-lmz#a Øa }=E/$&!L\*-97)1!#!lm)flm$&2&2O97:<2&2OB97*-/"(:>?$&:<"($&*-/¯®6 aOÊØ)0>*-;=)12
"%E){97*-/"(:>?$&:<"($&*-Ø:!L\*-L*-\"%$&*-:<2"(*tM5*-"%EØ97*-/"(:>?$&:<"($&*-Ç$&"%)1!#$&"(4A6D:/;X>)1:<
L*-L'2&:<"($&*-t;=)1/!#$B"%4{*-,D"(E/)GL\*-L)1\r!#L)197$&)
©ª E«¨ { }p¨wJ% ¦Lgw¬J N' ¡£¢T£}¤¥ ¦ ¦EgEw§¨ ¢S p¨ ¬®s w¯¨ p{¢S¨ °
TU
!F &
¾JI@K L Á-ÂNMb±&Q_¥¿ U ÂNs¡R%Àji
T<Y
+ ½ + [M Ý æ + Ë
KvcVÀ2UrKÀK¾IÂ
x g/a <z
lmE)1\)
+ M $B!®L'\)1¯<L*-L'2&:"%$&*-K;r)1!#$&"(4O6
+
Ëw$&!>)1:<¨L*-L'2&:"%$&*-t;=)1!#$&"%4{*-,D35$&NO)1m!#L)197$&)1!C:<97\p*-!#!C:<2&2-!#:>?L2B)1!#6<:/;=6
$&!"%E)9A*-"%:>?$&:<"($&*-t$&"%)1!#$&"(4a
}=E/)16
½ + Ê ð ½ Ä + M Ý +Ë Ç Ê ð
tL:2&)1*-)197*-2&*-354A6lm)+9A:/*-"/>)1:<!#'\p)"%$B>?)+;r$B\)197"%2B4A6_$&!#"%)1:;=6<lm)G97:<K)1!#"%$&>:<"()
$&"O, \p*->"(E/)NO*-2&'>?)*-,"%E)!#)1;=$&>?)1""(E/:"5E/:!C;r)1L*-!#$B"%)1;t';r)1\|N:\]45$&3!#)1;=$&>?)1h
"%:"($&*-m\]:"()Oa1}=E'!#6
²
²
½ ð
½ Ê ²
Ê ½ ½ ²
²
ð
½ Ä + M[Ý + Ë Ç Ê ð ½£Ä + MÝ + Ë Ç ð ½ Ä + M Ý + Ë Ç
ð
x g/a T<z
x g/a g<z
x g/a U<z
x g/a Y<z
lmE/)1\p)
$&!u"(E/)GNO*-2&'>?)+*-,/"(E/)G!#)1;=$&>?)1"%6
$&!uE)1$&35E/"Dx%"%E$&9A5)1!#!#zD*-,/"(E/)G!#)1;=$&>?)1"%:\]4{97*-2&'>?6
$&!u"%E)G!#)1;r$B>?)1/"(:"%$&*-K\]:"%)16
Ê/$&!u"%$B>?)G'/;=)1\©lmE$&97Em"%E)G!#:<>L2&)1;NO*-2&'>)+*-,/!#)1;r$B>?)1/"lm:!C, *-\]>)1;a
Þ/,%*-\]"('/:"%)12B4A61lm)'!#':2&2&4 7 r=5 :<\\]:/35)I!#:>?L2&$B/3~!#*"%E:<"5"(E/)I!#:>?L2B)\)1Lh
\)1!#)1"%!C:f9A*-!#"%:/""%$B>?)G$&/"()1\]NO:2ba
¤5*-!#!#$&2&$&H:"%$&*-Ë9AE:<9Af
) à{$B!t:ØL\*-L*-\"%$&*- *-,f$B/;=$&NO$&;=':<2&!KlmE/$&97E:9A"(':2&2&4,%*-!#h
!#$&2&$&H)1!a<%/972&';=)1!L\p)1;=:<"($&*-/635:<L!u$&t!#)1;=$&>)1/"(:<"($&*-6:/;?\p)1>?*-NO:2-, \p*->¬"%E)f!#)1;=$&h
>?)1"/;=')"%*{:/4~9A*-9A)1$BN:M52&)GL\*-97)1!#!aoMO!#)1\N)1;² :M5'/;=:<9A) ¼ $&!u"%E)1Cn
N`nDnD! &
¼2½ H à ½ Ä + M Ý +
Ë Ç à
x g/a j<z
«m*-lm)1NO)1\u"%E)0:M5*-N)+N:\]$B:<M52&)1!:<\p)G/*-"=;=)1"%)1\>?$&$&!#"($&9A6\]:"%E)1\C!#"%*-97E/:!#"%$B9a5Ê¥$&"(E
'/97E/:/35)1;97*-/*-"%:"%$B*-¥lm)¨lm$&2&2|/*-l¹L\p*-97)1)1;¥"(*?"(E/)mL\p*-M5:<M5$&2&$B!#"%$&90x !#"(*-9AE:<!#"($&97z
>?*-;=)12ba
ô$' m?ûOüIý(ý+1þ.+.-.+.3 ÿ ü0)øþ
²
¼)1/!#$B"%476?1+ 65$&!I:[*-$&!#!#*-?N:\]$&:"()fx%*-'"%L'"=*-,r:{[*-$B!#!#*-?L\p*-9A)1!#!*-,9A*-2B*-/$&H:<"($&*-p<6
lm$&"(E?$&"%)1!#$&"(4b+ 65*-,r"%E):<\p)1:';r)1\u97*-/!#$&;=)1\:<"($&*-/z aD}rE)!#:>?L2&)NO*-2&'>)16 65:<2&h
"%E*-'35E¥"(\]$&)1;w"(*ÇM M5)m5)1L"C9A*-!#"%:/"(6$B!!#'MoPR)19A"u"(*Ø"%E)m!#:>?L2&$&3X)1\]\p*-\%6lmE$&97E¥E/:!
x :LL\*-d<$&>?:"()12&45z:?K*-\]>?:2C;=$&!#"(\]$&M5'"($&*- x "(E/$&!{$&!~/*-"972&)1:/6©:!¨.f:<'!#!#$B:<;=$&!#"(\]$Bh
M5'"%$&*-wlK:<!~;=)1\]$&NO)1; , *-\f2&*-9A:"($&*-/6C*-"I!#9A:2&)NO:<\$&:<M52&)1!#6|9A, a@$&N$B:Si<iY6LatSAS<z a
±Qiq&QSLuMC¿vNKvNRsNR%Ã=ÁTR ¾¿ U0Â¡s
Tj
@)1;=$&>?)1"%:"%$B*-\:<"()167 6$&!'/5/*-lm6-M5'"D!#'LL*-!#)1;Ç"(*¨2&$B)0lm$&"(E/$B"(E/)+2&$&>$&"(!s{z # |Q6
lm$&"(E/$&~*-/)!#:>?L2&)OaA¤5*-!#!#$&2B$&H<:"($&*-~9AE:<9A)16.à 6Q$&!r'/5/*-lK{:!=lm)12&2&6AM5'"$&!r!#'LL*-!#)1;
"%*¨2&$&)0lK$&"%E$&"%E)02&$B>?$&"(!àCz # à{Q| 6lm$&"(E/$B*-)0!#:>?L2&)OaFI*-"%:>?$B/:"%$&*-$&"%)1!#$&"(4A6 6<$&!
'/5/*-lm:!Clm)12&2&6M5'"/$&!u!#'LL*-!#)1;"(*{2B$&)Glm$&"(E/$&t"(E/)G2&$&>$&"(! z # | 6, *-\|:<2&2-!#:>?L2B)1!
:<; !#L)197$&)1!a©ÊØ)>?*-;=)12*7 6 :/;à MO4:{'/$&,%*-\]>ª;=$&!#"(\]$BMO'"($&*-Ø:!lm)12&2ba©}=E/)2B)1/35"%E
*-,|35)1/)1\:<"($&*-, *-\u:35$&NO)1!#L)19A$&)1!$&!!#'LL*-!#)1;?"%*mM5)fO*-lmlm$&"(E97)1\]"(:<$B'9A)1\ph
"%:$&/"(476lmE/$B9AEE/:!x :LL\*-d<$&>?:"%)12B4Oz:0m*-\>?:25;r$B!#"%\$&M5'"%$&*-x%!#)1)f:M5*-N)1z a<}=E/'!lK)
L'" n
lm$&"(E/$&t!#:>?L2&)16
lm$&"(E/$&t!#:>?L2&)16
+ ´½ ³ Ä + MÇ¡Ý ³ Ä + Ë æµ Ä z # | ² ÇÇ
½.³ j¶ Ä + MÝ + Ë æ µ Ä z # | ÇÇ æ ·
² ¼@½
¸ ß Ä # à Ç
½ u ÄùÆ y # É y Ç
½ µ Ä z# | Ç
à ½ µ Äà z# à | Ç
½ µ Ä z# | Ç
2½ u ÄùÆ ~ # É ~ Ç
lm$&"(E/$&t:!ulm)12&2-:!C:<>*-/3K!#:>?L2B)1!a
¤O\p*->¬g/a S<ZGlm)GE/:NO)On
x%gDa z
x%gDa iz
x g/a S<Zz
x g/a SASz
x g/a S<z
x g/a S<Tz
x g/a S<gz
x g/a S<Uz
x g/a S<Yz
¼2½´¸ ß ¶ ³ ¶ Ä + M Ý u+ Ë æ µ # ÄÉ z # æ |µ ÇÇ }æz #u Äù| Æ y # É y Ç · # µ Ä àCz # à{| Ç"·
Ä·ÆT~ ~Ç Ä Ç
lmE/)1\p)
³ ß Äwe ¹pÇ $&!u:f$&!u[*-:f$B[!#!#*-*-$&!#!#NO*-t:\]NO$&::"%\])$&:lm"%)$&"(lKEt$&L"%EK:<\L:<:<>\:<)1"%>)1\ )1"%¹ )1\6 !ce 6
¸u Ä #É $ Ç $B!:¨m*-\>?:2/x%.0:'!#!#$&:<zNO:<\$&:"%)flm$&"(EÇ>?)1#:$ 6O:/;Ø!#"(:<;r:\p;Ç;=)1N$&:h
Æ
"%$&*-,¨
É ÄùÆ6:<# ; Ç
µ $B!:+'/$B, *-\]>qNO:\]$&:"%)*-t"%E)+$B/"()1\]NO:<2 Äº # Ç a
[*-Ä$&º !## !#*-Ç tL;=,
x g/a S<jz
» Ú Ä u½¼ Æ #¾ Ç ½ÆP¿ ¿ÀTuÁ g Ä`Â*Æ¡Ç
sr$B/*->?$B:<2-L;=,
» Ú Ä 4¼ u # » # ¾ Ç ½ T g u ug g » Ä Â » Ç ¿ Ä Â Ç
x g/a S<z
¾JI@K L Á-ÂNMb±&Q_¥¿ U ÂNs¡R%Àji
T<
KvcVÀ2UrKÀK¾IÂ
.0:'!#!#$&:mL;=,
N` !!! FnD".2
nD"& x g/a S<iz
» Ú ÄùÅ ¼ Æ # É #p¾ Ç ½ É Þ jSÀ ¿ÀXÁ:Á Â ùÄ ÅWj ÂÉ Æ¡Ç È
È Â
'/$B, *-\]>qL;=,
x g/a <Zz
» Ú ÄFÅ ¼ º # Ç ½ }=E/$&!K/)1)1;=!#6uL)1\E:<L!#6u:Çlm*-\p;*-,)1d<L2&:<:<"($&ÂÃ
*-©º a ÊØ)?97*-/!#$B;r)1\~"(E/)B97*-2&*-/$&H:h
"%$B*-/¯Cx lKE/:"%)1NO)1\0$&">?)1:/!~$&w"()1\]>?!~*-,IM5$&\"%E©V;=)1:<"(ECV$&>>?$&35\:<"($&*-CV)1>$&35\]:"%$B*-Ca a a
L\*-97)1!#!#)1!#z©M5)1$&3:¨\]:/;=*->?6D[*-$B!#!#*- L\p*-97)1!#!a}=E/){L\*-97)1!#!G*-,©97*-2&*-/$&H:"%$&*-6lm)
!#'LL*-!#)16|2B)1:<;=!#6='/;=)1\+9A*-!#"%:/"9A*-;=$&"%$B*-/!#6"(*Ç)1!#"(:<M52&$B!#E/>?)1"*-,:9AE:<\:<97"()1\]$&!#h
"%$B9IL*-L'2&:"%$&*-;=)1/!#$B"%476 +o6x '>?M5)1\C*-,$&;r$BN$&;=':2&!)1/97*-'/"()1\)1;$&t:'/$B":<\p)1:f$B
:<Ø$B/!#"(:<""($&>)K97'"%z%6lmE/$&97E $&!0"(E/)1X:m[*-$&!#!#*- N:\]$B:<"()~x §=ñ|a+g/a z#aIÊØ)¨:<\p)16DE/*-lKh
)1N)1$6D,%*-\97)1;X"%*)1!#"%$&>:<"(){"%E)¨;=)1/!#$B"%4Ç'!#$B/3Ç*-M5!#)1\]NO)1;¥:M5'/;=:/97)16 ¼ 6x%:K/'>M5)1\
*-,/,%*-!#!#$&2&$&H)1;$B/;=$&NO$&;=':<2&!u)19A*-'"%)1\p)1;$&m:+!#:<>L2&)1;N*-2&'>)G*-,D!#)1;=$&>?)1"%6_\p)1L$1h
!#)1/"($&/3:G\p)1:<!#*-:<M52&4f!#E/*-\""($&>?)$&/"()1\]NO:2lmE)1\)9A*-;r$B"%$&*-!C:<\p):<2&>*-!#"59A*-!#"%:/"(z 6
lmE/$B9AE¨$&!/PR'!#"5"%E);=)1/!#$&"(4Ö2&"()1\)1;t"(E/\p*-'35E¨"(E/)L\p*-9A)1!#!#)1!|*-,/!#)1;=$&>)1/"(:<"($&*-Kx%>?:L!
"%$B>?)16_*-/"(*:G!#)1;r$B>?)1/"O"(E/$&975/)1!#!#z 6NO*-2&'>?)!#:>?L2&$B/3~x >:<L!©"($&>)16:\p)1:<6o:/;t!#)1;=$&h
>?)1"%:"%$B*-K\]:"()*-/"(*~N*-2B'>?)1z 61:/;t,%*-!#!#$&2&$&H:"%$&*-¨x >:<L!©!#)1;=$&>)1/"(:<"($&*-¨N*-2B'>?)
Ö2&"()1\)1;Ç;=)1!#$&"%4*-"%*t:M5'/;=:<9A)1z a ·r*-2B'>?)0!#:>?L2B$&/3tE:<!:NO)1\]4t!#>:<2&2/>?)1:!#'\)1h
>?)1")1\\*-$61lmE/$B9AEm>:<4~M5))1!#"($&>?:"%)1;M54~"%E)m*-\]>:<2-;=$&!#"(\]$BMO'"($&*-m,%\*->¸\p)1L)1:<"()1;
>?)1:!#'$1>)1/"(!n5lK)"%\4t"%*t!#:>?L2B):9A*-!#"%:/"rNO*-2&'>?)165"(E/)!#"(*-9AE:<!#"($&97$&"(4$B!I$&/"(\p*-h
;='9A)1;MO4K*-'\$&:<M5$&2B$&"%4K"%*m;=*¨$&"L)1\],%)19A"(2&4aO@)1;=$&>)1/"(:<"($&*-\]:"%)16 76-$&!I!#'LL*-!#)1;Ç"(*
M5)097*-/!#"(:<"%65M5'"'/5/*-lKCnlm)09A:*-/2&4tL'"=\p*-'3OE2&$&>$&"(!I*-$B"rh=E)1\)16-'$&, *-\>
;=$&!#"%\$&M5'"%$B*-w$&!¨'!#)1; x §=ñ|ag/a S<z 6|MO'"$&,I"(E/)1\p)$B!¨!#*->)L\$&*-\$&/,%*-\]>:<"($&*-w:MO*-'"
"%E)f!#)1;=$&>)1/"(:<"($&*-\]:"()16<$&"/>?'!#"M5)G$&/97*-\]L*-\:<"()1;?E)1\)Oa ÊØ)G)1N)1t;=*{/*-"!#"(:<"()G"%E:<"
'/$&,%*-\]> ;=$&!#"(\]$&M5'"($&*-$B!"(E/)0L\p*-L)1\©'$&/,%*-\]>?:"($&N)fL\]$&*-\uE)1\)Oa§=d:9A"(2&4m"(E/)+!#:>?)
E/*-2&;=!u, *-\"%E)+,%*-!#!#$&2&$&H:"%$&*-K9AE:<9A)1X6 à|x §=ñ|a_g/a S<Tz#aAÞ2B"%$&>:<"()12&476<"(E/)G97*-/"(:<>$&/:"($&*-t$&!
:<2B!#*{>*-;=)12&)1;$Bt:0!#$&>$&2&:\©lm:4A69A*-!#$&;=)1\]$&3K*-2&4K2&$B>?$&"(!"(*~9A*-"%:>?$&:<"($&*-$&"%)1h
!#$&"(4¨:\)®5/*-lm¯-:fL\$&*-\]$ba
B[\p*-M5:<M5$&2B$&"%40"%E)1*-\]4$&!/*-"(E/$&3{M5'"-97*->?>*-K!#)1/!#)\)1;='97)1;¨"(*97:<2Bh
97'2&:<"($&*-¯
y=:<L2B:<97)
Ä
ôõó
ÅÑ÷ÇÆ )?ø*/1+.-pÆnÈ
Ç"(E/)~L\p)1N$&*-'!!#)197"($&*-Çlm)~E/:NO);r)1\$&NO)1;Ø"%E){L\p*-M5:<M5$&2B$&"%4;=$&!#"(\]$&M5'"($&*-Ø*-,:M5'/h
;r:/97)ux §=ñ|aQgDa SY<z a7%"!#E/*-'2&;¨M5)972&)1:\/M540*-lì"%E:<""(E/)u\p)12&:"%$&*-0MO)1"(lm)1)1:M5'/;=:<9A)
x *-M5!#)1\]NO)1;=z:<;?L*-L'2&:"%$B*-;=)1!#$&"%4Kx )1/97*-'/"()1\p)1;$&)197*-2&*-35$&97:<2O>?*-;=)12&!#6:/;*-, ´
h !Fd Épn"&
"%)1Ç2B*-*-O)1; , *-\$&ÇL:2&)1*-)19A*-2B*-3O45z©$B!+*-"©:{!#"%\:<$&35E"%,%*-\]lm:\;Ø*-)Oau8M5';r:/97)$&!G: `C H
\)1!#'2&"5*-,:9A*->L*-'/;L\*-97)1!#!#61lm$&"(EK;=)1/!#$B"%4M5)1$&3{*-2&4~*-/)*-,O$&"(!CL:<\:<>)1"%)1\!aQ "
!#E/*-'2&;MO)!#"(\p)1!#!#)1;tE/)1\p):<35:$&K"(E/:":M5'/;=:/97)I:<;;r)1!#$&"(4¨$&!u*-"/"(E/)!#:>?)16_:<;
"%E){"(lm*t"()1\]>!+!#E*-'2&;X/*-"|MO);=)12&$BMO)1\:<"()12&4t>$&d)1Ë; Ê> d0!dSm!ût `C H?ÉE/*-lK)1N)1$6_, *-\©"(E/)GL:2&)1*-M5$&*-2&*-35$&!#"(6<$&"$&!u:<9797)1!#!#$&M52&)*-/2&4¨N$B:f:M5'/;=:<9A)Oa
Ä $ô ' ÅÑ÷ÇÆ ý (%Æø*+.(*/,+.ÿÈ
JC'2&)1!*-,fL2&:'!#$&M52&)X$&/,%)1$19A)Ç"(\]:97)ØMO:97 "(* «m)1\p*-;r*-"('!#6:\*-';×UZZ s=FI6ulmE*
!#"%:"%)1;n®8;=)197$&!#$&*- lm:<!+lm$&!#)16=)1NO)1Ø"%E*-'35E $&"C2B)1;"%*;=$&!#:<!#"(\p*-'!f97*-/!#)1ñ5')1/97)1!#6
$&,"%E)G)1N$&;=)19A)G:"/E/:/;$&/;=$&97:"%)1;$&"DlK:<!u"(E/)+MO)1!#"*-/)+"%*{>?:5).E:/;"%E)G;r)197$&!#$&*-
lm:<!u,%*-*-2&$&!#E/6)1NO)1m"%E*-'35Em$&"/2B)1;"(*~"%E)GE/:LL$&)1!#"L*-!#!#$BMO2B)+97*-/!#)1ñ5')19A)1!#6<$&,/$&"lm:!
'/\p)1:<!#*-:<M52&)"(*~)1dL)197""(E/*-!#)G97*-/!#)1ñ5')1/97)1!a ¯x @$&NO$&:+S<iiY<6oLaoz # S<.T %#aoJC)1L2&:9A$B/3
B;=)19A$B!#$&*-/¯5lm$&"(EB$&, )1\p)1/97)1¯B645*-'E:<NO)f:f2&*-35$&97:<2O:<LL\p*-:9AE¨"%*¨"%E)f!#'MoPR)197"D"(E/:"Dlm:!
>?:;r)tM54Xs=:<45)1!x%S<jY<T
z # Sj % 6|:<; y=:L2&:9A)mx%S<S<
z # ?*-!#", *-\p35*-"%h
"%)1Ø,%*-\/)1:\]2B4ST<Z{45)1:<\!"%*M5)\)1;=$&!#97*-NO)1\)1;ØM5Ì
4 )1,(, \p)14O!x Si<Ti<z # jD %%g6 %:<45/)1!#6:<;
*-"%E)1\]!a
}rE)!#97E/)1>?)0*-,;=)1;='9A"($&NO)02&*-35$&9+$&!I"(E/'!n35$&NO)1:{97:'!#)16-lm)97:<$&/,%)1\$B"%!97*-/h
!#)1ñO')19A)1!a=ÊØ)165:<!IlK)12&2/:!I*-"(E/)1\!#97$&)1"%$&!#"(!;=*m, \p)1ñ5')1/"(2&476O,%:<97)0E)1\)f"%E)\p)1N)1\!#)On
0m& FS Cm&&NnD_n!&'ÍFn"& ÎwÉS*m&!¡m&¡"&d&H "!
Í&!dÎCIÏ }=E/$B!$&!u:m$&;r'97"($&N)2B*-3O$B9A6:0L2&:'!#$&M52&)$&, )1\p)1/97)Oa
FI*-d¨x%S<igY<zû# T<Y=% lm*-\O)1;Ø*-'"r"(E/)ñ5':/"($&"%:"($&N)0\'2&)1!*-,|97*-/!#$&!#"()1/"r2&*-35$&97:<2\)1:h
!#*-/$&3a_«m),%*-'/;t"(E/:"59A*-!#$&!#"%)19A4~97:<{*-/2B4{M5))1/!#'\p)1;m$&,O:<>*-'/"(!©*-,*-'\rM5)12&$&)1,
Ti
É&m!
¾JI2K L ÁÂNMbÐQ{Â=Ã=ÁTRK~ÁTR%ÀjiPU0ÂrÀKÃTR#ÁPÑ
g<Z
$&mNO:<\$&*-'!uL\*-L*-!#$B"%$&*-!97:<¨M5)+>:<LL)1;"(*~:<*-"%E)1\C!#)1"/*-,D\p)1:<2<L*-!#$&"($&N)+/'>M5)1\]!
lmE/$B9AEt*-M5)145)1;"%E)+'!#':2-\p'2&)1!u*-,/L\p*-MO:M5$&2&$&"(4{"%E)1*-\]4|n
`!Õó¡d&!DÏm&`
b!F
x U/a S<z
» Ú ÄÒ ¼ ¾ ¡Ç Ý » Ú Ò ¼ ¾ ½ :/;
x U/a <z
» Ú Ä Ò #pÓ ¼ ¾ Ç ½,» Ú ÄÒ ¼ ÓÔ#p¾ Ç§r » Ú Ä Ó ¼ ¾ Ç
«m)1\p)16 ;=)1/*-"()1!G"%E)~L\*-L*-!#$&"($&*-Ø"(E/:" $&!G"(\')16 ;=)1/*-"()1!+"(E/)~L\p*-L*-!#$&"($&*-
Ò *-"()"%E:<":2&2O"%E)0L\p*-M5:<M5$&2&h
"%E:<" $&!,%Ò :<2&!#)16¼ ¯®>?)1:/!I®35$&N)1¯B6-:/;Ç®6 ¯\p)1:<Ò ;=!uB:/;=¯am
Ò
$&"($&)1!:<\p)097*-/;=$&"($&*-:<2D*- ¾ 6OlmE/$B9AE;r)1*-"%)1!:2&2\)12&)1NO:/"M5:<97535\*-';Ø$&/,%*-\]>?:"($&*-
:<"-E:<;a1}=E)1\)$&!©/*0:<M5!#*-2&'"()IL\p*-MO:M5$&2&$&"(4:"-:<2&2<xw% )1,%,%\)145!=S<iTi0# j.%1E FI*-d+Si<gY# T<YD%E
@$&NO$&:Si<iYW# ST.%E :45/)1!ISi<igW# j<j.%% zCrÊ ¤5\p*-> "(E/)0!#'>¹:/;ÇL\p*-;='9A"\p'2&)1!x §=ñ5!aDUDa S6
UDa z 6-!#)1NO)1\]:2/'!#)1,%'2D\)1!#'2B"%!97:<M5);r)1\$&NO)1;a=8>?*-3"(E/)1> 6"(E/)~>?*-!#"|'!#)1, '2D:\p)
"%E)Gsr:45)1!#¯"(E/)1*-\p)1>
x U/a T<z
» Ú Ä Ò ¼ ËÓ #¾ Ç ½ » Ú Ä Ó ¼ » Ò #pÚ ¾ Ç§Ó r ¼» ¾ Ú ÄÒ ¼ ¾ Ç
Ä Ç
:/;>?:\35$&:<2&$B!#:<"($&*-
@B×
x U/a g<z
» Ú ÄÒ ¼ ¾ Ç ½)Ö T× » Ú Ä Ò #Ó ¼ ¾ Ç + Ó
}=E/)$B>?L*-\]"(:/97)0*-,rsr:45)1!#¯5"%E)1*-\)1> , *-\uL2&:'!#$&M52&)f$&/,%)1\)19A)fx $&;r'97"($&N)f2&*-35$&97z
M5)19A*->)1!:LL:\)1"OlKE/)1mlm)Glm\$&"() ¼ » ÊgE!ßN©! , *-\ # :<;Q+ Ê ,%*-\ Ó n
Ò
ðð
» Ú Ä ¼ » Êg !ß"!¼S+ ð Ê ð #¾ ÇØ » Ú Ä + ð Ê ð ¼S ¼ » ÊE!ß"! #p¾ ÇËr » Ú Ä ¼ » ÊgE!ßN!x U/¼ ¾a U<Ç z
*-\
» !Ê"Dß » Ú ð Ú ß º ßäÊ ¼ Ø
º ß ï º ß" E +¥Ù a eNàGÊ$ß e r » Dß » Ú ð Ú ß º ßÊ ¼
óNd!_!F x U/a Y<z
FI*-\p*-2&2&:\]4{UDa T6<U/a U<6UDa Y+)1/97:<L!#'2B:<"()1!u"%E)fL\p*-9A)1!#!*-,$&, )1\p)1/97)On_$&"/\)12&:"()1!"(E/)+L\p*-MOh
:<M5$&2B$&"%4 "%E:<""%E)E45L*-"%E)1!#$&!m$&!{"%\p')3O$BN)1w"(E/);=:<"(:<6"%* "%E)L\p*-M5:<M5$&2B$&"%4 "(E/:"Ilm)
lm*-'2&;XE/:NO)*-M5!#)1\]NO)1;Ç"%E);=:<"(:lm)1\p)0"(E/)E/45L*-"(E/)1!#$&!G"(\')Oa}=E/$&!$B!I"%E)L*-lm)1\*-,
s=:<45)1!#¯-"(E/)1*-\p)1>wa-m*-"%)f"%E:<"/"%E)0)1ñ5':<2B$&"%4K*-,r§=ñ|a-UDa T0lK:<!\)1L2&:97)1;M54mL\p*-L*-\]"($&*-h
:<2B$&"%4¨$&t§=ñ|aUDa U&E<"(E/$&!$&!Ö/)+, *-\CL:\]:>?)1"()1\)1!#"($&>?:"($&*-/6!#$B/97)f"(E/)+*->?$&"("()1;?;=)1/*->h
$&/:"(*-\$B!:/*-\>?:2&$&H:<"($&*-97*-/!#"(:<"%6-*-"r;=)1L)1;r$B/3m)1d<L2&$&97$&"%2B4m*-"(E/)fE/45L*-"(E/)1!#$&!
x @$BN$&:S<ii<Yr# S<T.%%z#a s=:<45)1!#$&:L\p*-MO:M5$&2&$&"(497:<~"('\]~"(E/)I§=ñ|aQgDa SYI$&!#$&;=)*-'"5"%*0\)1NO)1:<2
"%E)GL\*-M5:MO$B2&$&"(4{;=$&!#"(\]$BMO'"($&*-t*-*, Ú 6_"%E)GL*-L'2&:<"($&*-t;=)1/!#$B"%4a
M
Ä $ô Û,+EÜøþ.+1÷?ü~ü0) °,/13-.+1ü0/
ÊØ)!#E:<2&2'!#):<M5'/;=:/97)L;=,-:!|"(E/)2&$&5)12&$&E*-*-;t, '9A"($&*-~, *-\=)1!#"($&>?:"%$B*-{*-,5;=)1/!#$B"%4
L*-!#"%)1\$&*-\IL;=,©,%\*-> §rñ|auUDa Y/aC}=E'!#6Dlm)~/)1)1; "%*;=)1\]$BN)"(E/){:<M5';r:/97)L;=,Ö\!#" a
ÊØ)Glm$&2&2-'!#)G§=ñ|a_g/a S<&Y E1E/)19A)16_'!#$&3KL\p*-;r'97"O\'2&)Gx%§rñ|aoU/a z#n
» Ú Ä ¼ ¼ à # #p¾ Ç ½ ¼ g g ¼ g à Ä Â à Ç pR Ä Â Ç
x U/a j<z
ÐQ«±&QSLuMR%¿ MUrR%Ã=ÁTMRwvcVÁTR ¿ÀmÃ
gS
» Ú Ä ¼ # à¼ #¾ Ç ½Ý» Ú Ä ¼ ¼ à # #¾ ÇÞr » Ú Ä àf¼ ¾ Ç ½ ¼ g g ¼ g à Ä Â à Ç R r à{| àCz
Ä Â Ç
Â x%UDa z
²
ß @ àËá K á y e R ¿ÀXÁ c ß @ à§á K á y e
c
x%UDa iz
~ ² g Â ~
» Ú Ä ¼ # à # ¼ # # #p¾ Ç ½Ã² » Ú Ä ¼ # à¼ #¾ ÇÞr
» Ú Ä ¼ # à # # ¼ # # #p¾ Ç ½,» Ú Ä ¼ # à # 4¼ # # # #p¾ Ç§r | z x U/a S<Zz
Â ²
²
²
» Ú Ä ¼ # à # # # ¼ # #p¾ Ç ½,» Ú Ä # à # # ¼ # # #p¾ Ç¥r É Þ jSÀ ¿ÀXÁGÁ Â Ä Âj&É ÆPyÇ È
yÈ x U/Â a SASz
²
²y
» Ú Ä ¼ # à # # # # ¼ #p¾ Ç ½,» Ú Ä ¼ # à # # # ¼ # #p¾ Ç§r | {z x U/a S<z
Â
²
²
» Ú Ä ¼ # à # # # # # ¼ ¾ Ç ½Ý» Ú Ä ¼ # à # # # ¼ # #¾ ÇÞr É Þ jEÀ ¿ÀXÁGÁ Â Ä ÂfjÉ ÆT~.ÇÈ
~È x U/a ÂS<Tz
~
¤O\p*->¬>:<\p35$&/:2&$&H:<"($&*-¨x ² §=ñ|a1U/a g<zlm)E/:NO)On
²
@B×
» Ú Ä ¼ # à # # # # j¼ ¾ Ç ½ Ö ¾ » Ú Ä ¼ # à # # # # # ¼ ¾ Ç +
²
²
@B× @B×
» Ú Ä ¼ # à # # # ¼ ¾ Ç ½ Ö ¾ Ö ¾ » Ú Ä ¼ # à # # # # ¼ ¾ Ç + +f
æææ
:<;r6_Ö:<2&2B4
²
²
@B× @B× @B× @*× @B× @B×
» Ú Ä ¼ ¼ ¾ Ç ½ Ö ¾ Ö ¾ Ö ¾ Ö ¾ Ö ¾ Ö ¾ » Ú Ä ¼ # à # # # # # ¼ ¾ Ç + +f+ + +Y*+
à
x U/a S<gz
Ä ôN m?û+1ü~ûf)1+.-1û+]ý,-.+1ü0/1
7u5 65 4 â[BCüN?
A~<HBC> _?
9?
Z
AHZ
9
, ¾ $&;=$&9A:"()1!35\p*-!#!$B3O*-\]:/97)f:M5*-'"D"(E/)G!#$&"(':<"($&*-/6*-"%E)1\C"%E:<m:0O*-lm2&)1;=35)f"(E/:"
"%E)0L:\]:>?)1"()1\hã L)1\"%:$&!"(*K2&*-97:"%$&*-6"(E/)19A*-!#$&!#"()1/974m;=)1>?:/;=!"(E/:"D"(E/)fL\*-M5h
:<M5$&2&$B"%4 ;=)1/!#$&"(4 ,%'/97"%$B*-x L;=, z, *-\'×
ã !#E*-'2&; /*-"97E/:/35)lm$&"(E"(E/)NO:<2&')t*-,"%E)
*-,%,%!#)1"%6 ¾ ao}=E/$&!9A:KM5)Glm\$&"%"()1m;=*-lmm:!
Å
g<
x U/a S<Uz
» Ú Ä Ò ¼ ¾ Ç + Ò ½,» Ú ÄÒÝøÅ ¾ ¼ ¾ Ç + ÄÒÝÅ ¾ Ç
@$&9A) ¾ $&!u:f9A*-!#"%:/"(6+
Å
Ä Ò ÝøÅ ¾ Ç ½ + Ò 6_"%E'!
x U/a S<Yz
» Ú ÄÒ ¼ ¾ Ç ½ à eB!ÊCä
FI*->L2&)1"%)$&35/*-\:<9A):MO*-'"<: & / $B!|\p)1L\)1!#)1"%)1;M54f"%E)'$&, *-\>
L;=,#a
7u5 65 7 Y=üN?
».Z@_?
9?
Z
A.Z
9
@97:<2&)L:\]:>?)1"()1\]!:\p)"%E*-!#)K:!#!#*-9A$&:"()1; lK$&"%EX:¨!#$&H<)16*-\>?:35/$&"(';=)Oa ,ClK){\p)1:2&2&4
E/:N)K/*Ø$&;=)1::<M5*-'"u"(E/)t!#97:<2&)¨$&/NO*-2&NO)1;=6"(E/)tL\]$B*-\fL;=,>?'!#"MO)K$&/NO:<\$&:/"ulm$&"(E
\)1!#L)197"/"(*{!#"%\p)1"%97E/$B/356*-\C!#E\]$&O$B/356-*-,D"(E/$&!!#9A:2&)Oa<FIE:<35)f*-,>)1:<!#'\p)1>?)1"/'/$B"%!
>?'!#"D>:<5)+/*{;=$&,%,%)1\)19A)"%*{"%E)f:!#!#$&35/)1;L;=,#aÊØ)+97:<mlK\]$&"()f;=*-lmt"(E/$B!\p)1ñO'$B\)1h
>?)1"/*-,D97*-/!#$&!#"()1/974K:!
x U/a S<jz
» Ú Ä Ò ¼ ¾ Ç + Ò ½,» Ú Ä í Ò ¼ ¾ Ç + Ä í ÒfÇ
lmE)1\)_íÇ$&!G:¨L*-!#$B"%$&NO)~9A*-!#"%:/"]a©@$&9A)x+ í ½ íB+ 6O$&"97:<*-/2&4M5)!#:<"($&!#Ö)1;
Ä Ç Ò
M54
x U/a S<z
» Ú ÄÒ ¼ ¾ ÇØ h Ò
}=E/$&!L\]$&*-\u$&!9A:2&2&)1;:ËåG d&!HÏH&Q a5%"lm:!!#'3535)1!#"%)1;ÇM54j%)1,%,%\)145!Cx%S<iT<iz 6:/;
$&"\p)1L\p)1!#)1/"(!9A*->L2&)1"%)$&35/*-\:<9A):MO*-'""%E)N:2&')*-,:?!#97:<2B)tL:<\:<>)1"%)1\oa%"I$&!
)1ñ5'$&N:2&)1"/"(*{:+'/$B, *-\]>qL;=,, *-\"(E/)G2&*-35:\]$&"(E/>q*-, x @$&NO$&:+S<iiY@# S<T.% z n
Ò
» Ú Äwº ÄÒfÇ ¼ ¾ Ç ½ à eB!ÊCä
øû+EæS(*-.1+ ü0/
Ä ôÄ
ÊØ)G!#E/:2&2-!#"%:\]"O, \p*->¬"(E/)Gs=:<45)1!#¯<"%E)1*-\)1>6:!u35$&N)1K$&m§=ñ|a_U/a UDn
» Ú Ä ¼ » Êg !ß"!¼S+ ð Ê ð #¾ ÇØ » Ú Ä + ð Ê ð ¼S ¼ » ÊE!ß"! #p¾ ÇËr » Ú Ä ¼ » ÊgE!ßN!¼ ¾ Ç
Þ!#$&3 §=ñ|aKUDa Sg:<!"(E/)t2&$BO)12B$&E/*-*-;=6C:/;, )1,(, \p)145!#¯L\]$&*-\x%§=ñaKU/a S<zu, *-\f:<M5'/h
;=:<9A)16_lm)35)1"/"(E/)GL*-!#"()1\]$&*-\L;r,, *-\Ë+ n
M
²
²
× × × × × ×
» Ú Ä + M ¼ ¼ #¾ ÇØ Ö ¾ Ö ¾ Ö ¾ Ö ¾ Ö ¾ Ö ¾ » Ú Ä ¼ # à # # # # # ¼ ¾ Ç + ++ + +f%+à r ¼ x U/a S<iz
Ä Nô ç èOÿ
ùþ1øÿ½ø*/,-.(*-.+1ü0/
«m:N$&3;=$&,(Ö97'2&"%$B)1!lm$&"(EØE/:/;=2&$&3?§=ñ|auU/a S<i~M5*-"%EØ:/:2&45"($&9A:2&2&476O:<; '>?)1\]$B9A:2&2&4
x ;=')"(*!#$&df/)1!#"()1;t$&/"()135\]:"%$&*-!#z 6_lm)I\p)1!#*-\]"()1;t"(*!#$&>?'2B:<"($&*-Ca_ÊØ)I'!#)1;t§=ñ|a_g/a S<YI:!
:35)1/)1\:<"(*-\C*-,="%E)02&$&5)12&$BE/*-*-;Ø, '9A"($&*-©a5¤5*-\u"%E$&!IL'\L*-!#)16lm)+, )1;?$B":<M5'/;=:/97)1!
, \p*->q:'/$B, *-\]>¦;=$&!#"(\]$&M5'"($&*-3O)1)1\]:"%*-\]a-}rE)f'LL)1\u:/;2&*-lm)1\u2&$&>$&"%!*-,="%E)0'/$Bh
, *-\>¹;=$&!#"(\]$&M5'"($&*-Çx *-,r;=)1/!#$&"($&)1!#z|lm)1\)03O')1!#!#)1;X$&?"%E)>?://)1\*-,97'"%"($&3Oh%*-,%,r"(E/)
ÐQ«é&QSRFLus=ÂNÂ=ÀXÁDK~ÁTR ¿À
gT
H<)1\p*~"%:$&2&!u:, "()1\"(E/)GL\)1NO$&*-'!u!#$&>'2&:<"($&*-lm$&"(Etlm$&;=)1\|\]:/35)Oa8!u"(E/)G'2&"($&>?:"%)+35*-:<2
lm:<!C\:<"(E/)1\r"(*3O)1)1\]:"%)L2&:'!#$&M52&);=)1/!#$&"($&)1!#Y6 + 6"(E/:{"%*:!#!#)1!#!C"%E)1$&\rL\*-M5:MO$B2&$&"($&)1!#6
lm)K!#:>?L2&)1;¥"%E)K;=)1/!#$&"(4ÇL;=,C, *-\"(E/$B!L'\]L*-M !#)Oa}=E/)K;=)1!#$&"%4?L;r,C$B"%!#)12&,ulm:!0*-M5h
"%:$&/)1;Ø,%\*-> §=ñ|aDUDa U6'!#$&/3"(E/)35)1)1\]:"%)1;Ç2B$&5)12&$&E/*-*-;X,%'/97"%$&*-65:<;Ç"%Eê
) )1,(, \p)145!#¯
L\]$&*-\©,%*-\©:MO';=:<9A)Oa
» Ú Ä + M ¼ ¼ #¾ ÇØ.º ß ï º ßN E + æ ¼ x U/a <Zz
}rE)K;=)1/!#$B"%4ØL;=,ux $&X,%:<97"%6="(E/)¨;r)1!#$&"(4Ø9A;=, zClK:<!'!#)1;¥:<!f:tL2&:<'!#$BMO2B)K;=)1/!#$&"(4
N:2&')1!35)1/)1\:<"(*-\1nu:\:<;=*->¶NO:<\$&:"%)mE:<NO$&3Ø"%E)t!#:<>)mL;=,:!"(E/)t;=)1/!#$&"(4Xlm:!
*-MO"(:$&/)1;NO$&:G"%E)I$&/NO)1\]!#)"(\]:/!#,%*-\]>¸>?)1"(E/*-;=6_M5)19A:'!#)I"(E/)1\p)I$&!©:G*-/)1h%"%*-h%*-/)>:<Lh
L$&/3XM5)1"%lK)1)1¥"(E/)m97'>?'2&:"($&N)tL\p*-M5:<M5$&2B$&"%4Ø;=$&!#"(\]$BMO'"($&*- :<;w"%E)t\]:/35) # Z6 S % a "
9A:KM5)I!#E*-lmt"%E:<"OM54"%:5$&/3{:G'/$&,%*-\]>\]:/;=*->Ò'>?M5)1\$&¨"%E$&!u\]:/35)I:/;Ö/;=h
$&/3¨$&"%!C97*-\]\p)1!#L*-/;=$&3¨97*-*-\p;r$B/:"%)$&K"%E)9A'>'2&:<"($&NO)L\*-M5:M5$&2&$&"(4~;r$B!#"%\$&M5'"%$&*-tlK)
*-MO"(:$&t!#:<>L2&)1!Clm$&"(Et"(E/)G;=)1!#$&\)1;tL\p*-M5:<M5$&2B$&"%4~;=$&!#"(\]$&M5'"($&*-Ca
0.0012
0.0025
0.001
0.002
0.0008
0.0015
0.0006
0.001
0.0004
0.0005
0.0002
0
200
400
600
800
1000
1200
1400
0
200
1600
0.006
400
600
800
1000
1200
1400
1600
1000
1200
1400
1600
0.035
0.03
0.005
0.025
0.004
0.02
0.003
0.015
0.002
0.01
0.001
0
200
0.005
400
600
800
1000
1200
1400
0
200
1600
0.25
2.5
0.2
2
0.15
1.5
0.1
1
0.05
0.5
0
200
0
200
400
600
800
v %´5rp&w£&w w «m$&!#"(*-35\]:>?!2&)1:;r$B/3K"(*K;=)1!#$&"%4KL;r,/)1!#"%$&>:<"()1!, *-\ é 6 ê 6 ë 6 ë 6
fì 6:/; í $&"()1\]:"%$B*-/!a-[:<\:<>)1"%)1\©!#)1"("($&/35!lK)1\)On ÆPy ½ ä 6XÉ y ½ ä f / 6
400
600
800
1000
1200
1400
1600
400
600
800
1000
1200
1400
1600
g<g
}z ½ ä fî 6f| ½ ä jQ6
àCz ½ ä /Yï 6Xà}| ½ ä ïï 6 z ½ ä 6 | ½ ä 6 TÆ ~ ½ ä f 6
É ~ ½ ä 64+ Ë ½ f a78MO';=:<9A)lm:!uU<ZZ/a
}=E/)Ö35'\)1!~!#E/*-lèE/*-lê"(E/))1!#"($&>?:"%)*-,;=)1/!#$B"%4 L;r,, *-\:M5'/;=:/97)tx UZ<Z$&>h
L\*-NO)1!lm$&"(E$B/97\)1:!#$&/3¨/'>MO)1\u*-,$&"()1\]:"($&*-/!a- "D:LL)1:\]!u9A2B)1:<\C"(E/:"DSZ0ZZ<Zf$&"%)1\:<h
"%$B*-/!:\)f$&/!#',(Ö9A$B)1/"·/E lm)\p)197*->?>?)1;Ø"%*t'!#):"=2&)1:!#" ë $B"%)1\:<"($&*-/!a=[:<\:<>)1"%)1\!
lm)1\p)0!#)1"r"%*m Z/a Z<S Ø Z/a ZZZ<g $ é *-,r!#:<>L2&$&/3NO*-2&'>?)16O!#)1;=$&>?)1"%:"($&*-?\:<"()0*-,rZDa ZZ<0h
ZDa ZS< $ æ Û 61,%*-!#!#$&2&$&H:"%$&*-K9AE:<9A)*-,ZDa gUhZ/a U<U619A*- "%:>?$B/:"%$&*-K$&/"()1/!#$&"(4{*-,/Z/a ZS
h/Z/a Z<U61>?)1ð :m;=)1/!#$&"(4{, *-\97*-/"(:>?$&:<"($&*-t"(*¨SZ<ZZ $ a
È
çôõó ÅÑ÷ÇÆ -1ü~ù?ü~þ1ükÞÆòü0/?þpÆnÈ
¤O\p*->¬"(E/)G;=$&!#97'!#!#$&*-t*-,/\p)12&)1NO:<"O>*-;=)12&!u*-,D"%E)G@JC¤~*-t:<¨'/$&;=$&>)1/!#$&*-:<25)1/NO$&h
\*->?)1/"(:235\]:;=$&)1/"/$&@)19A"($&*-/a T0$&"DM5)19A:>?)+972&)1:<$6"(E/:""(E/)+!#:<"($&!#, :97"%*-\4K"(E/)1*-\p)1"%h
$&9A:25>?*-;=)125*-,ñ5':<"%$&"(:"%$&NO)+/$&97E/)+'"%$B2&$&H:<"($&*-/6:<!u\p)1L$1!#)1"%)1;M54K"(E/)+@JC¤56E:<!/*-"
MO)1)1{;=)1N)12B*-L)1;K:/;mL'M52&$&!#E)1;t45)1" aQ@)1NO)1\]:2_>?*-;=)12\p)1NO$&)1lm)1;K:M5*-N);=$&,%,%)1\$&{"%E)
!#E/:L)f*-,D"(E/)+@JC¤ E/)1NO)1\]"(E/)12&)1!#!#6<"%E)+"(*-L*-2&*-35$&97:<2OL\p*-L)1\]"($&)1!u*-,D:<2B2-"%E)f>*-;r)12B!:\)
9A*->>?*-Cn©@JC¤?!#E/*-'2&;M5){:m, '9A"($&*-X!#"(:<\"%$&3?:"©H)1\*-6D"(E/:Ø$&9A\p)1:<!#$B/3?"(*?:¨!#$&/h
3O2B)L)1:<mFx x>?*-;=)1z 65:/;Ø;=)197\)1:!#$&/3K"%*tH)1\*¨:<,%"%)1\lm:\;=!a/}=E/$&!97*->?>*-ÇL\p*-L)1\]"(4
2&)1;w"%E)tL\)1!#)1"u:<'"(E/*-\+"%*Ø"(E/)t$B;r)1:t"(*ØB"(E/\p*-lª:lm:4O¯=:2&2©$&\\)12B)1N:/"C$&, *-\>?:"%$&*-
9A*-!#$&;=)1\]$&3w"%E)?@JC¤w!#E:<L)16u'!#$&3w$&"%!¨"%*-L*-2B*-3O$B9A:2L\p*-L)1\]"($&)1!{*-/2&4a }=E/'!#6"%E)
L\)1!#)1"©>?)1"(E/*-;*-,u\p)19A*-!#"%\p'97"%$&*-XFx x$&/;=$&\p)19A"3O\:<;=$&)1":/:2&45!#$&!#zu$&!0M5:!#)1; 'L*-
"%E)f'$&>?*-;=:2&$&"(4K*-,D"(E/)+@JC¤|a Þ2&$&5)+"%\:<;=$&"($&*-/:2->?)1"(E/*-;=!#6<$&"/;=*-)1!/*-"D'"($&2&$&H)G:<4
*-"%E)1\:!#!#'>?L"($&*-/!:M5*-'""%E)@JC¤5!a%"r:"("%)1>L"%!"%*m$B/, )1\u"(E/)97*-\]\p)197"D"%*-L*-2B*-3O4*-,
"%E)f35\]:;=$&)1/":<2B*-/)16"(E/'!\p)1L2&:<97$&3¨!#:>?L2&)G!#97*-\)1!ulm$B"%E!#:>?L2&)G\]:/5!a<}=E$&!lK:<476
"%E)¨>)1"%E*-;*-N)1\p97*->?)1!G/:"%'\:<2B2&4?"(E/)~:\]"($&, :9A"(!G9A:'!#)1; MO4N$B*-2&:<"($&*-Ø*-,C:!#!#'>?Lh
"%$&*-!tx *-,G2&$&)1:<\$&"(4OzG"(E/: *-9A97'\~$& 972&:!#!#$&97:<2)1$&35)1/NO:<2B')1!#h M5:<!#)1; >?)1"(E/*-;=!mx%:<\p97E/h
:<;wE/*-\]!#)1!#E*-)m)1,(, )197"©*-,[F86DFI86/¥¼@zu"%E:<"C:\p)K'!#':2&2&4Ç®\)1>)1;r$B)1;r¯='/:"%'h
\]:2&2&4mx%2&$&5)0$&"(E/)fL*-L'2&:<\u¼F8z#a#}rE)0\p)12&:d:"%$&*-t"(*K"(*-L*-2&*-354t>?:5)1!"(E/)f>?)1"(E/*-;
:<2&!#*~$&;=)1L)1/;=)1/"*-,D"%E)GMO)1"(:+;r$BN)1\!#$&"%4a
çô$' ¯Ñø*(*ûp+./nk ,/,+1ÿ½ü0),(þ.+.-pÆ
8!C!#"%:"%)1;:M5*-N)161'$&>?*-;=:2&$&"(4¨*-,@JC¤5!$B!C"%E)9A)1"%\:<2:!#!#'>?L"($&*-m*-,"%E)35\]:;r$B)1/"
:<:<2&45!#$&!a«m*-lK)1N)1$6="%E)1$¨$&!/*?'/$&ñ5')tlm:4Ç"(*Çñ5':<"%$&,%4Ø"%E)m'/$B>?*-;=:<2B$&"%4X*-,u:
!#)1\]$&)1!I*-,r@JC¤5!IlmE)1?"(E/)'$&>?*-;=:2&$&"(4$&!I/*-"rL)1\],%)19A"(6$ba )Oa 6-lmE)1:2&2/"(E/)0\)1!#L*-!#)
, '/97"($&*-/!I:\p)+*-"!#"%\$&97"%2&4K'/$&>*-;r:2&6:/;V*-\u"(E/)14K97*-/"(:$&!#*->?)0*-$&!#)OaOÊØ)+E/:NO)
;r)1!#$B3O)1;"(E/){>?)1:!#'\)~"(E/:"©ñ5':<"%$&Ö)1!f:mB97*->?L:97"%)1!#!#¯r*-,C:KL:<"("%)1\Ç97\)1:"%)1; M54
:t!#)1\]$&)1!f*-,@JC¤O!#6:/;¥lm)Klm$B2&2"(\]4"%*Ç!#E*-l¹"(E/:"C$&"C:LL\*-d<$&>?:"%)1!#6/*-\+ñ5':/"($&Ö)1!#6
'/$&>*-;r:2&$&"(4Çñ5'$&"()¨lK)12&2ba}=E/$B!f$&!+M5)19A:'!#)~"%E)¨'$&>?*-;=:2=L:<"("%)1\Ç$&!+B97*->?L:9A"(¯D$&
"%E)f!#)1!#)+"(E/:"/E$&35EtN:2&')1!u"()1/;"%*~M5)G9A2&'!#"()1\p)1;"(*-35)1"%E)1\%6lmE$&2&!#"D2&*-lðNO:<2B')1!!#'\ph
\*-';"(E/)1>a
ÊØ)+'!#)1;:K$&;=)1:+*-,/:+"%*-L*-2B*-3O$B9A:252&$&/)1:\)12B:<!#"($&9/)1"(6<"(*~:<LL\p*-d$&>:<"()I"(E/)!#*-2&'h
"%$&*-K*-,D'/$&>*-;=:<2&$B"%4{>?:d$&>$&H:<"($&*-/6_>*-;r)12B)1;:!Clm$&"(E/$Bm/)1"O!#"%\:<$Bm>?$&$&>?$BH<:"%$B*-Ca
gU
kN!F m&
¾JI2K L ÁÂNM:éQ0MCÂ=¾I¿ÀmÃÁXMV¾ÁXR%¿À
g<Y
ÊØ)f$B/"(\*-;='97)+:t$&>:<35$&:<\4K697*->?L2B)1"%)12&4K9A*-/)197"%)1;/)1"(6\p)1L\)1!#)1"%)1;M54K:f9A*->h
L2&)1"()035\]:LECa8!#!#)1>M52&:<35)f!#:<>L2&)1!I97*-\]\p)1!#L*-/;Ç"(*m"(E/)035\:<LEN)1\"%$B9A)1!aÊØ)f$&/"(\p*-h
;='9A)I$B>?:3O$B/:\]4~, *-\p9A)1!C:>?*-3~"%E)N)1\"%$&97)1!#6_L\*-L*-\"%$B*-/:2"%*~"(E/)!#'>*-,/:2&2L\p*-;rh
'9A"(!*-,5;=)1/!#$B"%$&)1!|:<;m$&"%)1\ph NO)1\]"()1dI;=$&!#"(:<9A)1!#6o*-NO)1\=:<2B2!#L)197$&)1!ao}=E/)1!#), *-\p9A)1!r\p)1L\)1h
!#)1/"="(E/)"()1/;=)1/974t*-,r"%E)$&/;=$&NO$&;=':2&!M5)12&*-/35$&3"(*m"(E/)!#:>?)0!#L)19A$&)1!#65"(*m*-979A'L4
"%E)m!#:>?)m97*-/"($&/'*-'!#6'/, \:<35>)1/"()1;/$&97E/)Oa}=E/)m$B/;=$&NO$&;=':<2&!*-,)1NO)1\]4Ç!#L)197$&)1!
L\)1!#)1"$& "(E/)!#:<>L2&)®L'2&2&¯u"(E/)!#:<>L2&)1¯B!{2&*-97:<"($&*- "%* "%E)?\p)1!#L)19A"($&NO)¯BM5)1!#"I$&h
E/:M5$&"%:M52&)L2&:9A)1!#¯<*-m"(E/)35\]:;=$&)1/"(6_;r$B!#"%$&35'$&!#E/)1;M54¨E$&35Em9A*-9A)1"%\:<"($&*-m*-,/*-"%E)1\
9A*-h !#L)197$&Ö9~$&/;=$&NO$&;=':2&!a~y=)1"u"(E/)1\p)K:2&!#*ÇM5)m8¬L)1\>?'"(:<"($&*-,
À6r:!#!#*-9A$&:"()1;lm$&"(E
N)1\"%$B9A)1!f*-,"(E/)m35\:<LE©af}=E/$&!L)1\>?'"(:<"($&*- \)1L\p)1!#)1/"(!f"(E/)KL*-!#!#$&M52&)mx "(*-L*-2&*-35$&97:<2Bz
:<\\]:/35)1>?)1"*-,I"(E/)!#:>?L2&)1!{*-w"%E)35\:<;=$&)1" aÊØ)!#)1:\97E,%*-\"%E)!#"(:"%)*-,"(E/)
/)1"Clm$B"%EX>?$B/$&>'>¶!#"(\]:$&/6$õa )Oa 6!#'97EX:mL)1\]>'"%:"%$B*-Ã
ÀØ"%E:<">?$&$&>?$&H)1!"(E/)¨!#'>
*-,u$&/"()1\h%N)1\"%)1dK, *-\p9A)1!aIy=)1"C"%E)K$&"%)1\ph NO)1\]"()1dm,%*-\97)1!flK*-\]|n©"%E)K/)1"C\p)12&:d)1!G"(*?"(E/)
!#"%:"()¨*-,u>?$B/$&>'>¶!#"(\]:$&/6\p)1NO)1:<2&$B/3"%E'!"%E)¨:!#!#*-97$&:<"()1;¥L)1\>?'"(:<"($&*-F
À6\p)1L\)1h
!#)1/"($&/3"(E/)*-\p;r)1\$&/3*-,|N)1\"%$&97)1!IFx xØ!#:<>L2&)1!#z!#'97E?"(E/:"|$B/;=$&NO$&;=':<2D!#L)197$&)1!"()1/;
"%*t*-9797'L4'$&/"()1\]\p'L"()1;r6O97*->?L:9A"r/$&97E/)1!G:2&*-/3"(E/)L)1\>?'"(:<"($&*-?Fx xØ35\]:;r$B)1/"(z#a
¤5*-\]>?:2&$&H$&3¨"(E/)G"(:<!#{lm)G35)1":m*-MoPR)197"%$&NO)G, '9A"($&*-Cn
"%E'!
lmE/)1\p)
a
Ë ç
ç
à ½ â â â ¼ ñò I× ó ð æ ¼ñò áó ð æ ð ×iá
×å Û á å Û ð å Û
Ë
à ½ â ç â ×iá*æõ ñò ×Ió ñò áó
× å Û á å ÛLô
x Y/a S<z
x Y/a <z
ç
x Y/a T<z
õ ñò ×Ió ñò áó ½ ðâ Û ¼ñò ×Ió ð æ ¼ñ4ò áó ð
å
"%E'!
ç
x Y/a g<z
õ=× á ½ ðâ Û ¼ × ð æ ¼ á ð
å
«m*-lm)1NO)1\%6Q§rñ|aoY/a $&!:~$&/!#"(:<9A)*-,O:*-"%*-\$&*-'!#2&4~5/*-lm{35\]:LE/h%"%E)1*-\)1"($&97:<2_L\p*-MOh
2&)1>?6Q"%E)v':;r\:<"($&9©8!#!#$B3O>?)1"O[\p*-M52&)1>ðx v8[z%6QlmE)1\)*=à $&!|"%E)97*-!#"-, '/97"($&*-/6?¼ ¼
$&!"%E)+;=$&!#"(:/97)+>:<"(\]$Bd6*¼ õ #¼ $&!"(E/)o *-l¸>:<"(\]$Bd6À ß $&!"%E)fL*-!#$&"($&*-*-,D"(E/)+N)1\"%)1d0ô ß
$&m"(E/)GL)1\]>'"%:"($&*-ÌÀ 6:<; ¼ × ð $&!u"(E/)GL)1\],%*-\]>:<9AÄ )Ç *-,!#L)19A$&)1! ï $&m!#:>?L2&)ß a
v8[m$&!\*-'"($&/)12B4'!#)1;tM54*-L)1\]:"%$B*-¨\p)1!#)1:<\p97E/)1\]!="(*;=)1"%)1\>?$&)"(E/)I>*-!#"59A*->h
L:<97"=x $&?!#)1/!#)*-,o *-l 97*-!#"%z|L:<"("()1\]*-,©:<!#!#$B3O$&/3, :97$&2&$&"($&)1!"(*t2&*-9A:"($&*-/6$ba )Oa>?$&h
$&>?$BH<$&3Ç"(E/){"%*-"(:<2=97*-!#"C*-,C*-L)1\]:"%$B*-Ca Ø*-'\G>*-;r)12B6Dlm){!#)1)1?, *-\!#'97EX:Kx%2&$&/)1:\]z
"%*-L*-2B*-3O4K*-,D"%E)f)1"DlmE$&9AEt>$&/$B>?$&H)1!"(E/)+"%*-"(:2-!#"%\:<$&©a<}=E/)1\p)G)1d$&!#"(!:fN:!#"/2B$&"%)1\:<h
"%'\p)97*-/97)1\]/$B/3{"%E)+v8[a
çô$ m?ûOüIýwþ1øÿ °Oü{ûOÿ (þ.+Eö*(*-.+1ü0/
ÊØ)/)1)1;"(E/)L\p*-MO2B)1>"(*~MO), *-\]>'2&:"%)1;:!©:<¨$&/!#"(:/97)*-,/"(E/)v8[6_"%E'!C"%E)G\]:l
;=:<"(:x !#:>?L2&)1;=65*-\35)1)1\]:"%)1;Ø97*-)1/*-972&$&)16!#)1)M5)12&*-lKz>?'!#"|M5)"%\:<!#, *-\>?)1;Ø$&"%*
"%E)mv8[97:<!#)OaÊØ)m)1)1;w"%E)m;=$&!#"%:/97)m:/;w"(E/2
) o*-l>:<"(\]$B9A)1!f"%*Ø,%*-\]>?'2B:<"()m"(E/)
éQ«±&Q?ÁTImÂÌ÷ K LÃ¿ sTøR%Àji K sPi0¿ MR ÁTI2Ã
gj
v8[a-¼0$&!#"%:/97)>?:"%\$&d\)1L\p)1!#)1/"(!"(E/)t$&"%)1\ph !#:>?L2&)t;=$&!#"(:/97)1!*-"(E/)t35\]:;=$&)1/"]a
8!>)1/"($&*-/)1;Ç:M5*-N)16<lm)+9A:\)G:M5*-'"D"%*-L*-2B*-3O4t*-2&4a-}=E'!#6lm)+'!#)0$&"%)1\ph !#:>?L2&)
;r$B!#"%:/97)1!0\p)1L\)1!#)1"%)1; M54Ø"%E)K;=$&!#"(:<9A)1!fM5)1"%lm)1)1XL*-$&"%!0\)135'2&:\]2&4!#L:<97)1;¥*- :
2&$&/)Oa1ÊØ)G!#)1"/;=$&!#"(:<9A)M5)1"(lm)1)1m)1$&35E/M5*-\]!:<\M5$&"%\:<\$&2&4~"(*{S/ao}=E/)G;=$&!#"%:/97)>?:"(\]$&df$&ù
!
"%E'!n
úûû û
ý / ï æææ e Â j e Â e
ûû j
j ýjþ/ý ï æææ e æÂ ææ j ee Â j
ûû ý
j /ý /ï ï æÂ ææ
ûû
x%YDa Uz
½ ûûû / ý ýj j j ýj /ý ï
ô ûûü æï ææ /
ý j j /ý
ï
/
e Â j æææ ï / ý j j
e Â e Â j æææ ï / ý j e e Â e Â j æææ ïÿ/ ý j }rE)[o*-l¸>:<"(\]$Bd0$&!u97:<2&97'2&:"%)1;:!
üú ç ð
x%YDa Yz
õ ½ â× Û áâ Û Å × á[æ Å × ð
å å
¤}ø Fl
lmE/)1\p)
e $B!'>?M5)1\©*-,!#:<>L2&)1!#6
m
ï $&!u$&!u'"(E/>?)GM5;=)1)1\©/*-!#,/$&"(!#4{L*-)197,D$&!#)1L!#6)19A$B)1!cß \)1L\p)1!#)1/"($&/3"(E/)G!#:>?L2&)¥5Oa
×á
}rÅ E)IL\p*-MO2B)1>!#"(';=$&)1;tE/)1\p)I$&!©:Gv8[tlm$B"%E¨:+x%!#45>?>?)1"(\]$B9A61>*-/*-"(*-/$&976)1ñ5'$&;=$&!#h
j
j
! ¡ Fl
"%:/"(z}*-)1L2B$&"%H;=$&!#"%:/97)C>?:"(\]$&d<6AlmE$&97E$&!=*-/2&4f:<*-"%E)1\D, *-\>?'2&:"%$B*-*-,"(E/)ulm)1$&35E/"()1;
>?$&$&>?'>ª2B$&/)1:\:\]\:<35)1>?)1/"L\p*-M52&)1> x $B/y=8z#aAF*-/!#$&;=)1\]$B/3t"(E/)E:<\p;=/)1!#!I*-,
"%E)KL\p*-MO2B)1>?6"(E/)1\p){;=*)1d$&!#"©!#*->)K!#L)197$&:2r97:!#)1!f*-,u$&y=8¸"(E/:"C:\)~$& ³ E=E/*-lmh
)1N)1$6|*-'\f9A:!#)m$&!L\p*-M5:<M52&F
4 u
E:<\p;=6:<!)1NO)1 x%8/"($&h ¥*-/35)1z}<*-)1L2&$&"(Hv8[¥$&!
u ³ Â E:<\p;=61'/2&)1!#!u,%'\]"(E/)1\©97*-/³ !#"(\]Â :$&/"(!u:<\p)L*-!#)1;*-/"(*¨"(E/)G}<*-)1L2&$&"(H0>?:"(\]$&dDa
}\]:/!#,%*-\]>?)1;{;=:<"(::\p)"(E/)1~,%)1;K"(*f"(E/)v8[¨!#*-2&NO)1\1ao'"(L'"-*-,-"%E)v8[{L\*-97)1h
;r'\p)97*-/"(:<$&!"(E/)GM5)1!#"OL)1\]>?'"(:"%$&*-K*-,D!#:<>L2&)1!u, *-';x%!#E/*-'2&;M5)16$B;r)1:2&2&476_$&;=)1/h
"%$&97:2-lm$&"(E/6*-\©9A2B*-!#)+"(*-6"%E)+*-\$&35$&/:2->?*-;=)12&)1;!#)1ñ5')1/97)16<$õa )Oa 6 # j # ý # ä{ä}ä # e # ez a
Â
çôN öw÷?ø £ m |ü{þEæ0+./nk (þEk~ü~ûp+.-1÷ÿ
Uu5 65 4 :Ô ÿXBC9Hº[».?
A<.BC>
}rE)mv':;r\:<"($&98!#!#$&35>?)1/"[\p*-MO2B)1>¶x%v8[z$B!*-/)m*-,"(E/)m>*-!#";=$&,(Ö97'2&"uL\*-M5h
2&)1>?!G*-,"(E/)*-L)1\:<"($&*-!$1!#)1:\97E/6-:/;X"(E/)35\]:LE"%E)1*-\]4a "rlm:<!Ö\!#"|\p)197*-3O$&H)1;
MO4k*-*-L>?:/!:/; s=)19A5>:<Øx%S<iU<jGz # < %#a}=E)¨L\p*-M52&)1>$&!+'!#':<2&2B4?!#"(:<"()1; :!+, *-2&h
2&*-lm!n
.0$&NO)1 :<w$&"%)135)1@
\ e6u:<;Ë"(E/\p)1) e ew>:<"(\]$&97)1! ½ ¼ ×iá ¼ 6 ¸ ½ ¼ Ú × á ¼ 6u:<;
¼
à
¼

6
%
"
E
?
)
(
"
<
:
#
!

$B!K"(*Ö/;:ØL)1\>?r '"(:<"($&*- À6*-,G"(E/)!#)1ð " # j # ä{ä}ä # e K"(E/:"
½
×
á
>?$&$&>?$&H)1!
a
g<
ç à ñò ç ç ÚCñ4ò ñò
x Y/a j<z
â× å Û × ×Ió Ý â× å Û áâ å Û ð ×iá[æ ×Jó áó
:/; ¸ :\p)'!#':<2&2B497:<2B2&)1;X"%E)So *-lq:/; ;=$&!#"(:<9A)>:<"(\]$&d<6/\p)1!#L)19A"($&NO)12&4a 6/"(E/)
ç à × ñò ×Ió ;=*-)1!/*-"97*-/"(\]$&M5'"()"(*Ø"(E/)
9A*-!#">?:"(\]$&d<6$&!*-L"($&*-/:2C6:/;w"(E/)t"()1\]>
9A*->L2&)1d$B"%4X*-,"(E/)KL\*-M52&)1>6"(E/'!lm)t97:< *-× å, "(Û)1¥!#)1)K:,%*-\]>'2&:<"($&*-*-,"(E/)tv8[
lm$&"(E/*-'"$B" a }=E/)Xv8[ì>?:4 M5)X, *-\>?'2&:"()1;×$B >?:/4 )1ñO'$BN:2&)1/"f, *-\>?!a /)
*-,C"%E)1>$&!0:¨ñ5':<;=\]:"($&90Zh S¨L\*-35\]:>?>$&/3L\*-M52&)1>|# <%# .% 6DE)1/97)¨"(E/){/:>?)16:
352&*-M5:<2<>?$&$&>?$&H:"%$&*-¨L\*-M52&)1> # <%G# <Z.%% 61:<~$&"%)135)1\r2&$&)1:<\=L\p*-3O\:<> # <j% 61*-\=>$&d)1;
$&/"()135)1\©2&$&)1:<\|L\*-35\:<> # i&%# j.%G# j<i.% a
§=d"()1/!#$&NO)m\p)1!#)1:<\p97EÇE/:!0M5)1)1X9A*-;='9A"()1;w*- v8[asr*-"(EX)1d:9A"C:/;¥E/)1'\]$B!#"%$&9
!#*-2&'"($&*-/!)1d$&!#"]a1¤O*-\:<m)1d<9A)12B2&)1/"O\)1NO$&)1l*-Kv8[!#)1)_# <.% a
Uu5 65 7 Ð 6?
üTA ?
»ÒBC9H<~A}[
§=d:9A"©97*->?M5$&:<"(*-\]$B:<2r:<2B3O*-\$&"(E/>?!L\p*-NO$&;=)¨"(E/)¨L\*-M52&)1>¯B!0352&*-M5:2|*-L"($&>'>åx '!#'h
:<2B2&4t, *-\>?'2&:"%)1;Ø:!I>$&/$&>$&H:<"($&*-?"(:!#Oz a=¼0')"%*m"(E/)xu ³ E:<\p;=/)1!#!*-,r"(E/)v8[6
"%E)14¨97:mM5)+'"($&2&$BH<)1;*-/2&4K$&m97:<!#)G*-,D!#>:<2&25L\p*-M52&)1>?!#6Te & Â a1}rE)G!#$&>?L2&)1!#"/)1d:9A"
>?)1"(E/*-;=!0:\p){"(E/)¨)1/'>)1\]:"%$&NO){>?)1"(E/*-;=!a+}=E/)14?'!#)¨:m®M5\'"()K,%*-\97)~:<LL\p*-:<97E/¯"(*
"%E)L\*-M52&)1>61$ba )Oa 697*->?L2B)1"%)!#)1:\97ECaQ«K*-lm)1N)1$61"(E/)/'>M5)1\*-,/L*-"()1/"($&:2!#*-2&'"($&*-/!
35\*-lm!r)1dL2B*-!#$&N)12B4xèg h&Aj zlm$&"(E~"%E)!#$BH<)*-,5"%E)L\p*-M52&)1>?6.~
e x{x /'>M5)1\*-,O!#:>?L2B)1!#z#a
}=E/'!#61*-/2B4{NO)1\]40!#>?:2&2L\p*-M52&)1>?!|:<\p)"(\]:97"%:M52&)"(E/$&!lm:<4aQ§=N:2&':"%$B*-¨*-,5"(E/)I97*-!#"5*-,
:<!#!#$B3O>?)1"%!+$1ñ5'$&\p)1!
e !#"()1L!G:<; >'!#"M5)~\)1L)1:"%)1; egihj "($&>?)1!au¼')
"%*~"(E/$&!\p)1:<!#*-61)1/'>?)1\:<"($& NO)GÈ >?)1"(E/*-;=!u:<\p)I*-,D2&$B>?$&"()1;NO:2&'), *-\©Ä !#*-2BN$&Ç 3K"(E/)Gv8[a
kN" &¡ Fm!
ó ó
"FH@
ó
*-\p)~!#*-LE/$&!#"($&97:<"()1; )1d<:<97">)1"%E*-;=!f$&9A2B';r)~"(E/){BM5\]:/97E/h%:<;=h M5*-'/;=¯/x%s=srz%6
9A'"("($&/3wL2&:/)16:<;M5\]:/97E/h%:<;rh%9A'":2&35*-\]$B"%E>?!as=s$&!mM5:!#)1;*-Ë: $&;=)1:Ø*-,
M5\]:/97E/$&3O6AM5*-'/;=$&/356A:<;¨"(E/)u!#)12&)197"%$B*-\'2B)OaQ}rE)1!#)u:<2&35*-\$&"%E>?!='!#)u2&*-lm)1\DM5*-';r!
x !#)1)m)1d"u!#'M5!#)19A"($&*-z"(*ØMO*-'; "%E)tL\*-M52&)1>a~}=E/\p)1)K"(45L)1!*-,M5\]:/97E/$B/3Ø)1d$B!#"%6
/:>?)12&4|nx $&z"%E){!#$B/352&){:<!#!#$&35>?)1/"(6x $B$&z©L:$&\:!#!#$&35/>)1/"(6D:<; x%$&$&$&z\)12&:"($&N)L*-!#$Bh
"%$B*-/$&3a_s=slK:<!C:LL2&$&)1;"(*{"(E/)Gv8[M5Ã
4 # S< %# .j %G# S.i %#a
FI'"("%$B/3L2&:/):2&35*-\]$&"(E/>½'!#)1!{ y=[ x >?$Bd)1; $&/"()135)1\2&$&/)1:\L\p*-3O\:<>>?$&35z
, *-\>?'2&:"%$B*-/!r*-,"%E)uv8Ã
[ # <.Z %# S&i %<"%*+97*-/!#"(\'97""(E/)u>?:!#"%)1\/L\*-M52&)1>6Q:/;~"%E)!#2B:<NO)
L\*-M52&)1>6-lmE/$B9AE>?'!#"=M5)$& ³ a/}=E/)0!#2B:<NO)0L\p*-M52&)1> $B!I"%E)1!#*-2BN)1;Ç,%*-\"(E/)0$&/$&"($&:2
:<!#!#$B3O>?)1":<; *-L"($&>?:2uN:2&')1!{*-,IL\]$B>?:2:/; ;=':<2CNO:\]$&:M52&)1!~:<\p)t9A*->L'"%)1;a
,"%E);=':2©!#*-2&'"($&*-w*-,"(E/)!#2&:NO)tL\*-M52&)1>¶!#:<"($&!#Ö)1!~:<2B2©9A*-!#"%\:<$B/"(!{*-,"%E)t>?:!#h
"%)1\L\p*-MO2B)1>?65"%E)1?"(E/)*-L"($&>?:2D!#*-2&'"($&*-ÇE:<!MO)1)1:<97E/$B)1N)1;a"%E)1\]lm$&!#)165:"=2&)1:<!#"
*-/)*-,="(E/)f9A*-!#"%\:<$&"%!*-,r"(E/)0>?:!#"%)1\uL\p*-MO2B)1>¦$B!NO$&*-2&:"%)1;a%"(E/$B!I9A:!#)16"(E/)f>?:!#h
"%)1\L\p*-M52&)1>ê$&!0!#*-2BN)1;lK$&"%E Öd)1; ;=':<2=NO:<\$&:<M52&)1!+*-,u"%E)K!#2&:NO)¨L\p*-M52&)1>ê:<;¥"(E/)
!#*-2&'"($&*- $B!"%E)1X$&/L'"C"(*Ç"(E/)K!#2B:<NO)¨L\p*-M52&)1>waG}=E/){L\*-97)1!#!0$&!f\)1L)1:"()1; '"%$&2r:2&2
9A*-!#"%\:<$B/"(!*-,"%E)f>:<!#"()1\L\p*-M52&)1>¬:\)I,%'2&Ö2&2&)1;a1@*-2&'"($&*-t*-,D"(E/)G>?:!#"()1\L\p*-MO2B)1>
$&!I:2&*-lK)1\M5*-'/;=6-*-MoPR)197"%$BN),%'/97"%$B*-,%*-\:/4t,%)1:<!#$BMO2B)0!#)1"("%$&3t*-,="%E):<!#!#$B3O>?)1"
N:\]$B:<M52&)1!r$&!"(E/)'LL)1\M5*-'/;ao}rE):2&35*-\]$&"(E/>¸"()1\]>?$B/:"%)1!|lmE/)1~2&*-lm)1\=:/;m'LL)1\
M5*-'/;=!u>?)1)1"]a
s=\]:/97E/h%:<;rh%9A'"'!#)1!y=[x 2&$B/)1:\©L\*-35\:<>>?$&3Oz%6*-\C%y=[,%*-\]>'2&:<"($&*-*-,"(E/)
v8[o6r$&97*->?M5$&/:"($&*-wlm$&"(E:9A2&:!#!~*-,,%:<97)1"%h%;=)1Ö/$&3 $B/)1ñ5':<2B$&"%$B)1!{5*-lmw"%*XM5)
, '2&Ö2B2&)1;M54{:<2B2-, )1:!#$&M52&)G!#*-2&'"%$B*-/!a<}=E/)+>?)1"(E/*-;$&!:<2B!#*{\p)1, )1\\)1;t"(*~:<!u®L*-2&45E/)1;=\]:2
9A'"("($&/3L2&:<)1¯õaCs=\]:/97E/$&3L\p*-;='9A)1!GNO$&*-2&:"%$&*-!f*-,!#*->?){$&/)1ñ5':2&$&"($&)1!f:/;X"(E/*-!#)
:<\p)"(E/)1¨B97'"%h%*-,%,¯B6o$õa )Oa 61:;=;r)1;K"%*"(E/)*-\$&35$&/:2y=[V y=[m\p)12&:d:"%$B*-¨:/;t"(E/)IlKE/*-2&)
éQ«±&Q?ÁTImÂÌ÷ K LÃ¿ sTøR%Àji K sPi0¿ MR ÁTI2Ã
gi
L\*-97)1;='\)$B!+\p)1L)1:"%)1;a}=E/$&!G:LL\*-:97E97*->?M5$&)1!f"(E/)~, )1:"('\)1!I*-,9A'"("%$B/3L2&:<)16
:<;M5\]:/97E/h%:<;=h M5*-'/;t:2&35*-\]$&"(E/>!a
Uu5 65 z â[BLZ
9rÑ_BCº[>_;èZuA~<~ ?
A~<.BC>
yr*-lK)1\M5*-';r!:<\p)G'!#)1;?lm$B"%E:2&35*-\]$&"(E/>!L)1\],%*-\]>$&/3m:02&$&>?$B"%)1;Ç!#)1:\p9AEmx%)Oa 3a 6<"%E)
MO\:<9AEh :/;=h M5*-';rz aA.0*-*-;t2B*-lm)1\M5*-'/;=!!#E*-'2&;tM5)"($&35E/"(61:<;K)1:!#40"(*097*->?L'"()Oa
¤O*-\"(E/)v8[6Q"(E/)1\p)u)1d$&!#"<"%E\)1)u97:<"()135*-\]$&)1!r*-,2&*-lK)1\MO*-';=!a1}=E)Ö\!#"$&/972&';=)1!r"%E)
9A2&:!#!#$&97:<2.0$&2B>?*-\p)1h y=:<lK2&)1\uMO*-';Øx .fyrs=z=:/;Ø\p)12&:<"($&NO)1!a}=E/)!#)197*-/;Ø$B/972&';=)1!"%E)
)1$&35)1/NO:<2&')M5*-'/;=!x%§=·srz a}rE)"(E/$B\;{9A:"()13O*-\40$&!rM5:<!#)1;{*-~\)1h%, *-\>?'2&:"%$B*-/!r*-,-"%E)
v8[6<:/;35)1/)1\:<2&2B4¨\p)1ñ5'$&\)!#*-2&N$B/3K:f/'>MO)1\*-,/2&$&)1:<\:<!#!#$&35>?)1/"/L\*-M52&)1>!a
}rE)t.0$&2B>?*-\p)1h y=:<lK2&)1\0M5*-'/; $&!"(E/)>?*-!#", \p)1ñ5')1/"(2&4X'!#)1; 2&*-lK)1\0M5*-'/; , *-\
"%E)v8[5a] "Olm*-\]5!C$&
e # U<.Y % ao«m*-lm)1NO)1\%61$&"O;=)1"%)1\$&*-\]:"()1!ñ5'$&97O2B4{:!©"(E/)!#$&H)I*-,
"%E){v8[Ø$B/97\)1:!#)1!ar%>?L \p*-È N$&3.fy=sØ$&!G/*-""(\]$BN$&:2&65:/;Xlm:!!#E/*-lmÇ"(*M5x
) u ³
9A*->L2&)1"%@
) # %#a_yr$Bh [:\;=:2&*-!#h JC:>?:5\]$&!#E/:/h JC)1!#)1;=)MO*-'
; # <. %D$B!M5:!#)1;*-t*-LÂ h
"%$&>:<2O\p)1;r'97"($&*-t!#9AE)1>?)1!*-,="%E)fv8[a JC)1;r'97"($&*->?)1"(E/*-;=!lm)1\p)G$&/NO)1!#"($&35:<"()1;?$&
# &Y %# U.S %#a
§r$B3O)1N:2&')1h%MO:!#)1; M5*-'/;=!¨:\p)tMO:!#)1; *-w"%E)*-\"%E*-3O*-:<2u\p)12&:d:"%$&*-!~*-,"%E)
v8['!#$B/3K)1$B3O)1N:2&')1!C*-, o*-lð:/;;=$&!#"(:<9A)G>?:"(\]$&97)1!n
´{*n"&!
¸ ½ â ç ¹ × æ Æ ç ×@ Û
×å Û
x%YDa z
lmE/)1\p) :/; :\)~)1$&35)1/NO:2&')1!0*-,C"(E/)¨!#4O>>?)1"(\]$&9 o*-l :<;¥;=$&!#"(:<9A){>?:"(\]$&97)1!a
82&"%E*-'35¹ E"(E/)14¨Æ :<\p)G"%$&35E"%)1\C"(E/:"%E)f.fyrs:<;?ñ5'$&"()0)1:!#$&2&4¨9A*->L'"%)1;=6"(E/)14K;r)1"()1h
\]$&*-\:<"()ñ5'$&9752&4$&~)1:<\2&4!#"(:<35)1!|*-,-MO\:<9AE$&/3"(\p)1)16Q"(E/'!©M5)1$&3/*-"->'9AE{!#'$&"()1;m, *-\
"%E)+s=s>?)1"(E/*-;a
·|:\]$&:/97)0\p)1;='9A"($&*-2&*-lm)1\M5*-'/;=!lm)1\p)0$&"%\p*-;='9A)1;?MO:
4 # <. % a/}=E/)14t*-M5!#)1\]NO)1;
"%E:<"ulmE)1 "(E/)mNO:\]$&:/97)1!f*-6, o*-l¹:/;¥;r$B!#"%:/97)K>:<"(\]$&97)1!;=)197\)1:!#)16D"(E/)K.fy=sw$&/h
9A\p)1:<!#)1!#6:<;¥M5)197*->?)1!+>?:d$&>'>lmE/)1X\p*-lqN:\]$&:/97)1!G*-,C"%E)¨>:<"(\]$B9A)1!+M5)19A*->)
H<)1\p*raA}=E/)>?$&$&>?'>ðNO:<\$&:/97)C2&*-lm)1\DM5*-'/;¨9A:M5)u9A*->L'"%)1;{$&
e aQ "lK*-\]5!
lm)12&2-lmE)1mN:\]$B:<9A)1!C:\)E/$&35E/6lmE$&2&!#"D$&"O;=)1"%)1\$&*-\]:"()1!C"%*~"(E/).0y=s$&m 97:<È !#)"%E)14¨:\)
!#>?:2&2ba
Uu5 65 8Z
º[9H<HA~<üN
«m)1'\]$&!#"($&97!:\p)*-, "()1t'!#)1;"(*Ë:<;=2&)G2&:<\p35)v8[$B/!#"(:<9A)1!# %#a_Þ!#':<2&2B4A6"%E)fL\p*-h.= "! Fm&!
9A)1!#!E/:!u"%lm*{2&)1NO)12&!u*-,DE/)1'\$&!#"($&9A!n_"%E)G2&*-lm)1\C*-/)GM5)1$&3K"(E/)G2&*-97:<2-!#)1:\97E/6_lmE$&97Et$&!
"%E)1{;=\$&N)10MO4f:<'LL)1\/2&)1N)12_E)1'\]$&!#"($&976Q"(E/)!#*-h 97:<2&2B)1;K>?)1"(:h E/)1'\$&!#"($&9a7«m)1'\]$&!#"($&97!
9A:ÇL\p*-N$&;=)*-L"($&>?:2&6D*-\/)1:\]2&45h *-L"($&>:<2!#*-2&'"($&*-!0$&Ø:{\)1:!#*-/:M52&)"($&>?)Oau:<4
"%45L)1!u*-,DE/)1'\$&!#"($&9A!u"(*¨!#*-2BN)Gv8[t)1d$B!#" a1ÊØ)Glm$&2&2-35$&NO)G:f!#E*-\]"D*-NO)1\]NO$&)1lä
FI*-/!#"(\'97"($&*->?)1"(E/*-;=!r'!#':<2&2B4f!#"(:<\"<lK$&"%E:)1>L"%4+L)1\]>'"%:"%$B*-CaQ}=E/)1*-;=)1!
:<\p)$&"()1\]:"($&N)12B4:<;=;=)1;=6o>?:5$&/3~:!#!#$&35/>?)1"%!C"(*)1>?L"(4~2&*-97:<"($&*-/!C"(*)1/;t'LKlm$&"(EK:
9A*->L2&)1"%)L)1\]>'"%:"($&*-CaQ}=E/$B!r$B!|"(E/)u!#*-2&'"($&*-*-,"(E/)uv8[5aõ}=E/)u9A*-!#"%\p'97"%$&*-~E)1'\]$&!#h
"%$&9$&!u)1$&"(E/)1\©35\p)1)1;r4761*-\©!#*->)+2B*-9A:2-!#)1:<\p97ECa
±*`&d CFm
.0\p)1)1;r4~:2&35*-\]$&"(E/>q,%*-2&2&*-lm!"%E)G3O)1)1\]:2-$&;=)1:f*-,/"%E)+2B*-lm)1\CM5*-'/;MO'"/\)1!#L)197"%!
, )1:!#$&M5$&2&$&"(4a~}=E/'!$&"35\)1)1;=$&2&4Ø:!#!#$&35/!"(E/)tE$&35E/)1!#c" o*-lª"%*Ø"(E/)t!#>:<2B2&)1!#";=$&!#"(:/97)
:<NO:<$B2&:<M52&)Oa5}=E/)0)1d"=E/$B3OE)1!#N" o*-lÒ$&!I"(E/)1:!#!#$&35/)1;Ç"(*m"(E/)0)1d"!#>:<2&2B)1!#"r;=$&!#"(:/97)
$&,D"(E/$&!$&!u, )1:!#$&M52&)OaQ ,//*-"(6<$&"35*-)1!"(*~"%E)G/)1d"!#>?:2&2&)1!#";r$B!#"%:/97)16_:<;!#*{*-Ca
U<Z
±* aS]
&nD"S! m
] "FH
y=$&>?$B"%)1;)1'>?)1\:<"($&*-X>?)1"(E/*-;=!0>:<5)¨'!#)¨*-,u:Ø)1>?L$&\$&9A:2=*-M5!#)1\]NO:<"($&*-X"%E:<"
)1d:9A">?)1"(E/*-;=!*-, "()1t:<97E/$&)1NO)G:35*-*-;?:LL\*-d<$&>?:"($&N)!#*-2B'"%$&*-ñ5'$&97O2B4A6!#L)1;=$&/3
>?*-!#"*-,"(E/)K"%$&>)m*- !#2&$&35E/"$&>?L\p*-NO)1>?)1/"(!a}=E/)m$&;=)1:t$&!"(E/'!0"%*ÇL'"u:2&$&>$&"u*-
9A*->L'"%$B/3"%$B>?)165*-\'>?M5)1\*-,|!#"()1L!#65*-\:NO:<2B')*-,="%E)*-M1P )19A"($&NO), '9A"($&*-Ca8/h
*-"%E)1\lm:4$&!"(*t)1dL)1\]$B>?)1/"rlm$&"(E?"(E/)2B*-lm)1\IM5*-'/;n/"(E/)E/$B3OE)1\$&"r$&!L*-!#$&"($&*-)1;r6
"%E)G;r)1)1L)1\r:\)"(E/)97'"%G! EE/*-lK)1N)1$6<"(E/)G*-L"($&>?:2-!#*-2&'"($&*-t>?:4{MO)97'"(h *-,(, 6_"%*-1
* # < %#a
«m$&2B2972&$&>?M5$&3Ø>?)1"(E/*-;=!0!#"(:\]"Clm$&"(EX:<X$&$&"($&:<2|, )1:!#$&M52&)~!#*-2&'"($&*-/6|$&>?L\p*-N$B/3Ç$&"
$&"()1\]:"%$&NO)12&4ÇM54Ø2&*-97:2|!#)1:\97EX$& $&"%!0/)1$&35E/M5*-\pE/*-*-;a}rE$&!$&!0$1L)1:"%)1; '/"($&2©*Ç$&>h
L\*-NO)1>?)1"97: M5)t, *-'; $&"(E/)t/)1$B3OEM5*-\E*-*-;aK¤5';r:>?)1"%:2©,%)1:<"('\)1!f*-,E$&2&2
9A2B$&>?M5$&3K:\)I"(E/)G2&*-97:2-!#)1:<\p9AE61$&"(!!#97://$B/3K\p)135$&>?)16_:/;$&>L\*-NO)1>?)1"/\p'2&)Oa
.0JC8@[Ø!#"%:/;=!, *-\B.f\)1)1;=4tJC:/;=*->?$BH<)1;Ø8;=:L"%$&NO)@)1:\p9AE[\p*-9A)1;='\p)1¯õaD "r$&!
:?97*->?M5$&:<"($&*- *-,9A*-!#"%\p'9A"($&*- :<; E$&2&29A2B$&>?M5$&3:<2B3O*-\$&"(E/>?!aØ "lm:<!{:LL2&$&)1;
"%* ;=$&,(, )1\p)1/"GE/:\p; 9A*->MO$B/:"%*-\$&:<2*-L"($&>$&H<:"($&*- L\*-M52&)1>!$&/972&';=$&/3 v8[ # %#a
.0*-*-; !#*-2&'"%$B*-/!:\)97*-/!#"(\p'9A"()1;¥,%\*->"(E/)~:N:$&2&:M52&)~, )1:!#$&M52&)~!#L:<97)$&X9A*-!#"%\p'97h
"%$B*-¨LE:<!#)161lmE$&97E¨:\)"(E/)1{$&>?L\p*-N)1;K$&¨"(E/)2&*-97:<2<$&>?L\p*-N)1>)1/"-LE:<!#)IM54:2B*-9A:2
!#)1:<\p97EK$&m"(E/)G)1$&35E/M5*-\E*-*-;a
}:M5'x "(:<M5*-*-zD!#)1:\97EKlK:<!u$&"%\p*-;='9A)1;"(*{*-NO)1\p9A*->)+"(E/)G"(\]:LL$&/3{$&t2&*-97:2->?$&h
$&>?:M54Ø:<2B2&*-lm$&3 *-"*-2&4 $B>?L\p*-N)1>)1/"(6M5'"u:<2&!#*Ø;=)1"()1\]$&*-\:<"($&*- *-,"(E/)tL:\]"($&:2
!#*-2&'"($&*-lK$&"%E"(E/)f2&*-9A:2O!#)1:<\p9AEK>?*-NO)1&! # U&i %# YS %G# Y.Z %G# Y<. % a5}<*KL\p)1N)1"D"(E/)+:<2&35*-\$&"%E>
, \p*->97459A2B$&/356_"%E)I$&;=)1:G$&!C"(*\)1>)1>?M5)1\rN$&!#$B"%)1;t!#*-2&'"($&*-!$BK*-\p;r)1\="(*;=)1\]$&NO)I;=$&\p)19Ah
"%$B*-/!C, *-\r, '\"%E)1\=!#)1:<\p9AE©aQ*-NO)1!©"%*0N$&!#$B"%)1;t!#*-2&'"($&*-!:\p)L\p*-E/$&M5$&"()1;mx xK"%:M5'z 61:/;
:<\p)\p)13O$B!#"%)1\p)1;*-t:0"%:M5'2B$&!#" a}<:<M5'!#)1:<\p9AEK!#"%:\]"(!ulm$&"(E:t$&$&"%$B:<25, )1:!#$&M52&)+!#*-2&'"($&*-
:<;¥!#)12&)197"(!f"(E/){M5)1!#"C:<>*-/3Ç"(E/){/)1$&35EMO*-\!0*-M5"(:<$&)1;¥M54Ç*-/h "(:MO' >?*-NO)1!a}rE$&!
;=*-)1!/*-")19A)1!#!#:\]$B2&4X$&>?L\p*-N)t"(E/)t*-MoPR)197"($&N)t,%'/97"%$B*-Cam8¥:!#L$&\]:"($&*-¥97\]$&"()1\]$B*-
$&!G:K97*-/;=$&"($&*-ØlmE$&9AE6DlmE)1Ç, '2&Ö2B2&)1;=6/97:<9A)12&!G"(E/)~"(:<M5'X!#"%:"('!+*-,:¨>*-N)Oau@"%*-Lh
L$&/3¨9A\$&"()1\]$&*-6lmE)1t, '2&Ö2&2B)1;r6<!#"%*-L!"(E/)+:<2&35*-\$&"%E>wa¤5*-\C:m$&/"(\p*-;r'97"($&*-"%*{"%:M5'
!#)1:<\p97EK!#)1S
) # Y %#a
JC)1:9A"($&NO)¨!#)1:\97E?97*->?L2B)1>?)1/"(!0"(E/){2&*-97:<2=!#)1:\97EÇM54?:¨, )1)1;=M5:<97!#9AE)1>?)1!+"%E:<"
'!#)"%E)L:<!#"=E$&!#"%*-\4*-,|"%E)!#)1:<\p97E"(*t$&/97\p)1:<!#)"(E/)1$B\)1,(Ö9A$&)19A4t:/;X)1,(Ö9A:974 # SY %#a
@$&>L2&)>?:9AE$&/)G2&)1:\]$&/3{"()19AE/$&ñ5')1!:<\p)I'!#)1;"%*~"('/)GL:\]:>?)1"()1\]!C:/;"%*~;=)1"()1\h
>?$&)"%E)I:LL\*-L\$&:<"()MO:2&:/97)I*-,O;r$BN)1\!#$&Ö9A:"($&*-¨NO)1\]!#'!$&/"()1/!#$&Ö97:"%$&*-©aJC)1:9A"($&NO)
!#)1:<\p97E L\p*-L*-!#)1!m"(E/)Ç$B/"()13O\:<"($&*- *-,+!#$B>?L2&)Ø>)1>?*-\]45h%MO:!#)1;,%)1)1;rM5:9A¥!#9AE)1>?)1!
$&X2&*-97:<2r!#)1:<\p97EØ, *-\G"%E)K;=)1"()1\]>?$B/:"%$&*-X*-,u, \p)1)~L:<\:<>)1"%)1\!aG%X"%E)K\p)1:<97"%$BN){"%:M5'
!#)1:<\p97E/61$&¨L:<\"%$&97'2&:\%61:G!#$&>L2&)G, )1)1;=M5:<97!#97E/)1>)$&C o')19A)1!u"(E/)NO:<2&')*-,"%E)L\*-h
E/$&M5$&"($&*- L:<\:<>)1"%)1\f*-,"%E)?"(:<M5' !#)1:\97E/6C!#* "%E:<"I:?N:2&')*-,)1dL2&*-\:<"($&*-wNO)1\]!#'!
)1dL2&*-$B"%:"%$B*-Ç$&!G*-M5"%:$&/)1;=6"%E:<"r$&!+:<LL\p*-L\]$&:"()0, *-\"%E){2B*-9A:2D97E/:\]:9A"()1\]$&!#"($&97!*-,©"(E/)
"%:!#|am \p)1:<97"($&N)K"%:M5' !#)1:\p9AE "%E)BL\p*-E/$&M5$&"($&*-wL)1\]$B*-;r¯|$&!~;=)1"%)1\>?$&)1; "(E/\p*-'35E
, )1)1;=M5:<97x x¥\p)1:9A"($&NO)1z©>?)197E/:/$&!#>!;='\]$&3Ç"(E/)K!#)1:\p9AE©aG}=E/)¨L\*-E$&M5$&"($&*-XL)1\]$&*-;
$&/97\p)1:<!#)1!lmE)1Ø"%E)1\)$B!+:979A'>'2&:<"($&3)1NO$&;=)1/97)~"%E:<"|;r$BN)1\!#$&Ö9A:"($&*-Ç$&!G/)1)1;=)1;=6
$&"/;=)197\)1:!#)1!©lmE)1m"(E/$&!)1N$B;r)19A);=$&!#:LL)1:\]!a
@$&>'2&:"%)1;¨:</)1:2&$&/3flm:!|$&!#L$&\p)1;KM540L\p*-M52&)1>?!r*-,-!#"%:"($&!#"%$B9A:2_>?)197E/:/$&97!#6o:/;
9A: MO)K>?*-;=)12&)1;wM54Ø:< $&E/*->?*-35)1)1*-'!¨)1\p35*-;r$B9{¥:<\O*-NØ97E/:$&©a{}=E/)mM5:!#$&9~:<!#h
L)19A"/$&!"(E/)+:/:2&*-354Klm$&"(E"%E)1\]>*-;r45:<>$&9A!#6)1!#L)19A$&:2&2&4¨lm$&"(E"%E)flm:4K"(E/:"D>)1"%:2&!
9A*-*-2:<; :/)1:<2õa{}=E/)tLE4O!#$B9A:2©!#"(:<"()1!*-,:!#45!#"%)1>å:<\p)K:/:2&*-35*-'!~"%*Ø"(E/)t,%)1:<!#$&h
M52&)~!#*-2&'"%$B*-/!#6="%E)¨)1)1\354*-,C"%E)¨!#45!#"()1>9A*-\\)1!#L*-;=!f"(*"(E/){*-MoPR)197"%$&NO){, '/97"($&*-Ca
8?$&>L*-\]"(:<"|L\p*-L)1\]"(4*-,!#$&>'2&:"%)1;X://)1:2&$&3$&!G$&"%!:!#45>?L"(*-"%$B9097*-/NO)1\35)1/97)Oa
[\*-NO$&;=)1;K"(E/)$&/$&"($&:2"()1>?L)1\:<"('\)$&!©E$&35EK)1*-'3OE61$&"5E/:!©M5)1)1~L\*-NO)1;K"(E/:"5$&,5"%)1>h
L)1\]:"%'\p) ð :<"/$&"%)1\:<"($&*- ï $&!97E/*-!#)1!#'97Et"%E:<"/$&"!#:<"($&!#Ö)1!9A)1\"%:$&m97*-/;=$&"($&*-6-"%E)1
"%E)m!#45!#"%)1>¶lm$&2&29A*-N)1\p35)m"%*?"%E)t>?$&$&>?'>¶)1/)1\p3O4Ø97*-/Ö35'\:<"($&*-Ca~}=E/)1*-\p)1"%$&97:2
:<!#L)197"(!C*-,D"%E)G!#$&>?'2&:"()1;:/)1:<2B$&/3{:<\p)97*-N)1\p)1;=61)Oa 3|a 6_$& # g< %#a
±a
éQ«Ð&Q{ÂN®®R ¾JR%Â=Àm¾Ñ
US
.0)1/)1"($&9©:2&35*-\]$B"%E>?!:\p)$B/!#L$&\p)1;¨,%\*->úM5$&*-2B*-3O4ao}=E/)1$&\$&;=)1:$&!|"(*+:<;=:L""(E/))1N*-h
2&'"%$B*-/:\]4{>?)197E/:/$&!#>!,%\*->/:"%'\p)I"(*{97*->?M5$&:<"(*-\]$B:<2-*-L"($&>?$BH<:"%$B*-mL\*-M52&)1>!ao8
3O)1)1"%$B9:<2B3O*-\$&"(E/>ê!#"%:\]"(!+lm$&"(EØ:<Ø®$&/$&"($&:2=L*-L'2&:<"($&*-¯r*-,, )1:!#$&M52&)~!#*-2&'"%$B*- ®$&/;=$&h
N$&;=':2&!#¯õa}=E/){:<2B3O*-\$&"(E/>è!#)12&)19A"(!+L:<$&\!f*-,CL:\p)1/"(!f,%\*->"(E/)¨9A'\\)1"L*-L'2&:"%$B*-/6
'!#)1!f97\*-!#!#*-NO)1\\p'2&)1!f"(*L\*-;='97)B*-,(, !#L\]$B/35¯B6D"(E/){, )1:!#$&M52&)~!#*-2&'"($&*-/!f*-,C"%E)~9AE$&2&;
3O)1)1\]:"%$B*-CaI}=E/){*-,%,%!#L\]$&3?$&!+"%E)1X!#'M1P )19A"()1;¥"(*"(E/){B!#)12B)19A"($&*-/¯®6$ba )Oa 6D"%E)¨M5:;¥!#*-h
2&'"%$B*-/!0:\p);r$B!#9A:\;=)1;a}=E/$&!+L\p*-9A)1!#!G\p)1L)1:<"(!'/"($&2="%E)~!#"%*-LL$&3?97\]$&"()1\]$B*-Ø$&!G, '2&h
Ö2&2&)1;a=}=E):<2B3O*-\$&"(E/>¹97:M5)>*-;=$&Ö)1;ØM54t:<LL2&$B9A:"%$B*-*-,r>?'"(:<"($&*-6:/;V*-\>?$&h
3O\:<"($&*-6"(*$&>?L\p*-N)0"%E)ñO':2&$&"(4*-,"(E/)L*-L'2&:"%$B*-Ca¤5*-\$&"%\p*-;='9A"($&*-"%*35)1/)1"($&9
:<2&35*-\$&"%E>?!f!#)1,
) # <.S %*# & %J# Ti %[# Yg %*# SZ&T % au8ð'>?M5)1\I*-,©35)1/)1"($&9f:<2&35*-\$&"%E>?!flm)1\)
L\*-L*-!#)1;, *-\|"%E)+v8[Q6<!#)1S
) # S %=# &g %=# j %# SZ.Z %û# S<.Y % a
)1>?)1"($&9:<2&35*-\$&"%E>?!E/:N)G"(E/)1$&\/:>?)G;=)1\]$&NO)1;, \p*->¬"%E)G"%)1\>¬B>)1>?)1¯B6:+!#)12&, h
\)1L\p*-;='9A$&3m$&;=)1:x ::<:<2&*-354t*-,=35)1/)1z a¥)1>?)1!:\p)16:<!*-LL*-!#)1;Ø"%*m35)1)1!#6OL\p*-h
9A)1!#!#)1;¨:<;KL*-!#!#$&M52&4$B>?L\p*-N)1;¨MO4f"%E)$B/;=$&NO$&;=':<2&!|"%E:<"E/*-2&;m"(E/)1>aQ@*+:<\p)u"%E)E/45h
MO\$&;:<LL\p*-:9AE)1!#61$ba )Oa 61"(E/)97*->?M5$&:<"($&*-!*-,3O)1)1"%$B9:2&35*-\]$&"(E/>lm$&"(Em:+2&*-9A:2!#)1:\97E
# S&U %# g.Y %û# T.Z %û# Sg.Z %#a
8/"D!#45!#"()1>?!"(\]4{"(*K$&>$&"%:"()+"(E/)+M5)1E/:N$B*-\C*-,:<m:/"/9A*-2&*-4m$&!#)1:\97EK,%*-\C, *-*-;a
}rE)LE)1\*->*-/)"%\:<$B2C2&)1:<;=!~"(* :2&\p)1:<;=4X;=$&!#9A*-NO)1\p)1; !#*-'\p97)*-,,%*-*-;Ë:/; 35'$&;=)1!
"%E)m, '"('\)¨!#)1:<\p97EØ*-,:/"(!a0 "%)1!#$&"%4X*-,LE/)1\p*->?*-)K"(\]:$&2$&!0L\*-L*-\"%$&*-:<2|"%*?"%E)
:<>*-'/"©*-,©,%*-*-; ,%*-'/; $&Ç"(E/)~!#*-'\97)Oa%Ç:/"!#45!#"()1>?!+"%E)~LE/)1\p*->?*-/){"(\]:$&29A*-\ph
\)1!#L*-;r!"%*{:;r:L"($&N)G>)1>?*-\]476-:>?*-'/"*-,,%*-*-;Ç97*-\]\p)1!#L*-/;=!lK$&"%E"(E/)f*-M1P )19A"($&NO)
, '/97"($&*-/6u:/; "%E)!#)1:\p9AE :<\p)1:9A*-\\)1!#L*-;r!~"(*X"%E)!#L:97)*-,, )1:!#$&M52&)t!#*-2&'"($&*-/!a
8/"/!#45!#"()1>?!lm)1\p)$&/"(\*-;='97)1;MO,
4 # T.T % 6_:/;'!#)1;, *-\©v8[t!#*-2&NO$&3K$&:
# i<.j % a
m)1'\]:2-/)1"(lm*-\]5!E/:N),%*-'/;$&/97\)1:!#$&3¨'!#)G$&t"(E/)G:LL\*-d<$&>?:"%)!#*-2B'"%$&*-*-,
;r$B,%Ö97'2&"=*-L"%$B>?$&H:<"($&*-ÇL\p*-M52&)1>?!a L\]$&9A$BL2&)165/)1'\]:2/)1"%lK*-\]5!:<\p)0lK)12&2D!#'$&"()1;
"%*t"(E/)1!#)L\p*-M52&)1>?!#6-:!I"(E/)14t>$&/$&>$&H)16O$BL:\]:2&2&)12O, *-\>?6-:)1)1\354t, '9A"($&*-:<;
9A*-!#"%\:<$&"%!$&"%* lmE/$B9AE :Ë*-L"($&>?$BH<:"%$B*- L\*-M52&)1>ï9A:M5)Ø>?:LL)1;a Þ, *-\"%'h
/:"%)12&476>?:LL$&3 "(E/)X*-MoPR)197"%$BN)Ø,%'/97"%$&*-Ë:<;×97*-/!#"(\]:$&"%!*-/"(* : 35*-*-;ì)1/)1\p354
, '/97"($&*-"%'\/)1;~*-'";=$&,(Ö9A'2B"<,%*-\/97)1\]"(:<$&0L\*-M52&)1>!#6A$&9A2B';r$B/30"(E/)uv8[5aõ8w!#"(*-9AE:<!#h
"%$&9u)1'\]:2/)1"(lm*-\>?*-;=)12, *-\=!#*-2&NO$&3{"(E/)v8[mlm:!©L\*-L*-!#)1;KMOt
4 # T<S % Xa # Y&T %O35$&NO)1!
:<m*-NO)1\]NO$&)1lú*-,/)1'\]:2-/)1"(lm*-\O!u'!#)1;lm$&"(Em"(E/)Gv8[5a
"%E)1\>?)1"(E/*-;=!{L\*-L*-!#)1; , *-\0!#*-2&N$B/3¥"(E/)v8[w:\)t"(E/*-!#)M5:!#)1; *-w)1NO*-2&'h
"%$&*-:<\4XL\*-35\]:>?>$&/3 # S<Z.j %G# S<Z. % 6="(E/\p)1!#E/*-2&;w:979A)1L"($&/3 # g<.S %# jT %G# SZHi % 6r)1N*-2B'"%$&*-
!#"%\:<"()1354A6_>?$B3O\:<"($&*-t>*-;r)12-35)1)1"%$&9:<2B3O*-\$&"(E/>?6\p)1N)1\!#)I)12&$&>$&/:"%$B*->)1"%E*-;a
çô Ä
° 3+1ø*/,3Æ
}*:!#!#)1!#!"(E/)I)1,(Ö97$&)1/9740*-,5"(E/)v8[K>?)1"(E/*-;m*-,5!#)1\]$B:<"($&*-/61:!#)1\$&)1!*-,597*->?L:\]$&!#*-!
lm$&"(EÇ!#)1N)1\:<2/"%\:<;=$&"($&*-/:2D>)1"%E*-;r!GE:<NO)M5)1)1?\p'Ca}=E/\p)1)>?*-;=)12&!Glm)1\p)'"($&2&$&H)1;=6
/:>?)12&4"(E/).0:'!#!#$&:/6uM5)1"%:6C:/;Ë\p*-*-,>?*-;=)12baÇ}=E/)L:\]:>?)1"()1\]!~*-,"%E)>*-;=)12&!
lm)1\)!#)1""%* !#'9AEwNO:2&')1!~lmE/$&97E L\*-;='97)1; "%E)97*-)1/*-972&$&)1!K:LL)1:<\$&/3XNO$&!#':2&2&4
\)1:!#*-/:M52&)Oa}=E/)v8[ >)1"%E*-;Ëlm:!{"%)1!#"()1; 97*->?L:\p)1; lm$B"%Ew"(E/), *-2&2B*-lm$&/3w"(\]:h
;r$B"%$&*-:<2r*-/)1!n;=)1"(\)1;=)1; 97*-\]\p)1!#L*-/;=)19A)~:/:2&45!#$&!fx%¼§=FIJC8m8z%697*-\]\p)1!#L*-/h
;r)19A)f:<:<2B4O!#$B!I*-!#:<>L2&)1!#6-9A*-\\)1!#L*-;=)1/97)0:/:2&45!#$&!*-!#L)19A$B)1!#6\)197$&L\p*-9A:25:<NOh
)1\]:3O$B/356<:/;L\$&/97$&L:2-9A*->L*-/)1/"(!:<:<2&45!#$&!a
¤O$B3O'\p)+jDa S+x L:3O)GUY<z/!#E/*-lm!#6"(E/:"D"(E/)+v8[>)1"%E*-;?:LL)1:<\p)1;t!#'L)1\]$B*-\C"%*¨"%E)
"%\:<;=$&"($&*-/:2r*-/)1!$&X:mlK)12&2&h $B/, *-\>?)1;97:!#)On;r)1!#$&"($&)1!0lm)1\p){:mL\]$&*-\$|5*-lm/6r:<;
"%E)+35\:<;=$&)1"/lm:!C!#:<>L2&)1;'!#$&/3{\)135'2&:\!#L:97$&/3{*-,/!#:>?L2&)1!a
k d !"`!bc a
"!
U<
Uu57u5 4 ¹º[Ñ_Z
92BCr}[<~A.
FSNC&p! ÊØ)¨'!#)~M5*-"(EØ¯B/'>M5)1\*-,CE/$&"(!#¯B6D:/; 97*-\]\p)12&:<"($&*-Ç"(*:<!#!#)1!#!+lmE/)1"(E/)1\"(E/)~L\p)1!#)1/97)
*-,u:t3O\:<;=$&)1"Clm:!0;=)1"%)197"()1;¥M54Ø"%E)Kv8[6D$õa )Oa 6=lmE)1"%E)1\f"(E/)¨*-\]$&35$&:<2|:<;\)197*-/h
!#"%\p'97"%)1;¨*-\;=)1\]$B/3+*-,-!#:<>L2&)1!|:\p)C!#$&>?$&2B:<\]aom'>?M5)1\*-,E$&"%!|>?)1"(E/*-;m!#$B>?L2&4f9A*-'"%!
E/*-l¸>?:/4m"($&>)1!"(E/)0*-\$&35$&/:2O:<;?\p)19A*-!#"%\p'9A"()1;?!#)1\$&)1!x L)1\]>'"%:"($&*-/z:\)+$&;=)1/h
"%$B9A:2'L"%*~"(E/)G;=$&\p)19A"($&*-Ca
Uu57u5 7 Y=_Zu?
9H?
> 9?
> «üNBC9D9Z
».?
A<.BC>
FI*-\]\p)12&:"%$B*-t$&9A*-/)197"%$&*-lm$&"(E*-\;=$&:<25;=:"%:f$&!)1d<:<>$&/)1;N$B:\]:/m97*-\]\p)12&:"%$B*-/!a
JC:<~9A*-\\)12&:"($&*-¨"()1!#"O$&!©:G;=$&!#"%\$&M5'"%$B*-m, \p)1)"()1!#"5lmE/$&97Em;=)1"()1\]>?$B/)1!©lmE)1"%E)1\"(E/)1\p)
$&!{:>*-/*-"(*-/$&9\p)12&:<"($&*-M5)1"(lm)1)1"(lm* N:\]$&:M52&)1!at8¦>*-/*-"(*-/$&9t\p)12&:"%$B*-)1d$&!#"(!
lmE/)1Ø:/4$&/97\p)1:<!#)$&Ø*-)¨NO:\]$&:M52&)~$&!G$&/NO:<\$&:MO2B4?:!#!#*-9A$&:"()1; lm$B"%EØ)1$&"(E/)1\:m/*-h
;=)19A\p)1:<!#)*-\:G/*-h $&9A\p)1:!#)I$&m"(E/)*-"(E/)1\|N:\]$&:M52&)OaQ ¨"%E)\]:/~97*-\]\p)12&:<"($&*-{"%)1!#"O"(E/)
N:\]$B:<M52&)1!:<\p)G\)1L\p)1!#)1/"()1;MO4K"%E)1$&\u\]:/m*-\p;=)1\]!a-}rE'!#6-"%E)0"()1!#"$&!:;=$&!#"(\]$BMO'"($&*-h
, \p)1)Ç*-/)OaË82B"%E*-'3OEË"%E)Ø\]:/ 9A*-\\)12B:<"($&*-Ë97*-)1,(Ö9A$&)1"f97:ËM5)Ø$&/"()1\]L\p)1"()1; :<!t:
B!#"(\)135"%E¯*-,-"(E/)>?*-*-"%*-$&9u\)12&:"($&*-/6o"(E/))1/'>)1\]:"%$&*-~*-,-"(E/$&!|!#"%\p)1/35"(E~$&!!#*f9A*->h
L2&)1dG"%E:<"5"(E/)I\:<97*-\]\p)12&:<"($&*-~"()1!#"O>$&35E/"OM5)97*-/!#$&;=)1\p)1;m/*-h L:\]:>?)1"(\]$&9aQ}=E/) ¾
x '2&2=E/45L*-"%E)1!#$&!#zC*-,©"(E/){"%)1!#"|$&!+"%E:<"|"%E)1\)~$&!+/*>?*-*-"%*-$&9\)12B:<"($&*-ÇL\p)1!#)1/"|MO)1h
"%lK)1)1m"%E)GN:\]$&:M52&)1!aQ}=E/)G@L)1:\]>:<{\]:/{9A*-\\)1² 2B:<"($&*-K97*-)1,(Ö9A$&)1"$B!n
#
²
J½ Â â e e È Ä ÈÂ Ç
$&%
lmE)1\)
e
e 6
eK$&½ !u/ð'>ï MOÄùÅC)1\Çû*-Â ,DLð :<$B\]ï !Ä a ¼ Ç
x Y/a i<z
('
8/*-"(E/)1\x )1ñ5'$&NO:<2&)1"%z/, *-\]>'2&:+$&!
ò ç @ Ûó c e ï ¼ ò ç @ Û"ó
x Y/a S<Zz
ç È ò ç e ÛÛ ó ò ç @ ð Û"ó Ä ÇÂ È e
897"%':2&2&476<"(E/$B!$&!DPR'!#"/, *-\]>'2&:0,%*-\©[)1:\]!#*-/È¯®!97*-\]\p)12&:"%$B*-m9A*-)1,(Ö97$&)1/"O:<LL2B$&)1;"(*
$
%
e
½ â c ð ï Ä·ÅÇ=Â
\]:/5!a
}=E/)X2&)1NO)12*-,!#$&35/$BÖ9A:/97) $B!;=)1"()1\]>$&/)1;ìM54 97E/)1975$&/3 :<2B2L)1\]>?'"(:"%$&*-!*-,
\]:/5!$&Ç"(E/)!#:>?L2B):<; 97*-'/"($&3"(E/)~, \:<97"($&*-?,%*-\lmE$&9AE?"%E) $&!E/$B3OE)1\I"(E/:
"%E:<",%*-'/;a/8!"(E/)0/'>?M5)1\u*-,rL)1\]>?'"(:"%$&*-!I35\*-lK!lm$&"(Ã
E eg 6-"(E/$&!IL\p*-97)1;r'\p)+MO)1h
9A*->)1!!#*-*-NO)1\]4K"()1;=$&*-'!a¤5*-c\ e ý 6"(E/)+;r$B!#"%\$&M5'"%$&*-*-, ½ Þ e 9A:mM5)
1 :2-;r$B!#"%\$&M5'"%$&*-©a
Â
:<LL\p*-d$B>?:"%)1;tM54{:f!#"(:<;=:<\p;t/*-\>?
$&%
*)
Uu57u5 z Z
>_;[?
»~»69?
> «üNBC9H9XZ
».?
A~<HBC>
+$,%
-
Þ!#)I@L)1:\]>:<~*-\k)1;=:<2&2\]:/97*-\]\p)12&:<"($&*-¨9A*-)1,(Ö9A$B)1/"5"%*"()1!#"O"%E)I:<9797'\]:9A4*-,O\)1h
9A*-!#"%\p'97"%$&*-*-,|"(E/)0\]:/5!I*-?"(E/)03O\:<;=$&)1", *-\u:~!#$&/352&)0\'*-,|"(E/)>*-;=)12/x !#$B/352&)
>?*-;=)12&)1;w:/; \p)19A*-!#"%\p'9A"()1;w97*-)1/*-972&$&/)1z a¨«m*-lm)1NO)1$6|"(E/)t\p)1!#'2&"(!*-,\p)19A*-!#"%\p'9Ah
"%$B*-¥>?:4ÇNO:<\4Ç!#'M5!#"%:/"($&:2&2&4X'/;=)1\G97*-/!#"(:<"!#)1"("%$B/35!*-,"%E)mL:<\:<>)1"%)1\!f*-,"(E/)
>?*-;=)12&6-)1!#L)197$&:2&2&4KlKE/)1/'>?M5)1\u*-,=!#L)19A$B)1!$&N*-2&NO)1;Ø:$G2&*-l:<;V*-\u"(E/)f>?)1:
/$&97E/)*-NO)1\]2B:<Lm$B!C!#>?:2&2baoÊØ)>?$&35E"M5)I$&"%)1\p)1!#"()1;tE/*-lú"(E/)I>)1"%E*-;$B!C!#'9A97)1!#!#, '2$B
35)1/)1\]:2baDÊØ)'!#)>)1:<@L)1:\]>:<x *-\k)1/;=:2&2&zr\]:/t97*-\]\p)12&:"%$&*-97*-)1,%Ö97$&)1"r:!I:
>?)1:!#'\)OaQ%"/$&!u!#$&>L2&4
éQ«Ð&Q{ÂN®®R ¾JR%Â=Àm¾Ñ
UT
Ë ½ â u
$
$&%
:<;
x Y/a SASz
%
x Y/a S<z
ðË ½ â uð
lmE/)1\p)du¬$B!"(E/)G'>?M5)1\©*-,/\p)197*-/!#"(\'97"%$B*-/!$&/NO*-2&NO)1;$&K"%E)+"()1!#"]a
ÊØ)'!#)1; "%E$&!KL\p*-9A)1;='\p)t/*-"*-2&4:!¨:Ç"()1!#"IlmE)1"%E)1\~"%E)1\)$&!{:Ç97*-\]\p)12&:<"($&*-
MO)1"(lm)1)1"%E)0>*-;r)12B)1;Ç9A*-)1*-9A2B$&/)16-\p)1L\)1!#)1"%)1;M54m\]:/5! # j # ý # äIä # e 6<:<;Ç"(E/)0\p)1h
$
$
9A*-!#"%\p'9A"()1;9A*-)1*-9A2B$&/)1!#6_\p)1L\)1!#)1"%)1;¨MO4\:<5$&/35!C\p)1!#'2&"%$B/3, \p*->¸\)1L)1:"%)1;¨\'!
*-,"(E/)m>*-;r)12|ewv8[, *-\+)1:9AE !#)1"%"($&3 *-,L:\]:>?)1"()1\]!#6=M5'"\:<"(E/)1\G:!:>?)1:!#'\)
*-,D!#"%\p)1/35"(EK*-,"%E$&!u9A*-\\)12&:"($&*-Cao«m$&35EmNO:2&')1!C*-, Ë>?)1:K!#"(\*-3¨97*-\]\p)12&:"%$B*-/6_$ba )Oa 6
3O*-*-;K\)197*-/!#"(\'97"(:<M5$&2&$B"%4f*-,-"%E)35\]:;=$&)1/"<x \p)1L\)1!#)1"%)1;~M540\:<5!#z-, *-\D"(E/))1d:>?$&)1;
!#)1"%"($&/35!*-,D>?*-;=)12&¯®!uL:<\:<>)1"%)1\!a
$
%
Uu57u5 99H<.Zu;=?
>AHZuA
}rE)¤5\]$&)1;=>?:"%)1!#"² ¤5\]$B)1;r>:<Si<TjW# UZ% 65y=)1E/>:<S<ijUt# Y.%G³-$&!:~3O)1)1\]:2&$&H:<"($&*-
*-,"%E)@L)1:<\>?:¥\]:/ 97*-\]\p)12&:<"($&*-"()1!#"]a "$&!~:?"(lm*-h lm:4¥:/:2&45!#$&!~*-,\]:/5!a "
>?*-;=)12&!I\:<"($&/35!I*-,e \ P ';r35)1! \ xF?
x \p*-lm!#z=*- ï \ "(\p)1:<"(>?)1"%! \ x?x 97*-2&'>/!#z#a/}=E)0/'2B2
E/45L*-"%E)1!#$&!x ¾ z $&!r"%E:<"<"%E)u\]:"%$&35!|:\)C*-"\p)12&:<"()1;=6 $ba )Oa 6A"%E:<"<"%E)"(\p)1:<"(>?)1"%!97:</*-"
MO);=$&!#"%$B/35'$&!#E/)1;ao ~*-"(E/)1\=lm*-\p;=!#6 ¾ !#:4O!|"%E:<""%E);=$&!#"(\]$&M5'"($&*-/!©*-,5\:<O!rlm$&"(E/$B
\*-lm!f:<\p)~'/\p)12&:"%)1; MO)1"(lm)1)1Ø\p*-lm!a}rE)1\){:\)~"(lm*?"()1!#"CL:<\:<>)1"%)1\!n °:<; Ka
.#
/#
10
32
}rE)"%)1!#"5L:\]:>?)1"()1\ ò$&!©"(E/)!#*-h%9A:2&2&)1;mk)1;=:<2&2B¯B!C97*-)1,%Ö97$&)1/"5*-,O9A*-9A*-\p;=:<9A)OaQ%"5$&!
\)12&:"()1;m"%*~"(E/)I>)1:<¨\]:/~97*-\]\p)12&:<"($&*-{9A*-)1,(Ö97$&)1/"]aQ8/*-"(E/)1\|"%)1!#"OL:<\:<>)1"%)1\=$&! Kno$&,
E/$&35E{x x!#$&35/$BÖ9A:/"(z 61"(E/)9A*-2&'>/!©:\p);=$&,(, )1\p)1/":/;m"(E/)\*-lK!:\)9A*-\\)12B:<"()1;a7JC:/
*-\;=)1\]$B/3K$B!;=*-/)f$&t\p*-lm!#6:/;)1:<97Et\*-lð$&!'!#)1;?$B/;=)1L)1/;=)1/"/*-,"%E)f*-"(E/)1\!#6$ba )Oa 6
*-/2&4"%E)\p)12&:<"($&NO)0\:<Oh%*-\;=)1\!lm$&"(E/$BÇ)1:<97E\*-l:<\p)0'!#)1;a8!I$&"r$&!:~;r$B!#"%\$&M5'"%$&*-
, \p)1)"%)1!#"(6_"%E)1\):\)*~!#"%\p*-/3{:<!#!#'>L"%$B*-/!a
yr)1NO)12*-,O@$&35$&Ö9A:/97)OaoFI*-/!#'2B"/:G"%:M52&)I*-, N:2&')1!C,%*-\ xtTG:/1
; eü^ xtSU<6o*-\
xg+:<; eKu^ x/a_"(E/)1\lm$&!#)16'!#)G"(E/)GFIE$&h !#ñ5':\):LL\*-d<$&>?ï :"($&*-Ca1}=E/)GL\*-M5:M5$&2&$&"(4ï
;r$B!#"%\$&M5'"%$&*- *-, ';=)1\ ¾ 9A:XM5)¨:LL\*-d<$&>?:"()1; lm$B"%EX:
;=$&!#"%\$&M5'"%$B*- lK$&"%E
È
=
;
1
)
5
3
p
\
1
)
1
)
0
!
*

,
,
p
\
1
)
1
)
r
;
*
ê
>
&
$

,
%
"
E
m
)
/
'
>
5
M
1
)
f
\
*

,
A
9
*
&
2
'
>
/
#
!
6
w
c

g
*
ï Â ! eKcS<U/a
ï \+"(E/)m'>?M5)1\0*-,
\*-lm
ÊËE/)1"%*t'!#)"(E/)¤5\$&)1;=>?:"()1!#"%ÌØ}=E$&!L\*-97)1;='\)f!#E/*-'2&; /*-"rM5)'!#)1;ØlmE/)1
9A*->L:<\$&/3X\p)19A*-!#"%\p'9A"()1;!#)1\$&)1!0"(*Ç"(E/)m*-\$&35$&/:2©*-/)OaJC:"%E)1\%6='!#)m$B"C, *-\+:<!#!#)1!#!#h
$&/3m"(E/)Gñ5':2&$&"(4m*-,D\p)19A*-!#"%\p'9A"($&*-M5:<!#)1;*-L\p*-MO:M5$&2&$&!#"($&9!#:<>L2&$&/3¨, \p*->¬;=)1/!#$&"(4
L;r,¯B!#6lmE/)1Ø"(E/)~97*-\]\p)19A"r!#)1\]$&:"($&*-Ç$&!+/*-"|:KL\]$B*-\]$5/*-lm©a«m*-lm)1NO)1$6/:!+*-2&4?\p)1h
9A*-!#"%\p'9A"()1;w!#)1ñ5')1/97)1!0:$~'!#)1;,%*-\G:<:<2&45!#$&!#6$B"C>?)1:!#'\)1!+:t!#"%\p)1/35"(EX*-,C\)197*-/h
!#"%\p'9A"()1;?L:"("%)1\/6:/;/*-"$B"%!9A*-\\)12&:"($&*-mlm$&"(E"%E)f*-\$&35$&/:2OL:<"("%)1\Ca<}=E)1\)1,%*-\)16_$&"
>?$&35E/"rE/:LL)1"%E:<""(E/)fL\*-97)1;='\)G$&!$&/97*-\]\p)19A"/:<;Ç9A*-!#$&!#"()1/"(2&4\)1NO)1:<2B!:/*-"(E/)1\
L:<"("%)1\m$&m"(E/)G;=:"%:G"(E/:m"%E)G*-\]$&35$&:<25*-/)Oa
*0
42
2
42
5#
6
y m&_Fc"!=
Uu57u57 £BC9;BCrüu?
ºA<.BC>
7
¤O*-\K"%E)Ø\)197*-/!#"(\'97"($&*-:2&35*-\]$&"(E/>Ô;=*-)1!#¯B"+9A:\)?, *-\K"(E/)ØL*-2B:<\$&"%4 *-,f"%E)Ø\)197*-/h
!#"%\p'9A"()1; !#)1ñ5')1/97)16)Oa 3|a 6rSTgUYjiS<Z$&!"(E/)t!#:>?)K:<!SZijYUgT
S<6-lm)0/)1)1;ØÖ\]!#"="(*m;=)19A$B;r)flmE/$B9AE*-,|"(E/)"(lm*mL*-!#!#$BMO$B2&$&"($&)1!#6;=$&\p)197"*-\\p)1N)1\!#)1;?!#)1h
ñO')19A)16_$&!CL*-!#$B"%$&NO)12&4{9A*-\\)12B:<"()1;mlm$&"(EK*-\$&35$&/:2!#)1ñ5')1/97)16_:<;L$&9A'Lt"(E/)L\p*-L)1\
*-/)+, *-\"(E/)G"()1!#" a
] " =&d
98
U<g
ôõó
:
m?øû°ü~ûOÿ (*/,3ø 0ü °Õ),+.°X°Oøûø*/1-*)?ø*-1øûOÿ +./,+.-.+.3,øû+.(*-.+1üS/1
[)1\], *-\>?:/97)I*-,/!#)1NO)1K;=$&,(, )1\p)1/"!#)1\]$&:"%$B*-K"()19AE/$&ñ5')1!#6/:>?)12&4~"(E/)v':;r\:<"($&9C8!#h
!#$&35/>?)1"-[\*-M52&)1>Ù:<2B3O*-\$&"(E/>?6Q;r)1"(\p)1/;=)1;97*-\]\p)1!#L*-/;=)1/97)C:<:<2B4O!#$B!rx%¼§=FIJC8m8z%6
\)197$&L\p*-9A:2:N)1\:<35$&3x JC8z%619A*-\\)1!#L*-;r)19A):<:<2&45!#$&!C*-,!#:<>L2&)1!Cx F8z 61L\]$B/97$&L:<2
9A*->L*-/)1/"(!:/:2&45!#$&!Ix [F8z 6L\$&/97$&L:297*-*-\p;r$B/:"%)1!:<:<2B4O!#$B!Ix [FI*-8z%6:/;ÇL*-2B:<\
*-\;=$&:<"($&*-Çx%[z 6-lm)1\p)"()1!#"%)1;Ø*-Ç"(lm*t@JC¤>*-;r)12B!#6:<>)12&4A6O"(E/)M5)1"%:65:<;ØB\p*-*-,]¯
>?*-;=)12&!a}=E)+"()1!#"($&/3¨:<\\]:49A*-!#$&!#"%)1;*-,DSZf!#:>?L2&)1!#6!#L:9A)1Õ
; `Ü"d0*-t"(E/)G35\]:h
;r$B)1/"(6<97*->?L*-!#)1;*-,D'L"%*~Z<ZG!#L)197$&)1!a
;
5 465 4 ì0Z
A.?@B;[Z
»
Ê¥$&"(E"%E)fM5)1"(:>?*-;=)12&6<v8[972&)1:\]2&4{*-'"%L)1\, *-\>?!:<2&25*-"(E/)1\C"()1!#"%)1;!#)1\]$B:<"($&*->?)1"(E/h
*-;r!aC§=N)1?lm$&"(EÇ!#>?:2&2/'>M5)1\I*-,©!#L)197$&)1!$&/NO*-2&NO)1; $B":9AE$&)1N)1;X:M5*-'"|Z q)1,(Öh«óNFc
9A$&)19A476DlmE$&2&!#"C*-"(E/)1\!flm)1\p)~/)1:\]2&4H)1\*rau8Ø$&/"()1\)1!#"($&3?*-M5!#)1\]NO:<"($&*-Ølm:!G>?:;=)
"%E:<"lK$&"%E~v8[o67JC86Q:/;{¼§=FIJC8m86A"%E)u)1,%Ö97$&)1/974+$&>?L\p*-N)1;¨!#"%)1:;=$&2&4+lm$&"(E~$&/h
9A\p)1:<!#)1;/'>M5)1\*-,$B/;=)1L)1/;=)1/"!#L)197$&)1!$&/NO*-2&NO)1;a5m)1NO)1\]"(E/)12B)1!#!#6"%E)fv8[lm:!
:<2&lK:<45!+!#'L)1\]$&*-\"(*?*-"(E/)1\>)1"%E*-;r!f"%)1!#"()1;a}=E/'!#6$&"©:97E/$&)1NO)1; iZ ¦)1,(Ö97$&)1/974:"
<jf!#L)19A$&)1!#6lmE)1\)1:!C¼§=FIJC8m8ì;=$&;"%E)+!#:>?)G:"/:LL\*-d<$&>?:"()12&4~S<jZf$B/;=)1L)1/h
;r)1"u!#L)19A$&)1!0$&/NO*-2&NO)1;a§=d97)1L"u*-,JC86lmE$&97E¥lm:!:LL\*-d<$&>?:"%)12B4Ç*-,"(E/)K!#:<>)
)1,%Ö97$&)1/974:<!¼§=FIJC8K8¸x%'/)1d<L)19A"()1;X\)1!#'2&"(z 6O:2&2*-"%E)1\I>?)1"(E/*-;=!+"%)1!#"()1; lm)1\)
L)1\], *-\>?$&3KL*-*-\2&4|n"%E)14KM5)19A:>?)!#:"('\]:"%)1;N)1\4¨)1:\]2B4¨*-2&*-lð)1,(Ö9A$&)19A4{x F8×:"
:<LL\p*-daoU t61[FI86<[F*-86:/;L*-2&:\©*-\p;=$&/:"%$B*-mM5)12&*-lúS a
/<
=<
=<
/<
UU
&JÕm&F!
¾JI2K L ÁÂNM
U<Y
QSLÂNM®O¿ MKÀm¾IÂtKÀ2U sNRR ÁÃ
?>
1000
RA
QAP
800
DECORANA
number of hits
600
@
400
200
CA
PCoA, PCA, PO
0
0
20
40
60
80
140
160
180
200
§r,(Ö97$&)1/974G*-,;=$&,%,%)1\)1"_;r)1"()1\]>$&/$B!#"%$&9|!#)1\]$&:"($&*->?)1"(E/*-;=!=lm$&"(E"(E/)uM5)1"%:
>*-;=)12ba|·=)1\]"($&97:<2:<d<$&!I!#E/*-lK!+'>?M5)1\*-,|BE$&"%!#¯®6/$ba )Oa 6-L\p*-L)1\]2&4!#)1\]$B:<"()1;Ç"(\]$&:2&!
*-'"*-,S<ZZ<Z/atv8P
[ x ñ5':<;=\]:"($&9K:!#!#$&35/>)1/"IL\p*-M52&)1>Õ:2&35*-\]$&"(E/>6¼0§rFh
JC8K«
8 xt;r)1"(\p)1/;=)1;m97*-\]\p)1!#L*-/;=)1/97)I:/:2&45!#$&!#61JC«
8 xt\)197$&L\p*-9A:2:<NO)1\]:35$&/356
FÙ
8 x?97*-\]\p)1!#L*-/;=)19A)f:<:<2&45!#$&!*-,=!#:<>L2&)1!#6-[FIè
8 xÇL\]$&9A$BL:<2O9A*->L*-/)1"%!
:/:2&45!#$&!#6[FI*-
8 xXL\]$&9A$&L:2D97*-*-\;=$&:<"()1!:/:2&45!#$&!#6[
xØL*-2&:\*-\p;=$&/:"($&*-Ca
}=E)+L2B*-"/$&!uM5:<!#)1;*-tSg<jZZ<Z97:<2B9A'2&:"($&*-/!a
8!#*->?)1lKE/:"/!#$&>$&2&:\L:"%"()1\]{$&!C:9AE$&)1N)1;tlKE/)1K)1,(Ö97$&)1/974$&!C>?)1:!#'\p)1;m'!#$&/3{"(E/)
>?)1:K@L)1:\]>:<~\:<{97*-\]\p)12&:"%$B*-¨97*-)1,%Ö97$&)1" aov8[t$&!C:35:<$&{!#'L)1\]$B*-\"(*:<2&2*-"%E)1\
>?)1"(E/*-;=!#6/:2&"(E/*-'35EÇ*-"!#*tL\p*-/*-'/97)1;=2&4a "(!+)1,(Ö97$&)1/974t$&!G\)1:;=$&2&4t97*->?L:\)1;Ø"(*
"%E:<"u*-,JC8¬:<; ¼§=FIJC8m8a}=E/)1!#)m>)1"%E*-;=!:<97E/$&)1NO)1;w)1,(Ö9A$&)19A4Ø'L¥"%*ØS/a Z<Z/a
}=E/)14~:<\p)I,%*-2&2&*-lm)1;M54~[FI*-8 x :2&>?*-!#"OZ/a iz 6Q[FI8 :<;[ x :2&>?*-!#"OZDa Uz:/;=61Ö:<2&2B4A6
FI8 x :M5*-'"Z/a <z a
1
QAP, RA, DECORANA
0.9
PCoA
0.8
0.7
mean spearman
$&%
120
number of species
v ´5=+w &w
] & Ë
100
0.6
A
PCA
0.5
PO
0.4
0.3
0.2
CA
0.1
0
20
40
60
80
100
120
number of species
140
160
180
200
QFOGQSLÂNM®5¿ MKÀm¾Â¿ ®SUrR®®5ÂNMCÂ=ÀXÁ0U0ÂÁÂNMR%À2R Ã=ÁTR%¾ÃÂNMRK~ÁTR%¿ÀmÃ Uj
v %´5rp0&w w §=,(Ö9A$&)19A4G*-,;=$&,(, )1\p)1/"1;=)1"()1\]>$&/$&!#"($&9|!#)1\]$&:"%$B*->?)1"(E/*-;=!rlm$&"(E"%E)CMO)1"(:
>?*-;=)12baG·=)1\]"($&9A:2:d$&!f!#E/*-lm!"(E/)¨>?)1:Ø@L)1:\]>?:Ø\]:/9A*-\\)12B:<"($&*-X9A*-)1,(Öh
97$&)1/"r, \p*->¹SZ<ZZ"(\]$&:2&!arv8[ X
x ñ5':;r\:<"($&9G:!#!#$&35/>?)1"L\p*-M52&)1> :2&35*-\]$B"%E>?6
¼§=FIJC8m8 Ø
x ;=)1"%\p)1/;=)1;9A*-\\)1!#L*-;r)19A)f:<:<2B4O!#$B!#6OJC8ÙÇx \)197$&L\p*-9A:25:<NOh
)1\]:35$&/356oF8P{
x 9A*-\\)1!#L*-;=)1/97):/:2&45!#$&!*-,-!#:>?L2B)1!#6o[FI8 ¨x L\$&/97$&L:2<97*->?h
L*-/)1"%!:/:2&45!#$&!#6-[FI*-8ÙÇ
x L\]$&9A$BL:<2O9A*-*-\p;=$&/:"()1!:/:2&45!#$&!#65[Çx L*-2&:\u*-\h
>
;=$&/:"($&*-Ca1}=E/)GL2&*-"/$B!M5:!#)1;*-mS<gjZ<ZZ9A:2&97'2&:"%$&*-!a
;
5 465 7 VCWtBBCYXB;[Z
»
Ê¥$&"(E "(E/)B\p*-*-,]¯C>*-;r)12B6"(E/)v8[Ë!#)1\]$B:<"($&*- lm:!K)1NO)1w>?*-\p)?L\p*-/*-'/97)1;=2&4!#'h
L)1\]$&*-\I"(*t*-"(E/)1\I>)1"%E*-;r!G"()1!#"%)1;Xlm$B"%EÇ"(E/);=)1"()1\]>$&/$&!#"($&9f!#)1\]$&:"%$B*-ÇlmE/)1?/'>?M5)1\
*-,IE/$&"(!{lm:<!'!#)1; :!:>)1:<!#'\p)OaK8!~lm$&"(E"%E)MO)1"(:>?*-;=)12&6©v8[ :9AE$&)1N)1!)1,(Öh«bc
9A$&)19A4*-,©:MO*-'"|<Z q:"97:DaC!#$&dt!#L)197$&)1!#6/:/; "%E)~)1,%Ö97$&)1/974*-,©i*-;=)12&6<:"O:<M5*-'"/gZ+!#L)19A$&)1!C$B/NO*-2&N)1;a1}=E/)G!#:<>)"%\p)1/;=!u:!Clm$&"(Et"%E)MO)1"(:
>?*-;=)12<lK)1\)*-M5!#)1\]NO)1;n7)1,%Ö97$&)1/9740*-,5v8[6AJC86o:<;K¼§=FIJC8K8 $&>L\*-NO)1!lK$&"%E
$&/97\)1:!#$&3m/'>MO)1\u*-,=$&;r)1L)1;=)1/"!#L)197$&)1!$&N*-2BN)1;ÇlK$&"%E$&"%E)0:/:2&45!#$&G! E-E/*-lmh
)1N)1$6<M5*-"(EJC8Ù:/;¼§=FIJC8m8×2&)1NO)12-*-'":<\p*-'/;"%E)f'>?M5)1\C*-,!#L)197$&)1!uMO)1$B/3
U<Z6lKE/)1\p)"%E)14:97E/$&)1NO)"%E)1$&\>:<d<$&>?'>¹)1,%Ö97$&)1/974*-,:M5*-'"Z a|@'\]L\]$B!#$&/352&476
JC8×:35:<$Bm!#2&$&35E/"(2&4¨*-'"%L)1\, *-\]>!u¼§=FIJC8m8a
=<
<
/<
1000
number of hits
800
QAP
600
@
400
RA
200
DECORANA
CA, PCoA, PCA, PO
0
0
20
40
60
80
100
120
140
160
180
200
number of species
v %´5rp0&w ± w
§=,(Ö9A$&)19A4G*-,;=$&,(, )1\p)1/"1;=)1"()1\]>$&/$&!#"($&9|!#)1\]$&:"%$B*->?)1"(E/*-;=!rlm$&"(E"%E)uB\p*-*-,]¯
>?*-;=)12bar·r)1\"%$B9A:2/:d$&!!#E/*-lm!G/'>M5)1\*-,®E/$&"(!#¯B6O$ba )Oa 65L\*-L)1\2&4t!#)1\]$&:"()1;Ø"%\$&:<2B!
*-'"I*-,SZ<ZZ/av8ø
[ x ñO':;=\]:"%$B9K:!#!#$&35/>?)1"L\*-M52&)1>å:<2&35*-\$&"%E>?6u¼§=FIh
JC8m8 xt;=)1"($1;=)1;m9A*-\\)1!#L*-;=)1/97)I:<:<2B4O!#$B!#6JC«
8 xt\p)197$&L\*-97:2<:N)1\:<35$&356
FI8 x?97*-\]\p)1!#L*-/;=)1/97)f:/:2&45!#$&!I*-,=!#:>?L2&)1!#6[FIÙ
8 xL\]$&9A$&L:2O9A*->L*-/)1/"(!
:/:2&45!#$&!#6[F*-8 xØL\$&/97$&L:2D97*-*-\;=$&:<"()1!:<:<2B4O!#$B!#6[
xXL*-2&:\*-\p;r$B/:"%$&*-©a
}=E/)GL2&*-"$&!uMO:!#)1;*-mSg<jZ<ZZ97:<2&97'2&:"%$B*-/!a
&JÕ= !
¾JI2K L ÁÂNM
U<
?>
1
RA, DECORANA
QAP
PCoA
0.9
PCA
0.8
mean spearman
PO
0.7
A
0.6
0.5
CA
0.4
0.3
0
20
v ´5=+w º&w
40
60
80
100
120
140
160
180
200
number of species
§r,(Ö97$&)1/974G*-,;=$&,%,%)1\)1"_;r)1"()1\]>$&/$B!#"%$&9|!#)1\]$&:"($&*->?)1"(E/*-;=!=lm$&"(E"(E/)uB\p*-*-,]¯
>*-;=)12ba+·=)1\]"($&97:<2=:d$&!+!#E/*-lK!"%E)K>)1:<X@L)1:\]>:<Ç\:<Ç97*-\]\p)12&:<"($&*-Ø97*-)1,%Öh
97$&)1", \p*->¦S<ZZ<Z"(\]$B:<2&!arv8[ xØñO':;=\]:"%$B9+:!#!#$&35/>)1/"|L\*-M52&)1> :<2&35*-\$&"%E>?6
¼0§rFJC8m
8 xÇ;=)1"(\)1;r)1;9A*-\\)1!#L*-;=)1/97)0:/:2&45!#$&!#6-JC
8 xÇ\p)19A$BL\*-97:<25:Nh
)1\:<35$&356oFI8 xK97*-\]\p)1!#L*-/;=)1/97)u:<:<2&45!#$&!|*-,-!#:<>L2&)1!#6o[FI8 xKL\$&/97$&L:2_9A*->h
L*-)1/"(!:<:<2B4O!#$B!#6-[FI*-
8 xÇL\$&/97$&L:2/97*-*-\;=$&:<"()1!:/:2&45!#$&!#6-[
xÇL*-2B:<\*-\h
;=$&:<"($&*-©a}=E/)L2&*-"$&!MO:!#)1;t*-tSg<jZ<ZZ97:<2&97'2&:"%$B*-/!a
] & Ë
$&%
8 5M $&";=$&,(, )1\p)1/"-L:"("%)1\K$&!C*-M5"(:<$&)1;lmE/)1m)1,(Ö97$&)1/974$&!u>?)1:!#'\)1;t'!#$B/3{"%E)>?)1:
@L)1:\]>?:\]:/09A*-\\)12&:"($&*-¨97*-)1,(Ö9A$&)1" aQv8[¨$&!©:35:<$&~!#'L)1\$&*-\|"(*:2&2*-"%E)1\|>)1"%Eh
*-;=!a "r$&!G9A2&*-!#)12B4,%*-2&2&*-lm)1; M54JC8ú:/;X¼§=FIJC8K8a1}=E)1!#)>?)1"(E/*-;=!G:<97E/$&)1NO)1;
)1,%Ö97$&)19A4{*-N)1\CZ/a i<U/a}=E)14K:\)G, *-2B2&*-lm)1;?M54¨[FI*-8Ùx%:<2B>?*-!#"Z/a iUz 6_[FI8ìx Z/a <Uz 6_[
x :2&>?*-!#"ZDa z:/;=6_Ö/:2&2&476FI8 x :M5*-'"Z/a U<z a
ô$'
:
£mèþ.+1ÿ +.-.
8!>?)1"%$B*-/)1;w:MO*-NO)16="%E)tv8[!#)1\]$B:<"($&*- E/:!$&"(!2&$&>$&"%!M5)1$&3ØM5:<!#)1;*- :tB!#',%h
Ö9A$B)1/"(2&4*-NO)1\]2B:<LL$&397*->?L:97"|L:"%"()1\]¯D;=$&!#L2&:45)1; M54"(E/)~:<:<2B4OH)1;X9A*-)1*-9A2B$&/)Oa
}lm*{*-,"%E)f>*-;=)12&!'!#)1;=6:<>)12&4K"(E/)+.0:'!#!#$&::<;"(E/)fMO)1"(:0>*-;=)12&697*-/"(\*-25"(E/)
L:<"("()1\]Ø*-,u"%E)m35)1/)1\:<"()1; 97*-)1/*-972&$&)mNO$&:t"%':<M52&)¨L:<\:<>)1"%)1\!aG}<*?NO$&!#':2&$&H)K"(E/)
\]:/35)~*-,Cv8[X!#)1\]$&:"%$B*-Ø'!#:<M5$&2&$B"%476D:m!#)1\$&)1!G*-,C\)197*-/!#"(\'97"($&*-/!fMO:!#)1;X*-X>?*-;=)12&!
lm$&"(EO*-lmL:<\:<>)1"%)1\|!#)1"%"($&/35!IlK:<!\'©a¤O*-\uM5*-"(E>*-;=)12&!'!#)1;=6:0\)135'2&:\©:/;
\]:/;=*->ò!#:>?L2&$&3¥!#97E/)1>)1!Klm)1\p))1d:>?$&)1;a82&"%E*-'35E "(E/)\p)13O'2B:<\f!#:<>L2&$&/3
!#9AE)1>?)IlK:<!©,%:<\>*-\))1,%Ö97$&)1/"-"(E/:{"%E)I\]:/;=*->¸*-/)161$&"597*-'2&;tM5)I*-/2&4)1d<9A)1L"($&*-h
:<2B2&4¨\p)1:2&$&H)1;m'/;=)1\©\p)1:<2<9A$B\97'>?!#"(:<9A)1!a
5 765 4 ¸¹?
º_T<.?
>B;[Z
»
Ê¥$&"(Et"(E/)G.0:'!#!#$&:m>?*-;=)12&6"%E)1\)$B!:f!#$&/352&)GL:\]:>?)1"()1\%61"(E/)G>:<d<$&>?'>q"(*-2&)1\]:/97)16
Ê Ë*ÌGÍ 6lKE/$&97E ;=)1!#97\]$&M5)1!f"%E)Ko:"(/)1!#!#¯r*-,"(E/)K.0:'!#!#$&:<X97'\]NO)K'!#)1;"(*?>*-;=)12"(E/)
;
Qiq&QÇ÷ K LWsNRR#ÁÃ
Ui
>
!#L)19A$&)1!#¯C;=)1!#$&"%4 :<2B*-/3¥"(E/)35\]:;=$&)1/"]a}=E),%*-2&2&*-lm$&3!#)1\]$B)1!{*-,L2&*-"%!¨$&2&2&'!#"(\]:"()1!
E/*-lð9AE:<35$&/3¨>?:d$&>'>¬"%*-2B)1\]:/97)$&Co')19A)1!"%E)G)1,%Ö97$&)1/974~*-,Dv8[t!#)1\]$B:<"($&*-Ca
1000
100 species
800
number of hits
600
@
400
3 species
200
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
max tolerance
v %´5rp0&w £w
v8[X)1,(Ö9A$&)19A4lm$B"%EØ;=$&,(, )1\p)1/"=/'>M5)1\*-,©!#L)19A$B)1!#6/, *-\;r$B,%,%)1\)1"rL:h
\]:>?)1"()1\=!#)1"%"($&3O!a1m'>MO)1\=*-,OE/$&"(!©*-'"O*-,5S<ZZ<Z"%\$&:<2B!©lm:!©'!#)1;m:!©:>?)1:!#'\)
*-,C)1,(Ö9A$&)19A4aI*-;=)12=lm:<!f.0:'!#!#$&:/6lm$&"(E `ùC"!#:<>L2&)¨!#L:97$&/3|a:<d<$&h
>?'>¹"%*-2&)1\:<9A_
) Ê`ËJÌÍ0NO:<\$&)1;Ø, \p*->¹Z/a Z<S~"(*S/am'>MO)1\*-,!#L)197$&)1!$&N*-2&NO)1;
lm:!x%9A'\N)1!, \p*->q"%*-L"%*¨M5*-"%"(*->?z n-SZZ<6U<Z6Z6SU<6<S<Z6i66j6Y6U6g<6<:<;?T/a
}=E/)GL2&*-"$&!uMO:!#)1;*-mgT<Z<ZZ!#$&>'2&:<"($&*-!a
1
100 species
0.9
Spearman rho
0.8
0.7
B
0.6
0.5
3 species
0.4
0.3
0
v %´5rp0&w Ï w
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
max tolerance
v8[X)1,(Ö9A$&)19A4lm$B"%EØ;=$&,(, )1\p)1/"=/'>M5)1\*-,©!#L)19A$B)1!#6/, *-\;r$B,%,%)1\)1"rL:h
\]:>?)1"()1\=!#)1"%"($&3O!a1@L)1:\]>:<>)1:<{\]:/97*-\]\p)12&:"%$&*-~97*-)1,%Ö97$&)1" Ë *-,OS<ZZZ
$,%
±*"!!_ IÕ`Ü"
! H
¾JI2K L ÁÂNM
Y<Z
?>
"(\]$B:<2&!=lm$B"%E5/*-lK9A*-\\)197"<*-\p;=)1\lK:<!='!#)1;~:<!=:>?)1:!#'\)C*-,)1,%Ö97$&)1/974aA*-;=)12
lK:<!{.0:'!#!#$&:/6ulm$&"(ø
E ÜC"0!#:<>L2&)!#L:97$&/3|a?:d$&>'>ò"%*-2B)1\]:/97Ã
) Ê ËJÌÍ
NO:\]$&)1;, \p*->qZDa ZSf"(*KS/am'>?M5)1\C*-,=!#L)19A$B)1!$&N*-2BN)1;ÇlK:<!x 97'\]NO)1!,%\*->q"(*-L
"(*tM5*-"%"(*->?z nOSZ<Z6UZ<6-Z6S<U6-SZ<6-i6-<6-j6-Y6-U<6-g6-:<;ÇT/a}=E)L2&*-"=$&!IM5:!#)1;Ç*-
gT<ZZ<Z!#$B>?'2&:"%$B*-/!a
«! H
120
100
100 species
number of hits
80
@
60
40
20
3 species
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
max. tolerance
v ´5=+w &w
v8[ )1,(Ö97$&)1/974lK$&"%EØ;=$&,(, )1\p)1/"='>?M5)1\I*-,©!#L)197$&)1!#6/,%*-\I;=$&,(, )1\p)1/"=L:<h
\:<>)1"%)1\=!#)1"("%$B/35!a_K'>?M5)1\|*-,5E$&"%!C*-'"5*-,OS<ZZZI"%\$&:2&!lm:!©'!#)1;m:!©:>)1:<!#'\p)
*-,C)1,(Ö97$&)1/974aC*-;=)12lm:!G.0:'!#!#$&:<6Dlm$&"(E &ð!#:>?L2&)~!#L:9A$&3|a:d$&h
>'>ª"(*-2&)1\]:/97_
) Ê Ë*ÌGÍ NO:<\$&)1;Ø, \p*->¹Z/a Z<S"(*SDaK'>?M5)1\*-,©!#L)197$&)1!$&N*-2BN)1;
lK:<!x 97'\]NO)1!,%\*->q"(*-L?"(*KM5*-"("%*->z#nS<ZZ6UZ<6<Z6SU6SZ<6<i<66j6Y6U6g6:/;?T/a
}=E)+L2B*-"/$&!uM5:<!#)1;*-tgT<ZZ<Z!#$&>'2&:"%$&*-!a
1
100 species
0.9
number of hits
0.8
0.7
@
0.6
0.5
3 species
0.4
0.3
0
0.1
0.2
0.3
0.4
0.5
max. tolerance
0.6
0.7
0.8
0.9
1
Qiq&QÇ÷ K WL sNRR#ÁÃ
YS
v %´5rp0&w Ü w v8[X)1,(Ö9A$&)19A4lm$B"%EØ;=$&,(, )1\p)1/"=/'>M5)1\*-,©!#L)19A$B)1!#6/, *-\;r$B,%,%)1\)1"rL:h
\]:>?)1"()1\=!#)1"%"($&3O!a1@L)1:\]>:<>)1:<{\]:/97*-\]\p)12&:"%$&*-~97*-)1,%Ö97$&)1" Ë *-,OS<ZZZ
"(\]$&:2&!=lm$&"(E5/*-lm97*-\]\p)197"<*-\p;=)1\/lm:!='!#)1;{:!=:>)1:<!#'\p)C*-,)1,(Ö97$&)1/974a7*-;=)12
lm:!.0:'!#!#$&:/6©lm$B"%E&q
!#:>?L2B)t!#L:<97$&/3|am:d$&>'>å"(*-2&)1\]:/97)1Ê`Ë*ÌGÍ
>
$,%
NO:<\$&)1;,%\*->qZ/a Z<Sf"%*¨SDam'>M5)1\C*-,!#L)19A$&)1!$&/NO*-2&NO)1;?lm:!x%9A'\N)1!u,%\*->q"(*-L
"(*mM5*-"%"(*->?z nS<ZZ6U<Z6Z<6-SU6-S<Z6i6-<6-j6-Y<6-U6-g6-:<;ØTDa/}=E/)0L2&*-"|$B!IM5:<!#)1;Ç*-
gT<Z<ZZ!#$&>'2&:<"($&*-!a
100
80
60
40
20
0
0
0.2
0.4
0.6
0.8
1
v %´5rp0&w É w
y=*-lª)1,(Ö9A$B)1/974Ø.0:'!#!#$&:< >?*-;=)12©!#)1"("%$B/3|a¨m*-"()t"%E:<"@JC¤5!:\)¨/*-/h
*-NO)1\]2&:LL$&/3{$&m!#*->)G\)135$&*-!a
«m$&35E )1,%Ö97$&)1/974 lm:<!{:9AE$&)1N)1; , *-\\p)135'2&:\0!#:>?L2&)!#L:<97$&3¥!#97E/)1>?)16ulmE)1 "%E)
>?)1:!#'\)lm:<!¨"%E)Ç/'>M5)1\{*-,+E/$B"%!a¥}=E/$B!m>?)1:/!m"(E/:"lm)Ç$B/!#$&!#"()1; "%E:<""(E/)?:<M5h
!#*-2&'"%)12B49A*-\\)197""%*-L*-2&*-354lK:<!~\p)1N)1:2&)1;wM54 "(E/):/:2&45!#$&!a«m*-lK)1N)1$6©"(E/)$135'h
2&:<\G!#:>?L2&$B/3Ø!#97E/)1>?)K9A*-'2&;wE:<\p;=2&4?M5)¨)1N)1 :<LL\p*-d$B>?:"%)1; '/;=)1\G\)1:2r9A$&\p97'>?h
!#"%:/97)1!a ,lm)\)12&:d?"(E/)97*-/;=$&"($&*- *-,I:MO!#*-2B'"%)12&4 9A*-\\)197""%*-L*-2&*-35476u2&$&5)$Bw"%E)
9A:!#)lmE)1¨"(E/)>?)1:{@L)1:<\>?:{97*-\]\p)12&:"%$B*-{97*-)1,(Ö9A$&)1"-lm:!'!#)1;m:!:>)1:<!#'\p)*-,
)1,%Ö97$&)1/97456lK)3O)1"rñ5'$&"(){35*-*-; \)1!#'2B"%!lm$B"%EÇM5*-"(EÇ\p)13O'2B:<\:<;X\]:/;=*->¹!#:>?L2&$B/3
!#9AE)1>?)1!am}=E/)1/6:;=)197\)1:!#)1;)1,(Ö9A$&)19A4X*-979A'\\)1;wlKE/)1 Ê Ë*ÌGÍ lm:!{"(*-*X2&*-lG6C$ba )Oa 6
lmE/)1"(E/)*-NO)1\]2&:L*-,@JC¤5!{lK$&"%E$&"(E/)97*-)1/*-972&$&/)lm:!$&!#',%Ö97$&)1/""(* L\p*-;='9A)
'/$&ñ5')+!#*-2&'"%$B*-/!"(*~"%E)Gv8[a
5 765 7 ì0Z
A.?@B;[Z
»
Ê¥$&"(Ew"%E)MO)1"(:>?*-;=)12&6©"(E/)1\p)t:\)m"(lm*XL:\]:>?)1"()1\]!"(*XMO)t!#)1"(6©:<>)12&4 Ë*ÌGÍ 6©:<;
÷
ú, *-Ë*2&2&ÌG*-Í-lKa$&}/*-3t35!#)1)1"%E")1*-\%,6/!#"%$&E>?)14?'2&$&:p"($&o*-'/)1!#/6 97)KË*"(ÌGE/Í ){lm:<:!#45!>?!#)1>"/97)1*-"%\/4?!#"(*-:<,C"("E/"%){*{\ZD)1a U!#L6_:<*-; !#)~9AË*'ÌG\GÍ NN)1!:a\]$B%)1X;a1"%E )
ú
"%E$&!>:</)1$6_"%E)+:!#45>?>)1"%\4¨*-÷ ,D"(E/)G@JC¤{lm:!u9AE:<3O)1;a
;
¤O$B\]!#"(6O:~!#)1"=*-,!#$B>?'2&:"%$B*-/!lm:!9A:\]\$&)1;Ç*-'"=, *-\\p)13O'2B:<\u!#:>?L2&)!#L:9A$B/3|a=}=E)
$1!#'2&"(!~:<\p)m;=$&!#L2&:45)1; *-Ö3|a5j/a S<Z/a¨}=E/)t)1,(Ö9A$B)1/974 $B>?L\p*-N)1; \p)1>?:\]5:<M52&4ØlK$&"%E
$&/97\)1:!#$&3'>?M5)1\*-,!#L)197$&)1!I$&N*-2&NO)1;ar¤5*-\:97*-/!#"(:/"'>?M5)1\*-,!#L)197$&)1!#65"%E)
¾JI2K L ÁÂNM
Y<
,%*-\"%E))1:<\2&45h !#45>?>)1"%\$&97:<2C97:<!#)16 Ë*ÌGÍ ½
÷
?>
>?:d$&>'>ò)1,%Ö97$&)19A4 lm:!¨:9AE$&)1NO)1;
óN6 &IÕ`ùC"! H ú *Ë ÌGÍ a
1000
900
100 species
800
number of hits
700
@
50 species
600
500
400
300
200
100
4
5
6
7
8
9
10 species
15 species
20 species
3
0
0
5
10
15
20
gammamax
v ´5=+w éw
v8[)1,(Ö9A$&)19A4{lm$&"(E;=$&,%,%)1\)1"5/'>?M5)1\C*-,!#L)197$&)1!#6, *-\C;=$&,(, )1\p)1/"5L:<h
\:<>)1"%)1\=!#)1"("%$B/35!a_K'>?M5)1\|*-,5E$&"%!C*-'"5*-,OS<ZZZI"%\$&:2&!lm:!©'!#)1;m:!©:>)1:<!#'\p)
*-,)1,(Ö97$&)1/974a1*-;=)12-lm:!uMO)1"(:6lK$&"%Õ
E `Ü"©!#:>?L2B)+!#L:97$&/3|a Ë*ÌGÍlm:!uZDa U
"(E/\p*-'35E/*-'"(6 Ë*ÌGÍINO:\]$&)1;t,%\*->ZDa SG"%*Z/a1K'>?M5)1\*-,!#L)19A$&)1!C$B÷ /NO*-2&N)1;lm:!
x%9A'\N)1!, \p*->qú "(*-L?"(*KM5*-"%"(*->?z nS<ZZ<6UZ<6<<Z6SU<6<S<Z6i66j6Y6U6g6:/;?T/a}=E/)
L2B*-"D$&!uM5:<!#)1;*-mgg<gZZ<Z!#$&>'2&:"%$&*-!a
1
100 species
0.9
50
Spearman rho
0.8
0.7
B
20
0.6
15
10
0.5
0.4
3
0.3
0
v ´5=+w o&w
2
4
6
8
10
12
14
16
18
20
gammamax
v8[)1,(Ö97$&)1/974¨lK$&"%E;=$&,(, )1\p)1/"5/'>M5)1\*-,!#L)197$&)1!#6, *-\C;=$&,(, )1\p)1/"OL:<h
\:<>)1"%)1\=!#)1"("%$B/35!a_@L)1:<\>?:{>)1:<~\:<9A*-\\)12&:"($&*-¨97*-)1,(Ö9A$&)1" Ë *-,SZ<ZZ
$&%
YT
>
"(\]$&:2&!=lm$&"(E5/*-lm97*-\]\p)197"<*-\p;=)1\/lm:!='!#)1;{:!=:>)1:<!#'\p)C*-,)1,(Ö97$&)1/974a7*-;=)12
lm:!0M5)1"(:<6DlK$&"%E `Ü"!#:>?L2&){!#L:<97$&3a Ë*ÌGÍ lK:<!fZDa UK"(E/\p*-'35E/*-'"(6 Ë*ÌGÍ
NO:<\$&)1;,%\*->qZ/a S0"(*KZDam'>M5)1\C*-,!#L)19A$&)1!÷ $&/NO*-2&NO)1;?lm:!x%9A'\N)1!u,%\*->qú "(*-L
"(*mM5*-"%"(*->?z nS<ZZ6U<Z6Z<6-SU6-S<Z6i6-<6-j6-Y<6-U6-g6-:<;ØTDa/}=E/)0L2&*-"|$B!IM5:<!#)1;Ç*-
gg<gZ<ZZ!#$&>'2&:<"($&*-!a
&«!& H
90
80
70
number of hits
60
50
@
40
30
20
10
0
0
2
4
6
8
10
12
14
16
18
20
gammamax
v %´5rp0&w w
v8[)1,%Ö97$&)1/974{lm$&"(Et;r$B,%,%)1\)1"'>?M5)1\C*-,D!#L)197$&)1!#6,%*-\©;=$&,%,%)1\)1"L:h
\]:>?)1"()1\=!#)1"%"($&3O!a1m'>MO)1\=*-,OE/$&"(!©*-'"O*-,5S<ZZ<Z"%\$&:<2B!©lm:!©'!#)1;m:!©:>?)1:!#'\)
*-,)1,%Ö97$&)1/974a0*-;=)12lm:!M5)1"%:6=lm$&"(
E &!#:<>L2&)m!#L:9A$B/3|a Ë*ÌGÍ¨lm:!
Z/a U"(E/\p*-'35E/*-'"(6 Ë*ÌGÍN:\]$&)1;K, \p*->Z/a S"%*-LtZDaQK'>?M5)1\|*-,O!#L)197$&)1!©÷ $&N*-2&NO)1;
ú "%*-L"%*¨M5*-"%"(*->?z n-SZZ<6U<Z6Z6SU<6<S<Z6i66j6Y6U6g<6<:<;?T/a
lm:!x%9A'\N)1!, \p*->q
m*-"()0"(E/:"=)1,%Ö97$&)1/974K;=)197\)1:!#)1;:<M5*-'""()1"($&>?)1!9A*->L:<\p)1;?"(*K\p)135'2&:<\C97:!#)
x 45h%:<d<$&G! E_9A*->L:<\p)IÖ3|a j/a S<Zz#aQ}=E)L2&*-"D$&!uM5:<!#)1;*-mggg<ZZ<Z!#$B>?'2&:"%$B*-/!a
¾JI2K L ÁÂNM
Y<g
?>
1
0.9
Spearman rho
0.8
B
0.7
0.6
0.5
0.4
0
2
4
6
8
10
12
14
16
18
20
gammamax
v ´5=+w ± w
v8[)1,(Ö9A$&)19A4{lm$&"(E;=$&,%,%)1\)1"5/'>?M5)1\C*-,!#L)197$&)1!#6, *-\C;=$&,(, )1\p)1/"5L:<h
\:<>)1"%)1\=!#)1"("%$B/35!a_@L)1:<\>?:{>)1:<~\:<9A*-\\)12&:"($&*-¨97*-)1,(Ö9A$&)1" Ë¥*-,SZ<ZZ
"(\]$B:<2&!=lm$B"%E5/*-lK9A*-\\)197"<*-\p;=)1\lK:<!='!#)1;~:<!=:>?)1:!#'\)C*-,)1,%Ö97$&)1/974aA*-;=)12
lK:<!+M5)1"%:6/lm$B"%E &ú!#:>?L2B)¨!#L:9A$B/3|a Ë*ÌGÍ lm:!fZ/a U¨"(E/\p*-'35E/*-'"(6 ËJÌÍ
NO:\]$&)1;m,%\*->ðZ/a SI"%*-LK<Z/aAm'>MO)1\r*-,5!#L)19A$B)1!÷ $&N*-2&NO)1;tlm:!x%9A'\N)1!|, \p*->¸ú "(*-L
"(*tM5*-"%"(*->?z nOSZ<Z6UZ<6-Z6S<U6-SZ<6-i6-<6-j6-Y6-U<6-g6-:<;ÇT/a}=E)L2&*-"=$&!IM5:!#)1;Ç*-
ggg<ZZ<Z!#$B>?'2&:"%$B*-/!a
$
%
100
80
60
40
20
0
0
v ´5=+w ºw
0.2
0.4
0.6
0.8
1
y=*-lå)1,(Ö97$&)1/974¥M5)1"(:Ø>?*-;=)12!#)1"("%$B/3|am*-"%)"%E:<"G@JC¤5!m:\p)E)1:<NO$&2&4
:!#45>?>)1"%\$&9A:2ba
5 765 z 1W Zuº»A.
YU
>
;
}rE)G>?*-!#"/$B>?L*-\]"(:/"/;=$&,(, )1\p)1/97)$Bm)1,%Ö97$&)19A4~lm:!C*-M5!#)1\]NO)1;lKE/)1m;=$&,(, )1\p)1/"->)1:<h
!#'\)1!#6_/:>?)12B4{"(E/)'>?M5)1\*-,E/$&"(!#6:<;"(E/)>)1:<¨@L)1:\]>?:~\]:/~97*-\]\p)12&:<"($&*-¨9A*-h
)1,%Ö97$&)1/"(6Olm)1\)09A*->L:<\p)1;a=82&"(E/*-'35EÇ"(E/)1\p)lm:!:{E/'35);=\*-LÇ*-,|)1,%Ö97$&)19A4t>)1:<h
!#'\)1; :<!{/'>MO)1\*-,E$&"(!Klm$&"(E "%E)97E/:/35), \p*->ò\)135'2&:\"(*¥\]:/;=*->ò!#:>?L2&$B/3 Ü"! H2! m& !
!#9AE)1>?)16"%E)1\)lm:!¨*-2&4:Ç!#2B$&35E/"G;=$&,%,%)1\)19A)KlmE/)1 @L)1:\]>:<lK:<!{'!#)1;aØ}=E$&! ¡ Én"Cm
!#E/*-lm!¨"%E:<"lmE/$B2&)"(E/)\p)19A*-!#"%\p'97"%)1; !#)1ñ5')1/97)1!~:<\p)t/*-"S<ZZ ¹9A*-3O\p')1/"(6C"(E/)14 `!
!#"%$&2B2D9A*-"%:$&:3O*-*-;X;=)1:2*-,r$&/,%*-\]>:<"($&*-"%E:<"=97*-'2&;ØM5)$&/"()1\]L\p)1"()1;?:!I\)12B:<"()1;?"(*
"%E)+35\:<;=$&)1" a
?:/4t97:!#)16O"(E/)0)1,%Ö97$&)1/974tlm:!I$&9A\p)1:<!#$B/3lm$&"(E?$&9A\p)1:!#$&/3t'>?M5)1\*-,r$&/;=)1h
L)1/;=)1/"I!#L)197$&)1!~$&N*-2&NO)1; lm$&"(E/$& "(E/)!#"%';=4a%"lm:!~!#"%$&2B2NO$&!#$&M52&4 $&/97\p)1:<!#$&3 :"
S<ZZ?!#L)197$&)1!~$&/NO*-2&NO)1;a}=E/'!{$&,I97:<wM5)35)1/)1\]:2&2&4 \p)19A*->>?)1/;=)1; "%* $&N*-2&NO):<2&2
!#L)19A$&)1!:<"E:<;Çlm$&"(E"%E)0:/:2&45!#$&!am*-"\p)12&)1NO:<"D$&/,%*-\]>:<"($&*-/6-)Oa 3|a 6, \p*-> ;=)1L)1/h
;r)1"!#L)197$&)1!#6|*-\0!#L)197$&)1!E/:N$B/3X"%E)t!#:<>)m;=$&!#"(\]$&M5'"($&*-M54X9AE:<9A)16|9A:/97)12&!*-'"
:<'"(*->?:"%$B9A:2&2&4a
}rE)f.f:<'!#!#$B:<>?*-;=)125!#E/*-lK)1;Ç"%E:<""(E/)+v8[!#)1\]$&:"%$B*-lK*-\]5)1;?M5)1!#", *-\C:f!#$&/h
3O2B)K!#)1"("%$&3Ç*-, Ê`Ë*ÌGÍ~x :M5*-'"©Z/a ¨, *-\SZm!#:>?L2&)1!#Fz ErlK$&"%
E Ê`Ë*ÌGÍ{2&*-lK)1\"%E:<X"(E/)K*-L"($&h
>?'>NO:<2&')16)1,%Ö97$&)19A4;=\*-LL)1;Xñ5'$&97O2B4?"(*H)1\*raC "|$&!+"%E){\p)1!#'2&"|*-,©$&/!#',(Ö97$&)1/"
*-N)1\2&:<Lt97*-/"(:$&/)1;$&¨!#"%$&2B2-9A*->L:<97"L:"("%)1\¨*-,"%E)9A*-)1*-9A2&$B/)On1:<!C"(E/)1\p)I:\)I®35:<L!#¯,> dd!HC¶F µ H
lmE/)1\p)/*{"%lK*{!#L)197$&)1!C*-NO)1\]2&:L6_"%E)!#)1ñ5')1/97)+E:<!u!#)1NO)1\]:2)1ñ5'$&NO:<2B)1/"/*-L"($&>:<2-!#)1h !`C!
\]$&:"%$B*-/!#6:<;$B"$&!u"(E/)1¨:f>:<"("%)1\|*-,/97E/:/97)$&,/"(E/)97*-\]\p)197"O*-)G$&!C:<97E/$B)1N)1;tM54{v8[o6 &&d *Fm a
*-\©/*-"]a
"%E)*-"%E)1\0E/:/;=6©v8[w)1,(Ö97$&)1/974X;r\p*-LL)1;w!#2&*-lm2B4¥lm$&"(E Ê Ë*ÌGÍ $&/97\p)1:<!#$&3
:<M5*-NO)+$B"%!u*-L"($&>?'>qNO:<2B')16:/;¥V*-\©lm$&"(Et$&9A\p)1:<!#$B/3~\)1!#L*-!#)G:<!#45>?>)1"%\4¨$Bt"%E)
MO)1"(:+>?*-;=)125x $&9A\p)1:<!#$B/3 Ë*ÌGÍ h Ë*ÌGÍ ¼
z#a
"!
ú
/<
÷
ú<-P÷
Y<Y
¾JI2K L ÁÂNM
?>
(¥k{øúü0/ )ø*/,+.-.+1ø*
ôõó
C
D
¼)1/!#$&"(4¥$B!{"(E/)L\p*-L)1\fNO:<\$&:"%)t"(*XMO)'!#)1; lm$&"(Ew"(E/)35\]:;r$B)1/":<:<2&45!#$&!{xx\p)197*-/h
!#"%\p'9A"($&*-z 6/:!I;=)1/!#$B"%476*-"|)19A)1!#!#:\]$B2&4:<M5'/;=:/97)165!#E/*-lm!G"(E/)"(4OL$B9A:2/'$&>?*-;=:2
x *-\u*-"%E)1\]lm$B!#)9A*->L:<97"(zL:<"("%)1\*-,r;=$&!#"(\]$BMO'"($&*-©a}=E/'!#6lm)f>?$&35E"r97*-/!#$B;r)1\u:'!#h
:<35)+*-,v8[\p)19A*-!#"%\p'97"%$&*-:2&35*-\]$&"(E/> *-t:M5'/;=:<9A)1!u:!$B/:LL\*-L\$&:<"()16MO'"/!#)1)
2&:<"()1\]aQÞ/, *-\"%':<"()12&476AlK);=*G/*-"O*-lì"%E):9A"(':2oN:2&')1!=*-,;=)1/!#$B"%$&)1!#6AE/:N$B/30*-2&4
"%E)1$&\uL\*-M5:MO$B2&$&"(4¨;=$&!#"(\]$&M5'"($&*-/!x L;=,]¯®!#zD:"/E/:/;a}=E/'!#6<"%E)fL\p*-L)1\©'!#:3O)+$&!L\*-M5h
:<M5$&2&$B!#"%$&9a1 "/>)1:<!C"%E:<"/*~!#$&3O2B)fE4OL*-"(E/)1!#$B!:M5*-'""(E/)G/:"('\]:235\]:;r$B)1/"O*-\;=)1\r$&!
>?:;r.) E_$&!#"%)1:N; E<:+lmE*-2&)GMO'9AEt*-,x ;=$&,(, )1\p)1/"(2&4L\p*-MO:M52&)1zO*-\;=)1\]!C:\p)I35)1/)1\]:"()1;a
C
ô$'
(¥k{øúü0/ (ý,/1),(*/,3|ø*
D
Þ!#$&/3 v8[ x :!lm)12&2C:!*-"%E)1\;=)1"%)1\>?$&$&!#"($&9Az\)197*-/!#"(\p'9A"($&*-w*-:M5'/;=:<9A)1!0$&!
3O)1)1\]:2&2&4+/*-"97*-\]\p)197"%67'/"($&2_:<2B21:<M5'/;=:/97)1!=:<\p)©)1dL)197"()1;{"(*+2&$&)u$&::<\\*-lË/)1$&35E/h
MO*-\pE/*-*-;K*-,-;r)1!#$&"($&)1!aQ}=E/$&!|$&!|'!#':2&2&4f/*-"-"(\')'/"($&2:<2B21:<M5'/;=:/97)1!|:\p)CN)1\40E/$B3OE
x "(E/*-'!#:/;=!u*-,D$&/;=$&NO$&;=':2&!C, *-\|)1N)1\4{!#L)197$&)1!C$&K)1N)1\4{!#:>?L2B.) E"(E/$B!97*-/;=$&"($&*-t;=)1h
\]$&NO)1!C, \p*->"(E/)[*-$B!#!#*-m;=$&!#"%\$&M5'"%$B*-/z 6_!#:>?L2&$B/3~N*-2B'>?)16_:<;t!#)1;=$&>?)1"%:"%$B*-m\]:"%)
:<\p)97*-/!#"(:<"%6, *-!#!#$&2&$BH<:"%$B*-Ç9AE:<9A)0$&!G9A2&*-!#)"(*S<ZZ Òx "(E/$B!+;=)1\$&N)1!, \p*->¹"(E/)M5$&/*-h
>?$&:2;=$&!#"%\$&M5'"%$B*-/z 69A*-"%:>?$B/:"%$&*-?$&/"()1/!#$&"(4?$B!9A2&*-!#)~"(*H<)1\p*-65:<; >)1:<35)1/)1\]:h
"%$&*-t2B)1/35"%Et97*-/!#"(:/"]a a a
=<
¡m&î& b@d,&F !F !f!ê*m:` !!!rFm
!dF nD" ` "& ¦
Yj
Y<
¾I2K L ÁÂ¡M
&QÃVÃ
Ki0Â
FE
G
Òû-.+ 3+.(þmø *(ÿ½ù?þ1ø
5 465 4 ?
AH?
ôõó
H
JI
{ó
3K
M
L
}*K"()1!#"D"(E/)+lmE/*-2B)0L\p*-9A)1;='\p)16:f!#$&>?L2B)0:\]"($&Ö9A$B:<2-)1d<:<>L2&)GB\p'/h S7S¯-E/:!M5)1)1t35)1/h
)1\]:"%)1;'!#$&/3¨"%E2
) Î DÏoL\*-35\:<>aFI*->>?*-L:<\:<>)1"%)1\!ulm)1\)G!#)1""%*rn<L2B*-" x
Z<6O2&*-lm)1\)1/; xXZDa Z6O'LL)1\)1/; xXS/a Z6-*-NO)1\]2&:L xØZDa /a|.0:'!#!#$&:?>*-;r)12lK$&"%E\]:/h
;r*->2&4!#L:<97)1;Ç!#:>?L2&)1!E:<!M5)1)1'!#)1;a=:d$&>'>¹"(*-2&)1\]:/97S
) Ê Ë*ÌGÍ *-,"(E/).f:<'!#h
!#$&:<K>?*-;=)12-E/:!uMO)1)1K!#)1"/"(*{Z/a SDaQJC:/;=*->¬'>?M5)1\©!#)1)1;=!ulm)1\p)S<6_:/;UDa
}rE)G3O)1)1\]:"%)1;t;=)1!#$&"%$B)1!:\p)!#E/*-lmt$&K"%:M52&)iDa S6_:<;L2B*-"%"()1;*-KÖ3a#i/a S:/a
!#L)19A$B)1!
!& !
!& !
!& !
!& !
!& !
!& !
!& !
!& !
!& !
! !
S
ON
OP
OQ
OR
OS
OT
OU
OV
OW
N=X
Y
S
S
<S i
S
S
S
S
S
Sg
S
S<
gZ
S
UY
gZ<i
S
Y<i
S
Yg
S
j

S
Zi
gTY
U
S
YS
;r)1!#$&"($&)1!u:<"!#$&"%)1!
Yg
Y<g
U<
T<U
S
S
S
S
j
j<
<S
S<T

S
S
S
S
S
S
<Zi <Zi j<Z
<
g<TY g<TY S<Z Y<T
U
U
< S<j
S
S
S
S
YS
Y<S S?L2&)1!|lm)1\p)"(E/)1~!#E/',·o)1;K"(*0!#"(:\]"-lm$&"(E~:I\]:/;=*->ð*-\p;r)1\*-,-!#:>?L2B)1!a1}=E)1!#)
;r)1!#$&"($&)1!Klm)1\p), )1; "%* "%E
) Î nD"5¯CL\p*-3O\:<>å"%* >?:L "(E/)1>½*-/"(*¥:M5'/;=:/97)1!a
}rE'!#65lm)!#$&>'2&:<"()1;Ç'!#':2/!#"(:<\"%$B/3m;=:"%:,%\*-> "(E/)Ö)12&;?x Ö3|aAi/a SM5z#a}=E)0L:\]:>?)1h
"%)1\!#)1"%"($&3lK:<!;=*-/)0!#*t"%E:<"=)1d"(\p)1>?)12&4t:<\\*-l¸'/97)1\]"(:<$B/"($&)1!lm)1\p)0L'"r*-/"(*t:<2&2
L:<\:<>)1"%)1\!"(*{MO)G)1!#"($&>?:"()1;n ½ ZDa ZZ<&S ETÉ ½ Z/a Z<ZZZ<&S Ef z ½ Z/a ZZZ<&i Ef | ½ ZDa ZZ<S7S E
àz ½ ZDa iU E
à}| ½ SDa ZZ E z ½ ZDa &Z E Æ |y ½ Z/a Z<&S E y ½ S/a Z<&Z E
É ½ Z/a SDa
ZP
ÆT~
Yi
~
] &F!
¾JI2K L ÁÂNM Q{¾JKÃÂÃ=ÁNVUrR%ÂrÃ
j<Z
?[
5 465 7 ÔÑ[º[>_;[?
>üuZ,TZ
9H<H?
A~<HBC>
L
8M5'/;=:<9A)>?:"(\]$&d,%\*->ú"(E/)L\)1NO$&*-'!!#'M5!#)197"%$B*-{lK:<!|"%\:<!#L*-!#)1;m:<;K,%)1;K"(*0"(E/)
{ D&¶nD ûÏ_L\*-35\:<> "%*L\p)1L:<\p)0"(E/)~;=:<"(:~, *-\I"(E/t
) Î &&¶CÏ_L\p*-35\]:>¹"(*;=*"(E/)
v8[?!#)1\$&:<"($&*-*-"%E)1>wa@)1\$&:"%$&*-t\p)1NO)1:<2&)1;"(E/)0!#:>?L2B)0*-\p;r)1\onYTUSZjSgi
E_"(E/)G!#)1\]$B:<"()1;9A*-)1*-9A2&$B/)G*-,D:MO';=:<9A)1!C$&!uL2&*-"("()1;*-mÖ3|a#iDa S9a
JP=8
\8
5 465 z Z
>_<ApoèTZ
9D<.?
A~<HBC>
M
L
8M5'/;=:<9A)~>:<"(\]$&d,%\*->!#'M5!#)197"%$&*-Xi/a SDa SKlK:<!+'!#)1;¥"(*?35)1/)1\:<"(){:m"%)1!#*-\G*-,CT<Z
;=)1/!#$&"(4Ø>?:"%\$&97)1!0'!#$&3Ø"%E)KL\p*-3O\:<> Î &Ï<lmE$&9AE $&>?L2B)1>?)1/"(!)1ñ5':"%$&*- U/a Si
N$B:f!#$&>'2&:"%$&*-©a<}=E/'!#6"%E$&\]"(4{$&/;=)1L)1/;=)1"/)1!#"($&>?:"%)1!ulm)1\p)35)1/)1\:<"()1;, *-\©;=)1/!#$B"%4
*-,D)1NO)1\]4{!#L)19A$&)1!u:")1:97Em!#$&"()Oa¤5\*->Ò"%E$&!"()1/!#*-$6Y<+>?:"%\$&97)1!*-,/$&/,%)1\]\p)1;s=:45)1!#$&:<
;=)1/!#$&"($&)1!©x%9A:!#)1!ZZ<Z"(*ZY<Sz5lm)1\p)35)1/)1\:<"()1;mlm$&"(E Î &tÏL\p*-35\]:>wao}=E/)1!#)I>:<"(\]$&h
9A)1!ulm)1\p)G"%\:<!#L*-!#)1;:/;$&L'"D"%*{"(E/_
) Î D&¶nD ûÏ7L\*-35\]:>¬"(E/:"/L:!#!#)1;"(E/)1>q"(*
"%E)Gv8[!#)1\$&:"%$&*-KL\*-35\]:£
> Î &&¶CÏBa
5P
]P
^P=8
\8
}=E/)~Ö\]!#"Y<{9A:!#)1!L\p*-;r'97)1;X:¨E:<;=, '2*-,©E4OL*-"(E/)1!#)1!#6/lmE/$&97EØ:$L\p)1!#)1/"()1;
M5)12&*-lúx "(:<M|a i/a G:/;Ö3|a#i/a S<;=h%2&z#a
Y
Ö3|a#iDa S
;
)
,
3
E
$
P

2
>
97:<!#)
ZZ<Z
ZZ<S
ZZ<
ZZ<g
ZS<Y
ZS<
Z<Z
Z<g
Z<i
ZT<T
-* \p;r)1\
fYfT+U+S<Z+j0S+gfi+
fYfT+SZfU+j0S+gfi+
fYfT+U+j0SZfS+gfi+
fYfT+j+U0SZfS+gfi+
fYfT+SZfj+U0S+gfi+
fYfT+j+S<Z+U0S+gfi+
ffT+SZfU+j0S+gfi+Y
ffT+j+S<Z+U0S+gfi+Y
ffT+U+S<Z+j0S+gfi+Y
ffT+SZfj+U0S+gfi+Y
<»=³ É w w @)1NO)1\]:2x%/*-"+/)197)1!#!#:<\$&2&4w"(E/)ÇE$&35E/)1!#"f2&$&5)12&$&E*-*-;rzfE/45L*-"(E/)1!#)1!t:MO*-'"
!#:>?L2B)+*-\p;=)1\"(E/:":\p*-!#), \p*->¬"%E)GÖ\]!#"/YG9A:!#)1!u*-,/;=)1/!#$B"%4¨!#)1\]$&:"%$B*-Ca
QFOGQSK MÁTR®R ¾RK sÂ K Lus=Â CO
,_
jS
`
0
0
abundance
500
500
0
9
0
gradient
0
0
9
0
9
9
reconstructed gradient
f
e
inferred density
inferred density
500
hypothetical gradient
500
arbitrary order
d
0
c
b
abundance
population density
a
500
0
0
9
inferred density
[
500
0
0
9
a5b"cHdfehgZikj=d9lnm9bom9p]d9gZp\j=ehpqpqdnlng
csrht5j/ehpqbou vodfwJbopqxypqx=dfrhl9b z\bogZe^v
rhg{dfl.d9|=d9ehv"dniyu }kmndn|/dnl9ehv
x=}/j=r^p]x/dnmnd9m
¾JI2K L ÁÂNM Q{¾JKÃÂÃ=ÁNVUrR%ÂrÃ
j<
?[
0
9
0
0
9
500
0
9
0
0
9
k
inferred density
inferred density
j
0
500
500
0
0
9
l
inferred density
0
500
inferred density
500
i
h
inferred density
inferred density
g
500
0
0
9
~ZqZ9y/=J5H^"/===Z ¡¢"/£?^¤&¥¤&^"¥{£¥ ¡ J=¤&¥¦§¨
¦Z9/£¥]©4ªZ1/ªZ¢¥£«=¥h ¡/¬£=4 ¡=¥¦® ¡/¬¥¦ ¡ ¯¤&°²±q=³q©4h
h¤&¥¤&h¥²/¥£]¨J¦{9/£¥Z9h¤&¥ ¡9¢h£°]9¤&´ ¡=£=ªZ¢¥£/¥^ O¢ ¡µ
"¥¦]¨y¶55·=¦Z¤&H"]¨©=£µ{= ¡¸9//¨¹Z¤&¨ ¡ º]¨/{¤&h^¢99£9 ¡»¨¥
n¢¥¥¥¦Fn¤&ªZ/ªZ" ¡]k¶55·( ¡H"/¤&¥?¤&¥¼¥°]Hn£½£¥ ¡"] ¡©«¥¤&¯¨=*¨
h¤&¥¤&h¥4=]H¥¾¦Z¥9/"¹¨¤&£ f»¨"4]¨91=91¥¤&fh¨=¥¦Z f¥¾ ¡/¬µ
"¤&9£9¥¦?±]]¨¯ ¡H"/¤&¥¼¤&°¿¨ ¡=" ¡³¿ªZ»¥F¨¹Z¤&]¨ ¡ =¾À*h=
¨=1Á"n¢¥µqh=Âf¢ ¡£®/]n¹?¥/99¤&»Ã¢¥hH/"¥ °q¤&y==H=H k¤
ªZ² ¡=]£¿
Qiq&QSK M TR®R
[
ÅÄ
ÐJÑÓÒ
qÆÅÇqÈ5É§Ê,_yÈ5ËÌÉÊ`=Í
Î=Ï
ÔÖÕ{×ØHÙ®ÚfØÛJÜÝJÞJÛJßáàÜÝ3âÒ
ã1ä å1ä æ
çèéêè
-) /. 0 0 .21
? GF
E
I
H * % P/ 2 RQ (/D @ ( @2@ X0
(@ @ A\[])
@ ( @ @ ( @2@ 2 H a )
(
C2)
0
ë5ìí=îHïðñò^ð"í/ó4ôí=ï]íFõ¡öïy÷"înøìù]ú/û=ü¿ð"ìïöìôöôýï]þ®înöõ¡öÿ
!"#%$"'&(
)
0? 2
2
(KJ MN H );
S R)
V
@ ( @2@@ ZY0
) %_
@ ( `2`
( @ ô«í=ïí/ü
qõ¡öö?ìö /ïõ¡öòhïðþ&ì
ëõ¡öïOþ
óöõ
îHí=ìôþ&ÿ
Zõyþ
ðò Fðÿ
Zööì
ú²ÿ
{öìöîHí=ï]ð"þ&ìú
qþ&ó"óþ
ö
/õ¡öôðÿöìï]í=ï]ð"þ&ìîHí=ï]ö
í
ïþú
ökî9í
D
ôí/ïí
ZîHí=ÿ
9 óö
{þ&óøÿ¬ö
úyï]þ
{ö
î9þ
öõ¡öï]ù
qþ&î*í=óóZõ¡í/ÿ
ïþ
û ,óöì
Zï þ
0^
óöõ
fþ&ìö
qþ&îfí/ó"ó&õ öò^ðöõ
c HN 9 G (
í5õ¡ïí=ìôí/înô
óþ&ï]ïðì
î9þ
Zî9í/ÿ
8d6 $e& óþ&ï
a +) ;T
í=õºï ö
í=õ
Zî9í/ÿ
ZðïõJõ¡ï]í=ìôí=î9ô?ôöù
ú^úÿí
ú²í
kí=øõ¡õ¡ðí/ì
ZîHí=ôðöìï
¯ï ö
43"57698 ;: 5<=5> <
H
Zî9í/ÿ
õ¡í=ÿù
í ïöî
ú5ÿ
înö í/înöôï ö²ôí/ïíyÿí=ï]î9ð kïþ
\ï ö²í {þ
í=õ
óöõ5þ&ìï ö
öî9öJõ¡ð"ÿøóí=ï]öôøõ¡ðì
qînþ&ÿ
) 2 V R
ö²õ¡ò^î9ð ïï í=ïôðôí=óó,þ
¿õ¡í/ÿ
î9þ
/úõ öòhðöõ í=ìô
ò^þ&ìï]í=ÿðìí/ïðþ&ì¬îHí=ï]ö
ð"õ¡øí/óð /öô¬øõ¡ðì
ï í=ï
]þ&î
5õ¡ïîHí=ò^þ&ôí
{öìöîHí=ï]þ&î
ZöìöîHí=ïþ&îÿþ&ôöó
Fþ
í=ìô§ðïõºõ¡ï]í=ìôí=î9ô§ôö ð"í/ïðþ&ì
¯öî9ö
ï ö?÷ þ&î ¯í
î9þ&òhöõ¡õ¡öõyô«öõ¡òhîHð {öô½ðì
\õ¡í=ÿ
D b +V
%_
f 57<agh8 6 $i& H a + înþ
ZöìöîHí=ï]öô
Ï «õ í/òhðì
ðì
Zóö
3í½òhþ&öìþ&òhóðìö
ÿ
Î
ó"öÿöìïõï ö
í=õ
qþ&õ¡õ¡ðóð /í=ï]ð"þ&ìò í=ìòhö
ï ö
øõ¡ðì
ï öõ¡ö²ôöìõ¡ðïðöõ =í Zøìôí=ìòhöõ
í/î9í/ÿ¬öï]öî9õ
ðí=ïðþ&ì
ôöìõ¡ðï
í=õ
ïþ&óöîHí=ìòhöõ¡öïÅïþ
înþ&ÿ
÷"ôöìû=í Zøü
ï]ðì
Oô«öìõ¡ðïðöõ
ðï ÿí ð"ÿøÿ
ðï ÿí ðÿ¬øÿ
* + ,
@2@ BAC (ED E
@ ( 0 )
0 L
O
HUT WV
*) @ ( @
( @2@ V
@ (@
¯í/õòhî9öí=ïöô
]þ&óóþ
ð"ì
#!/bin/bash
# generate data using Gaussian model, rows are species
coenocline 0 1 < infile | den2abu | rm-zero-rows-cols 2 > gauss.dat
#
# plot raw data
mat2gri < gauss.dat> plt
gri p6.gri
gnome-gv p6.ps
#
#eof
,í/ìô
Q
/j
Æ
Î
0
¯í/õ*ú²û
û
í/ïïöîHì
Ï
Ï ²Ï ú
*ôöìõ¡ð"ï]ðöõ
ú
Ï û
Ï/Ï²Ï
Ï
Ï
/ú
* 2
ìþ&ï\ð"ìíînö Zøóí=î
0
=ú
=û
Ï
ú
ö
ú
û
öînö¿ïí {öì
Q 21 .
Q } Q ` 1 @ 1 *1
!V

î9þ
öî¿õ¡í/ÿ
û=úJû/û²û Ï
Î
öyî9öí=õ¡þ&ì
Ï
óöõ
(SD O
} ` @
Q2QRQ1*Q2.*Q
NNH G)
í=îHð"õ¡þ&ì
ú yú Jú yú Î
Ï=Î²Ï ²Ï
/û
21 2.
Q +Q *Q
2
qþ&îJòhþ&ÿ
ú^ú²ú=ûJú Ï
kí=øõ¡õ¡ðí=ìðõfï í/ïZï ö¿õ¡í/ÿ
ZîHí=ôðöìï
ôí/ïí
þ
Î
Î
öî qöòhï]ó
ö²îHí
Ç]Ê
64
Ï
D 2
Ä
gradient
5î9ð Zðìí=ó
ï ö
,Ê
0
þ&înôöî
û
Æ4È
400
)
+)
s"t=u"v\w!x2yKzy|{2y 9 \
;
Q+*1 . *} ` @
2Q
Q 1 . } ` Q @
} ` @
1 12Qb121b12.b1 1 } 1 ` . @ . ~. ~. .~Q .1 (D
!) %F
a
*
U (
û Î
\k-lm Wn on \pSq rn
È5Ì1Ä,Ê
a +
ï ö
=ú
/û
ï öyò^øî öõºí=î9öJìþ&ï
]î9þ&ÿ
îHí=ìôþ&ÿ
ZîHðô
qí Zøìôí/ìò^öõ þ&î9ôöînöôí=óþ&ì
óö
û Jû ²û
9 a 2T
Zî9í/ôðöìïóþ&þ
óð Zö²ï ðõ
óí=ò^öõ«þ&ì
lm 2m Wk =

ÅÄ,Ç ZÇqÆÅÇqÈ5É§Ê
Í È
c
yÈ5ËÌÉÊ
=Í
1
Î
70
0
0
64
gradient
)
~
M" ~F
9
stau"vrwxbz2y|y
o 2
0 (D a
Q+1
. } ` @
2Q 21 2. } ` @
2Q 21 2. } ` 2@
Q 1 . } ` Q @ Q WQ WQ Q2QWQ1WQ2.WQ Q } Q ` 1 @ 1 O1 W1 1QW121W1.G1
1 } 1 ` . @ . R. R. .2QR.21 H a /
" H N )
9 0 (
) 0
9
"V % (

ëýõ¡ö Zøöìòhökþ
í=ìô§õ¡í/ÿ
óöô
ú
Î
Ï=Ï5Ï
ú^úú=ûkú Ï
Ï
Ï
/ú
ìð"ÿþ&ôí/ó
í=îHïðñòhðí/ó&ôí=ï]í
qí Zøìôí/ìò^öõ
ú kú ú kú Î
=ú
Ï=Î5Ï 5Ï
=û
=û
Jí/óþ&ì
Ï
í=ïï]öî9ì¯þ
ZöìöîHí=ïöô¬ï înþ&ø
öJõ¡í=ÿ
ú
ú
û
û=úkû=ûû Ï
Ï
5ï ö
öì
èé
è
Zí5÷"ôöïöîHÿ¬ðìðõ¡ïðòhü
{þ&î9ðï ÿ
qþ&î*ï ö
5ë
ð"ÿ
kí=øõ¡õ¡ðí=ìÿ¬þ&ôöó
û û kû û Î
=ú
Î
ZîHí=ôðöìï
qøì
Zìþ
\õ öòhðöõ*ôðõ¡ïîHð Zøïðþ&ìðõºõ¡ï]ð"óó
*' ! +* *\M
D 9 /
) * WM " + ã1ä å1ä å
í
óöõºí=î9ö4ð"ìï öJò^þ&î9î9öòhï{þ&î9ôöî«úû
ì
=û
û
û
Ï
Ï kÏ ú
Ï
Ï û
Î
Zö ]þ&î9ö1î9öí=ó=í/ìí/ó Zõ¡ðõ
ðõ¡ð {ó"ö
²è
ZîHí=ôðöìïí=ìí=ó Zõ¡ðõ
óöÿ¬öìïöô
F~ W
%" = 2
¯í/õ¿ò^í=îHî9ðöô
ï ö
înþ
{î9í/ÿÖ÷
þ&øïøõ¡ðì
§ï ö
*ë
í=óù
Zí ôù ü /þ&ì§í Zøìôí/ìò^öõ
.
Î
/j
Æ
)
0 (
c)
H 2 %V 9c %H (D O
oV
9_ o" % ?
qðìõ¡ï]öí=ô?þ
ï]ð öó
í/ìô
«ô«öìõ¡ðïðöõ
qþ&î9ÿí=ïÅøõ¡ðì
ð
9 0 a
W
a 9 %?
2 % a
H
a
V 9;T
îHðþ&î¿ï]þï ö5í=ìí=ó Zõ¡ðõ Zï ö5ôí/ïí
®÷"î9í û Zí ù Zð Zü
öôí=ï]í
ðõ¡øí=óð =öô
öînö5ï öì?î9öí=îHî9í/ì
÷ {î9ðü =í=õ
Zöô?øõ¡ðì
#eof
70
0
64
gradient
,Ê
Ä
Ç]Ê
HV
V
öînöò^þ&ì
¬ï öînöõ¡øóïðì
î9ö {ðþ&øõ¡ó
0
Æ4È
öî9ï]öô?ïþí¾õ¡øðïù
qìþ&ï4÷"î9í ¯û Zí ü *í=õï ö¬ô«öìõ¡ðïðöõ
#!/bin/bash
#
# reconstruct using QAP, and write out sample order
itransp < data | raw2qap-big | gqapd-p > sample-order
#
itransp < data > tdata cat tdata sample-order > ini
rearr < ini | itransp | mat2gri > plt
gri p6.gri gnome-gv p6.ps
#
í Zóö
\k-lm Wn on \pSq rn
È5Ì1Ä,Ê
¯öî9öî9öó"í/ù
¬þ&î9ôöî
öòhï]þ&î
lm 2m Wk =
Í È

c
yÈ5ËÌÉÊ
stau"vrwxbz2y|y D c W
(W
V a
ö
5ë
òhþ&öìþ&òhóðìö
ë
Î=Î
ùqînöòhþ&ìõ¡ïî9øòhï]öô
)
) F
9
) 9 0
)
0^ (
þ&înô«öîkþ
U /=
);
"
Zøìôí=ìòhöõ
ïöîHÿð"ìðõ¡ïðòyÿí=ììöî¿þ
ö {öî
=Í
öînö
yí=îHïðñòhðí=ó*õ¡í/ÿ
Zøðïö4ðÿ
î9þ
öî9ó
óöõþ
{øïZòhþ&ì
Zî9í/ôðöìï«í=ìí=ó Zõ¡ðõ «øõ¡öô?ðìõ¡ïöí=ô?þ
íyô«ð"õ¡ï]ðìò^ïøìðÿ¬þ&ôí/ó
ðï
í=ò^ïü
í/ïïöîHì?öÿöî Zöô
í=õÅìøÿ¬öî9þ&øõÅóþ&ò^í=ó{þ
÷"øìð"ÿþ&ôí/ó"ðï
ðì
ï]ðÿ¬í Zí=ìô¬ðõ
ð"ï ¬ìþ&ðõ¡öü
]ÿöõ¡õ¡ðì
ø
¾ï]þ5í²ôöù
Oôöìõ¡ðïðöõ
þ
ù
Oí/óï þ&ø
Fï ö
9
)
í=ïï]öî9ì¼ð"õkìþ&ï*øìðÿþ&ôí=ó
a
{öî òhóþ&õ¡öïþøìð"ÿþ&ôí/ó"ðï ð"ì¬ï öõ¡öìõ¡öþ
ö÷"ìþ&ðõ¡öü
þ&øî*ôí/ïí
í=ï]ïöîHìöÿöî {öô
\
T M"
\
/V $ D ao a
% V ( a a E
H MM
9
a
9V (
ëÖôðõ¡ïðìòhï*ü"òhþ&ÿ
²í
]þ&îHÿð"ì
þ
b
ö {öî &ðõ4ìþ&ï«õ¡þ&ÿö
0 î9þ&òhöõ¡õ &ðì
) a
*í=ï öî /ðïînö î9öõ¡öìï]õºþ&øîºð Zìþ&î9í/ìò^öyþ
øöìò^ù
ï öïî9øöôí/ïí
ï öÿõ¡öó {öõ
¡
ã1ä å1ä
*' !+7 'M
èé
9é
9o $ )
0
%V 0 c 7 V \
9- Wa ¢ a
-)
£ \) )
£V 0 N (+D 0
W 9 H
a
% \^
a a N O )H H" 0
0 0 (
ë5õ4þ&ìó
ô
qõ¿þ
fôöìõ¡ðï]ð"öõ {ìþ&ïô«öìõ¡ðïðöõ4ï öÿõ¡öó öõ Zòhí/ì
þ&ì½ôöìõ¡ð"ï]ðöõkðõkðìï]î9ðìõ¡ð"ò^í=óó
ô«öìõ¡ðï
5ë
ô
Jï]þ¼þ
Zï]í=ðì
(í=ó Zþ&îHðï ÿ
þ&óö
ï]ðÿ¬í =ïþ&óöîHí=ìòhöõ

Zí Zðóð"õ¡ï]ðò
õ¡ðÿøó"í/ïðþ&ìõþ
înøìõ
îHí=ï öî ðïOðõ²í
înþ
Jôöìõ¡ðï
øõ ìþ&ï*íõ¡ðì
Zøìò
þ
í Zöõ¡ðí=ì
Zökí=ò ðö öô
{í/óøöõ *þ&ì
Zóöõ¡öîHð"í/ïðþ&ì
þ&ï öõ¡öõyþ&ì?õ¡í=ÿ
,õ¡öî9ðí=ï]ðþ&ì
\í/õðï*øõ¡öõkõ¡í=ÿ
ðò
ó"ðì
÷oï ö¯õ¡þ&óøïðþ&ìü ðõkþ
óö¾îHí=ì
Zðì
]î9þ&ÿ
ôöïöîHÿ¬ðìðõ¡ïðò
Zïí/ð"ìöô
í=ìô¼õ öò^ðöõ²þ
ù
í/ìô¬õ Zö
+ G
M
a
)
a V 9V (;D 0 W
/
)
0
H)
) 9V
/ / 9V a T¤\¥o¦ @ ( @@ 2§¥o¦ @ ( @2@@ 2¨©¦ @ ( @ ¨'ªE¦ @ ( @ (D 0 I
?
)
a 0
V 9V \
9)
2M b %V H=U T/«h©G¦ @ ( `2` U«ª¬¦ ( @ ?'©¦ @ ( @ Kª¦ @ ( @ 22¤M®¦ ( @ -§"®¦ @ ( @2@ (
5øðï]öìí=îHînþ
d)
ÿþ&ôöó
îHí=ÿöïöîHõ
þ
§þ
òhþ&ìñôöìòhöó"ðÿðïõ
qþ&î¿í¾ÿðìðÿøÿ
]ðôöìïðò^í=ó
í=ÿþ&øìïfþ
]þ&îÅí=óóõ¡í=ÿ
«ðìôð {ðôøí=óõ¡í=ÿ
úhú
öõ öòhðöõ
óöõ
Jú
D *) \ 2
ö
í/ïöô
qþ&óóþ
¯ðì
í {þ&øïõ¡í/ÿ
Zð {öì
þ&ìþ&ÿ
í/ìô
øïfþ&ìïþí=óó
í/õ
í/î9í/ÿ¬öï]öî9õ²ï]þí/ó"óþ
{þ&ó öô
ó"öõ {í=õJìþôöïí/ð"óöô
ô«öïí=ðóõþ&ì½óð qöí=ìô®ïí
û
¯í/õ
öî9ö
føìòhöîHïí/ðìï ð"ì
ðì
öînö
øõ ï ö5õ¡í=ÿ
qþ&îHÿ¬í/ïðþ&ì
{ð öì
í=ù
þ&ì¬õ¡öôðÿöìï]þ&óù
ú
qðôöìïðòhí/ó
ï ö
óö
ú
]þ&îí=óóZï öyõ öòhðöõ1ðì
¯öî9ö
ú
{þ&ó {öô
í=õ1ìþ
Jú
ú
)
H"
õ¡öîHðöõºþ
óöJîHí=ì
Zðì
V
" 9
ó"þ&ï]õ1î9ö înöõ¡öìïZõ¡ö {öîHí=ó
0
L
þ&ï öõ¡öõ
/í=ìô§înöóí/ïöôõ öòhðöõºô«ð"õ¡ï]î9ð Zøï]ðþ&ìõ
)d. ~
qþ&øïþ
=û
(
Zöìöînù
]ò^þ&öìþ&ò^ó"ðìö
}
/j
Æ
inferred density
Î
\k-lm Wn on \pSq rn
È5Ì1Ä,Ê
Æ4È
,Ê
Ä
Ç]Ê
1000
0
0
64
¯"°=±"²\³!´+µ¶|·2¶R¸N¹"ºM»¼a½H¾¿0À9¿/ÁÂÃÄ2ÅºMÆ9¾+»ÇÈr¾Ç?À%¿SÉWÊËWÌÍWÁbÁ7ÁWÁ2ËÎÌ2ÏÁ2ÉÐWÁÏbÁÍÑbÁÌ
Á2ÐGÁÊWÁ2ÑWÌ2ÌWÌÁGÁ2ÎWÌÊWÌ2ÉWÌÐGÌ2ËWÌÍWÌ2ÑWÌ2ÎOÉ2ÏWÉ2ÌWÉÁWÉ2ÍWÉÉGÉ2ÐWÉËWÉ2ÊWË2ÏOÉ2ÎWË2ÁWÉÑ
Ë2ÌË2ÊË2ÍË2ËË2ÐË2ÑOÍÌÊÏÊÌÍËÊÐÊËOËÎÊÉÊÍÊÁNÊ2ÊOËÉÍÉÊÑÍÏÊÎÍÁOÍÊÂ
Ò »ÅºMÄ2Ç!¾RÓNÀ%¼a½EÔMÕ;Â0ÑdÂ ËÂ
lm 2m Wk =

inferred density
Í È
c
yÈ5ËÌÉÊ
=Í
Î
`
1000
0
0
64
¯°a±"²r³´bµ2¶|Ö¶R¸N¹"ºM»¼½¾¿0À9¿SÌdÂ"ÃÄÅºMÆ9¾+»Ç!È\¾Ç?À9¿ÍÁWÉÊWËÌWÁÁÁ2ÉÎWÐÁ2ÏÁÍbÁËÑWÌ2ÏÁ2Ê
Á2ÌWÁÐWÁ2ÑGÌÌWÌ2ÊWÁÎWÌ2ÁGÌËWÌ2ÉWÌ2ÍWÌÐGÌ2ÑWÌÎWÉ2ÏWÉÌGÉ2ÁWÉËWÉ2ÉWÉ2ÍOÉ2ÊWÉ2ÐWËÏWÉ2ÎWÉÑGË2Á
Ë2ÌË2ÍË2ÊË2ÐË2ËË2ÑÍ2ÌÊ2ËÊ2ÏÊ2ÌÊ2ÐÊ2ÉÍ2ËÊ2ÊÍ2ÉOËNÎÊ2ÁÊ2ÎÊ2ÍÍ2ÏÊ2ÑË2ÉÍ2ÁÍ2ÊÂ
Ò »ÅºMÄÇ¾RÓNÀ9¼½NÔMÕ;ÂhÑÂ ÊdÂ
}@
/j
inferred density
Æ
\k-lm Wn on \pSq rn
È5Ì1Ä,Ê
Æ4È
,Ê
Ä
Ç]Ê
1000
0
0
64
¯"°=±"²\³!´+µ¶|×2¶R¸N¹"ºM»¼a½H¾¿0À9¿/ÉÂÃÄ2ÅºMÆ9¾+»ÇÈr¾Ç?À%¿SÉWÌ2ÏÎËWÍÊWÁÌWÁ2ÍÁ2ÉÐÁÁWÑÁ2ÏÁÌbÁÊ
Á2ËGÁÐWÁ2ÑWÌ2ÌWÁÎGÌ2ÉWÌÊWÌ2ÁWÌËGÌ2ÍWÌÐWÌ2ÑWÉ2ÏOÌ2ÎWÉ2ÌWÉÍWÉ2ÁWÉÉGÉ2ËWÉÐWÉ2ÊWÉ2ÎOË2ÏWÉ2ÑWËÁ
Ë2ÌË2ÊË2ÍË2ËÍ2ÌÊ2ÐOÊÏËÐÊËÊÉÊÌËÑOÍÉÍÏÊÁÊÍNË2ÎOÊÊÊÎÍËÊÑËÉÍÁOÍÊÂ
Ò »ÅºMÄ2Ç!¾RÓNÀ%¼a½EÔMÕ;Â0ÑdÂ Ê2Ø=ÑÂ ÍÂ
lm 2m Wk =

inferred density
Í È
c
yÈ5ËÌÉÊ
}
=Í
ú
1000
0
0
64
¯°a±"²r³´bµ2¶|Ù¶R¸N¹"ºM»¼½¾¿0À9¿SËdÂ"ÃÄÅºMÆ9¾+»Ç!È\¾Ç?À9¿ÌÏÍbÁWÉËWÊÌWÁÁÎWÐÁ2ÍÑWÁÏbÁÐÁ2ÉÁ2Ë
Á2ÌWÁÊWÌ2ÌGÌËWÁ2ÑWÌÊWÌ2ÁGÁÎWÌ2ÉWÌ2ÐWÌÎGÌ2ÍWÉÏWÌ2ÑWÉÌGÉ2ÁWÉÍWÉ2ÉWÉ2ËOÉ2ÊWÉ2ÐWËÏWÉ2ÎWÉÑGË2Á
Ë2ÌË2ÊË2ÍË2ËË2ÐÍ2ÌÊ2ÏË2ÑÊ2ÌÊ2ÐÊ2ËÊ2ÉË2ÎÊ2ÁÊ2ÍOÍNËÊ2ÊÍ2ÉÊ2ÑÍ2ÏË2ÉÊ2ÎÍ2ÁÍ2ÊÂ
Ò »ÅºMÄÇ¾RÓNÀ9¼½NÔMÕ;ÂhÑÂ ÊØaÑdÂ ÐÂ
/j
û
Æ
inferred density
}
\k-lm Wn on \pSq rn
È5Ì1Ä,Ê
Æ4È
,Ê
Ä
Ç]Ê
1000
0
0
64
¯"°=±"²\³!´+µ¶|µ2¶R¸N¹"ºM»¼a½H¾¿0À9¿/ÊÂÃÄ2ÅºMÆ9¾+»ÇÈr¾Ç?À%¿SÌ2ÏÉWÌÍWËÊWÁÎWÁÁÁ2ÏÐWÁ2ÉÁÌbÁËÁ2ÍÑ
Á2ÊGÁÐWÌ2ÁWÌ2ÌWÁÑGÁ2ÎWÌÊWÌ2ÉWÌËGÌ2ÍWÌÎWÌ2ÑWÌ2ÐOÉ2ÏWÉ2ÌWÉÍWÉ2ÁWÉÉGÉ2ËWÉÊWË2ÏWÉ2ÐOÉ2ÎWÉ2ÑWËÁ
Ë2ÌË2ÍË2ÊË2ËË2ÐÍ2ËOÊÏËÑÊÌÊËÊÉÊÐOÍÌÍÉÊÊÊÁNÊ2ÍOÍÏÊÎÊÑËÎËÉÍÊOÍÁÂ
Ò »ÅºMÄ2Ç!¾RÓNÀ%¼a½EÔMÕ;Â0ÑdÂ Ê2Ø=ÑÂ ÎÂ
lm 2m Wk =

inferred density
Í È
c
yÈ5ËÌÉÊ
}
=Í
=Ï
1000
0
0
64
¯°a±"²r³´bµ2¶|ÚÛ2¶/¸N¹"ºM»¼½¾¿0À9¿+ÍdÂ?ÃÄ2ÅºMÆ9¾G»ÇÈ\¾ÇSÀ9¿*ËÉOÍÁOÌÌ2ÏOÊÁÁÎOÁÉOÁ2ÍÐOÁÌOÑÁ2Ï
Á2ËWÁÐWÁ2ÊGÁÑWÌ2ÌWÌÉWÌ2ÁGÁÎWÌ2ËWÌ2ÊWÌÎGÌ2ÍWÌÑWÌ2ÐWÉÏGÉ2ÌWÉÍWÉ2ÁWÉ2ÉOÉ2ËWÉ2ÐWÉÊWÉ2ÎWËÏGÉ2Ñ
Ë2ÁbË2ÌËÍ~ËÊbËÐ~ÍÌË2ËbË2ÑÊ2ÏbÊ2ÌbÊ2ÐÊ2ÉbÊ2ËÍË~ÊÍbÊÁ~ËÎÊ2ÊbÍ2ÏÊÎ~ÍÉbÊÑ~ËÉÍ2ÁbÍ2ÊÂ
Ò »ÅºMÄÇ¾RÓNÀ9¼½NÔMÕ;ÂhÑÂ ÊØaÑdÂ ÑÂ
2Ü Ý~Þ2ßà2áâ=Þ2ã!äã!ä\åæ]ãUçWè"éÞ+â=áá
ñò À9ÕóôMÅ ò ¾ÇR»õ?¼½¾¿0¾O½¹"ºM»¼½¾¿0¾¿b¿0½H»ôMÆ9È ò ¾GÕ"¾ó¾ÇÄ2¼¾Èö¼»» ò ¼ÄÀ%óZ¼½¾À%ÇRÆ9À9÷"¾Æ9À9Ø ê ã ëâ=áIÞåì2ã;åéÞåí"éãrâ=ábî Þ2ï%â0ð
½»»ÈøÇ!Ä¼À9»¿0ù;À]Â ¾ùU¼½¾oÅ¾Ä2¿0ôMÇ!¾»õ/¼a½H¾À9ÇbÇ¾Æ9Ä2¼aÀ%úH¾NºMÇ» ò Ä ò À9Æ%À9¼aÀ%¾¿2Â¸N»ÓN¾ú¾Çaù;¼a½HÀ9¿GÀ9¿ â=2Þ ãràæ]áàãæ;áí"ã
û »ÅºMôM¼aÄ2¼aÀ%»óÄ2Æ9Æ9¹E¾ü¼Ç¾Å¾Æ9¹À9ó¼¾ó¿0À9ú¾b¼Ä2¿0÷ù¼a½H»ôMÕ½c¼½¾bÆ%À9÷"¾Æ9À9½»»È-Ç!Ä¼À9»¿IÄÇ¾+¼a½H¾
ý ºMÇ»ºM¾ÇUÄ2ó¿0ÓN¾Ç'þ¼a»G¼½¾*ºMÇ!» ò Æ9¾Åÿ»õ¿0¾ÇÀ%Ä¼À9»ó?Â
¼/À9¿OÄ2Æ9¿0»Õ»»È¬¼a»ZºM»À9óH¼R»ôM¼/¼a½HÄ¼¼a½H¾ ý Õ"»»Èø½¹"ºM»¼½¾¿0À9¿0þL¿0½H»ôMÆ9È ºMÇ»Èrô û ¾EÄ
Å»Ç¾ û »ÅºMÄ û ¼ û »¾ó» û Æ9À9ó¾ºMÄ¼¼a¾Ç!óÓNÀ9¼½¬Æ9¾¿0¿ ý ó»À%¿0¾þÀ9ó ¼½¾,ôMóHÀ9Å»È\Ä2ÆSºMÄ2¼a¼¾ÇóÂ
½HÀ9¿SÀ%¿ ò ¾ û Ä2ôM¿0¾*¼a½H¾¿0¾~½H¹"ºM»¼a½H¾¿0¾¿/ÄÇ¾ ò ôMÀ9Æ9¼M»óo¼½¾+¿0À9ÅôMÆ9Ä2¼¾ÈÈ\¾ó¿0À9¼À9¾¿0ù¼½ôM¿ó»¼
}Q
/j
Æ
\k-lm Wn on \pSq rn
È5Ì1Ä,Ê
Æ4È
,Ê
Ä
Ç]Ê
H a
) )
a S
2
'( D 0
"!$ < 6 ) V 9" B)
o
O)
" G a
M `( 1 `( @ a a ) M (`d( Q2'N
9G" )a) ) 7 2N 7N L65 ":27f (
ðìòhóøôðì
5ï öÅóþ&õ¡õþ
í Zøìô«í=ìòhö
øõ¡öô
qþ&îyðóóøõ¡ïîHí=ïðþ&ì
ï ö4÷"ìþ&ðõ¡öüð"ìñ
ö
&ð"ì
]öò^ïZþ
\õ¡í=ÿ
ÐJÑ
qþ&î9ÿí=ï]ð"þ&ìôøöÅïþkí=óó=ï ö
øõ ð"ïðõºïþ
Zõ
í=õí
Jïþ
ó"ðì
Zþ&þ&ô
ú
ò^í=ìôðôí=ï]ö
¯ðï ï í/ïZþ
õ¡ò öÿö
ð"ò
O×Õ{ÛJÚ
¬ÛÕ¾ß
¡
înþ&ò^öõ¡õ¡öõ«ï í=ï&ÿí ¯ôöìõ¡ðï þ&ìï]þ
Zö²ò^þ&ìò^ó"øô«öôï í=ï
fþ
\ï ö²í Zþ
qþ&îyí§õ¡þ&øìô
{ñ
{ö²õ¡ð
þ&ï öõ¡öõ
þ&ï öõ¡ðõ
qòhþ&ÿ
í=înö
öînöÅð"ïðõOò^í=øõ¡öôõ¡þ&óöó
5ï ö
¯í/õ
Õ
Û
ø b +
D
\
9V
a 9V )
< 6 8 $ 5 G ><=65 7: >
0 9) " D
a 27 M 0
5 f 2#%
" J %
2) 2 9 `2` } Q } (D +)
)
(
D
O)
;) a
!)
r)
)
+)
M" ( ¢ 2M 97 \
L
+ a
M
L V
` } 1 ` Q (
D a )
O)
M"
) \
0 9
2 E 0
(D 0 a ) a 0 H )
HV
9_
9 2 0 a
)
*)
M" (
V 0 %)R c
H£) a a"
);)
" ( ( 2M
0 9) ) a E
a ~
\ d 6 > 6 ( ( ) R 0 a *
(
J
N)
H ø
HV
H 2T+ 9 V 0
? a) G a
9
M
0^ %d 2V
) I E %)
G
0^ 9 \ aW
)
9)
H ! _
0 o 9VH U)
M ? )
9) H ! _
(KJ
`2` Q (
9V %V
" J 9
0
) a
\ )
2
2< 6 S# < 5
$%"f 576 $%"#%# 5U5 8 "# 5<=5 \5 "$% < 6 Hf 57698 $% 5<=5 fW$% 2< 6 65 # 57< 657<a5 6!<
> "$ < >R< 7 6 "# 57< > #% 6 7 $%# >/6 ": 5 $ fW$% 2< 6 6!5 ": 57<a55 : R >< #% 6 $ >
:2 6 >>5
D
d)
M" 2 %_ " # < $ 5 # < 5 2< 6 #%# 5
5 >> 6 "f < 6 < 6 7 5 # 57< f ?6 $ < r "5 :2# > 698 $ "#%#% 6 $% 55 2>> $7# 5 \< 6
8 2< 6 $ > f " 6 7 5<=5 < 6 !## 5 # 8d5< #%# 55 ": 2< 6 < 6 < >< ":
ã1ä 1ä æ
Zè
ðõfò^í=õ¡öÅõ¡ïøô
ò^þ&ó"ô«ù]ï]öÿ
!
é9é
í=õOôîHð {öì¾þ&ì¾ï ö4í Zøìô«í=ìòhö1ô«í=ïíÅþ&ìþ&õ¡ï]î9í/òhþ&ôõOôöîHð {öô
î9öð í/ó"ô#"%$þ&õ¡ï]í qí ð /ú
öºþ&õ¡ï]î9í/òhþ&ô
qí=øìí1ò^þ&ÿ¬öõ
ìöí=îï ö
Zþ&øìôí=î
-øöìð"ì
ö
qînþ&ÿ
½í=î9öíõ þ
ï ökõ í/óó"þ
þ&înô®ï]înþ&ø
õ
ðþ
Zöþ
ZîHí
ó"öõ
ðòhí/ó"ó
öî9í/ïö*í=ìô¾õ¡ø
]î9þ&ÿ
ø
qþ&õ¡õ¡ðóò^þ&ÿ¬ÿøìðï]ð"öõ4í/înö²þ
òhøîHînöìïùqö
íÿ¬ð öô
òhþ&í/õ¡ïí=ó
í
{ó"ðõ öô
î9öòhöìïí Zö
]î9þ&ÿ
ò^þ&í=õ¡ï]í=ó óí=ï]ù
«ï öõ¡ïøô
¼í=înöíðõ
Zùqí=î9òhï]ð"ò«ÿ¬í/î9ðìö
înþ
ð"ìòhöõ
þ&õ¡öô
þ&õ¡ïîHí=ò^þ&ô
óí=ï qþ&îHÿ
öì
Zöîfí=õ¡õ¡öÿ
õ¡óþ
í=õ¡õ¡öÿ
ð"î9þ&ìÿöìï
Zóí Zöõ
öõþ
Zóí Zö
.*
yþ&øïöî
þ&înô
ï]înþ&ø
ðï õ öò^ð"öõ5ðÿ
øõ &ï öí=øï þ&îHõ¿î9öòhþ
ï öJò^þ&í=õ¡ï]í=ó
óí=ï qþ&îHÿ
õ
þ&î9ï]öô
Zìð =öô
,*
þ&înô
qí=òhï]þ&î *ï ðõï
ö
þ&ìö
í=ìôï ö
þ&ìö
ö {öîHï öóöõ¡õ *ð
þ
ö
¯þ&î í
(
þ&ìó ï öJï þ¾öìôùqÿ¬öÿ
ï]înþ&ø
,*
í=øï þ&îHõ¯õ¡ï]í=ï]öï í/ïJï ö
Åï öõ¡ïøô
)(
{öï ööìï ö1òhþ&óôùqïöÿ
&
ú
'&
ìþ&îHï öî9ì
]î9þ&ÿ+ï ö¿õ¡öôðÿ¬öìïõ¡øî qí=ò^ö*õ¡í=ÿ
qþ&î9ÿõí=ìô®í=ô+* í/òhöìï*þ&øïöî
þ
înþ&ÿõðõ¡ïîHðòhï
öîHí=ï]öºðììöî«õ öó &õ¡öïïðì
{í=ï
]í/øìí/óî9ö ¯þ&î Zðì
{ð
Zÿöïî ½ðõï ö
ö
{í
înöõ¡øÿöô
í=î9öìïõ ð ]ïfþ
ôö ï õ
þ&øó"ôôðõ¡ï]þ&î9ïï öí/øïöò^þ&ó"þ
{ð"ò^í=ó
í/ïïöîHì
&ð
«õ¡ðï]öõ
ö
&ï öòhþ&îHînöòhïþ&î9ôöîHð"ì
þ
ò^þ&ìï]înþ&óóðì
«ï ö5óþ
öî¿ï]þ&óöî9í/ìò^ökóðÿð"ïOïþ
í/ïï]öî9ì
]õ¡í/ÿ
Zøï
/
¯ðóó
óöõ í/ó"þ&ì
§ï ö
{înöí=ï]öî
ï öõ¡öîHðí=ï]ð"þ&ì
Zí/ï
Zÿ¬öï]î9ðò
{î9í/ù
ôðöìï
þ&øîÿí0* þ&î
]í/òhðöõí=õ¡õ¡þ&ò^ð"í/ïðþ&ìõ§þ&òhò^øî9îHðì
î9þ&ìÿöìï]í=ó*õ¡öï]ïðì
Zøðóôø
í/ìô
{õ
qð
í {ö§õ öóïöînöô
õ¿í=ìôõ¡öôðÿöìï]õ
qðð
í ö²ö
{í=îHìí/òhóöù]ÿþ&óóøõ¡òhùqöò ð"ìþ&ôöîHÿ
ù
Zî {þ
=þ&í=ìõ¡öôðÿ¬öìïõ =í=ìô
ù
Zð {í/ó öJõ¡öôðÿ¬öìïõ
2
ö
õ öòhðöõyþ
6C
/
>;L
E6
6
¡
;8=< ?>?@
6 8GF
,*
þ&î9ôïînþ&ø
óí=ï qþ&îHÿ
76
ó"í/ï qþ&î9ÿõ
Zøóó"ö {õ
õ
ðï
õ¡öö
8F
ðï
ð"ï
6
ð"ù
]þ&î9öõ¡ïõ
Zî {þ
]þ&îHí=ÿðìð qöî
=þ&í=ì
Î)(
Zóí {öí=î9ö354
6
4 4 {öó
Zí=îHìí=òhóöù
Ï1&
înöð í=óô§ú
;89B
6 0H ;I
ôðõ¡ïðìòhïköì
]þ&îHí=ÿðìð qöî«ù
þ&õ¡ïîHí=òhþ&ô(í=õ¡õ¡öÿ
4 A
þ&înô¾ï]înþ&ø
í=õ¡õ¡öÿ
9
8)354 A
6
!6
4 ã1ä 1ä å
.*
]ððð
ï]þ
ð"ï ®òhþ&îHí=óóðìö¬í=ó Zí=ó
6
76
98
98 ;C
AD
A
KJ
C
9L
öºþ&øïöî
C 4
Zþ&øïöî
*ï ö¯òhþ&í/õ¡ïí/ó
ZöFî9öóí=ïöô
óí=ï ]þ&îHÿõ
þ&õ¡öôòhþ&í/õ¡ïí/ó
õ¡öôðÿ¬öìïõ
þ&îôöïí/ðó"õ1þ&ì¯óðï þ&óþ
6
:
]ð
3òhí=ì
òhþ&í=õ¡ï]í=ó
M3 ?6 Zóí {ö*ð"õfò í=îHí=ò^ïöîHð /öô
8=N
>;L
8/O
>;LR 6
;8)354 A
6
76 A
89354 C 4
;
98)P
354 6
4QD
L
çèéêè
D 2
9
)r. 0
.21 (\D (
V 9V ? X ) @ @2@2@
Q~1b. ~} @
2. } ` @
2Q 21 2. } 2@ Q
t ax
1 . 2} ` Q @ Q Q WQ ..b. } 2@
Q 1 . } ` }2@} } } } Q } 1
} . } +}2}+} `+` ` ` 1 ` . ` ` }
öí Zøìôí/ìò^öôí/ïí5ÿí=ï]î9ð ò^þ&ìõ¡ðõ¡ï]õ²þ
ò^þ&ìï]í=ðìöô¬û
S T
Ï
Ï
=Î
úkû
ï]þú
þ&õ¡ï]î9í/òhþ&ô
Ï
Î
Ï=ÎÏ Ï
/ú
û
Ï
ú
{í=ó öõ
úhúkú=ûú Ï
=û
Î
Ï
/ú5õ öòhðöõ4ð"ì
öîfò^ÿ
ú kú Î
Î Î ú
ú
Î û
ú
Î/ÏkÎ
ºþ
5õ¡í/ÿ
óöõ
öõ¡í/ÿ
óöõ
û
ï ö²õ¡öôðÿ¬öìï
û/úû/ûyû Ï
Î
Î
û kû û kû Î
Î=ÎÎ 5Î
ú
û kÏ kÏ ú
û
/Ï
Ï
lm 2m Wn k
.U WV
Wq 4k
5X!YZV
Ä
[X
}1
Wk
5V5Ë\KV
^]KX`_
Qb1b. b} ` @
2Q 21 2. } ` @
2Q 21 2.
x
`
`
Q
1
.
Q
Q
*
} 2@
2} @ Q +Q QQ*Q21*Q.*Q Q } Q ` 1 @ 1 *1 +1 1Q*121
1.+1 1 } 1 ` . @ . +. ~. .2Q*.1
. ` @ ` @ ` ` 1 1 @ 2.b. 1 }} @ `
=x2w \x
Q Q @+} . @ @ } @ Q } ` Q *Q @ 1*. 2Q .+1 @ ` Q 2Q
`
. } 1 }2} . } Q 2Q . 2Q @ `
5 < 2< 6 $% > : ""!#fW! > $ > @~@b@ ~Q @ @
@b}
@ @ @ . Q @b@ . @
@b@+@ . @~@ @~@~@ @+@~@~@ @ @~@+} .+Q @ @ . @+@ Q } @ } Q2Q~Q @~@+@ @
O6 8 $%#7$ 5 7"$%:2 5IQ
@ . @ @*@~@ 1+Q @ @ .+. @~@*@+@+@+@ Q~Q*Q @ ~. @
@ 2Q @+@~@+@b@ +.~Q ~. Q @ . @ Q @+} +.bQ @+@~@~@ @
r5 $ 2< 6 Mf 57698 $% 57<a5 }@ Q } 1 .
1R12. 2.R1. 2. @ . } 1 .
Q @ 12Q Q2. Q WQ2QW. } 1Q QWQ } . . 2} @ @ 1 @ @ . @ 2. . QWQ @
. 2} 2Q } Q } } Q 2@ ` @ @ 1~. @ Q 2Q~. Q . *.b1 @ . Q+1.
r5 $ 6 :2$ 5 $ 57<a5 @b@b@~@~@~@b@~@~@~@b@+@b@b@ @ Q } . @
@ @~@b@~@~@~@b@+@b@
@b@ @~@~@+@~@~@~@+@ @ @+@b@ Q @~@~@+@+@b@+@~@+@b@+@
< 6 ?# < 5 2@ @ 1 ` Q ` } 2} } ` 1 @
} } @ . @ Q 2. 2.
2Q 21 @2@ ` Q Q 1 @ @ Q 1 @ 21. Q . } 1
}@ 2.Qb1 } @ 2} Q 1
.Q @ @ Q @ 2.*.. @2@ 2@ @2@ 1Q . 2. } @2@ Q }2@ @ .
< 6 < 6 7G# 5< $ >!> $%f "f @ ` @b@~@b@~@~@ @b@~@ @b@~@~} QbQ @b@+@ . @b@~@b@+@b@
@+@b@+@ Q @+@b@+@~@+@b@+@+@ @~@+@b@ Q @ Q @ @ @ .+. @~@+@~@
< 6 < 6 7G"7:2 > 5 # 57< "f 2Q @b} @ Q
.b..~Q 2Q 2. @ . b. }
@b@ @+@ . @ ~Q @ @ Q @~@~@ . @ Q Q~.~Q @ .~Qb.+Qb. @~@b@+@b@~@ @ 2.bQ @b}
Q +.
< 6 < 6 7 65 fW$%: 5 # @ @b@+@~@+@~@+@+@b@+@~@ @ @b@+@~@+@~@+@+@b@+@~@+@~@+@
@b@ @~@~@+@~@~@~@+@+@b@+@~@+@b@+@~@~@~@+@+@b@+@~@+@b@+@~@+@b@+@+@b@
< 6 < 6 7 < >< ":2 @~@~@+@~@~@~@+@b@+@+@~@~@~@+@b@+@~@+@b@+@+@b@+@~@+@b@+@~@~@~@+@
@b@+@ 1 @~@+@~@~@~@+@+@b@+@~@+@b@+@~@~@~@+@+@b@+@~@+@b@+@~@+@b@+@
< 6 65S5<=65 @+@+@b@+@~@+@~@~@~@ @~@~@~@+@~@+@b@+@+@ @~@+@~@+@b@+@+@~@+@b@+@~@+@
@b@+@~@~@~@ Q~Q @~@ +. ~Q @ ~Q @+@+@b@+@~@+@b@+@
# h> "!## 5 7"$" 5 @ Q @+@ Q @b@+@~@+@+@~@~@ @b@+@ 2.*Q @+@~@+@+@~@~@~@ @ .
@+@ @~@+@~@~@~@+@+@b@+@ Q @b@+@~@~@~@+@+@b@+@~@+@ @~@+@b@+@+@
" 2< 6 r:2!#$ $ > @~@~@b@+@b@b@+@b@~@b@+@b@~@~@~@b@+@b@b@+@b@~@~@~@b@+@b@~@~@~@b@b@+@
@b@+@~@~@~@+@~@~@~@+@+@b@ @ @+@~@~@~@+@+@b@+@~@+@b@+@~@+@
$"f 576 $%"#%# 5R5 8 "# 57<a5/Q.b1.Q 2Q } Q } ` } 2. Q @ } @ 2@ 2Q
+QbQbQ b.~Q 2. . }~@b@ @ Q2Qb. @~@ .+.2Q 2Q }
@ . 21 } . @ } 2@
. } @ . 2. Q+Q } *Q 2Q
$"f 576 $%"#%# 5 "f 576 $% 5 } 1
+1. +1. 2. @ ~. }b@ Qb. @ ~Q @+@b@
@b@+@ . @~@ Q @~@~@ @b@+@ 1 @~@+@b@ @~@~@~@+@~@~@~@+@+@b@+@~@~@ Q @~@~@ . @
!fW$$ < 6 $%##% >!5I.+Q @+@+@+@+@*@~@+@*@~@+@*@~@+@ . @ }~@ 2Q @+}*@~@ . . @
@b@+@~@~@~@+@ 2@+@~@~@~@+@~@~@ 2Q . }
} 1 @+@b@+@ ~@+@~@ `
!fW$ < 6 65 # 5< 26!5<=5 b} Q @~} bQ @~} Q. 2Q
2.~. @ Q bQ~.b.
@ . 2Q @ @ . } .+Q 2. } Q @ . . 2Q @ 2.
} ~Qb. +. @ . @b} Q . @+@
.bQ @ Q
!fW$ < 6 65 #%# "# >5 @+@~@~@~@+@+@~@+@~@+@ @+@~@+@+@ @~} @~@ @+@+@~@+@~@+@
@b@+@ .~Q @+@~@~@~@+@+@ Q @~@+@ Q @~@~@~@ @b@+@~@+@b@+@~@+@b@+@+@
$ 6> f 5 "$ 5 $ 6 $%:2$ > @ } 2Q 2Q @ .+. } . } Q } 2. Q +Q @ Q+Q +Q
2Q~Q bQ +Q~.~Q @+@~@~@~@+@b@+@ Q @~@~@ Q } 2.~. 2Q } +Q @ 1
}
> $ 5S5 "fW$% 5<=5 @~@~@b@+@b@b@+@b@~@~@~@b@+@b@ @ @+@b@~@~@~@b@+@b@~@~@~@b@b@+@
@b@+@~@~@~@+@~@~@~@+@+@ @~@+@b@+@~@ @+@ @~@+@b@+@~@+@
SbadcfeGg
û
û
úkû
Ï ²Ï ú
Ï
Ï û
a T
h
ÎÎyÏ
û Î
Ï
=û
úhúkú=ûkú Ï
ûú/ûú ú
yÏ ²úhúû ²Ï yÎ²Ï
/ú
n
ú
ú
ûyû
n
û
yú yû
ú
Ï
ú
/o
yú Ï
?6
yû/ú
û
²û
ú
û=ú
Î/Ï
Ï
ú
Ï û
yû
Î
ûkú
ú ²ú Ï
Î
Ï=Ï
ú=ûú=û
û
û
û
û
û
û
Jû
ú/û
Jú Jû ²Ï Jú Ï û
5ú
ú
Î ú
Ï
ú=û5ú
²ú Jú=û
ûú =û
Ï kú
ú
Î
û
kû
û 5Ï
û kÏ ú
ûyûkû
yû
û Ï
ú=û/ûú
Ï
ú 5ú=û
ú
û
ú kû
ú
kú
yÎ
û
û Ï ú Ï kÏ
5û
Ï û
û
ú
kú=û
û
ûû
Î
Î kú
=û
û
ú
kú=û
û û
Ï
Î ú=û
ú
ú
û
6
ú
û Ï
ú
û
9
ú=û
û
yû yú yú
û
ú/û
ú
Ï
úhú
û
Ï
û
Ï
!6
kú
Ï
û
û
/ûyû
yú=û
354 A
=û
û
9
354 A
ú
=û
5ú 5ú=û=ûú^ú ú /ûkû
û
û/û
ú=ûyú/û
yû
û
Jú Ï
ú 5Ï
û kû kû kû Î
ú yÏ
û
ú
û
354 A
û²û
Ï
ú
Ï
yû
Åû
û
ú
û=úkû=ûkû Ï
/ú
ÏyÏ
ú
ûûkû
û
û
5û
/ûú
û
JÏ Jû ÏJÏ
Ï ú^ú
<
û
û
yû
4 5ú
û yú/û
û
ú Î
ú
²ûû²û
< ?>?@
ú
Î
/ú²ú Ï
û
ú=û
ú
ú
Ï
ú
/ú=û
d6
4 û
=û
ú
=ú
/ûyû yú=ûyû yû/úyú û
A
ú 5û
ú kú kú kú Î
/ú
Ï=ÎyÏ ²Ï
Ï
e TAjlk cfm
i
Î
Î
Ï
/ú
Î
ú
Î
Ï=Ï²Ï
ú Î
Ï
û kû kú
ú/ûyú
kû
û
ú=û
ú
kû
9
354 A
! 4
û
û
û
û
354 A
9
354 A
6
6
û
û
kûyû
yû
û
ûû
>
p
û
ú=û
û
p 6
4 ú
kú
ú=û
ú yú
û=û
ú
:
ú
6
ú
û
:
ú
û=ûú
û
=ûú=ûú
Ï Î ûú=ûkú=û
ú/û
A
B
B
û
Ï ûûûkûûkû
Î5Ï û
û/û
yú kû
6
û
Î
kû kûyû
6
û Ï
û
kû û=úkú
û
û
ú
û/û
ú
û
û
ú yú yú/û²ú
4 A
ú
ûkû
4 A
ú
ú/û
Ï
û
Ï
kú kú
kú
kû
+@
û
B
û
û
û=ûyú/û
kú
ûkû
ú yú kú
ú
²ú ²ú
û
û²û
Î
ú/ûyú kú=ûkú=ûkû
ú ûú/û
?6
ú ²û
û
ú/û
û
ú
kú
û
û
û
/ûyû û
û
û
B
ûkûyûú
r
yû
q
fú/û²ú
ú
ú ú ²ú
yú
yû
ú/û²ú
E6
û
û
ûû
û
ûyû ²ú
yú=ûú
ûkû
ú ²û ²ú=ûyû
ûkû
ÎÏ
yú
yû
ÏÏ
û
}.
/j
Y
\k-lm Wn on \pSq rn
sX5Ì1Ä+t
WY^X
+t
[uAt
Ä
?5 856 $ 5> < <a6 $7 5 #%$ > @~@+@b@+@+@b@+@~@~@~@~@~@+@b@+@~@~@~@+@b@+@+@b@+@~@~@~@+@b@
@~@+@b@+@ 1 @~@~@+@b@+@~@+@b@+@+@~@~@~@+@~@~@~@+@b@+@+@~@~@~@+@~@~@~@
3"5 2 6 > 2< 6 25 $ > > $ > Q . Q }b} . } Q } . . @ . . @ 2QbQ Qb. .
~Q @ Q+Q+. @ Q @+@ @+@ Q @~@+@~@ ~Q+.bQ+. } Q~.~Q+. @ @ +Q @ .
3 < 2< 6 #%# $%: 5 @ }b@@b@b@@~@@@b@b@ Q @@ @@~@ QQ @b@b@@@ @ .
}+@+@~@+@b@+@~@~@ Q+Q @+@~@+@b@ @
@b@+@~@~@~@+@+@ @~@ Q @+@
3 2 " 5L> @+@*@~@+@*@~@+@*@~@+@~@*@+@~@*@+@~@+@*@~@+@*@~@+@+@+@+@+@+@+@+@+@+@+@~@
@+@b@+@+@~@~@ @b@+@~@+@b@+@+@~@~@~@+@~@~@~@+@b@+@+@~@
\5 #fW!"#%# 5 #%$fW$%# 5 @b@+@b@+@b@+@b@~@~@~@~@~@ Q @ @b@ Q @+@b@~@~@~@~@~@~@~@~@~@b@
@ @+@+@~@~@~@ bQ @ Q @b@+@+@~@ @ ~Q~. @ Q }+@+@~@~@~@+@~@
\5 #fW77" 25 # 5 257<a5 2Q } .~Q @+} ~Q ~. @ QbQ~Q }~} .+.b.bQ~Q~Q~Qb. @ }+} Q
Q~Q
@+} @b@+@ } ~Q } @ Q @ +. } Q+Q~. }
@~@+@b@ Q
\5765 < 6 7$ > S >5 @ @+@b@ @+@+@b@+@~@+@b@+@~@+@+@ @~@+@b@+@~@+@+@b@+@~@+@b@
@~@+@b@+@+@~@~@~@+@b@ @+@b@+@+@~@~@~@+@~@ @+@b@+@+@~@~@~@+@~@
\5765 : >< f 5?5 6 $ 5< "f @+@~@+@*@~@+@+@+@+@+@~@*@+@~@+@*@~@ @+@*@~@+@+@+@+@+@~@
@~@+@b@+@+@~@~@~@+@b@+@~@+@b@+@+@~@~@~@+@~@~@ @b@+@+@~@~@~@+@~@~@~@+@
\5765 : >< f 5 " 6 f 5 "$ @+@~@+@+@ @~@+@+@~@+@~@+@+@~@+@~@+@+@~@+@~@+@+@~@+@~@+@+@~@
@~@+@b@+@+@~@~@~@+@b@+@~@+@b@+@+@~@~@~@+@~@~@~@+@b@+@+@~@~@~@+@~@~@
\5765 : >< f 5 #$ "f @b@b@~@b@~@b@b@~@b@~@b@b@~@b@~@b@b@ @~@b@b@ @~@b@b@~@b@
@~@+@b@+@+@~@~@~@+@b@+@~@+@b@+@+@~@~@~@+@~@~@~@+@b@+@+@~@~@~@+@~@~@~@
\5765 : >< f 5 6< #% ! > $ > @~@+@+@+@+@+@~@+@~@*@+@~@+@+@+@+@+@~@+@~@*@+@~@+@+@~@
@~@+@b@+@+@~@~@ @b@+@~@+@b@+@+@~@~@~@+@~@~@~@+@b@+@+@~@~@~@+@~@~@~@+@+@b@
\5765 : >< f 5 2576 $ 5 $#% Q ~QbQbQ . bQbQbQ bQ } bQ. Q Q } ..~Q @@
*. @ . @ Q @ Q~Q @ .
} @ . } @*} 2Q @ Q Q } . 2. @+@+@ @+@ *@ @
# < 6 65]8 $%#$ >UQ . @~} @ @
@ +Q @b@ .b. }~@ .~Q+QbQ @~@~@ 2.
@ .+. 2.*Q }~@ @ @ 2.~Q+.+. @ Q+Q } +Q~Q } 2Q }+} . }~@ Q @b@+@~@+@
7# 2 576 7# 57<a5 +Q @ @ @+@~@+@*@~@+@ +Q @~@*@+@~@ @*@+@~@+@ @+@+@ Q @~@
@~@ @+@ @~@~@+@ . @ @b@+@ @~@~@+@~@ @b@+@+@~@~@
7 < 7 6 $ > f 2< $#%$%:2 > @+@*@~@+@*@~@*@+@~@*@+@+@+@+@+@+@
@~@*@+@*@~@+@*@~@*@+@~@
@~@+@b@+@+@~@~@~@+@b@+@~@+@b@+@+@~@~@~@+@~@~@~@+@b@+@+@~@~@~@+@~@
\6 27 < 7 6 $ >;<a6 $ 8 "!## 5
@ ~. @~@b@b@~@~@~@b@~@b@+@ QbQ~Qb. @~@b@+@b@ @b@
@~@ @+@+@ ~Q @ Q @~@ Q @ @~@ ~Q @~@~@~@
@b@+@~@+@b@+@+@~@
\> ": 2< 6 \ 5 ": 5<=5 @*@~@+@~@ @~@+@*@~@+@~@+@+@~@+@*@ @~@+@+@~@+@*@~@+@~@+@+@~@
@~@+@b@+@+@~@~@~@+@b@ @+@b@+@+@~@~@~@+@~@ @+@b@+@+@~@~@~@+@~@
5 $%fW$#%$ >U> < <=6 $% 5 #%$ > @*@+@+@+@*@~@*@+@*@~@*@+@+@+@*@~@*@+@*@~@*@+@+@+@*@~@*@+@*@~@
@~@+@b@+@+@~@~@~@+@b@+@~@ @+@+@~@~@~@+@~@~@~@+@b@+@+@~@~@~@+@~@~@
6!<a> "$ < >?< 7 6 "# 5< > @ 2Q *Q @ @+}
@ } } @ @ Q2Q+1 *Q }b@
@ ~.. b. . } Q } .~Q. @@b}@ @ . @ . ` Q~Q } @ @ } } Q @
. 1 . 2Q ` }*}b@ .
"576> $% 2< 6 $%:2 5 65 :$$ @ . @
@+@ @~@+@~@ @ Q } } @~@ ~Q @~@ Q @
@ 2Q+Q~Q @+@~@~@ Q+. b. } Q @ Q @~@+@~@~@~@+}b@+@ @ ` ~. @ Q +@ Q
"576> $% 2< 6 $%:2 5 "" < $%#%$ 57<a5 @~@b@@~@@b@~@@b@~@@b@@~@b@@ @~@@b@b@b@b@b@b@@
@~@+@b@+@+@ @~@+@b@+@~@+@b@ @~@~@~@+@~@~@~@+@b@+@+@~@~@~@+@~@~@~@+@
#% 6 7 $# >6 : 5 $ } @ Q
@ Q bQ~QbQ~Q } .bQbQ }+} .~Qb.bQ @~} Q
Q @ . } Q~Q }+} Q+QbQ ~. } . @
. +@ @b@ +Q @
#% 6 7 $# >?> 1b. . Q. Q...~Q @} .QQbQ . @ @ .b..Q @
@ Q @ +Qb.+Q~.~Q~.+Q bQ ~Q+Qb.+.~.+Q 2. } 2Q @ ~@+@
@
#% 6 7 $# >> @ @b@~@ @~@b@~@b@b@~@b@~@b@b@ @~@b@ @~@b@ @b@~@b@b@~@b@
@~@+@b@+@+@~@~@~@ @+@~@+@b@+@+@~@~@~@+@~@~@~@+@b@+@+@~@~@~@
N
;6
û
4 ûû
/
4 ;
*ú ú ú
kûyû
4 76
ú
ú
û
Åû
ú=û
û
ûû
ú=û
û
ûyû
ûû
ú/û
û
yû
9 ;
kú
û
û
û=ûû
û
û
L
ú
ú
P
ú
û
û
û
P
û
ú/û
û
ú
P
¿û úhú
û
o
4 A
ú
û
û
ûyû
û
ûú
Ï
ûkû
Ï
û
û
û
û
;
P
û
û
d6
ú yû
û
C9C
6
ú
ú
P
;
P
;
P
;
û
;C
?v=6R6
û
>;L
û
I
û
;
P
ú/û
PG
²ú
4
kû
û
ú
ú
ûûû
ûyûkû
ú
ú
û/û
û
û
û
û
û
ú
Ï
ú yú/û
yú
ú
yû
û
û
û
yû
yû
û
6
4 û
ûkú=û
û
û
û
C
²û
ûûyû
kû
6
û ú ú/û
yú ²ú
ûû
Åûûû
û
û ²û
û
4
û
P
ú
kûkû
ú
4
9
P
ú
û
û
4
ú
ú=ûú
¿û
û
P
kú ûkû
ú ²ú
9
4
kú/û
²ú=ûú=û²ú/û²û
>
kûyû
P
C
w
û
û
/
û
;C
û
ú/û
ú
Ï=Î
6RC
kû
û
Î=Ï
û
yú
û
6 0H ;I
ûûû
ú
L+n
û
yû
û
û
ú
û
/ûyú/û
/ûú
Î
û
ú
û
ú
Ï
û
û
û
kÏ
ú/ûyú
ûkûú
yûyû
?6
û
û
ú
û
ûyûkû
Ï
ûû
yû
Ï
F
û
ú/ûyú
Î
ú/ûú
û
?6
F
F
ú
yú
û
ú
kú
Q6
4 û
û ú=û
ú
yû
F
fû
Ï
C
4 ú
6
ú ú/ûû Ï ú/ûkû Ï
Ï
F
E6
?6
Lx<
û
ûûû
kûûû
yû
û
kû
yú/ûyú
û
kú ²ú/û
kû
ûyú/ûyú Ï
ú/ûú
yú/û
Ï
û
ú
Ï
ú ²û
û
ûû
û
ú
ûyûyû
yÏ
û
ûû
û
û
lm 2m Wn k
.U WV
Wq 4k
5X!YZV
Ä
[X
Wk
5V5Ë\KV
}
^]KX`_
=Î
fW$% < 6 655 < $ >!<a57<a5Q ~Q +QbQ bQ+Q +. ~Q @ Q~Q~.+Qb. @~@~@
~.+.~Q~.~Q+Q @+@ @~@+@~@
@ @~@+@~@~@ Q @ Q }+@~@ @+@~@
fW$% < 6 65S5 "$ >
.~. ~} @ Q +Q b. ~Q } @ @ Q @ Q
@+@b@ .+.
Qb.+. 2Q @ Q @+@~@ Q~. Q } @ @ ~. @ Q @+@~@+@ .+Q~Q+Q } 1 @b@+@ Q
fW$% < 6 655 8 "# 57<a5 @~@~@+@b@+@b@+@~@~@~@+@b@ @ @~@~@~@~@+@b@+@~@~@~@+@b@+@
@b@+@~@~@~@+@~@~@~@+@+@b@+@ @b@+@~@~@~@+@+@b@+@~@+@b@+@~@+@b@+@+@
fW$% < 6 65 "$ 86 > > . ~. @
@ Q @ ~.+. } @ @ Qb.+Q }~} @ Q @
@b@+@ 2Q @ Q @ Q @ Q @
@ QQ @~}+@ .+Q 2.~Q +Q } Q.+1 @ Q +Q1 @ 2}+@~@~@+@
@b@ Q @~@~@
fW$% < 6 65S> !## 5 ~Q @~@b@ Q @b@~@b@ Q @b@b@~@ Q @b@ bQ @b@b@~@b@~@b@ @b@~@b@
Q @+@b@+@~@+@b@+@~@+@b@
@b@+@~@~@~@+@~@~@~@+@ @+@~@+@b@
fW$% < 6 65L> $fW$%#%$ >UQ @ @~@*@ +Q @+@*@ Q @ ` *Q*.~.*. @ @ @ Q @+@*@~@*@
@b@+@ @~@+@~@~@ }+@~@+@~@~@~@ b. @~@~@~@+@~@~@ Q @b@+@~@ Q
fW$% < 6 65S><=6 $ 5<=5 @b@b@+@b@ @~@b@+@b@b@~@b@~@b@+@b@
@b@+@b@b@~@b@~@b@+@b@
@b@+@~@~@~@+@~@~@~@+@+@b@+@~@ @+@~@~@~@+@+@b@+@~@+@b@+@~@+@b@+@
fW$% < 6 65 "": 57<a5 ` Q~Q } . @ } 2.+. 2Q
2Q
@+} Q } Q @ 2. Q
@ ~. }~@ } } 2Q @@ Q @ 2. bQ @ Q } @ } Q @ @ .+. }~@ @ Q ~Q b.2.
Q } Q2. 2Q . `
2@~@ Q 2Q*Q @
fW$% < 6 65> @+@~@+@+@~@+@~@+@+@b@+@~@+@~@+@+@~@+@~@+@+@~@~@~@+@~@+@+@~@+@~@+@
@b@+@~@~@~@+@ @~@+@+@b@+@ @ @~@~@~@+@+@b@+@~@+@b@+@~@+@b@
fW$% < 6 65> @b@+@+@b@+@~@~@~@+@b@+@~@~@~@ @+@ @+@~@~@~@~@~@+@b@+@~@~@~@+@
@b@+@~@~@~@+@~@~@~@+@+@b@+@~@+@b@+@~@~@~@+@+@b@+@~@+@b@+@~@+@b@
R >< #% 6 $ > :2 6 >!>5 Q } }2@ 2@ .2.bQ @ } 2.bQ @ @ Q 2} } 2} Q } 212Q QbQ2Q
QQWQ ` } @ Q ` Q WQ @ .WQ @ . ` } Q }2} ` } 2Q }2@W} @ QQ 2Q 21 } Q ` } .Q @ @
+1 ` @@ @ 1 Q
Q2. . @ }2@ ` 2Q21 }2@ . ~Q ` 21~Q Q
# < $ 5 # < 5 @*@+@~@+@+@+@+@+@~@*@+@~@+@~@*@+@ .+Q @+@+@+@~@+@*@~@+@~@*@+@~@+@+@ +Q
@b@+@~@~@~@+@~} . @+@+@b@+@~@+@b@ Q~Q @+@b@+@~@+@b@+@
< 6 !## 5S5 2>> 6 "f @~@~@b@~@b@b@~@b@~@~@~@b@b@~@b@~@b@b@+@b@~@b@~@b@b@~@b@~@~@~@b@
@b@ @ Q @+@+@~@+@b@+@~} . } @b@+@~@~@~@+@+@b@+@~} 1 Q21 @+@~@~@~@+@b@
< 6 !## 5 # 57<a5 @b@~@b@~@b@b@~@b@~@b@b@~@b@~@b@b@~@@b@~@b@~@b@b@~@b@~@b@b@~@b@~@b@
@ 1 @~@~@~@+@~@~@~@+@+@b@+@~@+@b@+@~@~@~@+@+@b@+@~@+@b@+@~@+@
< 6 < 6 7 5 # 5< "f @~@~@~@~@~@~@b@+@b@+@b@+@b@~@~@~@ ~Q @~@b@+@b@+@b@+@b@b@+@b@+@
@b@ Q~Q @~@+@~@~@~@+@ QbQ @~@+@b@+@~@~@~@+@+@ @+@~@~@+@+@b@+@~@~@
?6 $ 698 $ @b@+@b@~@~@~@b@+@b@+@b@b@+@b@~@~@~@~@~@b@+@b@~@~@~@~@~@b@+@b@b@+@
@b@ }+@~@+@b@+@ ~Q~Q @~@~@~@+@b@+@+@ 1~Q+Q ` @~@+@+@b@+@~@
"!##% 6 $ 5/5 >> $%# 5 @*@~@*@+@~@*@+@+@+@*@~@*@+@*@~@ *Q*Q @+@+@ @*@+@*@~@+@*@~@
@b@ .~. @~@+@~@~@ . @ Q @~@~@+@b@+@+@~@~@~@+@ 1 @~@~@+@~@~@~@
r< 6 08 2< 6 $% > f " 6 57<a5 @~@~@~@b@b@+@b@~@b@~@~@~@b@b@+@b} @b@~@b@+@b@~@b@+@b@
@b@+@~@~@~@ @+@+@~@~@~@+@~@~}~}+} Q @+@b@+@~@+@b@+@+@~@~@ Q 1 +@~@+@~@~@~@+@
F
6
E6
4 A
ûkû
yû
û
ûû
û
F
6
4 A
ú
?>?@
Oûkú Î
kû
F
yú
6
yûyû
kû
ûûyú=û
û
Î
û
ú
ú=û
kû
kû
yûû
û
yú=û
ûyû
Ï
ú
ú
yú
ûkûyû
û
Ï
6
4 A
yú
yû
ûyû
û
û
F
6
4 A
û=ûú yú
F
Ï kû=ûû=û
ú ²ú
ûú=û
6
4 A
û
ú=û
yûû
û yÏ
=û
Ï yÏ
û
û
û
Ï
û
Î
ú
û
²ú
yû
6
4 A
ú
=ú
ûû
ûû
6
4 A
û
F
ú Ï
4û
û
F
ú
²ú
û
û
û
Ï
û
ûûkû
û
F
/û
6
6
4 A
ú/ûú
ú/û
kú
û
Ï ûû ²û
Ï
F
û=ûkû ú
J
û/û
6
>;L
ú
/ûyú
Î
û
ú yú yû/ûyú=ûú
ú
ú
û
Î
û
Ï
û
yû
û
û kÎ
5Ï ûû
ú
ú Î
ú
ú ú
Ï ú
yÏ
ú kÏ
Ï
û
Î
ú
û
ú
Ï
ú Ï
Ï
ú =Ï
/ú
û
C 4
Ï
6
û
û
354 A
=û
û
?6 A
354 A
=û
Ï û
ú=û
û
354 A
ú yú
û
û
Ï =ú²û Ï û²ú
yÏ
3 ?6 ú=ûkú
û
û=û
û
ú û=ûyú/ûyû
Lx<
C
=û
yÏ û
û
4 A
û
L)n
û
F
ú
ú û=û
ú ÏyÏ
Ï/Ï
6
4 A
yÏ yú
ú
Ï
>;L
9
6
û
ú
N
>yL
ú
û
6
O
û
Ï
C 4
ú/û
kú=û
P
4
4 Î
!6
Î
)
x+zy|2y W
) ! D
ë
òhþ&í/õ¡ïþ
{øìôí/ìò^öõ²þ
þ&î í
û
ú/û
û
z ad{Gg
û
û
0
(
9)a)
*þ&õ¡ïîHí=ò^þ&ô½õ öò^ðöõyí=ïôð
î9þ&ÿ¬õ*ôðõ¡ï]î9ðòhï
Ï
a
]öî9öìïfõ¡ð"ï]öõyìöí=îJï öë5ïóí=ìïðò
}}
/j
Y
+t
%
I
Ä
[uAt
0
0
64
gradient
.|}|
õ¡í=ÿ
¡ ¡
WY^X
100
s"t=u"v\w!x+zy 2y W
ã1ä 1ä
\k-lm Wn on \pSq rn
sX5Ì1Ä+t
ë
ó"ðì
)
(
Zøìôí/ìò^öôí=ï]íþ
þ&î9ôöî
4þ&õ¡ïîHí=ò^þ&ô
þ¾ô«ð"õ¡ï]ðìò^ï
V 2 (
õ¡í=ÿ
í/ïï]öî9ì¯ðõºþ
óöõ¾ðì®ï ö§þ&îHð {ð"ìí=ó
A~îHí=ìôþ&ÿ
Zõ¡öî {í {ó"ö
** +M' '

²è
97 2
ë5õ*øõ¡øí/ó"ó
êèé
N
=í {øìôí/ìò^öJõ¡öî9ðí/ïðþ&ì
¯í/õºôþ&ìöJñî9õ¡ï
(
0 *öõ¡øóïõ¿í=î9öÅõ þ
M (0`d( (
ìþ&ìñ
ú=û
lm 2m Wn k
Ä
.U WV
Wq 4k
5X!YZV
[X
}`
Wk
5V5Ë\KV
^]KX`_
100
0
0
64
gradient
stau"vrwx2y2z2y {2y D / W
I
2
0
K
G
U 2Q Q
O1 GQ 121 .O1QGQ ` 1
. 2} ` 21b.21. 2Q @b}
)
W
E 0
a
9
9 a a
.|
ö
òhþ&öìþ&òhóðìö
5ë
) *
9 2
0
! (
) H
} Q 1 ` Q21 ` @ 1 } 1 Q2.1 Q OQ2Q 112.
` O. @ .
1 @ Q } 1 GQ @ Q
1 } 2@
Q
.2Q ` .. 2. (D b
H
a
N @ ( }2} (
(WD )
r) 2
0 0^
)
2
0
9
Ï û
ZîHí=ô«ð"öìï
=û
Ï
Î
û
¯í/õ²û
Ï ú
¾ú
Ï
=ûkú ú
ë
òhþ&îHînöóí/ïðþ&ìò^þ&ö ñò^ð"öìï
{øìôí/ìò^öõ
þ&ò^óð"ìö
í=ï]ïöîHì
¯öî9öøõ¡öô®í/õ
Ï
¯ðï
Î
ú
/ú
ú=ûú Ï
û
Ï
þ&ð"ìï1öõ¡ï]ðÿ¬í/ïþ&îHõkþ
{í
î9öõ¡øÿ¬öô
ZöìöîHí=óó ²í Zøìôí/ìïõ öòhðöõ
ú Î
Ï/ÎÏ
í=õºù
ú
Ï
=úkû
ú
¿ôöìõ¡ð"ï]ðöõ
,õ¡í=ÿ
û Ï
Î
Ï úû=û¾ú ¾û
í/ïöîOôö ï
í=õ÷"ìþ&ðõ Føìðÿ¬þ&ôí/óü
óöõþ
*öòhþ&ìõ¡ïînøò^ïöô¯þ&înôöîþ
Ï/Ï
/ú
û Î
{þ&õ¡ï]î9í/òhþ&ôõ¡í/ÿ
þ&ïö1ï í=ïð"ì
í1ìþ&ðõ øìðÿ¬þ&ô«í=ó í/ïïöîHìköÿ¬öî Zöô
ï ö
)
(
ù]î9öòhþ&ìõ¡ïî9øòhïöôþ&î9ôöîþ
Zí/õ¡öô¾þ&ìí Zøìôí=ìòhöõ
û¾úhúû
ö
ó"öõ«í=óþ&ì
/û
Ï
Ï
û/ú
Ï
öí=îHÿ¬í/ìî9í/ì
úhú/û
öînöõ¡øóïðì
Fòhþ&öìù
qþ&îyí {øìôí/ìï*õ öò^ðöõ fðïºðõ5ï ö¯ÿ¬í/ïïöîþ
ï ö¬í=ìí=ó Zõ¡ðõ¾ôöõ¡ð Zì®ï í/ï¿ï ö¬óöõ¡õ¾í Zøìôí/ìïÅõ öòhðöõ¾ò^þ&ìï]î9ð Zøï]öóöõ¡õï]þ
Zöìöî9í/ó
`@
/j
Y
ò^þ&ÿ
¡
a
@( (
í/òhïìöõ¡õï í/ì
õ¡öò^ïðþ&ìú
ã1ä 1ä

0
ï öí Zøìôí=ìï4õ öòhðöõôþ
\k-lm Wn on \pSq rn
sX5Ì1Ä+t
WY^X
7
' \ '"
9é
D
1
èé
(-D I
ðõ
¯ðóó
{öÿöìï]ð"þ&ìöô
{í=õ¡öôþ&ì®ôöìõ¡ðï]ð"öõ
í/î9í/ÿ¬öï]öî9õïþ
qðôöìï]ðòhí=ó ]þ&îfí=óóõ¡í=ÿ
ð"ô«øí=ó õ¡í/ÿ
óöõ
ökõ öòhðöõ
óð ]öí/ìô®ï]í
í=õòhí=îHîHð"öô3þ&øï4ñî9õ¡ï
Zö¯öõ¡ïðÿí=ï]öô
ó"öõ =í=õìþôöï]í=ðóöôð"ì
í/õ
Zð {öì
þ&ìþ&ÿ
Zð {öì
ú
þ&ì
óí=ò^ð"ì
ï ö
Zöìöî9í/ïöô(í
Zî9í/ôðöìï
¬ï ökõ¡í/ÿ
Zó §÷"înþ
ï ö5ÿðôôóö5þ
qþ&îºí/ó"óï ökõ öòhðöõ¿ðì
öînö
{þ&ó {öô
þ
{ðìô«ð"ù
ú
úhú
&í=õÅìþôöï]í=ðóõ1þ&ì
Jú
û
ú
öõ¡öî9ðí=ï]ðþ&ì
ë5óï þ&ø
óðÿð"ï]õþ
óö
ú
D
E 7 )L" (
a O
) a
`d( 21 ( M" HNV

% 9 ( )
9
2
a
) W
T 0 a
O 9c
N a a )
9"
óöõ²í/ó"þ&ì
)

" )
( @ 2¨ª¦ @ ( @ (
@ ( @ Kª ¦ @ ( @ 2
ðï ®ìí=îHînþ
øõ «ï öõ¡í=ÿ
qþ&î9ÿí=ï]ð"þ&ìþ&ìõ¡öôðÿ¬öìïþ&óþ
öî9ö
]ðôöìïðò^í=ó
í/õ
í/ìô
ðõÅõ¡ïîHð {ð"ì
í=óõ¡þ(ð"ì
Hé

R (bD 0
)
0
)
V
r r 9V = T'¤\W¥ ¦ @ ( @2@ '§¥W¦ @ ( @2@2@@2@ 2¨©r¦ @
D 0 )
0
V 9V r
9)
2M Z W 9V aU T*«0©¦ @ ( `2` «ª ¦ ( @ '©¦
M¤ ®W¦ ( @ §"®W¦ @ ( @@ (
ú
[uAt
'
/
è
B
öõ¡öîHðí=ï]ð"þ&ì
ò^þ&ìñôöìòhöþ&ì½ï ö
õ¡í/ÿ
Ä
û
ç
Ï
+t
Zøõ¡ï]ü
ï ö
ï öyõ¡í=ÿ
Zøìò Fþ
,þ&ÿ¬ö¾þ
ì
óökþ&înôöîHðì
]þ&îHïøìí=ï]öó
2 )
M (K`( M"
9 W
0 S V ) 9 (
) þ&ï öõ¡öõ5í {þ&øï*ï öò^þ&î9î9öòhïþ&înôöîJþ
ï öÿ
í=î9ö
înöõ¡öìïöô?þ&ì?ñ
í=îHð"öõÅînöÿí=î Zí Zó
,ÿ¬þ&õ¡ï«í Zøìôí=ìïõ öòhðöõ
Zî9í/ôðöìï ï øõ ï öî9ö5ðõJí
ó"öyïþ¾ï ö²óö qï{þ&îïþï ö²î9ð
Zð
þ&îHïðþ&ì
ïõ¡ð"ô«ö²þ
ú Ï
ï înþ&ø
ï öò^þ&öìþ&ò^ó"ðìö
þ
Oí=ÿ
í {öþ
í=ï]ïöîHì
ïðÿ¬íìöí/î
Zð Zøðï ðÿ
\ï öJòhþ&öìþ&òhóðìö
þ&õ¡öô
lm 2m Wn k
Ä
inferred density
.U WV
Wq 4k
5X!YZV
[X
`
Wk
5V5Ë\KV
^]KX`_
ú
5000
0
0
64
¯°a±"²r³´2¶2µ2¶|Ú 2¶R¸N¹"ºM»¼a½H¾¿0À9¿ÁÂ ½H¾ ñ Ø=»óHØ=È\¾ó¿0À%¼aÀ9¾¿bÇ!¾ û »ó¿0¼Ç!ô û ¼¾È »ÇÈr¾ÇR»õL»¿0Ø
¼ÇÄ û »ÈZ¿0ÄÅºMÆ9¾¿*»õ?ÄºMÇ¾¿0ôMÅ¾È û »¾ó» û Æ9À9ó¾Â ?¾ û »óH¿0¼aÇô û ¼¾È »ÇÈ\¾Ç/»õ¿0Ä2ÅØ
ºMÆ9¾¿IÄÆ%»óÕN¼½¾+Õ"ÇÄ2ÈrÀ%¾ó¼dÓNÄ2¿IÉÍ~ÉÐ~ÌËÉ2ËbÁ2ÎbÁ2ÑbÉ2ÉÊ2ÑbË2ÊbÌ2ÏbÁ2ÐbË2ÉÊ2ÎbÊ2ÐbË2ÍbÊ
Ì2ÉRËÌ*É2ÊRËËRÊ2Í*ÌÁRË2Ð*ÊÌRÊ2ÊRÌÎ*Á2ÍRÊËRË2Ñ*ÊÉRÊ2ÏRÊ2Á+Ë2ÎRË2ÏRËÁ*É2ÁRÌÌ*Á2ÊRÉÏRÁ*ÁÁ+Ì*Ì2Ñ
ÉWÉ2ÌÍÏWÍ2ÉÑWÉ2ÎWÍWÌÊbÍÊÁ2ËWÍ2ÌÁÏWÐWÌ2ÐËWÁ2ÌÎWÁ2ÉWÍËÉ2ÑWÍ2ÁÌÍÂ ½¾~ÃºM¾Ä2ÇÅÄ2ó
ÇÄ2ó÷ û »ÇÇ¾Æ9Ä¼À9»ó û »¾õÔ û À%¾ó¼ +ÓNÀ9¼½NÓNÄ2¼a¾ÇUÈr¾ºM¼½ÓÄ¿LØ=ÏÂ ÌÍ2Ð2ÎÉ2ÌdÂ
Q
K
!
q

/j
Y
û
inferred density
`
\k-lm Wn on \pSq rn
sX5Ì1Ä+t
WY^X
+t
Ä
[uAt
5000
0
0
64
¯"°=±"²\³!´2¶Kµ¶|Ú ¶/¸N¹"ºM»¼½¾¿0À9¿bÌdÂ ½H¾ ñ Øa»óØ=È\¾óH¿0À9¼aÀ%¾¿bÇ¾ û »óH¿0¼aÇô û ¼¾È »ÇÈ\¾ÇR»õL»¿0Ø
¼ÇÄ û »Èö¿0Ä2ÅºMÆ9¾¿+»õÄºMÇ!¾¿0ôMÅ¾È û »¾ó» û Æ9À9óH¾Â ?¾ û »óH¿0¼aÇô û ¼a¾Èö»Ç!È\¾ÇS»õU¿0ÄÅØ
ºMÆ%¾¿SÄ2Æ9»óÕ¼a½H¾bÕ"ÇÄ2È\À9¾ó¼HÓNÄ¿IÌ2ËÌÐ~ÉË~ÊÑ~ÁÎbËÉ~ËÊ~ÌÏ~ÁË~ÁÑÊ2ÎbÁ2ÐbÊ2ÐbË2ÍbÊbÌÉ
Ë2Ì*ËËRÊ2ÍRÉ2Ì+Ë2ÐRÊ2Ì+Ê2ÊRÌ2ÎRÁÍ*Ê2ËRËÑRÊ2É*ÊÏRÊ2ÁRËÎ*Ë2ÏRËÁRÉ2Á*ÌÌRÁ2Ê*ÉÏRÁ*Ì*Ì2ÑRÁ7Á*É2ÊRÌÁ
ÉWÍ2ÏWÍ2ÉÑWÍWÉÎWÌ2ÊÍ2ÊÉ2ÉWÍÌÁ2ÏWËWÎWÁ2ÌÐWÁÉbÉÑWÍ2ËÉ2ÐWÉÍÍ2ÁWÌ2ÍdÂ ½H¾bÃºM¾Ä2ÇÅÄó
Ç!ÄóH÷ û »ÇÇ¾Æ9Ä2¼aÀ%»ó û »¾õaÔ û À9¾ó¼ *ÓNÀ%¼a½EÓNÄ2¼¾ÇUÈ\¾ºM¼a½ÓNÄ2¿IØaÏdÂ Á2ÊÐ2Í2ËÑÂ
d
K
!
Z

lm 2m Wn k
Wq 4k
5X!YZV
Ä
inferred density
.U WV
[X
`
Wk
5V5Ë\KV
^]KX`_
Ï
5000
0
0
64
¯°a±"²r³´2¶2µ2¶|Ú·2¶R¸N¹"ºM»¼a½H¾¿0À9¿ÉÂ ½H¾ ñ Ø=»óHØ=È\¾ó¿0À%¼aÀ9¾¿bÇ!¾ û »ó¿0¼Ç!ô û ¼¾È »ÇÈr¾ÇR»õL»¿0Ø
¼ÇÄ û »ÈZ¿0ÄÅºMÆ9¾¿*»õ?ÄºMÇ¾¿0ôMÅ¾È û »¾ó» û Æ9À9ó¾Â ?¾ û »óH¿0¼aÇô û ¼¾È »ÇÈ\¾Ç/»õ¿0Ä2ÅØ
ºMÆ9¾¿IÄÆ%»óÕN¼½¾+Õ"ÇÄ2ÈrÀ%¾ó¼ÓÄ¿IÍË~ÁÉbÐbÎË~ÁÏ~ÌÐ~ÌÊÍ2ÊbÍ2ÌbÌ2ÏbÍ~ÉÎ~ÑÍ2ÉbÌ2ÁbÉÍ2Ï
ÁÁRÌRÉÏRÁRÁ2ÊRÌÌSÉÁRË2ÏRËÁSËÎRÊ2Á/Ê*ËRÊÏSËÑRÊ2ÉRÁÍSÊÊRÌ2ÎRÊÌSËÐRÌ2Ñ/É2ÌRËËRÊ2Í/É2ÊRËÌRÌ2É
ÊË2ÍÊ2ÐÊÎ~ÁÐbËÊÁ2ÑbË2ÉÁ2ÎÁ2ËbÉ2ÉÊÑÁ2ÌÉ2ËÌË~ÉÐbÉÑÍ2ÁbÉ2ÍÌ2ÍdÂ ½¾~ÃºM¾Ä2ÇÅÄ2ó
ÇÄ2ó÷ û »ÇÇ¾Æ9Ä¼À9»ó û »¾õÔ û À%¾ó¼ +ÓNÀ9¼½NÓNÄ2¼a¾ÇUÈr¾ºM¼½ÓÄ¿LÏÂ Ì2Í2ÎÌ2ÍÑÂ
K
!
q

q q
¾ü¼ù/¼½¾ û »óÔMÈ\¾ó û ¾-Æ9À9ÅÀ9¼a¿oÓN¾Ç¾ ò Ç»ÄÈ\¾ó¾ÈÂ ½ôM¿0ù/¼½¾-¿0Ä2ÅºMÆ9¾-ºMÄ2ÇÄ2Å¾¼¾Ç¿
À9È\¾ó¼À û ÄÆ?õa»ÇWÄÆ%Æ?¿0ÄÅºMÆ9¾¿ =ù?ÓN¾Ç¾
RÏÂ ÏÏ2Áù RÏÂ Ï2Ï2ÏÏ2Áù RÏdÂ Ï2ÏÐ2Ê2ù
Â ½H¾¿0ºM¾ û À9¾¿ºMÄ2ÇÄ2Å¾¼¾Ç¿ À9È\¾ó¼À û ÄÆrõ=»Ç*Ä2Æ9ÆU¼½¾¿0ºM¾ û À%¾¿À9óú»Æ9ú¾È =ù\ÓN¾Ç¾
§
¦
19/+}})1 ¡R5¢¤£/¥}
0¨
¶· ¶¸=¹Qº
©`ªG«¬
§
¯®x«°¬
²±;³´¬
5±=µ%¬
G¨
©
`Q
/j
Y
«0©I¦
'«ª¦
¼»R½ ¾
''©I¦ 'Kª¦ H¤M®N¦
M (0`d( 2. a M" `( `(
¿»½ À
inferred density
î9öõ¡öìï]öôþ&ìñ
¿»½ »
¼»R½?Á
ú ²ï î9þ&ø
\k-lm Wn on \pSq rn
sX5Ì1Ä+t
' ö§®E¦
ÃÂ½ »
í/ìô
WY^X
Ã»R½ »RÁ
+t
Ä
[uAt
(HD öî9öõ¡øó"ï]õ4í=înö
ú
5000
0
0
64
¯"°=±"²\³!´2¶Kµ¶|Ú2Ö¶/¸N¹"ºM»¼½¾¿0À9¿bËdÂ ½H¾ ñ Øa»óØ=È\¾óH¿0À9¼aÀ%¾¿bÇ¾ û »óH¿0¼aÇô û ¼¾È »ÇÈ\¾ÇR»õL»¿0Ø
¼ÇÄ û »ÈB¿0ÄÅºMÆ9¾¿»õSÄoºMÇ¾¿0ôMÅ¾È û »¾ó» û Æ9À9óH¾ù ò Ç»ÄÈ£Æ%À9ÅÀ9¼¿Gõ=»Ç+ºMÄÇ!ÄÅ¾¼a¾Ç!¿2Â
?¾ û »ó¿0¼Çô û ¼¾È,»ÇÈr¾ÇU»õM¿0ÄÅºMÆ9¾¿Ä2Æ9»óHÕ¼½¾+ÕÇ!ÄÈ\À9¾óH¼dÓNÄ2¿LÌË~ÉË~ÁÌ~ÁÎ~ËÉ~ËÊ
Á2ÑOËÍOÌÏOÁ2ÐÊ2ÎÊÊÐOË2ÌÌ2ÉÉ2ÌOËËOÊÍOÌ2ÁOÊ2ÌOËÐOÉÏOÁ2ÍÊ2ÊÌ2ÎOËÑOÊÉOÊ2ÏÊ2ËÊ2ÁOËÎ
É2ÁGËÁGË2ÏGÁÊGÌ2ÌWÌÑGÁÁOÁOÌGÉGÉÊGÍ2ÏOÍ2ÉGÉÎWÍOÑGÁËGÍ2ÊGÁÏWÌ2ÊGÊÑGÉ2ÉOÎGËGÍ2ÌOÐGÌ2ÐGÁÉ
Í2Ë+ÉÑ*É2Ð+Í2Á*ÉÍ*Ì2ÍdÂ ½H¾RÃºM¾ÄÇ!ÅÄ2óÇ!ÄóH÷ û »Ç!Ç!¾Æ9Ä2¼À9»ó û »¾õÔ û À9¾óH¼ RÓNÀ9¼½NÓNÄ2¼a¾Ç
È\¾ºM¼½NÓNÄ2¿LØ=ÏÂ Á2Í2ËÏ2ÐÉÂ
K
!

lm 2m Wn k
.U WV
inferred density
Ä
Wq 4k
5X!YZV
[X
`1
Wk
5V5Ë\KV
^]KX`_
5000
0
0
64
¯°a±"²r³´2¶2µ2¶|Ú×2¶R¸N¹"ºM»¼a½H¾¿0À9¿ÊÂ ½H¾ ñ Ø=»óHØ=È\¾ó¿0À%¼aÀ9¾¿bÇ!¾ û »ó¿0¼Ç!ô û ¼¾È »ÇÈr¾ÇR»õL»¿0Ø
¼ÇÄ û »ÈB¿0Ä2ÅºMÆ9¾¿b»õÄoºMÇ¾¿0ôMÅ¾È û »¾ó» û Æ9À9ó¾ù ò Ç!»Ä2È£Æ9À9ÅÀ9¼¿Wõ=»Ç+ºMÄÇ!ÄÅ¾¼a¾Ç!¿2Â
?¾ û »ó¿0¼Ç!ô û ¼a¾È»Ç!È\¾ÇU»õM¿0Ä2ÅºMÆ%¾¿Ä2Æ9»óÕ¼a½H¾~Õ"ÇÄ2È\À9¾ó¼HÓNÄ2¿Ì2ËbÉ2ËbÁ2ÌbÊ2ÑbÉ2ÉbÁ2Î
Á2ÑË2ÉÊOÁ2ÐË2ÊÊ2ÎOËÍOÊÐOÉ2ÎÌ2ÉÉ2ÊOÊÍOËËOË2ÐÊ2ÌÌ2ÑOÊÊOÌÎOÁ2ÍË2ÎË2ÑOÊÉOÊÏOË2ÏÊ2Á
Ê2ËWËÁWÁ2ÊWÉÁWÌ2ÌWÉ2ÏÁ7ÁGÌWÁGÉWÉ2ÌWÌÁWÍ2ÏWËÌWÍ2ÉWÍWÑWÌ2ÊWËOÁ2ÏÌ2ÐWÍÊWÁ2ËWÐGÎWÍWÌGÌÏWÁ2É
Í2Ë+É2Ñ*ÉÐ*Í2Á*ÉÍ*Ì2ÍdÂ ½¾RÃºM¾Ä2ÇÅÄóGÇ!ÄóH÷ û »ÇÇ¾Æ9Ä2¼aÀ%»ó û »¾õaÔ û À9¾ó¼ *ÓÀ9¼a½ÓNÄ2¼a¾Ç
È\¾ºM¼a½ÓNÄ¿?ØaÏdÂ Á2ÏÍ2Ì2ÏÍÂ
K
!

`.
/j
inferred density
Y
\k-lm Wn on \pSq rn
sX5Ì1Ä+t
WY^X
+t
Ä
[uAt
5000
0
0
64
¯"°=±"²\³!´2¶Kµ¶|Ú2Ù¶/¸N¹"ºM»¼½¾¿0À9¿bÍdÂ ½H¾ ñ Øa»óØ=È\¾óH¿0À9¼aÀ%¾¿bÇ¾ û »óH¿0¼aÇô û ¼¾È »ÇÈ\¾ÇR»õL»¿0Ø
¼ÇÄ û »ÈB¿0ÄÅºMÆ9¾¿»õSÄoºMÇ¾¿0ôMÅ¾È û »¾ó» û Æ9À9óH¾ù ò Ç»ÄÈ£Æ%À9ÅÀ9¼¿Gõ=»Ç+ºMÄÇ!ÄÅ¾¼a¾Ç!¿2Â
?¾ û »ó¿0¼Çô û ¼¾È-»Ç!È\¾ÇL»õ\¿0ÄÅºMÆ9¾¿SÄ2Æ9»óHÕE¼a½H¾Õ"ÇÄ2ÈrÀ%¾ó¼dÓNÄ2¿/Í2ËËWÁ2ÉÁÏbÐWÁÑWÎ
Í2ÌOÌÊGÍGÍÊGÑOÉÎGÍ2ÉGËÌGË2ËOÌ2ÑOÌÁGÍ2ÏOÁÁGÁÁ2ÍGÉÏGÁ2ÊGÌÌGÉ2ÁOË2ÏOËÁGÊ2ÁOÊ2ÏGËÎGË2ÑGÊÉ
Ê2ËWÊ2ÊWËÐWÌ2ÎWÉGÊÌWÊ2ÍWÌWÉÌWÉ2ÊWÌ2ÉWÊÎWË2ÍWÌÏWÊ2ÐWÊWÁ2ÐWÊÑWË2ÊWÁËWÁ2ÎWÉ2ÉWËÉWÌGÐWÁ2ÌWÉË
Ì2Ë+ÉÑ*É2Ð+Í2Á*ÉÍ*Ì2ÍdÂ ½H¾RÃºM¾ÄÇ!ÅÄ2óÇ!ÄóH÷ û »Ç!Ç!¾Æ9Ä2¼À9»ó û »¾õÔ û À9¾óH¼ RÓNÀ9¼½NÓNÄ2¼a¾Ç
È\¾ºM¼½NÓNÄ2¿LÏdÂ Ì2ËÐ2ÍË2ÏÂ
K
!

lm 2m Wn k
.U WV
inferred density
Ä
Wq 4k
5X!YZV
[X
`
Wk
5V5Ë\KV
^]KX`_
Î
5000
0
0
64
¯°a±"²r³´2¶2µ2¶|Úµ2¶R¸N¹"ºM»¼a½H¾¿0À9¿ÐÂ ½H¾ ñ Ø=»óHØ=È\¾ó¿0À%¼aÀ9¾¿bÇ!¾ û »ó¿0¼Ç!ô û ¼¾È »ÇÈr¾ÇR»õL»¿0Ø
¼ÇÄ û »ÈB¿0Ä2ÅºMÆ9¾¿b»õÄoºMÇ¾¿0ôMÅ¾È û »¾ó» û Æ9À9ó¾ù ò Ç!»Ä2È£Æ9À9ÅÀ9¼¿Wõ=»Ç+ºMÄÇ!ÄÅ¾¼a¾Ç!¿2Â
?¾ û »ó¿0¼Ç!ô û ¼a¾Èc»ÇÈr¾Çr»õd¿0Ä2ÅºMÆ9¾¿?Ä2Æ9»óHÕ¼½¾RÕ"ÇÄ2È\À9¾ó¼ÓNÄ2¿?ÁÌ+Î+Ë~Á2Ï*ÌÊ*Á2Ë~Í2Ê
ÑGÍÌWÉ2ÎWÍGÊWÍÉWÍ2ÏGÉÊWÁWÌ2ÁWÌ2ÎOÉ2ÏWÁÁWÉOÉ2ÁWÁ2ÊWÌÌWË2ÁGËÏWÊ2ËWÊÁWÊ2ÏWÊ2ÉWËÑWË2ÎGÁÍWÊ2Ê
É2ÌÊ2ÌÌËËÊÍOËÐËÌÌÑOÌ2ÉÊ2ÐÊ2ÎÉ2ÉË2ÊË2ÍÁ2ÐOÁÑÌÏÁÎOÌÐÊÑOÐË2ÉÉËÁ2ÉÍ2Ë
Ì2Ë+É2Ñ*ÍÁ*É2Ð*ÌÍ*É2ÍdÂ ½¾RÃºM¾Ä2ÇÅÄóGÇ!ÄóH÷ û »ÇÇ¾Æ9Ä2¼aÀ%»ó û »¾õaÔ û À9¾ó¼ *ÓÀ9¼a½ÓNÄ2¼a¾Ç
È\¾ºM¼a½ÓNÄ¿?ÏÂ ÌÑ2Á2ÎÌ2ÐdÂ
½H¾~¿0¾Ç!À9Ä2¼aÀ9»óEÕ"¾óH¾ÇÄ2¼a¾ÈoÄ ò ôMó û ½N»õM½H¹"ºM»¼a½H¾¿0¾¿Ä ò »ôM¼d¼a½H¾ û »Ç!Ç!¾ û ¼H»ÇÈ\¾Ç»õd¿0Ä2ÅØ
ºMÆ9¾¿Ä2Æ9»óHÕø¼½¾Õ"ÇÄ2ÈrÀ%¾ó¼Â Ã»Å¾ö»õ¼½¾Å Ä2Ç¾-ºMÇ!¾¿0¾óH¼a¾È4»ó ÔMÕ;Â\ÑÂ ÁÍZ¼½Ç»ôMÕ½
ÑdÂ Á2ÑdÂ ñ Æ9¼a½H»ôMÕ"½¼½¾b¿0Ä2ÅºMÆ%¾»Ç!È\¾Ç!À9óÕúHÄ2ÇÀ9¾¿Ç!¾ÅÄÇ!÷"Ä ò Æ9¹ù¼½¾ û »¾ó» û Æ9À9óH¾ºMÄ2¼a¼¾Çó
À9¿b¿0¼ÇÀ9÷"À9óHÕ"Æ9¹ ý Ç» ò ôM¿0¼aþùdÄ2óÈZÅô û ½ZÇ¾¿0¾Å ò Æ9¾¿*¼½¾OºMÄ¼¼¾Çó,¼½Ä2¼¾Å¾ÇÕ"¾Èõ=Ç»Å ¼a½H¾
K
!

`}
/j
Y
N õ¡öîHðí=ïðþ&ì
> "": 6 > "# <a>
96
¡
0
)
óð"ÿðïõ /í=ìôï í=ïþ
WY^X
\õ¡öî9ðí=ï]ðþ&ì¯þ&ìí Zøìô«í=ìòhöõ
+t
[uAt
Ä
(
cM7
ã1ä 1äÄ
6
ðï ìí/î9î9þ
\k-lm Wn on \pSq rn
sX5Ì1Ä+t
Å
Hé
D
H" a )
o a a
E
"
V
) a /
( 9

)
) V
E \N 7
9 +V H
(D 0
9 0
a
) E
G
) % a H a W (~D 0 a )
9" I) % a
(
) a +
o
V 0 % V
- ) (
M (`d( M `( 212=dN ö
a M" 9 (
a
0 % b
E M ) 9)) ;" H H a R=
\
RH" a
(
0
9
a +a
\H
ökìøóó
þ&ï öõ¡ðõJþ
ìþòhþ&îHînöóí=ï]ðþ&ì
õ¡ï]înøòhï]öô
ZîHí=ôðöìï
ÿí=ì
(òhþ&îHînöóí=ï]ð"þ&ì®ò^þ&ö ñò^ð"öìïMÆ
îHí=ì
Zöï ööì§ï ö
î9ö {öí=óöô(òhþ&öìþ&òhóðìö
í/ïï]öî9ì
í=ï]öî*ôö ï ¬í=ìô¬ï öî9öòhþ&ìù
{öÅî9ö* öòhïöô¯ôøö4ïþóþ
þ&õ¡ð"ï]ðþ&ìò^þ&øó"ôìþ&ï
ï ðõ¯ðõ
înþ
ðò (ðõînöÿí=î Zí Zó î9þ
ôðï]ð"þ&ìõ ðõ¾ÿ¬í/ðìó ¼õ {ÿ¬ÿöïîHðòhí=ó*í Zþ&øï1ï öÿðôôóöþ
ï]þí
Zînöí/ïí=ÿþ&øìïfþ
ï ö¯óö ]ï*þ&î²ï]þ
Zí/ï
fí/ÿ
ï öîHð
ï
ZÿöïîHð"òÅìí=ïøî9ö4þ
{ð {øð"ï §ðì
]î9þ&ÿ
ï ö
óí/òhðì
ï ö÷ Zóþ
înöõ¡øÿöô
óöï ö
ö {öîHï öóöõ¡õ ï öí/ìí/ó {õ¡ð"õînö öí=óöô¼íîHí=ï öîJînþ
ñ
Zõ
ú Ï
ï înþ&ø
ú
þ&înô«õ ï öí/ìí/ó {õ¡ð"õ
õ¡í/ÿ
óö4þ&înôöîHðì
ðò
Zöìöî9í/ïöô½í
5í/óþ&ì
¾ï ö
õ öò^ð"öõ¡ü,ôðõ¡ï]î9ð Zøï]ð"þ&ìí/ó"þ&ì
ÐJÑÈ
J
ø
Zö¯ìøÿ
înöõ¡øÿöô
ï ö
Zöîyþ
î9öõ¡øÿ¬öô
öînöõ¡öó"öò^ïöô
;
öî1÷oôðõ¡ï]í=ìòhöüïþ
ZîHí=ôðöìï
øõ ï ö
Zö²ò^þ&ìñîHÿ¬öô
{øõ¡ïOò^þ&öìþ&ò^óð"ìö
*ôð
?ò^þ&ìù
ðõ¾óöí=ôõ
í=ïï]öî9ì
MÇ
þ&øïºï öí/ìí/ó Zõ¡ðõ
qöînöìï
{øï{í²õ¡ðì
qò
ì¼í/ìþ&ï öî
þ&ï öõ¡öõþ&ìFï ö
Zóö
þ&ï öõ¡ðõºþ&ì¯ï ö
ZîHí=ôðöìï
2
R)
)
9 ( M" W
9
a
9G V W
9
R)
r
a /
)
õ¡öòhïðþ&ìõò^þ&ìï]í=ðìð"ì
ö) ;
?
)
)
( D
,
" R
ø
N ö 0 RN a
R)
"W)
9
(
a *
H
B
înþ
öí=î9ù
É¾Ü)¾ÚOÝËÊÝÜÛËÊÌÍÊÛJØÜ)ÎWÐÏÑÒÝJßáØÛ
þ&øîïöîHînöõ¡ïîHðí=ó5Óþ&óþ&òhöìö
#%" < 66 ><=6 $ 5 #
85>!<a6 27: >
öî9õ¡ðõ¡ï]öô(ï î9þ&ø
í=î Zðì
ZîHí=ôðöìï
ï]ð"ÿøÿü«þ&ì¼ï ö
ZîHí=ôðöìï{òhþ&øóô¬ìþ&ï
{ï ö
]í/òhïÅï í=ïJï ö
Zøõ¡ïºøìôöî
4ï ö
ï ö5õ¡í/ÿ
Zí/ófþ
{í/ó"øöõOþ
Zí Zó ½ô«øöïþ(ï ö
]þ&î4ï öðìôðînöò^ï
ò^í=ìï/ÿþ&ðõ¡ïøînö¿í=ìôï]öÿ
qí=øìí²þ
(ï ö
ïöîHînöõ¡ïîHðí=ó
¯þ&þ&ô«ó"í/ìô
ï ö
ïðþ&ì
ZîHí=ôðöìï
þ&óôõ þ&î
qí=ò^ïþ&îêü î9ö înöõ¡öìïöô
þ&þ&ôóí/ìô¬ù
ZîHí=ôðöìïõfð"ì5þ
ZîHí=õ¡õ¡óí/ìô
ë5óï þ&ø
qí=øìíþ
²óí=ìôõ¡ìí=ðóõ
Fï öînö
öî9ö¾õ¡ð Zìðñù
yï öwÓ¯þ&óþ&ò^öìö êï ö
öîHí=ï]ðþ&ì5ôøî9ðì
þ&ôõ*ðõºï]î9í/ôðïðþ&ìí=óó
ZîHí=õ¡õ¡óí/ìô
öï öîJï ð"õkí=õ¡õ¡øÿ
ï ö4÷"ïðÿ¬ö
öîHí=ï]øînö
Zí=õ¡ï]înþ
ù
®í {øìôí/ìï
ZîHí=ô«ð"öìïOí=ìí=ó Zõ¡ðõ
Zöóðö {öô§ï]þ
öõ¡ï]øôðöõ
öï öî²þ&ï öî
]í/øìí/ó=ÿð Zî9í/ïðþ&ì
ZöJòhþ&ìïî9þ&ó"óöô¬ÿ¬í/ð"ìó
öî9öòhí/î9îHðöô
þ&øïJï]þ¼õ¡öö
]í/òhï]þ&î9õð"ìòhóøôöô
ôðõ¡ïþ&îHï{ï ö
ðìòhóøôðì
Zöìöî9í/ó í/ïï]öî9ì¾þ
Zî9í/ôðöìï
c - !" -+
ã1ä 1
äæ
Ô
êé
Õyè
Öè
^é
é
+) \
9V c) a +)
)
) a
(HD )\P V
M
WP/ 7 ¢ a
) o
9 _ ` } 1 ` @ N

9V
£)
2
E) (D a
a
, ) O¢ G 9M ! ) ¢ 7
9_ -
V
) a
) * \
d
(
V a
9"
!N
)
!
\ ) O -
MN
~) V )
N)
2 )
L R (
í=ï]í
qþ&îï ð"õ¿òhí/õ¡öJõ¡ïøô
Óþ&óþ&òhöìöó"þ&ò^í=óðï
ðï ½í=ìô
þ
ï ö§ÿí=óí/òhþ
qí=øìí
Zøí/ìï]ðïí=ï]ð {öôí/ïíþ&ì
ðì
ï öìþ&î9ï öí/õ¡ïöîHì
þ
öÿð"í/ì?ò öî9ìþ&õ¡öÿ
þ
ÿöìï\þ
ÿøÿ
í5õ¡ïînþ&ø
]î9þ&ÿÖï ö
{ö¾þ
í
Ð-þ
]þ&õ¡õ¡ðóõ¡üOí Zøìôí=ìòhöõò^þ&ÿ¬ö
í=îHï«þ
ï ö
înö {ð"þ&ì
þ
öìö ó"í/ðì
Zóí ZöJþ
2
öÿð"í/ì
ó"í/ïöí/ø
\óí=ìô§õ¡ìí=ðóõ
&
qînþ&ÿ
Ù
¬ð"ìíkô«î
þ&þ&î
\ï ö`×{þ&øì
öÿð"í
Ø(
ökóþ&òhí/ó"ù
öî9öí=óõ¡þFï ö
öóþ&òhí/óð"ï Fðõ¾õ¡ðïøí/ïöô
öî9ð
í=ì
öî ¬þ
ðìòhþ&ÿ
ðí=ï]ó"í/ìï]ðò
þ&îHïðþ&ì§þ
öî9ö5òhþ&ìôðïðþ&ìõ
öînö
þ
/ö Fú
í=îHõ¡ï þ&ì?ï ö
ï öM$ðôùAÓþ&óþ&òhöìö
ð
óí/ìô¬õ¡ìí/ð"óõºþ
øò óö
ðò ?ðõyò í/î9í/òhï]öî9ð =öô
öî ï öóþ&òhí/óð"ï ð"õÅõ¡ðïøí/ïöô
]í/øìí/ó,í=õ¡õ¡öÿ
]í/øìíþ
í5ìöí=î5$í=óí
öînöôöõ¡ò^î9ð Zöô
ï öòhþ&ÿÿ¬øìðïðöõ4þ
$þ&înöþ
ìöí=îÅï ööô
îHðò
¯í=î9öÅô«öî9ð {öô
4öîHïþ
ï ö$ð"ô«ù
ó"öï]öôö öóù
þ&þ&ôóí=ìô¬þ
íõ¡ÿí=óó
qþ&î4ôö {öóþ
ï]ð"ù
Zþ&î Zö
ÿöìïOþ
*í
lm 2mOj
.Ú
z ad{Gg
Nq n
KV!ÛbV!YZtb\KtÌÛGX!\
`2`
\n W Wj
\sX!uÛ ÜV
1ÝGV
stË¤uX
LAYER
13
12
11
10b
10a
9
8b
8a
7
6
5
4
3
2
1
SPECIES / SAMPLE
-
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Acanthinula aculeata
0
0
1
0
0
3
0
20
3
51
0
0
0
0
0
Cochlodina laminata
0
1
2
5
16
5
3
6
1
32
6
4
1
0
1
Monachoides incarnata
0
6
3
4
16
26
9
26
2
122
5
10
2
1
1
Trichia unidentata
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
Vertigo pusilla
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
Alinda biplicata
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
Cepaea hortensis
0
1
1
0
0
0
9
1
0
2
0
1
0
0
0
Discus rotundatus
0
0
3
1
4
0
3
28
1
0
1
1
0
0
0
Aegopinella minor
0
1
3
1
7
3
0
6
0
24
0
2
0
0
0
Bradybaena fruticum
1
1
3
2
2
2
11
33
3
14
2
4
1
1
1
Helix pomatia
0
0
1
2
5
1
4
8
2
12
2
2
1
0
1
Clausilia pumila
0
5
1
3
8
10
2
8
2
30
0
3
1
0
1
Cecilioides acicula
0
0
0
0
0
0
0
1
0
0
0
1
1
4
16
Granaria frumentum
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
Helicella obvia
0
0
0
0
0
0
0
0
0
0
0
0
0
2
23
Helicopsis striata
0
1
3
1
1
1
1
1
0
0
0
0
0
1
1
Chondrula tridens
0
1
1
1
2
1
0
0
0
0
0
1
7
2
8
Pupilla sterri
0
11
6
16
4
3
6
0
9
3
1
4
29
2
1
Cepaea vindobonensis
0
0
0
2
1
0
0
0
2
8
2
3
1
1
1
Pupilla loessica
1
4
12
11
4
12
15
10
11
2
2
0
0
0
0
Pupilla muscorum
0
4
3
2
3
0
0
1
0
0
0
1
76
125
122
Truncatellina cylindrica
0
1
0
2
2
3
2
1
6
12
4
5
60
24
45
Vallonia costata
0
2
2
0
5
1
0
0
0
0
0
0
3
0
0
Vallonia excentrica
0
0
0
0
0
0
0
0
0
0
0
0
0
24
1
Vallonia pulchella
1
1
5
3
8
0
1
4
9
10
25
17
45
67
91
Vertigo pygmaea
0
0
0
0
1
0
5
1
1
3
9
2
30
36
45
Cochlicopa lubricella
0
0
1
0
7
1
2
0
0
0
3
4
8
45
18
Euomphalia strigella
0
1
2
1
1
1
7
3
2
0
0
0
1
0
1
Cochlicopa lubrica
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
Euconulus fulvus
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
Limacidae spp.
0
0
1
0
5
0
2
0
2
12
2
6
0
0
0
Punctum pygmaeum
0
0
4
1
6
0
3
4
0
33
7
0
0
0
0
Trichia cf. hispida
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
Vitrea contracta
0
2
7
4
32
25
2
51
4
4
5
1
1
0
0
Vitrina pellucida
0
0
0
0
2
0
1
1
4
0
0
0
0
0
0
Carychium tridentatum
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
Succinea oblonga
0
2
1
2
1
1
5
2
6
2
2
3
1
2
0
TOTAL
3
46
71
67
151
102
93
220
72
376
79
76
269
337
378
CHRONOLOGY
?
EA
EA
EA
EA
EA
EA
EA
SB
SB
SB
SA
SA
SR
SR
) 9))
0
)
a IP V
x+zy|2y W
( N

-P/ /¢ )
0
a ~ ( P/
\
¢ E M" 9 E M
7 o M
)
_ ` } 1 ` @ (
ë
{øìôí/ìò^öõþ
,ôð
,öòhï]ð"þ&ì3ìöí/îW$í=óí
qînþ&ÿ
ìøÿ
Ùë~lÙ
qînþ&ÿß-þ
qöînöìïõ öòhðöõþ
øò ó"ö
Zöî9öô¬óí Zöî9õ ,ú Ï
'~
ðí/ïóí=ìïðò
=ö ú
&
Ø(
,ø
þ
{öð"ì
öÿð"í
,óí=ìô¾õ¡ìí/ðó"õ«ð"ì5ï ö
wÓþ&óþ&òhöìö
ï öþ&óôöõ¡ï &úï ö
Zþ&î9öí=ó
,ë~
ø
í/ÿ
Zþ&øì
{í=ïóí/ìï]ð"ò
ÅöîHïþ
óöõ
Zöõ¡ï
Þ~
,ø
M

";T
í1õ¡ï]înþ&ø
í
öînöïí Zöì
(
înþ&ìþ&óþ
Zînöò^öìï
í/ïí
@2@
ú
/j
Y
/ H
a
)
§ ¥ ¨ © ¨ ª a
2
)
-í
Zöîú Ï
øí/ó"õ
Zðì
ï ðõyò^í=õ¡ö¾þ
]î9þ&ÿ
ï öyí=ìí=ó Zõ¡ðõ¿ôøö²ïþ¯ðïõ
¬ïþï înööõ öò^ð"öõ
*óí/ò Zðì
/í/ìô
ï]öî9ì
í=õ
¬ôðõ¡ï]ð"ì
ë
Zøðõ ð"ì
¯öóóZí/õ1õ öò^ð"öõ
\ôöìõ¡ðï
þ&þ&î
Zøìôí=ìòhökõ¡öî9ðí/ïðþ&ì
?ðì
+t
]í/øìí
[uAt
Ä
óö
í=îHí=ÿöïöîHõ
ö²î9öõ¡øóïõ*í=î9ö4õ þ
ï înööyð"ìôð {ðôù
í/õÅò^í=îHî9ðöô
qþ&îHÿ¬í/ïðþ&ìFí {þ&øïfõ¡í/ÿ
þ&øïñîHõ¡ï
bÇ
ì
í=ìô
Zí/õ¡öôþ&ì5í {øìôí/ìò^öõðõï ö1õ¡í/ÿ¬ö1í=õï í/ï
öõ¡ï]ð"ÿí=ï]öJþ
WY^X
o) 9
?) dT 9V
(W
(
0
0 H)
2
O
R]¤\¥h
I
0 I
L]« © « ª " © " ª ¤ ® § ® = a ~
a
a 9 9
a (D 0 M (h`( @ (
¯í/õ1ôðõ¡ò^í=înô«öô
Zöóþ&ì
\k-lm Wn on \pSq rn
sX5Ì1Ä+t
=ï ö
í=ï]ù
{í=õ¡öô¾þ&ì5ï ö¿ÿ¬í /ðÿøÿó"ð Zöóð þ&þ&ô
ì§þ&ìñ
û
50
0
0
14
gradient
2
) 9))
0
)
s"t=u"v\w!x+zy|{ y W
(
OP V
M
PS M¢ 2
(
E V
W
r
G.G1 ` Q
Q @W} (
(`d( Q2
a +) ÿ
) H 5 < $ "# 55 "#% 57<a57
% "$" 5 7#% 85 (
dà
5ë
ð"ì¼ï ö
õ¡öî9ðí=ï]ðþ&ì½þ&ì(í Zøìôí/ìò^öõkþ
4öî9ï]þ
{í¯õ¡ïî9þ&ø
¯ðò^öøìðÿ¬þ&ôí/ó
ï ö
Zî9í/ôðöìï
òhþ&înô«ð"ì
ïþï]þ
í/ïïöîHì
¯í/õ
ï]þ¾ïí
§îHð
ï
í
í=õ¿înö {öí/óöô
û
Ï
ò^þ&ó"øÿìù ðõ¡ö
õ¡öõ
ZöìöîHí=ï]öô
ë5óï þ&ø
Fï ö¯õ¡öîHð"í/ïðþ&ìFþ
þ&ï öõ¡ðõ²áÅû
ºõ¡í/ÿ
õ¡öîHðí=ïðþ&ì§î9öõ¡øóï ,ï öò^þ&öìþ&ò^óð"ìö
þ
ú
Zþ&ïï]þ&ÿ
ú
1óí/ìô
öÿ¬ðí
õ¡í/ÿ
õ¡ìí=ðóõ
Óþ&óþ&òhöìö
óöyþ&î9ôöî*í=óþ&ì
öòhðöõ4í=î9öþ&î9ôöînöôí=ò^ù
A~[n
óö ]ï
( W) )
@ 0 9))
M
9,)
7 H bV (h`( (
Zí=õ¡öô§þ&ìô«öìõ¡ðïðöõ
þ&ìó ï ö
þ
A
6
E6
9C
a
E
;
\ 9 I" M" a
) )
0 M
ö ï =ï öyõ¡öî9ðí=ï]ðþ&ì
qînþ&ÿ
qöînöìïõ öòhðöõ5þ
øò óö
*öòhþ&ìõ¡ïî9øòhïöô
¾ú^ú¾ú=û¾ú 5ú Ï
Î
A~´F 6
Åôð
,öòhïðþ&ì?ìöí=îË$í=óí
\ôöìõ¡ðï õ¡öîHðí=ï]ð"þ&ìí/înö4õ þ
óöõôð
¯í/õºòhí/î9îHðöô§þ&øï
õ þ
öôí=ì5ðÿ
qöînöôFõ¡ø
Zõ¡ï]í=ìïðí=óó
í=ï]ïöîHì§ôðô¬ìþ&ïò í/ì
ìþ&ìñ
û/ú
. @ H" a
(
7 (D \ï öyñîHõ¡ï
þ&ï öù
öî qöòhïøìðÿþ&ôí=ó í=ïï]öî9ì
Zö
]î9þ&ÿ
ï öí Zøìôí=ìòhö
{öî ÿ¬øò
öî9öõ¡øóïõ
lm 2mOj
Nq n
inferred density
.Ú
\n W Wj
\sX!uÛ ÜV
1ÝGV
stË¤uX
@
ú
ú
200
0
0
13
,¢ 2
)
) 9))
0
stau"vrwxbz2y|{ 2y W
)
P V
M
-P/ R¢
(~D M 0 )
2
J
( V
@ 0 O T "V (
; - V
H a
+} . +1 `
Q @ Q (
G HV N" a
9 U
2
!##% < "$fW7: 5 # 57<a< 6
0 a
0
a
) W
H ~.+1 ` Q
Q @~} (
6 5 #!:
H a *" a R ( ( V
) H
HV
L
0 O M
(OD )
H E
a
) E
7
9_ " 0
* % P /
0
K M
2
P 7
7
2 D 7
2
0 ¢ \" G)
9
2P
O
(D 9"

M
7
"P 7 M
2
% M" 2
E 7 2
2 D
(
K M
W) ) 0
,
)
9" (~D \;N 9"
9"
Q|
þ
5ë
kó"í/ìô
bÓ¯þ&óþ&ò^öìö
öÿ¬ðí
öì
Fõ¡öîHðí=ïðþ&ì
öñ
ZîHí=ôðöìï
ìðòhöÅòhþ&ÿ
í/ïïöîHì
í=õ
{íFõ¡ï]înþ&ø
{øînöõ þ
Ó
Ï
í=òhï{øìðÿþ&ôí=ó
]öîHînöô?ô«öìõ¡ðïðöõ²þ
í
ú Ï
õ5ï öðì
í=ï]ïöîHì
]öîHînöô
í=õOøì
ð"õõ þ
ì
Zöðì
û
Ï
ë5ò^òhþ&î9ôðì
ô«öî9ðì
í/óþ&ì
½þ
ø
öð"óöô
Zí/öìí
øìòhï]øÿ
ë
{ÿ¬í/öí
ø
þ&ÿí=ï]ðí
ö4÷"î9ð
â«í/ó"óþ&ìðí
?ï ö
«õ¡í/ÿ
Zí=õ¡öôþ&ìí Zøìù
óöõ4í=óþ&ì
§ï ö
ZîHí=ù
&ï í=ïfï ökî9ö {öí/ó"öô
þ&î9ôöîºðõJï öòhþ&îHînöòhïþ&î9ù
ZîHí=ôðöìï 4ï öõ öò^ð"öõ
ö÷"óö ]ï]üföìô
{ð óðòhí/ïí
Åö í/öí
øÿðó"óí
âfí=óóþ&ìðíö
þ&îHïöìõ¡ðõ
\ë5ö Zþ
dÓöóð"ò^þ
ù
Ø$þ&ìí/ù
ðìöóóí¯ÿ¬ðìþ&î
Åþ&ò óðòhþ
òhöìïîHðòhí
öô
ZîHí=ôðù
xâ*ðïî9öíò^þ&ìï]î9í/òhïí
ïü öìôðõOò í/î9í/òhï]öî9ðõ¡öô
øó"ò öóóí
Zînþ&ø
Åï ö
Åþ&ò óþ&ôðìíóí/ÿ¬ðìí=ïí
ðõ¡òhøõînþ&ïøìôí/ïøõ
4óí=øõ¡ðóðí
þ
íJóø
{í/ìô
ZîHðòhöóóí
înøìòhí/ïöóóðìí¯ò Zóðìù
ðóó"íkÿøõ¡òhþ&înøÿ
qïöî4í
þ&þ&ôóí/ìô
ö
?ïþFï öðîkïþ&óöîHí=ìòhöõ
xÓöóð
{öî ôðõ¡ïðìò^ï
ó"ö¯þ&înô«öîJí=óþ&ì
ZîHð"ö ðìõ öòhïðþ&ìFðïòhí/ì
ðóöï ö÷"î9ð
Zöõ¡ï]í=ïöô½ï í=ïï ö¾÷"óö ]ï]üöìô(ÿ¬ð
ïüföìôÿð
p 6
ðînþ&ìÿ¬öìïí/ó
î9ðò ðí¯øìðôöìïí/ïí
qînøï]ðòhøÿ
ìþ&ï
þ&ù
î9öõ¡øÿ¬öô
ú
¾ï ö4õ öòhðöõë5óð"ìôí
Zÿ¬í/öøÿ
{þ
qð
ú
öînö
5ï ö4í=ìí=ó Zõ¡ðõ
ðó"óíkóþ&öõ¡õ¡ð"ò^í /ë5òhí=ìï ðìøóíkí=ò^øó"öí/ïí
ò þ&ðôöõðìò^í=îHìí/ïí
ô«î9ðòhí
(õ¡þ&ÿ¬ö¬öì
Zî9í/ôðöìï1í=òhò^þ&înôðì
õ¡ðõ¿õ¡ïîHð"í/ïí
â«öî9ï]ð
þ&ï öõ¡ðõ
óöõí/óþ&ì
öìï{ðõ*ò í/î9í/òhïöîHð =öô
«î9í/ô
úhúú=ûyú yú Ï
ï]þ¯ï ðõ
Jõ¡í/ÿ
½ï ö
Î
øò óö
yú
ô«í=ìòhöõ Zï í/ïòhþ&îHînöõ þ&ìôõ4ïþï öînöò^þ&ìõ¡ï]înøò^ïöô?þ&înô«öîºþ
ô«ð"öìï
qöînöìïõ öò^ð"öõ
õkïþï ö
*öò^þ&ìõ¡ï]înøòhï]öôõ¡í=ÿ
úhúyú/ûyú ²ú
Oôð
,öòhïðþ&ììöí/î1$í/ó"í
þ&ï öõ¡ð"õ²áJû
í=õkînö öí=óöô
yû
Î
í {öõ¡ð"í/ì¬ðì
4öî9ï]þ
{ðînþ&ìÿ¬öìïí/ó {î9í/ôðöìï
øìð"ÿþ&ôí/ó
ë
þ&ì
õ¡ìí/ð"óõðìï ö
ï1înö înöõ¡öìï
ZîHí=õ¡õ¡óí=ìô
ïînö î9öõ¡öìï
öînöðõþ&ìöö ù
@
ú
/j
Y
û
þ
õ öò^ð"öõ
øïð
ø
ö {öî
A
öîHí=ïðþ&ì
ï ö
û=û
8d6 "! < :2 6 ><=5< $%
5<=< 6
öóó
>
ðÿ¬öðõ
+t
[uAt
Ä
óþ&ïïöô
/ö ú
ñ
Zöï öî
ðï §ï ö
þ&þ&ôóí=ìô
{øïþ&ìö5þ&ò^òhøîHînöìòhö
ðóóíyõ¡ï]öî9îHð í=înöÅÿí=î Zöôí=õ
&
Ï ú
þ&õ¡õ¡ð Zó
)(
õyí Zí=ðìï í=ï
Zöìöî9í/ïðì
þ&þ&îÅñï
¬í=ìôFðìõ öò^ïðì
]ö
þ&ï öõ¡ð /öô
Zöô
óþ&ïï]öô
ï
AÙ«ë
ù
Zî9í/õ¡õ¡óí=ìôü
ï ööì
öî9õ¡øõkïðÿö
ó"ö qï*ïþ?îHð
ð
÷ þ&þ&ôóí=ìô
ðìï]öìõ¡ðï §þ
ö
ù
í/ïï]öî9ì?ðõyõ þ
õ¡òhþ&î9öõþ&ì
þ&ìöõ²ÿ¬öí/ì¬÷ ZîHí=õ¡õ¡óí=ìôü
ï]ð"ÿøÿüðìï ö[Ù
{î9í/ôðù
qí=ò^ù
ì¼þ&ì
{öîHïðòhí/ó«í /ðõ
¯þþ
ðí/ïóí=ìïðòJðõ
Zõ¡öî í=ï]ð"þ&ìõ
înþ&ìþ&øìò^öô
qð"ð ï ö²ïøîHì¯ïþ¾÷ ZîHí=õ¡õ¡óí=ìôü=õ¡ööÿõºï]þ¾õ¡ïí/î9ïZö öìðìï öJóí ZöîOú
í/ìô®ìþ&ï1ðì(ó"í Zöî
-þ
qînþ&ÿ
ø
ïí
~îHí=ì
óöõ¡ò^þ&înöõ
öî9ö
õ¿ï]þ
Zí=õ¡öô?þ&ìôöìõ¡ð"ï]ðöõJînö {öí/óöô¬þ&ìó §í
qþ&ó"óþ
qð ï ö÷ þ&þ&ôóí=ìôFþ
{ðõ¡ð Zóö =í=ìô
Zî9þ&ø
öü"ó"ó\ñìôFï í=ï«í=óó
û Ï
ï ö
õ¡ò^þ&înöõJÿöí=ì÷ þ&þ&ôóí/ìôü
Þ-þ
í=õþ&îHð Zðìí/ó"ó ½õ¡ïí=ï]öô
&
Ï ú
)( d-þ
í/î9ï]õ¡ü/þ&ò^òhøîHînöô§ðìïðÿö²þ
/ö ?ú
&
ºû=û
)(
/ö ¾õ¡ïí/ïöõºï í/ï÷ ZîHí=ôøí/ó&ôö qþ&înöõ¡ïí/ïðþ&ì¯þ
\ó"í Zöî
þ
ø
í
ö öî Oð"ì
öîõ¡óþ
ö
í=ìô
15
score
6
=ö ¾ú
þ
í/înöyî9öÿ¬í/î {í Zóö
3
A-«þ
þ&ï öõ¡ðõkð"ï
ïðÿö Zõ¡í=ÿ
ï]þ&î²òhí/øõ¡ð"ì
-þ
Zóö
õ¡ööFï ö?þ
öìïï înþ&ø
ñ
óþ&öõ¡õ
þ&ï öõ¡öõ1ðõºÿøò ïþ&þ
þ
?ä
ð"ò
Zí=ò ïþï öôí=ï]í
qí=òhï«ï í=ïï ö5õ¡öîHðí=ïðþ&ì
í¯õ¡ðì
ÿöînöó
D
ðó"óíóþ&öõ¡õ¡ðòhí
í=ìôí=óóþ&òhòhøîHînöìòhöõOþ
qînþ&ÿ
î9þ&ÿÃï ö
í/ïïöîHìð"ì
7:2# 5 ": 28d657>> # 5 :
865 :2$% < 2 < > $ !:
ø
ö5ï]øî9ì
ð"óóí²óþ&öõ¡õ¡ðòhí
î9öôö þ&õ¡ðïöô
d4
WY^X
H V T M
2N 7c M L a b
( ¢ 9)r
0
7 2
H
)H M
) M
9
9 9
E)
L _ ` } 1dT @ ( ` @ (
J
a ) a
V
9 G
H G" a
U) U
H
0 9G. @ " ) (
D
) -H %_ %
b
M /
a ) HV
H)
(RD ? O öV
0 M (`d( (~D
W £)
) 9" L L?=
V
(
(UD !V
% 9"
%
! 2 T 9 a \
/
\
V 9 E 9 %
V
2 @ 2
+1
9 9
B" _ ` } 1T ` ` @ ^ V _ ` } 1dT M ( ` @ _
a %
)
) MM ) `
}(
ò^ö ïðþ&ì
þ
ã
\k-lm Wn on \pSq rn
sX5Ì1Ä+t
10
5
0
0
13
time
EA
SB
SA
SR
¯"°=±"²\³!´+µ¶ ¶RÃÄ2ÅºMÆ%¾W¿ û »Ç¾¿RúH¿2Â?¼À9Å¾ÂÃ û »Ç!¾¿R» ò ¼ÄÀ%ó¾ÈZõ=Ç»Å ¼½¾ ñ ¿0¾ÇÀ9Ä2¼aÀ%»ó
»óÄ ò ôMóÈ\Ä2ó û ¾¿/»õrÈrÀ%õaõa¾Ç!¾óH¼M¿0ºM¾ û À9¾¿S»õUÆ9Ä2óÈ-¿0óHÄÀ9Æ%¿+À%ó¼½¾ Ò ¾Ç!¼a»úÄG¿0¼aÇ»ôM½Ä
Ã¾ û ¼À9»ó-ó¾Ä2Ç £Ä2Æ9Ä Ò ½ô û ½Æ%¾ù \»½¾ÅÀ%Äùd¸»Æ9» û ¾óH¾Â À9Å¾OÇ!ôMóH¿~õaÇ!»Å Æ%¾õ=¼U¼»
Ç!À9Õ"½¼Â Ò ½HÇ!»óH»Æ9»Õ"¹ ñ \ºMÀ9Ä¼Æ9Ä2ó¼À û ùÃ Ãô ò"ò »Ç¾Ä2Æ9ùHÃ ñ Ãô ò Ä2¼aÆ%ÄóH¼aÀ û ù
Ã Ãô ò Ç¾ û ¾ó¼Â r»Ó ¿ û »Ç¾¿?ÄÇ¾SÀ%ó¼¾ÇºMÇ¾¼a¾ÈEÄ2¿ ý Ó»»ÈrÆ%ÄóHÈrþù½HÀ9Õ"½N¿ û »Ç!¾¿Ä2¿
ý Õ"ÇÄ2¿0¿0Æ9ÄóHÈ\þeÂ »¼a¾O¼½Ä2¼U¼½¾GÓN»»È\Æ9Ä2óÈZ»ºM¼aÀ9ÅôMÅ À9ó-¼½¾ \ºMÀ9Ä¼Æ9Ä2ó¼À û À9¿~Ó¾Æ9Æ
Ç¾ û »ÕóHÀ 2Ä ò Æ9¾Â
.ådå
^æ
é
ç
©bè ¿é

!

è
+ç
é
é
=ê
¦
è
ìë
q íq î
ïð¡5£}Kñ9Üòó+}
Ä2¼aÄIõ=»Çd¼½À%¿ û Ä2¿0¾?¿0¼aôMÈ\¹+ÄÇ¾?È\¾ÇÀ9ú¾ÈWõ=Ç»Å ¼½¾Lõ=Ä2ôMóÄI»õÆ9Ä2óÈG¿0óHÄÀ9Æ%¿;»õ¼½¾?¸»Æ9» û ¾óH¾
Æ9» û ÄÆ9À%¼a¹+»õ R» ò ¹"Æ9ÄSØ -¾¿0¼Ã¾ û ¼aÀ%»óó¾Ä2Ç R»óH¾ºMÇ!ôM¿0¹ù \»½¾ÅÀ9ÄÂ ½H¾LÄÕ"¾?À9¿\¸N»Æ9» û ¾ó¾Â
½¾IÆ9» û Ä2Æ9À9¼¹Ä2óÈ¼a½H¾SÅÄ2Æ9Ä û »õaÄôMóHÄSÓNÄ2¿UÈ\¾¿ û ÇÀ ò ¾È ò ¹ \» ¾÷~ÁÑ2ÎÑ Ñ2Ì =ù'Ó½¾Ç¾Ä2Æ9¿0»
¼a½H¾ "ôMÄ2ó¼À9¼aÄ2¼À9úH¾È\Ä¼Ä/»óOõ=»¿0¿0À9Æ9¿0þ2Ä ò ôMóHÈ\Äó û ¾¿ û »Å¾SõaÇ!»Å£Â ½H¾SÆ9» û ÄÆ%À9¼a¹bÀ9¿¿0À9¼ôMÄ¼¾È
À9ó,¼½¾W¿0»ôM¼½ÓN¾¿0¼¾Çó û »ÇóH¾ÇS»õ¼½¾ \»½H¾ÅÀ9Ä2ó RÄ2Ç¿0¼ùÀ9ó,ÄG¼»ºM»Õ"ÇÄ2ºM½À û ¿0À9¼aôMÄ2¼À9»ó
¿0À9ÅÀ%Æ9ÄÇU¼a»G¼½¾*ºMÇ!¾úÀ9»ôM¿?Æ9» û Ä2Æ9À9¼¹Â
ô
+õ
Aö
õ
=ç
[ê ÷ë
[ø
)ù
Zú
!ç
fõ
LAYER
9
8
7
6
5
4
3
2
1
0
SPECIES / SAMPLE
1
2
3
4
5
6
7
8
9
10
0
1
3
7
27
124
151
176
136
64
lm 2mOj
.Ú
Nq n
\n W Wj
\sX!uÛ ÜV
1ÝGV
@
stË¤uX
ú =Ï
LAYER
9
8
7
6
5
4
3
2
1
0
Acicula polita
0
0
0
0
0
6
7
2
0
0
Aegopinella pura
0
1
10
6
27
280
505
529
342
92
Clausilia cruciata
0
0
0
0
2
2
7
1
0
0
Cochlodina laminata
0
2
8
11
45
181
160
104
70
23
Discus ruderatus
0
193
51
196
190
154
86
15
17
0
Ena montana
0
0
0
0
0
0
0
6
9
3
Ena obscura
0
0
3
6
57
99
60
24
17
0
Helicodonta obvoluta
0
0
0
1
1
3
10
34
22
6
Isognomostoma isognomostoma
0
0
1
0
0
2
6
21
27
4
Macrogastra densestriata
0
0
0
0
0
0
1
2
0
0
Macrogastra plicatula
0
0
1
0
0
4
2
2
2
0
0
1
8
4
6
41
82
196
115
57
Orcula doliolum
0
1
2
1
3
48
46
4
1
0
Trichia unidentata bohemica
0
0
2
0
0
8
3
2
1
0
Vertigo pusilla
0
9
3
3
19
81
64
23
21
2
Vitrea diaphana
0
0
0
0
2
1
2
0
0
0
Alinda biplicata
0
0
13
1
10
135
220
240
184
269
Arianta arbustorum
0
0
0
11
19
0
1
1
1
0
Cepaea hortensis
0
0
0
1
0
6
2
9
10
1
Discus rotundatus
0
0
1
0
7
112
106
120
64
11
Limax sp.
0
0
0
0
1
7
10
12
3
0
Semilimax kotulai
0
19
5
2
0
0
0
0
0
0
Aegopinella minor
0
0
19
12
68
453
566
966
355
55
Bradybaena fruticum
0
2
4
8
39
37
21
18
14
0
Helix pomatia
0
0
0
0
0
0
1
2
6
0
Vitrea crystallina
1
0
3
0
0
0
0
0
0
0
Macrogastra ventricosa
0
0
0
0
0
1
6
5
2
0
Granaria frumentum
0
0
0
0
1
6
3
5
1
0
Helicopsis striata
0
6
4
1
0
1
0
0
0
0
Chondrula tridens
0
0
4
4
6
6
2
2
0
0
Pupilla sterri
0
0
4
2
1
1
0
0
0
0
Pupilla triplicata
0
0
0
0
0
0
1
0
0
0
Chondrina avenacea
0
0
0
0
0
0
0
2
7
104
Columella columella
0
213
23
6
0
0
0
0
0
0
Pupilla loessica
763
3
0
2
0
0
0
0
0
0
0
0
0
0
35
12
0
2
4
1
Vallonia costata
8
203
62
181
1574
1570
587
44
49
0
Vallonia excentrica
0
0
0
0
1
0
0
0
0
0
Vallonia pulchella
0
12
20
24
66
27
6
3
3
1
Vallonia tenuilabris
0
0
2
18
0
0
0
0
0
0
Vertigo pygmaea
0
0
3
1
6
0
4
4
1
0
Bulgarica nitidosa
0
0
2
0
0
25
22
12
4
2
0
23
14
21
52
96
50
4
6
0
0
0
2
5
30
29
17
14
16
0
Cochlicopa lubrica
1
356
89
27
3
0
0
0
0
0
Euconulus fulvus
1
35
11
10
16
24
25
18
9
7
Limacidae
0
3
2
16
12
6
11
23
13
0
@Q
ú
/j
Y
7
6
5
4
3
2
1
0
Nesovitrea hammonis
2
97
33
40
109
81
23
7
3
0
Punctum pygmaeum
0
125
27
30
94
153
93
40
179
146
Trichia sericea
0
132
35
13
10
0
2
0
0
0
Vertigo cf. arctica
0
19
3
0
1
0
0
0
0
0
Vitrea contracta
0
0
0
0
3
27
49
40
25
0
Vitrina pellucida
0
5
0
2
5
6
3
0
5
3
Clausilia dubia
0
0
0
1
0
0
0
2
1
1
Helicigona lapicida
0
0
1
0
0
1
2
29
20
12
Laciniaria plicata
0
0
0
0
0
2
1
2
0
0
Vertigo alpestris
0
67
8
5
0
1
1
2
2
0
Carychium tridentatum
0
5
10
8
45
513
589
143
142
0
Columella edentula
0
5
4
2
2
6
2
1
6
0
Nesovitrea petronella
0
0
0
1
11
11
2
0
0
0
Vertigo substriata
0
0
3
8
0
1
0
0
0
0
TOTAL
776
1538
503
698
2606
4390
3620
2913
1915
864
CHRONOLOGY
V
LV
PB
B
B
A
EA
LH
LH
R
) 9)a)
0
)
"
x*z2y y W
( *

0d¢ 2 -)
( P/
0 ` H a R H a^ @
";T
O 9 9
G 9 M¢ O 9
(
¢ ¢ 9
\
O
b)
_ ` } ` ` (
.û
ë
Zøìôí=ìòhöõJþ
2
}âý~1â*ðõ¡ïøóðí=ì
G~
ôð
]öî9öìïõ öò^ðöõJþ
þ&ìö î9øõ
Zöînöôóí Zöî9õ
þ
þ
Zöðì
ó"öìð Zóí=ò^ð"í/ó
]î9þ&ÿÃ-«þ
-
õ¡öî9ðí=ï]ðþ&ì
) =ÙëÎ~1Ù
&
=ö ¾ú
û
6
8 C96
A
6
\õ¡í=ÿ
ú²ï ö
ï ö
{þ&øì
2
ï ö
óöõ
Zöõ¡ï
=-âÐ~¯óí=ï]öqâ*ðõ¡ïøóðí=ì
{ó"í¯ùü?öõ¡ï
þ
öî9ö5ïí {öì
ðõºî9öòhöìï
s~
{ó"í/òhðí=ó
=-GÓÿ~¯óí=ï]ö¯Óþ&ó"þ&ò^öìö
ðí/ïóí=ìïðò
2
*
+ N
a *" a óöõ*í=óþ&ì
í/ÿ
]î9þ&ÿ
înþ&ìþ&ó"ù
înö {þ&înöí=ó
#~
*öò^öìï
(
Zí=õ¡öô½þ&ìFí Zøìôí/ìò^öõ
ö òhöóóöìïøìð"ÿþ&ôí/ó{òhþ&öìþ&òhóðìö
Oóí/ìôFõ¡ìí=ðóõyðì
xÓþ&óþ&òhöìö
öÿ¬ðí
ï öJþ&ó"ô«öõ¡ï
«þ&înöí=ó ^ëþ~¯ë5ïóí=ìïðò
kí/ïí
# 5 $ 5<=< 6 <
> " >!> $%$ >U< r 5 > [uAt
Ä
8
ìøÿ
N ;C 4
+t
9
öò^ïðþ&ì?ìöí=î
þ
WY^X
LAYER
z aQ{Gg
ë
\k-lm Wn on \pSq rn
sX5Ì1Ä+t
dT V
M (h`d( (2D 0 H
Q +1b. ~} ` @ (
í=õyò^í=îHî9ðöô½þ&øï*þ&ìFï öôí/ïí
í=ï]ïöîHì
þ&ï öï]ð"ò^í=ó
]õ¡öö²ñ
û Ï
ZîHí=ô«ð"öìï{ðõºú
û
Ï
ðïînö öí=óöôFí=ì
ö²òhþ&îHînöõ þ&ìôðì
¯þ&înô«öî
ú
Î
0 a
*
*
H
H
¬
I
/I
a W"£)
(/D ( a )
) a U M (`d( " 2$%#%# 5 #% >> $ 5 # "fW#%# 5 # "fW#%# 5 7 #%$ 5 # 6 $ 5 H5 ": fW$%#%$f 5 < "# 5 $
(?D 9"
0
) a M \ (
#%$: 5 $ #$% 5<=5 ( a
( " 7": 6 $ 5R5 ! 5 5 5 < $% "# 5R5 "#% 57<a5
N
7
V 9V \
9 2 R 9 a
a
a
( ( < $fW a
(
9 H
)
V N"
öõ
ðïö²ï öJìðòhöJòhþ&öìþ&òhóðìö
ôøò^öô
½í/ì
ZîHí=ï]ðþ&ìõ
öòhþ&óþ
øõ
´P 6R
?6
'35
9
öîHð
R6
Zðò^í=ó
íøìðÿþ&ôí=ó
;
ïõ¡ðôö¾þ
E6
qõ¡öö¾ñ
û Ï fðõyî9ö înöõ¡öìïöô
;8
*ï ö
ZîHí=ôðöìïfðõyþ&ò^òhø
98í/ìô1n
F
C 7
þ&ìö¾ÿ¬øõ¡ïOí=ó í {õ
Zî9í/ôðöìï
Zøïõ¡øòhò^öõ¡õ¡ð"þ&ì
õ¡öîHðí=ï]ð"þ&ì
î9þ&ù
ºþ&î¾ÿð"ù
76C
{þ&ó {öô
í/ïï]öî9ìînö öí=óöô
í=õ*ìþ&ï
qí=øìí=óº÷"õ¡øòhò^öõ¡õ¡ðþ&ìü
ZîHí=ôðöìï
;83
ó"öõJí/înö5ðì
þ&õ¡õ¡ð Zðóðï §ï í/ïìþ&ïï ököòhþ&óþ
òhí/øõ¡öJþ
*ï ö
?6
98=n
í/õ*ïþ¾ò^þ&ìò^óøôöJï í=ïð"ï
Zøï4îHí=ï öî
Ãö /ï]ð"ìòhïðì?ï öí/înöí
öînö5ôðí=ò î9þ&ìþ&øõyõ¡í=ÿ
ôöîHó Zðì
í=ï]ïöîHìþ&ìö
ï öóö ]ï]ÿ¬þ&õ¡ï*öìô½þ
;8x3
õ öò^ð"öõyìþ
Zðòhí/ó
Zð
ü(ð"ï
ö
Zöö Fðì
I
ðöô
6
8
\ö
¬ò^í=õ¡öõ
ÿ¬ðìô¼ï ö
,ð"õ4ï ökøìù
lm 2mOj
Nq n
.Ú
\n W Wj
\sX!uÛ ÜV
1ÝGV
stË¤uX
ú
@1
300
0
0
9
gradient
) 9)a)
0
)
stau"vrwxbz2y|{2y W
( !
"
U
07H¢ 2
M V
2 (
a +
Q ~~1 . b} ` @ (
H
(`d( 12
= )
) U 5 < $% "# ~5 5 "# 5<=5 % 6!< $ 8 > >!<a6 $ 57<a57 (
5ë
ðì
2
ï ö
þ
®õ¡öîHð"í/ïðþ&ì(þ&ì½í Zøìô«í=ìòhöõþ
Zóíù²ü?öõ¡ï
ìð"ò^ö5øìðÿþ&ôí=ó
í=óþ&ì
ï ö
ïþ¬ïí
îHð
ï
í/ïï]öî9ì
Zî9í/ôðöìï
6C
¯í/õJînö öí=óöô
í=õ¿ú
òhþ&óøÿìù ð"õ¡ö
A~
2
,öòhïðþ&ììöí/î
Ï
û
qînþ&ÿ
Î
Zþ&ïï]þ&ÿ
1ôð
]öî9öìï*õ öò^ð"öõþ
þ&ìö înøõ
í Zí/ð"ì
ú
óö ]ï
«þ
öÿðí
Åóí=ìô®õ¡ìí/ð"óõ
Ó¯þ&óþ&ò^öìö
*öòhþ&ìõ¡ïînøò^ïöô½õ¡í=ÿ
â«öî
ó"ö5þ&î9ôöî
öòhðöõ*í/înöJþ&înô«öînöôí=ò^òhþ&î9ôðì
~sn
R6
E6
ïþ¬ïþ
@.
ú
/j
Y
\k-lm Wn on \pSq rn
sX5Ì1Ä+t
WY^X
+t
[uAt
Ä
score
10
5
0
0
9
time
V
LV
PB
B
A
EA
LH
R
¯"°=±"²\³!´+µ¶ ¶RÃÄ2ÅºMÆ%¾W¿ û »Ç¾¿RúH¿2Â?¼À9Å¾ÂÃ û »Ç!¾¿R» ò ¼ÄÀ%ó¾ÈZõ=Ç»Å ¼½¾ ñ ¿0¾ÇÀ9Ä2¼aÀ%»ó
»óGÄ ò ôMóÈ\Äó û ¾¿r»õÈ\À9õõ=¾Ç¾ó¼¿0ºM¾ û À9¾¿r»õÆ9Ä2óÈ¿0óHÄÀ%Æ9¿UÀ9óG¼½¾ R» ò ¹"Æ9ÄSØ -¾¿0¼Ã¾ û Ø
¼À9»óEóH¾ÄÇ R»ó¾ºMÇôM¿0¹7ù r»½H¾ÅÀ9Ä2ù2¸N»Æ9» û ¾ó¾Â À%Å¾+Ç!ôMóH¿IõaÇ!»ÅÿÆ9¾õ=¼¼a»OÇÀ%Õ½H¼Â
?À9¿0¼aôMÆ%À9ÄóOÕ"Æ9Ä û À9Ä2Æ9ù Æ9Ä2¼a¾ ?À9¿0¼aôMÆ%À9ÄóHù
Ç¾ ò »Ç!¾Ä2Æ9ù \»Ç¾ÄÆ%ù ñ ñ ¼aØ
Æ%ÄóH¼aÀ û ù ñ \ºMÀ9Ä¼Æ9Ä2ó¼À û ù'Ã Ãô ò"ò »Ç¾Ä2Æ9ù7Ã ñ Ãô ò Ä2¼Æ9ÄóH¼aÀ û ù7Ã Ãô ò Ç!¾ û ¾ó¼
û ½HÇ!»óH»Æ9»Õ"¹Ä û7û »ÇÈrÀ%óÕG¼a» \» 2¾÷OÁ2Ñ2ÎÑ Ñ2Ì Â
.åd

!
wõ
õ
é
9ê
)è Îé
é
ç
è
+ç
§
q íq
÷ö
Qç
é
éK
é
;ç
Îé
ê ÷ë
1ø
°é
ç
é
+
Øù¨
ò1£
111¢KMÃòó+/)
Ä2¼aÄIõ=»Çd¼½À%¿ û Ä2¿0¾?¿0¼aôMÈ\¹+ÄÇ¾?È\¾ÇÀ9ú¾ÈWõ=Ç»Å ¼½¾Lõ=Ä2ôMóÄI»õÆ9Ä2óÈG¿0óHÄÀ9Æ%¿;»õ¼½¾?¸»Æ9» û ¾óH¾
Æ9» û ÄÆ9À%¼a¹W»õ"Ã÷"Ä2Æ9÷"ÄRóÄ2È Ò À9½H»úH»ô Ò Äú¾SóH¾ÄÇ RÄ2ÇÆ9¿0¼¾
óù \»½H¾ÅÀ9ÄÂ ñ Õ¾»õ"¼a½H¾/õ=Ä2ôMóÄ
9À ¿+¸N»Æ9» û ¾ó¾Â ½H¾Æ%» û Ä2Æ9À9¼¹Ä2óÈö¼a½H¾ÅÄÆ9Ä û »õ=Ä2ôMóÄÓÄ¿+È\¾¿ û Ç!À ò ¾È ò ¹ \» 2¾÷Á2ÑÎ2Ð
Ñ2Á =ùKÓN½¾Ç¾RÄ2Æ9¿0»G¼a½H¾ "ôMÄ2ó¼À9¼Ä¼À9ú¾+È\Ä2¼aÄ*»óEõa»¿0¿0À9Æ9¿0þÄ ò ôMóÈ\Äó û ¾¿ û »Å¾*õaÇ!»Å£Â
ô
Gõ
)ç
ø
Øù
#ê ÷ë
Mú
LAYER
9
8
7
6
5
4
3
2
1
0
SPECIES / SAMPLE
1
2
3
4
5
6
7
8
9
10
0
0
0
0
1
2
4
7
2
4
Acicula polita
0
0
0
0
2
1
1
0
0
0
Aegopinella pura
0
0
0
2
9
5
8
15
4
0
Cochlodina laminata
2
1
3
6
16
28
60
45
21
13
Discus ruderatus
0
2
0
5
0
1
0
0
0
0
Ena montana
0
0
1
0
0
2
2
5
2
0
Ena obscura
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
21
37
24
12
6
0
0
1
1
2
14
30
30
23
5
0
0
0
2
3
0
0
0
0
0
1
2
4
11
18
22
43
62
38
16
Oxychilus depressus
0
0
0
1
0
0
0
0
0
0
Semilimax semilimax
0
0
0
0
0
1
2
4
0
3
Sphyradium doliolum
0
0
1
1
7
0
0
0
0
0
Vertigo pusilla
0
1
0
0
1
0
0
0
0
0
Alinda biplicata
0
0
4
15
57
22
19
60
87
47
Cepaea hortensis
0
0
1
1
3
5
7
12
9
1
Discus rotundatus
1
0
2
4
58
70
104
111
26
16
Limax sp.
0
0
0
7
12
8
16
13
18
0
Aegopinella minor
1
2
5
7
20
21
47
92
40
47
Bradybaena fruticum
1
1
4
12
12
12
9
12
8
0
lm 2mOj
.Ú
Nq n
\n W Wj
\sX!uÛ ÜV
1ÝGV
@
stË¤uX
LAYER
9
8
7
Helix pomatia
1
0
1
Vitrea crystallina
0
0
2
Macrogastra ventricosa
0
0
0
Clausilia pumila
0
0
Urticicola umbrosa
0
Granaria frumentum
ú =Î
5
4
3
2
1
0
0
2
5
8
6
5
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
1
0
2
0
0
0
0
1
0
0
3
1
0
0
0
1
1
0
3
1
0
0
0
Helicopsis striata
1
6
2
2
0
0
0
0
0
0
Chondrula tridens
1
0
4
4
0
1
0
0
0
0
Pupilla sterri
0
1
1
0
0
0
0
0
0
0
Cepaea vindobonensis
0
0
0
0
0
0
0
1
0
0
Pupilla loessica
4
10
0
0
0
0
0
0
0
0
Pupilla muscorum
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
Vallonia costata
0
9
1
0
0
0
0
0
0
1
Vallonia pulchella
4
14
5
3
0
0
0
0
0
0
Bulgarica nitidosa
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
4
5
11
10
12
9
1
Cochlicopa lubrica
1
4
6
0
0
0
0
0
0
0
Euconulus fulvus
0
1
1
0
0
0
1
3
1
2
Limacidae & Agriolimacidae
1
4
2
6
4
16
23
28
15
0
Nesovitrea hammonis
0
3
1
1
0
0
0
1
1
24
Oxychilus cellarius
0
0
0
0
0
6
30
50
6
1
Punctum pygmaeum
0
0
0
0
0
0
2
6
4
5
Trichia plebeia
0
6
7
0
1
0
0
0
0
0
Vitrea contracta
0
0
0
0
3
3
0
0
0
0
Vitrina pellucida
0
0
0
1
1
0
0
0
1
0
Helicigona lapicida
0
0
0
2
3
10
16
18
15
2
Laciniaria plicata
0
0
0
1
0
1
0
2
1
0
Carychium tridentatum tridentatum
0
0
0
3
24
0
0
0
0
0
Succinea oblonga
0
2
1
0
0
0
0
0
0
0
TOTAL
19
72
63
106
274
293
482
622
351
196
CHRONOLOGY
PV-LV
PV-LV
PB-B
A
EA
EA
SB
SA-SR
SA-SR
R
z ad{Gg
x+zy2y W
V c
2 0 `
ë
þ
{þ&ø
) 9))
0
)
* 9
( L
H¢ 2
N)
( P/
a N ^ @
- 9 9
MM¢ 9¢
\
7M¢ M" 9d M
( +)
a o
_ ` } T 1.2 ( ` (
{øìôí/ìò^öõ*þ
,öò^ïðþ&ì
óí ZöîHõ
qöînöìïZõ öòhðöõºþ
QÓþ&ó"þ&ò^öìö
ï ö¯þ&óôöõ¡ï úï ö
GÙëÃ~¤Ù
~
Zînöò^öìï
D R
a 0 2 O)
)
a +
ö²í Zøìôí=ìòhö
\ôð
öÿ¬ðí
ó"öìð Zóí=ò^ð"í/ó
ëß~½ë5ï]ó"í/ìï]ðò
,ø
þ
Zöðì
~Ðâ*ðõ¡ï]øó"ðí/ì
M
6
Zþ&øì
óöõ
Zöõ¡ï
í=ï]í
qînþ&ÿ
V
ð~
,ø
-þ
=ö ú
öînöJïí Zöì
Ð~
Zþ&î9öí=ó
/Î
ëß~
qþ&î¾í=ì
qí=ò^ïþ&îOòhí/øõ¡ð"ì
ï ö
(
í/òhï]øí=óºþ
Zî9í/ôðöìï
²í=ì
â
Ð~
(
ú
í=ï]ïöîHì
HV
øìðôðÿöìõ¡ðþ&ìí=óÅöì
4ðù
Zöînöô
þ&înöí/ó
&
)
öîHí=ï]ð"þ&ì3þ
ø
ú
Zí/õ¡öô§õ¡öîHð"í/ïðþ&ìînö öí=óöôíìðòhö²øìðÿ¬þ&ô«í=ó
ï í/ï²õ öí {õ
ìøÿ
î9þ&ìþ&óþ
î9ö Zþ&înöí/ó
ïí
cP
"UTI
Z¢ %
7M
Zí=ó Zíìí/ô
]î9þ&ÿ
ðõînöòhöìï
x-âÿ~¼óí/ïö!â*ðõ¡ïøóðí=ì
ðí=ïóí/ìï]ð"ò
*öò^öìï
\óí=ìôõ¡ìí=ðóõ1ðìï ö
,í=ÿ
Î~
M (h`( 12
S qõ¡öö²ñ
ð"î9þ&ìÿöìïí=ó
û
@2}
/j
Y
ú
\k-lm Wn on \pSq rn
sX5Ì1Ä+t
WY^X
+t
Ä
[uAt
50
0
0
9
gradient
( J -
) - W
s"t=u"v\w!x+zy|{ y P
2
) %)a)
0
)
W 0 N 9
(
(
P 9 V £ \¢ r - V
`
(

a G
; OQ. } 1 @

H 2 ('`d( .2
= O)
)
5 < $ "# 55 "#% 57<a57 9" "$%" 5 #7 857 (
V a 9" ) ! (
)P V
M Z a 9 9ø
!
(J a a )
;
r o %
)I
) N
9
9 M \
I (rD 2M
0
a
) a W
a"N a
) (
2
0
V a W ` a )
) a 2
%' 0 "V %7K W V ( W)
0
R)
) E 2 `
} =\N O
M
) *
IV !
?
9 %)a) H 9
(rD 0 2
G 9 a
b
0
9
dû
4þ&öìþ&ò^ó"ðìö
í Zøìôí=ìòhöõkþ
Åð þ
{þ&ø
1ô«ð
,öòhï]ð"þ&ì
í=ï]ïöîHì
þ
*öòhþ&ìõ¡ïînøò^ïöô(õ¡í=ÿ
Óþ
A
6
öÿð"í
í/òhòhþ&î9ôðì
E6
ï]þ¾ïþ
í
,öòhï]ð"þ&ì
ZîHí=õ¡õ¡óí/ìôü
õ öò^ð"öõ
²ï ö
ZîHí=ôðöìï
í=ìô®õ¡ðôöþ
§îHð
1ï ö
{î9í/ôðöìïòhþ&øóô
{øï1ìþ
ï
óí=ò^öôþ&ì¾ï öÅóö ]ï]ÿ¬þ&õ¡ï,þ
þ
ðþ&øõ¡ó
ìí=ófòhþ&ÿ
þ&ìþ
í=înôï]þ
þ&õ¡ð"ï]ðþ&ì(þ
þ&õ¡ðïöyöìôõ1þ
ÿí Zìðïøôö
~'F 6
ï qþ&î í/înô
$(þ&î9öþ
Zï ö
Zöóðö {ö
1õ¡í=ÿ
ï ö
ZîHí=ôðöìï
ë
í/ïï]öî9ì
í=õkînö öí=óöô
¯í/õ²ú
ú ¾Ï
Î
]î9þ&ÿ
{þ&ïïþ&ÿ
ZîHí=ôðöìï
ðõ
~½óí
û
óö qï
ë5õ²ðì
ï ö5òhí/õ¡ö5þ
ÅöîHïþ
í
Zö?ðìï]öî î9öïöôýí/õ÷ þ&þ&ôóí=ìô
ðöô
öõ¡ð"ï]í=ï]ð"þ&ì
óöú
ðï
þ&þ&ôóí=ìô
öî9ökï ö5ÿþ&õ¡ï«þ
~óí
k÷"ÿí ð"ÿøÿ
{öî9õ
öî õ¡ð"ÿðóí=î
í=ìô
Zöî
ðò ½í=î9ö
óö
ô«ð
Oï ö
â*ðõ¡ïøóðí=ì
þ&þ&ôóí=ìôü
öînò^öìï]øí=óó
þ&õ¡õ¡ð Zðóðï ï í/ï«õ¡þ&ÿö5õ¡í=ÿ
ù
ðî9õ¡ï fï öóö qï
í/ìô®ìþ&ï
{î9í/ôðöìï
{öî =õ¡í=ÿ
ð"ìôðòhí/ïðì
þ&ì
{í=ó Zíìí=ô
qïöî«íyòhóþ&õ¡öîfðìõ öòhï]ð"þ&ìþ&ìöJìþ&ï]ðòhöõ*ï í=ï{ï ö
ó"öõúí/ìôû
øõ Zï öînöðõJí
fï ö
õ¡öî9ðí/ïðþ&ì
;C
{ð ?í/ÿ¬þ&øìïÅþ
öí/îºìöí/î¿ï öÿðôôóö5þ
5ë
¯õ 1ð"ì½ï ö
òhþ&óøÿìù ð"õ¡ö
ZîHí=ôðöìïºðõ5þ&ìó Fõ¡ò^í=înò^öó þ&ò^òhø
þ&õ¡ö5í
]î9þ
ìðÿ¬þ&ô«í=ó
þ&õ¡õ¡ð Zó
ðï í
]î9þ&ÿáï ö
{î9í/ôðöìï
ïþ§ï]í
ÿþ&õ¡ïí {øìôí/ìï\õ öò^ð"öõÅòhøóÿðìí/ïö
ðõ
¬ï ö
ö {öî {ï ö¾ðìïöî înöïí/ïðþ&ìð"õyìþ&ïOõ¡ïîHí=ð
õ¡ï]înþ&ø
{ïí=ðìöô
1óí/ìôõ¡ìí=ðóõ
GÓþ&óþ&òhöìö
óö¾þ&înôöî¿í=óþ&ì
öò^ðöõJí=înö5þ&î9ôöînöô
A~[n
õþ
]öî9öìïõ öò^ð"öõkþ
«ðõ
ðò
]í/øù
þ&õ¡ðïðþ&ìöô
]öîHðì
þ&ìó ¯ð"ì
í/î9í/ÿ¬öï]öî9õ &ìí=ÿöó
lm 2mOj
.Ú
Nq n
)a) 9V
5]85 $ >!< a
ö
\n W Wj
\sX!uÛ ÜV
7 H
2
]öò^ïð {ö*õ¡öô«ð"ÿöìïí=ï]ðþ&ì5î9í/ïöºò í/ì
ðì
2 )
ï öyøõ¡í ZöJþ
1ÝGV
stË¤uX
(D 0
Zöôøììþ&ïðò^öô

(
ð"õfõ þ&øóô
?)
\ÿöînöJí {øìôí/ìò^öõ
@`
ú
]þ&îOõ¡öîHð"í/ïðþ&ì
Zöºî9öí=ô¾í/õí
í/î9ìù
score
10
5
0
0
9
V
LV
PB−B
time
EA
A
SB
SA
SR
R
¯°a±"²r³´bµ2¶ Ö2¶/ÃÄ2ÅºMÆ9¾W¿ û »Ç¾¿+ú¿2Â¼aÀ%Å¾Â?Ã û »Ç¾¿R» ò ¼aÄ2À9óH¾ÈZõaÇ!»Å ¼a½H¾ ñ ¿0¾Ç!À9Ä2¼aÀ9»ó
»ó Ä ò ôMóÈ\Ä2ó û ¾¿b»õIÈrÀ%õaõa¾Ç!¾óH¼¿0ºM¾ û À%¾¿»õÆ%ÄóHÈ£¿0óÄ2À9Æ9¿WÀ9óZ¼½¾NÃ÷"Ä2Æ9÷"ÄoóÄ2È Ò À9Ø
½»ú»ôOÃ¾ û ¼À9»óHù \»½¾ÅÀ9Ä2ù¸N»Æ9» û ¾ó¾Â À9Å¾ÇôMó¿\õaÇ!»Å Æ%¾õ=¼2¼a»*ÇÀ%Õ½H¼Â Ò ½HÇ!»óH»Æ9Ø
»Õ"¹ ?À9¿0¼ôMÆ9À9Ä2ó,Õ"Æ9Ä û À%ÄÆ9ù Æ9Ä2¼¾ ?À9¿0¼ôMÆ9À9Ä2óù
Ç¾ ò »Ç¾Ä2Æ9ù \»Ø
Ç¾ÄÆ9ù ñ Bñ ¼Æ9Ä2ó¼À û ù ñ \ºMÀ9Ä2¼aÆ9Ä2ó¼À û ùUÃ Ãô òò »Ç¾ÄÆ%ùrÃ ñ Ãô ò Ä¼Æ9Ä2ó¼À û ù
Ã Ãô ò Ç¾ û ¾ó¼ È\Ä2¼aÀ%óÕ-Ä û7û »Ç!È\À9óHÕ-¼a» r» 2¾÷-Á2ÑÎ2Ð Ñ2Á ÂG¸NÀ%Õ½ö¿ û »Ç¾¿Ä2Ç!¾
À9óH¼a¾Ç!ºMÇ!¾¼¾ÈÄ2¿ ý Õ"Ç!Ä¿0¿0Æ9Ä2óÈ\þùÆ9»Ó ¿ û »Ç!¾¿Ä¿ ý ÓN»»È\Æ9Ä2óÈ\þiÂ »¼a¾¼½Ä2¼M¼½¾¿0Ä2ÅØ
ºMÆ9¾cÁ Æ9¾õ=¼Å»¿0¼ù /È\»¾¿óH»¼RÔM¼/ÓNÀ9¼½À9ó¼½¾cÕ"¾ó¾ÇÄ2ÆLºMÄ¼¼¾Çó *À9¼/À9óHÈ\À û Ä2¼¾¿
ý ÅÄüÀ9ÅôMÅ ÓN»»È\Æ9Ä2óÈ\þùMÓN½À9Æ%¾¼½¾ û »ÅºM»¿0À9¼aÀ%»ó ºM¾Ç û ¾ó¼ôMÄÆ U»õ?¼½¾õaÄôMóHÄ
À9¿/ú¾Ç¹¿0À9ÅÀ9Æ%ÄÇL¼»N¿0ÄÅºMÆ9¾¿SÌWÄ2óÈÉù¼½Ä2¼MÇÄ2ó÷"¾È,Ä2¿ ý ÅÄ2üÀ%ÅôMÅ ÕÇ!Ä¿0¿0Æ%ÄóHÈrþiÂ
óHÈ\¾¾ÈrùL»óH¾ÓN»ôMÆ9Èøó»¼*¾üºM¾ û ¼/ÓN»»È\Æ9Ä2óÈ Ä2¿0¿0¾Å ò Æ9Ä2Õ"¾¿À%ó¬¼½¾ ?À9¿0¼aôMÆ%À9Äó
Õ"Æ9Ä û À9Ä2Æ]Â Ç» ò Ä ò Æ9¹NÀ%¼MÈr¾Ä2Æ9¿ÓNÀ9¼½Ä2ócÄ2Ç¼À9õaÄ û ¼ ºMÇ¾¿0ôMÅÄ ò Æ9¹7ùºMÄÇ!ÄÅ¾¼a¾Ç!¿ÅÄºMØ
ºMÀ9óHÕÈ\¾ó¿0À9¼À9¾¿U»óH¼a»bÄ ò ôMóÈ\Ä2ó û ¾¿ û ½Ä2óÕ"¾È ò ¾¼ÓN¾¾óG¼½¾S¿0Ä2ÅºMÆ%¾¿0ù'ÓN½À%Æ9¿0¼"¼a½H¾
È\¾ó¿0À9¼À9¾¿*Ç¾ÅÄ2À9ó¾È-¼½¾W¿0Ä2Å¾ Ç!¾ û ÄÆ%Æ¼½Ä2¼;¼½¾WÄ2óÄ2Æ9¹"¿0À9¿RÓNÄ2¿ û Ä2ÇÇ!À9¾È,»ôM¼U»ó
å è"
í åí"éã!ä ù2ó»¼dÈ\¾ó¿0À%¼aÀ9¾¿ Â
.å
9ç
©
é
é
ê
é
+
!
W
bè
é
éÞ
Rç
é
+ç
§
é
ç
è
é
ç
é
#ê ÷ë
Ðø
)ù¨
¦
§
Ë¨
5©
§

?¨
E©
§
0¨
q íq í
Ì}q¥
´M
Ä¼ÄSõa»Ç¼½À9¿ û Ä¿0¾?¿0¼ôMÈ\¹~Ä2Ç!¾UÈr¾Ç!À9ú¾ÈOõaÇ!»Å ¼a½H¾Lõ=Ä2ôMóÄI»õÆ9Ä2óÈG¿0óÄ2À9Æ9¿\»õ¼½¾L¸N»Æ9» û ¾ó¾
Æ9» û Ä2Æ9À9¼¹»õ!?Äc÷"Ç!À ¾Å Ò Ä2ú¾ó¾Ä2Ç*ÃúÄ¼¹#"=Ä2óºM»È£Ã÷"Ä2Æ9»ôMù \»½H¾ÅÀ9ÄÂ ñ Õ"¾»õI¼a½H¾
õ=Ä2ôMóÄWÀ9¿R¸N»Æ%» û ¾óH¾Â ½H¾Æ9» û ÄÆ9À%¼a¹EÄ2óÈ,¼½¾bÅÄ2Æ9Ä û »õ=Ä2ôMóÄWÓÄ¿/È\¾¿ û ÇÀ ò ¾È ò ¹ \» 2¾÷
$ ¸»ÇÄ û ¾÷oÁ2ÑÑ2É Ñ2É aùÓN½H¾Ç!¾WÄ2Æ9¿0»o¼½¾ "ôMÄóH¼aÀ9¼Ä2¼aÀ9ú¾GÈ\Ä¼Ä»ó-õa»¿0¿0À9Æ9¿0þMÄ ò ôMóÈ\Äó û ¾¿
û »Å¾+õaÇ!»Å£Â
ô
ìë
ç
Ìø
'ê ÷ë
dù
ú
LAYER
9
8
7
6
5
4
3
2
1
SPECIES / SAMPLE
-
1
2
3
4
5
6
7
8
0
0
1
3
17
24
61
66
11
Aegopinella pura
0
0
0
2
32
29
45
46
5
Cochlodina laminata
0
0
1
10
46
43
49
28
12
Discus ruderatus
0
1
15
9
9
0
0
0
4
Ena montana
0
0
1
0
0
0
0
0
0
Ena obscura
0
0
0
1
11
6
1
0
2
0
0
0
0
1
3
7
4
2
0
0
0
0
1
2
0
0
0
0
0
0
2
9
1
0
0
0
ú^ú
@
LAYER
/j
Y
9
\k-lm Wn on \pSq rn
sX&%1Ä+t
WY^X
+t
Ä
[uAt
8
7
6
5
4
3
2
1
0
0
1
3
28
63
107
79
27
Oxychilus cf. depressus
0
1
0
0
0
0
0
0
0
Sphyradium doliolum
0
0
0
3
12
5
3
13
1
Trichia unidentata bohemica
0
0
0
0
7
7
5
3
2
Vertigo pusilla
0
0
0
0
7
9
13
13
6
Alinda biplicata
0
0
0
16
229
261
345
258
80
Arianta arbustorum
0
1
5
0
1
0
0
1
1
Cepaea hortensis
0
0
0
0
0
1
3
4
2
Discus rotundatus
0
0
0
7
26
21
3
1
18
Limax cf. cinereoniger
0
0
0
2
6
4
2
7
7
Oxychilus glaber
0
0
0
0
1
0
0
0
0
Semilimax kotulae
0
0
5
1
1
0
0
0
1
Aegopinella minor
0
0
0
15
64
73
124
447
26
Bradybaena fruticum
0
1
9
20
23
5
3
1
8
Helix pomatia
0
0
1
1
1
1
0
2
2
Clausilia pumilla
0
0
0
0
0
0
0
0
1
Granaria frumentum
0
0
0
25
177
260
390
156
31
Helicopsis striata
4
44
77
10
3
0
0
0
2
Chondrula tridens
0
0
1
10
7
0
0
0
1
Pupilla sterri
0
7
18
7
16
11
46
110
13
Pupilla triplicata
0
0
7
4
8
5
15
35
12
Chondrina avenacea
0
0
8
46
200
136
106
60
55
Pyramidula rupestris
0
0
0
0
0
6
2
8
6
Truncatellina claustralis
0
0
0
0
0
0
1
8
2
Pupilla muscorum
0
5
13
0
0
0
0
0
0
0
0
1
3
3
6
18
41
10
Vallonia costata
0
0
23
50
56
8
22
42
16
Vallonia pulchella
0
0
1
7
78
79
106
80
16
Vertigo pygmaea
0
0
0
0
0
0
1
0
0
Bulgarica nitidosa
0
0
1
9
93
165
239
118
69
0
1
8
12
71
13
12
7
10
0
1
3
15
42
28
31
30
14
Cochlicopa lubrica
0
6
1
0
0
0
0
0
0
Euconulus fulvus
0
0
6
2
8
4
4
5
6
Nesovitrea hammonis
0
0
0
3
3
1
1
0
1
Oxychilus cellarius
0
0
0
0
0
0
1
0
0
Punctum pygmaeum
0
0
2
0
3
0
3
1
9
Trichia sericea
0
6
125
13
1
0
0
0
0
Vitrea contracta
0
0
0
0
2
4
5
2
0
Clausilia dubia
0
0
1
1
14
2
4
2
0
Helicigona lapicida
0
0
0
0
2
5
11
11
3
Laciniaria plicata
0
0
0
0
0
1
0
0
0
Vertigo alpestris
0
1
7
3
0
0
0
0
2
Carychium tridentatum tridentatum
0
0
0
2
8
12
8
4
0
Nesovitrea petronella
0
0
4
8
6
0
0
0
0
TOTAL
4
75
346
325
1333
1304
1797
1693
496
CHRONOLOGY
V
LV
PB
B
A
EA
EA
SB-SA
SR
lm 2mOj
.Ú
Nq n
) 9))
x+zy)2y W
2¢ 2
` a
Z 9 %
\
( ~)
M
_
z ad{Gg
ë
,öòhï]ð"þ&ì
Zöðì
óðí=ì
{øìôí/ìò^öõþ
«þ
öÿðí
,ø
` G
o W
2
%V
Zöî
{í=õ¡öô
5ë
H
Zðì
,í=ÿ
Zþ&øì
-þ
)
N
=ö
"
ú^úhú
)
?
)
( P/
@
9\M¢ £
M" 9d
`` T 2Q 2
óöõ
Zöõ¡ï
ðõînöò^öìï
î9þ&ìþ&óþ
,ø
Óþ&îHí=ò^ö
S 9_ P 2V
2 0
"UT
9d¢ £¢ %
M
7M
( ` (
+**í
]î9þ&ÿÖìøÿ
Ñ~
Zóí=ò^ð"í/ó
ð~
&óí=ìôõ¡ìí=ðóõ«ðì¾ï ö
öînöJïí Zöì
Zþ&î9öí=ó
¾ú
úhú
Ï
ZîHð =öÿ
¯â
înö Zþ&î9öí=ó
ëß~
êïí
ø
ú
&
4í ö
Zöînöôóí {öî9õ
~ýâ*ðõ¡ï]øù
G~
þ&înöí/ó
Î~
Ï)(
9
L ) N Q
0 0 ! #$% > $ >b><=6 $ 5<=5 (
2
H (
]î9þ&ÿ
ï öí=ìí=ó Zõ¡ðõí=õðï
ï]þFí¬õ¡ðì
§õ¡öîHðí=ï]ð"þ&ì
0
( a^
7M¢
qöînöìï õ öò^ð"öõfþ
ðí=ïóí/ìï]ð"ò
]î9þ&ÿ
¯í/õôðõ¡òhí=î9ôöô
Zöóþ&ì
st('¤uX
1ÝGV
b-Qâ~óí=ïöKâ*ðõ¡ïøóðí=ì
GÙëÃ~¤Ù
í=ïí
Zînöò^öìï
ô«ð ðôøí=óõ
&ôð
ØÓþ&óþ&òhöìö
ï ö¯þ&óôöõ¡ï «úï ö
óöìð Zóí=òhðí/ó
ëß~½ë5ï]ó"í/ìï]ðò
-«í
\n W Wj
\sX!uÛ ÜV
Zóöõ öò^ð"öõ
í=õ
þ&þ&îyðì
]í/øìí
;
²B
qÿ¬öî9ö
§ðìù
õ¡øí/ó*í Zøìôí/ìò^ö
í=õ1òhí=îHîHð"öôþ&øïþ&ìï ö²î9öÿ¬í/ð"ìðì
õ¡í=ÿ
ó"öõ
)\ J /
," c )
( V a 2 H-,?5 6 $ !f ?5 "5 " < 6
G
H
E
o
9 a
) "
S %V 5> ; I> " >> $7O$%": !:
-
U ~< $fW ( ( )
" 9)L 75 <a< 6
`d( } (
M `( 2Q
ë5ìö /ò^öó"óöìïøìðÿþ&ôí=ó
þ&ì
í Zøìô«í=ìòhökôí=ï]í
í/ìô3ÿ¬þ&î9ö
ñ
ðì
õ
û ²í/ìô
í/õ
û
ð
ö
\ï ö
Zðöóôöô
ZîHí=ô«ð"öìïï]þ
înþ&ìþ&øìòhöôó (ï í=ïÅð"ìï ö¬òhí=õ¡öþ
ZîHí=ôðöìï
{õ
í=ï]ïöîHì§þ
înþ&ÿðõ¡öô?í¾înöí/ó
2
ï öõ¡öî9ðí=ï]ðþ&ì
Zöð"ìòhóøôöô
þ
qí=øìí=ó«õ¡øòhòhöõ¡õ¡ðþ&ì
Óþ
ù^ü?öõ¡ï
öò^ïðþ&ì
ìþ&ïºöòhþ&óþ
ðïõ¡öó
{ó"í
öî ]þ&îHÿ¬öô
ö {öî Zí Zí/ðì
*ï ö§ôîHð ù
qòhþ&ÿ
í=î9ö
?ä
ZI
>
3 ;
6
d6
/j
Y
ú^ú=û
\k-lm Wn on \pSq rn
sX&%1Ä+t
WY^X
+t
[uAt
Ä
50
0
0
7
gradient
s"t=u"v\w!x+zy|{.)y P
2
P V ¢ -
) %)a)
4þ&öìþ&ò^ó"ðìö
í Zøìôí=ìòhöõþ
Åí {ö
þ
Åô«ð
öÿð"í
òhþ&ìõ¡ïînøò^ïöô?õ¡í/ÿ
( J 0
)
( H a í=ï]ïöîHì
õþ
]öî9öìï¿õ öòhðöõ¾þ
ØÓþ&óþ&òhöìö
âöî
óöþ&înôöî*í/óþ&ì
- W
O 0 /* 9_
(
O V
(
M &} 0 .W1WQ
{ïí=ðìöô
4óí=ìô
)
]î9þ&ÿáï ö
õ¡ìí=ðóõ
5ìðò^öJøìðÿþ&ôí=ó
ï ö
ZîHí=ôðöìï
qînþ
í=ï]ïöîHì
í=õ
5ë
õ¡öî9ðí/ïðþ&ì
õ 4ðì®ï ö
*í
í=õ*î9ö {öí/ó"öô
Ï
û5ú
þ&ì
{î9ð =öÿ
*öù
öòhðöõ
lm12mOq =n GpSnn
Üu +Y
+uV!\
ú^ú Ï
H 2 ` ( 0 = W)
9" d > $ <=6 5 2 a< 6 "!## 5 (
< $% "# 5I5 "#% 57<a57
í=î9öþ&î9ôöînöôí=ò^òhþ&î9ôðì
R6
E6
ï]þ¾ïþ
ïþï]í
î9ð
ï
&òhþ&óøÿìù ðõ¡ö
A~'
]î9þ&ÿ
) M
Zþ&ïï]þ&ÿ
~Wn
ó"ö qï
5
D
score
10
5
0
0
7
time
LV
PB
B
A
EA
SB
SA
SR
¯°a±"²r³´bµ2¶ Ù2¶/ÃÄ2ÅºMÆ9¾W¿ û »Ç¾¿+ú¿2Â¼aÀ%Å¾Â?Ã û »Ç¾¿R» ò ¼aÄ2À9óH¾ÈZõaÇ!»Å ¼a½H¾ ñ ¿0¾Ç!À9Ä2¼aÀ9»ó
»ócÄ ò ôMóÈ\Ä2ó û ¾¿»õrÈ\À9õõ=¾Ç¾ó¼¿0ºM¾ û À9¾¿»õrÆ%ÄóHÈ-¿0óÄ2À9Æ9¿SÀ%ó¼½¾!?ÄW÷"Ç!À ¾Å Ò Ä2ú¾ù
\»½¾ÅÀ9Äù¸»Æ9» û ¾óH¾Â À9Å¾bÇ!ôMóH¿/õ=Ç»ÅÆ9¾õ=¼M¼»NÇÀ%Õ½H¼Â ?À9¿0¼ôMÆ9À9Ä2ócÕÆ%Ä û À9Ä2Æ9ù
Æ9Ä¼2¾ ?À9¿0¼ôMÆ9À9Ä2óù
Ç¾ ò »Ç!¾Ä2Æ9ù \»Ç!¾Ä2Æ9ù ñ cñ ¼Æ9ÄóH¼aÀ û ù ñ \ºMÀ9Ä¼Ø
Æ9Ä2ó¼À û ùÃ Ãô òò »Ç¾ÄÆ%ù'Ã ñ Ãô ò Ä¼Æ9Ä2ó¼À û ù'Ã Ãô ò Ç¾ û ¾ó¼Â »¼¾/¼a½HÄ¼¿ û »Ç¾¿
û ½Ä2óÕ"¾WÅ»óH»¼a»óHÀ û Ä2Æ9Æ9¹ÓNÀ9¼½,¼À9Å¾Â ½H¾WÕÇ!ÄÈ\À9¾óH¼ û »ôMÆ9Èó»¼ ò ¾WÀ9ó¼¾ÇºMÇ¾¼¾È
Ä2¿¾ û »Æ%»ÕÀ û Ä2ÆÄ2ó¹"Å»Ç¾ùU¼½»ôMÕ"½£¼½¾Ç¾NÀ9¿W¿0¼Ç!»óHÕ¾úHÀ9È\¾ó û ¾Nõa»Ç~ºMÇ¾¿0¾ó û ¾N»õ
¿0»Å¾c÷"À9óÈ »õ/Ä2ó£ôMóÀ%ÈrÀ%Å¾ó¿0À%»óÄ2ÆÕ"ÇÄ2È\À9¾ó¼ ¿0¾¾oÔMÕ;ÂÑdÂ Ì2Ð Â 3WóH¾oºM»¿0¿0À ò Æ9¾
À9óH¼a¾Ç!ºMÇ!¾¼Ä¼À9»óoÀ9¿¼a½HÄ¼\õ=Ä2ôMóÄ2Æ"ÅÀ9Õ"Ç!Ä¼À9»ó¿S»úH¾Ç!ÇÀ9È\¾È,¼½¾~¾ û »Æ9»Õ"À û Ä2ÆºMÄ2¼a¼¾Çó
ó¾Ó Ä2¿0¿0¾Å ò Æ9Ä2Õ"¾¿LÀ9óNÄ+¿0À9ÅÀ9Æ%ÄÇ û »ó¼¾ü¼HÄÇ¾ û »ÅºM»¿0¾È»õÄbóH¾Ó õ=Ä2ôMóÄÂ
.å
W
!
ìë

ç
ê
é
ç
+ç
é
éÌ
é
Øç
þé
é
é
ç
dè é
é
+
è
¦
§
Q¨
²©
46587
9;:<>=@?A<><@:BDC
½H¾bÓN½H»Æ9¾ºMÇ» û ¾È\ôMÇ¾R¼a¾¿0¼À9óHÕE¿0¼aÄ2Ç¼¾È\ùÄ2¿¼½¾~Æ9»Õ"À û »õM¼a½H¾bÅÄ2¼¼a¾Ç?È\¾ÅÄ2óÈ\¿0ùÓÀ9¼a½
ÄÇ!¼aÀ9Ô û À9Ä2Æ9Æ9¹Õ¾óH¾ÇÄ2¼a¾ÈZÈ\Ä¼Ä2ùÓN½H¾Ç!¾O¼a½H¾ û »ÇÇ¾ û ¼UÇ¾¿0ôMÆ9¼a¿*ÓN¾Ç¾O÷óH»ÓNóÀ9ó-Ä2ÈrúÄ2ó û ¾Â
¼?ÓNÄ2¿~È\¾Å»ó¿0¼ÇÄ2¼a¾Èö¼a½HÄ¼?ÓNÀ%¼a½FEbÄ2ôM¿0¿0À9Ä2óÃ HGÅ»Èr¾Ær¼½¾¿0¾Ç!À9Ä2¼aÀ9»ó-Ó»Ç÷"¿bÓN¾Æ%Æ
»ó ò »¼½-¿0ÅÄ2Æ9Æ\Ä2óÈZÆ9ÄÇÕ"¾WÈ\Ä¼Ä¿0¾¼¿2Â rú¾ó,¿0Æ9À%Õ½H¼?ôMó û ¾Ç¼ÄÀ%ó¼À9¾¿*À9ó¼Ç!»È\ô û ¾Èö¼»c¼a½H¾
ÄóHÄÆ9¹"¿0À9¿ ò ¹N¼a½H¾ \Ä2¹"¾¿0À9ÄóEÈ\¾óH¿0À9¼aÀ%¾¿SÈ\À9ÈóH»¼MÈ\À9¿0¼a»Ç!¼d¼½¾bÇ¾¿0ôMÆ9¼ ÓN½HÀ9Æ9¾b¼½¾Ç¾+ÓNÄ¿IÄ
ÅÀ9Æ9ÈúHÄ2ÇÀ%Ä¼À9»óbÀ%óW¿0ÄÅºMÆ9¾?»Ç!È\¾Çù7¼½¾ û »¾ó» û Æ9À9óH¾IÃ HG~ºMÄ2¼a¼¾ÇóbÇ!¾ÅÄÀ9óH¾ÈW¾¿0¿0¾ó¼À9Ä2Æ9Æ9¹
¼a½H¾+¿0Ä2Å¾Â
ø½À%Æ9¾ ò »¼a½oÄ2Ç¼À9Ô û À9ÄÆ¾üÄ2ÅºMÆ%¾¿0ùÕ"¾ó¾ÇÄ2¼¾È ò ¹N¼½¾ ý û »¾óH» û Æ%À9ó¾þºMÇ!»Õ"Ç!ÄÅùÈ\À9È
ÓN¾Æ9ÆÀ%ó¼½¾bÄ2óÄ2Æ9¹"¿0À9¿/»õrÄ ò ôMóHÈ\Äó û ¾¿ÄóHÈ,È\¾ó¿0À9¼À9¾¿ ¹À%¾Æ9È\¾È,¼a½H¾ û »ÇÇ¾ û ¼d¿0¾Ç!À9Ä2¼aÀ9»ó
»õS¿0Ä2ÅºMÆ9¾¿WÄ2¿ÓN¾Æ9ÆUÄ¿WÃ HG û »¾ó» û Æ9À9óH¾cºMÄ2¼¼a¾Ç!ó =ù\¼½¾EÇ¾¿0ôMÆ9¼¿W» ò ¼Ä2À9ó¾ÈBõaÇ!»Å ¼a½H¾
Ç!¾Ä2ÆÓN»Ç!Æ9ÈEÈ\Ä¼ÄRÓN¾Ç¾/ó»¼¿0» û Æ9¾ÄÇ!Æ9¹WÀ9óH¼a¾Ç!ºMÇ!¾¼Ä ò Æ9¾Â ½H¾ »Ç!ÓNÄ¹G»¿0¼ÇÄ û »È\¿Ä ò ôMóØ
ÈrÄ2ó û ¾+¿0¾ÇÀ9Ä2¼aÀ%»óc¿0½H»ÓN¾È,ÄóH»À9¿0¹EôMóÀ%Å»È\ÄÆÃ HG"¿Sõa»ÇL¼a½H¾~¼½Ç¾¾~»ÇL¿0»Å»¿0¼\È\»ÅÀ9Ø
óÄ2ó¼"¿0ºM¾ û À%¾¿0ù»¼a½H¾Ç;Ã HG"¿ ò ¾À9óHÕW¾À9¼½¾Ç\Åô û ½¼»»Wó»À%¿0¹7ù»Ç û ½HÄ»¼À û Ä2¼ÄÆ9ÆeÂ ½H¾SÈ\¾óØ
¿0À9¼a¹ ò Ä¿0¾È¿0¾ÇÀ9Ä2¼aÀ%»óÈ\À9ÈEó»¼HÀ9ÅºMÇ»ú¾/¼a½H¾RºMÄ¼¼¾ÇóOÄ¼"Ä2Æ9Æ9ùÅ»Ç¾»ú¾ÇaùÀ9¼Õ"¾ó¾Ç!Ä¼¾ÈNÄ
ò ôMó û ½o»õMÅôM¼aôMÄ2Æ9Æ9¹NÀ%ó û »ÅºMÄ2¼aÀ ò Æ9¾+½¹"ºM»¼½¾¿0¾¿Ä ò »ôM¼d¼½¾+¿0ÄÅºMÆ9¾+»Ç!È\¾ÇÄ2Æ9»óÕ¼a½H¾
½¹"ºM»¼a½H¾¿0À 2¾ÈZÕ"Ç!ÄÈ\À9¾óH¼Â õr¼a½H¾WÕ"ÇÄ2ÈrÀ%¾ó¼\À9¿RºMÇ¾¿0¾ó¼\Ä¼\Ä2Æ9Æ9ù"À9¼\ÓNÄ2¿RÅô û ½È\À9¿0¼»Ç¼¾È
ò ¹-»¼½¾Ç*¾õõ=¾ û ¼a¿0ùºMÇ!¾¿0ôMÅÄ ò Æ9¹,¿0¾È\À9Å¾ó¼ÄÇ!¹,Ä2óÈ ¼Ä2ºM½»ó»ÅÀ û ÄÆ]Â ¾¼aÄ2À9Æ9¾ÈöÀ9óõa»Ç!Ø
ÅÄ2¼aÀ9»ó-»ó-ºMÇ¾¿0ôMÅ¾È¿0¾È\À9Å¾ó¼Ä¼À9»ó-ÇÄ2¼¾¿0ùÄ2¿RÓN¾Æ9Æ\Ä¿*»ó,¼Ä2ºM½»ó»Å¹,ÓN¾Ç¾Wó»¼
Ä¼H½Ä2óÈÂ
r¾¼¼¾ÇRÇ!¾¿0ôMÆ9¼¿bÓ¾Ç!¾» ò ¼Ä2À9ó¾È£ÓÀ9¼a½ \»½¾ÅÀ9ÄóÆ9Ä2óÈ ¿0óÄ2À9Æ9¿2Â óöÄ2Æ9Ærõ=»ôMÇ*¿0¼aôMÈ\Ø
À9¾È¬¿0¾ û ¼À9»ó¿OÄÈ\À9¿0¼À9ó û ¼ÕÇ!ÄÈ\À9¾óH¼ÓÄ¿GºMÇ¾¿0¾ó¼ÂE¸»ÓN¾úH¾ÇùÄ2¿W¼a½H¾o¿0ÄÅºMÆ9¾¿GÓN¾Ç!¾
+
5è
`ç
©

ö
§
+
¨
¦
+
+
ìë
ç
ô
Ðç
2Q
/j
Y
ú^ú
0\ HV
V H
V
a
) 2* ~ 9_ ÿP V (
ôðí/ò înþ&ìþ&øõ
Zþ&ï ½öì
ö öì
þ&îHí=ó
ï öï]öÿ
ï ö²ò^í=õ¡öJþ
\ï ö
*í
r
a )
ðînþ&ìÿ¬öìïí/ó«í=ìôïöÿ
Zî9í/ôðöìï\þ
Zî9ð /öÿ
4í {ö
\k-lm Wn on \pSq rn
sX&%1Ä+t
þ&î9í/ó
öî9îHðôöôï öð"ì
WY^X
+t
Ä
[uAt
) a
ZîHí=ô«ð"öìïõkòhþ&øóô®ðìïöî ]öî9ö þ&î
øöìòhökþ
a ?)
í=óóZþ&ï öî
qí=ò^ïþ&îHõ1í=õ
í=õ
I6J
I
Ñ
K
>L¬Ü×)
ÛJØ)Ê
Õ{ÝË
(
)
H
9 L L
$% fW <a> "NM
U
S) 0
0 I)
)
#
a ra
2M 9 5 8 6 $ < f < 5< < 2 6 6 f >
; ?Td %-V
) o
HP
O
(D 0 )
L
9 W W)
9_
) - r a
9
L = WM ( * 0 9 a , W 9V 9
)
a ) \P/
W W 0
9 0
! / 9 a ö) ! 9
97
a
O
a )/ J
M)
)
0
a
9 0N
7 9
9 V 2 (D a *N ~
d V o" V M H
J 9V
?) a N
9 (bD , a
W
I
9U E
\ (UD %)a)
)
0
o %)a)
B H

+
) %)a)
a
(
)
)d a W'
)
S
0
2
0N :2!# 6 7 >> > 6 fW$% 8
! W 0
9 0 G a 9 a
9
5 "": 5 "
2M 9 a W W
( V a r 0 V
b
RaV
H
) 9_ H
"
H a c
(
) a 2c 0
2
D 0
H)
\ L
L 2 ;a¢ ( WV
)
)
V
9 \ O
(
a * 2 9
D
, \) 0 M H )
O 9_
V 9V E
H 2
( ¢ L
NP/ Q (
1
%
ë
ìö
ô«öïöîHÿ¬ðìð"õ¡ï]ðò¿í/ó {þ&î9ðï ÿ
ðõ
Zí=õ¡öô¯þ&ì5ï ö
øÿ
í¯òhþ&ÿ
í/ïï]öî9ì
öô
ö¯ï]í=õ Fþ
þ
Zìþ
Ç
5ë
îHðï ÿ
ï
,í=ïóöí/õ¡ïí
ð
{öï öî
1í¯óþ&ì
í=õõ þ
ìöÿ
þ
ðÿ¬í/ïöó
þ
î9þ
*ë
ò^þ&ìô«ð"ï]ðþ&ì§ðõºðÿ
ï ö
¯í/õ
ë
þ&îHïí/ìï /í/õºï ö
ï ö
{öïºí=ìFøìö Zøð {þ&ò^í=óînöõ¡øóï
5ë
õ¡þ
Zî9í/ôðöìïÿ¬øõ¡ï
qînþ&ÿ
ï ö
öî9öyøõ¡öôïþ
í§õ¡ðÿ
ZöìöîHí=ï]ö
öî qþ&î9ÿí=ìòhöJþ
Zþ&ï
ó"ö
Zøï¿í
øìô«înöôõ¿þ
5ë
{öî9öô
ï]öî9ì
1ï öóþ
í/ìô¼ïþí
þ
5ë
înþ&ò^öõ¡õ¡öõ
ï]í=ÿðìí/ïðþ&ì®í=ìô
øõ
ô«öí=ó
î9öòhðõ¡ö
ð"ï ï ö
þ
înþ
Óþ
óðì
í=ìô
ÿí
înþ&ò^öõ¡õ¡öõ5ðì
þ
þ
Zöïºï ðõînöù
Zöòhþ&ìõ¡ïî9øòhï]öô
]í/ìô
Zðòhí=ó\óðïöîHí=ï]øînöþ
öî9öðì
]öî9öìïïöõ¡ï\ò^í=õ¡öõ1ï]þí/õ¡õ¡öõ¡õ¿ï ö
\ôöï]öî9ÿðìðõ¡ï]ð"òÅõ¡öîHð"í/ïðþ&ì
ðò
øÿ
Zòhþ&ìù
í/ïùðO
öô
í=õ¯ïþ(ïî (ï]þ½ò^í=óòhøóí/ïöô«öìõ¡ðïðöõ
ö {öî Zðï
í=õJõ þ
øöìòhðì
îHí=ïö
(ï ö
ì?ï í=ï«õ¡ö öî9í/ó
]þ&õ¡õ¡ðóð =í=ï]ðþ&ì
òhþ&ìù
ZöìöîHí=ï]ðþ&ì(óöì
Zï
øóí/ïðþ&ì§ôöìõ¡ðïðöõ1þ&ìïþõ öòhðöõ¿í Zøìôí=ìòhöõ
ö
öî9ö*ïþ²øõ¡ö
î9þ
Zí {ð"óðõ¡ïðò
Oô«öìõ¡ðïðöõí=înöìö {öî4í=ò^òhöõ¡õ¡ð Zóö ð"ìõ¡ïöí/ô
ô
qõ ÿ¬í
Zìð =öJí/ìô¬ð"ì
þ&ï ôöï]öî9ÿðìðõ¡ï]ð"ò4í/ìô
ðì
?þ
ºô«öìõ¡ðï ?þ&ìïþ
{þ&ó öyï ö²ÿí=ðì
înþ
úhú
înþ&ò^öõ¡õ¡öõ*ï í=ïðì
Zí Zðó"ðõ¡ï]ð"òÅÿþ&ôöóõ
ï]öî
>
nWZn
ðì
¯ö
í Zöõ¡ðí=ì
í/ôFïþ
{í Zðóðï ¾ôðõ¡ï]î9ð Zøï]ð"þ&ìõ
òhþ&ìõ¡ïî9øòhïºôöìõ¡ðï
96
ðõ
]öî9öìï*ÿþ&ôöóðìï]înþ&ôøò^öô
{õ¡öôðÿöìï]í=ïðþ&ì
qöînöìòhöí Zþ&øï/ô«öìõ¡ðïðöõ
{í/ó"øöõyþ
õ¡ï]øôðöôñîHõ¡ï ïþ¾î9öòhþ
ô«í=ìòhö
ï öí=ìí=ó Zõ¡ðõ
þ&óøÿ¬ö5õ¡í/ÿ
ï öÿ
ïþÿ¬í Zö*í=ìðì
]öî9öìò^ö
ðì
!p 3
A
Zöî5þ
{öîHó"í
Zí=õ¡öôþ&ìõ öò^ð"öõÅí {øìôí/ìò^öõ
?õ¡öîHðí=ï]ð"þ&ìïþï öÿ
î9ö ¯þ&î Zðì
ï]þÿöìïðþ&ìõ¡þ&ÿöyþ
ðì
ïþ
øóí=ïðþ&ìôöìõ¡ð"ï]ðöõ {ìööô?ìþ&ïfìöò^öõ¡õ¡í=îHð"ó §ô«ð"õ óí í
ó §ï ö
õ¡ï]þ&ò í=õ¡ï]ð"ò
Zðï1ô«ð
í/ô
/í=ìô§ïîHí=ôðï]ð"þ&ìí=ó&ÿöï þ&ôõºþ
Zðòhí/ó"ó ®ìö /ïJõ¡ï]ö
A
Zóöÿ
öî9óí
þ
ZîHí=ô«ð"öìï*í=ìí=ó Zõ¡ðõ
ÿ¬þ&ôöó
ï þ&øõ¡í=ìôõ¿ô«ð
ë5õÅï ökôöïöîHÿ¬ðìðõ¡ïðòJõ¡öî9ðí/ïðþ&ìðõ
ï]î9í/î ï]þï ö
qí=ìô
Zöyòhþ
]öî9öìïÿþ&ôöóõ²ôðõ¡ò^øõ¡õ¡öôFðìöò^þ&óþ
óí/õ¡ï1ï þFô«öòhí=ô«öõ í=ìô
ºí=ïÅóöí=õ¡ï
ñòhðöìï¿ìøÿ
î9þ
¯þô«ð
öô¼ï]þ&ù
î9þ
]í/î 4õ¡ð Zìðñòhí=ìïó
ZöìöîHí=ï]þ&î
fñî9õ¡ï
qôöïî9öìôöô¼òhþ&îHînöõ þ&ìôöìò^ö¾í=ìí=ó Zõ¡ðõ
õ¡øóï {í¾÷"înöí/ó"ðõ¡ï]ð"ò^üZòhþ&öìþ&òhóðìö
ZîHí=ÿÿ¬öô
n
õ¡þ&ó {öîí/ó Zþ&ù
þ&õ¡ökìð"ò öõ4õ¡ð Zìðñòhí=ìïó þ
þ&óö
ï
]ï]öì
]þ&îHÿí=óð =öôí=õ5í/ì½ðìõ¡ïí=ìòhö
õðõôðõ¡ïðìò^ï *í/ìô3õ¡ø
ðï ï ökí=ìí=ó Zõ¡ðõ
Zö¾ò^ó"øÿ
5øí=ôîHí=ï]ðòkë5õ¡õ¡ð Zìÿöìï
øóí=î5þ&înô«ð"ìí=ï]ðþ&ì®í=ó Zþ&îHð"ï ÿ
öì®øìð"ÿþ&ôí/ó"ðï ½þ
õ öò^ðöõ¿ðõÅð"ìòhóøôöô
ZîHí=ô«ð"öìï,í=î9öºþ
øóí=ï]ð"þ&ì?ô«öìõ¡ðï ¬ïöìô¼ï]þ
Zóöÿ
)Ç
î9öõ¡öìï]öô
õ¡þ¯ï í=ïï öòhþ&öìþ&òhóðìöò^þ&ìõ¡ï]ð"ï]øïöõ
ðî9ðò^í=óó ®ï í=ï²õ¡öîHðí=ïðþ&ì3øõ¡ð"ì
5[Ù
í=õ
qøìòhïðþ&ìõþ&ì5ï ö
{î9í/ôðöìïºí/ìí/ó Zõ¡ðõ
Zðìí/ïþ&îHðí=ó
þ&øï öî qþ&î9ÿõyï í/ïfþ
ðì®ï ö¬òhí=õ¡öõ
înþ
{í=óøöõJþ
Åðìô«ð"î9öòhï
¯ì½òhþ&ÿ
öî í õ¾ï öÿþ&õ¡ï
õï]þ
ZîHí=ô«ð"öìïí=ìí=ó Zõ¡ðõ
]í/òhïï í=ï&ï ö1õ öò^ðöõ«înöõ þ&ìõ¡ö
øìðÿ¬þ&ô«í=ó
í=ò^ï
qþ&îOðìôðînöò^ï
í=ôï]þ
Zö
øöìòhöí Zøìù
öînö²ò^þ&ìõ¡ï]înøòhï]öô¬ðì
í ù
>
C=6
Ø>
2.
Sj
\5 > $ 5 $ 6 "U
2 "# 5< $7W:2 > $ < $% >
ì
í ïöî
ï]þôöîHð {ö²ï ö
>
ï öînöõ¡øóïþ
;Q6
¯öï]øî9ìöô
ï ö
ºï ö
Zìþ
õ \ð"ìï ö
õ¡í/ÿ
óðì
e
a T di'i
ï]ð"òõ¡öî9ðí=ï]ðþ&ì
5ë
õ¡þ&óøïðþ&ì
fð
ö
I
Zï 5þ
í
c
GT Tj
4í=îHóþ
Zöìöî9í/ïðþ&ì
g
Ri
ZöìöîHí=ï]þ&î
ï öõ¡öî9ðí/ïðþ&ì
ë5óï þ&ø
a
ÑÓÒ
ï]þ
õ¡ð"ô«ökô«þ
]í/õ
ú
]í/îJí=õï öí=øï þ&î
{öó"ðö öô(ï]þ
¯ðï þ&înôðìí=ïðþ&ì
û
ïþînöí/ó"ð /öOí¿õ¡ïþ&ò í/õ¡ù
í Zöõ¡ðí=ìFöõ¡ï]ðÿ¬í/ïöõþ
{öï ö
înþ
óðöô§ðìînöòhöìï
bL×LÕ{Ý
1ôöìõ¡ðïðöõ
ö
ZöìöîHí=ïþ&îêü î9í/ï öîï í=ì¯íJôðînöò^ï
öî
í=óöþ
{í/î9ðí/ìò^öÅþ
qþ&õ¡õ¡ðó"ð /í=ïðþ&ì
í=ìôí/õ¡õ¡þ&òhðí=ï]öô¾øìòhöîHïí=ðìïðöõ
ZöJøõ¡öô
þ&ï öõ¡öõ
¯ì
ôöõ¡ò^î9ð Zöõ
í=îHí=ÿöïöîHõí=õ
Zí=õ¡öô¾þ&ìö Zøí/ïðþ&ì
Zí/õ¡öôþ&ì
ØÕ{ÝJÚO×Ø)Ê#þx¾Õ
ë5õð"ìôðòhí/ïöô(ðì
)>
ìøÿ
/L.L.L
{öîÅþ
ðìôð {ðôøí=ó
ðì
í ï]öî
þ
í ï]þ
qöòhþ&óþ
înöõ¡öìï*ï öî9öõ¡øó"ï]õ ï ö
Zðòhí/ó,ó"ðï]öî9í/ïøînö
Õ{ÝËOÝJÛJÕ{Ú
Ò
í=ðîHõ«í=ìô
õ¡öõ
R6 !C
Zöî¿þ
]þ&î*ÿöînö
«õ¡í=ÿ
Ç
õ¡í=ÿ
Ï
óöõ
,ðï
,òhí/ìôðôí/ïö
ö
Zú Ï û =û
ðò
,ðìô«ð ðôøí=ó ò^þ&î9î9öõ þ&ìô«ù
þ&øóô
ì
qöî9îHðì
í/øïöòhþ&óþ
í=î9ôïí/õ
í=õ
{înþ&ø
ÿøõ¡ï \í=øï]þ&ÿ¬í/ïðòhí/óó
öò^þ&ó"þ
{ð"ò^í=ó
þ
{öí/ô
í=õ
înþ&ôøò^öÅí
]î9þ&ÿ
ºþ&ìó ï þ&õ¡ö
í=ï]ïöîHì¼ò^í=ì
?í/ìô
qøî9ï öîOðì
î9þ
Zï
{ÿ¬þ&î9ö
qí=ò^ð"öõ
Zøìò §þ
{ö
þ
Zï öðîþ
ö qøóó
ïðÿíJþ&ì¾ï ö
&í¾õ¡ï]î9í/ð
ï ]þ&î9ù
{øï{ìþ&ïìöòhöõ¡õ¡í/î9ðó
õ öò^ðöõ*í=òhò^þ&înôðì
¾ïþï öð"î
]þ&î4ôð
Jþ&ìö
½õ öò^ðöõ
øõ
Zþ&þ&ô
Zð {öõ¡ø
ò^í=ìôðôí=ï]öõ
Zøöõ¡ï]ð"þ&ìînöÿí=ðìõ
Zù
yðìí {øìôí/ìò^öù
þ
ïþk÷"ñó"ï]öîþ&øïü
þ&þ&ó
4í=îHó"þ
{öìöîHí=ï]öô¯ô«öìõ¡ðïðöõ*õ þ&øóô
Oïþ?ö Zøí/óð /öï öòhþ&ìïîHð Zøïðþ&ìõ
ò^þ&ÿ
{öô
]ñòhðöìïó
qþ&îkõ¡þ&øìô
]î9þ&ÿ
í Zøìôí=ìï
þ&ìöìïðìïî9þ&ôøòhöô
ö¯î9í/î9ðï
ï ö1í/ìõ öî\õ þ&øó"ô
î9þ
þ&ð"õ¡õ¡þ&ìðí=ì
þ&î²í Zøìôí=ìòhöþ
Zö¯4
Zí Zó
1íõ öòhðöõ
\ïþyìþ&îHÿ¬í/ó"ð /í=ïðþ&ì
öõ¡ïð Zí=ï]ðþ&ìð"õ1òhöîHïí=ðìó ¾ìööô«öô
Zî9í/ÿ
òhþ&ôöí=óõ¡þÿí {öõyøõ
þ&øï{ï ö4õ¡í=ÿ
qöînöìï«õ¡í/ÿ
ZöìöîHí=ï]ðþ&ì
qþ&î*ö {öî õ öò^ð"öõ
í/ÿ¬þ&ì
þ
óöõ²í/õ
qþ&õ¡õ¡ðó"ð /í=ïðþ&ì¯ò í=ìòhö
þ
öì
öì§ï öyîHí=ìôþ&ÿ
í/òhïó ï ö4õ¡í=ÿö¿ï î9þ&ø
]öî9öìï
ö¿þ
ï öyòhí=ìôðôí/ïö
qþ&õ¡õ¡ðó"ð /í=ïðþ&ìFðõînöÿþ
óí {õìþkînþ&óöºí/ì
5ï ö
þ&óö
Zí=õ¡öôõ¡öî9ðí=ï]ðþ&ìkï ö1÷oìþ&ðõ¡öüþ&òhòhøîHîHð"ì
Zö ]þ&î9öõ¡öî9ðí=ï]ðþ&ì
í/ìô¬î9í/înö²õ öò^ð"öõ¿ìþ
ö
ï ö
þ&ï öõ¡öõï í/ï
Zö
öï öîOï öË$þ&ìï]ö
Zøöõ¡ï]ð"þ&ìí/ó"õ¡þ5í/î9ðõ¡öõ
Zöìþ&î9ÿí=óð =öô
Zøï
þ&ï öù
öî ðõ¡öô¬ò^ó"í/õ¡õ¡ðñòhí=ï]ðþ&ì
þ&õ¡ðïðþ&ì¾þ
þ&øóôFï öì
Zþ&þ&ôòhóí=õ¡õ¡ðñòhí/ïðþ&ìþ
í ï]öî
þ&ï öõ¡öõ¡ü
óðì
øìõ¡ø
õ¡ðÿðó"í/îþ&înôöîHõð"ìïþòhóí=õ¡õ¡öõºò^þ&øóô
ðï 5ï öºô«öìõ¡ðï
ï ö²÷"ìþ&ð"õ
õ¡í/ÿ
qøõ¡ðì
öînö
=û
{ðõ¡í {ó"öyïþòhóí=õ¡õ¡ð
þ&ó öôõ öò^ðöõ
Zí/õ¡öôþ&ìö¿õ þ&øóôìþ&ï&þ&ò^òhøîí/ïí/óó
ë
ú
þ&ï öõ¡öõ¿ðìõ¡ï]öí=ô§ï ö²þ&óô¬þ&ìöõ
&ï öÅðì
í=ò^ïü fõ¡ÿþ&þ&ï ®ò^þ&öìþ&ò^ó"ðìö
þ&ï öõ¡öõ
Ï ú
ë5õ¯ÿ¬öìïðþ&ìöôðì
÷"òhþ&ÿ
/û
ðï §õ¡ðÿðó"í/îºþ&înô«öî
þ
ðì
þ&ï öõ¡öõ«ðõföìþ&îHÿ¬þ&øõ
/û
ZîHí=ô«ð"öìï &ï öðî¿ïþ&óöî9í/ìò^öõ &í=ìô?õ Zö õ
óöì
Zð
ð"ï
þ&înô«öî9õºò^þ&ÿ¬öþ&øï ,í=ìôò^í=óòhøóí/ïö²ï öó"ð Zöóð þ&þ&ô
í/ìô§øõ¡öyï öõ¡ö²òhóí=õ¡õ¡öõ*í/õºìö
ðì
ZöìöîHí=ï]öíînöí/óó
]î9ö Zøöìò^ðöõ
þ&î\înöóí/ïð {öºóð Zöóð þ&þ&ô«õfþ
Zöî\þ
óöõ Zð
þ&ï öõ¡öõÅð"ìïþò^ó"í/õ¡õ¡öõ
ôð
ï qþ&î ¯í/înô½ïþ
óö¾þ&î9ôöî òhþ&øìïfï ö
þ&ï öõ¡öõ
öî í õ ^í=õï ö¿ìøÿ
Zøðïö¯õ¡ïîHí=ð
ö ]øóó ¯înö öí=ï]ðì
þ&ï öõ¡ðõ
ðõ4ï ö5ìøÿ
L.L.L C=6 \ðï*ðõ
þ&ï öõ¡öõyí Zþ&øï«õ¡í/ÿ
îHí=ï]ð"þ&õfþ
+uV!\
-PS 2 ` +
9" ) % 9
)" a O)
* a, 9V a ) 9 H"
a 9 9
)H" a U
c
9V 9 9
) %V
0
O" (
2 0 a )
?" ;8dHefhgN d
) 2T ( ( 2. .2Q `2` @ . @ ` 1K1 ` } 1KQ KQ @K@2@2@2@K@@ H" a
< _M < :2 5 #iMR$ < +< ! $ 6 S)
9)= a bN )
2@ 0a M \V 2
8 r "f 6kj
" I U H M !V
H=
(
H" a
a
H) H
" ) a HV %V 0 ;=
) a a
0 0 0r
c " ) 9
% a)
0" ? M H )
oa
9
%O
~
) 0
(
P/ 2 ` % a H a R 9V M)
9
%
o
E
b)
¬H
a 0 M a
~
a
2
(D G
0
r a
0" ) a
/ (

N a RP W
0
6 f 5 #$ > U:2! > $ < $ >lj
9_ )
H %_ 9
G) 0
+N "
H £) 9_
V (*D ) 0
( 0 0 N 2 9~ >
2
H
9_ (
) a HV 9
9
D O 2 +) O) V
9 a M" (
N 0
9)a) ;) 9))
+ (
97 0 ~
) 9_
S]« © « ª a'
S] © ª ) Bn m
§ ® 2 ) %ö
9
( ! 0) %_
) V 0
7
EV ! 9
9
9
0 0?
Z) 7
0
H O)
9))
) (ED 0) 9_
7 E
O«h©
«ª 0 ø
%V
3 $ #%$ 7: 657< $% > 6
< > >
6
ó"öì
;T g
í/øï þ&îOìö {öîOõ¡í ðïí
d4
öìõ¡øò
5ø
Zøí=ï]ð"þ&ì
;T5T c
ËTj
Zðòhí=ó,þ&î9ôðìí/ïðþ&ì
õ¡öîHð"í/ïðþ&ìõ¡öî {öôí/õOíy÷oÿøóïð óö
I6J
í ïöî
Ù
øóí/ïðþ&ì§ôöìõ¡ðï
T
í Zöõ¡ðí=ì?ÿþ&ôöó
í/ó"öþ&öò^þ&óþ
ü?öºøõ¡öôíq$þ&ìï]ö
Zí {ð"óðõ¡ïðò²ÿþ&ôöóþ
þ
{þ&óøÿö êõ¡öôðÿ¬öìïí/ïðþ&ì¾îHí=ïö*í/ìô¯ï ö1øìòhöîHïí/ðìï yí {þ&øïðï
a
698 $% 85 ## < 8 < 6
î9þ
í Zöõ¡ðí/ìöõ¡ïðÿ¬í/ïö²þ
ò í/ìò^ö hòhþ&ìïí/ÿ¬ðìí=ï]ð"þ&ì5îHðõ
O
pSn n
WYZV!\sY^Û
P/ 2 I1W
b 2
)rP/ 2 IQ M
9V a ~¢ 2
)M ( r
c1 ( `
9
(6U ItWVYXNZ"w \x\[\wV =t x *)
a
) O¢ a
0 a R
N

?V
)
HbV
a 2 a7) 9_
7 0" a ) H
(
c a
wx+t ](^_Z"w Zw =x rtaw!x.^ ` tW] Z \x Z rx O
LP R
d

1 ( @
9_
7
(D H ( ( Z
ö¢ )
W
V
9 S" a ?
% ( M"Z V a N R ,
0 (
V 2 2M
= Ç
< ;4
rkRQTS2m
sX&%1Ä+t
Y
ú^ú
öî í õ
Zøï4í=óõ¡þ
qînöö
óð"ì
öóó
í/ìô
í/ìô
]î9þ&ÿ
{öö ð"ì
óð"ì
ðÿðó"í/î9ó
õ öò^ð"öõ
{þ&óøÿ¬ö¯ö ù
Jÿí
]î9ööó
í/ìô
Zí=ìô
Zööõ¡ï]ðÿ¬í/ïöôð"ìôö öìôöìïó
qþ&õ¡õ¡ðóð /í=ï]ð"þ&ìò í/ìò^öyò^í=ì
{í/î õ¡ð Zìðñò^í=ìïó ìþ&ïþ&ìó
õ öò^ðöõ¾í=ÿþ&ì
í=îHí=ÿöïöîHõ
Zö4õ öòhðñöô
í=îHí=ÿöïöîHõJöõ¡ïðÿí=ïù
þ&ï]öìï]ð"í/ó/ï]þòhþ&ìïí=ÿðìí/ïö
qþ&îí¬ò þ&õ¡öì
qþ&õ¡õ¡ðó"ð /í=ïðþ&ì®ò í/ìò^ö
õ¡í=ÿ
,öôðÿöìï]í=ï]ð"þ&ìî9í/ïöÅòhþ&øóô
Oí=ìô
(õ¡í=ÿ
óöõ
õ þ&øó"ô
qînþ&ÿ
ôð
qöînöìï
Zöò^þ&ìò^öð öô
2m m
QoS
rqYr
.U X!YqpË\sV´]
n
Üt('¤tG\FÄ
ÛGt
ú^ú
0
RV
0 a (
M H ))
(
: g5 ;& 5 g :;& 5 f g : < & ?
0 +
( 9
!
6 U$ 6 f 5< $% 5 7 <
7 ) a V
) 0 r
9_
)
) (KD *V R
) )
2O
r >5 f 2#% >
) 9 ( S) a
)
0
a )a) 9V
) V ! 2 H ( (
a 7
)
2 9V Z" a
)
!V ?a H 9 0 c \ ( a 0

2M 7 B " )
(J a 5 ": > 2!$ > "!::
0 0 0 % %)
0 MH7
)MV * )
9 a b
S *
)
a \¢ 2
9
\ %V
0 ,
(
V
) D
2V ) a ~¢ 2 ~ M )d
b" > "#: ~
O 2V
a
T
V aH
O
)
9V ) G
G
E 0 "
(D ) 0 (
V ) \
) J ) 9 %V
- ¬ 2M 2 ( 9
) 0
0 N N a 9 J
(
) a 9)
a
Z
0
2
9V Z)
V
ö
9c"ts 7: 5 #%I: 5<=5> <=>r>< $%##
fW$ >> $% 8
H HV
)
0 c)
(

í/õ²ÿí=ïîHðòhöõ²í/ìô¼ìþ&ïí=õ
C=6
ðï ðì
öòhï]þ&î9õ í=õ²ï ö ¬í=î9ö5ìþ
C=6
=í/ìô
ë5ìðìòhî9öí=õ¡öô§ò^í=înöJõ þ&øóô
þ
{öö ö í=òhïïîHí=ò þ
&ï ö
\ÿöí=õ¡øî9öÿ¬öìïþ
ðìï ð"õõ¡ï]ö þ
þ
í/óõ¡þ
{ö
{þ&óøÿö¿þ
\ðï
ö
Zí/ìí/ó Zõ¡ðõ
î9þ
}Ç
í=ðô¬ïþõ¡í/ÿ
&õ¡í/ÿ
{í/ó"øí Zóö
ìï ö
óöõ
ö öî ¬õ¡í=ÿ
þ
ó"öïí {öì
ð
ö
QÇ
óðì
þ&î9ï]ðþ&ìþ
{ö
þ&ðìïþ
{ðö
ðì
ï]þ&ïí=óï ðò Zìöõ¡õþ
]þ&îHïøìí=ï]öó
ÿí=ï]ðþ&ìòhþ&ìïöìï {õ¡þï í/ï
ö öìþ&ÿ¬ðïï]öôðìóí=õ¡ï
]þ&îHÿ¬í/ïðþ&ìÿí
/ 96
þ&ï öõ¡öõ
ö {öî
ZíJõ¡öôðÿ¬öìïþ&óþ
ï ö
í Zöõ¡ðí/ì
ÿöìïfþ
ïþ&ôí
Zþ&þ&ô½òhîHð"ï]öî9ðþ&ìþ
f÷"înöóí/ïð {öòhþ&ÿ
înöò^ðí Zóö
õ öò^ðöõfôöìõ¡ðïðöõ«õ þ&øóô
\ï ö²øìð ]þ&îHÿ
ë
{þ&þ&ô
þ&ìö /ïþ
înþ&ÿ
ï ðõ
þ&þ&îºðì§ðì
¯þ&îHóôü&ôí/ïí
I6J
@u#Ê#
í=õ
Zöìøÿ
ë5óõ¡þ
Oö
ó"öÿöìïöô
Zöî*þ
þ&õ¡õ¡ðù
í=ò^ïìöõ¡õ²þ
Oï ö5òhþ&öìþ&ù
{ö5ð"ìõ öòhï]öô
¯ïí=õ
Oï ö¾ôöõ¡ò^î9ð ï]ð öþ&ìö
þ&ìöìï]ðí=óôðõ¡ïîHð Zøïðþ&ìþ
ð"ï ¾ï ö1ÿøóïð óö
1þ
ï]ð"ÿí=ó
õfÿ¬þ&ô«öó=ðìõ¡ï]öí=ô
]î9þ&ÿÃí/ìöì
õ öòhðöõJí Zøìô«í=ìòhöõ4ðì
{ðî9þ&ìÿöìïOòhþ&ìïî9þ&óó"öô
qí=ò^ïþ&îfõ¡ïðóóZõ þ&øóô
ZöJóþ&þ
Zöô
qí=óÿþ&õ¡ïfðìù
M
înöôþ&ÿðìí/ìï]ó
qþ&îïþ¾ï]öõ¡ï{ï ö²ÿöï þ&ôþ&ìí
vÝJßáÝËÊ¬×)
ÜÝË
ÔÖÚ
D R ) E? (@w x* P/ ( ? ( V
"
/P ( ) a b
0 9 ) a b
^? ( 2V
2P/ ( ? (
w
9 ( ( ? (
*?V
2P/ ( w
W M (D G *
MM ( ) /V a 0 ) )MF "
)d
) *P/_ 7
M 72
o ( ? ( 2V ¢ 2" 2PS (
ö5í/øï þ&î¿ðõ
,ò
qþ&îºï ö
ðìô«î9ðò
,ø* ðï
í ø

ô«öîOï öí=øõ ðòhöõ1þ
*ö ø
{ó"ðò
sî
ZîHí=ï]ö ]øóïþ
Zðìô?óöí/ôöî9õ ð þ
ÌÓó"í/ôðó ÷kî
öí=ôöô
,ò
qþ&î
ï ö
L.L.L
]þ&î9ù
ðïï ök÷oò^þ&î9î9öòhï]ü&þ&ìö
Zðìõ¡ï]öí=ô¼þ
Zðòhí/óôí=ï]í¾òhþ&ìïí/ðìðì
õ¡þ&øìô÷oî9öí=ó
Ñ
Zö1ðÿ
Zóí Zöõ²ô«öî9ð {öô
{ó"öyöì
ë5óõ¡þ
¿ðìòhóøôöô
Zöïï]öîfõ¡ðÿøó"í/ïö²ï öyînöí=óòhí/õ¡öõ
í=óöþ&ìïþ&óþ
ï]í=ò^ï Oí=õ¡õ¡öÿ
öînö
í/ïïöîHìõÅí/înöïþ
{ìí/ÿ¬ðòhí/ó\ÿ¬þ&ôöóþ
Zöí
ø
í öyî9öí=ó&ò í=ìòhökïþ
]þ&îHïí ZóöJí=ìôïðÿö²òhþ&ìõ¡øÿð"ì
Oíô
¯þ&øóô
½þ
{ð öõ¡þ&øìô?înöõ¡øóï]õ í/ìô
î9þ&òhöôøî9öJð"õ¿ï í=ïí
Zöìöî9í/ïöôïþ
ö5õ¡ïðóóÿð"õ¡õyí
öó"þ
{ð"þ&óþ
òhí/õ¡öõ
Zö
ðõºðõºí=ìøìòhþ&ÿ
ö
¬ï ö
Zí õºðìõ¡öôðù
=í/ìôînö î9þ&ôøòhï]ð"þ&ì
ìþ&ï
/L.L.L
Zðõ¡ïõ þ&øóô
Zö4ö /ò^ó"øô«öô
Oí/ìô
înöõ¡öìïöô¬òhí=õ¡öõ¡ïøôðöõ
í/ïïöîHìü Zõ¡þï í=ïí/ó"ó\ò^í=ìôðôí=ï]ökò^þ&öìþ&ò^óð"ìö
ö {ö
íkõ¡ðì
Zî9í
>
!
{ö²óþ&õ¡ïí/óînöí=ô
]öò^ïð {ö5õ¡öôðÿöìï]í=ï]ð"þ&ì¼î9í/ïöü
þ&ìþ&ÿ
í {öõ¡ð"í/ìí=ìí=ó Zõ¡ðõ4ôðô
]ö
ö²ÿí=ðìò^í {öí/ï{þ
{ó"ö
,í=óóZï ö
qþ&î9ï
íõ¡öôðÿöìïóí ZöîÅôð {ðôöô
í/ðô®ÿ¬þ&î9öí=ïï]öìï]ðþ&ì½ï]þ?ïí
,øì
¬ö
ï\ðõ1í Zõ¡þ&óøïöó ìöòhöõ¡õ¡í/î ïþ
qøïøî9ö ^ï öÅí=õ¡õ¡ðõ¡ï]í=ìòhöÅþ
õ öò^ðöõ /öõ öò^ð"í/óó ¯ïþóð qöyõ¡ï]î9í/ïö Zðöõ ôöÿþ
øõ¡öô
{î9í/ÿ¬ÿðì
öóó í/õ«ïþkïî kïþyÿðìðÿð =öÅí=ì5öîHînþ&î°O
í=õ
Zþ&ï ìþ&ìõ¡öôðÿ¬öìïí/ïðþ&ìí=ó&í=ìôöînþ&õ¡ðþ&ìí=ó õ þ&øó"ô
ï öî9öõ þ&øóô
ò^óð"ìö
înþ
í/óó&ïðÿ¬öðìï]öî í=óõ1î9ö înöõ¡öìïöôðìï öyõ¡öôðÿöìï]í=î î9öòhþ&înô«õ
ÿöìïí=ï]ðþ&ì
þ
õ¡ÿí=óó
þ&øóôôþ
Zöï öînøóö í/õ²ï öînö¾ðõkíìööô¼ï]þ¬í/õ¡õ¡öõ¡õyï ö÷oö
õ¡øÿ
þ
ë
Zî9í/ÿ¬õ
+þ&ò
ðîHð
ï ö
sî
2
sî
í/înöó
í=îHí
{í/ó"øí Zóö5òhþ&ÿÿ¬öìïõ
Ç
ìõ¡ïðï]øïöyþ
Wþ&ò
Kî
köþ&óþ
í öó
sî bÇ
,ò &í/ìôÐkþ&ò
*ðï]ï
înþ=* öò^ï
ö
,ò
þ&î
ë5òhí/ôöÿ
þ&õ¡í
,ò
{í=ìÌÓþ&î9í/òhö
â«í/òhóí sÓþ&øõ¡í
í=îHð
í=õ
þ
Zõ¡í/ìöì
sî
,ò
x
&í/ìô
{ööìò^í=îHî9ðöôFþ&øïøìù
,òhðöìò^öõºþ
ï ö
=öò
C 96
ú^ú
}
Sj
Y
rkRQTS2m
sX&%1Ä+t
pSn n
WYZV!\sY^Û
+uV!\
?' ! {Y|+ ?
+ I*
y
z
^é
y
è
²å
æ{æ1ä 1ä æ
æ{æ1ä 1ä å

Zè
}~
abu2den-0.02.c
Generates posterior pdf for density from abundance.
Written by Peter Cejchan
Input (from stdin):
Output (to stdout):
Language: ISO C.
Depends on: GNU Scientific Library (GSL).
Written by: Peter Cejchan <[email protected]>
Compile: make -k
Tested on: Linux 2.2.10 / glibc 2.1.1 / gcc version 2.95.2 19991109
History:
version 0.01 (2000/02/17).
version 0.02 (2000/03/13): command-line parameter added.
License: GPL <http://www.gnu.org/copyleft/gpl.html>
__________________________________________________________________________*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <gsl_histogram.h>
#include <gsl_matrix.h>
#include <gsl_rng.h>
#include <gsl_sf_gamma.h>
/* #include "nrutil.h" */
#define PARFILE "abu2den.par"
#define PLOTFILE "plotfile.dat"
#define SEEDFILE "seeds"
gsl_rng *r; /* random number generator */
/* __________________________________________________________________________
d2a
__________________________________________________________________________*/
int d2a(
double Dp,
/* density (pure) */
úhú
`
ú/û
@
/j
Y
double
double
double
double
double
double
double
double
double
double
double
){
Dm,
V,
Sigma_v,
Rl,
Rh,
Cl,
Ch,
Ol,
Oh,
G,
Sigma_g
/*
/*
/*
/*
/*
/*
/*
/*
/*
/*
/*
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
[u
mean density for the species */
sample volume */
its std */
sedim. rate, lower... */
...upper limit */
fossiliz. chance, lower... */
...upper limit */
contaminat. intensity, lower... */
...upper limit */
length of a generation */
its std */
double gsl_ran_gaussian (const gsl_rng * R, double SIGMA);
double gsl_ran_flat (const gsl_rng * R, double A, double B);
unsigned int gsl_ran_poisson (const gsl_rng * R, double MU);
unsigned int gsl_ran_binomial (const gsl_rng * R, double P, unsigned int N);
double m, d;
int y, n;
/*
d= Dp + Dm*genuni(Ol, Oh)*gennor(V, Sigma_v)/(gennor(G, Sigma_g)*genuni(Rl, Rh)); */
d= (Dp + Dm*gsl_ran_flat (r,Ol,Oh))*(V+gsl_ran_gaussian (r,Sigma_v))/
((G+gsl_ran_gaussian (r,Sigma_g))*gsl_ran_flat (r,Rl,Rh));
m = gsl_ran_flat (r,Cl,Ch);
n = gsl_ran_poisson (r,d);
y = gsl_ran_binomial (r, m, n);
return(y);
}
/* __________________________________________________________________________
main
__________________________________________________________________________*/
int main(int argc, char *argv[]) {
gsl_histogram *h;
gsl_histogram_pdf *posterior;
double x, y, den, denmin, denmax, rnd;
unsigned long int seed = 1, bins=100,repeats = 1, iter=100000, i, abu;
FILE *plotfile, *seedfile, *parfile;
double gsl_ran_flat (const
int d2a(
double Dp,
double Dm,
double V,
double Sigma_v,
double Rl,
double Rh,
double Cl,
double Ch,
double Ol,
double Oh,
double G,
double Sigma_g
gsl_rng * R, double A, double B);
/*
/*
/*
/*
/*
/*
/*
/*
/*
/*
/*
sample volume */
its std */
...upper limit */
...upper limit */
...upper limit */
its std */
);
double
Dm,
V,
Sigma_v,
Rl,
Rh,
Cl,
Ch,
Ol,
Oh,
G,
/*
/*
/*
/*
/*
/*
/*
/*
/*
/*
sample volume */
its std */
...upper limit */
...upper limit */
...upper limit */
ú/û=ú
Sigma_g;
/* its std */
/* read in new seed */
if((seedfile = fopen(SEEDFILE,"r")) == NULL)
seed = 1;
else {
fscanf(seedfile, "%ld ", &seed);
fclose(seedfile);
}
/*do the RNG initialization*/
r = gsl_rng_alloc (gsl_rng_uni32);
gsl_rng_set (r, seed);
/* read in params */
if((parfile = fopen(PARFILE,"r")) ==
fprintf(stderr, "Model params file
return(1);
}
fscanf(parfile, "%lg %lg %lg %lg %lg %lg
&V, &Sigma_v, &Rl, &Rh, &Cl, &Ch, &Ol,
&Dm, &denmin, &denmax, &bins, &iter);
fclose(parfile);
NULL){
is missing. Exit.\n");
%lg %lg %lg %lg %lg %lg %lg %ld %ld",
&Oh, &G, &Sigma_g,
/* read-in the value of abu */
scanf ("%ld", &abu);
/* read-in the number of densities to be generated */
if (argc > 1)
repeats = atoi(argv[1]);
/* allocate histogram */
h = gsl_histogram_calloc_uniform (bins, denmin, denmax);
/* open plotfile */
if((plotfile = fopen(PLOTFILE,"w")) == NULL){
fprintf(stderr, "Cannot open output file. Exit.\n");
exit(1);
}
/* create likelihood x Jeffreys’ prior */
gsl_histogram_reset (h);
for (i = 0; i < iter; i++){
den = gsl_ran_flat (r,denmin, denmax);
y = d2a(den,Dm,V,Sigma_v,Rl,Rh,Cl,Ch,Ol,Oh,G,Sigma_g);
if (y==abu)
/* 1/den is the Jeffreys’ prior: is it done properly? */
gsl_histogram_accumulate (h, den, 1/den);
}
/* print out the histogram */
gsl_histogram_fprintf (plotfile, h, "%g", "%g") ;
fclose(plotfile);
/* create posterior pdf */
posterior = gsl_histogram_pdf_alloc (h);
/* sample it */
for (i = 0; i < repeats; i++){
rnd = gsl_rng_uniform_pos (r);
x = gsl_histogram_pdf_sample (posterior, rnd);
printf("%g ", x);
}
/* release memory */
gsl_histogram_free (h);
gsl_histogram_pdf_free (posterior);
gsl_rng_free (r);
/j
Y
ú/û=û
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
[u
/* etc... */
exit (0);
}
/* eof */
¡
M HMM*
y
æZæ1ä 1ä
²Õ
è
}~
adv-seeds.c
Advances seeds for random number generator and writes them to file.
compile: gcc adv-seeds.c -o adv-seeds -Wall
Written by P. Cejchan, 1999/09/23.
Compiled on Linux 2.2.10 / glibc 2.1.1 /
gcc version 2.95.1 19990809 (prerelease)
__________________________________________________________________________ */
#include <stdio.h>
#include <limits.h>
/* __________________________________________________________________________
main
__________________________________________________________________________
int main(void) {
long ij, kl, create = 0;
FILE *seedfile;
/* Read in old seeds */
if((seedfile = fopen(SEEDFILE,"r")) == NULL){
create = 1;
}
if(!create){
fscanf(seedfile, "%ld%ld", &ij, &kl);
fclose(seedfile);
}
else{
ij = 1;
kl = 0;
}
/* Create new seeds */
kl++;
if(kl >= LONG_MAX){
ij++;
kl = 1;
}
if(ij >= LONG_MAX){
ij = 1;
}
if((seedfile = fopen(SEEDFILE, "w")) == NULL) return(1);
fprintf(seedfile, "%ld %ld\n", ij, kl);
fflush(seedfile);
fclose(seedfile);
return(0);
}
/* eof */
y
æZæ1ä 1ä

* '
èÖ
^é
}~
ahisto-0.02.c
*/
ú/û Ï
Maps density onto abundance, and produces abundance histogram.
written by Peter Cejchan
Input (from stdin): density (double)
Output (to stdout): abundances (long)
Language: ISO C.
Depends on: Netlib routines from ranlib.c.
Compile: make -k
Tested on: Linux 2.2.10 /libc6 2.1.37/ gcc version 2.95.2 20000220
History:
version 0.01 (2000/03/17);
version 0.02 (2000/03/20) comman-line par;
__________________________________________________________________________*/
#include
#include
#include
#include
#include
#include
#include
<stdio.h>
<stdlib.h>
<math.h>
<gsl_histogram.h>
<gsl_matrix.h>
<gsl_rng.h>
<gsl_sf_gamma.h>
#define SEEDFILE "seed"
#define PARFILE "ahisto.par"
/* __________________________________________________________________________
main
__________________________________________________________________________
*/
gsl_histogram *h;
double
Dp,
/* species’ pure density */
Dm,
/* mean density for the species */
V,
/* sample volume */
Sigma_v,
/* its std */
Rl,
/* sedim. rate, lower... */
Rh,
/* ...upper limit */
Cl,
/* fossiliz. chance, lower... */
Ch,
Ol,
/* contaminat. intensity, lower... */
Oh,
G,
/* length of a generation */
Sigma_g,
/* its std */
m, d, abumin, abumax;
long y, seed, bins, iter, i, n;
int print = 0;
FILE *seedfile, *parfile, *plotfile;
/* read-in command-line arguments */
if (argc>1)
print = atoi(argv[1]);
2Q
/j
Y
ú/û
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
[u
if((parfile = fopen(PARFILE,"r")) == NULL){
fprintf(stderr, "Model params file is missing. Exit.\n");
return(1);
}
fscanf(parfile, "%lg %lg %lg %lg %lg %lg %lg %lg %lg %lg %lg %lg %lg %ld %ld",
&V, &Sigma_v, &Rl, &Rh, &Cl, &Ch, &Ol, &Oh, &G, &Sigma_g,
&Dm, &abumin, &abumax, &bins, &iter);
fclose(parfile);
seed = 0.0;
else {
fclose(seedfile);
}
/* read-in the value of density */
scanf ("%lg", &Dp);
h = gsl_histogram_calloc_uniform (bins, abumin, abumax);
/* open plotfile */
exit(1);
}
/* proper simulation of observations starts here */
for (i=0; i<iter; i++) {
d= (Dp + Dm*gsl_ran_flat(r, Ol, Oh))*(V+gsl_ran_gaussian(r, Sigma_v))/
((G+gsl_ran_gaussian(r, Sigma_g))*gsl_ran_flat(r, Rl, Rh));
m = gsl_ran_flat(r, Cl, Ch);
n = gsl_ran_poisson(r, d);
y = gsl_ran_binomial(r, m, n);
/* y is abundance */
gsl_histogram_accumulate (h, y, 1);
if (print)
printf("%ld ", y);
}
gsl_histogram_fprintf (plotfile, h, "%g", "%g");
fclose(plotfile);
gsl_rng_free (r);
/* etc... */
exit (0);
}
/* eof */
y
æZæ1ä 1ä
è
I
å
é
}~_nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
am2dt-0.03.c
21
ú/û
Generates a tensor of densities (vector of density matrices) from
an abundance matrix
Input (from stdin): number of species (=rows), number of samples
(= columns), matrix of abundances (specieswise)
Output (to files): prescribed number of matrices (a tensor) consisting of:
number of species (=rows), number of samples
(= columns), matrix of densities (specieswise);
Language: ISO C.
Compile: make -k
Tested on: Linux 2.2.10 / libc6 2.1.3-7 / gcc version
2.95.2 20000220
History:
version 0.01 (2000/03/27).
version 0.02 (2000/04/18): Makefile rewritten for libgsl0 v. 0.5+-1.
version 0.03 (2000/05/29): Serious bugs in indexing corrected!
Example: ./am2dt 5 < gauss.dat
__________________________________________________________________________*/
#include
#include
#include
#include
#include
#include
#include
#define
#define
#define
#define
<stdio.h>
<stdlib.h>
<math.h>
<gsl_histogram.h>
<gsl_matrix.h>
<gsl_rng.h>
<gsl_sf_gamma.h>
SPECPARFILE "spec.par"
SAMPPARFILE "samp.par"
COMPARFILE "com.par"
SEEDFILE "seeds"
/* __________________________________________________________________________
d2a
__________________________________________________________________________*/
int d2a(
double
double
double
double
double
double
double
double
double
double
double
double
){
Dp,
Dm,
V,
Sigma_v,
Rl,
Rh,
Cl,
Ch,
Ol,
Oh,
G,
Sigma_g
/*
/*
/*
/*
/*
/*
/*
/*
/*
/*
/*
/*
density (pure) */
sample volume */
its std */
...upper limit */
...upper limit */
...upper limit */
its std */
double m, d;
int y, n;
2.
/j
Y
ú/û
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
[u
d= (Dp + Dm*gsl_ran_flat (r,Ol,Oh))*(V+gsl_ran_gaussian (r,Sigma_v))/((G+gsl_ran_gaussian (r,Sigma_
m = gsl_ran_flat (r,Cl,Ch);
n = gsl_ran_poisson (r,d);
y = gsl_ran_binomial (r, m, n);
return(y);
}
/* __________________________________________________________________________
main
__________________________________________________________________________*/
gsl_histogram *h = NULL;
gsl_histogram_pdf *posterior = NULL;
double x, den, denmin, denmax, rnd, z,coeff,
Dm = 0,
V = 0,
/* sample volume */
Sigma_v = 0,
/* its std */
Rl = 0,
Rh = 0,
R = 0,
/* mean */
Cl = 0,
Ch = 0,
C = 0,
/* mean */
Ol = 0,
Oh = 0,
G = 0,
Sigma_g = 0;
/* its std */
unsigned long int seed = 1, bins=100,repeats = 1, iter=10000, i, j=0, k, abu, y, spec, samp, free;
FILE *seedfile, *parfile;
double gsl_ran_flat (const
int d2a(
double Dp,
double Dm,
double V,
double Sigma_v,
double Rl,
double Rh,
double Cl,
double Ch,
double Ol,
double Oh,
double G,
double Sigma_g
gsl_rng * R, double A, double B);
/*
/*
/*
/*
/*
/*
/*
/*
/*
/*
/*
sample volume */
its std */
...upper limit */
...upper limit */
...upper limit */
its std */
);
gsl_vector
*v,
*sigma_v,
*rl,
*rh,
*cl,
*ch,
*ol,
*oh,
*g,
*sigma_g;
/*
/*
/*
/*
/*
/*
/*
/*
/*
/*
sample volume */
its std */
...upper limit */
...upper limit */
...upper limit */
its std */
gsl_matrix
*ab;
/* abundances */
seed = 1;
else {
fclose(seedfile);
}
ú/û
/* read-in the number of density matrices to be generated */
if (argc > 1)
repeats = atoi(argv[1]);
/* read-in number of species, number of samples */
scanf ("%ld%ld", &spec, &samp);
/* read-in the abundance matrix */
ab = gsl_matrix_calloc (spec, samp);
for (i = 0; i < spec; i++){
for (j = 0; j < samp; j++){
scanf ("%lg", &z);
gsl_matrix_set (ab, i, j, z);
}
}
/* read-in common params */
if((parfile = fopen(COMPARFILE,"r")) == NULL){
fprintf(stderr, "Common params file is missing. Exit.\n");
exit(1);
}
fscanf(parfile, "%lg %ld %ld", &coeff, &bins, &iter);
/* read-in sample params */
v = gsl_vector_calloc (samp);
sigma_v = gsl_vector_calloc (samp);
rl = gsl_vector_calloc (samp);
rh = gsl_vector_calloc (samp);
if((parfile = fopen(SAMPPARFILE,"r")) == NULL){
fprintf(stderr, "Sample params file is missing. Exit.\n");
exit(1);
}
for (i = 0; i < samp; i++){
fscanf(parfile, "%lg", &z);
gsl_vector_set (v, i, z);
gsl_vector_set (sigma_v, i, z);
gsl_vector_set (rl, i, z);
gsl_vector_set (rh, i, z);
}
fclose(parfile);
/* read in species params */
cl = gsl_vector_calloc (spec);
ch = gsl_vector_calloc (spec);
ol = gsl_vector_calloc (spec);
oh = gsl_vector_calloc (spec);
g = gsl_vector_calloc (spec);
sigma_g = gsl_vector_calloc (spec);
if((parfile = fopen(SPECPARFILE,"r")) == NULL){
fprintf(stderr, "Species params file is missing. Exit.\n");
exit(1);
}
for (i = 0; i < spec; i++){
gsl_vector_set (cl, i, z);
gsl_vector_set (ch, i, z);
gsl_vector_set (ol, i, z);
gsl_vector_set (oh, i, z);
gsl_vector_set (g, i, z);
gsl_vector_set (sigma_g, i, z);
}
0
ú/û
}
/j
Y
\kRQ_Q0m
sX&%1Ä+t
fclose(parfile);
/* print out number of species, number of samples, number of repeats */
printf("%ld %ld %ld\n", spec, samp, repeats);
/* repeat for every species */
for (i = 0; i < spec; i++){
/* calculate mean density using point estimator */
Dm=0;
C = gsl_vector_get (cl, i);
G = gsl_vector_get (g, i);
for (j = 0; j < samp; j++) {
abu = gsl_matrix_get (ab, i, j);
V = gsl_vector_get (v, j);
R = gsl_vector_get (rl, j);
Dm += (abu*V*C)/(R*G);
}
Dm /= (double) samp;
/* read-in species params */
Cl = gsl_vector_get (cl, i);
Ch = gsl_vector_get (ch, i);
Ol = gsl_vector_get (ol, i);
Oh = gsl_vector_get (oh, i);
G = gsl_vector_get (g, i);
Sigma_g = gsl_vector_get (sigma_g, i);
/* repeat for every sample */
for (j = 0; j < samp; j++) {
/* read-in sample params */
V = gsl_vector_get (v, j);
Sigma_v = gsl_vector_get (sigma_v, j);
Rl = gsl_vector_get (rl, j);
Rh = gsl_vector_get (rh, j);
/* read-in the value of abundance */
abu = gsl_matrix_get (ab, i, j);
free = 0;
/* estimate denmin, denmax */
denmin = denmax = abu * (R*G)/(V*C);
if (denmin == 0.0) {
denmin = denmax = 0.1 * (R*G)/(V*C);
}
do {
if (free) {
}
denmin *= coeff;
denmax *= 1.0/coeff;
h = gsl_histogram_calloc_uniform (bins, denmin, denmax);
for (k = 0; k < iter; k++) {
den = gsl_ran_flat (r,denmin, denmax);
y = d2a(den,Dm,V,Sigma_v,Rl,Rh,Cl,Ch,Ol,Oh,G,Sigma_g);
if (y==abu) {
/* 1/den is the Jeffreys’ prior: is it done properly? */
gsl_histogram_accumulate (h, den, 1/den);
}
}
free = 1;
} while (gsl_histogram_get (h, bins-1) > 1 );
q
WX&%%tb\
[u
ú/û
`
/* sample it */
for (k = 0; k < repeats; k++){
printf("%g ", x);
}
printf("\n");
}
printf("\n");
}
printf("\n");
gsl_rng_free (r);
gsl_vector_free (v);
gsl_vector_free (sigma_v);
gsl_vector_free (rl);
gsl_vector_free (rh);
gsl_vector_free (cl);
gsl_vector_free (ch);
gsl_vector_free (ol);
gsl_vector_free (oh);
gsl_vector_free (g);
gsl_vector_free (sigma_g);
gsl_matrix_free (ab);
/* etc... */
exit (0);
}
/* _____________________________________________________________________ eof */
y
æ{æ1ä 1äÄ
\? !
+
}~
coenocline-0.07.h
Simulates data from a gaussian/beta/piecewise-linear response
function with different sampling (error) distributions.
Input: samples, number of species, maximum abundance.
Output: sampled abundances, rowwise, rows are species,
columns are samples.
Command-line params: generator type (0=gauss,1=beta,2=piecewiselinear), spacing of samples (0=regular, 1=random)
Common params (file): plot? (0/1), lower, upper end of the gradient, overlap;
Model-specific params (file):
gauss: max. tolerance
beta: max. alpha, max. gamma
piecewise-linear: background density;
Files: Reads a pair of seeds for random number generator from the file "seeds",
and model parametres from the file "params".
Written by P.Cejchan, initially based heavily on J.Oksanen, June 1997.
Language: ISO C
Compile: make -k
History:
was gaussgen.c, betagen.c , pwlgen.c
v 0.01 (1999/12/02): basic functionality
v 0.02: gnuplot plotting;
v 0.03 (2000/01/06): no zero-filled species
v 0.04 (2000/01/13): regular vs. random sampling
coenocline.c
v 0.05 (2000/01/14): beta, gauss, and piecewiselinear generators together;
v 0.06 (2000/01/21): treating allzero species removed; sampler splitted of
2@
/j
Y
ú Ï
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
[u
to a standalone program; params splitted to common and modelspecific;
v 0.07 (2000/02/10):
__________________________________________________________________________
*/
#include
#include
#include
#include
#include
#include
#include
<stdio.h>
<stdlib.h>
<math.h>
<time.h>
<string.h>
"nrutil.h"
"qsort.h"
/* cmd-line param 1: gen */
#define GAUSS 0
#define BETA 1
#define ROOF 2
/* cmd-line param 2: spacing */
#define REGULAR 0
#define RANDOM 1
#define
#define
#define
#define
#define
SEEDFILE "seeds"
C_PARFILE "common.par"
G_PARFILE "gauss.par"
B_PARFILE "beta.par"
GNUPLOTFILE "plot"
#define SHAPE 0.0
extern void setall (long, long);
extern float ranf ();
/* initialize rng */
/* uniform [0,1) */
void generate_points(float *arr, int k, float enda, float endb, int sampling);
float roof(float x, float a, float e, float m, float r);
float gauss(float x, float u, float t, float c);
float beta(float k, float a, float b, float alpha, float gamma, float x);
float ksol(float a, float b, float alpha, float gamma, float height);
void betapara(float pi, float m, float tau2, float *a, float *b);
/* eof */
/*
coenocline-0.07.c
__________________________________________________________________________*/
#include "coenocline-0.07.h"
/* __________________________________________________________________________
generate_points
__________________________________________________________________________
generates sampling points along the gradient
written by Peter Cejchan, 1998/11/18
*/
void generate_points(float *arr, int k, float enda, float endb, int spacing){
/* uniform [0,1) */
extern void ArraySort(int This[], CMPFUN fun_ptr, uint32 the_len);
int i;
int *aux;
/* auxilliary array to hold integers to be sorted */
aux = ivector(0, k);
switch (spacing){
case REGULAR:
default:
for (i=0; i<k; i++) {
arr[i] = enda + i*(endb-enda)/(float) (k - 1);
ú Ï ú
/* x = (float)i/(float)(nsimu-1)*span+enda; */
}
break;
case RANDOM:
for (i=0; i<k; i++) {
aux[i] = (int) 10000*ranf();
}
ArraySort(aux, cmpfun, k);
for (i=0; i<k; i++) {
arr[i] = aux[i]/10000.0;
}
break;
}
free_ivector(aux, 0, k);
return;
}
/* __________________________________________________________________________
roof
__________________________________________________________________________
‘roof’ (unimodal piecewise linear) response curve of a taxon on a gradient;
made up of linear segments
*/
float roof(float x, float a, float e, float u, float r){
/*
x
point on the gradient
a
amplitude, maximum abundance
e
excentricity = left/range
u
mean, position of max. abundance on the gradient
r
range of nonzero values of abundance
*/
float y;
if (x < u) y=x*(a/(e*r))+a-u*(a/(e*r));
else if (x < (u+r-r*e)) y=x*(-a)/(r-e*r)+a-u*(-a)/(r-e*r);
else y = 0;
return (y);
}
/* __________________________________________________________________________
gauss
__________________________________________________________________________
Returns the expected value from Gaussian response function
y = c*exp(-0.5(x-u)^2/t^2)
u
optimum
t
tolerance
c
maximum
x
point at which the function is evaluated
*/
float gauss(float x, float u, float t, float c)
{
return c*exp(-0.5*(x-u)*(x-u)/(t*t));
}
/* __________________________________________________________________________
beta
__________________________________________________________________________
Returns the expected value from beta response function
*/
/j
Y
ú Ï û
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
[u
float beta(float k, float a, float b, float alpha, float gamma,
float x)
{
float t2, t3;
/* Return zero if x is not in (a,b) */
if (x <= a || x >= b)
return 0;
/* Otherwise evaluate the beta-function at x */
t2 = pow(x-a,alpha);
t3 = pow(b-x,gamma);
return k*t2*t3;
}
/* __________________________________________________________________________
ksol
__________________________________________________________________________
The program asks the maximum height of the response function (to
the benefit of the user). Function ksol returns the value of k.
*/
float ksol(float a, float b, float alpha, float gamma, float height)
{
float t1, t4, t6, t11;
t1 = b-a;
t4 = t1/(alpha+gamma);
t6 = pow(alpha*t4, alpha);
t11= pow(gamma*t4, gamma);
return height/t6/t11;
}
/* __________________________________________________________________________
betapara
__________________________________________________________________________
For Beta-Binomial sampling model: Estimates the parameters a,b of
beta distribution from expected proportion (pi), binomial
denominator (m), and shape parameter (tau2). Solution (hopefully
correct) of Exercise 4.17 of McCullagh & Nelder 1989, helped by
Moore, Appl Stat 36, 8-14; 1987.
*/
void betapara(float pi, float m, float tau2, float *a, float *b)
{
float t1,t2,t3,t4;
t1 = tau2*m;
t2 = t1-m-tau2+1;
t3 = 1/(1+t1-tau2);
t4 = t2*t3;
*a = -t4*pi;
*b = t4*(pi-1);
}
/* __________________________________________________________________________
main
__________________________________________________________________________
Ranlib.c (Netlib repository) is used for random number generation.
To re-compile the program, you must either get these routines or
replace them with your favourite rng-routines.
*/
float x, u=0.0, t=0.0, c, mu, enda, endb, span, centre, span2, enda2, temp,
tmax, abumax, *points, alpha=0.0, gamma=0.0,
alphamax, gammamax, over, a=0.0, b=0.0, e=0.0, r=0.0, k=0.0;
ú Ï=Ï
int nsimu, i, nspec, j, plt,
/* command -line params */
gen=GAUSS,
spacing=REGULAR;
long seed1, seed2;
FILE
FILE
FILE
FILE
*seedfile;
*commonfile;
*parfile;
*plotfile = NULL;
/* read-in command-line arguments */
if (argc>1)
gen = atoi(argv[1]);
if (argc>2)
spacing = atoi(argv[2]);
/* initialize RNG */
fprintf(stderr, "Seed file is missing. Exit.\n");
return(1);
}
fscanf(seedfile, "%ld %ld", &seed1, &seed2);
fclose(seedfile);
setall(seed1,seed2);
/* read-in common params */
if((commonfile = fopen(C_PARFILE,"r")) == NULL){
fprintf(stderr, "Common params file is missing. Exit.\n");
return(1);
}
/* plot? lower, upper end of the gradient, overlap */
fscanf(commonfile, "%d %f %f %f", &plt, &enda, &endb, &over);
scanf ("%d", &nspec);
printf("%d ", nspec);
scanf ("%d", &nsimu);
printf("%d\n", nsimu);
scanf ("%f", &abumax);
/* number of species */
/* number of samples */
/* max abundance */
/* read-in model-specific params */
switch (gen) {
case GAUSS:
default:
if((parfile = fopen(G_PARFILE,"r")) == NULL){
return(1);
}
fscanf(parfile, "%f", &tmax);
fclose(parfile);
break;
case BETA:
if((parfile = fopen(B_PARFILE,"r")) == NULL){
return(1);
}
fscanf(parfile, "%f %f",&alphamax, &gammamax);
fclose(parfile);
break;
case ROOF:
break;
}
ú Ï
Q
/j
Y
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
/* plotting */
if (gen == ROOF) plt = 0;
if (plt) {
/* open plotfile */
if((plotfile = fopen(GNUPLOTFILE,"w")) == NULL){
exit(1);
}
/* print header */
fprintf(plotfile, "#!/usr/bin/gnuplot -persist\n#\n#\n");
switch (gen){
case GAUSS:
default:
fprintf(plotfile, "f(x) = c*exp(-0.5*(x-u)*(x-u)/(t*t))\n");
fprintf(plotfile, "set title \"Gaussian model tmax= %4.2f\"\n", tmax);
break;
case BETA:
fprintf(plotfile, "pow(t,u)= exp(log(t)*u)\n");
fprintf(plotfile, "f(x) = k*pow(x-a,alpha)*pow(b-x,gamma)\n");
fprintf(plotfile, "set title \"Beta model alphamax= %4.2f gammamax= %4.2f\"\n", alphamax, gammamax);
break;
}
fprintf(plotfile, "set xrange [%f:%f]\n", enda, endb);
fprintf(plotfile, "set yrange [0:%f]\n", abumax);
fprintf(plotfile, "plot ");
}
/* define the gradient */
if (endb < enda) {
temp = enda;
enda = endb;
endb = temp;
}
span = endb-enda;
centre = enda + 0.5*span;
span2 = (1.0+over)*span;
enda2 = centre - span2/2.0;
points = vector(0, nsimu);
generate_points(points, nsimu, enda, endb, spacing);
for (j = 0; j < nspec; j++) {
/* calculate parametres */
switch (gen){
case GAUSS:
default:
u = enda2 + span2*ranf();
/*
t = tmax* ranf();
/*
c = abumax* ranf();
/*
if (plt) {
fprintf(plotfile, "u=%f, t=%f,
if (j < nspec - 1)
fprintf(plotfile, ", ");
}
break;
case BETA:
/* species’max abundance */
c= abumax* ranf();
/* range endpoints a, b */
a = enda2 + span2*ranf();
b = enda2 + span2*ranf();
if (b < a) {
temp = a;
optimum (on the gradient) */
tolerance */
max abundance */
c=%f, f(x) notitle", u, t, c);
[u
ú Ï
a = b;
b = temp;
}
/* shape parameters alpha, gamma */
alpha = alphamax* ranf();
gamma = gammamax* ranf();
k = ksol(a, b, alpha, gamma, c);
if (plt) {
fprintf(plotfile, "k=%f, a=%f, b=%f, alpha=%f, gamma=%f, f(x) notitle", k, a, b, alpha, gamma);
if (j < nspec - 1)
fprintf(plotfile, ", ");
}
break;
case ROOF:
/* species’max abundance */
c = abumax* ranf();
/* range endpoints a, b */
a = enda2 + span2*ranf();
b = enda2 + span2*ranf();
if (b < a) {
temp = a;
a = b;
b = temp;
}
/* excentricity */
e = ranf();
/* range */
r = b-a;
/* mean */
u = a + e*r;
break;
}
for (i=0; i<nsimu; i++) {
x = points[i];
/* select generator */
switch (gen) {
case GAUSS:
default:
mu = gauss(x, u, t, c);
break;
case BETA:
mu = beta(k,a,b,alpha,gamma,x);
break;
case ROOF:
mu = roof(x, c, e, u, r);
break;
}
printf("%f ", mu);
}
printf ("\n");
}
if (plt)
fclose(plotfile);
/* free array */
free_vector(points, 0, nsimu);
return(0);
}
/* eof */
y
æ{æ1ä 1ä
}~
\
^é
1
ú Ï
.
/j
Y
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
[u
const-0.01.c
Generates m x n table of constant value.
Input (from stdin): m= # of rows, n= # of columns, value to be printed
Output (to stdout):m x n matrix of value
Language: ISO C.
Compile: make -k
History:
version 0.01 (2000/03/13).
__________________________________________________________________________*/
#include <stdio.h>
/* __________________________________________________________________________
main
__________________________________________________________________________*/
int rows, cols, c, i, j;
/* read number of rows and columns */
/*
rows = atoi(argv[1]); */
/*
cols = atoi(argv[2]); */
scanf ("%d%d%d", &rows, &cols, &c);
/* print out the table */
printf ("%d %d\n", rows, cols);
for (i=0; i< rows; i++) {
for (j=0; j< cols; j++)
printf ("%d ", c);
printf("\n");
}
exit (0);
}
/* eof */
y
æZæ1ä 1ä

\* *
²é
Ö
9é
}~
count-hits.c
Reads integer matrix from stdin, and counts rows that are monotonous.
Written by Peter Cejchan.
Input (from stdin): number of rows, number of columns, data matrix.
The matrix is readin rowwise, i.e., columns change fastest (innermost nest);
Output (to stdout): number of monotonous rows.
Language: ISO C.
Compile: make -k
2.95.2 20000220
History:
version 0.01 (1999/03/11).
version 0.02 (2000/04/07).
Example: ./count-hits < order
__________________________________________________________________________*/
#include <stdio.h>
.0
ú Ï
/* __________________________________________________________________________
main
__________________________________________________________________________*/
int main() {
int i, j, rows, cols, a, b, increasing, error=0, cnt=0;
scanf("%d%d", &rows, &cols);
for (i=0; i<rows; i++) {
scanf("%d%d", &a, &b);
if (a != b){
if (b > a) increasing = 1; else increasing = 0;
for (j=2; j<cols; j++) {
a= b;
scanf("%d", &b);
if ((increasing && (a > b)) || (!increasing && (a<b))) error = 1;
}
if (! error) cnt++;
error = 0;
} /* if */
}
printf("hits= %d\n", cnt);
return(0);
}
/* eof */
y
æ{æ1ä 1ä ã
+ *
²å1è
}~
den2abu-0.03.c
Maps density onto abundance.
written by Peter Cejchan
Input (from stdin): number of samples (int), number of species (int),
matrix of densities (float). Density matrix is read samplewise, i.e.,
species change fastest, samples slowest.
Output (to stdout):number of samples, number of species,
matrix of abundances. Abundance matrix is read samplewise, i.e.,
species change fastest, samples slowest.
Language: ISO C.
Compile: make -k
History:
version 0.01 (2000/01/28).
version 0.02 (2000/02/10): contamination included.
version 0.03 (2000/02/16): bug in abu gen corrected
__________________________________________________________________________*/
#include
#include
#include
#include
#include
#include
<stdio.h>
<stdlib.h>
<math.h>
<time.h>
<string.h>
"nrutil.h"
#define PARFILE "den2abu.par"
/* __________________________________________________________________________
genuni
2}
/j
Y
ú Ï
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
[u
__________________________________________________________________________*/
float genuni(float low, float high){
float range;
/* uniform [0,1) */
range = high-low;
return low + range * ranf();
}
/* __________________________________________________________________________
main
__________________________________________________________________________
*/
extern
extern
extern
extern
extern
void setall (long, long);
float ranf ();
long ignbin (long, float);
long ignpoi (float);
float gennor (float, float);
/*
/*
/*
/*
/*
initialize rng */
uniform [0,1) */
Binomial */
Poisson */
Normal */
float
*Dp,
/* species’ pure densities */
Dm,
V,
/* sample volume */
Sigma_v,
/* its std */
Rl,
Rh,
Cl,
Ch,
Ol,
Oh,
G,
Sigma_g,
/* its std */
m, x, d;
int y, rows, cols, i, j, n;
long seed1,seed2;
FILE *seedfile, *parfile;
return(1);
}
fscanf(parfile, "%f %f %f %f %f %f %f %f %f %f",
&V, &Sigma_v, &Rl, &Rh, &Cl, &Ch, &Ol, &Oh, &G, &Sigma_g);
fclose(parfile);
/* read in new seeds */
fprintf(stderr, "Seed file is missing. Exit.\n");
return(1);
}
fclose(seedfile);
/* read in number of rows, number of columns */
scanf ("%d%d", &rows, &cols);
Dp = vector(0, cols);
ú Ï
Dm = 0;
for (j = 0; j < cols; j++){
scanf("%f", &x);
Dp[j] = x;
Dm += x;
}
`
/* samples */
/* species */
for (j = 0; j < cols; j++){
/* species */
d= (Dp[j] + Dm*genuni(Ol, Oh))*gennor(V, Sigma_v)/(gennor(G, Sigma_g)*genuni(Rl, Rh));
m = genuni(Cl, Ch);
n = ignpoi(d);
y = ignbin(n, m);
printf("%d ", y);
}
printf("\n");
}
free_vector(Dp, 0, cols);
return(0);
}
/* eof */
y
y
æ{æ1ä 1ä æ
I
*é9å
²
}~
dt2dm-0.01.c
Generates a number of density matrices from density tensor.
Input (from stdin): number of species (=rows), number of samples
(= columns), number of repeats of readings of density, density tensor (rows, samples, repeats); repeats change fastest (innermost nest);
Output (to files): prescribed number of matrices (see the commandline parametre)consisting of:
number of species (=rows), number of samples
(= columns), matrix of densities (specieswise)
Language: ISO C.
Compile: make -k
2.95.2 20000220
History:
version 0.01 (2000/04/04).
Example: ./dt2dm 5 < tensor
__________________________________________________________________________*/
#include <stdio.h>
/* #include <stdlib.h> */
#include <string.h>
#include <gsl_rng.h>
#include "nrutil.h"
#define SEEDFILE "seed"
/* __________________________________________________________________________
main
__________________________________________________________________________*/
double z;
int i, j, k, spec, samp, matrices;
Q @
/j
Y
ú
unsigned long int seed = 1,
FILE *seedfile, *matrix;
float ***dty;
char *filename = "AAAAAA";
\kRQ_Q0m
sX&%1Ä+t
iter=10000, rnd;
seed = 1;
else {
fclose(seedfile);
}
/* read-in the number of density matrices to be generated */
if (argc > 1)
matrices = atoi(argv[1]);
else
matrices = 1;
/* readin number of species, number of samples, number of repeatings */
scanf ("%d%d%ld", &spec, &samp, &iter);
/* allocate output density tensor */
dty = f3tensor(0, spec, 0, samp, 0, iter);
/* read-in the density tensor */
for (i = 0; i < spec; i++){
for (j = 0; j < samp; j++){
for (k = 0; k < iter; k++){
scanf("%lg", &z);
dty[i][j][k]= (float) z;
}
}
}
/* generate matrices */
for (k = 0; k < matrices; k++){
/* open new file */
filename = l64a (k+2);
if((matrix = fopen(filename,"w")) == NULL){
fprintf(stderr, "Cannot open the output matrix file. Exit.\n");
exit(1);
}
/* print number of species, number of samples */
fprintf(matrix, "%d %d\n", spec, samp);
for (i = 0; i < spec; i++){
for (j = 0; j < samp; j++){
rnd = gsl_rng_uniform_int (r,iter);
fprintf(matrix, "%f ", dty[i][j][rnd]);
}
fprintf(matrix, "\n");
}
fclose(matrix);
}
gsl_rng_free (r);
/* etc... */
exit (0);
}
/* eof */
q
WX&%%tb\
[u
Q
ú =ú

|
y
²è|
æ{æ1ä 1ä æZæ
/*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*/
A Greedy Randomized Adaptive Search Procedure (GRASP)
for the
Quadratic Assignment Problem (QAP)
Authors: M.G.C. Resende (AT&T Bell Laboratories)
[[email protected]]
Y. Li (Pennsylvania State University)
[[email protected]]
P.M. Pardalos (University of Florida)
[[email protected]]
TOMS 22, 1 (Mar 1996) 104.
Netlib toms/754: gqapd.f -- translated by f2c (version 19951025).
Language: ANSI/ISO C.
Rewritten by Petr Cejchan, 1998/02/20.
#define FALSE 0
#define TRUE 1
/*
*
*
*
*
*
*
*
*
*
*
*
*
*
*/
This file includes the following functions:
gqapd
srtcst
stage1
stage2
savsol
local
mkbseq
insrtq
removq
evalij
randp
-
control subroutine for GRASP for QAP algorithm
sorts cost
stage 1 of GRASP construction phase
stage 2 of GRASP construction phase
saves current solution as best so far
2-exchange local search for QAP
makes permutation vector b = (1,2,...,n)
insert element into heap for sorting
remove element from heap
evaluates the cost effect of swapping i and j
random number generator function
/*
*
*/
int gqapd(int *n, int *n2, int *niter, float *alpha, float *beta, int *look4,
int *seed, int *f, int *d, int *a, int *b, int *srtf, int *srtif,
int *srtd, int *srtid, int *srtc, int *srtic, int *indexd,
int *indexf, int *cost, int *fdind, int *opta, int *bestv, int *iter)
{
/* System generated locals */
int i1;
/* Local variables */
static int objv, i, j, k, l;
extern int local(), stage1(), stage2(), savsol(),
srtcst();
/*
*
*
*
*
*
*
*
*
*
*
*
gqapd: Subroutine for finding an approximate solution of a
dense symmetric quadratic assignment problem.
Parameters:
infty - a large integer
Passed input
n
n2
niter alpha -
scalars:
dimension of qap problem
n * n
maximum number of GRASP iterations
phase 1 parameter
Q
/j
Y
ú =û
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
*
beta
- phase 1 parameter
*
look4 if permutation of cost look4 or less is found gqapd
*
returns that permutation
*
*
Passed input/output scalar:
*
seed
- random number generator seed
*
*
Passed output scalars:
*
bestv - cost of best assignment found
*
iter
- number of GRASP iterations taken
*
*
Passed input arrays:
*
f
- flow matrix stored as a 1-dimensional array,
*
row by row (dim = n2).
*
d
- distance matrix stored as a 1dimensional array,
*
row by row (dim = n2).
*
*
Passed work arrays:
*
a
- permutation vector (dim = n).
*
b
- permutation vector (dim = n).
*
srtf
- sorted F values
*
srtif - sorted F values (indices)
*
srtd
- sorted D values
*
srtid - sorted D values (indices)
*
srtc
- sorted cost values
*
srtic - sorted cost values (indices)
*
indexf - indices of facilities in unsorted cost matrix
*
indexd - indices of locations in unsorted cost matrix
*
cost
- sorted cost matrix
*
fdind - indices of sorted cost matrix
*
*
Passed output array:
*
opta
- best permutation vector (dim = n).
*
*
Local scalars and functions:
*
i
- facility index
*
j
- facility index
*
k
- location index
*
l
- location index
*
objv
- cost of permutation
*/
/*
Initialize cost of best assignment found to infinity. */
/* Parameter adjustments */
--opta;
--b;
--a;
--fdind;
--cost;
--indexf;
--indexd;
--srtic;
--srtc;
--srtid;
--srtd;
--srtif;
--srtf;
--d;
--f;
/* Function Body */
*bestv = 2147483647;
/* Sort the cost = f(i,j) * d(k,l) in increasing order to be used */
/* by the stage1 construction phase of GRASP. */
srtcst(n, n2, beta, &f[1], &d[1], &srtf[1], &srtif[1], &srtd[1], &
srtid[1], &srtc[1], &srtic[1], &indexd[1], &indexf[1], &cost[1], &
fdind[1]);
/* Do GRASP iterations. */
i1 = *niter;
[u
Q
ú
for (*iter = 1; *iter <= i1; ++(*iter)) {
/* Stage 1 of GRASP construction phase. */
stage1(n, n2, &i, &j, &k, &l, seed, alpha, beta, &objv, &indexd[1],
&indexf[1], &fdind[1], &cost[1], &a[1], &b[1]);
/* Stage 2 of GRASP construction phase. */
stage2(n, n2, &i, &j, &k, &l, seed, &objv, alpha, &f[1], &d[1], &
srtc[1], &srtic[1], &a[1], &b[1]);
/* Local search phase of GRASP. */
local(n, n2, &objv, &f[1], &d[1], &a[1], &b[1]);
/* If cost assignment is best so far, save permutation and */
/* cost of assignment. */
if (objv < *bestv) {
savsol(n, &objv, bestv, &a[1], &opta[1]);
/* If cost of assignment is at least as good as reque sted, */
/* return best permutation found. */
if (*bestv <= *look4) {
return 0;
}
}
/* L10: */
}
/* Adjust iteration counter for output. */
*iter = *niter;
return 0;
} /* gqapd */
/*
*
*/
int srtcst(int *n, int *n2, float *beta, int *f, int *d, int *srtf,
int *srtif, int *srtd, int *srtid, int *srtc, int *srtic,
int *indexd, int *indexf, int *cost, int *fdind)
{
int i1, i2, i3;
static int dind, find, i, j, nbeta, index, sizec, sized, sizef, dv,
fv;
extern int removq(), insrtq();
/*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
srtcst: Sorts cost = f(i,j)*d(k,l) in increasing order.
Passed input scalars:
n
- qap dimension
n2
- n * n
beta
- construction phase parameter
f
- flow matrix (row major order)
d
- distance matrix (row major order)
Passed work arrays:
srtf
- sorted flow matrix (values)
srtif - sorted flow matrix (indices)
srtd
- sorted distance matrix (values)
srtid - sorted distance matrix (indices)
srtc
- sorted cost matrix (values)
srtic - sorted cost matrix (indices)
Passed output arrays:
cost
- sorted cost matrix
Local scalars:
index - index
sizec - number of elements in cost heap
sized - number of elements in distance heap
sizef - number of elements in flow heap
Ï
Q2Q
/j
Y
ú
*
*
*
*
*
*
*
*
*
*
*
*
*/
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
dv
- distance value
fv
- flow value
dind
- distance index
find
- flow index
nbeta - number of candidates
i
- do loop index
j
- do loop index
Sort D in increasing order,
F in decreasing order (-F in increasing order).
Keep only the (n*n-n)*beta best elements in each sorting.
Initialize cardinalities of sorted sets of elements of D, F,
and cost.
--fdind;
--cost;
--indexf;
--indexd;
--srtic;
--srtc;
--srtid;
--srtd;
--srtif;
--srtf;
--d;
--f;
/* Function Body */
sized = 0;
sizef = 0;
sizec = 0;
/*
Insert all non-diagonal elements of D into D-priority heap */
/*
and all non-diagonal elements of -F into F-priority heap. */
index = 0;
i1 = *n;
for (i = 1; i <= i1; ++i) {
i2 = *n;
for (j = 1; j <= i2; ++j) {
++index;
if (i != j) {
insrtq(n2, &d[index], &index, &sized, &srtd[1], &srtid[1]);
i3 = -f[index];
insrtq(n2, &i3, &index, &sizef, &srtf[1], &srtif[1]);
}
/* L10: */
}
/* L20: */
}
/* Compute size of sorted sets. */
nbeta = *beta * (*n * *n - *n);
/* Remove the nbeta smallest D elements from D-priority heap and */
/* the nbeta smallest -F elements from F-priority heap. */
i1 = nbeta;
for (i = 1; i <= i1; ++i) {
removq(n2, &dv, &dind, &sized, &srtd[1], &srtid[1]);
removq(n2, &fv, &find, &sizef, &srtf[1], &srtif[1]);
/* Cost is product of sorted flow and distance. */
cost[i] = -dv * fv;
indexd[i] = dind;
indexf[i] = find;
/* Insert cost into cost priority-heap. */
insrtq(n2, &cost[i], &i, &sizec, &srtc[1], &srtic[1]);
/* L30: */
}
/* Remove nbeta sorted cost elements from cost priority-heap. */
i1 = nbeta;
for (i = 1; i <= i1; ++i) {
removq(n2, &cost[i], &fdind[i], &sizec, &srtc[1], &srtic[1]);
[u
Q21
ú
/* L40: */
}
return 0;
} /* srtcst */
/*
*
*/
int stage1(int *n, int *n2, int *i, int *j, int *k, int *l, int *seed,
float *alpha, float *beta, int *objv, int *indexd,
int *indexf, int *fdind, int *cost, int *a, int *b)
{
int i1;
static int dind, high, find;
extern double randp();
static float xrand;
static int ii, nselct, tmp;
/*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*/
stage1:
Builds the initial 2 assignments for the GRASP
construction phase (facility i to site k and
facility j to site l).
n
- qap dimension
n2
- n * n
alpha - construction phase parameter
beta
- construction phase parameter
seed
i
- facility index
j
- facility index
k
- location index
l
- location index
objv
- cost of initial 2 assignments
cost
- cost of assignment
Passed output arrays:
a
- permutation array
b
- permutation array
nselct - index of randomly selected element
dind
- distance index
find
- flow index
high
- upper bound of selection range
ii
- loop index
tmp
- temporary scalar
randp
- random number generator function
xrand
- dummy probability
/*
Initialize permutations. */
--b;
--a;
--cost;
--fdind;
--indexf;
--indexd;
/* Function Body */
i1 = *n;
for (ii = 1; ii <= i1; ++ii) {
a[ii] = ii;
b[ii] = ii;
/* L10: */
Q2.
/j
Y
ú
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
[u
}
/* Select element, at random, from the best (n*n-n)*alpha cost */
/* elements. */
xrand = randp(seed);
high = *alpha * *beta * (*n * *n - *n);
nselct = *seed / (2147483647 / high) + 1;
/* Initial assignment is facility i to location k */
/*
facility j to location l. */
/* Cost of initial assignment is f(i,j) * d(k,l). */
dind = indexd[fdind[nselct]];
find = indexf[fdind[nselct]];
*i = (find - 1) / *n + 1;
*j = find - (*i - 1) * *n;
*k = (dind - 1) / *n + 1;
*l = dind - (*k - 1) * *n;
*objv = cost[nselct];
/* Make initial assignments to permutation arrays: */
/* Assign facility
a[1] = *i;
a[*i] = 1;
b[1] = *k;
b[*k] = 1;
/* Assign facility
i1 = *n;
for (ii = 1; ii <=
if (a[ii] == *j)
tmp = a[2];
a[2] = *j;
a[ii] = tmp;
goto L30;
}
/* L20: */
}
L30:
i1 = *n;
for (ii = 1; ii <=
if (b[ii] == *l)
tmp = b[2];
b[2] = *l;
b[ii] = tmp;
goto L50;
}
/* L40: */
}
L50:
return 0;
} /* stage1 */
i to location k. */
j to location l. */
i1; ++ii) {
{
i1; ++ii) {
{
/*
*
*/
int stage2(int *n, int *n2, int *i, int *j, int *k, int *l, int *seed, int
float *alpha, int *f, int *d, int *srtc, int *srtic, int *a, int *b)
{
int i1, i2, i3, i4;
static int high, kinv, cost, linv, fdind;
extern double randp();
static float xrand;
static int sizec, akm1tn, blm1tn, anm1tn, bnm1tn, assign, nselct;
extern int removq(), insrtq();
static int tmp;
/*
*
*
*
stage2:
Builds a randomized greedy permutation starting from
the assignments made in stage1.
Permutation is returned in array a(*).
*objv,
Q 0
ú
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*/
n
- problem dimension
n2
- n * n
i
- facility index
j
- location index
k
- facility index
l
- location index
alpha - construction phase parameter
Passed input/output scalars:
seed
objv
- cost of assignment
f
- flow matrix
d
- distance matrix
Passed work arrays:
srtc
- sorted cost matrix (values)
srtic - sorted cost matrix (indices)
Passed input/output arrays:
a
- permutation array
b
- permutation array
high
- upper bound of selection range
assign - do loop counter of assignments
cost
- assignment cost
sizec - number of cost elemnets in cost heap
nselct - selected index
tmp
- temporary integer variable
kinv
- index of k in inverted permutation
linv
- index of l in inverted permutation
fdind - index of f d product
akm1tn - (a(k)-1)*n
blm1tn - (b(l)-1)*n
anm1tn - (a(n)-1)*n
bnm1tn - (b(n)-1)*n
randp - random number generator function
xrand - probability returned by random number generator
/* Main loop: Assignments 3,4,..,n-1 are made. */
--b;
--a;
--srtic;
--srtc;
--d;
--f;
/* Function Body */
i1 = *n - 1;
for (assign = 3; assign <= i1; ++assign) {
/* For all pairs not assigned yet, compute costs of all */
/* possible assignments, w.r.t. already-made assignments. */
sizec = 0;
i2 = *n;
for (*k = assign; *k <= i2; ++(*k)) {
akm1tn = (a[*k] - 1) * *n;
i3 = *n;
for (*l = assign; *l <= i3; ++(*l)) {
blm1tn = (b[*l] - 1) * *n;
cost = 0;
i4 = assign - 1;
for (*i = 1; *i <= i4; ++(*i)) {
/* Facility a(i) already assigned to location b(i): */
/* Cost of assigning facility a(k) to location b(l) */
/* relative to assignment of facility a(i) to */
/* location b(i). */
cost += f[akm1tn + a[*i]] * d[blm1tn + b[*i]];
/* L40: */
}
/* Insert cost element into cost-priority heap for */
/* sorting. */
i4 = akm1tn + b[*l];
Q }
/j
Y
ú
\kRQ_Q0m
sX&%1Ä+t
insrtq(n2, &cost, &i4, &sizec, &srtc[1], &srtic[1]);
/* L30: */
}
/* L20: */
}
/* Select assignment, at random, from the best alpha*sizec */
/* assignments. */
xrand = randp(seed);
high = *alpha * sizec;
nselct = *seed / (2147483647 / high) + 1;
i2 = nselct;
for (*i = 1; *i <= i2; ++(*i)) {
removq(n2, &cost, &fdind, &sizec, &srtc[1], &srtic[1]);
/* L50: */
}
/* Make assignment. */
*objv += cost;
kinv = (fdind - 1) / *n + 1;
linv = fdind - (kinv - 1) * *n;
i2 = *n;
for (*i = assign; *i <= i2; ++(*i)) {
if (a[*i] == kinv) {
*k = *i;
goto L70;
}
/* L60: */
}
L70:
i2 = *n;
for (*j = assign; *j <= i2; ++(*j)) {
if (b[*j] == linv) {
*l = *j;
goto L90;
}
/* L80: */
}
L90:
tmp = a[assign];
a[assign] = a[*k];
a[*k] = tmp;
tmp = b[assign];
b[assign] = b[*l];
b[*l] = tmp;
/* L10: */
}
anm1tn = (a[*n] - 1) * *n;
bnm1tn = (b[*n] - 1) * *n;
i1 = *n - 1;
for (*i = 1; *i <= i1; ++(*i)) {
*objv += f[anm1tn + a[*i]] * d[bnm1tn + b[*i]];
/* L100: */
}
*objv += *objv;
return 0;
} /* stage2 */
/*
*
*/
int savsol(int *n, int *objv, int *bestv, int *a, int *opta)
{
int i1;
static int i;
/*
*
*
*
*
savsol: Saves current best solution.
n
- problem dimension
objv
- objective function value
q
WX&%%tb\
[u
Q `
ú
*
*
*
*
*
*
*
*
*/
bestv - best objective function value so far
Passed input array:
a
- permutation array
Passed output array:
opta
- array of best permutation so far
Local scalar:
i
- loop index
--opta;
--a;
/* Function Body */
i1 = *n;
for (i = 1; i <= i1; ++i) {
opta[i] = a[i];
/* L10: */
}
*bestv = *objv;
return 0;
} /* savsol */
/*
*
*/
int local(int *n, int *n2, int *objv, int *f, int *d, int *a, int *b)
{
int i1, i2;
static int temp, i, j, xgain;
extern int evalij(), mkbseq();
static int improv;
/*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*/
local: Local 2-exchange on permutation array a.
Return improved permutation array a and objv.
n
- problem dimension
n2
- n * n
objv
- objective function value
f
- flow matrix
d
- distance matrix
a
- permutation array
b
- permutation array
Local scalars:
i
- loop index
j
- loop index
temp
- temp scalar used to swap a(i) and a(j)
xgain - gain from switch
improv - objective function improvement
/* Make array b(*) = (1,2,3,...,n) for local search. */
--b;
--a;
--d;
--f;
/* Function Body */
mkbseq(n, &a[1], &b[1]);
/*
Attempt to switch all pairs in permutation array a. */
L10:
improv = FALSE;
i1 = *n - 1;
1 @
/j
Y
ú
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
for (i = 1; i <= i1; ++i) {
i2 = *n;
for (j = i + 1; j <= i2; ++j) {
/*
Evaluate cost difference by adopting switch of a(
i) */
/*
and a(j). */
evalij(n, n2, &i, &j, &xgain, &f[1], &d[1], &a[1]);
/*
If switch improves cost, adopt it. */
if (xgain > 0) {
temp = a[i];
a[i] = a[j];
a[j] = temp;
*objv -= xgain;
improv = TRUE;
}
/* L30: */
}
/* L20: */
}
/* If no switch improves cost (improv=.false.), return; else repeat.
*/
if (improv) {
goto L10;
}
return 0;
} /* local */
/*
*
*/
int mkbseq(int *n, int *a, int *b)
{
int i1, i2;
static int i, j, tmp;
/*
*
mkbseq: Change permutation arrays a and b to make b = (1,2,...,n).
*
Passed input scalar:
*
n
- QAP dimension
*
*
a
- permutation array
*
b
- permutation array
*
Local scalars:
*
i
- loop index
*
j
- loop index
*
tmp
- temporary scalar
*/
--b;
--a;
/* Function Body */
i1 = *n - 1;
for (i = 1; i <= i1; ++i) {
i2 = *n;
for (j = i + 1; j <= i2; ++j) {
if (b[j] == i) {
b[j] = b[i];
b[i] = i;
tmp = a[i];
a[i] = a[j];
a[j] = tmp;
goto L20;
}
/* L10: */
}
[u
1
ú =ú
L20:
;
}
return 0;
} /* mkbseq */
/*
*
*/
int insrtq(int *n2, int *v, int *iv, int *sizeq, int *q, int *iq)
{
static int sq, tsz;
/*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*/
insrtq: Insert an element (v,iv) into a queue (q,iq).
n2
- n * n
v
- heap element (value)
iv
- heap element (index)
sizeq - size of heap
q
- heap (value)
iq
- heap (index)
Local scalars:
sq
- temporary size of heap
tsz
- temporary variable (sq/2)
Insert element into heap.
--iq;
--q;
/* Function Body */
++(*sizeq);
q[*sizeq] = *v;
iq[*sizeq] = *iv;
/*
Update heap to proper order. */
sq = *sizeq;
*v = q[sq];
*iv = iq[sq];
L10:
tsz = sq / 2;
if (tsz != 0) {
if (q[tsz] > *v) {
q[sq] = q[tsz];
iq[sq] = iq[tsz];
sq = tsz;
goto L10;
}
}
q[sq] = *v;
iq[sq] = *iv;
return 0;
} /* insrtq */
/*
*
*/
int removq(int *n2, int *v, int *iv, int *sizeq, int *q, int *iq)
{
static int vtmp, szqd2, j, k, ivtmp;
/*
*
*
*
*
*
*
removq: Remove smallest element (v,iv) from a priority
queue (q,iq).
Passed input scalar:
n2
- n * n
sizeq - size of heap
1
/j
Y
ú =û
*
*
*
*
*
*
*
*
*
*
*
*
*
*/
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
v
- smallest element in heap (value)
iv
- smallest element in heap (index)
q
- heap (value)
iq
- heap (index)
Local scalars:
vtmp
- tmp smallest element in heap (value)
ivtmp - tmp smallest element in heap (index)
k
- heap counter
j
- heap counter (2*k)
szqd2 - sizeq/2
Remove element from heap.
--iq;
--q;
/* Function Body */
*v = q[1];
*iv = iq[1];
q[1] = q[*sizeq];
iq[1] = iq[*sizeq];
--(*sizeq);
/* Update heap to proper order. */
k = 1;
vtmp = q[k];
ivtmp = iq[k];
szqd2 = *sizeq / 2;
L10:
if (k <= szqd2) {
j = k + k;
if (j < *sizeq) {
if (q[j] > q[j + 1]) {
++j;
}
}
if (vtmp > q[j]) {
q[k] = q[j];
iq[k] = iq[j];
k = j;
goto L10;
}
}
q[k] = vtmp;
iq[k] = ivtmp;
return 0;
} /* removq */
/*
*
*/
double randp(int *ix)
{
/* Initialized data */
static
static
static
static
int
int
int
int
a =
b15
b16
p =
16807;
= 32768;
= 65536;
2147483647;
float retval;
static int xalo, k, leftlo, fhi, xhi;
/*
*
*
*
*
randp: Portable pseudo-random number generator.
Reference: L. Schrage, "A More Portable Fortran
Random Number Generator", ACM Transactions on
Mathematical Software, Vol. 2, No. 2, (June, 1979).
[u
1
ú
Ï
*/
xhi = *ix / b16;
xalo = (*ix - xhi * b16) * a;
leftlo = xalo / b16;
fhi = xhi * a + leftlo;
k = fhi / b15;
*ix = xalo - leftlo * b16 - p + (fhi - k * b15) * b16 + k;
if (*ix < 0) {
*ix += p;
}
retval = (float) (*ix) * (float)4.656612875e-10;
return retval;
} /* randp */
/*
*
*/
int evalij(int *n, int *n2, int *i, int *j, int *xgain, int *f, int *d, int *a)
{
int i1;
static int dtmp1, dtmp2, im1tn, jm1tn, km1tn, k, aim1tn, ajm1tn,
akm1tn, ai, aj, ak;
/*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*/
evalij: Computes the gain in objective function by switching
the locations of facilities i and j (i < j).
n
- QAP dimension
n2
- n * n
i
- permutation array index
j
- permutation array index
Passed output scalar:
xgain - gain achieved by swapping i and j in
permutation
f
- flow matrix
d
- distance matrix
a
- permutation vector
Local scalars:
k
- do loop index
aim1tn - (a(i)-1)*n
ajm1tn - (a(j)-1)*n
akm1tn - (a(k)-1)*n
ai
- a(i)
aj
- a(j)
ak
- a(k)
im1tn - (i-1)*n
jm1tn - (j-1)*n
km1tn - (k-1)*n
dtmp1 - reusable distance computation
dtmp2 - reusable distance computation
--a;
--d;
--f;
/* Function Body */
*xgain = 0;
ai = a[*i];
aj = a[*j];
aim1tn = (ai - 1) * *n;
ajm1tn = (aj - 1) * *n;
im1tn = (*i - 1) * *n;
jm1tn = (*j - 1) * *n;
km1tn = 0;
i1 = *n;
12Q
/j
Y
ú
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
[u
for (k = 1; k <= i1; ++k) {
if (k != *i && k != *j) {
ak = a[k];
akm1tn = (ak - 1) * *n;
dtmp1 = d[km1tn + *i] - d[km1tn + *j];
dtmp2 = d[im1tn + k] - d[jm1tn + k];
*xgain = *xgain + dtmp1 * (f[akm1tn + ai] - f[akm1tn + aj]) +
dtmp2 * (f[aim1tn + ak] - f[ajm1tn + ak]);
}
km1tn += *n;
/* L20: */
}
dtmp1 = d[im1tn + *j] - d[jm1tn + *i];
*xgain += dtmp1 * (f[aim1tn + aj] - f[ajm1tn + ai]);
return 0;
} /* evalij */
/*--- end of file ---*/
y
æZæ1ä 1ä æå
* ' ?
Ö
^é

Zè
}~
histogram-0.01.c
Generates histogram.
Input (from stdin):
Output (to stdout):
Language: ISO C.
Compile: make -k
History:
version 0.01 (2000/02/16).
__________________________________________________________________________*/
#include
#include
#include
#include
#include
#include
<stdio.h>
<stdlib.h>
<math.h>
<gsl_histogram.h>
<gsl_matrix.h>
<gsl_rng.h>
#define PARFILE "abu2den.par"
/* __________________________________________________________________________
main
__________________________________________________________________________*/
gsl_vector *abu;
gsl_histogram *h;
gsl_histogram_pdf *posterior;
gsl_rng *r;
double x, y, abumax, abumin, rnd;
int bins, repeats = 1, rows, i;
unsigned long int seed = 1;
FILE *parfile, *plotfile;
return(1);
}
fscanf(parfile, "%d", &bins);
121
ú
fclose(parfile);
/* read-in the values, get min, max */
abumax = 0.0;
abumin = MAXDOUBLE;
scanf ("%d", &rows);
abu = gsl_vector_alloc (rows) ;
for (i = 0; i < rows; i++){
scanf ("%lg", &x);
gsl_vector_set(abu, i, x);
if(x < abumin) abumin = x;
if(x > abumax) abumax = x;
}
h = gsl_histogram_calloc_uniform (bins, abumin, abumax);
/* fill-in the histogram */
for (i = 0; i < rows; i++){
gsl_histogram_increment (h, gsl_vector_get(abu, i));
}
/* open plotfile */
exit(1);
}
gsl_histogram_fprintf (stdout, h, "%g", "%g") ;
gsl_histogram_reset (h);
for (i = 0; i < rows; i++){
y = gsl_vector_get(abu, i);
gsl_histogram_accumulate (h, y, 1/y);
}
/* sample it */
for (i = 0; i < repeats; i++){
printf("%g ", x);
}
gsl_rng_free (r);
/* etc... */
exit (0);
}
/* eof */
y
M¡
æ{æ1ä 1ä æ
|
Hé &è
}~
*
itransp.c
*
reads integer mmatrix from stdin, and outputs its
*
transpose to stdout
*
****************************************************************************/
#include <stdio.h>
12.
/j
Y
ú
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
[u
#define DIM 1000
void readm(int *rows, int *cols, int m[DIM][DIM]);
void transpose(int rows, int cols, int m[DIM][DIM]);
/**************************************************** ************************
*
readm
****************************************************************************/
void readm(int *rows, int *cols, int m[DIM][DIM]) {
int i, j;
scanf("%d%d", rows, cols );
for (i=0; i<*rows; i++) {
for (j=0; j<*cols; j++) {
scanf("%d", &m[i][j]);
}
}
}
/**************************************************** ************************
*
transpose
****************************************************************************/
void transpose(int rows, int cols, int m[DIM][DIM]) {
int i, j;
printf("%d %d\n", cols, rows );
for (i=0; i<cols; i++) {
for (j=0; j<rows; j++) {
printf("%d ", m[j][i]);
}
printf("\n");
}
}
/**************************************************** ************************
*
main
****************************************************************************/
int main(void) {
int rows=DIM, cols=DIM;
int m[DIM][DIM];
readm(&rows, &cols, m);
transpose(rows, cols, m);
return(0);
}
/* ---end of file--- */
y
æZæ1ä 1ä æ

?
èéHå
}~
mat2gri-0.01.c
Converts a matrix to a single column format for Gri.
Input: #rows #columns, data rowwise, on stdin.
Output: to stdout
Dependences: uses Gnu Scientific Library gsl.
compile: gcc mat2gri.c -o mat2gri
tested on: Linux 2.2.10 / glibc 2.1.1 / gcc version 2.95.2 19991109
History:
version 0.01 (1999/12/17)
_________________________________________________________________________ */
#include <stdio.h>
/* _________________________________________________________________________
main
1 0
ú
_________________________________________________________________________ */
int main(void) {
int i, j, x, rows, cols;
scanf("%d%d", &rows, &cols );
for (i = 0; i < rows; i++)
{
for (j = 0; j < cols; j++)
{
scanf("%d", &x);
printf("%d\n", x);
}
printf("\n", x);
}
return 0;
}
/* end of file */
y
+
æ{æ1ä 1ä æ
*i'_|

é
è
}~
monotonic-spear-0.02.c
Measures the mean monotonicity of a set of sequences.
Computes the mean spearman rank correlation coefficient of given
sequences (matrix rows) with monotonic (either increasing, or decreasing)
sequence. The better of the two is taken.
************************ WARNING *************************
NO TIES SHOULD BE PRESENT IN THE DATA !
**********************************************************
Implementation:
Here, we start with rank orders as input, so we do not calculate them.
Input: #rows #columns matrix of ranks in rows, rowwise, on stdin
Output: mean Spearman rank correlation coefficient (rho), on stdout
Written by Petr Cejchan 1999/07/02.
compile: make -k
Example: ./monotonic-spear < out-beta-qap
_________________________________________________________________________ */
#include <stdio.h>
/* _________________________________________________________________________
main
_________________________________________________________________________ */
int main(void) {
int i, j, rows, cols, d, d2, sum1, sum2, sum;
float rs, sum_rs, meanrho;
gsl_matrix * m;
/* read matrix */
scanf("%d%d", &rows, &cols );
m = gsl_matrix_alloc (rows, cols) ;
gsl_matrix_fscanf (stdin, m);
/* initialize */
sum_rs = 0;
for(i = 0; i < rows; i++){
sum1 = 0; sum2 = 0; sum = 0;
1 }
/j
Y
ú
/* for increasing sequence */
for(j = 0; j < cols; j++){
/* subtract the ranks of each pair of data.
d = gsl_matrix_get(m, i, j) - (j+1);
/* square each difference.
d2 = d * d;
\kRQ_Q0m
sX&%1Ä+t
*/
*/
/* sum the squared differences.
sum1 += d2;
*/
}
/* for decreasing sequence */
for(j = 0; j < cols; j++){
d = gsl_matrix_get(m, i, j) - (cols - j);
/* square each difference.
d2 = d * d;
*/
/* sum the squared differences.
sum2 += d2;
*/
}
/* take the lower sum */
if(sum1 < sum2) sum = sum1; else sum = sum2;
/* multiply the sum of squared differences by 6: this is 6S. */
/* r_s = 1 - {6S/(n^3-n)} */
rs = 1 - (6 * (float)sum/(float)(cols * cols * cols - cols));
sum_rs += rs;
}
meanrho = sum_rs / rows;
printf("mean Spearman rho = %f\n", meanrho);
return(0);
}
/* eof */
y
æZæ1ä 1ä æqÄ
" I7\"
å
}~
* ord2score.c
* a filter to convert an ordering of sample numbers
* into sample scores
*
* written by P. Cejchan, 1999/06/08
* language: ISO C
*/
/*
e.g.,
sample
sample
sample
sample
*/
numbers are: 1 2 3 4 5 6,
ordering is: 6 3 4 2 5 1,
scores are: 6 4 2 3 5 1.
numbers must be subsequent integers starting from 1
#include <stdio.h>
#include <stdlib.h>
#define DIM 10000
int main(void) {
int i, j, num, count;
int x;
int score[DIM];
int order[DIM];
/* read samples vector */
i= 0;
while (scanf("%d", &order[i]) != EOF)
i++;
/* read number of samples*/
num= i;
for(i=0; i< num; i++){
q
WX&%%tb\
[u
1 `
ú
/* count samples before this one, incl. this */
count= 0;
while(order[count] != i+1)
count++;
score[i]= count+1;
}
/* write out scores */
for(i=0; i<num; i++)
printf("%d ", score[i]);
printf("\n ");
return(0);
}
/* --- end of file --- */
y
+
æ{æ1ä 1ä æ

+²è|
Zèå
}~
raw2qap-big.c
Program to convert data input format from raw format to qap.
Reads an n by m data matrix and produces distance and flow matrices.
Raw data start with #rows, #columns, followed by data.
Species are columns, samples are rows.
Language: ISO C.
Input: number of rows, number of columns, data matrix rowwise.
Output: distance and flow matrix formatted for QAP input.
2.95.2-8 20000313 / libgsl0 0.5+-1
History:
version 0.01 (1999/03/10).
version 0.02 (2000/04/10): gsl rewrite, command-line param.
__________________________________________________________________________*/
#include <stdio.h>
#include <stdlib.h>
/* for abs */
#include <gsl/gsl_matrix.h>
#define NUM 1000.0
/* divide flows by NUM/maxflow */
/* __________________________________________________________________________
main
__________________________________________________________________________*/
int i, j, k, rows, cols, x, maxflow = 0, num, big = 0, z;
gsl_matrix
*matrix;
/* data matrix (int) */
/* read-in command-line params */
num = NUM;
if (argc > 1)
big = atoi(argv[1]);
if (argc > 2)
num = atoi(argv[2]);
/* read-in number of species, number of samples */
/* read-in the matrix */
matrix = gsl_matrix_calloc (rows, cols);
for (i = 0; i < rows; i++){
for (j = 0; j < cols; j++){
. @
/j
Y
ú
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
[u
scanf ("%d", &z);
gsl_matrix_set (matrix, i, j, z);
}
}
/* print dimension */
printf("%d\n\n", rows);
/* calculate distances between sequence’s equidistant nodes */
for (i = 0; i < rows; i++){
for (j = 0; j < rows; j++){
printf("%d ", abs(i - j));
}
printf("\n");
}
printf("\n");
if (big) {
/* calculate max flow */
maxflow = 0;
for (i = 0; i < rows; i++){
for (j = 0; j < rows; j++){
x = 0;
for (k = 0; k < cols; k++){
/* x += matrix[i][k] * matrix[j][k]; */
x += gsl_matrix_get (matrix, i, k)*gsl_matrix_get (matrix, j, k);
}
if(x > maxflow) maxflow = x;
}
}
}
/* calculate flows */
for (i = 0; i < rows; i++){
for (j = 0; j < rows; j++){
x = 0;
for (k = 0; k < cols; k++){
/* x += matrix[i][k] * matrix[j][k]; */
x += gsl_matrix_get (matrix, i, k)*gsl_matrix_get (matrix, j, k);
}
printf("%d ", big ? (num*x/maxflow): x);
}
printf("\n");
}
printf("\n");
exit(0);
}
/* eof */
y

æZæ1ä 1ä æ
" '
è
}
*
rearr.c
*
reads integer mmatrix and rearrangement vector from stdin,
*
and outputs rows-rearranged matrix
*
to stdout;
*
rearrangement vector uses numbers of rows starting from 1, (not 0)
*
shows which row will be printed next
*
input: rows, columns, matrix (rowwise), vector
*
****************************************************************************/
#include <stdio.h>
#define DIM 1000
void readall(int *rows, int *cols, int m[DIM][DIM], int v[DIM]);
void rearrange(int rows, int cols, int m[DIM][DIM], int v[DIM]);
.
ú =ú
/****************************************************************************
*
readall
****************************************************************************/
void readall(int *rows, int *cols, int m[DIM][DIM], int v[DIM]) {
int i, j;
/* read number of rows and number of columns */
scanf("%d%d", rows, cols );
/* read data matrix rowwise */
for (i=0; i<*rows; i++) {
for (j=0; j<*cols; j++) {
scanf("%d", &m[i][j]);
}
}
/* read rearrangement vector */
for (i=0; i<*rows; i++) scanf("%d", &v[i]);
}
/****************************************************************************
*
rearrange
****************************************************************************/
void rearrange(int rows, int cols, int m[DIM][DIM], int v[DIM]) {
int i, j;
printf("%d %d\n", rows, cols);
for (j=0; j<cols; j++) {
printf("%d ", m[v[i]1][j]); /* numbering of rows starts from 1 !!! */
}
printf("\n");
}
}
/****************************************************************************
*
main
****************************************************************************/
int main(void) {
int rows=DIM, cols=DIM;
int m[DIM][DIM];
int v[DIM];
readall(&rows, &cols, m, v);
rearrange(rows, cols, m, v);
return(0);
}
/* ---end of file--- */
y
æ{æ1ä 1ä æã

I" _\ '
}

}~
rm-zero-rows-cols-0.03.c
a filter to convert the integer matrix
containing rows/columns consisting solely of zeroes
into the matrix without such rows/columns.
Input: #rows, #columns, integer matrix (rowwise), on stdin
Output: to stdout
Params:
0 = replace,
1 = remove zero-filled rows & columns
2 = each entry increased by one
Language: ISO C.
Dependences: uses Gnu Scientific Library gsl.
Written by: Peter Cejchan.
compile: make -k
Language: ISO C
History:
.
/j
Y
ú =û
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
[u
version 0.01 (1999/12/21)
rows and columns were NOT removed
(to preserve the number of rows and columns throughout the computing),
but were slightly modified (by inserting 1s) instead
version 0.02 (2000/01/06): rows and cols are (optionally) really removed; Makefile; GSL rewrite;
version 0.03 (2000/01/12): optionally, all entries are x+= 1
_____________________________________________________________________ */
#include <stdio.h>
#include <math.h>
#define REPLACE 0
#define REMOVE 1
#define PLUSONE 2
int i, j, rows, cols, good, badrows, badcols;
int badrows2, badcols2, zeros = PLUSONE;
gsl_matrix *m;
gsl_vector *delrow = NULL;
gsl_vector *delcol = NULL;
if (argc>1) {
zeros = atoi(argv[1]);
}
else
zeros = PLUSONE;
/* read matrix */
scanf("%d%d", &rows, &cols);
m = gsl_matrix_alloc (rows, cols) ;
gsl_matrix_fscanf (stdin, m);
delrow = gsl_vector_alloc (rows) ;
delcol= gsl_vector_alloc (cols) ;
/* mark rows for deletion */
badrows = 0;
for(i=0;i<rows; i++){
good = 0;
gsl_vector_set(delrow, i, 0);
for(j=0; j< cols; j++){
if(gsl_matrix_get(m, i, j)!=0){
good = 1;
break;
}
}
if(!good) {
gsl_vector_set(delrow, i, 1);
badrows++;
}
}
/* mark columns for deletion */
badcols = 0;
for(i=0; i<cols; i++){
good = 0;
gsl_vector_set(delcol, i, 0);
for(j=0; j<rows; j++){
if(gsl_matrix_get(m, j, i)!=0){
good = 1;
break;
}
}
if(!good) {
gsl_vector_set(delcol, i, 1);
badcols++;
.
ú
}
}
switch (zeros) {
case REMOVE:
/* print # rows # columns */
printf("%d %d\n", rows - badrows, cols - badcols);
/* print data rowwise */
for(i=0;i < rows; i++){
if (! gsl_vector_get(delrow, i)){
if (! gsl_vector_get(delcol, j)) {
printf("%d\n", (int)gsl_matrix_get(m, i, j));
}
}
}
printf("\n");
}
break;
case REPLACE:
/* printf("%d %d\n", rows - badrows, cols - badcols); */
/* insert 1’s into zero rows */
badrows2=0;
for(i=0; i<rows; i++){
if (gsl_vector_get(delrow,i)) {
gsl_matrix_set(m, i, 0, 1);
badrows2++;
}
}
/* insert 1’s into zero columns */
badcols2=0;
for(i=0; i<cols; i++){
if (gsl_vector_get(delcol,i)){
gsl_matrix_set(m, 0, i, 1);
badcols2++;
}
}
/* print data rowwise */
printf("%d\n", (int) rint(gsl_matrix_get(m, i, j)));
}
printf("\n");
}
if((badrows!=badrows2) || (badcols!=badcols2)){
fprintf(stderr, "ERROR !");
return(1);
}
break;
case PLUSONE:
default:
/* print data + 1 rowwise */
printf("%d\n", (int) rint(gsl_matrix_get(m, i, j)) + 1);
}
printf("\n");
}
break;
}
gsl_matrix_free(m);
Ï
.2Q
/j
Y
ú
\kRQ_Q0m
sX&%1Ä+t
q
WX&%%tb\
[u
gsl_vector_free(delrow);
gsl_vector_free(delcol);
return(0);
}
/* eof */
y
y
æZæ1ä 1ä å

|
,è
}~
sampler-0.03.c
This is a sampler from a set of (Poisson/...) distributions,
with expected rates read from matrix on stdin, outputting matrix of
observed values drawn from proper Poisson (or other) distributions,
on stdout;
written by Peter Cejchan, based on J. Oksanen, 1997.
Input (from stdin):
Output (to stdout):
Language: ISO C.
Compile: make -k
History:
version 0.01 (1998/11/19).
version 0.02 (2000/01/13): ranlib.c, complete rewrite;
version 0.03 (2000/04/07): binomial denominator read from bdfile;
_____________________________________________________________________ */
#include
#include
#include
#include
#include
#define
#define
#define
#define
#define
<stdio.h>
<stdlib.h>
<math.h>
<time.h>
<string.h>
BERNOULLI 0
BINOM 1
POISSON 2
BETABIN 3
NEGBIN 4
#define BDFILE "bd"
#define SHAPEFILE "shapes"
/* __________________________________________________________________________
betapara
__________________________________________________________________________
For Beta-Binomial error model: Estimates the parameters a,b of
beta distribution from expected proportion (pi), binomial
denominator (m), and shape parameter (tau2). Solution (hopefully
correct) of Exercise 4.17 of McCullagh & Nelder 1989, helped by
Moore, Appl Stat 36, 8-14; 1987.
*/
void betapara(float pi, float m, float tau2, float *a, float *b)
{
float t1,t2,t3,t4;
t1 = tau2*m;
t2 = t1-m-tau2+1;
t3 = 1/(1+t1-tau2);
.21
ú
t4 = t2*t3;
*a = -t4*pi;
*b = t4*(pi-1);
}
/* __________________________________________________________________________
main
__________________________________________________________________________
*/
extern
extern
extern
extern
extern
extern
void setall (long, long);
float ranf ();
long ignbin (long, float);
long ignpoi (float);
float genbet (float, float);
float gengam (float, float);
/*
/*
/*
/*
/*
/*
initialize rng */
uniform [0,1) */
Binomial */
Poisson */
beta distribution */
gamma */
float mu, shape, aa, bb;
int rows, cols, i, resp=0, error = POISSON,
long seed1,seed2,bd;
FILE *shapefile=NULL, *seedfile, *bdfile;
j;
/* Read in new seeds */
seed1 = 1L;
seed2 = 1L;
}
else {
fclose(seedfile);
}
/* read-in the distribution type */
if (argc>1) {
error = atoi(argv[1]);
}
/*Do the RNG initialization*/
/* read-in the binomial denominator, bd (integer) */
if (error == BINOM || error == BETABIN) {
scanf ("%ld",&bd);
}
/* open file with overdispersion params for each species */
if (error == BETABIN || error == NEGBIN){
if((shapefile = fopen(SHAPEFILE,"r")) == NULL){
fprintf(stderr, "File with overdispersion params is missing. Exit.\n");
return(1);
}
}
/* read in number of rows, number of columns */
/* Proper simulation of observations starts here. Ugly ‘if (mu > 0.0)’
are needed since some (!) values of zero seem to cause FP errors in
ranlib.c. Please note the fall-through in BETABIN and NEGBIN.
*/
.2.
/j
Y
ú
\kRQ_Q0m
sX&%1Ä+t
for (j = 0; j < cols; j++){
scanf("%f", &mu);
muorig = mu; */
if (error == BINOM || error == BETABIN)
muorig *= bd; */
resp = 0;
switch (error) {
case BERNOULLI:
if (mu >= ranf()) resp=1;
else resp=0;
break;
case BETABIN:
fscanf(shapefile, "%f", &shape);
if (mu > 0.0) {
betapara(mu,bd,shape,&aa,&bb);
mu = genbet(aa,bb);
}
case BINOM:
if (mu > 0.0) resp = (int) ignbin(bd,mu);
else resp = 0;
break;
case NEGBIN:
fscanf(shapefile, "%f", &shape);
if (mu > 0.0) mu = gengam(1/(shape*mu),1/shape);
case POISSON:
default:
if (mu > 0.0) resp = (int) ignpoi(mu);
else resp = 0;
break;
}
printf("%d ", resp);
}
printf ("\n");
/*
/*
}
if (error == BETABIN || error == NEGBIN)
fclose(shapefile);
return(0);
}
/* end of file */
7\" M
y
æZæ1ä 1ä åæ
å
&è
}~
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*/
score2rank.c
A filter to convert scores from, e.g., DECORANA, to
sample ranks, without ties.
See:Maurice G. Kendall. Rank Correlation Methods.
Griffin, London, 4. edition, 1970.
Input: sample scores vector on stdin
Output: to stdout
Written by P. Cejchan, 1999/06/08.
compile: gcc score2rank.c -o score2rank
tested on: Linux 2.2.10 / glibc 2.1.1 /
gcc version egcs-2.91.66 (egcs-1.1.2 release)
#include <stdio.h>
#define DIM 1000
int main(void) {
int i, j, rows, cols, count, num;
int x;
float score[DIM];
int rank[DIM];
/* read sample scores vector */
i= 0;
q
WX&%%tb\
[u
. 0
ú
while (scanf("%f", &score[i]) != EOF)
i++;
/* read number of samples*/
num= i;
for(i=0; i< num; i++){
/* count scores lower than this */
count= 0;
for(j=0; j< num; j++){
if(score[j]<= score[i])
count++;
}
rank[i]= count;
}
/* write out scores */
for(i=0; i<num; i++)
printf("%d ", rank[i]);
printf("\n");
return(0);
}
/* --- end of file --- */
) )
1
0 } ` 2 1 . 2} Q 2 0 12 ` } @
02@ }2} @.0
o 7 0 @
% 21 @
% 01
0
021
)) a
9G
}
0 }
2Q2.
}
0 2 0 0
0 `
0
2.21
0
"7 2.
} Q
¢ KQ
9 0 0
0 o J @
0 a J 0
¢ +)
` +)
0
¢
9K121K.
0 0
! a
9 a 2Q }
Q }
P WKQ12121K12.
rK. `
\)a2Q
0 0 ` K1 . ` 0
*
a } @
V
.2 0
ü"înþ&þ
Hü qøìòhïðþ&ì
{û
&û
=û
Ï ú
ú
Ï
Ï
þ&ò =ú
òhþ&ÿÿ¬øìðï
í=òhï
òhþ&ÿ
öïðïðþ&ì
òhþ&ÿ
þ&õ¡ð"ï]ðþ&ìí/ó"ù {í/î9ðí/ïðþ&ì
Ï
òhþ&ÿ
û
í Zøìô«í=ìòhöJõ¡öîHð"í/ïðþ&ì
í/ô
0
H 0.0
.2 `
=V
H 0
0 `
a `
02Q `
2 .
2.2 0
2K1 2 ` }
)
K.
0
9 0
H
9 a 2Q }
bP WQ21
rPS
W W W1 21.1 1 0
M S)
0
a 0 } ` . 2} Q `
a
02@ ` @ `
9 9V
9 0 } 12 .
21 0
0
9 0
"
0 @ Q
%
% H1 1
0
% `
J .
)
7K1 . ..21
!
`
9V
0Q }
HV
}
HV
) a }
HV
a ` 21 0
HV
V 2 } `
HV
=
0

H
=û
ú
í/înò ¯ö
òhþ&ìïí=ÿðìí/ïðþ&ì
/ú
í/õ¡õ¡öÿ
Zóí Zöõ
í/õ¡õ¡öÿ
Zóö Zö
í/õ¡õ¡øÿ
ï]ð"þ&ì
í/õ¡õ¡øÿ
ï]ð"þ&ìõ ú=û ú
òhøïï]ðì
qøìò^ïðþ&ì
=ú
=ú
ôðõ¡ïîHð {øïðþ&ì
ò^í=õ¡öJõ¡ïøô
Ï
ò^þ&ö {þ&óøïðþ&ì
û
/ú
=ú
Ï
ú
óöõ =ú
ú^ú
=û
Ï
Zðòhí/ó&înöõ þ&ìõ¡ö²ÿ¬þ&ô«öó /ú
Zðòhí/ó
=ú
=ú
=ú
Zöî Züoõ1òhþ&ìòhö ï =ú
öìøÿöî9í/ïð {öJÿöï þ&ôõ
4ë
û
û/û
Ï
öòhþ&óþ
Ùóó"öì
ZîHí=ìò ùqí=ìôù]ò^øï
Zöìöî9í/ïþ&î
Ï
Ï
öòhþ&óþ
ö ñòhðöìò
Ï û
ZîHí=ìò ùqí=ìôù {þ&øìô§í/ó Zþ&î9ðï ÿ
ò^þ&öìþ&ò^ó"ðìö
Ï
ú/û
ôðõ¡ïí=ìòhöyÿ¬í/ïîHð
=ú
ò^þ&öìþ&ò^ó"ðìö =ú
Ï
Ï
ôðí=ò înþ&ìþ&øõºõ¡í/ÿ
Zðþ&ï]ð"ò^ù]ò^þ&ÿ¬ÿøìð"ï]ðöõ
Zðþ&ï]øî Zí/ïðþ&ì
Ï
úhú
ôöïî9öìôðì
û=ú
öï]íyÿþ&ôöó
û
ôöïî9öìôöô5ò^þ&î9î9öõ þ&ìô«öìò^ö*í=ìí=ó Zõ¡ðõ
ú
qøìò^ïðþ&ì
û
ôöïöîHÿ¬ðìðõ¡ïðò¿õ¡öîHðí=ï]ð"þ&ì
/û
Zöï]í
]øìòhï]ð"þ&ìõ =ú/û
ôöïöîHÿ¬ðìðõ¡ïðò /û
Zí Zöõ¡ðí=ì¯í=ìí=ó Zõ¡ðõ =ú^ú
öï]í
=ú
ðò
ôöõ¡òhîHð ïð {öJÿþ&ôöó =ú
úhú Ï
Zöóóùqõ í öôù
ë
ôöìõ¡ðï õ¡öîHð"í/ïðþ&ì
=û
Zöóóùqõ í öô
*ë
{î9í
ôöìõ¡ðï
Zÿöïî
Zí Zöõ¡ðí=ì
/ú
4ë
ôöÿ¬þ
=ú^ú
í Zöõ¡üï öþ&înöÿ
=ú
/û
óí=ìöJí=ó Zþ&îHð"ï ÿ
ÜÙ
û/ú
ë5øõ¡ï]ð"ì
ò^ô
ú/û
òhþ&îHînöõ þ&ìôöìò^öJí=ìí=ó Zõ¡ðõ =ú^ú
í/õ Zÿ¬ÿöïî
Zí/ï
òhþ&îHînöóí=ï]ð"þ&ì
òhþ&îHînöóí=ï]ð"þ&ìò^þ&ö ñòhðöìï
í/õ Zÿ¬ÿöïîHðò¿î9öõ þ&ìõ¡ö =ú
í/øïöòhþ&óþ
Ï
òhþ&ìòhö ï =ú
Zöìöî9í/ïöô§ôí/ïí úhú Ï
Zóí Zö
Ï û
òhþ&ìïðìøøÿ
qöòhï êúhú
í/õ¡õ¡öÿ
Ï
òhþ&ìõ¡ïînøò^ïðþ&ì§ÿöï þ&ôõ
Ï
í/î9ï]ð"ñò^ðí=óó
ú
òhþ&ìõ¡ïîHí=ðìï =ú
í/ó {þ&î9ðï ÿ
í/ìïõ Zõ¡ïöÿõ
/ú
òhþ&ìñôöìò^ö²óðÿ¬ðïõ
û
í/ìí/ó {õ¡ð"õ
í=ï]ïöîHì
û
ú
. }
ú
öì
ð"î9þ&ìÿöìï
öì
qí=ò^ïþ&î
öì
{î9í/ôðöìï
öì
í=îHðí Zóö
öì
ð"î9þ&ìÿöìïí=óù ZîHí=ôðöìï
ö Zøí=ï]ð"þ&ì
û=û
öînþ&õ¡ðþ&ì
Ï û
û
ú
û
/ú
û
. `
Nq
u\
[t
a `
öîHînþ&î
ú
û
0
öøî Zöò^þ&øõ
öøî Zöò^þ&øõºòhþ&ÿ

0 ` } 9 % \Q

H
U \Q `
) ` } @ @ .
V 7 01 @
U KQ }
2Q21
9 01
% H @ Q
r2Q }
W2Q 0
9 ` .0 1
1
"
01
7 } 12Q1
9 .2 0
N a \Q 0
N a
0KQ }
" a 0 ` }
} 0 } 0 9K1
H 0 }
9 0
2 } Q
0 } Q2
} 21
H 0 } K1 ` } MP WKQ21K12112.
MP WK121K12.
\)=KQ
)
212 0 ` 2 0 }
)
0
2Q.21
M " J .

H 2}

9 `
7 } 0 ` } 1
\)a2Q
9V
9 .
9 9 0
2 0
óí=ìô§õ¡ìí=ðóõ
Ï û
9V
a
öïðïþ&î =ú Ï
}
9
ö
í=øõ¡ïð ö²õ¡öí=î9ò
ö
þ&ìöìï]ð"í/ó&ôðõ¡ïîHð Zøïðþ&ì
)
/ú^ú
Zðõ¡ïðò4ö Zøí=ï]ðþ&ì
óþ
öî
0
0 } Q
) a 0 }
)
9 0
) %_ 2 0
J
a21
)
9 1
)
21 2.
)
J 2.
F 0 .
F
E)
}
N)
H 0
F
9 0 } 0 K1 } N J 21
)" 0 0
9 01 @
F
a 0
F £ @
F 0 .
F
9 0
a 0 } 2 12 0 ` "1 2
` @ ` } Q
9 0 2 0 0 1
Fb W'21 @ 0 1
r ` } @
\ 9 a 2Q `
2Q `
7
9 2.2
N
J
% ` } @ @ .
0 )) M @
" a 0 0 1 h1 0@ 00 ` 0 .
9 0 0 } `}
)
}
.
0
0 w )) 2
aKQ
91
úhú
ú
ú
$í=î
Ï û
qøìôí=ÿöìï]í=ó
{í=øõ¡õ¡ðí=ì
{í=øõ¡õ¡ðí=ì
ú
û
ìöøî9í/óìöï þ&î Zõ
úhú Ï
ìð"ò ö
=ú
{î9í/ôðöìï
Zú/û Zú Ï Zú
Zú
Zû
/û
úhú Ï úhú
{î9í/ôðöìïí=ìí=ó Zõ¡ðõ
ú^ú
ú Ï
û
*ë
{î9í/õ¡õ¡ó"í/ìô
{înööô
ú
ú
¾í/ó Zþ&î9ðï ÿ
öøîHð"õ¡ï]ðò
ðöî9í/înò ðòhí/ó,ÿ¬þ&ôöó /ú
Ó
û/û
ÿ¬þ&ô«öó /û=û û Ï
Óþ&óþ&òhöìö
ú
þ&îHõ¡öõ þ&öö
øÿ
û ú
qöòhï ú^ú
/ú
þ&ï öõ¡ðõ êû
=û
^úhú Ï
Ï
úhú
ðìôðînöò^ï
ðì
{î9í/ôðöìï\í=ìí=ó Zõ¡ðõ
]þ&îHÿí=ïðþ&ì
ðìïöìõ¡ðï
/û
Ï
ðìïöîHõ öòhðñòÅð"ìïöîHí=ò^ïðþ&ì
2
ö
qînö {õ¡ü îHð"þ&î
öìôí/ó"ó
úhú /û
=û
=û
=ú
û=ú
Ï
Ï
ù í=î9ôìöõ¡õ
ú
kþ&þ&ôí/ó"ó
=ú
ù í=î9ô
ìøó"ó
=û
Ü-G$õ
=ú^ú
ú
þ&î9ÿí=ó
{öìöï]ð"òÅí=ó Zþ&îHðï ÿ¬õ
Ü-G$
=û
Ï
=û
ÿøó"ï]ðôðÿ¬öìõ¡ðþ&ìí/óZõ¡òhí/ó"ðì
þ&ï öõ¡öõ
kóöí=õ¡þ&ìðí=ìòhþ&ìòhö ï
Ï û
ÿþ&ìþ&ï]þ&ìðò
/ú
{öìöîHí=ï]þ&îOþ
=ú
/ú
ÿþ&ôöó =ú
ú
ú
{ó"öÿ
$ðìx-ë
=ú
qøìò^ïðþ&ì
kí=øõ¡õ¡ðí/ìÿ¬þ&ôöó
û ú
Ç -
$
ú
=ú
]øìòhï]ð"þ&ì
înþ
ÿð {î9í/ïðþ&ì
kë!$õ =ú
=ú
ÿöÿ¬öï]ð"òÅí=ó Zþ&îHðï ÿ¬õ
ú
qøìôí=ÿöìï]í=ó&ìðò ö =ú
]í/øìí
ò í/ðìõ
$¤
Ï
qøìôí=ÿöìï]í=ó
Zþ
ÿí=õ¡ïöî
Ï
î9ðöôÿí=ìïöõ¡ï
/û=û
{þ&øìô
ÿí=óí=ò^þ
qí=ò^ïþ&îOí=ìí=ó Zõ¡ðõ =ú^ú
qþ&õ¡õ¡ðóð /í=ï]ð"þ&ì
=û
óþ
qí=ò^ðöõ
qí=ò^ïþ&î
úhú Ï
óð Zöóð þ&þ&ô
þ
þ&ï öõ¡ðõ
ïðÿøÿ
þ&înô«ð"ìí=ó
=ú
ú
û
Ï û
/û
þ&înô«ð"ìí=ï]ðþ&ì
û
5îHó"þ&ò^ð
5õ¡ïîHí=ò^þ&ôí
þ&õ¡ïîHí=ò^þ&ôõ
ú^ú Ï
í=óöþ&öò^þ&ó"þ
û
í=ï]ïöîHì
=úhú Ï
Ï
4ë
4þ&ë
ô
Ï
öî ]þ&îHÿ¬í/ìò^ö \ú
\ú
\ú
û/ú \û=û \û
û
öî ]þ&îHÿ¬í/ìò^öJþ
ïðÿøÿ
öîHÿ¬øï]í=ïðþ&ì
Zõ¡ðþ&ó"þ
þ&ðõ¡õ¡þ&ì
{ð"ò^í=ó
=ú
Ï
þ&ðõ¡õ¡þ&ìôðõ¡ïîHð Zøïðþ&ì
þ&óí=îOþ&înôðìí=ï]ð"þ&ì
þ
/û
=û
øóí=ï]ð"þ&ìôöìõ¡ðï
þ&õ¡ïöîHðþ&î
înöô«í=ïðþ&ì
ô
/û
=ú^ú
=ú
=ú
û
Ï
=û
Ï û
înöô«ð"ò^ïð {ö4ÿþ&ôöó =ú
îHð"ìòhð í/óò^þ&ÿ
înþ
{í Zðóðï
þ&ìöìïõÅí=ìí=ó Zõ¡ðõ
úhú
2@
Nq
0
ú
uA\
W'2Q..1 2'11.21 0 '. 0 1 0.0
W )
.1
W
021 }
W
K1 ` 2 2.
W 9V KQ 0
W
0@ 0
\?N 2.2 0
WK1.1 1 0

0" 0
" }
0
"K1

H1 ` Q
9V
1 @
9_ \ 21
9_
7 21. 0
o
a ` }
2Q21K1
" }
0 "21
0 1
0 2 12
0 R)
`
"
)=21 0
)
9 1
0 } 0
2 }
RV
}
H } .
H }
H } K.
R
Q
@
a
0
} 2.

1

+ aK1
0 } K1 0 .12 ` @ ` 0 @@
0 2 R
0
9
1
H.
"K1 @
0
.Q
0 o J @
2V R KQ }
5ë
5ë
=û
1
0 0 21 22Q2.
L )
}
0 ?)
H 12 0 0
!)
2 0
1 0 ` @ 0 "Q12
0 .
. K.2Q 2
9 0
0
.
@ Q
0
0 `
2
1 @
1
"
}
} 212 } 0
*
0
}
"Q21KQ2..
\ 0
0 2 o J @
a `
9 2 }
V
.
9)
9 } 0 }
9 } 0 0.0 " @@ .@ 0 " J }
7Q1
! }
!
0
V 2 }
V
.
¬ 0
H
r ` } @
=ú

0
0
0
0
J J
öí/î9ÿí=ì
§óðÿð"ï]õ
5ë
§õ¡öîHðí=ï]ð"þ&ì
5ë
§õ¡þ&ó öî
5ë
õ¡öîHðí=ïðþ&ì
!Ù
/ú
*í/ÿ¬öìõ
îHí=ì
Zö
îHí=ì
îHí=ì
î9öòhþ&ìõ¡ïînøò^ïöô
î9ö Zøóí=î«õ¡í/ÿ
ïöõ¡ï
ú/û
î9öõ þ&ìõ¡ö
î9ö ¯þ&î Zðì
ïþ
þ&óþ
ïþ
þ&óþ
Ï û
óö
õ¡í/ÿ
óöJí=î9öí û
õ¡í/ÿ
óðì
õ¡í/ÿ
óðì
õ¡í/ÿ
óðì
õ¡ò^í=óö
õ¡ò^þ&înö
=û
õ¡ò öÿ¬ö /û
=ú
õ¡ö Zøöìòhö
þ&ó"í/î9ðï
Ï
õ í ö
ú
í/î9í/ÿ¬öï]înöõ û=ú
õ¡ð Zìðñòhí=ìòhö
=û
õ¡ðÿøó"í/î9ï]ðþ&ì
=ú
õ¡ðÿøó"í/ïöô¬í=ììöí/ó"ðì
õ¡ðÿøó"í/ïöô¬òhþ&öìþ&òhóðìö
õ¡ðÿøó"í/ïðþ&ì
õ Zö öô
înþ
/û
Zóöÿ
û
í/ïï]öî9ì
ú
ú
=û
øìðïí/î þ&î Zí/ìðõ¡ÿõ =ú/û
{í=îHðí Zóö
Ï ú úhú
õ¡öîHðí=ïðþ&ì
û
{þ&óøÿ¬ö
ü
Ï
ðïïí Zöî
ü½ðõ¡òhþ&ìõ¡ðì§þ&înô«ð"ìí=ï]ðþ&ì
¯þ&þ&ô«ó"í/ìô
ú
û
úhú Ï
øìðïí/î þ&î Zí/ìðõ¡ÿ
Ï
õ¡ö Zøöìòhö
=ú
ú
øìðÿþ&ôí=óðï
Ï
û
ú=û
øìðÿþ&ôí=ó
=û
õ¡öôðÿöìï]í=ï]ð"þ&ìîHí=ï]ö
õ¡óí ö
øìðÿþ&ôí=ó
Ï û
õ¡öôðÿöìï]í=ï]ð"þ&ì
ôðõ¡ï]î9ð Zøï]ð"þ&ì
øìðÿþ&ôí=ó
ú
õ¡öôðÿöìï
û
{ðî9þ&ìÿöìï]í=ó ZîHí=ù
ôðöìï =ú
øìð qþ&î9ÿ
û
í=îHí=ÿöïî9ö
=û
=û
øìðôðÿöìõ¡ðþ&ìí=ó=öì
Ï
öî9î9þ&î
=ú
øìðôðÿöìõ¡ðþ&ìí=ó /ú/û
{þ&óøÿö /û
õ¡í/ÿ
û
Zðòhí/óZþ&înôðìí=ï]ð"þ&ì
ù]õ í öô
Ï
óö
=ú
í=îHí=ÿöïî9ö êú
øìò^öî9ï]í=ðìðï
ÿþ&ôöó =û
õ¡í/ÿ
ú
ïînöìô
/ú
*þ&þ
î9þ&þ
úhúhú
=ú
ïþ&óöî9í/ìò^ö
û/û
qøìò^ïðþ&ì
öï]ðïþ&î /ú Ï
úhú Ï
ïþ&óöî9í/ìò^ö
/û
/ú
ú
Ï û
ïðÿ¬ö
î9öõ¡þ&øînòhöõ ú
î9öõ þ&ìõ¡ö
ú^ú Ï
Ï
ïöõ¡ïðì
=û
óðì
ú
ïí {ø§õ¡öí=î9ò
{î9í/ôðöìï
î9ö Zøóí=î«õ í/òhðì
hú
û=û {û Ï {û
úhú^ú
/ú
/ú
î9öòhþ&ìõ¡ïînøò^ïðþ&ì
û
õ Zÿ¬ÿöïîHðò4înöõ þ&ìõ¡ö
êú
î9öí=óð =öôìð"ò ö =ú
=ú
õ¡øòhòhöõ¡õ¡ðþ&ì
=û
ú
ù]ÿþ&ôöó =ú
Ï
î9öí=òhï]ð {ö4õ¡öí=î9ò
î9öí=óð =öô
&ú
õ¡ïþ&ò í=õ¡ï]ðò
/û
¾òhþ&îHînöóí/ïðþ&ì
/ú
õ¡ïöìþ&öòhþ&øõ1ò^þ&ÿ
û
êú Ï
öî qþ&î9ÿí=ìòhö ú/û
ú
õ¡ïöìþ&öòhþ&øõ
/û
qøìò^ïðþ&ì
û
õ öòhðöõ¡ü
û
óð"ì
û=û
öî ]þ&îHÿ¬í/ìò^ö û
õ öòhðöõînöõ þ&ìõ¡ö
ú^úhú =úhú
*ë
õ¡í=ÿ
ú
õ öòhðöõ
û
îHí=ìôþ&ÿ
=û
õ öòhðöõ
§ö ]ñòhðöìò
5ë
[t
ú
/úhú
ú^úhú
&
( ( W ( \Z
9 ) o
9
(0D K 2} . 2} ` 120 ) aD `` 1 (
( (
(
( 8 0
0
%
$
`
(
<a57< T Q 2 0 .
( (
( )
)M)
7 9
H a
( 8 <=5< $ T Q 2Q ` ` 0 . (
9))
0
0
( (
( 7 -)
?) ~V 9 ( 8 <a57< $% Q T ` }@ (
( (
( ) 9V RM H !)
+V
a ~
)r )
0
9 /)
( 6 5 # #% 8 2 0@ T 11 ` 1 0@ ` } (
)
( (
(P
a 0
a (
" # >< | .T ` 2. 2 ` } 1 (
( (
(
\) 9 ) 0
0
HV
( 8 <a57< $% K. ` T Q.Q212 ` }.0 (
( (
( 6!> < $ > 7 2# 5 < 7f 2 < $ < $% 2 +P
!
V 2 1. 2} (
/ 0
2P W `` @ (
( (
(
H ) a HV
7 )? 2T O) W
0
V
V ( ><=65 #%$ 5
6 5 # <=5 2KQ @ T . 2.1 . @ `2` (
( (
( ¢ V
,¢ ( (
)
( 6 5 # 7# 8 . } T } ` ` } ` }@ (
H
( (
( w( F " ( P
) V

0
0
!V
! ( 6
5 # 8 <a57< $% $!" 1T Q 0 Q } 2 `2` Q (
( (
( ( 7 0 ( ( 7 w( ( (
0
0 W)
HV
M
;"
)
( 6 5 # 8 <a57< $% $% 21dT .1 } `` Q (
a)
(
2
ú
înþ
ø* í
ë
ë
Zóöÿ
Zînööô
Zöìöï]ðòí=ó Zþ&îHðï ÿ
öò ìðò^í=ó *ö þ&îHï
û =ù Ï
Ï
]þ&îkï ö
,óþ&í=ì
Zøí/ôîHí=ïðòí=õ¡õ¡ð Zìÿ¬öìï
,ò þ&þ&ó=þ
÷$í/ìí
Zöÿ¬öìï
Ç
=$
ú
&
$
(
û
ë5øõ¡ïðì
Ï/Ï
$
&Ïd(
Q
&
ë5øõ¡ïðì
Ï
1
.
,öí=înò ðì
]þ&îkíÿþ&ôöó
ë5øõ¡ïðì
õ¡ö²þ
înöóí=ï]ð {ö
$
> p
ë5øõ¡ïðì
R6 L $
4
4þ&ìïðìøøÿ
9L p
LØFR4
L
$þ&ôöóõ
ë5øõ¡ïðì
}
$
& d(
{þ
$
(
4ë
r 96
qþ&î
@
$
&õ öò^ð"öõ«înöõ þ&ìõ¡ö1ïþyöì
Þ
!
{ö Zöï]í=ï]ð"þ&ì
«ò í ïöî
í Zöõ¿û=ú
=û Ï
Åþ&ÿÿøìðï ½ï öù
ë5ò^í=ôöÿðò
$þ&ôöóóðì
þ
*ï ö¯öì
ðînþ&ìÿ¬öìïí/ó«ìð"ò ö¯þ
4
/ú
ú
Ï
(
ë5øõ¡ï]ðì¾í=ìôs$
$
í/ì
«ö í {ðþ&øî1þ
ZîHí=ôðöìï
í
þ&þ&ô
F
ë5øõ¡ïðì
=ë
Zöïí/ù qøìòhïðþ&ì
r 96
$
ÿ
óðòhí/ù
6
fö
r ;6
> p
4øîHînöìï
înþ
öîHðÿ¬öìïí/ó
4
ú
Zóöÿõfþ
Zöì
óí=ìïòhþ&ÿÿøù
ú
hú
{ðî9þ&ìÿöìï]í=ó
ï öþ&î
ZîHí=ù
r ;6 /D
û hú
=Ï
ð"ò þ&óõ
õ öòhðöõ²î9öõ þ&ìõ¡ö
Ç
n
û
ë5øõ¡ï]ðì
íìøïîHðöìï
>
ú/û
înöõ¡õ
óí=ìïõ
ò^þ&û¬óö öó"õ
ôðöìï]õí=ìôõ öòhðöõînöõ þ&ìõ¡öÅò^øî öõfðì¯înöóí=ï]ðþ&ìïþò^þ&ìï]ð"ìøøÿ
&
ú
ú
ë5øõ¡ï]ðì¬í/ìô
(
ú^ú
öînù
û
ó"í/ìïÅòhþ&ÿÿøìðï î9öõ þ&ìõ¡ö§ï]þ¼öóö {í/ïöô
ìðï]ð"öõ1í=óþ&ì
înöù
ú
qþ&î\ï ö1í=ìí=ó Zõ¡ðõ¡þ
>q<
$
d(
/ú
Ï
öïðïðþ&ì¬ð"ì
ë5øõ¡ï]ð"ì
ïðþ&ìõ
{í=óøö²ðìï ö
qînþ&ÿÃÿ¬þ&ìþ&òhøóïøî9ö
ò^þ&ìò^ö ï þ&î9ôðìí/ïðþ&ìÿ¬öï þ&ôõ =í=ìôìðò ö²ï öþ&î
ú
P
ë5øõ¡ï]ðì
ð"ö
&
öî qþ&î9ÿí=ìòhö
hú
Ï
þ&î í/ìôòhþ&ÿ
ú
{ð"ò^í=ó
r ;6
ZîHí=ôðöìïõ
&
Zõ¡ðþ&ó"þ
]þ&îHÿí=ìòhö
n
ï î9öö
^ú
Ï
ö Zöïí/ïðþ&ì(í=ìí=ó Zõ¡ðõ
öî ]þ&îHÿí=ìòhökð"ìÿøó"ï]ðõ öòhðöõ4ÿ¬ð ïøînöõ
(
`
qþ&î
Ï=Ï
ôðòhï]ð"þ&ì¬þ
&0d(
&
]þ&øîºþ&î9ôðìí/ïðþ&ìïöò ìð Zøöõ4í=õ¡õ¡øÿðì
úhú =û=ú ^ú
$
(
&
öî qþ&î9ÿí=ìòhöþ
qöînöìï&ìþ&ìùqó"ðìöí=î*õ öò^ð"öõ*î9öõ þ&ìõ¡öyÿ¬þ&ôöóõ
$
(
&
ú
ë5øõ¡ï]ð"ì
ôð
D
5ì§ìþ&ìùqóð"ìöí=îHõ öòhðöõ¿înöõ þ&ìõ¡öyÿþ&ôöóõ1ðì§þ&înô«ð"ìí=ï]ðþ&ì
=ú
Ï/Ï
þ
qøìò^ïðþ&ìõyïþí=ì
öîHï
öì
>
F
ú
0
ú
/í/ìô
û=ú
$ö
ë
Zöî9õ
Zî9í/ôðöìï
=û/ú
hú
öïöîHÿ¬ðìð"ì
ÿöí=ìõ²þ
í
ú
0
~k &%Mj
ÝGuÝGÛGuV&r
û
&
ë5øõ¡ïðì
ð /öô
2Q
ë
O
$
(
21
â
(
ú
í/ò öóöï
2.
(
ú
}
&
¾ï ö
`
$
@
4
(
û=ú
&
(
û=û
&
2Q
&
Ù
(
înþ
2.
(
Ù
û
0Q(
{í=õ¡öô
öî9í/óð
ú
=Ï
Ù
r ;6
înþ
6
õ¡ò öÿöyí
Zóöÿ
\ö í=òhïí=ìô
4
óðöôïþ
;
öøî9ðõ¡ï]ð"òÅòhøï]ïðì
r 96
Zóöÿ
{öî {ðö
!d6
=ú
ë5ì®þ
{öî {ðö
!d6
A4Ë3
p
î9þ
ë5ì®þ
A4`3
$í=îHïðì
ðò^õ
-Óøìï]ó
í=ø
ì
>
þ
9D
Zöìöïðòí=ó Zþ&ù
qû
ú
þ
Ï
Zöìöïðòí=ó Zþ&ù
ú
F
êí=ìôë
ðóóí=ìö
înþ
ú
/ú
ú Hú
Ï
*ò í ï]öîkëÃînö ð"ö
í {ö
þ
í/ìô
Ï
í/î9í/ó"óöó Zöìöïðò
> A
í Zöõ
öøîHðõ¡ïðò
,í=ì¤$í=ï]öþ
=ú
]þ&î
Åë
«ú
qÿ¬í/ìì
LØ
L
ú/û
qû
ðö5õ¡ïþ&öî9øì
{õ¡ÿ¬öï þ&ôö
=øîÅó"þ&öõ¡øì
þ&öììð Zöî
ó"ðò^í=ïðþ&ìõï]þ
ô«ð"õ¡ï]î9ð Zøï]ðþ&ì(þ
ú
øî {í=înô(í=ìô
í
Zöï ööì(í Zøìôí=ìòhöí/ìô
=ùqû
Zóöÿö
ð"ï
ë
0Ç !
ì
P
Zóöÿ
5ìï öînöóí=ï]ð"þ&ìõ ð
n
>
]þ&î*õ¡þ&ó {ù
û
$í=îHïðì
«øó"ó ºí/ìô
6
í=îHïðïðþ&ìðì
5ìï öyøõ¡ö²þ
ú =ú
Ï=Ï
n
{î9í/ÿ¬õ
öøîHð"õ¡ï]ðòhõ
Ï
2
Zõ înþ
ò í=ìòhöõ
Zøí/ôî9í/ïðòyí/õ¡õ¡ð Zìÿöìï
înöõ¡öí=î9ò ïþ
øî Zí=î9ô
ìøì
&
5
ì
Zí=ì
/D
=ú ^ú
>
«înþ
û
öìôöîHõ¡ü
«øó"ó ºí/ìô
O
õ öò^ðöõ
&
9
{øí=ôîHí=ï]ð"ò4í/õ¡õ¡ð {ìÿöìï
Zøí=ô«î9í/ïðòfí/õ¡õ¡ð Zìÿöìï
$þ&î
21
Zþ&øìô
Zóöÿ
ðöî
3
û
î9þ
Ù«ó"õ¡ö
ù
P
r ;6
F)n
Zóöÿ´ðìï ö4ôþ&ò^ïîHðìö4þ
øï]öî¿ðìïöìõ¡ð {ö5ÿøó"ï]ð {í=îHðí=ï]ökÿöï þ&ôõ²ðìöòhþ&óþ
ï ö
&
îHí=ìò í/ìô
qøìôí/ÿ¬öìïí/óõ
í=îHï&û
ú
ë
A
Ï
ò^þ&ÿ
(
û
î9þ
ðî9òhí
û
4
5
$í/ìó
û ÏQ(
hú
öî9í/ó"ð
qþ&î4ï ö
í=îHï{ú
öí=õ¡óö
îHðï ÿ¬õ
í
=ú
ï ö
=û
ÜF
öí=õ¡óö
îHðï ÿ¬õ
>
=ú
Ï
«í =í/î9í/íJí=ìô´Ó
{î9ðôÿöïí=ù öøî9ðõ¡ïðò^õ
GÇ l
ì
P
Zóöÿ
/Ï
óí/ìö¾ÿöï þ&ôõ
&
Ï
qþ&î9ÿøóí=ï]ð"þ&ì¬þ
$
Q(
înþ
öînöí/òhï]ð ö¾ïí Zø¼õ¡öí/înò
í=înô«õfõ¡þ&ó {ðì
2
6
û
òhþ&ìòhö ï
hú
L
í /í=îHí=í²í/ìô#Ó
(
íìö
&
=ú
4}L
^ú
Ï
ï öyî9öí=óù
ïøõOõ öòhðöõ
]þ&î4ï ö¾ò^þ&ìï]ð"ìøøÿ
í/î9í/ó"óöó
QâöîHõ¡í=ðóó"öõ
Zøí=ôîHí=ï]ðò*í=õ¡õ¡ð Zìÿ¬öìï
û
Ï
ú
ú=û
í /í=îHí=í²í/ìô
ðì
&
L $
Q(
ú
9v96 76
ë5ìöõ¡õ¡í 5ï]þ
L
ÿ¬þ&ôöó
í=ó Zð
öòhò ðþ&óó"ð
]û
«í Zöõ
Pb
ëìö
í/ìôsÙ
í/ïï]ð"ï]ðí=ìô
0Q(
&
{öÅöøòhí/ó
ú
Zøí/ôîHí=ïðò4í=õ¡õ¡ð Zìÿöìï
3
!d6
3
,ÿð"ï
înöø
7ä
ú
ú =ú /ú
Zñ
^ú
Ï
óðòhí/ïðþ&ìï]þï ö
&
$(öí/õ¡øînöÿöìïþ
Zøóöõ
{ðî9þ&ìÿöìï]í=ó/ìðò öõþ
qû
$
í=ìô
=Ï
&
}Ùì
ë5øõ¡ïðì
$(í/î
¯ðò þ&óõ ,í=ìô
Zøí/ìï]ðïí=ï]ð {öÅìðò ö
p
ú
_
(
H ( ( 7 0 cP ( ( (
) (
9_
9V T V
) MV
9" 0
7# 8 $% 5 # 7" 8d65 2>!. @ 20T . . 00 `2` @ (
( (
Dr( ( a ( r) (
8 <=5< $ } T 12Q 0 ` } `(
( ¢ ' ( M
( F (D 9 (
H"
=
2T W
~
9
; ( \6 7:$ 8> R< \56
5 ##%# P < $%fW$ 5< $7 #%# $ "f 0 `2` . (
6 5 #M7
(¢
F (D (OD %V 7 ( P
7f < $% 8K. T 2. Q @ `2` Q (
Dr( ¢ 2 (
(
2 9V R a
) $%# K<=65 > K> |K1 T 02@ Q } 0 . (
( ( ¢ 2_
( ¢ c
(
S) 9V
S
9
( W5 25 # > 56 *3 8 $ >< $% > 56!< 6 # 2
@ T .} 0 2@ Q2 ` } (
( ( ¢ 2_
( ( ( ¢
H 2M
)
) ~
%
r ( W5 5 # > 576 3 8 $ >< $% >> 576< 6 # 2 0 T ` Q ` }2@ (
( ( ¢ 2_
( ( ( ) c
*) G
9
U ( 6 5 #d P 2 65
< $% > > 56 7$% < 2 T `2` @2@ ` } (
( ¢ 7 ( ( ¢ 9 ¬ ( (
(
V V )R
9
( S"$ 6!> $ < f < $% 8 212 20T 1 } 2. ` `2` (

2T2 K)
( ¢ 7 ( ( ¢ 9 ¬ ( (
(
V V )R
9
2T 2
( S"$ 6!> $ < 7f < $ 8 212=Q20T 02@ } 2 `2` (
9 ¢ ( J( w( # < $ 56 $ 57< $ 6 "fW! <a5 # "<a57< $ >< $% >! 2
V )
9V
9V
"7 2 .@ 0 - (
V `2` (
( ¢ 'P (
( (
( %7
U
)
a
9
( \6 !:2$% 8d> U< x $ 6 : = < 6 5< $7 5 #
7 6 !"W s !" < $% # 8 6 $ < f >!; GQ @ .. Q 21r
P W ` } `(
(
!
M)
¢ w0( w0( 0 % 2
9
)
( f W5< | 2Q2 211 0 ` = ` } Q (
0
( ( ¢ (
H a O_
o
7 S_
( P 2 657< $% > > 576 \ 6 5 6 2.dT } Q @2} ` 0 (
0 Dr( ¢
( ( ¢ !
9 (
O) *
W
Z
( 6 2 5
a M
£
9
* 6 5 # P 2 6!5< $7 5 # > 576 2 T 0 .Q 2} .2 ` } (
$
ú ÏQ(
&
5X
ë
> ;
öøî9ðõ¡ï]ð"ò
Zøí/ôîHí=ïðõ¡ò öî
=ú
]þ&î
=ú
{øí=ôîHí=ï]ð"ò
Zøí=ôîHí=ï]ðò¯í/õ¡õ¡ð Zìÿöìï
ú Ï
Ï
Ï
hú
/Ï
^ú
înþ
=øþ&î9ôù
=Ï
{þ&þ&ó"öí/ì
Zóöÿõ
p 6
î9þ&ù
9
bk &%Mj
ÝbuAÝGÛbuAV&r
5X
0
_
ú =Ï
( (
(D N
0
} ( ( ¢ \ ( P M ( (
9
d ( J ¢ = 2. D F _2 2 `2` } (
` ( ( ¢
( 9 ( O>!> $ 8 "fW! <;5 8 f 57< $% 8 6 #!f >N 7# < $%
fW < 7: > MR$ < 6!<a6!5 6 865 f >;V
} Q )S3 < 6 +" < > $%Z!"7fW$ >
5 ":~f 5< !f 5< $ 5 # > >< f > ( H
2"K¢ H ` }2@ (
£ ( (KJ ( \5765 ##%# $f # 57< !: " 5 #$% 8ö5 ": s " < $% # 8 @ ( P/
6 $ < f N>
5 6 $: < : >V
} .. )3 < 6 < > $ f < 6
$!"( `2` Q (
( ( P/ (
7
9 a ) ;
9
( 6!< 7 6 !"\ < O>> 7$ 57< $% O> $ 5 \5 $ $ < $% > MR$ < $D P " %
P 2 65< $% 5 # > 576 `` 0 (
w V
( P %)a) ( 5 # $% 8 "# < $ 2576 $ 5< O 57<a5 (
G¢
V 7H

` .} 0 (
(P
(
% ( 9 _2_ (ID 0 BT 9_
"
) ( 65 >5 < $7 > 7 > >< f > 5 25 ":
6 " < $ >!2¢ 2.dT ` 2Q `2` . (
( 9V a
Q w( ( P
a V
) 0 a b"
) E ( P $ >! 1dT . 2} ` }2@ (
1 ( ( P ( ( ( "# < $ 2576 $ 5< O 5<=5 5 # 2> $ > ( ; " ` 0 (
( f
. ( Dr( P ( 2 77) 7
2 > |
2QdT . ` Q2. (
Dr( J( P ( ( ( P ( "# < $%:2$%fW > $% 5 # > 5 #%$ 8d"V
G1 ` ) "
0
86!5 > 7 ><=5< $ >!< $% >;5 ": 5 #$%: 6 5 7$%#$ < ( P/ % `` Q (
UF !_ 2 ( \6 5 7$%#$ < 5 ": 5 ":27f \6 >> N> \6 #%f >I5 ":
} F
# < $7 > ( W) 9V G 0 `` (
` ( 2V 0
( W5 ": +s < $ # 8 6 $ < f > ( N
o H \
" `2` (
Q @ ( ( 9""7H ( F ( ( ( "# < $ 2576 $ 5< 5 # > $ > 7# 8 $% 5 # 7fWf
"$ < $% > ( ( P/ öP
¢ ",
9
H ` .} 0 (
Dr( 7 (ND 0
Q F ( 7
;T r a 2M M
( 6 5 # f <=5
< $% 5 # > $% >! ` @ T 2. . 0 1 `2` (
Q ( ( \ (
HUT
) 7 ( 6 2 5 6 5 # +P 6!5< $7 5 # > 56 2Q.T 0 . } 2 `2` @ (
( ( M 7
Q
0V !
9
( 6 O <=> < hs > |.21T 1 @ . 2 ` 1 (
M _
(
QQ ( H ( 9 O) S
,V 0
8 <=5< $% K
1 c.T `2` 2 ` 1Q (
&
Ù
d(
û
Ù
øî Zí=î9ô
í=õ¡õ¡ð Zìÿ¬öìï
&
Ù
(
û
øî Zí/înô
Zóöÿ
Ó
öî9ð
F
&Ï
ü
2
ðì
ÿ¬öìï
înþ
(
û
&Ï/Ïd(
ë
}Ç
4þ&ó"þ&îHìð
þ
$
þ
ü
þ&î9ð
=ú
(
Zþ
í=ìô
ð
î9þ
ú /ú Ï
&Ï d(
-
í
(
?6
í/ìôÞ$
I
-«þ
ë
=ú
ü
(
?í=ìô
Ó
Ù
&
í=ì
(
Ó
I
öÿ
\þ
ïðÿð =í=ï]ðþ&ì
4
ò^þ&ÿ
C
/8EO
8
öï]ð"ï]þ&î9õ ,þ&îºï ö
Zn
C
4
þ&õ¡ï
4
ü½ðóö
ö
n
öò^ïí=ï]ðþ&ì
L r L9PGd4 L
>
RO
þ
D
í ÿ¬í/ìí/ìô´Ó¯í/óó /ú
4
P
wP
;C
û
n
6
O
ïþ&ì
4þ&ÿÿ¬øìðï
âfí=ì
þ&õ¡ïîHí=ìô
n
«ð"þ&óþ
4
>
*öðì
þ&óô
!6 D
3
p
í ÿ¬í/ì?í=ìôýÓí/ó"ó
,öîHð"öõ
înöõ þ&ó"ô
hú
Zõ¡ðþ&ó"þ
{öî
L
6
/û=ú^ú hú
û
{ð"õ¡ò öõ?øìô
QLØ<
ö ZöîÅöð"ìð Zö
ú
=íï]þ&þ&ó
<
*ë
Zöìöî9í/ó
r ;6
øî þ&õ¡öí=óù
>^3
!Q6
öî9í/ïðþ&ìí/óZînöõ¡öí/înò
p 6
;D
ú
,ð"ÿøóí=ï]öô¬í/ììöí=óðì
Zöî
í=òhò^ö ïðì
öîHð"þ&î1ïþ¯õ¡ð"ÿøóí=ï]öôí/ììöí=óðì
>
=öìí=îHïöì
Ùóóöì
õ¡ø
ú /ú /ú
Zóöõ¡ö
Ùóóöì
Ïd(
{ðò
hú
î9öõ¡õ =ú
,ò öøöî
öí/î9ðì
r ;6
&
{í=ìþ
{þ&óøÿö
9C
9C
P
dC
B
PGd4
/û
þ
ú
øóí=ï]ðþ&ìFí=ìô
Zþ&îHð"ï ÿÃí
&
@
/ú
øöò
(
ö5í/ìïfõ Zõ¡ïöÿ
hí/ìôînöí=õ¡þ&ìí {ó"ö1ö
`
ìð {öîHõ¡ðï
2
-þ&ìôþ&ì
/ú
DP
ú
îHí=ò^ö*í=ìô
6
O
,ïðî /í Zöîw
ð"õ =öôðïþ&î
þ
&
/þ
6
O
ìöõ
4þ
qþ&înô
ë
>n
{þ&øî9ìö
pGpGp
ú Ï ú =ú Ï
qînö Zøöìò
ë
ð
d(
$í=ìðö
Ï
d
×{þ&î
ö
â
í Zöìïõ
{öîHõ¡ð"ï í=ìô¬ï ökòhþ&ö þ&ó"øï]ðþ&ìþ
í=õ¡ï
Zí Zðóðï
îHðÿ¬ÿöïï
F
Zøí=ô«î9í/ïðò*í=õ¡õ¡ð Zìù
ú
4þ
&Ï d(
F Q$öó
:
]þ&î
=ú ^ú
&
D
!Q6
3
ú
4þ
&Ï
n
Óí=înò^þ&øî9ï/í=ìô
öîHí=ï]ð"ì
4þ&þ&óö ?í=ìô
×{þ&î
ú
û
öïðïðþ&ì
ü
(
; > A
>
A
6
\òhþ&þ
4þ&ììöóó
\òhþ&ÿ
AË3
qO
ùqû
Ó
(
: ;6
ì
4 ä
354 C
&Ï
n
6
¿þ
/ú
¾íkòhþ&óþ&ì
&Ï
n
{þ&óøÿö
`F
n
4óð
,í=ìKkðö Zþ
&Ï
76
5F
/ú
ëõ¡ïþ&ò í/õ¡ïðò1ìöøî9í/ó=ìöï þ&î 5í=ó Zþ&îHð"ï ÿ
{ó"öÿõ
&Ï
«öî9óðì
!6
F
O
;C
ú
(
ú
P
ó"í/ìì
Zøí/ôîHí=ïðò
6
þ
Zöî
âöîHóí
îHðì
>
B!4 C
9n°F
ö
ú
{þ&óøÿ¬öú
4
ðïõ¡þ&øóðõ
Ø$í
kî9í
n
Zõ
ý
:
öì¼í/ìô
A
í/înôí/ó"þ&õ \í/ìô¤-
ù *ö þ&î9ïú=û
í=ìô
A
&Ï d(
$
Åöóí
înþ
L
L
qþ&î*þ
ú /û
þ&ö Zþ&óþ
Ï
qþ&îHïõ¡ò îHð"ï]ïö¾ô«öî
ú
ú
Zðõ¡ò öõ {öî í/ó"ï]öìýôöîHõ¡öó Zöì
Ï =ú ^ú
{í=øõ¡í=óöì
Ï
{ö {öïí=ï]ðþ&ìõ Zøìôö
D
ú
Q
0
~k &%Mj
ÝGuÝGÛGuV&r
Q21
&
í=õ í=ÿ
ï]ðþ&ì5þ
Q2.
ë
(
Q0
Q(
ë
înöð í=óô
í=öþ
Q}
Q(
ë
{ðî9þ&ìÿöìï
í/õ¡õ¡öÿ
Q`
&
-
$
(
ú
î9öõ¡òhþ
1@
$
Q(
1
(
=ú
1
&
O
1
Ó
12Q
Ó
121
î
(
(
Ó
(
óþ
û
Q(
&
.
=ú
öî9í/ïö¯òhþ&í=õ¡ï]í=ó
qînþ&ÿ
öí=ï
òhþ&ÿ
öïðïðþ&ì
ú
Zõ¾ï]þ?í þ&ð"ô
ï ö§í=õ¡õ¡øÿ
r ;6
{í/î9ðí/ìò^ö
>
ïðþ&ìþ
n
¿ìþ&îHÿ¬í/ó"ðï
F
n
D
5ìï ö
{øí=ôîHí=ï]ð"ò¿í=õ¡õ¡ð Zìÿ¬öìï
înþ
Zóöÿ
=Ï
ðïï]í Zöî
4þ&öìþ&ò^ó"ðìö4õ¡ð"ÿøóí=ï]ð"þ&ì
ðï]ïí {öî
,ðÿøó"í/ïðþ&ì¾þ
4
p
Ï
&ò^þ&ÿ¬ÿøìðï
í/ïï]öî9ìõ
D
!6
4
ZîHð"ô
6
A4
ØÙì
Zö
Zóí=ìô
6
ú
6
A4F
4í/ÿ
Zö
6
ZîHðô
û
í ÿí=ì
í=ìô
Óí=óó -þ&ìù
óþ
öî
Ç
LØ3 ?6RC
{þ&øìô
ï ö
>
î9þ=* öòhïðþ&ì
ð"í
ðìôð {ðôøí/ó"ðõ¡ï]ð"òò^þ&ìò^ö ï¯þ
Ï
ú =û
^ú
/û
^ú
ï ö
{øí=ôîHí=ï]ð"òJí/õ¡õ¡ð Zìù
/ú
û
^ú
/Ï
û
óí/ìïí=õ¡õ¡þ&ò^ðí=ïðþ&ì
û
ö¬ðìôð ð"ô«øí=óðõ¡ïðòòhþ&ìòhö ï4þ
Ï
]þ&î1ï ö
< 6
ó"í/ìï4í/õ¡õ¡þ&òhðí=ï]ð"þ&ìõ
L
ú
öî
í Zøõ¡öí/înò í/ìô
{öî
í Zø
F}n
í/î9ï\ð
r ;6
3
!d6
ú
Ï
ú
ú
.@
&
kó"öí/õ¡þ&ì
4`<
1`
&
ï ö
,öôðÿ¬öìïí/î í=õ öòhï]õí=ìô
{õ öòhðöõOînöõ þ&ìõ¡ö4òhøî {öõOí=ìô¯þ
AL)3 ?6RC
4M<
-
Q(
6
4í=ÿ
O
Zóöÿ
L
ü
ë+ìö
óöí/õ¡þ&ì
1}
&
ü
!6
Ó
ë
ð"ï ðì
=ú
î9þ
< 6
õ¡ó"í/ìô«õ
Ï
ú
¿îHí=ì
Zí=î
Ó
3
{ó"í/ìô
kðó"ÿþ&înö
Q(
ú
^ú
O
ÿöìï
10
&
D
Ï
Ó
î9öõ¡õ
ðóóöî
12.
Ç
qî9í/ÿ¬ö þ&î Zõ
5õ¡ïîHí=ò^þ&ôõ5ðì(íòhþ&óôùqïöÿ
êú
kí=øò
QÙì
ô«þ&ì
&
×{í=ô«ö
ú Ï /ú
ìð {öîHõ¡ðï
&
hú
í/øò 5í=ìô
(
3
5øí/ôî9í/ïðòë5õ¡õ¡ð {ìÿöìï
û
Ï=Ï
&
qþ&îï ö
ú Ï/Ï /ú
=û
öøõ¡öþ
í/øò í=ìô
ÏQ(
û
=ú ú
&
qí ð
Oõ¡þ&ÿ¬ö¯înöõ¡øóïõ
î9ðö /öJí=ìô
Ó
;C
û
Q
(
=û
$þ&õ¡ïí
óð"ò^ðïðìï öí=ìí=ó Zõ¡ðõÅþ
ë
n
=û
ë5ìí=ìí=ó Zõ¡ðõþ
Ï û
&
:
Ï
î9ðöôÿí=ì
ðÿ
/ú Hú
ú
Zöóï
:
ñöó"ôôí/ïí
ú
ZîHð"ô«õ
¯öõ¡ï]öî9ì5ï]înþ&ÿõ ^ìþ&îHï öî9ì5ìþ&î í
{ó"í Zöõ
qînþ&ÿ
&
Zöó
înöð í=óô®í=ìô
öì
öìöïðòfÓ
Åþ&îHí=óóðìö®í/ó Zí=ókÿ¬í/öî9ó
Zï]ð"ò
=ú
l
O
í Zöõ*ú =Ï =ú
]þ&îÅï ö¾þ&î9ôðìí/ù
4
p
óí=ìöõ
6
öî9óí=ìô
kò í ï]öî
Zóöÿ
ë
*ìþ&ìù]ÿöïîHðòÿ¬øóïðôðÿöìõ¡ðþ&ìí=ófõ¡òhí=óðì
OðnW35F1F
sF
î9þ
í=îHðõ¡þ&ì?þ
õ¡ðÿøóí=ïöôòhþ&öìþ&òhóðìöõfí=ìô¾òhþ&öìþ
óöøînöìï*í=ìô
Q6
&
òhþ&ÿ
þ&ìöìï]õyí=ìí=ó Zõ¡ðõ²í/ìô¼înöòhð î9þ&òhí=óí öî9í Zðì
þ&óøÿ¬ökú þ
&
_
( w0( K( J 0 (
)
"
9
9
9
2V H) ( #% 8 2h1 } T 11 .12. 2 ` 00 (
)
w0( (KJ
( 5 : 6!5< $ 57>> $ 8 "fW <I5 ": 6 !# 57< !: 6 #!f >
P (J
6 $% > $% O $ > 6 < 5< !f 5< $ >U5 ":Y 6 < $ 5 # 7f
V
2. ) O
< 6 $!" 2 EF
N" c) ö
%
-c 2 0 }0 ( `2` Q (
(?J 9 ( P
9
) 2T
a M M S 9o ( 5 $% >! ` T 2Q } `` (
(J 9
(
2) 2 ( V
a'
0 ! ;T
! 0
( 5 $ > } T 121 0 Q2 `2` } (
( J( (!J
(
9 ) 0
0
V
) ( 8 <=5< $% MQ } T 0 1.
)
dT
b) aV } 1 ` } (
(J
(,D ) 2V )
a
( 6 5 # /< fW 6 $% 5 "<=5< $ >!< $% 5 # O>
9 )rV
> $ 5< $7 dT . 0 .1 Q 0.0 ` .0 (
(0J _
w(
( a *
9
( O $ > 6 < 2#%$!: 5< !f 5< $ >1dT } ` ` } ` } (
( F ( F ( ( ø 2 ( P
( 7# 8 1 T Q2Q..
Q1 ` 0 (
( F ( F ( ( ø 2 (
( 8
)
ab
<a57< $% T 2. ` 0 . (
( F ( w ( F 7 ( # < $ 56 $ 57< 5 5 # > $ > $%c7fWf ""$ < <a6 " < 6 ( P \
9V O 0KP r \ ` } (
( ( F ( 7fWf ""$ < ><=6 " < 6 5 : < S"$ ( P/ 2
9
H H r ` } Q (
( I -V W
(F
) b
9
H ( 5< !f 5< $% > > 576 2 0 T 0 0 0 ` `` (
( (F
( a
(
9V
) a "## 6 < # 1 T @ ` . (
( (F
(BD ( ##
9V
)/
6!6 < # 1 T 0 2. ` 0 (
J( F V (rD 6 5 #"7 f < $% 8 2 0T ` @
, ( P
@ . ` } `(
J( F V (ID 2
( r65 < L 57< f 5< $% 5 # \6 86!5 fWfW$% 8
?T
= < 6 h5 >
2!$ 5 i# >> " @ 20T 0 .Q ` Q2 M
`2` @ (
J( F V (D 2
(P
6 5 # 7f < $ 8 2 20T .Q 7 o
`2` @ (
$
(
îHðìò^ð í=óòhþ&ÿ
&
5X
kóþ
>
(
kóþ
ú
8QF
{öî
õ¡öí=î9ò
6
ë
/û
í Zøõ¡öí/înò ¾í=ìô
ï]øïþ&îHðí=ó
qú
P
>²O
ë5ø
í=îHïZðð
A
P
8
{øõ¡ïú
F}n
r 96
3
!d6
êû qú
Ï û
bk &%Mj
ÝbuAÝGÛbuAV&r
.
&
_
öîkí/ìôþ$
óþ
ìð öî9õ¡ðï þ
.
&
Ïd(
/I
.Q
C=6
Zøìí
Zí=îHí0* í=ì
*í=ì
]þ&î¿òhþ&ÿ
,þ
Zðìí/ïþ&îHðí=ó{þ
þ&óô
2
óø
qïÿí ï]þ¬õ¡þ
öîkë5ò^í=ôöÿðò
qïí/õ¡õ¡ð {ì
ø
Zóðõ öîHõ
öøîHí=óìöï þ&î
r 96
ï]ðÿ¬ð =í/ïðþ&ì
n
Zöî
A
ë5ôô«ð"õ¡þ&ìùü?öõ¡ó"ö
ü
(
F
«þ&øó"ô«öî ú
>n
@
í=óù
/6
D
/ú
Ù
(
.1
&
-í
4þ&óþ&îHí=ôþ¾í/ï
kþ&óô(í/ìô(ë
Zþ&îHð"ï ÿõ
&
1
0
ú
J( F V
( 2 ( 5 56 ( M
G M 0 0
9
V
H
)
P
H¢
`` 0 (

( ( ) 2 ) % T
(F

( 6 5 # O6< $ $ 5 # 65 # <
a /) 9_
MR 6 > `` . (
( ( F \ ! ( s " < $% # 8 6 $ < f > $ 56 +P < $fW$ 57< $% 5 ": 5 $%"
# 56 "$ 8 (
7 ` } `d(
( (F
( W %V
( (
S) a
)\V a
)r)
9 ( >!<a6!5 #%$ 5 6 5 # <a5 2 T `
. ` 1Q (
( (F
( (
V 8 M 5 ! > 7$7# |2 2 . } } 2 ` 12Q (
( F 9 = a ( 5 < $ <a57< $ 2# 5 < #% 8 ( ¢ " r
7M
W) \
\
H ` } (
w( ( F
( # 5 <M>!<a6!5< 8 $% >?5 ": 8 <=5< $% 6 >> > ( " "
` 0 `(
w( J( w (
( P ( ¢ 7 ( "# < $ 56 $ 5< L ( (
HI ( (D 5 # 2> $ > MR$ < 5 :2$% 8d> (
9 P 9)) 0 ( w( Q
O 5<=5
`` 1 (
(
(
( F ( w ( F 7 (
0
9 2T
V
9 ( 8 <=5< $ KQ dT Q 0 21 } ` }@ (
J( (
( = <=6 : " < $% > 576 (

F ( w0( F 9K1
`` @ (
(
( 9 ) )
V 2
G 9
( 6 5 # : 57< $% 5 # \> #% 8 2 2QdT Q 0 2QQ ` (
Dr( P ( M ( ¢ ( 2 H öP ( (2D ( 7
T 6 5 #;
)
0
H ( P
f < $% 8d 0 =Q20T Q 0 2Q 21 `` 1 (
w(
( J( (7J
( H ( %)a)a
)
R)
0
0
% ( 6 5 # Y 8 <=5< $7 $%" 2QT .0 Q2. `2` (
( P
#%: 6 $% 8 W56 6 f
F ( ( 7
! (

5 < $7# Kgg2K ?Q .Q Q 0 ` 1 0 (
( ( w
( (
( H T a M
)
0
% ( fW 6 $ 5 W5< 6!5 #%$ >!<a
Q 0 2 `2` (
0 T 0@ .
( Dr( w 2 ( \6 5 $#%$ < +< ! 6 ."< ;# 8 $%U > $!"( `2` Q (
( w )a)
( ! 6 6 5 $#%$ < ( P
0K
W) r ` `(
(
/û
5X
}*
þ&þ&ôí/óó
F
öòhï]ð öÿöï þ&ôõ
í=ì§öõ¡õ¡í þ&ìï öøõ¡ökþ
?ä
d8
O
ú
]þ&î*ï ökòhóí/õ¡õ¡ð"ñò^í=ï]ð"þ&ìþ
6
n
qí=òhï]þ&îºí=ìí=ó Zõ¡ðõ
r 96
>^<
4
ð"ðð
,ú
Ï
Ï ú
..
&
ü
(
.0
&
d(
Ùì
.}
&
d(
âö
þ&þ&ô«í=óó
LdP o
n
Zöï]í=ïðþ&ìí=ókòhóí=õ¡õ¡ðñò^í=ïðþ&ì+í=ìô
Rä
L
kînöð Zù ,ÿ¬ðï
6
Zóí=ìô
ú
öô«ð"ï]ðþ&ì
Ï
í Zöõ*ú
/ú
Z
4
«ó"í/ò
öóó
,ò^ð"öìïðñò
qþ&înô
=Ï
P
kî9ðÿö
{ö Zöï]í=ïðþ&ìí=ókòhþ&ìïðìøí
û êú
W
ü½ðóö
¿×{þ&î
ö
s×
ú
.`
&
(
Óí=ðî
î
n
öôðïðþ&ì
@
&0 d(
$
&0
î9þ
Ó
Óþ&ïöóóð"ì
&0/Ïd(
Óø
Q
-ðö
2
ë
íyò^þ&ÿ
1
/û
ü
(
ë
L
$
}
Ó
í {ìöõ
ö
]î9ö Zõ
=ú
=û
$
2
í=ìô
ìõyþ
í=îHðí Zóöõ*ðìï]þ
êû
=ú
ú
=ú hú
;C
C
/4
>
4
«ë
ìö
r ;6
F}n
ÿöï þ&ôõ
ë
ðöî9í/înò ðòhí/ó{õ¡öïþ
>
F
½î9öÿ¬í/î {õ
fÿ¬þ&ôöóõ
^ú
Ï
Ç ¤
ì
3
F
,þ&ÿ¬öîHõ
;C
/4
C
qþ&î
Ï
C ;6 ÜF4 ! L
¤B
^ú
øïï]ðì
ï ð"ì
Zõ®ðìÖþ&înôöî ýï ö
n
ú
P
îHð"ìòhð í/ó
Ï=Ï
Zí=ò öóþ&îJí=ò^òhö ï]í=ìòhö
ôöï]înöìôöô?òhþ&îHînöõ þ&ìôöìòhö¾í/ìí/ó {õ¡ð"õ
ú/û
Ù
4
5óô
î9öõ¡òhþ
r 96
Åþ&ìòhóøôðì
í Zöõ
í/ò Zõ¡þ&ì
ú Ï
&0 d(
ðìõ¡þ&ì
ALØ<
í=ìô¼ôþ
&00d(
õ¡í=þ
ú
&í/ìôÞ-
5ó
õ¡ïí=ï]ðõ¡ïðòhí/ó
P 4
í=ìô
=ú
Óøïò
6
.
&0
Ù
(
óö þ
> p d6
í ì
ú
Q6
ZöîHÿ¬í/ì
õ öòhðöõ*înöõ þ&ìõ¡ö²í/ìí/ó {õ¡ð"õ
&0
qõ
þ&ìôöìòhöí=ìí=ó Zõ¡ðõ í/ì
=û
1ìþ&ìù]ÿþ&ìþ&ï]þ&ìöï înöõ þ&ó"ô®í/òhò^ö ïðì
Óøðõ¡ÿ¬í/ì xÓ
(
4óð
=ú
ë5ìí=ó Zõ¡ðõºþ
r 96
!Q6
3
Zóö þ&þ&ô
öïî9öìô«öôFòhþ&îHînöí/õ
kí=øò
öôðïðþ&ì
þ&ìöìïõ
òhóí=õ¡õkþ
&0
î
{öô§þ&î9ôðìí/ïðþ&ìïöò ð Zøöî
kî9í ¯ùÓðó"ó
òhþ&ÿ
6
O
óí=ò
+Ùì
=ú
$ò
(
û
ºí=ìôÎü
í/ï í=ÿ
înöìïðòhöí=ìô#Óí/ó"ó
Óðóó"ðöî(í=ìô
(
ú
-
ë5ìôöîHõ¡þ&ì
A
Óðóóí=ìôÐÓ
ðÿ
&0
Ù
4
4
>
4óí=î9öìô«þ&ì
ú
î9öõ¡õ
qþ&înô
ú
Ï
6
ø
õ
ú
.
0
~k &%Mj
ÝGuÝGÛGuV&r
`
&0
_
( M)
J( ¢ ( 9 ) a R
%
( 6 5 6 5 #U P 2 65< $% 5 #
Z
> 56 2 T @ Q 2 ` 02} (
( ( \ ( f < $ < $%;(
\ P/ 92 " "
` } `(
Dr( ( !# WPW6 85 $ 7$ 8 5 >V
2@ ) 6 $% 8 6 6 $ > $%/= 6
f 57< $% $!" > ( K¢ H
9 !" " `2` 1 (
Dr( P ( ( w0( ¢
( %
(

W
f
)
%V
<=6 $% 5 1T 1 0 .2 ` 1 0 (
w0( ¢ (
( 0 ( "# < $:$fW! > $% 5 # > 5 #$% 8 (
0
9V 2M
( 2 W M
a
0M¢ V 9 0
`} (
( ( 2" T
)
9
)
( "< ": .s < |KQdT . `` ` } Q (
( ( 2 ( ! 6 $% 5 5 # 2< $ "U:2 > 6 5 $%#$ < > } (
( ( ( 56!5 fW <=6 $% > <a57< $ >< $ 5 # < 7: > \5> :ÿ 5 > (
7F 2 9K " ` 0 1 (
Dr(
w(
0) ( L
% ) G
( - ( (
= < 6 5< $7 5 #
9
a
\6 7:$ 8> b< q
7 6 !" \5765 ##%# 5 ": O $ ><=6 $ < !: f < $ 8O5 ": >< f > ` . ` Q
2 P WK ! " `2` @ ( + (
( %r ( (
(F (P (
( 0 ( F ( 0 H
~) G
9
( " 5 # > P 2 657< $% > > 576 2 `2` (
J(
( (
( 6 >< = < 6 ( ¢ d
J( * a
7 `0 (
( _ ( )
0 V 7 _ V V
M_
7 7
;V"_
c a
;
U ( fW$ 5
! <=65 #%$ > 2QT 21 Q 2 ` } 1 (
( _ ( ¢
% "4VH"_2
0" V 0
9 V (
> > #% > 6!5>! 2} T 121 2. ` ` } 0 (
( _ ( MV aV VG V
~_ 0V N 9
( > > #% ! > 7657>2Q @ T 1 0 0 2 ` } `d(
( _
0(
( ¢
9 "NVH"_2
0" b_ W %_
0V ( ~ 0 ( fW$ 5 <a6!5 #%$ >! dT . 21 `2` (
(
H ( ! 6 > <=5 "$ W5 : 6 6 !$ < " 8 P 2> $7# 8 $% "": < 8
: 6 f 56 $"! 5 76 5 # 8 ;(D K a ` } 1 (
(
F ( (
0
~" a K)
(
6 5 # 8 <=5< $7 $!" } T .@ 0 .2 `2` 0 (
-
(
2
í=ø
î9þ
qÿ¬í/ììí=ìô
Zóöÿ
øõ¡ð"ì
}2@
&
5X
Q(
2
ë
/û
«înþ&öò
û
=û=ú^ú
qþ&î«ï ö
p 6
þ&õ¡ðïðþ&ì
Zøí/ôîHí=ïðò*í/õ¡õ¡ð {ìÿöìï
;
r 96
>
ú
!
3
öôô
ë5ìí=ó Zþ&îHðï ÿ
{öìôöîHõ¡üôöòhþ&ÿ
*þ&øïóöô
í ÿ¬í/ì¯í/ìôÌÓí=óó
Zö
ö
¿×{þ&î
s×
ú
}
&
(
2
ú
þ
F
þ&ìöì
F
}
&
(
2
û
}
&
=ÏQ(
î9ðì
WO
Zöî
øõ Zí/ófí/ìô¤$
ü(ðõ
}Q
&
$
-í
(
ú
Zþ&ìö Zînþ
í
}1
&
-«í
(
}.
&
Ù
-
(
}.0
&
-ö
$ò
-ðÅí=ìô
Q(
Ç
>
}2}
×
$
}`
ú
/Ï
â
-«þ
`@
&
Q(
ú
*þ
$í=óí
=ö
`
&
ú
â
-«þ
(
ú
I
â
-«þ
(
3
û
`
`Q
&
&
-þ
õ
*
`1
(12
3
/ö í=ìô
×þ&î
óðù
lÓðó"óõ -þ&ìôþ&ì
ö {öîHó
Lú
s×
2
qïù
ú/û
O
>
Zøí/ôîHí=ïðòí/õ¡ù
F}OýO
FR4
ë5òhï]í
I
qþ&î
!Q6
3
/ú
°<
Zöìöïðò§í/ó {þ&î9ðï ÿ
P
í Zöõ
ú
Ï
Ï
î9öõ¡õ
«í=ìôð$
*í/ÿ¬í Zî9ðõ ìí/ì
Zøí/ôîHí=ïðòí=õ¡õ¡ð Zìÿ¬öìï
2
ìöî Zí=ìô
Zþ
Ù
înþ
Ó¯í/óó"öî
:
Zò
øó"þ
]í/øìíõ ó"í/ò þ
-«þ
*öõ¡öìôö
n
Zóöÿ
¯öî
>
D
înþ
-øöìðì
>w
/öìðì
þ&õ¡ï Zóí=ò^ð"í/óìð
/4
b-Qâ +$øöìò
¬ò^öî9ï]þ
ðõ¡ïþ&îHððfþ
{öõ¡ïî9þ&ø
{þ&ó"ìð
öì
=ö5ø?ÿí=óö
Zî9íy* ð"ì
<
=û =ú ^ú
*
{øÿ
öõ
Zìö
ö®õ Zí=óòhö®ìí=ôò^ð þ
þ&ø
^ú
Ï
/I
Ç
Óþ&î9í/òhö
î9õ¡ï {ð
î9ö {ðõ¡øìí
I94`I
<
þ&ôõ Zí/ó"þ&ø
C
O
$í=óí=ìõ¡þ&ì
r ;6
í=îHí=óóöó
þ&õ¡ï Zóí/òhðí=óìðõ¡þ&ø
O
(
C
LlF
ë
/I;4[I
=ö
í/ìí
{ó"ðò^í=ïðþ&ìõ
;C
ðþ&õ¡ïîHí=ï]ð {î9í/ñò
â
ÏQ(
{ó"öÿõí=ìô§ï öJóþ&òhí/ù
ú
êú
ë5ÿ¬ÿí=î öô«ð"ï]þ&î
/ìí/ÿ
û=û
=ö
{þ&ìö î9øõ
&
D
Ï
ò øò óö¯í`* ö* ð
`
ø
Ï
?C=6
]þ&îÅï ö
3
&
?v96
qþ&înô
ö
-þ&öï]õ¡ò
(
4
=ú
í/înôí/ó"þ&õ
{þ&øìôõ
&
L
×{þ&î
ë
4ë
-«ð
Q(
;C
LØP
ë5ìí öðÿ
&
ì
>
ú
5øí/ìï]ðïí=ï]ð {ö¯í
,í Zö
R
ö
$í=õ
õ¡ð Zìÿöìï
3
L
ÿí=ìì
îHí ùÓ¯ðóó
înþ
Ï
6
O
óí=ò^ö
ë5õ¡õ¡ð {ìÿöìï
û
ZF
×{þ&î
ö
öï í¾ò^þ&öìþ&ò^óð"ìö¾õ¡ðÿøó"í/ïþ&î4øõ¡ö qøóï]þ§òhí/ó"ð ZîHí=ï]öõ¡þ
6
F
í/înöJôöï]öòhïþ&îHõ
F
þ
Ï
Zöî
p
ò^í=ï]ð"þ&ìõyðì?ï öõ¡þ&òhðí=óõ¡ò^ð"öìòhöõ
ú
dÓ¯öðôöó
öò {ÿ¬í/ìì
öò^þ&ìþ&ÿðò¿í/òhï]ð ðïðöõ
2
{þ&óøÿö
«öî9óðì
ÿí=ìõºí/ìôl$
þ&þ
ï]ðþ&ìþ
7ä
>;D
;I
û
Zøÿ¿* öõ
ðþ&õ¡ïîHí=ï]ð Zî9í/ñò
q3
=û=û
C
I
ðöÿö
Ï
Zþ
Zó ø
6
úhú^ú /ú=û
8
^ú
I ; Q4
Zìö
/í
ZîHð /öÿ
Ï
q6
6
ä;6
,ïøïï Zí=îHï =ú
,ð"ÿøóí=ï]öôînöõ þ&ìõ¡öõ«ï]þ
F
=í í=ôìðÿ´õ {í ø
ú
Ï ú
þ&ï öï]ð"ò^í=ó qøìôí=ÿöìï]í=ó ìðò öõ
ú
ø
bk &%Mj
ÝbuAÝGÛbuAV&r
&
5X
_
0.0
` . F ( (
( ( ( 9_ EV )
H ( (
7 )
) 2
0
(
# :2!# K.2QdT 2. . 0.0 `` (
`0 (
(P
(D __
0
2M
a R
9
M (b 65 >5 < $% > 7 "_MR#!: 8 5 ": O 5<=5 8 $%" 6 $% 8
`` } (
` } P ( ( 0 ( ( 0
( (
( 9V )
9"M
( P !#% 8 $ 5
0 L
E
=V 2 V
` }.0 (
0 dT `
`` ( ( 2 ( ! 6 < $% 5 #2!#% 8 (
0M
9M 2 W ` 0 Q (
2M 7 a
@@ ( _ ¢ (LJ (
9
? ( D ~¢
\6 7!:$ 8d> < < = < 6 5< $7 5 # 6 "I7 s < $ # 8 6 $ < f >! 2 /Q2.1.Q 0 (

M) H `2` 0 (
)
ac
2T
@ ( ( 7 (
( 8 <=5< $ 0 dT 2Q.1 212. ` }.0 (
%V
IV ) 9)=
T
@ ( ( (
( 8 <a57< $% ) O" a
U )
a,
} T ` 0 @ ` } `(
( ( Ya <=6 7: " < $7 < s !" < $ # 8 6 $ < f > ( =D 0P \ @
W `2` . (
( ( $%f >5 ":fW < 7: > 8 <a57< $%
@Q (
#% 8 ( 72 " ` 0 Q (
( ( ( 0
) N
@1 (
( #% 8 2Q 0 T .Q2.Q .2Q } ` .. (
+
2 N
( 2# 5 < 7fWf ""$ < 5 : > $ > :2$ 6> $ < $ < 6!6 >!<a6 $ 5 # 8 >
@ . ( 0( <a57< $% V
) $ 5 # 7#%$ 57< $% 6 $% > L< \6 $ < $ > #% 8 $ 5 # 7$% < 2
( ¢ " d
2 D W
a O H 2
W) \ \ ` } (
( )
V
9 ) G
@0 ( 9
+ ( P 2 6!5< $7 > > 576 \6 7:$ 8> 2 21 ` 2. 0 ¢ `` ( H (
( W5 ": # < $% 56 f <a57< $% 2
@} ( ( W) 9V aG 0 ! `2` 0 (
9
( (
) a 0
H
@` (
2M
a
9
r ( P 2 <=6 "f 0 T @ 1
@ `` 1 (
-)
2T V
@ ( ( (
! ( 6 5 # 8 <a57< $% $!" T 0 ` } Q `2` (
$(í/óí=ìõ¡þ&ì )ü
(
ïí/óìðò ö
â
L
$í=ìð"ö
d(
Ù
ü?öõ¡ïÿí=ì
í=ìôl×
]øìòhï]ðþ&ìõkðìFíÿ¬þ&ôöó«þ
LEO
p
&
ú
û /ú =û
=þí=ìô§ë
õ¡ð Zìÿöìï
înþ
hú
-
×{í=ì
{öîHõ¡øõ
]øìôí/ÿ¬öìù
Zö
û
4þ&óþ&î9ìð
öJí=ìï{õ Zõ¡ï]öÿ
í
óðöôïþ¾ï ö
Zøí/ôîHí=ïðòºí/õ¡ù
N
pGpGp
Zóöÿ
*öí=óð =öô
*ò í í=îHîHí=óînöõ þ&ìõ¡ö¾ïþòhóðÿí=ïðòò í=ì
p
ú
&
$í/î
d(
õ öòhðöõ
ú
&
&
û=û
$í
$öî
d(
ú
4
3í/ìô
F
$þ&î
&
ú
2
í/ø
$ðìò
ú
$(ðìò
(
û
þ
]ÿí=ìì
ðì
&
$
$ë
&
Ç
Ù
(
ú
ü(ð"óö
ö
öìï]ðñò
â
d(
&
ú
&
úhú
d(
)Ùì
ëìö
ï]þ+ï ö
>
í Zöõ
/ú
û
í=ï]ïöîHìõ ï]þ&ù
hú
fò^þ&ÿ¬ÿøìð"ï
êïí=õ¡ÿí=ìðí
ë3ïöõ¡ï
í=ïï]öî9ìõ
Ç
$
öîHó"ðì
û
îHðì
ú
ð"õ¡õ¡öì
Ùóóöì
K×
înöõ¡õ
Åí/ÿ
{î9ðô
Zö
Ó
,ðÿ¬õ
!6
dC
B
Zóí=ìô
/ú
*öõ þ&ìõ¡ö§þ
qþ&înô
%Ç
>K
4ï înöö
ZîHí=õ¡õ¡öõ5ï]þFï þ
4
p
ZîHí=ôðöìï
hú
A4
P 6C
F
n
Zöî
ú
F
> A
þ&î Zðì
4
<
/
D
F
p
ÿöò í=ìð"õ¡ÿ
«ó"í/ò
4
öóó
,òhðù
û
ö ñò^ðöìïfö {þ&óøïðþ&ìí=î í=ó Zþ&îHðï ÿ
{ó"öÿ
]þ&îÅï ö
ÐP
ì
Zøí/ôîHí=ïðò²í/õ¡ù
í Zöõ¯û
/û
{öî
I
>
?6
p ìð {öîHõ¡ð"ï
!d6
4W3
înöõ¡õ
ðõ¡õ¡öì(í/ìôÎÓ
í=øó
í
óðòhí/ïðþ&ì§ïþï ö
Zøí/ôî9í/ïðò4í=õ¡õ¡ð Zìÿ¬öìï
ë
{ò í ïöî
×þ&î
ö
â
û=ú
î9þ&í=ò
P
ú
n
Zþ&ðõ5í=ìô
înþ
(
í
öôðï]þ&î
Zï ö1ÿï&ñöóôÿí=õ¡õ¡ð
öîHïðöõJþ
óí=ìïfò^þ&ÿ¬ÿøìð"ï ¬í/õ²í
õ¡ð Zìÿöìï
&
înþ
q
qþ&înô
ð"õ¡õ¡öì
â
ú
ö Zöïí/ïðþ&ì5þ
×{þ&î
õ¡ð Zìÿöìï
d(
ú
«í=öò
ú
fÿøóïðôðÿöìõ¡ðþ&ìí=óò^þ&ÿ¬ÿøìðï
í/ïöîOïí {ó"öJô«ö ï
¯ö ÿí=ì
ò í ï]öî
ú
þ&ÿ¬í/õ
n
Zþ&ðõ¾í/ìô°Ó
ö
{þ&óøÿ¬öJúyþ
&
ì
d6
n
öóó
õ¡þ&ðó"õ¿í=ìô§í
&
/ë
ú
$øöó"óöî9ùAþ&ÿ
(
ú
ð"í
ú
4
&
$þ&ìï]í=ìö
$øöóóöînùkþ&ÿ
(
ú
Zøõ
=ú
þ&ï öõ¡öõ²í Zþ&øï
$ðïò
ú /Ïd(
öøò^í=ó
ZîHí=ôðöìï
{öìöï]ð"òóþ&òhí/ó¾õ¡öí=î9ò
MÇ
>
ðÿøóí=ïðþ&ìþ
ðì
=úhú
ðóí=ôöó
înö öìõ¡ð öJÿ¬þ&ô«öó
fõ¡þ&ÿö
=Ï
ë
Zóöÿ
3
í=înô«õ*íyòhþ&ÿ
&
înþ
A
Zí/ì
(
ú
öî9õ¡ðï þ
{ðînþ&ìÿöìï]í=ó
,í=øìôöî9õ
înöðõ¡óö Zöì
Zøí=ô«î9í/ïðòí/õ¡õ¡ð Zìÿöìï
A
kð
ë5øõ¡ïðì
íyÿøóïðù {í=îHðí ZóöJöì
=û Ï û hú
$
(
ðò þ&óóõ í/ìôf$
Zøóöõ ë
î9öôðòhïöô
ÿ¬þ&ô«ð"ñò^í=ï]ð"þ&ì®þ
4ï î9öõ þ&óô
î9þ
5øí=ôîHí=ï]ðò²ë5õ¡ù
/ú
í/òhò^ö ïðì
Zóöÿ
F
I
6
½í=ìô
&ú
ðïõ
û
ú
Ó
ï öþ&î
5ö {ó"í/ìô
r ;6
,ïøôðöõyðì
>
qöììþ&õ¡òhí/ìô«ð"í/ì?ÿ¬ðî9öõ «î9öóö {í=ìòhöïþöò^þ&óþ
F
Ï
û
/û
hú
û
Zðòhí=ó
2}
~k &%Mj
0
ú
&
ÝGuÝGÛGuV&r
Z*
í
îHðìò^ð í=ó&òhþ&ÿ
/6
þ&î Zõ
&
ò í/ì
I
{öõ1ðìðì
û
-
úhú ÏQ(
ú
5îHóþ&òhð
ö
5înô«ð"ìí=ï]ðþ&ì
2Q
&
(
2
úhú
ööï
21
(
2
úhú
þ&î9öõ¡ï
2
ú
î
/Ï
2.
&
Ù
(
úhú
ðí=ì
&
0Q(
úhú
Ù
ðí=ì
}
Q(
úhú
ë
D
þ
Ó
ì
ü
ðïïí Zöî êöôðï]þ&î
dC L
L²F
L,8
í Zöõ
â
øì
kï ö?òhþ&óþ&î9í/ôþ
]î9þ&ìïyî9í/ì
ë5óóöì
4
ò í ïöî
ðó"í/ôöó
ðí
Zö
í/ïïöîHìõ¯þ
ï ð"ì
Zõ²ðìþ&înôöî
øï]ïðì
ðò Zöï]ïfí/ìô
óí=ò
ë
í
õ¡øò^òhöõ¡õ¡ðþ&ìí=óõ öòhðöõ²þ&ì
4þ&ÿ
=ë
n
6 D
öïðïðþ&ì(í=ìôìðò öï öþ&î
/ú
7
4}8
öï]ðïðþ&ìí=ìô§ìð"ò öyï öþ&î
&
9Ç
/LB
Åí/õ¡ö &í=ìô
,í/øìôöîHõ
Zí
>
^ú
/ú =ú
înöõ¡øóïõ¬øìôöî
r ;6
ú
Ï
Zí
¾þ&înôðìí=ï]ð"þ&ì
ôöï]înöìôöôFò^þ&î9î9öõ þ&ìôöìòhö5í/ìí/ó Zõ¡ðõ¡ô
û
í Zöõ*úhú
ü
{ö {öïí=ï]ðþ&ì
ìþ
{í/ìï]í ZöõJþ
/ú Ï ú
!6
Ï
ööï
ï öí/ô
þ
Zóí=ìòhö¿ÿ¬í/ïîHðòhöõ
>s3
õ öò^ðöõºôð {öîHõ¡ðï
&
ìõ¡ïí Zðó"ðï
óí=ìí=ï]ð"þ&ìõºí/ìôînöÿöôðöõ
5înöõ¡öÿ
öÓí Zøö
=û
þ&ìöìï]õ /í/ìôó"ðìöí=îìöøî9í/óìöïù
û
êú
@
û
hú
Ï
Ç
øïôí/ïíþ&înôöî
F
&
þ&ìöìï]õ /ÿðìþ&î*ò^þ&ÿ
Zõ¡í=ìöìýí/ìô$ðìò ðì
(
úhú=û
_
( ( 9 0
0
( 65 # < MR 6 7>K=120T ` 0 ` 12 `2` (
w0( W
7 4 ( (
a )
( 6 5 # & 8 7 H
H
T
%
$
%
$

"
`
`
(
<=5<
} T 2Q 0 2 0
(
(
( O ( ( ¬ G" 2
:
%
$
%
$
":
#
$
%
$
£
7
W
f
f
"
"$
%
$
PW6
5< 5 5>> 5<
< > W5 ": 2 8 < $ 2 2
Q ` } .2 D 2 ` 0 ( ( (ow O¢ ( (
( ( ( J +V ) £)
H T
)
0
9V ( 8 <=5< $ .0 T .21 02} ` 0} (
( H ( ( " ( F ( w0( ( P ( ¢ (
T
a \V 2 )
0
9 ( fW 6 $% 5 W57<
6!5 #%$ >!<a T ` 2.Q ` Q2 ` }2} (
( ( \( 6 < $% 5 #M#% 8 2 7 *P !7
.Q 2Q (
0KM
9M K W ` 0 . (
( ( 6( 6 < $ 5 #7# 8 6 $%"$ # >5 ": 5 #$% 5< $7 > 2 SP
7 ! ( ¢ 7"
7K
W) r \ ` } (
J( ( ¢ 2__ _ ( ! 9_
( Dr( (
)
2 ) 9
( #% 8 2"1 ` T 2Q } 2112
0
G
` 0} (
(F (
0" ( *
9 ,V ! HV oM H_
H
( $ <a6 $%#
V 7
9
) 2
-
5 | } T 2. ` 2@ Q ` 2@ (
P ( ( (D !
)d % 9
M
( "5 5 O .T ` 1 } ( ` .Q (
( Dr( ( a < 6!5 < $ \6 5 7$%#%$ < ( N
c H \ `2` . (
( Dr( (
2
c 2 2T D (
E
9 `2` 0 (
( ( 9V ( \5 > $ 5 < 6 $ 5 #e( W) o
( W)
R M
V aO 0 `2` . (
w0( ( (
( )
W"
)
( #% 8 21 T } ` @ ` 02@ (
( (D 2 ( P 657< $% > > 56 = <=6 : " < $%;(
\1
`2` (
( (D ( ( a ( 2M 7 a
%
( f < 6>r5 ": P 2 6!5< $7 > > 56 2 T 0 } `2` 1 (
( 9" 2V 2 " P ( w0( J( M¢ 2 OP ( ( (
( 8 <a57< $% 2.21T 2 ` } . (
a +
0
Ù
(
úhúhú
5X
öó"ó
=í
d
,ò^ð"öìïðñò
5î Zí=ìð =í=ï]ðþ&ìþ
íõ¡þ&ð"óÿþ&ðõ¡ïøî9ö
ò í ïöî
ØÙì
qþ&înô
Zóí=ìô
í/ì?í=õ¡õ¡öÿ
ZîHí=ôðöìï
Zóí Zö5þ
4
p
4þ&ÿ¬ù
ú
ú
*öí/î9ó
ú/û
=ú/û
ú
&
`
úhú
(
*í=ÿöìõ
þ
î9ôìøì
*øð"î
{þ&ì
í/ì
öî9õ¡ò ðöôöìí=îHïð Zö
&
P o
@
d(
ú=û
Rä L
ú=û/ú
(W2
&
ú=û/û
(W2
$
(
1
í=ì
ë
ú
.
&
(
ú=û
ú=û
0d(
Zöõ¡ï]ðÿ¬ÿï
Zöí=î Zöðïøì
ýøìô
,ôðöyô«øînò ÿö î9öînö
<
öînôöì
L1<
L
=û
9C
C
Ï û
Ï
4
âfí=ì
Zþ&îHí=ï]þ&î9ðöõÅðì
îHðìò^ð í/ó&òhþ&ÿ
þ&ìöìïí=ìí=ó Zõ¡ðõ¿ð"ì
ú
þ&õ¡ïîHí=ìô
înþ
*öðì
{í Zðóðï í=ìô
þ&óô
=ú
õ¡ïí/ïðõ¡ïðòhõ
ö
þ&ð"õ¡ù
]þ&î9ô
ìð"ù
=ú
Q6
qþ&înô
,òhðöìòhö
ø
Zóðòhí/ïðþ&ìõ
ë5ì½ö í=ÿðìí/ïðþ&ì½þ
Zðòhí/ó&ôí=ï]í
Åõ¡þ&ÿö§þ&înôðìí=ï]ð"þ&ì
4
/ú
=ú
înþ
{ó"öÿõ
Føõ¡öþ
û ^ú
Q6
5n
í í
p
$í=ò^ÿ¬ðóóí=ì
öôðïðþ&ì
û
Ù
ë
î9þ
&
ö Zï]öì
înöõ¡õ =ú
ë
Ó
(
ú=û
P
öóöòhï]înþ&ìðòhí=óó
õ¡ðÿøóí=ïöô¬öòhþ&óþ
&
I9d4 n
n< 94
ð ð"í
öî9õ¡ðï
Q
F
â*ðîHïøí=óóí
î9þ&òhöõ¡õ
qí Zï]þ&înöì
}*
Ï
ðö ZîHðõ¡ï
ú=û Ïd(
{öî Zóöðò öìôöì
ö²øõ¡öyí/ìô¬ðìï]öî î9öïí=ï]ðþ&ì¯þ
,ð"ö {î9ðõ¡ï
õ¡þ&ì
ú=û
¯ðî Zöìôö
hú
Ï
óð"öôînöõ¡öí=î9ò
&
&
û
*í=þ
í
&
ú
ÿöï þ&ôð Zôöî
/öìóðõ¡ïöìøìôí=ìôöînöìþ
í/ïö
Zóöÿ
ï]öî
÷
3
$
,ÿ¬ðï
î9í/í í=ìô
õ¡ðþ&ìí/ìô§ï ö
ë
Zöìöï]ðòyí
!d6
î9þ&í=ò §ïþï ö
ü
-þ&þ&ÿ¬í/ì
ü?öð
Zí=øõ¡õ¡ðí=ìî9öõ þ&ìõ¡ö²ÿþ&ôöó
/û=û ]ú
Zøí/ôî9í/ïðò²í/õ¡õ¡ð {ìÿöìï
/Ï
=Ï hú
ïöô¯í {öîHí {ð"ì
Ï =ú^ú
óþ
ú
Zðõ¡ïðò*înö Zî9öõ¡ù
bk &%Mj
ÝbuAÝGÛbuAV&r
5X
_
`
0
ú
( P (
( a )
% ( : 25 ":
} P ( w( J( r¢ 2
#% 8 $ 5 # > 56 } T 0 . ` }} (
` (D
( # 5 <>!<a6!5< 8 $ >\5 ": < \: 5 fW$% >M5 ": >!<a6 " < 6 \ 2# 5 < fWf ""$
< $% > (
w ` }2} (
9V 0K
a (b 6!5 > 7" 5 : $ |
@ ( w( 0" ( \V
Q2QdT . 0 0 . ` 0 (
( (
J H J( w0( %) ( H H
T 9
)
0
9 ( fW 6 $% 5 W57< 65 #%$ ><= ` T Q Q2Q2Q } ` .} 0 (
( (
(D P ( (
) -V
( T V
$%# |K. dT 2QQ2 ` } . (
( 7# 8 $% 5 #
( ( ø ( ) a "
7" 8d65 2>! 2.dT . }2@ ` 12. (
Q ( ( ø 2 ( ) 0 9
0 ( #% 8 $ 5 # " 865 > 2@ T 0 ` 2} ` . @ (
)
( $7# Q T .@ 0 2.Q2
1 ( ( ø 2 ( F
9 )V `.0(
. ( ( ¬ 2 ( 7fWf ""$ < $% >I5 ":W! > >< f > (
` 02@ (
( , ( ( ø 2 ( ( ø 2 (
x PW6 :2$% 57< $% 5 ":
0
# 57>> $ 5< $7 7fWf ""$ < $% > W5 ": > 8 < $ 2d 2 .2 D 2 ` 0 ( ( T( w HK ( V (
( PW6 :$ 57< $%~ # 5 < 7fWf ""$ < $% >!7V
I1 ) W5 :
} ( ( ø 77 Y 8 <=5< $% $%'i( w H" D ` 02} (
` ( ( ø 2
( ( ( ) 0 9_ T R
9 ) a
( #% 8 7Q.T Q ` 2Q21 2
` .21 (
2Q @ ( ( o ( ( ( H ( O !# 2fW < 6 $:+ < $%fW$ >!5< $7 < ! "$ " >
7 5> !:~7 8 !" < $% 5 # 8 6 $ < f >r5 ": > $%f "# 57< !: 5 "" 5 #$% 8dKV
` 1. )d3 < 6 < > $ f < 6 $%"'( `2` 1 (
2Q Dr( (
- ( ( ( F
9_
9V
" ( 6 5 # 8 <=5< $7 > $%" T 1 .} 0 2. @ 2 `` (
&
d(
ú=û
ïöî
p
&
(
ú=û
ü?í=ì
d(
ú Ï
&
Ù
ü?í=îHïöì
þ
ú
ë3ï öþ&î 5þ
n
{î9í/ôðöìï&í/ìí/ó {õ¡ð"õ
Ï ú Ï hú
A
hú
Ï
(
ú Ï ú
û
ìð {öîHõ¡ðï
ZöîHõ
Ï
înöìïðò^ö
=ú
P
ðó"ÿí=ì
îHð"ìòhöï]þ&ì
&
Ç
î9í/í kí=ìô
6
4
înöõ¡õ
îHðìò^öïþ&ì
6
!6
>
D
ú
/LQ3
þ&ó"øï]ðþ&ìí=ìô¬ï öìðò öyò^þ&ìò^ö ï
L;n
LØF
L
û
Zöî
öîHõ¡þ&ì
í=ìô
*þ
ó
øï]ïðì
kï ðì
n
\ôöïî9öìôöôò^þ&î9î9öõ þ&ìô«öìò^ö²í=ìí=ó Zõ¡ðõ
{õ«ðì5þ&înôöî hí1òhîHðïð Zøö
6
=ú=û
Ï
ú
&
ü
(
ú Ï û
ü?öóôþ&ì
ðÿ
þ&îHïí/ìò^ö
<
&
L
=ú
Ó
û Ï
ü
ú Ï/Ïd(
Ó
ü
&
âö
ü
ö5ðìïöìõ¡ðï þ
fòhþ&ÿ
{öô®ôðõ¡ïðìò^ïðþ&ì¼í/ìôõ¡þ&ÿöð"ÿ
Zöï]í=ïðþ&ì®þ
ú
öïðïðþ&ì
öî9õ¡øõ4ðïõ
óðòhí=ï]ðþ&ìõ
!L ;L
²ï ö
Zînöí/ï¿õ¡ÿþ
p
®ÿþ&øìï]í=ðìõ
^ú
â«ö
ðïï]í Zöî
Ó
(
ú Ï
û
Zöïí/ïðþ&ì¬þ
O
p
]þ&îHìð"í
,óí=øõ¡þ&ì
ú
(
ú Ï
-
{öîHó"þ&þ
ð"ï]ïí Zöî
O
&
í=ìôÞü
*í=ì¼þ
ðï]ïí {öî
Oï ö5õ¡ðõ Zð Zþ&øFÿþ&øìï]í=ðìõ þ&î9ö Zþ&ì¬í/ìô?ò^í=óðù
û
Ï
hú
Ï=Ï
îHí=ôðöìïfí/ìí/ó Zõ¡ðõ²þ
<
{ö Zöï]í=ïðþ&ì
L ;L
/û
û
=û
ú
&
Ó
ü
(
ú Ï
ïðþ&ì
&
Ó
ü
d(
ú Ï
ðïï]í Zöî
3
ðïï]í Zöî
^Ç
@
ú
&
Ó
&
$
!6
ü
$í/òhÿð"óóí=ì ÷-þ&ìôþ&ì
Zú5öôðù
Ó
ì
dC L
ü
ðï]ïí {öî {öô«ð"ï]þ&î
ALF
L.8
í {öõ
F
^í
öËÓ¯í Zøö
øì
ðï]ïí {öîí/ìô1ü
ïí/ð"ìõ êí=îHð =þ&ìí
!6
>
P
öôðïþ&î
>
ü
ËÇ
/LB
ö1Óí Zøö
Ï
øì
ð"ï]ïí Zöî
I
(
ú Ï
î
ü
C
4
ìï]înþ&ôøò^ïðþ&ì
>
=Ï
d(
ú Ï
!6
=ú
ë
âö
ðöîHð"ì
ZîHí=ôðöìïí/ìí/ó Zõ¡ðõfþ
þ&ó"øÿö
ûköôðïðþ&ì
Zöïí/ïðþ&ìþ
Åþ
÷B
D
=ú
&ï öºõ¡í=ìïíÅòhí/ïí/ó"ðìí¿ÿþ&øìù
Zï öÅõ¡þ&øï õ¡óþ
p
ö
4
/û
/û
&
ú
ü?þ&ì
d(K2
ú
×
í=ìô
C
ú /ú
ü?þ&ì
3
ü
(
þ
!d6
×{ööí/ìô
r 96
î9ðì
$ðïò
>qd4 C
!6
F
>q
9
&
ü
öóó
Zöî
{þ&óøÿö
²þ
?v96
6
ú
öìöîHí=óð =öô
=û
;
í=ôô«ð"ï]ð {öÿ¬þ&ô«öó"õ4ðì
û
ú
ú
ó"í/ìï«öòhþ&óù