"#$&% (')$*% )+ +,-++
% . /0% )+
132547689:4<;=>25?@ACBD>>FECGHIECGJK
LNMO7PRQSMTRUVXWYU!ZN[\7]YP_^:WYP_MV)`FUTRTRUa!UVN^
bCc7TRd3eXZNfCgCgCe
!"$#% & '
(*)+(,.-/1012345"/16+2*-7)))))))))))))))))))))))))))))) 8
(*):9;016<;/16+2*-;=>?;@*A"B16<;-DCEA;01-6+-FG*HI;J6+KL4KCE6+M*A"=+6+N223O;-3DP%HQ;=R
F*2*016+/1NKS)))))))))))))))))))))))))))))))) 8
(*))+(TP%HU;B?B1VA"5"6<;=W5;B1A2YXZ9[>\CEA;01-6+-F]))))))))))))) ^
(*)_:9;016<;/16+2*-;=`;@*A"B16<;-D=+A;01-6+-F)))))))))))))))))))) ^
(*)_)+(ba[-2*/1NA"0[V2*6+-/2YXZc6+A"de)))))))))))))))))))) f
(*)_)g9;016<;/16+2*-;=>?;@*A"B16<;-ICEA;01-6+-FD;-3IHhaij)))))))))) f
kelDm%!!"$n]oEm In]WpW .!
)+(,.-/1012345"/16+2*-7))))))))))))))))))))))))))))))q(*(
)er;4B1B16<;-hHh6+J/1401AOHh23A"=+B[;-3hP%Hs;=+F*2*016+/1NKt)))))))))))q(*(
)_:9;016<;/16+2*-;=>?;@*A"B16<;-hr;4B1B16<;-IHh6+J/1401AHh23A"=+B?,U)))))))))q(
)ue9;016<;/16+2*-;=>?;@*A"B16<;-hr;4B1B16<;-IHh6+J/1401AHh23A"=+B?,1,D)))))))))q("u
v:w?oEx% yz W! {
_)+(|PJVA"016+KDA"-/1B?2*-hB1@-/1NA"/16+53;/};)))))))))))))))))))q(~
_)e2*-5"=+4B16+2*-)))))))))))))))))))))))))))))) *
:% !" hn\n kv
u)+(|[6+B15"01A"/1A3A"-B16+/.@DHIHe)))))))))))))))))))))))) *_
u)+(*)+( [V/16+KD6+;/16+2*-O2YXs))))))))))))))))))))) u
u)+(*)[V/16+KD6+;/16+2*-O2YX[))))))))))))))))))) *8
u)+(*)_[V/16+KD6+;/16+2*-O2YXW[)))))))))))))))))))) *8
u)+(*)ua[-2*/1NA"0[V2*6+-/2YXZc6+A"de)))))))))))))))))))) *^
u):9;016<;/16+2*-;=`;@*A"B16<;-DHIHd?6+/1NIrHIHq))))))))))))))) *~
!#"%$#&('*),+*-.$0/1'2"
3?N6+B?01A"V2*01/;6+KDB?;/[;VV=+@6+-FOc*;016<;/16+2*-;=`;@*A"B16<;-h=+A;01-6+-FO/12L/.d2L5"=<;B1B[2YXZdA"=+=R
M-2d?- KD23A"=+B 4OF;4B1B16<;-zKD6+J/1401ALKD23A"=+BO;-3zN6+33A"-$HI;01M*2czKD23A"=+B)I9;016<; R
/16+2*-;=%`;@*A"B16<;-]<9[>?=+A;01-6+-FI6+BO;h01A"=<;/16+c*A"=+@7-A"d ;VV012;5}N /12IKD23A"=%=+A;01-6+-F
/1N;/%265 A"01BKh;-@;3c*;-/};F*A"B%01A"B1VA"5"//125"=<;B1B16+5;=HICI;-3LHhai7=+A;01-6+-F/1N;/%5;-
`AB1A"A"-7;B[;V;01/16+5"4=<;0?5;B1A2YXZ9[>]=+A;01-6+-F)
87 9;:&(/1:$0/1'2"*:%<*=:?>@BA0/1:"CD@B:&."*/ "*EGF2H:I*/ JK+GJLCD/8M@?N
<1/ O*'*'*)P:"*)RQSH :%<1E'%&(/8$(OGJ
CEA"/ TB?5"2*-B16+3A"0;V012*`;`6+=+6+B1/16+5?KD23A"=d?6+/1NhB12*KDA?2*`B1A"01c*A"3Ic*;016<;`=+A"B.UDGB12*KDA[N6+3 R
3A"-7c*;016<;`=+A"BBV ;-37KD23A"=WV;0};KDA"/1A"01BWO)%3?NAOF*2;=W2YX/1NAO=+A;01-6+-FDV0125"A"B1B6+B
/12YX -3h/1NA2*V/16+Kh;=c*;=+4A[2YXZW\F*6+c*A"-hB12*KDA[6+-B1/};-5"A"B[2YX[UD)
3?NA =+A;01-6+-FjV0125"A"B1B 6+BI/.@V6+5;=+=+@j32*-A Kh;J6+KL6+"6+-Fz/1NA KD23A"==+6+M*A"=+6+N223
\
]U,^W")%CEA"/ TB?3A_X -A
\
]UG^W(`
\
]UaVb^W
\
]Vb^U8W
1(*)+(
/1NA=+2*FYR =+6+M*A"=+6+N2232c?dW(`fedgih
\
]U,^W.5;-h/1NA"-I`AA"JV01A"B1B1A"37=+6+M*Aj4
c?dW(`fedgih
\
]UaVb^W#kDedgih
\
]Vb^U8W 1(*)*
3?NA[c*;016<;/16+2*-;=;VV012;5}NDB14VV2*B1A/1N;/%/1NA[/1014AN6+33A"-Lc*;016<;`=+A"B%V012*`;`6+=+6+/.@
\
]VI%5;-D`A;VV012J6+Kh;/1A"3`@O/1NA[36+B1/1016+`4/16+2*-D%lL<d?NA"01A%mD;01A[/1NA[36+B1/1016+`4/16+2*-
V;0};KDA"/1A"01B}")(n2L6+-/1A"F*0};/16+-FO2*4/BodA5;-hd?016+/1Aj4
c?dW(`p %ldoI.edgih
\
]VIaUG^WaqjVrkDp %ldoI.edgih
\
]Vb^U8WaqjV 1(*)_*
a X/1A"0; XA"d]Kh;-6+V4=<;/16+2-OdA5;-hd?016+/1AD(*)_O;B 4
\
d?NA"01A
LdmW8W(` p %l]VI edgih
\
]VIaUG^W
%l]VI
1(*)8*
h*^^\
0`p %l]VI edgih
%l]VI
\
]Vb^U8W
1(*)^*
3?NAC R36+c*A"01F*A"-5"Ah*^^\
L01A"V01A"B1A"-/z/1NA736+B1/};-5"Az`A"/.dA"A"-\/1NA ;VV012J6R
Kh;/1A"3IN6+33A"-7c*;016<;`=+A"B[36+B1/1016+`4/16+2*- X4-5"/16+2*-7;-37/1NAO01A;=%N6+33A"-7c*;016<;`=+A36+B R
/1016+`4/16+2*-
\
]Vb^U8W")
,./W5;-`A%V012c*A"3/1N;/*^^\
j6+-2*/1NA"0Wd2*013B#c?dWLdmW8Wd?6+/1NA4;=+6+/.@
6X %l%`
\
]Vb^U8W")
3?NAc*;016<;/16+2*-;==+A;01-6+-FL5"2*-B16+B1/1B[6+-h4B16+-FL/1NA=+2dA"0?`2*4-3LdmW8W?;B X4-5 R
/16+2*-7/12I2*V/16+KD6+"A6+-B1/1A;3z2YX /1NAL=+2*FYR=+6+M*A"=+6+N223W)a[- P%H =+6+M*AD;=+F*2*016+/1NKQd?6+/1Nz;-
;VV012J6+Kh;/1A"3DP B1/1A"VI5;-h`A4B1A"3#4
"!$#&%('*) "!+
4 X J7KD23A"=%V;0};KDA"/1A"01BO;/W-,*.0/G;-3z4V3;/1ADc*;016<; R
/16+2*-;=V;0};KDA"/1A"01BBmh/12LKh;J6+KL6+"A-LdmW8W")
12'*) "!+
4 X JLc*;016<;/16+2*-;=V;0};KDA"/1A"01B?;/?m3,}G;-3L4V3;/1AKD23A"=V;0};KDA"/1A"01B?W
/12OKh;J6+KD6"A-LdmW8W")
465*7(54 8&9;: <<>=@?0AB: C@A: <>?EDGFIHJLK?0: M3N-BNO
PjNA"-h%ldoI(`
\
]Vb^U8W%/1NA=+A;01-6+-FL;=+F*2*016+/1NK`A"5"2*KDA"B/1NA5"=<;B1B16+5;=WP%HU;=R
F*2*016+/1NK X2*0HICO/10};6+-6+-F?`A"5;4B1Ah*^^\
0`]?;-3/1NA%B1/1016+5"/=+2dA"0E`2*4-3@LdmW8W
6+BA4;=E/12O/1NA=+2*FYR=+6+M*A"=+6+N223W),.-D/1N6+B5;B1A/1NA;VV012J6+Kh;/1A"3DPZR B1/1A"Vh`A"5"2*KDA"B?;-
A"J;5"/OPZR B1/1A"V `A"5;4B1AD/1NALA"JVA"5"/};/16+2*- 6+B32*-ALd)0)/)L/1NAL/1014AL36+B1/1016+`4/16+2*-z;-3
-2*/?/1NA;VV012J6+Kh;/1A"3L2*-A*)
$Q 9;:&(/1:$0/1'2"*:%<RG:?>@BA0/1:"R<1@B:&."*/ "*E
a[-D6+KDV2*01/};-/%4B1A2YXZc*;016<;/16+2*-;==+A;01-6+-FO6+B/1NA;VV012J6+Kh;/16+2*-2YXZV2*B1/1A"016+2*0?3A"- R
B16+/16+A"B?6+-h`;@*A"B16<;-D=+A;01-6+-F)
CEA"/ TBO3A_X -A
\
]UO/1NAD=+6+M*A"=+6+N223I2YX ;DV012*`;`6+=+6+B1/16+5LKD23A"=%; X/1A"0O/1NADKD23A"=TB
V;0};KDA"/1A"01BBW\N;B?`A"A"-I6+-/1A"F*0};/1A"3h2*4/)%CEA"/ TB[d?016+/1Aj4
\
]UO(`
\
]U8W
\
dW2^UO
1(*)~*
;-3hB12 4
edgih
\
]UO(`fedgih
\
]U8W0kDedgih
\
dW2^UO 1(*)f*
a[F;6+-OdA?B14VV2*B1A?/1N;/%/1NA?01A;=V2*B1/1A"016+2*0%36+B1/1016+`4/16+2*-
\
dW2^UO5;-L`A[;VV012J R
6+Kh;/1A"3Od?6+/1Nh;36+B1/1016+`4/16+2*-TSdW2^UO/1N;/dA[d?6+=+=5;=+= U
"V3XWYYX) "!
;-3DB12
6+-/1A"F*0};/16+-FO2*4/?KD23A"=V;0};KDA"/1A"01BBWOGdA2*`/};6+-#4
\ p \ p \
Hh4=+/16+V=+@6+-FI/1NAIV012*`;`6+=+6+/.@
\
dW2^UOO/12*V$;-3$`2*/1/12*Ks`@SdW2^ULO;-3$01A;0 R
0};-F*6+-FOF*6+c*A"B 4
edgih
\
]UO(`LdWh"SdW2^UL ^^\
dW2^U1 1(*)+(*
d?NA"01A
LdW0`p SdW2^UO edgih
\
]U8W
\
dW2^UO
q W 1(*)+(*(
a[BL`A X2*01A*Gh"SdW2^UL ^^\
dW2^UO16+BL/1NA&C R36+c*A"01F*A"-5"Ah`A"/.dA"A"-j/1NAI;VV012J6R
Kh;/1AV2*B1/1A"016+2*0[36+B1/1016+`4/16+2*-I;-3h/1NA/1014AV2*B1/1A"016+2*0[36+B1/1016+`4/16+2*-W)>A"5;4B1AO2YX /1NA
X;5"/-h*^
\
($Od?6+/1NhA4;=+6+/.@Ld?NA"-I`
\
dA2*`/};6+-
edgih
\
]UO(LdW 1(*)+( *
HI;J6+KD6+"6+-FLdWWKDA;-BWKh;M*A/1NA?;VV012J6+Kh;/1AV2*B1/1A"016+2*0%;B5"=+2*B1A?;BV2*B1B16+`=+A
/12L/1NA/1014AV2*B1/1A"016+2*0)[B16+-FL>?;@*A"B?014=+A
\
]U8W(`
\
]UG^W
\
dWdA5;-hd?016+/1Aj4
LdW0`p SdW2^UL edgih
\
]U,^Waq W kh"SdW2^UL ^^\
dW1 1(*)+(_*
3?NA C R36+c*A"01F*A"-5"AL6+-7/1N6+B5;B1AL6+B/1NAL36+c*A"01F*A"-5"AD`A"/.dA"A"-z/1NAD;VV012J6+Kh;/R
6+-FzV2*B1/1A"016+2*0h;-3$/1NAhV016+2*0)f3?N6+BLKDA;-BO/1N;/D/1NA&4;-/16+/.@h"SdW2^UL ^^\
dW1
VA"-;=+6+"A"B[KD2*01A[5"2*KDV=+A"JOKD23A"=+B)
3?NAL`;@*A"B16<;- X0};KDA"d2*01Mh5;-7`ALA"J/1A"-3A"3 /12hKD23A"=+Bd?6+/1N7N6+33A"-7c*;016<;`=+A"B
Vz)%,.-h/1N6+B?5;B1ALdW%5;-I`Ad?016+/1/1A"-#4
LdWOaVI(`
p
SdWOaVb^UO edgih
\
]UaVI8W
SdWOaVb^UO
q W qjV 1(*)+("u
[B16+-F[/1NAZX2*=+=+2d?6+-F X;5"/12*016+;/16+2*-24SdWOaVb^UL0`SdW2^UOS]Vb^W;-3
\
]UaVI8W0`
\
]UaVb^W
\
dW?dA5;-hd?016+/1Aj4
LdWOaVI(`
p
SdW2^UOS]Vb^ULedgih
\
]VIaUG^W
S]Vb^UL
q WqjVkh"SdW2^UL ^^\
dW1q1(*)+(8*
3?NA X 01B1/O/1A"01Ks6+BO/1NAh;c*A"0};F*AD=+6+M*A"=+6+N2237d?N6+=+AL/1NADB1A"5"2*-3$/1A"01Ks6+BO/1NATC R
36+c*A"01F*A"-5"A?`A"/.dA"A"-L/1NA?;VV012J6+Kh;/16+-F%V2*B1/1A"016+2*0%;-3O/1NAV016+2*0)E,./5;-O`A3A"KD2*- R
B1/10};/1A"3 /1N;/d?NA"-q/1NA C R36+c*A"01F*A"-5"AL01A"345"A"BL/12z8^W j^ *edgihsd?N6+5}N
6+BL=+6+-A;0L6+- /1NAI-4KL`A"0O2YX V;0};KDA"/1A"01B ^W j^6.)A*)$AE)(*)+(_I5"2*0101A"B1V2*-3Bh/12z/1NA
>?;@*A"B16<;-h,.- X2*01Kh;/16+2*-L016+/1A"016+2*-W)
3?NA2*V/16+KD6+;/16+2*-2YX(*)+(_5;-D`A[32*-A4B16+-FO; X01A"A RX2*01K 2*V/16+KD6+;/16+2*-O;-3h;-
P%H R=+6+M*A;=+F*2*016+/1NK ;B?3A"B15"016+`A"3I6+-+()
%) "!+
4E5"2*KDV4/1AW/1NA%V2*B1/1A"016+2*0W2c*A"0E/1NA%N6+33A"--23A"BWB12*=+c6+-F LdWOaVI S]VI.`
O/12O2*`/};6+-#4
S]VI! "$#%&')(+*), 1(*)+(^*
3?NA-2*/};/16+2*-.-0/21
'
KDA;-B/1N;/?/1NA;c*A"0};F*A6+B?/};M*A"-hd)0)/SdW")
1 ) "!+
LdWOaVI SdW(`]O/12L2*`/};6+-#4
SdW! "$#%$&')(+*
\
dW 1(*)+(~*
3?NA-2*/};/16+2*-.-0/21
"
KDA;-B/1N;/?/1NA;c*A"0};F*A6+B?/};M*A"-hd)0)/S]VI")
,./ TB[6+KDV2*01/};-//12L-2*/16+5"A/1N;/?6X dA5}N22*B1A
\
dW?B145}NI/1N;/ SdW$WdW
\
dW
`A"=+2*-F*B[/12D/1NAOB};KDA X;KD6+=+@O6.)A*)
\
dW?6+B5"2*- 4F;/1A/12WdW"GW/1NA=+A;01-6+-FDV0125"A R
3401A"B[d?6+=+=B16+KDV=+@5"2*-B16+B1/1B[6+-D4V3;/16+-FON@VA"01V;0};KDA"/1A"01BG/10};-B X2*01KD6+-F/1NAV016+2*0
V;0};KDA"/1A"01B?6+-/12OV2*B1/1A"016+2*0[V;0};KDA"/1A"01B)
46554 N-D-?0M=@D6BNDGF-B?
a[-2*/1NA"0[d?;@D2YX=+22*M6+-FO/1NA2*V/16+KD6+;/16+2*-LV0125"A"B1Bd?;B?V012*V2*B1A"37`@hHh5;@I;-3
[A;=?<B1A"A ")%3?NA X 01B1/;B1B14KDV/16+2*-I6+B[/1N;//1NA"01AL6+B-2D365 A"01A"-5"AD`A"/.dA"A"-z=<; R
/1A"-/[c*;016<;`=+A"B?;-3IKD23A"=EV;0};KDA"/1A"01B 4%`2*/1Nh2YX /1NA"K 5"2*0101A"B1V2*-3B/12L4-2*`B1A"01c*A"3
B1/125}N;B1/16+5c*;016<;`=+A"B?;-3h5;-h`A/101A;/1A"372*-D/1NAB};KDA[=+A"c*A"=.)03?NAB1A"5"2*-37;B1B14KDV R
/16+2*-D6+B?5"2*-B16+3A"016+-FL/1NAO;VV012J6+Kh;/1A"3LV2*B1/1A"016+2*0 X;5"/12*016+;`=+Aj4
L[(`z
1(*)+(f*
d?NA"01AI6+B?/1NAA"-B1A"KL`=+A[2YX KD23A"=V;0};KDA"/1A"01B[;-3h=<;/1A"-/c*;016<;`=+A"B)
n2zdAh5;-$Kh;J6+KL6+"AL6+- /1NAhc*;016<;/16+2*-;=B1A"-B1A72YX /1NAh/1A"01K d?6+/1N$01A"B1VA"5"/h/12
M*A"A"V6+-FD;=+=2*/1NA"01B Yd?6+/1N`! [X JA"3W)
n2LdA5;-h01A"d?016+/1AD(*)+(_O;B 4
edgih
(` - edgih#"L]U$[$1%'&
(
*)1g+,.- 1(*)+( *
d?NA"01A-0/21,E3A"-2*/1A"B;-A"JVA"5"/};/16+2*-Od?6+/1N01A"B1VA"5"//12[/1NA36+B1/1016+`4/16+2*-O ,}]V,1")
n2L/};M6+-FOA"JV2*-A"-/16<;=+B?2YXZ`2*/1NhB16+3A"B[;-3h-2*01Kh;=+6+"6+-FdA2*`/};6+-#4
(`
0/
\ - edgih#"L]U$[$1%'&
(
1!243
0/
\ - edgih#"L]U$[$1
'&
(
1(*)**
3?N2*B1AA4;/16+2*-B[;01A5"2*4V=+A"3DA4;/16+2*-B?B16+-5"A/1NAB12*=+4/16+2*- X2*0?
3A"VA"-3B[2*-
A"JVA"5"/};/16+2*-B[d?6+/1Nh01A"B1VA"5"//12O/1NA2*/1NA"0 X;5"/12*01B
&
( )
n2D/1NAO2*V/16+KD6+;/16+2*-LV0125"A"B1B5"2*-B16+B1/1B6+-h6+-6+/16<;=+6+"6+-FA;5}N72YX /1NAL
;-3h/1NA"-
6+/1A"0};/16+c*A"=+@I4V3;/1ADA;5}N X;5"/12*0O;//16+KDAO4B16+-FIc*;=+4A"B5"2*KDV4/1A"3z34016+-FIV01A"c6+2*4B
6+/1A"0};/16+2*-B)
4655*7 H2: M3B:53BD6N-: C J:46(?0<>B: N K?0: M3N-BNO : N87 99 ;:
=<;B1B16+5;=Hhaiz=+A;01-6+-F5;-L`A[6+-/1A"01V01A"/1A"3I;B;B1VA"5"6<;=5;B1A[2YX c*;016<;/16+2*-;==+A;01- R
6+-F)32h2*`/};6+-7/1NADHhai X2*01KL4=<;/16+2*-h6+/ TBA"-2*4F*Nz/12hB1A"/L%l< ^UL`>=<%k;<?")
@01A"AA"-A"01F*@DKh;J6+KD6;/16+2*-O`A"5"2*KDA"B 4
ACB /4D
FE (
L< `
ACB / E
?HG
=<BkI<? edgih \
]U,^<
\
<qH<
`
ACB / E ?
edgih \
]UG^<?
\
<?1 1(*)(
G
/1NAOKh;J6+KL6+;/16+2-WGYX2*0[/1N6+B[01A;B12*-7N;B[`A"A"-73012*VVA"3W)rA"-A"0};=+6+;/16+2*-h/12DN6+33A"-
c*;016<;`=+A"B5;B1A6+B?A;B1@F*2*6+-F)
3?NADc*;016<;/16+2*-;=`;@*A"B16<;-z;VV012;5}NzF*A"-A"0};=+6+"A"BO/1NAhHhai]`A"5;4B1Ah6+/5;01016+A"B
6+- X2*01Kh;/16+2*-O;`2*4/%/1NA[4-5"A"01/};6+-/.@O6+-*W]A"c*A"-L6X 6+/ TB%2*-=+@O;-D;VV012J6+Kh;/16+2*-W)@40 R
/1NA"01KD2*01AD5"=<;B1B16+5;=[Hhai\32A"B1-#T/D;=+=+2d;-@zKD23A"=B1A"=+A"5"/16+2*-$;-3 32A"B1-#T/L`016+-F
;-@D6+- X2*01Kh;/16+2*-O2*-D/1NAKD23A"= 4;=+6+/.@)
b
7* !#"%$#&('*),+*-.$0/1'2"
[-A[2YX /1NA?KD2*B1/V2*V4=<;0KD23A"=d?6+3A"=+@O4B1A"3L6+-OB1VA"A"5}Nh01A"5"2*F*-6+/16+2*-O6+B%/1NA?KD6+J/1401A
2YX F;4B1B16<;-B)\,.-j/1N6+BD5}N;V/1A"0hdAId?6+=+=[F*6+c*AI;-j2c*A"01c6+A"dQ2YX 5"40101A"-/Id2*01MB X2*0
=+A;01-6+-F7c*;016<;/16+2*-;=%`;@*A"B16<;-$rHIH<`;B1A"3$2*-+( ;-3_ O; X/1A"0LF*6+c6+-FI; X;B1/
01A"c6+A"d\2YXZ5"=<;B1B16+5;=P%HU;=+F*2*016+/1NK7)
a[B%F*A"-A"0};=-2*/};/16+2*-dAd?6+=+=*3A"-2*/1A/1NA?V3 X );B1B125"6<;/1A"3Od?6+/1NL;5"2*KDV2*-A"-/1B
F*4;B1B16<;-B?KD6+J/1401A;B 4
\
^W.`
(
/ \
^W
(`
(
/
z
)+(
d?NA"01A
1 ( /
`([;-3DA;5}N
\
6+B?;F;4B1B16<;-D3A"-B16+/.@ X4-5"/16+2*-LV;0};KDA"/1A"016+"A"3
`@ W
`
)$CEA"/ TBL3A"-2*/1AId?6+/1N$`,,
,( /
/1NAhN6+33A"-$c*;016<;`=+A"BO/1N;/
6+-36+5;/1A/1NA5"2*KDV2*-A"-//1N;/?F*A"-A"0};/1A"3I/1NA - ,
2*`B1A"01c*;/16+2*-,")
7*87 :+*A0A0/1:" H/8I2$(+2&(@rH'*)G@B<1Ab:"*) QSH :%<1E'%&(/8$(OGJ
aj5"40101A"-/[;VV012;5}N X2*0ZX -36+-F2*V/16+Kh;=V;0};KDA"/1A"01B X2*0%/1NA[rHIH 5"2*-B16+B1/1B6+-L/1NA
;VV=+6+5;/16+2*-D2YXZ/1NAP%Hs;=+F*2*016+/1NK ;B?3A"B15"016+`A"3I6+-h/1NAV01A"c6+2*4B[5}N;V/1A"0)
,.- X;5"/O6+- /1NAh5;B1AI2YX ;zrHIH/1NAhV012*`;`6+=+6+/.@I2YX N6+33A"-$c*;016<;`=+A"B6+BL/1016+c R
6<;=4F*6+c*A"- ;-z2*`B1A"01c*;/16+2*-!,"G/1NADV012*`;`6+=+6+/.@I2YX /1NADN6+33A"-zc*;016<;`=+AC,,5;- `A
A"JV01A"B1B1A"3z;B 4
\
,,(`!, ^,10`
#"
\ "
, ^W "
1 ( / \
^W )*
n2z6+/ TBLV2*B1B16+`=+Ah/12z5"2*KDV4/1AD/1NAIA"J;5"/hPB1/1A"Vj6+- d?N6+5}N$/1NAIA"JVA"5"/};/16+2*-$6+B
32*-Ahd)0)/)z/1NAI/1014AhN6+33A"-$c*;016<;`=+AL36+B1/1016+`4/16+2*-B) a[VV=+@6+-FzP%H ;=+F*2*016+/1NK7G
dA"=+=EM-2d?-h4V3;/1A X2*01KL4=<;B X2*0[rHIHQV;0};KDA"/1A"01B?5;-h`A2*`/};6+-A"3W)
#"
` (
,( / \
, ^,"8W )_*
" ` 1 ,( / ,
\
, ^,"8W
1 ,( / \
, ^,"8W
)u
" ` 1 ,( / \
, ^,"8W",0k "
",#k "
1 ,( / \
, ^,"8W
)8*
7*$Q 9;:&(/1:$0/1'2"*:%<*=:?>@BA0/1:" :+*A0A0/1:" H/8I2$(+2&(@H'*)*N
@B<1Ar!
a[-O6+-/1A"01A"B1/16+-FO;VV=+6+5;/16+2*-2YX c*;016<;/16+2*-;=*`;@*A"B16<;-O=+A;01-6+-F[6+B%/1NA?rHIH /10};6+-6+-F)
CEA"/ TB?B1VA"5"6X@I;F;6+-L/1NAKD23A"= 4
\
^W(`
" (
/#
\
^W
0`
" ( / \
^,W8W
\
,*`!, ^W )^*
d?NA"01A
\
^,8W(`z
"
"
?;-3
\
,*`!, ^W.`
#"
)CEA"/ TB[3A_X -A5"2*- 4F;/1A
V016+2*01B%2*-OV;0};KDA"/1A"01B.Wf`
"
#"
"
") PzA5}N22*B1A?/1NA X2*=+=+2d?6+-F?5"2*-4F;/1A?V016+2*01B
X2*0V;0};KDA"/1A"01B?36+B1/1016+`4/16+2*-B 4
\
#"
(`hdm )~*
\
" ^ "
(` z " )f*
\
"
0` )*
d?NA"01Ah/3A"-2*/1A"B;L[6+016+5}N=+A"/36+B1/1016+`4/16+2*-WG z/;-2*01Kh;=36+B1/1016+`4/16+2*-h;-3
/?;@Pj6+B1N;01/?36+B1/1016+`4/16+2*-W)
CEA"/ TB3A_X -A-SdWW/1NA?;VV012J6+Kh;/16+2*-?2YX V;0};KDA"/1A"01BV2*B1/1A"016+2*0%;-3=+A"/ TB;B1B14KDA
/1N;/?6+/5;-h`A X;5"/12*016+"A"3h=+6+M*A SdW.`S
#"
"
S
"
"
")
[2d 6+/ TBWV2*B1B16+`=+A/12;VV=+@/1NA[P%H R=+6+M*A;=+F*2*016+/1NK]3A_X -A"3L6+- +( )W,.-/1NA[PZRB1/1A"V
dA2*`/};6+-#4
"
`S,2`!, ^
#"
"
/
.
.
(
.
(
. !"
)+(*
d?NA"01A
edgih#
#"
` - edgih
#"
1B` $?dm
"
0k%$?
"? m " ? )+(*(
edgih
" ` - edgih ^ "
^1B`
( /
$?1
"
](.kI *#kDedgih ^ "
^bqjedgih )+( *
&
' " ` B
"(
.0/
" )+(_*
3?N6+BA"JV01A"B1B16+2*-h6+BA46+c*;=+A"-/%/125"=<;B1B16+5;=WHIC7;5"5"4KL4=<;/12*0d?NA"01AV;0};KDA"/1A"01B
N;c*A%`A"A"-L6+-/1A"F*0};/1A"3O2*4/)$?,W6+B/1NA36+F;KDKD;ZX4-5"/16+2*-3A_X -A"3D;B0q(edgih)'%/jqH/W)
3?NA"-O6+-/1NAH RB1/1A"VO6+BWV2*B1B16+`=+A/12[4V3;/1A%V;0};KDA"/1A"01B2YX /1NAF;4B1B16<;-KD6+J/1401A"B
;BdA"=+=;B%-A"d$V;0};KDA"/1A"01BV2*B1/1A"016+2*01B/1N;/d?6+=+=N;c*A?/1NA?B};KDA X2*01K2YX V;0};KDA"/1A"01B
V016+2*01B?`A"5;4B1AO2YXZ/1NA5}N2*6+5"AdAN;c*A32*-AL<5"2*- 4F;/1AV016+2*01B}")
@2*0?/1NAF;4B1B16<;-hKD6+J/1401A?V;0};KDA"/1A"01B?dAd?6+=+=N;c*Aj4
"
` (
( / " " ` ( "
( /
"
W " ` (
" "
k "
"k "
)+("u
d?NA"01A "
`
"
)%i;0};KDA"/1A"01B?V2*B1/1A"016+2*01B[d?6+=+=EN;c*A[/1NAB};KDA X2*01K 2YXZV016+2*01B 4
S
#"
0`hdm
"
" S
" ^m "
(`z
"
" ' "
" S'
"
(`
"
" )+(8*
iW2*B1/1A"016+2*01B[V;0};KDA"/1A"01B?5;-h`A4V3;/1A"3 X2*=+=+2d?6+-F/1N6+B?014=+A"B 4
m " ` " m "
` " "
% "
% " " ` "
" ` " " ` " " " "
k% " " k
"
% 0 )+(^*
PzA5;-hA"JV01A"B1B/1NA;VV012J6+Kh;/1A?Kh;01F*6+-;==+6+M*A"=+6+N223I(*)+(8 4
` p S
#"
edgih
\
#"
S
#"
q
"( / p S'
" edgih
\
'
"
S'
" q ' "
" ( / p S
" ^' " edgih
\
" ^' "
S
" ^' " q "
"( /
( /
S, p S
edgih
\
,(^
S,
q
" ( /
( /
S, prp S'
"
S
" ^' " edgih
\
(^' " "
$,aq ' " q " )+(~*
@W6+01B1//1N01A"A?/1A"01KDB;01A(C R 36+B1/};-5"A?;-3/1NA=<;B1/W/.d2;01A/1NA?;c*A"0};F*A=+6+M*A"=+6+N223W)
`Sk,c
dmW8m #k
" ( /
,c
B "
("
B
(
k
" ( /
,c A "
("
" B " A
("
B "
1
" ( /
c E, )+(f*
d?NA"01A
c E,.` "
edgih
#"
k
( / "
edgih
"
" kBqjedgih -Dedgih
' "
k' " "
kDq2 "
)+( *
C\36+B1/};-5"A"Bh`A"/.dA"A"-]V016+2*0D;-3$V2*B1/1A"016+2*0D5;-j`AI6+-/1A"01V01A"/1A"3\;Bh;7KD23A"=
VA"-;=+6+/.@L/1A"01K;-3D/1NA X01A"AA"-A"01F*@2\5;-h`A4B1A"3h/12LB1A"=+A"5"/[/1NA`A"B1/[KD23A"=.)#3?NA
C7VA"-;=+/.@D01A"345"A"B/12L>,1jVA"-;=+6+;/16+2*-D/1A"01K d?NA"- 6.)A*)4
(
L
A
.`
( / edgih
\
0^W#k
edgih )**
d?NA"01A
6+B[/1NAO-4KL`A"0[2YXV;0};KDA"/1A"01B[6+-7;DKD23A"=W2YXB16+"A
A ) @2*0;hrHIH
` A
1(( q qdq]( *")
@B<1Ar!0!
a]365 A"01A"-/c*A"01B16+2*-D2YX c*;016<;/16+2*-;=`;@*A"B16<;-LF;4B1B16<;-DKD6+J/1401A"B%N;B%`A"A"-hV012*V2*B1A"3
`@D>6+B1N2*V_ )[@VA"01V;0};KDA"/1A"01B;01ANA"01AO2*V/16+KD6+"A"3h4B16+-FD;GT/.@VA TKh;J6+KO4K
=+6+M*A"=+6+N223$/1A"5}N-64Az6+-jd?N6+5}N]/1NA7c*;=+4A"Bh2YX /1NA7N@VA"01V;0};KDA"/1A"01B7;01A75}N2*B1A"-
/1272*V/16+KD6+"AO/1NADKh;01F*6+-;==+6+M*A"=+6+N22372YX /1NAh2*`B1A"01c*A"3$3;/};h6+-zd?N6+5}N /1NAhKD23A"=
V;0};KDA"/1A"01B?N;c*A`A"A"-I6+-/1A"F*0};/1A"3h2*4/)
3?NA KD6+J/1401A7KD23A"=6+BI01A R6+-/1A"01V01A"/1A"3 4B16+-F$/1NA =<;/1A"-/Ic*;016<;`=+A"B , ]d?6+/1N
,
(Od?NA"01A `s(* //+
1 ( / ,
b`s(*),3?NAh=<;/1A"-/c*;016<;`=+A"B01A"V01A"B1A"-/D/1NA
F;4B1B16<;-D/1N;/?F*A"-A"0};/1A"37/1NA hB};KDV=+A"B)CEA"/- `A/1NA3;/};B1A"/GdA5;-hd?016+/1Aj4
"L",^%$,0`
( /
( /
z0^
" 3 )(
3?NAO=<;/1A"-/?c*;016<;`=+A"B*,
I;01AL;O36+B15"01A"/1AL36+B1/1016+`4/16+2*-h/1N;/[3A"VA"-3B2*-IKD6+J6+-F
5"2A 5"6+A"-/1B
"L, ^
0` ( /
( / " 3
) *
3?NA"- dAD6+-/1012345"AD5"2*- 4F;/1ADV016+2*01BO2*-zKDA;-BO;-3z6+-c*A"01B1AD5"2c*;016<;-5"ADKh; R
/1016+J$<dAD32*-#T/-A"A"3 5"2*- 4F;/1ALV016+2*01BO2*-zdA"6+F*N/1B`A"5;4B1AI;-@d?;@7/1NA"@zd?6+=+=`A
6+-/1A"F*0};/1A"3h2*4/}")
"LW0`
( /
z
^ * )*_*
"L?0` 0 ^[ )u
d?NA"01A \6+BD; X JA"3jV;0};KDA"/1A"0G 76+BL/1NAI4-6+/OKh;/1016+JEG%;-3 :6+BD;2Pj6+B1N;01/
36+B1/1016+`4/16+2*-Dd?6+/1NhV;0};KDA"/1A"01B h;-3L),./?6+B?V2*B1B16+`=+A/12Od?016+/1Aj4
"L"h %$, ^
#`!"L",^%$, "L, ^ "LW "L? )*8*
[2d$c*;016<;/16+2*-;=`;@*A"B16<;-L=+A;01-6+-F5;-L`A[4B1A"3D/12OA"c*;=+4;/1A?N@VA"01V;0};KDA"/1A"01B)
Hh6+J6+-F5"2A 5"6+A"-/1B
d?6+=+=`A2*V/16+KD6+"A"3O6+-h;B1A"V;0};/1AHQB1/1A"VW).n2O6+-/1012345"6+-FO;-
;VV012J6+Kh;/16+-F36+B1/1016+`4/16+2*-hLdW6+/?6+B?V2*B1B16+`=+A/12Od?016+/1Aj4
edgih#"L",^
(`fedgih p "L"h8W2^
aq Wf`fedgih p LdW
"L"h8W2^
LdW
q Wfp LdW edgih
"L"h8W2^
LdW
q W)*^*
HI;M6+-F/1NA;B1B14KDV/16+2*-O/1N;/;VV012J6+Kh;/1A"3OV016+2*01B;01A[6+-3A"VA"-3A"-/G6+/%6+B%V2*B R
B16+`=+A/12Od?016+/1Aj4
L%$,0`] W1
?1
"
, )*~*
a[VV=+@6+-FOKDA"/1N23D3A"B15"016+`A"376+-7(*)_)+(*G*dA2*`/};6+-#4
"
, `
( / ( / \ " 3
)*f*
W ` ( /
z
^A (
( )*
? ` ( /
^ (
(
)_**
d?NA"01AOdAN;c*A[3A_X -A"3
\ 2`
\
1 (
( /
\ )_(
\
`0/
\ - edgih ^
^1
Dedgih
k (
- 1
k - 1
k -!
1
0-!
1[
)_ *
( ` - 1
( /
-,
1 )_*_*
A ( ` (
.0/
- 1
( /
-,
1 )_u
/(
` @
( /
-,
1 )_*8*
(
`
( /
#
-,
1k
( /
-,
1-
1
k- 1
( /
-,
10-!
1
( / -,
1 )_*^*
;-3I;B1B14KD6+-FO/1N;//1NAA"JVA"5"/1A"37c*;=+4A"B[;01Aj4
-, 1B`
\ )_*~*
-
1B`
A ( )_*f*
- 1B`
(
.0/
A ( A ( )_*
-
1B` (
(
.0/
)u*
- edgih ^
^1B`
" ( /
$?1
(
j(.k , * q(edgih BkDedgih ^ (
^ )u(
[-5"A[; X2*01K]2*-/1NA?;VV012J6+Kh;/1A"3[V016+2*01B j
"
6+B;B1B14KDA"3WG6+/W6+BWV2*B1B16+`=+A
/12L5"2*KDV4/1A[/1NA=+2dA"0`2*4-3h2*-h/1NAKh;01F*6+-;==+6+M*A"=+6+N223#4
cD` - edgih#"L",^%$,10- edgih#"L,$10-bedgih#"LW$10- edgih#"L?1
"
d?NA"01A
-bedgih#"L",^%$,$1B`
( /
( / -;,
1 ( - edgih ^
^1k
q
edgih
k (
-
1\#
k! -
1k - 1
0-
1[1 )u_*
- edgih#"L,$1B`
( /
( / -,
1 edgih
)u*u
- edgih#"LW$1B`
Sq
edgih
0k
( / - 1 )u8*
-bedgih#"L?$1B` jk q
edgih Bk
qdqBkj(
u
edgih
k " ( / edgih
](.kI,
edgih ^2^
kbqBkj(
( / - edgih ^%^1k
(
( / -
1 )u^*
- edgih "
,$1B`
( /
( / -,
1bedgih -;,
1 )u~*
- edgih (
1B`
(
/ k q
1(6bedgih
10
(
edgih ^ ( ^ )uf*
- edgih
?$1B`
( / k (
q (
edgih ^ ( ^$
"( /
edgih)' (
](.kI,
(
edgih ^ (
^
(
kbqk$(
- edgih ^
^1k
(
(
-
1[ )u2*
[-5"AD/1NAL`2*4-3z6+B5;=+5"4=<;/1A"3zdALN;c*AL;- ;VV012J6+Kh;/16+2*-D2YX edgih#"L",^
")D,./
6+B-2d V2*B1B16+`=+AD/1NA"- /12I01A RA"B1/16+Kh;/1AD-A"d c*;=+4A"B2YX
4B16+-F7/1NADB1275;=+=+A"3fT/.@VA
TWKh;J6+KO4KQ=+6+M*A"=+6+N2237/1A"5}N-64A*) [A"016+c6+-FI/1NAh=+2dA"0`2*4-3$;-3 B1A"/1/16+-F7/1NA
01A"B14=+/1B[/12L"A"012G6+/6+B?V2*B1B16+`=+A/12L5"2*KDV4/1A[-A"d\c*;=+4A"B2YX
)
` (
+
( / \ )8**
n2/1NA?c*;016<;/16+2*-;=`;@*A"B16<;-O=+A;01-6+-Fd?6+=+=*5"2*-B16+B1/1B%6+-O6+/1A"0};/16+c*A"=+@4V3;/16+-Fc*;016R
;/16+2*-;=V;0};KDA"/1A"01B[;-3hKD6+J6+-F5"2A 5"6+A"-/1B)
Q* QfI @?&(/ J@"%$0A'2" A#>G"%$(O*@?$0/1-K)G:$0:
,.-I2*013A"0/12DB1/143@I/1NAA 5;5"6+/.@h2YX/1N2*B1AO/1N01A"AL;VV012;5}NWGdA01A;=+6+"A"37B12*KDAB16+K R
V=+AOA"JVA"016+KDA"-/1B2*-7B1@-/1NA"/16+5L3;/};D6.)A*)O3;/};DF*A"-A"0};/1A"3 X012*KU;DM-2d?-7F;4B1B16<;-
KD6+J/1401A*)
PzAO4B1A"3z;DB16+KDV=+A_LF;4B1B16<;-IKD6+J/1401Ad?6+/1NIKDA;-G R GR 8)8L8 G36<;F*2YR
-;=W5"2c*;016<;-5"AKh;/1016+JL;-3I /_O /8O /O;B?KD6+J6+-F5"2A 5"6+A"-/1B 8***B};KDV=+A"BdA"01A
F*A"-A"0};/1A"3 X2*=+=+2d?6+-F/1N6+B?36+B1/1016+`4/16+2*-W)
@W6+01B1/h2YX ;=+=[dA7/1016+A"3j/12 X -3]/1NA75"2*0101A"5"/I36+KDA"-B16+2*-$2YX /1NA73;/};zB1A"/I4B16+-F
/1NAL>,15"016+/1A"016+2*-W)C@W6+F*401AD_)+(B1N2d?B/1NALV=+2*/2YX
(
L
A X4-5"/16+2*-72YX F;4B1B16<;-
KD6+J/1401A"B /1NAKh;J6+KL4K\6+B X2*0KG`_/1N;/?6+B?/1NAA_5 A"5"/16+c*A-4KL`A"02YX F;4B1B16<;-W)
2 4 6 8 10 12 14 16 18
−2.5
−2.4
−2.3
−2.2
−2.1
−2
−1.9 x 10 4
gaussian mixture
BIC(m)
@W6+F*401A_)+(j4W>,1<KhX4-5"/16+2*-D2YXZF;4B1B16<;-hKD6+J/1401A"B
3?NA"-dAz/1016+A"3\/1NAzc*;016<;/16+2*-;=[`;@*A"B16<;-\/1A"5}N-64Az3A"B15"016+`A"36+-]5"6+/1A;/1/16<;B
PzA-2*/16+5"A"3h/1N;/?01A"B14=+/1B[2YX /1NA9[>?rHIHz(B1/1012*-F*=+@D3A"VA"-3B2*-h/1NA5}N2*6+5"A2YX
/1NAO5"2c*;016<;-5"AKh;/1016+JLV016+2*01B)[,.- X;5"/[/1NAOc*;=+4A2YX 3A"/1A"01KD6+-A"B[/1NAOF;4B1B16<;-B
5"2*KDV2*-A"-/1B/1N;/32*KD6+-;/1A"B[2c*A"0/1NAL2*/1NA"01B)23?NA"01AjTBO;DB16+KDV=+Ad?;@h/12IB1A"AL/1N6+B
V012*`=+A"K 46+-75"=<;B1B16+5;=?P%Hd?NA"- c*A"01@ XA"dc*A"5"/12*01BL;01Ah;/1/1016+`4/1A"3 /127;hF;4B1B16<;-
5"2*KDV2*-A"-/G/1NAI5"2c*;016<;-5"AIKh;/1016+Jz01A"=<;/16+c*AI/12z/1N6+BD5"2*KDV2*-A"-/L`A"5"2*KDA"BDKD2*01A
;-3$KD2*01ALB16+-F*4=<;0D;-3 6+-$/1NAh=+6+KD6+/5;B1AI2YX4B1/L2*-Ahc*A"5"/12*0 X2*0O5"2*KDV2*-A"-/O6+/
`A"5"2*KDA"B;L"A"012hKh;/1016+JE)%,.-79[>?rHIHzG`A"5;4B1AL2YX V016+2*01BG6+/[5;--2*/[N;VVA"-7/1N;/
/1NA5"2c*;016<;-5"AKh;/1016+JO`A"5"2*KDA"B[B16+-F*4=<;0?;-3Id?NA"- 4B1/[2*-Ac*A"5"/12*0[6+B[;/1/1016+`4/1A"3
/12;F;4B1B16<;-O5"2*KDV2*-A"-/G/1NA[dA"6+F*N/01A"=<;/16+c*A/12/1N6+B%5"2*KDV2*-A"-/F*2/12"A"012)03?N6+B
V01A"c*A"-/1B X012*K 2c*A"0 X /1/16+-F)
[-D/1NA[2*/1NA"0B16+3A*G/1NA[c*;=+4A?2YX ?6+B/1NA[Kh;6+-5;4B1A2YXZ;-2*/1NA"0VNA"-2*KDA"-2*-
/.@V6+5;=W2YX c*;016<;/16+2*-;=`;@*A"B16<;-h=+A;01-6+-F 4/1NAOB1A"=X<RV014-6+-FL6.)A*)%3A"F*01A"AO2YXX01A"A"32*K
/1N;/?;01A-2*/?4B1A"3I;01AV014-A"3I2*4/)@2*0/1N6+B?01A;B12*-h5}N;-F*6+-FO/1NAc*;=+4A[2YX [5;-
3A"/1A"01KD6+-A/1NA-4KL`A"02YX F;4B1B16<;-D5"2*KDV2*-A"-/1B?/1N;/?d?6+=+=`AV014-A"3W)
325"2*01012*`2*0};/1A[/1N2*B1A?6+3A;BdA?014-LA"JVA"016+KDA"-/1Bd?6+/1NO365 A"01A"-/ c*;=+4A"B%d?NA"01A
b` .q D;-3 L6+B?;O4-6+/?Kh;/1016+JEGjqL6+B/1NAc*A"5"/12*0?36+KDA"-B16+2*-W)
@W6+F*401A[_)?B1N2d?B%/1NA?V=+2*/W2YX /1NA?-A"F;/16+c*AX01A"A?A"-A"01F*@ X4-5"/16+2*-O2YX /1NA?F;4B1B16<;-
KD6+J/1401A"Bd?6+/1N `\(*)
@W6+F*401Ah_)_DB1N2d?B/1NADV=+2*/2YX /1NAD-2*- R-A"F;/16+c*AL5"2*KDV2*-A"-/1B X4-5"/16+2*-z2YX /1NA
F;4B1B16<;-DKD6+J/1401A"B?d?6+/1N `(*)
1 2 3 4 5 6 7 8 9
6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5 x 10 4
gaussian mixtures
negative free energy
@W6+F*401A$_) 4[A"F;/16+c*A X01A"A$A"-A"01F*@ X4-5"/16+2*-\2YX F;4B1B16<;-KD6+J/1401A"B X2*0 `(
<9[>?rHIHz(
@012*K X F*401A7_)G/1NAI`A"B1/DKD23A"=?6+BD/1NAIKD23A"=?d?6+/1Nj_zF;4B1B16<;-BL/1N;/D5"2*0 R
01A"B1V2*-3BL/12IKD23A"=%4B1A"3 /12IF*A"-A"0};/1Ah3;/};) @W6+F*401AD_)_hB1N2d?BO/1N;/O;=+=%365 A"01A"-/
F;4B1B16<;-5"2*KDV2*-A"-/1BEN;c*A%-2*- R"A"0125"2A 5"6+A"-/1B;/E/1NAA"-3O2YX /1NA9[>?rHIH/10};6+- R
6+-F)
[2d]5"2*-B16+3A"0[/1NAB};KDA[A"JVA"016+KDA"-/?d?6+/1N `(**)
1 2 3 4 5 6 7 8 9 0
1 2 3 4 5 6 7 8 9
@W6+F*401A _)_ 4;[2*- R "A"012j5"2*KDV2*-A"-/1B X4-5"/16+2*-]2YX F;4B1B16<;-\KD6+J/1401A"B X2*0 `(
<9[>?rHIHz(
@W6+F*401AL_)uDB1N2d?B[/1NAL-A"F;/16+c*A X01A"AOA"-A"01F*@ 4[6+/1Bc*;=+4A6+-5"01A;B1A"BV012*F*01A"B1B16+c*A"=+@
d?NA"-L/1NA?5"2*KDV2*-A"-/1B-4KL`A"0F*2A"BZX012*K (/12_;-3O/1NA"-L6+B%5"2*-B1/};-/)CE22*M6+-F;/
/1NA-4KL`A"02YX -2*-h"A"012D5"2A 5"6+A"-/1B[6+- X F*401A_)8GdA5;-h-2*/16+5"A/1N;/?A"c*A"-Id?NA"-
/1NAL6+-6+/16<;=W-4KL`A"0[2YXF;4B1B16<;-75"2*KDV2*-A"-/1B[6+B`6+F*F*A"0/1NA"-z_GE/1NALKD23A"=WV014-A"B
X01A"A"32*K 3A"F*01A"Ah/1N;/D;01Ah5"2*-B16+3A"01A"3$4B1A"=+A"B1BD01A"5"2c*A"016+-Fz/1NAh2*016+F*6+-;=%-4KL`A"0O2YX
5"2*KDV2*-A"-/1B)C@2*0/1N6+B01A;B12*-$;=+=KD23A"=+Bd?6+/1N7KD2*01AO/1N;-z_hF;4B1B16<;-BN;c*AL/1NA
B};KDA?-A"F;/16+c*A X01A"A[A"-A"01F*@L6.)A*)/1NA"@LN;c*A?/1NA[B};KDA?-4KL`A"0%2YX -2*-D"A"012OF;4B1B16<;-W)
[2d7=+A"/ TBW5"2*KDV;01AW/1NA%2*016+F*6+-;=c*;=+4A"BEd?6+/1N[/1NA%01A"5"2c*A"01A"3O2*-Aj4E2*016+F*6+-;=dA"6+F*N/1B
;01AO)L)_O;-37)8 01A"5"2c*A"01A"37dA"6+F*N/1B;01AO)*uL)8**^O;-3I) 2*016+F*6+-;=EKDA;-B
;01A G RGR ;-3.8)88 01A"5"2c*A"01A"3hKDA;-B;01A )(*G) R (*)*^GR (*) 8)8[u)
2*016+F*6+-;=36<;F*2*-;=%5"2c*;016<;-5"ADKh;/1016+Jz;01A +(h)8 +(I( +(I( 01A"5"2c*A"01A"3j36<;F*2*-;=
5"2c*;016<;-5"AKh;/1016+JL;01A ))8* +(*)*~)*f +(*)*_)*^ )
,.-5"01A;B16+-F I/12h/1NALc*;=+4Ah(**L3;/};h;01AL5"=+4B1/1A"01A"3 6+-7/.d2D5"=+4B1/1A"01B)@2*0/1N6+B
01A;B12*-7/1NAO5}N2*6+5"AO2YX /1NA hc*;=+4A6+B;-I6+KDV2*01/};-/?6+B1B14AO3A"VA"-36+-Fh2*-I/1NAL;VV=+6R
5;/16+2*-W)
[2d=+A"/ TBD5"2*-B16+3A"0I/1NA72*/1NA"0I;VV012;5}NjdA73A"B15"016+`A"3;Bh9[>?rHIH )3?NA
VN6+=+2*B12*VN@D2YX /1N6+B[;VV012;5}NI6+B?B1=+6+F*N/1=+@L365 A"01A"-/)?,.- X;5"/[/1NA6+3A;O6+B?/12D6+-6+/16<;=+6+"A
/1NAIKD23A"=d?6+/1N$;IN6+F*N$-4KL`A"0O2YX F;4B1B16<;-$;-3 =+A"/L/1NAhKD23A"=?V014-6+-F76+/1B1A"=X )
a[F;6+-hV016+2*01B?2*-I/1NA5"2c*;016<;-5"AKh;/1016+JI<NA"01A V=<;@h; X4-3;KDA"-/};=012*=+A6+-h/1NA
F;4B1B16<;-I-4KL`A"0[/1N;/d?6+=+=WB1401c6+c*AL;/[/1NALA"-372YX/1NAO/10};6+-6+-F)*@W6+F*401AL_)^OV=+2*/1B
F;4B1B16<;-O-4KL`A"0%;//1NA?A"-3L2YX /1NA?/10};6+-6+-F[B1A"B1B16+2*- X4-5"/16+2*-O2YX 5"2c*;016<;-5"AKh;/1016+J
V016+2*01B)
PzA?5;-L-2*/16+5"A[/1N;/%4B16+-FV016+2*01B X2*0 j`A"/.dA"A"-z([;-3h(*VA"01KD6+/1B/1NA[5"2*0101A"5"/
A"c*;=+4;/16+2*-h2YX/1NAO2*016+F*6+-;=EF;4B1B16<;-I5"2*KDV2*-A"-/1B[d?N6+=+A=+2dA"0[c*;=+4A"B;=+=+2d?B?KD2*01A
5"2*KDV2*-A"-/1B?/12LB1401c6+c*A; X/1A"0?/1NAV014-6+-F)
1 2 3 4 5 6 7 8 9 6.8
6.9 7 7.1 7.2 7.3 7.4 x 10 4
gaussian mixtures
free negative energy
@W6+F*401A7_)u 4[A"F;/16+c*A X01A"AIA"-A"01F*@ X4-5"/16+2*-$2YX F;4B1B16<;-jKD6+J/1401A"B X2*0 f` (*
<9[>?rHIHz(
Q*87 '2"*-?< +*A0/1'2"
PJVA"016+KDA"-/1BOB1N2d /1N;/L9;016<;/16+2*-;=>?;@*A"B16<;- /1A"5}N-64AI5;- NA"=+V /12 X /LKD23A"=
/1273;/};I`A"/1/1A"0D/1N;- 5"=<;B1B16+5;=?/1A"5}N-64A"B)$a[-@d?;@7dAhKL4B1/-2*/16+5"Ah/1N;/O/1N2*B1A
;VV012;5}ND;01A?c*A"01@LB1A"-B16+`=+A[/12V016+2*0%5}N2*6+5"A<A"c*A"-D6X dA[/101@O/124B1A[-2*- R 6+- X2*01Kh;/16+c*A
V016+2*01B}14W5}N;-F*6+-FV016+2*01BZX -;=01A"B14=+/B1A"A"KDB%/125}N;-F*A[5"2*-B16+3A"0};`=+@)@401/1NA"01KD2*01A*G
;B6+/Wd?;B-2*/16+5"A6+- u G/1NA?KD23A"=*B1A"=X V014-6+-F[N;B-2/1NA"2*016+5;=A"c6+3A"-5"Aj4WdA?32*-#T/
N;c*AL;L/1NA"2*016+5;=%01A;B12*- X2*0[B};@6+-FD/1N;//1NALKD23A"=WB1A"=X V014-6+-FDd2*01MB5"2*0101A"5"/1=+@
`4/?V0};5"/16+5;=WA"c6+3A"-5"A*)
1 2 3 4 5 6 7 8 9 0
0.5 1 1.5 2 2.5 3 3.5 4
@W6+F*401AI_)8 4 [2*- R"A"012z5"2*KDV2*-A"-/1B X4-5"/16+2*- 2YX F;4B1B16<;- KD6+J/1401A"B X2*0 `s(*
<9[>?rHIHz(
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3 10 4
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
gaussian number
covariance prior
@W6+F*401A_)^ 4WF;4B1B16<;-h-4KL`A"0X4-5"/16+2*-D2YX 5"2c*;016<;-5"A[V016+2*0<9[>?rHIH *
,./ TBD;=+B12IV2*B1B16+`=+Ah/127/10};6+-j;- HIH 4B16+-F7c*;016<;/16+2*-;=%`;@*A"B16<;- =+A;01-6+-F)D3?NA
X 01B1/ X2*01KL4=<;/16+2*-72YX /1NAhV012*`=+A"K 5"2*KDA X012*K Hh5;@ 6+-8 d?N273A"B15"016+`A"3]/1NA
/10};6+-6+-Fh2YX ;D36+B15"01A"/1AD3A"-B16+/.@7HIHs4B16+-FI[6+016+5}N=+A"/36+B1/1016+`4/16+2*-B;BV016+2*01B)O,.-
-A"J/[B1A"5"/16+2*-hdAF*6+c*A3A"/};6+=+B?;`2*4/?/1N6+B?B12*=+4/16+2*-W)
G /1A0-.&(@?$0@)G@"*A0/8$ >KH H
CEA"/ TB[5"2*-B16+3A"0?/1NA X2*=+=+2d?6+-F-2*/};/16+2*-B 4
` ,X/$,* ///+$,
4WN6+33A"-hB1/};/1AB1A4A"-5"A*), W(///
V ` //$/
" ////
42*`B1A"01c*A"3IB1A4A"-5"Ah/ W(///\
` B G B `!"L,,0/.` ^,,(`! 14B1/};/1A/10};-B16+/16+2*-DV012*`;`6+=+6+/.@OKh;/1016+JE)
( `
G"L/3,#`
A ^,,(`! A"KD6+B1B16+2*-LV012*`;`6+=+6+/16+A"B
`
G
`!"L,X/.`! 6+-6+/16<;=B1/};/1A36+B1/1016+`4/16+2*-
<` (
4WKD23A"=TBV;0};KDA"/1A"01B)
`
(
(
(
4N@VA"01V;0};KDA"/1A"01B[/1N;/3A_X -AV016+2*0?2c*A"08<
r6+c*A"-hV;0};KDA"/1A"01B8<G6+/ TBV2*B1B16+`=+A/12Ld?016+/1Aj4
"L]VI}?^<(`
.0/
,( / B
""
,( /
"
#"
/ <u)+(
;-3 X2*0/1NAOV2*B1/1A"016+2*0V012*`;`6+=+6+/.@D2YX/1NALN6+33A"-7c*;016<;`=+A"BGW6+/ TB[V2*B1B16+`=+AO/12
d?016+/1Aj4
"L?^VI8W0`
(
"L]Vb^W
.0/
,( / B
""
,( /
"
#"
/ <u)*
d?NA"01A "L]Vb^W?6+B?/1NA-2*01Kh;=+6+;/16+2*-L5"2*-B1/};-/)?Hh5;@I;B1B14KDA"B?V016+2*0[V012*`; R
`6+=+6+/16+A"B2c*A"0 (
=+6+M*A[V012345"/[2YX [6+016+5}N=+A"/?36+B1/1016+`4/16+2*-D6.)A*)
"L
^)
((`!0 ) e+.-
B
////B )
( <u)_*
3?NAA"-B1A"KL`=+A=+A;01-6+-FO5"2*-B16+B1/1B6+-h;VV012J6+Kh;/16+-F/1NA36+B1/1016+`4/16+2*-D2YX N6+33A"-
c*;016<;`=+A"Bz;-3LV;0};KDA"/1A"01B?W]`@L;-LA"-B1A"KL`=+A?36+B1/1016+`4/16+2*-DL8W") PzA[;B1B14KDA
/1N;/?/1N6+B?36+B1/1016+`4/16+2*-D5;-h`AB1A"V;0};`=+AB145}NI/1N;/ 4
L8W(`]W1[
1
(
1E
<u)u
3?NA2*V/16+KD6+;/16+2*-O/};B1MD5"2*-B16+B1/?6+-hKD6+-6+KL6"6+-F/1NA X01A"AA"-A"01F*@2LL8W114
L0`Sk p p p
L8Wedgih
"L]VI}8W ^
L8W
<u)8*
3?NAhB1/10};/1A"F*@zV012*V2*B1A"3$`@ Hh5;@z5"2*-B16+B1/1BL6+-z6+/1A"0};/16+c*A"=+@z2*V/16+KD6+"AOA;5}N$
d?N6+=+A[M*A"A"V6+-FL2*/1NA"01B[5"2*-B1/};-/)
3?NA=+2*FYRV012*`;`6+=+6+/.@5;-h`Ad?016+/1/1A"-#4
edgih"L]VI}8W2^
#`
#
'&
( /
(
kj( edgih
B
( /
( /
kj( edgih
( /
(
k$( edgih
.0/
,( /
edgih
B
""
,( /
edgih
"
bedgih
#"
/ )1g+,.- /Q<u)^*
[2d]=+A"/ TB?5"2*-B16+3A"0?/1NA2*V/16+KD6+;/16+2*-O2YXZu)^)
54654 = 3B B :53BD6N DGF
CEA"/ TB;B1B14KDA/1N;/[36+B1/1016+`4/16+2*-B[}}h;01A X JA"3WGE;-3I=+A"/?5"2*-B16+3A"0/1NA X01A"A
A"-A"01F*@I;B[; X4-5"/16+2*-;=E2YX ?4
L ` k p
?
k
#
'&
( /
(
kj( edgih
B
W
.0/
,( /
edgih
B
""
k?edgih
)1g+,.- / <u)~*
/};M6+-FO6+-B1V6+0};/16+2*- X012*K /1NA>?;4K RPzA"=+5}ND;=+F*2*016+/1NK7G6+/ TB?V2*B1B16+`=+A/12Ld?016+/1Aj4
,(
`
=,,.`! 1$,,0/.` Y" <u)f*
;-3hB12G6+/ TB?V2*B1B16+`=+A/12Ld?016+/1Au)~ 4
L(` p
edgih
?
#
B
k$(
Y;)1g+,.- <u)*
d?NA"01A
`
.0/
,( / , (
(
<u)+(*
[B16+-FIr6+``B TB6+-A4;=+6+/.@G/1NAOA"JV01A"B1B16+2*-
G
L/ edgih
(
(
6+BKD6+-6+KL6+"A"3hd?6+/1N
01A"B1VA"5"//12DL/`@DL/(`
/
2
d?NA"01AI6+B?/1NA-2*01Kh;=+6+"6+-F5"2*-B1/};-/)
n2L/1NA36+B1/1016+`4/16+2*-I /1N;/?KD6+-6+KL6+"A?u)6+B?F*6+c*A"-h`@D;OV012345"/[2YX[6+016+5}N=+A"/
36+B1/1016+`4/16+2*-B 4
(` ) e+.- B ( /
( / <u)+(*(
5465*7 = 3B B :53BD6N DGF
a[VV=+@6+-F/1NA[B};KDAV0125"A"3401AdA[5;-L2*`/};6+-L;-;=+2*F*2*4BZX2*01KL4=<; X2*0%}d?6+/1N
,(
`
=,,.`! 1$/3,#`
A <u)+( *
`
W=,X/B`! <u)+(_*
5465 = 3B B :53BD6N DGF
[2d=+A"/ TB X J }[}
;-37=+A"/ TB5"2*-B16+3A"0/1NA X01A"ALA"-A"01F*@ 4B1/ X4-5"/16+2*-72YX
/1NAN6+33A"-hc*;016<;`=+A"B?nE)
LW1 `k
W p
?
.0/
,( /
edgih
B
""
bp
[
( ,( /
edgih
"
p
edgih
k edgih W )1g+,.- <u)+("u
CEA"/ TB[3A_X -A
B
`0/
\ p
?
edgih
B <u)+(8*
`0/
\ p
( edgih
<u)+(^*
`0/
\ p
3 <u)+(~*
;-3h=+A"/ TB?01A"d?016+/1Au)+("uL;B
LW1(`
Wedgih
W
.0/
,( / B
""
,( /
"
" /
Y )1g+,.- / <u)+(f*
3?NA2*V/16+Kh;=W?36+B1/1016+`4/16+2*-D6+B?F*6+c*A"-D`@ 4
W(`
(
%
.0/
,( / B
""
,( /
"
" /
<u)+( *
01A"=+A"c*;-/DV012*VA"01/16+A"Bh2YX WD36+B1/1016+`4/16+2*-j6.)A*)4;-/16+/16+A"B
4B16+-F$; X2*01d?;013 R
`;5}Md?;013$;=+F*2*016+/1NKU4B16+-F
B
)b3275"2*KDV4/1AD/1N2*B1Ahc*;=+4A"BG%/1NA X2*=+=+2d?6+-F
X2*01KL4=<;[5;-h`A4B1A"3#4
p ) e+.- \
edgih
\ ` $?
0k%$? <u)**
d?NA"01A
$?/(`
=
= /
edgih '%/*`
<u)(
5465 N-D-?0M=@D6BNDGF-B?
,./ TB6+-/1A"01A"B1/16+-FI/12h-2*/16+5"AO/1N;//1NALB};KDA4V3;/1A X2*01KL4=<;5;-z`AO2*`/};6+-A"374B16+-F
/1NADP%H R =+6+M*AL;=+F*2*016+/1NK 3A"B15"016+`A"3 6+-7B1A"5"/16+2*-j(*)_)O,.- X;5"/O;VV=+@6+-F X2*01KL4=<;h(*)+(^
dAN;c*Aj4
S !
#" &')(+*),
`
G D ( 1
G
D ( 1
G D (
<u) *
;-3h3A_X -6+-F
B
;B?6+-D/1NAV01A"c6+2*4B?B1A"5"/16+2*-hdA5;-Id?016+/1A
S$
.0/
,( /
B
""
,( /
"
" /
<u)*_*
@2*0E36+B1/1016+`4/16+2*-V;0};KDA"/1A"01BG=+A"/ TBE2*V/16+KD6+"AW6+/1BEV2*B1/1A"016+2*0W36+B1/1016+`4/16+2*-L
"}L
(
"}L
")
a[VV=+@6+-F X2*01KL4=<;O(*)+(~dAN;c*Aj4
L
1L
(
1L
$!
#" &')(+*
\ \ ( \ <u)u
-2d?6+-Fh/1N;/[6+016+5}N=+A"/[36+B1/1016+`4/16+2*-7N;B5"2*-4F;/1AOV016+2*01B6.)A*)O/1NAOV2*B1/1A"016+2*0
V012*`;`6+=+6+/.@hN;B/1NADB};KDA X2*01K2YX /1NADV016+2*0V012*`;`6+=+6+/.@GWL
"}L
(
"}L
[d?6+=+=
`A[6+016+5}N=+A"/?36+B1/1016+`4/16+2*-B)
L
1L
(
1L
1
D
1
1
\ \ ( \
<u)*8*
[A_X -6+-F
,( , (
;-3
;B6+-/1NA?V01A"c6+2*4BB1A"5"/16+2*-OdA2*`/};6+-#4
L
1L
(
1L
$!F
B
1 3
1 3
.0/
0
1
3
.0/
\ \ ( \
1<u)*^*
,./ TB?A;B1@D/12L2*`/};6+- X2*01KL4=<;B X2*0[L
"}L
(
"}L
14
?
(`!0 ) e+.- B
<u)*~*
(
(` ) e+.-
<u)*f*
(`! ) e+.-
<u)*
G87 9;:&(/1:$0/1'2"*:%<RG:?>@BA0/1:" KH H /8$(O H H
,.-7/1N6+B[B1A"5"/16+2*-7dAOA"J/1A"-3z/1NAOc*;016<;/16+2*-;=E`;@*A"B16<;-IHIH X0};KDA"d2*01MD/12h5"2*-/16+- R
42*4B3A"-B16+/.@IA"KD6+B1B16+2*-hV012*`;`6+=+6+/16+A"B?4B16+-FDc*;016<;/16+2*-;=E`;@*A"B16<;-7rHIHs3A"B15"016+`A"3
6+-hV01A"c6+2*4B?B1A"5"/16+2*-B)
CEA"/ TB[M*A"A"VI/1NAB};KDA-2*/};/16+2*-B2YX V01A"c6+2*4B?B1A"5"/16+2*- X2*0?HIHV;0};KDA"/1A"01B?`4/
X2*0/1NAA"KD6+B1B16+2*-LV012*`;`6+=+6+/16+A"B)W,.- X;5"/?-2djdA[d?6+=+=5"2*-B16+3A"0?5"2*-/16+-42*4B?A"KD6+B1B16+2*-
V012*`;`6+=+6+/16+A"BKD23A"=+A"3D`@h;OrHIHz)
CEA"/ TB?;B1B14KDA?/1N;/ ` 1 ) z
6+B/1NA[V3 X 2YX A"KD6+B1B16+2*-6+-LB1/};/1A 1)
,.-h/1NAc*;016<;/16+2*-;=`;@*A"B16<;- X0};KDA"d2*01MO=+A"/ TB?3A_X -AV016+2*01B?2*-D/1N6+B4;-/16+/16+A"B[;B 4
\
)
0`hdm <u)_**
\
^
(` z <u)_(
\
(` <u)_ *
,.-IrHIHHIHQ/1NA"01A;01A/.d2O365 A"01A"-/?N6+33A"-Dc*;016<;`=+A"BB1A4A"-5"A"B 4/1NAN6+3 R
3A"-DB1/};/1AB1A4A"-5"AOz;-3D/1NA[N6+33A"-DA"KD6+/1/16+-F[F;4B1B16<;-Bq;-3DdA[d?6+=+=;VV012J R
6+Kh;/1A[/1NA"6+0?V012*`;`6+=+6+/16+A"Bd?6+/1Nh;O36+B1/1016+`4/16+2*-hL\"),./ TB?V2*B1B16+`=+A/12Ld?016+/1Aj4
"L]VI}^W#`
.0/
, ( / B
""
,( /
"
#"
/ <u)_*_*
d?NA"01A
"
`)
"
z
"
"
<u)_u
6+B/1NA[V012*`;`6+=+6+/.@O2YX /1NA[A"KD6+B1B16+2*-O2YX /1NAK R/1NOF;4B1B16<;-L6+-D/1NA[BR/1NDB1/};/1A*)%;-3
-2d =+A"/ TB%/101@O/12;VV=+@/1NA[P%H R=+6+M*A?;=+F*2*016+/1NK7),.-L/1NA[H B1/1A"VDdA?B1N2*4=+3O5"2*KDV4/1Aj4
S\!
# #" &')(+*), <u)_*8*
d?NA"01A
- edgih
\
]aVb^W$1
'
1B`
p
.0/
,( /
edgih
B
""
p
D
p
D
p
D
,( /
edgih
"
p
edgih
#"
/
`
.0/
,( / p
0edgih
B
""
,( / p
D
p
D
p
D edgih
"
,( / p
edgih
#"
/
<u)_*^*
[A_X -6+-FL-2d
B
`0/
\ p
0edgih
B <u)_*~*
`0/
\ p
D
p
D
p
D
edgih <u)_*f*
`0/
\ p
jedgih
<u)_*
L\0
.0/
,( / B
""
,( /
"
" /
<u)u*
2*KDV4/};/16+2*-O2YX
B
;-3
5;-h`A32*-A4B16+-F X2*01KL4=<;[u)*G*d?N6+=+A?5"2*KDV4/}; R
/16+2*-D2YX
5;-h`A32*-A4B16+-FL01A"B14=+/1B X012*K )+()
3272*`/};6+-z/1NAhV012*`;`6+=+6+/.@zL"G%6+/ TBOA"-2*4F*N /127Kh;01F*6+-;=+6+"ALL\d?6+/1N
01A"B1VA"5"//12DH2*`/};6+-6+-F 4
L(`
L\
.0/
,( /
B
""
,( /
"
" /
` .0/
,( / B
""
,( /
"
" /
<u)u(
,./ TBW6+-/1A"01A"B1/16+-F[/12?-2*/16+5"A%/1N;/WLE6+BW-2*/E/1NA%36+B1/1016+`4/16+2*-dA2*`/};6+-Kh;01F*6+-;=R
6+"6+-F "L]aVb^W;-3z/1NA"-z5"2*KDV4/16+-FD/1NALV2*B1/1A"016+2*0OL")D,.- X;5"/B12*KDA"2*-A
Kh;@B14VV2*B1A/1N;/WLE5"2*4=+3`A%2*`/};6+-A"35"2*KDV4/16+-F0/
\
- edgih
1
"L]aVb^W1
`A"5;4B1AI"L2`
1
"L\")D3?NAhV012*`=+A"Ks6+- 32*6+-F76+/O6+BO/1N;/DLL;-3
L\O;01Ah-2*/OA"J;5"/DV012*`;`6+=+6+/16+A"B`4/ 4B1/L;VV012J6+Kh;/16+-F X4-5"/16+2*-WG;-3 B12
OdnD6+Bh-2*/h/1NAzV012*`;`6+=+6+/.@ 3A"-B16+/.@j/1N;/h5"2*KDA"B X012*K/1NA7Kh;01F*6+-;=+6+;/16+2*- 2YX
i?dnEGHI"),.-72*/1NA"0d2*013B6+/ TB[365 A"01A"-//12D6+-/1A"F*0};/1AO/1NAO=+2*F;016+/1NK 2YX ;LB14K/1N;-
6+-/1A"F*0};/16+-FI/1NADB14Ks2YX ;h=+2*F;016+/1NK7)D,.KDV2*01/};-/B1/};/16+B1/16+5"BO2YX /1NAIL\36+B R
/1016+`4/16+2*- 5;-$`A X2*4-3 4B16+-Fz/1NA X2*01d?;013 R `;5}Md?;013$;=+F*2*016+/1NKs2*0O/1NAI9[6+/1A"01`6
;=+F*2*016+/1NK7)
[2dj=+A"/ TB5"2*-B16+3A"0?/1NAH R B1/1A"V#4%4V3;/16+-F X2*01KL4=<; X2*0%/10};-B16+/16+2*-DV012*`;`6+=+6+/16+A"B
;-3L6+-6+/16<;=*B1/};/1A[V012*`;`6+=+6+/16+A"B%;01A[;=+KD2*B1/W/1NA?B};KDA`A"5;4B1AL\W6+B%Kh;01F*6+-;=R
6+"A"3Ld)0)/) d?N6+=+A4V3;/1A X2*01KL4=<;B X2*0F;4B1B16<;-OKD6+J/1401A"B365 A"01B) PzA5;-Ld?016+/1A
/1NAH R B1/1A"VI=+6+M*Aj4
S
S
SWS?S)".`
# #" &')(+*
\ \ \
W
\
?
\
)"q<u)u *
d?NA"01A
- edgih#"L]aVb^W$18D # (`
#
L\ ,
edgih
B
""
,
edgih
"
Dedgih
/
`
L
,
edgih
B
""
#
L\
,
edgih
"
Ledgih
/<u)u_*
[V3;/1A X2*01KL4=<;B X2*0
B ;-3
;01A;-;=+2*F*2*4BW/124V3;/16+-F X2*01KL4=<;?6+-O/1NA?V01A R
c6+2*4BB1A"5"/16+2*-Ld?6+/1NO/1NA?2*-=+@365 A"01A"-5"A[/1N;/L5"2*KDA"BZX012*K/1NA?Kh;01F*6+-;=+6;/16+2*-
2YX L\")
CEA"/ TB5"2*-B16+3A"0W-2dz4V3;/16+-F X2*01KL4=<; 4B1/ X2*0WF;4B1B16<;-BEV;0};KDA"/1A"01B 4W/1NA%V012*` R
=+A"K6+B;-;=+2*F*2*4B/12B16+KDV=+AF*4;B1B16<;-OKD6+J/1401A"B%d?6+/1NO/1NA[365 A"01A"-5"A[/1N;/%6+-LNA"01A[dA
N;c*A[/125"2*-B16+3A"0?/1NAB1/};/1A[V012*`;`6+=+6+/.@O/12*F*NA"/1A"0d?6+/1ND/1NA[5"2*KDV2*-A"-/V012*`;`6+=+6+/.@)
PzA[5;-Id?016+/1Aj4
#
L\
,
edgih
"
` ,
"
#
L=,,
A
,1edgih
"
` ,
L,,"
A
,. edgih
"
<u)u*u
d?NA"01AL
"
#
6+B[/1NAO;VV012J6+Kh;/1A"3DV012*`;`6+=+6+/.@ X2*0[`A"6+-FL6+-IB1/};/1A,O;/[/16+KDA-
;-3 X2*0EA"KD6+B1B16+2*-[2YX F;4B1B16<;-K7) 3?N6+BE/16+KDAWdA5;-d?016+/1A%L,,"
A
,1(`jL,,}1L
A
, ^,,.(`
L,,1
1
)3?N6+B6+B/1NAOB};KDAA"JV01A"B1B16+2*-z5"2*KDV4/1A"3I6+- )_L4B16+-FIL,,"
A
,.
6+-B1/1A;3z2YXB16+KDV=+@hL
A
")L,./KDA;-B[/1N;/4V3;/1A X2*01KL4=<;B X2*0F;4B1B16<;-7V;0};KDA R
/1A"01BL5;-z`AD2*`/};6+-B;BO6+-7B1A"5"/16+2*- )_D4B16+-F " # ` 1 " #
L,,"
A
,.6+-B1/1A;3 2YX
" ` 1 " )
+( a?/1/16<;BO)Wa]c*;016<;/16+2*-;=`;@*A"B16<;- X0};KDA"d2*01M X2*0F*0};VN6+5;=KD23A"=+B)
-#
U
V$!)
V@!>XW $V "V$!)$)V) "!@)
GE( G ***)
Pj6+--)>6+B1N2*VI)Hz)0n/10145"/1401A"37c*;016<;/16+2*-;=36+B1/1016+`4/16+2*-D6+-hc6+`A"B)
$!$!$#X'
VX)- "XW$V3 "!WW!V$!V3# " ") ")!T!) 6W# G ***_)
_ >6+B1N2*VL)Hz)2*0134-A;4OaO)9;016<;/16+2*-;=`;@*A"B16<;-OKD23A"=*B1A"=+A"5"/16+2*- X2*0WKD6+J/1401A
36+B1/1016+`4/16+2*-B)
$V !-"3#X)VTV3## $>%%XW'&"%#X)( )* +> "'$V3 , .-6V/
VT "XW $V3 "!WW!V$!V3# " ") ")01,V#/ V3V
GV;F*A"B *~*0 _u)
u! HI;5;@zO)))DCE25;=KD6+-6+KD;GB1@KDKDA"/101@I`01A;M6+-FI;-3zKD23A"=%V014-6+-FI6+-
c*;016<;/16+2*-;= X01A"AA"-A"01F*@hKD6+-6+KL6+;/162*-W)
8 HI;5;@hO)))P-B1A"KL`=+A[=+A;01-6+-F X2*0?N6+33A"-hKh;01M*2cOKD23A"=+B)