Efficient Algorithms for Lateral Gene Transfer Problems - IC

Efficient Algorithms for Lateral Gene Transfer
Problems
M. T. Hallett, J. Lagergren
A>20@-A>e>0A>>!ZCZ<A
Z<A>V!@R:i!
>
e>Vb`U@U>@PJIbA>K@*J,>@CgA>V}Z*A>@
JF: P: AP:
VA>BYC!@ªA2B!@* m@A>t79: ;: <:d‰ˆ!(BpVŠPˆ!.%‹$"d%1(2$!.3l4P&)(
@A>BG8UP!Z2P±H-`-\z5!mw!V!\,A>K>2@U0L‰ˆ!sg²
p .-+&).†ˆ!.‡o"V&2$!3&)3L!@–(2&>o>ˆ!s[³p .$%1p9ˆ!.:´”Y@µn71-`<!v
A>)A>VU!b`–U2>UA)G2UmA2>Wk!@–´2Am!
71-`<!v
A>)A>VU!b`ªU!2>UA)G^C@EA2>^M N OSSSO*M T @!A=@U2>e>`
b2JIV2}Z!a!8P}-Z!DA>ªW,\_A>[C!!y x @ªA>L@v
gZ¶@ZgH)F!IVA>)B!zA2B@*5>g@U2>e2`A>0w<l@
A>´·{>!C>@-A>¸<:±
!eJI
ZLA>V<@-A>l`nP<C
!yMDNPOSSSO*MRT[A>A=U!2>2!@<=A>mVA>)B!DA2B!@* >\X!@
JI)>FV@0WnA>2=A2B!@* >d-UUZ<P:
ABSTRACT
!#"$!%'&)(*$",+-&)./&0%1(2$!.354&)(
&)6!&).%13879: ;: <:=!>?!@-AB!DC@EA2B!@*5F@-A>BGIHA'J@
K2AL!C@
A2>FMDNPO*MRQOSSSPO*MRTK!@02UV8A2>W,:
X#A>H*A
!YZ[;<@PJIVC!\,A>[<]2222
C!C>^XHC!VU!_!@[
A>
A>UP!2Z@@2
A>@E!@-`=A>R>!2PF@FA>abA>BA>Z<>:Dcd@C
!A>EH!V!CUP,U!@2VBeA>@\XA>[<f>2UA>FA>
e2A>V!F!B<0gZA>!@hVViH-`hW:kjhbA>@h!Z
9\<JFV<@-A>l`m!@n$o%1p56Pp %1qFr<$!(2$s
&)%'&)(]A>eAIP!2Z<>
A>t@ZLH!8C@KA>AK>u!PJPiA>nHu2gZbABv
@Z2b`!UA>gV@uA>[C!@![!dmABewK!@u2eJkA>eA
x @@C
A>g*AF>2@V!ZE2U@>KA>AF>U!@U
A>>!C>@CFC!@,A2>DJIA>8A>2UyA2>z<H
@K!`<@V!/A>YJI@A>FUA>A'`VR!@@ZgH)
!A2B@*5>e>d2
9\HZAy@-A2B!UABHI@[C@B!1:zX=A>
H*A,!f!Z,;<@PJIVC!\!A>)V,>!2P@A>
bA>BA>Z<>=!22Z^VUbA>b`[A>AyA>^!UA>bA{`,!@:y|fbv
@`-\_Z2V@C0eAB!2AEHUA>>V!aC!@L2P}-Z@UYl>
~ !€ \<Z<@-ABeA>V!@a !Z@F<A>V
2U@>‚@
!/JIVUB
zA>d2U@>8>!2PH-`LA>^ZA>!>,@ ~ !€ :
¹y>b`FeA2A>A>A>IZ2aC@BV?EZA>!@2`=<v
KA>º!PJ» ªVA>BEA2B@*5>ª2ZUBi!KA>º.&)%1¼zˆ!(>½
sˆP†&" ~ Že¾\XŒ<\X € \R@2b>Pt2)B!a>Fw!@@C
A>
3>‡³%1(>&>&F%1(*$!.3l4P&)(z)BA>@m@
PXlHPA2> ~ \<\/ŽP¿<\
ŽŽ € :
À{@uK2ZH<A2>gA2B!@* 8!BA>@_\DK2ZHA2>LM^Áy!]
A2>M…@µ!@nCmÂm@!AgU@-AB!@P´@µM Á e>mUB!2@R\
@J’)2A>wªÃªF@A2><ZU#H-`ª2ZH/l<@CmÂ-\R@ªM Á
]A2B!@*52>PK2[!IA>g
!;=bA>I>-AIA>F2U!@KUBVm
Ã:m”Y@#A{JKVIV!HPA2>\XA>mÄÅ/Æ<ÇÈÉÉ´ÊYÈË_Ì_Í)Î
Ï É<È0>HÐ!2;IA> x @A>YV@gZ—@ZgH)]!a2ZHv
A2>A2B@* )z!BA>!@zA>ADA2B@* >’@A2>]V@-A>YA>
2U!@/:]d>!HÐ^;@PJI@KA>HEÑKÒYv'UA>=5!
Z@<>-!A>P8H@e2`LA2>aHZAy<>ew<
!H,A>YJIbA>@^ !Uv
A>!Ia ~ Ž¿ € :zjC-A>P>2@]!fA>=>!H…e>E!2
;@PJI@KA>[H8>Pw<
!HV=A>LJIA>@t[V!Ce>A>UE !Uv
A>!dZ@)Ig@PeYU!*Ad2U!>@C2UB ~ \ € :
1.
dUINTRODUCTION
!A>@R!>!ZyH!U)A>>V!2P}-Z@U@CF<>ƒ{UA>
Y>@5!>UtA>LJ„A>A=ZA>!@2`K>VA>@2
HA'J@0ABew0719: :A>E2UdA2>BGdU!@@!A^HEV@< 2>
5>!…E2V@CYC!@d1Vb`t711: :82@CYC!@dA2>eG,<ZIA>
!ZA>@2`m@-A>]2ZUB0=+-&).&L†!‡er" p1oB$%1p9ˆ!.\+-&)./&L"ˆ3B3>\
+-&)./&
o>ˆ!.6!&)(1+-&).oB&)\y!@n‰ˆ()pVŠPˆ!.%‹$"X+-&)./&
%1(*$!.3l4P&)(g712 ~  \
\Œ<\<\ŽP\ސ<\ŽPŒ € G):a‘dU@-A x @@CDP!2=!A>!A>P
A>gC@UFU!gZ@bA{`KA>KA>)>V@geJ’ZHV}-ZbA>Z
e“ UP”YV–•,@-A2>— k˜,@5!>
eA>VU\ “ Ue”YVš™Y@V2v
2bA{`-\ “ @-A2>P9\•!@\[›=AP:=K•,Z<A>œ<U@U\
<žŸŸ ¡¡-¢-£¤X¥ ¦£e§<¨ŸŸf¥*£ž
œ-A>-U);’˜,@5!>
eA>VU•,@-A>y@8›=AP:©YZ2v
UP!fc^@b`2^!@ª•,ZA>Yœ<UV@U\«E¬L\œA>-UB;<0\
œJ,P@R\­ !®¤Ÿ!¢!®<ž!¯žX¥9°¡y¥*¤! Permission to make digital or hard copies of part or all of this work or
personal or classroom use is granted without fee provided that copies are
not made or distributed for profit or commercial advantage and that copies
bear this notice and the full citation on the first page. To copy otherwise, to
republish, to post on servers, or to redistribute to lists, requires prior
specific permission and/or a fee.
RECOMB 2001, Montreal, Canada
© ACM 2001 1-58113-353-7/01/04…$5.00
149
##Z2u!@!A>)´>!UBÓA>eA#!t>v
U=U@2l<B!HA2A>@A>!@8e)XA>a!*Af2B!!`-P>:
À'A=VF2VFA>A>AF!V#A>mA>[Ô8Å/ÕÖ!×5ØËÇ×lÙRÌÎ*ÚaÙ_ÍÍ
>!H0\_@-A2>ZUP#@ ~  € :[À{@tA>F<>H0\/A>[@Z<A
U!@2*A>XI<V*A>@CZ2P=A2>aUP!P=A>]39r&2op‹&)3z%1(2&>&X!@
F2Az!f+-&)./&^%1(>&>&)3>:,>ZC[A>^!*A>ZVA>@
D+-&).&=†!‡<²
r" p9o>$!%1p1ˆ!.!@ª+-&)./&g"ˆ!3>3]@-A>\!@EHZVV<YKs[$)rrp .-+E
A>,C@IA2>aV@-A>YA>]2UaA2>5>!ÛJIU)[!@[Zv
A>@2`P@@C Zw<V!@A>@!=(2&2oBˆ.op1" p9$%1p9ˆ!.LUP!@H
)>VP_:mœZUB>!HFeH@*A>ZP)w<A>@2b`
712 ~ Ü \d¾\^Ž  \YŽe\YŽ ܀ !!@C!*A!A>>BG[!@š@š2B!
bÝ/>@ALU!@A>)w<A>:|[w!\a@ ~ Ž € #
V@C0Hv
A{J,@
!*AI!@B2A>^A2>IP[JIVUBm!eJI
dH!A>t‰<ˆ!3>%3>¼yp5%‹oB‰p .+E!@r<$!(*$!3>p %'&g†!‡er" p1oB$%1p9ˆ!.:
]!]5!>gZVA>dL</!XleA>B!_A2B!@* >
JIUBhKH!V!CUPVb`i2!Z@„71bAmUP!<A>Z>
!@-`š!2v
AB@-A[2UA>gIA>H!V!CUPI>!bA{`G8@nV2t
eA>v
eA>UP!b`ª2Z@´7 A>E x @bA>@ªY<>U2eG):^XA>EH*A
IZ<L;@eJIP<C<>V!ZEVEe[1!PJIbA>>v
2UAgA>#AgP!*Ag@!dA>2m<2bB!HVm>!2A>:À'@
!Z]<A>^C@^A2>^]
!
@-A>EA>d2UA2>
F@ ~ Ž\f\yŽ € H-`t
!@C>A>*5`<@C0U2AB!@HCv
UP`i2!Z@–U@bA>@:—|Z<2A>>>\IJu<>2*v
2Z=@-A2B!UABHA'`t2VVe=A>A>2L@-A>V!@Pª@ ~ Ž € \
V<@-A>l`2B_;`
eB!A>>]@Z<I1\!@2eJ
A>AaA>>U@UVVeA>V!@m<>HVÛHUyA2BUAB!HV]JI@
A>2FeB!A>)>^e>FHZ@_:
j–@EZ@<>-!A>PFA2>f>,Z2PEV@FA>z2ZHA2>yA2B!@*v
5]<1\-A>d@b`@!A>@!^·'A>¸E@A>dVzA>
U@<bA>V!@A>eAEA>[UB!2@´P<C
Â@AEHV@#A>UB!2@
2ZHA2>!:´j´Z2>-!A>PnA2>@nHZln!Z<@
2ZU)mJ]`tA>eAEA>[2A>V!y!B<8!]ZA>@uP
H-`[W#z>2UA>P/:ac^2\<@-`gVA>)B!A2B!@* ,wA>@<DA>
2A>V!y!B<EPuH-`uWh!@_\_@!ZE9\X!y2ZUB
)w<A>@2@>CZB!@-A>nA>ª>
@ºU@2*A>@-AP:n•,@v
2V<P\- ]w!V!\A>IC!@^!@[2U,A2>d@
|fCZ>EŽ
79G)\y71HGI>2R:EÀ{@#>-!A>Pt>2!@uzA>L2ZHA2>8A2B!@*v
5I9\J,YUP@mA2B!@* >ÞMi@A>gWV8A{J,8A2B@*5>ß
2ZHA2>8à—A>
e>Umá â=ãYO>â=ä>\ !VPJ#H-`KgA2B!@*5=aA>
2ZHA2>8å’A>
>U
á9æçOBæ
ä):I¬YPJP\A>Vd>U!@UVA>@
M„JIbA>nW–!=@KP@@C ZD@-A>><>ABA>@_:gÀ'@|fCv
Z<>Ž71HG)\@LU!@t2EA>AdA>8@U*A>F!zâÛ@ªàè@
WngZ*A]PYw<V*A>KP>dA>@mA>E@U*A>!d!yå’!@
çé@KWu!@@UIA>^!@U*A>]!Xâ8O>àÛ@
ãê@mWuLZ*A
PYw<*A>P>ZA>LA>Y!@U*A>!dDå’!@mçg:yV
@nA>Z>@µ8A>ALA>A2B!@* g5>ëA>m!@U*A>![!
âEOBãYO@måk@mMiA>åÛ^·'5!2J]eB¸[A2B@* )P:
À'UbAV@±H!A>±A>02ZH<A2>0A2B!@* m^!@
A>Ed! ~ Ž € 5!=U!v‹2UVA>!@R\A>)>8Y!@t!22Zv
A>!@KA>eA^!@b`m@FC!@F)^C!@=A2>719: :zC@=1`G
`mw<*AY@tC@EeAF!@-`m@-AY@0A>8ZA>!@ª!
A>mABew:±jh@ºgZbA>U
!F#C@ª>K*A>Zv
VeA>P0A>H8<>2@-AP\A>VdgZbA>VVUA'`K^>2ZPA>
H
A>[><ZUA=!I+-&).&†‡r" p9o>$!%1p9ˆ!.:E@P#@!AFHLA>
U!2:,œ<ZU)
LZbA>UbA{`[U!@-UUZ,A>>ZC
VA>BA2B!@*v
5I@A>!@:zXLU!A>Z<>^A>V]V<P<\JYV@-A2><ZUdA>
@!A>@u!]ì,²{$o%1p56Pp %1q!:c^@#ìXv'!UA>bA{`#2U@>K 8mC!@
A2>!@u2UFA2>[!eJIE!@b`#ì–UE!]C@gA>
2LZbAB!@Z2`Lw<*AyV@8A>]C!@!!_@[!@U*A2BABw:
|fC!Z>71UeG^2eJI=!@tw!VE
VA>BfA2B!@*5E2Uv
@>[A>eAIYPv'!UA>:
LU@-A2>HZA>!@d!yA>^!Y>L!d !VPJI:=À'@
œ UA>@š-\yJ,K@-A2>ZU
Zg@ABA>@_:nœUA>@ºªC
!Z
< mVeA>B!dC@KA2B!@* P:–À{@±œ<UA>!@  \zJ
2PJÞA>eALA>
ìXv'!UA>bA{`-\Dì’íîŽ!\y>2@ndA>L<>Hv
ïQ)>ñbò<
@Ñ0ÒYv‹UA>0HZ<AUP!@–Hª2!P±@±A>
ð 7‹ ó/ôeõIö 71ìn÷éøG ôö ø ôö_ù údù Q G)\]JI>ªøš
A>ª@Z[v
H)I!XA2B@*5>:,À'@0œUA>@0\J=2U>HE@KVC!!>bA>
5!m x wº@ZLH=A2B!@* >
øš5!
A>K2UV!^UP!2
^Ž)v'!UA>bA{`-\/1: :=A>8>2!@#JIVUB#!PJI= !=@b`ª!@
C!@
8C!@[ !b`A>0w<*A8@µ!@-`tABw<@n<Z>@CmA>
ZA>!@R:ëtVC!!>bA>ûC!@BeA>#±gZU)i2
V
2>ô UBºö<ù A2ú^>ù Q A>@nA>
C@B!I)>2V!@º!@´>Z@8V@nA>
ð 7‹
G):LüX!*A>b`-\_JL2PJÛA>eA=A>Žv'!UA>bA{`t<>Hv
ý\Y@–A>ªC@B!FUP2\YÑ0ÒYv‹UV)A>:kœ<UA>@ Ü
<AB![A>>2ZbA>F!b`<@C#ZC!>bA>[A>AB
l>»A>gVbA>BeA>Z>:0œ<UA>@µ¾mC!LK@ZgH)F!]!@
<>HVI!@
Z<A>Z>Eb>U)A>V!@]>VA>KA>LA>]J>;:
2.
<>ZDEFINITIONS
C!ZAaA>aP\J,JIVU@2V<z>-A>P[<>UA>P
A2>JI>^A>Fe>UI>F<b>UA>P
5>èA>^>-A]A>eJB<
A>
Ve[@nª2A>wgZ<ABC>mAL*A[:#j´
JI]UPV]2ZU)µKA2>K´(2ˆPˆ%'&>†
A2>:˜z`n0>-A>P´ !>*A
J,L!@ªZ@@ª!, ƒ{@-AY>-!A>ªA2>:^|!=>-A>P
5!>*Ayç±!@8I2A>ó wFÃY!çºA>y@<ZgHR!Z<A>C@C=>U
l>kÃg<@A>P[þ 71Ã<Gy@gA>^@ZLHa!R@C!@C8>U
eAIÃ[d@!A>P
þÿ,71Ã<G):y|!I2ZUBm8A2>YME\ 7 MYG,@!A>
bA>E2A8!2A>U8!@â87 M=GdA>E2A8I>ú U:m2AE!
PP!Ft>-!A>Pµ >*Amç m<@A>P 79çEGm711: :šA>
2A>ULJIbA>ZAgú Z<A>C@Ce>UBG):´#p5.%'&)(B.$",6!&)(B%1p9oB&)3
MÞ>
7 M=G 7 MYG):˜,A>nª+-&).&
%1(>&>&E!@´u39r&2op‹&)3
%1(2&>&Ee>gHV@2`#<>UA>PªA2>:gm(*ˆPˆ!%é!A2>8M’V
<@A>P
7 MYG):a=e>@-AI!a82A>w
Ã[@MiVd<@A>P
1
7
<
Ã
)
G
m
:
üRAEMkHª<>UA>PuH@2`#A2>:
jgJIVy> )
A>0A>2A>U
XO Á 2ZUBA>eAKá1ÃO ä)OPá1ÃO Á ä ±âL7 MYGF!
A>IU)VV>@!RÃL@[ME:fjh@U!@<@ú @-AyJIJIV/22Z
A>AD!UBL@-A>>@2A>wFÃ
7 MYG 7 MYG/!aI5AaUBV
<@A>P
*71Ã<GI!@ª[>VC!-A=UBVª@!A>P
!71Ã<G):=|
7 MYG)\!@-`g2A>wgÃL>PU)!Hd5>
mH-`[8<b>UA>PeA>
dª†-&)3)oB&).†$.%f n7 A>]P@]A>e
A ªV^[<2U@!@-A
/G):Lj´[<@A>gA>FH-`t
à X:Lj´[2ª>P`tA>
A ^!@n$.oB&)3>%‹ˆ!(d!aÃt7 #í Ã<G):yj´F>`KA>AdÃ
Ygr(*ˆ)r&)(
†&)3oB&).†$!.%^7 r(*ˆ)r&)($!.oB&)3>%‹ˆ!(*GE
X\Rb]
à –71Ãuí /G
@8Ã ! @8@!A>A>f>VeA>V!@2VgH`E
à " ª71
à # G):F,J2A>U
XO2
à $7 M=GI>p .o>ˆ!s^r<$!(2$³"V&^@tME\/b
@!%
A Ã!@m@!AI
à X:yj´=JIX2!A>I@!A>
L2V@CA>!@ª2'
A &)(+*FH
` (X:
ü_AYçkH8g>-!A>ª5!>*AP:^|=)2A>,
w -
79çEG)\
AYç/.
HFA>=>-!A>02ZHA2>F!zçÛU@2V*A>@Ca2A>U
79çEGX>PU)!HdH-`[<>UA>P[eA>a5>!
X:DüRAyM–Hd
>-A>PKA2>:]|!%021 ú 7 M=G)\A>"V&2$!3>%Io>ˆ!sLsˆ!.$!.oB&)3>%‹ˆ!(
3
0 @–M8\,J]>A2A>5
@ 4687 7 0ªG)\^ x @–! !VPJIßµb
0 ! &e
à *\=A>5
@ 4987 7 0tG ! ú Â8A>2JI23
\ 4987 7 0tG
V
A>L2A>wªÃ02ZU)tA>eA'0:1 71Ã<GIHZ<A'0;1 ú 7
/G] !UBu<>8<2U@!@-
A ´!,Ã:g|!=
<>1?7 MYG)\RAYAM @
HLA>[2ZHA2>[ú MÛ>-!A>´
A 46B7 C7 <=G):[j´gV)A ú C7 <=G
H
A>2ZH2A 7 MYG8@nMA@y:n|!
tbD(XOE\aJmZ2
4987F7 (XGO EGA>
@!A>3
46B7HFC7 &I(XO EH*!G):I|!Y[23
A <?J57 M=G)\
M ~ < € @!A>fA> !>*Az2ZH<A2>a@<ZUP8ú H-K
` <8:aüRAzç
H^= >*AI!@WF2U,A2>^2ZUB[A>eA 79çEG ! ú 7‹WaG):
^
V@3
C L FHM N Oß 79çEAG PQ7‹WaGy< x @P[z !VPJIß
L FHM N 71Ã<G ! 4987 N 7 ú F 71Ã<G2G):
césgSp R-&2†=+!(*$)r3
‰ Tiz=C!B[U!@-AB!@@C8e>U,yJ,
=Z@b>UA>tC:g[e>U=!TÞ>g@!A>P#âL7UTFG)\
A>^CIå
7UTFG)\<@A>d2A>U
7UTFG):aÀ‹ATê]8bw
CB!i!@±â K´2Age>U\IA>V
@ TXWnâ mZ2PšA>
<@A>dA>^bw<P[CB!JIbA>m>U]â8U7 TFG W8â8\<åU7 TFG)\<!@
2A>U=
7UTFG):|!LK2AEIPC!8å[A\ T5Wªå…V8< x @P
2V>b`-:acê†!p (>&2o%'&2†8sLSp R-&2†Loqo"V&fzdbw8CB!LJI>
!UB2A>w[!yA>!AB!/<C!>=-\-JIU)
U!@-AB!@,>U\!@
JIU)´U!@nH[A2BP>2PuV@uA>
b>U)A>V!@n!dVzbA>ge>U:
À‹yâ„=[2AY!y>U\A>@tå79â=G]<@A>dA>EZ@<>b`<V@C
Z@<>UA>PKP<C\/1: :då79â=G ! &7 RO2Ã<Gdß/á XO2Ã<
ä #
â *-S|!
RO2Y
à V7 MYG)\XAgÒ .Z M [ H[A>Z@V}Z071Z@b>UA>GYeA>
150
ABCDEF
(a) T
AC
Species Tree
DF
C
{A,C}
Transfer
D
S’
Direction of
Evolution
{A,C,E}
Gene Tree
B
E
(c)
{A,B,C,D,E,F}
BDF
ACE
A
(b)
F
Point in evolution
{B,D,F}
{D,F}
C
A
B
D
E
F
to A
to B
to C
to D
to E
to F
\]6^`_a)bdce fhg`ijkb-^bmlb$n8aobObtM3p$fCqriDstl5]vuvu9bm^HguwIxyblzgHao]6{}|bmwIx~ao]6qA]vl^dnIkbbO`{`uv_nI]9{`l€{H'nIkb^bmlbn8aobOb$]vlVg
w‚bmxƒ]6bmwna)bmb`pKfGxOi'jkbwI_qr|/]6z]vwI]6{`lºW Á {,Wd]v„‚Auv]6bm|…q+†nIkzbnˆ‡{u6gHn8bma)gHun8aogHl/wUbmaow]vl…\]6^`_a)b c‰fhqriIpŠ,{n8btnIkzgHn
nIkbu6gnbOaogHuna)gl/wUbOawIxokb„b-|{‰bwl{HntwgnI]vwU†‹nIkzb$x~{l/|/]6nI]9{`l/w]vlVŒbZl/]6nI]9{`lŽcdfhgHn8bma)gHu%j‘a)gHl/wCbOa’zxokb„bHi
wI]vl/xyb]9nx~{`l‰ng]6l/wg$|/]9aobmx~n8b|5„]6“zbm|}x~†x~u6b`p
A>LUP!2!:gj´LC
>
!y x @bA>@#!,ìXv'!UA>bA{`tHv
PJF:é|!ªŽ)v{UA>A'`-\,A>0Z@l}-ZmA2>ªU2>2@@CuA>
0VA>BA2B!@* g2U)ª7‹W Á O>â Á G= WiJIbA>´A>>
2At[V!H#!#Wè0A>#A2>M !HAB!@PÓ0 PJI:
üR)A
ç¶H0< x @PºH-}
` [79çEG ! 7‹W Á GL!@ºâL79çEG8V[A>
2At>Uºá (RGO E}
ä îâL7‹W Á G Wºâ Á 2ZUBéA>AªA>)>#
¡
ú
N
4
NZ¡ 7EG2ZUBiA>A0Ò ¢ M eV£´79â Á G%D&)EH*nJI>
£´79â Á G ! &)Ei‘
ß ¤m(XOPá (RGO Et
ä „â Á *:–|f@!b`-\]A[MÐHmA>
C@YA2>YHAB@P
5>èA>YU!@@UA>PU!@@-A]Dç
U!@AB@@
C 7‹W Á GLH-`-\z>UZ>2b`-\z2!2A2v‹UZ<A2A>@C2A>U
!DC>8:
HA'J@t
ª!@mÃ@mME:ycieA>0҄@08C!B!TÛPV<I
2'
A <”1•[7UTFGba!@K@b`mb [79ÒE+G –< !5— :
3.
üR)AWêTHE
Hm02MODEL
ULA2>K@MÞHmªC!@
A2>:ucèVA2v
BA2B!@*5IÝ/U)A>zA{J,ge>U=á(XOGEä)\á( Á OGE Á äyaW@@
>Uá XO>Ã<ä5>!îME‚/28!2A>@tzA>LZA>@ª><>v
2@-A>PµH-`há XO2Ã<äL-UUZ>
V!@Cšá (XO Eä8@±W\zA>
A2B!@* -UUZ<>\z!@A>>
!@@Cª!2A>@µ!dZA>@µ-UUZ>
!!@Cµá (Á9O EÁ äF@ºW:uXª<zA>\DJ2ZH/V
H!A>
>UDV@gWª!@8lU]@ge>U@8A>b>U)A>V!@gA>yA2B!@* HA'J@tA>8@)JI`#U>A>Pt2A>U:L|fCZ<>mŽ71UeG^2PJI
A>E2ZH/V2!@#W Á !,WºP0H-`A>EVA>BXA2B!@* >
@ª|fCZ<>[Ž71HG):
”Y@#mC!@8A2>LMk@#2U=A2>
W,\/Jg>
@-A>>*A>PF@E*A>ZVeA>V@CdA>z@VLZh@ZLH_!VA>B
A2B!@* >
A>eAK)wV!@
@i!@–ZA>!@2`±P!@@C!5Z
J]`LJI`gA>IC@dA2>dM±Vz@AP}-ZA>FA>I2UzA2>
W,:IÀ{@ªB^A>H8HC!VU!b`u!@@C! Z1\Z<g3)oB&).$!(Bp9ˆ
gZ*A]>A>*l`KA>^ PJI@C
U@*A2B!@-A>:
Ô8É Ï ×5Ì/×lÇ×lÙRÌèŽ!™
: ˜nVeA>B!A2B@* )f2UBR4ˆ!(,$^39r&2op‹&)3
%1(>&>&LWÛp 3g$gr<$!p ([7‹W Á O>â Á Gg¼f‰&)(>&LW Á p 3g$03B‡³>†!p 6Pp53Bp1ˆ!.µˆ*4EW
$!.†Yâ Á 1V&-á (XO Eäzƒß (ROE 7‹W Á Gƒ+
7‹WaG)O(Y! EH*g3B‡oB‰[%5‰$!%Cš
›ƒœ
Ÿmœ
Oœ
Ô8É Ï ×5Ì/×lÇ×lÙRÌk-™
: ˜nVeA>B!A2B@*5f2U@>]4ˆ!($d3‹r&2op‹&)3
%1(>&>&0Wî$!.†º$#+-&)./&#%1(2&B&
M p 3t$´%1(Bp r"V&t7‹W Á O>â Á OG¥G0¼f‰&)(>&
7‹W Á O2â Á Gzp 3y$Y"$!%'&)(*$"%1(2$!.3l4P&)(3)oB‰&)s
&4ˆ!(DWn$!.†¥
ßZ7‹W Á GP
~¦ ñ õ 3>‡oB‰0%5‰$!%Cš
%5‰&FsLpSR-&2†8+!(2$)r‰
WfÁƒWå79â^Á5GF†ˆe&)3=.ˆ!%o>ˆ!.%‹$!p .u$†!p1²
(>&2o%'&2†sgp R-&>†oqo"VB& ž
%5‰&g%‹$!p1"Dˆ*4[&>$oB‰u$!(2o[p .Kâ Á ‰$!38p .†-&9+!(>&>& › $!.†Kˆ!‡%9²
†-&9+!(>&>& Ÿ p .mW Á Wmâ Á žz$!.†
%5‰&Y‰&>$†ˆ{4F&2$oB‰t$(2o=p .
âdÁa‰$!3^p .†&‹+!(2&>& Ÿ $!.†ˆ!‡%9²
†-&9+!(>&>& › p .mW Á Wmâ Á œ
ƒ› œ
Ÿmœ
À'_J=
@[A>eAP\<Ad!@-`!@A]Z>@C8A>Y!Zv
A>@t>>2@-A>P#H-`#W,\X
ABewm
`ª@b`tP8@gU-`
!]!@-`#C@ª719: :A>[UP2! › ²'$o%1p 6Pp5%1qPG)\DA>@mleA>B!
A2B!@*ú 2UBú mZ@l}-Zb`n2U x m#C@KA2>KMÐ2ZU)
A>eA 7 MYG ! 7‹WaG):=jh@0Jg!eJ’ì•#’ŽLC@YA>
wv
*A8AE@-`ª@-AEZ<>@C
A>gZA>!@R\/A>F=@@C
Oœ
151
M ~ ¥/7<7‹WfÁ G2G € p 3Fo>ˆ!../&2o%'&2†0$!.†<7 MYG‘¥/7<7‹WDÁ5G2GB§
p 4=à N $!.†Ã Q $!(2&moB‰p1"†(>&).ºˆ*4FÃy¨ªp5.ªM¶$!.†Ã N O2à Q- ©
¥/7 7‹W Á G2BG žf%5‰&).0%5‰&)(>&8&R!p 3>%13ª( ¨ ¼yp5%5‰KoB‰p1"†!(2&).D(XNE$.†
Á « ¼f‰&)(2'
(/Q
p5.0W Á WKâ '
& (X=
N ! (/BQ ¬[3 œ % œ ~à ­ª¥/7 (`­9BG ž4ˆ!(
% ( ­
® ! ¿<OPŽ!OB « s[ˆ!(>&2ˆ!6!&)ˆ( žD%5‰&=†-v& ¯a.p %1p1ˆ!.mp5sYr" p‹&)3,%5‰$!‰
p 3I%5‰
& NZ¡ ²9s$ R!p s$"6!&)(B%'& R[3B‡oB‰%5‰$%Ryà ­rt¥/7 (`­9Gf4ˆ!(
† (`¨p 3E%5‰
& ÁN ²‹sLp .p s[$"X6!&)(B%'& Rª3>‡oB‰
® ! ¿<OŽO)O žd$.K
%5‰$!%Dà ¨ ,¥/7 (/hG ¬I§
p 4zÃNE$!.†=ÃQL$!(>&=oB‰p "†!(>&).tˆ{4zà ¨ p .g3
M žÃ<
N ¥/7 7‹W Á G2BG ž
Q ”
© ¥/7 7‹W Á G2BG žL%5‰&).h%5‰&)(>&u& R!p 3>%[$µoB‰p1"
$!.†ªÃ 5
† („ˆ*4
7‹WfÁ GFp .mWfÁ3 œ % œ Ã
Q ,¥/7 (/BG §
4ˆ!(&2$oB‰mÃ-…
7 MYGBž%5‰&[6!&)(B%1p9oB&)3=&I(±…[7‹W Á GFßÃ
¥/7 (/G *p .†!‡oB&L$
†!p (2&>o%'&2†Lr<$%5‰0p .mWfUÁ §
¥/7 (/GDp 3z™
$ ²'$!.%1p1oB‰$!p . ž4ˆ!(,&>$oB™
‰ (7‹W Á Gƒ&I7‹W Á G*Z§
ú
¥/´7 41G ! &o4´*ƒž4ˆ!(E$" " 4 7‹WaG
A>^<>H…A>[HE@-A2B!UABHE@ªC@B!1:]¬^eJ,P\ 2
VZfì´@
øR\-A>Y>!H—V x w<PBA>
A2BUAB!H:DÀ{@FA>,@)w<AX2UA>@_\J,,C,d !*A>yVC!!>bA>
5!IA>F2UV!XU!2F!]Ž)v'!UA>bA{`-:
j mJId>) A>-¥/7(/G8[A>³B$+K!'(R:±cÐVA>B
A2B@*52ù U@eù >VÓ7‹W Á O>â Á OG¥Gmtì²'$o%1p 6!&ªb!@é@`éb
emw µ~¶ NZ¡ ¥/7 (G ! ì,:LK%1(*$!.3l4P&)(g.‡s³B&)(^!=7‹W Á O>â Á O ¥G
JF: P: AP:yMê]A>Y2Z…edVzá (XO Eä ªâdÁR
ù &-á XO>Ã<ªä ªâL7 MYGz~ß ,¥/7 (/G)O'
à ¥/7 EG * ù ÷ ù ú 7 M ~ ¥/7 <7‹WyG2G € G ù · ŽS
ì²'$o%1p 6Pp5%1q±%1(2$.3l4P&)(.‡s³B&)(KWè@–ME\F<@A>P
ø ò 7‹WDO{M=G)\^KA>#@gZ A2B!@* t@ZLH!g!@-`hìXv
UA>A'`
VA>B/A2B@*5I2U@>K7‹WfÁ'O2â^Á9GO ¥Ga5!dW´@M8:
c¶ìRv{UA>A'`±VeA>B!=A2B@* )02U@>i7‹W Á OBâ Á GO ¥Gg5!tW
@tMÛJIA>#A2B!@* 8@ZLHFeAE*AFø#8U!P´mìzO2ø
"$%'&)(2$"X%1(*$!.3l4P&)(E3)oB&).$!(Bp9ˆ= YWº@ME:
Ê »/ÉÙ_ÈÉm¼ Ž!:½R‰&†-&2op 3>p9ˆ!.L6!&)()3>p9ˆ.
ˆ*4y%5‰&DìXξYØÇ×S¿R×lÇHÀ
øÎ2ÊYÈË_Ì/Í Ï É<È0r(2ˆ³"V&)sÐp 3]Ñ0Ò[²{o>ˆ!s^r"V&)%'& œ
°`œ
²Zœ
³ƒœ
jaH>8 ¸`=2U)>VHaPU)FA>a2bw=U!@bA>@:y•,@<v
< bA>V!@uŽYCZeB!@-A>=A>AA>^>-!Ad@
A>=2UVIA2>=U!2v
>2@<8A>0A>[>-!Ag!]A>C!@A2>t71!@
UP!@P
>ªC@B!ddA>A-@!Am
!@nA>BG)\IHZA
VPJImleA>B!^A2B!@*5>
A>´P0AB;@–lUh·{<>Z
A>A>8A>E>-!AE!IWD¸<:g•,@<bA>V!@n-\fm!@  CZeB!@-A>
A>AyA>A2>]Mšw<*A>zJIbA>@[A>]2UzA2>^WtV@
=U@v
@UA>P8
!@@f!@8^
@@fA>eAf>2U)A>aA><>UA>@
]!ZA>@uVV#H-`ªA>g>UFME:[[*A>ZleA>@
A>™
A (X
N ! (/Q=@#•,@bA>@#LA>C!A>)YJIbA>#•,@bA>@ 
<>!eJI^+-&).&E†‡r" p9o>$!%1p9ˆ!.#&)6!&).%13d712=|fCZ<>F-: G):,•,@v
2V<^g2A>wÃ2ZU)A>AI
à ¥/7 (/Gy Y2!'
(
7‹W Á G):
•,!@<A>!@=!@ Ü A>C)A>yJIbA>[A>I x @bA>@g!/VA>B
A2B@*5[2UB[5!>HlA>UP!2JI>A>>
H!A>ZA2v
C!@C
e>U]5>!îL2A>w
@KA>=C@=A2>=U2>2@mA>
VeA>B!yA2B!@*5>:[j[HgA>V=A>mHm!!V#>*A2>VU)v
A>!@R\/2@U8JI@t@-A>>>)A2A>P0@uHV!CUPz2@2\/A>
!@IA>eA=[C!@8w<*A>P0@0A>EC@E,gABew<@tA
2!ª@-A
@±A>0ZA>!@š><>2@-A>P±H-`šWÛHZA
@
<2U@@A[V@µA>m2ZH<A2>KEW Á >-A>PšH-Y
` ¥/7 (G8
U-`ª!yA>^C@K71Z@2^A>LC!@8J]! x >*AYA2B@*52>P
·{J]`<¸
!@
A>@A2B!@* 2>P–·'HU);¸gA>gA>]2ZHA2>eG):
üR!*A>b`-\aZ<L x @bA>@´F%1(2$!.354&)(m.‡<s[³B&)(E!2#v
2 )>I2Fw<l@eA>V!@R:ajh@Kì ! Ž\@`A>^>-!A^!
ME\+<7 M=G)\/HV!@C!=A>¥/7<7‹W Á G2G871H`0U@bA>@º7*ŽeGY@ªA>
< x @bA>V!@´!YŽv'!UA>bA{`G):|L¹
ì #èŽv'!U)A>VbA{`-\RA>FL@
!@C)a@U2>>b`LA>,UP2:D©YPJF\!@L22@U\!A>y2A>U
z
2ZHA2>EyMÓ
`KH!@CA>
¥/7 7‹W Á G2G):^Y
A>]w<*A>@UI ù ú 7 M ~ ¥/77‹WaG2G € G hù · Ž,A2B@*5>,<>V!ZDA>
A>
Z<A>V!@º2U>HPnH-`´W:tjU!,A>LyA>
·'wA>>@D¸m!@tZ2LbA^A>>ZCZA^A>E>
!@
A>,!)P:ac^@#·{@-A>>@<¸Ya!2F!22VHJI>
A2B!@* zgZ*AfAB!;]V!UJIbA>V@W:fÀ'Aaz!*`8A>=>b5`
A>AEy!ZF>2ZA>^ !FA>gwA>>@!D<a!20V
@µA>mV@-A>>@!]<1:º0<UP@šHmC@B!?P
2ZU)mA>A]A>FVA>BRA2B!@* >IA>eAIP=!@P>v
Z^A>A>E>-!
A <\!@0JIVUBtUP!Z2
¥/7 G@AYA>
Hg@
@-A>VUB@R\!2Ý/UAdA>d2A>UIA>!@A>Y>-AP:
ì
ø
ÁÈÙ_Ù `
Ï Â ºYbA2A>P_:
¬^PJ)P\- !,2
!!!Z,!Rìu!@ø[JI>^…
ì ºøR\
A>L<>HVî>
V@YA2B!U)AB!H:FjLC!g!ZEVC!!>bA>
@>-!aDU2>UA>@2^HPJFß
ìfÎ ¾YØÇS× ¿R×lÇ ÀnøÎ*ÊYÈË_Ì_Í Ï ÉÈK<>HV
ÃBl‚A_nye–c¶2UVmA2>uW—@–nC!@ªA2>ªM JIA>hìRv
UA>A'`@<ZgH
šø_:
Ä _n8‚A_n~em@VLZ A2B!@*5L@<ZgH=ø ’øe
XìXv'!U)A>VbA{`VA>)B!RA2B@*5Y2U@e>V!d5!YWµ!@
ME:
|!=A>8>
@)=!yA>=2UA>@R\/J,gJIVy22Z
A>A8W–Emú 2UFA2>!@tA>A=MkEmC!@LA2>ge
LlHX2)A 2ZUBmA>Adøòf7‹WfO*MYªG šø_:y|!^@`A{J,gA2>
M N O*M Q !@µ>Uá RO2Ã<N t
ä êâL7 M Q G)\yJJIVd!HZ2m@!ABeA>@
2C-A>b`ª@KZ2=LR~ÿ Å M )Æ 7
XO2Ã<G,A>
@!A>=A>F2A3&-á(XOEä‘
â87 M N G,Oß L yÅ M )Æ 7 (/G,í )Æ RˆO L yÅ M )Æ 7 EG )Æ Ã *-:
c’³>ˆP$!(*†=V8!bE79çBO <=GyJI)>=X
ç 1µMiVL<>UA>P
5!>*AdJIbA>!ZAd2VA>Pª)2A>VUI2ZUBKA>eA^þ óF 71Ã<G‘éŽ= ^5
à Ž79çEG[!@•
<Ç1È[7 MYGg@ZU
#2ZHA2>0!=M
U@-AB!@@t
C <7 MYG):L79=P!@dA>A=ç—YA>EZ@ù @t!,ù @ù ú ZgHX!ù · < ƒ*@-AaeA>: GL=o>ˆ!3>%<!D79çOB<=GX âL79çEG ÷
7 M ~ < € G Ž:zc„sˆ!6!&aV,!@>U^
 ªâL7 MYG):XÀ'Ad6$" p9† 79çBO <=G]bz!@m@b`K'\ Y2!
--7 M=G)\Â ! á RO 7 /G2ä
© ç¶KÂ ! á XO 8{7 /G2ä!@êá XGO 7 /G2ä ©
@éá XO *7 G2ä ’
çg:Óµ³>ˆP$!(*†±ˆ³%‹$p .ê³qns$e½p .-+ns[ˆ!6!&mšˆ!.i79çBO <=GV
795
ç W-&e~Â *BO <=G):[jgJIV,!22ZgA>eAE!,eYJ[
;
e>Fl/:
ü_A7‹W Á O2â Á GO ¥G^H[VA>ByA2B@* )E2U@e>K LW
@gME:a8"$%'&)(2$"%1(*$!.3l4P&)(B3a!/M±JF: P: AP:I7‹WfÁ‹OBâdÁ‹Oh¥GDyA>
5PJIV@C
2Ad!y>U
&á XO>Ã<ª
ä KâL7 MYGzOß ¤/á (XGO Eªä ªâ Á O ,¥/7 (/G,@
à t¥/7 EG *-S
ü_A7‹W Á O2â Á GO ¥G^H[VA>ByA2B@* )E2U@e>K LW
@êME:ëºHBÞ79çOB<=G0ªA>i³>ˆP$!(*† !M JF: P: AP:
7‹W Á O>â Á O ¥G8bÝéç¶[A>A2B!@* >
!YM…JF: P: AP:Û7‹W Á O>â Á OG¥G
@
< ! ¥/7 7‹W Á G2G)ª: ºYH2>YA>eAII7‹W Á O>â Á GO ¥G,!]A2B!@*v
58@ZgH)=ø´@#à FA>gHBu!MÛJF: P: AK7‹W Á O>â Á GO ¥G
A>@tA>gU*AE!à…P}-Z!Fø_:gc’HeBš79çBO <=G^Eì,O2øv
JI@LÝgA>>zVa@LìzO>ø8VeA>B!A2B!@* a2U@>[7‹W Á O>â Á GO ¥G
2ZU)LA>AI79çBO <=GDDA>]HeBg!MµJF: P: AP:I7‹W Á O>â Á GO ¥G):f
HB#79ç]ˆO <=G,V]U)`UVUFbݪA>)>Y]@LleA>B!/A2B!@* d2U)v
@>7‹W Á O>â Á hO ¥GD2ZU)LA>Ad79çBO <=GDyA>dHBg/MšJF: P: AP:
7‹WfÁ9O>â^Á9O ¥G):
|!IA{J,[HeBE79çOB<=G]!@#79ç Á Oˆ< Á G)\<J=J]>bA>
79çBO <=‘G Éê79ç Á BO < Á G
4.
j
@ACTIVITY
PJÞ)w@A>C!AND
@BTRANSFERS
>2!@n!IA>
ìXv'!U)A>VbA{`
ø<v9A2B!@*5
>!H 5!
ì…í Ž:•ºYZ x >*A>2ZbA
2eJI
152
(b)
(a)
(c)
abcd in g(abcde)
ac in g(abcd)
bd in g(abcd)
E
c in g(cd)
d in g(cd)
a in g(ab)
b in g(ab)
A
B
C
D
\]6^`_a)b}Ê+eYfhg‰itsl¹bO“+g`„‚/u6b…{3g•wIx~bmlgao]6{•‡]6nk”g‹|_‚Auv]vxygHnI]6{lpXfCqritsl¹bO“zg„‚Au6b${=g}wIx~bmlgay]9{•‡]6nIk¹nB‡{
wI]„ _/u6ngHlbO{`_/w,n8aogHl/wUbmaow~pË={HnIk”wIx~bmlgao]6{`w,gaobY|/]vwgu6u6{‡bm|¹q+†¹Ì{`l/|]6nI]6{`„
l  gHl/|XÌ3{`l/|/]6n]6{`’
l a)bw‚p‹fhxOisl
bO“zg„‚Au6b{H%g$wIx~bmlgHao]6{$‡]6nIk•gHx~nI]6z]6nˆ–
† Zp
b@t@`tb< ! < Á !@uç>1êç Á :8[e>UEÂ N OSSSOBÂ)
>$" %'&)(B.$%1p 6!&4ˆ!(*o)&2†
sˆ!6!&)3]by@K!@b`KbybAdVIA>FU!2
A>eAFA>[HB<LàENPOSSSPO2à !HAB!@PH-`#
!;@C
 N OSPSSO> @ªà’>A>*l`KA>^ PJI@CßzA>>Fdgø<O2ìXv9JI@
Í !U*
A Î^2ZUB#A>AEÏ
à ÉXÍ b!@t@b`tzA>>LE
øO*ìXv9JIV‹
@ Í Á YU*
A >ÎE2ZU)nA>Aà ­ ÉÐÍ Á 5!2!
® ~4 € :
ÚaÉm¼¼I˗-:%Õf&)%y79çOB<=G=³B&=N $[³>ˆP$!(2† œ ÕX&)%zØ ³B&Y%5‰&^3&)%zˆ*4
²9sgp5.p s[$"y6!&)(B%1p9oB&)3mˆ*
4 L `ÿ × FM N 7 (/G
$!.†t"V&)%IÂNOSSSOB ³B&
%5‰&gˆ‡<%l+ˆp .+K$(2o3z4)(2ˆs 6!&)(B%1p9oB&)3Lˆ*™
4 Ø œ%Ù 4 ù Ø ù #±ªì žy%5‰&).
 N OSSSOB) d$(>&L$!" %'&)().$!%1p 6!&4ˆ!(*oB&>†sˆ6!&)3=p .t79ç8O <=G œ
ÁÈÙRÙ `
c 22ZyA>Ad79ç=Á9OB<=Gfz@gì,O>ø<v9JIV@L2ZUBLA>A
Ï Â d
© â879ç Á G):zœ@U
7C<,O2çEGªÉé79ç Á OB<=G]@0ÂNOSSSO> 0
© âL79ç Á G)O
Â-NOPSSSO>Â 0
L `× F+¡M N 71Ã<G ! L `× F+¡´M N 7 /G)\/ 8!@-
` XO>
à …ØÛ:8¬Y@U\_H-`
üR
YŽ\A>,H!C^!‰ L × F‰¡´M N 71Ã<GRDUPB<@!bA{` ù Ø ù #ºì
@
!@-`[VeA>B!A2B@*5>2U@>E!y79ç Á 8O <=G):a,U@-A2Bv
UA>]A>F!22ZA>@A>AE79ç Á BO <=Gd!@0ì,O*øv9JI@R:
D5eJI@CYf@E!H*A2BUAf>2@F!A>yìXÎ ¾YØÇ×S¿_Î
l× ÇÀÓøÎ2ÊYÈË_Ì/Í Ï É<Ȗ!C>bA>0:Ûc %1()p56Pp9$"I(>&2†!‡o%1p9ˆ!.ºú @–
Heú B´79çOB<=GI^2 >PKH-`m5!=[!b>^!r
XO2Ã, 7‹WaG
7! 7
M açEG2GyJIVUBm>=2H@C!IV@KW´!J,_!]@Myç
>e@CYÃ8@L2!2A>UZ<A2A>@CYA>e>@-Aa!‰ @Wt!DJV
!I@KY
M çg:Djh@)dLA2><V_>P<ZUA>!@0d!22HF@
A>m!C!!>bA> AgJIV]H2 >P_:´üRA· ã H
A>2A
!IHB<N gà ! 79ç8O <=GFIU*AgA8!*ALø Ž
2ZUBA>eA
<Ž1VL ÿ M N 77‹WaG2G]!@ªç !¹— :düRA%Î !”Ñ :IEZ<A>Z<AY
A>^!C!!>bA>—V Î:fjd>A,A>d5PJIV@CgZ@A>/ã !V— :
ÚamÉ ¼¼IËk: Ö ˆ!(#&2$oB‰uÃVX[7‹WyGBžE%5‰&0.‡s[³)&)(0ˆ*4t ²
sgp5.p s[$"D6!&)()%1p9oB&)3ˆ*4LR ÿ M N N 71Ã<G[p 3Kkì#÷±ø œÖ ‡()%5‰&)()s[ˆ!(>&Bž
ù L ÿ M N N 71Ã<G ù ±71ìK÷nøG œ
Ž:]f!;EàÒtãk@0A^à8NPOSSPSO>à H=A>8HB<^!Hv
AB!@Pn5>! à»H`µ
;V@C#A>0A>)>@A>05!>U
IÂNOSSSO>Â :
:]|!mP!UBh!8àENPOSSSOBà \db8
à ­8VK!@–ìzO>øv9JI@R\IA
ã Ó d
¹
ã %&K
à *g!@m%
A ΐÓë@Rv7 Î)OŽ,±
÷ G,JI>
F
A>=U!*Ad!y
à ­*:
<:2F ù à ù ! ø · Ž\AY¹
ã Ó }
ã &eD
à *
 :28¹
ã Ó }
ã %&K
à *‘W&eà8NPOSSSO>à *:
ÁÈÙRÙ `
Ï Â ü_AF7‹W Á O>â Á GO ¥GzHYLì,O2øVA>BA2B!@*5>I2Uv
@ e>5!LW±@ªM8:FüRAEçkHLA>ùLù VA>)B!DA2B!@* >F,M
JF: P: AP:I7‹W Á O>â Á O¥GD!@[@A>IA>A ç šøR:Dœ<@UE7‹W Á O2â Á OG¥G
RìRv{UA>\eA>D@ZgH/+ v'@V
e2A>UR!H L `× FM N 71Ã<G
=
hìz:YÀ‹A^5eJI=A>A^A>E@ZgH)^
v‹V@
!_2v
A>U=L ÿ M N N 71Ã<GdV=Óì0÷šøR:LœV@ULM„!Y@2A>U=
@<C!>E@ZAB<C!>[Ž\ ù L ÿ M N N 71Ã<G ù ±<71ìm÷µøG):
ÚaÉm¼¼IË  :%Õf&)%d79çO8<=G[³)&[$ª³>ˆP$!(*†ª$!.†0"V&)%(YY7‹WyG
&)<7‹WaG* œ Õf&)%IÃh³B&K$- ²‹sLp .p5s$"y6!&)()%'&R0Ã}5LR`ÿ × N FHM N 7(/G
3>‡oB‰%5‰<$!%Y%5‰&)(2&
p 3[$D
}}LR`ÿ × N FHM N 7(/Gg¼ap %5‰ˆ!‡%‹†-&9+!(2&B& Ÿ p5.
MdI
ç„4ˆ!(8¼f‰p9oB‰Ã" œÙ 4^ÂN
$!.†ÂQm$!(2&[%5‰&
ˆ‡<%l+ˆp .+
$!(*o3Y4B(2ˆ!s %5‰&m6!&)()%1p1o)&)3Kˆ*4gÃY
ž %5‰&).µÂ N O> Q $!(2&0$" %'&)(B.$!%1p 6!&
4ˆ!(*oB&>†sˆ6!&)3=p .#79çOB=
< G œ
ÔYV=A>I
eAB=C@
HPJF\bAJ`,22H
A>gV<@-A>l`ºì÷´ø0bA>>@eA>V= !>UPKe@KgHeB
!U*
A "ºøR:XÀ'AaV2=5PJIz5>!„A>zV
ABIHeJºA>eA
A>E@ZLHd!yJ]`<^A>
UB2D<’^HZ@P0H-`ª Q)Q)ñbñbò<ò<ó/ó/ôeôeõ õ :ö
yôeóDNDDö-ù A>údù Q Ay!Zz!C>bA>Û>Z@y@gA> ð 7‹
71ìm÷µøG
G):
ÁÈÙRÙ `
Ï Â ü_‘A Ú-NPOSPSSˆO Ú H]A>^>U,!/A>deA>[5>
A>ÃV@0M±Içk!@0A3ÚªHFA>E!A>Y!ZA>C!@Cm>UE!r
X:
c^22ZYA>eA8C7 < Á O>ç Á GI^!@0ìzO>øv9JI@02ZUBKA>eA8C7 <O>çE‘G É
Q ª
© â879ç Á G):aœ<@U] N OB D
Q ª
© â879ç Á G)\!bAD !v
C7 < Á O>ç Á G)\!@g N O> © â879ç Á Gg712@U
PJIEA>K
A ڈO ÚNPOSSSO Ú º
Úo­'šâL79ç Á GYJIbA>
w<
! ® A>•
@ Ú ­ JZV±U!2>2@µA>´VA>BdA2B@*v
)>8H)A{J@n!@U*A>g@´<2U@@AP\f!2 Ú}šâL79ç=ÁlG
aÚ Ém¼¼IËЎ:Õf&)%/7‹W Á O>â Á OG¥Gz³)&$^"$!%'&)(2$"%1(*$!.3l4P&)(,3oB&).$!()p1ˆ
4ˆ!(YW„$!ó .†8M…¼ap %5‰ª"$!%'&)(2$"f%1(*$!.3l4P&)(B3Yç œÖ ˆ!(g&2$oB‰Ãu3$%1p 3B²
4)qp .+Fþ `× F 71Ã<G ! Z žzp %D‰ˆ"†3=%5‰$!%D
à t¥/7UL `× FHM N 71Ã<G2G œ
ÁÈÙRÙ `
Ï Â ºYbA2A>P/:
153
J,ZlªU2>2@tA>
VA>)B!fA2B!@* >YHA{J,@#!@U*A>!
@82U@!@-A)G):f¬^@U‘ L `× F+¡M N 71Ã<G ! L `× F+¡´M N 7 /G):fA
+\ L × F ¡ M N 71Ã<G]^@!AY!
@ v'!@-A>U)!@R:I^U!@-A2BUA>
A>E!22ZA>@A>AE79ç Á BO <=Gd!@0ì,O*øv9JI@R:
@KA>F!C!!>bA>ÐbAIJIVRH=2 >P_:zü_A^ã„H=A>=2A
&eD
à *8JI>Là ! 7 — O <7 MYG2G,=[HeB_:dü_™
A Î !¹Ñ :IcI5A>
A>=U!ZABeA>@KA>=Z<A>ZAI
Î:aj=>PAIA>Y !VPJ]v
@C[Z@-A>Rã !V— :
ÚaÉ ¼¼]Ëè-:%Õf&)%I79çOB<=Gg³B&[$m³BˆP$(2†yžI"V&)%A#³B&L%5‰&L(*ˆPˆ!%dˆ*4
M3ž,$!.†"V&)%Û ! M±]ç œ Õf&)%Ø ³)&E%5‰&L6!&)()%1p1o)&)3%
-7 MYG
3>‡oB‰%5‰$!C% š « › ¬%5‰&)(>&p 38.ˆt†!p (2Ü &>o%'&2†r<$!%5‰4)(2ˆ!s>u%‹ˆ
hp .
۞ « Ÿ ¬gþ Üó 7
/G ! OžI$.† « ¬ ú 7
/G ! ú 7 MdÁ5GL¼f‰&)(>&=MdÁdp 3
%5‰&o>ˆ!../&2o%'&2†o>ˆ!sYr<ˆ./&).%=ˆ*'
4 Û %‹ˆ0¼f‰p9oBt
‰ i³B&"ˆ!.-+!3 œ Õf&)%
ÂNPOSSSO> ³B&K%5‰&#ˆ‡<%l+ˆp .+n$!(*o3Kp ±
. Û ˆ*4m6!&)(B%1p9oB&)30p ±
. Ø œ
Ù 4m79ç]ˆO <=Gmp 3moqo" p9o0%5‰&). žE%5‰&).ºÂ N OSSSPO2o g$!(>&ª$" %'&)(B.$!%1p56!&
4ˆ!(2oB&2†s[ˆ!6!&)3=p .t79çBO <=G œ
!Ž :If;Fà0ãL\22Z=A>Adà ! 79çOB<=G
-:IüR)A]M Á Ó MYIçg:

: ÞaVUB;t
™NK@
!/)2A>
w (KJIUB0I Ad@KM Á
 :]À'%
(šVD
£Kv‹ AP\yA
à N O>à Q HmA>HeB[!HABV@P
5>!èà„H-`[
;V@CFA>^!bA>>@eA>
£ ezÂ-NPO2Â!Qe:
-:]2d‰ (
r Ýv‹ AP\-Aà8NO2à=Q]HIA>IHB<z!HABV@P
5>!Ðà—H-`
!;@C8A>EA>)>@A>
Ýe]Â N O>Â Q :
Ü :]À',à ­ FtŽO2ø<v‹JI@_\RALß
ã Ó V
㠙&K
à *@tV)
A ΙÓ
@Rv7 Î)O àI­'GzJI>
àI­aV]A>=U*A^!D
à ­
¾-:]2Fb ù à ù ! ø · Ž!\AY€
ã Ó d
ã &à8O *
Œ:]28€
ã Ó d
㠙&eD
à *‘W,&àENO2à=IQ *:
ÁÈÙ_Ù `
Ï Â 71À*<P<: G»©Y!A>UtA>eA
!K!@-`±HBê79ç Á O8<=G
2ZU)LA>Ad79çO8<=GªÉé79ç Á OB<=Ga!@&ÂNOPSSSO> *‰–=âL79ç ¨ G !V— \
bADV_A>eA L `× F+¡M N 7 /G ! L `× FHM N 7
/G !D!@-`'
ØÛ:
ÚaÉ ¼¼]Ë Ü : ½/&)3>%1p .-+
¼f‰&)%5‰&)(L$8+!p 6!&).u³>ˆP$!(2†Là p 3=oqo" p9o
ˆ(Fp 3E$Fì,O>øX²9¼ap .#o>$!.u³B&L†ˆ!.&Ep .ª%1p5s
& ð 7271øG ôù údù Q G=%1p s
& œ
ÁÈÙ_Ù `
Ï Â ºYbA2A>P_:
5.
™^@5!2ACTIVITY
A>Z@A>b`-\e@YA>1]ŽÎ¾YØÇ×S¿R×lÇHÀ
øÎ2ÊYÈË_Ì/Í Ï <É ÈDÁÈÙRÆ<Î
!Ö É¼êV^@A2BUAB!H:Y¬^PJ)P\A>>8w<*A>=[1*A> x w
BA>FC!>bA>î =A>^2UV!DUP2:Yj82U>H
bAd)>:
Ê »/ÉÙ_ÈÉm¼ -:½R‰&†-&2op 3>p9ˆ!.g6!&)()3>p9ˆ!.ˆ*4y%5‰&,ŽÎ¾YØÇ×S¿R×lÇHÀ
øÎ2ÊYÈË_Ì/Í Ï É<È$ÁÈÙRÆÖÉm¼Þp 3IÑ0Ò[²'o>ˆ!sYr"V&)%'& œ
ÁÈÙ_Ù `
Ï Â ºYbA2A>P_:
ü_AM Á 1…ME:šüR)
A (±HK!@–e>HbA2B2`µ2A>w´JIbA>
UBV<>@€(RNª!@V(/Qt@êW,:ÐüR)AÝ7(XOh(`­*O*M Á G
H#A>u2A
!8>Uná XO2Ã<}
ä âL7 M Á GK2ZUBiA>A L ¡UN M N 7
/Gºí™N(X\
L ¡ M N 71Ã<‘
G N (`­*\!!@3
Lª v‹@
!!K
@ L ÿ ¡UM N U7 L ¡ M N 7 /G2G):
ü_rA £´7 (XhO (`­*O*M Á GXH,A>,2Ay!>UIá XO*Ã<‘ä 0âL7 M Á GX2ZUB
A>
A L ¡´M N 7 /G ! (@
L ¡M N 71Ã<ªG ™NK( ­ :yc–2A>=
w (mª £´²
4$!%5!yM Á bù Ý ù £´7(XOh(XNO*ù M Á G ù ÷ ù £´7(XOG(/QO*M Á G ù 횐<‚-bAzÝ² 4$!%
5!8M Á bÝ Ý7 (RGO ( ­ O*M Á G 헏m!@
Ý7 (XGO ( ­ O*M Á G=U@-ABV@g@
e>UEá XO>Ã<äf2ZUBgA>e‘
A L ¡UM N 7 G ! (X\! ! ® ! ŽI ® ! ‚<!@
bAF,4$!%f5!=M Á bÝ´bA=
£Kv9 AY5!=M Á Ýv91A^ =M Á :=üRA
ØÛ7(XO*M Á GXH,A>z2Aa! v‹V@
!)2A>VUDÃL ÿ ¡´N M N 7(/G
2ZU)´A>A8A>>g
5VLR ÿ ¡UN M N 7 (/GYJIA>n!ZAB<C!>m0@
M Á JIU)šV
à " X:šÀ''
(š
£Kv‹ A[5!
M Á \,A>@ºA'J
bA>>@eA>Vt
£ïeEe
A (nV@uM Á gK!bL!d>UgÂNO>ÂQ
JI>d N @[ Q >]A>A{JF!ZA>C!@C8>Uyl>—=2A>w
ª ؒ7 (XO{M Á G):]À‹ (ª™
Ýv‹ AI YM Á \A>@mA{JA>)>@A>3
Ý
eLe
A (nV@´M Á VL0bL^>Uá XO2Ã<ä)OPá Á O>Ã Á äYJI>
7*ŽPG[á XO2Ã<ä)OPá Á9O2Ã-Á ä ±Ý7 (XGO ( ­ O{M^Á5G)\_ ! ® ! Ž[! ® ! -\]7‹G
L ¡UM N 7 G ! (X\!@79A
G !@K
Á e>
@
!D
@ (
!@
L ¡UM N 7 Á G)\<>2UA>b`-:
85PJIV@C0=Z<LŽÎ ¾YØÇS× ¿R×lÇ À±øÎ2ÊYÈË_Ì/Í Ï É<È#bv
C!!>bA>0:Dc^C@R\JI@z^A2><V>P<ZUA>@a22HV
˜y`A>Y
eABFHeJiJ,YUP@K25!>á
£î!@
Ý[e\
JIbA>ZAU>PA>@C[LU)`UVU=HB/\Z@-A>VA>>^@g!@C)IV
@-`1AI2A>w/:fjh@A>>=@L@CdI8 AI)2A>wJ
PFmŽ!O>øv9JI@R:
ÚaÉ ¼¼]Ëè¾-:%Õf&)%d79çOB<=G[³B&$ª³BˆP$(2† œÙ 4^ N O> Q $!(>&$" %'&)()²
. $!%1p 6!&,£ sˆ6!&)3ªp .µM¹gçKž[%5‰&).±ÂNO>ÂQº$(>&$" %'&)(B.$%1p 6!&
4ˆ!(2oB&2†
s[ˆ!6!&)3 œ
ÁÈÙ_Ù `
Ï Â ºYbA2A>P_:
ÚaÉ ¼¼]Ëތ%
: Õf&)%y79çOB<=G=$!.†[79ç=Á‹OB<=GF³B&^%1¼zˆ³>ˆP$!(2†!3^3>‡oB‰
%5‰<$!%d79ç]Oˆ<=G™ÉÛ79ç Á Oˆ<=G œ ˜=3>3>‡ús
&L%5‰$!%yà ¨ p 38$
6!&)()%'&Rtˆ*4dM
ÃN$!.†gÃQ œÙ 4 `× F 71ÃNBGLp 3E3&'r<$!(2$%'&>†E4)(*ˆ!s
ú ¼ap %5‰#F oB71‰Ã p1Q "G=†!(2p &).
.0…
M
]ç Á ža%5‰&).#á1~à ¨O2à N ª
ä ªç Á ˆ(Eá1~à ¨O2à Q ªä ªç Á œ
`×
ÁÈÙ_Ù `
Ï Â ºYbA2A>P_:
ÚaÉ ¼¼]Ëލ%
: Õf&)%X79ç]ˆO <=Gd³B&^$8³>ˆP$!(2† œ ˜Y3B3>‡s
&]%5‰$!%Ãy¨Fp 3]$
6!&)(B%'&R0ˆ*4Mè¼ap %5‰ªoB‰p1"†!ú (2&).Ã<N[$!.†EÃQ3>‡oB‰K%5‰$!%Iá1à ¨ O2ú ÃN)ä‘
© K
çKž,á1~à ¨ú O*à Q ä u
ç ž$!.† `× F 71à Q G8p53F3&'r<$(2$!%'&2†E4)(2ˆs 7 Md
çEGª
7 `× F 71ÃN)G‘W ú `× F 71ÃQPG2Gªp5.´M¹8ç œ”Ù 4ç=Á ! 79ç?
&-á1à ¨ O*Ã<N)ä *yG W&á1à ¨ O*ÃQPä *ƒžR%5‰&). « › ¬=%5‰&d6!&)(B%1p9oB&)3^ˆ*4dˆ!‡%‹†-&9+!(>&>&
M Lç Á p 3#& R$o%9" qº%5‰&t%5‰&#6!&)()%1p1o)&)3uˆ*4tˆ!‡%‹†-&9+!(2&B& Ÿ
Ÿ p .n”
p5.ª•
M ^ç $!.† « Ÿ ¬=4ˆ!(m&2$oB‰3B‡oB‰´6!&)()%'& Rt
zžL `× FHM N 7 /G !
L × F‰¡´M N 7 /G œ
ÁÈÙ_Ù `
Ï Â ºYbA2A>P_:
ÚaÉ ¼¼]Ë Ž¿<%
: ÕX&)%g79çBO <=Gª³B&ª$n³BˆP$(2† œ5Ù 4[ N O2 Q $(>&t$"b²
'% &)(B.$%1p 6!&=ݲ9sˆ!6!&)3[p5.0M‹YçKž^%5‰&).ÂNO2Â!Qt$!(2&$" %'&)(B.$%1p 6!&
4ˆ!(2oB&2†
s[ˆ!6!&)3 œ
ÁÈÙ_Ù `
Ï Â c^22ZEA>Ag79ç Á OB<=GdV=ªŽ!O>øv9JI@t2ZUBtA>A
79çOB<=GKÉÐ79ç=Á9OB<^Á1G):KüR)A8MdÁ Á ! ‹
M Yç=Á]@uA8MdÁ ! M‹
154
çg:ºüR)AD(±Hmu2A>w´JIbA>ºU)VV>@±(XN@±(/Q
@µM Á :
c^22ZgA>e
A Ý7 (XGO (XNO*MdÁ G=EUPB<V@!bA{`ºí—:Kc^22Z
A>eA,á RNPO2Ã<N)ä)Oá /QO>ÃQäRe>aA'Jd>UX!m Ý7 (XhO (XNO2M Á GR@YA>eA
L ¡´M N 7 XN)G ! (X:D˜y`gü_
=Ž\! !zeAaV!*AIŽ!!Z,! ® \7*ŽeG
A>,2A ú ¡ 7
­ Goú ú ¡ 71Ã ­ GXa2eBA>P85> ú ú ¡ 71Ã ­ ú GX@LM Á Á
!@7‹!GRA>z2A ¡ 7 `­‹GRD2BeA>P8l> 7 M Á IG ¡ 7 `­'G
@nM Á Á :uj„: 1: <: C:º!22ZA>A ® ! ŽK8A>[!!Z:˜z`
üR
[Œ
!@tü_
[[J8UP!@#22ZFA>eA[á XNPO2ÃN)%
ä ç Á :z¬^@UFÂ N O>Â Q >EA>)>@A>F5!>UPm:
1UA8A>AL2UEA2>g>t71U2
A>-Gg‡<" %1(2$s
&)%1(Bp9o\y2V@U
A>dZ@bA!XP!2Z<>@-AzV=%1p5s
&z@
C@^A2>]>=@!AP:
!*Ag*A2BVC!-A2 !2JBµwA>@2!@EA>ªZgy@v
ZUg<>HVYA>eA8>gA2>V!aA>KU!ZA>!:gÀ‹AE!P>
A>eAIbA>]J,FgZ*AI!PJÓ2!0·{H!Z@<Pm)2>!>¸[@mA>
*A>
A>!@gIA>V
gJgZ*A8Z2ª@JÞP!2Z<>
!ZA>@n712ZU)tY22H`t+-&).ˆ!sLp9o[†!p 3>%‹$!.oB&2G):FœU@_\
UZ<2>@-A>`LH!A>[=2UzA2>^@[C!@]A2>z>dC@!
@ZAP:›Y[A>>Ew<*A^ !*A=!C>A>^A>AdJIV x @mA>
2U]A2>YV@V?V@C8A>=@ZLHDVA>B_A2B@* )>\
C@L!@b`L^2Ay!C@A2>ˆ ïKbB_\J]e>]V!@@@CdA>
!b`mZY!C!!>bA>IA>V>C)FeAB!2A>d =HUA>>V<:À'A
J!ZVHIV@-A>>*A>V@CFA>8;@eJ±b{\@
>@U!1\-A>y
JIf!2[J,!>;
JIA>_\5!dw!\bB!_-`<C!@:
c^22Z]A>AÂNO>ÂQde>=A>)>@A>I >UP
ezA
(X:EÀ‹à…YA>LHeB#!HAB!@P#H-`ª
;V@CKÂ)­!@š79çOB<=G)\
A>@iA>U!*Aª![àïP}-Z!KA>uU*At!K79çOB=
< GmZŽ:
eA\-Jd
!;dFH<B!@U)@[@U>!2^A>IU*A,H`mŽ:
¬Y@U\Z<d!C>bA>Ð
!; ð 7‹ ô G,HB@UB:
üR)AA àá N O2à N ä)OSSSOPá `O2yà eä/!@3
à Á á
Á N O2Ã ÁN ä)OSPSSOPá
Áâ O*à âÁ ä
HYA'Jg2}Z@U]!ae>UI!RM8:yü_A%4 ! @R7OˆàeG,!@mA
ç ! W N ã­´ã ÿ N ) ­*:±j´J]>· bA> à…É N àÁIݒ7*ŽPGKá
`­*O>Ã~­‹ä !
á
Á­ O>à ­Á ä,5!dP!UBŽ ® ‹4 ŽE!@7‹G
4687NR7UL `× FHM N 7
` G)OˆL `
× FM N 71Ã~ G2G‘"™N
4687NX7UL `× FHM N 7
Á G)OˆL `× FM N 71à Á G2G)S
ÚamÉ ¼¼IËЎŽ!: Ù .º3ˆs
&0³(2$.oB‰±ˆ*4
%5‰&ª$" +ˆ!(Bp %5‰sKž8$t3&²
‡&).oB&Kˆ*4[s[ˆ!6!&)3E N OSPSSO> ô p53gs$†-&
3>‡oB‰´%5‰<$!%ža4ˆ!(gŽ
ø ž « › ¬ª7‹W W#Â-C7 &ÂNOSPSSO>Â)­C*!G)O<7 MYG2Gp53
$oqo" p9o « ¼f‰&)(>&
® k+
<7 M=GFp 3=%5‰&L(*ˆPˆ!%dˆ*4]%
M ¬)ž,$!.† « Ÿ ¬
C7 &ÂNOPSSSO>ÂeOô *-GO 7 MYG2GEp53E$
ŽO>øR²‹¼ap . œ
ä
ÁÈÙRÙ `
Ï Â ºYbA2A>P/:
6.
j´yPEXPERIMENTAL
y@-A>P^Zf!CRESULTS
>bA>7 A>`Fe>PlH
A -¡y¡ åræGçƒçoè~èƒèy¥2£¤R¥ ¦£§<¨!ŸŸf¥2£~ž çé<žŸŸ! ¡¡Oçoé<£)ê¨oë<¤£)ì GD!@
A2>PA>è!@m2B!A>*AI2)A>:,|fC!Z> Ü 2PJI]@=!D
<A>
!<2U@e>Y71ø !  Gf !yA>ABYl> ~ !€ J] !Z@
VKZ<LV@-ABA>@:2U@>0>2A>P@ ~ !€
@YXA>YE5Z@H-`Z<I!C>bA>èHZA@!A]2PJI@
)>:
|!Z0gA>2´n2U@>#<Ý/)0@b`i@hA>#!2v
)YyA>FA>>EA2B!@* >^V@ªA>8ìRvhÞD>!A>HUA>>Vv{-\+í_v
ÞD>!A>!H!U)A>>Vv{\^!@}
îCv ÞD>!A>!H!U)A>>V´V@P!C!:„
x lA>ê2U@e>V±bÝ/>ª2C@ x UP@A>b`/ß±A>>tnA2B!@* !!@CµA>u>Uul>ýA>u!@U*A>!ªgìRhv ÞD>!A>HUA>>Vv
Ž\]>±!@šH<>eJI@–!C\^!@±
íRCv ÞD>!A>!HUA>Bv>ŽªA>$
í_v
ÞD>!A>!H!U)A>>Vv>ŽHZ<A=@A2B@* )F5>îA>[e>UgHA'J@
A>[!@U*A>!8!%
&eì,O íA*PCv ÞD>!A>!H!U)A>>Vv{\a@ îCv Þa>A>!v
HUA>>V^A>
íyO>ìXCv ÞD>!A>!H!U)A>>Vv{:y]>CB!„A>-!;L!@
A>L!B<F!^ŽP¿2U@=A>>A>Z>@#!y<A>V
D2U@>
mA>2A>UZle0AB2A0@±!@±A>ªBm!8# J
@ZA>,5!L792A> x UllG]A2>IJIbA>ªI
!@-`!^gPP:
7.
OPEN
)>
>
@<ZPROBLEMS
gHY!5ZA>Z<>b>UA>!@F 8A>=J!>;:
|fb>*AP\bAJ!ZVµHK@-A>>*A>@C#A>@U>!BeA>KJC!A>
C @^!@[2U,A2>z@A>F!Z,R71HZAz*A>>2)>
A2B!U)AB!HbA{`G):c’>!=5!>gZVA>@u!=A>K<>2=A>
155
Species Tree
Gene Tree
8.~ Ž € •,REFERENCES
e>*A>@_\ “ :cE:_7‹!¿ ¿!¿GðZ@Cß,g@)Ji2ZA>@
~ €
~ €
~ €
~ €
~ Üe€
~¾ €
~Œ €
~ €
~ Ž¿ €
A>gA>=!*ABñeB!2bA>8-`<V!C@-`>U@UVVA>!@
>!H0: Ù t
. ò(>&)3>3>z: óu$!%5‰ œ+ô p1ˆ!3)op œ :
›FB”YZAB\˜d:V\¬Y\ õL:\ ðV!@C\/Y:\üR1\ “ :\
R>!R\ ð:@,
ö/!@C<\üa:X7*Ž¾%
G ºY@0*AB@U
HA'J@K-`<V!C@A>UYA2>`: ò](*ˆPo œ yŒ ÷ø˜d..‡$"
˜ùó#´² ú Ù ˜%ó2úqsYr<ˆ!3>p ‡sîˆ!
. ûFp 3)o(2&)%'
& ˜^" +ˆ!(Bp %5‰sg3ž
úürû%˜þý ÿe\_:  ¾ev   Ü :
›FB”YZAB\˜d:V\¬Y\ õL:\ ðV!@C\/Y:\üR1\ “ :\
R>!Rm\ ð:!@,
ö@C<\üa:_7*ŽP!
G ºY@A>^V@P2v‹U!*A
2ZH<A2>v9A2B!@* ^<V*AB@UFH)A{J@0-`<C!@A>U
A2>‰: ˜^" +ˆ!(Bp %5‰sgp1oB$=2UV!X22ZF@0U!Z<ABA>@!
H!V!C!`ª\_:_ŽP¾ Ü vBŽ-:
›=bJIUB\•^:|,:!@
ÞD!PH\ ð:›g:X7*Ž Ü G
‘^!@-A]>V?@-AB!_A2B!@*5^!@0ZUPA>@K!
‘dZH2UgC@IV@0¹yZH!U)A>>V[!@,
Þal*A>Vz: óuˆ!" œ
ô p9ˆ!" œ 6ˆ" œ \Rސ7 Ü G)\_:Œ¾! ŒŒ:
”Y-
@R\ “ :)AY1:f7*ŽP¾!Gd|fbA2A>@CgA>E”Y@
üR@P!C!8@-A>[bA>I2UI@PCß,ge>2@-`
*A2BA>C!`mVZ*A2BeA>P0H-`
UV<C!B^U@*A2>ZUA>P
5>!ÐCHV@K2P}-Z@U+: úq3B% œ ˆPˆ" œ \!Œ<:
”YZC \‘E:Ad!1:‘dU!@*A2>ZUA>@0a!@U@-A
UZVd-`<C!@‰: óuˆ"V&2o œ ò,‰q!"ˆ>+-&)./&)% œ $!.†
6ˆ" œ \ Ü \\R:_ŽPŒ!v{Ž<:
¬=V)A2AP\ “ :!@müXC>C>@R\ ð:f7‹¿¿¿GI©^J
c^C!!>bA>] IA>=›=ZUPA>!@v'üR!2 “ <1:  ÷vø
˜d..‡$
" ùüó ô ý \X;-`-<H\ ð!@R\<_:Ž Ü v>ŽeŒ<:
¬YV@_: ð<:X7*Ž¿GI‘dU!@*A2>ZUA>@CgA>=!VZ<A>@0
2P}-Z@UI2ZH<ƒ{UAIA>g>U!gHV@A>@mZ2@C
e>2@-`-: óu$!%5‰ œ+ô p9ˆ3op œ \!Œ<\R:/ŽŒev{¿¿<:
¬YV@_: ð<:X7*ŽGdcéZ<>*A>VUF)A>A>L>U@*A2>ZUA
A>Y*A>!2`m!a2P}-Z@U]2ZHƒ*UAIA>g>ULH@eA>V!@R:
œ óuˆ" œ 6ˆ" œ \ Ü \_: Ü v  ¿-:
¬YV@_\ ð<:V\ ðV!@C\Y:\<jn@C\üy:!@
ö!@C\«[:
7*ŽP!!™
G ºY@A>=U!w<bA{`!fU>@C
!ZA>@2`A2>r: ùyˆ!s³p .$!%‹ˆ!(Bp9$" òd$!%1%'&)(B.
óu$!%‹oB‰-p .+ « ùzòó¬Yý ÿ ² \üXüR©=•]œm!¾\R:/ŽP¾¾ev>Ž¿<:
Green Algae
Plants
Red & Brown
Algae
Cyanophora
Cyanobacteria
γ -Proteobacteria
β -Proteobacteria 2
β -Proteobacteria 1
α -Proteobacteria 2
α -Proteobacteria 1
Transfer
~ Ž!Ž € ¬YV@_\ð:\`ðV!@C\Y:V\jn@C\üy:!@ö@C\«[:
7*ŽP! Ü ™
G ºY@A>=U!w<bA{`
aU>@C
!ZA>@2`A2>`: ûFp 3)o(>&)%''
& ˜rr" p‹&2D
† óu$%5‰&)s$!%1p1o3B\
¾Ž!\R:_Žev>Ž Ü <:
~ ŽP € ¬Y!\¹I:•^:V\<j´>H`-\ “ :\@K‘^!LHZAP\<c8:
7*ŽP!%
G Þa-`!C@A>UFl<@UY ^>UgH@A>!@K@
›=@CZ=>Z‰: ó#ˆ" œ‰ô p9ˆ" œ 6ˆ" œ \/Ž Ü 79G)\R:
 ¿  ¿:
~ ސ € ºY2@R\”LH: ð:@mj-2\•^:‘E:_7*ŽP¾GIcd>UB
C@Ußz@Ke>JFª: ùz&"5" \Œ!<\_:!<Žv'!  :
~ Ž !€ ÞD!C!\‘E:<›g: “ :X7*Ž  G “ IHA'J@mA2>d!@
UV<*A>VU8@!b`<2^D*A>>VU!D22-UVA>@=!!@C
C@\!>C!@2^!@K>!: úq!3>% œzô p9ˆ" œ \  <\R:
!Œev{¾¾:
~ ŽP € ÞD!C!\‘E:<›g: “ :X7*ŽŒG^”Y@PR>ßyU>@C[C!@
!@m2UV^`<C!@IZ2V@Cg>U!@UPmA2>:
ô p9ˆp .P4ˆ()s[$!%1p9o3>\RŽ  \_:ŒŽPv'Œ!¿<:
~ Ž ܀ ÞD!C!\‘E:<›g: “ :@0•,>*A>!@R\ “ :c8:_7*ŽP!¾!G
|>!…C@YA>[!>C!@V2
X`<C!@-`/ßa‘^U@UVP
A2>d@A>=C@=A2>) ñe2UdA2>F>!H0:
óuˆ"V&2o‡<"$!™
( òz‰q!"ˆ>+-&)./&)%1p9o38$!.† 6ˆ" ‡%1p9ˆ!.\/¾-\R:
!Žv{  ¿<:
~ ŽP¾ € !@K¬=2P\cE:!@0•,<Z<>U)V1\”L:cE:X7*Ž!G
©Y)A{J>;
] ^2}Z@UFZ<A>V!@R: œ óuˆ" œ
6ˆ" œ \¾-\_:¾¾ev'Œ:
~ ŽŒ € j´-2\•^:X7*ŽP!Œ¾GI˜UA>>V!RZ<A>V!@R`: ótp9o(*ˆ³p9ˆ" œ
I&)6 œ \-Ž\R:!Žv{!¾Ž:
156