Inference of Transcriptional Regulation Relationships from Gene Expression Data Andrew T. Kwon Holger H. Hoos Dept. of Computer Science University of British Columbia Vancouver, BC, Canada Dept. of Computer Science University of British Columbia Vancouver, BC, Canada [email protected] [email protected] [email protected] !"#$%&'()#*'+,(%-+*. / +*.#$#$012(3" #45 6%((5*7#$89.:;/<#$ #=>':'"?'+4/#4@AB(#$ C':D 68(+=+4EF8/B8(+$GE +=.;H% (#=3/)( I;J3K8( "'-BL +$% #4?MN-00; O(P()QRM@#4S5('+$#$D8( (+=.#= C " ?;B%B(8#$TU0)/HVW#=+$X9.PZY[O\]=^_`_(I; KX;@<:'8#$B#= "'+a(% -+='#$3% ((Mb +$+aB(BE BG'5 0+$DL"c#$#=+=.G-O06'a-!#4#$P9((J!d2 -+4O#$"B#$8;'".O -O +$%'#47#=5 0+$L#=B()#$*/- #4#=Pe #4a'N'e#4fg()hi j-"0)/O2kN 'L(J3?'+=<8('c8 (+='#$ ` U P9()@B@-#$%I/B)#=8Q':'"L""L".61/B#$8; +$+4/)M G(P9()j& 0:'#=@0j(-+$(J ABSTRACT lBJ m?n oDpq<r,sut(vwxLrWr,yz{ |t;zip"}W~@#4!'"cc;#$8;'+, B8#=8(( Categories and Subject Descriptors % INTRODUCTION (#$8N%-+=. /!k2'XG#$,6I/BI(Z#$D@#=8:!'(#$ '"% ((c0#$"_U;'8'c ` 8? c8+$AT#$-BE --eI/Ii G8)+$+$#$%8((+$+$-+='e-8#$(JQV'Q E L'+"8((+$+g+$#4>8/8+=6D:'X96+= 8( M!8((+$+(;h5;P9e#$L+='8( G8('(8+4/N X#$%G(%-+=' /12 XD'28( +Ja? )/' eX.@(% -+=''2".28( +e +$(P9+=a2 XL.N +$(P(+': 8#$#$?'b8)+(8 #=(M' h8(#=BE ;? M'!0 ;? ?IE: 8#$#$ +WB#4"8;.#= :J ?')/U >(c(% -+=''L'?8()O'Q'(#$T8( E +$AB(".(%-+*.?c:'8#$B#= > %(((J`kBE #$% !#$)cO"'-B Si-8#= K 2P.#= -!".)j(/BG#= 12'XT. !#$)(ILKL )/3(('8:(Me L .&&X9/KSS0-I:'"B#=%C eL )/K#$ :') 0#$+$% #=8( +, 0+$((J 1C :G&I-B/?5(% -+=''/C12 XMR#4!#$Q(8('/ D";P9e!; N!; -Be6%>AB(#$&'@B#4fg() duO@ 8( "B(8G-+=c0GB(( 1. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage, and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. SAC 2003, Melbourne, Florida, USA © 2003 ACM 1-58113-624-2/03/03 ... 5.00. Raymond Ng Dept. of Computer Science University of British Columbia Vancouver, BC, Canada #$!#$)(Mg'Q D8; C 0P95 ?#$Q@#$8:S% ( 'a0(#$%j(% -+=';G0)/Q+$) XB#$%Q'(#4uAB(#$!+$(P9+=(JW>E #$+!(P9+= ()@'b8(Q #$89.:;/B@(;.8e8-+= i AB#$()e+4/C KL+=#$#4;C-O0>'2%(!. G#= M)(P9(-%(6%(j.>'2'WG+='% >kN XJ c#$89.:(/(8 += % /C'+$+=;@>;'8:eI-"B/c%(!AE #= OQ+*.%@8;'+= 0-b#4a +$G (bH8:" +$+$(%((MB' 55-I6;"cj(/B6L e -%C'"?A:'8>--+ #$i L'#$ ci QL #$P9Q -)j h.:BJ Ni 58; #$D5.P9:'+$+b%-+=. /S12'X I-8-M#$e#$>#$ :')6#=B()#$*/c% (e".6";P9!#4(8 (% -+=''/?(+='#$#$(J>Q-G!8( +$A&".-D b k2'XMaP9(3#$O#$ U; I/3:'XJKk3 8;Mh&' L )/c#4fg()eP.#= 0+$(Q )8(#='(C@#4C'(#$SAB(#$ 0(#=a@6 +$(P9(+$(M)@#$8:; h'a8(Q #$89.E :(/.:5'+= GB)(2 jB(()2@(;.82@#4cD8(E +$6#$8-BJb>;N(P9;MB'+$-%L#42L(/06#$8( +$M9#$ .:I#=+$+b8( :'#$QL#$%#$8; )!'-6'N#$i L.#= <E : #$#=%c&O8(+=+$-+*.D #=<+$(P9(+$(M,'"S8; SB-Q.P#= (;.8N@#4L-i-+g'"#$)(I#$%D#$'L'#$'a8; +=&(i)8(-j(#46;'8:?fg'(J d2h 0+$(ZB(;!#$G#$u u#=R".W #$"'E #$%@#=8:"'#4e'a% (e.P!#4(86(%-+=' /?#=):'8#$ %#$P9<+=.%-50O'G%?ABB(#$TB +=0:'#$; i #=89':(/':J SKT8; +$+$; 62 Y[R Y[i¡¢;£2'h"B#=%>'()#*'+(% -+=''/O #4bi %6AB(#$&.:! "(P +$-'6#$2 % #$IjB(P#$-aE @-#=%O;'+W &I/B)#$8G':O(J d2(L'#$"O'6#$O"'5#=5 % #$¤((_'5 +$+=;@(Jk B8#$L¥)M2j% #$P9@>0#$g.P9PB#$H'"jAB#$I#$%G'+$% #4 'Q +=P#$%DB0+='b""B#$%% (!(%-+='#$C"'#4(J@k B8#$mBM@NSB(()&3:'#$+=(AB+= '#$`'5 -c +$%'E #4?J>k< B(8#= C¦Mg2O#$8(-eDAB#$(): +u(-+4Q -B@ +$% #4§-#$%!; +g'"I/B)#$8e':!(JhVW#$"'+$+$/)MB#$ e8(8(+$-"B#=% (8#$c¨Q2>B.PB#=BQ!0#$-L'/O u- (-+$6'"c#$"B#$8;'G G#4(8#$ @ @i--QN XJ d2>.QG-O0a'uB(P#$-N 9'8(ai jAB:'8#$% (% -+='#$L#$i L.#= i ©#$8':(/O':Jhd2(@#$8+=- j: %#$%i #=+$D8 (+='#$ <'"'+$/B#$Q'"?8(+$-IE #$%5OG'+=#$8;.#$ hN;/9(#= ?kN X(J d2I#$5<ª¢ «:«Y]$\'[¬¢ TY[i¡¢;£ Mb@#$8:3(I5@ kNeP '#='0+$(,".2@#$%#48; ),+$#$;.,(+='#$#$!@#$D;'8 G0)/?(#4!®W;' 8('(+='#$<8()¯8#=;J5d28( +*.E #$5G"',0((5-;!;;P#$+4/D WN0" #$,'L )/G8(+$-IE 2. PRIOR WORK #=%c'"'+$/B((M'Q#4G#$QP9/c-i-+,#$S#$#=%@ 12DP.#= 0+$(N";P96GI%D%+$ 0" +g#$#$+='#4k/)JW#$L#$8'E :(/5#=@#$(N.:BM) @2-+=AB(8h@% ((h@#4L% E -+=' /5(+='#$#$hGAB#$0#4h%+$ 0" +$+4/#$#$+='a%(6AB(IE #$ ZB "+$((M6@#$8:8(-+*`0C(I;`-#$%UC8( (+=.#= RJDe.N(P9;MR@#$+$O#=G#$G%)K.!#=BE #$%&% ((e"'e".O% += 0"'+h#$#$+='#4k/)Mg#4Q)(Q e: X9D#$ '8(8( -)5 8O".D#$5 *(3: X9D#$'OL%-+=. % (6B-8h!ABa#$a#$°"-(86 #4a:'% 2% ( Jac E .P9;M928 (+='#$ 5I % +$/5;P9 -h%+$0 +"#$#$+='E #41/.P9Q'!+=)8( +$#$¤(;#$#$+='#4#$(G'#$#$%i ±8( "#4#$ + %-+=. /c+*.#$#$(J d22(8( "O!#=,GY£;²)Y>£)Y[1Yª[¬¢'&Y[i¡¢;£j0/DVW#$+$X9.P Y[Q\]=^<n m'M,@c)8(-;K#=B.PB#$%c+$)8;'+2;B%L(8E #$ &'0#$+$#4k/8".;OG aB(M9-8:L a8( +*.#$J d2e(%6B(8#$O8;'b -%( 8:%(6AB(IE #$ S8-P9GL#$Q@5L;³I'>8:"'%>#$AB(#$ +$(P(+>;B%(:!)8(8(-B;Mh "S(.P9(!-B#= -D;% (!i78( E #=B:'#$RJ5du&B-8(OL8('M5(%O8#$S -j-LQ-O0N ,;B%(@#$&125%(GAB(#$&8(-P( 'a".6j 6#4(8#$ &'".@@#4#=( 0+=>#$IE :'8(Q a; 8:C ;J!´>(5 #4>'G.O+$#$X9(+4/?L";P95 '8#$P.#$?(+='#$ #$S'!% #=P(?#$% ?8( (Jjk?8( +$8(-+=.#=% e8 M@ +$DL X9(h-6".a6;% (N". .''".5N-+=K% O+$;28('((JCd2L;B%(8E #$ O!#$D#4,8(-()Wi µ8( O +4/D#$h ()#= + '8#$P.#$?(+='#$ #$(J d2Q#4:c'B9 8:?#$jG- %G'N¶e\ ·9Y¸¬\ CgY[¹a¢ «º'¸Gn »BM ¦BM2¼J N;/9(#= 3k2'XC#=5c%': #$8; +h((:.#$K' 8"B#4#= "'+a#$"B(((8(5#$&O-+4#=P '#=.O 0"'0#$+$#$1/S#$IE #$0-#$RJµV'c% (?%-+=. /kN XH#$(8( M6C#4E 8;H 8/B8(+$#$8c%': U'QS2(/)(#= Hk2'X(B(()5 I-8- 6%&%-+=. /Uk2'XMh@#$+=&L' ':'>i Q5%': C(B(()>DI:'#$I#$8;'+h)/B BE #=O0(#$"L12 XJK´>(½¾(% -+='(O%(¿#4e " +4/#4h5#=>&B#4(8Q(%Di ±½À¿§#$D% :'RJQk ':N58( I-8NQ2(/)(#='&kN XM>;h5+$;. !12 X-#$%!0P9;?':J@>;2(P;M#=68;'0 8-B:'#$ +$+4/".:RMg(8(#= +$+4/<#4b!(': +,'(8Q' G%(GAB(#$ .:'Q:'X9(c#$)'8(8(-);J #$8( O:'X92+='8(2 -%D2(% -+=''2B#4(8+4/D0#$"B#=%e e:'%;?%(G 60)/0#$"B#=%' @(%-+=' > - 8( +$+=#$%#$6#$"B#4(8+4/)J 1WG#$6)/'(#$¤(#$%O".e% ( 8#$P '(@%DeM 2 -+=_A8S(?#$H(#4L.:#$?#$ +=+$;2(0/ 38( "B#$%U#=S#$eM@ 3 +$+G#$ +$+$;2;0)/ '+$+O#$ÀeJQd23AB(8:.#$N-+=0KP9; <#$#=0#4E #$RJUÄ>N-+=U +$<AB(8DS 0Pc8(:'#$T'-) e#$?+*(/H012((UkN8('(#$%<(P9()(JTd2c +4E %'#4: 8:XB6(5#4(8#= "'+,8 % ((MR-00;&Å(P9(M Å 0)/T8( +$8(-+=.#=%HC+= 'DCAB(#$`B +=<'&;'8 #$Q#$)P'+Jhd2(G(P()2#$%#4*/&QI:'G'WQ% (>AE #= .! C#$I:')IÁT@e5#$G C#$8( #$ AB#= M e8; M" 6(#4;Jad2-(M("B#=%O c +$LP +$-Mu'+=% #47L'XG;'8(P9()D !#$#$%3>M 8( I: )  MR'Q'+=+$#$%VbM(-+4#$%#$I#=%&'2(P()(J >a#=;'+8(#48(-I:'8((M#$R6)/B #=a 8#$P '#$% ZNO8('(8;M; 8:S(P9()G#$ -+*C0OL.8;?@#4 8('(#$%(P()j#$eJ duS'Æ&L'8:#$%C'Q8('(#$%S(P9()O@#$+= : X#$%& #=L'"( :'+b#=-(G#$)? 88(-;M2 ;Ç)-(8(5 +$#$%e h!(P()>I#$% G 0:'#$<-E #$8;'+j8( "'5°"8O+$#$X9(+$#$)U '"U§;PE #$%Cc(% -+=''/K(+='#$ #$RJ +$Mb#$8LN'OX. 0i ( "C@ D-+=C0)/B #=¤;<'Q (% -+='';M Na(P +$-'h0 !)/'(0)/Q #$%@h +4E %'#4±#$C0 SB#$8#$Q "?8:) #$%&5#$%E18 #$% (-+$;JhV j#$#$0#4 /%-+=.#= &(+=.#= #=(MNeIj8(E +$(jG(P9()@I#$%',Q% (!)/B (#$¤(;&0G#$BE #$0#$(K0/8 %#$%C;'8USVNMb'"KP#$8(&PBMb@#$+$  (L'#=5-8:"'%(RJd2(Mu2'È +$#$%5'" 8('#=%GI(h'hA+= #$;5 0.P9J,N(8;'-2j#$#$0#4 b% ( #$bAB#$%Q#4b#$°"-(82D2#$#$0#4;5% ( M9N#$jB(+=(/ (+='#$ #$012(&Q12OL #$j-8:" %;gJ du#$+$+$-I:'LL'#$3I: %O j +$%'#$?MhVW#$%-¼ -B+$#=(uhB)8((ui W¿G´QW¥'É9Ê.Ë G¿>Q>¥¥'¦  M;kN6% ( i µN/9; Ib% (2AB(#$O':e0:'#$;!iµ2'+=" '8 j'(INAB#$()en Ì.FJad2(e% (2'6X;@!";P9 ? 8#$P '#$c+*.#$#$#=: 8#$#$?(% -+='#$ J kC':QL8( ".5kN&% (DAB#= 8(-BP9((MN5I (8 BPL:(':UKI#$%3'5P9()(J (P9(). (8(#4"8D#$D#$)P +u(()65#4(8#$ +,8:"'%5 % (AB(#$38(-BP9L'!'D#$I: );Jcd28( P9#$ )8(e#$P9 +=P(2Qi+$+$.@#$%I(J ¼JjN'28;'+=8-+='#$%eN+$ 2'b( 8:D#$h#$);M'NNI 'Í) #$%K H+$#=%KHc:(Î.:S (.P9G )/&#$%#48; )e#$!()e#$cG8(-PQ"' L;/<+$;-5#$:.#= (J< ) #$%?#$ ';T0)/K+$#=#$%K@#=;_#$@#=8:`. (P9/#$D #$;M!.:#$)6@#4#$G8(#4"; @#=;'5.P: % ;RML'6L +$+#$%-+=.#$#$(>L;/ 0D(.P9(RJed25 +$%'#4±#$8; G) #$%L@#$BE ;#$¤(((MÏeM-)#=+#4j"N6@e>P9()jI#$% 0:'#$;L@#$Ï_ "ÏCÐ_¼G'G;Ç)-"'+O;'8?';MB' -)#$+gÏ_ÑÏbÒNÓ(ÔM@QÏbÒNÓ;Ô#$@!L'AB#$O-¾ +$+$;2; @#=;#$¤(J ¥J2>A;MB2!8; +$8(-+='GG+$5'6;'8?#$Q #$60 ; cQ) ;c':BJ mBJjVW#= +$+4/)M.h+= NP +$-W'a8(P9;G#=)@(P9(Jud2 3.1 Conversion of Data into Events d2c8('(+='#$_ 3;% ?(8#$UO8( U0cBE 8#=0(S'6! #45(6 a(8-?a!8( (+=.#= <i)8(-(OKL% += 0"'+jL'8:K @kN'"+$((Mb@#$+$ Q;B%!(8#$&)8(-(@?I %5+=)8( +uL.8((J +$MW8( +*.#$3S8;' !L X-'25(E ': +a(P#*B(8#=<L.:BMb'"(#4DS:'X9(!#$ '8(8( -)>5B#4(8#$ +$#4k/'h%-+=.#= J6`#$+$!5L(/&0 '0+$>O 8(8( .6(>'8 j@#4&2(/)(#= &12 X(M G )8#*.;c8( -B:'#$ +g8(I@8;'c0QP/#$% Jad2-(M Ni((+hL((<C(P(+$U? 0 += 8(;K<". 8( L(8h0 % +$0"'+ O+$)8; +#$#$+='#4k/D('-2 5: X : +>#=-(c#$)U 88(-;J<'+$H2 )? -& c 8(8+$#$<#$Q#$8(-:'#$ " +$+4/S¯8(#$()Q2(/)Jd2 P9()2"'a2>(8#$0e#=L#$28#$#=@B(#$%;L j(G8#$#*J d2?.ckNS1/B( e(%-+='#$T'c+$(P9(+j'>:'IE 8#=B#$BÁ 8#=P '#$ '"#$#$0#$#$ JQ1?5 8#$P '#$CB E 8((M>B-82'u% ( .fg(8Ne:'8#$#$ &B)8(( '%@-8D"',2B-8#$ 5:'2i h%jK#$8; ((J  P9(+4/)M)@#$#$0#4#$)8(2#$P9+$P9(h% Dà aB-8 B(8;'#$%B-8#= 3 @% (eJ 8#$P '#$K'O#$#$0#4E 3. THE EVENT METHOD 0.8 1.5 YGL207W Original YGL207W Smoothed YDR224C Original YDR224C Smoothed 0.6 1 0.4 Expression: ln(R/G) Expression: ln(R/G) 0.5 0.2 0 -0.2 0 -0.5 -1 -0.4 -1.5 -0.6 -0.8 -2 0 2 4 6 8 10 time 12 14 16 18 0 2 4 6 8 10 12 14 16 18 time Õ@ziÖ"suw.v×"ØÙsut(yz}uv_p"Ú5t(ÛuvHÜeÝvB}RtcÞvt;ÛupRßaàTÜeáRrWw.vB~;~;zip}µ{9sw'ÝvB~?ÚFp"wStâDpTãv|"~(t&Ö"vB}uvB~?äåæ2çègéê |}Wßä&ëcìç"çíRo î1ï pt;Û ï vÚFp"w.vL|"}Wß|Ú1tvBwD~.q<pgp"t(ÛWz}uÖS~;ÛupBâ}bðj|w.v{p}gÝvBw.t(vBß<z}RtpvBÝvB}gt>~(tw zi}uÖ~ñâÛWz{'Û|w.vLt;ÛuvB}|yziÖ}vßK|}WßK~;{pw'vBßaà +$GP +$-2O0Q8(+='#$;?'68I:')!  2'GBE ö | ï yivK×"Ø5÷{ p"w'z}uÖUÞ|t(w'ziá_ÚFp"wLt;ÛuvCÜ6ÝvB}Rt5Þvt;ÛupRß î ÉOø #$;0 ;&G(+=':'jòG".2(8#$( ù ú9û>5ø¼ ñGüÑÉBñQÉ<ø©ýµø¼ñGÉSø©þZø¼ñQú9ûÿõt;zq<v @8(): %e g6':G#$)ai 26% (@".2. u ß vByi|ã ï vtâDvv}t:â5p©vÝvB}Rt;~ à Úú9ûz~T}uvÖ"|t;z*Ývgñt;Ûv 0O8(+= #4;'G8(I: );JDd250-./+$P +4E < q | ; t { Û z G ~ " | ; ~ ; ~ i z Ö } v ß Í " | Q ~ b r B v u } |yitã"ñ~;z}u{v~;sW{ ÛUqS|t;{'ÛWz}uÖ -O".O(-+$#=U#$8((): % c >8(I: )P9() z~}upt|"yy*pâDvBßaàið '!?-;c8+*'#4i/S +$+W%()@ b!% #=P(AE #= '"+$h(%j@#4?+$!%';'6"'&  V #$% !0 -"'/S.8(+= #4"(3 G!MRO@#4<+= ù É j a þ ú9û> 9 ú > û 012((&Q0 -"'#$(6  M" "L>I>'>VNJ Â É É É ù ù V j þ 9 ú Q û É ý ú9û> V D; 8:K% (ABB(#$K8(-BP9MR#$!)8(D(-+4D#$ I#$%5'u(P()N8:".: 8(JaV'2 -2A#=(M268e L'#4A?'Q:'X9(Q#$)& 8(8( -)QD#$5(+=(/C0kN((C )'#$%O@#4&Ï3Ñm ?ò!Ñ`ÉBó ¥JNd2(G12P +4E kN(P9()@0(#$%8".;RM 6;@#$CdW'0+$¼Jjd2#$>L'E -(uNN8: (!(#4#$8; +$+4/)M u/G%.Pha#=% (IWB-O0 'a-!#4#$P9D-+4>@?(I;C0#$ += %#$8;'+a':(J #4AL#$@!i ¾'W#$#$+*.#4k/LL'#4AL-;O(P +$-".>.T2(+$+ kN%(GAB(#$ +$(@L'8:c-BeN X#$%)/B (#$(J d2(P9>I#$%e G¿G´QW¥'É9Ê.ô "¿Q>Q¥ ¥'¦  '.@ #$VW#$% -¼J d2a2(#$%),'"aL'8:((M ù ú9û>M9.N-8#$, a#$ +*(/Uú9û!J ú9û012(H&kN(P()#$8;'((Mj#$ 8('O#$G8; (C#$SL+=#$;'Q #= JQd2#$Q#$>L( #$¤( 3.2 Alignment of Event Strings e;_'h2@";P926P9()bI#$%(M)N@(;O!B#$ j 8a"'a#4gk2GP9()N.j)!'2 ".N*©; 8: ;M @G':!'25(P9()Q#$"B#$8;'L#$0+$(% -+='E #4!#$G-+$#$X9(+4/?'Q/°(8!L(%-+*. /C(+='#$ #$RJ '/O(+=.#= #=0)/5"B#=%>@0(IaL'8:012(L2kN +$#$;.#$B(+=(/_" +41/H2 L8:.P9 _AB()#*'+ I#$%j@#$+$Q: X#$%!Q#$G'"#$>(+=(/Bj#=)5 8(8-);J ( +4k/&'*e(P'+$-"'#$%0 &8((j(#$#$8;'+$+$/)J d2#$N 0+$(8;'06 B9'8;#$#=+=.+$/5QjB0+$(' l-IC ?#$'(#$Z;Ç)-(8(< +$#$%()(MGB#$fg()(P9() 0#$+$% #=8( +2;Ç)-(8(O +$#$%();W%#$P9SOkNc(P9QI#=%(M L'8:";P9c#4fg()2#=% )(Jk_-BL +$%'#4?M2?6E N58( ¯8#=+4/?#$Q(#4e0(IQ'+$#=% ()> 8(8 :#$% L'8:(Q''#$%(#$%QN(#$%)G" VuE1V(P9() S-#4: 0+4/HB";38( #$%S-8#$(&0(+$.eO-#$%< L'8:(JLd2#$!#$D#$% #4";<0/8( I: )DýµÉCøÀýZø¾¼;M B#4";P9#= DC>((+$(L BEK-8 +$%'#$õi ".C#$O-+4#$+$#$;` ù ú9û>'SVuE1V¾L'8:((JÄ>-C': % +$0"'+>;Ç)-(8(? +$#$%Cn Ê;e': X(#$ 8(8-) 8( (6*8((+$+$-+='>e +$(P9+=(Jj#$+$D8 ( "#$%#$BE #$>(+=(/B20kN((& +$#$%;P9()28:".: 8(JbQ +$5(; 8;'(c#$6 +$(P9(+$ G123%(&'C%)`#$"B#$8;'' 5(-B>".je#$6O(%9.#=P>#$Q+*(/)ÁT#$>N X)E a'()#*'+u(% -+=''/?(+='#$#$M#$eL(/& e0G- #$%K)/'(#$#$".% 8#$P '(L%eMa(P9O#= 'jB(8;'(N#$6 +=P9(+$(M0(8;'-j@+='aL(/5°"(8 O-I +42;/BL)8(8(-BL0'?(#4L8( -)'#$6J2d2 W 8'(M)-8:D b#4fgW" +4*E1+$#$P9(,'B#$fg()W6 (J '+$#=% ()6(-+4> b¿!´Qu¥ É9Ê;ô'"c¿Q>Q¥ ¥'¦  M"-6-#$% d2-(M,#45 ;'!;'"'0+$C #$%3'2(#$% D?@EF A'+$MB#$e;@?#$?VW#$%-BL¼ J L'8:(J )/(P9()j".@#$eL.8;L@#4  #$6 #$%;c -: +8( !'NÉJ  I: )e(P9()6"Q%#$> b-8(E : #$)k/)JGd2/C8( -+=C0OB-5& )/-O0e a; (MRi 3.3 Scoring Matrix Ä>-B,8('#=%>-8#$ O#$b0" (55>8('#$%Q8:(h'b#=#4E #$+$#$L<.-:.#= U e8((+$+$-+='6 '5'8E P#=- +(P9W8': 8(JWKN8; B-a#$,8(N#$68( #$% (Jad2-(M j/8; 6'#=c#$?#$#$%DQ'()#*'+ 1.5 YBL003C YBL002W 1 0.5 Expression: ln(R/G) 0 -0.5 -1 -1.5 -2 -2.5 -3 0 2 4 6 8 10 12 14 16 18 N¿G2ÉÉm  '"L¿G2ÉÉ9¥; time 1.5 Õ@ziÖsuw. v RØ ö ÛuvvBßuÖv~§Ú1psu}Wß ï ãÍt;Ûuv vBßuÖ"vÈßuvt(vB{ t;zip"}q<vt;ÛupRßz}Tt(ÛuvrWw.pbyivB~p"Ú6Ö"vB}uvB~Oä?å&æ2çègéBê |"}Wß ä&Ü>ì?×"×"×o îkï pyß¾yiz}uvB~'ð.à¾Ù}Wyiãt;ÛuvvBßuÖv~q<|w "vBßx |"}u ß Î{ |"} ï v<q<|t({ ÛuvBßHâzit;ÛTv|{ ÛHp"t;Ûuvw)à YGL207W YDR224C kO :h!'(N -N +$%'#4© % #$INAB#=I#$%GB(M 2>8(-8;L (#4#$8; +g8( ".:'#$P96'L 8G +4/E #$>',G(GkÁ_>8( (+=.#= <RMBG(% (8#$&gMB ">(P9()jRM &P '#$-j@ ;'+$EN += &I/B)#$8G':BJ 4. EXPERIMENTAL RESULTS 1 Expression: ln(R/G) 0.5 0 -0.5 -1 -1.5 -2 0 2 4 6 8 10 12 14 16 18 0"a¿!´QW¥'É9Ê; "¿QQ>¥¥.¦  Õ@ziÖ"suw.v çRØ ö âDp rW|"z*w ~©p"ÚTÖv}vÎváRrWw.v~;~;z*p}ÍrWw.pbyivB~ t(Ûu|t§~;{p"w.vßuz Nvw.vB}Rt(yiãÍz}Ít;Ûuv±{p"w.w.vByi|t;z*p}õ|}WßÍt;Ûuv vÝvB}gtq<vt;ÛupRßW~à î |ð: ä 5æNè"è oÆ|"}Wßä Oæaè"èçê ~;{p"w.v ÛuziÖÛ±zi} ï p"t;Û±q<vt;ÛupRßW~ñ|"~Ht;Ûuvã|w.vµ|yq<p~(tTzßuvB}Rt(z { |"y1à îkï ð:äåæ2çègéê |"}Wß`ä&ëcìç"çígo±~;{p"w.vKÛWz*ÖÛz}`t;Ûuv vÝvB}gtcqSvBt(ÛupRßañ ï stcw.vByi|t;z*Ývy*ãyipâ z}t;Ûuv3{pw'w.vByi|t;zip} qSvBt(ÛupRß ï vB{|"sW~(vÀpÚSt(Ûuvµt(vq<rbp"w.|"ycyi|Ö ï vt:â5vvB}t;Ûuv { p"w.w'vB~(rbp}Wßuz}uÖHvBÝvB}gt;~à %-+=. /3(+='#$ #$H 6%((0(#$%S8".;RMb/ .L #$%;K-: +h8('((J&VW#= +$+4/)MW#4j#$5&6E1V#$IE L.8RM( +4k/c(8(#4"(?0/ jþ`ÉøTþUø¼;@#$eO-+4#$+$#$; ù ú9û>J d2#$e8('#$%L'#4A& +$+$;@>-28() +>0(";P#$-6' - +$%'#$Æ#$UC:'#$+=(H'"K;'#$%'-+aj(/)J<d2L'E :'N )8(#='(@#4@8( #$%5L.#$AO8; 068:" %; 'a(8((./'8(8( :B#$%Q>j:'#$+=h @.:e".N.j0E #$% +4/B¤(;c0)/LG'+$% #4?JNV @-B6AB#$()(MP +$-( 'býSÑ`ÉBó Ê þSÑ`ÉBó mONG-;gJ time #$+$S<8('(+='#$Z#$&%).B(8#$%3 % +$0"'+!#=#$+='#41/0kN((`kN_;Ç)-(8((M>#$S(+=(/B?8; (-8D#46fg(8#$P9(@'>"#$%O%(!%-+=. /?(+=.#= E #$(J &A +$>i @#$@+$#$#$:.#$?#$@;@?#$VW#$%-BD¥J d2C;% <B(8#$ _I % +$/T)8(-(c C+$ E 8( +NL.8(G012((SkN?%(AB(#$ K8(-P((J`#$+$#4 #$#$ :')OS#*B()#4i/3% ((@#4_S#$%_(%'(c'Q+$)8; + #$#$+='#4k/&#$&>((8#$P9>AB(#$&'"+$((M#$j0#= j e-"B(#4: 0+$efg(8N #=% '#=%5N; X920-B2I#$+$+#$%#48; ) B +=a#$#=+=.#$#$((J  #=B,hAB(#$ DB +=u',%(( ¿G´QW¥'É9Ê.Í "Q¿ h!¼¼ ¼  ;@D#$OVW#$%-B2mN%(,. [email protected] U 8#=P '#$ U+*.#$#$H@#43;'83';J #$+$?0 U8('(+='#$`'"3(P9()3 #$% #$% 8 (C"'#$;Mh;B%?B(8#$ _8('(#4O:.+$; 08; -D'b c#=-¯8#=@-O0j',;B%(6L'8:;gJ 3.4 Comparison with Existing Methods B+=+$L'KY[N\]=^jn Ì.u -% j50-#=+=58( ((#$P9e8;':.E +$% -N'"8(+=+)8/8+=EF%-+=.;D% (W#$!a/)( I\ª:ª:¡B\ «¢ 5·9ª:Y¸ ª:Y«Y;¬¸¬\9YJd2/U';H<#$('Q#$89.:(/UAB#4E ()h#=@#=8:L/5)X6 +$(P(+; -B(()b j +$+ /);'IG%(!.Q(%-+='Q#$O#$)P +$(JDd2/(C8( O0#$; #$j-+4j@#$ Q0)/  Y[2\]=^jn ¥;5B-8(GD 8( ((#$P98( +$+=8#$ 5.:BJd2(Ic'+$(L2 I/B8: #$¤(;OQ'h'+=+28(+=+$h2-+=O0@'hj'jI: % #$S(#4!8((+$+b8/B8(+$JOd2(B#4fg()GeN(+$./9; K.(IL?8(+$+=.c'?I: % S +$"'E 8'?.(I;M (+$-#=.#= MR'"?.(IQ'   ¼.¨   ¥ Ì(:.-E (#$#$P9cO-:')(JHd2& ;UAB(#$ T+$(P9(+$L.c +$%C:'#$O @(IO +$AB(#$ H0)/<8() +j +$ AB#= ?+$(P9(+R;'-(()(J N(8( -2 B(+$+$L à W.:6u8( :'#$;GAB#= 5B += '6 +$+R(L;B#$%5*: (j#$e/9; Ij% ( MB-O0#=% .P9 ÉÉÉM,#4!j !(8((./<c"S&-0D N(% ( #$3 :B5;B-8(L;'8:U" 8JSVW#$+=X'PY[!\]=^3n m'j8E '(&D-02 WÌÌ Ì5X;@L: 8#=B#$"'+(%-+*.#$? #4(M #$8(+$-#$% ¦9Ê 8#$P '#$G C¥'¦¼D#$#$0#4#$(J6K!-;c +$"'E 8'N'"   ¥ ÌQ':>W h -bAB#$();J i "+4#$%c-BD +$+h%((G@#$&#$%#4"8;'D-50Q'2#$#$% .:< #=)O*Ë(?':<(MN2? "'+4/¤;HcX;@ (% -+='#$-0@-#=%Oe(G'+$% #4(J V ¾DÌÌ ÌXB;@c(%-+='#$C"'#4(M"G-50j'NB#$IE #$8!% (!'!8( -+=<0L'"'+$/B¤((Sj'Dm ¦9Ìci 5 +$"c': & _¦9¨ Ì'   ¥ Ì3.:;JZd2#$L;'".L '&.P9?¼;¥ ÉBM É ÉÉ #=0+$?"'#$5"'O8; H0L (U#$U +$"?':&;MW'"<.P95¥ ÉÉM ÉÉÉ #4G#$<   ¥ Ì?': ;JU1U&8)A e-B(P +$-".#$Ma(P9/3"'#$ Q% ( ".@)8(8(-B6#$Q+$#$I6 bÌ ÌÌX;@" #4@#$65-Q #4#=PJ KO-+=<'O".!0(8;'-+4/S(P9QC: X9( #4(8#= "'+=#41/K#$)C 8(8( -);MWN<8(''5#$ @S8".#$%L@#$5'Q12B(M+$;2#$% -50, R #=0+$6 #4h0/D +4kJhVW#$%-B(N¦>;@N.HL'/ -@ #$#$P9a2e -0/DjB(eb#$(#4hBE 8; #=.((M2@ P '#$(*ÉC_¼;ÉM ÉÉÉJ +$+j( ji ;8(': 0+4/)J dW'0+$K¥;@&SB(% (S D.P9+='0k2(C"'#4 4.1 Spellman’s Data Sets 70 90 event edge correlation 60 event edge correlation 80 number of true positives number of true positives 70 50 40 30 20 60 50 40 30 20 10 10 0 0 0 1000 2000 3000 4000 5000 top-k 6000 7000 8000 9000 10000 0 1000 2000 3000 4000 5000 top-k 6000 7000 8000 9000 10000 +$"DG': B 0   ¥'ÌG': Õ6z*Ösuw.vCíuØ ö w'suvep"~;zit;ziÝvSëczi~(t(w'z ï us t;z*p}W~LÚ1p"w ö p"r î ÉOø ø¼(É!:É ÉÉ)ð 4.2 Synthetic Data Sets ö | ï yivUçgØÙOÝvw'yi|rur,z}uÖ`ìvB~;sWyit(~?xcqSp}uÖ ö Ûuw.vvKÞZvBt(Û" N(8( -a h+=#$#4:'#$ W' (+$+=L' à ,':j(M'2N-; pRßW~ î x&yyjìvB~;sWyit(~# ö w'suv ep~;z*t;ziÝvCìvB~;sWyit;~'ð #4#$ +6I/)#$8?.:i & c:'#$+=(T(P +$-".E +$   ¥'Ì c $# & WQ +$% #4(JaV -6.:52NGB(#$%(5I (8(#48e('-2 R@(e +$% #4(Jhk -jA#=;M  hP(h)P9eÐ e)Ð h(+=% ' #$ m¥ $m É ÌB&Ê *¼ %%O¼É ¼ m¥ »B$m '¼ (&¥ %O%O»É ;' 8D.:6W8( #$I;! 8(-P9W#=% ;G@;K(% -+=''/ (=+ '#$ #$ 5: +$/5B-8((O8(-P((Jbd2j(% -+=''/  +*.#$<) Ð aB% ¼;» Ì(» %OÉ ¥¥¨ &¥ %OÉ 8(-B P9((Mg"'; .!/01/2IM@É&øeÑ436øeѧ¼;ÉMRNOB-8(; #$ -8:Oj(/&"'5.!/01/ 2 .!/01/ 2687 2-+=#4fg6@#$?E -(c0)/&!B(D +$%'#4(M"@(+$)X#$%'6Q E (8 eG'8 >+=#$I;0(+$;GJ>V >A +$M@#4S8-P9( ¼(ÉBM ÉÉ ÉU:'X#$% &0)/_; 8:`gJµe3 ?"' +¼ % m3' B -8((&(I@'>8( I:'6#$!(+=(/)M!.!/+01/ 2697 N-+=?0 G(-+4@-;c0)/& )/&[email protected]+= ?@#4;'8 >#$ EF#4i(5P9#$ :.!/01/2kJbÄ>-hI/B#$8j.:Qb: X9 ';Mb#$#$8;'#$%C'D(P()5<"!#$%#4"8;'+4/ e$+ +$;@#$%L 8 6#=)8#=B:'#$R B#4fg()"'#4L*Æc'12(J_dW'0+$S¥C +$ ;@5L-50! 6.P9+='#$%?-L#4#$P9L"'#$D@( ¼J<;h¢ ¸[F\ [&=W¬LY>DY]$\ ·@?!d2#$B(+=(/G0k2(8('E +$) XB#$%K'OLE¼(ÉBM ÉÉ É<: XB#$%0)/3;'8URJ3F#$ ( #$%!8:" %(N#=12!8(-P(2.>'+$2(/N8(I: );J PB#=B()j"'@Q#$@P9/+$#$+$G.P9+='M"#4b.e +$+J #=% "'+j8(-P9&.!/01/ 2A687 #$O%:.;30/<#$#4i#$% d2N(P(),GB-8;QN+$#$Ib ()#= +"¬iB¡-¬ ,¬i[F¢ «· ! . /+01/+2,0)/cDAB; -);J %-+=.#= '5N(+$+Mh0-5 D O12D'' B(#$%;&5"L#$#$0#$#$ (MB/L8( -+=& @0Q8".; ¥JCB:««YF²DB]$ \ «E=W¬LYF>DY]$\ ·G?hd2e#$6(+=(/B20kN((L8('E ( 8: ;J2>#$%OG'G"':'e e 0.P9MG(P() "B#$% 8:"'%6#$c128(-BP9(@.DP '#='0+$J #$% + Q -"5¥Êj-h#4#$P92#$#$0#4 /G(+=.#= #=,#$D 8(-P9F.!/01/ 2A687 #$a%(:';L0)/O#$@#4i#$%.!/01/ 2 0)/ '+$"e.:6;M '"¼.Êj#=!   ¥ Ìe.:6u@#$#$Dh E : "B+4/ 8(c -);J ¼(ÉBM ÉÉ Éc: XB#$%& #4(Je#=%cB#4fg()G".: QB-8(; 02(-+$(MB0-2+$;2;>-50N'-> #$#$P9Q 8#4E mBJ5H6\ «:[¬\]) < \ [Fª:¡¬i²@?,Ä>+4/5e8#$'"N12Q8-P9(u8; P '#$ @#46i-"RJ 0DL.8;R M" cG(IQ'a!8(-P9>.D+=+$;c@#4 d2@2eQT#=% #4"8( )2B0+$(a )8#*.;@#$ : "B§; % ((J #$% " +R8(-BP9C.!/01/ 2A687 #=j% (:';0/ 0:'#=;&(-+4@'6LB>Q "'+4/#$6#$8( 8(+$-#$P9 JNVW#4I;M : "B+4/8 %#$%<.!/01/+2W@#$#$O(8(#4;:'% J 08; -c 6) +$-#$H 6&.:BMaL )/K #4' % (D;2;< +$IG#=B()#=8( +hAB(#$<8(-P((MuL'X#=% ¦JC>G¬ IeY«Y[¬\]8J?Y¬=².¡[¬)²Q¢LKW2 Y[¸M?Wd2,12@8(-P(1.!/01/ 2 'OB: #$+$;C +4/B#$G#4¯8(-+4;J>FbIQ'b(D"'#$e@#$ ".!/0"/+2697Q"' L;³I';M,L'8:#$%&#$#$%;B%((Mu0- I %#$#$+='#4#$(5NL#=< 85(% -+=''/K #45'5'5+=( I ?(I G(8 -P('"+$+$;_@#4T:'" ;% ((J 0<#$BP+$P9;#$#$#=+=.".2(/(M><8( -+= #$%I% d2#$G#$!(IG'5 #4fg()#= +,2#=% )#=%M@#$#$% 8"(8(L-#$%&!' +4/B¤(#$%C.:BJ ;% (6'Q2#=% ;? '>"'& +$+$#=%L;% ((J e;2(P9;M9@(5@#$%BE: X#$%>" #4b-;O0)/D2 GNL8(';K'%9'#=I5/);'IO% (L': 0 ((M duU(P +$-".C;±<' +$% #4ci õ@#4<I/BE #$?j C'+4j(/B?8( J`#$+$L')/`"'#$'; #=8S':3(M62C8(-) ;TC-50L !-C #$#$P9 8H L'N8( O Gc ?B E "'#4>".e/ci-RJek? #=e8; M2O(;c 88(-e' #=S8( +$AgMR >2O-+*.;C%((>@#4& 0BP#$- 8!'D"'#$#$%N.!/+01/.&Ô @#4O.!/01/.Ô+61P.MW@&Q&#$!+*.E +*.#$#$J #$P9(+4/3L'+=+Mh -+=30&8 #=B;H 0L'8:D d2L;% &B(8#$ 3 ;3 O#= -D 0E "'#4#=%R.!/+01/.Ô?@#4_?:'" È 8(-P9 Jd2-(MhN&8(#4";3 +$(?J6d2!%': ?MX#$"B+4/cB'P#=(c0)/?#4e'#$%#$"'+b - (M : %': SQ&?'Gi S.!/0"/.ÔM,cL.8C@#43 )/S ¯8(-+$1/#="#$%5#=% #4"8( )6;% (@#=&L )/L%QB E .!/01/ Ô$TP -%U.!/+01/ Ô+6VP 2 -+=3Ç)-" +$#4i/K 5c- #$#$P9 +$((M(0)/!%#$P#$%>¤>8('2Q6#$%5 #$5 2%((J "'#4#=%JeK!%(:'(<'"c( I;?P9!>'2':'Q;'8 bP9(i 2>% (N".N(8(#=P;¤(D8( (MBe-E 8;.(%'/)MW(;P9: % ;<O :'+a-50G'2- #$#$P9 0O'@;% (5'!2i-KD%(j 5A((+4/S+$.GM -RJWh 8:':Ga8( :'#$;? ¼¼6#$% +8(-BP9(a c¼¼@: BE 8(-P((J?d2: %'5- #4#$P98(+= #4"8('#$Uj' @#$8?8( Ie-0j c>#=% #4"8( 8D',Q8 ((J ö | ï yivXRØxÝvw.|ÖvZY?s,q ï vwHp"Ú ö w'suv[6p~;zit;ziÝvB~KÚFw.pgq ÷gãu}gt;Ûuvt;z{ë|t(|K÷Rvt;~ î QQÑ¥9ð  (+='#$ hP() Q':  I: )ed2#=G>(+=;/ m¼J m»J Ì 1(% -+='>d2#$QQ(+=(/ ¥ ÊJ ¥ mmJ Ì ®,'#= +W?'8:#$% ¦ ¦J ¦9ÉJ >#$fg()#*'+R(#$%)#$% m BJ ¥ ¦)¨)J É O.5¥JLe'-'(+4/)MR28( -+=< !8( "'5i E L'8(& Qc(P()US"' >?;B%B(8#$ RM" 6!#$+$(():'#$ ? bGc".@2D" ;P #$+= 0+=Dj'Q- 0+$!L-8(DBEF¤(L8( G#= IQ' GI/B#$8G.:5 #46'jNQ(I;RJ d2j(-+4h+=#$I;#$du 0+$@¦G;H".aA8(b'N@®,'E #='+Q?.8#=%(MNcP9()32 L-#='< 8 (+='#$ ?gJWKe -+= 6"'NeP ):'%>E ³k;/);c0)/LG8('(+='#$C2 e#$#$#$;L@(#$ B(+=(/&2 @#$B-8((&OQ®,'#= +W?'8:#$%':O(J CONCLUSIONS ();§ +$% AND #4?MuFUTURE 8; +$+$;<CY WORK Y[eLY[i¡¢;£ M 'e8; &""& ()#= +u 8#$P '#$S c#$#=0#4#= "'#$@i % (OAB(#$<.:BJOd25(P9()Q#$G0" (S < X/Ti;'-B(? 5%AB(#$RM>-8 &#=SB(+=;/Bc " 'I/B/S0kN((K#$#$%S +$+$#$%S;% ((JC15#$58-BE :.#$"'+$+$/<¯8#=;JOd25#$G;@Sci 8( E ':'0+4/U<&8( +*.#$`'"U;% 8#$TO#= "B#=%5-G#4#$P9Q(%-+='#$? #4@i (+$+$L à j/);'I ':>(M) 5 -i b8( +*.#$5-BaI/B)#=82': (J2c'G(-+4ji #$jI-"B/8;'?0>i-c#$n 'J 1C+=#$% Q NO+$#$#4:'#$Q a5':L-(S#$S-QABE #$()(MN#$O2-+=_0?#$)(I#$%S8( #=L k/B(' #$%EkÇ)- +$#4k/H#=E1#=&':J +=BM@#$% :'#$%K#4E 89':(/?':O@#4?'6k/B(j'h#$ #X;@+$;% Q2-+= (+$5';@#$%e;@!h;'8:5 8( J  ;'#$%>@ b; +4E #$I#$8@I/B#$82':>,i b(I#$%ej'+=% #4b-+=5 +$ B.P9Oc0O#=)I#=%J <#=B; +hI/B#$8':&G2-+= 8N*© O'#4"8(#='+(% -+=''/k2'XG"'b#$8( ':'( '2L )/5;.-(2'6( +Q'2#$0+$eD'2#4a2-+= 0>!+=#='0+$Q#$"B#=8(' 2 W;e +$%'#4NN-+=L' @#4U%)gMh#$%BEkÇ)- +$#4k/3':J< B-8:U?k2'X<N-+=38( E #=BL?;'8#$X#$#$8(L'!P.#= -L".)j(/B(M2fg8 '6+4/B#$¤;'#$(8('/i O #=Dc0(8(L'8#$P9M i L.#= ? bB (#$?8+$AB(j8J6n ¨)M¼(É'J F2 -+=Z03B(#4: 0+=KTI-"B/`Kfg(8 8:"'%#$% !B-O0@'b(P9()@k/B(@ ?!'L 8(! ,!(P() RJuK6-;e(P()a1/N#$L-2AB#$()(M)0-B S8(-+=#$8; S#$c-O0LU".&SP9()cI#$% N-+*c(()@>%(DAB(#$?B +=e#$?'!:'#=+J d2jfg(8,'"N +$%'#4 à b"':', O#4b'L 8 -+*50N-Bb#$P9(I#$%9.;RJu`#$+$22@B#*D2#4#$8; + Ij#=8:)#$%Oe"':'NNQ-(RM)>Ç)-" +$#4k/L'u ':eNN222 X#$%e@#$5jL(/!.PNP9();!-Wi % #$#$% Q#$#$% 6#$)5G0(";P#$-@'WQ +$%'#$ !"':'@8:" %JjVW#= +$+4/)M#46#=e#$0+$G".>0)/-#$% 5+=)8( +W'+$#=% ()e +$% #4#$I; c uQ% += 0"'+W +$#$%() -(M6S'L 8(<'!S(P9()& 8-+=?0G#$.P9(&0)/L)8(-#=%L#$e G ?+$)8; +u8 % (6#= 5% (5AB(#$ <B "+$(e"'QL;/&°"8Q8( +$AgMg8( E B#4#= "'+(% -+=''/&(+=.#= #=(J Ä>8(eN!'Q+$*@@#$& ()#= +(% -+=''/c #4(M#$N2-+= 5. 0 @-(),Q(.P9j')/O-#$-a #4#$%hi 2: X9; +$#$I;JGÄ>D #$0+$O'B9 8:C#$eL':'#4#$P9D8(+$- (.P +b1G#$@5(% -+=''/&+*.#$#$0kN((c% ( 3eMb'"3  Mb )/K#$%38('(012((3% (  L;/0Q-6!6'8j".2/'e+*.;B-% % +4/)J6(.P#$%S-8:_ #42-+=T +$+$; ?'E ()#= +R8; #=.(j0Q+*'8(;c#$Q: X#=%(Jbe+$#$L.(+4/)M 2'68(50#$#$%DQ:'X9;"'#$#$%@#$O/B'(( T+*.%&i:'%() G-"B+4/#$%(%-+=' /T12'X -+=<0OI-"#$;gJLd:'#4#$P98(+$-B(.P'+bL;/C(+$#$ #$68()A;M 6#4eN-+=c(-+4>#$?8(+$-Ie'h%((6'e' 8( 8;c0)/(% -+=''/c(+='#$ #$(J ]P K+$#g-"'j 0>N+$OL- +=XB#$+$#$#$%X9#$ j;"P D +,#$+=#$ #$B08( +=GL(+4./(#4#$>C8( BX*?!>\ +=(B#4>'#4(N:-VWM+$#$+$'(X96J6.PNK('G+$"+,N @l-#$¤('+=- 6. ACKNOWLEDGMENTS +$D+$#=X6G"'XDe )/ -,(P#$22 R#$N a' .P#=#$%O-2@#4?P +$-"'0+$G-% %(I#$(J n4¼G¿OJ2':'C c5JV#$;BL J  ABEF(8#$8Q0"(/)#*' 8(+$-I#$%5 e%GAB#= .:BJkNHj«I¢;ªYY£ ¬)² ¸5¢LK ^@ ;F_a ?X¶ `!a$aGb'J n ¥;!DJlJ  CY[2\]=^ % ( E@#=Q: 8#$#$ + "'+4/#$6 WQ#4 #$8G8((+$+8/B8(+$Jg S¢]=c^ ;aY]] M"¥ 9'¨ dBÊ mM ¼;»» ÌBJ n m.S \5JVW#$+=X'PM" gJ" BX#$("M"'"&l:J ]#JIB()#$*/B#=%O% ( (%-+*. /&12'XBj*AB#$(): +g':BJk Hj«I¢;ªYY£ ¬)² ¸5L¢ Ke^@ ;F_a ?X¶ `!a$aGb'J n ¦'!5JV#$;L'M<JR#$#= +M":JBQ 8:L'M &OJ®W à ;J >#$%0(/)(#= ?kN X2'" +4/B¤(GABB(#$':BJ f¢ D«"\]WL¢ KE;h¢ e gR^R¶@¬¢]=^$M"Êm'EF¦)M -%-Ie¥'ÉÉ ÉBJ n ¨;Dd>J hG#=% )6 "?´5J -L RJ  (+$+=-+='e%9'G(8:+$%'/)J R %$%.jjGJ '#J #4;J ;- %'( +$+ %;X %.8(+ %.8((+$+$%9'(J (M ¼;»»ÊJ n . !J hQ2 Jki(8(G ,:'8#$#$ " +R(%-+='#$ (+='#$#$@@#4?%(GAB(#$ .:BJ"? I à (#$(M-0#4;LOQ;J  -e B8(#$(8(M>#$PJ ba#4#$  +$-O0#=M¥'ÉÉ9¥)J n Ê;5 gJeJe(;B+=L ?'"  JOJBK-8:J % (: + +$#$8; 0+=GOQ;.8ci e#$#=+=.#$#$(6#$c #$O 8(#=c;Ç)-(8(G'WkN'(#$(J f¢ D«"\]WL¢ Ke <¢ ]=^ ¶@¬¢]=^=MB¦ÌB ¦¦+m d)¦9¨ mMh¼(»9Ê'ÉBJ n Ì.D®,Jd>J" B(+$+$L RM"´5J B+$)8XM<VJ i5J ]" %jM \5JDJBF/);M h "J & e"JV-(M"8:<J;eJ  J h#$B(R(M"®WJ"Ä5#$P9J"Qa#=;@R#4M8O;'JN#$'cI ,(#$8(M +=+ 8/B8(+$E(%-+*.;c% ((@',>/)( I!¸\9ªª:¡\ «¢'O·ªY¸ ªY«Y;¬¸¬\)Yj#$89.:;/&)/B0#=#$¤;.#= J <¢]=^g¶@¬¢]=^WL¢ KG[i¡Y ;aY]] M»B m9¥ Ê +m d)m9¥'»9ÊMRQ8((O0G¼;»» ÌBJ n ».D®,J" B#4((M  J"´>+4/B-;M'"c!J B8:(#$(J  I-8#=% 0"(/)(#= c12 XLB(+$6',%GAB#= ?k2'X i#$8':(/c':J1R H2«¢;ª:YY£ ¬² ¸5L¢ KQ[i¡Y k6[]$\ [¬ª ·'l gB¢ ¸m¬ D΢ ;h¢ l gDB[F\'[¬¢ \ ]g¶@¬¢ ]$¢² · J"´>( ki L.#= )/I5 nÀdu(8: +$% /)M"¥ É ÉÉJ n4¼;É.!DJK#=(cJ ;aY]] DB]$\ E« ;h¢ e gD[F\ [¬¢ \ "£ ;h¢ 5< D¬ª:\'[¬¢ ¸ o¸¬)²O2² ¬Y:Y«Y£ p6YY[¬Sª ^@YF² DB]$\ [F¢'«E· q!Y[¹N¢'«º'¸Jg®b (#$(MQ(;J 9 @J h%J" "  -e 8(#$(8( Mckd>J=M B(B(O0@¥ ÉɼJ 7. REFERENCES
© Copyright 2026 Paperzz