!"$# &%'( )

*+*,-./*012435 67+8/9 ):;*<= > ?&A&BDCFEHG I.J)GK?ML*A&NFG*O @ P QSR)TUWVYXZQ\[ V$]_^/`a]bXZRdc(VeQSU$f(gShiQ\[gjQ k [hml QSUenohmV8pq]_^sr]Kgt+Q\nuVeQSU\vr]Kgt+Q\nuVeQSU\vdw$xzyj{*| }b~ Y€‚ƒ*€S„&…$†j‡Sˆi‰oŠ†j‹+€‚‡‚Œ€‚‰\ˆM€eŽ  OA&BDCF‘’AM“” •8–a—™˜›šdœš(-TVYno]b[žr$Q\nWQTUegtž`6Q\[ VeQSU Ÿb  f+T\¡¢—žh¤£¤£.rhml QSU¥r] T_¦v§0T\¡VYt]_Ue[+Qbv+w$x¨y   ©_Ÿ } ‰ªM‡Y‹7…=Ž(‡Sˆiª«‚¬qˆ­†YŠ¬ ®/¯_°«±1²8³j´W± µ¶·u¸&¹jº»¹‚¼a½+·¾W¶¿Mº»·W¹¹‚¶«ÀiÁ(ÂW¸MÿDÄŸMÂoÆ-Çj·uÀM·aº»¿ÉÈÊÂoÆ ÆËÂo¹jÌ;κͶ«Á(¶Ç0·W¿D· Ï ÈÊÂo¹j¿­À­¸&·Wº»¹‚¶Ç\ÐÂWÑjÀMº»Æ ºÍÒ·uÀMºÍÂo¹DÑj¸MÂWÓSÌͶÆÔWÁ)Ղ¶«¸M¶· ÑS·u¸MÀMº»È«ÖjÌ»·u¸ ¿MÈÊÂW¸&º»¹‚¼Æ˶«À­¸&º»È º»¿.Öj¿­¶Ç¥ÄÅÂW¸É¶«Îu·WÌ»Öj·uÀMº»¹‚¼6ÀMՂ¶/×YÖj·WÌ»ºÍÀi¾ÂWÄd·aÈ«·W¹jÇjº»Çj·uÀ­¶/ÆËÂǂ¶ÌÙØaÚ(ÂoÆ ÆËÂo¹jÌ; Öj¿­¶Ç¿MÈÊÂW¸&º»¹‚¼Æ˶«À­¸&º»È«¿«Ô(¿MÖjÈ&ÕÛ·W¿ ½(ÜMÚdÝ8Þaß7µ*Ô Ñj¸M¶«ÄŶ«¸ ÆËÂǂ¶Ì»¿ÉÀMÕj·uÀDàSÀËÀMՂ¶ Çj·uÀM·ËÁ(¶Ì»Ì'·W¹jÇÕj·ÎW¶ÉÌÍÂ1ÁH¸M¶«Ñj¸M¶¿­¶¹eÀM·uÀMºÍÂo¹=ÈÊÂoÆËÑSÌͶÊႺÍÀi¾ Ï ºÙØ ¶WØ*ÀMՂ¶.¹YÖjÆ.Ó¶«¸ÂWÄ ÑS·u¸&·WÆ˶«À­¶«¸&¿Ð&Ø Üâ¹$ÀMÕjº»¿ ÑS·uѶ«¸Ô'Á(¶s·u¸M¼oւ¶ ÀMÕj·uÀ.·ÆËÂǂ¶Ì ¿­¶ÌͶÈÊÀMºÍÂo¹¥Èʸ&ºÍÀ­¶«¸&º»· ÆÉÖj¿­À ·WÌ»¿­Â=º»¹jÈ«Ì»Öjǂ¶É·W¹‚ÂWÀMՂ¶«¸.º»ÆËÑÂW¸MÀM·W¹eÀãÑj¸MÂWѶ«¸MÀi¾6ÂWÄ+½+·¾W¶¿Mº»·W¹ ¹‚¶«ÀiÁ(ÂW¸Mÿ«Ô ¹j·WÆ˶Ì;ÉÀMՂ¶ºÍ¸äÅåæçÊèMçÊå\éç7é&êuë)ì\í»çMîWäðïðñuÔÁ)Õjº»È&Õ˺»¿ ¶ÊáÑÂo¹‚¶¹eÀMº»·WÌjº»¹ïðèMç&çÊò äÙóWïÅô ÂWÄ ÀMՂ¶ËÖj¹jǂ¶«¸&Ì;º»¹‚¼ ¼W¸&·uÑSÕ'Ø.õ¶ ǂ¶ÆËÂo¹j¿­À­¸&·uÀ­¶ËÀMÕj·uÀ À­¸&·WÇjºÍÀMºÍÂo¹j·WÌ_Æ˶«À­¸&º»È«¿ Æ ·¾ ¹‚ÂWÀbÇjº»¿­ÀMº»¹‚¼oÖjº»¿MÕãÓ¶«ÀiÁ(¶«¶¹Ë¹‚¶«ÀiÁ(ÂW¸Mÿ_Á)ºÍÀMÕÉǂ¸&·W¿­ÀMº»È«·WÌ»Ì;7Çjº÷ö¶«¸M¶¹eÀ_À­¸M¶«¶«Á)º»Ç‚ÀMÕj¿«Ø Üâ¹DÑS·u¸MÀMº»È«ÖjÌ»·u¸ÔuÁ(¶d¿MՂÂ1Á›ÀMÕj·uÀ*ºÍÀ º»¿ ×YÖjºÍÀ­¶Ì»ºÍÃW¶Ì;À­ÂÕj·ÎW¶)¹‚¶«ÀiÁ(ÂW¸Mÿ*ÀMÕj·uÀ ¸M¶«Ñ‚ø ¸M¶¿­¶¹eÀ È«ÌÍÂo¿­¶dÇjº»¿­À­¸&ºÍÓSւÀMºÍÂo¹j¿ Ï º»¹ÉÀ­¶«¸&Æ ¿bÂWÄùµ'øiÇjºÍÎW¶«¸M¼W¶¹jÈʶ8зW¹jÇËÕj·ÎW¶d¿Mº»Æ º»Ì»·u¸ ¸M¶«Ñj¸M¶¿­¶¹eÀM·uÀMºÍÂo¹úÈÊÂoÆËÑSÌͶÊႺÍÀi¾WԂÓSւÀ(Äð·WºÍ¸&Ì;ËÇjº÷ö¶«¸M¶¹eÀ(À­¸M¶«¶«Á)º»Ç‚ÀMÕj¿«Øbõ¶·WÌ»¿­Â˺»¹ø ÎW¶¿­ÀMºÍ¼o·uÀ­¶)ÀMՂ¶d¸M¶Ì»·uÀMºÍÂo¹j¿MÕjºÍÑS¿_Ó¶«ÀiÁ(¶«¶¹ ÀMՂ¶dÀ­¸M¶«¶«Á)º»Ç‚ÀMÕË·W¹jÇËÂWÀMՂ¶«¸(¿­À­¸&ÖjÈÊÀMւ¸&·WÌ Ñj¸MÂWѶ«¸MÀMºÍ¶¿'ÂWĂ¼W¸&·uÑSÕj¿ÀMÕj·uÀ_¿Mւ¼W¼W¶¿­À_¶Êû/È«ºÍ¶¹eÀÑj¸MÂWÓS·uÓSº»Ì»º»¿­ÀMº»È_À­¶¿­ÀM¿ÄÅÂW¸b·)×YÖjº»ÈMà ¶¿­ÀMº»Æ ·uÀMºÍÂo¹ÂWÄ_ÀMՂ¶À­¸M¶«¶«Á)º»Ç‚ÀMÕÇjւ¸&º»¹‚¼DÌͶ·u¸&¹jº»¹‚¼‚Ø ù ¶«¾YÁ(ÂW¸&Çj¿«ü_ýãþuñeçÿäÙþuå åç«ïðòKêuè 1ÿÔYí»çMþuèåjäÅå WÔSç  é«ämçÊåSïSäÅåæçÊèMçÊå\éçÊÔïðèMç&çÊò äÙóWïÅôeØ 

  !"#%$&"#')(+*)"#-,.!+/!01/2433,6572*.48393:"<;=!.4>?@"#&"@//!A; BDCFE:GHB:IJGKI2L2B:M#B:I1ENB:O !.!.4' "#!P/2433,Q"#63:"<;=!.4>?-R4S";-%"#!.TU"-V!.34'XW #&"#!.3Y!0"#Z3U0D43V)V!./\[U%"<*]3' JK^B:I '2/3,9;-%"#Y"#_V!./\[U%"<* (+*`23a!0b4!2[U9&"#!.3dcYe_Q;=f'!.3S"##&"#f3g"#a O "##'%"#!.3/ !X'/14/V:"#!.3V4%"#48h"#&"-i&"7R"4"#3,Q"#j'&"N)3'f3k3,j"# M#Bvuq57wZxf]y,.#V2/j4!.((/S"#V !X'/Z"#&"]\[?W /!.%"#zV!.3'%"#!.3/j3'3'3V{!.3,|}4:"Y!0P#3'!.~$48(/ € ‚Aƒf„\…2†%†%†%…4ƒP‡Xˆ "#!Q4!A$X'jQV!.V:"74!X'TV:"SWp0D!.4‰4443+"N&"#!.3f!0Š"#Š‹4!.3+" 4!.((/%"<*Y'S"#4(TU"#!.3Œ9uDzx\cf n:JqM\ŽE:JqŽXM#B !0-]57wQz'4V:"#'`V:*XV/V ,.#uD',?x O '3!"#'’‘“€”uH• …N– x O ;-4Y"# 3!X'f3—•sV!.444!.3'˜uD(+* !.3\Wp"#!&W  z9uq‘ …\¥ xZ;-4‘¦h%"#h', O 3' ¥ j"#94:"a!0-//@ž7Ÿ §#:"#4c a‹4!.3+"P'S"#4(TU"#!.3¨3V!X''} ‡ (+*¨"#z3:"<;=!.4>¨P,.%$.3y(+*¨"#z4!X'TV:"!0 "#hž7Ÿ Z©@¡u ƒf„N…2†%†%†%…4ƒP‡ x€’ª œ¬«„ ¡u ƒPœ¢&£ u ƒPœ x4x\c5@*"# M#BS"#4TV:"#T49;=23"#93?Ta(Q!0 GKI±?Bc³²!.P\[/ O "#!4V%0K*¨"# ž7Ÿ ³0D!.@63!X' ƒ ;-%"#´)43+"#;=_3'fµ&¶4!.((/%"#Œ9u ƒ €—· ¢A¸ u ƒ x4x O ;-4 ¸ u ƒ x7hS"#VT/8@44,.33+"="#!Q"#_43+"#7!0 ƒ c@¹j%$.3Q3:"<;=!.4> S"#4TV:"#T4Q‘ O /:"-ºuq‘Qx='3!"#j"#64443+"N&"#!.3]V!./\[U%"<*!0›‘Pc 572*.483 3:"<;=!.4>?64QT4'Y0D!. lM#r.»No+»GK®¼Gn:JqGHEQGKI2L2B:M#B:I1ENB:O Hc c-0D!._3S;=43, 4!.((/S"#Va½?T4 O 4TVN¾ »\B:®¼GHBDLPŽAl±+oJqGKIX¿O !.6R3'3,z"#!.S"#4!.64!.(XW (/%"<* Œ9uKÀ ¢ Á €iÂXxj!0-3`T3>?3!A;-3¨4:"a!07$48(/hÃÅÄÆÇ,.%$.3 B:ÈAGq±?B:I1ENB Á €³Â O !.›R3'3,j"#!.S"SW/%*6$48(/744,.33+"ÉÊU€’4,9Ë[XÌ@Œ9uKÉ ¢ Á € ÂXx O V2//'¾"# ­o2¯.GK­)ŽX­Ío\lrAn:J?Y w_ŸÔW<4'‰Õ Ö&×Hc ž=!.!.3/%*|T4't3U0D43V`/,.!.4%"# O 4TVNØ "# Ù ŽXI1E:JqGHr&IÚJqM#BNB uD!.)Ù r&GKIm Û<ÜzÝßÞ:à7à7Þ:áâ:ãHãqäËà7åAæHç Þ:áç á-èdâ#é:ê4ãqçëâ\á=áËêßæDì1Þ:íHîï ç æHêSípâNæHäËíHêŠçëãæHð&âNæ1ípâ\á&ñAÞ:àòNâ\íHçëâ\óËï ê4ãð&â#ò:êâ ô áËç æHêÔãqêßæ1Þ\õ+òNâ\ï äËê4ãSö÷KáæHðËçëãå&â\åêSí4ø:ì1ê™å&â\íqæHçëÝßäËïëâ\íHï éõ¬ÞAÝßä&ãÞ:ááËêßæDì1Þ:íHîAãìŠç æHð-óËç á&â\íHé=òNâ\íHçëâ\óËï ê4ãSù êßú2æHêSá&ñAç áËû=æHðËêíHê4ãqäËï æpã1æHÞû:êSáËêSípâ\ï ô áËç æHêñAÞ:àâ\ç á&ãdçëããDæHípâ\ç û:ðæqõ¬Þ:íHìdâ\ípñ+ö µ

JqM#BNB x-/,.!.4%"# Õ  ·&×Ô3'YV/!.4/%* 4/8&"#']"#!9%" È&oM\Gqo+»®B:m4B:®¼GK­)GKIoJqGHr&I "#VN3½?T Õ  O  O × O 4)\[U!.33+"#8/›3Y"#)4kzuK"#P'34!.3/%"<*x!0@/84,.S"j'3XW '3V4V!.4''¨(+*"#/,.!.4%"# O ;-VN¨h½?T%$/3+"Q"#!z"#4k9!0/84,.S" V/½?TQuD3?T   x .3'TV' h3P"# ­9r&M4o®X¿M4o\l^ !0Š57

w Ac+@,.##:"# hV2//'"# GKI±ŽENB# . ! h  # "    Õ Ë  ×   ± Gq±JK^XO JqM#BN B Gq±JK^ O 3'`h0D!.49//%*Y':R3'¾ 0D!.//!A;-c¾¹j%$.3}yuD'4V:"#'y!.PT3'4V:"#'xa,.#y‘ O "# Gq±JK^ !0 ƒPœ /!.3, !.4'43 , Pb"#Q3?Ta(Z!0 ƒPœ  Z3,.?(!.4_4V'3, ƒPœ  3 ?c_ Gq±JK^rßL    / . !  3 ,    '    3  ! # "   '        # "   h  9 Ë U [   aT  i;   U ' # " ]     / . !  3 , ?c7 GKI±ŽENB#±  JK^Bj¿M4o\l^ O O , j!.(U"N3'(+*PV!.33V:"#3,h"#b4V'3,Q3,.?(!.4@!0d2VN ¿M4o\l^ !0Š‘Ú/!.3 ƒPœ O ,.!.3,90D4!.- € ¨"# ! -€  ca3'TV'{;-'U"#/!.3 ,  O '3!"# ' ! O  "#);-'U"#{!0@"#)3'TV',.#/!.3 ,  O ;-/Q"#P3'TV'{;-'U"#"  !jZ"# 3aT3'TV' ;-'U"#]/!.3,P3+*f!.4'43,c #Š2433,Z572*.483)3:"<;=!.4>?›0D4!.Ø'&"N_Ô4V3+"#/%*Q(V!.3aV:"#%$.42 !0›4424VN¾Õ $&×Hc7eØ"<*XV2/™4!+VN]-(4'Y!.3z':R33, u  xP4V!.43,9:"#4V 0D!.-:$/T&"#3,)"#h½?T/%"<*f!0P,.%$.3]S"#4TV:"#T4 O 3'¨uHµ.x424VNYS"##&"#,*f0D!. "##2$.443,Y"#4V!0bV23''&"#9!X'/hT43, 4!.9/!XV2/"##3S0D!.49&"#!.3 uDc ,cÚ''3, O '/:"#3, O !.94:$.443,¾3F',.Ax\cÚe /2433,`/,.!.4%"#s"#3 424VNZ0D!._!X'/Š"#&"Z!.U"#k"#Q4V!.43,9:"#4V

c %-/8&"#'Y4!+VN 92* /4! T44!.P4!.j>?3!A;-/',.(!.TU"6"#P'!.93yuDc ,c94,.3/™3'\W 3'3Vh(:"<;=3YVS"N3f$48(/Nx"#!PV!.3S"##3 "#6424VNdc ž=!.!.3/%*|T4'Ú3U0D!.49&"#!.3XWp"#!.4:"#V]4V!.43,y:"#4Vz4TVNÚ]' 5 &Sž !. (])   # O * e &Sž O ( (+#y3' !"#4 O 4!A$X')9"##'-! ,`(:"<;=3{"#)VVT#V:* 3' "# V!./\[U%"<*`!0j !X'/(+*¨3k3,z"# 4T !0b"#z3V!X'3,{/3,"# !0Ô"#h!X'/@uDHc c@%"#-4443+"N&"#!.3YV!./\[U%"<*x73'z"#h3V!X'3,/3,"#z!0 "#a'&"N,.%$.3Y"#)!X'/ O ;-VN{_24T4'{(+*]"#a3,+&"#%$.)/!.,&W/!X!X' 3'9"#?T74  .V:"#="#Z!X'/44!.c²!.49//%* O "# ­)GKIGK­)ŽX­§±?BNnAE:M\G lJqGHr&I ®B:IX¿JK^ /u (])   #™x Õ 0 ×b4V!.4z!0Z572*.483}3:"<;=!.42 > 1 €Íuq‘ …\¥ xfuK;-VN}P½?T%$/3+" "#! 572*.483{3U0D!.49&"#!.3zV4%"#4!.3 O !.j' 5 &Sžx O Z':R3'  (])   #@uq‘ …\¥ 4¢ 3 xb€ 5 687:9 ºuq‘Q' x ;F/!.,¡u 3”¢ ‘ …\¥ x O ;-4 3 a]4:")!

0 <Í!.(4S$&"#!.3 uK"##33, '&"N+x O 3' ºuq‘Qx=="#63?Ta(!0™3'3'3+"b#:"#43''z"#!)4V%0K* "#až7Ÿ Zc-hR4S"_"#4¦!0›"#=  (])   #`4V!.4Q-"#h'4V4U"#!.3]/3,"#]!0Ô"# !X'/ O ;-/b"#Z4V!.3'"#4 O "#Z3,+&"#%$._/!.,&W/!X!X')!0Š"#Z!X'/,.%$.3 '&"N O "#=3?Ta(™!0(%"#™3''Q"#!_'4V4(@"#@'&"Nb,.%$.3h"#=!X'/Hc?T >@?dðË* ê ABDC/EDFû:ípâ\åËðjÞ\Hõ G`íHê4ãqäËï æpãõ¬íHÞ:àFÝßÞ:áËáËê4Ý<æHç áËJ û ILK\àâ\íHíHé2ç áËMû KMNdâ\ï ïXæHðËê=å&â\íHêSáæpãÞ\õêSò:êSíHé áËÞAñAê™ç * á G ó2é-â\á-äËá&ñAç íHê4Ý<æHê4ñbÝßï Pç OäËê:øæHðËêSá_ñAíHÞ:åËåËç áËûæHðËê›ñAç íHê4Ý<æHç Þ:á&â\ï ç æDé7Þ\õ?Þ\æHðËêSí1ê4ñAû:ê4ãSRö QjÞ:ípâ\ï û:ípâ\åËð&ãXó&â:ãqçëÝSâ\ï ï éâ\ï ï ÞNìaæHÞÔíHêSåËíHê4ãqêSáæXæHðËêŠãqêßæÞ\õ.ñAêSåêSá&ñAêSá&Ýßç ê4ãUêSá&ÝßÞAñAê4ñó2é›æHðËêdÞ:íHç û:ç á&â\ï2ñAç íHê4Ý<æHê4ñ û:ípâ\åËð@ìŠç æHðËÞ:äAææHðËêŠä&ãqêdÞ\õê4ñAû:êŠñAç íHê4Ý<æHç Þ:á&â\ï ç æDé:Hö ILSÞ\æHçëÝßêdæHð&âNæêSò:êSíHéå&â\ç íÞ\õ.áËÞAñAê4ãå&â\íqæHçëÝßç å&âNæHç áËû ç á_æHðËêãHâ\à7U ê THVXWYçëãÝßÞ:áËáËê4Ý<æHê4ñbç á_æHðËêà7Þ:ípâ\ï.û:ípâ\åË-ð N<ö Y

(] )#z0q2$.!.4@!X'/›"#&"@4'V:"='&"N6(:"4"#ZuD2$.b,./!.,&W/!X!X'xŠ3'

2$.f/!A;=a4443+"N&"#!.3¾V!./\[U%"<*.c Ób!A;=:$. O %"aQ3'3'3+"P!0-!"# !.S"N3+"_4!.S"#Z!0"#)/243' !X'/ O 3YS"#VT/8 O %"#Z3U0D43V)V!.)W /\[U%"<*.c9²!.j\[/ O ;=92* /243{"<;=!z3:"<;=!.4>?Q"#&"6R"6"#P'&"N ½?T//%* ;=// O 3'y2$.z4/8Q4443+"N&"#!.3yV!./\[U%"<* O *.:"P"#a"#4:;-'U"#Úuq3' "#4:0D!.4 O "#P3U0D43VzV!./\[U%"<*xaP½?T%"# 'L ,143+"2c &<3¾"#P O ;= 4!A$X'PS*XU"#!"#V uK;-%"#{3V4243,f3:"<;=!.4>?h4kAxb"#!.4:"#V2/›3/%*X4j3' 4!._4V2/:$X'3VZ4T,.,.S"#3,a"#&"74TVN 4%"#T&"#!.3=4b0D4½?T3+"-3!.T,. "#!4,.T60D!.bT43,9"#h"#4:;-'U"#z"#S"j'T43,9/2433, c gQ'!.3S"##&"#h"#&" "<;=! 3:"<;=!.4>?h2$X3, '#S"#V2//%*z'L ,143+"j"#4:;-'U"#692*Y½?T%"#a!0K"#3{44\W 43+"=V/!.4-'S"#4(TU"#!.3buD3)"#4!0  #1W<'%$.4,.3VAx3'2$.b4/8Ô3?Ta( !0™#:"#4huq3' "#?T-4/8@' 5 &S ž  (])   #g4V!.4Nx\' c (z!.4!A$. O ;=6'4V4(h V!.3S"#4TV:"#!.3z!0™"<;=!/84,.Z3&"#T#/ŠV/844-!0›57wb-"#&"-2$.6"#4!.S"<*.c &<3j"#Š O ;=4,.T›"#&"/2433,/,.!.4%"#4!.T/'j3V!.4!.#&"#Ô"#4:;-'U"# 6S"j!0@"#Z!X'/Ô4/V:"#!.3 V4%"#48UcQž=/24/%* O "#S"#3,"#a"#4:;-'U"#{!0 YV23''&"#!X'/='T43, /2433,YaTS"P($.S*¨ V3+"2c¨ž=!.TU"#3,]"# \[V:"@"#4:;-'U"#9!0Š6,.%$.3,.#9>?3!A;-39"#!h(_w_ŸÔW<4' O /%"#!.T,.)"#4Z4 !./%*X3!.8/¬Wp"#)T4S"#Va0D!.)TP(!.T3'3,Y"#f"#4:;-'U"#tÕ  O  ×Hc¨Ób!A;7W :$. O ;=Q'!93!"b3']"#!V!.TU"#6"#6"#4:;-'U"#]\[V:"#/%* O 3!.-;=Q3'Y,.!X!X' 4!2[U9&"#!.3!0Ô%"2¤U%"4 T V-"#!P2$.Q)½?TVN>4!.((/S"#V-"#S"-"#&"b44S"# ;-:"#h"#P"#4:;-'U"# .49//›3!.T,. ]!.j$.S*/84,.zuDHc c0qj0D4!. (3, .49//13!.T,.  ?x\

c gj;73+"-"#6V!./\[U%"<*!0Ô4TVNz"#S"-"#!P(j3'3'3+"_!0  O '3'3,a!.3/%*P!.39"#Z½?T/%"<*P!0d"#744S"#!.3f3'9"#Z#:"#@½?T3+"#¬W 0K*X3! , .49//X3!.T,. c²TS"#4!.4 O 43V="#424VNP›T4T//%*Q(4'P!.3)/!XV2/ "##3S0D!.49&"#!.3!0Ô"#QS"#4TV:"#T4fuDc ,c''3, O '/:"#3, O !.-4:$.443,f43,./ ',.Ax O "#_"#4:;-'U"#f"#S"-V23f(Z3V43+"N/H c gj3%"#8&"#b3f3+$.S"#,+&"#!.3!0 "#b4/8&"#!.34(:"<;=3fS"#4TV:"#T#/4!.S"#@!0Š,.#=3'"#bV!./\[U%"<* !03U0D43V=3h"#=,.#c &<3aS"#VT/8 O ;==\[U/!.4@"#=4/8&"#!.34™(:"<;=3 "#73?Ta(›!0#:"#4›3'')"#!Z4V%0K*Q"#73:"<;=!.4>a3'a"#="#4:;-'U"#)!0 "#-3:"<;=!.4>c4b3+$.S"#,+&"#!.34T,.,.S"= V3+"@4!.((/S"#V@"#S"#0D!.4\W 'V:"#3,Z"#"#4:;-'U"#P0D4!.v!"#buD2S*+Wp"#!&W


} 2 ]Ç jj v› at ™ ]!

&<3 "#-4V:"#!.3

O ;=h!.TU"#/3Z!.T-4/3S*44T/%"#b4T,.,.S"#3,P"#&"-%"--½?T%"# V!.!.3"#!Y3V!.T3+"#Q"<;=!{572*.483¨3:"<;=!.4>g!X'/h"#&"a4443+"P4/8 Ö

KL−divergence vs. treewidth difference 100 pairs of dags on 8 nodes, 28 edges

5

KL distance vs. treewidth distance 10K dags on 6 nodes 4

4.5

3.5 4

3

treewidth distance

treewidth difference

3 3.5

2.5

2

2.5

2

1.5 1.5

1 1

0.5

0.5

0

0

2

4

6

8

10

12

0

14

KL−divergence KL(P,Q)

I%âMN

0

0.05

0.1

0.15

0.2 0.25 KL distance

0.3

0.35

0.4

0.45

I¬ó-N

²Ô,.T4  ©buq+x="#4:;-'U"#z'L,143V9u+WßË[UNx$.44T #1W<'%$.4,.3VuWßË[UNx@0D!.  ·.·¾4 !0a#3'!./%*F,.3#&"#'Ú572*.483’3:"<;=!.4>?¾u  3!X' O µ  ',.Nx\c uD(xÔ"#4:;-'U"#'L ,143VQu +WßË[UNx™$.44T=S*X:"#4 V  #1W<'%$.4,.3VQuWßË[UNx›!.3  .S"#4!.3,&W?Z;-%"#  3!X'_V!.3S"#4TV:"#' T43,9"#J "#VN3½?Tc 'S"#4(TU"#!.3Q3'`*.:"P2$.$.S*`'L,143+"a"#4:;-'U"#Ëc g4!A;Æ"#&"a"#4 4)93+* 3:"<;=!.4>?h"#&"63V!X'V/!.4P'S"#4(TU"#!.3PuD24T4'(+* "#  m ±GKÈB:MH¿?B:I1ENB x O (TU"z2$.`¾4/8&"#%$./%*|/84,.{'L ,143V3F"#{"#4:;-'U"#dc§   mS±GKÈB:MH¿?B:I1ENB (:"<;=3y"<;=!{4!.((/%"<*'S"#4(TU"#!.3  }3 ' ]a':R3'} bu … .x € PÕ /!.,  Ë× O ;-4Z"#j\[UV:"N&"#!.3 ="N>3 ;-%"#f44V:"-"# ! Š

c g … … ;-//@T4f"# .S*X:"#4V2/   #1W<'%$.4,.3Vf':R3'}  u .x) € bu . x  bu … x\c ²Ô,.T4  uq+x™4!A;-   #1W<'%$.4,.3V7$.44T"#4:;-'U"#P'L ,143V0D!.  ‡ ·.·Z4 !0_#3'!./%*`,.3#&"#'}572*.483}3:"<;=!.4>?9!.2 3 ڀ  3!X');-%"#   € µ ',.c gP!.(4S$.3! V!.44/8&"#!.3Y(:"<;=3g"#a"#4:;-'U"#'L ,143V !3' "#  #1W<'%$.4,.3V©zV/!.4 'S"#4(TU"#!.3¨92*¨2$.]½?T%"# 'L ,143+"P"#4:;-'U"# O 3' $XVj$.4#Uc ²TS"#!.4 O ;=P4!A$X';72*{!0=V!.3S"#4TV:"#3,]57wb6"#&"64443+"aV/!.4 "@SÞ\æHêæHð&âNæ@Þ:äËí@â\á&â\ï éAãqçëã›çëã@â:ãqé2à7åAæHÞ\æHçëÝ\øUçö ê:ö_ì1ê-â:ãHãqäËà7ê-ãq$ ä #-Ýßç êSáæHï éQïëâ\íHû:êñËâNæpâjãqêßæpãSøãqÞ æHð&âNæì1êÝSâ\ájÝßÞ:à7å&â\íHê™æHðËê@ñAçëãDæHíHç óËäAæHç Þ:á&ãŠíHêSåËíHê4ãqêSáæHê4ñbó2é_ÝßÞ:à7åêßæHç áËûà7ÞAñAêSïëãñAç íHê4Ý<æHï é:øËç á&ãDæHê4â:ñ Þ\õÝßÞ:à7å&â\íHç áËû@æHðËêÝßÞ:íHíHê4ãqåÞ:á&ñAç áËû7ñËâNæpâ=ï ç î:êSï ç ðËÞ2ÞAñËãdä&ãqê4ñ_ç áZà7ÞAñAêSï %KãqêSï ê4Ý<æHç Þ:áZÝßíHç æHêSíHçëâËö 

'S"#4(TU"#!.37;-!.4h"#4:;-'U"#_V23](6$.S*z'L,143+"2c-¹j%$.3Y3+.3%"#8/ a57w 1ƀÆuq‘ …\¥ x4443+"#3, j‹4!.3+"_4!.((/%"<*f'S"#4(TU"#!.3]Œ9uDzx O ;=Q;-//V!.3XW S"#4TV:"Qf0q/%*z!0757wbh(+* 4,.3%RV23+"#/%*Y!X'%0K*X3,f‘ O 3'g&"j"#P#)"# >3,9)49//1'S"N3Vj(:"<;=3YŒ9uDzx73' %"#4!ˋ4V:"#!.3guD3"#4!0ÔS*X)W :"#4V  #1W<'%$.4,.3VAxŠ!.3+"#!-"#4:"Ô!0'S"#4(TU"#!.3ŠV!.34S"#3+"™;-%"#Q-!X'%R' ‘PcÔ-93)'2Z4-›"#&"4!A$/uD!.''%"#!.3x!H0 ;=2> h',. O Hc c™"# ',.9V!.444!.3'3,g"# ! ;=2> `4!.((/S"#Vf'3'3V9;-//3!"VN3,. aTVNf"#j'S"#4(TU"#!.39(TU"-92*94,.3%RV23+"#/%*9VN3,.Z"#jT3'4/%*X3,),.#z‘Pc QS"#43,"#Y!03Y',.Q(:"<;=3 "#6$48(/ ƒPœ 3']%"#b43+"jà O '3!"#'   œ uqÃax O V23(_½?T3+"#%R' O 0D!.@\[/ O (+*"#_aTU"#T/3U0D!.49&"#!.3P(:"<;=3 "#j"<;=!P$48(/ O -4!.!.4'z3gÕ Y ×@uD4Õ Y ׊0D!.':"N/Nx\c

  GKÈB:I`o_o°+BNn:GqoII1B:J =r&M 1§€§uq‘ …\¥ x ENr&IJpoGKIGKIX¿zo I1r2±?B ƒPœ oI±fGKJKn_loM#B:IJ à oI¾B#±A¿?B à ƒPœ GnQn2oGq±fJ?b;-%"# S"#4!.3,PV!.4 uDV!.3+"N33,a!.S"7!0"#j4!.((/%"<*P947!0"#jV!.444!.3'3,)'S"#4(TU"#!.3Nx 3'z;=2>zS*X:"#4Vh'L ,143VcbZ//!A;-"#!9> "#Q'S"#4(TU"#!.3-V/!.4 3' O &""#@#"# O "#!_2$.7-/84,.'L ,143V@36"#@"#4:;-'U"#dcž=/24/%* O "# 4!.S"#b!0›"#Q3:"<;=!.4>z;=QS"NS"#b;-%"# O ':"#436"#Q/%"#!0›"#h0q/%* "#@3:"<;=!.4>42;-3c@²!.@\[/ O %01"#_'S"#4(TU"#!.3P!04Vb;=,.+"#juD':R3' 3Y"#4j!0=aTU"#T/›3U0D!.49&"#!.3¨Õ Y ×Kx_j,./%*]3!.3XWb/84,.V!.3+"#4(TU"#!.3"#!6"#-aT/%"#¬W<3U0D!.49&"#!.3h3V!X''(+*)"#b3:"SW ;=!.4>Ux O "#3"#_3:"<;=!.4>aTS"=2$.Z93+* ;=2> a',.="#&"=V239(_4!A$.' ;-%"#!.TU"/!.43,gaTVN³VVT#V:*.c &<3|!.TV!.3S"#4TV:"#!.3uD4 ²Ô,.T4  uD(x4x O ;= S"NS"#';-%"##3'!.v',.¤?"#;7@,.!X!X'P3!.T,."#!h,.%$.-3:"<;=!.4>?=;-%"#49//  #1W<'S"N3V O *.:"h/84,./%*]'L ,143+"h,.#{S"#4TV:"#T40 c /_0=V!.T44 O !.T63/%*X4 V23]!.3/%*f(hV!.34'4' b4/3S*3']4½?T43,)0DTS"#b\[U43+"#_!.3 /84,.Z,.#¤™;=(/:$.a"#&"6;-%"#{3V4243, ,.#4k O ;=P;-//Ô!0K"#3!.(XW 4S$. "# 3V4243,{,+¾3`"#f"#4:;-'U"#}!.3,{57wbP4443+"#3,g4/8 'S"#4(TU"#!.3c



    j hÇ - !]: j › !}2  jj 

- !  ]: &<3f"#4V:"#!.3

O ;=j0D!XVT!.3f"#64443+"N&"#!.3zV!./\[U%"<*9S"-!0™"#j!X'/ 4/V:"#!.3V4%"#48Uc gb'!.3S"##&"#b%"#@3(/%"<*h"#!hV2U"#T4b"#b3U0D43V_V!.)W /\[U%"<*g(+*¨V!.3S"#4TV:"#3,Y"<;=!{#:"#4V0q/h!0_572*.483¾3:"<;=!.4>?P"#&" 2$. uqS*XU"#!"#V2//%*x74/84443+"N&"#!.3YV!./\[U%"<*`uK"#Q3?Ta(Z!0ËW #:"#4Nx O (TU"b'#S"#V2//%*9'L ,143+"b3U0D43V6V!./\[U%"<*{uK"#4:;-'U"#x\c wb!"#VÔ"#&"™749//&4443+"N&"#!.3hV!./\[U%"<*_'!XŠ3!"/%*_749//&"#4:;-'U"#dc ž=!.34'@64/ O ;=//¬W<>?3!A;-3\[/!01"#  = ¿M\Gq±O ;-4-"#b'4V:"#!.3 !0_//@$.S"#V2/huD!.4k!.3+"N/Kx6',.Pa0D4!.s/:0K"a"#! 4,.+"]uK0D4!. "#!.¨"#!{(!"4"#!. 44V:"#%$./%*x\2 c &p0_"# 3!X'94f(3S* O "#z,.4'¨4½?T4/4)"#3yÖ H ËW #:"#4czÓb!A;=:$. O %"hh2S*"#!]4"#&"Q"#"#4:;-'U"#`!0%"#6!.#/,.# )  ’uD3!"#V)"#&"6"#P!.#/›,.#6/42'U*Y"#483,.T/8&"#'x\¤3VP"#3U0DßW 3VV!./\[U%"<*Yj\[U!.33+"#8/" 3 ÔcP,.4' ;7hT4'g3}Õ µË×"#! 4!A$.P"# 0D!.//!A;-3,a4!.!.4%"#!.3dc ¡

  %  ØÕ µË× r&MB:ÈB:M\°  Y  JK^B:M#B B4¯.Gn:Jj±+oA¿Ën ‘ § € ‘9u Šx oI± ‘jÊ€ ‘ Ê u Š x :n ŽEN^zJK^oJ ºuq‘Qx|ºuq‘ Ê x Ô^B:M#B#oËn  uq‘Qx€tµ Ô^XGK®B  qu ‘ Ê x€  & ¡

.X6e_3'¬[1c w !A;Ø;=),.%$.aV!.3S"#4TV:"#!.3 4!.4'Y(!A$.c &<3Y0qV:" O %"_;-//(a4T V3+"j"#! b 4S"#4V:"!.T44/%$."#!j(S"#%"#=',. O 3P!.S"N3+"™0q/%*6!0S"#4TV:"#T4"#&"!08W "#344-3P$4!.T'8,.3!.43'94'V:"#!.34!.(/c›²!.\[/ O !.3bV23 "#3>]!0=f(S"#%"#Q,.#6f'8,.3!.4_3:"<;=!.4>Y;-%"# !.3PV!.!.33+"64XW 443+"#3,z3'3'3+"aT3>?3!A;-3$48(/Z"#!z(P'8,.3!.4'|uDc ,c O '424h!. V!.TU"#0qT/%"#Nx3'z"#h!"#-V!.!.33+"_4443+"#3,"#h!.(4S$.' S*XXW "#!.)V2T4'}(+*¨"#!.4zT3>?3!A;-3y$48(/zuD4 O 0D!.P\[/ O "#   (+%7Wß Z 3:"<;=!.4>`0D!.P'V2/7'8,.3!.4zÕ   × O !.a"#]57w§0D!.)V!.TU"#P3:"<;=!.4>¨0qT/%" '8,.3!.46Õ  Ö×Kx\c

"!$#

%'& BD“)(O*,+-('A & B

g3'P"#!j\[U(%"›"<;=!60q/!01',.›;-%"#a"###:"#›V!./\[U%"<*© 3 B#oËn:° Wp0q/%/ * . Ê € ‚ . ‡ Ê ˆ ;-%"#49//U"#4:;-'U"# O 3'9 ^oM4± Wp0q/%*/. Ê Ê € ‚ . ‡ Ê Ê ˆ ;-%"#]/84,.6"#4:;-'U"# O ; 40.ԇ Ê 3'1.ԇ Ê Ê 4h"#h0q/4S"#4V:"#']"#!W<3!X' 

',.cY5=!"#g0q/Z;-//(93!.3XW<\[U/V%"fuDHc cz,.%$.3¨(+*`]4!.((/S"#V)V!.3XW S"#4TV:"#!.3x\ c &<30qV:" O (!"#0q/Ô;-//(b3S"N3V=!01"#b#b#:"#4k' V!.3S"#4TV:"#!.3 O ;-VN ;=6':R3h3\[X"2c #Š:" "#}u … ˅ XxpW ±G -Ž+nAB:M (¨'4V:"#'—(S"#%"#Y,.# 3 ;-%"#  J./:0K"  3!X' O 2VN}!0Z',.4  O 3'  .4,.+" {3!X' O 4TVNFP"# '4V:"#!.3y!0j// ',._-0D4!.¦4,.+"-"#!9/:0K"2c- Z:R3Q M4oI±?r&­ u … ˅ XxpW<'L ,1T4 O V!.3S"#4TV:"#' (+* V!.33V:"#3,:$.S* /:0K"-3!X'Z"#!9)#3'!./%*9VN!.43]4T(4:"Z!0 4,.+"-3!X'  Ac ž=!.34'4TVNF#3'!. 'L ,1T4 3 ;-%"#y#:"#4Yu Q€ ;tµ.´ …  € µ.´ … a€’´x\ c #Š:" .ԇ Ê (@"#74!.((/%"<*j4V7!0 3 O Hc c™"#=4V7!0//?(S"#%"# ,.#=V!.3S"#4TV:"#'z(!A$.c@ž=/24/%* O "#b"#4:;-'U"#f!0Š"#_!.#/k' 3 7&" !.S"Zµ.´ ;   c gQ/ ‡ 4! 2$.Qºu 3 x@€u ;yµ.´x4µ&¶ |µ.´c7Q3?Ta(b!0›,.#  < ¶ u  x ‡  <¶c²!.7´P€—/!.,  O ;=_2$. ¢ .ԇ Ê ¢ €u  ‡  \x O 3P"#b0q/%*a  <¶  ¶  º]€u H \x O 3' !@€uD/!., Š
  GKJK^6lM#r.»No+»GK®¼GKJq°)oJÔ®B#oËn:J ±G -Ž+nAB:M_^oËnhJqM#BNB Gq±JK^  ;  &

; 

™u ;

 

µ›/3  x  a o M4oI±?r&­ u …˅ Xx m

  !

¡

.X6e_3'¬[1c &<3S"#VT/8 O 0D!."  Š€  ;    O  €    O 3' a€—/!.,  O ;=b2$.* !    ;  ;-%"#g4!.((/%"<* &"Q/2S"  ;#  ™u ;  „$ 1/!., Šx\c g92$.9':R3'`"<;=!Y/84,. 0q/b!0=(S"#%"#a',.j4TVN"#&"j"#P,.#63{(!"# 0q/b2$.%u H \x #:"#4 O *.:"Z"#a,.#_3]!.3Q0q/%*f2$.Q"#4:;-'U"#&  uD/!., Šx;-/6"# ,.#3a"#!"#›0q/%*h2$."#4:;-'U"#'  u H   x\cwb!"#V="#&""#7"#4:;-'U"#  *) +,-) +,-. #&"#!3Y"#jV24P(  u   ) +,-. x O ;-VN{6S*XU"#!"#V2//%* /84,._"#3 "# „ $  #&"#/ ! u  x7!.(U"N3' 3zŸ4!.!.4%"#!.3  c â\á&ñAÞ:à˜ñAç 3.ä&ãqêSípã-â\íHêZê OäËç òNâ\ï êSáæ7æHÞaæHðËêjû:ípâ\åËðãDæHíHä&Ý<æHäËíHêjÞ\õ F B54768-9 :<;>=@?BADC EDC>=@?BA56EGF<9GEGH EDF F EMLN9 COEB28-9>;QPJR ST2U8ødÝßäËíHíHêSáæHï éÝßÞ:á&ãqçëñAêSíHê4ñPæHÞ)óêZæHðËêhãDæpâNæHê %8Þ\õ%æHðËê %Kâ\íqæÝßÞAñAê4ãìŠðËêSá ÝßÞ:à@óËç áËê4ñ=ìŠç æHð7æHðËê™â\åËåËíHÞ:åËíHçëâNæHê1åËíHÞ:ó&â\óËç ï çëãDæHçë݊ñAê4ÝßÞAñAêS* í R VU8Xö W›â\ï ïëâ\û:êSíÝßÞAñAê4ãæHípâ\á&ãDõ¬Þ:íHàâ›óËï ÞAÝpî Þ\õZY=ç áËåËäAæóËç æpãç áæH Þ [â:ñËñAç æHç Þ:á&â\ï+å&â\íHç æDé %KÝpðËê4ÝpîóËç æpãSøËê4â:Ýpð_å&â\íHç æDé %KÝpðËê4ÝpîóËç æ™çëãÝßÞ:à7åËäAæHê4ñbõ¬Þ:íâ ãqäËó&ãqêßæŠÞ\7õ \ípâ\á&ñAÞ:à7ï é-ãqêSï ê4Ý<æHê4ñ_ç áËåËäAæóËç æpãSö 021

EB28-9>;JIGK



"! E

& *ËB˓ & B

(O'G*G

A ' (”

eÚ3&"#T#/d½?TS"#!.3f"#&"b447"#&"!0™"#j\[V:"b4/8&"#!.3(:"<;=3]ºu¼x=3' !Au¼x\c &<3h"#™4V:"#!.3h;==\[3"#='S"#4(TU"#!.36! 0 W<3!X'@',.›VV!.4'3,-"#! "#3?Ta(=!0d#:"#4cž=/24/%* O "#_9Ë[UaT˜V!./\[U%"<*)"#&"=!01"# V/½?TauK;-3 //$48(/=4_S;-4_'3'3+"\x O 3;-VNfV24Zº]€tµ ‡ ;  c ²Ô,.T4bµ64!A;-=!A; !2u¼x›'S"#4(TU"#'9=j0DT3V:"#!.3!0dºu ¼x O Hc c›%"4!A;- //!.44(/QV!.a(3&"#!.3b!0ZuDº …  x-4Z!A$.j//™3!.3XW<4!.!.4V6',.Z!.3{ RU[U']3?Ta(-!0Ô3!X'c The relationship between the number of parameters and w* for n=7 7

6

w*

5

4

3

2

1

20

30

40

50

60 70 80 number of parameters

90

100

110

120

² ,.T4hµX©U%-/8&"#!.34f(:"<;=3 ºu¼x73' !Au¼x\c@h4!./' VTS$.hV!.444!.3' Ô "#!z"#9Th(!.T3'd¤›"#9V!.444!.3'3,]3+"#,.QTh(!.T3'`h4!A;-3¨a S"#XWp;-46'!"4"#'z/3Ax\c

g='4%$.=(!.T3'Ô!.3J! O ;-VNQ\[U/83h"#@(!.T3'3,_VTS$.›3a²Ô,.T4 Y ëc µXc

(z!.4!A$.

&"4"N3'dc

O ;=h4!A;t"#&"b(!"# "#6/!A;=_3' "#hT-(!.T3'](/!A;’92*f(

¡

 %   Î  r = B:Mh»\r&ŽXI±\Ò 

 r&MhoI°9±+oA¿ ‘ rßLQr&M4±?B:M  

uq‘Qx!³/!.,ºuq‘Qx ` ; /!., 

†

¡

. ²Ô¬[ ',]‘§!07!.4'Ôc#Š:"Qºy()"#4443+"N&"#!.3gV!./\[U%"<* !0‘Pc-5@* "#Q2$.#,.3,4,.T3+" O "#4QaTS"_\[US"j&"_/2S"b!.3h$.S"#\[];-%"# /!.,uDº  ŠxP43+"#¤Z"#4:0D!.4 O "#Y!.#/k'}‘ fgV/½?T]!0j4k &"/2S" /!.,uDº  Šx   O ;-VNz4!A$.-"#64!.!.4%"#!.3dc

gP4!A;v"#&"6"#9(!A$.(!.T3'Z"#,.+"60D!.j49//›º¾3{"#P434"#&"6"#4 \[US"b',.7"#&"bV!.64(%"##4/%*V/!.4Z"#!%"2c $



 

¡

 %   &r M=B#o?EN^6GKIJ


 





 JK^B:M#B‡ B4¯.Gn:JKn7o7¿M4o\l^ ‘  GKJK^ 7  x4x & u ‡5 68



;



ßx€

!Auq‘

¡

. ²Ô¬[ !  „ c #Š:"7‘ Ô("#bV!./:"#-(S"#%"#,.#P;-%"#P"#b49// V!.!.33+"›!04k /!., 4TVNa"#&"//+"#7',.47'4V:„ "#'Q0D4!.Ú"#749// V!.!.33+"™"#!b"#„ =/84,.c &p"Ô™2S*6„ "#!Z4@"#&"  uq‘ Sx€ /!., Ôc /Z3Q"#@!"# 3' O ºuq‘ ßx€ /!.,    „$ u  ; /!., Šx\chV/8Æ24/%*90D!.//!A;-c















wb!"#Va"#&"j"#P(!.T3'{j3!"j"#,.+"6T "#!zf/!., ¾''%"#%$.a"#4 jºu  ‡ xZ€ µ ‡ ;  O 3 '  u  ‡ xh€ ;  uK;-4  ‡ '3!"#aV/½?TP!.3 y3!X'Nx O ;-/ "#a(!.T3' ,.%$.!  !Au  ‡ , x   ;y/!., Ôc6aV/8¦0D!.//!A;--0D4!.¦"#)V!.3+$.\[U%"<* !0™"#6(!.T3'dc

 

¡

  %  Î l+lB:M=»\r&ŽXI±\Ò µu    4x x   †



¡

.

 r&M@oI°Z±+oA¿ ‘ rßL7r&M4±?B:M    uq‘QxK/!.,uDºuq‘Qx ;

/Z%"4"#'uD4Õ Y ×Kx\c

 ™2"!    2 ] &<3g"#h4V:"#!.3g;=443+")4!.9!.(4S$&"#!.3Q!.3g!A;"#!]½?TVN>?/%*(!.T3'g"# "#4:;-'U"#'T43,h/2433,c g_'!Q3!"7&"4"#U"@"#!a4!2[U9&"#"#b"#4:;-'U"# uD/:"]/!.3{V!.TU"#g%"z\[V:"#/%*x\¤a"#f;=!.T/'’(`3’!A$.4>?//63³"#z4:"4"#3,c gaV!.34'Z!.4h4/8Ë[U'Y"N4>z!0"#S"#3,9;-:"#Z"#Q"#4:;-'U"# *  .49// 3!.T,. cf"#S"#Q;-//(9//!A;='{"#!]4h;-%"#49//4!.((/%"<* O 4!A$X'' "#:* 4Q$.S*Y0qS"9uD4T(/32_3Y"#)3?Ta(Z!0@3!X'j3Y"#)3:"<;=!.4>Ux\cQ ;=!.T/' //!A;tT_"#!VN!X!.4a(:"<;=3/%"#43&"#%$.h3:"<;=!.4>?Z;-%"#!.TU"jV:"#T//%* 3XW VT443,h"#Z\[U346!0Š4T333,a,.!X!X' uD(TU"aTVNf!.4b\[U34%$.Ax74!2[U9ËW "#!.3 /,.!.4%"#@0D!.':"#433,a"#j"#4:;-'U"#dc #Š:" ‘”€ uH• … – x'3!"#{"#V!./3+"guK"#!}¾V!./:"#{,.#x!0)3 T3'4V:"#'z,.#]‘Ú€vuH• …N– x O Hc c – € – ;-4 `="#Z4:"-!0™//!.44(/_',.-!.3,Q"#Z3!X'73z•Pc #Š:"T-/4! T4"#93!"N&"#!. 3 !2uq‘ … ‘QxQ€ !Auq‘Qx  !Au ‘Qx\c]²Ô4S" O ;=4!A;‰"#&"Q0D!.Q3+* ,.#]‘ O %"#_‘v!.-%"#-V!./3+" ‘vaTS"_2$.h/84,.j"#4:;-'U"# O Hc c"#&" !Auq‘ … ‘hx7 ¥ u Šx O ;-4  ]€ ¢ • ¢ c

# &$

#

#

#

(

¡

 % 

# %$ #

'#

 r&MhoI°ŽXI±GKM#BNE:J
·

¡

.X6e_3'¬[1c @4!X!0U!0X"#4!.!.4%"#!.3uD4@e_3'¬[xŠ4T,.,.S"#"#&"Ô3+*Z"<;=!&W<4''Q44!. 4!.((/S"#V-/,.!.4%"#0D!.@"#S"#3,h;-:"#-h,.%$.3,.#f‘Ú="#4:;-'U"#f&" !.S"b4!.6RU[U'Y3+"#,._´ O R4S"Z4!2[U9&"#"#h'34%"<*z!0‘‰(+*z#3'!./%* 4/V:"#3,¾¨49//_4:"z!06$.S"#\[—4 3'³!.TU"#TU"4"#3,`"#Y0D#V:"#!.3F!0h"# "#&"94z'ˋ#V3+"3¾"# ,.#dc}5@*¨"#]ž=43-! ,—(!.T3' O {#/f!0_4k Z4 T V3+"6"#!f,.:"Z;-%"#3 3''%"#%$.Q44!.j!0  ;-%"# 4!.((/%"<*z&"j/2S" \[U™u ;Zµ  x\¤7"#?T4:"4"#3, €   TP(!.T3')"#„  4!.((/%"<*g!0_44!. (+ *      X c &p0"#9S"#9&"#h/4h"#3   ;  ! uqh0D!.//!A;-60D4!. "#   4!X!0Nx O ;=64<‹4V:"2c?T-;=692*44Tj"#&"b‘   u  x@',. O Hc c›"#&"b‘ 444c X3VQ!.S"_/2433,/,.!.4%"#-4Q3V43+"N/ O Hc cb(4' !.3]/!XV2/',. "##3S0D!.49&"#!.3 O ;=f!.3/%*3'¨"#!Y4!A$X'3V43+"N/@"#4:;-'U"#¨VNVN>?¤73 !"#@;=!.4' O ;=j!.3/%*3'"#!)9>_4T4Z"#&"74TVN /!XV2/!X'%RV2&"#!.3'!)3!" 43 .V:"™/84,.@3V424›3h"#@"#4:;-'U"#dcž=/24/%* O 3!_',.›4!.T/'a(7'''Q"#!j 3!X' O ;-VN/42'U*h›!.4@"#3  43+"#buD43V7!.#/k2&"#!.3j;-//?3'TV' hV/½?T_!04k_!.4-"#3    x\cwb!"#V-"#&"="#=',.4Z(!.T3'@3V4#S* O (TU"f3!" 4 T V3+"guD4V2//b"# ,.4'|\[/Ax\c &p"f3!"f4'|"#!¨4 "#&" ''3,43,./h'4V:"#'Y',.aV233!"Z3V424h"#Q"#4:;-'U"#Y!0›"#a44T/%"#3, !.#/,.# (+*Y!.4h"#3Y!.3 uD4)e_3'¬[x\c ²TS"#4!.4 O %"b"#T43j!.TU" "#&" ­9rAn:J !.3\W<',.a\[X"#34!.3j'!3!"j3V424h"#Q"#4:;-'U"#Y0D!._T3'4V:"#' ,.#c²Ô,.T4 Y uD(x›4!A;-@"#-S"N&"#S"#V0D!."#b2$.#,.b3V424b3)"#4:;-'U"# !A$.//?!.3\W<',.7\[X"#34!.3 O ;-4 WßË[UÔV!.444!.3'›"#!b"#="#4:;-'U"#a!0"# 2$.#,.)\[X"#34!.3 O 3 ' +WßË[Ub,.%$._"#a3?Ta(j!0T3'4V:"#' ,.#_;-!.4 2$.#,.6\[X"#34!.3]"#6V!.444!.3'3,)"#4:;-'U"#dc 



"!

- 2

a  ! ! j

  T7"#!j,./%" O ;=-,.%$.-Z4>:"#VN9!0"#-4,.T3+"2cÔ-93a!.(4S$&"#!.3) Z "#&"=0D!.@VS"N39$/T=!0Šº]"#4Z\[US"Q?T,.Z3?Ta(=!0',.@;-%"#9ºY#)W :"#4 O ;-/h"#4P4Q3!"Z"#&"j93+*]',._;-%"# 4 T V3+"#/%*]49//"#4:;-'U"#dc 4:0D!.4 O 3!"›//+',.;-%"#Qº9#:"#4™V23a2$.=49//."#4:;-'U"# uq/%"#!.T,. "#4=\[US"›4TVN)',.Nx\¤."#&"Ô O "#4=aTS"›\[US"›',.;-%"#Q"#=#@#:"# V!./\[U%"<*f3'z);-!./j4V:"#4T¦!0™"#4:;-'U"#c ²Ô4S" O ;=@\[3›!A;`ºu ¼xŠ'S"#4(TU"#'6V4!.4™//',.Š!.3h,.%$.363?Ta( !03!X'PuD4)²Ô,.T4 Y x\ c /ZT_T4!.4)4ab"#!\[U/83z"#a(2$X!._!0"#  

'S"#4(TU"#!.3¨3'¨"#!{,.%$. Y0D/3,Y0D!.Q"#zS*XU"#!"#V O #&"#)"#3¨"#!{,.%$. 4,.!.4!.T7S"#9&"#¤$.S* V4T'6(!.T3'b464 T V3+"b0D!.7"#h4,.T3+"2c 5

6

Distribution of m over all unlabelled dags of order 8

x 10

3000

5

2500

2000 number of extensions

number of dags

4

3

1500

2

1000

1

500

0

0

50

100

150 m

I%âMN

200

250

0

300

2

3

4 5 treewidth of one−edge extensions (n=8)

I¬ó-N V

6

7

V

²Ô,.T4 Y ©7uq+x7'S"#4(TU"#!.3h!0',.›VV!.4'3,_"#!Zºu¼x\c7uD(x™eb$.#,.73V424 3f"#4:;-'U"#z!A$.b//d!.3\W<',.6\[X"#34!.3c &p"b4!.33+""#&"b!.S"-',.b46V!.3V3+"##&"#']!.3]P49//13?Ta(b!0Ôº $/Tc-ž=!.34'_/8(/' W<3!X'h',‘PcghV23Y44!XV8&"#h‘v;-%"#YP/32 !.4'43,z!073!X'  …    … y  3z3&"#T#/›;72*|uD4!z"#&"6"#4963!]',.P0D4!. ],.ßW_"#! ]/!A;=ßW<3?Ta(4'`3!X'Ax\cŠ# :"  œ '3!"#9"#‡ 3XW<',.49!03!X' 4 ¤Š3!"#VQ"#&"Z0D!.j//  O  œ  ;  c g)2$.)ºuq‘Qxb€ œ¬«„ µ  c ³&"j$/T



! 0Zºt4z44'|(+*y93+*¨',. Ǟ=/24/%*`"#]aT/%"#/V%"<*!0jº—'3'!.3 "#a3?Ta(j!0@'L,143+"j‡ S"#%"#!.3b!0@º O Hc c6!.4'4' 4½?T3VQ!03XW<',.4 u  „\…2†2†2†…  ‡ x=#&"#S0K*X3,  œ¬«„ µ  €—º3'  œ  ;  0D!.-/H/ 4c6aT/%"#/V%"<* !0@º¨Z"#)4T !A$.h//™4TVNS"#%"#!.3Z!0"#)3?Ta(j!0=/8(/'Y',.Z;-%"# "#63XW<',.4P4½?T3Vc]ž=/24/%* O "#P3?Ta(h! ‡ 07!.„ 4' ‡ 4 'g/8(//„ ' ',.6;-%"#  ,.%$.3y4½?T3V¾u  „\…2†2†2†…  ‡ xa)(!.T3''}(+*  .  .      … ;-VNy    9Ë[Uk' a;-3  œ € Bœ „ 0D!.P// 4cÚuDP44T/%"#3¾',.);- %"# ‡  ‡  ',.cëx ‡ X!g;-&"f$/T!06 ºÚV!.444!.3'F"#!g"#VN!.VY! 0  œ   gY 2 $. ‡   º€ œ¬«„ µ .   Y µ 2c &<3'' O "#h$/TZ4!.T3' Y µ . V!.444!.3'Y"#! "#j44f2>93"#j'S"#4(TU"#!.39!0™º›c7/42'U*"#4TZ0D!.749//$/T !0 Ôc²!.7\[/ O 0D!.'  ]€  "#j2>4!.T3' Y µ . €—Ö  uD46²Ô,.T4 Y +x\c @?dðËçëãŠá2äËà@óêSíŠçëãâ\åËåËíHÞ#úAç àâNæHêSï é# ! $ "%  &  > ! T .-/021 3*4  Û('*),+ - 5





 



µ

 

e /4!)3!"#V_"#&"7"#464_"<;=!P4/%08W<4/8VTS$.-3 ²Ô,.T4 Y  O !.36(!A$. _ "#9!"# O V!.444!.3'3,z"#!]!X''`3'`:$.3`$/Th!0ºu¼xj44V:"#%$./%*.c  V23¨(f24/%*\[U/83'¨(+*`!.(4S$X3, "#&")º|!0_Y', a!X''¨\[V:"#/%*;-3 "#P', h3{!X''{3?Ta(6!0=4!.T4VuDHc ca$.S"#Vj;-%"#{3XW<',.4·+x\c #Š:"

™u  … ´x)( "#z4!.((/%"<*g"#&"#3'!. W<3!X'z',g´¾4!.T4Vc— ‡ „

¶  O /%"#!0 ™u  … ´x;=4Z':"#43'(+* #Š4>!A$.VÕ   ×Hc %-!.T,./%* O ‡ ¶ ¶  ¶  ;-4     † Ö   3 ' )uH´x=)'V4243,)0DT3V:"#!.3f3z´9;-%"#$/T3{u  … µ.x\c ž=/24/%*]"#P#&"#!f,.4!A;-6\[U!.33+"#8//%*];-%"#g´c g2$. )uHµ.x   †   O 3V "#a#&"#!!0"#)3?Ta(Z!0@',._;-%"#{943,./Q4!.T4Va"#!"#a3?Ta(j!0',. ;-%"#P"<;=!Q4!.T4V=    † UO ;-VN9\[U/83;-+*P"#4_4-!.4',.;-%"# !X'' 3?Ta(-!0Ô# : "#4c wb!"#V7_44a'V424!0"#73?Ta(Ô!0',.›&0K"#Ôº(V!.›/84,."#3 ‡µ „ cÔ'T"#!j"#0qV:""#&"@//U',.;-%"#&"/2S"=µ ‡ „ #:"#4aTS" 2$.f3!X')!0=3XW<',.4P&"6/2S"u  ;Fµ.xauD43V)"#4PV23{(&"j!.S"j"#4 3!X'™;-%"#a3XW<',.4Zu  ; Y x O 3'a:$.3P%0"#=!"#u  ; Y x™3!X'Ô0D!.4Ø_V/½?T O "#j3?Ta(!0™#:"#4V23 (j&"-!.S" Y Aµ ‡   ¾µ ‡   ;  €tµ ‡ „ ;  x\c &p" b3!"Z4']"#!4Q"#&"_"#a3?Ta(_!04TVN ',.__!0›"#a#Q!.4'Zb"# 3?Ta(›!0',.›!.3zu  ;  x™3!X'c ?"N3/:*fÕ  Ë×,+2$.-3PS*X‡ U"#!"#V@0D!.4aT/8-0D!. "#3?Ta(!0/8(/' W<3!X'7',. O *X/'3,_"##&"#! . 0D!.Ô"#3?Ta(  !0',._!.3 g3!X'b;-%"# &"_/2S"6µ ‡ „ #:"#4b"#!9"#h"#!"N/3?Ta(Z!0 W 3!X'9',.¤3V9"#949//(Tg"#!z"#94,.+"Q!07"#9932>{7‹4TS")3 \[U!.33+"#8//%*94V2/'XW<'!A;-3z$.44!.3z!0™"#2>90D!.hu  ;  xpW<3!X'j',.c

 











Æ 2 !›!

™#'%"#!.3/.!X'/¬W<4/V:"#!.36V4%"#48-T4'Q0D!.™/2433,_572*.483a3:"<;=!.4>?Ô0q2$.!. !X'/h"#&")R"a"#f'&"N{3'¨2$. /!A;i4443+"N&"#!.3¾V!./\[U%"<*FuDHc c{"# 3?Ta(Š!0U#:"#43''6"#!-4V%0K*Z"#3:"<;=!.4>Ux\c›Ób!A;=:$. O "#!.4V4%"#48 '!j3!"›"N>-3+"#!jVV!.T3+""#V!./\[U%"<*Q!03U0D43V3a"#744T/%"#3,j3:"<;=!.4> O ;-VN9\[U!.33+"#8/3P"#b3:"<;=!.4>  ="#4:;-'U"#dcÓb43 O ;=_'!.3S"##&"#-"# !.S"N3V6!0T43,"#Q"#4:;-'U"# Z9S"Z!0!X'/™4/V:"#!.3]V4%"#48U c g 4!A;F"#&"@"#_V24@;-3"<;=!a3:"<;=!.4>?72$.Z'#S"#V2//%*a'L ,143+"="#4:;-'U"# O 3'*.:"Q4443+")V/!.4P'S"#4(TU"#!.39uD3{"#46! 0  #1W<'%$.4,.3VAx63'g2$. 4/8@4443+"N&"#!.3]V!./\[U%"#6uq3' "#?Tb4/87' 5 &S ž  (])   #g4V!.4Nx O 4 4 T V3+"#/%*z0D4½?T3+"2 c g)/4!94T,.,.S"64!.Q V3+"j4!.((/S"#Vj"#S"#_0D!.Z ½?TVN>S"#9&"#!.3f!0™"#j"#4:;-'U"#z'T43,P/2433,c Y

  jj   Õ  ×hšcge_c š V3+"4!2[U9&"#!.3 0D!."#483,.T/8&"#!.3 !0³3aT "#4:;-'U"#dc)&<3 JK^@r&I2L2B:M#B:I1ENBPr&I I1ENB:M\JpoGKIJq°fGKIYÐ_M\JqG 7E:Gqo®\IJ




Õ µË×6eQc™5=:*X,./k63'&Nc %-4dc/Z3{"#!.S"N3V)!07T43, "#4:;-'U"#g Q!X'/¬W<4/V:"#!.3V4%"#4!.3P0D!.=/2433,h(2*.483f3:"<;=!.4>?c &<3 Ž»­)GKJqJ?f"#&" 46 V3+"-0D!.3U0D43Vc™VN3V2/Š4!.S" O &ß 5 ( jc Uc `&"#4!.3 %-424VN ž=3+"# O µ·.·  c Õ Ö×Q¹)c ²=cž=!X!.c)PV!.TU"N&"#!.3/ÔV!./\[U%"<*]!0=4!.((/S"#VQ3U0D43V T43,572*.483 (/:0™3:"<;=!.4>?c Ð_M\JqG 7E:Gqo® \IJ?c&<3 Ñ=M#rAE & ( B:I JK^@r&I2L & r&I I1ENB:M\JpoGKIJq°YGKI`Ð_M\JqG 7E:Gqo®\IJ


Õ  ×%6c ZVN+"#c5=TVN>:"b/3&"#!.3d©eÚT3%0K*X3,a0D#:;=!.4>P0D!.74!.((/S"#V 3U0D43Vc &<3 Ñ=M#rAE &( =B:® L\JK ^ @r&I2L & r&I I1ENB:M\JpoGKIJq°{GKI¨Ð_M\JqG 7E:Gqo ® \IJ


Õ  ×h5_cUc_²4:*—3't acUcëž_c*(]V62*.c§eÅ4:$.!./TU"#!.3d©|5=/:0Q4!.,+&"#!.3³3 ,.#™;-%"#aV:*XV/c Ðb±È&oI1ENBNn=GK I hB:ŽXM4o® \I2L2r&M\­oJqGHr&IaÑ=M#rAENBNnNn:GKIX¿ °An:J493dc_e"#TU"#!.48/!.3Y/2433,9572*.483 3:"<;=!.4>? O "#VN3V2/Ô4\W !.S"-4ßWp"#ßW $  Wß·  cÔ™VN3V2/Š4!.S" O (zV4!.4!0K

" %-424VN O  $ $  c

Õ  ·&×/c #c #T4%"#k3{3'g acUc X,.//%"#cJ#Š!XV2/›V!.TU"N&"#!.3Y;-%"# 4!.(ËW (/%"#=!.3z,.#V2/dS"#4TV:"#T4Z3'f"#b/V2&"#!.39"#!P\[US"_S*XS"#c r&ŽXM\Io®ÔrßL6JK^" B !-r&°.o® JpoJqGn:JqGHE#o® rAE:GHB:Jq° # B:M\GHBNn -O  ·uHµ.x\© 0 µ.µ&Ö O  $   c 

Ö

Õ   × ac™eQc #Š4>!A$.Vc]3?Ta(Q!09Ë[U9/›$.S"#Va!0-z#3'!.ÅV:*XV/V ',.#dc ( ^BNr&M\°aÑ=M#r.» & Ð=l+l®¼GHE & O µ·U© Ö+·  XÖ+· $ O  $:  c

Õ  µË×h acUcëž_c4(]V62*93'%6cP(cXwb2/HcŠwb2X33!.3/%"›S0D!.493V-!0d/!A; '34%"<* 4%"<*VNVN> V!X' c  ®BNE:JqM#r&IGHE  B:JqJ?c &<3 Ño?E:G 7E !-GK­ \IJ)5=4!X' O Ó_½?3 `3, O 3' X3= , (]UHc &<3+"#//,.3+"4!.(XW 3,©hfV!.S"SW< V3+"a4!+VN"#!f0qT/%"6'8,.3!.4j3{V!.TU"#63:"<;=!.4>?c

Ž»­)GKJqJ
 



Õ   ×J(c X+;= O 5_c ²=c(z''/:"#!.3 O  ac šcŠÓbVN>493 O (cŠÓb34!.3 O šcUcŠÓb!.S$X%"#k O Óhc #Š933 O 3'y¹)c ²=cž=!X!.c{Ÿ4!.((/S"#V'8,.3!.4QT43, Y4:0D!.ßW aT/8&"#!.3Y!0"# &<3+"#43S"SW    (+%>?3!A;-/',.P(4©)&Ncd)4!.((/S"#V !X'/3'g3U0D43V9/,.!.4%"#c ύB:JK^r2±ËnfrßL \I2L2r&M\­oJqGHr&I`GKIgύB#±GHE:GKI1B:O Y ·U©ëµ&Ö   µ   O  $ $  c

Õ  Ë ×%6c ?"N3/:*.ce_V:*XV/V=!.43+"N&"#!.3™!0,.#c GnAE:M#B:Jh3U0D43Vc r&ŽXM\Io®rßLÐ_M\JqG 7E:Gqo® \IJ
1 j  

¡

 %  ÚÕ Y O µË×/ r&M{B:ÈB:M\°   Y  JK^B:M#BgB4¯.Gn:J9±+oA¿Ën ‘~€ ‘9u Šx oI± ‘ Ê €—‘ Ê u Šx n:ŽEN^JK^oJ ºuq‘Qx}ºuq‘ Ê x Ô^B:M#B#oËn  uq‘Qx€’µ Ô^XGK®B  uq‘ Ê x€  & ¡

. #Š:"Z‘‰(6"#hV!./:"#6(S"#%"#j,.# ;-%"# "#J"#!.V!.!.33+" !0=4k9µ4TVN"#&"6"#P'4V:"#!.3 !07//›',.6j0D4!. "#jV!.!.33+"6"#!f"# .(!"4"#!.{V!.!.33+"!0j4k+  ;ÚµXc #Š:"‘jÊ7(z"#    —4V:"N3,.T/8 ,.4'dcu X3Va"#P4!.!.4%"#!.3YZ!07S*XU"#!"#Va3&"#T4 O ;=P,.3!.4Q"#P44T)!0 '%$X4(/%"<*.cëx #Š:"h"#'4V:"#!.3!0//›$.S"#V2/_uD44dcf!.4k!.3+"N/Kx_',.Q3g‘jÊ 0

(a0D4!. /:0K"Z"#! 4,.+"uD44dca0D4!. "#!. "#! (!"4"#!.x\caž=/24/%* O "#P!.#/Ô,.# !0_‘ a"#4:;-'U"#|µ¨uD3!"#"#&"a"#f!.#/=,.#¨)/42'U*"#483,.T/8&"#'x O ;-/h"#a"#4:;-'U"#{!0"#)!.#/k'Y‘jʊ   Ôc g)!.3/%*]3' "#!f4!A;˜"#&"

ºuq‘Qx ºuq‘jʬx\c &<3'' O ºuq‘Qxj€‰Öu  ;³µ.x —µuDÖ #:"#4j0D!.62VNg!0@"# u ";—µ.x63!X')3g"#(!"4"#!. /:$./ O 3'¨!.34!.h0D!.Q2VN¨"#!.XW
 

KG JK^QlM#r.»No+»GK®¼GKJq°PoJ®B#oËn:J ±G -Ž+nAB:M_^oËnhJqM#BNB Gq±JK^  ;  & 

™u ;

; 

 !

 

gµ›/3  x  P o M4oI±?r&­ u …˅ Xx m 

¡

. &p"Q62S*{"#!]4!A;‰"#&"6"#"#4:;-'U"#g'!Xh3!"Q\[UV'  ;  O Hc c !.3 /4P"#3¾"#z4k !0_"#zV/½?T !.3¾"#z43+" uDHc c O 4,.+"\xQV!.!.33+"2c 4:0D!.4 O %"_4 T V_"#!94!A;Ø"#&"_"#Q!.#/k2&"#!.3fV23Y3''Y3'TVQ4TVN V/½?T6;-%"#z"#h4½?T4'Y4!.((/%"<*. c #Š: " ³3 ' v'3!"#h"#h/:0K"Z3'z"# 4,.+"V!.!.33+"#44V:"#%$./%*. c ³&"@›"#-4!.((/%"<*h"#&"@6›!0143+"#

… 3!"-V!.33V:"#']3f"#6!.#/k'f,.# ¡ UÕ ]3' | 463!"-V!.33V:"#'× €  ¡ UÕ  }©  £ u Ux   £ u Ux<× € u  ;    x     ! † 



#Š:"Œ ("# \[UV:"#'}3?Ta()!0b4)3¦"#&"4f3!")3'TV'dc`3 PÕ Œj×b€  !      ! … 3'¾(+* (]4>!A$  3½?T/%"<* O "#f4!.((/%"<*{"#&"a"#4 4P3!z!. 4a"#3`´ PÕ Œj×4TVN`',.h6&"h/2S"  ;  .´c?T6;=P;73+"h"# /84,.S"j´z4TVNY"#&"6´ PÕ Œj×  O 4! ´   ™u   ;}µ›/3  x O 4!A$X3,"#a/9Uc 

!

(1

¡

 % 

r&MhoI°ŽXI±GKM#BNE:J
!Auq‘

#

… ‘hx !uHµ!;

 Y x &

¡

.  #Š:" ?uq‘Qx3'  € !Auq‘Qx)'3!"#]"#]3?Ta(9!0j',.3'}"# "#4:;-„ 'U"#]!0,.#Y‘˜€ÆuH• …N– x O 44V:"#%$./%*.c &p"Z-2S*z"#!4Q"#&" ?uq‘Qx  u    x\c &<3'' O V!.34'"#_!.4'43,h!0™•Ú3k3,_"#-"#4:;-'U"#dc   ; š›$.S*9 $.S"#\[f3f•7'ˋ#V3+"="#!)&"7!.S"  ,.=!.4'4'$.S"#V7\[UVU"0D!. "#/8S"  ‡ $. S"#V O ;-VN O „ 3g"#9;=!.4S")V24 O 0D!.4Å]V/½?Tc]?Ta;=2$. ?uq‘Qx  œ¬«„ !    ! €   ;  u    x O 4!A$X3,"#V/8zc g3'6"#!-4!A;g"#&"









#

‘Qx!uHµ ;  Y x *;  c›e_44T"#„ V!.3+"##S*¤?"#3Z4/8Ô4,.T3+"4!A;- "#&""?u ‘Qx u4uHµ ;  Y x !;  ;  x ; u4uHµ ;  Y x !;  xu4uHµ ;  Y x !;  ; „  x\cÔ O !A;=:$. O V!.3+"##'V:"# ?u ‘ax€ u );  x.µ; ?uq‘Qx! u );  x.µ;    u    x\c &<3'' O ;=4/%*Y3'{"#! $.4%0K*Y"#&"j"#j/!A;=6(!.T3'j,.42&"#j"#3 "# TZ(!.T3'{,.%$.3 (+*]"#)44TU"#!.3 !. 3 !2u ‘Qx O ;-VN{4'TVj"#!4!A;-3, "#&" µ  u    x   ŵ  u ; xP!./'0D!.9//b·     ; ËO ;-4  € u Y ;  x Ôc g)2$.  +; ;  ¤!"#S;-4a"#)4!.!.4%"#!.3]"#4%$X8//%* !./'c›4:0D!.4Z%"=4 T V="#!Q4!A;³"#&"6u  Y ;  x  ³µuH' µ ;  Y x  O ;-VN VS"N3/%*9"#4Tc !Au

# 

#











#







¡

 %   r&MoI°±+oA¿ ‘  o+±+±GKIX¿o]n:GKIX¿®Bf±GKM#BNE:J
E#oII1r&J

¡

. &<3'' O %0‘§6"#4:;-'U"# O "#3"#49aTS"Q\[US"a3!.4'43, !0$.S"#V)P€  „\…2†2†2†…  ‡ 4TVN "#&"_0D!._2VN" O "#Q;-'U"#Y!0  œ Z&"Z!.S"!Qc e_44T9"#&"a;=f''¾]'4V:"#'¨',.  œ   ]uDV/24/%*%"Q4!.T/'¨3!"aV42&"# Y'4V:"#'¨V:*XV/f3¨‘Qx\cf!.#/k2&"#!.3{!0-"#fT,.3+"#'¾,.#¨3'TV 9V/½?TQ!.3 £ u  x ‚  œHˆ  c gh;-//V!.3S"#4TV:"h3Y!.4'43,!0"#_!.#/,.# ;-%"#{;-'U"#g&"h!.S "     c &<3{0qV:" O ;=9!.3/%*Y3'g"#!z!A$.   œ "#! "#3'g!0 ?2 c (z!A$X3,{3!X'f'!A;-3+;74'}3¨"# !.4'43,{V23y!.3/%*g'V424]%"#a;-'U"#dc );-'U"#{!0  a3' "#a;-'U"#{!0@:$.S*{3!X'P3 £ u  :xb;-//Ô3V424)(+* !.3c ž=/24/%* O "#;-'U"#`!0-3+*g!"#6$.S"#\[`;-%"#g3'\[g49//j"#3 _ 3  O ;-// 3!"bVN3,.c7Q!.3/%*;=!.4S*z4j"#h3,.?(!.4b!0  œ ;-%"#z3'\[z,.42&"#-"#3 "#&"b2$.Q3!A;Ø4V!./8&"#'zT O 3'z"#?Tb;-//d(h/3&"#'f(:0D!.4  œ 'T43, "#h3U0D43Vc-Ób!A;=:$. O //1"#&"_V23]3Y3 "#6;=!.4S"ZV24 O "#&"_:$.S* 4TVN¾3!X'9;-//,.:")V!.33V:"#'¨"# !  œ O 3V4243,Y%"#h;-'U"#¨(+*g!.3c ?Ta"# ;-'U"# !0Ô:$.S*z3!X'jV23z3V4246(+*z&"-!.S"-!.3c



 









Inference complexity as a model-selection criterion for ...

I n Pacific Rim International. Conference on ArtificialIntelligence, pages 399 -4 1 0, 1 998 . [1 4] I rina R ish, M ark Brodie, Haiqin Wang, and ( heng M a. I ntelligent prob- ing: a cost-efficient approach to fault diagnosis in computer networks. S ubmitted to IBM S ystems J ournal, 200 1 . [1 5 ] J. R issanen. M odeling by shortest ...

557KB Sizes 1 Downloads 439 Views

Recommend Documents

Components of Self-Complexity as Buffers for ...
Sep 29, 2007 - superior predictive power over the use of the SC-D measure. ... 1979) is a standard self-report scale of depression used widely in a variety of ...

Components of Self-Complexity as Buffers for ...
Sep 29, 2007 - by eight advanced clinical psychology students on a 0–3 scale for their ..... and the subjective nature of this measure are far from ideal and call ... The measure of depressive symptoms was the Center for Epidemiological.

Logical Omniscience as a Computational Complexity ...
stant specification for JL ∈ {J, JD, JT, J4, JD4, LP}, then JLCS as an epistemic system with simple reflected fragment rJLCS passes LOT (with respect to a certain proof system). In the last two statements, we assume that CS(·) is com- putable in p

Repeatability of clades as a criterion of reliability: a case ... - CiteSeerX
1 Present address: 315 Manter Hall, School of Biological Sciences, ... have some degree of naturalness, so acceptance a priori .... Early Eocene between 45–55 million years ago (Benton,. 1993 ..... ML method due to computer time limitation.

A Criterion for Demonstrating Natural Selection in the ...
Aug 8, 2006 - mentioned above by Cooke et al. on the Lesser Snow Goose (Anser caerulescens caerulescens) of La Pérouse Bay, Canada. To determine whether these studies are indeed rigorous in demonstrating natural selection in wild populations, we wil

Repeatability of clades as a criterion of reliability: a case ... - CiteSeerX
sider not only optimal trees but also near-optimal trees. (Hillis, 1995 ...... Ph.D. Dissertation, College of. William and Mary ..... Academic Press, San Diego, CA, pp.

A regularity criterion for the angular velocity component ...
In the case of the planar flow the weak solution is known to be unique and ..... [9] Uchovskii M.R., Yudovich B.I.: Axially symmetric flows of an ideal and viscous.

Ambiguity-Reduction: a Satisficing Criterion for ... - Semantic Scholar
tise of decision making in a domain consists of applying a set of rules, called here epistemic actions, which aim mainly at strengthening a belief structure before ...

A Robust Stopping Criterion for Agglomerative ...
ters are homogeneous in terms of speaker identity before every merging, by ... a pair of heterogeneous clusters where there are a small num- ber of feature samples ... computes difference between H0 and HA in terms of average log-likelihood ...

Optimal Sensor Placement with a Statistical Criterion for ...
[6] Meo M and Zumpano G (2005), On the optimal sensor placement techniques for a bridge structure, Engineering. Structures 27(10), 1488-1497. [7] Marano GC, Monti G, Quaranta G (2011), Comparison of different optimum criteria for sensor placement in

Ambiguity-Reduction: a Satisficing Criterion for ... - Semantic Scholar
tise of decision making in a domain consists of applying a set of rules, called here epistemic actions, which aim mainly at strengthening a belief structure before ...

AN IRREDUCIBILITY CRITERION FOR GROUP ...
Abstract. We prove a criterion for the irreducibility of an integral group representation ρ over the fraction field of a noetherian domain R in terms of suitably ...

AN IRREDUCIBILITY CRITERION FOR GROUP ...
Let G be a group, let R be a noetherian integral domain with fraction field K and .... be the residue field of Rp and the canonical quotient map, respectively.

Computational Precision of Mental Inference as Critical ... - Cell Press
2.9 Model fitting, fit validation, and number of parameters . . . . . . . . . . . . . . . . . . . . . . 33 ...... k=l var (fk(θnt) − fl(θnt) + εk − εl) to equal 2σ2 inf , where each εk is an ...

Computational Precision of Mental Inference as Critical ... - Cell Press
In both (A) and (B) error bars indicate s.e.m., and the black curve indicates the theoretical ..... shown for each variability type for the combination of biases that best fitted the subjects' behavior. ...... SciPy: Open source scientific tools for

Computational Precision of Mental Inference as Critical ... - Cell Press
Dec 1, 2016 - This experimental framework revealed that in contrast to current views, the ...... Kaufman, M.T., and Churchland, A.K. (2013). Cognitive ...

Auditory time-interval perception as causal inference on ... - Frontiers
Nov 28, 2012 - fore, revealing the temporal perception system is fundamental to ... that the temporal accuracy of our auditory system is higher than those for ...

Computational Precision of Mental Inference as Critical ... - Cell Press
Dec 1, 2016 - ability beyond what can be explained by the provided evidence and are thus ...... study. Drawing few samples results in noisy posterior distribu-.

Is Cognitive Science Usefully Cast as Complexity ...
Most work in cognitive science has treated empirical data as though they do yield ... error, ending in the correct course of action after all (e.g., Spivey, 2007), we ...

Auditory time-interval perception as causal inference on ... - Frontiers
Nov 28, 2012 - fore, revealing the temporal perception system is fundamental to understanding the sensory processing system, but it is not fully understood yet.

Satellite based land use and landscape complexity indices as ...
model. We used a simple linear least square model for all species groups with the exception of the threatened species where we used a poisson model because ..... Randomization, bootstrap and Monte-Carlo. Methods in biology. Chapman & Hall, New York.

A Language and an Inference Engine for Twitter ...
Oct 15, 2016 - People use online social networks to share huge amount of information: maybe too much? ... Twitter Filtering Rules. October 15th, 2016. 5 / 15 ...