Transcript
Technical Report
UCAM-CL-TR-554 ISSN 1476-2986
Number 554
Computer Laboratory
Towards a field theory for networks Jon Crowcroft
January 2003
15 JJ Thomson Avenue Cambridge CB3 0FD United Kingdom phone +44 1223 763500 http://www.cl.cam.ac.uk/
c 2003 Jon Crowcroft
Technical reports published by the University of Cambridge Computer Laboratory are freely available via the Internet: http://www.cl.cam.ac.uk/TechReports/ Series editor: Markus Kuhn ISSN 1476-2986
!" # $&%&')(+*,%.-0/1*,%3254 6 798;:<>=@?A: BDCFEHGIAJKC5L;MONQPHRAETSUL;VWCYX1RZCFBDM[C5LQ\]M^LQCF_9\]RZ`aNcb@RZC5C5LQ\]M@GFRZ\YL EHM[C5LQ\YL;G5CYEHM^de.L;NQRAf1G5L0CYX^L BDM[C5LQ\]M^LQCb@f^CYGJgLQhNiIjM1GYC5\]RAEHM[CYGkIjM GYIjf^\]NiL;GQl_X1EHGPmL;RAV@GC5I+EHM1M1InZRZCYEmIjMolaBDCRAPHGYISpRZqAL;G CYX^LGYCYf1V^rIAJsBDM[C5LQ\]M^LQC!C5\]RZ`aNZt@h!X1RZChuLSpEmdjX[CvNQRAPCYX^LG5L;RZ\wN]XxJKIA\!CYX^Lzyw{@|~}Qw{};|
Z{At nALQ\YrpV1Em`NQf1PmCQl9CuCYX^LvG]RASULvCYEHSpLAt,C5\]RZ`aN!NiIjM,C5\]IjP9NiIjM^dAL;G5CYEHIjMNiIjM[C5\YIjPK RAM1VUL;M^djETM^LQLQ\]EHM^d RZ\YLke.IACYXX^IACC5IAbEHNQGQl X1RZC!EHJRAGYX+Ni\YI>hvV1GY0RlqlRlwm
]jA|TwtNQRAGYNQRAV^L;G;tLQbEHV^L;SpEHNQGvRAM1V+G5IIjMxRZ\]LCYX^L M^IA\]S WX@RZCaEmJvCYX1LFC5\YL;M1V¡NiIjM[CYEHMf^L;GUJgIA\aM^LQC~huIA\Yq¢PHEHM1q NQRZb@RANQEmC£rC5I eL;NiIjSpLF@RZC5C5LQ\;t hvEmCYXpSpIA\YLL;¤[f@RAP1NQRZb@RANQEmC£rpEHM¥CYX^LvRANQNiL;GYGuRAM1VUNiIA\YLAtIA\ LQnAL;MSUIA\YLNQRZb@RANQEHC~rpEHM¥CYX^L!RANQNiL;GYG CYX1RAM CYX1LaNiIA\YLcRAGEHM0CYX^LpL;RZ\wPmr¢¦;§A¨Z©AGhvEHCYX¡¦Q©jªe@b@Gk«¬GknALQ\]GYf@G®e1bGPHEHM^qGEHM¯CYX^L !°!±.!¬²³_!5´!IhµNiIjf1PHVFhuLNiIAb.L> _X@EHGkEHGR
[email protected]\RZe.Ijf^CCYX^Lf1GYLaIAJ¶1L;PHV L;¤[f1RZCYEHIjM1GgLAld^l+dA\]R;nEmCYRZCYEmIjM1RAP·t3L;PHL;NiC5\]EHNQRAP¸t SpRZdjM^LQCYEHNZt¹G5C5\YIjM^d0RAM1Vºh¹L;RZq RZC5IjSaEHN»RAM1VºGYIxJgIA\YCYXkRAGzRcJf^CYf^\YLSUIV1L;P³JgIA\zSaRAM1RZdjEHM^d M^LQC~huIA\Yq¢C5\]RZ`NZl¼¯LxeL;PTEmLQnAL»CYX1RZCEHM½CYX1LJgf1CYf^\YLAtuIjM^L+NiIjf1PHV¾SUInALxJK\YIjS CYX1EHGUSUIV^L;P C5I+R»nALQ\YrcdAL;M^LQ\]RAP&b1\]L;GYNi\]Emb1CYEHnALC5L;NwX1M1EH¤f^LUJgIA\kV^L;GYEmdjM1ETM^dM1LQC~huIA\YqcNiIjM[C5\YIjPsIjM V1E¿.LQ\YL;M,C CYEHSUL;GYNQRAPHL;GQtEHM1NQPHf1V@EHM^dcC5\]RZ`aNFL;M^djETM^LQLQ\]EHM^d RAM@V¢CYX^LxGYLQCpIAJRAV1SpEHGYG]EmIjM¢RAM1V¾NiIjM1dAL;G5CYEmIjM NiIjM,C5\]IjPPHRhvGQl&¯L!RAPTG5IG5b.L;NQf1PHRZC5L!RZeIjf1C CYX^Lvf1GYLIAJ.CYX^L!GYRASpLvEHV^L;RkETMUhvEm\YL;PHL;GYGsM^LQC~huIA\YqGQl À Á Â0ÃÄŠƢǢÈÃÉ>ÅxÂ Ê Ë.ÌÍwÌpÎÍÌ¥Ï5Ð!ÑÒ.ÑÓ+ÔgÕoÎ,ÏiÔgÕÖÍÌÎ×ÑÕoÎØ.ÙKÌpÎ××wÚ.ÓxÛÏiÔgÑÕ.×ÔgÕ¯ÓÚ.ÜQË ÑÝ ÏiË.Ì¥Ð!ÑÍÞ0ÎØ9ÑÚÏÜÑÕ.ÖÌ×]ÏiÔKÑÕ ÜÑÕ^ÏÍÑÙsÎ[Õ.Òº×wÜQË.ÌÒÚ.ÙgÔKÕ.ÖxÑ[ݹÏÍiÎ[ß+ÜpÔgÕ¯ÏiËÌaà5Õ^ÏÌÍÕÌ>ÏkÐkË.ÔgÜQË ÐÌpá1Ú.Ì>×wÏiÔKÑÕ ÔgÕ¯ÏiË.ÔK×ÛoÎÛÌÍ>â ãäjåæOç èéåêAä,ë¸ìµí¯îîZï¹ð¼ñ³êjë·òó ÊË.ÌôoÍ×]ÏÔg×sÏËoÎ[Ï ÏiÍÎ[ß+Ü!ÔK×¹Êõö¢ÎÕÒÏiË.Î[ÏÎ[Û.Û.ÙgÔKÜZÎ[ÏÔgÑÕ×sÚ.×iÎÖÌ Ý·ÑÍwÓx×ÎpÓ+ÔT÷ÑÝøwÓ+ÔgÜ>ÌùUÎ[Õ.ÒÌÙgÌ>Û.ËoÎÕ^Ï×úûÙgÌ>Û.ËoÎÕ^Ï×!Î[ÍÌÙKÑÕ.ÖUÙgÔTüÌ>Ò&ýÏiË1Ú.×ÍwÌ×ÌÎÍÜQË+ÓxÎÔgÕ.ÙTþ Ü>ÑÕ.ÜÌ>Õ^ÏiÍiÎ,ÏiÌ×UÑÕ½×wÏÌZÎÒþº×wÏiÎ[ÏiÌØ9Ì>ËoÎZüÔKÑÚ.ÍÑÝÊõö¹ú&ÿºÔgÜ>Ì»ÎÍwÌüÌÍwþº×ËÑÍwÏUÙKÔKüÌÒ&ýØ.ÚÏzÕ@Ú Ó+ÌÍwÑÚ.×ú¢ÊËÌ0Ø9Ì>ËoÎZü@ÔgÑÚ.ÍÑÝÎÙÎ[ÍÖÌxÜÑÙKÙgÌÜÏiÔKÑÕ¼Ñ[ÝkÓxÔKÜÌcÔK×ÓxÎÔgÕÙKþ½ÏiÎÞÌ>Õ Î[×Ý·ÑÙgÙKÑAÐkÔgÕ.Ö Ï5þ@Û.ÔKÜZÎÙsË1Ú.ÓxÎÕ ×Ì×w×ÔKÑÕÎ[ÍÍÔTü[ÎÙ3×]ÏQÎ[ÏÔg×wÏÔgÜÎÙ&ØÌËoÎZü@ÔgÑÚÍú ë 1ä,åä[ç ³ë£ç å 1 ê òä í¯îZîZï³ðWñ êjë·ò9ó ÊËÌ×wÌÜÑÕ.Ò¯Î×w×Ú.Ó+ÛÏiÔKÑÕ+Ôg×ÏiËoÎ,ÏvÏË.Ìà5Õ1ÏÌÍwÕ.Ì>ÏÔg×Ë.Ô Ì>ÍiÎÍwÜQË.ÔgÜÎÙÔgÕ¢ÏË.ÌF×Ì>Õ.×ÌFÏiË.Î[ÏaÎÜÜ>Ì×w×Õ.ÌÏ5ÐÑÍÞ1×Î[ÍÌ»üÌ>Íwþ¢ÓÚ.ÜQË¡×ÙgÑAÐ!ÌÍUÏiË.ÎÕ¢ÏiË.̾øwÜ>ÑÍÌ>ù ÑÍkÜ>ÑÍÌ>×ú à5Õ.Ò.ÌÌ>Ò&ý×wÑÓxÌ+ÍÌ>×ÌÎÍÜQËOÔK×Ò.ÔKÍÌ>Ü>ÏiÌ>ÒÎ[ϽøwÓxÎÞ1ÔgÕ.Ö ÔTÏ×wÑù.â kÌÜ>ÌÕ^ÏÐ!ÑÍwÞ¼ÑÕ¼à5Õ^ÏiÌÍwÕ.Ì>ÏFÿºÌZÎ ×Ú.ÍwÌÓ+ÌÕ^ÏÎÕ.Ò Û.ÍwÑjü@ÔK×ÔgÑÕ.ÔgÕ.ÖFË.Î×Ø9Ì>ÌÕ ÓxÑ[ÏiÔKü[Î[ÏÌÒ¯Ø^þ0ÐkËoÎ,ÏkÑÕ.ÌpÓxÔKÖË^ÏÜÎÙgÙ3ÏË.ÌU×ÌÎÍÜQË Ý·ÑÍÏiËÌ à5Õ^ÏiÌÍwÕ.Ì>ÏûÍÙgÎÕ.Ö ÓxÑ@Ò.Ì>ÙDú z×pÐkÔKÏ˾ÏË.Ì+ö Ê ý³ÔgÓ+Û.ÙgÔKÜÔTÏzÔKÕ¡ÏË.ÔgÕÞ@ÔKÕ.Ö Ôg×aÎ0ÏiÍÎ[ß+ÜxÓxÎ[ÏiÍwÔT÷ºÏiËoÎ,Ï ËoÎ×zÎcÛ.ÍÌÝ·ÌÍwÌÕ.Ü>̻ݷÑÍ×wË.ÑÍ]ÏUÙgÔTüÌÒ3ý3ÎÕÒ½ÙgÑ@ÜZÎÙKÔ >ÌÒ ÜZÎÙKÙg×ýÑAüÌ>Í¥ÙgÑÕÖÌÍ>ý3ÎÕÒ½ÙgÑÕÖ 5Ò.ÔK×wÏiÎÕ.ÜÌ !ÏiË.ÔK× ÜÑÚÙgÒ Ø9ÌUÍwÌ ÌÕÝ·ÑÍwÜÌ>ÒØ^þ¯Û.ÍwÔgÜÔKÕ.Ö.ý.Ü>ÍÌÎ[ÏiÔKÕ.ÖÎ+×wÌÙTÝ Ý·Ú.ÙTôoÙgÙKÔgÕ.ÖaÛ.ÍÑÛ.Ë.Ì×]þú
!#"$%'(*)+ -,. %/ 10# 324"5 " 6 798;:< >=?@" 6)A ! :5 B %CD E - FG%*"/!#HG%/I 9 !#J (C 30B #K%/IL(M /!#J8 !# / #J8 L #% :5/ #;8 #$ #%N 8O" :5 P-:Q%/ ' :9 /8R:4%''S "6 #/!9 8O" :5 T 8Q 8U2A)V )WL@ X " H )Y:5 B %V F[Z )V #IB\]P H"S@8 @ " ^&BS:98(,9 798 $ %/&H:9% _ 5,. P 1FG%a`VbB U&^O< PcedWfg,h "SU0/ #(S #;6" 8O"8U%i )V #I 30B j"/` kD 3)+ 10# (S" _!# l)j "/5" D 1 )+ I9% 0 %/V m;/5" enSV)+ #%i($)V R /8*"S*" Z "[ FoO8 \4)A/%%p!# 3)q/[:9h O8 D@Z8 # \4 l0B/ W% # D " T,/%' &r 4 % 3& 8U8' &F j "S^nS, s88 e )V # IH 30B ` tu 5,h % 10# 9"Ss )V -"/!#P)A%%8O"S!# [8 / 8%%'&-]" 5 )V #Iuu" 5 # 8 ,h v "SU0B #()A"8O"6 P:4 S%/%/&5 1 FG 8/!(S68O"%%/ !# R " s :9/ #A,. 30# w xQyoz-{}|}~GSUyNNS
1 3yNz#Np<J{?oololzg u8O"S!# rJ,. "u" ! # FA$ ( ; " P #8 P 798s j)A%%h,h 8 #:9 T,. "^FG U,%/ (;8 #:9:5 i` xQyoz-j~G56z$v4plN}lolz dWS8/ &^)A%/%} [% !# A,. Q:58O" i`D_88 R )V #IBR)A/%% "SU0 E" E,/%/ &K K #:9S H: '0# %/&? 30# '9 #8 `cj" E 1 )+ #I)A/%% ,. 8 #:5 sr 8%/ U;S8 P* 1m 8'0# %/&^@:5 "i()A" P% 8&H/j /:5%'&8 ` " [ "SX (D)V K,. %/ 0 -"S<H"/[ 8 S ?FG%/n% " $ ; #!#/S% :5/ 9T/Fj" H )V # IuQ/% 5,h 1 )+ :5 H?- #8 (VP " #%?,. H,%/ H/ :9:5 < %'(o?Q - h 8%%/&/8 U X8 #`-c E ]"/Q8S,/%' (o)+ [ J 1=B H" D #. <!4!# ( #+8U%/! #. & F}" R:9 8O":5*FG #V 798R8 #$ #% 30# :L&:5 T # e F:5!#' R"S^8 $%'&;30/%,% ` cj" Q FW "S. s,h 4; h # u)+U&K "Ss"/:9!"Ls,. `;cj" 1=B 8/ #P # % i" * #. #%a`ocj" * , L LM 81/ #P I 18O" M :5 :9%/ :9 $O #D ` cj" P%A 8/ #; :9: + " P e; !!# e #:9 RFG P 81 `
¡ C¢9£u¢9¤¥T¦
§H¢9¨U©EªC«¢5¬
tu ; #h 6K&B : F;Z%U)A \FG #@<758;:5S!# :5 $9 "S58 #:9%/ %/&X! %/ ^" 8 U 8 5,h "SU0/ #s FjS # 30# Q 10# %* 8% (,Q8 '8%%'&E/8 . # @ :5 B %h"e8 #%/^% U^ 9@&B :5D8O"/ 8 P"Aj,. "HFG /,% (S; 798/ $U` cj" s # T%U)Ae:9!"LW,h P8O" # ;FG #:®nS %/^ " &.wV¯` ` U3lS°3
. !# U0' (S #h #/ Th #%/ j/; % 8 :5!# /8DnS %` lzB±N~¯U
G. :9 T. #% (S^ F8 # s:9 #:5 $:;²M M³ ´lµ¶<· ` ¸D 8 R "Sj " %3)AA"SU0 s )V 5 1m 8 (p # T :5. # %a(B" P " jS%a` ¹ FB8 # (lnS %/} #. C/Peº»?S8 (l)A"%/ CP,/ &_!# "P o%S`ke 3)+ 10# ( )+ _,h % 10# _ "SV" R 10# #%// #[ F} " T 1 )+ #I/FG8 _)A/%%S [ 3)+ A4C8%/ S8 1j:!98US8' &6)A'"-8 Q H5% $¼ ´ º<½cj" )V r 4:5 s8 #8 )A/ " 0B/ #` b #:9 T%U)AA"SU0# % U&,h ; #, 0 ,h #j" P 8 LD 0 #% H F )V # ILw ¾
!"#"%$&('%*)+,*).- (/.0 1324657098;:<&(= >@? !098,2A/=;B8=C5DE8-F&G=.*)&G=H*03=*I<),5J)&G(K*)J&(=H8/.!098,2A/=8=L&(2M)#=/N=;O0 09P092Q&(2RB8=;=B$!098J3B09092<=8;-F&(#)L=8;- B=O)J&G2SB8;B=;J)B8;E&G= TFUWVYX[Z ! \B09=]_^`=;) '05ba8&(dc aB8a e:$FaB8===&G092f$Fa@8C 998;BR $SaB8=8;-F&( _92B8g^ GGI $9*)&G=_&(=C#- 8;&h N(75J& *)i*&GP,'a@2'&G2d0 2P0929=;*&G092092P0 2J0 j)B=;L&(B=B (=B k,l]m
nOoKp`qrgpsPtbuwv#xKyjqr]zD{|zD}A~p1yuw
xKu
90 /Q2B'3Pe) 2&G=03 2 9K*)&(=H^D 2'Q*)&G=,&(=J20 ,)#0''=;&G*/*&G092f$& ,&(=,*)E2098 &(2M)#62SB8;2BH0iI 09/57 2RJ*03'B8B =#*)E 98==&G092Q0 WLH&(2Ai8B &(092M^*)E&G2R*B8;B=] 2QN#P0F'BG('Q =B dA ? 5J)B8;
=;=
0 Wh 8;9K09NF;O 2'A&G=, =;=J0 ,c6IFa&(B ( I=; GB(&GB2R &(=%'&G=;098;&(2)
?"71@6*+A)BC/ D'8"7 * &418"EF!! 1!GH)I J+1J *)4KL -"'+MN 7 O5PD)Q!'! C7&4 F+1") "*8R0R"S)'&(/"'J'PT&(8*LUV=FW:"7X J"1)'Y')1ZB -0[N* 8"7"AP\'D('']^ -"-+M0 +1* )'\)"[&()- * *)'"!G_ >?"`8"5R)F0(a+1G )SN/'&('b*c0)*8ad0 e]+*"!*)If+1G ?9:>#gh 0)*8CC"8"D8"J00d0 -)*""8C/0 &(11 b**8NKi)Oj&FJ".+1/Ykmln^oLUp":8"5')F)1?9%J)* ) )J")+* ' :#)* ID'+* GP8q -'G8'"!#e+1G J":K;*"* $*r"8".8"J0Pe J""'"!e*^ 05D'"!Be/" sDP J"r$9; $"1' %!! *!G t(+5UA=u>? J" q v/61 *)u'O#+*&F'0' 96Q/0+MAwx'&(*)+5-8"&('))'7+*G x"84[)0/* 1=u"?J)* ) Vs/" 1)) `yz -'''"!"*))Iw{w /05PD|"}8H"AP~Vs/ *))[8"1)' r9; e)&(""1)):9 80/'` :!! 1)).1"*))*=Q1 PH)' '"+1 *)[8"1+* *)(0 * P\J" )IP= >?"B J"'-')p&4/"*&(*G18)O+*G E5 -'+M")4'"+1 *)e"848"*+1 5)e9;J"+1'} ")58Y9 +* '"!jj' ! J"&F* Q9 '8"D'8J0$d0 -)*2"8RJ")'"!j""7! '}6)&4' &47)+5u)* I+*48"@6* *G'ND'T/0 &(1* b*"!\>#gh1XDJ"`)+5(")IP)I1& * r -'8"1 O/* "!F "!"87)+*'#"F
(DA
A0u q* ?r -8"* /* ^'!
!2 O( GH!! 1!G=Cc)&(4 OPD)1u"4'8"*`J"01))' ) *%9i)Ir)IM I5,"8
Q+*G {kml5^ox= 7 -0#')"[&41+M0")&<9; -!! 1!G'_ O1'?')*8a9:8") 'J"!YHM @:/* S)J +*5]/* ("1M'T9; &9:c] g "M]^d0 [08T+M""!"!("['"+1 *)5]8"*+1 *)+*)M )* ?A*`+M0"!'"!S"[/ O1 #'5 -) /61 ?*"8`J")1 ?9; & [ f O ¡0¢ Ki+1E))'+Q'"* "+* 5)0&FJ"./"'+5#8"1+* *)5U?"Z [O0£ a £'¡0¢ Ki!1&(1 '+:"+* 5)]8*+* 5)U O+*J"'8\+M0!"'!)S1*`&4 Q!** 'PZ [ 0£ f £'¡¤ 9;
¥ l ¦
= >?"')[')Q)Jt(+**G`/ D'8"S+* * !*"+1§"8)&(F9; &¨9O)IM"'.PvK+*+* 8""!CT 0.QJ""8* )IM8"'"!(9%+*G }"* IP©k«ªoEUA= e [D -" #8"r) /"/"Pr") '5 J""+Mj9©*"84)PD)*&() w2 e+*8"")p PS)&( 1 PT)&4/"Q+*D8"'!49%"E5 ¬w .e */" *)*G)Q(/6 * eE5 8HS"#9p'!1" 7+5~8"1 -0-)0 9%+5/"+*.P\)-79;J""+1'\9%'8\"8T&4msC"8` I?PJ`!1e#S6*"1+M= >?" l®¯B°-° "8"1/61"8"*+*r\>#gh±')-""1 -"'!F O+5T/"'P4 -}= >?"'),)u&( /" &4)'!B)"+*O,&(D8"*)% ²³M²0³^Ai´x³^µ59i %)0 Z%"&( ''D)]"/) PJj 51 )C - *8C1K"8C+*J'8j:!1! /""'+e8"')IM+*:Cr -' *'1))1VUp"Q&(
1)J" +*SPJJ")k¶o=4·#1)/*+1*PR"(&4 S0* [/q * 'N&("' - **))8"AD'+*1)PJ +*)J"&(%*"* [9; [9; O 8"'"!T'`&rJ".w/}$ Q9; [ ")&('))'5+Mc"/}¸C{9PJ ¹
!#"%$'&()*+, -. /0123!43*50*0*6**7%* %869 /%1:*<;=2*=0>3?@BA CD?E%GF> 09H*0$%1:?$I0JF> #E67K$I$LM*0INPO%QRNPS%QT1#!K*0>U*0VW> ?;X0Y[Z]\:^? - 7%@K.:!*)8FK0
M$I_;Ja`b(cA CDd !3E4*B#%5;= /0$e6:0>=*!*B J>*0*.U*!fg;=Ehi"%$0Bj7 lk3&m!nR;=i1<;XoEp86q>*Kr$L s6:*0f*!*. ? 0t6:!0*4u6:0># s6:!3*( jv?*0w+3!Y!*00U>mI% x3+*0y3!*G*<B />3I x?*0X ay:6%>* !r6>m#0Ftz080*J v;J**{j%j| #EFA } )$IWvc&3 28_*]*{Fm*{$~+E: +*8_ i*0>8>0*_ 36m0>#: s6:!*_%! W*1%!r 7I3*AGRoT1337*9 2t;=Js;J*DE!3*)I*{9 v*00>>% %:>3y0RF
M*$;)EFd#%.3 k#!fVW>#%*.E!dlrW>y%RF 9$%1 /$ >3a1m>r,$>y%1m!oo, #*0*9 ]$%0(8A
[7
7 B_I
7;X*0@l*$ v$ 2 *J v 0 -*!o$I $I @%x H5Lo
<)
* 9$:!hk#!B60* <) 1;J@5*{E%! #*0?*=UhE1%**
#$IH4Y 0 0y%Y!* J 2hFm3$ /YE%*s"!E%*
/>3*1i*D;X*)B]CDC! -!3 N sQRNP¡%Q|N's¢QRN¤£Q|N¥¢sQA ¦
¨ /D© D)¨ VW>6%j *0@!§ K$I $I @%,;=>!KU27*) /s;J*]CD7C ) ) 2s;X_*+ />8aA } ) c( ª « ¦ @H F:U#@W* <) >!,%*+$>*0 *056%>*? /0$¬Y§
*0§ I*87 _0>3*?E9HxA9CD3 <) %*9>#"% #{?8&m@#H>*0!o,E00Fr s®M¯:°a±W² ´³-µ¶%·¸ k#!aA¹. 0U$º*#%7k!3*B %.$>@L M*07#%$%AHCD0 07J>rC )¨ ¦ @:*DI 3F:U#%@Y>) /7oa13W>*D;=I»¼½s¾7%*.3!r3 c&:+ B% VW>#%a ¿tÀ-ÁÃÂsÄW¿IÅÆ¿sÂtÇMÈ Ç/ÅÆ3ÂsÇMÀ2É q@:*0
M,08j|;J0W( =)+ !>33!U-%*0*@"%!3yEF1# >*D$ 3$I
#%$80*I!Ê%*LW%j
ËJË?ÌÎÍÊÍ 2%r
<)
#$I*A
Ï #F13Kh$º>3*!fg3Y>3$>*{>*0K§6:{>#3Ð-5*4#%h#%* >4*{{Fr
3BÑ#s;J*+Y% FK5 $I0*+>%F1Ah1x%!4$>3*07%*IU2 #UX $*>0?WU->!3yEF1 *;Xm*]DD% % <) A
}
Ò
ÓrÔ[
5Õ ÖI×gØÙI[Ú9EÔ[Û I[ÛÜ[Ý
Órg7Ú9Ô[H I[Û
#E6H 0*0 ![o!. /) />3>0R;=K%I$Y%#$WJU*!4oo8&:* v*{r 0Ã #!$§A Ï >3>07;X0KK*D>!3* Þ
!#"$%'&#")(*+" ,#-'.% "0/."0/./12 "3'45!'.76' 4-' .%5 8/9." :;/(,<#,1='> ?A@CBD7EF2GHFI*JIKMLNOHB2B P +QR.S/"2TU25WVX,<4!# Y.!=VZ'4[\5!'&<"]&%^_&5;`aXa/9S:2:a! :a4&%5!a&%4bcdVef6'!4 g7ae/hh4'h4,i/9Zh*dVe!4ji/PVXVe'&%#"_.! "kl,#.%5 #&%"Z5!'jS"!# (/ma!4gKa4/.S,1^6 4&l4 5! ,<6_h*HVZ 4!gA/.%"na%k4!i/9,#'.%, ?A@CBD7EF2GHFI*JIK3wxEGd D' fGzy^dV{$/"/h%uk!#" |v&/ma,#.Ra"%P/jVX,1a+-'4'&h+5!'`T _&%.,#5 /9a,<'.,#,<.v 4 ,#.-%> ?ABD7E OmG}0~FcD'BKGd*B mu,<6'!.\aW./9a&4Wa%X/hh47/5;Ag7dVJ5 &#"_VZX/P6'',<"\" .,#//9." !^c!46,#5!k/9;/5;[va
e u`u uC /.[vua),<#c-'4l",<5!&,#'.Ag /9."hK',<.7a 4l5 &4:69/9a&4`S" cZ_&%a&/j,<.v 4 ,<. aVZ ( 'P >e/.%[a]c'¡ u!#<¢'4X5 '44 5fa,<'.X'./`],#&%." 4a/.",<.-S9C^£W¤cgK/."n/ 5 '.76 4/9a,<'.VX,1a+^,#./]j/9R/9u¥2h4,<.7RQCX¦§d¨9VX,#5;+,<.v4"&5! "k,<"P/]C&,#.-¢ #"% /X/.o'4-'/.,#,#.-kh4,<.5 , © l ª'u«Cu+Xu ¬an" <#,<.-^£W¤®%4'&-h&% b+Q¯¥2,<Sh%#on" /."°,<¢±C]h,#4,#5P/9e²§/#,<"/9,#'.³%ge´%> ¤j/"%vgµ²k>c¶c,#4,#&Ag·_>¸HVX#f'gY´%> u&4gj¤C45 !",#.%-'kX¥2,#-'5!']n¹»º'¼%gA²§/.%5 '&%6 4!g £eQkg*¥2!h%a!_(* 4dº'º'¼%> ¾½m¬:t ,#-v "¿¤C4'h*'4,#'./8¶/,<4.!À/."¿¤C4,#5!,#.-Á4À^£W¤C³N¤C,#<,#hh*®Âl 5;#,<.Ag)´ £e4dVZ5 49RQ^£££WÃÅÄF!ÆvÇ7ÈWÉÊvÊ2ËvÌjÍ Î*ËvϵÍÑÐ%ËjÍÒÎÓÊ9Ô2Ð7Õ'ÈÐ%ÊHÖÎÏ9Ç*ËdÈWÍÒÈKÌ×}> ÙØ9¬a£e'.- ,#'.ÚQ^6'',<"/.5!Û/."À£e.v4'<³g²_>Ü´'/5 '(%'.Ag_Ý_Þcß à2á9âuÞãZßoßåä æ7æ'gQ&-'&: dº'¼'¼2g¥;/9.%'4"çg£eQkghhç>ÜØ% è9TÑØ7½9º%> éè¬ÃX &45! h4,#5 ,<.- /." a !6'#&2a,#. 5 '.%-' :a,#. 5 .v4' ³ Ã>ê´%> ,<((* . /." ¶e> ¤> u <<'> Q&%a¢/9,#5 / Ø7ë Ä:dº'ºº7×f> ì ÇÇ7ÈWÉÊvÊ9ívívíeÍÌmÇ%ÐÇÌ7Ï7Ð9îWÍËÐ9ÖÍÑÐËµÍ Î2ÓÊÚÆvÕ2ÐïÓÊ'ðñòvÏµÍ ì Ç7Ö*Ï ¾ëm¬QR"%S,<,<'.£e.v4'*'4e^£W¤ó,#.Salô=.7 4.%!a³%gÃ^,<5;/4"$n'4:a,#!4W/.%"ôÑ/.¤C4a/9Pg£W/`T (4,<"-'õ^.,<6 4,<=t'4[,#.o¤C4'-4 Ùö9¬a/[v,<.-q4 !"ót'4[z,#.ó^!=VZ'4[v!boQ÷/]fTU 4!,#5Q./12,#_9l¥vVX,<a5;°¥2!46,#5! ·l,#5 ,#h%#,#.% ³%g%¥ .[9 4^!^/K,#.$¥ô:ø£Â¥Sh*',#&Å'.o£e']_&.,<5P/9,#'.%eQR45;,< 5}T a&4 ^/."n¤C425!'#!g Ä ¦¸'.%"'.Agõ ø×}ghhA>è7ùHT:ë'ùg¥2!h%P> dº'º9è> ¾ùm¬an" 4.£e.v4'¥v2:a!S³¢ÃÚ·l'4:Ñg%Q"",#'.2TÒz!#f'gô:¥%úeÀ¨HT:½¨%fT:ë9èv½ùº%g*dº'¼'º Ù¼9¬aÂl.o¤cdVe!4:T=¦/PVxÃX #/9a,<'.,#hZ aô=.7a!4.f^c'h*'<'-³go,#5;/<,#¶/<'&%'!g¤cfa4' ¶/#'&2a g£e4,#:a'^¶/#&%a' g2Q^£û¥2ô:£Ât¹»º'º%gúe':a'.çg¸dº'º'º%> ¼
"!# #!%$'&()*+$-,. 0/1243(5 67,8).*9/.:5;+<',=<'6>/ ?2A@B#,/.C/D@EC65 F/ FGH
I >;JLKNM'O-PNQK-R-RNM'"HTSU/8)V W)= $'YX[ZlZ f/xo!$ye-#,/{zo >|iD<)= F!j}j~$-,5F]~ {~6 U<'fw@E #,,E! 0i
<l5F /._ G-/$'&J)Sy-NM~ N)=#,lf ilC5 <)= F$-u+$-"&,#!2!#il67,jSy-NMftX/# f f N¡J¢.£0£'¤N N¡J¥w¦f¦¥.§¨L§E¥ª©«m¬_£'¤§0«'f®£m¡¯'¡¦N°_±k¥[" -²s§
aSUOb=Zb$f5F/(&$-,d</.5W&*iD<'_<'G-#
`
I N)=#,)=1g+t@}t d5F5F\b@E 5F$-/$-r> !<'5B},=</=<'!)= F$-/d$'&)=>
$y\-<'5}"$f! )*\3O-'PX?Q'K-K'KN`JQ'O-O-8Q'O^NP>t ³
aS^'b ³
<)=!$'0),$-59 Fb!#$-iDiC !<)= F$-)*+$-,. 0/J/._<'$yr,. !#/27r,.$-rs$',.)= F$-_<'57&<' ,././(<
/.)=<'6 5F F)*\'tA1pd5F5F\'2_Z<'C>5 5 $f$2fh<2 Sy--Pj´'$-C>,_<'5 $&Eµr7,="ª)$wE
³
/.U<',.!]"$f! F#)*\^->t
I N)=,.#)]",8ef !#/bC>/ >G¸<~Y# G-N)¹@,.$-r7$-,.) $-_<5dgL<' ,
"_<',. GpouJ@E1
´'$-ºu+,.$y+!#,$'&q)2s@E F5 Frrsµ!/.5 T2_3ouZ»uu
³
2 Sy--P>t