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/Zcaron /zcaron % 0x10 /caron /dotlessi % (unusual TeX characters available in, e.g., Lucida Bright) /dotlessj /ff /ffi /ffl /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef % very contentious; it's so painful not having quoteleft and quoteright % at 96 and 145 that we move the things normally found there down to here. /grave /quotesingle % 0x20 (ASCII begins) /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash % 0x30 /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question % 0x40 /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O % 0x50 /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore % 0x60 /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o % 0x70 /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /.notdef % rubout; ASCII ends % 0x80 /Euro /.notdef /quotesinglbase /florin /quotedblbase /ellipsis /dagger /daggerdbl /circumflex /perthousand /Scaron /guilsinglleft /OE /.notdef /.notdef /.notdef % 0x90 /.notdef /.notdef /.notdef /quotedblleft /quotedblright /bullet /endash /emdash /tilde /trademark /scaron /guilsinglright /oe /.notdef /.notdef /Ydieresis % 0xA0 /.notdef % nobreakspace /exclamdown /cent /sterling /currency /yen /brokenbar /section /dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen % Y&Y (also at 45); Windows' softhyphen /registered /macron % 0xD0 /degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered /cedilla /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown % 0xC0 /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla /Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis % 0xD0 /Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply
/Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls % 0xE0 /agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla /egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis % 0xF0 /eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def %%EndProcSet %%BeginProcSet: bbad153f.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmsy10 cmsy5 cmsy6 cmsy7 cmsy8 cmsy9 % /TeXbbad153fEncoding [ /minus /periodcentered /multiply /asteriskmath /divide /diamondmath /plusminus /minusplus /circleplus /circleminus /circlemultiply /circledivide /circledot /circlecopyrt /openbullet /bullet /equivasymptotic /equivalence /reflexsubset /reflexsuperset /lessequal /greaterequal /precedesequal /followsequal /similar /approxequal /propersubset /propersuperset /lessmuch /greatermuch /precedes /follows /arrowleft /arrowright /arrowup /arrowdown /arrowboth /arrownortheast /arrowsoutheast /similarequal /arrowdblleft /arrowdblright /arrowdblup /arrowdbldown /arrowdblboth /arrownorthwest /arrowsouthwest /proportional /prime /infinity /element /owner /triangle /triangleinv /negationslash /mapsto /universal /existential /logicalnot /emptyset /Rfractur /Ifractur /latticetop /perpendicular /aleph /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /union /intersection /unionmulti /logicaland /logicalor /turnstileleft /turnstileright /floorleft /floorright /ceilingleft /ceilingright /braceleft /braceright /angbracketleft /angbracketright /bar /bardbl /arrowbothv /arrowdblbothv /backslash /wreathproduct /radical /coproduct /nabla /integral /unionsq /intersectionsq /subsetsqequal /supersetsqequal /section /dagger /daggerdbl /paragraph /club /diamond /heart /spade /arrowleft /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /minus /periodcentered /multiply /asteriskmath /divide /diamondmath /plusminus /minusplus /circleplus /circleminus /.notdef /.notdef /circlemultiply /circledivide /circledot /circlecopyrt /openbullet /bullet /equivasymptotic /equivalence /reflexsubset /reflexsuperset /lessequal /greaterequal /precedesequal /followsequal /similar /approxequal /propersubset /propersuperset /lessmuch /greatermuch /precedes /follows /arrowleft /spade /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
] def %%EndProcSet %%BeginProcSet: f7b6d320.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmb10 cmbx10 cmbx12 cmbx5 cmbx6 cmbx7 cmbx8 cmbx9 cmbxsl10 % cmdunh10 cmr10 cmr12 cmr17cmr6 cmr7 cmr8 cmr9 cmsl10 cmsl12 cmsl8 % cmsl9 cmss10cmss12 cmss17 cmss8 cmss9 cmssbx10 cmssdc10 cmssi10 % cmssi12 cmssi17 cmssi8cmssi9 cmssq8 cmssqi8 cmvtt10 % /TeXf7b6d320Encoding [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /suppress /exclam /quotedblright /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /exclamdown /equal /questiondown /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /quotedblleft /bracketright /circumflex /dotaccent /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /endash /emdash /hungarumlaut /tilde /dieresis /suppress /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /suppress /dieresis /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] def %%EndProcSet %%BeginProcSet: 09fbbfac.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmsltt10 cmtt10 cmtt12 cmtt8 cmtt9 /TeX09fbbfacEncoding [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega /arrowup /arrowdown /quotesingle /exclamdown /questiondown /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /visiblespace /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright
/asciitilde /dieresis /visiblespace /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef /Omega /arrowup /arrowdown /quotesingle /exclamdown /questiondown /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /visiblespace /dieresis /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] def %%EndProcSet %%BeginProcSet: aae443f0.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmmi10 cmmi12 cmmi5 cmmi6 cmmi7 cmmi8 cmmi9 cmmib10 % /TeXaae443f0Encoding [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega /alpha /beta /gamma /delta /epsilon1 /zeta /eta /theta /iota /kappa /lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon /phi /chi /psi /omega /epsilon /theta1 /pi1 /rho1 /sigma1 /phi1 /arrowlefttophalf /arrowleftbothalf /arrowrighttophalf /arrowrightbothalf /arrowhookleft /arrowhookright /triangleright /triangleleft /zerooldstyle /oneoldstyle /twooldstyle /threeoldstyle /fouroldstyle /fiveoldstyle /sixoldstyle /sevenoldstyle /eightoldstyle /nineoldstyle /period /comma /less /slash /greater /star /partialdiff /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /flat /natural /sharp /slurbelow /slurabove /lscript /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /dotlessi /dotlessj /weierstrass /vector /tie /psi /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef /Omega /alpha /beta /gamma /delta /epsilon1 /zeta /eta /theta /iota /kappa /lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon /phi /chi /psi /tie /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] def %%EndProcSet %%BeginProcSet: texnansi.enc % @psencodingfile{ % author = "Y&Y, Inc.",
% version = "1.1", % date = "1 December 1996", % filename = "texnansi.enc", % email = "[e-mail]", % address = "45 Walden Street // Concord, MA 01742, USA", % codetable = "ISO/ASCII", % checksum = "xx", % docstring = "Encoding for fonts in Adobe Type 1 format for use with TeX." % } % % The idea is to have all 228 characters normally included in Type 1 text % fonts (plus a few more) available for typesetting. This is effectively % the character set in Adobe Standard Encoding, ISO Latin 1, plus a few more. % % Character code assignments were made as follows: % % (1) The character layout largely matches `ASCII' in the 32 -- 126 range, % except for `circumflex' in 94 and `tilde' in 126, to match `TeX text' % (`asciicircumflex' and `asciitilde' appear in 158 and 142 instead). % % (2) The character layout matches `Windows ANSI' in almost all places, % except for `quoteright' in 39 and `quoteleft' in 96 to match ASCII % (`quotesingle' and `grave' appear in 129 and 18 instead). % % (3) The character layout matches `TeX typewriter' used by CM text fonts % in most places (except for discordant positions such as hungarumlaut % (instead of braceright), dotaccent (instead of underscore) etc. % % (4) Remaining characters are assigned arbitrarily to the `control character' % range (0 -- 31), avoiding 0, 9, 10 and 13 in case we meet dumb software % - similarly one should really avoid 127 and 128 if possible. % In addition, the 8 open slots in Windows ANSI between 128 and 159 are used. % % (5) Y&Y Lucida Bright includes some extra ligatures and such; ff, ffi, ffl, % and `dotlessj,' these are included 11 -- 15, and 17. % % (6) Hyphen appears both at 45 and 173 for compatibility with both ASCII % and Windows ANSI. % % (7) It doesn't really matter where ligatures appear (both real, such as ffi, % and pseudo such as ---) since these should not be accessed directly, only % via ligature information in the TFM file. % % SAMPLE USAGE (in `psfonts.map' file for DVIPS): % % lbr LucidaBright "TeXnANSIEncoding ReEncodeFont" <texnansi.enc <lbr.pfb % % This tells DVIPS that the font called `lbr' in TeX has PostScript % FontName `LucidaBright.' It also asks DVIPS to expand the file `lbr.pfb' % into PFA form, to include the attached `texnansi.enc' encoding vector, % and to then actually reencode the font based on that encoding vector. % % Revised 1996 June 1 by adding second position for `fl' to avoid Acrobat bug. % Revised 1996 June 1 by adding second position for `fraction' for same reason. % Revised 1997 Oct 1 by adding cwm (used in boundary char TFM code) % Revised 1998 Mar 1 by adding Unicode for Euro character % /TeXnANSIEncoding [ /.notdef % 0
/Euro % /Uni20AC 1 /.notdef % 2 /.notdef % 3 /fraction % 4 /dotaccent % 5 /hungarumlaut % 6 /ogonek % 7 /fl % 8 /.notdef % /fraction % 9 not used (see 4), backward compatability only /cwm % 10 not used, except boundary char internally maybe /ff % 11 /fi % 12 /.notdef % /fl % 13 not used (see 8), backward compatability only /ffi % 14 /ffl % 15 /dotlessi % 16 /dotlessj % 17 /grave % 18 /acute % 19 /caron % 20 /breve % 21 /macron % 22 /ring % 23 /cedilla % 24 /germandbls % 25 /ae % 26 /oe % 27 /oslash % 28 /AE % 29 /OE % 30 /Oslash % 31 /space % 32 % /suppress in TeX text /exclam % 33 /quotedbl % 34 % /quotedblright in TeX text /numbersign % 35 /dollar % 36 /percent % 37 /ampersand % 38 /quoteright % 39 % /quotesingle in ANSI /parenleft % 40 /parenright % 41 /asterisk % 42 /plus % 43 /comma % 44 /hyphen % 45 /period % 46 /slash % 47 /zero % 48 /one % 49 /two % 50 /three % 51 /four % 52 /five % 53 /six % 54 /seven % 55 /eight % 56 /nine % 57 /colon % 58 /semicolon % 59
/less % 60 /equal % 61 /greater % 62 /question % 63 /at % 64 /A % 65 /B % 66 /C % 67 /D % 68 /E % 69 /F % 70 /G % 71 /H % 72 /I % 73 /J % 74 /K % 75 /L % 76 /M % 77 /N % 78 /O % 79 /P % 80 /Q % 81 /R % 82 /S % 83 /T % 84 /U % 85 /V % 86 /W % 87 /X % 88 /Y % 89 /Z % 90 /bracketleft % /backslash % /bracketright % /circumflex % /underscore % /quoteleft % /a % 97 /b % 98 /c % 99 /d % 100 /e % 101 /f % 102 /g % 103 /h % 104 /i % 105 /j % 106 /k % 107 /l % 108 /m % 109 /n % 110 /o % 111 /p % 112 /q % 113 /r % 114 /s % 115 /t % 116 /u % 117 /v % 118
% /exclamdown in Tex text % /questiondown in TeX text
91 92 93 94 95 96
% /quotedblleft in TeX text % /asciicircum in ASCII % /dotaccent in TeX text % /grave accent in ANSI
/w % 119 /x % 120 /y % 121 /z % 122 /braceleft % /bar % 124 /braceright % /tilde % 126 /dieresis % 127 /Lslash % /quotesingle % /quotesinglbase % /florin % 131 /quotedblbase % /ellipsis % 133 /dagger % 134 /daggerdbl % /circumflex % /perthousand % /Scaron % 138 /guilsinglleft % /OE % 140 /Zcaron % 141 /asciicircum % /minus % 143 /lslash % 144 /quoteleft % /quoteright % /quotedblleft % /quotedblright % /bullet % 149 /endash % 150 /emdash % 151 /tilde % 152 /trademark % /scaron % 154 /guilsinglright % /oe % 156 /zcaron % 157 /asciitilde % /Ydieresis % /nbspace % 160 /exclamdown % /cent % 162 /sterling % 163 /currency % 164 /yen % 165 /brokenbar % /section % 167 /dieresis % 168 /copyright % /ordfeminine % /guillemotleft % /logicalnot % /sfthyphen % /registered % /macron % 175 /degree % 176 /plusminus %
123 % /endash in TeX text % /emdash in TeX test 125 % /hungarumlaut in TeX text % /asciitilde in ASCII not used (see 168), use higher up instead 128 this position is unfortunate, but now too late to fix 129 130 132 135 136 137 139 142 145 146 147 148
153 155 158 159 % /space (no break space) 161
166 169 170 171 172 173 % /hyphen (hanging hyphen) 174 177
/twosuperior % /threesuperior % /acute % 180 /mu % 181 /paragraph % /periodcentered % /cedilla % 184 /onesuperior % /ordmasculine % /guillemotright % /onequarter % /onehalf % 189 /threequarters % /questiondown % /Agrave % 192 /Aacute % 193 /Acircumflex % /Atilde % 195 /Adieresis % /Aring % 197 /AE % 198 /Ccedilla % 199 /Egrave % 200 /Eacute % 201 /Ecircumflex % /Edieresis % /Igrave % 204 /Iacute % 205 /Icircumflex % /Idieresis % /Eth % 208 /Ntilde % 209 /Ograve % 210 /Oacute % 211 /Ocircumflex % /Otilde % 213 /Odieresis % /multiply % 215 /Oslash % 216 /Ugrave % 217 /Uacute % 218 /Ucircumflex % /Udieresis % /Yacute % 221 /Thorn % 222 /germandbls % /agrave % 224 /aacute % 225 /acircumflex % /atilde % 227 /adieresis % /aring % 229 /ae % 230 /ccedilla % 231 /egrave % 232 /eacute % 233 /ecircumflex % /edieresis % /igrave % 236
178 179 182 183 185 186 187 188 190 191 194 196
202 203 206 207
212 214 % OE in T1
219 220 223 226 228
234 235
/iacute % 237 /icircumflex % /idieresis % /eth % 240 /ntilde % 241 /ograve % 242 /oacute % 243 /ocircumflex % /otilde % 245 /odieresis % /divide % 247 /oslash % 248 /ugrave % 249 /uacute % 250 /ucircumflex % /udieresis % /yacute % 253 /thorn % 254 /ydieresis % ] def
238 239
244 246 % oe in T1
251 252 255 % germandbls in T1
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readonly def /FontBBox{-61 -250 999 759}readonly def /UniqueID 5000803 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def
/isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec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
0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /parenleftbig put dup 1 /parenrightbig put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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/version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY9 %!PS-AdobeFont-1.1: CMSY9 1.0 %%CreationDate: 1991 Aug 15 07:22:27 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def
end readonly def /FontName /CMSY9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-30 -958 1146 777}readonly def /UniqueID 5000819 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A 27D1663E0B62F461F6E40A5D6676D0037D33F24E2FAC2B0009AD3C8350CDF8CC 65BCA87979C36D14CB552E9A985E48BE4E88ECA16DF418749AF04FDD2B0E1380 D281BB2476BB45FF30946B247DFD7F57305FA87E50CA338121C71CDFDF927A9C 77FF14CB4A1D6D80356FB1171ED38C37702350497B44E42CE31DB2F493807DAA 15B887C671199A54C4C1294BC520F5538C15556BC43C9F62342B121C6DCD6C5F 491DA47FF360201EE21C08A781ED0589A6DF91B99FE118B9B29E4F068672E52F 1A06C514D91C4C937D4E642503392B1CD1BE8C2F499A1AD3753691F4D1DAB520 BDD769BAB70656DCE98FE5F77BE3D8633BECC0F8296D447419F73D58A556A872 53D139658EF30FE8E30E472DF06CA631B6F08402039CADB5B46166CEC30C10D0 0910E22AAA5632CB8F7FCB77BCD3BF38A5DABE2AC0CCABA535B03F338EFAA3E1 46480A4F905AE2C3E9000CB2F8519BFB4E0957F06C42602C10C0AF760AD41857 22664E61710936247988451E405A231578D43D8582F0904DAC9CD895E1404B6E E70669B1718F693EB4C8C9C610102905DD794D1AD2033F5CC015C5BA25AFC225 F70E4D61A8006C96CD099554110EBFFD0EE307BE01E75B825E46ADBB3C4702FE A3BCC8E48B8DAD4119C5D70579ACB5CA6693F17FA2F46195042088A93515D600 7EF1023FDE89E22515 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTT8 %!PS-AdobeFont-1.1: CMTT8 1.0 %%CreationDate: 1991 Aug 20 16:46:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def
/FontName /CMTT8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-5 -232 545 699}readonly def /UniqueID 5000830 def currentdict end currentfile eexec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325 4127 a 325 4189 a SDict begin [ /Color [0 1 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (cite.SGG2) cvn H.B /ANN pdfmark end 325 4189 a Black 1 w FK(],)f(and)h(it)g(has)g(been)h(found)g(to)f(still)g (contain)i(a)d(lar)n(ge)i(connected)i(component)f(e)n(v)o(en)e(with)f (a)h(1)p FG(=)p FK(3)g(fraction)i(of)70 4302 y(random)d(node)g (deletions.)70 4449 y SDict begin H.S end 70 4449 a 70 4449 a SDict begin 13.6 H.A end 70 4449 a 70 4449 a SDict begin [ /View [/XYZ H.V] /Dest (subsection.2.3) cvn H.B /DEST pdfmark end 70 4449 a 118 x Fs(2.3)99 b(F)n(aults)24 b(on)h(netw)o(orks)70 4632 y SDict begin H.S end 70 4632 a 70 4632 a SDict begin 13.6 H.A end 70 4632 a 70 4632 a SDict begin [ /View [/XYZ H.V] /Dest (subsubsection.2.3.1) cvn H.B /DEST pdfmark end 70 4632 a 114 x FI(2.3.1)91 b(Random)22 b(faults)70 4925 y FK(There)k(is)f(a)h (lar)n(ge)h(body)g(of)f(w)o(ork)g(on)g(node)h(and)f(edge)h(f)o(aults)g (that)g(occur)g(independently)j(at)c(random)h(in)e(a)h(general)70 5038 y(netw)o(ork.)36 b(H)5 b(\011)-35 b(astad,)26 b(Leighton,)i(and)e (Ne)n(wman)f([)p 0 0 .8 TeXcolorrgb 1638 5039 a SDict begin H.S end 1638 5039 a 0 0 .8 TeXcolorrgb -1 x FK(15)p 0 0 .8 TeXcolorrgb 1728 4976 a SDict begin H.R end 1728 4976 a 1728 5038 a SDict begin [ /Color [0 1 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (cite.HLN) cvn H.B /ANN pdfmark end 1728 5038 a Black 1 w FK(])g(address)j(the)d(problem)i(of)f(routing)h(when)f(there)h(are) f(node)g(and)70 5151 y(edge)g(f)o(aults)h(on)e(the)h(hypercube)i(which) d(occur)i(independently)j(at)25 b(random)h(with)f(some)h(probability)36 b FF(p)21 b FG(<)g FK(1.)34 b(The)o(y)p Black .8 .3 .3 TeXcolorrgb 1021 5401 a SDict begin H.S end 1021 5401 a .8 .3 .3 TeXcolorrgb 1023 5400 a Fv(T)t FC(H)t(E)t(O)t(RY)24 b(O)t(F)h Fv(C)t FC(O)t(M)t(P)t(U)t(T)t(I)t(N)t(G)p .8 .3 .3 TeXcolorrgb 1897 5344 a SDict begin H.R end 1897 5344 a 1897 5400 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype /URI /URI (http://dx.doi.org/10.4086/toc) >> /Subtype /Link H.B /ANN pdfmark end 1897 5400 a Black Fv(,)c(V)-11 b(olume)20 b(3)g(\(2007\),)e(pp.)25 b(1\22623)949 b(4)p Black eop end %%Page: 5 5 TeXDict begin 5 4 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop
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/M{setmiterlimit}bdf /n{newpath}bdf /N{newpath}bdf /q{gsave}bdf /Q{grestore}bdf /w{setlinewidth}bdf /Xic{matrix invertmatrix concat}bdf /Xq{matrix currentmatrix mark}bdf /XQ{cleartomark setmatrix}bdf /sepdef{ dup where not { AltsysSepDict } i if 3 1 roll exch put }bdf /st{settransfer}bdf /colorimage defed /_rci xdf /cntr 0 def /readbinarystring{ /cntr 0 def 2 copy readstring { { dup (\034) search { length exch pop exch dup length 0 ne { dup dup 0 get 32 sub 0 exch put /cntr cntr 1 add def } { pop 1 string dup 0 6 index read pop 32 sub put }ifelse 3 copy putinterval pop 1 add 1 index length 1 sub 1 index sub dup 0 le {pop pop exit}if getinterval } { pop exit } ifelse } loop }if cntr 0 gt { pop 2 copy dup length cntr sub cntr getinterval readbinarystring } if pop exch pop } bdf
/ /_NXLevel2 defed { _ _NXLevel2 not { /colorimage where { userdict eq { / /_rci false def } if } if } if } if / /md defed{ m md type /dicttype eq { / /colorimage where { m md eq { / /_rci false def }if }if /settransfer where { md eq { /st systemdict /settransfer get def }if }if }if }if /setstrokeadjust defed { true setstrokeadjust /C{curveto}bdf /L{lineto}bdf /m{moveto}bdf } { /dr{transform .25 sub round .25 add exch .25 sub round .25 add exch itransform}bdf /C{dr curveto}bdf /L{dr lineto}bdf /m{dr moveto}bdf / /setstrokeadjust{pop}bdf }ifelse / /privrectpath { 4 -2 roll m d dtransform round exch round exch idtransform 2 copy 0 lt exch 0 lt xor {dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto} {exch dup 0 rlineto exch 0 exch rlineto neg 0 rlineto} ifelse closepath }bdf /rectclip{newpath privrectpath clip newpath}def /rectfill{gsave newpath privrectpath fill grestore}def /rectstroke{gsave newpath privrectpath stroke grestore}def /_fonthacksave false def /currentpacking defed { /_bfh {/_fonthacksave currentpacking def false setpacking} bdf /_efh {_fonthacksave setpacking} bdf } { /_bfh {} bdf /_efh {} bdf
}ifelse /packedarray{array astore readonly}ndf / /` { f false setoverprint /-save0- save def 5 index concat pop storerect left bottom width height rectclip pop /MMdict_count countdictstack def /MMop_count count 1 sub def userdict begin /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath } bdf /currentpacking defed{true setpacking}if /min{2 copy gt{exch}if pop}bdf /max{2 copy lt{exch}if pop}bdf /xformfont { currentfont exch makefont setfont } bdf /fhnumcolors 1 statusdict begin /processcolors defed { pop processcolors } { /deviceinfo defed { deviceinfo /Colors known { pop deviceinfo /Colors get } if } if } ifelse end def % pix = x^2 + y^2 /printerRes gsave matrix defaultmatrix setmatrix 72 72 dtransform abs exch abs max grestore def /graycalcs [ { {Angle Frequency} { {GrayAngle GrayFrequency} {0 Width Height matrix defaultmatrix idtransform d dup mul exch dup mul add sqrt 72 exch div} {0 GrayWidth GrayHeight matrix defaultmatrix idtransform d dup mul exch dup mul add sqrt 72 exch div} ] def /calcgraysteps { forcemaxsteps { maxsteps }
{ /currenthalftone defed {currenthalftone /dicttype eq}{false}ifelse { currenthalftone begin HalftoneType 4 le {graycalcs HalftoneType 1 sub get exec} { HalftoneType 5 eq { Default begin {graycalcs HalftoneType 1 sub get exec} end } { {0 60} ifelse } ifelse end } { c currentscreen pop exch } ifelse p printerRes 300 max exch div exch 2 copy s sin mul round dup mul 3 1 roll c cos mul round dup mul a add 1 add d dup maxsteps gt {pop maxsteps} if d dup minsteps lt {pop minsteps} if } ifelse } bdf / /nextrelease defed { / /languagelevel defed not { / /framebuffer defed { 0 40 string framebuffer 9 1 roll 8 {pop} repeat dup 516 eq exch 520 eq or { /fhnumcolors 3 def /currentscreen {60 0 {pop pop 1}}bdf /calcgraysteps {maxsteps} bdf }if }if }if }if fhnumcolors 1 ne { /calcgraysteps {maxsteps} bdf } if /currentpagedevice defed { currentpagedevice /PreRenderingEnhance known { currentpagedevice /PreRenderingEnhance get { /calcgraysteps { forcemaxsteps
{maxsteps} {256 maxsteps min} ifelse } def } if } if } if /gradfrequency 144 def printerRes 1000 lt { /gradfrequency 72 def } if /adjnumsteps { dup dtransform abs exch abs max printerRes div gradfrequency mul round 5 max min }bdf /goodsep { spots exch get 4 get dup sepname eq exch (_vc_Registration) eq or }bdf /BeginGradation defed {/bb{BeginGradation}bdf} {/bb{}bdf} ifelse /EndGradation defed {/eb{EndGradation}bdf} {/eb{}bdf} ifelse / /bottom -0 def / /delta -0 def / /frac -0 def / /height -0 def / /left -0 def / /numsteps1 -0 def / /radius -0 def / /right -0 def / /top -0 def / /width -0 def / /xt -0 def / /yt -0 def / /df currentflat def / /tempstr 1 string def / /clipflatness currentflat def / /inverted? 0 currenttransfer exec .5 ge def / /tc1 [0 0 0 1] def / /tc2 [0 0 0 1] def /storerect{/top xdf /right xdf /bottom xdf /left xdf /width right left sub def /height top bottom sub def}bdf /concatprocs{ systemdict /packedarray known {dup type /packedarraytype eq 2 index type /packedarraytype eq or}{false}ifelse { /proc2 exch cvlit def /proc1 exch cvlit def proc1 aload pop proc2 aload pop proc1 length proc2 length add packedarray cvx }
{ /proc2 exch cvlit def /proc1 exch cvlit def /newproc proc1 length proc2 length add array def newproc 0 proc1 putinterval newproc proc1 length proc2 putinterval newproc cvx }ifelse }bdf /i{dup 0 eq { {pop df dup} {dup} ifelse /clipflatness xdf setflat }bdf version cvr 38.0 le {/setrgbcolor{ currenttransfer exec 3 1 roll currenttransfer exec 3 1 roll currenttransfer exec 3 1 roll setrgbcolor}bdf}if /vms {/vmsv save def} bdf /vmr {vmsv restore} bdf /vmrs{vmsv restore /vmsv save def}bdf /eomode{ {/filler /eofill load def /clipper /eoclip load def} {/filler /fill load def /clipper /clip load def} ifelse }bdf /normtaper{}bdf /logtaper{9 mul 1 add log}bdf /CD{ / /NF exch def { e exch dup /FID ne 1 index/UniqueID ne and {exch NF 3 1 roll put} {pop pop} ifelse }forall NF }bdf /MN{ 1 index length /Len exch def d dup length Len add s string dup L Len 4 -1 roll p putinterval d dup 0 4 -1 roll p putinterval }bdf /RC{4 -1 roll /ourvec xdf 256 string cvs(|______)anchorsearch {1 index MN cvn/NewN exch def cvn findfont dup maxlength dict CD dup/FontName NewN put dup /Encoding ourvec put NewN exch definefont pop}{pop}ifelse}bdf / /RF{ d dup F FontDirectory exch
k known { {pop 3 -1 roll pop} {RC} ifelse }bdf /FF{dup 256 string cvs(|______)exch MN cvn dup FontDirectory exch known {exch pop findfont 3 -1 roll pop} {pop dup findfont dup maxlength dict CD dup dup /Encoding exch /Encoding get 256 array copy 7 -1 roll {3 -1 roll dup 4 -2 roll put}forall put definefont} ifelse}bdf / /RCJ{4 -1 roll / /ourvec xdf 2 256 string cvs (|______) anchorsearch { {pop c cvn d dup FDFJ exch 1 index e eq { _ _bfh findfont _efh d dup m maxlength dict C CD d dup / /FontName 3 index p put d dup / /Encoding ourvec put 1 index e exch d definefont p pop } { {exch pop} ifelse } { {pop} ifelse }bdf / /RFJ{ d dup F FontDirectory exch k known { {pop 3 -1 roll pop} {RCJ} ifelse }bdf /hasfont { / /resourcestatus where { p pop /Font resourcestatus { pop pop true
} { false } ifelse } { dup FontDirectory exch known {pop true} { 256 string cvs (fonts/) exch MN status {pop pop pop pop true} {false} ifelse } ifelse } ifelse }bdf /FDFJ { d dup h hasfont n not { pop /Ryumin-Light-83pv-RKSJ-H h hasfont { /Ryumin-Light-83pv-RKSJ-H } { /Courier } i ifelse } if }bdf /FFJ{ _bfh d dup 2 256 string cvs ( (|______)exch MN c cvn d dup FontDirectory e exch known { e exch p pop f findfont 3 -1 roll p pop } { p pop
F FDFJ d dup findfont d dup maxlength dict C CD d dup dup / /Encoding exch / /Encoding get 2 256 array copy 7 -1 roll { 3 -1 roll d dup 4 -2 roll p put }forall p put d definefont } ifelse _efh }bdf /GS { dup hasfont { findfont exch makesetfont exch pop ts } { pop pop pop ts } ifelse } bdf / /RCK{4 -1 roll / /ourvec xdf 2 256 string cvs (|______) anchorsearch { {pop c cvn d dup FDFK exch 1 index e eq { _ _bfh findfont _efh d dup m maxlength dict C CD d dup / /FontName 3 index p put d dup / /Encoding ourvec put 1 index e exch
d definefont p pop } { {exch pop} ifelse } { {pop} ifelse }bdf / /RFK{ d dup F FontDirectory exch k known { {pop 3 -1 roll pop} {RCK} ifelse }bdf /hasfont { / /resourcestatus where { p pop /Font resourcestatus { pop pop true } { false } ifelse } { dup FontDirectory exch known {pop true} { 256 string cvs (fonts/) exch MN status {pop pop pop pop true} {false} ifelse } ifelse } ifelse }bdf /FDFK { d dup h hasfont n not { pop /JCsm h hasfont { /JCsm }
{ /Courier } i ifelse } if }bdf /FFK{ _bfh d dup 2 256 string cvs ( (|______)exch MN c cvn d dup FontDirectory e exch known { e exch p pop f findfont 3 -1 roll p pop } { p pop F FDFK d dup findfont d dup maxlength dict C CD d dup dup / /Encoding exch / /Encoding get 2 256 array copy 7 -1 roll { 3 -1 roll d dup 4 -2 roll p put }forall p put d definefont } ifelse _efh }bdf / /RCTC{4 -1 roll / /ourvec xdf 2 256 string cvs (|______) anchorsearch { {pop c cvn d dup FDFTC exch 1 index e eq { _ _bfh findfont _efh d dup
m maxlength dict C CD d dup / /FontName 3 index p put d dup / /Encoding ourvec put 1 index e exch d definefont p pop } { {exch pop} ifelse } { {pop} ifelse }bdf / /RFTC{ d dup F FontDirectory exch k known { {pop 3 -1 roll pop} {RCTC} ifelse }bdf /FDFTC { d dup h hasfont n not { pop /DFMing-Lt-HK-BF h hasfont { /DFMing-Lt-HK-BF } { /Courier } i ifelse } if }bdf /FFTC{ _bfh d dup 2 256 string cvs ( (|______)exch MN c cvn d dup FontDirectory e exch known { e exch p pop f findfont
3 -1 roll p pop } { p pop F FDFTC d dup findfont d dup maxlength dict C CD d dup dup / /Encoding exch / /Encoding get 2 256 array copy 7 -1 roll { 3 -1 roll d dup 4 -2 roll p put }forall p put d definefont } ifelse _efh }bdf /fps{ c currentflat e exch d dup 0 le{pop 1}if { dup setflat 3 index stopped { {1.3 mul dup 3 index gt{pop setflat pop pop stop}if} { {exit} ifelse }loop pop setflat pop pop }bdf /fp{100 currentflat fps}bdf / /clipper{clip}bdf /W{/clipper load 100 clipflatness dup setflat fps}bdf /AVec 256 array def AVec 0 /Helvetica findfont /Encoding get 0 256 getinterval putinterval /ANSIPatch[ 16#0/grave 16#1/acute 16#2/circumflex 16#3/tilde 16#4/macron 16#5/breve 16#6/dotaccent 16#7/dieresis 16#8/ring 16#9/cedilla 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase 16#83/florin 16#84/quotedblbase 16#85 /ellipsis 16#86/dagger 16#87/daggerdbl 16#89/perthousand 16#8A/Scaron 16#8B/guilsinglleft 16#8C/OE 16#91/quoteleft 16#92/quoteright 16#93 /quotedblleft 16#94/quotedblright 16#95/bullet 16#96/endash 16#97/emdash 16#99/trademark 16#9A/scaron 16#9B/guilsinglright 16#9C/oe 16#9F/Ydieresis 16#A0/space 16#A4/currency 16#A6/brokenbar 16#A7/section 16#A8/dieresis 16#A9/copyright 16#AA/ordfeminine 16#AB/guillemotleft 16#AC/logicalnot 16#AD/hyphen 16#AE/registered 16#AF/macron 16#B0/degree 16#B1/plusminus 16#B2/twosuperior 16#B3/threesuperior 16#B4/acute 16#B5/mu 16#B6/paragraph 16#B7/periodcentered 16#B8/cedilla 16#B9/onesuperior 16#BA/ordmasculine 16#BB/guillemotright 16#BC/onequarter 16#BD/onehalf
16#BE/threequarters 16#BF/questiondown 16#C0/Agrave 16#C1/Aacute 16#C2/Acircumflex 16#C3/Atilde 16#C4/Adieresis 16#C5/Aring 16#C6/AE 16#C7/Ccedilla 16#C8/Egrave 16#C9/Eacute 16#CA/Ecircumflex 16#CB/Edieresis 16#CC/Igrave 16#CD/Iacute 16#CE/Icircumflex 16#CF/Idieresis 16#D0/Eth 16#D1/Ntilde 16#D2/Ograve 16#D3/Oacute 16#D4/Ocircumflex 16#D5/Otilde 16#D6/Odieresis 16#D7/multiply 16#D8/Oslash 16#D9/Ugrave 16#DA/Uacute 16#DB/Ucircumflex 16#DC/Udieresis 16#DD/Yacute 16#DE/Thorn 16#DF/germandbls 16#E0/agrave 16#E1/aacute 16#E2/acircumflex 16#E3/atilde 16#E4/adieresis 16#E5/aring 16#E6/ae 16#E7/ccedilla 16#E8/egrave 16#E9/eacute 16#EA/ecircumflex 16#EB/edieresis 16#EC/igrave 16#ED/iacute 16#EE/icircumflex 16#EF/idieresis 16#F0/eth 16#F1/ntilde 16#F2/ograve 16#F3/oacute 16#F4/ocircumflex 16#F5/otilde 16#F6/odieresis 16#F7/divide 16#F8/oslash 16#F9/ugrave 16#FA/uacute 16#FB/ucircumflex 16#FC/udieresis 16#FD/yacute 16#FE/thorn 16#FF/ydieresis ] def 127 1 159 { AVec exch/bullet put } for ANSIPatch aload pop ANSIPatch length 2 idiv{AVec 3 1 roll put}repeat /DoPatch { dup /CharStrings known { setfont 0 1 255 { dup currentfont /Encoding get exch get currentfont /CharStrings get exch known {pop} {currentfont /Encoding get exch /bullet put} ifelse } for } {pop} ifelse } def /findheaderfont { AVec 256 array copy /FHT /|______Helvetica dup RF findfont def FHT DoPatch FHT } def end %. AltsysDict %%EndResource %%EndProlog %%BeginSetup AltsysDict begin _ _bfh _ _efh end %. AltsysDict %%EndSetup A AltsysDict begin /onlyk4{false}ndf /ccmyk{dup 5 -1 roll sub 0 max exch}ndf /cmyk2gray{ 4 -1 roll 0.3 mul 4 -1 roll 0.59 mul 4 -1 roll 0.11 mul add add add 1 min neg 1 add }bdf /setcmykcolor{1 exch sub ccmyk ccmyk ccmyk pop setrgbcolor}ndf /maxcolor { m max max max } ndf /maxspot { pop } ndf /setcmykcoloroverprint{4{dup -1 eq{pop 0}if 4 1 roll}repeat setcmykcolor}ndf /findcmykcustomcolor{5 packedarray}ndf
/setcustomcolor{exch aload pop pop 4{4 index mul 4 1 roll}repeat setcmykcolor pop}ndf /setseparationgray{setgray}ndf / /setoverprint{pop}ndf /currentoverprint false ndf /cmykbufs2gray{ 0 1 2 index length 1 sub { 4 index 1 index get 0 0.3 mul 4 index 2 index get 0 0.59 mul 4 index 3 index get 0 0.11 mul 4 index 4 index get add add add cvi 255 min 255 exch sub 2 index 3 1 roll put }for 4 1 roll pop pop pop }bdf /colorimage{ pop pop [ 5 -1 roll/exec cvx 6 -1 roll/exec cvx 7 -1 roll/exec cvx 8 -1 roll/exec cvx /cmykbufs2gray cvx ]cvx image } %. version 47.1 on Linotronic of Postscript defines colorimage incorrectly (rgb model only) version cvr 47.1 le statusdict /product get (Lino) anchorsearch{pop pop true}{pop false}ifelse and{userdict begin bdf end}{ndf}ifelse fhnumcolors 1 ne {/yt save def} if /customcolorimage{ aload pop (_vc_Registration) eq { pop pop pop pop separationimage } { /ik xdf /iy xdf /im xdf /ic xdf ic im iy ik cmyk2gray /xt xdf currenttransfer {dup 1.0 exch sub xt mul add}concatprocs st image } ifelse }ndf fhnumcolors 1 ne {yt restore} if fhnumcolors 3 ne {/yt save def} if /customcolorimage{ aload pop (_vc_Registration) eq { pop pop pop pop separationimage }
{ /ik xdf /iy xdf /im xdf /ic xdf 1 1.0 dup ic ik add min sub 1 1.0 dup im ik add min sub 1 1.0 dup iy ik add min sub /ic xdf /iy xdf /im xdf currentcolortransfer 4 1 roll { {dup 1.0 exch sub ic mul add}concatprocs 4 1 roll { {dup 1.0 exch sub iy mul add}concatprocs 4 1 roll { {dup 1.0 exch sub im mul add}concatprocs 4 1 roll setcolortransfer {/dummy xdf dummy}concatprocs{dummy}{dummy}true 3 colorimage } ifelse }ndf fhnumcolors 3 ne {yt restore} if fhnumcolors 4 ne {/yt save def} if /customcolorimage{ aload pop (_vc_Registration) eq { pop pop pop pop separationimage } { /ik xdf /iy xdf /im xdf /ic xdf currentcolortransfer {1.0 exch sub ik mul ik sub 1 add}concatprocs 4 1 roll {1.0 exch sub iy mul iy sub 1 add}concatprocs 4 1 roll {1.0 exch sub im mul im sub 1 add}concatprocs 4 1 roll {1.0 exch sub ic mul ic sub 1 add}concatprocs 4 1 roll setcolortransfer {/dummy xdf dummy}concatprocs{dummy}{dummy}{dummy} true 4 colorimage } ifelse }ndf fhnumcolors 4 ne {yt restore} if /separationimage{image}ndf /spotascmyk false ndf /newcmykcustomcolor{6 packedarray}ndf /inkoverprint false ndf / /setinkoverprint{pop}ndf / /setspotcolor { spots exch get dup 4 get (_vc_Registration) eq {pop 1 exch sub setseparationgray} {0 5 getinterval exch setcustomcolor} ifelse }ndf /currentcolortransfer{currenttransfer dup dup dup}ndf /setcolortransfer{st pop pop pop}ndf /fas{}ndf /sas{}ndf /fhsetspreadsize{pop}ndf / /filler{fill}bdf /F{gsave {filler}fp grestore}bdf /f{closepath F}bdf /S{gsave {stroke}fp grestore}bdf
/s{closepath S}bdf userdict /islevel2 systemdict /languagelevel known dup { pop systemdict /languagelevel get 2 ge } if put islevel2 not { /currentcmykcolor { 0 0 0 1 currentgray sub } ndf } if /tc { gsave setcmykcolor currentcmykcolor grestore } bind def /testCMYKColorThrough { tc add add add 0 ne } bind def /fhiscomposite where not { userdict /fhiscomposite islevel2 { gsave 1 1 1 1 setcmykcolor currentcmykcolor grestore add add add 4 eq } { 1 0 0 0 testCMYKColorThrough 0 1 0 0 testCMYKColorThrough 0 0 1 0 testCMYKColorThrough 0 0 0 1 testCMYKColorThrough and and and } ifelse put } { pop } ifelse / /bc4 [0 0 0 0] def /_lfp4 { 1 pop / /yt xdf / /xt xdf / /ang xdf storerect /taperfcn xdf /k2 xdf /y2 xdf /m2 xdf /c2 xdf /k1 xdf /y1 xdf /m1 xdf /c1 xdf c1 c2 sub abs m1 m2 sub abs y1 y2 sub abs k1 k2 sub abs m maxcolor c calcgraysteps mul abs round h height abs adjnumsteps
d dup 1 lt {pop 1} if 1 sub /numsteps1 xdf c currentflat mark c currentflat clipflatness / /delta top bottom sub numsteps1 1 add div def / /right right left sub def / /botsv top delta sub def { { W xt yt translate ang rotate xt neg yt neg translate d dup setflat /bottom botsv def 0 1 numsteps1 { numsteps1 dup 0 eq {pop pop 0.5} {div} ifelse taperfcn /frac xdf bc4 0 c2 c1 sub frac mul c1 add put bc4 1 m2 m1 sub frac mul m1 add put bc4 2 y2 y1 sub frac mul y1 add put bc4 3 k2 k1 sub frac mul k1 add put bc4 vc 1 index setflat { mark {newpath left bottom right delta rectfill}stopped {cleartomark exch 1.3 mul dup setflat exch 2 copy gt{stop}if} {cleartomark exit}ifelse }loop /bottom bottom delta sub def }for } gsave stopped grestore {exch pop 2 index exch 1.3 mul dup 100 gt{cleartomark setflat stop}if} {exit}ifelse }loop cleartomark setflat }bdf / /bcs [0 0] def /_lfs4 { / /yt xdf / /xt xdf / /ang xdf storerect /taperfcn xdf / /tint2 xdf / /tint1 xdf b bcs exch 1 exch put t tint1 tint2 sub abs b bcs 1 get maxspot c calcgraysteps mul abs round h height abs adjnumsteps d dup 2 lt {pop 2} if 1 sub /numsteps1 xdf c currentflat mark c currentflat clipflatness / /delta top bottom sub numsteps1 1 add div def / /right right left sub def
/ /botsv top delta sub def { { W xt yt translate ang rotate xt neg yt neg translate d dup setflat /bottom botsv def 0 1 numsteps1 { numsteps1 div taperfcn /frac xdf bcs 0 1.0 tint2 tint1 sub frac mul tint1 add sub put bcs vc 1 index setflat { mark {newpath left bottom right delta rectfill}stopped {cleartomark exch 1.3 mul dup setflat exch 2 copy gt{stop}if} {cleartomark exit}ifelse }loop /bottom bottom delta sub def }for } gsave stopped grestore {exch pop 2 index exch 1.3 mul dup 100 gt{cleartomark setflat stop}if} {exit}ifelse }loop cleartomark setflat }bdf /_rfs6 { / /tint2 xdf / /tint1 xdf b bcs exch 1 exch put / /inrad xdf / /radius xdf / /yt xdf / /xt xdf t tint1 tint2 sub abs b bcs 1 get maxspot c calcgraysteps mul abs round r radius inrad sub abs a adjnumsteps d dup 1 lt {pop 1} if 1 sub /numsteps1 xdf r radius inrad sub numsteps1 dup 0 eq {pop} {div} ifelse 2 div /halfstep xdf c currentflat mark c currentflat clipflatness { { d dup setflat W 0 1 numsteps1 { dup /radindex xdf numsteps1 dup 0 eq {pop pop 0.5} {div} ifelse /frac xdf bcs 0
tint2 tint1 sub frac mul tint1 add put bcs vc 1 index setflat { n newpath mark xt yt radius inrad sub 1 frac sub mul halfstep add inrad add 0 360 { arc radindex numsteps1 ne i inrad 0 gt or { x xt yt numsteps1 0 eq { inrad } { radindex 1 add numsteps1 div 1 exch sub radius inrad sub mul halfstep add inrad add }ifelse dup xt add yt moveto 360 0 arcn } if fill }stopped {cleartomark exch 1.3 mul dup setflat exch 2 copy gt{stop}if} {cleartomark exit}ifelse }loop }for } gsave stopped grestore {exch pop 2 index exch 1.3 mul dup 100 gt{cleartomark setflat stop}if} {exit}ifelse }loop cleartomark setflat }bdf /_rfp6 { 1 pop /k2 xdf /y2 xdf /m2 xdf /c2 xdf /k1 xdf /y1 xdf /m1 xdf /c1 xdf / /inrad xdf / /radius xdf / /yt xdf / /xt xdf c1 c2 sub abs m1 m2 sub abs y1 y2 sub abs k1 k2 sub abs m maxcolor c calcgraysteps mul abs round r radius inrad sub abs a adjnumsteps d dup 1 lt {pop 1} if 1 sub /numsteps1 xdf r radius inrad sub numsteps1 dup 0 eq {pop} {div} ifelse 2 div /halfstep xdf c currentflat mark c currentflat clipflatness { { d dup setflat W
0 1 numsteps1 { dup /radindex xdf numsteps1 dup 0 eq {pop pop 0.5} {div} ifelse /frac xdf bc4 0 c2 c1 sub frac mul c1 add put bc4 1 m2 m1 sub frac mul m1 add put bc4 2 y2 y1 sub frac mul y1 add put bc4 3 k2 k1 sub frac mul k1 add put bc4 vc 1 index setflat { n newpath mark xt yt radius inrad sub 1 frac sub mul halfstep add inrad add 0 360 { arc radindex numsteps1 ne i inrad 0 gt or { x xt yt numsteps1 0 eq { inrad } { radindex 1 add numsteps1 div 1 exch sub radius inrad sub mul halfstep add inrad add }ifelse dup xt add yt moveto 360 0 arcn } if fill }stopped {cleartomark exch 1.3 mul dup setflat exch 2 copy gt{stop}if} {cleartomark exit}ifelse }loop }for } gsave stopped grestore {exch pop 2 index exch 1.3 mul dup 100 gt{cleartomark setflat stop}if} {exit}ifelse }loop cleartomark setflat }bdf /lfp4{_lfp4}ndf /lfs4{_lfs4}ndf /rfs6{_rfs6}ndf /rfp6{_rfp6}ndf / /cvc [0 0 0 1] def /vc{ A AltsysDict /cvc 2 index put aload length dup 4 eq {pop dup -1 eq{pop setrgbcolor}{setcmykcolor}ifelse} {6 eq {sethexcolor} {setspotcolor} ifelse } ifelse } }bdf 0 setseparationgray / /imgr {-16128 -16128 16128 16128 } def / /bleed 0 def / /clpr {-16128 -16128 -144 -144 } def / /xs 1 def / /ys 1 def
/ /botx 0 def / /overlap 0 def / /wdist 18 def 0 2 mul fhsetspreadsize 0 0 ne {/df 0 def /clipflatness 0 def} if / /maxsteps 256 def / /forcemaxsteps false def / /minsteps 0 def userdict begin /AGDOrigMtx matrix currentmatrix def end vms -1687 -1884 translate / /currentpacking defed{false setpacking}if /spots[ 1 0 0 0 (Process Cyan) false newcmykcustomcolor 0 1 0 0 (Process Magenta) false newcmykcustomcolor 0 0 1 0 (Process Yellow) false newcmykcustomcolor 0 0 0 1 (Process Black) false newcmykcustomcolor ]def n [] 0 d 3.863708 M 1 w 0 j 0 J false setoverprint 0 i false eomode [0 0 0 1]vc vms 1988.3921 1929.8516 m 2011.3555 1919.0875 L 2007.2891 1930.0908 L 2281.8937 2031.0343 L 2277.5881 2042.5161 L 2002.9834 1941.5725 L 1998.917 1952.8151 L 1988.3921 1929.8516 L [1 0 1 0]vc f 0.25 w 1 j [0 0 0 1]vc S n 2177.3622 1927.6988 m 2167.3156 1950.9015 L 2163.01 1939.8981 L 1886.0133 2049.9314 L 1881.4685 2038.6888 L 2158.4651 1928.6556 L 2154.1595 1917.6523 L 2177.3622 1927.6988 L [0 0 0 0]vc f [0 0 0 1]vc S n 2096.2725 1927.6988 m 2086.2259 1951.1407 L
2081.9203 1940.1373 L 1806.3588 2049.9314 L 1801.814 2038.6888 L 2077.3754 1928.8948 L 2072.8306 1917.8915 L 2096.2725 1927.6988 L [0 0 0 0]vc f [0 0 0 1]vc S n 2023.0764 1932.7221 m 2012.5515 1955.9247 L 2008.4851 1944.6822 L 1726.9435 2049.9314 L 1722.6379 2038.6888 L 2004.1794 1933.4397 L 2000.113 1922.1971 L 2023.0764 1932.7221 L [0 0 0 0]vc f [0 0 0 1]vc S n 2253.907 1926.9812 m 2244.0997 1950.423 L 2239.5548 1939.4197 L 1964.2326 2049.9314 L 1959.6877 2038.6888 L 2235.01 1927.938 L 2230.7043 1916.9347 L 2253.907 1926.9812 L [0 0 0 0]vc f [0 0 0 1]vc S n 1748.711 1930.5692 m 1771.9136 1920.2835 L 1767.608 1931.2868 L 2044.6047 2038.6888 L 2040.0598 2049.9314 L 1763.3024 1942.7686 L 1758.9967 1953.7719 L 1748.711 1930.5692 L [1 0 1 0]vc f [0 0 0 1]vc S n 1828.6047 1930.0908 m 1851.8073 1919.5659 L 1847.7409 1930.5692 L 2124.4984 2032.2304 L 2120.4319 2043.7121 L 1843.4352 1942.051 L 1839.3688 1953.2935 L 1828.6047 1930.0908 L [1 0 1 0]vc
f [0 0 0 1]vc S n 1911.608 1927.938 m 1934.8107 1917.4131 L 1930.505 1928.4164 L 2204.1528 2031.0343 L 2199.8472 2042.5161 L 1926.1994 1939.8981 L 1922.1329 1950.9015 L 1911.608 1927.938 L [1 0 1 0]vc f [0 0 0 1]vc S n 1724.7907 2168.8151 m 1742.7309 2186.7553 L 1731.01 2186.7553 L 1731.01 2242.9679 L 1718.8107 2242.9679 L 1718.8107 2186.7553 L 1706.8505 2186.7553 L 1724.7907 2168.8151 L [1 0 1 0]vc f [0 0 0 1]vc S n 1804.206 2168.8151 m 1822.1462 2186.7553 L 1810.1861 2186.7553 L 1810.1861 2242.9679 L 1797.9867 2242.9679 L 1797.9867 2186.7553 L 1786.2658 2186.7553 L 1804.206 2168.8151 L [0 0 0 0]vc f [0 0 0 1]vc S n vmrs 1883.6213 2168.8151 m 1901.5615 2186.7553 L 1889.8406 2186.7553 L 1889.8406 2242.9679 L 1877.402 2242.9679 L 1877.402 2186.7553 L 1865.4419 2186.7553 L 1883.6213 2168.8151 L [1 0 1 0]vc f 0.25 w 1 j [0 0 0 1]vc S n
1963.0366 2168.8151 m 1980.9768 2186.7553 L 1969.2558 2186.7553 L 1969.2558 2242.9679 L 1957.0565 2242.9679 L 1957.0565 2186.7553 L 1945.0964 2186.7553 L 1963.0366 2168.8151 L [0 0 0 0]vc f [0 0 0 1]vc S n 2042.4519 2168.8151 m 2060.3921 2186.7553 L 2048.4319 2186.7553 L 2048.4319 2242.9679 L 2036.2326 2242.9679 L 2036.2326 2186.7553 L 2024.5117 2186.7553 L 2042.4519 2168.8151 L [1 0 1 0]vc f [0 0 0 1]vc S n 2122.3455 2167.6191 m 2140.2857 2185.5593 L 2128.5648 2185.5593 L 2128.5648 2241.7719 L 2116.3655 2241.7719 L 2116.3655 2185.5593 L 2104.4053 2185.5593 L 2122.3455 2167.6191 L [0 0 0 0]vc f [0 0 0 1]vc S n 2202 2166.1838 m 2219.9402 2184.124 L 2207.9801 2184.124 L 2207.9801 2240.3367 L 2195.7808 2240.3367 L 2195.7808 2184.124 L 2184.0598 2184.124 L 2202 2166.1838 L [1 0 1 0]vc f [0 0 0 1]vc S n 2279.7409 2166.1838 m 2297.6811 2184.3632 L 2285.721 2184.124 L 2285.721 2240.0975 L 2273.5216 2240.0975 L 2273.5216 2184.124 L 2261.5615 2184.124 L
2279.7409 2166.1838 L [0 0 0 0]vc f [0 0 0 1]vc S n 1783.8738 2164.7486 m 1786.7442 2192.4961 L 1776.6977 2184.3632 L 1736.0332 2234.5958 L 1725.7475 2226.2237 L 1766.1728 2175.9912 L 1756.1263 2167.8583 L 1783.8738 2164.7486 L [0 0 0 0]vc f [0 0 0 1]vc S n 1939.5947 2163.3134 m 1944.1396 2188.1905 L 1934.3323 2181.4928 L 1888.6445 2246.5559 L 1878.598 2239.3799 L 1924.2857 2174.5559 L 1914.7176 2167.6191 L 1939.5947 2163.3134 L [0 0 0 0]vc f [0 0 0 1]vc S n 2101.7741 2163.3134 m 2105.3622 2188.4297 L 2095.794 2181.2536 L 2047.2359 2246.5559 L 2037.4286 2239.3799 L 2086.2259 2174.0775 L 2076.6578 2166.9015 L 2101.7741 2163.3134 L [0 0 0 0]vc f [0 0 0 1]vc S n 2259.4087 2162.3566 m 2263.2359 2187.2337 L 2253.6678 2180.2968 L 2206.7841 2243.9247 L 2196.9768 2236.7486 L 2243.8605 2173.1207 L 2234.2924 2166.1838 L 2259.4087 2162.3566 L [0 0 0 0]vc f [0 0 0 1]vc S n vmrs
1747.0366 2163.7918 m 1772.1528 2167.8583 L 1762.5847 2174.7951 L 1808.9901 2239.3799 L 1799.1827 2246.5559 L 1752.5382 2181.9712 L 1742.9701 2188.9081 L 1747.0366 2163.7918 L [1 0 1 0]vc f 0.25 w 1 j [0 0 0 1]vc S n 1907.5416 2163.0742 m 1932.4186 2167.6191 L 1922.6113 2174.3167 L 1968.0598 2239.6191 L 1958.0133 2246.5559 L 1912.5648 2181.2536 L 1902.9967 2187.9513 L 1907.5416 2163.0742 L [1 0 1 0]vc f [0 0 0 1]vc S n 2062.0665 2164.9878 m 2087.1827 2168.0975 L 2077.8538 2175.2735 L 2127.1296 2237.9446 L 2117.5615 2245.3599 L 2068.2857 2182.928 L 2058.9568 2190.3433 L 2062.0665 2164.9878 L [1 0 1 0]vc f [0 0 0 1]vc S n 2222.8107 2161.8782 m 2247.9269 2165.9446 L 2238.3588 2172.8815 L 2284.5249 2236.5094 L 2274.4784 2243.6855 L 2228.5515 2180.0576 L 2218.7442 2186.9945 L 2222.8107 2161.8782 L [1 0 1 0]vc f [0 0 0 1]vc S n 2250.319 2051.845 m 2246.2525 2076.9613 L 2239.3156 2067.1539 L 2125.9336 2148.0044 L 2118.9967 2137.9579 L
2232.1396 2057.1074 L 2225.4419 2047.5393 L 2250.319 2051.845 L [0 0 0 0]vc f [0 0 0 1]vc S n 2144.113 2057.825 m 2168.7509 2052.0842 L 2162.5316 2062.1307 L 2282.8505 2136.5227 L 2276.3921 2146.8084 L 2156.3123 2072.4164 L 2150.093 2082.7021 L 2144.113 2057.825 L [1 0 1 0]vc f [0 0 0 1]vc S n 2173.5349 2052.3234 m 2169.2293 2077.6789 L 2162.2924 2067.6323 L 2045.8007 2149.2005 L 2038.8638 2139.3931 L 2155.3555 2057.5858 L 2148.6578 2048.0177 L 2173.5349 2052.3234 L [0 0 0 0]vc f [0 0 0 1]vc S n 2062.7841 2059.7387 m 2087.1827 2053.2802 L 2081.2027 2063.5659 L 2205.1097 2136.5227 L 2198.8904 2147.0476 L 2074.9834 2074.0908 L 2069.0033 2084.6157 L 2062.7841 2059.7387 L [1 0 1 0]vc f [0 0 0 1]vc S n 1828.1263 2057.825 m 1852.7641 2051.845 L 1846.7841 2061.8915 L 1966.1462 2134.1307 L 1959.9269 2144.4164 L 1840.3256 2072.4164 L 1834.3455 2082.7021 L 1828.1263 2057.825 L [1 0 1 0]vc f [0 0 0 1]vc S
n 1932.4186 2052.8018 m 1928.113 2078.1573 L 1921.1761 2068.35 L 1807.794 2149.2005 L 1800.618 2139.3931 L 1914.2392 2058.3034 L 1907.3024 2048.7353 L 1932.4186 2052.8018 L [0 0 0 0]vc f [0 0 0 1]vc S n vmrs 1853.9602 2053.9978 m 1849.4153 2079.1141 L 1842.7176 2069.0676 L 1728.3788 2149.2005 L 1721.4419 2139.3931 L 1835.7808 2059.2603 L 1828.8439 2049.4529 L 1853.9602 2053.9978 L [0 0 0 0]vc f 0.25 w 1 j [0 0 0 1]vc S n 1755.6479 2052.8018 m 1780.5249 2048.0177 L 1773.8273 2057.825 L 1887.2093 2134.1307 L 1880.2725 2144.4164 L 1767.1296 2067.8716 L 1760.4319 2077.9181 L 1755.6479 2052.8018 L [1 0 1 0]vc f [0 0 0 1]vc S n 1724.7907 2063.8051 m 1742.7309 2081.9845 L 1731.01 2081.9845 L 1731.01 2139.3931 L 1718.8107 2139.3931 L 1718.8107 2081.9845 L 1706.8505 2081.9845 L 1724.7907 2063.8051 L [1 0 1 0]vc f [0 0 0 1]vc S n 1804.206 2063.8051 m 1822.1462 2081.9845 L 1810.1861 2081.9845 L
1810.1861 2144.1772 L 1797.9867 2144.1772 L 1797.9867 2081.9845 L 1786.2658 2081.9845 L 1804.206 2063.8051 L [1 0 1 0]vc f [0 0 0 1]vc S n 1883.6213 2063.8051 m 1901.5615 2081.9845 L 1889.8406 2081.9845 L 1889.8406 2144.1772 L 1877.402 2144.1772 L 1877.402 2081.9845 L 1865.4419 2081.9845 L 1883.6213 2063.8051 L [0 0 0 0]vc f [0 0 0 1]vc S n 1962.0798 2063.8051 m 1980.2592 2081.7453 L 1968.299 2081.9845 L 1969.2558 2144.1772 L 1957.0565 2144.4164 L 1956.0997 2082.2237 L 1944.3788 2082.2237 L 1962.0798 2063.8051 L [0 0 0 0]vc f [0 0 0 1]vc S n 2042.4519 2063.8051 m 2060.3921 2081.9845 L 2048.4319 2081.9845 L 2048.4319 2144.1772 L 2036.2326 2144.1772 L 2036.2326 2081.9845 L 2024.5117 2081.9845 L 2042.4519 2063.8051 L [1 0 1 0]vc f [0 0 0 1]vc S n 2122.3455 2062.6091 m 2140.2857 2080.7885 L 2128.5648 2080.7885 L 2128.5648 2137.9579 L 2116.3655 2137.9579 L 2116.3655 2080.7885 L 2104.4053 2080.7885 L 2122.3455 2062.6091 L [1 0 1 0]vc f
[0 0 0 1]vc S n 2202 2061.1739 m 2219.9402 2079.3533 L 2207.9801 2079.3533 L 2207.9801 2141.7852 L 2195.7808 2141.7852 L 2195.7808 2079.3533 L 2184.0598 2079.3533 L 2202 2061.1739 L [0 0 0 0]vc f [0 0 0 1]vc S n 2279.7409 2061.1739 m 2297.6811 2079.3533 L 2285.721 2079.3533 L 2285.721 2141.7852 L 2273.5216 2141.7852 L 2273.5216 2079.3533 L 2261.5615 2079.3533 L 2279.7409 2061.1739 L [0 0 0 0]vc f [0 0 0 1]vc S n vmrs 1687.9535 1911.9114 m 1688.4319 1915.7387 L 1689.8671 1919.3267 L 1692.02 1922.9147 L 1695.1296 1926.2636 L 1698.7176 1929.134 L 1703.2625 1931.7652 L 1708.0465 1933.6789 L 1713.5482 1935.1141 L 1719.0499 1936.0709 L 1724.7907 1936.3101 L 1730.5316 1936.0709 L 1736.2725 1935.1141 L 1741.5349 1933.6789 L 1746.5582 1931.7652 L 1750.8638 1929.134 L 1754.6911 1926.2636 L 1757.5615 1922.9147 L 1759.9535 1919.3267 L 1761.1495 1915.7387 L 1761.6279 1911.9114 L 1761.1495 1908.0842 L 1759.9535 1904.2569 L 1757.5615 1900.6689 L 1754.6911 1897.3201 L 1750.8638 1894.4496 L 1746.5582 1892.0576 L 1741.5349 1889.9048 L 1736.2725 1888.4696 L
1730.5316 1887.5127 L 1724.7907 1887.2735 L 1719.0499 1887.5127 L 1713.5482 1888.4696 L 1708.0465 1889.9048 L 1703.2625 1892.0576 L 1698.7176 1894.4496 L 1695.1296 1897.3201 L 1692.02 1900.6689 L 1689.8671 1904.2569 L 1688.4319 1908.0842 L 1687.9535 1911.9114 L [0 0 0 0]vc f 0.25 w 1 j [0 0 0 1]vc S n 1767.3688 1911.9114 m 1767.8472 1915.7387 L 1769.0432 1919.3267 L 1771.4352 1922.9147 L 1774.3057 1926.2636 L 1778.1329 1929.134 L 1782.4386 1931.7652 L 1787.4618 1933.6789 L 1792.7243 1935.1141 L 1798.4651 1936.0709 L 1804.206 1936.3101 L 1809.9469 1936.0709 L 1815.4485 1935.1141 L 1820.9502 1933.6789 L 1825.7342 1931.7652 L 1830.2791 1929.134 L 1833.8671 1926.2636 L 1836.9768 1922.9147 L 1839.1296 1919.3267 L 1840.5648 1915.7387 L 1841.0432 1911.9114 L 1840.5648 1908.0842 L 1839.1296 1904.2569 L 1836.9768 1900.6689 L 1833.8671 1897.3201 L 1830.2791 1894.4496 L 1825.7342 1892.0576 L 1820.9502 1889.9048 L 1815.4485 1888.4696 L 1809.9469 1887.5127 L 1804.206 1887.2735 L 1798.4651 1887.5127 L 1792.7243 1888.4696 L 1787.4618 1889.9048 L 1782.4386 1892.0576 L 1778.1329 1894.4496 L 1774.3057 1897.3201 L 1771.4352 1900.6689 L 1769.0432 1904.2569 L 1767.8472 1908.0842 L
1767.3688 1911.9114 L [0 0 0 0]vc f [0 0 0 1]vc S n 1846.5449 1911.9114 m 1847.0233 1915.7387 L 1848.4585 1919.3267 L 1850.6113 1922.9147 L 1853.721 1926.2636 L 1857.5482 1929.134 L 1861.8538 1931.7652 L 1866.8771 1933.6789 L 1872.1396 1935.1141 L 1877.6412 1936.0709 L 1883.6213 1936.3101 L 1889.6014 1936.0709 L 1895.103 1935.1141 L 1900.3655 1933.6789 L 1905.3887 1931.7652 L 1909.6944 1929.134 L 1913.5216 1926.2636 L 1916.6313 1922.9147 L 1918.7841 1919.3267 L 1919.9801 1915.7387 L 1920.4585 1911.9114 L 1919.9801 1908.0842 L 1918.7841 1904.2569 L 1916.6313 1900.6689 L 1913.5216 1897.3201 L 1909.6944 1894.4496 L 1905.3887 1892.0576 L 1900.3655 1889.9048 L 1895.103 1888.4696 L 1889.6014 1887.5127 L 1883.6213 1887.2735 L 1877.6412 1887.5127 L 1872.1396 1888.4696 L 1866.8771 1889.9048 L 1861.8538 1892.0576 L 1857.5482 1894.4496 L 1853.721 1897.3201 L 1850.6113 1900.6689 L 1848.4585 1904.2569 L 1847.0233 1908.0842 L 1846.5449 1911.9114 L [0 0 0 0]vc f [0 0 0 1]vc S n 1926.1994 1911.9114 m 1926.6778 1915.7387 L 1928.113 1919.3267 L 1930.2658 1922.9147 L 1933.1362 1926.2636 L 1936.9635 1929.134 L 1941.5083 1931.7652 L
1946.2924 1933.6789 L 1951.5548 1935.1141 L 1957.2957 1936.0709 L 1963.0366 1936.3101 L 1968.7774 1936.0709 L 1974.5183 1935.1141 L 1979.7808 1933.6789 L 1984.804 1931.7652 L 1989.1097 1929.134 L 1992.9369 1926.2636 L 1995.8073 1922.9147 L 1997.9602 1919.3267 L 1999.3954 1915.7387 L 1999.8738 1911.9114 L 1999.3954 1908.0842 L 1997.9602 1904.2569 L 1995.8073 1900.6689 L 1992.9369 1897.3201 L 1989.1097 1894.4496 L 1984.804 1892.0576 L 1979.7808 1889.9048 L 1974.5183 1888.4696 L 1968.7774 1887.5127 L 1963.0366 1887.2735 L 1957.2957 1887.5127 L 1951.5548 1888.4696 L 1946.2924 1889.9048 L 1941.5083 1892.0576 L 1936.9635 1894.4496 L 1933.1362 1897.3201 L 1930.2658 1900.6689 L 1928.113 1904.2569 L 1926.6778 1908.0842 L 1926.1994 1911.9114 L [0 0 0 0]vc f [0 0 0 1]vc S n 2005.6146 1911.9114 m 2006.093 1915.7387 L 2007.2891 1919.3267 L 2009.4419 1922.9147 L 2012.5515 1926.2636 L 2016.3788 1929.134 L 2020.6844 1931.7652 L 2025.7077 1933.6789 L 2030.9701 1935.1141 L 2036.711 1936.0709 L 2042.4519 1936.3101 L 2048.1927 1936.0709 L 2053.6944 1935.1141 L 2059.196 1933.6789 L 2063.9801 1931.7652 L 2068.5249 1929.134 L 2072.113 1926.2636 L 2075.2226 1922.9147 L 2077.3754 1919.3267 L 2078.8107 1915.7387 L
2079.2891 1911.9114 L 2078.8107 1908.0842 L 2077.3754 1904.2569 L 2075.2226 1900.6689 L 2072.113 1897.3201 L 2068.5249 1894.4496 L 2063.9801 1892.0576 L 2059.196 1889.9048 L 2053.6944 1888.4696 L 2048.1927 1887.5127 L 2042.4519 1887.2735 L 2036.711 1887.5127 L 2030.9701 1888.4696 L 2025.7077 1889.9048 L 2020.6844 1892.0576 L 2016.3788 1894.4496 L 2012.5515 1897.3201 L 2009.4419 1900.6689 L 2007.2891 1904.2569 L 2006.093 1908.0842 L 2005.6146 1911.9114 L [0 0 0 0]vc f [0 0 0 1]vc S n 2085.5083 1910.4762 m 2085.9867 1914.3034 L 2087.422 1918.1307 L 2089.5748 1921.7187 L 2092.6844 1925.0676 L 2096.5117 1927.938 L 2100.8173 1930.33 L 2105.8406 1932.4828 L 2111.103 1933.9181 L 2116.6047 1934.8749 L 2122.3455 1935.1141 L 2128.3256 1934.8749 L 2133.8273 1933.9181 L 2139.0897 1932.4828 L 2144.113 1930.33 L 2148.4186 1927.938 L 2152.2459 1925.0676 L 2155.3555 1921.7187 L 2157.5083 1918.1307 L 2158.9435 1914.3034 L 2159.1827 1910.4762 L 2158.9435 1906.649 L 2157.5083 1903.0609 L 2155.3555 1899.4729 L 2152.2459 1896.124 L 2148.4186 1893.2536 L 2144.113 1890.6224 L 2139.0897 1888.7088 L 2133.8273 1887.2735 L 2128.3256 1886.3167 L 2122.3455 1886.0775 L 2116.6047 1886.3167 L 2111.103 1887.2735 L
2105.8406 1888.7088 L 2100.8173 1890.6224 L 2096.5117 1893.2536 L 2092.6844 1896.124 L 2089.5748 1899.4729 L 2087.422 1903.0609 L 2085.9867 1906.649 L 2085.5083 1910.4762 L [0 0 0 0]vc f [0 0 0 1]vc S n 2165.1628 1909.2802 m 2165.6412 1913.1074 L 2166.8372 1916.9347 L 2168.9901 1920.5227 L 2172.0997 1923.6323 L 2175.9269 1926.742 L 2180.2326 1929.134 L 2185.2558 1931.0476 L 2190.5183 1932.7221 L 2196.2592 1933.4397 L 2202 1933.9181 L 2207.7409 1933.4397 L 2213.2425 1932.7221 L 2218.7442 1931.0476 L 2223.5283 1929.134 L 2228.0731 1926.742 L 2231.6612 1923.6323 L 2234.7708 1920.5227 L 2236.9236 1916.9347 L 2238.3588 1913.1074 L 2238.8372 1909.2802 L 2238.3588 1905.4529 L 2236.9236 1901.6257 L 2234.7708 1898.0377 L 2231.6612 1894.928 L 2228.0731 1891.8184 L 2223.5283 1889.4264 L 2218.7442 1887.2735 L 2213.2425 1885.8383 L 2207.7409 1885.1207 L 2202 1884.6423 L 2196.2592 1885.1207 L 2190.5183 1885.8383 L 2185.2558 1887.2735 L 2180.2326 1889.4264 L 2175.9269 1891.8184 L 2172.0997 1894.928 L 2168.9901 1898.0377 L 2166.8372 1901.6257 L 2165.6412 1905.4529 L 2165.1628 1909.2802 L [0 0 0 0]vc f [0 0 0 1]vc S n
2242.6645 1909.2802 m 2243.1429 1913.1074 L 2244.3389 1916.9347 L 2246.7309 1920.5227 L 2249.6014 1923.6323 L 2253.4286 1926.742 L 2257.7342 1929.134 L 2262.7575 1931.0476 L 2268.2592 1932.7221 L 2274 1933.4397 L 2279.7409 1933.9181 L 2285.4818 1933.4397 L 2290.9834 1932.7221 L 2296.4851 1931.0476 L 2301.2691 1929.134 L 2305.814 1926.742 L 2309.402 1923.6323 L 2312.5117 1920.5227 L 2314.6645 1916.9347 L 2316.0997 1913.1074 L 2316.5781 1909.2802 L 2316.0997 1905.4529 L 2314.6645 1901.6257 L 2312.5117 1898.0377 L 2309.402 1894.928 L 2305.814 1891.8184 L 2301.2691 1889.4264 L 2296.4851 1887.2735 L 2290.9834 1885.8383 L 2285.4818 1885.1207 L 2279.7409 1884.6423 L 2274 1885.1207 L 2268.2592 1885.8383 L 2262.7575 1887.2735 L 2257.7342 1889.4264 L 2253.4286 1891.8184 L 2249.6014 1894.928 L 2246.7309 1898.0377 L 2244.3389 1901.6257 L 2243.1429 1905.4529 L 2242.6645 1909.2802 L [0 0 0 0]vc f [0 0 0 1]vc S n 1724.7907 1936.3101 m 1742.7309 1954.2503 L 1731.01 1954.2503 L 1731.01 2039.4064 L 1718.8107 2039.4064 L 1718.8107 1954.2503 L 1706.8505 1954.2503 L 1724.7907 1936.3101 L [1 0 1 0]vc f [0 0 0 1]vc S n
1804.206 1936.3101 m 1822.1462 1954.2503 L 1810.1861 1954.2503 L 1810.1861 2044.1905 L 1797.9867 2044.1905 L 1797.9867 1954.2503 L 1786.2658 1954.2503 L 1804.206 1936.3101 L [1 0 1 0]vc f [0 0 0 1]vc S n vmrs 1883.6213 1936.3101 m 1901.5615 1954.2503 L 1889.8406 1954.2503 L 1889.8406 2044.1905 L 1877.402 2044.1905 L 1877.402 1954.2503 L 1865.4419 1954.2503 L 1883.6213 1936.3101 L [1 0 1 0]vc f 0.25 w 1 j [0 0 0 1]vc S n 1963.0366 1936.3101 m 1980.7376 1954.4895 L 1969.0166 1954.4895 L 1968.0598 2044.4297 L 1955.8605 2044.1905 L 1956.8173 1954.2503 L 1944.8572 1954.2503 L 1963.0366 1936.3101 L [1 0 1 0]vc f [0 0 0 1]vc S n 2042.4519 1936.3101 m 2060.3921 1954.2503 L 2048.4319 1954.2503 L 2048.4319 2044.1905 L 2036.2326 2044.1905 L 2036.2326 1954.2503 L 2024.5117 1954.2503 L 2042.4519 1936.3101 L [0 0 0 0]vc f [0 0 0 1]vc S n 2122.3455 1935.1141 m 2140.2857 1953.0543 L 2128.5648 1953.0543 L 2128.5648 2042.9945 L
2116.3655 2042.9945 L 2116.3655 1953.0543 L 2104.4053 1953.0543 L 2122.3455 1935.1141 L [0 0 0 0]vc f [0 0 0 1]vc S n 2202 1933.9181 m 2219.9402 1951.8583 L 2207.9801 1951.8583 L 2207.9801 2036.7752 L 2195.7808 2036.7752 L 2195.7808 1951.8583 L 2184.0598 1951.8583 L 2202 1933.9181 L [0 0 0 0]vc f [0 0 0 1]vc S n 2279.7409 1933.9181 m 2297.6811 1951.8583 L 2285.721 1951.8583 L 2285.721 2036.7752 L 2273.5216 2036.7752 L 2273.5216 1951.8583 L 2261.5615 1951.8583 L 2279.7409 1933.9181 L [0 0 0 0]vc f [0 0 0 1]vc S n 1767.3688 2039.4064 m 1767.8472 2043.2337 L 1769.0432 2046.8217 L 1771.4352 2050.4098 L 1774.3057 2053.7586 L 1778.1329 2056.629 L 1782.4386 2059.2603 L 1787.4618 2061.1739 L 1792.7243 2062.6091 L 1798.4651 2063.5659 L 1804.206 2063.8051 L 1809.9469 2063.5659 L 1815.4485 2062.6091 L 1820.9502 2061.1739 L 1825.7342 2059.2603 L 1830.2791 2056.629 L 1833.8671 2053.7586 L 1836.9768 2050.4098 L 1839.1296 2046.8217 L 1840.5648 2043.2337 L 1841.0432 2039.4064 L 1840.5648 2035.34 L 1839.1296 2031.752 L 1836.9768 2028.1639 L
1833.8671 2024.8151 L 1830.2791 2021.9446 L 1825.7342 2019.5526 L 1820.9502 2017.3998 L 1815.4485 2015.9646 L 1809.9469 2015.0078 L 1804.206 2014.7686 L 1798.4651 2015.0078 L 1792.7243 2015.9646 L 1787.4618 2017.3998 L 1782.4386 2019.5526 L 1778.1329 2021.9446 L 1774.3057 2024.8151 L 1771.4352 2028.1639 L 1769.0432 2031.752 L 1767.8472 2035.34 L 1767.3688 2039.4064 L [0 0 0 0]vc f [0 0 0 1]vc S n 1846.5449 2039.4064 m 1847.0233 2043.2337 L 1848.4585 2046.8217 L 1850.6113 2050.4098 L 1853.721 2053.7586 L 1857.5482 2056.629 L 1861.8538 2059.2603 L 1866.8771 2061.1739 L 1872.1396 2062.6091 L 1877.6412 2063.5659 L 1883.6213 2063.8051 L 1889.6014 2063.5659 L 1895.103 2062.6091 L 1900.3655 2061.1739 L 1905.3887 2059.2603 L 1909.6944 2056.629 L 1913.5216 2053.7586 L 1916.6313 2050.4098 L 1918.7841 2046.8217 L 1919.9801 2043.2337 L 1920.4585 2039.4064 L 1919.9801 2035.34 L 1918.7841 2031.752 L 1916.6313 2028.1639 L 1913.5216 2024.8151 L 1909.6944 2021.9446 L 1905.3887 2019.5526 L 1900.3655 2017.3998 L 1895.103 2015.9646 L 1889.6014 2015.0078 L 1883.6213 2014.7686 L 1877.6412 2015.0078 L 1872.1396 2015.9646 L 1866.8771 2017.3998 L 1861.8538 2019.5526 L 1857.5482 2021.9446 L 1853.721 2024.8151 L
1850.6113 2028.1639 L 1848.4585 2031.752 L 1847.0233 2035.34 L 1846.5449 2039.4064 L [0 0 0 0]vc f [0 0 0 1]vc S n 1926.1994 2039.4064 m 1926.6778 2043.2337 L 1927.8738 2046.8217 L 1930.0266 2050.4098 L 1933.1362 2053.7586 L 1936.7243 2056.629 L 1941.0299 2059.2603 L 1945.814 2061.1739 L 1950.8372 2062.6091 L 1956.3389 2063.5659 L 1962.0798 2063.8051 L 1967.5814 2063.5659 L 1973.0831 2062.6091 L 1978.3455 2061.1739 L 1983.1296 2059.2603 L 1987.196 2056.629 L 1991.0233 2053.7586 L 1993.8937 2050.4098 L 1996.0465 2046.8217 L 1997.2425 2043.2337 L 1997.721 2039.4064 L 1997.2425 2035.34 L 1996.0465 2031.752 L 1993.8937 2028.1639 L 1991.0233 2024.8151 L 1987.196 2021.9446 L 1983.1296 2019.5526 L 1978.3455 2017.3998 L 1973.0831 2015.9646 L 1967.5814 2015.0078 L 1962.0798 2014.7686 L 1956.3389 2015.0078 L 1950.8372 2015.9646 L 1945.814 2017.3998 L 1941.0299 2019.5526 L 1936.7243 2021.9446 L 1933.1362 2024.8151 L 1930.0266 2028.1639 L 1927.8738 2031.752 L 1926.6778 2035.34 L 1926.1994 2039.4064 L [0 0 0 0]vc f [0 0 0 1]vc S n 2005.6146 2039.4064 m 2006.093 2043.2337 L 2007.2891 2046.8217 L 2009.4419 2050.4098 L
2012.5515 2053.7586 L 2016.3788 2056.629 L 2020.6844 2059.2603 L 2025.7077 2061.1739 L 2030.9701 2062.6091 L 2036.711 2063.5659 L 2042.4519 2063.8051 L 2048.1927 2063.5659 L 2053.6944 2062.6091 L 2059.196 2061.1739 L 2063.9801 2059.2603 L 2068.5249 2056.629 L 2072.113 2053.7586 L 2075.2226 2050.4098 L 2077.3754 2046.8217 L 2078.8107 2043.2337 L 2079.2891 2039.4064 L 2078.8107 2035.34 L 2077.3754 2031.752 L 2075.2226 2028.1639 L 2072.113 2024.8151 L 2068.5249 2021.9446 L 2063.9801 2019.5526 L 2059.196 2017.3998 L 2053.6944 2015.9646 L 2048.1927 2015.0078 L 2042.4519 2014.7686 L 2036.711 2015.0078 L 2030.9701 2015.9646 L 2025.7077 2017.3998 L 2020.6844 2019.5526 L 2016.3788 2021.9446 L 2012.5515 2024.8151 L 2009.4419 2028.1639 L 2007.2891 2031.752 L 2006.093 2035.34 L 2005.6146 2039.4064 L [0 0 0 0]vc f [0 0 0 1]vc S n vmrs 2085.5083 2037.9712 m 2085.9867 2041.7985 L 2087.422 2045.6257 L 2089.5748 2049.2137 L 2092.6844 2052.3234 L 2096.5117 2055.433 L 2100.8173 2057.825 L 2105.8406 2059.9779 L 2111.103 2061.4131 L 2116.6047 2062.3699 L 2122.3455 2062.6091 L 2128.3256 2062.3699 L 2133.8273 2061.4131 L 2139.0897 2059.9779 L 2144.113 2057.825 L 2148.4186 2055.433 L
2152.2459 2052.3234 L 2155.3555 2049.2137 L 2157.5083 2045.6257 L 2158.9435 2041.7985 L 2159.1827 2037.9712 L 2158.9435 2034.144 L 2157.5083 2030.3167 L 2155.3555 2026.9679 L 2152.2459 2023.6191 L 2148.4186 2020.7486 L 2144.113 2018.1174 L 2139.0897 2016.2038 L 2133.8273 2014.7686 L 2128.3256 2013.8118 L 2122.3455 2013.5725 L 2116.6047 2013.8118 L 2111.103 2014.7686 L 2105.8406 2016.2038 L 2100.8173 2018.1174 L 2096.5117 2020.7486 L 2092.6844 2023.6191 L 2089.5748 2026.9679 L 2087.422 2030.3167 L 2085.9867 2034.144 L 2085.5083 2037.9712 L [0 0 0 0]vc f 0.25 w 1 j [0 0 0 1]vc S n 2165.1628 2036.7752 m 2165.6412 2040.6024 L 2166.8372 2044.1905 L 2168.9901 2047.7785 L 2172.0997 2051.1274 L 2175.9269 2053.9978 L 2180.2326 2056.629 L 2185.2558 2058.5426 L 2190.5183 2059.9779 L 2196.2592 2060.9347 L 2202 2061.1739 L 2207.7409 2060.9347 L 2213.2425 2059.9779 L 2218.7442 2058.5426 L 2223.5283 2056.629 L 2228.0731 2053.9978 L 2231.6612 2051.1274 L 2234.7708 2047.7785 L 2236.9236 2044.1905 L 2238.3588 2040.6024 L 2238.8372 2036.7752 L 2238.3588 2032.948 L 2236.9236 2029.1207 L 2234.7708 2025.5327 L 2231.6612 2022.1838 L 2228.0731 2019.3134 L 2223.5283 2016.9214 L
2218.7442 2014.7686 L 2213.2425 2013.3333 L 2207.7409 2012.3765 L 2202 2012.1373 L 2196.2592 2012.3765 L 2190.5183 2013.3333 L 2185.2558 2014.7686 L 2180.2326 2016.9214 L 2175.9269 2019.3134 L 2172.0997 2022.1838 L 2168.9901 2025.5327 L 2166.8372 2029.1207 L 2165.6412 2032.948 L 2165.1628 2036.7752 L [0 0 0 0]vc f [0 0 0 1]vc S n 1687.9535 2039.4064 m 1688.4319 2043.2337 L 1689.8671 2046.8217 L 1692.02 2050.4098 L 1695.1296 2053.7586 L 1698.7176 2056.629 L 1703.2625 2059.2603 L 1708.0465 2061.1739 L 1713.5482 2062.6091 L 1719.0499 2063.5659 L 1724.7907 2063.8051 L 1730.5316 2063.5659 L 1736.2725 2062.6091 L 1741.5349 2061.1739 L 1746.5582 2059.2603 L 1750.8638 2056.629 L 1754.6911 2053.7586 L 1757.5615 2050.4098 L 1759.9535 2046.8217 L 1761.1495 2043.2337 L 1761.6279 2039.4064 L 1761.1495 2035.34 L 1759.9535 2031.752 L 1757.5615 2028.1639 L 1754.6911 2024.8151 L 1750.8638 2021.9446 L 1746.5582 2019.5526 L 1741.5349 2017.3998 L 1736.2725 2015.9646 L 1730.5316 2015.0078 L 1724.7907 2014.7686 L 1719.0499 2015.0078 L 1713.5482 2015.9646 L 1708.0465 2017.3998 L 1703.2625 2019.5526 L 1698.7176 2021.9446 L 1695.1296 2024.8151 L 1692.02 2028.1639 L 1689.8671 2031.752 L 1688.4319 2035.34 L
1687.9535 2039.4064 L [0 0 0 0]vc f [0 0 0 1]vc S n 2242.6645 2036.7752 m 2243.1429 2040.6024 L 2244.3389 2044.1905 L 2246.7309 2047.7785 L 2249.6014 2051.1274 L 2253.4286 2053.9978 L 2257.7342 2056.629 L 2262.7575 2058.5426 L 2268.2592 2059.9779 L 2274 2060.9347 L 2279.7409 2061.1739 L 2285.4818 2060.9347 L 2290.9834 2059.9779 L 2296.4851 2058.5426 L 2301.2691 2056.629 L 2305.814 2053.9978 L 2309.402 2051.1274 L 2312.5117 2047.7785 L 2314.6645 2044.1905 L 2316.0997 2040.6024 L 2316.5781 2036.7752 L 2316.0997 2032.948 L 2314.6645 2029.1207 L 2312.5117 2025.5327 L 2309.402 2022.1838 L 2305.814 2019.3134 L 2301.2691 2016.9214 L 2296.4851 2014.7686 L 2290.9834 2013.3333 L 2285.4818 2012.3765 L 2279.7409 2012.1373 L 2274 2012.3765 L 2268.2592 2013.3333 L 2262.7575 2014.7686 L 2257.7342 2016.9214 L 2253.4286 2019.3134 L 2249.6014 2022.1838 L 2246.7309 2025.5327 L 2244.3389 2029.1207 L 2243.1429 2032.948 L 2242.6645 2036.7752 L [0 0 0 0]vc f [0 0 0 1]vc S n 1687.9535 2144.1772 m 1688.4319 2148.2436 L 1689.8671 2151.8317 L 1692.02 2155.4197 L 1695.1296 2158.7686 L 1698.7176 2161.639 L 1703.2625 2164.2702 L
1708.0465 2166.1838 L 1713.5482 2167.6191 L 1719.0499 2168.5759 L 1724.7907 2168.8151 L 1730.5316 2168.5759 L 1736.2725 2167.6191 L 1741.5349 2166.1838 L 1746.5582 2164.2702 L 1750.8638 2161.639 L 1754.6911 2158.7686 L 1757.5615 2155.4197 L 1759.9535 2151.8317 L 1761.1495 2148.2436 L 1761.6279 2144.1772 L 1761.1495 2140.35 L 1759.9535 2136.7619 L 1757.5615 2133.1739 L 1754.6911 2129.825 L 1750.8638 2126.9546 L 1746.5582 2124.3234 L 1741.5349 2122.4098 L 1736.2725 2120.9745 L 1730.5316 2120.0177 L 1724.7907 2119.7785 L 1719.0499 2120.0177 L 1713.5482 2120.9745 L 1708.0465 2122.4098 L 1703.2625 2124.3234 L 1698.7176 2126.9546 L 1695.1296 2129.825 L 1692.02 2133.1739 L 1689.8671 2136.7619 L 1688.4319 2140.35 L 1687.9535 2144.1772 L [0 0 0 0]vc f [0 0 0 1]vc S n 1767.3688 2144.1772 m 1767.8472 2148.2436 L 1769.0432 2151.8317 L 1771.4352 2155.4197 L 1774.3057 2158.7686 L 1778.1329 2161.639 L 1782.4386 2164.2702 L 1787.4618 2166.1838 L 1792.7243 2167.6191 L 1798.4651 2168.5759 L 1804.206 2168.8151 L 1809.9469 2168.5759 L 1815.4485 2167.6191 L 1820.9502 2166.1838 L 1825.7342 2164.2702 L 1830.2791 2161.639 L 1833.8671 2158.7686 L 1836.9768 2155.4197 L 1839.1296 2151.8317 L 1840.5648 2148.2436 L
1841.0432 2144.1772 L 1840.5648 2140.35 L 1839.1296 2136.7619 L 1836.9768 2133.1739 L 1833.8671 2129.825 L 1830.2791 2126.9546 L 1825.7342 2124.3234 L 1820.9502 2122.4098 L 1815.4485 2120.9745 L 1809.9469 2120.0177 L 1804.206 2119.7785 L 1798.4651 2120.0177 L 1792.7243 2120.9745 L 1787.4618 2122.4098 L 1782.4386 2124.3234 L 1778.1329 2126.9546 L 1774.3057 2129.825 L 1771.4352 2133.1739 L 1769.0432 2136.7619 L 1767.8472 2140.35 L 1767.3688 2144.1772 L [0 0 0 0]vc f [0 0 0 1]vc S n 1846.5449 2144.1772 m 1847.0233 2148.2436 L 1848.4585 2151.8317 L 1850.6113 2155.4197 L 1853.721 2158.7686 L 1857.5482 2161.639 L 1861.8538 2164.2702 L 1866.8771 2166.1838 L 1872.1396 2167.6191 L 1877.6412 2168.5759 L 1883.6213 2168.8151 L 1889.6014 2168.5759 L 1895.103 2167.6191 L 1900.3655 2166.1838 L 1905.3887 2164.2702 L 1909.6944 2161.639 L 1913.5216 2158.7686 L 1916.6313 2155.4197 L 1918.7841 2151.8317 L 1919.9801 2148.2436 L 1920.4585 2144.1772 L 1919.9801 2140.35 L 1918.7841 2136.7619 L 1916.6313 2133.1739 L 1913.5216 2129.825 L 1909.6944 2126.9546 L 1905.3887 2124.3234 L 1900.3655 2122.4098 L 1895.103 2120.9745 L 1889.6014 2120.0177 L 1883.6213 2119.7785 L 1877.6412 2120.0177 L 1872.1396 2120.9745 L
1866.8771 2122.4098 L 1861.8538 2124.3234 L 1857.5482 2126.9546 L 1853.721 2129.825 L 1850.6113 2133.1739 L 1848.4585 2136.7619 L 1847.0233 2140.35 L 1846.5449 2144.1772 L [0 0 0 0]vc f [0 0 0 1]vc S n 1926.1994 2144.1772 m 1926.6778 2148.2436 L 1928.113 2151.8317 L 1930.2658 2155.4197 L 1933.1362 2158.7686 L 1936.9635 2161.639 L 1941.5083 2164.2702 L 1946.2924 2166.1838 L 1951.5548 2167.6191 L 1957.2957 2168.5759 L 1963.0366 2168.8151 L 1968.7774 2168.5759 L 1974.5183 2167.6191 L 1979.7808 2166.1838 L 1984.804 2164.2702 L 1989.1097 2161.639 L 1992.9369 2158.7686 L 1995.8073 2155.4197 L 1997.9602 2151.8317 L 1999.3954 2148.2436 L 1999.8738 2144.1772 L 1999.3954 2140.35 L 1997.9602 2136.7619 L 1995.8073 2133.1739 L 1992.9369 2129.825 L 1989.1097 2126.9546 L 1984.804 2124.3234 L 1979.7808 2122.4098 L 1974.5183 2120.9745 L 1968.7774 2120.0177 L 1963.0366 2119.7785 L 1957.2957 2120.0177 L 1951.5548 2120.9745 L 1946.2924 2122.4098 L 1941.5083 2124.3234 L 1936.9635 2126.9546 L 1933.1362 2129.825 L 1930.2658 2133.1739 L 1928.113 2136.7619 L 1926.6778 2140.35 L 1926.1994 2144.1772 L [0 0 0 0]vc f [0 0 0 1]vc S n
2005.6146 2144.1772 m 2006.093 2148.2436 L 2007.2891 2151.8317 L 2009.4419 2155.4197 L 2012.5515 2158.7686 L 2016.3788 2161.639 L 2020.6844 2164.2702 L 2025.7077 2166.1838 L 2030.9701 2167.6191 L 2036.711 2168.5759 L 2042.4519 2168.8151 L 2048.1927 2168.5759 L 2053.6944 2167.6191 L 2059.196 2166.1838 L 2063.9801 2164.2702 L 2068.5249 2161.639 L 2072.113 2158.7686 L 2075.2226 2155.4197 L 2077.3754 2151.8317 L 2078.8107 2148.2436 L 2079.2891 2144.1772 L 2078.8107 2140.35 L 2077.3754 2136.7619 L 2075.2226 2133.1739 L 2072.113 2129.825 L 2068.5249 2126.9546 L 2063.9801 2124.3234 L 2059.196 2122.4098 L 2053.6944 2120.9745 L 2048.1927 2120.0177 L 2042.4519 2119.7785 L 2036.711 2120.0177 L 2030.9701 2120.9745 L 2025.7077 2122.4098 L 2020.6844 2124.3234 L 2016.3788 2126.9546 L 2012.5515 2129.825 L 2009.4419 2133.1739 L 2007.2891 2136.7619 L 2006.093 2140.35 L 2005.6146 2144.1772 L [0 0 0 0]vc f [0 0 0 1]vc S n 2085.5083 2142.9812 m 2085.9867 2146.8084 L 2087.422 2150.6357 L 2089.5748 2154.2237 L 2092.6844 2157.3333 L 2096.5117 2160.443 L 2100.8173 2162.835 L 2105.8406 2164.9878 L 2111.103 2166.423 L 2116.6047 2167.1407 L 2122.3455 2167.6191 L 2128.3256 2167.1407 L 2133.8273 2166.423 L
2139.0897 2164.9878 L 2144.113 2162.835 L 2148.4186 2160.443 L 2152.2459 2157.3333 L 2155.3555 2154.2237 L 2157.5083 2150.6357 L 2158.9435 2146.8084 L 2159.1827 2142.9812 L 2158.9435 2139.1539 L 2157.5083 2135.3267 L 2155.3555 2131.7387 L 2152.2459 2128.629 L 2148.4186 2125.5194 L 2144.113 2123.1274 L 2139.0897 2121.2137 L 2133.8273 2119.5393 L 2128.3256 2118.8217 L 2122.3455 2118.3433 L 2116.6047 2118.8217 L 2111.103 2119.5393 L 2105.8406 2121.2137 L 2100.8173 2123.1274 L 2096.5117 2125.5194 L 2092.6844 2128.629 L 2089.5748 2131.7387 L 2087.422 2135.3267 L 2085.9867 2139.1539 L 2085.5083 2142.9812 L [0 0 0 0]vc f [0 0 0 1]vc S n vmrs 2165.1628 2141.7852 m 2165.6412 2145.6124 L 2166.8372 2149.2005 L 2168.9901 2152.7885 L 2172.0997 2156.1373 L 2175.9269 2159.0078 L 2180.2326 2161.639 L 2185.2558 2163.5526 L 2190.5183 2164.9878 L 2196.2592 2165.9446 L 2202 2166.1838 L 2207.7409 2165.9446 L 2213.2425 2164.9878 L 2218.7442 2163.5526 L 2223.5283 2161.639 L 2228.0731 2159.0078 L 2231.6612 2156.1373 L 2234.7708 2152.7885 L 2236.9236 2149.2005 L 2238.3588 2145.6124 L 2238.8372 2141.7852 L 2238.3588 2137.9579 L 2236.9236 2134.1307 L 2234.7708 2130.5426 L 2231.6612 2127.1938 L
2228.0731 2124.3234 L 2223.5283 2121.9314 L 2218.7442 2119.7785 L 2213.2425 2118.3433 L 2207.7409 2117.3865 L 2202 2117.1473 L 2196.2592 2117.3865 L 2190.5183 2118.3433 L 2185.2558 2119.7785 L 2180.2326 2121.9314 L 2175.9269 2124.3234 L 2172.0997 2127.1938 L 2168.9901 2130.5426 L 2166.8372 2134.1307 L 2165.6412 2137.9579 L 2165.1628 2141.7852 L [0 0 0 0]vc f 0.25 w 1 j [0 0 0 1]vc S n 2242.6645 2141.7852 m 2243.1429 2145.6124 L 2244.3389 2149.2005 L 2246.7309 2152.7885 L 2249.6014 2156.1373 L 2253.4286 2159.0078 L 2257.7342 2161.639 L 2262.7575 2163.5526 L 2268.2592 2164.9878 L 2274 2165.9446 L 2279.7409 2166.1838 L 2285.4818 2165.9446 L 2290.9834 2164.9878 L 2296.4851 2163.5526 L 2301.2691 2161.639 L 2305.814 2159.0078 L 2309.402 2156.1373 L 2312.5117 2152.7885 L 2314.6645 2149.2005 L 2316.0997 2145.6124 L 2316.5781 2141.7852 L 2316.0997 2137.9579 L 2314.6645 2134.1307 L 2312.5117 2130.5426 L 2309.402 2127.1938 L 2305.814 2124.3234 L 2301.2691 2121.9314 L 2296.4851 2119.7785 L 2290.9834 2118.3433 L 2285.4818 2117.3865 L 2279.7409 2117.1473 L 2274 2117.3865 L 2268.2592 2118.3433 L 2262.7575 2119.7785 L 2257.7342 2121.9314 L 2253.4286 2124.3234 L
2249.6014 2127.1938 L 2246.7309 2130.5426 L 2244.3389 2134.1307 L 2243.1429 2137.9579 L 2242.6645 2141.7852 L [0 0 0 0]vc f [0 0 0 1]vc S n 1687.9535 2242.9679 m 1688.4319 2246.7951 L 1689.8671 2250.6224 L 1692.02 2254.2104 L 1695.1296 2257.3201 L 1698.7176 2260.4297 L 1703.2625 2262.8217 L 1708.0465 2264.9745 L 1713.5482 2266.4098 L 1719.0499 2267.1274 L 1724.7907 2267.6058 L 1730.5316 2267.1274 L 1736.2725 2266.4098 L 1741.5349 2264.9745 L 1746.5582 2262.8217 L 1750.8638 2260.4297 L 1754.6911 2257.3201 L 1757.5615 2254.2104 L 1759.9535 2250.6224 L 1761.1495 2246.7951 L 1761.6279 2242.9679 L 1761.1495 2239.1407 L 1759.9535 2235.3134 L 1757.5615 2231.7254 L 1754.6911 2228.6157 L 1750.8638 2225.5061 L 1746.5582 2223.1141 L 1741.5349 2221.2005 L 1736.2725 2219.526 L 1730.5316 2218.8084 L 1724.7907 2218.33 L 1719.0499 2218.8084 L 1713.5482 2219.526 L 1708.0465 2221.2005 L 1703.2625 2223.1141 L 1698.7176 2225.5061 L 1695.1296 2228.6157 L 1692.02 2231.7254 L 1689.8671 2235.3134 L 1688.4319 2239.1407 L 1687.9535 2242.9679 L [0 0 0 0]vc f [0 0 0 1]vc S n 1767.3688 2242.9679 m 1767.8472 2246.7951 L 1769.0432 2250.6224 L
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dup (\034) search { length exch pop exch dup length 0 ne { dup dup 0 get 32 sub 0 exch put /cntr cntr 1 add def } { pop 1 string dup 0 6 index read pop 32 sub put }ifelse 3 copy putinterval pop 1 add 1 index length 1 sub 1 index sub dup 0 le {pop pop exit}if getinterval } { pop exit } ifelse } loop }if cntr 0 gt { pop 2 copy dup length cntr sub cntr getinterval readbinarystring } if pop exch pop } bdf / /_NXLevel2 defed { _ _NXLevel2 not { /colorimage where { userdict eq { / /_rci false def } if } if } if } if / /md defed{ m md type /dicttype eq { / /colorimage where { m md eq { / /_rci false def }if }if /settransfer where { md eq { /st systemdict /settransfer get def }if }if }if }if /setstrokeadjust defed {
true setstrokeadjust /C{curveto}bdf /L{lineto}bdf /m{moveto}bdf } { /dr{transform .25 sub round .25 add exch .25 sub round .25 add exch itransform}bdf /C{dr curveto}bdf /L{dr lineto}bdf /m{dr moveto}bdf / /setstrokeadjust{pop}bdf }ifelse / /privrectpath { 4 -2 roll m d dtransform round exch round exch idtransform 2 copy 0 lt exch 0 lt xor {dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto} {exch dup 0 rlineto exch 0 exch rlineto neg 0 rlineto} ifelse closepath }bdf /rectclip{newpath privrectpath clip newpath}def /rectfill{gsave newpath privrectpath fill grestore}def /rectstroke{gsave newpath privrectpath stroke grestore}def /_fonthacksave false def /currentpacking defed { /_bfh {/_fonthacksave currentpacking def false setpacking} bdf /_efh {_fonthacksave setpacking} bdf } { /_bfh {} bdf /_efh {} bdf }ifelse /packedarray{array astore readonly}ndf / /` { f false setoverprint /-save0- save def 5 index concat pop storerect left bottom width height rectclip pop /MMdict_count countdictstack def /MMop_count count 1 sub def userdict begin /showpage {} def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash newpath } bdf /currentpacking defed{true setpacking}if /min{2 copy gt{exch}if pop}bdf /max{2 copy lt{exch}if pop}bdf /xformfont { currentfont exch makefont setfont } bdf /fhnumcolors 1 statusdict begin /processcolors defed {
pop processcolors } { /deviceinfo defed { deviceinfo /Colors known { pop deviceinfo /Colors get } if } if } ifelse end def % pix = x^2 + y^2 /printerRes gsave matrix defaultmatrix setmatrix 72 72 dtransform abs exch abs max grestore def /graycalcs [ { {Angle Frequency} { {GrayAngle GrayFrequency} {0 Width Height matrix defaultmatrix idtransform d dup mul exch dup mul add sqrt 72 exch div} {0 GrayWidth GrayHeight matrix defaultmatrix idtransform d dup mul exch dup mul add sqrt 72 exch div} ] def /calcgraysteps { forcemaxsteps { maxsteps } { /currenthalftone defed {currenthalftone /dicttype eq}{false}ifelse { currenthalftone begin HalftoneType 4 le {graycalcs HalftoneType 1 sub get exec} { HalftoneType 5 eq { Default begin {graycalcs HalftoneType 1 sub get exec} end } { {0 60} ifelse } ifelse end } { c currentscreen pop exch } ifelse p printerRes 300 max exch div exch
2 copy s sin mul round dup mul 3 1 roll c cos mul round dup mul a add 1 add d dup maxsteps gt {pop maxsteps} if d dup minsteps lt {pop minsteps} if } ifelse } bdf / /nextrelease defed { / /languagelevel defed not { / /framebuffer defed { 0 40 string framebuffer 9 1 roll 8 {pop} repeat dup 516 eq exch 520 eq or { /fhnumcolors 3 def /currentscreen {60 0 {pop pop 1}}bdf /calcgraysteps {maxsteps} bdf }if }if }if }if fhnumcolors 1 ne { /calcgraysteps {maxsteps} bdf } if /currentpagedevice defed { currentpagedevice /PreRenderingEnhance known { currentpagedevice /PreRenderingEnhance get { /calcgraysteps { forcemaxsteps {maxsteps} {256 maxsteps min} ifelse } def } if } if } if /gradfrequency 144 def printerRes 1000 lt { /gradfrequency 72 def } if /adjnumsteps { dup dtransform abs exch abs max printerRes div gradfrequency mul round 5 max min }bdf /goodsep { spots exch get 4 get dup sepname eq exch (_vc_Registration) eq or }bdf /BeginGradation defed {/bb{BeginGradation}bdf} {/bb{}bdf}
ifelse /EndGradation defed {/eb{EndGradation}bdf} {/eb{}bdf} ifelse / /bottom -0 def / /delta -0 def / /frac -0 def / /height -0 def / /left -0 def / /numsteps1 -0 def / /radius -0 def / /right -0 def / /top -0 def / /width -0 def / /xt -0 def / /yt -0 def / /df currentflat def / /tempstr 1 string def / /clipflatness currentflat def / /inverted? 0 currenttransfer exec .5 ge def / /tc1 [0 0 0 1] def / /tc2 [0 0 0 1] def /storerect{/top xdf /right xdf /bottom xdf /left xdf /width right left sub def /height top bottom sub def}bdf /concatprocs{ systemdict /packedarray known {dup type /packedarraytype eq 2 index type /packedarraytype eq or}{false}ifelse { /proc2 exch cvlit def /proc1 exch cvlit def proc1 aload pop proc2 aload pop proc1 length proc2 length add packedarray cvx } { /proc2 exch cvlit def /proc1 exch cvlit def /newproc proc1 length proc2 length add array def newproc 0 proc1 putinterval newproc proc1 length proc2 putinterval newproc cvx }ifelse }bdf /i{dup 0 eq { {pop df dup} {dup} ifelse /clipflatness xdf setflat }bdf version cvr 38.0 le {/setrgbcolor{ currenttransfer exec 3 1 roll currenttransfer exec 3 1 roll currenttransfer exec 3 1 roll setrgbcolor}bdf}if /vms {/vmsv save def} bdf /vmr {vmsv restore} bdf /vmrs{vmsv restore /vmsv save def}bdf /eomode{ {/filler /eofill load def /clipper /eoclip load def} {/filler /fill load def /clipper /clip load def} ifelse
}bdf /normtaper{}bdf /logtaper{9 mul 1 add log}bdf /CD{ / /NF exch def { e exch dup /FID ne 1 index/UniqueID ne and {exch NF 3 1 roll put} {pop pop} ifelse }forall NF }bdf /MN{ 1 index length /Len exch def d dup length Len add s string dup L Len 4 -1 roll p putinterval d dup 0 4 -1 roll p putinterval }bdf /RC{4 -1 roll /ourvec xdf 256 string cvs(|______)anchorsearch {1 index MN cvn/NewN exch def cvn findfont dup maxlength dict CD dup/FontName NewN put dup /Encoding ourvec put NewN exch definefont pop}{pop}ifelse}bdf / /RF{ d dup F FontDirectory exch k known { {pop 3 -1 roll pop} {RC} ifelse }bdf /FF{dup 256 string cvs(|______)exch MN cvn dup FontDirectory exch known {exch pop findfont 3 -1 roll pop} {pop dup findfont dup maxlength dict CD dup dup /Encoding exch /Encoding get 256 array copy 7 -1 roll {3 -1 roll dup 4 -2 roll put}forall put definefont} ifelse}bdf / /RCJ{4 -1 roll / /ourvec xdf 2 256 string cvs (|______) anchorsearch { {pop c cvn d dup FDFJ exch 1 index e eq { _ _bfh findfont _efh d dup m maxlength dict
C CD d dup / /FontName 3 index p put d dup / /Encoding ourvec put 1 index e exch d definefont p pop } { {exch pop} ifelse } { {pop} ifelse }bdf / /RFJ{ d dup F FontDirectory exch k known { {pop 3 -1 roll pop} {RCJ} ifelse }bdf /hasfont { / /resourcestatus where { p pop /Font resourcestatus { pop pop true } { false } ifelse } { dup FontDirectory exch known {pop true} { 256 string cvs (fonts/) exch MN status {pop pop pop pop true} {false} ifelse } ifelse } ifelse }bdf /FDFJ { d dup
h hasfont n not { pop /Ryumin-Light-83pv-RKSJ-H h hasfont { /Ryumin-Light-83pv-RKSJ-H } { /Courier } i ifelse } if }bdf /FFJ{ _bfh d dup 2 256 string cvs ( (|______)exch MN c cvn d dup FontDirectory e exch known { e exch p pop f findfont 3 -1 roll p pop } { p pop F FDFJ d dup findfont d dup maxlength dict C CD d dup dup / /Encoding exch / /Encoding get 2 256 array copy 7 -1 roll { 3 -1 roll d dup 4 -2 roll p put }forall p put d definefont } ifelse _efh }bdf /GS { dup hasfont {
findfont exch makesetfont exch pop ts } { pop pop pop ts } ifelse } bdf / /RCK{4 -1 roll / /ourvec xdf 2 256 string cvs (|______) anchorsearch { {pop c cvn d dup FDFK exch 1 index e eq { _ _bfh findfont _efh d dup m maxlength dict C CD d dup / /FontName 3 index p put d dup / /Encoding ourvec put 1 index e exch d definefont p pop } { {exch pop} ifelse } { {pop} ifelse }bdf / /RFK{ d dup F FontDirectory exch k known { {pop 3 -1 roll pop} {RCK} ifelse }bdf /hasfont { / /resourcestatus where { p pop /Font resourcestatus { pop pop true
} { false } ifelse } { dup FontDirectory exch known {pop true} { 256 string cvs (fonts/) exch MN status {pop pop pop pop true} {false} ifelse } ifelse } ifelse }bdf /FDFK { d dup h hasfont n not { pop /JCsm h hasfont { /JCsm } { /Courier } i ifelse } if }bdf /FFK{ _bfh d dup 2 256 string cvs ( (|______)exch MN c cvn d dup FontDirectory e exch known { e exch p pop f findfont 3 -1 roll p pop } { p pop
F FDFK d dup findfont d dup maxlength dict C CD d dup dup / /Encoding exch / /Encoding get 2 256 array copy 7 -1 roll { 3 -1 roll d dup 4 -2 roll p put }forall p put d definefont } ifelse _efh }bdf / /RCTC{4 -1 roll / /ourvec xdf 2 256 string cvs (|______) anchorsearch { {pop c cvn d dup FDFTC exch 1 index e eq { _ _bfh findfont _efh d dup m maxlength dict C CD d dup / /FontName 3 index p put d dup / /Encoding ourvec put 1 index e exch d definefont p pop } { {exch pop} ifelse } { {pop} ifelse }bdf / /RFTC{ d dup F FontDirectory exch k known { {pop 3 -1 roll pop} {RCTC}
ifelse }bdf /FDFTC { d dup h hasfont n not { pop /DFMing-Lt-HK-BF h hasfont { /DFMing-Lt-HK-BF } { /Courier } i ifelse } if }bdf /FFTC{ _bfh d dup 2 256 string cvs ( (|______)exch MN c cvn d dup FontDirectory e exch known { e exch p pop f findfont 3 -1 roll p pop } { p pop F FDFTC d dup findfont d dup maxlength dict C CD d dup dup / /Encoding exch / /Encoding get 2 256 array copy 7 -1 roll { 3 -1 roll d dup 4 -2 roll p put }forall p put d definefont } ifelse _efh
}bdf /fps{ c currentflat e exch d dup 0 le{pop 1}if { dup setflat 3 index stopped { {1.3 mul dup 3 index gt{pop setflat pop pop stop}if} { {exit} ifelse }loop pop setflat pop pop }bdf /fp{100 currentflat fps}bdf / /clipper{clip}bdf /W{/clipper load 100 clipflatness dup setflat fps}bdf /AVec 256 array def AVec 0 /Helvetica findfont /Encoding get 0 256 getinterval putinterval /ANSIPatch[ 16#0/grave 16#1/acute 16#2/circumflex 16#3/tilde 16#4/macron 16#5/breve 16#6/dotaccent 16#7/dieresis 16#8/ring 16#9/cedilla 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase 16#83/florin 16#84/quotedblbase 16#85 /ellipsis 16#86/dagger 16#87/daggerdbl 16#89/perthousand 16#8A/Scaron 16#8B/guilsinglleft 16#8C/OE 16#91/quoteleft 16#92/quoteright 16#93 /quotedblleft 16#94/quotedblright 16#95/bullet 16#96/endash 16#97/emdash 16#99/trademark 16#9A/scaron 16#9B/guilsinglright 16#9C/oe 16#9F/Ydieresis 16#A0/space 16#A4/currency 16#A6/brokenbar 16#A7/section 16#A8/dieresis 16#A9/copyright 16#AA/ordfeminine 16#AB/guillemotleft 16#AC/logicalnot 16#AD/hyphen 16#AE/registered 16#AF/macron 16#B0/degree 16#B1/plusminus 16#B2/twosuperior 16#B3/threesuperior 16#B4/acute 16#B5/mu 16#B6/paragraph 16#B7/periodcentered 16#B8/cedilla 16#B9/onesuperior 16#BA/ordmasculine 16#BB/guillemotright 16#BC/onequarter 16#BD/onehalf 16#BE/threequarters 16#BF/questiondown 16#C0/Agrave 16#C1/Aacute 16#C2/Acircumflex 16#C3/Atilde 16#C4/Adieresis 16#C5/Aring 16#C6/AE 16#C7/Ccedilla 16#C8/Egrave 16#C9/Eacute 16#CA/Ecircumflex 16#CB/Edieresis 16#CC/Igrave 16#CD/Iacute 16#CE/Icircumflex 16#CF/Idieresis 16#D0/Eth 16#D1/Ntilde 16#D2/Ograve 16#D3/Oacute 16#D4/Ocircumflex 16#D5/Otilde 16#D6/Odieresis 16#D7/multiply 16#D8/Oslash 16#D9/Ugrave 16#DA/Uacute 16#DB/Ucircumflex 16#DC/Udieresis 16#DD/Yacute 16#DE/Thorn 16#DF/germandbls 16#E0/agrave 16#E1/aacute 16#E2/acircumflex 16#E3/atilde 16#E4/adieresis 16#E5/aring 16#E6/ae 16#E7/ccedilla 16#E8/egrave 16#E9/eacute 16#EA/ecircumflex 16#EB/edieresis 16#EC/igrave 16#ED/iacute 16#EE/icircumflex 16#EF/idieresis 16#F0/eth 16#F1/ntilde 16#F2/ograve 16#F3/oacute 16#F4/ocircumflex 16#F5/otilde 16#F6/odieresis 16#F7/divide 16#F8/oslash 16#F9/ugrave 16#FA/uacute 16#FB/ucircumflex 16#FC/udieresis 16#FD/yacute 16#FE/thorn 16#FF/ydieresis ] def 127 1 159 { AVec exch/bullet put } for ANSIPatch aload pop ANSIPatch length 2 idiv{AVec 3 1 roll put}repeat /DoPatch { dup /CharStrings known { setfont 0 1 255 { dup currentfont /Encoding get exch get currentfont /CharStrings get exch known {pop} {currentfont /Encoding get exch /bullet put} ifelse
} for } {pop} ifelse } def /findheaderfont { AVec 256 array copy /FHT /|______Helvetica dup RF findfont def FHT DoPatch FHT } def end %. AltsysDict %%EndResource %%EndProlog %%BeginSetup AltsysDict begin _ _bfh _ _efh end %. AltsysDict %%EndSetup A AltsysDict begin /onlyk4{false}ndf /ccmyk{dup 5 -1 roll sub 0 max exch}ndf /cmyk2gray{ 4 -1 roll 0.3 mul 4 -1 roll 0.59 mul 4 -1 roll 0.11 mul add add add 1 min neg 1 add }bdf /setcmykcolor{1 exch sub ccmyk ccmyk ccmyk pop setrgbcolor}ndf /maxcolor { m max max max } ndf /maxspot { pop } ndf /setcmykcoloroverprint{4{dup -1 eq{pop 0}if 4 1 roll}repeat setcmykcolor}ndf /findcmykcustomcolor{5 packedarray}ndf /setcustomcolor{exch aload pop pop 4{4 index mul 4 1 roll}repeat setcmykcolor pop}ndf /setseparationgray{setgray}ndf / /setoverprint{pop}ndf /currentoverprint false ndf /cmykbufs2gray{ 0 1 2 index length 1 sub { 4 index 1 index get 0 0.3 mul 4 index 2 index get 0 0.59 mul 4 index 3 index get 0 0.11 mul 4 index 4 index get add add add cvi 255 min 255 exch sub 2 index 3 1 roll put }for 4 1 roll pop pop pop }bdf /colorimage{ pop pop [ 5 -1 roll/exec cvx 6 -1 roll/exec cvx 7 -1 roll/exec cvx 8 -1 roll/exec cvx
/cmykbufs2gray cvx ]cvx image } %. version 47.1 on Linotronic of Postscript defines colorimage incorrectly (rgb model only) version cvr 47.1 le statusdict /product get (Lino) anchorsearch{pop pop true}{pop false}ifelse and{userdict begin bdf end}{ndf}ifelse fhnumcolors 1 ne {/yt save def} if /customcolorimage{ aload pop (_vc_Registration) eq { pop pop pop pop separationimage } { /ik xdf /iy xdf /im xdf /ic xdf ic im iy ik cmyk2gray /xt xdf currenttransfer {dup 1.0 exch sub xt mul add}concatprocs st image } ifelse }ndf fhnumcolors 1 ne {yt restore} if fhnumcolors 3 ne {/yt save def} if /customcolorimage{ aload pop (_vc_Registration) eq { pop pop pop pop separationimage } { /ik xdf /iy xdf /im xdf /ic xdf 1 1.0 dup ic ik add min sub 1 1.0 dup im ik add min sub 1 1.0 dup iy ik add min sub /ic xdf /iy xdf /im xdf currentcolortransfer 4 1 roll { {dup 1.0 exch sub ic mul add}concatprocs 4 1 roll { {dup 1.0 exch sub iy mul add}concatprocs 4 1 roll { {dup 1.0 exch sub im mul add}concatprocs 4 1 roll setcolortransfer {/dummy xdf dummy}concatprocs{dummy}{dummy}true 3 colorimage } ifelse }ndf fhnumcolors 3 ne {yt restore} if fhnumcolors 4 ne {/yt save def} if /customcolorimage{ aload pop (_vc_Registration) eq { pop pop pop pop separationimage } {
/ik xdf /iy xdf /im xdf /ic xdf currentcolortransfer {1.0 exch sub ik mul ik sub 1 add}concatprocs 4 1 roll {1.0 exch sub iy mul iy sub 1 add}concatprocs 4 1 roll {1.0 exch sub im mul im sub 1 add}concatprocs 4 1 roll {1.0 exch sub ic mul ic sub 1 add}concatprocs 4 1 roll setcolortransfer {/dummy xdf dummy}concatprocs{dummy}{dummy}{dummy} true 4 colorimage } ifelse }ndf fhnumcolors 4 ne {yt restore} if /separationimage{image}ndf /spotascmyk false ndf /newcmykcustomcolor{6 packedarray}ndf /inkoverprint false ndf / /setinkoverprint{pop}ndf / /setspotcolor { spots exch get dup 4 get (_vc_Registration) eq {pop 1 exch sub setseparationgray} {0 5 getinterval exch setcustomcolor} ifelse }ndf /currentcolortransfer{currenttransfer dup dup dup}ndf /setcolortransfer{st pop pop pop}ndf /fas{}ndf /sas{}ndf /fhsetspreadsize{pop}ndf / /filler{fill}bdf /F{gsave {filler}fp grestore}bdf /f{closepath F}bdf /S{gsave {stroke}fp grestore}bdf /s{closepath S}bdf userdict /islevel2 systemdict /languagelevel known dup { pop systemdict /languagelevel get 2 ge } if put islevel2 not { /currentcmykcolor { 0 0 0 1 currentgray sub } ndf } if /tc { gsave setcmykcolor currentcmykcolor grestore } bind def /testCMYKColorThrough { tc add add add 0 ne } bind def /fhiscomposite where not {
userdict /fhiscomposite islevel2 { gsave 1 1 1 1 setcmykcolor currentcmykcolor grestore add add add 4 eq } { 1 0 0 0 testCMYKColorThrough 0 1 0 0 testCMYKColorThrough 0 0 1 0 testCMYKColorThrough 0 0 0 1 testCMYKColorThrough and and and } ifelse put } { pop } ifelse / /bc4 [0 0 0 0] def /_lfp4 { 1 pop / /yt xdf / /xt xdf / /ang xdf storerect /taperfcn xdf /k2 xdf /y2 xdf /m2 xdf /c2 xdf /k1 xdf /y1 xdf /m1 xdf /c1 xdf c1 c2 sub abs m1 m2 sub abs y1 y2 sub abs k1 k2 sub abs m maxcolor c calcgraysteps mul abs round h height abs adjnumsteps d dup 1 lt {pop 1} if 1 sub /numsteps1 xdf c currentflat mark c currentflat clipflatness / /delta top bottom sub numsteps1 1 add div def / /right right left sub def / /botsv top delta sub def { { W xt yt translate ang rotate xt neg yt neg translate d dup setflat /bottom botsv def 0 1 numsteps1 { numsteps1 dup 0 eq {pop pop 0.5} {div} ifelse taperfcn /frac xdf bc4 0 c2 c1 sub frac mul c1 add put bc4 1 m2 m1 sub frac mul m1 add put bc4 2 y2 y1 sub frac mul y1 add put bc4 3 k2 k1 sub frac mul k1 add put bc4 vc 1 index setflat
{ mark {newpath left bottom right delta rectfill}stopped {cleartomark exch 1.3 mul dup setflat exch 2 copy gt{stop}if} {cleartomark exit}ifelse }loop /bottom bottom delta sub def }for } gsave stopped grestore {exch pop 2 index exch 1.3 mul dup 100 gt{cleartomark setflat stop}if} {exit}ifelse }loop cleartomark setflat }bdf / /bcs [0 0] def /_lfs4 { / /yt xdf / /xt xdf / /ang xdf storerect /taperfcn xdf / /tint2 xdf / /tint1 xdf b bcs exch 1 exch put t tint1 tint2 sub abs b bcs 1 get maxspot c calcgraysteps mul abs round h height abs adjnumsteps d dup 2 lt {pop 2} if 1 sub /numsteps1 xdf c currentflat mark c currentflat clipflatness / /delta top bottom sub numsteps1 1 add div def / /right right left sub def / /botsv top delta sub def { { W xt yt translate ang rotate xt neg yt neg translate d dup setflat /bottom botsv def 0 1 numsteps1 { numsteps1 div taperfcn /frac xdf bcs 0 1.0 tint2 tint1 sub frac mul tint1 add sub put bcs vc 1 index setflat { mark {newpath left bottom right delta rectfill}stopped {cleartomark exch 1.3 mul dup setflat exch 2 copy gt{stop}if} {cleartomark exit}ifelse }loop /bottom bottom delta sub def }for } gsave stopped grestore
{exch pop 2 index exch 1.3 mul dup 100 gt{cleartomark setflat stop}if} {exit}ifelse }loop cleartomark setflat }bdf /_rfs6 { / /tint2 xdf / /tint1 xdf b bcs exch 1 exch put / /inrad xdf / /radius xdf / /yt xdf / /xt xdf t tint1 tint2 sub abs b bcs 1 get maxspot c calcgraysteps mul abs round r radius inrad sub abs a adjnumsteps d dup 1 lt {pop 1} if 1 sub /numsteps1 xdf r radius inrad sub numsteps1 dup 0 eq {pop} {div} ifelse 2 div /halfstep xdf c currentflat mark c currentflat clipflatness { { d dup setflat W 0 1 numsteps1 { dup /radindex xdf numsteps1 dup 0 eq {pop pop 0.5} {div} ifelse /frac xdf bcs 0 tint2 tint1 sub frac mul tint1 add put bcs vc 1 index setflat { n newpath mark xt yt radius inrad sub 1 frac sub mul halfstep add inrad add 0 360 { arc radindex numsteps1 ne i inrad 0 gt or { x xt yt numsteps1 0 eq { inrad } { radindex 1 add numsteps1 div 1 exch sub radius inrad sub mul halfstep add inrad add }ifelse dup xt add yt moveto 360 0 arcn } if fill }stopped {cleartomark exch 1.3 mul dup setflat exch 2 copy gt{stop}if} {cleartomark exit}ifelse }loop
}for } gsave stopped grestore {exch pop 2 index exch 1.3 mul dup 100 gt{cleartomark setflat stop}if} {exit}ifelse }loop cleartomark setflat }bdf /_rfp6 { 1 pop /k2 xdf /y2 xdf /m2 xdf /c2 xdf /k1 xdf /y1 xdf /m1 xdf /c1 xdf / /inrad xdf / /radius xdf / /yt xdf / /xt xdf c1 c2 sub abs m1 m2 sub abs y1 y2 sub abs k1 k2 sub abs m maxcolor c calcgraysteps mul abs round r radius inrad sub abs a adjnumsteps d dup 1 lt {pop 1} if 1 sub /numsteps1 xdf r radius inrad sub numsteps1 dup 0 eq {pop} {div} ifelse 2 div /halfstep xdf c currentflat mark c currentflat clipflatness { { d dup setflat W 0 1 numsteps1 { dup /radindex xdf numsteps1 dup 0 eq {pop pop 0.5} {div} ifelse /frac xdf bc4 0 c2 c1 sub frac mul c1 add put bc4 1 m2 m1 sub frac mul m1 add put bc4 2 y2 y1 sub frac mul y1 add put bc4 3 k2 k1 sub frac mul k1 add put bc4 vc 1 index setflat { n newpath mark xt yt radius inrad sub 1 frac sub mul halfstep add inrad add 0 360 { arc radindex numsteps1 ne i inrad 0 gt or { x xt yt numsteps1 0 eq { inrad } { radindex 1 add numsteps1 div 1 exch sub radius inrad sub mul halfstep add inrad add }ifelse
dup xt add yt moveto 360 0 arcn } if fill }stopped {cleartomark exch 1.3 mul dup setflat exch 2 copy gt{stop}if} {cleartomark exit}ifelse }loop }for } gsave stopped grestore {exch pop 2 index exch 1.3 mul dup 100 gt{cleartomark setflat stop}if} {exit}ifelse }loop cleartomark setflat }bdf /lfp4{_lfp4}ndf /lfs4{_lfs4}ndf /rfs6{_rfs6}ndf /rfp6{_rfp6}ndf / /cvc [0 0 0 1] def /vc{ A AltsysDict /cvc 2 index put aload length dup 4 eq {pop dup -1 eq{pop setrgbcolor}{setcmykcolor}ifelse} {6 eq {sethexcolor} {setspotcolor} ifelse } ifelse } }bdf 0 setseparationgray / /imgr {-16128 -16128 16128 16128 } def / /bleed 0 def / /clpr {-16128 -16128 -144 -144 } def / /xs 1 def / /ys 1 def / /botx 0 def / /overlap 0 def / /wdist 18 def 0 2 mul fhsetspreadsize 0 0 ne {/df 0 def /clipflatness 0 def} if / /maxsteps 256 def / /forcemaxsteps false def / /minsteps 0 def userdict begin /AGDOrigMtx matrix currentmatrix def end vms -1812 -2013 translate / /currentpacking defed{false setpacking}if /spots[ 1 0 0 0 (Process Cyan) false newcmykcustomcolor 0 1 0 0 (Process Magenta) false newcmykcustomcolor 0 0 1 0 (Process Yellow) false newcmykcustomcolor 0 0 0 1 (Process Black) false newcmykcustomcolor ]def n [] 0 d 3.863708 M 1 w 0 j 0 J false setoverprint
0 i false eomode [0 0 0 1]vc vms 1900.1663 2130.0093 m 1978.6248 2208.707 L 1926.7178 2208.707 L 1926.7178 2305.1057 L 1873.3756 2305.1057 L 1873.3756 2208.707 L 1821.4686 2208.707 L 1900.1663 2130.0093 L [1 0 1 0]vc f 0.25 w 1 j [0 0 0 1]vc S n 2088.8972 2130.0093 m 2162.8108 2203.9229 L 2114.0135 2203.9229 L 2114.0135 2306.3017 L 2063.7809 2306.3017 L 2063.7809 2203.9229 L 2014.9836 2203.9229 L 2088.8972 2130.0093 L [0 0 0 0]vc f [0 0 0 1]vc S n 2040.5782 2120.202 m 2050.6248 2214.2086 L 2016.4188 2186.4611 L 1932.2194 2290.9927 L 1896.8175 2262.5276 L 1980.7776 2157.996 L 1946.3324 2130.2485 L 2040.5782 2120.202 L [0 0 0 0]vc f [0 0 0 1]vc S n 1953.0301 2118.0492 m 2027.4221 2130.0093 L 1998.957 2150.5807 L 2103.7278 2295.7768 L 2074.3058 2317.0658 L 1969.2959 2171.8698 L 1940.8307 2192.4412 L 1953.0301 2118.0492 L [1 0 1 0]vc f [0 0 0 1]vc S n 1812.6181 2071.6439 m
1813.0965 2077.3847 L 1814.2925 2083.3648 L 1816.4454 2089.1057 L 1819.555 2094.6073 L 1823.6214 2099.8698 L 1828.1663 2104.893 L 1833.6679 2109.4379 L 1839.8872 2113.7435 L 1846.5849 2117.81 L 1853.761 2121.1588 L 1861.6547 2124.0292 L 1869.7876 2126.1821 L 1878.1596 2128.0957 L 1886.7709 2129.2917 L 1895.6214 2129.7701 L 1904.4719 2129.7701 L 1913.3224 2129.2917 L 1922.1729 2128.0957 L 1930.545 2126.1821 L 1938.6779 2124.0292 L 1946.3324 2121.1588 L 1953.7477 2117.81 L 1960.4454 2113.7435 L 1966.6646 2109.4379 L 1971.9271 2104.893 L 1976.7111 2099.8698 L 1980.5384 2094.6073 L 1983.648 2089.1057 L 1985.8008 2083.3648 L 1987.2361 2077.3847 L 1987.7145 2071.6439 L 1987.2361 2065.6638 L 1985.8008 2059.6837 L 1983.648 2053.9429 L 1980.5384 2048.4412 L 1976.7111 2043.1787 L 1971.9271 2038.1555 L 1966.6646 2033.6106 L 1960.4454 2029.305 L 1953.7477 2025.4778 L 1946.3324 2021.8897 L 1938.6779 2019.0193 L 1930.545 2016.8665 L 1922.1729 2014.9528 L 1913.3224 2013.7568 L 1904.4719 2013.2784 L 1895.6214 2013.2784 L 1886.7709 2013.7568 L 1878.1596 2014.9528 L 1869.7876 2016.8665 L 1861.6547 2019.0193 L 1853.761 2021.8897 L 1846.5849 2025.4778 L 1839.8872 2029.305 L 1833.6679 2033.6106 L 1828.1663 2038.1555 L 1823.6214 2043.1787 L 1819.555 2048.4412 L 1816.4454 2053.9429 L
1814.2925 2059.6837 L 1813.0965 2065.6638 L 1812.6181 2071.6439 L [0 0 0 0]vc f [0 0 0 1]vc S n 2001.349 2071.6439 m 2001.8274 2077.3847 L 2003.2626 2083.3648 L 2005.4155 2089.1057 L 2008.5251 2094.6073 L 2012.3523 2099.8698 L 2017.1364 2104.893 L 2022.3988 2109.4379 L 2028.6181 2113.7435 L 2035.3158 2117.81 L 2042.7311 2121.1588 L 2050.3856 2124.0292 L 2058.5184 2126.1821 L 2066.8905 2128.0957 L 2075.741 2129.2917 L 2084.5915 2129.7701 L 2093.442 2129.7701 L 2102.2925 2129.2917 L 2110.9038 2128.0957 L 2119.2759 2126.1821 L 2127.4088 2124.0292 L 2135.3025 2121.1588 L 2142.4786 2117.81 L 2149.1763 2113.7435 L 2155.3955 2109.4379 L 2160.8972 2104.893 L 2165.442 2099.8698 L 2169.5085 2094.6073 L 2172.6181 2089.1057 L 2174.7709 2083.3648 L 2175.967 2077.3847 L 2176.4454 2071.6439 L 2175.967 2065.6638 L 2174.7709 2059.6837 L 2172.6181 2053.9429 L 2169.5085 2048.4412 L 2165.442 2043.1787 L 2160.8972 2038.1555 L 2155.3955 2033.6106 L 2149.1763 2029.305 L 2142.4786 2025.4778 L 2135.3025 2021.8897 L 2127.4088 2019.0193 L 2119.2759 2016.8665 L 2110.9038 2014.9528 L 2102.2925 2013.7568 L 2093.442 2013.2784 L 2084.5915 2013.2784 L 2075.741 2013.7568 L 2066.8905 2014.9528 L 2058.5184 2016.8665 L
2050.3856 2019.0193 L 2042.7311 2021.8897 L 2035.3158 2025.4778 L 2028.6181 2029.305 L 2022.3988 2033.6106 L 2017.1364 2038.1555 L 2012.3523 2043.1787 L 2008.5251 2048.4412 L 2005.4155 2053.9429 L 2003.2626 2059.6837 L 2001.8274 2065.6638 L 2001.349 2071.6439 L [0 0 0 0]vc f [0 0 0 1]vc S n 1812.6181 2305.1057 m 1813.0965 2311.0857 L 1814.2925 2316.8266 L 1816.4454 2322.5675 L 1819.555 2328.0691 L 1823.6214 2333.5708 L 1828.1663 2338.594 L 1833.6679 2343.1389 L 1839.8872 2347.4445 L 1846.5849 2351.2718 L 1853.761 2354.6206 L 1861.6547 2357.491 L 1869.7876 2359.8831 L 1878.1596 2361.5575 L 1886.7709 2362.7535 L 1895.6214 2363.4711 L 1904.4719 2363.4711 L 1913.3224 2362.7535 L 1922.1729 2361.5575 L 1930.545 2359.8831 L 1938.6779 2357.491 L 1946.3324 2354.6206 L 1953.7477 2351.2718 L 1960.4454 2347.4445 L 1966.6646 2343.1389 L 1971.9271 2338.594 L 1976.7111 2333.5708 L 1980.5384 2328.0691 L 1983.648 2322.5675 L 1985.8008 2316.8266 L 1987.2361 2311.0857 L 1987.7145 2305.1057 L 1987.2361 2299.1256 L 1985.8008 2293.3847 L 1983.648 2287.6439 L 1980.5384 2282.1422 L 1976.7111 2276.8797 L 1971.9271 2271.8565 L 1966.6646 2267.0724 L 1960.4454 2262.7668 L 1953.7477 2258.9395 L 1946.3324 2255.5907 L
1938.6779 2252.7203 L 1930.545 2250.3282 L 1922.1729 2248.6538 L 1913.3224 2247.4578 L 1904.4719 2246.7402 L 1895.6214 2246.7402 L 1886.7709 2247.4578 L 1878.1596 2248.6538 L 1869.7876 2250.3282 L 1861.6547 2252.7203 L 1853.761 2255.5907 L 1846.5849 2258.9395 L 1839.8872 2262.7668 L 1833.6679 2267.0724 L 1828.1663 2271.8565 L 1823.6214 2276.8797 L 1819.555 2282.1422 L 1816.4454 2287.6439 L 1814.2925 2293.3847 L 1813.0965 2299.1256 L 1812.6181 2305.1057 L [0 0 0 0]vc f [0 0 0 1]vc S n 2001.349 2306.3017 m 2001.8274 2312.2817 L 2003.2626 2318.2618 L 2005.4155 2324.0027 L 2008.5251 2329.5043 L 2012.3523 2334.7668 L 2017.1364 2339.79 L 2022.3988 2344.3349 L 2028.6181 2348.6405 L 2035.3158 2352.4678 L 2042.7311 2356.0558 L 2050.3856 2358.9263 L 2058.5184 2361.0791 L 2066.8905 2362.9927 L 2075.741 2364.1887 L 2084.5915 2364.6671 L 2093.442 2364.6671 L 2102.2925 2364.1887 L 2110.9038 2362.9927 L 2119.2759 2361.0791 L 2127.4088 2358.9263 L 2135.3025 2356.0558 L 2142.4786 2352.4678 L 2149.1763 2348.6405 L 2155.3955 2344.3349 L 2160.8972 2339.79 L 2165.442 2334.7668 L 2169.5085 2329.5043 L 2172.6181 2324.0027 L 2174.7709 2318.2618 L 2175.967 2312.2817 L 2176.4454 2306.3017 L 2175.967 2300.5608 L
2174.7709 2294.5807 L 2172.6181 2288.8399 L 2169.5085 2283.3382 L 2165.442 2278.0758 L 2160.8972 2273.0525 L 2155.3955 2268.5077 L 2149.1763 2264.202 L 2142.4786 2260.1356 L 2135.3025 2256.7867 L 2127.4088 2253.9163 L 2119.2759 2251.7635 L 2110.9038 2249.8498 L 2102.2925 2248.6538 L 2093.442 2248.1754 L 2084.5915 2248.1754 L 2075.741 2248.6538 L 2066.8905 2249.8498 L 2058.5184 2251.7635 L 2050.3856 2253.9163 L 2042.7311 2256.7867 L 2035.3158 2260.1356 L 2028.6181 2264.202 L 2022.3988 2268.5077 L 2017.1364 2273.0525 L 2012.3523 2278.0758 L 2008.5251 2283.3382 L 2005.4155 2288.8399 L 2003.2626 2294.5807 L 2001.8274 2300.5608 L 2001.349 2306.3017 L [0 0 0 0]vc f [0 0 0 1]vc S n 1947.2892 2309.6505 m 1947.5284 2312.2817 L 1948.9636 2314.913 L 1950.8773 2316.8266 L 1953.2693 2318.0226 L 1956.1397 2318.501 L 1959.0101 2318.0226 L 1961.4022 2316.8266 L 1963.3158 2314.913 L 1964.751 2312.2817 L 1965.2294 2309.6505 L 1964.751 2306.7801 L 1963.3158 2304.3881 L 1961.4022 2302.2352 L 1959.0101 2301.0392 L 1956.1397 2300.5608 L 1953.2693 2301.0392 L 1950.8773 2302.2352 L 1948.9636 2304.3881 L 1947.5284 2306.7801 L 1947.2892 2309.6505 L [0 0 0 0]vc f [0 0 0 1]vc
S n 1857.349 2309.6505 m 1857.8274 2312.2817 L 1859.0234 2314.913 L 1861.1763 2316.8266 L 1863.5683 2318.0226 L 1866.4387 2318.501 L 1869.0699 2318.0226 L 1871.7012 2316.8266 L 1873.6148 2314.913 L 1875.05 2312.2817 L 1875.2892 2309.6505 L 1875.05 2306.7801 L 1873.6148 2304.3881 L 1871.7012 2302.2352 L 1869.0699 2301.0392 L 1866.4387 2300.5608 L 1863.5683 2301.0392 L 1861.1763 2302.2352 L 1859.0234 2304.3881 L 1857.8274 2306.7801 L 1857.349 2309.6505 L [0 0 0 0]vc f [0 0 0 1]vc S n vmrs 1891.0766 2303.9096 m 1891.0766 2306.7801 L 1892.0334 2309.4113 L 1893.7078 2311.5641 L 1896.0998 2313.2385 L 1898.7311 2314.1954 L 1901.6015 2313.9562 L 1904.2327 2313.2385 L 1906.6248 2311.5641 L 1908.2992 2309.1721 L 1909.0168 2306.3017 L 1909.0168 2303.6704 L 1908.06 2300.8 L 1906.3856 2298.6472 L 1903.9935 2296.9728 L 1901.3623 2296.2552 L 1898.4919 2296.2552 L 1895.8606 2297.212 L 1893.7078 2298.8864 L 1892.0334 2301.0392 L 1891.0766 2303.9096 L [0 0 0 0]vc f 0.25 w 1 j [0 0 0 1]vc S n 1920.2593 2309.6505 m 1920.7377 2312.2817 L
1921.9337 2314.913 L 1923.8474 2316.8266 L 1926.4786 2318.0226 L 1929.1098 2318.501 L 1931.9802 2318.0226 L 1934.6115 2316.8266 L 1936.5251 2314.913 L 1937.7211 2312.2817 L 1938.1995 2309.6505 L 1937.7211 2306.7801 L 1936.5251 2304.3881 L 1934.6115 2302.2352 L 1931.9802 2301.0392 L 1929.1098 2300.5608 L 1926.4786 2301.0392 L 1923.8474 2302.2352 L 1921.9337 2304.3881 L 1920.7377 2306.7801 L 1920.2593 2309.6505 L [0 0 0 0]vc f [0 0 0 1]vc S n 1830.5583 2309.6505 m 1831.0367 2312.2817 L 1832.2327 2314.913 L 1834.1464 2316.8266 L 1836.7776 2318.0226 L 1839.4088 2318.501 L 1842.2792 2318.0226 L 1844.6713 2316.8266 L 1846.8241 2314.913 L 1848.0201 2312.2817 L 1848.4985 2309.6505 L 1848.0201 2306.7801 L 1846.8241 2304.3881 L 1844.6713 2302.2352 L 1842.2792 2301.0392 L 1839.4088 2300.5608 L 1836.7776 2301.0392 L 1834.1464 2302.2352 L 1832.2327 2304.3881 L 1831.0367 2306.7801 L 1830.5583 2309.6505 L [0 0 0 0]vc f [0 0 0 1]vc S n 2144.8706 2305.1057 m 2145.349 2307.9761 L 2146.545 2310.3681 L 2148.4586 2312.5209 L 2151.0899 2313.717 L 2153.9603 2314.1954 L 2156.5915 2313.717 L 2159.2228 2312.5209 L 2161.1364 2310.3681 L
2162.3324 2307.9761 L 2162.8108 2305.1057 L 2162.3324 2302.4744 L 2161.1364 2299.8432 L 2159.2228 2297.9296 L 2156.5915 2296.4944 L 2153.9603 2296.2552 L 2151.0899 2296.4944 L 2148.4586 2297.9296 L 2146.545 2299.8432 L 2145.349 2302.4744 L 2144.8706 2305.1057 L [0 0 0 0]vc f [0 0 0 1]vc S n 2055.1696 2305.1057 m 2055.648 2307.9761 L 2056.844 2310.3681 L 2058.7577 2312.5209 L 2061.3889 2313.717 L 2064.0201 2314.1954 L 2066.8905 2313.717 L 2069.2826 2312.5209 L 2071.4354 2310.3681 L 2072.6314 2307.9761 L 2073.1098 2305.1057 L 2072.6314 2302.4744 L 2071.4354 2299.8432 L 2069.2826 2297.9296 L 2066.8905 2296.4944 L 2064.0201 2296.2552 L 2061.3889 2296.4944 L 2058.7577 2297.9296 L 2056.844 2299.8432 L 2055.648 2302.4744 L 2055.1696 2305.1057 L [0 0 0 0]vc f [0 0 0 1]vc S n 2088.8972 2299.3648 m 2088.8972 2302.2352 L 2089.854 2304.8665 L 2091.5284 2307.2585 L 2093.9204 2308.9329 L 2096.5517 2309.6505 L 2099.4221 2309.6505 L 2102.0533 2308.6937 L 2104.2062 2307.0193 L 2105.8806 2304.6273 L 2106.8374 2301.996 L 2106.8374 2299.1256 L 2105.8806 2296.4944 L 2104.2062 2294.1023 L 2101.8141 2292.6671 L 2099.1829 2291.7103 L
2096.3125 2291.7103 L 2093.6812 2292.6671 L 2091.2892 2294.3415 L 2089.6148 2296.7336 L 2088.8972 2299.3648 L [0 0 0 0]vc f [0 0 0 1]vc S n 2117.8407 2305.1057 m 2118.3191 2307.9761 L 2119.7543 2310.3681 L 2121.6679 2312.5209 L 2124.06 2313.717 L 2126.9304 2314.1954 L 2129.8008 2313.717 L 2132.1929 2312.5209 L 2134.1065 2310.3681 L 2135.5417 2307.9761 L 2135.7809 2305.1057 L 2135.5417 2302.4744 L 2134.1065 2299.8432 L 2132.1929 2297.9296 L 2129.8008 2296.4944 L 2126.9304 2296.2552 L 2124.06 2296.4944 L 2121.6679 2297.9296 L 2119.7543 2299.8432 L 2118.3191 2302.4744 L 2117.8407 2305.1057 L [0 0 0 0]vc f [0 0 0 1]vc S n 2028.1397 2305.1057 m 2028.6181 2307.9761 L 2029.8141 2310.3681 L 2031.967 2312.5209 L 2034.359 2313.717 L 2037.2294 2314.1954 L 2039.8606 2313.717 L 2042.4919 2312.5209 L 2044.4055 2310.3681 L 2045.6015 2307.9761 L 2046.0799 2305.1057 L 2045.6015 2302.4744 L 2044.4055 2299.8432 L 2042.4919 2297.9296 L 2039.8606 2296.4944 L 2037.2294 2296.2552 L 2034.359 2296.4944 L 2031.967 2297.9296 L 2029.8141 2299.8432 L 2028.6181 2302.4744 L 2028.1397 2305.1057 L [0 0 0 0]vc f
[0 0 0 1]vc S n 1956.1397 2080.4944 m 1956.6181 2083.3648 L 1957.8141 2085.7568 L 1959.967 2087.6704 L 1962.359 2089.1057 L 1965.2294 2089.5841 L 1967.8606 2089.1057 L 1970.4919 2087.6704 L 1972.4055 2085.7568 L 1973.6015 2083.3648 L 1974.0799 2080.4944 L 1973.6015 2077.8631 L 1972.4055 2075.2319 L 1970.4919 2073.3183 L 1967.8606 2071.8831 L 1965.2294 2071.6439 L 1962.359 2071.8831 L 1959.967 2073.3183 L 1957.8141 2075.2319 L 1956.6181 2077.8631 L 1956.1397 2080.4944 L [0 0 0 0]vc f [0 0 0 1]vc S n 1866.4387 2080.4944 m 1866.9171 2083.3648 L 1868.1131 2085.7568 L 1870.0268 2087.6704 L 1872.658 2089.1057 L 1875.2892 2089.5841 L 1878.1596 2089.1057 L 1880.5517 2087.6704 L 1882.7045 2085.7568 L 1883.9005 2083.3648 L 1884.3789 2080.4944 L 1883.9005 2077.8631 L 1882.7045 2075.2319 L 1880.5517 2073.3183 L 1878.1596 2071.8831 L 1875.2892 2071.6439 L 1872.658 2071.8831 L 1870.0268 2073.3183 L 1868.1131 2075.2319 L 1866.9171 2077.8631 L 1866.4387 2080.4944 L [0 0 0 0]vc f [0 0 0 1]vc S n vmrs 1900.1663 2074.7535 m 1900.1663 2077.6239 L 1901.1231 2080.2552 L
1902.7975 2082.6472 L 1905.1895 2084.3216 L 1907.8208 2085.0392 L 1910.6912 2085.0392 L 1913.3224 2084.0824 L 1915.4753 2082.408 L 1917.1497 2080.016 L 1918.1065 2077.3847 L 1918.1065 2074.5143 L 1917.1497 2071.8831 L 1915.4753 2069.491 L 1913.0832 2067.8166 L 1910.452 2067.099 L 1907.5816 2067.099 L 1904.9503 2068.0558 L 1902.5583 2069.7302 L 1900.8839 2072.1223 L 1900.1663 2074.7535 L [0 0 0 0]vc f 0.25 w 1 j [0 0 0 1]vc S n 1929.1098 2080.4944 m 1929.5882 2083.3648 L 1931.0234 2085.7568 L 1932.9371 2087.6704 L 1935.3291 2089.1057 L 1938.1995 2089.5841 L 1941.0699 2089.1057 L 1943.462 2087.6704 L 1945.3756 2085.7568 L 1946.8108 2083.3648 L 1947.2892 2080.4944 L 1946.8108 2077.8631 L 1945.3756 2075.2319 L 1943.462 2073.3183 L 1941.0699 2071.8831 L 1938.1995 2071.6439 L 1935.3291 2071.8831 L 1932.9371 2073.3183 L 1931.0234 2075.2319 L 1929.5882 2077.8631 L 1929.1098 2080.4944 L [0 0 0 0]vc f [0 0 0 1]vc S n 1839.4088 2080.4944 m 1839.8872 2083.3648 L 1841.0832 2085.7568 L 1843.2361 2087.6704 L 1845.6281 2089.1057 L 1848.4985 2089.5841 L 1851.1297 2089.1057 L 1853.761 2087.6704 L
1855.6746 2085.7568 L 1856.8706 2083.3648 L 1857.349 2080.4944 L 1856.8706 2077.8631 L 1855.6746 2075.2319 L 1853.761 2073.3183 L 1851.1297 2071.8831 L 1848.4985 2071.6439 L 1845.6281 2071.8831 L 1843.2361 2073.3183 L 1841.0832 2075.2319 L 1839.8872 2077.8631 L 1839.4088 2080.4944 L [0 0 0 0]vc f [0 0 0 1]vc S n 2135.7809 2071.6439 m 2136.2593 2074.2751 L 2137.6945 2076.9063 L 2139.6081 2078.8199 L 2142.0002 2080.016 L 2144.8706 2080.4944 L 2147.741 2080.016 L 2150.1331 2078.8199 L 2152.0467 2076.9063 L 2153.4819 2074.2751 L 2153.9603 2071.6439 L 2153.4819 2068.7734 L 2152.0467 2066.3814 L 2150.1331 2064.2286 L 2147.741 2063.0326 L 2144.8706 2062.5542 L 2142.0002 2063.0326 L 2139.6081 2064.2286 L 2137.6945 2066.3814 L 2136.2593 2068.7734 L 2135.7809 2071.6439 L [0 0 0 0]vc f [0 0 0 1]vc S n 2046.0799 2071.6439 m 2046.5583 2074.2751 L 2047.7543 2076.9063 L 2049.9072 2078.8199 L 2052.2992 2080.016 L 2055.1696 2080.4944 L 2057.8008 2080.016 L 2060.4321 2078.8199 L 2062.3457 2076.9063 L 2063.5417 2074.2751 L 2064.0201 2071.6439 L 2063.5417 2068.7734 L 2062.3457 2066.3814 L 2060.4321 2064.2286 L 2057.8008 2063.0326 L
2055.1696 2062.5542 L 2052.2992 2063.0326 L 2049.9072 2064.2286 L 2047.7543 2066.3814 L 2046.5583 2068.7734 L 2046.0799 2071.6439 L [0 0 0 0]vc f [0 0 0 1]vc S n 2079.8075 2065.903 m 2079.8075 2068.5342 L 2080.7643 2071.4047 L 2082.4387 2073.5575 L 2084.8307 2075.2319 L 2087.462 2076.1887 L 2090.3324 2075.9495 L 2092.9636 2075.2319 L 2095.3557 2073.3183 L 2097.0301 2071.1655 L 2097.7477 2068.295 L 2097.7477 2065.6638 L 2096.7909 2062.7934 L 2095.1165 2060.6405 L 2092.7244 2058.9661 L 2090.0932 2058.0093 L 2087.2228 2058.2485 L 2084.5915 2058.9661 L 2082.4387 2060.8797 L 2080.7643 2063.0326 L 2079.8075 2065.903 L [0 0 0 0]vc f [0 0 0 1]vc S n 2108.9902 2071.6439 m 2109.4686 2074.2751 L 2110.6646 2076.9063 L 2112.5782 2078.8199 L 2115.2095 2080.016 L 2117.8407 2080.4944 L 2120.7111 2080.016 L 2123.3424 2078.8199 L 2125.256 2076.9063 L 2126.452 2074.2751 L 2126.9304 2071.6439 L 2126.452 2068.7734 L 2125.256 2066.3814 L 2123.3424 2064.2286 L 2120.7111 2063.0326 L 2117.8407 2062.5542 L 2115.2095 2063.0326 L 2112.5782 2064.2286 L 2110.6646 2066.3814 L 2109.4686 2068.7734 L 2108.9902 2071.6439 L [0 0 0 0]vc
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1906.6248 2287.4047 L 1912.844 2270.1821 L 1918.5849 2253.6771 L 1924.0866 2237.6505 L 1929.1098 2222.3415 L 1933.8939 2207.7502 L 1938.4387 2193.8764 L 1942.5052 2180.2419 L 1946.3324 2167.5641 L 1949.6812 2155.3648 L 1952.7909 2143.8831 L 1955.6613 2133.1189 L 1958.0533 2123.0724 L 1960.2062 2113.5043 L 1961.8806 2104.6538 L 1963.3158 2096.2817 L 1964.2726 2088.6273 L S n 1968.8175 2090.3017 m 1965.2294 2080.4944 L 1959.4885 2089.3449 L 1968.8175 2090.3017 L f n 2037.2294 2305.1057 m 2024.3125 2289.3183 L 2012.1131 2274.0093 L 2000.3922 2259.1787 L 1988.9105 2245.0658 L 1977.9072 2231.192 L 1967.6214 2217.7967 L 1957.8141 2204.8797 L 1948.4852 2192.4412 L 1939.6347 2180.2419 L 1931.5018 2168.9993 L 1923.6081 2157.996 L 1916.1929 2147.4711 L 1909.4952 2137.6638 L 1903.0367 2128.0957 L 1897.2959 2119.006 L 1892.0334 2110.6339 L 1887.2493 2102.501 L 1882.9437 2094.8465 L 1879.1165 2087.9096 L S n 1875.2892 2091.0193 m 1875.2892 2080.4944 L 1883.6613 2086.7136 L 1875.2892 2091.0193 L f n 2097.7477 2300.8 m 2084.5915 2284.5342 L 2071.6746 2268.7469 L 2059.4753 2253.4379 L 2047.9935 2238.8465 L 2036.751 2224.4944 L
2026.2261 2210.8598 L 2016.1796 2197.9429 L 2006.6115 2185.0259 L 1997.761 2172.8266 L 1989.3889 2161.3449 L 1981.256 2150.3415 L 1974.0799 2139.8166 L 1967.3822 2129.7701 L 1961.163 2120.4412 L 1955.4221 2111.3515 L 1950.3988 2102.9794 L 1945.854 2095.0857 L 1941.7876 2087.9096 L S n 1938.1995 2091.0193 m 1938.1995 2080.4944 L 1946.5716 2086.7136 L 1938.1995 2091.0193 L f n vmrs 2037.2294 2305.1057 m 2030.0533 2287.4047 L 2023.3557 2270.1821 L 2017.1364 2253.6771 L 2011.1563 2237.8897 L 2005.6547 2222.5807 L 2000.3922 2207.9894 L 1995.3689 2193.8764 L 1990.8241 2180.2419 L 1986.5184 2167.5641 L 1982.6912 2155.604 L 1979.3424 2144.1223 L 1976.2327 2133.1189 L 1973.3623 2123.0724 L 1971.2095 2113.5043 L 1969.0567 2104.6538 L 1967.3822 2096.2817 L 1966.1862 2088.6273 L 2.25 w 1 J 1 j [1 0 1 0]vc S n 1961.6414 2090.3017 m 1965.2294 2080.4944 L 1970.9703 2089.1057 L 1961.6414 2090.3017 L f n 2126.9304 2305.1057 m 2110.9038 2289.7967 L 2095.3557 2274.9661 L 2080.2859 2260.614 L 2065.9337 2246.7402 L 2052.2992 2233.1057 L 2038.9038 2219.9495 L
2026.4653 2207.2718 L 2014.266 2195.0724 L 2002.7842 2183.1123 L 1991.7809 2171.8698 L 1981.256 2160.8665 L 1971.4487 2150.5807 L 1962.359 2140.5342 L 1953.7477 2130.9661 L 1945.6148 2121.8764 L 1937.9603 2113.0259 L 1931.2626 2104.893 L 1924.8042 2096.9993 L 1919.0633 2089.5841 L 1913.8008 2082.6472 L S n 1910.6912 2086.4744 m 1909.0168 2076.1887 L 1918.3457 2080.9728 L 1910.6912 2086.4744 L f n 1929.1098 2309.6505 m 1937.9603 2291.7103 L 1946.3324 2274.4877 L 1954.2261 2257.7435 L 1961.8806 2241.717 L 1969.0567 2226.408 L 1975.7543 2211.5774 L 1981.9736 2197.2253 L 1987.9537 2183.3515 L 1993.9337 2170.1954 L 1998.957 2157.7568 L 2003.9802 2145.7967 L 2008.2859 2134.5542 L 2012.3523 2124.0292 L 2015.9404 2113.7435 L 2019.05 2104.4146 L 2021.9204 2095.5641 L 2024.3125 2087.192 L 2026.4653 2079.5376 L [0 0 0 1]vc S n 2030.7709 2081.6904 m 2028.1397 2071.6439 L 2021.6812 2079.5376 L 2030.7709 2081.6904 L f n 1929.1098 2309.6505 m 1942.0268 2292.4279 L 1954.2261 2275.6837 L 1965.7078 2259.6572 L 1976.9503 2244.109 L 1987.7145 2229.0392 L 1998.2394 2214.6871 L 2007.8075 2200.5741 L 2017.1364 2186.9395 L
2025.7477 2174.0226 L 2033.8806 2161.8233 L 2041.7743 2149.8631 L 2048.9503 2138.6206 L 2055.648 2127.8565 L 2061.8673 2117.5708 L 2067.6081 2108.0027 L 2072.8706 2098.6738 L 2077.4155 2090.0625 L 2081.7211 2082.1688 L 2085.5483 2074.5143 L S n 2089.1364 2077.6239 m 2088.8972 2067.099 L 2080.7643 2073.5575 L 2089.1364 2077.6239 L f n 1866.4387 2309.6505 m 1881.2693 2292.9063 L 1895.3822 2276.4013 L 1909.0168 2260.8532 L 1922.1729 2245.5442 L 1934.8507 2230.7136 L 1946.8108 2216.6007 L 1958.0533 2202.9661 L 1969.0567 2189.81 L 1979.3424 2176.893 L 1989.1497 2164.6937 L 1998.2394 2152.9728 L 2006.8507 2141.9694 L 2014.9836 2131.4445 L 2022.3988 2121.1588 L 2029.0965 2111.5907 L 2035.555 2102.7402 L 2041.2959 2094.1289 L 2046.3191 2085.996 L 2051.1032 2078.5807 L S n 2054.452 2081.9296 m 2055.1696 2071.6439 L 2046.3191 2077.3847 L 2054.452 2081.9296 L f n vmrs 1956.1397 2309.6505 m 1969.0567 2292.6671 L 1981.256 2276.4013 L 1993.4553 2260.614 L 2004.6979 2245.5442 L 2015.462 2230.7136 L 2025.9869 2216.6007 L 2035.7942 2202.7269 L 2045.1231 2189.5708 L 2053.7344 2176.6538 L 2062.1065 2164.6937 L
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1968.5782 2143.8831 L 1968.5782 2132.8797 L 1968.5782 2122.8332 L 1968.339 2113.2651 L 1967.8606 2104.4146 L 1967.143 2096.0425 L 1966.4254 2088.6273 L [1 0 1 0]vc S n 1971.2095 2089.1057 m 1965.2294 2080.4944 L 1961.8806 2090.5409 L 1971.2095 2089.1057 L f n 2153.9603 2305.1057 m 2147.741 2287.1655 L 2141.761 2269.9429 L 2136.2593 2253.1987 L 2130.9969 2236.9329 L 2125.9736 2221.6239 L 2121.4287 2206.5542 L 2117.1231 2192.4412 L 2113.0567 2178.3282 L 2109.2294 2165.4113 L 2105.8806 2152.9728 L 2102.7709 2141.0126 L 2099.9005 2129.7701 L 2097.5085 2119.2452 L 2095.3557 2109.1987 L 2093.442 2099.8698 L 2091.7676 2091.0193 L 2090.5716 2082.8864 L 2089.6148 2075.2319 L [0 0 0 1]vc S n 2085.0699 2076.9063 m 2088.8972 2067.099 L 2094.3988 2075.9495 L 2085.0699 2076.9063 L f n 2064.0201 2305.1057 m 2062.1065 2286.2086 L 2060.1929 2268.0292 L 2058.5184 2250.8067 L 2057.0832 2233.8233 L 2055.8872 2217.7967 L 2054.6912 2202.4877 L 2053.7344 2187.6572 L 2053.0168 2173.7834 L 2052.2992 2160.3881 L 2051.8208 2147.9495 L 2051.5816 2135.9894 L 2051.5816 2124.9861 L 2051.8208 2114.4611 L 2052.06 2104.6538 L
2052.5384 2095.5641 L 2053.0168 2087.192 L 2053.9736 2079.5376 L S n 2049.1895 2080.016 m 2055.1696 2071.6439 L 2058.2792 2081.4512 L 2049.1895 2080.016 L f n vmrs 2097.7477 2300.8 m 2095.8341 2282.1422 L 2093.9204 2264.4412 L 2092.246 2247.4578 L 2090.8108 2230.9528 L 2089.6148 2215.1655 L 2088.4188 2200.0957 L 2087.462 2185.5043 L 2086.7444 2171.8698 L 2086.266 2158.9528 L 2085.7876 2146.5143 L 2085.5483 2135.0326 L 2085.5483 2124.0292 L 2085.5483 2113.7435 L 2085.7876 2104.1754 L 2086.266 2095.3249 L 2086.9836 2087.192 L 2087.7012 2079.5376 L 2.25 w 1 J 1 j S n 2082.9171 2080.016 m 2088.8972 2071.6439 L 2092.246 2081.4512 L 2082.9171 2080.016 L f n 2064.0201 2305.1057 m 2069.761 2286.4479 L 2075.0234 2268.5077 L 2080.0467 2251.2851 L 2084.8307 2234.5409 L 2089.1364 2218.7535 L 2093.2028 2203.4445 L 2097.0301 2188.614 L 2100.3789 2174.7402 L 2103.4885 2161.3449 L 2106.359 2148.9063 L 2108.9902 2136.9462 L 2111.143 2125.7037 L 2113.0567 2115.1787 L 2114.7311 2105.3714 L 2115.9271 2096.0425 L 2116.8839 2087.6704 L 2117.6015 2079.7768 L
S n 2122.1464 2117.8407 2112.8175 2122.1464 f n vmr vmr end %%Trailer
2080.9728 2071.6439 2080.7336 2080.9728
m L L L
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%%DocumentProcessColors: Black %%ColorUsage:Color %%DocumentFonts: Helvetica %%+Helvetica-Bold %%+Helvetica-Oblique %%+Helvetica-BoldOblique %%+Times-Roman %%+Times-Bold %%+Times-Italic %%+Times-BoldItalic %%+Courier %%+Courier-Bold %%+Courier-Oblique %%+Courier-BoldOblique %%+Symbol %%DocumentSuppliedResources: procset Adobe_packedarray 2.0 0 %%+ procset Adobe_cmykcolor 1.1 0 %%+ procset Adobe_cshow 1.1 0 %%+ procset Adobe_customcolor 1.0 0 %%+ procset Adobe_typography_AI3 1.0 0 %%+ procset Adobe_Illustrator_AI3 1.0 0 %AI3_ColorUsage: Color %AI3_TemplateBox: 0 0 746 194 %AI3_TileBox: 0 0 746 194 %AI3_DocumentPreview: None %%Template: %%PageOrigin:0.0000 0.0000 %%EndComments %%BeginProlog %%BeginResource: procset Adobe_packedarray 2.0 0 %%Title: (Packed Array Operators) %%Version: 2.0 %%CreationDate: (8/2/90) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) userdict /Adobe_packedarray 5 dict dup begin put /initialize { /packedarray where { pop } { Adobe_packedarray begin Adobe_packedarray { dup xcheck { bind } if userdict 3 1 roll put } forall end } ifelse } def /terminate { } def /packedarray {
array astore readonly } def /setpacking { pop } def /currentpacking { false } def currentdict readonly pop end %%EndResource Adobe_packedarray /initialize get exec %%Title: (CMYK Color Operators) %%Version: 1.1 %%CreationDate: (1/23/89) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_cmykcolor 4 dict dup begin put /initialize { /setcmykcolor where { pop } { userdict /Adobe_cmykcolor_vars 2 dict dup begin put /_setrgbcolor /setrgbcolor load def /_currentrgbcolor /currentrgbcolor load def Adobe_cmykcolor begin Adobe_cmykcolor { dup xcheck { bind } if pop pop } forall end end Adobe_cmykcolor begin } ifelse } def /terminate { currentdict Adobe_cmykcolor eq { end } if } def /setcmykcolor { 1 sub 4 1 roll 3 {
3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat Adobe_cmykcolor_vars /_setrgbcolor get exec pop } def /currentcmykcolor { Adobe_cmykcolor_vars /_currentrgbcolor get exec 3 { 1 sub neg 3 1 roll } repeat 0 } def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_cshow 1.1 0 %%Title: (cshow Operator) %%Version: 1.1 %%CreationDate: (1/23/89) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_cshow 3 dict dup begin put /initialize { /cshow where { pop } { userdict /Adobe_cshow_vars 1 dict dup begin put /_cshow {} def Adobe_cshow begin Adobe_cshow { dup xcheck { bind } if userdict 3 1 roll put } forall end end } ifelse } def /terminate { } def /cshow { exch
Adobe_cshow_vars exch /_cshow exch put { 0 0 Adobe_cshow_vars /_cshow get exec } forall } def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_customcolor 1.0 0 %%Title: (Custom Color Operators) %%Version: 1.0 %%CreationDate: (5/9/88) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_customcolor 5 dict dup begin put /initialize { /setcustomcolor where { pop } { Adobe_customcolor begin Adobe_customcolor { dup xcheck { bind } if pop pop } forall end Adobe_customcolor begin } ifelse } def /terminate { currentdict Adobe_customcolor eq { end } if } def /findcmykcustomcolor { 5 packedarray } def /setcustomcolor { exch aload pop pop 4 { 4 index mul 4 1 roll } repeat 5 -1 roll pop
setcmykcolor } def /setoverprint { pop } def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_typography_AI3 1.0 0 %%Title: (Typography Operators)%%Version: 1.0 %%CreationDate:(5/31/90) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_typography_AI3 46 dict dup begin put /initialize { /TZ where { pop } { Adobe_typography_AI3 begin Adobe_typography_AI3 { dup xcheck { bind } if pop pop } forall end Adobe_typography_AI3 begin } ifelse } def /terminate { currentdict Adobe_typography_AI3 eq { end } if } def /modifyEncoding { /_tempEncode exch ddef /_pntr 0 ddef { counttomark -1 roll dup type dup /marktype eq { pop pop exit } { /nametype eq { _tempEncode /_pntr dup load dup 3 1 roll 1 add ddef 3 -1 roll
put } { /_pntr exch ddef } ifelse } ifelse } loop _tempEncode } def /TE { StandardEncoding 256 array copy modifyEncoding /_nativeEncoding exch def } def /TZ { /_useNativeEncoding exch def pop pop findfont dup length 2 add dict begin mark exch { 1 index /FID ne { def } if cleartomark mark } forall pop /FontName exch def counttomark 0 eq { Encoding StandardEncoding eq 1 _useNativeEncoding eq and { /Encoding _nativeEncoding def } if cleartomark } { /Encoding load 256 array copy modifyEncoding /Encoding exch def } ifelse FontName currentdict end definefont pop } def /tr { _ax _ay 3 2 roll } def /trj { _cx _cy _sp _ax _ay 6 5 roll } def
/a0 { /Tx { dup currentpoint 3 2 roll tr _psf newpath moveto tr _ctm _pss } ddef /Tj { dup currentpoint 3 2 roll trj _pjsf newpath moveto trj _ctm _pjss } ddef } def /a1 { W B } def /e0 { /Tx { tr _psf } ddef /Tj { trj _pjsf } ddef } def /e1 { W F } def /i0 { /Tx { tr sp } ddef /Tj { trj jsp } ddef } def /o0 { /Tx { tr sw rmoveto } ddef /Tj { trj swj rmoveto } ddef
} def /r0 { /Tx { tr _ctm _pss } ddef /Tj { trj _ctm _pjss } ddef } def /r1 { W S } def /To { pop _ctm currentmatrix pop } def /TO { Te _ctm setmatrix newpath } def /Tp { pop _tm astore pop _ctm setmatrix 2 dict begin /W {} def /h {} def } def /TP { end iTm 0 0 moveto } def /Tr { Te currentpoint newpath moveto dup 8 eq {pop 0} {dup 9 eq {pop 1} if} ifelse dup /_render exch ddef _renderStart exch get load exec } def /iTm { _ctm setmatrix _tm concat 0 _rise translate _hs 1 scale } def /Te { _render -1 eq {} {_renderEnd _render get dup null ne {load exec} {pop} ifelse} ifelse /_render -1 ddef } def /Tf { dup 1000 div /_fScl exch ddef exch findfont exch scalefont setfont } def /Tl { pop
0 exch _leading astore pop } def /Tt { pop } def /TW { 3 npop } def /Tw { /_cx exch ddef } def /Tc { /_ax exch ddef } def /Ts { /_rise exch ddef currentpoint iTm moveto } def /Ti { 3 npop } def /Tz { 100 div /_hs exch ddef iTm } def /Tq { pop } def /TX {pop} def /Tk { exch pop _fScl mul neg 0 rmoveto } def /T{ _hyphen Tx } def /TS { 0 eq {Tx} {Tj} ifelse } def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_Illustrator_AI3 1.0 0 %%Title: (Adobe Illustrator (R) Version 3.0 Full Prolog) %%Version: 1.0 %%CreationDate: (7/22/89) ()
%%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_Illustrator_AI3 71 dict dup begin put /initialize { userdict /Adobe_Illustrator_AI3_vars 55 dict dup begin put /_lp /none def /_pf {} def /_ps {} def /_psf {} def /_pss {} def /_pjsf {} def /_pjss {} def /_pola 0 def /_doClip 0 def /cf currentflat def /_tm matrix def /_renderStart [/e0 /r0 /a0 /o0 /i0 /i0 /i0 /i0] def /_renderEnd [null null null null /e1 /r1 /a1 /clip] def /_render -1 def /_rise 0 def /_ax 0 def /_ay 0 def /_cx 0 def /_cy 0 def /_leading [0 0] def /_ctm matrix def /_mtx matrix def /_sp 16#020 def /_hyphen (-) def /_fScl 0 def /_cnt 0 def /_hs 1 def /_nativeEncoding 0 def /_useNativeEncoding 0 def /_tempEncode 0 def /_pntr 0 def /Tx {} def /Tj {} def /CRender {} def /_AI3_savepage {} def /_gf null def /_cf 4 array def /_if null def /_of false def /_fc {} def /_gs null def /_cs 4 array def /_is null def /_os false def /_sc {} def /_pd 1 dict def /_ed 15 dict def /_pm matrix def /_fm null def /_fd null def /_fdd null def /_sm null def /_sd null def
/_sdd null def /_i null def Adobe_Illustrator_AI3 begin Adobe_Illustrator_AI3 dup /nc get begin { dup xcheck { bind } if pop pop } forall end end end Adobe_Illustrator_AI3 begin Adobe_Illustrator_AI3_vars begin newpath } def /terminate { end end } def /_ null def /ddef { Adobe_Illustrator_AI3_vars 3 1 roll put } def /xput { dup load dup length exch maxlength eq { dup dup load dup length 2 mul dict copy def } if load begin def end } def /npop { { pop } repeat } def /sw { dup length exch stringwidth exch 5 -1 roll 3 index 1 sub mul add 4 1 roll 3 1 roll 1 sub mul add } def /swj { dup 4 1 roll dup length exch stringwidth exch 5 -1 roll 3 index 1 sub mul add 4 1 roll 3 1 roll 1 sub mul add 6 2 roll /_cnt 0 ddef
{1 index eq {/_cnt _cnt 1 add ddef} if} forall pop exch _cnt mul exch _cnt mul 2 index add 4 1 roll 2 index add 4 1 roll pop pop } def /ss { 4 1 roll { 2 npop (0) exch 2 copy 0 exch put pop gsave false charpath currentpoint 4 index setmatrix stroke grestore moveto 2 copy rmoveto } exch cshow 3 npop } def /jss { 4 1 roll { 2 npop (0) exch 2 copy 0 exch put gsave _sp eq { exch 6 index 6 index 6 index 5 -1 roll widthshow currentpoint } { false charpath currentpoint 4 index setmatrix stroke }ifelse grestore moveto 2 copy rmoveto } exch cshow 6 npop } def /sp { { 2 npop (0) exch 2 copy 0 exch put pop false charpath 2 copy rmoveto } exch cshow 2 npop } def /jsp { { 2 npop (0) exch 2 copy 0 exch put _sp eq { exch 5 index 5 index 5 index 5 -1 roll widthshow
} { false charpath }ifelse 2 copy rmoveto } exch cshow 5 npop } def /pl { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } def /setstrokeadjust where {pop true setstrokeadjust /c { curveto } def /C /c load def /v { currentpoint 6 2 roll curveto } def /V /v load def /y { 2 copy curveto } def /Y /y load def /l { lineto } def /L /l load def /m { moveto } def } { /c { pl curveto } def /C /c load def /v { currentpoint 6 2 roll pl curveto } def /V /v load def
/y { pl 2 copy curveto } def /Y /y load def /l { pl lineto } def /L /l load def /m { pl moveto } def } ifelse /d { setdash } def /cf {} def /i { dup 0 eq { pop cf } if setflat } def /j { setlinejoin } def /J { setlinecap } def /M { setmiterlimit } def /w { setlinewidth } def /H {} def /h { closepath } def /N { _pola 0 eq { _doClip 1 eq {clip /_doClip 0 ddef} if newpath } { /CRender {N} ddef }ifelse } def /n {N} def /F { _pola 0 eq { _doClip 1 eq { gsave _pf grestore clip newpath /_lp /none ddef _fc
/_doClip 0 ddef } { _pf }ifelse } { /CRender {F} ddef }ifelse } def /f { closepath F } def /S { _pola 0 eq { _doClip 1 eq { gsave _ps grestore clip newpath /_lp /none ddef _sc /_doClip 0 ddef } { _ps }ifelse } { /CRender {S} ddef }ifelse } def /s { closepath S } def /B { _pola 0 eq { _doClip 1 eq gsave F grestore { gsave S grestore clip newpath /_lp /none ddef _sc /_doClip 0 ddef } { S }ifelse } { /CRender {B} ddef }ifelse } def /b { closepath B
} def /W { /_doClip 1 ddef } def /* { count 0 ne { dup type (stringtype) eq {pop} if } if _pola 0 eq {newpath} if } def /u {} def /U {} def /q {_pola 0 eq {gsave} if } def /Q { _pola 0 eq {grestore} if } def /*u { _pola 1 add /_pola exch ddef } def /*U { _pola 1 sub /_pola exch ddef _pola 0 eq {CRender} if } def /D {pop} def /*w {} def /*W {} def /` { /_i save ddef 6 1 roll 4 npop concat userdict begin /showpage {} def false setoverprint pop } def /~ { end _i restore } def /@ {} def /& {} def /O { 0 ne /_of exch ddef /_lp /none ddef
} def /R { 0 ne /_os exch ddef /_lp /none ddef } def /g { /_gf exch ddef /_fc { _lp /fill ne { _of setoverprint _gf setgray /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /G { /_gs exch ddef /_sc { _lp /stroke ne { _os setoverprint _gs setgray /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss
{ _sc jss } ddef /_lp /none ddef } def /k { _cf astore pop /_fc { _lp /fill ne { _of setoverprint _cf aload pop setcmykcolor /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /K { _cs astore pop /_sc { _lp /stroke ne { _os setoverprint _cs aload pop setcmykcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss {
_sc jss } ddef /_lp /none ddef } def /x { /_gf exch ddef findcmykcustomcolor /_if exch ddef /_fc { _lp /fill ne { _of setoverprint _if _gf 1 exch sub setcustomcolor /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /X { /_gs exch ddef findcmykcustomcolor /_is exch ddef /_sc { _lp /stroke ne { _os setoverprint _is _gs 1 exch sub setcustomcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss
} ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /dp { dup null eq { pop _dp 0 ne { 0 1 _dp 1 sub _dl mod { _da exch get 3 get } for _dp 1 sub _dl mod 1 add packedarray _da 0 get aload pop 8 -1 roll 5 -1 roll pop 4 1 roll definepattern pop } if } { _dp 0 ne _dp _dl mod 0 eq and { null dp } if 7 packedarray _da exch _dp _dl mod exch put _dp _dl mod _da 0 get 4 get 2 packedarray /_dp _dp 1 add def } ifelse } def /E { _ed begin dup 0 get type /arraytype ne { 0 { dup 1 add index type /arraytype eq { 1 add } { exit } ifelse } loop array astore } if /_dd exch def /_ury exch def /_urx exch def /_lly exch def /_llx exch def /_n exch def /_y 0 def /_dl 4 def
/_dp 0 def /_da _dl array def 0 1 _dd length 1 sub { /_d exch _dd exch get def 0 2 _d length 2 sub { /_x exch def /_c _d _x get _ ne def /_r _d _x 1 add get cvlit def _r _ ne { _urx _llx sub _ury _lly sub [1 0 0 1 0 0] [ /save cvx _llx neg _lly neg /translate cvx _c { nc /begin cvx } if _r dup type /stringtype eq { cvx } { {exec} /forall cvx } ifelse _c { /end cvx } if /restore cvx ] cvx /_fn 12 _n length add string def _y _fn cvs pop /_y _y 1 add def _fn 12 _n putinterval _fn _c false dp _d exch _x 1 add exch put } if } for } for null dp _n _dd /_pd end xput } def /fc { _fm dup concatmatrix pop } def /p { /_fm exch ddef 9 -2 roll _pm translate fc 7 -2 roll _pm scale fc 5 -1 roll _pm rotate fc 4 -2 roll exch 0 ne { dup _pm rotate fc
1 -1 _pm scale fc neg _pm rotate fc } { pop } ifelse dup _pm rotate fc exch dup sin exch cos div 1 0 0 1 0 6 2 roll _pm astore fc neg _pm rotate fc _pd exch get /_fdd exch ddef /_pf { save 0 1 _fdd length 1 sub { /_fd exch _fdd exch get ddef _fd 0 2 _fd length 2 sub { gsave 2 copy get dup _ ne { cvx exec _fc } { pop } ifelse 2 copy 1 add get dup _ ne { aload pop findfont _fm patternfill } { pop fill } ifelse grestore pop } for pop } for restore newpath } ddef /_psf { save 0 1 _fdd length 1 sub { /_fd exch _fdd exch get ddef _fd 0 2 _fd length 2 sub { gsave 2 copy get dup _ ne { cvx exec _fc }
{ pop } ifelse 2 copy 1 add get dup _ ne { aload pop findfont _fm 9 copy 6 npop patternashow } { pop 6 copy 3 npop ashow } ifelse grestore pop } for pop } for restore sw rmoveto } ddef /_pjsf { save 0 1 _fdd length 1 sub { /_fd exch _fdd exch get ddef _fd 0 2 _fd length 2 sub { gsave 2 copy get dup _ ne { cvx exec _fc } { pop } ifelse 2 copy 1 add get dup _ ne { aload pop findfont _fm 12 copy 6 npop patternawidthshow } { pop 9 copy 3 npop awidthshow } ifelse grestore pop } for pop } for restore swj rmoveto } ddef /_lp /none ddef } def /sc { _sm dup concatmatrix pop
} def /P { /_sm exch ddef 9 -2 roll _pm translate sc 7 -2 roll _pm scale sc 5 -1 roll _pm rotate sc 4 -2 roll exch 0 ne { dup _pm rotate sc 1 -1 _pm scale sc neg _pm rotate sc } { pop } ifelse dup _pm rotate sc exch dup sin exch cos div 1 0 0 1 0 6 2 roll _pm astore sc neg _pm rotate sc _pd exch get /_sdd exch ddef /_ps { save 0 1 _sdd length 1 sub { /_sd exch _sdd exch get ddef _sd 0 2 _sd length 2 sub { gsave 2 copy get dup _ ne { cvx exec _sc } { pop } ifelse 2 copy 1 add get dup _ ne { aload pop findfont _sm patternstroke } { pop stroke } ifelse grestore pop } for pop } for restore newpath } ddef /_pss { save 0 1 _sdd length 1 sub {
/_sd exch _sdd exch get ddef _sd 0 2 _sd length 2 sub { gsave 2 copy get dup _ ne { cvx exec _sc } { pop } ifelse 2 copy 1 add get dup _ ne { aload pop findfont _sm 10 copy 6 npop patternashowstroke } { pop 7 copy 3 npop ss } ifelse grestore pop } for pop } for restore pop sw rmoveto } ddef /_pjss { save 0 1 _sdd length 1 sub { /_sd exch _sdd exch get ddef _sd 0 2 _sd length 2 sub { gsave 2 copy get dup _ ne { cvx exec _sc } { pop } ifelse 2 copy 1 add get dup _ ne { aload pop findfont _sm 13 copy 6 npop patternawidthshowstroke } { pop 10 copy 3 npop jss } ifelse grestore pop } for pop } for restore
pop swj rmoveto } ddef /_lp /none ddef } def /A { pop } def /nc 3 dict def nc begin /setgray { pop } bind def /setcmykcolor { 4 npop } bind def /setcustomcolor { 2 npop } bind def currentdict readonly pop end /Z {findfont begin currentdict dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /FontName exch def dup length 0 ne {/Encoding Encoding 256 array copy def 0 exch {dup type /nametype eq {Encoding 2 index 2 index put pop 1 add} {exch pop} ifelse} forall} if pop currentdict dup end end /FontName get exch definefont pop} bind def currentdict readonly pop end setpacking /annotatepage { } def %%EndResource %%EndProlog %%BeginSetup Adobe_cshow /initialize get exec Adobe_customcolor /initialize get exec Adobe_typography_AI3 /initialize get exec Adobe_Illustrator_AI3 /initialize get exec %%BeginEncoding:_Helvetica Helvetica [ 39/quotesingle 96/grave 130/quotesinglbase 131/florin 132/quotedblbase 133/ellipsis 134/dagger 135/daggerdbl 136/circumflex 137/perthousand 138/Scaron 139/guilsinglleft 140/OE 145/quoteleft 146/quoteright 147/quotedblleft 148/quotedblright 149/bullet 150/endash 151/emdash 152/tilde 153/trademark 154/scaron 155/guilsinglright 156/oe 157/dotlessi 159/Ydieresis 164/currency 166/brokenbar 168/dieresis 169/copyright 170/ordfeminine 172/logicalnot 174/registered 175/macron 176/ring 177/plusminus 178/twosuperior 179/threesuperior 180/acute 181/mu 183/periodcentered 184/cedilla 185/onesuperior 186/ordmasculine 188/onequarter 189/onehalf 190/threequarters 192/Agrave 193/Aacute 194/Acircumflex 195/Atilde 196/Adieresis 197/Aring 198/AE 199/Ccedilla 200/Egrave 201/Eacute 202/Ecircumflex 203/Edieresis 204/Igrave 205/Iacute 206/Icircumflex 207/Idieresis 208/Eth 209/Ntilde 210/Ograve 211/Oacute 212/Ocircumflex 213/Otilde 214/Odieresis 215/multiply 216/Oslash
217/Ugrave 218/Uacute 219/Ucircumflex 220/Udieresis 221/Yacute 222/Thorn 223/germandbls 224/agrave 225/aacute 226/acircumflex 227/atilde 228/adieresis 229/aring 230/ae 231/ccedilla 232/egrave 233/eacute 234/ecircumflex 235/edieresis 236/igrave 237/iacute 238/icircumflex 239/idieresis 240/eth 241/ntilde 242/ograve 243/oacute 244/ocircumflex 245/otilde 246/odieresis 247/divide 248/oslash 249/ugrave 250/uacute 251/ucircumflex 252/udieresis 253/yacute 254/thorn 255/ydieresis ] /_Helvetica/Helvetica Z %%EndEncoding %%BeginEncoding:_Helvetica-Bold Helvetica-Bold [ 39/quotesingle 96/grave 130/quotesinglbase 131/florin 132/quotedblbase 133/ellipsis 134/dagger 135/daggerdbl 136/circumflex 137/perthousand 138/Scaron 139/guilsinglleft 140/OE 145/quoteleft 146/quoteright 147/quotedblleft 148/quotedblright 149/bullet 150/endash 151/emdash 152/tilde 153/trademark 154/scaron 155/guilsinglright 156/oe 157/dotlessi 159/Ydieresis 164/currency 166/brokenbar 168/dieresis 169/copyright 170/ordfeminine 172/logicalnot 174/registered 175/macron 176/ring 177/plusminus 178/twosuperior 179/threesuperior 180/acute 181/mu 183/periodcentered 184/cedilla 185/onesuperior 186/ordmasculine 188/onequarter 189/onehalf 190/threequarters 192/Agrave 193/Aacute 194/Acircumflex 195/Atilde 196/Adieresis 197/Aring 198/AE 199/Ccedilla 200/Egrave 201/Eacute 202/Ecircumflex 203/Edieresis 204/Igrave 205/Iacute 206/Icircumflex 207/Idieresis 208/Eth 209/Ntilde 210/Ograve 211/Oacute 212/Ocircumflex 213/Otilde 214/Odieresis 215/multiply 216/Oslash 217/Ugrave 218/Uacute 219/Ucircumflex 220/Udieresis 221/Yacute 222/Thorn 223/germandbls 224/agrave 225/aacute 226/acircumflex 227/atilde 228/adieresis 229/aring 230/ae 231/ccedilla 232/egrave 233/eacute 234/ecircumflex 235/edieresis 236/igrave 237/iacute 238/icircumflex 239/idieresis 240/eth 241/ntilde 242/ograve 243/oacute 244/ocircumflex 245/otilde 246/odieresis 247/divide 248/oslash 249/ugrave 250/uacute 251/ucircumflex 252/udieresis 253/yacute 254/thorn 255/ydieresis ] /_Helvetica-Bold/Helvetica-Bold Z %%EndEncoding %%BeginEncoding:_Helvetica-Oblique Helvetica-Oblique [ 39/quotesingle 96/grave 130/quotesinglbase 131/florin 132/quotedblbase 133/ellipsis 134/dagger 135/daggerdbl 136/circumflex 137/perthousand 138/Scaron 139/guilsinglleft 140/OE 145/quoteleft 146/quoteright 147/quotedblleft 148/quotedblright 149/bullet 150/endash 151/emdash 152/tilde 153/trademark 154/scaron 155/guilsinglright 156/oe 157/dotlessi 159/Ydieresis 164/currency 166/brokenbar 168/dieresis 169/copyright 170/ordfeminine 172/logicalnot 174/registered 175/macron 176/ring 177/plusminus 178/twosuperior 179/threesuperior 180/acute 181/mu 183/periodcentered 184/cedilla 185/onesuperior 186/ordmasculine 188/onequarter 189/onehalf 190/threequarters 192/Agrave 193/Aacute 194/Acircumflex 195/Atilde 196/Adieresis 197/Aring 198/AE 199/Ccedilla 200/Egrave 201/Eacute 202/Ecircumflex 203/Edieresis 204/Igrave 205/Iacute 206/Icircumflex 207/Idieresis 208/Eth 209/Ntilde 210/Ograve 211/Oacute 212/Ocircumflex 213/Otilde 214/Odieresis 215/multiply 216/Oslash 217/Ugrave 218/Uacute 219/Ucircumflex 220/Udieresis 221/Yacute 222/Thorn 223/germandbls 224/agrave 225/aacute 226/acircumflex 227/atilde 228/adieresis 229/aring 230/ae 231/ccedilla 232/egrave 233/eacute 234/ecircumflex 235/edieresis 236/igrave 237/iacute 238/icircumflex 239/idieresis 240/eth 241/ntilde 242/ograve 243/oacute 244/ocircumflex 245/otilde 246/odieresis 247/divide 248/oslash 249/ugrave 250/uacute 251/ucircumflex 252/udieresis 253/yacute 254/thorn 255/ydieresis ] /_Helvetica-Oblique/Helvetica-Oblique Z %%EndEncoding
%%BeginEncoding:_Helvetica-BoldOblique Helvetica-BoldOblique [ 39/quotesingle 96/grave 130/quotesinglbase 131/florin 132/quotedblbase 133/ellipsis 134/dagger 135/daggerdbl 136/circumflex 137/perthousand 138/Scaron 139/guilsinglleft 140/OE 145/quoteleft 146/quoteright 147/quotedblleft 148/quotedblright 149/bullet 150/endash 151/emdash 152/tilde 153/trademark 154/scaron 155/guilsinglright 156/oe 157/dotlessi 159/Ydieresis 164/currency 166/brokenbar 168/dieresis 169/copyright 170/ordfeminine 172/logicalnot 174/registered 175/macron 176/ring 177/plusminus 178/twosuperior 179/threesuperior 180/acute 181/mu 183/periodcentered 184/cedilla 185/onesuperior 186/ordmasculine 188/onequarter 189/onehalf 190/threequarters 192/Agrave 193/Aacute 194/Acircumflex 195/Atilde 196/Adieresis 197/Aring 198/AE 199/Ccedilla 200/Egrave 201/Eacute 202/Ecircumflex 203/Edieresis 204/Igrave 205/Iacute 206/Icircumflex 207/Idieresis 208/Eth 209/Ntilde 210/Ograve 211/Oacute 212/Ocircumflex 213/Otilde 214/Odieresis 215/multiply 216/Oslash 217/Ugrave 218/Uacute 219/Ucircumflex 220/Udieresis 221/Yacute 222/Thorn 223/germandbls 224/agrave 225/aacute 226/acircumflex 227/atilde 228/adieresis 229/aring 230/ae 231/ccedilla 232/egrave 233/eacute 234/ecircumflex 235/edieresis 236/igrave 237/iacute 238/icircumflex 239/idieresis 240/eth 241/ntilde 242/ograve 243/oacute 244/ocircumflex 245/otilde 246/odieresis 247/divide 248/oslash 249/ugrave 250/uacute 251/ucircumflex 252/udieresis 253/yacute 254/thorn 255/ydieresis ] /_Helvetica-BoldOblique/Helvetica-BoldOblique Z %%EndEncoding %%BeginEncoding:_Times-Roman Times-Roman [ 39/quotesingle 96/grave 130/quotesinglbase 131/florin 132/quotedblbase 133/ellipsis 134/dagger 135/daggerdbl 136/circumflex 137/perthousand 138/Scaron 139/guilsinglleft 140/OE 145/quoteleft 146/quoteright 147/quotedblleft 148/quotedblright 149/bullet 150/endash 151/emdash 152/tilde 153/trademark 154/scaron 155/guilsinglright 156/oe 157/dotlessi 159/Ydieresis 164/currency 166/brokenbar 168/dieresis 169/copyright 170/ordfeminine 172/logicalnot 174/registered 175/macron 176/ring 177/plusminus 178/twosuperior 179/threesuperior 180/acute 181/mu 183/periodcentered 184/cedilla 185/onesuperior 186/ordmasculine 188/onequarter 189/onehalf 190/threequarters 192/Agrave 193/Aacute 194/Acircumflex 195/Atilde 196/Adieresis 197/Aring 198/AE 199/Ccedilla 200/Egrave 201/Eacute 202/Ecircumflex 203/Edieresis 204/Igrave 205/Iacute 206/Icircumflex 207/Idieresis 208/Eth 209/Ntilde 210/Ograve 211/Oacute 212/Ocircumflex 213/Otilde 214/Odieresis 215/multiply 216/Oslash 217/Ugrave 218/Uacute 219/Ucircumflex 220/Udieresis 221/Yacute 222/Thorn 223/germandbls 224/agrave 225/aacute 226/acircumflex 227/atilde 228/adieresis 229/aring 230/ae 231/ccedilla 232/egrave 233/eacute 234/ecircumflex 235/edieresis 236/igrave 237/iacute 238/icircumflex 239/idieresis 240/eth 241/ntilde 242/ograve 243/oacute 244/ocircumflex 245/otilde 246/odieresis 247/divide 248/oslash 249/ugrave 250/uacute 251/ucircumflex 252/udieresis 253/yacute 254/thorn 255/ydieresis ] /_Times-Roman/Times-Roman Z %%EndEncoding %%BeginEncoding:_Times-Bold Times-Bold [ 39/quotesingle 96/grave 130/quotesinglbase 131/florin 132/quotedblbase 133/ellipsis 134/dagger 135/daggerdbl 136/circumflex 137/perthousand 138/Scaron 139/guilsinglleft 140/OE 145/quoteleft 146/quoteright 147/quotedblleft 148/quotedblright 149/bullet 150/endash 151/emdash 152/tilde 153/trademark 154/scaron 155/guilsinglright 156/oe 157/dotlessi 159/Ydieresis 164/currency 166/brokenbar 168/dieresis 169/copyright 170/ordfeminine 172/logicalnot 174/registered 175/macron 176/ring
177/plusminus 178/twosuperior 179/threesuperior 180/acute 181/mu 183/periodcentered 184/cedilla 185/onesuperior 186/ordmasculine 188/onequarter 189/onehalf 190/threequarters 192/Agrave 193/Aacute 194/Acircumflex 195/Atilde 196/Adieresis 197/Aring 198/AE 199/Ccedilla 200/Egrave 201/Eacute 202/Ecircumflex 203/Edieresis 204/Igrave 205/Iacute 206/Icircumflex 207/Idieresis 208/Eth 209/Ntilde 210/Ograve 211/Oacute 212/Ocircumflex 213/Otilde 214/Odieresis 215/multiply 216/Oslash 217/Ugrave 218/Uacute 219/Ucircumflex 220/Udieresis 221/Yacute 222/Thorn 223/germandbls 224/agrave 225/aacute 226/acircumflex 227/atilde 228/adieresis 229/aring 230/ae 231/ccedilla 232/egrave 233/eacute 234/ecircumflex 235/edieresis 236/igrave 237/iacute 238/icircumflex 239/idieresis 240/eth 241/ntilde 242/ograve 243/oacute 244/ocircumflex 245/otilde 246/odieresis 247/divide 248/oslash 249/ugrave 250/uacute 251/ucircumflex 252/udieresis 253/yacute 254/thorn 255/ydieresis ] /_Times-Bold/Times-Bold Z %%EndEncoding %%BeginEncoding:_Times-Italic Times-Italic [ 39/quotesingle 96/grave 130/quotesinglbase 131/florin 132/quotedblbase 133/ellipsis 134/dagger 135/daggerdbl 136/circumflex 137/perthousand 138/Scaron 139/guilsinglleft 140/OE 145/quoteleft 146/quoteright 147/quotedblleft 148/quotedblright 149/bullet 150/endash 151/emdash 152/tilde 153/trademark 154/scaron 155/guilsinglright 156/oe 157/dotlessi 159/Ydieresis 164/currency 166/brokenbar 168/dieresis 169/copyright 170/ordfeminine 172/logicalnot 174/registered 175/macron 176/ring 177/plusminus 178/twosuperior 179/threesuperior 180/acute 181/mu 183/periodcentered 184/cedilla 185/onesuperior 186/ordmasculine 188/onequarter 189/onehalf 190/threequarters 192/Agrave 193/Aacute 194/Acircumflex 195/Atilde 196/Adieresis 197/Aring 198/AE 199/Ccedilla 200/Egrave 201/Eacute 202/Ecircumflex 203/Edieresis 204/Igrave 205/Iacute 206/Icircumflex 207/Idieresis 208/Eth 209/Ntilde 210/Ograve 211/Oacute 212/Ocircumflex 213/Otilde 214/Odieresis 215/multiply 216/Oslash 217/Ugrave 218/Uacute 219/Ucircumflex 220/Udieresis 221/Yacute 222/Thorn 223/germandbls 224/agrave 225/aacute 226/acircumflex 227/atilde 228/adieresis 229/aring 230/ae 231/ccedilla 232/egrave 233/eacute 234/ecircumflex 235/edieresis 236/igrave 237/iacute 238/icircumflex 239/idieresis 240/eth 241/ntilde 242/ograve 243/oacute 244/ocircumflex 245/otilde 246/odieresis 247/divide 248/oslash 249/ugrave 250/uacute 251/ucircumflex 252/udieresis 253/yacute 254/thorn 255/ydieresis ] /_Times-Italic/Times-Italic Z %%EndEncoding %%BeginEncoding:_Times-BoldItalic Times-BoldItalic [ 39/quotesingle 96/grave 130/quotesinglbase 131/florin 132/quotedblbase 133/ellipsis 134/dagger 135/daggerdbl 136/circumflex 137/perthousand 138/Scaron 139/guilsinglleft 140/OE 145/quoteleft 146/quoteright 147/quotedblleft 148/quotedblright 149/bullet 150/endash 151/emdash 152/tilde 153/trademark 154/scaron 155/guilsinglright 156/oe 157/dotlessi 159/Ydieresis 164/currency 166/brokenbar 168/dieresis 169/copyright 170/ordfeminine 172/logicalnot 174/registered 175/macron 176/ring 177/plusminus 178/twosuperior 179/threesuperior 180/acute 181/mu 183/periodcentered 184/cedilla 185/onesuperior 186/ordmasculine 188/onequarter 189/onehalf 190/threequarters 192/Agrave 193/Aacute 194/Acircumflex 195/Atilde 196/Adieresis 197/Aring 198/AE 199/Ccedilla 200/Egrave 201/Eacute 202/Ecircumflex 203/Edieresis 204/Igrave 205/Iacute 206/Icircumflex 207/Idieresis 208/Eth 209/Ntilde 210/Ograve 211/Oacute 212/Ocircumflex 213/Otilde 214/Odieresis 215/multiply 216/Oslash 217/Ugrave 218/Uacute 219/Ucircumflex 220/Udieresis 221/Yacute 222/Thorn 223/germandbls 224/agrave 225/aacute 226/acircumflex 227/atilde 228/adieresis
229/aring 230/ae 231/ccedilla 232/egrave 233/eacute 234/ecircumflex 235/edieresis 236/igrave 237/iacute 238/icircumflex 239/idieresis 240/eth 241/ntilde 242/ograve 243/oacute 244/ocircumflex 245/otilde 246/odieresis 247/divide 248/oslash 249/ugrave 250/uacute 251/ucircumflex 252/udieresis 253/yacute 254/thorn 255/ydieresis ] /_Times-BoldItalic/Times-BoldItalic Z %%EndEncoding %%BeginEncoding:_Courier Courier [ 39/quotesingle 96/grave 130/quotesinglbase 131/florin 132/quotedblbase 133/ellipsis 134/dagger 135/daggerdbl 136/circumflex 137/perthousand 138/Scaron 139/guilsinglleft 140/OE 145/quoteleft 146/quoteright 147/quotedblleft 148/quotedblright 149/bullet 150/endash 151/emdash 152/tilde 153/trademark 154/scaron 155/guilsinglright 156/oe 157/dotlessi 159/Ydieresis 164/currency 166/brokenbar 168/dieresis 169/copyright 170/ordfeminine 172/logicalnot 174/registered 175/macron 176/ring 177/plusminus 178/twosuperior 179/threesuperior 180/acute 181/mu 183/periodcentered 184/cedilla 185/onesuperior 186/ordmasculine 188/onequarter 189/onehalf 190/threequarters 192/Agrave 193/Aacute 194/Acircumflex 195/Atilde 196/Adieresis 197/Aring 198/AE 199/Ccedilla 200/Egrave 201/Eacute 202/Ecircumflex 203/Edieresis 204/Igrave 205/Iacute 206/Icircumflex 207/Idieresis 208/Eth 209/Ntilde 210/Ograve 211/Oacute 212/Ocircumflex 213/Otilde 214/Odieresis 215/multiply 216/Oslash 217/Ugrave 218/Uacute 219/Ucircumflex 220/Udieresis 221/Yacute 222/Thorn 223/germandbls 224/agrave 225/aacute 226/acircumflex 227/atilde 228/adieresis 229/aring 230/ae 231/ccedilla 232/egrave 233/eacute 234/ecircumflex 235/edieresis 236/igrave 237/iacute 238/icircumflex 239/idieresis 240/eth 241/ntilde 242/ograve 243/oacute 244/ocircumflex 245/otilde 246/odieresis 247/divide 248/oslash 249/ugrave 250/uacute 251/ucircumflex 252/udieresis 253/yacute 254/thorn 255/ydieresis ] /_Courier/Courier Z %%EndEncoding %%BeginEncoding:_Courier-Bold Courier-Bold [ 39/quotesingle 96/grave 130/quotesinglbase 131/florin 132/quotedblbase 133/ellipsis 134/dagger 135/daggerdbl 136/circumflex 137/perthousand 138/Scaron 139/guilsinglleft 140/OE 145/quoteleft 146/quoteright 147/quotedblleft 148/quotedblright 149/bullet 150/endash 151/emdash 152/tilde 153/trademark 154/scaron 155/guilsinglright 156/oe 157/dotlessi 159/Ydieresis 164/currency 166/brokenbar 168/dieresis 169/copyright 170/ordfeminine 172/logicalnot 174/registered 175/macron 176/ring 177/plusminus 178/twosuperior 179/threesuperior 180/acute 181/mu 183/periodcentered 184/cedilla 185/onesuperior 186/ordmasculine 188/onequarter 189/onehalf 190/threequarters 192/Agrave 193/Aacute 194/Acircumflex 195/Atilde 196/Adieresis 197/Aring 198/AE 199/Ccedilla 200/Egrave 201/Eacute 202/Ecircumflex 203/Edieresis 204/Igrave 205/Iacute 206/Icircumflex 207/Idieresis 208/Eth 209/Ntilde 210/Ograve 211/Oacute 212/Ocircumflex 213/Otilde 214/Odieresis 215/multiply 216/Oslash 217/Ugrave 218/Uacute 219/Ucircumflex 220/Udieresis 221/Yacute 222/Thorn 223/germandbls 224/agrave 225/aacute 226/acircumflex 227/atilde 228/adieresis 229/aring 230/ae 231/ccedilla 232/egrave 233/eacute 234/ecircumflex 235/edieresis 236/igrave 237/iacute 238/icircumflex 239/idieresis 240/eth 241/ntilde 242/ograve 243/oacute 244/ocircumflex 245/otilde 246/odieresis 247/divide 248/oslash 249/ugrave 250/uacute 251/ucircumflex 252/udieresis 253/yacute 254/thorn 255/ydieresis ] /_Courier-Bold/Courier-Bold Z %%EndEncoding %%BeginEncoding:_Courier-Oblique Courier-Oblique [
39/quotesingle 96/grave 130/quotesinglbase 131/florin 132/quotedblbase 133/ellipsis 134/dagger 135/daggerdbl 136/circumflex 137/perthousand 138/Scaron 139/guilsinglleft 140/OE 145/quoteleft 146/quoteright 147/quotedblleft 148/quotedblright 149/bullet 150/endash 151/emdash 152/tilde 153/trademark 154/scaron 155/guilsinglright 156/oe 157/dotlessi 159/Ydieresis 164/currency 166/brokenbar 168/dieresis 169/copyright 170/ordfeminine 172/logicalnot 174/registered 175/macron 176/ring 177/plusminus 178/twosuperior 179/threesuperior 180/acute 181/mu 183/periodcentered 184/cedilla 185/onesuperior 186/ordmasculine 188/onequarter 189/onehalf 190/threequarters 192/Agrave 193/Aacute 194/Acircumflex 195/Atilde 196/Adieresis 197/Aring 198/AE 199/Ccedilla 200/Egrave 201/Eacute 202/Ecircumflex 203/Edieresis 204/Igrave 205/Iacute 206/Icircumflex 207/Idieresis 208/Eth 209/Ntilde 210/Ograve 211/Oacute 212/Ocircumflex 213/Otilde 214/Odieresis 215/multiply 216/Oslash 217/Ugrave 218/Uacute 219/Ucircumflex 220/Udieresis 221/Yacute 222/Thorn 223/germandbls 224/agrave 225/aacute 226/acircumflex 227/atilde 228/adieresis 229/aring 230/ae 231/ccedilla 232/egrave 233/eacute 234/ecircumflex 235/edieresis 236/igrave 237/iacute 238/icircumflex 239/idieresis 240/eth 241/ntilde 242/ograve 243/oacute 244/ocircumflex 245/otilde 246/odieresis 247/divide 248/oslash 249/ugrave 250/uacute 251/ucircumflex 252/udieresis 253/yacute 254/thorn 255/ydieresis ] /_Courier-Oblique/Courier-Oblique Z %%EndEncoding %%BeginEncoding:_Courier-BoldOblique Courier-BoldOblique [ 39/quotesingle 96/grave 130/quotesinglbase 131/florin 132/quotedblbase 133/ellipsis 134/dagger 135/daggerdbl 136/circumflex 137/perthousand 138/Scaron 139/guilsinglleft 140/OE 145/quoteleft 146/quoteright 147/quotedblleft 148/quotedblright 149/bullet 150/endash 151/emdash 152/tilde 153/trademark 154/scaron 155/guilsinglright 156/oe 157/dotlessi 159/Ydieresis 164/currency 166/brokenbar 168/dieresis 169/copyright 170/ordfeminine 172/logicalnot 174/registered 175/macron 176/ring 177/plusminus 178/twosuperior 179/threesuperior 180/acute 181/mu 183/periodcentered 184/cedilla 185/onesuperior 186/ordmasculine 188/onequarter 189/onehalf 190/threequarters 192/Agrave 193/Aacute 194/Acircumflex 195/Atilde 196/Adieresis 197/Aring 198/AE 199/Ccedilla 200/Egrave 201/Eacute 202/Ecircumflex 203/Edieresis 204/Igrave 205/Iacute 206/Icircumflex 207/Idieresis 208/Eth 209/Ntilde 210/Ograve 211/Oacute 212/Ocircumflex 213/Otilde 214/Odieresis 215/multiply 216/Oslash 217/Ugrave 218/Uacute 219/Ucircumflex 220/Udieresis 221/Yacute 222/Thorn 223/germandbls 224/agrave 225/aacute 226/acircumflex 227/atilde 228/adieresis 229/aring 230/ae 231/ccedilla 232/egrave 233/eacute 234/ecircumflex 235/edieresis 236/igrave 237/iacute 238/icircumflex 239/idieresis 240/eth 241/ntilde 242/ograve 243/oacute 244/ocircumflex 245/otilde 246/odieresis 247/divide 248/oslash 249/ugrave 250/uacute 251/ucircumflex 252/udieresis 253/yacute 254/thorn 255/ydieresis ] /_Courier-BoldOblique/Courier-BoldOblique Z %%EndEncoding %%BeginEncoding:_Symbol Symbol [ 39/quotesingle 96/grave 130/quotesinglbase 131/florin 132/quotedblbase 133/ellipsis 134/dagger 135/daggerdbl 136/circumflex 137/perthousand 138/Scaron 139/guilsinglleft 140/OE 145/quoteleft 146/quoteright 147/quotedblleft 148/quotedblright 149/bullet 150/endash 151/emdash 152/tilde 153/trademark 154/scaron 155/guilsinglright 156/oe 157/dotlessi 159/Ydieresis 164/currency 166/brokenbar 168/dieresis 169/copyright 170/ordfeminine 172/logicalnot 174/registered 175/macron 176/ring 177/plusminus 178/twosuperior 179/threesuperior 180/acute 181/mu 183/periodcentered 184/cedilla 185/onesuperior 186/ordmasculine
188/onequarter 189/onehalf 190/threequarters 192/Agrave 193/Aacute 194/Acircumflex 195/Atilde 196/Adieresis 197/Aring 198/AE 199/Ccedilla 200/Egrave 201/Eacute 202/Ecircumflex 203/Edieresis 204/Igrave 205/Iacute 206/Icircumflex 207/Idieresis 208/Eth 209/Ntilde 210/Ograve 211/Oacute 212/Ocircumflex 213/Otilde 214/Odieresis 215/multiply 216/Oslash 217/Ugrave 218/Uacute 219/Ucircumflex 220/Udieresis 221/Yacute 222/Thorn 223/germandbls 224/agrave 225/aacute 226/acircumflex 227/atilde 228/adieresis 229/aring 230/ae 231/ccedilla 232/egrave 233/eacute 234/ecircumflex 235/edieresis 236/igrave 237/iacute 238/icircumflex 239/idieresis 240/eth 241/ntilde 242/ograve 243/oacute 244/ocircumflex 245/otilde 246/odieresis 247/divide 248/oslash 249/ugrave 250/uacute 251/ucircumflex 252/udieresis 253/yacute 254/thorn 255/ydieresis ] /_Symbol/Symbol Z %%EndEncoding %%EndSetup u 0.000 0.000 0.000 [] 0 d 2.2500 w 0.000 0.000 0.000 1 j 260.9701 116.7309 261.4485 123.4286 262.8837 130.3654 265.2757 136.8239 268.3854 143.2824 272.4518 149.5017 277.4751 155.4817 283.2159 161.2226 289.9136 166.4850 297.0897 171.2691 304.9834 175.5748 313.3555 179.4020 322.2060 182.7508 331.5349 185.3821 341.3422 187.5349 351.1495 189.2093 361.1960 190.1661 371.4817 190.4053 381.7674 190.1661 391.8140 189.2093 401.6213 187.5349 411.4286 185.3821 420.7575 182.7508 429.6080 179.4020 437.9801 175.5748 445.8738 171.2691 453.0498 166.4850 459.7475 161.2226 465.4884 155.4817 470.5116 149.5017 474.5781 143.2824 477.6877 136.8239 480.0797 130.3654 481.5150 123.4286 481.9934 116.7309 481.5150 110.0332 480.0797 103.0963 0.000 k 1.000 K m L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L
477.6877 474.5781 470.5116 465.4884 459.7475 453.0498 445.8738 437.9801 429.6080 420.7575 411.4286 401.6213 391.8140 381.7674 371.4817 361.1960 351.1495 341.3422 331.5349 322.2060 313.3555 304.9834 297.0897 289.9136 283.2159 277.4751 272.4518 268.3854 265.2757 262.8837 261.4485 260.9701 B U u
96.6379 L 90.1794 L 83.9601 L 77.9801 L 72.2392 L 67.2159 L 62.1927 L 57.8870 L 54.0598 L 50.7110 L 48.0797 L 45.9269 L 44.2525 L 43.2957 L 43.0565 L 43.2957 L 44.2525 L 45.9269 L 48.0797 L 50.7110 L 54.0598 L 57.8870 L 62.1927 L 67.2159 L 72.2392 L 77.9801 L 83.9601 L 90.1794 L 96.6379 L 103.0963 L 110.0332 L 116.7309 L
0.000 0.000 0.000 0.000 k 4.0000 w 1.000 1.000 0.000 0.000 K 307.1362 98.3123 m 307.3754 102.1395 L 308.8106 105.9668 L 311.2027 109.7940 L 314.3123 113.3821 L 318.3787 116.7309 L 323.1628 119.6013 L 328.6645 122.4718 L 334.8837 124.8638 L 341.5814 126.7774 L 348.5183 128.4518 L 356.1728 129.6478 L 363.8272 130.3654 L 371.4817 130.6047 L 379.1362 130.3654 L 386.7907 129.6478 L 394.4452 128.4518 L 401.3821 126.7774 L 408.0797 124.8638 L 414.2990 122.4718 L 419.8007 119.6013 L
424.5847 428.6512 431.7608 434.1528 435.5880 435.8272 435.5880 434.1528 431.7608 428.6512 424.5847 419.8007 414.2990 408.0797 401.3821 394.4452 386.7907 379.1362 371.4817 363.8272 356.1728 348.5183 341.5814 334.8837 328.6645 323.1628 318.3787 314.3123 311.2027 308.8106 307.3754 307.1362 B U u
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FF(n)27 b FK(nodes)h(which)f(are)g(not)g(under)i(control)f(of)f(the)g (adv)o(ersary)i(and)f(if)e(there)i(are)f(no)g(more)g(than)70 2345 y FH(b)11 b FF(B)f FK(ln)g FF(n)23 b FK(data)h(items)g(that)g(map) g(to)f(the)h(node.)70 2452 y SDict begin H.S end 70 2452 a 70 2452 a SDict begin 13.6 H.A end 70 2452 a 70 2452 a SDict begin [ /View [/XYZ H.V] /Dest (theorem.4.3) cvn H.B /DEST pdfmark end 70 2452 a Black 96 x FI(De\002nition)h(4.3.)p Black 44 w FK(An)h FE(\()p FH(a)8 b FG(;)i FH(b)h FE(\))p FK(-good)29 b(path)e(is)f(a)h(path)g(through)i(the)e(b)n(utter\003y)h (netw)o(ork)f(from)g(a)f(top)h(supernode)j(to)c(a)70 2661 y(bottom)e(supernode)i(all)e(of)f(whose)h(supernodes)j(are)d FE(\()p FH(a)8 b FG(;)i FH(b)h FE(\))p FK(-good)25 b(supernodes.)70 2769 y SDict begin H.S end 70 2769 a 70 2769 a SDict begin 13.6 H.A end 70 2769 a 70 2769 a SDict begin [ /View [/XYZ H.V] /Dest (theorem.4.4) cvn H.B /DEST pdfmark end 70 2769 a Black 94 x FI(De\002nition)g(4.4.)p Black 43 w FK(A)g(top)h (supernode)j(is)d(called)h FE(\()p FH(g)8 b FG(;)i FH(a)e FG(;)i FH(b)h FE(\))p FK(-e)o(xpansi)n(v)o(e)29 b(if)d(there)h(e)o (xist)g FH(g)8 b FF(n)p FG(=)i FK(log)i FF(n)25 b FE(\()p FH(a)8 b FG(;)i FH(b)h FE(\))p FK(-good)29 b(paths)70 2976 y(that)24 b(start)g(at)f(this)h(supernode.)70 3147 y SDict begin H.S end 70 3147 a 70 3147 a SDict begin 13.6 H.A end 70 3147 a 70 3147 a SDict begin [ /View [/XYZ H.V] /Dest (subsection.4.3) cvn H.B /DEST pdfmark end 70 3147 a 101 x Fs(4.3)99 b(T)-9 b(echnical)26 b(lemmata)70 3429 y FK(F)o(ollo)n(wing)32 b(are)g(three)h(technical)i(lemmata)d(about)h (bipartite)h(e)o(xpanders)h(that)e(we)e(will)g(use)i(in)f(our)g (proofs.)56 b(The)70 3542 y(proof)29 b(of)g(the)g(\002rst)g(lemma)f(is) h(well)f(kno)n(wn)h([)p 0 0 .8 TeXcolorrgb 1558 3543 a SDict begin H.S end 1558 3543 a 0 0 .8 TeXcolorrgb -1 x FK(30)p 0 0 .8 TeXcolorrgb 1648 3480 a SDict begin H.R end 1648 3480 a 1648 3542 a SDict begin [ /Color [0 1 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (cite.Pinsker) cvn H.B /ANN pdfmark end 1648 3542 a Black 1 w FK(])g(\(see)g(also)g([)p 0 0 .8 TeXcolorrgb 2086 3543 a SDict begin H.S end 2086 3543 a 0 0 .8 TeXcolorrgb -1 x FK(26)p 0 0 .8 TeXcolorrgb 2176 3480 a SDict begin H.R end
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5118 y Fr(\000)p Fo(r)3507 5094 y Fn(0)3524 5118 y Fp(`)3552 5094 y Fn(0)3569 5118 y Fo(d)s Fp(=)p Fo(r)3670 5151 y FK(.)p Black .8 .3 .3 TeXcolorrgb 1000 5401 a SDict begin H.S end 1000 5401 a .8 .3 .3 TeXcolorrgb 1002 5400 a Fv(T)t FC(H)t(E)t(O)t(RY)h(O)t (F)f Fv(C)t FC(O)t(M)t(P)t(U)t(T)t(I)t(N)t(G)p .8 .3 .3 TeXcolorrgb 1876 5344 a SDict begin H.R end 1876 5344 a 1876 5400 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype /URI /URI (http://dx.doi.org/10.4086/toc) >> /Subtype /Link H.B /ANN pdfmark end 1876 5400 a Black Fv(,)e(V)-11 b(olume)19 b(3)i(\(2007\),)c(pp.)25 b(1\22623)928 b(11)p Black eop end %%Page: 12 12 TeXDict begin 12 11 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a Black 0 TeXcolorgray 70 199 a SDict begin H.S end 70 199 a 0 TeXcolorgray 0 TeXcolorgray 70 199 a SDict begin H.R end 70 199 a 70 199 a SDict begin [ /View [/XYZ H.V] /Dest (page.12) cvn H.B /DEST pdfmark end 70 199 a Black 1514 w Fv(A)t(.)25 b(F)t FC(I)t(A)m(T)f(A)t(N)t(D)h Fv(J)t(.)g(S)t FC(A)t(I)t(A)p Black 211 440 a FK(The)32 b(number)h(of)f(w)o(ays)g(to)g(choose)i(a)e (set)h FF(L)1659 407 y Fr(0)1712 440 y FK(of)f(the)h(appropriate)i (size)e(is)f(no)h(more)f(than)h FE(\()p FG(`)10 b FK(e)h FG(=`)3418 407 y Fr(0)3440 440 y FE(\))3475 407 y Fp(`)3503 383 y Fn(0)3557 440 y FK(and)32 b(the)70 553 y(number)27 b(of)e(w)o(ays)i(to)f(choose)h(a)f(set)g FF(R)1306 520 y Fr(0)1353 553 y FK(of)g(the)h(appropriate)i(size)d(is)g(no)g(more)g (than)h FE(\()p FF(r)12 b FK(e)g FG(=)p FF(r)3008 520 y Fr(0)3031 553 y FE(\))3066 520 y Fo(r)3094 496 y Fn(0)3115 553 y FK(.)36 b(So)25 b(the)h(probability)70 666 y(that)e(no)f(tw)o(o)g (subsets)j FF(L)c FK(of)i(size)g FG(`)1160 633 y Fr(0)1205 666 y FK(and)g FF(R)e FK(of)i(size)g FF(r)1737 633 y Fr(0)1782 666 y FK(ha)n(v)o(e)g(no)g(edge)g(between)h(them)f(is)f(no)h (more)f(than:)1470 813 y Fk(\022)1547 880 y FG(`)10 b FK(e)p 1547 920 89 4 v 1561 1004 a FG(`)1599 977 y Fr(0)1645 813 y Fk(\023)1712 835 y Fp(`)1740 811 y Fn(0)1775 941 y FM(\001)1813 840 y Fk(\020)1877 880 y FF(r)i FK(e)p 1877 920 88 4 v 1891 1004 a FF(r)1928 977 y Fr(0)1974 840 y Fk(\021)2029 863 y Fo(r)2057 838 y Fn(0)2091 941 y FM(\001)h FK(e)2169 904 y Fr(\000)2231 878 y Fh(r)2251 860 y Fn(0)2269 878 y Fi(`)2290 860 y Fn(0)2307 878 y Fh(d)p 2230 889 105 3 v 2272 927 a(r)2405 941 y FG(:)70 1204 y FK(Belo)n(w)22 b(we)h(solv)o(e)h(for)g(appropriate)j FF(d)h FK(such)c(that)g(this)g(probability)j(is)c(less)h(than)h(1)p FG(=)p FF(n)2789 1171 y FC(2)2827 1204 y FK(.)1710 1483 y
SDict begin H.S end 1710 1483 a 1710 1483 a SDict begin 13.6 H.A end 1710 1483 a 1710 1483 a SDict begin [ /View [/XYZ H.V] /Dest (equation.4.1) cvn H.B /DEST pdfmark end 1710 1483 a 1720 1354 a Fk(\022)1797 1421 y FG(`)10 b FK(e)p 1797 1462 89 4 v 1811 1545 a FG(`)1849 1519 y Fr(0)1895 1354 y Fk(\023)1962 1377 y Fp(`)1990 1352 y Fn(0)2024 1483 y FM(\001)2062 1382 y Fk(\020)2126 1421 y FF(r)i FK(e)p 2126 1462 88 4 v 2140 1545 a FF(r)2177 1519 y Fr(0)2224 1382 y Fk(\021)2278 1404 y Fo(r)2306 1380 y Fn(0)2340 1483 y FM(\001)h FK(e)2419 1445 y Fr(\000)2481 1419 y Fh(r)2501 1401 y Fn(0)2519 1419 y Fi(`)2540 1401 y Fn(0)2557 1419 y Fh(d)p 2480 1430 105 3 v 2522 1468 a(r)2682 1483 y FM(\024)82 b FK(1)p FG(=)p FF(n)2970 1445 y FC(2)p Black 3656 1483 a FK(\(4.1\))p Black 1088 1734 a FM(\()-15 b(\))201 b FG(`)1494 1696 y Fr(0)1527 1734 y FK(ln)1608 1606 y Fk(\022)1684 1672 y FG(`)10 b FK(e)p 1684 1713 89 4 v 1698 1796 a FG(`)1736 1770 y Fr(0)1783 1606 y Fk(\023)1862 1734 y FE(+)j FF(r)1983 1696 y Fr(0)2015 1734 y FK(ln)2096 1633 y Fk(\020)2160 1672 y FF(r)f FK(e)p 2160 1713 88 4 v 2174 1796 a FF(r)2211 1770 y Fr(0)2258 1633 y Fk(\021)2325 1734 y FM(\000)2418 1672 y FF(r)2455 1639 y Fr(0)2478 1672 y FG(`)2516 1639 y Fr(0)2539 1672 y FF(d)p 2418 1713 171 4 v 2485 1796 a(r)2682 1734 y FM(\024)82 b(\000)p FK(2)10 b(ln)h FF(n)p Black 569 w FK(\(4.2\))p Black 812 1985 a FM(\()-15 b(\))1232 1924 y FF(r)p 1191 1964 121 4 v 1191 2048 a(r)1228 2021 y Fr(0)1251 2048 y FG(`)1289 2021 y Fr(0)1331 1857 y Fk(\022)1398 1985 y FG(`)1436 1948 y Fr(0)1468 1985 y FK(ln)1549 1857 y Fk(\022)1626 1924 y FG(`)10 b FK(e)p 1626 1964 89 4 v 1640 2048 a FG(`)1678 2021 y Fr(0)1724 1857 y Fk(\023)1804 1985 y FE(+)j FF(r)1925 1948 y Fr(0)1957 1985 y FK(ln)2038 1884 y Fk(\020)2102 1924 y FF(r)f FK(e)p 2102 1964 88 4 v 2116 2048 a FF(r)2153 2021 y Fr(0)2200 1884 y Fk(\021)2267 1985 y FE(+)h FK(2)d(ln)g FF(n)2531 1857 y Fk(\023)2682 1985 y FM(\024)82 b FF(d)51 b FG(:)p Black 700 w FK(\(4.3\))p Black 70 2232 a(W)-7 b(e)22 b(get)i(step)g(\()p 0 0 .8 TeXcolorrgb 544 2233 a SDict begin H.S end 544 2233 a 0 0 .8 TeXcolorrgb -1 x FK(4.2)p 0 0 .8 TeXcolorrgb 657 2170 a SDict begin H.R end 657 2170 a 657 2232 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (equation.4.1) cvn H.B /ANN pdfmark end 657 2232 a Black FK(\))g(from)g(step)g (\()p 0 0 .8 TeXcolorrgb 1110 2233 a SDict begin H.S end 1110 2233 a 0 0 .8 TeXcolorrgb -1 x FK(4.1)p 0 0 .8 TeXcolorrgb 1223 2170 a SDict begin H.R end 1223 2170 a 1223 2232 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (equation.4.1) cvn H.B /ANN pdfmark end
1223 2232 a Black FK(\))g(in)f(the)h(abo)o(v) o(e)g(by)g(taking)h(the)e(logarithm)i(of)f(both)g(sides.)p 3765 2232 4 62 v 3769 2174 55 4 v 3769 2232 V 3822 2232 4 62 v 70 2327 a SDict begin H.S end 70 2327 a 70 2327 a SDict begin 13.6 H.A end 70 2327 a 70 2327 a SDict begin [ /View [/XYZ H.V] /Dest (theorem.4.6) cvn H.B /DEST pdfmark end 70 2327 a Black 93 x FI(Lemma)e(4.6.)p Black 42 w FF(Let)h FG(`;)10 b FF(r)-8 b FG(;)10 b(`)880 2387 y Fr(0)903 2420 y FG(;)g FF(r)975 2387 y Fr(0)998 2420 y FG(;)g FF(d)5 b FG(;)10 b FH(l)35 b FF(and)24 b(n)f(be)g(any)h(positive)i (values)f(wher)m(e)f FG(`)2533 2387 y Fr(0)2575 2420 y FM(\024)c FG(`)p FF(,)i(r)2786 2387 y Fr(0)2829 2420 y FM(\024)e FF(r)r(,)j FK(0)e FG(<)e FH(l)32 b FG(<)20 b FK(1)j FF(and)965 2669 y(d)i FM(\025)1310 2607 y FK(2)p FF(r)p 1136 2648 431 4 v 1136 2731 a(r)1173 2705 y Fr(0)1196 2731 y FG(`)1234 2705 y Fr(0)1256 2731 y FE(\()p FK(1)13 b FM(\000)g FH(l)e FE(\))1529 2705 y FC(2)1587 2541 y Fk(\022)1653 2669 y FG(`)1691 2631 y Fr(0)1724 2669 y FK(ln)1805 2541 y Fk(\022)1882 2607 y FG(`)f FK(e)p 1882 2648 89 4 v 1896 2731 a FG(`)1934 2705 y Fr(0)1980 2541 y Fk(\023)2059 2669 y FE(+)j FF(r)2180 2631 y Fr(0)2213 2669 y FK(ln)2293 2568 y Fk(\020)2358 2607 y FF(r)f FK(e)p 2358 2648 88 4 v 2372 2731 a FF(r)2409 2705 y Fr(0)2455 2568 y Fk(\021)2522 2669 y FE(+)h FK(2)d(ln)h FF(n)2787 2541 y Fk(\023)2910 2669 y FG(:)70 2921 y FF(Let)24 b(G)g(be)i(a)f(r)o (andom)h(bipartite)h(multigr)o(aph)g(with)f(left)f(side)h(L)e(and)i (right)h(side)f(R)e(wher)m(e)h FM(j)p FF(L)p FM(j)c FE(=)g FG(`)j FF(and)i FM(j)p FF(R)p FM(j)21 b FE(=)g FF(r)27 b(and)70 3034 y(eac)o(h)f(node)h(in)f(L)f(has)h(edg)o(es)h(to)f(d)k(r)o (andom)d(neighbor)o(s)i(in)d(R.)34 b(Then)26 b(with)g(pr)l(obability)j (at)d(least)h FK(1)14 b FM(\000)g FK(1)p FG(=)p FF(n)3482 3001 y FC(2)3520 3034 y FF(,)25 b(for)h(any)70 3147 y(set)c(L)243 3114 y Fr(0)285 3147 y FM(\032)d FF(L)i(wher)m(e)i FM(j)p FF(L)764 3114 y Fr(0)786 3147 y FM(j)d FE(=)f FG(`)959 3114 y Fr(0)981 3147 y FF(,)j(ther)m(e)h(is)f(no)h(set)g(R)1605 3114 y Fr(0)1646 3147 y FM(\032)c FF(R,)i(wher)m(e)i FM(j)p FF(R)2158 3114 y Fr(0)2180 3147 y FM(j)d FE(=)f FF(r)2352 3114 y Fr(0)2396 3147 y FF(suc)o(h)k(that)g(all)g(nodes)h(in) f(R)3247 3114 y Fr(0)3290 3147 y FF(shar)m(e)h(less)f(than)70 3260 y FH(l)11 b FG(`)169 3227 y Fr(0)191 3260 y FF(d)5 b FG(=)p FF(r)26 b(edg)o(es)f(with)e(L)806 3227 y Fr(0)828 3260 y FF(.)p Black 70 3447 a(Pr)l(oof)o(.)p Black 45 w FK(W)-7 b(e)29 b(will)h(use)g(the)g(probabilistic)j(method)e(to)e (sho)n(w)h(this.)48 b(W)-7 b(e)28 b(will)i(\002rst)f(\002x)g(a)g(set)h FF(L)3115 3414 y Fr(0)3161 3447 y FM(\032)23 b FF(L)29 b FK(of)h(size)g FG(`)3648 3414 y Fr(0)3699 3447 y FK(and)70 3560 y(a)h(set)i FF(R)330 3527 y Fr(0)377 3560 y FM(\032)25 b FF(R)31 b FK(of)h(size)h FF(r)877 3527 y Fr(0)932 3560 y FK(and)f(compute)i(the)f(probability)i(that)e(all)g(nodes)g(in)g FF(R)2705 3527 y Fr(0)2758 3560 y FK(share)g(less)g(than)g FH(l)11 b FG(`)3436 3527 y Fr(0)3459 3560 y FF(d)5 b FG(=)p FF(r)34 b FK(edges)70 3673 y(with)26 b FF(L)308 3640 y Fr(0)331 3673 y FK(.)38 b(If)27 b(this)h(bad)f(e)n(v)o(ent)h (occurs)g(then)g(the)g(total)g(number)g(of)f(edges)h(shared)g(between)h
FF(L)3069 3640 y Fr(0)3117 3673 y FK(and)f FF(R)3331 3640 y Fr(0)3379 3673 y FK(must)f(be)g(less)70 3786 y(than)g FH(l)11 b FF(r)350 3753 y Fr(0)373 3786 y FG(`)411 3753 y Fr(0)434 3786 y FF(d)5 b FG(=)p FF(r)r FK(.)39 b(Let)27 b FF(X)34 b FK(be)28 b(a)e(random)i(v)n(ariable)h(gi)n(ving)g(the)e (number)h(of)f(edges)h(shared)h(between)f FF(L)3343 3753 y Fr(0)3392 3786 y FK(and)f FF(R)3605 3753 y Fr(0)3627 3786 y FK(.)39 b(The)70 3899 y(probability)26 b(that)e(a)f(single)i (edge)g(from)e FF(L)1398 3866 y Fr(0)1443 3899 y FK(f)o(alls)h(in)g FF(R)1771 3866 y Fr(0)1816 3899 y FK(is)f FF(r)1936 3866 y Fr(0)1959 3899 y FG(=)p FF(r)i FK(so)f(by)g(linearity)h(of)f(e)o (xpectation,)i(E)p FE(\()p FF(X)9 b FE(\))19 b(=)h FF(r)3507 3866 y Fr(0)3530 3899 y FG(`)3568 3866 y Fr(0)3590 3899 y FF(d)5 b FG(=)p FF(r)r FK(.)211 4012 y(W)-7 b(e)22 b(can)i(then)h(say)e(that:)891 4262 y(Pr)982 4133 y Fk(\022)1049 4262 y FF(X)28 b FM(\024)1234 4200 y FH(l)11 b FF(r)1332 4167 y Fr(0)1355 4200 y FG(`)1393 4167 y Fr(0)1415 4200 y FF(d)p 1234 4241 232 4 v 1331 4324 a(r)1475 4133 y Fk(\023)1563 4262 y FE(=)19 b FK(Pr)p FE(\()p FF(X)29 b FM(\024)20 b FE(\()p FK(1)13 b FM(\000)g FH(d)e FE(\))f FK(E)o FE(\()p FF(X)f FE(\)\))20 b FM(\024)g FK(e)2600 4224 y Fr(\000)7 b FC(E)o FB(\()p Fo(X)f FB(\))p Fq(d)2839 4200 y Fl(2)2868 4224 y Fp(=)p FC(2)2984 4262 y FG(;)70 4514 y FK(where)23 b FH(d)32 b FE(=)19 b FK(1)13 b FM(\000)g FH(l)34 b FK(and)24 b(the)f(last)h(equation)i(follo)n(ws)e(by)g (Chernof)n(f)h(bounds)g(if)e(0)e FG(<)f FH(l)31 b FG(<)20 b FK(1.)211 4627 y(The)32 b(number)h(of)f(w)o(ays)g(to)g(choose)i(a)e (set)h FF(L)1659 4594 y Fr(0)1712 4627 y FK(of)f(the)h(appropriate)i (size)e(is)f(no)h(more)f(than)h FE(\()p FG(`)10 b FK(e)h FG(=`)3418 4594 y Fr(0)3440 4627 y FE(\))3475 4594 y Fp(`)3503 4570 y Fn(0)3557 4627 y FK(and)32 b(the)70 4740 y(number)27 b(of)e(w)o(ays)i(to)f(choose)h(a)f(set)g FF(R)1306 4707 y Fr(0)1353 4740 y FK(of)g(the)h(appropriate)i(size)d (is)g(no)g(more)g(than)h FE(\()p FF(r)12 b FK(e)g FG(=)p FF(r)3008 4707 y Fr(0)3031 4740 y FE(\))3066 4707 y Fo(r)3094 4683 y Fn(0)3115 4740 y FK(.)36 b(So)25 b(the)h(probability)70 4853 y(that)e(no)f(tw)o(o)g(subsets)j FF(L)837 4820 y Fr(0)882 4853 y FK(of)d(size)h FG(`)1182 4820 y Fr(0)1227 4853 y FK(and)g FF(R)1437 4820 y Fr(0)1482 4853 y FK(of)f(size)i FF(r)1782 4820 y Fr(0)1827 4853 y FK(ha)n(v)o(e)f(this)g(bad)g(e)n(v)o (ent)g(occur)h(is)1440 4982 y Fk(\022)1517 5049 y FG(`)10 b FK(e)p 1517 5090 89 4 v 1531 5173 a FG(`)1569 5147 y Fr(0)1615 4982 y Fk(\023)1682 5004 y Fp(`)1710 4980 y Fn(0)1745 5111 y FM(\001)1783 5010 y Fk(\020)1847 5049 y FF(r)i FK(e)p 1847 5090 88 4 v 1861 5173 a FF(r)1898 5147 y Fr(0)1945 5010 y Fk(\021)1999 5032 y Fo(r)2027 5008 y Fn(0)2061 5111 y FM(\001)h FK(e)2139 5073 y Fr(\000)2201 5047 y Fh(r)2221 5029 y Fn(0)2239 5047 y Fi(`)2260 5029 y Fn(0)2278 5047 y Fh(d)s Fj(d)2337 5029 y Fl(2)p 2201 5058 165 3 v 2260 5096 a(2)p Fh(r)2434 5111 y FG(:)p Black .8 .3 .3 TeXcolorrgb 1000 5401 a SDict begin H.S end 1000 5401 a .8 .3 .3 TeXcolorrgb 1002 5400 a Fv(T)t FC(H)t(E)t(O)t(RY)25 b(O)t(F)f Fv(C)t FC(O)t(M)t(P)t(U)t(T)t(I)t(N)t(G)p .8 .3 .3 TeXcolorrgb 1876 5344 a SDict begin H.R end 1876 5344 a 1876 5400 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype
/URI /URI (http://dx.doi.org/10.4086/toc) >> /Subtype /Link H.B /ANN pdfmark end 1876 5400 a Black Fv(,)e(V)-11 b(olume)19 b(3)i(\(2007\),)c(pp.)25 b(1\22623)928 b(12)p Black eop end %%Page: 13 13 TeXDict begin 13 12 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a Black 0 TeXcolorgray 70 199 a SDict begin H.S end 70 199 a 0 TeXcolorgray 0 TeXcolorgray 70 199 a SDict begin H.R end 70 199 a 70 199 a SDict begin [ /View [/XYZ H.V] /Dest (page.13) cvn H.B /DEST pdfmark end 70 199 a Black 948 w Fv(C)t FC(E)t(N)t(S)t(O)t(R)t (S)t(H)t(I)t(P)26 b Fv(R)t FC(E)t(S)t(I)t(S)t(T)n(A)t(N)t(T)e Fv(P)t FC(E)t(E)t(R)t Fv(-)t FC(T)s(O)t Fv(-)t(P)t FC(E)t(E)t(R)g Fv(N)t FC(E)t(T)t(W)s(O)t(R)t(K)t(S)p Black 70 440 a FK(Belo)n(w)e(we)h(solv)o(e)h(for)g(appropriate)j FF(d)h FK(such)c(that)g(this)g(probability)j(is)c(less)h(than)h(1)p FG(=)p FF(n)2789 407 y FC(2)2827 440 y FK(.)1805 785 y SDict begin H.S end 1805 785 a 1805 785 a SDict begin 13.6 H.A end 1805 785 a 1805 785 a SDict begin [ /View [/XYZ H.V] /Dest (equation.4.4) cvn H.B /DEST pdfmark end 1805 785 a 1815 657 a Fk(\022)1892 724 y FG(`)10 b FK(e)p 1892 764 89 4 v 1906 848 a FG(`)1944 821 y Fr(0)1990 657 y Fk(\023)2057 679 y Fp(`)2085 655 y Fn(0)2120 785 y FM(\001)2158 684 y Fk(\020)2222 724 y FF(r)i FK(e)p 2222 764 88 4 v 2236 848 a FF(r)2273 821 y Fr(0)2320 684 y Fk(\021)2374 706 y Fo(r)2402 682 y Fn(0)2436 785 y FM(\001)h FK(e)2514 748 y Fr(\000)2576 721 y Fh(r)2596 703 y Fn(0)2614 721 y Fi(`)2635 703 y Fn(0)2652 721 y Fh(d)s Fj(d)2711 703 y Fl(2)p 2576 732 165 3 v 2635 771 a(2)p Fh(r)2837 785 y FM(\024)83 b FK(1)p FG(=)p FF(n)3126 748 y FC(2)p Black 3656 785 a FK(\(4.4\))p Black 1149 1044 a FM(\()-15 b(\))202 b FG(`)1556 1006 y Fr(0)1588 1044 y FK(ln)1669 915 y Fk(\022)1746 982 y FG(`)10 b FK(e)p 1746 1023 89 4 v 1760 1106 a FG(`)1798 1080 y Fr(0)1844 915 y Fk(\023)1924 1044 y FE(+)j FF(r)2045 1006 y Fr(0)2077 1044 y FK(ln)2158 943 y Fk(\020)2222 982 y FF(r)f FK(e)p 2222 1023 88 4 v 2236 1106 a FF(r)2273 1080 y Fr(0)2320 943 y Fk(\021)2387 1044 y FM(\000)2480 982 y FF(r)2517 949 y Fr(0)2540 982 y FG(`)2578 949 y Fr(0)2600 982 y FF(d)5 b FH(d)2706 949 y FC(2)p 2480 1023 264 4 v 2571 1106 a FK(2)p FF(r)2837 1044 y FM(\024)83 b(\000)p FK(2)10 b(ln)h FF(n)p Black 413 w FK(\(4.5\))p Black 657 1295 a FM(\()-15 b(\))1209 1233 y FK(2)p FF(r)p 1036 1274 431 4 v 1036 1357 a(r)1073 1331 y Fr(0)1095 1357 y FG(`)1133 1331 y Fr(0)1156 1357
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4000 a(4)p Fh(r)2263 4014 y FG(:)70 4229 y FK(Belo)n(w)22 b(we)h(solv)o(e)h(for)g(appropriate)j FF(d)h FK(such)c(that)g(this)g (probability)j(is)c(less)h(than)h(1)p FG(=)p FF(n)2789 4196 y FC(2)2827 4229 y FK(.)1908 4457 y SDict begin H.S end 1908 4457 a 1908 4457 a SDict begin 13.6 H.A end 1908 4457 a 1908 4457 a SDict begin [ /View [/XYZ H.V] /Dest (equation.4.7) cvn H.B /DEST pdfmark end 1908 4457 a 1918 4356 a Fk(\020)1982 4395 y FF(r)12 b FK(e)p 1982 4436 88 4 v 1996 4519 a FF(r)2033 4493 y Fr(0)2080 4356 y Fk(\021)2135 4378 y Fo(r)2163 4354 y Fn(0)2196 4457 y FM(\001)h FK(e)2275 4419 y Fr(\000)2337 4393 y Fh(r)2357 4375 y Fn(0)2375 4393 y Fi(`)p Fh(d)s Fj(d)2455 4375 y Fl(2)p 2336 4404 147 3 v 2387 4442 a(4)p Fh(r)2580 4457 y FM(\024)82 b FK(1)p FG(=)p FF(n)2868 4419 y FC(2)p Black 3656 4457 a FK(\(4.7\))p Black 1404 4691 a FM(\()-15 b(\))201 b FF(r)1809 4654 y Fr(0)1842 4691 y FK(ln)1923 4591 y Fk(\020)1987 4630 y FF(r)12 b FK(e)p 1987 4671 88 4 v 2001 4754 a FF(r)2038 4728 y Fr(0)2085 4591 y Fk(\021)2152 4691 y FM(\000)2245 4630 y FF(r)2282 4597 y Fr(0)2305 4630 y FG(`)p FF(d)5 b FH(d)2449 4597 y FC(2)p 2245 4671 242 4 v 2325 4754 a FK(4)p FF(r)2580 4691 y FM(\024)82 b(\000)p FK(2)10 b(ln)h FF(n)p Black 671 w FK(\(4.8\))p Black 914 4909 a FM(\()-15 b(\))1467 4848 y FK(4)p FF(r)p 1293 4889 431 4 v 1293 4972 a(r)1330 4946 y Fr(0)1353 4972 y FG(`)p FE(\()p FH(b)1487 4946 y Fr(0)1522 4972 y FM(\000)13 b FK(1)p FE(\))1686 4946 y FC(2)1743 4808 y Fk(\020)1798 4909 y FF(r)1835 4872 y Fr(0)1868 4909 y FK(ln)1948 4808 y Fk(\020)2013 4848 y FF(r)f FK(e)p 2013 4889 88 4 v 2027 4972 a FF(r)2064 4946 y Fr(0)2110 4808 y Fk(\021)2177 4909 y FE(+)h FK(2)d(ln)h FF(n)2442 4808 y Fk(\021)2580 4909 y FM(\024)82 b FF(d)51 b FG(:)p Black 802 w FK(\(4.9\))p Black 70 5132 a(W)-7 b(e)22 b(get)i(step)g(\()p 0 0 .8 TeXcolorrgb 544 5133 a SDict begin H.S end 544 5133 a 0 0 .8 TeXcolorrgb -1 x FK(4.8)p 0 0 .8 TeXcolorrgb 657 5070 a SDict begin H.R end 657 5070 a 657 5132 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (equation.4.7) cvn H.B /ANN pdfmark end 657 5132 a Black FK(\))g(from)g(step)g(\()p 0 0 .8 TeXcolorrgb 1110 5133 a SDict begin H.S end 1110 5133 a 0 0 .8 TeXcolorrgb -1 x FK(4.7)p 0 0 .8 TeXcolorrgb 1223 5070 a SDict begin H.R end 1223 5070 a 1223 5132 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (equation.4.7) cvn H.B /ANN pdfmark end 1223 5132 a Black FK(\))g(in)f(the)h(abo)o(v)o(e)g(by)g(taking)h(the) e(logarithm)i(of)f(both)g(sides.)p 3765 5132 4 62 v 3769
5074 55 4 v 3769 5132 V 3822 5132 4 62 v Black .8 .3 .3 TeXcolorrgb 1000 5401 a SDict begin H.S end 1000 5401 a .8 .3 .3 TeXcolorrgb 1002 5400 a Fv(T)t FC(H)t(E)t(O)t(RY)h(O)t(F)f Fv(C)t FC(O)t(M)t(P)t(U)t(T)t(I)t(N)t(G)p .8 .3 .3 TeXcolorrgb 1876 5344 a SDict begin H.R end 1876 5344 a 1876 5400 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype /URI /URI (http://dx.doi.org/10.4086/toc) >> /Subtype /Link H.B /ANN pdfmark end 1876 5400 a Black Fv(,)e(V)-11 b(olume)19 b(3)i(\(2007\),)c(pp.)25 b(1\22623)928 b(13)p Black eop end %%Page: 14 14 TeXDict begin 14 13 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a Black 0 TeXcolorgray 70 199 a SDict begin H.S end 70 199 a 0 TeXcolorgray 0 TeXcolorgray 70 199 a SDict begin H.R end 70 199 a 70 199 a SDict begin [ /View [/XYZ H.V] /Dest (page.14) cvn H.B /DEST pdfmark end 70 199 a Black 1514 w Fv(A)t(.)25 b(F)t FC(I)t(A)m(T)f(A)t(N)t(D)h Fv(J)t(.)g(S)t FC(A)t(I)t(A)p Black 70 348 a SDict begin H.S end 70 348 a 70 348 a SDict begin 13.6 H.A end 70 348 a 70 348 a SDict begin [ /View [/XYZ H.V] /Dest (subsection.4.4) cvn H.B /DEST pdfmark end 70 348 a 92 x Fs(4.4)99 b Ff(\()p Fe(a)8 b Fd(;)j Fe(b)h Ff(\))p Fs(-good)24 b(super)o(nodes)70 527 y SDict begin H.S end 70 527 a 70 527 a SDict begin 13.6 H.A end 70 527 a 70 527 a SDict begin [ /View [/XYZ H.V] /Dest (theorem.4.8) cvn H.B /DEST pdfmark end 70 527 a Black 89 x FI(Lemma)g(4.8.)p Black 43 w FF(Let)h FH(a)8 b FG(;)i FH(d)868 583 y Fr(0)891 616 y FG(;)g FF(n)26 b(be)f(values)i(wher)m(e)f FH(a)j FG(<)21 b FK(1)p FG(=)p FK(2)26 b FF(and)h FH(d)2165 583 y Fr(0)2209 616 y FG(>)21 b FK(0)k FF(and)h(let)g(k)r FE(\()p FH(d)2781 583 y Fr(0)2803 616 y FG(;)10 b FH(a)e FE(\))26 b FF(be)f(a)h(value)g(that)h(depends)70 729 y(only)22 b(on)f FH(a)8 b FG(;)i FH(d)514 696 y Fr(0)557 729 y FF(and)22 b(assume)g(n)f(is)g(suf)n(\002ciently)k(lar)m(g)o(e)o (.)j(Let)21 b(eac)o(h)g(node)i(participate)h(in)d(k)r
FE(\()p FH(d)2966 696 y Fr(0)2989 729 y FG(;)10 b FH(a)e FE(\))i FK(ln)h FF(n)21 b(r)o(andom)h(middle)70 842 y(supernodes.)34 b(Then)24 b(r)m(emo)o(ving)i(any)f(set)f(of)g(n)p FG(=)p FK(2)h FF(nodes)h(still)f(leaves)g(all)g(b)n(ut)g FH(d)2598 809 y Fr(0)2620 842 y FF(n)p FG(=)10 b FK(ln)i FF(n)24 b(middle)h(supernodes)j(with)c(at)70 955 y(least)g FH(a)8 b FF(k)r FE(\()p FH(d)462 922 y Fr(0)485 955 y FG(;)i FH(a)e FE(\))i FK(ln)h FF(n)23 b(live)h(nodes.)p Black 70 1147 a(Pr)l(oof)o(.)p Black 45 w FK(F)o(or)35 b(simplicity)-6 b(,)39 b(we)34 b(will)h(assume)h(there)g(are)f FF(n)g FK(middle)h(supernodes)i(\(we)c(can)i(thro)n(w)f(out)g(an)o(y)h(e)o (xcess)70 1260 y(supernodes\).)211 1374 y(Let)31 b FG(`)24 b FE(=)g FF(n)p FK(,)33 b FG(`)659 1341 y Fr(0)706 1374 y FE(=)25 b FF(n)p FG(=)p FK(2,)34 b FF(r)27 b FE(=)d FF(n)p FK(,)33 b FF(r)1289 1341 y Fr(0)1337 1374 y FE(=)24 b FH(d)1488 1341 y Fr(0)1510 1374 y FF(n)p FG(=)10 b FK(ln)i FF(n)p FK(,)33 b FH(l)j FE(=)24 b FK(2)p FH(a)40 b FK(and)32 b FF(d)d FE(=)c FF(k)r FE(\()p FH(d)2581 1341 y Fr(0)2603 1374 y FG(;)10 b FH(a)e FE(\))i FK(ln)i FF(n)31 b FK(in)p 0 0 .8 TeXcolorrgb 3008 1375 a SDict begin H.S end 3008 1375 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 3316 1375 a SDict begin H.S end 3316 1375 a 0 0 .8 TeXcolorrgb -1 x FK(4.6)p 0 0 .8 TeXcolorrgb 3429 1312 a SDict begin H.R end 3429 1312 a 3429 1374 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.6) cvn H.B /ANN pdfmark end 3429 1374 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 3429 1312 a SDict begin H.R end 3429 1312 a 3429 1374 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.6) cvn H.B /ANN pdfmark end 3429 1374 a Black FK(.)53 b(W)-7 b(e)31 b(w)o(ant)70 1487 y(probability)g(less)e(than)g(1)p FG(=)p FF(n)979 1454 y FC(2)1045 1487 y FK(of)g(being)g(able)g(to)f (remo)o(v)o(e)h FF(n)p FG(=)p FK(2)g(nodes)g(and)g(ha)n(ving)h(a)e(set) h(of)f FH(d)3144 1454 y Fr(0)3167 1487 y FF(n)p FG(=)10 b FK(ln)h FF(n)28 b FK(supernodes)70 1600 y(all)c(with)g(less)h(than)h FH(a)8 b FF(k)r FE(\()p FH(d)908 1567 y Fr(0)930 1600 y FG(;)i FH(a)e FE(\))i FK(ln)i FF(n)24 b FK(li)n(v)o(e)g(nodes.)33 b(This)24 b(happens)j(pro)o(vided)f(that)f(the)g(number)g(of)g (connections)j(from)70 1713 y(each)c(supernode)i(is)e(bounded)h(as)f (in)p 0 0 .8 TeXcolorrgb 1266 1714 a SDict begin H.S end 1266 1714 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 1567 1714 a SDict begin H.S end 1567 1714 a 0 0 .8 TeXcolorrgb -1 x FK(4.6)p 0 0 .8 TeXcolorrgb 1680 1651 a SDict begin H.R end 1680 1651 a 1680 1713 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest
(theorem.4.6) cvn H.B /ANN pdfmark end 1680 1713 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 1680 1651 a SDict begin H.R end 1680 1651 a 1680 1713 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.6) cvn H.B /ANN pdfmark end 1680 1713 a Black FK(:)783 1967 y SDict begin H.S end 783 1967 a 783 1967 a SDict begin 13.6 H.A end 783 1967 a 783 1967 a SDict begin [ /View [/XYZ H.V] /Dest (equation.4.10) cvn H.B /DEST pdfmark end 783 1967 a FF(k)r FE(\()p FH(d)916 1930 y Fr(0)939 1967 y FG(;)10 b FH(a)e FE(\))i FK(ln)h FF(n)84 b FM(\025)1608 1906 y FK(4)10 b(ln)i FF(n)p 1458 1946 484 4 v 1458 2029 a FH(d)1514 2003 y Fr(0)1536 2029 y FF(n)p FE(\()p FK(1)h FM(\000)g FK(2)p FH(a)8 b FE(\))1903 2003 y FC(2)1961 1839 y Fk(\022)2038 1906 y FF(n)i FK(ln)q FE(\()p FK(2)g(e)r FE(\))p 2038 1946 293 4 v 2162 2029 a FK(2)2353 1967 y FE(+)2448 1906 y FH(d)2504 1873 y Fr(0)2526 1906 y FF(n)p 2447 1946 127 4 v 2447 2029 a FK(ln)g FF(n)2596 1967 y FM(\001)j FK(ln)2714 1839 y Fk(\022)2791 1906 y FK(ln)e FF(n)p 2791 1946 V 2815 2029 a FH(d)2871 2003 y Fr(0)2927 1839 y Fk(\023)3007 1967 y FE(+)i FK(2)d(ln)g FF(n)3271 1839 y Fk(\023)p Black 3611 1967 a FK(\(4.10\))p Black 1294 2216 a FE(=)1458 2155 y FK(2)g(ln)q FE(\()p FK(2)g(e)q FE(\))j FM(\001)g FK(ln)e FF(n)p 1458 2195 470 4 v 1473 2279 a FH(d)1529 2252 y Fr(0)1552 2279 y FE(\()p FK(1)i FM(\000)g FK(2)p FH(a)8 b FE(\))1874 2252 y FC(2)1950 2216 y FE(+)13 b FF(o)p FE(\()p FK(1)p FE(\))p Black 1417 w FK(\(4.11\))p Black 551 2464 a FM(\()-15 b(\))202 b FF(k)r FE(\()p FH(d)1053 2427 y Fr(0)1075 2464 y FG(;)10 b FH(a)e FE(\))84 b FM(\025)1530 2403 y FK(2)10 b(ln)r FE(\()p FK(2)g(e)q FE(\))p 1458 2443 439 4 v 1458 2527 a FH(d)1514 2500 y Fr(0)1536 2527 y FE(\()p FK(1)j FM(\000)g FK(2)p FH(a)8 b FE(\))1858 2500 y FC(2)1918 2464 y FE(+)13 b FF(o)p FE(\()p FK(1)p FE(\))46 b FG(:)p Black 1378 w FK(\(4.12\))p Black 3765 2714 4 62 v 3769 2656 55 4 v 3769 2714 V 3822 2714 4 62 v 70 2796 a SDict begin H.S end 70 2796 a 70 2796 a SDict begin 13.6 H.A end 70 2796 a 70 2796 a SDict begin [ /View [/XYZ H.V] /Dest (theorem.4.9) cvn H.B /DEST pdfmark end 70 2796 a Black 114 x FI(Lemma)21 b(4.9.)p Black 39 w FF(Let)h FH(b)11 b FG(;)f FH(d)854 2877 y Fr(0)877 2910 y FG(;)g FF(n)p FG(;)g FF(k)24 b(be)e(values)h(suc)o(h)g(that)f FH(b)30 b FG(>)19 b FK(1)p FF(,)i FH(d)2080 2877 y Fr(0)2122 2910 y FG(>)d FK(0)k FF(and)g(assume)h(n)f(is)g(suf)n(\002ciently)j (lar)m(g)o(e)o(.)k(Let)21 b(eac)o(h)70 3023 y(node)27 b(participate)i(in)d(k)12 b FK(ln)f FF(n)26 b(of)g(the)h(middle)f
(supernodes,)k(c)o(hosen)e(uniformly)g(at)e(r)o(andom.)37 b(Then)26 b(all)h(b)n(ut)g FH(d)3581 2990 y Fr(0)3603 3023 y FF(n)p FG(=)10 b FK(ln)i FF(n)70 3136 y(middle)24 b(supernodes)j(have)d(less)g(than)g FH(b)11 b FF(k)h FK(ln)f FF(n)23 b(participating)28 b(nodes)d(with)e(pr)l(obability)k (at)c(least)i FK(1)13 b FM(\000)g FK(1)p FG(=)p FF(n)3476 3103 y FC(2)3514 3136 y FF(.)p Black 70 3328 a(Pr)l(oof)o(.)p Black 45 w FK(F)o(or)35 b(simplicity)-6 b(,)39 b(we)34 b(will)h(assume)h(there)g(are)f FF(n)g FK(middle)h(supernodes)i(\(we)c (can)i(thro)n(w)f(out)g(an)o(y)h(e)o(xcess)70 3441 y(supernodes)f(and)e (the)f(lemma)g(will)g(still)h(hold\).)56 b(Let)32 b FG(`)24 b FE(=)h FF(n)p FK(,)34 b FF(r)27 b FE(=)e FF(n)p FK(,)34 b FF(r)2414 3408 y Fr(0)2462 3441 y FE(=)24 b FH(d)2613 3408 y Fr(0)2636 3441 y FF(n)p FG(=)10 b FK(ln)i FF(n)p FK(,)34 b FF(d)c FE(=)25 b FF(k)12 b FK(ln)e FF(n)32 b FK(and)h FH(b)3524 3408 y Fr(0)3572 3441 y FE(=)24 b FH(b)43 b FK(in)p 0 0 .8 TeXcolorrgb 70 3555 a SDict begin H.S end 70 3555 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 370 3555 a SDict begin H.S end 370 3555 a 0 0 .8 TeXcolorrgb -1 x FK(4.7)p 0 0 .8 TeXcolorrgb 483 3492 a SDict begin H.R end 483 3492 a 483 3554 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.7) cvn H.B /ANN pdfmark end 483 3554 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 483 3492 a SDict begin H.R end 483 3492 a 483 3554 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.7) cvn H.B /ANN pdfmark end 483 3554 a Black FK(.)29 b(Then)23 b(the)h(statement)h(in)f(this)g(lemma)f(holds)i(pro)o(vided)g(that:) 1137 3808 y SDict begin H.S end 1137 3808 a 1137 3808 a SDict begin 13.6 H.A end 1137 3808 a 1137 3808 a SDict begin [ /View [/XYZ H.V] /Dest (equation.4.13) cvn H.B /DEST pdfmark end 1137 3808 a FF(k)12 b FK(ln)f FF(n)83 b FM(\025)1688 3747 y FK(4)10 b(ln)h FF(n)p 1562 3788 435 4 v 1562 3871 a FH(d)1618 3845 y Fr(0)1640 3871 y FF(n)p FE(\()p FH(b)25 b FM(\000)13 b FK(1)p FE(\))1959 3845 y FC(2)2016 3680 y Fk(\022)2094 3747 y FH(d)2150 3714 y Fr(0)2173 3747 y FF(n)p 2093 3788 127 4 v 2093 3871 a FK(ln)e FF(n)2242 3808 y FM(\001)i FK(ln)2361 3680 y Fk(\022)2437 3747 y FK(ln)e FF(n)p 2437 3788 V 2461 3871 a FH(d)2517 3845 y Fr(0)2574 3680 y Fk(\023)2653 3808 y FE(+)i FK(2)d(ln)h FF(n)2918 3680 y Fk(\023)p Black 3611 3808 a FK(\(4.13\))p Black 905 4060 a FM(\()-15 b(\))201 b FF(k)85 b FM(\025)1763 3998 y FK(4)p 1562 4039 447 4 v 1562 4122 a FE(\()p FH(b)24 b FM(\000)13 b FK(1)p FE(\))1835 4096 y FC(2)1882 4122 y FK(ln)e FF(n)2031 4060 y FM(\001)i FK(ln)2150 3931
y Fk(\022)2227 3998 y FK(ln)e FF(n)p 2227 4039 127 4 v 2251 4122 a FH(d)2307 4096 y Fr(0)2376 4060 y FE(+)2508 3998 y FK(2)p 2469 4039 124 4 v 2469 4122 a FH(d)2525 4096 y Fr(0)2547 4122 y FF(n)2603 3931 y Fk(\023)2725 4060 y FG(:)p Black 861 w FK(\(4.14\))p Black 70 4311 a(The)23 b(right)h(hand)h(side)f(of)f(this)h(equation)i(goes)e(to)g(0)f (as)h FF(n)f FK(goes)h(to)g(in\002nity)-6 b(.)p 3765 4311 4 62 v 3769 4253 55 4 v 3769 4311 V 3822 4311 4 62 v 70 4413 a SDict begin H.S end 70 4413 a 70 4413 a SDict begin 13.6 H.A end 70 4413 a 70 4413 a SDict begin [ /View [/XYZ H.V] /Dest (theorem.4.10) cvn H.B /DEST pdfmark end 70 4413 a Black 95 x FI(Lemma)23 b(4.10.)p Black 43 w FF(Let)h FH(a)8 b FG(;)i FH(d)911 4475 y Fr(0)934 4508 y FG(;)g FF(n)24 b(be)h(values)h(suc)o(h)f(that)g FH(a)k FG(<)20 b FK(1)p FG(=)p FK(2)p FF(,)25 b FH(d)2174 4475 y Fr(0)2218 4508 y FG(>)20 b FK(0)k FF(and)h(let)g(k)r FE(\()p FH(d)2786 4475 y Fr(0)2809 4508 y FG(;)10 b FH(a)e FE(\))24 b FF(be)g(a)h(value)g(that)h(depends)70 4620 y(only)h(on)f FH(d)424 4587 y Fr(0)472 4620 y FF(and)h FH(a)33 b FF(and)27 b(assume)g(n)f(is)g(suf)n(\002ciently)k(lar)m(g)o (e)o(.)37 b(Let)26 b(eac)o(h)g(node)i(participate)h(in)d(k)r FE(\()p FH(d)3192 4587 y Fr(0)3215 4620 y FG(;)10 b FH(a)e FE(\))26 b FF(top)g(\(bottom\))70 4733 y(supernodes.)46 b(Then)28 b(r)m(emo)o(ving)i(any)f(set)f(of)h(n)p FG(=)p FK(2)g FF(nodes)g(still)g(leaves)h(all)f(b)n(ut)g FH(d)2655 4700 y Fr(0)2677 4733 y FF(n)p FG(=)10 b FK(ln)i FF(n)28 b(top)h(\(bottom\))g(supernodes)70 4846 y(with)23 b(at)g(least)i FH(a)8 b FF(k)r FE(\()p FH(d)735 4813 y Fr(0)757 4846 y FG(;)i FH(a)e FE(\))i FK(ln)i FF(n)23 b(live)h(nodes.)p Black 70 5038 a(Pr)l(oof)o(.)p Black 45 w FK(Let)f FG(`)d FE(=)g FF(n)p FK(,)j FG(`)761 5005 y Fr(0)804 5038 y FE(=)c FF(n)p FG(=)p FK(2,)24 b FF(r)f FE(=)d FF(n)p FG(=)10 b FK(ln)i FF(n)p FK(,)23 b FF(r)1535 5005 y Fr(0)1578 5038 y FE(=)d FH(d)1725 5005 y Fr(0)1747 5038 y FF(n)p FG(=)10 b FK(ln)i FF(n)p FK(,)23 b FH(l)31 b FE(=)20 b FK(2)p FH(a)31 b FK(and)24 b FF(d)i FE(=)19 b FF(k)r FE(\()p FH(d)2773 5005 y Fr(0)2796 5038 y FG(;)10 b FH(a)e FE(\))23 b FK(in)p 0 0 .8 TeXcolorrgb 3048 5039 a SDict begin H.S end 3048 5039 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 3348 5039 a SDict begin H.S end 3348 5039 a 0 0 .8 TeXcolorrgb -1 x FK(4.6)p 0 0 .8 TeXcolorrgb 3461 4976 a SDict begin H.R end 3461 4976 a 3461 5038 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.6) cvn H.B /ANN pdfmark end 3461 5038 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 3461 4976 a SDict begin H.R end 3461 4976 a 3461 5038 a
SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.6) cvn H.B /ANN pdfmark end 3461 5038 a Black FK(.)29 b(W)-7 b(e)23 b(w)o(ant)70 5151 y(probability)i(less)d(than)g(1)p FG(=)p FF(n)959 5118 y FC(2)1019 5151 y FK(of)g(being)h(able)f(to)g (remo)o(v)o(e)g FF(n)p FG(=)p FK(2)g(nodes)h(and)f(ha)n(ving)i(a)d(set) h(of)g FH(d)3039 5118 y Fr(0)3061 5151 y FF(n)p FG(=)10 b FK(ln)i FF(n)22 b FK(supernodes)j(all)p Black .8 .3 .3 TeXcolorrgb 1000 5401 a SDict begin H.S end 1000 5401 a .8 .3 .3 TeXcolorrgb 1002 5400 a Fv(T)t FC(H)t(E)t(O)t(RY)g(O)t(F)f Fv(C)t FC(O)t(M)t(P)t(U)t(T)t(I)t(N)t(G)p .8 .3 .3 TeXcolorrgb 1876 5344 a SDict begin H.R end 1876 5344 a 1876 5400 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype /URI /URI (http://dx.doi.org/10.4086/toc) >> /Subtype /Link H.B /ANN pdfmark end 1876 5400 a Black Fv(,)e(V)-11 b(olume)19 b(3)i(\(2007\),)c(pp.)25 b(1\22623)928 b(14)p Black eop end %%Page: 15 15 TeXDict begin 15 14 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a Black 0 TeXcolorgray 70 199 a SDict begin H.S end 70 199 a 0 TeXcolorgray 0 TeXcolorgray 70 199 a SDict begin H.R end 70 199 a 70 199 a SDict begin [ /View [/XYZ H.V] /Dest (page.15) cvn H.B /DEST pdfmark end 70 199 a Black 948 w Fv(C)t FC(E)t(N)t(S)t(O)t(R)t (S)t(H)t(I)t(P)26 b Fv(R)t FC(E)t(S)t(I)t(S)t(T)n(A)t(N)t(T)e Fv(P)t FC(E)t(E)t(R)t Fv(-)t FC(T)s(O)t Fv(-)t(P)t FC(E)t(E)t(R)g Fv(N)t FC(E)t(T)t(W)s(O)t(R)t(K)t(S)p Black 70 440 a FK(with)g(less)h(than)g FH(a)8 b FF(k)r FE(\()p FH(d)793 407 y Fr(0)815 440 y FG(;)i FH(a)e FE(\))i FK(ln)i FF(n)24 b FK(li)n(v)o(e)g(nodes.)33 b(W)-7 b(e)23 b(get)i(this)g(pro)o(vided)h (that)f(the)g(number)g(of)g(connections)j(from)c(each)70 553 y(supernode)i(is)d(bounded)j(as)e(in)p 0 0 .8 TeXcolorrgb 1077 554 a SDict begin H.S end 1077 554 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 1377 554 a SDict begin H.S end 1377 554 a 0 0 .8 TeXcolorrgb -1 x FK(4.6)p 0 0 .8 TeXcolorrgb 1490 491 a SDict begin H.R end 1490 491 a 1490 553 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.6) cvn H.B /ANN pdfmark end 1490 553 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb
1490 491 a SDict begin H.R end 1490 491 a 1490 553 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.6) cvn H.B /ANN pdfmark end 1490 553 a Black FK(:)761 758 y SDict begin H.S end 761 758 a 761 758 a SDict begin 13.6 H.A end 761 758 a 761 758 a SDict begin [ /View [/XYZ H.V] /Dest (equation.4.15) cvn H.B /DEST pdfmark end 761 758 a FF(k)r FE(\()p FH(d)894 721 y Fr(0)916 758 y FG(;)10 b FH(a)e FE(\))84 b FM(\025)1517 697 y FK(4)p 1298 738 484 4 v 1298 821 a FH(d)1354 795 y Fr(0)1377 821 y FF(n)p FE(\()p FK(1)13 b FM(\000)g FK(2)p FH(a)8 b FE(\))1744 795 y FC(2)1802 630 y Fk(\022)1879 697 y FF(n)i FK(ln)q FE(\()p FK(2)g(e)q FE(\))p 1879 738 293 4 v 2002 821 a FK(2)2194 758 y FE(+)2289 697 y FH(d)2345 664 y Fr(0)2367 697 y FF(n)p 2287 738 127 4 v 2287 821 a FK(ln)h FF(n)2436 758 y FM(\001)i FK(ln)q FE(\()p FK(1)p FG(=)p FH(d)2726 721 y Fr(0)2749 758 y FE(\))g(+)g FK(2)d(ln)h FF(n)3062 630 y Fk(\023)p Black 3611 758 a FK(\(4.15\))p Black 1135 1008 a FE(=)1371 946 y FK(2)f(ln)q FE(\()p FK(2)g(e)q FE(\))p 1298 987 439 4 v 1298 1070 a FH(d)1354 1044 y Fr(0)1377 1070 y FE(\()p FK(1)j FM(\000)g FK(2)p FH(a)8 b FE(\))1699 1044 y FC(2)1759 1008 y FE(+)13 b FF(o)p FE(\()p FK(1)p FE(\))46 b FG(:)p Black 1537 w FK(\(4.16\))p Black 3765 1208 4 62 v 3769 1150 55 4 v 3769 1208 V 3822 1208 4 62 v 70 1276 a SDict begin H.S end 70 1276 a 70 1276 a SDict begin 13.6 H.A end 70 1276 a 70 1276 a SDict begin [ /View [/XYZ H.V] /Dest (theorem.4.11) cvn H.B /DEST pdfmark end 70 1276 a Black 113 x FI(Lemma)23 b(4.11.)p Black 43 w FF(Let)g FH(b)11 b FG(;)f FH(d)906 1356 y Fr(0)929 1389 y FG(;)g FF(n)p FG(;)g FF(k)26 b(be)f(values)g(suc)o(h)g(that)g FH(b)32 b FG(>)20 b FK(1)p FF(,)k FH(d)2150 1356 y Fr(0)2193 1389 y FG(>)c FK(0)k FF(and)h(n)e(is)h(suf)n(\002ciently)k(lar)m(g)o(e) o(.)j(Let)24 b(eac)o(h)h(node)70 1501 y(participate)h(in)e(k)g(of)g (the)g(top)g(\(bottom\))h(supernodes)i(\(c)o(hosen)e(uniformly)g(at)e (r)o(andom\).)30 b(Then)24 b(all)g(b)n(ut)g FH(d)3442 1468 y Fr(0)3464 1501 y FF(n)p FG(=)10 b FK(ln)i FF(n)23 b(top)70 1614 y(\(bottom\))h(supernodes)j(consist)e(of)f(less)g(than)g FH(b)11 b FF(k)h FK(ln)f FF(n)23 b(nodes)i(with)f(pr)l(obability)i(at)e (least)g FK(1)13 b FM(\000)g FK(1)p FG(=)p FF(n)3218 1581 y FC(2)3256 1614 y FF(.)p Black 70 1764 a(Pr)l(oof)o(.)p Black 45 w FK(Let)24 b FG(`)c FE(=)g FF(n)p FK(,)j FF(r)g FE(=)d FF(n)p FG(=)10 b FK(ln)i FF(n)p FK(,)23 b FF(r)1183 1731 y Fr(0)1227 1764 y FE(=)d FH(d)1374 1731 y Fr(0)1396 1764 y FF(n)p FG(=)10 b FK(ln)i FF(n)p FK(,)23 b FF(d)j FE(=)20 b FF(k)25 b FK(and)f FH(b)2111 1731 y Fr(0)2154 1764 y FE(=)c FH(b)34 b FK(in)p 0 0 .8 TeXcolorrgb 2423 1765 a
SDict begin H.S end 2423 1765 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 2724 1765 a SDict begin H.S end 2724 1765 a 0 0 .8 TeXcolorrgb -1 x FK(4.7)p 0 0 .8 TeXcolorrgb 2837 1702 a SDict begin H.R end 2837 1702 a 2837 1764 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.7) cvn H.B /ANN pdfmark end 2837 1764 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 2837 1702 a SDict begin H.R end 2837 1702 a 2837 1764 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.7) cvn H.B /ANN pdfmark end 2837 1764 a Black FK(.)c(Then)24 b(the)g(statement)h(in)f(this)70 1877 y(lemma)f(holds)h(pro)o(vided)i(that:)1126 2083 y SDict begin H.S end 1126 2083 a 1126 2083 a SDict begin 13.6 H.A end 1126 2083 a 1126 2083 a SDict begin [ /View [/XYZ H.V] /Dest (equation.4.17) cvn H.B /DEST pdfmark end 1126 2083 a FF(k)84 b FM(\025)1608 2021 y FK(4)p 1414 2062 435 4 v 1414 2145 a FH(d)1470 2119 y Fr(0)1493 2145 y FF(n)p FE(\()p FH(b)24 b FM(\000)13 b FK(1)p FE(\))1811 2119 y FC(2)1868 1955 y Fk(\022)1946 2021 y FH(d)2002 1988 y Fr(0)2025 2021 y FF(n)p 1945 2062 127 4 v 1945 2145 a FK(ln)e FF(n)2094 2083 y FM(\001)i FK(ln)2213 1982 y Fk(\020)2296 2021 y FF(e)p 2277 2062 79 4 v 2277 2145 a FH(d)2333 2119 y Fr(0)2365 1982 y Fk(\021)2432 2083 y FE(+)g FK(2)d(ln)h FF(n)2697 1955 y Fk(\023)p Black 3611 2083 a FK(\(4.17\))p Black 1250 2334 a FE(=)1610 2273 y FK(4)p 1414 2313 437 4 v 1414 2397 a(ln)g FF(n)p FE(\()p FH(b)24 b FM(\000)13 b FK(1)p FE(\))1813 2370 y FC(2)1873 2334 y FM(\001)1911 2206 y Fk(\022)1978 2334 y FK(ln)2059 2233 y Fk(\020)2142 2273 y FF(e)p 2123 2313 79 4 v 2123 2397 a FH(d)2179 2370 y Fr(0)2212 2233 y Fk(\021)2278 2334 y FE(+)2372 2273 y FK(2)d(ln)h FF(n)p 2372 2313 182 4 v 2401 2397 a FH(d)2457 2370 y Fr(0)2479 2397 y FF(n)2563 2206 y Fk(\023)2686 2334 y FG(:)p Black 900 w FK(\(4.18\))p Black 70 2537 a(The)23 b(right)h(hand)h(side)f(of)f (this)h(equation)i(goes)e(to)g(0)f(as)h FF(n)f FK(goes)h(to)g (in\002nity)-6 b(.)p 3765 2537 4 62 v 3769 2479 55 4 v 3769 2537 V 3822 2537 4 62 v 70 2624 a SDict begin H.S end 70 2624 a 70 2624 a SDict begin 13.6 H.A end 70 2624 a 70 2624 a SDict begin [ /View [/XYZ H.V] /Dest (theorem.4.12) cvn H.B /DEST pdfmark end 70 2624 a Black 93 x FI(Cor)n(ollary)32 b(4.12.)p Black 46 w FF(Let)e FH(b)11 b FG(;)f FH(d)1001
2684 y Fr(0)1024 2717 y FG(;)g FF(n)p FG(;)g FF(k)32 b(be)f(values)g(suc)o(h)g(that)g FH(b)k FG(>)24 b FK(1)p FF(,)31 b FH(d)2289 2684 y Fr(0)2335 2717 y FG(>)24 b FK(0)30 b FF(and)h(n)e(is)i(suf)n(\002ciently)i(lar)m(g)o(e)o(.)50 b(Let)29 b(eac)o(h)70 2830 y(data)d(item)g(be)f(stor)m(ed)i(in)f(k)h (of)e(the)h(bottom)h(supernodes)i(\(c)o(hosen)e(uniformly)h(at)d(r)o (andom\).)37 b(Then)25 b(all)h(b)n(ut)h FH(d)3581 2797 y Fr(0)3603 2830 y FF(n)p FG(=)10 b FK(ln)i FF(n)70 2943 y(bottom)24 b(supernodes)j(have)d(less)g(than)g FH(b)11 b FF(k)h FK(ln)f FF(n)24 b(data)g(items)g(stor)m(ed)g(on)g(them)f(with) h(pr)l(obability)i(at)e(least)g FK(1)13 b FM(\000)g FK(1)p FG(=)p FF(n)3707 2910 y FC(2)3745 2943 y FF(.)p Black 70 3093 a(Pr)l(oof)o(.)p Black 45 w FK(Let)31 b(the)g(data)g(items)h (be)e(the)i(left)f(side)h(of)e(a)h(bipartite)i(graph)f(and)g(the)f (bottom)g(supernodes)k(be)c(the)g(right)70 3206 y(side.)e(The)23 b(proof)i(is)e(then)h(the)g(same)g(as)p 0 0 .8 TeXcolorrgb 1355 3207 a SDict begin H.S end 1355 3207 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 1656 3207 a SDict begin H.S end 1656 3207 a 0 0 .8 TeXcolorrgb -1 x FK(4.11)p 0 0 .8 TeXcolorrgb 1814 3144 a SDict begin H.R end 1814 3144 a 1814 3206 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.11) cvn H.B /ANN pdfmark end 1814 3206 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 1814 3144 a SDict begin H.R end 1814 3144 a 1814 3206 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.11) cvn H.B /ANN pdfmark end 1814 3206 a Black FK(.)p 3765 3206 4 62 v 3769 3148 55 4 v 3769 3206 V 3822 3206 4 62 v 70 3293 a SDict begin H.S end 70 3293 a 70 3293 a SDict begin 13.6 H.A end 70 3293 a 70 3293 a SDict begin [ /View [/XYZ H.V] /Dest (theorem.4.13) cvn H.B /DEST pdfmark end 70 3293 a Black 93 x FI(Cor)n(ollary)h(4.13.)p Black 42 w FF(Let)e FH(d)887 3353 y Fr(0)930 3386 y FG(>)d FK(0)p FF(,)i FH(a)28 b FG(<)20 b FK(1)p FG(=)p FK(2)p FF(,)k FH(b)31 b FG(>)20 b FK(1)p FF(.)28 b(Let)23 b(k)r FE(\()p FH(d)2009 3353 y Fr(0)2032 3386 y FG(;)10 b FH(a)e FE(\))p FF(,)23 b(be)g(a)g(value)i(depending)h(only)e(on)g FH(d)3359 3353 y Fr(0)3404 3386 y FF(and)g(assume)70 3499 y(n)31 b(is)h(suf)n(\002ciently)j(lar)m(g)o(e)o(.)55 b(Let)31 b(eac)o(h)h(node)h(appear)h(in)e(k)r FE(\()p FH(d)2004 3466 y Fr(0)2026 3499 y FG(;)10 b FH(a)e FE(\))32 b FF(top)g(supernodes,)37 b(k)r FE(\()p FH(d)2943 3466 y Fr(0)2966 3499 y FG(;)10 b FH(a)e FE(\))32 b FF(bottom)g(supernodes) 70 3612 y(and)22 b(k)r FE(\()p FH(d)360 3579 y Fr(0)382 3612 y FG(;)10 b FH(a)e FE(\))i FK(ln)i FF(n)21 b(middle)h(supernodes.) 32 b(Then)21 b(all)h(b)n(ut)g FH(d)1918 3579 y Fr(0)1941
3612 y FF(n)f(of)h(the)g(supernodes)j(ar)m(e)c FE(\()p FH(a)8 b FF(k)r FE(\()p FH(d)3037 3579 y Fr(0)3060 3612 y FG(;)i FH(a)e FE(\))p FG(;)i FH(b)h FF(k)r FE(\()p FH(d)3424 3579 y Fr(0)3448 3612 y FG(;)f FH(a)e FE(\)\))p FF(-good)70 3724 y(with)23 b(pr)l(obability)k FK(1)13 b FM(\000)g FF(O)p FE(\()p FK(1)p FG(=)p FF(n)1050 3691 y FC(2)1088 3724 y FE(\))p FF(.)p Black 70 3874 a(Pr)l(oof)o(.)p Black 45 w FK(Use)1439 4031 y FF(k)r FE(\()p FH(d)1572 3994 y Fr(0)1595 4031 y FG(;)d FH(a)e FE(\))21 b(=)1851 3970 y FK(10)p 1851 4010 91 4 v 1874 4094 a(3)1965 4031 y FM(\001)2085 3970 y FK(2)10 b(ln)r FE(\()p FK(2)g(e)q FE(\))p 2013 4010 439 4 v 2013 4094 a FH(d)2069 4067 y Fr(0)2091 4094 y FE(\()p FK(1)j FM(\000)g FK(2)p FH(a)8 b FE(\))2413 4067 y FC(2)70 4225 y FK(in)p 0 0 .8 TeXcolorrgb 174 4226 a SDict begin H.S end 174 4226 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 485 4226 a SDict begin H.S end 485 4226 a 0 0 .8 TeXcolorrgb -1 x FK(4.10)p 0 0 .8 TeXcolorrgb 643 4163 a SDict begin H.R end 643 4163 a 643 4225 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.10) cvn H.B /ANN pdfmark end 643 4225 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 643 4163 a SDict begin H.R end 643 4163 a 643 4225 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.10) cvn H.B /ANN pdfmark end 643 4225 a Black FK(.)62 b(Then)34 b(we)g(kno)n(w)g(that)h(no)f(more)h(than)g(3)p FH(d)2127 4192 y Fr(0)2150 4225 y FF(n)p FG(=)p FE(\()p FK(10)10 b(ln)j FF(n)p FE(\))34 b FK(top)h(supernodes)i(and)e(no)g (more)f(than)70 4338 y(3)p FH(d)171 4305 y Fr(0)194 4338 y FF(n)p FG(=)p FE(\()p FK(10)10 b(ln)j FF(n)p FE(\))27 b FK(bottom)h(supernodes)i(ha)n(v)o(e)e(less)f(than)h FH(a)8 b FF(k)r FE(\()p FH(d)2066 4305 y Fr(0)2089 4338 y FG(;)i FH(a)e FE(\))i FK(ln)h FF(n)27 b FK(li)n(v)o(e)g(nodes.)41 b(Ne)o(xt)27 b(plugging)i FF(k)r FE(\()p FH(d)3504 4305 y Fr(0)3527 4338 y FG(;)10 b FH(a)e FE(\))27 b FK(into)p 0 0 .8 TeXcolorrgb 70 4452 a SDict begin H.S end 70 4452 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 372 4452 a SDict begin H.S end 372 4452 a 0 0 .8 TeXcolorrgb -1 x FK(4.8)p 0 0 .8 TeXcolorrgb 485 4389 a SDict begin H.R end 485 4389 a 485 4451 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.8) cvn H.B /ANN pdfmark end 485 4451 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 485 4389 a SDict begin H.R end 485 4389 a 485 4451 a
SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.8) cvn H.B /ANN pdfmark end 485 4451 a Black 26 w FK(gi)n(v)o(es)f(that)h(no)e(more)h(than)h(3)p FH(d)1496 4418 y Fr(0)1519 4451 y FF(n)p FG(=)p FE(\()p FK(10)10 b(ln)j FF(n)p FE(\))25 b FK(middle)i(supernodes)i(ha)n(v)o(e)d (less)h(than)f FH(a)8 b FF(k)r FE(\()p FH(d)3378 4418 y Fr(0)3401 4451 y FG(;)i FH(a)e FE(\))i FK(ln)h FF(n)26 b FK(li)n(v)o(e)70 4564 y(nodes.)211 4677 y(Ne)o(xt)32 b(using)i FF(k)r FE(\()p FH(d)780 4644 y Fr(0)803 4677 y FG(;)10 b FH(a)e FE(\))32 b FK(in)p 0 0 .8 TeXcolorrgb 1073 4678 a SDict begin H.S end 1073 4678 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 1383 4678 a SDict begin H.S end 1383 4678 a 0 0 .8 TeXcolorrgb -1 x FK(4.11)p 0 0 .8 TeXcolorrgb 1541 4615 a SDict begin H.R end 1541 4615 a 1541 4677 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.11) cvn H.B /ANN pdfmark end 1541 4677 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 1541 4615 a SDict begin H.R end 1541 4615 a 1541 4677 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.11) cvn H.B /ANN pdfmark end 1541 4677 a Black 33 w FK(and)p 0 0 .8 TeXcolorrgb 1737 4679 a SDict begin H.S end 1737 4679 a 0 0 .8 TeXcolorrgb -2 x FK(Lemma)p 0 0 .8 TeXcolorrgb 2047 4679 a SDict begin H.S end 2047 4679 a 0 0 .8 TeXcolorrgb -2 x FK(4.9)p 0 0 .8 TeXcolorrgb 2160 4615 a SDict begin H.R end 2160 4615 a 2160 4677 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.9) cvn H.B /ANN pdfmark end 2160 4677 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 2160 4615 a SDict begin H.R end 2160 4615 a 2160 4677 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.9) cvn H.B /ANN pdfmark end 2160 4677 a Black 33 w FK(gi)n(v)o(es)h(that)h(no)f(more)g(than)g FH(d)3168 4644 y Fr(0)3191 4677 y FF(n)p FG(=)p FE(\()p FK(20)10 b(ln)j FF(n)p FE(\))33 b FK(of)f(the)70 4790 y(supernodes)j(can)e(ha)n (v)o(e)g(more)f(than)i FH(b)11 b FF(k)r FE(\()p FH(d)1469 4757 y Fr(0)1491 4790 y FG(;)f FH(a)e FE(\))i FK(ln)i FF(n)32 b FK(nodes)h(in)g(them.)55 b(Finally)-6 b(,)35 b(using)f FF(k)r FE(\()p FH(d)3070 4757 y Fr(0)3093 4790 y FG(;)10 b FH(a)e FE(\))32 b FK(in)p 0 0 .8 TeXcolorrgb 3362 4791 a
SDict begin H.S end 3362 4791 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 3671 4791 a SDict begin H.S end 3671 4791 a 0 0 .8 TeXcolorrgb -1 x FK(4.12)p 0 0 .8 TeXcolorrgb 3829 4728 a SDict begin H.R end 3829 4728 a 3829 4790 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.12) cvn H.B /ANN pdfmark end 3829 4790 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 3829 4728 a SDict begin H.R end 3829 4728 a 3829 4790 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.12) cvn H.B /ANN pdfmark end 3829 4790 a Black 70 4903 a FK(gi)n(v)o(es)c(that)g(no)g(more)f(than)i FH(d)1019 4870 y Fr(0)1041 4903 y FF(n)p FG(=)p FE(\()p FK(20)10 b(ln)j FF(n)p FE(\))28 b FK(of)g(the)g(bottom)g(supernodes)j (can)d(ha)n(v)o(e)g(more)g(than)g FH(b)11 b FF(k)r FE(\()p FH(d)3357 4870 y Fr(0)3380 4903 y FG(;)f FH(a)e FE(\))i FK(ln)i FF(n)27 b FK(data)70 5016 y(items)e(stored)i(at)f(them.)35 b(If)25 b(we)g(put)h(these)g(results)i(together)l(,)g(we)d(get)h(that)g (no)g(more)f(than)h FH(d)11 b FF(n)p FG(=)f FK(ln)i FF(n)26 b FK(supernodes)i(are)70 5128 y(not)23 b FE(\()p FH(a)8 b FF(k)r FE(\()p FH(d)441 5095 y Fr(0)464 5128 y FG(;)i FH(a)e FE(\))p FG(;)i FH(b)h FF(k)r FE(\()p FH(d)828 5095 y Fr(0)852 5128 y FG(;)f FH(a)e FE(\)\))p FK(-good)25 b(with)f(probability)i(1)13 b FM(\000)g FF(O)p FE(\()p FK(1)p FG(=)p FF(n)2241 5095 y FC(2)2279 5128 y FE(\))p FK(.)p 3765 5128 4 62 v 3769 5070 55 4 v 3769 5128 V 3822 5128 4 62 v Black .8 .3 .3 TeXcolorrgb 1000 5401 a SDict begin H.S end 1000 5401 a .8 .3 .3 TeXcolorrgb 1002 5400 a Fv(T)t FC(H)t(E)t(O)t(RY)25 b(O)t(F)f Fv(C)t FC(O)t(M)t(P)t(U)t(T)t(I)t(N)t(G) p .8 .3 .3 TeXcolorrgb 1876 5344 a SDict begin H.R end 1876 5344 a 1876 5400 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype /URI /URI (http://dx.doi.org/10.4086/toc) >> /Subtype /Link H.B /ANN pdfmark end 1876 5400 a Black Fv(,)e(V)-11 b(olume)19 b(3)i(\(2007\),)c(pp.)25 b(1\22623)928 b(15)p Black eop end %%Page: 16 16 TeXDict begin 16 15 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a Black 0 TeXcolorgray 70 199 a SDict begin H.S end 70 199 a 0 TeXcolorgray 0 TeXcolorgray 70 199 a SDict begin H.R end
70 199 a 70 199 a SDict begin [ /View [/XYZ H.V] /Dest (page.16) cvn H.B /DEST pdfmark end 70 199 a Black 1514 w Fv(A)t(.)25 b(F)t FC(I)t(A)m(T)f(A)t(N)t(D)h Fv(J)t(.)g(S)t FC(A)t(I)t(A)p Black 70 348 a SDict begin H.S end 70 348 a 70 348 a SDict begin 13.6 H.A end 70 348 a 70 348 a SDict begin [ /View [/XYZ H.V] /Dest (subsection.4.5) cvn H.B /DEST pdfmark end 70 348 a 92 x Fs(4.5)99 b Ff(\()p Fe(g)8 b Fd(;)j Fe(a)d Fd(;)j Fe(b)h Ff(\))p Fs(-expansi)o(v)o(e)24 b(super)o(nodes)70 526 y SDict begin H.S end 70 526 a 70 526 a SDict begin 13.6 H.A end 70 526 a 70 526 a SDict begin [ /View [/XYZ H.V] /Dest (theorem.4.14) cvn H.B /DEST pdfmark end 70 526 a Black 88 x FI(Theor)n(em)36 b(4.14.)p Black 50 w FF(Let)g FH(d)j FG(>)27 b FK(0)p FF(,)39 b FH(a)c FG(<)27 b FK(1)p FG(=)p FK(2)p FF(,)40 b FK(0)28 b FG(<)f FH(g)36 b FG(<)27 b FK(1)p FF(,)39 b FH(b)f FG(>)27 b FK(1)p FF(.)68 b(Let)36 b(k)r FE(\()p FH(d)11 b FG(;)f FH(a)e FG(;)i FH(g)e FE(\))36 b FF(be)h(a)f(value)h(depending)j(only)70 727 y(on)31 b FH(d)11 b FG(;)f FH(a)e FG(;)i FH(g)40 b FF(and)32 b(assume)h(n)e(is)h(suf)n(\002ciently)j(lar)m(g)o(e)o(.)54 b(Let)32 b(eac)o(h)g(node)h(participate)i(in)c(k)r FE(\()p FH(d)11 b FG(;)f FH(a)e FG(;)i FH(g)e FE(\))32 b FF(top)h(supernodes,) 70 840 y(k)r FE(\()p FH(d)11 b FG(;)f FH(a)e FG(;)i FH(g)e FE(\))19 b FF(bottom)i(supernodes)h(and)f(k)r FE(\()p FH(d)11 b FG(;)f FH(a)e FG(;)i FH(g)e FE(\))i FK(ln)h FF(n)20 b(middle)g(supernodes.)31 b(Then)19 b(all)h(b)n(ut)g FH(d)11 b FF(n)p FG(=)f FK(ln)i FF(n)19 b(top)h(supernodes)70 953 y(ar)m(e)j FE(\()p FH(g)8 b FG(;)i FH(a)e FF(k)r FE(\()p FH(d)j FG(;)f FH(a)e FE(\))p FG(;)i FH(b)h FF(k)r FE(\()p FH(d)g FG(;)f FH(a)e FE(\)\))p FF(-e)n(xpansive)29 b(with)24 b(pr)l(obability)i FK(1)13 b FM(\000)g FF(O)p FE(\()p FK(1)p FG(=)p FF(n)2449 920 y FC(2)2487 953 y FE(\))p FF(.)p Black 70 1123 a(Pr)l(oof)o(.)p Black 45 w FK(Assume)44 b(that)f(for)h(some)f(particular)j FF(k)r FE(\()p FH(d)11 b FG(;)f FH(a)e FG(;)i FH(g)e FE(\))43 b FK(that)h(more)f(than)h FH(d)11 b FF(n)p FG(=)f FK(ln)i FF(n)43 b FK(top)g(supernodes)k(are)c(not)70 1236 y FE(\()p FH(g)8 b FG(;)i FH(a)e FF(k)r FE(\()p FH(d)j FG(;)f FH(a)e FG(;)i FH(g)e FE(\))p FG(;)i FH(b)h FF(k)r FE(\()p FH(d)g FG(;)f FH(a)e FG(;)i FH(g)e FE(\))p FK(-e)o(xpansi)n(v)o(e.)106 b(Then)48 b(each)h(of)f(these)h(bad)f(top)h(supernodes)i(has)d FE(\()p FK(1)23 b FM(\000)e FH(g)8 b FF(n)p FE(\))p FG(=)i FK(ln)i FF(n)70 1349 y FK(paths)55 b(that)g(are)f(not)h FE(\()p FH(a)8 b FF(k)r FE(\()p FH(d)j FG(;)f FH(a)e FG(;)i FH(g)e FE(\))p FG(;)i FH(b)h FF(k)r FE(\()p FH(d)g FG(;)f FH(a)e FG(;)i FH(g)e FE(\)\))p FK(-good.)125 b(So)54 b(the)h(total)g(number)g(of)f(paths)i(that)f(are)f(not)70 1462 y FE(\()p FH(a)8 b FF(k)r FE(\()p FH(d)j FG(;)f
FH(a)e FG(;)i FH(g)e FE(\))p FG(;)i FH(b)h FF(k)r FE(\()p FH(d)g FG(;)f FH(a)e FG(;)i FH(g)e FE(\)\))p FK(-good)27 b(is)c(more)h(than)1717 1641 y FH(d)11 b FE(\()p FK(1)i FM(\000)g FH(g)8 b FE(\))p FF(n)2075 1608 y FC(2)p 1717 1682 396 4 v 1833 1773 a FK(ln)1904 1737 y FC(2)1951 1773 y FF(n)2168 1702 y FG(:)211 1921 y FK(W)-7 b(e)33 b(will)g(sho)n(w)h(there)h(is)f(a)g FF(k)r FE(\()p FH(d)11 b FG(;)f FH(a)e FG(;)i FH(g)e FE(\))34 b FK(such)h(that)f(this)h(e)n(v) o(ent)f(will)g(not)g(occur)h(with)f(high)h(probability)-6 b(.)63 b(Let)70 2034 y FH(d)126 2001 y Fr(0)168 2034 y FE(=)20 b FH(d)11 b FE(\()p FK(1)i FM(\000)g FH(g)8 b FE(\))23 b FK(and)h(let)1258 2195 y FF(k)r FE(\()p FH(d)11 b FG(;)f FH(a)e FG(;)i FH(g)e FE(\))21 b(=)1728 2134 y FK(10)p 1728 2174 91 4 v 1751 2257 a(3)1841 2195 y FM(\001)2079 2134 y FK(2)10 b(ln)q FE(\()p FK(2)g(e)q FE(\))p 1889 2174 673 4 v 1889 2257 a FH(d)h FE(\()p FK(1)i FM(\000)g FH(g)8 b FE(\)\()p FK(1)13 b FM(\000)g FK(2)p FH(a)8 b FE(\))2524 2231 y FC(2)2617 2195 y FG(:)70 2400 y FK(Then)21 b(we)f(kno)n(w)i(by)p 0 0 .8 TeXcolorrgb 735 2401 a SDict begin H.S end 735 2401 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 1034 2401 a SDict begin H.S end 1034 2401 a 0 0 .8 TeXcolorrgb -1 x FK(4.13)p 0 0 .8 TeXcolorrgb 1192 2338 a SDict begin H.R end 1192 2338 a 1192 2400 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.13) cvn H.B /ANN pdfmark end 1192 2400 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 1192 2338 a SDict begin H.R end 1192 2338 a 1192 2400 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.13) cvn H.B /ANN pdfmark end 1192 2400 a Black 21 w FK(that)g(with)f(high)h(probability)-6 b(,)25 b(there)e(are)e(no)h (more)f(than)h FH(d)11 b FE(\()p FK(1)g FM(\000)g FH(g)d FE(\))p FF(n)p FG(=)i FK(ln)i FF(n)21 b FK(supern-)70 2513 y(odes)h(that)f(are)h(not)g FE(\()p FH(a)8 b FF(k)r FE(\()p FH(d)j FG(;)f FH(a)e FG(;)i FH(g)e FE(\))p FG(;)i FH(b)h FF(k)r FE(\()p FH(d)g FG(;)f FH(a)e FG(;)i FH(g)e FE(\)\))p FK(-good.)32 b(W)-7 b(e)20 b(also)i(kno)n(w)f(that)h(each)g (of)f(these)h(supernodes)j(which)c(are)70 2626 y(not)h(good)i(cause)f (at)g(most)f FF(n)p FG(=)10 b FK(ln)i FF(n)22 b FK(paths)i(in)e(the)h (b)n(utter\003y)h(to)e(be)g(not)h FE(\()p FH(a)8 b FF(k)r FE(\()p FH(d)j FG(;)f FH(a)e FG(;)i FH(g)e FE(\))p FG(;)i FH(b)h FF(k)r FE(\()p FH(d)g FG(;)f FH(a)e FG(;)i FH(g)e FE(\)\))p FK(-good.)33 b(Hence)22 b(the)70 2739 y(number)28 b(of)f(paths)h(that)f(are)h(not)f FE(\()p FH(a)8 b FF(k)r FE(\()p FH(d)j FG(;)f FH(a)e FG(;)i FH(g)e FE(\))p FG(;)i FH(b)h FF(k)r FE(\()p FH(d)g FG(;)f FH(a)e FG(;)i FH(g)e FE(\)\))p FK(-good)31 b(is)c(no)g(more)g(than)h FH(d)11 b FE(\()p FK(1)j FM(\000)g FH(g)8 b FE(\))p FF(n)3264 2706 y FC(2)3302 2739 y FG(=)p FE(\()p FK(ln)3454 2703 y FC(2)3501 2739 y FF(n)p FE(\))27 b FK(which)70 2852 y(is)c(what)g(we)g(w)o(anted)h(to)g(sho)n(w)-6 b(.)p
3765 2852 4 62 v 3769 2794 55 4 v 3769 2852 V 3822 2852 4 62 v 70 2983 a SDict begin H.S end 70 2983 a 70 2983 a SDict begin 13.6 H.A end 70 2983 a 70 2983 a SDict begin [ /View [/XYZ H.V] /Dest (subsection.4.6) cvn H.B /DEST pdfmark end 70 2983 a 115 x Fs(4.6)99 b Ff(\()p Fe(a)8 b Fd(;)j Fe(b)h Ff(\))p Fs(-good)24 b(paths)h(to)g(data)g(items)70 3272 y FK(W)-7 b(e)22 b(will)i(use)g(the)g(follo)n(wing)h(lemma)e(to)h (sho)n(w)g(that)g(almost)g(all)g(the)g(nodes)h(are)f(connected)i(to)e (some)g(appropriately)70 3385 y(e)o(xpansi)n(v)o(e)h(top)f(supernode.) 70 3405 y SDict begin H.S end 70 3405 a 70 3405 a SDict begin 13.6 H.A end 70 3405 a 70 3405 a SDict begin [ /View [/XYZ H.V] /Dest (theorem.4.15) cvn H.B /DEST pdfmark end 70 3405 a Black 150 x FI(Lemma)19 b(4.15.)p Black 39 w FF(Let)h FH(d)29 b FG(>)17 b FK(0)p FF(,)k FH(e)k FG(>)17 b FK(0)j FF(and)i(n)e(be)h(suf)n(\002ciently)j(lar)m(g)o(e)o(.)k(Then)21 b(e)n(xists)h(a)f(constant)i(k)r FE(\()p FH(d)11 b FG(;)f FH(e)e FE(\))20 b FF(depending)k(only)70 3668 y(on)e FH(e)28 b FF(and)23 b FH(d)32 b FF(suc)o(h)23 b(that)f(if)g(eac)o(h)g (node)h(connects)i(to)d(k)r FE(\()p FH(d)11 b FG(;)f FH(e)e FE(\))21 b FF(r)o(andom)i(top)f(supernodes)j(then)e(with)f(high) h(pr)l(obability)-5 b(,)70 3781 y(any)24 b(subset)h(of)e(the)h(top)g (supernodes)j(of)c(size)h FE(\()p FK(1)13 b FM(\000)g FH(d)e FE(\))p FF(n)p FG(=)f FK(ln)i FF(n)23 b(can)h(be)g(r)m(eac)o (hed)g(by)g(at)f(least)i FE(\()p FK(1)13 b FM(\000)g FH(e)8 b FE(\))p FF(n)22 b(nodes.)p Black 70 3951 a(Pr)l(oof)o(.)p Black 45 w FK(W)-7 b(e)24 b(imagine)h(the)g FF(n)f FK(nodes)i(as)e(the) h(left)g(side)g(of)f(a)g(bipartite)j(graph)e(and)g(the)g FF(n)p FG(=)10 b FK(ln)i FF(n)24 b FK(top)g(supernodes)k(as)c(the)70 4064 y(right)32 b(side)g(and)f(an)h(edge)g(between)g(a)f(node)h(and)g (a)f(top)h(supernode)i(in)d(this)h(graph)g(if)f(and)h(only)g(if)f(the)h (node)g(and)70 4177 y(supernode)26 b(are)e(connected.)211 4290 y(F)o(or)d(the)i(statement)i(in)d(the)h(lemma)g(to)f(be)h(f)o (alse,)h(there)f(must)g(be)g(some)f(set)h(of)g FH(e)8 b FF(n)22 b FK(nodes)i(on)e(the)h(left)g(side)h(of)e(the)70 4403 y(graph)29 b(and)h(some)e(set)h(of)g FE(\()p FK(1)15 b FM(\000)g FH(d)c FE(\))p FF(n)p FG(=)f FK(ln)i FF(n)28 b FK(top)h(supernodes)j(on)d(the)g(right)g(side)h(of)e(the)h(graph)h (that)g(share)f(no)g(edge.)70 4516 y(W)-7 b(e)23 b(can)h(\002nd)g FF(k)r FE(\()p FH(d)11 b FG(;)f FH(e)e FE(\))23 b FK(lar)n(ge)i(enough) h(that)f(this)f(e)n(v)o(ent)h(occurs)g(with)f(probability)j(no)d(more)g (than)h(1)p FG(=)p FF(n)3331 4483 y FC(2)3393 4516 y FK(by)f(plugging)70 4629 y(in)f FG(`)d FE(=)g FF(n)p FK(,)j FG(`)441 4596 y Fr(0)483 4629 y FE(=)d FH(e)8 b FF(n)p FK(,)22 b FF(r)h FE(=)d FF(n)p FG(=)10 b FK(ln)i FF(n)23 b FK(and)h FF(r)1302 4596 y Fr(0)1345 4629 y FE(=)c(\()p FK(1)13 b FM(\000)g FH(d)e FE(\)\()p FF(n)p FG(=)f FK(ln)i FF(n)p FE(\))23 b FK(into)p 0 0 .8 TeXcolorrgb 2189 4630 a SDict begin H.S end
2189 4630 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 2489 4630 a SDict begin H.S end 2489 4630 a 0 0 .8 TeXcolorrgb -1 x FK(4.5)p 0 0 .8 TeXcolorrgb 2602 4567 a SDict begin H.R end 2602 4567 a 2602 4629 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.5) cvn H.B /ANN pdfmark end 2602 4629 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 2602 4567 a SDict begin H.R end 2602 4567 a 2602 4629 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.5) cvn H.B /ANN pdfmark end 2602 4629 a Black FK(.)29 b(The)23 b(bound)i(found)f(is:)609 4862 y SDict begin H.S end 609 4862 a 609 4862 a SDict begin 13.6 H.A end 609 4862 a 609 4862 a SDict begin [ /View [/XYZ H.V] /Dest (equation.4.19) cvn H.B /DEST pdfmark end 609 4862 a FF(k)r FE(\()p FH(d)11 b FG(;)f FH(e)e FE(\))83 b FM(\025)1264 4801 y FK(1)p 1107 4841 361 4 v 1107 4925 a FE(\()p FK(1)13 b FM(\000)g FH(d)e FE(\))p FH(e)d FF(n)1487 4734 y Fk(\022)1554 4862 y FH(e)g FF(n)13 b FM(\001)g FK(ln)1779 4761 y Fk(\020)1846 4801 y FK(e)p 1843 4841 48 4 v 1843 4925 a FH(e)1900 4761 y Fk(\021)1967 4862 y FE(+)2060 4801 y(\()p FK(1)g FM(\000)g FH(d)e FE(\))p FF(n)p 2060 4841 314 4 v 2154 4925 a FK(ln)g FF(n)2396 4862 y FM(\001)i FK(ln)2515 4734 y Fk(\022)2706 4801 y FK(e)p 2592 4841 268 4 v 2592 4925 a FE(\()p FK(1)g FM(\000)g FH(d)e FE(\))2870 4734 y Fk(\023)2949 4862 y FE(+)i FK(2)d(ln)h FF(n)3214 4734 y Fk(\023)p Black 3611 4862 a FK(\(4.19\))p Black 943 5127 a FE(=)1107 5059 y FK(ln)1187 4985 y Fk(\000)1242 5023 y FC(e)p 1239 5038 35 4 v 1239 5090 a Fq(e)1284 4985 y Fk(\001)p 1107 5106 219 4 v 1118 5189 a FK(1)i FM(\000)g FH(d)1348 5127 y FE(+)g FF(o)p FE(\()p FK(1)p FE(\))46 b FG(:)p Black 1948 w FK(\(4.20\))p Black Black .8 .3 .3 TeXcolorrgb 1000 5401 a SDict begin H.S end 1000 5401 a .8 .3 .3 TeXcolorrgb 1002 5400 a Fv(T)t FC(H)t(E)t(O)t(RY)25 b(O)t(F)f Fv(C)t FC(O)t(M)t(P)t(U)t(T)t(I)t(N)t(G)p .8 .3 .3 TeXcolorrgb 1876 5344 a SDict begin H.R end 1876 5344 a 1876 5400 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype /URI /URI (http://dx.doi.org/10.4086/toc) >> /Subtype /Link H.B /ANN pdfmark end 1876 5400 a Black Fv(,)e(V)-11 b(olume)19 b(3)i(\(2007\),)c(pp.)25 b(1\22623)928 b(16)p Black eop end %%Page: 17 17 TeXDict begin 17 16 bop 0 0 a
SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a Black 0 TeXcolorgray 70 199 a SDict begin H.S end 70 199 a 0 TeXcolorgray 0 TeXcolorgray 70 199 a SDict begin H.R end 70 199 a 70 199 a SDict begin [ /View [/XYZ H.V] /Dest (page.17) cvn H.B /DEST pdfmark end 70 199 a Black 948 w Fv(C)t FC(E)t(N)t(S)t(O)t(R)t (S)t(H)t(I)t(P)26 b Fv(R)t FC(E)t(S)t(I)t(S)t(T)n(A)t(N)t(T)e Fv(P)t FC(E)t(E)t(R)t Fv(-)t FC(T)s(O)t Fv(-)t(P)t FC(E)t(E)t(R)g Fv(N)t FC(E)t(T)t(W)s(O)t(R)t(K)t(S)p Black 3765 440 4 62 v 3769 382 55 4 v 3769 440 V 3822 440 4 62 v 211 657 a FK(W)-7 b(e)24 b(will)h(use)g(the)h(follo)n(wing)h(lemma)d(to)h (sho)n(w)g(that)h(if)f(we)g(can)g(reach)h FH(g)33 b FK(bottom)26 b(supernodes)i(that)e(ha)n(v)o(e)g(some)70 770 y(li)n(v)o(e)d(nodes)i (in)e(them)h(that)g(we)f(can)h(reach)g(most)g(of)f(the)h(data)g(items.) 70 771 y SDict begin H.S end 70 771 a 70 771 a SDict begin 13.6 H.A end 70 771 a 70 771 a SDict begin [ /View [/XYZ H.V] /Dest (theorem.4.16) cvn H.B /DEST pdfmark end 70 771 a Black 202 x FI(Lemma)31 b(4.16.)p Black 47 w FF(Let)g FH(g)8 b FG(;)i FF(n)p FG(;)g FH(e)40 b FF(be)32 b(any)g(positive)i (values)g(suc)o(h)e(that)h FH(e)f FG(>)24 b FK(0)p FF(,)34 b FH(g)f FG(>)24 b FK(0)p FF(.)54 b(Ther)m(e)32 b(e)n(xists)h(a)e(k)r FE(\()p FH(e)8 b FG(;)i FH(g)e FE(\))32 b FF(whic)o(h)70 1086 y(depends)c(only)f(on)g FH(e)8 b FG(;)i FH(g)33 b FF(suc)o(h)27 b(that)g(if)f(eac)o(h)h(bottom)g(supernode)i(holds)f(k) r FE(\()p FH(e)8 b FG(;)i FH(g)e FE(\))i FK(ln)h FF(n)26 b(r)o(andom)h(data)g(items,)g(then)g(any)70 1199 y(subset)e(of)e (bottom)h(supernodes)j(of)d(size)g FH(g)8 b FF(n)p FG(=)i FK(ln)h FF(n)24 b(holds)g FE(\()p FK(1)13 b FM(\000)g FH(e)8 b FE(\))p FF(n)23 b(unique)i(data)f(items.)p Black 70 1402 a(Pr)l(oof)o(.)p Black 45 w FK(W)-7 b(e)18 b(visualize)k(the)d FF(n)g FK(data)g(items)h(as)e(the)i(left)f(side)h(of)f(a)f(bipartite)j (graph)f(and)g(the)f FF(n)p FG(=)10 b FK(ln)i FF(n)19 b FK(bottom)g(supernodes)70 1514 y(as)k(the)h(right)g(side)g(of)g(this) g(graph.)29 b(There)24 b(is)f(an)h(edge)g(between)h(a)e(data)h(item)f (and)h(a)f(bottom)h(supernode)j(if)c(and)h(only)70 1627 y(if)34 b(the)h(bottom)h(supernode)i(contains)f(that)e(data)h(item.)62 b(The)35 b(bad)g(e)n(v)o(ent)h(is)e(that)i(there)g(is)e(some)h(set)g (of)g FH(g)8 b FF(n)p FG(=)i FK(ln)i FF(n)70 1740 y FK(supernodes)33 b(on)e(the)g(right)h(that)f(share)h(no)f(edge)g(with)g(some)f(set)h(of) g FH(e)8 b FF(n)30 b FK(data)h(items)g(on)g(the)g(right.)51 b(W)-7 b(e)30 b(will)g(\002nd)70 1853 y FF(k)r FE(\()p FH(e)8 b FG(;)i FH(g)e FE(\))24 b FK(lar)n(ge)j(enough)g(that)f(this)g (e)n(v)o(ent)g(occurs)h(with)e(probability)k(no)d(more)f(than)h(1)p FG(=)p FF(n)2881 1820 y FC(2)2920 1853 y FK(.)34 b(W)-7 b(e)24 b(do)i(this)g(by)f(plugging)70 1966 y(in)e FG(`)d FE(=)g FF(n)p FK(,)j FG(`)441 1933 y Fr(0)483 1966 y
FE(=)d FH(e)8 b FF(n)p FK(,)22 b FF(r)h FE(=)d FF(n)p FG(=)10 b FK(ln)i FF(n)p FK(,)23 b(and)h FF(r)1325 1933 y Fr(0)1368 1966 y FE(=)c FH(g)8 b FF(n)p FG(=)i FK(ln)h FF(n)23 b FK(into)p 0 0 .8 TeXcolorrgb 1918 1967 a SDict begin H.S end 1918 1967 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 2218 1967 a SDict begin H.S end 2218 1967 a 0 0 .8 TeXcolorrgb -1 x FK(4.5)p 0 0 .8 TeXcolorrgb 2331 1904 a SDict begin H.R end 2331 1904 a 2331 1966 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.5) cvn H.B /ANN pdfmark end 2331 1966 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 2331 1904 a SDict begin H.R end 2331 1904 a 2331 1966 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.5) cvn H.B /ANN pdfmark end 2331 1966 a Black FK(.)211 2083 y(W)-7 b(e)22 b(get:)1100 2345 y SDict begin H.S end 1100 2345 a 1100 2345 a SDict begin 13.6 H.A end 1100 2345 a 1100 2345 a SDict begin [ /View [/XYZ H.V] /Dest (equation.4.21) cvn H.B /DEST pdfmark end 1100 2345 a FF(k)r FE(\()p FH(e)8 b FG(;)i FH(g)e FE(\))i FK(ln)h FF(n)83 b FM(\025)1729 2284 y FK(ln)11 b FF(n)p 1723 2324 138 4 v 1723 2408 a FH(e)d(g)g FF(n)1881 2217 y Fk(\022)1976 2284 y FH(g)g FF(n)p 1958 2324 127 4 v 1958 2408 a FK(ln)j FF(n)2107 2345 y FM(\001)i FK(ln)2238 2284 y(e)p 2235 2324 45 4 v 2235 2408 a FH(g)2303 2345 y FE(+)g FH(e)8 b FF(n)13 b FM(\001)g FK(ln)2624 2284 y(e)p 2620 2324 48 4 v 2620 2408 a FH(e)2690 2345 y FE(+)g FK(2)d(ln)h FF(n)2955 2217 y Fk(\023)p Black 3611 2345 a FK(\(4.21\))p Black 868 2587 a FM(\()-15 b(\))201 b FF(k)r FE(\()p FH(e)8 b FG(;)i FH(g)e FE(\))83 b FM(\025)1723 2525 y FK(1)p 1723 2566 46 4 v 1723 2649 a FH(g)1791 2587 y FM(\001)13 b FK(ln)1923 2525 y(e)p 1920 2566 48 4 v 1920 2649 a FH(e)1990 2587 y FE(+)g FF(o)p FE(\()p FK(1)p FE(\))46 b FG(:)p Black 1306 w FK(\(4.22\))p Black 3765 2842 4 62 v 3769 2784 55 4 v 3769 2842 V 3822 2842 4 62 v 70 2994 a SDict begin H.S end 70 2994 a 70 2994 a SDict begin 13.6 H.A end 70 2994 a 70 2994 a SDict begin [ /View [/XYZ H.V] /Dest (subsection.4.7) cvn H.B /DEST pdfmark end 70 2994 a 120 x Fs(4.7)99 b(Connections)25 b(between)i Ff(\()p Fe(a)8 b Fd(;)j Fe(b)h Ff(\))p Fs(-good)24 b(super)o(nodes)70 3204 y
SDict begin H.S end 70 3204 a 70 3204 a SDict begin 13.6 H.A end 70 3204 a 70 3204 a SDict begin [ /View [/XYZ H.V] /Dest (theorem.4.17) cvn H.B /DEST pdfmark end 70 3204 a Black 91 x FI(Lemma)k(4.17.)p Black 45 w FF(Let)h FH(a)8 b FG(;)i FH(b)h FG(;)f FH(a)1028 3262 y Fr(0)1051 3295 y FG(;)g FF(n)29 b(be)g(any)h(positive)h(values)f(wher)m(e)f FH(a)2317 3262 y Fr(0)2363 3295 y FG(<)23 b FH(a)8 b FF(,)29 b FH(a)i FG(>)23 b FK(0)29 b FF(and)h(let)24 b(C)30 b(be)f(the)h(number)g(of)70 3408 y(supernodes)c(to)d(whic)o(h)g (eac)o(h)h(node)g(connects.)31 b(Let)22 b(X)31 b(and)18 b(Y)34 b(be)24 b(two)e(supernodes)27 b(that)c(ar)m(e)h(both)g FE(\()p FH(a)s FF(C)r FG(;)10 b FH(b)c FF(C)r FE(\))p FF(-good.)70 3521 y(Let)22 b(eac)o(h)h(node)h(in)f(X)30 b(have)24 b(edg)o(es)h(to)e(k)r FE(\()p FH(a)8 b FG(;)i FH(b)h FG(;)f FH(a)1632 3488 y Fr(0)1655 3521 y FE(\))22 b FF(r)o(andom)i(nodes)g(in)18 b(Y)34 b(wher)m(e)23 b(k)r FE(\()p FH(a)8 b FG(;)i FH(b)h FG(;)f FH(a)3002 3488 y Fr(0)3025 3521 y FE(\))22 b FF(is)h(a)g(value)h(depending)70 3634 y(only)h(on)g FH(a)8 b FG(;)i FH(b)35 b FF(and)25 b FH(a)775 3601 y Fr(0)798 3634 y FF(.)31 b(Then)25 b(with)f(pr)l (obability)k(at)d(least)g FK(1)13 b FM(\000)g FK(1)p FG(=)p FF(n)2229 3601 y FC(2)2268 3634 y FF(,)24 b(any)h(set)g(of)g FH(a)2755 3601 y Fr(0)2772 3634 y FF(C)12 b FK(ln)f FF(n)24 b(nodes)i(in)f(X)32 b(has)25 b(at)g(least)70 3747 y FH(a)135 3714 y Fr(0)152 3747 y FF(C)12 b FK(ln)f FF(n)23 b(live)h(neighbor)o(s) j(in)18 b(Y)12 b(.)p Black 70 3950 a(Pr)l(oof)o(.)p Black 45 w FK(Consider)33 b(the)f(e)n(v)o(ent)f(where)h(there)g(is)f(some)g (set)h(of)f FH(a)2144 3917 y Fr(0)2161 3950 y FF(C)12 b FK(ln)f FF(n)31 b FK(nodes)i(in)e FF(X)38 b FK(which)32 b(do)f(not)h(ha)n(v)o(e)g FH(a)3614 3917 y Fr(0)3631 3950 y FF(C)12 b FK(ln)f FF(n)70 4063 y FK(li)n(v)o(e)27 b(neighbors)k(in)23 b FF(Y)12 b FK(.)41 b(There)28 b(are)g FH(a)s FF(C)12 b FK(ln)f FF(n)28 b FK(li)n(v)o(e)g(nodes)h(in)23 b FF(Y)39 b FK(so)28 b(for)g(this)h(e)n(v)o(ent)f(to)g(happen,)j(there) e(must)f(be)g(some)70 4176 y(set)g(of)f FE(\()p FH(a)c FM(\000)14 b FH(a)565 4143 y Fr(0)587 4176 y FE(\))-5 b FF(C)12 b FK(ln)f FF(n)28 b FK(li)n(v)o(e)f(nodes)j(in)22 b FF(Y)39 b FK(that)28 b(share)h(no)f(edge)h(with)e(some)h(set)g(of)g FH(a)2827 4143 y Fr(0)2850 4176 y FF(d)15 b FK(ln)c FF(n)27 b FK(nodes)i(in)f FF(X)9 b FK(.)40 b(W)-7 b(e)27 b(note)70 4288 y(that)35 b(the)h(probability)i(that)d(there)h(are)g(tw)o(o)e (such)i(sets)g(which)f(share)h(no)f(edge)h(is)f(lar)n(gest)i(when)e FF(X)43 b FK(and)30 b FF(Y)46 b FK(ha)n(v)o(e)70 4401 y(the)30 b(most)f(possible)j(nodes.)49 b(Hence)30 b(we)f(will)g(\002nd) h(a)f FF(k)r FE(\()p FH(a)8 b FG(;)i FH(b)h FG(;)f FH(a)2168 4368 y Fr(0)2191 4401 y FE(\))30 b FK(lar)n(ge)h(enough)g(to)f(mak)o(e) g(this)g(bad)g(e)n(v)o(ent)h(occur)70 4514 y(with)36 b(probability)j(less)e(than)g(1)p FG(=)p FF(n)1200 4481 y FC(2)1274 4514 y FK(if)f(in)p 0 0 .8 TeXcolorrgb 1471 4515 a SDict begin H.S end 1471 4515 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 1784 4515 a SDict begin H.S end 1784 4515 a 0 0 .8 TeXcolorrgb
-1 x FK(4.5)p 0 0 .8 TeXcolorrgb 1897 4452 a SDict begin H.R end 1897 4452 a 1897 4514 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.5) cvn H.B /ANN pdfmark end 1897 4514 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 1897 4452 a SDict begin H.R end 1897 4452 a 1897 4514 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.5) cvn H.B /ANN pdfmark end 1897 4514 a Black 36 w FK(we)g(set)g FG(`)27 b FE(=)g FH(b)6 b FF(C)12 b FK(ln)f FF(n)p FK(,)39 b FF(r)30 b FE(=)d FH(b)6 b FF(C)12 b FK(ln)f FF(n)p FK(,)39 b FG(`)3209 4481 y Fr(0)3258 4514 y FE(=)27 b FH(a)3421 4481 y Fr(0)3438 4514 y FF(C)12 b FK(ln)f FF(n)p FK(,)39 b(and)70 4627 y FF(r)107 4594 y Fr(0)150 4627 y FE(=)19 b(\()p FH(a)i FM(\000)13 b FH(a)502 4594 y Fr(0)524 4627 y FE(\))-5 b FF(C)12 b FK(ln)f FF(n)p FK(.)29 b(When)23 b(we)g(do)h(this,)f(we)g(get)h(that)g FF(k)r FE(\()p FH(a)8 b FG(;)i FH(b)h FG(;)f FH(a)2223 4594 y Fr(0)2246 4627 y FE(\))23 b FK(must)h(be)f(greater)i(than)g(or)e (equal)i(to:)775 4764 y Fk(\022)1025 4831 y FH(b)p 852 4872 406 4 v 852 4955 a(a)917 4929 y Fr(0)939 4955 y FE(\()p FH(a)c FM(\000)13 b FH(a)1201 4929 y Fr(0)1223 4955 y FE(\))1268 4764 y Fk(\023)1348 4893 y FM(\001)1386 4764 y Fk(\022)1452 4893 y FH(a)1517 4855 y Fr(0)1550 4893 y FK(ln)1631 4764 y Fk(\022)1707 4831 y FH(b)22 b FK(e)p 1707 4872 112 4 v 1719 4955 a FH(a)1784 4929 y Fr(0)1829 4764 y Fk(\023)1908 4893 y FE(+)13 b(\()p FH(a)21 b FM(\000)13 b FH(a)2254 4855 y Fr(0)2275 4893 y FE(\))d FK(ln)2401 4764 y Fk(\022)2546 4831 y FH(b)22 b FK(e)p 2478 4872 249 4 v 2478 4955 a FH(a)f FM(\000)13 b FH(a)2705 4929 y Fr(0)2736 4764 y Fk(\023)2816 4893 y FE(+)2915 4831 y FK(2)p 2909 4872 59 4 v 2904 4955 a FF(C)2977 4764 y Fk(\023)3100 4893 y FG(:)p 3765 5151 4 62 v 3769 5093 55 4 v 3769 5151 V 3822 5151 4 62 v Black .8 .3 .3 TeXcolorrgb 1000 5401 a SDict begin H.S end 1000 5401 a .8 .3 .3 TeXcolorrgb 1002 5400 a Fv(T)t FC(H)t(E)t(O)t(RY)25 b(O)t(F)f Fv(C)t FC(O)t(M)t(P)t(U)t(T)t(I)t(N)t(G)p .8 .3 .3 TeXcolorrgb 1876 5344 a SDict begin H.R end 1876 5344 a 1876 5400 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype /URI /URI (http://dx.doi.org/10.4086/toc) >> /Subtype /Link H.B /ANN pdfmark end 1876 5400 a Black Fv(,)e(V)-11 b(olume)19 b(3)i(\(2007\),)c(pp.)25 b(1\22623)928 b(17)p Black eop end %%Page: 18 18 TeXDict begin 18 17 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a Black 0 TeXcolorgray
70 199 a SDict begin H.S end 70 199 a 0 TeXcolorgray 0 TeXcolorgray 70 199 a SDict begin H.R end 70 199 a 70 199 a SDict begin [ /View [/XYZ H.V] /Dest (page.18) cvn H.B /DEST pdfmark end 70 199 a Black 1514 w Fv(A)t(.)25 b(F)t FC(I)t(A)m(T)f(A)t(N)t(D)h Fv(J)t(.)g(S)t FC(A)t(I)t(A)p Black 70 348 a SDict begin H.S end 70 348 a 70 348 a SDict begin 13.6 H.A end 70 348 a 70 348 a SDict begin [ /View [/XYZ H.V] /Dest (subsection.4.8) cvn H.B /DEST pdfmark end 70 348 a 92 x Fs(4.8)99 b(Putting)25 b(it)g(all)f(together)70 614 y FK(W)-7 b(e)22 b(are)i(no)n(w)f(ready)i(to)e(gi)n(v)o(e)h(the)f (proof)i(of)p 0 0 .8 TeXcolorrgb 1468 615 a SDict begin H.S end 1468 615 a 0 0 .8 TeXcolorrgb -1 x FK(Theorem)p 0 0 .8 TeXcolorrgb 1818 615 a SDict begin H.S end 1818 615 a 0 0 .8 TeXcolorrgb -1 x FK(3.1)p 0 0 .8 TeXcolorrgb 1931 552 a SDict begin H.R end 1931 552 a 1931 614 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.3.1) cvn H.B /ANN pdfmark end 1931 614 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 1931 552 a SDict begin H.R end 1931 552 a 1931 614 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.3.1) cvn H.B /ANN pdfmark end 1931 614 a Black FK(.)p Black 70 801 a FF(Pr)l(oof)o(.)p Black 45 w FK(Let)36 b FH(d)11 b FG(;)f FH(a)e FG(;)i FH(g)e FG(;)i FH(a)832 768 y Fr(0)855 801 y FG(;)g FH(b)46 b FK(be)36 b(an)o(y)g(v)n(alues)h(such)g(that)f(0) 28 b FG(<)e FH(d)39 b FG(<)26 b FK(1,)39 b(0)27 b FG(<)g FH(a)35 b FG(<)26 b FK(1)p FG(=)p FK(2,)40 b(0)27 b FG(<)g FH(a)3160 768 y Fr(0)3209 801 y FG(<)g FH(a)8 b FK(,)38 b FH(b)g FG(>)27 b FK(1)35 b(and)70 914 y(0)20 b FG(<)g FH(g)28 b FG(<)20 b FK(1.)28 b(Let)761 1177 y FF(C)23 b FE(=)945 1115 y FK(10)p 945 1156 91 4 v 968 1239 a(3)1059 1177 y FM(\001)1296 1115 y FK(2)10 b(ln)r FE(\()p FK(2)g(e)q FE(\))p 1107 1156 673 4 v 1107 1239 a FH(d)h FE(\()p FK(1)i FM(\000)g FH(g)8 b FE(\)\()p FK(1)13 b FM(\000)g FK(2)p FH(a)8 b FE(\))1742 1213 y FC(2)1789 1177 y FG(;)192 b FF(T)31 b FE(=)2189 1109 y FK(ln)2270 1035 y Fk(\000)2324 1073 y FC(e)p 2322 1088 35 4 v 2322 1140 a Fq(e)2366 1035 y Fk(\001)p 2189 1156 219 4 v 2200 1239 a FK(1)13 b FM(\000)g FH(d)2418 1177 y FG(;)192 b FF(B)20 b FE(=)2812 1115 y FK(1)p 2812 1156 46 4 v 2812 1239 a FH(g)2877 1177 y FK(ln)2958 1076 y Fk(\020)3026 1115 y FK(e)p 3022
1156 48 4 v 3022 1239 a FH(e)3080 1076 y Fk(\021)70 1421 y FK(and)707 1562 y FF(D)g FE(=)884 1434 y Fk(\022)1133 1501 y FH(b)p 961 1541 406 4 v 961 1625 a(a)1026 1599 y Fr(0)1048 1625 y FE(\()p FH(a)h FM(\000)13 b FH(a)1310 1599 y Fr(0)1331 1625 y FE(\))1377 1434 y Fk(\023)d(\022)1520 1562 y FH(a)1585 1525 y Fr(0)1618 1562 y FK(ln)1699 1434 y Fk(\022)1776 1501 y FH(b)21 b FK(e)p 1776 1541 112 4 v 1788 1625 a FH(a)1853 1599 y Fr(0)1897 1434 y Fk(\023)1977 1562 y FE(+)13 b(\()p FH(a)20 b FM(\000)13 b FH(a)2322 1525 y Fr(0)2343 1562 y FE(\))d FK(ln)2470 1434 y Fk(\022)2615 1501 y FH(b)21 b FK(e)p 2546 1541 249 4 v 2546 1625 a FH(a)g FM(\000)13 b FH(a)2773 1599 y Fr(0)2804 1434 y Fk(\023)2884 1562 y FE(+)2984 1501 y FK(2)p 2977 1541 59 4 v 2972 1625 a FF(C)3045 1434 y Fk(\023)3168 1562 y FG(:)211 1772 y FK(Let)21 b(each)j(node)f(connect)h(to)18 b FF(C)23 b FK(top,)18 b FF(C)24 b FK(bottom)f(and)18 b FF(C)24 b FK(middle)f(supernodes.)31 b(Then)23 b(by)p 0 0 .8 TeXcolorrgb 3023 1773 a SDict begin H.S end 3023 1773 a 0 0 .8 TeXcolorrgb -1 x FK(Theorem)p 0 0 .8 TeXcolorrgb 3373 1773 a SDict begin H.S end 3373 1773 a 0 0 .8 TeXcolorrgb -1 x FK(4.14)p 0 0 .8 TeXcolorrgb 3531 1710 a SDict begin H.R end 3531 1710 a 3531 1772 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.14) cvn H.B /ANN pdfmark end 3531 1772 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 3531 1710 a SDict begin H.R end 3531 1710 a 3531 1772 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.14) cvn H.B /ANN pdfmark end 3531 1772 a Black FK(,)g(at)f(least)70 1885 y FE(\()p FK(1)15 b FM(\000)g FH(d)c FE(\))p FF(n)p FG(=)f FK(ln)i FF(n)28 b FK(top)i(supernodes)i(are)e FE(\()p FH(g)8 b FG(;)i FH(a)s FF(C)r FG(;)g FH(b)c FF(C)r FE(\))p FK(-e)o(xpansi)n(v)o(e.)49 b(Let)28 b(each)i(node)g(connect)i (to)d FF(T)39 b FK(top)30 b(supernodes.)70 1998 y(Then)20 b(by)p 0 0 .8 TeXcolorrgb 387 1999 a SDict begin H.S end 387 1999 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 685 1999 a SDict begin H.S end 685 1999 a 0 0 .8 TeXcolorrgb -1 x FK(4.15)p 0 0 .8 TeXcolorrgb 843 1936 a SDict begin H.R end 843 1936 a 843 1998 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.15) cvn H.B /ANN pdfmark end 843 1998 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 843 1936 a SDict begin H.R end 843 1936 a 843 1998 a
SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.15) cvn H.B /ANN pdfmark end 843 1998 a Black FK(,)h(at)f(least)i FE(\()p FK(1)10 b FM(\000)g FH(e)e FE(\))p FF(n)20 b FK(nodes)i(can)f(connect)i(to)d(some)h FE(\()p FH(g)8 b FG(;)i FH(a)s FF(C)r FG(;)g FH(b)c FF(C)r FE(\))p FK(-e)o(xpansi)n(v) o(e)24 b(top)d(supernode.)70 2111 y(Let)30 b(each)h(data)g(item)g(map)f (to)g FF(B)g FK(bottom)h(supernodes.)53 b(Then)31 b(by)p 0 0 .8 TeXcolorrgb 2268 2112 a SDict begin H.S end 2268 2112 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 2575 2112 a SDict begin H.S end 2575 2112 a 0 0 .8 TeXcolorrgb -1 x FK(4.16)p 0 0 .8 TeXcolorrgb 2733 2049 a SDict begin H.R end 2733 2049 a 2733 2111 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.16) cvn H.B /ANN pdfmark end 2733 2111 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 2733 2049 a SDict begin H.R end 2733 2049 a 2733 2111 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.16) cvn H.B /ANN pdfmark end 2733 2111 a Black FK(,)h(at)f(least)g FE(\()p FK(1)16 b FM(\000)f FH(e)8 b FE(\))p FF(n)30 b FK(nodes)i(ha)n(v)o(e)70 2223 y FE(\()p FH(a)s FF(C)r FG(;)10 b FH(b)c FF(C)r FE(\))p FK(-good)25 b(paths)g(to)e(at)h(least)g FE(\()p FK(1)13 b FM(\000)g FH(e)8 b FE(\))p FF(n)23 b FK(data)h(items.)211 2336 y(Finally)-6 b(,)32 b(let)d(each)i(node)f(in)g(a)f(middle)i (supernode)h(ha)n(v)o(e)f FF(D)d FK(random)j(connections)i(to)c(nodes)i (in)f(neighboring)70 2449 y(supernodes)36 b(in)c(the)h(b)n(utter\003y)h (netw)o(ork.)58 b(Then)33 b(by)p 0 0 .8 TeXcolorrgb 1812 2450 a SDict begin H.S end 1812 2450 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 2121 2450 a SDict begin H.S end 2121 2450 a 0 0 .8 TeXcolorrgb -1 x FK(4.17)p 0 0 .8 TeXcolorrgb 2279 2387 a SDict begin H.R end 2279 2387 a 2279 2449 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.17) cvn H.B /ANN pdfmark end 2279 2449 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 2279 2387 a SDict begin H.R end 2279 2387 a 2279 2449 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.4.17) cvn H.B /ANN pdfmark end 2279 2449 a Black FK(,)i(at)e(least)h FE(\()p FK(1)16 b FM(\000)g FH(e)8 b FE(\))p FF(n)32 b FK(nodes)i(can)f(broadcast)j(to)70 2562 y(enough)25 b(bottom)f(supernodes)j(so)d(that)g(the)o(y)g(can)f (reach)i(at)e(least)i FE(\()p FK(1)13 b FM(\000)g FH(e)8
b FE(\))p FF(n)22 b FK(data)i(items.)211 2675 y(Each)g(node)h(requires) i FF(T)35 b FK(links)25 b(to)f(connect)j(to)d(the)h(top)g(supernodes;)j (2)p FF(D)c FK(links)h(for)g(each)g(of)g(the)19 b FF(C)26 b FK(top)f(supern-)70 2788 y(odes)k(it)g(plays)h(a)e(role)i(in;)h(2)p FF(D)d FK(links)i(for)f(each)h(of)f(the)24 b FF(C)12 b FK(ln)f FF(n)28 b FK(middle)i(supernodes)i(it)d(plays)h(a)e(role)h (in)g(and)g FF(B)p FH(b)21 b FK(ln)11 b FF(n)70 2901 y FK(storage)27 b(for)e(each)i(of)e(the)c FF(C)27 b FK(bottom)f (supernodes)j(it)c(plays)i(a)e(role)h(in.)34 b(The)25 b(total)i(amount)f(of)g(memory)f(required)j(is)70 3014 y(thus)1409 3127 y FF(T)c FE(+)13 b FK(2)p FF(D)-5 b(C)14 b FE(+)8 b FF(C)k FK(ln)e FF(n)p FE(\()p FK(2)p FF(D)j FE(+)g FF(B)p FH(b)e FE(\))45 b FG(;)70 3292 y FK(which)23 b(is)h(less)g(than)g FF(k)776 3306 y FC(1)814 3292 y FE(\()p FH(e)8 b FE(\))i FK(log)h FF(n)23 b FK(for)h(some)g FF(k)1520 3306 y FC(1)1558 3292 y FE(\()p FH(e)8 b FE(\))22 b FK(dependent)27 b(only)d(on)g FH(e)8 b FK(.)211 3405 y(Our)24 b(search)i(algorithm)g(will)e(\002nd)g(paths)i(to)e(at)h(most) f FF(B)f FK(bottom)j(supernodes)i(for)c(a)g(gi)n(v)o(en)h(data)h(item)e (and)h(each)70 3518 y(of)e(these)i(paths)f(has)g(less)g(than)g(log)12 b FF(n)23 b FK(hops)h(in)g(it)f(so)h(the)f(search)i(time)f(is)f(no)h (more)f(than)1552 3720 y FF(k)1592 3734 y FC(2)1629 3720 y FE(\()p FH(e)8 b FE(\))i FK(log)i FF(n)20 b FE(=)g FF(B)10 b FK(log)h FF(n)46 b FG(:)211 3922 y FK(Each)31 b(supernode)k(contains)f(no)e(more)f(that)i FH(b)21 b FK(ln)11 b FF(n)31 b FK(nodes)i(and)f(in)g(each)g(search,)j(e)o(xactly) e FF(T)42 b FK(top)32 b(supernodes)70 4035 y(send)26 b(no)g(more)g(than)h FF(B)e FK(messages)i(so)f(the)h(total)g(number)g (of)e(messages)j(transmitted)g(during)g(a)d(search)j(is)e(no)g(more)70 4148 y(than)1388 4261 y FF(k)1428 4275 y FC(3)1466 4261 y FE(\()p FH(e)8 b FE(\))i FK(log)1710 4223 y FC(2)1758 4261 y FF(n)21 b FE(=)e(\()p FF(T)12 b(B)p FH(b)6 b FF(C)r FE(\))k FK(log)2348 4223 y FC(2)2395 4261 y FF(n)46 b FG(:)p 3765 4426 4 62 v 3769 4368 55 4 v 3769 4426 V 3822 4426 4 62 v 70 4569 a SDict begin H.S end 70 4569 a 70 4569 a SDict begin 13.6 H.A end 70 4569 a 70 4569 a SDict begin [ /View [/XYZ H.V] /Dest (section.5) cvn H.B /DEST pdfmark end 70 4569 a 149 x Ft(5)119 b(Modi\002cations)30 b(f)m(or)g(spam)f(r)n(esistant)g(distrib)n(uted)i(hash)f(table)70 4925 y FK(W)-7 b(e)22 b(no)n(w)h(describe)i(the)e(changes)j(in)d(the)g (netw)o(ork)i(necessary)h(for)d(the)h(spam)f(resistant)i(distrib)n (uted)i(hash)d(table.)30 b(W)-7 b(e)70 5038 y(only)29 b(sk)o(etch)i(the)e(required)i(proofs)g(since)f(the)f(ar)n(guments)i (are)e(based)i(on)e(slight)h(modi\002cations)h(to)e(the)g(proofs)i(of)p 0 0 .8 TeXcolorrgb 70 5152 a SDict begin H.S end 70 5152 a 0 0 .8 TeXcolorrgb -1 x FK(Section)p 0 0 .8 TeXcolorrgb 365 5151 a SDict begin H.S end 365 5151 a 0 0 .8 TeXcolorrgb FK(4)p 0 0 .8 TeXcolorrgb 410 5089 a SDict begin H.R end 410 5089 a 410 5151 a
SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (section.4) cvn H.B /ANN pdfmark end 410 5151 a 0 0 .8 TeXcolorrgb 0 0 .8 TeXcolorrgb 410 5089 a SDict begin H.R end 410 5089 a 410 5151 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (section.4) cvn H.B /ANN pdfmark end 410 5151 a Black FK(.)p Black .8 .3 .3 TeXcolorrgb 1000 5401 a SDict begin H.S end 1000 5401 a .8 .3 .3 TeXcolorrgb 1002 5400 a Fv(T)t FC(H)t(E)t(O)t(RY)25 b(O)t(F)f Fv(C)t FC(O)t(M)t(P)t(U)t(T)t(I)t(N)t(G) p .8 .3 .3 TeXcolorrgb 1876 5344 a SDict begin H.R end 1876 5344 a 1876 5400 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype /URI /URI (http://dx.doi.org/10.4086/toc) >> /Subtype /Link H.B /ANN pdfmark end 1876 5400 a Black Fv(,)e(V)-11 b(olume)19 b(3)i(\(2007\),)c(pp.)25 b(1\22623)928 b(18)p Black eop end %%Page: 19 19 TeXDict begin 19 18 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a Black 0 TeXcolorgray 70 199 a SDict begin H.S end 70 199 a 0 TeXcolorgray 0 TeXcolorgray 70 199 a SDict begin H.R end 70 199 a 70 199 a SDict begin [ /View [/XYZ H.V] /Dest (page.19) cvn H.B /DEST pdfmark end 70 199 a Black 948 w Fv(C)t FC(E)t(N)t(S)t(O)t(R)t (S)t(H)t(I)t(P)26 b Fv(R)t FC(E)t(S)t(I)t(S)t(T)n(A)t(N)t(T)e Fv(P)t FC(E)t(E)t(R)t Fv(-)t FC(T)s(O)t Fv(-)t(P)t FC(E)t(E)t(R)g Fv(N)t FC(E)t(T)t(W)s(O)t(R)t(K)t(S)p Black 211 440 a FK(The)j(\002rst)h(modi\002cation)i(is)d(that)i(rather)g(than)g(ha)n(v) o(e)f(a)g(constant)i(de)o(gree)f(e)o(xpander)h(between)f(tw)o(o)e (supernodes)70 553 y(connected)c(in)e(the)g(b)n(utter\003y)-6 b(,)22 b(we)e(will)h(ha)n(v)o(e)g(a)f(full)h(bipartite)i(graph)f (between)g(the)f(nodes)h(of)f(these)g(tw)o(o)g(supernodes.)70 666 y(Since)k(we)f(ha)n(v)o(e)i(insisted)h(that)f(the)g(total)g(number) g(of)f(adv)o(ersary)i(controlled)h(nodes)f(be)e(strictly)i(less)f(than) g FF(n)p FG(=)p FK(2,)f(we)70 778 y(can)k(guarantee)j(that)d(a)g(1)15 b FM(\000)g FH(e)35 b FK(fraction)c(of)e(the)g(paths)h(in)f(the)g(b)n (utter\003y)i(ha)n(v)o(e)f(all)f(supernodes)j(with)d(a)f(majority)j(of) 70 891 y(good)d(\(non-adv)o(ersary)j(controlled\))g(nodes.)41 b(In)27 b(particular)l(,)k(by)d(substituting)i(appropriate)h(v)n(alues) d(in)p 0 0 .8 TeXcolorrgb 3413 892 a SDict begin H.S end 3413 892 a 0 0 .8 TeXcolorrgb -1 x FK(Lemma)p 0 0 .8 TeXcolorrgb 3717 892 a
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% Get a DirectClass packet. % % Parameters: % red. % green. % blue. % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop compression 0 eq { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /DirectClassImage { % % Display a DirectClass image. % systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { DirectClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayDirectClassPacket } image } ifelse } bind def /GrayDirectClassPacket { % % Get a DirectClass packet; % % Parameters: % red % green
convert to grayscale.
% blue % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 eq { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /GrayPseudoClassPacket { % % Get a PseudoClass packet; convert to grayscale. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 eq { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /PseudoClassPacket { %
% Get a PseudoClass packet. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def compression 0 eq { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /PseudoClassImage { % % Display a PseudoClass image. % % Parameters: % class: 0-PseudoClass or 1-Grayscale. % currentfile buffer readline pop token pop /class exch def pop class 0 gt { currentfile buffer readline pop token pop /depth exch def pop /grays columns 8 add depth sub depth mul 8 idiv string def columns rows depth [ columns 0 0 rows neg 0 rows ] { currentfile grays readhexstring pop } image } { % % Parameters: % colors: number of colors in the colormap. % colormap: red, green, blue color packets. % currentfile buffer readline pop token pop /colors exch def pop /colors colors 3 mul def /colormap colors string def currentfile colormap readhexstring pop pop systemdict /colorimage known {
columns rows 8 [ columns 0 0 rows neg 0 rows ] { PseudoClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayPseudoClassPacket } image } ifelse } ifelse } bind def /DisplayImage { % % Display a DirectClass or PseudoClass image. % % Parameters: % x & y translation. % x & y scale. % label pointsize. % image label. % image columns & rows. % class: 0-DirectClass or 1-PseudoClass. % compression: 0-none or 1-RunlengthEncoded. % hex color packets. % gsave /buffer 512 string def /byte 1 string def /color_packet 3 string def /pixels 768 string def currentfile buffer readline pop token pop /x exch def token pop /y exch def pop x y translate currentfile buffer readline pop token pop /x exch def token pop /y exch def pop currentfile buffer readline pop token pop /pointsize exch def pop /Times-Roman findfont pointsize scalefont setfont x y scale currentfile buffer readline pop token pop /columns exch def token pop /rows exch def pop currentfile buffer readline pop token pop /class exch def pop currentfile buffer readline pop
token pop /compression exch def pop class 0 gt { PseudoClassImage } { DirectClassImage } ifelse grestore } bind def %%EndProlog %%Page: 1 1 %%PageBoundingBox: 0 0 64 45 userdict begin DisplayImage 0 0 64 45 12.000000 64 45 1 1 1 1 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF801FFFFFFFF FFFFF00007FFFFFFFFFFE00000FFFFFFFFFFC000007FFFFFFFFFC000003FFFFFFFFFC000 003FFFFFFFFF8000003FFFFFFFFF8000003FFFFFFFFF8000003FFFFFFFFF8000003FFFFF FFFF8000003FFFFFFFFF8000003FFFFFFFFF8000003FFFFFFFFF8000003FFFFFFFFF8000 003FFFFFFFFF8000007FFFFFFFFFC00000FFFFFFFFFFE00001FFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF end %%PageTrailer %%Trailer %%EOF %%EndDocument @endspecial 28 w(ac)p @beginspecial 0 @llx 0 @lly 64 @urx 45 @ury 32 @rwi @setspecial %%BeginDocument: tocdot.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: (ImageMagick) %%Title: (tocdot.eps) %%CreationDate: (Thu Jan 27 14:39:30 2005) %%BoundingBox: 0 0 64 45 %%HiResBoundingBox: 0 0 64 45 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 1 %%EndComments %%BeginDefaults %%EndDefaults %%BeginProlog % % Display a color image. The image is displayed in color on % Postscript viewers or printers that support color, otherwise % it is displayed as grayscale. % /DirectClassPacket { %
% Get a DirectClass packet. % % Parameters: % red. % green. % blue. % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop compression 0 eq { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /DirectClassImage { % % Display a DirectClass image. % systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { DirectClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayDirectClassPacket } image } ifelse } bind def /GrayDirectClassPacket { % % Get a DirectClass packet; % % Parameters: % red % green
convert to grayscale.
% blue % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 eq { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /GrayPseudoClassPacket { % % Get a PseudoClass packet; convert to grayscale. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 eq { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /PseudoClassPacket { %
% Get a PseudoClass packet. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def compression 0 eq { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /PseudoClassImage { % % Display a PseudoClass image. % % Parameters: % class: 0-PseudoClass or 1-Grayscale. % currentfile buffer readline pop token pop /class exch def pop class 0 gt { currentfile buffer readline pop token pop /depth exch def pop /grays columns 8 add depth sub depth mul 8 idiv string def columns rows depth [ columns 0 0 rows neg 0 rows ] { currentfile grays readhexstring pop } image } { % % Parameters: % colors: number of colors in the colormap. % colormap: red, green, blue color packets. % currentfile buffer readline pop token pop /colors exch def pop /colors colors 3 mul def /colormap colors string def currentfile colormap readhexstring pop pop systemdict /colorimage known {
columns rows 8 [ columns 0 0 rows neg 0 rows ] { PseudoClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayPseudoClassPacket } image } ifelse } ifelse } bind def /DisplayImage { % % Display a DirectClass or PseudoClass image. % % Parameters: % x & y translation. % x & y scale. % label pointsize. % image label. % image columns & rows. % class: 0-DirectClass or 1-PseudoClass. % compression: 0-none or 1-RunlengthEncoded. % hex color packets. % gsave /buffer 512 string def /byte 1 string def /color_packet 3 string def /pixels 768 string def currentfile buffer readline pop token pop /x exch def token pop /y exch def pop x y translate currentfile buffer readline pop token pop /x exch def token pop /y exch def pop currentfile buffer readline pop token pop /pointsize exch def pop /Times-Roman findfont pointsize scalefont setfont x y scale currentfile buffer readline pop token pop /columns exch def token pop /rows exch def pop currentfile buffer readline pop token pop /class exch def pop currentfile buffer readline pop
token pop /compression exch def pop class 0 gt { PseudoClassImage } { DirectClassImage } ifelse grestore } bind def %%EndProlog %%Page: 1 1 %%PageBoundingBox: 0 0 64 45 userdict begin DisplayImage 0 0 64 45 12.000000 64 45 1 1 1 1 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF801FFFFFFFF FFFFF00007FFFFFFFFFFE00000FFFFFFFFFFC000007FFFFFFFFFC000003FFFFFFFFFC000 003FFFFFFFFF8000003FFFFFFFFF8000003FFFFFFFFF8000003FFFFFFFFF8000003FFFFF FFFF8000003FFFFFFFFF8000003FFFFFFFFF8000003FFFFFFFFF8000003FFFFFFFFF8000 003FFFFFFFFF8000007FFFFFFFFFC00000FFFFFFFFFFE00001FFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF end %%PageTrailer %%Trailer %%EOF %%EndDocument @endspecial 27 w(il)p .8 .3 .3 TeXcolorrgb 297 3142 a SDict begin H.S end 297 3142 a .8 .3 .3 TeXcolorrgb -20 x Fa(http://www.math.tau.ac.i)o (l/~)o(fiat)p .8 .3 .3 TeXcolorrgb 1782 3059 a SDict begin H.R end 1782 3059 a 1782 3122 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype /URI /URI (http://www.math.tau.ac.il/~fiat) >> /Subtype /Link H.B /ANN pdfmark end 1782 3122 a Black 0 TeXcolorgray Black 0 TeXcolorgray 297 3392 a SDict begin H.S end 297 3392 a 0 TeXcolorgray 0 TeXcolorgray 297 3392 a SDict begin H.R end 297 3392 a 297 3392 a SDict begin [ /View [/XYZ H.V] /Dest (author.info.jared) cvn H.B /DEST pdfmark end 297 3392 a Black 23 w FK(Jared)h(Saia)p 0 0 .8 TeXcolorrgb 713 3405 a SDict begin H.S end 713 3405 a 0 0 .8 TeXcolorrgb -13 x Fv([About)19 b(the)i(author])p 0 0 .8 TeXcolorrgb 1334 3335 a
SDict begin H.R end 1334 3335 a 1334 3392 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (author.about.jared) cvn H.B /ANN pdfmark end 1334 3392 a Black 297 3505 a FK(Assistant)k (Professor)297 3618 y(Uni)n(v)o(ersity)g(of)e(Ne)n(w)f(Me)o(xico,)i (Alb)n(uquerque,)i(Ne)n(w)c(Me)o(xico)297 3731 y(saia)p @beginspecial 0 @llx 0 @lly 142 @urx 149 @ury 71 @rwi @setspecial %%BeginDocument: tocat.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: (ImageMagick) %%Title: (tocat.eps) %%CreationDate: (Thu Jan 27 14:39:24 2005) %%BoundingBox: 0 0 142 149 %%HiResBoundingBox: 0 0 142 149 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 1 %%EndComments %%BeginDefaults %%EndDefaults %%BeginProlog % % Display a color image. The image is displayed in color on % Postscript viewers or printers that support color, otherwise % it is displayed as grayscale. % /DirectClassPacket { % % Get a DirectClass packet. % % Parameters: % red. % green. % blue. % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop compression 0 eq { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /DirectClassImage
{
% % Display a DirectClass image. % systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { DirectClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayDirectClassPacket } image } ifelse } bind def /GrayDirectClassPacket { % % Get a DirectClass packet; convert to grayscale. % % Parameters: % red % green % blue % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 eq { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /GrayPseudoClassPacket
{
% % Get a PseudoClass packet; convert to grayscale. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 eq { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /PseudoClassPacket { % % Get a PseudoClass packet. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def compression 0 eq { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /PseudoClassImage
{
% % Display a PseudoClass image. % % Parameters: % class: 0-PseudoClass or 1-Grayscale. % currentfile buffer readline pop token pop /class exch def pop class 0 gt { currentfile buffer readline pop token pop /depth exch def pop /grays columns 8 add depth sub depth mul 8 idiv string def columns rows depth [ columns 0 0 rows neg 0 rows ] { currentfile grays readhexstring pop } image } { % % Parameters: % colors: number of colors in the colormap. % colormap: red, green, blue color packets. % currentfile buffer readline pop token pop /colors exch def pop /colors colors 3 mul def /colormap colors string def currentfile colormap readhexstring pop pop systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { PseudoClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayPseudoClassPacket } image } ifelse } ifelse } bind def /DisplayImage { % % Display a DirectClass or PseudoClass image.
% % Parameters: % x & y translation. % x & y scale. % label pointsize. % image label. % image columns & rows. % class: 0-DirectClass or 1-PseudoClass. % compression: 0-none or 1-RunlengthEncoded. % hex color packets. % gsave /buffer 512 string def /byte 1 string def /color_packet 3 string def /pixels 768 string def currentfile buffer readline pop token pop /x exch def token pop /y exch def pop x y translate currentfile buffer readline pop token pop /x exch def token pop /y exch def pop currentfile buffer readline pop token pop /pointsize exch def pop /Times-Roman findfont pointsize scalefont setfont x y scale currentfile buffer readline pop token pop /columns exch def token pop /rows exch def pop currentfile buffer readline pop token pop /class exch def pop currentfile buffer readline pop token pop /compression exch def pop class 0 gt { PseudoClassImage } { DirectClassImage } ifelse grestore } bind def %%EndProlog %%Page: 1 1 %%PageBoundingBox: 0 0 142 149 userdict begin DisplayImage 0 0 142 149 12.000000 142 149 1 1 1 1 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFFFFFFFFFFC00007FFFFFFFFFFFFFFFCFFFFFFFFFFFFFF800000FFFFFFFFFFFFFFFC FFFFFFFFFFFFF80000003FFFFFFFFFFFFFFCFFFFFFFFFFFFF00000001FFFFFFFFFFFFFFC FFFFFFFFFFFFE000000007FFFFFFFFFFFFFCFFFFFFFFFFFF0000000001FFFFFFFFFFFFFC FFFFFFFFFFFC0000000000FFFFFFFFFFFFFCFFFFFFFFFFE000000000003FFFFFFFFFFFFC FFFFFFFFFFC000003800001FFFFFFFFFFFFCFFFFFFFFFF0000007F00000FFFFFFFFFFFFC FFFFFFFFFC000007FFC00003FFFFFFFFFFFCFFFFFFFFFC00000FFFE00001FFFFFFFFFFFC FFFFFFFFFC00001FFFF80000FFFFFFFFFFFCFFFFFFFFE00000FFFFFE00007FFFFFFFFFFC FFFFFFFFE00003FFFFFF00003FFFFFFFFFFCFFFFFFFFE0001FFFFFFFC0001FFFFFFFFFFC FFFFFFFF80003FFFFFFFE0000FFFFFFFFFFCFFFFFFFF0000FFFFFFFFF0000FFFFFFFFFFC FFFFFFFF0003FFFFFFFFFC0007FFFFFFFFFCFFFFFFFE0003FFFFFFFFFE0003FFFFFFFFFC FFFFFFFC0003FFFFFFFFFF0000FFFFFFFFFCFFFFFFFC001FFFFFFFFFFF80007FFFFFFFFC FFFFFFF8001FFFFFFFFFFFC0007FFFFFFFFCFFFFFFF0001FFFFFFFFFFFE0007FFFFFFFFC FFFFFFE0007FFFFFFFFFFFF0003FFFFFFFFCFFFFFFE000FFFFFFFFFFFFF0001FFFFFFFFC FFFFFFC000FFFFFFFFFFFFF8001FFFFFFFFCFFFFFFC001FFFFFFFFFFFFFC001FFFFFFFFC FFFFFF8003FFFFFFFFFFFFFF000FFFFFFFFCFFFFFF8003FFFFFFFFFFFFFF800FFFFFFFFC FFFFFF0007FFFFFC0003FFFF8007FFFFFFFCFFFFFF000FFFFFE00000FFFF8003FFFFFFFC FFFFFF001FFFFE0000001FFFC001FFFFFFFCFFFFFF001FFFFC00000007FFE001FFFFFFFC FFFFFF003FFFC000000003FFE000FFFFFFFCFFFFFE003FFFC000000001FFE000FFFFFFFC FFFFFE007FFF8000000000FFF000FFFFFFFCFFFFFE007FFE00000000003FF0007FFFFFFC FFFFFE00FFFC00000000001FF8007FFFFFFCFFFFFE00FFF800001F00000FFC003FFFFFFC FFFFFE00FFF00001FFE00003FE003FFFFFFCFFFFFC00FFF00003FFF80001FE003FFFFFFC FFFFFC00FFE0003FFFFC0001FF003FFFFFFCFFFFFC01FFE0003FFFFE0000FF001FFFFFFC FFFFFC01FFC0007FFFFF0000FF001FFFFFFCFFFFFC01FF8001FFFFFFC000FF801FFFFFFC FFFFFC01FF8003FFFFFFE000FF801FFFFFFCFFFFFC01FF0007FFFFFFF000FFC01FFFFFFC FFFFFC01FF000FFFFFFFFC00FFC01FFFFFFCFFFFFC03FF000FFFFFFFFE00FFC01FFFFFFC FFFFFC03FF001FFFFFFFFE00FFC01FFFFFFCFFFFFC03FF001FFFFFFFFE00FFE01FFFFFFC FFFFFC03FE003FFFFFFFFE00FFE01FFFFFFCFFFFFC03FE007FFFFFFFFE01FFE01FFFFFFC FFFFFC03FE007FFFFFFFFE01FFE01FFFFFFCFFFFFC03FE00FFFFFFFFFE00FFE01FFFFFFC FFFFFC03FE00FFFFFFFFFE007FE01FFFFFFCFFFFFC03FE00FFFFFFFFFE003FE01FFFFFFC FFFFFC03FE00FFFFFFFFFE003FE01FFFFFFCFFFFFC03FE00FFFFFFFFFE003FE01FFFFFFC FFFFFC03FE00FFFFFFFFFC003FE01FFFFFFCFFFFFC03FE00FFFFFFFFFC001FE01FFFFFFC FFFFFC03FE007FFFFFFFFC001FE01FFFFFFCFFFFFC03FE007FFFFFFFF8000FE01FFFFFFC FFFFFC03FE003FFFFFFFF8000FE01FFFFFFCFFFFFC03FE001FFFFFFFF8000FE01FFFFFFC FFFFFC03FF001FFFFFFFF80007E01FFFFFFCFFFFFC03FF000FFFFFFFF80003E01FFFFFFC FFFFFC03FF0007FFFFFFF80003C01FFFFFFCFFFFFC03FF0007FFFFFFF80003801FFFFFFC FFFFFC03FF8001FFFFFFF80003001FFFFFFCFFFFFC03FF8001FFFFFFF00000001FFFFFFC FFFFFC03FFC000FFFFFFF00000001FFFFFFCFFFFFC03FFE0003FFFFFE00000001FFFFFFC FFFFFC03FFE0000FFFFF800000001FFFFFFCFFFFFC03FFF00007FFFF000400001FFFFFFC FFFFFC03FFF800003FFE000400003FFFFFFCFFFFFC03FFF800003FFC000400007FFFFFFC FFFFFC03FFFE0000000000040000FFFFFFFCFFFFFC03FFFE00000000000F0001FFFFFFFC FFFFFC03FFFF00000000000F0003FFFFFFFCFFFFFC03FFFFC0000000001F0007FFFFFFFC FFFFFC03FFFFF0000000007FFFFFFFFFFFFCFFFFFC03FFFFF800000000FFFFFFFFFFFFFC FFFFFC03FFFFFFC0000001FFFFFFFFFFFFFCFFFFFC03FFFFFFC0000003FFFFFFFFFFFFFC FFFFFC01FFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFC01FFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFC01FFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFC00FFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFC007FFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFC007FFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFC003FFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFC003FFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFE001FFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFE001FFFFFFFFFFFFFFFFFC03FFFFFFC FFFFFE0007FFFFFFFFFFFFFFFFC03FFFFFFCFFFFFF0003FFFFFFFFFFFFFFFFC03FFFFFFC FFFFFF8001FFFFFFFFFFFFFFFFC03FFFFFFCFFFFFF8000FFFFFFFFFFFFFFFFC03FFFFFFC FFFFFFC000FFFFFFFFFFFFFFFF803FFFFFFCFFFFFFC0007FFFFFFFFFFFFFFE003FFFFFFC FFFFFFE0003FFFFFFFFFFFFFF0003FFFFFFCFFFFFFE0000FFFFFFFFFFFFF80003FFFFFFC FFFFFFF80007FFFFFFFFFFFC00003FFFFFFCFFFFFFFC0001FFFFFFFFFFF000003FFFFFFC FFFFFFFE00007FFFFFFFFF8000003FFFFFFCFFFFFFFF00003FFFFFFFFF0000003FFFFFFC FFFFFFFF000007FFFFFFE00000007FFFFFFCFFFFFFFF80000000000000000001FFFFFFFC FFFFFFFFC000000000000000000FFFFFFFFCFFFFFFFFF000000000000000007FFFFFFFFC FFFFFFFFF80000000000000003FFFFFFFFFCFFFFFFFFFE000000000000000FFFFFFFFFFC FFFFFFFFFF800000000000007FFFFFFFFFFCFFFFFFFFFFC0000000000000FFFFFFFFFFFC
FFFFFFFFFFF800000000001FFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC end %%PageTrailer %%Trailer %%EOF %%EndDocument @endspecial 60 w(cs)p @beginspecial 0 @llx 0 @lly 64 @urx 45 @ury 32 @rwi @setspecial %%BeginDocument: tocdot.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: (ImageMagick) %%Title: (tocdot.eps) %%CreationDate: (Thu Jan 27 14:39:30 2005) %%BoundingBox: 0 0 64 45 %%HiResBoundingBox: 0 0 64 45 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 1 %%EndComments %%BeginDefaults %%EndDefaults %%BeginProlog % % Display a color image. The image is displayed in color on % Postscript viewers or printers that support color, otherwise % it is displayed as grayscale. % /DirectClassPacket { % % Get a DirectClass packet. % % Parameters: % red. % green. % blue. % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop compression 0 eq { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub {
pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /DirectClassImage { % % Display a DirectClass image. % systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { DirectClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayDirectClassPacket } image } ifelse } bind def /GrayDirectClassPacket { % % Get a DirectClass packet; convert to grayscale. % % Parameters: % red % green % blue % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 eq { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub {
pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /GrayPseudoClassPacket { % % Get a PseudoClass packet; convert to grayscale. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 eq { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /PseudoClassPacket { % % Get a PseudoClass packet. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def compression 0 eq { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub {
pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /PseudoClassImage { % % Display a PseudoClass image. % % Parameters: % class: 0-PseudoClass or 1-Grayscale. % currentfile buffer readline pop token pop /class exch def pop class 0 gt { currentfile buffer readline pop token pop /depth exch def pop /grays columns 8 add depth sub depth mul 8 idiv string def columns rows depth [ columns 0 0 rows neg 0 rows ] { currentfile grays readhexstring pop } image } { % % Parameters: % colors: number of colors in the colormap. % colormap: red, green, blue color packets. % currentfile buffer readline pop token pop /colors exch def pop /colors colors 3 mul def /colormap colors string def currentfile colormap readhexstring pop pop systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { PseudoClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayPseudoClassPacket } image } ifelse } ifelse
} bind def /DisplayImage { % % Display a DirectClass or PseudoClass image. % % Parameters: % x & y translation. % x & y scale. % label pointsize. % image label. % image columns & rows. % class: 0-DirectClass or 1-PseudoClass. % compression: 0-none or 1-RunlengthEncoded. % hex color packets. % gsave /buffer 512 string def /byte 1 string def /color_packet 3 string def /pixels 768 string def currentfile buffer readline pop token pop /x exch def token pop /y exch def pop x y translate currentfile buffer readline pop token pop /x exch def token pop /y exch def pop currentfile buffer readline pop token pop /pointsize exch def pop /Times-Roman findfont pointsize scalefont setfont x y scale currentfile buffer readline pop token pop /columns exch def token pop /rows exch def pop currentfile buffer readline pop token pop /class exch def pop currentfile buffer readline pop token pop /compression exch def pop class 0 gt { PseudoClassImage } { DirectClassImage } ifelse grestore } bind def %%EndProlog %%Page: 1 1 %%PageBoundingBox: 0 0 64 45 userdict begin DisplayImage 0 0 64 45 12.000000 64 45 1 1 1 1 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF801FFFFFFFF FFFFF00007FFFFFFFFFFE00000FFFFFFFFFFC000007FFFFFFFFFC000003FFFFFFFFFC000 003FFFFFFFFF8000003FFFFFFFFF8000003FFFFFFFFF8000003FFFFFFFFF8000003FFFFF FFFF8000003FFFFFFFFF8000003FFFFFFFFF8000003FFFFFFFFF8000003FFFFFFFFF8000 003FFFFFFFFF8000007FFFFFFFFFC00000FFFFFFFFFFE00001FFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF end %%PageTrailer %%Trailer %%EOF %%EndDocument @endspecial 28 w(unm)p @beginspecial 0 @llx 0 @lly 64 @urx 45 @ury 32 @rwi @setspecial %%BeginDocument: tocdot.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: (ImageMagick) %%Title: (tocdot.eps) %%CreationDate: (Thu Jan 27 14:39:30 2005) %%BoundingBox: 0 0 64 45 %%HiResBoundingBox: 0 0 64 45 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 1 %%EndComments %%BeginDefaults %%EndDefaults %%BeginProlog % % Display a color image. The image is displayed in color on % Postscript viewers or printers that support color, otherwise % it is displayed as grayscale. % /DirectClassPacket { % % Get a DirectClass packet. % % Parameters: % red. % green. % blue. % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop compression 0 eq { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub {
pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /DirectClassImage { % % Display a DirectClass image. % systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { DirectClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayDirectClassPacket } image } ifelse } bind def /GrayDirectClassPacket { % % Get a DirectClass packet; convert to grayscale. % % Parameters: % red % green % blue % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 eq { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub {
pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /GrayPseudoClassPacket { % % Get a PseudoClass packet; convert to grayscale. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 eq { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /PseudoClassPacket { % % Get a PseudoClass packet. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def compression 0 eq { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub {
pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /PseudoClassImage { % % Display a PseudoClass image. % % Parameters: % class: 0-PseudoClass or 1-Grayscale. % currentfile buffer readline pop token pop /class exch def pop class 0 gt { currentfile buffer readline pop token pop /depth exch def pop /grays columns 8 add depth sub depth mul 8 idiv string def columns rows depth [ columns 0 0 rows neg 0 rows ] { currentfile grays readhexstring pop } image } { % % Parameters: % colors: number of colors in the colormap. % colormap: red, green, blue color packets. % currentfile buffer readline pop token pop /colors exch def pop /colors colors 3 mul def /colormap colors string def currentfile colormap readhexstring pop pop systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { PseudoClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayPseudoClassPacket } image } ifelse } ifelse
} bind def /DisplayImage { % % Display a DirectClass or PseudoClass image. % % Parameters: % x & y translation. % x & y scale. % label pointsize. % image label. % image columns & rows. % class: 0-DirectClass or 1-PseudoClass. % compression: 0-none or 1-RunlengthEncoded. % hex color packets. % gsave /buffer 512 string def /byte 1 string def /color_packet 3 string def /pixels 768 string def currentfile buffer readline pop token pop /x exch def token pop /y exch def pop x y translate currentfile buffer readline pop token pop /x exch def token pop /y exch def pop currentfile buffer readline pop token pop /pointsize exch def pop /Times-Roman findfont pointsize scalefont setfont x y scale currentfile buffer readline pop token pop /columns exch def token pop /rows exch def pop currentfile buffer readline pop token pop /class exch def pop currentfile buffer readline pop token pop /compression exch def pop class 0 gt { PseudoClassImage } { DirectClassImage } ifelse grestore } bind def %%EndProlog %%Page: 1 1 %%PageBoundingBox: 0 0 64 45 userdict begin DisplayImage 0 0 64 45 12.000000 64 45 1 1 1 1 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF801FFFFFFFF FFFFF00007FFFFFFFFFFE00000FFFFFFFFFFC000007FFFFFFFFFC000003FFFFFFFFFC000 003FFFFFFFFF8000003FFFFFFFFF8000003FFFFFFFFF8000003FFFFFFFFF8000003FFFFF FFFF8000003FFFFFFFFF8000003FFFFFFFFF8000003FFFFFFFFF8000003FFFFFFFFF8000 003FFFFFFFFF8000007FFFFFFFFFC00000FFFFFFFFFFE00001FFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF end %%PageTrailer %%Trailer %%EOF %%EndDocument @endspecial 27 w(edu)p .8 .3 .3 TeXcolorrgb 297 3864 a SDict begin H.S end 297 3864 a .8 .3 .3 TeXcolorrgb -21 x Fa(http://www.cs.unm.edu/~s)o (aia)p .8 .3 .3 TeXcolorrgb 1591 3780 a SDict begin H.R end 1591 3780 a 1591 3843 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype /URI /URI (http://www.cs.unm.edu/~saia) >> /Subtype /Link H.B /ANN pdfmark end 1591 3843 a Black 70 4140 a Fb(ABOUT)28 b(THE)j(A)m(UTHORS)p 0 TeXcolorgray Black 0 TeXcolorgray 297 4320 a SDict begin H.S end 297 4320 a 0 TeXcolorgray 0 TeXcolorgray 297 4320 a SDict begin H.R end 297 4320 a 297 4320 a SDict begin [ /View [/XYZ H.V] /Dest (author.about.amos) cvn H.B /DEST pdfmark end 297 4320 a Black 24 w FK(A)t Fc(M)t(O)t(S)d FK(F)t Fc(I)t(A)l(T)e FK(graduated)g(from)e(the)p .8 .3 .3 TeXcolorrgb 1501 4321 a SDict begin H.S end 1501 4321 a .8 .3 .3 TeXcolorrgb -1 x FK(W)-7 b(eizmann)24 b(Institute)p .8 .3 .3 TeXcolorrgb 2205 4258 a SDict begin H.R end 2205 4258 a 2205 4320 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype /URI /URI (http://www.weizmann.ac.il/) >> /Subtype /Link H.B /ANN pdfmark end 2205 4320 a Black 26 w FK(in)f(1986.)30 b(His)23 b(advisor)i(w)o(as)p .8 .3 .3 TeXcolorrgb 3159 4321 a SDict begin H.S end 3159 4321 a .8 .3 .3 TeXcolorrgb -1 x FK(Adi)e(Shamir)p .8 .3 .3 TeXcolorrgb 3580 4258 a SDict begin H.R end 3580 4258 a 3580 4320 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype /URI /URI (http://www.weizmann.ac.il/math/profile/scientists/shamir-profile.html) >> /Subtype /Link H.B /ANN pdfmark end
3580 4320 a Black FK(.)433 4433 y(His)g(reseach)h(interests)i(include)e(online)h(algorithms,)g (cryptography)-6 b(,)26 b(data)e(mining,)g(web)e(search,)433 4546 y(and)i(peer)n(-to-peer)j(netw)o(orks.)k(He)22 b(also)i(enjo)o(ys) i(photography)g(and)e(sailing.)p 0 TeXcolorgray Black 0 TeXcolorgray 297 4816 a SDict begin H.S end 297 4816 a 0 TeXcolorgray 0 TeXcolorgray 297 4816 a SDict begin H.R end 297 4816 a 297 4816 a SDict begin [ /View [/XYZ H.V] /Dest (author.about.jared) cvn H.B /DEST pdfmark end 297 4816 a Black 24 w FK(J)o Fc(A)t(R)t(E)t(D)k FK(S)t Fc(A)t(I)t(A)d FK(graduated)h(from)d(the)p .8 .3 .3 TeXcolorrgb 1525 4835 a SDict begin H.S end 1525 4835 a .8 .3 .3 TeXcolorrgb -19 x FK(Uni)n(v)o(ersity)i(of) d(W)-7 b(ashington)p .8 .3 .3 TeXcolorrgb 2454 4754 a SDict begin H.R end 2454 4754 a 2454 4816 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype /URI /URI (http://www.cs.washington.edu/) >> /Subtype /Link H.B /ANN pdfmark end 2454 4816 a Black 26 w FK(in)23 b(2002.)29 b(His)23 b(advisor)i(w)o(as)p .8 .3 .3 TeXcolorrgb 3406 4817 a SDict begin H.S end 3406 4817 a .8 .3 .3 TeXcolorrgb -1 x FK(Anna)433 4928 y(Karlin)p .8 .3 .3 TeXcolorrgb 664 4866 a SDict begin H.R end 664 4866 a 664 4928 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype /URI /URI (http://www.cs.washington.edu/homes/karlin) >> /Subtype /Link H.B /ANN pdfmark end 664 4928 a Black FK(.)55 b(His)32 b(research)i(interests)g (include)g(randomized)h(algorithms,)h(distrib)n(uted)g(algorithms,)433 5041 y(and)24 b(graph)h(theory)-6 b(.)30 b(He)23 b(also)h(enjo)o(ys)h (hiking,)g(skiing,)g(and)f(mountain)h(biking.)p Black .8 .3 .3 TeXcolorrgb 1000 5401 a SDict begin H.S end 1000 5401 a .8 .3 .3 TeXcolorrgb 1002 5400 a Fv(T)t FC(H)t(E)t(O)t(RY)g(O)t(F)f Fv(C)t FC(O)t(M)t(P)t(U)t(T)t(I)t(N)t(G)p .8 .3 .3 TeXcolorrgb 1876 5344 a SDict begin H.R end 1876 5344 a 1876 5400 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype /URI /URI (http://dx.doi.org/10.4086/toc) >> /Subtype /Link H.B /ANN pdfmark end 1876 5400 a Black Fv(,)e(V)-11 b(olume)19 b(3)i(\(2007\),)c(pp.)25 b(1\22623)928 b(23)p Black eop end %%Trailer userdict /end-hook known{end-hook}if
%%EOF