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cleartomark %%EndFont %%BeginFont: CMCSC10 %!PS-AdobeFont-1.1: CMCSC10 1.0 %%CreationDate: 1991 Aug 18 17:46:49 % 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 (CMCSC10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMCSC10 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 19 /acute put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put readonly def /FontBBox{14 -250 1077 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % 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 (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 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 11 /alpha put dup 14 /delta put dup 59 /comma put dup 61 /slash put dup 84 /T put dup 97 /a put dup 98 /b put dup 105 /i put dup 106 /j put dup 110 /n put dup 112 /p put dup 116 /t put readonly def /FontBBox{37 -250 1349 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY5 %!PS-AdobeFont-1.1: CMSY5 1.0 %%CreationDate: 1991 Aug 15 07:21:16 % 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 (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 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 /minus put readonly def /FontBBox{21 -944 1448 791}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 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 44 /defines put readonly def /FontBBox{8 -463 1331 1003}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % 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 (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 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 1 /Delta put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put readonly def /FontBBox{-341 -250 1304 965}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 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 69 /E put dup 73 /I put dup 80 /P put dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 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 78 /N put readonly def /FontBBox{0 -504 2615 1004}readonly 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 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 14 /openbullet put dup 20 /lessequal put dup 21 /greaterequal put dup 24 /similar put dup 26 /propersubset put dup 33 /arrowright put dup 41 /arrowdblright put dup 47 /proportional put dup 49 /infinity put dup 50 /element put dup 56 /universal put dup 59 /emptyset put dup 66 /B put dup 69 /E put dup 70 /F put dup 78 /N put dup 79 /O put dup 82 /R put dup 84 /T put dup 91 /union put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 110 /backslash put dup 112 /radical put readonly def /FontBBox{-30 -958 1146 777}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % 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 (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 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 11 /alpha put dup 14 /delta put dup 17 /eta put dup 18 /theta put dup 23 /nu put dup 25 /pi put dup 28 /tau put dup 30 /phi put dup 31 /chi put dup 33 /omega put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 69 /E put dup 70 /F put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 102 /f put dup 103 /g put dup 105 /i put dup 106 /j put dup 107 /k put dup 110 /n put dup 112 /p put dup 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % 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 (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 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 10 /Omega put dup 22 /macron put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 61 /equal put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 91 /bracketleft put dup 93 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % 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 (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 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 11 /alpha put dup 14 /delta put dup 17 /eta put dup 18 /theta put dup 23 /nu put dup 25 /pi put dup 28 /tau put dup 31 /chi put dup 59 /comma put dup 61 /slash put dup 63 /star put dup 69 /E put dup 75 /K put dup 76 /L put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 89 /Y put dup 97 /a put dup 98 /b put dup 99 /c put dup 105 /i put dup 106 /j put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 120 /x put dup 121 /y put readonly def /FontBBox{11 -250 1241 750}readonly def currentdict end currentfile eexec 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % 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 (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 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 /minus put dup 21 /greaterequal put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 79 /O put dup 82 /R put dup 84 /T put dup 91 /union put dup 102 /braceleft put dup 103 /braceright put dup 110 /backslash put readonly def /FontBBox{-4 -948 1329 786}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: TeX-cmex9 %!PS-AdobeFont-1.0: TeX-cmex9 001.001 % Filtered by type1fix.pl 0.05 %%EndComments 13 dict dup begin /FontInfo 16 dict dup begin /Copyright (see\040copyright\040of\040original\040TeX\040font) def /FamilyName (TeX\040cmex9) def /FullName (TeX\040cmex9\040Regular) def /ItalicAngle 0 def /Notice (converted\040after\040April\0402001) def /UnderlinePosition -100 def /UnderlineThickness 50 def /Weight (Regular) def /isFixedPitch false def /version (001.001) def end readonly def /FontName /TeX-cmex9 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 8 /breve put dup 9 /macron put dup 16 /quotedblleft put dup 17 /quotedblright put dup 18 /quotedblbase put dup 19 /guillemotleft put dup 20 /guillemotright put dup 21 /endash put dup 32 /space put dup 33 /exclam put dup 34 /quotedbl put dup 35 /numbersign put dup 56 /eight put dup 58 /colon put dup 60 /less put dup 62 /greater put dup 80 /P put dup 81 /Q put dup 82 /R put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 100 /d put dup 101 /e put dup 104 /h put dup 105 /i put dup 110 /n put dup 111 /o put readonly def /FontBBox {-26 -2961 1503 773} readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA06DA87FC7163A5A2A756A598FAB07633 89DE8BAE4F093966CD2192CE95EB0F323A6BABFDACCFCF27D91F7869A0E46CA5 9AAF6905783E8AC1F3F9875A76F97187738432F8D14E61574CB292FFB9740871 66839799D8CAF6E0DFE00012EE6D46A2B3655F29705BE37FD5EDA1C765AA2CF5 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%%EndFont %%BeginFont: CMTI9 %!PS-AdobeFont-1.1: CMTI9 1.0 %%CreationDate: 1991 Aug 18 21:08:07 % 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 (CMTI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI9 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 14 /ffi put dup 46 /period put dup 65 /A put dup 67 /C put dup 68 /D put dup 71 /G put dup 77 /M put dup 80 /P put dup 82 /R put dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 121 /y put readonly def /FontBBox{-35 -250 1148 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % 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 (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 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 1 /Delta put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 16 /dotlessi put dup 18 /grave put dup 22 /macron put dup 34 /quotedblright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 126 /tilde put dup 127 /dieresis put readonly def /FontBBox{-39 -250 1036 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 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cleartomark %%EndFont %%BeginFont: CMBX9 %!PS-AdobeFont-1.1: CMBX9 1.0 %%CreationDate: 1991 Aug 20 16:36:25 % 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 (CMBX9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX9 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 44 /comma put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 73 /I put dup 77 /M put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 87 /W put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put readonly def /FontBBox{-58 -250 1195 750}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX7 %!PS-AdobeFont-1.1: CMBX7 1.0 %%CreationDate: 1991 Aug 20 16:35:49 % 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 (CMBX7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX7 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 44 /comma put dup 52 /four put dup 56 /eight put readonly def /FontBBox{-55 -250 1289 751}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % 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 (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 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 11 /ff put dup 12 /fi put dup 19 /acute put dup 28 /oslash put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put readonly def /FontBBox{-27 -250 1122 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6CC3F1E9AE32F234EB60FE7D E34995B1ACFF52428EA20C8ED4FD73E3935CEBD40E0EAD70C0887A451E1B1AC8 47AEDE4191CCDB8B61345FD070FD30C4F375D8418DDD454729A251B3F61DAE7C 8882384282FDD6102AE8EEFEDE6447576AFA181F27A48216A9CAD730561469E4 78B286F22328F2AE84EF183DE4119C402771A249AAC1FA5435690A28D1B47486 1060C8000D3FE1BF45133CF847A24B4F8464A63CEA01EC84AA22FD005E74847E 01426B6890951A7DD1F50A5F3285E1F958F11FC7F00EE26FEE7C63998EA1328B C9841C57C80946D2C2FC81346249A664ECFB08A2CE075036CEA7359FCA1E90C0 F686C3BB27EEFA45D548F7BD074CE60E626A4F83C69FE93A5324133A78362F30 8E8DCC80DD0C49E137CDC9AC08BAE39282E26A7A4D8C159B95F227BDA2A281AF A9DAEBF31F504380B20812A211CF9FEB112EC29A3FB3BD3E81809FC6293487A7 455EB3B879D2B4BD46942BB1243896264722CB59146C3F65BD59B96A74B12BB2 9A1354AF174932210C6E19FE584B1B14C00E746089CBB17E68845D7B3EA05105 EEE461E3697FCF835CBE6D46C75523478E766832751CF6D96EC338BDAD57D53B 52F5340FAC9FE0456AD13101824234B262AC0CABA43B62EBDA39795BAE6CFE97 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % 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. 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475 1[475 475 458 355 467 1[432 492 475 579 398 2[234 475 497 415 432 484 458 449 475 6[519 3[631 631 609 474 620 1[575 1[631 766 529 653 439 3[552 575 642 609 597 631 10[428 428 1[428 428 428 2[248 293 248 24[428 19[{}48 774.872 /CMCSC10 rf /Fv 138[673 471 478 475 2[606 673 1010 337 2[337 673 2[539 673 539 1[606 16[825 2[1111 2[623 5[926 2[909 18[337 1[337 44[{}21 1212.12 /CMR10 rf /Fw 137[736 774 542 550 574 736 774 697 774 1162 387 2[387 2[426 639 3[678 13[774 1045 4[1323 7[916 1[1007 67[{}20 1212.12 /CMBX10 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 8000dpi TeXDict begin %%BeginPaperSize: a4 a4 %%EndPaperSize end %%EndSetup %%Page: 1 1 TeXDict begin 1 0 bop 9766 15636 a Fw(Sequen)-39 b(tial)466 b(Mon)-39 b(te)465 b(Carlo)f(Samplers)h(for)g(Rare)f(Ev)-39 b(en)g(ts)9438 18514 y Fv(Adam)405 b(M.)e(Johansen,)i(Pierre)e(Del)g (Moral,)h(and)h(Arnaud)g(Doucet)9131 21464 y Fu(Abstra)-17 b(ct.)552 b Ft(W)-71 b(e)234 b(presen)-24 b(t)233 b(no)-24 b(v)g(el)235 b(sequen)-24 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Fk(;)f(s)30985 47360 y Fm(n)31552 47249 y Fj(g)366 b Fq(w)-28 b(e)366 b(shall)g(henceforth)g(think)h(of) 5146 48466 y(the)338 b(distribution)f(as)h(a)f(three)h(dimensional)h (one)e(o)-28 b(v)g(er)337 b(just)g(these)i(v)-57 b(ariables.)455 b(The)337 b(magnitude)h(of)g Fk(r)5146 49684 y Fq(is)j(termed)h(the)g (di\013eren)-28 b(tial)343 b(group)d(dela)-28 b(y)342 b(\(DGD\))h(and)e(is)g(the)h(quan)-28 b(tit)g(y)342 b(of)f(in)-28 b(terest.)7138 50902 y(One)340 b(option)e(for)g(a)h(prop)28 b(osal)339 b(distribution)g(is)g(an)f(up)28 b(date)340 b(mo)-28 b(v)g(e,)339 b(whic)-28 b(h)338 b(do)28 b(es)340 b(not)e(adjust)h(the)5146 52119 y(state)318 b(asso)28 b(ciated)318 b(with)g(a)f(particle)h(at)g(all,)323 b(but)318 b(do)28 b(es)318 b(correct)f(the)h(particle)g(w)-28 b(eigh)g(ts)317 b(to)h(accoun)-28 b(t)317 b(for)5146 53337 y(the)391 b(c)-28 b(hange)391 b(in)g(distribution)g(from)g(one)g(time)h(step)g (to)f(the)g(next.)605 b(This)391 b(has)g(incremen)-28 b(tal)392 b(w)-28 b(eigh)g(t)5146 54555 y(equal)393 b(to)f(the)h(ratio) g(of)f(the)g(densities)i(of)e(the)h(distribution)g(at)f(time)i Fk(t)e Fq(to)g(that)h(at)f(time)i Fk(t)261 b Fj(\000)h Fq(1.)608 b(A)5146 55772 y(priori)452 b(this)h(w)-28 b(ould)451 b(lead)i(v)-28 b(ery)453 b(fast)f(to)h(sample)g(degeneracy) -85 b(,)482 b(and)452 b(so)g(w)-28 b(e)452 b(also)h(apply)g(a)f(Mark) -28 b(o)g(v)5146 56990 y(k)g(ernel)368 b(of)f(the)h(correct)f(in)-28 b(v)-57 b(arian)-28 b(t)368 b(distribution)g(to)f(main)-28 b(tain)368 b(sample)h(div)-28 b(ersit)g(y)-85 b(.)534 b(W)-85 b(e)368 b(emplo)-28 b(y)g(ed)368 b(a)5146 58208 y(Metrop)28 b(olis-Hastings)329 b(k)-28 b(ernel)329 b(with)e(a)h(prop) 28 b(osal)327 b(whic)-28 b(h)327 b(randomly)h(selects)h(t)-28 b(w)g(o)327 b(indices)i(uniformly)5146 59425 y(b)28 b(et)-28 b(w)g(een)434 b(1)g(and)g Fk(n)g Fq(and)g(prop)28 b(oses)434 b(replacing)h(the)g Fk(\036)g Fq(and)f Fk(c)g Fq(v)-57 b(alues)436 b(b)28 b(et)-28 b(w)g(een)434 b(those)h(t)-28 b(w)g(o)433 b(indices)5146 60643 y(with)376 b(v)-57 b(alues)378 b(dra)-28 b(wn)375 b(from)h(the)i(uniform)e(distribution)h(o)-28 b(v)g(er)376 b([)p Fj(\000)p Fk(\031)36 b(;)172 b(\031)36 b Fq(])251 b Fj(\002)h Fq([)p Fj(\000)p Fq(1)p Fk(;)172 b Fq(1].)562 b(This)376 b(prop)28 b(osal)377 b(is)5146 61861 y(then)347 b(accepted)g(with)g(the)g(usual)g(Metrop)28 b(olis)348 b(acceptance)f(probabilit)-28 b(y)-85 b(.)472 b(Results)347 b(of)f(the)i(approac)-28 b(h)5146 63078 y(prop)28 b(osed)341 b(here)g(and)g(that)h(of)f([)p Fr(8)q Fq(])h(are)f(illustrated)h(in)g(\014gure)f(1.)7138 64296 y(2.3.3.)513 b Fp(Counting)436 b(Pr)-52 b(oblems.)513 b Fq(Coun)-28 b(ting)417 b(the)i(n)-28 b(um)g(b)28 b(er)418 b(of)g(w)-28 b(a)g(ys)417 b(of)h(\014lling)h(a)f(knapsac)-28 b(k)418 b(with)5146 65514 y(unique)377 b(com)-28 b(binations)377 b(of)f(ob)57 b(jects)377 b(of)f(kno)-28 b(wn)376 b(sizes)h(is)g(one)g (of)f(the)h(classic)g(coun)-28 b(ting)377 b(problems)f(of)5146 66731 y(computer)250 b(science,)271 b(see)251 b(for)f(example,)271 b([)p Fr(16)q Fq(].)426 b(In)250 b(its)h(simplest)h(form,)268 b(the)252 b(problem)e(is)h(this)g(one:)410 b(giv)-28 b(en)5146 67949 y(a)317 b(v)-28 b(ector,)324 b Fk(a)318 b Fq(of)g Fk(n)f Fq(ob)57 b(ject)319 b(sizes)f(and)g(a)g Fp(knapsack)426 b Fq(of)317 b(capacit)-28 b(y)319 b Fk(b)f Fq(w)-28 b(e)317 b(wish)h(to)g(estimate)h(the)g(n)-28 b(um)g(b)28 b(er)5146 69167 y(of)509 b(di\013eren)-28 b(t)509 b(com)-28 b(binations)510 b(of)f(ob)57 b(jects)509 b(whic)-28 b(h)508 b(will)i(\014t)f(within)g(the)h(knapsac)-28 b(k,)552 b(whic)-28 b(h)508 b(clearly)5146 70384 y(corresp)28 b(onds)338 b(to)h(the)g(n)-28 b(um)g(b)28 b(er)338 b(of)g(unique)i(0) 222 b Fj(\000)h Fq(1)339 b(v)-28 b(ectors)339 b Fk(x)g Fq(for)f(whic)-28 b(h)338 b(the)h(follo)-28 b(wing)339 b(inequalit)-28 b(y)341 b(is)5146 71602 y(satis\014ed:)5146 74147 y(\(2\))14221 b Fk(a)228 b Fj(\001)g Fk(x)285 b Fq(=)24330 72902 y Fm(P)23903 73201 y Fo(X)23981 75301 y Fm(i)p Fl(=1)25553 74147 y Fk(a)26095 74258 y Fm(i)26446 74147 y Fk(x)27026 74258 y Fm(i)27662 74147 y Fj(\024)g Fk(b:)p eop end %%Page: 8 8 TeXDict begin 8 7 bop 5146 3460 a Fl(8)9307 b(A.)277 b(M.)g(JOHANSEN,)h(P)-65 b(.)276 b(DEL)g(MORAL,)h(AND)g(A.)g(DOUCET) 5146 32905 y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 3586 @rwi @setspecial %%BeginDocument: dmgcomppdf.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: dmgpdfcomp.eps %%Creator: gnuplot 4.0 patchlevel 0 %%CreationDate: Mon Jul 25 12:11:43 2005 %%DocumentFonts: (atend) %%BoundingBox: 50 50 410 302 %%Orientation: Portrait %%EndComments /gnudict 256 dict def gnudict begin /Color true def /Solid false def /gnulinewidth 5.000 def /userlinewidth gnulinewidth def /vshift -46 def /dl {10.0 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /Rounded false def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /N {newpath moveto} bind def /C {setrgbcolor} bind def /f {rlineto fill} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse } def /BL { stroke userlinewidth 2 mul setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /AL { stroke userlinewidth 2 div setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /UL { dup gnulinewidth mul /userlinewidth exch def dup 1 lt {pop 1} if 10 mul /udl exch def } def /PL { stroke userlinewidth setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /LTw { PL [] 1 setgray } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def /BoxColFill { gsave Rec /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor fill grestore } def % % PostScript Level 1 Pattern Fill routine % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill { gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get 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Fq(])g(w)-28 b(ould)450 b(b)28 b(e)5146 49083 y(p)g(ossible,)457 b(this)433 b(is)g(a)g(m)-28 b(uc)g(h)432 b(more)h(c)-28 b(hallenging)434 b(problem)f(than)g(that)g(considered)g (there)h(in)f(whic)-28 b(h)5146 50301 y Fk(a)284 b Fq(=)h(\(1)p Fk(;)172 b(:)f(:)g(:)g(;)g Fq(4\))341 b(and)g(a)h(threshold)f(of)g Fk(b)284 b Fq(=)h(3)341 b(w)-28 b(as)341 b(emplo)-28 b(y)g(ed.)15895 52623 y Fr(3.)591 b(Dynamic)394 b(Rare)g(Ev)-33 b(en)g(t)393 b(Estimation)7138 54450 y Fq(Length)371 b(constrain)-28 b(ts)370 b(prev)-28 b(en)g(t)370 b(us)g(from)g(doing)h (more)f(than)h(illustrating)g(the)g(applicabilit)-28 b(y)372 b(of)5146 55667 y(our)c(approac)-28 b(h)368 b(to)i(the)g (dynamic)g(rare)f(ev)-28 b(en)g(t)370 b(estimation)h(problem,)377 b(and)370 b(pro)-28 b(viding)369 b(a)g(simple)i(to)-28 b(y)5146 56885 y(example)343 b(b)-28 b(y)341 b(w)-28 b(a)g(y)340 b(of)h(illustration.)457 b(F)-85 b(urther)341 b(details)h(will)g(b)28 b(e)342 b(presen)-28 b(ted)342 b(in)f([)p Fr(17)r Fq(].)7138 58103 y(Considering)258 b(the)h(space)g(on)f(whic)-28 b(h)258 b(the)h(paths)g(of)f(in)-28 b(terest)259 b(\(i.e.)429 b(those)259 b(starting)g(in)g(the)g(supp)28 b(ort)5146 59320 y(of)379 b Fk(\021)6861 59431 y Fl(0)7702 59320 y Fq(and)g(then)h(ev)-28 b(olving)382 b(according)d(to)h(the)g (la)-28 b(w)379 b(of)g(the)i(Mark)-28 b(o)g(v)379 b(c)-28 b(hain)379 b(un)-28 b(til)380 b(they)h(hit)f Fj(R)253 b([)f(T)k Fq(\))5146 60538 y(exist)13389 62379 y Fk(F)426 b Fq(=)15806 61134 y Fn(1)15643 61433 y Fo([)15550 63533 y Fm(i)p Fl(=2)17044 62379 y Fj(f)p Fk(i)p Fj(g)228 b(\002)g Fq(supp)o(\()p Fk(\021)22689 62490 y Fl(0)23151 62379 y Fq(\))f Fj(\002)h Fq(\()q Fk(E)284 b Fj(n)228 b Fq(\()p Fj(R)f([)g(T)256 b Fq(\)\))30995 61900 y Fm(i)p Fn(\000)p Fl(2)32620 62379 y Fj(\002)228 b(R)f([)g(T)255 b Fk(;)5146 64748 y Fq(where)385 b(w)-28 b(e)384 b(assume)i(that)f(the)h(supp)28 b(ort)385 b(of)g(the)h(initial)h(distribution)e(do)28 b(es)386 b(not)f(include)i(either)f(the)5146 65965 y(rare)397 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6011 a Fr(Algorithm)395 b(2)342 b Fq(An)f(SMC)g(algorithm)h(for)e(dynamic)j(rare)d(ev)-28 b(en)g(t)342 b(sim)-28 b(ulation.)p 5146 6471 39851 45 v 6170 7904 a Fk(t)355 b Fq(=)g(1.)583 b(Initialise)386 b(an)e(ensem)-28 b(ble)385 b(of)e Fk(N)491 b Fq(w)-28 b(eigh)g(ted)384 b(particle:)542 b Fr(for)384 b Fk(i)356 b Fq(=)g(1)384 b(to)g Fk(N)491 b Fr(do)768 b Fq(sample)384 b Fk(Y)44005 7395 y Fl(\()p Fm(i)p Fl(\))43777 8157 y(1)6170 9275 y Fq(from)329 b(the)h(la)-28 b(w)329 b(of)h(the)g(Mark)-28 b(o)g(v)329 b(c)-28 b(hain)330 b(un)-28 b(til)329 b(it)i(hits)f(either) g Fj(T)30337 9386 y Fl(1)31128 9275 y Fq(or)f Fj(R)p Fq(,)j(at)e(stopping)g(time)h Fk(\034)42130 8766 y Fl(\()p Fm(i)p Fl(\))42016 9528 y(1)43121 9275 y Fq(;)j(set)6170 11084 y Fk(W)7279 10574 y Fl(\()p Fm(i)p Fl(\))7137 11337 y(1)8554 11084 y Fq(=)285 b Fh(I)10022 11195 y Fn(T)10494 11323 y Fg(1)11153 9681 y Fo(\022)11906 11084 y Fk(X)12830 10574 y Fl(\()p Fm(i)p Fl(\))12752 11691 y Fm(\034)13216 11324 y Fg(\()p Fd(i)p 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Fq(b)28 b(efore)342 b Fj(R)p Fq(\).)6170 25502 y Fr(end)f(for)6170 27124 y Fq(W)-85 b(e)341 b(can)g(no)-28 b(w)341 b(estimate)i(the)f (quan)-28 b(tit)g(y)341 b(of)g(in)-28 b(terest:)456 b Fk(p)27661 26701 y Fm(?)28426 27124 y Fq(=)29882 26178 y Fm(T)29695 26377 y Fo(Q)29506 27976 y Fm(t)p Fl(=1)31299 26872 y Fq(^)31021 27124 y Fk(Z)31718 27235 y Fm(t)32431 27124 y Fq(with)341 b Fk(Z)35460 27235 y Fm(t)36116 27124 y Fq(=)37484 26716 y Fl(1)p 37330 26896 V 37330 27462 a Fm(N)38652 26178 y(N)38468 26377 y Fo(P)38347 27979 y Fm(i)p Fl(=1)39841 27124 y Fk(W)40950 26615 y Fl(\()p Fm(i)p Fl(\))40808 27358 y Fm(t)41941 27124 y Fq(.)p 5146 28560 39851 45 v 5146 31334 a(suc)-28 b(h)368 b(that)i(the)g(ma)57 b(jorit)-28 b(y)370 b(of)f(paths)g(reac)-28 b(hing)369 b Fj(T)24408 31445 y Fm(t)25150 31334 y Fq(b)28 b(efore)370 b Fj(R)f Fq(also)h(reac)-28 b(h)369 b Fj(T)34869 31445 y Fm(t)p Fl(+1)36638 31334 y Fq(b)28 b(efore)370 b Fj(R)p Fq(.)539 b(That)369 b(is,)5146 32552 y(the)394 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