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gstring 0 gindex getinterval true } def } if /FMVERSION { FMversion ne { /Times-Roman findfont 18 scalefont setfont 100 100 moveto (FrameMaker version does not match postscript_prolog!) dup = show showpage } if } def /FMLOCAL { FrameDict begin 0 def end } def /gstring FMLOCAL /gfile FMLOCAL /gindex FMLOCAL /orgxfer FMLOCAL /orgproc FMLOCAL /organgle FMLOCAL /orgfreq FMLOCAL /yscale FMLOCAL /xscale FMLOCAL /manualfeed FMLOCAL /paperheight FMLOCAL /paperwidth FMLOCAL /FMDOCUMENT { array /FMfonts exch def /#copies exch def FrameDict begin 0 ne dup {setmanualfeed} if /manualfeed exch def /paperheight exch def /paperwidth exch def /yscale exch def /xscale exch def currenttransfer cvlit /orgxfer exch def currentscreen cvlit /orgproc exch def /organgle exch def /orgfreq exch def setpapername manualfeed {true} {papersize} ifelse {manualpapersize} {false} ifelse {desperatepapersize} if end } def /pagesave FMLOCAL /orgmatrix FMLOCAL /landscape FMLOCAL /FMBEGINPAGE { FrameDict begin /pagesave save def 3.86 setmiterlimit /landscape exch 0 ne def landscape { 90 rotate 0 exch neg translate pop } {pop pop} ifelse xscale yscale scale /orgmatrix matrix def gsave } def /FMENDPAGE { grestore pagesave restore end showpage } def /FMFONTDEFINE { FrameDict begin findfont ReEncode 1 index exch definefont FMfonts 3 1 roll put end } def /FMFILLS { FrameDict begin array /fillvals exch def end } def /FMFILL { FrameDict begin fillvals 3 1 roll put end } def /FMNORMALIZEGRAPHICS { newpath 0.0 0.0 moveto 1 setlinewidth 0 setlinecap 0 0 0 sethsbcolor 0 setgray } bind def /fx FMLOCAL /fy FMLOCAL /fh FMLOCAL /fw FMLOCAL /llx FMLOCAL /lly FMLOCAL /urx FMLOCAL /ury FMLOCAL /FMBEGINEPSF { end /FMEPSF save def /showpage {} def FMNORMALIZEGRAPHICS [/fy /fx /fh /fw /ury /urx /lly /llx] {exch def} forall fx fy translate rotate fw urx llx sub div fh ury lly sub div scale llx neg lly neg translate } bind def /FMENDEPSF { FMEPSF restore FrameDict begin } bind def FrameDict begin /setmanualfeed { statusdict /manualfeed true put } def /max {2 copy lt {exch} if pop} bind def /min {2 copy gt {exch} if pop} bind def /inch {72 mul} def /pagedimen { paperheight sub abs 16 lt exch paperwidth sub abs 16 lt and {/papername exch def} {pop} ifelse } def /papersizedict FMLOCAL /setpapername { /papersizedict 14 dict def papersizedict begin /papername /unknown def /Letter 8.5 inch 11.0 inch pagedimen /LetterSmall 7.68 inch 10.16 inch pagedimen /Tabloid 11.0 inch 17.0 inch pagedimen /Ledger 17.0 inch 11.0 inch pagedimen /Legal 8.5 inch 14.0 inch pagedimen /Statement 5.5 inch 8.5 inch pagedimen /Executive 7.5 inch 10.0 inch pagedimen /A3 11.69 inch 16.5 inch pagedimen /A4 8.26 inch 11.69 inch pagedimen /A4Small 7.47 inch 10.85 inch pagedimen /B4 10.125 inch 14.33 inch pagedimen /B5 7.16 inch 10.125 inch pagedimen end } def /papersize { papersizedict begin /Letter {lettertray letter} def /LetterSmall {lettertray lettersmall} def /Tabloid {11x17tray 11x17} def /Ledger {ledgertray ledger} def /Legal {legaltray legal} def /Statement {statementtray statement} def /Executive {executivetray executive} def /A3 {a3tray a3} def /A4 {a4tray a4} def /A4Small {a4tray a4small} def /B4 {b4tray b4} def /B5 {b5tray b5} def /unknown {unknown} def papersizedict dup papername known {papername} {/unknown} ifelse get end /FMdicttop countdictstack 1 add def statusdict begin stopped end countdictstack -1 FMdicttop {pop end} for } def /manualpapersize { papersizedict begin /Letter {letter} def /LetterSmall {lettersmall} def /Tabloid {11x17} def /Ledger {ledger} def /Legal {legal} def /Statement {statement} def /Executive {executive} def /A3 {a3} def /A4 {a4} def /A4Small {a4small} def /B4 {b4} def /B5 {b5} def /unknown {unknown} def papersizedict dup papername known {papername} {/unknown} ifelse get end stopped } def /desperatepapersize { statusdict /setpageparams known { paperwidth paperheight 0 1 statusdict begin {setpageparams} stopped pop end } if } def /savematrix { orgmatrix currentmatrix pop } bind def /restorematrix { orgmatrix setmatrix } bind def /dmatrix matrix def /dpi 72 0 dmatrix defaultmatrix dtransform dup mul exch dup mul add sqrt def /freq dpi 18.75 div 8 div round dup 0 eq {pop 1} if 8 mul dpi exch div def /sangle 1 0 dmatrix defaultmatrix dtransform exch atan def /DiacriticEncoding [ /.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 /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quotesingle /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 /grave /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 /.notdef /Adieresis /Aring /Ccedilla /Eacute /Ntilde /Odieresis /Udieresis /aacute /agrave /acircumflex /adieresis /atilde /aring /ccedilla /eacute /egrave /ecircumflex /edieresis /iacute /igrave /icircumflex /idieresis /ntilde /oacute /ograve /ocircumflex /odieresis /otilde /uacute /ugrave /ucircumflex /udieresis /dagger /.notdef /cent /sterling /section /bullet /paragraph /germandbls /registered /copyright /trademark /acute /dieresis /.notdef /AE /Oslash /.notdef /.notdef /.notdef /.notdef /yen /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /ordfeminine /ordmasculine /.notdef /ae /oslash /questiondown /exclamdown /logicalnot /.notdef /florin /.notdef /.notdef /guillemotleft /guillemotright /ellipsis /.notdef /Agrave /Atilde /Otilde /OE /oe /endash /emdash /quotedblleft /quotedblright /quoteleft /quoteright /.notdef /.notdef /ydieresis /Ydieresis /fraction /currency /guilsinglleft /guilsinglright /fi /fl /daggerdbl /periodcentered /quotesinglbase /quotedblbase /perthousand /Acircumflex /Ecircumflex /Aacute /Edieresis /Egrave /Iacute /Icircumflex /Idieresis /Igrave /Oacute /Ocircumflex /.notdef /Ograve /Uacute /Ucircumflex /Ugrave /dotlessi /circumflex /tilde /macron /breve /dotaccent /ring /cedilla /hungarumlaut /ogonek /caron ] def /ReEncode { dup length dict begin { 1 index /FID ne {def} {pop pop} ifelse } forall 0 eq {/Encoding DiacriticEncoding def} if currentdict end } bind def /graymode true def /bwidth FMLOCAL /bpside FMLOCAL /bstring FMLOCAL /onbits FMLOCAL /offbits FMLOCAL /xindex FMLOCAL /yindex FMLOCAL /x FMLOCAL /y FMLOCAL /setpattern { /bwidth exch def /bpside exch def /bstring exch def /onbits 0 def /offbits 0 def freq sangle landscape {90 add} if {/y exch def /x exch def /xindex x 1 add 2 div bpside mul cvi def /yindex y 1 add 2 div bpside mul cvi def bstring yindex bwidth mul xindex 8 idiv add get 1 7 xindex 8 mod sub bitshift and 0 ne {/onbits onbits 1 add def 1} {/offbits offbits 1 add def 0} ifelse } setscreen {} settransfer offbits offbits onbits add div FMsetgray /graymode false def } bind def /grayness { FMsetgray graymode not { /graymode true def orgxfer cvx settransfer orgfreq organgle orgproc cvx setscreen } if } bind def /HUE FMLOCAL /SAT FMLOCAL /BRIGHT FMLOCAL /Colors FMLOCAL FMPrintInColor { /HUE 0 def /SAT 0 def /BRIGHT 0 def % array of arrays Hue and Sat values for the separations [HUE BRIGHT] /Colors [[0 0 ] % black [0 0 ] % white [0.00 1.0] % red [0.37 1.0] % green [0.60 1.0] % blue [0.50 1.0] % cyan [0.83 1.0] % magenta [0.16 1.0] % comment / yellow ] def /BEGINBITMAPCOLOR { BITMAPCOLOR} def /BEGINBITMAPCOLORc { BITMAPCOLORc} def /BEGINBITMAPTRUECOLOR { BITMAPTRUECOLOR } def /BEGINBITMAPTRUECOLORc { BITMAPTRUECOLORc } def /K { Colors exch get dup 0 get /HUE exch store 1 get /BRIGHT exch store HUE 0 eq BRIGHT 0 eq and {1.0 SAT sub setgray} {HUE SAT BRIGHT sethsbcolor} ifelse } def /FMsetgray { /SAT exch 1.0 exch sub store HUE 0 eq BRIGHT 0 eq and {1.0 SAT sub setgray} {HUE SAT BRIGHT sethsbcolor} ifelse } bind def } { /BEGINBITMAPCOLOR { BITMAPGRAY} def /BEGINBITMAPCOLORc { BITMAPGRAYc} def /BEGINBITMAPTRUECOLOR { BITMAPTRUEGRAY } def /BEGINBITMAPTRUECOLORc { BITMAPTRUEGRAYc } def /FMsetgray {setgray} bind def /K { pop } def } ifelse /normalize { transform round exch round exch itransform } bind def /dnormalize { dtransform round exch round exch idtransform } bind def /lnormalize { 0 dtransform exch cvi 2 idiv 2 mul 1 add exch idtransform pop } bind def /H { lnormalize setlinewidth } bind def /Z { setlinecap } bind def /fillvals FMLOCAL /X { fillvals exch get dup type /stringtype eq {8 1 setpattern} {grayness} ifelse } bind def /V { gsave eofill grestore } bind def /N { stroke } bind def /M {newpath moveto} bind def /E {lineto} bind def /D {curveto} bind def /O {closepath} bind def /n FMLOCAL /L { /n exch def newpath normalize moveto 2 1 n {pop normalize lineto} for } bind def /Y { L closepath } bind def /x1 FMLOCAL /x2 FMLOCAL /y1 FMLOCAL /y2 FMLOCAL /rad FMLOCAL /R { /y2 exch def /x2 exch def /y1 exch def /x1 exch def x1 y1 x2 y1 x2 y2 x1 y2 4 Y } bind def /RR { /rad exch def normalize /y2 exch def /x2 exch def normalize /y1 exch def /x1 exch def newpath x1 y1 rad add moveto x1 y2 x2 y2 rad arcto x2 y2 x2 y1 rad arcto x2 y1 x1 y1 rad arcto x1 y1 x1 y2 rad arcto closepath 16 {pop} repeat } bind def /C { grestore gsave R clip } bind def /FMpointsize FMLOCAL /F { FMfonts exch get FMpointsize scalefont setfont } bind def /Q { /FMpointsize exch def F } bind def /T { moveto show } bind def /RF { rotate 0 ne {-1 1 scale} if } bind def /TF { gsave moveto RF show grestore } bind def /P { moveto 0 32 3 2 roll widthshow } bind def /PF { gsave moveto RF 0 32 3 2 roll widthshow grestore } bind def /S { moveto 0 exch ashow } bind def /SF { gsave moveto RF 0 exch ashow grestore } bind def /B { moveto 0 32 4 2 roll 0 exch awidthshow } bind def /BF { gsave moveto RF 0 32 4 2 roll 0 exch awidthshow grestore } bind def /G { gsave newpath normalize translate 0.0 0.0 moveto dnormalize scale 0.0 0.0 1.0 5 3 roll arc closepath fill grestore } bind def /A { gsave savematrix newpath 2 index 2 div add exch 3 index 2 div sub exch normalize 2 index 2 div sub exch 3 index 2 div add exch translate scale 0.0 0.0 1.0 5 3 roll arc restorematrix stroke grestore } bind def /x FMLOCAL /y FMLOCAL /w FMLOCAL /h FMLOCAL /xx FMLOCAL /yy FMLOCAL /ww FMLOCAL /hh FMLOCAL /FMsaveobject FMLOCAL /FMoptop FMLOCAL /FMdicttop FMLOCAL /BEGINPRINTCODE { /FMdicttop countdictstack 1 add def /FMoptop count 4 sub def /FMsaveobject save def userdict begin /showpage {} def FMNORMALIZEGRAPHICS 3 index neg 3 index neg translate } bind def /ENDPRINTCODE { count -1 FMoptop {pop pop} for countdictstack -1 FMdicttop {pop end} for FMsaveobject restore } bind def /gn { 0 { 46 mul cf read pop 32 sub dup 46 lt {exit} if 46 sub add } loop add } bind def /str FMLOCAL /cfs { /str sl string def 0 1 sl 1 sub {str exch val put} for str def } bind def /ic [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0223 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0223 0 {0 hx} {1 hx} {2 hx} {3 hx} {4 hx} {5 hx} {6 hx} {7 hx} {8 hx} {9 hx} {10 hx} {11 hx} {12 hx} {13 hx} {14 hx} {15 hx} {16 hx} {17 hx} {18 hx} {19 hx} {gn hx} {0} {1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {11} {12} {13} {14} {15} {16} {17} {18} {19} {gn} {0 wh} {1 wh} {2 wh} {3 wh} {4 wh} {5 wh} {6 wh} {7 wh} {8 wh} {9 wh} {10 wh} {11 wh} {12 wh} {13 wh} {14 wh} {gn wh} {0 bl} {1 bl} {2 bl} {3 bl} {4 bl} {5 bl} {6 bl} {7 bl} {8 bl} {9 bl} {10 bl} {11 bl} {12 bl} {13 bl} {14 bl} {gn bl} {0 fl} {1 fl} {2 fl} {3 fl} {4 fl} {5 fl} {6 fl} {7 fl} {8 fl} {9 fl} {10 fl} {11 fl} {12 fl} {13 fl} {14 fl} {gn fl} ] def /sl FMLOCAL /val FMLOCAL /ws FMLOCAL /im FMLOCAL /bs FMLOCAL /cs FMLOCAL /len FMLOCAL /pos FMLOCAL /ms { /sl exch def /val 255 def /ws cfs /im cfs /val 0 def /bs cfs /cs cfs } bind def 400 ms /ip { is 0 cf cs readline pop { ic exch get exec add } forall pop } bind def /wh { /len exch def /pos exch def ws 0 len getinterval im pos len getinterval copy pop pos len } bind def /bl { /len exch def /pos exch def bs 0 len getinterval im pos len getinterval copy pop pos len } bind def /s1 1 string def /fl { /len exch def /pos exch def /val cf s1 readhexstring pop 0 get def pos 1 pos len add 1 sub {im exch val put} for pos len } bind def /hx { 3 copy getinterval cf exch readhexstring pop pop } bind def /h FMLOCAL /w FMLOCAL /d FMLOCAL /lb FMLOCAL /bitmapsave FMLOCAL /is FMLOCAL /cf FMLOCAL /wbytes { dup 8 eq {pop} {1 eq {7 add 8 idiv} {3 add 4 idiv} ifelse} ifelse } bind def /BEGINBITMAPBWc { 1 {} COMMONBITMAPc } bind def /BEGINBITMAPGRAYc { 8 {} COMMONBITMAPc } bind def /BEGINBITMAP2BITc { 2 {} COMMONBITMAPc } bind def /COMMONBITMAPc { /r exch def /d exch def gsave translate rotate scale /h exch def /w exch def /lb w d wbytes def sl lb lt {lb ms} if /bitmapsave save def r /is im 0 lb getinterval def ws 0 lb getinterval is copy pop /cf currentfile def w h d [w 0 0 h neg 0 h] {ip} image bitmapsave restore grestore } bind def /BEGINBITMAPBW { 1 {} COMMONBITMAP } bind def /BEGINBITMAPGRAY { 8 {} COMMONBITMAP } bind def /BEGINBITMAP2BIT { 2 {} COMMONBITMAP } bind def /COMMONBITMAP { /r exch def /d exch def gsave translate rotate scale /h exch def /w exch def /bitmapsave save def r /is w d wbytes string def /cf currentfile def w h d [w 0 0 h neg 0 h] {cf is readhexstring pop} image bitmapsave restore grestore } bind def /proc1 FMLOCAL /proc2 FMLOCAL /newproc FMLOCAL /Fmcc { /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 } bind def /ngrayt 256 array def /nredt 256 array def /nbluet 256 array def /ngreent 256 array def /gryt FMLOCAL /blut FMLOCAL /grnt FMLOCAL /redt FMLOCAL /indx FMLOCAL /cynu FMLOCAL /magu FMLOCAL /yelu FMLOCAL /k FMLOCAL /u FMLOCAL /colorsetup { currentcolortransfer /gryt exch def /blut exch def /grnt exch def /redt exch def 0 1 255 { /indx exch def /cynu 1 red indx get 255 div sub def /magu 1 green indx get 255 div sub def /yelu 1 blue indx get 255 div sub def /k cynu magu min yelu min def /u k currentundercolorremoval exec def nredt indx 1 0 cynu u sub max sub redt exec put ngreent indx 1 0 magu u sub max sub grnt exec put nbluet indx 1 0 yelu u sub max sub blut exec put ngrayt indx 1 k currentblackgeneration exec sub gryt exec put } for {255 mul cvi nredt exch get} {255 mul cvi ngreent exch get} {255 mul cvi nbluet exch get} {255 mul cvi ngrayt exch get} setcolortransfer {pop 0} setundercolorremoval {} setblackgeneration } bind def /tran FMLOCAL /fakecolorsetup { /tran 256 string def 0 1 255 {/indx exch def tran indx red indx get 77 mul green indx get 151 mul blue indx get 28 mul add add 256 idiv put} for currenttransfer {255 mul cvi tran exch get 255.0 div} exch Fmcc settransfer } bind def /BITMAPCOLOR { /d 8 def gsave translate rotate scale /h exch def /w exch def /bitmapsave save def colorsetup /is w d wbytes string def /cf currentfile def w h d [w 0 0 h neg 0 h] {cf is readhexstring pop} {is} {is} true 3 colorimage bitmapsave restore grestore } bind def /BITMAPCOLORc { /d 8 def gsave translate rotate scale /h exch def /w exch def /lb w d wbytes def sl lb lt {lb ms} if /bitmapsave save def colorsetup /is im 0 lb getinterval def ws 0 lb getinterval is copy pop /cf currentfile def w h d [w 0 0 h neg 0 h] {ip} {is} {is} true 3 colorimage bitmapsave restore grestore } bind def /BITMAPTRUECOLORc { gsave translate rotate scale /h exch def /w exch def /bitmapsave save def /is w string def ws 0 w getinterval is copy pop /cf currentfile def w h 8 [w 0 0 h neg 0 h] {ip} {gip} {bip} true 3 colorimage bitmapsave restore grestore } bind def /BITMAPTRUECOLOR { gsave translate rotate scale /h exch def /w exch def /bitmapsave save def /is w string def /gis w string def /bis w string def /cf currentfile def w h 8 [w 0 0 h neg 0 h] { cf is readhexstring pop } { cf gis readhexstring pop } { cf bis readhexstring pop } true 3 colorimage bitmapsave restore grestore } bind def /BITMAPTRUEGRAYc { gsave translate rotate scale /h exch def /w exch def /bitmapsave save def /is w string def ws 0 w getinterval is copy pop /cf currentfile def w h 8 [w 0 0 h neg 0 h] {ip gip bip w gray} image bitmapsave restore grestore } bind def /ww FMLOCAL /r FMLOCAL /g FMLOCAL /b FMLOCAL /i FMLOCAL /gray { /ww exch def /b exch def /g exch def /r exch def 0 1 ww 1 sub { /i exch def r i get .299 mul g i get .587 mul b i get .114 mul add add r i 3 -1 roll floor cvi put } for r } bind def /BITMAPTRUEGRAY { gsave translate rotate scale /h exch def /w exch def /bitmapsave save def /is w string def /gis w string def /bis w string def /cf currentfile def w h 8 [w 0 0 h neg 0 h] { cf is readhexstring pop cf gis readhexstring pop cf bis readhexstring pop w gray} image bitmapsave restore grestore } bind def /BITMAPGRAY { 8 {fakecolorsetup} COMMONBITMAP } bind def /BITMAPGRAYc { 8 {fakecolorsetup} COMMONBITMAPc } bind def /ENDBITMAP { } bind def end /ALDsave FMLOCAL /ALDmatrix matrix def ALDmatrix currentmatrix pop /StartALD { /ALDsave save def savematrix ALDmatrix setmatrix } bind def /InALD { restorematrix } bind def /DoneALD { ALDsave restore } bind def (3.0) FMVERSION 1 1 2 2 0 1 4 FMDOCUMENT 0 0 /Times-Italic FMFONTDEFINE 1 0 /Times-Roman FMFONTDEFINE 32 FMFILLS 0 0 FMFILL 1 .1 FMFILL 2 .3 FMFILL 3 .5 FMFILL 4 .7 FMFILL 5 .9 FMFILL 6 .97 FMFILL 7 1 FMFILL 8 <0f1e3c78f0e1c387> FMFILL 9 <0f87c3e1f0783c1e> FMFILL 10 FMFILL 11 FMFILL 12 <8142241818244281> FMFILL 13 <03060c183060c081> FMFILL 14 <8040201008040201> FMFILL 16 1 FMFILL 17 .9 FMFILL 18 .7 FMFILL 19 .5 FMFILL 20 .3 FMFILL 21 .1 FMFILL 22 0.03 FMFILL 23 0 FMFILL 24 FMFILL 25 FMFILL 26 <3333333333333333> FMFILL 27 <0000ffff0000ffff> FMFILL 28 <7ebddbe7e7dbbd7e> FMFILL 29 FMFILL 30 <7fbfdfeff7fbfdfe> FMFILL 595.3 841.9 0 FMBEGINPAGE 211.41 430.56 222.95 427.25 211.41 423.94 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162.27 330.69 165.57 330.8 4 Y V 164.45 365.75 165.58 330.78 2 L N 139.07 379.57 150.45 375.76 138.78 372.97 138.92 376.27 4 Y V 105.45 377.75 138.92 376.26 2 L N 180.15 348.43 182.95 336.76 174.39 345.18 177.27 346.81 4 Y V 166.45 366.25 177.28 346.8 2 L N 161.7 329.06 163.94 317.27 155.8 326.08 158.75 327.57 4 Y V 147.95 349.25 158.75 327.55 2 L N 126.68 369.88 135.95 362.25 124.05 363.81 125.37 366.85 4 Y V 103.45 376.25 125.37 366.84 2 L N 116.24 356.96 118.94 345.27 110.45 353.75 113.35 355.35 4 Y V 102.45 375.25 113.35 355.34 2 L N 7 X 90 450 9 9 159.95 373.25 G 0 X 90 450 9 9 159.95 373.25 A 7 X 90 450 9 9 141.95 355.25 G 0 X 90 450 9 9 141.95 355.25 A 7 X 90 450 9 9 123.95 337.25 G 0 X 90 450 9 9 123.95 337.25 A 7 X 90 450 9 9 114.95 400.25 G 0 X 90 450 9 9 114.95 400.25 A 7 X 90 450 9 9 96.95 382.25 G 0 X 90 450 9 9 96.95 382.25 A 7 X 90 450 9 9 186.95 328.25 G 0 X 90 450 9 9 186.95 328.25 A 7 X 90 450 9 9 168.95 310.25 G 0 X 90 450 9 9 168.95 310.25 A 0 18 Q (s) 40.95 431.25 T 0 14 Q (1) 47.95 426.75 T 1 F (observed) 54.94 438.45 T 0 18 Q (s) 231.95 430.63 T 0 14 Q (2) 238.95 426.13 T 1 F (observed) 245.94 437.83 T 0 18 Q (a) 40.95 407.25 T 0 14 Q (1) 49.94 402.75 T 0 18 Q (a) 233.95 407.63 T 0 14 Q (2) 242.94 403.13 T 0 18 Q (s) 213.95 266.51 T 0 14 Q (2) 220.95 262.01 T 1 F (predicted) 227.94 273.71 T 217.16 398.07 222.95 418.25 228.74 398.07 222.95 398.07 4 Y 4 X V 228.74 307.44 222.95 287.25 217.16 307.44 222.95 307.44 4 Y V 222.95 398.07 222.95 307.44 2 L 3 H 0 Z N 0 X (\050goal state\051) 623.95 411.29 T 400.41 430.56 411.95 427.25 400.41 423.94 400.41 427.25 4 Y V 258.95 427.25 400.41 427.25 2 L 1 H 2 Z N 397.06 293.75 402.92 283.29 392.4 289.05 394.73 291.4 4 Y V 258.95 427.25 394.75 291.37 2 L N 285.95 400.25 M 312.95 427.25 312.95 427.25 357.95 382.25 D 402.95 337.25 402.95 337.25 375.95 310.25 D 348.95 283.25 348.95 283.25 303.95 328.25 D 258.95 373.25 258.95 373.25 285.95 400.25 D O 285.95 400.25 375.95 310.25 2 L 3 H 7 X N 333.06 386.38 341.43 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376.25 314.37 366.84 2 L N 305.23 356.96 307.94 345.27 299.45 353.75 302.34 355.35 4 Y V 291.45 375.25 302.35 355.34 2 L N 7 X 90 450 9 9 348.95 373.25 G 0 X 90 450 9 9 348.95 373.25 A 7 X 90 450 9 9 330.95 355.25 G 0 X 90 450 9 9 330.95 355.25 A 7 X 90 450 9 9 312.95 337.25 G 0 X 90 450 9 9 312.95 337.25 A 7 X 90 450 9 9 303.95 400.25 G 0 X 90 450 9 9 303.95 400.25 A 7 X 90 450 9 9 285.95 382.25 G 0 X 90 450 9 9 285.95 382.25 A 7 X 90 450 9 9 375.95 328.25 G 0 X 90 450 9 9 375.95 328.25 A 7 X 90 450 9 9 357.95 310.25 G 0 X 90 450 9 9 357.95 310.25 A 0 18 Q (s) 420.95 430.63 T 0 14 Q (3) 427.95 426.13 T 1 F (observed) 434.94 437.83 T 0 18 Q (a) 422.95 407.63 T 0 14 Q (3) 431.94 403.13 T 0 18 Q (s) 402.95 266.51 T 0 14 Q (3) 409.95 262.01 T 1 F (predicted) 416.94 273.71 T 406.16 398.07 411.95 418.25 417.74 398.07 411.95 398.07 4 Y 4 X V 417.74 307.44 411.95 287.25 406.16 307.44 411.95 307.44 4 Y V 411.95 398.07 411.95 307.44 2 L 3 H 0 Z N 589.41 430.56 600.95 427.25 589.41 423.94 589.41 427.25 4 Y 0 X V 447.95 427.25 589.41 427.25 2 L 1 H 2 Z N 586.04 293.75 591.91 283.29 581.39 289.05 583.72 291.4 4 Y V 447.95 427.25 583.75 291.37 2 L N 474.95 400.25 M 501.95 427.25 501.95 427.25 546.95 382.25 D 591.95 337.25 591.95 337.25 564.95 310.25 D 537.95 283.25 537.95 283.25 492.95 328.25 D 447.95 373.25 447.95 373.25 474.95 400.25 D O 474.95 400.25 564.95 310.25 2 L 3 H 7 X N 522.05 386.38 530.42 377.78 518.76 380.64 520.41 383.51 4 Y 0 X V 500.45 394.75 520.44 383.48 2 L 0.5 H N 503.86 358.53 501.43 346.78 497.26 358.03 500.56 358.28 4 Y V 497.95 393.25 500.58 358.25 2 L N 549.69 342.46 558.44 334.26 546.67 336.57 548.18 339.52 4 Y V 526.95 350.25 548.18 339.51 2 L N 512.8 375.47 515.43 363.77 506.99 372.3 509.89 373.88 4 Y V 499.45 393.25 509.91 373.87 2 L N 531.41 323.7 540.42 315.78 528.58 317.72 529.99 320.71 4 Y V 508.45 330.75 530.02 320.68 2 L N 543.93 334.7 555.43 331.27 543.86 328.09 543.9 331.4 4 Y V 509.45 331.75 543.91 331.38 2 L N 546.87 330.9 543.93 319.27 540.26 330.69 543.56 330.8 4 Y V 542.45 365.75 543.58 330.78 2 L N 517.07 379.57 528.44 375.76 516.77 372.97 516.92 376.27 4 Y V 483.45 377.75 516.92 376.26 2 L N 558.15 348.43 560.94 336.76 552.39 345.18 555.27 346.81 4 Y V 544.45 366.25 555.28 346.8 2 L N 539.69 329.06 541.93 317.27 533.79 326.08 536.74 327.57 4 Y V 525.95 349.25 536.75 327.55 2 L N 504.68 369.88 513.95 362.25 502.05 363.81 503.36 366.85 4 Y V 481.45 376.25 503.37 366.84 2 L N 494.23 356.96 496.93 345.27 488.44 353.75 491.33 355.35 4 Y V 480.45 375.25 491.35 355.34 2 L N 7 X 90 450 9 9 537.95 373.25 G 0 X 90 450 9 9 537.95 373.25 A 7 X 90 450 9 9 519.95 355.25 G 0 X 90 450 9 9 519.95 355.25 A 7 X 90 450 9 9 501.95 337.25 G 0 X 90 450 9 9 501.95 337.25 A 7 X 90 450 9 9 492.95 400.25 G 0 X 90 450 9 9 492.95 400.25 A 7 X 90 450 9 9 474.95 382.25 G 0 X 90 450 9 9 474.95 382.25 A 7 X 90 450 9 9 564.95 328.25 G 0 X 90 450 9 9 564.95 328.25 A 7 X 90 450 9 9 546.95 310.25 G 0 X 90 450 9 9 546.95 310.25 A 1 18 Q (reward:) 616.02 430.63 T 0 F (R) 679.96 430.63 T (r) 591.95 266.51 T 0 14 Q (4) 598.95 262.01 T 1 F (predicted) 605.94 273.71 T (action) 484.97 309.71 T 595.16 398.07 600.95 418.25 606.74 398.07 600.95 398.07 4 Y 4 X V 606.74 307.44 600.95 287.25 595.16 307.44 600.95 307.44 4 Y V 600.95 398.07 600.95 307.44 2 L 3 H 0 Z N 0 X (model) 484.97 295.71 T (action) 295.97 309.71 T (model) 295.97 295.71 T (action) 106.97 309.29 T (model) 106.97 295.29 T FMENDPAGE %%EndDocument @endspecial 225 597 a fh(Figur)o(e)9 b(1)p fj(:)16 b fh(Episode:)e fj(Starti\ ng)d(with)f(the)g(initial)i(state)e fg(s)995 601 y fk(1)1009 597 y fj(,)h(the) f(action)f(sequence)e fg(a)1353 601 y fk(1)1368 597 y fg(;)f(a)1405 601 y fk (2)1420 597 y fg(;)g(a)1457 601 y fk(3)1482 597 y fj(was)k(observed)e(to)225 638 y(produce)g(the)i(\256nal)f(reward)g fg(R)p fj(.)16 b(The)8 b(domain)h (knowledge)f(represented)g(by)h(neural)g(network)g(action)g(models)g(is)225 680 y(used)f(to)h(post-facto)g(predict)g(and)f(analyze)g(each)g(step)g(of)i (the)f(observed)e(episode.)225 725 y 1500 3 v 60 x fu(ically)14 b(requires)h (lar)o(ge)g(amounts)f(of)h(training)e(data)i(\(which)f(will)g(be)h(costly)f (in)g(the)h(case)h(of)e(robot)225 831 y(learning\).)225 921 y fv(2.2)41 b(The) 11 b(analytical)d(component)j(of)f(EBNN)225 994 y fu(In)h(EBNN,)h(the)f(agent) g(exploits)f(its)g(domain)h(knowledge)g(to)f(extract)i(additional)d(shape)j (knowledge)225 1040 y(about)17 b(the)h(tar)o(get)f(function)f fq(Q)p fu(,)k (to)d(speed)h(convergence)g(and)g(reduce)g(the)g(number)g(of)f(training)225 1086 y(examples)11 b(required.)j(This)c(shape)g(knowledge,)g(represented)g (by)g(the)f(estimated)h fs(slope)g fu(of)g(the)f(tar)o(get)225 1131 y(functio\ n)k fq(Q)p fu(,)k(is)e(then)f(used)h(to)g(guide)f(the)h(generalization)f(proc\ ess.)30 b(More)15 b(speci\256cally)m(,)i(EBNN)225 1177 y(combines)12 b(the)g (above)g(inductive)f(learning)g(component)h(with)f(an)h(analytical)f(learning) h(component)225 1223 y(that)e(performs)g(the)g(following)e(three)i(steps)h (for)e(each)j(observed)e(training)f(episode:)256 1298 y(1.)21 b fv(Explain:) 16 b fu(Post-facto)11 b(predict)g(the)g(observed)g(episode)h(\(states)f(and)h (\256nal)f(reward\),)i(using)d(the)308 1344 y(action)h(models)g fr(M)592 1350 y fo(i)617 1344 y fu(\(c.f.)h(Fig.)f(1\).)17 b(Note)11 b(that)f(there)h(may)h (be)f(a)g(deviation)f(between)i(predicted)308 1389 y(and)e(observed)h(states,) g(since)f(the)g(domain)g(knowledge)g(is)g(only)f(approximately)g(correct.)256 1450 y(2.)21 b fv(Analyze:)26 b fu(Analyze)16 b(the)g(explanation)f(to)g(esti\ mate)i(the)e fs(slope)h fu(of)g(the)f(tar)o(get)h(function)f(for)308 1496 y (each)f(observed)e(state-action)g(pair)g fq(h)p fr(s)875 1502 y fo(k)896 1496 y fr(;)7 b(a)937 1502 y fo(k)957 1496 y fq(i)13 b fu(\()p fr(k)i fn(=)g fu (1)p fr(::)p fu(3\),)d(i.e.,)i(extract)e(the)h fs(derivative)f fu(of)g(the) 308 1541 y(\256nal)i(reward)h fr(R)f 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fq(r)343 1821 y fo(s)359 1825 y fe(k)379 1815 y fr(R)8 b fu (describe)h(the)f(dependence)h(of)f(the)g(\256nal)h(reward)f(upon)g(features) h(of)f(the)g(previous)f(states.)308 1872 y(They)k(provide)e(the)h fs(tar)n (get)g(slopes)p fu(,)h(denoted)e(by)1050 1861 y fl(d)1028 1872 y fq(r)1063 1878 y fo(s)1079 1882 y fe(k)1099 1872 y fq(Q)p fu(,)h(for)g(the)g(tar)o(get) g(function)f fq(Q)p fu(:)431 1949 y fl(d)412 1960 y fq(r)447 1966 y fo(s)463 1970 y ff(3)477 1960 y fq(Q)o fn(\()p fr(s)545 1966 y fm(3)563 1960 y fr(;)d (a)603 1966 y fm(3)620 1960 y fn(\))41 b(=)h fq(r)786 1966 y fo(s)802 1970 y ff(3)816 1960 y fr(R)34 b fn(=)954 1932 y fr(@)s(M)1019 1938 y fo(a)1037 1942 y ff(3)1051 1932 y fn(\()p fr(s)1086 1938 y fm(3)1104 1932 y fn(\))954 1950 y 166 2 v 1007 1988 a fr(@)r(s)1050 1994 y fm(3)431 2060 y fl(d)412 2071 y fq (r)447 2077 y fo(s)463 2081 y ff(2)477 2071 y fq(Q)o fn(\()p fr(s)545 2077 y fm(2)563 2071 y fr(;)6 b(a)603 2077 y fm(2)620 2071 y fn(\))41 b(=)h fq(r)786 2077 y fo(s)802 2081 y ff(2)816 2071 y fr(R)34 b fn(=)954 2043 y fr(@)s(M) 1019 2049 y fo(a)1037 2053 y ff(3)1051 2043 y fn(\()p fr(s)1086 2049 y fm(3) 1104 2043 y fn(\))954 2061 y 166 2 v 1007 2099 a fr(@)r(s)1050 2105 y fm(3) 1134 2071 y fq(\001)1160 2043 y fr(@)r(M)1224 2049 y fo(a)1242 2053 y ff(2) 1257 2043 y fn(\()p fr(s)1292 2049 y fm(2)1309 2043 y fn(\))1160 2061 y 166 2 v 1212 2099 a fr(@)s(s)1256 2105 y fm(2)431 2171 y fl(d)412 2182 y fq(r)447 2188 y fo(s)463 2192 y ff(1)477 2182 y fq(Q)o fn(\()p fr(s)545 2188 y fm(1) 563 2182 y fr(;)6 b(a)603 2188 y fm(1)620 2182 y fn(\))41 b(=)h fq(r)786 2188 y fo(s)802 2192 y ff(1)816 2182 y fr(R)34 b fn(=)954 2153 y fr(@)s(M)1019 2159 y fo(a)1037 2163 y ff(3)1051 2153 y fn(\()p fr(s)1086 2159 y fm(3)1104 2153 y fn(\))954 2172 y 166 2 v 1007 2210 a fr(@)r(s)1050 2216 y fm(3)1134 2182 y fq (\001)1160 2153 y fr(@)r(M)1224 2159 y fo(a)1242 2163 y ff(2)1257 2153 y fn (\()p fr(s)1292 2159 y fm(2)1309 2153 y fn(\))1160 2172 y 166 2 v 1212 2210 a fr(@)s(s)1256 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def /Legal {legal} def /Statement {statement} def /Executive {executive} def /A3 {a3} def /A4 {a4} def /A4Small {a4small} def /B4 {b4} def /B5 {b5} def /unknown {unknown} def papersizedict dup papername known {papername} {/unknown} ifelse get end stopped } def /desperatepapersize { statusdict /setpageparams known { paperwidth paperheight 0 1 statusdict begin {setpageparams} stopped pop end } if } def /savematrix { orgmatrix currentmatrix pop } bind def /restorematrix { orgmatrix setmatrix } bind def /dmatrix matrix def /dpi 72 0 dmatrix defaultmatrix dtransform dup mul exch dup mul add sqrt def /freq dpi 18.75 div 8 div round dup 0 eq {pop 1} if 8 mul dpi exch div def /sangle 1 0 dmatrix defaultmatrix dtransform exch atan def /DiacriticEncoding [ /.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 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@vscale 0.090000 @hscale @setspecial %%BeginDocument: pictures/robot_actions.ps /Mathdict 100 dict def Mathdict begin /Mlmarg 1.0 72 mul def /Mrmarg 1.0 72 mul def /Mbmarg 1.0 72 mul def /Mtmarg 1.0 72 mul def /Mwidth 8.5 72 mul def /Mheight 11 72 mul def /Mtransform { } bind def /Mnodistort true def /Mfixwid false def /Mfixdash false def /Mrot 0 def /Mpstart { MathPictureStart } bind def /Mpend { MathPictureEnd } bind def /Mscale { 0 1 0 1 5 -1 roll MathScale } bind def /ISOLatin1Encoding dup where { pop pop } { [ /.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 /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /minus /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 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent /dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron /space /exclamdown /cent /sterling /currency /yen /brokenbar /section /dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen /registered /macron /degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered /cedilla /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla /Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis /Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply /Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls /agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla /egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis /eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def } ifelse /MFontDict 50 dict def /MStrCat { exch dup length 2 index length add string dup 3 1 roll copy length exch dup 4 2 roll exch putinterval } def /MCreateEncoding { 1 index 255 string cvs (-) MStrCat 1 index MStrCat cvn exch (Encoding) MStrCat cvn dup where { exch get } { pop StandardEncoding } ifelse 3 1 roll dup MFontDict exch known not { 1 index findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding 3 index def currentdict end 1 index exch definefont pop MFontDict 1 index null put } if exch pop exch pop } def /ISOLatin1 { (ISOLatin1) MCreateEncoding } def /ISO8859 { (ISOLatin1) MCreateEncoding } def /Mcopyfont { dup maxlength dict exch { 1 index /FID eq { pop pop } { 2 index 3 1 roll put } ifelse } forall } def /Plain /Courier findfont Mcopyfont definefont pop /Bold /Courier-Bold findfont Mcopyfont definefont pop /Italic /Courier-Oblique findfont Mcopyfont definefont pop /MathPictureStart { gsave Mtransform Mlmarg Mbmarg translate /Mtmatrix matrix currentmatrix def /Mgmatrix matrix currentmatrix def } bind def /MathPictureEnd { grestore } bind def /MathSubStart { Momatrix Mgmatrix Mtmatrix Mlmarg Mrmarg Mbmarg Mtmarg Mwidth Mheight 11 -2 roll moveto Mtmatrix setmatrix currentpoint Mgmatrix setmatrix 13 -2 roll moveto Mtmatrix setmatrix currentpoint 2 copy translate /Mtmatrix matrix currentmatrix def /Mlmarg 0 def /Mrmarg 0 def /Mbmarg 0 def /Mtmarg 0 def 3 -1 roll exch sub /Mheight exch def sub /Mwidth exch def } bind def /MathSubEnd { /Mheight exch def /Mwidth exch def /Mtmarg exch def /Mbmarg exch def /Mrmarg exch def /Mlmarg exch def /Mtmatrix exch def dup setmatrix /Mgmatrix exch def /Momatrix exch def } bind def /Mdot { moveto 0 0 rlineto stroke } bind def /Mtetra { moveto lineto lineto lineto fill } bind def /Metetra { moveto lineto lineto lineto closepath gsave fill grestore 0 setgray stroke } bind def /Mistroke { flattenpath 0 0 0 { 4 2 roll pop pop } { 4 -1 roll 2 index sub dup mul 4 -1 roll 2 index sub dup mul add sqrt 4 -1 roll add 3 1 roll } { stop } { stop } pathforall pop pop currentpoint stroke moveto currentdash 3 -1 roll add setdash } bind def /Mfstroke { stroke currentdash pop 0 setdash } bind def /Mrotsboxa { gsave dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def grestore Msboxa 3 -1 roll /Mtmatrix 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