(original) (raw)

%!PS-Adobe-2.0 %%Creator: dvips 5.516 Copyright 1986, 1993 Radical Eye Software %%Title: top.dvi %%CreationDate: Sat May 13 23:12:06 1995 %%Pages: 51 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%EndComments %DVIPSCommandLine: dvips -o top.ps top %DVIPSSource: TeX output 1995.05.13:2311 %%BeginProcSet: tex.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR matrix currentmatrix dup dup 4 get round 4 exch put dup dup 5 get round 5 exch put setmatrix}N /@landscape{/isls true N}B /@manualfeed{ statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N 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def/fBitStretch true def /fg (Rvd\001\001\000\000\177) def /bdf{bind def}bind def /xdf{exch def}bdf /xl{neg exch neg translate}bdf /fp{pnsh 0 ne pnsv 0 ne and}bdf /nop{}bdf/lnop[/nop load]cvx bdf /vrb[ {fp{fg 6 get 0 ne{gsave stroke grestore}{gsave 1 setlinewidth pnsh pnsv scale stroke grestore}ifelse}if newpath}bind /eofill load dup /newpath load 2 index dup {clip newpath}bind {}bind dup 2 copy ]def currentscreen/spf xdf/rot xdf/freq xdf /doop{vrb exch get exec}bdf /psu{/tso xdf /fNote xdf/fBitStretch xdf/scaleby96 xdf/yflip xdf/xflip xdf /invertflag xdf/dbinvertflag invertflag statusdict begin version cvr 47.0 ge product (LaserWriter) eq not and end invertflag and {not}if def xflip yflip or{/noflips false def}if /pgs xdf 2 index .72 mul exch div/pys xdf div .72 mul/pxs xdf ppr astore pop/por xdf sn and/so xdf}bdf /tab{statusdict /11x17 known{statusdict begin /11x17 load end}{statusdict /setpage known{statusdict begin 792 1224 1 setpage end}{statusdict /setpageparams known{statusdict 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/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand/Acircumflex/Ecircumflex/Aacute /Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave/Oacute/Ocircumflex /apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron macvec 128 128 getinterval astore pop {}mark true/Courier/|______Courier 0 rf {/Metrics 21 dict begin/zero 600 def/one 600 def/two 600 def/three 600 def/four 600 def/five 600 def/six 600 def/seven 600 def/eight 600 def /nine 600 def/comma 600 def/period 600 def/dollar 600 def/numbersign 600 def/percent 600 def/plus 600 def/hyphen 600 def/E 600 def/parenleft 600 def/parenright 600 def/space 600 def currentdict end def currentdict/UniqueID known{/UniqueID 16#800000 def}if/FontBBox FontBBox 4 array astore def}mark true/Helvetica/|______Seattle 1 rf /oldsettransfer/settransfer load def /concatprocs{/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}def /settransfer{currenttransfer concatprocs oldsettransfer}def /PaintBlack{{1 exch sub}settransfer gsave newpath clippath 1 setgray fill grestore}def /od{(Rvd\001\001\000\000\177) fg copy pop txpose 1 0 mtx defaultmatrix dtransform exch atan/pa exch def newpath clippath mark {transform{itransform moveto}}{transform{itransform lineto}} {6 -2 roll transform 6 -2 roll transform 6 -2 roll transform {itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}} {{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}bdf /cd{}bdf /op{/sfl false def/pm save def}bdf /cp{ pop pop pm restore } bdf /px{0 3 1 roll tp tt}bdf /psb{/us save def}bdf /pse{us restore}bdf /ct 40 string def /nc{currentpoint initclip newpath gc{dup type dup/arraytype eq exch/packedarraytype eq or{exec}if} forall clip newpath moveto}def /kp{ct 0 2 index length 2 index 39 2 index put getinterval copy cvx exec mx3 currentmatrix pop}bdf /av 68 def end LW 1 eq userdict/a4small known not and{/a4small [[300 72 div 0 0 -300 72 div -120 3381] 280 3255 {statusdict/jobstate (printing) put 0 setblink margins exch 196 add exch 304 add 8 div round cvi frametoroket statusdict/jobstate (busy) put 1 setblink} /framedevice load 60 45{dup mul exch dup mul add 1.0 exch sub}/setscreen load {}/settransfer load/initgraphics load/erasepage load]cvx statusdict begin bind end readonly def}if md begin/bigs[lnop userdict/letter known{/letter load}{lnop}ifelse userdict/legal known{/legal load}{lnop}ifelse userdict/a4 known{/a4 load}{lnop}ifelse userdict/b5 known{/b5 load}{lnop}ifelse lnop lnop lnop /tab load]def /smalls[lnop userdict/lettersmall known{/lettersmall load}{userdict/note known{/note load}{lnop}ifelse}ifelse userdict/legal known{/legal load}{lnop}ifelse 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ps/lprep68.pro systemdict/currentpacking known{currentpacking true setpacking}if /LW{0}def /LW+{LW 2 eq}bind def /ok{systemdict/statusdict known dup{LW 0 gt and}if}bind def /md 250 dict def md begin /av 0 def /T true def/F false def/mtx matrix def/s75 75 string def/s8 8 string def/s1 ( ) def/pxs 1 def/pys 1 def 1 0 mtx defaultmatrix dtransform exch atan/pa exch def/nlw .24 def/ppr [-32 -29.52 762 582.48] def /pgs 1 def/por true def/xb 500 array def/so true def/tso true def/fillflag false def/pnm 1 def/fmv true def /sfl false def/ma 0 def/invertflag false def/dbinvertflag false def/xflip false def/yflip false def/noflips true def/scaleby96 false def/fNote true def/fBitStretch true def /fg (Rvd\001\001\000\000\177) def /bdf{bind def}bind def /xdf{exch def}bdf /xl{neg exch neg translate}bdf /fp{pnsh 0 ne pnsv 0 ne and}bdf /nop{}bdf/lnop[/nop load]cvx bdf /vrb[ {fp{fg 6 get 0 ne{gsave stroke grestore}{gsave 1 setlinewidth pnsh pnsv scale stroke grestore}ifelse}if newpath}bind /eofill load 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neg exch translate pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 translate }if yflip xflip not and{ ppr 1 get neg ppr 0 get neg translate }if }{ noflips{ translate pop pop 270 rotate 1 -1 scale }if xflip yflip and{ translate pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg translate }if xflip yflip not and{ translate pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 translate }if yflip xflip not and{ translate pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 exch translate }if }ifelse statusdict begin waittimeout 300 lt{ /waittimeout 300 def }if end scaleby96{ ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy translate .96 dup scale neg exch neg exch translate }if }bdf /fr{4 copy ppr aload pop 3 -1 roll add 3 1 roll exch add 6 2 roll 3 -1 roll sub 3 1 roll exch sub 3 -1 roll exch div 3 1 roll div exch scale pop pop xl}bdf /obl{{0.212557 mul}{pop 0}ifelse}bdf /sfd{ps fg 5 -1 roll get mul 100 div 0 ps 5 -1 roll obl ps neg 0 0 6a astore makefont setfont}bdf /fnt{findfont sfd}bdf /bt{sa 3 1 roll 3 index and put}bdf /sa(\000\000\000\000\000\000\000\000\000\000)def /fs{0 1 bt 1 2 bt 2 4 bt 3 8 bt 4 16 bt 5 32 bt 6 64 bt 7 128 bt sa exch 8 exch put}bdf /mx1 matrix def /mx2 matrix def /mx3 matrix def /bu{currentpoint currentgray currentlinewidth currentlinecap currentlinejoin currentdash exch aload length fg 5 sfl{1}{0}ifelse put pnsv pnsh 2t aload pop 3a aload pop mx2 aload pop mx1 aload pop mtx currentmatrix aload pop mx3 aload pop ps pm restore/ps xdf mx3 astore pop}bdf /bn{/pm save def mx3 setmatrix newpath 0 0 moveto ct dup 39 get 0 exch getinterval cvx exec mtx astore setmatrix mx1 astore pop mx2 astore pop 3a astore pop 2t astore pop/pnsh xdf/pnsv xdf gw /sfl fg 5 get 0 ne def array astore exch setdash setlinejoin setlinecap setlinewidth setgray moveto}bdf /fc{save vmstatus exch sub 50000 lt {(%%[|0|]%%)=print flush}if pop restore}bdf /tc{32768 div add 3 1 roll 32768 div add 2t astore pop}bdf /3a [0 0 0] 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neg rlineto}ifelse}ifelse closepath fill}if @2 @1 grestore moveto}ifelse}bdf /gw{/pnm fg 3 get fg 4 get div def}bdf /lw{fg exch 4 exch put fg exch 3 exch put gw pnsv pnsh pen}bdf /barc{/@1 xdf/@2 xdf/@3 xdf/@4 xdf/@5 xdf /@6 xdf/@7 xdf/@8 xdf gsave @5 @7 add 2 div @6 @8 add 2 div translate newpath 0 0 moveto @5 @7 sub @6 @8 sub mtx currentmatrix pop scale @1{newpath}if 0 0 0.5 @4 @3 arc @4 @3 sub abs 360 ge{closepath}if mtx setmatrix @2 doop grestore}bdf /ar{dup 0 eq barc}bdf /ov{0 exch 360 exch true barc}bdf /rc{/@t xdf currentpoint 6 2 roll newpath 4 copy 4 2 roll exch moveto 6 -1 roll lineto lineto lineto closepath @t doop moveto}bdf /mup{dup pnsh 2 div le exch pnsv 2 div le or}bdf /rr{/@1 xdf 2. div/@2 xdf 2. div/@3 xdf /@4 xdf/@5 xdf/@6 xdf/@7 xdf @7 @5 eq @6 @4 eq @2 mup or or{@7 @6 @5 @4 @1 rc} {@4 @6 sub 2. div dup @2 lt{/@2 xdf}{pop}ifelse @5 @7 sub 2. div dup @2 lt{/@2 xdf}{pop}ifelse @1 0 eq{/@2 @2 pnsh 2 div 2 copy gt{sub def}{0 pop4}ifelse}if currentpoint newpath @4 @6 add 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/BuildChar/bmbc load def end mfont definefont pop }bdf /wi LW 1 eq{{gsave 0 0 0 0 0 0 0 0 moveto lineto lineto lineto closepath clip stringwidth grestore}bind}{/stringwidth load}ifelse def /aps{0 get 124 eq}bdf /xc{s75 cvs dup}bdf /xp{put cvn}bdf /scs{xc 3 67 put dup 0 95 xp}bdf /sos{xc 3 79 xp}bdf /sbs{xc 1 66 xp}bdf /sis{xc 2 73 xp}bdf /sob{xc 2 79 xp}bdf /sss{xc 4 83 xp}bdf /dd{exch 1 index add 3 1 roll add exch}bdf /smc{moveto dup show}bdf /kwn{FontDirectory 1 index known{findfont exch pop}}bdf /gl{1 currentgray sub setgray}bdf /mm{/mfont 10 dict def mfont begin /FontMatrix [1 0 0 1 0 0] def /FontType 3 def /Encoding macvec def /df 4 index findfont def /FontBBox [0 0 1 1] def /xda xdf/mbc xdf /BuildChar{wd begin/cr xdf/fd xdf/cs s1 dup 0 cr put def fd/mbc get exec end}def exec end mfont definefont}bdf /ac{dup scs kwn{exch findfont dup length 1 add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall fmv{/Encoding macvec def}if/StrokeWidth nlw 1000 mul pys 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smc 0 ds da2 sub translate 0 0 smc da 0 smc da da smc 0 da smc gl da 2. div dup moveto show}bdf /aoc{fd/df get setfont gsave cs wi grestore setcharwidth gl cs 0 0 smc fd/df2 get setfont gl 0 0 moveto show}bdf /asc{/da .05 def fd/df get setfont gsave cs wi 1 index 0 ne{exch da add exch}if grestore setcharwidth cs da .01 add 0 smc 0 da translate gl 0 0 smc gl fd/df2 get setfont 0 0 moveto show}bdf /st{1000 mul usertime add dup 2147483647 gt{2147483647 sub}if def}bdf /the{usertime sub dup 0 lt exch -2147483648 gt and}bdf /6a 6 array def /2a 2 array def /3q 3 array def /qs{3 -1 roll sub exch 3 -1 roll sub exch}bdf /qa{3 -1 roll add exch 3 -1 roll add exch}bdf /qm{3 -1 roll 1 index mul 3 1 roll mul}bdf /qn{6a exch get mul}bdf /qA .166667 def/qB .833333 def/qC .5 def /qx{6a astore pop qA 0 qn qB 2 qn add qA 1 qn qB 3 qn add qB 2 qn qA 4 qn add qB 3 qn qA 5 qn add qC 2 qn qC 4 qn add qC 3 qn qC 5 qn add}bdf /qp{6 copy 12 -2 roll pop pop}bdf /qc{exch qp qx curveto}bdf /qi{{exch 4 copy 2a 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astore pop macvec 32/Times-Roman findfont/Encoding get 32 96 getinterval putinterval macvec dup 39/quotesingle put 96/grave put /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/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/blank/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge /ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand/Acircumflex/Ecircumflex/Aacute /Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave/Oacute/Ocircumflex /apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron macvec 128 128 getinterval astore pop {}mark true/Courier/|______Courier 0 rf {/Metrics 21 dict begin/zero 600 def/one 600 def/two 600 def/three 600 def/four 600 def/five 600 def/six 600 def/seven 600 def/eight 600 def /nine 600 def/comma 600 def/period 600 def/dollar 600 def/numbersign 600 def/percent 600 def/plus 600 def/hyphen 600 def/E 600 def/parenleft 600 def/parenright 600 def/space 600 def currentdict end def currentdict/UniqueID known{/UniqueID 16#800000 def}if/FontBBox FontBBox 4 array astore def}mark true/Helvetica/|______Seattle 1 rf /oldsettransfer/settransfer load def /concatprocs{/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}def /settransfer{currenttransfer concatprocs oldsettransfer}def /PaintBlack{{1 exch sub}settransfer gsave newpath clippath 1 setgray fill grestore}def /od{(Rvd\001\001\000\000\177) fg copy pop txpose 1 0 mtx defaultmatrix dtransform exch atan/pa exch def newpath clippath mark {transform{itransform moveto}}{transform{itransform lineto}} {6 -2 roll transform 6 -2 roll transform 6 -2 roll transform {itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}} {{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}bdf /cd{}bdf /op{/sfl false def/pm save def}bdf /cp{ pop pop pm restore } bdf /px{0 3 1 roll tp tt}bdf /psb{/us save def}bdf /pse{us restore}bdf /ct 40 string def /nc{currentpoint initclip newpath gc{dup type dup/arraytype eq exch/packedarraytype eq or{exec}if} forall clip newpath moveto}def /kp{ct 0 2 index length 2 index 39 2 index put getinterval copy cvx exec mx3 currentmatrix pop}bdf /av 68 def end LW 1 eq userdict/a4small known not and{/a4small [[300 72 div 0 0 -300 72 div -120 3381] 280 3255 {statusdict/jobstate (printing) put 0 setblink margins exch 196 add exch 304 add 8 div round cvi frametoroket statusdict/jobstate (busy) put 1 setblink} /framedevice load 60 45{dup mul exch dup mul add 1.0 exch sub}/setscreen load {}/settransfer load/initgraphics load/erasepage load]cvx statusdict begin bind end readonly def}if md begin/bigs[lnop userdict/letter known{/letter load}{lnop}ifelse userdict/legal known{/legal load}{lnop}ifelse userdict/a4 known{/a4 load}{lnop}ifelse userdict/b5 known{/b5 load}{lnop}ifelse lnop lnop lnop /tab load]def /smalls[lnop userdict/lettersmall known{/lettersmall load}{userdict/note known{/note load}{lnop}ifelse}ifelse userdict/legal known{/legal load}{lnop}ifelse userdict/a4small known{/a4small load}{lnop}ifelse userdict/b5 known{/b5 load}{userdict/note known{/note 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Fq(n)p Fw(])p Fp(g)h Fw(and)h(de\014ne)h (the)e(follo)o(wing)150 1095 y(cost)i(functional:)515 1207 y Fq(J)i Fw(=)610 1176 y(1)p 610 1196 23 2 v 610 1238 a(2)638 1207 y Fq(E)s Fp(f)705 1154 y Fi(N)733 1158 y Fe(\013)701 1166 y Fb(X)698 1257 y Fi(n)p Fn(=1)763 1207 y Fw(\()p Fo(y)810 1188 y Fh(\003)809 1218 y Fi(\013)833 1207 y Fw([)p Fq(n)p Fw(])10 b Fp(\000)g Fo(y)969 1214 y Fi(\013)994 1207 y Fw([)p Fq(n)p Fw(]\))1065 1188 y Fi(T)1091 1207 y Fw(\()p Fo(y)1138 1188 y Fh(\003)1137 1218 y Fi(\013)1161 1207 y Fw([)p Fq(n)p Fw(])g Fp(\000)h Fo(y)1298 1214 y Fi(\013)1322 1207 y Fw([)p Fq(n)p Fw(]\))p Fp(g)p Fq(;)290 b Fw(\(15\))150 1325 y(where)14 b Fq(\013)h Fw(is)f(an)g(index)i(across)d(target)g(tra)s(jectories)g(and)h Fo(y)1171 1332 y Fi(\013)1209 1325 y Fw(is)h(an)f(unkno)o(wn)g (function)h(of)f(the)150 1381 y(state)g Fo(x)289 1388 y Fi(\013)329 1381 y Fw(and)h(the)g(action)h Fo(u)661 1388 y Fi(\013)685 1381 y Fw(.)k(The)c(action)f Fo(u)977 1388 y Fi(\013)1017 1381 y 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rf /oldsettransfer/settransfer load def /concatprocs{/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}def /settransfer{currenttransfer concatprocs oldsettransfer}def /PaintBlack{{1 exch sub}settransfer gsave newpath clippath 1 setgray fill grestore}def /od{(Rvd\001\001\000\000\177) fg copy pop txpose 1 0 mtx defaultmatrix dtransform exch atan/pa exch def newpath clippath mark {transform{itransform moveto}}{transform{itransform lineto}} {6 -2 roll transform 6 -2 roll transform 6 -2 roll transform {itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}} {{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}bdf /cd{}bdf /op{/sfl false def/pm save def}bdf /cp{ pop pop pm restore } bdf /px{0 3 1 roll tp tt}bdf /psb{/us save def}bdf /pse{us restore}bdf /ct 40 string def /nc{currentpoint initclip newpath gc{dup type dup/arraytype eq exch/packedarraytype eq or{exec}if} forall clip newpath moveto}def /kp{ct 0 2 index length 2 index 39 2 index put getinterval copy cvx exec mx3 currentmatrix pop}bdf /av 68 def end LW 1 eq userdict/a4small known not and{/a4small [[300 72 div 0 0 -300 72 div -120 3381] 280 3255 {statusdict/jobstate (printing) put 0 setblink margins exch 196 add exch 304 add 8 div round cvi frametoroket statusdict/jobstate (busy) put 1 setblink} /framedevice load 60 45{dup mul exch dup mul add 1.0 exch sub}/setscreen load {}/settransfer load/initgraphics load/erasepage load]cvx statusdict begin bind end readonly def}if md begin/bigs[lnop userdict/letter known{/letter load}{lnop}ifelse userdict/legal known{/legal load}{lnop}ifelse userdict/a4 known{/a4 load}{lnop}ifelse userdict/b5 known{/b5 load}{lnop}ifelse lnop lnop lnop /tab load]def /smalls[lnop userdict/lettersmall known{/lettersmall load}{userdict/note known{/note load}{lnop}ifelse}ifelse userdict/legal known{/legal load}{lnop}ifelse userdict/a4small known{/a4small load}{lnop}ifelse userdict/b5 known{/b5 load}{userdict/note known{/note load}{lnop}ifelse}ifelse lnop lnop lnop /tab load]def end systemdict/currentpacking known{setpacking}if %%EndDocument 15 150 a %%BeginDocument: ps/recurrent.ps .9 dup scale md begin T T -130 -125 3170 2425 100 300 300 1 F F F F T T T psu (jordan; document: recurrent-Layer#1)jn 0 mf od op 0 0 xl 4 4 pen 1842 1342 gm (nc 0 0 3040 2300 6 rc)kp pr 1842 1342 pl 1818 1296 pl 1808 1304 pl 1799 1313 pl 1842 1342 pl 1 ep 1486 944 gm 1806 1302 lin 1279 1171 gm pr 1279 1171 pl 1247 1131 pl 1239 1141 pl 1232 1151 pl 1279 1171 pl 1 ep 965 931 gm 1237 1139 lin 1288 638 gm pr 1288 638 pl 1255 598 pl 1247 608 pl 1240 618 pl 1288 638 pl 1 ep 969 402 gm 1245 606 lin 1446 913 gm pr 1446 913 pl 1416 870 pl 1408 880 pl 1400 889 pl 1446 913 pl 1 ep 1181 681 gm 1406 878 lin 1696 1350 gm pr 1696 1350 pl 1672 1304 pl 1662 1313 pl 1653 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1963 pl 1 ep 1306 1769 gm 1306 1911 lin 1158 1963 gm pr 1158 1963 pl 1171 1913 pl 1158 1913 pl 1146 1913 pl 1158 1963 pl 1 ep 1156 1756 gm 1156 1911 lin 1179 1963 gm pr 1179 1963 pl 1215 1925 pl 1204 1919 pl 1193 1913 pl 1179 1963 pl 1 ep 1290 1761 gm 1202 1917 lin 64 gr 1125 1696 1196 1767 1 ov 0 gr 1125 1696 1196 1767 0 ov 64 gr 1275 1696 1346 1767 1 ov 0 gr 1275 1696 1346 1767 0 ov 1450 1334 gm (nc 1404 1333 1467 1600 6 rc)kp 1 setTxMode (Predicted)show 1513 1330 gm (nc 1467 1329 1529 1621 6 rc)kp (Next-State)show 1575 1409 gm (nc 1529 1408 1592 1554 6 rc)kp (Units)show 1450 1601 gm (nc 1404 1600 1467 1646 6 rc)kp (-)show 1450 2151 gm (nc 1404 2150 1467 2192 6 rc)kp (-)show F T cp cd end %%EndDocument endTexFig 150 1698 a Fw(Figure)18 b(10:)25 b(A)19 b(recurren)o(t)f(net)o(w)o (ork)f(with)h(a)g(forw)o(ard)f(mo)q(del.)29 b(The)18 b(b)q(o)o(xes)g(lab)q(eled)j(b)o(y)d(D's)150 1754 y(are)d(unit)h(dela)o (y)g(elemen)o(ts.)150 1888 y(where)21 b(the)g(Jacobian)h(matrices)f 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(of)d(the)g(p)q(erformance)h(error)e Fo(y)1211 175 y Fh(\003)1241 192 y Fp(\000)d Fo(y)k Fw(b)o(y)g(a)g(series)h(of)f (transp)q(ose)150 248 y(Jacobian)k(matrices,)g(sev)o(eral)f(of)g(whic)o (h)h(are)e(unkno)o(wn)i(a)e(priori.)33 b(Our)19 b(approac)o(h)g(to)f (esti-)150 304 y(mating)13 b(the)g(unkno)o(wn)h(factors)e(is)i(once)f (again)h(to)e(learn)i(forw)o(ard)e(mo)q(dels)i(of)f(the)g(underlying) 150 361 y(mappings)e(and)f(to)g(propagate)f(signals)j(bac)o(kw)o(ard)d (through)h(the)g(mo)q(dels.)19 b(Th)o(us)11 b(the)f(Jacobian)150 417 y(matrices)17 b(\()p Fq(@)s Fo(z)402 424 y Fi(\013)427 417 y Fq(=@)s Fo(u)506 424 y Fi(\013)530 417 y Fw(\),)g(\()p Fq(@)s Fo(z)646 424 y Fi(\013)670 417 y Fq(=@)s Fo(x)748 424 y Fi(\013)772 417 y Fw(\),)g(and)h(\()p Fq(@)s Fo(y)984 424 y Fi(\013)1008 417 y Fq(=@)s Fo(x)1086 424 y Fi(\013)1109 417 y Fw(\))g(in)g(Equations)f(17,)35 b(18,)17 b(and)g(19)g(are)150 474 y(all)e(replaced)h(b)o(y)e(estimated)g(quan)o(tities)h(in)g 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gsave newpath clippath 1 setgray fill grestore}def /od{(Rvd\001\001\000\000\177) fg copy pop txpose 1 0 mtx defaultmatrix dtransform exch atan/pa exch def newpath clippath mark {transform{itransform moveto}}{transform{itransform lineto}} {6 -2 roll transform 6 -2 roll transform 6 -2 roll transform {itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}} {{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}bdf /cd{}bdf /op{/sfl false def/pm save def}bdf /cp{ pop pop pm restore } bdf /px{0 3 1 roll tp tt}bdf /psb{/us save def}bdf /pse{us restore}bdf /ct 40 string def /nc{currentpoint initclip newpath gc{dup type dup/arraytype eq exch/packedarraytype eq or{exec}if} forall clip newpath moveto}def /kp{ct 0 2 index length 2 index 39 2 index put getinterval copy cvx exec mx3 currentmatrix pop}bdf /av 68 def end LW 1 eq userdict/a4small known not and{/a4small [[300 72 div 0 0 -300 72 div -120 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def/proc1 exch cvlit def/newproc proc1 length proc2 length add array def newproc 0 proc1 putinterval newproc proc1 length proc2 putinterval newproc cvx}def /settransfer{currenttransfer concatprocs oldsettransfer}def /PaintBlack{{1 exch sub}settransfer gsave newpath clippath 1 setgray fill grestore}def /od{(Rvd\001\001\000\000\177) fg copy pop txpose 1 0 mtx defaultmatrix dtransform exch atan/pa exch def newpath clippath mark {transform{itransform moveto}}{transform{itransform lineto}} {6 -2 roll transform 6 -2 roll transform 6 -2 roll transform {itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}} {{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}bdf /cd{}bdf /op{/sfl false def/pm save def}bdf /cp{ pop pop pm restore } bdf /px{0 3 1 roll tp tt}bdf /psb{/us save def}bdf /pse{us restore}bdf /ct 40 string def /nc{currentpoint initclip newpath gc{dup type dup/arraytype eq exch/packedarraytype eq or{exec}if} forall clip newpath moveto}def /kp{ct 0 2 index length 2 index 39 2 index put getinterval copy cvx exec mx3 currentmatrix pop}bdf /av 68 def end LW 1 eq userdict/a4small known not and{/a4small [[300 72 div 0 0 -300 72 div -120 3381] 280 3255 {statusdict/jobstate (printing) put 0 setblink margins exch 196 add exch 304 add 8 div round cvi frametoroket statusdict/jobstate (busy) put 1 setblink} /framedevice load 60 45{dup mul exch dup mul add 1.0 exch sub}/setscreen load {}/settransfer load/initgraphics load/erasepage load]cvx statusdict begin bind end readonly def}if md begin/bigs[lnop userdict/letter known{/letter load}{lnop}ifelse userdict/legal known{/legal load}{lnop}ifelse userdict/a4 known{/a4 load}{lnop}ifelse userdict/b5 known{/b5 load}{lnop}ifelse lnop lnop lnop /tab load]def /smalls[lnop userdict/lettersmall known{/lettersmall load}{userdict/note known{/note load}{lnop}ifelse}ifelse userdict/legal known{/legal load}{lnop}ifelse userdict/a4small known{/a4small load}{lnop}ifelse userdict/b5 known{/b5 load}{userdict/note known{/note load}{lnop}ifelse}ifelse lnop lnop lnop /tab load]def end systemdict/currentpacking known{setpacking}if %%EndDocument 479 150 a %%BeginDocument: ps/directinvfield.ps /Mfontsize 16 def /Mlmarg .5 72 mul def /Mrmarg .5 72 mul def /Mbmarg .5 72 mul def /Mtmarg .5 72 mul def /Mwidth 8.5 72 mul def /Mheight 11 72 mul def /Mtransform { } bind def /Mnodistort true def /Mpstart { MathPictureStart } bind def /Mpend { MathPictureEnd } bind def /Mscale { 0 1 0 1 5 -1 roll MathScale } bind def /Plain /Helvetica findfont def /Bold /Helvetica-Bold findfont def /Italic /Helvetica-Oblique findfont def /MathPictureStart { gsave Mtransform Mlmarg Mbmarg translate /Mtmatrix matrix currentmatrix def Plain Mfontsize scalefont setfont } bind def /MathPictureEnd { grestore showpage } 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 /Msboxa { newpath 5 -1 roll Mvboxa pop 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 [ 7 -2 roll 2 copy [ 3 1 roll 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def /Mvboxa { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def /Mbbox { 0 0 moveto false charpath flattenpath pathbbox newpath } bind def /Mmin { 2 copy gt { exch } if pop } bind def /Mmax { 2 copy lt { exch } if pop } bind def /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get show } for pop pop pop pop Mgmatrix setmatrix } bind def /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def /MathScale { Mwidth Mlmarg Mrmarg add sub Mheight Mbmarg Mtmarg add sub 0 0 moveto 1 index 0 lineto 2 copy lineto 0 1 index lineto clip newpath Mlp translate scale pop pop pop pop /Mgmatrix matrix currentmatrix def } bind def /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } bind def /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub div 4 1 roll exch sub div } bind def /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop exch 6 -1 roll Mlprun2 8 2 roll 4 -1 roll Mlprun2 6 2 roll 3 -1 roll Mlprun2 4 2 roll exch Mlprun2 6 2 roll } bind def /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def MathPictureStart 0 1 0 1 [ [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 setgray gsave gsave 0.002 setlinewidth /arrowdict 13 dict def /arrow { arrowdict begin /headlength exch def /halfheadthickness exch 2 div def /halfthickness exch 2 div def /tipy exch def /tipx exch def /taily exch def /tailx exch def /dx tipx tailx sub def /dy tipy taily sub def /savematrix matrix currentmatrix def tipx tailx eq tipy taily eq and { tailx taily Mdot } { /arrowlength dx dx mul dy dy mul add sqrt def /angle dy dx atan def /base arrowlength headlength sub def tailx taily translate angle rotate 0 halfthickness neg moveto base halfthickness neg lineto base halfheadthickness neg lineto arrowlength 0 lineto base halfheadthickness lineto base halfthickness lineto 0 halfthickness lineto closepath } ifelse savematrix setmatrix end } def newpath 0.300000 0.575000 0.307569 0.589589 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.300000 0.600000 0.307702 0.627387 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.300000 0.625000 0.310944 0.664157 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.300000 0.650000 0.316131 0.699226 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.300000 0.675000 0.322107 0.732211 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.300000 0.700000 0.327932 0.762923 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.300000 0.725000 0.333035 0.791262 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.300000 0.750000 0.337243 0.817122 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.300000 0.775000 0.340718 0.840377 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.300000 0.800000 0.343800 0.860920 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.300000 0.825000 0.346827 0.878707 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.300000 0.850000 0.350015 0.893809 .002 dup 3 mul dup 1.5 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dup 3 mul dup 1.5 mul arrow fill newpath 0.425000 0.775000 0.440687 0.787132 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.425000 0.800000 0.433152 0.812626 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.425000 0.825000 0.424710 0.836118 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.425000 0.850000 0.416272 0.857039 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.425000 0.875000 0.408677 0.875109 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.450000 0.575000 0.469915 0.574715 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.450000 0.600000 0.470466 0.598476 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.450000 0.625000 0.471726 0.622604 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.450000 0.650000 0.473101 0.647261 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.450000 0.675000 0.474002 0.672623 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.450000 0.700000 0.473845 0.698793 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.450000 0.725000 0.472084 0.725711 .002 dup 3 mul dup 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o(ard)f(mo)q(dels)j(is)f(relativ)o(ely)g(sligh)o(t.)27 b(Reasonably)952 2775 y(25)p eop %%Page: 26 26 26 25 bop 435 150 a 17037475 18418892 12301189 29864919 29338664 48283811 startTexFig 435 150 a %%BeginDocument: ps/lprep68.pro systemdict/currentpacking known{currentpacking true setpacking}if /LW{0}def /LW+{LW 2 eq}bind def /ok{systemdict/statusdict known dup{LW 0 gt and}if}bind def /md 250 dict def md begin /av 0 def /T true def/F false def/mtx matrix def/s75 75 string def/s8 8 string def/s1 ( ) def/pxs 1 def/pys 1 def 1 0 mtx defaultmatrix dtransform exch atan/pa exch def/nlw .24 def/ppr [-32 -29.52 762 582.48] def /pgs 1 def/por true def/xb 500 array def/so true def/tso true def/fillflag false def/pnm 1 def/fmv true def /sfl false def/ma 0 def/invertflag false def/dbinvertflag false def/xflip false def/yflip false def/noflips true def/scaleby96 false def/fNote true def/fBitStretch true def /fg (Rvd\001\001\000\000\177) def /bdf{bind def}bind def /xdf{exch def}bdf /xl{neg exch neg 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neg exch translate pop 1 -1 scale }if xflip yflip and{ pop exch neg exch translate 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg translate }if xflip yflip not and{ pop exch neg exch translate pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 translate }if yflip xflip not and{ ppr 1 get neg ppr 0 get neg translate }if }{ noflips{ translate pop pop 270 rotate 1 -1 scale }if xflip yflip and{ translate pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg translate }if xflip yflip not and{ translate pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 translate }if yflip xflip not and{ translate pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 exch translate }if }ifelse statusdict begin waittimeout 300 lt{ /waittimeout 300 def }if end scaleby96{ ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy translate .96 dup scale neg exch neg exch translate }if }bdf /fr{4 copy ppr aload pop 3 -1 roll add 3 1 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{@2 @1 moveto pnsh 0 rlineto pnlh pnsh add pnlv lineto 0 pnsv rlineto pnsh neg 0 rlineto @2 @1 pnsv add lineto}{pnlh pnlv moveto pnsh 0 rlineto 0 pnsv rlineto @2 pnsh add @1 pnsv add lineto pnsh neg 0 rlineto 0 pnsv neg rlineto}ifelse}ifelse closepath fill}if @2 @1 grestore moveto}ifelse}bdf /gw{/pnm fg 3 get fg 4 get div def}bdf /lw{fg exch 4 exch put fg exch 3 exch put gw pnsv pnsh pen}bdf /barc{/@1 xdf/@2 xdf/@3 xdf/@4 xdf/@5 xdf /@6 xdf/@7 xdf/@8 xdf gsave @5 @7 add 2 div @6 @8 add 2 div translate newpath 0 0 moveto @5 @7 sub @6 @8 sub mtx currentmatrix pop scale @1{newpath}if 0 0 0.5 @4 @3 arc @4 @3 sub abs 360 ge{closepath}if mtx setmatrix @2 doop grestore}bdf /ar{dup 0 eq barc}bdf /ov{0 exch 360 exch true barc}bdf /rc{/@t xdf currentpoint 6 2 roll newpath 4 copy 4 2 roll exch moveto 6 -1 roll lineto lineto lineto closepath @t doop moveto}bdf /mup{dup pnsh 2 div le exch pnsv 2 div le or}bdf /rr{/@1 xdf 2. div/@2 xdf 2. div/@3 xdf /@4 xdf/@5 xdf/@6 xdf/@7 xdf @7 @5 eq @6 @4 eq @2 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save def/@1 xdf/@2 xdf/@3 xdf/@4 xdf/@5 xdf/@6 @5 @3 4 add mul def dc translate scale/xdbit 1 1 idtransform abs/ydbit exch def abs def{0 0 1 ydbit add 1 10 rc clip}if @1 0 eq @1 4 eq or{1 setgray ydbit 0 1 ydbit add 1 2 rc}if @1 3 eq @1 7 eq or{1}{0}ifelse setgray/@9 @1 0 eq @1 1 eq @1 3 eq or or dbinvertflag xor def/@13 @6 def @2 fBitStretch or{/@10 @4 x4 def/@11 @3 x4 def/@12 @10 rb def/@13 @12 @11 mul def/@15 1 1 dtransform abs/calcY 1 index def round cvi/@14 exch def abs/calcX 1 index def round cvi scaleby96 not{1 add}if def/@16 @15 rb def/@17 @16 @14 mul def}if sn @13 60000 lt and @2 fBitStretch or and{mtx currentmatrix dup 1 get exch 2 get 0. eq exch 0. eq and @17 60000 lt and fBitStretch and{@16 3 bitshift @14 @9 [calcX 0 0 calcY 0 0]{@17 string @13 string currentfile @6 string readhexstring pop 1 index @4 @3 @5 @12 @2 smooth4 @10 @11 @12 dup string 5 index @15 @14 @16 dup string stretch}imagemask}{@12 x8 @11 @9 [@10 0 0 @11 0 0]{@13 string currentfile @6 string readhexstring 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setcachedevice} {Gnormsize dup scale width 0 XOffset YOffset bitwidth XOffset add bitheight YOffset add setcachedevice rowbytes 0 ne{ XOffset YOffset translate newpath 0 0 moveto bitwidth bitheight scale sn{ /xSmt bitwidth x4 def /ySmt bitheight x4 def /rSmt xSmt rb def rSmt x8 ySmt true [xSmt 0 0 ySmt neg 0 ySmt] {rSmt ySmt mul string CharData cr get 1 index bitwidth bitheight rowbytes rSmt tso smooth4} }{rowbytes 3 bitshift bitheight 4 add true [bitwidth 0 0 bitheight neg 0 bitheight 2 add] {CharData cr get} }ifelse imagemask }if }ifelse restore end end }bdf /bb{.96 exch div/Gnormsize mdf 2 index /Gkernmax mdf 1 index/Gdescent mdf 3 index div 4 1 roll 2 index div 1. 5 2 roll exch div 4 1 roll 4 array astore/FontBBox mdf }bdf /cdf{mfont/CharData get 3 1 roll put}bdf /bf{ mfont begin /FontType 3 def /FontMatrix [1 0 0 1 0 0] def /Encoding macvec def /BuildChar/bmbc load def end mfont definefont pop }bdf /wi LW 1 eq{{gsave 0 0 0 0 0 0 0 0 moveto lineto lineto lineto closepath clip stringwidth grestore}bind}{/stringwidth load}ifelse def /aps{0 get 124 eq}bdf /xc{s75 cvs dup}bdf /xp{put cvn}bdf /scs{xc 3 67 put dup 0 95 xp}bdf /sos{xc 3 79 xp}bdf /sbs{xc 1 66 xp}bdf /sis{xc 2 73 xp}bdf /sob{xc 2 79 xp}bdf /sss{xc 4 83 xp}bdf /dd{exch 1 index add 3 1 roll add exch}bdf /smc{moveto dup show}bdf /kwn{FontDirectory 1 index known{findfont exch pop}}bdf /gl{1 currentgray sub setgray}bdf /mm{/mfont 10 dict def mfont begin /FontMatrix [1 0 0 1 0 0] def /FontType 3 def /Encoding macvec def /df 4 index findfont def /FontBBox [0 0 1 1] def /xda xdf/mbc xdf /BuildChar{wd begin/cr xdf/fd xdf/cs s1 dup 0 cr put def fd/mbc get exec end}def exec end mfont definefont}bdf /ac{dup scs kwn{exch findfont dup length 1 add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall fmv{/Encoding macvec def}if/StrokeWidth nlw 1000 mul pys div ps div dup 12 lt{pop 12}if def /PaintType 2 def currentdict end definefont}ifelse}bdf /mb{dup sbs kwn{exch{pop}{bbc}{}mm}ifelse sfd}bdf /mo{dup sos kwn{exch{pop}{boc}{}mm}ifelse sfd}bdf /ms{dup sss kwn{exch{pop}{bsc}{}mm}ifelse sfd}bdf /ou{dup sos kwn{exch dup ac pop{scs findfont /df2 xdf}{aoc}{}mm}ifelse sfd}bdf /su{dup sss kwn{exch dup ac pop{scs findfont /df2 xdf}{asc}{}mm}ifelse sfd}bdf /ao{/fmv true def ou}bdf/as{/fmv true def su}bdf /vo{/fmv false def ou}bdf/vs{/fmv false def su}bdf /bbc{/da .03 def fd/df get setfont gsave cs wi 1 index 0 ne{exch da add exch}if grestore setcharwidth cs 0 0 smc da 0 smc da da smc 0 da moveto show}bdf /boc{/da 1 ps div def fd/df get setfont gsave cs wi 1 index 0 ne{exch da add exch}if grestore setcharwidth cs 0 0 smc da 0 smc da da smc 0 da smc gl da 2. div dup moveto show}bdf /bsc{/da 1 ps div def /ds .05 def/da2 da 2. div def fd/df get setfont gsave cs wi 1 index 0 ne{exch ds add da2 add exch}if grestore setcharwidth cs ds da2 add .01 add 0 smc 0 ds da2 sub translate 0 0 smc da 0 smc da da smc 0 da smc gl da 2. div dup moveto show}bdf /aoc{fd/df get setfont gsave cs wi grestore setcharwidth gl cs 0 0 smc fd/df2 get setfont gl 0 0 moveto show}bdf /asc{/da .05 def fd/df get setfont gsave cs wi 1 index 0 ne{exch da add exch}if grestore setcharwidth cs da .01 add 0 smc 0 da translate gl 0 0 smc gl fd/df2 get setfont 0 0 moveto show}bdf /st{1000 mul usertime add dup 2147483647 gt{2147483647 sub}if def}bdf /the{usertime sub dup 0 lt exch -2147483648 gt and}bdf /6a 6 array def /2a 2 array def /3q 3 array def /qs{3 -1 roll sub exch 3 -1 roll sub exch}bdf /qa{3 -1 roll add exch 3 -1 roll add exch}bdf /qm{3 -1 roll 1 index mul 3 1 roll mul}bdf /qn{6a exch get mul}bdf /qA .166667 def/qB .833333 def/qC .5 def /qx{6a astore pop qA 0 qn qB 2 qn add qA 1 qn qB 3 qn add qB 2 qn qA 4 qn add qB 3 qn qA 5 qn add qC 2 qn qC 4 qn add qC 3 qn qC 5 qn add}bdf /qp{6 copy 12 -2 roll pop pop}bdf /qc{exch qp qx curveto}bdf /qi{{exch 4 copy 2a astore aload pop qa .5 qm newpath moveto}{exch 2 copy 6 -2 roll 2 qm qs 4 2 roll}ifelse}bdf /qq{{qc 2a aload pop qx curveto}{exch 4 copy qs qa qx curveto}ifelse}bdf /pt{currentpoint newpath moveto}bdf /qf{/fillflag true def}bdf /ec{1 and 0 ne{0 doop}if grestore currentpoint newpath moveto/fillflag false def}bdf /eu{currentpoint fp{0 ep}{grestore newpath}ifelse moveto/fillflag false def}bdf /bp{currentpoint newpath 2 copy moveto}bdf /ef{gsave fillflag{gsave eofill grestore}if}bdf /sm{0 exch{@1 eq{1 add}if}forall}bdf /lshow{4 1 roll exch/@1 exch def{1 index wi pop sub 1 index sm dv 0 @1 4 -1 roll widthshow}{1 index wi pop sub 1 index dup sm 10 mul exch length 1 sub add dv dup 10. mul 0 @1 4 -1 roll 0 6 -1 roll awidthshow}ifelse}bdf /setTxMode{sa 9 2 index put 3 eq{1}{0}ifelse setgray}bdf /SwToSym{{}mark false/Symbol/|______Symbol 0 rf 0 sa 6 get 0 ne{pop 1}{sa 7 get 0 eq{pop 2}if}ifelse sa 1 get 0 ne/|______Symbol sa 4 get 0 ne{vs}{sa 3 get 0 ne{vo}{fnt}ifelse}ifelse}bdf /mc{0 3 1 roll transform neg exch pop}bdf /ul{dup 0 ne sa 2 get 0 ne and{gsave 0 0 /UnderlinePosition kif{mc}{ps -10 div}ifelse/UnderlineThickness kif{mc}{ps 15 div}ifelse abs setlinewidth neg rmoveto sa 4 get 0 ne{gsave currentlinewidth 2. div dup rmoveto currentpoint newpath moveto 2 copy rlineto stroke grestore}if sa 3 get sa 4 get or 0 ne{gsave gl 2 copy rlineto stroke grestore rlineto strokepath nlw pys div setlinewidth}{rlineto}ifelse stroke grestore}{pop}ifelse}bdf /sgt{2 copy known{get true}{pop pop false}ifelse}bdf /kif{currentfont dup/FontMatrix get exch/FontInfo sgt{true}{currentfont/df sgt {dup/FontInfo sgt{3 1 roll/FontMatrix get mtx concatmatrix exch true}{pop pop pop false} ifelse}{pop pop false}ifelse}ifelse{3 -1 roll sgt{exch true}{pop false}ifelse}{false}ifelse}bdf /blank/Times-Roman findfont/CharStrings get/space get def /macvec 256 array def /NUL/SOH/STX/ETX/EOT/ENQ/ACK/BEL/BS/HT/LF/VT/FF/CR/SO/SI /DLE/DC1/DC2/DC3/DC4/NAK/SYN/ETB/CAN/EM/SUB/ESC/FS/GS/RS/US macvec 0 32 getinterval astore pop macvec 32/Times-Roman findfont/Encoding get 32 96 getinterval putinterval macvec dup 39/quotesingle put 96/grave put /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/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/blank/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge /ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand/Acircumflex/Ecircumflex/Aacute /Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave/Oacute/Ocircumflex /apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron macvec 128 128 getinterval astore pop {}mark true/Courier/|______Courier 0 rf {/Metrics 21 dict begin/zero 600 def/one 600 def/two 600 def/three 600 def/four 600 def/five 600 def/six 600 def/seven 600 def/eight 600 def /nine 600 def/comma 600 def/period 600 def/dollar 600 def/numbersign 600 def/percent 600 def/plus 600 def/hyphen 600 def/E 600 def/parenleft 600 def/parenright 600 def/space 600 def currentdict end def currentdict/UniqueID known{/UniqueID 16#800000 def}if/FontBBox FontBBox 4 array astore def}mark true/Helvetica/|______Seattle 1 rf /oldsettransfer/settransfer load def /concatprocs{/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}def /settransfer{currenttransfer concatprocs oldsettransfer}def /PaintBlack{{1 exch sub}settransfer gsave newpath clippath 1 setgray fill grestore}def /od{(Rvd\001\001\000\000\177) fg copy pop txpose 1 0 mtx defaultmatrix dtransform exch atan/pa exch def newpath clippath mark {transform{itransform moveto}}{transform{itransform lineto}} {6 -2 roll transform 6 -2 roll transform 6 -2 roll transform {itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}} {{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}bdf /cd{}bdf /op{/sfl false def/pm save def}bdf /cp{ pop pop pm restore } bdf /px{0 3 1 roll tp tt}bdf /psb{/us save def}bdf /pse{us restore}bdf /ct 40 string def /nc{currentpoint initclip newpath gc{dup type dup/arraytype eq exch/packedarraytype eq or{exec}if} forall clip newpath moveto}def /kp{ct 0 2 index length 2 index 39 2 index put getinterval copy cvx exec mx3 currentmatrix pop}bdf /av 68 def end LW 1 eq userdict/a4small known not and{/a4small [[300 72 div 0 0 -300 72 div -120 3381] 280 3255 {statusdict/jobstate (printing) put 0 setblink margins exch 196 add exch 304 add 8 div round cvi frametoroket statusdict/jobstate (busy) put 1 setblink} /framedevice load 60 45{dup mul exch dup mul add 1.0 exch sub}/setscreen load {}/settransfer load/initgraphics load/erasepage load]cvx statusdict begin bind end readonly def}if md begin/bigs[lnop userdict/letter known{/letter load}{lnop}ifelse userdict/legal known{/legal load}{lnop}ifelse userdict/a4 known{/a4 load}{lnop}ifelse userdict/b5 known{/b5 load}{lnop}ifelse lnop lnop lnop /tab load]def /smalls[lnop userdict/lettersmall known{/lettersmall load}{userdict/note known{/note load}{lnop}ifelse}ifelse userdict/legal known{/legal load}{lnop}ifelse userdict/a4small known{/a4small load}{lnop}ifelse userdict/b5 known{/b5 load}{userdict/note known{/note load}{lnop}ifelse}ifelse lnop lnop lnop /tab load]def end systemdict/currentpacking known{setpacking}if %%EndDocument 435 150 a %%BeginDocument: ps/goaldirected.ps /Mfontsize 16 def /Mlmarg .5 72 mul def /Mrmarg .5 72 mul def /Mbmarg .5 72 mul def /Mtmarg .5 72 mul def /Mwidth 8.5 72 mul def /Mheight 11 72 mul def /Mtransform { } bind def /Mnodistort true def /Mpstart { MathPictureStart } bind def /Mpend { MathPictureEnd } bind def /Mscale { 0 1 0 1 5 -1 roll MathScale } bind def /Plain /Helvetica findfont def /Bold /Helvetica-Bold findfont def /Italic /Helvetica-Oblique findfont def /MathPictureStart { gsave Mtransform Mlmarg Mbmarg translate /Mtmatrix matrix currentmatrix def Plain Mfontsize scalefont setfont } bind def /MathPictureEnd { grestore showpage } 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 /Msboxa { newpath 5 -1 roll Mvboxa pop 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 [ 7 -2 roll 2 copy [ 3 1 roll 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def /Mvboxa { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def /Mbbox { 0 0 moveto false charpath flattenpath pathbbox newpath } bind def /Mmin { 2 copy gt { exch } if pop } bind def /Mmax { 2 copy lt { exch } if pop } bind def /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get show } for pop pop pop pop Mgmatrix setmatrix } bind def /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def /MathScale { Mwidth Mlmarg Mrmarg add sub Mheight Mbmarg Mtmarg add sub 0 0 moveto 1 index 0 lineto 2 copy lineto 0 1 index lineto clip newpath Mlp translate scale pop pop pop pop /Mgmatrix matrix currentmatrix def } bind def /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } bind def /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub div 4 1 roll exch sub div } bind def /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop exch 6 -1 roll Mlprun2 8 2 roll 4 -1 roll Mlprun2 6 2 roll 3 -1 roll Mlprun2 4 2 roll exch Mlprun2 6 2 roll } bind def /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def MathPictureStart 0 1 0 1 [ [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 setgray gsave gsave 0.002 setlinewidth /arrowdict 13 dict def /arrow { arrowdict begin /headlength exch def /halfheadthickness exch 2 div def /halfthickness exch 2 div def /tipy exch def /tipx exch def /taily exch def /tailx exch def /dx tipx tailx sub def /dy tipy taily sub def /savematrix matrix currentmatrix def tipx tailx eq tipy taily eq and { tailx taily Mdot } { /arrowlength dx dx mul dy dy mul add sqrt def /angle dy dx atan def /base arrowlength headlength sub def tailx taily translate angle rotate 0 halfthickness neg moveto base halfthickness neg lineto base halfheadthickness neg lineto arrowlength 0 lineto base halfheadthickness lineto base halfthickness lineto 0 halfthickness lineto closepath } ifelse savematrix setmatrix end } def newpath 0.300000 0.575000 0.310119 0.616503 .002 dup 3 mul dup 1.5 mul arrow fill newpath 0.300000 0.600000 0.314186 0.654903 .002 dup 3 mul 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rf /oldsettransfer/settransfer load def /concatprocs{/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}def /settransfer{currenttransfer concatprocs oldsettransfer}def /PaintBlack{{1 exch sub}settransfer gsave newpath clippath 1 setgray fill grestore}def /od{(Rvd\001\001\000\000\177) fg copy pop txpose 1 0 mtx defaultmatrix dtransform exch atan/pa exch def newpath clippath mark {transform{itransform moveto}}{transform{itransform lineto}} {6 -2 roll transform 6 -2 roll transform 6 -2 roll transform {itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}} {{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}bdf /cd{}bdf /op{/sfl false def/pm save def}bdf /cp{ pop pop pm restore } bdf /px{0 3 1 roll tp tt}bdf /psb{/us save def}bdf /pse{us restore}bdf /ct 40 string def 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def/proc1 exch cvlit def/newproc proc1 length proc2 length add array def newproc 0 proc1 putinterval newproc proc1 length proc2 putinterval newproc cvx}def /settransfer{currenttransfer concatprocs oldsettransfer}def /PaintBlack{{1 exch sub}settransfer gsave newpath clippath 1 setgray fill grestore}def /od{(Rvd\001\001\000\000\177) fg copy pop txpose 1 0 mtx defaultmatrix dtransform exch atan/pa exch def newpath clippath mark {transform{itransform moveto}}{transform{itransform lineto}} {6 -2 roll transform 6 -2 roll transform 6 -2 roll transform {itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}} {{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}bdf /cd{}bdf /op{/sfl false def/pm save def}bdf /cp{ pop pop pm restore } bdf /px{0 3 1 roll tp tt}bdf /psb{/us save def}bdf /pse{us restore}bdf /ct 40 string def /nc{currentpoint initclip newpath gc{dup type dup/arraytype eq exch/packedarraytype eq or{exec}if} forall clip newpath moveto}def /kp{ct 0 2 index length 2 index 39 2 index put getinterval copy cvx exec mx3 currentmatrix pop}bdf /av 68 def end LW 1 eq userdict/a4small known not and{/a4small [[300 72 div 0 0 -300 72 div -120 3381] 280 3255 {statusdict/jobstate (printing) put 0 setblink margins exch 196 add exch 304 add 8 div round cvi frametoroket statusdict/jobstate (busy) put 1 setblink} /framedevice load 60 45{dup mul exch dup mul add 1.0 exch sub}/setscreen load {}/settransfer load/initgraphics load/erasepage load]cvx statusdict begin bind end readonly def}if md begin/bigs[lnop userdict/letter known{/letter load}{lnop}ifelse userdict/legal known{/legal load}{lnop}ifelse userdict/a4 known{/a4 load}{lnop}ifelse userdict/b5 known{/b5 load}{lnop}ifelse lnop lnop lnop /tab load]def /smalls[lnop userdict/lettersmall known{/lettersmall load}{userdict/note known{/note load}{lnop}ifelse}ifelse userdict/legal known{/legal load}{lnop}ifelse userdict/a4small known{/a4small load}{lnop}ifelse userdict/b5 known{/b5 load}{userdict/note known{/note load}{lnop}ifelse}ifelse lnop lnop lnop /tab load]def end systemdict/currentpacking known{setpacking}if %%EndDocument 112 155 a %%BeginDocument: ps/waveforms1.ps .8 dup scale md begin T T -130 -125 3170 2425 100 300 300 1 F F F F T T T psu (Satchmo; document: figure-Layer#1)jn 0 mf od op 0 0 xl 1 1 pen 0 0 gm (nc 0 0 3040 2300 6 rc)kp 0 setlinecap currentscreen 3 1 roll pop pop 60 45 3 -1 roll setscreen 64 gr 2651 1610 2670 1646 1 rc 2651 1439 2670 1475 1 rc 2651 1269 2670 1304 1 rc 2651 1095 2670 1131 1 rc 2651 924 2670 960 1 rc 2651 754 2670 790 1 rc 4 4 pen 2634 771 gm 0 gr 2623 771 lin 2634 942 gm 2623 942 lin 2634 1112 gm 2623 1112 lin 2634 1286 gm 2623 1286 lin 2634 1457 gm 2623 1457 lin 2634 1627 gm 2623 1627 lin 2623 771 gm 2623 1627 lin 64 gr 2621 718 2640 754 1 rc 2639 703 gm 1 setTxMode 0 fs bu fc {}mark T /Helvetica /|______Helvetica 0 rf bn 33 fz bu fc 2 F /|______Helvetica fnt bn (0.0)show 64 gr 2451 718 2470 754 1 rc 2469 707 gm 1 setTxMode (1.0)show 64 gr 2281 718 2300 754 1 rc 2299 707 gm 1 setTxMode (2.0)show 64 gr 2108 718 2127 754 1 rc 2126 707 gm 1 setTxMode (3.0)show 64 gr 1938 718 1957 754 1 rc 1956 707 gm 1 setTxMode (4.0)show 2623 771 gm 0 gr 2623 759 lin 2538 771 gm 2538 765 lin 2453 771 gm 2453 759 lin 2368 771 gm 2368 765 lin 2283 771 gm 2283 759 lin 2195 771 gm 2195 765 lin 2110 771 gm 2110 759 lin 2025 771 gm 2025 765 lin 1940 771 gm 1940 759 lin 2623 771 gm 1940 771 lin 2620 771 gm 2609 792 lin 2620 771 gm 2620 771 lin 2609 792 gm 2601 813 lin 2609 792 gm 2609 792 lin 2601 813 gm 2590 834 lin 2601 813 gm 2601 813 lin 2590 834 gm 2579 858 lin 2590 834 gm 2590 834 lin 2579 858 gm 2566 879 lin 2579 858 gm 2579 858 lin 2566 879 gm 2552 900 lin 2566 879 gm 2566 879 lin 2552 900 gm 2535 921 lin 2552 900 gm 2552 900 lin 2535 921 gm 2519 942 lin 2535 921 gm 2535 921 lin 2519 942 gm 2502 963 lin 2519 942 gm 2519 942 lin 2502 963 gm 2483 987 lin 2502 963 gm 2502 963 lin 2483 987 gm 2467 1008 lin 2483 987 gm 2483 987 lin 2467 1008 gm 2448 1029 lin 2467 1008 gm 2467 1008 lin 2448 1029 gm 2434 1050 lin 2448 1029 gm 2448 1029 lin 2434 1050 gm 2420 1071 lin 2434 1050 gm 2434 1050 lin 2420 1071 gm 2412 1091 lin 2420 1071 gm 2420 1071 lin 2412 1091 gm 2406 1112 lin 2412 1091 gm 2412 1091 lin 2406 1112 gm 2406 1136 lin 2406 1112 gm 2406 1112 lin 2406 1136 gm 2409 1157 lin 2406 1136 gm 2406 1136 lin 2409 1157 gm 2420 1178 lin 2409 1157 gm 2409 1157 lin 2420 1178 gm 2431 1199 lin 2420 1178 gm 2420 1178 lin 2431 1199 gm 2442 1220 lin 2431 1199 gm 2431 1199 lin 2442 1220 gm 2448 1241 lin 2442 1220 gm 2442 1220 lin 2448 1241 gm 2439 1262 lin 2448 1241 gm 2448 1241 lin 2439 1262 gm 2420 1286 lin 2439 1262 gm 2439 1262 lin 2420 1286 gm 2385 1307 lin 2420 1286 gm 2420 1286 lin 2385 1307 gm 2341 1328 lin 2385 1307 gm 2385 1307 lin 2341 1328 gm 2294 1349 lin 2341 1328 gm 2341 1328 lin 2294 1349 gm 2242 1370 lin 2294 1349 gm 2294 1349 lin 2242 1370 gm 2193 1391 lin 2242 1370 gm 2242 1370 lin 2193 1391 gm 2143 1412 lin 2193 1391 gm 2193 1391 lin 2143 1412 gm 2102 1436 lin 2143 1412 gm 2143 1412 lin 2102 1436 gm 2064 1457 lin 2102 1436 gm 2102 1436 lin 2064 1457 gm 2031 1478 lin 2064 1457 gm 2064 1457 lin 2031 1478 gm 2009 1498 lin 2031 1478 gm 2031 1478 lin 2009 1498 gm 1992 1519 lin 2009 1498 gm 2009 1498 lin 1992 1519 gm 1981 1540 lin 1992 1519 gm 1992 1519 lin 1981 1540 gm 1979 1564 lin 1981 1540 gm 1981 1540 lin 1979 1564 gm 1984 1585 lin 1979 1564 gm 1979 1564 lin 1984 1585 gm 1992 1606 lin 1984 1585 gm 1984 1585 lin 1992 1606 gm 1992 1606 lin 64 gr 2684 1146 2714 1227 1 rc 2684 1146 2714 1227 1 rc 2125 607 2407 640 1 rc 2125 607 2407 640 1 rc nc ct 39 0 put 1 0 270 tp -14 0 206 0 tc 2273 423 gm tt 1 setTxMode 1 fs bu fc {}mark T /Helvetica-Bold /|______Helvetica-Bold 0 rf bn 42 fz bu fc 2 F /|______Helvetica-Bold fnt bn (tangential velocity)show te (nc 0 0 3040 2300 6 rc)kp 2678 1604 gm 0 fs 33 fz bu fc 2 F /|______Helvetica fnt bn (1.0)show 2678 1434 gm (0.8)show 2678 1263 gm (0.6)show 2678 1089 gm (0.4)show 2678 919 gm (0.2)show 2678 748 gm (0.0)show 2750 1145 gm 1 fs 42 fz bu fc 2 F /|______Helvetica-Bold fnt bn (time)show 754 208 gm 0 gr 743 208 lin 754 378 gm 743 378 lin 754 548 gm 743 548 lin 754 721 gm 743 721 lin 754 891 gm 743 891 lin 754 1061 gm 743 1061 lin 743 208 gm 743 1061 lin 64 gr 741 149 760 191 1 rc 759 131 gm 1 setTxMode 0 fs 33 fz bu fc 2 F /|______Helvetica fnt bn (-1.0)show 64 gr 513 155 532 191 1 rc 531 140 gm 1 setTxMode (0.0)show 64 gr 285 155 304 191 1 rc 303 140 gm 1 setTxMode (1.0)show 64 gr 57 155 76 191 1 rc 75 140 gm 1 setTxMode (2.0)show 743 208 gm 0 gr 743 196 lin 628 208 gm 628 202 lin 515 208 gm 515 196 lin 402 208 gm 402 202 lin 287 208 gm 287 196 lin 172 208 gm 172 202 lin 59 208 gm 59 196 lin 743 208 gm 59 208 lin 199 208 gm 199 229 lin 199 208 gm 199 208 lin 199 229 gm 199 250 lin 199 229 gm 199 229 lin 199 250 gm 199 271 lin 199 250 gm 199 250 lin 199 271 gm 199 295 lin 199 271 gm 199 271 lin 199 295 gm 199 316 lin 199 295 gm 199 295 lin 199 316 gm 199 336 lin 199 316 gm 199 316 lin 199 336 gm 199 357 lin 199 336 gm 199 336 lin 199 357 gm 199 378 lin 199 357 gm 199 357 lin 199 378 gm 199 399 lin 199 378 gm 199 378 lin 199 399 gm 199 423 lin 199 399 gm 199 399 lin 199 423 gm 202 444 lin 199 423 gm 199 423 lin 202 444 gm 202 465 lin 202 444 gm 202 444 lin 202 465 gm 205 486 lin 202 465 gm 202 465 lin 205 486 gm 205 507 lin 205 486 gm 205 486 lin 205 507 gm 207 527 lin 205 507 gm 205 507 lin 207 527 gm 210 548 lin 207 527 gm 207 527 lin 210 548 gm 216 572 lin 210 548 gm 210 548 lin 216 572 gm 218 593 lin 216 572 gm 216 572 lin 218 593 gm 224 614 lin 218 593 gm 218 593 lin 224 614 gm 229 635 lin 224 614 gm 224 614 lin 229 635 gm 238 656 lin 229 635 gm 229 635 lin 238 656 gm 246 677 lin 238 656 gm 238 656 lin 246 677 gm 254 697 lin 246 677 gm 246 677 lin 254 697 gm 265 721 lin 254 697 gm 254 697 lin 265 721 gm 276 742 lin 265 721 gm 265 721 lin 276 742 gm 287 763 lin 276 742 gm 276 742 lin 287 763 gm 301 784 lin 287 763 gm 287 763 lin 301 784 gm 314 805 lin 301 784 gm 301 784 lin 314 805 gm 328 826 lin 314 805 gm 314 805 lin 328 826 gm 342 847 lin 328 826 gm 328 826 lin 342 847 gm 356 870 lin 342 847 gm 342 847 lin 356 870 gm 369 891 lin 356 870 gm 356 870 lin 369 891 gm 383 912 lin 369 891 gm 369 891 lin 383 912 gm 397 933 lin 383 912 gm 383 912 lin 397 933 gm 411 954 lin 397 933 gm 397 933 lin 411 954 gm 424 975 lin 411 954 gm 411 954 lin 424 975 gm 438 999 lin 424 975 gm 424 975 lin 438 999 gm 449 1020 lin 438 999 gm 438 999 lin 449 1020 gm 460 1041 lin 449 1020 gm 449 1020 lin 460 1041 gm 460 1041 lin 0 0 2 5 3 2 dh 201 210 gm 201 231 lin rh 199 208 gm 199 208 lin 0 0 2 5 3 2 dh 201 231 gm 201 252 lin rh 199 229 gm 199 229 lin 0 0 2 5 3 2 dh 201 252 gm 204 273 lin rh 199 250 gm 199 250 lin 0 0 2 5 3 2 dh 204 273 gm 204 297 lin rh 202 271 gm 202 271 lin 0 0 2 5 3 2 dh 204 297 gm 207 318 lin rh 202 295 gm 202 295 lin 0 0 2 5 3 2 dh 207 318 gm 212 338 lin rh 205 316 gm 205 316 lin 0 0 2 5 3 2 dh 212 338 gm 218 359 lin rh 210 336 gm 210 336 lin 0 0 2 5 3 2 dh 218 359 gm 223 380 lin rh 216 357 gm 216 357 lin 0 0 2 5 3 2 dh 223 380 gm 231 401 lin rh 221 378 gm 221 378 lin 0 0 2 5 3 2 dh 231 401 gm 242 425 lin rh 229 399 gm 229 399 lin 0 0 2 5 3 2 dh 242 425 gm 253 446 lin rh 240 423 gm 240 423 lin 0 0 2 5 3 2 dh 253 446 gm 264 467 lin rh 251 444 gm 251 444 lin 0 0 2 5 3 2 dh 264 467 gm 281 488 lin rh 262 465 gm 262 465 lin 0 0 2 5 3 2 dh 281 488 gm 297 509 lin rh 279 486 gm 279 486 lin 0 0 2 5 3 2 dh 297 509 gm 314 529 lin rh 295 507 gm 295 507 lin 0 0 2 5 3 2 dh 314 529 gm 333 550 lin rh 312 527 gm 312 527 lin 0 0 2 5 3 2 dh 333 550 gm 355 574 lin rh 331 548 gm 331 548 lin 0 0 2 5 3 2 dh 355 574 gm 374 595 lin rh 353 572 gm 353 572 lin 0 0 2 5 3 2 dh 374 595 gm 396 616 lin rh 372 593 gm 372 593 lin 0 0 2 5 3 2 dh 396 616 gm 418 637 lin rh 394 614 gm 394 614 lin 0 0 2 5 3 2 dh 418 637 gm 440 658 lin rh 416 635 gm 416 635 lin 0 0 2 5 3 2 dh 440 658 gm 459 679 lin rh 438 656 gm 438 656 lin 0 0 2 5 3 2 dh 459 679 gm 476 699 lin rh 457 677 gm 457 677 lin 0 0 2 5 3 2 dh 476 699 gm 492 723 lin rh 474 697 gm 474 697 lin 0 0 2 5 3 2 dh 492 723 gm 506 744 lin rh 490 721 gm 490 721 lin 0 0 2 5 3 2 dh 506 744 gm 517 765 lin rh 504 742 gm 504 742 lin 0 0 2 5 3 2 dh 517 765 gm 528 786 lin rh 515 763 gm 515 763 lin 0 0 2 5 3 2 dh 528 786 gm 536 807 lin rh 526 784 gm 526 784 lin 0 0 2 5 3 2 dh 536 807 gm 542 828 lin rh 534 805 gm 534 805 lin 0 0 2 5 3 2 dh 542 828 gm 547 849 lin rh 540 826 gm 540 826 lin 0 0 2 5 3 2 dh 547 849 gm 550 872 lin rh 545 847 gm 545 847 lin 0 0 2 5 3 2 dh 550 872 gm 553 893 lin rh 548 870 gm 548 870 lin 0 0 2 5 3 2 dh 553 893 gm 556 914 lin rh 551 891 gm 551 891 lin 0 0 2 5 3 2 dh 556 914 gm 558 935 lin rh 554 912 gm 554 912 lin 0 0 2 5 3 2 dh 558 935 gm 558 956 lin rh 556 933 gm 556 933 lin 0 0 2 5 3 2 dh 558 956 gm 558 977 lin rh 556 954 gm 556 954 lin 0 0 2 5 3 2 dh 558 977 gm 558 1001 lin rh 556 975 gm 556 975 lin 0 0 2 5 3 2 dh 558 1001 gm 558 1022 lin rh 556 999 gm 556 999 lin 0 0 2 5 3 2 dh 558 1022 gm 558 1043 lin rh 556 1020 gm 556 1020 lin 556 1041 gm 556 1041 lin 64 gr 804 582 834 662 1 rc 804 582 834 662 1 rc 301 45 469 77 1 rc 301 45 469 77 1 rc 791 1038 gm 1 setTxMode (1.0)show 791 868 gm (0.8)show 791 698 gm (0.6)show 791 525 gm (0.4)show 791 355 gm (0.2)show 791 185 gm (0.0)show 863 580 gm 1 fs 42 fz bu fc 2 F /|______Helvetica-Bold fnt bn (time)show nc ct 39 0 put 1 0 270 tp -14 0 78 0 tc 379 13 gm tt (angle)show te (nc 0 0 3040 2300 6 rc)kp nc ct 39 0 put 1 0 270 tp -5 0 40 0 tc 288 63 gm tt 25 fz bu fc 2 F /|______Helvetica-Bold fnt bn (1)show te (nc 0 0 3040 2300 6 rc)kp 755 1343 gm 0 gr 744 1343 lin 755 1515 gm 744 1515 lin 755 1686 gm 744 1686 lin 755 1860 gm 744 1860 lin 755 2032 gm 744 2032 lin 755 2203 gm 744 2203 lin 744 1343 gm 744 2203 lin 757 1273 gm 1 setTxMode 0 fs 33 fz bu fc 2 F /|______Helvetica fnt bn (1.9)show 642 1273 gm (2.0)show 529 1273 gm (2.1)show 418 1273 gm (2.2)show 305 1273 gm (2.3)show 185 1273 gm (2.4)show 77 1273 gm (2.5)show 744 1343 gm 0 gr 744 1331 lin 686 1343 gm 686 1337 lin 629 1343 gm 629 1331 lin 574 1343 gm 574 1337 lin 516 1343 gm 516 1331 lin 458 1343 gm 458 1337 lin 401 1343 gm 401 1331 lin 346 1343 gm 346 1337 lin 288 1343 gm 288 1331 lin 230 1343 gm 230 1337 lin 172 1343 gm 172 1331 lin 117 1343 gm 117 1337 lin 60 1343 gm 60 1331 lin 744 1343 gm 60 1343 lin 640 1343 gm 640 1364 lin 640 1343 gm 640 1343 lin 640 1364 gm 637 1385 lin 640 1364 gm 640 1364 lin 637 1385 gm 631 1406 lin 637 1385 gm 637 1385 lin 631 1406 gm 626 1430 lin 631 1406 gm 631 1406 lin 626 1430 gm 618 1452 lin 626 1430 gm 626 1430 lin 618 1452 gm 607 1473 lin 618 1452 gm 618 1452 lin 607 1473 gm 596 1494 lin 607 1473 gm 607 1473 lin 596 1494 gm 579 1515 lin 596 1494 gm 596 1494 lin 579 1515 gm 557 1536 lin 579 1515 gm 579 1515 lin 557 1536 gm 535 1560 lin 557 1536 gm 557 1536 lin 535 1560 gm 508 1581 lin 535 1560 gm 535 1560 lin 508 1581 gm 478 1602 lin 508 1581 gm 508 1581 lin 478 1602 gm 445 1623 lin 478 1602 gm 478 1602 lin 445 1623 gm 409 1644 lin 445 1623 gm 445 1623 lin 409 1644 gm 370 1665 lin 409 1644 gm 409 1644 lin 370 1665 gm 332 1686 lin 370 1665 gm 370 1665 lin 332 1686 gm 291 1710 lin 332 1686 gm 332 1686 lin 291 1710 gm 252 1731 lin 291 1710 gm 291 1710 lin 252 1731 gm 214 1752 lin 252 1731 gm 252 1731 lin 214 1752 gm 181 1773 lin 214 1752 gm 214 1752 lin 181 1773 gm 150 1794 lin 181 1773 gm 181 1773 lin 150 1794 gm 128 1815 lin 150 1794 gm 150 1794 lin 128 1815 gm 112 1836 lin 128 1815 gm 128 1815 lin 112 1836 gm 104 1860 lin 112 1836 gm 112 1836 lin 104 1860 gm 104 1882 lin 104 1860 gm 104 1860 lin 104 1882 gm 112 1903 lin 104 1882 gm 104 1882 lin 112 1903 gm 128 1924 lin 112 1903 gm 112 1903 lin 128 1924 gm 150 1945 lin 128 1924 gm 128 1924 lin 150 1945 gm 183 1966 lin 150 1945 gm 150 1945 lin 183 1966 gm 222 1987 lin 183 1966 gm 183 1966 lin 222 1987 gm 266 2011 lin 222 1987 gm 222 1987 lin 266 2011 gm 318 2032 lin 266 2011 gm 266 2011 lin 318 2032 gm 370 2053 lin 318 2032 gm 318 2032 lin 370 2053 gm 425 2074 lin 370 2053 gm 370 2053 lin 425 2074 gm 483 2095 lin 425 2074 gm 425 2074 lin 483 2095 gm 541 2116 lin 483 2095 gm 483 2095 lin 541 2116 gm 599 2140 lin 541 2116 gm 541 2116 lin 599 2140 gm 653 2161 lin 599 2140 gm 599 2140 lin 653 2161 gm 706 2182 lin 653 2161 gm 653 2161 lin 706 2182 gm 706 2182 lin 0 0 2 5 3 2 dh 642 1345 gm 642 1366 lin rh 640 1343 gm 640 1343 lin 0 0 2 5 3 2 dh 642 1366 gm 639 1387 lin rh 640 1364 gm 640 1364 lin 0 0 2 5 3 2 dh 639 1387 gm 636 1408 lin rh 637 1385 gm 637 1385 lin 0 0 2 5 3 2 dh 636 1408 gm 628 1432 lin rh 634 1406 gm 634 1406 lin 0 0 2 5 3 2 dh 628 1432 gm 617 1454 lin rh 626 1430 gm 626 1430 lin 0 0 2 5 3 2 dh 617 1454 gm 603 1475 lin rh 615 1452 gm 615 1452 lin 0 0 2 5 3 2 dh 603 1475 gm 584 1496 lin rh 601 1473 gm 601 1473 lin 0 0 2 5 3 2 dh 584 1496 gm 559 1517 lin rh 582 1494 gm 582 1494 lin 0 0 2 5 3 2 dh 559 1517 gm 532 1538 lin rh 557 1515 gm 557 1515 lin 0 0 2 5 3 2 dh 532 1538 gm 499 1562 lin rh 530 1536 gm 530 1536 lin 0 0 2 5 3 2 dh 499 1562 gm 466 1583 lin rh 497 1560 gm 497 1560 lin 0 0 2 5 3 2 dh 466 1583 gm 430 1604 lin rh 464 1581 gm 464 1581 lin 0 0 2 5 3 2 dh 430 1604 gm 392 1625 lin rh 428 1602 gm 428 1602 lin 0 0 2 5 3 2 dh 392 1625 gm 356 1646 lin rh 390 1623 gm 390 1623 lin 0 0 2 5 3 2 dh 356 1646 gm 323 1667 lin rh 354 1644 gm 354 1644 lin 0 0 2 5 3 2 dh 323 1667 gm 293 1688 lin rh 321 1665 gm 321 1665 lin 0 0 2 5 3 2 dh 293 1688 gm 265 1712 lin rh 291 1686 gm 291 1686 lin 0 0 2 5 3 2 dh 265 1712 gm 246 1733 lin rh 263 1710 gm 263 1710 lin 0 0 2 5 3 2 dh 246 1733 gm 235 1754 lin rh 244 1731 gm 244 1731 lin 0 0 2 5 3 2 dh 235 1754 gm 229 1775 lin rh 233 1752 gm 233 1752 lin 0 0 2 5 3 2 dh 229 1775 gm 235 1796 lin rh 227 1773 gm 227 1773 lin 0 0 2 5 3 2 dh 235 1796 gm 246 1817 lin rh 233 1794 gm 233 1794 lin 0 0 2 5 3 2 dh 246 1817 gm 265 1838 lin rh 244 1815 gm 244 1815 lin 0 0 2 5 3 2 dh 265 1838 gm 293 1862 lin rh 263 1836 gm 263 1836 lin 0 0 2 5 3 2 dh 293 1862 gm 323 1884 lin rh 291 1860 gm 291 1860 lin 0 0 2 5 3 2 dh 323 1884 gm 356 1905 lin rh 321 1882 gm 321 1882 lin 0 0 2 5 3 2 dh 356 1905 gm 392 1926 lin rh 354 1903 gm 354 1903 lin 0 0 2 5 3 2 dh 392 1926 gm 430 1947 lin rh 390 1924 gm 390 1924 lin 0 0 2 5 3 2 dh 430 1947 gm 466 1968 lin rh 428 1945 gm 428 1945 lin 0 0 2 5 3 2 dh 466 1968 gm 499 1989 lin rh 464 1966 gm 464 1966 lin 0 0 2 5 3 2 dh 499 1989 gm 532 2013 lin rh 497 1987 gm 497 1987 lin 0 0 2 5 3 2 dh 532 2013 gm 559 2034 lin rh 530 2011 gm 530 2011 lin 0 0 2 5 3 2 dh 559 2034 gm 584 2055 lin rh 557 2032 gm 557 2032 lin 0 0 2 5 3 2 dh 584 2055 gm 603 2076 lin rh 582 2053 gm 582 2053 lin 0 0 2 5 3 2 dh 603 2076 gm 617 2097 lin rh 601 2074 gm 601 2074 lin 0 0 2 5 3 2 dh 617 2097 gm 628 2118 lin rh 615 2095 gm 615 2095 lin 0 0 2 5 3 2 dh 628 2118 gm 636 2142 lin rh 626 2116 gm 626 2116 lin 0 0 2 5 3 2 dh 636 2142 gm 639 2163 lin rh 634 2140 gm 634 2140 lin 0 0 2 5 3 2 dh 639 2163 gm 642 2184 lin rh 637 2161 gm 637 2161 lin 640 2182 gm 640 2182 lin 795 2182 gm 1 setTxMode (1.0)show 795 2010 gm (0.8)show 795 1839 gm (0.6)show 795 1665 gm (0.4)show 795 1493 gm (0.2)show 795 1322 gm (0.0)show 870 1720 gm 1 fs 42 fz bu fc 2 F /|______Helvetica-Bold fnt bn (time)show nc ct 39 0 put 1 0 270 tp -13 0 57 0 tc 400 1158 gm tt (angle)show te (nc 0 0 3040 2300 6 rc)kp nc ct 39 0 put 1 0 270 tp -5 0 45 0 tc 284 1183 gm tt 25 fz bu fc 2 F /|______Helvetica-Bold fnt bn (2)show te (nc 0 0 3040 2300 6 rc)kp 64 gr 1842 586 1872 666 1 rc 1842 586 1872 666 1 rc 1094 151 1114 187 1 rc nc ct 39 0 put 1 0 270 tp -5 0 40 0 tc 1218 63 gm tt 1 setTxMode (1)show te (nc 0 0 3040 2300 6 rc)kp 1728 1034 gm 0 fs 33 fz bu fc 2 F /|______Helvetica fnt bn (1.0)show 1728 864 gm (0.8)show 1728 694 gm (0.6)show 1728 521 gm (0.4)show 1728 351 gm (0.2)show 1728 181 gm (0.0)show 1801 576 gm 1 fs 42 fz bu fc 2 F /|______Helvetica-Bold fnt bn (time)show 1690 205 gm 0 gr 1679 205 lin 1690 375 gm 1679 375 lin 1690 545 gm 1679 545 lin 1690 719 gm 1679 719 lin 1690 889 gm 1679 889 lin 1690 1059 gm 1679 1059 lin 1679 205 gm 1679 1059 lin 1696 133 gm 1 setTxMode 0 fs 33 fz bu fc 2 F /|______Helvetica fnt bn (-2.0)show 1468 133 gm (-1.0)show 1243 137 gm (0.0)show 1010 137 gm (1.0)show 1679 205 gm 0 gr 1679 193 lin 1563 205 gm 1563 199 lin 1450 205 gm 1450 193 lin 1337 205 gm 1337 199 lin 1222 205 gm 1222 193 lin 1106 205 gm 1106 199 lin 993 205 gm 993 193 lin 1679 205 gm 993 205 lin 1183 205 gm 1189 226 lin 1183 205 gm 1183 205 lin 1189 226 gm 1191 247 lin 1189 226 gm 1189 226 lin 1191 247 gm 1194 268 lin 1191 247 gm 1191 247 lin 1194 268 gm 1197 292 lin 1194 268 gm 1194 268 lin 1197 292 gm 1197 312 lin 1197 292 gm 1197 292 lin 1197 312 gm 1197 333 lin 1197 312 gm 1197 312 lin 1197 333 gm 1197 354 lin 1197 333 gm 1197 333 lin 1197 354 gm 1194 375 lin 1197 354 gm 1197 354 lin 1194 375 gm 1194 396 lin 1194 375 gm 1194 375 lin 1194 396 gm 1189 420 lin 1194 396 gm 1194 396 lin 1189 420 gm 1186 441 lin 1189 420 gm 1189 420 lin 1186 441 gm 1183 462 lin 1186 441 gm 1186 441 lin 1183 462 gm 1178 483 lin 1183 462 gm 1183 462 lin 1178 483 gm 1175 504 lin 1178 483 gm 1178 483 lin 1175 504 gm 1169 525 lin 1175 504 gm 1175 504 lin 1169 525 gm 1164 545 lin 1169 525 gm 1169 525 lin 1164 545 gm 1161 569 lin 1164 545 gm 1164 545 lin 1161 569 gm 1161 590 lin 1161 569 gm 1161 569 lin 1161 590 gm 1161 611 lin 1161 590 gm 1161 590 lin 1161 611 gm 1161 632 lin 1161 611 gm 1161 611 lin 1161 632 gm 1167 653 lin 1161 632 gm 1161 632 lin 1167 653 gm 1172 674 lin 1167 653 gm 1167 653 lin 1172 674 gm 1180 695 lin 1172 674 gm 1172 674 lin 1180 695 gm 1189 719 lin 1180 695 gm 1180 695 lin 1189 719 gm 1197 740 lin 1189 719 gm 1189 719 lin 1197 740 gm 1205 760 lin 1197 740 gm 1197 740 lin 1205 760 gm 1213 781 lin 1205 760 gm 1205 760 lin 1213 781 gm 1222 802 lin 1213 781 gm 1213 781 lin 1222 802 gm 1227 823 lin 1222 802 gm 1222 802 lin 1227 823 gm 1233 844 lin 1227 823 gm 1227 823 lin 1233 844 gm 1235 868 lin 1233 844 gm 1233 844 lin 1235 868 gm 1238 889 lin 1235 868 gm 1235 868 lin 1238 889 gm 1241 910 lin 1238 889 gm 1238 889 lin 1241 910 gm 1241 931 lin 1241 910 gm 1241 910 lin 1241 931 gm 1241 952 lin 1241 931 gm 1241 931 lin 1241 952 gm 1238 972 lin 1241 952 gm 1241 952 lin 1238 972 gm 1235 996 lin 1238 972 gm 1238 972 lin 1235 996 gm 1233 1017 lin 1235 996 gm 1235 996 lin 1233 1017 gm 1227 1038 lin 1233 1017 gm 1233 1017 lin 1227 1038 gm 1227 1038 lin 0 0 2 5 3 2 dh 1224 207 gm 1226 228 lin rh 1222 205 gm 1222 205 lin 0 0 2 5 3 2 dh 1226 228 gm 1229 249 lin rh 1224 226 gm 1224 226 lin 0 0 2 5 3 2 dh 1229 249 gm 1237 270 lin rh 1227 247 gm 1227 247 lin 0 0 2 5 3 2 dh 1237 270 gm 1246 294 lin rh 1235 268 gm 1235 268 lin 0 0 2 5 3 2 dh 1246 294 gm 1259 314 lin rh 1244 292 gm 1244 292 lin 0 0 2 5 3 2 dh 1259 314 gm 1271 335 lin rh 1257 312 gm 1257 312 lin 0 0 2 5 3 2 dh 1271 335 gm 1287 356 lin rh 1269 333 gm 1269 333 lin 0 0 2 5 3 2 dh 1287 356 gm 1304 377 lin rh 1285 354 gm 1285 354 lin 0 0 2 5 3 2 dh 1304 377 gm 1323 398 lin rh 1302 375 gm 1302 375 lin 0 0 2 5 3 2 dh 1323 398 gm 1342 422 lin rh 1321 396 gm 1321 396 lin 0 0 2 5 3 2 dh 1342 422 gm 1364 443 lin rh 1340 420 gm 1340 420 lin 0 0 2 5 3 2 dh 1364 443 gm 1386 464 lin rh 1362 441 gm 1362 441 lin 0 0 2 5 3 2 dh 1386 464 gm 1408 485 lin rh 1384 462 gm 1384 462 lin 0 0 2 5 3 2 dh 1408 485 gm 1433 506 lin rh 1406 483 gm 1406 483 lin 0 0 2 5 3 2 dh 1433 506 gm 1458 527 lin rh 1431 504 gm 1431 504 lin 0 0 2 5 3 2 dh 1458 527 gm 1480 547 lin rh 1456 525 gm 1456 525 lin 0 0 2 5 3 2 dh 1480 547 gm 1499 571 lin rh 1478 545 gm 1478 545 lin 0 0 2 5 3 2 dh 1499 571 gm 1516 592 lin rh 1497 569 gm 1497 569 lin 0 0 2 5 3 2 dh 1516 592 gm 1527 613 lin rh 1514 590 gm 1514 590 lin 0 0 2 5 3 2 dh 1527 613 gm 1532 634 lin rh 1525 611 gm 1525 611 lin 0 0 2 5 3 2 dh 1532 634 gm 1529 655 lin rh 1530 632 gm 1530 632 lin 0 0 2 5 3 2 dh 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b(the)g(top)f(graphs,)g(the)h(dotted)f(line)i(is)g(the)e (reference)h(angle)150 2480 y(and)i(the)g(solid)i(line)f(is)g(the)f (actual)g(angle.)26 b(In)18 b(the)f(middle)i(graphs,)e(the)g(dotted)g (line)h(is)g(the)150 2536 y(feedbac)o(k)e(torque)e(and)i(the)f(solid)h (line)h(is)f(the)f(feedforw)o(ard)g(torque.)952 2775 y(34)p eop %%Page: 35 35 35 34 bop 112 155 a 27233649 34272297 2368143 5196759 29601792 39469056 startTexFig 112 155 a %%BeginDocument: ps/lprep68.pro systemdict/currentpacking known{currentpacking true setpacking}if /LW{0}def /LW+{LW 2 eq}bind def /ok{systemdict/statusdict known dup{LW 0 gt and}if}bind def /md 250 dict def md begin /av 0 def /T true def/F false def/mtx matrix def/s75 75 string def/s8 8 string def/s1 ( ) def/pxs 1 def/pys 1 def 1 0 mtx defaultmatrix dtransform exch atan/pa exch def/nlw .24 def/ppr [-32 -29.52 762 582.48] def /pgs 1 def/por true def/xb 500 array def/so true def/tso true def/fillflag false def/pnm 1 def/fmv true def /sfl false def/ma 0 def/invertflag false def/dbinvertflag false def/xflip false def/yflip false def/noflips true def/scaleby96 false def/fNote true def/fBitStretch true def /fg (Rvd\001\001\000\000\177) def /bdf{bind def}bind def /xdf{exch def}bdf /xl{neg exch neg translate}bdf /fp{pnsh 0 ne pnsv 0 ne and}bdf /nop{}bdf/lnop[/nop load]cvx bdf /vrb[ {fp{fg 6 get 0 ne{gsave stroke grestore}{gsave 1 setlinewidth pnsh pnsv scale stroke grestore}ifelse}if newpath}bind /eofill load dup /newpath load 2 index dup {clip newpath}bind {}bind dup 2 copy ]def currentscreen/spf xdf/rot xdf/freq xdf /doop{vrb exch get exec}bdf /psu{/tso xdf /fNote xdf/fBitStretch xdf/scaleby96 xdf/yflip xdf/xflip xdf /invertflag xdf/dbinvertflag invertflag statusdict begin version cvr 47.0 ge product (LaserWriter) eq not and end invertflag and {not}if def xflip yflip or{/noflips false def}if /pgs xdf 2 index .72 mul exch div/pys xdf div .72 mul/pxs xdf ppr astore pop/por xdf sn and/so xdf}bdf /tab{statusdict /11x17 known{statusdict begin 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statusdict begin waittimeout 300 lt{ /waittimeout 300 def }if end scaleby96{ ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy translate .96 dup scale neg exch neg exch translate }if }bdf /fr{4 copy ppr aload pop 3 -1 roll add 3 1 roll exch add 6 2 roll 3 -1 roll sub 3 1 roll exch sub 3 -1 roll exch div 3 1 roll div exch scale pop pop xl}bdf /obl{{0.212557 mul}{pop 0}ifelse}bdf /sfd{ps fg 5 -1 roll get mul 100 div 0 ps 5 -1 roll obl ps neg 0 0 6a astore makefont setfont}bdf /fnt{findfont sfd}bdf /bt{sa 3 1 roll 3 index and put}bdf /sa(\000\000\000\000\000\000\000\000\000\000)def /fs{0 1 bt 1 2 bt 2 4 bt 3 8 bt 4 16 bt 5 32 bt 6 64 bt 7 128 bt sa exch 8 exch put}bdf /mx1 matrix def /mx2 matrix def /mx3 matrix def /bu{currentpoint currentgray currentlinewidth currentlinecap currentlinejoin currentdash exch aload length fg 5 sfl{1}{0}ifelse put pnsv pnsh 2t aload pop 3a aload pop mx2 aload pop mx1 aload pop mtx currentmatrix aload pop mx3 aload pop ps pm restore/ps xdf mx3 astore pop}bdf /bn{/pm save def mx3 setmatrix newpath 0 0 moveto ct dup 39 get 0 exch getinterval cvx exec mtx astore setmatrix mx1 astore pop mx2 astore pop 3a astore pop 2t astore pop/pnsh xdf/pnsv xdf gw /sfl fg 5 get 0 ne def array astore exch setdash setlinejoin setlinecap setlinewidth setgray moveto}bdf /fc{save vmstatus exch sub 50000 lt {(%%[|0|]%%)=print flush}if pop restore}bdf /tc{32768 div add 3 1 roll 32768 div add 2t astore pop}bdf /3a [0 0 0] def /2t 2 array def /tp{3a astore pop}bdf /tt{mx2 currentmatrix pop currentpoint 2 copy 2t aload pop qa 2 copy translate 3a aload pop exch dup 0 eq {pop}{1 eq{-1 1}{1 -1}ifelse scale}ifelse rotate pop neg exch neg exch translate moveto}bdf /te{mx2 setmatrix}bdf /th{3 -1 roll div 3 1 roll exch div 2 copy mx1 scale pop scale/sfl true def}bdf /tu{1 1 mx1 itransform scale/sfl false def}bdf /ts{1 1 mx1 transform scale/sfl true def}bdf /fz{/ps xdf}bdf /dv{dup 0 ne{div}{pop}ifelse}bdf /pop4{pop pop pop pop}bdf /it{sfl{mx1 itransform}if}bdf /gm{exch it moveto}bdf/rm{it rmoveto}bdf /lm{currentpoint sfl{mx1 transform}if exch pop sub 0 exch it rmoveto}bdf /fm{statusdict/manualfeed known}bdf /se{statusdict exch/manualfeed exch put}bdf /mf{dup/ma exch def 0 gt{fm se/t1 5 st ok ma 1 gt and{/t2 0 st/t3 0 st statusdict/manualfeedtimeout 3600 put }if}if}bdf /jn{/statusdict where exch pop{statusdict exch /jobname exch put}if}bdf /pen{pnm mul/pnsh xdf pnm mul/pnsv xdf pnsh setlinewidth}bdf /min{2 copy gt{exch}if pop}bdf /max{2 copy lt{exch}if pop}bdf /dh{fg 6 1 put array astore dup {1 pxs div mul exch}forall astore exch pop exch pop exch setdash}bdf /ih[currentdash]def /rh{fg 6 0 put ih aload pop setdash}bdf /dl{gsave nlw pys div setlinewidth 0 setgray}bdf /dlin{exch currentpoint currentlinewidth 2 div dup translate newpath moveto lineto currentpoint stroke grestore moveto}bdf /lin{fg 6 get 0 ne{exch lineto currentpoint 0 doop moveto} {exch currentpoint/pnlv xdf/pnlh xdf gsave newpath/@1 xdf/@2 xdf fp{pnlh @2 lt{pnlv @1 ge {pnlh pnlv moveto @2 @1 lineto pnsh 0 rlineto 0 pnsv rlineto pnlh pnsh add pnlv pnsv add lineto pnsh neg 0 rlineto} {pnlh pnlv moveto pnsh 0 rlineto @2 pnsh add @1 lineto 0 pnsv rlineto pnsh neg 0 rlineto pnlh pnlv pnsv add lineto}ifelse}{pnlv @1 gt {@2 @1 moveto pnsh 0 rlineto pnlh pnsh add pnlv lineto 0 pnsv rlineto pnsh neg 0 rlineto @2 @1 pnsv add lineto}{pnlh pnlv moveto pnsh 0 rlineto 0 pnsv rlineto @2 pnsh add @1 pnsv add lineto pnsh neg 0 rlineto 0 pnsv neg rlineto}ifelse}ifelse closepath fill}if @2 @1 grestore moveto}ifelse}bdf /gw{/pnm fg 3 get fg 4 get div def}bdf /lw{fg exch 4 exch put fg exch 3 exch put gw pnsv pnsh pen}bdf /barc{/@1 xdf/@2 xdf/@3 xdf/@4 xdf/@5 xdf /@6 xdf/@7 xdf/@8 xdf gsave @5 @7 add 2 div @6 @8 add 2 div translate newpath 0 0 moveto @5 @7 sub @6 @8 sub mtx currentmatrix pop scale @1{newpath}if 0 0 0.5 @4 @3 arc @4 @3 sub abs 360 ge{closepath}if mtx setmatrix @2 doop grestore}bdf /ar{dup 0 eq barc}bdf /ov{0 exch 360 exch true barc}bdf /rc{/@t xdf currentpoint 6 2 roll newpath 4 copy 4 2 roll exch moveto 6 -1 roll lineto lineto lineto closepath @t doop moveto}bdf /mup{dup pnsh 2 div le exch pnsv 2 div le or}bdf /rr{/@1 xdf 2. div/@2 xdf 2. div/@3 xdf /@4 xdf/@5 xdf/@6 xdf/@7 xdf @7 @5 eq @6 @4 eq @2 mup or or{@7 @6 @5 @4 @1 rc} {@4 @6 sub 2. div dup @2 lt{/@2 xdf}{pop}ifelse @5 @7 sub 2. div dup @2 lt{/@2 xdf}{pop}ifelse @1 0 eq{/@2 @2 pnsh 2 div 2 copy gt{sub def}{0 pop4}ifelse}if currentpoint newpath @4 @6 add 2. div @7 moveto @4 @7 @4 @5 @2 arcto pop4 @4 @5 @6 @5 @2 arcto pop4 @6 @5 @6 @7 @2 arcto pop4 @6 @7 @4 @7 @2 arcto pop4 closepath @1 doop moveto}ifelse}bdf /pr{gsave newpath/pl{exch moveto/pl{exch lineto}def}def}bdf /pl{exch lineto}bdf /ep{dup 0 eq{{moveto}{exch lin}{}{(%%[|1|]%%)= flush}pathforall pop grestore}{doop grestore}ifelse currentpoint newpath moveto}bdf /gr{64. div setgray}bdf /pat{s8 copy pop 9.375 pa por not{90 add}if{1 add 4 mul cvi s8 exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and}setscreen gr}bdf /sg{freq rot/spf load setscreen gr}bdf /dc{transform round .5 sub exch round .5 sub exch itransform}bdf /sn{userdict/smooth4 known}bdf /x8{3 bitshift}bdf /x4{2 bitshift}bdf /d4{-2 bitshift}bdf /d8{-3 bitshift}bdf /rb{15 add -4 bitshift 1 bitshift}bdf /db{/@7 save def/@1 xdf/@2 xdf/@3 xdf/@4 xdf/@5 xdf/@6 @5 @3 4 add mul def dc translate scale/xdbit 1 1 idtransform abs/ydbit exch def abs def{0 0 1 ydbit add 1 10 rc clip}if @1 0 eq @1 4 eq or{1 setgray ydbit 0 1 ydbit add 1 2 rc}if @1 3 eq @1 7 eq or{1}{0}ifelse setgray/@9 @1 0 eq @1 1 eq @1 3 eq or or dbinvertflag xor def/@13 @6 def @2 fBitStretch or{/@10 @4 x4 def/@11 @3 x4 def/@12 @10 rb def/@13 @12 @11 mul def/@15 1 1 dtransform abs/calcY 1 index def round cvi/@14 exch def abs/calcX 1 index def round cvi scaleby96 not{1 add}if def/@16 @15 rb def/@17 @16 @14 mul def}if sn @13 60000 lt and @2 fBitStretch or and{mtx currentmatrix dup 1 get exch 2 get 0. eq exch 0. eq and @17 60000 lt and fBitStretch and{@16 3 bitshift @14 @9 [calcX 0 0 calcY 0 0]{@17 string @13 string currentfile @6 string readhexstring pop 1 index @4 @3 @5 @12 @2 smooth4 @10 @11 @12 dup string 5 index @15 @14 @16 dup string stretch}imagemask}{@12 x8 @11 @9 [@10 0 0 @11 0 0]{@13 string currentfile @6 string readhexstring pop 1 index @4 @3 @5 @12 @2 smooth4}imagemask}ifelse}{@5 3 bitshift @3 4 add @9 [@4 0 0 @3 0 2]{currentfile @6 string readhexstring pop}imagemask}ifelse @7 restore}bdf /multibit{/mbdeep exch def/mbY exch def/mbX exch def save mbX mbY mbdeep[mbX 0 0 mbY 0 0]{currentfile picstr readhexstring pop}image restore}bdf /wd 16 dict def /mfont 14 dict def /mdf{mfont wcheck not{/mfont 14 dict def}if mfont begin xdf end}bdf /cf{{1 index/FID ne{def}{pop pop}ifelse}forall}bdf/rf{/@1 exch def/@2 exch def FontDirectory @2 known{cleartomark pop}{findfont dup begin dup length @1 add dict begin cf{/Encoding macvec def}{Encoding dup length array copy/Encoding exch def counttomark 2 idiv{Encoding 3 1 roll put}repeat}ifelse pop exec currentdict end end @2 exch definefont pop}ifelse}bdf /bmbc{exch begin wd begin /cr xdf save CharTable cr 6 mul 6 getinterval{}forall /bitheight xdf/bitwidth xdf .96 div/width xdf Gkernmax add/XOffset xdf Gdescent add/YOffset xdf/rowbytes xdf rowbytes 255 eq{0 0 0 0 0 0 setcachedevice} {Gnormsize dup scale width 0 XOffset YOffset bitwidth XOffset add bitheight YOffset add setcachedevice rowbytes 0 ne{ XOffset YOffset translate newpath 0 0 moveto bitwidth bitheight scale sn{ /xSmt bitwidth x4 def /ySmt bitheight x4 def /rSmt xSmt rb def rSmt x8 ySmt true [xSmt 0 0 ySmt neg 0 ySmt] {rSmt ySmt mul string CharData cr get 1 index bitwidth bitheight rowbytes rSmt tso smooth4} }{rowbytes 3 bitshift bitheight 4 add true [bitwidth 0 0 bitheight neg 0 bitheight 2 add] {CharData cr get} }ifelse imagemask }if }ifelse restore end end }bdf /bb{.96 exch div/Gnormsize mdf 2 index /Gkernmax mdf 1 index/Gdescent mdf 3 index div 4 1 roll 2 index div 1. 5 2 roll exch div 4 1 roll 4 array astore/FontBBox mdf }bdf /cdf{mfont/CharData get 3 1 roll put}bdf /bf{ mfont begin /FontType 3 def /FontMatrix [1 0 0 1 0 0] def /Encoding macvec def /BuildChar/bmbc load def end mfont definefont pop }bdf /wi LW 1 eq{{gsave 0 0 0 0 0 0 0 0 moveto lineto lineto lineto closepath clip stringwidth grestore}bind}{/stringwidth load}ifelse def /aps{0 get 124 eq}bdf /xc{s75 cvs dup}bdf /xp{put cvn}bdf /scs{xc 3 67 put dup 0 95 xp}bdf /sos{xc 3 79 xp}bdf /sbs{xc 1 66 xp}bdf /sis{xc 2 73 xp}bdf /sob{xc 2 79 xp}bdf /sss{xc 4 83 xp}bdf /dd{exch 1 index add 3 1 roll add exch}bdf /smc{moveto dup show}bdf /kwn{FontDirectory 1 index known{findfont exch pop}}bdf /gl{1 currentgray sub setgray}bdf /mm{/mfont 10 dict def mfont begin /FontMatrix [1 0 0 1 0 0] def /FontType 3 def /Encoding macvec def /df 4 index findfont def /FontBBox [0 0 1 1] def /xda xdf/mbc xdf /BuildChar{wd begin/cr xdf/fd xdf/cs s1 dup 0 cr put def fd/mbc get exec end}def exec end mfont definefont}bdf /ac{dup scs kwn{exch findfont dup length 1 add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall fmv{/Encoding macvec def}if/StrokeWidth nlw 1000 mul pys div ps div dup 12 lt{pop 12}if def /PaintType 2 def currentdict end definefont}ifelse}bdf /mb{dup sbs kwn{exch{pop}{bbc}{}mm}ifelse sfd}bdf /mo{dup sos kwn{exch{pop}{boc}{}mm}ifelse sfd}bdf /ms{dup sss kwn{exch{pop}{bsc}{}mm}ifelse sfd}bdf /ou{dup sos kwn{exch dup ac pop{scs findfont /df2 xdf}{aoc}{}mm}ifelse sfd}bdf /su{dup sss kwn{exch dup ac pop{scs findfont /df2 xdf}{asc}{}mm}ifelse sfd}bdf /ao{/fmv true def ou}bdf/as{/fmv true def su}bdf /vo{/fmv false def ou}bdf/vs{/fmv false def su}bdf /bbc{/da .03 def fd/df get setfont gsave cs wi 1 index 0 ne{exch da add exch}if grestore setcharwidth cs 0 0 smc da 0 smc da da smc 0 da moveto show}bdf /boc{/da 1 ps div def fd/df get setfont gsave cs wi 1 index 0 ne{exch da add exch}if grestore setcharwidth cs 0 0 smc da 0 smc da da smc 0 da smc gl da 2. div dup moveto show}bdf /bsc{/da 1 ps div def /ds .05 def/da2 da 2. div def fd/df get setfont gsave cs wi 1 index 0 ne{exch ds add da2 add exch}if grestore setcharwidth cs ds da2 add .01 add 0 smc 0 ds da2 sub translate 0 0 smc da 0 smc da da smc 0 da smc gl da 2. div dup moveto show}bdf /aoc{fd/df get setfont gsave cs wi grestore setcharwidth gl cs 0 0 smc fd/df2 get setfont gl 0 0 moveto show}bdf /asc{/da .05 def fd/df get setfont gsave cs wi 1 index 0 ne{exch da add exch}if grestore setcharwidth cs da .01 add 0 smc 0 da translate gl 0 0 smc gl fd/df2 get setfont 0 0 moveto show}bdf /st{1000 mul usertime add dup 2147483647 gt{2147483647 sub}if def}bdf /the{usertime sub dup 0 lt exch -2147483648 gt and}bdf /6a 6 array def /2a 2 array def /3q 3 array def /qs{3 -1 roll sub exch 3 -1 roll sub exch}bdf /qa{3 -1 roll add exch 3 -1 roll add exch}bdf /qm{3 -1 roll 1 index mul 3 1 roll mul}bdf /qn{6a exch get mul}bdf /qA .166667 def/qB .833333 def/qC .5 def /qx{6a astore pop qA 0 qn qB 2 qn add qA 1 qn qB 3 qn add qB 2 qn qA 4 qn add qB 3 qn qA 5 qn add qC 2 qn qC 4 qn add qC 3 qn qC 5 qn add}bdf /qp{6 copy 12 -2 roll pop pop}bdf /qc{exch qp qx curveto}bdf /qi{{exch 4 copy 2a astore aload pop qa .5 qm newpath moveto}{exch 2 copy 6 -2 roll 2 qm qs 4 2 roll}ifelse}bdf /qq{{qc 2a aload pop qx curveto}{exch 4 copy qs qa qx curveto}ifelse}bdf /pt{currentpoint newpath moveto}bdf /qf{/fillflag true def}bdf /ec{1 and 0 ne{0 doop}if grestore currentpoint newpath moveto/fillflag false def}bdf /eu{currentpoint fp{0 ep}{grestore newpath}ifelse moveto/fillflag false def}bdf /bp{currentpoint newpath 2 copy moveto}bdf /ef{gsave fillflag{gsave eofill grestore}if}bdf /sm{0 exch{@1 eq{1 add}if}forall}bdf /lshow{4 1 roll exch/@1 exch def{1 index wi pop sub 1 index sm dv 0 @1 4 -1 roll widthshow}{1 index wi pop sub 1 index dup sm 10 mul exch length 1 sub add dv dup 10. mul 0 @1 4 -1 roll 0 6 -1 roll awidthshow}ifelse}bdf /setTxMode{sa 9 2 index put 3 eq{1}{0}ifelse setgray}bdf /SwToSym{{}mark false/Symbol/|______Symbol 0 rf 0 sa 6 get 0 ne{pop 1}{sa 7 get 0 eq{pop 2}if}ifelse sa 1 get 0 ne/|______Symbol sa 4 get 0 ne{vs}{sa 3 get 0 ne{vo}{fnt}ifelse}ifelse}bdf /mc{0 3 1 roll transform neg exch pop}bdf /ul{dup 0 ne sa 2 get 0 ne and{gsave 0 0 /UnderlinePosition kif{mc}{ps -10 div}ifelse/UnderlineThickness kif{mc}{ps 15 div}ifelse abs setlinewidth neg rmoveto sa 4 get 0 ne{gsave currentlinewidth 2. div dup rmoveto currentpoint newpath moveto 2 copy rlineto stroke grestore}if sa 3 get sa 4 get or 0 ne{gsave gl 2 copy rlineto stroke grestore rlineto strokepath nlw pys div setlinewidth}{rlineto}ifelse stroke grestore}{pop}ifelse}bdf /sgt{2 copy known{get true}{pop pop false}ifelse}bdf /kif{currentfont dup/FontMatrix get exch/FontInfo sgt{true}{currentfont/df sgt {dup/FontInfo sgt{3 1 roll/FontMatrix get mtx concatmatrix exch true}{pop pop pop false} ifelse}{pop pop false}ifelse}ifelse{3 -1 roll sgt{exch true}{pop false}ifelse}{false}ifelse}bdf /blank/Times-Roman findfont/CharStrings get/space get def /macvec 256 array def /NUL/SOH/STX/ETX/EOT/ENQ/ACK/BEL/BS/HT/LF/VT/FF/CR/SO/SI /DLE/DC1/DC2/DC3/DC4/NAK/SYN/ETB/CAN/EM/SUB/ESC/FS/GS/RS/US macvec 0 32 getinterval astore pop macvec 32/Times-Roman findfont/Encoding get 32 96 getinterval putinterval macvec dup 39/quotesingle put 96/grave put /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/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/blank/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge /ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand/Acircumflex/Ecircumflex/Aacute /Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave/Oacute/Ocircumflex /apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron macvec 128 128 getinterval astore pop {}mark true/Courier/|______Courier 0 rf {/Metrics 21 dict begin/zero 600 def/one 600 def/two 600 def/three 600 def/four 600 def/five 600 def/six 600 def/seven 600 def/eight 600 def /nine 600 def/comma 600 def/period 600 def/dollar 600 def/numbersign 600 def/percent 600 def/plus 600 def/hyphen 600 def/E 600 def/parenleft 600 def/parenright 600 def/space 600 def currentdict end def currentdict/UniqueID known{/UniqueID 16#800000 def}if/FontBBox FontBBox 4 array astore def}mark true/Helvetica/|______Seattle 1 rf /oldsettransfer/settransfer load def /concatprocs{/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}def /settransfer{currenttransfer concatprocs oldsettransfer}def /PaintBlack{{1 exch sub}settransfer gsave newpath clippath 1 setgray fill grestore}def /od{(Rvd\001\001\000\000\177) fg copy pop txpose 1 0 mtx defaultmatrix dtransform exch atan/pa exch def newpath clippath mark {transform{itransform moveto}}{transform{itransform lineto}} {6 -2 roll transform 6 -2 roll transform 6 -2 roll transform {itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}} {{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}bdf /cd{}bdf /op{/sfl false def/pm save def}bdf /cp{ pop pop pm restore } bdf /px{0 3 1 roll tp tt}bdf /psb{/us save def}bdf /pse{us restore}bdf /ct 40 string def /nc{currentpoint initclip newpath gc{dup type dup/arraytype eq exch/packedarraytype eq or{exec}if} forall clip newpath moveto}def /kp{ct 0 2 index length 2 index 39 2 index put getinterval copy cvx exec mx3 currentmatrix pop}bdf /av 68 def end LW 1 eq userdict/a4small known not and{/a4small [[300 72 div 0 0 -300 72 div -120 3381] 280 3255 {statusdict/jobstate (printing) put 0 setblink margins exch 196 add exch 304 add 8 div round cvi frametoroket statusdict/jobstate (busy) put 1 setblink} /framedevice load 60 45{dup mul exch dup mul add 1.0 exch sub}/setscreen load {}/settransfer load/initgraphics load/erasepage load]cvx statusdict begin bind end readonly def}if md begin/bigs[lnop userdict/letter known{/letter load}{lnop}ifelse userdict/legal known{/legal load}{lnop}ifelse userdict/a4 known{/a4 load}{lnop}ifelse userdict/b5 known{/b5 load}{lnop}ifelse lnop lnop lnop /tab load]def /smalls[lnop userdict/lettersmall known{/lettersmall load}{userdict/note known{/note load}{lnop}ifelse}ifelse userdict/legal known{/legal load}{lnop}ifelse userdict/a4small known{/a4small load}{lnop}ifelse userdict/b5 known{/b5 load}{userdict/note known{/note load}{lnop}ifelse}ifelse lnop lnop lnop /tab load]def end systemdict/currentpacking known{setpacking}if %%EndDocument 112 155 a %%BeginDocument: ps/waveforms2.ps .8 dup scale md begin T T -130 -125 3170 2425 100 300 300 1 F F F F T T T psu (Satchmo; document: waveforms2-Layer#1)jn 0 mf od op 0 0 xl 1 1 pen 0 0 gm (nc 0 0 3040 2300 6 rc)kp 0 setlinecap currentscreen 3 1 roll pop pop 60 45 3 -1 roll setscreen 64 gr 57 155 76 191 1 rc 4 4 pen 754 208 gm 0 gr 743 208 lin 754 378 gm 743 378 lin 754 548 gm 743 548 lin 754 721 gm 743 721 lin 754 891 gm 743 891 lin 754 1061 gm 743 1061 lin 743 208 gm 743 1061 lin 64 gr 741 149 760 191 1 rc 804 582 834 662 1 rc 804 582 834 662 1 rc 301 45 469 77 1 rc 301 45 469 77 1 rc 791 1038 gm 1 setTxMode 0 fs bu fc {}mark T /Helvetica /|______Helvetica 0 rf bn 33 fz bu fc 2 F /|______Helvetica fnt bn (1.0)show 791 868 gm (0.8)show 791 698 gm (0.6)show 791 525 gm (0.4)show 791 355 gm (0.2)show 791 185 gm (0.0)show 863 580 gm 1 fs bu fc {}mark T /Helvetica-Bold /|______Helvetica-Bold 0 rf bn 42 fz bu fc 2 F /|______Helvetica-Bold fnt bn (time)show nc ct 39 0 put 1 0 270 tp -14 0 78 0 tc 379 13 gm tt (angle)show te (nc 0 0 3040 2300 6 rc)kp nc ct 39 0 put 1 0 270 tp -5 0 40 0 tc 288 63 gm tt 25 fz bu fc 2 F /|______Helvetica-Bold fnt bn (1)show te (nc 0 0 3040 2300 6 rc)kp 755 1343 gm 0 gr 744 1343 lin 755 1515 gm 744 1515 lin 755 1686 gm 744 1686 lin 755 1860 gm 744 1860 lin 755 2032 gm 744 2032 lin 755 2203 gm 744 2203 lin 744 1343 gm 744 2203 lin 795 2182 gm 1 setTxMode 0 fs 33 fz bu fc 2 F /|______Helvetica fnt bn (1.0)show 795 2010 gm (0.8)show 795 1839 gm (0.6)show 795 1665 gm (0.4)show 795 1493 gm (0.2)show 795 1322 gm (0.0)show 870 1720 gm 1 fs 42 fz bu fc 2 F /|______Helvetica-Bold fnt bn (time)show nc ct 39 0 put 1 0 270 tp -13 0 57 0 tc 400 1158 gm tt (angle)show te (nc 0 0 3040 2300 6 rc)kp nc ct 39 0 put 1 0 270 tp -5 0 45 0 tc 284 1183 gm tt 25 fz bu fc 2 F /|______Helvetica-Bold fnt bn (2)show te (nc 0 0 3040 2300 6 rc)kp 64 gr 1842 586 1872 666 1 rc 1842 586 1872 666 1 rc nc ct 39 0 put 1 0 270 tp -5 0 40 0 tc 1218 63 gm tt 1 setTxMode (1)show te (nc 0 0 3040 2300 6 rc)kp 1728 1034 gm 0 fs 33 fz bu fc 2 F /|______Helvetica fnt bn (1.0)show 1728 864 gm (0.8)show 1728 694 gm (0.6)show 1728 521 gm (0.4)show 1728 351 gm (0.2)show 1728 181 gm (0.0)show 1801 576 gm 1 fs 42 fz bu fc 2 F /|______Helvetica-Bold fnt bn (time)show 1690 205 gm 0 gr 1679 205 lin 1690 375 gm 1679 375 lin 1690 545 gm 1679 545 lin 1690 719 gm 1679 719 lin 1690 889 gm 1679 889 lin 1690 1059 gm 1679 1059 lin 1679 205 gm 1679 1059 lin nc ct 39 0 put 1 0 270 tp -13 0 67 0 tc 1340 24 gm tt 1 setTxMode (torque)show te (nc 0 0 3040 2300 6 rc)kp 1732 2177 gm 0 fs 33 fz bu fc 2 F /|______Helvetica fnt bn (1.0)show 1732 2007 gm (0.8)show 1732 1837 gm (0.6)show 1732 1664 gm (0.4)show 1732 1494 gm (0.2)show 1732 1324 gm (0.0)show 1805 1719 gm 1 fs 42 fz bu fc 2 F /|______Helvetica-Bold fnt bn (time)show nc ct 39 0 put 1 0 270 tp -5 0 45 0 tc 1213 1187 gm tt 25 fz bu fc 2 F /|______Helvetica-Bold fnt bn (2)show te (nc 0 0 3040 2300 6 rc)kp nc ct 39 0 put 1 0 270 tp -13 0 68 0 tc 1340 1153 gm tt 42 fz bu fc 2 F /|______Helvetica-Bold fnt bn (torque)show te (nc 0 0 3040 2300 6 rc)kp 1688 1343 gm 0 gr 1677 1343 lin 1688 1514 gm 1677 1514 lin 1688 1685 gm 1677 1685 lin 1688 1859 gm 1677 1859 lin 1688 2030 gm 1677 2030 lin 1688 2201 gm 1677 2201 lin 1677 1343 gm 1677 2201 lin 64 gr 2397 2 2564 35 1 rc 2397 2 2564 35 1 rc 754 141 gm 1 setTxMode 0 fs 33 fz bu fc 2 F /|______Helvetica fnt bn (-1.0)show 530 143 gm (0.0)show 299 143 gm (1.0)show 70 143 gm (2.0)show 742 205 gm 0 gr 742 199 lin 629 205 gm 629 202 lin 514 205 gm 514 199 lin 400 205 gm 400 202 lin 287 205 gm 287 199 lin 172 205 gm 172 202 lin 58 205 gm 58 199 lin 742 205 gm 58 205 lin 198 205 gm 198 226 lin 199 248 lin 201 269 lin 202 291 lin 205 313 lin 209 334 lin 214 354 lin 221 376 lin 230 397 lin 239 419 lin 251 440 lin 264 462 lin 279 484 lin 295 505 lin 313 527 lin 333 548 lin 353 570 lin 375 592 lin 396 613 lin 417 633 lin 438 655 lin 458 676 lin 475 698 lin 491 719 lin 504 741 lin 516 763 lin 526 784 lin 534 806 lin 540 827 lin 544 849 lin 548 870 lin 551 892 lin 552 914 lin 555 934 lin 555 955 lin 556 977 lin 556 998 lin 556 1020 lin 556 1041 lin 0 0 2 5 3 2 dh 200 207 gm 32 gr 200 228 lin rh 0 0 2 5 3 2 dh 201 250 lin rh 0 0 2 5 3 2 dh 201 271 lin rh 0 0 2 5 3 2 dh 204 293 lin rh 0 0 2 5 3 2 dh 207 315 lin rh 0 0 2 5 3 2 dh 211 336 lin rh 0 0 2 5 3 2 dh 216 356 lin rh 0 0 2 5 3 2 dh 223 378 lin rh 0 0 2 5 3 2 dh 231 399 lin rh 0 0 2 5 3 2 dh 240 421 lin rh 0 0 2 5 3 2 dh 252 442 lin rh 0 0 2 5 3 2 dh 265 464 lin rh 0 0 2 5 3 2 dh 279 486 lin rh 0 0 2 5 3 2 dh 295 507 lin rh 0 0 2 5 3 2 dh 314 529 lin rh 0 0 2 5 3 2 dh 332 550 lin rh 0 0 2 5 3 2 dh 353 572 lin rh 0 0 2 5 3 2 dh 374 594 lin rh 0 0 2 5 3 2 dh 396 615 lin rh 0 0 2 5 3 2 dh 418 635 lin rh 0 0 2 5 3 2 dh 439 657 lin rh 0 0 2 5 3 2 dh 459 678 lin rh 0 0 2 5 3 2 dh 476 700 lin rh 0 0 2 5 3 2 dh 492 721 lin rh 0 0 2 5 3 2 dh 505 743 lin rh 0 0 2 5 3 2 dh 517 765 lin rh 0 0 2 5 3 2 dh 528 786 lin rh 0 0 2 5 3 2 dh 534 808 lin rh 0 0 2 5 3 2 dh 541 829 lin rh 0 0 2 5 3 2 dh 546 851 lin rh 0 0 2 5 3 2 dh 550 872 lin rh 0 0 2 5 3 2 dh 553 894 lin rh 0 0 2 5 3 2 dh 554 916 lin rh 0 0 2 5 3 2 dh 557 936 lin rh 0 0 2 5 3 2 dh 557 957 lin rh 0 0 2 5 3 2 dh 558 979 lin rh 0 0 2 5 3 2 dh 558 1000 lin rh 0 0 2 5 3 2 dh 558 1022 lin rh 0 0 2 5 3 2 dh 559 1043 lin rh 1692 139 gm 1 setTxMode (-3.0)show 1580 139 gm (-2.0)show 1466 139 gm (-1.0)show 1353 146 gm (0.0)show 1241 146 gm (1.0)show 1127 146 gm (2.0)show 1014 146 gm (3.0)show 1678 207 gm 0 gr 1678 201 lin 1621 207 gm 1621 204 lin 1564 207 gm 1564 201 lin 1506 207 gm 1506 204 lin 1449 207 gm 1449 201 lin 1392 207 gm 1392 204 lin 1336 207 gm 1336 201 lin 1279 207 gm 1279 204 lin 1222 207 gm 1222 201 lin 1165 207 gm 1165 204 lin 1107 207 gm 1107 201 lin 1050 207 gm 1050 204 lin 994 207 gm 994 201 lin 1678 207 gm 994 207 lin 1341 207 gm 1388 228 lin 1433 250 lin 1470 271 lin 1501 293 lin 1526 314 lin 1544 335 lin 1559 355 lin 1569 377 lin 1575 398 lin 1577 420 lin 1576 441 lin 1572 463 lin 1561 484 lin 1544 506 lin 1518 527 lin 1481 549 lin 1431 570 lin 1367 591 lin 1296 613 lin 1222 633 lin 1155 654 lin 1101 676 lin 1065 697 lin 1049 719 lin 1050 740 lin 1065 762 lin 1087 783 lin 1112 804 lin 1140 826 lin 1168 847 lin 1193 869 lin 1215 890 lin 1235 912 lin 1251 932 lin 1266 953 lin 1279 975 lin 1291 996 lin 1304 1017 lin 1317 1039 lin 0 0 2 5 3 2 dh 1338 209 gm 32 gr 1338 230 lin rh 0 0 2 5 3 2 dh 1338 252 lin rh 0 0 2 5 3 2 dh 1338 273 lin rh 0 0 2 5 3 2 dh 1338 295 lin rh 0 0 2 5 3 2 dh 1338 316 lin rh 0 0 2 5 3 2 dh 1339 337 lin rh 0 0 2 5 3 2 dh 1339 357 lin rh 0 0 2 5 3 2 dh 1339 379 lin rh 0 0 2 5 3 2 dh 1339 400 lin rh 0 0 2 5 3 2 dh 1339 422 lin rh 0 0 2 5 3 2 dh 1339 443 lin rh 0 0 2 5 3 2 dh 1339 465 lin rh 0 0 2 5 3 2 dh 1339 486 lin rh 0 0 2 5 3 2 dh 1339 508 lin rh 0 0 2 5 3 2 dh 1339 529 lin rh 0 0 2 5 3 2 dh 1339 551 lin rh 0 0 2 5 3 2 dh 1339 572 lin rh 0 0 2 5 3 2 dh 1339 593 lin rh 0 0 2 5 3 2 dh 1339 615 lin rh 0 0 2 5 3 2 dh 1339 635 lin rh 0 0 2 5 3 2 dh 1338 656 lin rh 0 0 2 5 3 2 dh 1338 678 lin rh 0 0 2 5 3 2 dh 1338 699 lin rh 0 0 2 5 3 2 dh 1338 721 lin rh 0 0 2 5 3 2 dh 1338 742 lin rh 0 0 2 5 3 2 dh 1338 764 lin rh 0 0 2 5 3 2 dh 1338 785 lin rh 0 0 2 5 3 2 dh 1338 806 lin rh 0 0 2 5 3 2 dh 1338 828 lin rh 0 0 2 5 3 2 dh 1338 849 lin rh 0 0 2 5 3 2 dh 1338 871 lin rh 0 0 2 5 3 2 dh 1338 892 lin rh 0 0 2 5 3 2 dh 1338 914 lin rh 0 0 2 5 3 2 dh 1338 934 lin rh 0 0 2 5 3 2 dh 1338 955 lin rh 0 0 2 5 3 2 dh 1338 977 lin rh 0 0 2 5 3 2 dh 1338 998 lin rh 0 0 2 5 3 2 dh 1338 1019 lin rh 0 0 2 5 3 2 dh 1338 1041 lin rh 757 1286 gm 1 setTxMode (1.9)show 624 1286 gm (2.0)show 488 1286 gm (2.1)show 348 1286 gm (2.2)show 212 1286 gm (2.3)show 79 1286 gm (2.4)show 742 1342 gm 0 gr 742 1336 lin 673 1342 gm 673 1339 lin 605 1342 gm 605 1336 lin 538 1342 gm 538 1339 lin 470 1342 gm 470 1336 lin 402 1342 gm 402 1339 lin 333 1342 gm 333 1336 lin 265 1342 gm 265 1339 lin 198 1342 gm 198 1336 lin 130 1342 gm 130 1339 lin 61 1342 gm 61 1336 lin 742 1342 gm 61 1342 lin 617 1342 gm 617 1363 lin 616 1385 lin 610 1406 lin 601 1428 lin 588 1449 lin 570 1471 lin 546 1491 lin 517 1512 lin 483 1534 lin 445 1555 lin 404 1577 lin 361 1598 lin 316 1620 lin 274 1641 lin 234 1663 lin 197 1684 lin 167 1706 lin 144 1727 lin 131 1749 lin 127 1769 lin 132 1790 lin 148 1812 lin 172 1833 lin 202 1855 lin 239 1876 lin 278 1898 lin 320 1919 lin 364 1941 lin 406 1962 lin 445 1984 lin 482 2005 lin 513 2027 lin 541 2048 lin 563 2068 lin 580 2090 lin 592 2111 lin 600 2133 lin 604 2154 lin 605 2176 lin 0 0 2 5 3 2 dh 619 1344 gm 32 gr 619 1365 lin rh 0 0 2 5 3 2 dh 616 1387 lin rh 0 0 2 5 3 2 dh 612 1408 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scale dot grestore gsave 0.412699 0.519576 translate 0.002000 dup scale dot grestore gsave 0.424442 0.509236 translate 0.002000 dup scale dot grestore gsave 0.438527 0.501028 translate 0.002000 dup scale dot grestore gsave 0.454697 0.496010 translate 0.002000 dup scale dot grestore gsave 0.472305 0.495361 translate 0.002000 dup scale dot grestore gsave 0.500000 0.500000 translate 0.071387 neg 0.148758 scale link grestore gsave 0.428613 0.648758 translate 0.004000 dup scale joint grestore gsave 0.428613 0.648758 translate 0.046967 0.152951 neg scale link grestore gsave 0.475580 0.495806 translate 0.004000 dup scale joint grestore grestore gsave .25 .2 translate 0.002000 setlinewidth /cmtx matrix currentmatrix def gsave 0.375000 0.625000 translate 0.010000 dup scale button grestore gsave 0.625000 0.625000 translate 0.010000 dup scale button grestore gsave 0.500000 0.500000 translate 0.150000 dup scale base grestore gsave 0.500000 0.500000 translate 0.004000 dup scale joint grestore gsave 0.375028 0.624398 translate 0.002000 dup scale dot grestore gsave 0.375342 0.622589 translate 0.002000 dup scale dot grestore gsave 0.376507 0.619544 translate 0.002000 dup scale dot grestore gsave 0.379233 0.615270 translate 0.002000 dup scale dot grestore gsave 0.384199 0.609910 translate 0.002000 dup scale dot grestore gsave 0.391884 0.603822 translate 0.002000 dup scale dot grestore gsave 0.402415 0.597609 translate 0.002000 dup scale dot grestore gsave 0.415369 0.592019 translate 0.002000 dup scale dot grestore gsave 0.429667 0.587642 translate 0.002000 dup scale dot grestore gsave 0.443832 0.584549 translate 0.002000 dup scale dot grestore gsave 0.456446 0.582285 translate 0.002000 dup scale dot grestore gsave 0.466569 0.580206 translate 0.002000 dup scale dot grestore gsave 0.474011 0.577845 translate 0.002000 dup scale dot grestore gsave 0.479147 0.574997 translate 0.002000 dup scale dot grestore gsave 0.482526 0.571591 translate 0.002000 dup scale dot grestore gsave 0.484648 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gsave 0.542817 0.625589 translate 0.002000 dup scale dot grestore gsave 0.565394 0.626487 translate 0.002000 dup scale dot grestore gsave 0.584975 0.627255 translate 0.002000 dup scale dot grestore gsave 0.600806 0.627863 translate 0.002000 dup scale dot grestore gsave 0.612434 0.628302 translate 0.002000 dup scale dot grestore gsave 0.619805 0.628607 translate 0.002000 dup scale dot grestore gsave 0.623371 0.628843 translate 0.002000 dup scale dot grestore gsave 0.624181 0.629062 translate 0.002000 dup scale dot grestore gsave 0.500000 0.500000 translate 0.162918 0.026131 neg scale link grestore gsave 0.662918 0.473869 translate 0.004000 dup scale joint grestore gsave 0.662918 0.473869 translate 0.038762 neg 0.155234 scale link grestore gsave 0.624156 0.629102 translate 0.004000 dup scale joint grestore grestore MathPictureEnd %%EndDocument endTexFig 150 2440 a Fw(Figure)15 b(24:)k(P)o(erformance)13 b(on)i(the)f (\014rst)g(learning)i(trial)f(as)f(a)g(function)h(of)f(the)g(learning)i (rate.)952 2775 y(37)p eop %%Page: 38 38 38 37 bop 237 150 a 23286743 20721254 8485847 26510049 31772590 47231303 startTexFig 237 150 a %%BeginDocument: ps/lprep68.pro systemdict/currentpacking known{currentpacking true setpacking}if /LW{0}def /LW+{LW 2 eq}bind def /ok{systemdict/statusdict known dup{LW 0 gt and}if}bind def /md 250 dict def md begin /av 0 def /T true def/F false def/mtx matrix def/s75 75 string def/s8 8 string def/s1 ( ) def/pxs 1 def/pys 1 def 1 0 mtx defaultmatrix dtransform exch atan/pa exch def/nlw .24 def/ppr [-32 -29.52 762 582.48] def /pgs 1 def/por true def/xb 500 array def/so true def/tso true def/fillflag false def/pnm 1 def/fmv true def /sfl false def/ma 0 def/invertflag false def/dbinvertflag false def/xflip false def/yflip false def/noflips true def/scaleby96 false def/fNote true def/fBitStretch true def /fg (Rvd\001\001\000\000\177) def /bdf{bind def}bind def /xdf{exch def}bdf /xl{neg exch neg translate}bdf /fp{pnsh 0 ne pnsv 0 ne and}bdf /nop{}bdf/lnop[/nop load]cvx bdf /vrb[ {fp{fg 6 get 0 ne{gsave stroke grestore}{gsave 1 setlinewidth pnsh pnsv scale stroke grestore}ifelse}if newpath}bind /eofill load dup /newpath load 2 index dup {clip newpath}bind {}bind dup 2 copy ]def currentscreen/spf xdf/rot xdf/freq xdf /doop{vrb exch get exec}bdf /psu{/tso xdf /fNote xdf/fBitStretch xdf/scaleby96 xdf/yflip xdf/xflip xdf /invertflag xdf/dbinvertflag invertflag statusdict begin version cvr 47.0 ge product (LaserWriter) eq not and end invertflag and {not}if def xflip yflip or{/noflips false def}if /pgs xdf 2 index .72 mul exch div/pys xdf div .72 mul/pxs xdf ppr astore pop/por xdf sn and/so xdf}bdf /tab{statusdict /11x17 known{statusdict begin /11x17 load end}{statusdict /setpage known{statusdict begin 792 1224 1 setpage end}{statusdict /setpageparams known{statusdict begin 792 1224 0 1 setpageparams end}if}ifelse}ifelse}bdf /txpose{ pxs pys scale ppr aload pop por{ noflips{ pop exch neg exch translate pop 1 -1 scale }if xflip yflip and{ pop exch neg exch translate 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg translate }if xflip yflip not and{ pop exch neg exch translate pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 translate }if yflip xflip not and{ ppr 1 get neg ppr 0 get neg translate }if }{ noflips{ translate pop pop 270 rotate 1 -1 scale }if xflip yflip and{ translate pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg translate }if xflip yflip not and{ translate pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 translate }if yflip xflip not and{ translate pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 exch translate }if }ifelse statusdict begin waittimeout 300 lt{ /waittimeout 300 def }if end scaleby96{ ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy translate .96 dup scale neg exch neg exch translate }if }bdf /fr{4 copy ppr aload pop 3 -1 roll add 3 1 roll exch add 6 2 roll 3 -1 roll sub 3 1 roll exch sub 3 -1 roll exch div 3 1 roll div exch scale pop pop xl}bdf /obl{{0.212557 mul}{pop 0}ifelse}bdf /sfd{ps fg 5 -1 roll get mul 100 div 0 ps 5 -1 roll obl ps neg 0 0 6a astore makefont setfont}bdf /fnt{findfont sfd}bdf /bt{sa 3 1 roll 3 index and put}bdf /sa(\000\000\000\000\000\000\000\000\000\000)def /fs{0 1 bt 1 2 bt 2 4 bt 3 8 bt 4 16 bt 5 32 bt 6 64 bt 7 128 bt sa exch 8 exch put}bdf /mx1 matrix def /mx2 matrix def /mx3 matrix def /bu{currentpoint currentgray currentlinewidth currentlinecap currentlinejoin currentdash exch aload length fg 5 sfl{1}{0}ifelse put pnsv pnsh 2t aload pop 3a aload pop mx2 aload pop mx1 aload pop mtx currentmatrix aload pop mx3 aload pop ps pm restore/ps xdf mx3 astore pop}bdf /bn{/pm save def mx3 setmatrix newpath 0 0 moveto ct dup 39 get 0 exch getinterval cvx exec mtx astore setmatrix mx1 astore pop mx2 astore pop 3a astore pop 2t astore pop/pnsh xdf/pnsv xdf gw /sfl fg 5 get 0 ne def array astore exch setdash setlinejoin setlinecap setlinewidth setgray moveto}bdf /fc{save vmstatus exch sub 50000 lt {(%%[|0|]%%)=print flush}if pop restore}bdf /tc{32768 div add 3 1 roll 32768 div add 2t astore pop}bdf /3a [0 0 0] def /2t 2 array def /tp{3a astore pop}bdf /tt{mx2 currentmatrix pop currentpoint 2 copy 2t aload pop qa 2 copy translate 3a aload pop exch dup 0 eq {pop}{1 eq{-1 1}{1 -1}ifelse scale}ifelse rotate pop neg exch neg exch translate moveto}bdf /te{mx2 setmatrix}bdf /th{3 -1 roll div 3 1 roll exch div 2 copy mx1 scale pop scale/sfl true def}bdf /tu{1 1 mx1 itransform scale/sfl false def}bdf /ts{1 1 mx1 transform scale/sfl true def}bdf /fz{/ps xdf}bdf /dv{dup 0 ne{div}{pop}ifelse}bdf /pop4{pop pop pop pop}bdf /it{sfl{mx1 itransform}if}bdf /gm{exch it moveto}bdf/rm{it rmoveto}bdf /lm{currentpoint sfl{mx1 transform}if exch pop sub 0 exch it rmoveto}bdf /fm{statusdict/manualfeed known}bdf /se{statusdict exch/manualfeed exch put}bdf /mf{dup/ma exch def 0 gt{fm se/t1 5 st ok ma 1 gt and{/t2 0 st/t3 0 st statusdict/manualfeedtimeout 3600 put }if}if}bdf /jn{/statusdict where exch pop{statusdict exch /jobname exch put}if}bdf /pen{pnm mul/pnsh xdf pnm mul/pnsv xdf pnsh setlinewidth}bdf /min{2 copy gt{exch}if pop}bdf /max{2 copy lt{exch}if pop}bdf /dh{fg 6 1 put array astore dup {1 pxs div mul exch}forall astore exch pop exch pop exch setdash}bdf /ih[currentdash]def /rh{fg 6 0 put ih aload pop setdash}bdf /dl{gsave nlw pys div setlinewidth 0 setgray}bdf /dlin{exch currentpoint currentlinewidth 2 div dup translate newpath moveto lineto currentpoint stroke grestore moveto}bdf /lin{fg 6 get 0 ne{exch lineto currentpoint 0 doop moveto} {exch currentpoint/pnlv xdf/pnlh xdf gsave newpath/@1 xdf/@2 xdf fp{pnlh @2 lt{pnlv @1 ge {pnlh pnlv moveto @2 @1 lineto pnsh 0 rlineto 0 pnsv rlineto pnlh pnsh add pnlv pnsv add lineto pnsh neg 0 rlineto} {pnlh pnlv moveto pnsh 0 rlineto @2 pnsh add @1 lineto 0 pnsv rlineto pnsh neg 0 rlineto pnlh pnlv pnsv add lineto}ifelse}{pnlv @1 gt {@2 @1 moveto pnsh 0 rlineto pnlh pnsh add pnlv lineto 0 pnsv rlineto pnsh neg 0 rlineto @2 @1 pnsv add lineto}{pnlh pnlv moveto pnsh 0 rlineto 0 pnsv rlineto @2 pnsh add @1 pnsv add lineto pnsh neg 0 rlineto 0 pnsv neg rlineto}ifelse}ifelse closepath fill}if @2 @1 grestore moveto}ifelse}bdf /gw{/pnm fg 3 get fg 4 get div def}bdf /lw{fg exch 4 exch put fg exch 3 exch put gw pnsv pnsh pen}bdf /barc{/@1 xdf/@2 xdf/@3 xdf/@4 xdf/@5 xdf /@6 xdf/@7 xdf/@8 xdf gsave @5 @7 add 2 div @6 @8 add 2 div translate newpath 0 0 moveto @5 @7 sub @6 @8 sub mtx currentmatrix pop scale @1{newpath}if 0 0 0.5 @4 @3 arc @4 @3 sub abs 360 ge{closepath}if mtx setmatrix @2 doop grestore}bdf /ar{dup 0 eq barc}bdf /ov{0 exch 360 exch true barc}bdf /rc{/@t xdf currentpoint 6 2 roll newpath 4 copy 4 2 roll exch moveto 6 -1 roll lineto lineto lineto closepath @t doop moveto}bdf /mup{dup pnsh 2 div le exch pnsv 2 div le or}bdf /rr{/@1 xdf 2. div/@2 xdf 2. div/@3 xdf /@4 xdf/@5 xdf/@6 xdf/@7 xdf @7 @5 eq @6 @4 eq @2 mup or or{@7 @6 @5 @4 @1 rc} {@4 @6 sub 2. div dup @2 lt{/@2 xdf}{pop}ifelse @5 @7 sub 2. div dup @2 lt{/@2 xdf}{pop}ifelse @1 0 eq{/@2 @2 pnsh 2 div 2 copy gt{sub def}{0 pop4}ifelse}if currentpoint newpath @4 @6 add 2. div @7 moveto @4 @7 @4 @5 @2 arcto pop4 @4 @5 @6 @5 @2 arcto pop4 @6 @5 @6 @7 @2 arcto pop4 @6 @7 @4 @7 @2 arcto pop4 closepath @1 doop moveto}ifelse}bdf /pr{gsave newpath/pl{exch moveto/pl{exch lineto}def}def}bdf /pl{exch lineto}bdf /ep{dup 0 eq{{moveto}{exch lin}{}{(%%[|1|]%%)= flush}pathforall pop grestore}{doop grestore}ifelse currentpoint newpath moveto}bdf /gr{64. div setgray}bdf /pat{s8 copy pop 9.375 pa por not{90 add}if{1 add 4 mul cvi s8 exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and}setscreen gr}bdf /sg{freq rot/spf load setscreen gr}bdf /dc{transform round .5 sub exch round .5 sub exch itransform}bdf /sn{userdict/smooth4 known}bdf /x8{3 bitshift}bdf /x4{2 bitshift}bdf /d4{-2 bitshift}bdf /d8{-3 bitshift}bdf /rb{15 add -4 bitshift 1 bitshift}bdf /db{/@7 save def/@1 xdf/@2 xdf/@3 xdf/@4 xdf/@5 xdf/@6 @5 @3 4 add mul def dc translate scale/xdbit 1 1 idtransform abs/ydbit exch def abs def{0 0 1 ydbit add 1 10 rc clip}if @1 0 eq @1 4 eq or{1 setgray ydbit 0 1 ydbit add 1 2 rc}if @1 3 eq @1 7 eq or{1}{0}ifelse setgray/@9 @1 0 eq @1 1 eq @1 3 eq or or dbinvertflag xor def/@13 @6 def @2 fBitStretch or{/@10 @4 x4 def/@11 @3 x4 def/@12 @10 rb def/@13 @12 @11 mul def/@15 1 1 dtransform abs/calcY 1 index def round cvi/@14 exch def abs/calcX 1 index def round cvi scaleby96 not{1 add}if def/@16 @15 rb def/@17 @16 @14 mul def}if sn @13 60000 lt and @2 fBitStretch or and{mtx currentmatrix dup 1 get exch 2 get 0. eq exch 0. eq and @17 60000 lt and fBitStretch and{@16 3 bitshift @14 @9 [calcX 0 0 calcY 0 0]{@17 string @13 string currentfile @6 string readhexstring pop 1 index @4 @3 @5 @12 @2 smooth4 @10 @11 @12 dup string 5 index @15 @14 @16 dup string stretch}imagemask}{@12 x8 @11 @9 [@10 0 0 @11 0 0]{@13 string currentfile @6 string readhexstring pop 1 index @4 @3 @5 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dup scale width 0 XOffset YOffset bitwidth XOffset add bitheight YOffset add setcachedevice rowbytes 0 ne{ XOffset YOffset translate newpath 0 0 moveto bitwidth bitheight scale sn{ /xSmt bitwidth x4 def /ySmt bitheight x4 def /rSmt xSmt rb def rSmt x8 ySmt true [xSmt 0 0 ySmt neg 0 ySmt] {rSmt ySmt mul string CharData cr get 1 index bitwidth bitheight rowbytes rSmt tso smooth4} }{rowbytes 3 bitshift bitheight 4 add true [bitwidth 0 0 bitheight neg 0 bitheight 2 add] {CharData cr get} }ifelse imagemask }if }ifelse restore end end }bdf /bb{.96 exch div/Gnormsize mdf 2 index /Gkernmax mdf 1 index/Gdescent mdf 3 index div 4 1 roll 2 index div 1. 5 2 roll exch div 4 1 roll 4 array astore/FontBBox mdf }bdf /cdf{mfont/CharData get 3 1 roll put}bdf /bf{ mfont begin /FontType 3 def /FontMatrix [1 0 0 1 0 0] def /Encoding macvec def /BuildChar/bmbc load def end mfont definefont pop }bdf /wi LW 1 eq{{gsave 0 0 0 0 0 0 0 0 moveto lineto lineto lineto closepath clip stringwidth 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y Fv(Discussion)150 2278 y Fw(In)d(this)g(pap)q (er)g(w)o(e)f(ha)o(v)o(e)g(argued)g(that)g(the)g(sup)q(ervised)i (learning)g(paradigm)e(is)h(broader)f(than)150 2334 y(is)21 b(commonly)g(assumed.)36 b(The)21 b(distal)g(sup)q(ervised)h(learning)g (framew)o(ork)d(extends)i(sup)q(er-)150 2391 y(vised)d(learning)f(to)f (problems)h(in)h(whic)o(h)f(desired)h(v)m(alues)g(are)e(a)o(v)m (ailable)i(only)g(for)d(the)i(distal)p 150 2430 660 2 v 187 2457 a Fm(19)219 2473 y Fl(This)11 b(tec)o(hnique)h(can)f(b)q(e)f (considered)i(as)f(an)f(example)i(of)e(using)h(sup)q(ervised)i (learning)f(algorithms)h(to)d(solv)o(e)150 2519 y(a)j(reinforcemen)o(t) h(learning)i(problem)e(\(see)f(b)q(elo)o(w\).)952 2775 y Fw(41)p eop %%Page: 42 42 42 41 bop 150 192 a Fw(consequences)15 b(of)e(a)g(learner's)g(actions)h (and)g(not)f(for)g(the)g(actions)h(themselv)o(es.)19 b(This)14 b(is)g(a)g(sig-)150 248 y(ni\014can)o(t)g(w)o(eak)o(ening)f (of)g(the)g(classical)i(notion)e(of)g(the)g(\\teac)o(her")g(in)h(the)f 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y(uttering)f(the)f(form)g(\\w)o(ater,")f(and)i(ma)o(y)f (utilize)i(the)f(acoustic)g(represen)o(tation)f(of)h(\\w)o(ater")150 1754 y(as)c(a)h(distal)h(target)d(for)i(learning)h(the)f(articulatory)f (mo)o(v)o(emen)o(ts)g(for)g(expressing)i(a)f(desire)h(to)150 1810 y(drink,)d(ev)o(en)g(though)e(the)i(other)e(p)q(erson)i(uses)f (the)g(w)o(ater)f(to)g(douse)i(a)e(\014re.)19 b(Finally)l(,)14 b(when)f(the)150 1867 y(learner)k(is)g(acquiring)h(an)e(in)o(v)o(erse)h (mo)q(del,)g(as)f(in)h(the)g(sim)o(ulations)g(rep)q(orted)g(in)g(this)g (pap)q(er,)150 1923 y(the)e(in)o(ten)o(tion)h(is)g(ob)o(viously)g(a)o (v)m(ailable)h(b)q(ecause)f(it)f(is)h(the)f(same)g(as)g(desired)i (outcome.)241 1980 y(Our)12 b(conception)h(of)f(distal)h(sup)q(ervised) g(learning)g(problem)g(as)f(a)f(set)h(of)g(training)g(pairs)g(is)150 2036 y(of)i(course)h(an)f(abstraction)g(that)g(m)o(ust)g(b)q(e)h(elab)q (orated)g(when)g(dealing)h(with)f(complex)g(tasks.)150 2093 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Fw(A)o(tk)o(eson,)f(C.)h (G.,)f(&)h(Reink)o(ensmey)o(er,)h(D.)f(J.)g(\(1988\).)j(Using)d(asso)q (ciativ)o(e)h(conten)o(t-address-)241 1678 y(able)j(memories)f(to)f (con)o(trol)h(rob)q(ots.)28 b Fx(IEEE)18 b(Confer)n(enc)n(e)f(on)h(De)n (cision)g(and)h(Contr)n(ol)p Fw(.)241 1735 y(San)c(F)l(rancisco,)g(CA.) 150 1828 y(Barto,)f(A.)i(G.)f(\(1989\).)k(F)l(rom)c(c)o(hemotaxis)h(to) f(co)q(op)q(erativit)o(y:)21 b(Abstract)15 b(exercises)i(in)f(neu-)241 1885 y(ronal)k(learning)i(strategies.)35 b(In)21 b(R.)f(M.)g(Durbin,)i (R.)e(C.)g(Maill,)j(&)d(G.)g(J.)g(Mitc)o(hison)241 1941 y(\(Eds.\),)14 b Fx(The)i(c)n(omputing)g(neur)n(one)p Fw(.)j(Reading,)d(MA:)f(Addison-W)l(esley)i(Publishers.)150 2035 y(Barto,)g(A.)g(G.,)h(Sutton,)f(R.)h(S.,)g(&)g(Anderson,)g(C.)f (W.)g(\(1983\).)26 b(Neuronlik)o(e)19 b(adaptiv)o(e)f(ele-)241 2092 y(men)o(ts)13 b(that)f(can)i(solv)o(e)f(di\016cult)h(learning)h (con)o(trol)e(problems.)20 b Fx(IEEE)13 b(T)m(r)n(ansactions)f(on)241 2148 y(Systems,)j(Man,)h(and)g(Cyb)n(ernetics)p Fw(,)d Fx(SMC-13)p Fw(,)h(834-846.)150 2242 y(Bec)o(k)o(er,)k(S.)f(&)h(Hin)o (ton,)g(G.)f(E.)g(\(1989\).)26 b Fx(Sp)n(atial)18 b(c)n(oher)n(enc)n(e) f(as)h(an)h(internal)e(te)n(acher)i(for)g(a)241 2298 y(neur)n(al)d(network)p Fw(.)k(\(T)l(ec)o(h.)g(Rep.)g(CR)o (G-TR-89-7\).)f(T)l(oron)o(to:)g(Univ)o(ersit)o(y)d(of)f(T)l(oron)o (to.)150 2392 y(Carlson,)g(A.)g(B.)g(\(1986\).)j Fx(Communic)n(ation)e (Systems)p Fw(.)i(New)e(Y)l(ork:)j(McGra)o(w-Hill.)150 2486 y(Craig,)d(J.)h(J.)f(\(1986\).)23 b Fx(Intr)n(o)n(duction)17 b(to)g(R)n(ob)n(otics)p Fw(.)24 b(Reading,)18 b(MA:)e(Addison-W)l (esley)i(Pub-)241 2542 y(lishers.)952 2775 y(45)p eop %%Page: 46 46 46 45 bop 150 192 a Fw(Gelfand,)15 b(I.)h(M.)e(&)i(F)l(omin,)f(S.)g(V.) g(\(1963\).)j Fx(Calculus)e(of)g(variations)p Fw(.)k(Englew)o(o)q(o)q (d)c(Cli\013s,)f(N.)241 248 y(J.:)20 b(Pren)o(tice-Hall.)150 340 y(Go)q(o)q(dwin,)k(G.)d(C.)h(&)h(Sin,)h(K.)e(S.)g(\(1984\).)39 b Fx(A)n(daptive)23 b(\014ltering)e(pr)n(e)n(diction)i(and)f(c)n(ontr)n (ol)p Fw(.)241 396 y(Englew)o(o)q(o)q(d)16 b(Cli\013s,)f(NJ:)g(Pren)o (tice-Hall.)150 488 y(Grossb)q(erg,)d(S.)h(\(1987\).)k(Comp)q(etitiv)o (e)c(learning:)20 b(F)l(rom)12 b(in)o(teractiv)o(e)h(activ)m(ation)h (to)e(adaptiv)o(e)241 545 y(resonance.)20 b Fx(Co)n(gnitive)15 b(Scienc)n(e)p Fw(,)e(11,)h(23-63.)150 636 y(Hin)o(ton,)20 b(G.)f(E.)g(&)h(Sejno)o(wski,)g(T.)f(J.)g(\(1986\).)31 b(Learning)20 b(and)g(relearning)g(in)g(Boltzmann)241 693 y(mac)o(hines.)k(In)17 b(D.)f(E.)g(Rumelhart)h(&)g(J.)f(L.)g (McClelland)j(\(Eds.\),)c Fx(Par)n(al)r(lel)i(distribute)n(d)241 749 y(pr)n(o)n(c)n(essing)p Fw(:)h Fx(V)m(olume)e(1)p Fw(,)f(282-317.)j(Cam)o(bridge,)d(MA:)f(MIT)h(Press.)150 841 y(Hogan,)23 b(N.)f(\(1984\).)39 b(An)22 b(organising)g(principle)j (for)d(a)g(class)g(of)g(v)o(olun)o(tary)f(mo)o(v)o(emen)o(ts.)241 898 y Fx(Journal)16 b(of)h(Neur)n(oscienc)n(e)p Fw(,)c Fx(4)p Fw(,)i(2745-2754.)150 989 y(Jordan,)j(M.)f(I.)h(\(1983\).)26 b Fx(Mental)18 b(pr)n(actic)n(e)p Fw(.)27 b(Unpublished)21 b(dissertation)d(prop)q(osal,)g(Cen)o(ter)241 1046 y(for)c(Human)i (Information)f(Pro)q(cessing,)g(Univ)o(ersit)o(y)h(of)f(California,)h (San)f(Diego.)150 1138 y(Jordan,)22 b(M.)f(I.)g(\(1986\).)36 b(Serial)22 b(order:)32 b(A)21 b(parallel,)j(distributed)f(pro)q (cessing)f(approac)o(h.)241 1194 y(\(T)l(ec)o(hnical)17 b(Rep)q(ort)e(8604\).)k(La)c(Jolla,)h(CA:)e(Univ)o(ersit)o(y)i(of)f (California,)h(San)f(Diego.)150 1286 y(Jordan,)j(M.)f(I.)g(\(1988\).)25 b Fx(Sup)n(ervise)n(d)18 b(le)n(arning)f(and)h(systems)g(with)h(exc)n (ess)e(de)n(gr)n(ess)g(of)h(fr)n(e)n(e-)241 1343 y(dom)p Fw(.)j(\(COINS)16 b(T)l(ec)o(h.)21 b(Rep.)g(88-27\).)e(Amherst,)c(MA:)g (Univ)o(ersit)o(y)h(of)f(Massac)o(h)o(usetts,)241 1399 y(Computer)g(and)g(Information)g(Sciences.)150 1491 y(Jordan,)f(M.)g (I.,)g(&)g(Rosen)o(baum,)h(D.)e(A.)h(\(1989\).)k(Action.)i(In)15 b(M.)f(I.)g(P)o(osner)g(\(Ed.\),)f Fx(F)m(ounda-)241 1547 y(tions)j(of)g(Co)n(gnitive)f(Scienc)n(e)p Fw(.)j(Cam)o(bridge,)d (MA:)g(MIT)g(Press.)150 1639 y(Jordan,)k(M.I.)g(\(1990\).)28 b(Motor)18 b(learning)i(and)f(the)g(degrees)g(of)f(freedom)h(problem.) 31 b(In)20 b(M.)241 1696 y(Jeannero)q(d)c(\(Ed.\),)e Fx(A)o(ttention)h(and)i(Performanc)n(e,)f(XIII)p Fw(.)d(Hillsdale,)k (NJ:)e(Erlbaum.)150 1787 y(Jordan,)f(M.)f(I.,)h(&)g(Jacobs,)g(R.)g(A.)f (\(1990\).)18 b(Learning)d(to)e(con)o(trol)h(an)f(unstable)i(system)f (with)241 1844 y(forw)o(ard)20 b(mo)q(deling.)41 b(In)23 b(D.)e(T)l(ouretzky)h(\(Ed.\),)g Fx(A)n(dvanc)n(es)e(in)i(Neur)n(al)g (Information)241 1900 y(Pr)n(o)n(c)n(essing)14 b(Systems)h(2)p Fw(.)20 b(San)c(Mateo,)d(CA:)i(Morgan)f(Kaufmann.)150 1992 y(Ka)o(w)o(ato,)g(M.)g(\(1990\).)19 b(Computational)c(sc)o(hemes)h (and)f(neural)i(net)o(w)o(ork)d(mo)q(dels)i(for)f(forma-)241 2049 y(tion)e(and)f(con)o(trol)g(of)h(m)o(ultijoin)o(t)g(arm)f(tra)s (jectory)l(.)17 b(In)c(W.)f(T.)g(Miller,)i(I)q(I)q(I,)g(R.)e(S.)h (Sutton,)241 2105 y(&)i(P)l(.)g(J.)g(W)l(erb)q(os)h(\(Eds.\),)e Fx(Neur)n(al)i(Networks)g(for)g(Contr)n(ol)p Fw(.)j(Cam)o(bridge:)h (MIT)15 b(Press.)150 2197 y(Ka)o(w)o(ato,)20 b(M.,)h(F)l(uruk)m(a)o(w)o (a,)g(K.,)h(&)f(Suzuki,)i(R.)d(\(1987\).)35 b(A)21 b(hierarc)o(hical)h (neural-net)o(w)o(ork)241 2253 y(mo)q(del)16 b(for)f(con)o(trol)g(and)g (learning)h(of)f(v)o(olun)o(tary)g(mo)o(v)o(emen)o(t.)k Fx(Biolo)n(gic)n(al)c(Cyb)n(ernetics)p Fw(,)241 2310 y Fx(57)p Fw(,)g(169-185.)150 2402 y(Kirk,)h(D.)e(E.)h(\(1970\).)j Fx(Optimal)e(c)n(ontr)n(ol)g(the)n(ory)p Fw(.)k(Englew)o(o)q(o)q(d)c (Cli\013s,)f(NJ:)g(Pren)o(tice-Hall.)150 2494 y(Kohonen,)f(T.)f (\(1982\).)k(Self-organized)e(formation)e(of)g(top)q(ologically)i (correct)e(feature)g(maps.)241 2550 y Fx(Biolo)n(gic)n(al)i(Cyb)n (ernetics)p Fw(,)e Fx(43)p Fw(,)i(56-69.)952 2775 y(46)p eop %%Page: 47 47 47 46 bop 150 192 a Fw(Kup)q(erstein,)19 b(M.)d(\(1988\).)22 b(Neural)c(mo)q(del)f(of)g(adaptiv)o(e)f(hand-ey)o(e)i(co)q(ordination) g(for)e(single)241 248 y(p)q(ostures.)k Fx(Scienc)n(e)p Fw(,)13 b Fx(239)p Fw(,)i(1308-1311.)150 342 y(LeCun,)h(Y.)f(\(1985\).) k(A)d(learning)g(sc)o(heme)g(for)f(asymmetric)g(threshold)i(net)o(w)o (orks.)i Fx(Pr)n(o)n(c)n(e)n(e)n(d-)241 398 y(ings)c(of)i(Co)n(gnitiva) e(85)p Fw(.)20 b(P)o(aris,)15 b(F)l(rance.)150 492 y(LeCun,)20 b(Y.)e(\(1987\).)27 b Fx(Mo)n(d)o(\022)-22 b(eles)18 b(c)n(onnexionnistes)f(de)i(l'appr)n(entissage)p Fw(.)28 b(Unpublished)21 b(do)q(c-)241 549 y(toral)15 b(dissertation,)g(Univ)o (ersit)o(\023)-21 b(e)15 b(de)h(P)o(aris,)e(VI.)150 642 y(Linsk)o(er,)k(R.)f(\(1988\).)22 b(Self-organization)c(in)g(a)e(p)q (erceptual)i(net)o(w)o(ork.)24 b Fx(Computer)p Fw(,)17 b Fx(21)p Fw(,)h(105-)241 699 y(117.)150 793 y(Ljung,)d(L.)h(&)f(S\177) -23 b(oderstr\177)g(om,)14 b(T.)h(\(1986\).)j Fx(The)n(ory)e(and)g(pr)n (actic)n(e)g(of)h(r)n(e)n(cursive)e(identi\014c)n(ation)p Fw(.)241 849 y(Cam)o(bridge:)20 b(MIT)15 b(Press.)150 943 y(Miller,)i(W.)e(T.)g(\(1987\).)k(Sensor-based)d(con)o(trol)g(of)f 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b(Iden)o(ti\014cation)d(and)e(con)o(trol)f(of)h(dynamical)241 1563 y(systems)k(using)h(neural)h(net)o(w)o(orks.)23 b Fx(IEEE)16 b(T)m(r)n(ansactions)f(on)j(Neur)n(al)f(Networks)p Fw(,)f Fx(1)p Fw(,)h(4-)241 1619 y(27.)150 1713 y(Nguy)o(en,)k(D.)d(&)i (Widro)o(w,)g(B.)g(\(1989\).)31 b(The)20 b(truc)o(k)f(bac)o(k)o(er-upp) q(er:)30 b(An)20 b(example)g(of)f(self-)241 1770 y(learning)c(in)g (neural)h(net)o(w)o(orks.)i(In:)i Fx(Pr)n(o)n(c)n(e)n(e)n(dings)13 b(of)j(the)f(International)f(Joint)h(Confer-)241 1826 y(enc)n(e)g(on)h(Neur)n(al)g(Networks)p Fw(,)f Fx(2)p Fw(,)g(357-363.)j(Piscata)o(w)o(a)o(y)l(,)c(NJ:)h(IEEE)g(Press.)150 1920 y(P)o(ark)o(er,)k(D.)g(\(1985\).)32 b Fx(L)n(e)n(arning-lo)n(gic)p Fw(.)f(\(T)l(ec)o(h.)i(Rep.)i(TR-47\).)e(Cam)o(bridge,)20 b(MA:)f(MIT)241 1976 y(Sloan)d(Sc)o(ho)q(ol)g(of)e(Managemen)o(t.)150 2070 y(Robinson,)k(A.)e(J.)h(&)g(F)l(allside,)i(F.)d(\(1989\).)23 b(Dynamic)17 b(reinforcemen)o(t)g(driv)o(en)h(error)e(propa-)241 2127 y(gation)d(net)o(w)o(orks)f(with)h(application)i(to)d(game)h(pla)o (ying.)20 b Fx(Pr)n(o)n(c)n(e)n(e)n(dings)12 b(of)i(Neur)n(al)g(Infor-) 241 2183 y(mation)i(Systems)p Fw(.)j(American)d(Institute)g(of)f(Ph)o (ysics.)150 2277 y(Rosen)o(blatt,)g(F.)f(\(1962\).)19 b Fx(Principles)c(of)h(neur)n(o)n(dynamics)p Fw(.)j(New)c(Y)l(ork:)20 b(Spartan.)150 2371 y(Rumelhart,)g(D.)e(E.)g(\(1986\).)28 b(Learning)20 b(sensorimotor)e(programs)f(in)i(parallel)h(distributed) 241 2427 y(pro)q(cessing)c(systems.)j Fx(US-Jap)n(an)c(Joint)h(Seminar) f(on)h(Comp)n(etition)g(and)g(Co)n(op)n(er)n(ation)241 2484 y(in)g(Neur)n(al)g(Nets,)f(II)p Fw(.)f(Unpublished)k(presen)o (tation.)952 2775 y(47)p eop %%Page: 48 48 48 47 bop 150 192 a Fw(Rumelhart,)21 b(D.)e(E.,)g(Hin)o(ton,)i(G.)e (E.,)g(Williams,)j(R.)e(J.)f(\(1986\).)31 b(Learning)20 b(in)o(ternal)h(rep-)241 248 y(resen)o(tations)f(b)o(y)h(error)f (propagation.)36 b(In)22 b(D.)e(E.)g(Rumelhart)h(&)h(J.)e(L.)h (McClelland)241 304 y(\(Eds.\),)f Fx(Par)n(al)r(lel)g(distribute)n(d)h (pr)n(o)n(c)n(essing)p Fw(:)27 b Fx(V)m(olume)21 b(1)p Fw(,)g(318-363.)33 b(Cam)o(bridge,)21 b(MA:)241 361 y(MIT)15 b(Press.)150 455 y(Rumelhart,)i(D.)e(E.,)g(Smolensky)l(,)i(P)l(.,)e (McClelland,)j(J.)e(L.)g(&)g(Hin)o(ton,)g(G.)f(E.)h(\(1986\).)k(Sc)o (he-)241 511 y(mata)e(and)h(sequen)o(tial)h(though)o(t)e(pro)q(cesses)i (in)f(PDP)g(mo)q(dels.)32 b(In)19 b(D.)g(E.)f(Rumelhart)241 568 y(&)k(J.)g(L.)g(McClelland)i(\(Eds.\),)f Fx(Par)n(al)r(lel)f (distribute)n(d)h(pr)n(o)n(c)n(essing)p Fw(:)31 b Fx(V)m(olume)22 b(2)p Fw(,)i(7-57.)241 624 y(Cam)o(bridge,)15 b(MA:)f(MIT)h(Press.)150 718 y(Rumelhart,)j(D.)e(E.)g(&)i(Zipser,)f(D.)f(\(1986\).)24 b(F)l(eature)16 b(disco)o(v)o(ery)h(b)o(y)g(comp)q(etitiv)o(e)h (learning.)241 774 y(In)e(D.)f(E.)g(Rumelhart)h(&)g(J.)f(L.)g (McClelland)j(\(Eds.\),)c Fx(Par)n(al)r(lel)i(distribute)n(d)g(pr)n(o)n (c)n(essing)p Fw(:)241 831 y Fx(V)m(olume)g(1)p Fw(,)f(151-193.)j(Cam)o (bridge,)d(MA:)f(MIT)i(Press.)150 925 y(Sc)o(hmidh)o(ub)q(er,)e(J.)d (H.)f(\(1990\).)17 b(An)12 b(on-line)h(algorithm)e(for)f(dynamic)i (reinforcemen)o(t)g(learning)241 981 y(and)20 b(planning)i(in)f (reactiv)o(e)f(en)o(vironmen)o(ts.)35 b(In:)c Fx(Pr)n(o)n(c)n(e)n(e)n (dings)18 b(of)j(the)g(International)241 1038 y(Joint)13 b(Confer)n(enc)n(e)f(on)i(Neur)n(al)f(Networks)p Fw(,)g Fx(2)p Fw(,)g(253-258.)k(Piscata)o(w)o(a)o(y)l(,)11 b(NJ:)i(IEEE)g (Press.)150 1131 y(Sutton,)e(R.)f(S.)g(\(1984\).)17 b Fx(T)m(emp)n(or)n(al)10 b(cr)n(e)n(dit)i(assignment)e(in)h(r)n(einfor)n (c)n(ement)g(le)n(arning)p Fw(.)16 b(\(COINS)241 1188 y(T)l(ec)o(h.)k(Rep.)g(84-02\).)e(Amherst,)c(MA:)g(Univ)o(ersit)o(y)h (of)e(Massac)o(h)o(usetts,)g(Computer)h(and)241 1244 y(Information)h(Sciences.)150 1338 y(Sutton,)i(R.)g(S.)g(\(1988\).)24 b(Learning)18 b(to)e(predict)i(b)o(y)f(the)g(metho)q(ds)g(of)g(temp)q (oral)g(di\013erences.)241 1395 y Fx(Machine)f(L)n(e)n(arning)p Fw(,)d Fx(3)p Fw(,)i(9-44.)150 1488 y(Sutton,)i(R.)g(S.)g(\(1990\).)23 b(In)o(tegrated)16 b(arc)o(hitectures)i(for)e(learning,)i(planning,)h (and)e(reacting)241 1545 y(based)22 b(on)f(appro)o(ximating)g(dynamic)i (programming.)38 b Fx(Pr)n(o)n(c)n(e)n(e)n(dings)19 b(of)k(the)f (Seventh)241 1601 y(International)15 b(Confer)n(enc)n(e)f(on)i(Machine) g(L)n(e)n(arning)p Fw(.)150 1695 y(W)l(erb)q(os,)f(P)l(.)g(\(1974\).)j Fx(Beyond)f(r)n(e)n(gr)n(ession:)i(New)d(to)n(ols)g(for)g(pr)n(e)n (diction)g(and)h(analysis)e(in)h(the)241 1751 y(b)n(ehavior)n(al)g (scienc)n(es)p Fw(.)i(Unpublished)g(do)q(ctoral)d(dissertation,)g(Harv) m(ard)g(Univ)o(ersit)o(y)l(.)150 1845 y(W)l(erb)q(os,)f(P)l(.)f (\(1987\).)18 b(Building)f(and)d(understanding)h(adaptiv)o(e)f (systems:)19 b(A)13 b(statistical/n)o(u-)241 1902 y(merical)g(approac)o (h)e(to)g(factory)g(automation)f(and)i(brain)h(researc)o(h.)18 b Fx(IEEE)12 b(T)m(r)n(ansactions)241 1958 y(on)k(Systems,)f(Man,)h (and)g(Cyb)n(ernetics)p Fw(,)d Fx(17)p Fw(,)i(7-20.)150 2052 y(Widro)o(w,)i(B.)g(&)g(Ho\013,)g(M.)f(E.)h(\(1960\).)24 b(Adaptiv)o(e)18 b(switc)o(hing)g(circuits.)27 b Fx(Institute)17 b(of)i(R)n(adio)241 2108 y(Engine)n(ers,)13 b(Western)h(Ele)n(ctr)n (onic)e(Show)j(and)f(Convention,)f(Convention)g(R)n(e)n(c)n(or)n(d)p Fw(,)g Fx(Part)241 2165 y(4)p Fw(,)i(96-104.)150 2259 y(Widro)o(w,)f(B.,)h(&)g(Stearns,)f(S.)h(D.)f(\(1985\).)k Fx(A)n(daptive)e(signal)f(pr)n(o)n(c)n(essing)p Fw(.)i(Englew)o(o)q(o)q (d)f(Cli\013s,)241 2315 y(NJ:)f(Pren)o(tice-Hall.)952 2775 y(48)p eop %%Page: 49 49 49 48 bop 791 192 a Fv(App)r(endix)22 b(A)150 293 y Fw(T)l(o)11 b(obtain)h(an)g(expression)g(for)g(the)f(gradien)o(t)h(of)f(Equation)h (16,)f(w)o(e)h(utilize)i(a)d(con)o(tin)o(uous-time)150 349 y(analog,)j(deriv)o(e)h(a)f(necessary)h(condition,)g(and)g(then)f (con)o(v)o(ert)g(the)h(result)f(in)o(to)h(discrete)g(time.)150 406 y(T)l(o)c(simplify)j(the)e(exp)q(osition)h(w)o(e)e(compute)h (partial)h(deriv)m(ativ)o(es)f(with)h(resp)q(ect)f(to)f(the)h(actions) 150 462 y Fo(u)h Fw(instead)h(of)f(the)h(w)o(eigh)o(ts)f Fo(w)q Fw(.)18 b(The)c(resulting)g(equations)g(are)f(con)o(v)o(erted)g (in)o(to)g(gradien)o(ts)h(for)150 519 y(the)h(w)o(eigh)o(ts)g(b)o(y)g (prem)o(ultiplying)j(b)o(y)d(the)g(transp)q(ose)g(of)g(the)g(Jacobian)h (matrix)f(\()p Fq(@)s Fo(u)p Fq(=@)s Fo(w)o Fw(\).)241 575 y(Let)i Fo(u)p Fw(\()p Fq(t)p Fw(\))g(represen)o(t)f(an)h(action)g (tra)s(jectory)e(and)i(let)g Fo(y)q Fw(\()p Fq(t)p Fw(\))f(represen)o (t)h(a)g(sensation)g(tra-)150 632 y(jectory)l(.)36 b(These)21 b(tra)s(jectories)f(are)g(link)o(ed)j(in)e(the)g(forw)o(ard)e (direction)j(b)o(y)f(the)g(dynamical)150 688 y(equations:)869 744 y(_)861 745 y Fo(x)12 b Fw(=)h Fq(f)5 b Fw(\()p Fo(x)p Fq(;)j Fo(u)p Fw(\))150 828 y(and)881 885 y Fo(y)13 b Fw(=)g Fq(g)r Fw(\()p Fo(x)p Fw(\))p Fq(:)241 968 y Fw(The)j(action)g (v)o(ector)g Fo(u)f Fw(is)i(assumed)f(to)f(dep)q(end)j(on)e(the)g (curren)o(t)g(state)f(and)h(the)g(target)150 1024 y(v)o(ector:)845 1081 y Fo(u)d Fw(=)g Fq(h)p Fw(\()p Fo(x)p 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Fo(y)543 1680 y Fh(\003)572 1699 y Fp(\000)e Fo(y)q Fw(\))664 1680 y Fi(T)691 1699 y Fw(\()p Fo(y)738 1680 y Fh(\003)767 1699 y Fp(\000)g Fo(y)q Fw(\))f(+)i([)p Fq(f)5 b Fw(\()p Fo(x)p Fq(;)j Fo(u)p Fw(\))g Fp(\000)1129 1698 y Fw(_)1121 1699 y Fo(x)p Fw(])1162 1680 y Fi(T)1189 1699 y Fo(\010)i Fw(+)g([)p Fq(h)p Fw(\()p Fo(x)p Fq(;)e Fo(y)1417 1680 y Fh(\003)1434 1699 y Fw(\))i Fp(\000)h Fo(u)p Fw(])1550 1680 y Fi(T)1577 1699 y Fo(\011)p Fq(:)150 1811 y Fw(The)21 b(Lagrange)g(m)o(ultipliers)i(ha)o(v)o(e)d(an)h(in)o(terpretation)g(as) g(sensitivities)i(of)d(the)h(cost)g(with)150 1868 y(resp)q(ect)e(to)f (v)m(ariations)h(in)644 1867 y(_)637 1868 y Fo(x)f Fw(and)h Fo(y)q Fw(,)f(resp)q(ectiv)o(ely)l(.)32 b(Because)20 b(these)e(sensitivities)j(b)q(ecome)150 1924 y(partial)14 b(deriv)m(ativ)o(es)g(when)g(the)f(problem)h(is)g(con)o(v)o(erted)e(to) h(discrete)h(time,)g(w)o(e)f(are)f(in)o(terested)150 1981 y(in)k(solving)g(for)f Fo(\011)p Fw(\()p Fq(t)p Fw(\).)241 2037 y(A)k(necessary)g(condition)i(for)e(an)g(optimizing)h (solution)g(is)g(that)e(it)i(satisfy)f(the)g(Euler-)150 2094 y(Lagrange)c(equations)g(\(Gelfand)h(&)f(F)l(omin,)g(1963\):)818 2186 y Fq(@)s(L)p 818 2207 58 2 v 820 2248 a(@)s Fo(x)891 2217 y Fp(\000)949 2186 y Fq(d)p 941 2207 41 2 v 941 2248 a(dt)991 2186 y(@)s(L)p 991 2207 58 2 v 993 2248 a(@)1027 2247 y Fw(_)1020 2248 y Fo(x)1066 2217 y Fw(=)e(0)150 2330 y(and)818 2365 y Fq(@)s(L)p 818 2386 V 819 2427 a(@)s Fo(u)891 2396 y Fp(\000)949 2365 y Fq(d)p 941 2386 41 2 v 941 2427 a(dt)991 2365 y(@)s(L)p 991 2386 58 2 v 992 2427 a(@)1027 2426 y Fw(_)1019 2427 y Fo(u)1066 2396 y Fw(=)g(0)150 2490 y(at)18 b(eac)o(h)g(momen)o(t)g(in)h(time.)30 b(These)19 b(equations)g(are)f(the)g(equiv)m(alen)o(t)i(in)f(function)h (space)e(of)150 2546 y(the)d(familiar)h(pro)q(cedure)g(of)f(setting)g (the)h(partial)f(deriv)m(ativ)o(es)i(equal)f(to)e(zero.)952 2775 y(49)p eop %%Page: 50 50 50 49 bop 241 192 a Fw(Substituting)16 b(for)f Fq(L)p Fw(\()p Fq(t)p Fw(\))g(and)g(simplifying)j(w)o(e)d(obtain:)605 312 y(_)592 324 y Fo(\010)e Fw(=)g Fp(\000)731 293 y Fq(@)s(f)p 731 313 55 2 v 731 355 a(@)s Fo(x)790 275 y Fi(T)818 324 y Fo(\010)c Fp(\000)917 293 y Fq(@)s(k)p 916 313 V 916 355 a(@)s Fo(x)975 275 y Fi(T)1003 324 y Fo(\011)g Fw(+)1106 293 y Fq(@)s(g)p 1104 313 V 1104 355 a(@)s Fo(x)1163 275 y Fi(T)1191 324 y Fw(\()p Fo(y)1238 305 y Fh(\003)1266 324 y Fp(\000)i Fo(y)q Fw(\))150 435 y(and)853 511 y Fo(\011)h Fw(=)960 481 y Fq(@)s(f)p 959 501 56 2 v 959 543 a(@)s Fo(u)1020 462 y Fi(T)1047 511 y Fo(\010)p Fq(:)241 605 y Fw(Using)j(an)g(Euler)h(appro)o(ximation,)f (these)g(equations)g(can)g(b)q(e)h(written)f(in)h(discrete)g(time)150 661 y(as)f(recurrence)h(relations:)327 782 y Fo(\010)p Fw([)p Fq(n)10 b Fp(\000)g Fw(1])i(=)h Fo(\010)p Fw([)p Fq(n)p Fw(])d(+)g Fq(h)733 751 y(@)s(f)p 733 772 55 2 v 733 813 a(@)s Fo(x)793 733 y Fi(T)820 782 y Fo(\010)p Fw([)p Fq(n)p Fw(])f(+)i Fq(h)998 751 y(@)s(k)p 997 772 V 997 813 a(@)s Fo(x)1056 733 y Fi(T)1084 782 y Fo(\011)p Fw([)p Fq(n)p Fw(])e Fp(\000)i Fq(h)1266 751 y(@)s(g)p 1264 772 V 1264 813 a(@)s Fo(x)1323 733 y Fi(T)1351 782 y Fw(\()p Fo(y)1398 763 y Fh(\003)1416 782 y Fw([)p Fq(n)p Fw(])f Fp(\000)g Fo(y)q Fw([)p Fq(n)p Fw(]\))95 b(\(27\))150 894 y(and)796 970 y Fo(\011)p Fw([)p Fq(n)p Fw(])12 b(=)956 939 y Fq(@)s(f)p 955 959 56 2 v 955 1001 a(@)s Fo(u)1016 921 y Fi(T)1043 970 y Fo(\010)p Fw([)p Fq(n)p Fw(])p Fq(;)572 b Fw(\(28\))150 1063 y(where)13 b Fq(h)f Fw(is)h(the)g (sampling)g(p)q(erio)q(d)h(of)e(the)g(discrete)h(appro)o(ximation.)19 b(T)l(o)12 b(utilize)j(these)e(recur-)150 1120 y(rence)i(relations)g (in)g(a)f(discrete-time)i(net)o(w)o(ork,)d(the)i(sampling)g(p)q(erio)q (d)h Fq(h)f Fw(is)g(absorb)q(ed)g(in)g(the)150 1176 y(net)o(w)o(ork)c (appro)o(ximations)i(of)f(the)h(con)o(tin)o(uous-time)g(mappings.)20 b(The)13 b(net)o(w)o(ork)e(appro)o(xima-)150 1233 y(tion)18 b(of)g Fq(f)23 b Fw(m)o(ust)17 b(also)h(include)j(an)c(iden)o(tit)o(y)i (feedforw)o(ard)e(comp)q(onen)o(t)h(to)g(accoun)o(t)g(for)f(the)150 1289 y(initial)g(autoregressiv)o(e)d(term)g(in)h(Equation)g(27.)k(Prem) o(ultiplication)e(of)d(Equation)g(28)g(b)o(y)h(the)150 1346 y(transp)q(ose)f(of)g(the)h(Jacobian)g(matrix)f(\()p Fq(@)s Fo(u)p Fq(=@)s Fo(w)o Fw(\))h(then)f(yields)i(Equations)f(17,)28 b(18,)14 b(and)g(19)g(in)150 1402 y(the)h(main)h(text.)792 1545 y Fv(App)r(endix)23 b(B)150 1647 y Fw(The)13 b(net)o(w)o(orks)f (used)h(in)h(all)g(of)e(the)h(sim)o(ulations)h(w)o(ere)f(standard)f (feedforw)o(ard)h(connectionist)150 1703 y(net)o(w)o(orks)h(\(see)h (Rumelhart,)h(Hin)o(ton,)f(&)h(Williams,)g(1986\).)241 1760 y Fx(A)n(ctivation)c(functions)p Fw(|The)f(input)i(units)f(and)g (the)f(output)g(units)i(of)e(all)h(net)o(w)o(orks)e(w)o(ere)150 1816 y(linear)16 b(and)g(the)f(hidden)i(units)f(w)o(ere)f(logistic)h (with)g(asymptotes)e(of)h Fp(\000)p Fw(1)g(and)g(1.)241 1873 y Fx(Input)d(and)h(tar)n(get)f(values)p Fw(|In)g(the)f(kinematic)h (arm)e(sim)o(ulations,)j(the)e(join)o(t)g(angles)g(w)o(ere)150 1929 y(represen)o(ted)17 b(using)h(the)f(v)o(ector)f([cos\()p Fq(q)844 1936 y Fn(1)875 1929 y Fp(\000)926 1911 y Fi(\031)p 926 1918 22 2 v 928 1945 a Fn(2)953 1929 y Fw(\))p Fq(;)8 b Fw(cos)n(\()p Fq(q)1089 1936 y Fn(2)1109 1929 y Fw(\))p Fq(;)g Fw(cos)o(\()p Fq(q)1246 1936 y Fn(3)1266 1929 y Fw(\)])1297 1913 y Fi(T)1323 1929 y Fw(.)25 b(The)18 b(Cartesian)e(targets)150 1985 y(w)o(ere)f(scaled)h(to)f(lie)h(b)q(et)o (w)o(een)g Fp(\000)p Fw(1)f(and)g(1)g(and)h(fed)f(directly)i(in)o(to)e (the)g(net)o(w)o(ork.)241 2042 y(In)h(the)f(dynamic)h(arm)f(sim)o (ulations,)h(all)g(v)m(ariables|join)o(t)h(angles,)e(angular)h(v)o(elo) q(cities,)150 2098 y(angular)h(accelerations,)h(and)f(torques|w)o(ere)f (scaled)i(and)f(fed)g(directly)i(in)o(to)d(the)h(net)o(w)o(ork.)150 2155 y(The)c(scaling)h(factors)e(w)o(ere)g(c)o(hosen)h(suc)o(h)g(that)f (the)h(scaled)h(v)m(ariables)g(ranged)f(appro)o(ximately)150 2211 y(from)h Fp(\000)p Fw(1)i(to)e(1.)241 2268 y Fx(Initial)h(weights) p Fw(|Initial)i(w)o(eigh)o(ts)e(w)o(ere)f(c)o(hosen)h(randomly)g(from)g (a)f(uniform)h(distribu-)150 2324 y(tion)g(on)h(the)f(in)o(terv)m(al)h ([)p Fp(\000)p Fw(0)p Fq(:)p Fw(5)p Fq(;)8 b Fw(0)p Fq(:)p Fw(5].)241 2381 y Fx(Hidden)17 b(units)p Fw(|A)g(single)i(la)o(y)o(er)d (of)h(50)f(hidden)j(units)e(w)o(as)f(used)i(in)g(all)f(net)o(w)o(orks.) 24 b(No)150 2437 y(attempt)12 b(w)o(as)h(made)g(to)g(optimize)i(the)e (n)o(um)o(b)q(er)h(of)f(the)g(hidden)i(units)f(or)f(their)h (connectivit)o(y)l(.)241 2494 y Fx(Par)n(ameter)j(values)p Fw(|A)f(learning)g(rate)f(of)g(0.1)g(w)o(as)f(used)i(in)h(all)f(of)f (the)h(kinematic)h(arm)150 2550 y(sim)o(ulations.)k(The)15 b(momen)o(tum)g(w)o(as)f(set)h(to)g(0.5.)952 2775 y(50)p eop %%Page: 51 51 51 50 bop 241 192 a Fw(In)19 b(the)f(dynamic)i(arm)e(sim)o(ulations,)h (a)f(learning)i(rate)e(of)g(0.1)f(w)o(as)h(used)h(in)g(all)g(cases,)150 248 y(except)c(for)e(the)i(sim)o(ulation)g(sho)o(wn)f(in)h(Figure)g(24) f(in)h(whic)o(h)g(the)f(learning)i(rate)e(w)o(as)f(manip-)150 304 y(ulated)j(explicitly)l(.)23 b(No)15 b(momen)o(tum)f(w)o(as)h(used) h(in)g(the)f(dynamic)h(arm)e(sim)o(ulations.)792 448 y Fv(App)r(endix)22 b(C)150 549 y Fw(The)16 b(dynamic)h(arm)e(w)o(as)g (mo)q(deled)i(using)g(rigid-b)q(o)q(dy)h(mec)o(hanics.)k(The)16 b(link)i(lengths)e(w)o(ere)150 606 y(0)p Fq(:)p Fw(33)d(m)i(for)f(the)h (pro)o(ximal)g(link)h(and)f(0)p Fq(:)p Fw(32)e(m)i(for)f(the)h(distal)g (link.)21 b(The)15 b(masses)g(of)f(the)h(links)150 662 y(w)o(ere)g(2)p Fq(:)p Fw(52)f(kg)h(and)h(1)p Fq(:)p Fw(3)e(kg.)241 718 y(The)k(mass)f(w)o(as)f(assumed)i(to)f(b)q(e)h (distributed)h(uniformly)g(along)e(the)h(links.)28 b(The)18 b(mo-)150 775 y(men)o(ts)i(of)f(inertia)i(of)e(the)h(links)i(ab)q(out)d (their)i(cen)o(ters)f(of)f(mass)g(w)o(ere)h(therefore)g(giv)o(en)g(b)o (y)150 831 y Fq(I)170 838 y Fi(i)200 831 y Fw(=)c Fq(m)291 838 y Fi(i)305 831 y Fq(l)320 815 y Fn(2)319 843 y Fi(i)340 831 y Fq(=)p Fw(12,)g(yielding)j(0)p Fq(:)p Fw(023)d(kg)c Fp(\001)f Fw(m)852 815 y Fn(2)889 831 y Fw(and)17 b(0)p Fq(:)p Fw(012)f(kg)c Fp(\001)f Fw(m)1221 815 y Fn(2)1257 831 y Fw(for)17 b(the)g(pro)o(ximal)h(and)f(distal)150 888 y(links,)f(resp)q(ectiv)o(ely)l(.)952 2775 y(51)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF