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%!PS-Adobe-2.0 %%Creator: dvips 5.516 Copyright 1986, 1993 Radical Eye Software %%Title: cbcltr.dvi %%CreationDate: Sat Apr 13 19:29:17 1996 %%Pages: 12 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%EndComments %DVIPSCommandLine: dvips -o cbcltr.ps cbcltr.dvi %DVIPSSource: TeX output 1996.04.13:1928 %%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 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y(con)o(tact)f(with,)g(the)f(actual)i(v)o(elo)q(cit)o (y)g(do)q(es)f(not)g(coincide)h(with)f(the)-75 2700 y(nominal)g(v)o (elo)q(cit)o(y)m(.)1013 -71 y Fs(\(MME\))f(and)g(sho)o(w)f(ho)o(w)h (its)g(parameters)f(can)i(b)q(e)f(estimated.)1013 -25 y(The)h(rest)h(of)f(the)g(pap)q(er)h(is)f(organized)g(as)g(follo)o(ws:) k(Section)c(2)1013 20 y(de\014nes)g(the)g(problem,)e(in)h(section)h(3)f (the)h(learning)f(algorithm)1013 66 y(is)j(deriv)o(ed,)h(section)g(4)f (presen)o(ts)i(a)e(sim)o(ulated)e(example)h(and)1013 112 y(section)h(5)f(discusses)i(other)f(asp)q(ects)h(relev)n(an)o(t)f (to)f(the)h(imple-)1013 157 y(men)o(tation)12 b(and)h(directions)i(for) e(further)i(w)o(ork.)1013 251 y Fr(2)74 b(Reac)n(habilit)n(y)18 b(Graphs)h(and)g(Mark)n(o)n(v)1097 309 y(Mixtures)e(of)i(Exp)r(erts) 1013 380 y Fs(F)m(or)12 b(an)o(y)g(assem)o(bly)g(of)g(ob)r(jects,)i (the)g(space)g(of)e(all)g(the)h(relativ)o(e)1013 426 y(degrees)e(of)e(freedom)g(of)h(the)g(ob)r(jects)h(in)e(the)i(assem)o (bly)e(is)g(called)1013 472 y(the)i Fo(c)n(on\014gur)n(ation)j(sp)n(ac) n(e)d Fs(\(C-space\).)19 b(Ev)o(ery)12 b(p)q(ossible)f(con\014g-)1013 517 y(uration)h(of)g(the)h(assem)o(bly)e(is)i(represen)o(ted)i(b)o(y)e (a)f(unique)g(p)q(oin)o(t)1013 563 y(in)e(the)h(C-space)h(and)e(mo)o(v) o(emen)o(t)e(in)j(the)g(real)f(space)i(maps)e(in)o(to)1013 609 y(con)o(tin)o(uous)f(tra)r(jectories)j(in)d(the)i(C-space.)17 b(The)11 b(sets)g(of)e(p)q(oin)o(ts)1013 654 y(corresp)q(onding)k(to)g (eac)o(h)g(state)g(of)f(con)o(tact)h(create)h(a)f(partition)1013 700 y(o)o(v)o(er)g(the)g(C-space.)19 b(Because)c(tra)r(jectories)f(are) g(con)o(tin)o(uous,)e(a)1013 746 y(p)q(oin)o(t)e(can)i(mo)o(v)o(e)e (from)f(a)i(state)i(of)d(con)o(tact)i(only)f(to)g(one)h(of)e(the)1013 791 y(neigh)o(b)q(oring)j(states)j(of)e(con)o(tact)h(.)20 b(This)15 b(can)f(b)q(e)h(depicted)h(b)o(y)1013 837 y(a)11 b(directed)h(graph)g(with)f(v)o(ertices)h(represen)o(ting)i(states)e (of)f(con-)1013 883 y(tact)j(and)f(arcs)i(for)f(the)g(p)q(ossible)g (transitions)g(b)q(et)o(w)o(een)h(them,)1013 928 y(called)c(the)i Fo(r)n(e)n(achability)f(gr)n(aph)p Fs(.)17 b(If)12 b(no)f(constrain)o (ts)i(on)e(the)i(v)o(e-)1013 974 y(lo)q(cities)f(are)i(imp)q(osed,)d (then)j(in)e(the)i(reac)o(habilit)o(y)e(graph)g(eac)o(h)1013 1020 y(state)g(of)g(con)o(tact)g(is)g(connected)i(to)e(all)f(its)h (neigh)o(b)q(ours.)17 b(But)c(if)1013 1065 y(the)g(range)h(of)e(v)o (elo)q(cities)i(restricted,)h(the)e(connectivit)o(y)h(of)e(the)1013 1111 y(graph)j(decreases)j(and)d(the)i(connections)f(are)g(generally)f (non-)1013 1157 y(symmetric.)g(Figure)d(1)g(sho)o(ws)h(an)f(example)f (of)g(a)h(C-space)h(and)1013 1202 y(its)20 b(reac)o(habilit)o(y)f (graph)h(for)g(v)o(elo)q(cities)g(with)g(only)f(p)q(ositiv)o(e)1013 1248 y(comp)q(onenets.)f(On)c(the)h(other)f(hand,)g(longer)g(mo)o(v)o (emen)o(t)d(du-)1013 1294 y(rations)i(b)q(et)o(w)o(een)h(observ)n (ations)g(could)f(allo)o(w)e(more)i(than)g(one)1013 1339 y(state)g(transition)g(to)f(o)q(ccur,)i(leading)e(to)h(an)f(e\013ectiv) o(e)j(increase)1013 1385 y(in)e(the)h(n)o(um)o(b)q(er)g(of)f(neigh)o(b) q(ours)h(of)f(a)h(state.)1061 1431 y(Ideally)m(,)g(in)h(the)h(absence)h (of)e(noise,)h(the)g(states)h(of)d(con)o(tact)1013 1476 y(and)f(ev)o(ery)h(transition)f(through)g(the)h(graph)f(can)h(b)q(e)g (p)q(erfectly)1013 1522 y(observ)o(ed.)21 b(T)m(o)14 b(deal)h(with)f(the)h(uncertain)o(t)o(y)h(in)e(the)h(measure-)1013 1568 y(men)o(ts,)21 b(w)o(e)f(will)f(attac)o(h)i(probabilities)f(to)g (the)h(arcs)g(of)f(the)1013 1613 y(graph)9 b(in)g(the)h(follo)o(wing)d (w)o(a)o(y:)15 b(Let)10 b(us)g(denote)h(b)o(y)e Fk(Q)1841 1619 y Fj(i)1864 1613 y Fs(the)h(set)h(of)1013 1659 y(con\014gurations) f(corresp)q(onding)i(to)f(state)h(of)e(con)o(tact)i Fk(i)f Fs(and)g(let)1013 1705 y(the)f(mo)o(v)o(emen)o(t)e(of)h(a)h(p)q(oin)o (t)g Fk(x)f Fs(with)h(uniform)e(nominal)f(v)o(elo)q(cit)o(y)1013 1750 y Fk(v)16 b Fs(for)e(a)g(time)f(\001)p Fk(T)20 b Fs(b)q(e)15 b(giv)o(en)f(b)o(y)g Fk(x)p Fs(\()p Fk(t)c Fs(+)f(\001)p Fk(T)d Fs(\))13 b(=)f Fk(f)1814 1735 y Fi(\003)1834 1750 y Fs(\()p Fk(x;)7 b(v)q(;)g Fs(\001)p Fk(T)f Fs(\);)1013 1796 y(b)q(oth)17 b Fk(x)g Fs(and)g Fk(v)i Fs(are)e(v)o(ectors)i(of)d(same)g(dimension)g(as)h(the)h(C-)1013 1842 y(space.)g(No)o(w,)13 b(let)h Fk(x)1329 1827 y Fi(0)1340 1842 y Fk(;)k(v)1391 1827 y Fi(0)1417 1842 y Fs(b)q(e)c(the)g(noisy)f (measuremen)o(ts)g(of)g(the)1013 1887 y(true)j(v)n(alues)g Fk(x;)21 b(v)q(;)h(x)15 b Fh(2)f Fk(Q)1454 1893 y Fj(j)1487 1887 y Fs(and)i Fk(P)6 b Fs([)p Fk(x;)h(v)q Fh(j)p Fk(x)1715 1872 y Fi(0)1725 1887 y Fk(;)g(v)1765 1872 y Fi(0)1776 1887 y Fk(;)g(j)r Fs(])16 b(the)g(p)q(oste-)1013 1933 y(rior)11 b(distribution)g(of)h Fk(x;)17 b(v)d Fs(giv)o(en)d(the)h (measuremen)o(ts)g(and)f(the)1013 1979 y(state)g(of)g(con)o(tact)h(.)17 b(Then,)12 b(the)f(probabilit)o(y)f(of)g(transition)h(to)g(a)1013 2024 y(state)i Fk(i)f Fs(from)e(a)i(giv)o(en)g(state)h Fk(j)i Fs(in)d(time)f(\001)p Fk(T)17 b Fs(can)c(b)q(e)g(expressed)1013 2070 y(as:)1040 2202 y Fk(P)6 b Fs([)p Fk(i)p Fh(j)p Fk(x)1135 2184 y Fi(0)1145 2202 y Fk(;)h(v)1185 2184 y Fi(0)1196 2202 y Fk(;)g(j)r Fs(])23 b(=)1324 2145 y Fg(Z)1347 2239 y Fi(f)p Fj(x;v)q Fi(j)p Fj(x)p Fi(2)p Fj(Q)1488 2243 y Ff(j)1503 2239 y Fj(;f)1532 2231 y Fe(\003)1550 2239 y Fn(\()p Fj(x;v)q(;)p Fn(\001)p Fj(T)t Fn(\))p Fi(2)p Fj(Q)1732 2243 y Ff(i)1745 2239 y Fi(g)1398 2202 y Fk(P)6 b Fs([)p Fk(x;)h(v)q Fh(j)p Fk(x)1543 2184 y Fi(0)1552 2202 y Fk(;)g(v)1592 2184 y Fi(0)1604 2202 y Fk(;)g(j)r Fs(])p Fk(dx)g(dv)23 b Fs(=)g Fk(a)1849 2208 y Fj(ij)1878 2202 y Fs(\()p Fk(x)1918 2184 y Fi(0)1930 2202 y Fk(;)7 b(v)1970 2184 y Fi(0)1982 2202 y Fs(\))1972 2283 y(\(1\))1013 2329 y(W)m(e)14 b(de\014ne)i(a)e(transition)g (probabilit)o(y)f(matrix)g Fk(A)g Fs(=)h([)p Fk(a)1904 2335 y Fj(j)r(i)1932 2329 y Fs(])1944 2313 y Fj(m)1944 2339 y(i;j)r Fn(=1)1013 2380 y Fs(and)19 b(assume)g(a)g(measuremen)o(t) g(noise)g Fk(p)p Fs([)p Fk(x)1713 2365 y Fi(0)1724 2380 y Fh(j)p Fk(q)i Fs(=)g Fk(i;)7 b(x)21 b Fh(2)f Fk(Q)1988 2386 y Fj(i)2002 2380 y Fs(].)1013 2426 y(This)h(allo)o(ws)g(us)h(to)g (construct)i(a)e(Hidden)g(Mark)o(o)o(v)f(Mo)q(del)1013 2472 y(\(HMM\))11 b(with)f(output)g Fk(x)h Fs(ha)o(ving)e(a)h(con)o (tinous)h(emission)e(prob-)1013 2517 y(abilit)o(y)e(distribution)j Fk(p)f Fs(and)h(where)g(the)h(state)f(of)f(con)o(tact)i(pla)o(ys)1013 2563 y(the)k(role)g(of)f(a)h(hidden)g(state)h(v)n(ariable.)j(Our)d (main)d(goal)g(is)i(to)1013 2609 y(estimate)e(this)h(mo)q(del)e(from)g (observ)o(ed)j(data.)1061 2654 y(T)m(o)c(giv)o(e)g(a)g(general)h (statemen)o(t)f(of)g(the)h(problem)e(w)o(e)i(will)e(as-)1013 2700 y(sume)j(that)g(all)g(p)q(osition,)g(v)o(elo)q(cit)o(y)g(and)g (force)i(measuremen)o(ts)965 2727 y(1)p eop %%Page: 2 3 2 2 bop -50 -112 a 13948346 14506278 5723013 17958420 32627752 46047232 startTexFig -50 -112 a %%BeginDocument: cbcltr-2dspace.ps save /d_sv_obj exch def userdict /IslandDrawDict 300 dict dup begin put /bdef {bind def} bind def /E {exch} bdef /FF {findfont} bdef /MF {makefont} bdef /RO {rotate} bdef /SC {scale} bdef /SF {setfont} bdef /SG {setgray} bdef /TR {translate} bdef /bp {lj lw rgb} bdef /bpbw {lj lw setgray} bdef /c {curveto} bdef /cl {closepath} bdef /fi {eofill} bdef /g {setgray} bdef /gr {grestore} bdef /gs {gsave} bdef /l {lineto} bdef /lj {setlinejoin} bdef /lw {setlinewidth} bdef /m {moveto} bdef /n {newpath} bdef /nx {/x E def} bdef /r {rmoveto} bdef /rl {rlineto} bdef /rgb {setrgbcolor} bdef /s {show} bdef /sd {setdash} bdef /sp {x 0 rmoveto} bdef /ss {currentpoint pop E m} bdef /st {stroke} bdef /BPSIDE 32 def %% pixels per pattern side /PATFREQ 3.0 def %% pattern pixels per mm /dp_mat [PATFREQ 0 0 PATFREQ 0 0] def /dp_pw BPSIDE def %% pattern pixel width /dp_ph BPSIDE def %% pattern pixel height /dp_w dp_pw PATFREQ div def %% pattern mm width /dp_h dp_ph PATFREQ div def %% pattern mm height /savemat matrix def /topmat matrix def /patmat matrix def /ncpoint errordict /nocurrentpoint get def errordict begin /nocurrentpoint { dup /pathbbox load eq {pop 0 0 1 1} {ncpoint} ifelse } bdef end /ar { %% sa ea sx sy rot tx ty matrix currentmatrix 8 1 roll TR RO SC n 0 0 1 5 3 roll arc setmatrix } bdef /arn { %% sa ea sx sy rot tx ty TR RO SC matrix currentmatrix 8 1 roll n 0 0 1 5 3 roll arcn setmatrix } bdef /el { %% sx sy rot tx ty matrix currentmatrix 6 1 roll TR RO SC n 0 0 1 0 360 arc setmatrix cl } bdef /image_raster { %% sw sh sd dw dh xs ys TR SC /sd E def /sh E def /sw E def /imagebuf sw sd mul 7 add 8 idiv string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop} image } bdef /imagemask_raster { TR SC /sh E def /sw E def /imagebuf sw 7 add 8 idiv string def sw sh false [sw 0 0 sh 0 0] {currentfile imagebuf readhexstring pop} imagemask } bdef /dither_color_raster { % bool sw sh sd dw dh xs ys TR SC /sd E def /sh E def /sw E def sd 8 eq and { /imagebuf 3 string def /grayval 1 string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop pop imagebuf 0 get 0.299 mul imagebuf 1 get 0.587 mul add imagebuf 2 get 0.114 mul add cvi grayval exch 0 exch put grayval } image } { /imagebuf sw 3 mul sd mul 7 add 8 idiv string def sh { currentfile imagebuf readhexstring pop pop } repeat } ifelse } bdef /image_color_raster { % bool sw sh sd dw dh xs ys /colorimage where not { dither_color_raster } { pop TR SC /sd E def /sh E def /sw E def pop /imagebuf sw 3 mul sd mul 7 add 8 idiv string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop} false 3 colorimage } ifelse } bdef /patpath { /inv E def topmat setmatrix pathbbox %% get lo - hi indecies /hy E dp_h div floor cvi def /hx E dp_w div floor cvi def /ly E dp_h div floor cvi def /lx E dp_w div floor cvi def lx 1 hx { dp_w mul ly 1 hy { dp_h mul E dup 3 1 roll E patmat currentmatrix pop TR dp_pw dp_ph inv dp_mat dp_proc imagemask patmat setmatrix } for pop } for } bdef /setpattern { /blue E def /green E def /red E def /freq E def /bwidth E def /bpside E def /bstring E def /onbits 0 def /offbits 0 def freq 0 {/y E def /x E def /xindex x 1 add 2 div bpside mul cvi def /yindex y 1 add 2 div bpside mul cvi def bstring yindex bwidth mul xindex 8 idiv add get not 1 7 xindex 8 mod sub bitshift and 0 ne {/onbits onbits 1 add def 1} {/offbits offbits 1 add def 0} ifelse } setscreen {} settransfer systemdict /setcmykcolor known { /fact 1 onbits offbits onbits add div sub def 1 red sub fact mul 1 green sub fact mul 1 blue sub fact mul 0 setcmykcolor } { offbits offbits onbits add div setgray} ifelse } bdef /dmatrix matrix def /dpi 72 0 dmatrix defaultmatrix dtransform dup mul E dup mul add sqrt def /B {gs bp st gr} bdef %% brush: gr lw lj /Bbw {gs bpbw st gr} bdef %% brush: gr lw lj /F {gs rgb eofill gr} bdef %% fill: gr /Fbw {gs setgray eofill gr} bdef %% fill: gr /PB {gs lj lw setpattern st gr} bdef /PF {gs eoclip patpath gr} bdef /BB {gs rgb lj lw strokepath clip patpath gr} bdef /xdef {exch def} bdef /clip_region { /ht xdef /wd xdef /bm xdef /lm xdef newpath lm bm moveto 0 ht rlineto wd 0 rlineto 0 ht neg rlineto closepath clip } bdef /reencode_small_dict 12 dict def /ReencodeSmall { reencode_small_dict begin /new_codes_and_names exch def /new_font_name exch def /base_font_name exch def /base_font_dict base_font_name findfont def /newfont base_font_dict maxlength dict def base_font_dict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName new_font_name put new_codes_and_names aload pop new_codes_and_names length 2 idiv { newfont /Encoding get 3 1 roll put } repeat new_font_name newfont definefont pop end %reencode_small_dict } def /extended_Zapf [ 8#223 /a89 8#224 /a90 8#225 /a93 8#226 /a94 8#227 /a91 8#230 /a92 8#231 /a205 8#232 /a85 8#233 /a206 8#234 /a86 8#235 /a87 8#236 /a88 8#237 /a95 8#240 /a96 ] def /extended_Standard [ 29 /thorn 30 /yacute 31 /divide 128 /Acircumflex 129 /Adieresis 130 /Agrave 131 /Aring 132 /Atilde 133 /Ccedilla 134 /Eacute 135 /Ecircumflex 136 /Edieresis 137 /Egrave 138 /Iacute 139 /Icircumflex 140 /Idieresis 141 /Igrave 142 /Ntilde 143 /Oacute 144 /Ocircumflex 145 /Odieresis 146 /Ograve 147 /Otilde 148 /Scaron 149 /Uacute 150 /Ucircumflex 151 /Udieresis 152 /Ugrave 153 /Ydieresis 154 /Zcaron 155 /aacute 156 /acircumflex 157 /adieresis 158 /agrave 159 /aring 160 /atilde 161 /exclamdown 162 /cent 163 /sterling 164 /fraction 165 /yen 166 /florin 167 /section 168 /currency 169 /quotesingle 170 /quotedblleft 171 /guillemotleft 172 /guilsinglleft 173 /guilsinglright 174 /fi 175 /fl 176 /plusminus 177 /endash 178 /dagger 179 /daggerdbl 180 /periodcentered 181 /twosuperior 182 /paragraph 183 /bullet 184 /quotesinglbase 185 /quotedblbase 186 /quotedblright 187 /guillemotright 188 /ellipsis 189 /perthousand 190 /threesuperior 191 /questiondown 192 /mu 193 /grave 194 /acute 195 /circumflex 196 /tilde 197 /macron 198 /breve 199 /dotaccent 200 /dieresis 201 /onesuperior 202 /ring 203 /cedilla 204 /onequarter 205 /hungarumlaut 206 /ogonek 207 /caron 208 /emdash 209 /ccedilla 210 /copyright 211 /eacute 212 /ecircumflex 213 /edieresis 214 /egrave 215 /iacute 216 /icircumflex 217 /idieresis 218 /igrave 219 /logicalnot 220 /minus 221 /ntilde 222 /oacute 223 /ocircumflex 224 /odieresis 225 /AE 226 /onehalf 227 /ordfeminine 228 /ograve 229 /otilde 230 /registered 231 /scaron 232 /Lslash 233 /Oslash 234 /OE 235 /ordmasculine 236 /trademark 237 /uacute 238 /ucircumflex 239 /udieresis 240 /ugrave 241 /ae 242 /ydieresis 243 /zcaron 244 /Aacute 245 /dotlessi 246 /threequarters 247 /Eth 248 /lslash 249 /oslash 250 /oe 251 /germandbls 252 /multiply 253 /Yacute 254 /Thorn 255 /eth ] def /extended_Symbol [ ] def /extend_font { % stack: fontname newfontname exch dup (ZapfDingbats) eq { cvn exch cvn extended_Zapf ReencodeSmall } { dup (Symbol) eq { cvn exch cvn extended_Symbol ReencodeSmall } { cvn exch cvn extended_Standard ReencodeSmall } ifelse } ifelse } bind def /extend_font_name { % stack: font_name_string dup length 1 add string /extended_font_name exch def extended_font_name 0 (_) putinterval extended_font_name 1 3 -1 roll putinterval extended_font_name } bind def /gf { /f exch def f cvn where { f exch begin cvn load exec setfont end } { f 0 f length 8 sub getinterval dup /localfont exch extend_font_name def localfont extend_font localfont findfont /xsz f f length 4 sub 4 getinterval cvi def /ysz f f length 8 sub 4 getinterval cvi def [ xsz 0 0 ysz neg 0 0 ] makefont dup f cvn exch def setfont } ifelse } bind def /ul { % space drop thickness gs currentpoint currentlinewidth currentpoint n m 6 -3 roll lw 0 exch r 0 rl st lw m gr } bind def /nxtab { currentpoint pop 1000.0 mul cvi tab mod tab exch sub 1000.0 div 0 rmoveto } bind def /nx { /x exch def } bind def 0. nx gsave 2.83465 -2.83465 scale 0 -279.4 translate topmat currentmatrix pop n 50.722 63.556 m 152.47 63.556 l gsave 0 0 0 0.176 0 B grestore n 151.86 63.556 m 151.86 165 l gsave 0 0 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cl 0 0 0 F n 36.056 165 m 170.14 165 l gsave 0 0 0 0 0 B grestore n 50.722 34.833 m 51.556 37.333 l 49.889 37.333 l cl 0 0 0 F n 50.722 174.78 m 50.722 37.333 l gsave 0 0 0 0 0 B grestore n 78.833 124.97 m 133.53 107.86 l n 133.53 107.86 m 131.39 109.4 l 130.89 107.81 l cl 0 0 0 F n 78.833 124.97 m 131.14 108.61 l gsave 0 0 0 0 0 B grestore n savemat currentmatrix pop [1 0 0 1 158.889 181.194] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Helvetica04000400) gf 0.00 0.00 0.00 rgb (x) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 63.25 42.7778] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Helvetica04000400) gf 0.00 0.00 0.00 rgb (y) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 121 100.222] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Helvetica04000400) gf 0.00 0.00 0.00 rgb (v) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 89.8333 55.9167] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Helvetica04000400) gf 0.00 0.00 0.00 rgb (A) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 160.111 108.167] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Helvetica04000400) gf 0.00 0.00 0.00 rgb (B) s savemat setmatrix userdict /#copies 1 put grestore end d_sv_obj restore %%EndDocument endTexFig 883 206 a 16884804 9472573 24602378 36903567 33351352 42692362 startTexFig 883 206 a %%BeginDocument: cbcltr-reach.ps save /d_sv_obj exch def userdict /IslandDrawDict 300 dict dup begin put /bdef {bind def} bind def /E {exch} bdef /FF {findfont} bdef /MF {makefont} bdef /RO {rotate} bdef /SC {scale} bdef /SF {setfont} bdef /SG {setgray} bdef /TR {translate} bdef /bp {lj lw rgb} bdef /bpbw {lj lw setgray} bdef /c {curveto} bdef /cl {closepath} bdef /fi {eofill} bdef /g {setgray} bdef /gr {grestore} bdef /gs {gsave} bdef /l {lineto} bdef /lj {setlinejoin} bdef /lw {setlinewidth} bdef /m {moveto} bdef /n {newpath} bdef /nx {/x E def} bdef /r {rmoveto} bdef /rl {rlineto} bdef /rgb {setrgbcolor} bdef /s {show} bdef /sd {setdash} bdef /sp {x 0 rmoveto} bdef /ss {currentpoint pop E m} bdef /st {stroke} bdef /BPSIDE 32 def %% pixels per pattern side /PATFREQ 3.0 def %% pattern pixels per mm /dp_mat [PATFREQ 0 0 PATFREQ 0 0] def /dp_pw BPSIDE def %% pattern pixel width /dp_ph BPSIDE def %% pattern pixel height /dp_w dp_pw PATFREQ div def %% pattern mm width /dp_h dp_ph PATFREQ div def %% pattern mm height /savemat matrix def /topmat matrix def /patmat matrix def /ncpoint errordict /nocurrentpoint get def errordict begin /nocurrentpoint { dup /pathbbox load eq {pop 0 0 1 1} {ncpoint} ifelse } bdef end /ar { %% sa ea sx sy rot tx ty matrix currentmatrix 8 1 roll TR RO SC n 0 0 1 5 3 roll arc setmatrix } bdef /arn { %% sa ea sx sy rot tx ty TR RO SC matrix currentmatrix 8 1 roll n 0 0 1 5 3 roll arcn setmatrix } bdef /el { %% sx sy rot tx ty matrix currentmatrix 6 1 roll TR RO SC n 0 0 1 0 360 arc setmatrix cl } bdef /image_raster { %% sw sh sd dw dh xs ys TR SC /sd E def /sh E def /sw E def /imagebuf sw sd mul 7 add 8 idiv string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop} image } bdef /imagemask_raster { TR SC /sh E def /sw E def /imagebuf sw 7 add 8 idiv string def sw sh false [sw 0 0 sh 0 0] {currentfile imagebuf readhexstring pop} imagemask } bdef /dither_color_raster { % bool sw sh sd dw dh xs ys TR SC /sd E def /sh E def /sw E def sd 8 eq and { /imagebuf 3 string def /grayval 1 string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop pop imagebuf 0 get 0.299 mul imagebuf 1 get 0.587 mul add imagebuf 2 get 0.114 mul add cvi grayval exch 0 exch put grayval } image } { /imagebuf sw 3 mul sd mul 7 add 8 idiv string def sh { currentfile imagebuf readhexstring pop pop } repeat } ifelse } bdef /image_color_raster { % bool sw sh sd dw dh xs ys /colorimage where not { dither_color_raster } { pop TR SC /sd E def /sh E def /sw E def pop /imagebuf sw 3 mul sd mul 7 add 8 idiv string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop} false 3 colorimage } ifelse } bdef /patpath { /inv E def topmat setmatrix pathbbox %% get lo - hi indecies /hy E dp_h div floor cvi def /hx E dp_w div floor cvi def /ly E dp_h div floor cvi def /lx E dp_w div floor cvi def lx 1 hx { dp_w mul ly 1 hy { dp_h mul E dup 3 1 roll E patmat currentmatrix pop TR dp_pw dp_ph inv dp_mat dp_proc imagemask patmat setmatrix } for pop } for } bdef /setpattern { /blue E def /green E def /red E def /freq E def /bwidth E def /bpside E def /bstring E def /onbits 0 def /offbits 0 def freq 0 {/y E def /x E def /xindex x 1 add 2 div bpside mul cvi def /yindex y 1 add 2 div bpside mul cvi def bstring yindex bwidth mul xindex 8 idiv add get not 1 7 xindex 8 mod sub bitshift and 0 ne {/onbits onbits 1 add def 1} {/offbits offbits 1 add def 0} ifelse } setscreen {} settransfer systemdict /setcmykcolor known { /fact 1 onbits offbits onbits add div sub def 1 red sub fact mul 1 green sub fact mul 1 blue sub fact mul 0 setcmykcolor } { offbits offbits onbits add div setgray} ifelse } bdef /dmatrix matrix def /dpi 72 0 dmatrix defaultmatrix dtransform dup mul E dup mul add sqrt def /B {gs bp st gr} bdef %% brush: gr lw lj /Bbw {gs bpbw st gr} bdef %% brush: gr lw lj /F {gs rgb eofill gr} bdef %% fill: gr /Fbw {gs setgray eofill gr} bdef %% fill: gr /PB {gs lj lw setpattern st gr} bdef /PF {gs eoclip patpath gr} bdef /BB {gs rgb lj lw strokepath clip patpath gr} bdef /xdef {exch def} bdef /clip_region { /ht xdef /wd xdef /bm xdef /lm xdef newpath lm bm moveto 0 ht rlineto wd 0 rlineto 0 ht neg rlineto closepath clip } bdef /reencode_small_dict 12 dict def /ReencodeSmall { reencode_small_dict begin /new_codes_and_names exch def /new_font_name exch def /base_font_name exch def /base_font_dict base_font_name findfont def /newfont base_font_dict maxlength dict def base_font_dict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName new_font_name put new_codes_and_names aload pop new_codes_and_names length 2 idiv { newfont /Encoding get 3 1 roll put } repeat new_font_name newfont definefont pop end %reencode_small_dict } def /extended_Zapf [ 8#223 /a89 8#224 /a90 8#225 /a93 8#226 /a94 8#227 /a91 8#230 /a92 8#231 /a205 8#232 /a85 8#233 /a206 8#234 /a86 8#235 /a87 8#236 /a88 8#237 /a95 8#240 /a96 ] def /extended_Standard [ 29 /thorn 30 /yacute 31 /divide 128 /Acircumflex 129 /Adieresis 130 /Agrave 131 /Aring 132 /Atilde 133 /Ccedilla 134 /Eacute 135 /Ecircumflex 136 /Edieresis 137 /Egrave 138 /Iacute 139 /Icircumflex 140 /Idieresis 141 /Igrave 142 /Ntilde 143 /Oacute 144 /Ocircumflex 145 /Odieresis 146 /Ograve 147 /Otilde 148 /Scaron 149 /Uacute 150 /Ucircumflex 151 /Udieresis 152 /Ugrave 153 /Ydieresis 154 /Zcaron 155 /aacute 156 /acircumflex 157 /adieresis 158 /agrave 159 /aring 160 /atilde 161 /exclamdown 162 /cent 163 /sterling 164 /fraction 165 /yen 166 /florin 167 /section 168 /currency 169 /quotesingle 170 /quotedblleft 171 /guillemotleft 172 /guilsinglleft 173 /guilsinglright 174 /fi 175 /fl 176 /plusminus 177 /endash 178 /dagger 179 /daggerdbl 180 /periodcentered 181 /twosuperior 182 /paragraph 183 /bullet 184 /quotesinglbase 185 /quotedblbase 186 /quotedblright 187 /guillemotright 188 /ellipsis 189 /perthousand 190 /threesuperior 191 /questiondown 192 /mu 193 /grave 194 /acute 195 /circumflex 196 /tilde 197 /macron 198 /breve 199 /dotaccent 200 /dieresis 201 /onesuperior 202 /ring 203 /cedilla 204 /onequarter 205 /hungarumlaut 206 /ogonek 207 /caron 208 /emdash 209 /ccedilla 210 /copyright 211 /eacute 212 /ecircumflex 213 /edieresis 214 /egrave 215 /iacute 216 /icircumflex 217 /idieresis 218 /igrave 219 /logicalnot 220 /minus 221 /ntilde 222 /oacute 223 /ocircumflex 224 /odieresis 225 /AE 226 /onehalf 227 /ordfeminine 228 /ograve 229 /otilde 230 /registered 231 /scaron 232 /Lslash 233 /Oslash 234 /OE 235 /ordmasculine 236 /trademark 237 /uacute 238 /ucircumflex 239 /udieresis 240 /ugrave 241 /ae 242 /ydieresis 243 /zcaron 244 /Aacute 245 /dotlessi 246 /threequarters 247 /Eth 248 /lslash 249 /oslash 250 /oe 251 /germandbls 252 /multiply 253 /Yacute 254 /Thorn 255 /eth ] def /extended_Symbol [ ] def /extend_font { % stack: fontname newfontname exch dup (ZapfDingbats) eq { cvn exch cvn extended_Zapf ReencodeSmall } { dup (Symbol) eq { cvn exch cvn extended_Symbol ReencodeSmall } { cvn exch cvn extended_Standard ReencodeSmall } ifelse } ifelse } bind def /extend_font_name { % stack: font_name_string dup length 1 add string /extended_font_name exch def extended_font_name 0 (_) putinterval extended_font_name 1 3 -1 roll putinterval extended_font_name } bind def /gf { /f exch def f cvn where { f exch begin cvn load exec setfont end } { f 0 f length 8 sub getinterval dup /localfont exch extend_font_name def localfont extend_font localfont findfont /xsz f f length 4 sub 4 getinterval cvi def /ysz f f length 8 sub 4 getinterval cvi def [ xsz 0 0 ysz neg 0 0 ] makefont dup f cvn exch def setfont } ifelse } bind def /ul { % space drop thickness gs currentpoint currentlinewidth currentpoint n m 6 -3 roll lw 0 exch r 0 rl st lw m gr } bind def /nxtab { currentpoint pop 1000.0 mul cvi tab mod tab exch sub 1000.0 div 0 rmoveto } bind def /nx { /x exch def } bind def 0. nx gsave 2.83465 -2.83465 scale 0 -279.4 translate topmat currentmatrix pop n savemat currentmatrix pop [1 -0 -0 1 139.93 77.485] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Helvetica01800180) gf 0.00 0.00 0.00 rgb (C) s savemat setmatrix n savemat currentmatrix pop [1 -0 -0 1 163.628 56.326] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Helvetica01800180) gf 0.00 0.00 0.00 rgb (G) s savemat setmatrix n savemat currentmatrix pop [1 -0 -0 1 155.729 71.278] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Helvetica01800180) gf 0.00 0.00 0.00 rgb (B stick) s savemat setmatrix n savemat currentmatrix pop [1 -0 -0 1 167.014 80.306] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Helvetica01800180) gf 0.00 0.00 0.00 rgb (B slide) s savemat setmatrix n savemat currentmatrix pop [1 -0 -0 1 146.419 61.968] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Helvetica01800180) gf 0.00 0.00 0.00 rgb (A stick) s savemat setmatrix n savemat currentmatrix pop [1 -0 -0 1 135.134 54.916] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Helvetica01800180) gf 0.00 0.00 0.00 rgb (A slide) s savemat setmatrix n 143.74 74.583 m 163.2 57.232 l gsave 0 0 0 0 0 B grestore n 160.63 58.583 m 163.2 57.232 l 161.57 59.636 l 0 0 0 F n 160.63 58.583 m 163.2 57.232 l 161.57 59.636 l gsave 0 0 0 0 0 B grestore n 144.58 75.852 m 154.88 71.62 l gsave 0 0 0 0 0 B grestore n 152 72.04 m 154.88 71.62 l 152.54 73.345 l 0 0 0 F n 152 72.04 m 154.88 71.62 l 152.54 73.345 l gsave 0 0 0 0 0 B grestore n 142.19 73.877 m 148.53 62.734 l gsave 0 0 0 0 0 B grestore n 146.53 64.836 m 148.53 62.734 l 147.75 65.534 l 0 0 0 F n 146.53 64.836 m 148.53 62.734 l 147.75 65.534 l gsave 0 0 0 0 0 B grestore n 144.44 77.404 m 164.62 78.532 l gsave 0 0 0 0 0 B grestore n 161.84 77.67 m 164.62 78.532 l 161.76 79.079 l 0 0 0 F n 161.84 77.67 m 164.62 78.532 l 161.76 79.079 l gsave 0 0 0 0 0 B grestore n 140.64 73.877 m 138.94 55.963 l gsave 0 0 0 0 0 B grestore n 138.51 58.838 m 138.94 55.963 l 139.91 58.705 l 0 0 0 F n 138.51 58.838 m 138.94 55.963 l 139.91 58.705 l gsave 0 0 0 0 0 B grestore n 162.64 67.389 m 164.9 58.079 l gsave 0 0 0 0 0 B grestore n 163.55 60.654 m 164.9 58.079 l 164.92 60.987 l 0 0 0 F n 163.55 60.654 m 164.9 58.079 l 164.92 60.987 l gsave 0 0 0 0 0 B grestore n 173.78 76.134 m 166.87 58.079 l gsave 0 0 0 0 0 B grestore n 167.22 60.966 m 166.87 58.079 l 168.54 60.461 l 0 0 0 F n 167.22 60.966 m 166.87 58.079 l 168.54 60.461 l gsave 0 0 0 0 0 B grestore n 153.61 58.361 m 162.5 55.963 l gsave 0 0 0 0 0 B grestore n 159.59 56.017 m 162.5 55.963 l 159.96 57.379 l 0 0 0 F n 159.59 56.017 m 162.5 55.963 l 159.96 57.379 l gsave 0 0 0 0 0 B grestore n 147.12 53.565 m 162.22 53.847 l gsave 0 0 0 0 0 B grestore n 149.93 54.323 m 147.12 53.565 l 149.96 52.912 l 0 0 0 F n 149.93 54.323 m 147.12 53.565 l 149.96 52.912 l gsave 0 0 0 0 0 B grestore n 159.41 53.089 m 162.22 53.847 l 159.38 54.499 l 0 0 0 F n 159.41 53.089 m 162.22 53.847 l 159.38 54.499 l gsave 0 0 0 0 0 B grestore n 151.22 58.22 m 142.75 55.822 l gsave 0 0 0 0 0 B grestore n 148.69 56.772 m 151.22 58.22 l 148.31 58.129 l 0 0 0 F n 148.69 56.772 m 151.22 58.22 l 148.31 58.129 l gsave 0 0 0 0 0 B grestore n 145.27 57.269 m 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y(and)e(to)h(represen)o(t)h(it)e(b)o(y)h(a)f(di\013eren)o(t)h (function)f(\(i.e)g(a)g(di\013eren)o(t)-75 2262 y(set)k(of)f (parameters)g Fk(\022)275 2268 y Fj(k)296 2262 y Fs(\))g(on)g(eac)o(h)h (of)e(the)i(sub)q(domains;)e(when)-75 2308 y Fk(f)t Fs(\()p Fk(u;)7 b(\022)27 2314 y Fj(k)48 2308 y Fs(\))15 b(will)e(b)q(ear)j(ph) o(ysical)e(signi\014cance,)h(the)h(name)d Fo(move-)-75 2354 y(ment)h(mo)n(del)e Fs(will)f(b)q(e)i(to)f(them,)g(but)h(in)f (general)g(eac)o(h)h Fk(f)t Fs(\()p Fk(u;)7 b(\022)900 2360 y Fj(k)921 2354 y Fs(\))-75 2399 y(will)12 b(b)q(e)j(refered)g(to) f(as)g(a)g Fo(mo)n(dule)p Fs(.)-26 2445 y(The)19 b(ev)o(olution)f(of)g Fk(q)i Fs(is)e(con)o(trolled)h(b)o(y)f(a)h(Mark)o(o)o(v)f(c)o(hain)-75 2491 y(whic)o(h)c(dep)q(ends)h(on)f Fk(u)g Fs(and)f(of)h(a)f(set)i(of)e (parameters)h Fk(W)828 2497 y Fj(j)846 2491 y Fs(:)-75 2548 y Fk(a)-53 2554 y Fj(ij)-24 2548 y Fs(\()p Fk(u)p Fs(\()p Fk(t)p Fs(\))p Fk(;)7 b(W)121 2554 y Fj(j)139 2548 y Fs(\))k(=)h Fk(P)6 b(r)q Fs([)p Fk(q)q Fs(\()p Fk(t)p Fs(+1\))11 b(=)h Fk(i)p Fh(j)p Fk(q)q Fs(\()p Fk(t)p Fs(\))f(=)h Fk(j;)7 b(u)p Fs(\()p Fk(t)p Fs(\)])34 b Fk(t)11 b Fs(=)h(0)p Fk(;)7 b Fs(1)p Fk(;)g(:)g(:)g(:)-75 2606 y Fs(with)64 2624 y Fg(X)88 2712 y Fj(i)131 2663 y Fk(a)153 2669 y Fj(ij)182 2663 y Fs(\()p Fk(u;)g(W)280 2669 y Fj(j)297 2663 y Fs(\))12 b(=)g(1)34 b Fk(j)14 b Fs(=)e(1)p Fk(;)7 b(:)g(:)g(:)e(;)i(m)23 b Fh(8)p Fk(u;)7 b(W)777 2669 y Fj(j)794 2663 y Fk(:)78 b Fs(\(2\))1013 1166 y(Figure)14 b(2)h(depicts)h(this)f(arc)o(hitecture.)23 b(It)15 b(can)g(b)q(e)g(easily)g(seen)1013 1212 y(that)j(this)h(mo)q (del)f(generalizes)h(the)h(mixture)d(of)i(exp)q(erts)h(ar-)1013 1258 y(c)o(hitecture)c([7],)e(to)h(whic)o(h)g(it)g(reduces)i(in)e(the)g (case)i(where)f Fk(a)1996 1264 y Fj(ij)1013 1303 y Fs(are)h(indep)q (enden)o(t)i(of)e Fk(j)j Fs(\(the)e(columns)e(of)h Fk(A)h Fs(are)f(all)g(equal\).)1013 1349 y(It)h(b)q(ecomes)g(the)h(mo)q(del)e (of)g([1])g(when)i Fk(A)f Fs(and)g Fk(f)23 b Fs(are)c(neural)1013 1395 y(net)o(w)o(orks.)i(A)15 b(mo)q(del)f(where)i(the)f(Mark)o(o)o(v)f (c)o(hain)h(transitions)1013 1440 y(are)i(implemen)o(ted)f(b)o(y)h(a)g (recurren)o(t)j(net)o(w)o(ork)e(w)o(as)f(prop)q(osed)1013 1486 y(in)c([3)o(].)1013 1579 y Fr(3)56 b(An)19 b(EM)f(Algorithm)f(for) i(MME)1013 1651 y Fs(T)m(o)26 b(estimate)g(the)i(v)n(alues)f(of)f(the)i (unkno)o(wn)f(parameters)1013 1697 y Fk(\033)1038 1682 y Fn(2)1056 1697 y Fk(;)f(W)1133 1703 y Fj(k)1154 1697 y Fk(;)f(\022)1210 1703 y Fj(k)1231 1697 y Fk(;)h(k)20 b Fs(=)g(1)p Fk(;)7 b(:)g(:)g(:)t(;)g(m)38 b Fs(giv)o(en)18 b(the)h(sequence)h(of)e(ob-)1013 1742 y(serv)n(ations)1206 1727 y Fn(2)1238 1742 y Fk(u)p 1262 1731 53 2 v 14 x Fn(0)p Fj(;T)1314 1742 y Fk(;)c(y)p 1360 1731 V 14 x Fn(0)p Fj(;T)1413 1742 y Fk(;)k(T)f(>)12 b Fs(0)h(and)h(a)g(prior)f (probabilit)o(y)g(of)1013 1795 y(the)h(initial)e(state)1315 1866 y Fk(\031)1339 1872 y Fj(j)1356 1866 y Fs(\(0\))23 b(=)h Fk(P)6 b(r)q Fs([)p Fk(q)q Fs(\(0\))k(=)i Fk(j)r Fs(])p Fk(:)1013 1937 y Fs(the)f Fo(Exp)n(e)n(ctation)h(Maximization)f Fs(\(EM\))g([4)o(])f(algorithm)e(will)h(b)q(e)1013 1983 y(used.)1061 2028 y(The)21 b(EM)g(algorithm)e(is)h(an)h(iterativ)o(e)f (pro)q(cedure)j(whic)o(h)1013 2074 y(con)o(v)o(erges)11 b(asymptotically)e(to)h(a)h(lo)q(cal)f(maxim)n(um)c(of)k(the)i(lik)o (e-)1013 2120 y(liho)q(o)q(d)17 b(function.)33 b(It)19 b(requires)i(the)e(in)o(tro)q(duction)g(of)f(unob-)1013 2165 y(serv)o(ed)g(v)n(ariables,)f(whic)o(h,)h(in)e(our)i(case)g(will)e (b)q(e)i(the)g(hidden)1013 2218 y(state)13 b(v)n(ariables)g Fh(f)p Fk(q)q Fs(\()p Fk(t)p Fs(\))p Fh(g)1394 2197 y Fj(T)1394 2231 y(t)p Fn(=0)1450 2218 y Fs(.)18 b(Then)c(it)e(attempts)h (to)g(maximi)o(ze)1013 2264 y(a)i Fo(c)n(omplete)i Fs(lik)o(eliho)q(o)q (d)d(function)i Fk(l)1590 2270 y Fj(c)1623 2264 y Fs(whic)o(h)h(dep)q (ends)g(on)f(the)1013 2309 y(extended)f(set)g(of)e(v)n(ariables.)1061 2355 y(This)d(pro)q(cess)h(is)e(iterativ)o(e,)h(eac)o(h)g(iteration)g (comprising)d(t)o(w)o(o)1013 2401 y(steps.)19 b(The)13 b(\014rst)h(step)h(\(Exp)q(ectation)f(or)f(E\))h(\014nds)f(the)h (distri-)1013 2446 y(bution)k(of)h(the)g(unobserv)o(ed)h(v)n(ariables)f (giv)o(en)f(the)i(observ)o(ed)1013 2492 y(v)n(ariables)d(and)h(the)h (curren)o(t)g(estimates)f(of)g(the)g(parameters;)1013 2538 y(then)c(it)g(computes)g(the)g(exp)q(ectation)h(of)e Fk(l)1688 2544 y Fj(c)1720 2538 y Fs(w.r.t.)k(this)d(distri-)1013 2583 y(bution.)p 1013 2608 250 2 v 1064 2635 a Fm(2)1082 2651 y Fd(s)p 1100 2642 68 2 v 11 x Fc(t)1112 2667 y Fb(1)1128 2662 y Fc(;t)1149 2667 y Fb(2)1178 2651 y Fq(=)c Fp(f)h Fd(s)p Fq(\()p Fd(t)1295 2655 y Fm(1)1312 2651 y Fq(\))p Fd(;)6 b(s)p Fq(\()p Fd(t)1391 2655 y Fm(1)1413 2651 y Fq(+)f(1\))p Fd(;)i(:)f(:)g(:)g(;)g(s)p Fq(\()p Fd(t)1615 2655 y Fm(2)1632 2651 y Fq(\))p Fp(g)11 b Fq(denotes)h(the)g (sequence)1013 2700 y(of)g(v)n(alues)j(of)d(the)h(v)n(ariable)j Fd(s)c Fq(o)o(v)o(er)h(the)h(time)f(in)o(terv)n(al)i Fd(t)1844 2704 y Fm(1)1861 2700 y Fd(;)6 b(:)g(:)g(:)g(;)g(t)1960 2704 y Fm(2)1977 2700 y Fq(.)965 2727 y Fs(2)p eop %%Page: 3 4 3 3 bop 334 -112 a 20247620 11840716 7301775 17629511 34666987 33548697 startTexFig 334 -112 a %%BeginDocument: cbcltr-mme.ps save /d_sv_obj exch def userdict /IslandDrawDict 300 dict dup begin put /bdef {bind def} bind def /E {exch} bdef /FF {findfont} bdef /MF {makefont} bdef /RO {rotate} bdef /SC {scale} bdef /SF {setfont} bdef /SG {setgray} bdef /TR {translate} bdef /bp {lj lw rgb} bdef /bpbw {lj lw setgray} bdef /c {curveto} bdef /cl {closepath} bdef /fi {eofill} bdef /g {setgray} bdef /gr {grestore} bdef /gs {gsave} bdef /l {lineto} bdef /lj {setlinejoin} bdef /lw {setlinewidth} bdef /m {moveto} bdef /n {newpath} bdef /nx {/x E def} bdef /r {rmoveto} bdef /rl {rlineto} bdef /rgb {setrgbcolor} bdef /s {show} bdef /sd {setdash} bdef /sp {x 0 rmoveto} bdef /ss {currentpoint pop E m} bdef /st {stroke} bdef /BPSIDE 32 def %% pixels per pattern side /PATFREQ 3.0 def %% pattern pixels per mm /dp_mat [PATFREQ 0 0 PATFREQ 0 0] def /dp_pw BPSIDE def %% pattern pixel width /dp_ph BPSIDE def %% pattern pixel height /dp_w dp_pw PATFREQ div def %% pattern mm width /dp_h dp_ph PATFREQ div def %% pattern mm height /savemat matrix def /topmat matrix def /patmat matrix def /ncpoint errordict /nocurrentpoint get def errordict begin /nocurrentpoint { dup /pathbbox load eq {pop 0 0 1 1} {ncpoint} ifelse } bdef end /ar { %% sa ea sx sy rot tx ty matrix currentmatrix 8 1 roll TR RO SC n 0 0 1 5 3 roll arc setmatrix } bdef /arn { %% sa ea sx sy rot tx ty TR RO SC matrix currentmatrix 8 1 roll n 0 0 1 5 3 roll arcn setmatrix } bdef /el { %% sx sy rot tx ty matrix currentmatrix 6 1 roll TR RO SC n 0 0 1 0 360 arc setmatrix cl } bdef /image_raster { %% sw sh sd dw dh xs ys TR SC /sd E def /sh E def /sw E def /imagebuf sw sd mul 7 add 8 idiv string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop} image } bdef /imagemask_raster { TR SC /sh E def /sw E def /imagebuf sw 7 add 8 idiv string def sw sh false [sw 0 0 sh 0 0] {currentfile imagebuf readhexstring pop} imagemask } bdef /dither_color_raster { % bool sw sh sd dw dh xs ys TR SC /sd E def /sh E def /sw E def sd 8 eq and { /imagebuf 3 string def /grayval 1 string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop pop imagebuf 0 get 0.299 mul imagebuf 1 get 0.587 mul add imagebuf 2 get 0.114 mul add cvi grayval exch 0 exch put grayval } image } { /imagebuf sw 3 mul sd mul 7 add 8 idiv string def sh { currentfile imagebuf readhexstring pop pop } repeat } ifelse } bdef /image_color_raster { % bool sw sh sd dw dh xs ys /colorimage where not { dither_color_raster } { pop TR SC /sd E def /sh E def /sw E def pop /imagebuf sw 3 mul sd mul 7 add 8 idiv string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop} false 3 colorimage } ifelse } bdef /patpath { /inv E def topmat setmatrix pathbbox %% get lo - hi indecies /hy E dp_h div floor cvi def /hx E dp_w div floor cvi def /ly E dp_h div floor cvi def /lx E dp_w div floor cvi def lx 1 hx { dp_w mul ly 1 hy { dp_h mul E dup 3 1 roll E patmat currentmatrix pop TR dp_pw dp_ph inv dp_mat dp_proc imagemask patmat setmatrix } for pop } for } bdef /setpattern { /blue E def /green E def /red E def /freq E def /bwidth E def /bpside E def /bstring E def /onbits 0 def /offbits 0 def freq 0 {/y E def /x E def /xindex x 1 add 2 div bpside mul cvi def /yindex y 1 add 2 div bpside mul cvi def bstring yindex bwidth mul xindex 8 idiv add get not 1 7 xindex 8 mod sub bitshift and 0 ne {/onbits onbits 1 add def 1} {/offbits offbits 1 add def 0} ifelse } setscreen {} settransfer systemdict /setcmykcolor known { /fact 1 onbits offbits onbits add div sub def 1 red sub fact mul 1 green sub fact mul 1 blue sub fact mul 0 setcmykcolor } { offbits offbits onbits add div setgray} ifelse } bdef /dmatrix matrix def /dpi 72 0 dmatrix defaultmatrix dtransform dup mul E dup mul add sqrt def /B {gs bp st gr} bdef %% brush: gr lw lj /Bbw {gs bpbw st gr} bdef %% brush: gr lw lj /F {gs rgb eofill gr} bdef %% fill: gr /Fbw {gs setgray eofill gr} bdef %% fill: gr /PB {gs lj lw setpattern st gr} bdef /PF {gs eoclip patpath gr} bdef /BB {gs rgb lj lw strokepath clip patpath gr} bdef /xdef {exch def} bdef /clip_region { /ht xdef /wd xdef /bm xdef /lm xdef newpath lm bm moveto 0 ht rlineto wd 0 rlineto 0 ht neg rlineto closepath clip } bdef /reencode_small_dict 12 dict def /ReencodeSmall { reencode_small_dict begin /new_codes_and_names exch def /new_font_name exch def /base_font_name exch def /base_font_dict base_font_name findfont def /newfont base_font_dict maxlength dict def base_font_dict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName new_font_name put new_codes_and_names aload pop new_codes_and_names length 2 idiv { newfont /Encoding get 3 1 roll put } repeat new_font_name newfont definefont pop end %reencode_small_dict } def /extended_Zapf [ 8#223 /a89 8#224 /a90 8#225 /a93 8#226 /a94 8#227 /a91 8#230 /a92 8#231 /a205 8#232 /a85 8#233 /a206 8#234 /a86 8#235 /a87 8#236 /a88 8#237 /a95 8#240 /a96 ] def /extended_Standard [ 29 /thorn 30 /yacute 31 /divide 128 /Acircumflex 129 /Adieresis 130 /Agrave 131 /Aring 132 /Atilde 133 /Ccedilla 134 /Eacute 135 /Ecircumflex 136 /Edieresis 137 /Egrave 138 /Iacute 139 /Icircumflex 140 /Idieresis 141 /Igrave 142 /Ntilde 143 /Oacute 144 /Ocircumflex 145 /Odieresis 146 /Ograve 147 /Otilde 148 /Scaron 149 /Uacute 150 /Ucircumflex 151 /Udieresis 152 /Ugrave 153 /Ydieresis 154 /Zcaron 155 /aacute 156 /acircumflex 157 /adieresis 158 /agrave 159 /aring 160 /atilde 161 /exclamdown 162 /cent 163 /sterling 164 /fraction 165 /yen 166 /florin 167 /section 168 /currency 169 /quotesingle 170 /quotedblleft 171 /guillemotleft 172 /guilsinglleft 173 /guilsinglright 174 /fi 175 /fl 176 /plusminus 177 /endash 178 /dagger 179 /daggerdbl 180 /periodcentered 181 /twosuperior 182 /paragraph 183 /bullet 184 /quotesinglbase 185 /quotedblbase 186 /quotedblright 187 /guillemotright 188 /ellipsis 189 /perthousand 190 /threesuperior 191 /questiondown 192 /mu 193 /grave 194 /acute 195 /circumflex 196 /tilde 197 /macron 198 /breve 199 /dotaccent 200 /dieresis 201 /onesuperior 202 /ring 203 /cedilla 204 /onequarter 205 /hungarumlaut 206 /ogonek 207 /caron 208 /emdash 209 /ccedilla 210 /copyright 211 /eacute 212 /ecircumflex 213 /edieresis 214 /egrave 215 /iacute 216 /icircumflex 217 /idieresis 218 /igrave 219 /logicalnot 220 /minus 221 /ntilde 222 /oacute 223 /ocircumflex 224 /odieresis 225 /AE 226 /onehalf 227 /ordfeminine 228 /ograve 229 /otilde 230 /registered 231 /scaron 232 /Lslash 233 /Oslash 234 /OE 235 /ordmasculine 236 /trademark 237 /uacute 238 /ucircumflex 239 /udieresis 240 /ugrave 241 /ae 242 /ydieresis 243 /zcaron 244 /Aacute 245 /dotlessi 246 /threequarters 247 /Eth 248 /lslash 249 /oslash 250 /oe 251 /germandbls 252 /multiply 253 /Yacute 254 /Thorn 255 /eth ] def /extended_Symbol [ ] def /extend_font { % stack: fontname newfontname exch dup (ZapfDingbats) eq { cvn exch cvn extended_Zapf ReencodeSmall } { dup (Symbol) eq { cvn exch cvn extended_Symbol ReencodeSmall } { cvn exch cvn extended_Standard ReencodeSmall } ifelse } ifelse } bind def /extend_font_name { % stack: font_name_string dup length 1 add string /extended_font_name exch def extended_font_name 0 (_) putinterval extended_font_name 1 3 -1 roll putinterval extended_font_name } bind def /gf { /f exch def f cvn where { f exch begin cvn load exec setfont end } { f 0 f length 8 sub getinterval dup /localfont exch extend_font_name def localfont extend_font localfont findfont /xsz f f length 4 sub 4 getinterval cvi def /ysz f f length 8 sub 4 getinterval cvi def [ xsz 0 0 ysz neg 0 0 ] makefont dup f cvn exch def setfont } ifelse } bind def /ul { % space drop thickness gs currentpoint currentlinewidth currentpoint n m 6 -3 roll lw 0 exch r 0 rl st lw m gr } bind def /nxtab { currentpoint 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119.22 115.11 m 125.28 115.11 l gsave 0 0 0 0.564 0 B grestore n 119.39 142.19 m 137.31 142.19 l gsave 0 0 0 0.564 0 B grestore n 104.27 158.58 m 128.33 158.58 l gsave 0 0 0 0.564 0 B grestore n 104.41 171.07 m 140.1 171.07 l gsave 0 0 0 0.564 0 B grestore n 70.247 141.87 m 81.109 141.87 l gsave 0 0 0 0.564 0 B grestore n 78.288 141.16 m 81.109 141.87 l 78.288 142.57 l gsave 0 0 0 0.564 0 B grestore n 70.106 114.5 m 70.106 141.87 l gsave 0 0 0 0.564 0 B grestore n 92.746 123.67 m 92.746 123.59 92.683 123.53 92.605 123.53 c 92.527 123.53 92.464 123.59 92.464 123.67 c 92.464 123.75 92.527 123.81 92.605 123.81 c 92.683 123.81 92.746 123.75 92.746 123.67 c gsave 0 0 0 0 0 B grestore n 92.746 127.2 m 92.746 127.08 92.683 126.99 92.605 126.99 c 92.527 126.99 92.464 127.08 92.464 127.2 c 92.464 127.31 92.527 127.41 92.605 127.41 c 92.683 127.41 92.746 127.31 92.746 127.2 c gsave 0 0 0 0 0 B grestore n 92.746 130.58 m 92.746 130.5 92.683 130.44 92.605 130.44 c 92.527 130.44 92.464 130.5 92.464 130.58 c 92.464 130.66 92.527 130.72 92.605 130.72 c 92.683 130.72 92.746 130.66 92.746 130.58 c gsave 0 0 0 0 0 B grestore n savemat currentmatrix pop [1 -0 -0 1 90.278 117.851] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Times-Roman02800280) gf 0.00 0.00 0.00 rgb (f) s savemat setmatrix n savemat currentmatrix pop [1 -0 -0 1 90.278 144.935] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Times-Roman02800280) gf 0.00 0.00 0.00 rgb (f) s savemat setmatrix n savemat currentmatrix pop [1 -0 -0 1 92.252 145.23] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Courier02400240) gf 0.00 0.00 0.00 rgb (m) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 92.8867 117.712] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Courier02000200) gf 0.00 0.00 0.00 rgb (1) s savemat setmatrix n savemat currentmatrix 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cl 0 0 0 F n 104.26 142 m 109.42 142 l gsave 0 0 0 0.352 0 B grestore n 118.01 144.14 m 117.49 144.63 116.76 144.9 116.05 144.86 c 115.33 144.84 114.63 144.52 114.14 143.99 c 113.65 143.46 113.39 142.74 113.42 142.02 c 113.44 141.3 113.77 140.6 114.3 140.12 c 114.82 139.63 115.55 139.36 116.26 139.39 c 116.98 139.42 117.68 139.74 118.17 140.27 c 118.66 140.79 118.92 141.52 118.89 142.24 c 118.87 142.88 118.61 143.51 118.17 143.99 c gsave 0 0 0 0.352 0 B grestore n 116.03 139.1 m 114.84 135.54 l 117.21 135.54 l cl 0 0 0 F n 116.03 135.54 m 116.03 130.39 l gsave 0 0 0 0.352 0 B grestore n 128.18 117.79 m 129.37 121.35 l 127 121.35 l cl 0 0 0 F n 128.18 121.35 m 128.18 158.43 l gsave 0 0 0 0.352 0 B grestore n 139.94 144.83 m 141.13 148.39 l 138.76 148.39 l cl 0 0 0 F n 139.94 148.39 m 139.94 171.11 l gsave 0 0 0 0.352 0 B grestore 2.9792 2.75 0 92.201 165 el gsave 0 0 0 0.352 0 B grestore 2.9792 2.75 0 92.576 172.56 el gsave 0 0 0 0.352 0 B grestore 2.9792 2.75 0 92.34 157.65 el gsave 0 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(Helvetica03200320) gf 0.00 0.00 0.00 rgb () s(Symbol03200320) gf 0 0 m 0 ss (n) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 110.458 106.944] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Helvetica02000200) gf 0.00 0.00 0.00 rgb (1) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 110.153 137.194] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m /tab 283.00 1000.0 mul cvi def 0 0 m 0 ss (Helvetica02000200) gf 0.00 0.00 0.00 rgb (m) s savemat setmatrix n 48.278 99.611 m 172.94 99.611 l 172.94 184.56 l 48.278 184.56 l cl gsave 0.498 0.498 0.498 0 0 B grestore userdict /#copies 1 put grestore end d_sv_obj restore %%EndDocument endTexFig 477 725 a Fs(Figure)14 b(2:)k(The)c(Mark)o(o)o(v)f(Mixture)h(of)g(Exp) q(erts)h(arc)o(hitecture)-26 857 y(The)d(Maximization)c(\(M\))k(step)h (reassigns)f(to)g(the)g(unkno)o(wn)-75 903 y(parameters)25 b(the)h(v)n(alues)f(whic)o(h)g(maxim)o(ize)e(the)i(exp)q(ected)-75 949 y(complete)13 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Fs(,)24 b(eac)o(h)f(of)e(them)g(ha)o(ving)g(a)1013 297 y(new)15 b(parameter)g(as)h(co)q(e\016cien)o(t.)24 b(But)15 b(eac)o(h)h(additional)e(v)n(ari-)1013 343 y(able)f(a\013ects) i(only)e(one)h(of)f(the)h(6)g(exp)q(erts)h(\(see)g(App)q(endix)f(A\).) 1013 389 y(Therefore,)i(b)o(y)f(including)f(the)i(additional)d(v)n (ariables)i(only)f(in)1013 434 y(the)k(mo)q(dels)e(that)h(dep)q(end)i (on)e(them,)g(w)o(e)h(ha)o(v)o(e)f(an)h(insignif-)1013 480 y(ican)o(t)g(increase)i(in)e(the)h(n)o(um)o(b)q(er)f(of)g (parameters.)32 b(T)m(o)17 b(a)o(v)o(oid)1013 526 y(in\014nite)c(input) g(v)n(alues)g(the)g(the)h(v)n(alues)f(of)g Fk(v)1717 532 y Fj(x)1738 526 y Fk(;)18 b(v)1788 532 y Fj(y)1821 526 y Fs(w)o(ere)c(lo)o(w)o(er-)1013 571 y(b)q(ounded)g(b)o(y)g(the)g (small)e(constan)o(t)i Fk(V)1611 577 y Fj(min)1687 571 y Fs(=)e(1)p Fk(=)p Fs(50.)1061 620 y Fa(Implemen)o(tati)o(on)21 b(of)j(the)f(transition)d(probabilit)n(y)1013 666 y(matrix:)c Fs(T)m(o)d(implem)o(en)o(t)e(the)i(transition)g(matrix)e Fk(A)i Fs(w)o(e)g(used)1013 711 y(a)d(bank)h(of)f Fo(gating)i(networks) p Fs(,)f(one)g(for)f(eac)o(h)h(column)f(of)g Fk(A)p Fs(.)17 b(Ex-)1013 757 y(amining)9 b(\014gure)k(1)f(it)h(is)f(easy)h(to)f(see)i (that)f(there)g(exist)g(exp)q(erts)1013 803 y(that)i(share)h(the)g (same)e(\014nal)g(state)i(of)f(con)o(tact)h(\(for)f(instance,)1013 848 y Fa(A)i(stic)o(k)d Fs(and)h Fa(A)i(slide)c Fs(b)q(oth)i(represen)o (t)i(mo)o(v)o(emen)o(ts)c(whose)1013 894 y(\014nal)j(p)q(osition)h(is)h (on)f(surface)i Fa(A)p Fs(\).)e(Since)h(transition)f(proba-)1013 940 y(bilities)12 b(dep)q(end)j(only)e(on)g(the)h(\014nal)f(p)q (osition)g(the)h(columns)f(of)1013 985 y(the)j(matrix)e Fk(A)i Fs(corresp)q(onding)g(to)g(these)h(exp)q(erts)h(are)e(equal.) 1013 1031 y(This)c(brings)h(the)g(n)o(um)o(b)q(er)f(of)g(distinct)h (gating)e(net)o(w)o(orks)i(to)g(4.)1061 1080 y(The)f(b)q(oundaries)f (of)g(the)g(decision)h(regions)f(are)g(curv)o(ed)h(sur-)1013 1125 y(faces,)e(so)f(that)h(to)f(implemen)o(t)d(eac)o(h)k(of)f(them)g 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(set)i(are)f(roughly)g(equal.)30 b(The)1013 1735 y(distribution)18 b(o)o(v)o(er)h(v)o(elo)q(cities)h(and)f(the)g(sequence)j(length)d Fk(T)1013 1781 y Fs(w)o(ere)d(c)o(hosen)g(so)f(as)g(to)g(meet)g(this)g (requiremen)o(t.)21 b(The)16 b(\()p Fk(x;)d(y)q Fs(\))1013 1826 y(v)n(alues)e(obtained)g(b)o(y)h(sim)o(ulation)c(w)o(ere)13 b(corrupted)g(with)e(gaus-)1013 1872 y(sian)i(additiv)o(e)g(noise)h (with)g(standard)g(deviation)f Fk(\033)q Fs(.)1061 1921 y(In)h(the)g(M)f(step,)h(the)g(parameters)g(of)f(the)h(gating)e(net)o (w)o(orks)1013 1966 y(w)o(ere)18 b(up)q(dated)g(b)o(y)f(gradien)o(t)h (ascen)o(t,)g(with)g(a)f(\014xed)h(n)o(um)o(b)q(er)1013 2012 y(of)c(ep)q(o)q(c)o(hs)j(for)e(eac)o(h)h(M)g(step.)24 b(App)q(endix)16 b(C)f(sho)o(ws)h(ho)o(w)f(the)1013 2058 y(gradien)o(t)d(w)o(as)h(computed.)k(W)m(e)12 b(used)i(w)o(eigh)o(ted)f (least)g(squares)1013 2103 y(estimation)d(for)i(the)g(mo)o(v)o(emen)o (t)e(mo)q(dels)h(parameters.)17 b(T)m(o)12 b(en-)1013 2149 y(sure)i(that)g(mo)q(dels)e(and)h(gates)h(are)g(correctly)h (coupled,)e(initial)1013 2195 y(v)n(alues)j(for)h Fk(\022)i Fs(are)f(c)o(hosen)g(around)f(the)h(true)g(v)n(alues.)27 b(In)17 b(the)1013 2240 y(presen)o(t)h(case,)h(this)e(is)g(not)g(an)g (unrealistic)g(assumption.)26 b Fk(W)1013 2286 y Fs(w)o(as)19 b(initialized)g(with)g(small)f(random)g(v)n(alues.)36 b(Because)22 b(of)1013 2332 y(the)d(long)f(time)f(to)i(con)o(v)o (ergence,)i(only)d(a)h(small)d(n)o(um)o(b)q(er)j(of)1013 2377 y(runs)12 b(ha)o(v)o(e)g(b)q(een)i(p)q(erformed.)j(The)12 b(observ)o(ed)i(v)n(ariance)e(of)f(the)1013 2423 y(results)19 b(o)o(v)o(er)f(test)h(sets)h(w)o(as)e(extremely)f(small,)g(so)h(that)g (the)1013 2469 y(v)n(alues)13 b(presen)o(ted)j(here)f(can)f(b)q(e)h (considered)g(as)f(t)o(ypical.)1061 2517 y(Three)i(criteria)e(w)o(ere)h (used)g(to)f(measure)g(the)h(p)q(erformance)1013 2563 y(of)c(the)i(learning)e(algorithm:)j(exp)q(erts')g(parameters)e (deviation)1013 2609 y(from)e(the)j(true)g(v)n(alues,)f(square)i(ro)q (ot)e(of)g(prediction)g(MSE)h(and)1013 2654 y(hidden)g(state)h (misclassi\014caton.)j(Because)e(training)d(w)o(as)h(p)q(er-)1013 2700 y(formed)f(on)i(a)g(distribution)f(that)i(is)e(not)h(exp)q(ected)j (to)d(app)q(ear)965 2727 y(4)p eop %%Page: 5 6 5 5 bop 525 -112 a 14208860 10893473 8025374 26312704 21247508 40061091 startTexFig 525 -112 a %%BeginDocument: cbcltr-gate.ps save /d_sv_obj exch def userdict /IslandDrawDict 300 dict dup begin put /bdef {bind def} bind def /E {exch} bdef /FF {findfont} bdef /MF {makefont} bdef /RO {rotate} bdef /SC {scale} bdef /SF {setfont} bdef /SG {setgray} bdef /TR {translate} bdef /bp {lj lw rgb} bdef /bpbw {lj lw setgray} bdef /c {curveto} bdef /cl {closepath} bdef /fi {eofill} bdef /g {setgray} bdef /gr {grestore} bdef /gs {gsave} bdef /l {lineto} bdef /lj {setlinejoin} bdef /lw {setlinewidth} bdef /m {moveto} bdef /n {newpath} bdef /nx {/x E def} bdef /r {rmoveto} bdef /rl {rlineto} bdef /rgb {setrgbcolor} bdef /s {show} bdef /sd {setdash} bdef /sp {x 0 rmoveto} bdef /ss {currentpoint pop E m} bdef /st {stroke} bdef /BPSIDE 32 def %% pixels per pattern side /PATFREQ 3.0 def %% pattern pixels per mm /dp_mat [PATFREQ 0 0 PATFREQ 0 0] def /dp_pw BPSIDE def %% pattern pixel width /dp_ph BPSIDE def %% pattern pixel height /dp_w dp_pw PATFREQ div def %% pattern mm width /dp_h dp_ph PATFREQ div def %% pattern mm height /savemat matrix def /topmat matrix def /patmat matrix def /ncpoint errordict /nocurrentpoint get def errordict begin /nocurrentpoint { dup /pathbbox load eq {pop 0 0 1 1} {ncpoint} ifelse } bdef end /ar { %% sa ea sx sy rot tx ty matrix currentmatrix 8 1 roll TR RO SC n 0 0 1 5 3 roll arc setmatrix } bdef /arn { %% sa ea sx sy rot tx ty TR RO SC matrix currentmatrix 8 1 roll n 0 0 1 5 3 roll arcn setmatrix } bdef /el { %% sx sy rot tx ty matrix currentmatrix 6 1 roll TR RO SC n 0 0 1 0 360 arc setmatrix cl } bdef /image_raster { %% sw sh sd dw dh xs ys TR SC /sd E def /sh E def /sw E def /imagebuf sw sd mul 7 add 8 idiv string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop} image } bdef /imagemask_raster { TR SC /sh E def /sw E def /imagebuf sw 7 add 8 idiv string def sw sh false [sw 0 0 sh 0 0] {currentfile imagebuf readhexstring pop} imagemask } bdef /dither_color_raster { % bool sw sh sd dw dh xs ys TR SC /sd E def /sh E def /sw E def sd 8 eq and { /imagebuf 3 string def /grayval 1 string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop pop imagebuf 0 get 0.299 mul imagebuf 1 get 0.587 mul add imagebuf 2 get 0.114 mul add cvi grayval exch 0 exch put grayval } image } { /imagebuf sw 3 mul sd mul 7 add 8 idiv string def sh { currentfile imagebuf readhexstring pop pop } repeat } ifelse } bdef /image_color_raster { % bool sw sh sd dw dh xs ys /colorimage where not { dither_color_raster } { pop TR SC /sd E def /sh E def /sw E def pop /imagebuf sw 3 mul sd mul 7 add 8 idiv string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop} false 3 colorimage } ifelse } bdef /patpath { /inv E def topmat setmatrix pathbbox %% get lo - hi indecies /hy E dp_h div floor cvi def /hx E dp_w div floor cvi def /ly E dp_h div floor cvi def /lx E dp_w div floor cvi def lx 1 hx { dp_w mul ly 1 hy { dp_h mul E dup 3 1 roll E patmat currentmatrix pop TR dp_pw dp_ph inv dp_mat dp_proc imagemask patmat setmatrix } for pop } for } bdef /setpattern { /blue E def /green E def /red E def /freq E def /bwidth E def /bpside E def /bstring E def /onbits 0 def /offbits 0 def freq 0 {/y E def /x E def /xindex x 1 add 2 div bpside mul cvi def /yindex y 1 add 2 div bpside mul cvi def bstring yindex bwidth mul xindex 8 idiv add get not 1 7 xindex 8 mod sub bitshift and 0 ne {/onbits onbits 1 add def 1} {/offbits offbits 1 add def 0} ifelse } setscreen {} settransfer systemdict /setcmykcolor known { /fact 1 onbits offbits onbits add div sub def 1 red sub fact mul 1 green sub fact mul 1 blue sub fact mul 0 setcmykcolor } { offbits offbits onbits add div setgray} ifelse } bdef /dmatrix matrix def /dpi 72 0 dmatrix defaultmatrix dtransform dup mul E dup mul add sqrt def /B {gs bp st gr} bdef %% brush: gr lw lj /Bbw {gs bpbw st gr} bdef %% brush: gr lw lj /F {gs rgb eofill gr} bdef %% fill: gr /Fbw {gs setgray eofill gr} bdef %% fill: gr /PB {gs lj lw setpattern st gr} bdef /PF {gs eoclip patpath gr} bdef /BB {gs rgb lj lw strokepath clip patpath gr} bdef /xdef {exch def} bdef /clip_region { /ht xdef /wd xdef /bm xdef /lm xdef newpath lm bm moveto 0 ht rlineto wd 0 rlineto 0 ht neg rlineto closepath clip } bdef /reencode_small_dict 12 dict def /ReencodeSmall { reencode_small_dict begin /new_codes_and_names exch def /new_font_name exch def /base_font_name exch def /base_font_dict base_font_name findfont def /newfont base_font_dict maxlength dict def base_font_dict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName new_font_name put new_codes_and_names aload pop new_codes_and_names length 2 idiv { newfont /Encoding get 3 1 roll put } repeat new_font_name newfont definefont pop end %reencode_small_dict } def /extended_Zapf [ 8#223 /a89 8#224 /a90 8#225 /a93 8#226 /a94 8#227 /a91 8#230 /a92 8#231 /a205 8#232 /a85 8#233 /a206 8#234 /a86 8#235 /a87 8#236 /a88 8#237 /a95 8#240 /a96 ] def /extended_Standard [ 29 /thorn 30 /yacute 31 /divide 128 /Acircumflex 129 /Adieresis 130 /Agrave 131 /Aring 132 /Atilde 133 /Ccedilla 134 /Eacute 135 /Ecircumflex 136 /Edieresis 137 /Egrave 138 /Iacute 139 /Icircumflex 140 /Idieresis 141 /Igrave 142 /Ntilde 143 /Oacute 144 /Ocircumflex 145 /Odieresis 146 /Ograve 147 /Otilde 148 /Scaron 149 /Uacute 150 /Ucircumflex 151 /Udieresis 152 /Ugrave 153 /Ydieresis 154 /Zcaron 155 /aacute 156 /acircumflex 157 /adieresis 158 /agrave 159 /aring 160 /atilde 161 /exclamdown 162 /cent 163 /sterling 164 /fraction 165 /yen 166 /florin 167 /section 168 /currency 169 /quotesingle 170 /quotedblleft 171 /guillemotleft 172 /guilsinglleft 173 /guilsinglright 174 /fi 175 /fl 176 /plusminus 177 /endash 178 /dagger 179 /daggerdbl 180 /periodcentered 181 /twosuperior 182 /paragraph 183 /bullet 184 /quotesinglbase 185 /quotedblbase 186 /quotedblright 187 /guillemotright 188 /ellipsis 189 /perthousand 190 /threesuperior 191 /questiondown 192 /mu 193 /grave 194 /acute 195 /circumflex 196 /tilde 197 /macron 198 /breve 199 /dotaccent 200 /dieresis 201 /onesuperior 202 /ring 203 /cedilla 204 /onequarter 205 /hungarumlaut 206 /ogonek 207 /caron 208 /emdash 209 /ccedilla 210 /copyright 211 /eacute 212 /ecircumflex 213 /edieresis 214 /egrave 215 /iacute 216 /icircumflex 217 /idieresis 218 /igrave 219 /logicalnot 220 /minus 221 /ntilde 222 /oacute 223 /ocircumflex 224 /odieresis 225 /AE 226 /onehalf 227 /ordfeminine 228 /ograve 229 /otilde 230 /registered 231 /scaron 232 /Lslash 233 /Oslash 234 /OE 235 /ordmasculine 236 /trademark 237 /uacute 238 /ucircumflex 239 /udieresis 240 /ugrave 241 /ae 242 /ydieresis 243 /zcaron 244 /Aacute 245 /dotlessi 246 /threequarters 247 /Eth 248 /lslash 249 /oslash 250 /oe 251 /germandbls 252 /multiply 253 /Yacute 254 /Thorn 255 /eth ] def /extended_Symbol [ ] def /extend_font { % stack: fontname newfontname exch dup (ZapfDingbats) eq { cvn exch cvn extended_Zapf ReencodeSmall } { dup (Symbol) eq { cvn exch cvn extended_Symbol ReencodeSmall } { cvn exch cvn extended_Standard ReencodeSmall } ifelse } ifelse } bind def /extend_font_name { % stack: font_name_string dup length 1 add string /extended_font_name exch def extended_font_name 0 (_) putinterval extended_font_name 1 3 -1 roll putinterval extended_font_name } bind def /gf { /f exch def f cvn where { f exch begin cvn load exec setfont end } { f 0 f length 8 sub getinterval dup /localfont exch extend_font_name def localfont extend_font localfont findfont /xsz f f length 4 sub 4 getinterval cvi def /ysz f f length 8 sub 4 getinterval cvi def [ xsz 0 0 ysz neg 0 0 ] makefont dup f cvn exch def setfont } ifelse } bind def /ul { % space drop thickness gs currentpoint currentlinewidth currentpoint n m 6 -3 roll lw 0 exch r 0 rl st lw m gr } bind def /nxtab { currentpoint pop 1000.0 mul cvi tab mod tab exch sub 1000.0 div 0 rmoveto } bind def /nx { /x exch def } bind def 0. nx gsave 2.83465 -2.83465 scale 0 -279.4 translate topmat currentmatrix pop n 72.504 130.44 m 72.504 83.328 l 76.736 83.328 l 76.736 130.44 l 72.504 130.44 l cl gsave 0 0 0 0 0 B grestore n 72.504 115.49 m 72.504 110.41 l 76.736 110.41 l 76.736 115.49 l 72.504 115.49 l cl gsave 0 0 0 0 0 B grestore n 95.074 121.41 m 95.074 92.356 l 99.305 92.356 l 99.305 121.41 l 95.074 121.41 l cl gsave 0 0 0 0 0 B grestore n 108.61 121.41 m 108.61 92.404 l 113.98 92.404 l 113.98 121.41 l 108.61 121.41 l cl gsave 0 0 0 0 0 B grestore n 101.56 105.61 m 101.85 105.61 l 101.56 105.61 l cl gsave 0 0 0 0 0 B grestore n 95.215 110.27 m 95.215 105.61 l 99.305 105.61 l 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ldef /j /setlinejoin ldef /cap /setlinecap ldef /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef /portraitMode 0 def /landscapeMode 1 def /dpi2point 0 def /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath fill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { 2 copy moveto lineto stroke } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 363 216 6024 4806 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef /Helvetica /ISOLatin1Encoding 144 FMSR /Helvetica /ISOLatin1Encoding 96 FMSR /Helvetica /ISOLatin1Encoding 144 FMSR /Helvetica /ISOLatin1Encoding 96 FMSR /Helvetica /ISOLatin1Encoding 144 FMSR /Helvetica /ISOLatin1Encoding 96 FMSR /Helvetica /ISOLatin1Encoding 144 FMSR /Helvetica /ISOLatin1Encoding 96 FMSR /Helvetica /ISOLatin1Encoding 144 FMSR /Helvetica /ISOLatin1Encoding 96 FMSR /Helvetica /ISOLatin1Encoding 144 FMSR /Helvetica /ISOLatin1Encoding 96 FMSR /Helvetica /ISOLatin1Encoding 144 FMSR 1 j c1 0 0 6917 5187 PR 6 w DO 4 w SO 6 w c0 899 4615 mt 6258 4615 L 899 389 mt 6258 389 L 899 4615 mt 899 389 L 6258 4615 mt 6258 389 L 899 4615 mt 899 4615 L 6258 4615 mt 6258 4615 L 899 4615 mt 6258 4615 L 899 4615 mt 899 389 L 899 4615 mt 899 4615 L 899 4615 mt 899 4561 L 899 389 mt 899 443 L 859 4784 mt (0) s 1569 4615 mt 1569 4561 L 1569 389 mt 1569 443 L 1529 4784 mt (5) s 2239 4615 mt 2239 4561 L 2239 389 mt 2239 443 L 2159 4784 mt (10) s 2909 4615 mt 2909 4561 L 2909 389 mt 2909 443 L 2829 4784 mt (15) s 3579 4615 mt 3579 4561 L 3579 389 mt 3579 443 L 3499 4784 mt (20) s 4248 4615 mt 4248 4561 L 4248 389 mt 4248 443 L 4168 4784 mt (25) s 4918 4615 mt 4918 4561 L 4918 389 mt 4918 443 L 4838 4784 mt (30) s 5588 4615 mt 5588 4561 L 5588 389 mt 5588 443 L 5508 4784 mt (35) s 6258 4615 mt 6258 4561 L 6258 389 mt 6258 443 L 6178 4784 mt (40) s 899 4615 mt 926 4615 L 6258 4615 mt 6231 4615 L 899 4615 mt 953 4615 L 6258 4615 mt 6204 4615 L /Helvetica /ISOLatin1Encoding 96 FMSR /Helvetica /ISOLatin1Encoding 144 FMSR 595 4668 mt (10) s /Helvetica /ISOLatin1Encoding 96 FMSR 755 4579 mt (-4) s /Helvetica /ISOLatin1Encoding 144 FMSR 899 4361 mt 926 4361 L 6258 4361 mt 6231 4361 L 899 4212 mt 926 4212 L 6258 4212 mt 6231 4212 L 899 4106 mt 926 4106 L 6258 4106 mt 6231 4106 L 899 4024 mt 926 4024 L 6258 4024 mt 6231 4024 L 899 3957 mt 926 3957 L 6258 3957 mt 6231 3957 L 899 3901 mt 926 3901 L 6258 3901 mt 6231 3901 L 899 3852 mt 926 3852 L 6258 3852 mt 6231 3852 L 899 3808 mt 926 3808 L 6258 3808 mt 6231 3808 L 899 3770 mt 926 3770 L 6258 3770 mt 6231 3770 L 899 3770 mt 953 3770 L 6258 3770 mt 6204 3770 L /Helvetica /ISOLatin1Encoding 96 FMSR /Helvetica /ISOLatin1Encoding 144 FMSR 595 3823 mt (10) s /Helvetica /ISOLatin1Encoding 96 FMSR 755 3734 mt (-3) s /Helvetica /ISOLatin1Encoding 144 FMSR 899 3515 mt 926 3515 L 6258 3515 mt 6231 3515 L 899 3367 mt 926 3367 L 6258 3367 mt 6231 3367 L 899 3261 mt 926 3261 L 6258 3261 mt 6231 3261 L 899 3179 mt 926 3179 L 6258 3179 mt 6231 3179 L 899 3112 mt 926 3112 L 6258 3112 mt 6231 3112 L 899 3056 mt 926 3056 L 6258 3056 mt 6231 3056 L 899 3007 mt 926 3007 L 6258 3007 mt 6231 3007 L 899 2963 mt 926 2963 L 6258 2963 mt 6231 2963 L 899 2925 mt 926 2925 L 6258 2925 mt 6231 2925 L 899 2925 mt 953 2925 L 6258 2925 mt 6204 2925 L /Helvetica /ISOLatin1Encoding 96 FMSR /Helvetica /ISOLatin1Encoding 144 FMSR 595 2978 mt (10) s /Helvetica /ISOLatin1Encoding 96 FMSR 755 2889 mt (-2) s /Helvetica /ISOLatin1Encoding 144 FMSR 899 2670 mt 926 2670 L 6258 2670 mt 6231 2670 L 899 2521 mt 926 2521 L 6258 2521 mt 6231 2521 L 899 2416 mt 926 2416 L 6258 2416 mt 6231 2416 L 899 2334 mt 926 2334 L 6258 2334 mt 6231 2334 L 899 2267 mt 926 2267 L 6258 2267 mt 6231 2267 L 899 2210 mt 926 2210 L 6258 2210 mt 6231 2210 L 899 2161 mt 926 2161 L 6258 2161 mt 6231 2161 L 899 2118 mt 926 2118 L 6258 2118 mt 6231 2118 L 899 2079 mt 926 2079 L 6258 2079 mt 6231 2079 L 899 2079 mt 953 2079 L 6258 2079 mt 6204 2079 L /Helvetica /ISOLatin1Encoding 96 FMSR /Helvetica /ISOLatin1Encoding 144 FMSR 595 2132 mt (10) s /Helvetica /ISOLatin1Encoding 96 FMSR 755 2043 mt (-1) s /Helvetica /ISOLatin1Encoding 144 FMSR 899 1825 mt 926 1825 L 6258 1825 mt 6231 1825 L 899 1676 mt 926 1676 L 6258 1676 mt 6231 1676 L 899 1571 mt 926 1571 L 6258 1571 mt 6231 1571 L 899 1489 mt 926 1489 L 6258 1489 mt 6231 1489 L 899 1422 mt 926 1422 L 6258 1422 mt 6231 1422 L 899 1365 mt 926 1365 L 6258 1365 mt 6231 1365 L 899 1316 mt 926 1316 L 6258 1316 mt 6231 1316 L 899 1273 mt 926 1273 L 6258 1273 mt 6231 1273 L 899 1234 mt 926 1234 L 6258 1234 mt 6231 1234 L 899 1234 mt 953 1234 L 6258 1234 mt 6204 1234 L /Helvetica /ISOLatin1Encoding 96 FMSR /Helvetica /ISOLatin1Encoding 144 FMSR 595 1287 mt (10) s /Helvetica /ISOLatin1Encoding 96 FMSR 755 1198 mt (0) s /Helvetica /ISOLatin1Encoding 144 FMSR 899 980 mt 926 980 L 6258 980 mt 6231 980 L 899 831 mt 926 831 L 6258 831 mt 6231 831 L 899 725 mt 926 725 L 6258 725 mt 6231 725 L 899 643 mt 926 643 L 6258 643 mt 6231 643 L 899 577 mt 926 577 L 6258 577 mt 6231 577 L 899 520 mt 926 520 L 6258 520 mt 6231 520 L 899 471 mt 926 471 L 6258 471 mt 6231 471 L 899 428 mt 926 428 L 6258 428 mt 6231 428 L 899 389 mt 926 389 L 6258 389 mt 6231 389 L 899 389 mt 953 389 L 6258 389 mt 6204 389 L /Helvetica /ISOLatin1Encoding 96 FMSR /Helvetica /ISOLatin1Encoding 144 FMSR 595 442 mt (10) s /Helvetica /ISOLatin1Encoding 96 FMSR 755 353 mt (1) s /Helvetica /ISOLatin1Encoding 144 FMSR 899 4615 mt 6258 4615 L 899 389 mt 6258 389 L 899 4615 mt 899 389 L 6258 4615 mt 6258 389 L 899 389 mt 899 389 L 6258 389 mt 6258 389 L gs 899 389 5360 4227 MR c np 134 4 134 3 134 4 134 3 134 3 134 3 134 4 134 5 134 7 134 12 134 28 134 14 134 14 134 15 134 16 134 18 134 21 134 26 134 29 133 53 134 43 134 106 134 44 134 21 134 120 134 32 134 126 134 140 134 217 134 250 134 274 134 -156 134 -673 134 392 134 428 134 360 134 429 134 880 134 39 1033 789 40 MP stroke DO 134 0 134 0 134 0 134 0 134 0 134 0 134 0 133 0 134 0 134 0 134 0 134 0 134 0 134 0 134 1 134 0 134 0 134 0 134 0 134 1 134 0 134 9 134 3 134 3 134 14 134 81 134 893 1033 744 28 MP stroke DA 134 0 134 0 134 0 134 0 134 0 134 1 134 0 134 0 134 973 1033 775 10 MP stroke DD 134 0 134 0 134 1 134 -1 134 1 134 1 134 2 134 1601 1033 776 9 MP stroke /Helvetica /ISOLatin1Encoding 192 FMSR gr DD /Helvetica /ISOLatin1Encoding 192 FMSR 541 3547 mt -90 rotate (standard prediction error) s 90 rotate 1973 4979 mt (EM iterations | backprop epochs/2000) s SO end eplot epage end showpage %%EndDocument endTexFig 930 -65 a 14682517 10893473 3552215 12695879 36179968 38811238 startTexFig 930 -65 a %%BeginDocument: cbcltr-lcg.ps /MathWorks 150 dict begin /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef /portraitMode 0 def /landscapeMode 1 def /dpi2point 0 def /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath fill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { 2 copy moveto lineto stroke } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 432 260 5955 4762 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef /Helvetica /ISOLatin1Encoding 144 FMSR 1 j c1 0 0 6917 5187 PR 6 w DO 4 w SO 6 w c0 899 4615 mt 6258 4615 L 899 389 mt 6258 389 L 899 4615 mt 899 389 L 6258 4615 mt 6258 389 L 899 4615 mt 899 4615 L 6258 4615 mt 6258 4615 L 899 4615 mt 6258 4615 L 899 4615 mt 899 389 L 899 4615 mt 899 4615 L 899 4615 mt 899 4561 L 899 389 mt 899 443 L 859 4784 mt (0) s 1569 4615 mt 1569 4561 L 1569 389 mt 1569 443 L 1529 4784 mt (5) s 2239 4615 mt 2239 4561 L 2239 389 mt 2239 443 L 2159 4784 mt (10) s 2909 4615 mt 2909 4561 L 2909 389 mt 2909 443 L 2829 4784 mt (15) s 3579 4615 mt 3579 4561 L 3579 389 mt 3579 443 L 3499 4784 mt (20) s 4248 4615 mt 4248 4561 L 4248 389 mt 4248 443 L 4168 4784 mt (25) s 4918 4615 mt 4918 4561 L 4918 389 mt 4918 443 L 4838 4784 mt (30) s 5588 4615 mt 5588 4561 L 5588 389 mt 5588 443 L 5508 4784 mt (35) s 6258 4615 mt 6258 4561 L 6258 389 mt 6258 443 L 6178 4784 mt (40) s 899 4615 mt 953 4615 L 6258 4615 mt 6204 4615 L 784 4668 mt (0) s 899 4087 mt 953 4087 L 6258 4087 mt 6204 4087 L 664 4140 mt (0.1) s 899 3559 mt 953 3559 L 6258 3559 mt 6204 3559 L 664 3612 mt (0.2) s 899 3030 mt 953 3030 L 6258 3030 mt 6204 3030 L 664 3083 mt (0.3) s 899 2502 mt 953 2502 L 6258 2502 mt 6204 2502 L 664 2555 mt (0.4) s 899 1974 mt 953 1974 L 6258 1974 mt 6204 1974 L 664 2027 mt (0.5) s 899 1445 mt 953 1445 L 6258 1445 mt 6204 1445 L 664 1498 mt (0.6) s 899 917 mt 953 917 L 6258 917 mt 6204 917 L 664 970 mt (0.7) s 899 389 mt 953 389 L 6258 389 mt 6204 389 L 664 442 mt (0.8) s 899 4615 mt 6258 4615 L 899 389 mt 6258 389 L 899 4615 mt 899 389 L 6258 4615 mt 6258 389 L 899 389 mt 899 389 L 6258 389 mt 6258 389 L gs 899 389 5360 4227 MR c np 134 0 134 1 134 -1 134 0 134 0 134 0 134 -2 134 -2 134 0 134 0 134 2 134 2 134 1 134 0 134 2 134 0 134 2 134 2 134 -2 133 2 134 12 134 13 134 33 134 7 134 16 134 -2 134 9 134 10 134 30 134 41 134 118 134 -191 134 -61 134 181 134 320 134 442 134 552 134 876 134 1574 1033 618 40 MP stroke DO 134 5 134 -5 134 -5 134 15 134 -10 134 -5 134 15 133 -5 134 5 134 -5 134 -5 134 -5 134 10 134 -5 134 -5 134 15 134 -5 134 -5 134 -5 134 2 134 9 134 27 134 55 134 22 134 132 134 253 134 1983 1033 1786 28 MP stroke DA 134 3 134 18 134 -1 134 -1 134 -18 134 6 134 13 134 5 134 479 1033 3722 10 MP stroke DD 134 0 134 0 134 0 134 0 134 0 134 -5 134 3 134 518 1033 3722 9 MP stroke /Helvetica /ISOLatin1Encoding 192 FMSR gr DD /Helvetica /ISOLatin1Encoding 192 FMSR 610 3440 mt -90 rotate (% misclassified states) s 90 rotate 1973 4979 mt (EM iterations | backprop epochs/2000) s SO end eplot epage end showpage %%EndDocument endTexFig 388 671 a Fs(\(a\))926 b(\(b\))-75 767 y(Figure)15 b(4:)20 b(Prediction)15 b(standard)g(error)h(\(MSE)694 752 y Fn(1)p Fj(=)p Fn(2)747 767 y Fs(\))f(\(a\))g(and)g(p)q(ercen)o(tage)h (of)f(wrong)f(exp)q(ert)j(c)o(hoices)e(\(misclassi\014ed)f(states\))j (\(b\))-75 812 y(on)c(the)i(training)e(set)h(during)g(learning)f(for)g (the)h(MME)g(and)g(ME)g(mo)q(dels.)j(The)d(abscissa)g(w)o(as)g(scaled)g (according)g(to)f(the)i(n)o(um)o(b)q(er)-75 858 y(of)e(bac)o (kpropagation)g(ep)q(o)q(c)o(hs)i(for)e(the)h(t)o(w)o(o)f(mo)q(dels.)k (|)c(MME,)h(no)f(noise;)h Fh(\001)7 b(\001)g(\001)12 b Fs(MME,)h(noise)h(0)p Fk(:)p Fs(2;)e({)i Fh(\001)f Fs({)g(ME,)h(no)f(noise;)g({)h({)f(ME,)-75 904 y(noise)h(0)p Fk(:)p Fs(2.)-50 1040 y 14682517 10419816 2960179 12564316 36245749 40192655 startTexFig -50 1040 a %%BeginDocument: cbcltr-mset.ps /MathWorks 150 dict begin /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef /portraitMode 0 def /landscapeMode 1 def /dpi2point 0 def /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath fill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { 2 copy moveto lineto stroke } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 329 9 6078 5036 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef /Helvetica /ISOLatin1Encoding 144 FMSR 1 j c1 0 0 6917 5187 PR 6 w DO 4 w SO 6 w c0 899 4615 mt 6258 4615 L 899 389 mt 6258 389 L 899 4615 mt 899 389 L 6258 4615 mt 6258 389 L 899 4615 mt 899 4615 L 6258 4615 mt 6258 4615 L 899 4615 mt 6258 4615 L 899 4615 mt 899 389 L 899 4615 mt 899 4615 L 899 4615 mt 899 4561 L 899 389 mt 899 443 L 859 4784 mt (0) s 2239 4615 mt 2239 4561 L 2239 389 mt 2239 443 L 2139 4784 mt (0.1) s 3579 4615 mt 3579 4561 L 3579 389 mt 3579 443 L 3479 4784 mt (0.2) s 4918 4615 mt 4918 4561 L 4918 389 mt 4918 443 L 4818 4784 mt (0.3) s 6258 4615 mt 6258 4561 L 6258 389 mt 6258 443 L 6158 4784 mt (0.4) s 899 4615 mt 953 4615 L 6258 4615 mt 6204 4615 L 784 4668 mt (0) s 899 4192 mt 953 4192 L 6258 4192 mt 6204 4192 L 584 4245 mt (0.01) s 899 3770 mt 953 3770 L 6258 3770 mt 6204 3770 L 584 3823 mt (0.02) s 899 3347 mt 953 3347 L 6258 3347 mt 6204 3347 L 584 3400 mt (0.03) s 899 2925 mt 953 2925 L 6258 2925 mt 6204 2925 L 584 2978 mt (0.04) s 899 2502 mt 953 2502 L 6258 2502 mt 6204 2502 L 584 2555 mt (0.05) s 899 2079 mt 953 2079 L 6258 2079 mt 6204 2079 L 584 2132 mt (0.06) s 899 1657 mt 953 1657 L 6258 1657 mt 6204 1657 L 584 1710 mt (0.07) s 899 1234 mt 953 1234 L 6258 1234 mt 6204 1234 L 584 1287 mt (0.08) s 899 812 mt 953 812 L 6258 812 mt 6204 812 L 584 865 mt (0.09) s 899 389 mt 953 389 L 6258 389 mt 6204 389 L 664 442 mt (0.1) s 899 4615 mt 6258 4615 L 899 389 mt 6258 389 L 899 4615 mt 899 389 L 6258 4615 mt 6258 389 L 899 389 mt 899 389 L 6258 389 mt 6258 389 L gs 899 389 5360 4227 MR c np gr 863 2629 mt 935 2629 L 899 2593 mt 899 2665 L 2203 3305 mt 2275 3305 L 2239 3269 mt 2239 3341 L 3543 2502 mt 3615 2502 L 3579 2466 mt 3579 2538 L 4882 1657 mt 4954 1657 L 4918 1621 mt 4918 1693 L 6222 812 mt 6294 812 L 6258 776 mt 6258 848 L gs 899 389 5360 4227 MR c np gr 36 36 899 2417 FO 36 36 2239 3220 FO 36 36 3579 2502 FO 36 36 4918 1657 FO 36 36 6258 685 FO gs 899 389 5360 4227 MR c np gr 863 4426 mt 935 4498 L 935 4426 mt 863 4498 L 2203 3987 mt 2275 4059 L 2275 3987 mt 2203 4059 L 3543 3396 mt 3615 3468 L 3615 3396 mt 3543 3468 L 4882 2762 mt 4954 2834 L 4954 2762 mt 4882 2834 L 6222 2212 mt 6294 2284 L 6294 2212 mt 6222 2284 L gs 899 389 5360 4227 MR c np gr 863 3601 mt 935 3601 L 899 3565 mt 899 3637 L 863 3565 mt 935 3637 L 935 3565 mt 863 3637 L 2203 4066 mt 2275 4066 L 2239 4030 mt 2239 4102 L 2203 4030 mt 2275 4102 L 2275 4030 mt 2203 4102 L 3543 3685 mt 3615 3685 L 3579 3649 mt 3579 3721 L 3543 3649 mt 3615 3721 L 3615 3649 mt 3543 3721 L 4882 3263 mt 4954 3263 L 4918 3227 mt 4918 3299 L 4882 3227 mt 4954 3299 L 4954 3227 mt 4882 3299 L 6222 2798 mt 6294 2798 L 6258 2762 mt 6258 2834 L 6222 2762 mt 6294 2834 L 6294 2762 mt 6222 2834 L gs 899 389 5360 4227 MR c np /Helvetica /ISOLatin1Encoding 216 FMSR gr /Helvetica /ISOLatin1Encoding 216 FMSR 2811 4997 mt (input noise level) s 530 4569 mt -90 rotate (prediction standard error - input noise level) s 90 rotate 2651 258 mt (Training distribution) s end eplot epage end showpage %%EndDocument endTexFig 930 1040 a 14682517 10419816 2960179 12564316 36245749 40192655 startTexFig 930 1040 a %%BeginDocument: cbcltr-mseu.ps /MathWorks 150 dict begin /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef /portraitMode 0 def /landscapeMode 1 def /dpi2point 0 def /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath fill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { 2 copy moveto lineto stroke } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 329 9 6078 5036 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef /Helvetica /ISOLatin1Encoding 144 FMSR 1 j c1 0 0 6917 5187 PR 6 w DO 4 w SO 6 w c0 899 4615 mt 6258 4615 L 899 389 mt 6258 389 L 899 4615 mt 899 389 L 6258 4615 mt 6258 389 L 899 4615 mt 899 4615 L 6258 4615 mt 6258 4615 L 899 4615 mt 6258 4615 L 899 4615 mt 899 389 L 899 4615 mt 899 4615 L 899 4615 mt 899 4561 L 899 389 mt 899 443 L 859 4784 mt (0) s 2239 4615 mt 2239 4561 L 2239 389 mt 2239 443 L 2139 4784 mt (0.1) s 3579 4615 mt 3579 4561 L 3579 389 mt 3579 443 L 3479 4784 mt (0.2) s 4918 4615 mt 4918 4561 L 4918 389 mt 4918 443 L 4818 4784 mt (0.3) s 6258 4615 mt 6258 4561 L 6258 389 mt 6258 443 L 6158 4784 mt (0.4) s 899 4615 mt 953 4615 L 6258 4615 mt 6204 4615 L 784 4668 mt (0) s 899 4145 mt 953 4145 L 6258 4145 mt 6204 4145 L 584 4198 mt (0.01) s 899 3676 mt 953 3676 L 6258 3676 mt 6204 3676 L 584 3729 mt (0.02) s 899 3206 mt 953 3206 L 6258 3206 mt 6204 3206 L 584 3259 mt (0.03) s 899 2737 mt 953 2737 L 6258 2737 mt 6204 2737 L 584 2790 mt (0.04) s 899 2267 mt 953 2267 L 6258 2267 mt 6204 2267 L 584 2320 mt (0.05) s 899 1798 mt 953 1798 L 6258 1798 mt 6204 1798 L 584 1851 mt (0.06) s 899 1328 mt 953 1328 L 6258 1328 mt 6204 1328 L 584 1381 mt (0.07) s 899 859 mt 953 859 L 6258 859 mt 6204 859 L 584 912 mt (0.08) s 899 389 mt 953 389 L 6258 389 mt 6204 389 L 584 442 mt (0.09) s 899 4615 mt 6258 4615 L 899 389 mt 6258 389 L 899 4615 mt 899 389 L 6258 4615 mt 6258 389 L 899 389 mt 899 389 L 6258 389 mt 6258 389 L gs 899 389 5360 4227 MR c np gr 863 3019 mt 935 3019 L 899 2983 mt 899 3055 L 2203 3394 mt 2275 3394 L 2239 3358 mt 2239 3430 L 3543 2502 mt 3615 2502 L 3579 2466 mt 3579 2538 L 4882 1516 mt 4954 1516 L 4918 1480 mt 4918 1552 L 6222 483 mt 6294 483 L 6258 447 mt 6258 519 L gs 899 389 5360 4227 MR c np gr 36 36 899 2549 FO 36 36 2239 3253 FO 36 36 3579 2408 FO 36 36 4918 1469 FO 36 36 6258 483 FO gs 899 389 5360 4227 MR c np gr 863 4109 mt 935 4181 L 935 4109 mt 863 4181 L 2203 4156 mt 2275 4228 L 2275 4156 mt 2203 4228 L 3543 3734 mt 3615 3806 L 3615 3734 mt 3543 3806 L 4882 3311 mt 4954 3383 L 4954 3311 mt 4882 3383 L 6222 2936 mt 6294 3008 L 6294 2936 mt 6222 3008 L gs 899 389 5360 4227 MR c np gr 863 3535 mt 935 3535 L 899 3499 mt 899 3571 L 863 3499 mt 935 3571 L 935 3499 mt 863 3571 L 2203 4145 mt 2275 4145 L 2239 4109 mt 2239 4181 L 2203 4109 mt 2275 4181 L 2275 4109 mt 2203 4181 L 3543 3723 mt 3615 3723 L 3579 3687 mt 3579 3759 L 3543 3687 mt 3615 3759 L 3615 3687 mt 3543 3759 L 4882 3347 mt 4954 3347 L 4918 3311 mt 4918 3383 L 4882 3311 mt 4954 3383 L 4954 3311 mt 4882 3383 L 6222 2878 mt 6294 2878 L 6258 2842 mt 6258 2914 L 6222 2842 mt 6294 2914 L 6294 2842 mt 6222 2914 L gs 899 389 5360 4227 MR c np /Helvetica /ISOLatin1Encoding 216 FMSR gr /Helvetica /ISOLatin1Encoding 216 FMSR 2811 4997 mt (input noise level) s 530 4569 mt -90 rotate (prediction standard error - input noise level) s 90 rotate 2553 258 mt (Uniform V distribution) s end eplot epage end showpage %%EndDocument endTexFig 388 1746 a Fs(\(a\))926 b(\(b\))-50 1759 y 14682517 10419816 4078469 12564316 36245749 40192655 startTexFig -50 1759 a %%BeginDocument: cbcltr-ngt.ps /MathWorks 150 dict begin /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef /portraitMode 0 def /landscapeMode 1 def /dpi2point 0 def /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath fill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { 2 copy moveto lineto stroke } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 529 9 5878 5036 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef /Helvetica /ISOLatin1Encoding 144 FMSR 1 j c1 0 0 6917 5187 PR 6 w DO 4 w SO 6 w c0 899 4615 mt 6258 4615 L 899 389 mt 6258 389 L 899 4615 mt 899 389 L 6258 4615 mt 6258 389 L 899 4615 mt 899 4615 L 6258 4615 mt 6258 4615 L 899 4615 mt 6258 4615 L 899 4615 mt 899 389 L 899 4615 mt 899 4615 L 899 4615 mt 899 4561 L 899 389 mt 899 443 L 859 4784 mt (0) s 2239 4615 mt 2239 4561 L 2239 389 mt 2239 443 L 2139 4784 mt (0.1) s 3579 4615 mt 3579 4561 L 3579 389 mt 3579 443 L 3479 4784 mt (0.2) s 4918 4615 mt 4918 4561 L 4918 389 mt 4918 443 L 4818 4784 mt (0.3) s 6258 4615 mt 6258 4561 L 6258 389 mt 6258 443 L 6158 4784 mt (0.4) s 899 4615 mt 953 4615 L 6258 4615 mt 6204 4615 L 784 4668 mt (0) s 899 4145 mt 953 4145 L 6258 4145 mt 6204 4145 L 784 4198 mt (1) s 899 3676 mt 953 3676 L 6258 3676 mt 6204 3676 L 784 3729 mt (2) s 899 3206 mt 953 3206 L 6258 3206 mt 6204 3206 L 784 3259 mt (3) s 899 2737 mt 953 2737 L 6258 2737 mt 6204 2737 L 784 2790 mt (4) s 899 2267 mt 953 2267 L 6258 2267 mt 6204 2267 L 784 2320 mt (5) s 899 1798 mt 953 1798 L 6258 1798 mt 6204 1798 L 784 1851 mt (6) s 899 1328 mt 953 1328 L 6258 1328 mt 6204 1328 L 784 1381 mt (7) s 899 859 mt 953 859 L 6258 859 mt 6204 859 L 784 912 mt (8) s 899 389 mt 953 389 L 6258 389 mt 6204 389 L 784 442 mt (9) s 899 4615 mt 6258 4615 L 899 389 mt 6258 389 L 899 4615 mt 899 389 L 6258 4615 mt 6258 389 L 899 389 mt 899 389 L 6258 389 mt 6258 389 L gs 899 389 5360 4227 MR c np gr 863 1680 mt 935 1680 L 899 1644 mt 899 1716 L 2203 1586 mt 2275 1586 L 2239 1550 mt 2239 1622 L 3543 1338 mt 3615 1338 L 3579 1302 mt 3579 1374 L 4882 1042 mt 4954 1042 L 4918 1006 mt 4918 1078 L 6222 774 mt 6294 774 L 6258 738 mt 6258 810 L gs 899 389 5360 4227 MR c np gr 36 36 899 1582 FO 36 36 2239 1516 FO 36 36 3579 1244 FO 36 36 4918 985 FO 36 36 6258 798 FO gs 899 389 5360 4227 MR c np gr 863 4213 mt 935 4285 L 935 4213 mt 863 4285 L 2203 3922 mt 2275 3994 L 2275 3922 mt 2203 3994 L 3543 3476 mt 3615 3548 L 3615 3476 mt 3543 3548 L 4882 3053 mt 4954 3125 L 4954 3053 mt 4882 3125 L 6222 2640 mt 6294 2712 L 6294 2640 mt 6222 2712 L gs 899 389 5360 4227 MR c np gr 863 2197 mt 935 2197 L 899 2161 mt 899 2233 L 863 2161 mt 935 2233 L 935 2161 mt 863 2233 L 2203 2173 mt 2275 2173 L 2239 2137 mt 2239 2209 L 2203 2137 mt 2275 2209 L 2275 2137 mt 2203 2209 L 3543 2032 mt 3615 2032 L 3579 1996 mt 3579 2068 L 3543 1996 mt 3615 2068 L 3615 1996 mt 3543 2068 L 4882 1845 mt 4954 1845 L 4918 1809 mt 4918 1881 L 4882 1809 mt 4954 1881 L 4954 1809 mt 4882 1881 L 6222 1610 mt 6294 1610 L 6258 1574 mt 6258 1646 L 6222 1574 mt 6294 1646 L 6294 1574 mt 6222 1646 L gs 899 389 5360 4227 MR c np /Helvetica /ISOLatin1Encoding 216 FMSR gr /Helvetica /ISOLatin1Encoding 216 FMSR 2811 4997 mt (input noise level) s 730 3558 mt -90 rotate (% misclassified states) s 90 rotate 2651 258 mt (Training distribution) s end eplot epage end showpage %%EndDocument endTexFig 930 1759 a 14682517 10419816 4078469 12564316 36245749 40192655 startTexFig 930 1759 a %%BeginDocument: cbcltr-ngu.ps /MathWorks 150 dict begin /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef /portraitMode 0 def /landscapeMode 1 def /dpi2point 0 def /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath fill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { 2 copy moveto lineto stroke } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 529 9 5878 5036 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef /Helvetica /ISOLatin1Encoding 144 FMSR 1 j c1 0 0 6917 5187 PR 6 w DO 4 w SO 6 w c0 899 4615 mt 6258 4615 L 899 389 mt 6258 389 L 899 4615 mt 899 389 L 6258 4615 mt 6258 389 L 899 4615 mt 899 4615 L 6258 4615 mt 6258 4615 L 899 4615 mt 6258 4615 L 899 4615 mt 899 389 L 899 4615 mt 899 4615 L 899 4615 mt 899 4561 L 899 389 mt 899 443 L 859 4784 mt (0) s 2239 4615 mt 2239 4561 L 2239 389 mt 2239 443 L 2139 4784 mt (0.1) s 3579 4615 mt 3579 4561 L 3579 389 mt 3579 443 L 3479 4784 mt (0.2) s 4918 4615 mt 4918 4561 L 4918 389 mt 4918 443 L 4818 4784 mt (0.3) s 6258 4615 mt 6258 4561 L 6258 389 mt 6258 443 L 6158 4784 mt (0.4) s 899 4615 mt 953 4615 L 6258 4615 mt 6204 4615 L 784 4668 mt (0) s 899 3911 mt 953 3911 L 6258 3911 mt 6204 3911 L 784 3964 mt (1) s 899 3206 mt 953 3206 L 6258 3206 mt 6204 3206 L 784 3259 mt (2) s 899 2502 mt 953 2502 L 6258 2502 mt 6204 2502 L 784 2555 mt (3) s 899 1798 mt 953 1798 L 6258 1798 mt 6204 1798 L 784 1851 mt (4) s 899 1093 mt 953 1093 L 6258 1093 mt 6204 1093 L 784 1146 mt (5) s 899 389 mt 953 389 L 6258 389 mt 6204 389 L 784 442 mt (6) s 899 4615 mt 6258 4615 L 899 389 mt 6258 389 L 899 4615 mt 899 389 L 6258 4615 mt 6258 389 L 899 389 mt 899 389 L 6258 389 mt 6258 389 L gs 899 389 5360 4227 MR c np gr 863 1910 mt 935 1910 L 899 1874 mt 899 1946 L 2203 1812 mt 2275 1812 L 2239 1776 mt 2239 1848 L 3543 1424 mt 3615 1424 L 3579 1388 mt 3579 1460 L 4882 1058 mt 4954 1058 L 4918 1022 mt 4918 1094 L 6222 600 mt 6294 600 L 6258 564 mt 6258 636 L gs 899 389 5360 4227 MR c np gr 36 36 899 1903 FO 36 36 2239 1868 FO 36 36 3579 1530 FO 36 36 4918 1100 FO 36 36 6258 636 FO gs 899 389 5360 4227 MR c np gr 863 3952 mt 935 4024 L 935 3952 mt 863 4024 L 2203 3741 mt 2275 3813 L 2275 3741 mt 2203 3813 L 3543 3382 mt 3615 3454 L 3615 3382 mt 3543 3454 L 4882 2959 mt 4954 3031 L 4954 2959 mt 4882 3031 L 6222 2551 mt 6294 2623 L 6294 2551 mt 6222 2623 L gs 899 389 5360 4227 MR c np gr 863 2185 mt 935 2185 L 899 2149 mt 899 2221 L 863 2149 mt 935 2221 L 935 2149 mt 863 2221 L 2203 2150 mt 2275 2150 L 2239 2114 mt 2239 2186 L 2203 2114 mt 2275 2186 L 2275 2114 mt 2203 2186 L 3543 1939 mt 3615 1939 L 3579 1903 mt 3579 1975 L 3543 1903 mt 3615 1975 L 3615 1903 mt 3543 1975 L 4882 1657 mt 4954 1657 L 4918 1621 mt 4918 1693 L 4882 1621 mt 4954 1693 L 4954 1621 mt 4882 1693 L 6222 1375 mt 6294 1375 L 6258 1339 mt 6258 1411 L 6222 1339 mt 6294 1411 L 6294 1339 mt 6222 1411 L gs 899 389 5360 4227 MR c np /Helvetica /ISOLatin1Encoding 216 FMSR gr /Helvetica /ISOLatin1Encoding 216 FMSR 2811 4997 mt (input noise level) s 730 3558 mt -90 rotate (% misclassified states) s 90 rotate 2553 258 mt (Uniform V distribution) s end eplot epage end showpage %%EndDocument endTexFig 390 2465 a Fs(\(c\))h(\(d\))-75 2553 y(Figure)13 b(5:)k(T)m(est)c(set) h(p)q(erformance)f(of)f(the)i(MME)f(and)f(ME)i(mo)q(dels)d(for)i(v)n (arious)f(lev)o(els)h(of)f(the)i(input)e(noise)h Fk(\033)1694 2559 y Fj(in)1741 2553 y Fs(on)g(t)o(w)o(o)f(di\013eren)o(t)-75 2599 y(distribuitons.)17 b(\(a\))c(and)f(\(b\):)18 b(\(Prediction)13 b(MSE\))734 2584 y Fn(1)p Fj(=)p Fn(2)793 2599 y Fh(\000)6 b Fk(\033)855 2605 y Fj(in)889 2599 y Fs(;)13 b(\(c\))g(and)f(\(d\):)18 b(the)13 b(p)q(ercen)o(tage)h(of)e(misclassi\014ed)g(states.)18 b Fh(\002)13 b Fs({)f(MME,)-75 2645 y(no)i(noise;)f(*)h({)f(MME)i (noise)f(0)p Fk(:)p Fs(2;)e Fh(\016)i Fs({)f(ME,)h(no)f(noise;)h(+)g({) g(ME,)f(noise)h(0)p Fk(:)p Fs(2.)965 2727 y(6)p eop %%Page: 7 8 7 7 bop 98 -112 a 27707273 11840716 9077882 20326563 39929528 33482915 startTexFig 98 -112 a %%BeginDocument: cbcltr-pred.ps save /d_sv_obj exch def userdict /IslandDrawDict 300 dict dup begin put /bdef {bind def} bind def /E {exch} bdef /FF {findfont} bdef /MF {makefont} bdef /RO {rotate} bdef /SC {scale} bdef /SF {setfont} bdef /SG {setgray} bdef /TR {translate} bdef /bp {lj lw rgb} bdef /bpbw {lj lw setgray} bdef /c {curveto} bdef /cl {closepath} bdef /fi {eofill} bdef /g {setgray} bdef /gr {grestore} bdef /gs {gsave} bdef /l {lineto} bdef /lj {setlinejoin} bdef /lw {setlinewidth} bdef /m {moveto} bdef /n {newpath} bdef /nx {/x E def} bdef /r {rmoveto} bdef /rl {rlineto} bdef /rgb {setrgbcolor} bdef /s {show} bdef /sd {setdash} bdef /sp {x 0 rmoveto} bdef /ss {currentpoint pop E m} bdef /st {stroke} bdef /BPSIDE 32 def %% pixels per pattern side /PATFREQ 3.0 def %% pattern pixels per mm /dp_mat [PATFREQ 0 0 PATFREQ 0 0] def /dp_pw BPSIDE def %% pattern pixel width /dp_ph BPSIDE def %% pattern pixel height /dp_w dp_pw PATFREQ div def %% pattern mm width /dp_h dp_ph PATFREQ div def %% pattern mm height /savemat matrix def /topmat matrix def /patmat matrix def /ncpoint errordict /nocurrentpoint get def errordict begin /nocurrentpoint { dup /pathbbox load eq {pop 0 0 1 1} {ncpoint} ifelse } bdef end /ar { %% sa ea sx sy rot tx ty matrix currentmatrix 8 1 roll TR RO SC n 0 0 1 5 3 roll arc setmatrix } bdef /arn { %% sa ea sx sy rot tx ty TR RO SC matrix currentmatrix 8 1 roll n 0 0 1 5 3 roll arcn setmatrix } bdef /el { %% sx sy rot tx ty matrix currentmatrix 6 1 roll TR RO SC n 0 0 1 0 360 arc setmatrix cl } bdef /image_raster { %% sw sh sd dw dh xs ys TR 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} ifelse } { pop pop } ifelse } forall newfont /FontName new_font_name put new_codes_and_names aload pop new_codes_and_names length 2 idiv { newfont /Encoding get 3 1 roll put } repeat new_font_name newfont definefont pop end %reencode_small_dict } def /extended_Zapf [ 8#223 /a89 8#224 /a90 8#225 /a93 8#226 /a94 8#227 /a91 8#230 /a92 8#231 /a205 8#232 /a85 8#233 /a206 8#234 /a86 8#235 /a87 8#236 /a88 8#237 /a95 8#240 /a96 ] def /extended_Standard [ 29 /thorn 30 /yacute 31 /divide 128 /Acircumflex 129 /Adieresis 130 /Agrave 131 /Aring 132 /Atilde 133 /Ccedilla 134 /Eacute 135 /Ecircumflex 136 /Edieresis 137 /Egrave 138 /Iacute 139 /Icircumflex 140 /Idieresis 141 /Igrave 142 /Ntilde 143 /Oacute 144 /Ocircumflex 145 /Odieresis 146 /Ograve 147 /Otilde 148 /Scaron 149 /Uacute 150 /Ucircumflex 151 /Udieresis 152 /Ugrave 153 /Ydieresis 154 /Zcaron 155 /aacute 156 /acircumflex 157 /adieresis 158 /agrave 159 /aring 160 /atilde 161 /exclamdown 162 /cent 163 /sterling 164 /fraction 165 /yen 166 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105.01 l 62.251 110.34 l 56.918 110.34 l cl eoclip gsave n 56.918 110.34 m 56.918 105.01 l 62.251 105.01 l 62.251 110.34 l 56.918 110.34 l cl eoclip n 56.918 110.34 m 56.918 105.01 l 62.251 105.01 l 62.251 110.34 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 56.918 105.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 62.251 105.01 m 62.251 99.677 l 67.585 99.677 l 67.585 105.01 l 62.251 105.01 l cl eoclip gsave n 62.251 105.01 m 62.251 99.677 l 67.585 99.677 l 67.585 105.01 l 62.251 105.01 l cl eoclip gsave n 62.251 105.01 m 62.251 99.677 l 67.585 99.677 l 67.585 105.01 l 62.251 105.01 l cl eoclip n 62.251 105.01 m 62.251 99.677 l 67.585 99.677 l 67.585 105.01 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.334 62.251 99.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 62.251 110.34 m 62.251 105.01 l 67.585 105.01 l 67.585 110.34 l 62.251 110.34 l cl eoclip gsave n 62.251 110.34 m 62.251 105.01 l 67.585 105.01 l 67.585 110.34 l 62.251 110.34 l cl eoclip gsave n 62.251 110.34 m 62.251 105.01 l 67.585 105.01 l 67.585 110.34 l 62.251 110.34 l cl eoclip n 62.251 110.34 m 62.251 105.01 l 67.585 105.01 l 67.585 110.34 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.333 62.251 105.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 67.585 105.01 m 67.585 99.677 l 72.918 99.677 l 72.918 105.01 l 67.585 105.01 l cl eoclip gsave n 67.585 105.01 m 67.585 99.677 l 72.918 99.677 l 72.918 105.01 l 67.585 105.01 l cl eoclip gsave n 67.585 105.01 m 67.585 99.677 l 72.918 99.677 l 72.918 105.01 l 67.585 105.01 l cl eoclip n 67.585 105.01 m 67.585 99.677 l 72.918 99.677 l 72.918 105.01 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.334 67.585 99.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 67.585 110.34 m 67.585 105.01 l 72.918 105.01 l 72.918 110.34 l 67.585 110.34 l cl eoclip gsave n 67.585 110.34 m 67.585 105.01 l 72.918 105.01 l 72.918 110.34 l 67.585 110.34 l cl eoclip gsave n 67.585 110.34 m 67.585 105.01 l 72.918 105.01 l 72.918 110.34 l 67.585 110.34 l cl eoclip n 67.585 110.34 m 67.585 105.01 l 72.918 105.01 l 72.918 110.34 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 67.585 105.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 72.918 105.01 m 72.918 99.677 l 78.251 99.677 l 78.251 105.01 l 72.918 105.01 l cl eoclip gsave n 72.918 105.01 m 72.918 99.677 l 78.251 99.677 l 78.251 105.01 l 72.918 105.01 l cl eoclip gsave n 72.918 105.01 m 72.918 99.677 l 78.251 99.677 l 78.251 105.01 l 72.918 105.01 l cl eoclip n 72.918 105.01 m 72.918 99.677 l 78.251 99.677 l 78.251 105.01 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.334 72.918 99.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 72.918 110.34 m 72.918 105.01 l 78.251 105.01 l 78.251 110.34 l 72.918 110.34 l cl eoclip gsave n 72.918 110.34 m 72.918 105.01 l 78.251 105.01 l 78.251 110.34 l 72.918 110.34 l cl eoclip gsave n 72.918 110.34 m 72.918 105.01 l 78.251 105.01 l 78.251 110.34 l 72.918 110.34 l cl eoclip n 72.918 110.34 m 72.918 105.01 l 78.251 105.01 l 78.251 110.34 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 72.918 105.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 78.251 105.01 m 78.251 99.677 l 83.585 99.677 l 83.585 105.01 l 78.251 105.01 l cl eoclip gsave n 78.251 105.01 m 78.251 99.677 l 83.585 99.677 l 83.585 105.01 l 78.251 105.01 l cl eoclip gsave n 78.251 105.01 m 78.251 99.677 l 83.585 99.677 l 83.585 105.01 l 78.251 105.01 l cl eoclip n 78.251 105.01 m 78.251 99.677 l 83.585 99.677 l 83.585 105.01 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.334 78.251 99.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 78.251 110.34 m 78.251 105.01 l 83.585 105.01 l 83.585 110.34 l 78.251 110.34 l cl eoclip gsave n 78.251 110.34 m 78.251 105.01 l 83.585 105.01 l 83.585 110.34 l 78.251 110.34 l cl eoclip gsave n 78.251 110.34 m 78.251 105.01 l 83.585 105.01 l 83.585 110.34 l 78.251 110.34 l cl eoclip n 78.251 110.34 m 78.251 105.01 l 83.585 105.01 l 83.585 110.34 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.333 78.251 105.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 83.585 105.01 m 83.585 99.677 l 88.918 99.677 l 88.918 105.01 l 83.585 105.01 l cl eoclip gsave n 83.585 105.01 m 83.585 99.677 l 88.918 99.677 l 88.918 105.01 l 83.585 105.01 l cl eoclip gsave n 83.585 105.01 m 83.585 99.677 l 88.918 99.677 l 88.918 105.01 l 83.585 105.01 l cl eoclip n 83.585 105.01 m 83.585 99.677 l 88.918 99.677 l 88.918 105.01 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.334 83.585 99.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 83.585 110.34 m 83.585 105.01 l 88.918 105.01 l 88.918 110.34 l 83.585 110.34 l cl eoclip gsave n 83.585 110.34 m 83.585 105.01 l 88.918 105.01 l 88.918 110.34 l 83.585 110.34 l cl eoclip gsave n 83.585 110.34 m 83.585 105.01 l 88.918 105.01 l 88.918 110.34 l 83.585 110.34 l cl eoclip n 83.585 110.34 m 83.585 105.01 l 88.918 105.01 l 88.918 110.34 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 83.585 105.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 88.918 105.01 m 88.918 99.677 l 94.251 99.677 l 94.251 105.01 l 88.918 105.01 l cl eoclip gsave n 88.918 105.01 m 88.918 99.677 l 94.251 99.677 l 94.251 105.01 l 88.918 105.01 l cl eoclip gsave n 88.918 105.01 m 88.918 99.677 l 94.251 99.677 l 94.251 105.01 l 88.918 105.01 l cl eoclip n 88.918 105.01 m 88.918 99.677 l 94.251 99.677 l 94.251 105.01 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.334 88.918 99.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 88.918 110.34 m 88.918 105.01 l 94.251 105.01 l 94.251 110.34 l 88.918 110.34 l cl eoclip gsave n 88.918 110.34 m 88.918 105.01 l 94.251 105.01 l 94.251 110.34 l 88.918 110.34 l cl eoclip gsave n 88.918 110.34 m 88.918 105.01 l 94.251 105.01 l 94.251 110.34 l 88.918 110.34 l cl eoclip n 88.918 110.34 m 88.918 105.01 l 94.251 105.01 l 94.251 110.34 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 88.918 105.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 94.251 105.01 m 94.251 99.677 l 99.585 99.677 l 99.585 105.01 l 94.251 105.01 l cl eoclip gsave n 94.251 105.01 m 94.251 99.677 l 99.585 99.677 l 99.585 105.01 l 94.251 105.01 l cl eoclip gsave n 94.251 105.01 m 94.251 99.677 l 99.585 99.677 l 99.585 105.01 l 94.251 105.01 l cl eoclip n 94.251 105.01 m 94.251 99.677 l 99.585 99.677 l 99.585 105.01 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.334 94.251 99.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 94.251 110.34 m 94.251 105.01 l 99.585 105.01 l 99.585 110.34 l 94.251 110.34 l cl eoclip gsave n 94.251 110.34 m 94.251 105.01 l 99.585 105.01 l 99.585 110.34 l 94.251 110.34 l cl eoclip gsave n 94.251 110.34 m 94.251 105.01 l 99.585 105.01 l 99.585 110.34 l 94.251 110.34 l cl eoclip n 94.251 110.34 m 94.251 105.01 l 99.585 105.01 l 99.585 110.34 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.333 94.251 105.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 99.585 105.01 m 99.585 99.677 l 104.92 99.677 l 104.92 105.01 l 99.585 105.01 l cl eoclip gsave n 99.585 105.01 m 99.585 99.677 l 104.92 99.677 l 104.92 105.01 l 99.585 105.01 l cl eoclip gsave n 99.585 105.01 m 99.585 99.677 l 104.92 99.677 l 104.92 105.01 l 99.585 105.01 l cl eoclip n 99.585 105.01 m 99.585 99.677 l 104.92 99.677 l 104.92 105.01 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.334 99.585 99.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 99.585 110.34 m 99.585 105.01 l 104.92 105.01 l 104.92 110.34 l 99.585 110.34 l cl eoclip gsave n 99.585 110.34 m 99.585 105.01 l 104.92 105.01 l 104.92 110.34 l 99.585 110.34 l cl eoclip gsave n 99.585 110.34 m 99.585 105.01 l 104.92 105.01 l 104.92 110.34 l 99.585 110.34 l cl eoclip n 99.585 110.34 m 99.585 105.01 l 104.92 105.01 l 104.92 110.34 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 99.585 105.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 104.92 105.01 m 104.92 99.677 l 110.25 99.677 l 110.25 105.01 l 104.92 105.01 l cl eoclip gsave n 104.92 105.01 m 104.92 99.677 l 110.25 99.677 l 110.25 105.01 l 104.92 105.01 l cl eoclip gsave n 104.92 105.01 m 104.92 99.677 l 110.25 99.677 l 110.25 105.01 l 104.92 105.01 l cl eoclip n 104.92 105.01 m 104.92 99.677 l 110.25 99.677 l 110.25 105.01 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.334 104.918 99.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 104.92 110.34 m 104.92 105.01 l 110.25 105.01 l 110.25 110.34 l 104.92 110.34 l cl eoclip gsave n 104.92 110.34 m 104.92 105.01 l 110.25 105.01 l 110.25 110.34 l 104.92 110.34 l cl eoclip gsave n 104.92 110.34 m 104.92 105.01 l 110.25 105.01 l 110.25 110.34 l 104.92 110.34 l cl eoclip n 104.92 110.34 m 104.92 105.01 l 110.25 105.01 l 110.25 110.34 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 104.918 105.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 110.25 105.01 m 110.25 99.677 l 115.58 99.677 l 115.58 105.01 l 110.25 105.01 l cl eoclip gsave n 110.25 105.01 m 110.25 99.677 l 115.58 99.677 l 115.58 105.01 l 110.25 105.01 l cl eoclip gsave n 110.25 105.01 m 110.25 99.677 l 115.58 99.677 l 115.58 105.01 l 110.25 105.01 l cl eoclip n 110.25 105.01 m 110.25 99.677 l 115.58 99.677 l 115.58 105.01 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.334 110.251 99.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 110.25 110.34 m 110.25 105.01 l 115.58 105.01 l 115.58 110.34 l 110.25 110.34 l cl eoclip gsave n 110.25 110.34 m 110.25 105.01 l 115.58 105.01 l 115.58 110.34 l 110.25 110.34 l cl eoclip gsave n 110.25 110.34 m 110.25 105.01 l 115.58 105.01 l 115.58 110.34 l 110.25 110.34 l cl eoclip n 110.25 110.34 m 110.25 105.01 l 115.58 105.01 l 115.58 110.34 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.333 110.251 105.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 115.58 105.01 m 115.58 99.677 l 120.92 99.677 l 120.92 105.01 l 115.58 105.01 l cl eoclip gsave n 115.58 105.01 m 115.58 99.677 l 120.92 99.677 l 120.92 105.01 l 115.58 105.01 l cl eoclip gsave n 115.58 105.01 m 115.58 99.677 l 120.92 99.677 l 120.92 105.01 l 115.58 105.01 l cl eoclip n 115.58 105.01 m 115.58 99.677 l 120.92 99.677 l 120.92 105.01 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.334 115.585 99.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 115.58 110.34 m 115.58 105.01 l 120.92 105.01 l 120.92 110.34 l 115.58 110.34 l cl eoclip gsave n 115.58 110.34 m 115.58 105.01 l 120.92 105.01 l 120.92 110.34 l 115.58 110.34 l cl eoclip gsave n 115.58 110.34 m 115.58 105.01 l 120.92 105.01 l 120.92 110.34 l 115.58 110.34 l cl eoclip n 115.58 110.34 m 115.58 105.01 l 120.92 105.01 l 120.92 110.34 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.333 115.585 105.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 120.92 105.01 m 120.92 99.677 l 126.25 99.677 l 126.25 105.01 l 120.92 105.01 l cl eoclip gsave n 120.92 105.01 m 120.92 99.677 l 126.25 99.677 l 126.25 105.01 l 120.92 105.01 l cl eoclip gsave n 120.92 105.01 m 120.92 99.677 l 126.25 99.677 l 126.25 105.01 l 120.92 105.01 l cl eoclip n 120.92 105.01 m 120.92 99.677 l 126.25 99.677 l 126.25 105.01 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.334 120.918 99.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 120.92 110.34 m 120.92 105.01 l 126.25 105.01 l 126.25 110.34 l 120.92 110.34 l cl eoclip gsave n 120.92 110.34 m 120.92 105.01 l 126.25 105.01 l 126.25 110.34 l 120.92 110.34 l cl eoclip gsave n 120.92 110.34 m 120.92 105.01 l 126.25 105.01 l 126.25 110.34 l 120.92 110.34 l cl eoclip n 120.92 110.34 m 120.92 105.01 l 126.25 105.01 l 126.25 110.34 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 120.918 105.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore grestore n 130.09 167.14 m 122.6 167.14 l 122.6 101.29 l 130.09 101.29 l 130.09 167.14 l cl 0 0 1 F 1 1 1 setrgbcolor /dp_proc pat0 def false PF gsave n 167.86 201.6 m 152.89 201.6 l 152.89 69.905 l 167.86 69.905 l 167.86 201.6 l cl eoclip gsave n 120.92 105.01 m 120.92 99.677 l 126.25 99.677 l 126.25 105.01 l 120.92 105.01 l cl eoclip gsave n 120.92 105.01 m 120.92 99.677 l 126.25 99.677 l 126.25 105.01 l 120.92 105.01 l cl eoclip gsave n 120.92 105.01 m 120.92 99.677 l 126.25 99.677 l 126.25 105.01 l 120.92 105.01 l cl eoclip n 120.92 105.01 m 120.92 99.677 l 126.25 99.677 l 126.25 105.01 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.334 120.918 99.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 120.92 110.34 m 120.92 105.01 l 126.25 105.01 l 126.25 110.34 l 120.92 110.34 l cl eoclip gsave n 120.92 110.34 m 120.92 105.01 l 126.25 105.01 l 126.25 110.34 l 120.92 110.34 l cl eoclip gsave n 120.92 110.34 m 120.92 105.01 l 126.25 105.01 l 126.25 110.34 l 120.92 110.34 l cl eoclip n 120.92 110.34 m 120.92 105.01 l 126.25 105.01 l 126.25 110.34 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 120.918 105.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 120.92 115.68 m 120.92 110.34 l 126.25 110.34 l 126.25 115.68 l 120.92 115.68 l cl eoclip gsave n 120.92 115.68 m 120.92 110.34 l 126.25 110.34 l 126.25 115.68 l 120.92 115.68 l cl eoclip gsave n 120.92 115.68 m 120.92 110.34 l 126.25 110.34 l 126.25 115.68 l 120.92 115.68 l cl eoclip n 120.92 115.68 m 120.92 110.34 l 126.25 110.34 l 126.25 115.68 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 120.918 110.343 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 120.92 121.01 m 120.92 115.68 l 126.25 115.68 l 126.25 121.01 l 120.92 121.01 l cl eoclip gsave n 120.92 121.01 m 120.92 115.68 l 126.25 115.68 l 126.25 121.01 l 120.92 121.01 l cl eoclip gsave n 120.92 121.01 m 120.92 115.68 l 126.25 115.68 l 126.25 121.01 l 120.92 121.01 l cl eoclip n 120.92 121.01 m 120.92 115.68 l 126.25 115.68 l 126.25 121.01 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.334 120.918 115.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 120.92 126.34 m 120.92 121.01 l 126.25 121.01 l 126.25 126.34 l 120.92 126.34 l cl eoclip gsave n 120.92 126.34 m 120.92 121.01 l 126.25 121.01 l 126.25 126.34 l 120.92 126.34 l cl eoclip gsave n 120.92 126.34 m 120.92 121.01 l 126.25 121.01 l 126.25 126.34 l 120.92 126.34 l cl eoclip n 120.92 126.34 m 120.92 121.01 l 126.25 121.01 l 126.25 126.34 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 120.918 121.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 120.92 131.68 m 120.92 126.34 l 126.25 126.34 l 126.25 131.68 l 120.92 131.68 l cl eoclip gsave n 120.92 131.68 m 120.92 126.34 l 126.25 126.34 l 126.25 131.68 l 120.92 131.68 l cl eoclip gsave n 120.92 131.68 m 120.92 126.34 l 126.25 126.34 l 126.25 131.68 l 120.92 131.68 l cl eoclip n 120.92 131.68 m 120.92 126.34 l 126.25 126.34 l 126.25 131.68 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 120.918 126.343 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 120.92 137.01 m 120.92 131.68 l 126.25 131.68 l 126.25 137.01 l 120.92 137.01 l cl eoclip gsave n 120.92 137.01 m 120.92 131.68 l 126.25 131.68 l 126.25 137.01 l 120.92 137.01 l cl eoclip gsave n 120.92 137.01 m 120.92 131.68 l 126.25 131.68 l 126.25 137.01 l 120.92 137.01 l cl eoclip n 120.92 137.01 m 120.92 131.68 l 126.25 131.68 l 126.25 137.01 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.334 120.918 131.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 120.92 142.34 m 120.92 137.01 l 126.25 137.01 l 126.25 142.34 l 120.92 142.34 l cl eoclip gsave n 120.92 142.34 m 120.92 137.01 l 126.25 137.01 l 126.25 142.34 l 120.92 142.34 l cl eoclip gsave n 120.92 142.34 m 120.92 137.01 l 126.25 137.01 l 126.25 142.34 l 120.92 142.34 l cl eoclip n 120.92 142.34 m 120.92 137.01 l 126.25 137.01 l 126.25 142.34 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 120.918 137.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 120.92 147.68 m 120.92 142.34 l 126.25 142.34 l 126.25 147.68 l 120.92 147.68 l cl eoclip gsave n 120.92 147.68 m 120.92 142.34 l 126.25 142.34 l 126.25 147.68 l 120.92 147.68 l cl eoclip gsave n 120.92 147.68 m 120.92 142.34 l 126.25 142.34 l 126.25 147.68 l 120.92 147.68 l cl eoclip n 120.92 147.68 m 120.92 142.34 l 126.25 142.34 l 126.25 147.68 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 120.918 142.343 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 120.92 153.01 m 120.92 147.68 l 126.25 147.68 l 126.25 153.01 l 120.92 153.01 l cl eoclip gsave n 120.92 153.01 m 120.92 147.68 l 126.25 147.68 l 126.25 153.01 l 120.92 153.01 l cl eoclip gsave n 120.92 153.01 m 120.92 147.68 l 126.25 147.68 l 126.25 153.01 l 120.92 153.01 l cl eoclip n 120.92 153.01 m 120.92 147.68 l 126.25 147.68 l 126.25 153.01 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 120.918 147.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 120.92 158.34 m 120.92 153.01 l 126.25 153.01 l 126.25 158.34 l 120.92 158.34 l cl eoclip gsave n 120.92 158.34 m 120.92 153.01 l 126.25 153.01 l 126.25 158.34 l 120.92 158.34 l cl eoclip gsave n 120.92 158.34 m 120.92 153.01 l 126.25 153.01 l 126.25 158.34 l 120.92 158.34 l cl eoclip n 120.92 158.34 m 120.92 153.01 l 126.25 153.01 l 126.25 158.34 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 120.918 153.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 120.92 163.68 m 120.92 158.34 l 126.25 158.34 l 126.25 163.68 l 120.92 163.68 l cl eoclip gsave n 120.92 163.68 m 120.92 158.34 l 126.25 158.34 l 126.25 163.68 l 120.92 163.68 l cl eoclip gsave n 120.92 163.68 m 120.92 158.34 l 126.25 158.34 l 126.25 163.68 l 120.92 163.68 l cl eoclip n 120.92 163.68 m 120.92 158.34 l 126.25 158.34 l 126.25 163.68 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 120.918 158.343 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 120.92 169.01 m 120.92 163.68 l 126.25 163.68 l 126.25 169.01 l 120.92 169.01 l cl eoclip gsave n 120.92 169.01 m 120.92 163.68 l 126.25 163.68 l 126.25 169.01 l 120.92 169.01 l cl eoclip gsave n 120.92 169.01 m 120.92 163.68 l 126.25 163.68 l 126.25 169.01 l 120.92 169.01 l cl eoclip n 120.92 169.01 m 120.92 163.68 l 126.25 163.68 l 126.25 169.01 l cl gsave eoclip savemat currentmatrix pop [ 5.333 0 0 5.333 120.918 163.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 126.25 105.01 m 126.25 99.677 l 131.58 99.677 l 131.58 105.01 l 126.25 105.01 l cl eoclip gsave n 126.25 105.01 m 126.25 99.677 l 131.58 99.677 l 131.58 105.01 l 126.25 105.01 l cl eoclip gsave n 126.25 105.01 m 126.25 99.677 l 131.59 99.677 l 131.59 105.01 l 126.25 105.01 l cl eoclip n 126.25 105.01 m 126.25 99.677 l 131.59 99.677 l 131.59 105.01 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.334 126.251 99.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 126.25 110.34 m 126.25 105.01 l 131.58 105.01 l 131.58 110.34 l 126.25 110.34 l cl eoclip gsave n 126.25 110.34 m 126.25 105.01 l 131.58 105.01 l 131.58 110.34 l 126.25 110.34 l cl eoclip gsave n 126.25 110.34 m 126.25 105.01 l 131.59 105.01 l 131.59 110.34 l 126.25 110.34 l cl eoclip n 126.25 110.34 m 126.25 105.01 l 131.59 105.01 l 131.59 110.34 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.333 126.251 105.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 126.25 115.68 m 126.25 110.34 l 131.58 110.34 l 131.58 115.68 l 126.25 115.68 l cl eoclip gsave n 126.25 115.68 m 126.25 110.34 l 131.58 110.34 l 131.58 115.68 l 126.25 115.68 l cl eoclip gsave n 126.25 115.68 m 126.25 110.34 l 131.59 110.34 l 131.59 115.68 l 126.25 115.68 l cl eoclip n 126.25 115.68 m 126.25 110.34 l 131.59 110.34 l 131.59 115.68 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.333 126.251 110.343 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 126.25 121.01 m 126.25 115.68 l 131.58 115.68 l 131.58 121.01 l 126.25 121.01 l cl eoclip gsave n 126.25 121.01 m 126.25 115.68 l 131.58 115.68 l 131.58 121.01 l 126.25 121.01 l cl eoclip gsave n 126.25 121.01 m 126.25 115.68 l 131.59 115.68 l 131.59 121.01 l 126.25 121.01 l cl eoclip n 126.25 121.01 m 126.25 115.68 l 131.59 115.68 l 131.59 121.01 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.334 126.251 115.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 126.25 126.34 m 126.25 121.01 l 131.58 121.01 l 131.58 126.34 l 126.25 126.34 l cl eoclip gsave n 126.25 126.34 m 126.25 121.01 l 131.58 121.01 l 131.58 126.34 l 126.25 126.34 l cl eoclip gsave n 126.25 126.34 m 126.25 121.01 l 131.59 121.01 l 131.59 126.34 l 126.25 126.34 l cl eoclip n 126.25 126.34 m 126.25 121.01 l 131.59 121.01 l 131.59 126.34 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.333 126.251 121.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 126.25 131.68 m 126.25 126.34 l 131.58 126.34 l 131.58 131.68 l 126.25 131.68 l cl eoclip gsave n 126.25 131.68 m 126.25 126.34 l 131.58 126.34 l 131.58 131.68 l 126.25 131.68 l cl eoclip gsave n 126.25 131.68 m 126.25 126.34 l 131.59 126.34 l 131.59 131.68 l 126.25 131.68 l cl eoclip n 126.25 131.68 m 126.25 126.34 l 131.59 126.34 l 131.59 131.68 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.333 126.251 126.343 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 126.25 137.01 m 126.25 131.68 l 131.58 131.68 l 131.58 137.01 l 126.25 137.01 l cl eoclip gsave n 126.25 137.01 m 126.25 131.68 l 131.58 131.68 l 131.58 137.01 l 126.25 137.01 l cl eoclip gsave n 126.25 137.01 m 126.25 131.68 l 131.59 131.68 l 131.59 137.01 l 126.25 137.01 l cl eoclip n 126.25 137.01 m 126.25 131.68 l 131.59 131.68 l 131.59 137.01 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.334 126.251 131.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 126.25 142.34 m 126.25 137.01 l 131.58 137.01 l 131.58 142.34 l 126.25 142.34 l cl eoclip gsave n 126.25 142.34 m 126.25 137.01 l 131.58 137.01 l 131.58 142.34 l 126.25 142.34 l cl eoclip gsave n 126.25 142.34 m 126.25 137.01 l 131.59 137.01 l 131.59 142.34 l 126.25 142.34 l cl eoclip n 126.25 142.34 m 126.25 137.01 l 131.59 137.01 l 131.59 142.34 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.333 126.251 137.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 126.25 147.68 m 126.25 142.34 l 131.58 142.34 l 131.58 147.68 l 126.25 147.68 l cl eoclip gsave n 126.25 147.68 m 126.25 142.34 l 131.58 142.34 l 131.58 147.68 l 126.25 147.68 l cl eoclip gsave n 126.25 147.68 m 126.25 142.34 l 131.59 142.34 l 131.59 147.68 l 126.25 147.68 l cl eoclip n 126.25 147.68 m 126.25 142.34 l 131.59 142.34 l 131.59 147.68 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.333 126.251 142.343 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 126.25 153.01 m 126.25 147.68 l 131.58 147.68 l 131.58 153.01 l 126.25 153.01 l cl eoclip gsave n 126.25 153.01 m 126.25 147.68 l 131.58 147.68 l 131.58 153.01 l 126.25 153.01 l cl eoclip gsave n 126.25 153.01 m 126.25 147.68 l 131.59 147.68 l 131.59 153.01 l 126.25 153.01 l cl eoclip n 126.25 153.01 m 126.25 147.68 l 131.59 147.68 l 131.59 153.01 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.333 126.251 147.677 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101808080804040404020202020 1010101008080808040404040202020201010101 savemat setmatrix grestore grestore grestore grestore gsave n 126.25 158.34 m 126.25 153.01 l 131.58 153.01 l 131.58 158.34 l 126.25 158.34 l cl eoclip gsave n 126.25 158.34 m 126.25 153.01 l 131.58 153.01 l 131.58 158.34 l 126.25 158.34 l cl eoclip gsave n 126.25 158.34 m 126.25 153.01 l 131.59 153.01 l 131.59 158.34 l 126.25 158.34 l cl eoclip n 126.25 158.34 m 126.25 153.01 l 131.59 153.01 l 131.59 158.34 l cl gsave eoclip savemat currentmatrix pop [ 5.334 0 0 5.333 126.251 153.01 ] concat 1 1 1 setrgbcolor 32 32 1 1 0 0 imagemask_raster 808080804040404020202020101010100808080804040404020202020101010180808080 404040402020202010101010080808080404040402020202010101018080808040404040 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2677 y Fs(\()p Fk(t)p Fs(\))1624 2619 y Fg(\024)1651 2649 y Fk(\030)1669 2655 y Fj(ik)1701 2649 y Fs(\()p Fk(t)p Fs(\))p 1651 2668 98 2 v 1655 2706 a Fk(\015)1676 2712 y Fj(k)1697 2706 y Fs(\()p Fk(t)p Fs(\))1762 2677 y Fh(\000)10 b Fk(a)1826 2683 y Fj(ik)1858 2677 y Fs(\()p Fk(t)p Fs(\))1905 2619 y Fg(\025)954 2727 y Fs(10)p eop %%Page: 11 12 11 11 bop 492 -112 a 15250861 10893473 9933045 11643371 27562557 24207687 startTexFig 492 -112 a %%BeginDocument: cbcltr-altgate.ps save /d_sv_obj exch def userdict /IslandDrawDict 300 dict dup begin put /bdef {bind def} bind def /E {exch} bdef /FF {findfont} bdef /MF {makefont} bdef /RO {rotate} bdef /SC {scale} bdef /SF {setfont} bdef /SG {setgray} bdef /TR {translate} bdef /bp {lj lw rgb} bdef /bpbw {lj lw setgray} bdef /c {curveto} bdef /cl {closepath} bdef /fi {eofill} bdef /g {setgray} bdef /gr {grestore} bdef /gs {gsave} bdef /l {lineto} bdef /lj {setlinejoin} bdef /lw {setlinewidth} bdef /m {moveto} bdef /n {newpath} bdef /nx {/x E def} bdef /r {rmoveto} bdef /rl {rlineto} bdef /rgb {setrgbcolor} bdef /s {show} bdef /sd {setdash} bdef /sp {x 0 rmoveto} bdef /ss {currentpoint pop E m} bdef /st {stroke} bdef /BPSIDE 32 def %% pixels per pattern side /PATFREQ 3.0 def %% pattern pixels per mm /dp_mat [PATFREQ 0 0 PATFREQ 0 0] def /dp_pw BPSIDE def %% pattern pixel width /dp_ph BPSIDE def %% pattern pixel height /dp_w dp_pw PATFREQ div def %% pattern mm width /dp_h dp_ph PATFREQ div def %% pattern mm height /savemat matrix def /topmat matrix def /patmat matrix def /ncpoint errordict /nocurrentpoint get def errordict begin /nocurrentpoint { dup /pathbbox load eq {pop 0 0 1 1} {ncpoint} ifelse } bdef end /ar { %% sa ea sx sy rot tx ty matrix currentmatrix 8 1 roll TR RO SC n 0 0 1 5 3 roll arc setmatrix } bdef /arn { %% sa ea sx sy rot tx ty TR RO SC matrix currentmatrix 8 1 roll n 0 0 1 5 3 roll arcn setmatrix } bdef /el { %% sx sy rot tx ty matrix currentmatrix 6 1 roll TR RO SC n 0 0 1 0 360 arc setmatrix cl } bdef /image_raster { %% sw sh sd dw dh xs ys TR SC /sd E def /sh E def /sw E def /imagebuf sw sd mul 7 add 8 idiv string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop} image } bdef /imagemask_raster { TR SC /sh E def /sw E def /imagebuf sw 7 add 8 idiv string def sw sh false [sw 0 0 sh 0 0] {currentfile imagebuf readhexstring pop} imagemask } bdef /dither_color_raster { % bool sw sh sd dw dh xs ys TR SC /sd E def /sh E def /sw E def sd 8 eq and { /imagebuf 3 string def /grayval 1 string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop pop imagebuf 0 get 0.299 mul imagebuf 1 get 0.587 mul add imagebuf 2 get 0.114 mul add cvi grayval exch 0 exch put grayval } image } { /imagebuf sw 3 mul sd mul 7 add 8 idiv string def sh { currentfile imagebuf readhexstring pop pop } repeat } ifelse } bdef /image_color_raster { % bool sw sh sd dw dh xs ys /colorimage where not { dither_color_raster } { pop TR SC /sd E def /sh E def /sw E def pop /imagebuf sw 3 mul sd mul 7 add 8 idiv string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop} false 3 colorimage } ifelse } bdef /patpath { /inv E def topmat setmatrix pathbbox %% get lo - hi indecies /hy E dp_h div floor cvi def /hx E dp_w div floor cvi def /ly E dp_h div floor cvi def /lx E dp_w div floor cvi def lx 1 hx { dp_w mul ly 1 hy { dp_h mul E dup 3 1 roll E patmat currentmatrix pop TR dp_pw dp_ph inv dp_mat dp_proc imagemask patmat setmatrix } for pop } for } bdef /setpattern { /blue E def /green E def /red E def /freq E def /bwidth E def /bpside E def /bstring E def /onbits 0 def /offbits 0 def freq 0 {/y E def /x E def /xindex x 1 add 2 div bpside mul cvi def /yindex y 1 add 2 div bpside mul cvi def bstring yindex bwidth mul xindex 8 idiv add get not 1 7 xindex 8 mod sub bitshift and 0 ne {/onbits onbits 1 add def 1} {/offbits offbits 1 add def 0} ifelse } setscreen {} settransfer systemdict /setcmykcolor known { /fact 1 onbits offbits onbits add div sub def 1 red sub fact mul 1 green sub fact mul 1 blue sub fact mul 0 setcmykcolor } { offbits offbits onbits add div setgray} ifelse } bdef /dmatrix matrix def /dpi 72 0 dmatrix defaultmatrix dtransform dup mul E dup mul add sqrt def /B {gs bp st gr} bdef %% brush: gr lw lj /Bbw {gs bpbw st gr} bdef %% brush: gr lw lj /F {gs rgb eofill gr} bdef %% fill: gr /Fbw {gs setgray eofill gr} bdef %% fill: gr /PB {gs lj lw setpattern st gr} bdef /PF {gs eoclip patpath gr} bdef /BB {gs rgb lj lw strokepath clip patpath gr} bdef /xdef {exch def} bdef /clip_region { /ht xdef /wd xdef /bm xdef /lm xdef newpath lm bm moveto 0 ht rlineto wd 0 rlineto 0 ht neg rlineto closepath clip } bdef /reencode_small_dict 12 dict def /ReencodeSmall { reencode_small_dict begin /new_codes_and_names exch def /new_font_name exch def /base_font_name exch def /base_font_dict base_font_name findfont def /newfont base_font_dict maxlength dict def base_font_dict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName new_font_name put new_codes_and_names aload pop new_codes_and_names length 2 idiv { newfont /Encoding get 3 1 roll put } repeat new_font_name newfont definefont pop end %reencode_small_dict } def /extended_Zapf [ 8#223 /a89 8#224 /a90 8#225 /a93 8#226 /a94 8#227 /a91 8#230 /a92 8#231 /a205 8#232 /a85 8#233 /a206 8#234 /a86 8#235 /a87 8#236 /a88 8#237 /a95 8#240 /a96 ] def /extended_Standard [ 29 /thorn 30 /yacute 31 /divide 128 /Acircumflex 129 /Adieresis 130 /Agrave 131 /Aring 132 /Atilde 133 /Ccedilla 134 /Eacute 135 /Ecircumflex 136 /Edieresis 137 /Egrave 138 /Iacute 139 /Icircumflex 140 /Idieresis 141 /Igrave 142 /Ntilde 143 /Oacute 144 /Ocircumflex 145 /Odieresis 146 /Ograve 147 /Otilde 148 /Scaron 149 /Uacute 150 /Ucircumflex 151 /Udieresis 152 /Ugrave 153 /Ydieresis 154 /Zcaron 155 /aacute 156 /acircumflex 157 /adieresis 158 /agrave 159 /aring 160 /atilde 161 /exclamdown 162 /cent 163 /sterling 164 /fraction 165 /yen 166 /florin 167 /section 168 /currency 169 /quotesingle 170 /quotedblleft 171 /guillemotleft 172 /guilsinglleft 173 /guilsinglright 174 /fi 175 /fl 176 /plusminus 177 /endash 178 /dagger 179 /daggerdbl 180 /periodcentered 181 /twosuperior 182 /paragraph 183 /bullet 184 /quotesinglbase 185 /quotedblbase 186 /quotedblright 187 /guillemotright 188 /ellipsis 189 /perthousand 190 /threesuperior 191 /questiondown 192 /mu 193 /grave 194 /acute 195 /circumflex 196 /tilde 197 /macron 198 /breve 199 /dotaccent 200 /dieresis 201 /onesuperior 202 /ring 203 /cedilla 204 /onequarter 205 /hungarumlaut 206 /ogonek 207 /caron 208 /emdash 209 /ccedilla 210 /copyright 211 /eacute 212 /ecircumflex 213 /edieresis 214 /egrave 215 /iacute 216 /icircumflex 217 /idieresis 218 /igrave 219 /logicalnot 220 /minus 221 /ntilde 222 /oacute 223 /ocircumflex 224 /odieresis 225 /AE 226 /onehalf 227 /ordfeminine 228 /ograve 229 /otilde 230 /registered 231 /scaron 232 /Lslash 233 /Oslash 234 /OE 235 /ordmasculine 236 /trademark 237 /uacute 238 /ucircumflex 239 /udieresis 240 /ugrave 241 /ae 242 /ydieresis 243 /zcaron 244 /Aacute 245 /dotlessi 246 /threequarters 247 /Eth 248 /lslash 249 /oslash 250 /oe 251 /germandbls 252 /multiply 253 /Yacute 254 /Thorn 255 /eth ] def /extended_Symbol [ ] def /extend_font { % stack: fontname newfontname exch dup (ZapfDingbats) eq { cvn exch cvn extended_Zapf ReencodeSmall } { dup (Symbol) eq { cvn exch cvn extended_Symbol ReencodeSmall } { cvn exch cvn extended_Standard ReencodeSmall } ifelse } ifelse } bind def /extend_font_name { % stack: font_name_string dup length 1 add string /extended_font_name exch def extended_font_name 0 (_) putinterval extended_font_name 1 3 -1 roll putinterval extended_font_name } bind def /gf { /f exch def f cvn where { f exch begin cvn load exec setfont end } { f 0 f length 8 sub getinterval dup /localfont exch extend_font_name def localfont extend_font localfont findfont /xsz f f length 4 sub 4 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1212 y(mo)q(del)c Fk(j)65 1197 y Fi(0)88 1212 y Fs(in)g(the)i(time)e(in)o(terv)n(al)g(\() p Fk(t;)d(t)t Fs(+)t(1])i(giv)o(en)i(that)g(the)h(state)-75 1258 y(of)h(con)o(tact)i(at)e(time)g Fk(t)h Fs(w)o(as)g Fk(k)q Fs(.)k(W)m(e)13 b(ha)o(v)o(e)h(that)141 1332 y Fk(a)163 1338 y Fj(ik)218 1332 y Fs(=)279 1293 y Fg(X)273 1382 y Fj(j)289 1374 y Fe(0)300 1382 y Fi(!)p Fj(i)351 1332 y Fk(g)371 1338 y Fj(k)q(j)406 1330 y Fe(0)441 1332 y Fs(=)497 1293 y Fg(X)513 1382 y Fj(j)529 1374 y Fe(0)564 1332 y Fk(G)597 1338 y Fj(k)q(ij)644 1330 y Fe(0)655 1332 y Fk(g)675 1338 y Fj(k)q(j)710 1330 y Fe(0)-75 1454 y Fs(The)j(structure)i(of)e(the)g(net)o(w)o(ork)g(is)g(giv)o(en)f(in)h (\014gure)g(7.)27 b(The)-75 1500 y(elemen)o(ts)14 b(of)g(the)g(matrix)f (G)g(are)i(1)f(or)g(0,)f(indicating)g(whether)-75 1545 y(mo)q(dule)f Fk(j)90 1530 y Fi(0)116 1545 y Fs(leads)i(to)g(state)h (of)e(con)o(tact)i Fk(i)f Fs(or)g(not.)-26 1591 y(The)i(function)f(to)g (b)q(e)i(maxim)o(ized)c(has)j(the)g(same)f(form)e(as)-75 1636 y(ab)q(o)o(v)o(e,)j(with)g(the)h(indices)g Fk(i;)c(j)19 b Fs(b)q(oth)e(running)f(no)o(w)g(o)o(v)o(er)g(the)-75 1682 y(states)f(of)e(con)o(tact)i(.)j(Then)c(its)g(gradien)o(t)g (w.r.t.)j Fk(g)731 1688 y Fj(k)q(j)766 1680 y Fe(0)792 1682 y Fs(is)317 1756 y Fk(@)r(J)364 1762 y Fj(W)p 314 1775 92 2 v 314 1813 a Fk(@)r(g)358 1819 y Fj(k)q(j)393 1811 y Fe(0)434 1784 y Fs(=)496 1756 y Fk(\030)514 1762 y Fj(ik)p 494 1775 55 2 v 494 1813 a Fk(a)516 1819 y Fj(ik)-75 1887 y Fs(where)c Fk(i)f Fs(is)f(the)i(state)f(of)f(con)o (tact)i(to)e(whic)o(h)h(mo)o(v)o(emen)o(t)d(mo)q(del)-75 1932 y Fk(j)-56 1917 y Fi(0)-31 1932 y Fs(leads)14 b(\(i.e.)j Fk(j)179 1917 y Fi(0)203 1932 y Fh(!)11 b Fk(i)p Fs(\).)18 b(The)13 b(ab)q(o)o(v)o(e)g(relationship)g(sho)o(ws)g(that)-75 1978 y(all)k(the)h(gates')g(outputs)h(corresp)q(onding)f(to)g(the)h (same)e(state)-75 2024 y(of)12 b(con)o(tact)h(receiv)o(e)h(the)f(same)f (error)i(signal)d(and)i(therefore)h(no)-75 2069 y(comp)q(etition)e(can) j(o)q(ccur)g(b)q(et)o(w)o(een)g(them.)954 2727 y(11)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF