{VERSION 6 0 "IBM INTEL LINUX" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 47 "MTH 455 A DISCRE TE LINEAR AGE-STRUCTURED MODEL" }{TEXT -1 64 "\nJR 2/1/2005 age_struc tured.mws\nSee Haberman, Section 35, p138." }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 288 "# SET UP THE MATRIX A\nrestart:\nwith(LinearAlgebr a):\nM:=3;\nb:=[0,1.7,0.5,0]; # birth rates\nd:=[0.2,0.1,0.6,0.9 ]; # death rates\nA:=[seq([seq(0,col=0..M)],row=0..M)]: #fill A with \+ zeros\nfor col from 0 to M-1 do\n A[1,col+1]:=b[col+1];\n A[col+2, col+1]:=1-d[col+1];\nend do:\nevalm(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG7&\"\"!$\"# %\"dG7&$\"\"#!\" \"$\"\"\"F($\"\"'F($\"\"*F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matr ixG6#7&7&\"\"!$\"# " 0 "" {MPLTEXT 1 0 655 "# SOME USEFUL PROCEDURES\n\n# MUTLIPLY VECTOR N BY MATRIX A\nappl y_A:=(A,N)->convert(evalm(A&*N),list):\n\n# NORMALIZE A VECTOR\nnormal iz:=proc(N)\n local tot,i,Nlocal;\n Nlocal:=N;\n tot:=0;\n for i from 1 to nops(N) do tot:=tot+abs(N[i]); end do:\n unassign('i'): \n for i from 1 to nops(N) do Nlocal[i]:=N[i]/tot; end do:\n# for \+ i from 1 to nops(N) do Nlocal[i]:=N[i]/N[1]; end do:\n return Nlocal ;\nend proc:\n\n# MAKE A HISTOGRAM OF A VECTOR\nmy_histogram:=proc(N) \n local n,i,r;\n n:=nops(N);\n for i from 0 to n-1 do\n r[i ]:=plottools[rectangle]([i,N[i+1]],[i+1,0],color=pink);\n end do:\n \+ return plots[display](seq(r[i],i=0..n-1));\nend proc:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "N:=[1,0,0,0]; # WHAT HAPPENS IF WE START WITH JUST BABIES?\nfor t from 1 to 30 do\n N:=apply_A(A,N) ;\nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&\"\"\"\"\"!F'F' " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"\"!F'$\"\")!\"\"F&F&" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"$O\"!\"#$\"\"!F*$\"#sF(F) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"$g$!\"$$\"%)3\"F($\"\"! F,$\"$)GF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"&'\\=!\"%$\"% !)GF($\"%#z*F($\"\"!F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"& ?z*!\"&$\"'oz9F($\"&?f#F($\"&o\"RF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"NG7&$\"(c]k#!\"'$\"'gLyF($\"(7%\"NG7&$\")!ov*>!\"($\")[/;@F($\"(S-0(F($\"([oK&F( " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"*;)y\\R!\")$\"*Sa!)f\"F ($\"*KSW!>F($\")g4?GF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"+ SE\"*oO!\"*$\"+G0$)fJF($\"+g*[#Q9F($\"*Ghxh(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"+yj$34'!\"*$\"+7,8NHF($\"+vu%Q%GF($\"+Se*Hv& !#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"+G\\k6k!\"*$\"+-\"pE ([F($\"+,rhTEF($\"+!**Qv8\"F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"N G7&$\"+BgM/'*!\"*$\"+UfJH^F($\"+#>-aQ%F($\"+Sokc5F(" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"NG7&$\"+?QD\"4\"!\")$\"+=oZ$o(!\"*$\"+[VQ;YF+$\"+ x3;a%\"NG7&$\"+w-,P:!\")$\"+g0 .I()!\"*$\"+O\"H^\"pF+$\"+RPbY=F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"NG7&$\"+_;')H=!\")$\"+@#3'H7F($\"+/v-dy!\"*$\"+a;0mFF-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"+^`=$[#!\")$\"+A$*)QY\"F($\"+*RZm5\" F($\"+-5\"G9$!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"+Yb$>/ $!\")$\"+\"G[l)>F($\"+!R+vJ\"F($\"+'f*eEW!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"+tA)e.%!\")$\"+P%[NV#F($\"+`M*yy\"F($\"+g:+q _!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"+q!z4.&!\")$\"+=eq GKF($\"+$f$>!>#F($\"+7Qd^r!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\" NG7&$\"+(o'*Qe'!\")$\"+cKyCSF($\"+O_$e!HF($\"+sVxg()!\"*" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"NG7&$\"+`\"\\]H)!\")$\"+]t6n_F($\"+I\\IAOF($ \"+%4MB;\"F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"+'>Dl2\"!\" ($\"+A$Rgj'!\")$\"+:cSSZF+$\"+s>#*[9F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"+mp9l8!\"($\"+o:?7')!\")$\"+!RNC(fF+$\"+YA;'*=F+" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"+Ogpi%\"NG7&$\" +X*[TC#!\"($\"+Ho:59F($\"+d\"e!H)*!\")$\"+kDR+JF-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"+<&>())G!\"($\"+c\">`z\"F($\"+Y69p7F($\"+jKi JR!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"+QJh'o$!\"($\"+9c (4J#F($\"+Ssy:;F($\"+%ekl2&!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"NG7&$\"+k@bOZ!\"($\"+50H\\HF($\"+`!y)z?F($\"+g*[JY'!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"+$*Gt`g!\"($\"+J$)!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&$\"+t;*)ox!\" ($\"+9j)H%[F($\"+evJ5MF($\"+%eW<1\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 285 "# SAME EXPERIMENT, BUT MAKE AN ANIMATED HISTOGRAM TH IS TIME\nN:=[1,0,0,0];\nhisto[0]:=my_histogram(convert(N,list)):\nfor \+ t from 1 to 30 do\n N:=apply_A(A,N);\n histo[t]:=my_histogram(conv ert(N,list)):\nend do: unassign('t'):\nplots[display]( seq( histo[t], \+ t=0..30 ), insequence=true );\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"NG7&\"\"\"\"\"!F'F'" }}{PARA 13 "" 1 "" {GLPLOT2D 203 193 193 {PLOTDATA 2 "6#-%(ANIMATEG6A7&-%)POLYGONSG6$7&7$$\"\"!F-$\"\"\"F-7$F.F .7$F.F,7$F,F,-%'COLOURG6&%$RGBGF/$\"*w6%Hv!\"*$\"+9Vygz!#5-F(6$7&F17$$ \"\"#F-F,F@F1F3-F(6$7&F@7$$\"\"$F-F,FFF@F3-F(6$7&FF7$$\"\"%F-F,FLFFF37 &-F(6$7&F2F1F1F2F3-F(6$7&7$F.$\"\")!\"\"7$FAFWF@F1F3FCFI7&-F(6$7&7$F,$ \"$O\"!\"#7$F.FjnF1F2F3F=-F(6$7&7$FA$\"#sF\\o7$FGFboFFF@F3FI7&-F(6$7&7 $F,$\"$g$!\"$7$F.FjoF1F2F3-F(6$7&7$F.$\"%)3\"F\\p7$FAFbpF@F1F3FC-F(6$7 &7$FG$\"$)GF\\p7$FMFipFLFFF37&-F(6$7&7$F,$\"&'\\=!\"%7$F.FaqF1F2F3-F(6 $7&7$F.$\"%!)GFcq7$FAFiqF@F1F3-F(6$7&7$FA$\"%#z*Fcq7$FGF`rFFF@F3FI7&-F (6$7&7$F,$\"&?z*!\"&7$F.FhrF1F2F3-F(6$7&7$F.$\"'oz9Fjr7$FAF`sF@F1F3-F( 6$7&7$FA$\"&?f#Fjr7$FGFgsFFF@F3-F(6$7&7$FG$\"&o\"RFjr7$FMF^tFLFFF37&-F (6$7&7$F,$\"(c]k#!\"'7$F.FftF1F2F3-F(6$7&7$F.$\"'gLyFht7$FAF^uF@F1F3-F (6$7&7$FA$\"(7!\"(7$F.FdvF1F2F3-F(6$7&7$F.$\")[/;@Ffv7$FAF\\w F@F1F3-F(6$7&7$FA$\"(S-0(Ffv7$FGFcwFFF@F3-F(6$7&7$FG$\"([oK&Ffv7$FMFjw FLFFF37&-F(6$7&7$F,$\"*;)y\\R!\")7$F.FbxF1F2F3-F(6$7&7$F.$\"*Sa!)f\"Fd x7$FAFjxF@F1F3-F(6$7&7$FA$\"*KSW!>Fdx7$FGFayFFF@F3-F(6$7&7$FG$\")g4?GF dx7$FMFhyFLFFF37&-F(6$7&7$F,$\"+SE\"*oOF97$F.F`zF1F2F3-F(6$7&7$F.$\"+G 0$)fJF97$FAFgzF@F1F3-F(6$7&7$FA$\"+g*[#Q9F97$FGF^[lFFF@F3-F(6$7&7$FG$ \"*Ghxh(F97$FMFe[lFLFFF37&-F(6$7&7$F,$\"+yj$34'F97$F.F]\\lF1F2F3-F(6$7 &7$F.$\"+7,8NHF97$FAFd\\lF@F1F3-F(6$7&7$FA$\"+vu%Q%GF97$FGF[]lFFF@F3-F (6$7&7$FG$\"+Se*Hv&F<7$FMFb]lFLFFF37&-F(6$7&7$F,$\"+G\\k6kF97$F.Fj]lF1 F2F3-F(6$7&7$F.$\"+-\"pE([F97$FAFa^lF@F1F3-F(6$7&7$FA$\"+,rhTEF97$FGFh ^lFFF@F3-F(6$7&7$FG$\"+!**Qv8\"F97$FMF__lFLFFF37&-F(6$7&7$F,$\"+BgM/'* F97$F.Fg_lF1F2F3-F(6$7&7$F.$\"+UfJH^F97$FAF^`lF@F1F3-F(6$7&7$FA$\"+#>- aQ%F97$FGFe`lFFF@F3-F(6$7&7$FG$\"+Sokc5F97$FMF\\alFLFFF37&-F(6$7&7$F,$ \"+?QD\"4\"Fdx7$F.FdalF1F2F3-F(6$7&7$F.$\"+=oZ$o(F97$FAF[blF@F1F3-F(6$ 7&7$FA$\"+[VQ;YF97$FGFbblFFF@F3-F(6$7&7$FG$\"+x3;a/$Fdx7$F.Fhhl F1F2F3-F(6$7&7$F.$\"+\"G[l)>Fdx7$FAF_ilF@F1F3-F(6$7&7$FA$\"+!R+vJ\"Fdx 7$FGFfilFFF@F3-F(6$7&7$FG$\"+'f*eEWF97$FMF]jlFLFFF37&-F(6$7&7$F,$\"+tA )e.%Fdx7$F.FejlF1F2F3-F(6$7&7$F.$\"+P%[NV#Fdx7$FAF\\[mF@F1F3-F(6$7&7$F A$\"+`M*yy\"Fdx7$FGFc[mFFF@F3-F(6$7&7$FG$\"+g:+q_F97$FMFj[mFLFFF37&-F( 6$7&7$F,$\"+q!z4.&Fdx7$F.Fb\\mF1F2F3-F(6$7&7$F.$\"+=eqGKFdx7$FAFi\\mF@ F1F3-F(6$7&7$FA$\"+$f$>!>#Fdx7$FGF`]mFFF@F3-F(6$7&7$FG$\"+7Qd^rF97$FMF g]mFLFFF37&-F(6$7&7$F,$\"+(o'*Qe'Fdx7$F.F_^mF1F2F3-F(6$7&7$F.$\"+cKyCS Fdx7$FAFf^mF@F1F3-F(6$7&7$FA$\"+O_$e!HFdx7$FGF]_mFFF@F3-F(6$7&7$FG$\"+ sVxg()F97$FMFd_mFLFFF37&-F(6$7&7$F,$\"+`\"\\]H)Fdx7$F.F\\`mF1F2F3-F(6$ 7&7$F.$\"+]t6n_Fdx7$FAFc`mF@F1F3-F(6$7&7$FA$\"+I\\IAOFdx7$FGFj`mFFF@F3 -F(6$7&7$FG$\"+%4MB;\"Fdx7$FMFaamFLFFF37&-F(6$7&7$F,$\"+'>Dl2\"Ffv7$F. FiamF1F2F3-F(6$7&7$F.$\"+A$Rgj'Fdx7$FAF`bmF@F1F3-F(6$7&7$FA$\"+:cSSZFd x7$FGFgbmFFF@F3-F(6$7&7$FG$\"+s>#*[9Fdx7$FMF^cmFLFFF37&-F(6$7&7$F,$\"+ mp9l8Ffv7$F.FfcmF1F2F3-F(6$7&7$F.$\"+o:?7')Fdx7$FAF]dmF@F1F3-F(6$7&7$F A$\"+!RNC(fFdx7$FGFddmFFF@F3-F(6$7&7$FG$\"+YA;'*=Fdx7$FMF[emFLFFF37&-F (6$7&7$F,$\"+Ogpi())GFfv7$F.F]imF1F2F3-F(6 $7&7$F.$\"+c\">`z\"Ffv7$FAFdimF@F1F3-F(6$7&7$FA$\"+Y69p7Ffv7$FGF[jmFFF @F3-F(6$7&7$FG$\"+jKiJRFdx7$FMFbjmFLFFF37&-F(6$7&7$F,$\"+QJh'o$Ffv7$F. FjjmF1F2F3-F(6$7&7$F.$\"+9c(4J#Ffv7$FAFa[nF@F1F3-F(6$7&7$FA$\"+Ssy:;Ff v7$FGFh[nFFF@F3-F(6$7&7$FG$\"+%ekl2&Fdx7$FMF_\\nFLFFF37&-F(6$7&7$F,$\" +k@bOZFfv7$F.Fg\\nF1F2F3-F(6$7&7$F.$\"+50H\\HFfv7$FAF^]nF@F1F3-F(6$7&7 $FA$\"+`!y)z?Ffv7$FGFe]nFFF@F3-F(6$7&7$FG$\"+g*[JY'Fdx7$FMF\\^nFLFFF37 &-F(6$7&7$F,$\"+$*Gt`gFfv7$F.Fd^nF1F2F3-F(6$7&7$F.$\"+J$)Fdx7$ FMFi_nFLFFF37&-F(6$7&7$F,$\"+t;*)oxFfv7$F.Fa`nF1F2F3-F(6$7&7$F.$\"+9j) H%[Ffv7$FAFh`nF@F1F3-F(6$7&7$FA$\"+evJ5MFfv7$FGF_anFFF@F3-F(6$7&7$FG$ \"+%eW<1\"Ffv7$FMFfanFLFFF3" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 381 "# SAME EXPERIMENT, BUT THIS TIME NORMALIZE POPULATION \n# IN ORDER TO SEE BETTER WHAT'S HAPPENING TO THE AGE-DISTRIBUTION\nN:=[1,0,0,0];\nhisto[0]:=my_histogram(conver t(N,list)):\nfor t from 1 to 30 do\n N:=apply_A(A,N);\n N:=normali z(N);\n print(N); \n histo[t]:=my_histogram(convert(N,list)):\n end do: unassign('t'):\nplots[display]( seq( histo[t], t=0..30 ), inse quence=true );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7&\"\"\"\"\"!F 'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"\"!F%$\"+++++5!\"*F$F$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+Q:YQl!#5$\"\"!F($\"+i%Q:Y$F&F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+>Ftt?!#5$\"+06GniF&$\"\"!F*$\" +wh)*e;F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+\"e\"HMf!#5$\"+1kCS #*!#6$\"+yPoTJF&$\"\"!F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+[gz[ J!#5$\"+'p!=eZF&$\"+j$[]L)!#6$\"+>%=&f7F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+$)4CQa!#5$\"+\"*)*e5;F&$\"+;G+QFF&$\"+#4j;8#!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+V)\\Gt$!#5$\"+:rCaRF&$\"+:kZ<8 F&$\"+ZiEa**!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+*H^o5&!#5$\"+ *Q$>m?F&$\"+[HLiCF&$\"+GOAYO!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$ \"+w/ejS!#5$\"+**ft*\\$F&$\"+QD'Hf\"F&$\"+%*)4sV)!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+T*eT*[!#5$\"+)))f%eBF&$\"+8<6&G#F&$\"+JXpAY!#6 " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+&e>kD%!#5$\"+)peZB$F&$\"+Txl `xY!#5$\"+qzecEF&$\"+?_I/@F&$\"+Rp9>c!#6" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+Dh\\RW!#5$\"+=()>$)HF&$\"+sHA1>F &$\"+w=#3r'!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+C9!fi%!#5$\"+M \\1FFF&$\"+\"\\i:1#F&$\"+A:rae!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7 &$\"+.$=4[%!#5$\"+wF&$\"+U2e?l!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+6ST%f%!#5$\"+=3LqFF&$\"+#oA`.#F&$\"+)*[K**f!#6" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+fC,1X!#5$\"+p1!=*GF&$\"+\")Qlh> F&$\"+1*H`S'!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+s$R^d%!#5$\"+ 0b\"oz#F&$\"++.E>?F&$\"+E#[y3'!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7 &$\"+Q)\\7_%!#5$\"+bM'3(GF&$\"+U=Nu>F&$\"+T'[`L'!#6" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#7&$\"++9OjX!#5$\"+\\#**H\"GF&$\"+7_W4?F&$\"+J8%>9'!#6 " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+>]^IX!#5$\"+hC8eGF&$\"+8H2#) >F&$\"+Ghz#H'!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+%4shb%!#5$\" +by(G#GF&$\"+bSX.?F&$\"+A*f\\<'!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# 7&$\"+TN:OX!#5$\"+NZQ]GF&$\"+OF&$\"+l)**oE'!#6" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#7&$\"+3my^X!#5$\"+CQ!*GGF&$\"+T%*z**>F&$\"+C85&>'!#6 " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+eneRX!#5$\"+csmXGF&$\"+$yK'* )>F&$\"+/?8^i!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+CD6\\X!#5$\" ++#yD$GF&$\"+75d(*>F&$\"+&o#Q2i!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# 7&$\"+cynTX!#5$\"+^RzUGF&$\"+$Qv8*>F&$\"+n\"G:C'!#6" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#7&$\"+!Q#[ZX!#5$\"+G\"=[$GF&$\"+WD@'*>F&$\"+)\\p[@'!# 6" }}{PARA 13 "" 1 "" {GLPLOT2D 210 219 219 {PLOTDATA 2 "6#-%(ANIMATEG 6A7&-%)POLYGONSG6$7&7$$\"\"!F-$\"\"\"F-7$F.F.7$F.F,7$F,F,-%'COLOURG6&% $RGBGF/$\"*w6%Hv!\"*$\"+9Vygz!#5-F(6$7&F17$$\"\"#F-F,F@F1F3-F(6$7&F@7$ $\"\"$F-F,FFF@F3-F(6$7&FF7$$\"\"%F-F,FLFFF37&-F(6$7&F2F1F1F2F3-F(6$7&7 $F.$\"+++++5F97$FAFWF@F1F3FCFI7&-F(6$7&7$F,$\"+Q:YQlF<7$F.FinF1F2F3F=- F(6$7&7$FA$\"+i%Q:Y$F<7$FGF`oFFF@F3FI7&-F(6$7&7$F,$\"+>Ftt?F<7$F.FhoF1 F2F3-F(6$7&7$F.$\"+06GniF<7$FAF_pF@F1F3FC-F(6$7&7$FG$\"+wh)*e;F<7$FMFf pFLFFF37&-F(6$7&7$F,$\"+\"e\"HMfF<7$F.F^qF1F2F3-F(6$7&7$F.$\"+1kCS#*!# 67$FAFeqF@F1F3-F(6$7&7$FA$\"+yPoTJF<7$FGF]rFFF@F3FI7&-F(6$7&7$F,$\"+[g z[JF<7$F.FerF1F2F3-F(6$7&7$F.$\"+'p!=eZF<7$FAF\\sF@F1F3-F(6$7&7$FA$\"+ j$[]L)Fgq7$FGFcsFFF@F3-F(6$7&7$FG$\"+>%=&f7F<7$FMFjsFLFFF37&-F(6$7&7$F ,$\"+$)4CQaF<7$F.FbtF1F2F3-F(6$7&7$F.$\"+\"*)*e5;F<7$FAFitF@F1F3-F(6$7 &7$FA$\"+;G+QFF<7$FGF`uFFF@F3-F(6$7&7$FG$\"+#4j;8#Fgq7$FMFguFLFFF37&-F (6$7&7$F,$\"+V)\\Gt$F<7$F.F_vF1F2F3-F(6$7&7$F.$\"+:rCaRF<7$FAFfvF@F1F3 -F(6$7&7$FA$\"+:kZ<8F<7$FGF]wFFF@F3-F(6$7&7$FG$\"+ZiEa**Fgq7$FMFdwFLFF F37&-F(6$7&7$F,$\"+*H^o5&F<7$F.F\\xF1F2F3-F(6$7&7$F.$\"+*Q$>m?F<7$FAFc xF@F1F3-F(6$7&7$FA$\"+[HLiCF<7$FGFjxFFF@F3-F(6$7&7$FG$\"+GOAYOFgq7$FMF ayFLFFF37&-F(6$7&7$F,$\"+w/ejSF<7$F.FiyF1F2F3-F(6$7&7$F.$\"+**ft*\\$F< 7$FAF`zF@F1F3-F(6$7&7$FA$\"+QD'Hf\"F<7$FGFgzFFF@F3-F(6$7&7$FG$\"+%*)4s V)Fgq7$FMF^[lFLFFF37&-F(6$7&7$F,$\"+T*eT*[F<7$F.Ff[lF1F2F3-F(6$7&7$F.$ \"+)))f%eBF<7$FAF]\\lF@F1F3-F(6$7&7$FA$\"+8<6&G#F<7$FGFd\\lFFF@F3-F(6$ 7&7$FG$\"+JXpAYFgq7$FMF[]lFLFFF37&-F(6$7&7$F,$\"+&e>kD%F<7$F.Fc]lF1F2F 3-F(6$7&7$F.$\"+)peZB$F<7$FAFj]lF@F1F3-F(6$7&7$FA$\"+Txl`xYF<7$F.FjblF1F2F3-F(6$7&7$F.$\"+qzecEF<7$FAFaclF@F1F3-F(6$7 &7$FA$\"+?_I/@F<7$FGFhclFFF@F3-F(6$7&7$FG$\"+Rp9>cFgq7$FMF_dlFLFFF37&- F(6$7&7$F,$\"+Dh\\RWF<7$F.FgdlF1F2F3-F(6$7&7$F.$\"+=()>$)HF<7$FAF^elF@ F1F3-F(6$7&7$FA$\"+sHA1>F<7$FGFeelFFF@F3-F(6$7&7$FG$\"+w=#3r'Fgq7$FMF \\flFLFFF37&-F(6$7&7$F,$\"+C9!fi%F<7$F.FdflF1F2F3-F(6$7&7$F.$\"+M\\1FF F<7$FAF[glF@F1F3-F(6$7&7$FA$\"+\"\\i:1#F<7$FGFbglFFF@F3-F(6$7&7$FG$\"+ A:raeFgq7$FMFiglFLFFF37&-F(6$7&7$F,$\"+.$=4[%F<7$F.FahlF1F2F3-F(6$7&7$ F.$\"+wF<7$FGF_ilFFF@F3-F(6$7& 7$FG$\"+U2e?lFgq7$FMFfilFLFFF37&-F(6$7&7$F,$\"+6ST%f%F<7$F.F^jlF1F2F3- F(6$7&7$F.$\"+=3LqFF<7$FAFejlF@F1F3-F(6$7&7$FA$\"+#oA`.#F<7$FGF\\[mFFF @F3-F(6$7&7$FG$\"+)*[K**fFgq7$FMFc[mFLFFF37&-F(6$7&7$F,$\"+fC,1XF<7$F. F[\\mF1F2F3-F(6$7&7$F.$\"+p1!=*GF<7$FAFb\\mF@F1F3-F(6$7&7$FA$\"+\")Qlh >F<7$FGFi\\mFFF@F3-F(6$7&7$FG$\"+1*H`S'Fgq7$FMF`]mFLFFF37&-F(6$7&7$F,$ \"+s$R^d%F<7$F.Fh]mF1F2F3-F(6$7&7$F.$\"+0b\"oz#F<7$FAF_^mF@F1F3-F(6$7& 7$FA$\"++.E>?F<7$FGFf^mFFF@F3-F(6$7&7$FG$\"+E#[y3'Fgq7$FMF]_mFLFFF37&- F(6$7&7$F,$\"+Q)\\7_%F<7$F.Fe_mF1F2F3-F(6$7&7$F.$\"+bM'3(GF<7$FAF\\`mF @F1F3-F(6$7&7$FA$\"+U=Nu>F<7$FGFc`mFFF@F3-F(6$7&7$FG$\"+T'[`L'Fgq7$FMF j`mFLFFF37&-F(6$7&7$F,$\"++9OjXF<7$F.FbamF1F2F3-F(6$7&7$F.$\"+\\#**H\" GF<7$FAFiamF@F1F3-F(6$7&7$FA$\"+7_W4?F<7$FGF`bmFFF@F3-F(6$7&7$FG$\"+J8 %>9'Fgq7$FMFgbmFLFFF37&-F(6$7&7$F,$\"+>]^IXF<7$F.F_cmF1F2F3-F(6$7&7$F. $\"+hC8eGF<7$FAFfcmF@F1F3-F(6$7&7$FA$\"+8H2#)>F<7$FGF]dmFFF@F3-F(6$7&7 $FG$\"+Ghz#H'Fgq7$FMFddmFLFFF37&-F(6$7&7$F,$\"+%4shb%F<7$F.F\\emF1F2F3 -F(6$7&7$F.$\"+by(G#GF<7$FAFcemF@F1F3-F(6$7&7$FA$\"+bSX.?F<7$FGFjemFFF @F3-F(6$7&7$FG$\"+A*f\\<'Fgq7$FMFafmFLFFF37&-F(6$7&7$F,$\"+TN:OXF<7$F. FifmF1F2F3-F(6$7&7$F.$\"+NZQ]GF<7$FAF`gmF@F1F3-F(6$7&7$FA$\"+OF<7 $FGFggmFFF@F3-F(6$7&7$FG$\"+l)**oE'Fgq7$FMF^hmFLFFF37&-F(6$7&7$F,$\"+3 my^XF<7$F.FfhmF1F2F3-F(6$7&7$F.$\"+CQ!*GGF<7$FAF]imF@F1F3-F(6$7&7$FA$ \"+T%*z**>F<7$FGFdimFFF@F3-F(6$7&7$FG$\"+C85&>'Fgq7$FMF[jmFLFFF37&-F(6 $7&7$F,$\"+eneRXF<7$F.FcjmF1F2F3-F(6$7&7$F.$\"+csmXGF<7$FAFjjmF@F1F3-F (6$7&7$FA$\"+$yK'*)>F<7$FGFa[nFFF@F3-F(6$7&7$FG$\"+/?8^iFgq7$FMFh[nFLF FF37&-F(6$7&7$F,$\"+CD6\\XF<7$F.F`\\nF1F2F3-F(6$7&7$F.$\"++#yD$GF<7$FA Fg\\nF@F1F3-F(6$7&7$FA$\"+75d(*>F<7$FGF^]nFFF@F3-F(6$7&7$FG$\"+&o#Q2iF gq7$FMFe]nFLFFF37&-F(6$7&7$F,$\"+cynTXF<7$F.F]^nF1F2F3-F(6$7&7$F.$\"+^ RzUGF<7$FAFd^nF@F1F3-F(6$7&7$FA$\"+$Qv8*>F<7$FGF[_nFFF@F3-F(6$7&7$FG$ \"+n\"G:C'Fgq7$FMFb_nFLFFF37&-F(6$7&7$F,$\"+!Q#[ZXF<7$F.Fj_nF1F2F3-F(6 $7&7$F.$\"+G\"=[$GF<7$FAFa`nF@F1F3-F(6$7&7$FA$\"+WD@'*>F<7$FGFh`nFFF@F 3-F(6$7&7$FG$\"+)\\p[@'Fgq7$FMF_anFLFFF3" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve \+ 4" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 42 "THE RELEVANCE OF THE EIGENDATA OF MATRIX A" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "Am:=convert(A,Matrix); # \"Eigenvectors\" needs inpu t of type \"Matrix\"\n#Eigenvalues(Am);\n(vals,vecs):=Eigenvectors(Am) :\neigvals:=vals;\neigvecs:=evalm(vecs);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#AmG-%'RTABLEG6%\"*O=jM\"-%'MATRIXG6#7&7&\"\"!$\"#%(eigvalsG-%'RTABLEG6%\"*#**zb8-%'MAT RIXG6#7&7#^$$\"3`l1fn\\-\"G\"!#<$\"\"!F37#^$$!2W***************F1F27#^ $$!3k`m!fn\\-\"G!#=F27#^$$\"3adEATRpn@!#NF2&%'VectorG6#%'columnG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%(eigvecsGK%'matrixG6#7&7&^$$\"+ckb-z !#5$\"\"!F/^$$!+!\\F&zmF-F.^$$\"+#GyW>'!#6F.^$$!+kmL\">\"!#DF.7&^$$\"+ Pf9N\\F-F.^$$\"+#*>iV`F-F.^$$!+`eRjF-F.^$$!+)Ro#Q!)F-F.^$$\"+++++5!\"*F.Q(pprint16\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 176 "C1:=Column(vecs,1); # THE \+ DOMINANT EIGENVECTOR\n# COMPARE WITH SIMULATION (SCALE SO FIRST ELEMEN T IS 1)\nC1/C1[1];\nN/N[1]; # N STORES THE POPULATION AT THE END OF OU R SIMULATION" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#C1G-%'RTABLEG6%\"*# *G?N\"-%'MATRIXG6#7&7#^$$\"3')z!)zbkb-z!#=$\"\"!F37#^$$\"3k5z\\Pf9N\\F 1F27#^$$\"3<'Q^y1[sY$F1F27#^$$\"38/(HV3[E3\"F1F2&%'VectorG6#%'columnG " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*GeHP\"-%'MATRIXG6#7 &7#^$$\"3?(\\l.++++\"!#<$\"\"!F17#^$$\"3Z&4v?G**\\C'!#=F07#^$$\"3v1A7- =](Q%F6F07#^$$\"3&*)3<(zs**p8F6F0&%'VectorG6#%'columnG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+++++5!\"*$\"+H)=QB'!#5$\"+W#4(*Q%F)$\"+!fhmO \"F)" }}}{PARA 0 "" 0 "" {TEXT -1 121 "OBSERVE THAT THE AGE DISTRIBUTI ON OF THE POPULATION IS SETTLING INTO THAT\nGIVEN BY THE DOMINANT EIGE NVECTOR OF MATRIX A.\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "?Ma trix" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "?Vector" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "?Column" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{MARK "13 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 134631836 135579992 135202892 137295828 }{RTABLE M7R0 I6RTABLE_SAVE/134631836X,%)anythingG6"6"[gl!"%!!!#1"%"%""!$"")!""F'F'$"#