FWS  x   p   C?    
	   1. start  I    z'uJ4  f |/Hlc>UQ0gj`\L u10o-Xllj       #    VQː     51 hiUΘi  #    VQː f    51 hiUΘi  #    VQː      51 hiUΘi "                      逿 #    VQː     -X1kCLs`  #    VQː f    -O chsZ`  #    VQː      -O chsZ` "   	                  	   
 . 0 Y  hEe!{ay% 5O=^zT+qn
DF2v%'ȝn5fuﶣBS#ZtZۓ{zq*RJU mL/$T\ (˩UC,ta-Hw Ҫ*K7 wherX-~vV]f8 5hz[Z]
Ǯq2e7	qܺn9(OL3jPf_YQv;FrVhh),Dmkt9m ja,ٌs9fGU ڪ 5fvOtd%i3@- ̗,iL^Z1bd
Sh[MC~yh:<p 5ix*W}సS-B۩  5gek~\'/j& |BAB@ 4?ݷnZn|

6phuЀL\8lNmʰр鐃TUk\oyv 5gv!^'|z6!o 5O,☲N9}מn08U(U_n  5lyWF Z1⇵\2 5f݆ˀnS9 3 !=qҙ:t%*PyJR60h.lWmk6f4 sYLM0=4Ϛˀ)Ӏ)ll: g45gHiujԨ="xT5  LVc`9@2]% ؈ynP9hy2V#i. A 5kf S4h䋉E~?
#A
 yWTfUFLpYkdk\O[G{S$pLJBm K 5hNf @&C$|#N@Y	K|7jxi
L&(0 M} _Mw߉ϻNVcQ 5wi; &	]{vQ-MEů6Xӗw >dpQ]fsi_ 5jw"crj7#E# 5lyF䯎ߞ]g>oF7<Ò "p@  5dLxWn]wIZI-pB`6Vp!),eԕ3Ųkt]4ہo;W{~Bdl5fJNHI 5 	\c[! .A 5hwSZiw4k\3\ lMZ 09TI ַvZnRͳAs[ bwu;ӷL  Xj:r׾A 5eDiȤPU0"yk@ \ѠFXf%=\O ..m|]rP 
*q/q˛$xܷv 5Nl'(f7WYt7a;g 5hQKc,,@b$F (qr^28D w0!+{mk@VR"ЍZ5Ft ڷrkk>ͽim`
ܩɼ(knա 5akMer,B2%JHR n1/z`	4nٺ<7Ŷ6P 5Nn*re޹FKyK[gQ@ "   
 Verdana ABCDFGIKNOPRSTWacekstx3    h3    

  c.'\ "@DSd2   P     x;  (    %H\<fq9312:aڸT8.>L	gcL	|V[}>uC?yT!å"Ar8tH.T\G4>o9ޱ)&?;pjsqT88@\=qu8/sZ0+t(/CAy6     C    UP    (    5/9 J J3V[->_.  rӚPP   !; R     % 4 5ew^-~bv%پx6@5I6f8M 5@D{(<wf"#A任7     Times New Roman+-=    XTT  
 0O   =1P!  C:8"  A	0 C    UP (    5/9 J J3V[->_.  rӚPP %  eA; '  ; (  }1P+  1],   -  @Y .  82@/  @Z    ]QU;  `^X ѥ^nڂ Z H.eye2y]> _ s[iH.c_     eRezj Ag 5p>xEr،!s:,>     %`^X ѥ^nڂ Z H.eye2y]> _ s[iH.cAX`DQjQu88YTm?d3'xFOWk+ :`  q  !=   ]QU;  `^X ѥ^nڂ Z H.eye2y]> _ s[iH.c_           5`!s:,J;v   As,s,T ȬB' Z -*r1L@     %`r1&ԣppl=MfO"<5gV 1Y5Efu-mAX3 hįSmAp\- 	2m<2@	<_].G / -\ƀt  C   ]QU;  `^X ѥ^nڂ Z H.eye2y]> _ s[iH.c_     `^X ѥ^nڂ Z H.eye2ybB5     %`*:,J;v   As,s,T Ȭp ˝J@!AX&ԣppl=MfO"<5gV 1Y5Efu-mr1 w  eAM   ]QU;  `^X ѥ^nڂ Z H.eye2y]> _ s[iH.c_           5`!s:,J;v   As,s,T ȬS~cOOijJm);i"_*      %eRezj Ah M Khi繖* LVFORth8~P _eΏAm _B6uX`^N"RSʣmc%4	<2x]X gԵG\ƀz  }     ʂ       ]QU;  `^X ѥ^nڂ Z H.eye2y]> _ s[iH.c_     NL'\ΰKNݶ2      %`*s:2mJ?N ;g :*݌&d/_vz`TVgR!AX9 4ibW۶.@d{b̞Edd/.F \R`    A   ʇ @     x @     `  0@  H    z'`@Z   f śVbMv  L tu1ژc&S :Ř    ?     _sans   	-    o	 0           (  TARGET OUTPUT   (  
p Ј X 	@    @ Ȉ @   P ,  -8 $@    :   : 1@  	-    o	 0           (  TARGET OUTPUT   (  0 G H ?`@    U  U  L@   4 @ bp b  Z@@   <6  o ph g@   }    z'`Zt  fƭ 셄ՠSc) )Lvv	f; & )͍Z	@1N; SP& S::L)bw[`L[   	/    w@0           (  OUTPUT NEURODES   t	-    o	 0           (  TARGET OUTPUT   (  Dk  }P }؈ u @   L $ H @   L@ $0   @   U  ( 0 x@   ]B ,  @        z`Z  @{!S5h)`
|*
gGSv=^dӌ+xl	+qqfȲGBjST	Ύ;;S z`X V V͍Z 셄ՠSc) )Lvv	f; & ś    	-    o	 0           (  TARGET OUTPUT   (	/    w@0           (  HIDDEN NEURODES   跰	/     w@0           (  OUTPUT NEURODES    tЈ  ]x ,  X@   e` 0  ΀ @   m  4h $ 8@   g 8؈ (`  @   > 8H (Ј  @        ! z`Z   @{!S5h)`
|*
gGSv=^dӌ+xl	+qqfȲ)͍Z	@1N; SP& S::L)bw[`L[셄ՠSc) )Lvv	f; & ś A`L[665hd,& :O@Lc0ǨL u10h  ! 	-   " o	 0           (  TARGET OUTPUT  " (	.   # o 0           (  INPUT NEURODES  # \	/   $ w@0           (  OUTPUT NEURODES  $ t	/   % w@0           (  HIDDEN NEURODES  % 跰   = -@ $@  
쀈 A( 1 )@  À A 1  )h@  2j E, 5, -#@        & z`Zh  fƭ 셄ՠSc) )Lvv	f; & GBjST	Ύ;;S z`X V V͍Z 셄ՠSc) )Lvv	f; & ś ?q0n.,ՠlc>`3;2,x6 /t*VbMv  L tu1ژc&S :Řllj   & 	-   ' o	 0           (  TARGET OUTPUT  ' (	-   ( o	 0           (  TARGET OUTPUT  ( (	-   ) o	 0           (  TARGET OUTPUT  ) (	/   * w@0           (  OUTPUT NEURODES  * t	-   + o	 0           (  TARGET OUTPUT  + (	/   , w@0           (  HIDDEN NEURODES  , 跰	-   - o	 0           (  TARGET OUTPUT  - (	.   . o 0           (  INPUT NEURODES 	 . \	-   / o 0           (  INPUT PATTERN 
 / )4 Uƈ I9x 9:  11H@  䈈 MF =Gp 5>@  	 MTX =T 5L(@        	 
     
   buttons ?    
   2. buttons  Q  0 xLG`Z4   fƭ 셄ՠSc) )Lvv	f; & GBjST	Ύ;;S z`X V V͍Z 셄ՠSc) )Lvv	f; & ś ?q0n.,ՠlc>`3;2,x6 /t*VbMv  L tu1ژc&S :Řllj ^ST`*|o3N <%@ c`Z7n>, m`t  0 	-   1 o	 0           (  TARGET OUTPUT  1 (	-   2 o	 0           (  TARGET OUTPUT  2 (	-   3 o	 0           (  TARGET OUTPUT  3 (	/   4 w@0           (  OUTPUT NEURODES  4 t	-   5 o	 0           (  TARGET OUTPUT  5 (	/   6 w@0           (  HIDDEN NEURODES  6 跰	-   7 o	 0           (  TARGET OUTPUT  7 (	.   8 o 0           (  INPUT NEURODES 	 8 \	w   9 && 0          (  Click 'Next' button to progress one sectionClick 'Back' button to go back one section 
 9 S	-   : o 0           (  INPUT PATTERN  : )4   -   ;                        ; b` (   <                     < b   Z0@         	 
    ?    

   3. input1   = x:Gu`Z4  f fƭ "jSUD
gGSx!q2,xb`
\W   {!a5h)`
|*
gGSv=Be0Y+xl	+qqfƭ )͍Z	@1N; SP& S::L)bw[`L[셄ՠSc) )Lvv	f; & ś =	@1N; SP& S::L)bw[`L[665h /t*VbMv  L tu1ژc&S :Řllj ^Sg`*|Zo3ө=J=3}[Z ś G@  =  	/   > w@0           (  OUTPUT NEURODES  > t	/   ? w@0           (  HIDDEN NEURODES  ? 跰	-   @ o	 0           (  TARGET OUTPUT  @ (	.   A o 0           (  INPUT NEURODES  A \	x   B X& 0          (  The input pattern values propagate forwardsto the input neurodes in the neural network  B SP	-   C o 0           (  INPUT PATTERN  C )4 i   D x i  fP fdf : CIL
gGSl?̦ u1@m)1ƭ ؁%Ä*1Z9`'ht !Q1̴S   D     E xj N  

 a T9 PF  G 	܃F = E0U pP F 9 ,PP :G H܃A VeG d ܃Z r"Dv $sh9 &P9 (L  E     ,   F                       F b` @  !5` A+! C4" A	*% eA5p' 5`( +@  !/ A&! C/" A%h% eE/' /( &@  !*  E p! C)" A% eE*X' 	* (  p@  !$ IЉ! D!ʒ " D (% eI$Ј' $( @  ! M0! D!ʏ8" D `% eI@' ( 0@  !@ M! D!ʌp" D % eI' @( @  ! Q	! D!̉" D Ј% eM(' ( 	@  !  UP! Fs!" F"% eM'  ( P@  !` >! Fs!" FED% eM	' `( @        t w z }     ?    

   4. thresh \  G xCu`Z\  f |/Hlc>UQ0gj`\L u10o-Xllj   fƭ 셄ՠSc) )Lvv	f; & )͍Z	@1N; SP& S::L)bw[`L[셄ՠSc) )Lvv	f; & ś >U665hd,& :O@Lc0ǨL u10o0n.(/p& V:=L`XsUt$Xscaրz_Кlc`  G 	-   H o	 0           (  TARGET OUTPUT  H (	-   I o	 0           (  TARGET OUTPUT  I (	-   J o	 0           (  TARGET OUTPUT  J (	/   K w@0           (  OUTPUT NEURODES  K t	-   L o	 0           (  TARGET OUTPUT  L (	/   M w@0           (  HIDDEN NEURODES  M 跰	-   N o	 0           (  TARGET OUTPUT 	 N (	.   O o 0           (  INPUT NEURODES 
 O \	   P T?8 0          (  If  the value arriving at a neurode is over athreshold (red) value then the neurodewill output a positive value, zero otherwise  P QF0,   Q                       Q b`'  ! >{@  !H  >c`  !  >{@  C  @  eA     |! J<P" J9#  Cp$  [ % eQ&  e1H' ( |)  H*  M  R ]QU;  `^X ѥ^nڂ Z H.eye2y]> _ s[iH.c_          Nzjst+ Y2ٞ稨s'x,!s:2mJ?N ;g 1IPsm?d3'xFOWk+ :>      %`1 hįSmAp\- 	2m<2@	<_].G / -AX&ԣppl=MfO"<5gV 1Y5Efu-mr1 = R !  S ]QU;  `^X ѥ^nڂ Z H.eye2y]> _ s[iH.c_           -QMӭV&Bd6cgX^o*G / H*z2yjr1&ԣppl=MfO"<5s!QAJz0 ˝J@      LǝN ;g :*݌&d/_w=ܵ3-֟L:`9`DQjQ      %`^gYFMGl]eQ{̞Ey<k]X bjZۣ.cAX
9`F%zj Ah M Khi繖* LVFORth8~P _eΏAm _BA S CX  eA  T ]QU;  `^X ѥ^nڂ Z H.eye2y]> _ s[iH.c_           -QMӭV&Bd6cgX^o*G / H*z2yjr1&ԣppl=MfO"<5s2먠=4nߪY@FҐMkS>i$:|       LǝN ;g :*݌&d/_w=ܵ3-֟L*>åR!s:2mJ?|      %`*:,J;v   As,s,T Ȭp ˝J@`d.cgYFMGl]eQ{̞Ey<k]X bjZۣ\ T e   h  ʂ k   n  A q ʇ @   ! " % ' (  C  >` C栈 > ` ͠ ʛ@   # ;@$ 3Հ& ʣ)  * @  C@ >ø C` >Û 3ݠ + ʳݠ $  ؈# ;$ 3 & ʣ) $؈* (@  C@ >ˡ J  E` K  C@  H  㘈# C@$ ;& ʫ@) ( * p@  F` A Sۭ NӇ  ӷ  ː@ K 3  +# CӠ$ ;& ʫ) * 0@  Kc F[ \` W @  @ C@  ;# C $ ;`& ʫ ) l밈*  @  P K  e  `x@ K C~ ӥ [  Sx # C$ ;& ʫ) x*  @  U Pv  n ip  v   k`  cp# K $ C`& ʳ) K * Cv`@  [C  V;m@ wk  rci` Ô  m@ [  ڃ   {i@# K$ Cv& ʳ@) @* m@  `@ [d S {Kb  ` d @ ѓ  ̋a# K $ Ci`& ʳ) Ë* d@  eۂ` `[ ;@ 3Z ; 3[ む ȫ   ãZ`# K$ C[& ʳ ) {* s\ @  k+y f#R y S  {y sS  y y  R# Ku $ CN@& ʳw) 3y* +S @  psp kkJ  r K q  J` kq  r@  K# Sg$ K@& ʻi) q * J`@  ug pA  k  D` h` A +h` j  D # SZ $ K3@& ʻ\@) ܣh`* כA@  {_  v8` c < +_ #9  _ c`  <# SL$ K%& ʻN) [_* S8@  SV@ {K/ \@ 5 kW  c0@ V [  5 # S? $ K@& ʻA ) V* 0 @  M & T .  ȣN@ Û' sN  #T  -# [1$ S
& 3`) M* ' @  S;  K@ {M` s& =` Ż C=  3M   +&@# [#$ R & %) <`* @  S$  J` ʻ4  ų@ ʫ& Ţ +& ;2   3@# [`$ R& @) %* @  S  J` ʫ Ţ ʛ  Œ@  +  "# [$ R & 
) * @       	 
           # $ ) * h k ?    
   5. hidden1 \  U x7u`Z\ f fƭ "jSUD
gGSx!q2,xb`
\W   fƭ 셄ՠSc) )Lvv	f; & )͍Z	@1N; SP& S::L)bw[`L[셄ՠSc) )Lvv	f; & ś A`L[665hd,& :O@Lc0ǨL u10h/sf X==\SaTtݼXSaT^,l3  U 	-   V o	 0           (  TARGET OUTPUT  V (	-   W o	 0           (  TARGET OUTPUT  W (	-   X o	 0           (  TARGET OUTPUT  X (	/   Y w@0           (  OUTPUT NEURODES  Y t	-   Z o	 0           (  TARGET OUTPUT  Z (	/   [ w@0           (  HIDDEN NEURODES  [ 跰	-   \ o	 0           (  TARGET OUTPUT 	 \ (	.   ] o 0           (  INPUT NEURODES 
 ] \	   ^ tk8 0          (  The values feeding forward into a hiddenneurode are combined together as a weightedsum which is thresholded to give an output  ^ F0,   _                    '   _ b`;   "    :   `  Ԡ  `   `!  Ԡ& ʂ '  : (  :   ` ]QU;  `^X ѥ^nڂ Z H.eye2y]> _ s[iH.c_               "5``F%zj Ah M Khi繖* LVFORy!	.tzm)NT%̅l0"(ɵ(u:  %uq{̞Ey<k]u~"{])ͷ"4|       %`*s:2mJ?N ;g :*݌&d/_vz`TVgR!AYTNݵr   &\%4 &d+#')t4} ( /GҐ/!s:, _ `    a ]QU;  `^X ѥ^nڂ Z H.eye2y]> _ s[iH.c_               "5``F%zj Ah M Khi繖* LVFORy)??vR 'ZJ@ⓕ?`<!s:2mJ?N ;g 1I]sm?d3'xFOWk|v(5SZ=~_~,3mȍ1|@      %`*:,J;v   As,s,T Ȭp ˝J@`d.cgYFMGl]eQ{̞Ey<k]X bjZۣb a ʂ e  @  &  R  J@ ʢ   Ҹ   b! Z ' `( @  R` J ʺ` `   b@! Z' ڠ(  @  R J    @ 
  b! Z '  ( ʀ@  R  J@ 
` 򣀈 |  j ! b`' ҹ@( Һ @      ʛ u   ꩠ! ' @( ˂@  j  ~by` " @ m   ! x@' ƺ( β@@  :` {2n 2@  e  J`! Bm' Â ( ڕ@  } wd  : j  b^@  r! jc ' B( 
 @  yҀ  tY` J| B}` :V   ! X`' 
 ( 2@  vu qN Zu  "u O   t! M' u( bv @  sjj nbD  bm` n  G`  j ! C@' j( ފk`@  p:`  k29` re f ?  *_`! "8' Z``( `@  m
U h. ] ^ Ⱥ8   ZT! R. ' "U( V@@  iJ d$  |V  ԚW@ ϒ0  J@! z#' K@( 
K@  f@@ a uN zO r(  ?! ' @( :A @  e1 `
 nF ZH  R!@  1@! 
' 1( 3 @  e  耈 g?  :@` 2   ! ' ! ( "@  e@   ez( .  @   ! `' `(  @   c eb    ! ' ( @        	 
   n q ?    
   6. output1 e  b x2u`Z\  f fƭ "jSUD
gGSx!q2,xb`
\W   {!a5h)`
|*
gGSv=Be0Y+xl	+qqfƭ GBjST	Ύ;;S z`X V V͍Z 셄ՠSc) )Lvv	f; & ś ?q0n.,ՠlc>`3;2,x6   Ԃ<UDf?>Y EM2`7m0N8tV =  b  	-   c o	 0           (  TARGET OUTPUT  c (	-   d o	 0           (  TARGET OUTPUT  d (	-   e o	 0           (  TARGET OUTPUT  e (	/   f w@0           (  OUTPUT NEURODES  f t	-   g o	 0           (  TARGET OUTPUT  g (	/   h w@0           (  HIDDEN NEURODES 	 h 跰	-   i o	 0           (  TARGET OUTPUT 
 i (	.   j o 0           (  INPUT NEURODES  j \	   k _8 0          (  The values feeding forward into an outputneurode are combined as a weighted sumwhich is thresholded to give a final output value  k F0,   l                    ;   l b`O  ʇ  w!   G   7   ˗Ā  ) G    `   ! @"  A '  (  )   *  `g  m ]QU;  `^X ѥ^nڂ Z H.eye2y]> _ s[iH.c_               "`J40"(ɵ(u:  묪6v2S@鸼ƞ	`Fr1 hįSmAp\- 	2m<2@	<_]/<!=V  _eΏAm ?Iʟxm3      %eRezj Ah M Khi繖* LVFORth8~P _eΏAm _B6uX`^N"RSʣmc%4	<2x]X gԵG\ƀe m ,  n ]QU;  `^X ѥ^nڂ Z H.eye2y]> _ s[iH.c_          .8B6uXvq)@pl=MfOۼγ"R/      %`*:,J;v   As,s,T Ȭp ˝J@!AX`DQjQu88YTm?d3'xFOWk+ :`  h n A 6  o ]QU;  `^X ѥ^nڂ Z H.eye2y]> _ s[iH.c_          B6uXv. (Ȯ%k݌&dnO-l0"(ɵ(u:  %_      %eRezj Ah M Khi繖* LVFORth8~P _eΏAm ?`FX
fE6ΧSuFcJh2ydv=b+3kn k o ʇ @          ! ' (  i ΀" ؀) y`* q@    t "  ) q* i @  ִ   " ٫) i * a@@  Y  ž " ٕ ) i@* ao@   c" ~) a* YX@  ʵ " h ) Yh* QB @  ʥH " Q) QR * I+`@  ʤ퀈 R" ; ) Q;`* I@  ʔ   " $) I$* @ @      	 
       ?    
   7. comparison1   p xQWx&W\  f ‑]u' 1HhҘ`q:-  f śVbMv  L tu1ژc&S :ŘBjST	Ύ;;S z`X V V͍Z eSVbMv  L tu1ژc&S :Ř4-	@1N; SP& S::L)bw[`L[665h /uD|lljXMZu61
0gj`PL c`
`
\W   ETzQ>`cٍϓ@<4 
c|0
'l;0f =0T  p 	-   q o	 0           (  TARGET OUTPUT  q (	-   r o	 0           (  TARGET OUTPUT  r (	-   s o	 0           (  TARGET OUTPUT  s (	/   t w@0           (  OUTPUT NEURODES  t t	-   u o	 0           (  TARGET OUTPUT  u (	/   v w@0           (  HIDDEN NEURODES 	 v 跰	-   w o	 0           (  TARGET OUTPUT 
 w (	.   x o 0           (  INPUT NEURODES  x \	   y _8 0          (  The output values are compared withthe target output that corresponds withthe given input to the neural network  y F0	-   z oM 0           (  ACTUAL OUTPUT  z <   ,   {                    O   { b`Y  ʄ8  s "  ) A * 8@@    U "   )   * @+ `,  ŀ- Y . 2@/ Y@    s " @ )  * @+ c ,  - Y . 2@/ Y@  `   "  ) @6 * x@+ f ,  - XY . P2@/  Y@    r} "  ) 1* 'Ј+ h, ̀- Y . 2@/ @Y@    5 "   )  - * |#P+ k, B- Y . 2@/ Y@    q " @ ) `(* Ї+ Ÿ, L- pY . h2@/ Y`@  @   "  ) $ * <P+ ܅ć, cX- (Y .  2@/  Y@@    q] " ~ )  * Ї+ E·, #b- Y . 2@/ @Y@@     "  l )  * P+ ڇ, n- Y . 2@/ @H@      	 
      ?    
	   8. error e  | xLGxtW\  f fƮ"jU)y]JS)!q2tu|`Z   \!a5o*\.'J)v=Be0!bـ!jƫGBjST	Ύ;;S z`X V V͍Z 셄ՠSc) )Lvv	f; & ś =	@1N; SP& S::L)bw[`L[665h   1zQ>`َ <ؙ@ 
c0
#l; J& =(T  | 	/   } w@0           (  OUTPUT NEURODES  } t	/   ~ w@0           (  HIDDEN NEURODES  ~ 跰	.    o 0           (  INPUT NEURODES   \	    48 0          (  The error between the target outputand actual processed output is calculatedError = Target Output - Actual Output   F0	1    oX& 0          (  ERRORCALCULATION   \0	   ,                       Y  
  b`c  h  p " @Z ) * \Ї+ , M- @Y . 82@/ `@     5AU@R/P     Times New Roman-    X't  
    WP  0  z1   2      XTT 
    0 3  r뤊4  8@5  @6  7  8   9  P8@    XWA  	   :  p)h@ @ @   " ) * + , - . / 0 1 2 3 4 5 @ 6  9 80: )X@ 6  9 8(: ()P@ 6  9 `:  @ 6  9 @: Ȥ@ 6 ʃ 9 @ : 耤@ 6 c 7 8 9 @: 耻@@      
 ?    
   9. backprop e   x3Wua\  f .|/Hlc>UQ0gj`\L u10o-Xllj   C!a5h)`
|*
gGSv=Be0Y+xl	+qqfƭ )͍Z	@1N; SP& S::L)bw[`L[셄ՠSc) )Lvv	f; & ś C10o0n.,ՠlc>`3;2+   TzQZ`%3ù@=,L }1GMMS68ډ0f<U   	/    w@0           (  OUTPUT NEURODES   t	/    w@0           (  HIDDEN NEURODES   跰	.    o 0           (  INPUT NEURODES   \	    n8 0          (  The error values are back-propagated throughthe network to adjust the weights to give anoutput closer to the target for the given input   QF0	,    o 0           (  ERROR VALUES   <@ c    x WV  fP fH:l?UUS +Lvz28UTfśbLpSBZ)0 	      xj U  

 J $ăG ܃R 4I Ѓ 	G ܃F = E0U pP F ,9 :PP HG V܃A d eG r"܃Z $Dv &sh9 (P9 *L 
  P   ,                       c    b`m 6 T67 
8 9 A : @ 6 47 !`8 9 A#: `@ 6 耈7 8 8 `9 A:`:  @ 6 B 7 O 8 (@9 AP: @ 6  7 e8 ? 9 Ag: , @ 6  7 |8 V 9 A~ : B@ 6 ɶM7 8 l9 A: Y@@ 6 ɖ7 8 9 A@: o@ 6 v7 @8 9 A: 聆@ 6 gY 7  8 `9 A`: 聝 @       ?    
   10. weights 0   xauc^\  f fƭ "jSUD
gGSx!q2,xb`
\W   )ƭ 셄ՠSc) )Lvv	f; & @BjST	Ύ;;S z`X V V͍Z nlljXMZu61
0gj`PL c`
  zQZ`%3ϒ@<  
cL0
3l; =<T   	/    w@0           (  OUTPUT NEURODES   t	/    w@0           (  HIDDEN NEURODES   跰	.    o 0           (  INPUT NEURODES   \	    p30          (  Positive error helps to reinforce theweights, negative error reduces theweights and zero error has no effect   QF0,                       m    b`w   G   ʇ      ѹ   쀊!  #  쀊$  &  9`'  y 6 G 7  8 @9 A : 聳@    eb      ! `# @$ ր&   ' Ġ@  e ez( .    !  #  $ @& ' @@  e` g?  :@` z   ! # $ & !@' @  e-  nF ZH  ޚ  /@! # /`$ & 2 ' @  e= uN` zO ׺@  >`! 
# B?@$ :& j@'  @  i
H@ |rV  ԚW@   I ! "`# zI$ r# & :K ' z@ 6 7 8 9 :  lBS  b] ^ #  S! - # T`$ -& 
U' J`@      x;  (        %I.o4ˋ_L!j74Fp9Zp_0\i[}s1+A->y wC:pCwk*ґ Q:R$*D.{#7XXN8]P9Nk8 .L:~hK#:ᏹYΘ	`^CJM	:mNlʂve    o] Re f "+   r^`! j7# _ $ 8@& ``' % @     x;  (        P    %H._C+_8r..=֫쇍$AHKZp]L;W`p,Lvi/Kuᏻ@8]Ψp=Pp!Zʄ8tH.T`#=QC[2\u;Ϗx(.\:.1!ԫO49guC!}htKRlpNlveTt(    rh :m  n  B2  Bi ! :B`# 2i$ *B& ޢk ' /@      x;  (    P        %H.\:hqW>kjQ":jUqp%Ƙ%p1:`K8`Ko pct8qT8p'{x)!å"IrI\G4d;fhpKu,yՕ8@s:ᏹYΘ	`^CJM	:mNlʂve    us@ *t "u b:`  
s! M # jt@$ bM& ru' ײ:`@      x;  (        P    %H.jDy4Oz(Ays^VyƘ%p1:`K8`Ko pct8qT8p'{x)!å"ArJw2\u?;׏9ݓC)'^E͊r^hW:izF>uQlu8/sZ0+t(/CAy6"P	`    y*~  | B}` B   ~! W# ~$ X & B`' ԂE @      x;  (    P        %I.TCߚYo:A#yXC1*4%s\%̭8.0KuCᏸctq;^4h%@p .pT8q8N-eB:R$*0CJDH=y;Q;prN15K9,p"I^!;M8	:mPNlstnh    |b 
@ j  I   ! b`# `$ b& 
 ' JO@  `    Q@  r! jm # " $ m@& ڕ' Z@@  ڞ  ⓠ @ X  :! 2w# b$ Zw& Ϊ`' e @   қ` ʛ 
`  
 ! `# ɚ $ Ē`& z ' Ǻo@  R` £  򣀈 2h   j! b# ҷ$ ʐ& Һ`'  @  R  Ȫ @ Ro  b`! Z# `$ ʡ&  ' @  R   ` Z   b ! Z@#  $ ²@& ' `@  R ʢ    b! Z # $  & `'  @      ?    
   11. proportional error 0   x.WucW\ f |/Hlc>UQ0gj`\L u10o-Xllj   G!a5h)`
|*
gGSv=Be0Y+xl	+qqfƭ @BjST	Ύ;;S z`X V V͍Z n& śVbMv  L tu1ژc&S :Ř  TQZ`53ù=eL }2GMLS60i0f<U   	/    w@0           (  OUTPUT NEURODES   t	/    w@0           (  HIDDEN NEURODES   跰	.    o 0           (  INPUT NEURODES   \	    48 0          (  The error at a hidden neurode is the sum of theoutput neurode error contributions proportionalto the size of the weights joining the neurodes   QF0,                       w    b`   b  b     ʂ   b     ʂ `    b  `! Ԡ"  ʂ # ʂ$ z%   &  ' @       ! # $ & '  S  ʫ$` ʛ    +$` [	"  %  @  S/  ʋJ ʳ/  3/  J ["  % / @  SH  R H  SH  CR ['" * % H @  +S@ CZ ūS@ {S@ Z [7 " 9 % S@@  |c\ c  \ C\ c  SF@" ʻH % \@  vf k  #f f +k  SU`" ʻW % ۃf@  pp  Ss  [p  p  s  Sd" ʻf % Kp @  ky {  y y s{  Ks" ʻu % y@  eS@   Ӄ@ S@   K" ʳ % Ӄ@@  _ }k    Ի  K" ʳ % @  YÖ sÓ  C 㖀 c  K " ʳ % c@  T  j#@     @ C " ʫ % # @  N; `{@  k @ C@" ʫ % p@  H{` V۫@ ` +` K@ C΀" ʫ % @  C  M3` K    x؈ Cݠ" ʫ % ( @  C  CӼ@ 3  ʳ  ( ;" ʣ % $@@  C  C㠈   ʛ   ;" ʣ %  @     0   x.WucW\ f |/Hlc>UQ0gj`\L u10o-Xllj   )ƭ 셄ՠSc) )Lvv	f; & @BjST	Ύ;;S z`X V V͍Z nlljXMZu61
0gj`PL c`
  TQZ`53ù=eL }2GMLS60i0f<U   	/    w@0           (  OUTPUT NEURODES   t	/    w@0           (  HIDDEN NEURODES   跰	.    o 0           (  INPUT NEURODES   \	    48 0          (  The error at a hidden neurode is the sum of theoutput neurode error contributions proportionalto the size of the weights joining the neurodes   QF0 ! ! C eA  C" eA% @       " % @     	 
   = A \ _ b e h k ?    
   12. input 2    x:Gu`Z\  f fƭ "jSUD
gGSx!q2,xb`
\W   {!a5h)`
|*
gGSv=Be0Y+xl	+qqfƭ )͍Z	@1N; SP& S::L)bw[`L[셄ՠSc) )Lvv	f; & ś =	@1N; SP& S::L)bw[`L[665h /t*VbMv  L tu1ژc&S :Řllj   @f@YY|~*V@jYc
~Zq0>xU@ >   	/    w@0           (  OUTPUT NEURODES   t	/    w@0           (  HIDDEN NEURODES   跰	-    o	 0           (  TARGET OUTPUT   (	.    o 0           (  INPUT NEURODES   \	s    X& 0          (  The input pattern values propagate forwardsonce again through the changed network   SP	-    o 0           (  INPUT PATTERN 	  )4 D   E     ,                           b`   !;   =1P!  C:8"  A	0%  eA; '  ; (  }1P+  1],   -  @Y .  82@/  @Z R  !U  C[  ^   a  ʂ d   g  A j  ʇ @  !5` A+! C4" A	*% eA5p' 5`( +@  !/ A&! C/" A%h% eE/' /( &@  !*  E p! C)" A% eE*X' 	* (  p@  !$ IЉ! D!ʒ " D (% eI$Ј' $( @  ! M0! D!ʏ8" D `% eI@' ( 0@  !@ M! D!ʌp" D % eI' @( @  ! Q	! D!̉" D Ј% eM(' ( 	@  !  UP! Fs!" F"% eM'  ( P@  !` >! Fs!" FED% eM	' `( @      	  U X [ ^ a d g j ?    
   13. diff weights e   x+u`Z\  f |/Hlc>UQ0gj`\L u10o-Xllj   fƭ 셄ՠSc) )Lvv	f; & )͍Z	@1N; SP& S::L)bw[`L[셄ՠSc) )Lvv	f; & ś >U665hd,& :O@Lc0ǨL u10o0n.+   Q*`ِ=o̲ 2GMLS680f? W   	-    o	 0           (  TARGET OUTPUT   (	-    o	 0           (  TARGET OUTPUT   (	-    o	 0           (  TARGET OUTPUT   (	/    w@0           (  OUTPUT NEURODES   t	-    o	 0           (  TARGET OUTPUT   (	/    w@0           (  HIDDEN NEURODES 	  跰	-    o	 0           (  TARGET OUTPUT 
  (	.    o 0           (  INPUT NEURODES   \	    d8 0          (  The weights that were adjusted on the previousiteration of the backpropagation techniquemay cause the output to be different    QF0,                           b`  ! >{@  !H  >c`  !  >{@  C  @  eA     |! J<P" J9#  Cp$  [ % eQ&  e1H' ( |)  H*  2 R !6 S C9  eA= T F   I  ʂ L   O  A R ʇ @   ! " % ' (  C  >` C栈 > ` ͠ ʛ@   # ;@$ 3Հ& ʣ)  * @  C@ >ø C` >Û 3ݠ + ʳݠ $  ؈# ;$ 3 & ʣ) $؈* (@  C@ >ˡ J  E` K  C@  H  㘈# C@$ ;& ʫ@) ( * p@  F` A Sۭ NӇ  ӷ  ː@ K 3  +# CӠ$ ;& ʫ) * 0@  Kc F[ \` W @  @ C@  ;# C $ ;`& ʫ ) l밈*  @  P K  e  `x@ K C~ ӥ [  Sx # C$ ;& ʫ) x*  @  U Pv  n ip  v   k`  cp# K $ C`& ʳ) K * Cv`@  [C  V;m@ wk  rci` Ô  m@ [  ڃ   {i@# K$ Cv& ʳ@) @* m@  `@ [d S {Kb  ` d @ ѓ  ̋a# K $ Ci`& ʳ) Ë* d@  eۂ` `[ ;@ 3Z ; 3[ む ȫ   ãZ`# K$ C[& ʳ ) {* s\ @  k+y f#R y S  {y sS  y y  R# Ku $ CN@& ʳw) 3y* +S @  psp kkJ  r K q  J` kq  r@  K# Sg$ K@& ʻi) q * J`@  ug pA  k  D` h` A +h` j  D # SZ $ K3@& ʻ\@) ܣh`* כA@  {_  v8` c < +_ #9  _ c`  <# SL$ K%& ʻN) [_* S8@  SV@ {K/ \@ 5 kW  c0@ V [  5 # S? $ K@& ʻA ) V* 0 @  M & T .  ȣN@ Û' sN  #T  -# [1$ S
& 3`) M* ' @  S;  K@ {M` s& =` Ż C=  3M   +&@# [#$ R & %) <`* @  S$  J` ʻ4  ų@ ʫ& Ţ +& ;2   3@# [`$ R& @) %* @  S  J` ʫ Ţ ʛ  Œ@  +  "# [$ R & 
) * @      	 
            # $ ) * I L ?    
   14. weight effect e   xNu`Z\  f fƭ "jSUD
gGSx!q2,xb`
\W   fƭ 셄ՠSc) )Lvv	f; & )͍Z	@1N; SP& S::L)bw[`L[셄ՠSc) )Lvv	f; & ś A`L[665hd,& :O@Lc0ǨL u10k   I? WDf8>O z~d)0*:n`
0@<!a    	-    o	 0           (  TARGET OUTPUT   (	-    o	 0           (  TARGET OUTPUT   (	-    o	 0           (  TARGET OUTPUT   (	/    w@0           (  OUTPUT NEURODES   t	-    o	 0           (  TARGET OUTPUT   (	/    w@0           (  HIDDEN NEURODES 	  跰	-    o	 0           (  TARGET OUTPUT 
  (	.    o 0           (  INPUT NEURODES   \	    8 0          (  Some of the weights joining the hiddenneurodes to the output neruodes werechanged during backpropagation   F0,                           b`   "    :   `  Ԡ  `   `!  Ԡ& ʂ '  : (  : @ `  C a ʂ F  @  &  R  J@ ʢ   Ҹ   b! Z ' `( @  R` J ʺ` `   b@! Z' ڠ(  @  R J    @ 
  b! Z '  ( ʀ@  R  J@ 
` 򣀈 |  j ! b`' ҹ@( Һ @      ʛ u   ꩠ! ' @( ˂@  j  ~by` " @ m   ! x@' ƺ( β@@  :` {2n 2@  e  J`! Bm' Â ( ڕ@  } wd  : j  b^@  r! jc ' B( 
 @  yҀ  tY` J| B}` :V   ! X`' 
 ( 2@  vu qN Zu  "u O   t! M' u( bv @  sjj nbD  bm` n  G`  j ! C@' j( ފk`@  p:`  k29` re f ?  *_`! "8' Z``( `@  m
U h. ] ^ Ⱥ8   ZT! R. ' "U( V@@  iJ d$  |V  ԚW@ ϒ0  J@! z#' K@( 
K@  f@@ a uN zO r(  ?! ' @( :A @  e1 `
 nF ZH  R!@  1@! 
' 1( 3 @  e  耈 g?  :@` 2   ! ' ! ( "@  e@   ez( .  @   ! `' `(  @   c eb    ! ' ( @       	 
    O R ?    
   15. diff outputs [   xGGu`Z\  f fƭ "jSUD
gGSx!q2,xb`
\W   {!a5h)`
|*
gGSv=Be0Y+xl	+qqfƭ GBjST	Ύ;;S z`X V V͍Z 셄ՠSc) )Lvv	f; & ś ?q0n.,ՠlc>`3;2,x6 /[ W9>H: i*1î jcٲ    	-    o	 0           (  TARGET OUTPUT   (	-    o	 0           (  TARGET OUTPUT   (	-    o	 0           (  TARGET OUTPUT   (	/    w@0           (  OUTPUT NEURODES   t	-    o	 0           (  TARGET OUTPUT   (	/    w@0           (  HIDDEN NEURODES   跰	-    o	 0           (  TARGET OUTPUT 	  (	.    o 0           (  INPUT NEURODES 
  \	    <8 0          (  The weighted sums arriving at the output neurodes are therefore different to beforewhich results in a different network output   F0,                           b`  ʇ  w!   G   7   ˗Ā  ) G    `   ! @"   #  @'  (  )   *  `F ` 0   ]QU;  `^X ѥ^nڂ Z H.eye2y]> _ s[iH.c_          bl 4+c+]j`vSȼ	d.cgYFMGYP\g      %`r1&ԣppl=MfO"<5gV 1Y5Efu-mAX3 hįSmAp\- 	2m<2@	<_].G / -r1 I  A L o ʇ @          ! ' (  i ΀" ؀# ѱ) y`* q@    t "  # ћ@) q* i @  ִ   " ٫# ф) i * a@@  Y  ž " ٕ # n@) i@* ao@   c" ~# W) a* YX@  ʵ " h # A@) Yh* QB @  ʥH " Q# *) QR * I+`@  ʤ퀈 R" ; # @) Q;`* I@  ʔ   " $# ) I$* @ @       	 
     ?    
   16. compare2    xQWx&W\  f ‑]u' 1HhҘ`q:-  f śVbMv  L tu1ژc&S :ŘBjST	Ύ;;S z`X V V͍Z eSVbMv  L tu1ژc&S :Ř4-	@1N; SP& S::L)bw[`L[665h /uD|lljXMZu61
0gj`PL c`
`
\P^-H,هʝ(0ɠ̚ m1OMLQ6V@Yd  	-    o	 0           (  TARGET OUTPUT   (	-    o	 0           (  TARGET OUTPUT   (	-    o	 0           (  TARGET OUTPUT   (	/    w@0           (  OUTPUT NEURODES   t	-    o	 0           (  TARGET OUTPUT   (	/    w@0           (  HIDDEN NEURODES   跰	-    o	 0           (  TARGET OUTPUT 	  (	.    o 0           (  INPUT NEURODES 
  \	    ?8 0          (  The output values are compared withthe target output once again: this timeonly the right hand output is incorrect   F0	-    oM 0           (  ACTUAL OUTPUT   <  ,                           b`  ʄ8  s "  # @) A * 8@@        	 
       ?     R   xWa@Z\   fƭ 셄ՠSc) )Lvv	f; & BjST	Ύ;;S z`X V V͍Z 셄ՠSc) )Lvv	f; & ś 4-	@1N; SP& S::L)bw[`L[665h /t*{òVbMv  L tu1ژc&S :Řllj ^LJ' }21d	pF i*.Ý 4קʀ    	-    o	 0           (  TARGET OUTPUT   (	-    o	 0           (  TARGET OUTPUT   (	-    o	 0           (  TARGET OUTPUT   (	/    w@0           (  OUTPUT NEURODES   t	-    o	 0           (  TARGET OUTPUT   (	/    w@0           (  HIDDEN NEURODES   跰	-    o	 0           (  TARGET OUTPUT   (	.    o 0           (  INPUT NEURODES 	  \	    8 0          (  The process of forwards and backwards propagationcontinues until the neural network produces thecorrect target output for each given training input 
  QF0	-    oM 0           (  ACTUAL OUTPUT   <   ,                           b` 1    h҂  @ 

  
c.'\@            YZ04    UP     51 hiUΘi  (    %X1Z  4    UP f    51 hiUΘi  (    %X1Z  4    UP      51 hiUΘi  (    %X1Z   1    UP      (    %1 ´Zchs`L -                            -b` 3    hS@` ɀ 

  bs$*l
            5Z @   
