Date received: Sat Dec  2 16:00:29 1989

ART2, like ART1 is defined in two ways; as a dynamic system of
differential equations, and as a practical implementation.  For a
class assignment we were required to implement the latter.  I can give
you source code for the assignment, without any guarantee that it is
really correct- in fact there were some problems- in part (c)1 Gail
wrote "B,C & D should be null (no activation) after F0 processing.
With theta = 0.6 (they are quenched)" and in part (c)2 she wrote
"B,C,D should drop to zero after F0 processing" and her final comment
was "Your simulation, for the most part, is correct.  In part (c) you
should observe null output vectors for patterns B,C & D.  Check this-"
So, I hope this is of some use to you, if only to set the parameters.



		CN 550 SIMULATION ASSIGNMENT 4
		==============================


			Steve Lehar (slehar@bucasb.BU.EDU)

INTRODUCTION

This simulation was an extension of an earlier simulation of the front
end of ART2 (Lehar 1989).  In the previous work the F0 and F1 layers
were implemented, and in this model the F2 layer has been completed,
the model is excercised on a variety of vectors, and its performance
is compared to the leader algorithm and the ART1 model.

ALGORITHM

Figure 1 shows the general flow of activation through the ART2 model,
in a manner consistant with a biological implementation.  The format
of this figure was designed to clarify the major data flow in the
model.  The inputs arrive at the bottom, and the information
propagates generally upwards, with some feedback paths looping back
down.  For clarity the figure only shows three data paths, though of
course any number of them could be accomodated.  At alternating stages
of the algorithm normalization takes place, such as from w' to x', and
v' to u'.  This is represented in the figure by the crisscross
pathways, which represent on-center off-surround interactions, that
is, the straight through vertical paths are excitatory, whereas the
crossover pathways are inhibitory.  In the interests of clarity, the
reset mechanism is not depicted.

The overall architecture consists of three sets of layers, F0, F1 and F2.
F0 serves as a buffer to isolate the input lines from the top-down
activity of the network, and to normalize the input pattern.  F1 performs
further normalization, and integrates the bottom-up and top-down
influences.  F2 encodes the high level abstraction of the input patterns,
and is connected to F1 through a bi-directional adaptive filter.
The learning rate on the adaptive filter is such that a pattern must
resonate by means of a bottom-up top-down match in order for learning
to occur.

The overall algorithm is as follows.  The input data is presented at
F0, and F0 is iterated 10 times until the values stabilize.  F1 is
then iterated for 10 iterations until its values reach equilibrium.
Finally, another 10 iterations are performed simultaneously with F1
and F2 until equilibrium is achieved, testing for reset.  (In all
these loops, test runs confirmed that 10 iterations were plenty for
equilibrium to occur) If the reset flag has been set in these
iterations, all the nodes in F1 and F2 are re-initialized and the above
procedure for F1 and F2 is repeated until no further reset occurs.

Learning of the stabilized resonant pattern follows by updating the bottom-up
and top-down weights, and F1 is recomputed with the new top-down values.  This
procedure is repeated for 1000 iterations, which tests showed was easily
sufficient for equilibrium to occur.  The algorithm is now ready for the next
input pattern.

The equations that describe the flow of data through the net are
defined below.

F0 EQUATIONS:

	w'(i) = I(i) + a * u(i)					A1
	p'(i) = u'(i)						A2
	x'(i) = w'(i) / (e + ||w||)				A3
	q'(i) = p'(i) / (e + ||p||)				A4
	v'(i) = f(x'(i)) + b * f(q'(i))				A5
	u'(i) = v'(i) / (e + ||v||)				A6

F1 EQUATIONS:

	w(i) = q'(i) + a * u(i)					A7
	p(i) = u(i)						A8
	x(i) = w(i) / (e + ||w||)				A9
	q(i) = p(i) / (e + ||p||)				A10
	v(i) = f(x(i)) + b * f(q(i))				A11
	u(i) = v(i) / (e + ||v||)				A12

where a=5, e=0.00001, b=5, theta=0.3, and the notation ||x|| denotes
the L2 norm of x.  The function f(x) is a threshold linear function
such that f(x)=0 for x <= theta, and f(x) = x for x > theta.
In the simulations the equations were computed in the sequence shown
for each pass through the loop.  A reset vector is also calculated
to record the match between the top-down expectation and the bottom-up
priming, as follows:

RESET EQUATION:

	r(i) = (q1(i) + c * p(i)) / (e + ||q1|| + ||c*p||)	A13

Bottom-up (zup) and top-down (zdn) weights between p and F2 were
initialized as follows:-

LTM EQUATIONS:

	zup(i,j) = 1/(0.2 * sqrt(m))				A14
	zdn(j,i) = 0						A15

where m is the number of nodes in F1.  The F2 values were computed
using the formula-


F2 EQUATIONS:

	F2(j) = f2(j) + SUMi( p(i) * zup(i,j) )			A16

	F2(j) = E 0.8 if F2(j) = MAXi(F2(i)),
		  0   otherwise			L		A17

A16 is applied first, and then A17 finds the maximal node, and sets it
to 0.8, while setting all other nodes to zero.  This is an extreme
contrast enhancement, or winner-take-all choice operation.



RESULTS

The algorithm was run on a variety of input patterns
with a variety of parameter values.  A record of data was printed
for each presentation of an input vector to show the state of the
system after learning that vector. The format of the data record
is as follows:-

  INPUT PATTERN: the input pattern presented

  RESET: when a reset occurs, the word "RESET" appears in a line by itself
	after the input pattern.

  PARAMETERS: rho is the vigilance, normr is the norm of the reset vector,
	winner is maximal F2 node, and 'learning' indicates that the LTM
	weights were modified.

  F1 VALUES: the values of nodes w,x,v,u,p and q in F1 are presented.

  F2 VALUES: the F2 values are presented before the winner-take-all
	competition

  F2 WINNER: the winning F2 node from the line above is indicated

  LTM WEIGHTS: the last two lines display the bottom-up and top-down weights
	from the p nodes to the winning F2 node.  Since it is only these
	weights	that change in each cycle, it is unnecessary to print the
	other weights.  The differential equation determines that these weights
	track the value of the p nodes, so that the similarity of these weights
	to the p nodes indicates that sufficient iterations have been performed

PART (a)1     BINARY INPUT PATTERNS
==================================
The following patterns were presented to the network with vigilance set to 0.98

A 1 1 1 1 1 0 0 0 0 0
B 1 0 0 0 0 0 0 0 0 1
C 0 1 0 1 0 1 0 1 0 1
D 0 0 0 1 1 1 1 0 0 0
A 1 1 1 1 1 0 0 0 0 0
B 1 0 0 0 0 0 0 0 0 1
C 0 1 0 1 0 1 0 1 0 1
D 0 0 0 1 1 1 1 0 0 0
E 1 1 0 0 0 0 0 0 1 1 no learning
F 0 0 0 0 1 1 0 0 0 0 no learning


 A:   1.00  1.00  1.00  1.00  1.00  0.00  0.00  0.00  0.00  0.00
rho= 0.98 normr= 1.00	winner=0 learning
w:    2.68  2.68  2.68  2.68  2.68  0.00  0.00  0.00  0.00  0.00
x:    0.45  0.45  0.45  0.45  0.45  0.00  0.00  0.00  0.00  0.00
v:    2.68  2.68  2.68  2.68  2.68  0.00  0.00  0.00  0.00  0.00
u:    0.45  0.45  0.45  0.45  0.45  0.00  0.00  0.00  0.00  0.00
p:    2.24  2.24  2.24  2.24  2.24  0.00  0.00  0.00  0.00  0.00
q:    0.45  0.45  0.45  0.45  0.45  0.00  0.00  0.00  0.00  0.00
F2:   3.54  3.54  3.54  3.54  3.54  3.54  3.54  3.54
     ;WINS;
zup0: 2.24  2.24  2.24  2.24  2.24  0.00  0.00  0.00  0.00  0.00
zdn0: 2.24  2.24  2.24  2.24  2.24  0.00  0.00  0.00  0.00  0.00

 B:   1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  1.00
rho= 0.98 normr= 1.00	winner=1 learning
w:    4.24  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  4.24
x:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
v:    4.24  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  4.24
u:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
p:    3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54
q:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
F2:   1.58  2.24  2.24  2.24  2.24  2.24  2.24  2.24
           ;WINS;
zup1: 3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54
zdn1: 3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54

 C:   0.00  1.00  0.00  1.00  0.00  1.00  0.00  1.00  0.00  1.00
rho= 0.98 normr= 1.00	winner=2 learning
w:    0.00  2.68  0.00  2.68  0.00  2.68  0.00  2.68  0.00  2.68
x:    0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45
v:    0.00  2.68  0.00  2.68  0.00  2.68  0.00  2.68  0.00  2.68
u:    0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45
p:    0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24
q:    0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45
F2:   2.00  1.58  3.54  3.54  3.54  3.54  3.54  3.54
                 ;WINS;
zup2: 0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24
zdn2: 0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24

 D:   0.00  0.00  0.00  1.00  1.00  1.00  1.00  0.00  0.00  0.00
rho= 0.98 normr= 1.00	winner=3 learning
w:    0.00  0.00  0.00  3.00  3.00  3.00  3.00  0.00  0.00  0.00
x:    0.00  0.00  0.00  0.50  0.50  0.50  0.50  0.00  0.00  0.00
v:    0.00  0.00  0.00  3.00  3.00  3.00  3.00  0.00  0.00  0.00
u:    0.00  0.00  0.00  0.50  0.50  0.50  0.50  0.00  0.00  0.00
p:    0.00  0.00  0.00  2.50  2.50  2.50  2.50  0.00  0.00  0.00
q:    0.00  0.00  0.00  0.50  0.50  0.50  0.50  0.00  0.00  0.00
F2:   2.24  0.00  2.24  3.16  3.16  3.16  3.16  3.16
                       ;WINS;
zup3: 0.00  0.00  0.00  2.50  2.50  2.50  2.50  0.00  0.00  0.00
zdn3: 0.00  0.00  0.00  2.50  2.50  2.50  2.50  0.00  0.00  0.00

 A:   1.00  1.00  1.00  1.00  1.00  0.00  0.00  0.00  0.00  0.00
rho= 0.98 normr= 1.00	winner=0 learning
w:    2.68  2.68  2.68  2.68  2.68  0.00  0.00  0.00  0.00  0.00
x:    0.45  0.45  0.45  0.45  0.45  0.00  0.00  0.00  0.00  0.00
v:    2.68  2.68  2.68  2.68  2.68  0.00  0.00  0.00  0.00  0.00
u:    0.45  0.45  0.45  0.45  0.45  0.00  0.00  0.00  0.00  0.00
p:    2.24  2.24  2.24  2.24  2.24  0.00  0.00  0.00  0.00  0.00
q:    0.45  0.45  0.45  0.45  0.45  0.00  0.00  0.00  0.00  0.00
F2:  25.00  7.91 10.00 11.18 17.68 17.68 17.68 17.68
     ;WINS;
zup0: 2.24  2.24  2.24  2.24  2.24  0.00  0.00  0.00  0.00  0.00
zdn0: 2.24  2.24  2.24  2.24  2.24  0.00  0.00  0.00  0.00  0.00

 B:   1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  1.00
rho= 0.98 normr= 1.00	winner=1 learning
w:    4.24  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  4.24
x:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
v:    4.24  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  4.24
u:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
p:    3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54
q:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
F2:   7.91 25.00  7.91  0.00 11.18 11.18 11.18 11.18
           ;WINS;
zup1: 3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54
zdn1: 3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54

 C:   0.00  1.00  0.00  1.00  0.00  1.00  0.00  1.00  0.00  1.00
rho= 0.98 normr= 1.00	winner=2 learning
w:    0.00  2.68  0.00  2.68  0.00  2.68  0.00  2.68  0.00  2.68
x:    0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45
v:    0.00  2.68  0.00  2.68  0.00  2.68  0.00  2.68  0.00  2.68
u:    0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45
p:    0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24
q:    0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45
F2:  10.00  7.91 25.00 11.18 17.68 17.68 17.68 17.68
                 ;WINS;
zup2: 0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24
zdn2: 0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24

 D:   0.00  0.00  0.00  1.00  1.00  1.00  1.00  0.00  0.00  0.00
rho= 0.98 normr= 1.00	winner=3 learning
w:    0.00  0.00  0.00  3.00  3.00  3.00  3.00  0.00  0.00  0.00
x:    0.00  0.00  0.00  0.50  0.50  0.50  0.50  0.00  0.00  0.00
v:    0.00  0.00  0.00  3.00  3.00  3.00  3.00  0.00  0.00  0.00
u:    0.00  0.00  0.00  0.50  0.50  0.50  0.50  0.00  0.00  0.00
p:    0.00  0.00  0.00  2.50  2.50  2.50  2.50  0.00  0.00  0.00
q:    0.00  0.00  0.00  0.50  0.50  0.50  0.50  0.00  0.00  0.00
F2:  11.18  0.00 11.18 25.00 15.81 15.81 15.81 15.81
                       ;WINS;
zup3: 0.00  0.00  0.00  2.50  2.50  2.50  2.50  0.00  0.00  0.00
zdn3: 0.00  0.00  0.00  2.50  2.50  2.50  2.50  0.00  0.00  0.00

 E:   1.00  1.00  0.00  0.00  0.00  0.00  0.00  0.00  1.00  1.00
RESET
rho= 0.98 normr= 0.75	winner=3
w:    1.12  3.14  0.31  2.56  0.31  1.86  0.00  1.86  0.50  2.49
x:    0.20  0.56  0.06  0.46  0.06  0.33  0.00  0.33  0.09  0.45
v:    0.00  0.56  0.00  3.21  2.26  2.93  2.19  0.33  0.00  0.45
u:    0.00  0.10  0.00  0.59  0.42  0.54  0.40  0.06  0.00  0.08
p:    0.12  0.53  0.06  2.51  2.06  2.37  2.00  0.37  0.00  0.40
q:    0.03  0.12  0.01  0.55  0.45  0.52  0.44  0.08  0.00  0.09
F2:  11.82  1.85 13.83 22.36 16.49 16.49 16.49 16.49
                       ;WINS;
zup3: 0.00  0.00  0.00  2.50  2.50  2.50  2.50  0.00  0.00  0.00
zdn3: 0.00  0.00  0.00  2.50  2.50  2.50  2.50  0.00  0.00  0.00

 F:   0.00  0.00  0.00  0.00  1.00  1.00  0.00  0.00  0.00  0.00
RESET
rho= 0.98 normr= 0.74	winner=1
w:    0.30  2.50  0.30  2.77  1.31  2.66  0.00  1.83  0.00  1.83
x:    0.05  0.46  0.05  0.51  0.24  0.49  0.00  0.34  0.00  0.34
v:    3.28  0.46  0.00  0.51  0.00  0.49  0.00  0.34  0.00  3.96
u:    0.63  0.09  0.00  0.10  0.00  0.09  0.00  0.06  0.00  0.76
p:    2.89  0.50  0.06  0.55  0.12  0.39  0.00  0.37  0.00  3.20
q:    0.66  0.11  0.01  0.13  0.03  0.09  0.00  0.08  0.00  0.73
F2:   9.22 21.51 11.19  2.66 12.77 12.77 12.77 12.77
           ;WINS;
zup1: 3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54
zdn1: 3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54





PART (a)2     BINARY INPUT PATTERNS
==================================
The same patterns were presented with the vigilance now set to 0.85

 A:   1.00  1.00  1.00  1.00  1.00  0.00  0.00  0.00  0.00  0.00
rho= 0.85 normr= 1.00	winner=0 learning
w:    2.68  2.68  2.68  2.68  2.68  0.00  0.00  0.00  0.00  0.00
x:    0.45  0.45  0.45  0.45  0.45  0.00  0.00  0.00  0.00  0.00
v:    2.68  2.68  2.68  2.68  2.68  0.00  0.00  0.00  0.00  0.00
u:    0.45  0.45  0.45  0.45  0.45  0.00  0.00  0.00  0.00  0.00
p:    2.24  2.24  2.24  2.24  2.24  0.00  0.00  0.00  0.00  0.00
q:    0.45  0.45  0.45  0.45  0.45  0.00  0.00  0.00  0.00  0.00
F2:   3.54  3.54  3.54  3.54  3.54  3.54  3.54  3.54
     ;WINS;
zup0: 2.24  2.24  2.24  2.24  2.24  0.00  0.00  0.00  0.00  0.00
zdn0: 2.24  2.24  2.24  2.24  2.24  0.00  0.00  0.00  0.00  0.00

 B:   1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  1.00
rho= 0.85 normr= 1.00	winner=1 learning
w:    4.24  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  4.24
x:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
v:    4.24  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  4.24
u:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
p:    3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54
q:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
F2:   1.58  2.24  2.24  2.24  2.24  2.24  2.24  2.24
           ;WINS;
zup1: 3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54
zdn1: 3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54

 C:   0.00  1.00  0.00  1.00  0.00  1.00  0.00  1.00  0.00  1.00
rho= 0.85 normr= 1.00	winner=2 learning
w:    0.00  2.68  0.00  2.68  0.00  2.68  0.00  2.68  0.00  2.68
x:    0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45
v:    0.00  2.68  0.00  2.68  0.00  2.68  0.00  2.68  0.00  2.68
u:    0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45
p:    0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24
q:    0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45
F2:   2.00  1.58  3.54  3.54  3.54  3.54  3.54  3.54
                 ;WINS;
zup2: 0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24
zdn2: 0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24

 D:   0.00  0.00  0.00  1.00  1.00  1.00  1.00  0.00  0.00  0.00
rho= 0.85 normr= 1.00	winner=3 learning
w:    0.00  0.00  0.00  3.00  3.00  3.00  3.00  0.00  0.00  0.00
x:    0.00  0.00  0.00  0.50  0.50  0.50  0.50  0.00  0.00  0.00
v:    0.00  0.00  0.00  3.00  3.00  3.00  3.00  0.00  0.00  0.00
u:    0.00  0.00  0.00  0.50  0.50  0.50  0.50  0.00  0.00  0.00
p:    0.00  0.00  0.00  2.50  2.50  2.50  2.50  0.00  0.00  0.00
q:    0.00  0.00  0.00  0.50  0.50  0.50  0.50  0.00  0.00  0.00
F2:   2.24  0.00  2.24  3.16  3.16  3.16  3.16  3.16
                       ;WINS;
zup3: 0.00  0.00  0.00  2.50  2.50  2.50  2.50  0.00  0.00  0.00
zdn3: 0.00  0.00  0.00  2.50  2.50  2.50  2.50  0.00  0.00  0.00

 A:   1.00  1.00  1.00  1.00  1.00  0.00  0.00  0.00  0.00  0.00
rho= 0.85 normr= 1.00	winner=0 learning
w:    2.68  2.68  2.68  2.68  2.68  0.00  0.00  0.00  0.00  0.00
x:    0.45  0.45  0.45  0.45  0.45  0.00  0.00  0.00  0.00  0.00
v:    2.68  2.68  2.68  2.68  2.68  0.00  0.00  0.00  0.00  0.00
u:    0.45  0.45  0.45  0.45  0.45  0.00  0.00  0.00  0.00  0.00
p:    2.24  2.24  2.24  2.24  2.24  0.00  0.00  0.00  0.00  0.00
q:    0.45  0.45  0.45  0.45  0.45  0.00  0.00  0.00  0.00  0.00
F2:  25.00  7.91 10.00 11.18 17.68 17.68 17.68 17.68
     ;WINS;
zup0: 2.24  2.24  2.24  2.24  2.24  0.00  0.00  0.00  0.00  0.00
zdn0: 2.24  2.24  2.24  2.24  2.24  0.00  0.00  0.00  0.00  0.00

 B:   1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  1.00
rho= 0.85 normr= 1.00	winner=1 learning
w:    4.24  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  4.24
x:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
v:    4.24  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  4.24
u:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
p:    3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54
q:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
F2:   7.91 25.00  7.91  0.00 11.18 11.18 11.18 11.18
           ;WINS;
zup1: 3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54
zdn1: 3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54

 C:   0.00  1.00  0.00  1.00  0.00  1.00  0.00  1.00  0.00  1.00
rho= 0.85 normr= 1.00	winner=2 learning
w:    0.00  2.68  0.00  2.68  0.00  2.68  0.00  2.68  0.00  2.68
x:    0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45
v:    0.00  2.68  0.00  2.68  0.00  2.68  0.00  2.68  0.00  2.68
u:    0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45
p:    0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24
q:    0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45  0.00  0.45
F2:  10.00  7.91 25.00 11.18 17.68 17.68 17.68 17.68
                 ;WINS;
zup2: 0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24
zdn2: 0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24  0.00  2.24

 D:   0.00  0.00  0.00  1.00  1.00  1.00  1.00  0.00  0.00  0.00
rho= 0.85 normr= 1.00	winner=3 learning
w:    0.00  0.00  0.00  3.00  3.00  3.00  3.00  0.00  0.00  0.00
x:    0.00  0.00  0.00  0.50  0.50  0.50  0.50  0.00  0.00  0.00
v:    0.00  0.00  0.00  3.00  3.00  3.00  3.00  0.00  0.00  0.00
u:    0.00  0.00  0.00  0.50  0.50  0.50  0.50  0.00  0.00  0.00
p:    0.00  0.00  0.00  2.50  2.50  2.50  2.50  0.00  0.00  0.00
q:    0.00  0.00  0.00  0.50  0.50  0.50  0.50  0.00  0.00  0.00
F2:  11.18  0.00 11.18 25.00 15.81 15.81 15.81 15.81
                       ;WINS;
zup3: 0.00  0.00  0.00  2.50  2.50  2.50  2.50  0.00  0.00  0.00
zdn3: 0.00  0.00  0.00  2.50  2.50  2.50  2.50  0.00  0.00  0.00

 E:   1.00  1.00  0.00  0.00  0.00  0.00  0.00  0.00  1.00  1.00
rho= 0.85 normr= 0.92	winner=1
w:    4.04  0.50  0.00  0.00  0.00  0.00  0.00  0.00  0.50  4.04
x:    0.70  0.09  0.00  0.00  0.00  0.00  0.00  0.00  0.09  0.70
v:    4.24  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  4.24
u:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
p:    3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54
q:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
F2:   7.91 25.00  7.91  0.00 11.18 11.18 11.18 11.18
           ;WINS;
zup1: 3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54
zdn1: 3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54

 F:   0.00  0.00  0.00  0.00  1.00  1.00  0.00  0.00  0.00  0.00
rho= 0.85 normr= 0.93	winner=3
w:    0.00  0.00  0.00  2.42  3.28  3.28  2.42  0.00  0.00  0.00
x:    0.00  0.00  0.00  0.42  0.57  0.57  0.42  0.00  0.00  0.00
v:    0.00  0.00  0.00  2.91  3.08  3.08  2.91  0.00  0.00  0.00
u:    0.00  0.00  0.00  0.48  0.51  0.51  0.48  0.00  0.00  0.00
p:    0.00  0.00  0.00  2.48  2.51  2.51  2.48  0.00  0.00  0.00
q:    0.00  0.00  0.00  0.50  0.50  0.50  0.50  0.00  0.00  0.00
F2:  11.18  0.00 11.18 25.00 15.81 15.81 15.81 15.81
                       ;WINS;
zup3: 0.00  0.00  0.00  2.50  2.50  2.50  2.50  0.00  0.00  0.00
zdn3: 0.00  0.00  0.00  2.50  2.50  2.50  2.50  0.00  0.00  0.00


PART (b)1     REAL VALUED INPUT PATTERNS
========================================
The following patterns were presented to the network with vigilance set to 0.98


 A:   1.00  0.80  0.60  0.40  0.20  0.00  0.00  0.00  0.00  0.00
rho= 0.98 normr= 1.00	winner=0 learning
w:    4.24  3.39  2.55  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    0.71  0.57  0.42  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    4.24  3.39  2.55  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    0.71  0.57  0.42  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    3.54  2.83  2.12  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    0.71  0.57  0.42  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:   2.68  2.68  2.68  2.68  2.68  2.68  2.68  2.68
     ;WINS;
zup0: 3.54  2.83  2.12  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn0: 3.54  2.83  2.12  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 B:   1.00  0.70  0.50  0.20  0.00  0.00  0.20  0.50  0.70  1.00
RESET
rho= 0.98 normr= 1.00	winner=7 learning
w:    3.48  2.43  0.00  0.00  0.00  0.00  0.00  0.00  2.43  3.48
x:    0.58  0.41  0.00  0.00  0.00  0.00  0.00  0.00  0.41  0.58
v:    3.48  2.43  0.00  0.00  0.00  0.00  0.00  0.00  2.43  3.48
u:    0.58  0.41  0.00  0.00  0.00  0.00  0.00  0.00  0.41  0.58
p:    2.90  2.03  0.00  0.00  0.00  0.00  0.00  0.00  2.03  2.90
q:    0.58  0.41  0.00  0.00  0.00  0.00  0.00  0.00  0.41  0.58
F2:   3.19  3.11  3.11  3.11  3.11  3.11  3.11  3.11
                                               ;WINS;
zup7: 2.90  2.03  0.00  0.00  0.00  0.00  0.00  0.00  2.03  2.90
zdn7: 2.90  2.03  0.00  0.00  0.00  0.00  0.00  0.00  2.03  2.90

 C:   0.00  0.50  1.00  0.50  0.00  0.00  0.50  1.00  0.50  0.00
rho= 0.98 normr= 1.00	winner=1 learning
w:    0.00  0.00  4.24  0.00  0.00  0.00  0.00  4.24  0.00  0.00
x:    0.00  0.00  0.71  0.00  0.00  0.00  0.00  0.71  0.00  0.00
v:    0.00  0.00  4.24  0.00  0.00  0.00  0.00  4.24  0.00  0.00
u:    0.00  0.00  0.71  0.00  0.00  0.00  0.00  0.71  0.00  0.00
p:    0.00  0.00  3.54  0.00  0.00  0.00  0.00  3.54  0.00  0.00
q:    0.00  0.00  0.71  0.00  0.00  0.00  0.00  0.71  0.00  0.00
F2:   1.50  2.24  2.24  2.24  2.24  2.24  2.24  0.00
           ;WINS;
zup1: 0.00  0.00  3.54  0.00  0.00  0.00  0.00  3.54  0.00  0.00
zdn1: 0.00  0.00  3.54  0.00  0.00  0.00  0.00  3.54  0.00  0.00

 D:   0.00  0.00  0.30  0.50  0.80  0.80  0.50  0.30  0.00  0.00
rho= 0.98 normr= 1.00	winner=2 learning
w:    0.00  0.00  0.00  2.25  3.60  3.60  2.25  0.00  0.00  0.00
x:    0.00  0.00  0.00  0.37  0.60  0.60  0.37  0.00  0.00  0.00
v:    0.00  0.00  0.00  2.25  3.60  3.60  2.25  0.00  0.00  0.00
u:    0.00  0.00  0.00  0.37  0.60  0.60  0.37  0.00  0.00  0.00
p:    0.00  0.00  0.00  1.87  3.00  3.00  1.87  0.00  0.00  0.00
q:    0.00  0.00  0.00  0.37  0.60  0.60  0.37  0.00  0.00  0.00
F2:   0.00  0.00  3.08  3.08  3.08  3.08  3.08  0.00
                 ;WINS;
zup2: 0.00  0.00  0.00  1.87  3.00  3.00  1.87  0.00  0.00  0.00
zdn2: 0.00  0.00  0.00  1.87  3.00  3.00  1.87  0.00  0.00  0.00

 E:   1.00  0.50  0.00  0.00  0.00  0.00  0.00  0.00  0.50  1.00
rho= 0.98 normr= 1.00	winner=7 learning
w:    3.69  2.10  0.00  0.00  0.00  0.00  0.00  0.00  2.10  3.69
x:    0.61  0.35  0.00  0.00  0.00  0.00  0.00  0.00  0.35  0.61
v:    3.66  2.14  0.00  0.00  0.00  0.00  0.00  0.00  2.14  3.66
u:    0.61  0.36  0.00  0.00  0.00  0.00  0.00  0.00  0.36  0.61
p:    3.05  1.79  0.00  0.00  0.00  0.00  0.00  0.00  1.79  3.05
q:    0.61  0.36  0.00  0.00  0.00  0.00  0.00  0.00  0.36  0.61
F2:  15.97  0.00  0.00 15.57 15.57 15.57 15.57 25.00
                                               ;WINS;
zup7: 3.05  1.79  0.00  0.00  0.00  0.00  0.00  0.00  1.79  3.05
zdn7: 3.05  1.79  0.00  0.00  0.00  0.00  0.00  0.00  1.79  3.05

 F:   0.00  0.00  0.00  0.50  1.00  1.00  0.50  0.00  0.00  0.00
rho= 0.98 normr= 1.00	winner=2 learning
w:    0.00  0.00  0.00  2.03  3.73  3.73  2.03  0.00  0.00  0.00
x:    0.00  0.00  0.00  0.34  0.62  0.62  0.34  0.00  0.00  0.00
v:    0.00  0.00  0.00  2.05  3.71  3.71  2.05  0.00  0.00  0.00
u:    0.00  0.00  0.00  0.34  0.62  0.62  0.34  0.00  0.00  0.00
p:    0.00  0.00  0.00  1.72  3.09  3.09  1.72  0.00  0.00  0.00
q:    0.00  0.00  0.00  0.34  0.62  0.62  0.34  0.00  0.00  0.00
F2:   0.00  0.00 25.00 15.40 15.40 15.40 15.40  0.00
                 ;WINS;
zup2: 0.00  0.00  0.00  1.72  3.09  3.09  1.72  0.00  0.00  0.00
zdn2: 0.00  0.00  0.00  1.72  3.09  3.09  1.72  0.00  0.00  0.00

 A:   1.00  0.80  0.60  0.40  0.20  0.00  0.00  0.00  0.00  0.00
rho= 0.98 normr= 1.00	winner=0 learning
w:    4.24  3.39  2.55  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    0.71  0.57  0.42  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    4.24  3.39  2.55  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    0.71  0.57  0.42  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    3.54  2.83  2.12  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    0.71  0.57  0.42  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00  7.50  0.00 13.42 13.42 13.42 13.42 15.84
     ;WINS;
zup0: 3.54  2.83  2.12  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn0: 3.54  2.83  2.12  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 B:   1.00  0.70  0.50  0.20  0.00  0.00  0.20  0.50  0.70  1.00
rho= 0.98 normr= 1.00	winner=7 learning
w:    3.55  2.33  0.00  0.00  0.00  0.00  0.00  0.00  2.33  3.55
x:    0.59  0.39  0.00  0.00  0.00  0.00  0.00  0.00  0.39  0.59
v:    3.56  2.31  0.00  0.00  0.00  0.00  0.00  0.00  2.31  3.56
u:    0.59  0.38  0.00  0.00  0.00  0.00  0.00  0.00  0.38  0.59
p:    2.97  1.92  0.00  0.00  0.00  0.00  0.00  0.00  1.92  2.97
q:    0.59  0.38  0.00  0.00  0.00  0.00  0.00  0.00  0.38  0.59
F2:  15.84  0.00  0.00 15.31 15.31 15.31 15.31 25.00
                                               ;WINS;
zup7: 2.97  1.92  0.00  0.00  0.00  0.00  0.00  0.00  1.92  2.97
zdn7: 2.97  1.92  0.00  0.00  0.00  0.00  0.00  0.00  1.92  2.97

 C:   0.00  0.50  1.00  0.50  0.00  0.00  0.50  1.00  0.50  0.00
rho= 0.98 normr= 1.00	winner=1 learning
w:    0.00  0.00  4.24  0.00  0.00  0.00  0.00  4.24  0.00  0.00
x:    0.00  0.00  0.71  0.00  0.00  0.00  0.00  0.71  0.00  0.00
v:    0.00  0.00  4.24  0.00  0.00  0.00  0.00  4.24  0.00  0.00
u:    0.00  0.00  0.71  0.00  0.00  0.00  0.00  0.71  0.00  0.00
p:    0.00  0.00  3.54  0.00  0.00  0.00  0.00  3.54  0.00  0.00
q:    0.00  0.00  0.71  0.00  0.00  0.00  0.00  0.71  0.00  0.00
F2:   7.50 25.00  0.00 11.18 11.18 11.18 11.18  0.00
           ;WINS;
zup1: 0.00  0.00  3.54  0.00  0.00  0.00  0.00  3.54  0.00  0.00
zdn1: 0.00  0.00  3.54  0.00  0.00  0.00  0.00  3.54  0.00  0.00

 D:   0.00  0.00  0.30  0.50  0.80  0.80  0.50  0.30  0.00  0.00
rho= 0.98 normr= 1.00	winner=2 learning
w:    0.00  0.00  0.00  2.18  3.64  3.64  2.18  0.00  0.00  0.00
x:    0.00  0.00  0.00  0.36  0.61  0.61  0.36  0.00  0.00  0.00
v:    0.00  0.00  0.00  2.17  3.65  3.65  2.17  0.00  0.00  0.00
u:    0.00  0.00  0.00  0.36  0.61  0.61  0.36  0.00  0.00  0.00
p:    0.00  0.00  0.00  1.80  3.04  3.04  1.80  0.00  0.00  0.00
q:    0.00  0.00  0.00  0.36  0.61  0.61  0.36  0.00  0.00  0.00
F2:   0.00  0.00 25.00 15.21 15.21 15.21 15.21  0.00
                 ;WINS;
zup2: 0.00  0.00  0.00  1.80  3.04  3.04  1.80  0.00  0.00  0.00
zdn2: 0.00  0.00  0.00  1.80  3.04  3.04  1.80  0.00  0.00  0.00


PART (b)2     REAL VALUED INPUT PATTERNS
========================================
The following patterns were presented to the network with vigilance set to 0.85



 A:   1.00  0.80  0.60  0.40  0.20  0.00  0.00  0.00  0.00  0.00
rho= 0.85 normr= 1.00	winner=0 learning
w:    4.24  3.39  2.55  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    0.71  0.57  0.42  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    4.24  3.39  2.55  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    0.71  0.57  0.42  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    3.54  2.83  2.12  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    0.71  0.57  0.42  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:   2.68  2.68  2.68  2.68  2.68  2.68  2.68  2.68
     ;WINS;
zup0: 3.54  2.83  2.12  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn0: 3.54  2.83  2.12  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 B:   1.00  0.70  0.50  0.20  0.00  0.00  0.20  0.50  0.70  1.00
rho= 0.85 normr= 0.91	winner=0 learning
w:    4.58  3.41  0.00  0.00  0.00  0.00  0.00  0.00  0.41  0.58
x:    0.80  0.59  0.00  0.00  0.00  0.00  0.00  0.00  0.07  0.10
v:    4.79  3.60  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    0.80  0.60  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    3.99  3.01  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    0.80  0.60  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00 13.41 13.41 13.41 13.41 13.41 13.41 13.41
     ;WINS;
zup0: 3.99  3.01  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn0: 3.99  3.01  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 C:   0.00  0.50  1.00  0.50  0.00  0.00  0.50  1.00  0.50  0.00
rho= 0.85 normr= 1.00	winner=1 learning
w:    0.00  0.00  4.24  0.00  0.00  0.00  0.00  4.24  0.00  0.00
x:    0.00  0.00  0.71  0.00  0.00  0.00  0.00  0.71  0.00  0.00
v:    0.00  0.00  4.24  0.00  0.00  0.00  0.00  4.24  0.00  0.00
u:    0.00  0.00  0.71  0.00  0.00  0.00  0.00  0.71  0.00  0.00
p:    0.00  0.00  3.54  0.00  0.00  0.00  0.00  3.54  0.00  0.00
q:    0.00  0.00  0.71  0.00  0.00  0.00  0.00  0.71  0.00  0.00
F2:   0.00  2.24  2.24  2.24  2.24  2.24  2.24  2.24
           ;WINS;
zup1: 0.00  0.00  3.54  0.00  0.00  0.00  0.00  3.54  0.00  0.00
zdn1: 0.00  0.00  3.54  0.00  0.00  0.00  0.00  3.54  0.00  0.00

 D:   0.00  0.00  0.30  0.50  0.80  0.80  0.50  0.30  0.00  0.00
rho= 0.85 normr= 1.00	winner=2 learning
w:    0.00  0.00  0.00  2.25  3.60  3.60  2.25  0.00  0.00  0.00
x:    0.00  0.00  0.00  0.37  0.60  0.60  0.37  0.00  0.00  0.00
v:    0.00  0.00  0.00  2.25  3.60  3.60  2.25  0.00  0.00  0.00
u:    0.00  0.00  0.00  0.37  0.60  0.60  0.37  0.00  0.00  0.00
p:    0.00  0.00  0.00  1.87  3.00  3.00  1.87  0.00  0.00  0.00
q:    0.00  0.00  0.00  0.37  0.60  0.60  0.37  0.00  0.00  0.00
F2:   0.00  0.00  3.08  3.08  3.08  3.08  3.08  3.08
                 ;WINS;
zup2: 0.00  0.00  0.00  1.87  3.00  3.00  1.87  0.00  0.00  0.00
zdn2: 0.00  0.00  0.00  1.87  3.00  3.00  1.87  0.00  0.00  0.00

 E:   1.00  0.50  0.00  0.00  0.00  0.00  0.00  0.00  0.50  1.00
rho= 0.85 normr= 0.92	winner=0 learning
w:    4.86  2.98  0.00  0.00  0.00  0.00  0.00  0.00  0.32  0.63
x:    0.85  0.52  0.00  0.00  0.00  0.00  0.00  0.00  0.06  0.11
v:    5.07  3.20  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    0.85  0.53  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    4.22  2.68  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    0.84  0.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00  0.00  0.00 11.07 11.07 11.07 11.07 11.07
     ;WINS;
zup0: 4.22  2.68  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn0: 4.22  2.68  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 F:   0.00  0.00  0.00  0.50  1.00  1.00  0.50  0.00  0.00  0.00
rho= 0.85 normr= 1.00	winner=2 learning
w:    0.00  0.00  0.00  2.03  3.73  3.73  2.03  0.00  0.00  0.00
x:    0.00  0.00  0.00  0.34  0.62  0.62  0.34  0.00  0.00  0.00
v:    0.00  0.00  0.00  2.05  3.71  3.71  2.05  0.00  0.00  0.00
u:    0.00  0.00  0.00  0.34  0.62  0.62  0.34  0.00  0.00  0.00
p:    0.00  0.00  0.00  1.72  3.09  3.09  1.72  0.00  0.00  0.00
q:    0.00  0.00  0.00  0.34  0.62  0.62  0.34  0.00  0.00  0.00
F2:   0.00  0.00 25.00 15.40 15.40 15.40 15.40 15.40
                 ;WINS;
zup2: 0.00  0.00  0.00  1.72  3.09  3.09  1.72  0.00  0.00  0.00
zdn2: 0.00  0.00  0.00  1.72  3.09  3.09  1.72  0.00  0.00  0.00

 A:   1.00  0.80  0.60  0.40  0.20  0.00  0.00  0.00  0.00  0.00
rho= 0.85 normr= 0.97	winner=0 learning
w:    4.77  3.48  0.42  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    0.81  0.59  0.07  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    4.87  3.50  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    0.81  0.58  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    4.06  2.91  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    0.81  0.58  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00  0.00  0.00 10.91 10.91 10.91 10.91 10.91
     ;WINS;
zup0: 4.07  2.91  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn0: 4.07  2.91  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 B:   1.00  0.70  0.50  0.20  0.00  0.00  0.20  0.50  0.70  1.00
rho= 0.85 normr= 0.92	winner=0 learning
w:    4.66  3.30  0.00  0.00  0.00  0.00  0.00  0.00  0.41  0.58
x:    0.81  0.57  0.00  0.00  0.00  0.00  0.00  0.00  0.07  0.10
v:    4.89  3.47  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    0.82  0.58  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    4.08  2.89  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    0.82  0.58  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00  0.00  0.00 11.03 11.03 11.03 11.03 11.03
     ;WINS;
zup0: 4.08  2.89  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn0: 4.08  2.89  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 C:   0.00  0.50  1.00  0.50  0.00  0.00  0.50  1.00  0.50  0.00
rho= 0.85 normr= 1.00	winner=1 learning
w:    0.00  0.00  4.24  0.00  0.00  0.00  0.00  4.24  0.00  0.00
x:    0.00  0.00  0.71  0.00  0.00  0.00  0.00  0.71  0.00  0.00
v:    0.00  0.00  4.24  0.00  0.00  0.00  0.00  4.24  0.00  0.00
u:    0.00  0.00  0.71  0.00  0.00  0.00  0.00  0.71  0.00  0.00
p:    0.00  0.00  3.54  0.00  0.00  0.00  0.00  3.54  0.00  0.00
q:    0.00  0.00  0.71  0.00  0.00  0.00  0.00  0.71  0.00  0.00
F2:   0.00 25.00  0.00 11.18 11.18 11.18 11.18 11.18
           ;WINS;
zup1: 0.00  0.00  3.54  0.00  0.00  0.00  0.00  3.54  0.00  0.00
zdn1: 0.00  0.00  3.54  0.00  0.00  0.00  0.00  3.54  0.00  0.00

 D:   0.00  0.00  0.30  0.50  0.80  0.80  0.50  0.30  0.00  0.00
rho= 0.85 normr= 1.00	winner=2 learning
w:    0.00  0.00  0.00  2.18  3.64  3.64  2.18  0.00  0.00  0.00
x:    0.00  0.00  0.00  0.36  0.61  0.61  0.36  0.00  0.00  0.00
v:    0.00  0.00  0.00  2.17  3.65  3.65  2.17  0.00  0.00  0.00
u:    0.00  0.00  0.00  0.36  0.61  0.61  0.36  0.00  0.00  0.00
p:    0.00  0.00  0.00  1.80  3.04  3.04  1.80  0.00  0.00  0.00
q:    0.00  0.00  0.00  0.36  0.61  0.61  0.36  0.00  0.00  0.00
F2:   0.00  0.00 25.00 15.21 15.21 15.21 15.21 15.21
                 ;WINS;
zup2: 0.00  0.00  0.00  1.80  3.04  3.04  1.80  0.00  0.00  0.00
zdn2: 0.00  0.00  0.00  1.80  3.04  3.04  1.80  0.00  0.00  0.00



PART (c)1     THETA = 0.6
=========================
part (b)1 was repeated with theta = 0.6


 A:   1.00  0.80  0.60  0.40  0.20  0.00  0.00  0.00  0.00  0.00
rho= 0.98 normr= 1.00	winner=0 learning
w:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:   1.58  1.58  1.58  1.58  1.58  1.58  1.58  1.58
     ;WINS;
zup0: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn0: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 B:   1.00  0.70  0.50  0.20  0.00  0.00  0.20  0.50  0.70  1.00
rho= 0.98 normr= 1.00	winner=1 learning
w:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:   5.00  1.58  1.58  1.58  1.58  1.58  1.58  1.58
           ;WINS;
zup1: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn1: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 C:   0.00  0.50  1.00  0.50  0.00  0.00  0.50  1.00  0.50  0.00
rho= 0.98 normr= 1.00	winner=0 learning
w:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00 25.00  7.91  7.91  7.91  7.91  7.91  7.91
     ;WINS;
zup0: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn0: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 D:   0.00  0.00  0.30  0.50  0.80  0.80  0.50  0.30  0.00  0.00
rho= 0.98 normr= 1.00	winner=1 learning
w:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00 25.00  7.91  7.91  7.91  7.91  7.91  7.91
           ;WINS;
zup1: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn1: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 E:   1.00  0.50  0.00  0.00  0.00  0.00  0.00  0.00  0.50  1.00
RESET
rho= 0.98 normr= 1.00	winner=7 learning
w:    4.24  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  4.24
x:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
v:    4.24  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  4.24
u:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
p:    3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54
q:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
F2:   3.54  3.54  2.24  2.24  2.24  2.24  2.24  2.24
                                               ;WINS;
zup7: 3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54
zdn7: 3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54

 F:   0.00  0.00  0.00  0.50  1.00  1.00  0.50  0.00  0.00  0.00
rho= 0.98 normr= 1.00	winner=2 learning
w:    0.00  0.00  0.00  0.00  4.24  4.24  0.00  0.00  0.00  0.00
x:    0.00  0.00  0.00  0.00  0.71  0.71  0.00  0.00  0.00  0.00
v:    0.00  0.00  0.00  0.00  4.24  4.24  0.00  0.00  0.00  0.00
u:    0.00  0.00  0.00  0.00  0.71  0.71  0.00  0.00  0.00  0.00
p:    0.00  0.00  0.00  0.00  3.54  3.54  0.00  0.00  0.00  0.00
q:    0.00  0.00  0.00  0.00  0.71  0.71  0.00  0.00  0.00  0.00
F2:   0.00  0.00  2.24  2.24  2.24  2.24  2.24  0.00
                 ;WINS;
zup2: 0.00  0.00  0.00  0.00  3.54  3.54  0.00  0.00  0.00  0.00
zdn2: 0.00  0.00  0.00  0.00  3.54  3.54  0.00  0.00  0.00  0.00

 A:   1.00  0.80  0.60  0.40  0.20  0.00  0.00  0.00  0.00  0.00
rho= 0.98 normr= 1.00	winner=0 learning
w:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00 25.00  0.00  7.91  7.91  7.91  7.91 17.68
     ;WINS;
zup0: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn0: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 B:   1.00  0.70  0.50  0.20  0.00  0.00  0.20  0.50  0.70  1.00
rho= 0.98 normr= 1.00	winner=1 learning
w:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00 25.00  0.00  7.91  7.91  7.91  7.91 17.68
           ;WINS;
zup1: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn1: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 C:   0.00  0.50  1.00  0.50  0.00  0.00  0.50  1.00  0.50  0.00
rho= 0.98 normr= 1.00	winner=0 learning
w:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00 25.00  0.00  7.91  7.91  7.91  7.91 17.68
     ;WINS;
zup0: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn0: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 D:   0.00  0.00  0.30  0.50  0.80  0.80  0.50  0.30  0.00  0.00
rho= 0.98 normr= 1.00	winner=1 learning
w:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00 25.00  0.00  7.91  7.91  7.91  7.91 17.68
           ;WINS;
zup1: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn1: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00



PART (c)2     THETA = 0.6
=========================
part (b)2 was repeated with theta = 0.6


 A:   1.00  0.80  0.60  0.40  0.20  0.00  0.00  0.00  0.00  0.00
rho= 0.98 normr= 1.00	winner=0 learning
w:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:   1.58  1.58  1.58  1.58  1.58  1.58  1.58  1.58
     ;WINS;
zup0: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn0: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 B:   1.00  0.70  0.50  0.20  0.00  0.00  0.20  0.50  0.70  1.00
rho= 0.98 normr= 1.00	winner=1 learning
w:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:   5.00  1.58  1.58  1.58  1.58  1.58  1.58  1.58
           ;WINS;
zup1: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn1: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 C:   0.00  0.50  1.00  0.50  0.00  0.00  0.50  1.00  0.50  0.00
rho= 0.98 normr= 1.00	winner=0 learning
w:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00 25.00  7.91  7.91  7.91  7.91  7.91  7.91
     ;WINS;
zup0: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn0: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 D:   0.00  0.00  0.30  0.50  0.80  0.80  0.50  0.30  0.00  0.00
rho= 0.98 normr= 1.00	winner=1 learning
w:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00 25.00  7.91  7.91  7.91  7.91  7.91  7.91
           ;WINS;
zup1: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn1: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 E:   1.00  0.50  0.00  0.00  0.00  0.00  0.00  0.00  0.50  1.00
RESET
rho= 0.98 normr= 1.00	winner=7 learning
w:    4.24  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  4.24
x:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
v:    4.24  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  4.24
u:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
p:    3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54
q:    0.71  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.71
F2:   3.54  3.54  2.24  2.24  2.24  2.24  2.24  2.24
                                               ;WINS;
zup7: 3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54
zdn7: 3.54  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  3.54

 F:   0.00  0.00  0.00  0.50  1.00  1.00  0.50  0.00  0.00  0.00
rho= 0.98 normr= 1.00	winner=2 learning
w:    0.00  0.00  0.00  0.00  4.24  4.24  0.00  0.00  0.00  0.00
x:    0.00  0.00  0.00  0.00  0.71  0.71  0.00  0.00  0.00  0.00
v:    0.00  0.00  0.00  0.00  4.24  4.24  0.00  0.00  0.00  0.00
u:    0.00  0.00  0.00  0.00  0.71  0.71  0.00  0.00  0.00  0.00
p:    0.00  0.00  0.00  0.00  3.54  3.54  0.00  0.00  0.00  0.00
q:    0.00  0.00  0.00  0.00  0.71  0.71  0.00  0.00  0.00  0.00
F2:   0.00  0.00  2.24  2.24  2.24  2.24  2.24  0.00
                 ;WINS;
zup2: 0.00  0.00  0.00  0.00  3.54  3.54  0.00  0.00  0.00  0.00
zdn2: 0.00  0.00  0.00  0.00  3.54  3.54  0.00  0.00  0.00  0.00

 A:   1.00  0.80  0.60  0.40  0.20  0.00  0.00  0.00  0.00  0.00
rho= 0.98 normr= 1.00	winner=0 learning
w:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00 25.00  0.00  7.91  7.91  7.91  7.91 17.68
     ;WINS;
zup0: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn0: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 B:   1.00  0.70  0.50  0.20  0.00  0.00  0.20  0.50  0.70  1.00
rho= 0.98 normr= 1.00	winner=1 learning
w:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00 25.00  0.00  7.91  7.91  7.91  7.91 17.68
           ;WINS;
zup1: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn1: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 C:   0.00  0.50  1.00  0.50  0.00  0.00  0.50  1.00  0.50  0.00
rho= 0.98 normr= 1.00	winner=0 learning
w:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00 25.00  0.00  7.91  7.91  7.91  7.91 17.68
     ;WINS;
zup0: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn0: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

 D:   0.00  0.00  0.30  0.50  0.80  0.80  0.50  0.30  0.00  0.00
rho= 0.98 normr= 1.00	winner=1 learning
w:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
x:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
v:    6.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
u:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
p:    5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
q:    1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
F2:  25.00 25.00  0.00  7.91  7.91  7.91  7.91 17.68
           ;WINS;
zup1: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
zdn1: 5.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

ANALYSIS

PART A

The function of the F0 layer is to serve as a two-stage normalization
filter.  There is a combination of feedback loops that contrast
enhance the input pattern, combined with normalization filters that
prevent the values from becomming excessive.  Significantly though,
the feedback gains a and b are 3 and 5 respectively, which means that
at the corresponding nodes the feedback signal is favored over the
feed forward input by those gain values.  This stage of filtering is
required in order to make the algorithm independant of the absolute
value of the input signal, and respond only to relative values.

The F1 layer is composed of exactly the same kind of normalization
filter, except that the top-down F2 layer is in the same feedback
loop as F1, and with such strong gain settings, would have the potential
to swamp out any inputs.  This is the purpose of separating F0 and
F1, where F1 is isolated from top-down feedback.  There is an extra
level of normalization in F1 in the connection from p through q back
to v.  This serves to normalize the influence of the top-down filter
before it is fed back into F1.

A comparison of the clustering capabilities of ART1, ART2 and the
leader algorithm is provided below.  All the algorithms are parameter
dependant, so 'typical' values were selected for this comparison.
Perhaps it would be more fair to compare 'best' parameters for each
algorithm, or robustness across parameter ranges.  The fundamental
problem of course is that it is impossible to rate clustering
performance in any impartial way.  The notion of an ideal clustering
scheme only has meaning when the data represents some physical
quantities which are being clustered for some specific application.
If the vector represents color, form, weight ... for instance, then
clustering would depend on wether your application domain is
industrial furniture, where color is irrelevant, household furniture,
where color is important, or fabric where color is everything and form
is irrelivant.  Examining clusterings by eye for instance as below
puts a strong emphasis on spatial grouping, to which the human eye is
exquisitely sensitive.  In the furniture example such grouping is
completely irrelevant, since adjacency of color, form, weight ... is
not defined in any meaningful space.

PART B

The assignment for this section states "discuss how the network learns
these patterns in the fast learning mode".  Well, there's not much to
say- it assigns a new F2 node for each input pattern and thats that.
The fact that further discussion is required suggests to me that my
simulation is incomplete or incorrect in some way.  This is not only
entirely possible, but even likely.  In an algorithm of this level of
complexity it would be truely surprising if it were to work first
time.  After three days and one night of almost non-stop programming I
have managed to exorcise all of the programming bugs, and even the
more obvious algorithmic bugs.  My LTM weights do track the values of
the p nodes, as instructed by the differential equation, for instance.
As to whether the output is as it should be however, there is no way
for me to tell.  All I can say is that it looks o.k. to me, and leave
it at that.  With this kind of algorithm with intensive and nested
feedback loops and bottom-up top-down interactions my intuitions
abandon me entirely for all but the most general of observations.

ALGORITHMIC COMPARISONS
=======================

LEADER ALGORITHM threshold = 1.0
================================

BINARY DATA:

A: 1 1 1 1 1 0 0 0 0 0

B: 1 0 0 0 0 0 0 0 0 1
E: 1 1 0 0 0 0 0 0 1 1

C: 0 1 0 1 0 1 0 1 0 1

D: 0 0 0 1 1 1 1 0 0 0
F: 0 0 0 0 1 1 0 0 0 0

REAL DATA:

A: 1.0 0.8 0.6 0.4 0.2 0.0 0.0 0.0 0.0 0.0
B: 1.0 0.7 0.5 0.2 0.0 0.0 0.2 0.5 0.7 1.0
E: 1.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.5 1.0

C: 0.0 0.5 1.0 0.5 0.0 0.0 0.5 1.0 0.5 0.0

D: 0.0 0.0 0.3 0.5 0.8 0.8 0.5 0.3 0.0 0.0
F: 0.0 0.0 0.0 0.5 1.0 1.0 0.5 0.0 0.0 0.0

ART1 ALGORITHM slow learning rho=.4
===================================

BINARY DATA:

A: 1 1 1 1 1 0 0 0 0 0
B: 1 0 0 0 0 0 0 0 0 1

C: 0 1 0 1 0 1 0 1 0 1
D: 0 0 0 1 1 1 1 0 0 0
F: 0 0 0 0 1 1 0 0 0 0

E: 1 1 0 0 0 0 0 0 1 1

ART2 ALGORITHM fast learning rho=.85
===================================

BINARY DATA:

A: 1 1 1 1 1 0 0 0 0 0

B: 1 0 0 0 0 0 0 0 0 1
E: 1 1 0 0 0 0 0 0 1 1

C: 0 1 0 1 0 1 0 1 0 1

D: 0 0 0 1 1 1 1 0 0 0
F: 0 0 0 0 1 1 0 0 0 0

REAL DATA:

A: 1.0 0.8 0.6 0.4 0.2 0.0 0.0 0.0 0.0 0.0
B: 1.0 0.7 0.5 0.2 0.0 0.0 0.2 0.5 0.7 1.0
E: 1.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.5 1.0

C: 0.0 0.5 1.0 0.5 0.0 0.0 0.5 1.0 0.5 0.0

D: 0.0 0.0 0.3 0.5 0.8 0.8 0.5 0.3 0.0 0.0
F: 0.0 0.0 0.0 0.5 1.0 1.0 0.5 0.0 0.0 0.0



REFERENCES

Lehar 1989	CN550 Assignment 3, CNS program, Boston University

