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system. This is the case when the average life span reaches minimum value and the
average number of types of antibodies - maximum. The concentration decreases
immediately and the types of antibodies are eliminated from the system. The new
ones which replaced the eliminated types live shortly too. The second behavior is
the case where all the antibodies live forever and the life span is maximal while the
average number of antibodies - minimal. In the first case the suppression pressure
is stronger than the activation one. The concentration of all the types of antibod-
ies goes down just after their appearance in the system so the set of antigens is
continuously changing. Just the opposite situation is in the second case where the
activation pressure is much stronger than the suppression and the concentrations
of each of the types of antibodies quickly reach maximum level. So the set of types
is constant from the beginning till the end of experiment. None of the two cases
represents a system which would be able to learn anything.
The most promising case is the result where the life span as well as the average
number of types of antibodies is between the minimum and the maximum value.
Unfortunately there are measures that do not satisfy this requirement. Especially
when we look at the life span it can be seen that for Russel and Rao (with and with-
out T), Sokal and Michener (with and without T), Rogers and Tanimoto without
T, Kulzinski without T, Yule, Hamming and
r
-contiguous bits matching rule it is
very dicult or even impossible to find the values for thresholds
at
and
st
giving
the requested behavior of the system. The remaining measures allows to be tuned
and in those cases it is expected that the system will construct a stable set of de-
pendencies between types of antibodies.
4.2
Histograms of Ages of Antibodies
To confirm our conjectures based on the average life span and average number of
types of antibodies we gathered more detailed information about the lifetime of
types of antibodies appearing during the experiments. Figures 3 and 4 present sam-
ple histograms with mortality of types respecting to their maximum age for three
different settings of thresholds
at
and
st
.
The histograms in Figures 3 and 4 represent distribution for the lifetime of ob-
jects representing types of antibodies in the system. The histograms
3.a
(
at
=0
.
6
st
=0
.
7) and
4.a
(
at
=0
.
2
st
=0
.
3) obtained for Jaccard and Needham anity
measure without and with transformation T represent the most requested situa-
tion. It can be seen that there is a set of objects living for short and even very short
time but there are also the types of antibodies which live longer or even for the time
of the entire experiment, and so the distribution stretches out to the right. Between
these two extremes there are also some types of antibodies which live neither very
short nor forever albeit among them there could be also those which were created in
the middle of the experiment and which lived till the end of the test. Besides it can
be seen that the histogram obtained with transformation T is more regular than
the one without T. This observation indicates that the transformation T makes
results of Jaccard and Needham anity measure more predictable.
The histograms
3.b
and
4.b
(both obtained with
at
=0
.
1
st
=0
.
5) as well as
3.c
and
4.c
(both obtained with
at
=0
.
6
st
=0
.
1) represent the system working with
