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where (14) originates from both (7), (8) and (9), (15) - from (10), and (16) -
from (11). The transformed Hamming distance turns to the formula
d
HT
=
b
.
4
Tuning the Network
In the first phase of our research we observed the dynamics of the model i.e. the
change of concentration of different types of antibodies. The change is expressed
by life spans of the objects since the objects with high concentration live longer
(and even
forever
, i.e. as long as the experiment continues) while the ones with
decreasing concentration quickly reach the minimum value and are eliminated from
the system. This way the life span of the objects tells a lot about the environment
where they have to live. Another parameter good for observing the properties of
the system is average number of types of antibodies. For better understanding of
the graphs it necessary to note, that in contrast to other network models the size
of repertoire of types of antibodies was fixed. Therefore new types were recruited
only if some other disappeared and made room in the repertoire.
This group of experiments was performed for the system without antigens thus
just the first and the second rule of interactions influenced on the concentration
levels. Verification of ability of the system to build a stable structure of interactions
was the goal of this part of experiments. This group of experiments allowed us also
to tune the system. The role of selected measures as well as the two thresholds
mentioned above,
at
and
st
which control the sensitivity of the antibodies were
compared in these experiments.
4.1
Average Life Span and Average Number of Antibodies
The results of experiments with different values of thresholds
at
and
st
are pre-
sented in Figure 1 (average life span of types of antibodies) and 2 (average number
of types of antibodies). Each of the figures consist of eight graphs for eight an-
ity measures and for six of them (7) - (10) and
r
-contiguous bits rule two versions
of measures were tested: without and with transformation T. Thus for each of the
six there are two landscapes in the graph except for the Yule a
nity measure (12)
which can not be applied with transformation T and the Hamming - applied just
with transformation T. Every experiment was repeated 20 times therefore every
point in the graphs is the mean of the obtained 20 average life spans or average
numbers of types of antibodies.
The activation factor
η
a
was set to 1.11111 and the suppression factor
η
s
-to
0.9. The thresholds
st
and
at
for Hamming distance and
r
-contiguous bits rule
changed from 1 to 15 with step 1 while for the remaining six measures - from 0.1
to 0.9 with step 0.1. For all the cases minimum level of concentration was set to 0.1
and the maximum - to 9999. The population consisted of 1000 objects representing
different types of antibodies and every experiment took 500 iterations. Thus the
minimum average number of types of antibodies in the system is 1000 and their
maximum average life span is 500.
There are two extreme behaviors observed in the graphs. The first behavior is the
case where all the types of antibodies die immediately after introduction into the
