Information Technology Reference
In-Depth Information
S
1
S
5
S
2
S
3
S
4
S
6
Fig. 6.
A visualization of the six-group structure taken from [12]. The size of the boxes
corresponds to the group size. The lines show possible links between vertices of the
groups and their thickness is a measure of the number of links.
graph at some time step. We clearly see the central and the peripheral part of
the idiotypic network.
We were able to explain this sophisticated structure by means of an 11-
dimensional pattern module. From this we can derive the correct group sizes
and the observed links between the groups. Also the observation, that
S
1
and
S
4
decay into subgroups [20], can be fully understood. Table 4 gives the mapping
{
S
i
}→{S
j
}
. For example, groups
S
8
,
S
9
,
S
10
,
S
11
,and
S
12
are the subgroups of the empirical group
S
1
. Their calculated size
adds to 1124, which is
exactly
the statistically measured size of group
|
S
i
|
and the derived group sizes
S
1
.
Table 4.
The pattern module of the six groups structure
S
1
S
2
S
3
S
4
S
5
S
6
S
7
S
8
S
9
S
10
S
11
S
12
empirical group
S
4
S
4
S
4
S
5
S
6
S
3
S
2
S
1
S
1
S
1
S
1
S
1
group size
2
22
110
330
660
924
924
660
330
110
22
2
Applying (5) we can also calculate the number of links from a given vertex
v
i
∈ S
i
to vertices in group
S
j
. The results are given in Table 5. This table is
identical
to
the table of measured links in [20]. The non-integer number of links of
v
1
S
1
is
∈
due to the division of
S
1
into subgroups. (They are weighted averages.)
In contrast to the static patterns that emerge for low influx
I
in this struc-
ture we also find perfect matches and 1-mismatch links, but they are simply
outnumbered by the 2-mismatch links.
