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sustained by the network form sharp line-boundaries which separate the space
into tolerant and non-tolerant regions. Figure 2 shows new evidence that within
these non-tolerant or reactive regions, the tolerance varies quite widely; in fig-
ure 2, the darker the shading, the more reactive the spot. Blank (white) regions
are those in which any cell is tolerated. Highly intolerant regions are created
when the recognition regions of a number of cells overlap, thus providing high
stimulation to a cell. It is interesting to observe that the heterogeneous and
homogeneous approaches result in markedly different different divisions of the
space. Furthermore, increasing the upper-limit is expected to lead to thicker
boundaries between zones (see [10]) — however,figure 2 shows that an entirely
different pattern of reactivity is observed at the upper limit
U
is increased from
10
,
000 to 200
,
000.
5.2
Network Properties
Table 1 compares the physical properties of the networks evolved over 10,000 iter-
ations for various values of
U
, in both the homogeneous and heterogeneous cases.
These results show average values obtained using 100 different seed values (with
the same set of seeds used for homogeneous and heterogeneous experiments).
Firstly, as previously shown in figure 1, the size of the networks increases as
U
increases, and as we switch from a homogeneous birth dynamics to a heteroge-
neous dynamics. The maximum and average degree increase with increasing
U
,
as does the cluster coecient. A heterogeneous model tends to lead to networks
with lower clustering coecient and lower average degree than a homogeneous
model for any given
U
. All differences are statistically significant.
Table 1.
Physical properties of homogeneous/heterogeneous networks obtained after
10,000 iterations from the same seed value
homo hetero
10,000 100,000 200,000 10,000 100,000 200,000
Number of Nodes
167.8
357.6
786.5
326.9
986.7
1286.2
Max Degree
29.4
58.0
121.2
37.7
117.9
165.6
Average Degree
4.7
7.9
14.3
3.7
8.9
12.5
Clustering Coecient 0.022
0.023
0.027
0.016
0.016
0.017
Although the maximum degree increases with
U
, due to cells being able to
achieve a higher stimulation from multiple connections before being penalised,
figure 3 also clearly shows that the the maximum degree fluctuates up and down;
this is just a consequence of the concentration rule; the concentration of the cell
with maximum degree with be gradually reduced to zero due the high stimulation
it will inevitably receive at which point it is removed from the system. Following
this, a eventually a new cell will likely take its place and begin to acquire new
connections; the cycle will then repeat.
