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that it only contains birth-dynamics, i.e. there is no mechanism by which nodes
may disappear due to environmental constraints, and therefore nodes can in-
crease in concentration indefinitely. This is clearly unrealistic from a biological
perspective, and likely impacts on the type of networks we can expect to obtain
from such a model.
Therefore, in this paper, we present an analysis of an alternative model which
in keeping with biologically motivated spirit of [4] is type-based and depends on
node concentration, yet includes complete birth and death dynamics as in [5]. We
investigate whether the inclusion of a complete dynamics can lead to a scale-free
distribution in a network with an exogenous production scheme. The experiments
are performed using an integer-value shape-space. Much of the previous work in
this area has made use of binary shape-space — this partly has historical roots,
dating back to the first ideas in AIS proposed by Farmer [8], but also has some
advantages in the richness of matching-rules it facilitates. However, using an
integer shape-space only provides an interesting comparison to existing work
with binary shape-spaces, but has advantages from the engineering perspective
in that it lends itself more readily to the kind of real-world engineering problems
we wish to address with AIS technology, and in that the networks can be readily
visualised. The next section presents the model used and discusses the differences
between it and the general model proposed in [4].
3
Immunological Model
The model used in this paper has previously been presented in [2,10,9] and is
shown in outline below.
1. Generate at random a new antibody cell at location (x,y) with radius
r
and
add to the simulation with concentration 10.
2. Calculate the stimulation
S
Ab
of each antibody cell present according to
equation 1
3. For each cell present, if
L<S
Ab
<U
, increase the concentration of the cell
by 1, otherwise decrease it by 1, where
L
and
U
represent a lower and upper
stimulation limit, respectively.
4. Remove any cells whose concentration has reached 0.
5. Repeat
)+
cells
E
Ab
||
Ab
||
S
Ab
=
A
c
(
r
−||
A
−
E
c
(
r
−||
E
−
)
( )
antigens
A
In equation 1,
Ab
represents the complementary position of an antibody
Ab
.
A
c
/E
c
represents the
concentration
of the antigen
A
or antibody
E
,and
r
rep-
resents the recognition radius of the cell. Although the generic equation given
covers the most general case in which a simulation can contain both antibodies
and antigens, in all simulations reported in this paper, no antigens are added,
therefore only idiotypic interactions between cells are considered.
