Information Technology Reference
In-Depth Information
are very similar. However, there is a difference between both functions because the
function of (27) decreases linearly from the center to the border of the affinity region,
whereas the function of (28) decreases exponentially as can be seen from figure 7.
5 Conclusion
General aspects of the structure and the dynamics of shape-spaces were presented in
this paper. Emphasis was laid on a clear definition of distance functions and it was
argued that in
n
-based shape-spaces only metrics should be used as such functions.
It was shown that
ℜ
-balls (used as recognition regions) have different shapes depend-
ing on the type of the distance function. Several distance functions used in Hamming
shape-spaces were examined and it turned out that not all of them are metrics.
With respect to the dynamics, an affinity function was defined as a function by
which an element
i
exerts affinity on other elements and its value is determined by the
distance between
i
and the other elements. The distance determines the shape of the
recognition or affinity region of
i
, and the affinity function its varying size. It was
illustrated which impact different distance metrics have on affinity functions. In
particular it was shown how the similarity measure of Rogers and Tanimoto, though
not being a distance function, can be used to define an affinity function.
The affinity function is the basis for the definition of the dynamics of a shape-
space. This has to be worked out in more detail, which means, it must be described
how the functions
a
(
t
) and
b
(
t
) change over time. In [1] they are linked to each other.
This has the advantage that the size of the affinity region can be kept fixed and only
the function
a
(
t
) (or
C
(
i
,
t
)) has to be defined. In [1], it is defined as a function of the
total affinity exerted on an immune element
i
by all other immune elements.
In a further developed simulation system the influence of the affinity on the
concentration of elements should be defined in a more elaborated way. For instance
the influence of other elements like cytokines, which have a different dynamics,
should be taken into account. The concentration of antigens should be treated
differently from that of the antibodies (as is already done in [1]) and it should be
taken into consideration that it cannot only decrease but also increase which means
that the immune response fails.
ε
References
[1]
H. Bersini. Self-assertion versus self-recognition: A tribute to Francisco Varela.
In
Proceedings of ICARIS 2002
. Canterbury, 2002.
[2]
R.J. De Boer. Information processing in immune systems: Clonal selection
versus idiotypic network models.
Cell to Cell Signalling
:
From Experiments to
Theoretical Models
. Academic Press, 1989, 285 - 302.
[3]
R.J. De Boer and A.S. Perelson. Size and connectivity as emergent properties of
a developing immune network.
J. of Theoretical Biology
, 149, 1990, 381 - 424.
[4]
L. De Castro and J. Timmis.
Artificial Immune Systems
:
A new Computational
Intelligence Approach
. Springer, 2002.
[5]
V. Detours, H. Bersini, J. Stewart, and F. Varela. Development of an idiotypic
network in shape-space.
J. of Theoretical Biology
, 170, 1994.
