B Cell–Inspired Algorithms - Immunological Computation: Theory and Applications - page 143

where x j denotes the j th antigen presented to the IN. Hence, information about
all the antigens that have been presented earlier to the network is used to compute
the current stimulation level of each D-W-B cell. Also, corresponding equations to
update the infl uence radii can be derived by making

∂ sX

i

()

0

∂

2

i

thus obtaining

1

we W

ij i J , 1

sx ()

(5.25) i j

2

iJ ,

∑

, w ij denotes f i ( x j ), and σ i , J the radio of infl uence of i th
D-W-B cell after presenting ( J

where W f () x

iJ , 1 i j

−

1) antigens, which is defi ned as

1

e Ww d

eW

2 2

iJ , 1 iJ , 1 iJ iJ ,

2

(5.26)

1

2 ( w )

ij ,

iJ , 1 iJ ,

where d iJ denotes the distance from D-W-B cell i to the J th encountered antigen.
In this model, a dynamic stimulation factor α ( t ) is also incorporated in the
calculation of the D-W-B cell stimulation level. h is is done by allowing groups of
D-W-B cells to have a stimulation coe cient that will cause the formation of sub-
networks of D-W-B cell that can self-sustain, even after the antigen that caused their
creation disappears from the environment. However, a limit should be specifi ed on the
time span that these patterns would contribute to the network dynamics so as to avoid
the imposition of any additional superfl uous (computational and storage) burden on
the IN by such patterns. h us, an annealing schedule is proposed for this stimulation
factor, that is, this stimulation coe cient decreases with the age of the subnet.
In the absence of a recent antigen that succeeds in stimulating a given subnet,
the age of the D-W-B cell increases to 1 with each antigen presented to the immune
system. However, if a new antigen succeeds in stimulating a given subnet, then its
age is reset to 0. h erefore, those subnets that are very old will gradually die, unless
they become restimulated by recent relevant antigens. Incorporating a dynamic
suppression factor in the computation of the D-W-B cell stimulation level is also
a more reasonable way to take internal interactions into account. h e suppression
factor is not intended to control the proliferation and redundancy in the population
of the D-W-B cells. It is important to note that the eff ect of positive stimulation
is to provide a memory mechanism to the IN; however, suppression provides a
mechanism to have the D-W-B cells compete to avoid redundancy.