Information Technology Reference
In-Depth Information
Δc
1
(
t
)=
c
i
(
t
)
η
s
(1
S
B
2
B
(
t
)
−A
B
2
B
(
t
)
pop size
c
i
(
t
)
−
)
−
iff S
B
2
B
(
t
)
>A
B
2
B
(
t
)
,
(1)
A
B
2
B
(
t
)
−S
B
2
B
(
t
)
pop size
c
i
(
t
)
η
a
(1
c
i
(
t
)
−
)
−
iff S
B
2
B
(
t
)
<A
B
2
B
(
t
)
Δc
2
(
t
)=
c
i
(
t
)
η
s
−
c
i
(
t
)
iff
(
S
B
2
B
(
t
)=0)
∧
(
A
B
2
B
(
t
)=0)
,
(2)
0
otherwise
Δc
3
(
t
)=
c
i
(
t
)
η
A
B
2
A
(
t
)
c
i
(
t
)
,
−
(3)
a
Δc
4
(
t
)=
c
i
(
t
)
η
s
−
c
i
(
t
)
iff
(
S
B
2
B
(
t
)=0)
∧
(
A
B
2
A
(
t
)=0)
,
(4)
0
otherwise
In case of a model including antigens a new concentration for the objects
representing types of antigens has to be evaluated too. Since the change in the
concentration level of each type of antigens depends on its natural continuous
proliferation in the organism (5th rule) and the number of types of antibodies
which recognize the given type of antigens (3rd rule) the new concentration
c
j
(
t
)
of the object representing
j
-th type of antigen is evaluated as follows:
c
j
(
t
+1)=
c
j
(
t
)
η
pro
pop size
S
B
2
A
pop size
−
(5)
where
η
pro
is an antigens' proliferation factor where
η
pro
>
1 (in our experiments
η
pro
was equal
η
a
).
3An yM su s
The shape space model described above is still not complete because we have
not defined a relation for the shapes in the defined space yet. Binary pattern
matching problem belongs to classic and a set of different similarity or distance
functions was already proposed [1]. It is closely connected with a problem of
classification of binary patterns (see e.g. [9] for discussion). In our case it is
assumed that the significance of the bits in the patterns is the same for all the
bits. So eventually the following set of anity measures was selected for tests [7]:
1. Russel and Rao, 2. Jaccard and Needham, 3. Kulzinski, 4. Sokal and Michener,
5. Rogers and Tanimoto, 6. Yule. They were compared with a Hamming distance
and a
r
-contiguous bits matching rule.
For the formal description we shall use the following definition of the binary
strings:
X, Y
N
and the following reference variables:
a
=
i
=1
ξ
i
,ξ
i
=
1
∈{
0
,
1
}
X
i
=
Y
i
=1
,
0
otherwise
.
b
=
i
=1
ξ
i
,ξ
i
=
1
X
i
=1
,Y
i
=0
,
0
otherwise
.
c
=
i
=1
ξ
i
,ξ
i
=
1
(6)
X
i
=0
,Y
i
=1
,
0
otherwise
.
d
=
i
=1
ξ
i
,ξ
i
=
1
X
i
=
Y
i
=0
,
0
otherwise
.
Note, that the total:
a
+
b
+
c
+
d
is a constant value and equals
n
, i.e. the length
of the binary string. Tested anity measures are as follows:
