Biomedical Engineering Reference
In-Depth Information
Remark4.4
To.calculate.the.regional.similarity.of.ξ
1
.in.region.
V
1
.and.ξ
2
.in.region.
V
2
,.let.
=
v
f
T
(
ξ
,
V
1
. and.
)
v
=
f
T
(
ξ
,
V
2
;. then. the. regional. similarity. can. be. calcu-
)
1
1
2
2
lated.as
∏
m
−
1
(
)
δ
(
f
(
ξ
,
V f
),
(
ξ
,
V
))
= δ
v v
,
=
d v j v j
(
( ),
( ))
.
(4.11)
T
1
1
T
2
2
1
2
1
2
.
j
=
0
where.
m
.is.the.size.of.region.
V
1
.and.
V
2
.(the.size.of.both.regions.must.be.the.
same)..For.simplicity,
δ
(
f
(
ξ
,
V f
),
(
ξ
,
V
))
≡ ∆ ξ
(
,
V
;
ξ
,
V
)
.
(4.12)
.
T
1
1
T
2
2
1
1
2
2
Example4.2
Consider.two.schemata.
ξ =
*01* 1* *
.and.
ξ
=
0 * *1* 01
.and.two.regions.
2
[
]
[
]
with.
2, 4
.and.
V
=
4, 6
;.the.regional.similarity.of. ξ .in.
V
.and. ξ .in.
V
=
V
.is.calculated.as
.
∆ ξ
(
,
V
;
ξ
,
V
)
= δ
(1* 1,
* 01)
=
d
(1, *)
×
d
(*, 0)
×
d
(1, 1) 0.5 1 1 0.5
=
×
×
=
1
1
2
2
.
4.2.2 exact Schema evolution equation for Copy-and-Paste
Now.consider.a.primary.schemata.competition.set.
S
.with.
o
(
ξ
)
=
n
,
ξ ∈
S
,.
i
i
n
and.hence.
size S
(
)
=
2
≡
M
..The.deining.length.of.schema.ξ
i
.is.
L
=
p
−
p
1
,.
ξ
d
2
with.
max( ( )
2
. denoting. the. bit. locations. of. the.
first. and. last. actual. bits,. respectively.. It. is. assumed. that. a. copy-and-paste.
operation.is.performed.on.schemata.ξ
p
=
min(
f
L
(
ξ
))
. and.
p
=
f
L
ξ
1
i
i
m n
, ..A.transposon.of.length.
L
g
.is.
copied.from.
ξ
m
.at.position.
c
.and.pasted.into.position.
k
.of. ξ
n
,.and.the.resul-
tant.schema.is.denoted.as.
′
ξ
∈
S
ξ
n
.
Figure 4.2.
d
epicts. the. operation. for. which. some. important. notations. are.
given.as.follows:
1.
Transposonregion
:.
= + − + + − − .
specifies.the.bit.locations.of.selected.transposons.in. ξ
m
,.which.fall.
into.the.defining.length.region.
p
G
[ max(
c
p
k
, 0), min(
c
p
L
k L
,
1)]
c k
,
1
1
d
g
[
,
p
]
.of.the.targeted.schema.ξ,.after.
1
2
pasting;
2.
Pastedregion
:.
V
=
[max(
p k
,
),min(
p
+
L k L
,
+
−
1)]
.specifies.the.bit.
k
1
1
d
g
locations.within.the.region.
p
[
,
p
2
.of.ξ.where.the.transposon.is.pasted;
]
1
3.
Unchangedregion
:.
V
[
p
,min(
p
L k
,
1)]
[max(
p k L
,
),
p
L
]
.
′ =
+
−
+
+
k
1
1
d
1
g
1
d
specifies.the.bit.locations.of.ξ.within.the.region.
p
[
,
p
2
.but.not.belong-
]
1
ing.to.
V
k
.
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