Biomedical Engineering Reference
In-Depth Information
By. considering. all. the. possible. combinations. of.
c
. and.
k
,. the.
,
k
,
c
m
n
m
n
destructive.rate.
PD
A
.of.ξ
is.then.computed.as
L L
−
L L
−
g
g
p
L L
∑
∑
1
2
∑
cut
g
[
]
PD
=
1
− ∆ ξ
( ,
I
;
ξ
,
G
) ( ,
∆ ξ
M
;
ξ
,
M
′
)
A
c
,
k
c
,
c
,
k
c
,
k
c
,
k
3
m m
n m m
m m
m m
(
−
+
1)
c
=
0
c
=
0
k
∉κ
(
c
)
n
m
m
m
∑
[
]
+
1
− ∆ ξ
( ,
I
;
ξ
,
G
) ( ,
∆ ξ
M
;
ξ
,
M
′
)
c
,
k
c
,
c
,
k
c
,
k
c
,
k
n
n
m n
n
n
n
n
n
k
∉κ
(
c
)
.
n
n
.
.
(4.38)
where. κ
(
c
)
=
(
c
,
c
+
L
]
,.
p
cut
. is. the. operational. rate. of. the. cut-and-paste.
m
m
m
g
1
operation,.and.the.factor.
.indicates.the.probability.of.selecting.a.par-
1)
3
(
L L
g
−
+
ticular.set.of
c
( , , )
.
The.occurrence.probability.of.case.A.is.given.by
(
,
c
,
k
)
.or.
c
c
k
m
n
m
m
n
n
E t
A
( )
=
P
( , )
ξ
t P
( , )
.
ξ
t
(4.39)
.
Hence.the.expected.destruction.of.ξ.in.this.case.is.computed.as
(
)
( )
P
ξ
,
t
=
PD E t
×
A
A
A
p
L L
cut
g
=
3
(
−
+
1)
L L
−
L L
−
g
g
∑
∑
1
2
∑
[
]
×
1
− ∆ ξ
( ,
I
;
ξ
,
G
) ( ,
∆ ξ
M
;
ξ
,
M
′
)
c
,
k
c
,
c
,
k
c
,
k
c
,
k
m m
n m m
m m
m m
c
=
0
c
=
0
k
∉κ
(
c
)
n
m
m
m
∑
[
]
(
)
(
)
+
1
− ∆ ξ
( ,
I
;
ξ
,
G
) ( ,
∆ ξ
M
;
ξ
,
M
′
)
P
ξ
,
t P
ξ
,
t
c
,
k
c
,
c
,
k
c
,
k
c
,
k
n
n
m n
n
n
n
n
n
k
∉κ
(
c
)
..
n
n
.
.
(4.40)
CaseB
(
ξ
= ξ
m
.and.ξ =
n
).
In.this.case,.one.of.the.schemata.is.ξ,.while.another.is.not..Without.duplica-
tion,.we.only.consider.having.ξ
.and. ξ
∈
S
).or.(ξ ∈
m
n
= ξ
.and.ξ
∈
.
S
m
n
To.have.ξ.destroyed,.that.is,.
,.the.condition.must.be
ξ
′
≠ ξ
m
(
)
(
)
∆ ξ
,
I
;
ξ
′
,
I
∆ ξ
,
M
;
ξ
′
,
M
≠
1
c
,
k
m c
,
k
c
,
k
m
c
,
k
m m
m m
m m
m m
.
(4.41)
(
)
(
)
⇒ ∆ ξ
,
I
;
ξ
,
G
∆ ξ
,
M
;
ξ
,
M
′
≠
1
c
,
k
n
c
,
c
,
k
c
,
k
c
,
k
.
m m
n m m
m m
m m
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