Biomedical Engineering Reference
In-Depth Information
Z
Z´
flip rightmost bit
G
c,k
0 0 1 1
1
1 0
0 0 ... 1
1 0
0 0 ... 1
0 0 1 1
0
(a)
flip rightmost bit
ξ
m
G
c,k
(b)
1 0
0 0 ... 1
0 0 1 1
1
0 0 1 1
0
1 0
0 0 ... 1
G
c,k
(c)
1 0
0 0 ... 1
0 0 1 1 1
ξ
n
ξ
n
0 0 1 1 1
1 0
0 0 ... 1
1 1 0
0 0 ... 1
0 0 1 1
1
V
k
V
k
ξ
i
ξ
i
1 0
0 0 ... 1
0 0 1 1 1
1 0
*
0 0 ... 1
*
0 0 1 1 1
*
U
c,k
=
N
Figure a.5
Visualization.of.the.proof.of.Lemma.4.5.
.
.
Hence,.if.some.actual.bits.are.not.copied.in.the.transposon,.we.have
∑
∑
∆ ξ
(
,
V
;
ξ
,
G
)
−
∆ ξ
(
,
V
;
ξ
,
G
)
=
0.
i
k
m
c k
,
i
k
m
c k
,
ξ
∈
Z
ξ
∈ ′
Z
.
.
m
m
.
b..For.any.copying.position
c
,.which.causes.all.the.actual.bits.of.
ξ
.
to. be. located. inside.
G
c k
,. if.
k
≠.
c
,. that. is,. any. actual. bit. in.
v
. is.
compared.with.the.don't-care.bit.in.
v
,.it.is.possible.to.find.a.cor-
responding.
,
ξ
∈
Z
′
.by.flipping.the.rightmost.of.those.actual.bits,.
m
′
such.that
∆ ξ
(
,
V
;
ξ
,
G
)
= ∆ ξ
(
,
V
;
ξ
,
G
).
.
i
k
m
c k
,
i
k
m
'
c k
,
.
.
. Hence,.if.all.actual.bits.are.copied.in.the.transposon.and.some.of.
those.are.compared.with.don't-care.bits.after.they.are.pasted,
∑
∑
∆ ξ
(
,
V
;
ξ
,
G
)
−
∆ ξ
(
,
V
;
ξ
,
G
)
=
0.
i
k
m
c k
,
i
k
m
c k
,
ξ
∈
Z
ξ
∈ ′
Z
.
.
m
m
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