Biomedical Engineering Reference
In-Depth Information
Deinition4.6
The.
distributionmatrix
.for.schema.
ξ
.under.the.copy-and-paste.operation.
ξ ∈
S
is.defined.as
( )
( )
( )
i
i
i
a
a
a
11
12
1
M
( )
i
( )
i
( )
i
a
a
a
( )
i
.
(4.55)
A
=
21
22
2
M
( )
( )
( )
i
i
i
a
a
a
M
M
MM
1
2
.
where.
M
.is.the.size.of.
S
ξ
.
Remark4.5
ξ ∈
ξ
,.
A
i
)
(
For.each.schema.
.only.depends.on.the.JG.length.
L
g
.
S
Remark4.6
[
]
( )
i
∈
0, 1
.
We.deine.a.state.vector.at.time.
t
.as
P
(
ξ
ξ
, )
t
1
P
(
, )
t
( )
=
2
Y t
.
(4.56)
P
(
ξ
, )
t
M
.
then.(4.53).can.be.rewritten.as
(
)
i
P
(
ξ
,
t
+
1)
=
Y t A Y t
′
( )
( )
=
y t
(
+
1)
.for.
i
=
1,.2,.….,.
M
,.
(4.57)
i
i
.
where.
Y
( )
.denotes.the.transpose.of.
Y
(
t
),.and.
y t
i
( )
.is.the.
i
th.element.of.
Y
(
t
)..
′
Based.on.the.deinition.of.
P
,.one.has
(
ξ
, )
t
i
M
M
∑
∑
.
(4.58)
y t
( )
=
P
(
ξ
, ) 1
t
=
∀
t
i
i
.
i
=
1
i
=
1
Equation. (4.57)
.
is. regarded. as. the. state. transition. equation,. revealing. the.
dynamics.of.the.copy-and-paste.transposition.
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