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
Based.on.the.deinition.given.in . Equation.(4.54) ,. a mn
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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