Information Technology Reference
In-Depth Information
hind this phenomena is that various physical factors like road and center point take
temporally varied roles in the course of local growth. In the first one, road is more
important than center at time T
1
, but less important at T
2
. It means that local growth
occurs along road first and then moves to the center. The third one takes an opposite
effect. If we use
D
to denote the total amount of local growth,
D
l
for the lower part
along road,
D
u
for the upper part along road,
D
c
for the center part and
D
t
for the con-
tinuous development till time
t
. Hereby, D=
D
n
=
D
l
+
D
u
+
D
c
. W
r
and W
c
represent the
weight value of factor ROAD and CENTER respectively. We are able to detect the
following rules:
Convergence
Sequence
Divergence
T
1
T
3
T
2
T
2
T
1
T
2
T
1
T
1
T
2
Fig. 1.
Temporal Heterogeneity
In Convergence: if D
t
< D
l
+ D
u
, W
r
→1, W
c
→0 (at T
1
); if D
t
> D
l
+ D
u
, W
r
→0, W
c
→1
(at T
2
);
In Sequence: if D
t
< D
l
, W
r
→1, W
c
→0 ( at T
1
); if D
t
> D
l
and D
t
< D
l
+ D
c
, W
r
→0,
W
c
→1 (at T
2
); if D
t
> D
l
+ D
c
and D
t
< D, W
r
→1, W
c
→0 (at T
3
);
In Divergence: if D
t
< D
c
, W
r
→0, W
c
→1 (at T
1
); if D
t
> D
c
and D
t
< D, W
r
→1, W
c
→0
(at T
2
).
Here, symbol "→" means "approaching to or close to". The three cases imply that the
temporal complexity could be represented and understood through dynamic weighting.
It means that factor weight is a function of temporal development amount, i.e.
(2)
W
i
(t) = f
i
(D
t
)
In principle, the function
f
i
(D
t
)
should be continuous, which may be a step linear or
more complicated non-linear function. In practice, the function
f
i
(D
t
)
has to be simpli-
fied through
discretization. It implies that the whole period needs to be divided into
few cases
t
1
~t
n
, each with varied weight values.
