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,
r
esear
ch
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w
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tr
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o
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ar
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m
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lated
an
n
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g
[
2
-
4
]
.
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o
p
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b
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L
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d
y
[
9
-
13
]
.
L
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d
y
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la
w
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s
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s
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esear
c
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[
14
-
17
]
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s
p
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th
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H
id
d
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Ma
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Mo
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HM
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[
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HM
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t
h
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b
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[
19
-
25
].
T
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I
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Vo
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8
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
8
:
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9
1
–
2
9
8
292
u
s
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B
au
m
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W
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g
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r
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m
[
1
8
]
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T
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en
w
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p
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ed
to
a
class
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f
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T
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ARCH
M
E
T
H
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v
e
r
g
e
t
o
a
g
lo
b
a
l
m
in
i
m
u
m
,
a
m
ed
iu
m
o
r
r
a
p
i
d
c
o
o
lin
g
to
s
p
ee
d
u
p
th
e
s
e
ar
ch
w
h
en
n
o
im
p
r
o
v
em
en
t
in
s
o
lu
ti
o
n
o
cc
u
r
s
(
Fig
u
r
e
1
).
Fig
u
r
e
1
.
Ma
r
k
o
v
ch
ai
n
f
o
r
s
im
u
lated
an
n
ea
li
n
g
al
g
o
r
ith
m
T
h
e
Hid
d
en
Ma
r
k
o
v
Mo
d
el
ca
n
b
e
d
ef
in
ed
as 5
-
tu
p
le
w
h
er
e:
a.
S=
{
,
,
}
is
s
et
o
f
h
id
d
en
s
tates,
w
h
ic
h
is
r
esp
ec
tiv
e
l
y
:
s
lo
w
,
m
ed
iu
m
a
n
d
r
ap
id
co
o
lin
g
.
b.
: is S
A
w
it
h
a
s
lo
w
L
u
n
d
y
d
ec
r
ea
s
e
la
w
,
t
h
e
co
o
lin
g
f
ac
to
r
is
.
c.
:
is
th
e
s
a
m
e
v
ar
ia
n
t
o
f
s
i
m
u
l
ated
an
n
ea
lin
g
,
w
h
er
e
th
e
co
o
lin
g
la
w
is
f
a
s
ter
th
an
th
e
p
r
ev
io
u
s
o
n
e
d.
: is L
u
n
d
y
s
i
m
u
lated
an
n
ea
li
n
g
v
ar
ia
n
t
w
it
h
w
h
er
e
th
e
r
ap
id
co
o
lin
g
la
w
e.
is
th
e
s
et
o
f
th
e
o
b
s
er
v
a
tio
n
p
er
s
tate.
f.
is
a
tr
an
s
itio
n
p
r
o
b
a
b
ilit
y
m
atr
ix
,
w
h
er
e
is
th
e
p
r
o
b
ab
ilit
y
t
h
at
th
e
s
tate
at
ti
m
e
is
,
is
g
i
v
e
n
w
h
e
n
t
h
e
s
tate
at
ti
m
e
is
g.
is
th
e
i
n
itial p
r
o
b
ab
ilit
y
,
w
h
er
e
is
th
e
p
r
o
b
ab
ilit
y
o
f
b
ein
g
i
n
th
e
s
tate
.
h.
is
th
e
o
b
s
er
v
atio
n
p
r
o
b
ab
ilit
ies,
w
h
er
e
is
th
e
p
r
o
b
a
b
ilit
y
o
f
o
b
s
er
v
in
g
in
s
tate
.
T
h
is
o
b
s
er
v
atio
n
s
m
atr
i
x
o
f
h
id
d
en
m
ar
k
o
v
m
o
d
el
is
esti
m
ate
d
at
ea
r
ly
s
tag
e
b
y
Ma
x
i
m
u
m
L
ik
e
lih
o
o
d
E
s
ti
m
a
tio
n
(
M
L
E
)
.
T
h
e
m
ai
n
p
u
r
p
o
s
e
o
f
th
is
m
o
d
el
is
to
esti
m
ate
s
tate
s
eq
u
e
n
ce
S
th
at
b
est
ex
p
lai
n
s
t
h
e
o
b
s
er
v
atio
n
s
eq
u
en
ce
O.
T
o
g
en
er
at
e
th
e
o
b
s
er
v
ab
le
s
eq
u
en
ce
o
f
HM
M
m
o
d
el.
W
e
u
s
e
a
p
r
o
g
r
ess
i
o
n
r
ate
d
escr
ib
ed
in
E
q
u
atio
n
(
1
)
,
an
d
a
m
ea
s
u
r
e
o
f
th
e
ac
ce
p
ta
n
ce
r
ate
o
f
th
e
p
r
o
p
o
s
ed
s
o
lu
tio
n
d
escr
ib
ed
in
E
q
u
atio
n
(
2
)
.
(
1
)
W
h
er
e
in
E
q
u
atio
n
(
1
)
,
th
e
n
u
m
b
er
o
f
p
r
o
p
o
s
al
is
th
e
n
u
m
b
er
o
f
s
o
l
u
tio
n
g
en
er
ated
b
y
t
h
e
n
ei
g
h
b
o
r
h
o
o
d
f
u
n
ctio
n
i
n
ea
ch
i
ter
atio
n
,
i
n
n
er
an
d
o
u
ter
lo
o
p
ar
e
th
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
iter
atio
n
s
es
tab
lis
h
ed
f
o
r
S
A
to
f
i
n
d
th
e
b
est s
o
l
u
tio
n
.
(
2
)
I
n
E
q
u
atio
n
(
2
)
,
th
e
n
u
m
b
er
o
f
ac
ce
p
ted
s
o
lu
tio
n
s
at
iter
atio
n
t
is
th
e
ac
cu
m
u
lated
n
u
m
b
er
o
f
ac
ce
p
ted
s
o
lu
tio
n
u
n
til
t
h
e
c
u
r
r
en
t
iter
at
io
n
;
an
d
li
k
e
th
e
E
q
.
1
,
n
u
m
b
e
r
o
f
p
r
o
p
o
s
al
is
th
e
n
u
m
b
er
o
f
s
o
lu
tio
n
g
e
n
er
ated
d
u
r
in
g
th
e
s
ea
r
ch
.
T
h
e
ac
ce
p
t
an
ce
r
ate
,
an
d
th
e
p
r
o
g
r
ess
io
n
r
ate
ar
e
th
en
u
s
ed
to
g
e
n
er
a
te
a
s
eq
u
e
n
ce
o
f
class
f
r
o
m
a
s
et
o
f
r
u
les as
f
o
ll
o
w
:
a.
: little d
ec
r
ea
s
e
o
f
ac
ce
p
tan
ce
r
ate.
b.
: n
o
i
m
p
r
o
v
e
m
en
t in
co
s
t
f
u
n
c
tio
n
ev
e
n
i
f
th
e
p
r
o
g
r
ess
io
n
r
at
e
is
less
t
h
a
n
5
0
%.
c.
: a
g
r
ea
t d
ec
r
ea
s
e
o
f
ac
ce
p
tan
c
e
r
ate.
d.
: a
litt
le
in
cr
ea
s
e
o
f
ac
ce
p
ta
n
c
e
r
ate.
e.
: a
h
u
g
e
in
cr
ea
s
e
o
f
ac
ce
p
tan
c
e
r
ate.
Ra
p
id
C
o
o
li
n
g
M
e
d
iu
m
Co
o
li
n
g
S
lo
w
Co
o
li
n
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
S
elf
-
Tu
n
ed
S
imu
la
ted
A
n
n
ea
lin
g
A
lg
o
r
ith
m
u
s
in
g
Hid
d
en
Ma
r
ko
v
Mo
d
el
(
Mo
h
a
med
La
la
o
u
i
)
293
Du
r
in
g
t
h
e
r
u
n
a
s
et
o
f
o
b
s
er
v
atio
n
is
g
en
er
ated
as
f
o
llo
w
:
A
l
g
o
r
ith
m
1
: G
e
n
er
ate_
Ob
s
er
v
atio
n
Input:
ρ,
Rule_1(
,
Rule_2(
, Rule_3(
,
b b
Rule_4(
, Rule_5(
Output
: O Current Observation
If
Rule_1(
==TRUE
then
O
1
End
If
Rule_2(
==TRUE
then
O
2
End
If
Rule_3(
==TRUE
then
O
3
End
If
Rule_4(
==TRU
E
then
O
4
End
If
Rule_5(
==TRUE
then
O
5
End
Return
O
T
h
e
p
u
r
p
o
s
e
o
f
th
i
s
m
o
d
el
is
t
o
esti
m
a
te
s
tate
S t
h
at
b
es
t e
x
p
lain
s
t
h
e
o
b
s
er
v
a
tio
n
s
eq
u
e
n
c
e
O.
Giv
e
n
th
e
o
b
s
er
v
atio
n
s
eq
u
e
n
ce
an
d
a
m
o
d
el
.
Firstl
y
,
w
e
e
s
ti
m
ate
th
e
tr
an
s
itio
n
a
n
d
e
m
is
s
io
n
p
r
o
b
ab
ilit
ies
f
r
o
m
t
h
e
f
ir
s
t
s
eq
u
en
ce
o
f
o
b
s
er
v
a
tio
n
u
s
in
g
a
s
u
p
er
v
is
ed
tr
ai
n
in
g
.
I
n
w
h
ic
h
,
w
e
co
u
n
t
f
r
eq
u
en
c
ies o
f
tr
a
n
s
m
i
s
s
io
n
s
a
n
d
e
m
i
s
s
io
n
s
o
f
t
h
e
m
o
d
el:
A
l
g
o
r
ith
m
2
: M
L
E
Input:
Output:
A
=(
,
B
=
)
For
i = 1 to T
-
1
do
End
For
i = 1 to T
do
End
For
i = 1 to 3
do
=
∑
and
=
∑
End
For
to
3
do
For
j=1
to
3
do
End
For
t=1
to
do
End
End
Return
T
h
en
w
e
u
s
e
th
e
Viter
b
i to
s
el
ec
t th
e
co
r
r
esp
o
n
d
in
g
s
tate
s
e
q
u
en
ce
th
a
t b
est e
x
p
lai
n
s
o
b
s
er
v
atio
n
s
,
s
ec
o
n
d
l
y
,
t
h
e
B
au
m
W
elc
h
ad
j
u
s
ts
t
h
e
m
o
d
el
p
ar
a
m
eter
s
to
m
ax
i
m
ize
|
i.e
.
,
th
e
p
r
o
b
ab
ilit
y
o
f
t
h
e
o
b
s
er
v
atio
n
s
eq
u
en
ce
g
i
v
en
t
h
e
m
o
d
el.
2
.
1
.
Vit
er
bi
A
lg
o
rit
h
m
Af
ter
m
o
d
el
p
ar
a
m
eter
s
d
ef
i
n
itio
n
,
th
e
Viter
b
i
alg
o
r
it
h
m
is
u
s
ed
to
b
u
ild
HM
M
cla
s
s
i
f
icatio
n
p
r
o
ce
s
s
.
T
h
is
alg
o
r
ith
m
is
u
s
e
d
to
co
m
p
u
te
t
h
e
m
o
s
t p
r
o
b
ab
l
e
p
ath
as
w
ell
as it
s
p
r
o
b
ab
ilit
y
.
A
l
g
o
r
ith
m
3
: V
iter
b
i
Input:
S
, A = (
,
B =
)
,
Output:
the most probable sequence of states
For i =
do
and
End
{Initialization}
For
t = 2 to T
do
For
j=1 to 3
do
and
End
End
;
For t
to 1 do
End
Return
2
.
2
.
B
a
u
m
Welc
h
A
lg
o
rit
h
m
T
h
e
B
au
m
–
W
elch
a
lg
o
r
it
h
m
i
s
u
s
ed
to
ad
j
u
s
t
th
e
p
ar
a
m
eter
s
o
f
HM
M.
T
h
is
tr
ai
n
i
n
g
s
tep
i
s
b
ased
o
n
Fo
r
w
ar
d
-
B
ac
k
w
ar
d
alg
o
r
ith
m
.
2
.
2
.
1
.
F
o
rwa
rd
A
lg
o
rit
h
m
T
h
e
f
ir
s
t
alg
o
r
ith
m
u
s
ed
b
y
t
h
e
B
au
m
-
W
elc
h
alg
o
r
ith
m
is
th
e
Fo
r
w
ar
d
alg
o
r
ith
m
.
T
h
is
alg
o
r
ith
m
r
etu
r
n
s
th
e
f
o
r
w
ar
d
v
ar
iab
le
d
ef
in
ed
as
t
h
e
p
r
o
b
ab
ilit
y
o
f
t
h
e
p
ar
tial
o
b
s
er
v
atio
n
s
eq
u
e
n
ce
u
n
t
il
ti
m
e
t,
w
it
h
s
tate
at
ti
m
e
t,
(
t)
=
(
|
)
,
a
n
d
w
e
d
ef
in
e
|
as
th
e
p
r
o
b
a
b
ilit
y
o
f
th
e
o
b
s
er
v
atio
n
s
eq
u
e
n
ce
g
iv
e
n
t
h
e
m
o
d
el
.
A
l
g
o
r
ith
m
4
: Fo
r
w
ar
d
Input
:
S
=
O
=
,
A
=
(
)
B
=
,
Output:
,
|
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
8
:
2
9
1
–
2
9
8
294
For
to
do
End
For
to
T
-
1
do
For
to
do
(
∑
)
End
End
|
∑
Return
|
2
.
2
.
2
.
B
a
ck
w
a
rd
A
lg
o
rit
h
m
T
h
e
s
ec
o
n
d
al
g
o
r
ith
m
u
s
ed
b
y
B
au
m
-
W
elc
h
B
ac
k
w
ar
d
.
T
h
is
alg
o
r
it
h
m
ca
lc
u
late
s
t
h
e
b
ac
k
w
ar
d
v
ar
iab
le
d
ef
in
ed
as t
h
e
p
r
o
b
a
b
ilit
y
o
f
t
h
e
p
ar
tial o
b
s
er
v
atio
n
s
eq
u
e
n
ce
af
ter
ti
m
e
,
g
i
v
en
s
t
ate
:
|
A
l
g
o
r
ith
m
5
: B
ac
k
w
ar
d
Input
: S=
O=
A=
(
)
B=
,
Output
:
:the probability of the partial observation sequence
For
to
do
End
For
to
do
For
to
do
∑
End
End
Return
T
h
e
B
au
m
-
W
elc
h
is
th
e
n
u
s
e
d
to
r
e
-
esti
m
ate
t
h
e
p
ar
a
m
ete
r
s
o
f
th
e
m
o
d
el
,
w
h
ich
m
a
x
i
m
izes
th
e
p
r
o
b
a
b
ilit
y
o
f
t
h
e
o
b
s
er
v
atio
n
s
eq
u
en
ce
.
T
h
is
al
g
o
r
ith
m
i
s
d
escr
ib
ed
as f
o
llo
w
:
A
l
g
o
r
ith
m
6
: B
au
m
-
W
elc
h
Input
:
S=
O=
A=
(
)
B=
,
,
|
Output:
̅
̅
̅
̅
Repeat
|
F
o
rward
;
β
Backward(
O, A, B,
)
For
t=1
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T
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3
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do
|
End
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End
End
For
k=1
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T
do
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i=1
to
3
do
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j=1
to
3
do
̅
;
̅
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∑
;
̅
∑
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End
End
End
While
(
|
increase)
Return
̅
̅
2
.
3
.
T
he
H
y
bridi
za
t
io
n
o
f
H
M
M
a
nd
SA
I
n
th
e
f
o
llo
w
i
n
g
w
e
w
ill
i
m
p
l
e
m
en
t
a
v
ar
ian
t
s
i
m
u
la
ted
an
n
ea
lin
g
b
ased
o
n
h
id
d
en
Ma
r
k
o
v
m
o
d
els.
T
h
e
in
ter
est
b
eh
i
n
d
h
y
b
r
id
i
za
tio
n
th
e
s
i
m
u
lated
an
n
ea
l
in
g
w
it
h
th
e
H
MM
is
to
i
m
p
r
o
v
e
th
e
S
A’
s
p
er
f
o
r
m
a
n
ce
.
A
l
g
o
r
ith
m
7
: H
MM
-
S
A
al
g
o
r
i
th
m
Data
: The objective function
Initialization
O:Empty
observation
sequence,
initial temperature,
final
temperature,
:starting point, cmp
,
:progression rate,
:acceptance rate,
n
0:temperature stage
Repeat
Repeat
u is a Random vector from the uniform distribution over
If
then
else
Generate a pseudo
-
random number
∈
If
then
End
End
Until
equmbrium is approached sufficiently closely at
Update(
,
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
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N:
2
0
8
8
-
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A
S
elf
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n
ed
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ted
A
n
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ith
m
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d
en
Ma
r
ko
v
Mo
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el
(
Mo
h
a
med
La
la
o
u
i
)
295
Generate
-
Observation
If
then
;
MLE
;
state
Viterbi
; cmp
cmp
;
else
;
Baum
-
Welch(O,A,B) ; state
Viterbi(O,A,B)
End
Cooling_law
Cooling_law
Until
indicating that the system is frozen
3.
E
XP
E
R
I
M
E
NT
T
h
e
ex
p
er
i
m
e
n
t
w
as
d
esi
g
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ed
to
m
ea
s
u
r
e
th
e
e
f
f
ec
t
s
o
f
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y
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izatio
n
o
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HM
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n
d
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n
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to
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o
w
h
o
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r
ap
p
r
o
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h
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n
i
m
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r
o
v
e
th
e
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o
l
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tio
n
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u
alit
y
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w
e
h
a
v
e
ch
o
s
en
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v
e
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en
c
h
m
ar
k
f
u
n
c
tio
n
s
s
e
lecte
d
f
r
o
m
th
e
liter
at
u
r
e
(
T
ab
le
1
)
.
T
ab
le
1
.
B
en
ch
m
ar
k
f
u
n
ctio
n
s
N
a
me
F
u
n
c
t
i
o
n
F
o
r
mu
l
a
S
i
x
-
H
u
mp
C
a
me
l
(
)
L
e
v
y
N
°
1
3
Q
u
a
d
r
i
c
∑
(
∑
)
T
a
b
l
e
t
∑
S
p
h
e
r
e
∑
T
h
e
p
r
o
p
o
s
ed
h
y
b
r
id
izatio
n
o
f
S
A
al
g
o
r
ith
m
a
n
d
HM
M
w
as
co
d
ed
in
Scilab
p
r
o
g
r
a
m
m
i
n
g
lan
g
u
a
g
e
an
d
ex
p
er
i
m
e
n
ts
w
er
e
co
n
d
u
cted
o
n
a
P
C
w
it
h
an
I
n
te
l
C
o
r
e
i7
-
5
5
0
0
U
2
.
4
0
GHz
(
4
C
P
Us)
an
d
8
GB
o
f
R
A
M.
T
h
e
h
y
b
r
id
izatio
n
o
f
S
A
a
n
d
HM
M
h
a
v
e
b
ee
n
te
s
ted
u
s
i
n
g
t
h
e
b
en
c
h
m
ar
k
f
u
n
ctio
n
s
p
r
ese
n
ted
ab
o
v
e.
E
ac
h
f
u
n
ctio
n
w
a
s
te
s
ted
o
v
e
r
3
0
tr
ials
.
W
e
eli
m
i
n
ated
t
h
e
ef
f
ec
ts
o
f
o
th
er
f
ac
to
r
s
w
h
ic
h
p
la
y
a
n
i
m
p
o
r
tan
t
r
o
le
in
th
e
p
er
f
o
r
m
a
n
ce
o
f
al
g
o
r
ith
m
,
b
y
ch
o
o
s
i
n
g
th
e
s
a
m
e
s
tar
tin
g
p
o
in
ts
f
o
r
all
m
eth
o
d
s
(
in
ea
c
h
r
u
n
)
a
n
d
th
eir
lo
ca
tio
n
w
a
s
ch
o
s
en
to
b
e
f
ar
f
r
o
m
b
a
s
in
s
o
f
at
tr
ac
tio
n
o
f
g
lo
b
al
m
in
i
m
a.
Als
o
,
w
e
h
a
v
e
ch
o
s
e
n
t
h
e
s
a
m
e
in
itial
ac
ce
p
tan
ce
p
r
o
b
ab
ilit
y
an
d
an
id
en
tical
len
g
t
h
o
f
th
e
in
n
er
an
d
o
u
ter
lo
o
p
s
.
T
h
e
in
it
ial
te
m
p
er
atu
r
e,
,
h
av
e
b
ee
n
ca
lc
u
lated
f
r
o
m
m
e
an
en
er
g
y
r
is
e
s
d
u
r
in
g
t
h
e
in
it
ializatio
n
.
B
ef
o
r
e
th
e
s
tar
t o
f
t
h
e
S
A
,
t
h
e
m
ea
n
v
alu
e
o
f
co
s
t
r
is
e
s
is
esti
m
ate
d
b
y
a
co
n
s
tan
t
n
u
m
b
er
o
f
m
o
v
es
eq
u
al
to
1
0
0
.
T
h
en
,
in
iti
al
te
m
p
er
atu
r
e
is
ca
lcu
la
ted
u
s
i
n
g
t
h
e
f
o
llo
w
i
n
g
f
o
r
m
u
la
[
26
]
,
w
h
er
e
is
th
e
i
n
it
ial
a
v
er
ag
e
p
r
o
b
ab
ilit
y
o
f
ac
ce
p
tan
ce
an
d
is
ta
k
en
eq
u
a
l to
0
.
9
5
.
T
h
e
len
g
t
h
o
f
o
b
s
er
v
ed
s
eq
u
en
ce
w
as c
h
o
s
e
n
eq
u
al
t
o
1
0
.
3
.
1
.
Nu
m
er
ica
l
R
es
ults
T
h
e
co
m
p
u
tatio
n
al
r
es
u
lt
s
a
n
d
s
tati
s
ti
ca
l
an
al
y
s
e
s
ar
e
s
u
m
m
ar
ized
in
T
ab
le
2
.
I
t
p
r
o
v
id
es
th
e
d
etail
s
o
f
th
e
r
es
u
lts
f
o
r
th
e
test
f
u
n
ctio
n
s
.
T
h
e
o
v
er
all
b
est
s
o
lu
ti
o
n
o
f
th
e
to
tal
3
0
r
ep
licatio
n
s
is
s
h
o
w
n
i
n
b
o
ld
.
HM
M
-
S
A
p
r
o
v
id
es
t
h
e
b
est
s
o
lu
tio
n
f
o
r
th
e
test
f
u
n
ct
io
n
s
,
.
I
n
g
en
er
al,
HM
M
-
S
A
alg
o
r
ith
m
o
v
er
co
m
es t
h
e
class
ical
v
ar
ia
n
ts
in
all
b
e
n
ch
m
ar
k
f
u
n
c
tio
n
s
.
T
ab
le
2
.
R
esu
lts
co
m
p
ar
i
s
o
n
s
b
et
w
ee
n
HM
M
-
S
A
a
n
d
th
e
cla
s
s
ical
S
A
F
u
n
c
t
i
o
n
s
H
M
M
-
S
A
C
S
A
b
e
s
t
-
1
.
0
3
2
E
+
0
0
-
1
.
0
3
1
E
+
0
0
m
e
a
n
-
1
.
0
3
2
E
+
0
0
-
1
.
0
3
1
E
+
0
0
b
e
s
t
3
.
7
6
8
E
-
0
6
1
.
3
7
1
E
-
0
5
m
e
a
n
7
.
8
6
4
E
-
0
2
6
.
9
4
4
E
-
0
2
b
e
s
t
2
.
0
1
3
E
-
0
7
6
.
6
7
1
E
-
0
6
m
e
a
n
6
.
1
8
1
E
-
0
6
4
.
0
0
0
E
-
0
3
b
e
s
t
9
.
9
0
3
E
-
0
7
7
.
1
1
2
E
-
0
6
m
e
a
n
6
.
6
4
3
E
-
0
5
1
.
4
3
2
E
-
0
3
b
e
s
t
4
.
3
1
1
E
-
0
9
8
.
7
4
5
E
-
0
6
m
e
a
n
4
.
6
6
2
E
-
0
6
1
.
1
5
5
E
-
0
3
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
8
:
2
9
1
–
2
9
8
296
3
.
2
.
Co
m
pa
riso
n
of
C
o
nv
er
g
ence
P
er
f
o
r
m
a
nce
T
o
o
b
tain
f
u
r
th
er
in
s
i
g
h
t
s
i
n
to
th
e
co
n
v
er
g
en
ce
b
eh
a
v
io
r
o
u
r
ap
p
r
o
ac
h
,
HM
M
-
S
A
m
eth
o
d
w
as
co
m
p
ar
ed
to
t
h
e
clas
s
ical
S
A
.
E
x
p
er
i
m
e
n
ts
w
er
e
d
esi
g
n
ed
t
o
m
ea
s
u
r
e
t
h
e
e
f
f
ec
t
s
o
f
t
h
e
h
y
b
r
id
izatio
n
o
f
S
A
an
d
HM
M
p
r
ese
n
ted
i
n
t
h
e
p
r
ev
io
u
s
s
ec
t
io
n
.
I
t
w
a
s
n
o
ticed
th
at
t
h
e
H
MM
-
S
A
ca
n
co
n
v
er
g
e
r
ap
id
l
y
to
g
lo
b
al
m
i
n
i
m
u
m
.
T
h
e
ti
m
e
g
ai
n
ed
i
n
ea
r
l
y
s
tag
e
ca
n
b
e
u
s
ed
to
co
n
v
er
g
e
to
a
b
etter
s
o
lu
tio
n
.
T
h
is
b
eh
a
v
io
r
i
s
d
ep
icted
in
F
ig
u
r
e
2
.
Fig
u
r
e
2
.
C
o
m
p
ar
is
o
n
o
f
H
M
M
-
S
A
a
n
d
th
e
cla
s
s
ical
S
A
3
.
3
.
Sta
t
is
t
ica
l
A
na
ly
s
is
W
e
p
er
f
o
r
m
ed
a
Ma
n
n
–
W
h
it
n
e
y
–
W
ilco
x
o
n
(
MW
W
)
test
[
27
]
to
d
eter
m
i
n
e
w
h
et
h
er
th
e
alg
o
r
it
h
m
r
ea
ch
a
s
ig
n
i
f
ica
n
t
p
er
f
o
r
m
a
n
ce
.
W
e
ch
o
o
s
e
th
is
s
tat
is
tical
test
b
ec
au
s
e
w
e
h
a
v
e
t
w
o
h
e
u
r
is
tics
to
co
m
p
ar
e.
T
h
e
Ma
n
n
–
W
h
it
n
e
y
–
W
ilco
x
o
n
test
co
m
p
ar
es
w
h
et
h
er
th
er
e
is
an
y
d
if
f
er
en
ce
f
r
o
m
t
w
o
al
g
o
r
ith
m
s
.
T
h
e
n
u
ll
h
y
p
o
t
h
esi
s
s
ay
s
th
at
th
e
t
w
o
alg
o
r
ith
m
s
h
av
e
t
h
e
s
am
e
m
ea
n
s
(
)
an
d
th
e
alter
n
ati
v
e
h
y
p
o
t
h
esi
s
s
a
y
s
t
h
at
t
w
o
al
g
o
r
ith
m
s
h
av
e
a
d
if
f
er
en
t
m
e
an
s
(
)
.
A
cc
o
r
d
in
g
to
tab
le
3
,
f
o
r
f
u
n
ctio
n
s
,
th
e
p
-
v
alu
e
is
les
s
th
a
n
t
h
e
s
ig
n
i
f
ica
n
ce
le
v
el
o
f
.
W
e
ca
n
r
ej
ec
t
th
e
n
u
ll
h
y
p
o
t
h
esi
s
,
s
o
w
e
ca
n
co
n
cl
u
d
e
th
at
o
u
r
h
y
b
r
id
izatio
n
o
f
H
MM
an
d
SA
o
u
tp
er
f
o
r
m
s
t
h
e
class
ical
i
n
s
ta
n
ce
o
f
S
A
.
T
ab
le
3
.
S
tatis
tical
an
al
y
s
i
s
f
o
r
b
en
ch
m
ar
k
f
u
n
ctio
n
s
4.
CO
NCLU
SI
O
N
I
n
t
h
is
s
t
u
d
y
,
w
e
p
r
o
p
o
s
ed
a
s
elf
-
tu
n
i
n
g
ca
p
ab
ilit
y
o
f
s
i
m
u
la
ted
an
n
ea
li
n
g
b
ased
o
n
Hid
d
en
Ma
r
k
o
v
Mo
d
el.
T
o
test
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ld
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e
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r
s
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ed
.
RE
F
E
R
E
NC
E
S
[1
]
S
.
Kirk
p
a
tri
k
,
"
Op
ti
m
iza
ti
o
n
b
y
sim
u
late
d
a
n
n
e
a
li
n
g
,
"
S
c
ien
c
e
,
v
o
l.
2
2
0
,
No
.
4
5
9
8
,
6
7
1
–
6
8
0
,
1
9
8
3
.
[2
]
E.
A
a
rts,
F
.
d
e
Bo
n
t
,
E.
Ha
b
e
r
s,
a
n
d
P
.
v
a
n
L
a
a
rh
o
v
e
n
,
"
P
a
ra
ll
e
l
Im
p
le
m
e
n
tatio
n
s
o
f
th
e
S
tat
isti
c
a
l
Co
o
li
n
g
A
l
g
o
rit
h
m
,
"
In
teg
ra
ti
o
n
,
th
e
VL
S
I
J
o
u
rn
a
l
,
Vo
l.
4
,
2
0
9
-
2
3
8
,
1
9
8
6
.
[3
]
A
.
C
a
so
tt
o
,
F
.
Ro
m
e
o
a
n
d
A
.
S
a
n
g
io
v
a
n
n
i
-
Vin
c
e
n
telli
,
"
A
P
a
ra
ll
e
l
S
im
u
la
te
d
An
n
e
a
li
n
g
Al
g
o
rit
h
m
fo
r
th
e
Pl
a
c
e
me
n
t
o
f
M
a
c
ro
-
Ce
ll
s,
"
P
r
o
c
e
e
d
in
g
s
o
f
th
e
IEE
E
In
ter
n
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
C
o
m
p
u
ter
-
A
id
e
d
De
sig
n
,
3
0
-
3
3
,
1
9
8
6
.
[4
]
E.
A
a
rts,
a
n
d
J.
Ko
rst,
"
S
im
u
late
d
A
n
n
e
a
li
n
g
a
n
d
Bo
l
tzm
a
n
n
M
a
c
h
in
e
s:
A
S
to
c
h
a
stic
A
p
p
ro
a
c
h
to
Co
m
b
in
a
to
ria
l
Op
ti
m
iza
ti
o
n
a
n
d
Ne
u
ra
l
Co
m
p
u
t
in
g
,
"
J
o
h
n
W
il
e
y
&
S
o
n
s
,
1
9
8
9
.
[5
]
A
.
Kr.
Ya
d
a
v
a
n
d
a
l.
,
“
D
e
sig
n
Op
ti
m
iza
ti
o
n
o
f
Hi
g
h
-
F
re
q
u
e
n
c
y
P
o
w
e
r
T
r
a
n
sf
o
r
m
e
r
b
y
Ge
n
e
ti
c
A
lg
o
rit
h
m
a
n
d
S
im
u
late
d
A
n
n
e
a
li
n
g
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
En
g
in
e
e
rin
g
,
V
o
l.
1
,
No
.
2
,
p
p
.
1
0
2
~
1
0
9
,
2
0
1
1
[6
]
P
.
Ilam
a
th
i,
V
.
S
e
ll
a
d
u
ra
i,
K.
Ba
la
m
u
ru
g
a
n
,
“
P
re
d
ictiv
e
M
o
d
e
ll
i
n
g
a
n
d
Op
ti
m
iza
ti
o
n
o
f
P
o
w
e
r
P
la
n
t
Nitro
g
e
n
Ox
id
e
s E
m
is
sio
n
”
,
I
AE
S
I
n
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
Arti
f
icia
l
I
n
telli
g
e
n
c
e
(
IJ
-
AI)
,
V
o
l.
1
,
N
o
.
1
,
p
p
.
1
1
~
1
8
,
,
2
0
1
2
.
[7
]
Q.
Ch
e
n
a
n
d
a
l.
,
“
S
im
u
late
d
A
n
n
e
a
li
n
g
A
lg
o
rit
h
m
f
o
r
F
rictio
n
P
a
ra
m
e
ter
s
Id
e
n
ti
f
ica
ti
o
n
”
,
T
EL
KOM
NIKA
(
T
e
lec
o
mm
u
n
ica
ti
o
n
Co
mp
u
ti
n
g
El
e
c
tro
n
ics
a
n
d
C
o
n
tro
l
)
,
V
o
l
.
1
1
,
No
.
1
,
p
p
.
2
4
5
~
2
5
2
,
2
0
1
3
.
[8
]
M
.
L
u
n
d
y
a
n
d
A
.
M
e
e
s,
"
Co
n
v
e
r
g
e
n
c
e
o
f
a
n
A
n
n
e
a
li
n
g
A
l
g
o
rit
h
m
,
"
M
a
th
e
ma
ti
c
a
l
Pro
g
ra
mm
in
g
,
V
o
l
3
4
,
p
p
1
1
1
-
1
2
4
,
1
9
8
6
.
[9
]
W
.
A
.
Kh
a
n
a
a
n
d
D.
R.
H
a
y
h
u
rst,
"
Co
m
p
u
ter
-
a
id
e
d
p
a
rt
p
ro
g
ra
m
se
g
m
e
n
tatio
n
a
n
d
re
c
o
n
stru
c
t
io
n
f
o
r
m
in
i
m
iza
ti
o
n
o
f
m
a
c
h
in
e
to
o
l
re
sid
e
n
c
e
ti
m
e
"
,
In
t.
J
.
Co
mp
u
ter
In
teg
ra
ted
M
a
n
u
fa
c
t
u
rin
g
,
Vo
l.
4
,
No
.
5
,
3
0
0
-
3
1
4
,
1
9
9
1
.
[1
0
]
A
.
Af
i
f
i
a
n
d
D.
R.
Ha
y
h
u
rst,
"
Co
m
p
u
ter
-
a
id
e
d
p
a
rt
p
r
o
g
ra
m
o
p
ti
m
iza
ti
o
n
o
f
m
u
lt
i
-
c
o
m
p
o
n
e
n
t
p
a
ll
e
t
re
sid
e
n
c
e
ti
m
e
in
a
m
a
c
h
in
in
g
c
e
n
tre
f
o
r
c
a
n
n
e
d
c
y
c
les
a
n
d
c
u
tt
e
r
to
o
l
c
o
m
p
e
n
sa
ti
o
n
"
,
I
n
t.
J
.
Co
m
p
u
ter
I
n
teg
ra
ted
M
a
n
u
f
a
c
tu
ri
n
g
,
V
o
l
.
8
,
No
.
1
,
1
-
2
0
,
1
9
9
5
.
[1
1
]
A
.
Af
i
f
i,
D.R.
Ha
y
h
u
rst
a
n
d
W
.
A.
Kh
a
n
,
"
No
n
-
p
r
o
d
u
c
ti
v
e
to
o
l
p
a
t
h
o
p
t
im
isa
ti
o
n
o
f
m
u
lt
i
-
to
o
l
p
a
rt
p
ro
g
ra
m
m
e
s,
"
In
t
J
A
d
v
M
a
n
u
f
T
e
c
h
n
o
l
,
5
5
:1
0
0
7
–
1
0
2
3
,
2
0
1
1
.
[1
2
]
R.
Ba
i,
J.
Blaz
e
w
i
c
z
,
E.
K.
Bu
rk
e
,
G
.
K
e
n
d
a
ll
a
n
d
B.
M
c
Co
ll
u
m
,
"
A
si
m
u
late
d
a
n
n
e
a
li
n
g
h
y
p
e
r
-
h
e
u
risti
c
m
e
th
o
d
o
lo
g
y
f
o
r
f
lex
ib
le d
e
c
isio
n
su
p
p
o
rt,
"
4
OR
-
Q J Op
e
r
Re
s,
1
0
:4
3
–
6
6
,
2
0
1
2
.
[1
3
]
S
.
Ya
n
g
a
n
d
J.
M
a
rc
io
M
a
c
h
a
d
o
,
"
A
S
e
l
f
-
L
e
a
rn
in
g
S
im
u
late
d
A
n
n
e
a
li
n
g
A
l
g
o
rit
h
m
f
o
r
G
lo
b
a
l
Op
ti
m
iza
ti
o
n
s
o
f
El
e
c
tro
m
a
g
n
e
ti
c
De
v
ic
e
s,
"
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
M
a
g
n
e
ti
c
s
,
V
o
l
.
3
6
,
N°
.
4
,
2
0
0
0
.
[1
4
]
S
.
S
u
n
,
F
.
Z
h
u
g
e
a
n
d
S
.
A
.
Na
p
e
l,
"
Lea
rn
in
g
e
n
h
a
n
c
e
d
sim
u
late
d
a
n
n
e
a
li
n
g
,
"
Ap
p
li
e
d
I
n
telli
g
e
n
c
e
,
Vo
l.
2
8
,
Iss
u
e
1
,
p
p
8
3
-
9
9
,
2
0
0
8
.
[1
5
]
S
.
J.
Je
o
n
g
a
n
d
K
-
S
.
Kim
,
"
T
h
e
e
ff
icie
n
t
se
a
r
c
h
m
e
th
o
d
o
f
sim
u
late
d
a
n
n
e
a
li
n
g
u
si
n
g
f
u
z
z
y
lo
g
ic
c
o
n
tro
ll
e
r,
"
Exp
e
rt
S
y
ste
ms
wit
h
Ap
p
li
c
a
ti
o
n
s
3
6
,
7
0
0
9
9
-
7
1
0
3
,
2
0
0
9
.
[1
6
]
R.
Be
ll
io
a
n
d
S
.
Ce
sc
h
ia,
"
F
e
a
t
u
re
-
b
a
se
d
t
u
n
i
n
g
o
f
sim
u
late
d
a
n
n
e
a
li
n
g
a
p
p
li
e
d
t
o
t
h
e
c
u
rricu
lu
m
-
b
a
s
e
d
c
o
u
rse
ti
m
e
tab
li
n
g
p
ro
b
lem
,
"
J
o
u
rn
a
l
o
f
Co
mp
u
ter
s &
Op
e
ra
ti
o
n
s R
e
se
a
rc
h
,
6
5
,
8
3
–
9
2
,
2
0
1
6
.
[1
7
]
L
.
Ra
b
in
e
r,
"
A
tu
t
o
ria
l
o
n
h
id
d
e
n
ma
rk
o
v
mo
d
e
ls
a
n
d
se
lec
ted
a
p
p
li
c
a
ti
o
n
s
in
sp
e
e
c
h
re
c
o
g
n
it
io
n
,
"
P
r
o
c
e
e
d
in
g
s
o
f
th
e
IEE
E
,
7
7
(2
),
2
5
7
–
2
8
6
,
1
9
8
9
.
[1
8
]
O.
A
o
u
n
,
M
.
S
a
r
h
a
n
i
a
n
d
A
.
El
A
f
i
a
,
"
Hid
d
e
n
m
a
rk
o
v
m
o
d
e
l
c
las
sif
i
e
r
f
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(
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l
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t
o
f
V
a
lu
e
A
n
a
l
y
sis T
o
o
ls.
Evaluation Warning : The document was created with Spire.PDF for Python.