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m
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th
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AI
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o
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ls
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e
n
e
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te
sta
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su
lt
s
with
v
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ry
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n
g
d
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g
re
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s
o
f
a
c
c
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ra
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y
.
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we
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r,
d
e
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s
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ts
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s
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ig
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th
e
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e
e
d
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sy
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e
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e
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th
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t
AI
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su
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ra
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ti
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K
ey
w
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r
d
s
:
AI
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ass
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ted
r
esear
ch
m
eth
o
d
o
l
o
g
y
Gen
er
ativ
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AI
Gr
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ca
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L
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is
Statis
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ep
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rticle
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n
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r th
e
CC B
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SA
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se
.
C
o
r
r
e
s
p
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nd
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A
uth
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r
:
Vale
r
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Ok
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lich
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Kaz
ar
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I
n
s
titu
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o
f
Dig
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r
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m
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Ar
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1.
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D
UCT
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O
N
Desp
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win
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s
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f
g
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r
ativ
e
ar
tific
ial
in
tellig
en
ce
(
AI
)
in
g
r
ad
u
ate
r
esear
ch
[
1
]
,
[
2
]
,
th
er
e
is
a
lack
o
f
em
p
ir
ically
test
ab
le
cr
iter
ia
f
o
r
ev
alu
atin
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th
e
m
eth
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d
o
lo
g
ical
ad
m
is
s
ib
ilit
y
o
f
AI
-
g
en
e
r
ated
s
tatis
t
ical
r
esu
lt
s
.
So
,
a
m
e
th
o
d
o
lo
g
ically
s
ig
n
if
ican
t
q
u
esti
o
n
ar
is
es:
d
o
s
u
ch
to
o
ls
en
s
u
r
e
s
tatis
tica
l
co
r
r
ec
tn
ess
wh
en
p
er
f
o
r
m
in
g
s
tan
d
ar
d
q
u
a
n
titativ
e
an
aly
s
is
p
r
o
ce
d
u
r
es?
Sev
er
al
s
tu
d
ies
[
3
]
–
[
5
]
d
em
o
n
s
tr
ate
th
e
s
u
s
tain
ed
in
ter
est
o
f
r
esear
ch
er
s
in
g
r
ad
u
ate
-
lev
el
r
esear
c
h
an
d
s
tu
d
e
n
t
p
r
o
jects.
Ho
wev
er
,
th
e
p
r
o
b
lem
o
f
its
m
eth
o
d
o
lo
g
ical
a
d
m
is
s
ib
ilit
y
with
in
th
e
f
r
a
m
ewo
r
k
o
f
class
ical
s
tatis
tica
l
p
r
o
ce
d
u
r
es
r
em
ain
s
in
s
u
f
f
icien
tly
em
p
ir
ically
s
tu
d
ied
.
L
in
ea
r
r
e
g
r
ess
io
n
,
wid
ely
u
s
ed
in
g
r
ad
u
ate
-
lev
el
r
esear
c
h
in
th
e
f
ield
s
o
f
ed
u
ca
tio
n
,
e
co
n
o
m
ics,
en
g
in
ee
r
in
g
an
d
s
o
cial
s
cien
ce
s
,
r
ep
r
esen
ts
a
m
o
r
e
c
o
m
p
lex
u
s
e
ca
s
e
o
f
AI
to
o
ls
.
Ho
wev
er
,
p
r
e
v
io
u
s
wo
r
k
s
[
1
]
,
[
2
]
d
ea
lt
with
th
e
p
r
o
ce
s
s
in
g
o
f
s
ca
led
d
ata
a
n
d
d
id
n
o
t
to
u
c
h
u
p
o
n
t
h
e
co
n
s
tr
u
ctio
n
o
f
r
e
g
r
ess
io
n
m
o
d
els.
Mo
s
t
ex
is
tin
g
p
u
b
lic
atio
n
s
f
o
cu
s
o
n
th
e
p
e
d
ag
o
g
ical
asp
ec
ts
o
f
AI
a
p
p
licatio
n
[
6
]
–
[
1
6
]
o
r
o
n
th
e
au
to
m
atio
n
o
f
ed
u
ca
tio
n
al
task
s
[
1
7
]
,
[
1
8
]
.
At
th
e
s
am
e
tim
e,
th
e
is
s
u
e
o
f
q
u
an
titativ
e
co
m
p
ar
ab
ilit
y
o
f
r
esu
lts
an
d
r
ep
r
o
d
u
cib
ilit
y
o
f
th
e
an
aly
tical
p
r
o
ce
d
u
r
e
wh
e
n
u
s
in
g
AI
r
em
ain
s
in
s
u
f
f
icien
tly
v
er
if
ied
em
p
ir
ically
[
1
9
]
.
I
n
co
r
r
ec
t
r
eg
r
ess
io
n
co
e
f
f
icien
ts
ca
n
af
f
ec
t
ev
alu
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r
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ts
,
th
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ass
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m
en
ts
,
p
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co
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cl
u
s
io
n
s
,
an
d
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tu
d
en
t r
esear
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q
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ality
.
T
h
er
e
ar
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p
r
ac
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n
o
s
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d
ie
s
b
ased
o
n
p
r
e
-
s
p
ec
if
ied
q
u
an
t
itativ
e
th
r
esh
o
ld
s
o
f
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2875
ac
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p
tab
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s
tatis
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d
ev
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T
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to
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in
p
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f
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r
m
in
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lin
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with
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lev
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R
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m
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−
Do
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r
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co
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icien
ts
(
A,
B
)
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R
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in
th
e
p
r
e
-
estab
lis
h
ed
th
r
esh
o
ld
o
f
ac
ce
p
tab
le
s
tatis
t
ical
d
ev
iatio
n
r
elativ
e
to
th
e
Mic
r
o
s
o
f
t
E
x
ce
l
alg
o
r
ith
m
ic
b
e
n
ch
m
a
r
k
ca
lcu
l
atio
n
(
T
r
en
d
lin
e
OL
S)?
(
R
Q1
)
T
h
e
f
o
llo
win
g
ac
ce
p
tab
le
th
r
e
s
h
o
ld
v
alu
es
ar
e
ad
o
p
ted
:
d
ev
iatio
n
o
f
th
e
r
eg
r
ess
io
n
co
ef
f
i
cien
t
less
th
an
±
1
%
f
r
o
m
th
e
r
ef
e
r
en
ce
v
alu
e;
d
ev
iatio
n
o
f
R
²
less
th
a
n
±
0
.
0
1
;
d
e
v
iatio
n
o
f
th
e
p
r
ed
i
cted
v
alu
e
less
th
an
±
5
%.
E
x
ce
ed
in
g
th
e
th
r
esh
o
ld
v
alu
es
is
co
n
s
id
er
ed
a
v
io
latio
n
o
f
th
e
p
r
in
cip
le
o
f
m
eth
o
d
o
lo
g
ical
eq
u
iv
alen
ce
.
−
I
s
th
e
s
tr
u
ctu
r
al
r
ep
r
o
d
u
ci
b
ilit
y
o
f
th
e
o
r
d
in
a
r
y
least
s
q
u
ar
es
(
OL
S)
p
r
o
ce
d
u
r
e
m
ain
tain
ed
wh
en
u
s
in
g
d
if
f
er
en
t A
I
to
o
ls
with
a
f
ix
e
d
p
r
o
m
p
t a
n
d
id
e
n
tical
in
p
u
t
d
at
aset?
(
R
Q2
)
T
h
e
r
e
p
r
o
d
u
cib
ilit
y
o
f
a
c
o
m
p
u
tatio
n
al
p
r
o
ce
d
u
r
e
is
d
ef
i
n
ed
as:
co
r
r
ec
t
d
escr
ip
tio
n
o
f
th
e
lin
ea
r
r
eg
r
ess
io
n
Y
=
A
×
X
+
B
;
ca
lcu
latio
n
an
d
o
u
t
p
u
t
o
f
th
e
co
ef
f
icien
ts
A
an
d
B
;
ca
lcu
latio
n
an
d
o
u
tp
u
t
o
f
R
²;
ca
lcu
latio
n
an
d
o
u
tp
u
t
o
f
t
h
e
p
r
ed
icted
r
esu
lt
f
o
r
2
0
3
0
.
Vio
l
atio
n
o
f
ea
ch
elem
e
n
t
is
co
n
s
id
er
ed
a
v
io
latio
n
o
f
r
ep
r
o
d
u
cib
ilit
y
.
−
Un
d
er
wh
at
m
et
h
o
d
o
lo
g
ical
c
o
n
d
itio
n
s
ca
n
th
e
u
s
e
o
f
AI
b
e
co
n
s
id
er
ed
ac
ce
p
tab
le
with
o
u
t
v
io
latin
g
th
e
r
eq
u
ir
em
e
n
ts
o
f
s
tatis
tical
co
r
r
ec
tn
ess
an
d
ac
ad
em
ic
r
esp
o
n
s
ib
ilit
y
?
(
R
Q3
)
Acc
ep
tab
ilit
y
is
co
n
s
id
er
ed
to
b
e
ac
h
iev
ed
wh
e
n
th
e
f
o
llo
w
in
g
co
n
d
itio
n
s
ar
e
s
im
u
ltan
eo
u
s
ly
m
et:
co
m
p
lian
ce
o
f
th
e
r
esu
lts
with
th
e
th
r
esh
o
l
d
v
alu
es;
tr
an
s
p
a
r
en
cy
o
f
th
e
s
tr
u
ctu
r
e
o
f
th
e
r
e
q
u
est;
ch
ec
k
o
f
th
e
r
esu
lts
b
y
th
e
r
esear
ch
er
;
m
ain
ten
an
ce
o
f
t
h
e
r
esear
ch
er
’
s
r
esp
o
n
s
ib
ilit
y
f
o
r
in
ter
p
r
etatio
n
.
T
h
e
m
eth
o
d
o
lo
g
y
b
ases
o
n
th
e
AI
-
ass
is
ted
r
esear
ch
m
eth
o
d
o
lo
g
y
ap
p
r
o
ac
h
[
1
9
]
–
[
2
2
]
.
W
ith
in
th
is
ap
p
r
o
ac
h
,
AI
to
o
ls
ar
e
v
iewe
d
s
tr
ictly
as
m
ec
h
an
is
m
s
th
at
s
u
p
p
o
r
t
th
e
ex
ec
u
tio
n
o
f
estab
lis
h
ed
an
aly
tical
p
r
o
ce
d
u
r
es,
with
o
u
t
ch
an
g
in
g
th
eir
m
et
h
o
d
o
lo
g
ical
o
r
e
p
is
tem
o
lo
g
ical
f
o
u
n
d
atio
n
s
.
AI
p
r
o
m
p
ts
[
1
]
,
[
2
]
ar
e
co
n
ce
p
tu
alize
d
as
ad
d
itio
n
al
co
m
p
u
tatio
n
al
to
o
ls
f
o
r
ca
lcu
latin
g
s
tan
d
ar
d
s
tatis
tical
co
e
f
f
icien
ts
[
2
3
]
,
[
2
4
]
.
T
h
eir
u
s
e
is
ac
ce
p
ted
o
n
ly
t
o
th
e
ex
ten
t
t
h
at
th
e
class
ical
r
eq
u
ir
em
e
n
ts
o
f
lin
ea
r
r
eg
r
ess
io
n
an
aly
s
is
ar
e
p
r
eser
v
ed
.
T
h
e
r
esear
ch
f
r
am
ew
o
r
k
is
b
a
s
ed
o
n
th
r
ee
in
ter
r
elate
d
p
r
in
c
ip
les:
i)
t
h
e
p
r
in
cip
le
o
f
m
eth
o
d
o
lo
g
ical
eq
u
iv
alen
ce
(
r
esu
lts
o
b
tain
ed
u
s
in
g
AI
s
h
o
u
ld
r
em
ain
q
u
an
ti
tativ
ely
co
m
p
ar
ab
le
with
r
ef
er
en
ce
ca
lcu
latio
n
s
)
;
ii
)
th
e
p
r
in
cip
le
o
f
p
r
o
ce
d
u
r
al
r
ep
r
o
d
u
cib
ilit
y
(
th
e
u
s
e
o
f
A
I
to
o
ls
s
h
o
u
ld
p
r
eser
v
e
th
e
s
tr
u
ctu
r
e
an
d
lo
g
ical
co
n
s
is
ten
cy
o
f
th
e
OL
S
p
r
o
c
ed
u
r
e)
;
an
d
iii
)
th
e
p
r
in
ci
p
le
o
f
lim
ited
ap
p
licab
ilit
y
(
AI
to
o
ls
ca
n
ass
is
t
in
ca
lcu
latio
n
s
,
b
u
t
d
o
n
o
t
r
ep
la
ce
th
e
r
esear
ch
er
an
d
th
eir
in
ter
p
r
etiv
e
r
esp
o
n
s
ib
ilit
y
)
.
T
h
is
co
n
ce
p
t
d
o
es
n
o
t
aim
to
r
ev
is
e
ed
u
ca
tio
n
al
m
et
h
o
d
o
lo
g
y
[
2
5
]
,
[
2
6
]
o
r
s
tatis
ti
ca
l
th
eo
r
y
[
2
3
]
,
[
2
4
]
.
I
ts
p
u
r
p
o
s
e
is
to
d
ef
in
e
th
e
ad
m
is
s
ib
ilit
y
an
d
lim
itatio
n
s
o
f
u
s
in
g
AI
in
r
esear
ch
[
2
7
]
u
n
d
er
clea
r
ly
d
ef
in
e
d
m
eth
o
d
o
lo
g
ical
co
n
d
itio
n
s
.
First o
f
all,
at
th
e
g
r
ad
u
ate
-
lev
el
[
1
9
]
,
[
2
2
]
.
2.
M
E
T
H
O
D
2
.
1
.
Resea
rc
h
des
ig
n
a
nd
a
na
ly
t
ica
l pro
ce
du
re
T
h
e
an
aly
s
is
f
o
cu
s
ed
o
n
v
e
r
if
y
in
g
wh
et
h
er
th
e
AI
t
o
o
l
s
r
ep
r
o
d
u
ce
th
e
s
tan
d
ar
d
al
g
o
r
ith
m
ic
im
p
lem
en
tatio
n
o
f
th
e
OL
S
m
eth
o
d
an
d
wh
eth
e
r
th
e
o
b
tain
e
d
r
esu
lts
r
em
ain
with
in
th
e
ac
ce
p
tab
le
s
tatis
tica
l
d
ev
iatio
n
r
elativ
e
t
o
th
e
b
en
c
h
m
ar
k
ca
lc
u
latio
n
.
T
h
e
b
u
ilt
-
in
lin
ea
r
tr
en
d
lin
e
f
u
n
ctio
n
o
f
Mic
r
o
s
o
f
t
E
x
ce
l
(
I
n
s
er
t
→
C
h
ar
t
→
Ad
d
T
r
e
n
d
lin
e
→
Dis
p
lay
E
q
u
atio
n
an
d
R
²)
,
e
x
ec
u
ted
in
W
in
d
o
ws
1
0
,
was
u
s
ed
as
th
e
b
en
ch
m
ar
k
alg
o
r
ith
m
ic
ca
lcu
latio
n
.
T
h
is
to
o
l
im
p
lem
e
n
ts
th
e
s
tan
d
ar
d
OL
S
alg
o
r
ith
m
f
o
r
esti
m
atin
g
th
e
co
ef
f
icien
ts
o
f
a
lin
ea
r
m
o
d
el
an
d
ca
lcu
latin
g
t
h
e
co
ef
f
icien
t o
f
d
eter
m
in
atio
n
(
R
²)
.
T
h
e
em
p
ir
ical
b
asis
co
n
s
is
ted
o
f
f
iv
e
tim
e
s
er
ies
[
1
]
,
d
if
f
er
i
n
g
in
th
e
len
g
th
o
f
o
b
s
er
v
atio
n
s
(
f
r
o
m
7
to
2
1
u
n
its
)
an
d
th
e
d
y
n
am
ics
o
f
th
e
in
d
icato
r
s
.
T
h
ese
s
er
ies
ar
e
tak
en
f
r
o
m
th
e
au
th
o
r
'
s
r
esear
ch
p
r
ac
tice,
t
h
e
f
ir
s
t
o
f
wh
ich
was
p
u
b
lis
h
ed
i
n
th
e
p
ap
er
[
7
]
.
T
h
e
r
an
g
e
o
f
v
alu
es
o
f
th
e
d
ep
en
d
e
n
t
v
ar
ia
b
les
v
ar
ied
in
s
ca
le
b
etwe
en
th
e
s
er
ies.
T
h
is
m
ad
e
it
p
o
s
s
ib
le
to
test
th
e
r
o
b
u
s
tn
ess
o
f
th
e
r
ep
r
o
d
u
cib
ilit
y
o
f
OL
S
at
d
if
f
er
en
t
o
r
d
er
s
o
f
m
ag
n
itu
d
e.
E
x
tr
em
e
o
u
tlier
s
a
n
d
s
tr
u
ctu
r
al
b
r
ea
k
s
wer
e
n
o
t
d
etec
ted
.
Fo
r
ea
ch
d
ata
s
et,
an
id
en
tical
s
tr
u
ctu
r
e
o
f
th
e
an
aly
tical
p
r
o
ce
d
u
r
e
an
d
a
f
ix
ed
q
u
er
y
f
o
r
m
u
latio
n
wer
e
u
s
ed
wh
en
ac
ce
s
s
in
g
AI
to
o
ls
.
Mo
r
eo
v
er
,
th
e
b
asic
ass
u
m
p
t
io
n
s
o
f
class
ical
s
in
g
le
-
f
ac
to
r
lin
ea
r
r
eg
r
ess
io
n
(
lin
ea
r
it
y
o
f
th
e
r
elatio
n
s
h
ip
,
in
d
ep
en
d
en
ce
o
f
o
b
s
er
v
atio
n
s
,
an
d
s
tab
ilit
y
o
f
th
e
er
r
o
r
v
ar
ian
ce
)
wer
e
o
b
s
er
v
ed
.
I
n
-
d
ep
th
an
aly
s
is
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
15
,
No
.
4
,
Au
g
u
s
t
20
26
:
2
8
7
4
-
2
8
8
2
2876
r
esid
u
als
an
d
test
in
g
f
o
r
h
eter
o
s
ce
d
asti
city
wer
e
n
o
t
p
er
f
o
r
m
ed
.
At
th
e
s
am
e
tim
e,
p
ar
am
etr
ic
r
o
b
u
s
tn
ess
was
test
ed
th
r
o
u
g
h
a
co
m
p
ar
is
o
n
o
f
co
ef
f
icien
ts
an
d
p
r
e
d
icted
v
a
lu
es with
in
th
e
s
tatis
tical
to
ler
an
ce
f
r
am
ewo
r
k
.
T
h
e
an
aly
tical
p
r
o
ce
s
s
f
o
r
p
r
o
ce
s
s
in
g
ea
ch
d
ata
s
er
ies
in
cl
u
d
ed
:
f
o
r
m
aliza
tio
n
o
f
a
lin
ea
r
m
o
d
el
o
f
th
e
f
o
r
m
Y
=
A
×
X
+
B
;
esti
m
atio
n
o
f
c
o
ef
f
icien
ts
A
an
d
B
;
ca
lcu
latio
n
o
f
th
e
co
ef
f
icien
t
o
f
d
eter
m
in
atio
n
(
R
²)
,
t
-
s
tatis
tic,
an
d
p
-
v
al
u
e.
T
h
e
co
m
p
ar
ab
ilit
y
o
f
th
e
r
es
u
lts
was
ass
e
s
s
ed
with
in
a
p
r
e
-
d
ef
in
ed
s
y
s
tem
o
f
s
tatis
t
ical
to
ler
an
ce
s
(
s
tatis
t
ic
al
to
ler
an
ce
f
r
am
ewo
r
k
)
.
T
h
u
s
,
th
e
s
tu
d
y
was
d
esig
n
ed
as
a
test
ab
le
m
o
d
el:
if
th
e
r
esu
lts
f
ell
o
u
ts
id
e
th
e
estab
lis
h
ed
lim
its
,
th
e
ass
u
m
p
tio
n
o
f
s
tatis
tical
co
m
p
ar
ab
ilit
y
wo
u
ld
b
e
co
n
s
id
er
ed
r
ef
u
ted
.
T
h
is
en
s
u
r
es
th
e
f
alsi
f
iab
ilit
y
o
f
th
e
m
eth
o
d
o
lo
g
ical
s
tatem
en
t
an
d
r
ed
u
ce
s
th
e
r
is
k
o
f
u
n
cr
itical
in
ter
p
r
etatio
n
o
f
n
u
m
er
ical
s
im
ilar
ity
as
ev
id
en
ce
o
f
co
r
r
ec
tn
ess
[
2
7
]
,
[
2
8
]
.
R
esp
o
n
s
ib
ilit
y
f
o
r
th
e
in
ter
p
r
etatio
n
o
f
th
e
r
esu
lts
an
d
co
n
tr
o
l
o
v
e
r
th
e
c
o
r
r
ec
tn
ess
o
f
th
e
ca
lc
u
latio
n
s
r
em
ain
e
d
with
th
e
r
esear
ch
er
at
all
s
tag
es o
f
th
e
an
aly
s
is
.
2
.
2
.
AI
t
o
o
ls
a
nd
co
m
pa
riso
n str
a
t
eg
y
T
h
e
au
t
h
o
r
s
u
s
ed
f
o
u
r
g
en
e
r
ativ
e
m
o
d
els:
C
h
atGPT
4
.
0
,
Dee
p
Seek
v
3
.
2
(
Dee
p
Seek
Ma
th
-
B
ase
v
er
s
io
n
7
B
)
,
Gem
in
i
3
Pro
,
an
d
Gr
o
k
4
.
1
.
All
to
o
ls
wer
e
p
u
b
licly
av
ailab
le,
allo
win
g
s
tu
d
en
ts
to
ap
p
ly
AI
to
o
ls
in
th
eir
g
r
ad
u
ate
-
le
v
el
r
esear
ch
.
T
o
m
in
im
ize
v
ar
ia
b
ilit
y
,
a
f
ix
ed
q
u
e
r
y
s
tr
u
ctu
r
e
was
u
s
ed
:
u
s
e
an
id
en
tical
s
o
u
r
ce
d
ataset;
in
s
tr
u
ct
th
e
m
o
d
el
to
p
er
f
o
r
m
OL
S
l
in
ea
r
r
e
g
r
ess
io
n
f
o
r
Y
=
A
×
X
+
B
;
o
u
tp
u
t
A,
B
,
R
²,
t
-
s
tatis
tic,
an
d
p
-
v
alu
e;
a
n
d
in
s
tr
u
ct
th
e
m
o
d
el
n
o
t
to
ap
p
ly
ad
d
itio
n
al
d
ata
tr
an
s
f
o
r
m
a
tio
n
s
.
T
h
e
p
r
o
m
p
t
d
id
n
o
t
c
o
n
tain
an
y
in
s
tr
u
cti
o
n
s
o
n
th
e
in
ter
p
r
etatio
n
o
f
th
e
r
esu
lts
an
d
d
i
d
n
o
t
i
n
clu
d
e
an
y
e
v
alu
ativ
e
s
tatem
en
ts
.
T
h
e
f
o
llo
win
g
p
a
r
am
eter
s
wer
e
u
s
ed
f
o
r
co
m
p
ar
is
o
n
:
A
an
d
B
co
ef
f
icien
ts
;
th
e
co
e
f
f
icien
t
o
f
d
eter
m
in
atio
n
(
R
²)
;
th
e
p
r
esen
ce
an
d
ac
cu
r
ac
y
o
f
th
e
lev
el
o
f
s
tatis
tical
s
ig
n
if
ican
ce
(
p
-
v
alu
e
)
;
an
d
th
e
p
r
ed
icted
v
al
u
e
f
o
r
2
0
3
0
(
m
an
u
ally
ca
lcu
lated
f
o
r
th
e
s
elec
te
d
f
iv
e
-
y
ea
r
h
o
r
izo
n
to
2
0
3
0
)
.
T
h
e
b
u
ilt
-
in
t
r
en
d
lin
e
f
u
n
ctio
n
in
Mic
r
o
s
o
f
t
E
x
ce
l
ca
lcu
lates
A,
B
,
an
d
R
²
co
ef
f
icien
ts
,
b
u
t
d
o
es
n
o
t
ca
lcu
late
p
-
v
alu
es.
T
h
er
e
f
o
r
e
,
p
-
v
alu
es
wer
e
u
s
ed
s
o
lely
as
an
ad
d
itio
n
al
in
d
icato
r
o
f
th
e
p
r
o
c
ed
u
r
al
co
m
p
leten
ess
o
f
th
e
AI
to
o
ls
.
T
h
ey
wer
e
n
o
t
u
s
ed
as
an
el
em
en
t
o
f
d
ir
ec
t
q
u
an
titativ
e
c
o
m
p
ar
is
o
n
with
th
e
b
en
ch
m
ar
k
.
C
o
m
p
a
r
is
o
n
s
wer
e
co
n
d
u
cte
d
with
in
th
e
s
tatis
tical
d
ev
iatio
n
th
r
esh
o
l
d
s
d
escr
ib
ed
b
ef
o
r
e
.
T
h
e
au
th
o
r
s
d
id
n
o
t
aim
to
id
en
tif
y
a
“
b
est
”
AI
to
o
l
an
d
d
id
n
o
t
in
ter
p
r
et
m
in
im
al
n
u
m
er
ical
d
if
f
er
en
ce
s
as
a
b
asis
f
o
r
r
an
k
in
g
m
o
d
els.
T
h
e
c
o
m
p
ar
is
o
n
s
tr
ateg
y
f
o
cu
s
ed
o
n
v
er
i
f
y
in
g
th
e
co
n
d
itio
n
s
o
f
m
eth
o
d
o
l
o
g
ical
eq
u
iv
alen
ce
a
n
d
p
r
o
ce
d
u
r
al
r
e
p
r
o
d
u
cib
ilit
y
wh
en
u
s
in
g
th
e
AI
to
o
ls
.
2
.
3
.
St
a
t
is
t
ica
l
t
o
lera
nce
f
ra
m
ewo
rk
T
o
en
s
u
r
e
th
e
v
er
if
iab
ilit
y
o
f
t
h
e
r
esu
lts
an
d
p
r
ev
e
n
t a
r
b
itra
r
y
in
ter
p
r
etatio
n
o
f
n
u
m
er
ical
s
im
ilar
ities
,
a
s
y
s
tem
o
f
s
tatis
t
ical
to
ler
an
ce
s
was in
tr
o
d
u
ce
d
in
th
e
s
tu
d
y
.
Acc
ep
tab
le
d
ev
iatio
n
lim
its
ar
e
s
et
as
[
2
3
]
,
[
2
4
]
:
f
o
r
th
e
r
eg
r
ess
io
n
co
ef
f
icien
ts
(
A,
B
)
–
less
th
an
±
1
%
f
r
o
m
th
e
r
ef
e
r
en
ce
v
alu
e;
f
o
r
th
e
d
eter
m
in
atio
n
co
ef
f
icien
t (
R
²)
–
less
th
an
±
0
.
0
1
;
f
o
r
th
e
p
r
ed
icted
v
al
u
e
–
l
ess
th
an
±
5
%.
T
h
e
s
y
s
tem
o
f
s
tatis
tical
to
ler
an
ce
s
s
er
v
es
as
a
cr
iter
io
n
f
o
r
ass
ess
in
g
th
e
m
eth
o
d
o
lo
g
ical
eq
u
iv
alen
ce
o
f
th
e
r
esu
lts
o
b
tain
ed
u
s
in
g
AI
to
o
ls
r
elativ
e
to
th
e
r
e
f
er
en
ce
ca
lcu
l
atio
n
(
W
in
d
o
ws 1
0
).
T
h
e
th
r
esh
o
ld
v
alu
es
wer
e
s
elec
ted
to
b
alan
ce
co
m
p
u
tatio
n
al
s
en
s
itiv
ity
an
d
in
ter
p
r
etativ
e
s
tab
ilit
y
o
f
th
e
m
o
d
el.
Min
o
r
d
is
cr
ep
an
cies
in
th
e
r
esu
lts
m
ay
ar
is
e
d
u
e
to
r
o
u
n
d
in
g
an
d
ca
l
cu
latio
n
p
r
ec
is
io
n
.
Ho
wev
er
,
th
e
y
s
h
o
u
ld
n
o
t
al
ter
th
e
tr
e
n
d
s
lo
p
e
,
th
e
co
ef
f
icien
t
o
f
d
eter
m
in
atio
n
,
o
r
t
h
e
f
o
r
ec
ast
r
esu
lt.
Dev
iatio
n
s
ex
ce
ed
in
g
th
e
th
r
esh
o
ld
v
alu
es
ar
e
c
o
n
s
id
er
ed
a
v
i
o
latio
n
o
f
t
h
e
p
r
in
cip
le
o
f
m
eth
o
d
o
lo
g
ical
eq
u
iv
alen
ce
.
E
x
ce
e
d
in
g
th
e
t
h
r
esh
o
ld
v
alu
es
co
n
s
titu
tes
g
r
o
u
n
d
s
f
o
r
r
ejec
tin
g
th
e
ass
u
m
p
tio
n
o
f
s
tatis
tical
co
m
p
ar
ab
ilit
y
.
T
h
u
s
,
th
e
t
h
r
esh
o
ld
s
y
s
tem
s
er
v
es
to
v
e
r
if
y
t
h
e
ass
u
m
p
tio
n
th
at
m
et
h
o
d
o
lo
g
ical
eq
u
iv
alen
ce
is
co
n
s
id
er
ed
c
o
n
f
ir
m
e
d
o
n
ly
if
t
h
e
q
u
a
n
titativ
ely
s
p
ec
if
ied
th
r
esh
o
ld
v
alu
es a
r
e
m
et.
2
.
4
.
Repro
du
cibili
t
y
,
ha
llu
cina
t
io
n r
is
k
a
nd
m
et
ho
do
lo
g
ica
l
co
ntr
o
l
R
ep
r
o
d
u
cib
ilit
y
o
f
t
h
e
p
r
o
ce
d
u
r
e
is
d
ef
in
ed
as
th
e
s
im
u
ltan
eo
u
s
f
u
lf
illme
n
t
o
f
th
e
f
o
llo
win
g
co
n
d
itio
n
s
:
c
o
r
r
ec
tn
ess
o
f
th
e
m
o
d
el
Y
=
A
×
X
+
B
;
n
o
c
h
an
g
es
t
o
th
e
in
p
u
t
d
ata;
ca
lcu
latio
n
o
f
th
e
co
ef
f
icien
ts
A
an
d
B
u
s
in
g
s
tan
d
ar
d
OL
S
lo
g
ic;
ca
lcu
latio
n
o
f
th
e
co
e
f
f
icien
t
o
f
d
eter
m
in
atio
n
(
R
²)
;
an
d
co
r
r
ec
tn
ess
o
f
th
e
f
o
r
ec
ast
f
o
r
2
0
3
0
.
N
u
m
er
ical
d
is
cr
ep
an
cie
s
with
in
th
e
lim
its
s
et
w
ith
in
t
h
e
th
r
esh
o
ld
v
alu
e
s
ar
e
n
o
t in
ter
p
r
ete
d
as a
v
io
latio
n
o
f
r
e
p
r
o
d
u
cib
ilit
y
.
T
h
is
is
cr
u
cial
to
co
n
s
id
er
th
e
r
is
k
o
f
s
to
ch
asti
c
v
ar
iab
ilit
y
in
g
en
er
ativ
e
m
o
d
els.
T
h
e
ar
c
h
itectu
r
e
o
f
lar
g
e
lan
g
u
ag
e
m
o
d
els
is
p
r
o
b
ab
ilis
tic
in
n
atu
r
e.
T
h
is
m
ea
n
s
th
at
ev
en
with
th
e
s
am
e
q
u
er
y
,
m
in
o
r
v
ar
iatio
n
s
in
th
e
n
u
m
er
ical
r
esu
lts
ar
e
p
o
s
s
ib
le.
T
h
e
s
tu
d
y
u
s
ed
a
f
ix
e
d
q
u
er
y
s
tr
u
ctu
r
e,
an
d
ca
lcu
latio
n
s
we
r
e
p
er
f
o
r
m
ed
with
m
in
im
al
v
a
r
iab
ilit
y
in
th
e
g
en
er
atio
n
p
ar
a
m
eter
s
.
I
f
s
ig
n
if
ican
t
d
ev
iatio
n
s
wer
e
id
en
tifie
d
,
th
e
r
esu
lts
wer
e
r
e
-
ch
ec
k
ed
.
I
n
th
e
co
n
tex
t
o
f
t
h
is
s
tu
d
y
,
AI
h
allu
cin
atio
n
is
d
ef
in
e
d
as
th
e
g
en
er
atio
n
o
f
s
tatis
tically
p
lau
s
ib
le
b
u
t
co
m
p
u
tatio
n
ally
in
c
o
r
r
ec
t
r
esu
lts
d
u
e
to
th
e
p
r
o
b
a
b
ilis
tic
n
atu
r
e
o
f
t
h
e
la
n
g
u
a
g
e
m
o
d
el.
T
o
m
in
im
ize
th
is
r
is
k
,
th
e
f
o
llo
win
g
m
eth
o
d
o
lo
g
ical
co
n
tr
o
l
m
ea
s
u
r
es
wer
e
ap
p
lied
:
u
s
e
o
f
a
r
ef
er
en
ce
alg
o
r
it
h
m
ic
ca
lcu
latio
n
f
o
r
co
m
p
ar
is
o
n
;
in
tr
o
d
u
ctio
n
o
f
th
r
esh
o
ld
s
f
o
r
ac
ce
p
tab
le
d
ev
iatio
n
s
;
f
ix
e
d
q
u
er
y
s
tr
u
ctu
r
e;
av
o
i
d
an
ce
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
E
va
lu
a
tin
g
th
e
meth
o
d
o
lo
g
ic
a
l a
d
mis
s
ib
ilit
y
o
f g
en
era
tive
A
I
to
o
ls
fo
r
lin
ea
r
…
(
V
a
lery
Oku
lich
-
K
a
z
a
r
in
)
2877
in
ter
p
r
etiv
e
i
n
s
tr
u
ctio
n
s
in
th
e
task
f
o
r
m
u
latio
n
;
m
an
d
ato
r
y
v
er
i
f
icatio
n
o
f
r
esu
lts
b
y
t
h
e
r
esear
ch
e
r
.
T
h
is
s
tu
d
y
d
o
es
n
o
t
ass
u
m
e
ep
is
te
m
ic
eq
u
iv
ale
n
ce
b
etwe
en
g
en
er
ativ
e
m
o
d
els
an
d
s
p
ec
ialized
s
tatis
tical
s
o
f
twar
e.
AI
to
o
ls
ar
e
co
n
s
id
er
e
d
p
u
r
ely
as p
r
o
b
ab
ilis
tic
s
y
s
tem
s
r
eq
u
ir
in
g
ex
ter
n
al
alg
o
r
ith
m
ic
v
er
if
icatio
n
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
Resul
t
s
re
la
t
ed
t
o
RQ
1
T
h
e
r
esu
lts
o
f
ca
lc
u
latin
g
t
h
e
lin
ea
r
r
e
g
r
ess
io
n
co
e
f
f
icien
ts
t
o
an
s
wer
R
Q1
ar
e
p
r
esen
ted
i
n
T
ab
le
1
.
At
f
ir
s
t
g
lan
ce
,
th
e
d
ata
in
T
ab
le
1
d
e
m
o
n
s
tr
ate
th
e
n
u
m
e
r
ical
co
m
p
ar
a
b
ilit
y
o
f
t
h
e
r
es
u
lts
o
b
tain
ed
u
s
in
g
v
ar
io
u
s
AI
to
o
ls
with
th
e
b
e
n
ch
m
ar
k
alg
o
r
ith
m
ic
ca
lcu
latio
n
in
Mic
r
o
s
o
f
t
E
x
ce
l
(
T
r
e
n
d
li
n
e
OL
S).
Ho
wev
er
,
a
p
r
o
p
e
r
ass
ess
m
en
t
o
f
co
m
p
ar
ab
ilit
y
r
eq
u
ir
es
a
q
u
an
titativ
e
an
aly
s
is
o
f
d
ev
iatio
n
s
r
elativ
e
to
estab
lis
h
ed
s
tatis
t
ical
d
ev
iatio
n
th
r
esh
o
ld
s
.
T
h
e
co
r
r
esp
o
n
d
in
g
ca
lc
u
latio
n
s
ar
e
p
r
esen
ted
i
n
T
ab
le
2
.
T
ab
le
1
.
L
in
ea
r
r
eg
r
ess
io
n
an
a
ly
s
is
f
o
r
ex
am
p
le
-
1
u
s
in
g
v
ar
i
o
u
s
AI
to
o
ls
I
n
d
i
c
a
t
o
r
C
h
a
t
G
P
T
4
.
0
D
e
e
p
S
e
e
k
v
3
.
2
G
e
mi
n
i
3
p
r
o
G
r
o
k
4
.
1
M
i
c
r
o
s
o
f
t
Ex
c
e
l
R
e
g
r
e
ssi
o
n
c
o
e
f
f
i
c
i
e
n
t
А
1
0
3
0
8
.
0
0
1
0
3
0
8
.
0
0
1
0
3
0
8
.
0
0
9
5
4
1
.
8
0
1
0
3
0
8
.
0
0
R
e
g
r
e
ssi
o
n
c
o
e
f
f
i
c
i
e
n
t
B
1
0
7
0
6
9
.
0
0
9
6
7
6
1
.
0
0
9
6
7
6
0
.
9
0
1
0
4
7
2
2
.
7
0
9
6
7
6
1
.
0
0
D
e
t
e
r
m
i
n
a
t
i
o
n
c
o
e
f
f
i
c
i
e
n
t
R
2
0
.
9
7
6
8
0
.
9
7
6
5
0
.
9
8
8
9
0
.
9
7
3
4
0
.
9
7
6
8
S
i
g
n
i
f
i
c
a
n
c
e
l
e
v
e
l
p
0
.
0
0
0
0
0
.
0
0
0
0
0
.
0
0
0
0
0
.
0
0
0
2
-
F
o
r
e
c
a
st
f
o
r
2
0
3
0
2
5
1
3
8
1
.
0
0
2
4
1
0
7
3
.
0
0
2
4
1
0
7
3
.
2
0
2
2
8
7
9
6
.
4
0
2
4
1
0
7
3
.
0
0
T
ab
le
2
s
h
o
ws
th
at
Dee
p
Seek
v
3
.
2
f
u
lly
co
m
p
lies
with
th
e
estab
lis
h
ed
th
r
esh
o
ld
s
.
All
in
d
icato
r
s
ar
e
with
in
th
e
ac
ce
p
tab
le
s
tatis
tical
d
ev
iatio
n
,
co
n
f
ir
m
in
g
m
eth
o
d
o
l
o
g
ical
eq
u
iv
alen
ce
f
o
r
th
is
ex
am
p
le.
C
h
atGPT
4
.
0
d
em
o
n
s
tr
ates a
n
ex
ce
s
s
o
f
th
e
ac
ce
p
tab
le
d
ev
iatio
n
f
o
r
th
e
ab
s
o
lu
te
ter
m
(
B
)
b
y
m
o
r
e
th
an
1
0
%.
Ho
wev
er
,
th
e
p
r
e
d
icted
v
al
u
e
r
em
ain
s
with
in
±
5
%,
in
d
icatin
g
a
p
ar
tial
v
io
latio
n
o
f
p
ar
a
m
e
tr
ic
s
tab
ilit
y
wh
ile
m
ain
tain
in
g
p
r
ac
tical
co
m
p
ar
ab
ilit
y
o
f
th
e
f
o
r
ec
ast.
Gem
in
i
3
Pro
ex
ce
e
d
s
th
e
ac
ce
p
tab
l
e
th
r
esh
o
ld
f
o
r
R
²
(
Δ
=0
.
0
1
2
1
>
0
.
0
1
)
.
Desp
ite
m
ain
tain
in
g
h
ig
h
ex
p
lan
ato
r
y
p
o
w
er
o
f
th
e
m
o
d
el,
th
e
f
o
r
m
al
eq
u
iv
alen
ce
cr
iter
io
n
is
n
o
t
m
et.
Gr
o
k
4
.
1
d
em
o
n
s
tr
ates
d
ev
iatio
n
s
in
s
ev
er
al
p
ar
am
eter
s
,
in
clu
d
in
g
co
ef
f
icien
ts
an
d
p
r
ed
icte
d
v
alu
e,
wh
ich
d
o
es
n
o
t
allo
w
u
s
to
co
n
f
ir
m
m
eth
o
d
o
lo
g
ical
e
q
u
iv
alen
ce
f
o
r
t
h
is
ex
am
p
le.
T
h
u
s
,
th
e
r
esu
lts
o
f
R
Q1
in
d
icate
a
d
if
f
er
e
n
tiated
n
atu
r
e
o
f
s
tatis
tical
co
m
p
ar
ab
ilit
y
.
W
h
ile
m
ain
tain
in
g
th
e
s
tr
u
ctu
r
al
co
r
r
ec
tn
ess
o
f
th
e
m
o
d
el,
th
e
q
u
an
titativ
e
s
tab
ilit
y
o
f
th
e
p
ar
am
eter
s
d
ep
en
d
s
o
n
th
e
AI
to
o
l
u
s
ed
.
T
ab
le
2
.
Dev
iatio
n
an
aly
s
is
r
elativ
e
to
b
en
c
h
m
ar
k
c
alcu
latio
n
(
E
x
am
p
le
-
1)
To
o
l
ΔA
(
%)
ΔB
(
%)
ΔR
²
ΔF
o
r
e
c
a
st
(
%)
W
i
t
h
i
n
t
o
l
e
r
a
n
c
e
?
C
h
a
t
G
P
T
4
.
0
0
.
0
0
+
1
0
.
6
4
0
.
0
0
0
0
+
4
.
2
7
P
a
r
t
i
a
l
(
B
)
D
e
e
p
S
e
e
k
v
3
.
2
0
.
0
0
0
.
0
0
0
.
0
0
0
0
0
.
0
0
Y
e
s
G
e
mi
n
i
3
P
r
o
0
.
0
0
−
0
.
0
0
+
0
.
0
1
2
1
+
0
.
0
0
N
o
(
R
²)
G
r
o
k
4
.
1
−
7
.
4
4
+
8
.
2
2
−
0
.
0
0
3
4
−
5
.
0
9
No
Ex
c
e
l
(
B
e
n
c
h
m
a
r
k
)
–
–
–
–
–
3
.
2
.
Resul
t
s
re
la
t
ed
t
o
RQ
2
T
o
f
in
d
th
e
an
s
wer
to
R
Q2
,
th
e
f
o
llo
win
g
f
o
u
r
ex
a
m
p
les
wer
e
u
s
ed
,
as
s
ee
n
in
T
a
b
le
3
.
T
h
e
d
ata
p
r
esen
ted
in
T
ab
le
3
d
em
o
n
s
tr
ate
s
tatis
tical
co
ef
f
icien
ts
an
d
p
r
ed
icted
v
alu
es
f
o
r
lin
ea
r
r
eg
r
ess
io
n
u
s
in
g
AI
p
r
o
m
p
ts
ac
r
o
s
s
f
o
u
r
a
d
d
itio
n
al
em
p
ir
ical
ex
am
p
les
wit
h
d
if
f
er
en
t
d
ata
c
h
ar
ac
ter
is
tics
.
R
ep
r
o
d
u
cib
ilit
y
an
aly
s
is
was
p
er
f
o
r
m
ed
i
n
tw
o
s
tag
es:
s
tr
u
ctu
r
al
r
ep
r
o
d
u
ci
b
ilit
y
test
in
g
(
f
u
ll
OL
S
p
r
o
ce
d
u
r
e)
;
q
u
a
n
titativ
e
ass
es
s
m
en
t
o
f
d
ev
iatio
n
s
r
elativ
e
to
th
e
Mic
r
o
s
o
f
t
E
x
ce
l
r
ef
er
en
ce
ca
lcu
latio
n
with
in
th
e
s
tatis
t
ical
to
ler
an
ce
f
r
am
ewo
r
k
.
I
n
all
ex
am
p
les,
th
e
n
eu
r
al
n
etwo
r
k
s
co
r
r
ec
tly
f
o
r
m
alize
d
th
e
Y
=
A
×
X
+
B
m
o
d
el
an
d
s
h
o
we
d
co
ef
f
icien
ts
an
d
R
²
,
as
s
h
o
w
n
in
T
ab
le
4
.
I
n
ter
m
s
o
f
t
h
e
OL
S
p
r
o
ce
d
u
r
e
s
tr
u
ctu
r
e,
r
ep
r
o
d
u
cib
ilit
y
is
co
n
f
ir
m
e
d
.
T
h
e
p
ictu
r
e
r
eg
ar
d
in
g
q
u
an
titativ
e
s
tab
ilit
y
is
s
ig
n
if
ican
tly
m
o
r
e
co
m
p
lex
.
Fo
r
ex
am
p
le,
f
o
r
Dee
p
Seek
v
3
.
2
,
d
e
v
iatio
n
s
r
e
m
ain
with
in
th
e
estab
lis
h
ed
t
h
r
esh
o
ld
s
in
all
f
o
u
r
e
x
am
p
le
s
(
T
ab
le
4
)
.
T
h
u
s
,
m
eth
o
d
o
l
o
g
ical
eq
u
i
v
alen
ce
is
co
n
s
is
ten
tly
co
n
f
ir
m
e
d
.
Fo
r
C
h
atGPT
4
.
0
an
d
Gem
in
i
3
Pro
,
s
ig
n
if
ican
t
d
ev
iatio
n
s
i
n
th
e
in
ter
ce
p
t
(
B
)
ar
e
o
b
s
er
v
ed
in
m
o
s
t
ex
am
p
les
(
T
ab
le
4
)
.
Ho
wev
e
r
,
th
e
s
lo
p
e
co
e
f
f
icien
ts
(
B
)
a
r
e
v
ir
tu
ally
id
e
n
tical.
R
²
r
em
ain
s
s
tab
le
in
m
o
s
t
ca
s
es.
Pre
d
icted
v
alu
es
ar
e
o
f
t
en
with
in
±
5
%
o
r
cl
o
s
e
to
th
e
lim
it.
T
h
is
in
d
icate
s
p
ar
tial
p
a
r
am
etr
ic
in
s
tab
ilit
y
wh
ile
m
ain
tain
in
g
th
e
o
v
er
all
s
tr
u
ctu
r
e
o
f
t
h
e
lin
ea
r
r
elatio
n
s
h
ip
.
Fo
r
Gr
o
k
4
.
1
,
ex
am
p
le
-
3
d
em
o
n
s
tr
ates
a
f
u
n
d
am
en
tally
d
if
f
er
en
t
p
atter
n
o
f
d
ev
iatio
n
s
:
Δ
A
=
+1
3
.
1
2
%,
Δ
B
=
+4
2
1
.
3
4
%,
Δ
R
²
=
+0
.
1
9
5
8
,
Δ
Fo
r
e
ca
s
t
=
+2
9
.
8
9
%
(
T
ab
le
4
)
.
T
h
is
m
ay
b
e
d
u
e
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
15
,
No
.
4
,
Au
g
u
s
t
20
26
:
2
8
7
4
-
2
8
8
2
2878
s
tr
u
ctu
r
al
d
e
v
iatio
n
o
f
th
e
m
o
d
el.
I
n
th
is
ca
s
e,
R
²
in
cr
ea
s
es
f
r
o
m
0
.
7
6
5
5
to
0
.
9
5
1
3
.
T
h
is
s
i
g
n
if
ican
tly
ch
an
g
es
th
e
in
ter
p
r
etatio
n
o
f
th
e
ex
p
l
an
ato
r
y
p
o
wer
o
f
th
e
m
o
d
el.
I
n
th
is
ca
s
e,
th
e
s
tati
s
tical
t
o
ler
an
ce
f
r
am
ew
o
r
k
r
ec
o
r
d
s
a
v
i
o
latio
n
o
f
m
eth
o
d
o
lo
g
ical
eq
u
i
v
alen
ce
.
T
h
u
s
,
th
e
r
ep
r
o
d
u
cib
ilit
y
o
f
th
e
p
r
o
ce
d
u
r
e
d
o
es
n
o
t
m
ea
n
th
e
q
u
an
titativ
e
s
tab
ilit
y
o
f
t
h
e
p
ar
am
eter
s
.
T
h
e
d
if
f
e
r
en
ce
b
etwe
en
s
tr
u
ctu
r
al
r
ep
r
o
d
u
cib
ilit
y
(
th
e
f
o
r
m
al
im
p
le
m
en
tatio
n
o
f
OL
S)
an
d
p
ar
am
etr
ic
s
tab
ilit
y
(
co
m
p
lia
n
ce
with
estab
lis
h
ed
to
ler
an
ce
s
)
was
d
em
o
n
s
tr
ated
in
T
ab
le
4
.
Stru
ctu
r
al
r
ep
r
o
d
u
cib
ilit
y
was
c
o
n
f
ir
m
e
d
f
o
r
all
AI
to
o
ls
.
Qu
an
titativ
e
s
tab
ilit
y
is
s
p
ec
if
ic.
Dee
p
Seek
d
em
o
n
s
tr
ates
s
tab
ilit
y
.
C
h
atGPT
an
d
Gem
i
n
i
d
em
o
n
s
tr
ate
p
ar
tial
s
tab
ilit
y
.
Gr
o
k
4
.
1
d
em
o
n
s
tr
ates
in
s
tab
ilit
y
with
ce
r
tain
d
atasets
.
T
h
u
s
,
R
Q2
r
ec
eiv
es
a
d
if
f
er
en
tiated
a
n
s
wer
:
AI
to
o
ls
r
ep
r
o
d
u
ce
th
e
an
aly
tical
s
tr
u
ctu
r
e
o
f
OL
S,
b
u
t
n
u
m
er
ical
s
tab
ilit
y
v
ar
ies an
d
r
eq
u
ir
es m
an
d
ato
r
y
ex
ter
n
al
v
er
if
icatio
n
.
T
ab
le
3
.
T
esti
n
g
th
e
r
ep
r
o
d
u
ci
b
ilit
y
o
f
an
aly
tical
p
r
o
ce
d
u
r
es
f
o
r
f
o
u
r
v
ar
io
u
s
AI
t
o
o
ls
(
ex
a
m
p
les
2
–
5)
To
o
l
А
В
R
2
p
-
v
a
l
u
e
F
o
r
e
c
a
st
f
o
r
2
0
3
0
Ex
a
m
p
l
e
-
2
C
h
a
t
G
P
T
4
.
0
7
5
7
.
90
-
1
6
4
.
9
0
0
.
8
8
4
2
0
.
0
0
0
0
2
8
6
3
5
.
3
0
D
e
e
p
S
e
e
k
v
3
.
2
7
5
7
.
8
0
-
9
2
1
.
3
0
0
.
8
8
4
2
0
.
0
0
0
0
2
7
8
7
5
.
1
0
G
e
mi
n
i
3
p
r
o
7
5
7
.
9
0
-
1
6
4
.
9
0
0
.
9
0
4
3
0
.
0
0
0
0
2
8
6
3
5
.
3
0
G
r
o
k
4
.
1
7
5
7
.
9
0
-
1
6
4
.
9
0
0
.
8
8
4
2
0
.
0
0
0
0
2
8
6
3
5
.
3
0
Ex
c
e
l
(
B
e
n
c
h
m
a
r
k
)
7
5
7
.
9
0
-
9
2
2
.
8
0
0
.
8
8
4
2
-
2
7
8
7
7
.
4
0
Ex
a
m
p
l
e
-
3
C
h
a
t
G
P
T
4
.
0
5
8
6
2
.
20
2
4
0
7
.
9
0
0
.
7
6
5
5
0
.
0
0
0
0
1
0
7
9
2
7
.
5
0
D
e
e
p
S
e
e
k
v
3
.
2
5
8
6
1
.
6
0
-
3
4
5
0
.
5
0
0
.
7
6
5
4
0
.
0
0
0
0
1
0
2
0
7
6
.
0
0
G
e
mi
n
i
3
p
r
o
5
8
6
1
.
6
0
2
4
1
1
.
2
0
0
.
7
6
5
4
0
.
0
0
0
0
1
0
7
9
2
0
.
0
0
G
r
o
k
4
.
1
6
7
4
8
.
5
0
1
1
0
9
9
.
2
0
0
.
9
5
1
3
0
.
0
0
0
0
1
3
2
5
7
2
.
2
0
Ex
c
e
l
(
B
e
n
c
h
m
a
r
k
)
5
8
6
2
.
2
0
-
3
4
5
4
.
3
0
0
.
7
6
5
5
-
1
0
2
0
6
5
.
3
0
Ex
a
m
p
l
e
-
4
C
h
a
t
G
P
T
4
.
0
1
1
6
8
.
8
0
2
2
4
.
2
0
0
.
8
9
0
1
0
.
0
0
0
1
1
7
7
5
6
.
2
0
D
e
e
p
S
e
e
k
v
3
.
2
1
1
6
8
.
8
0
-
9
4
4
.
6
0
0
.
8
8
9
8
0
.
0
0
0
1
1
6
5
8
7
.
4
0
G
e
mi
n
i
3
p
r
o
1
1
6
8
.
8
0
-
9
4
4
.
6
0
0
.
8
8
4
4
0
.
0
0
0
7
1
6
5
8
7
.
4
0
G
r
o
k
4
.
1
1
1
6
8
.
8
0
2
2
4
.
2
0
0
.
8
9
0
1
0
.
0
0
0
1
1
7
7
5
6
.
2
0
Ex
c
e
l
(
B
e
n
c
h
m
a
r
k
)
1
1
6
8
.
8
0
-
9
4
4
.
6
0
0
.
8
9
0
1
-
1
6
5
8
7
.
4
0
Ex
a
m
p
l
e
-
5
C
h
a
t
G
P
T
4
.
0
3
2
7
.
80
4
0
2
5
.
3
0
0
.
9
3
3
3
0
.
0
0
0
0
8
9
4
2
.
3
0
D
e
e
p
S
e
e
k
v
3
.
2
3
2
7
.
8
0
3
6
9
7
.
5
0
0
.
9
3
3
0
0
.
0
0
0
0
8
6
1
4
.
5
0
G
e
mi
n
i
3
p
r
o
3
2
7
.
8
0
4
0
2
5
.
3
0
0
.
9
3
3
3
0
.
0
0
0
0
8
9
4
2
.
3
0
G
r
o
k
4
.
1
3
5
4
.
6
0
4
2
1
6
.
0
0
0
.
9
4
4
0
0
.
0
0
0
0
9
5
3
5
.
0
0
Ex
c
e
l
(
B
e
n
c
h
m
a
r
k
)
3
2
7
.
8
0
3
6
9
7
.
5
0
0
.
9
3
3
3
-
8
6
1
4
.
5
0
T
ab
le
4
.
Su
m
m
a
r
y
o
f
d
e
v
iatio
n
s
r
elativ
e
to
b
en
c
h
m
ar
k
(
ex
a
m
p
les
2
–
5)
To
o
l
ΔA
(
%)
ΔB
(
%)
ΔR
²
ΔF
o
r
e
c
a
st
(
%)
W
i
t
h
i
n
t
o
l
e
r
a
n
c
e
?
Ex
a
m
p
l
e
-
2
C
h
a
t
G
P
T
4
.
0
0
.
0
0
+
8
2
.
1
2
0
.
0
0
0
0
+
2
.
7
2
N
o
(
B
)
D
e
e
p
S
e
e
k
v
3
.
2
0
.
0
0
0
.
1
6
0
.
0
0
0
0
−
0
.
0
1
Y
e
s
G
e
mi
n
i
3
P
r
o
0
.
0
0
+
8
2
.
1
2
+
0
.
0
2
0
1
+
2
.
7
2
N
o
(
R
²
,
B
)
G
r
o
k
4
.
1
0
.
0
0
+
8
2
.
1
2
0
.
0
0
0
0
+
2
.
7
2
N
o
(
B
)
Ex
a
m
p
l
e
-
3
C
h
a
t
G
P
T
4
.
0
0
.
0
0
+
1
6
9
.
7
0
0
.
0
0
0
0
+
5
.
7
5
No
D
e
e
p
S
e
e
k
v
3
.
2
−
0
.
0
1
0
.
1
1
0
.
0
0
0
1
+
0
.
0
1
Y
e
s
G
e
mi
n
i
3
P
r
o
−
0
.
0
1
+
1
6
9
.
8
4
0
.
0
0
0
1
+
5
.
7
4
No
G
r
o
k
4
.
1
+
1
3
.
1
2
+
4
2
1
.
3
4
+
0
.
1
9
5
8
+
2
9
.
8
9
No
Ex
a
m
p
l
e
-
4
C
h
a
t
G
P
T
4
.
0
0
.
0
0
+
1
2
3
.
7
3
0
.
0
0
0
0
+
7
.
0
5
No
D
e
e
p
S
e
e
k
v
3
.
2
0
.
0
0
0
.
0
0
0
.
0
0
0
3
0
.
0
0
Y
e
s
G
e
mi
n
i
3
P
r
o
0
.
0
0
0
.
0
0
−
0
.
0
0
6
4
0
.
0
0
Y
e
s
G
r
o
k
4
.
1
0
.
0
0
+
1
2
3
.
7
3
0
.
0
0
0
0
+
7
.
0
5
No
Ex
a
m
p
l
e
-
5
C
h
a
t
G
P
T
4
.
0
0
.
0
0
+
8
.
8
7
0
.
0
0
0
0
+
3
.
8
0
N
o
(
B
)
D
e
e
p
S
e
e
k
v
3
.
2
0
.
0
0
0
.
0
0
0
.
0
0
0
3
0
.
0
0
Y
e
s
G
e
mi
n
i
3
P
r
o
0
.
0
0
+
8
.
8
7
0
.
0
0
0
0
+
3
.
8
0
N
o
(
B
)
G
r
o
k
4
.
1
+
8
.
1
8
+
1
4
.
0
2
+
0
.
0
1
0
7
+
1
0
.
6
8
No
3
.
3
.
Resul
t
s
re
la
t
ed
t
o
RQ
3
T
h
e
em
p
ir
ical
r
esu
lts
allo
w
u
s
to
in
f
er
th
e
co
n
d
itio
n
s
f
o
r
ac
ce
p
tab
le
u
s
e
o
f
AI
[
1
9
]
b
a
s
ed
o
n
th
e
o
b
s
er
v
ed
d
ev
iatio
n
s
(
T
ab
les
2
an
d
4
)
.
T
h
e
e
m
p
ir
ical
r
esu
lts
allo
w
u
s
to
co
n
clu
d
e
th
at
th
e
an
aly
s
is
d
em
o
n
s
tr
ated
th
r
ee
d
is
tin
ct
em
p
ir
ical
p
atter
n
s
:
co
m
p
lete
p
ar
am
etr
ic
s
tab
ilit
y
with
in
th
e
g
iv
en
to
ler
an
ce
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
E
va
lu
a
tin
g
th
e
meth
o
d
o
lo
g
ic
a
l a
d
mis
s
ib
ilit
y
o
f g
en
era
tive
A
I
to
o
ls
fo
r
lin
ea
r
…
(
V
a
lery
Oku
lich
-
K
a
z
a
r
in
)
2879
th
r
esh
o
ld
s
(
Dee
p
Seek
v
3
.
2
in
all
ex
am
p
les);
p
a
r
tial
p
ar
am
etr
ic
in
s
tab
ilit
y
p
r
im
ar
ily
a
f
f
e
ctin
g
th
e
in
ter
ce
p
t
v
alu
es
(
C
h
atGPT
4
.
0
an
d
Gem
in
i
3
Pro
)
;
an
d
s
tr
u
ctu
r
al
d
ev
iatio
n
b
e
y
o
n
d
th
e
to
ler
an
ce
th
r
esh
o
ld
s
s
im
u
ltan
eo
u
s
ly
af
f
ec
tin
g
th
e
s
lo
p
e,
R
²,
an
d
th
e
p
r
ed
icted
o
u
tco
m
e
(
Gr
o
k
4
.
1
in
ex
am
p
le
3
)
.
T
h
ese
p
atter
n
s
allo
w
u
s
to
f
o
r
m
u
late
f
o
u
r
em
p
ir
ically
b
ased
to
ler
a
n
ce
co
n
d
i
tio
n
s
.
−
C
o
n
d
itio
n
1
:
q
u
a
n
titativ
e
v
alid
atio
n
.
T
h
e
p
r
esen
ce
o
f
th
r
esh
o
ld
v
io
latio
n
s
in
a
n
u
m
b
er
o
f
AI
to
o
ls
in
d
icate
s
th
at
th
e
r
eg
r
ess
io
n
p
ar
am
eter
s
g
en
e
r
ated
b
y
th
e
A
I
ca
n
n
o
t
b
e
ac
ce
p
ted
with
o
u
t
v
er
if
icatio
n
b
y
th
e
r
esear
ch
er
.
T
h
e
u
s
e
o
f
AI
to
o
ls
is
p
er
m
is
s
ib
le
o
n
ly
if
:
i
)
th
e
co
e
f
f
icien
ts
an
d
p
r
ed
ict
ed
v
alu
es
ar
e
clo
s
e
to
th
e
r
ef
er
e
n
ce
ca
lcu
lati
o
n
s
;
ii
)
th
e
d
ev
iatio
n
s
ar
e
esti
m
ated
with
in
p
r
e
d
eter
m
in
ed
to
ler
an
ce
s
.
−
C
o
n
d
itio
n
2
:
s
en
s
itiv
ity
to
co
ef
f
icien
t
B
.
I
n
s
ev
e
r
al
ex
am
p
les
(
T
ab
les
2
an
d
4
)
,
d
ev
iatio
n
s
m
o
s
t
o
f
ten
af
f
ec
ted
th
e
in
te
r
ce
p
t
(
B
)
,
w
h
ile
th
e
s
lo
p
e
(
A)
o
f
ten
r
e
m
ain
ed
s
tab
le.
A
ch
an
g
e
in
th
e
in
ter
ce
p
t
ca
n
s
ig
n
if
ican
tly
af
f
ec
t
f
o
r
ec
ast
v
alu
es.
T
h
u
s
,
ch
ec
k
in
g
th
e
s
tab
ilit
y
o
f
th
e
i
n
ter
ce
p
t
a
n
d
in
d
e
p
en
d
e
n
t
co
n
f
ir
m
atio
n
o
f
f
o
r
ec
ast ca
lcu
latio
n
s
ar
e
r
eq
u
ir
e
d
wh
en
d
ev
i
atio
n
s
ex
ce
ed
±
1
%.
−
C
o
n
d
itio
n
3
:
R
²
s
tab
ilit
y
th
r
esh
o
ld
.
I
n
ex
am
p
le
3
,
th
e
Gr
o
k
4
.
1
n
eu
r
al
n
etwo
r
k
d
em
o
n
s
tr
ates
th
at
a
s
ig
n
if
ican
t
d
ev
iatio
n
in
R
²
(
+0
.
1
9
5
8
)
ca
n
f
u
n
d
am
e
n
tally
ch
an
g
e
th
e
in
ter
p
r
etatio
n
o
f
th
e
m
o
d
el.
I
n
s
u
ch
ca
s
es,
th
e
u
s
e
o
f
AI
ca
n
n
o
t
b
e
co
n
s
id
er
ed
m
eth
o
d
o
lo
g
ically
eq
u
i
v
alen
t.
T
h
e
r
ef
o
r
e,
th
e
a
cc
ep
tab
ilit
y
o
f
u
s
e
r
eq
u
ir
es d
ev
iatio
n
s
in
R
²
with
in
±
0
.
0
1
.
−
C
o
n
d
itio
n
4
:
r
esear
ch
er
r
esp
o
n
s
ib
ilit
y
an
d
co
n
tr
o
l
.
E
m
p
ir
ic
al
d
ata
co
n
f
ir
m
th
at
AI
to
o
ls
r
ep
r
o
d
u
ce
th
e
co
m
p
u
tatio
n
al
s
tr
u
ctu
r
e,
b
u
t
m
ay
v
a
r
y
i
n
n
u
m
er
ical
p
r
ec
i
s
io
n
.
T
h
er
e
f
o
r
e,
th
e
ac
ce
p
tab
ilit
y
o
f
u
s
e
is
co
n
d
itio
n
e
d
b
y
:
i
)
th
e
r
esear
ch
er
’
s
ab
ilit
y
t
o
in
ter
p
r
et
s
ta
tis
tical
p
ar
am
eter
s
[
2
2
]
;
ii
)
v
er
if
icatio
n
o
f
r
esu
lts
;
ii
i
)
a
r
ef
u
s
al
to
r
eg
ar
d
AI
r
esu
lts
a
s
ep
is
tem
ically
au
to
n
o
m
o
u
s
.
T
ak
en
to
g
eth
e
r
,
th
e
o
b
tain
ed
r
esu
lts
d
em
o
n
s
tr
ate
th
at
AI
p
r
o
m
p
ts
ca
n
b
e
co
n
s
id
er
e
d
a
n
a
cc
ep
tab
le
m
ea
n
s
o
f
m
eth
o
d
o
l
o
g
ical
s
u
p
p
o
r
t,
b
u
t n
o
t a
s
a
s
tan
d
al
o
n
e
an
al
y
tical
to
o
l
[
2
0
]
.
3
.
4
.
Dis
cus
s
io
n
T
h
e
o
b
tain
e
d
r
esu
lts
allo
w
u
s
to
clar
if
y
th
e
m
et
h
o
d
o
lo
g
ic
al
s
tatu
s
o
f
u
s
in
g
AI
in
g
r
ad
u
ate
-
lev
el
r
esear
ch
[
1
]
,
[
2
]
f
o
r
lin
ea
r
r
eg
r
ess
io
n
an
aly
s
is
.
First,
th
e
r
es
u
lts
o
f
R
Q1
an
d
R
Q2
d
em
o
n
s
tr
ate
th
at
g
en
er
ativ
e
AI
to
o
ls
r
ep
r
o
d
u
ce
th
e
s
tr
u
ct
u
r
e
o
f
th
e
OL
S
p
r
o
ce
d
u
r
e.
H
o
wev
er
,
th
eir
n
u
m
er
ical
s
tab
ilit
y
is
n
o
t
co
n
s
tan
t.
Fu
ll
p
ar
am
etr
ic
eq
u
iv
ale
n
ce
was
n
o
t
co
n
f
ir
m
e
d
f
o
r
all
m
o
d
els.
T
h
er
ef
o
r
e,
m
eth
o
d
o
l
o
g
ical
eq
u
iv
alen
ce
is
co
n
d
itio
n
al
an
d
d
ep
en
d
s
o
n
co
m
p
lian
ce
with
estab
lis
h
ed
s
tatis
tica
l
d
ev
iatio
n
th
r
esh
o
ld
s
.
Seco
n
d
,
th
e
id
en
tifie
d
d
e
v
iatio
n
s
in
th
e
i
n
ter
ce
p
t
an
d
,
in
s
o
m
e
ca
s
es,
in
R
²
d
em
o
n
s
tr
ate
th
at
s
tr
u
ctu
r
al
r
ep
r
o
d
u
cib
ilit
y
d
o
es
n
o
t
g
u
a
r
an
tee
p
a
r
am
etr
ic
s
tab
i
lity
.
T
h
is
d
is
tin
ctio
n
is
o
f
f
u
n
d
am
en
tal
im
p
o
r
tan
ce
f
o
r
g
r
ad
u
ate
-
lev
el
r
esear
ch
,
wh
er
e
co
ef
f
icien
t
v
al
u
es
d
ir
e
ctly
in
f
lu
en
ce
th
e
s
tu
d
y
'
s
co
n
clu
s
io
n
s
.
T
h
ir
d
,
th
e
r
esu
lts
o
f
R
Q3
co
n
f
ir
m
th
e
p
r
in
cip
le
o
f
lim
ited
a
d
m
is
s
ib
ilit
y
:
AI
to
o
ls
ca
n
b
e
u
s
ed
as
an
au
x
iliar
y
c
o
m
p
u
tatio
n
al
m
ec
h
an
is
m
,
p
r
o
v
id
ed
th
at
th
ey
ar
e
q
u
a
n
titativ
ely
v
er
if
ied
,
th
e
p
r
o
ce
d
u
r
e
is
tr
an
s
p
ar
en
t,
a
n
d
r
esear
ch
er
c
o
n
tr
o
l
is
m
ain
tain
ed
[
6
]
,
[
2
2
]
.
E
m
p
ir
ical
d
ata
d
o
n
o
t su
p
p
o
r
t th
ei
r
ep
is
tem
ic
au
to
n
o
m
y
.
T
h
e
id
en
tifie
d
d
is
tin
ctio
n
b
et
wee
n
s
tr
u
ctu
r
al
r
ep
r
o
d
u
cib
ilit
y
an
d
p
ar
am
etr
ic
s
tab
ilit
y
clar
if
ies
th
e
m
eth
o
d
o
l
o
g
ical
s
tatu
s
o
f
AI
i
n
ed
u
ca
tio
n
al
r
esear
ch
.
A
n
u
m
b
er
o
f
p
u
b
licatio
n
s
co
n
s
id
er
n
eu
r
al
n
etwo
r
k
s
as
a
to
o
l
f
o
r
o
p
tim
izatio
n
o
f
ac
a
d
em
ic
ac
tiv
ity
[
9
]
,
[
1
1
]
,
[
1
4
]
,
[
2
9
]
.
Ho
wev
e
r
,
th
e
o
b
tain
ed
em
p
ir
ical
d
ata
d
em
o
n
s
tr
ate
th
at
co
m
p
u
tatio
n
al
s
u
p
p
o
r
t
is
n
o
t
id
en
tical
t
o
th
e
s
tab
ilit
y
o
f
s
tatis
tical
r
esu
lts
.
As
f
o
r
ed
u
ca
tio
n
al
ev
alu
atio
n
,
ev
en
m
in
o
r
d
ev
i
atio
n
s
in
AI
-
g
en
er
ated
r
eg
r
e
s
s
io
n
o
u
tp
u
ts
m
ay
in
f
lu
en
ce
th
e
ass
e
s
s
m
en
t
o
f
g
r
ad
u
ate
r
esear
ch
q
u
ality
an
d
th
e
v
alid
ity
o
f
th
esis
co
n
clu
s
io
n
s
.
T
h
is
p
o
in
t
b
ec
o
m
es
p
a
r
ticu
lar
ly
r
elev
an
t
f
o
r
em
p
ir
ical
ed
u
ca
tio
n
al
s
tu
d
ies
wh
er
e
s
tatis
tical
r
esu
lts
d
ir
ec
tly
in
f
o
r
m
p
e
d
ag
o
g
ical
r
ec
o
m
m
en
d
atio
n
s
.
Fo
r
ex
am
p
le,
a
c
o
m
p
a
r
ativ
e
s
tu
d
y
o
f
m
e
d
ia
s
tu
d
en
ts
in
d
if
f
er
en
t
c
o
u
n
tr
ies
s
tatis
tica
lly
d
em
o
n
s
tr
ated
a
s
ig
n
if
ican
t
p
r
ef
er
en
ce
f
o
r
v
is
u
al
lear
n
in
g
m
eth
o
d
s
o
v
er
au
d
ito
r
y
o
n
es,
wh
ich
led
to
co
n
cr
ete
r
ec
o
m
m
en
d
atio
n
s
f
o
r
a
d
ap
tin
g
lectu
r
e
f
o
r
m
ats
in
h
ig
h
er
ed
u
ca
tio
n
[
3
0
]
.
T
h
u
s
,
th
e
s
tu
d
y
s
h
if
ts
th
e
d
is
cu
s
s
io
n
ab
o
u
t th
e
u
s
e
o
f
AI
in
ed
u
ca
ti
o
n
f
r
o
m
th
e
lev
el
o
f
tech
n
o
lo
g
ical
ef
f
icien
cy
[
1
3
]
–
[
1
8
]
,
[
2
5
]
,
[
2
6
]
to
th
e
lev
el
o
f
m
eth
o
d
o
l
o
g
ical
ad
m
is
s
ib
ilit
y
.
AI
to
o
ls
ca
n
b
e
in
teg
r
ated
in
to
th
e
r
esear
ch
in
f
r
astru
ctu
r
e
o
f
g
r
ad
u
ate
-
lev
el
ed
u
ca
tio
n
[
1
9
]
–
[
2
2
]
,
b
u
t th
eir
u
s
e
r
eq
u
ir
es m
ain
tain
in
g
th
e
r
esp
o
n
s
ib
ilit
y
o
f
th
e
r
esear
ch
er
.
An
ad
d
itio
n
al
lim
itatio
n
is
th
e
o
p
ac
ity
o
f
th
e
g
en
er
ativ
e
m
o
d
el
ar
ch
itectu
r
e
(
m
o
d
el
o
p
ac
ity
)
[
3
1
]
.
T
h
e
u
s
er
h
as
n
o
ac
ce
s
s
to
t
h
e
i
n
ter
n
al
alg
o
r
ith
m
ic
p
r
o
ce
s
s
in
g
m
ec
h
an
is
m
s
an
d
p
o
s
s
ib
le
h
id
d
en
co
m
p
u
tatio
n
al
s
tag
es.
Giv
en
th
is
o
p
ac
ity
,
ex
t
er
n
al
q
u
a
n
titativ
e
v
er
if
icatio
n
o
f
th
e
r
esu
lts
b
ec
o
m
es
a
n
ec
e
s
s
ar
y
co
n
d
itio
n
f
o
r
m
eth
o
d
o
l
o
g
ical
r
eliab
ilit
y
.
T
h
e
ap
p
r
o
ac
h
is
v
alid
ated
wh
en
p
ar
am
etr
ic
s
tab
ilit
y
c
o
n
d
itio
n
s
ar
e
m
et
[
2
7
]
,
b
u
t
d
o
es
n
o
t
au
to
m
atica
lly
im
p
ly
th
e
m
eth
o
d
o
l
o
g
ical
eq
u
iv
ale
n
ce
o
f
all
AI
t
o
o
ls
.
E
m
p
i
r
ical
d
ata
clar
if
y
th
e
ap
p
licab
ilit
y
o
f
AI
-
ass
is
ted
r
es
ea
r
ch
m
eth
o
d
o
lo
g
y
in
t
h
e
co
n
t
ex
t o
f
q
u
an
titativ
e
an
aly
s
is
.
4.
CO
NCLU
SI
O
N
T
h
e
r
esu
lts
s
h
if
t
th
e
d
is
cu
s
s
io
n
o
f
AI
u
s
e
in
g
r
a
d
u
ate
-
lev
el
r
esear
ch
f
r
o
m
t
h
e
lev
el
o
f
tec
h
n
o
lo
g
ical
ef
f
ec
tiv
en
ess
to
th
e
lev
el
o
f
m
eth
o
d
o
lo
g
ical
a
d
m
is
s
ib
ilit
y
.
T
h
e
em
p
ir
ical
d
ata
clar
if
y
th
e
lim
its
o
f
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
15
,
No
.
4
,
Au
g
u
s
t
20
26
:
2
8
7
4
-
2
8
8
2
2880
ap
p
licatio
n
o
f
AI
-
ass
is
ted
r
esear
ch
m
eth
o
d
o
lo
g
y
in
q
u
a
n
titativ
e
an
aly
s
is
:
it
s
u
s
e
is
p
er
m
is
s
ib
le
o
n
ly
if
th
e
co
n
d
itio
n
s
o
f
p
a
r
am
etr
ic
s
tab
ilit
y
an
d
r
esear
ch
co
n
tr
o
l
a
r
e
m
et.
T
h
e
au
t
o
m
atic
m
eth
o
d
o
lo
g
ical
eq
u
iv
alen
ce
o
f
g
en
er
ativ
e
m
o
d
els is
n
o
t c
o
n
f
i
r
m
ed
.
I
n
ter
m
s
o
f
p
r
ac
tical
s
ig
n
if
i
ca
n
ce
,
th
e
s
tu
d
y
’
s
r
esu
lts
allo
w
f
o
r
th
e
f
o
r
m
u
latio
n
o
f
ca
u
tio
u
s
m
eth
o
d
o
l
o
g
ical
r
ec
o
m
m
en
d
at
io
n
s
h
o
w
to
u
s
e
AI
to
o
ls
wh
en
p
e
r
f
o
r
m
in
g
lin
ea
r
r
eg
r
ess
io
n
in
g
r
ad
u
ate
-
le
v
el
r
esear
ch
.
First,
th
e
u
s
e
o
f
AI
is
o
n
ly
p
er
m
is
s
ib
le
if
th
e
o
b
tain
ed
co
ef
f
icien
ts
an
d
p
r
ed
icted
v
alu
es
ar
e
q
u
an
titativ
ely
v
er
if
ied
with
in
p
r
ed
eter
m
in
e
d
s
tatis
tical
d
e
v
iatio
n
to
ler
an
ce
s
.
Seco
n
d
,
t
h
e
co
ef
f
icien
t
(
B
)
r
eq
u
ir
es
s
p
ec
ial
atten
tio
n
,
as
th
is
p
ar
am
eter
ex
h
ib
its
th
e
g
r
ea
test
v
ar
iab
ilit
y
an
d
m
a
y
i
n
f
lu
en
ce
p
r
ed
ictiv
e
r
esu
lts
.
T
h
ir
d
,
if
t
h
e
d
eter
m
in
atio
n
co
e
f
f
icien
t
(
R
²)
ex
h
ib
its
s
ig
n
if
ican
t
d
ev
iatio
n
s
,
u
s
i
n
g
th
e
AI
r
esu
lts
with
o
u
t
f
u
r
th
er
v
er
if
icatio
n
i
s
m
eth
o
d
o
l
o
g
ically
u
n
ac
ce
p
t
ab
le.
T
h
is
m
a
y
af
f
ec
t
th
e
in
ter
p
r
etatio
n
o
f
t
h
e
m
o
d
el
’
s
ex
p
lan
ato
r
y
p
o
wer
.
T
h
e
o
b
tain
ed
r
esu
lts
ar
e
co
n
tex
tu
al
in
n
atu
r
e.
T
h
ey
r
elate
ex
c
lu
s
iv
ely
to
s
in
g
le
-
f
ac
to
r
lin
ea
r
r
eg
r
ess
io
n
with
a
f
ix
ed
p
r
o
m
p
t
s
tr
u
ctu
r
e
.
T
h
e
y
d
o
n
o
t
im
p
l
y
a
r
an
k
in
g
o
f
A
I
to
o
ls
o
u
ts
id
e
t
h
is
m
eth
o
d
o
l
o
g
ical
co
n
te
x
t.
T
h
er
e
ar
e
s
ev
er
al
l
im
itatio
n
s
o
f
th
e
s
tu
d
y
.
First,
th
e
an
aly
s
is
was
l
im
ited
to
a
s
in
g
le
-
v
ar
iate
lin
ea
r
r
eg
r
ess
io
n
s
tu
d
y
.
T
h
e
r
esu
lts
o
b
tain
ed
ca
n
n
o
t
b
e
au
to
m
at
ically
g
en
er
alize
d
to
m
u
ltiv
a
r
iate
o
r
n
o
n
lin
ea
r
m
o
d
els.
Su
ch
m
o
d
els
h
av
e
h
ig
h
er
p
a
r
am
etr
ic
s
en
s
itiv
ity
an
d
co
m
p
u
tatio
n
al
co
m
p
lex
ity
.
Seco
n
d
,
th
e
s
tu
d
y
f
o
cu
s
ed
o
n
th
e
m
eth
o
d
o
lo
g
ica
l
v
alid
ity
o
f
th
e
ca
lcu
latio
n
s
.
T
h
e
s
tu
d
y
was
n
o
t
o
n
th
e
s
ele
ctio
n
o
f
th
e
b
est
AI
to
o
l
o
r
th
e
p
e
d
ag
o
g
ical
ef
f
ec
ts
o
f
AI
u
s
e.
T
h
e
im
p
ac
t
o
f
AI
ap
p
licatio
n
o
n
t
h
e
d
ev
elo
p
m
en
t
o
f
m
aster
’
s
s
tu
d
en
ts
’
r
esear
ch
co
m
p
eten
c
ies
r
eq
u
ir
es
s
ep
ar
ate
an
aly
s
is
.
T
h
ir
d
,
th
e
r
esu
lts
wer
e
o
b
t
ain
ed
with
a
f
ix
e
d
q
u
er
y
s
tr
u
ctu
r
e
a
n
d
s
p
ec
if
ic
v
er
s
io
n
s
o
f
th
e
AI
to
o
ls
.
Giv
en
th
e
d
y
n
am
ic
n
atu
r
e
o
f
n
e
u
r
al
n
etwo
r
k
d
ev
elo
p
m
e
n
t,
s
u
b
s
eq
u
e
n
t
v
er
s
io
n
s
m
ay
ex
h
ib
it
a
d
if
f
e
r
en
t
d
eg
r
ee
o
f
p
ar
am
etr
ic
s
tab
il
ity
.
Ho
wev
er
,
th
is
p
o
s
s
ib
ilit
y
r
eq
u
ir
es
em
p
ir
ical
v
er
if
icatio
n
a
n
d
ca
n
n
o
t
b
e
a
s
s
u
m
ed
n
o
r
m
ativ
ely
.
A
p
r
o
m
is
in
g
d
ir
ec
tio
n
f
o
r
f
u
r
th
er
r
esear
ch
is
a
lo
n
g
itu
d
i
n
al
an
aly
s
is
o
f
th
e
s
tab
ili
ty
o
f
r
esu
lts
wh
en
u
p
d
atin
g
AI
to
o
ls
,
as
well
a
s
an
ass
es
s
m
en
t o
f
th
eir
ap
p
licab
ilit
y
in
m
o
r
e
co
m
p
le
x
s
tatis
tical
p
r
o
ce
d
u
r
es.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
is
r
esear
ch
h
as
b
ee
n
f
u
n
d
e
d
b
y
th
e
g
r
an
t
“Ap
p
licatio
n
o
f
h
y
b
r
id
s
war
m
i
n
tellig
en
ce
alg
o
r
ith
m
s
in
th
e
d
ev
elo
p
m
e
n
t
o
f
p
r
o
ac
tiv
e
m
u
lti
-
ag
en
t
s
y
s
tem
s
f
o
r
th
e
d
ig
ital
ed
u
ca
tio
n
al
en
v
ir
o
n
m
e
n
t”
o
f
th
e
Scien
ce
C
o
m
m
ittee
o
f
th
e
Min
is
tr
y
o
f
Scien
ce
an
d
Hig
h
er
E
d
u
ca
tio
n
o
f
th
e
R
ep
u
b
lic
o
f
Kaz
ak
h
s
tan
(
No
.
AP2
6
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9
6
0
2
3
)
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
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E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT
)
to
r
ec
o
g
n
ize
in
d
iv
id
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Na
m
e
o
f
Aut
ho
r
C
M
So
Va
Fo
I
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Vi
Su
P
Fu
Vale
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y
Ok
u
lich
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Kaz
ar
in
✓
✓
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✓
✓
✓
✓
✓
✓
Kan
at
Ko
zh
ak
h
m
et
✓
✓
✓
✓
✓
✓
✓
✓
✓
C
:
C
o
n
c
e
p
t
u
a
l
i
z
a
t
i
o
n
M
:
M
e
t
h
o
d
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o
g
y
So
:
So
f
t
w
a
r
e
Va
:
Va
l
i
d
a
t
i
o
n
Fo
:
Fo
r
mal
a
n
a
l
y
s
i
s
I
:
I
n
v
e
s
t
i
g
a
t
i
o
n
R
:
R
e
so
u
r
c
e
s
D
:
D
a
t
a
C
u
r
a
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o
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:
W
r
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:
W
r
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g
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v
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Vi
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P
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T
ST
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M
E
NT
Au
th
o
r
s
s
tate
n
o
co
n
f
lict o
f
in
t
er
est.
DATA AV
AI
L
AB
I
L
I
T
Y
T
h
e
au
th
o
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s
co
n
f
ir
m
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d
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p
p
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e
f
in
d
in
g
s
o
f
th
is
s
tu
d
y
ar
e
av
ailab
le
with
in
th
e
ar
ticle
an
d
its
s
u
p
p
lem
en
tar
y
m
ater
ia
ls
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
E
va
lu
a
tin
g
th
e
meth
o
d
o
lo
g
ic
a
l a
d
mis
s
ib
ilit
y
o
f g
en
era
tive
A
I
to
o
ls
fo
r
lin
ea
r
…
(
V
a
lery
Oku
lich
-
K
a
z
a
r
in
)
2881
RE
F
E
R
E
NC
E
S
[
1
]
V
.
O
k
u
l
i
c
h
-
K
a
z
a
r
i
n
,
“
N
e
w
C
h
a
t
G
P
T
3
.
5
I
n
st
r
u
c
t
i
o
n
(
P
r
o
m
p
t
)
t
o
C
a
l
c
u
l
a
t
e
S
t
a
t
i
st
i
c
a
l
I
n
d
i
c
a
t
o
r
s
f
o
r
S
t
u
d
e
n
t
G
r
a
d
u
a
t
i
o
n
P
r
o
j
e
c
t
s,
”
WS
E
AS
T
ra
n
s
a
c
t
i
o
n
s
o
n
C
o
m
p
u
t
e
r R
e
sea
r
c
h
,
v
o
l
.
1
2
,
p
p
.
3
0
7
–
3
1
7
,
2
0
2
4
,
d
o
i
:
1
0
.
3
7
3
9
4
/
2
3
2
0
1
8
.
2
0
2
4
.
1
2
.
3
0
.
[
2
]
V
.
O
k
u
l
i
c
h
-
K
a
z
a
r
i
n
,
“
S
t
a
t
i
s
t
i
c
s
U
si
n
g
N
e
u
r
a
l
N
e
t
w
o
r
k
s
i
n
t
h
e
C
o
n
t
e
x
t
o
f
S
u
st
a
i
n
a
b
l
e
D
e
v
e
l
o
p
me
n
t
G
o
a
l
9
.
5
,
”
S
u
s
t
a
i
n
a
b
i
l
i
t
y
,
v
o
l
.
1
6
,
n
o
.
19
,
2
0
2
4
,
d
o
i
:
1
0
.
3
3
9
0
/
s
u
1
6
1
9
8
3
9
5
.
[
3
]
H.
H
.
Y
a
n
g
a
n
d
Y
.
-
T.
L
i
n
,
“
H
o
w
K
n
o
w
l
e
d
g
e
S
h
a
r
i
n
g
a
n
d
C
o
h
e
si
o
n
B
e
c
o
m
e
K
e
y
s t
o
a
S
u
c
c
e
ssf
u
l
G
r
a
d
u
a
t
i
o
n
P
r
o
j
e
c
t
f
o
r
S
t
u
d
e
n
t
s
f
r
o
m D
e
s
i
g
n
C
o
l
l
e
g
e
,
”
S
AG
E
O
p
e
n
,
v
o
l
.
1
2
,
n
o
.
3
,
2
0
2
2
,
d
o
i
:
1
0
.
1
1
7
7
/
2
1
5
8
2
4
4
0
2
2
1
1
2
1
7
8
5
.
[
4
]
J.
O
.
C
o
n
n
e
r
,
“
S
t
u
d
e
n
t
E
n
g
a
g
e
m
e
n
t
i
n
a
n
I
n
d
e
p
e
n
d
e
n
t
R
e
sea
r
c
h
P
r
o
j
e
c
t
:
T
h
e
I
n
f
l
u
e
n
c
e
o
f
C
o
h
o
r
t
C
u
l
t
u
r
e
,
”
J
o
u
r
n
a
l
o
f
Ad
v
a
n
c
e
d
Ac
a
d
e
m
i
c
s
,
v
o
l
.
2
1
,
n
o
.
1
,
p
p
.
8
–
3
8
,
2
0
0
9
,
d
o
i
:
1
0
.
1
1
7
7
/
1
9
3
2
2
0
2
X
0
9
0
2
1
0
0
1
0
2
.
[
5
]
R
.
H
e
r
z
a
l
l
a
h
,
“
P
r
a
c
t
i
c
a
l
l
y
O
r
i
e
n
t
e
d
D
e
si
g
n
P
r
o
j
e
c
t
s
i
n
M
e
c
h
a
t
r
o
n
i
c
s
E
n
g
i
n
e
e
r
i
n
g
:
A
C
a
s
e
S
t
u
d
y
o
f
D
e
s
i
g
n
Ex
p
e
r
i
e
n
c
e
s
a
n
d
O
u
t
c
o
m
e
s,”
I
n
t
e
rn
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
t
ri
c
a
l
E
n
g
i
n
e
e
r
i
n
g
&
E
d
u
c
a
t
i
o
n
,
v
o
l
.
4
7
,
n
o
.
1
,
p
p
.
3
1
–
4
6
,
2
0
1
0
,
d
o
i
:
1
0
.
7
2
2
7
/
I
JEEE.
4
7
.
1
.
4
.
[
6
]
M
.
P
.
B
a
b
a
n
o
ğ
l
u
,
T.
Ö
.
K
a
r
a
t
a
ş
,
a
n
d
E.
D
ü
n
d
a
r
,
“
E
n
v
i
si
o
n
i
n
g
t
h
e
F
u
t
u
r
e
o
f
A
I
-
A
ssi
st
e
d
EFL
Te
a
c
h
i
n
g
a
n
d
L
e
a
r
n
i
n
g
:
C
o
n
c
e
p
t
u
a
l
R
e
p
r
e
se
n
t
a
t
i
o
n
s
o
f
P
r
o
sp
e
c
t
i
v
e
Te
a
c
h
e
r
s
,”
S
AG
E
O
p
e
n
,
v
o
l
.
1
5
,
n
o
.
2
,
2
0
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