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K
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:
B
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Data
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Dif
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tial a
p
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CC B
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C
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A
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Sal
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c.
th
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
p
r
im
ar
y
s
ig
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al
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s
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al
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en
tific
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n
d
u
r
in
g
t
h
e
d
ata
s
tr
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m
[
1
]
.
T
h
is
r
esear
ch
'
s
p
r
im
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f
o
cu
s
is
id
en
tify
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m
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w
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in
d
ata
s
tr
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m
s
,
p
ar
ticu
lar
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p
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asizin
g
th
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elem
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t
o
f
tim
e.
T
h
e
o
b
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is
to
en
h
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ce
th
e
e
f
f
icien
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o
f
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s
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b
s
et
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p
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ata
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m
s
th
r
o
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a
s
eq
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n
tial
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f
ex
p
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f
ac
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ac
c
u
r
ate
a
n
d
r
ap
id
an
o
m
al
y
d
etec
tio
n
[
2
]
,
[
3
]
.
A
s
ig
n
if
ican
t
c
h
allen
g
e
in
tim
e
-
b
ased
an
o
m
aly
id
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tific
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,
esp
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in
t
h
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c
o
n
tex
t
o
f
m
o
b
ile
r
o
b
o
ts
u
s
ed
in
r
o
u
g
h
ter
r
ain
r
escu
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m
is
s
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n
s
,
is
th
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ass
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ciate
d
c
o
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t
o
f
tr
a
n
s
itio
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in
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th
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d
ata
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tr
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f
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o
m
o
n
e
g
e
o
g
r
ap
h
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r
eg
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t
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an
o
th
er
[
4
]
.
T
h
is
co
s
t
p
r
im
ar
ily
ar
is
es
f
r
o
m
t
h
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m
o
v
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m
en
t
o
f
r
o
b
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ts
.
Var
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s
ap
p
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x
im
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alg
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r
ith
m
s
h
a
v
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b
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d
ev
elo
p
ed
to
ad
d
r
ess
th
is
is
s
u
e,
with
th
e
B
r
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m
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tio
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alg
o
r
ith
m
b
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a
p
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in
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t
ch
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d
u
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ex
p
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m
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ag
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g
tim
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co
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-
ef
f
ec
tiv
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m
o
d
el
c
o
n
s
tr
u
ctio
n
[
5
]
.
Ho
wev
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r
,
t
h
e
s
tan
d
ar
d
B
r
o
wn
ian
m
o
tio
n
alg
o
r
ith
m
f
ac
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ch
allen
g
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in
clu
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g
h
an
d
lin
g
v
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d
atasets
,
m
em
o
r
y
lim
itatio
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s
,
an
d
th
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in
a
b
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to
ad
a
p
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to
a
b
eh
av
io
r
-
b
ased
s
y
s
tem
with
in
f
in
ite
v
ar
ian
ce
[
6
]
,
[
7
]
.
T
o
ad
d
r
ess
th
e
ch
allen
g
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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o
wca
s
e
d
if
f
er
en
tiatio
n
in
er
r
atic
m
o
tio
n
s
[
9
]
,
[
1
0
]
.
I
n
p
r
esen
tin
g
t
h
e
m
in
im
u
m
B
r
o
wn
ian
m
o
tio
n
u
s
in
g
s
to
c
h
asti
c
d
if
f
er
en
tial
ap
p
r
o
x
im
at
io
n
an
d
o
p
tim
is
tic
o
p
tim
izatio
n
,
th
e
p
ath
is
d
ep
i
cted
in
tim
e
in
ter
v
als,
ea
ch
f
u
r
th
er
d
iv
id
e
d
in
to
s
u
b
-
i
n
ter
v
al
s
[
1
1
]
.
T
h
e
cr
itical
o
b
jectiv
e
is
to
d
eter
m
in
e
h
o
w
ea
ch
s
u
b
-
in
ter
v
al
s
h
o
u
l
d
b
e
r
ep
r
esen
ted
with
in
th
e
en
tire
tim
e
in
ter
v
al.
T
h
is
in
v
o
lv
es
th
e
s
elec
tio
n
o
f
a
m
a
th
em
atica
l
m
o
d
el,
in
th
is
ca
s
e,
s
to
ch
asti
c
d
if
f
e
r
en
tial
eq
u
atio
n
s
(
SDE)
,
an
d
a
n
o
p
tim
izatio
n
tech
n
iq
u
e
,
s
p
ec
if
ically
an
o
p
tim
is
tic
o
p
tim
i
za
tio
n
alg
o
r
ith
m
[
1
2
]
.
I
n
s
u
m
m
ar
y
,
th
is
p
ap
e
r
in
tr
o
d
u
ce
s
an
in
n
o
v
ativ
e
ap
p
r
o
ac
h
to
tack
le
th
e
ch
allen
g
es a
s
s
o
ciate
d
with
tim
e
-
b
ased
an
o
m
aly
id
en
tific
atio
n
,
p
ar
ticu
lar
ly
in
m
o
b
ile
r
o
b
o
t
s
,
b
y
p
r
esen
tin
g
th
e
s
to
ch
a
s
tic
d
if
f
er
en
tial
ap
p
r
o
x
im
ati
o
n
an
d
o
p
tim
is
tic
o
p
tim
izatio
n
o
f
B
r
o
wn
ia
n
m
o
tio
n
as
a
m
o
r
e
ef
f
ec
tiv
e
alter
n
ativ
e
to
th
e
tr
ad
itio
n
al
B
r
o
wn
ian
m
o
tio
n
alg
o
r
ith
m
[
1
3
]
.
T
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
p
r
o
v
id
es
s
ev
er
al
k
ey
co
n
tr
ib
u
tio
n
s
to
en
h
a
n
ce
co
s
t
ef
f
icien
cy
an
d
im
p
r
o
v
e
an
o
m
aly
d
etec
tio
n
a
cc
u
r
ac
y
in
r
o
b
o
tic
s
y
s
tem
s
.
On
e
o
f
its
p
r
im
ar
y
ad
v
an
tag
es
is
th
e
s
ig
n
if
ican
t
r
ed
u
ctio
n
in
ex
p
en
s
es
r
elate
d
to
th
e
m
o
v
em
en
t
o
f
m
o
b
ile
r
o
b
o
ts
,
p
ar
ticu
lar
ly
d
u
r
in
g
th
e
p
r
o
ce
s
s
o
f
d
etec
tin
g
an
o
m
alies
in
d
ata
s
tr
ea
m
s
[
1
4
]
.
B
y
em
p
lo
y
in
g
a
m
at
h
e
m
atica
l
m
o
d
el
t
h
at
ap
p
r
o
x
i
m
ates
th
e
m
in
im
al
B
r
o
wn
ian
m
o
tio
n
p
ath
,
th
e
m
eth
o
d
ef
f
ec
ti
v
ely
m
in
im
izes
u
n
n
ec
ess
ar
y
r
o
b
o
t
m
o
v
em
en
ts
,
th
er
eb
y
c
o
n
s
er
v
in
g
b
o
th
en
e
r
g
y
a
n
d
r
eso
u
r
ce
s
.
B
r
o
wn
ian
m
o
tio
n
,
o
f
ten
ass
o
ciate
d
with
r
a
n
d
o
m
m
o
v
em
e
n
t
p
atter
n
s
,
is
s
tr
ea
m
lin
ed
h
e
r
e
to
lim
it
r
o
b
o
t
m
o
v
e
m
en
t,
f
o
cu
s
in
g
o
n
p
ath
way
s
with
m
i
n
im
al
d
e
v
iatio
n
.
T
h
is
tar
g
eted
m
o
v
em
e
n
t
s
tr
ateg
y
n
o
t
o
n
l
y
s
av
es
o
p
er
atio
n
al
c
o
s
ts
b
u
t
als
o
ex
ten
d
s
th
e
o
p
er
atio
n
al
life
s
p
an
o
f
r
o
b
o
tic
c
o
m
p
o
n
en
ts
b
y
r
ed
u
ci
n
g
wea
r
an
d
tear
o
n
th
e
m
ac
h
in
e
r
y
[
1
5
]
.
I
n
ad
d
itio
n
to
co
s
t
s
av
in
g
s
,
th
e
ap
p
r
o
ac
h
em
p
lo
y
s
an
a
d
v
a
n
ce
d
m
ath
em
atica
l
f
r
am
ewo
r
k
b
ased
o
n
s
to
ch
ast
ic
d
if
f
er
en
tial
eq
u
atio
n
s
(
SD
E
s
)
to
r
ef
in
e
t
h
e
p
r
ec
is
io
n
o
f
th
e
m
in
im
al
p
ath
ap
p
r
o
x
im
atio
n
.
B
y
lev
er
a
g
in
g
SDEs,
th
e
s
y
s
tem
ca
n
d
y
n
am
ically
ad
ju
s
t
to
u
n
p
r
ed
ictab
le
f
ac
to
r
s
th
at
im
p
ac
t
r
o
b
o
t
m
o
v
em
en
t
a
n
d
d
ata
co
l
lectio
n
[
1
6
]
.
T
h
is
ad
d
ed
la
y
er
o
f
m
ath
em
atica
l
r
ig
o
r
en
h
a
n
ce
s
th
e
ac
cu
r
ac
y
o
f
th
e
B
r
o
wn
ian
m
o
tio
n
m
o
d
el,
en
s
u
r
in
g
th
at
th
e
r
o
b
o
ts
f
o
llo
w
a
p
at
h
clo
s
e
to
th
e
m
in
im
al
d
is
tan
ce
r
e
q
u
ir
e
d
to
d
etec
t a
n
o
m
alies e
f
f
ec
tiv
ely
.
T
h
e
u
s
e
o
f
SDEs e
n
s
u
r
es th
at
th
e
ap
p
r
o
ac
h
ad
ap
ts
well
to
f
lu
ctu
atin
g
co
n
d
itio
n
s
,
wh
ich
ar
e
c
o
m
m
o
n
in
r
ea
l
-
wo
r
ld
ap
p
licatio
n
s
wh
e
r
e
r
o
b
o
tic
s
y
s
tem
s
en
co
u
n
ter
v
ar
ied
te
r
r
ain
s
an
d
o
b
s
tacle
s
[
1
7
]
–
[
2
0
]
.
T
h
is
r
esu
lts
in
a
r
o
b
u
s
t
s
y
s
tem
wh
er
e
th
e
ac
cu
r
ac
y
o
f
an
o
m
al
y
d
etec
tio
n
r
em
ai
n
s
h
ig
h
,
ev
en
u
n
d
er
ch
allen
g
in
g
c
o
n
d
itio
n
s
.
T
o
im
p
r
o
v
e
th
e
a
p
p
r
o
ac
h
,
a
n
o
p
tim
is
tic
o
p
tim
izatio
n
tech
n
i
q
u
e
is
in
co
r
p
o
r
ated
to
ef
f
ec
tiv
ely
tack
le
co
n
tin
u
o
u
s
o
p
tim
izatio
n
c
h
allen
g
es
ass
o
ciate
d
with
B
r
o
wn
ian
m
o
ti
o
n
[
1
6
]
.
T
h
is
f
r
a
m
ewo
r
k
p
lay
s
a
v
ital
r
o
le
in
id
en
tify
i
n
g
th
e
o
p
tim
al
p
ath
s
f
o
r
r
o
b
o
ts
,
s
tr
ik
in
g
a
b
alan
ce
b
etwe
en
m
in
im
izin
g
p
ath
len
g
t
h
an
d
m
ax
im
izin
g
th
e
p
r
o
b
ab
ilit
y
o
f
an
o
m
al
y
d
etec
tio
n
.
B
y
f
o
cu
s
in
g
o
n
o
p
tim
izin
g
th
e
r
o
b
o
t'
s
p
ath
,
th
e
m
eth
o
d
s
ig
n
if
ican
tly
in
cr
ea
s
es
th
e
ch
an
ce
s
o
f
ac
cu
r
ately
id
en
tif
y
in
g
an
o
m
alies
with
o
u
t
n
ec
ess
itatin
g
ex
ten
s
iv
e
m
o
v
em
en
t.
T
h
is
o
p
tim
izatio
n
p
r
o
ce
s
s
d
o
es
n
o
t
s
o
lely
f
o
cu
s
o
n
id
en
tify
in
g
an
o
m
alies
b
u
t
also
em
p
h
asizes
ef
f
icien
t
r
eso
u
r
ce
allo
ca
tio
n
,
m
in
im
izin
g
co
m
p
u
tatio
n
al
p
o
wer
,
an
d
u
ltima
tely
r
e
d
u
cin
g
th
e
tim
e
an
d
co
s
t
in
v
o
lv
ed
in
an
o
m
aly
d
etec
ti
o
n
.
An
ad
d
itio
n
al
asp
ec
t
o
f
th
is
m
eth
o
d
o
lo
g
y
is
its
em
p
h
asis
o
n
ac
cu
r
ately
p
in
p
o
in
tin
g
th
e
m
o
s
t
lik
ely
m
in
im
u
m
p
ath
o
f
B
r
o
wn
ia
n
m
o
tio
n
with
in
a
s
p
ec
if
ic
tim
e
f
r
a
m
e,
a
f
ea
tu
r
e
t
h
at
s
ig
n
if
ican
tly
en
h
an
ce
s
th
e
ef
f
ec
tiv
en
ess
o
f
an
o
m
aly
d
ete
ctio
n
[
2
1
]
.
T
h
e
p
r
o
p
o
s
ed
a
p
p
r
o
ac
h
ef
f
ec
tiv
ely
n
ar
r
o
ws
d
o
wn
t
h
e
s
et
o
f
p
r
o
b
ab
le
p
ath
s
,
f
o
cu
s
in
g
o
n
ac
c
u
r
ately
id
en
tify
in
g
t
h
e
m
in
im
u
m
p
ath
th
at
ex
h
i
b
its
B
r
o
wn
ian
m
o
tio
n
ch
a
r
ac
ter
is
tics
.
T
h
is
en
s
u
r
es
th
at
a
n
o
m
alie
s
in
ex
ten
s
iv
e
d
ata
s
tr
ea
m
s
ar
e
d
etec
ted
p
r
o
m
p
tly
an
d
with
m
in
im
al
r
eso
u
r
ce
co
n
s
u
m
p
tio
n
,
r
ed
u
cin
g
u
n
n
ec
ess
ar
y
r
o
b
o
tic
m
o
v
em
en
ts
.
T
h
e
ti
m
e
-
b
o
u
n
d
n
atu
r
e
o
f
th
is
id
en
tific
atio
n
p
r
o
ce
s
s
f
u
r
th
er
en
h
a
n
ce
s
th
e
s
y
s
tem
'
s
r
esp
o
n
s
iv
en
ess
,
en
ab
lin
g
r
ea
l
-
tim
e
d
etec
tio
n
o
f
ir
r
eg
u
lar
ities
.
B
y
m
ain
tain
in
g
h
ig
h
p
r
ec
is
io
n
in
an
o
m
aly
d
et
ec
tio
n
wh
ile
o
p
er
atin
g
u
n
d
er
r
eso
u
r
ce
co
n
s
tr
ain
ts
,
th
e
ap
p
r
o
ac
h
b
ec
o
m
es
h
ig
h
ly
s
u
itab
le
f
o
r
a
p
p
licatio
n
s
wh
er
e
b
o
th
ac
cu
r
ac
y
an
d
o
p
er
atio
n
al
ef
f
icien
cy
ar
e
cr
itical,
s
u
ch
as
au
to
n
o
m
o
u
s
n
av
ig
atio
n
,
d
is
aster
r
esp
o
n
s
e,
an
d
e
n
v
ir
o
n
m
en
tal
m
o
n
ito
r
in
g
in
ch
allen
g
in
g
ter
r
ain
s
.
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21
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in
teg
er
s
.
0
is
p
o
s
itiv
e
wh
en
th
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s
p
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ic
d
ata
s
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es
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d
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th
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m
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m
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Su
p
p
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r
t
h
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tak
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m
,
1
is
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e
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d
its
p
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a
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d
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its
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r
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ied
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wn
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Fig
u
r
e
1
.
Fig
u
r
e
1
.
Stru
ctu
r
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o
f
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m
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tio
n
[
2
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T
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d
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m
o
v
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n
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s
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d
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r
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e
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t
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o
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co
s
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in
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u
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(
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Ass
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aid
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is
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n
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1
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C
o
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s
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er
th
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B
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m
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(
(
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Un
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m
ly
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u
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S a
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ip
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t
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or
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1
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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2
7
2
2
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8
6
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1
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Ma
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20
2
5
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1
9
-
30
22
Fro
m
(
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,
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T
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,
ad
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itio
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al
ly
co
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if
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in
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o
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m
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7
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,
a
m
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m
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ize
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r
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
Op
timiz
in
g
r
o
b
o
t a
n
o
m
a
ly
d
et
ec
tio
n
th
r
o
u
g
h
s
to
ch
a
s
tic
d
iffer
en
tia
l
a
p
p
r
o
xima
tio
n
…
(
B
r
a
n
esh
M.
P
illa
i
)
23
T
h
is
s
tu
d
y
ef
f
ec
tiv
ely
d
em
o
n
s
tr
ates
th
e
co
n
n
ec
tio
n
b
etwe
en
th
e
o
u
tco
m
es
an
d
ap
p
r
o
x
im
atio
n
s
o
b
tain
ed
f
r
o
m
th
e
p
r
o
v
id
ed
s
to
ch
asti
c
d
if
f
er
en
tial
eq
u
atio
n
an
d
th
eir
ass
o
ciatio
n
with
th
e
p
ath
wis
e
d
if
f
er
en
tial
eq
u
atio
n
,
as
r
ef
er
e
n
ce
d
in
s
o
u
r
ce
s
[
4
]
–
[
7
]
.
Mo
r
e
s
p
ec
if
ically
,
it
s
h
o
wca
s
es
h
o
w
th
e
s
o
lu
tio
n
C
f
o
r
th
e
p
ath
wis
e
d
if
f
er
en
tial
(
7
)
ca
n
b
e
in
f
er
r
ed
f
r
o
m
th
e
r
esp
o
n
s
e
A
co
r
r
esp
o
n
d
in
g
to
t
h
e
s
to
ch
asti
c
eq
u
atio
n
(
1
)
.
I
t'
s
cr
u
cial
to
em
p
h
asize
th
at
th
is
s
tatem
en
t
is
m
ad
e
u
n
d
er
th
e
ass
u
m
p
tio
n
th
at
eq
u
atio
n
6
p
o
s
s
ess
es
a
u
n
iq
u
e
g
lo
b
al
s
o
lu
tio
n
,
th
er
e
b
y
g
u
ar
a
n
teein
g
th
e
u
n
iq
u
en
ess
o
f
th
e
lo
ca
l so
l
u
tio
n
f
o
r
eq
u
at
io
n
1
.
T
h
is
p
ap
er
estab
lis
h
es
a
clea
r
lin
k
b
etwe
en
th
e
s
o
lu
tio
n
s
an
d
esti
m
atio
n
s
o
f
s
to
ch
asti
c
an
d
p
ath
wis
e
d
if
f
er
en
tial
e
q
u
atio
n
s
[
2
4
]
,
[
2
5
]
.
Ad
d
itio
n
ally
,
it
u
n
d
er
s
co
r
es
th
e
s
ig
n
if
ica
n
ce
o
f
u
n
iq
u
e
co
n
d
itio
n
s
,
p
ar
ticu
lar
ly
in
th
e
c
o
n
tex
t
o
f
(
6
)
an
d
its
im
p
licatio
n
s
f
o
r
eq
u
atio
n
1
.
L
et
L
r
e
p
r
esen
t
th
e
s
o
lu
tio
n
to
(
2
)
.
I
t
is
well
estab
lis
h
ed
th
at
th
e
s
o
lu
tio
n
is
in
v
er
tib
le
in
th
e
n
eig
h
b
o
r
h
o
o
d
N
o
f
(
0
,
0
,
0
).
(
,
,
)
∈
,
⟼
(
(
,
,
)
,
,
)
h
as th
e
o
p
p
o
s
ite.
K
s
tan
d
s
f
o
r
th
e
m
a
p
p
in
g
th
at
p
r
o
v
id
es
(
(
,
,
)
,
,
)
=
an
d
(
(
,
,
)
,
,
)
=
I
n
ar
ea
ar
o
u
n
d
u
s
,
th
e
m
atr
ix
eq
u
iv
alen
ce
h
o
ld
s
in
(
1
4
)
.
(
,
,
)
=
(
(
(
,
,
)
,
,
)
)
−
1
(
1
4
)
B
y
u
s
in
g
(
2
)
,
th
e
o
b
tain
(
1
5
)
a
n
d
(
1
6)
.
(
,
,
)
=
−
∑
(
,
,
)
=
0
(
,
)
(
1
5
)
(
,
,
)
=
−
∑
(
,
,
)
(
(
,
,
)
,
,
)
=
0
(
1
6
)
B
y
p
lu
g
g
in
g
th
e
p
ar
am
eter
s
o
f
th
e
+
1
-
v
alu
ed
p
r
o
ce
d
u
r
e
(
(
)
,
(
)
)
in
to
th
e
s
to
ch
asti
c
eq
u
atio
n
f
o
r
a
n
ex
p
r
ess
io
n
K
(
z,
y
,
t)
,
g
et
(
1
7
)
,
(
(
)
,
(
)
,
)
−
(
(
0
)
,
(
0
)
,
0
)
(
1
7
)
=
∑
∫
(
(
(
)
,
(
)
,
)
)
(
)
+
∫
(
(
(
)
,
(
)
,
)
)
(
)
0
0
=
0
+
∫
(
(
(
)
,
(
)
,
)
)
0
=
∑
∫
(
(
(
)
,
(
)
,
)
)
(
(
)
,
)
0
=
0
−
∑
∫
(
(
)
,
(
)
,
)
0
=
0
(
(
(
)
,
(
)
,
)
,
(
)
,
)
B
u
t
(
)
=
(
(
(
)
,
(
)
,
)
,
(
)
,
)
an
d
(
1
4
)
h
o
ld
s
,
h
en
ce
(
)
≔
(
(
)
,
(
)
,
)
(
1
8
)
s
atis
f
ies
th
e
p
ath
-
wis
e
(
6
)
o
n
an
in
d
i
v
id
u
al
s
ca
le.
Similar
ly
,
it
m
ay
estab
lis
h
th
at
(
)
≔
(
(
)
,
(
)
,
)
s
atis
f
ies
th
e
p
ath
-
wis
e
(
1
1
)
o
n
a
p
ar
ticu
lar
s
ca
le.
L
et
B
r
a
p
p
r
o
x
im
ate
a
p
r
o
p
o
r
tio
n
ate
B
r
o
wn
ian
m
o
tio
n
B
z
.
L
et
,
:
∗
(
0
,
)
b
e
p
r
e
d
eter
m
in
e
d
in
(
1
9
)
an
d
(
2
0
)
,
(
)
=
0
+
∫
(
(
)
,
)
+
∫
(
(
)
,
)
(
)
.
0
0
(
1
9
)
(
)
=
0
+
∫
(
(
)
,
)
+
∫
(
(
)
,
)
(
)
.
0
0
(
2
0
)
w
h
er
e
∈
ℤ
,
ac
ce
p
ts
,
with
h
ig
h
p
r
o
b
ab
ilit
y
,
a
s
in
g
le
lo
ca
l
s
o
lu
ti
o
n
o
n
th
e
s
am
e
in
ter
v
al
(
t
1
,
t
2
)
(
wh
er
e
t
0
is
o
u
ts
id
e
o
f
Z
b
u
t
s
till
p
ar
t
o
f
th
e
in
ter
v
al)
.
I
n
ad
d
itio
n
,
th
e
f
o
llo
win
g
ap
p
r
o
x
im
ate
r
esu
lt
h
as
b
ee
n
o
b
tain
ed
in
(
2
1
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
1
9
-
30
24
.
(
l
im
→
∞
s
up
‖
(
)
−
(
)
‖
=
0
)
=
1
(
2
1
)
P
ro
blem
2
Fin
d
th
e
n
ea
r
er
l
o
ca
tio
n
f
r
o
m
th
e
s
o
u
r
ce
p
o
in
t
wh
er
e
th
e
d
ata
s
tr
ea
m
W
b
eg
in
s
an
d
d
ef
in
e
o
p
tim
al
p
ath
f
o
r
th
e
d
at
a
s
tr
ea
m
W
m
o
v
es f
r
o
m
o
n
e
p
o
in
t to
an
o
th
er
p
o
in
t.
P
ro
o
f
(
a
)
T
h
e
an
ticip
ated
q
u
a
n
tity
o
f
n
ea
r
-
o
p
tim
al
lo
ca
tio
n
s
f
o
r
an
y
b
is
co
n
s
tr
ain
ed
in
(
2
2
)
,
ℚ
[
(
)
]
≤
6
2
2
(
2
2
)
I
t
f
ix
es
th
e
v
alu
e
o
f
≜
(
1
2
)
.
T
h
e
s
p
ee
d
o
f
g
r
o
wth
o
f
(
)
,
th
e
q
u
an
tity
o
f
-
n
ea
r
-
o
p
tim
al
lo
ca
tio
n
s
in
[
0
,
1
]
o
f
th
e
f
o
r
m
/
2
,
is
m
ea
s
u
r
ed
b
y
th
e
n
ea
r
-
o
p
tim
ality
d
i
m
en
s
io
n
in
d
im
en
s
io
n
o
n
e
wit
h
th
e
p
s
eu
d
o
-
d
is
tan
ce
(
,
)
=
(
|
−
|
)
.
I
t
s
h
o
ws
th
at,
in
g
e
n
er
al,
th
is
q
u
an
tity
g
r
o
ws
at
a
co
n
s
tan
t
r
ate
r
eg
a
r
d
in
g
b
.
T
h
is
im
p
lies
th
at
th
er
e
e
x
is
ts
a
m
etr
ic
w
h
er
e
t
h
e
B
r
o
wn
ia
n
is
L
ip
s
ch
itz
with
lik
elih
o
o
d
at
least
1
−
an
d
h
as
a
n
ea
r
-
o
p
tim
ality
asp
ec
t =
0
w
ith
=
(
(
1
/
)
)
.
T
h
e
(
(
1
/
)
)
ter
m
,
o
r
ig
in
atin
g
f
r
o
m
th
e
s
tan
d
ar
d
DOO
er
r
o
r
f
o
r
d
eter
m
in
is
tic
f
u
n
ctio
n
o
p
tim
is
atio
n
,
an
d
a
d
if
f
e
r
en
t
(
(
1
/
)
)
ter
m
,
o
r
ig
in
atin
g
f
r
o
m
t
h
e
n
ee
d
to
ad
ju
s
t
o
u
r
p
s
eu
d
o
-
d
i
s
tan
ce
ℒ
s
u
ch
th
at
th
e
B
r
o
wn
ian
is
ℒ
-
L
ip
s
ch
itz
with
lik
elih
o
o
d
1
-
,
to
g
eth
e
r
r
e
p
r
esen
t
th
e
f
in
ali
s
ed
s
tu
d
y
d
if
f
icu
lty
b
o
u
n
d
.
C
o
m
b
in
i
n
g
t
h
ese
two
b
o
u
n
d
s
y
ield
s
an
u
p
p
er
lim
it o
n
s
am
p
le
co
m
p
lex
ity
o
f
(
2
(
1
/
)
)
.
P
ro
o
f
(
b)
A
B
r
o
wn
ian
m
o
ti
o
n
wh
o
s
e
o
p
tim
u
m
O
is
r
ea
ch
ed
f
o
r
th
e
in
itial
tim
e
at
th
e
lo
ca
tio
n
d
escr
ib
ed
as is
d
en
o
ted
b
y
U
a
n
d
th
e
B
r
o
wn
ian
m
ea
n
d
er
0
+
ca
n
b
e
d
ef
in
e
d
as in
(
2
3
)
,
0
+
≜
−
(
1
−
.
1
)
√
1
(
2
3
)
1
+
≜
−
(
1
+
(
1
−
1
)
)
√
1
−
1
(
2
4
)
T
h
en
th
e
th
e
o
r
em
1
d
ec
lar
es t
h
at
+
≦
0
+
≦
1
+
an
d
t
1
ch
an
g
es r
eg
ar
d
less
o
f
b
o
t
h
0
+
1
+
.
Fo
r
ea
ch
p
o
s
itiv
e
in
teg
er
,
it
e
s
tab
lis
h
es
a
m
ax
im
u
m
co
n
s
tr
ain
t
o
n
th
e
p
r
e
d
icted
am
o
u
n
t
o
f
-
n
ea
r
-
o
p
tim
al
p
o
s
itio
n
s
b
>0
an
d
a
n
y
v
alu
es o
f
>
0
.
ℚ
[
(
)
]
=
ℚ
[
∑
1
{
(
2
)
>
−
}
2
=
0
]
=
∑
ℚ
[
1
{
(
2
)
>
−
}
]
2
=
0
=
∑
ℚ
[
1
{
{
(
2
)
>
−
∩
2
≤
1
}
∪
{
(
2
)
>
−
∩
2
>
1
}
}
]
2
=
0
=
∑
ℚ
[
1
{
0
+
(
1
−
1
2
)
<
√
1
∩
2
≤
1
}
]
2
=
0
+
∑
ℚ
[
1
{
1
+
(
2
–
1
1
−
1
)
<
√
1
−
1
∩
2
>
1
}
]
2
=
0
Sin
ce
t1
ch
an
g
es
r
eg
ar
d
less
o
f
0
+
1
+
,
u
tili
zin
g
t
h
e
ab
o
v
e
e
q
u
atio
n
with
C
=
(
0
+
,
1
+
)
,
D=
t1
a
n
d
f
u
n
ctio
n
in
(
2
5
)
,
:
(
0
,
1
)
,
→
∑
(
[
1
{
0
(
1
−
1
2
)
<
√
∩
2
≤
}
]
+
1
{
1
(
2
–
1
1
−
)
<
√
1
−
∩
2
>
}
)
2
=
0
(
2
5
)
it h
as su
f
f
icien
t e
v
id
en
ce
t
o
ass
er
t th
at.
ℚ
[
(
)
]
=
ℚ
[
(
,
)
]
≤
s
up
ℚ
[
(
,
)
]
≤
s
u
p
{
∑
ℚ
[
1
{
0
+
(
1
−
2
)
<
√
∩
2
≤
}
]
2
=
0
}
+
s
u
p
{
∑
ℚ
[
1
{
1
+
(
2
–
1
−
)
<
√
1
−
∩
2
>
}
]
2
=
0
}
=
s
up
{
∑
ℝ
{
0
+
(
1
−
2
)
<
√
}
⌊
2
⌋
=
0
}
+
s
up
{
∑
ℝ
{
1
+
(
2
–
1
−
)
<
√
1
−
}
2
=
⌊
2
⌋
}
=
2
s
up
{
∑
ℝ
{
0
+
(
1
−
2
)
<
√
}
⌊
2
⌋
=
0
}
=
2
s
up
{
1
+
2
+
3
+
4
}
(
2
6
)
w
h
er
e
(
2
6
)
is
ex
p
an
d
ed
as
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
Op
timiz
in
g
r
o
b
o
t a
n
o
m
a
ly
d
et
ec
tio
n
th
r
o
u
g
h
s
to
ch
a
s
tic
d
iffer
en
tia
l
a
p
p
r
o
xima
tio
n
…
(
B
r
a
n
esh
M.
P
illa
i
)
25
1
=
∑
ℝ
[
0
+
(
1
−
2
)
<
√
]
⌊
2
2
⌋
=
0
,
2
=
∑
ℝ
[
0
+
(
1
−
2
)
<
√
]
⌊
2
2
⌋
=
⌈
2
2
⌉
,
3
=
∑
ℝ
[
0
+
(
1
−
2
)
<
√
]
,
⌊
2
⌋
−
⌈
2
2
⌉
=
⌈
2
2
⌉
4
=
∑
ℝ
[
0
+
(
1
−
2
)
<
√
]
⌊
2
⌋
=
⌊
2
⌋
−
⌈
2
2
⌉
.
Giv
en
th
at
1
is
th
e
h
ig
h
est
p
o
s
s
ib
le
lik
elih
o
o
d
,
it
m
a
y
s
im
p
l
y
p
lace
a
lim
it
o
n
1
4
as
2
2
,
to
o
b
tain
th
at
1
+
4
≤
2
(
2
2
)
.
B
y
ac
cu
m
u
latin
g
a
cr
o
s
s
th
e
B
r
o
wn
ian
m
ea
n
d
er
d
is
tr
ib
u
tio
n
p
ar
am
eter
s
,
it c
an
n
o
w
p
lace
u
p
p
er
a
n
d
lo
we
r
b
o
u
n
d
s
o
n
th
e
r
est o
f
t
h
e
p
o
s
s
ib
ilit
ies o
cc
u
r
r
in
g
in
t
h
e
af
o
r
em
en
tio
n
ed
f
o
r
m
u
la.
ℝ
[
0
+
(
)
<
]
=
2
√
2
∫
e
x
p
(
−
2
2
)
√
∗
2
0
∫
e
x
p
(
−
2
2
(
1
−
)
)
√
(
1
−
)
∗
2
0
≤
2
√
(
1
−
)
(
.
2
)
∫
2
0
e
x
p
(
−
2
2
)
≤
2
3
3
√
(
1
−
)
(
.
2
)
≤
2
3
3
(
1
−
)
√
(
1
−
)
(
.
2
)
=
2
3
√
2
(
√
(
1
−
)
)
3
T
h
e
lim
it is
th
en
ap
p
lied
t
o
th
e
s
u
m
o
f
2
3
.
2
+
3
=
∑
ℝ
[
0
+
(
1
−
2
)
<
√
]
⌊
2
2
⌋
=
⌈
2
2
⌉
+
∑
ℝ
[
0
+
(
1
−
2
)
<
√
]
⌊
2
⌋
−
⌈
2
2
⌉
=
⌈
2
2
⌉
≤
∑
2
3
√
2
(
√
√
(
1
−
2
√
2
)
)
3
+
⌊
2
2
⌋
=
⌈
2
2
⌉
∑
2
3
√
2
(
√
√
(
1
−
2
√
2
)
)
3
⌊
2
⌋
−
⌈
2
2
⌉
=
⌈
2
2
⌉
≤
∑
1
6
√
(
√
√
√
2
)
3
+
⌊
2
2
⌋
=
⌈
2
2
⌉
∑
1
6
√
(
√
√
1
−
2
)
3
≤
⌊
2
⌋
−
⌈
2
2
⌉
=
⌈
2
2
⌉
∑
1
6
√
(
√
√
√
2
)
3
+
⌊
2
2
⌋
=
⌈
2
2
⌉
∑
1
6
√
(
√
√
⌊
2
⌋
2
+
2
)
3
⌊
2
⌋
−
⌈
2
2
⌉
=
⌈
2
2
⌉
Swap
p
in
g
o
u
t t
h
e
in
d
e
x
in
g
as
=
−
′
+
⌊
2
⌋
,
d
is
co
v
er
th
e
f
o
llo
win
g
,
2
+
3
≤
(
2
2
)
3
/
2
6
√
(
∑
1
3
/
2
⌊
2
2
⌋
=
⌈
2
2
⌉
+
∑
1
3
/
2
⌊
2
⌋
−
⌈
2
2
⌉
=
⌈
2
2
⌉
)
≤
(
2
2
)
3
2
3
√
∑
1
3
2
∝
=
⌈
2
2
⌉
≤
(
2
2
)
3
2
3
√
3
√
⌈
2
2
⌉
≤
1
√
2
2
≤
2
2
,
wh
er
e
it wa
s
u
tili
ze
d
f
o
r
a
n
y
th
in
g
in
th
e
p
r
ev
io
u
s
r
o
w
0
>
0
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
1
9
-
30
26
∑
1
3
2
∝
=
0
≤
1
0
3
2
+
∑
∫
1
3
2
=
−
1
∝
=
0
+
1
1
0
3
2
+
∫
1
3
2
=
∝
0
1
0
3
2
+
2
√
0
≤
3
√
0
At
lo
n
g
last
,
th
e
o
b
tain
e
d
(
2
7
)
,
∀
,
1
+
2
+
3
+
4
≤
3
2
2
(
2
7
)
Hen
ce
,
ℚ
[
(
)
]
≤
6
2
2
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
I
n
th
e
MA
T
L
AB
im
p
lem
en
tatio
n
,
a
s
er
ies
o
f
n
u
m
e
r
ical
test
s
wer
e
co
n
d
u
cted
to
ass
es
s
th
e
p
er
f
o
r
m
an
ce
o
f
a
tech
n
i
q
u
e
f
o
r
ev
alu
atin
g
th
e
m
o
v
em
e
n
t
co
s
t
o
f
d
ata
s
tr
ea
m
s
.
T
h
i
s
p
r
o
ce
s
s
in
v
o
lv
ed
ass
ig
n
in
g
s
p
ec
if
ic
co
s
t
v
alu
es
to
th
e
m
o
v
em
en
t
o
f
d
ata
s
tr
ea
m
s
.
On
e
k
ey
p
ar
am
eter
,
d
e
n
o
t
ed
as
̂
,
was
s
et
to
0
,
s
im
p
lify
in
g
th
e
ca
lcu
latio
n
b
y
n
eg
atin
g
th
e
co
n
tr
i
b
u
tio
n
o
f
λ
to
th
e
co
s
t
f
u
n
ctio
n
.
T
h
e
s
y
s
tem
u
tili
ze
d
a
p
r
o
b
a
b
ilit
y
d
is
tr
ib
u
tio
n
wh
er
e
π
=
0
an
d
f
o
llo
wed
a
s
tan
d
ar
d
n
o
r
m
al
d
is
tr
ib
u
tio
n
o
f
n
(
0
,
1
)
,
wh
ich
was
ess
en
tial
f
o
r
d
etec
tin
g
d
ata
s
tr
ea
m
m
o
v
e
m
en
ts
with
in
a
d
ef
i
n
ed
r
a
n
g
e.
T
h
e
e
x
p
er
im
e
n
t
ai
m
ed
to
e
v
alu
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
b
y
s
im
u
latin
g
a
s
er
i
es
o
f
d
ata
s
tr
ea
m
s
an
d
m
ea
s
u
r
in
g
th
e
ass
o
ciate
d
m
o
v
em
en
t
co
s
ts
.
Ho
wev
er
,
a
n
o
tab
le
lim
itatio
n
a
r
is
es
wh
en
λ
is
s
et
to
0
,
as
it
b
e
co
m
es
im
p
o
s
s
ib
le
to
ca
lcu
late
th
e
o
p
tim
al
m
o
v
em
en
t
co
s
t
u
n
d
er
s
u
c
h
co
n
d
itio
n
s
.
Desp
ite
th
is
,
th
e
ex
p
er
i
m
en
t
p
r
o
ce
ed
ed
b
y
g
en
er
atin
g
tar
g
et
d
ata
s
tr
ea
m
v
alu
es
with
a
p
r
o
b
ab
ilit
y
o
f
0
.
1
an
d
f
o
llo
win
g
a
n
o
r
m
al
d
is
tr
ib
u
tio
n
o
f
m
ea
n
0
an
d
v
ar
ian
ce
1
,
n
(
0
,
1
)
.
T
h
is
p
r
o
b
ab
ilis
tic
g
en
e
r
atio
n
allo
we
d
f
o
r
a
co
n
t
r
o
lled
y
et
b
asic
e
n
v
ir
o
n
m
e
n
t
in
wh
ich
th
e
tech
n
iq
u
e
co
u
ld
b
e
ev
al
u
ated
.
Fo
r
th
e
s
im
u
latio
n
,
t
h
e
s
tan
d
ar
d
d
ata
s
tr
ea
m
was
m
o
d
eled
u
s
in
g
a
d
is
tr
ib
u
tio
n
with
a
m
ea
n
o
f
0
an
d
a
h
ig
h
er
v
a
r
ian
ce
o
f
1
.
7
,
allo
win
g
th
e
s
y
s
tem
to
co
m
p
ar
e
th
e
p
er
f
o
r
m
an
ce
b
etwe
en
th
e
g
en
er
ated
tar
g
et
d
ata
s
tr
ea
m
an
d
th
e
s
tan
d
ar
d
o
n
e.
T
h
is
d
if
f
er
e
n
ce
in
d
is
tr
ib
u
tio
n
en
a
b
led
th
e
m
eth
o
d
to
ass
ess
h
o
w
well
it
co
u
ld
d
etec
t
an
d
ev
alu
ate
m
o
v
em
en
ts
ac
r
o
s
s
v
ar
ied
d
ata
p
atter
n
s
.
Acc
o
r
d
in
g
to
th
e
r
esu
lts
,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
p
r
o
d
u
ce
d
a
1
5
%
p
r
o
b
ab
ilit
y
f
o
r
d
etec
tin
g
t
h
e
v
alu
es
0
an
d
1
,
m
ar
k
in
g
th
ese
as k
ey
p
o
in
ts
o
f
in
ter
est
with
in
th
e
d
ata
s
tr
ea
m
'
s
m
o
v
em
en
t.
Desp
ite
th
e
in
s
ig
h
ts
g
ain
ed
,
t
h
er
e
wer
e
o
b
s
er
v
a
b
le
s
h
o
r
tco
m
in
g
s
.
Sp
ec
if
ically
,
th
e
m
o
v
e
m
en
t
co
s
t
f
o
r
0
r
ea
ch
ed
its
m
ax
im
u
m
,
al
o
n
g
with
its
ass
o
ciate
d
er
r
o
r
r
ate.
T
h
is
in
d
icate
s
th
at
wh
ile
th
e
m
eth
o
d
m
ay
o
f
f
er
s
o
m
e
b
en
e
f
its
,
s
u
ch
as
d
etec
tin
g
m
o
v
em
en
ts
in
d
ata
s
tr
ea
m
s
,
its
ef
f
o
r
ts
to
p
r
o
v
id
e
o
p
tim
al
r
esu
lts
u
n
d
er
ce
r
tain
co
n
d
itio
n
s
,
p
a
r
ticu
lar
l
y
wh
en
λ
is
s
et
to
0
.
T
o
en
h
an
ce
th
e
ex
p
e
r
im
en
t,
it
wo
u
ld
b
e
b
en
ef
icial
to
in
tr
o
d
u
ce
a
m
o
r
e
co
m
p
lex
s
ce
n
ar
io
with
v
ar
ied
p
ar
am
eter
v
alu
es
an
d
co
n
d
itio
n
s
to
f
u
lly
ass
ess
th
e
tech
n
iq
u
e'
s
ef
f
ec
tiv
en
ess
an
d
lim
itatio
n
s
.
Fig
u
r
e
2
p
r
esen
ts
a
co
m
p
a
r
ativ
e
v
is
u
aliza
tio
n
o
f
th
r
ee
d
is
tin
ct
d
ata
s
am
p
les,
lab
eled
as
s
am
p
le
1
,
s
am
p
le
2
,
an
d
s
am
p
le
3
,
ea
c
h
d
elin
ea
ted
b
y
a
u
n
i
q
u
e
c
o
lo
r
—
b
lack
,
r
e
d
,
a
n
d
b
lu
e,
r
esp
ec
tiv
el
y
.
Sam
p
le
1
ex
h
ib
its
a
s
m
all
KL
d
iv
e
r
g
en
ce
(
0
|
|
1
)
an
d
(
1
|
|
0
)
,
in
d
icatin
g
a
p
r
ed
icted
o
v
er
s
h
o
o
t
ap
p
r
o
ac
h
in
g
ze
r
o
.
Sam
p
le
2
h
as
a
s
m
a
ll
er
r
o
r
p
r
o
p
o
r
tio
n
wh
er
e
(
=
0
)
,
an
d
f
o
r
a
lar
g
er
p
r
o
p
o
r
tio
n
,
it
s
h
o
ws
a
l
ar
g
e
v
alu
e,
d
en
o
ted
b
y
(
1
-
β)/α
,
wh
ich
lead
s
to
d
ata
s
tr
ea
m
ter
m
in
atio
n
.
I
n
th
e
ca
s
e
o
f
s
am
p
le
3
,
wh
ich
h
as
a
lar
g
e
v
alu
e,
t
h
e
p
r
im
a
r
y
g
o
al
o
f
th
e
a
n
aly
s
is
is
to
r
ed
u
ce
th
e
n
u
m
b
er
o
f
alg
o
r
ith
m
ch
a
n
g
es b
ef
o
r
e
c
o
r
r
ec
tly
id
en
tify
in
g
th
e
tar
g
et
d
at
a
s
tr
ea
m
.
Fig
u
r
e
2
.
Sam
p
les with
KL
d
i
v
er
g
en
ce
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
Op
timiz
in
g
r
o
b
o
t a
n
o
m
a
ly
d
et
ec
tio
n
th
r
o
u
g
h
s
to
ch
a
s
tic
d
iffer
en
tia
l
a
p
p
r
o
xima
tio
n
…
(
B
r
a
n
esh
M.
P
illa
i
)
27
All
th
r
ee
s
am
p
les
f
o
llo
w
a
s
im
ilar
tr
en
d
with
th
eir
o
wn
p
e
cu
liar
ch
a
r
ac
ter
is
tics
.
Sam
p
le
1
(
b
lack
)
ex
h
ib
its
a
s
tead
y
,
alm
o
s
t
lin
ea
r
d
ec
lin
e
u
n
til
it
f
latten
s
o
u
t
t
o
war
d
s
th
e
e
n
d
o
f
th
e
d
o
m
ain
.
Sam
p
le
2
(
r
e
d
)
is
ch
ar
ac
ter
ized
b
y
a
s
ig
n
if
ica
n
t
o
s
cillatio
n
b
ef
o
r
e
s
h
a
r
p
l
y
d
r
o
p
p
in
g
,
i
n
d
icatin
g
a
v
a
r
iab
le
r
esp
o
n
s
e
o
r
m
ea
s
u
r
em
en
t
b
ef
o
r
e
r
ea
ch
in
g
a
s
im
ilar
lev
el
a
s
s
am
p
le
1
to
war
d
s
th
e
en
d
.
Sam
p
le
3
(
b
lu
e)
m
ir
r
o
r
s
th
e
o
s
cillatio
n
s
ee
n
in
s
am
p
le
2
,
b
u
t
with
a
less
p
r
o
n
o
u
n
ce
d
in
itial
d
r
o
p
an
d
a
d
ee
p
er
f
i
n
al
d
escen
t.
T
h
is
co
m
p
ar
is
o
n
allo
ws
f
o
r
an
ea
s
y
ass
es
s
m
en
t
o
f
th
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s
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ilar
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d
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r
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les
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Fig
u
r
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3
p
r
esen
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a
tim
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ies
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r
ap
p
r
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atio
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ata
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ics
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atin
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4
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ates
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Fig
u
r
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5
s
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en
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u
m
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ts
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4
0
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d
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g
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e
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ip
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ile,
Fig
u
r
e
6
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n
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asts
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3
.
Sto
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r
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4
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ath
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ased
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RE
F
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NC
E
S
[
1
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R
.
A
.
A
r
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a
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a
b
e
e
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,
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E.
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h
me
d
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.
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mr
a
n
,
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d
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:
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.
[
2
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R
.
H
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.
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n
,
Y
.
Q
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o
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.
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a
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g
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P
.
Z
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si
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n
Evaluation Warning : The document was created with Spire.PDF for Python.