Talk - HKU

!
"
"
###
&'
"
"
(
)
(
*
(
&
*
+
#
$
%
1
(
-
"
)
.
#
#
#
&
/
0
(
$
( #
,
2
$
#
Recorded Temperature
30
Current Temperature
x1
y0
20
)3 4 3!)
5 4 ) 5!
6
7
10
x0
y1
0
F
$
x
y
1
2
( #
9
2
$
#
&'
Recorded Temperature
Bound for Current Temperature
30
y0
20
)
x0
10
0
x
F
y
$
( #
9
8
2
$
#
&'
Recorded Temperature
'
Bound for Current Temperature
30
)
20
y0
10
6
x0
0
;
F
$
x
y
:
3
$
=
#
!
#
5
#
%
9
7
#
)!<3>
!,3>
7
0
/
#
#
$
<
6
@#
#
6
D
7
A6 BBC
*
# A
3,C
7
7
*
'
D
7
6
*
AD63%C
#
7
$
?
4
D
(
7
9
(
7
7
)
$
B
2
-
(
*
/
-
*
- /0
/
0
0
- /
0
$
55
5
E
2
fi(x,t) – uncertainty pdf
Ti.a(t)
[li(t)
9)
ui(t)]
Uncertainty Interval
Ui(t)
!
)
*
A6 BBC
$
5%
$
5
F
#
!
7
/A
"
!
/7
/G
%
C
0
*
0
H3I
0
(
#
7
$
!#
*
7
#
!
*
7
$
5,
6
$
&
F &
#
9
$
#
9$
6
); 6
#
(
&
( $
$ 2 $ 2 )$
6
,3@;
9FF$ 92 $ 92 )$
6
;
6
53@
;
7
7
$
92 $
+ 0
9
51
5!=
*
*
-
9
/-
0 #
/
&
+
0
$
58
7
92 $
%!
=
T4
T3
T2
T1
0
0
J
K
#
-5 -% -, -1
*
#
$
5:
9
-%
T4
T3
T2
0
l2
l1
l3
l4
l5
x x+dx
=-%
l3
l2
%
∈A % ,C -%
!
f 2 ( x) • (1 − P1 ( x))dx +
l3
#
l4
l3
l2
f 2 ( x) • ∏ (1 − Pk ( x))dx +
k =1, 3
$
l5
l4
f 2 ( x) • (1 − P1 ( x))dx
f 2 ( x) •
∏ (1 − P ( x))dx
k =1, 3, 4
k
5<
8
$
F
# L
7
L
"Which sensor, among 4, has the minimum reading?"
100%
(assuming only 1 answer exists, if values are known precisely)
100%
T2
T3
Sensors
T4
25%
25%
0%
T1
50%
25%
0%
0%
0%
25%
75%
25%
Probability
Probability
75%
50%
25%
100%
T1
T2
T3
Sensors
T4
0%
7
$
5?
( # $
$
"Is reading of sensor i in range [l,u] ?"
7
L L L L#
7
0
0
0
#
#
#
l
533>
9$
b)
M B8>! %
M 8>! %/B8>
M 83>!
%/
Score =
u
a)
c)
A
0
C0
| pi − 0.5 |
0.5
Score _ of _ an _ ERQ =
$
1
| pi − 0.5 |
| R | i∈R 0.5
5B
9
$
9& (
$
/5"
%0
"Which sensor, among n, has the minimum reading?"
MG
/-
0I
G
/-5 ,3>0 /-% 13>0 /-, ,3>0I
'
#
D
' M A53 %3C
7
2
2 ) FF
*
9$
/
0
#
"
$
$
9& (
N/O0
%3
$
O /O5 P O #
n
H (X ) =
i =1
/
/
D
p ( X i ) log 2
/%"
%0
/O50 P
/O 00
1
p( X i )
∃ ! /O 0 M 5
/
00
OQ
%
30
7
!
Score _ of _ Entity _ Aggr _ Query = − H ( R )× | B |
/
#
0
#/
'
0
$
%5
10
&(
$
"What is the minimum value among n sensors?"
!
G /)0 !) ∈ A
A53 %3C
CI
/)0 R A53 %3C
u
H ( X ) = − p ( x ) log2 p ( x )dx
l
2
#
O#
Score _ of _ Value _ Aggr _ Query = − H ( X )
$
=
( # $
E
-
%%
7
#
7
7
$
%,
11
E
/
E S
0
T
.
/
. S T
2 2 T
2)
T
0
- #
#
)
$
9)
#
%1
!
5
5333
#
#
L
2 L7
$
%8
12
9)
2
!
3
3
3
#
3
$
R
/λ0
533
$
9
'
#
%:
92 $
0
-0.5
-1
Score
-1.5
Glb_RR
Loc_RR
MinMin
MaxUnc
-2
-2.5
-3
-3.5
-4
-4.5
200
250
300
350
Bandwidth
$
400
450
500
%<
13
9
'
#
-
0.9
0.8
Glb_RR
Loc_RR
MinMin
MaxUnc
0.7
Time (sec)
0.6
0.5
0.4
0.3
0.2
0.1
0
250
300
350
400
450
500
Bandwidth
$
6
%?
!
0
7
0
0
0
)
7
7
0
7
7
7
0
#
#
7
$
%B
14
=
&"
'(
###
"
"
U
)%
( *
###
U
"
R
(*
###
U
"
"
$
92 $
,3
,!9
T4
T3
T2
T1
x
0
x x+dx
. %/)0
-%
=-% ∈ A) )V )C -%
#
%/)0 W/5& 5/)00 )
/)0
$
-5
H -%
,5
15
+)
0)
,
- ../D 6
$
(
-
2
=
</,0 5BBB
,
'% /
$
*
5B =
999
=
= 9=
,-
D
X6
#
'
&
=
(2 =
E2D %33%
$
9
'
,%
#
1.4
1.2
1
Uncertainty
)
%33,
/ D
+
Glb_RR
Loc_RR
MinMin
MaxUnc
MinExpEntr
0.8
0.6
0.4
0.2
0
200
250
300
350
400
450
500
Bandwidth
$
,,
16