!

! "#$%&'(! )* +



2 !

2 #

2 ;

!$ !%

#

& .2

!% &

& *

#

! $

(

! − )

*

"

!

8 8

*

*

2

* * 0

/

1 2 3 0 /1 45! 67 + * 2 8 8 * * 0 /1 2 * 49$:7 + 2 3 8 * $ 2 2 $ 2 8 8 * 2 * 2 * * ! 2 8 8 * $ $2 * * 0 * 8 ! 2 8 8 2 * 2 * $ 2 2 2 2 0 /1 2 * 2 2 2 8 * 2 * * * * ! * 88 * ! 2 2 8 * 8

2 88 * ! * ! 0 /1 2 * * / $ 2 * * ! * 8 1 ! 8 ; ! 0 " .0 " 2 /2 ! * 8 2 < $ 0 " <0 " 2 * 2 * $ 0 " 0" 28 8 2 8 ! * < $ " <0 "

3 4&$5%7 -

,- ./ "- ., 0

+ *

8

! "

'

* *

22 2 +

* 3

8 2 0 /1 2 8 ) 2 ) 2 2

*

22 $8 4557! $ * 0 8 ! 22 8 ; 22 * 8 <0 " # * ! ! ; 2 22 4567! 8 8 <0 " * 0 !* 8 <0 " 2 ! * 2 * = ! $ 2 * * ! <0 " * 8 ; 22 * <0 " ! 2 <0 " ; 2 2 4&$5>7! 8 2 88 8 ? ! 32 ! * ! * 2 2 * ; ) ! 2 $8 2 + 22 2 2 45%7 ; 8 2 * 2 @ 22 8

+

*

2

8

8 ;

*

; 2 + ;

8 2

$8

* 2

22

22

+

8

3

!

+ !5

2

*+ 2 2

*!

2

8

8 2

* 5≤*≤1

*

* 3 2

* !

!5 ≥

-

! 6 ≥D ≥

!1

5

+ <0 "

2

+

+ 2

-

2 2

2 $8

45%7

2 3

+ 2 +

+ 22 45%7 8 8 22 3

8 * 2 8 *

;

* F

+ 2 2 2

3

"

!F BΣ

$ !

8 8

8

* 8

*

8

) ! 45%7

8 * 2 2

+ 8 *

$

; 22

*

-

2

+

* 0 /1 2 ! 2 2 * 8

2

! 5≤ ≤ ,! 5 ≤ F! 2

*

+

*

)

2

8

2$

5 !F

"

2

*

F

A <

!

A

) ! !* !

<0 "

' " 45%7!

;

1 3

+

* !

9

8F 1

Σ Σ

B5 FB5

2

≤1 -

B

,

A 2

6

0 /1 2 * !* 3 ,×1 *

3

3



!F

*

2 *

2 88 3

22 2 8 ! 2 2 8$ 2 ) 2 3 2 2 2 22 2 2 22

!F

BF

1

-

"

!

!F B Σ

!

8

! +

BF

+

2

;

!

-

8

+

"

8F

8 !F ×

!F

(

* ,

1

Σ Σ

!F B-

B5 FB5

? .= 1 )- - 1 ,, 1

! F ≥ ! F G5 * ! F ∈ C'! 5E

* B, 8 0 /1 2 * B, 8 <0 " ; 8 2 * B 3C15! 16! D ! 1,E B8 8 <0 " ! * 5 ≤ - < ,1 B + 3 ,×1! * !F * ! 5 ≤ ≤ ,! 5 ≤ F ≤ 1 2 F <0 " 8 +

1 -

#

+ 1 3 45%7 45%7! 3 , × 1G5 ! * * ! 5 ≤ ≤ ,! ' ≤ F ≤ 1 2 F <0 " 8 + * + 3

* H5I , *!

!

+

3 !F = !

! 5≤ ≤ ,! 5≤ F ≤ 1$5

;

* 3

!

2

8 32 22 8 * * $ 2 2 * * ! + $ * * 2 8 ; 22 * ! F! ! D ! * !

J

F!

F

8 H5I

*

!

* $

2 2 + 2 8 + 8 8

2

+

J

!

)

3 ! 3!

3!

D

>

*

!

8

*

* *

? .?.) /

!* 5! 6! D !

5!

5 ! 5!

6! 5 !

! 6 !D! 6! 6 ! D !

J !

F! J

F

!

*

22

0 /1 2

* ;

+ 8 8

* + - 8 5 8

2

3 8

45%7 - 8 5 2 0 /1 2 * > ; 8 * - 8 5 - 8 5! 15B 16B 19 B 1> B 9 1( B6 ( *! ' ) !1B 3 C15! 16! 19! 1(! 1>E B 9 2 2 $ ! 2 + 3 - 8 6 * 5 - 8 5 ' 5 - 8 6 ! !5 B !6 B !9 B ! 8 -BK

!5 G !6 G !9 8 2

6

5

45%7! 8 +

* 6! 5 = ! * (! 5 ! !

' (( ' (K ' >6 ' (( ' %(

' (5 ' 9: ' (( ' >5 ' 6>

8 M M - @ " <0 " <0 " " <0 " 2 H I H " <0 "I 8 <0 " 2 " <0 " 2 H

- 8 *

8

*

5! 5 J

22

2 3 ' 59 ' 59 ' '9 ' 5> ' 'K

(! 5 ! -

, , -

K

6 - = 6 + 1 3 2 2 - 8 5 ' >% ' >9 ' (: ' %% ' 9%

' 5> ' 5> ' '( ' 5> ' 55

!

- 1 ".1?

*

O -P

M M

8

! *

2 I

$ 2 3 8 , B 2 B1 B- , 8 B" 0 2 3

* 8 * 2

8

2 - @ 3

P) )

-

2 *

N M M) ! 5 ! D!

*

H !

* ! 1$5 !

I ; + !1

B . ,1 × 3 !

,1

+ ;

' '6 ' '6 ' '5 ' '' ' '(

,

8 2 2 3

8

(

45%7!

-

5!

6! 5 %

' '6 ' '6 ' '5 ' '' ' '(

A

= !*

%!

2 2 5

- = 5 + 1

* 6 3! * ' 5>

!* !

0

K

2 8

M MN

2

5

5

!9 !

- 8 6

< $ *

!6 G !9 !

*

H I 3 - <0 " * ! " ) ← 8 2 * !5< " ) ≤ ,1 " <0 " ← 8 <0 " 2 " ) * ! 5 ≤ " <0 " ≤ - ) 5 ≤ - < ,1! 8 5 ≤ " <0 " < ,1 22 ! " ) > " <0 " ← L 2 + 2 2 H " ) I 3 2 2 ! 2 H I + ←) H I

2

! 2 2 3 2 * 8 2

2

5

←) 3! M MN " <0 " 7← "

4 " )

3

!

2

$

!

,1 × 9 * +

3

* 8

M M 3

*

8

2 2

M M

←"

%

8 $

8 *

2 ,! 1! -! 2 ←*

D -

- 2 2 2*

5! 6! D ! *

! F! ! D !

L. -#1

3H M F

;

! 2

+ +

! !

*

3! 2

M M

2 -

I ) ; B

; 3 !

B " " ; B "6 ; B -

; B ,1 × ,1 G 6 " G " 6 G * "B ; B ,1 × ,1 G ! 2 * $ 2 3 ! 2 2 2 8 2 * 2 $ 2 3 ,616-6

) ! < '!

45%7!

A -

2 !

8$ *

2 8

)

* 8 ; 2 2 22 45%7 2 2 22

22 *

8$ 2 8$

2 + <0 " <

3 * + - 8 9! * ! ,

+ 3 - 8 9 2 8 >

*

9 0 ! 8 % 45%7 * - 8 ( -

8 22 22

8 3

8

45%7! 3

22

+ ' 9: -

6 = ! 2

(

' >5 *

+ 2

2 2 1

3! * - 8 %

) 3 8

! - 8 K

2 2 22

2 ! 8$ 2 2

2 2 $

" # !

( 0 1

- 8 9

45%7 -B%

5 5 5 5 5

5 ' ' ' '

' '6 ' '> ' '5 ' 5% ' '(

- = > * 2 2 2 - 8 9

+ $

' >% ' >% ' (: ' :' ' 9%

1

' 5> ' 5: ' '( ' 6& ' 55 - =

5 * 8

' 59 ' 59 ' '9 ' 59 ' 'K

- = "

3!

' ' ' ' '

3 !

- = % 0 " 1 3! 2 2 22 -B%

' '6 ' '> ' '5 ' 5% ' '(

5 5 5 5 5

' ' ' 5 '

' ' ' ' '

*

45%7 8

' (5 ' 9: ' (( ' >5 ' 6>

2 3

! 8

3 2

45%7!

2

-)

- = 9 + 1 45%7!

3 2 ( $

' (5 22 ! - 8 > 3! 3

! >'' 45%7 2

2 * 3 2 + 3 2 2 ! - 8 : ) ! 5( * > - 8 :! 8 , B 5( 1B> 0 -! 8 * 8 6( 8 2 2 ! 3 ) - 8 & 8 8 2 2 * * 2 3 >!6 %!6 8 3 >!6 ! %!6 K! 9 8 32 * < - 8 :!

' :' ' >% ' >% ' (: ' 9%

( 6 5 9 >

K

3

5 5 5 5 5

' 6& ' 5: ' 5% ' 5> ' 55

>! 5 B ' 9%! ) ! 2 %! 6 8 >! 5 J K! 6 2 2 * < 3 2 ! 45%7! ; 8 2 2 22

( 6 ( 5 >

6 6 9 6 6

%! 5 B ' (9

22

%

>! 6 %! 5 ! !

%

K

2

22 6:66('' ,616-6 $ 2 * 2 2 * - 8 5'

8 -

$8

".,"

) .,)

22 2 <0 "

8

2 2

0 /1 2 2

< $ * 2

2 -

3 2 ) 8

9 9 6 9 9

* >

A

"

6 > 9 5 9

K! 6 B ' 9(

3 K! 9

3!

2

' '> ' '( ' '( ' '6 ' '5

+

8

2 0 2 8

)

2 2 2 * 3 8 8 3

8 2 2

2

* 22 2

!

- = ' >% ' >& ' (: ' :& ' 9% ' (9 ' :: ' >9 ' 6& ' K& ' >% ' %5 ' >K ' 99 - = ' :& ' :: ' K& ' %5 ' >& ' >K ' >% ' >% ' >9 ' (: ' (9 ' 9: ' 9% ' 9( ' 99 ' 6& ' 66 ' 65

:

+

' 5> ' 65 ' '( ' 9: ' 55 ' 55 ' 9( ' 5' ' ': ' 66 ' 5: '5 ' 5( ' '>

' '6 ' '> ' '5 ' 5% ' '( ' '6 ' 55 ' '6 ' '' ' 5' ' '> ' '5 ' '6 ' '6

& ( K 5' 56 6 59 55 5 : 9 % ( > K 5( & 5' 6

3 5 5 5 5 5 5 5 5 5 5 5 6 5 6 5 5 6 6

' 5: ' 5% ' 5> ' 5( ' 55 ' 55 ' 55 '5 '5 '5 ' ': ' '% ' '% ' '> ' '> ' '> ' '> ' '(

1

55 ( 5 59 K % > 56 5' : & 5' ( 5( 55 K 6 > <

6 9 6 6 9 6 6 6 9 6 6 ( ( 6 9 ( 9 9

- =

3!

' '' ' '6 ' '' ' '% ' '' ' '' ' '> ' '5 ' '' ' '% ' '6 ' '' ' '5 ' ''

' '' ' '' ' '' ' '6 ' '' ' '' ' '6 ' '' ' '' ' '9 ' '5 ' '' ' '' ' ''

) - 8 : ' '( ' '9 ' '6 ' '6 ' '6 ' '6 ' '6 ' '6 ' '6 ' '6 ' '6 ' '5 ' '5 ' '5 ' '5 ' '5 ' '

2 4>7

9 5' 5( 59 55 : K % ( 6 5 59 56 55 : 9 5( 5(

6 > 9 9 ( 9 > 9 > ( 9 ( 9 > ( 9 > (

' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '

59 56 56 & & & : % % > > 9 9 6 5 5

> > ( > ( 9 > > ( > ( > ( > > (

," )

457 = 1 F ! Q.2 " , * R! , * P 1 L *$# ! 5&&K 467 * , ) F ! Q.2 , * ? ? 2 R! 1 ? 8 ! 5&&: 497 !1 , = * !Q 2 / 0 0 /1 .2 , * R! 9 " . 0 .2 " , * 0 .", @ 6''%! " ) != ! ! 2 55$59! 6''% 4(7 = * ! 1 , ! 1 2 1 ! Q # ) 0 0 /1 .2 , * R! - *! A 66! , 9! 22 5&&$ 6'(! 1 $S 6''>

5' 0 2

"

1 - 8 : < -B6(

5

5

'

'

'

5

5

'

'

'

5

'

'

'

'

5

5

5

'

'

5

5

'

'

'

5

5

'

'

'

5

5

'

'

'

5

'

'

'

'

5

'

'

'

'

5

5

'

'

'

5

5

'

'

'

5

'

'

'

'

5

5

'

'

'

5

'

'

'

'

3!

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

A Simple Approach for Optimal Allocation of ...

topology of all-optical wide area network, few nodes may require less number of .... utilization for different nodes, the proposed algorithm chooses the nodes ...

163KB Sizes 1 Downloads 257 Views

Recommend Documents

A Simple Model of Optimal Population Coding for ...
Aug 14, 2014 - 39.2%. 17.0%. 7.3%. 36.2%. 37.0%. 34.1%. 33.5%. Figure 4. Image reconstruction examples. We compare reconstructions from two different ...

Genetic evolutionary algorithm for optimal allocation of ...
Given a set of connections between the source-destination node-pairs, the algorithm to ..... advantages of natural genetic system. In this article, more ..... rence on Wireless and Optical Communications Networks – 2006. (WOCN'06), IEEE ...

Genetic evolutionary algorithm for optimal allocation of ...
Keywords WDM optical networks · Optimal wavelength converter ... network may employ wavelength converters to increase the ..... toward the next generation.

Approach for Optimal Reconfiguration of a Distribution System
an important position and customers ask more and more ... concept of distribution system reconfiguration for loss .... estimate SAIFI using the relationship: ( )2. 1.

Optimal Allocation Mechanisms with Single ... - Semantic Scholar
Oct 18, 2010 - [25] Milgrom, P. (1996): “Procuring Universal Service: Putting Auction Theory to Work,” Lecture at the Royal Academy of Sciences. [26] Myerson ...

A Cooperative Approach to Queue Allocation of ...
Then it holds that x ∈ C(vA) if and only if ui + wj = Uij for each ... Let Π(S, O(S)) denote the set of all bijections from S to O(S).1 The permutation game (N,vP ) is.

Optimal Resource Allocation for Multiuser MIMO-OFDM ...
tiplexing (OFDM), a broadband frequency-selective channel is decoupled into ... strong candidate for next generation wireless systems, like 4th generation ...

Heavy traffic optimal resource allocation algorithms for ...
Aug 27, 2014 - b School of ECEE, 436 Goldwater Center, Arizona State University, Tempe, AZ 85287, USA ... We call these requests jobs. The cloud service ...

Optimal Power Allocation for Fading Channels in ...
Jul 8, 2008 - communication network (SCN) to opportunistically operate in the ...... Telecommunications Conference (GLOBECOM07), Washington. DC, USA ...

Optimal Quantization and Bit Allocation for ...
Etienne Marcheret, Vaibhava Goel, Peder A. Olsen. IBM T. J. Watson Research, Yorktown Heights, NY, USA ... The first stage, level 1, relies on a set of Gaussians. G to convert an input d-dimensional feature vector xt to offset .... terms of the produ

Optimal Feedback Allocation Algorithms for Multi-User ...
a weighted sum-rate maximization at each scheduling instant. We show that such an .... station has perfect knowledge of the channel state m[t] in every time slot.

Optimal Allocation Mechanisms with Single ... - Semantic Scholar
Oct 18, 2010 - We study revenue-maximizing allocation mechanisms for multiple heterogeneous objects when buyers care about the entire ..... i (ci,cLi)], where (pLi)z denotes the probability assigned to allocation z by pLi. The timing is as follows: S

Optimal sequential treatment allocation
Dec 12, 2017 - treatment) and obtaining more precise information later (by postponing the measurement). In addition, we argue that the desirability of a treatment cannot be measured only by its ex- pected outcome. A sensible welfare function must tak

A New Approach for Optimal Capacitor Placement in ...
financial resources, electric utilities usually implement gradually intermediate non-optimal ... power compensation planning in large scale energy companies.

A Simple Distant Supervision Approach for the ... - Stanford NLP Group
the organizers, Wikipedia, and web snippets. Our implementation .... host cities tend to be capitals, which neither follows logically, nor happens to be true, ...

A Simple Approach to Synthesis of Linear Arrays
2. The Optimization Procedure. Consider a linear array composed of N ... (2) where is real and positive, and m a m θ is an angle between 0 and π radians.

Optimal Allocation Mechanisms with Single-Dimensional ... - DII UChile
Oct 18, 2010 - the allocation of “sponsored-link” positions on a search engine: Each .... virtual surpluses, the solution derived via pointwise optimization is not ...

Using Cat Models for Optimal Risk Allocation of P&C ...
ment of computer software models that cal- ... respective probability distribution functions, FY(y) and .... order to optimally grow the business of a (re-)insurer? We.

A Model of Contiguity for Spatial Unit Allocation
Dec 4, 2003 - Institute for Geoinformation, Technical University of Vienna, Vienna, Austria .... territories regardless of the degree of compactness.

Utility-Optimal Dynamic Rate Allocation under Average ...
aware applications that preserves the long-term average end- to-end delay constraint ...... Service Management, IEEE Transactions on, vol. 4, no. 3, pp. 40–49,.

Optimal and Fair Transmission Rate Allocation Problem ...
lular networks where the service infrastructure is provided by fixed bases, and also incorporates ... In section 3, we define the problem, the adopted notation and.

optimal allocation with ex-post verification and limited penalties
The proof of Lemma 2 is in the online appendix. By Lemma 2 and the assumption that v(x) ..... r∗ , is outside the domain [n−1 n. , 1], as n ≥ ¯n implies 1 r∗ > 1 n.

optimal allocation with ex-post verification and limited penalties
social value of giving the prize to an agent is privately known by this agent. The ...... (19). Fn−1(xr) = (1 − c)r. The solution of problem (Pr) is thus. (20) gr(x) =.