HAL Id: hal-01703319
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Elastic Time Computation in QoS-Driven Hypermedia
Presentations
Bruno Bachelet, Philippe Mahey, Rogério Rodrigues, Luiz Soares
To cite this version:
Bruno Bachelet, Philippe Mahey, Rogério Rodrigues, Luiz Soares. Elastic Time Computation in QoS-Driven Hypermedia Presentations. Multimedia Systems, Springer Verlag, 2007, 12 (6), pp.461-478. �10.1007/s00530-006-0067-4�. �hal-01703319�
Elastic Time Computation in QoS-Driven Hypermedia Presentations
Bruno Bachelet and Philippe Mahey1
LIMOS, UMR 6158-CNRS,
Université Blaise-Pascal, BP 10125, 63173 Aubière, France.
Rogério Rodrigues and Luiz Fernando Soares2
Departamento de Informática, PUC-Rio, Rio de Janeiro, Brazil.
Research Report LIMOS/RR04-16
1{bachelet,mahey}@isima.fr 2{rogerio,lfgs}@inf.puc-rio.br
Abstract
The development of hypermedia/multimedia systems requires the implementation of an element, usually known as formatter, which is in charge of receiving the specification of a document and controlling its presentation. In order to orchestrate the presentation, formatters should build a pre-sentation plan that will contain the scheduling time for each document object and the inter media-object synchronization information, including those whose time of occurrence cannot be predicted, like relationships coming from user interaction. Besides orienting the presentation scheduling, the plan will guide prefetching, reservation and adaptation mechanisms in charge of maintaining the presentation quality of service. Adjustment in the duration of media objects is one of the most important adaptation techniques in order to maintain spatio-temporal relationships specified in a hypermedia document. Elastic time computation accomplishes this goal by stretching and shrinking the ideal duration of media objects. This paper presents new elastic time algorithms for adjusting the hypermedia document presentation in order to avoid temporal inconsistencies. The algorithms explore the flexibility offered by some hypermedia models in the definition of media object durations, choosing objects to be stretched or shrunk in order to obtain the best possible quality of presentation. Our proposals are based on the out-of-kilter and the cost-scaling methods for minimum-cost flow problems on temporal graphs. An aggregation procedure enhances the basic algorithm offering more flexibility in modeling real-life situations in comparison with other previous work based on linear programming.
Keywords: hypermedia presentation, elastic time computation, minimum-cost flow and tension.
Résumé
Le développement de systèmes hypermédia/multimédia requiert l’implémentation d’un élément, généralement connu sous le nom de formateur, chargé de recevoir les spécifications d’un document et de contrôler sa présentation. Afin d’orchestrer la présentation, les formateurs doivent construire un plan de la présentation qui contiendra la date planifiée de chaque objet du document et des informations de synchronisation inter-objet, incluant celles où la date d’occurrence ne peut pas être prévue, comme les relations issues d’interactions avec l’utilisateur. En plus d’orienter la pla-nification de la présentation, le plan guidera les mécanismes de mise en cache, de réservation et d’adaptation en charge de maintenir la qualité de la présentation. L’ajustement de la durée des objets multimédia est l’une des plus importantes techniques d’adaptation pour assurer les relations spatio-temporelles spécifiées dans un document hypermédia. Le calcul de temps élastique réalise cet objectif en étirant ou contractant la durée idéale de présentation des objets multimédia. Cet article présente de nouveaux algorithmes de calcul de temps élastique pour ajuster la présentation de documents hypermédia, afin d’éviter les inconsistences temporelles. Les algorithmes explorent la flexibilité offerte par certains modèles hypermédia dans la définition de la durée des objets mul-timédia, choisissant les objets qui doivent être étirés ou contractés pour obtenir la meilleure qualité possible pour la présentation. Nos propositions reposent sur des méthodes de mise à conformité et de mise à l’échelle pour des problèmes de flot de coût minimum dans des graphes temporels. Une procédure d’agrégation améliore l’algorithme de base pour offrir plus de flexibilité dans la modélisation de situations réelles en comparaison avec de précédents travaux reposant sur la pro-grammation linéaire.
Mots clés : présentation hypermédia, calcul de temps élastique, flot et tension de coût minimum. Acknowledgements / Remerciements
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3 E , & . 3 E , 0? &) > & " ") A( 4 $$ & 8) 3 > 0 " , $ $ + " ( ( 3 + 0 " ,
$$ 8) 3 > + . 0 > $ +
$ 3" > @&) " >A $ $ , " ( & & 3" > $ " 3" > ") 8) " 0 (
+ 2 !
& $ 3 0" &)" . & 0+ 3 "" > , & ( % + . + " , 3 > & T > D ≤ ≤ ∈ ∈ ∈ ∈ $ F U $ U $ F $ θ θ θ θ .61
' 8) "+ 3" F 0 " + " 3 , + " . 71 D
{
} {
}
[
$ F]
U $ F $ U $ $ $ Fθ θ θ θ .661> θ & 3 " &) ( H & .61 @ ) 3 0" &)" F A " ,) " .661 $ +( % & , ) " 3 0" 0+ "3 , ) )"& 0 " & " $ > $ ) 3 & 33 & 3 & &)" &) , & )$ (
+ " &
4 + $ " & 8) 33 ", $ 0 ) & " 0" $( > )"" ( % > θ ≤θ$ ) , 0 3 ) & 3 >
0 & > ) $ E , + $ 0" ( 7 $ F $)$ , ") & $ & & " & ) ( 3 θ "" 3 θ$ ) &
3 " , > $ 0" 9H &?; =( # &
4 ", $ " ) ) $ &( 7 & & "
π & 0 > & & & & ( E > 3 " > " , & 3 "" > , + 3 & 3 "" 0 ∈ =@G A D π −π ≤ @GA > @GA " , 3 .6661( & 3 & 3 0" > " E 3 " ) θ$ ≤π −π ≤θ$ F( P , 0 E $ " + & .6661 > > )"& " E > $ F A G @ θ π π − ≤ = & @ A > $ A G @ θ π π − ≤ =− ( 7 ) & 3 & > , $ & 3 $ , " , > "" . / 1 & )0" &D > F , . / 1 & θ$ F > . / 1 && & > & −θ$ @ 3( % ,) A( , 3 ", $ 3 ! ""$ & % & 94 ;<= 3 & & > , " & 3 3 0" ( 7 $ & 3
) @ > > 0 $ 3 & & , . 3 , 9! <=A( H > > ) ") 0" 3 $ J "$ 3 0" K > $ + 0 , &) , ) $ ( θ $ θ 9θ /θ $= ! " 2 # 7 3 $ 0" $( + - . 1 3 / -7 3 $ & & 3+ 3 @$ $ .
> , & )$ 3 0 ") & 3 $ & " &) ") A & 3 ) 3 E " $ & 9%)"E = 3 " & $ $)$ 0" $ 9#" L = "
( # "+ $ " & ,"+ "+ $ " ", $ 0 "+ )& & 9H &?; = 0) 3 $ F "" " > 3 ) ) ( 7 ) 3 E " ", $
<
$ " &) " $ & > ) & & 3" > "+ ) " $ " + &( 7 $ & , $ ) & 0) & $ , "" > , $) $ 3" F 0 " + & $ & ( 7 E + " E " ) > " " $ " +
& 3 ( N & > E & 3 D > " @% ,) A &
F $ @% ,) 'A( & > E " ) 3 " , θ > 3" >ϕ ( % " E " ) & 0+ % ,) 0 & 3 F > % ,) 0'( 0 & 3 .θ / ϕ 1 " ) > & ( N "+ 3 "" 3 , E " $ $)$ @ $ " + & ( ( A( "" & 33 )" + 0 , "" E " ) ( N 3 F " > 3 $ 3 > " ( 7 > & )
F ( 7 ") ,+ & 3 $ 9#" L = & 9H &?; = " , $ $)$ 0" $ > " ( (a1) (b1) ^ θ c ϕ θ 0 u u u u c2u -c1u c1u c2u θ θmin max θumax θumin u u θu ^ θu c 0 u c'u (a2) (b2) u u ϕu θumax θumin θu θ θmin θ^ max θu u ^ θu ! " 4 # *A 3) ( 0*A I " ) ( * A # > " ( *'A F $ ( + 5 6 % > " 3+ 3 , , D ( 0 " > E " ) '( 0 E " ) <( . " 3 E " ) ( " 3 E " ) (
% , + $) 0 & 3" > $) 0 & & &
$ > & E " ) ( % , + ' $) 0
& & 3" > $) 0 &( , < & E " ( % , + < "+ 3" > 0 $ & 3 & > ) $ E , $ ) 3 E " > " 3 , + "+ 0 , &(
% "" > , $ " > E 3 %)"E 9%)"E = > D
• 3 , + > 3 & + " , 3 > 3" > 0
& & ) , 3 > 0 &G
• 3 , + ' > 3 & + " , 3 > 3" > 0
& ) , 3 > 0 & &(
7 $ "" > ) 3 "" > , ", $ $ 3 E " ) D
algorithm improveArc:
if (u is below the curve) then
find a cycle γ to decrease the flow of u or a cut ϖ to increase the tension of u;
if (cycle found) then
find λ the maximum value the flow on γ can be decreased; ϕ = ϕ – λγ;
else (cut found)
find µ the maximum value the tension on ϖ can be increased; θ = θ + µϖ;
end if;
else /* u is above the curve */
find a cycle γ to increase the flow of u or a cut ϖ to decrease the tension of u; if (cycle found) then
find λ the maximum value the flow on γ can be increased; ϕ = ϕ + λγ;
else (cut found)
find µ the maximum value the tension on ϖ can be decreased; θ = θ - µϖ;
end if; end if;
7 ) > 3 "" > , $ & $ E "" E " & $ , $ $)$ ( 7 $ & ?) " ) ", $ ) "+ & &"+ )
3 , ) " "" E " D
algorithm linearInKilter: make θ compatible;
ϕ = 0;
while (an arc u is out-of-kilter) do for all arc u do
if (u out-of-kilter) then improveArc(u); end for;
end while;
+ (
7 $ & " , "+ & 33 3 , " F ( & & ) "+ & ) & $ " E " ) + " ) @ , A $) 0 3 ) & & 3" > @ A + " @ ) A $) 0 $ & 3 &( 7 3" > @ A 3 ""
+ " @ ) A $ & 3 &( H > 3" > & $ & 3 &
$ G + 0 $ & 3 & , $ ( 3 E " ) $ & 3 . " & " " @% ,) 0 A " E > > " 0" $ E " @0+ , , 3" > A > ) " , E " ) ( 3 , "
$ , , 3" > 3 E " > "" ) $ ""+ $ E ) 3 E " ( & & 0" $ & "" ) ) 3 E " 8) > F $ E " ) 0+ ) ( N ) $ & & 3 " 0 , ""
F $ E " ) & 3 > $ F $ 3 ) (
7 &) & ) " > 0 & & ( $$ & & > > E F $ & , "+ $ & 3 & "+ , >
F $ ( N ) " 0 " > ", $ 3 $ & > D
algorithm convexInKilter:
ε = 0.1 sup{θ$ F −θ$ , u in U}; while (ε > p) do
make all arcs in-kilter with precision ε; /* Uses algorithm linearInKilter. */
ε = sup{0.1ε,p}; end while;
+ * - " /
-7 & $ & & $ , " ) D 0 , "" E " ) ( H > > + $ & 8) & 33 ( 0 & ", $ "" &
3 $ $)$ 3" > 0" $ 94 ;<= & 0 & 94 H ;;=( 4 & ε 3 "" 3 , " ε 3 3 $ E " ) $ ( ( ) , + % ,) L( ε ε ε ε ε ε θ ϕ θ θ θ $ ' 8 8 V ! " 7 #ε 7 ", $ > , ") 3 ε + 3 0" 0 ) "+ ε $ "( 0 & $ F@ $ G $ FA 0 " θ θ ε ∈ = = ) ") 94 ;<=( 0 " & 3 ε< @> )$0 3 & , A + ε $ " $ " 94 ;<=( 7 ", $ &) ε ") $ E , ε9 $ " 3 $ ε $ " ( 3 ) 3 ", $ 8) & 0 ) & 3" > " : 8/8; > 8 0 3 + 3 0" 9! <=( 7 $ &) 3 ", $ 0 & 3 "" > D algorithm dualCostScaling: π = 0; ε = A; ϕ = 0; while (ε ≥ 1/n) do
make π ε-optimal;
ε = ε/2;
end while;
E , ε9 $ " 3 $ ε $ " & 3 & 3 "" > ( % )& 3" > 0) " ( ( 3" > ") 3 ) & "+ ) @ % ,) A( H 3" > " > 3 & +$ @ ( ( 3 + & A G @ A G @ = − = = ϕ ϕ "> + 3 &A( θ ϕ ε ' θ ϕ ' ε ' ' ε ' -ε ' ' ' . 1 . 1 ! " 8 # < 7 > ) $ , + 3 $ ε9 E " ) ", $ $ 3+ 3" > " >( 7 3 & , F & ( ( & > A G @ A G @ > − = = ϕ ϕ
( 7 F 3 3" > > & > 3 $ &? ( > & > 3 $ , > 3" > 0 &) & ) , , > 3" > 0 &( 7 & + " ", $ 3" > 3 & & & "+ 3
0 0 " > ) 94 ;<=( 3 3" > 0 "+ ) & & "
& & 3 ε9 @% ,) 0A 3 3 $ , & & 3
) , , ( 7 ) $ & ""+ & 3" > + ) F 3 3" >( & $ + 3 $ E " ) ( 7 > "
&) $ E ε $ " 0 & 3 "" > D
algorithm makeEpsilonOptimal: build pseudo-flow ϕ;
while (an excess node i exists) do q = = =@GA − @GA ϕ ϕ ; while (q>0) do
if (an arc u=(i;j) can increase its flow without leaving its kilter curve) then increase ϕu to its maximum;
else if (an arc u=(j;i) can decrease its flow without leaving its kilter curve) then decrease ϕu to its minimum;
else πi = πi - ε/2; end while; end while; + + - 9 / -4" ), ) > $ & > E + , > , " 3 , @ 5< A 0 ) + 0 $ + $$ 3 ) > + $ &
L $ " , ( & & " , , )" 3 $ F 3 "" " @ , "" " A 0 > > & @ + . "" " A & + " 3 $ & 0+ , 0) " $ + "" " , ( H > + $ & $ " , F "+ "" "( N F " " 3 $ " " $ & " & > , "" " 0) + " ( ) , "" & 8) "" " , B # , ( N 3 $ & "" & ,, , " 0" $ # , & > F " >
F & 8) B # , (
+ + ,
-% $ ""+ # , , 0 &) & $ " , 3 & @ I " 8) A( ) "+ + , 0 ) & 0+ " 3 >
0 D
• 8) " @ A " ,D -.$/ 1 & > ) (-.$/ 1 & 9-. / 1 0+ &) 3 $ & & @% ,) ; A( 7 "
0 & ( & 9 & & (3 9(
• # "" " " ,D -.$/ 1 )0 ) & 0+ > "" " (-.$/ 1 & 9-.$/ 1 > $ & @% ,) ;0A( 7 " 0 & ( & 9 & & ( 9(
$ $ . 1 $ $ . 1 ' ' ! " : # 5<
& "" " " , & ) & $ 5< ( 7 # " 0 + > # , 0+ 0 + "" & 5< ( % ,) > # 3 # , ( 3 9! < = F " > 3 & ) " $ ( 3 $ $ ! " ) # #$ 5< 4 > 0+ % ,) $ 3 4"" T $ " " "" "( "+ " "" "D " E , 3 0? ! > & 3 0? " 0 E "" " +(
! " " ! ! " " ! " ! " ! " ! " ! ! " ! " ' ! " " ! " ! " ! 3 " ! " ! 3 3 " ! " ! 3 " ! 3 ! 3 " 3 ' = 5< ! " # " + + - "" " - ; 7 ,, , $ & > "" > " , $ $)$ 0" $ "+ # , 0 &) & 9! < =( 7 ", $ > E # & & 3 $
# , , ) "+D & , # " ", $ )$ $ " 3 > )0, $ " & " E > & 3 $ $ 0" 8) E"+ 0) "& $ " 3 > " # " ( H , 3 $ " 3
$ " 3 # " 0) " 3 ""+ 3 (
% $ & 3 3 # , 0 ) # , "+ & & & "+ " & ( 7 3 θ 3 # , & 3 & 0 > ) & , ( ( θ=π −π ( 7 , 33 ", $ $ $)$ 3) ), 3 # , , $) 0 & 3 &( 7 3) 3 $ " > $ 3 & , ") D = = ∈ $ $ ) 0 ,@ A $ @θ Aθ
4 3) F $ $)$ 3) & & F( N + > 3 &
&) 0) "& 3) 3 # " ( ) & > "" " )0, , & ,' & ) $ $)$ 3) ), &
' , ) "+ E > ( 7 $ $)$ 3) ' , , ) + 3 # " , +,' , 0+D A @ A @ $ ' ' ' ' $ ) $ ) ) , , $ $ $ , ,+ = = + + 4 F " & 9! < = 3) 0 0) " " $ & , "+ %. 1 > )$ 3 3 0 3) , ) & ' , ) @% ,) ' A(
; ), ,' ), ),' @ A ),' ), ), ,' @0A ! " # " 7 $ $)$ 3) ' , , ) 3 # " , ,' D A @ A @ ' ' $ ) $ ) ) , , , , = + 7 $ " )$ 3 3) 0 0) " " & , %. 1 @% ,) '0A( 7 3)"" & " 3 ,, , 8) & 9! < =( H > $ &)
, 3 $ " > ," # " 0 > > & 0) "& , $ $)$ 3) & > # " (3 9 @ ( 9A( 7 &) ,
> & 3 ( ( > # " ) " & ( 4 $ $ $ $)$ 3) 3 > " , E > $ E , + & 3+ $ $)$ ") & ) 0) "& $ $)$ ( + + * 9 H+ $ & $ " , + " # , @ (,( " % ,) A( H > + 8) $ $ " F( 3 ) ) "" " & 3 > && & 0 E +( N 3 # ) 0 $ ) > 3 + ""+ 3 $ "" " , ( 4 5< >5< ,-.*/01 ) $ " 3 $ $ " )0 3 07 ⊂ 0 3 $ , $ E $ , , ,7-.*/0?071 "" "( 7 @07@ @0@ "" & 5< 3 , ,( 7 ") & > $ + 3 , & ) 0 , "" " + 3 ,( % $ & 3 + & , B # , 0) > 3 ) $ 3 , > $ "" # ) 0 @ " ) & 3 $ + $ & 3 "& W $ 3+ , "&A(
4 ,, , $ & 0 ) & J K B # , & &) " " , 0 " 33 ) 3 E " # , @ 7 0" A >
$ & "" & ) " $ $)$ 0" $ B # , ( 7 > $0 ,, , & ) 3 E " 8) 0 & # & $
'
5 $ #
N "" 5< 3 , , # )0, 3 ,( 4
5< 3 , P 3 & ? # $
> ) ,( 9! <0= & ) > + 0 J, &K # & $ 3
) ( 7 $ & > 3 # & $ A 3 , ,( 7 $ $)$ 0" $ " & # $ 3 A > ,, , $ &( 7 ) 3 $ A A $ $)$ 3) ) & $ " θ* E > A 0 ," ,, , & > F > " 3) -) & * θ ( ) # 7 $ & $ F ) # $ 0 E , ( 4
&& , 0+ ,, , & > , 0) "& , , " , ,( , > 2 =@* G0 A=@∅G∅A ,, , & -.$/ 1 && & ( (
{ }
G G{ }
A @* $ 02 = −∪ −∪ (
7 >"+ && & $ + 0 ) 3 E " @ & "+ A 0 ) 3
$ " 3" > $) 0 4 & E 3" > " > > " , 2 ( % ) "+ "+ ) 3 E " 3 + " ) $ & 3+ "+ 3" > 3 0 3 $ & > 3 > 9! <0=( E " > " 2 $ " & ,, , & 0 && &( 7 4&?) $
H > && , , 0 ) ( & ,, , & -.$/ 1G $ " θ 3 $ + 0 8) " & 33 3 " π −π$( 7 0
& ) , $ $)$ 3) ) 3 $ ""+ & $ 3 # $ ,, , & 0 & ( 7 $ ) 0 3 $ & " $ F " &
9! <0=(
# $ " ,
% & 3 ) > )$ " & $ 3 #
& $ A ) 3 & & " & 3 # $ A 0 " ,
# $ A A BA ( 5 $ $ & & 9! <0= )
& F 3 + , ( 5) , ) # $ && & 3 "" > , " & (
4 0" $ > && , ,, , & -.$/ 1 , 2 D $ +0 & & $ & " & 3 2 0 ) + $ "+ && 3 ,, , & 3 , 2 ( H )"& 0 " & 0+ > " # $ A & , $ E , ) $ & 0" ( 4"" 3 # $ A 0 ), 0 E , 2 @ ( ( 2 +=2 ∪A −
{ }
A( N "" 3 (7 & >0 E 3 8) 0 ,, # $ && & 0 & ," ,, , & 3 "+ " & 0 ) & > "" 0 ) "+ 0 & & 3
'
& && & ( 7 " 0 F $ "+ 33 $ 3 > "" 0 0 ), 0 E , "+ & ( 7 ) > & $ > + ""+ " , # $ ( 9! <0= 8) " # $ " &) , )$0 $ $)$ +( 3 I " # + 43 " , ,, , & -.$/ 1 )" $) 0 E " E > " , 2 $ "( 7 ) E > , , 3 > & 3 & " > 3" > $) " D & & > ) )$ E " ) 3) 9! <0=( % 3 # $ A " : / ; 0 & 3 &( )
3 $ & & $ " & 3 # $ > + "
[
ϕGϕ]
> ϕ 3" > 3 > " , 2( % & , 3" > ϕ 3 3 # $ A ) 3 & 3 0" 3" > ϕ # $ @> && & " A( ) 0" $ & " " " > E 3" > 0" $ 0 3 ) & 94 ;<=(4", $
7 3 "" > , ", $ )$$ . > " 3 ) $ &(
algorithm reconstruction:
find SP-decomposition A=
{ }
A =(( ; let H be an empty graph;for all (SP-component A∈A) do
find minimum cost tension for A using aggregation; let u=(x;y) be the aggregated arc of A ;
while (exists A with A <A and ($∈A and ∈A )) do split A ;
find tension for each arc of A using ) ; find flow for each arc of A ;
end while; add arc u in H;
find minimum cost tension for H using out-of-kilter; end for;
for all (aggregated arc u in H) do split A ;
find tension for each arc of A using ) ; end for;
+ 2 9
CF $ ) " , $ & )$ & " , " $ " , 0 3 $ &
$ 0 3 ", $ & 3 & 33 0? 3) (
3 > " 3) @> ")& $ )$ & $ $ F $ 3) A $ )"& 0 F & & " , $$ , & " E P #IL( 7 0" '
L
''
& < " $ 3 $ & > > " ( 7 0" 33 & 3 > $ & 0 # , @7 0" A & B # , @7 0" ' & <A( 7 0"
> 3 $ 3 # , > . ( 7 0" ' > )" > . 3
B # , ( 7 0" < ) 3 $ 3 $ & 3 ) #
) 0 (
)" F & & " H. ) & )F , + $(
N ) & P -- '(; $ " & 0? & 3 ) $ " $ $ & ( 7 )" $ 3 3 & $"+ , & , ( ! $ F@ $ G $ FA 0 " θ θ ∈ = & A G @ $ F ' 0 ! ∈ = 3 F & (444( < ,6 3 & ' 3 & ' & ' "" " & ' ' ( ( ' ( ( (<' ( ( L ( < (<; ( ( ; ( < ('< ( ' (' ( ' ;( (; ( ( <<( ; ( <(<' (<< <;(L< '( (' (<' <'( ( < ;( ( L # C 5< 7 0" ,, , 8) " "+ 0 $ 33 + 3
$ & ( H > , & " 3 " + $ & + . (
< ,6 3 & ' 3 & ' & ' 9 & ' ' ( ( ' ( < ( ('< ( ( L ( (' ( L ( ; ( ' ( ( ( (' ' L( ( ( L (; < (L; <(' <(' (;L < ( ('L ( '( ; ' ;( ( < (L ( ' # C >5< .5< -DE1 7 0" ' > # ) 0 W ) $ & 0 $
33 " , , @ & & ' A > ," ) 3 E " $ & 3 $ "" @0 " > & & ' A( 7 > + , & $ & #
$ & > $ " &) , ) E + , &
3 $ ( %) 3 $ 0 3 ) & 9! <0=( &=' ,6 3 & ' 3 & ' & ' 9 & ' ' '( ( '(' ( < L( '(' '( ( ' ( < '( < '('L (L L ' ( '( '( '( < ' ( L '( < '( ' '(' ; ' ( <( L '( '( '
'<
' (<' <('L '( ' '(L
<L(< <( '( (
' ( ( L '( ' ( <
* # C >5< 5< .F44 G444 1
"+ ) 3 E " $ & & " > F & 33 0" ( 7 0" > 0
> 0? 3) " 8) 3) @ 4 F A & 3 )"
( 7 3 $ & ) "+ 0 & & $ " $ (
> 3 & ' ( ; '( <( < ( '(' + # C $ .(44 D44 1
2
1
- "
9
4 $ " $ $ $ 0 $ & ) 0+ & $ $ $ ,)" & )$ ( H > ) & 0" 0 0 &" & "+ &) , ) $ ( 3 ) "+ &) , ) $ $ $ @ ) & 33 3 $ F &
$ " A & & "+ > 3 & )$ " &+ 0 &( 7 & " + & " $ 3 $ 0 " + $ ) $ $ ( C ), + . 0 & 3 > "" " 8) " +( 7
> + 3 $ & "+ ) , 0 $ " $ & ) $ &?) $ 0)
" , $ $ $ 3 & & )$ &) ,
0 0 " + 3 &?) $ &) , ) $ (
7 $ & 0) "& 3 , " ( ! & " & )$ 0? @ A 3 & 0 3 + 8) & 0 " + & 3 & $ 8) ( 7
&& 3 3 , , $ $ + $ & 3 $ $ "+
&) 0 0 " + 3 &?) $ &) , & )$ ) $ 0) " $ $ . 0? " , & $ ? (
7 3 , " 0 0) " 0 & "+ " 3 $ ( H >
$ " E ) F > 3 $ ) 3 $
$ 3 H+ $ & + $ C − 33 , $ @ A − @& " + & ? $ & 0+ > E , + $ $ & " + & $ G
" 0" 0 &> & G (A + 3 8) 0? " , " 0 " + 3 ) ( 3 , " $ + & & 0 $ " & " (
C ) 3 $ 0 0 & 3 $ & B ,
$ $ ( ) & > "" ) 0 $ $ $ "
3 & ) H+ $ & + $ C( H > > E
, " , " , + $ & E & 3 ) $ " $ ( 7 ) ) $) 0 $ " + & 0) "& 3 , " 0 & "+ )$ 0 )
C 3 $ $ ( " , 3 0) "& , " > & " ) 9M HI;L I 7 =(
'
4 " , ) " 3 , $ $ 0 & & & > D $ " & F ) ( 4 $ " $ 3 , " , &( 5) , F )
3 , " &)" & & $ & ,, , &?) $ > 0" $ $ ) (
3 3 , " 0) " > ) ) & B 8) 3
0? $) 0 $ & 0 & $ 3 & 3 0? 3 ( 3 B 8) 0 & & 3 + " B 0" & ) 3 , " )"& 0
&(
$ H+ $ & C > & "" > B , "" ) @ 3 $AG 3 F $ " + $ & + $ ) , $$) & $ " $ & 0+
> E > ) B ,) ( " 3 , $ 3 0? )"&
0 $ &( 3 $ $ 0 > $ & ) & $ 3 $
) 3 , " )"& " 0 &(
+ & $ & , 3 + 0" " $) 0
&?) & & ,"+( & + $ & 3 + " $ & 3 & 3 , " $) 0 &?) &(
4
(
4 3 $ & &) , $ " $ " ) & 0" 3 $ + 0) "& , > " " ) )" " $) 0 ") & &) , ) $
0? $ & & ) " 0? > ) & 0" &) (
5) , ) $ F 3 $ ) ) , ""+ & C
3 $ $ > $ + ) , " (
4 & ) ) " " 0 &?) & &) +
&?) $ 3 , " ( 3 + $ $ " & , 3 & )$ 0? 0 ,) & & & " " )"& 0 &?) &(
# $ , 3 $ F 0 " @ & )& F & " + A )"& " 0 $ & & $ & > & & $ 0" & 0+
" & " 3 + . $ , & )$ 0? (
, " 3 + , " $ & & "
)"& 0 &?) &( C + $ " , & $ + 0 8) & )" "+ $ $ " + 3 & )$ (
& $ & 3"+ & $) 0 & & 3 0" ( $ $ " $ $ ) $ + 0 + " $ $ . 0" $ @$ & 3+ ,
0 &) A(
7
"
(
7 /
-4 3 $ & &) , ) $ $ $ & & "+ > 3 & )$ " &+ 0 &( 7 & " + & " $ 0 " + 3 3 $ $ )
'
3 )" & )$ ( H > "+ ) $ ) & 0" 0 0 &" &( 7 > + 3 $ & ) 0 $ " $ & ) $ &?) $ (
N ) $ $ $ ) &?) $ &) F & &) 3
)0 8) )"& 0 $ ) & " )") $ & $ " $ $ + 0 $ " &( 7 3 $ )"& ) , " $ ", $ > & , F &) 3 " &+ & & " $ $ ) 8) $ ( 7 ) " $
$ ) )"& 0 " 0" ", $ )"& E 3 3 )" $ ) & 0 3 + $ $ & $ " )") 3 $ $) 0 & 3"+( 5 & , + 3 $ $ " $ " )") $ + 8) ) $)$ " )") 0 + $ F ( H > " E , 0 E )" 3 3 $$ . 3 + $ & & )$ @" $ " A $ " $ ", $ 3 ), 0 ) & " $ ( " ) > 0" ) $ 8) E
+ . $ " & & $ ) , > " &)" ( ) & $ " , 3 % ,) < & ) $ " " &+ 0 $ ) & 3 , (
N & 3+ & 33 3 $ $ ) &) , D
! " ) # H ) I ) II ) I ) II ) )' )< ) A ! " * # 8 $
• 4 & " + 3 $ & 0? $ & 3+ , " , 3
3 ) % ,) <(
• 4 ) & 0" 3 ) " E 0) >
3 3 F $ " )J % ,) <( • 7 ) & & (,( )F % ,) <(
7 9 " .
-) 3 E " $ & " 0" ( & ," & " + )( & ) & 3 & " + $ ! & A )"& ( 7 $ )(773)9 )G3)D$) 0 ) E & )F77 &( N 3
3 3 )(77 & & 3 )(773)9 )G3)D 8) " 3 )F77(
7 ) E " +$ & $ +0 $ 0" @ ( ( ) 3
0 ) & A( 7 & ) $ $ &) 3 ) 3 E " $ & @ 3( A & "+ ) " 0 $ E " ( % " &+ 0 &
'
0 ) & 3 F & &) ( 4 3 , ) 3 E " & 3
&) "" $ 0" > $ ") F 3 3
+ . E " ) & + . &)"
$ "( "+ 3 > 3 $ $ &) 8) & @> 3
&) %.K 1 > )$0 3 , & K
0" & 3 $ & 3 + . 9! <=A(
3 ) & 0" && )J $ " , A ,+ > "" 0 " 3 $ ( 4 3 )J & & &
3 )J 8) " 3 )F77( 7 "" "+ E " 0 ) $ " $ $ " &)" 3 )J 0 & $ & ""+ & & 3
3 $ " , ( ) 3 + . 0" $ "
&)" 3 ) &(
3 ) & & )F A $ , > "" 0 "+ 0) $ ""+ & & , > $ " , ( 7 )F77 $ & 0) 3" >
" > 3 & +$ 3 & A & H( 7 0 " 3 ) && & 0 > A & H > 3" > 8) " 3" > 3 )F77 )"" &
0 ) & ( 7 "+ ) 3 E " 0)
+ . "> + 0" ( E ) ) $ " &)" 0 3 ) & > 3 > 3 $ $ &) " & (
7 * - "" "
7 )&+ # , 3 0 , 3 " $ $ ) 3 $ "
&)" ( 4 F " & ,, , 8) > " $ $)$ 0" $ # , & "+ & $ " 0) " & $ $)$ 3) & 3 $ "" > " $ &?)
3 > " # , $ ""+( 7 )$ ) "" " 0 " & 0+ ," @ 3 ) > $) $ $ " F 3) 0) "" 3) 3)""+
& & ) 3 E " 8) A & 3 ) 8) (
7 3 0 & & ) ,, , 8) $ " $ $ )
$ $)$ 3) 3 "" " $ + "" " 3 $ " , & +
) $ &) , ) $ & ) $ $ 3 ) 3 E " ( 7 8)
$ $ , 0) & 0 ), ), & 3+ ) > , , 3 (
8 9
?
@
7 % 3"+ + $ 3 $ 9!): ;< !): ;<0= &) & & 3 $ " @ $ &)" & . $ )F " + &)" A( " & "
> $ " & F ) ( 3 $ & >0 E % 3"+ F ) " @ $ " , A $ " $ " 3 $ E , & 33 )" $ " $ 3 ) $ &?) $ (
C" $ $ ) 0 && & % 3"+ & 9I ; =( H > + "+ & $ & " > > " F 3) @% 3"+ $ & " 0 & " > $ & " 0 & + " A( 7 + " $ > $ " F $ & >
) 0" "+ 3 $ " $ & ( 4 & ) & ) " F & & $ & " , " F 3) & , $ " & 3 $ " +
'L
% 3"+ & 3 $ ) & > F 3 3 ,
$ $ (
& ) 9 '= ) , & + $ 3 $)" $ & & )$ 0 & $ " $ , $ & 0? ( 7 + $ " 33 $ " 3" F 0 " + ), $ & 0? &) 3 > 0 & 3 & "
0" , " > & ) " $ ") (
$ " & ) 3 $ $ ) 3 & 0" @ A 0? F & &) @ A & 0) "& $ " , $ & H 7# @2
5 < A( 7 , 0 & & & ) " (
5) , F ) 3 $ $ 33 &) 3 $ & 0? &
$ $ > F & ") ( N + & ) 3) )
+ . " & & ) 3 $ " &?) $ ", $ 0) > ) & , $ . $ ( 7 $ , " 8) E"+ 3 & >
, $ 3 &) " ( 7 & ) 3 $ " $
&) 3 ) & 0" & 3+ 3 & 8) &) &?) $ (
7 & ) 3 $ & & " > 3 , & F & & ) ( 4" ), 33 , ", $ 3 " $ & 3"+ ") ) , &+
> ) , 0 ) 8) " )" (
$ " 3 $ % & 3 $ @ $ & % & #" + A 9 ;<= 0) "& ,
3 $ " & & & 3+ $ $ 3 ( ! 3 P
" + $ " $ 3 9N< = & )$ + $ 3 $ $
F 0 & & 0) " $ &?) $ $ &( '( &) 3 " 3 & 3 , 0? &) "" > " $ $ ) 0) " E & ) $ " 0" 3 $ ) , & & 8) " +( 4 ) ""+ > > , , > F & $$ & " $ $ ) ", $ (
M , "( 9M HI;L= & " & $ $ 3 &)" , $)" $ & ( H > " "+ & & )$ F ") "+ 0 & & 0" " &
& 0" $ & 0? &) ( 5) , & )$ ) $ $
$ 0? ) " 3 , &) > F & &) > & " ( 3 ) " &) $ & & + $ ) &)" , ", $ 3
" )" , 0? &) & $ $ " ,$
+ . ( N + ", $ 3 $ & 0? E ,
&) ( " $ $ ) 0 & $ " 0" 3 $ ) , & & 8) " +(
% ""+ $ $$ " ), $ " & ) & & " >
" $ $ ) 3 $ $$ 0 ) > "+ &?) $
) ) $ & F 0+ $ " ) 3 " $ " ( H+ # " + F $ " 3 & 0+ JCF 7 "E , H & K 9 & = > & , "(
'
: !
!
?
@
7 > ", $ 3 " $ $ ) ( 3 $ 0 & J ) 3 E " K $ & 3 $ $)$ 0" $ > "" > $) $ 3" F 0 " + $ & " " " 3 ) ( 7 ", $ , " & " > , " F 3) ( 4 J&) " " ,K " & > 0" $ $ $)$ 3" > 0" $ " & > > "" E > J " ,K $ &( 7 $ & 0 & & 3 0 , , $ " $ (! ", $ F "+ $ & & 0 ) 3 $ $ " F $ & ) & ) > E > & " , > > " (
& 0 ) & &) , ) $ " $ $ ) )"& 0 " 0"
", $ )"& E 3 3 )" $ ) & 0 3 + $ $ & $ " )") 3 $ $) 0 & 3"+( 7 3 ) 3 E " $ & > 0 & & ) $ ) & ) & L(
4 > $ & 33 , $ " 3 $ & 0 & 3 ) ) 3 $ " , "" & J ,, , K " &( N E , "+ > > " F 3) ,, , & ) 8) $ , "" " 3 $ " ( 7 8) & 33 ") $ $ E $ & "+ ) 0" 0 ) & $ " $ ", $ 0) " & " ) $ ) , > 0 " 3 ) $ $ ) ( 7) , 0 E 3 , " & 0 , , 3 0" & ) & 3 3) ) > E( 7 3 , " # $ " 0" $ 8) , ) 3 ) & F $ > " &+ ) & & " $ 9 '=( 4 ") 3 "" " ,
" 0 & " & ) , ,, , 8) 9! =( 4" ), " $ " F + 3 $ & F " )" > , & " 0 D 3 & &
, 0" $ " & ( & Q#- (
7 )" & "" > ")& & , " 0 "+ & 3 ) ) 3) ( H > 3 & 3) " # $ " 0" $ $) 0 , &(
7 & , " ) ""+ & 0+ & $ " , 0+ && , > & =( & =9 & D 3 " E , =( =9 & , & & &) &
> " E , & & =( & =9 " & "+( 7 3 ) , " > " " & 0+ $ " , ( 7 0 $ $)$ & $ F $)$ 0" &) 3 ,
& $ " ) 0) > & 3 3 F , =( =9 &) )"& 3 0 " + & $ (
P " , 3"+ ) & ) & L " ) , "" " & ,, , ( 0 & & ) ,, , 8) $ " $ $ )
$ $)$ 3) 3 "" " $ + "" " 3 $ " , &
+ ) $ &) , ) $ & ) $ $ 3 ) 3 E " ( 7
8) $ $ , 0) & 0 ), ), & 3+ ) > ,
';
, & , 3) 3 '( &) " 3 & 3 , 0? &) "" > , " $ $ ) 0) $ " 0" 3 $ ) , & &
8) " +( N > , , > F & $$ & " $ $ ) ", $ (
% ""+ $ & 0? &) 0 "+ &?) & 0) $ ) > ) ) $ & ( N " & > "+ &) &?) $ ) ) $ &
0 & $ " ) 3 " $ " ( H+ # " 3 + . & )& & & F $ " 3 & 0+ C7H 9 & = > & , " 3 $ &( N
> > E , $)" $ & "+ 3 & 3 #CP )& & & & )& "+ 3 #CP & & (
7 3 " , " , " $ $ ) ", $ > " + 0" 3 $ " )" & &?) $ > ) ) " " , @ " , $ $)$A 3
8) " +(
9 1
94 ;<= 4 )? (I( , 7( ( " M(!( > E %" > # H "" ;;<( 94 H ;;= 4 )? (I( H 0 )$ 5( ( " M(!( " , F , 5) " > E %" > # 0" $( L = ) 5 ")$ ;;; ( < ( 94"" <= 4"" M(%( J , I >" ,& 0 ) 7 $ " " K( ) ")8 ' @ A $0 ; < ( <' <(9! <= ! " !( & " $ & 0"X$ & + & " & )$
+ $ & ( # 5 7 !" # " " $ % & % ( " M N - O ( 9! < = ! " !( + #( $)$ F 7 # 0" $ # "" " P ( C" C% % C ")$ <L ' < ( '' '< ( 9! <0= ! " !( + #( $)$ F # > 7 # 0" $ B) # "" " P ( < ; !" # " + " $ % & % ' <( " M 944G CC4G(P 9! = ! " !( 4,, , 4 3 $)$ ! + 7 # 0" $( !" # " + " $ % & % ' ( " M 944D CC4D4Q 9! P '= ! , ( P )" H ) 4( # , $$ ? )F )F & ( 5) & ; '(
9! IN;;= ! "" ( I" N( N & " M( J4 & 4& ,+ 3 )" $ & # K(
")8 8 " & 4 0 ;;;( 9!): ;< = !) ( ( : ""> , #(7( J4) $ 7 $ " + ) $ K ")8 ) 8 " 3 4 ;;< ( < < ( 9!): ;<0= !) ( ( : ""> , #(7( J4) $ ""+ P , &)" 3 )" $ & 5 )$ K( ")8 8 5 R , Y " , @'A $0 ;;< ( L( 9! = !)" $ 5( (%(P( & ,) (%( ( JB # , 4&
H+ $ & % $ K 7 " 3 7 " & 0 # & M ! . " + ' (
95 4 = 5 + 4(I( "0 5( 40 >& P(5( J4 ) " % $ > E & 7 "E 3 ) ,
& # + , 3 F 4> 4 " K( 2 ) .2) 1 R
<
95 ; = 5 . ( #( J7 $ $ # & " 3 7 $ & )" $ & 3 $ K
< (F ) " < = : , . ;;
( ' ; '< (
95)I ; = 5)& 4( I $ ( J ) ) & 7 $ " $ 3 )" $ & 5 K( <
### S 8 A 8 5 !") ) E
4 4),) ;; (
9%)"E = %)"E 5( ( J4 ) 3 I " & 3 $ " %" > # 0" $ K( 5 "8 R
" 8 "( ; ; ( 'L(
9H &?; = H &? ( # 0"X$ & ) ) , Z 4", $ $ " F ( # 5 7
& " & "" % ;; (
9M HI;L= M , 7( H $ M( I $ ( J4 # &)" , $ 3 )" $ & #
+ . K( ### ) 8 ) 5 > & ;;L ( <L; < ( 9I 7 = I M( 7 B( J# 3 &)" , 3 $ H+ $ & K ### ) ) )) 944( H " E % " & M) ' ( 9I ; = I $ ( , M( J )" $ & 5 )$ > C" 7 $ K( < ")8 8 7PF [ % 4 $0 ;; (
9I"P%;;= I" N( P ( % &" ( J & # Z P "" + 3 & ) , +K( ###
) 8 ) 5 . )857PP1 %" "+ M) ;;;(
9 '= + \& ( 0 + $ " ( ( J5 " , > ) &) + . &
$)" $ & K( 8 " R I")> 4 & $ #)0" @<A
5 $0 ' ' ( ' < '< (
9 P ; = " 7( P 3 4( J + . & , & " 3 )" $ & 0? K( ###
R 5 " ) @<A 4 " ;; ( < 'L(
9 '= & (7( 0 ( ( (%(P( J4) $ &)" , 3 H+ $ & 5 )$
> C" 7 $ K( < < L ' ' ( ;(
9 ) '= ) ") & 5( ( (%(P( JQ ] Q7 $ " D $ ,
CF & ) N 0 4) , ,) , K = C 2 8
R 7 +" P $ "( ' ' ( <; ;(
9 ) <= ) ") & 5( ( J " H+ $ & 4) , ,) , D $ , ) &
CF K # 5 7 3 $ 5 $ # & M ! . " ' <( " M 944GO4GO O 9# ; = # . )8) (M( " 7(5( ( J4 7 $ " 3 % $ > E 3 )" $ & + . K( ### R 5 " ) .5 M 5 8 ) 1 @ A M ) + ;; ( < ( 9#" L = #" M( ( 4 ) 3 I " 4", $ 3 " , $)$ # " # 0" $ ( 8 < ;L ( 'L '; 9 E = E 3 "" (7( > E %" > & $ . ( M( N " +( ; (
9 <= & ,) (%( (%(P J & & 0? B # , 4&
% $ K ")8 5 A # P 0" % $0 ' <(
9 & = & ,) (%( ) & ,) #( ( % ?^ !( Y " ( (%(P( J & &
C" 7 $ 4& # D , 3 7 "E , H & 7 " > H+ $ &
% $ K 7 " 3 7 " & 0 # & M ! . " ' (
9 ;<= )$ P( M M( )"" & I( ( !)" $ 5( J % &D 4 # C $
<
9 = (%(P( & ,) (%( ) ") & 5( ( J & " , 4) , & % $ ,
H+ $ & 5 )$ H+ # + $K ")8 8 5 R , Y " ,
@'A ' ( < (
9N< = N "& N & N 0 )$ @N< A( J + . & )" $ & , ,) , @
<'
(
7 " 3 $ $)$ 0" $ & 0 & "") & + $ " F $ " & , + . 3 > ( 7 0 $ @$ )$ $ $ F & " 8) A > "" 0 $ & 3 3 "" > , $ & " C9D
$ . @θ A+ '@θ'A )0? θ −θ'= $ F $ θ θ θ ≤ ≤ $ F ' ' $ ' θ θ θ ≤ ≤
N ) θS<θS' > θS & θS' & " &) & " =θS' −θS( /
& 0? 3) $ θS −θ +θS'−θ' ( −& 0 > & " ") =@θSGθS'A & θ −θ'= ( E , % ,)
$ " ") ) 8) 0) ) ) 3 0 " ( 3 3 F , θ
0 > θS & θS' θ' " & &) & 0 > θS & θS'( % ,) ") & 0+ 3)"" ,$ 9@θSGθSAG@θS'GθS'A=( θ θ θ $ θ' $ θ' θ' θ' θ θ' θ V V V V ! " + # % $ 0 ") > "+ 0? & & F 3 θ =θS θ' =θS' − =θS(
<< 6 ; & 0? 3)
( ) ( )
' ' ' ' S S $ θ −θ +θ −θ ( ) " & & @ $ 'A 0 > & " ") =@θSGθS'A & θ −θ'= ( 4 $ "+ F $ " ") "> + ) 8) ( , " ? 3 @θSGθS'A '= −θ θ ( % ,) ") & 0+ 5 > ' S ' S ' ' = − + =θ θ θ θ ( " 0 0? 8) ""+ & &( θ θ θ $ θ' $ θ' θ' θ' θ θ θ $ θ' $ θ' θ' θ θ' ' θ ' V V V V ! " 2 # % $ * / / ( & 0? 3) $ $ F{
θS −θ GθS' −θ'}
( H > + $ $ . $ F $ " 0 ") & @ $ ∞A 0 > & " ") =@θSGθS'A &'=
−θ
θ ( $ " ") ) 8) @ F $ " 0) , " A
