From 3c56b3b02a655b0e8048c31ca707edfc14e923c7 Mon Sep 17 00:00:00 2001 From: couchot Date: Thu, 28 Nov 2013 11:54:46 +0100 Subject: [PATCH 1/1] jout dossier seminaire --- sem1305/#assync.tex# | 31 + sem1305/#problematique5.tex# | 24 + sem1305/Hexagones.jpg | Bin 0 -> 31034 bytes sem1305/RCapproche.tex.bak | 6 + sem1305/assync.tex | 28 + sem1305/assync.tex~ | 16 + sem1305/beamerthemefemto.sty | 217 ++++ sem1305/caracteristique.tex.bak | 15 + sem1305/caracteristique2.tex.bak | 13 + sem1305/cv.tex | 8 + sem1305/cv.tex~ | 2 + sem1305/formalisation.tex~ | 1 + sem1305/formalisationenergie.tex | 13 + sem1305/formalisationenergie.tex.bak | 12 + sem1305/formalisationenergie.tex~ | 12 + sem1305/formalisationflux.tex | 32 + sem1305/formalisationflux.tex~ | 31 + sem1305/formalisationglobale.tex | 18 + sem1305/formalisationglobale.tex~ | 15 + sem1305/formalisationsimplifiee.tex | 21 + sem1305/formalisationsimplifiee.tex~ | 19 + sem1305/interation1.tex | 23 + sem1305/interation1.tex~ | 24 + sem1305/interation2.tex | 45 + sem1305/interation2.tex~ | 24 + sem1305/lagrange.tex | 25 + sem1305/lagrange.tex~ | 25 + sem1305/lagrangeoperateur.tex | 24 + sem1305/lagrangeoperateur.tex~ | 24 + sem1305/logo-CNRS.jpg | Bin 0 -> 31161 bytes sem1305/logo-ENSMM.jpg | Bin 0 -> 41727 bytes sem1305/logo-FEMTO.jpg | Bin 0 -> 24217 bytes sem1305/logo-UFC.jpg | Bin 0 -> 27379 bytes sem1305/logo-UTBM.jpg | Bin 0 -> 9120 bytes sem1305/main.aux | 79 ++ sem1305/main.log | 1620 ++++++++++++++++++++++++++ sem1305/main.nav | 51 + sem1305/main.out | 3 + sem1305/main.pdf | Bin 0 -> 380433 bytes sem1305/main.snm | 0 sem1305/main.tex | 114 ++ sem1305/main.tex.bak | 113 ++ sem1305/main.tex~ | 113 ++ sem1305/main.thm | 0 sem1305/main.toc | 5 + sem1305/merci.tex | 1 + sem1305/pbprng.tex.bak | 28 + sem1305/qualitePRNG.tex.bak | 11 + sem1305/rem0.tex | 13 + sem1305/rem0.tex.bak | 13 + sem1305/rem0.tex~ | 0 sem1305/rem1.tex | 51 + sem1305/rem1.tex~ | 51 + sem1305/reseau.png | Bin 0 -> 86702 bytes sem1305/sense.jpg | Bin 0 -> 9829 bytes sem1305/texput.log | 21 + sem1305/wsn.png | Bin 0 -> 64834 bytes 57 files changed, 3035 insertions(+) create mode 100644 sem1305/#assync.tex# create mode 100644 sem1305/#problematique5.tex# create mode 100644 sem1305/Hexagones.jpg create mode 100644 sem1305/RCapproche.tex.bak create mode 100644 sem1305/assync.tex create mode 100644 sem1305/assync.tex~ create mode 100644 sem1305/beamerthemefemto.sty create mode 100644 sem1305/caracteristique.tex.bak create mode 100644 sem1305/caracteristique2.tex.bak create mode 100644 sem1305/cv.tex create mode 100644 sem1305/cv.tex~ create mode 100644 sem1305/formalisation.tex~ create mode 100644 sem1305/formalisationenergie.tex create mode 100644 sem1305/formalisationenergie.tex.bak create mode 100644 sem1305/formalisationenergie.tex~ create mode 100644 sem1305/formalisationflux.tex create mode 100644 sem1305/formalisationflux.tex~ create mode 100644 sem1305/formalisationglobale.tex create mode 100644 sem1305/formalisationglobale.tex~ create mode 100644 sem1305/formalisationsimplifiee.tex create mode 100644 sem1305/formalisationsimplifiee.tex~ create mode 100644 sem1305/interation1.tex create mode 100644 sem1305/interation1.tex~ create mode 100644 sem1305/interation2.tex create mode 100644 sem1305/interation2.tex~ create mode 100644 sem1305/lagrange.tex create mode 100644 sem1305/lagrange.tex~ create mode 100644 sem1305/lagrangeoperateur.tex create mode 100644 sem1305/lagrangeoperateur.tex~ create mode 100644 sem1305/logo-CNRS.jpg create mode 100644 sem1305/logo-ENSMM.jpg create mode 100644 sem1305/logo-FEMTO.jpg create mode 100644 sem1305/logo-UFC.jpg create mode 100644 sem1305/logo-UTBM.jpg create mode 100644 sem1305/main.aux create mode 100644 sem1305/main.log create mode 100644 sem1305/main.nav create mode 100644 sem1305/main.out create mode 100644 sem1305/main.pdf create mode 100644 sem1305/main.snm create mode 100644 sem1305/main.tex create mode 100644 sem1305/main.tex.bak create mode 100644 sem1305/main.tex~ create mode 100644 sem1305/main.thm create mode 100644 sem1305/main.toc create mode 100644 sem1305/merci.tex create mode 100644 sem1305/pbprng.tex.bak create mode 100644 sem1305/qualitePRNG.tex.bak create mode 100644 sem1305/rem0.tex create mode 100644 sem1305/rem0.tex.bak create mode 100644 sem1305/rem0.tex~ create mode 100644 sem1305/rem1.tex create mode 100644 sem1305/rem1.tex~ create mode 100644 sem1305/reseau.png create mode 100644 sem1305/sense.jpg create mode 100644 sem1305/texput.log create mode 100644 sem1305/wsn.png diff --git a/sem1305/#assync.tex# b/sem1305/#assync.tex# new file mode 100644 index 0000000..b5a9dd5 --- /dev/null +++ b/sem1305/#assync.tex# @@ -0,0 +1,31 @@ +\begin{itemize} +\item Calculs effectués sur chaque n{\oe}ud: réécriture de +$$ +w_l^{(k+1)} = w_l^{(k+1)} + \theta^{(k)}. \left( \sum_{i \in N} a_{il}.q_i^{(k)} \right) +$$ +\item Conditions pour la convergence asynchrone du calcul\footnote{Nedić, A., Bertsekas, D. P., \& Borkar, V. S. (2001). Distributed asynchronous incremental subgradient methods. Studies in Computational Mathematics, 8, 381-407.} +\begin{itemize} +\item Majoration des sous-gradients par une constante $C$ +\item $\theta$: sous la forme $\omega / t^{q}$ avec $3/4 < q \leq 1$ + \end{itemize} +\item Premières expérimentations: +\begin{itemize} +\item Pour chaque variable $X$ à modifier: + $X^{k+1} = f(X^{k}) if \textit{random()}B-;7)=E*FbO!GB`811cC*3CqU3)a0Y@C2o@Lug9LXU zAb9XIxu5%azdBW?>N{so)%vsc?A_ga^;+FmU;XgwVFf^|X!#v;> z02>nv8w(Q~8w(o;2OAfk1Roy{5C1U{F#*Yw$5d2L9#c|2rDJ7yO2bS`Ny*5~$jrvh z!O20*z{AJ$oR9T6$Me4rLBqkp!NW_ZtU3t*9UTn~6AKpy6Bi2u6Lljx0D}~h>>0lt z7P+>2=wl`UK}(OMI_#G^x}H7b%<_fxEJClWKP0dI#-Xrk`1abX2vF$a7}ywi|4yT!V_;&DJ|olSm$Srv=^k3wL;iS` zf{9tc<3r*2?}s@60R~EXQVddn4B$?el!TNN?f-WmCmN1<`-?N4B^M1t09Fz*x$7Y- zp>*|Trn*_X?M)lS-F`yiw!q7m6jF}oRSTw<1qm;3DQS_#q=R-I+;vDXk2kFxle(!& z`won;Vy78kS22b0#MKA_bO~nQGe&sPQX%>K%_z(eb{@UDZy(;YKJVyOFI1NWsQNkk zU*RfpPO_&j@A`55=rlSBM+Tn^-bQMW;3FWGJ(H`QlDBr^^NkMxBRXKPPngdUL*_@d 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zwrYgMUtOOs)611r<2Pw)Wc#a#S6=Q&qdS%!Q7`iwP$8d+GMqCw|Bs#U-*wD&8GUig z+|)w6N5?p8W(#MmD5fl&Nm@Op`ts=yubt3C+03g?wSRwl9R)NfTX8y|`KVcfT_dQy^7+573I{mEsH zzd)JjzYoWQO_VOkafboA7Qc%zd&BtEF~f^yp3D$EyqUNYIZ;8IYzOxgE{RtaMN4mh z5Cd-^@yZtaN$~{rg^l!4Cc1rq^VE>&>o(c=EUcGvJyF|9%F8L9Y1C&AX9p)?mwYVI zM8E5n%#koVA7jZhHm~;Z`$5y7!Kw}j^a#$gKNQ1Y1!T1*D~uv$i+x`+T^r>84;N*x zj;gah@VyCC!yW~&4&YuznxX|?sP~n;Uur@leTs*Nngi^V;PVUTt9Ndk1pRlLKPeM1CIIMI|JiP7W8$A>k-Z=fdu`sl3}d~m8#h$*F; z7ZgG=ZFtiEg(Zp@c~y!R*IXWdjT#`Z)DV1&q5W(QIBCyF-QhvVK$h%(ZTw9qg?hJc zrD@SGo>p*yzw1yQl1V|Exx0PP3%e&{Z030wwpn$yx*uQJ)Azlk$Yu-O%UDtlz|N7;3>)5$sc4oBvoh^Sa z0%TY1qimd5jmggKLDQ(HT_W?ZmZ;S50_XpSeZ>FP{QD2p1F=owiql@%8gJ~PdUH5q uMgq54o#j0u;A%CjzfBQ!br&MQp{$P_{si} > 0$}. +\item Distorsion bornée: \alert<2>{$\sigma^2 e^{-\gamma . R_h.P_{sh}^{}2/3} \leq D_h$}. +\item Charge initiale du n{\oe}ud $i$: $B_i$ +\item Puissance dissipée au n{\oe}ud $i$: +$$ +P_{si}+ P_{ti} + P_{ri}= +\alert<2>{P_{si}+ \sum_{l \in L}a_{il}^{+}.c^s_l.y_l + +\sum_{l \in L} a_{il}^{-}.c^r.y_l \leq q.B_i}. +$$ + +\end{itemize} + diff --git a/sem1305/formalisationenergie.tex.bak b/sem1305/formalisationenergie.tex.bak new file mode 100644 index 0000000..7d873ec --- /dev/null +++ b/sem1305/formalisationenergie.tex.bak @@ -0,0 +1,12 @@ +\begin{itemize} +\item Puissance d'encodage au n{\oe}ud $i$: $P_{si}$, \alert<2>{$P_{si} > 0$}. +\item Distortion bornée: \alert<2>{$\sigma^2 e^{-\gamma . R_h.P_{sh}^{}2/3} \leq D_h$}. +\item Puissance dissipée au n{\oe}ud $i$: +$$ +P_{si}+ P_{ti} + P_{ri}= +\alert<2>{P_{si}+ \sum_{l \in L}a_{il}^{+}.c^s_l.y_l + +\sum_{l \in L} a_{il}^{-}.c^r.y_l}. +$$ + +\end{itemize} + diff --git a/sem1305/formalisationenergie.tex~ b/sem1305/formalisationenergie.tex~ new file mode 100644 index 0000000..397f606 --- /dev/null +++ b/sem1305/formalisationenergie.tex~ @@ -0,0 +1,12 @@ +\begin{itemize} +\item Puissance d'encodage au n{\oe}ud $i$: $P_{si}$, \alert<2>{$P_{si} > 0$}. +\item Distorsion bornée: \alert<2>{$\sigma^2 e^{-\gamma . R_h.P_{sh}^{}2/3} \leq D_h$}. +\item Puissance dissipée au n{\oe}ud $i$: +$$ +P_{si}+ P_{ti} + P_{ri}= +\alert<2>{P_{si}+ \sum_{l \in L}a_{il}^{+}.c^s_l.y_l + +\sum_{l \in L} a_{il}^{-}.c^r.y_l}. +$$ + +\end{itemize} + diff --git a/sem1305/formalisationflux.tex b/sem1305/formalisationflux.tex new file mode 100644 index 0000000..4e20fd8 --- /dev/null +++ b/sem1305/formalisationflux.tex @@ -0,0 +1,32 @@ +%\vspace{-2em} +\begin{itemize} +\item Article publiée en 2009\footnote{Yifeng He; Lee, I.; Ling Guan, "Distributed Algorithms for Network Lifetime Maximization in Wireless Visual Sensor Networks," Circuits and Systems for Video Technology, IEEE Transactions on , vol.19, no.5, pp.704,718, May 2009} +\item Graphe orienté fort. connexe, +$a_{il} = +\left\{ + \begin{array}{rl} + 1 & \textrm{si $l=(i,\_)$ } \\ + -1 & \textrm{si $l=(\_,i)$} \\ + 0 & \textrm{sinon} + \end{array} + \right.$ +\item $V$ l'ensemble des capteurs vidéos de $N$. +\item Encodage de la vidéo au n{\oe}ud $h$ au taux $R_h$, \alert<2>{$R_h \geq 0$} \\ + $\leadsto$ Taux de production $\eta_{hi}$ du n{\oe}ud $i$ pour la session $h$ + $\eta_{hi} = +\left\{ + \begin{array}{rl} + R_h & \textrm{si $i$ est $h$} \\ + -R_h & \textrm{si $i$ est le puits} \\ + 0 & \textrm{sinon} + \end{array} + \right.$ +\item Flux de la session $h$ dans l'arc $l$: $x_{hl}$, \alert<2>{$x_{hl}\geq 0$} +\item Pour $y_l$ la somme des flux dans $l$: +\alert<2>{$\forall l \in L +\sum_{h \in V}x_{hl} = y_l$} +\item Conservation du flux: +\alert<2>{$\forall h \in V, \forall i \in N +\sum_{l \in L }a_{il}x_{hl} = \eta_{hi}$} +\end{itemize} + diff --git a/sem1305/formalisationflux.tex~ b/sem1305/formalisationflux.tex~ new file mode 100644 index 0000000..07fd5de --- /dev/null +++ b/sem1305/formalisationflux.tex~ @@ -0,0 +1,31 @@ +%\vspace{-2em} +\begin{itemize} +\item Graphe orienté fort. connexe, +$a_{il} = +\left\{ + \begin{array}{rl} + 1 & \textrm{si $l=(i,\_)$ } \\ + -1 & \textrm{si $l=(\_,i)$} \\ + 0 & \textrm{sinon} + \end{array} + \right.$ +\item $V$ l'ensemble des capteurs vidéos de $N$. +\item Encodage de la vidéo au n{\oe}ud $h$ au taux $R_h$, \alert<2>{$R_h>0$} \\ + $\leadsto$ Taux de production $\eta_{hi}$ du n{\oe}ud $i$ pour la session $h$ + $\eta_{hi} = +\left\{ + \begin{array}{rl} + R_h & \textrm{si $i$ est $h$} \\ + -R_h & \textrm{si $i$ est le puits} \\ + 0 & \textrm{sinon} + \end{array} + \right.$ +\item Flux de la session $h$ dans l'arc $l$: $x_{hl}$, \alert<2>{$x_{hl}>0$} +\item Pour $y_l$ la somme des flux dans $l$: +\alert<2>{$\forall l \in L +\sum_{h \in V}x_{hl} = y_l$} +\item Conservation du flux: +\alert<2>{$\forall h \in V, \forall i \in N +\sum_{l \in L }a_{il}x_{hl} = \eta_{hi}$} +\end{itemize} + diff --git a/sem1305/formalisationglobale.tex b/sem1305/formalisationglobale.tex new file mode 100644 index 0000000..1530578 --- /dev/null +++ b/sem1305/formalisationglobale.tex @@ -0,0 +1,18 @@ +\begin{itemize} +\item Trouver $R$, $x$, $P_s$ minimisant $q$ t.q. + +\item $\sum_{l \in L }a_{il}x_{hl} = \eta_{hi},\forall h \in V, \forall i \in N $ + +\item $ \sum_{h \in V}x_{hl} = y_l,\forall l \in L$ +\item $\dfrac{\ln(\sigma^2/D_h)}{\gamma.P_{sh}^{2/3}} \leq R_h \forall h \in V$ + +\item $P_{si}+ \sum_{l \in L}a_{il}^{+}.c^s_l.y_l + +\sum_{l \in L} a_{il}^{-}.c^r.y_l \leq q.B_i, \forall i \in N$ + +\item $x_{hl}\geq0, \forall h \in V, \forall l \in L$ + +\item $R_h \geq 0, \forall h \in V$ + +\item $P_{sh} > 0,\forall h \in V$ + +\end{itemize} diff --git a/sem1305/formalisationglobale.tex~ b/sem1305/formalisationglobale.tex~ new file mode 100644 index 0000000..0b97c95 --- /dev/null +++ b/sem1305/formalisationglobale.tex~ @@ -0,0 +1,15 @@ +$$ +\begin{array}{rl} + +$$ + + +\item Puissance d'encodage au n{\oe}ud $i$: $P_{si}$, \alert<2>{$P_{si} > 0$}. +\item Distorsion bornée: \alert<2>{$\sigma^2 e^{-\gamma . R_h.P_{sh}^{}2/3} \leq D_h$}. +\item Charge initiale du n{\oe}ud $i$: $B_i$ +\item Puissance dissipée au n{\oe}ud $i$: +$$ +P_{si}+ P_{ti} + P_{ri}= +\alert<2>{P_{si}+ \sum_{l \in L}a_{il}^{+}.c^s_l.y_l + +\sum_{l \in L} a_{il}^{-}.c^r.y_l \leq q.B_i}. +$$ diff --git a/sem1305/formalisationsimplifiee.tex b/sem1305/formalisationsimplifiee.tex new file mode 100644 index 0000000..4889d50 --- /dev/null +++ b/sem1305/formalisationsimplifiee.tex @@ -0,0 +1,21 @@ +\begin{itemize} +\item Trouver $R$, $x$, $P_s$, $q_i$ minimisant $\sum_{i \in N }q_i^2$ t.q. + +\item $\sum_{l \in L }a_{il}x_{hl} = \eta_{hi},\forall h \in V, \forall i \in N $ + +\item $\dfrac{\ln(\sigma^2/D_h)}{\gamma.P_{sh}^{2/3}} \leq R_h, \forall h \in V$ + +\item $P_{si}+ \sum_{l \in L}a_{il}^{+}.c^s_l.\left( \sum_{h \in V}x_{hl} \right) + +\sum_{l \in L} a_{il}^{-}.c^r.\left( \sum_{h \in V}x_{hl} \right) \leq q.B_i, \forall i \in N$ + +\item $\sum_{i \in N} a_{il}.q_i = 0 \forall l \in L$ + +\item $x_{hl}\geq0, \forall h \in V, \forall l \in L$ + +\item $R_h \geq 0, \forall h \in V$ + +\item $P_{sh} > 0,\forall h \in V$ + +\item $q_i > 0,\forall i \in N$ + +\end{itemize} diff --git a/sem1305/formalisationsimplifiee.tex~ b/sem1305/formalisationsimplifiee.tex~ new file mode 100644 index 0000000..5783373 --- /dev/null +++ b/sem1305/formalisationsimplifiee.tex~ @@ -0,0 +1,19 @@ +\begin{itemize} +\item Trouver $R$, $x$, $P_s$ minimisant $\sum_{i \in N }q_i^2$ t.q. + +\item $\sum_{l \in L }a_{il}x_{hl} = \eta_{hi},\forall h \in V, \forall i \in N $ + +\item $\dfrac{\ln(\sigma^2/D_h)}{\gamma.P_{sh}^{2/3}} \leq R_h \forall h \in V$ + +\item $P_{si}+ \sum_{l \in L}a_{il}^{+}.c^s_l.\left( \sum_{h \in V}x_{hl} \right) + +\sum_{l \in L} a_{il}^{-}.c^r.\left( \sum_{h \in V}x_{hl} \right) \leq q.B_i, \forall i \in N$ + +\item $\sum_{i \in N} a_{il}.q_i = 0 forall l \in L$ + +\item $x_{hl}\geq0, \forall h \in V, \forall l \in L$ + +\item $R_h \geq 0, \forall h \in V$ + +\item $P_{sh} > 0,\forall h \in V$ + +\end{itemize} diff --git a/sem1305/interation1.tex b/sem1305/interation1.tex new file mode 100644 index 0000000..c7a89e1 --- /dev/null +++ b/sem1305/interation1.tex @@ -0,0 +1,23 @@ +\begin{itemize} +\item +$ u_{hi}^{(k+1)} = u_{hi}^{(k)} - \theta^{(k)}. \left( + \eta_{hi}^{(k)} - \sum_{l \in L }a_{il}x_{hl}^{(k)} \right) $ +\item +$v_{h}^{(k+1)}= \max\left\{0,v_{h}^{(k)} - \theta^{(k)}.\left( R_h^{(k)} - \dfrac{\ln(\sigma^2/D_h)}{\gamma.(P_{sh}^{(k)})^{2/3}} \right)\right\}$ +\item + $\begin{array}{rcl} + \lambda_{i}^{(k+1)} = \lambda_{i}^{(k)} - \theta^{(k)}&.&\left( + q^{(k)}.B_i - + \sum_{l \in L}a_{il}^{+}.c^s_l.\left( \sum_{h \in V}x_{hl}^{(k)} \right) \right. \\ + && - \left. \sum_{l \in L} a_{il}^{-}.c^r.\left( \sum_{h \in V}x_{hl}^{(k)} \right) - P_{si}^{(k)} \right) +\end{array} +$ + +\item +$w_l^{(k+1)} = w_l^{(k+1)} + \theta^{(k)}. \left( \sum_{i \in N} a_{il}.q_i^{(k)} \right)$ + + +\item +$\theta^{(k)} = \omega / t^{1/2}$ +\end{itemize} + diff --git a/sem1305/interation1.tex~ b/sem1305/interation1.tex~ new file mode 100644 index 0000000..863d0c5 --- /dev/null +++ b/sem1305/interation1.tex~ @@ -0,0 +1,24 @@ +Trouver $R$, $x$, $P_s$, $q_i$ minimisant +$$ +\begin{array}{l} + L(R,x,P_s,q,u,v,\lambda,w)= \\ + \sum_{i \in N }q_i^2 + \sum_{h \in V, l \in L }\delta.x_{hl}^2 ++ \sum_{h \in V }\delta.R_{h}^2 \\ ++ \sum_{h \in V }\sum_{i \in N } u_{hi} \left(\sum_{l \in L }a_{il}x_{hl} - \eta_{hi}\right) \\ ++ \sum_{h \in V}v_{h}.\left( \dfrac{\ln(\sigma^2/D_h)}{\gamma.P_{sh}^{2/3}} - R_h \right) \\ ++ \sum_{i \in N} \lambda_{i}. \left( P_{si}+ \sum_{l \in L}a_{il}^{+}.c^s_l.\left( \sum_{h \in V}x_{hl} \right) \right. +\\ +\qquad \qquad \qquad + \left. \sum_{l \in L} a_{il}^{-}.c^r.\left( \sum_{h \in V}x_{hl} \right) - q.B_i \right) \\ ++ \sum_{l \in L} w_l. \left( \sum_{i \in N} a_{il}.q_i \right) +\end{array} +$$ +\begin{itemize} +\item $x_{hl}\geq0, \forall h \in V, \forall l \in L$ + +\item $R_h \geq 0, \forall h \in V$ + +\item $P_{sh} > 0,\forall h \in V$ + +\item $q_i > 0,\forall i \in N$ + +\end{itemize} diff --git a/sem1305/interation2.tex b/sem1305/interation2.tex new file mode 100644 index 0000000..af326e2 --- /dev/null +++ b/sem1305/interation2.tex @@ -0,0 +1,45 @@ +\begin{enumerate} +\item +$q_i^{(k)} = \arg\min_{q_i>0} +\left( +q^2 + q. +\left( +\sum_{l \in L } a_{il}w_l^{(k)}- +\lambda_i^{(k)}B_i +\right) +\right)$ + +\item +$ +P_{sh}^{(k)} += +\arg \min_{p > 0} +\left( +v_h^{(k)}.\dfrac{\ln(\sigma^2/D_h)}{\gamma p ^{2/3}} + \lambda_h^{(k)}p +\right) +$ + +\item +$ +R_h^{(k)} += +\arg \min_{r \geq 0 } +\left( +\delta r^2 +-v_h^{(k)}.r - \sum_{i \in N} u_{hi}^{(k)} \eta_{hi} +\right) +$ +\item +$ +x_{hl}^{(k)} = +\arg \min_{x \geq 0} +\left( +\delta.x^2 + x. +\sum_{i \in N} \left( +\lambda_{i}^{(k)}.(c^s_l.a_{il}^{+} + +c^r. a_{il}^{-} )+ + u_{hi}^{(k)} a_{il} +\right) +\right) + $ +\end{enumerate} diff --git a/sem1305/interation2.tex~ b/sem1305/interation2.tex~ new file mode 100644 index 0000000..863d0c5 --- /dev/null +++ b/sem1305/interation2.tex~ @@ -0,0 +1,24 @@ +Trouver $R$, $x$, $P_s$, $q_i$ minimisant +$$ +\begin{array}{l} + L(R,x,P_s,q,u,v,\lambda,w)= \\ + \sum_{i \in N }q_i^2 + \sum_{h \in V, l \in L }\delta.x_{hl}^2 ++ \sum_{h \in V }\delta.R_{h}^2 \\ ++ \sum_{h \in V }\sum_{i \in N } u_{hi} \left(\sum_{l \in L }a_{il}x_{hl} - \eta_{hi}\right) \\ ++ \sum_{h \in V}v_{h}.\left( \dfrac{\ln(\sigma^2/D_h)}{\gamma.P_{sh}^{2/3}} - R_h \right) \\ ++ \sum_{i \in N} \lambda_{i}. \left( P_{si}+ \sum_{l \in L}a_{il}^{+}.c^s_l.\left( \sum_{h \in V}x_{hl} \right) \right. +\\ +\qquad \qquad \qquad + \left. \sum_{l \in L} a_{il}^{-}.c^r.\left( \sum_{h \in V}x_{hl} \right) - q.B_i \right) \\ ++ \sum_{l \in L} w_l. \left( \sum_{i \in N} a_{il}.q_i \right) +\end{array} +$$ +\begin{itemize} +\item $x_{hl}\geq0, \forall h \in V, \forall l \in L$ + +\item $R_h \geq 0, \forall h \in V$ + +\item $P_{sh} > 0,\forall h \in V$ + +\item $q_i > 0,\forall i \in N$ + +\end{itemize} diff --git a/sem1305/lagrange.tex b/sem1305/lagrange.tex new file mode 100644 index 0000000..186b680 --- /dev/null +++ b/sem1305/lagrange.tex @@ -0,0 +1,25 @@ +\begin{itemize} +\item Trouver $R$, $x$, $P_s$, $q_i$ minimisant $\sum_{i \in N }q_i^2$ t.q. + +\item $\sum_{l \in L }a_{il}x_{hl} = \eta_{hi},\forall h \in V, \forall i \in N$ +\alert{$ \leadsto$ $u_{hi}$} + +\item $\dfrac{\ln(\sigma^2/D_h)}{\gamma.P_{sh}^{2/3}} \leq R_h, \forall h \in V$ +\alert{$ \leadsto$ $v_{h}$} +\item $P_{si}+ \sum_{l \in L}a_{il}^{+}.c^s_l.\left( \sum_{h \in V}x_{hl} \right) + +\sum_{l \in L} a_{il}^{-}.c^r.\left( \sum_{h \in V}x_{hl} \right) \leq q.B_i, \forall i \in N$ +\alert{$ \leadsto$ $\lambda_{i}$} + +\item $\sum_{i \in N} a_{il}.q_i = 0 \forall l \in L$ +\alert{$ \leadsto$ $w_{l}$} + + +\item $x_{hl}\geq0, \forall h \in V, \forall l \in L$ + +\item $R_h \geq 0, \forall h \in V$ + +\item $P_{sh} > 0,\forall h \in V$ + +\item $q_i > 0,\forall i \in N$ + +\end{itemize} diff --git a/sem1305/lagrange.tex~ b/sem1305/lagrange.tex~ new file mode 100644 index 0000000..f1b8aa4 --- /dev/null +++ b/sem1305/lagrange.tex~ @@ -0,0 +1,25 @@ +\begin{itemize} +\item Trouver $R$, $x$, $P_s$, $q_i$ minimisant $\sum_{i \in N }q_i^2$ t.q. + +\item $\sum_{l \in L }a_{il}x_{hl} = \eta_{hi},\forall h \in V, \forall i \in N$ +\alert{$ \leadsto$ $u_{hi}$} + +\item $\dfrac{\ln(\sigma^2/D_h)}{\gamma.P_{sh}^{2/3}} \leq R_h, \forall h \in V$ +\alert{$ \leadsto$ $v_{h}$} +\item $P_{si}+ \sum_{l \in L}a_{il}^{+}.c^s_l.\left( \sum_{h \in V}x_{hl} \right) + +\sum_{l \in L} a_{il}^{-}.c^r.\left( \sum_{h \in V}x_{hl} \right) \leq q.B_i, \forall i \in N$ +\alert{$ \leadsto$ $\lambda_{i}$} + +\item $\sum_{i \in N} a_{il}.q_i = 0 \forall l \in L$ +\alert{$ \leadsto$ $w_{l}$ + + +\item $x_{hl}\geq0, \forall h \in V, \forall l \in L$ + +\item $R_h \geq 0, \forall h \in V$ + +\item $P_{sh} > 0,\forall h \in V$ + +\item $q_i > 0,\forall i \in N$ + +\end{itemize} diff --git a/sem1305/lagrangeoperateur.tex b/sem1305/lagrangeoperateur.tex new file mode 100644 index 0000000..dfe1aa2 --- /dev/null +++ b/sem1305/lagrangeoperateur.tex @@ -0,0 +1,24 @@ +Trouver $R$, $x$, $P_s$, $q_i$ minimisant +$$ +\begin{array}{l} + L(R,x,P_s,q,u,v,\lambda,w)= \\ + \sum_{i \in N }q_i^2 + \alert<2>{\sum_{h \in V, l \in L } \delta.x_{hl}^2} ++ \alert<2>{\sum_{h \in V }\delta.R_{h}^2} \\ ++ \sum_{h \in V }\sum_{i \in N } u_{hi} \left(\sum_{l \in L }a_{il}x_{hl} - \eta_{hi}\right) \\ ++ \sum_{h \in V}v_{h}.\left( \dfrac{\ln(\sigma^2/D_h)}{\gamma.P_{sh}^{2/3}} - R_h \right) \\ ++ \sum_{i \in N} \lambda_{i}. \left( P_{si}+ \sum_{l \in L}a_{il}^{+}.c^s_l.\left( \sum_{h \in V}x_{hl} \right) \right. +\\ +\qquad \qquad \qquad + \left. \sum_{l \in L} a_{il}^{-}.c^r.\left( \sum_{h \in V}x_{hl} \right) - q.B_i \right) \\ ++ \sum_{l \in L} w_l. \left( \sum_{i \in N} a_{il}.q_i \right) +\end{array} +$$ +\begin{itemize} +\item $x_{hl}\geq0, \forall h \in V, \forall l \in L$ + +\item $R_h \geq 0, \forall h \in V$ + +\item $P_{sh} > 0,\forall h \in V$ + +\item $q_i > 0,\forall i \in N$ + +\end{itemize} diff --git a/sem1305/lagrangeoperateur.tex~ b/sem1305/lagrangeoperateur.tex~ new file mode 100644 index 0000000..863d0c5 --- /dev/null +++ b/sem1305/lagrangeoperateur.tex~ @@ -0,0 +1,24 @@ +Trouver $R$, $x$, $P_s$, $q_i$ minimisant +$$ +\begin{array}{l} + L(R,x,P_s,q,u,v,\lambda,w)= \\ + \sum_{i \in N }q_i^2 + \sum_{h \in V, l \in L }\delta.x_{hl}^2 ++ \sum_{h \in V }\delta.R_{h}^2 \\ ++ \sum_{h \in V }\sum_{i \in N } u_{hi} \left(\sum_{l \in L }a_{il}x_{hl} - \eta_{hi}\right) \\ ++ \sum_{h \in V}v_{h}.\left( \dfrac{\ln(\sigma^2/D_h)}{\gamma.P_{sh}^{2/3}} - R_h \right) \\ ++ \sum_{i \in N} \lambda_{i}. \left( P_{si}+ \sum_{l \in L}a_{il}^{+}.c^s_l.\left( \sum_{h \in V}x_{hl} \right) \right. +\\ +\qquad \qquad \qquad + \left. \sum_{l \in L} a_{il}^{-}.c^r.\left( \sum_{h \in V}x_{hl} \right) - q.B_i \right) \\ ++ \sum_{l \in L} w_l. \left( \sum_{i \in N} a_{il}.q_i \right) +\end{array} +$$ +\begin{itemize} +\item $x_{hl}\geq0, \forall h \in V, \forall l \in L$ + +\item $R_h \geq 0, \forall h \in V$ + +\item $P_{sh} > 0,\forall h \in V$ + +\item $q_i > 0,\forall i \in N$ + +\end{itemize} diff --git a/sem1305/logo-CNRS.jpg b/sem1305/logo-CNRS.jpg new file mode 100644 index 0000000000000000000000000000000000000000..9a7bdced2d0de5f2fa95e6ebc947b6c79b2e55b4 GIT binary patch literal 31161 zcmbTdWmp}})-AelcXtTx?(P;KxVuAe2=4Cg?he7-f)m_5xVt-Nz3-N9@AG^=?zy#| z>Y82MC8K)In$J_`3uJ10R$8b z90C#w8U_{)ctaC102Bla3=|v;0siRI0X0FIsjT{4DU@@_><0jx(^BWNh2y*MC9# z8`=LiU;+QXko_Cj|KM5$z=MGRA08MAKoIcwLRH`g`&Xof0jqY8jrL)-Y)6weE)1Gy zhuCTrYzuphe~kV4cCsz6N>C7Qz`xvT%QvHi}~ z$z#H5<%Gz|c(F6}I$-hv+R3VSEzq!IUFcA$FUvit#D-E!a;&sWU=|nL2zxDOUD<1iON6XG5!qrNQb%< z+1J{GFFqjiYR6Dl>jTvwI!!Mc>e6_ zh37vV_IH!4HsdBq7=HrjOnJ#Z0o@Av{p>g0tAIXmdr6Oja=%i>P*IH?la~2cGW^-4 z@ovJW)Exz+q$pjyHPuf*3YJ(iRD%mq4u9n`AM>?>@HL1OW#X&Aed|prsWs7qe*T-i z^;Bh0xq`MX0aGmu!2-Hp;A~2pTtEa>9_W9@%FWF+%SFeHjmbFef#MuVE?5Zi_xGA~ zWA^jCV}wo`J!$+cDvVpo0l}~qAJ%S;hyATt61xr2=@H56o}RpO?dg1)`ugR`VsUV5 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+%\renewtheorem{theorem}[theorem]{Théorème} + + + +\newcommand{\inputFrameb}[2]{ +\frame{ +\frametitle{#1} +%\begin{small} +\input{#2} +%\end{small} +}} + +\newcommand{\Nats}[0]{\ensuremath{\mathds{N}}} +\newcommand{\Z}[0]{\ensuremath{\mathbb{Z}}} +\newcommand{\R}[0]{\ensuremath{\mathds{R}}} +\newcommand{\Bool}[0]{\ensuremath{\mathds{B}}} +\newcommand{\StratSet}[0]{\ensuremath{\mathbb{S}}} + + +\newcommand{\fc}[1]{\ensuremath{\overline{#1}}} +%\renewcommand\footnotelayout{\tiny} +\let\oldfootnotesize\footnotesize +\renewcommand*{\footnotesize}{\oldfootnotesize\scriptsize} + +\usepackage{graphicx} +\DeclareGraphicsExtensions{.jpg, .png , .pdf, .bmp, .pdftex} + + +\title[Durée de vie d'un réseau de capteurs vidéos]{Optimisation de la durée de vie d'un réseau de capteurs vidéos} + +\author[couchot@femto-st.fr]{Jean-Fran\c{c}ois {\sc Couchot}, Ahmed \sc{Mostefaoui}} + +\institute[Institut FEMTO-ST]{\textit{Institut FEMTO-ST - Département DISC- Équipe AND}} + +\date[AMTECH'13]{31 Mai 2013} + +% ____ _____ ____ _ _ _____ +% | _ \| ____| __ )| | | |_ _| +% | | | | _| | _ \| | | | | | +% | |_| | |___| |_) | |_| | | | +% |____/|_____|____/ \___/ |_| +% + +%\newcommand{\Bool}[0]{\ensuremath{\mathds{B}}} + +\begin{document} +\setbeamertemplate{background}{\titrefemto} + +\begin{frame}[plain] +\titlepage +\end{frame} + +\setbeamertemplate{background}{\pagefemto} + +% \begin{frame}{Plan} +\setbeamertemplate{section in toc}[sections numbered] +% \tableofcontents +% \end{frame} + +\frame{\frametitle{Plan}\tableofcontents[hideallsubsections]} + +\section{Problématique générale} +\frame{\frametitle{Plan}\tableofcontents[currentsection,hideallsubsections]} +\inputFrameb{Contexte: réseau de capteurs vidéos}{cv} +\inputFrameb{Formalisation: réseau et flux}{formalisationflux} +\inputFrameb{Formalisation: énergie}{formalisationenergie} +\inputFrameb{Formulation globale}{formalisationglobale} +\inputFrameb{Formulation simplifiée}{formalisationsimplifiee} + + +\section{Démarche d'optimisation} +\frame{\frametitle{Plan}\tableofcontents[currentsection,hideallsubsections]} +\inputFrameb{Multiplicateurs de Lagrange\footnote{Palomar, D.P.; Mung Chiang, "A tutorial on decomposition methods for network utility maximization," Selected Areas in Communications, IEEE Journal on , vol.24, no.8, pp.1439,1451, Aug. 2006}}{lagrange} +\inputFrameb{Opérateur de Lagrange}{lagrangeoperateur} +\inputFrameb{Approche itérative: variables duales}{interation1.tex} +\inputFrameb{Approche itérative: variables primaires}{interation2.tex} + + +\section{Travaux en cours} +\frame{\frametitle{Plan}\tableofcontents[currentsection,hideallsubsections]} +\inputFrameb{Analyse des résultats}{rem0.tex} +\inputFrameb{Approche itérative: quelques remarques}{rem1.tex} +\inputFrameb{Approche itérative assynchrone}{assync.tex} +\inputFrameb{Merci}{merci.tex} + + +% \section{Conclusion et perspectives} +% \frame{\frametitle{Plan}\tableofcontents[currentsection,hideallsubsections]} + +\end{document} +% _____ ___ _ _ +% | ___|_ _| \ | | +% | |_ | || \| | +% | _| | || |\ | +% |_| |___|_| \_| +% diff --git a/sem1305/main.tex.bak b/sem1305/main.tex.bak new file mode 100644 index 0000000..1b4b24b --- /dev/null +++ b/sem1305/main.tex.bak @@ -0,0 +1,113 @@ +\documentclass{beamer} +\usepackage{beamerthemefemto} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{amsfonts,amsmath,amssymb,stmaryrd,dsfont} +\usepackage[french]{babel} +\usepackage{algorithm2e} +\usepackage{alltt} +%\usepackage[amsmath,thmmarks,thref,framed]{ntheorem} + + + + +%\theoremstyle{plain} +%\theoremsymbol{\ensuremath{\clubsuit}} +%\theoremseparator{.} +%\theoremprework{\hrulefill} +%\theorempostwork{\hrulefill\newline} +%\renewtheorem{theorem}[theorem]{Théorème} + + + +\newcommand{\inputFrameb}[2]{ +\frame{ +\frametitle{#1} +%\begin{small} +\input{#2} +%\end{small} +}} + +\newcommand{\Nats}[0]{\ensuremath{\mathds{N}}} +\newcommand{\Z}[0]{\ensuremath{\mathbb{Z}}} +\newcommand{\R}[0]{\ensuremath{\mathds{R}}} +\newcommand{\Bool}[0]{\ensuremath{\mathds{B}}} +\newcommand{\StratSet}[0]{\ensuremath{\mathbb{S}}} + + +\newcommand{\fc}[1]{\ensuremath{\overline{#1}}} +%\renewcommand\footnotelayout{\tiny} +\let\oldfootnotesize\footnotesize +\renewcommand*{\footnotesize}{\oldfootnotesize\scriptsize} + +\usepackage{graphicx} +\DeclareGraphicsExtensions{.jpg, .png , .pdf, .bmp, .pdftex} + + +\title[durée de vie d'un réseau de capteurs vidéos]{Optimisation de la durée de vie d'un réseau de capteurs vidéos} + +\author[couchot@femto-st.fr]{Jean-Fran\c{c}ois {\sc Couchot}, Ahmed \sc{Mostefaoui}} + +\institute[Institut FEMTO-ST]{\textit{Institut FEMTO-ST - Département DISC- Équipe AND}} + +\date[AMTECH'13]{31 Mai 2013} + +% ____ _____ ____ _ _ _____ +% | _ \| ____| __ )| | | |_ _| +% | | | | _| | _ \| | | | | | +% | |_| | |___| |_) | |_| | | | +% |____/|_____|____/ \___/ |_| +% + +%\newcommand{\Bool}[0]{\ensuremath{\mathds{B}}} + +\begin{document} +\setbeamertemplate{background}{\titrefemto} + +\begin{frame}[plain] +\titlepage +\end{frame} + +\setbeamertemplate{background}{\pagefemto} + +% \begin{frame}{Plan} +\setbeamertemplate{section in toc}[sections numbered] +% \tableofcontents +% \end{frame} + +\frame{\frametitle{Plan}\tableofcontents[hideallsubsections]} + +\section{Problématique générale} +\frame{\frametitle{Plan}\tableofcontents[currentsection,hideallsubsections]} +\inputFrameb{Contexte: réseau de capteurs vidéos}{cv} +\inputFrameb{Formalisation: réseau et flux}{formalisationflux} +\inputFrameb{Formalisation: énergie}{formalisationenergie} +\inputFrameb{Formulation globale}{formalisationglobale} +\inputFrameb{Formulation simplifiée}{formalisationsimplifiee} + +\section{Démarche d'optimisation} +\frame{\frametitle{Plan}\tableofcontents[currentsection,hideallsubsections]} +\inputFrameb{Multiplicateurs de Lagrange}{lagrange} +\inputFrameb{Opérateur de Lagrange}{lagrangeoperateur} +\inputFrameb{Approche itérative: variables duales}{interation1.tex} +\inputFrameb{Approche itérative: variables primaires}{interation2.tex} + + +\section{Travaux en cours} +\frame{\frametitle{Plan}\tableofcontents[currentsection,hideallsubsections]} +\inputFrameb{Analyse des résultats}{rem0.tex} +\inputFrameb{Approche itérative: quelques remarques}{rem1.tex} +\inputFrameb{Approche itérative assynchrone}{assync.tex} +\inputFrameb{Merci}{merci.tex} + + +% \section{Conclusion et perspectives} +% \frame{\frametitle{Plan}\tableofcontents[currentsection,hideallsubsections]} + +\end{document} +% _____ ___ _ _ +% | ___|_ _| \ | | +% | |_ | || \| | +% | _| | || |\ | +% |_| |___|_| \_| +% diff --git a/sem1305/main.tex~ b/sem1305/main.tex~ new file mode 100644 index 0000000..19c164f --- /dev/null +++ b/sem1305/main.tex~ @@ -0,0 +1,113 @@ +\documentclass{beamer} +\usepackage{beamerthemefemto} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{amsfonts,amsmath,amssymb,stmaryrd,dsfont} +\usepackage[french]{babel} +\usepackage{algorithm2e} +\usepackage{alltt} +%\usepackage[amsmath,thmmarks,thref,framed]{ntheorem} + + + + +%\theoremstyle{plain} +%\theoremsymbol{\ensuremath{\clubsuit}} +%\theoremseparator{.} +%\theoremprework{\hrulefill} +%\theorempostwork{\hrulefill\newline} +%\renewtheorem{theorem}[theorem]{Théorème} + + + +\newcommand{\inputFrameb}[2]{ +\frame{ +\frametitle{#1} +%\begin{small} +\input{#2} +%\end{small} +}} + +\newcommand{\Nats}[0]{\ensuremath{\mathds{N}}} +\newcommand{\Z}[0]{\ensuremath{\mathbb{Z}}} +\newcommand{\R}[0]{\ensuremath{\mathds{R}}} +\newcommand{\Bool}[0]{\ensuremath{\mathds{B}}} +\newcommand{\StratSet}[0]{\ensuremath{\mathbb{S}}} + + +\newcommand{\fc}[1]{\ensuremath{\overline{#1}}} +%\renewcommand\footnotelayout{\tiny} +\let\oldfootnotesize\footnotesize +\renewcommand*{\footnotesize}{\oldfootnotesize\scriptsize} + +\usepackage{graphicx} +\DeclareGraphicsExtensions{.jpg, .png , .pdf, .bmp, .pdftex} + + +\title[Durée de vie d'un réseau de capteurs vidéos]{Optimisation de la durée de vie d'un réseau de capteurs vidéos} + +\author[couchot@femto-st.fr]{Jean-Fran\c{c}ois {\sc Couchot}, Ahmed \sc{Mostefaoui}} + +\institute[Institut FEMTO-ST]{\textit{Institut FEMTO-ST - Département DISC- Équipe AND}} + +\date[AMTECH'13]{31 Mai 2013} + +% ____ _____ ____ _ _ _____ +% | _ \| ____| __ )| | | |_ _| +% | | | | _| | _ \| | | | | | +% | |_| | |___| |_) | |_| | | | +% |____/|_____|____/ \___/ |_| +% + +%\newcommand{\Bool}[0]{\ensuremath{\mathds{B}}} + +\begin{document} +\setbeamertemplate{background}{\titrefemto} + +\begin{frame}[plain] +\titlepage +\end{frame} + +\setbeamertemplate{background}{\pagefemto} + +% \begin{frame}{Plan} +\setbeamertemplate{section in toc}[sections numbered] +% \tableofcontents +% \end{frame} + +\frame{\frametitle{Plan}\tableofcontents[hideallsubsections]} + +\section{Problématique générale} +\frame{\frametitle{Plan}\tableofcontents[currentsection,hideallsubsections]} +\inputFrameb{Contexte: réseau de capteurs vidéos}{cv} +\inputFrameb{Formalisation: réseau et flux}{formalisationflux} +\inputFrameb{Formalisation: énergie}{formalisationenergie} +\inputFrameb{Formulation globale}{formalisationglobale} +\inputFrameb{Formulation simplifiée}{formalisationsimplifiee} + +\section{Démarche d'optimisation} +\frame{\frametitle{Plan}\tableofcontents[currentsection,hideallsubsections]} +\inputFrameb{Multiplicateurs de Lagrange\footnote{Palomar, D.P.; Mung Chiang, "A tutorial on decomposition methods for network utility maximization," Selected Areas in Communications, IEEE Journal on , vol.24, no.8, pp.1439,1451, Aug. 2006}}{lagrange} +\inputFrameb{Opérateur de Lagrange}{lagrangeoperateur} +\inputFrameb{Approche itérative: variables duales}{interation1.tex} +\inputFrameb{Approche itérative: variables primaires}{interation2.tex} + + +\section{Travaux en cours} +\frame{\frametitle{Plan}\tableofcontents[currentsection,hideallsubsections]} +\inputFrameb{Analyse des résultats}{rem0.tex} +\inputFrameb{Approche itérative: quelques remarques}{rem1.tex} +\inputFrameb{Approche itérative assynchrone}{assync.tex} +\inputFrameb{Merci}{merci.tex} + + +% \section{Conclusion et perspectives} +% \frame{\frametitle{Plan}\tableofcontents[currentsection,hideallsubsections]} + +\end{document} +% _____ ___ _ _ +% | ___|_ _| \ | | +% | |_ | || \| | +% | _| | || |\ | +% |_| |___|_| \_| +% diff --git a/sem1305/main.thm b/sem1305/main.thm new file mode 100644 index 0000000..e69de29 diff --git a/sem1305/main.toc b/sem1305/main.toc new file mode 100644 index 0000000..9600787 --- /dev/null +++ b/sem1305/main.toc @@ -0,0 +1,5 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {french} +\beamer@sectionintoc {1}{Probl\IeC {\'e}matique g\IeC {\'e}n\IeC {\'e}rale}{3}{0}{1} +\beamer@sectionintoc {2}{D\IeC {\'e}marche d'optimisation}{11}{0}{2} +\beamer@sectionintoc {3}{Travaux en cours}{17}{0}{3} diff --git a/sem1305/merci.tex b/sem1305/merci.tex new file mode 100644 index 0000000..0519ecb --- /dev/null +++ b/sem1305/merci.tex @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/sem1305/pbprng.tex.bak b/sem1305/pbprng.tex.bak new file mode 100644 index 0000000..058a792 --- /dev/null +++ b/sem1305/pbprng.tex.bak @@ -0,0 +1,28 @@ +\vspace{-1em} +\begin{scriptsize} +\begin{alltt} +111000100100000100010101100001010001110011100000 +010000010001101011001010001101110000111101111010 +100111111001110111001001110011010100100011111000 +100000000111111010110111000111101000101111011010 +\end{alltt} +\end{scriptsize} +\vspace{-1em} +\begin{itemize} +\item PRNG: algorithme déterministe de + génération de nombres suivant certaines propriétés de hasard +\item Utilisation en technologies mobiles: +\begin{itemize} +\item Clefs d'échange sur le réseau (WEP, HTTPS, chiffrement) +\item Mesure de distances (GPS) +\end{itemize} +\item Devrait être cryptographiquement sécurisé: +\begin{itemize} +\item Passer avec succes des tests statistiques (NIST, U01,\ldots) +\item Pour une séquence aléatoire donnée de $k$ bits: + aucun algorithme en temps polynomial + pouvant prédire le $k+1$ème avec une probabilité supérieure à 50\% +\item Connaître l'état $s$ de l'algorithme ne permet pas + de reconstruire les nombres aléatoires générés jusqu'à $s$. +\end{itemize} +\end{itemize} diff --git a/sem1305/qualitePRNG.tex.bak b/sem1305/qualitePRNG.tex.bak new file mode 100644 index 0000000..79c8dc1 --- /dev/null +++ b/sem1305/qualitePRNG.tex.bak @@ -0,0 +1,11 @@ +Evaluation des algorithmes: +\begin{itemize} +\item + Génération aléatoire de fonctions vérifiant + les critères du théorème précédent + et méthode constructive pour en générer~\footnote{Jacques Bahi, Jean-François Couchot, Christophe Guyeux, and Adrien Richard. On the Link Between Strongly Connected Iteration Graphs and Chaotic Boolean Discrete-Time Dynamical Systems. In FCT'11, 18th Int. Symp. on Fundamentals of Computation Theory, volume 6914 of LNCS, Oslo, Norway, pages 126--137, August 2011} +\item Succès à toutes les batteries de test~\footnote{Jacques Bahi, Xiaole Fang, Christophe Guyeux, and Qianxue Wang. Suitability of chaotic iterations schemes using XORshift for security applications. JNCA, Journal of Network and Computer Applications, *(*):***--***, 2013. Note: Accepted manuscript. To appear.} +\item Preuve de crypto sécurité et comparaison de complexité~\footnote{A Complexity Approach for Steganalysis. Journées Codes et Stéganographie, Hôtel de la Monnaie, Rennes, France, March 2012} + + +\end{itemize} diff --git a/sem1305/rem0.tex b/sem1305/rem0.tex new file mode 100644 index 0000000..6883003 --- /dev/null +++ b/sem1305/rem0.tex @@ -0,0 +1,13 @@ +\begin{itemize} +\item Validité du remplacement de $\sum_{i \in N }q_i^2$ par + $\sum_{i \in N }q_i^2 + {\sum_{h \in V, l \in L } \delta.x_{hl}^2} ++ {\sum_{h \in V }\delta.R_{h}^2}$? +\item Résultats expérimentaux avec $\delta = 0,2$ +\begin{itemize} +\item $q_i \approx 0,105$ et $0,1 \leq R_h \leq 0,15$ +\item $\sum_{i \in N }q_i^2 \approx 0.11$ vs. +$\sum_{i \in N }q_i^2 + {\sum_{h \in V, l \in L } \delta.x_{hl}^2} ++ {\sum_{h \in V }\delta.R_{h}^2} \geq 0,20$ +\item Non négligeable! +\end{itemize} +\end{itemize} diff --git a/sem1305/rem0.tex.bak b/sem1305/rem0.tex.bak new file mode 100644 index 0000000..944c8bf --- /dev/null +++ b/sem1305/rem0.tex.bak @@ -0,0 +1,13 @@ +\begin{itemize} +\item Validité du remplacement de $\sum_{i \in N }q_i^2$ par + $\sum_{i \in N }q_i^2 + {\sum_{h \in V, l \in L } \delta.x_{hl}^2} ++ {\sum_{h \in V }\delta.R_{h}^2}$? +\item Résultats experimentaux avec $\delta = 0,2$ +\begin{itemize} +\item $q_i \approx 0,105$ et $0,1 \leq R_h \leq 0,15$ +\item $\sum_{i \in N }q_i^2 \approx 0.11$ vs. +$\sum_{i \in N }q_i^2 + {\sum_{h \in V, l \in L } \delta.x_{hl}^2} ++ {\sum_{h \in V }\delta.R_{h}^2} \geq 0,20$ +\item Non négligeable! +\end{itemize} +\end{itemize} diff --git a/sem1305/rem0.tex~ b/sem1305/rem0.tex~ new file mode 100644 index 0000000..e69de29 diff --git a/sem1305/rem1.tex b/sem1305/rem1.tex new file mode 100644 index 0000000..fe7ef1e --- /dev/null +++ b/sem1305/rem1.tex @@ -0,0 +1,51 @@ +\begin{enumerate} +\item +$q_i^{(k)} = \arg\min_{q_i>0} +\left( +q^2 + q. +\left( +\sum_{l \in L } a_{il}w_l^{(k)}- +\lambda_i^{(k)}B_i +\right) +\right)$ + +\item +$ +P_{sh}^{(k)} += +\arg \min_{p > 0} +\left( +v_h^{(k)}.\dfrac{\ln(\sigma^2/D_h)}{\gamma p ^{2/3}} + \lambda_h^{(k)}p +\right) +$ + +\item +$ +R_h^{(k)} += +\arg \min_{r \geq 0 } +\left( +\delta r^2 +-v_h^{(k)}.r - \sum_{i \in N} u_{hi}^{(k)} \eta_{hi} +\right) +$ +\item +$ +x_{hl}^{(k)} = +\arg \min_{x \geq 0} +\left( +\delta.x^2 + x. +\sum_{i \in N} \left( +\lambda_{i}^{(k)}.(c^s_l.a_{il}^{+} + +c^r. a_{il}^{-} )+ + u_{hi}^{(k)} a_{il} +\right) +\right) + $ +\end{enumerate} +\begin{itemize} +\item Toutes les fonctions sont dérivables! +\item $ \leadsto$ pour 1. 3. 4., calcul direct du min! +\item 2. str. décroissante si $\lambda_h^{(k)}$ $\leadsto$ l'argmin est infini! +\item Convexité de 3. et 4. artificielle? Arbitraire? +\end{itemize} diff --git a/sem1305/rem1.tex~ b/sem1305/rem1.tex~ new file mode 100644 index 0000000..b234d5c --- /dev/null +++ b/sem1305/rem1.tex~ @@ -0,0 +1,51 @@ +\begin{enumerate} +\item +$q_i^{(k)} = \arg\min_{q_i>0} +\left( +q^2 + q. +\left( +\sum_{l \in L } a_{il}w_l^{(k)}- +\lambda_i^{(k)}B_i +\right) +\right)$ + +\item +$ +P_{sh}^{(k)} += +\arg \min_{p > 0} +\left( +v_h^{(k)}.\dfrac{\ln(\sigma^2/D_h)}{\gamma p ^{2/3}} + \lambda_h^{(k)}p +\right) +$ + +\item +$ +R_h^{(k)} += +\arg \min_{r \geq 0 } +\left( +\delta r^2 +-v_h^{(k)}.r - \sum_{i \in N} u_{hi}^{(k)} \eta_{hi} +\right) +$ +\item +$ +x_{hl}^{(k)} = +\arg \min_{x \geq 0} +\left( +\delta.x^2 + x. +\sum_{i \in N} \left( +\lambda_{i}^{(k)}.(c^s_l.a_{il}^{+} + +c^r. a_{il}^{-} )+ + u_{hi}^{(k)} a_{il} +\right) +\right) + $ +\end{enumerate} +\begin{itemize} +\item Toutes les fonctions sont dérivables! +\item $ \leadsto$ le min de 1. 3. 4. se calcule directement! +\item 2. str. décroissante si $\lambda_h^{(k)}$ $\leadsto$ l'argmin est infini! +\item Convexité de 3. et 4. artificielle? 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