From 3c56b3b02a655b0e8048c31ca707edfc14e923c7 Mon Sep 17 00:00:00 2001
From: couchot <jf.couchot@gmail.com>
Date: Thu, 28 Nov 2013 11:54:46 +0100
Subject: [PATCH] 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:
+  $X^{k+1} =  f(X^{k}) if \textit{random()}<T else X^{k}$
+\item Convergence pour 
+Synchrone
+1 746
+2 1580
+3 4490
+4 7257
+5 8541
+6 10000
+7 9189
+8 10000
+9 10000
+10 10000
+
+
+
+\end{itemize}
+\end{itemize}
diff --git a/sem1305/#problematique5.tex# b/sem1305/#problematique5.tex#
new file mode 100644
index 0000000..6385a47
--- /dev/null
+++ b/sem1305/#problematique5.tex#
@@ -0,0 +1,24 @@
+
+
+\begin{minipage}{0.45\textwidth}
+\includegraphics[width=4cm]{lunettes.png}
+\end{minipage}
+\hspace{0.5cm}
+\begin{minipage}{0.45\textwidth}
+\includegraphics[width=3cm]{iwatch.jpg}
+\end{minipage}
+
+\begin{itemize}
+
+\item Nouvelles technologies (lunettes, montres) et nouvelles 
+  fonctionnalités 
+
+
+
+% Utilisabilité 
+\item Analyse d'utilisation d'applications, d'interfaces utilisateur, 
+  convivialité des applications e t des systèmes mobiles
+\item \ldots 
+\end{itemize}
+
+
diff --git a/sem1305/Hexagones.jpg b/sem1305/Hexagones.jpg
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diff --git a/sem1305/RCapproche.tex.bak b/sem1305/RCapproche.tex.bak
new file mode 100644
index 0000000..518b745
--- /dev/null
+++ b/sem1305/RCapproche.tex.bak
@@ -0,0 +1,6 @@
+\begin{itemize}
+\item Données chiffrées grâce aux courbes elliptiques: 
+  sécurité, efficacité 
+\item Encryptions homomorphes: aggrégation sécurisée sans cryptage/décryptage 
+  à chaque n{\oe}ud
+\end{itemize}
diff --git a/sem1305/assync.tex b/sem1305/assync.tex
new file mode 100644
index 0000000..480ac5f
--- /dev/null
+++ b/sem1305/assync.tex
@@ -0,0 +1,28 @@
+\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:
+  $X^{k+1} =  f(X^{k}) if \textit{random()}<T else X^{k}$
+\item Convergence pour 
+Synchrone
+1 746
+2 1580
+3 4490
+4 7257
+5 8541
+6 10000
+7 9189
+8 10000
+9 10000
+10 10000
+\end{itemize}
+\end{itemize}
diff --git a/sem1305/assync.tex~ b/sem1305/assync.tex~
new file mode 100644
index 0000000..477ba18
--- /dev/null
+++ b/sem1305/assync.tex~
@@ -0,0 +1,16 @@
+\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:
+  $X^{k+1} =  f(X^{k}) if \textit{random()<T else X^{k}$
+\item Convergence pour  
+\end{itemize}
diff --git a/sem1305/beamerthemefemto.sty b/sem1305/beamerthemefemto.sty
new file mode 100644
index 0000000..252d2fa
--- /dev/null
+++ b/sem1305/beamerthemefemto.sty
@@ -0,0 +1,217 @@
+%-------------------------------------------------------------------------------
+% LaTeX Beamer theme "femto" from the femto-st evaluation model (2011) JM Nicod and PC Heam (LIFC)
+% 
+% author: Christophe Varnier et passage au ".sty" par G. Laurent
+%         Joel Abadie (12/06/2012) rajout de fonctionnalites tikzpicture
+%         Jean-Marc Nicod (logo + reglage pied de page)
+%-------------------------------------------------------------------------------
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{beamerthemefemto}[2012/06/05 beamer theme femto package]
+\RequirePackage{times}
+\RequirePackage{tikz}
+%-------------------------------------------------------------------------------
+
+%      _         _             _                     _                     
+%  ___| |_ _   _| | ___    ___| |_    ___ ___  _   _| | ___ _   _ _ __ ___ 
+% / __| __| | | | |/ _ \  / _ \ __|  / __/ _ \| | | | |/ _ \ | | | '__/ __|
+% \__ \ |_| |_| | |  __/ |  __/ |_  | (_| (_) | |_| | |  __/ |_| | |  \__ \
+% |___/\__|\__, |_|\___|  \___|\__|  \___\___/ \__,_|_|\___|\__,_|_|  |___/
+%          |___/                                                           
+%
+
+% commande permettant de dessiner une page de fond
+% appel depuis le document par : \setbeamertemplate{background}{\titrefemto}
+\newcommand{\titrefemto}{
+\begin{tikzpicture}
+	%definition du node centre au dimension de la page
+	\node[minimum height=\paperheight, minimum width=\paperwidth](centre) {};
+	% placement des logos en bas à gauche
+	\matrix[above right=4mm, ampersand replacement=\&] at (centre.south west){
+		\node[anchor=center]{\includegraphics[width=7mm]{logo-UFC.jpg}}; \&
+		\node[anchor=center]{\includegraphics[width=6mm]{logo-CNRS.jpg}}; \&
+		\node[anchor=center]{\includegraphics[width=13mm]{logo-ENSMM.jpg}}; \&
+		\node[anchor=center]{\includegraphics[width=12mm]{logo-UTBM.jpg}}; \\
+	};
+	%placement des logos en haut à droite
+	\node[below left, inner sep=0] at (centre.north east) {\includegraphics[width=5.5cm]{Hexagones.jpg}};
+	%placement des logos en haut à gauche
+%	\node[below right=6mm] at (centre.north west) {\includegraphics[width=2.8cm]{Femto-logo_couleur-2012.png}};
+	\node[below right=6mm] at (centre.north west) {\includegraphics[width=2.8cm]{logo-FEMTO.jpg}};
+\end{tikzpicture}
+}
+
+% commande permettant de dessiner une page de fond
+% appel depuis le document par : \setbeamertemplate{background}{\pagefemto}
+\newcommand{\pagefemto}{
+\begin{tikzpicture}
+	% definition du node centre au dimension de la page
+	\node[minimum height=\paperheight, minimum width=\paperwidth](centre) {};
+	% placement des logos en bas à gauche
+%	\node[above right=3mm] at (centre.south west) {\includegraphics[width=1.2cm]{Femto-logo_couleur-2012.png}};
+	\node[above right=0.75mm] at ([shift={(0.25,0)}]centre.south west) {\includegraphics[width=1.2cm]{logo-FEMTO.jpg}};
+	%placement des logos en haut à droite
+	\node[below left, inner sep=0](hexa) at (centre.north east) {\includegraphics[width=3.9cm]{Hexagones.jpg}};
+	%trace des traits
+	\coordinate (A) at ([shift={(0.5,-1.4)}]centre.north west);
+	\coordinate (B) at (A-| hexa.west);
+	\draw[BleuFemtoTitre] (A) -- ([xshift=-3mm]B);
+	%trait inferieur
+%	\coordinate (A) at ([shift={(0.5,1.1)}]centre.south west);
+	\coordinate (A) at ([shift={(0.5,.8)}]centre.south west);
+%	\coordinate (B) at ([shift={(-0.5,1.1)}]centre.south east);
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+	\draw[BleuFemtoTitre] (A) -- (B);
+\end{tikzpicture}
+}
+
+% \definecolor{GreenYellow}{cmyk}{0.15,0,0.69,0} % PANTONE 388
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+% \definecolor{Violet}{cmyk}{0.79,0.88,0,0} % PANTONE VIOLET
+% \definecolor{RoyalPurple}{cmyk}{0.75,0.90,0,0} % PANTONE 267
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+% \definecolor{Blue}{cmyk}{1.,1.,0,0} % PANTONE BLUE-072
+% \definecolor{Cerulean}{cmyk}{0.94,0.11,0,0} % PANTONE 3005
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+% \definecolor{Turquoise}{cmyk}{0.85,0,0.20,0} % PANTONE (312+313)
+% \definecolor{TealBlue}{cmyk}{0.86,0,0.34,0.02} % PANTONE 3145
+% \definecolor{Aquamarine}{cmyk}{0.82,0,0.30,0} % PANTONE 3135
+% \definecolor{BlueGreen}{cmyk}{0.85,0,0.33,0} % PANTONE 320
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+% \definecolor{SeaGreen}{cmyk}{0.69,0,0.50,0} % PANTONE 3268
+% \definecolor{Green}{cmyk}{1.,0,1.,0} % PANTONE GREEN
+% \definecolor{ForestGreen}{cmyk}{0.91,0,0.88,0.12} % PANTONE 349
+% \definecolor{PineGreen}{cmyk}{0.92,0,0.59,0.25} % PANTONE 323
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+% \definecolor{Gray}{cmyk}{0,0,0,0.50} % PANTONE COOL-GRAY-8
+\definecolor{DarkGray}{cmyk}{0,0,0,0.80} % PANTONE COOL-GRAY-8
+% \definecolor{Black}{cmyk}{0,0,0,1.} % PANTONE PROCESS-BLACK
+% \definecolor{White}{cmyk}{0,0,0,0} % No PANTONE match
+
+% ajout des couleurs Femto
+\definecolor{BleuFemtoTitre}{cmyk}{0.94,0.83,0,0.01}
+\definecolor{BleuFemtoTexte}{cmyk}{0.92,0.54,0.05,0.09}
+\definecolor{BleuFemto}{RGB}{39,84,148}
+\definecolor{BleuClairFemto}{RGB}{66,153,214}
+\definecolor{VertFemto}{RGB}{175,203,81}
+\definecolor{GrisClairFemto}{RGB}{177,179,180}
+\definecolor{GrisFemto}{RGB}{112,127,135}
+
+\usetheme{default}
+
+\setbeamertemplate{navigation symbols}{}
+
+\setbeamercolor{structure}{fg=DarkGray}
+
+% _                       _       _         _   _ _            
+%| |_ ___ _ __ ___  _ __ | | __ _| |_ ___  | |_(_) |_ _ __ ___ 
+%| __/ _ \ '_ ` _ \| '_ \| |/ _` | __/ _ \ | __| | __| '__/ _ \
+%| ||  __/ | | | | | |_) | | (_| | ||  __/ | |_| | |_| | |  __/
+% \__\___|_| |_| |_| .__/|_|\__,_|\__\___|  \__|_|\__|_|  \___|
+%                  |_|                                         
+
+%\pgfdeclareimage[height=\paperheight,width=\paperwidth]{titrefemto}{TitreFemto.png}
+
+\setbeamertemplate{title page}
+{
+\vskip 10mm 
+\usebeamerfont{title}\usebeamercolor[fg]{title}\LARGE\textcolor{BleuFemto}\inserttitle
+\newline\newline
+\normalsize\textcolor{GrisFemto}\insertauthor
+\newline
+\vskip 1mm
+\textcolor{GrisFemto}\insertinstitute
+\newline\newline
+\footnotesize\textcolor{GrisFemto}\insertdate
+}
+
+% _                       _       _                                
+%| |_ ___ _ __ ___  _ __ | | __ _| |_ ___   _ __   __ _  __ _  ___ 
+%| __/ _ \ '_ ` _ \| '_ \| |/ _` | __/ _ \ | '_ \ / _` |/ _` |/ _ \
+%| ||  __/ | | | | | |_) | | (_| | ||  __/ | |_) | (_| | (_| |  __/
+% \__\___|_| |_| |_| .__/|_|\__,_|\__\___| | .__/ \__,_|\__, |\___|
+%                  |_|                     |_|          |___/      
+
+%\pgfdeclareimage[height=\paperheight,width=\paperwidth]{pagefemto}{PageFemto.png}
+
+\setbeamertemplate{frametitle}{\vspace{6mm}\hspace{-5mm}\Large\bf\textcolor{BleuFemto} \insertframetitle}
+
+% pour les block
+\definecolor{fondFemtotableau}{rgb}{1,0.71,0.754}
+\setbeamertemplate{blocks}[rounded]
+\setbeamercolor{block title}{fg=BleuClairFemto!60,bg=BleuFemto}
+\setbeamercolor{block body}{bg=GrisClairFemto!40,fg=GrisFemto!50!black}
+\setbeamerfont{block title}{series=\bfseries}
+\setbeamercolor{title in head/foot}{fg=gray}
+\newenvironment{femtoBlock}[1]{%
+  \textcolor{BleuFemto}{\normalsize\textbf{#1}}\normalsize}
+
+\setbeamertemplate{footline}
+{%
+  \leavevmode%
+  \vspace{-2mm}%
+  \hbox{\begin{beamercolorbox}[wd=.85\paperwidth,ht=2.5ex,dp=-2.5ex,leftskip=.3cm plus1fill,rightskip=.3cm]{author in head/foot}%
+    \usebeamerfont{author in head/foot} \hfill \textcolor{GrisFemto}{\insertshortinstitute}
+  \end{beamercolorbox}%
+  \begin{beamercolorbox}[wd=.15\paperwidth,right,ht=2.5ex,dp=1.8ex,leftskip=.3cm,rightskip=.3cm plus1fil]{title in head/foot}%
+    \usebeamerfont{title in head/foot} \hfill \textcolor{BleuFemto}{\insertframenumber\ / \inserttotalframenumber}\hspace{0.25cm}
+  \end{beamercolorbox}}%
+  \vskip 10pt%
+}
+
+\setbeamertemplate{itemize item}[circle]
+\setbeamertemplate{itemize subitem}[circle]
+
+\partopsep=0ex % espace apres les blocks et avant le contenu
+\topsep=5ex % debut du texte du slide
+\parsep=0ex
+\itemsep=0ex 
+
+%-------------------------------------------------------------------------------
+
diff --git a/sem1305/caracteristique.tex.bak b/sem1305/caracteristique.tex.bak
new file mode 100644
index 0000000..c21f7b2
--- /dev/null
+++ b/sem1305/caracteristique.tex.bak
@@ -0,0 +1,15 @@
+\begin{minipage}{0.45\textwidth}
+\includegraphics[width=4cm]{nexus.png}
+\end{minipage}
+\begin{minipage}{0.45\textwidth}
+\includegraphics[width=4cm]{sense.jpg}
+\end{minipage}
+\begin{itemize}
+\item Interfaces de communication $\leadsto$ réseaux ad hoc, Internet
+\item Programmable $VHDL$, \ldots, java (Android) 
+\item Des données embarquées, \ldots, persistentes (cloud)
+\item Environnement multimédia $\leadsto$ en entrée, en sortie
+\item Outils pour la localisation $\leadsto$ GPS, cartes 
+\end{itemize}
+
+
diff --git a/sem1305/caracteristique2.tex.bak b/sem1305/caracteristique2.tex.bak
new file mode 100644
index 0000000..8bfa2e9
--- /dev/null
+++ b/sem1305/caracteristique2.tex.bak
@@ -0,0 +1,13 @@
+\begin{itemize}
+\item Conséquences de la mobilité:
+\begin{itemize}
+\item Energie en quantité limitée $\leq $ 8 Wh
+\item Environnement ouvert avec attaques possibles 
+\item Hardware limité (processeur, mémoire,\ldots) 
+\end{itemize}
+\item Optimisation 
+\begin{itemize}
+\item De la complexité algorithmique, mémoire, des communications
+\item Sécurisation du processus
+\end{itemize}
+\end{itemize}
diff --git a/sem1305/cv.tex b/sem1305/cv.tex
new file mode 100644
index 0000000..24bfbce
--- /dev/null
+++ b/sem1305/cv.tex
@@ -0,0 +1,8 @@
+\vspace{-1em}
+\includegraphics[width=9cm]{reseau.png}
+\vspace{-3em}
+\begin{itemize}
+\item Objectif: maximiser la durée de vie du réseau $T_{\textit{net}}$
+\item Objectif équivalent: minimiser l'inverse $q = \dfrac{1}{T_{\textit{net}}}$ 
+\end{itemize} 
+
diff --git a/sem1305/cv.tex~ b/sem1305/cv.tex~
new file mode 100644
index 0000000..c4027ad
--- /dev/null
+++ b/sem1305/cv.tex~
@@ -0,0 +1,2 @@
+\begin{itemize}
+\item 
\ No newline at end of file
diff --git a/sem1305/formalisation.tex~ b/sem1305/formalisation.tex~
new file mode 100644
index 0000000..35933e6
--- /dev/null
+++ b/sem1305/formalisation.tex~
@@ -0,0 +1 @@
+\begin{itemize}
\ No newline at end of file
diff --git a/sem1305/formalisationenergie.tex b/sem1305/formalisationenergie.tex
new file mode 100644
index 0000000..ca1dad2
--- /dev/null
+++ b/sem1305/formalisationenergie.tex
@@ -0,0 +1,13 @@
+\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 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
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diff --git a/sem1305/main.snm b/sem1305/main.snm
new file mode 100644
index 0000000..e69de29
diff --git a/sem1305/main.tex b/sem1305/main.tex
new file mode 100644
index 0000000..0f33120
--- /dev/null
+++ b/sem1305/main.tex
@@ -0,0 +1,114 @@
+\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.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? Arbitraire?
+\end{itemize}
diff --git a/sem1305/reseau.png b/sem1305/reseau.png
new file mode 100644
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-- 
2.39.5