From 653872b9a3bd32a568456f5e145167da236fbcab Mon Sep 17 00:00:00 2001 From: couturie Date: Tue, 6 Mar 2012 08:57:18 +0100 Subject: [PATCH] suppression fichier ~ --- combMExp.tex~ | 13 ------------ combMXpl.tex~ | 9 -------- combMixed.tex~ | 28 ------------------------- combMixedTheo.tex~ | 15 ------------- introModes.tex~ | 32 ---------------------------- introMotivations.tex~ | 13 ------------ introRIter.tex~ | 49 ------------------------------------------- introRunning.tex~ | 18 ---------------- 8 files changed, 177 deletions(-) delete mode 100755 combMExp.tex~ delete mode 100755 combMXpl.tex~ delete mode 100755 combMixed.tex~ delete mode 100755 combMixedTheo.tex~ delete mode 100755 introModes.tex~ delete mode 100755 introMotivations.tex~ delete mode 100755 introRIter.tex~ delete mode 100755 introRunning.tex~ diff --git a/combMExp.tex~ b/combMExp.tex~ deleted file mode 100755 index d7f5a64..0000000 --- a/combMExp.tex~ +++ /dev/null @@ -1,13 +0,0 @@ -\begin{exampleblock}{} - -\begin{itemize} -\item Our Prototype: confirmation of convergence -of mixed asynchronous iterations with uniform delays -\item Mixed iterations with - $SCC(1)=\{1,2\}$, - $SCC(3)=\{3\}$ and $SCC(4)=\{4,5\}$ -\begin{center} - \includegraphics[width=2.5cm]{../xpl_iteration_final.ps} -\end{center} -\end{itemize} -\end{exampleblock} diff --git a/combMXpl.tex~ b/combMXpl.tex~ deleted file mode 100755 index 58d7514..0000000 --- a/combMXpl.tex~ +++ /dev/null @@ -1,9 +0,0 @@ - -\begin{exampleblock}{} -\begin{itemize} -\item Connection graph: -\begin{center} -\includegraphics[width=3cm]{../xplgraph.ps} -\end{center} -\end{itemize} -\end{exampleblock} diff --git a/combMixed.tex~ b/combMixed.tex~ deleted file mode 100755 index a22a809..0000000 --- a/combMixed.tex~ +++ /dev/null @@ -1,28 +0,0 @@ -\begin{itemize} -\item Intuition: - \begin{itemize} - \item Nodes that may introduce cyclic iterations: grouped - \item Nodes inside each group: synchronized at each other - \item Nodes of distinct groups: keeping asynchronism - \end{itemize} -\item Formalization: - \begin{itemize} - \item Group: SCC of the connection graph - \item Mixed iterations of DN with Uniform Delays: - \begin{itemize} - \item $S_{ij}^t$ is $t$ if $i \in SCC(j)$. - \item $ - \begin{array}{l} - \forall p_0,p_1,q_0,q_1,t \, .\, - \quad ( - p_1 \in SCC(p_0) \land - q_1 \in SCC(q_0))\\ - \qquad \Rightarrow - S_{p_0q_0}^{t} = - S_{p_1q_1}^{t} - \end{array} - $ - \end{itemize} - \end{itemize} -\item Elements in the same SCC: cannot be differentiated -\end{itemize} diff --git a/combMixedTheo.tex~ b/combMixedTheo.tex~ deleted file mode 100755 index f686b77..0000000 --- a/combMixedTheo.tex~ +++ /dev/null @@ -1,15 +0,0 @@ -\newcommand{\Nats}[0]{\ensuremath{\mathbb{N}}} - -\begin{Theorem}{} - Given an initial configuration $X^0 = (X_1^0, \ldots, X_n^0)$ and a - strategy $(J^t)^{t \in \Nats}$. If chaotic iterations with strategy - $(J^t)^{t \in \Nats}$ converge to some fixed-point, then mixed iterations with - uniform delays with the same strategy $(J^t)^{t \in \Nats}$ converge to the - same fixed-point. -\end{Theorem} -\begin{Proof} -\begin{itemize} -\item Element renaming wrt. a partial order -\item Induction on the SCC index -\end{itemize} -\end{Proof} diff --git a/introModes.tex~ b/introModes.tex~ deleted file mode 100755 index ab0ce9e..0000000 --- a/introModes.tex~ +++ /dev/null @@ -1,32 +0,0 @@ -\begin{itemize} - \item \emph{Strategy}: sequence of elements updated at time $t$; - \begin{itemize} - \item $n*n$ diagonal matrix: $J_{ii}^t = 1$ iff $X_i \in E_i$ - is updated at time $t$ - \end{itemize} - \item \emph{Visibility Dates}: sequence of the more recent dates where - components know values of other ones - \begin{itemize} - \item $n*n$ matrix $S_{ij}^t$: highest $t'$ - s.t. $t' \le t$ and $X_j^{t'}$ is accessible for $i$ - \item Communcation delays from $j$ to $i$: $t - S_{ij}^t$ - \end{itemize} - \item \emph{Iterations modes}: -\[ -X^{t+1}= (I -J^t)X^t + J^t -\left( -\begin{array}{c} -F_1 -\left( X_1^{S_{11}^t},\ldots, X_{n}^{S_{1{n}}^t} \right) \\ -\vdots \\ -F_{n} \left( X_1^{S_{{n}1}^t},\ldots, X_{n}^{S_{{n}{n}}^t} \right) -\end{array} -\right) -\] -\begin{itemize} -\item Parallel mode: $J^t=I$ and $S^t=(t)$ -\item Chaotic mode: $S^t=(t)$ -\item Asynchronous: no constraint -\end{itemize} -\end{itemize} - diff --git a/introMotivations.tex~ b/introMotivations.tex~ deleted file mode 100755 index db5c024..0000000 --- a/introMotivations.tex~ +++ /dev/null @@ -1,13 +0,0 @@ -\begin{itemize} -\item<1-3> Objectives: ``similar behaviors'' in asynchronous iterations - as in some chaotic iterations -\item<2-3> Issues: -\begin{itemize} -\item Strengthening the convergence conditions of chaotic mode -\item Lightly introduce synchronism into asynchronous modes [ABCVS05] -\end{itemize} -\item<3> \alert{Proof of convergence conjecture} -\end{itemize} - - - diff --git a/introRIter.tex~ b/introRIter.tex~ deleted file mode 100755 index 601d302..0000000 --- a/introRIter.tex~ +++ /dev/null @@ -1,49 +0,0 @@ -\begin{exampleblock}{} -\begin{itemize} -\only<1>{\item Parallel iterations: convergence -\begin{center} -\includegraphics[width=8cm]{../implementation/para_iterate_dec.ps} -\end{center}} -\only<2>{\item Chaotic iterations: divergence with $J^t=\{24;15;14;15;\ldots\}$ -\begin{center} -\includegraphics[width=4cm]{../chao_iterate_excerpt.ps} -\end{center}} -\only<3>{\item Asynchronous iterations: divergence even with $J^t=I$ -\begin{itemize} -\item $S^t = \left( -\begin{array}{lllll} -t & t' & t & t & t \\ -t & t & t & t & t \\ -t & t & t & t & t \\ -t & t & t & t & t\\ -t & t & t & t & t \\ -\end{array} -\right) -\textrm{ where } -t' = \left\{ -\begin{array}{l} -t \textrm{ if t is even;} \\ -t-1 \textrm{ otherwise.} -\end{array} -\right. -$ -\item -$ -\begin{array}{rcl} -X^{2k+1} & =& F(X^{2k}) \\ -X^{2k} & =& \left( -\begin{array}{l} -F_1(X_1^{2k-1},X_2^{2k-2},X_3^{2k-1},X_4^{2k-1},X_5^{2k-1}) \\ -F_2(X^{2k-1})\\ -\vdots \\ -F_5(X^{2k-1}) -\end{array} -\right). -\end{array} -$ - -$\rightarrow$ cycle between 3 and 11. -\end{itemize} -} -\end{itemize} -\end{exampleblock} diff --git a/introRunning.tex~ b/introRunning.tex~ deleted file mode 100755 index a212770..0000000 --- a/introRunning.tex~ +++ /dev/null @@ -1,18 +0,0 @@ -\begin{exampleblock}{} -\begin{itemize} -\item Five elements $1 \le i \le 5$ taking their value $X_i$ in $\{0,1\}$ -\item Configuration: a binary number in 0,1,\ldots,31 -\item Dynamic: a map -\[ -F(X)= \left \{ -\begin{array}{lll} -f_1(X_1,X_2,X_3,X_4,X_5) & = & X_1 \overline{X_2} + \overline{X_1} X_2 \\ -f_2(X_1,X_2,X_3,X_4,X_5) & = & \overline{X_1 + X_2} \\ -f_3(X_1,X_2,X_3,X_4,X_5) & = & X_3 \overline{X_1} \\ -f_4(X_1,X_2,X_3,X_4,X_5) & = & X_5 \\ -f_5(X_1,X_2,X_3,X_4,X_5) & = & \overline{X_3} + X_4 -\end{array} -\right. -\] -\end{itemize} -\end{exampleblock} -- 2.39.5