87 lines
3.1 KiB
TeX
87 lines
3.1 KiB
TeX
\begin{frame}{Système, Modèle, Formalisme}
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\framesubtitle{Définitions}
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\begin{center}
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%\includegraphics[height=3cm]{vector/stub-formlism-model-system}
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\begin{tikzpicture}[
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%font=\small
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node distance=1cm and 3cm]
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\node[draw] (model) {Modèle};
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\node[draw,below right=2cm of model] (system) {Système};
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\node[draw,right=of model] (formalism) {Formalisme};
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\draw[shorten <=3pt,shorten >=3pt,-Stealth] (formalism) to
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node[auto,swap,font=\small] {description} (model);
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\draw[shorten <=3pt,shorten >=3pt,very thick,line cap=round,<->,
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out=170,in=-70] (system) to node[auto,font=\small] {sémantique} (model);
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%node[auto,font=\small] {explique}
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\coordinate (absconc) at ($(barycentric cs:model=1,system=1) + (5cm,0)$);
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\draw [dashed] (barycentric cs:model=1,system=1) -- +(6cm,0) -- +(-3cm,0);
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\node[label=above:Abstrait,label=below:Concret] at (absconc) {};
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\end{tikzpicture}
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\end{center}
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%
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\begin{itemize}
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\item \structure{Système}\\
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\small objet d'étude décomposé en parties
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\medskip
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\item \structure{Modèle}\\
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\small vue simplifiée du système (abstraction) dont l'existence est
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dépendante du système
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\medskip
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\item \structure{Formalisme}\\
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\small langage, support d'expression du modèle
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\end{itemize}
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\end{frame}
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\begin{frame}{Système, Modèle, Formalisme}
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\framesubtitle{Points de vue sur les systèmes de Lindenmayer, $(\Sigma,w_0,P)$}
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\begin{itemize}
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\item \emph{L-System} comme \structure{formalisme} \\
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{\small support de la description de la croissance des plantes}
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\item \emph{L-System} comme \structure{modèle} \\
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{\small modèle de calcul comme $\lambda$-calcul, machines de Turing,
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grammaires de Chomsky, …}
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\item \emph{L-System} comme \structure{système} \\
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{\small objet d'étude formel dont un modèle pourrait être les fonctions de
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croissance}
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\end{itemize}
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\medskip
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\begin{columns}
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\column{.33\textwidth}
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\includegraphics[height=.4\textheight]{raster/lsystem-formalism}
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\column{.33\textwidth}
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\includegraphics[height=.4\textheight]{vector/lsystem-model}
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\column{.33\textwidth}
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%\includegraphics[width=\textwidth]{raster/lsystem-system}
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\begin{tikzpicture}
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\node[draw, text width=.9\textwidth] {\small
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$$f(n) = | w_n |$$
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$ \left\{\begin{array}{l}
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a \rightarrow ab\\
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b \rightarrow b
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\end{array}\right. \qquad f(n) = n+1$
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\medskip
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$ \left\{\begin{array}{l}
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a \rightarrow b\\
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b \rightarrow ab
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\end{array}\right. \qquad f(n) = \text{fib}(n)$
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};
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\end{tikzpicture}\\
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\end{columns}
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\begin{columns}[t]
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\column{.4\textwidth}\centering
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\mkCitation{P. Prusinkiewicz, A. Lindenmayer: “The algorithmic beauty of plants (the virtual laboratory)”, 1990}
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\column{.6\textwidth}\centering
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\mkCitation{G. Rozenberg, A. Salomaa: “The mathematical theory of L-Systems”, DAIMI Report Series, 3(33), 1974}
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\end{columns}
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\end{frame}
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