111 lines
6.1 KiB
TeX
111 lines
6.1 KiB
TeX
\begin{frame}
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\frametitle{Localiser l'activité}
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\centering
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\input{vector/active-equation.tikz}
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\begin{columns}
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\column{.65\textwidth}\centering
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\input{vector/active-quiescent-reprensentation.tikz}
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\column{.35\textwidth}
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\end{columns}
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\end{frame}
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\begin{frame}[label=this one]
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\frametitle{Simulations \mgs et sous-collection active}
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\begin{itemize}
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\item Trajectoires dans \mgs
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\begin{center}
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\begin{tikzpicture} [scale=0.4,baseline,
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cell/.style={minimum size=0.35cm}]
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\fill (0.65,0.65) rectangle (8.35,8.35);
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\foreach \p/\c in%
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{ { (1,8)/forest},{(2,8)/forest},{(3,8)/forest},{(4,8)/forest},{(5,8)/forest},{(6,8)/forest},{(7,8)/forest},{(8,8)/forest}%
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,{(1,7)/forest},{(2,7)/forest},{(3,7)/forest},{(4,7)/forest},{(5,7)/forest},{(6,7)/forest},{(7,7)/forest},{(8,7)/forest}%
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,{(1,6)/forest},{(2,6)/forest},{(3,6)/fire}, {(4,6)/fire}, {(5,6)/forest},{(6,6)/forest},{(7,6)/forest},{(8,6)/forest}%
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,{(1,5)/forest},{(2,5)/forest},{(3,5)/forest},{(4,5)/fire}, {(5,5)/forest},{(6,5)/forest},{(7,5)/forest},{(8,5)/forest}%
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,{(1,4)/forest},{(2,4)/forest},{(3,4)/forest},{(4,4)/forest},{(5,4)/forest},{(6,4)/forest},{(7,4)/forest},{(8,4)/forest}%
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,{(1,3)/forest},{(2,3)/forest},{(3,3)/forest},{(4,3)/forest},{(5,3)/forest},{(6,3)/forest},{(7,3)/forest},{(8,3)/forest}%
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,{(1,2)/forest},{(2,2)/forest},{(3,2)/forest},{(4,2)/forest},{(5,2)/forest},{(6,2)/forest},{(7,2)/forest},{(8,2)/fire}%
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,{(1,1)/forest},{(2,1)/forest},{(3,1)/forest},{(4,1)/forest},{(5,1)/forest},{(6,1)/forest},{(7,1)/forest},{(8,1)/fire}}
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\node[cell,fill=\c,draw=white,line width=1pt] at \p {};
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\node at (4.5,0) {$C^0$};
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\end{tikzpicture}
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\hfill
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\begin{tikzpicture} [scale=0.4,baseline,
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cell/.style={minimum size=0.35cm}]
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\fill (0.65,0.65) rectangle (8.35,8.35);
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\foreach \p/\c in%
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{ { (1,8)/forest},{(2,8)/forest},{(3,8)/forest},{(4,8)/forest},{(5,8)/forest},{(6,8)/forest},{(7,8)/forest},{(8,8)/forest}%
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,{(1,7)/forest},{(2,7)/fire}, {(3,7)/fire}, {(4,7)/fire}, {(5,7)/fire}, {(6,7)/forest},{(7,7)/forest},{(8,7)/forest}%
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,{(1,6)/forest},{(2,6)/fire}, {(3,6)/ashes}, {(4,6)/ashes}, {(5,6)/fire}, {(6,6)/forest},{(7,6)/forest},{(8,6)/forest}%
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,{(1,5)/forest},{(2,5)/fire}, {(3,5)/fire}, {(4,5)/ashes}, {(5,5)/fire}, {(6,5)/forest},{(7,5)/forest},{(8,5)/forest}%
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,{(1,4)/forest},{(2,4)/forest},{(3,4)/fire}, {(4,4)/fire}, {(5,4)/fire}, {(6,4)/forest},{(7,4)/forest},{(8,4)/forest}%
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,{(1,3)/forest},{(2,3)/forest},{(3,3)/forest},{(4,3)/forest},{(5,3)/forest},{(6,3)/forest},{(7,3)/fire}, {(8,3)/fire}%
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,{(1,2)/forest},{(2,2)/forest},{(3,2)/forest},{(4,2)/forest},{(5,2)/forest},{(6,2)/forest},{(7,2)/fire}, {(8,2)/ashes}%
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,{(1,1)/forest},{(2,1)/forest},{(3,1)/forest},{(4,1)/forest},{(5,1)/forest},{(6,1)/forest},{(7,1)/fire}, {(8,1)/ashes}}
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\node[cell,fill=\c,draw=white,line width=1pt] at \p {};
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\node at (4.5,0) {$C^1 = T(C^0)$};
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\end{tikzpicture}
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\hfill
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\begin{tikzpicture} [scale=0.4,baseline,
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cell/.style={minimum size=0.35cm}]
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\fill (0.65,0.65) rectangle (8.35,8.35);
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\foreach \p/\c in%
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{ { (1,8)/fire}, {(2,8)/fire}, {(3,8)/fire}, {(4,8)/fire}, {(5,8)/fire}, {(6,8)/fire}, {(7,8)/forest},{(8,8)/forest}%
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,{(1,7)/fire}, {(2,7)/ashes}, {(3,7)/ashes}, {(4,7)/ashes}, {(5,7)/ashes}, {(6,7)/fire}, {(7,7)/forest},{(8,7)/forest}%
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,{(1,6)/fire}, {(2,6)/ashes}, {(3,6)/ashes}, {(4,6)/ashes}, {(5,6)/ashes}, {(6,6)/fire}, {(7,6)/forest},{(8,6)/forest}%
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,{(1,5)/fire}, {(2,5)/ashes}, {(3,5)/ashes}, {(4,5)/ashes}, {(5,5)/ashes}, {(6,5)/fire}, {(7,5)/forest},{(8,5)/forest}%
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,{(1,4)/fire}, {(2,4)/fire}, {(3,4)/ashes}, {(4,4)/ashes}, {(5,4)/ashes}, {(6,4)/fire}, {(7,4)/fire}, {(8,4)/fire}%
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,{(1,3)/forest},{(2,3)/fire}, {(3,3)/fire}, {(4,3)/fire}, {(5,3)/fire}, {(6,3)/fire}, {(7,3)/ashes}, {(8,3)/ashes}%
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,{(1,2)/forest},{(2,2)/forest},{(3,2)/forest},{(4,2)/forest},{(5,2)/forest},{(6,2)/fire}, {(7,2)/ashes}, {(8,2)/ashes}%
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,{(1,1)/forest},{(2,1)/forest},{(3,1)/forest},{(4,1)/forest},{(5,1)/forest},{(6,1)/fire}, {(7,1)/ashes}, {(8,1)/ashes}}
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\node[cell,fill=\c,draw=white,line width=1pt] at \p {};
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\node at (4.5,0) {$C^2 = T(C^1) = T^2(C^0)$};
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\end{tikzpicture}
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\end{center}
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\item Décomposition de l'activité et trajectoires
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\begin{itemize}
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\item \textcolor{active}{Sous-collection active $A_i$} et
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\textcolor{quiescent}{sous-collection quiescente $Q_i$}
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\item Décomposition de la relation d'évolution
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\[ A^{i+1} + Q^{i+1} = T(A^i + Q^i) \]
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\end{itemize}
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\end{itemize}
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\end{frame}
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\begin{frame}{Relation entre $A^{i+1},Q^{i+1}$ et $A^i,Q^i$}
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$$ A^{i+1} + Q^{i+1} = T(A^i + Q^i) $$
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\begin{itemize}
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\item Sous-collection \textcolor{frontier}{frontière $F^i$}
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\end{itemize}
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\begin{columns}
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\column{.5\textwidth}
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\begin{enumerate}
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\item \structure{Propriété} $T(A^i + Q^i) = T(A^i \mid Q^i) + Q^i$
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\item \structure{Propriété} $| A^{i+1} | \subseteq | A^i + F^i |$
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\item \structure{Propriété} $| Q^i - F^i | \subseteq | Q^{i+1} |$
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\item \structure{Définition} $F^i = \text{Lk}(A^i)$
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\item \structure{Remarque} $T(A^i \mid Q^i) = T(A^i \mid F^i)$
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\item \structure{Résultat} $C^{i+1} = T(A^i \mid F^i) + F^i + (Q^i - F^i)$
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\end{enumerate}
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\column{.5\textwidth}
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$$ \text{Lk} \left(
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\tikz[baseline] \node {\includegraphics[width=2cm]{vector/operateursS}};
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\right) =
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\tikz[baseline] \node {\includegraphics[width=2cm]{vector/operateursLkS}};
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$$
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\end{columns}
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\bigskip
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\[
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\left\{
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\arraycolsep=1.4pt%\def\arraystretch{2.2}
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\begin{array}{rl}
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A^0 &= \text{PatMatch}_T(C^0)\\
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A^{i+1} &= \text{PatMatch}_T\left[ T(A^i \mid \text{Lk}(A^i)) + \text{Lk}(A^i) \right]
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\end{array}
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\right.
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\]
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\end{frame}
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