More changes to two step computation figure.
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334b78c526
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42d44a6c4b
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@ -56,25 +56,32 @@
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%pdb cylinder
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\node[cylinder, text width=0.28\textwidth, align=center, draw=black, text=blue, cylinder uses custom fill, cylinder body fill=blue!10, aspect=0.12, minimum height=5cm, minimum width=2.5cm, cylinder end fill=blue!50, shape border rotate=90] (cylinder) at (0, 0) {
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\tabcolsep=0.1cm
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\begin{tabular}{>{\footnotesize}c | >{\footnotesize}c >{\footnotesize}c >{\footnotesize}c}
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$OnTime$ & City$_\ell$ & $\Phi$ & \textbf{p}\\
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\hline
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& Buffalo & $L_a$ & 0.9 \\
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& Chicago & $L_b$ & 0.5\\
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& Bremen & $L_c$ & 0.5\\
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& Zurich & $L_d$ & 1.0\\
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\renewcommand{\aboverulesep}{0pt}
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\renewcommand{\belowrulesep}{0pt}
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\begin{tabular}{>{\small}c >{\small}c >{\small}c}
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\multicolumn{3}{c}{$\boldsymbol{OnTime}$}\\
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\toprule
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City$_\ell$ & $\Phi$ & \textbf{p}\\
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\midrule
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Buffalo & $L_a$ & 0.9 \\
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Chicago & $L_b$ & 0.5\\
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Bremen & $L_c$ & 0.5\\
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Zurich & $L_d$ & 1.0\\
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\end{tabular}\\
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\tabcolsep=0.05cm
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\begin{tabular}{ >{\scriptsize}c | >{\scriptsize}c >{\scriptsize}c >{\scriptsize}c >{\scriptsize}c}
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$Route$ & $\text{City}_1$ & $\text{City}_2$ & $\Phi$ & \textbf{p} \\
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\hline
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& Buffalo & Chicago & $R_a$ & 1.0 \\
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& Chicago & Zurich & $R_b$ & 1.0 \\
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%\captionof{table}{Route}
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\begin{tabular}{>{\footnotesize}c >{\footnotesize}c >{\footnotesize}c >{\footnotesize}c}
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\multicolumn{4}{c}{$\boldsymbol{Route$}}\\
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\toprule
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$\text{City}_1$ & $\text{City}_2$ & $\Phi$ & \textbf{p} \\
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\midrule
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Buffalo & Chicago & $R_a$ & 1.0 \\
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Chicago & Zurich & $R_b$ & 1.0 \\
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%& $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ \\
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& Chicago & Bremen & $R_c$ & 1.0 \\
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Chicago & Bremen & $R_c$ & 1.0 \\
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\end{tabular}};
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%label below cylinder
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\node[below=0.2 cm of cylinder]{$\pdb$};
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\node[below=0.2 cm of cylinder]{{\LARGE$ \pdb$}};
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%First arrow
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\node[single arrow, right=0.25 of cylinder, draw=black, fill=black!65, text=white, minimum height=0.75cm, minimum width=0.25cm](arrow1) {\textbf{Step 1}};
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\node[above=of arrow1](arrow1Label) {$\query$};
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@ -83,10 +90,14 @@
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%Query output (output of step 1)
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\node[rectangle, right=0.175 of arrow1, draw=black, text=purple, fill=purple!15, minimum height=4.5cm, minimum width=2cm](rect) {
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\tabcolsep=0.075cm
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\begin{tabular}{ >{\small}c | >{\small}c >{\small}c >{\centering\arraybackslash\small}m{1.95cm}}
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$\query$ & City & $\Phi$ & Circuit\\% & $\expct_{\idb \sim \probDist}[\query(\db)(t)]$ \\ \hline
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\hline \\\\[-3.5\medskipamount]
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& Buffalo & $L_a R_a$ &\resizebox{!}{10mm}{
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%\captionof{table}{Q}
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\begin{tabular}{>{\normalsize}c >{\normalsize}c >{\centering\arraybackslash\small}m{1.95cm}}
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\multicolumn{3}{c}{$\boldsymbol{\query(\pdb)}$}\\
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\toprule
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City & $\Phi$ & Circuit\\% & $\expct_{\idb \sim \probDist}[\query(\db)(t)]$ \\ \hline
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\midrule
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%\hline \\\\[-3.5\medskipamount]
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Buffalo & $L_a R_a$ &\resizebox{!}{10mm}{
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\begin{tikzpicture}[thick]
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\node[gen_tree_node](sink) at (0.5, 0.8){$\boldsymbol{\circmult}$};
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\node[gen_tree_node](source1) at (0, 0){$L_a$};
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@ -95,43 +106,66 @@
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\draw[->] (source2)--(sink);
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\end{tikzpicture}% & $0.5 \cdot 1.0 + 0.5 \cdot 1.0 = 1.0$
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}\\% & $0.9$ \\
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& Chicago & $L_b R_b + L_b R_c$&\resizebox{!}{16mm} {
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\begin{tikzpicture}[thick]
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\node[gen_tree_node] (a2) at (0, 0){$R_b$};
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\node[gen_tree_node] (b2) at (1, 0){$L_b$};
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\node[gen_tree_node] (c2) at (2, 0){$R_c$};
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%level 1
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\node[gen_tree_node] (a1) at (0.5, 0.8){$\boldsymbol{\circmult}$};
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\node[gen_tree_node] (b1) at (1.5, 0.8){$\boldsymbol{\circmult}$};
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%level 0
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\node[gen_tree_node] (a0) at (1.0, 1.6){$\boldsymbol{\circplus}$};
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%edges
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\draw[->] (a2) -- (a1);
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\draw[->] (b2) -- (a1);
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\draw[->] (b2) -- (b1);
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\draw[->] (c2) -- (b1);
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\draw[->] (a1) -- (a0);
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\draw[->] (b1) -- (a0);
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\end{tikzpicture}
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}\\
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Chicago & $L_b R_b + L_b R_c$&
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\resizebox{!}{16mm} {
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\begin{tikzpicture}[thick]
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\node[gen_tree_node] (a1) at (1, 0){$R_b$};
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\node[gen_tree_node] (b1) at (2, 0){$R_c$};
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%level 1
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\node[gen_tree_node] (a2) at (0.75, 0.8){$L_b$};
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\node[gen_tree_node] (b2) at (1.5, 0.8){$\boldsymbol{\circplus}$};
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%level 0
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\node[gen_tree_node] (a3) at (1.1, 1.6){$\boldsymbol{\circmult}$};
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%edges
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\draw[->] (a1) -- (b2);
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\draw[->] (b1) -- (b2);
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\draw[->] (a2) -- (a3);
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\draw[->] (b2) -- (a3);
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\end{tikzpicture}
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}\\
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%%%%%%%%%%%
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%Non factorized circuit%
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%%%%%%%%%%%
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%\resizebox{!}{16mm} {
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%\begin{tikzpicture}[thick]
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% \node[gen_tree_node] (a2) at (0, 0){$R_b$};
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% \node[gen_tree_node] (b2) at (1, 0){$L_b$};
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% \node[gen_tree_node] (c2) at (2, 0){$R_c$};
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% %level 1
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% \node[gen_tree_node] (a1) at (0.5, 0.8){$\boldsymbol{\circmult}$};
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% \node[gen_tree_node] (b1) at (1.5, 0.8){$\boldsymbol{\circmult}$};
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% %level 0
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% \node[gen_tree_node] (a0) at (1.0, 1.6){$\boldsymbol{\circplus}$};
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% %edges
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% \draw[->] (a2) -- (a1);
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% \draw[->] (b2) -- (a1);
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% \draw[->] (b2) -- (b1);
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% \draw[->] (c2) -- (b1);
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% \draw[->] (a1) -- (a0);
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% \draw[->] (b1) -- (a0);
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% \end{tikzpicture}
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% }\\
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\end{tabular}
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};
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%label below rectangle
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\node[below=0.2cm of rect]{$\query(\pdb)$};
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\node[below=0.2cm of rect]{{\LARGE $\query(\pdb)$}};
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%Second arrow
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\node[single arrow, right=0.25 of rect, draw=black, fill=black!65, text=white, minimum height=0.75cm, minimum width=0.25cm](arrow2) {\textbf{Step 2}};
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%Expectation computation; (output of step 2)
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\node[rectangle, right=0.25 of arrow2, rounded corners, draw=black, fill=red!15, text=red, minimum height=4.5cm, minimum width=2cm](rrect) {
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\tabcolsep=0.09cm
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\begin{tabular}{>{\footnotesize}c | >{\footnotesize}c >{\footnotesize}m{1.95cm}}
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$\query$ & City & $\mathbb{E}[\poly(\vct{X})]$\\
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\hline
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& Buffalo & $1.0 \cdot 0.9 = 0.9$\\
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& Chicago & $(0.5 \cdot 1.0) + $\newline $\hspace{0.2cm}(0.5 \cdot 1.0)$\newline $= 1.0$\\
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%\captionof{table}{Q}
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\begin{tabular}{>{\small}c >{\centering\arraybackslash\small}m{1.95cm}}
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\multicolumn{2}{c}{$\expct\pbox{\poly(\vct{X})}$}\\
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\toprule
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City & $\mathbb{E}[\poly(\vct{X})]$\\
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\midrule[0.02em]
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Buffalo & $1.0 \cdot 0.9 = 0.9$\\
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Chicago & $(0.5 \cdot 1.0) + $\newline $\hspace{0.2cm}(0.5 \cdot 1.0)$\newline $= 1.0$\\
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\end{tabular}
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};
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%label of rounded rectangle
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\node[below=0.2cm of rrect]{$\expct\pbox{\poly(\vct{X})}$};
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\node[below=0.2cm of rrect]{{\LARGE $\expct\pbox{\poly(\vct{X})}$}};
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\end{tikzpicture}
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}
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\caption{Two step model of computation}
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