variance.tex
Paper VI: Transfer Semigroups: Stochastic, Bayesian, Fractional, and PDE Realizations
variance.tex
This is the original TeX manuscript source. Use the paper’s PDF for typeset equations.
1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \path[draw=black,fill=black!8] (0.7,2.05) rectangle (10.546154,2.8);
4 \path[draw=black,fill=black!20] (10.546154,2.05) rectangle (11.13956,2.8);
5 \path[draw=black,fill=black!36] (11.13956,2.05) rectangle (13.2,2.8);
6 \draw[black!60] (5.623077,2.8) -- (5.623077,3.05);
7 \draw[black!60] (5.623077,3.05) -- (3,3.28);
8 \node[font=\small,align=center,font=\small] at (3,3.73) {mean\\$\frac{256}{25}$};
9 \draw[black!60] (10.842857,2.8) -- (10.842857,3.05);
10 \draw[black!60] (10.842857,3.05) -- (9.2,3.28);
11 \node[font=\small,align=center,font=\small] at (9.2,3.73) {between blocks\\$\frac{108}{175}$};
12 \draw[black!60] (12.16978,2.8) -- (12.16978,3.05);
13 \draw[black!60] (12.16978,3.05) -- (12.25,3.28);
14 \node[font=\small,align=center,font=\small] at (12.25,3.73) {within blocks\\$\frac{15}{7}$};
15 \node[font=\small,align=center,font=\scriptsize] at (7,4.55) {Weighted squared norms: total $13$};
16 \node[font=\small,align=center,font=\scriptsize] at (2.3,0.7) {$D_0f=\left[\begin{matrix}\frac{16}{5}\\\frac{16}{5}\\\frac{16}{5}\\\frac{16}{5}\end{matrix}\right]$};
17 \node[font=\small,align=center,font=\scriptsize] at (6.9,0.7) {$D_1f=\left[\begin{matrix}- \frac{6}{5}\\- \frac{6}{5}\\\frac{18}{35}\\\frac{18}{35}\end{matrix}\right]$};
18 \node[font=\small,align=center,font=\scriptsize] at (11.5,0.7) {$D_2f=\left[\begin{matrix}-2\\1\\- \frac{12}{7}\\\frac{9}{7}\end{matrix}\right]$};
19 \end{tikzpicture}
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