variance.tex

Paper VI: Transfer Semigroups: Stochastic, Bayesian, Fractional, and PDE Realizations

variance.tex

Download original file

This is the original TeX manuscript source. Use the paper’s PDF for typeset equations.

Read the typeset paper

Skip source text

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}

Back to source controls

Other PDFs for this work

Original file and source record

This copy matches the recorded source file. Its publication here does not change the work’s review status.

SHA-256: ad8e2050542cf0bfb9f47b0dc594d0585c4edd2a17f2bef0e22bb683f16fdefe

Original source on GitHub

Back to Paper VI: Transfer Semigroups: Stochastic, Bayesian, Fractional, and PDE Realizations