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

Download original file

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

Read the typeset paper

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 \node[font=\small,align=center,font=\small] at (1.6,4.4) {Path};
4 \node[font=\small,align=center,font=\small] at (4.4,4.4) {probability};
5 \node[font=\small,align=center,font=\small] at (7,4.4) {weight};
6 \node[font=\small,align=center,font=\small] at (9.5,4.4) {terminal};
7 \node[font=\small,align=center,font=\small] at (12,4.4) {contribution};
8 \node[font=\small,align=center,font=\small] at (1.6,3.8) {\texttt{0000}};
9 \node[font=\small,align=center] at (4.4,3.8) {$27/64$};
10 \node[font=\small,align=center] at (7,3.8) {$1$};
11 \node[font=\small,align=center] at (9.5,3.8) {$2$};
12 \node[font=\small,align=center] at (12,3.8) {$27/32$};
13 \draw[black!18,line width=.3pt] (0.6,3.58) -- (13.4,3.58);
14 \node[font=\small,align=center,font=\small] at (1.6,3.33) {\texttt{0001}};
15 \node[font=\small,align=center] at (4.4,3.33) {$9/64$};
16 \node[font=\small,align=center] at (7,3.33) {$1$};
17 \node[font=\small,align=center] at (9.5,3.33) {$1$};
18 \node[font=\small,align=center] at (12,3.33) {$9/64$};
19 \node[font=\small,align=center,font=\small] at (1.6,2.86) {\texttt{0010}};
20 \node[font=\small,align=center] at (4.4,2.86) {$3/64$};
21 \node[font=\small,align=center] at (7,2.86) {$1/2$};
22 \node[font=\small,align=center] at (9.5,2.86) {$2$};
23 \node[font=\small,align=center] at (12,2.86) {$3/64$};
24 \draw[black!18,line width=.3pt] (0.6,2.64) -- (13.4,2.64);
25 \node[font=\small,align=center,font=\small] at (1.6,2.39) {\texttt{0011}};
26 \node[font=\small,align=center] at (4.4,2.39) {$9/64$};
27 \node[font=\small,align=center] at (7,2.39) {$1/2$};
28 \node[font=\small,align=center] at (9.5,2.39) {$1$};
29 \node[font=\small,align=center] at (12,2.39) {$9/128$};
30 \node[font=\small,align=center,font=\small] at (1.6,1.92) {\texttt{0100}};
31 \node[font=\small,align=center] at (4.4,1.92) {$3/64$};
32 \node[font=\small,align=center] at (7,1.92) {$1/2$};
33 \node[font=\small,align=center] at (9.5,1.92) {$2$};
34 \node[font=\small,align=center] at (12,1.92) {$3/64$};
35 \draw[black!18,line width=.3pt] (0.6,1.7) -- (13.4,1.7);
36 \node[font=\small,align=center,font=\small] at (1.6,1.45) {\texttt{0101}};
37 \node[font=\small,align=center] at (4.4,1.45) {$1/64$};
38 \node[font=\small,align=center] at (7,1.45) {$1/2$};
39 \node[font=\small,align=center] at (9.5,1.45) {$1$};
40 \node[font=\small,align=center] at (12,1.45) {$1/128$};
41 \node[font=\small,align=center,font=\small] at (1.6,0.98) {\texttt{0110}};
42 \node[font=\small,align=center] at (4.4,0.98) {$3/64$};
43 \node[font=\small,align=center] at (7,0.98) {$1/4$};
44 \node[font=\small,align=center] at (9.5,0.98) {$2$};
45 \node[font=\small,align=center] at (12,0.98) {$3/128$};
46 \draw[black!18,line width=.3pt] (0.6,0.76) -- (13.4,0.76);
47 \node[font=\small,align=center,font=\small] at (1.6,0.51) {\texttt{0111}};
48 \node[font=\small,align=center] at (4.4,0.51) {$9/64$};
49 \node[font=\small,align=center] at (7,0.51) {$1/4$};
50 \node[font=\small,align=center] at (9.5,0.51) {$1$};
51 \node[font=\small,align=center] at (12,0.51) {$9/256$};
52 \node[font=\small,align=center,font=\scriptsize] at (7,-0.22) {Total probability $=1$; weighted terminal expectation $=311/256$.};
53 \end{tikzpicture}

Back to source controls

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