diff options
Diffstat (limited to 'buch/chapters/80-wahrscheinlichkeit')
| -rw-r--r-- | buch/chapters/80-wahrscheinlichkeit/google.tex | 40 | ||||
| -rw-r--r-- | buch/chapters/80-wahrscheinlichkeit/images/Makefile | 8 | ||||
| -rw-r--r-- | buch/chapters/80-wahrscheinlichkeit/images/spielB.pdf | bin | 0 -> 9917 bytes | |||
| -rw-r--r-- | buch/chapters/80-wahrscheinlichkeit/images/spielB.tex | 59 | ||||
| -rw-r--r-- | buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.pdf | bin | 0 -> 14592 bytes | |||
| -rw-r--r-- | buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.tex | 59 | ||||
| -rw-r--r-- | buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf | bin | 120558 -> 120558 bytes | |||
| -rw-r--r-- | buch/chapters/80-wahrscheinlichkeit/parrondo.tex | 88 |
8 files changed, 128 insertions, 126 deletions
diff --git a/buch/chapters/80-wahrscheinlichkeit/google.tex b/buch/chapters/80-wahrscheinlichkeit/google.tex index 3616760..ca78b3d 100644 --- a/buch/chapters/80-wahrscheinlichkeit/google.tex +++ b/buch/chapters/80-wahrscheinlichkeit/google.tex @@ -41,46 +41,6 @@ zerstört. \begin{figure} \centering \includegraphics{chapters/80-wahrscheinlichkeit/images/internet.pdf} -%\begin{tikzpicture}[>=latex,thick] -%\foreach \x in {0,3,6,9}{ -% \foreach \y in {0,3}{ -% \fill[color=white] ({\x},{\y}) circle[radius=0.3]; -% \draw ({\x},{\y}) circle[radius=0.3]; -% } -%} -%\node at (0,3) {$1$}; -%\node at (0,0) {$2$}; -%\node at (3,3) {$3$}; -%\node at (3,0) {$4$}; -%\node at (6,3) {$5$}; -%\node at (6,0) {$6$}; -%\node at (9,3) {$7$}; -%\node at (9,0) {$8$}; -%% 1 -%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (0,3) -- (3,3); -%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (0,3) -- (0,0); -%% 2 -%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (0,0) to[out=-20,in=-160] (3,0); -%% 3 -%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (3,3) -- (6,3); -%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (3,3) -- (0,0); -%% 4 -%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (3,0) -- (6,3); -%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (3,0) -- (6,0); -%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (3,0) to[out=160,in=20] (0,0); -%% 5 -%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (6,3) -- (9,3); -%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (6,3) -- (9,0); -%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (6,3) -- (6,0); -%% 6 -%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (6,0) to[out=20,in=160] (9,0); -%% 7 -%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (9,3) .. controls (7.5,4) .. (6,4) -- (3,4) .. controls (1.5,4) .. (0,3); -%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (9,3) to[out=-110,in=110] (9,0); -%% 8 -%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (9,0) to[out=-160,in=-20] (6,0); -%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (9,0) to[out=70,in=-70] (9,3); -%\end{tikzpicture} \caption{Modell-Internet als Beispiel für die Link-Matrix und die Google-Matrix. \label{buch:figure:modellinternet}} \end{figure} diff --git a/buch/chapters/80-wahrscheinlichkeit/images/Makefile b/buch/chapters/80-wahrscheinlichkeit/images/Makefile index b04f6ff..8d34217 100644 --- a/buch/chapters/80-wahrscheinlichkeit/images/Makefile +++ b/buch/chapters/80-wahrscheinlichkeit/images/Makefile @@ -5,7 +5,8 @@ # all: dreieck.pdf trenn.pdf vergleich.pdf vergleich.jpg \ positiv.pdf positiv.jpg diffusion.png diffusion.pdf \ - konvex.pdf internet.pdf markov.pdf markov2.pdf markov3.pdf + konvex.pdf internet.pdf markov.pdf markov2.pdf markov3.pdf \ + spielB.pdf spielBtilde.pdf # Visualisierung diffusion in einer primitiven Matrix diffusion.pdf: diffusion.tex diffusion.jpg @@ -71,3 +72,8 @@ markov2.pdf: markov2.tex markov3.pdf: markov3.tex pdflatex markov3.tex +spielB.pdf: spielB.tex + pdflatex spielB.tex + +spielBtilde.pdf: spielBtilde.tex + pdflatex spielBtilde.tex diff --git a/buch/chapters/80-wahrscheinlichkeit/images/spielB.pdf b/buch/chapters/80-wahrscheinlichkeit/images/spielB.pdf Binary files differnew file mode 100644 index 0000000..466974d --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/spielB.pdf diff --git a/buch/chapters/80-wahrscheinlichkeit/images/spielB.tex b/buch/chapters/80-wahrscheinlichkeit/images/spielB.tex new file mode 100644 index 0000000..92989ed --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/spielB.tex @@ -0,0 +1,59 @@ +% +% spielB.tex -- Zutandsdiagramm für Spiel B +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\R{2} +\def\r{0.5} +\coordinate (A) at (0,\R); +\coordinate (B) at ({\R*sqrt(3)/2},{-0.5*\R}); +\coordinate (C) at ({-\R*sqrt(3)/2},{-0.5*\R}); + +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (B); +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (C); +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) -- (B); + +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=90,in=-30] (A); +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) to[out=90,in=-150] (A); +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=-150,in=-30] (C); + +\pgfmathparse{0.93*\R} +\xdef\Rgross{\pgfmathresult} + +\node at (30:\Rgross) {$\frac34$}; +\node at (150:\Rgross) {$\frac14$}; +\node at (-90:\Rgross) {$\frac14$}; + +\pgfmathparse{0.33*\R} +\xdef\Rklein{\pgfmathresult} + +\node at (-90:\Rklein) {$\frac34$}; +\node at (30:\Rklein) {$\frac9{10}$}; +\node at (150:\Rklein) {$\frac1{10}$}; + +\fill[color=white] (A) circle[radius=\r]; +\draw (A) circle[radius=\r]; +\node at (A) {$0$}; + +\fill[color=white] (B) circle[radius=\r]; +\draw (B) circle[radius=\r]; +\node at (B) {$2$}; + +\fill[color=white] (C) circle[radius=\r]; +\draw (C) circle[radius=\r]; +\node at (C) {$1$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.pdf b/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.pdf Binary files differnew file mode 100644 index 0000000..7812c9c --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.pdf diff --git a/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.tex b/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.tex new file mode 100644 index 0000000..b2d4b01 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.tex @@ -0,0 +1,59 @@ +% +% spielBtilde.tex -- Zustandsdiagramm des modifzierten Spiels +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\R{2.5} +\def\r{0.5} +\coordinate (A) at (0,\R); +\coordinate (B) at ({\R*sqrt(3)/2},{-0.5*\R}); +\coordinate (C) at ({-\R*sqrt(3)/2},{-0.5*\R}); + +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (B); +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (C); +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) -- (B); + +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=90,in=-30] (A); +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) to[out=90,in=-150] (A); +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=-150,in=-30] (C); + +\pgfmathparse{0.93*\R} +\xdef\Rgross{\pgfmathresult} + +\node at (30:\Rgross) {$\frac34-\varepsilon$}; +\node at (150:\Rgross) {$\frac14+\varepsilon$}; +\node at (-90:\Rgross) {$\frac14+\varepsilon$}; + +\pgfmathparse{0.32*\R} +\xdef\Rklein{\pgfmathresult} + +\node at (-90:\Rklein) {$\frac34-\varepsilon$}; +\node at (30:\Rklein) {$\frac9{10}+\varepsilon$}; +\node at (150:\Rklein) {$\frac1{10}-\varepsilon$}; + +\fill[color=white] (A) circle[radius=\r]; +\draw (A) circle[radius=\r]; +\node at (A) {$0$}; + +\fill[color=white] (B) circle[radius=\r]; +\draw (B) circle[radius=\r]; +\node at (B) {$2$}; + +\fill[color=white] (C) circle[radius=\r]; +\draw (C) circle[radius=\r]; +\node at (C) {$1$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf Binary files differindex c6173ce..b7215b4 100644 --- a/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf +++ b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf diff --git a/buch/chapters/80-wahrscheinlichkeit/parrondo.tex b/buch/chapters/80-wahrscheinlichkeit/parrondo.tex index 3bdba9a..a62d813 100644 --- a/buch/chapters/80-wahrscheinlichkeit/parrondo.tex +++ b/buch/chapters/80-wahrscheinlichkeit/parrondo.tex @@ -61,48 +61,7 @@ Fälle recht gross, in einem Fall aber sehr klein. \subsubsection{Übergangsmatrix im Spiel $B$} \begin{figure} \centering -\begin{tikzpicture}[>=latex,thick] -\def\R{2} -\def\r{0.5} -\coordinate (A) at (0,\R); -\coordinate (B) at ({\R*sqrt(3)/2},{-0.5*\R}); -\coordinate (C) at ({-\R*sqrt(3)/2},{-0.5*\R}); - -\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (B); -\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (C); -\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) -- (B); - -\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=90,in=-30] (A); -\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) to[out=90,in=-150] (A); -\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=-150,in=-30] (C); - -\pgfmathparse{0.93*\R} -\xdef\Rgross{\pgfmathresult} - -\node at (30:\Rgross) {$\frac34$}; -\node at (150:\Rgross) {$\frac14$}; -\node at (-90:\Rgross) {$\frac14$}; - -\pgfmathparse{0.33*\R} -\xdef\Rklein{\pgfmathresult} - -\node at (-90:\Rklein) {$\frac34$}; -\node at (30:\Rklein) {$\frac9{10}$}; -\node at (150:\Rklein) {$\frac1{10}$}; - -\fill[color=white] (A) circle[radius=\r]; -\draw (A) circle[radius=\r]; -\node at (A) {$0$}; - -\fill[color=white] (B) circle[radius=\r]; -\draw (B) circle[radius=\r]; -\node at (B) {$2$}; - -\fill[color=white] (C) circle[radius=\r]; -\draw (C) circle[radius=\r]; -\node at (C) {$1$}; - -\end{tikzpicture} +\includegraphics{chapters/80-wahrscheinlichkeit/images/spielB.pdf} \caption{Zustandsdiagramm für das Spiel $B$, Zustände sind die Dreierreste des Kapitals. \label{buch:wahrscheinlichkeit:fig:spielB}} @@ -454,51 +413,10 @@ U^t (G\odot B) p \] wie erwartet. -\subsubsection{Das modifizierte Spiel $B$} +\subsubsection{Das modifizierte Spiel $\tilde{B}$} \begin{figure} \centering -\begin{tikzpicture}[>=latex,thick] -\def\R{2.5} -\def\r{0.5} -\coordinate (A) at (0,\R); -\coordinate (B) at ({\R*sqrt(3)/2},{-0.5*\R}); -\coordinate (C) at ({-\R*sqrt(3)/2},{-0.5*\R}); - -\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (B); -\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (C); -\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) -- (B); - -\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=90,in=-30] (A); -\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) to[out=90,in=-150] (A); -\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=-150,in=-30] (C); - -\pgfmathparse{0.93*\R} -\xdef\Rgross{\pgfmathresult} - -\node at (30:\Rgross) {$\frac34-\varepsilon$}; -\node at (150:\Rgross) {$\frac14+\varepsilon$}; -\node at (-90:\Rgross) {$\frac14+\varepsilon$}; - -\pgfmathparse{0.32*\R} -\xdef\Rklein{\pgfmathresult} - -\node at (-90:\Rklein) {$\frac34-\varepsilon$}; -\node at (30:\Rklein) {$\frac9{10}+\varepsilon$}; -\node at (150:\Rklein) {$\frac1{10}-\varepsilon$}; - -\fill[color=white] (A) circle[radius=\r]; -\draw (A) circle[radius=\r]; -\node at (A) {$0$}; - -\fill[color=white] (B) circle[radius=\r]; -\draw (B) circle[radius=\r]; -\node at (B) {$2$}; - -\fill[color=white] (C) circle[radius=\r]; -\draw (C) circle[radius=\r]; -\node at (C) {$1$}; - -\end{tikzpicture} +\includegraphics{chapters/80-wahrscheinlichkeit/images/spielBtilde.pdf} \caption{Zustandsdiagramm für das modifizerte Spiel $\tilde{B}$, Zustände sind die Dreierreste des Kapitals. Gegenüber dem Spiel $B$ |