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-rw-r--r--buch/chapters/80-wahrscheinlichkeit/google.tex40
-rw-r--r--buch/chapters/80-wahrscheinlichkeit/images/Makefile8
-rw-r--r--buch/chapters/80-wahrscheinlichkeit/images/spielB.pdfbin0 -> 9917 bytes
-rw-r--r--buch/chapters/80-wahrscheinlichkeit/images/spielB.tex59
-rw-r--r--buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.pdfbin0 -> 14592 bytes
-rw-r--r--buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.tex59
-rw-r--r--buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdfbin120558 -> 120558 bytes
-rw-r--r--buch/chapters/80-wahrscheinlichkeit/parrondo.tex88
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
new file mode 100644
index 0000000..466974d
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/spielB.pdf
Binary files differ
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
new file mode 100644
index 0000000..7812c9c
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.pdf
Binary files differ
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
index c6173ce..b7215b4 100644
--- a/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf
+++ b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf
Binary files differ
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 $B$