merge conflict

main/nonergodicity.tex

@@ -14,18 +14,18 @@ P = \begin{pmatrix}
 \frac{1}{2} & 0 & \frac{1}{2} & 0 & 0\\
 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0\\
 0 & 0 & \frac{1}{2} & 0 & \frac{1}{2}\\
-0 & 0 & 0 & 0 & 1  
+0 & 0 & 0 & 0 & 1
 \end{pmatrix}
 \]
 
-%可重启的随机游走
+%可重启的随机游走矩阵
 \[
 P = \begin{pmatrix}
 0 & 0 & 1 & 0 & 0 &  \\
 \frac{1}{2} & 0 & \frac{1}{2} & 0 & 0\\
 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0\\
 0 & 0 & \frac{1}{2} & 0 & \frac{1}{2}\\
-0 & 0 & 1 & 0 & 0  
+0 & 0 & 1 & 0 & 0
 \end{pmatrix}
 \]
 
@@ -42,26 +42,7 @@ P = \begin{pmatrix}
 \]
 
 %随机游走pic
-\begin{tikzpicture}
-    \node[draw, rectangle, fill=gray!50] (DEAD) at (-2,0) ;
-    \node[draw, rectangle, fill=gray!50] (DEAD2) at (10,0) ;
-    \node[draw, circle] (A) at (0,0) {A};
-    \node[draw, circle] (B) at (2,0) {B};
-    \node[draw, circle] (C) at (4,0) {C};
-    \node[draw, circle] (D) at (6,0) {D};
-    \node[draw, circle] (E) at (8,0) {E};
-  
-    \draw[->] (A) -- (DEAD);
-    \draw[->] (B) -- (A);
-    \draw[->] (B) to [bend left=30] (C);
-    \draw[->] (C) to [bend left=30] (B);
-    \draw[->] (C) to [bend left=30] (D);
-    \draw[->] (D) to [bend left=30] (C);
-    \draw[->] (D) -- (E);
-    \draw[->] (E) -- (DEAD2);
-  
-    \draw[->] ([yshift=4ex]C.north) -- ([yshift=4.5ex]C.south);
-  \end{tikzpicture}
+\input{pic/randomWalk}
 
 设两个上三角矩阵为( A ) 和 ( B )，它们的形式分别为：
 
@@ -93,24 +74,7 @@ c_{ij}=\sum_{k=1}^{n} a_{ik}b_{kj}
 $N=1+Q^1+Q^2……$
 
 % “重启”随机游走 pic
-\begin{tikzpicture}
-  
-    \node[draw, circle] (A) at (0,0) {A};
-    \node[draw, circle] (B) at (2,0) {B};
-    \node[draw, circle] (C) at (4,0) {C};
-    \node[draw, circle] (D) at (6,0) {D};
-    \node[draw, circle] (E) at (8,0) {E};
-  
-    \draw[->] (A.north) to [bend left=30] (C.north)
-    \draw[->] (B) -- (A);
-    \draw[->] (B) to [bend left=30] (C);
-    \draw[->] (C) to [bend left=30] (B);
-    \draw[->] (C) to [bend left=30] (D);
-    \draw[->] (D) to [bend left=30] (C);
-    \draw[->] (D) -- (E);
-    \draw[->] (E.south) to [bend left=30] (C.south)
-  
-\end{tikzpicture}
+\input{pic/randomWalkRestart}
 
 
 

main/paradox.tex

@@ -79,7 +79,7 @@ N = \begin{pmatrix}
 \end{pmatrix}
 ]
 
-% 带截断的圣彼得堡悖论 
+% 带截断的圣彼得堡悖论
 \begin{table}[ht]
   \centering
   \begin{tabular}{|c|c|c|}
@@ -94,7 +94,7 @@ N = \begin{pmatrix}
   30 & 186.15 & +156.15 \\
   \hline
   \end{tabular}
-  \end{table}
+\end{table}
 
 
 

pic/2048example.tex

@@ -21,26 +21,25 @@
     
             
             
-            \node (p1) at(-10,16) {\includegraphics[height=3.0cm,width=3cm]{main/2048pic/2_1.png}};
-            
-            
-            \node (p2) at(-3,16) {\includegraphics[height=3.0cm,width=3cm]{main/2048pic/2_2.png}};
-            
-            \node (p3) at(3,16) {\includegraphics[height=3.0cm,width=3cm]{main/2048pic/3_1.png}};
-            
-            \node (p4) at(10,16) {\includegraphics[height=3.0cm,width=3cm]{main/2048pic/3_2.png}};
-        
+            \node (p1) at(-10,16) {\includegraphics[height=3.0cm,width=3cm]{main/2048pic/2_1}};
+
+            
+            \node (p2) at(-3,16) {\includegraphics[height=3.0cm,width=3cm]{main/2048pic/2_2}};
+
+            \node (p3) at(3,16) {\includegraphics[height=3.0cm,width=3cm]{main/2048pic/3_1}};
+
+            \node (p4) at(10,16) {\includegraphics[height=3.0cm,width=3cm]{main/2048pic/3_2}};
+
             \draw [-] (p1.north) -- (s11.south);
             \draw [-] (p2.north) -- (s12.south);
             \draw [-] (p3.north) -- (s21.south);
             \draw [-] (p4.north) -- (s22.south);
-                
-            
-            \node (p5) at(-7,30) {\includegraphics[height=3.0cm,width=3cm]{main/2048pic/0.png}};
+
+            \node (p5) at(-7,30) {\includegraphics[height=3.0cm,width=3cm]{main/2048pic/0}};
             
-            \node (p6) at(10,25) {\includegraphics[height=3.0cm,width=3cm]{main/2048pic/2_0.png}};
-    
-            \node (p7) at(-10,25) {\includegraphics[height=3.0cm,width=3cm]{main/2048pic/2_0.png}};
+            \node (p6) at(10,25) {\includegraphics[height=3.0cm,width=3cm]{main/2048pic/2_0}};
+
+            \node (p7) at(-10,25) {\includegraphics[height=3.0cm,width=3cm]{main/2048pic/2_0}};
             
             \draw [-] (st.west) -- (p5.east);
             \draw [-] (as1.west) -- (p7.east);

pic/randomWalk.tex

+\begin{tikzpicture}
+    \node[draw, rectangle, fill=gray!50] (DEAD) at (-2,0) ;
+    \node[draw, rectangle, fill=gray!50] (DEAD2) at (10,0) ;
+    \node[draw, circle] (A) at (0,0) {A};
+    \node[draw, circle] (B) at (2,0) {B};
+    \node[draw, circle] (C) at (4,0) {C};
+    \node[draw, circle] (D) at (6,0) {D};
+    \node[draw, circle] (E) at (8,0) {E};
+
+    \draw[->] (A) -- (DEAD);
+    \draw[->] (B) -- (A);
+    \draw[->] (B) to [bend left=30] (C);
+    \draw[->] (C) to [bend left=30] (B);
+    \draw[->] (C) to [bend left=30] (D);
+    \draw[->] (D) to [bend left=30] (C);
+    \draw[->] (D) -- (E);
+    \draw[->] (E) -- (DEAD2);
+
+    \draw[->] ([yshift=4ex]C.north) -- ([yshift=4.5ex]C.south);
+\end{tikzpicture}
\ No newline at end of file

pic/randomWalkRestart.tex

+\begin{tikzpicture}
+
+    \node[draw, circle] (A) at (0,0) {A};
+    \node[draw, circle] (B) at (2,0) {B};
+    \node[draw, circle] (C) at (4,0) {C};
+    \node[draw, circle] (D) at (6,0) {D};
+    \node[draw, circle] (E) at (8,0) {E};
+
+    \draw[->] (A.north) to [bend left=30] (C.north)
+    \draw[->] (B) -- (A);
+    \draw[->] (B) to [bend left=30] (C);
+    \draw[->] (C) to [bend left=30] (B);
+    \draw[->] (C) to [bend left=30] (D);
+    \draw[->] (D) to [bend left=30] (C);
+    \draw[->] (D) -- (E);
+    \draw[->] (E.south) to [bend left=30] (C.south)
+
+\end{tikzpicture}
\ No newline at end of file