JackieLin0123/SciTikZ-Bench huggingface dataset:
\documentclass[tikz,border=10pt]{standalone}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
  \def\XSTART{0}
  \def\YSTART{3}
  \def\YDIAONE{2.5}
  \def\YDIATWO{2}
  \def\YCURVE{2}
  \def\XCURVE{2}
  \def\XEND{15}
  \def\XONESTART{2}
  \def\XONEDELTA{2}
  \def\DD{0.5}

  \def\YEND{\YSTART+\YCURVE+\YDIATWO}
  \def\XCURVESTART{\XEND/2-\XSTART/2-\XCURVE/2}
  \def\XCURVESTARTUP{\XEND/2-\XSTART/2-\XCURVE}
  \def\XCURVEEND{\XEND/2-\XSTART/2 + \XCURVE/2}
  \def\XONEEND{\XONESTART+\XONEDELTA}
  \def\XTWOSTART{\XCURVEEND+\XONESTART}
  \def\XTWODELTA{\XONEDELTA*\YDIAONE*\YDIAONE/\YDIATWO/\YDIATWO}
  \def\XTWOEND{\XTWOSTART+\XTWODELTA}
  \def\YTWOMIDDLE{\YSTART+\YCURVE+\YDIATWO/2}
  \def\YONEMIDDLE{\YSTART+\YDIAONE/2}
  \def\GROUND{\YSTART/4}

  \tikzset{
      partial ellipse/.style args={#1:#2:#3}{
          insert path={+ (#1:#3) arc (#1:#2:#3)}
      },
      dimen/.style={<->,>=latex,thin,
        every rectangle node/.style={fill=white,midway,font=\sffamily}},
  }

  \draw (\XSTART,\YSTART) -- (\XCURVESTART,\YSTART)
    to[out=0, in=180, looseness=0.75]
      (\XCURVEEND,{\YSTART+\YCURVE}) -- (\XEND,{\YSTART+\YCURVE});
  \draw (\XSTART,{\YSTART+\YDIAONE}) -- (\XCURVESTARTUP,{\YSTART+\YDIAONE})
    to[out=0, in=180, looseness=0.75] (\XCURVEEND,\YEND) -- (\XEND,\YEND);

  \draw [fill=gray] (\XONESTART,\YSTART) coordinate (BA)
    rectangle (\XONEEND,{\YSTART+\YDIAONE}) coordinate (BB);
  \draw [fill=lightgray](\XONESTART,\YONEMIDDLE) node [below] {$A_1$}
    ellipse ({\YDIAONE/6} and {\YDIAONE/2});
  \draw [fill=gray,dashed](\XONEEND,\YONEMIDDLE)
    ellipse ({\YDIAONE/6} and {\YDIAONE/2});
  \draw (\XONEEND,\YONEMIDDLE)
    [partial ellipse=-90:90:{\YDIAONE/6} and {\YDIAONE/2}];

  \draw [fill=gray] (\XTWOSTART,{\YSTART+\YCURVE}) coordinate (CA)
    rectangle (\XTWOEND,{\YSTART+\YCURVE+\YDIATWO}) coordinate (CB);
  \draw [fill=lightgray] (\XTWOSTART,\YTWOMIDDLE) node [below] {$A_2$}
    ellipse ({\YDIATWO/6} and {\YDIATWO/2});
  \draw [fill=gray,dashed](\XTWOEND,\YTWOMIDDLE)
    ellipse ({\YDIATWO/6} and {\YDIATWO/2});
  \draw (\XTWOEND,{\YSTART+\YCURVE+\YDIATWO/2})
    [partial ellipse=-90:90:{\YDIATWO/6} and {\YDIATWO/2}];

  \draw [fill=gray] (0,0) rectangle  (\XEND,\GROUND);

  \draw ($(BA)+(0,\YDIAONE)$) -- ++(0,\DD) coordinate (D1) -- +(0,5pt);
  \draw (BB) -- ++(0,\DD) coordinate (D2) -- +(0,5pt);
  \draw [dimen] (D1) -- (D2) node {$v_1dt$};

  \draw ($(BA)!0.5!(BB)$) -- ++(5pt,0) coordinate (E) -- +(5pt,0);
  \draw [dimen] let \p{E}=(E) in (\x{E},\GROUND) -- (E) node {$h_1$};
  \draw [style=->](\XSTART,\YONEMIDDLE) -- (\XONESTART,\YONEMIDDLE)
    node [midway,above] {$p_1$};

  \draw ($(CA)+(0,\YDIATWO)$) -- ++(0,\DD) coordinate (D1) -- +(0,5pt);
  \draw (CB) -- ++(0,\DD) coordinate (D2) -- +(0,5pt);
  \draw [dimen] (D1) -- (D2) node {$v_2dt$};

  \draw ($(CA)!0.5!(CB)$) -- ++(5pt,0) coordinate (D) -- +(5pt,0);
  \draw [dimen] let \p{D}=(D) in (\x{D},\GROUND) -- (D) node {$h_2$};
  \draw [style=->](\XCURVEEND,\YTWOMIDDLE) -- (\XTWOSTART,\YTWOMIDDLE)
    node [midway,above] {$p_2$};
\end{tikzpicture}
\end{document}
\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{math}

\begin{document}
\tdplotsetmaincoords{70}{100}
\begin{tikzpicture}[tdplot_main_coords]
    \pgfmathsetmacro{\r}{2}
    % Base of the truncated cylinder
    \draw[thick,fill=cyan!35,opacity=0.75] plot[domain=0:6.2832,smooth,variable=\t] ({\r*cos(\t r)},{\r*sin(\t r)},{0.0});
    \draw[red,thick,dashed] plot[domain=1.570796327:4.71238898,smooth,variable=\t] ({\r*cos(\t r)},{\r*sin(\t r)},{0.0}); 
    % Vertical wall (back, external radius)
    \fill[gray!35,opacity=0.5] (0,\r,0) 
        -- plot[domain=1.571:4.71238898,smooth,variable=\t] ({\r*cos(\t r)},{\r*sin(\t r)},{0})
        -- (0,-\r,4) 
        -- plot[domain=4.71238898:1.571,smooth,variable=\t] ({\r*cos(\t r)},{\r*sin(\t r)},{4.0-\r*sin(\t r)})
        -- (0,\r,0);	
    % Vertical wall (front, external radius)
    \fill[cyan!35,opacity=0.5] (0,-\r,0) 
        -- plot[domain=-1.571:1.571,smooth,variable=\t] ({\r*cos(\t r)},{\r*sin(\t r)},{0}) 
        -- (0,\r,2.0) 
        -- plot[domain=1.571:-1.571,smooth,variable=\t] ({\r*cos(\t r)},{\r*sin(\t r)},{4.0-\r*sin(\t r)}) 
        -- (0,-\r,0);
    % section of the plane (cut by a plane)
    \draw[thick] plot[domain=0:6.2832,smooth,variable=\t] ({\r*cos(\t r)},{\r*sin(\t r)},{4.0-\r*sin(\t r)});
    % The cylinder (vertical wall)
    \foreach \angulo in {0,0.05,...,6.3}{
        \pgfmathparse{2.0*cos(\angulo r)}
        \pgfmathsetmacro{\px}{\pgfmathresult}
        \pgfmathparse{2.0*sin(\angulo r)}
        \pgfmathsetmacro{\py}{\pgfmathresult}
        \draw[cyan] (\px,\py,0) -- (\px,\py,4.0-\py);
    }
    \fill[cyan!35,opacity=0.75] plot[domain=0:6.2832,smooth,variable=\t] ({\r*cos(\t r)},{\r*sin(\t r)},{4.0-\r*sin(\t r)});
    % Circumferences bounding the cylinder
    \draw[red,thick] plot[domain=0:6.2831853,smooth,variable=\t] ({\r*cos(\t r)},{\r*sin(\t r)},{4.0-\r*sin(\t r)}); 
    \draw[red,thick] plot[domain=-1.570796327:1.570796327,smooth,variable=\t] ({\r*cos(\t r)},{\r*sin(\t r)},{0.0}); 
    % lengths and indication of points
    \draw[dash dot dot] (0,0,-1) -- (0,0,6);
    \draw[dash dot dot] (0,-\r,6) -- (0,\r,2);
    \draw[dash dot dot] (-\r,0,4) -- (\r,0,4);
    \draw[dash dot dot] (0,0,4) -- (0,\r+1.5,4);
    \draw[dash dot dot] (-\r,0,0) -- (\r,0,0);
    \draw[dash dot dot] (0,-\r-1.0,0) -- (0,\r+1.5,0);
    \draw[dash dot dot] (0,-\r-1.0,6) -- (0,-\r,6);
    \draw[dash dot dot] (0,\r,5.5) -- (0,\r,2) -- (0,\r+1,2);
    \draw[thick,<->] (0,0,5) -- (0,\r,5) node [midway,fill=white] {$r$};
    \draw[thick,<->] (0,\r+0.5,0) -- (0,\r+0.5,2) node [midway,fill=white] {$h_{1}$};
    \draw[thick,<->] (0,-\r-0.5,0) -- (0,-\r-0.5,6) node [midway,fill=white] {$h_{2}$};
    \draw[thick,<->] (0,\r+1.0,0) -- (0,\r+1.0,4) node [midway,fill=white] {$h$};
\end{tikzpicture}
\end{document}
\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{automata, positioning, arrows}

\tikzset{
  node distance=2.5cm,
  every state/.style={semithick, fill=gray!10},
  initial text={},
  double distance=2pt,
  every edge/.style={draw, ->, >=stealth', auto, semithick},
  vertex/.style={state, minimum size=5mm, fill=gray!10, inner sep=0pt, font=\tiny},
  vertexsmall/.style={state, minimum size=4mm, fill=gray!10, inner sep=0pt, font=\tiny},
  base/.style={draw, ->, >=stealth', auto, semithick, font=\tiny, sloped, pos=0.5, above},
  SE/.style={base, thick},
  SN/.style={base, dashed, thick},
  E/.style={base, color=gray!60, thin},
  FE/.style={base, dotted, color=gray!60, thin}
}

\begin{document}
\begin{tikzpicture}
  \foreach \phi in {0,...,3}{
    \node[vertex] (\phi) at (360/8 * \phi:2cm) {$w_\phi$};
  }
  \foreach \phi in {4,...,7}{
    \node[vertex] (\phi) at (360/8 * \phi:2cm) {};
  }
  \draw (1) edge[SE] node {$+\Delta$} (0)
             edge[SN] node {$-\Delta$} (2)
             edge[E] node {} (6)
        (3) edge[SE] node {$+\Delta$} (2)
             edge[SE] node {$-\Delta$} (0)
             edge[E] node {} (6)
        (5) edge[E] node {} (4)
             edge[E] node {} (2)
             edge[E] node {} (0)
        (7) edge[E] node {} (6);
\end{tikzpicture}
\end{document}
\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.9}
\tikzset{immagine/.style={above right, inner sep=0pt, outer sep=0pt}}
\pgfplotscreateplotcyclelist{mycolorlist}{%
	blue,every mark/.append style={fill=blue!80!black},mark=*\\%
	red,every mark/.append style={fill=red!80!black},mark=square*\\%
	green!60!black,every mark/.append style={fill=green!80!black},mark=otimes*\\%
	red,mark=star\\%
	blue,every mark/.append style={fill=blue!80!black},mark=diamond*\\%
	red,densely dashed,every mark/.append style={solid,fill=red!80!black},mark=*\\%
	green!60!black,densely dashed,every mark/.append style={solid,fill=green!80!black},mark=square*\\%
	black,densely dashed,every mark/.append style={solid,fill=gray},mark=otimes*\\%
	blue,densely dashed,mark=star,every mark/.append style=solid\\%
	red,densely dashed,every mark/.append style={solid,fill=red!80!black},mark=diamond*\\%
}

\begin{document}
\begin{tikzpicture}[scale=0.8]
\begin{loglogaxis}[
small,
xlabel=Dofs, title={$L = 256$},
cycle list name=mycolorlist]
% GAMG classical
\addplot coordinates {
	(20007, 0.61384)
	(40011, 1.0748)
	(80007, 3.4119)
	(160028, 7.899)
	(320020, 17.728)
	(640035, 31.062)
	(1280053, 81.295)
	(2560065, 200.05)
};
% GAMG with aggregation
\addplot coordinates {
	(20007, 0.80825)
	(40011, 1.0095)
	(80007, 2.7438)
	(160028, 6.6927)
	(320020, 12.949)
	(640035, 21.867)
	(1280053, 68.561)
	(2560065, 153.04)
};
% BoomerAMG
\addplot coordinates {
	(20007, 0.095413)
	(40011, 0.21166)
	(80007, 0.42168)
	(160028, 0.92577)
	(320020, 1.9803)
	(640035, 4.0734)
	(1280053, 8.6757)
	(2560065, 19.306)
};
% ML
\addplot coordinates {
	(20007, 0.82717)
	(40011, 0.84182)
	(80007, 2.9882)
	(160028, 6.9114)
	(320020, 12.307)
	(640035, 19.958)
	(1280053, 59.375)
	(2560065, 122.13)
};
% SuperLU
\addplot coordinates {
	(20007, 0.22203)
	(40011, 0.5914)
	(80007, 1.6566)
	(160028, 4.7524)
	(320020, 15.251)
	(640035, 44.929)
	(1280053, 141.91)
	(2560065, 434.59)
};
% UMFPACK
\addplot coordinates {
	(20007, 0.1465)
	(40011, 0.31841)
	(80007, 0.80297)
	(160028, 2.0617)
	(320020, 6.0724)
	(640035, 15.798)
};
% MUMPS
\addplot coordinates {
	(20007, 0.20897)
	(40011, 0.46142)
	(80007, 0.96547)
	(160028, 2.2502)
	(320020, 4.7861)
	(640035, 11.106)
	(1280053, 27.182)
	(2560065, 68.077)
};
\addplot coordinates {
	(20007, 0.2357)
	(40011, 0.50776)
	(80007, 1.16)
	(160028, 2.4988)
	(320020, 5.5394)
	(640035, 13.835)
	(1280053, 30.348)
	(2560065, 78.262)
};
% Pastix
\addplot coordinates {
	(20007, 0.23317)
	(40011, 0.51628)
	(80007, 1.1609)
	(160028, 2.3292)
	(320020, 5.2971)
	(640035, 12.573)
	(1280053, 25.432)
	(2560065, 70.057)
};
\end{loglogaxis}
\end{tikzpicture}
\end{document}
\documentclass[border=5pt]{standalone}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[xscale=1, yscale=0.9]
\node (v14) at (-3,3) {\large $y_{1,5}$};
\node (v15) at (-3,2) {\large $y_{1,4}$};
\node (v17) at (-3,1) {\large $y_{1,3}$};
\node (v19) at (-3,0) {\large $y_{1,2}$};
\node (v21) at (-3,-1) {\large $y_{1,1}$};
\node (v23) at (-1.5,-1) {\large $y_{2,1}$};
\node (v24) at (-1.5,0) {\large $y_{2,2}$};
\node (v25) at (-1.5,1) {\large $y_{2,3}$};
\node (v26) at (-1.5,2) {\large $y_{2,4}$};
\node (v27) at (-1.5,3) {\large $y_{2,5}$};
\node (v28) at (0,-1) {\large $y_{3,1}$};
\node (v29) at (0,0) {\large $y_{3,2}$};
\node (v30) at (0,1) {\large $x_{3,3}$};
\node (v31) at (0,2) {\large $x_{3,4}$};
\node (v32) at (0,3) {\large $x_{3,5}$};
\node (v37) at (1.5,3) {\large $x_{4,5}$};
\node (v36) at (1.5,2) {\large $x_{4,4}$};
\node (v35) at (1.5,1) {\large $x_{4,3}$};
\node (v34) at (1.5,0) {\large $x_{4,2}$};
\node (v33) at (1.5,-1) {\large $x_{4,1}$};
\node (v38) at (3,-1) {\large $x_{5,1}$};
\node (v39) at (3,0) {\large $x_{5,2}$};
\node (v40) at (3,1) {\large $x_{5,3}$};
\node (v41) at (3,2) {\large $x_{5,4}$};
\node (v42) at (3,3) {\large $x_{5,5}$};
\node (v13) at (4.5,3) {\large $x_{6,5}$};
\node (v16) at (4.5,2) {\large $x_{6,4}$};
\node (v18) at (4.5,1) {\large $x_{6,3}$};
\node (v20) at (4.5,0) {\large $x_{6,2}$};
\node (v22) at (4.5,-1) {\large $x_{6,1}$};

\draw [blue] (v21) -- (v19) -- (v17) -- (v15) -- (v14);
\draw [blue] (v23) -- (v24) -- (v25) -- (v26) -- (v27);
\draw [blue] (v28) -- (v29) -- (v30) -- (v31) -- (v32);
\draw [blue] (v33) -- (v34) -- (v35) -- (v36) -- (v37);
\draw [blue] (v38) -- (v39) -- (v40) -- (v41) -- (v42);
\draw [blue] (v22) -- (v20) -- (v18) -- (v16) -- (v13);

\node at (1,-2.4) {\large space $n$};
\node [rotate=90] at (-4,1) {\large imaginary-time $L$};

\draw [blue, dotted, thick] (v14) -- (v27) -- (v32) -- (v37) -- (v42) -- (v13);
\draw [blue, dotted, thick] (v15) -- (v26) -- (v31) -- (v36) -- (v41) -- (v16);
\draw [blue, dotted, thick] (v17) -- (v25) -- (v30) -- (v35) -- (v40) -- (v18);
\draw [blue, dotted, thick] (v19) -- (v24) -- (v29) -- (v34) -- (v39) -- (v20);
\draw [blue, dotted, thick] (v21) -- (v23) -- (v28) -- (v33) -- (v38) -- (v22);

\node (v43) at (0.5,3.5) {};
\node (v44) at (-0.5,3.5) {};
\node (v45) at (-0.5,0.5) {};
\node (v46) at (0.5,0.5) {};
\node (v47) at (0.5,-1.5) {};
\node (v48) at (-0.5,-1.5) {};
\draw [red, dashed] (v43.center) -- (v44.center) -- (v45.center) -- (v46.center) -- (v47.center) -- (v48.center);
\end{tikzpicture}

\end{document}
\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows,positioning}

\tikzset{
    >=stealth',
    observedrect/.style={
        rectangle,
        rounded corners,
        draw=black, thick,
        minimum width=6em,
        minimum height=2em,
        font=\footnotesize,
        text centered,
        fill=black!10!white
    },
    latent/.style={
        circle,
        rounded corners,
        draw=black, thick, dashed,
        minimum width=2.2em,
        minimum height=2.2em,
        font=\footnotesize,
        text centered
    },
    pil/.style={
        ->,
        thick,
        shorten <=2pt,
        shorten >=2pt
    }
}

\begin{document}
\begin{tikzpicture}[->,shorten >=0pt,shorten <=0pt,node distance=3em,thick]
\node[observedrect](1){Treatment};
\node[observedrect, above left=of 1](2){Randomiser};
\node[observedrect, right=of 1](3){Outcome};
\node[latent, above left=of 3](4){U};
\path[]
	(2) edge (1)
	(1) edge (3)
	(4) edge (3);
\end{tikzpicture}
\end{document}
\documentclass{standalone}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{shapes,automata,positioning}

\newcommand{\nbit}[2]{{#2}_{#1}}
\newcommand{\repl}[3]{\$^{#3}_{#1, #2}}

\begin{document}
\begin{tikzpicture}[node distance=2cm,on grid,auto]
   \node[state] (q_0)   {$q_0$};
   \node[state] (q_1) [right=of q_0] {$q_1$};
   \node[state] (q_2) [right=of q_1] {$q_2$};
   \node[state] (q_3) [right=of q_2] {$q_3$};
   \path[->]
    (q_0) edge [bend left]  node [above] {$\nbit{1}{0}$} (q_1)
          edge [bend right] node [below] {$\repl{1}{1}{1}$} (q_1)
    (q_1) edge [bend left]  node [above] {$\repl{2}{0}{0}$} (q_2)
          edge [bend right] node [below] {$\nbit{2}{1}$} (q_2)
    (q_2) edge [bend left]  node [above] {$\nbit{3}{0}$} (q_3)
          edge [bend right] node [below] {$\repl{3}{1}{1}$} (q_3);
\end{tikzpicture}
\end{document}
\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\tikzset{vtx/.style={inner sep=1.7pt, outer sep=0pt, circle, fill, draw}}

\begin{document}
\begin{tikzpicture}[scale=1.0]
\draw 
(0,0) node[vtx](x){}
(1,0) node[vtx](y){}
(60:1) node[vtx](z){}
(y)--++(60:1) node[vtx](w){}--(z)
(x)--(y)--(z)--(x)
(2,0) node[vtx](xx){}
(w)--(xx);
\draw(1,-0.5) node{$H_1$};
\end{tikzpicture}
\end{document}
\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows,decorations.markings}

\begin{document}
\begin{tikzpicture}
\filldraw[fill=gray!20, line width=2pt] (-6,0) circle [radius=1.5] node {$Q,M$};
\filldraw[fill=gray!20, line width=2pt] (0,0) circle [radius=1.5] node {$Q,M'$};
\draw[dotted,line width=1pt] (0,0) circle [radius=1.7];
\draw[line width=2pt,color=gray] (0,0) circle [radius=2];
\node at (0,2.4) {$m=M-M'$};
\end{tikzpicture}
\end{document}
\documentclass[border=5pt]{standalone}
\usepackage{amssymb,amsmath}
\usepackage{tikz}
\usetikzlibrary{automata,arrows}

\begin{document}
\begin{tikzpicture}
    \node (nodo01) at (0,0) {$c_{0}$};

    \node (nodo11) at (-2,-1) {$c_{1}$};
    \node (nodo12) at (-1,-1) {$c_{2}$};
    \node (nodo13) at (0,-1) {$\ldots$};
    \node (nodo14) at (1,-1) {$c_{n-1}$};
    \node (nodo15) at (2,-1) {$c_{n}$};

    \node (nodo21) at (-3,-2) {$c_{1,1}$};
    \node (nodo22) at (-2,-2) {$c_{1,2}$};
    \node (nodo23) at (-1,-2) {$c_{2,2}$};
    \node (nodo25) at (0,-2) {...};
    \node (nodo26) at (1,-2) {$c_{n-1,k}$};
    \node (nodo27) at (2.3,-2) {$c_{n,1}$};
    \node (nodo28) at (3.3,-2) {$\ldots$};
    \node (nodo29) at (4.3,-2) {$c_{n,m}$};

    \node (nodo31) at (-3,-3) {...};
    \node (nodo32) at (-2,-3) {...};
    \node (nodo33) at (-1,-3) {...};
    \node (nodo35) at (0,-3)  {...};
    \node (nodo36) at (1,-3)  {...};
    \node (nodo37) at (2.3,-3) {...};
    \node (nodo38) at (4.3,-3) {...};

    \draw (nodo01) -- (nodo11);
    \draw (nodo01) -- (nodo12);
    \draw (nodo01) -- (nodo14);
    \draw (nodo01) -- (nodo15);

    \draw (nodo11) -- (nodo21);
    \draw (nodo12) -- (nodo22);
    \draw (nodo12) -- (nodo23);
    \draw (nodo14) -- (nodo26);
    \draw (nodo15) -- (nodo27);
    \draw (nodo15) -- (nodo29);

    \draw [dotted] (nodo21) -- (nodo31);
    \draw [dotted] (nodo22) -- (nodo32);
    \draw [dotted] (nodo23) -- (nodo33);
    \draw [dotted] (nodo26) -- (nodo36);
    \draw [dotted] (nodo27) -- (nodo37);
    \draw [dotted] (nodo29) -- (nodo38);
\end{tikzpicture}
\end{document}
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usetikzlibrary{positioning}

\begin{document}
\begin{tikzpicture}[scale=0.86]
\begin{axis}[
    axis x line=bottom,
    axis y line=left,
    xtick={0.05},
    xticklabels={0},
    ytick={-1,0},
    yticklabels={$u_{\max}$,0},
    every axis x label/.style={
        at={(ticklabel* cs:1.05)},
        anchor=west,
    },
    every axis y label/.style={
        at={(ticklabel* cs:1.05)},
        anchor=south,
    },
    domain=0.05:2.5,
    samples=100,
    xlabel=$\rho$,
    ylabel=$\alpha$,
    legend cell align=left,
    legend pos=north east
]
\addplot[smooth,thick,purple]{((3*exp(3*x)-1*exp(1*x))/(exp(3*x)-exp(1*x)))-((4*exp(4*x)+exp(-x))/(exp(4*x)-exp(-x)))};
\addplot[smooth,thick,dashed,green]{((3*exp(3*x)-1*exp(1*x))/(exp(3*x)-exp(1*x)))-((4*exp(4*x)-0.5*exp(0.5*x))/(exp(4*x)-exp(0.5*x)))};
\addplot[smooth,thick,dash dot,green]{((3*exp(3*x)+exp(-x))/(exp(3*x)-exp(-x)))-((4*exp(4*x)-1*exp(1*x))/(exp(4*x)-exp(1*x)))};
\legend{$u_0>u_{1}$ and $\underline{u}>\overline{u}$, $u_0<u_{1}$ and $\underline{u}>\overline{u}$, $u_0<u_{1}$ and $\underline{u}<\overline{u}$};
\addplot[smooth,dotted]{-1};
\addplot[smooth,dashed]{0};
\end{axis}
\end{tikzpicture}
\end{document}
\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows.meta, decorations.markings}

\tikzset{
    >=Stealth,
    mid arrow/.style={
        postaction={decorate, decoration={
            markings,
            mark=at position 0.5 with {\arrow{>}}
        }}
    }
}

\begin{document}
\begin{tikzpicture}[scale=1.6, rotate=19]
    \foreach \i/\label in {0/D_1, 1/D_2, 2/D_3, 3/D_4, 4/D_5} {
        \coordinate (D\i) at ({72*\i}:1);
        \fill (D\i) circle (0.05cm);
        \node[anchor={72*\i+180}] at (D\i) {$\label$};
    }

    \foreach \i in {0,...,4} {
        \pgfmathtruncatemacro{\next}{mod(\i+1,5)}
        \draw[->, mid arrow] (D\i) -- (D\next);
    }
\end{tikzpicture}
\end{document}
\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning, decorations.pathreplacing}

\tikzset{
    ns/.style={
        inner sep=0mm, outer sep=0mm,
        append after command={
            [very thick]
            (\tikzlastnode.north west) edge (\tikzlastnode.north east)
            (\tikzlastnode.south west) edge (\tikzlastnode.south east)
        }
    },
    wens/.style={
        inner sep=0mm, outer sep=0mm,
        append after command={
            [very thick]
            (\tikzlastnode.north west) edge (\tikzlastnode.south west)
            (\tikzlastnode.north east) edge (\tikzlastnode.south east)
            (\tikzlastnode.north west) edge (\tikzlastnode.north east)
            (\tikzlastnode.south west) edge (\tikzlastnode.south east)
        }
    },
    wns/.style={
        inner sep=0mm, outer sep=0mm,
        append after command={
            [very thick]
            (\tikzlastnode.north west) edge (\tikzlastnode.south west)
            (\tikzlastnode.north west) edge (\tikzlastnode.north east)
            (\tikzlastnode.south west) edge (\tikzlastnode.south east)
        }
    },
    ens/.style={
        inner sep=0mm, outer sep=0mm,
        append after command={
            [very thick]
            (\tikzlastnode.north east) edge (\tikzlastnode.south east)
            (\tikzlastnode.north west) edge (\tikzlastnode.north east)
            (\tikzlastnode.south west) edge (\tikzlastnode.south east)
        }
    },
    e/.style={
        inner sep=0mm, outer sep=0mm,
        append after command={
            [very thick]
            (\tikzlastnode.north east) edge (\tikzlastnode.south east)
        }
    },
    w/.style={
        inner sep=0mm, outer sep=0mm,
        append after command={
            [very thick]
            (\tikzlastnode.north west) edge (\tikzlastnode.south west)
        }
    }
}

\begin{document}
\begin{tikzpicture}[scale=0.6, every node/.style={scale=0.6}]
    \node[circle] (t0) at (0,0) {$w$};
    \node[wens, minimum height=6mm, minimum width=5mm, align=center, right=0mm of t0] (t1) {$1$};
    \node[wens, minimum height=6mm, minimum width=40mm, align=center, right=0mm of t1] (t2) {$\ldots$};
    \node[ens, minimum height=6mm, minimum width=10mm, align=center, right=0mm of t2] (t3) {$\ell'$};
    \node[ens, minimum height=6mm, minimum width=10mm, align=center, right=0mm of t3] (t4) {$\ell'+1$};
    \node[ns, minimum height=6mm, minimum width=20mm, align=center, right=0mm of t4] (t5) {$\ldots$};
    \node[wns, minimum height=6mm, minimum width=10mm, align=center, right=0mm of t5] (t6) {$\ell$};
    \node[wens, minimum height=6mm, minimum width=15mm, align=center, right=0mm of t6] (t7) {$\ldots$};

    \draw[decoration={brace,raise=5pt, amplitude=5pt},decorate] (t1.north) -- node[above=10pt, xshift=-5mm]{$(t-1)$-universal $\Rightarrow M[\ell',t-1]$} (t3.north);
    \draw[decoration={brace,raise=5pt, amplitude=5pt},decorate] (t4.north) -- node[above=10pt, xshift=5mm]{universal $\Rightarrow \sigma - \Delta(\ell'+1,\ell)$} (t6.north);
\end{tikzpicture}
\end{document}
\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing,arrows,calc}

\begin{document}
\begin{tikzpicture}[baseline=-20, scale=.4]
 \draw[thick] (1.5,-1) -- (3.5,-1);  \draw[thick] (5.6,-1) -- (9,-1); 
  \draw[fill] (1.5,-1) circle (3pt);  
 \draw[fill] (3,-1) circle (3pt);  
    \node at (4.5,-1) {$\cdots$};  
 \draw[fill] (6,-1) circle (3pt); 
 \draw[fill] (7.5,-1) circle (3pt);  
 \draw[fill] (9,-1) circle (3pt);  

 \draw[thick] (8.9,-2.1) rectangle (9.1,-1.9);
 \draw[thick] (9,-1) -- (9,-1.9);
 \node at (1.5,-.5) {$\scriptscriptstyle v_1$} ;
 \node at (3,-.5) {$\scriptscriptstyle v_2$} ;
 \node at (6,-.5) {$\scriptscriptstyle v_{n-2}\ $} ;
 \node at (7.5,-.5) {$\scriptscriptstyle v_{n-1}$} ;
 \node at (9,-.5) {$\scriptscriptstyle v_{n}$} ;
 \node at (9,-2.6) {$\scriptscriptstyle v_{n+1}$} ;
\end{tikzpicture}
\end{document}