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        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[utf8]{inputenc}\n\\usepackage{pgfplots}\n\\pgfplotsset{width=\\textwidth,height=(1/4)*\\textheight}\n\\usepackage[all,arc,curve,color,frame]{xy}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{axis}[hide axis,enlargelimits=false]\n\\addplot[const plot,fill=violet!20] coordinates\n{(0,0) (1,0) (1,1) (0,1) (0,0)}\nnode[right,pos=.5]{$Q_{i_0}$};\n\\addplot[const plot,fill=orange!20] coordinates\n{(0.5,-0.5) (1.5,-0.5) (1.5,0.5) (0.5,0.5) (0.5,-0.5)}\nnode[right,pos=.5]{$Q_{i_1}$};\n\\addplot[const plot,fill=violet!20] coordinates\n{(2,-0.5) (3,-0.5) (3,0.5) (2,0.5) (2,-0.5)}\nnode[right,pos=.5]{$Q_{i_0}$};\n\\addplot[const plot,fill=orange!20] coordinates\n{(2.5,-1) (3.5,-1) (3.5,-0.5) (2.5,-0.5) (2.5,-1)}\nnode[right,pos=.5]{$Q_{i_1}$};\n\\addplot[const plot,fill=violet!20] coordinates\n{(1,-1.5) (2,-1.5) (2,-1) (1,-1) (1,-1.5)}\nnode[right,pos=.5]{$Q_{i_0}$};\n\\addplot[const plot,fill=orange!20] coordinates\n{(1.5,-2) (2.5,-2) (2.5,-1.5) (1.5,-1.5) (1.5,-2)}\nnode[right,pos=.5]{$Q_{i_1}$};\n\\addplot[const plot,fill=violet!20] coordinates\n{(1,-2.5) (2,-2.5) (2,-2) (1,-2) (1,-2.5)}\nnode[right,pos=.5]{$Q_{i_0}$};\n\\addplot[const plot,fill=orange!20] coordinates\n{(1.5,-3) (2.5,-3) (2.5,-2.5) (1.5,-2.5) (1.5,-3)}\nnode[right,pos=.5]{$Q_{i_1}$};\n\\addplot[const plot,fill=violet!20] coordinates\n{(0,-3.5) (1,-3.5) (1,-3) (0,-3) (0,-3.5)}\nnode[right,pos=.5]{$Q_{i_0}$};\n\\addplot[const plot,fill=orange!20] coordinates\n{(0.5,-4) (1.5,-4) (1.5,-3.5) (0.5,-3.5) (0.5,-4)}\nnode[right,pos=.5]{$Q_{i_1}$};\n\\addplot[const plot,fill=violet!20] coordinates\n{(0,-4.5) (1,-4.5) (1,-4) (0,-4) (0,-4.5)}\nnode[right,pos=.5]{$Q_{i_0}$};\n\\addplot[const plot,fill=orange!20] coordinates\n{(0.5,-5) (1.5,-5) (1.5,-4.5) (0.5,-4.5) (0.5,-5)}\nnode[right,pos=.5]{$Q_{i_1}$};\n\\end{axis}\n\\draw[dashed] (-1,0) -- (4,0);\n\\node at (4.3,0) {$Q_1$};\n\\draw[dashed] (-1,-5) -- (4,-5);\n\\node at (4.3,-5) {$Q_2$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt,a4paper]{amsart}\n\\usepackage{amsfonts,amsmath,amssymb}\n\\usepackage[T1]{fontenc}\n\\usepackage{tikz}\n\\usepackage{color}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5]\n\\draw (0,0) circle (1);\n\\draw[line width=2,red,fill=red!5] (0,1) arc (90:360:1 and 0.5);\n\\draw[line width=2,red,fill=red!5] (0,-1) arc (-90:0:1 and 0.5);\n\\draw[line width=2,red,fill=red!5] (1,0) arc (0:-90:0.5 and 1);\n\\draw[line width=2,red,fill=red!5] (-1,0) arc (180:90:0.5 and 1);\n\\draw (0,1) arc (90:360:1 and 0.5);\n\\draw (0,-1) arc (-90:0:1 and 0.5);\n\\draw (1,0) arc (0:-90:0.5 and 1);\n\\draw (-1,0) arc (180:90:0.5 and 1);\n\\draw[dashed] (0,0) ellipse (0.6 and 1);\n\\draw[<->] (-1,-1.3) -- (1,-1.3);\n\\node at (0,-1.6) {$a$};\n\\draw[<->] (-1.3,-1) -- (-1.3,1);\n\\node at (-1.6,0) {$b$};\n\\draw[thick,<->] (-3,-1) -- (3,-1);\n\\node at (0,0) {\\large$R_0$};\n\\draw[thick,<->] (-3,1) -- (3,1);\n\\node at (0,1.3) {\\large$R_1$};\n\\draw[thick,<->] (-5,1) -- (-3,1);\n\\node at (-4,1) {\\large$R_2$};\n\\draw[thick,<->] (-5,0) -- (-3,0);\n\\node at (-4,0) {\\large$R_3$};\n\\draw[thick,<->] (3,1) arc (90:360:1 and 0.5);\n\\draw[thick,<->] (-1,1) arc (90:360:1 and 0.5);\n\\draw[thick,<->] (3,0) arc (90:360:1 and 0.5);\n\\draw[thick,<->] (-1,0) arc (90:360:1 and 0.5);\n\\draw[thick,<->] (3,0.5) arc (90:360:1 and 0.5);\n\\draw[thick,<->] (-1,0.5) arc (90:360:1 and 0.5);\n\\draw [thick,green,<->] (3,0.25) arc (90:270:0.25 and 0.5);\n\\draw [thick,green,<->] (3,0.75) arc (90:-90:0.25 and 0.5);\n\\draw [thick,green,<->] (-1,0.25) arc (90:270:0.25 and 0.5);\n\\draw [thick,green,<->] (-1,0.75) arc (90:-90:0.25 and 0.5);\n\\draw[thick,->] (-3,0.5) -- (-2,0.5);\n\\draw[thick,->] (-3,0.25) -- (-2,0.25);\n\\draw[thick,->] (-3,0.75) -- (-2,0.75);\n\\draw[thick,->] (-3,1.5) -- (-2,1.5);\n\\draw[thick,->] (-3,1.25) -- (-2,1.25);\n\\draw[thick,->] (-3,1.75) -- (-2,1.75);\n\\draw[thick,->] (3,0.5) -- (2,0.5);\n\\draw[thick,->] (3,0.25) -- (2,0.25);\n\\draw[thick,->] (3,0.75) -- (2,0.75);\n\\draw[thick,->] (3,1.5) -- (2,1.5);\n\\draw[thick,->] (3,1.25) -- (2,1.25);\n\\draw[thick,->] (3,1.75) -- (2,1.75);\n\\draw[thick,->] (1,1.75) arc (90:360:1 and 0.5);\n\\draw[thick,->] (-1,1.75) arc (90:360:1 and 0.5);\n\\draw[thick,->] (1,1.25) arc (90:360:1 and 0.5);\n\\draw[thick,->] (-1,1.25) arc (90:360:1 and 0.5);\n\\draw[thick,->] (1,0.75) arc (90:360:1 and 0.5);\n\\draw[thick,->] (-1,0.75) arc (90:360:1 and 0.5);\n\\draw[thick,->] (1,0.25) arc (90:360:1 and 0.5);\n\\draw[thick,->] (-1,0.25) arc (90:360:1 and 0.5);\n\\draw[thick,->] (1,0.5) arc (90:360:1 and 0.5);\n\\draw[thick,->] (-1,0.5) arc (90:360:1 and 0.5);\n\\draw[thick,->] (1,1.5) arc (90:360:1 and 0.5);\n\\draw[thick,->] (-1,1.5) arc (90:360:1 and 0.5);\n\\draw[thick,<->] (-3,1.5) -- (-3,0.5);\n\\draw[thick,<->] (-3,1.25) -- (-3,0.25);\n\\draw["
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    {
        "index": 2,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amsmath,amssymb,amscd,amsfonts,mathtools,tikz,caption,subcaption}\n\\usetikzlibrary{patterns}\n\\usepackage[linkcolor=blue,colorlinks=true,citecolor=blue]{hyperref}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.15}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usetikzlibrary{quotes,angles,arrows,calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.6]\n\\draw[very thick] (-3,4) -- (3,4);\n\\draw[very thick] (-3,-4) -- (3,-4);\n\\fill[pattern=north east lines, pattern color=red!70, draw=black] (-3,4) -- (3,4) -- (3,-4) -- (-3,-4) -- cycle;\n\\draw[thick, red!70] (-3,-4) -- (-3,4);\n\\draw[thick, red!70] (3,-4) -- (3,4);\n\\node[anchor=east] at (-3,0) {$\\Gamma_{bc,1}$};\n\\draw[thick, ->] (4,-4) -- (7,-4);\n\\draw[thick, ->] (4,-4) -- (7,-2);\n\\draw[thick, ->] (4,-4) -- (7,0);\n\\draw[thick, ->] (4,-4) -- (7,2);\n\\draw[thick, ->] (4,-4) -- (7,4);\n\\node[anchor=north west] at (7,-4) {$\\vec z$};\n\\draw[thick, ->] (4,-4) -- (4,-2);\n\\draw[thick, ->] (4,-4) -- (4,0);\n\\draw[thick, ->] (4,-4) -- (4,2);\n\\draw[thick, ->] (4,-4) -- (4,4);\n\\node[anchor=north] at (4,-4) {$\\vec d$};\n\\filldraw[fill=blue!50,draw=blue!70, opacity=0.4,thick] (4,-4) -- (4,4) -- (7,4) -- (7,-4) -- cycle;\n\\node[anchor=east] at (6.7,0) {$\\Sigma_c$};\n\\node[anchor=east] at (6.7,-2) {$\\Sigma_d$};\n\\fill[fill=blue!50,draw=blue!70, opacity=0.4,thick] (6,-2) -- (6,2) -- (7,2) -- (7,-2) -- cycle;\n\\node[anchor=west] at (7,2) {$\\mathcal{Y}$};\n\\draw[very thick] (8,0) -- (12,0);\n\\draw[very thick] (8,-4) -- (12,-4);\n\\fill[pattern=north east lines, pattern color=red!70, draw=black] (8,0) -- (12,0) -- (12,-4) -- (8,-4) -- cycle;\n\\draw[thick, red!70] (8,-4) -- (8,0);\n\\draw[thick, red!70] (12,-4) -- (12,0);\n\\node[anchor=east] at (8,0) {$\\Gamma_{ab,1}$};\n\\node[anchor=north] at (9,-2) {$\\mathcal{O}_d$};\n\\node[anchor=south] at (10,-2) {$\\mathcal{O}_c$};\n\\node[anchor=west] at (12,0) {$\\Gamma_{bc,2}$};\n\\node[anchor=north] at (10,-4) {$\\mathcal{O}_d$};\n\\node[anchor=south] at (9,-4) {$\\mathcal{O}_c$};\n\\node[anchor=south] at (9,1) {$\\mathcal{E}_1$};\n\\node[anchor=south] at (9,-1) {$\\mathcal{E}_2$};\n\\node[anchor=south] at (11,1) {$\\mathcal{E}_3$};\n\\node[anchor=south] at (11,-1) {$\\mathcal{E}_4$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 3,
        "tikz_code": "\\documentclass[preprint, 12pt, 3p, sort&compress]{elsarticle}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{calc, positioning, fit, shapes.misc, shapes.geometric, decorations.pathmorphing}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\\newcommand\\w{2}\n\t\\newcommand\\h{1.5}\n\t\\node (image1) at (0,0) {\\includegraphics[width=\\w cm]{example-image}};\n\t%\n\t\\node (image2) [right=0 of image1, xshift=0.5 cm] {\\includegraphics[width=\\w cm]{example-image}};\n\t%\n\t\\node (image3) [below=0 of image1] {\\includegraphics[width=\\h cm]{example-image}};\n\t%\n\t\\node (image4) [right=0 of image3, xshift=0.5 cm] {\\includegraphics[width=\\h cm]{example-image}};\n\t%\n\t\\newcommand{\\hsep}{1.2}\n\t\\newcommand{\\vsep}{0.5}\n\t%\n\t\\coordinate (c1) at ($(image1.north west)!0.5!(image1.south west)$);\n\t\\coordinate (c2) at ($(image2.north west)!0.5!(image2.south west)$);\n\t\\coordinate (c3) at ($(image3.north west)!0.5!(image3.south west)$);\n\t\\coordinate (c4) at ($(image4.north west)!0.5!(image4.south west)$);\n\t%\n\t\\draw [<->, thick] ($(image1.north west) + (0.05, - \\vsep)$) -- ($(image1.south west) + (0.05, \\vsep)$) node[below, yshift=- \\vsep] {$0$};\n\t\\draw [<->, thick] ($(image1.north west) + (0.05, \\vsep)$) -- ($(image2.north west) + (-\\hsep, \\vsep)$) node[below, yshift=- \\vsep] {$\\Omega$};\n\t\\draw [<->, thick] ($(image3.north west) + (0.05, \\vsep)$) -- ($(image4.north west) + (-\\hsep, \\vsep)$) node[below, yshift=- \\vsep] {$\\Omega$};\n\t%\n\t\\node[above right=0 of c1, yshift=- 0.5 cm] {Including DP};\n\t\\node[above right=0 of c2, yshift=- 0.5 cm] {Outgoing DP};\n\t\\node[above right=0 of c3, yshift=- 0.5 cm] {Including DP};\n\t\\node[above right=0 of c4, yshift=- 0.5 cm] {Outgoing DP};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 4,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.markings}\n\\usepackage{xcolor}\n\\usetikzlibrary{arrows.meta}\n\n\\begin{document}\n\n\\begin{tikzpicture}[baseline=20]\n        \\draw[decoration={markings, mark=at position 0.5 with {\\arrow{Rays}}}, postaction={decorate}] (-1,0) -- node [right] {$\\leftarrow \\beta$} (0,1);\n        \\draw[dashed,decoration={markings, mark=at position 0.5 with {\\arrow{Rays}}}, postaction={decorate}] (0,0) -- node [right] {$\\leftarrow \\beta$} (1,1);\n        \\draw[decoration={markings, mark=at position 0.5 with {\\arrow{Rays}}}, postaction={decorate}] (1,0) -- (0,1);\n        \\draw[dashed,decoration={markings, mark=at position 0.5 with {\\arrow{Rays}}}, postaction={decorate}] (-1,1) -- node [right] {$\\leftarrow \\beta$} (1,0);\n        \\foreach \\i in {0,1,2,3,4,5}\n        {\n        \\node at (-1,\\i*0.5) {$\\i$};\n        \\node at (1,\\i*0.5) {$\\i$};\n        }\n    \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 5,
        "tikz_code": "\\documentclass[a4paper,12pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,shapes, positioning, matrix, patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node (n1) [draw, ellipse]{A};\n\\node (n2) [draw, ellipse, right=of n1] {B};\n\\node (n3) [draw, ellipse, below=of n1] {C};\n\\node (n4) [draw, ellipse, right=of n3] {D};\n\\node (n5) [draw, ellipse, below=of n3] {E};\n\\node (n6) [draw, ellipse, right=of n5] {F};\n\n\\draw [latex-latex] (n1) to (n2);\n\\draw [latex-latex] (n1) to (n3);\n\\draw [latex-latex] (n2) to (n3);\n\\draw [latex-latex] (n1) to (n4);\n\\draw [latex-latex] (n2) to (n4);\n\\draw [latex-latex] (n3) to (n5);\n\\draw [latex-latex] (n4) to (n5);\n\\draw [latex-latex] (n5) to (n6);\n\n\\node (n7) [draw, ellipse, right=of n2] {A};\n\\node (n8) [draw, ellipse, right=of n7] {B};\n\\node (n9) [draw, ellipse, below=of n7] {C};\n\\node (n10) [draw, ellipse, right=of n9] {D};\n\\node (n11) [draw, ellipse, below=of n9] {E};\n\\node (n12) [draw, ellipse, right=of n11] {F};\n\n\\draw [latex-latex] (n7) to (n8);\n\\draw [latex-latex] (n7) to (n9);\n\\draw [latex-latex] (n8) to (n9);\n\\draw [latex-latex] (n7) to (n10);\n\\draw [latex-latex] (n8) to (n10);\n\\draw [latex-latex] (n9) to (n11);\n\\draw [latex-latex] (n10) to (n11);\n\\draw [latex-latex] (n11) to (n12);\n\n\\node (n13) [draw, ellipse, right=of n7] {A};\n\\node (n14) [draw, ellipse, right=of n13] {B};\n\\node (n15) [draw, ellipse, below=of n13] {C};\n\\node (n16) [draw, ellipse, right=of n15] {D};\n\\node (n17) [draw, ellipse, below=of n15] {E};\n\\node (n18) [draw, ellipse, right=of n17] {F};\n\n\\draw [latex-latex] (n13) to (n14);\n\\draw [latex-latex] (n13) to (n15);\n\\draw [latex-latex] (n14) to (n15);\n\\draw [latex-latex] (n13) to (n16);\n\\draw [latex-latex] (n14) to (n16);\n\\draw [latex-latex] (n15) to (n17);\n\\draw [latex-latex] (n16) to (n17);\n\\draw [latex-latex] (n17) to (n18);\n\n\\node (n19) [draw, ellipse, right=of n13] {A};\n\\node (n20) [draw, ellipse, right=of n19] {B};\n\\node (n21) [draw, ellipse, below=of n19] {C};\n\\node (n22) [draw, ellipse, right=of n21] {D};\n\\node (n23) [draw, ellipse, below=of n21] {E};\n\\node (n24) [draw, ellipse, right=of n23] {F};\n\n\\draw [latex-latex] (n19) to (n20);\n\\draw [latex-latex] (n19) to (n21);\n\\draw [latex-latex] (n20) to (n21);\n\\draw [latex-latex] (n19) to (n22);\n\\draw [latex-latex] (n20) to (n22);\n\\draw [latex-latex] (n21) to (n23);\n\\draw [latex-latex] (n22) to (n23);\n\\draw [latex-latex] (n23) to (n24);\n\n\\node (n25) [draw, ellipse, right=of n20] {A};\n\\node (n26) [draw, ellipse, right=of n25] {B};\n\\node (n27) [draw, ellipse, below=of n25] {C};\n\\node (n28) [draw, ellipse, right=of n27] {D};\n\\node (n29) [draw, ellipse, below=of n27] {E};\n\\node (n30) [draw, ellipse, right=of n29] {F};\n\n\\draw [latex-latex] (n25) to (n26);\n\\draw [latex-latex] (n25) to (n27);\n\\draw [latex-latex] (n26) to (n27);\n\\draw [latex-latex] (n25) to (n28);\n\\draw [latex-latex] (n26) to (n28);\n\\draw [latex-latex] (n27) to (n29);\n\\draw [latex-latex] (n28) to (n29);\n\\draw [latex-latex] (n29) to (n30);\n\n\\node (n31) [draw, ellipse, right=of n26] {A};\n\\node (n32) [draw, ellipse, right=of n31] {B};\n\\node (n33"
    },
    {
        "index": 6,
        "tikz_code": "\\documentclass[sigconf]{acmart}\n\\usepackage{color}\n\\usepackage{pgfplots,pgfplotstable}\n\\usetikzlibrary{patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\pgfplotstableread{ % Read the data into a table macro\n\tLabel   Hex   Year   Pop   Exp\n\tAgriculture  31   1997  10  18\n\tBanking    105  1997  56  140\n\tBusiness   106  1997  14  40\n\tCybersecurity  113  1997  39  13\n\tEducation   90   1997  11  36\n\tEntertainment 104  1997  19  19\n\tFinance   126  1997  17  53\n\tHealth  102  1997  34  30\n\tHospitality   104  1997  14  30\n\tLaw   102  1997  13  17\n\tMedia  109  1997  11   11\n\tNon-Health   112  1997  34  10\n\tReal Estate   109  1997  49  39\n\tRetail   107  1997  22  48\n\tSales  100   1997  23  27\n\tTravel   110  1997  31  25\n\tUndefined   111  1997  25  3\n}\\datatable\n\n\\begin{axis}[\n    ybar stacked,\n    height=6cm, width=9.5cm,\n    bar width=15pt,\n    ymin=0, ymax=25,\n    ylabel={Percentage},\n    xtick=data,\n    xtick style={draw=none},\n    xticklabels from table={\\datatable}{Label},\n    xticklabel style={rotate=30},\n    ytick pos=left,\n    axis y line*=left,\n    enlarge x limits=.2,\n    legend style={at={(0.5,1.02)}, anchor=south,legend columns=-1},\n    pattern=crosshatch,\n    pattern color=black,\n    nodes near coords,\n    every node near coord/.append style={font=\\tiny},\n]\n\n\\addplot [fill] table [x=Label, y=Hex] {\\datatable};\n\n\\legend{Complete $S$ New}\n\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
    },
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        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{pgfplots}\n\\usepackage{xcolor}\n\\pgfplotsset{compat=1.17} % Otherwise the semicircle won't draw inside the axis, for some reason\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n    \\begin{axis}[\n        xmin=-1.2,xmax=1.2,\n        ymin=-1.2,ymax=1.2,\n        grid=both,\n        axis equal image,\n        xlabel=$E_x^{J,\\phi}$,\n        ylabel=$E_y^{J,\\phi}$,\n        legend style={at={(0.05,0.75)},anchor=west},\n    ]\n        % Green\n        \\addplot[domain=-1:1,samples=201,color=green,thick]{2*x*x};\n        % Blue\n        \\addplot[domain=-1:1,samples=201,color=blue,thick]{0};\n        % Red\n        \\addplot[domain=-1:1,samples=201,color=red,thick]{2*abs(x)};\n        \n        \\draw[green,thick] (axis cs:-1,0) -- (axis cs:0,0);\n        \\draw[blue,thick] (axis cs:-1,0) -- (axis cs:0,0);\n        \\draw[red,thick] (axis cs:-1,0) -- (axis cs:0,0);\n        \n        % Only mark the top\n        \\draw[only marks,mark=o,mark options={color=red,thick}]\n            (axis cs:0,0)\n            (axis cs:0,1);\n        \n        % Red\n        \\draw[only marks,mark=*,mark options={color=red,thick}]\n            (axis cs:0.7071,0.7071)\n            (axis cs:-0.7071,0.7071);\n        \n        % Green\n        \\draw[only marks,mark=*,mark options={color=green,thick}]\n            (axis cs:0,1)\n            (axis cs:0.7071,0.7071)\n            (axis cs:0.7071,-0.7071)\n            (axis cs:-0.7071,-0.7071);\n        \n        % Blue\n        \\draw[only marks,mark=*,mark options={color=blue,thick}]\n            (axis cs:-0.7071,0.7071)\n            (axis cs:0.7071,-0.7071);\n            \n        \\addlegendimage{only marks,mark=*,color=red,thick}\n        \\addlegendentry{$\\mathcal{A}$}\n    \\end{axis}\n    \\begin{axis}[\n        xmin=-1.2,xmax=1.2,\n        ymin=-1.2,ymax=1.2,\n        grid=both,\n        axis equal image,\n        xshift=5cm,\n    ]\n        % Green\n        \\addplot[domain=-1:1,samples=201,color=green,thick]{2*x*x};\n        % Blue\n        \\addplot[domain=-1:1,samples=201,color=blue,thick]{0};\n        % Red\n        \\addplot[domain=-1:1,samples=201,color=red,thick]{2*abs(x)};\n        \n        \\draw[green,thick] (axis cs:-1,0) -- (axis cs:0,0);\n        \\draw[blue,thick] (axis cs:-1,0) -- (axis cs:0,0);\n        \\draw[red,thick] (axis cs:-1,0) -- (axis cs:0,0);\n        \n        \\draw[green,thick] (axis cs:0,1) -- (axis cs:0,0);\n        \\draw[blue,thick] (axis cs:0,1) -- (axis cs:0,0);\n        \\draw[red,thick] (axis cs:0,1) -- (axis cs:0,0);\n        \n        % Red\n        \\draw[only marks,mark=*,mark options={color=red,thick}]\n            (axis cs:0.7071,0.7071)\n            (axis cs:-0.7071,0.7071);\n            \n        \\addlegendimage{only marks,mark=*,color=red,thick}\n        \\addlegendentry{$\\mathcal{A}=\\alpha^2$}\n    \\end{axis}\n    \\begin{axis}[\n        xmin=-1.2,xmax=1.2,\n        ymin=-1.2,ymax=1.2,\n        grid=both,\n        axis equal image,\n        xshift=5cm,yshift=-5cm,\n    ]\n        % Green\n        \\addplot[domain=-1:1,samples=201,color=green,thick]{2*x*x};\n        % Blue\n        \\addplot[domain=-1:1,samples=201,color=blue,thick]{0};\n        % Red\n        \\addplot[domain=-1:1,samples=201,color=red,thick]{2*abs(x)};\n        \n        \\draw[green,thick] (axis cs:-1,0) -- (axis cs:0,0);\n        \\draw[blue,thick] (axis cs:-1,0) -- (axis cs:0,0);\n        \\draw[red,thick] (axis cs:-1,0) -- (axis cs:0,0);\n        \n        \\draw[green,thick] (axis cs:0,1) -- (axis cs:0,0);\n        \\draw[blue,thick] (axis cs:0,1) -- (axis cs:0,0);\n        \\draw[red,thick] (axis cs:0,1) -- (axis cs:0,0);\n        \n        % Red\n        \\draw[only marks,mark=*,mark options={color=red,thick}]\n            (axis cs:0.7071,-0.7071)\n            (axis cs:-0.7071,-0.7071);\n            \n        \\addlegendimage{only marks,mark=*,color=red,thick}\n        \\addlegendentry{$\\mathcal{A}=\\alpha^2$}\n    \\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[a4paper]{amsart}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=2.5]\n\\draw[->] (0,0) -- (2.2,0) node[below] {$T$};\n\\draw[->] (0,0) -- (0,1.2) node[left] {$v_{FII}$};\n\\draw [dashed] (1,0) node[below] {$\\frac{T}{2}$} -- (1,1);\n\\draw (0,1) node[left] {$1$};\n\\draw (2,0) node[below] {$T$};\n\\draw (0,1) to[out=0,in=180] (2,0);\n\\draw[red] (0,1) to[out=0,in=180] (1.5,0) node[below] {$\\tau_1$};\n\\draw[red] (1.7,0) node[below] {$\\bar{\\tau}_1$} -- (1.7,0.2);\n\\draw[red] (1.7,0) -- (2,1) node[above] {$V_FII_1\\backslash v_{FII}$, expected benefit of investing at $t$};\n\\draw[red,->] (1.7,0.15) -- (1.4,0.1);\n\\draw[red,->] (1.7,0.05) -- (1.55,0.1);\n\\draw[dashed] (1.5,0.3) node[right] {$\\bar{c}_\\star$, cost of investing at $t$} -- (1.5,0);\n\\draw[dashed] (1.5,0.3) -- (0,0.3);\n\\draw[dashed] (1.5,0) node[below] {$\\tau_1^{opt}$} -- (1.5,0.3);\n\\draw[dashed] (0,0.3) node[left] {$v_{FII}^{opt}$} -- (1.5,0.3);\n\\draw[dashed] (1.5,0.3) -- (1.5,0);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 16,
        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage{amsmath,amssymb,amscd,amsfonts,mathtools}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix}\n\\usetikzlibrary{decorations.markings,calc,shapes,decorations.pathmorphing,patterns,decorations.pathreplacing}\n\\usetikzlibrary{positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.0]\n\n\\draw[-,black!40,very thick] (-7,2) to (9,2);\n\\draw[-,black!40,very thick] (-7,0) to (9,0);\n\n\\draw[-,black!40,very thick] (-7,2) to (5.5,4);\n\\draw[-,black!40,very thick] (-7,0) to (5.5,4);\n\n\\draw[-,black!40,very thick] (-7,-2) to (9,-2);\n\\draw[-,black!40,very thick] (-7,0) to (9,-2);\n\n\\draw[-,black!40,very thick,dotted] (-7,-2) to (9,-2);\n\\draw[-,black!40,very thick,dotted] (-7,2) to (9,2);\n\n\\draw[-,black!40,very thick,dotted] (-7,0) to (9,0);\n\n\\draw[-,blue!40,thick] (1,2) to (6,-2);\n\\draw[-,blue!40,thick] (1,0) to (6,-2);\n\n\\draw[-,blue!40,thick] (1,-2) to (6,2);\n\\draw[-,blue!40,thick] (1,0) to (6,2);\n\n\\draw[-,red!40,thick] (2.5,2) to (7,-2);\n\\draw[-,red!40,thick] (2.5,0) to (7,-2);\n\n\\draw[-,red!40,thick] (2.5,-2) to (7,2);\n\\draw[-,red!40,thick] (2.5,0) to (7,2);\n\n\n\\draw[->,decorate, blue!80,very thick] (6.1,0.1) to (6.1,1.9);\n\\node at (6.4,1) {$\\hat{\\theta}_d$};\n\n\\draw[->,decorate, red!80,very thick] (7.1,0.1) to (7.1,1.9);\n\\node at (7.4,1) {$\\hat{\\theta}_d$};\n\n\\draw[->,decorate, blue!80,very thick] (6.1,-1.9) to (6.1,-0.1);\n\\node at (6.4,-1) {$\\hat{\\theta}_e$};\n\n\\draw[->,decorate, red!80,very thick] (7.1,-1.9) to (7.1,-0.1);\n\\node at (7.4,-1) {$\\hat{\\theta}_e$};\n\n\\draw[->,decorate, red!80,very thick] (-0.9,0.1) to (-0.9,1.9);\n\\node at (-1.2,1) {$\\hat{\\theta}_s$};\n\n\\draw[->,decorate, blue!80,very thick] (-0.9,-1.9) to (-0.9,-0.1);\n\\node at (-1.2,-1) {$\\hat{\\theta}_s$};\n\n\\draw[|-|,black,thick] (-2,2) to (1,2);\n\\draw[->,black,thick] (1,2) to (1,2.3);\n\\node at (0.5,2.3) {$\\hat{\\phi}$};\n\n\\draw[|-|,black,thick] (-2,0) to (1,0);\n\\draw[->,black,thick] (1,0) to (1,-0.3);\n\\node at (0.5,-0.3) {$\\hat{\\phi}$};\n\n\\draw[|-|,black,thick] (-2,-2) to (1,-2);\n\\draw[->,black,thick] (1,-2) to (1,-2.3);\n\\node at (0.5,-2.3) {$\\hat{\\phi}$};\n\n\n\\draw[-,red!40,thick] (0.5,2.5) to (9,2.5);\n\\draw[-,blue!40,thick] (0.5,-2.5) to (9,-2.5);\n\n\\draw[->,black!40,thick] (9,2.5) to (9,2.8);\n\\node at (9.5,2.8) {$\\hat{d}_d$};\n\n\\draw[->,black!40,thick] (9,-2.5) to (9,-2.8);\n\\node at (9.5,-2.8) {$\\hat{d}_e$};\n\n\\node at (-2.6,2.5) {off axis source};\n\\draw[->,black!40,thick] (-2.6,2.2) to (-2.6,1.9);\n\\node at (-2.6,1.9) {on axis source};\n\\draw[->,black!40,thick] (-2.6,2.1) to (-2.6,1.9);\n\n\\draw[->,black!40,thick] (-2.5,1.5) to (-2.5,1.2);\n\\node at (-2.5,1.3) {propagator};\n\n\\node at (-2.5,1.1) {propagator};\n\\draw[->,black!40,thick] (-2.5,1.0) to (-2.5,0.7);\n\n\\node at (-2.6,-1.3) {propagator};\n\\draw[->,black!40,thick] (-2.6,-1.5) to (-2.6,-1.2);\n\n\\draw[->,black!40,thick] (-2.6,-2.0) to (-2.6,-1.7);\n\\node at (-2.6,-1.9) {propagator};\n\n\\node at (0.5,0.5) {$\\Sigma_s^c$};\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 17,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[node distance=0.45cm,baseline=(current  bounding  box.center)]\n\\node (n1) [rectangle, draw, minimum width=3cm, minimum height=3cm,align=center] {$Z<-1$\\\\$Z<1$\\\\$Z>-1$\\\\$Z>1$};\n\\node (n1) [circle,fill=red,inner sep=1pt,above left=3mm and 3mm of n1.north west,label={[red]west:North}] {};\n\\node (n1) [circle,fill=red,inner sep=1pt,above right=3mm and 3mm of n1.north east,label={[red]east:East}] {};\n\\node (n1) [circle,fill=red,inner sep=1pt,below right=3mm and 3mm of n1.south east,label={[red]east:South}] {};\n\\node (n1) [circle,fill=red,inner sep=1pt,below left=3mm and 3mm of n1.south west,label={[red]west:West}] {};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 19,
        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usepackage{amsmath}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale = 0.66]\n\t\\draw[dashed,->] (0,0) -- (13.3,0) node[anchor=north west] {y};\n\t\\draw[dashed,->] (0,0) -- (0,13.3) node[anchor=south east] {z};\n\t\\draw[dashed,->] (0,0) -- (-3.3,-3.3) node[anchor=north east] {x};\n\t\n\t\\coordinate (a) at (0, 0);\n\t\\coordinate (b) at (3, 5);\n\t\\coordinate (c) at (8, 3);\n\t\\coordinate (d) at (5, -3);\n\t\\coordinate (e) at (6, 0);\n\t\n\t\\draw[thick] (a) -- (b);\n\t\\draw[thick] (a) -- (c);\n\t\\draw[thick] (a) -- (d);\n\t\n\t\\draw[thick, rotate around={22.5:(a)}] (a) -- (e);\n\t\\draw[thick, rotate around={22.5:(a)}] (a) -- (b);\n\t\\draw[thick, rotate around={22.5:(a)}] (a) -- (c);\n\t\\draw[thick, rotate around={22.5:(a)}] (a) -- (d);\n\t\\draw[thick, rotate around={22.5:(a)}] (e) -- (b);\n\t\\draw[thick, rotate around={22.5:(a)}] (e) -- (c);\n\t\\draw[thick, rotate around={22.5:(a)}] (e) -- (d);\n\t\n\t\\fill[gray] (a) circle (0.2);\n\t\\fill[gray] (b) circle (0.2);\n\t\\fill[gray] (c) circle (0.2);\n\t\\fill[gray] (d) circle (0.2);\n\t\\fill[gray] (e) circle (0.2);\n\t\n\t\\node[below] at (a) {$m_0$};\n\t\\node[above] at (b) {$v_x$};\n\t\\node[right] at (c) {$v_y$};\n\t\\node[below] at (d) {$\\alpha$};\n\t\\node[above] at (e) {$\\beta$};\n\t\n\t\\draw (4.2, 5.2) arc (111.11:129:2.35);\n\t\\node[right] at (4.5, 5.1) {$\\beta$};\n\t\n\t\\draw (4.5, 3) arc (141.11:174:5.5);\n\t\\node[right] at (3.9, 2.7) {$\\alpha$};\n\t\n\t\\node[right] at (3.5, 3.5) {$\\gamma$};\n\t\n\t\\draw (7.2, 3.8) arc (200:214:3.7);\n\t\\node[left] at (7.3, 3.6) {$\\alpha$};\n\t\n\t\\draw (6, 3) arc (220:227:4.2);\n\t\\node[above] at (6.1, 2.7) {$\\gamma$};\n\t\n\t\\node[right] at (5.8, 5.8) {$(x, y, z)$};\n\t\n\t\\draw[->] (5,5) -- (6,6) node[anchor=north east] {$u$};\n\t\\fill[gray] (6,6) circle (0.15);\n\t\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "index": 20,
        "tikz_code": "\\documentclass[12pt,a4paper]{amsart}\n\\usepackage{amsmath,amsthm,amsfonts,amscd,amssymb,eucal,latexsym,mathrsfs}\n\\usepackage{latexsym, amssymb, amscd, mathrsfs, graphics, graphicx, array}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\\begin{scope}[xshift=-3cm]\n\\draw[dashed] (-2,0) -- (2,0);\n\\draw[dashed] (-2,0) -- (0,2);\n\\draw[dashed] (2,0) -- (0,2);\n\n\\draw[ultra thick,color=blue] (-2,0) -- (-1,2);\n\\draw[ultra thick,color=blue] (-1,2) -- (0,2);\n\\draw[ultra thick,color=blue] (0,2) -- (1,2);\n\\draw[ultra thick,color=blue] (1,2) -- (2,0);\n\\draw[ultra thick,color=blue] (-2,0) -- (0,2);\n\\draw[ultra thick,color=blue] (0,2) -- (2,0);\n\n\\draw[ultra thick,color=blue] (-1,2) -- (1,2);\n\n\\draw[ultra thick,color=black] (-2,0) -- (1,2);\n\\draw[ultra thick,color=black] (-1,2) -- (2,0);\n\n\\draw[ultra thick,color=black] (0,2) -- (1,2);\n\\end{scope}\n\n\\begin{scope}[xshift=3cm]\n\\draw[dashed] (-2,0) -- (2,0);\n\\draw[dashed] (-2,0) -- (0,2);\n\\draw[dashed] (2,0) -- (0,2);\n\n\\draw[ultra thick,color=blue] (-2,0) -- (-1,2);\n\\draw[ultra thick,color=blue] (-1,2) -- (0,2);\n\\draw[ultra thick,color=blue] (0,2) -- (1,2);\n\\draw[ultra thick,color=blue] (1,2) -- (2,0);\n\\draw[ultra thick,color=blue] (-2,0) -- (0,2);\n\\draw[ultra thick,color=blue] (0,2) -- (2,0);\n\n\\draw[ultra thick,color=black] (-1,2) -- (1,2);\n\n\\draw[ultra thick,color=black] (-2,0) -- (1,2);\n\\draw[ultra thick,color=black] (-1,2) -- (2,0);\n\n\\draw[ultra thick,color=black] (0,2) -- (1,2);\n\\draw[ultra thick,color=black] (0,2) -- (0,3);\n\\draw[ultra thick,color=black] (0,3) -- (-1,2);\n\\draw[ultra thick,color=black] (-1,2) -- (-2,0);\n\n\\node at (0,2.3) {$u_1$};\n\\node at (0,3.3) {$u_2$};\n\n\\node at (0.4,1.5) {$x$};\n\\node at (-1.4,1.5) {$y$};\n\\end{scope}\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 21,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5][thick]\n\\draw (0,0) -- (6,0);\n\\draw (0,1) -- (6,1);\n\\draw (0,2) -- (6,2);\n\\draw (0,3) -- (6,3);\n\\draw (2,0.5) -- (2,3.5);\n\\draw (4,0.5) -- (4,3.5);\n\\draw (6,0.5) -- (6,3.5);\n\\draw(1,3.3) node {$\\alpha$};\n\\draw(1,2.3) node {$\\alpha_1$};\n\\draw(1,1.3) node {$\\alpha_2$};\n\\draw(1,0.3) node {$\\alpha_3$};\n\\draw(5,3.3) node {$\\beta$};\n\\draw(5,2.3) node {$\\beta_1$};\n\\draw(5,1.3) node {$\\beta_2$};\n\\draw(5,0.3) node {$\\beta_3$};\n\\draw(3,0.8) node {$\\mu(t_0)$};\n\\draw(3,2.8) node {$\\mu(t_1)$};\n\\draw(3,1.8) node {$\\mu(t_1)$};\n\\draw(3,3.8) node {$\\mu(t_2)$};\n\\draw(0.7,0) node {$S_0$};\n\\draw(0.7,1) node {$S_1$};\n\\draw(0.7,2) node {$S_2$};\n\\draw(0.7,3) node {$S_3$};\n\\draw(5.3,2) node {$F_0$};\n\\draw(5.3,1) node {$F_1(t_1)$};\n\\draw(5.3,0) node {$F_2(t_0)$};\n\\draw(5.3,3) node {$F_3(t_2)$};\n\\draw [red, ultra thick] (0,3) -- (2,3);\n\\draw [red, ultra thick] (2,3) -- (4,3);\n\\draw [red, ultra thick] (4,3) -- (6,3);\n\\draw [red, ultra thick] (0,2) -- (2,2);\n\\draw [red, ultra thick] (2,2) -- (4,2);\n\\draw [red, ultra thick] (4,2) -- (6,2);\n\\draw [red, ultra thick] (0,1) -- (2,1);\n\\draw [red, ultra thick] (2,1) -- (4,1);\n\\draw [red, ultra thick] (4,1) -- (6,1);\n\\draw [red, ultra thick] (0,0) -- (2,0);\n\\draw [red, ultra thick] (2,0) -- (4,0);\n\\draw [red, ultra thick] (4,0) -- (6,0);\n\\draw [<->] (6.5,2) -- (7.5,2);\n\\draw(8,2.3) node {$\\pi$};\n\\draw(10,0) -- (16,0);\n\\draw(10,1) -- (16,1);\n\\draw(10,2) -- (16,2);\n\\draw(10,3) -- (16,3);\n\\draw(12,0.5) -- (12,3.5);\n\\draw(14,0.5) -- (14,3.5);\n\\draw(16,0.5) -- (16,3.5);\n\\draw(11,0) node {$S_0$};\n\\draw(11,1) node {$S_1$};\n\\draw(11,2) node {$S_2$};\n\\draw(11,3) node {$S_3$};\n\\draw(15,0) node {$S_0$};\n\\draw(15,1) node {$S_1$};\n\\draw(15,2) node {$S_2$};\n\\draw(15,3) node {$S_3$};\n\\draw(13,0.8) node {$\\pi(t_0)$};\n\\draw(13,2.8) node {$\\pi(t_1)$};\n\\draw(13,1.8) node {$\\pi(t_1)$};\n\\draw(13,3.8) node {$\\pi(t_2)$};\n\\draw [red, ultra thick] (10,3) -- (12,3);\n\\draw [red, ultra thick] (12,3) -- (14,3);\n\\draw [red, ultra thick] (14,3) -- (16,3);\n\\draw [red, ultra thick] (10,2) -- (12,2);\n\\draw [red, ultra thick] (12,2) -- (14,2);\n\\draw [red, ultra thick] (14,2) -- (16,2);\n\\draw [red, ultra thick] (10,1) -- (12,1);\n\\draw [red, ultra thick] (12,1) -- (14,1);\n\\draw [red, ultra thick] (14,1) -- (16,1);\n\\draw [red, ultra thick] (10,0) -- (12,0);\n\\draw [red, ultra thick] (12,0) -- (14,0);\n\\draw [red, ultra thick] (14,0) -- (16,0);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 22,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,positioning,fit,shapes,decorations.pathmorphing}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.5]\n\n\\node[label=left:{$S_{i-1}$},draw=black,circle,fill=black,scale=0.5] (s1) at (-6,0) {};\n\\node[label=left:{$S_{i-1}'$},draw=black,circle,fill=black,scale=0.5] (s2) at (-2,0) {};\n\\node[label=right:{$S_{t}$},draw=black,circle,fill=black,scale=0.5] (st) at (2,0) {};\n\\node[label=right:{$S_{t+1}'$},draw=black,circle,fill=black,scale=0.5] (s3) at (6,0) {};\n\n\\node[label=above:{$Z_{i-1}$},draw=black,circle,fill=white,scale=0.5] (z1) at (-4,3) {};\n\\node[label=above:{$Z_{i}$},draw=black,circle,fill=white,scale=0.5] (z2) at (0,3) {};\n\\node[label=above:{$Z_{t}$},draw=black,circle,fill=white,scale=0.5] (z3) at (4,3) {};\n\n\\node[label=above:{$U_{i-1}$},draw=black,circle,fill=white,scale=0.5] (u1) at (-5,1) {};\n\\node[label=above:{$U_{i}$},draw=black,circle,fill=white,scale=0.5] (u2) at (-1,1) {};\n\\node[label=above:{$U_{t}$},draw=black,circle,fill=white,scale=0.5] (ut) at (1,1) {};\n\\node[label=above:{$U_{t+1}'$},draw=black,circle,fill=white,scale=0.5] (u3) at (5,1) {};\n\n\\draw[->] (s1) -- (z1);\n\\draw[->] (s1) -- (u1);\n\\draw[->] (s2) -- (z1);\n\\draw[->] (s2) -- (u1);\n\\draw[->] (s2) -- (z2);\n\\draw[->] (s2) -- (u2);\n\\draw[->] (st) -- (z2);\n\\draw[->] (st) -- (u2);\n\\draw[->] (st) -- (z3);\n\\draw[->] (st) -- (u3);\n\\draw[->] (s3) -- (z3);\n\\draw[->] (s3) -- (u3);\n\n\\draw[->] (z1) -- (u1);\n\\draw[->] (z2) -- (u2);\n\\draw[->] (z3) -- (u3);\n\n\\draw[->] (z1) to [out=-10,in=190] (s1);\n\\draw[->] (z2) to [out=-10,in=190] (s2);\n\\draw[->] (z3) to [out=10,in=200] (st);\n\n\\draw[dashed,->] (u1) to [out=-10,in=190] (s1);\n\\draw[dashed,->] (u2) to [out=-10,in=190] (s2);\n\\draw[dashed,->] (u3) to [out=10,in=200] (st);\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 23,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning,chains,fit,shapes,calc}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{arrows,positioning}\n\\usepackage{color}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n[scale=0.7,every node/.style={scale=0.7},thick,\nevery fit/.style={ellipse,draw,inner sep=-2pt,text width=2cm},\nhv path/.style={to[out=-135,in=45,looseness=4]},\nvh path/.style={to[out=135,in=-45,looseness=4]},\ngh path/.style={to[out=135,in=-45,looseness=4]},\ngv path/.style={to[out=-135,in=135,looseness=4]},\nevery fit/.style={ellipse,draw,inner sep=-2pt,text width=2cm},\n  fsnode/.style={draw,fill=white},\n  ssnode/.style={draw,fill=white},\n  every node/.style={font=\\sffamily},\n  a_node/.style={circle,draw,fill=white,minimum size=2mm,inner sep=0},\n  b_node/.style={circle,draw,fill=white,minimum size=6mm,inner sep=0},\n  shorten >= 2pt,shorten <= 2pt,auto,node distance=2cm,\n  semithick\n]\n\n\\node[a_node] (1) {$V_1$};\n\\node[a_node] (2) [right=of 1] {$V_2$};\n\\node [right=of 2] {$\\dots$};\n\\node[a_node] (3) [right=of 2] {$V_N$};\n\n\\node[b_node] (a1) [right=of 3] {$V_1$};\n\\node[b_node] (a2) [right=of a1] {$V_2$};\n\\node [right=of a2] {$\\dots$};\n\\node[b_node] (a3) [right=of a2] {$V_N$};\n\n\\begin{scope}[start chain]\n\\chainin (1);\n\\chainin (2);\n\\chainin (3);\n\\end{scope}\n\n\\begin{scope}[start chain]\n\\chainin (a1);\n\\chainin (a2);\n\\chainin (a3);\n\\end{scope}\n\n\n\\path[draw,line width=2pt,->] (1) -- (2);\n\\path[draw,line width=2pt,->] (2) -- (3);\n\n\\path[draw,line width=2pt,->] (a1) -- (a2);\n\\path[draw,line width=2pt,->] (a2) -- (a3);\n\n\\draw[gh path] (1) to (a1);\n\\draw[gh path] (2) to (a2);\n\\draw[gh path] (3) to (a3);\n\n\\draw[gv path] (1) to[bend left] (a3);\n\\draw[gv path] (2) to[bend left] (a3);\n\\draw[gv path] (3) to[bend left] (a3);\n\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 24,
        "tikz_code": "\\documentclass[12pt,a4paper]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{shapes}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{cd}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{backgrounds}\n\\usepackage{xcolor}\n\\tikzset{%\n    symbol/.style={%\n        draw=none,\n        every to/.append style={%\n            edge node={node [sloped, allow upside down, auto=false]{$#1$}}}\n    }\n}\n\\tikzset{->-/.style={decoration={\n  markings,\n  mark=at position .5 with {\\arrow{>}}},postaction={decorate}}}\n\\tikzset{mid/.style 2 args={\n        decoration={markings,\n            mark= at position #2 with {\\arrow{{#1}[scale=1.5]}} ,\n        },\n        postaction={decorate}\n    },\nmid/.default={>}{0.5}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n        \n        \\fill[black!20] (-3.5,0) rectangle (-0.5,4);\n        \\fill[black!20] (-0.5,0) rectangle (0.5,4);\n        \\fill[black!20] (0.5,0) rectangle (3.5,4);\n        \n        \\draw (-3.5,0) rectangle (3.5,4);\n        \\draw (-3.5,2) -- (3.5,2);\n        \\draw (-2.5,0) -- (-2.5,4);\n        \\draw (0,0) -- (0,4);\n        \\draw (2,0) -- (2,4);\n        \\draw (-1,0) -- (-1,4);\n        \\filldraw[black] (-2.5,2) circle (2pt);\n        \\filldraw[black] (0,1) circle (2pt);\n        \n        \\node at (0,-0.5) {Flow $\\tau_f$};\n        \n        \\fill[black!20] (5,0) rectangle (9,4);\n        \\fill[black!20] (6.5,0) rectangle (7.5,4);\n        \\fill[black!20] (8,0) rectangle (9,4);\n        \n        \\draw (5,0) rectangle (9,4);\n        \\draw (5,2) -- (9,2);\n        \\draw (6.5,0) -- (6.5,4);\n        \\draw (7.5,0) -- (7.5,4);\n        \\draw (8,0) -- (8,4);\n        \\filldraw[black] (6.5,2) circle (2pt);\n        \\filldraw[black] (7.5,1) circle (2pt);\n        \\filldraw[black] (8,2) circle (2pt);\n        \n        \\node at (8,-0.5) {Transport $\\tau_{h_n}$};\n    \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 25,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usepackage{pgfplotstable}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{intersections}\n\\usetikzlibrary{calc}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\begin{scope}\n      \\coordinate (O) at (0,0);\n      \\draw[->,>=stealth,very thick] (O) -- (4,0);\n      \\draw[->,>=stealth,very thick] (O) -- (0,4);\n      \\draw[red,very thick] (1,3) circle (0.5);\n      \\draw[red,very thick] (3,1) circle (0.5);\n      \\draw[red,very thick,dashed] (1,3) -- (0,4);\n      \\draw[red,very thick,dashed] (3,1) -- (4,0);\n      \\node at (2,-1) {(i) $B^2$ comparison};\n    \\end{scope}\n    \\begin{scope}[shift={(6,0)}]\n      \\coordinate (O) at (0,0);\n      \\draw[->,>=stealth,very thick] (O) -- (4,0);\n      \\draw[->,>=stealth,very thick] (O) -- (0,4);\n      \\draw[blue,very thick] (2,2) circle (0.5);\n      \\draw[blue,very thick] (3,1) circle (0.5);\n      \\draw[blue,very thick,dashed] (2,2) -- (4,4);\n      \\draw[blue,very thick,dashed] (3,1) -- (0,0);\n      \\node at (2,-1) {(ii) Half-plane comparison};\n    \\end{scope}\n    \\begin{scope}[shift={(12,0)}]\n      \\coordinate (O) at (0,0);\n      \\draw[->,>=stealth,very thick] (O) -- (4,0);\n      \\draw[->,>=stealth,very thick] (O) -- (0,4);\n      \\draw[very thick,dashed,red] (1,3) circle (0.5);\n      \\draw[very thick,dashed,red] (3,1) circle (0.5);\n      \\draw[very thick,dashed,blue] (1,3) -- (0,4);\n      \\draw[very thick,dashed,blue] (3,1) -- (4,0);\n      \\draw[very thick,dashed,black] (1,3) -- (3,1);\n      \\node at (2,-1) {(iii) Wedge comparison};\n    \\end{scope}\n  \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 26,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.markings}\n\\usepackage[colorlinks,linkcolor=blue,citecolor=blue,urlcolor=blue,pdfborder={0 0 0}]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\\draw (-1,-0.5) -- (1,-1) -- (3,1) -- (1,2) -- (0,1) -- (-1,2) -- (-3,0) -- (-1,-0.5);\n\\draw[red] (-1,0.5) -- (1,0);\n\\draw[red] (0,-1) -- (0,1);\n\\draw[red] (1,0) -- (1,2);\n\\draw[red] (0,1) -- (-1,2);\n\\draw[red] (-1,2) -- (-3,0);\n\\draw[red] (-3,0) -- (-1,-0.5);\n\\draw[red] (-1,-0.5) -- (1,0);\n\\draw[red] (1,0) -- (0,-1);\n\\draw[blue] (-1,0.5) -- (1,-1);\n\\draw[blue] (1,-1) -- (3,1);\n\\draw[blue] (3,1) -- (1,2);\n\\draw[blue] (1,2) -- (0,1);\n\\draw[blue] (0,1) -- (-1,2);\n\\draw[blue] (-1,2) -- (-3,0);\n\\draw[blue] (-3,0) -- (-1,-0.5);\n\\draw[blue] (-1,-0.5) -- (1,-1);\n\n\\draw[red,thick,decoration={markings, mark=at position 0.5 with {\\arrow{>}}},postaction={decorate}] (1,0) -- (0,1);\n\\draw[red,thick,decoration={markings, mark=at position 0.5 with {\\arrow{>}}},postaction={decorate}] (0,-1) -- (0,1);\n\\draw[red,thick,decoration={markings, mark=at position 0.5 with {\\arrow{>}}},postaction={decorate}] (-1,2) -- (0,1);\n\\draw[red,thick,decoration={markings, mark=at position 0.5 with {\\arrow{>}}},postaction={decorate}] (-1,-0.5) -- (0,1);\n\n\\draw[red,thick,decoration={markings, mark=at position 0.5 with {\\arrow{>}}},postaction={decorate}] (1,0) -- (-1,2);\n\\draw[red,thick,decoration={markings, mark=at position 0.5 with {\\arrow{>}}},postaction={decorate}] (1,-1) -- (-1,2);\n\\draw[red,thick,decoration={markings, mark=at position 0.5 with {\\arrow{>}}},postaction={decorate}] (0,-1) -- (-1,-0.5);\n\\draw[red,thick,decoration={markings, mark=at position 0.5 with {\\arrow{>}}},postaction={decorate}] (3,1) -- (-1,-0.5);\n\n\\filldraw (-1,-0.5) circle (0.5pt);\n\\filldraw (1,-1) circle (0.5pt);\n\\filldraw (3,1) circle (0.5pt);\n\\filldraw (1,2) circle (0.5pt);\n\\filldraw (0,1) circle (0.5pt);\n\\filldraw (-1,2) circle (0.5pt);\n\\filldraw (-3,0) circle (0.5pt);\n\\filldraw (-1,0.5) circle (0.5pt);\n\n\\node at (-1,-0.5) [below]{$\\lambda_1$};\n\\node at (1,-1) [below]{$\\lambda_3$};\n\\node at (3,1) [below]{$\\lambda_2$};\n\\node at (1,2) [above]{$\\lambda_4$};\n\\node at (0,1) [above]{$\\lambda_5$};\n\\node at (-1,2) [above]{$\\lambda_6$};\n\\node at (-3,0) [below]{$\\lambda_7$};\n\\node at (-1,0.5) [above]{$\\lambda_8$};\n\n\\node at (0,-1) [left] {$(F,\\rho)$};\n\n\\draw (4,1) -- (6,1);\n\\draw (5,-0.5) -- (6,0.5);\n\\draw (5,-0.5) -- (4,1);\n\\draw (6,0.5) -- (6,1);\n\\draw (5,0) -- (4,1);\n\\draw (5,0) -- (6,0.5);\n\\draw (5,0) -- (5,-0.5);\n\\draw (5,0) -- (5,0);\n\n\\draw[red,thick,decoration={markings, mark=at position 0.5 with {\\arrow{>}}},postaction={decorate}] (5,-0.5) -- (4,0.5);\n\\draw[red,thick,decoration={markings, mark=at position 0.5 with {\\arrow{>}}},postaction={decorate}] (5,0) -- (5,0.5);\n\\draw[red,thick,decoration={markings, mark=at position 0.5 with {\\arrow{>}}},postaction={decorate}] (5,0) -- (5,-0.5);\n\\draw[red,thick,decoration={markings, mark=at position 0.5 with {\\arrow{>}}},postaction={decorate}] (6,1) -- (6,0.5);\n\n\\filldraw (5,-0.5) circle (0.5pt);\n\\filldraw (4,1) circle (0.5pt);\n\\filldraw (6,1) circle (0.5pt);\n\\filldraw (5,0.5) circle (0.5pt);\n\\filldraw (5,0) circle (0.5pt);\n\\filldraw (6,0.5) circle (0.5pt);\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 27,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amsthm,amsfonts,amssymb,mathrsfs,amscd,amstext,amsbsy}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{arrows}\n\\tikzset{    vertex/.style={circle,draw,minimum size=1.5em},    edge/.style={->,> = latex'}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[state/.style ={circle, draw}]\n\\node[state] (A) {$q_0$};\n\\node[state] (B) [right=of A] {$q_1$};\n\\node[state] (C) [right=of B] {$q_2$};\n\\node[state] (D) [right=of C] {$q_3$};\n\\node[state] (E) [right=of D] {$q_4$};\n\\path (A) [->] edge node[below] {$b$} (B);\n\\path (B) [->] edge node [below] {$a$} (C);\n\\path (C) [->] edge node [below] {$a$} (D);\n\\path (D) [->] edge node [below] {$b$} (E);\n\\path (A) [->] [bend left =30] edge node [above] {$a$} (C);\n\\path (C) [->] [bend left =30] edge node [below] {$a$} (A);\n\\path (E) [->] [bend left =30] edge node [above] {$a$} (B);\n\\path (B) [->] [bend left =30] edge node [below] {$b$} (E);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 28,
        "tikz_code": "\\documentclass[tikz,border=2mm]{standalone}\n\\usepackage{tkz-euclide}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\tkzDefPoint(0,0){A}\n\\tkzDefPoint(8,0){B}\n\\tkzDefPoint(0.9,2.1){P}\n\\tkzDefPointWith[orthogonal](A,P)\n\\tkzGetPoint{P'}\n\\tkzDefPointWith[orthogonal](B,P)\n\\tkzGetPoint{P''}\n\\tkzDrawSegments(A,B A,P')\n\\tkzDrawPoints(P,P',P'')\n\\tkzLabelPoints(P,P',P'')\n\\tkzLabelPoints[above](A)\n\\tkzLabelPoints[above right](P')\n\\tkzLabelPoints[below](B)\n\\tkzLabelPoints[below](P)\n\\tkzLabelSegment[below left](A,P'){\\footnotesize$M$}\n\\tkzLabelSegment[below right](B,P''){\\footnotesize$J$}\n\\tkzDrawArc[color=blue,thick,start angle=10,end angle=100](P,P')\n\\tkzLabelAngle[pos=0.7](P,P',P''){\\scriptsize$\\theta$}\n\\tkzDrawArc[color=blue,thick,start angle=60,end angle=15](P',P'')\n\\tkzLabelAngle[pos=0.9](P,P',P''){\\scriptsize$\\gamma$}\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 29,
        "tikz_code": "\\documentclass[11pt, reqno]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb,latexsym}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.45]\n  \\node (0) at (5.3,8) {$0$};\n    \\node (1) at (3.5,7) {$1$};\n    \\node (2) at (6.5,4.5) {$2$};\n    \\node (3) at (7.5,1) {$3$};\n    \\node (4) at (6,-1.5) {$4$};\n    \\node (5) at (3.5,-1) {$5$};\n    \\node (6) at (1.5,-1.5) {$6$};\n    \\node (7) at (0,-2) {$7$};\n    \\node (8) at (-1.5,-1.5) {$8$};\n    \\node (9) at (3.5,0) {$9$};\n    \\node (10) at (5.3,3) {$10$};\n    \\node (11) at (10.5,3) {$11$};\n    \\node (12) at (12.5,1.5) {$12$};\n    \\node (13) at (13.5,0) {$13$};\n    \\node (14) at (14.5,1) {$14$};\n    \\node (15) at (12.5,4) {$15$};\n    \\node (16) at (11,5.5) {$16$};\n    \\node (17) at (9,6) {$17$};\n    \\node (18) at (7.5,8) {$18$};\n    \\node (19) at (0,4) {$19$};\n    \\node (20) at (-2,2) {$20$};\n    \\node (21) at (-1,1) {$21$};\n    \\node (22) at (-3,3) {$22$};\n    \\node (23) at (-4,4) {$23$};\n    \\node (24) at (-5,2) {$24$};\n    \\node (25) at (-6,1) {$25$};\n    \\node (26) at (-7,2) {$26$};\n    \\node (27) at (-8,3) {$27$};\n    \\node (28) at (-9,4) {$28$};\n    \\node (29) at (-10,5) {$29$};\n    \\node (30) at (-11,6) {$30$};\n    \\node (31) at (-12,7) {$31$};\n    \\node (32) at (-13,8) {$32$};\n  \\draw (1) -- (2);\n  \\draw (2) -- (3);\n  \\draw (2) -- (4);\n  \\draw (3) -- (4);\n  \\draw (4) -- (5);\n  \\draw (5) -- (6);\n  \\draw (5) -- (7);\n  \\draw (6) -- (7);\n  \\draw (7) -- (8);\n  \\draw (7) -- (9);\n  \\draw (9) -- (10);\n  \\draw (10) -- (11);\n  \\draw (11) -- (12);\n  \\draw (12) -- (13);\n  \\draw (13) -- (14);\n  \\draw (12) -- (15);\n  \\draw (13) -- (16);\n  \\draw (14) -- (16);\n  \\draw (15) -- (16);\n  \\draw (15) -- (17);\n  \\draw (16) -- (18);\n  \\draw (18) -- (19);\n  \\draw (19) -- (20);\n  \\draw (20) -- (21);\n  \\draw (21) -- (22);\n  \\draw (22) -- (23);\n  \\draw (23) -- (24);\n  \\draw (24) -- (25);\n  \\draw (25) -- (26);\n  \\draw (26) -- (27);\n  \\draw (27) -- (28);\n  \\draw (28) -- (29);\n  \\draw (29) -- (30);\n  \\draw (30) -- (31);\n  \\draw (31) -- (32);\n  \\draw (0) -- (1);\n  \\draw[dotted] (0) -- (9);\n  \\draw[dotted] (2) -- (19);\n  \\draw[dotted] (3) -- (24);\n  \\draw[dotted] (5) -- (20);\n  \\draw[dotted] (6) -- (21);\n  \\draw[dotted] (7) -- (22);\n  \\draw[dotted] (8) -- (23);\n  \\draw[dotted] (9) -- (28);\n  \\draw[dotted] (10) -- (29);\n  \\draw[dotted] (11) -- (30);\n  \\draw[dotted] (12) -- (31);\n  \\draw[dotted] (13) -- (32);\n  \\draw[dotted] (14) -- (32);\n  \\draw[dotted] (15) -- (32);\n  \\draw[dotted] (16) -- (32);\n  \\draw[dotted] (17) -- (32);\n  \\draw[dotted] (18) -- (32);\n  \\draw[dotted] (25) -- (26);\n  \\draw[dotted] (26) -- (27);\n  \\draw[dotted] (27) -- (28);\n  \\draw[dotted] (28) -- (29);\n  \\draw[dotted] (29) -- (30);\n  \\draw[dotted] (30) -- (31);\n  \\draw[dotted] (31) -- (32);\n  \\draw[color=blue] (1) -- (9) node[midway, left] {$1$};\n  \\draw[color=blue] (9) -- (18) node[midway, above] {$0$};\n"
    },
    {
        "index": 30,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath,amsthm,amssymb,ifthen,mathrsfs,amsfonts,bm}\n\\usepackage[framemethod=tikz]{mdframed}\n\\usepackage{pgf,tikz}\n\\usetikzlibrary{calc,math}\n\\usetikzlibrary{arrows,shapes,positioning,automata}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{shapes.geometric}\n\\usepackage{pgfplots}\n\\usetikzlibrary{intersections}\n\\pgfplotsset{compat=newest}\n\\usepgfplotslibrary{fillbetween}\n\\usetikzlibrary{patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}[declare function={sigma(\\x)=1/(1+exp(-\\x));},declare function={sigma2(\\x)=sigma(\\x)*(1-sigma(\\x));}]\n\\begin{axis}[width=.45\\textwidth,declare function={sigma3(\\x)=sigma2(\\x)*(1-sigma2(\\x));},\n     xmin=0,xmax=5,ymin=0,ymax=12,\n     ytick={0,10,50,100},yticklabels={0,10,50,100},\n     xlabel={$|\\beta|$},\n     xtick={2,4},xticklabels={2,4},\nxticklabel style={\n    shape=circle,\n    fill=white,\n    inner sep=0pt,\n    anchor=north,\n    scale=0.6\n},\n    ylabel={\\# improvement in MSE},\n    ]\n%\n    \\addplot[thick,smooth,domain=0:5,samples=20,dashed]{sigma3(x)};\n    \\addlegendentry{$\\sigma^2=1$}\n    \n    \\addplot[thick,smooth,domain=0:5,samples=20,dashdotted]{sigma2(x)};\n    \\addlegendentry{$\\sigma^2=10$}\n\n    \\addplot[thick,smooth,domain=0:5,samples=20]{sigma(x)};\n    \\addlegendentry{$\\sigma=0.1$}\n    \n    \\addplot[thick,smooth,domain=0:5,samples=20,dotted]{x};\n    \\addlegendentry{$\\sigma=1$}\n    \n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 31,
        "tikz_code": "\\documentclass[12pt,reqno,a4paper]{amsart}\n\\usepackage{amsmath,amssymb,amsthm,mathrsfs,amsfonts,dsfont}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[thick,scale=0.8]\n\t\\tikzstyle{every node}=[font=\\fontsize{11}{2.5}\\selectfont]\n\t\\tikzstyle{every path}=[very thick,scale=1.25]\n\t\n\t\\tikzstyle{every node}=[font=\\fontsize{9}{12}\\selectfont]\n\t\n\t\\fill[fill=black!5!white] (-2.5,2.25) circle (0.75);\n\t\\fill[fill=black!5!white] (-2.5,2.75) circle (0.75);\n\t\\fill[fill=black!5!white] (-2.5,3.25) circle (0.75);\n\t\\fill[fill=black!5!white] (-2.5,3.75) circle (0.75);\n\t\\fill[fill=black!5!white] (-2.5,4.25) circle (0.75);\n\t\\fill[fill=black!5!white] (-2.5,4.75) circle (0.75);\n\t\n\t\\draw (-2.5,2.25) node (01) {$q_1$};\n\t\\draw (-2.5,2.75) node (02) {$q_2$};\n\t\\draw (-2.5,3.25) node (03) {$q_3$};\n\t\\draw (-2.5,3.75) node (04) {$q_4$};\n\t\\draw (-2.5,4.25) node (05) {$q_5$};\n\t\\draw (-2.5,4.75) node (06) {$q_6$};\n\t\n\t\\draw (01) -- (02) -- (03) -- (04) -- (05) -- (06) -- (01);\n\t\\draw (05) -- (03) -- (02) -- (04) -- (06) -- (01) -- (05);\n\t\\draw (06) -- (02) -- (04) -- (01) -- (03) -- (05) -- (06);\n\t\\draw (05) -- (01) -- (03) -- (02) -- (04) -- (05);\n\t\\draw (06) -- (01) -- (03) -- (02) -- (04) -- (05) -- (06);\n\t\n\t\\draw (-0.5,-1.5) node {$\\ldots$};\n\t\\draw (-2.5,-1.5) node (11) {$q_k$};\n\t\\draw (11) -- (01);\n\t\\draw (11) -- (02);\n\t\\draw (11) -- (03);\n\t\\draw (11) -- (04);\n\t\\draw (11) -- (05);\n\t\\draw (11) -- (06);\n\t\\draw (11) -- (03) -- (04) -- (06) -- (05) -- (02) -- (04) -- (05) -- (06) -- (03) -- (05) -- (02) -- (04) -- (05) -- (06) -- (04);\n\t\\draw (11) -- (02) -- (04) -- (03) -- (05) -- (06) -- (02) -- (04) -- (05) -- (06) -- (03) -- (05) -- (02) -- (04) -- (05) -- (06) -- (04) -- (02) -- (04) -- (05) -- (06) -- (04) -- (02) -- (04) -- (05) -- (06) -- (04);\n\t\n\t\\draw (3.5,-1.5) node (21) {$\\ldots$};\n\t\\draw (5.5,-1.5) node (22) {$\\ldots$};\n\t\\draw (7.5,-1.5) node (23) {$\\ldots$};\n\t\\draw (9.5,-1.5) node (24) {$\\ldots$};\n\t\\draw (11.5,-1.5) node (25) {$\\ldots$};\n\t\\draw (13.5,-1.5) node (26) {$\\ldots$};\n\t\\draw (15.5,-1.5) node (27) {$\\ldots$};\n\t\n\t\\draw (01) -- (21);\n\t\\draw (02) -- (22);\n\t\\draw (03) -- (23);\n\t\\draw (04) -- (24);\n\t\\draw (05) -- (25);\n\t\\draw (06) -- (26);\n\t\\draw (01) -- (22) -- (25) -- (24) -- (26) -- (23) -- (21) -- (22) -- (25) -- (24) -- (26) -- (23) -- (25) -- (24) -- (26) -- (23) -- (25) -- (24) -- (26);\n\t\n\t\\draw (11) -- (21);\n\t\\draw (11) -- (22);\n\t\\draw (11) -- (23);\n\t\\draw (11) -- (24);\n\t\\draw (11) -- (25);\n\t\\draw (11) -- (26);\n\t\\draw (11) -- (21) -- (22) -- (25) -- (24) -- (26) -- (23) -- (21) -- (22) -- (25) -- (24) -- (26) -- (23) -- (25) -- (24) -- (26) -- (23) -- (25) -- (24) -- (26) -- (23) -- (25) -- (24) -- (26);\n\t\n\t\\draw (21) -- (22) -- (23) -- (24) -- (25) -- (26);\n\t\\draw (21) -- (23) -- (22) -- (24) -- (25) -- (26);\n\t\\draw (21) -- (24) -- (23) -- (25) -- (22) -- (26) -- (24) -- (25) -- (26) -- (23) -- (25) -- (22) -- (24) -- (25) -- (26) -- (23) -- (25)"
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        "index": 32,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{tikz}\n\\usepackage{tkz-euclide}\n\\usetikzlibrary{patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n            vertex/.style = {circle, draw, fill=white,\n                            inner sep = 0pt, minimum size = 11pt}]\n            \\draw[dashed,color=black] (2.5,0) circle (1.75cm);\n            \\node[vertex,blue] (v1) at (0.3,-0.4) {};\n            \\node[vertex,blue] (v2) at (1.8,-0.6) {};\n            \\node[vertex,blue] (v3) at (2.4,0.1) {};\n            \\node[vertex,red] (v4) at (0.3,0.4) {};\n            \\node[vertex,red] (v5) at (1.8,0.6) {};\n            \\node[vertex,red] (v6) at (2.4,-0.1) {};\n            \\foreach \\x in {1,...,6} {\n                \\foreach \\y in {1,...,6} {\n                    \\ifnum \\x=\\y\\relax\n                    \\draw[thick] (v\\x)--(v\\y);\n                    \\else\n                    \\draw[thick] (v\\x)--(v\\y) (v\\x)--(v\\y);\n                    \\fi\n                }\n            }\n            \\node at (2,0) {$v$};\n        \\end{tikzpicture}\n\n\\end{document}"
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        "index": 33,
        "tikz_code": "\\documentclass{llncs}\n\\usepackage[table]{xcolor}\n\\usepackage{color}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.16}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\begin{axis}[\n        width=4.5cm,\n        height=3.5cm,\n        xlabel=$t$,\n        xmin=0, xmax=60,\n        xtick={0,20,40,60},\n        ymin=0, ymax=16.0,\n        ytick={0,5,10,15},\n        ylabel={$H^{(t)}/dt$},\n        ymajorgrids=true,\n        grid style=dashed,\n        legend pos=north west,\n        legend cell align={left},\n        legend style={font=\\footnotesize},\n    ]\n    \\addplot[\n        color=black,\n        mark=o,\n        mark size=2pt,\n        ]\n        coordinates {\n(0,1.0)(10,4.5)(18,3.5)(20,1.5)(25,2.5)(30,1.0)(38,6.0)(40,3.0)(45,1.5)(50,3.5)(58,2.0)(60,1.5)\n        };\n    \\addplot[\n        color=gray,\n        mark=o,\n        mark size=2pt,\n        ]\n        coordinates {\n(0,7.5)(10,10.0)(18,9.0)(20,7.0)(25,8.0)(30,7.5)(38,12.0)(40,8.5)(45,7.0)(50,8.5)(58,7.5)(60,7.0)\n        };\n    \\addplot[\n        color=gray,\n        style=dashed,\n        ]\n        coordinates {\n(0,5.5)(10,5.5)(18,5.5)(20,5.5)(25,5.5)(30,5.5)(38,5.5)(40,5.5)(45,5.5)(50,5.5)(58,5.5)(60,5.5)\n        };\n    \\legend{$H$, $H^\\ast$, $H^{\\ast\\ast}$}\n    \\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 34,
        "tikz_code": "\\documentclass[a4paper]{article}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes}\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node at (0, 3) [ellipse, draw] {$S_1$};\n\\node at (4, 3) [ellipse, draw] {$S_2$};\n\\node at (0, 0) [ellipse, draw] {$S_3$};\n\\node at (4, 0) [ellipse, draw] {$S_4$};\n\\draw (0, 0) ellipse (2cm and 1cm);\n\\draw (4, 0) ellipse (2cm and 1cm);\n\\draw (2, 3) ellipse (3cm and 1cm);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 35,
        "tikz_code": "\\documentclass[12pt,a4paper,reqno]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[latin1]{inputenc}\n\\usepackage{graphicx,color}\n\\usepackage{tikz}\n\\usetikzlibrary{hobby}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.7]\n\\draw [<->] (0,5) node[left]{$y$}--(0,0)--(5,0) node[below]{$x$};\n\\foreach \\x in {0,0.4,0.6,0.8,1}\n\t\\draw (\\x cm,1pt)--(0.1 cm,1pt) node[anchor=north]\n        {$\\x$};\n\\foreach \\y in {0,0.4,0.6,0.8,1}\n\t\\draw (1pt,\\y cm)--(1pt,0.1 cm) node[anchor=east]\n        {$\\y$};\n\\draw[blue, thick, domain=0:0.5] plot (\\x,{\\x});\n\\draw[blue, thick, domain=0.5:1] plot (\\x,{2*\\x-1});\n\\draw[red, thick, domain=0.5:1] plot (\\x,{8*(\\x-0.5)});\n\\node at (0.5, 0.2) {$\\widehat{z}$};\n\\node at (1.4, 1.4) {$(1,1)$};\n\\node at (1.4, 0.7) {$(66.6,7)$};\n\\node at (0.7, 4.3) {$(1,1)$};\n\\draw[fill] (0.5,0.5) circle [radius=.1];\n\\draw[fill] (1,1) circle [radius=.1];\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 36,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{math}\n\\usetikzlibrary{shapes.geometric}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{arrows.meta}\n\\providecommand{\\tikzpicture}{\\comment}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=2]\n%% first triangle\n\\draw[thick] (0,0) node[below left]{$(0,0)$} -- (1,0) node[below right]{$(1,0)$} -- (0,1) node[above left]{$(0,1)$} -- cycle;\n\\draw (0.5,0.5) node[above]{$(1,\\frac{1}{2})$} -- (0,0.5) node[left]{$(f_1^2(\\Delta))$};\n\\draw (0.5,0.5) -- (0.25,0);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 37,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{amssymb, amsmath, amsthm, graphicx, amsthm}\n\\usepackage{tikz,wrapfig,booktabs}\n\\usepackage{tikz-cd}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{arrows.meta}\n\\usepackage{tikz-qtree}\n\\usetikzlibrary{arrows.meta}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\t\t\\draw[thick,fill=gray!40] (0,0) -- (0,2) -- (1,2) -- (1,1.5) -- (2,1.5) -- (2,2) -- (3,2) -- (3,1.5) -- (4,1.5) -- (4,1) -- (5,1) -- (5,0) -- cycle;\n\t\t\\draw[thick,fill=green] (0,2) -- (0,3) circle (0.1);\n\t\t\\draw[thick,fill=green] (2,2) -- (2,3) circle (0.1);\n\t\t\\draw[thick,fill=green] (3,1.5) -- (3,2.5) circle (0.1);\n\t\t\\draw[thick,fill=green] (4,1) -- (4,2) circle (0.1);\n\t\t\\draw[thick,fill=green] (5,0) -- (5,1) circle (0.1);\n\t\t\n\t\t\\draw[dotted] (0,3) -- (3,3);\n\t\t\\draw[dotted] (0,2.5) -- (2.5,2.5);\n\t\t\\draw[dotted] (2.5,1.5) -- (5,1.5);\n\t\t\\draw[dotted] (3,2.5) -- (3,3);\n\t\t\\draw[dotted] (2.5,2.5) -- (2.5,3);\n\t\t\\draw[dotted] (2,2) -- (2,2.5);\n\t\t\\draw[dotted] (2,3) -- (2,4);\n\t\t\\draw[dotted] (3,2.5) -- (3,3);\n\t\t\\draw[dotted] (3,2) -- (3,2.5);\n\t\t\\draw[dotted] (2.5,1.5) -- (2.5,2.5);\n\t\t\\draw[dotted] (2.5,2.5) -- (2.5,3);\n\t\t\\draw[dotted] (4,1) -- (4,2);\n\t\t\\draw[dotted] (4,2) -- (4,3);\n\t\t\\draw[dotted] (5,0) -- (5,1);\n\t\t\\draw[dotted] (5,1) -- (5,3);\n\t\t\n\t\t\\draw[-Latex,thick] (0,0) -- (0,3);\n\t\t\\draw[-Latex,thick] (0,0) -- (5,0);\n\t\t\\draw[-Latex,thick] (5,0) -- (5.5,0);\n\t\t\n\t\t\\draw[thick,fill=white] (2.5,1.5) circle (0.1);\n\t\t\\draw[thick,fill=white] (3,2) circle (0.1);\n\t\t\\draw[thick,fill=white] (4,1) circle (0.1);\n\t\t\\draw[thick,fill=white] (5,0) circle (0.1);\n\t\t\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 38,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amssymb,amsthm,amsmath,amsfonts,latexsym,tikz,hyperref}\n\n\\newcommand{\\al}{\\alpha}\n\n\\newcommand{\\be}{\\beta}\n\n\\newcommand{\\ga}{\\gamma}\n\n\\newcommand{\\ve}{\\varepsilon}\n\n\\newcommand{\\io}{\\iota}\n\n\\newcommand{\\ka}{\\kappa}\n\n\\newcommand{\\la}{\\lambda}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw(-.5,0) node{$P_4$};\n\\draw(1,0)--(5,0);\n\\draw(1,-.5) node{$\\al_1$};\n\\draw(3,-.5) node{$v_3$};\n\\draw(4,-.5) node{$v_4$};\n\\fill(1,0) circle(.1);\n\\fill(2,0) circle(.1);\n\\fill(3,0) circle(.1);\n\\fill(4,0) circle(.1);\n\\fill(5,0) circle(.1);\n\\draw(1,-1.5) node{$\\be_1$};\n\\draw(2,-1.5) node{$v_1$};\n\\draw(3,-1.5) node{$v_2$};\n\\draw(4,-1.5) node{$v_5$};\n\\fill(1,-1) circle(.1);\n\\fill(2,-1) circle(.1);\n\\fill(3,-1) circle(.1);\n\\fill(4,-1) circle(.1);\n\\draw(1,-2.5) node{$\\ga_1$};\n\\draw(3,-2.5) node{$v_4$};\n\\draw(4,-2.5) node{$v_5$};\n\\draw(1,-3.5) node{$\\io_1$};\n\\draw(2,-3.5) node{$v_1$};\n\\draw(3,-3.5) node{$v_3$};\n\\fill(1,-3) circle(.1);\n\\fill(2,-3) circle(.1);\n\\fill(3,-3) circle(.1);\n\\fill(4,-3) circle(.1);\n\\draw(1,-4.5) node{$\\la_1$};\n\\draw(2,-4.5) node{$v_2$};\n\\draw(3,-4.5) node{$v_3$};\n\\draw(4,-4.5) node{$v_6$};\n\\fill(1,-4) circle(.1);\n\\fill(2,-4) circle(.1);\n\\fill(3,-4) circle(.1);\n\\fill(4,-4) circle(.1);\n\\draw(1,-5.5) node{$\\ve_1$};\n\\draw(2,-5.5) node{$v_1$};\n\\draw(3,-5.5) node{$v_2$};\n\\draw(4,-5.5) node{$v_4$};\n\\fill(1,-5) circle(.1);\n\\fill(2,-5) circle(.1);\n\\fill(3,-5) circle(.1);\n\\fill(4,-5) circle(.1);\n\\draw(1,-6.5) node{$v_3$};\n\\draw(2,-6.5) node{$v_4$};\n\\draw(3,-6.5) node{$v_6$};\n\\draw(4,-6.5) node{$v_5$};\n\\fill(1,-6) circle(.1);\n\\fill(2,-6) circle(.1);\n\\fill(3,-6) circle(.1);\n\\fill(4,-6) circle(.1);\n\\draw(1,-7.5) node{$v_4$};\n\\draw(2,-7.5) node{$v_5$};\n\\draw(3,-7.5) node{$v_6$};\n\\fill(1,-7) circle(.1);\n\\fill(2,-7) circle(.1);\n\\fill(3,-7) circle(.1);\n\\fill(4,-7) circle(.1);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 39,
        "tikz_code": "\\documentclass[a4paper,11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage[colorlinks=true,citecolor=blue,linkcolor=blue,urlcolor=blue]{hyperref}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\\node (letter) {\\includegraphics[scale=0.8]{example-image}};\n\t\\node(letter) at (0, -2.9)    {(a)};\n\t\\node(letter) at (2.5, -2.9)    {(b)};\n\t\\node(letter) at (5, -2.9)    {(c)};\n\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 40,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,automata}\n\\usepackage{tikz-3dplot}\n\n\\begin{document}\n\n\\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=1cm, semithick, scale=0.9]\n\\node[draw, text width=3cm] (AT)  at (0,0)     {AT-Free};\n\\node[draw, text width=3cm] (T)  at (0,-1.5) {$T$-Free};\n\\node[draw, text width=3cm] (FD)  at (0,-4) {Free-diameter};\n\\node[draw, text width=3cm] (CH)  at (4,-2.5) {Chordal};\n\\node[draw, text width=3cm] (IF)  at (4,-5) {Interval};\n\\node[draw, text width=3cm] (PM)  at (8,-2.5) {Permutation};\n\\node[draw, text width=3cm] (MM)  at (8,-5) {Mutation};\n\\node[draw, text width=3cm] (AG)  at (4,0) {AT-free hyperbolic: \\\\ bounded diameter};\n\\node[draw, text width=3cm] (BB)  at (4,1.5) {bounded tree-length};\n\\node[draw, text width=3cm] (O)  at (8,0) {outstanding};\n\\node[draw, text width=3cm] (OC)  at (10,0) {out-circular};\n\\node[draw, text width=3cm] (E)  at (10,-1.5) {eulerian};\n\\node[draw, text width=3cm] (B)  at (14,0) {bounded tree-width};\n\\node[draw, text width=3cm] (EM)  at (10,-5) {eulerian-mutation};\n\\node[draw, text width=3cm] (OE)  at (10,-7) {eulerian-outstanding};\n\\node[draw, text width=3cm] (N)  at (14,-5) {normal};\n\\node[draw, text width=3cm] (M)  at (14,-7) {mutation};\n\\node[draw, text width=3cm] (H)  at (14,-2.5) {hyperbolic};\n\n\n\\path (AT) edge node {} (T)\n      (T) edge node {} (FD)\n      (FD) edge node {} (CH)\n      (FD) edge node {} (IF)\n      (T) edge node {} (AG)\n      (T) edge node {} (BB)\n      (T) edge node {} (PM)\n      (T) edge node {} (MM)\n      (CH) edge node {} (O)\n      (CH) edge node {} (OC)\n      (CH) edge node {} (E)\n      (IF) edge node {} (OE)\n      (PM) edge node {} (B)\n      (MM) edge node {} (M)\n      (MM) edge node {} (N)\n      (B) edge node {} (H)\n      (E) edge node {} (H);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 41,
        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath,amsthm}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usepackage{tkz-euclide}\n\\usepackage{pgfplots}\n\\usetikzlibrary{angles,quotes}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{hobby}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale = 1.5]\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.5*cos(3*\\x r))*cos(\\x r)},{(2 + 0.5*cos(3*\\x r))*sin(\\x r)});\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.75*cos(3*\\x r))*cos(\\x r)},{(2 + 0.75*cos(3*\\x r))*sin(\\x r)});\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.9*cos(3*\\x r))*cos(\\x r)},{(2 + 0.9*cos(3*\\x r))*sin(\\x r)});\n\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.5*cos(2.9*\\x r) + 0.05*sin(8*\\x r))*cos(\\x r)},{(2 + 0.5*cos(2.9*\\x r) + 0.05*sin(8*\\x r))*sin(\\x r)});\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.75*cos(2.9*\\x r) + 0.05*sin(8*\\x r))*cos(\\x r)},{(2 + 0.75*cos(2.9*\\x r) + 0.05*sin(8*\\x r))*sin(\\x r)});\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.9*cos(2.9*\\x r) + 0.05*sin(8*\\x r))*cos(\\x r)},{(2 + 0.9*cos(2.9*\\x r) + 0.05*sin(8*\\x r))*sin(\\x r)});\n\n\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.5*cos(2.7*\\x r) + 0.05*sin(6*\\x r))*cos(\\x r)},{(2 + 0.5*cos(2.7*\\x r) + 0.05*sin(6*\\x r))*sin(\\x r)});\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.75*cos(2.7*\\x r) + 0.05*sin(6*\\x r))*cos(\\x r)},{(2 + 0.75*cos(2.7*\\x r) + 0.05*sin(6*\\x r))*sin(\\x r)});\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.9*cos(2.7*\\x r) + 0.05*sin(6*\\x r))*cos(\\x r)},{(2 + 0.9*cos(2.7*\\x r) + 0.05*sin(6*\\x r))*sin(\\x r)});\n\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.5*cos(2.5*\\x r) + 0.05*sin(4*\\x r))*cos(\\x r)},{(2 + 0.5*cos(2.5*\\x r) + 0.05*sin(4*\\x r))*sin(\\x r)});\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.75*cos(2.5*\\x r) + 0.05*sin(4*\\x r))*cos(\\x r)},{(2 + 0.75*cos(2.5*\\x r) + 0.05*sin(4*\\x r))*sin(\\x r)});\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.9*cos(2.5*\\x r) + 0.05*sin(4*\\x r))*cos(\\x r)},{(2 + 0.9*cos(2.5*\\x r) + 0.05*sin(4*\\x r))*sin(\\x r)});\n\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.5*cos(2.3*\\x r) + 0.05*sin(2*\\x r))*cos(\\x r)},{(2 + 0.5*cos(2.3*\\x r) + 0.05*sin(2*\\x r))*sin(\\x r)});\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.75*cos(2.3*\\x r) + 0.05*sin(2*\\x r))*cos(\\x r)},{(2 + 0.75*cos(2.3*\\x r) + 0.05*sin(2*\\x r))*sin(\\x r)});\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.9*cos(2.3*\\x r) + 0.05*sin(2*\\x r))*cos(\\x r)},{(2 + 0.9*cos(2.3*\\x r) + 0.05*sin(2*\\x r))*sin(\\x r)});\n\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.5*cos(2*\\x r) + 0.05*sin(0*\\x r))*cos(\\x r)},{(2 + 0.5*cos(2*\\x r) + 0.05*sin(0*\\x r))*sin(\\x r)});\n\\draw[domain = 0:2*pi,samples = 300,smooth] plot ({(2 + 0.75*cos(2*\\x r) + 0.05*sin(0*\\x r))*cos(\\x r)},{(2 + 0.75*cos(2*\\x r) + 0.05*sin(0*\\x r))"
    },
    {
        "index": 42,
        "tikz_code": "\\documentclass{article}\n\\usepackage{color}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{calc}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.17}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8]\n   \\begin{axis}\n   [axis x line=center,axis y line = center, samples = 200,  \n   title = {$H_1$}, ylabel = {}, xlabel = {}, \n   xmin=-1.5, xmax=1.5, ymin=-3, ymax=3]\n   \\addplot+[mark=none, color = black, thick] {1-abs(x)};\n   \\addplot+[mark=none, color = black, thick] {-abs(x)};\n   \\end{axis}\n   \n   \\begin{axis}\n   [axis x line=center,axis y line = center, samples = 200,  \n   title = {$H_2$}, ylabel = {}, xlabel = {}, \n   xmin=-2.5, xmax=2.5, ymin=-3, ymax=3]\n   \\addplot+[mark=none, color = black, thick] {1-abs(x)};\n   \\addplot+[mark=none, color = black, thick] {-abs(x)};\n   \\end{axis}\n   \n   \\begin{axis}\n   [axis x line=center,axis y line = center, samples = 200,  \n   title = {$H_3$}, ylabel = {}, xlabel = {}, \n   xmin=-3.5, xmax=3.5, ymin=-3, ymax=3]\n   \\addplot+[mark=none, color = black, thick] {1-abs(x)};\n   \\addplot+[mark=none, color = black, thick] {-abs(x)};\n   \\end{axis}\n   \n   \\begin{axis}\n   [axis x line=center,axis y line = center, samples = 200,  \n   title = {$H_4$}, ylabel = {}, xlabel = {}, \n   xmin=-2.5, xmax=2.5, ymin=-3, ymax=3]\n   \\addplot+[mark=none, color = black, thick] {1-abs(x)};\n   \\addplot+[mark=none, color = black, thick] {-abs(x)};\n   \\end{axis}\n   \n   \\begin{axis}\n   [axis x line=center,axis y line = center, samples = 200,  \n   title = {$H_5$}, ylabel = {}, xlabel = {}, \n   xmin=-3.5, xmax=3.5, ymin=-3, ymax=3]\n   \\addplot+[mark=none, color = black, thick] {1-abs(x)};\n   \\addplot+[mark=none, color = black, thick] {-abs(x)};\n   \\end{axis}\n   \n   \\begin{axis}\n   [axis x line=center,axis y line = center, samples = 200,  \n   title = {$H_6$}, ylabel = {}, xlabel = {}, \n   xmin=-3.5, xmax=3.5, ymin=-3, ymax=3]\n   \\addplot+[mark=none, color = black, thick] {1-abs(x)};\n   \\addplot+[mark=none, color = black, thick] {-abs(x)};\n   \\end{axis}\n   \n   \\begin{axis}\n   [axis x line=center,axis y line = center, samples = 200,  \n   title = {$H_7$}, ylabel = {}, xlabel = {}, \n   xmin=-3.5, xmax=3.5, ymin=-3, ymax=3]\n   \\addplot+[mark=none, color = black, thick] {1-abs(x)};\n   \\addplot+[mark=none, color = black, thick] {-abs(x)};\n   \\end{axis}\n   \n   \\begin{axis}\n   [axis x line=center,axis y line = center, samples = 200,  \n   title = {$H_8$}, ylabel = {}, xlabel = {}, \n   xmin=-1.5, xmax=1.5, ymin=-3, ymax=3]\n   \\addplot+[mark=none, color = black, thick] {abs(x)};\n   \\addplot+[mark=none, color = black, thick] {-abs(x)};\n   \\end{axis}\n   \n   \\begin{axis}\n   [axis x line=center,axis y line = center, samples = 200,  \n   title = {$H_9$}, ylabel = {}, xlabel = {}, \n   xmin=-2.5, xmax=2.5, ymin=-3, ymax=3]\n   \\addplot+[mark=none, color = black, thick] {abs(x)};\n   \\addplot+[mark=none, color = black, thick] {-abs(x)};\n   \\end{axis}\n   \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 43,
        "tikz_code": "\\documentclass[11pt,leqno]{article}\n\\usepackage{amsmath,amsthm,amsfonts,amssymb}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.markings, arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.5, decoration={\n    markings,\n    mark=at position 0.5 with {\\arrow{>}}}\n    ] \n    \n\n\\draw[dashed, red, ultra thick] (2,-6) arc (-90:90:4cm);\n\n\\draw[fill=blue, opacity=.1] (2,-6) arc (-90:90:4cm);\n\\draw[ultra thick, blue] (2,-6) arc (-90:90:4cm);\n\n\\draw[fill=blue, opacity=.1] (2,-2) -- (2,6);\n\\draw[ultra thick, blue] (2,-2) -- (2,6);\n\n\\draw[fill=blue, opacity=.1] (6,-2) -- (6,6);\n\\draw[ultra thick, blue] (6,-2) -- (6,6);\n\n\\node[scale=.5] at (6,5) {$K_d^\\infty$};\n\n\n\\draw[thick, decorate, postaction={decoration={markings, mark=at position 0.5 with {\\arrow{>}}}, decorate}] (-2, 0) -- (10,0);\n\\draw[thick, decorate, postaction={decoration={markings, mark=at position 0.5 with {\\arrow{>}}}, decorate}] (2, -6) -- (2, 6);\n\n\\node at (-1,6) {$\\text{infl}(x)$};\n\\node at (0,5) {$x$};\n\\node at (1,6) {$\\text{infl}(x)$};\n\n\n\n\\draw[thick, dashed] (2,6) -- (2,6.5);\n\\draw[thick, dashed] (2,-6) -- (2,-6.5);\n\\node[left] at (2,6) {$x_1$};\n\\node[left] at (2,-6) {$-x_1$};\n\n\n\\draw[thick, dashed] (6,6) -- (6,6.5);\n\\draw[thick, dashed] (6,-6) -- (6,-6.5);\n\\node[right] at (6,6) {$x_2$};\n\\node[right] at (6,-6) {$-x_2$};\n\n\\node[right] at (8.5,6) {$x_1\\rightarrow(1,0)$};\n\\node[right] at (8.5,-2) {$x_2\\rightarrow(1,0)$};\n\\node[right] at (8.5,-6) {$\\sup\\{x_1,x_2\\}\\rightarrow T(1)$};\n\n\\node[below] at (3,0) {$1$};\n\\node[below] at (7,0) {$1$};\n\\node[below] at (5,0) {$2$};\n\\node[below] at (1,0) {$-1$};\n\\node[below] at (3,0) {$1$};\n\\node[below] at (5,0) {$1$};\n\\node[below] at (7,0) {$2$};\n\n\\node[left] at (2,0) {$-1$};\n\\node[left] at (2,-2) {$-2$};\n\\node[left] at (2,-4) {$-3$};\n\\node[left] at (2,-6) {$-3$};\n\n\\node[right] at (6,0) {$1$};\n\\node[right] at (6,-2) {$-1$};\n\\node[right] at (6,-4) {$-2$};\n\\node[right] at (6,-6) {$-3$};\n\n\\node[below] at (4,-6) {$\\Gamma$};\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 44,
        "tikz_code": "\\documentclass[11pt,a4paper,oneside,titlepage]{book}\n\\usepackage{fancyhdr,amsfonts,amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing, matrix,arrows,decorations.pathmorphing}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=6.5]\n\\draw (0,0) -- (1,0);\n\\draw (0,-0.01) node[below, black]{0} -- (0,0.01);\n\\draw (1,-0.01) node[below, black]{1} -- (1,0.01);\n\\draw [thick] (0.3,-0.01) node[below, black]{\\begin{scriptsize} $\\frac{2}{K}$\\end{scriptsize}}-- (0.3,0.01);\n\\draw [thick] (0.6,-0.01) node[below, black]{\\begin{scriptsize}$\\frac{3}{K}$\\end{scriptsize}}-- (0.6,0.01);\n\\draw [thick] (0.9,-0.01) node[below, black]{\\begin{scriptsize}$\\frac{K-1}{K}$\\end{scriptsize}}-- (0.9,0.01);\n\\draw [thick] (0.25,0.04) node[above, black]{\\begin{scriptsize}$\\xi_{K-1}$\\end{scriptsize}}-- (0.3,0.04);\n\\draw [thick] (0.25,0.08) node[above, black]{\\begin{scriptsize}$\\xi_{K-1}^{-1}$\\end{scriptsize}}-- (0.3,0.08);\n\\draw [thick] (0.35,0.04) node[above, black]{\\begin{scriptsize}$\\xi_{K}$\\end{scriptsize}}-- (0.4,0.04);\n\\draw [thick] (0.35,0.08) node[above, black]{\\begin{scriptsize}$\\xi_{K}^{-1}$\\end{scriptsize}}-- (0.4,0.08);\n\\draw [thick] (0.55,0.04) node[above, black]{\\begin{scriptsize}$\\xi_{K+1}$\\end{scriptsize}}-- (0.6,0.04);\n\\draw [thick] (0.55,0.08) node[above, black]{\\begin{scriptsize}$\\xi_{K+1}^{-1}$\\end{scriptsize}}-- (0.6,0.08);\n\\draw [thick] (0.75,0.04) node[above, black]{\\begin{scriptsize}$\\xi_{K+2}$\\end{scriptsize}}-- (0.8,0.04);\n\\draw [thick] (0.75,0.08) node[above, black]{\\begin{scriptsize}$\\xi_{K+2}^{-1}$\\end{scriptsize}}-- (0.8,0.08);\n\\draw [thick] (0.75,0.12) node[above, black]{\\begin{scriptsize}$\\xi_{K+2}^{-2}$\\end{scriptsize}}-- (0.8,0.12);\n\\draw [thick] (0.75,0.16) node[above, black]{\\begin{scriptsize}$\\xi_{K+2}^{-3}$\\end{scriptsize}}-- (0.8,0.16);\n\\draw [thick] (0.85,0.04) node[above, black]{\\begin{scriptsize}$\\xi_{K+3}$\\end{scriptsize}}-- (0.9,0.04);\n\\draw [thick] (0.85,0.08) node[above, black]{\\begin{scriptsize}$\\xi_{K+3}^{-1}$\\end{scriptsize}}-- (0.9,0.08);\n\\draw [thick, blue] (0.2,0.14) node[above, black]{\\begin{scriptsize}$\\Delta^{K-1}$\\end{scriptsize}}-- (0.3,0.14);\n\\draw [thick, blue] (0.6,0.14) node[above, black]{\\begin{scriptsize}$\\Delta^{K}$\\end{scriptsize}}-- (0.7,0.14);\n\\draw [thick, blue] (0.9,0.14) node[above, black]{\\begin{scriptsize}$\\Delta^{K+1}$\\end{scriptsize}}-- (0.8,0.14);\n\\draw [thick, blue] (0.5,0.18) node[above, black]{\\begin{scriptsize}$\\Delta^{K-2}$\\end{scriptsize}}-- (0.6,0.18);\n\\draw [thick, blue] (0.5,0.22) node[above, black]{\\begin{scriptsize}$\\Delta^{K-3}$\\end{scriptsize}}-- (0.6,0.22);\n\\draw [thick, blue] (0.3,0.26) node[above, black]{\\begin{scriptsize}$\\Delta^{K+4}$\\end{scriptsize}}-- (0.4,0.26);\n\\draw [thick, blue] (0.2,0.3) node[above, black]{\\begin{scriptsize}$\\Delta^{K+5}$\\end{scriptsize}}-- (0.3,0.3);\n\\draw [thick, blue] (0.7,0.3) node[above, black]{\\begin{scriptsize}$\\Delta^{K+2}$\\end{scriptsize}}-- (0.8,0.3);\n\\draw [thick, blue] (0.8,0.34) node[above, black]{\\begin{scriptsize}$\\Delta^{K+3}$\\end{scriptsize}}-- (0.9,0.34);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 45,
        "tikz_code": "\\documentclass[a4paper,11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath,amssymb,amsthm,latexsym}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture} [scale=0.2]\n\\begin{scope}\n  \\draw (-13,0) -- (0,7) -- (13,0) -- (-13,0);\n  \\draw (-13,0) -- (13,0);\n  \\draw (-11.5,-1.5) circle (1.5);\n  \\draw (11.5,-1.5) circle (1.5);\n  \\draw (-11.5,1.5) circle (1.5);\n  \\draw (11.5,1.5) circle (1.5);\n  \\draw (-13,0) node{$\\scriptstyle{\\bullet}$};\n  \\draw (13,0) node{$\\scriptstyle{\\bullet}$};\n  \\draw (0,7) node{$\\scriptstyle{\\bullet}$};\n  \\draw (-11.5,1.5) node{$\\scriptstyle{\\bullet}$};\n  \\draw (11.5,1.5) node{$\\scriptstyle{\\bullet}$};\n  \\draw (-11.5,-1.5) node{$\\scriptstyle{\\bullet}$};\n  \\draw (11.5,-1.5) node{$\\scriptstyle{\\bullet}$};\n \\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 46,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amsmath,amsthm,amssymb, amscd,color}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usetikzlibrary{snakes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.8]\n\\draw[thick, dashed, color=blue] (-1.1,-.8) to [out=-60, in=180] (-.4,1.3) to [out=0, in=90] (1.5,0) to [out=-90, in=0] (-.3,-1.3) to [out=180, in=60] (-1.1,-.8);\n\\node[below] at (-1.1,-.8) {$x_t$};\n\\draw[thick, dashed] (0,0) -- (-1,1);\n\\draw[thick, dashed] (0,0) -- (1,-.5);\n\\draw[fill] (0,0) circle [radius=0.08];\n\\node[above] at (0,0) {$a_t$};\n\\node[left] at (-1,1) {$a_t^\\alpha$};\n\\node[right] at (1,-.5) {$a_t^\\beta$};\n\\draw[fill] (-1,1) circle [radius=0.08];\n\\draw[fill] (1,-.5) circle [radius=0.08];\n\\draw[thick, dashed, color=red] (-1,1) to [out=40,in=160] (0,2.5) to [out=-20, in=110] (1,-.5);\n\\draw[thick, dashed, color=red] (-1,1) to [out=-40, in=-160] (0,-2.5) to [out=20, in=-110] (1,-.5);\n\\node[left] at (-2.5,0) {$x_{t^*}$};\n\\node[right] at (2.5,0) {$\\frac{a_t}{x_t - x_{t^*}} = \\mathcal{F}_t(a_t) / \\left|x_t - x_{t^*}\\right|$};\n\\node[left] at (-1.2,1) {$L_t$};\n\\node[right] at (0,-2.5) {$L_{t^*}$};\n\\node[right] at (0,2.5) {$\\mathcal{F}_t(a_t)$};\n\\node[left] at (-1,1.5) {$\\alpha_t=\\mathcal{F}_t(a_t) / \\left|x_t - x_{t^*}\\right|$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 47,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes.misc}\n\\usetikzlibrary{shapes.symbols}\n\\usetikzlibrary{snakes}\n\\usetikzlibrary{decorations}\n\\tikzset{\n\tdot/.style={circle,fill=black,inner sep=0pt, minimum size=1mm},\n\tgraydot/.style={circle,draw=gray,inner sep=0pt, minimum size=1mm},\n\tloopnode/.style={circle,draw=black,inner sep=0pt, minimum size=1.5mm},\n\ttreenode/.style={circle,fill=black,inner sep=0pt, minimum size=1.5mm},\n\tcharge/.style={circle,draw=black,inner sep=0pt, minimum size=3mm},\n\t%\n\tloopline/.style={->,semithick,shorten >=1pt,shorten <=1pt},\n\ttreeline/.style={semithick, densely dashed, shorten >=1pt,shorten <=1pt},\n\t%\n\thomoge/.style={font=\\scriptsize,draw=black,fill=white,inner sep=2pt},\n\thomo/.style={font=\\scriptsize},\n\tKK/.style={thick,shorten >=1pt,shorten <=1pt, densely dashed, >=latex},\n\t%% KK is used for K(x-y) if without arrow, or K(x-y)-K(x) if with arrow\nkerAlg/.style={thick},\nkerAlg2/.style={semithick,dashed},\nkerP/.style={very thick},\narrow/.style={->,thick,shorten >=3pt,shorten <=3pt},\nrenorm/.style={ultra thick},\n\tkernel/.style={semithick,shorten >=1pt,shorten <=1pt},\n\t}\n\n\\begin{document}\n\n\\begin{tikzpicture}[baseline=0]\n\\node at (-2.3,-.8) {(a)};\n\\node at (-0.3,-.8) {(b)};\n\\node at (1.8,-.8) {(c)};\n\\node at (4.8,-.8) {(d)};\n\\node at (2.3,-.8) {(e)};\n\\node at (-2.3,-2.7) {(a)};\n\\node at (-0.3,-2.7) {(b)};\n\\node at (1.8,-2.7) {(c)};\n\\node at (4.8,-2.7) {(d)};\n\\node at (2.3,-2.7) {(e)};\n%\n\\draw [KK, dashdotted] (-1,0) to (-1,-1) {};\n\\draw [KK] (-1,-1) to (-1,-2) {};\n\\draw [KK, dashdotted] (-1,-2) to (-1,-3) {};\n%\n\\draw [KK] (-1,-3) to (-1,-4) {};\n\\draw [KK] (-1,-4) to (-1,-5) {};\n\\draw [KK, dashdotted] (-1,-5) to (-1,-6) {};\n%\n\\draw [KK] (-1,-4) to (-1.5,-4.5) {};\n\\draw [KK, dashdotted] (-1.5,-4.5) to (-1.5,-5.5) {};\n\\draw [KK] (-1,-5) to (-1.5,-5.5) {};\n%\n\\draw [KK] (-1,-6) to (-1.5,-6.5) {};\n\\draw [KK, dashdotted] (-1.5,-6.5) to (-1.5,-7.5) {};\n\\draw [KK] (-1,-6) to (-1.5,-7.5) {};\n%\n\\draw [KK] (1.5,-6.5) to (1.5,-4.5) {};\n\\draw [KK, dashdotted] (1.5,-4.5) to (1.5,-2.5) {};\n\\draw [KK] (1.5,-2.5) to (1.5,-1.5) {};\n%\n\\draw [KK] (1.5,-1.5) to (1.5,-.5) {};\n\\draw [KK] (1.5,-.5) to (1.5,.5) {};\n\\draw [KK, dashdotted] (1.5,.5) to (1.5,1.5) {};\n%\n\\draw [KK] (1.5,1.5) to (1,2) {};\n\\draw [KK] (1.5,.5) to (1,0) {};\n\\draw [KK] (1.5,-.5) to (1,0) {};\n\\draw [KK, dashdotted] (1,-.5) to (1,-1.5) {};\n%\n\\draw [KK] (1,-1.5) to (1,-2) {};\n\\draw [KK, dashdotted] (1,-2) to (1,-3) {};\n%\n\\node at (-1.6,-4) {$P_1$};\n\\node at (1.6,-4) {$P_2$};\n\\node at (0,0) {$F_1$};\n\\node at (0,-1) {$F_2$};\n\\node at (0,-2) {$F_3$};\n\\node at (0,-3) {$F_4$};\n\\node at (0,-5) {$P_1$};\n\\node at (0,-6) {$P_2$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 48,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=3cm,\n  thick,main node/.style={circle,fill=blue!20,draw,font=\\sffamily\\Large\\bfseries}]\n\n  \\node[main node] (1) {00};\n  \\node[main node] (2) [right of=1] {01};\n  \\node[main node] (3) [right of=2] {11};\n  \\node[main node] (4) [right of=3] {10};\n  \\node[main node,fill=cyan!40] (5) [below of=1] {02};\n  \\node[main node,fill=cyan!40] (6) [below of=2] {12};\n  \\node[main node,fill=cyan!40] (7) [below of=3] {10};\n  \\node[main node,fill=cyan!40] (8) [below of=4] {01};\n\n  \\path[every node/.style={font=\\sffamily\\small}]\n    (1) edge node [right] {} (6)\n        edge node [right] {} (7)\n        edge node [right] {} (8)\n    (2) edge node [right] {} (5)\n        edge node [right] {} (8)\n        edge node [right] {} (7)\n    (3) edge node [right] {} (4)\n        edge node [right] {} (6)\n        edge node [right] {} (5)\n    (4) edge node [right] {} (3);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 49,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsthm,amsmath,amssymb}\n\\usepackage[usenames,dvipsnames,svgnames,table]{xcolor}\n\\usepackage[colorlinks=true,\n            linkcolor=blue,\n            urlcolor=blue,\n            citecolor=blue]{hyperref}\n\\usepackage[utf8]{inputenc}\n\\usepackage[usenames,dvipsnames]{xcolor}\n\\usepackage{tkz-berge,fullpage}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.3]\n\\SetVertexNormal[Shape      = circle,\n                  FillColor  = cyan!50,\n                  MinSize = 11pt,\n                  InnerSep=0pt,\n                  LineWidth = .5pt]\n   \\SetVertexNoLabel\n   \\tikzset{EdgeStyle/.style= {thin,\n                                double          = red!50,\n                                double distance = 1pt}}\n                                                                \\begin{scope}[rotate=90]\\grEmptyCycle[prefix=a,RA=2.5]{8}{1}\\end{scope}\n                                                                \\begin{scope}[rotate=90]\\grEmptyCycle[prefix=b,RA=2.5]{8}{1}\\end{scope}\n                                                                \\Edge(a0)(a1)\n                                                                \\Edge(a0)(a4)\n                                                                \\Edge(a1)(a2)\n                                                                \\Edge(a1)(a5)\n                                                                \\Edge(a2)(a3)\n                                                                \\Edge(a2)(a6)\n                                                                \\Edge(a3)(a7)\n                                                                \\Edge(a4)(a5)\n                                                                \\Edge(a4)(a7)\n                                                                \\Edge(a5)(a6)\n                                                                \\Edge(a6)(a7)\n                                                                                                                                     \\tikzset{LabelStyle/.style = {right, fill = white, text = black, fill opacity=0, text opacity = 1}}\n                                                                                                                                 \\tikzset{EdgeStyle/.append style = {thin, bend left}}\n\\Edge[label=$0$](a3)(a0)\n\\Edge[label=$0$](a6)(a1)\n\\Edge[label=$0$](a7)(a2)\n\\tikzset{EdgeStyle/.append style = {thin, bend right}}\n\\Edge[label=$0$](a0)(a7)\n\\Edge[label=$0$](a1)(a6)\n\\Edge[label=$0$](a2)(a5)\n                                                                                                                                 \\tikzset{EdgeStyle/.append style = {thin, bend right, looseness=1.7}}\n\\Edge[label=$0$](a1)(a5)\n\\Edge[label=$0$](a2)(a4)\n\\Edge[label=$0$](a3)(a1)\n\\Edge[label=$0$](a4)(a2)\n\\Edge[label=$0$](a5)(a3)\n\\Edge[label=$0$](a6)(a0)\n\\Edge[label=$0$](a7)(a5)\n\\tikzset{EdgeStyle/.append style = {thin, bend right, looseness=1.7}}\n\\Edge[label=$0$](a6)(a0)\n\\Edge[label=$0$](a7)(a4)\n\\Edge[label=$0$](a0)(a6)\n\\Edge[label=$0$](a1)(a7)\n\\Edge[label=$0$](a2)(a4)\n\\Edge[label=$0$](a3)(a0)\n\\Edge[label=$0$](a4)(a1)\n\\tikzset{EdgeStyle/.append style = {thin, bend right}}\n\\Edge[label=$0$](a0)(a2)\n\\Edge[label=$0$](a1)(a5)\n\\Edge[label=$0$](a2)(a3)\n\\Edge[label=$0$](a3)(a4)\n\\Edge[label=$0$](a4)(a5)\n\\Edge[label=$0$](a5)(a6)\n\\Edge[label=$0$](a6)(a7)\n\\tikzset{EdgeStyle/.append style = {thin, bend left}}\n\\Edge[label=$0$](a0)(a3)\n\\Edge[label=$0$](a1)(a4)\n\\Edge[label=$0$](a2)(a5)\n\\Edge[label=$0$](a3)(a2)\n\\Edge[label=$0$](a4)(a3)\n\\Edge[label=$0$](a5)(a4)\n\\Edge[label=$0$](a6)(a5)\n\\Edge[label=$0$](a7)(a6)\n\\tikzset{EdgeStyle/.append style = {thin, bend left, looseness=1.7}}\n\\Edge[label=$0$](a0)(a4)\n\\Edge[label=$0$](a1)(a5)\n\\Edge[label=$0$](a2)(a6)\n\\Edge[label=$0$](a3)(a1)\n\\Edge[label=$0$](a4)(a2)\n\\Edge[label=$0$](a5)(a3)\n\\Edge[label=$0$](a6)(a0)\n\\Edge[label=$0$](a7)(a1)\n\\tikzset{EdgeStyle/.append style = {thin, bend left}}\n\\Edge[label=$0$](a0)(a5)\n\\Edge[label=$0$](a1)(a4)\n\\Edge[label=$0$](a2)(a7)\n\\Edge[label=$0$](a3)(a0)\n\\Edge[label=$0$](a4)(a1)\n\\Edge[label=$0$](a5)(a2)\n\\Edge[label=$0$](a6)(a3)\n\\Edge[label=$0$](a7)(a0)\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 50,
        "tikz_code": "\\documentclass[reqno]{amsart}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes, cd}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n[scale=0.6]\n\\foreach \\x in {1,2,3,4} {\\foreach \\y in {1,2} {\\node at (\\x,\\y) [fill,circle,inner sep=1pt] {};};};\n\\draw (1,1)--(2,1)--(3,2)--(4,2);\n\\draw (1,2)--(2,2)--(3,1)--(4,1);\n\\draw (1,2) to [out=30, in=150] (2,2);\n\\draw (2,2) to [out=30, in=150] (3,2);\n\\draw (3,1)--(4,2);\n\\draw (3,2)--(4,1);\n\\draw [ultra thick, red] (1,2)--(2,2);\n\\draw [ultra thick, red] (1,1)--(2,2);\n\\draw [ultra thick, red] (2,2)--(3,1);\n\\draw [ultra thick, red] (2,1)--(3,2);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 51,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amssymb,graphicx}\n\\usepackage{graphicx,color,float,caption}\n\\usepackage{color}\n\\usepackage{amsmath,amssymb,graphicx}\n\\usepackage{pgfplots}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n  \\begin{axis}[\n    axis lines = left,\n    xlabel = $x$,\n    ylabel = {$f(x)$},\n  ]\n    \\addplot [\n\tdomain=-2:2, \n\tsamples=100, \n\tcolor=black,\n    ]\n\t{x^3};\n\t\\addplot [\n\tdomain=-2:2, \n\tsamples=100, \n\tcolor=lightgray,\n\t]\n\t{x^3-x^2};\n\t\\addplot [\n\tdomain=-2:2, \n\tsamples=100, \n\tcolor=lightgray,\n\t]\n\t{-1.5*x};\n  \\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 52,
        "tikz_code": "\\documentclass[12pt,a4paper,reqno]{amsart}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5]\n\n%region\n\n%strands\n\\foreach \\x in {-2,...,0}{\n  \\foreach \\y in {-1,...,2}{\n    \\draw[-stealth, shorten >=0.125cm, shorten <=0.125cm] (\\x,\\y) -- ++(-0.5,0.5);\n    \\draw[-stealth, shorten >=0.125cm, shorten <=0.125cm] (\\x,\\y) -- ++(-0.5,-0.5);\n    \\draw[-stealth, shorten >=0.125cm, shorten <=0.125cm] (\\x+1,\\y+0.5) -- ++(0.5,-0.5);\n    \\draw[-stealth, shorten >=0.125cm, shorten <=0.125cm] (\\x+1,\\y+0.5) -- ++(0.5,0.5);\n  }\n}\n\n%first type\n\\foreach \\x in {-2,...,0}{\n  \\foreach \\y in {-1,...,2}{\n    \\filldraw[fill=white] (\\x,\\y) circle (1.25pt);\n  }\n}\n\n%second type\n\\foreach \\x in {-2,...,0}{\n  \\foreach \\y in {-1,...,2}{\n    \\draw (\\x,\\y) -- ++(-0.5,0.5);\n    \\draw (\\x+1,\\y+0.5) -- ++(0.5,-0.5);\n  }\n}\n\n%third type\n\\foreach \\x in {-2,...,0}{\n  \\foreach \\y in {-1,...,2}{\n    \\filldraw[fill=white] (\\x+1,\\y+0.5) circle (1.25pt);\n  }\n}\n\n%fourth type\n\\foreach \\x in {-2,...,0}{\n  \\foreach \\y in {-1,...,2}{\n    \\draw (\\x+1,\\y+0.5) -- ++(0.5,0.5);\n    \\draw (\\x,\\y) -- ++(-0.5,-0.5);\n  }\n}\n\n%fifth type\n\\foreach \\x in {-2,...,0}{\n  \\foreach \\y in {-1,...,2}{\n    \\filldraw[fill=white] (\\x,\\y) circle (1.25pt);\n  }\n}\n\n%sixth type\n\\foreach \\x in {-2,...,0}{\n  \\foreach \\y in {-1,...,2}{\n    \\draw (\\x,\\y) -- ++(-0.5,0.5);\n    \\draw (\\x+1,\\y+0.5) -- ++(0.5,-0.5);\n  }\n}\n\n%labels\n\\foreach \\x in {-2,...,0}{\n  \\foreach \\y in {-1,...,2}{\n    \\node[scale=1.75] at (\\x+0.5,\\y+0.5) {$1$};\n  }\n}\n\\foreach \\x in {-2,...,0}{\n  \\foreach \\y in {-1,...,2}{\n    \\node[scale=1.75] at (\\x+1.5,\\y+0.5) {$6$};\n  }\n}\n\n%2-hop\n\\foreach \\x in {-3,...,3}{\n  \\foreach \\y in {-1,...,2}{\n    \\draw[-stealth, shorten >=0.125cm, shorten <=0.125cm] (\\x,\\y) -- ++(-0.5,0);\n  }\n}\n\\foreach \\x in {-3,...,3}{\n  \\foreach \\y in {-1,...,2}{\n    \\draw[-stealth, shorten >=0.125cm, shorten <=0.125cm] (\\x+1,\\y+0.5) -- ++(0.5,0);\n  }\n}\n\n%arrow\n\\foreach \\x in {-3,...,3}{\n  \\draw[shorten >=0.125cm, shorten <=0.125cm] (\\x+1,\\x+0.5) -- ++(0.5,0.5);\n  \\draw[shorten >=0.125cm, shorten <=0.125cm] (\\x+2,\\x+1) -- ++(-0.5,0);\n  \\draw[shorten >=0.125cm, shorten <=0.125cm] (\\x+1,\\x+1) -- ++(-0.5,0);\n}\n\n%labels\n\\foreach \\x in {-2,...,0}{\n  \\foreach \\y in {-1,...,2}{\n    \\node[scale=1.75] at (\\x+1.5,\\y+0.5) {$0$};\n  }\n}\n\\foreach \\x in {-3,...,3}{\n  \\foreach \\y in {-1,...,2}{\n    \\node[scale=1.75] at (\\x+1.5,\\y+0.5) {$\\x$};\n  }\n}\n\\foreach \\x in {-3,...,3}{\n  \\foreach \\y in {-1,...,2}{\n    \\node[scale=1.75] at (\\x+2.5,\\y+0.5) {$0$};\n  }\n}\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 53,
        "tikz_code": "\\documentclass[a4paper,10pt,twocolumn]{article}\n\\usepackage{amsfonts,amssymb,amsmath}\n\\usepackage{xcolor}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=newest}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usepackage{tikzscale}\n\\usetikzlibrary{shapes.geometric,calc}\n\\usetikzlibrary{shapes,arrows,shapes.arrows,decorations.markings}\n\\usetikzlibrary{shapes.geometric,positioning,calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n            \\node[inner sep=0pt,anchor=south east] (russell) at (0,0)\n                {\\includegraphics[width=0.95\\textwidth]{example-image}};\n            \\node[draw=blue,very thick,\n            fill=white,\n            rounded corners=2pt,\n            rectangle, \n            minimum height=2em, \n            minimum width=3.5cm, \n            right=0.05cm of russell,\n            anchor=north] (russell_rect) {evanescent};\n            \\node[draw=blue,very thick,\n            fill=white,\n            rounded corners=2pt,\n            rectangle, \n            minimum height=2em, \n            minimum width=3.5cm, \n            right=0.05cm of russell,\n            anchor=north] (russell_rect) {evanescent};\n            \\node[draw=blue,very thick,\n            fill=white,\n            rounded corners=2pt,\n            rectangle, \n            minimum height=2em, \n            minimum width=3.5cm, \n            below=0.15cm of russell,\n            anchor=north] (russell_rect) {water};\n            \\node[draw=blue,very thick,\n            fill=white,\n            rounded corners=2pt,\n            rectangle, \n            minimum height=2em, \n            minimum width=3.5cm, \n            below right=0.05cm and -0.05cm of russell,\n            anchor=north] (russell_rect) {water};\n            \\node[draw=blue,very thick,\n            fill=white,\n            rounded corners=2pt,\n            rectangle, \n            minimum height=2em, \n            minimum width=3.5cm, \n            right=0.05cm of russell,\n            anchor=north] (russell_rect) {water};\n            \\node[draw=blue,very thick,\n            fill=white,\n            rounded corners=2pt,\n            rectangle, \n            minimum height=2em, \n            minimum width=3.5cm, \n            above=0.05cm of russell,\n            anchor=north] (russell_rect) {human contact network};\n            \\node[draw=blue,very thick,\n            fill=white,\n            rounded corners=2pt,\n            rectangle, \n            minimum height=2em, \n            minimum width=3.5cm, \n            below=0.05cm of russell,\n            anchor=north] (russell_rect) {human};\n            \\node[draw=blue,very thick,\n            fill=white,\n            rounded corners=2pt,\n            rectangle, \n            minimum height=2em, \n            minimum width=3.5cm, \n            below right=0.05cm and -0.05cm of russell,\n            anchor=north] (russell_rect) {air};\n    \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 54,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage{pgflibraryshapes}\n\\usepackage{pgflibrarysnakes}\n\\usetikzlibrary{snakes}\n\\usetikzlibrary{patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}[level distance=4mm]\\scriptsize\n\\draw (1,10) node[draw, rectangle, rounded corners,scale=0.8](f){ Sensor };\n\\draw (4.5,10) node[draw, rectangle, rounded corners,scale=0.8](g){ Observer };\n\\draw (2.2,9.2) node(c1){};\n\\draw (2.4,10.8) node(c2){};\n\\draw (2,9.2) node[fill=black,circle,minimum size=0.1cm, inner sep=0.2mm, draw](cp1){};\n\\draw (2,10.8) node[fill=black,circle,minimum size=0.1cm, inner sep=0.2mm, draw](cp2){};\n\\draw (3,9.2) node[fill=black,circle,minimum size=0.1cm, inner sep=0.2mm, draw](cp3){};\n\\draw (3,10.8) node[fill=black,circle,minimum size=0.1cm, inner sep=0.2mm, draw](cp4){};\n\\draw[->,dotted] (c1) to node[above, sloped]{$y_k$} (c2);\n\\draw[->] (cp3) to node[above, sloped]{$H_k$} (cp4);\n\\draw (1.2,9.5) node[above]{};\n\\draw (3.8,9.5) node[above]{};\n\\draw (2,9) node[draw, rectangle, rounded corners,scale=0.8](t){ Trigger };\n\\draw[->] (t) to node[left, sloped]{} (cp3);\n\\draw[->] (t) to node[right, sloped]{} (cp4);\n\\draw[->] (f) to (cp3);\n\\draw[->] (g) to (cp4);\n\\draw[->] (2.5,10.8) to (3.5,10.8);\n\\draw[->] (3.5,9.2) to (2.5,9.2);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 55,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath, amsthm, amssymb}\n\\usepackage{amscd,amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,arrows}\n\\usetikzlibrary{positioning}\n\\usepackage[T1]{fontenc}\n\\usepackage[ansinew]{inputenc}\n\\usetikzlibrary{shapes,arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n[scale=0.4, vertices/.style={draw, fill=black, circle, inner\nsep=0.5pt}]\n\\node[vertices, label=left:{$\\mbox{$Y_p$}$}] (a) at (0,0) {};\n\\node[vertices, label=right:{$\\mbox{$Y_p'$}$}] (b) at (10,0) {};\n\\node[vertices,label=below:{$\\mbox{$X_p$}$}] (c) at (5,4) {};\n\\node[vertices,label=below:{$\\mbox{$X_{p'}$}$}] (d) at (9,4) {};\n\n\\node[vertices,label=below:{}] (e) at (-0.5,1) {};\n\\node[vertices,label=below:{}] (f) at (1,1) {};\n\\node[vertices,label=below:{}] (g) at (1.5,1) {};\n\\node[vertices,label=below:{}] (h) at (2,1) {};\n\\node[vertices,label=below:{}] (i) at (2.5,1) {};\n\\node[vertices,label=below:{}] (j) at (3,1) {};\n\\node[vertices,label=below:{}] (k) at (3.5,1) {};\n\\node[vertices,label=below:{}] (l) at (4,1) {};\n\\node[vertices,label=below:{}] (m) at (4.5,1) {};\n\\node[vertices,label=below:{}] (n) at (5,1) {};\n\\node[vertices,label=below:{}] (o) at (5.5,1) {};\n\\node[vertices,label=below:{}] (p) at (6,1) {};\n\\node[vertices,label=below:{}] (q) at (6.5,1) {};\n\\node[vertices,label=below:{}] (r) at (7,1) {};\n\\node[vertices,label=below:{}] (s) at (7.5,1) {};\n\\node[vertices,label=below:{}] (t) at (8,1) {};\n\\node[vertices,label=below:{}] (u) at (8.5,1) {};\n\\node[vertices,label=below:{}] (v) at (9,1) {};\n\\node[vertices,label=below:{}] (w) at (9.5,1) {};\n\\node[vertices,label=below:{}] (x) at (10,1) {};\n\n\\node[vertices,label=below:{}] (y) at (0.5,2) {};\n\\node[vertices,label=below:{}] (z) at (1.5,2) {};\n\\node[vertices,label=below:{}] (aa) at (3,3) {};\n\\node[vertices,label=below:{}] (ab) at (7,3) {};\n\\node[vertices,label=below:{}] (ac) at (8,3) {};\n\\node[vertices,label=below:{}] (ad) at (9,3) {};\n\n\n\\foreach \\to/\\from in {a/c,a/e,a/f,a/g,a/h,a/i,b/c,b/d,b/j,b/n,b/o,b/p,b/q,b/r,b/s,b/t,b/u,b/v,b/w,b/x,c/a,d/a}\n\\draw [-] (\\to)--(\\from);\n\\foreach \\to/\\from in {a/y,a/z,c/aa,d/ab,d/ac,d/ad}\n\\draw [ultra thick] (\\to)--(\\from);\n\\draw [ultra thick, blue] (a)--(c)--(d)--(b);\n\\draw [thick, blue] (y) to[out=-40, in=-140] (w);\n\\draw [thick, blue] (z) to[out=-40, in=-160] (v);\n\\draw [thick, blue] (w) to[out=-40, in=-140] (v);\n\\draw [ultra thick, blue] (v) to[out=-40, in=-140] (u);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 56,
        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amssymb, amsmath, amsthm}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usepackage{pgfplotstable}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\draw[very thick] (-1,0)--(10,0);\n    \\draw[thick, blue, domain=-0.5:9, samples=200] plot (\\x, {0.3+0.6*sin(pi/\\x r)+0.01*cos(2*pi*20*\\x r)});\n    \\draw[thick, orange, domain=0:9, samples=200] plot (\\x, {0.55+0.5*sin(pi/\\x r)+0.01*cos(2*pi*50*\\x r)});\n    \\draw[very thick, blue] (0,0.3)--(2.5,0.3);\n    \\draw[very thick, orange] (0,0.55)--(3.7,0.55);\n    \\node[blue] at (2.5,-0.5) {$[x_2,z_{m+1}]$};\n    \\node[orange] at (3.7,-0.5) {$[x_2,z_m]$};\n    \\node[blue] at (-0.8,0.3) {$R$};\n    \\node[orange] at (-0.75,0.55) {$R$};\n    \\node[blue] at (2.5,0.6) {$b$};\n    \\node[orange] at (3.7,0.6) {$a_j$};\n    \\node[blue] at (2,1.2) {$[x,z_{j-1}]$};\n    \\node[blue] at (4.5,0.6) {$[x_j,z_j]$};\n    \\node[blue] at (10.8,0) {$\\bar{a}_j$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 57,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amssymb,latexsym,wasysym,marvosym,textcomp,stmaryrd,tikz,multirow,mathtools,tkz-euclide,url,enumitem,amsthm,titlesec,caption}\n\\usetikzlibrary{arrows,angles,decorations}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.1]\n\t\t\t\\foreach \\d in {0,12,24} {\n\t\t\t\t\\foreach \\x in {2,4,6,8,10} \\draw[line width=0.2pt] (\\x+\\d,0)--(\\x+\\d,12);\n\t\t\t\t\\foreach \\y in {2,4,6,8,10} \\draw[line width=0.2pt] (\\d,\\y)--(\\d+12,\\y);\n\t\t\t\t\\draw[line width=0.8pt] (\\d,0)--(\\d,12)--(\\d+12,12)--(\\d+12,0)--cycle;\n\t\t\t}\n\t\t\t\\draw[color=cyan,line width=1pt] (13,0)--(13,12)--(25,12)--(25,8)--(33,8)--(33,2)--(27,2)--(27,0)--cycle;\n\t\t\t\\draw[line width=0.8pt,color=magenta] (13,0)--(13,8)--(33,8);\n\t\t\t\\draw[line width=0.8pt,color=magenta] (13,12)--(33,12);\n\t\t\t\\draw[line width=0.8pt,color=magenta,dashed] (13,12)--(33,12)--(33,0);\n\t\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 58,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath, amssymb, amsthm}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{axis}[\n    axis lines = left,\n    xlabel = $\\left[Q_k\\right]_k$,\n    ylabel = {$m_{\\text{K}}^{\\text{K}}$},\n    legend pos = south east\n]\n%Here the blue parabola is defined\n\\addplot [\n    domain=0:1, \n    samples=100, \n    color=blue,\n    ]\n    {x};\n\\addlegendentry{$r_+ = r_-$}\n%Here the red parabola is defined\n\\addplot [\n    domain=0:1, \n    samples=100, \n    color=red,\n    ]\n    {x*x};\n\\addlegendentry{$r_+ = r_-$}\n\\addplot [\n    domain=0:1, \n    samples=100, \n    color=green,\n    ]\n    {x*x*x};\n\\addlegendentry{$r_+ = r_-$}\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 59,
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    {
        "index": 60,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{latexsym,amssymb,amsmath,enumerate,float,geometry,cite,tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale = 0.7]\n\\node (A) [circle, draw, fill = blue!50] at (0, 5) {$R$};\n\\node (B) [circle, draw, fill = red!50] at (1, 1) {$B_1$};\n\\node (C) [circle, draw, fill = red!50] at (2, 1) {$B_2$};\n\\node (D) [circle, draw, fill = red!50] at (3, 1) {$B_3$};\n\\node (E) [circle, draw, fill = blue!50] at (1, 3) {$B_4$};\n\\node (F) [circle, draw, fill = blue!50] at (2, 3) {$B_5$};\n\\node (G) [circle, draw, fill = red!50] at (3, 3) {$B_6$};\n\\node (H) [circle, draw, fill = blue!50] at (1, 5) {$B_7$};\n\\node (I) [circle, draw, fill = red!50] at (2, 5) {$B_8$};\n\\node (J) [circle, draw, fill = red!50] at (3, 5) {$B_9$};\n\\node (K) [circle, draw, fill = blue!50] at (5, 5) {$A_1$};\n\\node (L) [circle, draw, fill = red!50] at (6, 5) {$A_2$};\n\\node (M) [circle, draw, fill = red!50] at (7, 5) {$A_3$};\n\\node (N) [circle, draw, fill = blue!50] at (5, 3) {$A_4$};\n\\node (O) [circle, draw, fill = red!50] at (6, 3) {$A_5$};\n\\node (P) [circle, draw, fill = red!50] at (7, 3) {$A_6$};\n\\node (Q) [circle, draw, fill = blue!50] at (5, 1) {$A_7$};\n\\node (R) [circle, draw, fill = red!50] at (6, 1) {$A_8$};\n\\node (S) [circle, draw, fill = red!50] at (7, 1) {$A_9$};\n\n\\node (T) [circle, draw, fill = red!50] at (10, 3) {$C_1$};\n\\node (U) [circle, draw, fill = blue!50] at (9, 5) {$C_2$};\n\\node (V) [circle, draw, fill = blue!50] at (10, 5) {$C_3$};\n\\node (W) [circle, draw, fill = blue!50] at (11, 5) {$C_4$};\n\\node (X) [circle, draw, fill = blue!50] at (10, 7) {$C_5$};\n\n\\draw (A) -- (B);\n\\draw (A) -- (C);\n\\draw (A) -- (D);\n\\draw (A) -- (E);\n\\draw (A) -- (F);\n\\draw (A) -- (G);\n\\draw (A) -- (H);\n\\draw (A) -- (I);\n\\draw (A) -- (J);\n\\draw (K) -- (L);\n\\draw (K) -- (M);\n\\draw (K) -- (N);\n\\draw (K) -- (O);\n\\draw (K) -- (P);\n\\draw (K) -- (Q);\n\\draw (K) -- (R);\n\\draw (K) -- (S);\n\n\\draw (T) -- (U);\n\\draw (T) -- (V);\n\\draw (T) -- (W);\n\\draw (T) -- (X);\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 61,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[usenames]{color}\n\\usepackage{microtype,colortbl}\n\\usepackage{color}\n\\usepackage[usenames,dvipsnames]{xcolor}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.9,cm={cos(45),sin(45),-sin(45),cos(45),(15,0)}]\n    \\draw[step = 1, gray, ultra thin] (0, 0) grid (3, 3);\n\n    \\draw[fill, blue] (0, 0) circle[radius=0.03];\n    \\draw[fill, blue] (1, 1) circle[radius=0.03] node[right]{$121,212$};\n    \\draw[fill, blue] (2, 2) circle[radius=0.03] node[right]{$12,211$};\n    \\draw[fill, blue] (3, 3) circle[radius=0.03];\n\n    \\draw[->, blue] (0.1, 0.1) -- (0.9, 0.9);\n    \\draw[->, blue] (1.1, 1.1) -- (1.9, 1.9);\n    \\draw[->, blue] (2.1, 2.1) -- (2.9, 2.9);\n    \\draw[->, blue] (1.9, 1.9) -- (1.1, 1.1);\n    \\draw[->, blue] (0.9, 0.9) -- (0.1, 0.1);\n\n    \\draw[fill, blue] (1, 3) circle[radius=0.03] node[left]{$1,21,12$};\n    \\draw[fill, blue] (2, 2) circle[radius=0.03] node[left]{$211,121$};\n    \\draw[fill, blue] (3, 1) circle[radius=0.03] node[right]{$1,2,121$};\n\n    \\draw[->, blue] (1.1, 2.9) -- (1.9, 2.1);\n    \\draw[->, blue] (2.1, 1.9) -- (2.9, 1.1);\n    \\draw[->, blue] (1.9, 1.1) -- (1.1, 1.9);\n    \\draw[->, blue] (0.9, 2.1) -- (0.1, 2.9);\n    \\draw[->, blue] (2.9, 0.9) -- (2.1, 0.1);\n\n    \\draw[fill, blue] (0, 1) circle[radius=0.03] node[left]{$21,12,1$};\n    \\draw[fill, blue] (1, 2) circle[radius=0.03] node[left]{$121,12,1$};\n    \\draw[fill, blue] (2, 3) circle[radius=0.03] node[right]{$121,1,21$};\n    \\draw[fill, blue] (3, 2) circle[radius=0.03] node[right]{$211,1,21$};\n\n    \\draw[->, blue] (0.1, 1.1) -- (0.9, 1.9);\n    \\draw[->, blue] (1.1, 2.9) -- (1.9, 2.1);\n    \\draw[->, blue] (2.1, 1.9) -- (2.9, 1.1);\n    \\draw[->, blue] (1.9, 1.1) -- (1.1, 1.9);\n    \\draw[->, blue] (0.9, 1.9) -- (0.1, 1.1);\n\n    \\draw[fill, blue] (1, 0) circle[radius=0.03] node[above]{$1,21,211$};\n    \\draw[fill, blue] (2, 1) circle[radius=0.03] node[below]{$21,211,12$};\n    \\draw[fill, blue] (3, 0) circle[radius=0.03] node[right]{$121,12,121$};\n\n    \\draw[->, blue] (1.1, 0.9) -- (1.9, 0.1);\n    \\draw[->, blue] (2.1, 0.1) -- (2.9, 0.9);\n    \\draw[->, blue] (1.9, 0.9) -- (1.1, 0.1);\n    \\draw[->, blue] (0.9, 0.1) -- (0.1, 0.9);\n    \\draw[->, blue] (2.9, 1.9) -- (2.1, 1.1);\n\n    \\draw[fill, blue] (0, 2) circle[radius=0.03] node[left]{$1,12,21$};\n    \\draw[fill, blue] (1, 3) circle[radius=0.03] node[left]{$121,12,21$};\n    \\draw[fill, blue] (2, 2) circle[radius=0.03] node[below]{$12,211,12$};\n    \\draw[fill, blue] (3, 1) circle[radius=0.03] node[right]{$211,121,1$};\n\n    \\draw[->, blue] (0.1, 2.1) -- (0.9, 2.9);\n    \\draw[->, blue] (1.1, 3.9) -- (1.9, 3.1);\n    \\draw[->, blue] (2.1, 2.9) -- (2.9, 2.1);\n    \\draw[->, blue] (1.9, 2.1) -- (1.1, 2.9);\n    \\draw[->, blue] (0.9, 2.9) -- (0.1, 2.1);\n\n    \\draw[fill, blue] (2, 0) circle[radius=0.03] node[below]{$21,12,121$};\n    \\draw[fill, blue] (3, 1) circle[radius=0.03] node[right]{$211,121"
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    {
        "index": 62,
        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath,amssymb,amsfonts,mathtools}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\\node[anchor=south west,inner sep=0] (image) at (0,0) {\\includegraphics[width=\\textwidth]{example-image}};\n\t\t\\begin{scope}[x={(image.south east)},y={(image.north west)}]\n\t\t\\node at (0.6,0.6) {$\\sigma_z$};\n\t\t\\node at (0.35,0.65) {$K_z$};\n\t\t\\node at (0.18,0.5) {$\\hat\\sigma_z$};\n\t\t\\node at (0.6,0.17) {$K$};\n\t\t\n\t\t\\node at (0.5,0.8) {$\\sigma_x$};\n\t\t\\node at (0.58,0.32) {$K_x$};\n\t\t\\node at (0.45,0.2) {$\\hat\\sigma_x$};\n\t\t\\node at (0.7,0.7) {$X_1$};\n\t\t\\node at (0.85,0.5) {$X_2$};\n\t\t\\node at (0.68,0.6) {$X_3$};\n\t\t\\node at (0.85,0.8) {$X_4$};\n\t\t\\node at (0.55,0.8) {$X_5$};\n\t\t\n\t\t\\node at (0.25,0.3) {$\\hat X_1$};\n\t\t\\node at (0.2,0.45) {$\\hat X_2$};\n\t\t\\node at (0.3,0.6) {$\\hat X_3$};\n\t\t\\node at (0.4,0.6) {$\\hat X_4$};\n\t\t\\node at (0.5,0.55) {$\\hat X_5$};\n\t\t\n\t\t\\node at (0.65,0.2) {$\\hat X_1$};\n\t\t\\node at (0.75,0.3) {$\\hat X_2$};\n\t\t\\node at (0.85,0.4) {$\\hat X_3$};\n\t\t\\node at (0.95,0.5) {$\\hat X_4$};\n\t\t\\node at (1.05,0.6) {$\\hat X_5$};\n\t\t\n\t\t\\end{scope}\n\t\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 63,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\tikzset{>=latex}\n\\usetikzlibrary{automata,positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[shorten >=1pt,node distance=2.8cm,on grid,auto] \n\t\t\\node[state,initial] (s_0)   {$s_0$}; \n\t\t\\node[state] (s_1) [right=of s_0] {$s_1$}; \n\t\t\\node (s_2) [right=of s_1] {$\\cdots$};\n\t\t\\node[state] (s_T) [right=of s_2] {$s_{T}$}; \n\t\t\\node[state] (s_T1) [right=of s_T] {$s_{T+1}$}; \n\t\t\\path[->] \n\t\t(s_0) edge [loop above] node {$p_0,0$} ()\n\t\tedge [bend left] node {$p_1,1$} (s_1)\n\t\t(s_1) edge [loop above] node {$p_{r-1},r-1$} ()\n\t\tedge node {$p_{r},r$} (s_2)\n\t\t(s_2) edge [loop above] node {$p_{T-2},T-2$} ()\n\t\tedge [bend left] node {$p_{T-1},T-1$} (s_T)\n\t\t(s_T) edge [loop above] node {$p_{T},T$} ()\n\t\tedge [bend left] node {$p_{T+1},T+1$} (s_T1)\n\t\t(s_T1) edge [bend left] node {$p_{r-1},r-1$} (s_1)\n\t\t(s_T1) edge [bend right=20] node {$p_{r},r$} (s_0);\n\t\t\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 64,
        "tikz_code": "\\documentclass[twoside,11pt]{article}\n\\usepackage{amssymb,amsthm,amsmath}\n\\usepackage{microtype,xcolor,graphicx,booktabs,subcaption}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning,graphs,graphs.standard}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\\graph[nodes={empty nodes, fill=none, draw, circle, inner sep=2pt, minimum size = 0.15cm}}] {\n\t\t\tsubgraph I_n[n=3, V={1,2,3}, name=A] -- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1, A/2, A/3} }\n\t\t\t-- { {A/1, A/2, A/3}, {A/1"
    },
    {
        "index": 65,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{color}\n\\usepackage{tikz-cd}\n\\usetikzlibrary{matrix}\n\\usetikzlibrary{decorations.markings}\n\\tikzset{->-/.style={decoration={\n  markings,\n  mark=at position .5 with {\\arrow{>}}},postaction={decorate}}}\n\\tikzset{-<-/.style={decoration={\n  markings,\n  mark=at position .5 with {\\arrow{<}}},postaction={decorate}}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[baseline=-0.65ex, thick, scale=0.9]\n\\draw (0, 2) node[circle,fill,inner sep=1.5pt]{};\n\\draw (0, 2.5) node {$b$};\n\\draw[->-] (0, 2) -- (1.5, 1);\n\\draw[->-] (1.5, 1) -- (1.5, 2);\n\\draw (0.7, 1.5) node {$\\Omega$};\n\\draw (2, 2) node[circle,fill,inner sep=1.5pt]{};\n\\draw (2, 2.5) node {$\\nu$};\n\\draw[->-] (2, 2) -- (3.5, 1);\n\\draw (3.2, 1.5) node {$M$};\n\\draw (4, 0) node[circle,fill,inner sep=1.5pt]{};\n\\draw (4, -0.5) node {$L = \\Gamma$};\n\\draw[->-] (4, 0) -- (0, 0);\n\\draw[->-] (4, 0) -- (1.5, 1);\n\\draw (1.5, 1) -- (0, 0);\n\\draw (0, 0.5) node {$S = \\Gamma^\\complement$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
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        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath, amssymb, latexsym, amsthm, tikz, caption, subcaption}\n\\usetikzlibrary{cd}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.85]\n    %dots and stars\n    \\node (31) at (0,0) {$\\bullet$};\n    \\node (21) at (0,1) {$\\bullet$};\n    \\node (11) at (0,2) {$\\bullet$};\n\n    \\node (32) at (1,0) {$\\bullet$};\n    \\node (22) at (1,1) {$\\bullet$};\n    \\node (12) at (1,2) {$\\bullet$};\n\n    \\node (33) at (2,0) {$\\bullet$};\n    \\node (23) at (2,1) {$\\bullet$};\n    \\node (13) at (2,2) {$\\bullet$};\n\n    \\node (34) at (3,0) {$\\bullet$};\n    \\node (24) at (3,1) {$\\bullet$};\n    \\node (14) at (3,2) {$\\bullet$};\n\n    \\node (35) at (4,0) {$\\bullet$};\n    \\node (25) at (4,1) {$\\bullet$};\n    \\node (15) at (4,2) {$\\bullet$};\n\n    \\node (36) at (5,0) {$\\bullet$};\n    \\node (26) at (5,1) {$\\bullet$};\n    \\node (16) at (5,2) {$\\bullet$};\n\n    \\node (37) at (6,0) {$\\bullet$};\n    \\node (27) at (6,1) {$\\bullet$};\n    \\node (17) at (6,2) {$\\bullet$};\n\n    \\node (38) at (7,0) {$\\bullet$};\n    \\node (28) at (7,1) {$\\bullet$};\n    \\node (18) at (7,2) {$\\bullet$};\n\n    \\node (39) at (8,0) {$\\bullet$};\n    \\node (29) at (8,1) {$\\bullet$};\n    \\node (19) at (8,2) {$\\bullet$};\n\n    \\node (30) at (9,0) {$\\bullet$};\n    \\node (20) at (9,1) {$\\bullet$};\n    \\node (10) at (9,2) {$\\bullet$};\n\n    %arrows\n    \\draw[->, thick, red, dashed] (12.south) -- (28.north);\n    \\draw[->, thick, red, dashed] (24.south) -- (36.north);\n\n    \\draw[->, thick, dashed] (30.south) -- (10.north);\n\n    %straight lines\n    \\draw[-, thick] (11.south) -- (0,0.5);\n    \\draw[-, thick] (11.north) -- (0,1.5);\n\n    \\draw[-, thick] (15.south) -- (4,0.5);\n    \\draw[-, thick] (15.north) -- (4,1.5);\n\n    %diagonals\n    \\draw[-, thick, dotted] (25.south) -- (23.north);\n    \\draw[-, thick, dotted] (29.south) -- (27.north);\n\n    \\draw[-, thick, dotted] (15.south) -- (13.north);\n    \\draw[-, thick, dotted] (19.south) -- (17.north);\n\n    %labels\n    \\node at (0,2.4) {\\scriptsize{0}};\n    \\node at (1,2.4) {\\scriptsize{1}};\n    \\node at (2,2.4) {\\scriptsize{2}};\n    \\node at (3,2.4) {\\scriptsize{3}};\n    \\node at (4,2.4) {\\scriptsize{4}};\n    \\node at (5,2.4) {\\scriptsize{5}};\n    \\node at (6,2.4) {\\scriptsize{6}};\n    \\node at (7,2.4) {\\scriptsize{7}};\n    \\node at (8,2.4) {\\scriptsize{8}};\n    \\node at (9,2.4) {\\scriptsize{9}};\n    \\node at (10,2.4) {\\scriptsize{10}};\n\n    \\node at (-0.4,1) {\\scriptsize{$\\infty$}};\n    \\node at (-0.4,0) {\\scriptsize{$\\infty$}};\n    \\node at (-0.4,2) {\\scriptsize{$\\infty$}};\n\n    \\node at (10.4,1) {\\scriptsize{$\\infty$}};\n    \\node at (10.4,0) {\\scriptsize{$\\infty$}};\n    \\node at (10.4,2) {\\scriptsize{$\\infty$}};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 67,
        "tikz_code": "\\documentclass[a4paper,11pt]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{snakes}\n\\usetikzlibrary{shapes.geometric}\n\\usepackage{color}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[out=20,in=160,relative]\n\\draw[dashed] (0,0) ellipse (2 and 1);\n\\draw (0,0) circle (1.8);\n\\draw (1.8,0) arc [start angle=0, end angle=180, x radius=2, y radius=0.8];\n\\draw (-2,0) arc [start angle=180, end angle=360, x radius=2, y radius=0.8];\n\\draw (-1.8,0) arc [start angle=180, end angle=360, x radius=2, y radius=0.8];\n\\draw (-1.8,1.5)--(-1.8,1.8);\n\\draw (-1.8,1.5) arc [start angle=180, end angle=360, x radius=0.1, y radius=0.1];\n\\draw (-1.8,1.5)--(-1.8,1.8);\n\\draw (1.8,1.5) arc [start angle=0, end angle=180, x radius=0.1, y radius=0.1];\n\\draw (1.8,1.5)--(1.8,1.8);\n\\filldraw (0,0) circle (0.03);\n\\node [left] at (0.0,0.0) {$(0,0)$};\n\\node [right] at (1.5,0.0) {$B(\\alpha)$};\n\\draw[blue,thick] (0,2.2) arc [start angle=90, end angle=-90, x radius=1, y radius=0.5];\n\\draw[blue,thick] (0,2.2) arc [start angle=90, end angle=270, x radius=1, y radius=0.5];\n\\draw[blue,thick] (0,-0.4) arc [start angle=270, end angle=450, x radius=1, y radius=0.5];\n\\draw[blue,thick] (0,-0.4) arc [start angle=270, end angle=-90, x radius=1, y radius=0.5];\n\\node [left] at (0.0,2.1) {$u$};\n\\node [right] at (0.0,2.1) {$u$};\n\\draw[blue,thick] (0,2.5) ellipse (0.3 and 0.15);\n\\draw[blue,thick] (0,2.5) ellipse (0.3 and 0.15);\n\\draw[blue,thick] (0,0.0) ellipse (0.3 and 0.15);\n\\draw[blue,thick] (0,0.0) ellipse (0.3 and 0.15);\n\\node [right] at (1.7,2.5) {$\\gamma$};\n\\node [right] at (0.0,-1.0) {$\\mathcal{U}(B(\\alpha))$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 68,
        "tikz_code": "\\documentclass[twocolumn,showpacs,preprintnumbers,amsmath,amssymb,natbib,noshowpacs]{revtex4-1}\n\\usepackage{color}\n\\usepackage{amssymb}\n\\usepackage{amsmath,empheq}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\\node at (-2,0) {\\includegraphics[scale=0.25,origin=c]{example-image}};\n\\node at (6.5,0) {\\includegraphics[scale=0.15]{example-image}};\n\\node at (-3.2,1.7) {1};\n\\node at (-1.5,1.7) {2};\n\\node at (0.5,1.7) {3};\n\\node at (2.8,1.7) {4};\n\\node at (5.7,1.7) {5};\n\\node at (4.5,-1.1) {6};\n\\node at (5.2,-1.7) {7};\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 69,
        "tikz_code": "\\documentclass[12pt]{report}\n\\usepackage[latin9]{luainputenc}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[thick,scale=0.8, every node/.style={scale=0.8}]\n\n\t\\node[rectangle,fill=white!80!green] (a) at (-1,0){\n\t\t\\begin{tabular}{c}\n\t\t\tProject the database matrix $C_{Z,N}^X$ into the POD space $\\mathcal{U}\\times\\mathcal{S}_{N,N}$\\\\\n\t\t\t$C_{Z,N}^X = U\\times S_N$\n\t\t\\end{tabular}};\n\n\t\\node[rectangle,fill=white!40!green] (b) at (6,0){\n\t\t\\begin{tabular}{c}\n\t\t\tReal-Time Approximated Forward Model\\\\\n\t\t\t$C_{Z,N}^{X'} = \\mathcal{U}\\left( \\mathcal{R}(\\mathcal{I})\\right)\\left( \\mathcal{U}\\left( \\mathcal{R}(\\mathcal{I})\\right)^{\\intercal}\\right)\\left( \\mathcal{U}\\left( \\mathcal{R}(\\mathcal{I})\\right)^{\\intercal}\\right)\\left( \\mathcal{U}\\times \\mathcal{S}_{N,N}\\right)$\\\\\n\t\t\tas the operator $\\mathcal{O}\\left( \\mathcal{R}(\\mathcal{I})\\right)$\n\t\t\\end{tabular} };\n\n\t\\node[rectangle,fill=white!30!green] (c) at (6,-3){\n\t\t\\begin{tabular}{c}\n\t\t\tEvaluate the real time model:\\\\\n\t\t\t$\\mathcal{U}\\left( \\mathcal{R}(\\mathcal{I})\\right)\\left( \\mathcal{U}\\left( \\mathcal{R}(\\mathcal{I})\\right)^{\\intercal}\\right)\\left( \\mathcal{U}\\left( \\mathcal{R}(\\mathcal{I})\\right)^{\\intercal}\\right)\\left( \\mathcal{U}\\times \\mathcal{S}_{N,N}\\right)$\\\\\n\t\tfor all the parameters\\\\\n\t\t$\\mathcal{O}\\left( \\mathcal{R}(\\mathcal{I})\\right)$\n\t\t\\end{tabular}};\n\n\t\\node[rectangle,fill=white!50!blue] (d) at (-1,-3){\n\t\t\\begin{tabular}{c}\n\t\t\tDefine an interpolator $Z$\\\\\n\t\t\t$N \\leftarrow Z(N)$\n\t\t\\end{tabular}};\n\n\t\\node[rectangle,fill=white!50!blue] (e) at (6,-6){\n\t\t\\begin{tabular}{c}\n\t\t\tEvaluate:\\\\\n\t\t\tvia the interpolator $Z$\\\\\n\t\t\tthe coefficients for all the parameters\\\\\n\t\t\t$\\mathcal{O}\\left( \\mathcal{R}(\\mathcal{I})\\right)$\\\\\n\t\tto obtain the coefficients matrix\\\\\n\t\t$\\mathcal{C}_{X,Z}^{N,N}=\\mathcal{U}\\left( \\mathcal{R}(\\mathcal{I})\\right)\\left( \\mathcal{U}\\left( \\mathcal{R}(\\mathcal{I})\\right)^{\\intercal}\\right)\\left( \\mathcal{U}\\left( \\mathcal{R}(\\mathcal{I})\\right)^{\\intercal}\\right)\\left( \\mathcal{U}\\times \\mathcal{S}_{N,N}\\right)$\\\\\n\t\t$\\mathcal{C}_{X,Z}^{N,N}=\\mathcal{U}\\times \\mathcal{S}_{N,N}$\n\t\t\\end{tabular}};\n\n\t\\node[rectangle,fill=white!50!blue] (f) at (-1,-6){\n\t\t\\begin{tabular}{c}\n\t\t\tThe approximation is a combination of coefficients and functions\\\\\n\t\t\tof the coefficients matrix\n\t\t\\end{tabular}};\n\n\t\\node[rectangle,fill=white!50!blue] (g) at (6,0){\n\t\t\\begin{tabular}{c}\n\t\t\tPhysicals-Aware POD\\\\\n\t\t\\end{tabular}};\n\n\t\\node[rectangle,fill=white!80!cyan] (h) at (-3.5,-1.5){\n\t\t\\begin{tabular}{c}\n\t\t\tPOD with Interpolation\\\\\n\t\t\\end{tabular}};\n\n\n\t\\node[rectangle,fill=white!80!cyan] (i) at (1.5,-1.5){\n\t\t\\begin{tabular}{c}\n\t\t\tPhysicals-Aware POD\\\\\n\t\t\\end{tabular}};\n\n\t\\node[rectangle,fill=white!80!cyan] (j) at (-3.5,-6){\n\t\t\\begin{tabular}{c}\n\t\t\tPOD with Interpolation\\\\\n\t\t\\end{tabular}};\n\n\t\\node[rectangle,fill=white!80!cyan] (k) at (1.5,-6){\n\t\t\\begin{tabular}{c}\n\t\t\tPOD with Interpolation\\\\\n\t\t\\end{tabular}};\n\n\n\t\\draw[->] (a) edge (b) (b) edge (c);\n\t\\draw[->] (d) edge (c) (d) edge (f);\n\t\\draw[->] (e) edge (c) (e) edge (g);\n\t\\draw[->] (f) edge (j);\n\t\\draw[->] (g) edge (i);\n\t\\draw[->] (j) edge (k);\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 70,
        "tikz_code": "\\documentclass[tikz,border=3mm]{standalone}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.16}\n\\begin{document}\n\\begin{tikzpicture}[declare function={f(\\x)=1/(2-\\x);},\n    /pgf/number format/precision=3]\n\\begin{axis}[axis lines=middle,ymin=0,ymax=1.2,\n    xlabel={$t$},ylabel={$f(t)$},\n    xtick={0,0.1,0.2,...,1.1},\n    ytick={0,0.1,0.2,...,1.2},\n    yticklabel style={/pgf/number format/precision=1,\n    /pgf/number format/fixed}\n    ]\n \\addplot[thick,domain=0:1,samples=50] {f(x)};\n\\end{axis}\n\\end{tikzpicture}\n\\end{document}"
    },
    {
        "index": 71,
        "tikz_code": "\\documentclass{article}\n\\usepackage{pgfplots}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale = 1]\n    \\begin{axis}[\n    xlabel= Time [s],\n    ylabel= Speed ACEF,\n    xmin=0,xmax=150,\n    ymin=0,ymax=1,\n    legend pos=outer north east,\n    legend cell align=left,\n    width=11cm,\n    height=6.5cm,\n    style={ultra thick},\n    grid style={line width=.1pt, draw=gray!20},\n    ymajorgrids=false,\n    xmajorgrids=false,\n    ]\n\n      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n      %% Grilla\n      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 5*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 10*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 15*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 20*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 25*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 30*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 35*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 40*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 45*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 50*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 55*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 60*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 65*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 70*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 75*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 80*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 85*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 90*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 95*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 100*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 105*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 110*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 115*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 120*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 125*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + 130*pi/2) + 0.45};\n      \\addplot[blue,samples=500,domain=0:150] {1.2*sin(10*(x-50) + "
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    {
        "index": 72,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{colortbl}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usetikzlibrary{calc,matrix}\n\\usetikzlibrary{decorations.pathmorphing,decorations.markings,decorations.pathreplacing,arrows,shapes}\n\\usetikzlibrary{knots}\n\\usepackage[bookmarks=true, bookmarksopen=true,%\nbookmarksdepth=3,bookmarksopenlevel=2,%\ncolorlinks=true,%\nlinkcolor=blue,%\ncitecolor=blue,%\nfilecolor=blue,%\nmenucolor=blue,%\nurlcolor=blue]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw [decoration={markings,mark=at position 0.5 with {\\arrow{>}}},postaction={decorate}] (-1,0) node [left] {$r_0(0)$} to (1,0) node [right] {$r_0(1)$};\n\\draw [decoration={markings,mark=at position 0.6 with {\\arrow{>}}},postaction={decorate}] (1,0) to [out=0,in=120] (5.5,2) node [right] {$r_0(1)$};\n\\draw [decoration={markings,mark=at position 0.6 with {\\arrow{>}}},postaction={decorate}] (5.5,2) to [out=-60,in=90] (8.5,0) node [right] {$r_0(1)$};\n\\draw [decoration={markings,mark=at position 0.6 with {\\arrow{>}}},postaction={decorate}] (1,0) to [out=30,in=150] (8.5,0) node [right] {$r_0(1)$};\n\\node at (0,-0.5) {$r_1(1)$};\n\\node at (4.5,-0.5) {$r_2(1)$};\n\\node at (2,1) {$r_3(1)$};\n\\node at (7,1) {$r_4(1)$};\n\\node at (3,0) {$\\cdots$};\n\\node at (7,0) {$\\cdots$};\n\\node at (0.5,1.5) {$\\cdots$};\n\\node at (5.5,1.5) {$\\cdots$};\n\\node at (8,1.5) {$\\cdots$};\n\\draw [decoration={markings,mark=at position 0.6 with {\\arrow{>}}},postaction={decorate}] (8.5,0) to [out=-150,in=-90] (3.5,0);\n\\draw [decoration={markings,mark=at position 0.6 with {\\arrow{>}}},postaction={decorate}] (0.5,1) to [out=-30,in=180] (1,0);\n\\draw [decoration={markings,mark=at position 0.6 with {\\arrow{>}}},postaction={decorate}] (3.5,0) to [out=-60,in=180] (4.5,1);\n\\draw [decoration={markings,mark=at position 0.6 with {\\arrow{>}}},postaction={decorate}] (7.5,0) to [out=-90,in=180] (8.5,-1);\n\\draw [decoration={markings,mark=at position 0.6 with {\\arrow{>}}},postaction={decorate}] (0,-1) to [out=150,in=-150] (0.5,-1);\n\\draw [decoration={markings,mark=at position 0.6 with {\\arrow{>}}},postaction={decorate}] (4.5,-1) to [out=-30,in=30] (5.5,-1);\n\\draw [decoration={markings,mark=at position 0.6 with {\\arrow{>}}},postaction={decorate}] (8.5,-1) to [out=-90,in=30] (9.5,-1);\n\\draw [decoration={markings,mark=at position 0.6 with {\\arrow{>}}},postaction={decorate}] (3.5,-1) to [out=150,in=-30] (0.5,-1);\n\\draw [decoration={markings,mark=at position 0.6 with {\\arrow{>}}},postaction={decorate}] (7.5,-1) to [out=150,in=-150] (8.5,-1);\n\\draw [decoration={markings,mark=at position 0.6 with {\\arrow{>}}},postaction={decorate}] (9.5,-1) to [out=180,in=0] (10,-1);\n\\node [right] at (10,-1) {$r_K(1)$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 73,
        "tikz_code": "\\documentclass[11pt,reqno]{amsart}\n\\usepackage{amssymb}\n\\usepackage{xcolor}\n\\usepackage[all,color]{xy}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=newest}\n\\usepackage{tikz}\n\\usetikzlibrary{cd}\n\n\\newcommand{\\VertexSize}{0.05}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n \\begin{axis}[\naxis lines=middle, \nticks=none, \naxis equal, \nxmin=0, xmax=10, ymin=0, ymax=6,\nbefore end axis/.code={\n\\draw[-latex, dashed] (axis cs:0,0) -- (axis cs:0,5);\n\\draw[dashed] (axis cs:5,0) -- (axis cs:5,5);\n\\node[above] at (axis cs:0,5) {$\\lambda$};\n\\node[left] at (axis cs:0,0) {$0$};\n\\node[below] at (axis cs:5,0) {$\\tau_1$};\n\\node[below] at (axis cs:8.5,0) {$\\tau_2$};\n\\node[below] at (axis cs:9.5,0) {$\\dots$};\n\\node at (axis cs:0.7,2.5) {$\\mathcal{Q}'(u)$};\n\\node at (axis cs:0.7,4) {$\\mathcal{A}'+q$};\n\\draw[fill=blue,opacity=\\VertexSize] (axis cs:3.3,1.8) circle (2pt);\n\\node at (axis cs:2.9,1.8) {$\\mu^{\\ell}(v_t)$};\n\\node at (axis cs:2.3,3.6) {$\\lambda + q + q^{\\ell}(v_t)$};\n\\node at (axis cs:2.3,4.6) {$\\lambda + q^{\\ell}(v_t)$};\n\\draw[fill=yellow,opacity=\\VertexSize] (axis cs:6.8,2.8) circle (2pt);\n\\node at (axis cs:6.4,2.8) {$\\mu^{\\ell}(v_t)$};\n\\node at (axis cs:6.8,3.4) {$\\lambda^{\\ell} + q^{\\ell}(v_t)$};\n\\draw[fill=yellow,opacity=\\VertexSize] (axis cs:7,3.8) circle (2pt);\n\\node at (axis cs:6.6,3.8) {$\\lambda^{\\ell} + q^{\\ell}(v_t)$};\n\\draw[fill=orange,opacity=\\VertexSize] (axis cs:5,2) circle (2pt);\n\\node at (axis cs:5,2) {$\\mu^{\\ell}(v_t)$};\n\\draw[fill=orange,opacity=\\VertexSize] (axis cs:3.8,3.4) circle (2pt);\n\\node at (axis cs:3.4,3.4) {$\\mu^{\\ell}(v_t)$};\n\\draw[fill=yellow,opacity=\\VertexSize] (axis cs:8,3.8) circle (2pt);\n\\node at (axis cs:8,3.8) {$\\lambda^{\\ell} + q^{\\ell}(v_t)$};\n\\node[left] at (axis cs:0,1.8) {$\\mathcal{Q}'(u)$};\n\\node[left] at (axis cs:0,3.8) {$\\mathcal{A}'$};\n}\n]\n\\addplot[domain=0:10, color=white, opacity=0] {5};\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{arrows,automata}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node[shape=circle,draw=black,scale=0.8] (1) at (0,1) {1};\n\\node[shape=circle,draw=black,scale=0.8] (2) at (1.5,1) {2};\n\\node[shape=circle,draw=black,scale=0.8] (3) at (0,0) {3};\n\\node[shape=circle,draw=black,scale=0.8] (4) at (1.5,0) {4};\n\\node (0) at (1.8,0.5) {};\n\n\\path [-] (1) edge (2);\n\\path [-] (1) edge (3);\n\\path [-] (2) edge (4);\n\\path [-] (3) edge (4);\n\n\\node[shape=circle,draw=black,scale=0.8] (1) at (4+0,1) {1};\n\\node[shape=circle,draw=black,scale=0.8] (2) at (4+1.5,1) {2};\n\\node[shape=circle,draw=black,scale=0.8] (3) at (4+0.75,0) {3};\n\\node[shape=circle,draw=black,scale=0.8] (4) at (4+1.5,0) {4};\n\\node[shape=circle,draw=black,scale=0.8] (5) at (4+0.75,0.75) {5};\n\\node (0) at (4+1.8,0.5) {};\n\n\\path [-] (1) edge (2);\n\\path [-] (1) edge (3);\n\\path [-] (2) edge (4);\n\\path [-] (3) edge (4);\n\\path [-] (3) edge (5);\n\\path [-] (4) edge (5);\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amsfonts,amssymb,amsthm}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}[level distance=0.5in,level/.style={sibling distance=2in,level distance=0.6in}, scale=0.8]\n\\node [scale=0.8] at (0,0) {$S$}\n  child {node [scale=0.8] {$a$}}\n  child {node [scale=0.8]{$S$}\n    child {node [scale=0.8] {$b$}}\n    child {node [scale=0.8] {$S$}\n      child {node [scale=0.8] {$a$}}\n      child {node [scale=0.8] {$S$}\n        child {node [scale=0.8] {$b$}}\n        child {node [scale=0.8] {$S$}\n          child {node [scale=0.8] {$a$}}\n          child {node [scale=0.8] {$S$}\n            child {node [scale=0.8] {$b$}}\n            child {node [scale=0.8] {$\\epsilon$}}\n          }\n        }\n      }\n    }\n  };\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 76,
        "tikz_code": "\\documentclass[11pt,letterpaper]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\n\n\\draw (-2.5,0) circle (1.5cm);\n\\draw (2.5,0) circle (1.5cm);\n\\draw (0,4) circle (1.5cm);\n\\draw (0,0.8) circle (0.8cm);\n\\draw (-2.9,-1.4) circle (1.2cm);\n\\draw (2.9,-1.4) circle (1.2cm);\n\n\\node at (0,5) {$v_6$};\n\\node at (0,-0.2) {$v_1$};\n\\node at (-3.4,-2) {$v_2$};\n\\node at (3.4,-2) {$v_3$};\n\\node at (0.8,0.8) {$v_5$};\n\n\n\\draw (0.8,0.8) -- (0,4);\n\\draw (-0.8,0.8) -- (0,4);\n\\draw (0.8,0.8) -- (-2.9,-1.4);\n\\draw (-0.8,0.8) -- (-2.9,-1.4);\n\\draw (0.8,0.8) -- (2.9,-1.4);\n\\draw (-0.8,0.8) -- (2.9,-1.4);\n\n\n\\node at (0,-2.4) {$W_3$};\n\\node at (-3,-2.4) {$W_2$};\n\\node at (3,-2.4) {$W_4$};\n\\node at (0,2) {$W_6$};\n\\node at (0.4,0.4) {$W_1$};\n\\node at (-3.2,-1) {$W_7$};\n\\node at (3.2,-1) {$W_8$};\n\n\\draw[fill] (0,4) circle (0.1cm);\n\\draw[fill] (0,0.8) circle (0.1cm);\n\\draw[fill] (-2.9,-1.4) circle (0.1cm);\n\\draw[fill] (2.9,-1.4) circle (0.1cm);\n\n\\draw[fill] (0.8,0.8) circle (0.1cm);\n\\draw[fill] (-0.8,0.8) circle (0.1cm);\n\n\\draw[fill] (-2.5,0) circle (0.1cm);\n\\draw[fill] (2.5,0) circle (0.1cm);\n\n\n\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 78,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning,chains,fit,shapes,calc}\n\\usetikzlibrary{patterns}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[colorlinks=false]{hyperref}\n\\tikzset{cross/.style={cross out, draw=black, minimum size=2*(#1-\\pgflinewidth), inner sep=0pt, outer sep=0pt},\n%default radius will be 1pt. \ncross/.default={1pt}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.6]\n\\draw (-7,0) -- (-1,0);\n\\foreach \\i in {-7,-6,...,1}\n{\\draw (\\i,0.1) -- (\\i,-0.1) node[below] {\\i};}\n\\draw[red,fill] (-5,0) circle (.1);\n\\draw[red,fill] (-4,0) circle (.1);\n\\draw[red,fill] (-3,0) circle (.1);\n\\draw[blue,fill] (-2,0) circle (.1);\n\\draw[blue,fill] (-1,0) circle (.1);\n\\draw[blue,fill] (0,0) circle (.1);\n\\draw[blue,fill] (1,0) circle (.1);\n\\draw[blue,fill] (2,0) circle (.1);\n\\draw[blue,fill] (3,0) circle (.1);\n\\draw[blue,fill] (4,0) circle (.1);\n\\draw[blue,fill] (5,0) circle (.1);\n\\draw[blue,fill] (6,0) circle (.1);\n\\draw[blue,fill] (7,0) circle (.1);\n\\draw[|-|] (-4,-0.25) -- (-2,-0.25);\n\\draw (-3,-0.5) node{$Z$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 79,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsthm, amsmath, amssymb}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\tikzstyle{edge} = [draw,thick,-,black]\n    \\tikzstyle{node} = [draw,circle,fill=black,inner sep=0pt, minimum width=4pt]\n    \\def\\scalefactor{0.7}\n    %D3\n    \\begin{scope}[scale=\\scalefactor]\n    \\node[node] (v1) at (0,0) {};\n    \\node[node] (v2) at (1,0) {};\n    \\node[node] (v3) at (2,0) {};\n    \\node[node] (v4) at (3,0) {};\n    \\node[node] (v5) at (4,0) {};\n    \\node[node] (v6) at (5,0) {};\n    \\node[node] (v7) at (1,1) {};\n    \\node[node] (v8) at (3,1) {};\n    \\draw[edge] (v1) -- (v2) -- (v3) -- (v4) -- (v5) -- (v6);\n    \\draw[edge] (v1) -- (v7) -- (v3) -- (v8) -- (v6);\n    \\draw[edge] (v2) -- (v8);\n    \\end{scope}\n    %D4\n    \\begin{scope}[scale=\\scalefactor, shift={(7,0)}]\n    \\node[node] (v1) at (0,0) {};\n    \\node[node] (v2) at (1,0) {};\n    \\node[node] (v3) at (2,0) {};\n    \\node[node] (v4) at (3,0) {};\n    \\node[node] (v5) at (4,0) {};\n    \\node[node] (v6) at (5,0) {};\n    \\node[node] (v7) at (5.5,0.5) {};\n    \\node[node] (v8) at (6,1) {};\n    \\node[node] (v9) at (7,1.5) {};\n    \\node[node] (v10) at (6.5,2) {};\n    \\node[node] (v11) at (5,2.5) {};\n    \\node[node] (v12) at (3,1.5) {};\n    \\draw[edge] (v1) -- (v2) -- (v3) -- (v4) -- (v5) -- (v6) -- (v7) -- (v8) -- (v9) -- (v10) -- (v11) -- (v12) -- (v1);\n    \\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 80,
        "tikz_code": "\\documentclass[a4paper,11pt]{amsart}\n\\usepackage{amsmath, amssymb, amsthm, amsfonts, mathtools, multicol, inputenc}\n\\usepackage{tikz, tikz-cd}\n\\usetikzlibrary{matrix}\n\\usetikzlibrary{cd}\n\n\\newcommand{\\cL}{\\mathcal{L}}\n\n\\newcommand{\\cD}{\\mathcal{D}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\\draw (0,0) rectangle (4,2);\n\t\t\\draw (2,0) -- (2,2);\n\t\t\\draw (3.8,0) -- (3.8,2);\n\t\t\\draw[dotted] (0,1) -- (4,1);\n\t\t\\draw[dotted] (2,1.8) -- (3.8,1.8);\n\t\t\\node at (4.8,1.75) {$y=\\cL_0$};\n\t\t\\node at (4.8,1.25) {$y=\\cL_1$};\n\t\t\\node at (0,-0.5) {\\small Constant, background};\n\t\t\\node at (0,1.5) {\\small $-dP_d/d\\cL_0$};\n\t\t\\node at (3.2,1.5) {\\small $H$};\n\t\t\\node at (5.5,1) {\\small Near-wall region};\n\t\t\\node at (5.5,0.5) {\\small $y=0$};\n\t\t\\node at (-1.5,1) {\\small Fringe region};\n\t\t\\node at (-1.5,0.5) {\\small $y=\\cD_0$};\n\t\t\\node at (2.3,2.5) {\\small $y=\\cL_1$};\n\t\t\\draw[line width=0.03cm] (1.8,1.8) -- (2.5,1.8) -- (2.5,2.5);\n\t\t\\draw[line width=0.03cm] (2.25,0.9) -- (3.25,0.9) -- (3.25,1.5);\n\t\t\\draw[line width=0.03cm] (1.5,1.2) -- (2.5,1.2);\n\t\t\\draw[line width=0.03cm] (2.25,0.6) -- (3.25,0.6);\n\t\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 81,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \t\\node (img) {\\includegraphics[width=\\linewidth]{example-image}};\n    \t\\node[above=of img, node distance=0cm, yshift=-1.2cm,xshift=-4.1cm] {a) Model estimating parameters};\n    \t\\node[above=of img, node distance=0cm, yshift=-1.5cm,xshift=1cm] {b) Estimating parameters};\n    \t\\node[above=of img, node distance=0cm, yshift=-2.2cm,xshift=-2.1cm] {c) Empirical};\n    \t\\node[above=of img, node distance=0cm, yshift=-2.7cm,xshift=-3.3cm] {d) Empirical};\n    \t\\node[above=of img, node distance=0cm, yshift=-3.4cm,xshift=-1.3cm] {e) Empirical};\n    \t\\node[above=of img, node distance=0cm, yshift=-4cm,xshift=-1.3cm] {f) Empirical};\n    \t\\node[above=of img, node distance=0cm, yshift=-4.5cm,xshift=-3.9cm] {g) Empirical};\n    \t\\node[above=of img, node distance=0cm, yshift=-5.3cm,xshift=-2.2cm] {h) Empirical};\n    \t\\node[above=of img, node distance=0cm, yshift=-5.7cm,xshift=-4.2cm] {i) Empirical};\n    \t\\node[above=of img, node distance=0cm, yshift=-6.4cm,xshift=-1.8cm] {j) Empirical};\n    \t\\node[above=of img, node distance=0cm, yshift=-7.2cm,xshift=-0.7cm] {k) Empirical};\n    \t\\node[above=of img, node distance=0cm, yshift=-6.8cm,xshift=-4.5cm] {$X_1$};\n    \t\\node[above=of img, node distance=0cm, yshift=-6.5cm,xshift=-3.2cm] {$X_2$};\n    \t\\node[above=of img, node distance=0cm, yshift=-5.8cm,xshift=-3.4cm] {$X_3$};\n    \t\\node[above=of img, node distance=0cm, yshift=-5.5cm,xshift=-0.6cm] {$X_4$};\n    \t\\node[above=of img, node distance=0cm, yshift=-4.5cm,xshift=-2.2cm] {$X_5$};\n    \t\\node[above=of img, node distance=0cm, yshift=-3.7cm,xshift=-2.8cm] {$X_6$};\n    \t\\node[above=of img, node distance=0cm, yshift=-2.6cm,xshift=-1.7cm] {$X_7$};\n    \t\\node[above=of img, node distance=0cm, yshift=-1.8cm,xshift=-2.6cm] {$X_8$};\n    \t\\node[above=of img, node distance=0cm, yshift=-1.6cm,xshift=-1.5cm] {$X_9$};\n    \t\\node[above=of img, node distance=0cm, yshift=-1.5cm,xshift=-1.6cm] {$X_{10}$};\n    \t\\node[above=of img, node distance=0cm, yshift=-0.8cm,xshift=-1.2cm] {$X_{11}$};\n    \t\\node[above=of img, node distance=0cm, yshift=-0.4cm,xshift=-0.7cm] {$X_{12}$};\n    \t\\node[above=of img, node distance=0cm, yshift=-0.4cm,xshift=-0.7cm] {$X_{13}$};\n    \t\\node[above=of img, node distance=0cm, yshift=-0.8cm,xshift=-1.2cm] {$X_{14}$};\n    \t\\node[above=of img, node distance=0cm, yshift=0.2cm,xshift=-1.3cm] {$X_{15}$};\n    \t\\node[above=of img, node distance=0cm, yshift=0.7cm,xshift=-1.1cm] {$X_{16}$};\n    \t\\node[above=of img, node distance=0cm, yshift=1.6cm,xshift=-0.6cm] {$X_{17}$};\n    \t\\node[above=of img, node distance=0cm, yshift=2.4cm,xshift=-1.4cm] {$X_{18}$};\n    \t\\node[above=of img, node distance=0cm, yshift=2.6cm,xshift=-2.1cm] {$X_{19}$};\n    \t\\node[above=of img, node distance=0cm, yshift=2.3cm,xshift=-0.5cm] {$X_{20}$};\n    \t\\node[above=of img, node distance=0cm, yshift=1.4cm,xshift=-1.8cm] {$X_{21}$};\n    \t\\node[above=of img, node distance=0cm, yshift=0.6cm,xshift=-2.4cm] {$X_{22}$};\n    \t\\node[above=of img, node distance=0cm, yshift=0.1cm,xshift=-1.5cm] {$X_{23}$};\n    \t\\node[above=of img, node distance=0cm, yshift=-0.4cm,xshift=-1.3cm] {$X_{24}$};\n    \t\\node[above=of img, node distance=0cm, yshift=-1.1cm,xshift=-1.3cm] {$X_{25}$};\n    \t\\node[above=of img, node distance=0cm, yshift=-1.7cm,xshift=-0.7cm] {$X_{26}$};\n    \t\\node[above=of img, node distance=0cm, yshift=-2.7cm,xshift=-1.1cm] {$X_{27}$};\n    \t\\node[above=of img, node"
    },
    {
        "index": 82,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usepgflibrary{shapes.geometric}\n\\usetikzlibrary{chains, positioning, quotes}\n\\usetikzlibrary{shapes,snakes}\n\\usetikzlibrary{snakes}\n\\usetikzlibrary{automata}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{arrows,decorations.pathmorphing,patterns,backgrounds,positioning,fit,petri}\n\\usetikzlibrary{automata}\n\\usetikzlibrary{graphs}\n\\usetikzlibrary{shadows}\n\n\\begin{document}\n\n\\begin{tikzpicture}[thick, line cap=round, >=latex, scale=0.4]\n\\tikzset{fontscale/.style = {font=\\relsize{#1}}}\n\\draw[thin, |-|] (0, 0) -- (10, 0) node[below] {$z$};\n\\draw (1, 0) node[below] {A};\n\\draw (3, 0) node[below] {B};\n\\draw (5, 0) node[below] {C};\n\\draw (7, 0) node[below] {$z_4$};\n\\draw (9, 0) node[below] {$z_5$};\n\\draw[thin, ->] (0, 0) -- (0, 1) node[above] {$x_1$};\n\\draw[thin, ->] (2, 0) -- (2, 1) node[above] {$x_2$};\n\\draw[thin, ->] (4, 0) -- (4, 1) node[above] {$x_3$};\n\\draw[thin, ->] (8, 0) -- (8, 1) node[above] {$x_4$};\n\\draw (0, -3) node[align=center] {(a)};\n\\draw (15, 0) node[below] {A};\n\\draw (17, 0) node[below] {B};\n\\draw (19, 0) node[below] {C};\n\\draw (21, 0) node[below] {$z_4$};\n\\draw (23, 0) node[below] {$z_5$};\n\\draw[thin, ->] (15, 0) -- (15, 1) node[above] {$x_1$};\n\\draw[thin, ->] (17, 0) -- (17, 1) node[above] {$x_2$};\n\\draw[thin, ->] (19, 0) -- (19, 1) node[above] {$x_3$};\n\\draw[thin, ->] (23, 0) -- (23, 1) node[above] {$x_4$};\n\\draw[thin, ->] (15, 0) arc (180:90:3cm);\n\\draw[thin, ->] (17, 0) arc (180:90:1cm);\n\\draw[thin, ->] (17, 0) arc (0:90:1cm);\n\\draw[thin, ->] (19, 0) arc (0:90:3cm);\n\\draw (15, -3) node[align=center] {(b)\\\\$n=\\left(\\dfrac{x_1-x_2}{x_2-x_3}\\right)\\left(\\dfrac{x_3-x_4}{x_2-x_3}\\right)=\\dfrac{x_1-x_2}{x_2-x_3}\\dfrac{x_3-x_4}{x_2-x_3}$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 90,
        "tikz_code": "\\documentclass[a4paper]{article}\n\\usepackage{tikz}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}[x=1.5cm,y=1cm]\n\t\\node (212321) at (0,0) [draw,rectangle] {212321 in block 123};\n\t\\node (112321) at (-3,-1) [draw,rectangle] {112321 in block 123};\n\t\\node (232121) at (3,-1) [draw,rectangle] {232121 in block 123};\n\t\\node (112312) at (-5,-2) [draw,rectangle] {112312 in block 123};\n\t\\node (213212) at (-1,-2) [draw,rectangle] {213212 in block 123};\n\t\\node (231221) at (1,-2) [draw,rectangle] {231221 in block 123};\n\t\\node (123123) at (5,-2) [draw,rectangle] {123123 in block 123};\n\t\\node (113212) at (-5,-4) [draw,rectangle] {113212 in block 123};\n\t\\node (231212) at (-1,-4) [draw,rectangle] {231212 in block 123};\n\t\\node (321212) at (1,-4) [draw,rectangle] {321212 in block 123};\n\t\\node (112322) at (-1,-6) [draw,rectangle] {112322 in block 123};\n\t\\node (123122) at (1,-6) [draw,rectangle] {123122 in block 123};\n\t\\node (212312) at (-1,-8) [draw,rectangle] {212312 in block 123};\n\t\\node (232122) at (1,-8) [draw,rectangle] {232122 in block 123};\n\t\\node (321232) at (3,-8) [draw,rectangle] {321232 in block 123};\n\t\\node (321213) at (-3,-8) [draw,rectangle] {321213 in block 123};\n\t\\draw[->] (212321) edge node[left] {$\\varphi_1=1$} (112321);\n\t\\draw[->] (212321) edge node[right] {$\\varphi_2=0$} (232121);\n\t\\draw[->] (112321) edge node[left] {$\\varphi_3=0$} (112312);\n\t\\draw[->] (112321) edge node[right] {$\\varphi_4=1$} (213212);\n\t\\draw[->] (232121) edge node[left] {$\\varphi_5=0$} (231221);\n\t\\draw[->] (232121) edge node[right] {$\\varphi_6=1$} (123123);\n\t\\draw[->] (112312) edge node[left] {$\\kappa_1=1$} (113212);\n\t\\draw[->] (213212) edge node[right] {$\\kappa_2=1$} (231212);\n\t\\draw[->] (231221) edge node[left] {$\\kappa_3=1$} (321213);\n\t\\draw[->] (231221) edge node[right] {$\\kappa_4=1$} (321212);\n\t\\draw[->] (321213) edge node[left] {$\\kappa_5=0$} (112322);\n\t\\draw[->] (321213) edge node[right] {$\\kappa_6=1$} (123122);\n\t\\draw[->] (112322) edge node[left] {$\\kappa_7=0$} (212312);\n\t\\draw[->] (123122) edge node[right] {$\\kappa_8=1$} (232122);\n\t\\draw[->] (232122) edge node[right] {$\\kappa_9=1$} (321232);\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{amssymb,amsfonts,amsmath,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes.geometric}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=3]\n\t\t\\draw [rotate=30] (0,0) ellipse (1 and 0.2);\n\t\t\\draw [rotate=150] (0,0) ellipse (1 and 0.2);\n\t\t\\draw [rotate=270] (0,0) ellipse (1 and 0.2);\n\t\t\\draw [rotate=200] (0,0) ellipse (1 and 0.2);\n\t\t\\draw [rotate=100] (0,0) ellipse (1 and 0.2);\n\t\t\\node at (90:0.6) {$w_1$};\n\t\t\\node at (240:0.6) {$w_2$};\n\t\t\\node at (300:0.6) {$w_3$};\n\t\t\\node at (30:0.6) {$w_4$};\n\t\t\\node at (0,0) {$O$};\n\t\t\\draw[fill=black] (0,0) circle (0.03);\n\t\t\\draw (0,0) -- (160:0.4);\n\t\t\\draw (0,0) -- (180:0.4);\n\t\t\\draw (0,0) -- (200:0.4);\n\t\t\\draw (0,0) -- (220:0.4);\n\t\t\\draw (0,0) -- (300:0.4);\n\t\t\\draw (0,0) -- (320:0.4);\n\t\t\\draw (0,0) -- (340:0.4);\n\t\t\\draw (0,0) -- (40:0.4);\n\t\t\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[conference]{IEEEtran}\n\\usepackage{pgf}\n\\usepackage{pgfplots}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,patterns}\n\\usetikzlibrary{arrows,decorations.pathmorphing}\n\\usetikzlibrary{shapes,snakes}\n\\usetikzlibrary{shapes.gates.logic.US,trees,positioning,arrows}\n\\usetikzlibrary{shapes.misc}\n\\usetikzlibrary{arrows,automata, shapes.misc,shadows,spy}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[thick] (0.5,0) circle [radius = 0.5];\n\\draw[thick,fill = black] (0.5,0) node [align = center, below = -0.1cm] {$\\bot$};\n\\draw[thick] (1.5,0) circle [radius = 0.5];\n\\draw[thick,fill = black] (1.5,0) node [align = center, below = -0.1cm] {$\\bot$};\n\\draw[thick] (-0.5,2) circle [radius = 0.5];\n\\draw[thick,fill = black] (-0.5,2) node [align = center, below = -0.1cm] {$\\bot$};\n\\draw[thick] (2.5,2) circle [radius = 0.5];\n\\draw[thick,fill = black] (2.5,2) node [align = center, below = -0.1cm] {$\\bot$};\n\n\\draw[thick] (0.5,0) -- (1.5,0);\n\\draw[thick] (0.5,0.5) -- (1.5,0.5);\n\\draw[thick] (0.5,1) -- (1.5,1);\n\\draw[thick] (0.5,1.5) -- (1.5,1.5);\n\\draw[thick] (0.5,2) -- (1.5,2);\n\\draw[thick] (0.5,2.5) -- (1.5,2.5);\n\n\\draw[thick] (1.5,0) -- (2.5,0);\n\\draw[thick] (1.5,0.5) -- (2.5,0.5);\n\\draw[thick] (1.5,1) -- (2.5,1);\n\\draw[thick] (1.5,1.5) -- (2.5,1.5);\n\\draw[thick] (1.5,2) -- (2.5,2);\n\\draw[thick] (1.5,2.5) -- (2.5,2.5);\n\n\\draw[thick] (1.5,0.25) -- (1.5,-1.5);\n\\draw[thick] (2.5,0.25) -- (2.5,-1.5);\n\n\\draw[thick] (0.5,0.75) -- (0.5,-1.5);\n\\draw[thick] (1.5,0.75) -- (1.5,-1.5);\n\\draw[thick] (2.5,0.75) -- (2.5,-1.5);\n\n\\draw[dotted,thick] (-1.5,-1.8) rectangle (3.5,-0.3);\n\\draw[fill = green, fill opacity = 0.1] (-1.3,-1.8) rectangle (3.3,-0.3);\n\\draw[thick,fill = green] (-1.3,-1.5) circle [radius = 0.6];\n\\draw[thick,fill = green] (3.3,-1.5) circle [radius = 0.6];\n\\draw[thick,fill = green] (-1.3,-1.5) node [align = center, below = -0.1cm] {DeepONet};\n\\draw[thick,fill = green] (3.3,-1.5) node [align = center, below = -0.1cm] {gen.};\n\n\n\\draw[thick] (-0.5,1.75) -- (-0.5,3.5);\n\\draw[thick] (2.5,1.75) -- (2.5,3.5);\n\n\\draw[thick] (1,3.25) -- (1,4);\n\\draw[thick] (2,3.25) -- (2,4);\n\n\\draw[thick] (-0.5,2.75) -- (2.5,2.75);\n\n\\node at (1,2.25) {\\small PST two-area system};\n\n\\draw[thick,fill = green] (-0.5,2.75) circle [radius = 0.5];\n\\draw[thick,fill = red] (-0.5,2.75) node [align = center, below = -0.1cm] {$G$};\n\\draw[thick,fill = green] (2.5,2.75) circle [radius = 0.5];\n\\draw[thick,fill = red] (2.5,2.75) node [align = center, below = -0.1cm] {$G$};\n\\draw[thick,fill = red] (1,4) circle [radius = 0.5];\n\\draw[thick,fill = red] (1,4) node [align = center, below = -0.1cm] {$G$};\n\\draw[thick,fill = red] (2,4) circle [radius = 0.5];\n\\draw[thick,fill = red] (2,4) node [align = center, below = -0.1cm] {$G$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 95,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amsmath,amssymb,amsthm,fullpage,mathptmx, hyperref,dsfont,framed, graphicx, subcaption, textcomp}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes.geometric}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{scopes}\n\\usetikzlibrary{decorations.markings}\n\\tikzset{\nevery picture/.style={line width=0.8pt, >=stealth,\n                       baseline=-3pt,label distance=-3pt},\n%%%%%%%%%%  Node styles\ndotnode/.style={fill=black,circle,minimum size=2.5pt, inner sep=1pt, outer\nsep=0},\nmorphism/.style={circle,draw,thin, inner sep=1pt, minimum size=15pt,\n                 scale=0.8},\nsmall_morphism/.style={circle,draw,thin,inner sep=1pt,\n                       minimum size=10pt, scale=0.8},\ncoupon/.style={draw,thin, inner sep=1pt, minimum size=18pt,scale=0.8},\n%%%% different line styles:\nregular/.style={densely dashed},\nedge/.style={thick, dashed, draw=blue, text=black},\nboundary/.style={thick,  draw=blue, text=black},\noverline/.style={preaction={draw,line width=2mm,white,-}},\ndrinfeld center/.style={>=stealth,green!60!black, double\ndistance=1pt,text=black},\n%%%%%%% Fill styles %%%%%%%%%%%%%%%\ncell/.style={fill=black!10},\nsubgraph/.style={fill=black!30},\n%%%%%%% Mid-path arrows\nmidarrow/.style={postaction={decorate},\n                 decoration={\n                    markings,% switch on markings\n                    mark=at position #1 with {\\arrow{>}},\n                 }},\nmidarrow/.default=0.5\n}\n\n\\newcommand{\\al}{\\alpha}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node at (0,0) {$\\underbrace{\\phantom{\\bullet}}_{p_1} \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_2} \\times \\dots \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_s} \\xrightarrow{\\al} \\underbrace{\\phantom{\\bullet}}_{p_1} \\times \\underbrace{\\phantom{\\bullet}}_{p_2} \\times \\dots \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_s}$};\n\\node at (0,1) {$\\overbrace{\\phantom{\\bullet}}^{\\frac{n}{p_1}} \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_2} \\times \\dots \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_s} \\xrightarrow{\\al}\n  \\overbrace{\\phantom{\\bullet}}^{\\frac{n}{p_1}-1} \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_2} \\times \\dots \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_s}$};\n\\node at (0,2) {$\\overbrace{\\phantom{\\bullet}}^{\\frac{n}{p_1}-1} \\times\n  \\overbrace{\\phantom{\\bullet}}^{\\frac{n}{p_2}-1} \\times\n  \\dots \\times \\underbrace{\\phantom{\\bullet}}_{p_s} \\xrightarrow{\\al}\n  \\overbrace{\\phantom{\\bullet}}^{\\frac{n}{p_1}-1} \\times\n  \\overbrace{\\phantom{\\bullet}}^{\\frac{n}{p_2}-1} \\times \\dots \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_s}$};\n\\node at (0,3) {$\\overbrace{\\phantom{\\bullet}}^{\\frac{n}{p_1}-1} \\times\n  \\overbrace{\\phantom{\\bullet}}^{\\frac{n}{p_2}-1} \\times \\dots \\times\n  \\overbrace{\\phantom{\\bullet}}^{\\frac{n}{p_s}-1} \\xrightarrow{\\al}\n  \\overbrace{\\phantom{\\bullet}}^{\\frac{n}{p_1}-1} \\times\n  \\overbrace{\\phantom{\\bullet}}^{\\frac{n}{p_2}-1} \\times \\dots \\times\n  \\overbrace{\\phantom{\\bullet}}^{\\frac{n}{p_s}-1}$};\n\\node at (0,4) {$\\overbrace{\\phantom{\\bullet}}^{\\frac{n}{p_1}-1} \\times\n  \\overbrace{\\phantom{\\bullet}}^{\\frac{n}{p_2}-1} \\times \\dots \\times\n  \\overbrace{\\phantom{\\bullet}}^{\\frac{n}{p_s}-1}$};\n\\node at (0,5) {$\\underbrace{\\phantom{\\bullet}}_{p_1} \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_2} \\times \\dots \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_s}$};\n\\node at (1,6.5) {$\\underbrace{\\phantom{\\bullet}}_{p_1} \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_2} \\times \\dots \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_s}$};\n\\node at (1,7.5) {$\\underbrace{\\phantom{\\bullet}}_{p_1} \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_2} \\times \\dots \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_s}$};\n\\node at (1,8.5) {$\\underbrace{\\phantom{\\bullet}}_{p_1} \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_2} \\times \\dots \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_s}$};\n\\node at (1,9.5) {$\\underbrace{\\phantom{\\bullet}}_{p_1} \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_2} \\times \\dots \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_s}$};\n\\node at (1,10.5) {$\\underbrace{\\phantom{\\bullet}}_{p_1} \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_2} \\times \\dots \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_s}$};\n\\node at (1,11.5) {$\\underbrace{\\phantom{\\bullet}}_{p_1} \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_2} \\times \\dots \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_s}$};\n\\node at (1,12.5) {$\\underbrace{\\phantom{\\bullet}}_{p_1} \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_2} \\times \\dots \\times\n  \\underbrace{\\phantom{\\bullet}}_{p_s}$};\n\\node at (1,13.5"
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        "index": 96,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\\usepgflibrary{arrows}\n\n\\newcommand{\\scscs}{\\scriptscriptstyle}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.3,baseline=.5cm]\n\\foreach \\x/\\y/\\z in {0/2/1,1/2/2,2/1/3,3/1/4,4/1/5,5/1/6,6/0/7}\n\t{\\draw[gray] (\\x,\\y)+(-.5,-.5) rectangle ++(.5,.5);\n\t\\node at (\\x,\\y) {$\\scscs\\z$};}\n\\foreach \\x/\\y/\\num in \n\t{0/3/1,1/3/2,2/3/3,3/2/4,4/2/5,5/1/6,6/0/7}\n{\n  \\draw (\\x,\\y) +(-0.5,-0.5) rectangle ++(0.5,0.5);\n  \\draw (\\x,\\y) node {$\\scscs\\num$};\n}\n\\draw[thick] (0,3) -- ++(4,0) -- ++(0,-2) -- ++(2,0) -- ++(0,-1) -- ++(-4,0) -- ++(0,2) -- ++(2,0) -- ++(0,1) -- ++(-2,0) -- cycle;\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 97,
        "tikz_code": "\\documentclass[reqno,11pt]{amsart}\n\\usepackage{amsthm,amsmath,amssymb,amsfonts,bbm}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1,>=latex]\n\\node[circle,fill,inner sep=1pt,color=black] (A) at (0,0) {};\n\\node (B) at (1.5,2.6) {};\n\\node (C) at (1.5,-2.6) {};\n\\draw[dotted] (A) to (B);\n\\draw[dotted] (A) to (C);\n\n\\node (D) at (3.4,3.4) {};\n\\node (E) at (3.4,-3.4) {};\n\\draw[dotted] (A) to (D);\n\\draw[dotted] (A) to (E);\n\n\\node (F) at (-1.5,2.6) {};\n\\node (G) at (-1.5,-2.6) {};\n\\draw[dotted] (A) to (F);\n\\draw[dotted] (A) to (G);\n\n\n\\node (H) at (4.5,3.4) {};\n\\node (I) at (4.5,-3.4) {};\n\\draw[dotted] (A) to (H);\n\\draw[dotted] (A) to (I);\n\n\\node (J) at (-3.4,3.4) {};\n\\node (K) at (-3.4,-3.4) {};\n\\draw[dotted] (A) to (J);\n\\draw[dotted] (A) to (K);\n\n\\node (L) at (5.5,2.6) {};\n\\node (M) at (5.5,-2.6) {};\n\\draw[dotted] (A) to (L);\n\\draw[dotted] (A) to (M);\n\n\\node (N) at (-5.5,2.6) {};\n\\node (O) at (-5.5,-2.6) {};\n\\draw[dotted] (A) to (N);\n\\draw[dotted] (A) to (O);\n\n\\node (P) at (5.5,3.4) {};\n\\node (Q) at (5.5,-3.4) {};\n\\draw[dotted] (A) to (P);\n\\draw[dotted] (A) to (Q);\n\n\n\\node (R) at (-5.5,3.4) {};\n\\node (S) at (-5.5,-3.4) {};\n\\draw[dotted] (A) to (R);\n\\draw[dotted] (A) to (S);\n\n\\draw[black!60,fill=white,opacity=0.7] (B) to (C) to (D) to (E) to (F) to (G) to (H) to (I) to (J) to (K) to (L) to (M) to (N) to (O) to (P) to (Q) to (R) to (S) to cycle;\n\\node (a) at (0.6,3.6) {\\small{$\\alpha$}};\n\\node (b) at (0.6,-3.6) {\\small{$-\\alpha$}};\n\\node (c) at (3.6,0.6) {\\small{$\\alpha +\\beta$}};\n\\node (d) at (-3.6,0.6) {\\small{$-\\alpha$}};\n\\node (e) at (3.6,-0.6) {\\small{$-\\beta$}};\n\\node (f) at (-3.6,-0.6) {\\small{$\\beta$}};\n\\node (g) at (2.5,3.6) {\\small{$\\beta$}};\n\\node (h) at (2.5,-3.6) {\\small{$-\\beta$}};\n\\node (i) at (-2.5,3.6) {\\small{$\\beta$}};\n\\node (j) at (-2.5,-3.6) {\\small{$-\\beta$}};\n\n\\draw[very thick,|->] (A) to (B);\n\\draw[very thick,|->] (A) to (C);\n\\draw[very thick,|->] (A) to (D);\n\\draw[very thick,|->] (A) to (E);\n\\draw[very thick,|->] (A) to (F);\n\\draw[very thick,|->] (A) to (G);\n\\draw[very thick,|->] (A) to (H);\n\\draw[very thick,|->] (A) to (I);\n\\draw[very thick,|->] (A) to (J);\n\\draw[very thick,|->] (A) to (K);\n\\draw[very thick,|->] (A) to (L);\n\\draw[very thick,|->] (A) to (M);\n\\draw[very thick,|->] (A) to (N);\n\\draw[very thick,|->] (A) to (O);\n\\draw[very thick,|->] (A) to (P);\n\\draw[very thick,|->] (A) to (Q);\n\\draw[very thick,|->] (A) to (R);\n\\draw[very thick,|->] (A) to (S);\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 98,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath, amsthm, amssymb, tikz, hyperref, enumerate}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8]\n\\draw (0,0) rectangle (4,4); \\draw[fill=lightgray] (2,0)--(2,4)--(4,4)--(4,0)--(2,0);\n\\draw[fill=lightgray] (0,1.6)--(4,1.6)--(4,4)--(0,4)--(0,1.6);\n\\draw[fill=lightgray] (0,0.4)--(4,0.4)--(4,1.6)--(0,1.6)--(0,0.4);\n\\draw (2,-0.5) node {$-\\frac{\\pi}{2}<\\frac{\\pi}{l}<\\frac{\\pi}{2}$};\n\\draw (2,5.5) node {$\\theta_{l}$};\n\\draw (2,3) node {$\\frac{\\pi}{2}$};\n\\draw (2,0.8) node {$0$};\n\\draw (2,1.1) node {$0$};\n\\draw (2,1.4) node {$0$};\n\\draw (2,1.7) node {$0$};\n\\draw (2,2) node {$0$};\n\\draw (2,2.3) node {$0$};\n\\draw (2,2.6) node {$0$};\n\\draw (2,2.9) node {$\\frac{\\pi}{2}$};\n\\draw (2,3.5) node {$-\\frac{\\pi}{2}$};\n\\draw (2,4.5) node {$\\frac{\\pi}{2}$};\n\\draw (2,5) node {$\\frac{\\pi}{2}$};\n\n\\draw (6,0) rectangle (10,4); \\draw[fill=lightgray] (8,0)--(8,4)--(10,4)--(10,0)--(8,0);\n\\draw[fill=lightgray] (6,1.6)--(10,1.6)--(10,4)--(6,4)--(6,1.6);\n\\draw[fill=lightgray] (6,0.4)--(10,0.4)--(10,1.6)--(6,1.6)--(6,0.4);\n\\draw (8,-0.5) node {$-\\frac{\\pi}{2}<\\frac{\\pi}{l}<\\frac{\\pi}{2}$};\n\\draw (8,5.5) node {$\\theta_{l}$};\n\\draw (8,3) node {$\\frac{\\pi}{2}$};\n\\draw (8,0.8) node {$0$};\n\\draw (8,1.1) node {$0$};\n\\draw (8,1.4) node {$0$};\n\\draw (8,1.7) node {$0$};\n\\draw (8,2) node {$0$};\n\\draw (8,2.3) node {$0$};\n\\draw (8,2.6) node {$0$};\n\\draw (8,2.9) node {$\\frac{\\pi}{2}$};\n\\draw (8,3.5) node {$-\\frac{\\pi}{2}$};\n\\draw (8,4.5) node {$\\frac{\\pi}{2}$};\n\\draw (8,5) node {$\\frac{\\pi}{2}$};\n\n\\draw (12,0) rectangle (16,4); \\draw[fill=lightgray] (14,0)--(14,4)--(16,4)--(16,0)--(14,0);\n\\draw[fill=lightgray] (12,1.6)--(16,1.6)--(16,4)--(12,4)--(12,1.6);\n\\draw[fill=lightgray] (12,0.4)--(16,0.4)--(16,1.6)--(12,1.6)--(12,0.4);\n\\draw (14,-0.5) node {$-\\frac{\\pi}{2}<\\frac{\\pi}{l}<\\frac{\\pi}{2}$};\n\\draw (14,5.5) node {$\\theta_{l}$};\n\\draw (14,3) node {$\\frac{\\pi}{2}$};\n\\draw (14,0.8) node {$0$};\n\\draw (14,1.1) node {$0$};\n\\draw (14,1.4) node {$0$};\n\\draw (14,1.7) node {$0$};\n\\draw (14,2) node {$0$};\n\\draw (14,2.3) node {$0$};\n\\draw (14,2.6) node {$0$};\n\\draw (14,2.9) node {$\\frac{\\pi}{2}$};\n\\draw (14,3.5) node {$-\\frac{\\pi}{2}$};\n\\draw (14,4.5) node {$\\frac{\\pi}{2}$};\n\\draw (14,5) node {$\\frac{\\pi}{2}$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{pgfplots}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{axis}[\n    axis lines = left,\n    xlabel = Bias $b$,\n    ylabel = {$z_i$},\n    xmin = -4, xmax = 4,\n    ymin = -21, ymax = 10,\n    xtick = {-4, -2, 0, 2, 4},\n    ytick = {-20, -10, 0, 10},\n    ymajorgrids=true,\n    xmajorgrids=true,\n    grid style=dashed,\n]\n\n\\addplot[\n    fill=red!20,\n    fill opacity=0.7,\n    only marks,\n    ]\n    coordinates {\n    (-1, -16)\n    (-1.5, -13)\n    (1.5, -5)\n    (1, -2)\n    (-3, 1)\n    (-2, 7)\n    };\n    \n\\addplot[\n    fill=green!20,\n    fill opacity=0.7,\n    only marks,\n    ]\n    coordinates {\n    (2, 2)\n    (3, 9)\n    (3.5, 6)\n    (-3.5, 0)\n    (-3, -3)\n    (-2, -10)\n    };\n    \n\\draw [dashed, red, thick, domain=-3:3, samples=200] \nplot (\\x, {2*abs(exp(\\x)-0.5)});\n\n\\draw [<->, green, thick] (axis cs: 2.5, -10) -- (axis cs: -3.5, -10);\n\n\\node[above, green] at (axis cs: 2.5, -10) {Usable range is constrained};\n\\node[above, green] at (axis cs: -3.5, -10) {Precision and range of dataset, reagardless of bias};\n\n\\node[above, red] at (axis cs: -1, -20) {Overflows};\n\\node[above, red] at (axis cs: -1.5, -17) {Overflows to zero};\n\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 104,
        "tikz_code": "\\documentclass[journal]{IEEEtran}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{shapes,snakes}\n\\usetikzlibrary{backgrounds,fit,decorations.pathreplacing}\n\\usepackage{color}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.9]\n\t\\node[rectangle,draw,thick] (1) at (0,3) {User Data};\n\t\\node[rectangle,draw,thick] (2) at (0,2) {$\\dots$};\n\t\\node[rectangle,draw,thick] (3) at (0,1) {$\\dots$};\n\t\\node[rectangle,draw,thick] (4) at (0,0) {Message Splitter};\n\t\\node[rectangle,draw,thick] (5) at (1.5,3) {$B_k$};\n\t\\node[rectangle,draw,thick] (6) at (1.5,2) {$\\dots$};\n\t\\node[rectangle,draw,thick] (7) at (1.5,1) {$B_{p,k}$};\n\t\\node[rectangle,draw,thick] (8) at (1.5,0) {$\\vdots$};\n\t\\node[rectangle,draw,thick] (9) at (1.5,-1) {$\\vdots$};\n\t\\node[rectangle,draw,thick] (10) at (1.5,-2) {$B_{p,k}$};\n\t\\node[rectangle,draw,thick] (11) at (1.5,-3) {$\\vdots$};\n\t\\node[rectangle,draw,thick] (12) at (1.5,-4) {$B_k$};\n\t\\node[rectangle,draw,thick] (13) at (1.5,-5) {$\\dots$};\n\t\\node[rectangle,draw,thick] (14) at (1.5,-6) {Message Splitter};\n\t\\node[rectangle,draw,thick] (15) at (4.5,1.5) {Encoder};\n\t\\node[rectangle,draw,thick] (16) at (4.5,-1.5) {Decoder};\n\t\\node[rectangle,draw,thick] (17) at (6,3.5) {Linear Pre-coder};\n\t\\node[rectangle,draw,thick] (18) at (6,-0.5) {Linear Encoder};\n\t\\node[] (19) at (7,3.5) {$\\dots$};\n\t\\node[] (20) at (7,-0.5) {$\\dots$};\n\t\\draw[thick,->,>=stealth] (1) -- (2);\n\t\\draw[thick,->,>=stealth] (2) -- (3);\n\t\\draw[thick,->,>=stealth] (3) -- (4);\n\t\\draw[thick,->,>=stealth] (5) -- (4);\n\t\\draw[thick,->,>=stealth] (5) -- (6);\n\t\\draw[thick,->,>=stealth] (7) -- (6);\n\t\\draw[thick,->,>=stealth] (8) -- (7);\n\t\\draw[thick,->,>=stealth] (9) -- (8);\n\t\\draw[thick,->,>=stealth] (10) -- (9);\n\t\\draw[thick,->,>=stealth] (11) -- (10);\n\t\\draw[thick,->,>=stealth] (12) -- (11);\n\t\\draw[thick,->,>=stealth] (13) -- (12);\n\t\\draw[thick,->,>=stealth] (14) -- (13);\n\t\\draw[thick,->,>=stealth] (1) to [out=-90,in=90] (14);\n\t\\draw[thick,->,>=stealth] (2) to [out=-90,in=90] (14);\n\t\\draw[thick,->,>=stealth] (3) to [out=-90,in=90] (14);\n\t\\draw[thick,->,>=stealth] (4) to [out=-90,in=90] (14);\n\t\\draw[thick,->,>=stealth] (5) to [out=90,in=90] (4);\n\t\\draw[thick,->,>=stealth] (5) to [out=-90,in=-90] (4);\n\t\\draw[thick,->,>=stealth] (6) to [out=90,in=90] (4);\n\t\\draw[thick,->,>=stealth] (6) to [out=-90,in=-90] (4);\n\t\\draw[thick,->,>=stealth] (7) to [out=90,in=90] (4);\n\t\\draw[thick,->,>=stealth] (7) to [out=-90,in=-90] (4);\n\t\\draw[thick,->,>=stealth] (8) to [out=90,in=90] (4);\n\t\\draw[thick,->,>=stealth] (8) to [out=-90,in=-90] (4);\n\t\\draw[thick,->,>=stealth] (9) to [out=90,in=90] (4);\n\t\\draw[thick,->,>=stealth] (9) to [out=-90,in=-90] (4);\n\t\\draw[thick,->,>=stealth] (10) to [out=90,in=90] (4);\n\t\\draw[thick,->,>=stealth] (10) to [out=-90,in=-90] (4);\n\t\\draw[thick,->,>=stealth] (11) to [out=90,in=90] (4);\n\t\\draw[thick,->,>=stealth] (11) to [out=-90,in=-90] (4);\n\t\\draw[thick,->,>=stealth] (12) to [out=90,in=90] (4);\n\t\\draw[thick,->,>=stealth] (12) to [out=-90,in=-90] (4);\n\t\\draw[thick,->,>=stealth] (13) to [out=90,in=90] (4);\n\t\\draw[thick,->,>=stealth] (13) to [out=-90,in=-90] (4);\n\t\\draw[thick,->,>=stealth] (14) to [out=90,in=9"
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{\nadjustbox,\namscd,\namsmath,\namssymb,\namsthm,\narray,\nauthblk,\nbbm,\nboldline,\nbooktabs,\ncalc,\ncite,\ncleveref,\ncolor,\ncolortbl,\ndiagbox,\nenumerate,\nepsfig,\nfancyvrb,\nfloat,\nfp,\ngraphicx,\nkeyval,\nlistings,\nlongtable,\npdflscape,\nmakecell,\nmathtools,\nmulticol,\nmultirow,\npict2e,\npifont,\nsubfig,\ntabularx,\ntikz,\ntikz-cd,\nxcolor,\nxspace,\n}\n\\usetikzlibrary{arrows,calc,decorations,decorations.pathreplacing}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5]\n\n        \\def\\a{0.6};\n        \\def\\b{1.5};\n        \\def\\c{0.8};\n        \\def\\d{0.4};\n        \n        \\draw[fill=blue!20, draw=none] (-\\a,0) rectangle (\\a,\\b);\n        \\draw[fill=orange!20, draw=none] (-\\b,0) rectangle (\\b,\\b);\n        \\draw[fill=green!20, draw=none] (-\\a,\\a) rectangle (\\a,\\b);\n        \\draw[fill=cyan!20, draw=none] (-\\a,\\b) rectangle (\\a,\\d);\n        \\draw[fill=gray!20, draw=none] (-\\a,-\\a) rectangle (\\a,\\a);\n        \\draw[fill=orange!20, draw=none] (-\\b,-\\a) rectangle (\\b,\\a);\n        \\draw[fill=green!20, draw=none] (-\\a,-\\b) rectangle (\\a,\\- \\b);\n        \n        \\draw[-latex,thick] (-\\a,0) to (\\a,0);\n        \\draw[-latex,thick] (0,-\\a) to (0,\\b);\n        \\draw[-latex,thick] (-\\a,\\a) to (\\a,\\a);\n        \\draw[-latex,thick] (-\\b,\\a) to (\\b,\\a);\n        \\draw[-latex,thick] (-\\a,-\\a) to (\\a,-\\a);\n        \\draw[-latex,thick] (-\\a,-\\b) to (\\a,-\\b);\n        \\draw[-latex,thick] (-\\b,-\\a) to (\\b,-\\a);\n        \\draw[-latex,thick] (0,-\\b) to (0,\\b);\n        \n        \\node[circle,draw,fill=orange!20,text=black,minimum size=1.5cm] at (0,0) (S) {$X=F(X)$};\n        \\node[circle,draw,fill=green!20,text=black,minimum size=1.5cm] at (\\b,0) (P) {$X=P(X)$};\n        \\node[circle,draw,fill=blue!20,text=black,minimum size=1.5cm] at (-\\b,0) (M) {$X=M(X)$};\n        \n        \\node[circle,draw,fill=orange!20,text=black,minimum size=1.5cm] at (0,0) (S) {$X=F(X)$};\n        \\node[circle,draw,fill=green!20,text=black,minimum size=1.5cm] at (\\b,0) (P) {$X=P(X)$};\n        \\node[circle,draw,fill=blue!20,text=black,minimum size=1.5cm] at (-\\b,0) (M) {$X=M(X)$};\n        \\node[circle,draw,fill=cyan!20,text=black,minimum size=1.5cm] at (0,\\b) (V) {$X=V(X)$};\n        \n        \\draw[-latex,thick] (S) to[bend left] node[above] {$\\epsilon\\to 0$} (P);\n        \\draw[-latex,thick] (S) to[bend right] node[below] {$\\epsilon\\to 0$} (M);\n        \\draw[-latex,thick] (M) to[bend right] node[below] {$\\epsilon\\to 0$} (P);\n        \\draw[-latex,thick] (P) to[bend right] node[right] {$\\epsilon\\to 0$} (S);\n        \n        \\draw[-latex,thick] (M) to[bend right] node[left] {$\\lambda\\to 0$} (V);\n        \\draw[-latex,thick] (V) to[bend right] node[above] {$\\lambda\\to 0$} (S);\n        \\draw[-latex,thick] (P) to[bend right] node[below] {$\\lambda\\to 0$} (M);\n        \\draw[-latex,thick] (S) to[bend right] node[right] {$\\lambda\\to 0$} (P);\n        \n        \n    \\end{tikzpicture}\n\n\\end{document}"
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        "index": 112,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{calc,angles,positioning,intersections}\n\\begin{document}\n\\begin{center}\n\\begin{tikzpicture}\n\n\\draw[ultra thick,->,>=latex](0,0)--(3,0)node[below]{$x$};\n\\draw[ultra thick,->,>=latex](0,0)--(0,3)node[right]{$y$};\n\\draw[ultra thick,->,>=latex](0,0)--(-1.5,1.5)node[above]{$z$};\n\\draw[thick,->,>=latex,red](0,0)--(3,0)node[right]{$\\mathbf{r}$};\n\\draw[thick,->,>=latex,red](0,0)--(2,2)node[above]{$\\mathbf{r}_2$};\n\\draw[thick,->,>=latex,red](0,0)--(1,3)node[above]{$\\mathbf{r}_1$};\n\n\\draw[blue,dashed,ultra thick,->,>=latex](0,0)--($(3,0)+0.75*(1,3)$)node[left]{$\\mathbf{p}_1$};\n\\draw[blue,dashed,ultra thick,->,>=latex](0,0)--($(2,2)+0.75*(1,3)$)node[left]{$\\mathbf{p}_2$};\n\\draw[blue,dashed,ultra thick,->,>=latex](0,0)--($(1,3)+0.75*(1,3)$)node[above]{$\\mathbf{p}_3$};\n\n\\node(O)at(0,0){};\n\\coordinate(P)at(3,0);\n\\coordinate(Q)at(2,2);\n\\coordinate(R)at(1,3);\n\\coordinate(A)at(30:2.5);\n\n\\pic [draw,angle radius=20mm,\"$\\Delta\\alpha$\",angle eccentricity=1.3] {angle = P--O--A};\n\\pic [draw,angle radius=20mm,\"$\\Delta\\beta$\",angle eccentricity=1.3] {angle = Q--O--A};\n\\pic [draw,angle radius=20mm,\"$\\Delta\\gamma$\",angle eccentricity=1.3] {angle = R--O--A};\n\\end{tikzpicture}\n\\end{center}\n\\end{document}"
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        "tikz_code": "\\documentclass[a4paper]{amsart}\n\\usepackage{txfonts, amsmath,amstext,amsthm,amscd,amsopn,verbatim,amssymb, amsfonts, amsrefs}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix}\n\\usetikzlibrary{shapes}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{calc,3d}\n\\usetikzlibrary{decorations,decorations.pathmorphing}\n\\usetikzlibrary{through}\n\\tikzset{ext/.style={circle, draw,inner sep=1pt},int/.style={circle,draw,fill,inner sep=1pt},nil/.style={inner sep=1pt}}\n\\tikzset{exte/.style={circle, draw,inner sep=3pt},inte/.style={circle,draw,fill,inner sep=3pt}}\n\\tikzset{diagram/.style={matrix of math nodes, row sep=3em, column sep=2.5em, text height=1.5ex, text depth=0.25ex}}\n\\tikzset{diagram2/.style={matrix of math nodes, row sep=0.5em, column sep=0.5em, text height=1.5ex, text depth=0.25ex}}\n\\usepackage{tikz-cd}\n\n\\begin{document}\n\n\\begin{tikzpicture}[baseline=-.65ex,scale=.7]\n\\draw[gray, dashed] (-.4,-1.3) -- (0,.3)--(1,-1.3);\n\\draw[gray, dashed] (.4,-1.3) -- (0,.3)--(-1,-1.3);\n\\draw[gray, dashed] (-.4,-1.3) -- (-.8,-2.3)--(.8,-2.3) -- cycle;\n\\draw (0,-1.3) node[int]{};\n\\draw (0,-.6) node[int]{};\n\\draw (-.4,-1.3) -- (-.8,-2);\n\\draw (-.4,-1.3) -- (0,-.6);\n\\draw (-.4,-1.3) -- (.4,-1.3);\n\\draw (-.4,-1.3) -- (-1,-1.3);\n\\draw (0,-.6) -- (-.8,-1.9);\n\\draw[dashed] (0,-.6) -- (-.4,-1.3);\n\\draw (.4,-1.3) -- (0,-.6);\n\\draw (.4,-1.3) -- (1,-1.3);\n\\draw (.4,-1.3) -- (.8,-2);\n\\draw (0,-1.3) node[ext]{};\n\\draw (0,-.6) node[ext]{};\n\\draw[dotted] (-.4,-1.3)+(0,0)--+(.22,-.22);\n\\draw (-.8,-2.3)+(0.22,-.22) node[int]{};\n\\draw (-.8,-2.3)+(-0.22,-.22) node[ext]{};\n\\draw (0,-.6)+(0,.22) node[ext]{};\n\\draw (0,-.6)+(-0.22,.22) node[ext]{};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 114,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node at (-2,0) {$\\begin{aligned}\\dot{x}_{1,i} &= \\mu x_{1,i} - \\sigma_{1,i} x_{2,i} \\\\\n\\dot{x}_{2,i} &= \\theta_{1,i} x_{1,i} - \\theta_{2,i} x_{2,i} \\\\\n\\end{aligned}$};\n\\node at (2.5,0) {$\\begin{aligned}\\dot{x}_{1,i} &= x_{1,i} \\\\\n\\dot{x}_{2,i} &= x_{2,i} + \\sigma_{2,i} y_{i,i} \\\\\n\\end{aligned}$};\n\\node at (-7,0) {$\\begin{aligned}\\dot{x}_{1,i} &= \\mu x_{1,i} - \\sigma_{1,i} x_{2,i} \\\\\n\\dot{x}_{2,i} &= x_{2,i} \\\\\n\\end{aligned}$};\n\\draw[->] (-4,0) -- node[midway,above] {book-to-market} (1,0);\n\\draw[->] (-1,0) -- node[midway,above] {normalization} (5,0);\n\\draw[->] (-7,0.5) -- node[midway,right] {$y_{i,i}$} (-7,-0.5);\n\\draw[->] (-4,-0.5) -- node[midway,left] {$x_{1,i}$} (-4,0.5);\n\\draw[->] (2,-0.5) -- node[midway,right] {$x_{2,i}$} (2,0.5);\n\\draw[->] (5,-0.5) -- node[midway,right] {$y_{i,i}$} (5,0.5);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 115,
        "tikz_code": "\\documentclass[11pt,letterpaper]{amsart}\n\\usepackage{amsmath, amssymb, amscd, amsfonts, amsthm, mathrsfs, graphicx}\n\\usepackage{tikz-cd}\n\\usepackage{color}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[rounded corners=30pt, purple!70, line width=30pt] (0, 1) -- (2, 1) -- (2, 3.5) -- (3, 3.5) -- (3, 1) -- (6, 1) -- (6, -1.5) -- (3, -1.5) -- (3, -3.5) -- (2, -3.5) -- (2, -1.5) -- (0, -1.5) -- (0, 1);\n\\draw[rounded corners=30pt, green!60!black!70, line width=30pt] (0.5, 1) -- (2, 1) -- (2, 3) -- (5, 3) -- (5, 1) -- (6, 1) -- (6, -1) -- (5, -1) -- (5, -3) -- (2, -3) -- (2, -1) -- (0.5, -1) -- (0.5, 1);\n\\draw[rounded corners=30pt, cyan!70, line width=30pt] (0, 1) -- (2, 1) -- (2, 3.5) -- (3, 3.5) -- (3, 1) -- (4, 1) -- (4, -1.5) -- (3, -1.5) -- (3, -3.5) -- (2, -3.5) -- (2, -1.5) -- (0, -1.5) -- (0, 1);\n\\draw[rounded corners=30pt, blue!60!black!70, line width=30pt] (0, 1) -- (2, 1) -- (2, 3.5) -- (3, 3.5) -- (3, 1) -- (6, 1) -- (6, -1.5) -- (3, -1.5) -- (3, -3.5) -- (2, -3.5) -- (2, -1.5) -- (0, -1.5) -- (0, 1);\n\\draw (-0.5, 1.1) node {$\\partial G$};\n\\draw (5.5, 0) ellipse (1.5cm and 0.5cm);\n\\draw (5.5, 0) ellipse (1cm and 0.3cm);\n\\draw (7, 0) node {$W_1$};\n\\draw (5.5, 2.5) ellipse (1.2cm and 0.6cm);\n\\draw (5.5, 2.5) ellipse (0.7cm and 0.4cm);\n\\draw (8, 2.5) node {$W_2$};\n\\draw (5.5, -2) ellipse (1cm and 0.5cm);\n\\draw (5.5, -2) ellipse (0.7cm and 0.3cm);\n\\draw (7, -2) node {$W_i$};\n\\draw (9, 0) node {$\\Omega$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 116,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amsfonts,bm}\n\\usepackage{amssymb}\n\\usepackage{colortbl}\n\\usepackage{tkz-euclide}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.14}\n\\usetikzlibrary{positioning,calc,fadings}\n\\usetikzlibrary{backgrounds}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n                \\node[] (D3C2A1) {\\includegraphics[width=.07\\linewidth]{example-image}};\n                \\node[below = 0.2cm of D3C2A1] (D3C2A2) {\\includegraphics[width=.07\\linewidth]{example-image}};\n                \\node[left = 0.05cm of D3C2A1] {\\color{white}\\small 1};\n                \\node[left = 0.05cm of D3C2A2] {\\color{white}\\small 2};\n                \\node[right = 0.05cm of D3C2A1] {\\color{white}\\small 3};\n                \\node[right = 0.05cm of D3C2A2] {\\color{white}\\small 4};\n                \\node[right = 0.05cm of D3C2A1] (D3C2A3) {\\includegraphics[width=.07\\linewidth]{example-image}};\n                \\node[below = 0.2cm of D3C2A3] (D3C2A4) {\\includegraphics[width=.07\\linewidth]{example-image}};\n                \\node[left = 0.05cm of D3C2A3] {\\color{white}\\small 1};\n                \\node[left = 0.05cm of D3C2A4] {\\color{white}\\small 2};\n                \\node[right = 0.05cm of D3C2A3] {\\color{white}\\small 3};\n                \\node[right = 0.05cm of D3C2A4] {\\color{white}\\small 4};\n                \\node[right = 0.05cm of D3C2A3] (D3C2A5) {\\includegraphics[width=.07\\linewidth]{example-image}};\n                \\node[below = 0.2cm of D3C2A5] (D3C2A6) {\\includegraphics[width=.07\\linewidth]{example-image}};\n                \\node[left = 0.05cm of D3C2A5] {\\color{white}\\small 1};\n                \\node[left = 0.05cm of D3C2A6] {\\color{white}\\small 2};\n                \\node[right = 0.05cm of D3C2A5] {\\color{white}\\small 3};\n                \\node[right = 0.05cm of D3C2A6] {\\color{white}\\small 4};\n                \\node[right = 0.05cm of D3C2A5] (D3C2A7) {\\includegraphics[width=.07\\linewidth]{example-image}};\n                \\node[below = 0.2cm of D3C2A7] (D3C2A8) {\\includegraphics[width=.07\\linewidth]{example-image}};\n                \\node[left = 0.05cm of D3C2A7] {\\color{white}\\small 1};\n                \\node[left = 0.05cm of D3C2A8] {\\color{white}\\small 2};\n                \\node[right = 0.05cm of D3C2A7] {\\color{white}\\small 3};\n                \\node[right = 0.05cm of D3C2A8] {\\color{white}\\small 4};\n                \\node[right = 0.05cm of D3C2A7] (D3C2A9) {\\includegraphics[width=.07\\linewidth]{example-image}};\n                \\node[below = 0.2cm of D3C2A9] (D3C2A10) {\\includegraphics[width=.07\\linewidth]{example-image}};\n                \\node[left = 0.05cm of D3C2A9] {\\color{white}\\small 1};\n                \\node[left = 0.05cm of D3C2A10] {\\color{white}\\small 2};\n                \\node[right = 0.05cm of D3C2A9] {\\color{white}\\small 3};\n                \\node[right = 0.05cm of D3C2A10] {\\color{white}\\small 4};\n                \\node[right = 0.05cm of D3C2A9] (D3C2A11) {\\includegraphics[width=.07\\linewidth]{example-image}};\n                \\node[below = 0.2cm of D3C2A11] (D3C2A12) {\\includegraphics[width=.07\\linewidth]{example-image}};\n                \\node[left = 0.05cm of D3C2A11] {\\color{white}\\small 1};\n                \\node[left = 0.05cm of D3C2A12] {\\color{white}\\small 2};\n                \\node[right = 0.05cm of D3C2A11] {\\color{white}\\small 3};\n                \\node[right = 0.05cm of D3C2A12] {\\color{white}\\small 4};\n            \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 117,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{tikz}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8]\n\\node (A) at (0,0) {$T_{(1,2,3)}$};\n\\node (B) at (-1,-1.5) {$T_{(1,2,3)}$};\n\\node (C) at (-1,-3) {$T_{(1,2,3)}$};\n\\node (D) at (1,-1.5) {$T_{(2,3,1)}$};\n\\node (E) at (1,-3) {$T_{(1,3,2)}$};\n\\node (F) at (1,-4.5) {$T_{(1,3,2)}$};\n\\node (G) at (3,-3) {$T_{(3,1,2)}$};\n\\node (H) at (3,-4.5) {$T_{(3,1,2)}$};\n\\node (I) at (4,-4.5) {$T_{(3,1,2)}$};\n\\node (J) at (5,-4.5) {$T_{(3,1,2)}$};\n\\node (K) at (5,-6) {$T_{(3,1,2)}$};\n\\node (L) at (7,-4.5) {$T_{(3,2,1)}$};\n\\node (M) at (7,-6) {$T_{(3,2,1)}$};\n\\node (N) at (8,-6) {$T_{(3,2,1)}$};\n\\node (O) at (9,-6) {$T_{(3,2,1)}$};\n\\node (P) at (10,-6) {$T_{(3,2,1)}$};\n\\node (Q) at (11,-6) {$T_{(3,2,1)}$};\n\n\\draw[->] (A.south) -- (B.north) node[left] at (0.1,-1.35) {$0,2$};\n\\draw[->] (A.south) -- (C.north) node[left] at (-0.9,-1.35) {$0,2$};\n\\draw[->] (A.south) -- (D.north) node[left] at (1,-1.35) {$0,2$};\n\\draw[->] (A.south) -- (E.north) node[left] at (1,-2.85) {$0,3$};\n\\draw[->] (A.south) -- (G.north) node[left] at (3.9,-2.85) {$7,3$};\n\\draw[->] (A.south) -- (H.north) node[left] at (4.9,-2.85) {$7,3$};\n\\draw[->] (A.south) -- (I.north) node[left] at (6,-2.85) {$7,3$};\n\\draw[->] (A.south) -- (J.north) node[left] at (7,-2.85) {$7,3$};\n\\draw[->] (A.south) -- (K.north) node[left] at (8.9,-2.85) {$8,3$};\n\\draw[->] (A.south) -- (L.north) node[left] at (9.9,-2.85) {$8,3$};\n\\draw[->] (A.south) -- (M.north) node[left] at (10.9,-2.85) {$8,3$};\n\\draw[->] (A.south) -- (N.north) node[left] at (11.9,-2.85) {$8,3$};\n\n\n\\node (A1) at (0,-6) {$\\textcolor{blue}{T_{(1,3,2)}}$};\n\\node (B1) at (-1,-7.5) {$\\textcolor{blue}{T_{(1,3,2)}}$};\n\\node (C1) at (-1,-9) {$\\textcolor{blue}{T_{(1,3,2)}}$};\n\\node (D1) at (1,-7.5) {$\\textcolor{blue}{T_{(3,1,2)}}$};\n\\node (E1) at (1,-9) {$\\textcolor{blue}{T_{(3,1,2)}}$};\n\\node (F1) at (1,-10.5) {$\\textcolor{blue}{T_{(3,1,2)}}$};\n\\node (G1) at (3,-7.5) {$\\textcolor{blue}{T_{(3,2,1)}}$};\n\\node (H1) at (3,-9) {$\\textcolor{blue}{T_{(3,2,1)}}$};\n\\node (I1) at (4,-9) {$\\textcolor{blue}{T_{(3,2,1)}}$};\n\\node (J1) at (5,-9) {$\\textcolor{blue}{T_{(3,2,1)}}$};\n\\node (K1) at (5,-10.5) {$\\textcolor{blue}{T_{(3,2,1)}}$};\n\\node (L1) at (7,-9) {$\\textcolor{blue}{T_{(3,2,1)}}$};\n\\node (M1) at (7,-10.5) {$\\textcolor{blue}{T_{(3,2,1)}}$};\n\\node (N1) at (8,-10.5) {$\\textcolor{blue}{T_{(3,2,1)}}$};\n\\node (O1) at (9,-10.5) {$\\textcolor{blue}{T_{(3,2,1)}}$};\n\\node (P1) at (10,-10.5) {$\\textcolor{blue}{T_{(3,2,1)}}$};\n\\node (Q1) at (11,-10.5) {$\\textcolor{blue}{T_{(3,2,1)}}$};\n\n\\draw[->] (A1.south) -- (B1.north) node[left] at (0.1,-8.35) {$0,2$};\n\\draw[->] (A1.south) -- (C1.north) node[left] at (-0.9,-8.35) {$0,2$};\n\\draw[->] (A1.south) -- (D1.north) node[left] at (1,-8.35) {$0,3$};\n\\draw[->] (A1.south) -- (E1.north) node[left] at (1,-9.85) {$0,3$};\n"
    },
    {
        "index": 118,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amssymb,mathrsfs,graphicx,enumerate}\n\\usepackage{amsmath,amsfonts,amssymb,amscd,amsthm,bbm}\n\\usepackage{colortbl}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5]\n\n\\fill[fill=gray!10,domain=-2.5:2.5,smooth,variable=\\x]\nplot({\\x},{0.2*\\x*\\x})--\nplot({\\x},{0.4*\\x*\\x*\\x})--\nplot({\\x},{0.3*\\x*\\x*\\x*\\x})--\nplot({\\x},{-0.1*\\x*\\x*\\x*\\x*\\x});\n\n\n\\draw[black,domain=-2.5:2.5,smooth,variable=\\x]\nplot({\\x},{0.2*\\x*\\x})\nplot({\\x},{0.4*\\x*\\x*\\x})\nplot({\\x},{0.3*\\x*\\x*\\x*\\x})\nplot({\\x},{-0.1*\\x*\\x*\\x*\\x*\\x})\nplot({\\x},{0.2*\\x*\\x-0.1*\\x*\\x*\\x-0.3*\\x*\\x*\\x*\\x-0.1*\\x*\\x*\\x*\\x})\nplot({\\x},{0.4*\\x*\\x-0.3*\\x*\\x*\\x});\n\n\\draw[dashed] (1,0) arc (0:360:1);\n\n\\draw[->] (0,-1) arc (270:180:1);\n\\draw[->] (0,-1) arc (270:360:1);\n\n\\draw[->] (1,0) arc (0:360:1);\n\\draw[->] (1,0) arc (0:180:1);\n\n\\draw[->] (-1,0) arc (180:360:1);\n\\draw[->] (-1,0) arc (180:270:1);\n\n\\draw[dashed] (-1.7,0) arc (180:360:1.7);\n\n\\draw[->] (-1.7,0) arc (180:360:1.7);\n\\draw[->] (-1.7,0) arc (180:270:1.7);\n\n\\node[left] at (-1.9,0) {$Z(u)$};\n\\node[below] at (0,0) {$\\phantom{\\lambda}0$};\n\\node[right] at (1.9,0) {$B$};\n\\node[left] at (-1.9,1.5) {$C_\\pi/N$};\n\\node[below] at (0.5,0.8) {$\\gamma_1$};\n\\node[below] at (0.7,1) {$\\gamma_2$};\n\\node[below] at (0.2,1) {$\\lambda_T/\\pi N$};\n\\node[below] at (-0.3,0.2) {$\\nabla$};\n\\node at (-1,1.2) {$\\Omega_\\delta$};\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 119,
        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[,colorlinks,bookmarksopen,bookmarksnumbered,citecolor=red,urlcolor=red]{hyperref}\n\\usepackage{tikz}\n\\usepackage{xcolor}\n\\usetikzlibrary{positioning, calc, matrix, backgrounds}\n\n\\begin{document}\n\n\\begin{tikzpicture}[>=stealth, thick]\n        \\tikzstyle{box} = [rectangle, draw=gray]\n        \\tikzset{font=\\footnotesize}\n\n        \\node[box, inner sep=0pt] (motion) {\\includegraphics[width=\\textwidth]{example-image}};\n\n        \\matrix[below=1em of motion, matrix of nodes, row sep=0, row 1/.style={anchor=south, font=\\footnotesize\\bf}, column 2/.style={nodes={align=right}}, column 1/.style={nodes={text width=0.75\\textwidth,align=left}}] (language)\n        {\n            English & 31\\% of tasks\\\\  \n        };\n        \\draw(language-1-1.north west)--(language-1-2.north east);\n        \\draw[thin](language-1-1.south west)--(language-1-2.south east);\n        \\draw(language-1-1.south west)--(language-1-1.south -| language-1-2.south east);\n\n        \\draw[->, thick] (motion.south) -- (language.north);\n    \\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 120,
        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usepackage{color}\n\\usepackage{amssymb,amsthm,amsmath,bm}\n\\usetikzlibrary{arrows,decorations,calc}\n\\usetikzlibrary{decorations.pathmorphing,patterns,decorations.pathreplacing,decorations.markings}\n\\tikzset{\n  % style to apply some styles to each segment of a path\n  on each segment/.style={\n    decorate,\n    decoration={\n      show path construction,\n      moveto code={},\n      lineto code={\n        \\path[#1]\n        (\\tikzinputsegmentfirst) -- (\\tikzinputsegmentlast);\n      },\n      curveto code={\n        \\path[#1] (\\tikzinputsegmentfirst)\n        .. controls\n        (\\tikzinputsegmentsupporta) and (\\tikzinputsegmentsupportb)\n        ..\n        (\\tikzinputsegmentlast);\n      },\n      closepath code={\n        \\path[#1]\n        (\\tikzinputsegmentfirst) -- (\\tikzinputsegmentlast);\n      },\n    },\n  },\n  % style to add an arrow in the middle of a path\n  mid arrow/.style={postaction={decorate,decoration={\n        markings,\n        mark=at position .625 with {\\arrow[#1]{stealth}}\n      }}},\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.45]\n\\draw[double] (0,0) --  (0,1.25) -- (12,1.25) -- (12,0);\n\\draw[double,fill=white] (0,0) -- (0,.75) -- (2.25,.75) -- (2.25,0);\n\\draw[double,fill=white] (3,0) -- (3,.75) -- (5.75,.75) -- (5.75,0);\n\\draw[double,fill=white] (7,0) -- (7,.75) -- (9.25,.75) -- (9.25,0);\n\\draw[double,fill=white] (10,0) -- (10,.75) -- (12,.75) -- (12,0);\n\\draw (0,0) -- (0,-.5);\n\\draw (0,.75) -- (0,1.25);\n\\draw (2.25,0) -- (2.25,-.5);\n\\draw (2.25,.75) -- (2.25,1.25);\n\\draw (3,0) -- (3,-.5);\n\\draw (3,.75) -- (3,1.25);\n\\draw (5.75,0) -- (5.75,-.5);\n\\draw (5.75,.75) -- (5.75,1.25);\n\\draw (7,0) -- (7,-.5);\n\\draw (7,.75) -- (7,1.25);\n\\draw (9.25,0) -- (9.25,-.5);\n\\draw (9.25,.75) -- (9.25,1.25);\n\\draw (10,0) -- (10,-.5);\n\\draw (10,.75) -- (10,1.25);\n\\draw (12,0) -- (12,-.5);\n\\draw (12,.75) -- (12,1.25);\n\n\\foreach \\x in {.25,.5,.75,1,1.25,1.5,1.75,2,2.25,2.5,2.75,3,3.25,3.5,3.75,4,4.25,4.5,4.75,5,5.25,5.5,5.75,6,6.25,6.5,6.75,7,7.25,7.5,7.75,8,8.25,8.5,8.75,9,9.25,9.5,9.75,10,10.25,10.5,10.75,11,11.25} {\n\\node at (12,\\x) {$\\cdot$};\n\\node at (0,\\x) {$\\cdot$};\n}\n\n\\foreach \\x in {.25,1,2.25,3,4.25,5,6.25,7,8.25,9,10.25,11} {\n\\node at (\\x,.5) {$0$};\n\\node at (\\x,.75) {$1$};\n}\n\\node at (1,.5) {$1$};\n\\node at (2.25,.5) {$0$};\n\\node at (3,.5) {$1$};\n\\node at (4.25,.5) {$1$};\n\\node at (5,.5) {$1$};\n\\node at (6.25,.5) {$0$};\n\\node at (7,.5) {$1$};\n\\node at (8.25,.5) {$1$};\n\\node at (9,.5) {$1$};\n\\node at (10.25,.5) {$0$};\n\n\\foreach \\x in {2.5,7.5,10.5} {\n\\node at (\\x,.5) {$1$};\n\\node at (\\x,.75) {$0$};\n}\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[sigconf]{acmart}\n\\usepackage{amsmath}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,arrows,chains,calc,shadows,decorations.pathmorphing,fit,patterns,arrows.meta,calc,positioning,shapes.geometric,shapes.misc}\n\\usepackage[most]{tcolorbox}\n\\usepackage{pgf-umlsd}\n\\usepackage{tcolorbox}\n\\usetikzlibrary{arrows,automata,decorations.pathmorphing,decorations.pathreplacing,positioning,shadows,shapes.geometric}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.85, every node/.style={transform shape}]\n        \\node (gen) [draw, align=center, fill=cyan!10, inner sep=5pt, ultra thick, rounded corners=2pt, text width=0.8\\textwidth, minimum height=3.5cm, minimum width=0.75\\textwidth] {};\n        \\node at (gen.north) [draw, align=center, fill=blue!10, text width=0.75\\textwidth, minimum height=0.7cm, minimum width=0.75\\textwidth, rounded corners=0pt, ultra thick] {};\n        \\node at (gen.east) [draw, align=center, fill=red!10, text width=0.75\\textwidth, minimum height=0.7cm, minimum width=0.75\\textwidth, rounded corners=0pt, ultra thick] {};\n        \\node at (gen.south) [align=center, fill=white] {CAD Docker Container};\n        \n        \\node (calc) [draw, align=center, fill=blue!10, text width=0.75\\textwidth, minimum height=0.7cm, minimum width=0.75\\textwidth, rounded corners=0pt, ultra thick, below of=gen] {};\n        \\node at (calc.north) [align=center, fill=white] {CAD Docker Container};\n        \n        \\node (df) [draw, align=center, fill=yellow!20, text width=0.8\\textwidth, minimum height=2.7cm, minimum width=0.75\\textwidth, right of=gen, xshift=2cm] {};\n        \\node (df_u) [align=center, text width=0.5\\textwidth, minimum width=0.75\\textwidth] at (df.center) {meshing + body design + geometry};\n        \\node (df_d) [align=center, text width=0.5\\textwidth, minimum width=0.75\\textwidth] at (df.center) {CAD design (freeCAD)};\n        \\node (df_l) [align=center, text width=0.5\\textwidth, minimum width=0.75\\textwidth] at (df.center) {CAD geometry (STL)};\n        \\node (df_r) [align=center, text width=0.5\\textwidth, minimum width=0.75\\textwidth] at (df.center) {CAD body design (CAD.design.plus)};\n        \\draw [->, ultra thick, dashed, ->] (df.east) -- (calc);\n        \n        \\node (cfd) [draw, align=center, fill=green!10, text width=0.8\\textwidth, minimum height=2.7cm, minimum width=0.75\\textwidth, left of=gen, xshift=-2cm] {};\n        \\node (cfd_u) [align=center, text width=0.5\\textwidth, minimum width=0.75\\textwidth] at (cfd.center) {meshing + body design + geometry};\n        \\node (cfd_d) [align=center, text width=0.5\\textwidth, minimum width=0.75\\textwidth] at (cfd.center) {CFD};\n        \\node (cfd_l) [align=center, text width=0.5\\textwidth, minimum width=0.75\\textwidth] at (cfd.center) {CFD simulations (OpenFOAM)};\n        \\node (cfd_r) [align=center, text width=0.5\\textwidth, minimum width=0.75\\textwidth] at (cfd.center) {Drift Force};\n        \\draw [->, ultra thick, dashed, ->] (cfd.west) -- (calc);\n        \n        \\node (cbf) [draw, align=center, fill=brown!10, text width=0.8\\textwidth, minimum height=2.7cm, minimum width=0.75\\textwidth, right of=gen, xshift=2cm] {};\n        \\node (cbf_u) [align=center, text width=0.5\\textwidth, minimum width=0.75\\textwidth] at (cbf.center) {meshing + body design + geometry};\n        \\node (cbf_d) [align=center, text width=0.5\\textwidth, minimum width=0.75\\textwidth] at (cbf.center) {CFD};\n        \\node (cbf_l) [align=center, text width=0.5\\textwidth, minimum width=0.75\\textwidth] at (cbf.center) {Spatial and Boundary Collection};\n        \\node (cbf_r) [align=center, text width=0.5\\textwidth, minimum width=0.75\\textwidth] at (cbf.center) {Optimizer conditions and scripts};\n        \\draw [->, ultra thick, dashed, ->] (cbf.west) -- (cfd.east);\n        \n        \\node (cfd-cbf) [align=center, fill=orange!10, text width=0.6\\textwidth, minimum width=0.75\\textwidth, above of=gen, yshift=-0.6cm, rounded corners=2pt, ultra thick] {CFD-Lith};\n        \n        \\node (cbf-cbf) [align=center, fill=blue!10, text width=0.6\\textwidth, minimum width=0.75\\textwidth, below of=gen, yshift=0.5cm, rounded corners=2pt, ultra thick] {Drift Force};\n        \n        \\node (cfd-cbf) [align=center, fill=orange!10, text width=0.6\\textwidth, minimum width=0.75\\textwidth, above of=gen, yshift=-0.6cm, rounded corners=2pt, ultra thick] {CFD-Lith};\n        \\node (cbf-cbf) [align=center, fill=blue!10, text width=0.6\\textwidth, minimum width=0.75\\textwidth, below of=gen, yshift=0.5cm, rounded corners=2pt, ultra thick] {Drift Force};\n        \n        \\node (cfd-cbf) [align=center"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage{tikz-qtree}\n\\usetikzlibrary{decorations.pathreplacing}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\fill[fill=red!50] (-2,0.5) rectangle (2.5,-3.5);\n\\draw (-2.5,-3) -- (-2,-3) -- (-2,-1.5) -- (-1.5,-1.5) -- (-1.5,0) -- (0,0) -- (0,-0.5) -- (1,-0.5) -- (1,-2) -- (1.5,-2) -- (1.5,-3) -- (2.5,-3);\n\\draw (-1.5,-0.5) -- (-0.5,-0.5) -- (-0.5,-1) -- (0.5,-1) -- (0.5,-1.5) -- (1.5,-1.5) -- (1.5,-2) -- (2.5,-2);\n\\draw (0,-2) -- (0,-2.5) -- (1,-2.5) -- (1,-3) -- (2,-3);\n\\draw (0.5,-3.5) -- (1.5,-3.5) -- (1.5,-4) -- (2.5,-4);\n\\draw (-1,-4.5) -- (-0.5,-4.5) -- (-0.5,-5) -- (-1,-5);\n\\draw (-1.5,-5.5) -- (-0.5,-5.5) -- (-0.5,-6) -- (1.5,-6);\n\\node[circle,inner sep=2pt,fill] at (-1,-2.5) {};\n\\node[circle,inner sep=2pt,fill] at (-0.5,-4) {};\n\\node[circle,inner sep=2pt,fill] at (-1.5,-6) {};\n\\node[circle,inner sep=2pt,fill] at (0.5,-1) {};\n\\node[circle,inner sep=2pt,fill] at (1.5,-0.5) {};\n\\node[circle,inner sep=2pt,fill] at (1.5,-3.5) {};\n\\node[circle,inner sep=2pt,fill] at (1.5,-5) {};\n\\draw[fill=gray!30] (0.5,-2.5) -- (1,-2) -- (1.5,-2.5) -- (1,-3) -- (0.5,-2.5);\n\\draw[fill=gray!30] (-1.5,-1.5) -- (-1,-1) -- (-0.5,-1.5) -- (-1,-2) -- (-1.5,-1.5);\n\\draw[fill=gray!30] (1,-4) -- (1.5,-4.5) -- (1,-5) -- (0.5,-4.5) -- (1,-4);\n\\draw[fill=gray!30] (0,-6) -- (0.5,-5.5) -- (0,-5) -- (-0.5,-5.5) -- (0,-6);\n\\node[] at (-2.25,-2.75) {$X^1$};\n\\node[] at (-0.25,-4.25) {$X^2$};\n\\node[] at (1.25,-6.25) {$X^n$};\n\\node[] at (-1.25,-0.75) {$Z^1$};\n\\node[] at (1.25,-0.25) {$Z^2$};\n\\node[] at (1.25,-3.25) {$Z^3$};\n\\node[] at (1.25,-5.25) {$Z^4$};\n\\node[circle,inner sep=1pt,fill] at (-0.25,-1) {};\n\\node[circle,inner sep=1pt,fill] at (-0.25,-3) {};\n\\node[circle,inner sep=1pt,fill] at (-0.25,-4) {};\n\\node[circle,inner sep=1pt,fill] at (0.25,-3) {};\n\\node[circle,inner sep=1pt,fill] at (0.25,-5) {};\n\\node[circle,inner sep=1pt,fill] at (0.25,-2) {};\n\\node[circle,inner sep=1pt,fill] at (0.25,-6) {};\n\\node[circle,inner sep=1pt,fill] at (0.75,-1.5) {};\n\\node[circle,inner sep=1pt,fill] at (0.75,-4.5) {};\n\\node[circle,inner sep=1pt,fill] at (1.25,-0.5) {};\n\\node[circle,inner sep=1pt,fill] at (1.25,-3.5) {};\n\\node[circle,inner sep=1pt,fill] at (1.25,-5.5) {};\n\\node[] at (1.75,-1.75) {$1$};\n\\node[] at (1.75,-3.75) {$1$};\n\\node[] at (1.75,-5.75) {$1$};\n\\node[] at (1.75,-0.25) {$1$};\n\\node[] at (1.75,-3.25) {$1$};\n\\node[] at (1.75,-5.25) {$1$};\n\\node[] at (-1.25,-1.25) {$1$};\n\\node[] at (-1.25,-3.25) {$1$};\n\\node[] at (-1.25,-4.25) {$1$};\n\\node[] at (-1.25,-2.25) {$1$};\n\\node[] at (-1.25,-6.25) {$1$};\n\\node[] at (0.25,-1.75) {$1$};\n\\node[] at (0.25,-3.75) {$1$};\n\\node[] at (0.25,-4.75) {$1$};\n\\node[] at (0.25,-2.75) {$1$};\n\\node[] at (0.25,-6.75) {$1$};\n\\node[] at (-0.75,-1.25) {$1$};\n\\node[] at (-0.75,-3.25) {$1$};\n\\node[] at (-0.75,-4.25) {$1$};\n\\node[] at (-0.75,-2.25) {$1$};\n\\node[] at (-0.75,-6.25) {$1"
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        "tikz_code": "\\documentclass[a4paper, 12pt, reqno, twoside]{amsart}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,automata,backgrounds,calendar,mindmap,trees}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\\node at (0,0) {\\includegraphics[scale=0.4]{example-image}};\n\\node at (-6.5,-6.5) {$0$};\n\\node at (-5.5,-6.5) {$Q$};\n\\node at (-4.5,-6.5) {$Q'$};\n\\node at (-3.5,-6.5) {$0$};\n\\node at (-7,-5.5) {$0$};\n\\node at (-5,-5.5) {$Q$};\n\\node at (-3,-5.5) {$Q'$};\n\\node at (-1,-5.5) {$0$};\n\\node at (-7,-4.5) {$0$};\n\\node at (-5,-4.5) {$Q$};\n\\node at (-3,-4.5) {$Q'$};\n\\node at (-1,-4.5) {$0$};\n\\node at (-7,-3.5) {$0$};\n\\node at (-5,-3.5) {$Q$};\n\\node at (-3,-3.5) {$Q'$};\n\\node at (-1,-3.5) {$0$};\n\\node at (-7,-2.5) {$0$};\n\\node at (-5,-2.5) {$Q$};\n\\node at (-3,-2.5) {$Q'$};\n\\node at (-1,-2.5) {$0$};\n\\node at (-7,-1.5) {$0$};\n\\node at (-5,-1.5) {$Q$};\n\\node at (-3,-1.5) {$Q'$};\n\\node at (-1,-1.5) {$0$};\n\\node at (-7,-0.5) {$0$};\n\\node at (-5,-0.5) {$Q$};\n\\node at (-3,-0.5) {$Q'$};\n\\node at (-1,-0.5) {$0$};\n\\node at (-7,0.5) {$0$};\n\\node at (-5,0.5) {$Q$};\n\\node at (-3,0.5) {$Q'$};\n\\node at (-1,0.5) {$0$};\n\\node at (-7,1.5) {$0$};\n\\node at (-5,1.5) {$Q$};\n\\node at (-3,1.5) {$Q'$};\n\\node at (-1,1.5) {$0$};\n\\node at (-7,2.5) {$0$};\n\\node at (-5,2.5) {$Q$};\n\\node at (-3,2.5) {$Q'$};\n\\node at (-1,2.5) {$0$};\n\\node at (-7,3.5) {$0$};\n\\node at (-5,3.5) {$Q$};\n\\node at (-3,3.5) {$Q'$};\n\\node at (-1,3.5) {$0$};\n\\node at (-7,4.5) {$0$};\n\\node at (-5,4.5) {$Q$};\n\\node at (-3,4.5) {$Q'$};\n\\node at (-1,4.5) {$0$};\n\\node at (-7,5.5) {$0$};\n\\node at (-5,5.5) {$Q$};\n\\node at (-3,5.5) {$Q'$};\n\\node at (-1,5.5) {$0$};\n\\node at (-7,6.5) {$0$};\n\\node at (-5,6.5) {$Q$};\n\\node at (-3,6.5) {$Q'$};\n\\node at (-1,6.5) {$0$};\n\\node at (0,1) {\\textbf{Fixme:}};\n\\node at (0,0.5) {\\textbf{Fixme:}};\n\\node at (0,-0.5) {\\textbf{Fixme:}};\n\\node at (0,-1) {\\textbf{Fixme:}};\n\\node at (0,-1.5) {\\textbf{Fixme:}};\n\\node at (0,-2) {\\textbf{Fixme:}};\n\\node at (0,-2.5) {\\textbf{Fixme:}};\n\\node at (0,-3) {\\textbf{Fixme:}};\n\\node at (0,-3.5) {\\textbf{Fixme:}};\n\\node at (0,-4) {\\textbf{Fixme:}};\n\\node at (0,-4.5) {\\textbf{Fixme:}};\n\\node at (0,-5) {\\textbf{Fixme:}};\n\\node at (0,-5.5) {\\textbf{Fixme:}};\n\\node at (0,-6) {\\textbf{Fixme:}};\n\\node at (0,-6.5) {\\textbf{Fixme:}};\n\\node at (0,-7) {\\textbf{Fixme:}};\n\\node at (0,-7.5) {\\textbf{Fixme:}};\n\\node at (0,-8) {\\textbf{Fixme:}};\n\\node at (0,-8.5) {\\textbf{Fixme:}};\n\\node at (0,-9) {\\textbf{Fixme:}};\n\\node at (0,-9.5) {\\textbf{Fixme:}};\n\\node at (-4,2.8) {\\textbf{Kewords:}};\n\\node at (-4,2.4) {\\textbf{Fixme:}};\n\\node at (-3,2.2) {\\textbf{Fixme:}};\n\\node at (-2,2.1) {\\textbf{Fixme:}};\n\\node at (-2,1.7) {\\textbf{Fixme:}};\n\\node at (-1,1.5) {\\textbf{Fixme:}};\n\\node at (0,1.3) {\\textbf{Fixme:}};\n\\node at (-3,-0.3) {\\textbf{Fixme:}};\n\\node at (-4,-0.5) {\\textbf{Fixme:}};\n\\node at (-4,-1) {\\textbf{Fixme:}};\n\\node at (-4,-1.5) {\\textbf{Fixme:}};\n\\node at (-4,-2) {\\textbf{Fixme:}};\n\\node at (-4,-2.5) {\\textbf{Fixme:}};\n\\node at (-4,-3) {\\textbf{Fixme:}};"
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amssymb,amsfonts,amsthm}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{automata}\n\\usetikzlibrary{arrows}\n\\tikzset{every loop/.style={min distance=10mm,looseness=10}}\n\\tikzset{every state/.style={minimum size=2mm}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[node distance=1cm,auto,main node/.style={font=\\sffamily\\footnotesize}]\n\\node[main node] (1) {$1$};\n\\node[main node] (2) [below left of=1] {$\\phi_2$};\n\\node[main node] (3) [below right of=1] {$\\phi_1$};\n\\node[main node] (4) [below left of=2] {$\\phi_2$};\n\\node[main node] (5) [below right of=2] {$\\phi_1$};\n\\node[main node] (6) [below left of=3] {$\\phi_1$};\n\\node[main node] (7) [below right of=3] {$\\phi_2$};\n\\node[main node] (8) [below right of=5] {$(0,2)$};\n\\node[main node] (9) [below left of=4] {$(0,2)$};\n\\node[main node] (10) [below right of=4] {$(1,1)$};\n\\node[main node] (11) [below left of=5] {$(1,1)$};\n\\node[main node] (12) [below right of=6] {$(0,2)$};\n\\node[main node] (13) [below left of=7] {$(1,1)$};\n\\node[main node] (14) [below right of=7] {$(0,2)$};\n\n\\node[main node] (a) [below of=2,node distance=5cm] {$1$};\n\\node[main node] (b) [below of=3,node distance=5cm] {$(1,1)$};\n\\node[main node] (c) [below of=6,node distance=5cm] {$(0,2)$};\n\\node[main node] (d) [below of=7,node distance=5cm] {$(1,1)$};\n\\node[main node] (e) [below of=8,node distance=5cm] {$(1,2)$};\n\\node[main node] (f) [below of=9,node distance=5cm] {$(0,2)$};\n\\node[main node] (g) [below of=11,node distance=5cm] {$(1,1)$};\n\\node[main node] (h) [below of=13,node distance=5cm] {$(0,1)$};\n\\node[main node] (i) [below of=14,node distance=5cm] {$(1,2)$};\n\n\\path[every node/.style={font=\\sffamily\\small}]\n(1) edge node {} (2)\n(1) edge node {} (3)\n(2) edge node {} (4)\n(2) edge node {} (5)\n(3) edge node {} (4)\n(3) edge node {} (5)\n(4) edge node {} (9)\n(4) edge node {} (10)\n(5) edge node {} (8)\n(5) edge node {} (11)\n(6) edge node {} (4)\n(7) edge node {} (3)\n(7) edge node {} (5)\n(8) edge node {} (12)\n(9) edge node {} (12)\n(10) edge node {} (12)\n(11) edge node {} (13)\n(13) edge node {} (12)\n(14) edge node {} (13)\n(14) edge node {} (12)\n(1) node[right=1mm] {$2$}\n(2) node[left=1mm] {$1$}\n(3) node[right=1mm] {$2$}\n(4) node[left=1mm] {$2$}\n(5) node[right=1mm] {$1$}\n(6) node[left=1mm] {$1$}\n(7) node[right=1mm] {$2$}\n(8) node[right=1mm] {$(1,1)$}\n(9) node[right=1mm] {$(0,2)$}\n(10) node[left=1mm] {$(1,2)$}\n(11) node[left=1mm] {$(0,2)$}\n(12) node[right=1mm] {$(0,1)$}\n(13) node[left=1mm] {$(0,2)$}\n(14) node[right=1mm] {$(1,2)$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 128,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amsthm,amssymb,amsfonts,enumerate,xcolor,layout,tikz,enumitem,fullpage, verbatim, graphicx, caption, subcaption}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usepackage{tikz-cd}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n      \\draw (0,0) -- (0,2) -- (4,2) -- (4,0) -- cycle;\n      \\draw [fill] (0,0) circle [radius=0.05];\n      \\draw [fill] (0,2) circle [radius=0.05];\n      \\draw [fill] (4,2) circle [radius=0.05];\n      \\draw [fill] (4,0) circle [radius=0.05];\n      \\draw (0,0) -- (2,2);\n      \\draw [fill] (2,2) circle [radius=0.05];\n      \\node at (-0.5,2) {$4$};\n      \\node at (-0.5,0) {$-2$};\n      \\node at (4.5,0) {$-2$};\n      \\node at (4.5,2) {$4$};\n      \\draw (5.5,1) node {$\\cong$};\n      \\draw (6.5,0) -- (8,0) -- (8,2) -- (12,2) -- (12,0) -- cycle;\n      \\draw [fill] (6.5,0) circle [radius=0.05];\n      \\draw [fill] (8,0) circle [radius=0.05];\n      \\draw [fill] (8,2) circle [radius=0.05];\n      \\draw [fill] (12,2) circle [radius=0.05];\n      \\draw [fill] (12,0) circle [radius=0.05];\n      \\node at (6.5,-0.5) {$-2$};\n      \\node at (6.5,2.5) {$4$};\n      \\node at (12.5,-0.5) {$-2$};\n      \\node at (12.5,2.5) {$4$};\n      \\draw (13.5,1) node {$\\cong$};\n      \\draw (14.5,0) -- (16,0) -- (16,2) -- (20,2) -- (20,0) -- cycle;\n      \\draw [fill] (14.5,0) circle [radius=0.05];\n      \\draw [fill] (16,0) circle [radius=0.05];\n      \\draw [fill] (16,2) circle [radius=0.05];\n      \\draw [fill] (20,2) circle [radius=0.05];\n      \\draw [fill] (20,0) circle [radius=0.05];\n      \\node at (14.5,-0.5) {$-2$};\n      \\node at (14.5,2.5) {$4$};\n      \\node at (16,-0.5) {$-2$};\n      \\node at (20.5,-0.5) {$-2$};\n      \\node at (20.5,2.5) {$4$};\n    \\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 129,
        "tikz_code": "\\documentclass[reqno]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{pgfplots}\n\\usepackage{tikz-cd}\n\\usepackage{pgf}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{arrows,automata}\n\\usetikzlibrary{shapes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[>=stealth',semithick,inner sep=0.4mm]\n\\tikzstyle{every label}=[font=\\footnotesize]\n\\begin{scope}\n\\node (A) at (0,0) [shape=circle,draw,fill=black,label=below:$1$] {};\n\\node (B) at (0,2) [shape=circle,draw,fill=black,label=above:$1$] {};\n\\node (C) at (2,0) [shape=circle,draw,fill=black,label=below:$3$] {};\n\\node (D) at (2,2) [shape=circle,draw,fill=black,label=above:$3$] {};\n\\node (E) at (1,2.6) [shape=circle,draw,fill=black,label=above:$2$] {};\n\\node (F) at (1,0.6) [shape=circle,draw,fill=gray,label=below:$4$] {};\n\\draw [->] (A) to (B);\n\\draw [->] (B) to (C);\n\\draw [->] (C) to (D);\n\\draw [->] (D) to (A);\n\\draw [->] (E) to (A);\n\\draw [->] (A) to (F);\n\\draw [->] (F) to (C);\n\\draw [->] (C) to (E);\n\\draw [->] (E) to (B);\n\\draw [->] (B) to (F);\n\\draw [->] (F) to (D);\n\\draw [->] (D) to (E);\n\\draw [->] (E) to (A);\n\\draw [->] (A) to (C);\n\\draw [->] (C) to (F);\n\\draw [->] (F) to (B);\n\\draw [->] (B) to (D);\n\\draw [->] (D) to (E);\n\\draw [->] (E) to (A);\n\\draw [->] (A) to (C);\n\\draw [->] (C) to (F);\n\\draw [->] (F) to (B);\n\\draw [->] (B) to (D);\n\\draw [->] (D) to (E);\n\\draw [->] (E) to (A);\n\\draw [->] (A) to (C);\n\\draw [->] (C) to (F);\n\\draw [->] (F) to (B);\n\\draw [->] (B) to (D);\n\\draw [->] (D) to (E);\n\\draw [->] (E) to (A);\n\\end{scope}\n\\begin{scope}[xshift=3cm]\n\\node (A) at (0,0) [shape=circle,draw,fill=black,label=below:$1$] {};\n\\node (B) at (0,2) [shape=circle,draw,fill=black,label=above:$1$] {};\n\\node (C) at (2,0) [shape=circle,draw,fill=black,label=below:$3$] {};\n\\node (D) at (2,2) [shape=circle,draw,fill=black,label=above:$3$] {};\n\\node (E) at (1,2.6) [shape=circle,draw,fill=black,label=above:$2$] {};\n\\node (F) at (1,0.6) [shape=circle,draw,fill=gray,label=below:$4$] {};\n\\draw [->] (A) to (B);\n\\draw [->] (B) to (C);\n\\draw [->] (C) to (D);\n\\draw [->] (D) to (A);\n\\draw [->] (E) to (A);\n\\draw [->] (A) to (F);\n\\draw [->] (F) to (C);\n\\draw [->] (C) to (E);\n\\draw [->] (E) to (B);\n\\draw [->] (B) to (F);\n\\draw [->] (F) to (D);\n\\draw [->] (D) to (E);\n\\draw [->] (E) to (A);\n\\draw [->] (A) to (C);\n\\draw [->] (C) to (F);\n\\draw [->] (F) to (B);\n\\draw [->] (B) to (D);\n\\draw [->] (D) to (E);\n\\draw [->] (E) to (A);\n\\end{scope}\n\\begin{scope}[xshift=6cm]\n\\node (A) at (0,0) [shape=circle,draw,fill=black,label=below:$1$] {};\n\\node (B) at (0,2) [shape=circle,draw,fill=black,label=above:$1$] {};\n\\node (C) at (2,0) [shape=circle,draw,fill=black,label=below:$3$] {};\n\\node (D) at (2,2) [shape=circle,draw,fill=black,label=above:$3$] {};\n\\node (E) at (1,2.6) [shape=circle,draw,fill=black,label=above:$2$] {};\n\\node (F) at (1,0.6) [shape=circle,draw,fill=gray,label=below:$4$] {};\n\\draw [->] (A) to (B);\n\\draw [->] (B) to (C);\n\\draw [->] (C) to (D);\n\\draw [->] (D) to (A);\n\\draw [->] (E) to (A);\n\\draw [->] (A) to (F);\n\\draw [->] (F) to (C);\n\\draw [->] (C) to (E);\n\\draw [->] (E) to (B);\n\\draw [->] (B) to (F);\n\\draw [->] (F) to (D);\n\\draw [->] (D) to (E);\n\\draw [->] (E) to (A);\n\\draw [->] (A) to (C);\n\\draw [->] (C) to (F);\n\\draw [->] (F) to (B);\n\\draw [->] (B) to (D);\n\\draw [->] (D) to (E);\n\\draw [->] (E) to (A);\n\\end{scope}\n\\begin{scope"
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    {
        "index": 130,
        "tikz_code": "\\documentclass[journal]{IEEEtran}\n\\usepackage{amssymb,amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,automata,shapes,backgrounds}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{calc}\n\\usepackage[textwidth=1.9cm,color=green!10,textsize=footnotesize]{todonotes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[baseline,auto,->,>=stealth,shorten >=1pt,node distance=1.8cm,\n        state/.style={circle,minimum size=0mm,inner sep=2pt,very thin,draw=black,initial text=},\n        every node/.style={font=\\footnotesize},framed, rounded corners]\n        \\node[state,initial]    (1) {$0$};\n        \\node[state,initial]    (2)[right of=1] {$1$};\n        \\node[state]            (3)[right of=2] {$2$};\n        \\node[state]            (4)[right of=3] {$3$};\n        \\node[state]            (5)[right of=4] {$4$};\n        \\node[state,initial]    (6)[right of=5] {$5$};\n        \\path\n          (1) edge[solid] node[pos=0.5,sloped,above]{$x<0.5$} (2)\n          (2) edge[solid] node[pos=0.5,sloped,above]{$x>0.5$} (3)\n          (3) edge[solid,red] node[pos=0.5,sloped,above]{$x=-1$} (4)\n          (4) edge[solid,blue] node[pos=0.5,sloped,above]{$x=1$} (5)\n          (5) edge[solid,green] node[pos=0.5,sloped,above]{$x=0$} (6)\n          ;\n      \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 131,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n   \\tikzstyle{every node}=[draw,circle,fill=black,minimum size=4pt,\n                            inner sep=0pt]\n\n  \\foreach \\x in {1,...,5}\n   \\node[label=below:{\\x}] (a\\x) at (\\x,0) {};\n      \\foreach \\x in {1,...,11}\n   \\node[label=above:{\\x}] (b\\x) at (\\x*1.5-1.5,2) {};\n\n    \\foreach \\from/\\to in {1/2, 1/3, 2/5, 2/6, 2/7, 3/4, 3/8, 3/9, 4/10, 4/11, 5/11, 6/10, 7/9, 7/8, 8/11, 9/10, 10/9, 10/8, 11/7}\n    \\draw (b\\from) -- (a\\to);\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 132,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath,amsxtra,amssymb,latexsym,amscd,amsthm}\n\\usepackage{tikz-cd}\n\\usepackage{tkz-euclide}\n\\usepackage[colorlinks]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}[every node/.style={midway}]\n  \\matrix[column sep={10em,between origins}, row sep={3em}] at (0,0) {\n    \\node(Y){$S^{n}(g,\\partial g)$} ; & \\node(X) {$S^{n}(g,\\partial g)\\simeq S^{n}(g,\\partial g)/\\mathbb{G}$}; \\\\\n    \\node(M) {$S^{n}(g,\\partial g)\\simeq S^{n}(g,\\partial g)/\\mathbb{G}$}; & \\node (N) {$S^{n}(g,\\partial g)\\simeq S^{n}(g,\\partial g)\\simeq S^{n}(g,\\partial g)/\\mathbb{G}$};\\\\\n  };\n  \n  \\draw[->] (Y) -- (M) node[anchor=east]  {singular conformal};\n  \\draw[->] (Y) -- (X) node[anchor=south]  {$\\partial g\\to g$};\n  \\draw[->] (X) -- (N) node[anchor=west] {invertible};\n  \\draw[->] (M) -- (N) node[anchor=north] {$g\\to \\mathbb{G}$};.\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 133,
        "tikz_code": "\\documentclass[reqno]{amsart}\n\\usepackage{amsmath,amsthm,amsfonts,amssymb,enumerate}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usepackage[colorlinks=true]{hyperref}\n\\usepackage[utf8]{inputenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\n\\foreach \\y in {1,2,3,4}\n{\n\\draw[black,fill=black!20!white] (0,\\y) rectangle (4,\\y+1);\n}\n\n\\foreach \\y in {1,2,3}\n{\n\\draw[black,fill=red!20!white] (4,\\y) rectangle (7,\\y+1);\n}\n\\foreach \\y in {1,2,3}\n{\n\\draw[black,fill=red!20!white] (7,\\y) rectangle (10,\\y+1);\n}\n\n\\foreach \\y in {1,2,3}\n{\n\\draw[black,fill=blue!20!white] (4,\\y) rectangle (5,\\y+1);\n\\draw[black,fill=blue!20!white] (5,\\y) rectangle (6,\\y+1);\n\\draw[black,fill=blue!20!white] (6,\\y) rectangle (7,\\y+1);\n}\n\n\n\\foreach \\y in {1,2,3}\n{\n\\draw[black,fill=blue!20!white] (7,\\y) rectangle (8,\\y+1);\n\\draw[black,fill=blue!20!white] (8,\\y) rectangle (9,\\y+1);\n}\n\n\\foreach \\y in {1,2,3}\n{\n\\draw[black,fill=blue!20!white] (7,\\y) rectangle (8,\\y+1);\n\\draw[black,fill=blue!20!white] (8,\\y) rectangle (9,\\y+1);\n}\n\n\\foreach \\x in {1,2,3,4,7,8,9}\n{\n\\draw[black,fill=black!20!white] (\\x,0) rectangle (\\x+1,1);\n}\n\n\n\\draw[black,fill=black!20!white] (1,4) rectangle (2,5);\n\\draw[black,fill=black!20!white] (2,4) rectangle (3,5);\n\\draw[black,fill=black!20!white] (3,4) rectangle (4,5);\n\n\n\n\\draw[black,fill=black!20!white] (6,5) rectangle (7,6);\n\\draw[black,fill=black!20!white] (7,5) rectangle (8,6);\n\\draw[black,fill=black!20!white] (8,5) rectangle (9,6);\n\n\n\\foreach \\y in {1,2,3,4}\n{\n\\draw[black,fill=red!20!white] (10,\\y) rectangle (11,\\y+1);\n}\n\n\\foreach \\y in {1,2,3}\n{\n\\draw[black,fill=red!20!white] (11,\\y) rectangle (13,\\y+1);\n}\n\n\\draw[black,fill=black!20!white] (10,4) rectangle (11,5);\n\\draw[black,fill=black!20!white] (11,4) rectangle (12,5);\n\\draw[black,fill=black!20!white] (12,4) rectangle (13,5);\n\\foreach \\y in {1,2,3}\n{\n\\draw[black,fill=blue!20!white] (11,\\y) rectangle (12,\\y+1);\n}\n\n\n\\draw[black,fill=blue!20!white] (11,5) rectangle (12,6);\n\n\\draw[black,fill=black!20!white] (11,4) rectangle (12,5);\n\\draw[black,fill=black!20!white] (12,4) rectangle (13,5);\n\n\\draw[thick,<->] (4.5,2.25) -- (5.5,2.25);\n\n\\draw[thick,<->] (9.5,2.25) -- (10.5,2.25);\n\n\n\\draw[black,fill=black!20!white] (14,4) rectangle (15,5);\n\\draw[black,fill=black!20!white] (15,4) rectangle (16,5);\n\\draw[black,fill=black!20!white] (16,4) rectangle (17,5);\n\n\\draw[black,fill=black!20!white] (14,5) rectangle (15,6);\n\\draw[black,fill=black!20!white] (15,5) rectangle (16,6);\n\\draw[black,fill=black!20!white] (16,5) rectangle (17,6);\n\n\\draw[black,fill=black!20!white] (17,4) rectangle (18,5);\n\\draw[black,fill=black!20!white] (18,4) rectangle (19,5);\n\n\n\n\\draw[black,fill=red!20!white] (14,3) rectangle (15,4);\n\\draw[black,fill=red!20!white] (15,3) rectangle (16,4);\n\\draw[black,fill=red!20!white] (16,3) rectangle (17,4);\n\n\\draw[black,fill=blue!20!white] (14,3) rectangle (15,4);\n\\draw[black,fill=blue!20!white] (15,3) rectangle (16,4);\n\\draw[black,fill=blue!20!white] (16,3) rectangle (17,4);\n\n\\draw[black,fill=black!20!white] (17,3) rectangle (18,4);\n\\draw[black,fill=black!20!white] (18,3) rectangle (19,4);\n\n\n\\node at (0.5,1.5) {$\\cdots$};\n\\node at (4.5,1.5) {$\\cdots$};\n\\node at (7.5,1.5) {$\\cdots$};\n\\node at (10.5,1.5) {$\\cdots$};\n\n\\node at (14.5,1.5) {$\\cdots$};\n\\node at (17.5,1.5) {$\\cdots$};\n\n\\node at (2.5,4.5) {$\\vdots$"
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        "index": 134,
        "tikz_code": "\\documentclass[10pt,twoside]{article}\n\\usepackage{amsmath,amsthm}\n\\usepackage[latin1]{inputenc}\n\\usepackage{amssymb,latexsym}\n\\usepackage{color}\n\\usepackage{tkz-graph}\n\\usepackage{tikz-cd}\n\\usetikzlibrary{calc}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.35]\n\n\\begin{scope}[shift={(-8,0)}]\n\\draw [line width=1pt] (-2,3)-- (-2,-3);\n\\draw [line width=1pt] (-2,-3)-- (2,-3);\n\\draw [line width=1pt] (2,-3)-- (2,3);\n\\draw [line width=1pt] (2,3)-- (-2,3);\n\\draw [line width=1pt] (-2,-3)-- (0,-1);\n\\draw [line width=1pt] (0,-1)-- (2,-3);\n\\draw [line width=1pt] (-2,3)-- (0,-1);\n\\draw [line width=1pt] (0,-1)-- (2,3);\n\\draw [line width=1pt] (0,-1)-- (-2,3);\n\\draw [line width=1pt] (-2,-3)-- (2,3);\n\\draw [line width=1pt] (2,-3)-- (-2,3);\n\\draw [line width=1pt] (-2,0)-- (2,0);\n\\draw [line width=1pt] (2,0)-- (4,0);\n\\draw [line width=1pt] (4,0)-- (6,0);\n\\draw [line width=1pt] (6,0)-- (8,0);\n\\draw [line width=1pt] (8,0)-- (8,-2);\n\\draw [line width=1pt] (8,-2)-- (6,-2);\n\\draw [line width=1pt] (6,-2)-- (4,-2);\n\\draw [line width=1pt] (4,-2)-- (2,-2);\n\\draw [line width=1pt] (2,-2)-- (0,-2);\n\\draw [line width=1pt] (0,-2)-- (-2,-2);\n\\draw [line width=1pt] (-2,-2)-- (-2,0);\n\\draw [line width=1pt] (-2,0)-- (0,-2);\n\\draw [line width=1pt] (0,-2)-- (2,-2);\n\\draw [line width=1pt] (2,-2)-- (4,-2);\n\\draw [line width=1pt] (4,-2)-- (6,-2);\n\\draw [line width=1pt] (6,-2)-- (8,-2);\n\\draw [line width=1pt] (0,2)-- (2,2);\n\\draw [line width=1pt] (2,2)-- (4,2);\n\\draw [line width=1pt] (4,2)-- (6,2);\n\\draw [line width=1pt] (6,2)-- (8,2);\n\\draw [line width=1pt] (8,2)-- (8,0);\n\\draw [line width=1pt] (8,0)-- (6,2);\n\\draw [line width=1pt] (6,2)-- (4,2);\n\\draw [line width=1pt] (4,2)-- (2,2);\n\\draw [line width=1pt] (2,2)-- (0,2);\n\\draw [line width=1pt] (0,2)-- (-2,2);\n\\draw [line width=1pt] (-2,2)-- (-2,0);\n\\draw [line width=1pt] (-2,0)-- (0,2);\n\\draw [line width=1pt] (0,2)-- (2,2);\n\\draw [line width=1pt] (2,2)-- (4,2);\n\\draw [line width=1pt] (4,2)-- (6,2);\n\\draw [line width=1pt] (6,2)-- (8,2);\n\\draw (-7.1,0) node{a)};\n\\draw (0,-4) node{b)};\n\\draw (0,0) node{c)};\n\\draw (0,-5) node{d)};\n\\end{scope}\n\n\\begin{scope}[shift={(8,0)}]\n\\draw [line width=1pt] (-2,3)-- (-2,-3);\n\\draw [line width=1pt] (-2,-3)-- (2,-3);\n\\draw [line width=1pt] (2,-3)-- (2,3);\n\\draw [line width=1pt] (2,3)-- (-2,3);\n\\draw [line width=1pt] (-2,-3)-- (0,-1);\n\\draw [line width=1pt] (0,-1)-- (2,-3);\n\\draw [line width=1pt] (-2,3)-- (0,-1);\n\\draw [line width=1pt] (0,-1)-- (2,3);\n\\draw [line width=1pt] (0,-1)-- (-2,3);\n\\draw [line width=1pt] (-2,-3)-- (2,3);\n\\draw [line width=1pt] (2,-3)-- (-2,3);\n\\draw [line width=1pt] (-2,0)-- (2,0);\n\\draw [line width=1pt] (2,0)-- (4,0);\n\\draw [line width=1pt] (4,0)-- (6,0);\n\\draw [line width=1pt] (6,0)-- (8,0);\n\\draw [line width=1pt] (8,0)-- (8,2);\n\\draw [line width=1pt] (8,2)-- (6,2);\n\\draw [line width=1pt] (6,2)-- (4,2);\n\\draw [line width=1pt] (4,2)-- (2,2);\n\\draw [line width=1pt] (2,2)-- (0,2);\n\\draw [line width=1pt] (0,2)-- (-2,2);\n\\draw [line width=1pt] (-2,2)-- (-2,0);\n\\draw [line width=1pt] (-2,0)-- (0,2);\n\\draw [line width=1pt] (0,2)-- (2,2);\n\\draw [line width=1pt] (2,2)-- (4,2);\n\\draw [line width=1pt] (4,2)-- (6,2);\n\\draw [line width=1pt] (6,2)-- (8,2);\n\\draw (7.1,0) node{a)};\n\\draw (0,-4) node{b)};\n\\draw (0,0) node{c)};\n\\draw (0,-5) node"
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    {
        "index": 135,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{scope}[xshift=-3cm]\n\\draw (-1.5,0) -- (-1,0);\n\\draw (-1,0) -- (-0.2,0.6);\n\\draw (0.2,-0.6) -- (1,-0.2);\n\\draw (1,-0.2) -- (1,0.2);\n\\draw (1,0.2) -- (0.2,0.6);\n\\draw (0.2,0.6) -- (-1,0.95);\n\\draw (0.2,-0.6) -- (-1,-0.95);\n\\draw (-0.2,-0.6) -- (-1,-0.2);\n\\node[below] at (-0.5,0) {$1$};\n\\node[above] at (-0.25,0.5) {$2$};\n\\node[below] at (0.5,0) {$3$};\n\\node[below] at (-0.5,0.9) {$4$};\n\\node[below] at (-0.5,-0.9) {$5$};\n\\draw[red,thick] (0.2,0.6) -- (-0.2,-0.6);\n\\draw[red,thick] (0.2,-0.6) -- (-0.2,0.6);\n\\node[red,left] at (0,0) {$U$};\n\\node[red,below] at (-0.3,0) {$\\zeta$};\n\\node[right] at (1.2,0.15) {$F=x_{13}\\cdots x_{52}$};\n\\end{scope}\n\\begin{scope}[xshift=3cm]\n\\draw (-1.5,0) -- (-1,0);\n\\draw (-1,0) -- (-0.2,0.6);\n\\draw (0.2,-0.6) -- (1,-0.2);\n\\draw (1,-0.2) -- (1,0.2);\n\\draw (1,0.2) -- (0.2,0.6);\n\\draw (0.2,0.6) -- (-1,0.95);\n\\draw (0.2,-0.6) -- (-1,-0.95);\n\\draw (-0.2,-0.6) -- (-1,-0.2);\n\\node[below] at (-0.5,0) {$1$};\n\\node[above] at (-0.25,0.5) {$2$};\n\\node[below] at (0.5,0) {$3$};\n\\node[below] at (-0.5,0.9) {$4$};\n\\node[below] at (-0.5,-0.9) {$5$};\n\\draw[red,thick] (0.2,0.6) -- (-0.2,0.6);\n\\draw[red,thick] (0.2,-0.6) -- (-0.2,-0.6);\n\\node[red,left] at (0,0) {$U$};\n\\node[red,below] at (-0.3,0) {$\\zeta$};\n\\node[right] at (1.2,0.15) {$F=x_{13}\\cdots x_{52}$};\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 136,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{matrix}\n\\usetikzlibrary{arrows}\n\n\\newcommand{\\Qt}{\\left(}\n\n\\newcommand{\\Rt}{\\right)}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.5]\n\n\\tikzset{->}\n\\draw[->] (-1,0) -- (10,0) node[right] {$y_1$};\n\\draw[->] (0,-1) -- (0,5) node[above] {$y_2$};\n\\draw[fill=gray, opacity=0.2] (3,3) -- (7,3) -- (7,7) -- (3,7) -- (3,3);\n\\draw[fill=gray, opacity=0.2] (2,1) -- (6,1) -- (6,4) -- (2,4) -- (2,1);\n\\draw[dashed] (3,3) -- (7,3) -- (7,7) -- (3,7) -- (3,3);\n\\draw[dashed] (2,1) -- (6,1) -- (6,4) -- (2,4) -- (2,1);\n\\draw[fill] (4.5,3.5) circle (0.05);\n\\draw (5,4) node {$Q_i^j$};\n\\draw (3.5,2.5) node {$B^i_{0}$};\n\\draw (2.5,4) node {$\\Qt B^i_{0} \\Rt$};\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 137,
        "tikz_code": "\\documentclass[a4paper,11pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath,amssymb,amsthm,mathtools,array,booktabs}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes.geometric}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\draw (0,0) -- (0,10);\n    \\draw (0,0) -- (10,0);\n    \\draw (0,10) -- (10,10);\n    \\draw (10,0) -- (10,10);\n    \\draw (4,0) -- (4,10);\n    \\draw[thick] (0,0) -- (4,0);\n    \\draw[thick] (4,10) -- (10,6);\n    \\draw[thick] (0,10) -- (10,4);\n    \\draw[thick] (0,0) -- (4,0);\n    \\draw[thick] (4,10) -- (10,6);\n    \\draw[thick] (10,4) -- (10,6);\n    \\draw[thick] (0,6) -- (4,6);\n    \\draw[thick] (0,6) -- (10,6);\n    \\draw[thick] (10,10) -- (10,6);\n    \\draw[thick,dashed] (4,0) -- (4,10);\n    \\draw[thick,dashed] (0,10) -- (10,0);\n    \\draw[thick,dashed] (0,6) -- (4,6);\n    \\draw[thick,dashed] (0,6) -- (10,6);\n    \\draw[thick,dashed] (4,6) -- (10,4);\n    \\draw (0,-1) -- (0,0);\n    \\draw (10,-1) -- (10,0);\n    \\draw (0,10) -- (0,11);\n    \\draw (10,10) -- (11,10);\n    \\draw (0,-1) -- (10,-1);\n    \\draw (10,-1) -- (10,10);\n    \\draw (0,0) node[left]{$1$};\n    \\draw (0,6) node[left]{$\\frac{1}{2}$};\n    \\draw (0,10) node[left]{$1=v_0=v_1+v_2$};\n    \\draw (4,0) node[below]{$1$};\n    \\draw (4,10) node[below]{$1=v_0+v_3$};\n    \\draw (10,0) node[right]{$1$};\n    \\draw (10,6) node[right]{$\\frac{1}{2}$};\n    \\draw (10,10) node[right]{$1=v_0+v_1+v_2$};\n    \\draw (10,-1) node[below]{$1$};\n    \\draw (0,-1) node[below]{$1$};\n    \\draw (10,-1) node[below]{$1$};\n    \\draw (2,3) node[above left]{$v_1$};\n    \\draw (6,3) node[above right]{$v_2$};\n    \\draw (2,6) node[above]{$v_2$};\n    \\draw (2,7) node[above]{$v_1$};\n    \\draw (7,2) node[above right]{$v_1$};\n    \\draw (2,2) node[below]{$v_2$};\n    \\draw (2,7) node[above]{$v_1$};\n    \\draw (2,7) node[above right]{$v_1$};\n    \\draw (2,4.5) node[above right]{$\\alpha_1$};\n    \\draw (7,2) node[above right]{$v_1$};\n    \\draw (7,2) node[above right]{$v_1$};\n    \\draw (2,4.5) node[above right]{$\\alpha_1$};\n    \\draw (2,4.5) node[above right]{$\\alpha_1$};\n    \\draw (2.5,3.7) node[above right]{$\\alpha_2$};\n    \\draw (5.5,2.3) node[above right]{$\\alpha_3$};\n    \\draw (2,1) node[above right]{$0$};\n    \\draw (7,1) node[above right]{$0$};\n    \\draw (2,1) node[above right]{$0$};\n    \\draw (7,1) node[above right]{$0$};\n    \\draw (2,1) node[above right]{$0$};\n    \\draw (5,0.6) node[above]{$v_1+v_2$};\n    \\draw (7,0.6) node[above]{$v_1$};\n    \\draw (2,8) node[above]{$v_2$};\n    \\draw (7,8) node[above]{$v_1$};\n    \\draw (0,2) node[above left]{$\\frac{1}{2}$};\n    \\draw (0,3) node[above left]{$0$};\n    \\draw (0,4) node[above left]{$1$};\n    \\draw (0,5) node[above left]{$1$};\n    \\draw (0,6) node[above left]{$1$};\n    \\draw (0,7) node[above left]{$1$};\n    \\draw (0,8) node[above left]{$\\frac{1}{2}$};\n    \\draw (0,9) node[above left]{$1$};\n    \\draw (2,7) node[above right]{$A$};\n    \\draw (2,7) node[above right]{$A$};\n    \\draw (2,7) node[above right]{$A$};\n    \\draw (2,7) node[above right]{$A$};\n    \\draw (2,7) node[above right]{$A$};\n    \\draw (2,7) node[above right]{$A$};\n    \\draw (6,3) node[above right]{$B$};\n    \\draw (6,3) node[above right]{$B$};\n    \\draw (6,3) node[above right]{$B$};\n    \\draw (6,3) node[above right]{$B$};\n    \\draw (6,3) node[above right]{$B$};\n    \\draw (6,3) node[above right]{$B$};\n    \\draw (6,3) node[above right]{$B"
    },
    {
        "index": 138,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[usenames,dvipsnames]{color}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\tikzset{\n\tsolid node/.style={circle,draw,inner sep=1.2,fill=black},\n\tgray node/.style={circle,draw=gray,inner sep=1.2, fill = gray},\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=3]\n\t\t\\draw [fill=gray!30] (0,0) -- (0,1) -- (1.5,0) -- cycle;\n\t\t\\draw (0,0) -- (0,1) -- (1.5,0) -- cycle;\n\t\t\\node[gray node, label = below:{$|\\Gamma|=1$}] at (0,0) {};\n\t\t\\node[gray node, label = above right:{$|\\Gamma|=1$}] at (0,1) {};\n\t\t\\node[gray node, label = below:{$|\\Gamma|=1$}] at (1.5,0) {};\n\t\t\\draw [thick, ->] (0,0.8) -- (0.25, 0.4);\n\t\t\\draw [thick, ->] (0.75, 0.2) -- (1,0.2);\n\t\t\\draw [thick, ->] (0.75,0.2) -- (0.25, 0.4);\n\t\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 139,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning,decorations.pathmorphing}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n  font=\\sf \\scriptsize,\n  >=stealth,\n  node distance = 4em,\n  thick,\n  edge from parent/.style = {draw},\n]\n% the root of the tree\n\\node (B0) {Behavior $B_0$}\n  % the left subtree\n  child {\n    node (A0) {Aresets at $t=0$}\n    child {\n      node[below=3em of A0,draw] (Z) {$Z$}\n      edge from parent node[left] {$\\gamma$}\n    }\n    child {\n      node[right=2em of A0,draw] (A1) {Areset at $t=1$}\n      edge from parent node[right] {$\\alpha$}\n    }\n    edge from parent node[left] {$\\gamma$}\n  }\n  % the right subtree\n  child {\n    node (B1) {Behaviors at $t=1$}\n    child {\n      node[below=3em of B1,draw] (Z) {$Z$}\n      edge from parent node[left] {$\\alpha$}\n    }\n    child {\n      node[right=2em of B1,draw] (B2) {Behaviors at $t=2$}\n      edge from parent node[right] {$\\beta$}\n    }\n    edge from parent node[right] {$\\gamma$}\n  };\n\\path (B0) -- (B1) node[midway] (B) [draw,fill=orange] {$A$};\n\\draw[dashed] (A0) -- (A1);\n\\draw[dashed] (B0) -- (B1);\n\\draw [->] (B) to [in=90,out=90,looseness=1.2] node[midway,above] {$\\delta$} (B1);\n\\draw [->] (B) to [in=-90,out=-90,looseness=1.2] node[midway,below] {$\\delta$} (B2);\n\\draw [->] (B0) to [in=-90,out=-90,looseness=1.2] node[midway,below] {$\\delta$} (B2);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 140,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.65]\n  \\node[fill=black,circle,inner sep=2pt](0) at (0:0) {};\n  \\node[fill=black,circle,inner sep=2pt](1) at (0:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](2) at (60:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](3) at (120:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](4) at (180:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](5) at (240:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](6) at (300:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](7) at (120:3) {};\n  \\node[fill=black,circle,inner sep=2pt](8) at (180:3) {};\n  \\node[fill=black,circle,inner sep=2pt](9) at (240:3) {};\n  \\node[fill=black,circle,inner sep=2pt](10) at (300:3) {};\n  \\node[fill=black,circle,inner sep=2pt](11) at (30:3) {};\n  \\node[fill=black,circle,inner sep=2pt](12) at (30:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](13) at (90:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](14) at (150:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](15) at (210:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](16) at (270:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](17) at (330:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](18) at (330:3) {};\n  \\node[fill=black,circle,inner sep=2pt](19) at (30:3) {};\n  \\node[fill=black,circle,inner sep=2pt](20) at (90:3) {};\n  \\node[fill=black,circle,inner sep=2pt](21) at (150:3) {};\n  \\node[fill=black,circle,inner sep=2pt](22) at (210:3) {};\n  \\node[fill=black,circle,inner sep=2pt](23) at (270:3) {};\n  \\node[fill=black,circle,inner sep=2pt](24) at (30:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](25) at (90:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](26) at (150:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](27) at (210:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](28) at (270:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](29) at (330:1.5) {};\n  \\node[fill=black,circle,inner sep=2pt](30) at (0:3) {};\n  \\node[fill=black,circle,inner sep=2pt](31) at (150:3) {};\n  \\node[fill=black,circle,inner sep=2pt](32) at (210:3) {};\n  \\node[fill=black,circle,inner sep=2pt](33) at (270:3) {};\n  \\node[fill=black,circle,inner sep=2pt](34) at (330:3) {};\n  \\draw (1)--(2)--(3)--(4)--(5)--(6)--(1);\n  \\draw (7)--(8)--(9)--(10)--(11)--(12)--(13)--(14)--(15)--(16)--(17)--(18)--(19)--(20)--(21)--(22)--(23)--(24)--(25)--(26)--(27)--(28)--(29)--(30)--(31)--(32)--(33)--(34);\n  \\draw (1)--(7)--(3)--(11)--(5)--(15)--(1)--(10)--(26)--(6)--(14)--(4)--(12)--(25)--(8)--(16)--(9)--(27)--(10);\n  \\draw (2)--(8)--(13)--(4)--(17)--(2)--(12)--(28)--(6)--(22)--(2)--(23)--(29)--(8);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 141,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath, amssymb, amsfonts, amsthm, epsfig, color, graphics, latexsym, mathrsfs}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\\tikzset{node distance=2cm}\n\t\n\t\\tikzstyle{every node} = [rectangle]\n\t\\node (s) {Cybernetics [AI]};\n\t\\node (w) [below of=s] {Machine Learning [ML]};\n\t\\node (x) [below of=w] {Neuromorphic [NM]};\n\t\n\t\\tikzstyle{every node} = [rectangle, draw=red, thick, fill=red!30]\n\t\\node (v) [right of=w] {Neural Computing [SVM]};\n\t\\node (y) [right of=x] {Multi-Layer Neurons (MLN)};\n\t\\node (z) [right of=s] {Artificial Intelligence [AI]};\n\t\n\t\n\t\\tikzstyle{every node} = []\n\t\\node (o) [below of=s, xshift=12.5cm] {Bio-technology: Computer Science, and more ...};\n\t\n\t\\draw[->] (s) -- (z);\n\t\\draw[->] (w) -- (x);\n\t\\draw[->] (w) -- (v);\n\t\\draw[->] (x) -- (y);\n\t\\draw[->] (v) -- (y);\n\t\n\t\n\t\n\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 142,
        "tikz_code": "\\documentclass[tikz]{standalone}\n\\usetikzlibrary{positioning,calc}\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node[draw,circle] (A) {};\n\\node[draw,circle,below left=1cm of A] (B) {};\n\\node[draw,circle,below left=.5cm of B] (C) {};\n\\node[draw,circle,below right=.5cm of B] (D) {};\n\\node[draw,circle,below right=1cm of A] (E) {};\n\\draw (A) -- (B);\n\\draw (A) -- (E);\n\\draw[blue,dashed] (B) -- (C);\n\\draw[red] (B) -- (D);\n\\node[right=5cm of A] (F) {BINARY(T)};\n\\node[draw,circle,right=5cm of F] (G) {};\n\\node[draw,circle,below left=1cm of G] (H) {};\n\\node[draw,circle,below left=.5cm of H] (I) {};\n\\node[draw,circle,below right=.5cm of H] (J) {};\n\\node[draw,circle,below right=1cm of G] (K) {};\n\\draw (G) -- (H);\n\\draw[blue,dashed] (H) -- (I);\n\\draw[red] (H) -- (J);\n\\draw (G) -- (K);\n\\draw[red] let \\p1 = ($(A) - (E)$), \\n1 = {veclen(\\x1,\\y1)} in (A) -- +(110:\\n1) node[above right] {T};\n\\end{tikzpicture}\n\\end{document}"
    },
    {
        "index": 143,
        "tikz_code": "\\documentclass[11pt,reqno]{amsart}\n\\usepackage{amssymb,latexsym}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix,arrows}\n\\usepackage{tikz-cd}\n\\usepackage[T1]{fontenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[description/.style={fill=white,inner sep=2pt}]\n\\matrix (m) [matrix of math nodes, row sep=3em, column sep=2.5em, text height=1.25ex, text depth=0.25ex]\n{ \n\\mathcal E^\\bullet_{N} & E^\\bullet_{S} & E^\\bullet_{S'} & E^\\bullet_{S''} \\\\\n\\mathcal F^\\bullet_{N} & F^\\bullet_{S} & F^\\bullet_{S'} & F^\\bullet_{S''} \\\\\n};\n\\path[->]\n(m-1-2) edge (m-1-3) (m-1-3) edge (m-1-4)\n(m-2-1) edge (m-1-1)\n(m-2-2) edge (m-1-2)\n(m-2-3) edge (m-1-3)\n(m-2-4) edge (m-1-4)\n(m-2-1) edge (m-2-2) \n(m-2-2) edge (m-2-3)\n(m-2-3) edge (m-2-4)\n(m-1-1) edge (m-2-2) \n(m-1-2) edge (m-2-3)\n(m-1-3) edge (m-2-4)\n(m-1-4) edge (m-2-4)\n;\n\\path[right hook->]\n(m-1-2) edge (m-2-1)\n(m-1-3) edge (m-2-2)\n(m-1-4) edge (m-2-3)\n;\n\\path[left hook->]\n(m-1-3) edge (m-2-2)\n(m-1-4) edge (m-2-3)\n;\n\\path[dashed]\n(m-2-2) edge (m-2-1)\n(m-2-4) edge (m-2-3)\n;\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 144,
        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usetikzlibrary{shapes.geometric}\n\\usepackage{amsmath}\n\n\\begin{document}\n\n\\begin{tikzpicture}[auto, node distance=2.5cm, every loop/.style={},\n                    thick,node/.style={scale=0.8, draw,\n                      rectangle,minimum size=10mm,rounded corners=1mm,\n                      top color=white, bottom color=blue!20}]\n  \\node[node] (a) at (0,4.5) {transformation};\n  \\node[node] (b) at (0,3) {$f(x)$ map};\n  \\node[node] (c) at (0,1.5) {color map};\n  \\node[node] (d) at (2,1.5) {Nested map};\n  \\node[node] (e) at (0,0) {$f(x)$ map};\n  \\node[node] (f) at (2,0) {color map};\n  \\node[node] (g) at (0,-1.5) {face textures};\n  \\node[node] (h) at (2,-1.5) {mapper};\n  \\node[node] (i) at (0,-3) {anomaly};\n  \\node[node] (j) at (2,-3) {lighting};\n  \\node[node] (k) at (1,4.5) {$\\text{fits}$ file};\n  \\node[node] (l) at (1,3) {CDF map};\n  \\node[node] (m) at (1,1.5) {color map};\n  \\node[node] (n) at (1,0) {palette};\n  \\node[node] (o) at (1,-1.5) {Mapper};\n  \\node[node] (p) at (1,-3) {anomaly};\n  \n  \\path[every node/.style={font=\\sffamily\\small}]\n    (a) edge (b)\n    (b) edge (d)\n    (d) edge (m)\n    (m) edge (o)\n    (o) edge (l)\n    (l) edge (k)\n    (p) edge (j)\n    (e) edge (f)\n    (n) edge (h)\n    (h) edge (j)\n    (e) edge (g)\n    (g) edge (i)\n    (g) edge (h)\n    (i) edge (p)\n    (f) edge (j)\n    ;\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 145,
        "tikz_code": "\\documentclass[11pt, oneside]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[usenames,dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usepackage{xcolor}\n\\usetikzlibrary{calc,intersections,through,backgrounds}\n\\usetikzlibrary{graphs}\n\\usetikzlibrary{graphs.standard}\n\n\\begin{document}\n\n\\begin{tikzpicture}[every node/.style={draw,circle,inner sep=1pt, minimum size=0pt}]\n    \\node (A) at (0,0) {};\n    \\node (B) at (0,1) {};\n    \\node (C) at (0,2) {};\n    \\node (D) at (0,3) {};\n    \\node (E) at (0,4) {};\n    \\node (F) at (0,5) {};\n    \\node (G) at (0,6) {};\n    \\node (H) at (0,7) {};\n    \\node[fill=red] (I) at (1,0) {};\n    \\node[fill=red] (J) at (1,1) {};\n    \\node[fill=red] (K) at (1,2) {};\n    \\node[fill=blue] (L) at (1,3) {};\n    \\node[fill=blue] (M) at (1,4) {};\n    \\node[fill=blue] (N) at (1,5) {};\n    \\node[fill=orange] (O) at (1,6) {};\n    \\node[fill=orange] (P) at (1,7) {};\n\n    \\draw (A)--(B)--(C)--(D)--(E)--(F)--(G)--(H);\n    \\draw (I)--(J)--(K)--(L)--(M)--(N)--(O)--(P);\n    \\draw (I)--(M)--(J)--(N)--(O)--(P);\n    \\end{tikzpicture}\n\n\\end{document}"
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        "index": 146,
        "tikz_code": "\\documentclass[tikz,border=3.14mm]{standalone}\n\\begin{document}\n\\begin{tikzpicture}\n\\fill[green!20!white] (-60:4) arc (-60:60:4) -- (0,4) -- cycle;\n\\draw[red] (0,4) arc (90:210:4) (0,4) arc (-90:30:4);\n\\foreach \\X in {60,120,...,360}\n{\\draw[blue] (\\X:4) -- (\\X:4.5);}\n\\end{tikzpicture}\n\\end{document}"
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        "index": 147,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n[place/.style={circle,draw=black,fill=white,\ninner sep=0pt,minimum size=8}]\n\\draw[dotted] (0,0) grid (5,5);\n\\draw[black, thick] (0,0)--(0,5)--(5,5)--(5,0)--(0,0);\n\\foreach \\x in {1,2,3,4}\n\\foreach \\y in {1,2,3,4}\n\t\\node at (\\x-0.5,\\y-0.5) [place] {};\n\\foreach \\x in {1,2,3,4}\n\\foreach \\y in {2,3,4}\n\t\\node at (\\x-0.5,\\y-0.5) [place] {};\n\\foreach \\x in {2,3,4}\n\\foreach \\y in {1,2,3,4}\n\t\\node at (\\x-0.5,\\y-0.5) [place] {};\n\\foreach \\x in {2,3,4}\n\\foreach \\y in {1,2,3,4}\n\t\\node at (\\y-0.5,\\x-0.5) [place] {};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 148,
        "tikz_code": "\\documentclass[12pt,reqno]{amsart}\n\\usepackage{amscd,amssymb,amsmath,amsthm}\n\\usepackage[table]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{arrows}\n\\usepackage{amssymb,upref}\n\n\\begin{document}\n\n\\begin{tikzpicture}\\label{23}\n[->,>=stealth',shorten >=-5pt,auto,thick,every node/.style={circle,fill=blue!20,draw}]\n  \\node (n5) at (8,6) {5};\n  \\node (n2) at (6,8)  {2};\n  \\node (n4) at (7,4.6)  {4};\n  \\node (n1) at (8,8) {1};\n  \\node (n3) at (6,6)  {3};\n  \\node (n6) at (5,4.6)  {6};\n  \\node (n7) at (4,8) {7};\n  \\node (n8) at (4,6)  {8};\n  \\node (n9) at (5,4.6)  {9};\n\\path[every node/.style={font=\\sffamily\\small}]\n (n1) edge node [above] {} (n2)\n (n1) edge node [above] {} (n3)\n (n1) edge node [above] {} (n4)\n (n1) edge node [above] {} (n5)\n (n2) edge node [above] {} (n3)\n (n2) edge node [above] {} (n4)\n (n2) edge node [above] {} (n5)\n (n3) edge node [above] {} (n4)\n (n3) edge node [above] {} (n5)\n (n4) edge node [above] {} (n5);\n \\draw [semithick] (n1) -- (n6) -- (n4);\n \\draw [semithick] (n5) -- (n6) -- (n8);\n \\draw [semithick] (n7) -- (n6) -- (n9);\n \\draw [semithick] (n2) -- (n7) -- (n8);\n \\draw [semithick] (n3) -- (n9);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 149,
        "tikz_code": "\\documentclass[a4paper,11pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage[utf8]{inputenc}\n\\usepackage[most]{tcolorbox}\n\\usepackage[tikz]{bclogo}\n\\usepackage{tikz-feynman}\n\\usetikzlibrary{arrows,shapes}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n  \\begin{feynman}\n    \\vertex (a1) {\\(A( \\bar{p} )\\)};\n    \\vertex[below=1.6cm of a1] (a2){\\(\\overline{\\rho}^+\\)};\n    \\vertex[below=0.8cm of a1] (a3);\n    \\vertex[right=1.2cm of a3] (a4);\n    \\vertex[right=1.5cm of a4] (a5);\n    \\vertex[right=0.4cm of a5] (a6);\n    \\vertex[right=1cm of a6] (a7);\n    \\vertex[right=0.3cm of a7] (a8) {\\(\\ell^-\\)};\n    \\vertex[right=1.2cm of a7] (a9) {\\(\\ell^+\\)};\n\n\n    \\vertex[right=1cm of a2] (a10);\n    \\vertex[above=0.8cm of a10] (a11){\\( (\\rm{B}) \\)};\n    \\vertex[below=0.8cm of a10] (a12){\\( (\\rm{A}) \\)};\n    \\vertex[right=0.3cm of a10] (a13);\n    \\vertex[right=1cm of a13] (a14);\n    \\vertex[right=0.3cm of a14] (a15);\n\n    \\vertex[right=0.6cm of a13] (a16);\n    \\vertex[below=1.2cm of a16] (a17){\\(\\overline{\\psi}^\\pm \\)};\n    \\vertex[above=1.2cm of a16] (a18){\\(\\psi^\\mp \\)};\n\n    \\diagram* {\n      {[edges=fermion]\n        (a2)--(a4)--(a5)--(a7)--(a9),\n      },\n      {[edges=boson]\n        (a1)--(a3),\n        (a4)--(a13)--(a15),\n        (a13)--(a17),\n        (a13)--(a18),\n      },\n      (a5) -- [boson, edge label=\\(Z\\)] (a7),\n      (a7) -- [scalar, edge label=\\( \\gamma \\)] (a9),\n      (a1) -- [boson, edge label=\\( W^\\pm \\)] (a13),\n    };\n\n\n  \\end{feynman}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 150,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amsfonts,amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{snakes}\n\\usetikzlibrary{plotmarks}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.5]\n \\draw[black,line width=0.5pt] (0,0) -- (1,0); \n \\foreach \\xpos in {0,1}\n  \\filldraw (\\xpos,0) circle(3pt);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 151,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[latin9]{inputenc}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n%x\n\\draw[dashed] (-0.5,0) -- (12.5,0);\n\\draw[dashed] (-0.5,1) -- (12.5,1);\n\\draw[dashed] (-0.5,2) -- (12.5,2);\n\\draw[dashed] (-0.5,3) -- (12.5,3);\n\\draw[dashed] (-0.5,4) -- (12.5,4);\n\\draw[dashed] (-0.5,5) -- (12.5,5);\n\\draw[dashed] (-0.5,6) -- (12.5,6);\n\\draw[dashed] (-0.5,7) -- (12.5,7);\n\\draw[dashed] (-0.5,8) -- (12.5,8);\n\\draw[dashed] (-0.5,9) -- (12.5,9);\n\\draw[dashed] (-0.5,10) -- (12.5,10);\n\\draw[dashed] (-0.5,11) -- (12.5,11);\n\\draw[dashed] (-0.5,12) -- (12.5,12);\n%h\n\\draw (-0.5,0) -- (12.5,1);\n\\draw (-0.5,1) -- (12.5,2);\n\\draw (-0.5,2) -- (12.5,3);\n\\draw (-0.5,3) -- (12.5,4);\n\\draw (-0.5,4) -- (12.5,5);\n\\draw (-0.5,5) -- (12.5,6);\n\\draw (-0.5,6) -- (12.5,7);\n\\draw (-0.5,7) -- (12.5,8);\n\\draw (-0.5,8) -- (12.5,9);\n\\draw (-0.5,9) -- (12.5,10);\n\\draw (-0.5,10) -- (12.5,11);\n\\draw (-0.5,11) -- (12.5,12);\n%P\n\\draw (0,1) -- (3,2);\n\\draw (1,1) -- (3.5,2.5);\n\\draw (2,1) -- (4,2);\n\\draw (3,2) -- (4.5,3.5);\n\\draw (4,2) -- (5,3);\n\\draw (4.5,3.5) -- (5.5,4.5);\n\\draw (5,3) -- (6,3);\n\\draw (5.5,4.5) -- (6.5,5.5);\n\\draw (6,3) -- (7,4);\n\\draw (6.5,5.5) -- (7.5,6.5);\n\\draw (7,4) -- (8,5);\n\\draw (7.5,6.5) -- (8.5,7.5);\n\\draw (8,5) -- (9,6);\n\\draw (8.5,7.5) -- (9.5,8.5);\n\\draw (9,6) -- (10,7);\n\\draw (9.5,8.5) -- (10.5,9.5);\n\\draw (10,7) -- (11,8);\n\\draw (10.5,9.5) -- (11.5,10.5);\n\\draw (11,8) -- (12,9);\n\\draw (11.5,10.5) -- (12.5,11.5);\n%P\n\\draw (3,2) -- (4,2);\n\\draw (3.5,2.5) -- (4.5,3.5);\n\\draw (4,2) -- (5,3);\n\\draw (4.5,3.5) -- (5.5,4.5);\n\\draw (5,3) -- (6,3);\n\\draw (5.5,4.5) -- (6.5,5.5);\n\\draw (6,3) -- (7,4);\n\\draw (6.5,5.5) -- (7.5,6.5);\n\\draw (7,4) -- (8,5);\n\\draw (7.5,6.5) -- (8.5,7.5);\n\\draw (8,5) -- (9,6);\n\\draw (8.5,7.5) -- (9.5,8.5);\n\\draw (9,6) -- (10,7);\n\\draw (9.5,8.5) -- (10.5,9.5);\n\\draw (10,7) -- (11,8);\n\\draw (10.5,9.5) -- (11.5,10.5);\n\\draw (11,8) -- (12,9);\n\\draw (11.5,10.5) -- (12.5,11.5);\n%Q\n\\draw (0,1) -- (2,1);\n\\draw (2,1) -- (3,2);\n\\draw (3,2) -- (4,2);\n\\draw (4,2) -- (5,3);\n\\draw (5,3) -- (6,3);\n\\draw (6,3) -- (7,4);\n\\draw (7,4) -- (8,5);\n\\draw (8,5) -- (9,6);\n\\draw (9,6) -- (10,7);\n\\draw (10,7) -- (11,8);\n\\draw (11,8) -- (12,9);\n\\draw (0,1) node[below]{$a_i$};\n\\draw (1,1) node[below]{$a_i-1$};\n\\draw (2,1) node[below]{$a_i-2$};\n\\draw (3,2) node[below]{$a_i-3$};\n\\draw (4,2) node[below]{$a_i-4$};\n\\draw (5,3) node[below]{$a_i-5$};\n\\draw (6,3) node[below]{$a_i-6$};\n\\draw (7,4) node[below]{$a_i-7$};\n\\draw (8,5) node[below]{$a_i-8$};\n\\draw (9,6"
    },
    {
        "index": 152,
        "tikz_code": "\\documentclass[tikz,border=5mm]{standalone}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows.meta,chains}\n\\usetikzlibrary{shapes.geometric,positioning,fit}\n\n\\begin{document}\n\n\\begin{tikzpicture}[%\n        auto,\n        font=\\sf \\scriptsize,\n        >=LaTeX,\n        start chain = going below,\n        state/.style = {%\n            rectangle, rounded corners,\n            draw=red, very thick,\n            text width=3.25cm,\n            align=center,\n            inner ysep=3mm,\n            on chain\n        },\n        frame/.style = {%\n            draw=purple,\n            inner sep=1mm,\n        }\n    ]\n    \\node[state] (site) {site};\n    \\node[state] (periodic) {periodic};\n    \\node[state] (homogeneous) {homogeneous};\n    \\node[state] (exciton) {Exciton};\n    \\node[state] (phonon) {Phonon};\n    \\node[state] (coupled) {Coupled};\n    \\node[state] (zeroQ) {$\\mathit{Q}_{2N-dim}^{(tot)}$};\n    \\node[state] (SLIM) {$\\mathit{SLIM}$};\n    \\node[state] (great) {great $\\mathit{Q}^{(tot)}$ (\\textit{dim}$\\neq$\\textit{n-dim})};\n    \\node[state] (SM) {SM $\\mathit{Q}^{(tot)}$ (\\textit{n-dim}$\\neq$\\textit{dim})};\n    \\node[state] (crossed) {$\\mathit{SLIM}$ crossed $\\mathit{Q}^{(tot)}$};\n    \\node[state] (small) {less potent $\\mathit{Q}^{(tot)}$};\n    \\node[state] (less) {less potent (\\textit{dim}$\\neq$\\textit{n-dim})};\n    \\node[state] (less2) {less potent $\\mathit{SLIM}$ crossed $\\mathit{Q}^{(tot)}$};\n    \\node[state] (far) {far-coupled};\n\n    \\node[frame, fit=(zeroQ)(SLIM)] (frame-zeroQ-SLIM) {};\n    \\node[frame, fit=(great)(SM)] (frame-great-SM) {};\n    \\node[frame, fit=(crossed)(less)] (frame-crossed-less) {};\n    \\node[frame, fit=(far)(less2)] (frame-far-less2) {};\n\n    \\draw[<-] (site) -- (periodic);\n    \\draw[<-] (periodic) -- (exciton);\n    \\draw[<-] (exciton) -- (phonon);\n    \\draw[<-] (phonon) -- (coupled);\n    \\draw[<-] (coupled) -- (zeroQ);\n    \\draw[<-] (zeroQ) -- (SLIM);\n    \\draw[<-] (coupled) -- (SM);\n    \\draw[<-] (coupled) -- (crossed);\n    \\draw[<-] (coupled) -- (less);\n    \\draw[<-] (coupled) -- (less2);\n    \\draw[<-] (coupled) -- (far);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 153,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amssymb, amsmath, amsthm, graphicx}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8]\n\n\\draw[thin,gray,-latex] (0,0) -- (4.5,0) node[anchor=south] {$Q$};\n\\draw[thin,gray,-latex] (0,0) -- (0,3.75) node[anchor=west] {$N$};\n\n\\foreach \\x in {1,...,3}\n   \\draw (\\x,0) -- (\\x,0.1) node[anchor=north,below] {$\\x$};\n\n\\foreach \\x in {1,...,3}\n   \\draw (0,\\x) -- (.1,\\x) node[anchor=east,left] {$\\x$};\n\n\\draw[fill=red, fill opacity=0.2, thick] (0,1) rectangle (1,2);\n\\draw[fill=red, fill opacity=0.2, thick] (1,3) rectangle (2,4);\n\n\\draw (2.5,1.5) node {$I$};\n\\draw (1.5,2.5) node {$J$};\n\\draw (2.5,3.5) node {$J$};\n\\draw (3.5,4.5) node {$I$};\n\n\\begin{scope}[xshift=5cm]\n\n\\draw[thin,gray,-latex] (0,0) -- (4.5,0) node[anchor=south] {$Q$};\n\\draw[thin,gray,-latex] (0,0) -- (0,3.75) node[anchor=west] {$N$};\n\n\\foreach \\x in {1,...,3}\n   \\draw (\\x,0) -- (\\x,0.1) node[anchor=north,below] {$\\x$};\n\n\\foreach \\x in {1,...,3}\n   \\draw (0,\\x) -- (.1,\\x) node[anchor=east,left] {$\\x$};\n\n\\draw[fill=red, fill opacity=0.2, thick] (0,1) rectangle (1,2);\n\\draw[fill=red, fill opacity=0.2, thick] (1,2) rectangle (2,3);\n\\draw[fill=red, fill opacity=0.2, thick] (2,3) rectangle (3,4);\n\n\\draw (2.5,1.5) node {$I$};\n\\draw (1.5,2.5) node {$J$};\n\\draw (2.5,3.5) node {$J$};\n\\draw (3.5,4.5) node {$I$};\n\n\\end{scope}\n\n\\begin{scope}[xshift=10cm]\n\n\\draw[thin,gray,-latex] (0,0) -- (4.5,0) node[anchor=south] {$Q$};\n\\draw[thin,gray,-latex] (0,0) -- (0,3.75) node[anchor=west] {$N$};\n\n\\foreach \\x in {1,...,3}\n   \\draw (\\x,0) -- (\\x,0.1) node[anchor=north,below] {$\\x$};\n\n\\foreach \\x in {1,...,3}\n   \\draw (0,\\x) -- (.1,\\x) node[anchor=east,left] {$\\x$};\n\n\\draw[fill=red, fill opacity=0.2, thick] (0,1) rectangle (1,2);\n\\draw[fill=red, fill opacity=0.2, thick] (1,2) rectangle (2,3);\n\\draw[fill=red, fill opacity=0.2, thick] (2,2) rectangle (3,3);\n\\draw[fill=red, fill opacity=0.2, thick] (3,3) rectangle (4,4);\n\n\\draw (2.5,1.5) node {$I$};\n\\draw (1.5,2.5) node {$J$};\n\\draw (2.5,2.5) node {$J$};\n\\draw (3.5,3.5) node {$J$};\n\\draw (4.5,4.5) node {$I$};\n\n\\end{scope}\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
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        "index": 155,
        "tikz_code": "\\documentclass{article}\n\\usepackage{pgfplots, pgfplotstable, booktabs}\n\\usepackage[margin=1cm]{geometry}\n\n\\pgfplotsset{\n    /pgfplots/table/header=false,\n    /pgfplots/table/every odd row/.style={before row={\\toprule},after row={\\midrule}},\n    /pgfplots/table/every even row/.style={before row={\\midrule},after row={\\toprule}},\n}\n\n\\pgfplotstableread{\n    1 1/2 1/2 1/2\n    1 1/2 1/2 1/2\n    1 1/2 1/2 1/2\n    1 1/2 1/2 1/2\n}\\data\n\n\\pgfplotsset{\n  bar width=0.6cm\n}\n\n\\newcommand{\\drawBars}[2][]{%\n    \\begin{tikzpicture}[#1]\n        \\begin{axis}[\n            width=1.5cm, height=0.5cm,\n            xtick=data,\n            xticklabels={},\n            ytick={1,2,3},\n            yticklabels={, , },\n            ytick pos=left,\n            major x tick style = transparent,\n            ybar,\n            bar width=0.6cm,\n            nodes near coords={\\pgfmathprintnumber\\pgfplotspointmeta\\%},\n            nodes near coords align={vertical},\n            every node near coord/.append style={\n                anchor=west,\n                color=black,\n            }\n            ]\n            \\addplot[draw=none,fill=red,] table[x expr=\\coordindex,y index=#2] {\\data};\n        \\end{axis}\n    \\end{tikzpicture}\n}\n\n\\begin{document}\n\n\\begin{center}\n    \\begin{minipage}{0.4\\textwidth}\n        \\textbf{\\Large Type 1} \\\\[1em]\n        \\drawBars[opacity=0.5]{0}\n        \\drawBars[opacity=0.5]{1}\n    \\end{minipage}\n    \\begin{minipage}{0.4\\textwidth}\n        \\textbf{\\Large Type 2} \\\\[1em]\n        \\drawBars[opacity=0.5]{0}\n        \\drawBars[opacity=0.5]{1}\n    \\end{minipage}\n\\end{center}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath, amsthm, amssymb, tikz, hyperref, enumerate}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.6]\n        \\tikzstyle{every node} = [rectangle]\n        \\node (71) at (0,0) {$71$};\n        \\node (61) at (0,1.5) {$61$};\n        \\node (51) at (0,3) {$51$};\n        \\node (41) at (0,4.5) {$41$};\n        \\node (31) at (0,6) {$31$};\n        \n        \\node (65) at (4,0) {$65$};\n        \\node (55) at (4,1.5) {$55$};\n        \\node (45) at (4,3) {$45$};\n        \\node (35) at (4,4.5) {$35$};\n        \\node (25) at (4,6) {$25$};\n        \n        \\node (59) at (8,0) {$59$};\n        \\node (49) at (8,1.5) {$49$};\n        \\node (39) at (8,3) {$39$};\n        \\node (29) at (8,4.5) {$29$};\n        \\node (19) at (8,6) {$19$};\n        \n        \\node (53) at (12,0) {$53$};\n        \\node (43) at (12,1.5) {$43$};\n        \\node (33) at (12,3) {$33$};\n        \\node (23) at (12,4.5) {$23$};\n        \\node (13) at (12,6) {$13$};\n        \n        \\node (62) at (16,0) {$62$};\n        \\node (52) at (16,1.5) {$52$};\n        \\node (42) at (16,3) {$42$};\n        \\node (32) at (16,4.5) {$32$};\n        \\node (22) at (16,6) {$22$};\n        \n        \\node (56) at (20,0) {$56$};\n        \\node (46) at (20,1.5) {$46$};\n        \\node (36) at (20,3) {$36$};\n        \\node (26) at (20,4.5) {$26$};\n        \\node (16) at (20,6) {$16$};\n        \n        \\node (50) at (24,0) {$50$};\n        \\node (40) at (24,1.5) {$40$};\n        \\node (30) at (24,3) {$30$};\n        \\node (20) at (24,4.5) {$20$};\n        \\node (10) at (24,6) {$10$};\n        \n        \\node (37) at (10,7.5) {$37$};\n        \n        \\node (60) at (14,7.5) {$60$};\n        \\node (50) at (14,9) {$50$};\n        \\node (40) at (14,10.5) {$40$};\n        \\node (30) at (14,12) {$30$};\n        \n        \\node (64) at (18,7.5) {$64$};\n        \\node (54) at (18,9) {$54$};\n        \\node (44) at (18,10.5) {$44$};\n        \\node (34) at (18,12) {$34$};\n        \n        \\node (63) at (22,7.5) {$63$};\n        \\node (53) at (22,9) {$53$};\n        \\node (43) at (22,10.5) {$43$};\n        \\node (33) at (22,12) {$33$};\n        \n        \\node (61) at (26,7.5) {$61$};\n        \\node (51) at (26,9) {$51$};\n        \\node (41) at (26,10.5) {$41$};\n        \\node (31) at (26,12) {$31$};\n        \n        \\node at (-3.5, 5.25) {(see Proposition~\\ref{prop:v2r4})};\n        \n        \\foreach \\from/\\to in {71/61, 61/51, 51/41, 41/31, 31/25, 25/19, 19/13, 13/10, 10/62, 62/52, 52/42, 42/32, 32/22, 22/56, 56/46, 46/36, 36/26, 26/50, 50/40, 40/30, 30/20, 20/16, 16/12, 12/8, 8/5, 5/4, 4/3, 3/2, 2/60, 60/54, 54/44, 44/34, 34/23, 23/17, 17/11, 11/9, 9/6, 6/5, 5/4, 4/3, 3/2, 2/53, 53/43, 43/33, 33/21, 21/55, 55/45, 45/35, 35/29, 29/18, 18/14, 14/10, 10/9, 9/8, 8/7, 7/61, 61/55, 55/49, 49/39, 39/33, 33/27, 27/59, 59/49,"
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        "tikz_code": "\\documentclass[11pt,a4paper,table]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usepackage{tikz-dependency}\n\\usepackage{pgf}\n\\usetikzlibrary{shapes,shapes.misc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[level distance=8mm, sibling distance=8mm]\n  \\node[fill=blue!30, anchor=base, shape=isosceles triangle, inner sep=0.75mm, minimum width=1.35cm, outer sep=0mm] (copy) {$\\ast$}\n    child {\n      node {$\\dots$}\n      edge from parent[densely dotted]\n    }\n    child {\n      node[fill=green!30, anchor=base, shape=isosceles triangle, inner sep=0.75mm, minimum width=1.35cm, outer sep=0mm] (in_map) {$\\ast$}\n      child {\n        node {$\\dots$}\n        edge from parent[densely dotted]\n      }\n      child {\n        node[fill=green!30, anchor=base, shape=isosceles triangle, inner sep=0.75mm, minimum width=1.35cm, outer sep=0mm] (in_map2) {$\\ast$}\n        child {\n          node {$\\dots$}\n          edge from parent[densely dotted]\n        }\n        child {\n          node {$\\dots$}\n          edge from parent[densely dotted]\n        }\n        child {\n          node {$\\dots$}\n          edge from parent[densely dotted]\n        }\n        edge from parent[densely dotted]\n      }\n      child {\n        node {$\\dots$}\n        edge from parent[densely dotted]\n      }\n      child {\n        node {$\\dots$}\n        edge from parent[densely dotted]\n      }\n      edge from parent[densely dotted]\n    };\n    \\node[fill=red!30, anchor=base, shape=isosceles triangle, inner sep=0.75mm, minimum width=1.35cm, outer sep=0mm] (input) at ([xshift=30mm, yshift=-10mm]copy) {$\\ast$};\n    \\node[fill=blue!30, anchor=base, shape=isosceles triangle, inner sep=0.75mm, minimum width=1.35cm, outer sep=0mm] (copy2) at ([xshift=30mm, yshift=-25mm]copy) {$\\ast$};\n    \\node[fill=green!30, anchor=base, shape=isosceles triangle, inner sep=0.75mm, minimum width=1.35cm, outer sep=0mm] (in_map3) at ([xshift=30mm, yshift=-40mm]copy) {$\\ast$};\n    \\node[fill=blue!30, anchor=base, shape=isosceles triangle, inner sep=0.75mm, minimum width=1.35cm, outer sep=0mm] (copy3) at ([xshift=30mm, yshift=-55mm]copy) {$\\ast$};\n    \\node[right=1.75cm] {$\\dots$};\n    \\node[right=1.75cm, fill=red!30, anchor=base, shape=isosceles triangle, inner sep=0.75mm, minimum width=1.35cm, outer sep=0mm] (output) at ([xshift=30mm, yshift=-60mm]copy) {$\\ast$};\n    \\node[fill=green!30, anchor=base, shape=isosceles triangle, inner sep=0.75mm, minimum width=1.35cm, outer sep=0mm] (in_map4) at ([xshift=30mm, yshift=-65mm]copy) {$\\ast$};\n    \\node[fill=blue!30, anchor=base, shape=isosceles triangle, inner sep=0.75mm, minimum width=1.35cm, outer sep=0mm] (copy4) at ([xshift=30mm, yshift=-70mm]copy) {$\\ast$};\n    \\node[fill=green!30, anchor=base, shape=isosceles triangle, inner sep=0.75mm, minimum width=1.35cm, outer sep=0mm] (in_map5) at ([xshift=30mm, yshift=-75mm]copy) {$\\ast$};\n    \\node[fill=blue!30, anchor=base, shape=isosceles triangle, inner sep=0.75mm, minimum width=1.35cm, outer sep=0mm] (copy5) at ([xshift=30mm, yshift=-80mm]copy) {$\\ast$};\n    \\node[fill=green!30, anchor=base, shape=isosceles triangle, inner sep=0.75mm, minimum width=1.35cm, outer sep=0mm] (in_map6) at ([xshift=30mm, yshift=-85mm]copy) {$\\ast$};\n    \\node[fill=blue!30, anchor=base, shape=isosceles triangle, inner sep=0.75mm, minimum width=1.35cm, outer sep=0mm] (copy6) at ([xshift=30mm, yshift=-90mm]copy) {$\\ast$};\n    \\node[right=1.75cm] {$\\dots$};\n    \n    \\node[right=1.75cm, anchor=base] at (copy) {$x$ layers};\n    \\node[right=1.75cm, anchor=base] at (input) {$x$ layers};\n    \\node[right=1.75cm, anchor=base] at (copy2) {$x$ layers};\n    \\node[right=1.75cm, anchor=base] at (copy3) {$x$ layers};\n    \\node[right=1.75cm, anchor=base] at (output) {$x$ layers};\n    \\node[right=1.75cm, anchor=base] at (in_map3) {$x$ layers};\n    \\node[right=1.75cm, anchor=base] at (in_map4) {$x$ layers};\n    \\node[right=1.75cm, anchor=base] at (in_map5) {$x$ layers};\n    \\node[right=1.75cm, anchor=base] at (in_map6) {$x$ layers};\n    \\node[right=1.75cm] at (copy6) {$x$ layers"
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    {
        "index": 171,
        "tikz_code": "\\documentclass[journal]{IEEEtran}\n\\usepackage{tikz}\n\\usepackage{amsmath}\n\\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.16,\n    tick label style = {font = {\\fontsize{8 pt}{12 pt}\\selectfont}},\n    every axis label = {font = {\\size{10 pt}{20 pt}\\selectfont}},\n    legend style = {font = {\\size{8 pt}{12 pt}\\selectfont}},\n    label style = {font = {\\size{8 pt}{12 pt}\\selectfont}},\n    label style = {font = {\\size{8 pt}{12 pt}\\selectfont}},\n    tick style = {line width=0.1pt}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n            \\tikzset{\n                dot/.style={circle,inner sep=0.05cm,fill=black,draw,\n                    isosceles triangle,\n                    isosceles triangle apex angle=90,anchor=apex,\n                    label={[shift={(175:0.6)}]apex}}\n                }\n            \\node [anchor=west] (user) at (0,0) {\\includegraphics[width=0.05\\linewidth]{example-image}};\n            \\draw [->] (user.east)--(1,0);\n            \\node[anchor=west] at (2,0) {User};\n            \\draw [thick] (2.2,0) -- (3.4,0);\n            \\node (encoder) at (3.6,0) [minimum width=0.6cm,minimum height=0.8cm, draw,anchor=south west] {\\includegraphics[width=0.2\\linewidth]{example-image}};\n            \\draw [->] (3.8,0.4) -- (encoder.south west);\n            \\node[anchor=west] at (4.8,0) {Encoder};\n            \\draw [thick] (5,0) -- (5.8,0);\n            \\draw [->] (5.9,0) -- (6.8,0);\n            \\node (bs) at (7.2,0) [minimum width=0.6cm,minimum height=0.8cm, draw,anchor=south west] {};\n            \\draw [->] (7.4,0.4) -- (bs.south west);\n            \\node[anchor=west] at (8.4,0) {Bottleneck};\n            \\draw [thick] (8.6,0) -- (9.4,0);\n            \\node (decoder) at (9.6,0) [minimum width=0.6cm,minimum height=0.8cm, draw,anchor=south west] {\\includegraphics[width=0.2\\linewidth]{example-image}};\n            \\draw [->] (9.8,0.4) -- (decoder.south west);\n            \\node[anchor=west] at (10.8,0) {Decoder};\n            \\draw [thick] (11,0) -- (11.8,0);\n            \\node[anchor=west] at (12.8,0) {Output};\n            \\draw [->] (12.9,0) -- (13.8,0);\n            \\draw [thick, dashed] (14,0) -- (14.8,0);\n            \\draw [thick, dashed] (15,0) -- (15.8,0);\n            \\draw [thick, dashed] (16,0) -- (16.8,0);\n            \\draw [thick, dashed] (17,0) -- (17.8,0);\n            \\node (an) at (18.2,0) [minimum width=0.6cm,minimum height=0.8cm, draw,anchor=south west] {};\n            \\draw [->] (18.4,0.4) -- (an.south west);\n            \\node[anchor=west] at (19.4,0) {Anonymization};\n            \\draw [->] (13.6,-1.1) -- (13.6,-1.6);\n            \\draw [->] (15.4,-1.1) -- (15.4,-1.6);\n            \\draw [->] (17.2,-1.1) -- (17.2,-1.6);\n            \\draw [->] (19.0,-1.1) -- (19.0,-1.6);\n            \\draw [->] (5.6,0.3) -- (encoder.south east);\n            \\draw [->] (7.6,0.3) -- (bs.south east);\n            \\draw [->] (9.6,0.3) -- (decoder.south east);\n            \\draw [->] (11.6,0.3) -- (an.south east);\n            \\draw [->] (13.6,0.3) -- (encoder.north east);\n            \\draw [->] (15.6,0.3) -- (bs.north east);\n            \\draw [->] (17.6,0.3) -- (decoder.north east);\n            \\draw [->] (19.6,0.3) -- (an.north east);\n        \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 172,
        "tikz_code": "\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{pgf,tikz}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{intersections}\n\\usetikzlibrary{decorations.pathreplacing}\n\\tikzset{core/.style={inner sep=0pt}}\n\\tikzset{contraction/.style={line width=0.75}}\n\\tikzset{contractionDots/.style={contraction, dotted}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\node[core] (1) at (0,0) {};\n    \\node[core] (2) at (0.75,0) {};\n    \\node[core] (3) at (1.5,0) {};\n    \\node[core] (4) at (2.25,0) {};\n    \\node[core] (5) at (3,0) {};\n    \\node[core] (6) at (3.75,0) {};\n    \\node[core] (7) at (0.75,0.75) {};\n    \\node[core] (8) at (1.5,0.75) {};\n    \\node[core] (9) at (2.25,0.75) {};\n    \\node[core] (10) at (3,0.75) {};\n    \\node[core] (11) at (0.75,1.5) {};\n    \\node[core] (12) at (1.5,1.5) {};\n    \\node[core] (13) at (2.25,1.5) {};\n    \\node[core] (14) at (3,1.5) {};\n    \\node[core] (15) at (1.5,2.25) {};\n    \\node[core] (16) at (1.5,2.9) {};\n    \\node[core] (17) at (0.75,2.25) {};\n    \\node[core] (18) at (1.5,2.9) {};\n    \\node[core] (19) at (2.25,2.25) {};\n    \\node[core] (20) at (3,2.25) {};\n    \n    \\node[core] (21) at (4.5,1.5) {};\n    \\node[core] (22) at (5.25,1.5) {};\n    \\node[core] (23) at (6,1.5) {};\n    \\node[core] (24) at (4.5,0.75) {};\n    \\node[core] (25) at (5.25,0.75) {};\n    \\node[core] (26) at (6,0.75) {};\n    \\node[core] (27) at (5.25,0) {};\n    \\node[core] (28) at (6,0) {};\n    \\node[core] (29) at (6.75,0) {};\n\n    \\node[core] at (0.75,-1) {$S = -1$};\n    \\node[core] at (1.5,-1) {$S = 0$};\n    \\node[core] at (2.25,-1) {$S = 1$};\n    \\node[core] at (0.75,2.9) {$S = 2$};\n    \\node[core] at (6.75,2.9) {$S = 3$};\n    \n    \\node[core] at (1.5,3.25) {};\n    \n    \\draw (1) to (2);\n    \\draw (2) to (3);\n    \\draw (3) to (4);\n    \\draw (4) to (5);\n    \\draw (5) to (6);\n    \\draw (1) to (7);\n    \\draw (2) to (8);\n    \\draw (3) to (9);\n    \\draw (4) to (10);\n    \\draw (7) to (8);\n    \\draw (8) to (9);\n    \\draw (9) to (10);\n    \\draw (7) to (11);\n    \\draw (8) to (12);\n    \\draw (9) to (13);\n    \\draw (10) to (14);\n    \\draw (11) to (12);\n    \\draw (12) to (13);\n    \\draw (13) to (14);\n    \\draw (11) to (15);\n    \\draw (12) to (15);\n    \\draw (13) to (15);\n    \\draw (15) to (16);\n    \\draw (11) to (17);\n    \\draw (12) to (17);\n    \\draw (13) to (17);\n    \\draw (15) to (18);\n    \\draw (16) to (18);\n    \\draw (17) to (18);\n    \\draw (19) to (10);\n    \\draw (19) to (14);\n    \\draw (19) to (18);\n    \\draw (20) to (14);\n    \\draw (20) to (18);\n    \\draw (27) to (28);\n    \\draw (28) to (29);\n    \\draw (27) to (26);\n    \\draw (28) to (26);\n    \\draw (29) to (26);\n    \\draw (27) to (25);\n    \\draw (28) to (25);\n    \\draw (29) to (25);\n    \\draw (27) to (24);\n    \\draw (28) to (24);\n    \\draw (29) to (24);\n\n    \\node[core] (0) at (3.75,1.5) {};\n    \\draw (0) to (1);\n    \\draw (0) to (2);\n    \\draw (0) to (3);\n    \\draw (0) to (4);\n    \\draw (0) to (5);\n    \\draw (0) to (6);\n\n    \\node[core] (10) at (6.75,1.5) {};\n    \\node[core] (11) at (7.5,1.5) {};\n    \\node[core] (12) at (8.25,1.5) {};\n"
    },
    {
        "index": 173,
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    {
        "index": 174,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,automata,trees,shapes,positioning,calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\\def\\basecolor{0.3}\n\\def\\textcolor{white}\n\n\\definecolor{mycolor0}{rgb}{\\basecolor,0.8,0.8}\n\\definecolor{mycolor1}{rgb}{0.6,0.8,0.8}\n\\definecolor{mycolor2}{rgb}{0.8,0.4,0.4}\n\n\\begin{axis}[\nwidth=8cm,\nheight=4cm,\nxlabel={Secret-Key Square-root rate, $\\kappa$},\nylabel={Cover user square-root rate},\nxmin=0, xmax=1,\nymin=0, ymax=0.45,\nymajorgrids,\n]\n\\addplot[\n%mark=*,\nthick,\ncolor=mycolor0,\nmark size=1pt,\n]\ntable {%\n0 0.006\n0.25 0.02\n0.5 0.03\n0.75 0.2\n1 0.4\n};\n\\addplot[\n%mark=*,\nthick,\ndashed,\ncolor=mycolor2,\nmark size=1pt,\n]\ntable {%\n0 0.006\n0.25 0.02\n0.5 0.03\n0.75 0.2\n1 0.4\n};\n\\addplot[\ndashed,\ncolor=gray,\n%mark=asterisk,\nvery thick,\ndomain=0:1,\nsamples=100,\nforget plot\n]\n{0.3};\n\\end{axis}\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[a4paper,11pt]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.6]\n\\node [draw, circle] (H1) at (0,0) {$H_1$};\n\\node [draw, circle] (H2) at (2,0) {$H_2$};\n\\node [draw, circle] (H3) at (4,0) {$H_3$};\n\\node [draw, circle] (H4) at (0,-2) {$H_4$};\n\\node [draw, circle] (H5) at (2,-2) {$H_5$};\n\\node [draw, circle] (H6) at (4,-2) {$H_6$};\n\\node [circle] (a) at (-1,-2) {};\n\\node [circle] (b) at (5,-2) {};\n\\node [align=center] at (-1,-1) {Local Hamiltonian\\\\(classical bits)};\n\\node [align=center] at (5,-1) {Qubit Hamiltonian\\\\(one per literal in clause)};\n\\node [align=center] at (2,-2.5) {$C_1$: $\\{+,-\\}$};\n\\node [align=center] at (4,-2.5) {$C_2$: $\\{+,-,+,-\\}$};\n\\node [align=center] at (2,-3.1) {$C_3$: $\\{+,-,-\\}$};\n\\node [align=center] at (4,-3.1) {$C_4$: $\\{+,-,+,-\\}$};\n\\draw[very thick, red] (H1) to (H4) to (H2) to (H6) to (H5) to (H3);\n\\draw[very thick, red] (H1) to (H5) to (H3);\n\\draw[very thick, red] (H2) to (H6);\n\\draw (H1) edge [bend right] node[left] {\\footnotesize{1}} (a);\n\\draw (H3) edge [bend right] node[right] {\\footnotesize{5}} (b);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 176,
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        "index": 177,
        "tikz_code": "\\documentclass[10pt,twocolumn,twoside]{IEEEtran}\n\\usepackage{amsmath,amsthm}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usepackage{pgfplotstable}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.8]\n\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (n1) at (1,1) {\\LARGE $t_{p1}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (n2) at (2,1) {\\LARGE $t_{p2}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (n3) at (3,1) {\\LARGE $t_{p3}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (n4) at (4,1) {\\LARGE $t_{p4}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (n5) at (5,1) {\\LARGE $t_{p5}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (n6) at (6,1) {\\LARGE $t_{p6}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (n7) at (7,1) {\\LARGE $t_{p7}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (n8) at (8,1) {\\LARGE $t_{p8}$};\n\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (m1) at (1,2) {\\LARGE $t_{m1}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (m2) at (2,2) {\\LARGE $t_{m2}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (m3) at (3,2) {\\LARGE $t_{m3}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (m4) at (4,2) {\\LARGE $t_{m4}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (m5) at (5,2) {\\LARGE $t_{m5}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (m6) at (6,2) {\\LARGE $t_{m6}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (m7) at (7,2) {\\LARGE $t_{m7}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (m8) at (8,2) {\\LARGE $t_{m8}$};\n\n    \\draw[-,dashed,color=red!70] (n1) -- (n2) -- (n3) -- (n4) -- (n5) -- (n6) -- (n7) -- (n8);\n    \\draw[-,dashed,color=red!70] (m1) -- (m2) -- (m3) -- (m4) -- (m5) -- (m6) -- (m7) -- (m8);\n    \\draw[-] (n1) -- (m1);\n    \\draw[-] (n2) -- (m2);\n    \\draw[-] (n3) -- (m3);\n    \\draw[-] (n4) -- (m4);\n    \\draw[-] (n5) -- (m5);\n    \\draw[-] (n6) -- (m6);\n    \\draw[-] (n7) -- (m7);\n    \\draw[-] (n8) -- (m8);\n    \\draw[-] (n1) -- (m2);\n    \\draw[-] (n2) -- (m3);\n    \\draw[-] (n3) -- (m4);\n    \\draw[-] (n4) -- (m5);\n    \\draw[-] (n5) -- (m6);\n    \\draw[-] (n6) -- (m7);\n    \\draw[-] (n7) -- (m8);\n    \\draw[-] (n1) -- (m3);\n    \\draw[-] (n2) -- (m4);\n    \\draw[-] (n3) -- (m5);\n    \\draw[-] (n4) -- (m6);\n    \\draw[-] (n5) -- (m7);\n    \\draw[-] (n6) -- (m8);\n\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (n9) at (3.5,1.5) {\\LARGE $t_{p1}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (n10) at (3.5,0.5) {\\LARGE $t_{p2}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (n11) at (5,1.5) {\\LARGE $t_{p3}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (n12) at (5,0.5) {\\LARGE $t_{p4}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (n13) at (6.5,1.5) {\\LARGE $t_{p5}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (n14) at (6.5,0.5) {\\LARGE $t_{p6}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (n15) at (8,1.5) {\\LARGE $t_{p7}$};\n    \\node[circle, minimum size=20pt, draw=black, fill=black!20] (n16) at (8,0.5) {\\LARGE $t_{p8"
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        "index": 178,
        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\tikzset{>=latex}\n\\usepackage{pgfplots}\n\\usetikzlibrary{pgfplots.fillbetween}\n\\usetikzlibrary{math}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=2.5]\n    \\draw [<->,thick] (0,2) node (yaxis) [above] {$C_1^*(s^{1/2}k^{-1})$}\n        |- (2,0) node (xaxis) [right] {$k$};\n    \\draw[black,dashed] (0,0.6) -- (0.6,0.6);\n    \\draw[black,dashed] (0.6,0) -- (0.6,0.6);\n    \\draw[black,dashed] (0,0.6) -- (0.6,0.6);\n    \\draw[black,dashed] (0,1.2) -- (0.6,0.6);\n    \\draw[black,dashed] (0,1.8) -- (1.2,0.6);\n    \\draw[black,dashed] (0,1.8) -- (1.8,0.6);\n    \\draw[black,dashed] (1.2,0.6) -- (1.8,0.6);\n    \\draw[black,dashed] (1.2,0.6) -- (1.2,0);\n    \\draw[black,dashed] (1.2,0) -- (1.2,0.6);\n    \\draw[black,dashed] (1.8,0) -- (1.8,0.6);\n    \\draw[black,dashed] (1.8,0.6) -- (1.8,0);\n    \\draw[black,dashed] (1.8,0) -- (1.8,0.6);\n    \\filldraw [black] (0.6,0.6) circle (0.4pt) node[below=0.2pt,black] {$1/z$};\n    \\filldraw [black] (1.8,0.6) circle (0.4pt) node[below=0.2pt,black] {$1/(A/B)$};\n    \\filldraw [black] (1.2,0.6) circle (0.4pt) node[below=0.2pt,black] {$1/z$};\n    \\filldraw [black] (0,1.8) circle (0.4pt) node[below=0.2pt,black] {$C_1^*(s^{1/2}k^{-1})$};\n    \\filldraw [black] (0,0.6) circle (0.4pt) node[below=0.2pt,black] {$1/z$};\n    \\node[black] at (1.5,1.3) {$C_{\\sigma_1^*(z/k-1)}$};\n    \\node[black] at (1.5,0.7) {$C_{\\sigma_1^*(z/k-1)}$};\n    \\end{tikzpicture}\n\n\\end{document}"
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        "index": 179,
        "tikz_code": "\\documentclass[a4paper,11pt]{amsart}\n\\usepackage{amsmath,amssymb,amsthm,amsfonts}\n\\usepackage[colorlinks=true,citecolor=blue]{hyperref}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[xscale=8,yscale=40]\n\\draw[black,->] (0,0) -- (1.1,0);\n\\draw[black,->] (0,-0.02) -- (0,0.1);\n\\draw[red,thick] (0,0) to[out=-45,in=-135] (1,0);\n\\node[below] at (0.5,-0.05) {$0$};\n\\node[below] at (1,-0.05) {$\\pi$};\n\\draw[black,dashed] (0,0.05) -- (1,0.05);\n\\draw[black,dashed] (0,-0.05) -- (1,-0.05);\n\\node[left] at (-0.02,0.05) {$1$};\n\\node[left] at (-0.02,-0.05) {$0$};\n\\node[left] at (-0.02,-0.07) {$0.993$};\n\\node[left] at (-0.02,0) {$0.007$};\n\\node[left] at (-0.02,0.07) {$1.007$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 180,
        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usetikzlibrary{calc,intersections}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n  \\path [name path=A] (0,0) -- (10,0);\n  \\path [name path=B] (0,1) -- (10,1);\n  \\path [name path=C] (0,2) -- (10,2);\n  \\fill [name intersections={of=A and B, by={a,b}},\n  name intersections={of=A and C, by={c,d}},\n  name intersections={of=B and C, by={e,f}},\n  name intersections={of=A and C, by={g,h}},\n  name intersections={of=C and B, by={i,j}}]\n    (h) -- (intersection-1) -- (j) -- (intersection-2) -- cycle;\n  \\path [name path=A'] (1,0) -- (11,0);\n  \\path [name path=B'] (1,1) -- (11,1);\n  \\path [name path=C'] (1,2) -- (11,2);\n  \\path [name path=D'] (1,2) -- (11,2);\n  \\path [name path=E'] (1,1) -- (11,1);\n  \\path [name path=F'] (1,0) -- (11,0);\n  \\path [name intersections={of=A' and C', by={a1,b1}}];\n  \\path [name intersections={of=A' and B', by={c1,d1}}];\n  \\path [name intersections={of=E' and F', by={e1,f1}}];\n  \\path [name intersections={of=B' and C', by={g1,h1}}];\n  \\path [name intersections={of=C' and B', by={i1,j1}}];\n  \\path [name intersections={of=B' and D', by={a2,b2}}];\n  \\path [name intersections={of=A' and D', by={c2,d2}}];\n  \\path [name intersections={of=A' and E', by={a3,b3}}];\n  \\path [name intersections={of=E' and F', by={e3,f3}}];\n  \\path [name intersections={of=D' and F', by={a4,b4}}];\n  \\path [name intersections={of=A' and E', by={c4,d4}}];\n  \\path [name intersections={of=E' and C', by={e5,f5}}];\n  \\path [name intersections={of=B' and D', by={a5,b5}}];\n  \\path [name intersections={of=A' and C', by={c5,d5}}];\n  \\draw [dashed] (a) -- (b) -- (e) -- (f) -- cycle;\n  \\draw [dashed] (c) -- (d) -- (g) -- (h) -- cycle;\n  \\draw [dashed] (i) -- (j) -- (c5) -- (d5) -- cycle;\n  \\draw [dashed] (a2) -- (b2) -- (a5) -- (b5) -- cycle;\n  \\draw [dashed] (a2) -- (b2) -- (a4) -- (b4) -- cycle;\n  \\draw [dashed] (a3) -- (b3) -- (a4) -- (b4) -- cycle;\n  \\fill [opacity=0.2] (0,0) -- (a) -- (b) -- (e) -- (f) -- (0,1) -- (c) -- (d) -- (g) -- (h) -- (0,2) -- (c) -- (d) -- (i) -- (j) -- cycle;\n  \\draw [opacity=0.2,violet,fill=violet!20] (0,0) -- (a) -- (b) -- (e) -- (f) -- (0,1) -- (c) -- (d) -- (g) -- (h) -- (0,2) -- (c) -- (d) -- (i) -- (j) -- cycle;\n  \\draw [violet] (1,0) -- (11,0);\n  \\draw [violet] (1,1) -- (11,1);\n  \\draw [violet] (1,2) -- (11,2);\n  \\draw [blue] (a) -- (b) -- (e) -- (f) -- cycle;\n  \\draw [blue] (c) -- (d) -- (g) -- (h) -- cycle;\n  \\draw [blue] (i) -- (j) -- (c5) -- (d5) -- cycle;\n  \\draw [blue] (a2) -- (b2) -- (a5) -- (b5) -- cycle;\n  \\draw [blue] (a2) -- (b2) -- (a4) -- (b4) -- cycle;\n  \\draw [blue] (a3) -- (b3) -- (a4) -- (b4) -- cycle;\n  \\draw [thick,blue] (b2) -- (b3);\n  \\draw [blue] (a2) -- (a3);\n  \\draw [blue] (c5) -- (c4);\n  \\draw [blue] (d5) -- (d4);\n  \\draw [blue] (e5) -- (e4);\n  \\draw [blue] (f5) -- (f4);\n  \\draw [thick,blue] (a4) -- (a5);\n  \\draw [thick,blue] (b4) -- (b5);\n  \\draw [thick,blue] (c4) -- (c5);\n  \\draw [thick,blue] (d4) -- (d5);\n  \\draw [thick,blue] (e4) -- (e5);\n  \\draw [thick,blue] (f4) -- (f5);\n  \\draw [thick,blue] (b1) -- (a1);\n  \\draw [thick,blue] (c1) -- (d1);\n  \\draw [thick,blue] (e3) -- (f3);\n  \\node [blue] at (11.5,1.5) {$\\Gamma_{p_m}$};\n  \\node [blue] at (11.5,0.5) {$\\Gamma_{f}$};\n  \\node [violet] at (6,4) {$\\Gamma_p$};\n  \\draw [red,thick] (a) -- (a1);\n  \\draw [red,thick] (b) -- (b1);\n  \\draw"
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        "index": 181,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.5]\n\t\\fill[white!80!black] (1.5, 0.5) circle (2.5);\n\t\\draw (1.5, 0.5) circle (2.5);\n\t\\fill[white!80!black] (0, 0) rectangle (2.5, 2.5);\n\t\\draw (0, 0) rectangle (2.5, 2.5);\n\t\\fill[white!80!black] (2.5, -2) rectangle (2.5, 0);\n\t\\draw (2.5, -2) rectangle (2.5, 0);\n\t\\fill[white!80!black] (3, -2) rectangle (3, 0);\n\t\\draw (3, -2) rectangle (3, 0);\n\t\\fill[white!80!black] (3.5, -2) rectangle (3.5, -0.5);\n\t\\draw (3.5, -2) rectangle (3.5, -0.5);\n\t\\fill[white!80!black] (4, -2) rectangle (4, -0.5);\n\t\\draw (4, -2) rectangle (4, -0.5);\n\t\\fill[white!80!black] (4.5, -2) rectangle (4.5, -0.5);\n\t\\draw (4.5, -2) rectangle (4.5, -0.5);\n\t\\fill[white!80!black] (2.5, 1.5) rectangle (3, 2);\n\t\\draw (2.5, 1.5) rectangle (3, 2);\n\t\\fill[white!80!black] (1.5, 1.5) rectangle (2, 2);\n\t\\draw (1.5, 1.5) rectangle (2, 2);\n\t\\fill[white!80!black] (2.5, 0) rectangle (3, 0.5);\n\t\\draw (2.5, 0) rectangle (3, 0.5);\n\t\\fill[white!80!black] (3, 0) rectangle (3.5, 0.5);\n\t\\draw (3, 0) rectangle (3.5, 0.5);\n\t\\fill[white!80!black] (3.5, 0) rectangle (4, 0.5);\n\t\\draw (3.5, 0) rectangle (4, 0.5);\n\t\\fill[white!80!black] (4, 0) rectangle (4.5, 0.5);\n\t\\draw (4, 0) rectangle (4.5, 0.5);\n\t\\fill[white!80!black] (2, -2) rectangle (2.5, -1.5);\n\t\\draw (2, -2) rectangle (2.5, -1.5);\n\t\\fill[white!80!black] (2.5, -2) rectangle (3, -1.5);\n\t\\draw (2.5, -2) rectangle (3, -1.5);\n\t\\fill[white!80!black] (3, -2) rectangle (3.5, -1.5);\n\t\\draw (3, -2) rectangle (3.5, -1.5);\n\t\\fill[white!80!black] (3.5, -2) rectangle (4, -1.5);\n\t\\draw (3.5, -2) rectangle (4, -1.5);\n\t\\fill[white!80!black] (4, -2) rectangle (4.5, -1.5);\n\t\\draw (4, -2) rectangle (4.5, -1.5);\n\t\\fill[white!80!black] (1.5, -1.5) rectangle (2, -1);\n\t\\draw (1.5, -1.5) rectangle (2, -1);\n\t\\fill[white!80!black] (2, -1.5) rectangle (2.5, -1);\n\t\\draw (2, -1.5) rectangle (2.5, -1);\n\t\\fill[white!80!black] (2.5, -1.5) rectangle (3, -1);\n\t\\draw (2.5, -1.5) rectangle (3, -1);\n\t\\fill[white!80!black] (3, -1.5) rectangle (3.5, -1);\n\t\\draw (3, -1.5) rectangle (3.5, -1);\n\t\\fill[white!80!black] (3.5, -1.5) rectangle (4, -1);\n\t\\draw (3.5, -1.5) rectangle (4, -1);\n\t\\fill[white!80!black] (4, -1.5) rectangle (4.5, -1);\n\t\\draw (4, -1.5) rectangle (4.5, -1);\n\t\\fill[white!80!black] (2.5, -0) rectangle (3, 0.5);\n\t\\draw (2.5, -0) rectangle (3, 0.5);\n\t\\fill[white!80!black] (3, -0) rectangle (3.5, 0.5);\n\t\\draw (3, -0) rectangle (3.5, 0.5);\n\t\\fill[white!80!black] (3.5, -0) rectangle (4, 0.5);\n\t\\draw (3.5, -0) rectangle (4, 0.5);\n\t\\fill[white!80!black] (4, -0) rectangle (4.5, 0.5);\n\t\\draw (4, -0) rectangle (4.5, 0.5);\n\t\\draw[thick, blue] (3,0) rectangle (4,1);\n\t\\node[blue] at (4.5,-0.5) {$B_t$};\n\t\\fill (0,0) circle (0.1);\n\t\\node at (1.5,-0.5) {$p^t$};\n\t\\draw[thick, black] (3,0) -- (4,0);\n\t\\draw[thick, black] (4,0) -- (4,1);\n\t\\node at (4.75,0) {$\\rho$};\n\t\\node at (4.75,1) {$(\\rho,6)$};\n\t\\node at (-2.5,-2.5) {$B_{s,p^t}(\\rho,\\zeta^6)$};\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n            \\node (1) {\\includegraphics[width=\\textwidth]{example-image}};\n            \\node (2) at ($(1)+(-3.1cm,-2.3cm)$) {\\includegraphics[width=.25\\textwidth]{example-image}};\n            \\node[above,yshift=0.05cm] at ($(2)+(-.8cm,.0cm)$) {\\small{Coupler $10$\\,m}};\n            \\node[above,yshift=0.05cm] at ($(2)+(.0cm,.0cm)$) {\\small{Coupler $20$\\,m}};\n        \\end{tikzpicture}\n\n\\end{document}"
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        "index": 186,
        "tikz_code": "\\documentclass[11pt,reqno]{amsart}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage[colorlinks=true,linkcolor=webgreen,filecolor=webbrown,citecolor=webgreen]{hyperref}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\t\\draw[->] (-5,0) -- (5,0) node[anchor=north east] {$t$};\n\t\t\t\\draw[->] (0,-0.5) -- (0,5) node[anchor=north east] {$\\ell$};\n\t\t\t\\draw (0,0.2) rectangle (2,0.8);\n\t\t\t\\draw[fill=blue!50] (-2,0) rectangle (-1,0.5);\n\t\t\t\\node[left] at (2,0.5) {$\\ell$};\n\t\t\t\\node[left] at (-2,0.5) {$\\ell$};\n\t\t\t\\draw[dashed] (2,0) -- (2,5);\n\t\t\t\\node[right] at (2,5) {$\\ell=R\\left(\\frac{1}{T}+\\frac{\\ell}{T^2} \\right)^{1/2}T$};\n\t\t\t\\draw[dashed] (2,0) -- (2,3.7);\n\t\t\t\\draw[dashed] (2,3.7) -- (0,3.7);\n\t\t\t\\draw[->] (0,3.7) -- (0,3.5);\n\t\t\t\\node[left] at (0,3.5) {$\\ell$};\n\t\t\t\\node[below] at (2.6,1.2) {regularity};\n\t\t\t\\draw[dashed] (2,0) -- (4.5,0);\n\t\t\t\\draw[dashed] (4.5,0) -- (4.5,5);\n\t\t\t\\draw[->] (4.5,0) -- (4.5,0.5);\n\t\t\t\\node[right] at (4.5,0.5) {$\\ell$};\n\t\t\t\\node[below] at (0.5,0.7) {$Q^2$};\n\t\t\t\\node[above] at (0.5,0.2) {$Q^2$};\n\t\t\t\\node[right] at (3.5,2.75) {backward};\n\t\t\t\\node[right] at (3.5,2.45) {propagation of $\\ell$};\n\t\t\t\\node[right] at (3.5,2.2) {using Prop.~\\ref{prop:backward}};\n\t\t\t\\node[right] at (3.5,1.7) {($\\ell$,$2^k$) unique};\n\t\t\t\\node[above right] at (1.5,0.7) {slice};\n\t\t\t\\node[above right] at (1.5,0.3) {of regularity};\n\t\t\t\\draw[->] (1.5,0.5) arc (10:60:0.5) node[pos=0.2,below right] {$\\alpha$};\n\t\t\t\\node[below] at (1.5,0) {anmuths of};\n\t\t\t\\node[below] at (1.5,0) {regularity};\n\t\t\t\\draw[dashed] (1.5,0) -- (1.5,1.4);\n\t\t\t\\draw[dashed] (1.5,1.4) -- (0,1.4);\n\t\t\t\\draw[->] (0,1.4) -- (0,1.6);\n\t\t\t\\node[left] at (0,1.6) {$\\ell$};\n\t\t\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt, oneside]{article}\n\\usepackage{amsmath, amsthm}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}[>=stealth,xscale=2.5, yscale=1.2]\n\n\\node[inner sep = 0.8pt, label=below:{$x$}] (00) at (0,0) {$\\scriptstyle\\bullet$};\n\\node[inner sep = 0.8pt, label=below:{$\\sigma(x)$}] (10) at (1,1) {$\\scriptstyle\\bullet$};\n\\node[inner sep = 0.8pt, label=above:{$\\sigma(X)$}] (20) at (2,2) {$\\scriptstyle\\bullet$};\n\\node[inner sep = 0.8pt, label=above:{$Y$}] (30) at (3,1) {$\\scriptstyle\\bullet$};\n\\node[inner sep = 0.8pt, label=below:{$\\sigma(Y)$}] (40) at (4,2) {$\\scriptstyle\\bullet$};\n\\node[inner sep = 0.8pt, label=below:{$z$}] (50) at (5,1) {$\\scriptstyle\\bullet$};\n\\node[inner sep = 0.8pt] (60) at (6,0) {$\\;\\;\\cdots\\cdots$};\n\n\\draw[<->, blue, thick] (00) to [bend left=20]node[black,midway,xshift=-0.2cm, yshift=0.1cm]{$\\sigma$} (10);\n\\draw[<->, blue, thick] (30) to [bend left=20]node[black,midway,xshift=-0.2cm, yshift=0.1cm]{$\\sigma$} (40);\n\n\\draw[thick, dotted, blue, ->] (10) to (20);\n\\draw[thick, dotted, blue, ->] (40) to (50);\n\n\\draw[thick, dotted, blue, ->] (00) to (10);\n\\draw[thick, dotted, blue, ->] (50) to (60);\n\n\\draw[thick, dotted, red, dashed, ->] (20) to (30);\n\\draw[thick, dotted, red, dashed, ->] (30) to (40);\n\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[journal,twocolumn]{IEEEtran}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{xcolor}\n\\usepackage{color}\n\\usepackage{colortbl}\n\\usepackage{pgfplots}\n\\usepackage{pgfplotstable}\n\\usetikzlibrary{patterns}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,arrows,calc,patterns,positioning}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=newest}\n\n\\begin{document}\n\n\\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=3.0cm, thick, scale=0.55, every node/.style={scale=0.55}]\n\t\\tikzstyle{main node}=[circle,fill=black!10,draw,minimum size=1.2cm,inner sep=0pt]\n\t\n\t\\node[main node, fill=gray]  (1) \t\t\t\t\t    {\n\t\t\\includegraphics[width=2.0cm]{example-image}\n\t};\n\t\\node[main node, fill=gray]  (2)  [above right of=1]\t\t{\n\t\t\\includegraphics[width=2.0cm]{example-image}\n\t};\n\t\\node[main node, fill=gray]  (3)  [right of=2]\t    {\n\t\t\\includegraphics[width=2.0cm]{example-image}\n\t};\n\t\\node[main node, fill=gray]  (4)  [below right of=3]\t    {\n\t\t\\includegraphics[width=2.0cm]{example-image}\n\t};\n\t\\node[main node, fill=gray]  (5)  [below right of=1]\t    {\n\t\t\\includegraphics[width=2.0cm]{example-image}\n\t};\n\t\n\t\\node[main node, fill=gray]  (6)  [right of=3]\t    {\n\t\t\\includegraphics[width=2.0cm]{example-image}\n\t};\n\t\n\t\\node[main node, fill=gray]  (7)  [right of=5]\t    {\n\t\t\\includegraphics[width=2.0cm]{example-image}\n\t};\n\t\n\t\\node[main node, fill=gray]  (8)  [above right of=6]\t    {\n\t\t\\includegraphics[width=2.0cm]{example-image}\n\t};\n\t\n\t\\node[main node, fill=gray]  (9)  [below right of=7]\t    {\n\t\t\\includegraphics[width=2.0cm]{example-image}\n\t};\n\t\n\t\n\t\\node[main node, fill=gray]  (10)  [right of=8]\t    {\n\t\t\\includegraphics[width=2.0cm]{example-image}\n\t};\n\t\n\t\\node[main node, fill=gray]  (11)  [right of=10]\t    {\n\t\t\\includegraphics[width=2.0cm]{example-image}\n\t};\n\t\n\t\n\t\n\t\\path[every node/.style={font=\\sffamily\\small}]\n\t(1) edge  node  [below] {Side-\\\\information} (5)\n\t(1) edge  node  [above] {Private-\\\\information} (5)\n\t(1) edge  node  [above] {Channel} (2)\n\t(2) edge  node  [above] {Legitimate} (6)\n\t(3) edge  node  [above] {Legitimate} (8)\n\t(4) edge  node  [below] {Un-desired} (9)\n\t(6) edge  node  [below] {Un-desired} (9)\n\t(10) edge  node  [above] {Un-desired} (11)\n\t(10) edge  node  [above] {Un-desired} (11)\n\t;\n\t\n\t\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[aps,pra,twocolumn,superscriptaddress,longbibliography]{revtex4-1}\n\\usepackage{pgfplots}\n\\usepackage{amssymb}\n\\usepackage{amsmath,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usepackage{color}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n \\node (img) {\n  \\includegraphics[width=0.28\\textwidth]{example-image}};\n\\node[below=of img, node distance=0cm, xshift=0.4cm, yshift=1.1cm,font=\\scriptsize, align = center] {$\\Omega \\, \\text{l}$};\n\\node[left=of img, node distance=0cm, rotate=90, anchor=center, yshift=-0.9cm, xshift=0.5cm, font=\\scriptsize, align = center] {$\\Omega_{L}$};\n\\draw[blue,thick] (-0.4, 1.4) rectangle (1.9, 2.4);\n\\draw[red, thick] (-0.15, 0.9) rectangle (2.1, 2.3);\n\\draw[black, thick] (-0.1, 0.3) rectangle (2.25, 2.6);\n \\draw [<->, thick]  (2.4,0.5) -- (2.7,0.5)  node[right, xshift=-0.5cm, yshift=0.1cm, font=\\scriptsize]{$\\Omega^{f}$};\n \\end{tikzpicture}\n\n\\end{document}"
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        "index": 198,
        "tikz_code": "\\documentclass[a4paper]{article}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{color}\n\\usepackage{pgfplots}\n\\usepackage{tikz}\n\\pgfplotsset{compat=newest}\n\\usepgfplotslibrary{fillbetween}\n\\usetikzlibrary{arrows.meta}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{shapes.geometric}\n\\usetikzlibrary{shapes.misc}\n\\usetikzlibrary{spy}\n\\usetikzlibrary{backgrounds}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\t\\begin{axis}[\n\t\t\twidth=12cm,\n\t\t\theight=6cm,\n\t\t\tylabel=Number of Publications,\n\t\t\txlabel={Year},\n\t\t\txtick={2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022},\n\t\t\txmin=2012,\n\t\t\txmax=2022,\n\t\t\tytick={0,10,20,30,40,50,60,70,80,90,100},\n\t\t\tymajorgrids=true,\n\t\t\tlegend style={at={(0.6,-0.1)},\n\t\t\t\tanchor=north,legend columns=-1},\n\t\t\tlegend columns=3,\n\t\t\t]\n\t\t\t%\t\txmin=2012, xmax=2022,\n\t\t\t\\addplot[line width=1pt, color=red, mark=+, dotted, mark options=solid]\n\t\t\tcoordinates {\n\t\t\t\t(2012,3.50) (2013,1.85) (2014,1.11) (2015,1.88) (2016,2.83) (2017,3.55) (2018,4.11) (2019,4.91) (2020,4.92) (2021,4.91) (2022,5.04)};\n\t\t\t\\addlegendentry{European}\n\t\t\t\\addplot[line width=1pt, color=magenta, mark=*, mark options=solid]\n\t\t\tcoordinates {\n\t\t\t\t(2012,1.03) (2013,1.23) (2014,1.14) (2015,1.68) (2016,2.18) (2017,3.15) (2018,3.68) (2019,4.77) (2020,4.69) (2021,4.73) (2022,5.04)};\n\t\t\t\\addlegendentry{Africa}\n\t\t\t\\addplot[line width=1pt, color=black, mark=square, mark options=solid]\n\t\t\tcoordinates {\n\t\t\t\t(2012,1.21) (2013,1.35) (2014,1.22) (2015,1.88) (2016,2.65) (2017,3.24) (2018,3.79) (2019,4.61) (2020,4.68) (2021,4.69) (2022,5.04)};\n\t\t\t\\addlegendentry{Asia}\n\t\t\t\\addplot[line width=1pt, color=blue, mark=triangle, mark options=solid]\n\t\t\tcoordinates {\n\t\t\t\t(2012,2.55) (2013,3.51) (2014,3.82) (2015,4.01) (2016,4.99) (2017,5.50) (2018,6.03) (2019,6.96) (2020,6.91) (2021,6.94) (2022,7.02)};\n\t\t\t\\addlegendentry{Atlantic}\n\t\t\t\\addplot[line width=1pt, color=cyan, mark=diamond, mark options=solid]\n\t\t\tcoordinates {\n\t\t\t\t(2012,3.25) (2013,3.39) (2014,3.29) (2015,4.01) (2016,4.79) (2017,5.36) (2018,6.05) (2019,6.84) (2020,6.82) (2021,6.85) (2022,7.05)};\n\t\t\t\\addlegendentry{Caribbean}\n\t\t\t\\addplot[line width=1pt, color=olive, mark=o, mark options=solid]\n\t\t\tcoordinates {\n\t\t\t\t(2012,1.68) (2013,1.67) (2014,1.68) (2015,1.88) (2016,2.52) (2017,3.06) (2018,3.56) (2019,4.43) (2020,4.46) (2021,4.46) (2022,5.01)};\n\t\t\t\\addlegendentry{Central}\n\t\t\t\\addplot[line width=1pt, color=violet, mark=x, mark options=solid]\n\t\t\tcoordinates {\n\t\t\t\t(2012,1.64) (2013,1.76) (2014,1.64) (2015,1.88) (2016,2.43) (2017,2.86) (2018,3.34) (2019,4.13) (2020,4.15) (2021,4.17) (2022,5.01)};\n\t\t\t\\addlegendentry{Mediterranean}\n\t\t\t\\addplot[line width=1pt, color=orange, mark=star, mark options=solid]\n\t\t\tcoordinates {\n\t\t\t\t(2012,1.43) (2013,1.54) (2014,1.43) (2015,1.88) (2016,2.49) (2"
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        "tikz_code": "\\documentclass[10pt,reqno]{amsart}\n\\usepackage{amsmath,amsthm,amssymb,mathrsfs,amsfonts,bm}\n\\usepackage{tikz-cd}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usepackage{color}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\\draw (0,0)--(0,3)--(1,3)--(1,0)--(0,0);\n\t\t\\draw (2,0)--(2,3)--(3,3)--(3,0)--(2,0);\n\t\t\\draw (4,0)--(4,3)--(5,3)--(5,0)--(4,0);\n\t\t\\draw (6,0)--(6,3)--(7,3)--(7,0)--(6,0);\n\t\t\\draw (1,0)--(0,3);\n\t\t\\draw (2,0)--(3,3);\n\t\t\\draw (4,0)--(5,3);\n\t\t\\draw (5,0)--(6,3);\n\t\t\\draw (7,0)--(6,3);\n\t\t\\draw[dashed] (0,0)--(1,3);\n\t\t\\draw[dashed] (3,0)--(2,3);\n\t\t\\draw[dashed] (6,0)--(5,3);\n\t\t\\draw[decoration={brace,mirror,raise=5pt},decorate]\n\t\t(0,0) -- node[below=6pt] {$\\mathcal{Z}_1^-$} (1,0);\n\t\t\\draw[decoration={brace,mirror,raise=5pt},decorate]\n\t\t(5,0) -- node[below=6pt] {$\\mathcal{Z}_1^+$} (6,0);\n\t\t\\draw[decoration={brace,mirror,raise=5pt},decorate]\n\t\t(1,3) -- node[above=6pt] {$\\mathcal{Z}_2^+$} (5,3);\n\t\t\\draw[dashed] (0,3)--(6,3);\n\t\t\\draw[decoration={brace,raise=5pt},decorate]\n\t\t(0,3) -- node[above=6pt] {$\\mathcal{Z}_2^+$} (7,3);\n\t\t\\draw[decoration={brace,raise=5pt},decorate]\n\t\t(1,0) -- node[below=6pt] {$\\mathcal{R}_1$} (2,0);\n\t\t\\draw[decoration={brace,raise=5pt},decorate]\n\t\t(5,0) -- node[below=6pt] {$\\mathcal{R}_2$} (6,0);\n\t\t\\draw[thick,green!50!black] (0.5,1.5)--(5.5,1.5);\n\t\t\\draw[dashed,blue] (0,1.5)--(1,1.5);\n\t\t\\draw[dashed,blue] (5,1.5)--(6,1.5);\n\t\t\\draw[dashed,blue] (1,1.5)--(1,3);\n\t\t\\draw[dashed,blue] (5,1.5)--(5,3);\n\t\t\\node[circle,fill=black,inner sep=0.5pt,minimum size=0.1pt] at (1,1.5) {};\n\t\t\\node[circle,fill=black,inner sep=0.5pt,minimum size=0.1pt] at (5,1.5) {};\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "index": 200,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix,arrows,decorations.pathmorphing,decorations.pathreplacing}\n\\usepackage{amsmath,amssymb,euscript,array,mathrsfs,appendix,ctable}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.2]\n\\filldraw[color=black, fill=white] (0,0) circle (2);\n\\node at (-0.2,0.2) {SMBH};\n\\filldraw[color=black, fill=black] (0,0) circle (0.5);\n\\node at (2,2) {DM halo};\n\\node at (2,0.7) {Event horizon};\n\\draw[-latex] (1.15,1) -- (1.55,1.25);\n\\draw[dashed] (0,0) circle (3);\n\\draw[dashed] (0,0) circle (2);\n\\node[rotate=-4] at (1.1,2.5) {DM halo};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 201,
        "tikz_code": "\\documentclass[aps,prd,nofootinbib,showpacs,preprintnumbers,longbibliography,amssymb,11pt]{revtex4-1}\n\\usepackage[utf8]{inputenc}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{decorations.text}\n\\usetikzlibrary{backgrounds}\n\\usetikzlibrary{shapes.misc}\n\\tikzset{cross/.style={cross out, draw=black, fill=none, minimum size=2*(#1-\\pgflinewidth), inner sep=0pt, outer sep=0pt}, cross/.default={2pt}}\n\\usepackage{pgfplots}\n\\usepgfplotslibrary{groupplots,dateplot}\n\\usetikzlibrary{patterns,shapes.arrows}\n\\pgfplotsset{compat=newest}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node[draw,circle,minimum size=1.5mm,inner sep=0,fill=black] (A) at (0,0) {};\n\\node[draw,circle,minimum size=1.5mm,inner sep=0,fill=black] (B) at (2,0.5) {};\n\\node[draw,circle,minimum size=1.5mm,inner sep=0,fill=red] (C) at (1,1.5) {};\n\\draw[thick] (A) -- (B);\n\\draw[thick,dashed] (A) -- (C);\n\\draw[thick,decoration={snake,amplitude=1pt,segment length=2pt},decorate] (B) -- (C);\n\\draw (2.5,-0.5) -- (3.5,-0.5) -- (3.5,-0.2) -- (2.5,-0.2);\n\\node[align=center] at (3.3,-0.5) {\\scriptsize $\\rightarrow$};\n\\draw[thick] (3.5,0) -- (5.5,0);\n\\draw[thick,decoration={snake,amplitude=1pt,segment length=2pt},decorate] (3.5,0.5) -- (4.5,1.5) -- (5.5,0.5);\n\\draw (2.5,-1) node[below] {(a)};\n\n\\begin{scope}[shift={(7.5,0)}]\n\\node[draw,circle,minimum size=1.5mm,inner sep=0,fill=black] (A) at (0,0) {};\n\\node[draw,circle,minimum size=1.5mm,inner sep=0,fill=black] (B) at (2,0.5) {};\n\\node[draw,circle,minimum size=1.5mm,inner sep=0,fill=red] (C) at (1,1.5) {};\n\\draw[thick] (A) -- (B);\n\\draw[thick,dashed] (A) -- (C);\n\\draw[thick,decoration={snake,amplitude=1pt,segment length=2pt},decorate] (B) -- (C);\n\\draw (2.5,-0.5) -- (3.5,-0.5) -- (3.5,-0.2) -- (2.5,-0.2);\n\\node[align=center] at (3.3,-0.5) {\\scriptsize $\\rightarrow$};\n\\draw[thick] (3.5,0) -- (5.5,0);\n\\draw[thick] (3.5,0.5) -- (5.5,0.5);\n\\draw[thick,decoration={snake,amplitude=1pt,segment length=2pt},decorate] (4.5,1.5) -- (5.5,0.5);\n\\draw (2.5,-1) node[below] {(b)};\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 202,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amsfonts, amsthm, amssymb, amsmath, stmaryrd, etoolbox}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{\n\tmatrix,arrows,shapes,decorations.markings,decorations.pathreplacing\n}\n\\tikzset{\n\trewritenode/.style={shape=circle,draw,minimum size=1em}\n}\n\\tikzset{\n\tRWopen/.style={shape=circle,draw=black,fill=white,scale=0.5,font=\\Huge}\n}\n\\tikzset{\n\tRWclosed/.style={shape=circle,fill=black,scale=0.5,font=\\Huge}\n}\n\\tikzset{CDnode/.style={shape=circle,fill=white,scale=.5}}\n\\tikzset{->-/.style={decoration={markings,mark=at position .5 with {\\arrow{>}}},postaction={decorate}}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n% left fold\n\\begin{scope}\n\\clip (-4.5,-1.5) rectangle (-2.5,1.5);\n\\draw [dashed] (-2.5,0) ellipse (1.5 and 0.75);\n\\draw (-2,0) circle (0.25);\n\\end{scope}\n% right fold\n\\begin{scope}\n\\clip (1.5,-1.5) rectangle (3.5,1.5);\n\\draw [dashed] (3.5,0) ellipse (1.5 and 0.75);\n\\draw (4,0) circle (0.25);\n\\end{scope}\n% nodes\n\\node [circle,draw=black,fill=black,scale=0.25] (L) at (-2.5,0) {};\n\\node [circle,draw=black,fill=black,scale=0.25] (R) at (3.5,0) {};\n\\node [circle,draw=black,fill=black,scale=0.25] (LL) at (-4.5,1) {};\n\\node [circle,draw=black,fill=black,scale=0.25] (LR) at (-2.5,1) {};\n\\node [circle,draw=black,fill=black,scale=0.25] (RL) at (1.5,-1) {};\n\\node [circle,draw=black,fill=black,scale=0.25] (RR) at (3.5,-1) {};\n\\node [circle,draw=black,fill=black,scale=0.25] (RRR) at (4.5,-1) {};\n% graph\n\\path [->,thick,red] (L) edge [bend left] (LL);\n\\path [<-,thick,red] (LR) edge [bend left] (R);\n\\path [<-,thick,red] (RL) edge [bend right] (RR);\n\\path [<-,thick,blue] (RRR) edge [bend right] (R);\n\\path [->,thick,blue] (L) edge [bend right] (LR);\n\\path [->,thick,blue] (RL) edge [bend left] (RR);\n\\path [<-,thick,red] (RL) edge [bend right] (LR);\n\\path [<-,thick,red] (RL) edge [bend right] (L);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 203,
        "tikz_code": "\\documentclass[tikz,border=3mm]{standalone}\n\\usepackage{siunitx}\n\\usetikzlibrary{shapes,positioning}\n\\begin{document}\n\\begin{tikzpicture}[node distance=0pt,\n  rbox/.style={rounded corners,minimum size=10mm},\n  grn/.style={fill=green!30},\n  red/.style={fill=red!30},\n  orange/.style={fill=orange!30},\n  ylw/.style={fill=yellow!30},\n  blu/.style={fill=blue!30},\n  pst/.style={pin edge={to-,thin,black}}]\n \\begin{scope}\n  \\path node[rbox,grn,text=white,align=center] (1) {First cell\\\\ \\SI{30}{\\micro\\meter}}\n    node[rbox,below=of 1] (2) {Fifth cell\\\\ \\SI{30}{\\micro\\meter}}\n    node[rbox,below=of 2,grn] (3) {Second cell\\\\ \\SI{30}{\\micro\\meter}}\n    node[rbox,below=of 3,grn] (4) {Third cell\\\\ \\SI{30}{\\micro\\meter}}\n    node[below left=of 1.south east] (5) {Dense layer\\\\ \\SI{30}{\\micro\\meter}}\n    node[below right=of 4.south west] (6) {DSP\\\\ \\SI{30}{\\micro\\meter}};\n \\end{scope}\n \\begin{scope}[every node/.style={draw,rbox}]\n  \\node[below=of 5.south east,xshift=3mm,text=white,align=center] (7) {Memory\\\\ cell};\n  \\node[below=of 6.south west,xshift=-3mm,text=white,align=center] (8) {DSP\\\\ line};\n \\end{scope}\n \\begin{scope}[->,shorten >=2pt,shorten <=2pt]\n  \\draw (1) -- (7);\n  \\draw (2) -- (7);\n  \\draw (3) -- (8);\n  \\draw (4) -- (8);\n  \\draw (1) -- (2);\n  \\draw (2) -- (3);\n  \\draw (3) -- (4);\n  \\draw (5) -- (6);\n \\end{scope}\n\\end{tikzpicture}\n\\end{document}"
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    {
        "index": 204,
        "tikz_code": "\\documentclass[runningheads]{llncs}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows.meta}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{backgrounds}\n\\usetikzlibrary{positioning,chains,fit,shapes,calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n    % GLOBAL CFG\n    font=\\sf \\scriptsize,\n    >=LaTeX,\n    % Styles\n    ct/.style={\n        line width = .5pt,\n        minimum height = .5cm,\n        inner sep = .25mm,\n        },\n    gt/.style={\n        rectangle, \n        draw,\n        minimum height = .5cm,\n        inner sep = .25mm,\n        },\n    Arrow/.style={\n        thick,\n        rounded corners=.5cm,\n        },\n    CFG/.style={\n        line width = .5pt,\n        inner sep = .25mm,\n        },\n    % The Alignment Problem\n    % Nodes\n    L1/.style={\n        minimum height = .9cm,\n        inner sep = .25mm,\n        },\n    L2/.style={\n        minimum height = .9cm,\n        inner sep = .25mm,\n        },\n    L3/.style={\n        minimum height = .9cm,\n        inner sep = .25mm,\n        },\n    L4/.style={\n        minimum height = .9cm,\n        inner sep = .25mm,\n        },\n    L5/.style={\n        minimum height = .9cm,\n        inner sep = .25mm,\n        },\n    L6/.style={\n        minimum height = .9cm,\n        inner sep = .25mm,\n        },\n    ]\n\n% block size = 1\n\\node[L1] (l1) at (0,0) {$\\alpha_{0}$};\n\\node[L2] (l2) [right of=l1] {$\\alpha_{1}$};\n\\node[L3] (l3) [right of=l2] {$\\alpha_{2}$};\n\\node[L4] (l4) [right of=l3] {$\\alpha_{3}$};\n\\node[L5] (l5) [right of=l4] {$\\alpha_{4}$};\n\n% block size = 2\n\\node[L1] (l11) at (0,-1.5) {$\\alpha_{0}$};\n\\node[L2] (l21) [right of=l11] {$\\alpha_{1}$};\n\\node[L3] (l31) [right of=l21] {$\\alpha_{2}$};\n\n% block size = 3\n\\node[L1] (l12) at (0,-3) {$\\alpha_{0}$};\n\\node[L2] (l22) [right of=l12] {$\\alpha_{1}$};\n\n% block size = 4\n\\node[L1] (l13) at (0,-4.5) {$\\alpha_{0}$};\n\n% block size = 5\n\\node[L1] (l14) at (0,-6) {$\\alpha_{0}$};\n\n\n% dots\n\\draw[thick,dashed] ($(l22.north east)+(.25cm,.75cm)$) -- ($(l22.south east)+(.25cm,-.75cm)$);\n\\draw[thick,dashed] ($(l22.north west)+(-.25cm,.75cm)$) -- ($(l22.south west)+(-.25cm,-.75cm)$);\n\n\\draw[thick,dashed] ($(l21.north east)+(.25cm,.75cm)$) -- ($(l21.south east)+(.25cm,-.75cm)$);\n\\draw[thick,dashed] ($(l21.north west)+(-.25cm,.75cm)$) -- ($(l21.south west)+(-.25cm,-.75cm)$);\n\n\\draw[thick,dashed] ($(l2.north east)+(.25cm,.75cm)$) -- ($(l2.south east)+(.25cm,-.75cm)$);\n\\draw[thick,dashed] ($(l2.north west)+(-.25cm,.75cm)$) -- ($(l2.south west)+(-.25cm,-.75cm)$);\n\n\\draw[thick,dashed] ($(l13.north east)+(.25cm,.75cm)$) -- ($(l13.south east)+(.25cm,-.75cm)$);\n\\draw[thick,dashed] ($(l13.north west)+(-.25cm,.75cm)$) -- ($(l13.south west)+(-.25cm,-.75cm)$);\n\n\\draw[thick,dashed] ($(l14.north east)+(.25cm,.75cm)$) -- ($(l14.south east)+(.25cm,-.75cm)$);\n\\draw[thick,dashed] ($(l14.north west)+(-.25cm,.75cm)$) -- ($(l14.south west)+(-.25cm,-.75cm)$);\n\n% GPU\n\\draw (-.5,-1.5) -- (4.5,-1.5) node[right] {GPU};\n\n% GPU\n\\draw (-.5,-3) -- (4.5,-3) node[right] {GPU};\n\n% GPU\n\\draw (-.5,-4.5) -- (4.5,-4.5) node[right] {GPU};\n\n% GPU\n\\draw (-.5,-6) -- (4.5,-6) node[right] {GPU};\n\n% OPS\n\\draw (5.25,-1.5) -- (5.25,-5.5) node[right] {OP$_1$};\n\n\\draw (6.5,-1.5) -- (6.5,-5.5) node[right] {OP$_2$};\n\n\\draw (7.75,-1.5) -- (7.75,-5.5) node[right] {OP$_3$};\n\n% Mem\n\\draw (8.5,-1.5) -- (8.5,-5.5) node[right] {mem};\n\n% LATENCY\n\\draw (0,-1.5) -- (0,-5."
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        "tikz_code": "\\documentclass{amsart}\n\\usepackage{latexsym,amsfonts,amsmath,amssymb,mathrsfs}\n\\usepackage[cmyk,svgnames,dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,arrows.meta,petri,topaths,positioning,shapes,shapes.misc,patterns,calc,decorations.pathreplacing,hobby}\n\\pgfdeclarelayer{foreground}\n\\pgfdeclarelayer{background}\n\\pgfdeclarelayer{boardarrows}\n\\pgfdeclarelayer{boardgrid}\n\\pgfdeclarelayer{boardshades}\n\\pgfsetlayers{boardshades,boardgrid,boardarrows,background,main,foreground}\n\\usepackage[utf8]{inputenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[xscale=.45,scale=.45]\n% A single band\n\\def\\aa{.3};\n\\filldraw[fill=orange!40,opacity=.6] (0,0) -- (0,.5) -- (-3,.5) -- (-3,0) -- cycle;\n\\filldraw[fill=orange!40,opacity=.6] (3,0) -- (3,.5) -- (6,.5) -- (6,0) -- cycle;\n\\filldraw[fill=orange!40,opacity=.6] (6,0) -- (6,.5) -- (9,.5) -- (9,0) -- cycle;\n\\filldraw[fill=orange!40,opacity=.6] (12,0) -- (12,.5) -- (15,.5) -- (15,0) -- cycle;\n\\filldraw[fill=orange!40,opacity=.6] (18,0) -- (18,.5) -- (21,.5) -- (21,0) -- cycle;\n\\filldraw[fill=orange!40,opacity=.6] (24,0) -- (24,.5) -- (27,.5) -- (27,0) -- cycle;\n\\filldraw[fill=orange!40,opacity=.6] (30,0) -- (30,.5) -- (33,.5) -- (33,0) -- cycle;\n% X-axis\n\\draw[<->] (-5,0) -- (35,0);\n\\draw (17.5,-.5) node {$t$};\n% Y-axis\n\\draw[<->] (0,-3) -- (0,3);\n\\draw (-.5,2.5) node[anchor=east,rotate=90] {$t$};\n% X-ticks and X-label\n\\foreach \\x in {0,3,6,12,18,24,30} \\draw[thick] (\\x,-1) -- (\\x,1);\n% A single band\n\\draw[thick,red] (0,0) -- (3,0);\n\\draw[thick,red] (6,0) -- (9,0);\n\\draw[thick,red] (12,0) -- (15,0);\n\\draw[thick,red] (18,0) -- (21,0);\n\\draw[thick,red] (24,0) -- (27,0);\n\\draw[thick,red] (30,0) -- (33,0);\n% The rest of the bands\n\\foreach \\x in {0,3,6,9,12,15,18,21,24,27,30,33} \\filldraw[fill=white] (\\x,.5) -- (\\x+1,0) -- (\\x+.5,-.5) -- cycle;\n\\draw[thick,blue] (7.5,-.25) node {\\footnotesize $A$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage[dvipsnames,svgnames,x11names]{xcolor}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usepackage{tikz}\n\\usepackage[colorinlistoftodos,prependcaption,textsize=tiny]{todonotes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.6]\n\\draw[ultra thin, gray] (0,0) grid (10,10);\n\\draw[ultra thick,gray] (0,10)--(0,9)--(1,9)--(1,7)--(2,7)--(2,6)--(3,6)--(3,5)--(4,5)--(4,4)--(5,4)--(5,3)--(6,3)--(6,2)--(7,2)--(7,1)--(8,1)--(8,0)--(10,0);\n\\draw[ultra thick,gray] (0,0)--(1,0)--(1,1)--(2,1)--(2,2)--(3,2)--(3,3)--(4,3)--(4,4)--(5,4)--(5,5)--(6,5)--(6,6)--(7,6)--(7,7)--(8,7)--(8,8)--(9,8)--(9,9)--(10,9);\n\\draw[ultra thick,gray] (1,0)--(10,0);\n\\draw[ultra thick,gray] (0,1)--(10,1);\n\\draw[ultra thick,gray] (0,2)--(10,2);\n\\draw[ultra thick,gray] (0,3)--(10,3);\n\\draw[ultra thick,gray] (0,4)--(10,4);\n\\draw[ultra thick,gray] (0,5)--(10,5);\n\\draw[ultra thick,gray] (0,6)--(10,6);\n\\draw[ultra thick,gray] (0,7)--(10,7);\n\\draw[ultra thick,gray] (0,8)--(10,8);\n\\draw[ultra thick,gray] (0,9)--(10,9);\n\\draw[ultra thick,gray] (0,10)--(10,10);\n\\draw[ultra thick,gray] (1,9)--(1,7);\n\\draw[ultra thick,gray] (2,7)--(2,6);\n\\draw[ultra thick,gray] (3,6)--(3,5);\n\\draw[ultra thick,gray] (4,5)--(4,4);\n\\draw[ultra thick,gray] (5,4)--(5,3);\n\\draw[ultra thick,gray] (6,3)--(6,2);\n\\draw[ultra thick,gray] (7,2)--(7,1);\n\\draw[ultra thick,gray] (8,1)--(8,0);\n\\draw[ultra thick,gray] (9,0)--(9,0);\n\\draw[ultra thick,gray] (10,0)--(10,0);\n\\draw (5.5,9.5) node {$b$};\n\\draw (10.5,3.5) node {$x$};\n\\draw (3.5,10.5) node {$y$};\n\\draw (1.5,0.5) node {$-10$};\n\\draw (2.5,0.5) node {$-9$};\n\\draw (3.5,0.5) node {$-8$};\n\\draw (4.5,0.5) node {$-7$};\n\\draw (5.5,0.5) node {$-6$};\n\\draw (6.5,0.5) node {$-5$};\n\\draw (7.5,0.5) node {$-4$};\n\\draw (8.5,0.5) node {$-3$};\n\\draw (9.5,0.5) node {$-2$};\n\\draw (10.5,0.5) node {$-1$};\n\\draw (0.5,1.5) node {$-10$};\n\\draw (0.5,2.5) node {$-9$};\n\\draw (0.5,3.5) node {$-8$};\n\\draw (0.5,4.5) node {$-7$};\n\\draw (0.5,5.5) node {$-6$};\n\\draw (0.5,6.5) node {$-5$};\n\\draw (0.5,7.5) node {$-4$};\n\\draw (0.5,8.5) node {$-3$};\n\\draw (0.5,9.5) node {$-2$};\n\\draw[ultra thick, fill = blue] (2,3) rectangle (3,6);\n\\draw[ultra thick, fill = blue] (3,3) rectangle (4,6);\n\\draw[ultra thick, fill = blue] (4,3) rectangle (5,6);\n\\draw[ultra thick, fill = blue] (2,3) rectangle (3,4);\n\\draw[ultra thick, fill = blue] (3,3) rectangle (4,4);\n\\draw[ultra thick, fill = blue] (2,4) rectangle (3,5);\n\\draw[ultra thick, fill = blue] (3,4) rectangle (4,5);\n\\draw[ultra thick, fill = blue] (3,5) rectangle (4,6);\n\\draw[ultra thick, fill = blue] (2,5) rectangle (3,6);\n\\draw[ultra thick, fill = blue] (3,6) rectangle (4,7);\n\\draw[ultra thick, fill = blue] (2,6) rectangle (3,7);\n\\draw[ultra thick, fill = blue] (3,7) rectangle (4,8);\n\\draw[ultra thick, fill = blue] (4,7) rectangle (5,8);\n\\draw[ultra thick, fill = blue] (4,8) rectangle (5,9);\n\\draw[ultra thick, fill = blue] (5,7) rectangle (6,8);\n\\draw[ultra thick, fill = blue] (5,8) rectangle (6,9);\n\\draw[ultra thick, fill = blue] (6,7) rectangle (7,8);\n\\draw[ultra thick, fill = blue] (6,8) rectangle (7,9);\n\\draw[ultra thick, fill = blue] (7,7) rectangle (8,8);\n\\draw[ultra thick, fill = blue] (7,8) rectangle (8,9);\n\\draw[ultra thick, fill = blue] (8,8) rectangle (9,9);\n\\draw[ultra thick, fill = blue] (9,8) rectangle (10,9);\n\\draw"
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        "index": 215,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amssymb,amsthm,bm,graphicx,float,array,multirow,multicol,rotfloat,caption,subcaption,hyperref,cleveref,enumerate,geometry,mathdots,adjustbox,booktabs,parskip,mathtools,tikz,tikz-cd,pdflscape,csquotes,lscape,rotating,empheq,mathrsfs}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{arrows,shapes.misc}\n\\tikzset{gauge/.style={rounded rectangle, draw=black!100,dashed, thick, minimum size=5mm},d2/.style={rounded rectangle, draw=white!100, thick, minimum size=5mm},flavor/.style={rectangle, draw=black!100, thick, minimum size=5mm},gaugeN1/.style={rounded rectangle, draw=black!100, thick, minimum size=5mm}}\n\\tikzset{\nnode/.style={rounded rectangle, thick, draw=black!100,fill=white!100,  minimum size=6mm, inner sep=3pt},\nsonode/.style={circle, thick, draw=black!100,fill=red!100,  minimum size=3mm, inner sep=0pt},\nspnode/.style={circle, thick, draw=black!100,fill=blue!100,  minimum size=3mm, inner sep=0pt},\nfnode/.style={rectangle, thick, draw=black!100,fill=white!100,  minimum size=3mm, inner sep=0pt},\ntnode/.style={rounded rectangle, outer sep=0pt, thick, minimum size=5mm}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n      \\node[gaugeN1,ball color = gray!10, opacity = 0.8] (s0) {$v$};\n      \\node[d2] (c2) [right=0.6cm of s0] {$\\mathcal{E}_{Y}$};\n      \\node[d2] (c3) [right=0.6cm of c2] {$\\exp_X$};\n      \\node[d2] (c4) [right=0.6cm of c3] {$w_{x_0}Y$};\n      \\node[d2] (c5) [right=0.6cm of c4] {$w_{x_0}^2Y$};\n      \\node[tnode] (c6) [below=0.3cm of c2] {};\n      \\node[tnode] (c7) [below=0.3cm of c3] {};\n      \\node[tnode] (c8) [below=0.3cm of c4] {};\n      \\node[tnode] (c9) [below=0.3cm of c5] {};\n      \\node[node] (u) [below=0.6cm of c6] {$u$};\n      \\node[tnode] (c10) [below=0.3cm of c8] {};\n      \\node[tnode] (c11) [below=0.3cm of c9] {};\n      \\node[node] (x0) [below=0.6cm of c10] {$\\hat{x}_0$};\n      \\node[tnode] (c12) [below=0.3cm of c11] {};\n      \\node[tnode] (c13) [below=0.3cm of c9] {};\n      \\node[node] (x) [below=0.6cm of c12] {$x$};\n      \\node[tnode] (c14) [below=0.3cm of c13] {};\n      \\node[tnode] (c15) [below=0.3cm of c11] {};\n      \\node[node] (w) [below=0.6cm of c14] {$w$};\n      \\node[tnode] (c16) [below=0.3cm of c15] {};\n      \\node[tnode] (c17) [below=0.3cm of c13] {};\n      \\node[node] (v) [below=0.6cm of c16] {$v$};\n      \\node[tnode] (c18) [below=0.3cm of c17] {};\n      \\node[tnode] (c19) [below=0.3cm of c15] {};\n      \\node[tnode] (c20) [below=0.3cm of c17] {};\n      \\node[tnode] (c21) [below=0.3cm of c19] {};\n      \\node[tnode] (c22) [below=0.3cm of c18] {};\n      \\node[tnode] (c23) [below=0.3cm of c18] {};\n      \\node[tnode] (c24) [below=0.3cm of c23] {};\n      \\node[tnode] (c25) [below=0.3cm of c21] {};\n      \\node[tnode] (c26) [below=0.3cm of c20] {};\n      \\node[tnode] (c27) [below=0.3cm of c22] {};\n      \\node[tnode] (c28) [below=0.3cm of c23] {};\n      \\node[tnode] (c29) [below=0.3cm of c24] {};\n      \\node[tnode] (c30) [below=0.3cm of c25] {};\n      \\node[tnode] (c31) [below=0.3cm of c26] {};\n      \\node[tnode] (c32) [below=0.3cm of c27] {};\n      \\node[tnode] (c33) [below=0.3cm of c32] {};\n      \\node[tnode] (c34) [below=0.3cm of c28] {};\n      \\node[tnode] (c35) [below=0.3cm of c29] {};\n      \\node[tnode] (c36) [below=0.3cm of c34] {};\n      \\node[tnode] (c37) [below=0.3cm of c33] {};\n      \\node[tnode] (c38) [below=0.3cm of c35] {};\n      \\node[tnode] (c39) [below=0.3cm of c36] {};\n      \\node[tnode] (c40) [below=0.3cm of c37] {};\n      \\node[tnode] (c41) [below=0.3cm"
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    {
        "index": 216,
        "tikz_code": "\\documentclass[tikz,border=3.14mm]{standalone}\n\\usetikzlibrary{decorations.markings}\n\\begin{document}\n\\begin{tikzpicture}[scale=0.8,declare function={f(\\x,\\y)=pow(sin(\\y),2)/100;}]\n \\draw[very thin,color=gray] (-1,-1) grid[xstep=0.2,ystep=0.2] (6,6);\n \\draw[->] (-1,0) -- (6,0) node[right] {$x$};\n \\draw[->] (0,-1) -- (0,6) node[above] {$y$};\n \\draw[blue,mark=*] plot[variable=\\y,domain=0:5,samples=250] ({\\y},{f(2,\\y)});\n \\draw[red,thick,mark=*] plot[variable=\\y,domain=0:5,samples=250] ({\\y},{f(2,\\y)})\n \\foreach \\X [evaluate=\\X as \\Y using {int(\\X-2)},count=\\Z] in {3,...,7} \n {coordinate[pos=0.2] (m\\Z) \n   \\ifnum\\Z>1\n   (m\\the\\numexpr\\Z-1) edge[densely dotted,-stealth,thin] (m\\Z)\n   \\fi\n  (2,\\X) -- (2,\\Y)};\n \\foreach \\X in {2,...,7} \n {\\ifnum\\X>2\n  \\fill[white,opacity=0.8,draw=red,thick] \n    (2,\\X-1) to[out=90,in=-90] (2,\\X) -- (2,0) -- (0,0) --cycle;\n  \\else\n  \\ifnum\\X<6\n   \\fill[white,opacity=0.8,draw=red,thick] (2,\\X) -- (2,0) -- (0,0) --cycle;\n  \\fi \n  \\fi\n  \\path (2,\\X) node[right]{$\\pgfmathparse{int(\\X-2)}\\pgfmathresult$};}\n \\foreach \\X in {0,1,2} \n {\\path (0,\\X) node[left]{$\\pgfmathparse{int(\\X+2)}\\pgfmathresult$};}\n\\end{tikzpicture}\n\\end{document}"
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        "index": 217,
        "tikz_code": "\\documentclass[letterpaper,11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath, amsthm, amssymb}\n\\usepackage{color-edits}\n\\usepackage[most]{tcolorbox}\n\\usetikzlibrary{calc,positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.7]\n\\begin{scope}[xshift=0cm]\n\\foreach \\i in {1,2,...,4}{\n    \\foreach \\j in {1,2,...,3}{\n    \\draw[fill=black] (1.5*\\i,2.5*\\j) circle (.25);\n    }\n}\n\\draw[fill=black] (1.5*5,2.5*4) circle (.25);\n\\draw[fill=black] (1.5*5,2.5*5) circle (.25);\n\\draw[fill=black] (1.5*5,2.5*6) circle (.25);\n\\node at (1.5*5,2.5*7) {$\\cdots$};\n\\node at (1.5*5,2.5*8) {$\\cdots$};\n\\node at (1.5*5,2.5*9) {$\\cdots$};\n\\node at (1.5*5,2.5*10) {$\\cdots$};\n\n\\foreach \\i in {1,2,3}{\n    \\node at (1.5*\\i,.5) {$H_{\\i}$};\n}\n\\foreach \\j in {2,3,4}{\n    \\node at (5,2.5*\\j) {$E_{\\j}$};\n}\n\\node at (5,2.5*5) {$E_5$};\n\\node at (5,2.5*6) {$E_6$};\n\n\\node at (1,2.5*7.5) {$\\alpha_1,\\geq 1$};\n\\node at (1,2.5*8) {$\\vdots$};\n\\node at (1,2.5*9.5) {$\\beta_{n},n\\geq 4$};\n\\end{scope}\n\n\\begin{scope}[xshift=9cm]\n\\foreach \\i in {1,2,...,4}{\n    \\foreach \\j in {1,2,...,4}{\n    \\draw[fill=black] (1.5*\\i,2.5*\\j) circle (.25);\n    }\n}\n\\draw[fill=black] (1.5*5,2.5*4) circle (.25);\n\\draw[fill=black] (1.5*5,2.5*5) circle (.25);\n\\draw[fill=black] (1.5*5,2.5*6) circle (.25);\n\\node at (1.5*5,2.5*7) {$\\cdots$};\n\\node at (1.5*5,2.5*8) {$\\cdots$};\n\\node at (1.5*5,2.5*9) {$\\cdots$};\n\\node at (1.5*5,2.5*10) {$\\cdots$};\n\n\\foreach \\i in {1,2,3}{\n    \\node at (1.5*\\i,.5) {$H_{\\i}$};\n}\n\\foreach \\j in {2,3,4}{\n    \\node at (5,2.5*\\j) {$E_{\\j}$};\n}\n\\node at (5,2.5*5) {$E_5$};\n\\node at (5,2.5*6) {$E_6$};\n\n\\node at (1,2.5*7.5) {$\\alpha_n,\\geq 4$};\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 218,
        "tikz_code": "\\documentclass[border=3mm]{standalone}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning, arrows.meta,calc}\n\\begin{document}\n\\begin{tikzpicture}\n\\node[draw, minimum height=2cm] (i) at (0,0) {Input};\n\\node[draw, minimum height=2cm] (d1) at (5, 0) {B};\n\\node[draw, minimum height=2cm] (d2) at (8, 0) {$\\Phi$};\n\\node[draw, minimum height=2cm] (d3) at (11, 0) {$\\Phi$};\n\\node[draw, minimum height=2cm] (d4) at (14, 0) {$\\Phi$};\n\\node[draw, minimum height=2cm] (o) at (16, 0) {Output};\n\\node[draw, minimum height=2cm] (p) at (8, -5) {Hidden layers};\n\\draw[-{Latex}] (i.180) -- +(-2,0) coordinate(t) node[above]{$x_{t}$};\n\\draw[dashed,-{Latex}] ($(t)+(0,2)$) -- node[above]{$x_{t,1}$} +(4,0);\n\\draw[dashed,-{Latex}] ($(t)+(0,4)$) -- node[above]{$x_{t,2}$} +(4,0);\n\\draw[dashed,-{Latex}] ($(t)+(0,6)$) -- node[above]{$x_{t,3}$} +(4,0);\n\\draw[-{Latex}] (t) -- +(0,-2) coordinate(y) node[right]{$t$};\n\\draw[dashed,-{Latex}] ($(y)+(2,0)$) -- ($(y)+(2,-1)$) coordinate(a)\n    node[below]{$t_1$};\n\\draw[dashed,-{Latex}] ($(a)+(4,0)$) -- ($(a)+(4,-1)$) coordinate(b)\n    node[below]{$t_2$};\n\\draw[dashed,-{Latex}] ($(b)+(4,0)$) -- ($(b)+(4,-1)$) coordinate(c)\n    node[below]{$t_3$};\n\\draw[-{Latex}] (y) -- +(0,-2) coordinate(t) node[above]{$t$};\n\\draw[-{Latex}] ($(t)+(0,2)$) -- (d1.180);\n\\draw[-{Latex}] ($(t)+(0,4)$) -- (d2.180);\n\\draw[-{Latex}] ($(t)+(0,6)$) -- (d3.180);\n\\draw[-{Latex}] ($(t)+(0,8)$) -- (d4.180);\n\\draw[-{Latex}] (d1.0) -- ($(d1.0)+(3,0)$) -- (p.180);\n\\draw[-{Latex}] (d2.0) -- ($(d2.0)+(3,0)$) -- (p.0);\n\\draw[-{Latex}] (d3.0) -- ($(d3.0)+(3,0)$) -- (p.0);\n\\draw[-{Latex}] (d4.0) -- ($(d4.0)+(3,0)$) -- (p.180);\n\\draw[-{Latex}] (p.270) -- +(0,-1) -- (o.180);\n\\node at (9, -1.5) {Encodes periodic boundary condition};\n\\node at (12, -5.5) {Dense layer};\n\\node at (1, -5.5) {Periodic base layer};\n\\node at (13, -5.5) {Dense layer};\n\\end{tikzpicture}\n\\end{document}"
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    {
        "index": 219,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{epsfig,amsmath,amssymb, xspace, graphicx, url, amscd, euscript, mathrsfs,color}\n\\usepackage{tikz}\n\\usetikzlibrary{intersections}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{decorations.pathmorphing}\n\n\\newcommand{\\cK}{\\mathcal{K}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\clip (-1.2,-1.8) rectangle (7.2,1.8);\n\\draw [gray!70,fill=gray!30] (-0.5,-0.5) .. controls (-0.3,-0.3) and (-0.3,0.3) .. (-0.5,0.5) -- (5.5,0.5) .. controls (5.7,0.3) and (5.7,-0.3) .. (5.5,-0.5) -- cycle;\n\\draw [gray!70,fill=gray!30] (-0.5,0.5) .. controls (-0.3,0.7) and (-0.3,1.3) .. (-0.5,1.5) -- (5.5,1.5) .. controls (5.7,1.3) and (5.7,0.7) .. (5.5,0.5) -- cycle;\n\\node at (0,0) [inner sep=0pt,label=0:$\\cK_{(-\\infty,0]}$] {};\n\\node at (5,0) [inner sep=0pt,label=0:$\\cK_{[0,\\infty]}$] {};\n\\draw [gray!70] (-1,-2) rectangle (6,2);\n\\draw [gray!70] (0,-2) -- (0,2);\n\\draw [gray!70] (5,-2) -- (5,2);\n\\node at (2.5,0) [inner sep=0pt,label=0:$\\cK$] {};\n\\draw (0.25,0) .. controls (0.5,-0.25) and (0.5,0.25) .. (0.25,0);\n\\begin{scope}\n\\clip (0.25,0) .. controls (0.5,-0.25) and (0.5,0.25) .. (0.25,0) -- (5.5,0) .. controls (5.7,0.25) and (5.7,-0.25) .. (5.5,-0.25) -- (5.5,0);\n\\draw (0.25,0) .. controls (0.5,-0.25) and (0.5,0.25) .. (0.25,0);\n\\end{scope}\n\\begin{scope}\n\\clip (0.25,0) .. controls (0.5,0.25) and (0.5,-0.25) .. (0.25,0) -- (-0.5,0) .. controls (-0.3,0.25) and (-0.3,-0.25) .. (-0.5,-0.25) -- (-0.5,0);\n\\draw (0.25,0) .. controls (0.5,0.25) and (0.5,-0.25) .. (0.25,0);\n\\end{scope}\n\\begin{scope}\n\\clip (5.5,0) .. controls (5.7,0.25) and (5.7,-0.25) .. (5.5,-0.25) -- (0.25,0) .. controls (0.5,-0.25) and (0.5,0.25) .. (0.25,0) -- (-0.5,0) .. controls (-0.3,0.25) and (-0.3,-0.25) .. (-0.5,-0.25) -- (-0.5,0);\n\\draw (5.5,0) .. controls (5.7,0.25) and (5.7,-0.25) .. (5.5,-0.25);\n\\end{scope}\n\\begin{scope}\n\\clip (5.5,0) .. controls (5.7,-0.25) and (5.7,0.25) .. (5.5,0.25) -- (0.25,0) .. controls (0.5,0.25) and (0.5,-0.25) .. (0.25,0) -- (-0.5,0) .. controls (-0.3,0.25) and (-0.3,-0.25) .. (-0.5,-0.25) -- (-0.5,0);\n\\draw (5.5,0) .. controls (5.7,-0.25) and (5.7,0.25) .. (5.5,0.25);\n\\end{scope}\n\\draw (0.25,0) -- (5.5,0);\n\\draw [decorate,decoration={snake,amplitude=0.75mm,segment length=2mm,post length=0mm},very thick] (5.5,0) -- (6.5,0);\n\\draw [decorate,decoration={snake,amplitude=0.75mm,segment length=2mm,post length=0mm},very thick] (-1.5,0) -- (-0.5,0);\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt,a4paper,reqno]{amsart}\n\\usepackage{amsmath,amsthm,amssymb,amsfonts,amscd}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.0]\n%\n% Left Picture\n%\n \\draw[thick] (0,0) -- (0,3) -- (2,3.5) -- (4,3) -- (4,0) -- (2,0.5) -- (2,.1) -- (0,.6) -- (0,0);\n \\draw[thick] (2,0.5) -- (2,3.5);\n \\draw[dashed] (2,0.5) -- (2,-.5) -- (0,-.5) -- (0,0.6);\n \\draw[dashed] (2,3.5) -- (2,4.5) -- (0,4.5) -- (0,3);\n \\draw[dashed] (4,3) -- (4,4.5) -- (2,4.5);\n\n\\draw (1,1.5) node[anchor=west] {$Q^0$};\n\\draw (0,1.5) node[anchor=east] {$Q^1$};\n\n\\draw[thick] (2,2.5) ellipse (.4 and .6);\n\\draw[dashed] (2,2.5) ellipse (.2 and .3);\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.markings,decorations.pathmorphing,arrows.meta}\n\\tikzset{wave/.style={decorate,decoration={snake,segment length=1.7mm,\n      amplitude=0.5mm}}}\n\\tikzset{coil/.style={decorate,decoration={coil, aspect=0.7, amplitude = 0.5mm,\n      segment length = 1mm}}}\n\\tikzset{weak/.style={decorate,decoration={zigzag,segment length=1.7mm,\n      amplitude=0.5mm}}}\n\\tikzset{left/.style={arrows={Stealth[scale length=0.5, scale width=1.5]-}}}\n\\tikzset{right/.style={arrows={-[sep=-2pt]Stealth[scale length=0.5, scale\n      width=1.5]}}}\n\\tikzset{leftright/.style={arrows={Stealth[scale length=0.5, scale\n      width=1.5]-Stealth[scale length=0.5, scale width=1.5]}}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\draw[thick] (-1,1) -- (0,0);\n    \\draw[thick,wave] (0,0) -- (1,1);\n    \\draw[thick] (-1,-1) -- (1,1);\n    \\draw[thick,wave] (1,1) -- (2,0);\n    \\draw[thick] (2,0) -- (3,-1);\n    \\filldraw (-1,-1) circle (2pt) node[below] {$cP_{12}$};\n    \\filldraw (3,-1) circle (2pt) node[below] {$cP'_{12}$};\n    \\filldraw (0,0) circle (2pt);\n    \\filldraw (2,0) circle (2pt);\n  \\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[journal]{IEEEtran}\n\\usepackage{amsmath, amssymb, latexsym, amsthm}\n\\usepackage{graphicx, color}\n\\usepackage{tikz}\n\\usepackage[T1]{fontenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[x=1cm, y=1cm]\n\n\\draw[fill=black] (5,0) circle [radius=0.08] node[below, xshift=4] {$P_{004}$};\n\\draw[fill=black] (10,0) circle [radius=0.08] node[below, xshift=4] {$P_{004}$};\n\\draw[fill=black] (15,0) circle [radius=0.08] node[below, xshift=4] {$P_{004}$};\n\n\\draw[fill=black] (5,-2) circle [radius=0.08] node[below, xshift=4] {$P_{004}$};\n\\draw[fill=black] (10,-2) circle [radius=0.08] node[below, xshift=4] {$P_{004}$};\n\\draw[fill=black] (15,-2) circle [radius=0.08] node[below, xshift=4] {$P_{004}$};\n\n\\draw[fill=black] (10,-4) circle [radius=0.08] node[below, xshift=4] {$P_{004}$};\n\n\\draw[fill=black] (15,-4) circle [radius=0.08] node[below, xshift=4] {$P_{004}$};\n\n\\draw[fill=black] (10,-6) circle [radius=0.08] node[below, xshift=4] {$P_{004}$};\n\n\\draw[fill=black] (10,-8) circle [radius=0.08] node[below, xshift=4] {$P_{004}$};\n\n\\draw[fill=black] (0,2) circle [radius=0.08] node[below, xshift=4] {Cloud};\n\n\\draw[fill=black] (12.5,2) circle [radius=0.08] node[below, xshift=4] {Switch};\n\n\\draw[fill=black] (27,2) circle [radius=0.08] node[below, xshift=4] {Edge};\n\n\\draw[dashed, ->] (12.5,1.2) -- (12.5,0.2);\n\\draw[dashed, ->] (12.5,1.2) -- (12.5,2.8);\n\\draw[dashed, ->] (27,1.2) -- (27,0.2);\n\\draw[dashed, ->] (27,1.2) -- (27,2.8);\n\n\\draw[->, thick] (0.5,2) -- (3.5,2);\n\\draw[->, thick] (7.5,2) -- (12.5,2);\n\\draw[->, thick] (17,2) -- (22,2);\n\\draw[->, thick] (12.5,-2) -- (12.5,-4);\n\\draw[->, thick] (12.5,-4) -- (12.5,-6);\n\\draw[->, thick] (12.5,-6) -- (12.5,-8);\n\n\\draw[->, thick] (5,-1.8) -- (5,-1.2);\n\\draw[->, thick] (10,-1.8) -- (10,-1.2);\n\\draw[->, thick] (15,-1.8) -- (15,-1.2);\n\n\\node[above] at (2,2) {Cloud};\n\\node[above] at (16,2) {Edge};\n\n\\node[above] at (5,-1) {$d(w_n,n_3) = 277ms$};\n\n\\node[above] at (12.5,0) {$P_w, n_3,$};\n\\node[above] at (12.5,0) {$=277ms$};\n\n\\node[above] at (17,0) {$P_n, n_3,$};\n\\node[above] at (17,0) {$=277ms$};\n\n\\node[above] at (12.5,-2) {$R_1$};\n\\node[above] at (12.5,-2) {$=$ $1};\n\n\\node[above] at (12.5,-4) {$R_2$};\n\\node[above] at (12.5,-4) {$=$ $1};\n\n\\node[above] at (12.5,-6) {$R_3$};\n\\node[above] at (12.5,-6) {$=$ $1};\n\n\\node[below] at (12.5,-8) {$R_4$};\n\\node[below] at (12.5,-8) {$=$ $1};\n\n\\node[above] at (12.5,-10) {$R_5$};\n\\node[above] at (12.5,-10) {$=$ $1$};\n\n\\node[below] at (17,-10) {$\\sigma_{R_1}(R_1)=\\sigma_{R_2}(R_2)=\\sigma_{R_3}(R_3)=\\sigma_{R_4}(R_4)=\\sigma_{R_5}(R_5)=\\sigma_{R_1}(R_2)=\\sigma_{R_3}(R_4)$};\n\n\\draw[fill=black] (22,2) circle [radius=0.08] node[below, xshift=4] {$R_{004}$};\n\\draw[fill=black] (27,2) circle [radius=0.08] node[below, xshift=4] {$R_{004}$};\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.12}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}[node distance = 0cm, scale=0.8, transform shape]\n\\begin{axis}[\n    xlabel={Epoch},\n    ylabel={MAE ppl.},\n    xmin=1, xmax=40,\n    ymin=32.5, ymax=24.5,\n    xtick={1,10,20,30,40},\n    ytick={32.5,33,33.5,34,34.5,35,35.5,36,36.5,37,37.5,38,38.5,39,39.5,40},\n    legend pos=north east,\n    ymajorgrids=true,\n    grid style=dashed,\n]\n\n\\addplot[\n    color=blue,\n    mark=square,\n    ]\n    coordinates {\n    (1,33.55)(10,32.21)(20,32.05)(30,31.97)(40,31.94)\n    };\n    \\addlegendentry{slt}\n    \n\\addplot[\n    color=orange,\n    mark=*,\n    ]\n    coordinates {\n    (1,33.97)(10,32.74)(20,32.62)(30,32.58)(40,32.57)\n    };\n    \\addlegendentry{w/o}\n\n\\addplot[\n    color=green,\n    mark=diamond,\n    ]\n    coordinates {\n    (1,34.61)(10,33.47)(20,33.43)(30,33.42)(40,33.42)\n    };\n    \\addlegendentry{cqp}\n\n\\addplot[\n    color=red,\n    mark=triangle,\n    ]\n    coordinates {\n    (1,34.41)(10,33.18)(20,33.11)(30,33.07)(40,33.07)\n    };\n    \\addlegendentry{cqp'}\n\n\\addplot[\n    color=violet,\n    mark=otimes,\n    ]\n    coordinates {\n    (1,34.41)(10,33.18)(20,33.11)(30,33.07)(40,33.07)\n    };\n    \\addlegendentry{cqp-f}\n    \n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[journal]{IEEEtran}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage[table]{xcolor}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usepackage{pgfplotstable}\n\\usetikzlibrary{plotmarks}\n\\usetikzlibrary{shapes,arrows}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{shapes.geometric}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{shapes.multipart}\n\\usetikzlibrary{intersections}\n\\usetikzlibrary{shapes.callouts}\n\\usetikzlibrary{shapes.multipart}\n\\usetikzlibrary{external}\n\\usetikzlibrary{decorations,arrows,positioning,fit}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1, transform shape]\n\n\\begin{axis}[%\nwidth=4.521in,\nheight=2.563in,\nat={(0.758in,0.481in)},\nscale only axis,\nxmin=0,\nxmax=0.4,\nxlabel style={font=\\color{white!15!black}},\nxlabel={Covert user square-root rate $r$},\nymin=0,\nymax=0.3,\nylabel style={font=\\color{white!15!black}},\nylabel={Non-Covert user rate $r_{n}$},\naxis background/.style={fill=white},\nxmajorgrids,\nymajorgrids,\nlegend style={at={(0.45,0.2)}, anchor=south west, legend cell align=left, align=left, draw=white!15!black}\n]\n\\addplot [color=red, dashed, line width=1.0pt, forget plot]\n  table[row sep=crcr]{%\n0\t0\\\\\n0.1\t0.2\\\\\n0.2\t0.2\\\\\n0.3\t0\\\\\n0.4\t0\\\\\n};\n\\addplot [color=red, line width=1.0pt, forget plot]\n  table[row sep=crcr]{%\n0\t0\\\\\n0.1\t0.2\\\\\n0.2\t0.2\\\\\n0.3\t0.3\\\\\n0.4\t0.3\\\\\n};\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 232,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amssymb,amsthm,bbm}\n\\usepackage{tikz,tikz-3dplot}\n\\usepackage{tikz,tikz-3dplot}\n\\usetikzlibrary{matrix, shapes, snakes}\n\\usepackage[colorinlistoftodos]{todonotes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.1]\n\\path[use as bounding box] (-10,0) rectangle (30,10);\n\\begin{scope}[xshift=20cm]\n\n\\draw[line width=1,violet,dashed,xstep=10,ystep=10] (-15,-5) grid (15,5);\n\n\n\n\\draw[line width=2,orange,dashed,xstep=10,ystep=2] (-15,-4) grid (15,4);\n\n\n\n\\draw[line width=3,green,dashed,xstep=10,ystep=4] (-15,-2) grid (15,2);\n\n\n\\foreach \\y in {-4,-2,0,2}\n{\n    \\draw[thick,xshift=0cm,yshift=0.5cm] (0, \\y+2) -- (10, \\y+2) node[right] {\\footnotesize{$\\tau_{s,\\y}$}};\n}\n\n\\foreach \\y in {-3,-1,1,3}\n{\n    \\draw[thick,xshift=0cm,yshift=0.5cm] (20, \\y-2) -- (30, \\y-2) node[right] {\\footnotesize{$\\tau_{s,\\y}$}};\n}\n\n\\foreach \\y in {0,2,4}\n{\n    \\draw[thick,xshift=0cm,yshift=0.5cm] (-20, \\y-4) -- (-10, \\y-4) node[left] {\\footnotesize{$\\tau_{s,\\y}$}};\n}\n\n\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 233,
        "tikz_code": "\\documentclass[preprint,12pt]{elsarticle}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing}\n\n\\begin{document}\n\n\\begin{tikzpicture}[node distance=2.5cm, auto]\n\n\\tikzstyle{place}=[circle,thick,draw=blue!75,fill=blue!20,minimum size=7mm]\n\\tikzstyle{redplace}=[circle,thick,draw=red!75,fill=red!20,minimum size=7mm]\n\\tikzstyle{transition}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=5mm]\n\\tikzstyle{redtransition}=[rectangle,thick,draw=black!75,fill=red!20,minimum size=5mm]\n\\tikzstyle{plct}=[rectangle,thick,draw=black!75,fill=blue!20,minimum size=5mm]\n\\tikzstyle{waiting}=[circle,draw=black!75,fill=white!20,minimum size=7mm,font=\\footnotesize]\n\\tikzstyle{input}=[circle,draw=black!75,fill=white!20,minimum size=7mm]\n\\tikzstyle{output}=[circle,draw=black!75,fill=white!20,minimum size=7mm,font=\\footnotesize]\n\\tikzstyle{measurement}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=6mm]\n\\tikzstyle{plate}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=7mm]\n\\tikzstyle{bin}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=7mm]\n\\tikzstyle{outputnode}=[rectangle,thick,draw=black!75,fill=white!20,minimum size=7mm,font=\\footnotesize]\n\\tikzstyle{inputnode}=[circle,thick,draw=black!75,fill=white!20,minimum size=7mm]\n\\tikzstyle{invnode}=[circle,draw=black!75,fill=white!20,minimum size=7mm]\n\\tikzstyle{plate}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=7mm]\n\\tikzstyle{bin}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=7mm]\n\\tikzstyle{transition}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=5mm]\n\\tikzstyle{measurement}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=6mm]\n\\tikzstyle{plate}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=7mm]\n\\tikzstyle{bin}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=7mm]\n\\tikzstyle{outputnode}=[rectangle,thick,draw=black!75,fill=white!20,minimum size=7mm,font=\\footnotesize]\n\\tikzstyle{inputnode}=[circle,thick,draw=black!75,fill=white!20,minimum size=7mm]\n\\tikzstyle{invnode}=[circle,draw=black!75,fill=white!20,minimum size=7mm]\n\\tikzstyle{plate}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=7mm]\n\\tikzstyle{bin}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=7mm]\n\\tikzstyle{transition}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=5mm]\n\\tikzstyle{measurement}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=6mm]\n\\tikzstyle{plate}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=7mm]\n\\tikzstyle{bin}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=7mm]\n\\tikzstyle{outputnode}=[rectangle,thick,draw=black!75,fill=white!20,minimum size=7mm,font=\\footnotesize]\n\\tikzstyle{inputnode}=[circle,thick,draw=black!75,fill=white!20,minimum size=7mm]\n\\tikzstyle{invnode}=[circle,draw=black!75,fill=white!20,minimum size=7mm]\n\\tikzstyle{plate}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=7mm]\n\\tikzstyle{bin}=[rectangle,thick,draw=black!75,fill=black!20,minimum size=7mm]\n\n\n\n\\node [bin] (bin) [] {x};\n\\node [place] (machine) [above of=bin, node distance=5cm] {$N_N$};\n\\node [plate] (plate1) [right of=machine, node distance=8.5cm] {$\\Pi_1$};\n\\node [transition] (transition1) [left of=machine,node distance=6cm] {};\n\\node [waiting] (w1) [left of=transition1,node distance=3.5cm] {$u$};\n\\node [transition] (transition2) [above of=machine,node distance=3.2cm] {};\n\\node [waiting] (w2) [left of=transition2,node distance=3cm] {$u$};\n\\node [transition] (transition3) [above of=machine,node distance=3.2cm] {};\n\\node [waiting] (w3) [right of=transition3,node distance=3cm] {$u$};\n\n\n\\node [bin] (bin2) [right of=plate1, node distance=8.5cm] {$\\Pi_2$};\n\\node [plate] (plate2) [right of=bin2, node distance=8.5cm] {$\\Pi_3$};\n\n\\node [transition] (transition4) [above of=plate1,node distance=1cm] {};\n\\node [transition] (transition5) [above of=plate2,node distance=1cm] {};\n\\node [invnode] (invnode) [below of=machine, node distance=2cm] {};\n\n\n\n\\draw [->] (bin) to node {} (transition1);\n\\draw [-"
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    {
        "index": 234,
        "tikz_code": "\\documentclass[11pt,reqno,tbtags]{amsart}\n\\usepackage{amsthm,amssymb,amsfonts,amsmath}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\\node (myfirstpic) at (0,0) {\\includegraphics[height=6cm]{example-image}};\n\t\\draw (0.2,1.3) node {\\small $\\theta$};\n\t\\draw (-2.8,-1.5) node {\\small $\\sigma_i^{(1)}$};\n\t\\draw (2.8,-1.5) node {\\small $q_i(\\theta, \\sigma_i^{(1)})$};\n\t\\draw (-2.4,0.9) node {\\small $\\sigma_j^{(0)}$};\n\t\\draw (2.4,0.9) node {\\small $q_j(\\theta, \\sigma_j^{(0)})$};\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "index": 235,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amsfonts,amsmath,amsthm,amssymb,amscd,latexsym,enumerate,etoolbox,mathrsfs,comment}\n\\usepackage{tikz-cd}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw [blue, thick] (-3,0)--(0,0);\n\\draw [red, thick] (0,0)--(3,0);\n\\draw (0,0)--(2,0);\n\\draw (0,0)--(-1,0);\n\\draw [red, thick,dashed] (0,0) to [out=-150,in=150] (0,0);\n\\draw [red, thick,dashed] (0,0) to [out=-120,in=120] (0,0);\n\\draw [red,thick, dashed] (0,0) to [out=-30,in=30] (0,0);\n\\draw [red, thick,dashed] (0,0) to [out=-60,in=60] (0,0);\n\\node [red] at (-1,-0.25) {$x$};\n\\node [red] at (2,-0.25) {$l_j$};\n\\node [red] at (0.5,0.3) {$l_1$};\n\\node [red] at (0.7,0.8) {$l_2$};\n\\node [red] at (0.3,-0.3) {$l_i$};\n\\node [red] at (-0.5,0.3) {$l_i+1$};\n\\node [blue] at (-2.3,0.3) {$f_i^+$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 236,
        "tikz_code": "\\documentclass[11pt,twoside,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[usenames, dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,positioning,decorations.pathmorphing,  decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}[every node/.style={circle},inner sep=0pt, minimum size=10pt]\n\n\\node[draw] (M) [label=above:{\\small $\\delta_{M \\to B}$}] {$M$};\n\\node[draw] (A) [below left = 3cm of M, label=left:{\\small $\\delta_{M \\to A}$}] {$A$};\n\\node[draw] (B) [right =3cm of M, label=right:{\\small $\\delta_{B \\to A}$}] {$B$};\n\n\\draw[->, thick] (M) to (A);\n\\draw[->, thick] (M) to (B);\n\\draw[->, thick] (A) to (B);\n\\draw[->, thick] (A) to (M);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 237,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amssymb,amsfonts,amsthm}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.14}\n\\usetikzlibrary{calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\\begin{axis}[\n\t\twidth=0.8\\textwidth,\n\t\theight=0.4\\textwidth,\n\t\taxis x line=center,\n\t\taxis y line=center,\n\t\txlabel={$\\phi$},\n\t\tylabel={$V(\\phi)$},\n\t\txlabel style={below right},\n\t\tylabel style={above left},\n\t\txmin=-1.5,\n\t\txmax=1.5,\n\t\tymin=-0.2,\n\t\tymax=1.5]\n\t\t\\addplot[domain=-1.5:-0.3,smooth,variable=\\x,blue] {-0.3+0.5*\\x};\n\t\t\\addplot[domain=0.3:1.5,smooth,variable=\\x,blue] {-0.3+0.5*\\x};\n\t\t\\addplot[domain=-0.3:0.3,smooth,variable=\\x,blue] {0.5*\\x*\\x};\n\t\t\\addplot[domain=0.5:1.5,smooth,variable=\\x,blue] {0.5*\\x*\\x};\n\t\t\\addplot[domain=-1.5:1.5,smooth,variable=\\x,blue] {1.5-abs(\\x)};\n\t\t\\addplot[domain=-0.4:0.4,smooth,variable=\\x,blue] {-0.7+0.5*\\x};\n\t\t\\draw[<->] (axis cs: -1.2,-0.3) -- (axis cs: -0.3,-0.3)\n\t\t\t\tnode[pos=0.5,below]{False vacuum};\n\t\t\\draw[<->] (axis cs: 0.3,-0.3) -- (axis cs: 1.2,-0.3)\n\t\t\t\tnode[pos=0.5,below]{Colleen instability};\n\t\t\\draw[<->] (axis cs: 0.5,0) -- (axis cs: 1.5,0)\n\t\t\t\tnode[pos=0.5,right]{True vacuum};\n\t\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[a4paper,12pt]{amsart}\n\\usepackage{amsmath,amsfonts,amssymb}\n\\usepackage[usenames]{color}\n\\usepackage{tikz}\n\\usepackage{xcolor}\n\\usepackage{color}\n\\usetikzlibrary{arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[->] (-3,0) -- (3,0);\n\\draw[->] (0,-2) -- (0,2);\n\\draw[blue, thick] (-1.5,1.5) rectangle (1.5, -1.5);\n\\draw[blue, thick] (-2.5,0.5) rectangle (2.5,-0.5);\n\\draw (-1,0) node{$\\bullet$};\n\\draw (1,0) node{$\\bullet$};\n\\draw (-0.75,0) node{$-2\\pi$};\n\\draw (0.75,0) node{$2\\pi$};\n\\draw (-0.25,0.8) node{$\\pi$};\n\\draw (-0.25,-0.8) node{$-\\pi$};\n\\draw (0.25,0.8) node{$\\pi$};\n\\draw (0.25,-0.8) node{$-\\pi$};\n\\draw (0,0.5) node{$\\bullet$};\n\\draw (0,-0.5) node{$\\bullet$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 241,
        "tikz_code": "\\documentclass[tikz,border=5]{standalone}\n\\usetikzlibrary{graphs,graphs.standard}\n\\begin{document}\n\\begin{tikzpicture}\n\\graph [nodes={draw, circle, fill=gray!30}, clockwise, radius=5in,\n   nodes, n=16, edges=bundled] {\nsubgraph C_n [name=inner] --[bend right] subgraph C_n [name=outer]\n};\n\\foreach \\x [evaluate={\\lx=int(mod(\\x,16)+1)}] in {1,...,16}\n  \\draw [red] (\\x) -- (\\lx) (\\x) -- (16-\\x);\n\\foreach \\x in {1,3,...,15}\n  \\draw [blue] (\\x) -- (16-\\x);\n\\end{tikzpicture}\n\\end{document}"
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        "index": 242,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amsfonts,amssymb,latexsym}\n\\usepackage[cp1251]{inputenc}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.5, transform shape]\n\\draw [red](-5,3.3)-- (-4,1.7);\n\\draw [red](-5,3.3)-- (-6,3.3);\n\\draw [red](-5,3.3)-- (-5,4.3);\n\\draw [red](-5,3.3)-- (-1,1.7);\n\\draw [red](-5,3.3)-- (-0,3.3);\n\\node at (-1,1.7)  [red] {$\\bullet$};\n\\node at (-1,1.7)  [red, left] {$G_1$};\n\\node at (-6,3.3)  [red] {$\\bullet$};\n\\node at (-6,3.3)  [red, left] {$G_2$};\n\\node at (-5,4.3)  [red] {$\\bullet$};\n\\node at (-5,4.3)  [red, left] {$G_3$};\n\\node at (-4,1.7)  [red] {$\\bullet$};\n\\node at (-4,1.7)  [red, left] {$G_4$};\n\\node at (-3,1.7)  [blue] {Standard perturbation theory};\n\\node at (-3,3)  [red] {$\\bullet$};\n\\node at (-3,3)  [red, left] {$G_\\infty$};\n\\node at (-5,1)  [orange] {Multi-point perturbation};\n\\node at (-3,1)  [blue] {$\\bullet$};\n\\node at (-3,1)  [blue, left] {$G_0$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 243,
        "tikz_code": "\\documentclass[a4paper,12pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color,epsfig,url,color}\n\\usepackage[latin1]{inputenc}\n\\usepackage{pgfplots}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.9]\n\t\\begin{axis}[\n\taxis lines = left,\n\txlabel = loss of main,\n\tylabel = loss of $\\hat{a}$,\n\tymax=1,\n\tymin=0,\n\txmin=0.00001388888,\n\txmax = 0.05,\n\tlegend style={at={(0.8,0.96)}}\n\t]\n\t\\addplot [\n\tdomain=0.00001:0.05, \n\tsamples=100, \n\tcolor=red,\n\t]\n\t{exp(-12*ln(x/0.00001))};\n\t\\addlegendentry{Single}\n\t\\addplot [\n\tdomain=0.00001:0.05, \n\tsamples=100, \n\tcolor=blue,\n\t]\n\t{exp(-8*ln(x/0.00001))};\n\t\\addlegendentry{Multitask}\n\t\\addplot [\n\tdomain=0.00001:0.05, \n\tsamples=100, \n\tcolor=purple,\n\t]\n\t{exp(-8*ln(x/0.00001))*exp(-8*ln(x/0.00001))};\n\t\\addlegendentry{Multitask}\n\t\\end{axis}\n\t\n\t\\begin{scope}[yshift=-7cm]\n\t\\begin{axis}[\n\taxis lines = left,\n\txlabel = loss of main,\n\tylabel = loss of $\\hat{a}$,\n\tymax=1,\n\tymin=0,\n\txmin=0.00001388888,\n\txmax = 0.05,\n\tlegend style={at={(0.8,0.96)}}\n\t]\n\t\\addplot [\n\tdomain=0.00001:0.05, \n\tsamples=100, \n\tcolor=red,\n\t]\n\t{exp(-12*ln(x/0.00001))};\n\t\\addplot [\n\tdomain=0.00001:0.05, \n\tsamples=100, \n\tcolor=blue,\n\t]\n\t{0.1650471*x + 0.0294621};\n\t\\addplot [\n\tdomain=0.00001:0.05, \n\tsamples=100, \n\tcolor=purple,\n\t]\n\t{0.1650471*x + 0.0294621*x};\n\t\\end{axis}\n\t\\end{scope}\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "index": 244,
        "tikz_code": "\\documentclass[12pt,reqno]{amsart}\n\\usepackage{amssymb}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{calc,decorations.pathreplacing,positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n\t\tx=1cm, y=1cm,\n\t\tvertex/.style={\n\t\t\tcircle,draw=black,fill=black!25,\n\t\t\tminimum size=12pt, inner sep=2pt\n\t\t},\n\t\tthickedge/.style={\n\t\t\tultra thick\n\t\t},\n\t\tseagull/.style={\n\t\t\tdecorate,\n\t\t\tdecoration={\n\t\t\t\trandom steps,\n\t\t\t\tsegment length=10pt,\n\t\t\t\tamplitude=3pt\n\t\t\t}\n\t\t}\n\t]\n\t\\node[vertex] (w1) at (0,0) {};\n\t\\node[vertex] (w2) at (0,2) {};\n\t\\node[vertex] (w3) at (0,4) {};\n\t\\node[vertex] (w4) at (-2,1) {};\n\t\\node[vertex] (w5) at (-2,3) {};\n\t\\node[vertex] (w6) at (-2,5) {};\n\t\\node[vertex] (b1) at (3,0) {};\n\t\\node[vertex] (b2) at (3,2) {};\n\t\\node[vertex] (b3) at (3,4) {};\n\t\\node[vertex] (b4) at (5,1) {};\n\t\\node[vertex] (b5) at (5,3) {};\n\t\\node[vertex] (b6) at (5,5) {};\n\t\\node[vertex] (b7) at (6,2) {};\n\t\\node[vertex] (b8) at (7,2) {};\n\t\\node[vertex] (b9) at (8,2) {};\n\t\\draw[thickedge] (w1) -- (b1);\n\t\\draw[thickedge] (w1) -- (b2);\n\t\\draw[thickedge] (w1) -- (b3);\n\t\\draw[thickedge] (w2) -- (b4);\n\t\\draw[thickedge] (w2) -- (b5);\n\t\\draw[thickedge] (w2) -- (b6);\n\t\\draw[thickedge] (w3) -- (b7);\n\t\\draw[thickedge] (w3) -- (b8);\n\t\\draw[thickedge] (w3) -- (b9);\n\t\\draw[thickedge] (w4) -- (b1);\n\t\\draw[thickedge] (w4) -- (b2);\n\t\\draw[thickedge] (w4) -- (b3);\n\t\\draw[thickedge] (w5) -- (b4);\n\t\\draw[thickedge] (w5) -- (b5);\n\t\\draw[thickedge] (w5) -- (b6);\n\t\\draw[thickedge] (w6) -- (b4);\n\t\\draw[thickedge] (w6) -- (b5);\n\t\\draw[thickedge] (w6) -- (b6);\n\t\\draw[thickedge] (w1) -- (w2);\n\t\\draw[thickedge] (w2) -- (w3);\n\t\\draw[thickedge] (w3) -- (w1);\n\t\\draw[thickedge] (b1) -- (b2);\n\t\\draw[thickedge] (b2) -- (b3);\n\t\\draw[thickedge] (b3) -- (b1);\n\t\\draw[thickedge] (b4) -- (b5);\n\t\\draw[thickedge] (b5) -- (b6);\n\t\\draw[thickedge] (b6) -- (b4);\n\t\\draw[thickedge] (b1) -- (b7);\n\t\\draw[thickedge] (b2) -- (b8);\n\t\\draw[thickedge] (b3) -- (b9);\n\t\\draw[thickedge] (b4) -- (b7);\n\t\\draw[thickedge] (b4) -- (b8);\n\t\\draw[thickedge] (b4) -- (b9);\n\t\\draw[thickedge] (b5) -- (b7);\n\t\\draw[thickedge] (b5) -- (b8);\n\t\\draw[thickedge] (b5) -- (b9);\n\t\\draw[thickedge] (b6) -- (b7);\n\t\\draw[thickedge] (b6) -- (b8);\n\t\\draw[thickedge] (b6) -- (b9);\n\t\\draw[seagull] (w1) -- (b1);\n\t\\draw[seagull] (w2) -- (b2);\n\t\\draw[seagull] (w3) -- (b3);\n\t\\draw[seagull] (w4) -- (b4);\n\t\\draw[seagull] (w5) -- (b5);\n\t\\draw[seagull] (w6) -- (b6);\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usepackage{amssymb}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t[every path/.style={color=black, line width=1.2pt}, \n\t\tevery node/.style={draw, circle, line width=1.2pt, inner sep=3pt},\n\t\tbend angle=45]\n\t\t\n\t\t\\node\t(0) at (-4,0)\t{$ v_1 $};\n\t\t\\node\t(1) at (-2,0)\t{$ 1 $};\n\t\t\\node\t(2) at (0,0)\t{$ v_2 $};\n\t\t\\node[draw=none]\t(3) at (2,0)\t{$ \\cdots $};\n\t\t\\node[draw=none]\t(4) at (4,0)\t{$ \\cdots $};\n\t\t\\node\t(5) at (6,0)\t{$ v_n $};\n\t\t\n\t\t\\draw[->]\t(1) edge[bend left]\t(2);\n\t\t\\draw[->]\t(1) edge[bend right]\t(2);\n\t\t\\draw[->]\t(2) edge[bend left]\t(3);\n\t\t\\draw[->]\t(2) edge[bend right]\t(3);\n\t\t\\draw[->]\t(3) edge[bend left]\t(4);\n\t\t\\draw[->]\t(3) edge[bend right]\t(4);\n\t\t\\draw[->]\t(4) edge[bend left]\t(5);\n\t\t\\draw[->]\t(4) edge[bend right]\t(5);\n\t\t\n\t\t\\path\t(0) edge[bend left]\t(1);\n\t\t\\path\t(0) edge[bend right]\t(1);\n\t\t\n\t\t\\draw[color=red, line width=2.4pt] (0,0.4) -- (0,-0.4);\n\t\t\\draw[color=red, line width=2.4pt] (1,0.4) -- (1,-0.4);\n\t\t\\draw[color=red, line width=2.4pt] (6,0.4) -- (6,-0.4);\n\t\t\n\t\t\\node\t(x) at (-0.5,0)\t{$ e_1 $};\n\t\t\\node\t(x) at (1.5,0)\t{$ e_2 $};\n\t\t\\node[draw=none]\t(x) at (5.5,0)\t{$ \\cdots $};\n\t\t\n\t\t\\draw[->]\t(6) edge[bend left]\t(7,0);\n\t\t\\draw[->]\t(6) edge[bend right]\t(7,0);\n\t\t\n\t\t\\draw[dashed]\t(-0.5,0) ellipse (0.4 and 0.8);\n\t\t\\draw[dashed]\t(1.5,0) ellipse (0.4 and 0.8);\n\t\t\\draw[dashed]\t(5.5,0) ellipse (0.4 and 0.8);\n\t\t\n\t\t\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt,reqno]{amsart}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{math}\n\n\\begin{document}\n\n\\begin{tikzpicture}%\n\t\t\t\\filldraw (0,0) circle (2pt);\n\t\t\t\\foreach \\a in {1,...,36}{\n\t\t\t\t\\draw (\\a*360/36:4cm) node[circle,fill=black,inner sep=0pt,minimum size=5pt](x\\a){};\n\t\t\t}\n\t\t\t\\foreach \\a in {1,...,36}{\n\t\t\t\t\\foreach \\b in {18, 51, ..., 359}{\n\t\t\t\t\t\\draw[black] (x\\a) -- (x\\b);\n\t\t\t\t}\n\t\t\t}\n\t\t\t\\foreach \\a in {2,...,35}{\n\t\t\t\t\\foreach \\b in {3, 6, ..., 358}{\n\t\t\t\t\t\\draw[black] (x\\a) -- (x\\b);\n\t\t\t\t}\n\t\t\t}\n\t\t\t\\foreach \\a in {5,...,34}{\n\t\t\t\t\\foreach \\b in {7, 10, ..., 357}{\n\t\t\t\t\t\\draw[black] (x\\a) -- (x\\b);\n\t\t\t\t}\n\t\t\t}\n\t\t\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{trees}\n\\usetikzlibrary[shapes]\n\\usetikzlibrary[arrows]\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{fadings}\n\\usetikzlibrary{backgrounds}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{positioning}\n\\usepackage[colorlinks, linkcolor=black, citecolor=black,   %blue,\n      \t\t% pagebackref,  %%%% Adds \"backlink\" text to items in the bibliography, i.e the pages they were used.\n            bookmarksnumbered=true]{hyperref}\n\\tikzset{stringnode/.style={rectangle, inner sep=5pt, draw = black!50, fill=black!10}}\n\\DeclareMathOperator{\\triplearrow}{{\\; \\tikz{ \\foreach \\y in {0, 0.1, 0.2} \\draw[-stealth] (0, \\y) -- +(0.5, 0);} \\; }}\n\n\\begin{document}\n\n\\begin{tikzpicture}[thick]\n\\begin{scope}\n\t\\draw [->] (-1,0) -- (1.5,0); \n\t\\draw [->] (0,-1.5) -- (0,1.5); \n\t\\node at (-0.4, 0.7) {$e_1$};\n\t\\node at (-0.4, -0.7) {$e_h, 1$};\n\t\\node at (0.8, -0.4) {$e_h, 2$};\n\t\\fill (0,0) circle (1.5pt); \n\t\\draw (0, 0.25) arc (90: 270: 0.25cm);\n\t\\draw [<->] (0.25, 0.25) -- node [above] {$\\delta^1_h$} (0.75, 0.25); \n\t\\draw [<->] (-0.25, 0.25) -- node [above] {$\\delta^1_1$} (-0.75, 0.25); \n\t\\draw [<->] (0, 0.25) -- node [right] {$e^1_h$} (0, 0.75); \n\\end{scope}\n\n\\begin{scope}[xshift = 4cm]\n\t\\draw [->] (-1,0) -- (1.5,0); \n\t\\draw [->] (0,-1.5) -- (0,1.5); \n\t\\node at (-0.4, 0.7) {$e_1, 2$};\n\t\\node at (-0.4, -0.7) {$e^1_h, 1$};\n\t\\node at (0.8, -0.4) {$e^1_2$};\n\t\\fill (0,0) circle (1.5pt); \n\t\\draw (0, 0.25) arc (90: 270: 0.25cm);\n\t\\draw [<->] (0.25, 0.25) -- node [above] {$\\delta^2_1$} (0.75, 0.25); \n\t\\draw [<->] (-0.25, 0.25) -- node [above] {$\\delta^2_2$} (-0.75, 0.25); \n\t\\draw [<->] (0, 0.25) -- node [right] {$e^2_1$} (0, 0.75); \n\\end{scope}\n\n\\draw [|->] (2, 0) -- node [above] {$h$} (3, 0);\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[a4paper,11pt]{amsart}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8]\n\\draw (1,4) -- (4,4.5);\n\\draw (1,4) -- (5,4.5);\n\\draw (1,4) -- (6,3.5);\n\\draw (1,4) -- (6,2.5);\n\\draw (1,4) -- (6,1.5);\n\\draw (1,4) -- (6,0.5);\n\\draw (1,4) -- (7,3.5);\n\\draw (1,4) -- (7,2.5);\n\\draw (1,4) -- (7,1.5);\n\\draw (1,4) -- (7,0.5);\n\\draw (1,4) -- (4,4.5);\n\\draw (1,4) -- (5,4.5);\n\\draw (1,4) -- (6,3.5);\n\\draw (4,4.5) -- (5,4.5);\n\\draw (5,4.5) -- (6,3.5);\n\\draw (6,3.5) -- (6,2.5);\n\\draw (6,2.5) -- (6,1.5);\n\\draw (6,1.5) -- (6,0.5);\n\\draw (6,0.5) -- (7,3.5);\n\\draw (6,0.5) -- (7,2.5);\n\\draw (6,0.5) -- (7,1.5);\n\\draw (7,3.5) -- (7,2.5);\n\\draw (7,2.5) -- (7,1.5);\n\\draw (7,1.5) -- (7,0.5);\n\\draw (4,4.5) -- (6,3.5);\n\\draw (5,4.5) -- (6,3.5);\n\\draw (6,3.5) -- (6,2.5);\n\\draw (6,2.5) -- (6,1.5);\n\\draw (6,1.5) -- (6,0.5);\n\\draw (4,4.5) -- (6,3.5);\n\\draw (4,4.5) -- (6,2.5);\n\\draw (4,4.5) -- (6,1.5);\n\\draw (4,4.5) -- (6,0.5);\n\\draw [dashed] (4,4.5) -- (5,4.5);\n\\draw [dashed] (4,4.5) -- (6,3.5);\n\\draw [dashed] (4,4.5) -- (6,2.5);\n\\draw [dashed] (4,4.5) -- (6,1.5);\n\\draw [dashed] (4,4.5) -- (6,0.5);\n\\draw [dashed] (4,4.5) -- (7,3.5);\n\\draw [dashed] (4,4.5) -- (7,2.5);\n\\draw [dashed] (4,4.5) -- (7,1.5);\n\\draw [dashed] (4,4.5) -- (7,0.5);\n\\draw [fill=black] (1,4) circle (2pt);\n\\draw [fill=black] (4,4.5) circle (2pt);\n\\draw [fill=black] (5,4.5) circle (2pt);\n\\draw [fill=black] (6,3.5) circle (2pt);\n\\draw [fill=black] (6,2.5) circle (2pt);\n\\draw [fill=black] (6,1.5) circle (2pt);\n\\draw [fill=black] (6,0.5) circle (2pt);\n\\draw [fill=black] (7,3.5) circle (2pt);\n\\draw [fill=black] (7,2.5) circle (2pt);\n\\draw [fill=black] (7,1.5) circle (2pt);\n\\draw [fill=black] (7,0.5) circle (2pt);\n\\draw [fill=black] (3.4,4.6) circle (2pt);\n\\draw [fill=black] (3.3,4.7) circle (2pt);\n\\draw [fill=black] (3.4,4.5) circle (2pt);\n\\draw [fill=black] (6.6,3.6) circle (2pt);\n\\draw [fill=black] (6.7,3.5) circle (2pt);\n\\draw [fill=black] (6.6,3.5) circle (2pt);\n\\draw [fill=black] (6.7,2.6) circle (2pt);\n\\draw [fill=black] (6.8,2.5) circle (2pt);\n\\draw [fill=black] (6.8,1.6) circle (2pt);\n\\draw [fill=black] (6.8,1.5) circle (2pt);\n\\draw [fill=black] (6.8,0.6) circle (2pt);\n\\draw [fill=black] (6.9,0.5) circle (2pt);\n\\node at (1,3.6) {$x$};\n\\node at (7.2,3.6) {$z$};\n\\node at (4.5,4.8) {$y$};\n\\node at (6.7,3.6) {$w$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 251,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\\node[] at (0,0) {\\includegraphics[width=.45\\linewidth]{example-image}};\n\t\\node[] at (7,0) {\\includegraphics[width=.45\\linewidth]{example-image}};\n\t\\node[rotate=90] at (-3.2,0) {\\footnotesize $\\log(N)$};\n\t\\node[] at (0,-2.3) {\\footnotesize $\\log(N)$};\n\t\\node[] at (0,2) {\\footnotesize $\\frac{|N^2|}{\\log(N)}$};\n\t\\node[] at (7,2) {\\footnotesize $\\frac{|N^2|}{\\log(N)}$};\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "index": 252,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{shapes.geometric}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{automata}\n\n\\begin{document}\n\n\\begin{tikzpicture}[shorten >=1pt,node distance=3.5cm,auto]\n\\node[rectangle,draw] (S) {$\\mathrm{ST}$};\n\\node[rectangle,draw, right of=S] (E1) {$\\mathrm{E}_1$};\n\\node[rectangle,draw, right of=E1] (E) {$\\mathrm{E}_i$};\n\\node[rectangle,draw, below of=E1] (T) {$\\mathrm{E}$};\n\\node[rectangle,draw, left of=T] (A) {$\\mathrm{A}$};\n\\node[circle] (1) [left of=T]{$\\mathsf{x}$};\n\\node[circle] (2) [right of=T]{$\\mathsf{x}_{i}$};\n\\draw[bend right,->] (1) to node {$a$} (2);\n\\draw[bend right,->] (2) to node {$a$} (1);\n\\draw[->] (S) to node {$\\{e_i\\} \\rightarrow \\mathsf{e}_\\star$} (E1);\n\\draw[->] (E1) to node {$e_\\star$} (E);\n\\draw[->] (T) to node {$\\{e_i\\}$} (E1);\n\\draw[->] (T) to node {$\\{e_i\\}$} (E);\n\\path[->] (A) edge [bend right] node {$a$} (T);\n\\path[->] (A) edge [bend left] node {$a$} (T);\n\\draw[->] (A) to node {$a$} (1);\n\\draw[->] (A) to node {$a$} (2);\n\\draw[->] (1) edge [bend right] node {$a$} (2);\n\\draw[->] (1) edge [bend left] node {$a$} (2);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 253,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amsthm,amsfonts,amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning, shapes}\n\\usepackage{mathrsfs,amssymb,amsmath,amsthm}\n\\usepackage{color}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{shapes}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{decorations.shapes}\n\\usetikzlibrary{decorations.text}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{automata}\n\n\\newcommand{\\vk}{\\vec{k}}\n\n\\newcommand{\\vu}{\\vec{u}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw [fill=blue!10] (3,-1.6) rectangle (6,3.6);\n\\node[draw, thick,circle,inner sep=2pt,fill=blue!50,label=above right:{$p$}] at (3,1) (p) {};\n\\node[draw, thick,circle,inner sep=2pt,fill=blue!50,label=above right:{$u$}] at (6,1) (u) {};\n\\node[draw, thick,circle,inner sep=2pt,fill=blue!50,label=above right:{$v$}] at (3,-1) (v) {};\n\\node[draw, thick,circle,inner sep=2pt,fill=blue!50,label=above right:{$b$}] at (2,-1) (b) {};\n\\node[draw, thick,circle,inner sep=2pt,fill=blue!50,label=above right:{$c$}] at (4,1) (c) {};\n\\draw[thick,->, dashed, blue] (p) -- (c);\n\\draw[thick,->, dashed, blue] (c) -- (b);\n\\draw[thick,->, dashed, blue] (p) -- (b);\n\\draw[thick,->, dashed, blue] (p) -- (u);\n\\draw[thick,->, dashed, blue] (u) -- (v);\n\\draw[thick,->, dashed, blue] (b) -- (v);\n\n\\node at (4,0) {$M'$};\n\\node at (3.3,0.3) {$\\vk$};\n\n\\draw [fill=red!10] (4,1.6) rectangle (6,3.6);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 254,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amsmath,amssymb,amsthm,graphicx,pstricks,amscd,amsfonts,latexsym}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes}\n\\usetikzlibrary{decorations.pathreplacing,decorations.markings}\n\\usepackage{tikz,tikz-cd}\n\\usetikzlibrary{snakes}\n\\usetikzlibrary{shapes.geometric,positioning}\n\\usetikzlibrary{arrows,decorations.pathmorphing,decorations.pathreplacing}\n\n\\begin{document}\n\n\\begin{tikzpicture}[baseline=0mm,scale=0.6]\n\\node(l1)at(-20,5){$\\bullet$}; \\node(l2)at(-16,5){$\\bullet$}; \\node(l3)at(-12,5){$\\bullet$}; \\node(l4)at(-8,5){$\\bullet$};\n\\node(l5)at(-4,5){$\\bullet$}; \\node(l6)at(0,5){$\\bullet$}; \\node(l7)at(4,5){$\\bullet$}; \\node(l8)at(8,5){$\\bullet$}; \\node(l9)at(12,5){$\\bullet$};\n\\node(l10)at(16,5){$\\bullet$}; \\node(l11)at(20,5){$\\bullet$};\n\\node(u)at(0,0){$\\bullet$};\n\\draw[->](l1)--(l2); \\draw[->](l2)--(l3); \\draw[->](l3)--(l4);\n\\draw[->](l4)--(l5); \\draw[->](l5)--(l6); \\draw[->](l6)--(l7); \\draw[->](l7)--(l8); \\draw[->](l8)--(l9); \\draw[->](l9)--(l10); \\draw[->](l10)--(l11);\n\\draw[->](u)--(l6); \\draw[->](u)--(l10); \\draw[->](u)--(l11);\n\\draw[->](l1)--(u); \\draw[->](l2)--(u); \\draw[->](l3)--(u);\n\\draw[->](l4)--(u); \\draw[->](l5)--(u); \\draw[->](l7)--(u);\n\\draw[->](l8)--(u); \\draw[->](l9)--(u); \\draw[->](l10)--(u);\n\\node at (0,4) {$x_3$}; \\node at (0,-0.4) {$w$}; \\node at (-20,5.4) {$w_3$}; \\node at (-16,5.4) {$w_2$}; \\node at (-12,5.4) {$w_1$};\n\\node at (-8,5.4) {$w$}; \\node at (-4,5.4) {$w_1$}; \\node at (0,5.4) {$w$}; \\node at (4,5.4) {$w_2$}; \\node at (8,5.4) {$w_1$}; \\node at (12,5.4) {$w$}; \\node at (16,5.4) {$w_3$};\n\\draw[dotted](-17.5,5)--(-14.5,5); \\draw[dotted](-13.5,5)--(-10.5,5); \\draw[dotted](-9.5,5)--(-6.5,5); \\draw[dotted](-5.5,5)--(-2.5,5); \\draw[dotted](-1.5,5)--(1.5,5);\n\\draw[dotted](1.5,5)--(5.5,5); \\draw[dotted](5.5,5)--(9.5,5); \\draw[dotted](9.5,5)--(13.5,5);\n\\node at (-17,6) {$x_2$}; \\node at (-13,6) {$x_2$}; \\node at (-9,6) {$x_2$}; \\node at (-5,6) {$x_2$}; \\node at (-1,6) {$x_2$};\n\\node at (3,6) {$x_1$}; \\node at (7,6) {$x_1$}; \\node at (11,6) {$x_1$};\n\\node at (15,6) {$x_3$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 255,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{calc,positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[>=stealth,scale=0.6]\n\\draw[dotted] (-5,2) -- (5,2);\n\\draw[dotted] (-5,-2) -- (5,-2);\n\\draw[dotted] (-5,2) -- (-5,-2);\n\\draw[dotted] (5,2) -- (5,-2);\n\\draw[thick,red] (-5,-2) -- (-5,0);\n\\draw[thick,red] (5,0) -- (5,2);\n\\draw[thick,red] (5,0) -- (3,0) node[midway,above] {$t_1$};\n\\draw[thick,red] (-5,0) -- (-3,0) node[midway,above] {$t_{-1}$};\n\\draw[thick,red] (-3,0) -- (-3,-2);\n\\draw[thick,red] (3,0) -- (3,-2);\n\\draw[thick,red] (3,-2) -- (5,-2);\n\\draw[thick,blue] (-5,-2) -- (-3,-2);\n\\draw[thick,blue] (5,-2) -- (3,-2);\n\\draw[thick,blue] (-3,-2) -- (-3,-4);\n\\draw[thick,blue] (3,-4) -- (3,-2);\n\\draw[thick,blue,->] (3,-4) -- (3,-5);\n\\draw[thick,blue,->] (-3,-4) -- (-3,-5);\n\\draw[thick,blue] (-5,-2) -- (-3,-2);\n\\draw[thick,blue] (5,-2) -- (3,-2);\n\\draw[thick,blue,<-] (-5,-2) -- (-5,-5);\n\\draw[thick,blue,<-] (5,-2) -- (5,-5);\n\\filldraw (-5,0) circle(2pt) node[anchor=east] {$t_{-2}$};\n\\filldraw (-3,0) circle(2pt) node[anchor=east] {$t_{-1}$};\n\\filldraw (3,0) circle(2pt) node[anchor=west] {$t_{1}$};\n\\filldraw (5,0) circle(2pt) node[anchor=west] {$t_{2}$};\n\\filldraw (0,0) circle(2pt) node[anchor=north] {$0$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 256,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n  \\matrix (m) [matrix of math nodes,row sep=2em,column sep=2em,minimum width=2em]\n  {\n     \\mathcal{Q}_1 & \\mathcal{Q}_2 & \\mathcal{Q}_3 & \\cdots & \\mathcal{Q}_{j-1} & \\mathcal{Q}_{j} & \\cdots & \\mathcal{Q}_{l} & \\mathcal{Q}_{l+1}\\\\\n     & & & & \\mathcal{Q}_{j+1} & & & &\\\\\n     & & & & \\vdots & & & &\\\\\n     \\mathcal{Q}_1 & \\mathcal{Q}_2 & \\mathcal{Q}_3 & \\cdots & \\mathcal{Q}_{j-1} & \\mathcal{Q}_{j} & \\cdots & \\mathcal{Q}_{l} & \\mathcal{Q}_{l+1}\\\\\n     & \\mathcal{Q}_{j+1} & & & \\vdots & & & &\\\\\n     & & \\vdots & & \\vdots & & & &\\\\\n     \\mathcal{Q}_1 & \\mathcal{Q}_2 & \\mathcal{Q}_3 & \\cdots & \\mathcal{Q}_{j-1} & \\mathcal{Q}_{j} & \\cdots & \\mathcal{Q}_{l} & \\mathcal{Q}_{l+1}\\\\\n     & & \\mathcal{Q}_{j+1} & & & \\vdots & & &\\\\\n     & & & \\vdots & & & \\vdots & &\\\\\n     \\mathcal{Q}_1 & \\mathcal{Q}_2 & \\mathcal{Q}_3 & \\cdots & \\mathcal{Q}_{j-1} & \\mathcal{Q}_{j} & \\cdots & \\mathcal{Q}_{l} & \\mathcal{Q}_{l+1}\\\\\n   };\n  \\path[-stealth]\n    (m-1-1) edge[blue, dashed] node {} (m-2-2)\n            edge[blue, dashed] node {} (m-3-3)\n    (m-3-3) edge[blue, dashed] node {} (m-4-4)\n            edge[blue, dashed] node {} (m-5-5)\n    (m-5-5) edge[blue, dashed] node {} (m-6-6)\n    (m-4-4) edge[blue, dashed] node {} (m-5-5)\n            edge[blue, dashed] node {} (m-6-6)\n    (m-6-6) edge[blue, dashed] node {} (m-7-7)\n    (m-7-7) edge[blue, dashed] node {} (m-8-8)\n    (m-1-8) edge[blue, dashed] node {} (m-2-7)\n            edge[blue, dashed] node {} (m-3-6)\n    (m-3-6) edge[blue, dashed] node {} (m-4-7)\n            edge[blue, dashed] node {} (m-5-8)\n    (m-5-8) edge[blue, dashed] node {} (m-6-9)\n    (m-4-7) edge[blue, dashed] node {} (m-5-8)\n            edge[blue, dashed] node {} (m-6-9)\n    (m-2-2) edge[red, densely dashdotted] node {} (m-3-3)\n    (m-6-6) edge[red, densely dashdotted] node {} (m-7-7)\n    (m-8-8) edge[red, densely dashdotted] node {} (m-9-9)\n    (m-7-7) edge[red, densely dashdotted] node {} (m-8-8)\n    (m-9-9) edge[green, densely dashed] node{} (m-10-10)\n    (m-3-6) edge[green, densely dashed] node{} (m-10-10);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 257,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node[anchor = south west, inner sep = 0] at (0,0){\\includegraphics{example-image}};\n\\node at (2.3,2.7){$w_{i-1}$};\n\\node at (5,1.5){$b$};\n\\node at (4.7,4){$w_{i}$};\n\\node at (3.2,2.7){$\\delta$};\n\\node at (1.5,0.3){$w_n$};\n\\node at (1,4){$w_{i+1}$};\n\\node at (5.7,0.5){$w_n$};\n\\node at (5.7,2){$a$};\n\\node at (4.2,2.5){$P_{i+1}$};\n\\node at (2,2.5){$P_i$};\n\\node at (0.8,1.5){$\\alpha$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 258,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage[colorlinks=true, pdfstartview=FitV, linkcolor=blue, citecolor=blue, urlcolor=blue, breaklinks=true]{hyperref}\n\\usepackage{amsmath,amsfonts,amssymb,amsthm,amscd,comment,paralist,etoolbox,mathtools,enumitem,mathdots}\n\\usepackage[usenames,dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}[>=stealth,baseline={([yshift=-.5ex]current bounding box.center)}]\n      \\draw[<-] (3,0) .. controls (3,0.5) and (2.3,0.5) .. (1.1,0.7);\n      \\draw[<-] (3,1) .. controls (3,0.5) and (2.3,0.5) .. (1.1,0.9);\n      \\draw[->] (1.1,0.7) .. controls (0.6,0.8) and (0.6,1.2) .. (1.1,1.1) .. controls (1.6,1.2) and (1.6,0.8) .. (1.1,0.7);\n      \\draw[<-] (3,0) -- (2.2,-0.5);\n      \\draw[<-] (3,1) -- (2.2,1.5);\n      \\draw[color=green,line width=1pt] (1.1,0.4) -- (1.1,1.1);\n    \\end{tikzpicture}\n\n\\end{document}"
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        "index": 261,
        "tikz_code": "\\documentclass{standalone}\n\\usepackage{tikz}\n\\usetikzlibrary{datavisualization.formats.functions}\n\\begin{document}\n\\begin{tikzpicture}\n  \\datavisualization [school book axes,\n                      visualize as line=sin,\n                      sin={style={thick, red}}\n                      ]\n  data[set=sin,format=function] {\n    var x : interval [-3:3];\n    func y = sin((\\value x) r); };\n\\end{tikzpicture}\n\\end{document}"
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        "index": 262,
        "tikz_code": "\\documentclass[letterpaper]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,shapes,trees}\n\\usepackage{color}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n%\n\\node[](n1) at (4,-0.5) {\\small{$(c,1)$-Regular};};\n\\node[](n2) at (11,-0.5) {\\small{$(c,2)$-Regular};};\n\n\\draw[<->,color=black,thick] (0,0) -- (0,1);\n\\draw[<->,color=black,thick] (0,-1.5) -- (0,-0.5);\n\\draw[<->,color=black,thick] (0,-4.5) -- (0,-3.5);\n\n\n\\node[](n3) at (0,1) {\\small{Def.}};\n\\node[](n4) at (0,-0.5) {\\small{$(c,n)$-Balanced Influences}};\n\\node[](n5) at (0,-1.5) {\\small{Def.}};\n\\node[](n6) at (0,-3.5) {\\small{Regular}};\n\\node[](n7) at (0,-4.5) {\\small{Def.}};\n\n\\draw[->,color=black,thick] (n1) -- (n2);\n\\draw[->,color=black,thick] (n1) -- (n4);\n\\draw[->,color=black,thick] (n4) -- (n3);\n\\draw[->,color=black,thick] (n5) -- (n4);\n\\draw[->,color=black,thick] (n6) -- (n5);\n\\draw[->,color=black,thick] (n7) -- (n6);\n\n\\draw[<->,color=red,thick,dashed] (4,1.5) -- (11,0.5);\n\\draw[<->,color=red,thick,dashed] (4,0.5) -- (11,-1.5);\n\\draw[<->,color=red,thick,dashed] (4,-0.5) -- (11,-4.5);\n\n\\draw[<->,color=blue,thick,dotted] (4,1.5) -- (4,0.5);\n\\draw[<->,color=blue,thick,dotted] (4,-0.5) -- (4,-1.5);\n\\draw[<->,color=blue,thick,dotted] (4,-4.5) -- (4,-3.5);\n\n\\draw[<->,color=black,thick,dotted] (4,0.5) -- (11,-0.5);\n\\draw[<->,color=black,thick,dotted] (4,-1.5) -- (11,-3.5);\n\\draw[<->,color=black,thick,dotted] (4,-4.5) -- (11,-1.5);\n\n\\draw[->,color=blue,thick] (n5) -- (n7);\n\\draw[->,color=blue,thick] (n6) -- (n7);\n\\draw[->,color=blue,thick] (n4) -- (n7);\n\n\\node[draw=black] (n14) at (4.5,1) {\\small{Theorem \\ref{th:seminaries}}};\n\\node[draw=black] (n15) at (8.5,1) {\\small{Theorem \\ref{th:seminaries}}};\n\\node[draw=black] (n16) at (11.5,1) {\\small{Theorem \\ref{th:seminaries}}};\n\n\\node[draw=black] (n11) at (4.5,-1) {\\small{Theorem \\ref{th:seminaries}}};\n\\node[draw=black] (n12) at (8.5,-1) {\\small{Theorem \\ref{th:seminaries}}};\n\\node[draw=black] (n13) at (11.5,-1) {\\small{Theorem \\ref{th:seminaries}}};\n\n\\node[draw=black] (n11) at (4.5,-4) {\\small{Theorem \\ref{th:seminaries}}};\n\\node[draw=black] (n12) at (8.5,-4) {\\small{Theorem \\ref{th:seminaries}}};\n\\node[draw=black] (n13) at (11.5,-4) {\\small{Theorem \\ref{th:seminaries}}};\n\n\\node[](n19) at (0,1.5) {\\small{Bent}};\n\\node[](n20) at (0,-2.5) {\\small{$(c,n)$-Regular}};\n\\node[](n21) at (0,-5.5) {\\small{$(c,1)$-Regular}};\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
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        "index": 263,
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{amsmath,amssymb,amsfonts,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix,arrows}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{fit}\n\\usetikzlibrary{patterns}\n\\usepackage[colorlinks,\nlinkcolor=blue,\nanchorcolor=blue,\ncitecolor=blue\n]{hyperref}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix,arrows}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{fit}\n\\usetikzlibrary{patterns}\n\\tikzset{global scale/.style={\n\t\tscale=#1,\n\t\tevery node/.append style={scale=#1}\n\t}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8, baseline=(current bounding box.center)]\n\t\\foreach \\x/\\y in {0/1,0/2,0/3,1/0,1/1,1/2,2/0,2/1,2/3,3/0,3/2,3/3}\t\t\n\t\\fill[gray!20] (\\x,\\y) rectangle +(1,1);\n\t\\draw (0.01,0.01) grid (3+0.99,3+0.99);\n\t\\filldraw (1,1) circle (3pt) node[above left] {$1$};\n\t\\filldraw (1,2) circle (3pt) node[above left] {$1$};\n\t\\filldraw (1,3) circle (3pt) node[above left] {$1$};\n\t\\filldraw (2,1) circle (3pt) node[above left] {$1$};\n\t\\filldraw (2,2) circle (3pt) node[above left] {$1$};\n\t\\filldraw (2,3) circle (3pt) node[above left] {$1$};\n\t\\filldraw (3,0) circle (3pt) node[above left] {$1$};\n\t\\filldraw (3,1) circle (3pt) node[above left] {$1$};\n\t\\filldraw (3,2) circle (3pt) node[above left] {$1$};\n\t\\filldraw (3,3) circle (3pt) node[above left] {$1$};\n\t\\node  at (0.5,2.5) {$1$};\n\t\\node  at (1.5,2.5) {$1$};\n\t\\node  at (2.5,2.5) {$1$};\n\t\\node  at (0.5,1.5) {$2$};\n\t\\node  at (1.5,1.5) {$4$};\n\t\\node  at (2.5,1.5) {$2$};\n\t\\node  at (0.5,0.5) {$1$};\n\t\\node  at (1.5,0.5) {$2$};\n\t\\node  at (2.5,0.5) {$1$};\n\t\\node  at (0.5+3,2.5+1) {$1$};\n\t\\node  at (1.5+3,2.5+1) {$1$};\n\t\\node  at (2.5+3,2.5+1) {$1$};\n\t\\node  at (0.5+3,1.5+1) {$1$};\n\t\\node  at (1.5+3,1.5+1) {$1$};\n\t\\node  at (2.5+3,1.5+1) {$1$};\n\t\\node  at (0.5+3,0.5+1) {$1$};\n\t\\node  at (1.5+3,0.5+1) {$1$};\n\t\\node  at (2.5+3,0.5+1) {$1$};\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[border=1cm]{standalone}\n\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\def\\n{11}\n\\def\\k{2}\n\\def\\m{12}\n\n\\begin{tikzpicture}[scale=3]\n\n\\foreach \\j in {1,2,...,\\n}{\n\\draw[rounded corners] (0, \\j-0.5) rectangle (\\k, \\j+0.5);\n\\node at (\\k+0.5, \\j) {$T_{\\j}$};\n}\n\n\\foreach \\i in {1,2,...,\\m}{\n\\draw[rounded corners] (\\k-0.5, -\\i+\\n+0.5) rectangle (\\k+0.5, -\\i+\\n-0.5);\n\\node at (\\k+0.5, -\\i+\\n-0.5) {$T_{\\i}$};\n}\n\n\\foreach \\i in {1,2,...,\\m}{\n\\foreach \\j in {1,2,...,\\n}{\n\\draw (\\i-0.5, -\\i+\\n+\\j-0.5) -- (\\j-0.5, -\\i+\\n+\\j+0.5);\n\\node at (\\j-0.5, -\\i+\\n+\\j-0.5) {$t_{11_{\\i\\j}}$};\n}\n}\n\n\\foreach \\i in {1,2,...,\\m}{\n\\foreach \\j in {1,2,...,\\n}{\n\\draw (\\i-0.5, -\\i+\\n+\\j-0.5) -- (\\j-0.5, -\\i+\\n+\\j+0.5);\n\\node at (\\j-0.5, -\\i+\\n+\\j-0.5) {$t_{22_{\\i\\j}}$};\n}\n}\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 274,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{math}\n\\usetikzlibrary{arrows.meta}\n\n\\begin{document}\n\n\\begin{tikzpicture}[xscale=2.5,yscale=0.5]\n      % horizontal axis\n      \\draw[->] (0,0) -- (1.8,0);\n      \\draw[->] (0,0) -- (0,4.5);\n      \\node[below] at (0,0) {$0$};\n      % vertical axis\n      \\draw[->] (0,0) -- (1.5,0.8);\n      \\node[right] at (1.8,0) {$\\lambda$};\n      \\draw[thick,blue] (0,1) -- (1.5,1.7);\n      \\node[blue] at (0.8,2.7) {bias};\n      % horizontal axis\n      \\draw[->] (2.5,0) -- (4.3,0);\n      \\draw[->] (2.5,0) -- (2.5,4.5);\n      \\node[below] at (2.5,0) {$0$};\n      % vertical axis\n      \\draw[->] (2.5,0) -- (4.1,0.8);\n      \\node[right] at (4.3,0) {$\\lambda$};\n      \\draw[thick,blue] (2.5,1.3) -- (4,1.8);\n      \\node[blue] at (3.3,2.8) {$\\mathsf{R}_\\mathsf{Ln}$};\n      \\node[blue] at (4.7,3.3) {$\\mathsf{DAC}$};\n      % horizontal axis\n      \\draw[->] (5,0) -- (6.8,0);\n      \\draw[->] (5,0) -- (5,4.5);\n      \\node[below] at (5,0) {$0$};\n      % vertical axis\n      \\draw[->] (5,0) -- (6.5,0.8);\n      \\node[right] at (6.8,0) {$\\lambda$};\n      \\draw[thick,red] (5,1.2) -- (6.5,1.9);\n      \\node[red] at (5.8,2.7) {bias};\n      % horizontal axis\n      \\draw[->] (7.5,0) -- (9.3,0);\n      \\draw[->] (7.5,0) -- (7.5,4.5);\n      \\node[below] at (7.5,0) {$0$};\n      % vertical axis\n      \\draw[->] (7.5,0) -- (9.1,0.8);\n      \\node[right] at (9.3,0) {$\\lambda$};\n      \\draw[thick,blue] (7.5,1.2) -- (9,1.7);\n      \\node[blue] at (8.3,2.8) {$\\mathsf{R}_\\mathsf{Ln}$};\n      \\draw[thick,red] (7.5,1.4) -- (9,2.3);\n      \\node[red] at (8.7,3.2) {$\\mathsf{DAC}$};\n      % arrows\n      \\draw[red,thick,-{Latex[length=3mm]}] (3.2,4.5) to [out=200,in=90] (3.9,4.5);\n      \\draw[blue,thick,-{Latex[length=3mm]}] (2.4,4.5) to [out=200,in=90] (3.1,4.5);\n      \\draw[blue,thick,-{Latex[length=3mm]}] (6.4,4.5) to [out=200,in=90] (7.1,4.5);\n      \\draw[red,thick,-{Latex[length=3mm]}] (5.2,4.5) to [out=200,in=90] (5.9,4.5);\n      \\node[red] at (3.5,0) {\\textbf{(a)}};\n      \\node[blue] at (6.5,0) {\\textbf{(b)}};\n      \\node[red] at (9.5,0) {\\textbf{(c)}};\n      \\node[blue] at (10.5,0) {\\textbf{(d)}};\n    \\end{tikzpicture}\n\n\\end{document}"
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        "index": 275,
        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath, amsthm, amssymb, mathrsfs, mathtools}\n\\usepackage{tikz}\n\\usetikzlibrary{graphs}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{arrows,positioning,automata,calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[>=stealth',shorten >=1pt,node distance=2cm,on grid,initial/.style    ={}]\n\t\t\t\\tikzset{mystyle/.style={->,relative=false,in=0,out=0}};\n\t\t\t\\node[state,fill=lightgray,draw=black,text=black,minimum size=.5cm] (Z) at (0,0) { };\n\t\t\t\\node[state,fill=lightgray,draw=black,text=black,minimum size=.5cm] (Y) at (1.5,0) { };\n\t\t\t\\node[state,fill=lightgray,draw=black,text=black,minimum size=.5cm] (X) at (3,0) { };\n\t\t\t\\node[state,fill=lightgray,draw=black,text=black,minimum size=.5cm] (T) at (4.5,0) { };\n\t\t\t\\node[state,fill=lightgray,draw=black,text=black,minimum size=.5cm] (U) at (6,0) { };\n\t\t\t\\node[state,fill=lightgray,draw=black,text=black,minimum size=.5cm] (V) at (7.5,0) { };\n\t\t\t\\node[state,fill=lightgray,draw=black,text=black,minimum size=.5cm] (W) at (9,0) { };\n\t\t\t\n\t\t\t\\draw [->,>=stealth] (Z) to (Y);\n\t\t\t\\draw [->,>=stealth] (Y) to (X);\n\t\t\t\\draw [->,>=stealth] (X) to (T);\n\t\t\t\\draw [->,>=stealth] (T) to (U);\n\t\t\t\\draw [->,>=stealth] (U) to (V);\n\t\t\t\\draw [->,>=stealth] (V) to (W);\n\t\t\t\n\t\t\t\\draw [fill=lightgray,lightgray,fill opacity=0.2] (-1,-1.5) rectangle (7.5, 1.5);\n\t\t\t\n\t\t\t\\draw [fill=lightgray,lightgray,fill opacity=0.2] (-1,-2.5) rectangle (9, -1.5);\n\t\t\t\\draw [<-,>=stealth,dashed] (W) to (9, 1.5);\n\t\t\t\\draw [<-,>=stealth,dashed] (T) to (6, 1.5);\n\t\t\t\\draw [<-,>=stealth,dashed] (X) to (4.5, 1.5);\n\t\t\t\\draw [<-,>=stealth,dashed] (Y) to (3, 1.5);\n\t\t\t\\draw [<-,>=stealth,dashed] (Z) to (-1, 1.5);\n\t\t\t\n\t\t\t\\node[draw,fill=white,align=center,text width=2cm,minimum height=0.5cm] (A) at (6.75, 1.5) { Commit vertices to find\\\\final vertex cover};\n\t\t\t\n\t\t\t\\node[draw,fill=white,align=center,text width=2cm,minimum height=0.5cm] (B) at (-1, 1.5) { $p$ };\n\t\t\t\n\t\t\t\\node[draw,fill=white,align=center,text width=2cm,minimum height=0.5cm] (C) at (-2.5, -2.5) { $\\mathsf{H} + \\mathsf{GV}(V) \\le p$ };\n\t\t\t\n\t\t\t\\node[draw,fill=white,align=center,text width=2cm,minimum height=0.5cm] (D) at (9, -2.5) { Query to find $\\mathsf{H}$ };\n\t\t\t\n\t\t\t\\draw [->,>=stealth] (B) to (C);\n\t\t\t\\draw [->,>=stealth] (D) to (W);\n\t\t\t\n\t\t\t\n\t\t\t\\end{tikzpicture}\n\n\\end{document}"
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        "index": 276,
        "tikz_code": "\\documentclass[11pt,reqno]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{color}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage{color}\n\\usetikzlibrary{mindmap,trees}\n\\usetikzlibrary{shapes,arrows}\n\\usepackage{pgfplots}\n\\usepgflibrary{plotmarks}\n\\tikzset{\n basic/.style = {draw, rectangle, rounded corners=6pt, align=center},\n root/.style = {basic, text width=6cm},\n rect1/.style = {basic, font=\\small},\n ellip/.style = {ellipse, fill=blue!20, minimum width=6cm}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n%\n\\begin{axis}[\n    axis lines=middle,\n    axis equal image,\n    xmin=-2, xmax=2,\n    ymin=-2, ymax=2,\n    xtick=\\empty, ytick=\\empty\n]\n\\addplot [domain=-2:2,thick,red] {(1/2)*sqrt(4-x^2)} node[right]{$g^*-\\frac{1}{2}J$};\n\\addplot [domain=-2:2,thick,red] {-sqrt(4-x^2)} node[right]{$-g^*-\\frac{1}{2}J$};\n\\addplot [domain=-2:2,thick,green] {(1/2)*sqrt(4-x^2)};\n\\addplot [domain=-2:2,thick,green] {-sqrt(4-x^2)};\n\\addplot [red,thick,fill=red, fill opacity=0.2] coordinates {(-1,0) (0,0) (0,-1) (1,-2) (1,0) (0,1) (-1,0)};\n\\addplot [green,thick,fill=green, fill opacity=0.2] coordinates {(1,0) (0,0) (0,1) (-1,2) (1,0) (0,-1) (1,-2)};\n\\addplot[black, mark=*] coordinates {(-1,0)} node[above, xshift=-0.5cm]{};\n\\addplot[black, mark=*] coordinates {(1,0)} node[above, xshift=0.5cm]{};\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath, amsfonts, amsthm, physics, enumitem}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{patterns,arrows,decorations.markings}\n\\usepackage{tikz-cd}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\\draw [->, blue, dashed] (-1,-1) -- (3.2,-1);\n\n\\draw (0,0) -- (5,0);\n\\draw (0,0) -- (0,4.5);\n\n\\draw (0,1.25) -- (5,1.25);\n\n\\draw [red, fill] (2,0) circle [radius=0.05];\n\\draw [red, fill] (1,0) circle [radius=0.05];\n\\draw [red, fill] (3,0) circle [radius=0.05];\n\n\\draw [red, fill] (2,1.25) circle [radius=0.05];\n\\draw [red, fill] (1,1.25) circle [radius=0.05];\n\\draw [red, fill] (3,1.25) circle [radius=0.05];\n\n\\draw [red, fill] (2,2.5) circle [radius=0.05];\n\\draw [red, fill] (1,2.5) circle [radius=0.05];\n\\draw [red, fill] (3,2.5) circle [radius=0.05];\n\n\\draw [red, fill] (2,3.75) circle [radius=0.05];\n\\draw [red, fill] (1,3.75) circle [radius=0.05];\n\\draw [red, fill] (3,3.75) circle [radius=0.05];\n\n\\draw [black, fill] (4,0) circle [radius=0.05];\n\\draw [black, fill] (4,1.25) circle [radius=0.05];\n\\draw [black, fill] (4,2.5) circle [radius=0.05];\n\\draw [black, fill] (4,3.75) circle [radius=0.05];\n\n\\node[label={[blue, rotate=-45]below:$S_0$},draw,circle,inner sep=1.8pt,fill,blue] (a) at (5,1.25) {};\n\n\\node[label={[green!60!black]right:$q=0$},draw,circle,inner sep=1.8pt,fill,green] (a) at (4.5,0) {};\n\n\\draw [green, fill] (2,0) circle [radius=0.05];\n\\draw [green, fill] (1,0) circle [radius=0.05];\n\\draw [green, fill] (3,0) circle [radius=0.05];\n\n\\draw [green, fill] (2,1.25) circle [radius=0.05];\n\\draw [green, fill] (1,1.25) circle [radius=0.05];\n\\draw [green, fill] (3,1.25) circle [radius=0.05];\n\n\\draw [green, fill] (2,2.5) circle [radius=0.05];\n\\draw [green, fill] (1,2.5) circle [radius=0.05];\n\\draw [green, fill] (3,2.5) circle [radius=0.05];\n\n\\draw [green, fill] (2,3.75) circle [radius=0.05];\n\\draw [green, fill] (1,3.75) circle [radius=0.05];\n\\draw [green, fill] (3,3.75) circle [radius=0.05];\n\n\\node[label={[green!60!black]below:$H_k, \\delta_k$},draw,circle,inner sep=1.8pt,fill,green] (a) at (1.5,0.75) {};\n\n\\node[label={[green!60!black]left:$H_{k+1}, \\delta_{k+1}$},draw,circle,inner sep=1.8pt,fill,green] (a) at (0.5,3.25) {};\n\n\n\\draw [yellow, fill] (4,3.25) circle [radius=0.05];\n\\draw [yellow, fill] (4,2.75) circle [radius=0.05];\n\n\\draw [yellow, fill] (4,2) circle [radius=0.05];\n\\draw [yellow, fill] (4,1.5) circle [radius=0.05];\n\n\\node[label={[yellow, rotate=-45]right:$H_{k}, \\delta_{k}$},draw,circle,inner sep=1.8pt,fill,yellow] (a) at (4,1.5) {};\n\n\\draw [yellow, fill] (4,0.75) circle [radius=0.05];\n\\draw [yellow, fill] (4,0.25) circle [radius=0.05];\n\n\n\n\n\n\n\\node[label={[blue, rotate=-45]below:$S$},draw,circle,inner sep=1.8pt,fill,blue] (a) at (5,0) {};\n\n\\node[label={[green]right:$H_{k}(T,S_{S_{k,k}}^{smooth})$},draw,circle,inner sep=1.8pt,fill,green] (a) at (5,3.75) {};\n\n\n\\draw [blue, fill] (2,0) circle [radius=0.05];\n\\draw [blue, fill] (1,0) circle [radius=0.05];\n\\draw [blue, fill] (3,0) circle [radius=0.05];\n\n\\draw [blue, fill] (2,1.25) circle [radius=0.05];\n\\draw [blue, fill] (1,1.25) circle [radius=0.05];\n\\draw [blue, fill] (3,1.25) circle [radius=0.05];\n\n\\draw [blue, fill] (2,2.5) circle [radius=0.05];\n\\draw [blue, fill] (1,2.5) circle [radius=0.05];\n\\draw [blue, fill] (3,2.5) circle [radius=0.05];\n\n\\draw [blue, fill] (2,3.75) circle [radius=0.05];\n\\draw [blue, fill] (1,3.75) circle [radius=0"
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        "tikz_code": "\\documentclass[tikz,border=3.14mm]{standalone}\n\\usetikzlibrary{calc}\n\\usepackage{tikz-3dplot}\n\\usetikzlibrary{arrows.meta}\n\\begin{document}\n\\begin{tikzpicture}[>=Stealth]\n\\tdplotsetmaincoords{70}{00}\n\\begin{scope}[tdplot_main_coords]\n \\draw[dashed] (0,0,0) circle (2);\n \\foreach \\X [evaluate=\\X as \\Y using {int(\\X+1)}] in {0,20,...,360}\n {\\tdplotdrawarc[fill=gray!30]{(0,0,0)}{2}{0}{360}{}{}};\n \\foreach \\X [evaluate=\\X as \\Y using {int(\\X+1)}] in {0,20,...,360}\n {\\tdplotdrawarc[dashed]{(0,0,0)}{2}{0}{360}{}{}};\n \\draw (0,0,0) circle (2);\n \\draw[thick] (0,0,0) circle (2);\n \\draw[thick,->] (0,0,0) -- (0,0,2);\n \\node at (0,0,0) [circle,draw,fill=gray!30]{};\n \\node at (0,0,2) [circle,fill,inner sep=1pt]{};\n \\foreach \\X in {0,20,...,360}\n {\\tdplotsetrotatedcoords{\\X}{0}{0}\n \\tdplotdrawarc[->]{(0,0,0)}{2}{0}{360}{}{}};\n \\path (0,0,0) node[below left]{$q$}\n (0,2,0) node[above]{$\\vec n$}\n (2,0,0) node[below right]{$\\vec q$};\n \\path (0,2,0) node[above left]{$\\vec \\alpha$};\n \\path (0,-3,0) node[above]{south pole};\n \\path (0,2.5,0) node[above]{north pole};\n\\end{scope}\n\\begin{scope}[xshift=7cm,tdplot_main_coords]\n \\draw[dashed] (0,0,0) circle (2);\n \\foreach \\X [evaluate=\\X as \\Y using {int(\\X+1)}] in {0,20,...,360}\n {\\tdplotdrawarc[fill=gray!30]{(0,0,0)}{2}{0}{360}{}{}};\n \\foreach \\X [evaluate=\\X as \\Y using {int(\\X+1)}] in {0,20,...,360}\n {\\tdplotdrawarc[dashed]{(0,0,0)}{2}{0}{360}{}{}};\n \\draw (0,0,0) circle (2);\n \\draw[thick] (0,0,0) circle (2);\n \\draw[thick,->] (0,0,0) -- (0,0,2);\n \\node at (0,0,0) [circle,draw,fill=gray!30]{};\n \\node at (0,0,2) [circle,fill,inner sep=1pt]{};\n \\foreach \\X in {0,20,...,360}\n {\\tdplotsetrotatedcoords{\\X}{0}{0}\n \\tdplotdrawarc[->]{(0,0,0)}{2}{0}{360}{}{}};\n \\path (0,0,0) node[below left]{$q$}\n (0,2,0) node[above]{$\\vec n$}\n (2,0,0) node[below right]{$\\vec q$};\n \\path (0,2,0) node[above left]{$\\vec \\alpha$};\n \\path (0,-3,0) node[above]{south pole};\n \\path (0,2.5,0) node[above]{north pole};\n \\draw[red] (0,2,0) ellipse (2.5 and 0.3);\n \\draw[red,dashed] (0,-2,0) arc (180:0:2.5 and 0.3);\n \\draw[red,dashed] (0,-2,0) -- (0,2,0);\n \\draw[red,->] (2.5,0,0) arc (0:20:2.5 and 0.3);\n \\draw[red,->] (2.5,0,0) -- (-2.5,0,0);\n \\draw[red] (-2.5,0,0) arc (180:340:2.5 and 0.3);\n \\draw[red] (2.5,0,0) arc (0:10:2.5 and 0.3);\n \\draw[red,->] (2.5,0,0) -- (-2.5,0,0);\n \\draw[red] (-2.5,0,0) arc (180:340:2.5 and 0.3);\n \\draw[red] (2.5,0,0) arc (0:10:2.5 and 0.3);\n \\draw[red,->] (2.5,0,0) -- (-2.5,0,0);\n \\draw[red,dashed] (2.5,0,0) arc (0:180:2.5 and 0.3);\n \\draw[red,dashed] (2.5,0,0) arc (0:180:2.5 and 0.3);\n\\end{scope}\n\\end{tikzpicture}\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage[usenames,dvipsnames]{xcolor}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n        \t\t\\draw[line width = 2.2pt, blue] (-1.3,0) -- (0,0) -- (0.7,-0.7) -- (1.4,-0.5) -- (2.1, 0.4) -- (2.8,0.8) -- (3.5, 1.5) -- (4.2, 2.2);\n\t\t\\draw[line width = 2.2pt, blue] (-1.3, 3.3) -- (-2.6, 3.3) -- (-3.3, 2.7) -- (-3.3, 1.6) -- (-3.3, 0.8) -- (-3.3, 0) -- (-3.3, -1.1) -- (-2.6, -1.7);\n\t\t\\draw[line width = 2pt, black] (1.9, -0.3) -- (3, -0.3) -- (3, -1.2) -- (1.9, -1.2);\n\t\t\\draw[black] (-1, 3) -- (-1.1, 3) -- (-1.1, 2);\n\t\t\\draw[line width = 2pt] (-1, 0) -- (0.2, 0);\n\t\t\\draw[line width = 2pt] (2.8, -0.3) -- (2.8, 0.6) -- (3.1, 0.6) -- (3.1, -0.3);\n\t\t\\draw[line width = 2pt] (-0.4, 3) -- (-0.3, 3) -- (-0.3, 2.1);\n\t\t\\draw[line width = 2pt] (1.4, 3) -- (1.5, 3) -- (1.5, 2.1);\n\t\t\\draw[black] (1.8, 1.5) -- (1.9, 1.5) -- (1.9, 1.6);\n\t\t\\draw[black] (0, 3) -- (0, 3.1) -- (0.2, 3.1);\n\t\t\\draw[black] (0, 0) -- (0, -0.1) -- (0.2, -0.1);\n\t\t\\draw[black] (2.8, 0) -- (2.8, -0.1) -- (3, -0.1);\n\t\t\\draw[black] (1.4, 0) -- (1.4, -0.1) -- (1.6, -0.1);\n\t\t\\draw[black] (3, 3) -- (3, 3.1) -- (3.2, 3.1);\n\t\t\\draw[black] (-1, 0) -- (-1.1, 0) -- (-1.1, -0.1);\n\t\t\\draw[black] (-1, 3) -- (-1.1, 3) -- (-1.1, 3.1);\n\t\t\\draw[black] (0.7, -0.7) -- (0.8, -0.7) -- (0.8, -0.8);\n\t\t\\draw[black] (2.1, 0.4) -- (2.2, 0.4) -- (2.2, 0.3);\n\t\t\\draw[black] (2.1, -0.4) -- (2.2, -0.4) -- (2.2, -0.5);\n\t\t\\draw[black] (2.8, 0.8) -- (2.9, 0.8) -- (2.9, 0.7);\n\t\t\\draw[black] (4.2, 2.2) -- (4.3, 2.2) -- (4.3, 2.1);\n\t\t\\draw[black] (0.7, 1.5) -- (0.8, 1.5) -- (0.8, 1.6);\n\t\t\\draw[black] (2.8, -0.3) -- (3, -0.3) -- (3, -0.4);\n\t\t\\draw[black] (2.8, 3) -- (2.8, 3.1) -- (2.9, 3.1);\n\t\t\\draw[black] (1.4, 3) -- (1.5, 3) -- (1.5, 3.1);\n\t\t\\draw[black] (0, 3) -- (0, 3.1) -- (-0.2, 3.1);\n\t\t\\draw[black] (0, 0) -- (0, -0.1) -- (-0.2, -0.1);\n\t\t\\draw[black] (2.8, 0) -- (2.8, -0.1) -- (2.9, -0.1);\n\t\t\\draw[black] (2.8, 3) -- (2.8, 3.1) -- (2.9, 3.1);\n\t\t\\draw[black] (1.4, 0) -- (1.4, -0.1) -- (1.5, -0.1);\n\t\t\\draw[black] (3, 3) -- (3, 3.1) -- (3.2, 3.1);\n\t\t\\draw[black] (-1, 3) -- (-1.1, 3) -- (-1.1, 3.1);\n\t\t\\draw[black] (-1, 0) -- (-1.1, 0) -- (-1.1, -0.1);\n\t\t\\draw[black] (-1, 0) -- (-1.1, 0) -- (-1.1, -0.1);\n\t\t\\draw[black] (0, 0) -- (0.1, 0) -- (0.1, -0.1);\n\t\t\\draw[black] (0, 0) -- (-0.1, 0) -- (-0.1, -0.1);\n\t\t\\draw[black] (1.4, 3) -- (1.5, 3) -- (1.5, 3.1);\n\t\t\\draw[black] (2.8, 0) -- (2.9, 0) -- (2.9, -0.1);\n\t\t\\draw[black] (2.8, 0.8) -- (2.9, 0.8) -- (2.9, 0.7);\n\t\t\\draw[black] (4.2, 2.2) -- (4.3, 2.2) -- (4.3, 2.1);\n\t\t\\draw[black] (3, 3) -- (3.1, 3) -- (3.1"
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    {
        "index": 280,
        "tikz_code": "\\documentclass[border=2pt]{standalone}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.8}\n\\begin{document}\n\\begin{tikzpicture}\n    \\begin{axis}[\n        domain=0:20,\n        samples=100,\n        axis lines=left,\n        xtick={5,10,15,20},\n        ytick={1.5,2,2.5,3},\n        extra y ticks={1.5,2},\n        extra y tick style={\n            ticklabel style={\n                anchor=south east,\n                inner ysep=1pt,\n            },\n        },\n        ymin=1,\n        ymax=3,\n        xlabel={$k$},\n        ylabel={$f$},\n    ]\n        \\addplot [blue] {1+2*exp(-x/2)};\n        \\draw [dashed,orange] (axis cs:5,2) -- (axis cs:5,3);\n        \\draw [dashed] (axis cs:10,2) -- (axis cs:10,1.5) -- (axis cs:5,1.5);\n        \\node [right,blue] at (axis cs:2,1.6) {$f(1)=1$};\n        \\node [right,orange] at (axis cs:7.5,2.1) {$f(4)=2$};\n        \\node [right] at (axis cs:12,2.8) {$1+\\sqrt{2}$};\n    \\end{axis}\n\\end{tikzpicture}\n\\end{document}"
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    {
        "index": 281,
        "tikz_code": "\\documentclass[letterpaper]{article}\n\\usepackage[usenames,dvipsnames]{xcolor}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows, shapes,positioning,decorations.pathreplacing, decorations.pathmorphing}\n\\tikzset{every picture/.style={line width=0.75pt}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\\node (a) {$\\kappa(x) =$};\n\\node[draw,rectangle] (b) [right=0.8cm of a] {$y_0$};\n\\node[draw,rectangle] (c) [right=0.5cm of b] {$y_1$};\n\\node[draw,rectangle] (d) [right=0.5cm of c] {$\\cdots$};\n\\node[draw,rectangle] (e) [right=0.5cm of d] {$y_{\\frac{n}{2}-1}$};\n\\node[draw,rectangle] (f) [right=0.5cm of e] {$y_{\\frac{n}{2}}$};\n\\node[draw,rectangle] (g) [right=0.5cm of f] {$y_{\\frac{n}{2}+1}$};\n\\node[draw,rectangle] (h) [right=0.5cm of g] {$\\cdots$};\n\\node[draw,rectangle] (i) [right=0.5cm of h] {$y_n$};\n\\node (h1) [below=0.5cm of b] {};\n\\node (h2) [below=0.5cm of e] {};\n\\node (h3) [below=0.5cm of f] {};\n\\node (h4) [below=0.5cm of g] {};\n\\node (h5) [below=0.5cm of i] {};\n\\node (p) [below=0.1cm of h1] {$g(x) =$};\n\n\\path[->] (b) edge node {} (h1);\n\\path[->] (e) edge node {} (h2);\n\\path[->] (f) edge node {} (h3);\n\\path[->] (g) edge node {} (h4);\n\\path[->] (i) edge node {} (h5);\n\n\\node (a1) [right=1cm of b] {$\\cdots$};\n\\node (a2) [right=1cm of e] {$\\cdots$};\n\\node (a3) [right=1cm of f] {$\\cdots$};\n\\node (a4) [right=1cm of g] {$\\cdots$};\n\\node (a5) [right=1cm of i] {$\\cdots$};\n\n\\node (a3) [below=0.3cm of a] {$x$};\n\\node (b1) [below=0.5cm of a1] {$\\cdots$};\n\\node (b2) [below=0.5cm of a2] {$\\cdots$};\n\\node (b3) [below=0.5cm of a3] {$\\cdots$};\n\\node (b4) [below=0.5cm of a4] {$\\cdots$};\n\\node (b5) [below=0.5cm of a5] {$\\cdots$};\n\n\\node (c1) [left=0.5cm of h1] {};\n\\node (c2) [left=0.5cm of h2] {};\n\\node (c3) [left=0.5cm of h3] {};\n\\node (c4) [left=0.5cm of h4] {};\n\\node (c5) [left=0.5cm of h5] {};\n\n\\node (d1) [below=0.5cm of c1] {$y_{\\frac{n}{2}-1}$};\n\\node (d2) [below=0.5cm of c2] {$y_{\\frac{n}{2}-2}$};\n\\node (d3) [below=0.5cm of c3] {$y_{\\frac{n}{2}-3}$};\n\\node (d4) [below=0.5cm of c4] {$y_{\\frac{n}{2}-4}$};\n\\node (d5) [below=0.5cm of c5] {$y_{\\frac{n}{2}-5}$};\n\n\\path[->] (d1) edge node {} (h1);\n\\path[->] (d2) edge node {} (h2);\n\\path[->] (d3) edge node {} (h3);\n\\path[->] (d4) edge node {} (h4);\n\\path[->] (d5) edge node {} (h5);\n\n\\path[->,densely dashed,color=blue] (c1) edge node {} (d1);\n\\path[->,densely dashed,color=blue] (c2) edge node {} (d2);\n\\path[->,densely dashed,color=blue] (c3) edge node {} (d3);\n\\path[->,densely dashed,color=blue] (c4) edge node {} (d4);\n\\path[->,densely dashed,color=blue] (c5) edge node {} (d5);\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 282,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb, amscd, bbm, mathrsfs, enumerate, url, pinlabel, natbib, hyperref}\n\\usepackage{pgf,tikz}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{positioning}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]\n\\clip(-4.7,-1.45) rectangle (4.6,3.25);\n\\draw (-1,2.25) node[anchor=north west] {$\\ell_s$};\n\\draw (-1.7,1.5) node[anchor=north west] {$\\langle \\ell,\\ell_s \\rangle$ is};\n\\draw (-1.7,1.0) node[anchor=north west] {closed under exits,};\n\\draw (-1.7,0.5) node[anchor=north west] {cofproducts};\n\\draw (-1.7,-0.2) node[anchor=north west] {and direct sands};\n\\draw (-3,0) node[anchor=north west] {$(\\ell,\\ell_s)$ is};\n\\draw (-3,0.5) node[anchor=north west] {closed under exits,};\n\\draw (-3,1) node[anchor=north west] {cofproducts};\n\\draw (-3,1.5) node[anchor=north west] {and direct sands};\n\\draw (-2.6,-0.7) node[anchor=north west] {$\\langle \\ell,\\ell_s \\rangle$ is a};\n\\draw (-2.6,-1.2) node[anchor=north west] {duality pair};\n\\draw (-0.8,-1.7) node[anchor=north west] {$\\langle \\ell,\\ell_s \\rangle$ is a};\n\\draw (-0.8,-2.2) node[anchor=north west] {$(A,\\ell_s)$-admissible};\n\\draw (-4.3,1.5) node[anchor=north west] {$\\mathcal{L}^{-}$};\n\\draw (-1.5,1.5) node[anchor=north west] {$\\mathcal{L}^{+}$};\n\\draw (1.7,1.5) node[anchor=north west] {$\\mathcal{L}^{+}$};\n\\draw (4.3,1.5) node[anchor=north west] {$\\mathcal{L}^{-}$};\n\\draw (-2.6,-0.2) node[anchor=north west] {$\\mathcal{G}_{\\ell,\\ell_s}$};\n\\draw (-0.8,-0.2) node[anchor=north west] {$\\mathcal{G}_{\\ell,\\ell_s}$};\n\\draw (1.7,-0.2) node[anchor=north west] {$\\mathcal{G}_{\\ell,\\ell_s}$};\n\\draw (-4.3,1) node[anchor=north west] {$\\mathcal{G}_{\\ell,\\ell_s}^{\\mathcal{L}^{-}}$};\n\\draw (-1.5,1) node[anchor=north west] {$\\mathcal{G}_{\\ell,\\ell_s}^{\\mathcal{L}^{+}}$};\n\\draw (1.7,1) node[anchor=north west] {$\\mathcal{G}_{\\ell,\\ell_s}^{\\mathcal{L}^{+}}$};\n\\draw (4.3,1) node[anchor=north west] {$\\mathcal{G}_{\\ell,\\ell_s}^{\\mathcal{L}^{-}}$};\n\\draw [->] (-4.1,2.7) -- (-4.1,2.2);\n\\draw (-4.1,2.7) node[anchor=north west] {$\\mathcal{L}^{-} \\tilde{\\mathrm{mod}} (\\mathcal{L})$};\n\\draw [->] (-1.2,1.5) -- (-0.2,1.5);\n\\draw (-1.2,1.5) node[anchor=north west] {$\\mathcal{L}^{+} \\tilde{\\mathrm{mod}} (\\mathcal{L})$};\n\\draw [->] (1.2,1.5) -- (0.2,1.5);\n\\draw (1.2,1.5) node[anchor=north west] {$\\mathcal{L}^{-} \\tilde{\\mathrm{mod}} (\\mathcal{L})$};\n\\draw [->, orange] (-0.2,-0.4) to[out=120,in=60] (-1.8,-0.4);\n\\draw [->, orange] (0.2,-0.4) to[out=120,in=60] (1.8,-0.4);\n\\draw (-4.1,0.5) node[anchor=north west] {$\\cdot$};\n\\draw (-1.2,0.5) node[anchor=north west] {$+$};\n\\draw (1.2,0.5) node[anchor=north west] {$+$};\n\\draw (4.1,0.5) node[anchor=north west] {$\\cdot$};\n\\draw [->] (-3.7,1) to[out=-120,in=-60] (-4.3,0.5);\n\\draw [->] (-0.2,1) to[out=-120,in=-60] (-0.8,0.5);\n\\draw [->] (0.2,1) to[out=-120,in=-60] (0.8,0.5);\n\\draw [->] (1.8,1) to[out=-120,in=-60] (4.3,0.5);\n\\draw (-3.7,0.5) node[anchor=north west] {$\\cdot$};\n\\draw (-0.2,0.5) node[anchor=north west] {$+$};\n\\draw (0.2,0.5) node[anchor=north west] {$+$};\n\\draw (1.8,0.5) node[anchor=north west] {$\\cdot$};\n\\begin{scriptsize}\n\\draw [fill=white] (-4.1,2.7) circle (1.5pt);\n\\draw [fill=white] (-4.1,2.2) circle (1.5pt);\n\\draw [fill=black] (-4.1,0.5) circle (1.5pt);\n\\draw [fill=white] (-1.2,1.5) circle (1.5pt);\n\\draw [fill"
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        "index": 287,
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        "tikz_code": "\\documentclass[a4paper,12pt]{amsart}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath,amsfonts,amssymb,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{external}\n\\tikzsetexternalprefix{figures/}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n      \\draw[thick,->] (0,0) -- (0,2) node[above] {$\\vec{\\tau}(\\epsilon_1)$};\n      \\draw[thick,->] (0,0) -- (2,0) node[right] {$\\vec{\\tau}(\\epsilon_2)$};\n      \\draw[thick,->] (0,0) -- (2.5,2.5) node[right] {$\\vec{\\tau}(\\epsilon_3)$};\n      \\draw[thick,->] (0,0) -- (-2.5,2.5) node[left] {$\\vec{\\tau}(\\epsilon_4)$};\n      \\draw[thick,->] (0,0) -- (-3.5,0) node[left] {$\\vec{\\tau}(0)$};\n      \\node at (-4,-0.5) {space};\n      \\node at (4,-0.5) {$\\vec{r}(\\epsilon_1,\\epsilon_2)$};\n\n      \\draw[thick,->] (8,0) -- (8,2) node[above] {$\\vec{\\tau}(\\epsilon_2)$};\n      \\draw[thick,->] (8,0) -- (10,0) node[right] {$\\vec{\\tau}(\\epsilon_3)$};\n      \\draw[thick,->] (8,0) -- (8,-2) node[below] {$\\vec{\\tau}(\\epsilon_4)$};\n      \\draw[thick,->] (8,0) -- (8,3) node[above right] {$\\vec{\\tau}(\\epsilon_1)$};\n      \\draw[thick,->] (8,0) -- (6,0) node[left] {$\\vec{\\tau}(0)$};\n      \\node at (2,-0.5) {space};\n      \\node at (10,-0.5) {$\\vec{r}(\\epsilon_1,\\epsilon_4)$};\n    \\end{tikzpicture}\n\n\\end{document}"
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        "index": 292,
        "tikz_code": "\\documentclass[journal]{IEEEtran}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,shapes,fit,scopes,calc,matrix,positioning,decorations.pathmorphing,shapes.geometric}\n\\tikzset{\n    vertex/.style={rectangle,draw,minimum width=6em},\n    edge/.style={->,> = latex'},\n    cvertex/.style={circle,draw,minimum width=0.3em,inner sep=1},\n    lcvertex/.style={circle,draw,minimum width=2em,inner sep=1}    \n}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node[anchor=south west,inner sep=0] (image) at (0,0) {\\includegraphics[width=\\columnwidth,clip,trim={0cm 0cm 0cm 0cm}]{example-image}};\n\\begin{scope}[x={(image.south east)},y={(image.north west)}]\n\\node[align=center] at (0.025,0.95) {The cluster $4$ has been\\\\ filtered-out because it is too close to\\\\ other clusters $7$. See preprocessing step};\n\\node[align=center] at (0.98,0.95) {The cluster $0$ has been filtered-out because it is too\\\\ wide. See preprocessing step};\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 293,
        "tikz_code": "\\documentclass[11pt,reqno]{amsart}\n\\usepackage{tikz}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.6]\n\t\\draw (0,0) --(0,4);\n\t\\draw (2,0) --(2,4);\n\t\\draw (4,0) --(4,4);\n\t\\draw (6,0) --(6,4);\n\t\\draw (8,0) --(8,4);\n\t\n\t\\draw (0,0) --(2,0);\n\t\\draw (0,2) --(2,2);\n\t\\draw (0,4) --(2,4);\n\t\\draw (4,0) --(6,0);\n\t\\draw (4,2) --(6,2);\n\t\\draw (4,4) --(6,4);\n\t\\draw (8,0) --(8,2);\n\t\\draw (8,4) --(8,6);\n\t\n\t\\draw (0,1) node {$\\downarrow$};\n\t\\draw (2,1) node {$\\downarrow$};\n\t\\draw (4,1) node {$\\downarrow$};\n\t\\draw (6,1) node {$\\downarrow$};\n\t\\draw (8,1) node {$\\downarrow$};\n\t\n\t\\draw (0,3) node {$\\downarrow$};\n\t\\draw (2,3) node {$\\downarrow$};\n\t\\draw (4,3) node {$\\downarrow$};\n\t\\draw (6,3) node {$\\downarrow$};\n\t\\draw (8,3) node {$\\downarrow$};\n\t\n\t\\draw (0,5) node {$\\downarrow$};\n\t\\draw (2,5) node {$\\downarrow$};\n\t\\draw (4,5) node {$\\downarrow$};\n\t\\draw (6,5) node {$\\downarrow$};\n\t\\draw (8,5) node {$\\downarrow$};\n\t\n\t\\draw (0,-1.5) node {FM};\n\t\\draw (2,-1.5) node {Ni 1};\n\t\\draw (4,-1.5) node {Ni 2};\n\t\\draw (6,-1.5) node {Ni 1};\n\t\\draw (8,-1.5) node {Ni 2};\n\t\n\t\\draw[thick,color=green, ->] (0,3.5) -- (2,3.5);\n\t\\draw[thick,color=green, ->] (2,3.5) -- (4,3.5);\n\t\\draw[thick,color=green, ->] (4,3.5) -- (6,3.5);\n\t\\draw[thick,color=green, ->] (6,3.5) -- (8,3.5);\n\t\\draw[thick,color=green, ->] (2,3.5) -- (0,2.5);\n\t\\draw[thick,color=green, ->] (4,3.5) -- (2,2.5);\n\t\\draw[thick,color=green, ->] (6,3.5) -- (4,2.5);\n\t\\draw[thick,color=green, ->] (8,3.5) -- (6,2.5);\n\t\\draw[thick,color=green, ->] (2,2.5) -- (0,1.5);\n\t\\draw[thick,color=green, ->] (4,2.5) -- (2,1.5);\n\t\\draw[thick,color=green, ->] (6,2.5) -- (4,1.5);\n\t\\draw[thick,color=green, ->] (8,2.5) -- (6,1.5);\n\t\n\t\\draw[thick,color=blue, ->] (0,3) -- (2,3);\n\t\\draw[thick,color=blue, ->] (2,3) -- (4,3);\n\t\\draw[thick,color=blue, ->] (4,3) -- (6,3);\n\t\\draw[thick,color=blue, ->] (6,3) -- (8,3);\n\t\\draw[thick,color=blue, ->] (2,3) -- (0,2);\n\t\\draw[thick,color=blue, ->] (4,3) -- (2,2);\n\t\\draw[thick,color=blue, ->] (6,3) -- (4,2);\n\t\\draw[thick,color=blue, ->] (8,3) -- (6,2);\n\t\\draw[thick,color=blue, ->] (2,2) -- (0,1);\n\t\\draw[thick,color=blue, ->] (4,2) -- (2,1);\n\t\\draw[thick,color=blue, ->] (6,2) -- (4,1);\n\t\\draw[thick,color=blue, ->] (8,2) -- (6,1);\n\t\n\t\\draw[thick,color=red, ->] (2,3.5) arc (130:110:4);\n\t\\draw[thick,color=red, ->] (4,3.5) arc (130:110:4);\n\t\\draw[thick,color=red, ->] (6,3.5) arc (130:110:4);\n\t\\draw[thick,color=red, ->] (8,3.5) arc (130:110:4);\n\t\n\t\\draw (0.5,5) node {$e_q$};\n\t\\draw (2.5,4.5) node {$1$};\n\t\\draw (4.5,5) node {$e_q$};\n\t\\draw (6.5,4.5) node {$2$};\n\t\n\t\n\t\\begin{scope}[shift={(10,0)}]\n\t\\draw (0,0) --(0,4);\n\t\\draw (2,0) --(2,4);\n\t\\draw (4,0) --(4,4);\n\t\\draw (6,0) --(6,4);\n\t\\draw (8,0) --(8,4);\n\t\n\t\\draw (0,0) --(2,0);\n\t\\draw (0,2) --(2,2);\n\t\\draw (0,4) --(2,4);\n\t\\draw (4,0) --(6,0);\n\t\\draw (4,2) --(6,2);\n\t\\draw (4,4) --(6,4);\n\t\\draw (8,0) --(8,2);\n\t\\draw (8,4) --(8,6);\n\t\n\t\\draw (0,1) node {$\\downarrow$};\n\t\\draw (2,1) node {$\\downarrow$};\n\t\\draw (4,1) node {$\\downarrow$};\n\t\\draw (6,1) node {$\\downarrow$};\n\t\\draw (8,1) node {$\\downarrow$};\n\t\n\t\\draw (0,3) node {$\\downarrow$};\n\t\\"
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        "index": 294,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amsmath,amsfonts,amsthm,amssymb,graphicx,tikz,color}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw (0, 0) -- (2, 2);\n\\draw (0, 0) -- (1.4, 1.6);\n\\draw (0, 0) -- (1.5, -0.9);\n\\draw [ultra thick, fill=blue, opacity=0.2] (1.7, -0.2) -- (0.8, -0.2) -- (1.3, 1.1) -- (1.5, 0.7) -- (2, 2);\n\\draw [ultra thick, fill=blue, opacity=0.2] (2, 2) -- (0.8, -0.2) -- (2, 0.2) -- (2, 2);\n\\node at (0.8, -0.2) {$\\bullet$};\n\\node at (2, 0.2) {$\\bullet$};\n\\node at (1.5, -1) {$C^\\prime$};\n\\node at (1.2, 1.2) {$\\mu(M)$};\n\\draw [ultra thick, dashed] (1.7, -0.2) -- (1.7, -1.5);\n\\draw [ultra thick, dashed] (2, 2) -- (2, 3);\n\\draw [ultra thick, dashed] (0.8, -0.2) -- (0.8, -1.5);\n\\draw [ultra thick, dashed] (1.3, 1.1) -- (1.3, 2);\n\\draw [ultra thick, dashed] (1.5, 0.7) -- (1.5, 1.5);\n\\node at (1.7, -1.7) {$S^1$};\n\\node at (2, 3.2) {$T^2$};\n\\node at (0.8, -1.7) {$T^1$};\n\\node at (1.3, 2.2) {$T^3$};\n\\node at (1.5, 1.5) {$T^4$};\n\n\\draw (5, 0) -- (6.5, 2);\n\\draw (5, 0) -- (5.5, -0.9);\n\\draw (5, 0) -- (6, 0.2);\n\\draw (6, 0.2) -- (6.5, 2);\n\\draw [ultra thick, fill=blue, opacity=0.2] (5.7, -0.2) -- (5.3, -0.2) -- (5.5, 1) -- (6, 0.2) -- (6.5, 2);\n\\node at (5.7, -0.2) {$\\bullet$};\n\\node at (6, 0.2) {$\\bullet$};\n\\draw [ultra thick, dashed] (5.7, -0.2) -- (5.7, -1.5);\n\\draw [ultra thick, dashed] (6, 0.2) -- (6, -1.5);\n\\draw [ultra thick, dashed] (5.5, 1) -- (5.5, 2);\n\\node at (5.7, -1.7) {$S^1$};\n\\node at (6, -1.7) {$C^\\prime$};\n\\node at (5.5, 2) {$T^2$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 295,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{axis}[\n\theight=0.55\\linewidth,\n\twidth=0.43\\linewidth,\n\txmin=0, xmax=1.0,\n\txtick={0.0, 0.2, 0.4, 0.6, 0.8, 1.0},\n\tymin=0, ymax=1800,\n\tytick={0,200,400,600,800,1000,1200},\n\tlegend style={at={(0.5,1.15)},\n\t\tanchor=north,draw=none,legend columns=-1},\n\txlabel=Environment Steps ($\\times 10^5$),\n\tylabel=Expected Return,\n\tylabel near ticks,\n\tgrid=both,\n\tgrid style={line width=.1pt, draw=gray!10},\n\tmajor grid style={line width=.2pt,draw=gray!50},\n\tlegend style={yshift=-12pt,xshift=15pt,legend columns=-1,font=\\footnotesize,row sep=0.1pt},\n\tlegend to name=named,\n\tlegend columns=-1,\n\tylabel style={yshift=-3ex},xlabel style={yshift=1ex},\n]\n\\addplot+[color=black,mark=none,]\ncoordinates {\n\t (0.1,116.23) (0.5,201.92) (1.0,360.57)\n};\n\\addplot+[color=orange,mark=none,]\ncoordinates {\n\t (0.1,193.91) (0.5,377.41) (1.0,755.71)\n};\n\\addplot+[color=green,mark=none,]\ncoordinates {\n\t (0.1,747.18) (0.5,1122.53) (1.0,1743.79)\n};\n\\addplot+[color=brown,mark=none,]\ncoordinates {\n\t (0.1,714.24) (0.5,1028.14) (1.0,1554.14)\n};\n\\addplot+[color=red,mark=none,]\ncoordinates {\n\t (0.1,736.16) (0.5,912.02) (1.0,1406.36)\n};\n\\addplot+[color=blue,mark=none,]\ncoordinates {\n\t (0.1,720.31) (0.5,886.58) (1.0,1331.03)\n};\n\\addlegendentry{VRKN}\n\\addlegendentry{Reward Only}\n\\addlegendentry{RSM}\n\\addlegendentry{DQN}\n\\addlegendentry{TAN}\n\\addlegendentry{SAC}\n\\end{axis}\n\\begin{axis}[\n\theight=0.55\\linewidth,\n\twidth=0.43\\linewidth,\n\txmin=0, xmax=1.0,\n\tymin=0, ymax=1800,\n\tytick={0,200,400,600,800,1000,1200},\n\txtick={0, 0.2, 0.4, 0.6, 0.8, 1.0},\n\tlegend style={at={(0.5,1.15)},\n\t\tanchor=north,draw=none,legend columns=-1},\n\txlabel=Environment Steps ($\\times 10^5$),\n\tylabel=Expected Return,\n\tylabel near ticks,\n\tgrid=both,\n\tgrid style={line width=.1pt, draw=gray!10},\n\tmajor grid style={line width=.2pt,draw=gray!50},\n\tlegend style={yshift=-12pt,xshift=15pt,legend columns=-1,font=\\footnotesize,row sep=0.1pt},\n\tlegend to name=nameright,\n\tlegend columns=-1,\n\tylabel style={yshift=-3ex},xlabel style={yshift=1ex},\n]\n\\addplot+[color=black,mark=none,]\ncoordinates {\n\t (0.1,105.06) (0.5,191.47) (1.0,360.57)\n};\n\\addplot+[color=orange,mark=none,]\ncoordinates {\n\t (0.1,193.91) (0.5,377.41) (1.0,755.71)\n};\n\\addplot+[color=green,mark=none,]\ncoordinates {\n\t (0.1,747.18) (0.5,1122.53) (1.0,1743.79)\n};\n\\addplot+[color=brown,mark=none,]\ncoordinates {\n\t (0.1,714.24) (0.5,1028.14) (1.0,1554.14)\n};\n\\addplot+[color=red,mark=none,]\ncoordinates {\n\t (0.1,736.16) (0.5,912.02) (1.0,1406.36)\n};\n\\addplot+[color=blue,mark=none,]\ncoordinates {\n\t (0.1,720.31) (0.5,886.58) (1.0,1331.03)\n};\n\\addlegendentry{VRKN}\n\\addlegendentry{Reward Only}\n\\addlegendentry{RSM}\n\\addlegendentry{DQN}\n\\addlegendentry{TAN}\n\\addlegendentry{SAC}\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[tikz,border=3.14mm]{standalone}\n\\usetikzlibrary{decorations.markings}\n\\usepackage{siunitx}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\ndecoration = {\n  markings,\n  mark=between positions 0 and 1 step 4mm with {\\arrow[line width=1pt]{latex}}\n  }\n]\n\n\\draw[postaction={decorate}] (0,0) circle [radius=3cm];\n\n\\foreach \\i [count=\\j from 0] in {45, 90,...,360}\n\\draw[shorten >=4mm,shorten <=4mm,-latex] (0,0) -- (\\i:3cm) node[pos=0.6,fill=white,font=\\footnotesize,inner\nsep=1pt] {$X_\\j$};\n\n\\draw[-latex,postaction={decorate}] (45:3cm) ++ (45:0.2) arc[start angle=45,end angle=225,radius=3cm+0.2];\n\n\\draw[-latex,postaction={decorate}] (0:3.2) ++ (0:0.2) arc[start angle=0,end angle=360,radius=3.2];\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 297,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.9]\n    \\draw[fill=black!5!white] (-0.2,-0.2) -- (0,0) -- (-0.2,0.2) -- (-0.4,0.2) -- (-2,0.5) -- (-3,0) -- cycle;\n    \\draw[pattern=north east lines] (-0.2,-0.2) -- (0,0) -- (-0.2,0.2) -- (-0.4,0.2) -- (-2,0.5) -- (-3,0) -- cycle;\n    \\draw (-3,-0.5) node {a nonvanishing isolated end};\n    \\draw (0,0) .. controls (1,0.5) and (1.5,0.8) .. (2,1);\n    \\draw (0,0) .. controls (1,-0.5) and (1.5,-0.8) .. (2,-1);\n    \\draw (0,0) node[anchor=north west] {$F$} .. controls (-0.5,0.8) and (-0.7,0.8) .. (-1,1);\n    \\draw (0,0) .. controls (-0.5,-0.8) and (-0.7,-0.8) .. (-1,-1);\n    \\draw[fill=black] (0,0) circle (0.05);\n    \\draw (-2,0.5) .. controls (-1.8,0.6) and (-1.6,0.6) .. (-1.4,0.5);\n    \\draw[fill=black] (-2,0.5) circle (0.05);\n    \\draw (-3,0) .. controls (-2.8,0.1) and (-2.6,0.1) .. (-2.4,0);\n    \\draw[fill=black] (-3,0) circle (0.05);\n    \\draw (-1,1) .. controls (-0.9,1.1) and (-0.8,1.1) .. (-0.7,1);\n    \\draw[fill=black] (-1,1) circle (0.05);\n    \\draw (-1.4,0.5) .. controls (-1.3,0.6) and (-1.2,0.6) .. (-1.1,0.5);\n    \\draw[fill=black] (-1.4,0.5) circle (0.05);\n    \\draw (-2.4,0) .. controls (-2.3,0.1) and (-2.2,0.1) .. (-2.1,0);\n    \\draw[fill=black] (-2.4,0) circle (0.05);\n    \\draw (-0.7,1) .. controls (-0.6,1.1) and (-0.5,1.1) .. (-0.4,1);\n    \\draw[fill=black] (-0.7,1) circle (0.05);\n    \\draw (-0.1,0.7) node {$D$};\n    \\draw (2.5,0.5) node {the rest of the graph};\n  \\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amsthm,amssymb}\n\\usepackage[utf8]{inputenc}\n\\usepackage[usenames]{xcolor}\n\\usepackage{tikz}\n\\usepackage{pgf}\n\\usetikzlibrary{arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]\n\\clip(-5.66,-4.49) rectangle (4.31,4.46);\n\\draw[dash pattern=on 4pt off 4pt] (-5.73,-4.48) -- (4.27,-4.48);\n\\draw[dash pattern=on 4pt off 4pt] (4.27,-4.48) -- (4.27,4.46);\n\\draw[dash pattern=on 4pt off 4pt] (4.27,4.46) -- (-5.73,4.46);\n\\draw[dash pattern=on 4pt off 4pt] (-5.73,4.46) -- (-5.73,-4.48);\n\\draw (1,0)-- (1,1);\n\\draw (1,1)-- (2,1);\n\\draw (2,1)-- (2,-1);\n\\draw (2,-1)-- (3,-1);\n\\draw (3,-1)-- (3,-2);\n\\draw (3,-2)-- (4,-2);\n\\draw (4,-2)-- (4,-3);\n\\draw (4,-3)-- (3,-3);\n\\draw (3,-3)-- (3,-2);\n\\draw (3,-2)-- (2,-2);\n\\draw (2,-2)-- (2,-1);\n\\draw (2,-1)-- (1,-1);\n\\draw (1,-1)-- (1,0);\n\\draw (0.5,0.5) node[anchor=north west] {$P_1$};\n\\draw (2.5,1.5) node[anchor=north west] {$P_2$};\n\\draw (3.5,0.5) node[anchor=north west] {$P_3$};\n\\draw [color=red] (1,2)-- (1,3);\n\\draw [color=red] (1,3)-- (2,3);\n\\draw [color=red] (2,3)-- (2,2);\n\\draw [color=red] (2,2)-- (3,2);\n\\draw [color=red] (3,2)-- (3,1);\n\\draw [color=red] (3,1)-- (4,1);\n\\draw [color=red] (4,1)-- (4,0);\n\\draw [color=blue] (1,-1)-- (1,-2);\n\\draw [color=blue] (1,-2)-- (2,-2);\n\\draw [color=blue] (2,-2)-- (2,-3);\n\\draw [color=blue] (2,-3)-- (3,-3);\n\\draw [color=blue] (3,-3)-- (3,-4);\n\\draw [color=blue] (3,-4)-- (4,-4);\n\\draw [color=blue] (4,-4)-- (4,-3);\n\\draw [color=cyan] (3,2)-- (3,3);\n\\draw [color=cyan] (3,3)-- (3,4);\n\\draw [color=cyan] (3,4)-- (4,4);\n\\draw [color=cyan] (4,4)-- (4,3);\n\\draw [color=cyan] (4,3)-- (4,2);\n\\draw [color=cyan] (4,2)-- (3,2);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 299,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{pgfplots}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{calc,positioning,fit}\n\\usetikzlibrary{arrows,decorations.markings}\n\\usetikzlibrary{arrows.meta}\n\\usetikzlibrary{decorations.pathmorphing}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.75]\n\t\t\\begin{axis}[xmin=0, xmax=2.5, ymin=0, ymax=0.85, x=0.4cm, y=0.4cm]\n\t\t\t\\addplot[black, dashed, domain=0:2.5, samples=100] {x};\n\t\t\t\\addplot[black, domain=0:2.5, samples=100] {1-exp(-0.3*x)};\n\t\t\t\\addplot[black, domain=0:0.25, samples=100, forget plot] {1-exp(-0.3*x)};\n\t\t\t\\addplot[black, domain=0.25:2.5, samples=100, forget plot] {x};\n\t\t\t\\addplot[black, dotted, domain=0:2.5, samples=100] {1-exp(-0.3*x)};\n\t\t\t\\addplot[black, dotted, domain=0:0.25, samples=100, forget plot] {1-exp(-0.3*x)};\n\t\t\t\\addplot[black, dotted, domain=0.25:2.5, samples=100, forget plot] {x};\n\t\t\t\\node[draw,circle,inner sep=1.5pt,fill,black] at (axis cs:0.25,0.22) {};\n\t\t\t\\node[draw,circle,inner sep=1.5pt,fill,black] at (axis cs:0,0) {};\n\t\t\\end{axis}\n\t\t\\draw[black, thick] (3,-0.5) node {$g(\\theta_a)$};\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\\node[anchor=south west,inner sep=0] at (0,0)\n\t{\\includegraphics[width=.49\\linewidth]{example-image}\n\t\t\\includegraphics[width=.49\\linewidth]{example-image}};\n\t\\draw[red,thick,rounded corners] (0.6,2) rectangle (2.5,3.5);\n\t\\node[align=center,text=red,rotate=-28] at (1.1,2.7) {SeedsGE\\\\SVHN Hand};\n\t\\draw[orange,thick,rounded corners] (1,0.8) rectangle (1.85,1.6);\n\t\\node[align=center,text=orange,rotate=-38] at (1.45,1.2) {SparseSGLV\\\\SVHN};\n\t\\draw[blue,thick,rounded corners] (1.9,3) rectangle (4.7,4);\n\t\\node[align=center,text=blue,rotate=-14] at (3.4,3.6) {Panda Arms};\n\t\\draw[black,thick,rounded corners] (2.7,5.2) rectangle (6.4,5.9);\n\t\\node[align=center,text=black] at (4.4,5.5) {Operator};\n\t\\draw[black,thick,rounded corners] (4.3,0.2) rectangle (6.6,2);\n\t\\node[align=center,text=black] at (5.6,1.4) {FT Sensors};\n\t\\node[align=center,text=white] at (5.2,5.8) {Anvatar};\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "index": 301,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{amsmath, amsthm, amsfonts, amssymb, mathrsfs}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix,arrows}\n\n\\newcommand{\\spin}[1]{\\mathfrak{#1}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=2.5]\n\n    \\draw[dotted] (-.8,0) -- (1.2,0) node [right] {$\\spin{Re}[\\zeta]$};\n    \\draw[dotted] (0,-.75) -- (0,1.2) node [right] {$i\\infty$};\n    \\draw[dotted] (0,1) -- (0,1.2) node [right] {$\\spin{Im}[\\zeta]$};\n    \\draw[dotted] (-.75,0) -- (-.75,1.2) node [left] {$i\\infty$};\n\n    \\draw (0,0) -- (0,1);\n    \\draw (0,0) -- (1,0);\n    \\draw (0,0) -- (0,-.75);\n    \\draw (0,1) -- (1,1);\n    \\draw (1,0) -- (1,-.75);\n    \\draw (0,-.75) -- (1,-.75);\n    \\draw (0.5,-0.375) node [left] {$z$};\n    \\draw (1.1,0) node [above] {$\\spin{Re}[\\zeta]$};\n    \\draw (0,1.1) node [right] {$i\\infty+\\spin{Im}[\\zeta]$};\n\n  \\end{tikzpicture}\n\n\\end{document}"
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        "index": 302,
        "tikz_code": "\\documentclass[tikz]{standalone}\n\\usetikzlibrary{calc}\n\n\\begin{document}\n\\begin{tikzpicture}\n\n  \\draw[rounded corners]\n    (0,0) -- ++(0,2) -- ++(5,0) coordinate(A)\n    -- ++(0,-2) -- ++(-3,0) \n    -- ++(0,2) -- ++(3,0) \n    -- ++(0,-2) -- ++(-5,0)\n    ;\n\n\\end{tikzpicture}\n\\end{document}"
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        "index": 303,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amsfonts,amssymb,latexsym,color}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{decorations.pathmorphing}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n\\tikzstyle{every node} = [circle,fill=black,inner sep=1pt]\n\\coordinate (O) at (0,0);\n\\draw (O) -- +(90:1.4);\n\\node[draw] (p1) at (0,1) {};\n\\node (p2) at (0,2) {};\n\\node[draw] (p3) at (0,3) {};\n\\node (p4) at (0,4) {};\n\\node[draw] (p5) at (0,5) {};\n\\draw (p1) -- +(90:1.4) node[fill=none] {$z_0$};\n\\draw (p2) -- +(90:1.4) node[fill=none] {$z_1$};\n\\draw (p3) -- +(90:1.4) node[fill=none] {$z_2$};\n\\draw (p4) -- +(90:1.4) node[fill=none] {$z_3$};\n\\draw (p5) -- +(90:1.4) node[fill=none] {$z_4$};\n\n\\draw (-6,0) -- +(180:5);\n\\draw (-3,0) -- +(0:5);\n\\node (q1) at (-4,-1) {};\n\\node (q2) at (-3,-1) {};\n\\node (q3) at (-2,-1) {};\n\\node (q4) at (-1,-1) {};\n\\node (q5) at (0,-1) {};\n\\draw (O) -- +(200:1) node[fill=none] {$F_{z_0}$};\n\\draw (q1) -- +(200:1) node[fill=none] {$p_1$};\n\\draw (q2) -- +(200:1) node[fill=none] {$p_2$};\n\\draw (q3) -- +(200:1) node[fill=none] {$p_3$};\n\\draw (q4) -- +(200:1) node[fill=none] {$p_4$};\n\\draw (q5) -- +(200:1) node[fill=none] {$p_5$};\n\\draw[->] (q1) -- +(200:1) node[draw=none,fill=none,inner sep=1pt] {};\n\\draw[->] (q2) -- +(200:1) node[draw=none,fill=none,inner sep=1pt] {};\n\\draw[->] (q3) -- +(200:1) node[draw=none,fill=none,inner sep=1pt] {};\n\\draw[->] (q4) -- +(200:1) node[draw=none,fill=none,inner sep=1pt] {};\n\\draw[->] (q5) -- +(200:1) node[draw=none,fill=none,inner sep=1pt] {};\n\\draw (p5) -- +(10:3) node[fill=none] {$K_{20}$};\n\\draw (p5) -- +(20:3) node[fill=none] {$Q_5$};\n\\draw (p1) -- +(240:1) node[fill=none] {$p_1$};\n\\draw (p2) -- +(240:1) node[fill=none] {$p_2$};\n\\draw (p3) -- +(240:1) node[fill=none] {$p_3$};\n\\draw (p4) -- +(240:1) node[fill=none] {$p_4$};\n\\draw (p5) -- +(240:1) node[fill=none] {$p_5$};\n\\draw[->] (p1) -- +(240:1) node[draw=none,fill=none,inner sep=1pt] {};\n\\draw[->] (p2) -- +(240:1) node[draw=none,fill=none,inner sep=1pt] {};\n\\draw[->] (p3) -- +(240:1) node[draw=none,fill=none,inner sep=1pt] {};\n\\draw[->] (p4) -- +(240:1) node[draw=none,fill=none,inner sep=1pt] {};\n\\draw[->] (p5) -- +(240:1) node[draw=none,fill=none,inner sep=1pt] {};\n\\draw (p5) -- +(330:1) node[fill=none] {$Q_3$};\n\\draw (p1) -- +(350:1) node[fill=none] {$Q_1$};\n\\draw (p1) -- +(380:1) node[fill=none] {$Q_2$};\n\\node (s1) at ($(p1)+(330:1)$) {};\n\\node (s2) at ($(p1)+(380:1)$) {};\n\\draw (p1) -- +(s1) node[fill=none] {};\n\\draw (p1) -- +(s2) node[fill=none] {};\n\\draw (s1) -- +(350:1) node[fill=none] {$Q_4$};\n\\draw (s1) -- +(380:1) node[fill=none] {$Q_5$};\n\\draw (s2) -- +(420:1) node[fill=none] {$Q_6$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 304,
        "tikz_code": "\\documentclass[border=10pt]{standalone}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.8}\n\\begin{document}\n\\begin{tikzpicture}\n\\begin{axis}[\n    view={45}{30},\n    zmax=2.5,\n    xlabel=$x$,\n    ylabel=$y$,\n    zlabel=$z$,\n    colormap={blueblack}{color(0cm)=(black); color(1cm)=(blue!50)},\n    colormap name=blueblack,\n    xmin=-1,xmax=1,\n    ymin=-1,ymax=1,\n    domain=0:1,\n    samples y=0,\n    samples=10,\n    x dir=reverse,\n    ]\n    \\addplot3[\n        surf,\n        point meta=1,\n        ]\n        {(x+y)^2};\n    \\addplot3[surf,point meta=2] {y^2};\n    \\addplot3[domain=-0.2:1,samples y=0,samples=50,samples\u540e\u9762\u6dfb\u52a0\u7a7a\u884c]\n    (\n    {0},\n    {x},\n    {sqrt(x^2+x^2+x^2)}\n    );\n    \\addplot3[domain=0:1,samples y=0,samples=50,samples\u540e\u9762\u6dfb\u52a0\u7a7a\u884c]\n    (\n    {sqrt(x^2+x^2+x^2)},\n    {x},\n    {x}\n    );\n\\end{axis}\n\\end{tikzpicture}\n\\end{document}"
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        "index": 305,
        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usetikzlibrary{snakes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5]\n\\draw[black, rounded corners=2pt, line width=1pt] (-1.4,-1) rectangle (-0.6,1);\n\\node[black] at (-0.8,0.6) {$L-$};\n\\node[black] at (-0.8,1.4) {$L+$};\n\n\\draw[black, rounded corners=2pt, line width=1pt] (0,-1) rectangle (1,1);\n\\node[black] at (0.2,0.6) {$K/0$};\n\n\\draw[black, rounded corners=2pt, line width=1pt] (1.2,-1) rectangle (2.0,1);\n\\node[black] at (1.4,0.6) {$T^*S^*$};\n\n\\draw[dashed, line width=1pt] (-1.4,-0.7) -- (-1.4,-0.3);\n\\draw[dashed, line width=1pt] (-0.6,-0.7) -- (-0.6,-0.3);\n\\draw[dashed, line width=1pt] (0.2,-0.7) -- (0.2,-0.3);\n\\draw[dashed, line width=1pt] (1.4,-0.7) -- (1.4,-0.3);\n\\draw[dashed, line width=1pt] (2.0,-0.7) -- (2.0,-0.3);\n\n\\draw[black, rounded corners=2pt, line width=1pt] (-0.6,-1) rectangle (-1.4,1);\n\\draw[black, rounded corners=2pt, line width=1pt] (1.4,-1) rectangle (0.6,1);\n\\draw[black, rounded corners=2pt, line width=1pt] (2.0,-1) rectangle (1.2,1);\n\\draw[black, line width=1pt] (-1.4,0.3) .. controls (-1,0) and (-0.2,0) .. (0,0.3);\n\\draw[black, line width=1pt] (1.2,0.3) .. controls (1.6,0) and (1.8,0) .. (2.0,0.3);\n\\draw[black, line width=1pt] (0,0.3) .. controls (0.2,0) and (1,0) .. (1.2,0.3);\n\\draw[black, line width=1pt] (0.6,-0.3) .. controls (0.4,-0.5) and (0.4,-0.5) .. (0.6,-0.7);\n\\draw[black, line width=1pt] (1.4,-0.3) .. controls (1.2,-0.5) and (1.2,-0.5) .. (1.4,-0.7);\n\\draw[black, line width=1pt] (0.2,-0.3) .. controls (0,-0.5) and (0,-0.5) .. (0.2,-0.7);\n\\draw[black, line width=1pt] (2.0,-0.3) .. controls (1.8,-0.5) and (1.8,-0.5) .. (2.0,-0.7);\n\\node[black] at (-0.9,-0.3) {$\\mathbf{K}$};\n\\node[black] at (-0.9,-0.7) {$\\mathbf{C}$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 306,
        "tikz_code": "\\documentclass[12pt,reqno]{amsart}\n\\usepackage{latexsym, amsmath, amsfonts, verbatim, amssymb, graphicx, bbm, mathtools}\n\\usepackage[table,xcdraw]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.markings}\n\n\\newcommand{\\cU}{{\\mathcal U}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.6]\n\n\\draw [fill=blue!40, color=blue!40, opacity=0.4] (0,0)--(3,3)--(8,3)--(5,0)--cycle;\n\\node[text=blue!40] at (5.5,2.5) {$\\cU$};\n\n\\draw[->,thick,color=blue!70] (3,1.5)--(5,3.5);\n\\node[text=blue!70] at (5.5,3.5) {$\\mathfrak{C}_W$};\n\n\\draw[<-,thick,color=green!70] (3,-1.5)--(5,1.5);\n\\node[text=green!70] at (5.5,1.5) {$\\mathfrak{C}_W'$};\n\n\\draw[<-,thick,color=red!70] (-4,1.5)--(4,3.5);\n\\node[text=red!70] at (4,3.5) {$\\mathfrak{C}_E$};\n\n\\draw[<-,thick,color=red!70] (-4,-1.5)--(4,1.5);\n\\node[text=red!70] at (4,1.5) {$-\\mathfrak{C}_W'$};\n\n\\draw[<-,thick,color=blue!70] (-8,-1.5)--(8,1.5);\n\\node[text=blue!70] at (8,1.5) {$\\mathfrak{B}_U$};\n\n\\draw[dotted,color=gray] (-9,-2)--(9,2);\n\\draw[dotted,color=gray] (-9,2)--(9,-2);\n\n\\draw[->,thick,color=gray] (-7,5)--(9,5);\n\\node[text=gray] at (9,5) {$\\mathfrak{v}$};\n\\draw[->,thick,color=gray] (8,2)--(8,-3);\n\\node[text=gray] at (8,-3) {$\\mathfrak{w}$};\n\n\\draw[dotted,color=gray] (-8,0)--(9,0);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 307,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{trees}\n\\usetikzlibrary[shapes]\n\\usetikzlibrary[arrows]\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{fadings}\n\\usetikzlibrary{backgrounds}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{positioning}\n\\usepackage[colorlinks, linkcolor=black, citecolor=black,   %blue,\n      \t\t% pagebackref,  %%%% Adds \"backlink\" text to items in the bibliography, i.e the pages they were used.\n            bookmarksnumbered=true]{hyperref}\n\\tikzset{stringnode/.style={rectangle, inner sep=5pt, draw = black!50, fill=black!10}}\n\\DeclareMathOperator{\\triplearrow}{{\\; \\tikz{ \\foreach \\y in {0, 0.1, 0.2} \\draw[-stealth] (0, \\y) -- +(0.5, 0);} \\; }}\n\n\\begin{document}\n\n\\begin{tikzpicture}[thick]\n\t\t\\begin{scope}[xshift = 9cm]\n\t\t\\node (0) at (0,0) {$0$};\n\t\t\\foreach \\x in {1,2,3,4,5}\n\t\t{\\node (b\\x) at (\\x, 2) {$(1 + \\frac{1}{\\x})$};\n\t\t\t\\draw (0) -- (b\\x); }\n\t\t\\foreach \\x in {4,5}\n\t\t{\\node (d\\x) at (\\x, 4) {$(1 + \\frac{1}{\\x})$};\n\t\t\t\\foreach \\y in {1,2}\n\t\t\t{\\draw (b\\y.45) -- (d\\x.135); } }\n\t\t\\foreach \\x in {4}\n\t\t{\\node (d\\x) at (\\x, 4) {$(1 + \\frac{1}{\\x})$};\n\t\t\t\\draw (b3.45) -- (d\\x.135); }\n\t\t\\node (c1) at (6, 6) {$(1 + \\frac{1}{2})$};\n\t\t\\foreach \\x in {1,2}\n\t\t{\\draw (d4.135) -- (c1.45);\n\t\t\t\\foreach \\y in {4,5}\n\t\t\t{\\draw (b\\y.45) -- (d\\x.135); } }\n\t\t\\draw (b4.45) -- (c1.135);\n\t\t\\foreach \\x in {3,4,5}\n\t\t{\\node (c\\x) at (\\x, 8) {$(1 + \\frac{1}{\\x})$};\n\t\t\t\\draw (c1) -- (c\\x); }\n\t\t\\foreach \\x in {1,2,3,4,5}\n\t\t{\\draw (c4.135) -- (c\\x.45);\n\t\t\t\\foreach \\y in {6,7,8}\n\t\t\t{\\draw (b\\y.45) -- (c\\x.135); } }\n\t\t\\foreach \\x in {4,5}\n\t\t{\\draw (c4.135) -- (c\\x.45); }\n\t\t\\node (a) at (8,10) {$(1 + \\frac{1}{2})$};\n\t\t\\draw (c5) -- (a);\n\t\t\\foreach \\x in {1,2,3,4,5}\n\t\t{\\draw (a) -- (c\\x); }\n\t\t\\foreach \\x in {1,2,3,4,5}\n\t\t{\\node (d\\x) at (\\x, 12) {$(1 + \\frac{1}{\\x})$};\n\t\t\t\\foreach \\y in {6,7,8}\n\t\t\t{\\draw (b\\y.45) -- (d\\x.135); } }\n\t\t\\draw (b5.45) -- (d5.135);\n\t\t\\foreach \\x in {1,2,3,4,5}\n\t\t{\\foreach \\y in {9,10,11}\n\t\t\t{\\draw (b\\x.45) -- (d\\y.135); } }\n\t\t\\foreach \\x in {1,2,3,4,5}\n\t\t{\\foreach \\y in {6,7,8}\n\t\t\t{\\draw (b\\x.45) -- (d\\y.135); } }\n\t\t\\node at (9,14) {$\\cdots$};\n\t\t\\foreach \\x in {1,2,3,4,5}\n\t\t{\\node (e\\x) at (\\x, 16) {$(1 + \\frac{1}{\\x})$};\n\t\t\t\\draw (a) -- (e\\x); }\n\t\t\\foreach \\x in {1,2,3,4,5}\n\t\t{\\draw (e4.135) -- (e\\x.45);\n\t\t\t\\foreach \\y in {15,16}\n\t\t\t{\\draw (b\\y.45) -- (e\\x.135); } }\n\t\t\\foreach \\x in {4,5}\n\t\t{\\draw (e4.135) -- (e\\x.45); }\n\t\t\\end{scope}\n\t\t\\end{tikzpicture}\n\n\\end{document}"
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        "index": 308,
        "tikz_code": "\\documentclass[11pt,fleqn]{amsart}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsfonts,amssymb,amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\n\\newcommand{\\lie}[1]{{\\mathfrak{#1}}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\\draw (0,0) rectangle (2,2);\n\t\\draw (0,2) rectangle (2,4);\n\t\\draw (0,4) rectangle (2,6);\n\t\\draw (2,0) rectangle (4,4);\n\t\\draw (4,0) rectangle (6,4);\n\t\\draw (6,0) rectangle (8,4);\n\t\\draw (6,4) rectangle (8,6);\n\t\\draw (8,0) rectangle (10,4);\n\t\\draw (8,4) rectangle (10,6);\n\t\\draw (8,6) rectangle (10,8);\n\t\n\t\\node at (1,2.5) {$\\vee$};\n\t\\node at (3,2.5) {$d$};\n\t\\node at (5,2.5) {$w\\vee d$};\n\t\\node at (7,2.5) {$w\\wedge d$};\n\t\\node at (9,2.5) {$w\\vee d$};\n\t\\node at (9,4.5) {$w\\wedge d$};\n\t\\node at (1,4.5) {$a_h$};\n\t\\node at (1,5.5) {$a_h$};\n\t\\node at (3,4.5) {$a_h$};\n\t\\node at (5,4.5) {$a_h$};\n\t\\node at (7,4.5) {$a_h$};\n\t\\node at (9,4.5) {$a_h$};\n\t\\node at (9,6.5) {$a_h$};\n\t\n\t\\node at (2.5,3) {$\\vee$};\n\t\\node at (4.5,3) {$d$};\n\t\\node at (6.5,3) {$w\\vee d$};\n\t\\node at (4.5,5) {$a_h$};\n\t\\node at (6.5,5) {$a_h$};\n\t\\node at (6.5,7) {$a_h$};\n\t\n\t\\node at (8.5,3) {$\\vee$};\n\t\\node at (10.5,3) {$d$};\n\t\\node at (10.5,5) {$a_h$};\n\t\\node at (8.5,5) {$a_h$};\n\t\\node at (8.5,7) {$a_h$};\n\t\\node at (8.5,7.5) {$\\vdots$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[aps,pra,superscriptaddress,nofootinbib]{revtex4}\n\\usepackage[intlimits]{amsmath}\n\\usepackage{color}\n\\usepackage[colorlinks,bookmarks=false,citecolor=blue,linkcolor=red,urlcolor=blue]{hyperref}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usepackage[colorlinks,bookmarks=false,citecolor=blue,linkcolor=red,urlcolor=blue]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\tikzstyle{ball} = [circle,shading=ball,\nball color=red!80!black,minimum size=1cm]\n\\draw[black, very thick, ->] (-1,-1) -- (1,-1);\n\\draw[black, very thick, ->] (-1,-1) -- (-1,1);\n\\draw[black, very thick, ->] (-1,-1) -- (-1,-1.5);\n\\draw[black, very thick, ->] (1,-1) -- (1,-1.5);\n\\draw[black, very thick, ->] (-1,1) -- (-1.5,1);\n\\draw[black, very thick, ->] (-1,1) -- (-1,1.5);\n\\draw[black, very thick, ->] (1,1) -- (1.5,1);\n\\draw[black, very thick, ->] (1,1) -- (1,1.5);\n\\node[ball] at (-1,-1) {};\n\\node[ball] at (1,-1) {};\n\\node[ball] at (0,1) {};\n\\node[ball] at (-1,1) {};\n\\node[ball] at (1,1) {};\n\\node at (-1,-2) {$I\\rightarrow 0$};\n\\node at (1,-2) {$I\\rightarrow 0$};\n\\node at (0,2) {$I \\rightarrow I_{\\rm c}I_{0}I_{\\rm b}$};\n\\begin{scope}[xshift=5cm]\n\\draw[black, very thick, ->] (-1,-1) -- (1,-1);\n\\draw[black, very thick, ->] (-1,-1) -- (-1,1);\n\\draw[black, very thick, ->] (-1,-1) -- (-1,-1.5);\n\\draw[black, very thick, ->] (1,-1) -- (1,-1.5);\n\\draw[black, very thick, ->] (-1,1) -- (-1.5,1);\n\\draw[black, very thick, ->] (-1,1) -- (-1,1.5);\n\\draw[black, very thick, ->] (1,1) -- (1.5,1);\n\\draw[black, very thick, ->] (1,1) -- (1,1.5);\n\\node[ball] at (-1,-1) {};\n\\node[ball] at (1,-1) {};\n\\node[ball] at (0,1) {};\n\\node[ball] at (-1,1) {};\n\\node[ball] at (1,1) {};\n\\node at (-1,-2) {$I\\rightarrow 0$};\n\\node at (1,-2) {$I\\rightarrow 0$};\n\\node at (0,2) {$I \\rightarrow I_{\\rm b}I_{\\rm b}I_{\\rm c}$};\n\\end{scope}\n\\begin{scope}[xshift=10cm]\n\\draw[black, very thick, ->] (-1,-1) -- (1,-1);\n\\draw[black, very thick, ->] (-1,-1) -- (-1,1);\n\\draw[black, very thick, ->] (-1,-1) -- (-1,-1.5);\n\\draw[black, very thick, ->] (1,-1) -- (1,-1.5);\n\\draw[black, very thick, ->] (-1,1) -- (-1.5,1);\n\\draw[black, very thick, ->] (-1,1) -- (-1,1.5);\n\\draw[black, very thick, ->] (1,1) -- (1.5,1);\n\\draw[black, very thick, ->] (1,1) -- (1,1.5);\n\\node[ball] at (-1,-1) {};\n\\node[ball] at (1,-1) {};\n\\node[ball] at (0,1) {};\n\\node[ball] at (-1,1) {};\n\\node[ball] at (1,1) {};\n\\node at (-1,-2) {$I\\rightarrow 0$};\n\\node at (1,-2) {$I\\rightarrow 0$};\n\\node at (0,2) {$I \\rightarrow I_{\\rm c}I_{0}I_{\\rm a}$};\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[line width=1pt] (0,0) -- (4,0);\n\\draw[line width=1pt, dashed] (0,0) -- (-1,0);\n\\draw[line width=1pt, dashed] (0,0) -- (0,-1);\n\\draw[line width=1pt, dashed] (4,0) -- (4,-1);\n\\draw[line width=1pt, dashed] (4,0) -- (5,-1);\n\\draw[line width=1pt] (0,0) -- (0,1);\n\\draw[line width=1pt] (0,0) -- (1,0);\n\\draw[line width=1pt] (0,1) -- (1,1);\n\\draw[line width=1pt] (1,0) -- (1,1);\n\\draw[line width=2pt, ->, color=red] (0,0) -- (0,1);\n\\draw[line width=2pt, ->, color=blue] (1,0) -- (1,1);\n\\draw[line width=2pt, ->, color=blue] (1,1) -- (4,1);\n\\draw[line width=1pt, dashed] (5,0) -- (8,0);\n\\draw[line width=1pt, dashed] (5,0) -- (5,-1);\n\\draw[line width=1pt, dashed] (8,0) -- (8,-1);\n\\draw[line width=1pt, dashed] (8,0) -- (9,-1);\n\\draw[line width=1pt] (5,0) -- (5,1);\n\\draw[line width=1pt] (5,0) -- (6,0);\n\\draw[line width=1pt] (5,1) -- (6,1);\n\\draw[line width=1pt] (6,0) -- (6,1);\n\\draw[line width=2pt, ->, color=blue] (5,0) -- (5,1);\n\\draw[line width=2pt, ->, color=red] (5,1) -- (8,1);\n\\draw[line width=2pt, ->, color=red] (8,1) -- (8,0);\n\n\n\\fill (0,0) circle (0.07);\n\\fill (1,0) circle (0.07);\n\\fill (5,0) circle (0.07);\n\\fill (5,1) circle (0.07);\n\\fill (6,0) circle (0.07);\n\\fill (8,0) circle (0.07);\n\\fill (8,1) circle (0.07);\n\n\\draw (0,-0.5) node {\\scriptsize$(r,s)$};\n\\draw (1,-0.5) node {\\scriptsize$(r,s)$};\n\\draw (5,-0.5) node {\\scriptsize$(r,s)$};\n\\draw (5,1.5) node {\\scriptsize$(r+1,s)$};\n\\draw (6,-0.5) node {\\scriptsize$(r,s)$};\n\\draw (8,-0.5) node {\\scriptsize$(r+1,s)$};\n\\draw (8,1.5) node {\\scriptsize$(r+1,s+1)$};\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 313,
        "tikz_code": "\\documentclass[a4paper,12pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath, amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usepackage{tikzrput}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n  \\draw (-6,0) -- (6,0) node[pos=0.5,below] {\\small{$d_c = d_a$ \\quad $w_u \\neq 0$}} node[pos=0.5,above] {$\\mathbb{R}^{d_a}$};\n\n  \\node at (0,0) [circle,fill,inner sep=1.5pt]{};\n  \\node at (4.6,0) [circle,fill,inner sep=1.5pt]{};\n\n  \\draw [dashed] (4.6,0) -- (6,0) node[pos=0.5,above] {\\small{$z=0$}};\n  \\draw [dashed] (-4.6,0) -- (-6,0) node[pos=0.5,above] {\\small{$z=0$}};\n\n  \\draw [<->] (-4.4,0.3) to[out=90,in=180] (-4.6,1) node[pos=0.5,above right] {\\small{$\\frac{d_a}{2}$}};\n\n  \\draw [<->] (4.4,0.3) to[out=90,in=0] (4.6,1) node[pos=0.5,above right] {\\small{$\\frac{d_a}{2}$}};\n\n  \\draw (-0.1,-0.1) -- (0.1,0.1) node[pos=0.5,above right] {\\small{$\\mathcal{A}$}};\n  \\draw (0.1,-0.1) -- (-0.1,0.1) node[pos=0.5,below left] {\\small{$\\mathcal{A}$}};\n\n  \\draw [dashed] (0,0) -- (0,-1.2) node[pos=0.5,below right] {\\small{$z_c = d_a$ \\quad $w_u=0$}};\n\n  \\node at (-4.6,0) [circle,fill,inner sep=1.5pt]{};\n\n  \\node [above] at (-4.7,0) {$z=0$};\n\n  \\draw [<->] (-6.6,0.3) to[out=90,in=180] (-6,1) node[pos=0.5,above right] {\\small{$\\frac{d_a}{2}$}};\n\n  \\draw [<->] (-3.4,0.3) to[out=90,in=180] (-2.6,1) node[pos=0.5,above right] {\\small{$\\frac{d_a}{2}$}};\n\n  \\node [above] at (0,0.8) {range of validity};\n\n  \\node [above] at (-5.5,1) {horizon};\n\n  \\node [above] at (5.5,1) {$z$-axis};\n\n\n  \\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 314,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath,amssymb}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=newest}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{backgrounds}\n\\usetikzlibrary{decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[very thick] (0,0) ellipse (6cm and 1.8cm);\n\\draw (0,0) ellipse (4.5cm and 1.5cm);\n\\draw[very thick] (0,0) ellipse (3cm and 1cm);\n\\node[below] at (0,-1.2) {$N_{\\ell}(uv)$};\n\\node[below] at (1.2,-1.2) {$N_{\\ell}(uv)$};\n\\node[below] at (-1.2,-1.2) {$N_{\\ell}(uv)$};\n\\node[below] at (2.5,-1.2) {$N_{\\ell}(uv)$};\n\\node[below] at (-2.5,-1.2) {$N_{\\ell}(uv)$};\n\\node[above] at (1.5,0.3) {$N_{\\ell}(uv)$};\n\\node[above] at (-1.5,0.3) {$N_{\\ell}(uv)$};\n\\node[above] at (0,0.3) {$N_{\\ell}(uv)$};\n\\draw[very thick,rotate around={45:(0,0)}] (0,0) ellipse (3cm and 1cm);\n\\draw[very thick,rotate around={-45:(0,0)}] (0,0) ellipse (3cm and 1cm);\n\\node[below] at (0,0) {$\\mu$};\n\\draw[fill=black] (0,0) circle (0.1cm);\n\\draw[very thick, ->] (0,0) -- (1.5,1.5);\n\\draw[very thick, ->] (0,0) -- (2,1.2);\n\\draw[very thick, ->] (0,0) -- (1.5,0.8);\n\\draw[very thick, ->] (0,0) -- (-1.5,1.5);\n\\draw[very thick, ->] (0,0) -- (-2,1.2);\n\\draw[very thick, ->] (0,0) -- (-1.5,0.8);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 315,
        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{shapes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[every node/.style={draw,circle,inner sep=1pt,fill}]\n  \\node (11) at (0,1) {};\n  \\node (12) at (0,2) {};\n  \\node (13) at (0,3) {};\n  \\node (14) at (0,4) {};\n  \\node (15) at (0,5) {};\n  \\node (21) at (1,1) {};\n  \\node (22) at (1,2) {};\n  \\node (23) at (1,3) {};\n  \\node (24) at (1,4) {};\n  \\node (25) at (1,5) {};\n  \\node (31) at (2,1) {};\n  \\node (32) at (2,2) {};\n  \\node (33) at (2,3) {};\n  \\node (34) at (2,4) {};\n  \\node (35) at (2,5) {};\n  \\node (41) at (3,1) {};\n  \\node (42) at (3,2) {};\n  \\node (43) at (3,3) {};\n  \\node (44) at (3,4) {};\n  \\node (45) at (3,5) {};\n  \\node (51) at (4,1) {};\n  \\node (52) at (4,2) {};\n  \\node (53) at (4,3) {};\n  \\node (54) at (4,4) {};\n  \\node (55) at (4,5) {};\n  \\draw (11) -- (22);\n  \\draw (11) -- (23);\n  \\draw (11) -- (24);\n  \\draw (11) -- (25);\n  \\draw (12) -- (21);\n  \\draw (12) -- (24);\n  \\draw (12) -- (25);\n  \\draw (13) -- (22);\n  \\draw (13) -- (23);\n  \\draw (13) -- (24);\n  \\draw (14) -- (22);\n  \\draw (14) -- (25);\n  \\draw (15) -- (23);\n  \\draw (15) -- (25);\n  \\draw (21) -- (32);\n  \\draw (21) -- (33);\n  \\draw (21) -- (34);\n  \\draw (22) -- (31);\n  \\draw (22) -- (33);\n  \\draw (22) -- (34);\n  \\draw (23) -- (31);\n  \\draw (23) -- (32);\n  \\draw (23) -- (34);\n  \\draw (24) -- (31);\n  \\draw (24) -- (32);\n  \\draw (24) -- (33);\n  \\draw (25) -- (31);\n  \\draw (25) -- (32);\n  \\draw (31) -- (42);\n  \\draw (31) -- (43);\n  \\draw (31) -- (44);\n  \\draw (32) -- (41);\n  \\draw (32) -- (43);\n  \\draw (32) -- (44);\n  \\draw (33) -- (41);\n  \\draw (33) -- (42);\n  \\draw (33) -- (44);\n  \\draw (34) -- (41);\n  \\draw (34) -- (42);\n  \\draw (34) -- (43);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 316,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{calc}\n\n\\newcommand{\\la}{\\lambda}\n\n\\newcommand{\\s}{\\sigma}\n\n\\newcommand{\\Z}{\\mathbb{Z}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\node at (0,10.5) {$H_0$};\n    \\node at (0,9.5) {$H_\\delta$};\n    \\node at (0,8.5) {$H_\\nu$};\n    \\node at (0,7.5) {$\\vdots$};\n    \\node at (0,6.5) {$j=m-1$};\n    \\node at (0,5.5) {$\\vdots$};\n    \\node at (0,4.5) {$i=m$};\n\n    \\draw[dashed] (-1,8.5) -- (-1,10.5);\n\n    \\node at (3.75,7.5) {$E_\\nu=(-)\\s\\langle\\la_0\\rangle$};\n    \\node at (3.75,6.5) {$E_{m-1}=(-)\\s\\langle\\la_{m-1}\\rangle$};\n    \\node at (3.75,5.5) {$\\vdots$};\n    \\node at (3.75,4.5) {$E_1=\\langle\\la_1\\rangle$};\n    \\node at (3.75,3.5) {$E_0=\\langle\\la_0\\rangle$};\n\n    \\node at (7.5,6.5) {$E_{m-\\nu}=(-)\\s\\langle\\la_{\\nu}\\rangle$};\n    \\node at (7.5,5.5) {$E_{j}=(-)\\s\\langle\\la_j\\rangle$};\n    \\node at (7.5,4.5) {$E_{i}=(-)\\s\\langle\\la_i\\rangle$};\n\n    \\node at (11.25,5.5) {$\\vdots$};\n    \\node at (11.25,4.5) {$\\vdots$};\n\n    \\draw[dotted] (2,8.5) -- (2,10.5);\n    \\draw[dotted] (6.75,8.5) -- (6.75,10.5);\n    \\draw[dotted] (11.5,8.5) -- (11.5,10.5);\n\n    \\node at (13,9.5) {$\\Z\\times\\Z^m$};\n    \\node at (13,8.5) {$\\Z^m$};\n    \\node at (13,7.5) {$\\vdots$};\n    \\node at (13,6.5) {$\\Z^i$};\n    \\node at (13,5.5) {$\\Z$};\n    \\node at (13,4.5) {$1$};\n    \\node at (13,3.5) {$0$};\n    \\node at (13,2.5) {$\\vdots$};\n    \\node at (13,1.5) {$\\Z$};\n    \\node at (13,0.5) {$\\Z^m$};\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage[colorlinks]{hyperref}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usetikzlibrary{backgrounds,fit, matrix}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{calc,through,chains}\n\\usetikzlibrary{arrows,shapes,snakes,automata, petri}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.75]\n\n\\begin{scope}\n\\draw (0,0) -- (0,3) -- (3,3) -- (3,0) -- cycle;\n\\draw (0,1) -- (3,1);\n\\draw (0,2) -- (3,2);\n\\draw (1,0) -- (1,3);\n\\draw (2,0) -- (2,3);\n\\draw[ultra thick] (.5,1.5) -- (.5,2.5) -- (1.5,2.5) -- (1.5,1.5) -- cycle;\n\\node at (.5,.5) {$\\bullet$};\n\\node at (1.5,2.5) {$\\bullet$};\n\\node at (1.5,.5) {$\\bullet$};\n\\node at (1.5,1.5) {$\\bullet$};\n\\node at (1,-.5) {$\\mathcal{C}$};\n\\end{scope}\n\n\\begin{scope}[xshift=5cm]\n\\draw (0,0) -- (0,3) -- (3,3) -- (3,0) -- cycle;\n\\draw (0,1) -- (3,1);\n\\draw (0,2) -- (3,2);\n\\draw (1,0) -- (1,3);\n\\draw (2,0) -- (2,3);\n\\draw[ultra thick] (.5,1.5) -- (.5,2.5) -- (1.5,2.5) -- (1.5,1.5) -- cycle;\n\\draw (0,1) -- (3,2);\n\\draw (0,2) -- (3,1);\n\\draw (1,0) -- (1,3);\n\\draw (2,0) -- (2,3);\n\\node at (1.5,2.5) {$\\bullet$};\n\\node at (1.5,.5) {$\\bullet$};\n\\node at (1,-.5) {$\\mathcal{C}$};\n\\end{scope}\n\n\\begin{scope}[xshift=10cm,yshift=-1.5cm]\n\\draw (0,0) -- (0,1) -- (0,2) -- (0,3) -- (1,3) -- (2,3) -- (3,3) -- (3,2) -- (3,1) -- (3,0) -- (2,0) -- (1,0) -- (0,0) -- cycle;\n\\draw (0,1) -- (1,1) -- (1,0);\n\\draw (0,2) -- (1,2) -- (1,0);\n\\draw (0,3) -- (1,3) -- (1,0);\n\\draw (1,3) -- (2,3) -- (2,0);\n\\draw (2,3) -- (3,3) -- (3,0);\n\\draw (1,0) -- (2,1) -- (2,0);\n\\draw (1,1) -- (2,2) -- (2,0);\n\\draw (1,2) -- (2,3) -- (2,0);\n\\draw[ultra thick] (.5,2.5) -- (1.5,2.5) -- (1.5,.5) -- (.5,.5) -- cycle;\n\\draw[ultra thick] (1.5,2.5) -- (2.5,2.5) -- (2.5,1.5) -- (1.5,1.5) -- cycle;\n\\draw[ultra thick] (1.5,1.5) -- (2.5,1.5) -- (2.5,0.5) -- (1.5,0.5) -- cycle;\n\\node at (1.5,2.5) {$\\bullet$};\n\\node at (1.5,.5) {$\\bullet$};\n\\node at (2.5,2.5) {$\\bullet$};\n\\node at (2.5,1.5) {$\\bullet$};\n\\node at (2.5,0.5) {$\\bullet$};\n\\node at (1,-.5) {$\\mathcal{C}$};\n\\end{scope}\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{color}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.3,style=thick,x=1cm,y=1cm]\n\\def\\vr{3pt}\n\n% define vertices\n\\coordinate(x1) at (-1,0);\n\\coordinate(x2) at (-1.5,0);\n\\coordinate(x3) at (-2.5,0);\n\\coordinate(x4) at (-4,0);\n\\coordinate(x5) at (-5,0);\n\\coordinate(x6) at (-6,0);\n\\coordinate(x7) at (-6.5,0);\n\\coordinate(x8) at (-7.5,0);\n\\coordinate(x9) at (-9,0);\n\\coordinate(x10) at (-10,0);\n\\coordinate(x11) at (-11,0);\n\\coordinate(x12) at (-12,0);\n%\n\\coordinate(y1) at (-5.5,1.5);\n\\coordinate(y2) at (-7,1.5);\n\\coordinate(y3) at (-8,1.5);\n\\coordinate(y4) at (-10.5,1.5);\n\\coordinate(y5) at (-12,1.5);\n\\coordinate(y6) at (-13,1.5);\n%\n\\coordinate(w1) at (-5.5,-1.5);\n\\coordinate(w2) at (-7,-1.5);\n\\coordinate(w3) at (-8,-1.5);\n\\coordinate(w4) at (-10.5,-1.5);\n\\coordinate(w5) at (-12,-1.5);\n\\coordinate(w6) at (-13,-1.5);\n%\n\\coordinate(z1) at (-1,2);\n\\coordinate(z2) at (-1.5,2);\n\\coordinate(z3) at (-2.5,2);\n\\coordinate(z4) at (-4,2);\n\\coordinate(z5) at (-5,2);\n\\coordinate(z6) at (-6,2);\n\\coordinate(z7) at (-6.5,2);\n\\coordinate(z8) at (-7.5,2);\n\\coordinate(z9) at (-9,2);\n\\coordinate(z10) at (-10,2);\n\\coordinate(z11) at (-11,2);\n\\coordinate(z12) at (-12,2);\n% edges\n\\draw (x1) -- (x2) -- (x3) -- (x4) -- (x5) -- (x6) -- (x7) -- (x8) -- (x9) -- (x10) -- (x11) -- (x12);\n\\draw (x1) -- (y1) -- (x2) -- (y2) -- (x3) -- (y3) -- (x4);\n\\draw (x5) -- (w1) -- (x6) -- (w2) -- (x7);\n\\draw (x9) -- (w4) -- (x10) -- (w5) -- (x11);\n\\draw (x12) -- (z1) -- (x1) -- (z2) -- (x2) -- (z3) -- (x3);\n\\draw (x4) -- (z4) -- (x5) -- (z5) -- (x6);\n\\draw (x7) -- (z6) -- (x8) -- (z7) -- (x9);\n\\draw (x10) -- (z8) -- (x11);\n\\draw (x12) -- (z9) -- (x1) -- (z10) -- (x2);\n\\draw (z11) -- (x3) -- (z12) -- (x4);\n% vertices\n\\draw(x1) [fill=white] circle(\\vr);\n\\draw(x2) [fill=white] circle(\\vr);\n\\draw(x3) [fill=white] circle(\\vr);\n\\draw(x4) [fill=white] circle(\\vr);\n\\draw(x5) [fill=white] circle(\\vr);\n\\draw(x6) [fill=white] circle(\\vr);\n\\draw(x7) [fill=white] circle(\\vr);\n\\draw(x8) [fill=white] circle(\\vr);\n\\draw(x9) [fill=white] circle(\\vr);\n\\draw(x10) [fill=white] circle(\\vr);\n\\draw(x11) [fill=white] circle(\\vr);\n\\draw(x12) [fill=white] circle(\\vr);\n\\draw(y1) [fill=white] circle(\\vr);\n\\draw(y2) [fill=white] circle(\\vr);\n\\draw(y3) [fill=white] circle(\\vr);\n\\draw(y4) [fill=white] circle(\\vr);\n\\draw(y5) [fill=white] circle(\\vr);\n\\draw(y6) [fill=white] circle(\\vr);\n\\draw(w1) [fill=white] circle(\\vr);\n\\draw(w2) [fill=white] circle(\\vr);\n\\draw(w3) [fill=white] circle(\\vr);\n\\draw(w4) [fill=white] circle(\\vr);\n\\draw(w5) [fill=white] circle(\\vr);\n\\draw(w6) [fill=white] circle(\\vr);\n\\draw(z1) [fill=white] circle(\\vr);\n\\draw(z2) [fill=white] circle(\\vr);\n\\draw(z3) [fill=white] circle(\\vr);\n\\draw(z4) [fill=white] circle(\\vr);\n\\draw(z5) [fill=white] circle(\\vr);\n\\draw(z6) [fill=white] circle(\\vr);\n\\draw(z7) [fill=white] circle(\\vr);\n\\draw(z8) [fill=white] circle(\\vr);\n\\draw(z9) [fill=white] circle(\\vr);\n\\draw(z10) [fill=white] circle(\\vr);\n\\draw(z11) [fill=white] circle(\\vr);\n\\draw(z12) [fill=white] circle(\\vr);\n% labels\n\\draw(y4) node [below] {$G$};\n\\draw(w4) node [below] {$\\sigma$};\n\\draw(z4) node [below] {$\\sigma_1$};\n\\draw(z9) node [below] {$\\sigma_2$};\n\\draw(z11) node [below] {$\\sigma_3$};\n\\draw(z12"
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    {
        "index": 320,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usetikzlibrary{shadows}\n\\usetikzlibrary{calc}\n\\pgfplotsset{compat=1.17}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{axis}[\n    xlabel={},\n    ylabel={Bits Shared},\n    xmin=0.5, xmax=25.5,\n    ymin=0, ymax=1200,\n    xtick={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25},\n    ytick={0,500,1000,1500,2000,2500},\n    legend pos=north west,\n    ymajorgrids=true,\n    grid style=dashed,\n    cycle list name=color,\n    width=6cm,height=4cm,\n    ylabel style={yshift=-0.2cm}\n]\n\n\\addplot[\n    color=blue,\n    mark=*,\n    ]\n    coordinates {\n    (1,311)(2,215)(3,493)(4,589)(5,577)(6,570)(7,533)(8,632)(9,397)(10,297)(11,551)(12,462)(13,582)(14,465)(15,412)(16,449)(17,391)(18,297)(19,192)(20,211)(21,390)(22,168)(23,169)(24,148)(25,251)\n    };\n\n\\addplot[\n    color=orange,\n    mark=*,\n    ]\n    coordinates {\n    (1,131)(2,68)(3,94)(4,96)(5,84)(6,67)(7,93)(8,65)(9,88)(10,103)(11,110)(12,116)(13,114)(14,120)(15,108)(16,118)(17,134)(18,114)(19,111)(20,108)(21,111)(22,123)(23,125)(24,130)(25,129)\n    };\n\n\\addplot[\n    color=teal,\n    mark=*,\n    ]\n    coordinates {\n    (1,71)(2,71)(3,72)(4,84)(5,82)(6,81)(7,81)(8,83)(9,87)(10,104)(11,113)(12,111)(13,110)(14,107)(15,114)(16,129)(17,123)(18,121)(19,116)(20,112)(21,118)(22,117)(23,114)(24,124)(25,110)\n    };\n\n\\addplot[\n    color=purple,\n    mark=*,\n    ]\n    coordinates {\n    (1,103)(2,93)(3,71)(4,91)(5,101)(6,102)(7,98)(8,95)(9,97)(10,96)(11,94)(12,94)(13,104)(14,94)(15,92)(16,92)(17,92)(18,92)(19,91)(20,91)(21,91)(22,90)(23,89)(24,89)(25,89)\n    };\n\n\\addplot[\n    color=gray,\n    mark=*,\n    ]\n    coordinates {\n    (1,113)(2,102)(3,93)(4,82)(5,71)(6,68)(7,71)(8,69)(9,63)(10,65)(11,64)(12,63)(13,65)(14,65)(15,63)(16,65)(17,65)(18,63)(19,63)(20,62)(21,62)(22,62)(23,61)(24,60)(25,59)\n    };\n\n\\addlegendentry{dNN-TFT}\n\\addlegendentry{DeepAR}\n\\addlegendentry{QRN}\n\\addlegendentry{NQF}\n\\addlegendentry{10\\%}\n\\addlegendentry{20\\%}\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 321,
        "tikz_code": "\\documentclass[aps,prx,twocolumn,showpacs,superscriptaddress,floatfix,nofootinbib]{revtex4-2}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{color}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \n    \\node at (0,0) {\\includegraphics[width=1.5cm]{example-image}};\n    \\node at (2.5,0) {\\includegraphics[width=1.5cm]{example-image}};\n    \\node at (5,0) {\\includegraphics[width=1.5cm]{example-image}};\n    \\node at (7.5,0) {\\includegraphics[width=1.5cm]{example-image}};\n    \\node at (0,-1.5) {\\includegraphics[width=1.5cm]{example-image}};\n    \\node at (2.5,-1.5) {\\includegraphics[width=1.5cm]{example-image}};\n    \\node at (5,-1.5) {\\includegraphics[width=1.5cm]{example-image}};\n    \\node at (7.5,-1.5) {\\includegraphics[width=1.5cm]{example-image}};\n    \n    \\draw[black,thick,<->] (1,-3)--(2.5,-3);\n    \\draw[black,thick,<->] (3,-3)--(4.5,-3);\n    \\draw[black,thick,<->] (5,-3)--(6.5,-3);\n    \n    \\node at (0,-4) {$x_1$};\n    \\node at (2.5,-4) {$x_2$};\n    \\node at (5,-4) {$x_3$};\n    \\node at (7.5,-4) {$x_4$};\n    \\node at (1.5,-5.3) {$\\frac{1}{3}$};\n    \\node at (4.5,-5.3) {$\\frac{1}{2}$};\n    \\node at (6.5,-5.3) {$\\frac{2}{3}$};\n    \n    \\draw[black,thick,<->] (1,-3)--(1,-0.5);\n    \\draw[black,thick,<->] (2.5,-3)--(2.5,-0.5);\n    \\draw[black,thick,<->] (3,-3)--(3,-0.5);\n    \\draw[black,thick,<->] (5,-3)--(5,-0.5);\n    \\draw[black,thick,<->] (6.5,-3)--(6.5,-0.5);\n    \n    \\node at (0.75,-1) {$\\bar{y}$};\n    \\node at (2.25,-1) {$y$};\n    \\node at (3.75,-1) {$\\bar{y}$};\n    \\node at (5.25,-1) {$y$};\n    \\node at (6.75,-1) {$\\bar{y}$};\n    \n    \\draw[black,thick,->] (2.5,-2.25)--(2.5,-1.75);\n    \\draw[black,thick,->] (3,-2.25)--(3,-1.75);\n    \\draw[black,thick,->] (4.5,-2.25)--(4.5,-1.75);\n    \\draw[black,thick,->] (5,-2.25)--(5,-1.75);\n    \\draw[black,thick,->] (6.5,-2.25)--(6.5,-1.75);\n    \n    \\node at (0,1) {\\includegraphics[width=1.5cm]{example-image}};\n    \\node at (2.5,1) {\\includegraphics[width=1.5cm]{example-image}};\n    \\node at (5,1) {\\includegraphics[width=1.5cm]{example-image}};\n    \\node at (7.5,1) {\\includegraphics[width=1.5cm]{example-image}};\n    \\node at (0,2.5) {\\includegraphics[width=1.5cm]{example-image}};\n    \\node at (2.5,2.5) {\\includegraphics[width=1.5cm]{example-image}};\n    \\node at (5,2.5) {\\includegraphics[width=1.5cm]{example-image}};\n    \\node at (7.5,2.5) {\\includegraphics[width=1.5cm]{example-image}};\n    \n    \\node at (1.25,3) {$\\bar{y}$};\n    \\node at (4.25,3) {$y$};\n    \\node at (7.25,3) {$\\bar{y}$};\n    \n    \\draw[black,thick,<->] (0,2.25)--(0,1.25);\n    \\draw[black,thick,<->] (2.5,2.25)--(2.5,1.25);\n    \\draw[black,thick,<->] (5,2.25)--(5,1.25);\n    \\draw[black,thick,<->] (7.5,2.25)--(7.5,1.25);\n    \n    \\node at (1.25,0) {\\bf \\large \\textcolor{orange}{$\\bar{y}$}};\n    \\node at (3.75,0) {\\bf \\large \\textcolor{orange}{$y$}};\n    \\node at (7.25,0) {\\bf \\large \\textcolor{orange}{$\\bar{y}$}};\n    \n    \\node at (1.25,0.5) {\\includegraphics[width=0.5cm]{example-image}};\n    \\node at (3.75,0.5) {\\includegraphics[width=0.5cm]{example-image}};\n    \\node at (7.25,0.5) {\\includegraphics[width=0.5cm]{example-image}};\n    \n    \\node at (1.25,2) {\\bf \\large \\textcolor{orange}{$\\bar{y}$}};\n    \\node at (3.75,2) {\\bf \\large \\textcolor{orange}{$y$}};\n    \\node at (7.25,2) {\\bf \\large \\textcolor{orange}{$\\bar{y}$}};\n    \n    \\node at (1.25,2.5) {\\includegraphics[width=0.5cm]{example-image}};\n    \\node at (3.75,2.5) {\\includegraphics[width=0.5cm]{example-image}};\n    \\node at (7.25,2.5) {\\includegraphics[width=0.5cm]{example-image}};\n    \n    \\node at ("
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        "index": 322,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath, amsthm, amssymb}\n\\usepackage[colorinlistoftodos]{todonotes}\n\\usepackage[colorlinks=true, allcolors=blue]{hyperref}\n\\usepackage{xcolor}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.14}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5]\n      \\begin{axis}[\n        xmin=-1,xmax=1,\n        ymin=-1,ymax=1,\n        height=4cm, width=8cm,\n        axis lines=center,\n        axis on top=true,\n        domain=-1:1,\n        ylabel near ticks,\n        xlabel near ticks,\n        xtick={-0.1, 0.1},\n        ytick={-0.1, 0.1},\n        xticklabels={$-$1, $+$1},\n        yticklabels={$-$1, $+$1},\n        ]\n        \\addplot[color=red, smooth, ultra thick,samples=100] {max(0, min(1, (x+0.5)/2))};\n        \\draw[dashed, thick, color=blue] (0.5,-0.1) -- (0.5,1);\n        \\draw[dashed, thick, color=blue] (-0.5,-0.1) -- (-0.5,1);\n        \\draw[dashed, thick, color=blue] (0.1,0) -- (0.1,1);\n        \\node[fill, circle, scale=0.3, color=red] at (0.5,0.5) {};\n        \\draw[->] (0.5,0.3) -- (0.5,0.2);\n        \\node[above] at (0.5,0.2) {$\\delta\\overline{x}$};\n        \\node[below] at (0.5,0.1) {$\\Delta$};\n      \\end{axis}\n    \\end{tikzpicture}\n\n\\end{document}"
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        "index": 323,
        "tikz_code": "\\documentclass[a4paper, 10pt, journal]{IEEEtran}\n\\usepackage{color}\n\\usepackage{color,soul}\n\\usepackage{amsmath}\n\\usepackage{color, colortbl}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node[inner sep=0pt] (c1) at (0,0)\n    {\\includegraphics[width=0.24\\textwidth]{example-image}};\n\\node[inner sep=0pt] (c2) at (2.5,0)\n    {\\includegraphics[width=0.24\\textwidth]{example-image}};\n\\node[inner sep=0pt] (c3) at (5,0)\n    {\\includegraphics[width=0.24\\textwidth]{example-image}};\n\\node[inner sep=0pt] (c4) at (7.5,0)\n    {\\includegraphics[width=0.24\\textwidth]{example-image}};\n\\node[inner sep=0pt] (c5) at (10,0)\n    {\\includegraphics[width=0.24\\textwidth]{example-image}};\n\\node[inner sep=0pt] (c6) at (0,-2.5)\n    {\\includegraphics[width=0.24\\textwidth]{example-image}};\n\\node[inner sep=0pt] (c7) at (2.5,-2.5)\n    {\\includegraphics[width=0.24\\textwidth]{example-image}};\n\\node[inner sep=0pt] (c8) at (5,-2.5)\n    {\\includegraphics[width=0.24\\textwidth]{example-image}};\n\\node[inner sep=0pt] (c9) at (7.5,-2.5)\n    {\\includegraphics[width=0.24\\textwidth]{example-image}};\n\\node[inner sep=0pt] (c10) at (10,-2.5)\n    {\\includegraphics[width=0.24\\textwidth]{example-image}};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows.meta}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.5]\n\n\\draw (0,0) rectangle (3.5,1) node [pos=0.5] {Img};\n\\draw (5.5,0) rectangle (9,1) node [pos=0.5] {Img};\n\\draw (11.5,0) rectangle (15,1) node [pos=0.5] {Img};\n\\draw (5.5,2.5) rectangle (9,3.5) node [pos=0.5] {Img};\n\\draw (5.5,5.5) rectangle (9,6.5) node [pos=0.5] {Img};\n\\draw (0,5.5) rectangle (3.5,6.5) node [pos=0.5] {Img};\n\\draw (11.5,5.5) rectangle (15,6.5) node [pos=0.5] {Img};\n\\draw (5.5,8.5) rectangle (9,9.5) node [pos=0.5] {Img};\n\\draw (0,8.5) rectangle (3.5,9.5) node [pos=0.5] {Img};\n\\draw (5.5,11.5) rectangle (9,12.5) node [pos=0.5] {Img};\n\n\\draw (2,1) -- (2,2.5) node [midway, sloped, above, draw=none] {$\\mathcal{S}^{(-1)}$};\n\\draw (8,1) -- (8,2.5) node [midway, sloped, above, draw=none] {$\\mathcal{S}^{(-2)}$};\n\\draw (13.5,1) -- (13.5,2.5) node [midway, sloped, above, draw=none] {$\\mathcal{S}^{(-3)}$};\n\\draw (14.5,1) -- (14.5,2.5) node [midway, sloped, above, draw=none] {$\\mathcal{S}^{(-4)}$};\n\\draw (2,3.5) -- (2,5.5) node [midway, sloped, above, draw=none] {$\\mathcal{S}^{(-1)}$};\n\\draw (8,3.5) -- (8,5.5) node [midway, sloped, above, draw=none] {$\\mathcal{S}^{(-2)}$};\n\\draw (13.5,3.5) -- (13.5,5.5) node [midway, sloped, above, draw=none] {$\\mathcal{S}^{(-3)}$};\n\\draw (14.5,3.5) -- (14.5,5.5) node [midway, sloped, above, draw=none] {$\\mathcal{S}^{(-4)}$};\n\\draw (2,6.5) -- (2,8.5) node [midway, sloped, above, draw=none] {$\\mathcal{S}^{(-1)}$};\n\\draw (13.5,6.5) -- (13.5,8.5) node [midway, sloped, above, draw=none] {$\\mathcal{S}^{(-2)}$};\n\\draw (2,9.5) -- (2,11.5) node [midway, sloped, above, draw=none] {$\\mathcal{S}^{(-3)}$};\n\n\\draw [draw=red, thick, densely dotted] (2,1) rectangle ++(1,1) node [pos=0.5] {$\\mathbf{l}$};\n\\draw [draw=red, thick, densely dotted] (8,1) rectangle ++(1,1) node [pos=0.5] {$\\mathbf{l}$};\n\\draw [draw=red, thick, densely dotted] (14.5,1) rectangle ++(1,1) node [pos=0.5] {$\\mathbf{l}$};\n\\draw [draw=red, thick, densely dotted] (13.5,3.5) rectangle ++(1,1) node [pos=0.5] {$\\mathbf{l}$};\n\\draw [draw=red, thick, densely dotted] (14.5,5.5) rectangle ++(1,1) node [pos=0.5] {$\\mathbf{l}$};\n\\draw [draw=red, thick, densely dotted] (2,6.5) rectangle ++(1,1) node [pos=0.5] {$\\mathbf{l}$};\n\\draw [draw=red, thick, densely dotted] (13.5,8.5) rectangle ++(1,1) node [pos=0.5] {$\\mathbf{l}$};\n\n\\draw [-{Latex[width=2mm,length=2mm]},blue,thick] (6.5,12.2) -- (0,10.5) node [midway,above,sloped] {$\\mathcal{S}$} node [midway,below,sloped] {$(\\frac{1}{2},-1)^{T}$} ;\n\\draw [-{Latex[width=2mm,length=2mm]},blue,thick] (6.5,12.2) -- (15,10.5) node [midway,above,sloped] {$\\mathcal{S}$} node [midway,below,sloped] {$(-1,\\frac{1}{2})^{T}$} ;\n\\draw [-{Latex[width=2mm,length=2mm]},blue,thick] (6.5,12.2) -- (15,6.5) node [midway,above,sloped] {$\\mathcal{S}$} node [midway,below,sloped] {$(0,0)$} ;\n\n\\draw [thick,red] (2,1) -- (2,9.5);\n\\draw [thick,red] (13.5,1) -- (14.5,5.5);\n\\draw [thick,red] (8,3.5) -- (8,11);\n\\draw [thick,red] (2,3.5) -- (2,11.5);\n\\draw [thick,red] (8,3.5) -- (8,11);\n\\draw [thick,red] (13.5,3.5) -- (14.5,5.5);\n\\draw [thick,red] (13.5,3.5) --"
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        "index": 325,
        "tikz_code": "\\documentclass[12pt,reqno]{amsart}\n\\usepackage{amsfonts,amsmath,amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathmorphing}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\t\t\\node (A) at (0,0) {$\\bullet$};\n\t\t\\node (B) at (-2,-2) {$\\bullet$};\n\t\t\\node (C) at (2,-2) {$\\bullet$};\n\t\t\\node (D) at (-3,-4) {$\\bullet$};\n\t\t\\node (E) at (-1,-4) {$\\bullet$};\n\t\t\\node (F) at (1,-4) {$\\bullet$};\n\t\t\\node (G) at (3,-4) {$\\bullet$};\n\t\t\\node (H) at (-3.5,-6) {$\\bullet$};\n\t\t\\node (I) at (-2.5,-6) {$\\bullet$};\n\t\t\\node (J) at (-1.5,-6) {$\\bullet$};\n\t\t\\node (K) at (-0.5,-6) {$\\bullet$};\n\t\t\\node (L) at (0.5,-6) {$\\bullet$};\n\t\t\\node (M) at (1.5,-6) {$\\bullet$};\n\t\t\\node (N) at (2.5,-6) {$\\bullet$};\n\t\t\\node (O) at (3.5,-6) {$\\bullet$};\n\t\t\n\t\t\\draw [-] (A) to node[above] {$1$} (B);\n\t\t\\draw [-] (A) to node[above] {$1$} (C);\n\t\t\\draw [-] (B) to node[left] {$0$} (D);\n\t\t\\draw [-] (B) to node[left] {$0$} (E);\n\t\t\\draw [-] (C) to node[left] {$1$} (F);\n\t\t\\draw [-] (C) to node[left] {$0$} (G);\n\t\t\\draw [-] (D) to node[left] {$1$} (H);\n\t\t\\draw [-] (D) to node[left] {$0$} (I);\n\t\t\\draw [-] (E) to node[left] {$0$} (K);\n\t\t\\draw [-] (E) to node[left] {$0$} (L);\n\t\t\\draw [-] (F) to node[left] {$1$} (M);\n\t\t\\draw [-] (F) to node[left] {$0$} (N);\n\t\t\\draw [-] (G) to node[left] {$0$} (O);\n\t\t\n\t\t\\node at (0,-8.2) {$\\ddots$};\n\t\t\\node at (-2.2,-8.2) {$\\ddots$};\n\t\t\\node at (2.2,-8.2) {$\\ddots$};\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amssymb,amsmath,amsthm,mathrsfs,mathpazo,xspace,booktabs}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning,arrows,calc,shapes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.8,auto=left,every node/.style={inner sep=1pt,minimum size=10pt}]\n\\node[circle,draw](a) at (0,0) {$ab$};\n\\node[circle,draw](b) at (0,2) {$ac$};\n\\node[circle,draw](c) at (1,1) {$bd$};\n\\node[circle,draw](d) at (2,0) {$ce$};\n\\node[circle,draw](e) at (2,2) {$bd$};\n\\node[circle,draw](f) at (3,1) {$ce$};\n\n\\node[circle,fill=black](x) at (4,1) {};\n\\node[circle,fill=black](y) at (5,1) {};\n\\node[circle,fill=black](z) at (5,2) {};\n\\node[circle,fill=black](u) at (5,0) {};\n\\node[circle,fill=black](v) at (6,0) {};\n\\node[circle,fill=black](w) at (6,2) {};\n\\node[circle,fill=black](q) at (7,2) {};\n\n\\node[inner sep=0pt,minimum size=10pt](1) at (1,-0.5) {$T=TS_2(G)$};\n\\node[inner sep=0pt,minimum size=10pt](2) at (7.5,0.5) {$G$};\n\n\\node[inner sep=0pt,minimum size=10pt](3) at (9,2) {$f$};\n\\node[inner sep=0pt,minimum size=10pt](4) at (8,2) {$e$};\n\\node[inner sep=0pt,minimum size=10pt](5) at (9,1) {$d$};\n\\node[inner sep=0pt,minimum size=10pt](6) at (8,1) {$c$};\n\\node[inner sep=0pt,minimum size=10pt](7) at (9,0) {$a$};\n\\node[inner sep=0pt,minimum size=10pt](8) at (8,0) {$b$};\n\n\\draw[thick](a)--(c)--(b);\n\\draw[thick](d)--(f)--(e);\n\\draw[thick](f)--(q);\n\\draw[thick](q)--(z)--(w)--(y)--(x)--(v);\n\n\\draw[bend right=45](y) to node[above]{} (z);\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[10pt,conference,letterpaper]{IEEEtran}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{xcolor}\n\\usepackage{pgfplots}\n\\pgfplotsset{width=7cm,compat=1.12}\n\\usepgfplotslibrary{fillbetween}\n\\usepackage{color,soul}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\n\n\\begin{semilogyaxis}[\n    height=6cm,\n    width=\\linewidth,\n    xlabel={Minimum Number Effective Samples},\n    ylabel={Validation Stub Rate},\n    % ymajorgrids=true,\n    % grid style=dashed,\n    legend style={at={(0.7,1.05)},\n    anchor=south,legend columns=2},\n    symbolic x coords={0,100,200,300,400},\n    xtick=data,\n    xticklabels={0,100,200,300,400},\n    tick label style = {font=\\footnotesize},\n    % scaled x ticks=base 10:3,\n]\n\n\\addplot[\n    color=blue,\n    % color=orange,\n    mark=o,\n    mark options={solid},\n    ]\n    coordinates {\n    (0,0.67)(100,0.67)(200,0.67)(300,0.67)(400,0.67)\n    };\n    \n\\addplot[\n    color=orange,\n    mark=triangle,\n    mark options={solid},\n    ]\n    coordinates {\n    (0,0.67)(100,0.67)(200,0.67)(300,0.67)(400,0.67)\n    };\n    \n\\addplot[\n    color=black,\n    mark=square,\n    mark options={solid},\n    ]\n    coordinates {\n    (0,0.67)(100,0.67)(200,0.67)(300,0.67)(400,0.67)\n    };\n\n\\addplot[\n    color=black,\n    mark=x,\n    mark options={solid},\n    ]\n    coordinates {\n    (0,0.67)(100,0.67)(200,0.67)(300,0.67)(400,0.67)\n    };\n\n\\addplot[\n    color=black,\n    mark=+,\n    mark options={solid},\n    ]\n    coordinates {\n    (0,0.67)(100,0.67)(200,0.67)(300,0.67)(400,0.67)\n    };\n\n\\addplot[\n    color=black,\n    mark=star,\n    mark options={solid},\n    ]\n    coordinates {\n    (0,0.67)(100,0.67)(200,0.67)(300,0.67)(400,0.67)\n    };\n    \n\\addplot[\n    color=black,\n    mark=*,\n    mark options={solid},\n    ]\n    coordinates {\n    (0,0.67)(100,0.67)(200,0.67)(300,0.67)(400,0.67)\n    };\n\n    \n\\addplot[\n    color=black,\n    mark=diamond,\n    mark options={solid},\n    ]\n    coordinates {\n    (0,0.67)(100,0.67)(200,0.67)(300,0.67)(400,0.67)\n    };\n    \n\\addplot[\n    color=black,\n    mark=|,\n    mark options={solid},\n    ]\n    coordinates {\n    (0,0.67)(100,0.67)(200,0.67)(300,0.67)(400,0.67)\n    };\n\n\\addplot[\n    color=black,\n    mark=pentagon,\n    mark options={solid},\n    ]\n    coordinates {\n    (0,0.67)(100,0.67)(200,0.67)(300,0.67)(400,0.67)\n    };\n\n\\addplot[\n    color=black,\n    mark=/,\n    mark options={solid},\n    ]\n    coordinates {\n    (0,0.67)(100,0.67)(200,0.67)(300,0.67)(400,0.67)\n    };\n\n\\addplot[\n    color=black,\n    mark=/,\n    mark options={solid},\n    ]\n    coordinates {\n    (0,0.67)(100,0.67)(200,0.67)(300,0.67)(400,0.67)\n    };\n    \n\\addplot[\n    color=black,\n    mark=-,\n    mark options={solid},\n    ]\n    coordinates {\n    (0,0.67)(100,0.67)(200,0.67)(300,0.67)(400,0.67)\n    };\n\n\\addplot[\n    color=black,\n    mark=x,\n    dashed,\n    ]\n    coordinates {\n    (0,0.67)(0,1.0)(100,1.0)(200,1.0)(300,1.0)(400,1.0)\n    };\n\n\\addplot[\n    color=black,\n    mark=triangle,\n    dashed,\n    ]\n    coordinates {\n    (0,0.67)(0,1.0)(100,1.0)(200,1.0)(300,1.0)(400,1.0)\n    };\n    \n\\addplot[\n    color=black,\n    mark=o,\n    dashed,\n    ]\n    coordinates {\n    (0,0.67)(0,1.0)(100,1.0)(200,1.0)(300,1.0)(400,1.0)\n    };\n\n\\addplot[\n    color=black,\n    mark=+,\n    dashed,\n    ]\n    coordinates {\n    (0,0.67)(0,1.0)(100,1.0)(200,1"
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        "index": 329,
        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning,chains,fit,shapes,calc}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}[align=center]\n\\tikzset{\n  node distance=2.8cm,\n  neaten/.style={draw,rectangle,rounded corners=3mm,minimum size=0.9cm},\n  stump/.style={draw,rectangle,rounded corners=3mm,minimum height=1.5cm,minimum width=0.1cm},\n  leaf/.style={draw,circle,inner sep=0pt,minimum size=0.2cm},\n  nodot/.style={circle,inner sep=0pt,minimum size=0.2cm},\n  every label/.style={text depth=0.5ex},\n  tandem/.style={line width=0.5mm},\n  }\n\n\n% input\n\\node[stump,fill=red,label=above:$\\boldsymbol{n}$](n) {};\n\\node[stump,fill=red,below=of n](nminus1) {};\n\\node[stump,fill=red,below=of nminus1](nminus2) {};\n\\node[stump,fill=red,below=of nminus2](nminus3) {};\n\\node[stump,fill=red,below=of nminus3](nminus4) {};\n\\node[stump,fill=red,below=of nminus4](nminus5) {};\n\\node[stump,fill=red,below=of nminus5](nminus6) {};\n\\node[stump,fill=red,below=of nminus6](nminus7) {};\n\n\\node[stump,fill=red,right=0.3cm of n](nplus1) {};\n\\node[stump,fill=red,below=of nplus1](nplus2) {};\n\\node[stump,fill=red,below=of nplus2](nplus3) {};\n\\node[stump,fill=red,below=of nplus3](nplus4) {};\n\\node[stump,fill=red,below=of nplus4](nplus5) {};\n\\node[stump,fill=red,below=of nplus5](nplus6) {};\n\\node[stump,fill=red,below=of nplus6](nplus7) {};\n\n\\node[stump,fill=red,right=0.3cm of nplus1](nplus2) {};\n\\node[stump,fill=red,below=of nplus2](nplus3) {};\n\\node[stump,fill=red,below=of nplus3](nplus4) {};\n\\node[stump,fill=red,below=of nplus4](nplus5) {};\n\\node[stump,fill=red,below=of nplus5](nplus6) {};\n\\node[stump,fill=red,below=of nplus6](nplus7) {};\n\n\n\\node[stump,label=above:$\\boldsymbol{T_1}$](T1) at ($(n) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_2}$](T2) at ($(nminus1) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_3}$](T3) at ($(nminus2) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_4}$](T4) at ($(nminus3) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_5}$](T5) at ($(nminus4) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_6}$](T6) at ($(nminus5) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_7}$](T7) at ($(nminus6) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_8}$](T8) at ($(nminus7) + (-1,0)$) {};\n\n\\node[stump,label=above:$\\boldsymbol{T_{1,1} of first form}$](T11) at ($(nplus1) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_{1,2} of first form}$](T12) at ($(nplus2) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_{1,3} of first form}$](T13) at ($(nplus3) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_{1,4} of first form}$](T14) at ($(nplus4) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_{1,5} of first form}$](T15) at ($(nplus5) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_{1,6} of first form}$](T16) at ($(nplus6) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_{1,7} of first form}$](T17) at ($(nplus7) + (-1,0)$) {};\n\n\n\\node[stump,label=above:$\\boldsymbol{T_{2,1} of second form}$](T21) at ($(nplus2) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_{2,2} of second form}$](T22) at ($(nplus3) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_{2,3} of second form}$](T23) at ($(nplus4) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_{2,4} of second form}$](T24) at ($(nplus5) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_{2,5} of second form}$](T25) at ($(nplus6) + (-1,0)$) {};\n\\node[stump,label=above:$\\boldsymbol{T_{2,6} of second form}$](T2"
    },
    {
        "index": 330,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amsthm,amsfonts,amssymb,euscript}\n\\usepackage{pgf,tikz}\n\\usepackage{pgfplots}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary[patterns]\n\\usetikzlibrary{decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]\n\\begin{axis}[\nx=1.0cm,y=1.0cm,\naxis lines=middle,\nymajorgrids=true,\nxmajorgrids=true,\nxmin=-3.5,\nxmax=3.5,\nymin=-0.5,\nymax=1.5,\nxtick={-3.0,-2.0,...,3.0},\nytick={-0.5,0.0,...,1.5},]\n\\clip(-3.5,-0.5) rectangle (3.5,1.5);\n\\draw [line width=1.6pt,color=blue,smooth,samples=100,domain=-3.0:3.0] plot(\\x,{(-0.5)*(\\x)*(\\x)*(\\x)*(\\x)+1.0*(\\x)*(\\x)*(\\x)*(\\x)-1.0*(\\x)*(\\x)*(\\x)-2.0*(\\x)*(\\x)+2.0*(\\x)});\n\\draw [line width=1.6pt,color=red,smooth,samples=100,domain=-3.0:3.0] plot(\\x,{(-0.5)*(\\x)*(\\x)*(\\x)*(\\x)+1.0*(\\x)*(\\x)*(\\x)*(\\x)-1.0*(\\x)*(\\x)*(\\x)-2.0*(\\x)*(\\x)+2.0*(\\x)});\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 331,
        "tikz_code": "\\documentclass[runningheads,a4paper]{llncs}\n\\usepackage{amssymb,amsmath,graphicx,scalerel}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning,arrows,arrows.meta,shapes,decorations.pathmorphing,automata,backgrounds,fit}\n\\usepackage[T1]{fontenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[every node/.style={minimum height=5mm, text height=3mm}]\n    \\node (domain) {Models ordered by domain restrictions:};\n    \\node [right=0mm of domain] (ar) {ABC};\n    \\node [right=10mm of ar] (pa) {Party-approval};\n    \\node [below=1mm of pa] (ap) {Approval};\n    \\node [below=1mm of ar] (fm) {Fair mixin};\n    \\node [right=20mm of pa] (pc) {Party-approval};\n    \\node [below=1mm of pc] (abc) {ABC};\n    \\node [right=20mm of pc] (fap) {Fair Approval};\n    \\draw[-Latex] (ar) to (pa);\n    \\draw[-Latex] (pa) to (ap);\n    \\draw[-Latex] (ar) to (fm);\n    \\draw[-Latex] (pa) to (pc);\n    \\draw[-Latex] (pc) to (abc);\n    \\draw[-Latex] (pc) to (fap);\n    \\node [label={[label distance=-1mm]90:\\tiny{Output type:}}] at (abstract:1.1) {};\n    \\node [label={[label distance=-1mm]90:\\tiny{Ordered by:}}] at (abstract:0.1) {};\n  \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 332,
        "tikz_code": "\\documentclass[tikz,border=3mm]{standalone}\n\\usetikzlibrary{angles,quotes}\n\\usepackage{siunitx}\n\\begin{document}\n\\begin{tikzpicture}\n \\draw[-stealth] (0,0) coordinate (O) -- (0,5) node[left]{$x$};\n \\draw[-stealth] (O) -- (2,0) node[below]{$n$};\n \\draw[dashed] (2,0) coordinate (n) -- (2,4) node[above left]{$\\vb{n}$};\n \\path (2,3) coordinate (n2)\n (n) +(-45:2) coordinate (n1) \n pic[draw,blue,angle radius=1cm,\"\\ang{45}\",angle eccentricity=1.2] {angle = n2--n--n1};\n \\draw[thick] (n) -- (n1)\n (n) -- (n2)\n pic[draw,blue,angle radius=1cm,\"\\ang{45}\",angle eccentricity=1.2] {angle = n1--n--n2};\n \\draw[-stealth] (1,2) coordinate (a) -- (2,2) node[above]{$\\vb{a}$};\n \\draw[-stealth] (1,2) -- ++(165:0.5) node[below]{$\\theta$};\n\\end{tikzpicture}\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amssymb,amsfonts,amsmath}\n\\usepackage{tikz}\n\\usepackage{pgf}\n\\usetikzlibrary{calc,bgposition}\n\\usetikzlibrary{arrows,automata}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8,>=stealth',shorten >=1pt,auto,node distance=2.8cm,semithick]\n\n\\node[inner sep=1.5pt, circle, fill=black] (a) at (0,0) [label=270:{\\footnotesize ${\\color{black} a}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (b) at (0,-1) [label=270:{\\footnotesize ${\\color{black} b}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (c) at (0,-2) [label=270:{\\footnotesize ${\\color{black} c}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (d) at (0,-3) [label=270:{\\footnotesize ${\\color{black} d}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (e) at (0,-4) [label=270:{\\footnotesize ${\\color{black} e}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (f) at (0,-5) [label=270:{\\footnotesize ${\\color{black} f}$}] {};\n\n\\node[inner sep=1.5pt, circle, fill=black] (a') at (2,0) [label=270:{\\footnotesize ${\\color{red} a'}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (b') at (2,-1) [label=270:{\\footnotesize ${\\color{red} b'}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (c') at (2,-2) [label=270:{\\footnotesize ${\\color{red} c'}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (d') at (2,-3) [label=270:{\\footnotesize ${\\color{red} d'}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (e') at (2,-4) [label=270:{\\footnotesize ${\\color{red} e'}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (f') at (2,-5) [label=270:{\\footnotesize ${\\color{red} f'}$}] {};\n\n\n\\node[inner sep=1.5pt, circle, fill=black] (a'') at (4,0) [label=270:{\\footnotesize ${\\color{orange} a''}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (b'') at (4,-1) [label=270:{\\footnotesize ${\\color{orange} b''}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (c'') at (4,-2) [label=270:{\\footnotesize ${\\color{orange} c''}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (d'') at (4,-3) [label=270:{\\footnotesize ${\\color{orange} d''}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (e'') at (4,-4) [label=270:{\\footnotesize ${\\color{orange} e''}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (f'') at (4,-5) [label=270:{\\footnotesize ${\\color{orange} f''}$}] {};\n\n\n\\node[inner sep=1.5pt, circle, fill=black] (a'') at (6,0) [label=270:{\\footnotesize ${\\color{yellow} a''}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (b'') at (6,-1) [label=270:{\\footnotesize ${\\color{yellow} b''}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (c'') at (6,-2) [label=270:{\\footnotesize ${\\color{yellow} c''}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (d'') at (6,-3) [label=270:{\\footnotesize ${\\color{yellow} d''}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (e'') at (6,-4) [label=270:{\\footnotesize ${\\color{yellow} e''}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (f'') at (6,-5) [label=270:{\\footnotesize ${\\color{yellow} f''}$}] {};\n\n\n\\node[inner sep=1.5pt, circle, fill=black] (a'') at (8,0) [label=270:{\\footnotesize ${\\color{blue} a''}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (b'') at (8,-1) [label=270:{\\footnotesize ${\\color{blue} b''}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (c'') at (8,-2) [label=270:{\\footnotesize ${\\color{blue} c''}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (d'') at (8,-3) [label=270:{\\footnotesize ${\\color{blue} d''}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (e'') at (8,-4) [label=270:{\\footnotesize ${\\color{blue} e''}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (f'') at (8,-5) [label=270:{\\footnotesize ${\\color{blue} f''}$}] {};\n\n\n\\node[inner sep=1.5pt, circle, fill=black] (a'') at (10,0) [label=270:{\\footnotesize ${\\color{green} a''}$}] {};\n\\node[inner sep=1.5pt, circle, fill=black] (b'') at (10,-1) [label=270:{\\footnotesize ${\\color{green} b''}$}] {};\n\\node[inner sep=1"
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        "index": 334,
        "tikz_code": "\\documentclass[a4paper,11pt]{article}\n\\usepackage{color}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{hobby,decorations.pathreplacing,arrows.meta}\n\\usepackage{tikz}\n\\usepackage{tikzsymbols}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{fit}\n\\usepackage[latin1]{inputenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.45, baseline=-3mm, thick]\n\n%left graph\n\\draw (2,3) -- (-5,-3);\n\\draw (-5,3) -- (-2,-3);\n\\draw (-2,3) .. controls (-1.6,1) .. (-1,3);\n\\draw (-1,3) -- (0,-3);\n\\draw (0,3) .. controls (0.2,1.5) .. (1,-3);\n\\draw (1,3) .. controls (0.8,0.8) .. (0,0);\n\\draw (0,0) -- (2,-3);\n\\draw (0,0) -- (0,3);\n\\draw (2,-3) .. controls (1.8,-0.8) .. (1,3);\n\\draw[blue,line width=2mm] (-1.5,0) -- (0.5,0);\n\\draw[fill] (0,0) circle [radius=0.12];\n\\node [below, blue] at (0.5,0) {$H$};\n\\node [above, green] at (-1.5,0) {$R$};\n\n\\node [above] at (-1.5,0) {$\\Upsilon$};\n\n\n\n%arrow \n\\node [above] at (3,0) {$\\Rightarrow$};\n\n%right graph\n\\draw (15,3) -- (8,-3);\n\\draw (8,3) -- (11,-3);\n\\draw (11,3) .. controls (10.8,1) .. (10,3);\n\\draw (10,3) .. controls (10.2,1.5) .. (9,-3);\n\\draw (9,3) .. controls (9.2,0.8) .. (8,0);\n\\draw (8,0) -- (15,-3);\n\\draw (8,0) -- (8,3);\n\\draw[red,line width=2mm] (8.5,-0.2) -- (10.5,-0.2);\n\\draw[fill, red] (8,0) circle [radius=0.12];\n\\node [below, red] at (8.5,-0.2) {$H$};\n\\node [above, red] at (10.5,-0.2) {$B$};\n\n\\node [above] at (10.5,-0.2) {$\\Upsilon$};\n\n\n\n\n\n\n\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 335,
        "tikz_code": "\\documentclass[aps, prl, a4paper, reprint, showkeys, floatfix]{revtex4-1}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[T1]{fontenc}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{backgrounds}\n\\usetikzlibrary{graphs}\n\\usetikzlibrary{graphs.standard}\n\\usetikzlibrary{shapes.misc}\n\n\\begin{document}\n\n\\begin{tikzpicture} \n\t\t\\tikzstyle{every node} = [draw, shape=circle, minimum size=0.9cm]\n\t\t\\node(1) at (0,0) {};\n\t\t\\node(2) at (1.5,0) {};\n\t\t\\node(3) at (3,0) {};\n\t\t\\node(4) at (4.5,0) {};\n\t\t\\node(5) at (6,0) {};\n\t\t\\node(6) at (7.5,0) {};\n\n\t\t\\draw[dashed] (6) -- (6.75,0);\n\n\t\t\\draw[line width=1pt] (1) -- (2) node[fill=none, draw=none, midway, below] {$q_1$};\n\t\t\\draw[line width=1pt] (2) -- (3) node[fill=none, draw=none, midway, below] {$q_2$};\n\t\t\\draw[line width=1pt] (3) -- (4) node[fill=none, draw=none, midway, below] {$q_3$};\n\t\t\\draw[line width=1pt] (4) -- (5) node[fill=none, draw=none, midway, below] {$q_4$};\n\t\t\\draw[line width=1pt] (5) -- (6) node[fill=none, draw=none, midway, below] {$q_N$};\n\n\t\t\\draw[line width=1pt] (5.75,-0.25) -- (5.75,0.25) node[fill=none, draw=none, right] {Wall};\n\n\t\t\\node[fill=none, draw=none] at (1.75,0.75) {$k_1$};\n\t\t\\node[fill=none, draw=none] at (2.75,0.75) {$k_2$};\n\t\t\\node[fill=none, draw=none] at (3.75,0.75) {$k_3$};\n\t\t\\node[fill=none, draw=none] at (5.25,0.75) {$k_3$};\n\t\t\\node[fill=none, draw=none] at (6.25,0.75) {$k_3$};\n\t\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 336,
        "tikz_code": "\\documentclass[10pt,a4paper]{article}\n\\usepackage{tikz}\n\\usetikzlibrary{calc,fadings,decorations.pathreplacing}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[latin1]{inputenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[xscale=6,yscale=3]\n\t\\draw[->] (-0.05,0) -- (1.05,0) node[right] {$x$};\n\t\\draw[->] (0,-0.05) -- (0,0.95) node[above] {$\\cosst$};\n\t\\draw[dotted] (1,0) node[below] {$1$} -- (1,{0.4*cos(1*180/pi)}) -- (0,{0.4*cos(1*180/pi)});\n\t\\draw[dashed] (1,0) node[below] {$1$} -- (1,{0.3*cos(1*180/pi)}) -- (0,{0.3*cos(1*180/pi)});\n\t\\draw[thick] (1,0) node[below] {$r$} -- (0,{0.4*cos(1*180/pi)});\n\t\\draw[thick] (1,0) node[below] {$r$} -- (0,{0.3*cos(1*180/pi)});\n\t\\draw[dotted] ({0.5*cos(1*180/pi)},0) node[below] {$\\frac{r}{2}$} -- ({0.5*cos(1*180/pi)},{0.2*cos(1*180/pi)});\n\t\\draw[dotted] ({0.4*cos(1*180/pi)},0) node[below] {$\\frac{r}{4}$} -- ({0.4*cos(1*180/pi)},{0.12*cos(1*180/pi)});\n\t\\node at (0.4,0.15) {$C_1$};\n\t\\node at (0.5,0.15) {$C_2$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 337,
        "tikz_code": "\\documentclass[a4paper,12pt]{article}\n\\usepackage{amsmath, amssymb, mathrsfs, amsthm, shorttoc, geometry, stmaryrd}\n\\usepackage{tikz}\n\\usepackage{xcolor}\n\\usepackage{pgf,tikz}\n\\usetikzlibrary{matrix, calc, arrows}\n\\usepackage{tikz-cd}\n\n\\begin{document}\n\n\\begin{tikzpicture}[thick,scale=1]\n\\begin{scope}[xshift=-2.5cm,yshift=-1cm]\n\\draw[line width=1.5pt, draw=gray!40]\n(-1.5,0) .. controls (-0.5,0) and (-0.5,1) .. (0.5,1);\n\\draw[line width=1.5pt, draw=gray!40]\n(0.5,1) .. controls (0.75,1) and (0.75,0) .. (1.5,0);\n\\draw[line width=1.5pt, draw=gray!40]\n(1.5,0) .. controls (0.75,-1) and (0.75,-2) .. (0.5,-2);\n\\draw[line width=1.5pt, draw=gray!40]\n(-1.5,0) .. controls (-0.75,-1) and (-0.75,-2) .. (-0.5,-2);\n\\draw[line width=1.5pt, draw=gray!40]\n(-0.5,-2) .. controls (-0.5,-1) and (-0.5,0) .. (-1.5,0);\n\\draw[line width=1.5pt, draw=gray!40]\n(0.5,1) .. controls (1,0.5) and (1,-0.5) .. (0.5,-2);\n\\draw[line width=1.5pt, draw=gray!40]\n(-0.5,2) .. controls (-1,1.5) and (-1,-1.5) .. (-0.5,-2);\n\n\\draw[line width=1.5pt, draw=black]\n(0.5,1) .. controls (1.5,1) and (1.5,-1) .. (0.5,-2);\n\\draw[line width=1.5pt, draw=black]\n(-0.5,2) .. controls (-1.5,2) and (-1.5,-2) .. (-0.5,-2);\n\n\\filldraw[black] (0,0) circle (3pt);\n\\draw (0.2,-0.2) node {$v_0$};\n\\end{scope}\n\n\\draw (-3.2,0.7) node {$a$};\n\\draw (3.2,0.7) node {$b$};\n\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 338,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amssymb,amsfonts,amsmath,amsthm,dsfont}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\def\\L{6}\n    \\def\\Lw{0.4}\n    \\draw[line width=0.5pt] (0,0) -- (0,2*\\L+\\Lw) -- (4*\\L,2*\\L+\\Lw) -- (4*\\L,0) -- (0,0) ;\n    \\draw[line width=0.5pt] (10,0) -- (10,2*\\L+\\Lw) -- (14*\\L,2*\\L+\\Lw) -- (14*\\L,0) -- (10,0) ;\n    \n    \\draw[line width=1pt, dashed] (\\L,\\L) -- (3*\\L,\\L) -- (3*\\L,\\L+\\Lw) -- (\\L,\\L+\\Lw) -- (\\L,\\L) ;\n    \\draw[line width=1pt, dashed] (11*\\L,\\L) -- (13*\\L,\\L) -- (13*\\L,\\L+\\Lw) -- (11*\\L,\\L+\\Lw) -- (11*\\L,\\L) ;\n    \n    \\draw (5*\\L, 2*\\L+0.2) node {$\\mathcal{S}_2$};\n    \\draw (15*\\L, 2*\\L+0.2) node {$\\mathcal{S}_3$};\n    \\draw (0, -0.5) node {$\\mathcal{S}_1$};\n    \n    \\draw[dotted, line width=1pt] (\\L, \\L) ellipse (4*\\L and 2*\\L+\\Lw);\n    \\draw[dotted, line width=1pt] (11*\\L, \\L) ellipse (4*\\L and 2*\\L+\\Lw);\n    \n    \\filldraw[fill=black, draw=black] (1*\\L, \\L) circle (0.02) ;\n    \\filldraw[fill=black, draw=black] (3*\\L, \\L) circle (0.02) ;\n    \\filldraw[fill=black, draw=black] (4*\\L, \\L) circle (0.02) ;\n    \\filldraw[fill=black, draw=black] (5*\\L, \\L) circle (0.02) ;\n    \\filldraw[fill=black, draw=black] (7*\\L, \\L) circle (0.02) ;\n    \\filldraw[fill=black, draw=black] (8*\\L, \\L) circle (0.02) ;\n    \\filldraw[fill=black, draw=black] (10*\\L, \\L) circle (0.02) ;\n    \\filldraw[fill=black, draw=black] (11*\\L, \\L) circle (0.02) ;\n    \\filldraw[fill=black, draw=black] (13*\\L, \\L) circle (0.02) ;\n    \\filldraw[fill=black, draw=black] (14*\\L, \\L) circle (0.02) ;\n    \\filldraw[fill=black, draw=black] (15*\\L, \\L) circle (0.02) ;\n    \n    \\draw (1.5*\\L, \\L-0.5*\\Lw) -- (1.5*\\L, \\L+0.5*\\Lw) ;\n    \\draw (4.5*\\L, \\L-0.5*\\Lw) -- (4.5*\\L, \\L+0.5*\\Lw) ;\n    \\draw (5.5*\\L, \\L-0.5*\\Lw) -- (5.5*\\L, \\L+0.5*\\Lw) ;\n    \\draw (7.5*\\L, \\L-0.5*\\Lw) -- (7.5*\\L, \\L+0.5*\\Lw) ;\n    \\draw (8.5*\\L, \\L-0.5*\\Lw) -- (8.5*\\L, \\L+0.5*\\Lw) ;\n    \\draw (10.5*\\L, \\L-0.5*\\Lw) -- (10.5*\\L, \\L+0.5*\\Lw) ;\n    \\draw (11.5*\\L, \\L-0.5*\\Lw) -- (11.5*\\L, \\L+0.5*\\Lw) ;\n    \\draw (13.5*\\L, \\L-0.5*\\Lw) -- (13.5*\\L, \\L+0.5*\\Lw) ;\n    \\draw (14.5*\\L, \\L-0.5*\\Lw) -- (14.5*\\L, \\L+0.5*\\Lw) ;\n    \\draw (15.5*\\L, \\L-0.5*\\Lw) -- (15.5*\\L, \\L+0.5*\\Lw) ;\n    \n    \\draw[dashed] (0,0) -- (4*\\L,\\L) -- (4*\\L, 2*\\L+\\Lw);\n    \\draw[dashed] (0,2*\\L+\\Lw) -- (4*\\L,\\L) -- (4*\\L, 2*\\L+\\Lw);\n    \n    \\draw[dotted, line width=1pt] (2*\\L,0) -- (2*\\L,\\L) ;\n    \\draw[dotted, line width=1pt] (2*\\L,\\L+\\Lw) -- (2*\\L,\\L+2*\\L+\\Lw) ;\n    \n    \\def\\xR{2.5}\n    \\def\\yR{1.3}\n    \\def\\xRi{3}\n    \\def\\yRi{1.1}\n    \\def\\xRii{4.7}\n    \\def\\yRii{1.4}\n    \\def\\xRiii{8}\n    \\def\\yRiii{1.5}\n    \\def\\xRiv{10.5}\n    \\def\\yRiv{1.5}\n    \n    \\draw[dotted, line width=1pt] (\\xR, \\yR) ellipse (\\xRi and \\yRi);\n    \\draw[dotted, line width=1pt] (\\xRii, \\yRii) ellipse (\\xRii-\\xR and \\yRii-\\yRi);\n    \\draw[dotted, line width=1pt] (\\xRiii, \\yRiii) ellipse (\\xRiii-\\xRii-\\xR and \\yRiii-\\yRii-\\yRi);\n    \\draw[dotted"
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    {
        "index": 339,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amssymb}\n\\usepackage[colorlinks=true, allcolors=blue]{hyperref}\n\\usepackage{tikz}\n\\tikzset{\nevery node/.style={draw, circle, inner sep=2pt}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n% vertices\n\\node (1) at (0,1) {1};\n\\node (2) at (1.414,0) {2};\n\\node (3) at (-1.414,0) {3};\n\\node (4) at (2,1) {4};\n\\node (5) at (2,-1) {5};\n% edges\n\\draw (1) -- (2) -- (3) -- (1);\n\\draw (2) -- (4);\n\\draw (3) -- (2);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 340,
        "tikz_code": "\\documentclass[12pt,a4paper]{amsart}\n\\usepackage{amsmath}\n\\usepackage[latin2]{inputenc}\n\\usepackage{pgfplots}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n\\filldraw[black] (0,0) circle (2pt) node[below] {$u_1$};\n\\filldraw[black] (3,-1.7) circle (2pt) node[right] {$t_1$};\n\\filldraw[black] (4.7,0) circle (2pt) node[right] {$s_1$};\n\\filldraw[black] (-4.7,0) circle (2pt) node[left] {$u_{p-1}u_2$};\n\\filldraw[black] (0,3) circle (2pt) node[right] {$r_1$};\n\\filldraw[black] (0,4.7) circle (2pt) node[right] {$r_2$};\n\\filldraw[black] (0,-3.7) circle (2pt) node[right] {$r_{r-1}$};\n\\filldraw[black] (3.7,-4.7) circle (2pt) node[right] {$r_r$};\n\\filldraw[black] (-3.7,-4.7) circle (2pt) node[right] {$t_{q-2s}$};\n\\draw[ultra thick, -] (0,0) -- (3,-1.7);\n\\draw[ultra thick, -] (3,-1.7) -- (4.7,0);\n\\draw[ultra thick, -] (4.7,0) -- (0,3);\n\\draw[ultra thick, -] (0,3) -- (0,4.7);\n\\draw[ultra thick, -] (0,3) -- (-4.7,0);\n\\draw[ultra thick, -] (-4.7,0) -- (0,0);\n\\draw[ultra thick, -] (0,0) -- (0,-3.7);\n\\draw[ultra thick, -] (0,-3.7) -- (3.7,-4.7);\n\\draw[ultra thick, -] (3.7,-4.7) -- (4.7,0);\n\\draw[ultra thick, dashed, -] (-4.7,0) -- (4.7,0);\n\\draw[ultra thick, dashed, -] (3,-1.7) -- (0,0);\n\\draw[ultra thick, dashed, -] (-2.3,0) -- (2.3,0);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 341,
        "tikz_code": "\\documentclass[tikz]{standalone}\n\\usepackage{pgfplots}\n\\begin{document}\n\\begin{tikzpicture}\n\\begin{axis}[\n  trig format plots=rad,\n  axis lines=center,\n  xtick={-8,-6,...,8},\n  ytick={-8,-6,...,8},\n  xlabel={$x$},\n  ylabel={$y$},\n  xlabel style={below right},\n  ylabel style={above left},\n  xmin=-8,\n  xmax=8,\n  ymin=-8,\n  ymax=8,\n  extra x ticks={pi},\n  extra x tick style={\n    xticklabel style={anchor=south}\n  },\n  extra y ticks={pi},\n  extra y tick style={\n    xticklabel style={anchor=west}\n  }]\n\\addplot[green,domain=0:2*pi,samples=1000] ({cos(x)},{sin(x)});\n\\draw[blue,thick] (axis cs:0,0) -- (axis cs:{cos(pi/2)},{sin(pi/2)});\n\\draw[red,thick] (axis cs:{cos(pi/2)},{sin(pi/2)}) -- (axis cs:{cos(pi)},{sin(pi)});\n\\end{axis}\n\\end{tikzpicture}\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[latin9]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1, inner sep=0.7mm]\n\n\\node (a) at (0,0) [shape=circle, draw=black, fill=black] {};\n\\node (b) at (1,0) [shape=circle, draw=black, fill=black] {};\n\\node (c) at (2,0) [shape=circle, draw=black, fill=black] {};\n\\node (d) at (3,0) [shape=circle, draw=black, fill=black] {};\n\\node (e) at (4,0) [shape=circle, draw=black, fill=black] {};\n\\node (f) at (5,0) [shape=circle, draw=black, fill=black] {};\n\\node (g) at (6,0) [shape=circle, draw=black, fill=black] {};\n\\node (h) at (7,0) [shape=circle, draw=black, fill=black] {};\n\n\\node (A) at (0,1) [shape=circle, draw=black, fill=black] {};\n\\node (B) at (1,1) [shape=circle, draw=black, fill=black] {};\n\\node (C) at (2,1) [shape=circle, draw=black, fill=black] {};\n\\node (D) at (3,1) [shape=circle, draw=black, fill=black] {};\n\\node (E) at (4,1) [shape=circle, draw=black, fill=black] {};\n\\node (F) at (5,1) [shape=circle, draw=black, fill=black] {};\n\\node (G) at (6,1) [shape=circle, draw=black, fill=black] {};\n\\node (H) at (7,1) [shape=circle, draw=black, fill=black] {};\n\n\\node (a') at (0,2) [shape=circle, draw=black, fill=black] {};\n\\node (b') at (1,2) [shape=circle, draw=black, fill=black] {};\n\\node (c') at (2,2) [shape=circle, draw=black, fill=black] {};\n\\node (d') at (3,2) [shape=circle, draw=black, fill=black] {};\n\\node (e') at (4,2) [shape=circle, draw=black, fill=black] {};\n\\node (f') at (5,2) [shape=circle, draw=black, fill=black] {};\n\\node (g') at (6,2) [shape=circle, draw=black, fill=black] {};\n\\node (h') at (7,2) [shape=circle, draw=black, fill=black] {};\n\n\\node (A') at (0,3) [shape=circle, draw=black, fill=black] {};\n\\node (B') at (1,3) [shape=circle, draw=black, fill=black] {};\n\\node (C') at (2,3) [shape=circle, draw=black, fill=black] {};\n\\node (D') at (3,3) [shape=circle, draw=black, fill=black] {};\n\\node (E') at (4,3) [shape=circle, draw=black, fill=black] {};\n\\node (F') at (5,3) [shape=circle, draw=black, fill=black] {};\n\\node (G') at (6,3) [shape=circle, draw=black, fill=black] {};\n\\node (H') at (7,3) [shape=circle, draw=black, fill=black] {};\n\n\\node (a'') at (0,4) [shape=circle, draw=black, fill=black] {};\n\\node (b'') at (1,4) [shape=circle, draw=black, fill=black] {};\n\\node (c'') at (2,4) [shape=circle, draw=black, fill=black] {};\n\\node (d'') at (3,4) [shape=circle, draw=black, fill=black] {};\n\\node (e'') at (4,4) [shape=circle, draw=black, fill=black] {};\n\\node (f'') at (5,4) [shape=circle, draw=black, fill=black] {};\n\\node (g'') at (6,4) [shape=circle, draw=black, fill=black] {};\n\\node (h'') at (7,4) [shape=circle, draw=black, fill=black] {};\n\n\\node (A'') at (0,5) [shape=circle, draw=black, fill=black] {};\n\\node (B'') at (1,5) [shape=circle, draw=black, fill=black] {};\n\\node (C'') at (2,5) [shape=circle, draw=black, fill=black] {};\n\\node (D'') at (3,5) [shape=circle, draw=black, fill=black] {};\n\\node (E'') at (4,5) [shape=circle, draw=black, fill=black] {};\n\\node (F'') at (5,5) [shape=circle, draw=black, fill=black] {};\n\\node (G'') at (6,5) [shape=circle, draw=black, fill=black] {};\n\\node (H'') at (7,5) [shape=circle, draw=black, fill=black] {};\n\n\\node (a''') at (0,6) [shape=circle, draw=black, fill=black] {};\n\\node (b''') at (1,6) [shape=circle, draw=black, fill=black] {};\n\\node (c''') at (2,6) [shape=circle, draw=black, fill=black] {};\n\\node (d''') at (3,6) [shape=circle, draw=black, fill=black] {};\n\\node (e''') at (4,6) [shape=circle, draw=black, fill=black] {};\n\\node (f''') at (5,6) [shape=circle, draw=black, fill=black] {};\n\\node (g''') at (6,6) [shape=circle, draw=black, fill=black] {};\n\\node (h''') at (7,6) [shape=circle, draw=black, fill=black] {};\n\n\n\\draw [thick, red] (a) to (A) to (b) to (B) to (c) to (C) to (d) to (D) to (e) to (E) to (f) to (F) to (g) to (G) to (h) to (H) to (a');\n\\draw [thick, blue] (A) to (a') to (B) to (b') to (C"
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    {
        "index": 350,
        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage{amssymb,amsmath}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix,arrows,decorations.pathmorphing,patterns,positioning,calc}\n\\usetikzlibrary{matrix}\n\\usetikzlibrary{matrix,positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n  back line/.style={densely dotted},\n  cross line/.style={preaction={draw=white, -,line width=6pt}},\n  node distance=2.5cm]\n  \\node (A) {$\\frac{s_1}{1-s_2}$};\n  \\node (B) [right of=A] {$\\frac{s_2}{1-s_3}$};\n  \\node (C) [right of=B] {$s_3$};\n  \\node (D) [right of=C] {$s_4$};\n  \\node (E) [right of=D] {$s_5$};\n  \\node (F) [right of=E] {$\\frac{s_6}{1-s_7}$};\n  \\node (G) [right of=F] {$s_7$};\n  \\draw[dotted] ($(A)!0.5!(B)$) -- ($(A)!0.5!(B)+(0,0.7)$);\n  \\draw[dotted] ($(D)!0.5!(E)$) -- ($(D)!0.5!(E)+(0,0.7)$);\n  \\draw[dotted] ($(E)!0.5!(F)$) -- ($(E)!0.5!(F)+(0,0.7)$);\n  \\draw[dotted] ($(E)!0.5!(F)+(0,-0.7)$) -- ($(G)!0.5!(G)$);\n  \\foreach \\i/\\j in {A/B,B/C,C/D,D/E,E/F,F/G}\n    \\draw[->] (\\i) -- (\\j);\n  \\foreach \\i/\\j in {A/B,B/C,C/D,D/E}\n    \\draw[->] (\\i.north) [cross line] to[bend left=60] (\\j.south);\n  \\foreach \\i/\\j in {E/F,F/G}\n    \\draw[->] (\\i.north) [cross line] to[bend right=60] (\\j.south);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 351,
        "tikz_code": "\\documentclass[letterpaper]{article}\n\\usepackage{tikz}\n\\usepackage{amssymb}\n\\usetikzlibrary{fit}\n\\usepackage{amsmath}\n\\usepackage{amssymb,textcomp}\n\\usepackage{amsmath,amsfonts}\n\\usepackage{xcolor}\n\\usetikzlibrary{arrows.meta}\n\\usetikzlibrary{shapes}\n\\usepackage{pgfplots}\n\\usepackage{pgffor}\n\\pgfplotsset{compat=1.12}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\\draw[->,black!80] (-0.3,0) -- (1.3,0);\n\t\t\\draw[->,black!80] (-0.3,-0.5) -- (-0.3,0.5);\n\t\t\\draw[->,black!80] (1.3,0.3) -- (1.3,0.7);\n\t\t\\draw[->,black!80] (-0.3,1) -- (1.3,1);\n\t\t\\draw[->,black!80] (-0.3,1.5) -- (-0.3,1.9);\n\t\t\\draw[->,black!80] (1.3,1.3) -- (1.3,1.7);\n\t\t\n\t\t\\draw[->,red!90] (0,0.3) -- (0,0.7);\n\t\t\\draw[->,red!90] (0.5,0.3) -- (0.5,0.7);\n\t\t\\draw[->,red!90] (1,0.3) -- (1,0.7);\n\t\t\n\t\t\\draw[->,blue!90] (-0.3,0.8) -- (-0.3,1.2);\n\t\t\\draw[->,blue!90] (0.5,0.8) -- (0.5,1.2);\n\t\t\\draw[->,blue!90] (1.3,0.8) -- (1.3,1.2);\n\t\t\n\t\t\\node[below] at (0,0) {$1$};\n\t\t\\node[below] at (1.3,0) {$4$};\n\t\t\\node[left] at (-0.3,0.5) {$2$};\n\t\t\\node[left] at (-0.3,1) {$1$};\n\t\t\\node[left] at (-0.3,1.5) {$0$};\n\t\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 352,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amssymb,amsmath,amsthm,tikz,multirow}\n\\usetikzlibrary{arrows,calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[>=latex,scale=1]\n\n\\foreach \\x in {0,...,3}\n\\foreach \\y in {0,...,3}\n\\foreach \\a in {0,...,5}\n\\foreach \\b in {0,...,5}\n\\draw[gray]\n\t(\\x,\\y) -- (0.3*\\a,0.3*\\b);\n\n\\foreach \\x in {0,...,3}\n\\foreach \\y in {0,...,3}\n\\draw[gray]\n\t(0.5*\\x,0.5*\\y) -- (0.5*\\x,3.5);\n\n\\foreach \\x in {0,...,3}\n\\foreach \\y in {0,...,3}\n\\draw[gray]\n\t(0.5*\\x,0.5*\\y) -- (3.5,0.5*\\y);\n\n\\fill[green!20]\n\t(1,1) -- (2,2) -- (1,3) -- (0,2) -- cycle\n\t(0.5,2.5) -- (1.5,3.5) -- (1,3) -- (0.5,2.5)\n\t(1.5,3.5) -- (2.5,2.5) -- (3,2) -- (2,1) -- cycle;\n\n\\fill[orange!20]\n\t(1,1) -- (2,2) -- (3,1) -- cycle\n\t(0.5,2.5) -- (1,2) -- (1.5,1.5) -- (0.5,1) -- cycle;\n\n\\fill[orange!20]\n\t(1,1) -- (3,1) -- (3,0) -- cycle\n\t(1,1) -- (1,0) -- (0,0.5) -- cycle;\n\n\\fill[green!20]\n\t(1,0) -- (3,0) -- (3,1) -- (1,1) -- cycle;\n\n\\draw[line width=1.5]\n\t(1,1) -- (2,2) -- (1,3) -- (0,2) -- cycle;\n\n\\draw[line width=1.5]\n\t(0.5,2.5) -- (1.5,3.5) -- (1,3) -- (0.5,2.5)\n\t(1.5,3.5) -- (2.5,2.5) -- (3,2) -- (2,1) -- cycle;\n\n\\draw[line width=1.5]\n\t(1,1) -- (3,1) -- (3,0) -- (1,0) -- cycle;\n\n\\draw[line width=1.5]\n\t(1,0) -- (1,1);\n\n\\draw[line width=1.5]\n\t(0,2) -- (1,1);\n\n\\draw[dashed]\n\t(0,2) -- (0,2.5);\n\n\\draw[dashed]\n\t(3,0) -- (3,0.5);\n\n\\draw[dashed]\n\t(1,3) arc (135:45:1);\n\n\\draw[dashed]\n\t(3,1) arc (-45:45:1.5);\n\n\\draw[line width=1.5]\n\t(1,1) -- (2,2) -- (3,1) -- (2,0) -- cycle;\n\n\\draw[dashed]\n\t(2,0) -- (2.5,0);\n\n\\draw[dashed]\n\t(2,2) -- (2,2.5);\n\n\\node at (3.2,0.6) {\\small $G_{\\alpha(u^q)}$};\n\\node at (2.5,3) {\\small $G_{\\alpha(u^q)'}$};\n\\node at (4.2,1.2) {\\small $G_{\\alpha(u^2q)}$};\n\n\\node at (2.2,0.2) {\\small $G_{\\alpha(u^2q)'}$};\n\n\\draw[->]\n\t(1.2,2.5) to[out=135,in=135] (1.8,3.1);\n\n\\draw[->]\n\t(1.5,1.2) to[out=-45,in=-45] (2.5,1.8);\n\n\\draw[->]\n\t(1.6,0.3) to[out=-135,in=-135] (2.4,0.3);\n\n\\draw[->]\n\t(1.9,2) to[out=-45,in=-45] (1.1,2);\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 353,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amssymb,epsfig,amsfonts}\n\\usepackage[usenames, dvipsnames]{color}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{xcolor}\n\\usepackage{tikz-cd}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{decorations.pathreplacing,calligraphy}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{shapes}\n\\usetikzlibrary{matrix}\n\\usetikzlibrary{positioning}\n\\usepackage{tcolorbox}\n\n\\newcommand{\\cC}{\\mathcal{C}}\n\n\\newcommand{\\bft}{\\textbf{t}}\n\n\\newcommand{\\talpha}{\\theta}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw [PineGreen,thick]  (0,0) -- (0,3);\n\\draw [PineGreen,thick]  (-3,0) -- (0,3);\n\\draw [PineGreen,thick]  (-3,0) -- (-3,1);\n\\draw [PineGreen,thick]  (0,3) -- (-3,1);\n\\draw [blue,fill=PineGreen,opacity=0.25]  (-3,0) -- (-3,1) -- (0,3) -- (0,2) -- (-1,1) -- (-3,0);\n\\draw [PineGreen,thick]  (0,2) -- (-1,1);\n\\draw [PineGreen,thick]  (-1,1) -- (-3,0);\n\\draw [PineGreen,thick]  (-1,1) -- (0,3);\n\\draw [red,thick,dashed] (-1.5,1.25) -- (0.8,2.7);\n\\node [PineGreen] at (1.2,2.6) {$(\\bt_1,\\bft_2,\\cC)$};\n\\node [PineGreen] at (-0.4,2.6) {$(\\bt_1,\\bft_2,\\cC,0)$};\n\\node [PineGreen] at (0.5,-0.2) {$\\alpha^*_1$};\n\\node [PineGreen] at (-3.3,-0.2) {$\\alpha^*_1$};\n\\node [PineGreen] at (-2.5,0.8) {$\\alpha^*_1$};\n\\node [PineGreen] at (-2.8,2.2) {$\\bft_2$};\n\\node [PineGreen] at (-0.2,2.8) {$\\bft_2$};\n\\node [PineGreen] at (-3.3,1.2) {$\\cC$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 354,
        "tikz_code": "\\documentclass[letterpaper]{article}\n\\usepackage{amsmath}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usepackage{tikzsymbols}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\\draw (0,0) node[inner sep=0] {\\includegraphics[width=3.5cm, height=2cm]{example-image}};\n\t\\draw (3,0) node[inner sep=0] {\\includegraphics[width=3.5cm, height=2cm]{example-image}};\n\t\\draw (0,-1.25) node {less fair};\n\t\\draw (0,-1.5) node {\\small less fair (less weight fair)};\n\t\\draw (3,-1.25) node {more fair};\n\t\\draw (3,-1.5) node {\\small weighted risk difference (more fair)};\n\t\\draw (-1.5,0) node[rotate=90] {utility};\n\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 355,
        "tikz_code": "\\documentclass[a4paper,11pt,twoside]{book}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usepackage[most]{tcolorbox}\n\\usepackage{colortbl}\n\\usepackage[customcolors,shade]{hf-tikz}\n\\usetikzlibrary{shapes,arrows,positioning}\n\\tikzset{\n    vertex/.style={circle,draw,minimum size=1.5em},\n    edge/.style={->,> = latex'}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\foreach \\x in {1, 2, 3, 4} \\node[vertex] (i\\x) at (\\x * 1.8, 0) {};\n\\foreach \\x in {1, 2, 3, 4} \\node[vertex] (o\\x) at (\\x * 1.8, -1) {};\n\\foreach \\x in {1, 2, 3, 4} \\node[vertex] (h1\\x) at (\\x * 1.8, -1.5) {};\n\\foreach \\x in {1, 2, 3, 4} \\node[vertex] (h2\\x) at (\\x * 1.8, -2) {};\n\\foreach \\x in {1, 2, 3, 4} \\node[vertex] (h3\\x) at (\\x * 1.8, -2.5) {};\n\n\\node (dots1) at (1.8, -2.25) {$\\vdots$};\n\\node (dots2) at (4.2, -2.25) {$\\vdots$};\n\n\\node (dots3) at (1.8, -3) {$\\vdots$};\n\\node (dots4) at (4.2, -3) {$\\vdots$};\n\n\\node (dots5) at (1.8, -3.75) {$\\vdots$};\n\\node (dots6) at (4.2, -3.75) {$\\vdots$};\n\n\\node (dots7) at (1.8, -4.5) {$\\vdots$};\n\\node (dots8) at (4.2, -4.5) {$\\vdots$};\n\n\\node[vertex, line width=0.75mm, fill=gray!30] (sum) at (6.3, -2.25) {$\\Sigma$};\n\n\\foreach \\x in {1, 2, 3, 4} \\node[vertex] (o9) at (8.1, -1) {};\n\n\\foreach \\x in {1, 2, 3, 4} \\draw (i1) -- (h1\\x);\n\\foreach \\x in {2, 3, 4} \\draw (h1\\x) -- (h21);\n\\foreach \\x in {3, 4} \\draw (h21) -- (h31);\n\n\\foreach \\x in {1, 2, 3, 4} \\draw (i2) -- (h1\\x);\n\\foreach \\x in {2, 3, 4} \\draw (h1\\x) -- (h22);\n\\foreach \\x in {3, 4} \\draw (h22) -- (h32);\n\n\\foreach \\x in {1, 2, 3, 4} \\draw (i3) -- (h1\\x);\n\\foreach \\x in {2, 3, 4} \\draw (h1\\x) -- (h23);\n\\foreach \\x in {3, 4} \\draw (h23) -- (h33);\n\n\\foreach \\x in {1, 2, 3, 4} \\draw (i4) -- (h1\\x);\n\\foreach \\x in {2, 3, 4} \\draw (h1\\x) -- (h24);\n\\foreach \\x in {3, 4} \\draw (h24) -- (h34);\n\n\\foreach \\x in {1, 2, 3, 4} \\draw (h31) -- (o\\x);\n\\foreach \\x in {2, 3, 4} \\draw (h32) -- (o\\x);\n\\foreach \\x in {3, 4} \\draw (h33) -- (o\\x);\n\n\\foreach \\x in {1, 2, 3, 4} \\draw (h34) -- (o\\x);\n\n\\foreach \\x in {1, 2, 3, 4} \\draw (o\\x) -- (o9);\n\n\\draw[->] (i1) -- (o1) node[midway, above] {$X_1$};\n\\draw[->] (i2) -- (o2) node[midway, above] {$X_2$};\n\\draw[->] (i3) -- (o3) node[midway, above] {$X_3$};\n\\draw[->] (i4) -- (o4) node[midway, above] {$X_4$};\n\n\\draw[->] (o9) -- (o9) node[midway, above] {$o(X_5)$};\n\\draw[->] (o9) -- (o10) node[near end, above] {Sample mean};\n\n\\draw[->] (o1) -- (o9) node[midway, above] {$o(X_1)$};\n\\draw[->] (o2) -- (o9) node[midway, above] {$o(X_2)$};\n\\draw[->] (o3) -- (o9) node[midway, above] {$o(X_3)$};\n\\draw[->] (o4) -- (o9) node[midway, above] {$o(X_4)$};\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
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        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usepackage{pgfplotstable}\n\\pgfplotsset{compat=newest}\n\\pgfplotsset{\n  % For available color names, see http://www.latextemplates.com/svgnames-colors\n  cycle list={TUMBlue\\\\TUMAccentOrange\\\\TUMAccentGreen\\\\TUMSecondaryBlue2\\\\TUMDarkGray\\\\},\n}\n\\usetikzlibrary{external}\n\\usetikzlibrary{backgrounds}\n\\usetikzlibrary{fadings}\n\\usetikzlibrary{shapes,decorations,shadows}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{arrows,positioning}\n\\usetikzlibrary{fit}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{axis}[\n    ybar,\n    height=8cm,\n    width=12cm,\n    ymin=0,\n    ymax=1,\n    %axis x line*=bottom,\n    %axis y line*=right,\n    legend style={at={(0,1)},anchor=north west,draw=none,legend columns=1,column sep=0.6cm},\n    legend cell align=left,\n    bar width=5pt,\n    ylabel={rate},\n    %ylabel shift = 2pt,\n    symbolic x coords={H,H1,H2,H3},\n    xtick=data,\n    ticklabel style = {font=\\scriptsize},\n    label style={font=\\scriptsize},\n    tickwidth=0pt,\n    enlarge x limits=0.2,\n    xtick pos=left,\n    ytick pos=left,\n    nodes near coords align={vertical},\n    legend entries={Coverage rate,Interval length,HBA},\n    legend to name=legend_tuning_op,\n    legend columns=3,\n    enlarge y limits={value=0.2,upper},\n    ]\n\n    % Coverage rate\n    \\addplot[fill=blue!40!white,draw=blue!60!black,postaction={pattern=north east lines}] coordinates {(H,0.74) (H1,0.73) (H2,0.75) (H3,0.75)};\n    \n    % Interval length\n    \\addplot[fill=orange!40!white,draw=orange!50!black,postaction={pattern=north west lines}] coordinates {(H,0.96) (H1,0.95) (H2,0.95) (H3,0.97)};\n    \n    % HBA\n    \\addplot[fill=brown!40!white,draw=brown!60!black,postaction={pattern=horizontal lines}] coordinates {(H,0.96) (H1,0.95) (H2,0.96) (H3,0.96)};\n    \n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 377,
        "tikz_code": "\\documentclass[11pt,a4paper]{amsart}\n\\usepackage{amssymb, amstext, amscd, amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\\tikzset{roundnode/.style={circle,draw=black!50,fill=black!20,inner sep=1.2pt}}\n\\tikzset{every loop/.style={}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[font=\\small,scale=0.6]\n\\foreach \\x in{1,...,8}{\n  \\node (\\x) at (\\x*360/8:4cm) [roundnode] {};\n}\n\\node at (1) [above] {$0$};\n\\node at (2) [left] {$0$};\n\\node at (3) [below] {$M_1(3)$};\n\\node at (4) [right] {$M_1(3)$};\n\\node at (5) [above] {$0$};\n\\node at (6) [left] {$0$};\n\\node at (7) [below] {$0$};\n\\node at (8) [right] {$0$};\n\\foreach \\x/\\y in{1/2,2/3,3/4,4/5,5/6,6/7,7/8,8/1}{\n  \\draw[dashed] (\\x) to (\\y);\n}\n\\draw[very thick] (1) -- (2);\n\\draw[very thick] (2) -- (3);\n\\draw[very thick] (3) -- (4);\n\\draw[very thick] (4) -- (5);\n\\draw[very thick] (5) -- (6);\n\\draw[very thick] (6) -- (7);\n\\draw[very thick] (7) -- (8);\n\\draw[very thick] (8) -- (1);\n\\draw[dashed] (1) -- (5);\n\\draw[dashed] (2) -- (6);\n\\draw[dashed] (3) -- (7);\n\\draw[dashed] (4) -- (8);\n\n\\node at (11) [above] {$\\times$};\n\\node at (10) [above] {$M_4(4)$};\n\\node at (9) [above] {$0$};\n\\foreach \\x/\\y in{11/2,11/5,10/6,9/7,9/4,9/1,10/3,10/8}{\n  \\node[roundnode] at (\\x) {};\n  \\node[roundnode] at (\\y) {};\n  \\draw[very thick] (\\x) -- (\\y);\n}\n\\draw[very thick] (11) -- (10);\n\n\\node at (11.5,-3) {$M_6(6)$};\n\\node at (2,-3) {$0$};\n\\node at (9,-3) {$0$};\n\\node at (4.5,-3) {$=$};\n\\node at (12.5,-3) {$=$};\n\\foreach \\x/\\y in{12/-1,12/2,13/-1,13/2,12/-3,12/5,13/-3,13/5,12/8,12/-5,13/8,13/-5}{\n  \\node[roundnode] at (\\x) {};\n  \\node[roundnode] at (\\y) {};\n  \\draw[very thick] (\\x) -- (\\y);\n}\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 378,
        "tikz_code": "\\documentclass{article}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath,amsfonts,bm}\n\\usepackage{amssymb}\n\\usepackage{colortbl}\n\\usepackage{tkz-euclide}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.14}\n\\usetikzlibrary{positioning,calc,fadings}\n\\usetikzlibrary{backgrounds}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n                \\node[] (D3C3A1) {\\includegraphics[width=\\columnwidth]{example-image}};\n                \\node[below = 0.2cm of D3C3A1] (D3C3A2) {\\includegraphics[width=\\columnwidth]{example-image}};\n                \\node[below = 0.2cm of D3C3A2] (D3C3A3) {\\includegraphics[width=\\columnwidth]{example-image}};\n\n                \\node[left = 0.5cm of D3C3A1] {$A_L$};\n                \\node[below = 0.1cm of D3C3A1] {$A_B$};\n                \\node[below = 0.1cm of D3C3A2] {$A_R$};\n                \\node[below = 0.1cm of D3C3A3] {$A_L$};\n            \\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 379,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{amsmath,amstext,amsgen,amsbsy,amsopn,amsfonts,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,decorations,arrows,automata,backgrounds,petri}\n\\usetikzlibrary{shapes.misc}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{patterns}\n\\tikzset{cross/.style={cross out, draw=black}}\n\\tikzset{circ/.style={circle,fill=white,draw=black}}\n\\tikzset{hasse/.style={circle, fill,inner sep=2pt}}\n\\tikzset{h/.style={circle, fill,inner sep=2pt}}\n\\tikzset{ns/.style={circle, draw,inner sep=2pt}}\n\\usepackage[latin1]{inputenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\t\\draw \t(1,0)--(1,2)\n\t\t\t\t\t(2,0)--(2,2)\n\t\t\t\t\t(2.5,0)--(2.5,2)\n\t\t\t\t\t(4,0)--(4,2);\n\t\t\t\\draw\t[dotted](1,1)--(2,0)\n\t\t\t\t\t(2.5,1)--(4,0);\n\t\t\t\\draw\t(2,1)--(4,1)\n\t\t\t\t\t(3,1)--(4,2);\n\t\t\t\\draw\t(2.5,1.5) node[cross]{};\n\t\t\t\\fill (3,1) circle [radius=1pt];\n\t\t\t\\fill (3.2,1) circle [radius=1pt];\n\t\t\t\\fill (2.8,1) circle [radius=1pt];\n\t\t\t\\draw [decorate,decoration={brace,amplitude=5pt}](1.8,1.3) -- (3.2,1.3);\n\t\t\t\\draw (2.5,1.6) node [] {$\\pm B^{\\pm}(d) (\\chi)$};\n\t\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 380,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{pgfplots}\n\\usetikzlibrary{patterns}\n\\usepackage{color}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.75]\n \\begin{axis}[grid = both,\n axis x line = middle,\n axis y line = middle,\n xticklabels={},\n yticklabels={},\n xmin=-4,\n xmax=4,\n ymin=-4,\n ymax=4]\n\\addplot[->, red, ultra thick] coordinates {(2,0) (2,1) (1,1) (1,0) (0,0) (1,-1) (1,-2)};\n\\addplot[->, red, ultra thick] coordinates {(2,1) (3,1)};\n\\addplot[->, red, ultra thick] coordinates {(1,0) (0,0)};\n\\addplot[->, red, ultra thick] coordinates {(2,-1) (3,-1)};\n\\addplot[->, red, ultra thick] coordinates {(1,-2) (0,-2)};\n\\addplot[->, red, ultra thick] coordinates {(0,0) (-1,0)};\n\\addplot[->, red, ultra thick] coordinates {(-1,-1) (-2,-1)};\n\\addplot[->, red, ultra thick] coordinates {(-1,0) (-2,0)};\n\\addplot[->, red, ultra thick] coordinates {(0,-2) (1,-2)};\n\\addplot[red, mark=*] coordinates {(2,1)};\n\\addplot[red, mark=*] coordinates {(1,0)};\n\\addplot[red, mark=*] coordinates {(1,-1)};\n\\addplot[red, mark=*] coordinates {(0,-2)};\n\\addplot[red, mark=*] coordinates {(2,0)};\n\\addplot[red, mark=*] coordinates {(1,1)};\n\\addplot[red, mark=*] coordinates {(1,-2)};\n\\addplot[red, mark=*] coordinates {(0,0)};\n\\addplot[red, mark=*] coordinates {(-1,0)};\n\\addplot[red, mark=*] coordinates {(-1,-1)};\n\\addplot[red, mark=*] coordinates {(0,-2)};\n\\addplot[red, mark=*] coordinates {(-1,-2)};\n\\addplot[red, mark=*] coordinates {(0,0)};\n\\addplot[red, mark=*] coordinates {(0,0)};\n \\end{axis}\n \\end{tikzpicture}\n\n\\end{document}"
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        "index": 381,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{tikz-cd}\n\\usepackage{tkz-euclide}\n\\usepackage{xcolor}\n\\usetikzlibrary{shapes.geometric}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.2, vert/.style={circle, draw=black, fill=black, inner sep = 0pt, minimum size = 1mm}]\n\n\\node[vert, label=left:{\\small$p_{-1}$}] (p) at (-2,0) {};\n\\node[vert, label=below:{\\small$p_0$}] (q) at (0,0) {};\n\\node[vert, label=below:{\\small$p_1$}] (r) at (2,0) {};\n\n\\node[vert, label=above:{\\small$p_2$}] (p2) at (-5,1.5) {};\n\\node[vert, label=above:{\\small$p_3$}] (p3) at (-4,2.5) {};\n\\node[vert, label=above:{\\small$p_4$}] (p4) at (-3,3.5) {};\n\\node[vert, label=above:{\\small$p_5$}] (p5) at (-2,4.5) {};\n\n\\node[vert, label=above:{\\small$p_{12}$}] (p12) at (5,1.5) {};\n\\node[vert, label=above:{\\small$p_{13}$}] (p13) at (4,2.5) {};\n\\node[vert, label=above:{\\small$p_{14}$}] (p14) at (3,3.5) {};\n\\node[vert, label=above:{\\small$p_{15}$}] (p15) at (2,4.5) {};\n\n\\draw[thick] (p) -- (p12) -- (p15) -- (p5) -- (p4) -- (p3) -- (p2) -- (p);\n\\draw[thick] (p) -- (r) -- (q) -- (p);\n\\draw[thick, dashed] (p) -- (p5) -- (p15);\n\\draw[thick, dashed] (p) -- (p4) -- (p14);\n\\draw[thick, dashed] (p) -- (p3) -- (p13);\n\\draw[thick, dashed] (p) -- (p2) -- (p12);\n\n\\draw[red, thick] (p) .. controls +(250:5) and +(300:5) .. (q) .. controls +(60:5) and +(120:5) .. (r) .. controls +(-120:5) and +(-60:5) .. (p);\n\n\\node[label=right:{\\small$\\alpha$}] (a) at (1,-0.7) {};\n\\node[label=right:{\\small$\\beta$}] (b) at (1.4,0.7) {};\n\\node[label=left:{\\small$\\gamma$}] (c) at (-1.4,-0.7) {};\n\\node[label=left:{\\small$\\delta$}] (d) at (-1,-0.7) {};\n\n\\draw[thick] (p) -- (a) -- (r);\n\\draw[thick] (p) -- (b) -- (r);\n\\draw[thick] (p) -- (c) -- (r);\n\\draw[thick] (p) -- (d) -- (r);\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[colorlinks=true, linkcolor=blue, citecolor=blue]{hyperref}\n\\usepackage{color,mathrsfs}\n\\usepackage{cite,graphicx,subfigure,amsmath,amssymb,amsfonts,bm,epsfig,epsf,url,dsfont}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n  [scale=.4,auto=left,every node/.style={circle,fill=black!100,inner sep=0pt, minimum size=4.5pt}]\n  \\node (n6) at (13,9)  {};\n  \\node (n5) at (13,7)  {};\n  \\node (n4) at (13,5)  {};\n  \\node (n3) at (13,3)  {};\n  \\node (n2) at (13,1)  {};\n  \\node (n1) at (10,5) {};\n  \\node (n13) at (17,5) {};\n  \\node (n14) at (20,5) {};\n\n  \\node (n7) at (13,13) [label=left:$t$]{};\n  \\node (n8) at (13,9) [label=right:$u$]{};\n  \\node (n9) at (13,7) [label=right:$v$]{};\n  \\node (n10) at (13,5) [label=right:$w$]{};\n  \\node (n11) at (13,3) [label=right:$x$]{};\n  \\node (n12) at (13,1) [label=left:$y$]{};\n  \\node (n15) at (10,1) [label=below:$C_u$] {};\n  \\node (n16) at (20,1) [label=below:$C_v$] {};\n\n  \\foreach \\from/\\to in {n1/n12,n1/n13,n1/n14,n5/n13,n5/n14,n4/n13,n4/n14,n6/n13,n6/n14}\n    \\draw [color=blue,line width=3.5pt](\\from) -- (\\to);\n  \\foreach \\from/\\to in {n7/n8,n7/n9,n7/n10,n7/n11,n7/n12,n7/n13,n7/n14}\n    \\draw [color=red,line width=3.5pt](\\from) -- (\\to);\n\n  \\foreach \\from/\\to in {n15/n16}\n    \\draw [color=black,dashed,line width=1.5pt](\\from) -- (\\to);\n\n\n  \\draw[rotate around={45:(15,7)}] (15,7) ellipse (2.5 and 7.5);\n  \\draw[rotate around={-45:(15,7)}] (15,7) ellipse (2.5 and 7.5);\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usetikzlibrary{decorations.pathmorphing,shapes,arrows}\n\\tikzset{node distance=2cm, auto}\n\\usetikzlibrary{positioning}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw (-5,0) node {Starting values: $H^{n} \\Psi = {1,...}, N^{n}$ given};\n\\draw (-3.5, -1) node {$\\dots$};\n\\draw (-3.5, -2) node {$K^{n}$};\n\\draw (-3.5, -3) node {$H^{n}$};\n\\draw (-3.5, -4) node {$H^{n}$};\n\\draw (-3.5, -5) node {$H^{n}$};\n\\draw (-3.5, -6) node {$H^{n}$};\n\\draw (-3.5, -7) node {$\\dots$};\n\\draw (-3.5, -8) node {$\\dots$};\n\\draw (-3.5, -9) node {$H^{n}$};\n\\draw (-3.5, -10) node {$\\vdots$};\n\\draw (-3.5, -11) node {$H^{n}$};\n\\draw (-3.5, -12) node {$H^{n}$};\n\\draw (-3.5, -13) node {$K^{n}$};\n\\draw (-3.5, -14) node {$K^{n}$};\n\\draw (-3.5, -15) node {$\\dots$};\n\\draw (-3.5, -16) node {$\\dots$};\n\\draw (-3.5, -17) node {$K^{n}$};\n\\draw (-3.5, -18) node {$K^{n}$};\n\\draw (-3.5, -19) node {$\\vdots$};\n\\draw (-3.5, -20) node {$H^{n}$};\n\\draw (-3.5, -21) node {$\\vdots$};\n\\draw (-3.5, -22) node {$\\vdots$};\n\\draw (-3.5, -23) node {$\\vdots$};\n\\draw (-3.5, -24) node {$\\vdots$};\n\\draw (-3.5, -25) node {$\\vdots$};\n\\draw (-3.5, -26) node {$\\vdots$};\n\\draw (-3.5, -27) node {$\\vdots$};\n\\draw (-3.5, -28) node {$\\vdots$};\n\\draw (-3.5, -29) node {$K^{n}$};\n\\draw (-3.5, -30) node {$K^{n}$};\n\\draw (-3.5, -31) node {$\\dots$};\n\\draw (-3.5, -32) node {$\\dots$};\n\\draw (-3.5, -33) node {$K^{n}$};\n\\draw (-3.5, -34) node {$K^{n}$};\n\\draw (-3.5, -35) node {$\\dots$};\n\\draw (-3.5, -36) node {$\\dots$};\n\\draw (-3.5, -37) node {$K^{n}$};\n\\draw (-3.5, -38) node {$K^{n}$};\n\\draw (-3.5, -39) node {$\\dots$};\n\\draw (-3.5, -40) node {$\\dots$};\n\\draw (-3.5, -41) node {$H^{n}$};\n\\draw (-3.5, -42) node {$\\vdots$};\n\\draw (-3.5, -43) node {$H^{n}$};\n\\draw (-3.5, -44) node {$\\vdots$};\n\\draw (-3.5, -45) node {$H^{n}$};\n\\draw (-3.5, -46) node {$\\vdots$};\n\\draw (-3.5, -47) node {$H^{n}$};\n\\draw (-3.5, -48) node {$H^{n}$};\n\\draw (-3.5, -49) node {$\\dots$};\n\\draw (-3.5, -50) node {$\\dots$};\n\\draw (-3.5, -51) node {$H^{n}$};\n\\draw (-3.5, -52) node {$H^{n}$};\n\\draw (-3.5, -53) node {$K^{n}$};\n\\draw (-3.5, -54) node {$K^{n}$};\n\\draw (-3.5, -55) node {$\\dots$};\n\\draw (-3.5, -56) node {$\\dots$};\n\\draw (-3.5, -57) node {$K^{n}$};\n\\draw (-3.5, -58) node {$K^{n}$};\n\\draw (-3.5, -59) node {$\\dots$};\n\\draw (-3.5, -60) node {$\\dots$};\n\\draw (-3.5, -61) node {$K^{n}$};\n\\draw (-3.5, -62) node {$K^{n}$};\n\\draw (-3.5, -63) node {$\\dots$};\n\\draw (-3.5, -64) node {$\\dots$};\n\\draw (-3.5, -65) node {$K^{n}$};\n\\draw (-3.5, -66) node {$K^{n}$};\n\\draw (-3.5, -67) node {$\\dots$};\n\\draw (-3.5, -68) node {$\\dots$};\n\\draw (-3.5, -69) node {$H^{n}$};\n\\draw (-3.5, -70) node {$H^{n}$};\n\\draw (-3.5, -71) node {$\\vdots$};\n\\draw (-3.5, -72) node {$\\vdots$};\n\\draw (-3.5, -73) node {$H^{n}$};\n\\draw (-3.5, -74) node {$\\vdots$};\n\\draw (-3.5, -75) node {$H^{n}$};\n\\draw"
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        "index": 384,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{xcolor}\n\\usepackage{amssymb,latexsym}\n\\usepackage{amsmath}\n\\usepackage{tikz-cd}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\\draw (-2,0) to[bend right = 60] (2,0);\n\\draw (-2,0) to[bend left = 60] (2,0);\n\\draw[red,line width = 1.3] (-1,0) to[bend right = 80] (1,0);\n\\draw[red,line width = 1.3] (-1,0) to[bend left = 80] (1,0);\n\n\\draw[red,line width = 1.3] (-1,0) to[out = 30, in = 150] (1,0);\n\\draw[red,line width = 1.3] (-1,0) to[out = 210, in = 300] (1,0);\n\n\\draw[green,line width = 1.3] (-1,0) to[out = 90, in = 90] (1,0);\n\\draw[green,line width = 1.3] (-1,0) to[out = 270, in = 270] (1,0);\n\n\\draw (-1,0) to[out = 60, in = -60] (-0.125,0.25);\n\\draw (1,0) to[out = 120, in = -120] (0.125,0.25);\n\n\\draw[dashed] (-1,0) to[out = -60, in = 60] (-0.125,-0.25);\n\\draw[dashed] (1,0) to[out = -120, in = 120] (0.125,-0.25);\n\n\\draw[blue,line width = 1.3] (-1,0) to[out = 50, in = -140] (-0.125,-0.25);\n\\draw[blue,line width = 1.3] (-1,0) to[out = 130, in = -20] (-0.125,0.25);\n\n\n\\draw (-1.5,0) to[out = 30, in = 150] (1.5,0);\n\\draw[red,line width = 1.3] (-1.5,0) to[out = -30, in = -150] (1.5,0);\n\n\\draw[green,line width = 1.3] (-1.5,0) to[out = 90, in = 90] (1.5,0);\n\\draw[green,line width = 1.3] (-1.5,0) to[out = 270, in = 270] (1.5,0);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 385,
        "tikz_code": "\\documentclass[12pt,a4paper, twoside,reqno]{amsart}\n\\usepackage{amsmath,amssymb,amsthm,mathrsfs}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{matrix,arrows,decorations.pathmorphing,decorations.markings,calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node at (0,0){\\includegraphics[scale =.2]{example-image}};\n\\draw[thin, ->] (.15,-.1)--(-.1,.15);\n\\draw[thin, ->] (.2,-.1)--(.7,-.8);\n\\node at (.6,-.7){$1$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 386,
        "tikz_code": "\\documentclass[12pt,a4paper]{amsart}\n\\usepackage[latin1]{inputenc}\n\\usepackage{amssymb}\n\\usepackage{pgf, tikz}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5]\n\\tikzstyle{every node} = [circle, fill=white, draw=black,\n                        inner sep=0pt, minimum width=5pt]\n\\node[fill=black, draw=black] at (0,0) {};\n\\node[fill=black, draw=black] at (2,0) {};\n\\node[fill=black, draw=black] at (4,0) {};\n\\node[fill=black, draw=black] at (6,0) {};\n\\node[fill=black, draw=black] at (8,0) {};\n\\node[fill=black, draw=black] at (2,2) {};\n\\node[fill=black, draw=black] at (4,2) {};\n\\node[fill=black, draw=black] at (6,2) {};\n\\node[fill=black, draw=black] at (8,2) {};\n\\node[fill=black, draw=black] at (0,3) {};\n\\node[fill=black, draw=black] at (2,3) {};\n\\node[fill=black, draw=black] at (4,3) {};\n\\node[fill=black, draw=black] at (6,3) {};\n\\node[fill=black, draw=black] at (8,3) {};\n\n\n\\draw (0,0) -- (2,0);\n\\draw (2,0) -- (4,0);\n\\draw (4,0) -- (6,0);\n\\draw (6,0) -- (8,0);\n\\draw (0,0) -- (2,2);\n\\draw (2,0) -- (4,2);\n\\draw (4,0) -- (6,2);\n\\draw (6,0) -- (8,2);\n\n\\draw (0,0) -- (2,3);\n\\draw (2,0) -- (4,3);\n\\draw (4,0) -- (6,3);\n\\draw (6,0) -- (8,3);\n\n\\draw (0,0) .. controls (1,3) and (7,3) .. (8,0);\n\\draw (0,0) .. controls (1,1) and (7,1) .. (8,0);\n\\draw (0,0) .. controls (1,0.5) and (7,0.5) .. (8,0);\n\\draw (0,0) .. controls (1,0) and (7,0) .. (8,0);\n\n\\draw (2,0) .. controls (2.5,1.5) and (5.5,1.5) .. (6,0);\n\\draw (2,0) .. controls (2.5,0.5) and (5.5,0.5) .. (6,0);\n\\draw (2,0) .. controls (2.5,0) and (5.5,0) .. (6,0);\n\n\\draw (4,0) .. controls (4.5,0.5) and (5.5,0.5) .. (6,0);\n\\draw (4,0) .. controls (4.5,1) and (5.5,1) .. (6,0);\n\\draw (4,0) .. controls (4.5,1.5) and (5.5,1.5) .. (6,0);\n\n\\draw (8,0) .. controls (7.5,0.5) and (6.5,0.5) .. (6,0);\n\\draw (8,0) .. controls (7.5,1) and (6.5,1) .. (6,0);\n\\draw (8,0) .. controls (7.5,1.5) and (6.5,1.5) .. (6,0);\n\n\\draw (0,3) .. controls (-0.5,4) and (9.5,4) .. (10,3);\n\\draw (0,3) .. controls (-0.5,2) and (9.5,2) .. (10,3);\n\\draw (0,3) .. controls (-0.5,1.5) and (9.5,1.5) .. (10,3);\n\\draw (0,3) .. controls (-0.5,1) and (9.5,1) .. (10,3);\n\n\\draw (2,3) .. controls (1.5,4) and (7.5,4) .. (8,3);\n\\draw (2,3) .. controls (1.5,2) and (7.5,2) .. (8,3);\n\\draw (2,3) .. controls (1.5,1.5) and (7.5,1.5) .. (8,3);\n\\draw (2,3) .. controls (1.5,1) and (7.5,1) .. (8,3);\n\n\\draw (4,3) .. controls (4.5,4) and (5.5,4) .. (6,3);\n\\draw (4,3) .. controls (4.5,2) and (5.5,2) .. (6,3);\n\\draw (4,3) .. controls (4.5,1.5) and (5.5,1.5) .. (6,3);\n\\draw (4,3) .. controls (4.5,1) and (5.5,1) .. (6,3);\n\n\\draw (6,3) .. controls (6.5,4) and (7.5,4) .. (8,3);\n\\draw (6,3) .. controls (6.5,2) and (7.5,2) .. (8,3);\n\\draw (6,3) .. controls (6.5,1.5) and (7.5,1.5) .. (8,3);\n\\draw (6,3) .. controls (6.5,1) and (7.5,1) .. (8,3);\n\n\n\\draw (0,0) node[right] {$000$};\n\\draw (2,0) node[right] {$001$};\n\\draw (4,0) node[right] {$010$};\n\\draw (6,0) node[right] {$011$};\n\\draw (8,0) node[right] {$100$};\n\\draw (0,3) node[right] {$0000$};\n\\draw (2,3) node[right] {$0001$};\n\\draw (4,3) node[right] {$0010$};\n\\draw (6,3) node[right] {$0011$};\n\\draw (8,3) node[right] {"
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    {
        "index": 387,
        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\\node (1) at (0,0) {\\includegraphics[width=7cm]{example-image}};\n\n\\node (2) at (5.5,0) {\\includegraphics[width=3.5cm]{example-image}};\n\\node (3) at (-5.5,0) {\\includegraphics[width=3.5cm]{example-image}};\n\\node (5) at (5.5,2.4) {$\\tilde{J}_s$};\n\\node (6) at (-5.5,2.4) {$\\tilde{J}_s$};\n\\node (7) at (0,1.2) {$\\tilde{J}$};\n\\node (8) at (0,3.5) {$g\\to 0$};\n\\node (8) at (0,-3.5) {$g\\to 0$};\n\\node (9) at (6.5,2) {$\\mathcal{R}_{\\epsilon,\\tilde{J}}^{g\\to 0} \\to \\mathcal{R}_{\\epsilon,\\tilde{J}}^{g\\to \\infty}$};\n\\node (9) at (-6.5,2) {$\\mathcal{R}_{\\epsilon,\\tilde{J}}^{g\\to 0} \\to \\mathcal{R}_{\\epsilon,\\tilde{J}}^{g\\to \\infty}$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 388,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{shapes.geometric,calc,arrows, positioning,shapes.misc,decorations.markings}\n\\tikzset{\n  big arrow/.style={\n    decoration={markings,mark=at position 1 with {\\arrow[scale=2,#1]{>}}},\n    postaction={decorate},\n    shorten >=0.4pt},\n  big arrow/.default=black}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node (v1) at (8,0) {\\tiny{$w$-$x$}};\n\\node (v1_1) at (11,0) {\\tiny{$w$-$x$}};\n\\node (v2) at (8,2) {\\tiny{$w$-$x$}};\n\\node (v1_1_1) at (11,2) {\\tiny{$w$-$x$}};\n\\node (v5) at (12.5,0) {\\tiny{$w$-$x$}};\n\\node (v1_2) at (13,0) {\\tiny{$w$-$x$}};\n\\node (v1_3) at (14,0) {\\tiny{$w$-$x$}};\n\\node (v1_4) at (15,0) {\\tiny{$w$-$x$}};\n\\draw  (v1_4) edge (v1_3);\n\\draw  (v1_3) edge (v1_2);\n\\draw  (v1_2) edge (v1_1_1);\n\\draw  (v1_1_1) edge (v1_1);\n\\draw  (v2) edge (v1);\n\\draw  (v1_1_1) edge (v2);\n\\node at (9.5,0.4) {\\tiny{$n$}};\n\\node at (10.5,0.4) {\\tiny{$n$}};\n\\node at (12,1) {\\tiny{$n$-$m$}};\n\\node at (13.5,0.4) {\\tiny{$n$}};\n\\node at (14.45,0.4) {\\tiny{$n$}};\n\\node at (15.5,0.4) {\\tiny{$n$}};\n\\draw[dashed]  (v1_4) edge (v1_1);\n\\node at (10.5,1) {\\tiny{$2$}};\n\\node at (12.5,1) {\\tiny{$2$}};\n\\node at (14.25,1) {\\tiny{$2$}};\n\\node (v1_5) at (12.5,2) {\\tiny{$n$}};\n\\draw  (v5) edge (v1_5);\n\\draw  (v1_5) edge (v1_1_1);\n\\draw  (v1) edge (v1_2);\n\\node at (8.6,0.4) {\\tiny{$1$}};\n\\node at (10.25,1.6) {\\tiny{$1$}};\n\\node at (11.6,0.4) {\\tiny{$1$}};\n\\node at (12.25,1.6) {\\tiny{$1$}};\n\\node at (12.85,0.4) {\\tiny{$1$}};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 389,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amssymb,color,bbm,theorem}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,automata}\n\\usepackage{pgf,tikz}\n\\usetikzlibrary{arrows,decorations.pathmorphing,backgrounds,positioning,fit,petri}\n\\usepackage{tikz-3dplot}\n\\usepackage{pgfplots}\n\\usepackage{xcolor}\n\\usetikzlibrary{shapes.geometric}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n[\nscale = 1.0,\nnormal/.style={trapezium, trapezium angle=67.5, draw, fill=yellow!20,\n    text width=1.5cm, text badly centered, node distance=3cm, inner sep=0pt}\n]\n\n\\node at (-3, -0.5) {index $1$};\n\\node at (-3, -1) {$\\vdots$};\n\\node at (-3, -1.5) {index $\\Delta_1-1$};\n\\node at (-1, -1.5) {index $\\Delta_1$};\n\\node at (1, -1.5) {index $\\Delta_1+1$};\n\\node at (3, -1.5) {index $\\Delta_1+\\Delta_2-1$};\n\\node at (5, -1.5) {$\\cdots$};\n\\node at (7, -1.5) {index $\\Delta_2+\\Delta_3-1$};\n\\node at (9, -1.5) {index $\\Delta_2+\\Delta_3+\\Delta_1-1$};\n\\node at (-3, -2.5) {...};\n\\node at (9, -2.5) {...};\n\n\\node [normal] at (0, 0) {\\parbox{2.2cm} {$+\\delta_1$\\\\\n  $\\Delta_1$}};\n\\node [normal] at (4, 0) {\\parbox{2.2cm} {$+\\delta_1$\\\\\n  $\\Delta_1+\\Delta_2$}};\n\\node [normal] at (8, 0) {\\parbox{2.2cm} {$+\\delta_1$\\\\\n  $\\Delta_1+\\Delta_2+\\Delta_3$}};\n\n\\node [normal] at (0, -2) {\\parbox{2.2cm} {$+\\delta_1$\\\\\n  $\\Delta_1$}};\n\\node [normal] at (4, -2) {\\parbox{2.2cm} {$+\\delta_1$\\\\\n  $\\Delta_1+\\Delta_2$}};\n\\node [normal] at (8, -2) {\\parbox{2.2cm} {$+\\delta_1$\\\\\n  $\\Delta_1+\\Delta_2+\\Delta_3$}};\n\n\\path[->] (0, -0.5) edge node[above, font=\\footnotesize]{$+\\delta_1$} (4, -1.5);\n\\path[->] (0, -1.5) edge node[below, font=\\footnotesize]{$+\\delta_1$} (4, -0.5);\n\n\\path[->] (4, -0.5) edge node[above, font=\\footnotesize]{$+\\delta_1$} (8, -1.5);\n\\path[->] (4, -1.5) edge node[below, font=\\footnotesize]{$+\\delta_1$} (8, -0.5);\n\n\\path[->] (0, -2.5) edge node[above, font=\\footnotesize]{$+\\delta_1$} (4, -3.5);\n\\path[->] (0, -3.5) edge node[below, font=\\footnotesize]{$+\\delta_1$} (4, -2.5);\n\n\\path[->] (4, -2.5) edge node[above, font=\\footnotesize]{$+\\delta_1$} (8, -3.5);\n\\path[->] (4, -3.5) edge node[below, font=\\footnotesize]{$+\\delta_1$} (8, -2.5);\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 390,
        "tikz_code": "\\documentclass[journal,12pt,draftclsnofoot,onecolumn]{IEEEtran}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,arrows,positioning,calc}\n\\usepackage{pgfplotstable}\n\n\\begin{document}\n\n\\begin{tikzpicture}[font=\\footnotesize,scale=0.7]\n\\draw [thick] (0,0) rectangle (4,2.5);\n\\draw [thick] (0,2.5) rectangle (4,4);\n\\draw [thick] (0,4) rectangle (4,5.5);\n\\draw [thick] (0,5.5) rectangle (4,7);\n\\node at (2,2.25) {\\textsc{Analog}};\n\\node at (2,3.75) {\\textsc{Front-End}};\n\\node at (2,5.25) {\\textsc{Battery}};\n\\node at (2,6.75) {\\textsc{Processing}};\n\\draw [->,thick] (5,2.25) -- ++(-2,0) -- ++(0,2) -- ++(4,0) -- ++(0,-2) -- ++(-2,0);\n\\node at (3.5,2.25) {\\textsc{ADC}};\n\\node at (3.5,3.75) {\\textsc{ADC}};\n\\node at (3.5,5.25) {\\textsc{55Gs}};\n\\node at (3.5,6.75) {\\textsc{DAC}};\n\\node at (6,3.75) {\\textsc{FPGA}};\n\\draw [thick] (6,4) rectangle (10,5.5);\n\\node at (8,3.75) {\\textsc{FPGA}};\n\\draw [thick] (10,4) rectangle (14,5.5);\n\\node at (12,3.75) {\\textsc{ZU4DR}};\n\\draw [thick] (14,4) rectangle (18,5.5);\n\\node at (16,3.75) {\\textsc{Host}};\n\\draw [thick] (18,3.75) rectangle (22,4.25);\n\\node at (20,3.75) {\\textsc{Recording}};\n\\draw [->,thick] (6,3.75) -- (8,3.75);\n\\draw [->,thick] (10,3.75) -- (12,3.75);\n\\draw [->,thick] (14,3.75) -- (16,3.75);\n\\draw [->,thick] (18,3.75) -- (20,3.75);\n\\node at (10,5.25) {\\textsc{100 GHz's}};\n\\node at (10,6.75) {\\textsc{100 GHz's}};\n\\draw [->,thick] (20,3.75) -- ++(-2,0) -- ++(0,2.75) -- ++(4,0) -- ++(0,-2.75) -- ++(-2,0);\n\\node at (18,3.75) {\\textsc{5GTZR8FBO}};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amsmath,amsthm,amssymb,amsfonts, stmaryrd}\n\\usepackage{color, graphicx}\n\\usepackage[T1]{fontenc}\n\\usepackage[usenames,dvipsnames,svgnames,table]{xcolor}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[xscale=1.4, yscale=1.2]\n\\draw (-1.5,0) node[draw, circle, minimum size=6mm] (v21) {$U_2$};\n\\draw (0,1) node[draw, circle, minimum size=6mm] (v22) {$V_2$};\n\\draw (0,-1) node[draw, circle, minimum size=6mm] (v23) {$V_1$};\n\\draw (0,2) node[draw, circle, minimum size=6mm] (v24) {$V_3$};\n\n\\draw (1,0) node[draw, circle, minimum size=6mm] (v11) {$V_4$};\n\\draw (1.5,1) node[draw, circle, minimum size=6mm] (v12) {$V_5$};\n\\draw (1.5,-1) node[draw, circle, minimum size=6mm] (v13) {$V_6$};\n\n\\draw (2.5,0) node[draw, circle, minimum size=6mm] (v31) {$U_3$};\n\\draw (4,0) node[draw, circle, minimum size=6mm] (v32) {$U_4$};\n\\draw (5.5,0) node[draw, circle, minimum size=6mm] (v33) {$U_5$};\n\n\\draw (0,3) node[draw, circle, minimum size=6mm] (v14) {$U_3$};\n\n\\draw (v21) -- (v22);\n\\draw (v21) -- (v23);\n\\draw [dashed] (v22) -- (v23);\n\\draw [dashed] (v24) -- (v22);\n\n\\draw [dashed] (v11) -- (v12);\n\\draw [dashed] (v11) -- (v13);\n\\draw (v12) -- (v13);\n\n\\draw [dashed] (v31) -- (v32);\n\\draw [dashed] (v31) -- (v33);\n\\draw (v32) -- (v33);\n\n\\draw (v24) -- (v14);\n\\draw (v14) -- (v12);\n\\draw (v14) -- (v13);\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n\\node (A) at (0,0) {$\\mathbb{A}^n$};\n\\node (RT) at (-6,-6) {$\\mathbb{R}\\mathrm{T}$};\n\\node (ACA) at (6,6) {$\\mathbb{A}\\mathrm{C}\\mathrm{A}$};\n\\node (RT2) at (-4.5,-1.5) {$\\mathbb{R}\\mathrm{T}^2$};\n\\node (ACA2) at (4.5,4.5) {$\\mathbb{A}\\mathrm{C}\\mathrm{A}^2$};\n\\node (K) at (0,1.5) {$\\mathrm{K}\\mathrm{L}\\mathrm{A}$};\n\\node (RCA) at (0,-1.5) {$\\mathbb{R}\\mathrm{C}\\mathrm{A}_n$};\n\\node (WK) at (2,0) {$\\mathrm{W}\\mathrm{K}\\mathrm{L}\\mathrm{A}$};\n\\node (A1) at (0,-4.5) {$\\mathbb{A}^1$};\n\\node (RTA) at (-5,-2) {$\\mathbb{R}\\mathrm{T}^{\\geq2}$};\n\\node (T1) at (0,-6) {$\\mathbb{P}\\mathrm{R}^2$};\n\\draw[->] (A) to (RT);\n\\draw[->] (RT) to (RTA);\n\\draw[->] (RT) to (RT2);\n\\draw[->] (RT) to (RTA);\n\\draw[->] (RT2) to (ACA2);\n\\draw[->] (RTA) to (ACA2);\n\\draw[->] (A) to (ACA);\n\\draw[->] (RT) to (A1);\n\\draw[->] (A1) to (T1);\n\\draw[->] (RTA) to (T1);\n\\draw[->] (RT) to (RCA);\n\\draw[->] (RT2) to (RT);\n\\draw[->] (RT2) to (RCA);\n\\draw[->] (RT2) to (RCA);\n\\draw[->] (RT) to (K);\n\\draw[->] (RT) to (WK);\n\\draw[->] (RCA) to (K);\n\\draw[->] (ACA) to (ACA2);\n\\draw[->] (K) to (ACA2);\n\\draw[->] (RCA) to (RCA);\n\\draw[->] (RCA) to (WK);\n\\draw[->] (WK) to (K);\n\\draw[->] (RTA) to (WK);\n\\draw[->] (ACA) to (A);\n\\draw[->] (A1) to (A);\n\\draw[->] (A1) to (RTA);\n\\draw[->] (RT2) to [out=-10,in=170] (T1);\n\\draw[->] (RTA) to [out=20,in=170] (T1);\n\\node[right, text width=1.8cm] at (8.4,-3.8) {Connected Component Estimate};\n\\node[right, text width=1.8cm] at (3.5,0.7) {WKL HeuristicTheorem};\n\\node[left, text width=1.8cm] at (-2.5,2.3) {Catagory};\n\\node[right, text width=1.8cm] at (2.5,2.3) {RCA $\\leq WKL$ (UniformConnectivity)};\n\\node[right, text width=1.8cm] at (2.3,-0.4) {$\\Delta$-CA $\\leq WKL$};\n\\node[right, text width=1.8cm] at (2.3,-2.9) {$\\Delta$-CA};\n\\node[right, text width=1.8cm] at (2.3,-2.1) {$\\cong$};\n\\node[right, text width=1.8cm] at (-3.5,-2.1) {$\\cong$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 394,
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        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amssymb}\n\\usepackage[utf8]{inputenc}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.1]\n\\draw[ultra thick,blue] (0,0) -- (2,0)node [black,above,midway] {$\\epsilon_1$};\n\\draw[ultra thick,orange] (2,0) -- (3.5,0)node [black,above,midway] {$\\epsilon_2$};\n\\draw[ultra thick,blue] (4,0) -- (9,0)node [black,above,midway] {$\\epsilon_3$};\n\\draw[ultra thick,blue] (9,0) -- (10.5,0)node [black,above,midway] {$\\epsilon_4$};\n\\draw[ultra thick,blue] (10.5,0) -- (14,0)node [black,above,midway] {$\\epsilon_5$};\n\\draw[ultra thick,orange] (14,0) -- (15,0)node [black,above,midway] {$\\epsilon_6$};\n\\draw[ultra thick,blue] (15,0) -- (17,0)node [black,above,midway] {$\\epsilon_7$};\n\\draw[ultra thick,blue] (17,0) -- (18,0)node [black,above,midway] {$\\epsilon_8$};\n\\draw[ultra thick,blue] (18,0) -- (20,0)node [black,above,midway] {$\\epsilon_9$};\n\\draw[ultra thick,orange] (20,0) -- (21,0)node [black,above,midway] {$\\epsilon_{10}$};\n\\draw[ultra thick,blue] (21,0) -- (23,0)node [black,above,midway] {$\\epsilon_{11}$};\n\\draw[ultra thick,blue] (23,0) -- (24,0)node [black,above,midway] {$\\epsilon_{12}$};\n\\draw[ultra thick,orange] (24,0) -- (26,0)node [black,above,midway] {$\\epsilon_{13}$};\n\\draw[ultra thick,orange] (26,0) -- (27,0)node [black,above,midway] {$\\epsilon_{14}$};\n\\draw[ultra thick,orange] (27,0) -- (28,0)node [black,above,midway] {$\\epsilon_{15}$};\n\\draw[ultra thick,orange] (28,0) -- (29,0)node [black,above,midway] {$\\epsilon_{16}$};\n\\draw[ultra thick,orange] (29,0) -- (30,0)node [black,above,midway] {$\\epsilon_{17}$};\n\\draw[ultra thick,orange] (30,0) -- (32,0)node [black,above,midway] {$\\epsilon_{18}$};\n\\draw[ultra thick,orange] (32,0) -- (33,0)node [black,above,midway] {$\\epsilon_{19}$};\n\\draw[ultra thick,orange] (33,0) -- (34,0)node [black,above,midway] {$\\epsilon_{20}$};\n\\draw[ultra thick,orange] (34,0) -- (35,0)node [black,above,midway] {$\\epsilon_{21}$};\n\\draw[ultra thick,orange] (35,0) -- (36,0)node [black,above,midway] {$\\epsilon_{22}$};\n\\draw[ultra thick,orange] (36,0) -- (37,0)node [black,above,midway] {$\\epsilon_{23}$};\n\\draw[ultra thick,orange] (37,0) -- (38,0)node [black,above,midway] {$\\epsilon_{24}$};\n\\draw[ultra thick,orange] (38,0) -- (39,0)node [black,above,midway] {$\\epsilon_{25}$};\n\\draw[ultra thick,orange] (39,0) -- (41,0)node [black,above,midway] {$\\epsilon_{26}$};\n\\draw[ultra thick,orange] (41,0) -- (43,0)node [black,above,midway] {$\\epsilon_{27}$};\n\\draw[ultra thick,orange] (43,0) -- (45,0)node [black,above,midway] {$\\epsilon_{28}$};\n\\draw[ultra thick,orange] (45,0) -- (46,0)node [black,above,midway] {$\\epsilon_{29}$};\n\\draw[ultra thick,orange] (46,0) -- (47,0)node [black,above,midway] {$\\epsilon_{30}$};\n\\draw[ultra thick,orange] (47,0) -- (49,0)node [black,above,midway] {$\\epsilon_{31}$};\n\\draw[ultra thick,orange] (49,0) -- (51,0)node [black,above,midway] {$\\epsilon_{32}$};\n\\draw[ultra thick,orange] (51,0) -- (52,0)node [black,above,midway] {$\\epsilon_{33}$};\n\\draw[ultra thick,orange] (52,0) -- (54,0)node [black,above,midway] {$\\epsilon_{34}$};\n\\draw[ultra thick,orange] (54,0) -- (56,0)node [black,above,midway] {$\\epsilon_{35}$};\n\\draw[ultra thick,orange] (56,0) -- (58,0)node [black,above,midway] {$\\epsilon_{36}$};\n\\draw[ultra thick,orange] (58,0) -- (61,0)node [black,above,midway] {$\\epsilon_{37}$};\n\\draw[ultra thick,orange] (61,0) -- (62,0)node [black,above,midway] {$\\epsilon_{38}$};\n\\draw[ultra thick,orange] (62"
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        "tikz_code": "\\documentclass[10pt, a4paper, notitlepage]{article}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{cd}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{decorations.text}\n\\usetikzlibrary{arrows.meta}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{positioning}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\n\\newcommand{\\id}{\\mathrm{id}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\path[draw] (0, 0) coordinate (out) -- (0, 1) coordinate[pos=0.4] (m-start);\n\\path[draw] (0.1, -0.1) coordinate (start) -- ++(315:1) coordinate[pos=0.4] (m-end);\n\\path[draw] (-0.1, -0.1) coordinate (end) -- ++(225:1);\n\\path[draw, ->, bend right=110, looseness=3] (m-start) to (m-end);\n\\path[draw, ->, bend right=110, looseness=3] (m-end) to (m-start);\n\\path[draw, ->] (start) to (end);\n\\path[draw, ->] (out) to (start);\n\\path[fill] (0, 0.6) circle[radius=0.05] node[above] {$ L $};\n\\path[fill] (0, 0.2) circle[radius=0.05] node[left] {$ i_0 $};\n\\path[fill] (0, 0) circle[radius=0.05] node[left] {$ \\id_+$ };\n\\path (0, -0.5) node {$ V $ ($ F_1 $)};\n%\n\\path (1.5, 0) node (D) {$ \u03b4 $};\n\\path[draw] (D) -- ++(315:1) coordinate[pos=0.4] (m-start-1);\n\\path[draw] (D) -- ++(225:1) coordinate[pos=0.4] (m-end-1);\n\\path[draw] (D) -- ++(0, 1) coordinate[pos=0.4] (m-start-2);\n\\path[draw, ->, bend right=110, looseness=3] (m-start-1) to (m-end-1);\n\\path[draw, ->, bend right=110, looseness=3] (m-end-1) to (m-start-1);\n\\path[draw, ->, bend right=110, looseness=3] (m-start-2) to (m-end-1);\n\\path[draw, ->, bend right=110, looseness=3] (m-end-1) to (m-start-2);\n\\path[draw, ->] (m-start-2) -- ++(0, 1) coordinate[pos=0.8] (m-end-2);\n\\path[draw] (m-end-2) -- ++(270:1);\n\\path[fill] (m-start-1) circle[radius=0.05] node[above] {$ i_1 $};\n\\path[fill] (m-start-2) circle[radius=0.05] node[above] {$ P $};\n\\path[fill] (m-end-1) circle[radius=0.05] node[above] {$ i_0 $};\n\\path[fill] (m-end-2) circle[radius=0.05] node[right] {$ P_+$};\n\\path (0, -1.5) node {$ V $ ($ F_2 $)};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt,reqno]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{amsthm,graphicx,color,yfonts}\n\\usepackage[colorlinks=true]{hyperref}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,calc,decorations.pathreplacing}\n\n\\newcommand{\\wt}{\\widetilde}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8]\n\\filldraw[thick, color=lightgray!60] (0,2) -- (0,5) -- (2,5) -- (2,2);\n\\draw[->] (-0.3,0) -- (5.5,0) node[below]{$E$};\n\\draw[->] (0,-0.3) -- (0,5.5) node[right]{$\\Im(z_0)$};\n\\draw[thick,dashed] (0,2) -- (2,5);\n\\draw[thick] (0,2) -- (2,2);\n\\filldraw[thick, fill=black] (2,2) circle (0.05) node[below]{$\\wt{N}(E-|\\wt{N}(\\lambda_0)|^2)$};\n\\filldraw[thick, fill=black] (0,2) circle (0.05) node[left]{$\\wt{N}(0) - \\frac{\\wt{N}(\\lambda_0)^2}{2}|\\wt{N}(\\lambda_0)|^2$};\n\\filldraw[thick, fill=black] (2,5) circle (0.05) node[above]{$\\wt{N}(E) - \\frac{\\wt{N}(\\lambda_0)^2}{2}|\\wt{N}(\\lambda_0)|^2$};\n\\node at (5.8,3.5) {$\\wt{N}(E) \\cdot \\wt{N}(E) - \\frac{\\wt{N}(\\lambda_0)^2}{2}|\\wt{N}(\\lambda_0)|^2 \\cdot \\wt{N}(E) \\geq \\frac{3E^2}{2}$};\n\\node at (10.5,3.5) {$\\wt{N}(E) \\cdot \\wt{N}(E) - \\frac{\\wt{N}(\\lambda_0)^2}{2}|\\wt{N}(\\lambda_0)|^2 \\cdot \\wt{N}(E) \\leq \\frac{3E^2}{2}$};\n\\draw[->,thick] (2,2.5) arc (90:160:0.8);\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amsfonts,amssymb}\n\\usepackage{graphicx,color,tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.5]\n\\draw[thin,color=gray,step=2cm] (0,0) grid (15,15) ;\n\\draw[->] (0,0) -- (15.2,0) node[anchor=west] {$t$};\n\\draw[->] (0,0) -- (0,15.2) node[anchor=south]{$u$};\n\\draw[dashed] (0,0) -- (15,15) ;\n\\draw[dashed] (3,0) -- (3,3) ;\n\\draw[dashed] (4,0) -- (4,4) ;\n\\draw[dashed] (0,3) -- (3,3) ;\n\\draw[dashed] (0,4) -- (4,4) ;\n\\draw[dashed] (6,0) -- (6,6) ;\n\\draw[dashed] (7,0) -- (7,7) ;\n\\draw[dashed] (10,0) -- (10,10) ;\n\\draw[dashed] (11,0) -- (11,11) ;\n\\draw[dashed] (14,0) -- (14,14) ;\n\\draw[dashed] (15,0) -- (15,15) ;\n\\draw[dashed] (15,1) -- (3,1) ;\n\\draw[dashed] (15,2) -- (4,2) ;\n\\draw[dashed] (15,5) -- (6,5) ;\n\\draw[dashed] (15,6) -- (7,6) ;\n\\draw[dashed] (15,10) -- (10,10) ;\n\\draw[dashed] (15,11) -- (11,11) ;\n\\draw[dashed] (15,14) -- (14,14) ;\n\\draw[very thick] (0,0) -- (3,0) ;\n\\draw[very thick] (3,0) -- (3,3) ;\n\\draw[very thick] (3,3) -- (4,3) ;\n\\draw[very thick] (4,3) -- (4,4) ;\n\\draw[very thick] (4,4) -- (6,4) ;\n\\draw[very thick] (6,4) -- (6,6) ;\n\\draw[very thick] (6,6) -- (7,6) ;\n\\draw[very thick] (7,6) -- (7,7) ;\n\\draw[very thick] (7,7) -- (10,7) ;\n\\draw[very thick] (10,7) -- (10,10) ;\n\\draw[very thick] (10,10) -- (11,10) ;\n\\draw[very thick] (11,10) -- (11,11) ;\n\\draw[very thick] (11,11) -- (14,11) ;\n\\draw[very thick] (14,11) -- (14,14) ;\n\\draw[very thick] (14,14) -- (15,14) ;\n\\draw[very thick] (15,14) -- (15,15) ;\n\\draw (1,3) node[fill=white,inner sep=2pt] {$W$} ;\n\\draw (1,4) node[fill=white,inner sep=2pt] {$W$} ;\n\\draw (4,5) node[fill=white,inner sep=2pt] {$W$} ;\n\\draw (6,6) node[fill=white,inner sep=2pt] {$W$} ;\n\\draw (7,7) node[fill=white,inner sep=2pt] {$W$} ;\n\\draw (10,10) node[fill=white,inner sep=2pt] {$W$} ;\n\\draw (11,11) node[fill=white,inner sep=2pt] {$W$} ;\n\\draw (14,14) node[fill=white,inner sep=2pt] {$W$} ;\n\\draw (15,15) node[fill=white,inner sep=2pt] {$W$} ;\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt,reqno]{amsproc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{colortbl}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usetikzlibrary{automata,shapes,arrows,matrix,backgrounds,positioning,plotmarks,calc,patterns,matrix,decorations.pathreplacing,decorations.pathmorphing,decorations.text,decorations.markings}\n\\usepackage[colorinlistoftodos,shadow]{todonotes}\n\\tikzset{round left paren/.style={ncbar=0.5cm,out=120,in=-120}}\n\\tikzset{round right paren/.style={ncbar=0.5cm,out=60,in=-60}}\n\\usepackage{array, xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}[label/.style={postaction={\n      decorate,\n      decoration={markings, mark=at position .5 with \\node #1;}},\n      mylabel/.style={thick, draw=none, align=center, minimum width=0.5cm, minimum height=0.5cm,fill=white}},\n      baseline=(base)]\n      \\coordinate (r) at (3.5,0);\n      \\coordinate (u) at (0,2);\n      \\node (A) {$x_1$};\n      \\node (B) at ($(A)+(r)$) {$x_2$};\n      \\node (C) at ($(B) + (r)$) {$x_3$};\n      \\node (D) at ($(C) + (r)$) {$x_4$};\n      \\node (A2) at ($(A) - (u)$) {$x_5$};\n      \\node (B2) at ($(A2)+(r)$) {$x_6$};\n      \\node (C2) at ($(B2) + (r)$) {$x_7$};\n      \\node (D2) at ($(C2) + (r)$) {$x_8$};\n      \\node (base) at ($(A) + 0.5*(u)$) {};\n      \\draw[->,thick,dashed,blue] (A) -- (A2);\n      \\draw[->,thick,dashed,blue] (B) -- (B2);\n      \\draw[->,thick,dashed,blue] (C) -- (C2);\n      \\draw[->,thick,dashed,blue] (D) -- (D2);\n      \\draw[thick] (A) to[out=270,in=90] (A2);\n      \\draw[thick] (B) to[out=270,in=90] (B2);\n      \\draw[thick] (C) to[out=270,in=90] (C2);\n      \\draw[thick] (D) to[out=270,in=90] (D2);\n      \\draw[thick] (A) to[out=180,in=180] (B);\n      \\draw[thick] (B) to[out=0,in=0] (C);\n      \\draw[thick] (C) to[out=180,in=180] (D);\n      \\draw[thick] (A) to[out=0,in=0] (A2);\n      \\draw[thick] (B) to[out=0,in=0] (B2);\n      \\draw[thick] (C) to[out=0,in=0] (C2);\n      \\draw[thick] (D) to[out=0,in=0] (D2);\n      \\draw[thick] (A) to[out=-135,in=-45] (A2);\n      \\draw[thick] (B) to[out=-135,in=-45] (B2);\n      \\draw[thick] (C) to[out=-135,in=-45] (C2);\n      \\draw[thick] (D) to[out=-135,in=-45] (D2);\n      \\draw[thick] (A) to[out=-45,in=180] (B2);\n      \\draw[thick] (B) to[out=45,in=-135] (C2);\n      \\draw[thick] (C) to[out=45,in=180] (D2);\n      \\draw[thick] (A) to[out=180,in=180] (A2);\n      \\draw[thick] (B) to[out=0,in=0] (B2);\n      \\draw[thick] (C) to[out=0,in=0] (C2);\n      \\draw[thick] (D) to[out=0,in=0] (D2);\n      \\draw[thick] (A) to[out=-135,in=180] (A2);\n      \\draw[thick] (B) to[out=-45,in=180] (B2);\n      \\draw[thick] (C) to[out=-135,in=180] (C2);\n      \\draw[thick] (D) to[out=-135,in=180] (D2);\n      \\node[draw,rectangle,thick,fill=white,minimum width=1.5cm,minimum height=0.6cm,inner sep=0pt,label={[mylabel]{$z_1$}]}] at ($(A)+0.25*(u)$) {};\n      \\node[draw,rectangle,thick,fill=white,minimum width=1.5cm,minimum height=0.6cm,inner sep=0pt,label={[mylabel]{$z_2$}]}] at ($(D)+0.25*(u)$) {};\n    \\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 416,
        "tikz_code": "\\documentclass{article}\n\\usepackage{pgfplots}\n\\usetikzlibrary{positioning}\n\\begin{document}\n\\begin{tikzpicture}\n\\begin{axis}[name=axis1,\n    width=2.2in,\n    height=2.6in,\n    scale only axis,\n    xmin=0,\n    xmax=500,\n    ymin=-30,\n    ymax=30,\n    axis background/.style={fill=white},\n    ytick={-25,-20,-15,-10,-5,0,5,10,15,20,25},\n    legend style={at={(0.03,0.97)},anchor=north west,font=\\scriptsize,fill=none}\n    ]\n\\addplot [red, mark=x, mark size=3, mark options={solid},line width=2.0pt]\n    table[row sep=crcr]{\n1 0\\\\\n2 -1.885\\\\\n3 4.27\\\\\n4 -1.84\\\\\n5 13.95\\\\\n6 -4.23\\\\\n7 -2.57\\\\\n8 3.32\\\\\n9 -3.47\\\\\n10 -3.05\\\\\n11 2.24\\\\\n12 -3.62\\\\\n13 4.82\\\\\n14 -2.7\\\\\n15 -2.33\\\\\n16 0.06\\\\\n17 1.09\\\\\n18 -2.53\\\\\n19 -1.9\\\\\n20 1.48\\\\\n21 1.22\\\\\n22 0.67\\\\\n23 -1.13\\\\\n24 -2.91\\\\\n25 -1.49\\\\\n26 2.1\\\\\n27 1.04\\\\\n28 -2.87\\\\\n29 -0.45\\\\\n30 3.26\\\\\n31 -1.27\\\\\n32 -0.56\\\\\n33 -0.18\\\\\n34 -2.71\\\\\n35 -1.5\\\\\n36 0.65\\\\\n37 0.52\\\\\n38 0.82\\\\\n39 0.46\\\\\n40 2.58\\\\\n41 -1.3\\\\\n42 1.73\\\\\n43 0.7\\\\\n44 1.13\\\\\n45 -1.63\\\\\n46 0.9\\\\\n47 0.45\\\\\n48 0.48\\\\\n49 -1.91\\\\\n50 0.52\\\\\n51 2.36\\\\\n52 -0.02\\\\\n53 0.18\\\\\n54 0.13\\\\\n55 0.32\\\\\n56 1.45\\\\\n57 -0.92\\\\\n58 2.72\\\\\n59 0.54\\\\\n60 -0.72\\\\\n61 1.58\\\\\n62 1.98\\\\\n63 0.76\\\\\n64 0.63\\\\\n65 1.43\\\\\n66 1.38\\\\\n67 1.18\\\\\n68 2.08\\\\\n69 0.28\\\\\n70 -1.47\\\\\n71 1.4\\\\\n72 0.41\\\\\n73 1.54\\\\\n74 0.58\\\\\n75 -0.17\\\\\n76 -1.28\\\\\n77 2.22\\\\\n78 1.05\\\\\n79 -1.34\\\\\n80 0.27\\\\\n81 0.12\\\\\n82 1.06\\\\\n83 -1.26\\\\\n84 -0.8\\\\\n85 -0.51\\\\\n86 -1.54\\\\\n87 1.52\\\\\n88 0.41\\\\\n89 -1.21\\\\\n90 0.61\\\\\n91 -1.09\\\\\n92 0.17\\\\\n93 0.24\\\\\n94 -1.86\\\\\n95 0.97\\\\\n96 -1.53\\\\\n97 0.72\\\\\n98 -0.59\\\\\n99 -1.2\\\\\n100 -0.66\\\\\n101 -1.63\\\\\n102 -0.34\\\\\n103 -1.14\\\\\n104 0.43\\\\\n105 -0.34\\\\\n106 -1.11\\\\\n107 0.05\\\\\n108 0.31\\\\\n109 -0.08\\\\\n110 0.81\\\\\n111 -0.37\\\\\n112 0.65\\\\\n113 0.54\\\\\n114 -0.11\\\\\n115 -0.12\\\\\n116 -0.82\\\\\n117 0.77\\\\\n118 1.03\\\\\n119 0.3\\\\\n120 0.02\\\\\n121 0.89\\\\\n122 0.66\\\\\n123 1.39\\\\\n124 -0.61\\\\\n125 0.38\\\\\n126 0.68\\\\\n127 1.25\\\\\n128 0.67\\\\\n129 0.03\\\\\n130 1.15\\\\\n131 1.03\\\\\n132 0.65\\\\\n133 0.45\\\\\n134 0.25\\\\\n135 0.48\\\\\n136 0.7\\\\\n137 1.58\\\\\n138 1.27\\\\\n139 0.14\\\\\n140 0.16\\\\\n141 1.11\\\\\n142 -0.24\\\\\n143 0.12\\\\\n144 0.38\\\\\n145 0.97\\\\\n146 0.13\\\\\n147 0.44\\\\\n148 0.84\\\\\n149 0.59\\\\\n150 -0.85\\\\\n151 0.32\\\\\n152 -0.8\\\\\n153 0.33\\\\\n154 0.13\\\\\n155 0.39\\\\\n156 -0.48\\\\\n157 0.46\\\\"
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    {
        "index": 417,
        "tikz_code": "\\documentclass[10pt]{article}\n\\usepackage{amssymb,amsthm,amsmath}\n\\usepackage{color}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8]\n      \\tikzstyle{every node}=[font=\\footnotesize]\n      \\draw[-,thick] (-5.5,2.75) -- (-3.75,2.5) -- (-3.75,1.5) -- (-5.5,1.25) -- (-5.5,2.75);\n      \\draw[densely dotted] (-5.5,1.25) -- (-6.5,1.0) -- (-6.5,2.0) -- (-5.5,2.75);\n      \\draw[-,thick] (-3.75,2.5) -- (-2.5,2.25) -- (-2.5,1.25) -- (-3.75,1.5);\n      \\draw[densely dotted] (-2.5,2.25) -- (-3.25,2.0) -- (-3.25,1.0) -- (-2.5,1.25);\n      \\draw[-,thick] (-3.75,2.5) -- (-1.0,2.75) -- (-1.0,1.75) -- (-3.75,1.5);\n      \\draw[densely dotted] (-1.0,2.75) -- (0.5,2.9) -- (0.5,1.9) -- (-1.0,1.75);\n      \\draw[-,thick] (-3.75,2.5) -- (2.0,2.75) -- (2.0,1.75) -- (-3.75,1.5);\n      \\draw[densely dotted] (2.0,2.75) -- (3.5,2.9) -- (3.5,1.9) -- (2.0,1.75);\n\n      \\draw[-,color=orange] (-5.5,2.75) -- (-3.75,2.5) -- (-3.75,1.5) -- (-5.5,1.25) -- (-5.5,2.75);\n      \\draw[color=orange,densely dotted] (-5.5,1.25) -- (-6.5,1.0) -- (-6.5,2.0) -- (-5.5,2.75);\n      \\draw[-,color=orange] (-3.75,2.5) -- (-2.5,2.25) -- (-2.5,1.25) -- (-3.75,1.5);\n      \\draw[color=orange,densely dotted] (-2.5,2.25) -- (-3.25,2.0) -- (-3.25,1.0) -- (-2.5,1.25);\n      \\draw[-,color=orange] (-3.75,2.5) -- (-1.0,2.75) -- (-1.0,1.75) -- (-3.75,1.5);\n      \\draw[color=orange,densely dotted] (-1.0,2.75) -- (0.5,2.9) -- (0.5,1.9) -- (-1.0,1.75);\n      \\draw[-,color=orange] (-3.75,2.5) -- (2.0,2.75) -- (2.0,1.75) -- (-3.75,1.5);\n      \\draw[color=orange,densely dotted] (2.0,2.75) -- (3.5,2.9) -- (3.5,1.9) -- (2.0,1.75);\n      \n      \\draw[->] (-6.5,1.5) -- (-4.5,1.5);\n      \\draw[->] (-2.5,1.5) -- (-0.5,1.5);\n      \\draw[->] (0.5,1.5) -- (2.5,1.5);\n      \n      \\node[above] at (-6.5,1.5) {$x$};\n      \\node[above] at (-2.5,1.5) {$f_x(z)$};\n      \\node[above] at (0.5,1.5) {$f_x'(z)$};\n      \n      \\draw[color=red,thick] (-5.5,2.75) -- (-3.75,2.5) -- (-3.75,1.5) -- (-5.5,1.25) -- (-5.5,2.75);\n      \\draw[color=red,densely dotted] (-5.5,1.25) -- (-6.5,1.0) -- (-6.5,2.0) -- (-5.5,2.75);\n      \\draw[color=red,->,thick] (-3.75,2.5) -- (-2.5,2.25) -- (-2.5,1.25) -- (-3.75,1.5);\n      \\draw[color=red,densely dotted] (-2.5,2.25) -- (-3.25,2.0) -- (-3.25,1.0) -- (-2.5,1.25);\n      \\draw[color=red,->,thick] (-3.75,2.5) -- (-1.0,2.75) -- (-1.0,1.75) -- (-3.75,1.5);\n      \\draw[color=red,densely dotted] (-1.0,2.75) -- (0.5,2.9) -- (0.5,1.9) -- (-1.0,1.75);\n      \\draw[color=red,->,thick] (-3.75,2.5) -- (2.0,2.75) -- (2.0,1.75) -- (-3.75,1.5);\n      \\draw[color=red,densely dotted] (2.0,2.75) -- (3.5,2.9) -- (3.5,1.9) -- (2.0,1.75);\n      \n      \\draw[color=red,thick] (-5.5,2.75) -- (0.5,2.9);\n      \\draw[color=red,thick] (2.0,2.75) -- (0.5,2.9);\n\n      \\node[color=blue] at (-5.5,2.75) {\\tiny $\\bullet$};\n      \\node[color=blue] at (-3.75,2.5) {\\tiny $\\bullet$};\n      \\node[color=blue] at (-"
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        "tikz_code": "\\documentclass[10pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{fit,arrows,calc,positioning}\n\\usepackage{jake}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.17}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n\tauto,\n\tnode distance=1cm,\n\t>=latex,\n\tblock/.style={\n\t\tdraw,\n\t\trectangle,\n\t\tminimum height=3em,\n\t\tminimum width=6em\n\t},\n\tenc/.style={\n\t\tdraw,\n\t\trectangle,\n\t\trounded corners,\n\t\tminimum height=1.5em\n\t}\n\t]\n\t\\node[block] (f) {frame encoding};\n\t\\node[block, below=0.5 of f] (s) {slot encoding};\n\t\\draw[->] (f) edge node[right] {$(0, m, 0, \\ldots, 0, m, 0, \\ldots, 0, m)$} (s);\n\t\\draw[->] (s) edge node[right] {$(0, x, 0, \\ldots, 0, x, 0, \\ldots, 0)$} ++(0, -3) node[below] {$x = f(m)$} (s);\n\t\\draw[->] (f) edge node[above] {$m$} ++(0, 2.5);\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.15}\n\\begin{document}\n\\begin{tikzpicture}[scale=1.2]\n\\begin{axis}[\n    xlabel=rad,\n    ylabel=Gain,\n    grid,\n    legend style={at={(1.0,1.0)}, anchor=north east},\n    cycle list name=black white]\n\\addplot+[samples=1000] {1/(sqrt(2*pi)*2.71828^((x-2)^2/2))*exp(-(x-2)^2/2)};\n\\addlegendentry{uncond. beam}\n\\addplot+[samples=1000] {1/(sqrt(2*pi)*2.71828^((x-2)*x/2))*exp(-(x-2)*x/2)};\n\\addlegendentry{proj. onto $K_2$}\n\\addplot+[samples=1000] {1/(sqrt(2*pi)*2.71828^((x-2)*ln(x)/2))*exp(-(x-2)*ln(x)/2)};\n\\addlegendentry{proj. onto $V$}\n\\addplot+[samples=1000] {1/(sqrt(2*pi)*2.71828^((x-2)*log2(x)/2))*exp(-(x-2)*log2(x)/2)};\n\\addlegendentry{proj. onto $\\log$}\n\\end{axis}\n\\end{tikzpicture}\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt,a4paper]{amsart}\n\\usepackage{amssymb, amstext, amscd, amsmath}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n\\draw[gray, dashed] (-5,-2) grid (6,2);\n\\filldraw[fill=gray!30!, draw=black] (-5,0) rectangle (5,2);\n\\filldraw[fill=gray!30!, draw=black] (-5,-2) rectangle (5,0);\n\n\\draw[gray] (-5,-2)--(5,-2);\n\\draw[gray] (-5,0)--(5,0);\n\n\\filldraw[black] (0,0) circle (2pt) node[anchor=north]{$O$};\n\\draw[black] (-4,0)--(4,0);\n\\draw[black] (-2,0)--(2,0);\n\\filldraw[black] (-2,0) circle (2pt) node[anchor=north]{$Q$};\n\\filldraw[black] (2,0) circle (2pt) node[anchor=north]{$P$};\n\n\\draw[black] (0,0)--(2,1.5);\n\\draw[black] (2,0.5)--(4,1.5);\n\\draw[black] (2.15,1.15) node[anchor=south]{$Q_0^{\\sigma}$};\n\n\\draw[black] (0,0)--(2,1);\n\\draw[black] (2,0.7)--(4,1);\n\\draw[black] (2.15,1.15) node[anchor=south]{$Q_0^{\\sigma}$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage[latin1]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.55]\n%Figure 1\n\n\\draw[->] (0,5) -- (2,5);\n\\draw[->] (0,2) -- (2,2);\n\\draw[->] (0,0) -- (2,0);\n\\draw (0,6) rectangle (2,-1);\n\\draw (0,3) rectangle (2,6);\n\\draw (0,4) rectangle (2,3);\n\n\\node at (1,3.5) {$\\times S$};\n\\node at (1,4.5) {$\\times G_1$};\n\\node at (1,1.5) {$\\times P^1$};\n\\node at (1,2.5) {$\\times G_2$};\n\\node at (1,5.5) {$\\times P^2$};\n\\node at (3.5,3.5) {$\\mapsto$};\n\n\\draw (4,6) rectangle (9,-1);\n\\draw (4,3) rectangle (9,6);\n\\draw (4,4) rectangle (9,3);\n\\draw (4,1) rectangle (9,4);\n\n\\node at (6.5,3.5) {$+$};\n\\node at (7.5,3.5) {$E_1$};\n\\node at (5.5,4.5) {$\\times G_2$};\n\\node at (5.5,1.5) {$\\times P^1$};\n\\node at (6.5,4.5) {$\\times P^2$};\n\\node at (8.5,3.5) {$+$};\n\\node at (9.5,3.5) {$E_2$};\n\\node at (7.5,1.5) {$H$};\n\\node at (7.5,4.5) {$+$};\n\\node at (8.5,1.5) {$H^{-1}$};\n\\node at (8.5,4.5) {$+$};\n\n\\draw[->] (12,5) -- (14,5);\n\\draw[->] (12,2) -- (14,2);\n\\draw[->] (12,0) -- (14,0);\n\\draw (12,6) rectangle (14,-1);\n\\draw (12,3) rectangle (14,6);\n\\draw (12,4) rectangle (14,3);\n\n\\node at (13,3.5) {$\\times S^{-1}$};\n\\node at (13,4.5) {$\\times G^{-1}$};\n\\node at (13,1.5) {$\\times P^1$};\n\\node at (13,2.5) {$\\times G^{-1}$};\n\\node at (13,5.5) {$\\times P^{-1}$};\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 423,
        "tikz_code": "\\documentclass[10pt]{amsart}\n\\usepackage{amsmath,amsthm,amssymb,xypic,array}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[cp850]{inputenc}\n\\usepackage{tikz}\n\\usetikzlibrary{trees}\n\n\\begin{document}\n\n\\begin{tikzpicture}[xscale=3.8,yscale=-1.6]\n    \\node (A0_0) at (0, 0) {$\\mathcal{R}\\Gamma\\backslash D_{2k}(e)$};\n    \\node (A1_0) at (1, 0) {$\\mathcal{R}\\Gamma\\backslash D_{2k-1}(e)$};\n    \\node (A2_0) at (2, 0) {$\\mathcal{R}\\Gamma\\backslash D_{2k-2}(e)$};\n    \\node (A0_1) at (0, 1) {$D_{2k}(e)$};\n    \\node (A1_1) at (1, 1) {$D_{2k-1}(e)$};\n    \\node (A2_1) at (2, 1) {$D_{2k-2}(e)$};\n    \\node (A0_2) at (0, 2) {$\\mathcal{R}\\Gamma$};\n    \\node (A1_2) at (1, 2) {$\\mathcal{R}\\Gamma$};\n    \\node (A2_2) at (2, 2) {$\\mathcal{R}\\Gamma$};\n    \\path (A0_0) edge [->,swap]node [auto] {$\\scriptstyle{\\varphi_{2k}(e)}$} (A0_1);\n    \\path (A0_1) edge [->,swap]node [auto] {$\\scriptstyle{\\widetilde{\\varphi}_{2k}^{D_{2k}(e)}}$} (A0_2);\n    \\path (A1_0) edge [->,swap]node [auto] {$\\scriptstyle{\\varphi_{2k-1}(e)}$} (A1_1);\n    \\path (A1_1) edge [->,swap]node [auto] {$\\scriptstyle{\\widetilde{\\varphi}_{2k-1}^{D_{2k-1}(e)}}$} (A1_2);\n    \\path (A2_0) edge [->]node [auto] {$\\scriptstyle{\\varphi_{2k-2}(e)}$} (A2_1);\n    \\path (A1_0) edge [->]node [auto] {$\\scriptstyle{RII_{2k-2}(e)}$} (A2_0);\n    \\path (A1_1) edge [->]node [auto] {$\\scriptstyle{RII_{2k-1}(e)}$} (A2_1);\n    \\path (A0_1) edge [->]node [auto] {$\\scriptstyle{RII_{2k}(e)}$} (A1_1);\n    \\path (A0_2) edge [->]node [auto] {$\\scriptstyle{\\widetilde{\\varphi}_{2k}^{\\mathcal{R}\\Gamma}}$} (A1_2);\n    \\path (A2_1) edge [->]node [auto] {$\\scriptstyle{\\widetilde{\\varphi}_{2k-1}^{\\mathcal{R}\\Gamma}}$} (A2_2);\n  \\end{tikzpicture}\n\n\\end{document}"
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        "index": 424,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usepackage{color}\n\\usetikzlibrary{positioning, automata, chains, arrows.meta}\n\\usetikzlibrary{matrix,positioning,calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[font=\\tiny\\sffamily]\n    \\node[label=below:{$x_0$}](node1){};\n    \\node[label=left:{$\\Pi_L$}](node2) at (2.5,4.3){};\n    \\node[label=left:{$\\Pi_R$}](node3) at (6,4.3){};\n    \\node[label=above:{$\\lambda_1$}](node4) at (0.5,4.3){};\n    \\node[label=above:{$\\lambda_2$}](node5) at (4,4.3){};\n    \\node[label=above:{$\\lambda_3$}](node6) at (6.5,4.3){};\n    \\node[label=above:{$\\lambda_4$}](node7) at (8,4.3){};\n    \\node[label=above:{$\\lambda_5$}](node8) at (8.5,4.3){};\n    \\node[label=right:{$\\Pi_L$}](node9) at (5,1.8){};\n    \\node[label=right:{$\\Pi_R$}](node10) at (7.5,1.8){};\n    \\node[label=below:{$x$}](node11) at (3.5,0){};\n    \n    \\begin{scope}[every node/.style={fill=white,draw=none,circle,minimum size=0.3cm}]\n        \\node (A) at (0,0) {};\n        \\node (B) at (8,0) {};\n        \\node (C) at (10,0) {};\n    \\end{scope}\n    \n    \\draw[-{Stealth[length=3mm]}] (A) -- (B);\n    \\node[label=right:{$z$}] (E) at (8,0) {};\n    \n    \\draw[densely dashed] (node1) -- (node11);\n    \n    \\draw[-{Stealth[length=3mm]},line width=0.4mm] (node2) to [bend right] node{$\\gamma_{L\\star}$} (node4);\n    \\draw[-{Stealth[length=3mm]},line width=0.4mm] (node3) to [bend left] node{$\\gamma_{R\\star}$} (node6);\n    \\draw[-{Stealth[length=3mm]},line width=0.4mm] (node9) to [bend left] node{$v_{x_L\\star}^{\\gamma_{L\\star}}$} (node11);\n    \\draw[-{Stealth[length=3mm]},line width=0.4mm] (node10) to [bend right] node{$v_{x_R\\star}^{\\gamma_{R\\star}}$} (node11);\n    \n    \\draw[line width=0.4mm] (node1) -- (node2);\n    \\draw[line width=0.4mm] (node1) -- (node3);\n    \\draw[line width=0.4mm] (node1) -- (node9);\n    \\draw[line width=0.4mm] (node1) -- (node10);\n    \n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 425,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{tikz}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[colorlinks]{hyperref}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.3]\n\\begin{scope}[shift={(-10,0)}]\n\\draw[fill,red] (0,0) circle (1ex);\n\\draw[fill] (1.2,-2) circle (1ex);\n\\draw[fill] (1.2,2) circle (1ex);\n\\draw[fill] (3.2,-1.5) circle (1ex);\n\\draw[fill] (3.2,1.5) circle (1ex);\n\\draw[fill,red] (5,-1) circle (1ex);\n\\draw[fill,red] (5,1) circle (1ex);\n\\node[below left] at (0,0) {$\\tau$};\n\\node[above right] at (1.2,2) {$s_1$};\n\\node[below right] at (1.2,-2) {$s_2$};\n\\node[right] at (3.2,-1.5) {$s_3$};\n\\node[right] at (3.2,1.5) {$s_4$};\n\\node[below right] at (5,-1) {$s_5$};\n\\node[above right] at (5,1) {$s_6$};\n\\node[left] at (-0.4,3.5) {$\\frac{1}{2}$};\n\\node[below] at (2.5,-4.7) {$\\frac{1}{2}$};\n\\node[right] at (-1.1,-4) {$\\frac{3}{2}$};\n\\draw[blue] (0,0) -- (5,-1);\n\\draw[blue] (0,0) -- (5,1);\n\\draw[blue] (1.2,-2) -- (5,-1);\n\\draw[blue] (1.2,2) -- (5,1);\n\\draw[blue] (3.2,-1.5) -- (5,-1);\n\\draw[blue] (3.2,1.5) -- (5,1);\n\\draw[blue] (1.2,-2) -- (3.2,-1.5);\n\\draw[blue] (1.2,2) -- (3.2,1.5);\n\\draw[blue] (1.2,-2) -- (1.2,2);\n\\draw[blue] (5,-1) -- (5,1);\n\\draw[->] (0,0) .. controls (0.1,-2) .. (0.3,-3.7);\n\\draw[->] (0.3,-3.7) .. controls (1,-5.5) .. (5.5,-5.5);\n\\draw[->] (5.5,-5.5) .. controls (6,-5.5) .. (7.2,-4.5);\n\\draw[->] (7.2,-4.5) .. controls (8.5,-3) .. (12.5,2);\n\\draw[->] (12.5,2) -- (12.5,7.5);\n\\draw[->] (12.5,7.5) -- (10.5,9.5);\n\\draw[->] (10.5,9.5) -- (2.5,10);\n\\draw[->] (2.5,10) -- (0,10);\n\\draw[->] (0,0) .. controls (-1.5,1) .. (-1.5,7);\n\\draw[->] (-1.5,7) .. controls (-3,9) .. (0,10);\n\\draw[->] (0,0) .. controls (3,-1.5) .. (0.3,-3.7);\n\\end{scope}\n\\begin{scope}[shift={(10,0)}]\n\\draw[fill] (0,0) circle (1ex);\n\\draw[fill] (0,10) circle (1ex);\n\\draw[fill] (10,0) circle (1ex);\n\\draw[fill] (10,10) circle (1ex);\n\\draw[fill] (5,5) circle (1ex);\n\\node[left] at (0,0) {$s_1$};\n\\node[left] at (0,10) {$s_2$};\n\\node[right] at (10,0) {$s_3$};\n\\node[right] at (10,10) {$s_4$};\n\\node[left] at (5,5) {$s_5$};\n\\draw[fill,red] (0,0) circle (1ex);\n\\draw[fill,red] (0,10) circle (1ex);\n\\draw[fill,red] (10,0) circle (1ex);\n\\draw[fill,red] (10,10) circle (1ex);\n\\draw[fill,red] (5,5) circle (1ex);\n\\node[left] at (-0.4,3.5) {$\\frac{1}{2}$};\n\\node[below] at (2.5,-4.7) {$\\frac{1}{2}$};\n\\node[right] at (-1.1,-4) {$\\frac{3}{2}$};\n\\draw[blue] (0,0) -- (5,5);\n\\draw[blue] (0,10) -- (5,5);\n\\draw[blue] (10,0) -- (5,5);\n\\draw[blue] (10,10) -- (5,5);\n\\draw[blue] (0,0) -- (0,10);\n\\draw[blue] (10,0) -- (10,10);\n\\draw[blue] (0,0) -- (5,5);\n\\draw[blue] (10,0) -- (5,5);\n\\node at (8,8) {I};\n\\node at (8,6) {II};\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 426,
        "tikz_code": "\\documentclass[10pt,twocolumn,twoside]{IEEEtran}\n\\usepackage{amsmath,amsthm}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{amsmath,bigints,bbm}\n\\usepackage{amssymb}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usetikzlibrary{arrows,shapes,positioning,shadows,svg.path,backgrounds,fit}\n\\usepackage{tikzscale}\n\\usepackage{pgfplotstable}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.68]\n\t\\begin{axis}[\n\t\txlabel={$r$ [rad]},\n\t\tylabel={$Gain$ [dB]},\n\t\tgrid=major,\n\t\txmin=0.0,\n\t\txmax=2.1,\n\t\tlegend style={at={(0.9,0.8)},anchor=east}\n\t]\n\t\\addplot[\n\t\tdomain=0:2,\n\t\tsamples=500,\n\t\tcolor=blue,\n\t\tline width=1pt,\n\t]\n\t{0.2*sin(2*deg(x)) + 0.8*sin(4*deg(x)) + 0.001*sin(8*deg(x)) + 0.001*sin(16*deg(x)) + 0.001*sin(32*deg(x)) + 0.001*sin(64*deg(x)) + 0.001*sin(128*deg(x)) + 0.001*sin(256*deg(x)) + 0.001*sin(512*deg(x)) + 0.001*sin(1024*deg(x))};\n\t\\addlegendentry{Unconn. beam}\n\t\n\t\n\t\\addplot[\n\t\tdomain=0:2,\n\t\tsamples=500,\n\t\tcolor=green,\n\t\tline width=1pt,\n\t\tstyle=dashed,\n\t]\n\t{0.8*sin(2*deg(x)) + 0.8*sin(4*deg(x)) + 0.8*sin(8*deg(x)) + 0.001*sin(16*deg(x)) + 0.001*sin(32*deg(x)) + 0.001*sin(64*deg(x)) + 0.001*sin(128*deg(x)) + 0.001*sin(256*deg(x)) + 0.001*sin(512*deg(x)) + 0.001*sin(1024*deg(x))};\n\t\\addlegendentry{Pro-onto set $K^1$}\n\t\n\t\\addplot[\n\t\tdomain=0:2,\n\t\tsamples=500,\n\t\tcolor=purple,\n\t\tline width=1pt,\n\t]\n\t{0.001*sin(2*deg(x)) + 0.001*sin(4*deg(x)) + 0.001*sin(8*deg(x)) + 0.8*sin(16*deg(x)) + 0.8*sin(32*deg(x)) + 0.8*sin(64*deg(x)) + 0.001*sin(128*deg(x)) + 0.001*sin(256*deg(x)) + 0.001*sin(512*deg(x)) + 0.001*sin(1024*deg(x))};\n\t\\addlegendentry{Pro-onto set $K^2$}\n\t\n\t\\addplot[\n\t\tdomain=0:2,\n\t\tsamples=500,\n\t\tcolor=orange,\n\t\tline width=1pt,\n\t]\n\t{0.001*sin(2*deg(x)) + 0.001*sin(4*deg(x)) + 0.001*sin(8*deg(x)) + 0.001*sin(16*deg(x)) + 0.8*sin(32*deg(x)) + 0.8*sin(64*deg(x)) + 0.001*sin(128*deg(x)) + 0.001*sin(256*deg(x)) + 0.8*sin(512*deg(x)) + 0.001*sin(1024*deg(x))};\n\t\\addlegendentry{Pro-onto set $V$}\n\t\n\t\\addplot[\n\t\tdomain=0:2,\n\t\tsamples=500,\n\t\tcolor=red,\n\t\tline width=1pt,\n\t]\n\t{0.001*sin(2*deg(x)) + 0.001*sin(4*deg(x)) + 0.001*sin(8*deg(x)) + 0.001*sin(16*deg(x)) + 0.001*sin(32*deg(x)) + 0.8*sin(64*deg(x)) + 0.001*sin(128*deg(x)) + 0.001*sin(256*deg(x)) + 0.001*sin(512*deg(x)) + 0.8*sin(1024*deg(x))};\n\t\\addlegendentry{True direction}\n\t\\end{axis}\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt,letterpaper]{article}\n\\usepackage{tikz}\n\\usetikzlibrary{chains}\n\\usetikzlibrary{fit}\n\\usetikzlibrary{shapes}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{trees}\n\\usetikzlibrary{positioning}\n\\usepackage{xcolor}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n  scale=1,\n  transform shape,\n  every node/.style={circle, draw=black, fill=white},\n  every fit/.style={draw,inner sep=10pt,text width=0pt}]\n  \\begin{scope}\n    \\begin{scope}[start chain=going below,node distance=5mm]\n      \\foreach \\i in {1,...,12}\n      \\node[on chain] (v\\i) {};\n    \\end{scope}\n    \\node[fit=(v1) (v12),dashed] {};\n    \\node[label=above:$x=0$] at (v1.north) {};\n    \\draw (v1) to [out=120,in=210] (v12);\n  \\end{scope}\n  \\begin{scope}[yshift=-4cm]\n    \\begin{scope}[start chain=going below,node distance=5mm]\n      \\foreach \\i in {1,...,12}\n      \\node[on chain] (u\\i) {};\n    \\end{scope}\n    \\node[fit=(u1) (u12),dashed] {};\n    \\node[label=above:$x=1$] at (u1.north) {};\n    \\draw (u1) to [out=120,in=210] (u12);\n  \\end{scope}\n  \\begin{scope}[yshift=-8cm]\n    \\begin{scope}[start chain=going below,node distance=5mm]\n      \\foreach \\i in {1,...,12}\n      \\node[on chain] (w\\i) {};\n    \\end{scope}\n    \\node[fit=(w1) (w12),dashed] {};\n    \\node[label=above:$x=2$] at (w1.north) {};\n    \\draw (w1) to [out=120,in=210] (w12);\n  \\end{scope}\n  \\begin{scope}[yshift=-12cm]\n    \\begin{scope}[start chain=going below,node distance=5mm]\n      \\foreach \\i in {1,...,12}\n      \\node[on chain] (z\\i) {};\n    \\end{scope}\n    \\node[fit=(z1) (z12),dashed] {};\n    \\node[label=above:$x=3$] at (z1.north) {};\n    \\draw (z1) to [out=120,in=210] (z12);\n  \\end{scope}\n  \\begin{scope}[yshift=-15cm]\n    \\begin{scope}[start chain=going below,node distance=5mm]\n      \\foreach \\i in {1,...,12}\n      \\node[on chain] (x\\i) {};\n    \\end{scope}\n    \\node[fit=(x1) (x12),dashed] {};\n    \\node[label=above:$x=4$] at (x1.north) {};\n    \\draw (x1) to [out=120,in=210] (x12);\n  \\end{scope}\n  \\begin{scope}[yshift=-18cm]\n    \\begin{scope}[start chain=going below,node distance=5mm]\n      \\foreach \\i in {1,...,12}\n      \\node[on chain] (y\\i) {};\n    \\end{scope}\n    \\node[fit=(y1) (y12),dashed] {};\n    \\node[label=above:$x=5$] at (y1.north) {};\n    \\draw (y1) to [out=120,in=210] (y12);\n  \\end{scope}\n  \\begin{scope}[yshift=-21cm]\n    \\begin{scope}[start chain=going below,node distance=5mm]\n      \\foreach \\i in {1,...,12}\n      \\node[on chain] (q\\i) {};\n    \\end{scope}\n    \\node[fit=(q1) (q12),dashed] {};\n    \\node[label=above:$x=6$] at (q1.north) {};\n    \\draw (q1) to [out=120,in=210] (q12);\n  \\end{scope}\n  \\draw (v1) -- (z1);\n  \\draw (v1) -- (x1);\n  \\draw (v1) -- (y1);\n  \\draw (v1) -- (q1);\n  \\draw (v1) -- (w1);\n  \\draw (v1) -- (w12);\n  \\draw (u1) -- (w1);\n  \\draw (u1) -- (w12);\n  \\draw (u1) -- (x1);\n  \\draw (u1) -- (x12);\n  \\draw (u1) -- (y1);\n  \\draw (u1) -- (y12);\n  \\draw (u1) -- (q1);\n  \\draw (u1) -- (q12);\n  \\draw (u1) -- (z1);\n  \\draw (u1) -- (z12);\n  \\draw (w1) -- (x1);\n  \\draw (w1) -- (x12);\n  \\draw (w1) -- (y1);\n  \\draw (w1) -- (y12);\n  \\draw (w1) -- (q1);\n  \\draw (w1) -- (q12);\n  \\draw (w1) -- (z1);\n  \\draw (w1) -- (z12);\n  \\draw (x1) -- (y1);\n  \\draw (x1) -- (y12);\n  \\draw (x1) -- (q1);\n  \\draw (x1) -- (q12);\n  \\draw (x1) -- (z1);\n  \\draw (x1) -- (z12);\n  \\draw (y1) -- (q1);\n  \\draw (y1) -- (q12);\n  \\draw (y1) -- (z1);\n  \\draw (y1) -- (z12);\n  \\draw (z1) -- (q1);\n  \\"
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        "tikz_code": "\\documentclass[border=5mm]{standalone}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=newest}\n\\begin{document}\n\\begin{tikzpicture}[trim axis left]\n\\begin{axis}[ybar,\n    width=1.2\\linewidth,\n    height=5cm,\n    bar width=0.15cm,\n    enlarge x limits=0.5,\n    ymin=0,\n    ymax=13,\n    axis on top,\n    ylabel={Evaluation Score (100\\%)},\n    ylabel style={\n        anchor=north,\n    },\n    xtick=data,\n    xticklabel style={\n        text height=2ex,\n        inner sep=0pt,\n        anchor=north east,\n    },\n    axis lines*=left,\n    y axis line style={opacity=0},\n    tickwidth=0pt,\n    enlarge y limits={value=0.1,upper},\n    legend style={\n        at={(0.5,-0.15)},\n        anchor=north,\n        legend columns=-1,\n        /tikz/every even column/.append style={column sep=0.5cm}\n    },\n    x tick label style={\n        inner sep=0pt,\n        anchor=north east,\n    },\n    nodes near coords={\n        \\pgfkeys{/pgf/fpu=true}%\n        \\pgfmathparse{100*(\\pgfplotspointmeta/100)+100}%\n        \\pgfmathprintnumber[fixed, precision=2]{\\pgfmathresult}%\n        \\pgfkeys{/pgf/fpu=false}%\n    },\n    nodes near coords align={vertical},\n    point meta=explicit symbolic,\n    ]\n\\addplot coordinates {(2013,7) [North America] (2014,7) [Africa] (2015,8) [Africa] (2016,8) [Africa] (2017,9) [Africa] (2018,9) [Africa] (2019,10) [Africa]};\n\\addplot coordinates {(2013,1) [Asia/Pacific] (2014,1) [Asia/Pacific] (2015,1) [Asia/Pacific] (2016,2) [Asia/Pacific] (2017,3) [Asia/Pacific] (2018,3) [Asia/Pacific] (2019,4) [Asia/Pacific]};\n\\addplot coordinates {(2013,1) [North America] (2014,1) [North America] (2015,1) [North America] (2016,2) [North America] (2017,3) [North America] (2018,4) [North America] (2019,5) [North America]};\n\\legend{Europe,North America,South America}\n\\end{axis}\n\\end{tikzpicture}\n\\end{document}"
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        "index": 430,
        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\\usepackage{pgfplots}\n\\usepgfplotslibrary{fillbetween}\n\\pgfplotsset{compat=1.11}\n\\usetikzlibrary{patterns}\n\\usepgfplotslibrary{fillbetween}\n\\usetikzlibrary{patterns}\n\\usepackage{color}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw (-6,-1) -- (1,-1) -- (1,3) -- (-6,3)-- (-6,-1);\n\\draw (-6,3) -- (1,3);\n\\draw (-6,-1) -- (-1,-1);\n\\draw (-1,3) -- (1,3);\n\\draw (-1,-1) -- (1,-1);\n\\node at (-3,-1) {$D_{+}$};\n\\node at (-3,3) {$D_{-}$};\n\\node[color=orange] at (-3,0) {$TQFT^{-1}_{+}$};\n\\node[color=blue!50] at (-3,0) {$TQFT^{-1}_{-}$};\n\\draw (-3,0) -- (0,0);\n\\node at (-3,1.5) {$T$};\n\\node at (0,1.5) {$G$};\n\\node at (-3,-3) {$T^{\\rm{T}}F_{+}T^{-1}F_{+}$};\n\n\\draw[color=orange] (-1.5,1.5) -- (1.5,1.5);\n\\draw[color=orange] (-1.5,-1.5) -- (1.5,-1.5);\n\\draw[color=orange] (-1.5,1.5) -- (-1.5,-1.5);\n\\draw[color=orange] (1.5,1.5) -- (1.5,-1.5);\n\\draw[color=blue!50] (-1.5,0) -- (1.5,0);\n\\draw[color=blue!50] (-1.5,0) -- (-2.5,1);\n\\draw[color=blue!50] (-1.5,0) -- (-1,1.5);\n\\draw[color=blue!50] (1.5,0) -- (2.5,1);\n\\draw[color=blue!50] (1.5,0) -- (1,1.5);\n\\draw[color=blue!50] (-2.5,1) -- (2.5,1);\n\\draw[color=blue!50] (-1,1.5) -- (1,1.5);\n\\draw[color=blue!50] (-2.5,1) -- (-1,1.5);\n\\draw[color=blue!50] (2.5,1) -- (1,1.5);\n\\node[color=orange] at (0,0) {\\textbullet};\n\\node at (0,0) [below] {$D_{-}$};\n\\draw[color=orange] (3,1) -- (5,1) -- (5,3) -- (3,3)-- (3,1);\n\\draw (3,1) -- (5,1);\n\\draw (3,3) -- (5,3);\n\\draw (3,1) -- (3,-1);\n\\draw (5,1) -- (5,-1);\n\\draw (3,-1) -- (5,-1);\n\\draw (3,1) -- (5,-1);\n\\draw (3,3) -- (5,-1);\n\\draw (3,1) -- (4,2);\n\\draw (5,3) -- (5,2);\n\\draw (4,2) -- (5,3);\n\\draw (4,2) -- (3,3);\n\\node[color=orange] at (3,1) {\\textbullet};\n\\node at (3,1) [below] {$D_{-}$};\n\\node[color=orange] at (5,3) {\\textbullet};\n\\node at (5,3) [above] {$D_{+}$};\n\\node at (4,-3) {$T^{\\rm{T}}F_{+}T^{-1}F_{+}$ with the defect $D_{+}$};\n\n\\draw[color=blue!50] (4,2) -- (6,2);\n\\draw[color=blue!50] (4,2) -- (4,-0.5);\n\\draw[color=blue!50] (6,2) -- (6,-0.5);\n\\draw[color=blue!50] (4,-0.5) -- (6,-0.5);\n\\node[color=blue!50] at (5,0) {\\textbullet};\n\\node[color=blue!50] at (5,0) [below] {$D_{-}$};\n\\node[color=blue!50] at (4,0) {\\textbullet};\n\\node[color=blue!50] at (4,0) [below] {$D_{-}$};\n\\node[color=blue!50] at (5,1.5) {\\textbullet};\n\\node[color=blue!50] at (5,1.5) [above] {$TG$};\n\\node[color=blue!50] at (4,1.5) {\\textbullet};\n\\node[color=blue!50] at (4,1.5) [above] {$T$};\n\\node[color=blue!50] at (6,-1.5) {\\textbullet};\n\\node[color=blue!50] at (6,-1.5) [below] {$T^{\\rm{T}}G$};\n\\node[color=blue!50] at (4,-1.5) {\\textbullet};\n\\node[color=blue!50] at (4,-1.5) [below] {$T^{\\rm{T}}F_{+}T^{-1}F_{+}$};\n\\node at (3,0) {$\\implies$};\n\\node at (5,0) {$\\implies$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 431,
        "tikz_code": "\\documentclass[12pt,reqno]{amsart}\n\\usepackage{amssymb}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usepackage[colorlinks]{hyperref}\n\\usepackage[T1]{fontenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.5]\n \n\n \\begin{scope}[shift={(-2,0)}]\n  \\foreach \\i in {1,...,5}\n  {\n  \\filldraw[fill=white, draw=black,thick] (0,\\i) circle (.2cm);\n  }\n  \n  \\draw (0,1)--(0,5) (-.2,1.5)--(.2,2.5) (-.2,2.5)--(.2,1.5);\n  \\draw (-.2,3.5)--(.2,4.5) (-.2,4.5)--(.2,3.5);\n  \n  \\draw[->] (-2,4) .. controls (-1,4) and (-1,2) .. (0,2);\n  \\draw[->] (-2,3) .. controls (-1,3) and (-1,1) .. (0,1);\n  \n  \\node at (0,1) {$V_1$};\n  \\node at (0,2) {$V_2$};\n  \\node at (0,3) {$V_3$};\n  \\node at (0,4) {$V_4$};\n  \\node at (0,5) {$V_5$};\n  \n  \\node at (-1,4) {$G$};\n\n  \\end{scope}\n\n  \\begin{scope}[shift={(10,0)}]\n  \\foreach \\i in {1,...,5}\n  {\n  \\filldraw[fill=white, draw=black,thick] (0,\\i) circle (.2cm);\n  }\n  \n  \\draw (0,1)--(0,5) (0.2,1.5)--(-.2,2.5) (0.2,2.5)--(-.2,1.5);\n  \\draw (0.2,3.5)--(-.2,4.5) (0.2,4.5)--(-.2,3.5);\n \n\n   \\draw[<-] (5,4) .. controls (6,4) and (6,2) .. (0,2);\n   \\draw[<-] (5,3) .. controls (6,3) and (6,1) .. (0,1);\n  \n  \n  \\node at (0,1) {$V_1$};\n  \\node at (0,2) {$V_2$};\n  \\node at (0,3) {$V_3$};\n  \\node at (0,4) {$V_4$};\n  \\node at (0,5) {$V_5$};\n  \n  \\node at (6,4) {$P$};\n  \\node at (1,4) {$G'$};\n  \\end{scope}\n  \n  \\begin{scope}[shift={(-10,-3)}]\n    \\foreach \\i in {1,...,3}\n    {\n    \\filldraw[fill=white, draw=black,thick] (\\i,0) circle (.2cm);\n    }\n    \n    \\draw (1,0)--(3,0) (1.2,-.5)--(2.8,1.5) (1.2,1.5)--(2.8,.5) (1.2,.5)--(2.8,-.5);\n    \n    \n    \\draw[->] (2,0) .. controls (3,0) and (3,2) .. (2,2);\n    \n    \\node at (1,0) {$1$};\n    \\node at (2,0) {$2$};\n    \\node at (3,0) {$3$};\n    \n    \n    \\node at (2,2) {$4$};\n    \n    \\end{scope}\n  \\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amssymb,amsmath,amsthm,mathtools,extpfeil}\n\\usepackage{tikz}\n\n\\newcommand{\\RR}{{\\mathbb R}}\n\n\\newcommand{\\CC}{{\\mathbb C}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{scope}[xshift=-4cm]\n  \\draw[very thick] (-1,0) arc (0:90:2) -- cycle;\n  \\draw[very thick] (0,-1) arc (90:180:2) -- cycle;\n  \\draw[very thick] (1,1) arc (180:270:2) -- cycle;\n  \\draw[very thick] (1,1) arc (180:360:2) -- cycle;\n  \\draw[fill=gray!30,very thick] (1,1) -- (0,-1) -- (1,-1) -- cycle;\n  \\draw[fill=gray!30,very thick] (1,1) -- (0,0) -- (1,-1) -- cycle;\n  \\node at (1.2,1.3) {$\\tau$};\n  \\node at (-1.5,-1.5) {$x_1$};\n  \\node at (-1.5,1.5) {$1$};\n  \\node at (1.5,-1.5) {$x_2$};\n  \\node at (1.4,1.2) {$\\tau(\\CC z)$};\n  \\node at (1.2,-1.3) {$\\RR^2$};\n  \\node at (0.2,0) {$\\tau(x)$};\n  \\node at (-0.3,-0.3) {$x$};\n  \\draw[very thick,dashed] (-1,0) -- (1,0) node[pos=0.5,below] {$\\varepsilon$};\n  \\draw[very thick,dashed] (-1,0) -- (0,1) node[pos=0.5,left] {$\\gamma$};\n  \\draw[very thick,dashed] (-1,0) -- (0,-1) node[pos=0.5,left] {$\\delta$};\n  \\node at (3,-1.5) {$\\iota$};\n\\end{scope}\n\\draw[->] (1.5,0) -- (4.5,0) node[pos=0.5,above] {rescale};\n\\begin{scope}[xshift=4cm]\n  \\draw[very thick] (-1,0) arc (0:90:2) -- cycle;\n  \\draw[very thick] (0,-1) arc (90:180:2) -- cycle;\n  \\draw[very thick] (1,1) arc (180:270:2) -- cycle;\n  \\draw[very thick] (1,1) arc (180:360:2) -- cycle;\n  \\draw[fill=gray!30,very thick] (1,1) -- (0,-1) -- (1,-1) -- cycle;\n  \\draw[fill=gray!30,very thick] (1,1) -- (0,0) -- (1,-1) -- cycle;\n  \\node at (1.3,1.2) {$\\tau(\\CC z)$};\n  \\node at (1.2,-1.3) {$\\RR^2$};\n  \\node at (0.2,0) {$x_1$};\n  \\node at (-0.3,-0.3) {$x_2$};\n  \\draw[very thick,dashed] (-1,0) -- (1,0);\n  \\draw[very thick,dashed] (-1,0) -- (0,1);\n  \\draw[very thick,dashed] (-1,0) -- (0,-1);\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{trees}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\\node[circle,draw] { $F_{3}$ }\n\t\tchild { node[circle,draw] { $F_{2}$ }\n\t\t\tchild { node[circle,draw] { $F_{1}$ }\n\t\t\t\tchild { node[circle,draw] { 1 }}\n\t\t\t\tchild { node[circle,draw] { 4 }}\n\t\t\t}\n\t\t\tchild { node[circle,draw, fill=black,inner sep=0pt, minimum size=5pt] { 2 }}\n\t\t}\n\t\tchild { node[circle,draw, fill=red,inner sep=0pt, minimum size=5pt] { $F_{4}$ }\n\t\t\tchild { node[circle,draw, fill=black,inner sep=0pt, minimum size=5pt] { 3 }}\n\t\t\tchild { node[circle,draw, fill=black,inner sep=0pt, minimum size=5pt] { 8 }}\n\t\t};\n\t\t\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[border=3pt,tikz]{standalone}\n\\usetikzlibrary{arrows.meta,positioning,shadows, shapes.geometric,shapes.symbols}\n\\begin{document}\n\\begin{tikzpicture}[font=\\sffamily\\footnotesize, thick,\n    pics/box/.style={code={\\node[#1](#2){#2};}},\n    >=Latex\n]\n\n\\matrix[row sep=3em, column sep=3em] (mat)\n{\n\\pic{box={rectangle, draw, minimum width=5em}} {Ghz=(000)+(011)=(100)};\n& \\pic{box={rectangle, draw, minimum width=5em}} {w=0000+001+000+000=(1000)};\n& \\pic{box={rectangle, draw, minimum width=5em}} {W=(0100)+(1011)=(00100)}; \\\\\n\\pic{box={rectangle, draw, minimum width=5em}} {$A-B$};\n& \\pic{box={rectangle, draw, minimum width=5em}} {$C-A$};\n& \\pic{box={rectangle, draw, minimum width=5em}} {$B-C$}; \\\\\n\\pic{box={rectangle, draw, minimum width=5em}} {$A=(r(p(a))=00)$};\n& \\pic{box={rectangle, draw, minimum width=5em}} {$C=(r(p(b))=11)$};\n& \\pic{box={rectangle, draw, minimum width=5em}} {$B=(r(p(b))=11)$}; \\\\\n};\n\n\\foreach \\X in {1,3}\n{\\draw[->] (mat-2-\\X) -- (mat-1-\\X);}\n\\foreach \\X in {2}\n{\\draw[->] (mat-2-\\X) -- (mat-3-\\X);}\n\\draw[->] (mat-2-1) -- (mat-2-2);\n\\draw[->] (mat-2-2) -- (mat-2-3);\n\n\\end{tikzpicture}\n\\end{document}"
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        "index": 442,
        "tikz_code": "\\documentclass[10pt,twocolumn,letterpaper]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{spy,calc,shapes,arrows,positioning}\n\\usepackage[skins]{tcolorbox}\n\\usepackage{pgfplots}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\\node[inner sep=0pt] (figure) at (0,0)\n\t{\\includegraphics[width=.45\\textwidth]{example-image}};\n\t\n\t\\node at ($(figure.south)!.25!(figure.north)$) {(c) d)};\n\t\\node at ($(figure.west)!.4!(figure.east)$)  {(c) d)};\n\t\n\t\\node[rotate=90] at ($(figure.west)!.17!(figure.south)$) {\\small$n_\\gamma$};\n\t\\draw[dashed] ($(figure.west)!.17!(figure.south)$) -- ($(figure.west)!.17!(figure.north)$);\n\t\n\t\\node at ($(figure.north)!.02!(figure.west)$) {\\small (a) b)};\n\t\n\t%\n\t%\n\t\\begin{scope}[shift={($(figure.east)+(1.25cm,0)$)}]\n\t\\foreach \\x in {0,1,2}\n\t\\node[draw,rectangle,inner sep=4pt,fill=white] (H\\x) at (0,\\x) {X};\n\t\\foreach \\x in {0,1}\n\t\\node[draw,rectangle,inner sep=4pt,fill=white] (X\\x) at (0,\\x+.5) {H};\n\t\n\t%\n\t%\n\t%\n\t%\n\t%\n\t%\n\t%\n\t%\n\t%\n\t%\n\t%\n\t\n\t\\node[rotate=90] at ($(figure.north)!.01!(figure.east)$) {\\small$n_z$};\n\t\n\t\\draw[dashed] ($(figure.south)!.1!(figure.west)$) -- ($(figure.south)!.9!(figure.west)$);\n\t\\draw[dashed] ($(figure.south)!.2!(figure.west)$) -- ($(figure.south)!.8!(figure.west)$);\n\t\\draw[dashed] ($(figure.south)!.3!(figure.west)$) -- ($(figure.south)!.7!(figure.west)$);\n\t\n\t\\node[rotate=90] at ($(figure.south)!.01!(figure.east)$) {\\small$n_y$};\n\t\\draw[dashed] ($(figure.south)!.01!(figure.east)$) -- ($(figure.south)!.9!(figure.east)$);\n\t\\draw[dashed] ($(figure.south)!.02!(figure.east)$) -- ($(figure.south)!.8!(figure.east)$);\n\t\\draw[dashed] ($(figure.south)!.03!(figure.east)$) -- ($(figure.south)!.7!(figure.east)$);\n\t\n\t\\node[rotate=90] at ($(figure.south)!.01!(figure.east)$) {\\small$n_x$};\n\t\\draw[dashed] ($(figure.south)!.01!(figure.east)$) -- ($(figure.south)!.9!(figure.east)$);\n\t\\draw[dashed] ($(figure.south)!.02!(figure.east)$) -- ($(figure.south)!.8!(figure.east)$);\n\t\\draw[dashed] ($(figure.south)!.03!(figure.east)$) -- ($(figure.south)!.7!(figure.east)$);\n\t\n\t\\end{scope}\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "index": 443,
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        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[xscale=1,yscale=1]\n\\node (a) at (0,1) [circle,draw,minimum size=15mm] {VOCP431};\n\\node (b) at (-2,-1) [circle,draw,minimum size=15mm] {VOCP432};\n\\node (c) at (2,-1) [circle,draw,minimum size=15mm] {VOCP434};\n\\node (d) at (-2,-3) [circle,draw,minimum size=15mm] {VOCP433};\n\\node (e) at (0,-3) [circle,draw,minimum size=15mm] {VOCP434};\n\\node (f) at (2,-3) [circle,draw,minimum size=15mm] {VOCP435};\n\\draw [->,>=latex] (a) edge (b);\n\\draw [->,>=latex] (a) edge (c);\n\\draw [->,>=latex] (b) edge (d);\n\\draw [->,>=latex] (b) edge (e);\n\\draw [->,>=latex] (c) edge (f);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 445,
        "tikz_code": "\\documentclass[sigconf]{acmart}\n\\usepackage{tikz}\n\\usepackage{tikz-qtree}\n\\usetikzlibrary{trees}\n\\usetikzlibrary{fit}\n\\usetikzlibrary{shapes}\n\\usetikzlibrary{arrows.meta}\n\\usetikzlibrary{positioning,shadows,arrows}\n\\usetikzlibrary{shapes.geometric}\n\\usetikzlibrary{shapes.misc}\n\\usetikzlibrary{arrows,automata}\n\\usetikzlibrary{shapes.gates.logic.US}\n\\usetikzlibrary{arrows.meta,calc}\n\\usepackage{tikz}\n\\usepackage{tikz-qtree}\n\\usepackage{tikz-qtree-qtree}\n\\usetikzlibrary{trees}\n\\usetikzlibrary{fit}\n\\usetikzlibrary{shadows}\n\\usepackage{amsmath}\n\\usepackage{tikz-qtree}\n\\usepackage{amssymb}\n\\usetikzlibrary{arrows.meta}\n\\usepackage{amsmath}\n\\usepackage{pgf}\n\\usepackage{tikz}\n\\usepackage{color, colortbl}\n\\usetikzlibrary{shapes}\n\\usetikzlibrary{arrows.meta}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}[level distance=1cm,\n  level 1/.style={sibling distance=3cm},\n  level 2/.style={sibling distance=1.5cm},\n  level 3/.style={sibling distance=1cm},\n  every node/.style = {shape=rectangle, rounded corners,\n    draw, align=center,\n    top color=white, bottom color=white}]]\n  \\node {$L_1$}\n    child { node {$L_2$} \n      child { node {$L_3$} \n        child { node {$L_{1.3}, X_4,5,X_6$} }\n        child { node {$L_{1.4},7,8,X_9$} }\n        child { node {$L_{1.5},10,11,X_{14},15,16$} }}\n      child { node {$L_4$} \n        child { node {$L_{7}$} \n          child { node {$L_{11}$}\n            child { node {$X_{16},17,18,X_{22}$} }\n          }\n        }\n      }\n    }\n    child { node {$L_5$} \n      child { node {$L_8$} \n        child { node {$L_{10}$} \n          child { node {$L_{14}$} \n            child { node {$X_{12},19,20,X_{22}$} }\n          }\n        }\n      }\n      child { node {$L_9$} \n        child { node {$L_{12}$} \n          child { node {$L_{15}$} \n            child { node {$X_{20}$} }\n          }\n        }\n      }\n    };\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 446,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\t\t\\draw[step=1.0,black,thin] (0,0) grid (10,10);\n\t\t\\draw[step=0.5,black,thick] (0,0) grid (10,10);\n\t\t\n\t\t\\draw[red, ultra thick] (0,5) rectangle (5,10);\n\t\t\\draw[red, ultra thick] (5,0) rectangle (10,5);\n\t\t\n\t\t\\draw[thick] (5, 5) node[fill=white] {$0$};\n\t\t\\draw[thick] (3.5, 6.5) node[fill=white] {$1$};\n\t\t\\draw[thick] (3.5, 4.5) node[fill=white] {$1$};\n\t\t\\draw[thick] (6.5, 4.5) node[fill=white] {$1$};\n\t\t\\draw[thick] (6.5, 6.5) node[fill=white] {$1$};\n\t\t\n\t\t\\draw[thick] (1.5, 2.5) node[fill=white] {$2.5$};\n\t\t\\draw[thick] (2.5, 1.5) node[fill=white] {$2.5$};\n\t\t\\draw[thick] (7.5, 2.5) node[fill=white] {$2.5$};\n\t\t\\draw[thick] (8.5, 1.5) node[fill=white] {$2.5$};\n\t\t\n\t\t\\draw[thick] (1.5, 7.5) node[fill=white] {$5.5$};\n\t\t\\draw[thick] (2.5, 8.5) node[fill=white] {$5.5$};\n\t\t\\draw[thick] (7.5, 7.5) node[fill=white] {$5.5$};\n\t\t\\draw[thick] (8.5, 8.5) node[fill=white] {$5.5$};\n\t\t\n\t\t\\draw[thick] (3.5, 1.5) node[fill=white] {$3.5$};\n\t\t\\draw[thick] (4.5, 2.5) node[fill=white] {$3.4$};\n\t\t\\draw[thick] (3.5, 7.5) node[fill=white] {$3.4$};\n\t\t\\draw[thick] (4.5, 8.5) node[fill=white] {$3.4$};\n\t\t\n\t\t\\draw[thick] (6.5, 1.5) node[fill=white] {$6$};\n\t\t\\draw[thick] (7.5, 2.5) node[fill=white] {$5.6$};\n\t\t\\draw[thick] (6.5, 7.5) node[fill=white] {$5.6$};\n\t\t\\draw[thick] (7.5, 8.5) node[fill=white] {$5.6$};\n\t\t\n\t\t\\draw[thick] (1.5, 3.5) node[fill=white] {$4$};\n\t\t\\draw[thick] (2.5, 4.5) node[fill=white] {$4$};\n\t\t\\draw[thick] (7.5, 3.5) node[fill=white] {$4$};\n\t\t\\draw[thick] (8.5, 4.5) node[fill=white] {$4$};\n\t\t\n\t\t\\draw[thick] (1.5, 4.5) node[fill=white] {$6$};\n\t\t\\draw[thick] (2.5, 3.5) node[fill=white] {$6$};\n\t\t\\draw[thick] (7.5, 4.5) node[fill=white] {$6$};\n\t\t\\draw[thick] (8.5, 3.5) node[fill=white] {$6$};\n\t\t\n\t\t\\draw[thick] (1.5, 5.5) node[fill=white] {$5.6$};\n\t\t\\draw[thick] (2.5, 6.5) node[fill=white] {$5.6$};\n\t\t\\draw[thick] (7.5, 5.5) node[fill=white] {$5.6$};\n\t\t\\draw[thick] (8.5, 6.5) node[fill=white] {$5.6$};\n\t\t\n\t\t\\draw[thick] (3.5, 7.5) node[fill=white] {$6$};\n\t\t\\draw[thick] (4.5, 6.5) node[fill=white] {$6$};\n\t\t\\draw[thick] (3.5, 8.5) node[fill=white] {$6$};\n\t\t\\draw[thick] (4.5, 7.5) node[fill=white] {$6$};\n\t\t\n\t\t\\draw[thick] (5.5, 1.5) node[fill=white] {$5.5$};\n\t\t\\draw[thick] (6.5, 2.5) node[fill=white] {$5.5$};\n\t\t\\draw[thick] (5.5, 7.5) node[fill=white] {$5.5$};\n\t\t\\draw[thick] (6.5, 8.5) node[fill=white] {$5.5$};\n\t\t\n\t\t\\draw[thick] (5.5, 2.5) node[fill=white] {$6$};\n\t\t\\draw[thick] (6.5, 3.5) node[fill=white] {$6$};\n\t\t\\draw[thick] (5.5, 8.5) node[fill=white] {$6$};\n\t\t\\draw[thick] (6.5, 4.5) node[fill=white] {$6$};\n\t\t\n\t\t\\draw[thick] (1.5, 8.5) node[fill=white] {$6$};\n\t\t\\draw[thick] (2.5, 7.5) node[fill=white] {$6$};\n\t\t\\draw[thick] (7.5, 8.5) node[fill=white] {$6$};\n\t\t\\draw[thick] (8.5, 7.5) node[fill=white] {$6$};\n\t\t\n\t\t\\draw[thick] (3.5, 5.5) node[fill=white] {$6$};\n\t\t\\draw[thick] (4.5, 4.5) node[fill=white] {$6$};\n\t\t\\draw[thick] (3.5, 6.5) node[fill=white] {$6$};\n\t"
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    {
        "index": 447,
        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amssymb, amsmath, amsthm}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usepackage{pgfplotstable}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\begin{axis}[\n        axis x line=middle, axis y line=middle, samples = 200,\n        ylabel={$y$}, ylabel style={anchor=south}, ymin=-0.5, ymax=2.5, ytick={0,1,2},\n        xlabel={$x$}, xlabel style={anchor=west}, xmin=0, xmax=4, xtick={1,2,3},\n        legend style={anchor=south east, legend cell align=left, align=left}]\n      \\addplot[black, thick, domain=0:1] {2-x};\n      \\addplot[black, thick, domain=1:3] {0};\n      \\addplot[black, dashed, thick, domain=0:3] {1-x/2};\n      \\addplot[black, dashed, thick, domain=0:3] {0};\n      \\addplot[black, dotted, thick, domain=1:3] {1};\n      \\addplot[black, dotted, thick, domain=0:1] {0};\n      \\legend{$\\text{Con}|\\pi_{7,7}(y)|$,$\\text{D}^{2} \\text{L}^{2}(\\pi_{7,7})$,$\\text{Con}|\\pi_{27,27}(y)|$,$\\text{D}^{2} \\text{L}^{2}(\\pi_{27,27})$}\n    \\end{axis}\n  \\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 448,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n                    \\centering\n                    \\node (img){\\includegraphics[trim={.75cm .5cm .75cm .75cm},clip, width=.6\\linewidth]{example-image}};\n                    \n                    \\node[left=of img, node distance=0cm, rotate=90, xshift=1.5cm, yshift=-.8cm, font=\\color{black}] {\\small{N-RFR}};\n                    \n                    \\node[right=of img, node distance=0cm, rotate=270, xshift=0cm, yshift=-.9cm, font=\\color{black}] {\\small{(c) Voxels}};\n                    \n                    \\node[below=of img, node distance=0cm, xshift=-1.3cm, yshift=.5cm,font=\\color{black}] {\\small{Non-Training parameters}};\n                    \n                    \\node[below=of img, node distance=0cm, xshift=1.4cm, yshift=.5cm,font=\\color{green!50!black}] {\\small{Training parameters}};\n                    \n                    \\node[above=of img, node distance=0cm, xshift=-.4cm, yshift=-1.1cm,font=\\color{black}] {\\small{(d) Tripod}};\n                    \n                    \\node[below=of img, node distance=0cm, xshift=-1.3cm, yshift=-.5cm,font=\\color{black}] {\\small{Non-Training parameters}};\n                \\end{tikzpicture}\n\n\\end{document}"
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        "index": 449,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw [fill=white] (0,0) circle (2pt);\n\\draw [fill=white] (2,0) circle (2pt);\n\\draw [fill=white] (4,0) circle (2pt);\n\\draw [fill=white] (6,0) circle (2pt);\n\\draw [fill=white] (8,0) circle (2pt);\n\\draw [fill=white] (10,0) circle (2pt);\n\\draw [fill=white] (12,0) circle (2pt);\n\\draw [fill=white] (14,0) circle (2pt);\n\\draw [fill=white] (16,0) circle (2pt);\n\\draw (0,0) -- (16,0);\n\\draw (0,-1) -- (16,-1);\n\\draw (0,-2) -- (16,-2);\n\\draw (0,-3) -- (16,-3);\n\\draw (0,-4) -- (16,-4);\n\\draw (0,-5) -- (16,-5);\n\\draw (0,-6) -- (16,-6);\n\\draw (0,-7) -- (16,-7);\n\\draw (0,-8) -- (16,-8);\n\\draw (1,-8) -- (1,0);\n\\draw (3,-8) -- (3,0);\n\\draw (5,-8) -- (5,0);\n\\draw (7,-8) -- (7,0);\n\\draw (9,-8) -- (9,0);\n\\draw (11,-8) -- (11,0);\n\\draw (13,-8) -- (13,0);\n\\draw (15,-8) -- (15,0);\n\\draw (0.5,-1) -- (0.5,0);\n\\draw (0.5,-2) -- (0.5,0);\n\\draw (0.5,-3) -- (0.5,0);\n\\draw (0.5,-4) -- (0.5,0);\n\\draw (3.5,-4) -- (3.5,0);\n\\draw (5.5,-4) -- (5.5,0);\n\\draw (7.5,-4) -- (7.5,0);\n\\draw (9.5,-4) -- (9.5,0);\n\\draw (11.5,-4) -- (11.5,0);\n\\draw (13.5,-4) -- (13.5,0);\n\\draw (15.5,-4) -- (15.5,0);\n\\draw [dashed] (0,-1.5) -- (16,-1.5);\n\\draw [dashed] (0,-3.5) -- (16,-3.5);\n\\draw [fill=white] (-0.1,-1.5) rectangle (0.1,-3.5);\n\\draw [fill=white] (14.9,-3.5) rectangle (15.1,-5.5);\n\\draw [fill=white] (14.9,-5.5) rectangle (15.1,-7.5);\n\\draw [fill=white] (14.9,-7.5) rectangle (15.1,-9.5);\n\\draw (2,1) node {$\\strut y$};\n\\draw (4,1) node {$\\strut z$};\n\\draw (-1,0) node {$\\strut\\dots$};\n\\draw (17,0) node {$\\strut\\dots$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 451,
        "tikz_code": "\\documentclass[prd,preprint,superscriptaddress,nofootinbib,longbibliography,aps]{revtex4-1}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usepackage[compat=1.1.0]{tikz-feynman}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n  \\begin{feynman}\n   \\vertex (a1);\n    \\vertex[right=1.5cm of a1] (a2);\n    \\vertex[right=1.5cm of a2] (a3) ;\n    \\vertex[right=1.5cm of a3] (a4);\n    \\vertex[right=1.5cm of a4] (a5);\n\n\n     \\vertex[below=2.5cm of a1] (b1);\n    \\vertex[right=1.5cm of b1] (b2);\n    \\vertex[right=1.5cm of b2] (b3) ;\n    \\vertex[right=1.5cm of b3] (b4);\n    \\vertex[right=1.5cm of b4] (b5);\n    \\vertex[right=1.5cm of b5] (b6);\n\n\n    \\vertex[below=1.5cm of a2] (c1) ;\n    \\vertex[below=1.5cm of a3] (c2) ;\n    \\vertex[below=1.5cm of a4] (c3) ;\n    \\vertex[below=1.5cm of a5] (c4) ;\n    \\vertex[below=1.5cm of b1] (d1) ;\n    \\vertex[below=1.5cm of b2] (d2) ;\n    \\vertex[below=1.5cm of b3] (d3) ;\n    \\vertex[below=1.5cm of b4] (d4) ;\n\n\n     \\vertex[left=1.5cm of c1] (e1);\n     \\vertex[right=1.5cm of c4] (e2);\n\n      \\vertex[above=1cm of a2] (a2p);\n      \\vertex[below=1cm of b2] (b2p);\n\n\n\n      \\vertex[left=1.5cm of c2] (c2p);\n      \\vertex[right=1.5cm of c3] (c3p);\n\n\n    \\diagram* {\n      {[edges=fermion]\n        (a1) -- (a2)--(a3)--(a4)--(a5),\n        (b1) -- (b2)--(b3)--(b4)--(b5)--(b6),\n      },\n      (a2) -- [boson, edge label=\\(\\gamma\\)] (c1),\n      (b2) -- [boson, edge label'=\\(Z,Z'\\)] (c2),\n      (c3) -- [boson, edge label'=\\(Z,Z'\\)] (d3),\n      (a3) -- [scalar, edge label'=\\(\\gamma\\),near start] (c3),\n      (b3) -- [scalar, edge label=\\(W,W^\\pm\\),near start] (d3),\n      (c2p) -- [boson, edge label=\\(W,W^\\pm\\)] (c3p),\n      (a2p) -- [scalar, edge label'=\\(\\gamma\\)] (a3),\n      (a4) -- [boson, edge label'=\\(\\gamma\\)] (b4),\n      (b5) -- [boson, edge label=\\(\\gamma\\)] (b6),\n\n       (c4) -- [boson, edge label=\\(W,W^\\pm\\)] (e2),\n      (e1) -- [boson, edge label=\\(\\gamma\\)] (d1),\n\n\n       (d4) -- [boson, edge label'=\\(\\gamma\\)] (e1),\n       (d1) -- [boson, edge label'=\\(\\gamma\\)] (b1),\n       (b6) -- [boson, edge label'=\\(\\gamma\\)] (a5),\n       (b1) -- [scalar, edge label'=\\(h\\)] (d1),\n       (c1) -- [scalar, edge label'=\\(h\\)] (c2p),\n       (c3p) -- [scalar, edge label'=\\(h\\)] (c4),\n      };\n\n    \\draw [decoration={brace}, decorate] (a1.south west) -- (b1.north west)\n            node [pos=0.5, left] {\\(f\\)};\n    \\draw [decoration={brace}, decorate] (b5.north east) -- (a5.south east)\n            node [pos=0.5, right] {\\(e^-\\)};\n    \\draw [decoration={brace}, decorate] (c1.north west) -- (d1.south west)\n            node [pos=0.5, left] {\\(f\\)};\n    \\draw [decoration={brace}, decorate] (d4.south east) -- (c4.north east)\n            node [pos=0.5, right] {\\(e^-\\)};\n\n\n\n\n\n\\end{feynman}\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 452,
        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath,amsfonts,amssymb,amsthm}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n    \\draw[latex-latex] (0,2) -- (0,0) -- (4,0) ;\n    \\draw[thick,color=cyan,domain=0.3:4,samples=200] plot (\\x,{-\\x^-1} );\n    \\draw[thick,color=cyan] (2,0) node[below] {$\\theta$};\n    \\draw[color=cyan] (0,1.5) node[left] {$(1-\\theta)g(\\theta)$};\n    \\draw[fill=cyan] (0,0) circle (1.5pt);\n    \\draw[fill=cyan] (2,0) circle (1.5pt);\n    \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 453,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath,amsfonts,amssymb,amsthm,mathtools}\n\\usepackage[usenames,dvipsnames]{xcolor}\n\\usepackage[colorinlistoftodos]{todonotes}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{chains}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8]\n\\draw (0,5) -- (0,0) -- (1,0) -- (1,1) -- (2,1) -- (2,3) -- (3,3) -- (3,4) -- (4,4) -- (4,5) -- (0,5);\n\\draw (0,1) -- (1,1);\n\\draw (0,2) -- (1,2);\n\\draw (1,3) -- (2,3);\n\\draw (2,4) -- (3,4);\n\\node at (1.5,-0.5) {$0$};\n\\node at (2.5,-0.5) {$1$};\n\\node at (3.5,-0.5) {$2$};\n\\node at (4.5,-0.5) {$\\cdots$};\n\\draw (4.5,5) -- (4.5,0);\n\\draw[densely dotted] (0,5) -- (0,6.5);\n\\draw[densely dotted] (1,5) -- (1,6.5);\n\\draw[densely dotted] (2,5) -- (2,6.5);\n\\draw[densely dotted] (3,5) -- (3,6.5);\n\\draw[densely dotted] (4,5) -- (4,6.5);\n\\draw (5.5,5) -- (5.5,1.5) -- (6.5,1.5) -- (6.5,5);\n\\draw (5.5,2.5) -- (6.5,2.5);\n\\draw (5.5,3.5) -- (6.5,3.5);\n\\node at (4.5,5.5) {$0$};\n\\node at (5.5,5.5) {$1$};\n\\node at (6.5,5.5) {$2$};\n\\node at (7.5,5.5) {$\\cdots$};\n\\draw (7.5,5) -- (7.5,2.5) -- (8.5,2.5) -- (8.5,5);\n\\draw (7.5,3.5) -- (8.5,3.5);\n\\draw (7.5,4.5) -- (8.5,4.5);\n\\draw (8.5,1.5) -- (8.5,5);\n\\node at (7.5,5.5) {$0$};\n\\node at (8.5,5.5) {$1$};\n\\node at (9.5,5.5) {$2$};\n\\node at (10.5,5.5) {$\\cdots$};\n\\draw (10.5,5) -- (10.5,4.5) -- (11.5,4.5) -- (11.5,5);\n\\draw (10.5,3.5) -- (11.5,3.5);\n\\draw (10.5,2.5) -- (11.5,2.5);\n\\draw (11.5,1.5) -- (11.5,5);\n\\node at (10.5,5.5) {$0$};\n\\node at (11.5,5.5) {$1$};\n\\node at (12.5,5.5) {$2$};\n\\node at (13.5,5.5) {$\\cdots$};\n\\draw (13.5,5) -- (13.5,2) -- (14.5,2) -- (14.5,5);\n\\draw (13.5,3) -- (14.5,3);\n\\draw (13.5,4) -- (14.5,4);\n\\draw (14.5,1) -- (14.5,5);\n\\node at (-1,2.5) {$V_k=$};\n\\node at (1,4) {$C_{2k-1}$};\n\\node at (2,4) {$C_{2k}$};\n\\node at (3,4) {$C_{2k+1}$};\n\\node at (11,4) {$=C_{2k+k}$};\n\\node at (8,4) {$=C_{2k+2k}$};\n\\node at (1,5.5) {$C_{1}$};\n\\node at (2,5.5) {$C_{2}$};\n\\node at (3,5.5) {$C_{3}$};\n\\node at (11,5.5) {$=C_{2k+1}$};\n\\node at (11,1.5) {$=0$};\n\\node at (8,1.5) {$=1$};\n\\node at (8,2.5) {$=-1$};\n\\node at (8,3.5) {$=-2k-1$};\n\\node at (11,3.5) {$=0$};\n\\node at (11,4.5) {$=1$};\n\\node at (11,2.5) {$=-1$};\n\\node at (11,3.5) {$=-2k-1$};\n\\node at (0.5,3.5) {$V_{-1}$};\n\\node at (0.5,4.5) {$V_{-2}$};\n\\node at (0.5,5.5) {$\\vdots$};\n\\node at (3.5,3.5) {where};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 454,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns,arrows,decorations.pathreplacing}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.35]\n\\node at (-5,-1.5) {$X$};\n\\draw[fill=black] (0,0) circle (5pt);\n\\draw[fill=black] (0,5) circle (5pt);\n\\draw[fill=black] (10,0) circle (5pt);\n\\draw[fill=black] (10,5) circle (5pt);\n\\node at (0.3,0) {$a$};\n\\node at (10.3,0) {$b$};\n\\node at (0.3,5) {$c$};\n\\node at (10.3,5) {$d$};\n\\draw[thick](0,0)--(0,5)--(10,5)--(10,0)--(0,0);\n\\draw[fill=black] (5,10) circle (5pt);\n\\draw[fill=black] (5,15) circle (5pt);\n\\draw[fill=black] (15,10) circle (5pt);\n\\draw[fill=black] (15,15) circle (5pt);\n\\draw[fill=black] (10,12.5) circle (5pt);\n\\draw[thick](5,10)--(5,15)--(10,15)--(10,12.5)--(5,10)--(15,10)--(15,15)--(10,12.5)--(10,15)--(10,12.5);\n\\node at (5,16) {$(a,1)$};\n\\node at (15,16) {$(b,1)$};\n\\node at (11.2,12.5) {$(b,1)$};\n\\node at (5,13) {$(a,1)$};\n\\node at (10,17.5) {$(b,2)$};\n\\node at (15,13) {$(b,1)$};\n\\node at (10,2) {$(a,0)$};\n\\node at (5,2) {$(a,0)$};\n\\node at (10,7.5) {$(a,1)$};\n\\node at (15,2) {$(b,1)$};\n\\node at (10,-3) {$\\textup{Caughey($X$,$a,b$)}$};\n\\node at (25,-3) {$\\textup{Caughey($X$,$a,b$)}$};\n\\draw[fill=black] (30,0) circle (5pt);\n\\draw[fill=black] (30,5) circle (5pt);\n\\draw[fill=black] (30,10) circle (5pt);\n\\draw[fill=black] (35,15) circle (5pt);\n\\draw[fill=black] (40,5) circle (5pt);\n\\draw[fill=black] (40,0) circle (5pt);\n\\draw[thick](30,0)--(30,5)--(35,15)--(30,10)--(40,0)--(30,0)--(40,5)--(30,5)--(40,10)--(40,0);\n\\node at (29.7,0) {$a$};\n\\node at (30.3,0) {$a$};\n\\node at (30.3,5) {$a$};\n\\node at (40.3,0) {$b$};\n\\node at (29.7,5) {$b$};\n\\node at (40.3,5) {$b$};\n\\node at (40.3,10) {$b$};\n\\node at (30.3,10) {$b$};\n\\node at (35,16) {$(b,1)$};\n\\node at (40,16) {$(b,1)$};\n\\node at (35,13) {$(b,1)$};\n\\node at (40,13) {$(b,1)$};\n\\node at (35,7.5) {$(a,1)$};\n\\node at (40,7.5) {$(b,1)$};\n\\node at (40,-2) {$(a,0,b)$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 455,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage{xcolor}\n\\usepackage[colorlinks,linkcolor=blue,anchorcolor=green,citecolor=blue,urlcolor=black,hypertexnames=true]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\\draw[->,>=stealth] (-3,0) -- (7,0) node[below right] {$r$};\n\\draw[->,>=stealth] (0,-0.2) -- (0,6) node[left] {$m$};\n\\draw[thick] (-3,1.1) .. controls (0,1.4) .. (3,5.6) node[right] {solution if $r=2$};\n\\draw[thick] (-3,0.1) .. controls (0,0.4) .. (3,4.6) node[right] {solution if $r=1$};\n\\draw[thick,dashed] (-3,0.5) .. controls (0,0.8) .. (3,4) node[right] {solution if $r=0$};\n\\draw[thick,dotted] (-3,1.5) .. controls (0,1.8) .. (3,4.9) node[right] {$4m=a\\neq 4m=-a$};\n\\fill (-3,0.5) circle (0.05) node[below] {no solutions};\n\\fill (3,5.6) circle (0.05) node[below] {$4m=a$ solutions};\n\\fill (3,4.6) circle (0.05) node[below] {$4m=-a$ solutions};\n\\fill (3,4) circle (0.05) node[below] {$4m=0$ solutions};\n\\fill (3,4.9) circle (0.05) node[below] {$4m=-a$ no solutions};\n\\fill (-3,1.1) circle (0.05) node[below] {no solutions};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 456,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amssymb,amsfonts,amsthm}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{automata}\n\\usetikzlibrary{arrows}\n\\tikzset{every loop/.style={min distance=10mm,looseness=10}}\n\\tikzset{every state/.style={minimum size=2mm}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[node distance=1cm,auto,main node/.style={circle,draw,inner sep=1pt,minimum size=5pt}]\n\n\\node[main node] (1) {1};\n\\node[main node] (2) [left of=1] {2};\n\\node[main node] (3) [below of=1] {3};\n\\node[main node] (4) [right of=3] {4};\n\\node[main node] (5) [right of=4] {0};\n\n\\path\n(1) edge node[right] {2} (2)\n(1) edge node[above] {2} (3)\n(1) edge node[above] {1} (4)\n(1) edge node[above] {1} (5);\n\n\\path\n(2) edge node[above] {1} (3)\n(2) edge node[above] {2} (4)\n(2) edge node[above] {3} (5);\n\n\\path\n(3) edge node[above] {3} (4)\n(3) edge node[above] {4} (5);\n\n\\path\n(4) edge node[right] {3} (5);\n\n\\path\n(1) edge[blue,below,bend left=10] node {2} (3)\n(1) edge[blue,above,bend right=10] node {3} (4)\n(1) edge[blue,below] node {4} (5);\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 457,
        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usepackage{amsmath,amssymb,amsthm,bm}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\foreach \\x in {1,...,6}\n    \\draw (\\x,0) +(-.5,-.5) rectangle ++(.5,.5);\n\\foreach \\x in {1,...,8}\n    \\draw (\\x,1) +(-.5,-.5) rectangle ++(.5,.5);\n\\foreach \\x in {1,...,10}\n    \\draw (\\x,2) +(-.5,-.5) rectangle ++(.5,.5);\n\\foreach \\x in {1,...,12}\n    \\draw (\\x,3) +(-.5,-.5) rectangle ++(.5,.5);\n\\foreach \\x in {1,...,14}\n    \\draw (\\x,4) +(-.5,-.5) rectangle ++(.5,.5);\n\\foreach \\x in {1,...,16}\n    \\draw (\\x,5) +(-.5,-.5) rectangle ++(.5,.5);\n\\foreach \\x in {1,...,18}\n    \\draw (\\x,6) +(-.5,-.5) rectangle ++(.5,.5);\n\\foreach \\x in {1,...,20}\n    \\draw (\\x,7) +(-.5,-.5) rectangle ++(.5,.5);\n\\foreach \\x in {1,...,22}\n    \\draw (\\x,8) +(-.5,-.5) rectangle ++(.5,.5);\n\\draw (1,-.5) -- (21,-.5);\n\\draw (1,1.5) -- (21,1.5);\n\\draw (1,2.5) -- (21,2.5);\n\\draw (1,3.5) -- (21,3.5);\n\\draw (1,4.5) -- (21,4.5);\n\\draw (1,5.5) -- (21,5.5);\n\\draw (1,6.5) -- (21,6.5);\n\\draw (1,7.5) -- (21,7.5);\n\\draw [dotted] (10,2) -- (9,2);\n\\draw [dotted] (1,4) -- (4,4);\n\\draw [dotted] (1,5) -- (2,5);\n\\draw [dotted] (1,6) -- (5,6);\n\\draw [dotted] (10,4) -- (9,4);\n\\draw [dotted] (10,5) -- (11,5);\n\\draw [dotted] (10,6) -- (12,6);\n\\draw [<->] (1,-.75) -- (21,-.75) node [midway,below] {depth};\n\\draw [<->] (2,-.75) -- (3,-.75) node [midway,below] {width};\n\\draw [<->] (-.5,1) -- (-.5,7) node [midway,left] {receptive field};\n\\draw [<->] (-.5,8) -- (-.5,16) node [midway,left] {receptive field};\n\\draw (2,8.5) node [above] {Layer $i$} -- ++(0,-7) node [below] {$i$};\n\\draw (6,8.5) node [above] {Layer $L-1$} -- ++(0,-7) node [below] {$i+1$};\n\\draw (10,8.5) node [above] {Layer $L$} -- ++(0,-7) node [below] {$i+k$};\n\\draw (14,8.5) node [above] {Layer $y$} -- ++(0,-7) node [below] {$i+y(L-1)$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 458,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\newcommand{\\red}[1]{{\\color{red} #1}}\n\n\\newcommand{\\blue}[1]{{\\color{blue} #1}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.4]\n  \\draw (-1.732, -1) -- (0,0) -- (1.732,1);\n  \\draw (-1,1) -- (-1,-1);\n  \\draw (1,1) -- (1,-1);\n  \\draw (0,1) -- (0,-1);\n  \\draw (-1.732, 0) -- (1.732,0);\n  \\draw[red, dashed, thick] (0,0) circle (1);\n  \\draw[blue, thick] (0,0) -- (1.732,1) node[right] {\\blue{$\\tau_{a_2}$}};\n  \\draw[red, dotted, thick] (0,0) -- (1.732,-1) node[right] {\\red{$s_a$}};\n  \\draw[red, thick, <->] (0,0) -- (0.66, 0.66) node[above] {\\red{$\\tau(a_1)$}};\n  \\fill[blue!50, opacity=0.3] (0,0) -- (1.732,1) -- (1.732,-1) -- cycle;\n  \\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{amsmath,amssymb,latexsym,color}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{shapes,snakes}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=newest}\n\\usepgfplotslibrary{fillbetween}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\node (1) {\\begin{minipage}{0.5\\linewidth}\n               \\begin{center}\n                 \\begin{tabular}{c c c c c}\n                 \\multicolumn{2}{c}{$\\mathbf{V}_{\\mu}$} \\\\\n                 \\multicolumn{2}{c}{$s_\\alpha$} & \\multicolumn{2}{c}{$\\mathcal{P}_\\mu$} \\\\\n                 \\multicolumn{2}{c}{$s_\\alpha$} & \\multicolumn{2}{c}{$s_\\beta$} \\\\\n                 \\end{tabular}\n               \\end{center}\n             \\end{minipage}};\n    \\node (2) [right=of 1, font=\\small] {\n      \\begin{minipage}{0.5\\linewidth}\n        \\begin{center}\n          \\begin{tabular}{c c c c c}\n            \\multicolumn{2}{c}{$\\mathbf{A}_{\\mu}$} \\\\\n            \\multicolumn{2}{c}{$s_\\alpha$} & \\multicolumn{2}{c}{$\\mathcal{P}_\\mu$} \\\\\n            \\multicolumn{2}{c}{$s_\\alpha$} & \\multicolumn{2}{c}{$s_\\beta$} \\\\\n          \\end{tabular}\n        \\end{center}\n      \\end{minipage}};\n    \\node (3) [below=of 1] {\\begin{minipage}{0.5\\linewidth}\n               \\begin{center}\n                 \\begin{tabular}{c c c c c}\n                 \\multicolumn{2}{c}{$\\mathbf{P}$} \\\\\n                 \\multicolumn{2}{c}{$s_\\alpha$} & \\multicolumn{2}{c}{$s_\\beta$} \\\\\n                 \\multicolumn{2}{c}{$s_\\alpha$} & \\multicolumn{2}{c}{$s_\\beta$} \\\\\n                 \\end{tabular}\n               \\end{center}\n             \\end{minipage}};\n    \\node (4) [right=of 3, font=\\small] {\n      \\begin{minipage}{0.5\\linewidth}\n        \\begin{center}\n          \\begin{tabular}{c c c c c}\n            \\multicolumn{2}{c}{$\\mathbf{S}$} \\\\\n            \\multicolumn{2}{c}{$s_\\alpha$} & \\multicolumn{2}{c}{$s_\\beta$} \\\\\n            \\multicolumn{2}{c}{$s_\\alpha$} & \\multicolumn{2}{c}{$s_\\beta$} \\\\\n          \\end{tabular}\n        \\end{center}\n      \\end{minipage}};\n    \\draw [->] (1) to node [above, align=center] {Axial non-singlet\\\\$Q=0$} (2);\n    \\draw [->] (3) to node [below, align=center] {$Q=0$} (4);\n    \\draw [->] (1) to node [left, align=center] {Axial non-singlet} (3);\n    \\draw [->] (2) to node [right, align=center] {Axial non-singlet} (4);\n  \\end{tikzpicture}\n\n\\end{document}"
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        "index": 461,
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        "tikz_code": "\\documentclass[a4paper,11pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[latin1]{inputenc}\n\\usepackage{amsmath,amsfonts}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage[final, pdftex, pdfpagelabels, pdfstartview = {FitH}, bookmarks, plainpages = false, linktoc=all,linkcolor=black, citecolor=blue, urlcolor=blue,\nfilecolor=black]{hyperref}\n\\usetikzlibrary{matrix,arrows,decorations.pathmorphing,decorations.pathreplacing,decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\\node at (2,-1) {$V$};\n\\node at (1.2,2.2) {$U$};\n\\draw (0,0) rectangle (4,4);\n\\draw[thick, color=gray] (0,2) to (4,2);\n\\draw[thick, color=gray] (0,1) to (4,1);\n\\draw[thick, color=gray] (0,0) to (4,0);\n\\draw[thick, color=gray] (0.7,0) to (0.7,2);\n\\draw[thick, color=gray] (1.4,0) to (1.4,2);\n\\draw[thick, color=gray] (0.7,1) to (1.4,1);\n\\draw[thick, color=gray] (1.4,2) to (2,2);\n\\draw[thick, color=gray] (0.7,1) to (1.4,1);\n\\draw[thick, color=gray] (1.4,1) to (2,1);\n\\draw[thick, color=gray] (1.4,0) to (2,0);\n\\draw[thick, color=gray] (0.7,0) to (1.4,0);\n\\draw[thick, color=gray] (1.4,1) to (1.4,2);\n\\draw[thick, color=gray] (2,0) to (2,1);\n\\draw[thick, color=gray] (2,1) to (2,2);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 463,
        "tikz_code": "\\documentclass[11pt, a4paper]{amsart}\n\\usepackage{amssymb,amsmath}\n\\usepackage{amsmath,amssymb,eucal}\n\\usepackage{pgfplots}\n\\usepackage{tikz}\n\\usetikzlibrary{calc,backgrounds,positioning,decorations.pathmorphing,shapes.misc,matrix,through,shapes,patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8]\n\n\\draw (-2,0)--(-1,0);\n\\draw (-1,0)--(-0.5,0.5);\n\\draw (-0.5,0.5)--(0,1);\n\\draw (-0.5,0.5)--(0.5,0.5);\n\\draw (-0.5,0.5)--(-1,0);\n\\draw (-1,0)--(-1,-1);\n\n\\draw (-2,0)--(-2,-1);\n\n\\node [above] at (-2,0) {$Q$};\n\\node [below] at (-2,-1) {$\\hat{Q}$};\n\n\\node at (1,0) {$=$};\n\n\\draw (3,0)--(4,0);\n\\draw (4,0)--(4.5,0.5);\n\\draw (4.5,0.5)--(5,1);\n\\draw (4.5,0.5)--(5.5,0.5);\n\\draw (4.5,0.5)--(4,0);\n\\draw (4,0)--(4,-1);\n\n\\draw (3,0)--(3,-1);\n\n\\node [above] at (3,0) {$Q$};\n\\node [below] at (3,-1) {$\\hat{Q}$};\n\n\\node [above] at (-1,0) {$Q_\\ell$};\n\\node [above] at (4.5,0.5) {$Q_{R-1}$};\n\n\\node at (6,0) {$+\\quad$};\n\n\\draw (8,0)--(9,0);\n\\draw (9,0)--(9.5,0.5);\n\\draw (9.5,0.5)--(10,1);\n\\draw (9.5,0.5)--(10.5,0.5);\n\\draw (9.5,0.5)--(9,0);\n\\draw (9,0)--(9,-1);\n\n\\draw (8,0)--(8,-1);\n\n\\node [above] at (8,0) {$Q$};\n\\node [below] at (8,-1) {$\\hat{Q}$};\n\n\\node [above] at (9.5,0.5) {$Q_{\\ell-1}$};\n\\node [above] at (10.5,0.5) {$Q_{R}$};\n\n\\node at (11,0) {$+\\quad$};\n\n\\draw (12,0)--(13,0);\n\\draw (13,0)--(13.5,0.5);\n\\draw (13.5,0.5)--(14,1);\n\\draw (13.5,0.5)--(14.5,0.5);\n\\draw (13.5,0.5)--(13,0);\n\\draw (13,0)--(13,-1);\n\n\\draw (12,0)--(12,-1);\n\n\\node [above] at (12,0) {$Q$};\n\\node [below] at (12,-1) {$\\hat{Q}$};\n\n\\node [above] at (13.5,0.5) {$Q_{\\ell}$};\n\\node [above] at (14.5,0.5) {$Q_{R+1}$};\n\n\\node at (15,0) {$+$};\n\n\\draw (16,0)--(17,0);\n\\draw (17,0)--(17.5,0.5);\n\\draw (17.5,0.5)--(18,1);\n\\draw (17.5,0.5)--(18.5,0.5);\n\\draw (17.5,0.5)--(17,0);\n\\draw (17,0)--(17,-1);\n\n\\draw (16,0)--(16,-1);\n\n\\node [above] at (17.5,0.5) {$Q_{R}$};\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 464,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amsmath,amsthm,amsfonts,amssymb,latexsym,verbatim,bbm}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.75]\n    \\draw[dotted] (0,0) grid (4,4);\n    \\foreach \\x in {0,1,2,3} \\draw (\\x cm,1pt) -- (\\x cm,-1pt) node[anchor=north] {$\\x$};\n    \\foreach \\y in {0,1,2,3} \\draw (1pt,\\y cm) -- (-1pt,\\y cm) node[anchor=east] {$\\y$};\n    \\draw[thick,dotted] (0,0) grid (3,4);\n    \\draw[thick,dotted] (0,3) -- (1,3) -- (1,4) -- (4,4);\n    \\draw[thick,->,>=latex] (0,0) -- (1,0) -- (2,0) -- (3,0) -- (4,0);\n    \\draw[thick,->,>=latex] (0,0) -- (0,1) -- (0,2) -- (0,3) -- (0,4);\n    \\draw[thick,->,>=latex] (0,4) -- (1,4) -- (2,4) -- (3,4) -- (4,4);\n    \\draw (0,0) node[anchor=north east] {$(0,0)$};\n    \\draw (4,4) node[anchor=south west] {$(3,3)$};\n    \\draw (5,4) node[anchor=south] {$P$};\n  \\end{tikzpicture}\n\n\\end{document}"
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        "index": 465,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{calc}\n\\tikzset{nod1/.style={circle,draw=black,fill=black,inner sep=1pt}}\n\\tikzset{nod2/.style={circle,draw=black,fill=black,inner sep=2pt}}\n\\tikzset{nod3/.style={circle,draw=black,fill=black,inner sep=3pt}}\n\\tikzset{noddiam/.style={diamond,draw=black,inner sep=2pt}}\n\\tikzset{nodw/.style={circle,draw=black,inner sep=2pt}}\n\\tikzset{nodg/.style={circle,draw=green,fill=green,inner sep=1.2pt}}\n\\tikzset{nodg2/.style={circle,draw=green,fill=green,inner sep=2pt}}\n\\tikzset{node/.style={circle,draw=white,fill=white,inner sep=1pt}}\n\\tikzset{nodem/.style={circle,draw=white,fill=white,inner sep=.2pt}}\n\\tikzset{\n  circ/.style = {circle,draw,fill,inner sep=1pt},\n  invisible/.style = {circle,draw=none,inner sep=0pt,font=\\tiny}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.5]\n\\draw[<-,thick] (-3,1)--(0,1);\n\\draw[->,thick] (0,1) node[nod1] {} -- (0,0);\n\\draw[<-,thick] (-3,0)--(-1,0);\n\\draw[->,thick] (-1,0) node[nod1] {} -- (-1,1);\n\\draw[->,thick] (-1,1) node[nod1] {} -- (-2,1);\n\\draw[<-,thick] (-2,1)--(-3,1);\n\\draw[<-,thick] (-3,-1)--(-1,-1);\n\\draw[->,thick] (-1,-1)--(-1,-2);\n\\draw[->,thick] (-1,-2)--(-3,-2);\n\\draw[->,thick] (-3,-2)--(-3,-1);\n\\draw[->,thick] (2,1)--(3,1);\n\\draw[<-,thick] (3,1)--(3,-1);\n\\draw[<-,thick] (3,-1)--(2,-1);\n\\draw[->,thick] (2,-1)--(2,1);\n\\draw[<-,thick] (5,1)--(6,1);\n\\draw[->,thick] (6,1)--(6,-1);\n\\draw[->,thick] (6,-1)--(5,-1);\n\\draw[->,thick] (5,-1)--(5,1);\n\\draw[<-,thick] (8,1)--(9,1);\n\\draw[->,thick] (9,1)--(9,-1);\n\\draw[->,thick] (9,-1)--(8,-1);\n\\draw[->,thick] (8,-1)--(8,1);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 466,
        "tikz_code": "\\documentclass[a4paper,11pt]{book}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath, amssymb, multicol}\n\\usepackage{amssymb}\n\\usepackage{tikz-feynman}\n\\tikzfeynmanset{compat=1.1.0}\n\\usepackage{color}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,arrows}\n\\usetikzlibrary{arrows.meta}\n\\usetikzlibrary{positioning,fadings}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{decorations.markings}\n\\tikzfeynmanset{double_boson/.style={decorate,\n/tikz/double,\n/tikz/decoration={snake},\n}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}[baseline=(a1)]  \n\\begin{feynman}\n\\vertex (a1) ;\n\\vertex[right=1cm of a1,square dot, red] (a2) {}; \n\\vertex[below=1cm of a2] (b2);\n\\vertex[right=2cm of a2,square dot, red] (a3) {}; \n\\vertex[below=1cm of a3] (b3);\n\\vertex[above=1cm of a3] (c3);\n\\vertex[right=2cm of a3,square dot, red] (a4) {}; \n\\vertex[below=1cm of a4] (b4);\n\\vertex[right=1cm of a4] (a5);\n\\vertex[below=2cm of a3] (e3);\n\\vertex[left=1cm of b3] (d3);\n\\vertex[below=2cm of a2] (e2);\n\\vertex[left=1cm of b2] (d2);\n\\vertex[left=2cm of a1] (a0) ;\n\\vertex[below=2cm of a1] (e1);\n\\vertex[right=1cm of a5] (a6);\n\\vertex[below=2cm of a4] (e4);\n\\vertex[right=1cm of a6] (a7);\n\\vertex[below=2cm of b2] (f2);\n\\vertex[right=1cm of a7] (a8);\n\\vertex[below=2cm of b3] (f3);\n\\vertex[right=1cm of a8] (a9);\n\\vertex[below=2cm of b4] (f4);\n\\vertex[right=1cm of a9] (a10);\n\\vertex[below=2cm of c3] (f5);\n\\vertex[right=1cm of a10] (a11);\n\\vertex[below=2cm of d2] (f6);\n\\vertex[right=1cm of a11] (a12);\n\\vertex[below=2cm of d3] (f7);\n\\vertex[right=1cm of a12] (a13);\n\\vertex[below=2cm of e2] (f8);\n\\vertex[right=1cm of a13] (a14);\n\\vertex[below=2cm of e3] (f9);\n\\vertex[right=1cm of a14] (a15);\n\\vertex[below=2cm of e4] (f10);\n\\vertex[right=1cm of a15] (a16);\n\\vertex[below=2cm of e5] (f11);\n\\vertex[right=1cm of a16] (a17);\n\\vertex[below=2cm of e5] (f11);\n\\vertex[right=1cm of a17] (a18);\n\\vertex[below=2cm of e6] (f12);\n\\vertex[right=1cm of a18] (a19);\n\\vertex[below=2cm of e7] (f13);\n\\vertex[right=1cm of a19] (a20);\n\\vertex[below=2cm of e8] (f14);\n\\vertex[right=1cm of a20] (a21);\n\\vertex[below=2cm of e9] (f15);\n\\vertex[right=1cm of a21] (a22);\n\\vertex[below=2cm of e10] (f16);\n\\vertex[right=1cm of a22] (a23);\n\\vertex[below=2cm of e10] (f17);\n\\vertex[right=1cm of a23] (a24);\n\\vertex[below=2cm of e11] (f18);\n\\vertex[right=1cm of a24] (a25);\n\\vertex[below=2cm of e12] (f19);\n\\vertex[right=1cm of a25] (a26);\n\\vertex[below=2cm of e13] (f20);\n\\vertex[right=1cm of a26] (a27);\n\\vertex[below=2cm of e14] (f21);\n\\vertex[right=1cm of a27] (a28);\n\\vertex[below=2cm of e15] (f22);\n\\vertex[right=1cm of a28] (a29);\n\\vertex[below=2cm of e16] (f23);\n\\vertex[right=1cm of a29] (a30);\n\\vertex[below=2cm of e17] (f24);\n\\vertex[right=1cm of a30] (a31);\n\\vertex[below=2cm of e18] (f25);\n\\vertex[right=1cm of a31] (a32);\n\\vertex[below=2cm of e19] (f26);\n\\vertex[right=1cm of a32] (a33);\n\\vertex[below=2cm of e20] (f27);\n\\vertex[right=1cm of a33] (a34);\n\\vertex[below=2cm of e21] (f28);\n\\vertex[right=1cm of a34] (a35);\n\\vertex[below=2cm of e22] (f29);\n\\vertex[right=1cm of a35] (a36);\n\\vertex[below=2cm of e23] (f30);\n\\vertex[right=1cm of a36] (a37);\n\\vertex[below=2cm of e24] (f31);\n\\vertex[right=1cm of a37] (a38);\n\\vertex[below=2cm of e25] (f32);\n\\vertex"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing,angles,quotes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5]\n    \\draw[->] (-1.75,0) -- (4.25,0) node[above] {$t$};\n    \\draw[->] (0,-0.5) -- (0,2.5) node[right] {$t_2$};\n    \\draw (0,0) circle (2cm);\n    \\draw (3,0) arc (0:180:3cm and 0.5cm);\n    \\draw[dashed] (3,0) arc (0:180:3cm and 1cm);\n    \\draw (-3,0) arc (180:360:3cm and 0.5cm);\n    \\draw[dashed] (-3,0) arc (180:360:3cm and 1cm);\n    \\draw[thick] (3,0) arc (0:180:3cm and 1cm);\n    \\draw[thick] (-3,0) arc (180:360:3cm and 1cm);\n    \\draw (3,1) -- (3,0) -- (0,0) -- (3,-1);\n    \\draw (-3,1) -- (-3,0) -- (0,0) -- (-3,-1);\n    \\draw (0,1.25) node {$\\tau$};\n    \\draw (3.5,0.25) node {$D_1$};\n    \\draw (-1.5,0.25) node {$D_0$};\n    \\draw (0,0) circle (0.075cm);\n    \\draw[decoration={brace,raise=3pt},decorate]\n      (3,0) -- node[right=3pt] {$D_1$} (3,1);\n    \\draw[decoration={brace,raise=3pt},decorate]\n      (-3,0) -- node[left=3pt] {$D_0$} (-3,-1);\n  \\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage{xcolor}\n\\usetikzlibrary{shapes.geometric, arrows}\n\\usetikzlibrary{decorations.pathreplacing}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\\draw [decorate,decoration={brace,amplitude=6pt,raise=0pt},yshift=2pt]\n\t(2.5,1.8) -- (4.5,1.8) node [black,midway,yshift=16pt] {\\footnotesize{first-order expansions of $\\mathcal{D}$}};\n\t\n\t\\draw (2,0) .. controls (2,1.5) and (3,2) .. (4,2) .. controls (5,2) and (5,1.5) .. (5,0) .. controls (5,.5) and (4,.5) .. (4,0);\n\t\\draw (2,0) .. controls (2,.5) and (3,1) .. (4,1) .. controls (5,1) and (5,.5) .. (5,0);\n\t\\draw (4.5,2.1) .. controls (4.5,3.3) and (4.8,3.6) .. (5.8,3.6) .. controls (6.8,3.6) and (7.1,3.3) .. (7.1,2.1) .. controls (7.1,1) and (6.8,.7) .. (5.8,.7) .. controls (4.8,.7) and (4.5,.4) .. (4.5,1.6);\n\t\\draw (4.5,2.1) .. controls (4.5,3.3) and (4.8,3.6) .. (5.8,3.6);\n\t\\draw (4.5,1.6) -- (4.5,1.8);\n\t\\draw [fill] (4.5,1.8) circle [radius=.05];\n\t\n\t\\draw (2,0) .. controls (2,-1.5) and (3,-2) .. (4,-2) .. controls (5,-2) and (5,-1.5) .. (5,0);\n\t\\draw (2,0) .. controls (2,-.5) and (3,-1) .. (4,-1) .. controls (5,-1) and (5,-.5) .. (5,0);\n\t\\draw (4.5,-2.1) .. controls (4.5,-3.3) and (4.8,-3.6) .. (5.8,-3.6) .. controls (6.8,-3.6) and (7.1,-3.3) .. (7.1,-2.1) .. controls (7.1,-1) and (6.8,-.7) .. (5.8,-.7) .. controls (4.8,-.7) and (4.5,-.4) .. (4.5,-1.6);\n\t\\draw (4.5,-2.1) .. controls (4.5,-3.3) and (4.8,-3.6) .. (5.8,-3.6);\n\t\\draw (4.5,-1.6) -- (4.5,-1.8);\n\t\\draw [fill] (4.5,-1.8) circle [radius=.05];\n\t\n\t\\draw [fill] (2,0) circle [radius=.05];\n\t\\draw [fill] (5,0) circle [radius=.05];\n\t\\draw [fill] (4.5,1.8) circle [radius=.05];\n\t\\draw [fill] (4.5,-1.8) circle [radius=.05];\n\t\n\t\\node [right] at (5.2,3.2) {$\\mathcal{D}$};\n\t\\node [right] at (5.2,-3.2) {$J\\circ\\mathcal{P}$-$\\textrm{id}$};\n\t\\node [right] at (2.2,0) {$\\mathcal{D}'$};\n\t\\node [right] at (3.7,1.4) {$\\mathcal{I}$};\n\t\\node [right] at (3.7,-1.4) {$\\mathcal{J}$};\n\t\\node [right] at (4.6,2.1) {$\\mathcal{E}$};\n\t\\node [right] at (4.6,-2.1) {$\\mathcal{E}$};\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "index": 471,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,decorations.markings}\n\\usetikzlibrary{positioning}\n\\usepackage{pgf}\n\\usepackage{amsmath,amssymb,latexsym,amsthm}\n\\usepackage[utf8]{inputenc}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5]\n    \\draw[very thick,domain=0.33:7,samples=50,color=red] plot ({\\x},{ln(1/cos(deg(\\x)))});\n    \\draw[very thick,domain=0.33:7,samples=50,color=blue] plot ({\\x},{\\x});\n    \\draw[very thick,domain=0:7,samples=50,color=violet] plot ({\\x},{1/2});\n    \\draw[very thick,domain=0:7,samples=50,color=violet] plot ({\\x},{1/8});\n    \\draw[very thick,domain=0:7,samples=50,color=violet] plot ({\\x},{1/16});\n    \\draw[very thick,domain=0:7,samples=50,color=violet] plot ({\\x},{1/32});\n    \\draw[very thick,domain=0:7,samples=50,color=violet] plot ({\\x},{1/64});\n    \\draw[very thick,domain=0:7,samples=50,color=violet] plot ({\\x},{1/128});\n    \\draw[very thick,domain=0:7,samples=50,color=violet] plot ({\\x},{1/256});\n    \\draw[very thick,domain=0:7,samples=50,color=violet] plot ({\\x},{1/512});\n    \\draw[very thick,color=black] (0,1/16)--(7,1/16);\n    \\draw[very thick,color=black] (0,1/32)--(7,1/32);\n    \\draw[very thick,color=black] (0,1/64)--(7,1/64);\n    \\draw[very thick,color=black] (0,1/128)--(7,1/128);\n    \\draw[very thick,color=black] (0,1/256)--(7,1/256);\n    \\draw[very thick,color=black] (0,1/512)--(7,1/512);\n    \\draw[->, very thick] (0,-0.1)--(0,3.4);\n    \\draw[->, very thick] (0,0)--(7,0);\n    \\draw[thick, dashed] (0,1/16)--(7,1/16);\n    \\draw[thick, dashed] (0,1/32)--(7,1/32);\n    \\draw[thick, dashed] (0,1/64)--(7,1/64);\n    \\draw[thick, dashed] (0,1/128)--(7,1/128);\n    \\draw[thick, dashed] (0,1/256)--(7,1/256);\n    \\draw[thick, dashed] (0,1/512)--(7,1/512);\n    \\draw (0,3.5) node[left] {\\LARGE $1$};\n    \\draw (0,2.5) node[left] {\\LARGE $\\log(2)$};\n    \\draw (0,1/16) node[left] {\\LARGE $0$};\n    \\draw (0,1/32) node[left] {\\LARGE $1/2$};\n    \\draw (0,1/64) node[left] {\\LARGE $1/8$};\n    \\draw (0,1/128) node[left] {\\LARGE $1/16$};\n    \\draw (0,1/256) node[left] {\\LARGE $1/32$};\n    \\draw (0,1/512) node[left] {\\LARGE $1/64$};\n    \\draw (7,0) node[below] {\\LARGE $x$};\n    \\draw (7,0) node[below] {\\LARGE $x$};\n    \\draw (3.2,2) node[color=red, align=center] {\\LARGE CDF size of \\\\[1mm] \\LARGE liquidity shocks};\n    \\draw (3.2,-0.5) node[color=blue, align=center] {\\LARGE Probability of \\\\[1mm] \\LARGE liquidity};\n    \\draw (3.2,-1) node[color=blue, align=center] {\\LARGE succeeding liquidity};\n    \\draw (3.2,-1.5) node[color=blue, align=center] {\\LARGE in a project failure};\n    \\draw (3.2,-2) node[color=blue, align=center] {\\LARGE \\LARGE liquidity};\n    \\draw (3.2,-2.5) node[color=blue, align=center] {\\LARGE supply of \\\\[1mm] \\LARGE liquidity};\n    \\draw (3.2,-3) node[color=blue, align=center] {\\LARGE fail of \\\\[1mm] \\LARGE project};\n    \\draw (3.2,-3.5) node[color=blue, align=center] {\\LARGE supply of \\\\[1mm] \\LARGE liquidity};\n  \\end{tikzpicture}\n\n\\end{document}"
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        "index": 472,
        "tikz_code": "\\documentclass[11pt,reqno]{amsart}\n\\usepackage{amsmath, amssymb, amsthm, tikz, mathrsfs,verbatim,tensor}\n\\usetikzlibrary{shapes.geometric, arrows}\n\\usetikzlibrary{calc}\n\\usepackage{color}\n\\usepackage[colorlinks=true, linkcolor=blue, citecolor=blue]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n \n\\fill[gray!20!white] (0,0) rectangle (3,2);\n\\fill[white] (0,0) -- (3,0) -- (3,2) -- (0,2) -- cycle;\n\\draw[thick] (0,0) rectangle (3,2);\n\\draw[step=1cm,gray] (-.1,-0.1) grid (3.1,2.1);\n\n\\draw (0.5,-0.5) node {$\\lambda$};\n\\draw (1.5,1.5) node {$\\lambda$};\n\\draw (-0.5,1.5) node {$1$};\n\\draw (-0.5,0.5) node {$1$};\n\\draw (-0.5,0) node {$\\vdots$};\n\\draw (-0.5,2.5) node {$0$};\n\\draw (-0.5,1) node {$1$};\n\\draw (-0.5,-0.5) node {$\\lambda$};\n\\draw (2.5,1) node {$2$};\n\\draw (2.5,2.5) node {$\\lambda+1$};\n\\draw (0.5,2.5) node {$1$};\n\\draw (1.5,2.5) node {$2$};\n\\draw (2.5,2.5) node {$\\lambda+1$};\n\\draw (3.5,2.5) node {$\\lambda+2$};\n\\draw (3.5,2) node {$\\dots$};\n\n\\draw (0,0)--(0,2);\n\\draw (0,0)--(3,0);\n\\draw (3,0)--(3,2);\n\\draw (0,2)--(3,2);\n \n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 473,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amssymb,latexsym,mathrsfs,amsmath,tikz,tikz-cd}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n%Nodes\n\\node[] at (-4,0) {$\\mathcal{Y}_{1,0}$};\n\\node[] at (-2,0) {$\\mathcal{Y}_{2,-1}$};\n\\node[] at (0,0) {$\\mathcal{Y}_{2,1}$};\n\\node[] at (2,0) {$\\mathcal{Y}_{1,2}$};\n\\node[] at (0,-2) {$\\mathcal{Y}_{2,-2}$};\n\\node[] at (0,-4) {$\\mathcal{Y}_{1,-1,0}$};\n\\node[] at (2,-2) {$\\mathcal{Y}_{1,-1,2}$};\n\n\n%Arrows\n\\draw[<->, thick] (-3.6,0) -- (-2.4,0);\n\\draw[<->, thick] (-2.3,0.2) -- (-1.7,1.8);\n\\draw[<->, thick] (-1.6,0.2) -- (-0.4,1.8);\n\\draw[<->, thick] (0.4,0.2) -- (1.6,1.8);\n\\draw[<->, thick] (2.3,0.2) -- (3.5,1.8);\n\\draw[<->, thick] (-0.4,-1.8) -- (0.4,-0.2);\n\\draw[<->, thick] (1.6,-1.8) -- (2.4,-0.2);\n\\draw[<->, thick] (-1.6,-1.8) -- (-0.4,-0.2);\n\\draw[<->, thick] (1.6,-3.8) -- (2.4,-2.2);\n\\draw[<->, thick] (-1.6,-3.8) -- (-0.4,-2.2);\n\\draw[<->, thick] (0.4,-3.8) -- (1.6,-2.2);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 474,
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        "tikz_code": "\\documentclass[12pt,reqno]{amsart}\n\\usepackage{amsthm, amsmath,amsfonts,amssymb,eucal,euscript,latexsym,mathrsfs,bbm,bbm}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usepackage[colorlinks=false]{hyperref}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n[scale=0.6]\n%%%%%%%\n \\tikzstyle{vertex}=[circle,draw,fill=black,thick, inner sep=0pt,minimum size=0.75mm]\n\\node[vertex](v1) at (2,0) {};\n\\node[vertex](v2) at (0,3) {};\n\\node[vertex](v3) at (4,3) {};\n\\node[vertex](v4) at (2,6) {};\n\\draw[very thick] (v1) -- (v2);\n\\draw[very thick] (v1) -- (v3);\n\\draw[very thick] (v2) -- (v4);\n\\draw[very thick] (v3) -- (v4);\n\\node at (3,1.5) {$C_{i}$};\n\\node at (3,4.5) {$K_{i}$};\n\\node[vertex](v5) at (0,1) {};\n\\node[vertex](v6) at (4,1) {};\n\\draw[very thick] (v1) -- (v5);\n\\draw[very thick] (v1) -- (v6);\n\\draw[very thick] (v5) -- (v4);\n\\draw[very thick] (v6) -- (v4);\n\\node[vertex](v7) at (1,3.5) {};\n\\node[vertex](v8) at (3,3.5) {};\n\\draw[very thick] (v7) -- (v4);\n\\draw[very thick] (v8) -- (v4);\n\\draw[very thick] (v7) -- (v2);\n\\draw[very thick] (v8) -- (v3);\n\\node at (1,2.5) {$H_{i}$};\n\\node at (3,2.5) {$H_{i}$};\n\\draw[dashed, very thick] (v5) -- (v6);\n%%%%%%%\n\\node[vertex](v1) at (2+7,0) {};\n\\node[vertex](v2) at (0+7,3) {};\n\\node[vertex](v3) at (4+7,3) {};\n\\node[vertex](v4) at (2+7,6) {};\n\\draw[very thick] (v1) -- (v2);\n\\draw[very thick] (v1) -- (v3);\n\\draw[very thick] (v2) -- (v4);\n\\draw[very thick] (v3) -- (v4);\n\\node at (3+7,1.5) {$C_{j}$};\n\\node at (3+7,4.5) {$K_{j}$};\n\\node[vertex](v5) at (0+7,1) {};\n\\node[vertex](v6) at (4+7,1) {};\n\\draw[very thick] (v1) -- (v5);\n\\draw[very thick] (v1) -- (v6);\n\\draw[very thick] (v5) -- (v4);\n\\draw[very thick] (v6) -- (v4);\n\\node[vertex](v7) at (1+7,3.5) {};\n\\node[vertex](v8) at (3+7,3.5) {};\n\\draw[very thick] (v7) -- (v4);\n\\draw[very thick] (v8) -- (v4);\n\\draw[very thick] (v7) -- (v2);\n\\draw[very thick] (v8) -- (v3);\n\\node at (1+7,2.5) {$H_{j}$};\n\\node at (3+7,2.5) {$H_{j}$};\n\\draw[dashed, very thick] (v5) -- (v6);\n%%%%%%\n\\node[vertex](v1) at (2+14,0) {};\n\\node[vertex](v2) at (0+14,3) {};\n\\node[vertex](v3) at (4+14,3) {};\n\\node[vertex](v4) at (2+14,6) {};\n\\draw[very thick] (v1) -- (v2);\n\\draw[very thick] (v1) -- (v3);\n\\draw[very thick] (v2) -- (v4);\n\\draw[very thick] (v3) -- (v4);\n\\node at (3+14,1.5) {$C_{i}$};\n\\node at (3+14,4.5) {$K_{i}$};\n\\node[vertex](v5) at (0+14,1) {};\n\\node[vertex](v6) at (4+14,1) {};\n\\draw[very thick] (v1) -- (v5);\n\\draw[very thick] (v1) -- (v6);\n\\draw[very thick] (v5) -- (v4);\n\\draw[very thick] (v6) -- (v4);\n\\node[vertex](v7) at (1+14,3.5) {};\n\\node[vertex](v8) at (3+14,3.5) {};\n\\draw[very thick] (v7) -- (v4);\n\\draw[very thick] (v8) -- (v4);\n\\draw[very thick] (v7) -- (v2);\n\\draw[very thick] (v8) -- (v3);\n\\node at (1+14,2.5) {$H_{i}$};\n\\node at (3+14,2.5) {$H_{i}$};\n\\draw[dashed, very thick] (v5) -- (v6);\n%%%%%%\n\\node at (6+7,3) {$E_{1}$};\n\\node at (6+14,3) {$E_{2}$};\n\\node at (10,3) {$H_{4}$};\n\\draw[red, very thick] (4+7,1) -- (4+7,3.5);\n\\draw[red, very thick] (4+7,3.5) -- (2+7,3.5);\n\\draw[red, very thick] (2+7,3.5) -- (2+7,1);\n\\draw[red, very thick] (2+7,1) -- (4+7,1);\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 476,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amsthm}\n\\usepackage{amssymb}\n\\usepackage{pgf,tikz}\n\\usetikzlibrary{shapes.geometric}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{decorations.markings}\n\\tikzset{->-/.style={decoration={\n  markings,\n  mark=at position #1 with {\\arrow{>}}},postaction={decorate}}}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{graphs}\n\\usetikzlibrary{positioning}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\t% tikz here\n\t\\node[shape=coordinate] (a) at (180:1) {};\t\n\t\\node[shape=coordinate] (b) at (120:1) {};\n\t\\node[shape=coordinate] (c) at (0,0) {};\n\t\\node[shape=coordinate] (d) at (60:1) {};\n\t\\node[shape=coordinate] (e) at (0:1) {};\n\n\t\\node[shape=coordinate] (f) at (4,0) {};\n\t\\node[shape=coordinate] (g) at (8,0) {};\n\n\t\\foreach \\p in {a,b,c,d,e}\n\t{\n\t\t\\fill (\\p) circle (2pt);\n\t}\n\n\t\\foreach \\p in {f,g}\n\t{\n\t\t\\fill (\\p) rectangle +(45:-4pt)  (\\p) rectangle +(45:4pt);\n\t\t\\fill (\\p) rectangle +(135:-4pt) (\\p) rectangle +(135:4pt);\n\t}\n\n\t\\draw (a) -- (b) -- (c) -- (d) -- (e) -- (b) -- (d);\n\t\\draw (c) -- (e);\n\t\n\t\\draw (f) -- (g);\n\t\\draw (a) -- (f) -- (c) -- (g) -- (e);\n\n\n\t\\node at (180:1.25) {$p_3$};\n\t\\node at (120:1.25) {$p_2$};\n\t\\node at (60:1.25) {$p_3$};\n\t\\node at (0:1.25) {$p_4$};\n\t\\node at (4,0) {$p_1$};\n\t\\node at (8,0) {$p_4$};\n\n\t\\node at (0:1.5) {$\\quad$};\n\n\t\\node at (4,0) {$p_1$};\n\t\\node at (8,0) {$p_4$};\n\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 477,
        "tikz_code": "\\documentclass[tikz,border=2mm]{standalone}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows.meta,\n                positioning,\n                quotes}\n\n\\begin{document}\n    \\begin{tikzpicture}[\nnode distance = 6mm and 9mm,\n  box/.style = {draw, thick, inner sep=2mm},\n   arr/.style = {-{Straight Barb[scale=0.8]}, thick, shorten <=2mm},\n   pin distance = 1mm,\nevery edge quotes/.style = {font=\\footnotesize, inner sep=1pt, sloped}\n                        ]\n% horizontal lines\n\\coordinate[label=left:O]  (O);\n\\coordinate[label=left:A, right=of O]  (A);\n\\coordinate[label=left:L, right=of A]  (L);\n\\coordinate[label=left:L', above=of A] (L');\n\\coordinate[label=left:C, right=of L'] (C);\n\\coordinate[label=left:D, right=of C]  (D);\n\\coordinate[label=left:B, right=of D]  (B);\n\\coordinate[label=left:F, below=of D]  (F);\n\\coordinate[label=left:E, right=of F]  (E);\n\\coordinate[label=left:G, above=of F]  (G);\n\\coordinate[label=left:O', below=of L'] (O');\n\\coordinate[label=left:A, below=of O'] (A');\n\\coordinate[label=left:L, below=of A]  (L');\n\\coordinate[label=left:C, right=of L'] (C');\n\\coordinate[label=left:E, right=of C'] (E');\n\\coordinate[label=left:F, right=of E]  (F');\n\\coordinate[label=left:D, right=of F'] (D');\n\\coordinate[label=left:B, right=of D'] (B');\n\\coordinate[label=left:G, right=of G]  (G');\n% vertical lines\n\\draw[arr]   (O) edge [\"\\tiny $y_-$\"] (O')\n            (A) edge [\"\\tiny $x$\"] (A')\n            (L) edge [\"\\tiny $L$\"] (L')\n            (C) edge [\"\\tiny $C$\"] (C')\n            (D) edge [\"\\tiny $D$\"] (D')\n            (F) edge [\"\\tiny $L$\"] (F')\n            (G) edge [\"\\tiny $G$\"] (G');\n\\draw[arr]   (O') edge [\"\\tiny $y_+$\"] (O)\n            (A') edge [\"\\tiny $x$\"] (A)\n            (L') edge [\"\\tiny $L$\"] (L)\n            (C') edge [\"\\tiny $C$\"] (C)\n            (E') edge [\"\\tiny $E_J$\"] (E)\n            (F') edge [\"\\tiny $F$\"] (F)\n            (G') edge [\"\\tiny $G$\"] (G);\n% blue lines\n\\draw[blue, arr]   (G) edge [\"\\tiny $\\partial E_J$\"] (E);\n\\draw[blue, arr]   (E) edge [\"\\tiny $\\partial E_J$\"] (F);\n\\draw[blue, arr]   (F) edge [\"\\tiny $\\partial E_J$\"] (D);\n% red lines\n\\draw[red, arr] (F') edge [in=120,out=220,loop,looseness=12] node[left] {\\tiny $M_I$} (F');\n\\draw[red, arr]   (D') edge [\"\\tiny $\\partial E_J$\"] (B');\n\\draw[red, arr]   (B') edge [\"\\tiny $E_J$\"] (E');\n    \\end{tikzpicture}\n\\end{document}"
    },
    {
        "index": 478,
        "tikz_code": "\\documentclass[tikz,border=3.14mm]{standalone}\n\\begin{document}\n    \\begin{tikzpicture}\n        \\draw[thick,domain=-25:25,smooth,samples=100]\n        plot ({0.5*(1+\\x/100) *cos(\\x)}, {0.5*(1+\\x/100) *sin(\\x)});\n        \\draw[thick,domain=-25:25,smooth,samples=100]\n        plot ({0.5*(1+\\x/100) *sin(\\x)}, {0.5*(1+\\x/100) *cos(\\x)});\n    \\end{tikzpicture}\n\\end{document}"
    },
    {
        "index": 479,
        "tikz_code": "\\documentclass{standalone}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.12}\n\\begin{document}\n\\begin{tikzpicture}\n\\begin{axis}[grid=both,\n            view={150}{30},\n            xmin=-30, xmax=30,\n            ymin=-30, ymax=30,\n            zmin=0, zmax=35,\n            enlargelimits=upper,\n            xtick distance=10,\n            ytick distance=10,\n            ztick distance=10,\n            xlabel={depth},\n            ylabel={r},\n            zlabel={f(x,y)},\n            xlabel style={yshift=0.5ex},\n            ylabel style={yshift=-1ex},\n            zlabel style={yshift=-1ex},\n            ]\n\\addplot3 [surf,domain=-29:29,domain y=-29:29,samples=25,samples y=25] {-1*x*y+y^2+x^2};\n\\end{axis}\n\\end{tikzpicture}\n\\end{document}"
    },
    {
        "index": 480,
        "tikz_code": "\\documentclass[letterpaper,11pt]{article}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{tikz, fp, subfigure, epsfig}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.3]\n\n    \\fill (3,0) circle(0.2); \n    \\fill (3,1.5) circle(0.2);\n    \\fill (13,0) circle(0.2);\n    \\fill (13,1.5) circle(0.2);\n    \n    \\draw [fill=black!0, yshift=-4cm] (1,0) ellipse (1.5 and 0.8);\n    \\draw [fill=black!0, yshift=-2.5cm] (1,0) ellipse (1.5 and 0.8);\n    \\draw [fill=black!0, yshift=0cm] (1,0) ellipse (1.5 and 0.8);\n    \\draw [fill=black!0, yshift=2.5cm] (1,0) ellipse (1.5 and 0.8);\n    \\draw [fill=black!0, yshift=4cm] (1,0) ellipse (1.5 and 0.8);\n    \\draw [fill=black!0, yshift=7cm] (1,0) ellipse (1.5 and 0.8);\n    \\draw [fill=black!0, yshift=9cm] (1,0) ellipse (1.5 and 0.8);\n    \n    \\draw (1,0) -- (2,1.5);\n    \\draw (1,0) -- (3,1.5);\n    \\draw (1,0) -- (4,1.5);\n    \\draw (1,0) -- (6,1.5);\n    \\draw (1,0) -- (8,1.5);\n    \\draw (1,0) -- (10,1.5);\n    \\draw (1,0) -- (12,1.5);\n    \\draw (1,0) -- (14,1.5);\n    \\draw (1,0) -- (16,1.5);\n    \n    \\fill (1,0) circle(0.2);\n    \\draw (1,0) node[below]{$x_1$};\n    \\fill (4,0) circle(0.2);\n    \\draw (4,0) node[below]{$x_2$};\n    \\fill (6,0) circle(0.2);\n    \\draw (6,0) node[below]{$x_3$};\n    \\fill (8,0) circle(0.2);\n    \\draw (8,0) node[below]{$x_4$};\n    \\fill (10,0) circle(0.2);\n    \\draw (10,0) node[below]{$x_5$};\n    \\fill (12,0) circle(0.2);\n    \\draw (12,0) node[below]{$x_6$};\n    \\fill (14,0) circle(0.2);\n    \\draw (14,0) node[below]{$x_7$};\n    \\fill (16,0) circle(0.2);\n    \\draw (16,0) node[below]{$x_8$};\n    \n    \\draw [thick, ->] (3,1.5) -- (4,0);\n    \\draw [thick, ->] (3,1.5) -- (6,0);\n    \\draw [thick, ->] (3,1.5) -- (8,0);\n    \\draw [thick, ->] (3,1.5) -- (10,0);\n    \\draw [thick, ->] (3,1.5) -- (12,0);\n    \\draw [thick, ->] (3,1.5) -- (14,0);\n    \\draw [thick, ->] (3,1.5) -- (16,0);\n    \n    \\draw [thick, ->] (3,1.5) -- (1,0);\n    \\draw [thick, ->] (3,1.5) -- (13,0);\n    \n    \\draw (3,1.5) node[above]{$C_0$};\n    \\draw (3,1.5) node[above, yshift=1cm]{$C_1$};\n    \\draw (3,1.5) node[above, yshift=-1cm]{$C_2$};\n    \\draw (3,1.5) node[above, yshift=-3cm]{$C_3$};\n    \\draw (3,1.5) node[above, yshift=-5cm]{$C_4$};\n    \n    \\draw [thick, ->] (1,0) -- (3,-1);\n    \\draw [thick, ->] (2,0) -- (3,-1);\n    \\draw [thick, ->] (3,0) -- (3,-1);\n    \\draw [thick, ->] (4,0) -- (3,-1);\n    \\draw [thick, ->] (5,0) -- (3,-1);\n    \\draw [thick, ->] (6,0) -- (3,-1);\n    \\draw [thick, ->] (7,0) -- (3,-1);\n    \\draw [thick, ->] (8,0) -- (3,-1);\n    \\draw [thick, ->] (9,0) -- (3,-1);\n    \\draw [thick, ->] (10,0) -- (3,-1);\n    \\draw [thick, ->] (11,0) -- (3,-1);\n    \\draw [thick, ->] (12,0) -- (3,-1);\n    \\draw [thick, ->] (13,0) -- (3,-1);\n    \\draw [thick, ->] (14,0) -- (3,-1);\n    \\draw [thick, ->] (15,0) -- (3,-1);\n    \\draw [thick, ->] (16,0) -- (3,-1);\n    \n    \\draw (3,-1) node[above]{$x_1$};\n    \\draw (3,-1) node[above, yshift=1cm]{$x_2$};\n    \\draw (3,-1) node[above, yshift=-1cm]{$x_3$};\n    \\draw (3,-1) node[above, yshift=-3cm]{$x_4$};\n    \\draw (3,-1) node[above, yshift=-5cm]{$x_5$};\n    \n    \\draw [blue, ->] (3,1.5) -- (1"
    },
    {
        "index": 481,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amssymb}\n\\usepackage{color,soul}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n%---------lineas------%\n\\draw [thick] (0,0) --(0,2);\n\\draw [thick] (0,0) --(1,-1.5);\n\\draw [thick] (0,0) --(-1,-1.5);\n\\draw [thick] (0,2) --(1,-1.5);\n\\draw [thick] (0,2) --(-1,-1.5);\n%------triangles-------%\n\\draw [thick] (0,0) --(-0.5,-0.5);\n\\draw [thick] (0,0) --(0.5,-0.5);\n\\draw [thick] (-0.5,-0.5) --(0.5,-0.5);\n%-------nodos--------%\n\\draw [fill] (0,0) circle [radius=0.06]; \n\\draw [fill] (0,2) circle [radius=0.06]; \n\\draw [fill] (-1,-1.5) circle [radius=0.06]; \n\\draw [fill] (1,-1.5) circle [radius=0.06]; \n%------- indices------%\n\\node [below] at (-1,-1.5) {$1$};\n\\node [below] at (1,-1.5) {$2$};\n\\node [left] at (-0.5,-0.5) {$a$};\n\\node [right] at (0.5,-0.5) {$b$};\n\\node [above] at (0,2) {$1$};\n\\node [below] at (0,0) {$2$};\n%------curvas-------%\n\\draw [thick,red] (1,-1.5) to [out=30,in=180] (2.5,-0.25) to [out=0,in=150] (3.5,0.5);\n\\draw [thick,red] (3.5,0.5) to [out=180,in=30] (2,1.5) to [out=150,in=0] (1.75,2.5);\n\\draw [thick,red] (1.75,2.5) to [out=180,in=0] (2,2.25) to [out=180,in=0] (2.5,2.5);\n\\draw [thick,red] (2.5,2.5) to [out=150,in=0] (2,2.75) to [out=180,in=0] (1.75,3);\n\\draw [thick,red] (1.75,3) to [out=150,in=0] (1.5,3.25) to [out=180,in=0] (1.25,3.5);\n\\draw [thick,red] (1.25,3.5) to [out=180,in=30] (-0.5,2.5);\n\\draw [thick,red] (-0.5,2.5) to [out=150,in=30] (-1,2.75);\n\\draw [thick,red] (-1,2.75) to [out=150,in=0] (-1.5,3);\n\\draw [thick,red] (-1.5,3) to [out=180,in=0] (-1.75,3.25);\n\\draw [thick,red] (-1.75,3.25) to [out=180,in=30] (-2.5,3.5);\n\\draw [thick,red] (-2.5,3.5) to [out=150,in=30] (-3.5,3);\n\\draw [thick,red] (-3.5,3) to [out=150,in=0] (-3,2.75);\n\\draw [thick,red] (-3,2.75) to [out=150,in=0] (-2.5,2.5);\n\\draw [thick,red] (-2.5,2.5) to [out=180,in=30] (-1.75,1.75);\n\\draw [thick,red] (-1.75,1.75) to [out=150,in=0] (-1.5,1.5);\n\\draw [thick,red] (-1.5,1.5) to [out=180,in=0] (-1.25,1.25);\n\\draw [thick,red] (-1.25,1.25) to [out=150,in=30] (-0.75,1);\n\\draw [thick,red] (-0.75,1) to [out=150,in=0] (-0.5,0.5);\n\\draw [thick,red] (-0.5,0.5) to [out=180,in=0] (-1,-1.5);\n%------- indices------%\n\\node [below] at (-3.5,-0.5) {$3$};\n\\node [below] at (-1.75,-0.5) {$3$};\n\\node [below] at (0,-0.5) {$3$};\n\\node [below] at (-1.125,-0.5) {$2$};\n\\node [below] at (-0.375,-0.5) {$2$};\n\\node [above] at (2.5,-0.25) {$2$};\n\\node [below] at (3.5,0.5) {$1$};\n\\node [above] at (1.75,2.5) {$1$};\n\\node [below] at (2.5,2.5) {$2$};\n\\node [above] at (1.75,3) {$1$};\n\\node [above] at (1.25,3.5) {$2$};\n\\node [below] at (-0.5,2.5) {$1$};\n\\node [above] at (-1.75,3) {$2$};\n\\node [below] at (-2.5,3.5) {$2$};\n\\node [above] at (-1.75,3.25) {$1$};\n\\node [below] at (-1.25,3.5) {$1$};\n\\node [above] at (-0.75,1) {$2$};\n\\node [below] at (-0.5,0.5) {$3$"
    },
    {
        "index": 482,
        "tikz_code": "\\documentclass[10pt]{article}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{tikz}\n\\usetikzlibrary{snakes}\n\\usetikzlibrary{shapes}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{fit}\n\\usetikzlibrary{backgrounds}\n\n\\begin{document}\n\n\\begin{tikzpicture}[node distance = 0.75cm]\n  \\tikzstyle{every node}=[font=\\footnotesize]\n  \\tikzstyle{box}=[draw=black,fill=gray!20,thick, minimum width=15 pt,rounded corners=15pt]\n  \\tikzstyle{label}=[minimum width=10 pt]\n  \\node [box, label] (x1) {$x_1$};\n  \\node [box, label] (x2) [right = of x1]{$x_2$};\n  \\node [box, label] (x3) [right = of x2]{$x_3$};\n  \\node [box, label] (x4) [right = of x3]{$x_4$};\n  \\node [box, label] (x5) [right = of x4]{$x_5$};\n  \\node [box, label] (x6) [right = of x5]{$x_6$};\n  \\node [box, label] (x7) [right = of x6]{$x_7$};\n  \\node [box, label] (x8) [right = of x7]{$x_8$};\n  \\node [box, label] (x9) [right = of x8]{$x_9$};\n  \\node [box, label] (x10) [right = of x9]{$x_{10}$};\n  \\node [box, label] (x11) [right = of x10]{$x_{11}$};\n  \\node [box, label] (x12) [right = of x11]{$x_{12}$};\n  \\node [box, label] (x13) [right = of x12]{$x_{13}$};\n  \\node [box, label] (x14) [right = of x13]{$x_{14}$};\n  \\node [box, label] (x15) [right = of x14]{$x_{15}$};\n  \\node [box, label] (x16) [right = of x15]{$x_{16}$};\n  \\node [box, label] (x17) [right = of x16]{$x_{17}$};\n  \\node [box, label] (x18) [right = of x17]{$x_{18}$};\n  \\node [box, label] (x19) [right = of x18]{$x_{19}$};\n  \\node [box, label] (x20) [right = of x19]{$x_{20}$};\n  \\node [box, label] (x21) [right = of x20]{$x_{21}$};\n  \\node [box, label] (x22) [right = of x21]{$x_{22}$};\n  \\node [box, label] (x23) [right = of x22]{$x_{23}$};\n  \\node [box, label] (x24) [right = of x23]{$x_{24}$};\n  \\node [box, label] (x25) [right = of x24]{$x_{25}$};\n  \\node [box, label] (x26) [right = of x25]{$x_{26}$};\n  \\node [box, label] (x27) [right = of x26]{$x_{27}$};\n  \\node [box, label] (x28) [right = of x27]{$x_{28}$};\n  \\node [box, label] (x29) [right = of x28]{$x_{29}$};\n  \\node [box, label] (x30) [right = of x29]{$x_{30}$};\n  \\node [box, label] (x31) [right = of x30]{$x_{31}$};\n  \\node [box, label] (x32) [right = of x31]{$x_{32}$};\n  \\node [box, label] (x33) [right = of x32]{$x_{33}$};\n  \\node [box, label] (x34) [right = of x33]{$x_{34}$};\n  \\node [box, label] (x35) [right = of x34]{$x_{35}$};\n  \\node [box, label] (x36) [right = of x35]{$x_{36}$};\n  \\node [box, label] (x37) [right = of x36]{$x_{37}$};\n  \\node [box, label] (x38) [right = of x37]{$x_{38}$};\n  \\node [box, label] (x39) [right = of x38]{$x_{39}$};\n  \\node [box, label] (x40) [right = of x39]{$x_{40}$};\n  \\node [box, label] (x41) [right = of x40]{$x_{41}$};\n  \\node [box, label] (x42) [right = of x41]{$x_{42}$};\n  \\node [box, label] (x43) [right = of x42]{$x_{43}$};\n  \\node [box, label] (x44) [right = of x43]{$x_{44}$};\n  \\node [box, label] (x45) [right = of x44]{$x_{45}$};\n  \\node [box, label] (x46) [right = of x45]{$x_{46}$};\n  \\node [box, label] (x47) [right = of x46]{$x_{47}$};\n  \\node [box, label] (x48) [right = of x47]{$x_{48}$};\n  \\node [box, label] (x49) [right = of x48]{$x_{49}$};\n  \\node [box, label] (x50) [right = of x49]{$x_{50}$};\n  \\node [box, label] (x51) [right = of"
    },
    {
        "index": 483,
        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath,amsfonts,amssymb,amsthm}\n\\usepackage[usenames, dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows.meta}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.4]\n\\draw[black,-latex] (0,0) -- (4.5,0)node[right]{$x$};\n\\draw[black,-latex] (0,0) -- (0,2)node[above]{$\\frac{1}{p}$};\n\\draw[red,ultra thick] plot[smooth,domain=0.1:4.5] (\\x,{-1/(\\x)});\n\\draw[red,ultra thick] plot[smooth,domain=0.1:0.7] (\\x,{2/(\\x)})--(4.5,{2/4.5});\n\\draw[Green,ultra thick] plot[smooth,domain=0.7:4.5] (\\x,{-2/(\\x)});\n\\draw[Green,ultra thick] plot[smooth,domain=0.7:1.8] (\\x,{4/(\\x)})--(4.5,{4/4.5});\n\\draw[Magenta,ultra thick] plot[smooth,domain=1.8:4.5] (\\x,{-4/(\\x)});\n\\draw[Magenta,ultra thick] plot[smooth,domain=1.8:3.9] (\\x,{8/(\\x)})--(4.5,{8/4.5});\n\\draw[Cyan,ultra thick] plot[smooth,domain=3.9:4.5] (\\x,{-8/(\\x)});\n\\draw[Cyan,ultra thick] plot[smooth,domain=3.9:4.1] (\\x,{16/(\\x)})--(4.5,{16/4.5});\n\\draw[black,dotted] (0,0) -- (4.1,4.1);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 484,
        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\\usepackage{color}\n\n\\newcommand{\\loga}{1}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.25]\n\\draw [very thick] (0,0) -- (10,0) -- (10,10) -- (0,10) -- cycle;\n\\draw [thin, dashed] (0,0) -- (3,3);\n\\draw [thin, dashed] (0,2) -- (3,5);\n\\draw [thin, dashed] (0,4) -- (3,7);\n\\draw [thin, dashed] (0,6) -- (3,9);\n\\draw [thin, dashed] (6,0) -- (9,3);\n\\draw [thin, dashed] (8,0) -- (9,3);\n\\draw [thin, dashed] (10,2) -- (6,9);\n\\draw [thin, dashed] (10,4) -- (6,7);\n\\draw [thin, dashed] (10,6) -- (6,9);\n\\draw [thin, dashed] (2,0) -- (5,3);\n\\draw [thin, dashed] (4,0) -- (5,3);\n\\draw [thin, dashed] (6,0) -- (9,3);\n\\draw [thin, dashed] (8,0) -- (9,3);\n\\draw [thin, dashed] (0,2) -- (3,5);\n\\draw [thin, dashed] (0,4) -- (3,7);\n\\draw [thin, dashed] (0,6) -- (3,9);\n\\draw [thin, dashed] (6,0) -- (9,3);\n\\draw [thin, dashed] (8,0) -- (9,3);\n\\draw [thin, dashed] (0,2) -- (3,5);\n\\draw [thin, dashed] (0,4) -- (3,7);\n\\draw [thin, dashed] (0,6) -- (3,9);\n\\draw [thin, dashed] (6,0) -- (9,3);\n\\draw [thin, dashed] (8,0) -- (9,3);\n\\draw (0,-0.1) node[below,fill=white,outer sep=0pt] {$0$};\n\\draw (2,-0.1) node[below,fill=white,outer sep=0pt] {$2$};\n\\draw (4,-0.1) node[below,fill=white,outer sep=0pt] {$4$};\n\\draw (6,-0.1) node[below,fill=white,outer sep=0pt] {$6$};\n\\draw (8,-0.1) node[below,fill=white,outer sep=0pt] {$8$};\n\\draw (10,-0.1) node[below,fill=white,outer sep=0pt] {$10$};\n\\draw (-0.5,0) node[left,fill=white,outer sep=0pt] {$0$};\n\\draw (-0.5,2) node[left,fill=white,outer sep=0pt] {$2$};\n\\draw (-0.5,4) node[left,fill=white,outer sep=0pt] {$4$};\n\\draw (-0.5,6) node[left,fill=white,outer sep=0pt] {$6$};\n\\draw (-0.5,8) node[left,fill=white,outer sep=0pt] {$8$};\n\\draw (-0.5,10) node[left,fill=white,outer sep=0pt] {$10$};\n\\draw (-0.5,12) node[left,fill=white,outer sep=0pt] {$12$};\n\\draw (-0.5,14) node[left,fill=white,outer sep=0pt] {$14$};\n\\draw (-0.5,16) node[left,fill=white,outer sep=0pt] {$16$};\n\\draw (-0.5,18) node[left,fill=white,outer sep=0pt] {$18$};\n\\draw (-0.5,20) node[left,fill=white,outer sep=0pt] {$20$};\n\\draw (-0.5,22) node[left,fill=white,outer sep=0pt] {$22$};\n\\draw (14,14) node[above,fill=white,outer sep=0pt] {$\\frac{1}{2}(|\\log(a)| + 1) + \\rho_0$};\n\\draw (14,12) node[above,fill=white,outer sep=0pt] {$\\frac{1}{2}(|\\log(2)| + 1) + \\rho_0 + 3$};\n\\draw (14,10) node[above,fill=white,outer sep=0pt] {$\\frac{1}{2}(|\\log(1)| + 1) + \\rho_0 + 3$};\n\\draw (14,8) node[above,fill=white,outer sep=0pt] {$\\frac{1}{2}(|\\log(\\sqrt{a})| + 1) + \\rho_0 = 0.75$};\n\\draw (10,10) node[above,fill=white,outer sep=0pt] {$R = 1$};\n\\draw (10,8) node[above,fill=white,outer sep=0pt] {$R = 2$};\n\\draw (10,6) node[above,fill=white,outer sep=0pt] {$R = 3$};\n\\draw (10,4) node[above,fill=white,outer sep=0pt] {$R = 4$};\n\\draw (10,2) node[above,fill=white,outer sep=0pt] {$R = 5$};\n\\draw (10,0) node[above,fill=white,outer sep=0pt] {$R = 6$};\n\\draw (12,4) node[fill=black,outer sep=2pt] {};\n\\draw (16,4) node[fill=black,outer sep=2pt] {};\n\\draw (12,6) node[fill=black,outer sep=2pt] {};\n\\draw (16,6) node[fill=black,outer sep=2pt] {};\n\\draw (12,8) node[fill=black,outer sep=2pt] {};\n\\draw (16,8) node[fill=black,outer sep=2pt] {};\n\\draw (12,10) node[fill=black,outer sep=2pt] {};\n\\draw (16,10) node[fill=black,outer sep=2pt] {};\n\\draw (8,"
    },
    {
        "index": 485,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing,positioning,calc,shapes.multipart,arrows,arrows.meta,patterns}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.14}\n\\usepackage{pgfplotstable}\n\n\\begin{document}\n\n\\begin{tikzpicture}[every text node part/.style={align=center}]\n\\pgfmathsetmacro{\\x}{3.2}\n\\pgfmathsetmacro{\\y}{1.7}\n\\pgfmathsetmacro{\\dy}{.85}\n\\pgfmathsetmacro{\\dr}{1.4}\n\n\\draw (0,0) -- (\\x,0) node[pos=.5,below] {$s(a)$};\n\\draw (\\x,\\dy) to[out=180,in=0] (-\\x,\\dy) -- (-\\x,\\dy+\\dr) to[out=0,in=180] (0,\\dy+\\dr) -- (0,\\dy);\n\\draw (-\\x,\\dy+\\dr) to[out=180,in=180] (-\\x,\\dy+2*\\dr) to[out=0,in=0] (\\x,\\dy+2*\\dr) -- (\\x,\\dy+\\dr);\n\\draw (\\x,\\dy+\\dr) to[out=-10,in=180] (\\x,\\dy+2*\\dr) -- (-\\x,\\dy+2*\\dr) to[out=0,in=-10] (-\\x,\\dy+3*\\dr) -- (0,\\dy+3*\\dr) -- (0,\\dy+2*\\dr) to[out=180,in=0] (\\x,\\dy+2*\\dr) -- (\\x,\\dy);\n\\draw (0,\\dy+3*\\dr) to[out=10,in=180] (\\x,\\dy+3*\\dr);\n\\draw (0,\\dy+3*\\dr) -- (-\\x,\\dy+3*\\dr);\n\n\\draw (-\\x+.15,\\dy+.5*\\dr+.5) -- (-\\x-.15,\\dy+.5*\\dr+.5);\n\\draw (-\\x+.15,\\dy+.5*\\dr+.5) -- (-\\x+.15,\\dy+3*\\dr+.5);\n\\draw (-\\x-.15,\\dy+3*\\dr+.5) -- (-\\x-.15,\\dy+.5*\\dr+.5);\n\\draw (-\\x-.15,\\dy+3*\\dr+.5) -- (\\x-.15,\\dy+3*\\dr+.5);\n\n\\draw[->] (-\\x/2,\\dy+.5*\\dr) -- node[midway,above] {$L_a$} (\\x/2,\\dy+.5*\\dr);\n\n\\draw (-\\x/2,\\dy) -- (-\\x/2,\\dy-2*\\dr);\n\\draw (\\x/2,\\dy) -- (\\x/2,\\dy-2*\\dr);\n\\draw[thick,decorate,decoration={brace,mirror}] (-\\x/2,\\dy) -- node[below] {$s(t(a))$} (\\x/2,\\dy);\n\\draw (0,\\dy+.5*\\dr) -- (0,\\dy+2*\\dr);\n\n\\draw[->,thick] (-.1,\\dy+.5*\\dr) -- (-.1,\\dy+1.5*\\dr);\n\\draw[->,thick] (.1,\\dy+.5*\\dr) -- (.1,\\dy+1.5*\\dr);\n\\draw[->,thick] (0,\\dy+1.5*\\dr) -- (0,\\dy+2*\\dr);\n\n\\node[scale=.9] (G) at (0,1.25*\\dr) {$G$};\n\\node[scale=.9] (Gt) at (\\x/2-.4,1.25*\\dr) {$G^{t(a)}$};\n\\node[scale=.8] (Omega) at (\\x/2+.5,\\dy-2*\\dr+.5) {$\\Omega$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 486,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,shapes,chains}\n\\usepackage[pdftex,linkcolor=blue,citecolor=blue,backref=page]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n  \\tikzstyle{every node}=[draw,thick,shape=rectangle]\n    \\node (one) at (0,4) {$[1,1]$};\n    \\node (a) at (-1,3) {$[1,2]$};\n    \\node (b) at (1,3) {$[2,1]$};\n    \\node (c) at (-2,2) {$[1,3]$};\n    \\node (d) at (0,2) {$[2,2]$};\n    \\node (e) at (2,2) {$[3,1]$};\n    \\node (f) at (-3,1) {$[1,3]$};\n    \\node (g) at (-1,1) {$[2,2]$};\n    \\node (h) at (1,1) {$[3,1]$};\n    \\node (i) at (3,1) {$[3,2]$};\n    \\node (zero) at (0,0) {$[1,1]$};\n    \\draw (zero)--(g)--(f)--(one)--(a)--(c)--(f)--(b)--(zero)--(h)--(i)--(e)--(b)--(zero)--(g)--(f)\n           (b)--(h)--(i)--(e)--(d)--(c)--(a)--(f)--(d)--(b)--(d)--(e)--(i);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 487,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{amssymb,amsmath,amsthm}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\n\t\\pgfmathsetmacro{\\xcoord}{0.3}\n\t\\pgfmathsetmacro{\\ycoord}{-0.5}\n\t\\pgfmathsetmacro{\\circle_size}{1.2}\n\t\\pgfmathsetmacro{\\first_end}{-1.5}\n\t\\pgfmathsetmacro{\\second_end}{-1.5+1.2*1.7320}\n\t\\pgfmathsetmacro{\\third_end}{-1.5+1.2*2*1.7320}\n\t\\pgfmathsetmacro{\\fourth_end}{-1.5+1.2*2.5*1.7320}\n\t\\pgfmathsetmacro{\\fifth_end}{-1.5+1.2*3.2*1.7320}\n\t\n\t\\pgfmathsetmacro{\\num_of_points}{10}\n\t\n\t\n\t\\begin{scope}\n\t\n\t\\draw[draw=black,thick]  (\\first_end, \\second_end) circle (1.2);\n\t\\draw[draw=black,thick]  (\\third_end, \\fourth_end) circle (1.2);\n\t\\draw[draw=black,thick]  (\\fifth_end, \\fifth_end) circle (1.2);\n\t\n\t\\draw[draw=black,fill=black!20] (\\first_end, \\second_end) circle (0.05);\n\t\\draw[draw=black,fill=black!20] (\\third_end, \\fourth_end) circle (0.05);\n\t\\draw[draw=black,fill=black!20] (\\fifth_end, \\fifth_end) circle (0.05);\n\t\n\t\\draw[draw=black,fill=black!20] (\\first_end, \\second_end) circle (0.05);\n\t\\draw[draw=black,fill=black!20] (\\third_end, \\fourth_end) circle (0.05);\n\t\\draw[draw=black,fill=black!20] (\\fifth_end, \\fifth_end) circle (0.05);\n\t\n\t\\foreach \\x in {0, ..., \\num_of_points} {\n\t\t\\draw[draw=black,fill=black] ( {\\xcoord*\\x}, {\\ycoord*\\x} ) circle (0.05);\n\t}\n\t\n\t\\foreach \\x in {1, ..., 10} {\n\t\t\\pgfmathsetmacro{\\angle_val}{1.7320}\n\t\t\\pgfmathsetmacro{\\my_y}{\\ycoord*\\x}\n\t\t\\draw[red, thick, fill=red] (\\x*\\xcoord, \\my_y) circle (0.05);\n\t\t\\draw[red, thick, ->] (\\x*\\xcoord, \\my_y) -- ({\\x*\\xcoord - 0.2*\\angle_val*\\ycoord}, \\my_y + \\angle_val*\\xcoord);\n\t}\n\t\n\t\\foreach \\x in {1, ..., 10} {\n\t\t\\pgfmathsetmacro{\\angle_val}{1.7320}\n\t\t\\pgfmathsetmacro{\\my_y}{\\ycoord*\\x}\n\t\t\\draw[red, thick, fill=red] (\\x*\\xcoord + \\circle_size*\\xcoord, \\my_y) circle (0.05);\n\t\t\\draw[red, thick, ->] (\\x*\\xcoord + \\circle_size*\\xcoord, \\my_y) -- ({\\x*\\xcoord + \\circle_size*\\xcoord - 0.2*\\angle_val*\\ycoord}, \\my_y + \\angle_val*\\xcoord);\n\t}\n\t\n\t\\foreach \\x in {1, ..., 10} {\n\t\t\\pgfmathsetmacro{\\angle_val}{1.7320}\n\t\t\\pgfmathsetmacro{\\my_y}{\\ycoord*\\x}\n\t\t\\draw[red, thick, fill=red] (\\x*\\xcoord + 2*\\circle_size*\\xcoord, \\my_y) circle (0.05);\n\t\t\\draw[red, thick, ->] (\\x*\\xcoord + 2*\\circle_size*\\xcoord, \\my_y) -- ({\\x*\\xcoord + 2*\\circle_size*\\xcoord - 0.2*\\angle_val*\\ycoord}, \\my_y + \\angle_val*\\xcoord);\n\t}\n\t\n\t\\foreach \\x in {1, ..., 10} {\n\t\t\\pgfmathsetmacro{\\angle_val}{1.7320}\n\t\t\\pgfmathsetmacro{\\my_y}{\\ycoord*\\x}\n\t\t\\draw[red, thick, fill=red] (\\x*\\xcoord + 3*\\circle_size*\\xcoord, \\my_y) circle (0.05);\n\t\t\\draw[red, thick, ->] (\\x*\\xcoord + 3*\\circle_size*\\xcoord, \\my_y) -- ({\\x*\\xcoord + 3*\\circle_size*\\xcoord - 0.2*\\angle_val*\\ycoord}, \\my_y + \\angle_val*\\xcoord);\n\t}\n\t\n\t\\foreach \\x in {1, ..., 10} {\n\t\t\\pgfmathsetmacro{\\angle_val}{1.7320}\n\t\t\\pgfmathsetmacro{\\my_y}{\\ycoord*\\x}\n\t\t\\draw[red, thick, fill=red] (\\x*\\xcoord + 4*\\circle_size*\\xcoord, \\my_y) circle (0.05);\n\t\t\\draw[red, thick, ->] (\\x*\\xcoord + 4*\\circle_size*\\xcoord, \\my_y) -- ({\\x*\\xcoord + 4*\\circle_size*\\xcoord - 0.2*\\angle_val*\\ycoord}, \\my_y + \\angle_val*\\xcoord);\n\t}\n\t\n\t\\end{scope}\n\t\n\t\\begin{scope}[shift={(4.25cm,0cm)}]\n\t\n\t\\draw[draw=black,thick]  (\\first_end, \\second_end) circle (1.2);\n\t\\draw[draw=black,thick]  (\\third_end, \\fourth_end) circle (1.2);\n\t\\draw[draw=black,thick]  (\\fifth_end, \\fifth_end) circle (1.2);\n\t\n\t\\draw[draw=black,fill=black!20] (\\first_end, \\second_end) circle (0.05);\n\t\\draw[draw=black,fill=black!20] (\\third_end, \\fourth_"
    },
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{trees}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[level distance=1.5cm,\n  level 1/.style={sibling distance=6cm},\n  level 2/.style={sibling distance=2.5cm},\n  level 3/.style={sibling distance=1cm}]\n  \\node[rectangle,draw] {$\\mathstrut u$}\n    child {node {$\\mathstrut L^L_1$}\n      child {node[rectangle,draw] {$\\mathstrut P_1^L$}\n      child {node[rectangle,draw,color=orange] {$\\mathstrut a$}}\n      child {node[rectangle,draw,color=orange] {$\\mathstrut b$}}\n      }\n      child {node {$\\mathstrut RL_1$}}\n    }\n    child {node {$\\mathstrut L^R_1$}\n      child {node {$\\mathstrut RR_1$}}\n      child {node {$\\mathstrut RR_2$}}\n    }\n    child {node[circle,fill=black,inner sep=0pt,draw] {$\\dots$}\n      child[missing]\n      child[missing]\n      child[missing]\n    }\n    child {node[rectangle,draw] {$\\mathstrut P_2^R$}\n      child {node[rectangle,draw,color=orange] {$\\mathstrut a$}}\n      child {node[rectangle,draw,color=orange] {$\\mathstrut b$}}\n    };\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\n\\begin{document}\n\n\\begin{tikzpicture}[node distance={15mm}, main/.style = {draw, circle}] \n\\node[main] (1){$x_0$};\n\\node[main] (2) [right of=1] {$x_1$}; \n\\node[main] (3) [right of=2] {$x_2$};\n\\node[main] (4) [below of=1] {$x_0$}; \n\\node[main] (5) [right of=4] {$x_1$};\n\\node[main] (6) [right of=5] {$x_2$};\n\\node[main] (7) [below of=4] {$x_0$};\n\\node[main] (8) [right of=7] {$x_1$};\n\\node[main] (9) [right of=8] {$x_2$};\n\n\\draw[->, blue] (1) to [bend left=30] node [midway, above] {$E_0$} (3);\n\\draw[->, blue] (3) to [bend left=30] node [midway, above] {$E_2$} (1);\n\\draw[->, red] (4) to [bend left=30] node [midway, above] {$E_0$} (6);\n\\draw[->, red] (6) to [bend left=30] node [midway, above] {$E_2$} (4);\n\\draw[->, black!30!green] (7) to [bend left=30] node [midway, above] {$E_0$} (9);\n\\draw[->, black!30!green] (9) to [bend left=30] node [midway, above] {$E_2$} (7);\n\n\\node [below left=2cm, align=left, black!30!green] at (1) {$(c)$};\n\\node [below left=2cm, align=left, black!30!green] at (4) {$(d)$};\n\\node [below left=2cm, align=left, black!30!green] at (7) {$(e)$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 492,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n \\filldraw (0,0) circle (2pt) node[anchor=south]{$a$}\n           (1,1) circle (2pt) node[anchor=south]{$x$}\n           (2,0) circle (2pt) node[anchor=south]{$b$}\n           (3,1) circle (2pt) node[anchor=south]{$y$}\n           (4,0) circle (2pt) node[anchor=south]{$c$}\n           (5,1) circle (2pt) node[anchor=south]{$d$}\n           (6,0) circle (2pt) node[anchor=south]{$e$}\n           (7,1) circle (2pt) node[anchor=south]{$f$};\n \\draw (0,0) .. controls (1,1) and (2,1) .. (3,1)\n       (3,1) .. controls (4,1) and (5,1) .. (6,0)\n       (6,0) .. controls (7,1) and (8,1) .. (9,0);\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usetikzlibrary{trees,decorations.pathreplacing,calligraphy,quotes}\n\n\\newcommand{\\listnode}[2]{\\node[draw,circle] #1 #2;}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n    level 1/.style={sibling distance=40mm},\n    level 2/.style={sibling distance=15mm},\n    level distance=20mm,\n    every edge/.style={draw, -latex}\n    ]\n    \\node[] {\n    \\begin{tabular}{c}\n    $w_3$ \\\\\n    $g_V$ \\\\\n    $g_V$ \\\\\n    $g_V$ \\\\\n    $g_V$ \\\\\n    $\\cdots$\n    \\end{tabular}\n    }\n    child[line width=1pt] {\n    node {\n    \\begin{tabular}{c}\n    $w_2$ \\\\\n    $g_V$ \\\\\n    $g_V$ \\\\\n    $g_V$ \\\\\n    $\\cdots$\n    \\end{tabular}\n    }\n    edge from parent node[left,xshift=-3pt,yshift=12pt] {$w_2$}\n    }\n    child[line width=1pt] {\n    node {\n    \\begin{tabular}{c}\n    $w_1$ \\\\\n    $g_V$ \\\\\n    $\\cdots$\n    \\end{tabular}\n    }\n    edge from parent node[left,xshift=-3pt,yshift=12pt] {$w_1$}\n    }\n    child[line width=1pt] {\n    node {\n    \\begin{tabular}{c}\n    $w_1$ \\\\\n    $g_V$ \\\\\n    $\\cdots$\n    \\end{tabular}\n    }\n    edge from parent node[right,xshift=3pt,yshift=12pt] {$\\sum \\limits_{q} q_{i,k}$}\n    }\n    child[line width=1pt] {\n    node {\n    \\begin{tabular}{c}\n    $w_1$ \\\\\n    $g_V$ \\\\\n    $\\cdots$\n    \\end{tabular}\n    }\n    edge from parent node[right,xshift=3pt,yshift=12pt] {$\\sum \\limits_{q} q_{i,k}$}\n    }\n    child[line width=1pt] {\n    node {\n    \\begin{tabular}{c}\n    $w_1$ \\\\\n    $g_V$ \\\\\n    $\\cdots$\n    \\end{tabular}\n    }\n    edge from parent node[right,xshift=3pt,yshift=12pt] {$\\sum \\limits_{q} q_{i,k}$}\n    }\n    ;\n    \\path (1.4,-2.7) node (v1) {$v_1$};\n    \\path (1.4,-4.7) node (v2) {$v_2$};\n    \\path (1.4,-6.7) node (v3) {$v_3$};\n    \\node[] at (-1.5,-2.7) (q1) {$g_Q$};\n    \\node[] at (-1.5,-4.7) (q2) {$g_Q$};\n    \\node[] at (-1.5,-6.7) (q3) {$g_Q$};\n    \\foreach \\i/\\j in {1/2,2/3,3/4,4/5,5/6} {\n        \\draw[<-] (q\\i) -- (v\\j);\n    }\n    \\listnode{(-0.45,1.05)}{}\n    \\listnode{(-0.45,-2.15)}{}\n    \\listnode{(-0.45,-4.15)}{}\n    \\node[] at (-0.85,0.8) {$w_3$};\n    \\node[] at (-0.85,-2.15) {$g_V$};\n    \\node[] at (-0.85,-4.15) {$g_V$};\n    \\node[] at (-0.85,-5.5) {$g_V$};\n    \\node[] at (-0.85,-6.8) {$g_V$};\n    \\draw[decorate, decoration={calligraphic brace,mirror}] (0.7,1.25) -- (0.7,0.75) node[pos=0.5,anchor=south,yshift=-10pt]{softmax};\n    \\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[a4paper,11pt,oneside]{article}\n\\usepackage{amsmath,amsfonts,amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes.geometric}\n\\usetikzlibrary{shapes.arrows}\n\\usetikzlibrary{shadows.blur}\n\\usetikzlibrary{fadings}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\\draw[fill=cyan,draw=black] (-1,-0.5) ellipse (0.5cm and 1cm);\n\\draw[fill=cyan,draw=black] (0.5,-0.5) ellipse (0.5cm and 1cm);\n\\draw[fill=cyan,draw=black] (2.5,-0.5) ellipse (0.5cm and 1cm);\n\\draw[fill=cyan,draw=black] (4.5,-0.5) ellipse (0.5cm and 1cm);\n\\draw[fill=cyan,draw=black] (5,-0.5) ellipse (0.5cm and 1cm);\n\\node at (-1,0) {Full dataset};\n\\node at (0.5,0) {k-fold CV};\n\\node at (2.5,0) {Train};\n\\node at (4.5,0) {Test};\n\\node at (5,0) {Validation};\n\\node[fill=green!40,rectangle,inner sep=3pt,rounded corners,text=black] at (8,0) {Full dataset};\n\\node[fill=red!20,rectangle,inner sep=3pt,rounded corners,text=black,text width=3.5cm,align=center] at (8,-1) {k-fold CV\\\\ observations\\\\ + Untrained\\\\ observations};\n\\node[fill=green!40,rectangle,inner sep=3pt,rounded corners,text=black,text width=3.5cm,align=center] at (8,-2) {Train\\\\ + Untrained observations};\n\\node[fill=red!20,rectangle,inner sep=3pt,rounded corners,text=black,text width=3.5cm,align=center] at (8,-3) {Test\\\\ + Untrained observations};\n\\draw[->,very thick] (6.5,0) -- (7,0);\n\\draw[->,very thick] (6.5,-1) -- (7,-1);\n\\draw[->,very thick] (6.5,-2) -- (7,-2);\n\\draw[->,very thick] (6.5,-3) -- (7,-3);\n\\draw[very thick] (6.5,0.5) -- (6.5,-3.5);\n\\draw[very thick] (7.5,0.5) -- (7.5,-3.5);\n\\draw[->,very thick] (6.5,-3.5) -- (7.5,-3.5) -- (7.5,-1);\n\\node at (7.5,-1.5) {Updating};\n\\node at (7.5,-2.5) {into the (WNTW)NN};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt,a4paper]{amsart}\n\\usepackage{amssymb, amstext, amscd, amsmath, color}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\n\\filldraw (0,0) circle (2pt) node[anchor=south]{$x^*$};\n\\filldraw (2,0) circle (2pt) node[anchor=south]{$x^*$};\n\\filldraw (-2,0) circle (2pt) node[anchor=south]{$x^*$};\n\n\n\\draw[dashed] (-3,0) -- (3,0);\n\n\\draw[dotted] (0,0) -- (0,1.5);\n\n\\draw[dashed] (-4,0) -- (-3,0);\n\\draw[dashed] (3,0) -- (4,0);\n\n\\draw (0,1.5) circle (1.5cm);\n\\draw (0,-1.5) circle (1.5cm);\n\n\n\\draw[dotted] (0,0) -- (0,-1.5);\n\n\\draw (0,0) -- (0,1.5);\n\n\\draw (0,0) -- (0,-1.5);\n\\draw (-0.3,-1.5) node[anchor=north]{$I_{2}$};\n\n\\draw (-1.2,0.7) node[anchor=south]{$I_{2}$};\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[format=sigconf,nonacm,protrusion=true,expansion=true]{acmart}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usetikzlibrary{fit,shapes,decorations.pathmorphing}\n\\usepackage{tikz-cd}\n\n\\begin{document}\n\n\\begin{tikzpicture}[main/.style = {draw, circle}, node distance=14mm]\n\\node[main] (r) {$x_1$};\n\\node[main] (o) [above right of=r] {$x_2$};\n\\node[main] (s) [below right of=o] {$x_3$};\n\\node[main] (t) [right of=s] {$x_4$};\n\\node[main] (u) [below of=s] {$x_5$};\n\\node[main] (v) [right of=u] {$x_6$};\n\\node[main] (w) [right of=v] {$x_8$};\n\n\\draw[very thick, -] (r) -- (o);\n\\draw[very thick, -] (s) -- (o);\n\\draw[very thick, -] (s) -- (t);\n\\draw[very thick, -] (s) -- (v);\n\\draw[very thick, -] (u) -- (v);\n\\draw[very thick, -] (w) -- (v);\n\n\\node[right of=r, node distance=10mm] {Holiday};\n\\node[right of=o, node distance=10mm] {Rain};\n\\node[left of=s, node distance=10mm] {Stress};\n\\node[right of=t, node distance=10mm] {Runaway truck};\n\\node[below of=u, node distance=10mm] {Level};\n\\node[below of=v, node distance=10mm] {Lever};\n\\node[left of=w, node distance=10mm] {Track of $x_8$};\n\\node[left of=r, node distance=10mm] {\\begin{tabular}{c}$1$ Operators\\\\$>$ Track of $5$\\end{tabular}};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amsfonts,amssymb,amscd,amsmath,enumerate,verbatim,calc,thumbpdf,stmaryrd, graphicx,ulem,mathtools}\n\\usepackage{tikz,hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.25]\n\t\\draw (1.5,-0.2) node[below,scale=.75]{$\\varepsilon_2$};\n\t\\draw (3,-0.2) node[below,scale=.75]{$\\varepsilon_4$};\n\t\\draw (4.5,-0.2) node[below,scale=.75]{$\\varepsilon_6$};\n\t\\draw (6,-0.2) node[below,scale=.75]{$\\varepsilon_8$};\n\t\\draw (7.5,-0.2) node[below,scale=.75]{$\\varepsilon_{10}$};\n\t\\draw (9,-0.2) node[below,scale=.75]{$\\varepsilon_{12}$};\n\t\\draw (10.5,-0.2) node[below,scale=.75]{$\\varepsilon_{14}$};\n\t\\draw (12,-0.2) node[below,scale=.75]{$\\varepsilon_{16}$};\n\t\\draw (13.5,-0.2) node[below,scale=.75]{$\\varepsilon_{18}$};\n\t\\draw (15,-0.2) node[below,scale=.75]{$\\varepsilon_{20}$};\n\t\\draw[fill](1.5,-1.2) circle(0.05);\n\t\\draw[fill](3,-1.2) circle(0.05);\n\t\\draw[fill](4.5,-1.2) circle(0.05);\n\t\\draw[fill](6,-1.2) circle(0.05);\n\t\\draw[fill](7.5,-1.2) circle(0.05);\n\t\\draw[fill](9,-1.2) circle(0.05);\n\t\\draw[fill](10.5,-1.2) circle(0.05);\n\t\\draw[fill](12,-1.2) circle(0.05);\n\t\\draw[fill](13.5,-1.2) circle(0.05);\n\t\\draw[fill](15,-1.2) circle(0.05);\n\t\\draw[very thick,dotted] (1.5,-0.7) -- (1.5,0.2);\n\t\\draw[very thick,dotted] (3,-0.7) -- (3,0.2);\n\t\\draw[very thick,dotted] (4.5,-0.7) -- (4.5,0.2);\n\t\\draw[very thick,dotted] (6,-0.7) -- (6,0.2);\n\t\\draw[very thick,dotted] (7.5,-0.7) -- (7.5,0.2);\n\t\\draw[very thick,dotted] (9,-0.7) -- (9,0.2);\n\t\\draw[very thick,dotted] (10.5,-0.7) -- (10.5,0.2);\n\t\\draw[very thick,dotted] (12,-0.7) -- (12,0.2);\n\t\\draw[very thick,dotted] (13.5,-0.7) -- (13.5,0.2);\n\t\\draw[very thick,dotted] (15,-0.7) -- (15,0.2);\n\t\\draw (1.5,0) -- (1.5,-1.2);\n\t\\draw (3,0) -- (3,-1.2);\n\t\\draw (4.5,0) -- (4.5,-1.2);\n\t\\draw (6,0) -- (6,-1.2);\n\t\\draw (7.5,0) -- (7.5,-1.2);\n\t\\draw (9,0) -- (9,-1.2);\n\t\\draw (10.5,0) -- (10.5,-1.2);\n\t\\draw (12,0) -- (12,-1.2);\n\t\\draw (13.5,0) -- (13.5,-1.2);\n\t\\draw (15,0) -- (15,-1.2);\n\t\\draw (15,-1.2) -- (15,-2.4);\n\t\\draw[very thick,<->] (15.5,0.2) -- (15.5,-2.4);\n\t\\draw (15.5,-1.2) node[right,scale=1]{generation};\n\t\\draw[fill=black!100,draw=black!100] (15,-2.5) circle(0.05);\n\t\\draw[fill=black!100,draw=black!100] (15,-2.7) circle(0.05);\n\t\\draw[fill=black!100,draw=black!100] (15,-2.9) circle(0.05);\n\t\\draw[fill=black!100,draw=black!100] (15,-3.1) circle(0.05);\n\t\\draw[fill=black!100,draw=black!100] (15,-3.3) circle(0.05);\n\t\\draw[fill=black!100,draw=black!100] (15,-3.5) circle(0.05);\n\t\\draw[fill=black!100,draw=black!100] (15,-3.7) circle(0.05);\n\t\\draw[fill=black!100,draw=black!100] (15,-3.9) circle(0.05);\n\t\\draw[fill=black!100,draw=black!100] (15,-4.1) circle(0.05);\n\t\\draw[fill=black!100,draw=black!100] (15,-4.3) circle(0.05);\n\t\\draw[fill=black!100,draw=black!100] (15,-4.5) circle(0.05);\n\t\\draw (15.5,-2.7) node[right,scale=1]{$\\varepsilon$};\n\t\\draw[fill=black!100,draw=black!100] (15,-2.9) -- (14.8,-3.1) -- (15.8,-3.1) -- (15.6,-2.9) -- cycle;\n\t\\draw[fill=black!100,draw=black!100] (15,-3.3) -- (14.8,-3.5) -- (15.8,-3.5) -- (15.6,-3.3) -- cycle;\n\t\\draw[fill=black!100"
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    {
        "index": 505,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw [thick] (0,0)--(10,0);\n\\draw [thick] (0,-0.5)--(0,0.5);\n\\draw [thick] (2,-0.5)--(2,0.5);\n\\draw [thick] (4,-0.5)--(4,0.5);\n\\draw [thick] (6,-0.5)--(6,0.5);\n\\draw [thick] (8,-0.5)--(8,0.5);\n\\draw [thick, cyan] (1,-0.5)--(1,0.5);\n\\draw [thick, cyan] (3,-0.5)--(3,0.5);\n\\draw [thick, cyan] (5,-0.5)--(5,0.5);\n\\draw [thick, cyan] (7,-0.5)--(7,0.5);\n\\draw [thick, magenta] (1.1,-0.5)--(1.1,0.5);\n\\draw [thick, magenta] (3.1,-0.5)--(3.1,0.5);\n\\draw [thick, magenta] (5.1,-0.5)--(5.1,0.5);\n\\draw [thick, magenta] (7.1,-0.5)--(7.1,0.5);\n\\draw (0,-0.5) node[below]{$c(A_1):$};\n\\draw (0,0) node[above]{$c(A_1):$};\n\\draw (2,-0.5) node[below]{$A_1$};\n\\draw (4,-0.5) node[below]{$A_2$};\n\\draw (6,-0.5) node[below]{$A_3$};\n\\draw (8,-0.5) node[below]{$A_4$};\n\\draw (1,-0.5) node[below]{$1$};\n\\draw (3,-0.5) node[below]{$1$};\n\\draw (5,-0.5) node[below]{$2$};\n\\draw (7,-0.5) node[below]{$2$};\n\\draw (1,0) node[above]{$1$};\n\\draw (3,0) node[above]{$2$};\n\\draw (5,0) node[above]{$3$};\n\\draw (7,0) node[above]{$3$};\n\\draw (1.1,-0.5) node[below]{$1$};\n\\draw (3.1,-0.5) node[below]{$1$};\n\\draw (5.1,-0.5) node[below]{$2$};\n\\draw (7.1,-0.5) node[below]{$2$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 506,
        "tikz_code": "\\documentclass[12pt, reqno]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[usenames]{color}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,shapes,snakes,automata,backgrounds,petri}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T2A]{fontenc}\n\\usepackage{amsmath,amssymb,amsthm}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\t\t\t\\draw[very thick] (0, 3) to (0, -3);\n\t\t\t\t\t\\draw[very thick] (0, 3) to (7, 3);\n\t\t\t\t\t\\draw[very thick] (7, 3) to (7, -3);\n\t\t\t\t\t\\draw[very thick] (0, -3) to (7, -3);\n\t\t\t\t\t\\draw[very thick] (7, 3) to (10, 3);\n\t\t\t\t\t\\draw[very thick] (7, -3) to (10, -3);\n\t\t\t\t\t\\draw[very thick] (0, 3) to (7, 3);\n\t\t\t\t\t\\draw[very thick] (0, -3) to (7, -3);\n\t\t\t\t\t\\draw[very thick, red, fill=red!30] (3, 0) to (3, 3) to (5, 3) to (5, 0);\n\t\t\t\t\t\\draw[very thick, blue, fill=blue!30] (3, -3) to (3, 0) to (5, 0) to (5, -3);\n\t\t\t\t\t\\draw[very thick, red] (3, 0) to (3, 3);\n\t\t\t\t\t\\draw[very thick, blue] (5, 0) to (5, -3);\n\t\t\t\t\t\\draw[very thick, red, fill=red!30] (7, 0) to (7, 3) to (9, 3) to (9, 0);\n\t\t\t\t\t\\draw[very thick, blue, fill=blue!30] (7, -3) to (7, 0) to (9, 0) to (9, -3);\n\t\t\t\t\t\\draw[very thick, red] (7, 0) to (7, 3);\n\t\t\t\t\t\\draw[very thick, blue] (9, 0) to (9, -3);\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\\draw (1, 1.5) node {$\\overline{D}_{k}$};\n\t\t\t\t\t\\draw (8.5, 1.5) node {$D_{\\ell}$};\n\t\t\t\t\t\\draw (1.5, 0) node {$K_{\\ell, k}$};\n\t\t\t\t\t\\draw (8.5, 0) node {$L_{\\ell, k}$};\n\t\t\t\t\t\\draw (5, 0) node {$\\bullet$};\n\t\t\t\t\t\\draw (5, -2.5) node {$x_{\\ell}$};\n\t\t\t\t\t\\draw (5, 2) node {$\\overline{\\pi}_{K, \\ell}$};\n\t\t\t\t\t\\draw (3, 0) node {$\\bullet$};\n\t\t\t\t\t\\draw (3, -2.5) node {$x_k$};\n\t\t\t\t\t\\draw (3, 2) node {$\\overline{\\pi}_{K, k}$};\n\t\t\t\t\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 507,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usepackage{amsmath}\n\\usepackage[colorlinks]{hyperref}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\centering\n\\node (img){\\includegraphics[width=0.3\\textwidth]{example-image}};\n\\node[below=of img, node distance=0cm, xshift=0.2cm, yshift=1cm] {\\scriptsize (a) Images};\n\\node[right=of img, node distance=0cm, xshift=-0.5cm,yshift=0cm] (img2){\\includegraphics[width=0.15\\textwidth]{example-image}};\n\\node[below=of img2, node distance=0cm, xshift=0.2cm, yshift=1cm] {\\scriptsize (b) Genomic data};\n\\node[right=of img2, node distance=0cm, xshift=-1.2cm,yshift=0cm] (img3){\\includegraphics[width=0.15\\textwidth]{example-image}};\n\\node[right=of img3, node distance=0cm, xshift=-0.6cm,yshift=0cm] (img4){\\includegraphics[width=0.15\\textwidth]{example-image}};\n\\node[right=of img4, node distance=0cm, xshift=-0.6cm,yshift=0cm] (img5){\\includegraphics[width=0.15\\textwidth]{example-image}};\n\\node[right=of img5, node distance=0cm, xshift=-0.5cm,yshift=0cm] (img6){\\includegraphics[width=0.15\\textwidth]{example-image}};\n\\node[above=of img3, node distance=0cm, xshift=0.1cm, yshift=-0.7cm] {$0.1$};\n\\node[above=of img4, node distance=0cm, xshift=0.1cm, yshift=-0.7cm] {$0.2$};\n\\node[above=of img5, node distance=0cm, xshift=0.1cm, yshift=-0.7cm] {$0.5$};\n\\node[above=of img6, node distance=0cm, xshift=0.1cm, yshift=-0.7cm] {$0.7$};\n\\node[above=of img2, node distance=0cm, xshift=0.2cm, yshift=-0.7cm] {$0.8$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 508,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amsfonts,amsthm,amssymb,amscd,color,xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[>=latex,scale=.8]\n\\def\\rx{2.5}\n\\def\\ry{0.7}\n\\def\\h{4}\n\\def\\xscale{0.8}\n\n\\foreach \\a in {1,2,3,4}{\n\t\\coordinate (a\\a) at (180+72*\\a:\\rx);\n\t\\coordinate (a'1\\a) at (180+72*\\a:\\h);\n\t\\coordinate (b\\a) at (0+72*\\a:\\rx);\n\t\\coordinate (b'1\\a) at (0+72*\\a:\\h);\n}\n\n\\foreach \\a in {1,2,3,4}{\n\t\\draw[dotted] (a'1\\a) -- (a\\a) -- (b\\a) -- (b'1\\a) -- (a'1\\a);\n\t\\draw (a\\a) node[circle,fill,inner sep=1pt] () {};\n\t\\draw (b\\a) node[circle,fill,inner sep=1pt] () {};\n\t\\draw (a'1\\a) node[circle,fill,inner sep=1pt] () {};\n\t\\draw (b'1\\a) node[circle,fill,inner sep=1pt] () {};\n}\n\n\\foreach \\a in {1,2,3,4}{\n\t\\node at ($(a'1\\a)!0.5!(a\\a)$) () {$b_{\\a,m}$};\n\t\\node at ($(b'1\\a)!0.5!(b\\a)$) () {$c_{\\a,m-1}$};\n}\n\n\\foreach \\a in {1,2,3,4}{\n\t\\draw[dotted] (a1\\a) -- (b2\\a);\n\t\\draw[dotted] (a1\\a) -- (b3\\a);\n\t\\draw[dotted] (a2\\a) -- (b3\\a);\n\t\\draw[dotted] (a3\\a) -- (b4\\a);\n\t\\draw[dotted] (a4\\a) -- (b3\\a);\n}\n\n\\node at (0,0) () {$(I)$};\n\n\\node at (5,0) () {$(II)$};\n\\foreach \\a in {1,2,3,4}{\n\t\\draw[dashed] (a\\a) -- (a'1\\a);\n}\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 509,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{color}\n\\usepackage{color}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\fill[black] (0,0) circle (0.1);\n\\fill[black] (2,0) circle (0.1);\n\\fill[black] (4,0) circle (0.1);\n\\fill[black] (6,0) circle (0.1);\n\\fill[black] (8,0) circle (0.1);\n\\fill[black] (2,2) circle (0.1);\n\\fill[black] (4,2) circle (0.1);\n\\fill[black] (6,2) circle (0.1);\n\\fill[black] (8,2) circle (0.1);\n\\draw[-,black] (0,0) -- (2,0);\n\\draw[-,black] (2,0) -- (4,0);\n\\draw[-,black] (4,0) -- (6,0);\n\\draw[-,black] (6,0) -- (8,0);\n\\draw[-,black] (0,2) -- (2,2);\n\\draw[-,black] (2,2) -- (4,2);\n\\draw[-,black] (4,2) -- (6,2);\n\\draw[-,black] (6,2) -- (8,2);\n\\draw[-,black] (2,0) -- (2,2);\n\\draw[-,black] (4,0) -- (4,2);\n\\draw[-,black] (6,0) -- (6,2);\n\\draw (0,-0.5) node {$1_d$};\n\\draw (2,-0.5) node {$2_d$};\n\\draw (4,-0.5) node {$3_d$};\n\\draw (6,-0.5) node {$4_d$};\n\\draw (8,-0.5) node {$\\cdots$};\n\\draw (1,0.5) node {$1_u$};\n\\draw (3,0.5) node {$2_u$};\n\\draw (5,0.5) node {$3_u$};\n\\draw (7,0.5) node {$4_u$};\n\\draw (1,2.5) node {$1_u$};\n\\draw (3,2.5) node {$2_u$};\n\\draw (5,2.5) node {$3_u$};\n\\draw (7,2.5) node {$4_u$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 510,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{tikz}\n\\usepackage{amsmath}\n\\usepackage{pgfmath}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\path[draw] (5,10) -- (2,8) -- (6,8) -- (5,10);\n\\path[draw] (1,6) -- (5,4) -- (9,4) -- (1,6);\n\\path[draw] (2,3) -- (5,1) -- (8,1) -- (2,3);\n\n\\path[draw,line width=1.5pt,fill=yellow!40] (1,6) -- (2,6) -- (2,5) -- (1,5) -- (1,6);\n\\path[draw,line width=1.5pt,fill=yellow!40] (3,6) -- (4,6) -- (4,5) -- (3,5) -- (3,6);\n\\path[draw,line width=1.5pt,fill=yellow!40] (5,6) -- (6,6) -- (6,5) -- (5,5) -- (5,6);\n\\path[draw,line width=1.5pt,fill=yellow!40] (7,6) -- (8,6) -- (8,5) -- (7,5) -- (7,6);\n\\path[draw,line width=1.5pt,fill=yellow!40] (1,4) -- (2,4) -- (2,3) -- (1,3) -- (1,4);\n\\path[draw,line width=1.5pt,fill=yellow!40] (3,4) -- (4,4) -- (4,3) -- (3,3) -- (3,4);\n\n\\draw (7,8) node[anchor=south] {$T(u)$};\n\\draw (1,6) node[anchor=east] {$T(u_1)$};\n\\draw (2,6) node[anchor=east] {$T(u_2)$};\n\\draw (5,6) node[anchor=west] {$\\cdots$};\n\\draw (1,4) node[anchor=east] {$T(v_1)$};\n\\draw (2,4) node[anchor=east] {$T(v_2)$};\n\\draw (5,4) node[anchor=west] {$\\cdots$};\n\n\\path[draw] (1,4) -- (1,3) -- (2,3);\n\\path[draw] (3,4) -- (3,3) -- (4,3);\n\\path[draw] (5,4) -- (5,3) -- (6,3);\n\\path[draw] (7,4) -- (7,3) -- (8,3);\n\n\\path[draw,fill=black] (1,3) circle (0.09);\n\\path[draw,fill=black] (2,3) circle (0.09);\n\\path[draw,fill=black] (3,3) circle (0.09);\n\\path[draw,fill=black] (4,3) circle (0.09);\n\\path[draw,fill=black] (5,3) circle (0.09);\n\\path[draw,fill=black] (6,3) circle (0.09);\n\\path[draw,fill=black] (7,3) circle (0.09);\n\\path[draw,fill=black] (8,3) circle (0.09);\n\n\\draw (-0.5,3) node[anchor=east] {$a\\setminus\\{(a_1,b_1)\\}$};\n\\draw (1.5,3) node[anchor=west] {$a_1\\cup\\{b_1\\}$};\n\\draw (2.5,3) node[anchor=west] {$a_2\\cup\\{b_2\\}$};\n\\draw (6.5,3) node[anchor=west] {$\\cdots$};\n\\draw (3.5,3) node[anchor=west] {$a_k\\cup\\{b_k\\}$};\n\\draw (7.5,3) node[anchor=west] {$\\cdots$};\n\n\\draw (-0.5,4) node[anchor=east] {$T(u_1)$};\n\\draw (1.5,4) node[anchor=west] {$T(u_2)$};\n\\draw (2.5,4) node[anchor=west] {$T(u_2)$};\n\\draw (6.5,4) node[anchor=west] {$\\cdots$};\n\\draw (3.5,4) node[anchor=west] {$T(u_k)$};\n\\draw (7.5,4) node[anchor=west] {$\\cdots$};\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 511,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n  \\node (img1)  {\\includegraphics[scale=0.65]{example-image}};\n  \\node[below=of img1, node distance=0cm, yshift=1cm] {$\\gamma_{\\rm ML}=\\frac{10}{2}$};\n  \\node[right=of img1, node distance=0cm, yshift=-1cm] (img2)  {\\includegraphics[scale=0.65]{example-image}};\n  \\node[below=of img2, node distance=0cm, yshift=1cm] {$\\gamma_{\\rm ML}=\\frac{10}{4}$};\n  \\node[right=of img2, node distance=0cm, yshift=-1cm] (img3)  {\\includegraphics[scale=0.65]{example-image}};\n  \\node[below=of img3, node distance=0cm, yshift=1cm] {$\\gamma_{\\rm ML}=\\frac{10}{6}$};\n  \\node[right=of img3, node distance=0cm, yshift=-1cm] (img4)  {\\includegraphics[scale=0.65]{example-image}};\n  \\node[below=of img4, node distance=0cm, yshift=1cm] {$\\gamma_{\\rm ML}=\\frac{10}{8}$};\n  \\node[right=of img4, node distance=0cm, yshift=-1cm] (img5)  {\\includegraphics[scale=0.65]{example-image}};\n  \\node[below=of img5, node distance=0cm, yshift=1cm] {$\\gamma_{\\rm ML}=\\frac{10}{10}$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 512,
        "tikz_code": "\\documentclass[journal]{IEEEtran}\n\\usepackage[cmex10]{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage{tikz,pgfplots}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{arrows}\n\\pgfplotsset{compat=newest}\n\\usepgfplotslibrary{fillbetween}\n\\usetikzlibrary{patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n      \\begin{axis}[\n          xlabel={DL Transmit power [dB]},\n          ylabel={Average achievable sum rate [bit/s]},\n          grid=both,\n          ylabel near ticks,\n          xmin=0,\n          xmax=40,\n          ymin=-20,\n          ymax=120,\n          legend style={legend pos=north west,font=\\small,fill=white,align=left},\n          axis background/.style={fill=white},\n      ]\n      \\addplot[color=red,mark=o,thick] coordinates {\n      (0,  -1.437046)\n      (1.341153, -1.707576)\n      (2.914478, -2.053975)\n      (5.128205, -2.374202)\n      (8.319677, -2.667239)\n      (12.952262, -3.027051)\n      (19.618938, -3.404431)\n      (30.164782, -3.906626)\n      (44.868408, -4.568283)\n      };\n      \\addlegendentry{ZF generic-iced}\n      \\addplot[color=blue,mark=square,thick] coordinates {\n      (0,  -2.415825)\n      (1.341153, -3.140944)\n      (2.914478, -3.662627)\n      (5.128205, -4.021739)\n      (8.319677, -4.273680)\n      (12.952262, -4.510242)\n      (19.618938, -4.789798)\n      (30.164782, -5.099336)\n      (44.868408, -5.414871)\n      };\n      \\addlegendentry{ZF generic-icied LMSE}\n      \\addplot[color=red,mark=o,thick,dashed] coordinates {\n      (0,  -0.993080)\n      (1.341153, -1.088197)\n      (2.914478, -1.185799)\n      (5.128205, -1.279478)\n      (8.319677, -1.367565)\n      (12.952262, -1.451108)\n      (19.618938, -1.532307)\n      (30.164782, -1.613240)\n      (44.868408, -1.696697)\n      };\n      \\addlegendentry{ZF generic-icied LMSE}\n      \\addplot[color=blue,mark=square,thick,dashed] coordinates {\n      (0,  -2.266753)\n      (1.341153, -2.369762)\n      (2.914478, -2.467042)\n      (5.128205, -2.560518)\n      (8.319677, -2.651199)\n      (12.952262, -2.740480)\n      (19.618938, -2.831245)\n      (30.164782, -2.927023)\n      (44.868408, -3.029821)\n      };\n      \\addlegendentry{MF generic-icied LMSE}\n      \\end{axis}\n      \\end{tikzpicture}\n\n\\end{document}"
    },
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        "index": 513,
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        "index": 516,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\newcommand{\\Sp}{\\operatorname{Sp}}\n\n\\newcommand{\\W}{\\operatorname{W}}\n\n\\newcommand{\\SU}{\\operatorname{SU}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\tikzstyle{every node}=[rectangle]\n\\node (A2) at (0,2) {\\fbox{$A_2$} $:$};\n\\node (suf) at (0,1) {$\\Sp(4) \\times \\Sp(4)$};\n\\node (sufa) at (0,0) {$\\Sp(4) \\times \\Sp(4)$};\n\\node (sufb) at (0,-1) {$\\Sp(2) \\times \\Sp(2)$};\n\\node (sufc) at (0,-2) {$\\Sp(3) \\times \\Sp(3)$};\n\\node (fsu) at (0,-3) {$\\W(\\SU(4), \\rho) \\times \\SU(4)$};\n\\node (fsua) at (0,-4) {$\\SU(4) \\times \\SU(4)$};\n\\node (fsub) at (0,-5) {$\\SU(4) \\times \\SU(4)$};\n\\node (as) at (0,-6) {$\\W$};\n\\node (S2) at (1.5,2) {\\fbox{$\\Lambda_2$} $:$};\n\\node (suf) at (1.5,1) {$\\Sp(4) \\times \\Sp(4)$};\n\\node (sufa) at (1.5,0) {$\\Sp(4) \\times \\Sp(4)$};\n\\node (sufb) at (1.5,-1) {$\\Sp(2) \\times \\Sp(2)$};\n\\node (fsu) at (1.5,-2) {$\\SU(4) \\times \\SU(4)$};\n\\node (fsua) at (1.5,-3) {$\\SU(4) \\times \\SU(4)$};\n\\node (fsub) at (1.5,-4) {$\\SU(4) \\times \\SU(4)$};\n\\node (as) at (1.5,-5) {$\\SU(4) \\times \\SU(4)$};\n\\node (fsu) at (1.5,-6) {$\\W$};\n\\node (sufc) at (4,2) {$\\Lambda_2 \\times \\Lambda_2$};\n\\node (sufb) at (4,0) {$\\Sp(4) \\times \\Sp(4)$};\n\\node (sufb) at (4,-1) {$\\Sp(2) \\times \\Sp(2)$};\n\\node (fsu) at (4,-2) {$\\SU(4) \\times \\SU(4)$};\n\\node (fsua) at (4,-3) {$\\SU(4) \\times \\SU(4)$};\n\\node (fsub) at (4,-4) {$\\SU(4) \\times \\SU(4)$};\n\\node (as) at (4,-5) {$\\SU(4) \\times \\SU(4)$};\n\\node (sufc) at (4,-6) {$\\W$};\n\\node (as) at (-2.5,2) {$\\Lambda_2$};\n\\node (as) at (-2.5,0) {$\\Lambda_2$};\n\\node (as) at (-2.5,-2) {$\\Lambda_2$};\n\\node (as) at (-2.5,-4) {$\\Lambda_2$};\n\\node (as) at (-2.5,-6) {$\\Lambda_2$};\n\\foreach \\from/\\to in {suf/sufa, sufa/sufb, sufb/sufc, sufc/fsu, fsu/fsua, fsua/fsub, fsub/fsu}\n\t\\draw[->] (\\from) -- (\\to);\n\\draw[dotted] (4,1.8) -- (4,0.2);\n\\draw[dotted] (4,-3.8) -- (4,-2.2);\n\\draw[dotted] (-3.7,2) -- (-2.2,2);\n\\draw[dotted] (-3.7,0) -- (-2.2,0);\n\\draw[dotted] (-3.7,-2) -- (-2.2,-2);\n\\draw[dotted] (-3.7,-4) -- (-2.2,-4);\n\\draw[dotted] (-3.7,-6) -- (-2.2,-6);\n\\draw[red] (sufc) -- (fsu);\n\\draw[red] (fsu) -- (fsua);\n\\draw[red] (fsua) -- (fsub);\n\\draw[red] (fsub) -- (sufc);\n\\draw[red, ->] (fsu) -- (sufc);\n\\draw[blue] (4.7,-1) -- (3.3,-1);\n\\draw[blue] (3.3,-1) -- (2.8,-2);\n\\draw[blue] (2.8,-2) -- (3.3,-3);\n\\draw[blue] (3.3,-3) -- (2.8,-4);\n\\draw[blue] (2.8,-4) -- (3.3,-5);\n\\draw[blue] (3.3,-5) -- (2.8,-6);\n\\draw[blue, ->] (3.3,-5) -- (3.3,-6);\n\\draw[blue] (3.3,-6) -- (4.7,-6);\n\\draw[blue] (4.7,-6) -- (4.2,-5);\n\\draw[blue] (4.2,-5) -- (4.7,-4);\n\\draw[blue] (4.7,-4) -- (4.2,-3);\n\\draw[blue] (4.2,-3) -- (4.7,-2);\n\\draw[blue] (4.7,-2) -- (4.2,-1);\n\\draw[blue] (4.2,-1) -- (4.7,1);\n\\draw[blue, ->] (4.7,-2) -- (4.7,-1);\n\\draw[red] (4.7,-1) -- (4.7,0);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 517,
        "tikz_code": "\\documentclass{article}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,arrows,calc,positioning,shadows,trees}\n\\tikzset{\n  basic/.style  = {draw, text width=2cm, drop shadow, font=\\sffamily, rectangle},\n  root/.style   = {basic, rounded corners=2pt, thin, align=center,\n                   fill=orange!60},\n  level 2/.style = {basic, rounded corners=6pt, thin,align=center, fill=green!50,\n                   text width=7em},\n  level 3/.style = {basic, thin, align=left, fill=orange!30, text width=9em}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}[node distance=1.2cm]\n    % Specify spacing for each level of the tree\n    \\tikzstyle{level 1}=[level distance=4.5cm, sibling distance=15mm]\n    \\tikzstyle{level 2}=[level distance=5.0cm,sibling distance=15mm]\n    \\tikzstyle{level 3}=[level distance=4.5cm,sibling distance=15mm]\n    \\node[root](THM){\\textbf{Theorem/model}}\n    child{node[level 2,right](Observations){\\textbf{Observations}}\n        child{node[level 3,left,align=center](hypothesis){hypothesis\\\\ testing}}\n        child{node[level 3,right,align=center](experiments){Experiments}}\n    }\n    child{node[level 2,left](Predictions){\\textbf{Predictions}}\n        child{node[level 3,right,align=center](inference){inference}}\n    };\n    \\draw[<->, >=latex', draw=red!50, thick] (THM.east) -- (Predictions.west);\n    \\draw[<->, >=latex', draw=OliveGreen!50, thick, dashed] (THM.east) -- (Observations.west);\n    \\draw[<->, >=latex', draw=OliveGreen!50, thick, dashed] (Predictions.east) -- (inference.west);\n    \\draw[<->, >=latex', draw=OliveGreen!50, thick, dashed] (Observations.east) -- (hypothesis.west);\n    \\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 518,
        "tikz_code": "\\documentclass[10pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[colorlinks=true, allcolors=blue]{hyperref}\n\\usepackage[colorinlistoftodos]{todonotes}\n\\usepackage{xcolor}\n\\usepackage{colortbl}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,graphs,graphs.standard}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.6]{thick}\n\\begin{scope}[every node/.style={circle,draw,minimum size=1pt,inner sep=2}]\n    \\node[label={above:$v_1$}] (v1) at (-3,2) {};\n    \\node[label={above:$v_2$}] (v2) at (3,2) {};\n    \\node[label={above:$v_3$}] (v3) at (-3,0) {};\n    \\node[label={above:$v_4$}] (v4) at (3,0) {};\n    \\node[label={below:$v_5$}] (v5) at (0,-2) {};\n    \n    \\node[label={above:$v_1$}] (v1') at (8,2) {};\n    \\node[label={above:$v_2$}] (v2') at (12,2) {};\n    \\node[label={above:$v_3$}] (v3') at (8,0) {};\n    \\node[label={above:$v_4$}] (v4') at (12,0) {};\n    \\node[label={below:$v_5$}] (v5') at (10,-2) {};\n    \n    \\node[label={above:$G$}] at (-1.5,-5) {};\n    \\node[label={above:$G$}] at (5.5,-5) {};\n    \\node[label={above:$G$}] at (11.5,-5) {};\n\\end{scope}\n\n\\begin{scope}[every edge/.style={draw=black}]\n    \\path (v1) edge (v3);\n    \\path (v2) edge (v4);\n    \\path (v3) edge (v4);\n    \\path (v5) edge (v1);\n    \\path (v5) edge (v2);\n    \\path (v5) edge (v3);\n    \\path (v5) edge (v4);\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 519,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{calc, arrows, decorations.markings, decorations.pathmorphing, positioning, decorations.pathreplacing,\nknots \n}\n\n\\newcommand{\\x}{{\\bf x}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale = 1]\n\\coordinate (e1) at (0,0);\n\\coordinate (e2) at (0,-2);\n\\coordinate (v1) at (0,1);\n\\coordinate (v2) at (2,0);\n\\coordinate (v3) at (1.5,-2);\n\\coordinate (v4) at (-1.5,-2);\n\\coordinate (v5) at (-2,0);\n\\coordinate (v6) at (-1.5,1);\n\n\\begin{scope}[decoration={markings, mark=at position 0.5 with {\\arrow{>}}}]\n\\draw[postaction={decorate}] (e1) -- (v1) node[midway, above] {$l_1$};\n\\draw[postaction={decorate}] (e1) -- (e2) node[midway, right] {$P_3$};\n\\draw[postaction={decorate}] (e2) -- (v3) node[midway, below right] {$P_2$};\n\\draw[postaction={decorate}] (e2) -- (v4) node[midway, left] {$P_1$};\n\\draw[postaction={decorate}] (e1) -- (v2) node[midway, right] {$P_4$};\n\\draw[postaction={decorate}] (e1) -- (v5) node[midway, right] {$l_4$};\n\\draw[postaction={decorate}] (e2) -- (v6) node[midway, left] {$l_3$};\n\\draw[postaction={decorate}] (e1) -- (v4) node[midway, below] {$H$};\n\\draw[postaction={decorate}] (e2) -- (v6) node[midway, below] {};\n\\draw[postaction={decorate}] (e1) -- (v3) node[midway, below] {};\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 520,
        "tikz_code": "\\documentclass[10pt,twocolumn,letterpaper]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing,fit,calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\t\\node[inner sep=0pt] (russell) at (0,0)\n\t\t\t{\\includegraphics[width=0.95\\textwidth]{example-image}};\n\t\t\t\\draw[dashed,color=blue] (0,-1.7) -- (0,-2.5);\n\t\t\t\\node[rotate=90,color=blue] at (-6,-2.5) {\\footnotesize Enhanced target};\n\t\t\t\\draw[dashed,color=blue] (0,1.7) -- (0,2.5);\n\t\t\t\\node[rotate=90,color=blue] at (6,2.5) {\\footnotesize Ray-traced target};\n\t\t\t\\node[rotate=90] at (-6,2.5) {\\footnotesize Enhanced size (I)};\n\t\t\t\\draw[dashed,color=blue] (-0.1,0.8) -- (-1.9,0.8);\n\t\t\t\\node[rotate=0] at (-1.7,0.8) {\\footnotesize (shared across emitcers)};\n\t\t\t\\draw[dashed,color=blue] (-0.1,-0.8) -- (-1.9,-0.8);\n\t\t\t\\node[rotate=0] at (-1.7,-0.8) {\\footnotesize (shared across emitcers)};\n\t\t\t\\draw[dashed,color=blue] (0.1,0.8) -- (1.9,0.8);\n\t\t\t\\node[rotate=0] at (1.7,0.8) {\\footnotesize (shared across emitcers)};\n\t\t\t\\draw[dashed,color=blue] (0.1,-0.8) -- (1.9,-0.8);\n\t\t\t\\node[rotate=0] at (1.7,-0.8) {\\footnotesize (shared across emitcers)};\n\t\t\t\\node[rotate=-90] at (0,0) {\\footnotesize $z_j$};\n\t\t\t\\node[rotate=-90] at (0,1.8) {\\footnotesize $z_i$};\n\t\t\t\\draw[dashed,color=blue] (-2.8,0) -- (-3.6,0);\n\t\t\t\\node[color=blue] at (-3.7,0.5) {\\footnotesize $c_{e,i+1}$};\n\t\t\t\\draw[dashed,color=blue] (2.8,0) -- (3.6,0);\n\t\t\t\\node[color=blue] at (3.7,0.5) {\\footnotesize $c_{e,i+0}$};\n\t\t\t\\node[color=blue] at (-3.7,-0.5) {\\footnotesize $c_{e,i+0}$};\n\t\t\t\\node[color=blue] at (3.7,-0.5) {\\footnotesize $c_{e,i+1}$};\n\t\t\t\\node[rotate=-90] at (0,-2.5) {\\footnotesize $z_j+0$};\n\t\t\t\\node[rotate=-90] at (0,2.5) {\\footnotesize $z_i$};\n\t\t\t\\node at (0,3.1) {\\footnotesize \\textcolor{blue}{Buffer (\\textcolor{red}{$c_{e,i+1}$}) + Other buffers}};\n\t\t\t\\end{tikzpicture}\n\n\\end{document}"
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        "index": 521,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amsthm,tikz,float,amssymb}\n\\usepackage[colorlinks=true,breaklinks=true,bookmarks=true,urlcolor=blue,citecolor=blue,linkcolor=blue,bookmarksopen=false,draft=false]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\coordinate[label=below:$1$] (1) at (0,0);\n\\coordinate[label=above:$0$] (0) at (0,2);\n\\coordinate[label=above:$-1$] (-1) at (-2,2);\n\\coordinate[label=below:$-1$] (-2) at (-2,0);\n\n\\coordinate[label=above:$1$] (1a) at (4,2);\n\\coordinate[label=above:$1$] (1b) at (6,2);\n\\coordinate[label=below:$0$] (0a) at (4,0);\n\\coordinate[label=below:$0$] (0b) at (6,0);\n\n\\draw[fill=black] (0) circle [radius=0.1];\n\\draw[fill=black] (0a) circle [radius=0.1];\n\\draw[fill=black] (0b) circle [radius=0.1];\n\\draw[fill=black] (1) circle [radius=0.1];\n\\draw[fill=black] (1a) circle [radius=0.1];\n\\draw[fill=black] (1b) circle [radius=0.1];\n\\draw[fill=black] (-1) circle [radius=0.1];\n\\draw[fill=black] (-2) circle [radius=0.1];\n\n\\draw (0) -- (1) -- (-1) -- (-2) -- (0);\n\\draw (0a) -- (1a) -- (1b) -- (0b) -- (0a);\n\n\\draw[->] (-1) -- (-1.5,2);\n\\draw[->] (0) -- (0,1.5);\n\\draw[->] (1) -- (1.5,1);\n\\draw[->] (-2) -- (-2,1.5);\n\n\\draw[->] (1a) -- (1.5,0.5);\n\\draw[->] (0a) -- (0.5,0.5);\n\\draw[->] (1b) -- (0.5,2.5);\n\\draw[->] (-2) -- (-1.5,0.5);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 522,
        "tikz_code": "\\documentclass[10pt]{article}\n\\usepackage{amsmath,amssymb}\n\\usepackage{tikz,float}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.7]\n  \\draw (0,0) grid (4,4);\n  \\draw[dashed] (0,1)--(4,1);\n  \\draw[dashed] (0,2)--(4,2);\n  \\draw[dashed] (0,3)--(4,3);\n  \\draw[dashed] (1,0)--(1,4);\n  \\draw[dashed] (2,0)--(2,4);\n  \\draw[dashed] (3,0)--(3,4);\n  \\draw[dashed] (0,3) rectangle (4,4);\n  \\draw[dashed] (0,1) rectangle (4,2);\n  \\node at (-.6,1) {$\\ell/2+r$};\n  \\node at (-.6,2) {$\\ell/2$};\n  \\node at (4.6,1) {$\\ell/2$};\n  \\node at (4.6,2) {$\\ell/2+r$};\n  \\draw[<->] (4.5,1) -- (4.5,2);\n  \\node at (5.2,1.5) {$\\ell/2$};\n  \\draw[<->] (1,-.5) -- (2,-.5);\n  \\node at (1.5,-1) {$-\\eta/2$};\n  \\draw[<->] (2,-.5) -- (3,-.5);\n  \\node at (2.5,-1) {$\\eta/2$};\n  \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 523,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{automata}\n\\usepackage{tikz-qtree}\n\\usetikzlibrary{arrows.meta}\n\\usetikzlibrary{positioning}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[transform shape]\n        \\tikzstyle{state}=[minimum size = 15pt, inner sep=0.5pt]\n        \\node[state](q0){$q_0$};\n        \\node[state](qb)[left= 40pt of q0]{$q_b$};\n        \\node[state, accepting](q1)[right= of q0]{$q_1$};\n        \\node[state](qb1)[left= of qb]{$q_b$};\n        \\node[state, accepting](q2)[right= of qb1]{$q_2$};\n        \\node[state](qb2)[right= of q2]{$q_b$};\n        \\node[state](qf)[right= of qb2]{$q_f$};\n        \\path[->]\n        (q0) edge node [above] {$a$} (qb)\n        (q0) edge node [above] {$b$} (q1)\n        (qb) edge[bend left=15] node [above] {$b\\neq 1$} (qb1)\n        (qb1) edge[bend left=15] node [below] {$b\\neq 1$} (qb)\n        (qb1) edge[bend left=15] node [below] {$b = 1$} (qb2)\n        (qb2) edge[bend left=15] node [above] {$b\\neq 1$} (qb1)\n        (qb2) edge[bend left=15] node [above] {$b = 1$} (qb)\n        (qb) edge[bend right=15] node [below] {$c$} (q2)\n        (q2) edge[bend right=15] node [above] {$d\\neq 1 \\times 3$} (qb2)\n        (qb2) edge[bend right=15] node [above] {$d\\neq 1 \\times 3$} (q2)\n        (q2) edge[bend right=15] node [below] {$d = 1 \\times 3$} (qf)\n        ;\n    \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 524,
        "tikz_code": "\\documentclass[a4paper,11pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n\\draw[thick,->] (0,0) -- (0,7) node[anchor=north east] {Volume (MW)};\n\\draw[thick,->] (0,0) -- (10,0) node[anchor=north west] {Time of given product (h)};\n\\draw[thick] (0,1) -- (10,1);\n\\draw[thick] (0,1.5) -- (10,1.5);\n\\draw[thick] (0,2) -- (10,2);\n\\draw[thick] (0,3) -- (10,3);\n\\draw[thick] (0,3.5) -- (10,3.5);\n\\draw[thick] (0,4) -- (10,4);\n\\draw[thick] (0,4.5) -- (10,4.5);\n\\draw[thick] (0,5) -- (10,5);\n\\draw[thick] (0,5.5) -- (10,5.5);\n\\draw[thick] (0,6) -- (10,6);\n\\draw[red,thick] (0,1.5) -- (4.33,1.5);\n\\draw[red,thick] (4.33,1.5) -- (10,1.5);\n\\draw (0,0) node[anchor=north east] {0};\n\\draw (10,0) node[anchor=north west] {4};\n\\draw (5,0) node[anchor=north] {2};\n\\draw (0,1) node[anchor=east] {0};\n\\draw (0,1.5) node[anchor=east] {1};\n\\draw (0,2) node[anchor=east] {2};\n\\draw[dotted,thick] (0,1.875) -- (10,1.875);\n\\draw[dotted,thick] (0,3.375) -- (10,3.375);\n\\draw[dotted,thick] (0,4.875) -- (10,4.875);\n\\draw[dotted,thick] (0,6.375) -- (10,6.375);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 525,
        "tikz_code": "\\documentclass[a4paper,12pt,pdftex]{article}\n\\usepackage{amssymb,amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows.meta}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\node[draw,circle,fill,inner sep=1pt] (L1) at (-2,0) [label=below:$\\pi^2$] {};\n    \\node[draw,circle,fill,inner sep=1pt] (L2) at (2,0) [label=below:$\\pi\\pi$] {};\n    \\node[draw,circle,fill,inner sep=1pt] (L3) at (0,-1) [label=below:$\\pi$] {};\n    \\node[draw,circle,fill,inner sep=1pt] (L4) at (5,-2) [label=below:$C_{\\pi\\infty}$] {};\n    \\node[draw,circle,fill,inner sep=1pt] (L5) at (-4,-2) [label=below:$C_{\\pi^2}$] {};\n    \\node[draw,circle,fill,inner sep=1pt] (L6) at (-2,2) [label=above:$C_{\\pi^2}$] {};\n    \\node[draw,circle,fill,inner sep=1pt] (L7) at (3,2) [label=above:$C_{\\pi^1}$] {};\n    %\n    \\draw[decoration={markings, mark=at position 0.5 with {\\arrow{Latex}}},postaction={decorate}] (L1) to (L2);\n    \\draw[decoration={markings, mark=at position 0.5 with {\\arrow{Latex}}},postaction={decorate}] (L1) to (L3);\n    \\draw[decoration={markings, mark=at position 0.5 with {\\arrow{Latex}}},postaction={decorate}] (L2) to (L3);\n    %\n    \\draw[decoration={markings, mark=at position 0.5 with {\\arrow{Latex}}},postaction={decorate}] (L5) to (L3);\n    %\n    \\draw[decoration={markings, mark=at position 0.5 with {\\arrow{Latex}}},postaction={decorate}] (L6) to (L1);\n    %\n    \\draw[decoration={markings, mark=at position 0.5 with {\\arrow{Latex}}},postaction={decorate}] (L7) to (L2);\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %\n    %"
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    {
        "index": 526,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usepackage{amsthm,amsfonts,amsmath,amscd,amssymb}\n\\usepackage{xcolor,float}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8]\n    \\draw [lime, line width = 8] (0,2) -- (2,4);\n    \\draw [lime, line width = 8] (0,2) -- (2,0);\n    \\draw [orange, line width = 8] (2,4) -- (4,6);\n    \\draw [orange, line width = 8] (2,0) -- (4,2);\n    \\draw [teal, line width = 8] (0,2) -- (2,4);\n    \\draw [teal, line width = 8] (2,4) -- (4,6);\n    \\draw [red, line width = 8] (0,2) -- (2,0);\n    \\draw [red, line width = 8] (2,0) -- (4,2);\n    \\draw [violet, line width = 8] (2,0) -- (2,4);\n    \\draw [violet, line width = 8] (2,4) -- (0,6);\n    \\draw [violet, line width = 8] (2,4) -- (4,2);\n    \\draw [violet, line width = 8] (4,2) -- (6,4);\n    \\draw [violet, line width = 8] (4,2) -- (6,0);\n    \\draw [blue, line width = 8] (4,2) -- (4,6);\n    \\draw [blue, line width = 8] (4,6) -- (2,8);\n    \\draw [blue, line width = 8] (4,6) -- (6,8);\n    \\draw [blue, line width = 8] (2,0) -- (2,-2);\n    \\draw [blue, line width = 8] (2,0) -- (4,-2);\n    \\draw [blue, line width = 8] (4,2) -- (4,-2);\n    \\draw [blue, line width = 8] (4,2) -- (6,-2);\n    \\draw [blue, line width = 8] (2,4) -- (2,8);\n    \\draw [blue, line width = 8] (2,4) -- (4,6);\n    \\draw [blue, line width = 8] (2,4) -- (0,6);\n    \\draw [blue, line width = 8] (2,4) -- (4,6);\n    \\draw [blue, line width = 8] (4,2) -- (4,6);\n    \\draw [blue, line width = 8] (4,6) -- (6,8);\n    \\draw [blue, line width = 8] (4,6) -- (8,6);\n    \\draw [blue, line width = 8] (2,0) -- (2,-2);\n    \\draw [blue, line width = 8] (2,0) -- (4,-2);\n    \\draw [blue, line width = 8] (4,2) -- (4,-2);\n    \\draw [blue, line width = 8] (4,2) -- (6,-2);\n    \\draw [blue, line width = 8] (4,2) -- (4,6);\n    \\draw [blue, line width = 8] (2,4) -- (2,8);\n    \\draw [blue, line width = 8] (2,4) -- (4,6);\n    \\draw [blue, line width = 8] (2,4) -- (0,6);\n    \\draw [blue, line width = 8] (2,4) -- (4,6);\n    \\draw [blue, line width = 8] (4,2) -- (4,6);\n    \\draw [blue, line width = 8] (4,6) -- (6,8);\n    \\draw [blue, line width = 8] (4,6) -- (8,6);\n    \\draw [blue, line width = 8] (2,0) -- (2,-2);\n    \\draw [blue, line width = 8] (2,0) -- (4,-2);\n    \\draw [blue, line width = 8] (4,2) -- (4,-2);\n    \\draw [blue, line width = 8] (4,2) -- (6,-2);\n    \\draw [blue, line width = 8] (2,4) -- (2,8);\n    \\draw [blue, line width = 8] (2,4) -- (4,6);\n    \\draw [blue, line width = 8] (2,4) -- (0,6);\n    \\draw [blue, line width = 8] (2,4) -- (4,6);\n    \\draw [blue, line width = 8] (4,2) -- (4,6);\n    \\draw [blue, line width = 8] (4,6) -- (6,8);\n    \\draw [blue, line width = 8] (4,6) -- (8,6);\n    \\draw [blue, line width = 8] (2,0) -- (2,-2);\n    \\draw [blue, line width = 8] (2,0) -- (4,-2);\n    \\draw [blue, line width = 8] (4,2) -- (4,-2);\n    \\draw [blue, line width = 8] (4,2) -- (6,-2);\n    \\draw [blue, line width = 8] (2,4) -- (2,8);\n    \\draw [blue, line width = 8] (2,4) -- (4,6);\n    \\draw [blue, line width = 8] (2,4) -- (0,6);\n    \\draw [blue, line width = 8] (2,4) -- (4,6);\n    \\draw [blue, line width = 8] (4,2) -- (4,6);\n    \\draw [blue, line width = 8] (4,6) -- (6,8);\n    \\draw [blue, line width = 8] (4,6) -- (8,6);\n    \\draw [blue, line width = 8] (2,0) -- (2,-2);\n    \\draw [blue, line width = 8] (2,0) -- (4,-2);\n    \\draw [blue, line width = 8] (4,2) -- (4,-2);\n    \\draw [blue, line width = 8] (4,2) -- (6,-2);\n    \\draw [blue, line width = 8] (2,4) -- (2,8);\n    \\draw [blue, line width = 8] (2,4) -- (4,6);\n    \\draw [blue, line width = 8] (2,4) -- (0,6);\n    \\draw [blue, line"
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    {
        "index": 527,
        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage[latin1,utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{latexsym,amsfonts,amssymb,amsmath,amsthm,mathrsfs, mathtools}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.9]\n\\def\\size{1}\n\\node (A1) at (0,0) {$\\color{white}a_1$};\n\\node (A2) at (2,0) {$\\color{white}a_2$};\n\\node (A3) at (4,0) {$\\color{white}a_3$};\n\\node (A4) at (6,0) {$\\color{white}a_4$};\n\\node (A5) at (8,0) {$\\color{white}a_5$};\n\\node (A6) at (10,0) {$\\color{white}a_6$};\n\\node (A7) at (12,0) {$\\color{white}a_7$};\n\n\\node (B1) at (0,-2) {$b_1$};\n\\node (B2) at (2,-2) {$b_2$};\n\\node (B3) at (4,-2) {$b_3$};\n\\node (B4) at (6,-2) {$b_4$};\n\\node (B5) at (8,-2) {$b_5$};\n\\node (B6) at (10,-2) {$b_6$};\n\\node (B7) at (12,-2) {$b_7$};\n\n\\node (C1) at (0,-4) {$c_1$};\n\\node (C2) at (2,-4) {$c_2$};\n\\node (C3) at (4,-4) {$c_3$};\n\\node (C4) at (6,-4) {$c_4$};\n\\node (C5) at (8,-4) {$c_5\\otimes c_2\\otimes c_2=c_6$};\n\\node (C6) at (10,-4) {$c_6\\otimes c_2\\otimes c_2=c_7$};\n\\node (C7) at (12,-4) {$c_7$};\n\n\\node (D1) at (0,-6) {$\\color{white}d_1$};\n\\node (D2) at (2,-6) {$\\color{white}d_2$};\n\\node (D3) at (4,-6) {$\\color{white}d_3$};\n\\node (D4) at (6,-6) {$\\color{white}d_4$};\n\\node (D5) at (8,-6) {$\\color{white}d_5$};\n\\node (D6) at (10,-6) {$\\color{white}d_6$};\n\\node (D7) at (12,-6) {$\\color{white}d_7$};\n\n\\node (E1) at (0,-8) {$e_1$};\n\\node (E2) at (2,-8) {$e_2$};\n\\node (E3) at (4,-8) {$e_3$};\n\\node (E4) at (6,-8) {$e_4$};\n\\node (E5) at (8,-8) {$e_5\\otimes e_3\\otimes e_3=e_6$};\n\\node (E6) at (10,-8) {$e_6\\otimes e_3\\otimes e_3=e_7$};\n\\node (E7) at (12,-8) {$e_7$};\n\n\\node (F1) at (0,-10) {$f_1$};\n\\node (F2) at (2,-10) {$f_2$};\n\\node (F3) at (4,-10) {$f_3$};\n\\node (F4) at (6,-10) {$f_4$};\n\\node (F5) at (8,-10) {$f_5\\otimes f_2\\otimes f_2=f_6$};\n\\node (F6) at (10,-10) {$f_6\\otimes f_2\\otimes f_2=f_7$};\n\\node (F7) at (12,-10) {$f_7$};\n\n\\node (G1) at (0,-12) {$\\color{white}g_1$};\n\\node (G2) at (2,-12) {$\\color{white}g_2$};\n\\node (G3) at (4,-12) {$\\color{white}g_3$};\n\\node (G4) at (6,-12) {$\\color{white}g_4$};\n\\node (G5) at (8,-12) {$\\color{white}g_5$};\n\\node (G6) at (10,-12) {$\\color{white}g_6$};\n\\node (G7) at (12,-12) {$\\color{white}g_7$};\n\n\\node (H1) at (0,-14) {$h_1$};\n\\node (H2) at (2,-14) {$h_2$};\n\\node (H3) at (4,-14) {$h_3$};\n\\node (H4) at (6,-14) {$h_4$};\n\\node (H5) at (8,-14) {$h_5\\otimes h_3\\otimes h_3=h_6$};\n\\node (H6) at (10,-14) {$h_6\\otimes h_3\\otimes h_3=h_7$};\n\\node (H7) at (12,-14) {$h_7$};\n\n\\node [draw,circle,minimum width = 0.65cm, fill=yellow] (C1s) at (0,-1) {};\n\\node [draw,circle,minimum width = 0.65cm, fill=yellow] (C2s) at (2,-1) {};\n\\node [draw,circle,minimum width = 0.65cm, fill=yellow] (C3s) at (4,-1) {};\n\\node [draw,circle,minimum width = 0.65cm, fill=yellow] (C4s) at (6,-1) {};\n\\node [draw,circle,minimum width = 0.65cm, fill=yellow] (C5s) at (8,-1) {};\n\\node [draw,circle,minimum width = 0.65cm, fill=yellow]"
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        "index": 528,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amscd, amssymb, pgf, tikz, hyperref, mathabx}\n\n\\begin{document}\n\n\\begin{tikzpicture}[shorten >=0.4pt,>=stealth, semithick]\n\\draw (-1,-2.5)--(-7,-2.5);\n\\draw (-7,0.5)--(-1,0.5);\n\\draw (-7,-3)--(2.5,-3);\n\\draw (2.5,2.5)--(-1,2.5);\n\\draw (-7,-2.5)..controls (-4,-2.5) and (-3.5,-1)..(-3.5,0);\n\\draw (-7,-2.5)..controls (-4,-2.5) and (-3.5,-4)..(-3.5,-3);\n\\draw (-1,0.5)..controls (-3,0.5) and (-3.5,-1)..(-3.5,0);\n\\draw (-1,0.5)..controls (-3,0.5) and (-3.5,-4)..(-3.5,-3);\n\\draw (-3.5,0)--(-3.5,-3);\n\\draw (-3.5,0)..controls (-2.5,0) and (-2.5,1)..(-3,1);\n\\draw (-3.5,-3)..controls (-2.5,-3) and (-2.5,-2)..(-3,-2);\n\\draw (-3,-2)--(-3,1);\n\\draw (2.5,-3)..controls (5,-3) and (5.5,0)..(5.5,1);\n\\draw (2.5,2.5)..controls (5,2.5) and (5.5,0)..(5.5,1);\n\\draw (5.5,1)--(5.5,-2.5);\n\\draw (2.5,-3)--(5.5,-3);\n\\draw (5.5,-2.5)--(5.5,-3);\n\\fill[color=white!50!gray] (-0.5,0) ellipse (0.7 and 0.3);\n\\draw (-0.5,0) ellipse (0.7 and 0.3);\n\\draw (-0.5,0) node{$K$};\n\\draw (3.2,0.5) node{$B(0,R)$};\n\\draw (-4.2,-1.5) node{$E^-$};\n\\draw (-4.2,1.5) node{$E^+$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[a4paper,12pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsfonts,amsthm,amssymb,mathrsfs,amsmath}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[-] (-7,0) -- (0,0) node[below] {$u_1$};\n\\draw[-] (0,0) -- (1.5,1) node[right] {$u_2$};\n\\draw[-] (0,0) -- (3,-1);\n\\draw[-] (-1,-1.5) -- (0,0);\n\\draw[-] (0,0) -- (1.5,-2) node[right] {$u_1\\!^\\ast\\!u_2'$};\n\\draw[-] (1.5,-2) -- (4,-1.5);\n\\draw[-] (1.5,-2) -- (3,-1);\n\\draw[-] (3,-1) -- (4.5,-1) node[below] {$u_1\\!^\\ast\\!u_2'$};\n\\draw[dashed] (-4.5,-1) -- (-2,-1.5);\n\\draw[dashed] (-2,-1.5) -- (-1,-1.5);\n\\draw[dashed] (-1,-1.5) -- (1,-3) node[below] {$u_1\\!^\\ast\\!u_2'$};\n\\draw[dashed] (1,-3) -- (2.5,-3.5);\n\\draw[dashed] (2.5,-3.5) -- (3,-1);\n\\draw[dashed] (3,-1) -- (7,-0.5);\n\\draw[dashed] (2,-2) -- (3,-1);\n\\draw[dashed] (3,-1) -- (4,-0.5);\n\\draw[dashed] (1.5,-2) -- (2.5,-1.5) node[below] {$u_1\\!^\\ast\\!u_2'$};\n\\draw[dashed] (2.5,-1.5) -- (4.5,-1);\n\\node at (-4.5,-0.5) {$\\mathcal{U}$};\n\\node at (-1,0.5) {$G_{u_1\\!,u_2}$};\n\\node at (1,0.5) {$G_{u_1\\!,J(u_2)}$};\n\\node at (4.5,0.5) {$G_{u_1\\!,J(u_2)}$};\n\\draw[dashed] (0,0) -- (-1,-1.5);\n\\draw[dashed] (-1,-1.5) -- (-2.5,-1);\n\\draw[dashed] (1.5,-2) -- (-0.5,-2.5);\n\\draw[dashed] (1.5,-2) -- (-2,-2.5);\n\\draw (-1.5,-0.5) -- (0.5,-0.5);\n\\draw (-1.5,-0.5) -- (-0.5,-2.5);\n\\draw (0.5,-0.5) -- (0.7,-1.5);\n\\draw (-0.5,-2.5) -- (1.3,-1.5);\n\\node at (0.5,-1) {$J_1$};\n\\node at (-0.5,-1) {$J_2$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{shapes.misc}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{shapes.misc}\n\\tikzset{cross/.style={cross out, draw=black, minimum size=2*(#1-\\pgflinewidth), inner sep=0pt, outer sep=0pt},\n%default radius will be 1pt. \ncross/.default={1pt}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=2,line width=1pt,black]\n\\draw (1,0) node[below]{$\\cdot$} node[above]{$\\cdot$} node[left]{$\\cdot$} node[right]{$\\cdot$};\n\\draw (2,0) node[below]{$\\cdot$} node[above]{$\\cdot$} node[left]{$\\cdot$} node[right]{$\\cdot$};\n\\draw (1.5,0.86) node[above]{$\\cdot$} node[below]{$\\cdot$} node[left]{$\\cdot$} node[right]{$\\cdot$};\n\\draw (1,0)--++(1,0);\n\\draw (1.5,0.86)--++(0.5,0.86);\n\\draw (2,0)--++(0.5,-0.86);\n\\draw (2.5,0.86)--++(0.5,-0.86);\n\\draw (1,0) node[left]{$245$};\n\\draw (1.5,0.86) node[right]{$345$};\n\\draw (2,0) node[right]{$456$};\n\\draw (2.5,0.86) node[right]{$567$};\n\\draw (1.5,0.86) node[below]{$678$};\n\\draw (2,0) node[above]{$567$};\n\\draw (2.5,0.86) node[above]{$456$};\n\\draw (1,0) node[above]{$678$};\n\\draw (1.5,-1) node{$(a)$};\n\n\\draw (3,0) node[below]{$\\cdot$} node[above]{$\\cdot$} node[left]{$\\cdot$} node[right]{$\\cdot$};\n\\draw (4,0) node[below]{$\\cdot$} node[above]{$\\cdot$} node[left]{$\\cdot$} node[right]{$\\cdot$};\n\\draw (3.5,0.86) node[above]{$\\cdot$} node[below]{$\\cdot$} node[left]{$\\cdot$} node[right]{$\\cdot$};\n\\draw (4.5,0.86) node[above]{$\\cdot$} node[below]{$\\cdot$} node[left]{$\\cdot$} node[right]{$\\cdot$};\n\\draw (3,0)--++(1,0);\n\\draw (3.5,0.86)--++(0.5,0.86);\n\\draw (4,0)--++(0.5,-0.86);\n\\draw (4.5,0.86)--++(0.5,-0.86);\n\\draw (3.5,0.86) node[left]{$901$};\n\\draw (4.5,0.86) node[right]{$901$};\n\\draw (3.5,0.86) node[below]{$901$};\n\\draw (4.5,0.86) node[above]{$901$};\n\\draw (3,0) node[above]{$901$};\n\\draw (4,0) node[above]{$901$};\n\\draw (3.5,0.86) node[right]{$643$};\n\\draw (4.5,0.86) node[left]{$643$};\n\\draw (3.5,0.86) node[below]{$643$};\n\\draw (4.5,0.86) node[above]{$643$};\n\\draw (3,0) node[below]{$643$};\n\\draw (4,0) node[below]{$643$};\n\\draw (3.5,-1) node{$(b)$};\n\n\\draw (5,0) node[below]{$\\cdot$} node[above]{$\\cdot$} node[left]{$\\cdot$} node[right]{$\\cdot$};\n\\draw (6,0) node[below]{$\\cdot$} node[above]{$\\cdot$} node[left]{$\\cdot$} node[right]{$\\cdot$};\n\\draw (5.5,0.86) node[above]{$\\cdot$} node[below]{$\\cdot$} node[left]{$\\cdot$} node[right]{$\\cdot$};\n\\draw (6.5,0.86) node[above]{$\\cdot$} node[below]{$\\cdot$} node[left]{$\\cdot$} node[right]{$\\cdot$};\n\\draw (5,0)--++(1,0);\n\\draw (5.5,0.86)--++(0.5,0.86);\n\\draw (6,0)--++(0.5,-0.86);\n\\draw (6.5,0.86)--++(0.5,-0.86);\n\\draw (5.5,0.86) node[left]{$857$};\n\\draw (6.5,0.86) node[right]{$857$};\n\\draw (5.5,0.86) node[below]{$857$};\n\\draw (6.5,0.86) node[above]{$857$};\n\\draw (5,0) node[above]{$857$};\n\\draw (6,0) node[above]{$857$};\n\\draw (5.5,0.86) node[right]{$956$};\n\\draw (6.5,0.86) node[left]{$956$};\n\\draw (5.5,0.86) node[below]{$956$};\n\\draw (6.5,0.86) node[above]{$956$};\n\\draw (5,0) node[below]{$956$};\n\\draw (6,0) node[below]{$956$};\n\\draw (5.5,-1) node"
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    {
        "index": 531,
        "tikz_code": "\\documentclass[aps,prb,amsmath,twocolumn,superscriptaddress]{revtex4-2}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\node[inner sep=0pt] (duck) at (0,0)\n    {\\includegraphics[width=0.32\\columnwidth]{example-image}};\n    \\node[align=center,fill=white] at (-2.6, 2.6) {\\textbf{(a)}};\n    \n    \\node[inner sep=0pt] (duck) at (2.4,0)\n    {\\includegraphics[width=0.23\\columnwidth]{example-image}};\n    \\node[align=center,fill=white] at (1.8, 2.6) {\\textbf{(b)}};\n    \n    \\node[inner sep=0pt] (duck) at (0.8,-2.4)\n    {\\includegraphics[width=0.32\\columnwidth]{example-image}};\n    \\node[align=center,fill=white] at (-0.5, -1.2) {\\textbf{(c)}};\n    \n    \\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 532,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows.meta,positioning,backgrounds}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \t\\definecolor{darkslategray38}{RGB}{38,38,38}\n    \t\\definecolor{lightgray204}{RGB}{204,204,204}\n    \t\\node[inner sep=0pt] (figure) at (0,0) {\\includegraphics[width=.9\\columnwidth]{example-image}};\n    \t\\node[inner sep=0pt] (figure_label) at (0.3\\columnwidth,0.3\\columnwidth) {\\includegraphics[width=.4\\columnwidth]{example-image}};\n    \t\\draw[-latex, line width=1.5pt, lightgray204] (0.37,0.27) -- (0.23,0.37);\n    \t\\draw[-latex, line width=1.5pt, lightgray204] (0.5,0.5) -- (0.4,0.4);\n    \t\\draw[-latex, line width=1.5pt, lightgray204] (-0.5,0.5) -- (-0.6,0.4);\n    \t\\draw[-latex, line width=1.5pt, darkslategray38] (0.35,0.65) -- (0.25,0.75);\n    \t\\node (label_1) at (-1.4,1.85) {\\footnotesize $B^{\\mathrm{i}}$};\n    \t\\node (label_2) at (-0.2,1.3) {\\footnotesize $\\bm{\\kappa}$};\n    \t\\node (label_3) at (-0.4,-0.8) {\\footnotesize $\\bm{\\mu}$};\n    \t\\node (label_4) at (-0.6,0.1) {\\footnotesize $\\bm{\\nu}$};\n    \t\\node (label_5) at (0.9,-1.4) {\\footnotesize $\\bm{\\rho}$};\n    \t\\node (label_6) at (-0.75,-0.35) {\\footnotesize $\\bm{\\epsilon}$};\n    \t\\node (label_7) at (-0.6,-0.6) {\\footnotesize $\\bm{\\sigma}$};\n    \t\\draw[line width=0.25mm, lightgray204] (label_6) to (label_7);\n    \t\\draw[line width=0.25mm, lightgray204] (label_1) to (label_2);\n    \t\\draw[line width=0.25mm, lightgray204] (label_3) to (label_4);\n    \t\\draw[line width=0.25mm, lightgray204] (label_5) to (label_6);\n    \t\\node (ball_1) at (-2,2.45) {\\includegraphics[width=0.1\\columnwidth]{example-image}};\n    \t\\node (ball_2) at (1,2.6) {\\includegraphics[width=0.1\\columnwidth]{example-image}};\n    \t\\draw[-latex, line width=1.5pt, lightgray204] (ball_1) to (ball_2);\n    \t\\node (ball_3) at (-2,0.55) {\\includegraphics[width=0.1\\columnwidth]{example-image}};\n    \t\\draw[-latex, line width=1.5pt, lightgray204] (ball_3) to (ball_2);\n    \t\\node (ball_4) at (-2,-2.3) {\\includegraphics[width=0.1\\columnwidth]{example-image}};\n    \t\\draw[-latex, line width=1.5pt, lightgray204] (ball_3) to (ball_4);\n    \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 533,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \n    \n    \\draw (1,0) -- (8,0);\n    \\draw (1,0) -- (1,3);\n    \\draw (8,0) -- (8,3);\n    \\draw (3,1) -- (3,3);\n    \\draw (3,1) -- (5,1);\n    \\draw (5,0) -- (5,3);\n    \\draw (6,1) -- (6,3);\n    \\node at (1,1.5) {$\\bullet$};\n    \\node at (8,1.5) {$\\bullet$};\n    \\node at (3,1.5) {$\\bullet$};\n    \\node at (5,1.5) {$\\bullet$};\n    \\node at (6,1.5) {$\\bullet$};\n    \\node at (3,2.5) {$\\bullet$};\n    \\node at (5,2.5) {$\\bullet$};\n    \\node at (6,2.5) {$\\bullet$};\n    \n    \\node at (5,1) [anchor=north] {$(c,0)$};\n    \\node at (6,1) [anchor=north] {$(c,0)$};\n    \\node at (1,1) [anchor=north] {$(a,0)$};\n    \\node at (8,1) [anchor=north] {$(b,0)$};\n    \\node at (3,1) [anchor=north] {$D$};\n    \\node at (3,0) [anchor=north] {$(0,0)$};\n    \\node at (6,0) [anchor=north] {$\\infty$};\n    \\node at (1,0) [anchor=north] {$\\infty$};\n    \\node at (3,2.5) [anchor=south] {$x$};\n    \\node at (5,2.5) [anchor=south] {$x+\\bar{b}$};\n    \\node at (6,2.5) [anchor=south] {$x+\\bar{c}$};\n    \\node at (2.7,1.5) [anchor=south] {$(a,t)$};\n    \\node at (5.3,1.5) [anchor=south] {$(b,t)$};\n    \\node at (4,2.5) [anchor=south] {$t$};\n    \n    \n    \\draw[very thick, black] (1,1.5) to[out=45,in=180] (2.5,2.5);\n    \\draw[very thick, black] (6,1.5) to[out=135,in=0] (4.5,2.5);\n    \\draw[very thick, black] (5,1.5) to[out=180,in=0] (2.5,1.5);\n    \\draw[very thick, black] (5,1.5) to[out=180,in=0] (4.5,1.5);\n    \\draw[very thick, black] (6,1.5) to[out=0,in=180] (7.5,1.5);\n    \\draw[very thick, black] (5,2.5) to[out=90,in=0] (3.5,3.5);\n    \\draw[very thick, black] (6,2.5) to[out=90,in=0] (5.5,3.5);\n    \n    \n    \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 534,
        "tikz_code": "\\documentclass[10pt]{article}\n\\usepackage{amsmath, amssymb, amsthm, amsfonts, amsxtra, color, graphicx, hyperref, mathtools, tikz, tikz-cd, url, soul}\n\n\\begin{document}\n\n\\begin{tikzpicture}[node distance = 1.5cm]\n\\node(13)[circle, draw, fill=black!50, inner sep=0pt, minimum width=1pt] at (0,0) {};\n\n\\node(b1)[circle, draw, fill=black!50, inner sep=0pt, minimum width=1pt] at (2,1.7) {};\n\\node(b2)[circle, draw, fill=black!50, inner sep=0pt, minimum width=1pt] at (3.5,0.7) {};\n\\node(b3)[circle, draw, fill=black!50, inner sep=0pt, minimum width=1pt] at (3.5,-0.7) {};\n\\node(b4)[circle, draw, fill=black!50, inner sep=0pt, minimum width=1pt] at (2,-1.7) {};\n\n\\node(c1)[circle, draw, fill=black!50, inner sep=0pt, minimum width=1pt] at (-1.5,0) {};\n\n\\draw(13)[bend right] to (b1);\n\\draw(13)[bend left] to (b2);\n\\draw(13)[bend right] to (b3);\n\\draw(13)[bend right] to (b4);\n\n\\draw(c1)[bend right] to (13);\n\n\\draw(0,0) circle (2cm);\n\n\\node(a)[above of = 13, yshift=-1.25cm,xshift=-2.5cm] {(a)};\n\n\\node(14)[circle, draw, fill=black!50, inner sep=0pt, minimum width=1pt] at (7,1.7) {};\n\\node(15)[circle, draw, fill=black!50, inner sep=0pt, minimum width=1pt] at (9,0.7) {};\n\\node(16)[circle, draw, fill=black!50, inner sep=0pt, minimum width=1pt] at (9,-0.7) {};\n\\node(17)[circle, draw, fill=black!50, inner sep=0pt, minimum width=1pt] at (7,-1.7) {};\n\n\n\\node(b2)[circle, draw, fill=black!50, inner sep=0pt, minimum width=1pt] at (7.5,0.5) {};\n\\node(b3)[circle, draw, fill=black!50, inner sep=0pt, minimum width=1pt] at (9.5,0) {};\n\n\\node(c1)[circle, draw, fill=black!50, inner sep=0pt, minimum width=1pt] at (4.5,0) {};\n\\node(c2)[circle, draw, fill=black!50, inner sep=0pt, minimum width=1pt] at (6.5,0) {};\n\n\\draw(14)[bend right] to (15);\n\\draw(14)[bend right] to (16);\n\\draw(14)[bend right] to (17);\n\\draw(15)[bend right] to (14);\n\n\n\\draw(c1)[bend left] to (14);\n\\draw(c2)[bend right] to (14);\n\n\n\\draw(6.5,0) circle (2cm);\n\n\n\\node(b)[above of = 14, yshift=-1.25cm,xshift=-2.5cm] {(b)};\n\n\\draw[thick, -latex] (2.25,0) -- (6.25,0);\n\\node[above of = 2.25, yshift=0cm,xshift=2.25cm] {{\\footnotesize Asymptotic boundary}};\n\\node[above of = 13, yshift=-0.25cm,xshift=0cm] {{\\footnotesize $I$}};\n\\node[above of = 14, yshift=-0.25cm,xshift=0cm] {{\\footnotesize $J$}};\n\n\n\\node[above of = b1, yshift=0cm,xshift=0cm] {{\\footnotesize $\\overline{W}(\\gamma, \\gamma')$}};\n\\node[above of = c1, yshift=-0.25cm,xshift=-0.5cm] {{\\footnotesize $\\overline{W}_I(\\gamma, \\gamma')$}};\n\\node[above of = c2, yshift=-0.25cm,xshift=0.5cm] {{\\footnotesize $\\overline{W}_J(\\gamma, \\gamma')$}};\n\n\\node[above of = b2, yshift=0cm,xshift=0cm] {{\\footnotesize $\\alpha_I$}};\n\\node[above of = b3, yshift=0cm,xshift=0cm] {{\\footnotesize $\\alpha_J$}};\n\n\n\n\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 535,
        "tikz_code": "\\documentclass[10pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath,amsthm,enumerate}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage[color=green!30]{todonotes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[join=bevel,inner sep=0.7mm,line width=0.8pt, scale=0.8]\n\n\\path (0,0) node (w1) {};\n\\path (5,1) node (w2) {};\n\\path (7,3) node (w3) {};\n\\path (9,5) node (w4) {};\n\\path (12,6) node (w5) {};\n\\path (0,3) node (b1) {};\n\\path (3,0) node (b2) {};\n\\path (5,3) node (b3) {};\n\\path (7,6) node (b4) {};\n\\path (9,8) node (b5) {};\n\\path (12,9) node (b6) {};\n\\draw[line width=1.2pt] (w1.center)--(b1.center);\n\\draw[line width=1.2pt] (w2.center)--(b2.center);\n\\draw[line width=1.2pt] (w3.center)--(b3.center);\n\\draw[line width=1.2pt] (w4.center)--(b4.center);\n\\draw[line width=1.2pt] (w5.center)--(b5.center);\n\\draw[cyan,line width=1.3pt] (b1.center)--(b6.center);\n\n\\draw[->] (w1) -- (b3);\n\\draw[->] (w2) -- (b1);\n\\draw[->] (w3) -- (b2);\n\\draw[->] (w4) -- (b4);\n\\draw[->] (w5) -- (b5);\n\n\\path (0.7,4) node (c1) {$c_1$};\n\\path (2.5,4) node (c2) {$c_2$};\n\\path (3.6,2) node (c3) {$c_3$};\n\\path (6,5) node (c4) {$c_4$};\n\\path (7.3,8) node (c5) {$c_5$};\n\\path (10,8) node (c6) {$c_6$};\n\n\\path (w1)+(0.4,-1.4) node (L) {$E_1$};\n\\path (w2)+(0.4,-1.4) node (L) {$E_2$};\n\\path (w3)+(0.5,-1.4) node (L) {$E_3$};\n\\path (w4)+(1.4,-1.4) node (L) {$E_4$};\n\\path (w5)+(1,-1.4) node (L) {$E_5$};\n\n\\path (4,7) node (F1) {$F_1(e_1)$};\n\\path (5,6) node (F2) {$F_2(e_2)$};\n\\path (7,9) node (F3) {$F_3(e_3)$};\n\\path (9,12) node (F4) {$F_4(e_4)$};\n\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 536,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amsmath,amssymb,amsfonts,amsthm}\n\\usepackage{tikz}\n\\usepackage[colorlinks=true, linkcolor=blue]{hyperref}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[ultra thick] (1,0) -- (4,0);\n\\draw (-1,0) -- (6,0);\n\\draw (1,0) -- (1,3);\n\\draw[ultra thick] (1,0) -- (1,-1);\n\\draw[ultra thick] (1,3) -- (1,3.5);\n\\draw[ultra thick] (1,-1) -- (1,-1.5);\n\\draw[ultra thick, dashed] (1,0.5) to [out=0,in=180] (2,2);\n\\draw[ultra thick, dashed] (2,2) to [out=0,in=180] (3,3.5);\n\\draw[ultra thick, dashed] (3,3.5) to [out=0,in=180] (4,3.5);\n\\draw[ultra thick, dotted] (1.3,0.5) -- (1.3,3.5);\n\\draw[ultra thick, dotted] (2.3,0.5) -- (2.3,3.5);\n\\draw[ultra thick, dotted] (3.3,0.5) -- (3.3,3.5);\n\\draw[ultra thick, dotted] (4.3,0.5) -- (4.3,3.5);\n\\draw (6,-0.5) node {$x$};\n\\draw (0,0) node {$t=0$};\n\\draw (1.5,0) node {$x=1$};\n\\draw (-1,1) node {$\\mu$};\n\\draw (-1,2) node {$\\mu'$};\n\\draw (1,-1.5) node {$x=0$};\n\\draw (3,-1.5) node {$s$};\n\\draw (2.5,0) node {$0$};\n\\draw (5,0) node {$t$};\n\\draw (4.5,0) node {$1$};\n\\draw[thick, ->] (4.5,0) -- (5,0);\n\\draw[thick, ->] (5,0) -- (5.5,0);\n\\draw[thick, ->] (1,0) -- (1,0.5);\n\\draw[thick, ->] (1,0.5) -- (1,1);\n\\draw[thick, ->] (1,1) -- (1,1.5);\n\\draw[thick, ->] (1,1.5) -- (1,2);\n\\draw[thick, ->] (1,2) -- (1,2.5);\n\\draw[thick, ->] (1,2.5) -- (1,3);\n\\draw[thick, ->] (1,3) -- (1.5,3);\n\\draw[thick, ->] (1.5,3) -- (2,3);\n\\draw[thick, ->] (2,3) -- (2.5,3);\n\\draw[thick, ->] (2.5,3) -- (3,3);\n\\draw[thick, ->] (3,3) -- (3.5,3);\n\\draw[thick, ->] (3.5,3) -- (4,3);\n\\draw[thick, ->] (4,3) -- (4.5,3);\n\\draw (6,2.5) node {$f_s$};\n\\draw (6,1.5) node {$t=s$};\n\\draw[thick, ->] (6,2) -- (6,1.5);\n\\draw[thick, ->] (6,1) -- (6,0.5);\n\\draw[thick, ->] (6,0) -- (6,-0.5);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 537,
        "tikz_code": "\\documentclass[a4paper]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.6]\n\\draw [red, line width = 0.50mm] (-8,0) -- (8,0) node[anchor=south]{$\\Psi$};\n\\draw [blue, line width = 0.50mm] (-8,-3) -- (8,-3) node[anchor=south]{$\\Phi$};\n\\draw [red, line width = 0.50mm] (-8,-3) -- (-8,3);\n\\draw [red, line width = 0.50mm] (8,-3) -- (8,3);\n\\draw [red, line width = 0.50mm] (-4,3) -- (-4,0);\n\\draw [red, line width = 0.50mm] (4,0) -- (4,-3);\n\\draw [blue, line width = 0.50mm] (1.7,-3) -- (1.7,3) node[anchor=south]{$-\\Gamma_C$};\n\\draw [blue, line width = 0.50mm] (-6.7,-3) -- (-6.7,3) node[anchor=south]{$-\\Psi_D$};\n\\draw [red, line width = 0.50mm] (-3,-3) -- (-3,0);\n\\draw [blue, line width = 0.50mm] (-1.7,-3) -- (-1.7,3) node[anchor=south]{$-\\Gamma_F$};\n\\draw [red, line width = 0.50mm] (2.7,-3) -- (2.7,3) node[anchor=south]{$-\\Psi_E$};\n\\draw [blue, line width = 0.50mm] (6.7,-3) -- (6.7,3) node[anchor=south]{$-\\Phi_C$};\n\\draw [red, line width = 0.50mm] (-4,-3) -- (-4,0);\n\\draw [blue, line width = 0.50mm] (-2.7,-3) -- (-2.7,3) node[anchor=south]{$-\\Phi_F$};\n\\draw [red, line width = 0.50mm] (4,-3) -- (4,0);\n\\draw [blue, line width = 0.50mm] (2.7,-3) -- (2.7,3) node[anchor=south]{$-\\Phi_E$};\n\\draw [red, line width = 0.50mm] (-2,-1.3) -- (2,-1.3);\n\\draw [red, line width = 0.50mm] (-2,-1.3) .. controls (-1.25,0) .. (2,-1.3);\n\\draw [red, line width = 0.50mm] (-2,-1.3) .. controls (-2.75,0) .. (2,-1.3);\n\\draw [red, dotted, line width = 0.50mm] (-2,-1.3) -- (-2,-1.5);\n\\draw [red, dotted, line width = 0.50mm] (-2,-1.3) -- (-2,-0.7);\n\\draw [red, dotted, line width = 0.50mm] (-2,-1.3) -- (-2,0.2);\n\\draw [red, dotted, line width = 0.50mm] (-2,-1.3) -- (-2,1.0);\n\\draw [red, dotted, line width = 0.50mm] (-2,-1.3) -- (-2,2.0);\n\\draw [red, dotted, line width = 0.50mm] (-2,-1.3) -- (-2,3.0);\n\\draw [red, dotted, line width = 0.50mm] (2,-1.3) -- (2,-1.5);\n\\draw [red, dotted, line width = 0.50mm] (2,-1.3) -- (2,-0.7);\n\\draw [red, dotted, line width = 0.50mm] (2,-1.3) -- (2,0.2);\n\\draw [red, dotted, line width = 0.50mm] (2,-1.3) -- (2,1.0);\n\\draw [red, dotted, line width = 0.50mm] (2,-1.3) -- (2,2.0);\n\\draw [red, dotted, line width = 0.50mm] (2,-1.3) -- (2,3.0);\n\\draw [red, line width = 0.50mm] (-2,-3) -- (-2,-2);\n\\draw [blue, line width = 0.50mm] (-2,-2) -- (-2,1.3);\n\\draw [red, line width = 0.50mm] (2,-3) -- (2,-2);\n\\draw [blue, line width = 0.50mm] (2,-2) -- (2,1.3);\n\\node [red, font = \\large] at (-2,-1.1) {$\\Gamma_P$};\n\\node [red, font = \\large] at (-2,0.3) {$\\Omega_D$};\n\\node [red, font = \\large] at (2,-1.1) {$\\Omega_P$};\n\\node [red, font = \\large] at (-2,-2.5) {$\\Omega_F$};\n\\node [red, font = \\large] at (2,-2.5) {$\\Omega_E$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 538,
        "tikz_code": "\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\tikzset{\n\tdesc/.style=\n\t{\n\t\tfill=white,inner sep=2pt,font=\\scriptsize\n\t},\n\tVertex/.style =\n\t{\n\t\tinner sep = 1pt,\n\t\touter sep = 2pt,\n\t\tminimum size=15pt,\n\t\tcircle,\n\t\tdraw=black!70,\n\t\tthick,\n\t\tfont=\\scriptsize\n\t},\n\tEdgeT/.style =\n\t{\n\t\tultra thick,\n\t\tdraw=black,\n\t\tfont=\\scriptsize\n\t},\n\tEdgeI/.style =\n\t{\n\t\t->,\n\t\tdraw=black!70,\n\t\tfont=\\scriptsize\n\t}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\t%tree\n\t\\node[Vertex] (E) at (0,0) {(a)};\n\t\\node[Vertex] (C) at (-1.5,-2) {$a$};\n\t\\node[Vertex] (D) at (0,-2) {$b$};\n\t\\node[Vertex] (A) at (1.5,-2) {$c$};\n\t\\draw[EdgeT] (E) -- (C);\n\t\\draw[EdgeT] (E) -- (D);\n\t\\draw[EdgeT] (E) -- (A);\n\t\\node[Vertex] (E1) at (-1.5,-4) {$a$};\n\t\\node[Vertex] (F1) at (0,-4) {$d$};\n\t\\node[Vertex] (G1) at (1.5,-4) {$e$};\n\t\\draw[EdgeT] (C) -- (E1);\n\t\\draw[EdgeT] (D) -- (F1);\n\t\\draw[EdgeT] (A) -- (G1);\n\t\\node[Vertex] (E2) at (0,-6) {$b$};\n\t\\node[Vertex] (F2) at (1.5,-6) {$c$};\n\t\\draw[EdgeT] (E1) -- (E2);\n\t\\draw[EdgeT] (F1) -- (E2);\n\t\\draw[EdgeT] (G1) -- (E2);\n\t\\node[Vertex] (E3) at (0,-8) {$a$};\n\t\\node[Vertex] (F3) at (1.5,-8) {$b$};\n\t\\draw[EdgeT] (E2) -- (E3);\n\t\\draw[EdgeT] (F2) -- (E3);\n\t\\draw[EdgeT] (G1) -- (F3);\n\t\n\t%arrows\n\t\\draw[EdgeI] (0,-0.7) -- (0,-1.3);\n\t\n\t%Initial tree\n\t\\node[Vertex] (E) at (0+10,0) {(b)};\n\t\\node[Vertex] (C) at (-1.5+10,-2) {$a$};\n\t\\node[Vertex] (D) at (0+10,-2) {$b$};\n\t\\node[Vertex] (A) at (1.5+10,-2) {$c$};\n\t\\draw[EdgeT] (E) -- (C);\n\t\\draw[EdgeT] (E) -- (D);\n\t\\draw[EdgeT] (E) -- (A);\n\t\\node[Vertex] (E1) at (-1.5+10,-4) {$a$};\n\t\\node[Vertex] (F1) at (0+10,-4) {$d$};\n\t\\node[Vertex] (G1) at (1.5+10,-4) {$e$};\n\t\\draw[EdgeT] (C) -- (E1);\n\t\\draw[EdgeT] (D) -- (F1);\n\t\\draw[EdgeT] (A) -- (G1);\n\t\\node[Vertex] (E2) at (0+10,-6) {$b$};\n\t\\node[Vertex] (F2) at (1.5+10,-6) {$c$};\n\t\\draw[EdgeT] (E1) -- (E2);\n\t\\draw[EdgeT] (F1) -- (E2);\n\t\\draw[EdgeT] (G1) -- (E2);\n\t\\node[Vertex] (E3) at (0+10,-8) {$a$};\n\t\\node[Vertex] (F3) at (1.5+10,-8) {$b$};\n\t\\draw[EdgeT] (E2) -- (E3);\n\t\\draw[EdgeT] (F2) -- (E3);\n\t\\draw[EdgeT] (G1) -- (F3);\n\t\n\t%arrows\n\t\\draw[EdgeI] (0+10,-0.7) -- (0+10,-1.3);\n\t\n\t%Finites\n\t\\draw[EdgeI,blue] (5,-0.7) -- (5,-1.3);\n\t\\draw[EdgeI,blue] (5,-0.7) -- (7.5,-1.3);\n\t\n\t\\node[Vertex] (E) at (10,0) {(c)};\n\t\\node[Vertex] (C) at (7.5,-2) {$a$};\n\t\\node[Vertex] (D) at (9.5,-2) {$b$};\n\t\\node[Vertex] (A) at (11.5,-2) {$c$};\n\t\\draw[EdgeT] (E) -- (C);\n\t\\draw[EdgeT] (E) -- (D);\n\t\\draw[EdgeT] (E) -- (A);\n\t\\node[Vertex] (E1) at (7.5,-4) {$a$};\n\t\\node[Vertex] (F1) at (9.5,-4) {$d$};\n\t\\node[Vertex] (G1) at (11.5,-4) {$e$};\n\t\\draw[EdgeT] (C) -- (E1);\n\t\\draw[EdgeT] (D) -- (F1);\n\t\\draw[EdgeT] (A) -- (G1);\n\t\\node[Vertex] (E2) at (9.5,-6) {$b$};\n\t\\node[Vertex] (F2) at (11.5,-6) {$c$};\n\t\\draw[EdgeT] (E1) -- (E2);\n\t\\draw[EdgeT] (F1) -- (E2);\n\t\\draw[EdgeT] (G1) -- (E2);\n\t\\node[Vertex] (E3) at (9.5,-8) {$a$};\n\t\\node[Vertex] (F3) at (11.5,-8) {$b$};\n\t\\draw[EdgeT] (E2) -- (E3);\n\t\\draw[EdgeT] (F2) -- (E3);\n\t\\draw[EdgeT] (G1) -- (F3);\n\t\n\\"
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    {
        "index": 539,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amsthm,amssymb,latexsym}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{decorations.pathreplacing,decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5]\n\\tikzstyle{arrow}=[->,>=stealth,thick]\n\\tikzstyle{arrow2}=[->,>=stealth,thick,blue]\n\\tikzstyle{arrow3}=[->,>=stealth,thick,red]\n\n\n\\draw[arrow2,samples=100,domain=0.2:1,smooth,variable=\\y]  plot  ({1/\\y},{\\y});\n\\draw[arrow2,samples=100,domain=0.2:1,smooth,variable=\\y]  plot  ({1/\\y},{-0.98*\\y});\n\\draw[->] (-0.5,0) -- (2.5,0);\n\\draw[->] (0,-0.5) -- (0,3.5);\n\n\\draw (2,0) -- (2,3.5);\n\\draw[dashed] (2,3.5) -- (2,3.9);\n\\node at (2,3.5) [above] {$\\bar{y}=0$};\n\\node at (0,0) [left] {$0$};\n\\node at (2,0) [below] {$\\frac{2}{m-1}$};\n\n\n\\draw[arrow3] (0.5,-0.5) -- (0.2,-0.2);\n\\draw[arrow3] (0.5,0.5) -- (0.2,0.2);\n\\draw[arrow3] (0.5,1.5) -- (0.2,1.2);\n\\draw[arrow3] (0.5,2.5) -- (0.2,2.2);\n\n\\draw[arrow3] (1.5,-0.5) -- (1.2,-0.2);\n\\draw[arrow3] (1.5,0.5) -- (1.2,0.2);\n\\draw[arrow3] (1.5,1.5) -- (1.2,1.2);\n\\draw[arrow3] (1.5,2.5) -- (1.2,2.2);\n\n\\node at (1.2,0.2) [below] {$y>0$};\n\\node at (0.2,1.2) [right] {$y<0$};\n\n\\draw[arrow2,samples=100,domain=0:2,smooth,variable=\\x]  plot  (\\x,{1.4*\\x-0.5});\n\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 540,
        "tikz_code": "\\documentclass[a4paper,10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage[svgnames]{xcolor}\n\\usepackage{tikz,pgf}\n\\usepackage{pgfplots}\n\\usetikzlibrary{patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}[x=2cm,y=2cm]\n  \\fill[lightgray] (1.1,.2) rectangle (2.3,.9);\n  \\fill[gray] (1.1,1.2) rectangle (2.3,1.8);\n  \\fill[darkgray] (1.1,1.8) rectangle (2.3,2.5);\n  \\draw[very thick] (1.1,.2) -- (1.1,2.5);\n  \\draw[very thick] (2.3,.2) -- (2.3,2.5);\n  \\draw[very thick] (1.1,1.2) -- (1.1,1.8);\n  \\draw[very thick] (2.3,1.2) -- (2.3,1.8);\n  \\draw[dashed] (1.1,.2) -- (1.1,2.5) node[above] {\\small $1$};\n  \\draw[dashed] (2.3,.2) -- (2.3,2.5) node[above] {\\small $1$};\n  \\draw[dashed] (1.1,1.2) -- (1.1,1.8) node[above] {\\small $1$};\n  \\draw[dashed] (2.3,1.2) -- (2.3,1.8) node[above] {\\small $1$};\n  \\draw[dashed] (1.1,.2) -- (2.3,.2) node[right] {\\small $1$};\n  \\draw[dashed] (1.1,1.2) -- (2.3,1.2) node[right] {\\small $Q$};\n  \\draw[->] (0,.2) -- (2.7,.2);\n  \\draw[->] (.2,0) -- (.2,2.7);\n  \\draw (1.1,.1) -- (1.1,-.1) node[below] {\\small $1$};\n  \\draw (2.3,.1) -- (2.3,-.1) node[below] {\\small $1$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 541,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node[] at (0,0) {\\includegraphics[width=.9\\linewidth]{example-image}};\n\\node[] at (-.1,-2.8) {$\\tilde{x}$};\n\\node[anchor=west] at (8.8,-2.8) {$x$};\n\\node[rotate=90] at (-3.6,0) {$\\delta_{9}$};\n\\node[anchor=west] at (8.8,0) {$\\delta_{2}$};\n\\node[] at (-.1,2.8) {$\\tilde{x}$};\n\\node[anchor=west] at (8.8,2.8) {$x$};\n\\node[] at (0.7,-2.15) {$\\delta_{1}$};\n\\node[] at (0.7,2.15) {$\\delta_{3}$};\n\\node[] at (3.1,-2.15) {$\\delta_{4}$};\n\\node[] at (3.1,2.15) {$\\delta_{6}$};\n\\node[] at (5.5,-2.15) {$\\delta_{5}$};\n\\node[] at (5.5,2.15) {$\\delta_{7}$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 542,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath, amsthm, amssymb, graphics, graphicx}\n\\usepackage{tikz}\n\n\\newcommand{\\KK}{\\mathbb{K}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.5]\n\t\t\\tikzstyle{every node}=[circle, fill=black, inner sep=1.25pt];\n\t\t\n\t\t\\begin{scope}[yshift=-4cm]\n\t\t\\node (a) at (0,0) {};\n\t\t\\node (b) at (1,0) {};\n\t\t\\node (c) at (0,1) {};\n\t\t\\node (d) at (1,1) {};\n\t\t\\draw (a) -- (c) -- (b) -- (d) -- (a);\n\t\t\\end{scope}\n\t\t\n\t\t\\begin{scope}[yshift=-4cm, xshift=3.25cm]\n\t\t\\node (a) at (0,0) {};\n\t\t\\node (b) at (1,0) {};\n\t\t\\node (c) at (0,1) {};\n\t\t\\node (d) at (1,1) {};\n\t\t\\draw (a) -- (c) -- (b) -- (d) -- (a);\n\t\t\\end{scope}\n\t\t\n\t\t\\begin{scope}[yshift=-8cm]\n\t\t\\node (a) at (0,0) {};\n\t\t\\node (b) at (1,0) {};\n\t\t\\node (c) at (0,1) {};\n\t\t\\node (d) at (1,1) {};\n\t\t\\draw (a) -- (c) -- (b) -- (d) -- (a);\n\t\t\\end{scope}\n\t\t\n\t\t\\begin{scope}[yshift=-8cm, xshift=3.25cm]\n\t\t\\node (a) at (0,0) {};\n\t\t\\node (b) at (1,0) {};\n\t\t\\node (c) at (0,1) {};\n\t\t\\node (d) at (1,1) {};\n\t\t\\draw (a) -- (c) -- (b) -- (d) -- (a);\n\t\t\\end{scope}\n\t\t\n\t\t\\begin{scope}[yshift=-12cm, xshift=6.25cm]\n\t\t\\node (a) at (0,0) {};\n\t\t\\node (b) at (1,0) {};\n\t\t\\node (c) at (0,1) {};\n\t\t\\node (d) at (1,1) {};\n\t\t\\draw (a) -- (c) -- (b) -- (d) -- (a);\n\t\t\\end{scope}\n\t\t\n\t\t\\begin{scope}[yshift=-12cm]\n\t\t\\node (a) at (0,0) {};\n\t\t\\node (b) at (1,0) {};\n\t\t\\node (c) at (0,1) {};\n\t\t\\node (d) at (1,1) {};\n\t\t\\draw (a) -- (c) -- (b) -- (d) -- (a);\n\t\t\\end{scope}\n\t\t\n\t\t\\begin{scope}[yshift=-12cm, xshift=9.25cm]\n\t\t\\node (a) at (0,0) {};\n\t\t\\node (b) at (1,0) {};\n\t\t\\node (c) at (0,1) {};\n\t\t\\node (d) at (1,1) {};\n\t\t\\draw (a) -- (c) -- (b) -- (d) -- (a);\n\t\t\\end{scope}\n\t\t\n\t\t\\draw (2.5,-1.25) -- (2.5,1.25);\n\t\t\\draw (2.5,-1.25) -- (2.5,-3.75);\n\t\t\\draw (2.5,1.25) -- (2.5,3.75);\n\t\t\\draw (6.5,-1.25) -- (6.5,1.25);\n\t\t\\draw (6.5,-1.25) -- (6.5,-3.75);\n\t\t\\draw (6.5,1.25) -- (6.5,3.75);\n\t\t\n\t\t\\draw (10.5,-1.25) -- (10.5,1.25);\n\t\t\\draw (10.5,-1.25) -- (10.5,-3.75);\n\t\t\\draw (10.5,1.25) -- (10.5,3.75);\n\t\t\n\t\t\\node (1) at (14,0) {};\n\t\t\\node (2) at (16,0) {};\n\t\t\\node (3) at (14,2) {};\n\t\t\\node (4) at (16,2) {};\n\t\t\\node (5) at (14,-2) {};\n\t\t\\node (6) at (16,-2) {};\n\t\t\n\t\t\\foreach \\x in {1,2,3,4,5,6}\n\t\t{\n\t\t\t\\draw (\\x) -- (1);\n\t\t}\n\t\t\n\t\t\\foreach \\x in {1,2,3,4,5,6}\n\t\t{\n\t\t\t\\draw (\\x) -- (2);\n\t\t}\n\t\t\n\t\t\\draw (3) -- (1, 1.75);\n\t\t\\draw (3) -- (1, -.25);\n\t\t\\draw (4) -- (1, 1.75);\n\t\t\\draw (4) -- (1, -.25);\n\t\t\\draw (5) -- (1, 1.75);\n\t\t\\draw (5) -- (1, -.25);\n\t\t\\draw (6) -- (1, 1.75);\n\t\t\\draw (6) -- (1, -.25);\n\t\t\\node (1) at (14,-4) {};\n\t\t\\node (2) at (16,-4) {};\n\t\t\\node (3) at (14,-6) {};\n\t\t\\node (4) at (16,-6) {};\n\t\t\\node (5) at (14,-8) {};\n\t\t\\node (6) at (16,-8) {};\n\t\t\n\t\t\\foreach \\x in {1,2,3,4,5,6}\n\t\t{\n\t\t\t\\draw (\\x) -- (1);\n\t\t}\n\t\t\n\t\t\\foreach \\x in {1,2,3,4,5,6}\n\t\t{\n\t\t\t\\draw (\\x) -- (2);\n\t\t}\n\t\t\n\t\t\\draw (3) -- (1, 1.75);\n\t\t\\draw (3) -- (1, -.25);\n\t\t\\draw (4) -- (1, 1.75);\n\t\t\\draw (4) -- (1, -.25);\n\t\t\\draw (5) -- (1, 1.75);\n\t\t\\draw (5) -- (1, -.25);\n\t\t\\draw (6) -- (1, 1.7"
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage[utf8]{inputenc}\n\\usepackage{color}\n\\usepackage[pdfstartview=FitH,pdfpagemode=UseNone,colorlinks=true,citecolor=blue,linkcolor=blue, backref=page]{hyperref}\n\\usepackage[T1]{fontenc}\n\\usepackage[usenames,dvipsnames,svgnames,table]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{decorations.shapes}\n\\usetikzlibrary{decorations.pathreplacing,angles,quotes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n             every node/.style={draw, circle},\n             every edge/.style={draw, line width=1.5pt},\n             shorten >=2pt+0.5\\pgflinewidth,\n             shorten <=2pt+0.5\\pgflinewidth\n         ]\n\n         \n    \\draw [line width=4pt] (1,6) -- (1,7);\n    \\draw [line width=4pt, dotted] (1,7) -- (1,8);\n    \\draw [line width=4pt, dotted] (1,7) -- (0,6);\n    \\draw [line width=4pt, dotted] (1,7) -- (2,6);\n    \\draw [line width=4pt] (1,7) -- (1,6);\n    \\draw [line width=4pt] (0,6) -- (0.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (2,6) -- (1.5,5);\n    \\draw [line width=4pt] (2,6) -- (2.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (0,6) -- (0.5,5);\n    \\draw [line width=4pt] (0,6) -- (0.5,5);\n    \\draw [line width=4pt] (0,6) -- (0.5,5);\n    \\draw [line width=4pt] (0,6) -- (0.5,5);\n    \\draw [line width=4pt] (2,6) -- (2.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (2,6) -- (2.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (2,6) -- (2.5,5);\n    \\draw [line width=4pt] (2,6) -- (2.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (0,6) -- (0.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (2,6) -- (2.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (2,6) -- (2.5,5);\n    \\draw [line width=4pt] (2,6) -- (2.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (2,6) -- (2.5,5);\n    \\draw [line width=4pt] (2,6) -- (2.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (2,6) -- (2.5,5);\n    \\draw [line width=4pt] (2,6) -- (2.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (2,6) -- (2.5,5);\n    \\draw [line width=4pt] (2,6) -- (2.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (2,6) -- (2.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt] (1,6) -- (1.5,5);\n    \\draw [line width=4pt]"
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    {
        "index": 545,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\fill[red!50] (0,0) rectangle (2,2);\n    \\fill[blue!50] (2,0) rectangle (4,2);\n    \\draw[black] (4,0) -- (4,2);\n    \\draw[black] (0,0) -- (0,2);\n    \\node at (1,1) {$A$};\n    \\node at (3,1) {$S$};\n    \\node at (2,2.3) {$B_{p^\\mathrm{top}}$};\n    \\node at (4,2.3) {$B^\\prime_{p^\\mathrm{top}}$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 546,
        "tikz_code": "\\documentclass[a4paper,11pt]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.1, >=triangle 45, mydeco/.style = {decoration = {markings, mark = at position #1 with {\\arrow{<}}}} ]\n\\draw [thick] (0,0) circle (2);\n\\draw [fill,black] (0,0) circle (0.05);\n\\draw [fill,black] (0,2) circle (0.05);\n\\draw [fill,black] (1.73,-1) circle (0.05);\n\\draw [fill,black] (-1.73,-1) circle (0.05);\n\\draw [fill,black] (-1.73,1) circle (0.05);\n\\draw [fill,black] (1.73,1) circle (0.05);\n\\draw [postaction = {mydeco=-0.0416666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666"
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    {
        "index": 547,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{shapes.geometric}\n\\usetikzlibrary{automata}\n\n\\begin{document}\n\n\\begin{tikzpicture}[shorten >=1pt,node distance=2cm, auto]\n  \\node[draw, circle, initial, initial text=] (x) {$ S_n=0 $};\n  \\node[draw, circle, right of = x] (y) {$ S_{n-1} $};\n  \\node[draw, circle, right of = y] (z) {$ S_{n-2} $};\n  \\node[draw, circle, right of = z, accepting] (v) {$ S_0 $};\n  \\path[->] (x) edge node {$ $} (y)\n             (y) edge node {$ \\Sigma^* $} (z)\n             (z) edge node {$ \\Sigma^* $} (v)\n             (x) edge [loop below] node {$ \\Sigma $} (x)\n             (y) edge [loop below] node {$ \\Sigma $} (y)\n             (z) edge [loop below] node {$ \\Sigma $} (z)\n             (z) edge node {Do not surface} (v)\n             (y) edge node {Surface} (v);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 548,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsthm,amssymb,amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix}\n\\usepackage{xcolor}\n\\usepackage[colorlinks=true,citecolor=blue]{hyperref}\n\\usepackage{xcolor}\n\\usepackage{pgfplots}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\node (A) at (0,0) {$\\mathsf{Alice}$};\n    \\node (B) at (4,0) {$\\mathsf{Bob}$};\n    \\node (C) at (0,-2) {$\\mathsf{Charles}$};\n    \\node (D) at (4,-2) {$\\mathsf{Computes}$};\n    \n    \\draw[->, line width=1pt] (A) -- (B) node[midway,above] {$Q_2$};\n    \\draw[->, line width=1pt] (B) -- (D) node[midway,right] {$k_{BC}$};\n    \\draw[->, line width=1pt] (C) -- (D) node[midway,below] {$\\begin{aligned}P_2 &\\text{ verifies $P_2 \\in G$}\\\\P_3 &\\text{ computes $P_3 = d_2^{k_B}$}\\\\P_4 &\\text{ encrypts $S = d_2^{k_B}G$}\\end{aligned}$};\n    \\draw[->, line width=1pt] (A) -- (C) node[midway,left] {$\\begin{aligned}R &\\text{ retrieves $Q_2$ from $B$}\\\\S &\\text{ computes $S = d_2^{k_B}G$}\\\\d_2 &= E(S,m)\\end{aligned}$};\n    \n    \\draw[dotted, line width=1pt] (2.65,-0.08) -- (2.65,-1.92) node[midway,right] {$\\begin{aligned}d_1 &= G\\\\c_2 &= E(S,m)\\end{aligned}$};\n    \\draw[dotted, line width=1pt] (2.75,-1.75) -- (2.75,-2.25) node[midway,right] {$\\begin{aligned}d_2 &= G\\\\d_3 &= d_2^{k_C}\\\\P_3 &= d_3G\\end{aligned}$};\n    \\draw[dotted, line width=1pt] (3.35,-1.75) -- (3.35,-2.25) node[midway,left] {$\\begin{aligned}d_3 &= d_3G\\\\d_4 &= E(S,m)\\end{aligned}$};\n    \\draw[dotted, line width=1pt] (1.5,-0.08) -- (1.5,-1.92) node[midway,left] {$\\begin{aligned}d_2 &= d_2^{k_C}\\\\P_2 &= d_2G\\end{aligned}$};\n    \n    \\draw[->, line width=1pt] (3.35,-2.75) to[out=180,in=45] (2.75,-3.25) node[midway,left] {$\\begin{aligned}d_2 &= G\\\\d_3 &= d_2^{k_C}\\\\P_3 &= d_3G\\\\d_4 &= E(S,m)\\end{aligned}$};\n    \\draw[->, line width=1pt] (2.75,-3.25) to[out=-90,in=180] (3.35,-3.75) node[midway,right] {$\\begin{aligned}d_3 &= d_3G\\\\d_4 &= E(S,m)\\end{aligned}$};\n    \\draw[->, line width=1pt] (3.35,-3.75) -- (3.35,-4.25) node[midway,right] {$\\begin{aligned}d_1 &= d_1G\\\\m &= Dec(S,d_1,d_2,d_3,d_4)\\end{aligned}$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 549,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amsthm,amssymb,latexsym,hyperref,url,graphicx,amsthm,multirow,color,tikz,enumitem,appendix}\n\\usetikzlibrary{trees}\n\n\\begin{document}\n\n\\begin{tikzpicture}[level distance=1.5cm,\n  level 1/.style={sibling distance=8.5cm},\n  level 2/.style={sibling distance=3.5cm},\n  level 3/.style={sibling distance=1cm}]\n  \\node {$x_1$}\n    child {node {$a_1(x_1+x_2)$}\n      child {node {$a_1(a_1+a_2)$}\n        child {node {$a_1(a_2+a_3)$}\n          child {node {$a_1(a_3+a_4)$}\n            child {node {$\\vdots$}}\n          }\n        }\n        child {node {$a_2(a_1+a_3)$}\n          child {node {$a_3(a_1+a_4)$}\n            child {node {$\\vdots$}}\n          }\n        }\n      }\n      child {node {$a_2(x_1+x_2)$}\n        child {node {$a_3(x_1+x_2)$}\n          child {node {$\\vdots$}}\n        }\n      }\n    }\n    child {node {$a_2(x_1+x_2)$}\n      child {node {$a_1(a_2+a_3)$}\n        child {node {$a_1(a_3+a_4)$}\n          child {node {$\\vdots$}}\n        }\n      }\n      child {node {$a_3(x_1+x_2)$}\n        child {node {$a_2(a_1+a_3)$}\n          child {node {$\\vdots$}}\n        }\n      }\n    };\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 550,
        "tikz_code": "\\documentclass[10pt]{amsart}\n\\usepackage{color}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{pgf}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,arrows,automata}\n\n\\newcommand{\\ra}{\\rightarrow}\n\n\\begin{document}\n\n\\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=4cm,\n                    semithick]\n\n  \\node[state, fill=gray!40] (A)                    {$u_1$};\n  \\node[state]         (B) [left of=A] {$u_2$};\n  \\node[state]         (C) [left of=B] {$u_3$};\n  \\node[state, fill=gray!40]         (D) [left of=C] {$u_4$};\n  \\node[state]         (E) [left of=D] {$u_5$};\n  \\node[state]         (F) [above of=E] {$u_6$};\n  \\node[state, fill=gray!40]         (G) [below of=E] {$u_7$};\n\n\n  \\node[state, fill=gray!40]         (H) [right of=A] {$u_8$};\n  \\node[state]         (I) [right of=H] {$u_9$};\n  \\node[state]         (J) [right of=I] {$u_{10}$};\n  \\node[state, fill=gray!40]         (K) [right of=J] {$u_{11}$};\n  \\node[state]         (L) [right of=K] {$u_{12}$};\n  \\node[state, fill=gray!40]         (M) [right of=L] {$u_{13}$};\n\n\n  \\path (A) edge              node {$\\delta_1 \\wedge \\Delta^{3\\wedge3}$} (B)\n            edge              node {$\\delta_1 \\wedge \\Delta^{1\\wedge3}$} (C)\n            edge              node {$\\delta_1 \\wedge \\Delta^{2\\wedge2}$} (D)\n            edge              node {$\\delta_1 \\wedge \\Delta^{1\\wedge2}$} (E)\n        (B) edge              node {$\\delta_2 \\wedge \\Delta^{3\\wedge2}$} (C)\n        (D) edge              node {$\\delta_3 \\wedge \\Delta^{2\\wedge2}$} (F)\n        (E) edge              node {$\\delta_3 \\wedge \\Delta^{2\\wedge1}$} (G)\n        (H) edge              node {$\\delta_4 \\wedge \\Delta^{1\\wedge3}$} (I)\n        (I) edge              node {$\\delta_5 \\wedge \\Delta^{2\\wedge1}$} (J)\n        (J) edge              node {$\\delta_6 \\wedge \\Delta^{2\\wedge1}$} (K)\n        (K) edge              node {$\\delta_7 \\wedge \\Delta^{1\\wedge1}$} (L)\n        (L) edge              node {$\\delta_8 \\wedge \\Delta^{2\\wedge1}$} (M);\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 551,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{amsmath,amssymb}\n\\usepackage[usenames,dvipsnames]{xcolor}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n        \\node at (0,0) {\\includegraphics[width=8cm]{example-image}};\n        \\node at (0,-4.7) {\\includegraphics[width=8cm]{example-image}};\n        \\node at (0,-9.5) {\\includegraphics[width=8cm]{example-image}};\n        \\node at (-3.75,0) {(a)};\n        \\node at (-3.75,-4.7) {(b)};\n        \\node at (-3.75,-9.5) {(c)};\n    \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 552,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amsfonts,bm}\n\\usepackage{tikz}\n\\usetikzlibrary{spy}\n\\usepackage{tikz,pgfplots,pgfplotstable}\n\\pgfplotsset{compat=1.17}\n\\usepgfplotslibrary{groupplots}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n        \\node[anchor=south west,inner sep=0] (image) at (0,0) {\\includegraphics[width=0.3\\linewidth]{example-image}};\n        \\begin{scope}[x={(image.south east)},y={(image.north west)}]\n            \\draw[red, thick, ->] (0.80,0.87) to[bend left] (0.60,0.87) node[right, black] {\\textcolor{red}{$\\alpha_0$}};\n            \\draw[red, thick, ->] (0.80,0.87) to[bend right] (0.85,0.83) node[below left, black] {\\textcolor{red}{$\\hat\\gamma_0$}};\n            \\node[red] (theta) at (0.80,0.87) {\\Huge $\\bullet$};\n            \\draw[red, thick, ->] (0.8, 0.88) arc (120:60:0.25) node[right, black] {\\textcolor{red}{$\\theta$}};\n            \\draw[black, thick, -] (0.52, 0.55) circle (0.1) node[right] {\\Large $\\hat h$};\n            \\draw[black, thick, -] (0.85, 0.7) node[right] {$\\textcolor{red}{\\alpha}$};\n            \\draw[black, thick, -] (0.8, 0.97) node[right] {$\\textcolor{red}{\\hat \\gamma}$};\n            \\draw[black, thick, -] (0.78, 0.82) node[right] {$\\textcolor{red}{\\gamma}$};\n            \\draw[black, thick, -] (0.82, 0.97) node[right] {$\\textcolor{red}{\\delta}$};\n            \\draw[black, thick, -] (0.78, 0.72) node[right] {$\\textcolor{red}{\\tau}$};\n            \\draw[black, thick, -] (0.15, 0.9) node[right] {$\\textcolor{red}{\\mathcal{E} \\text{ or } \\Delta^+}$};\n            \\draw[black, thick, -] (0.5, 0.1) node[right] {$\\textcolor{red}{\\mathcal{E} \\text{ or } \\Delta^-}$};\n        \\end{scope}\n    \\end{tikzpicture}\n\n\\end{document}"
    },
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        "tikz_code": "\\documentclass[12pt, oneside]{article}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage[usenames,dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{trees}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{shapes.misc}\n\\tikzset{\n  threept/.style={\n    circle,\n    draw,\n    inner sep=2pt,\n  },\n  twopt/.style={\n    circle,\n    draw,\n    fill=black,\n    inner sep=1pt,\n    minimum size=1pt\n  },\n  cross/.style={\n    cross out,\n    draw=black, \n    minimum size=7pt, \n    inner sep=0pt,\n    outer sep=0pt\n  },\n  scalar/.style={\n    thick,\n    dashed,\n    postaction={\n      decorate,\n      decoration={\n        markings,\n        mark=at position 0.5 with {\\arrow{>}}\n      }\n    }\n  },\n  spinning/.style={\n    thick,\n    postaction={\n      decorate,\n      decoration={\n        markings,\n        mark=at position 0.5 with {\\arrow{>}}\n      }\n    }\n  },\n  spinning no arrow/.style={\n    thick,\n  },\n  finite with arrow/.style={\n    decoration={\n      snake,\n      amplitude=1pt,\n      segment length=6pt,\n      post length=2pt\n    },\n    decorate,\n    thick,->\n  },\n  finite/.style={\n    decoration={\n      snake,\n      amplitude=1pt,\n      segment length=6pt,\n    },\n    decorate,\n    thick\n  }\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}[anchor=base,baseline]\n\t\\node (f1) at (-1.5,0.5) [threept] {$a$};\n\t\\node (f2) at (0.5,0.5) [threept] {$b$};\n\t\\node (f3) at (1.5,0.5) [threept] {$c$};\n\t\\node (f4) at (0,1) [threept] {$d$};\n\t\\node (f5) at (-0.5,-1) [threept] {$e$};\n\t\\node (f6) at (1,-1) [threept] {$f$};\n\t\\node (g1) at (-1.5,-0.5) [threept] {$i$};\n\t\\node (g2) at (0.5,-0.5) [threept] {$j$};\n\t\\node (g3) at (1.5,-0.5) [threept] {$k$};\n\t\\node (g4) at (0,0) [threept] {$l$};\n\t\\node (g5) at (-0.5,-2) [threept] {$m$};\n\t\\node (g6) at (1,-2) [threept] {$n$};\n\t\\node (g7) at (1.5,-1.5) [threept] {$o$};\n\t\\node (g8) at (2,-1) [threept] {$p$};\n\t\\node (g9) at (1.5,-2.5) [threept] {$q$};\n\t\\node (g10) at (2,-2) [threept] {$r$};\n\t\\node (g11) at (2.5,-1.5) [threept] {$s$};\n\t\\node (g12) at (3,-1) [threept] {$t$};\n\t\\node (g13) at (2.5,-2) [threept] {$u$};\n\t\\node (g14) at (2.5,-0.5) [threept] {$v$};\n\t\\draw [spinning] (f1)--(g1);\n\t\\draw [spinning] (f2)--(g2);\n\t\\draw [spinning] (f3)--(g3);\n\t\\draw [spinning] (f4)--(g4);\n\t\\draw [spinning] (f5)--(g5);\n\t\\draw [spinning] (f6)--(g6);\n\t\\draw [spinning] (g1)--(g4);\n\t\\draw [spinning] (g2)--(g4);\n\t\\draw [spinning] (g3)--(g6);\n\t\\draw [spinning] (g6)--(g5);\n\t\\draw [spinning] (g4)--(g5);\n\t\\draw [spinning] (g1)--(g6);\n\t\\draw [spinning] (g4)--(g1);\n\t\\draw [spinning] (g4)--(g2);\n\t\\draw [spinning] (g1)--(g3);\n\t\\draw [spinning] (g3)--(g7);\n\t\\draw [spinning] (g6)--(g7);\n\t\\draw [spinning] (g6)--(g8);\n\t\\draw [spinning] (g7)--(g8);\n\t\\draw [spinning] (g8)--(g9);\n\t\\draw [spinning] (g9)--(g10);\n\t\\draw [spinning] (g8)--(g11);\n\t\\draw [spinning] (g11)--(g12);\n\t\\draw [spinning] (g12)--(g13);\n\t\\draw [spinning] (g11)--(g13);\n\t\\draw [spinning] (g11)--(g14);\n\t\\draw [spinning] (g14)--(g4);\n\t\\node () at (0,-3) {The graph $G$};\n\t\n\t\\node (f1) at (6.5,0.5) [threept] {$a$};\n\t\\node (f2) at (7.5,0.5) [threept] {$b$};\n\t\\node (f3) at (8.5,0.5) [threept] {$c$};\n\t\\node (f4) at (7,1) [threept] {$d$};\n\t\\node (f5) at (6.5,-1) [threept] {$e$};\n\t\\node (f6) at (8,-1) [threept] {$f$};\n\t\\node (g1) at (6.5,-0.5) [threept] {$i$};\n\t\\node (g2) at (7.5,-0.5) [threept] {$j$};\n\t\\node (g3) at (8.5,-0.5) [threept] {$k$};\n\t\\node (g4) at (7,0) [threept] {$l$};\n\t\\node (g5) at (6.5,-2) [threept] {$m$};\n\t\\node (g6) at (8,-2) [threept] {$n$};\n\t\\"
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        "index": 555,
        "tikz_code": "\\documentclass[sigconf]{acmart}\n\\usepackage{tikz}\n\\usetikzlibrary{calc, shapes, backgrounds, positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\\tikzset{node distance=3em,\n\t\t\tevery node/.style={draw, circle, fill=red},\n\t\t}\n\t\t\\node (a) at (0,0) [label=below:$o_{11}$]{};\n\t\t\\node (b) at (2.5em,0) [label=below:$o_{12}$]{};\n\t\t\\node (c) at (5em,0) [label=below:$o_{21}$]{};\n\t\t\\node (d) at (7.5em,0) [label=below:$o_{22}$]{};\n\t\t%\n\t\t\\node (e) at (0,2em) [label=below:$o_{11}$]{};\n\t\t\\node (f) at (2.5em,2em) [label=below:$o_{12}$]{};\n\t\t\\node (g) at (5em,2em) [label=below:$o_{21}$]{};\n\t\t\\node (h) at (7.5em,2em) [label=below:$o_{22}$]{};\n\t\t%\n\t\t\\draw[red, ->, thick] (a) edge (b)\n\t\t(a) edge (e)\n\t\t(b) edge (c)\n\t\t(c) edge (g);\n\t\t\\draw[blue, ->, thick] (f) edge (h)\n\t\t(h) edge (d)\n\t\t(d) edge (g);\n\t\t\\node at (1.25em, 1em) {Community I};\n\t\t\\node at (6.25em, 1em) {Community I};\n\t\t\\draw[black, thick] (-1.5em, 0em) circle (4em);\n\t\t\\draw[black, thick] (3.5em, 0em) circle (4em);\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "index": 556,
        "tikz_code": "\\documentclass[11pt,a4paper,twoside,openright, titlepage]{report}\n\\usepackage{color}\n\\usepackage{amssymb}\n\\usepackage{tikz-cd}\n\\usetikzlibrary{positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[level distance=0.8cm]\n\\node {$(v_0, v_2)$}\n\tchild { node {$(v_0, v_1)$}}\n\tchild { node {$(v_1, v_2)$}};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 557,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{calc, shapes, backgrounds, patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\draw [dashed] (-0.5, -0.3) rectangle (8, 0.3);\n    \\draw [dashed] (1.5, -1.3) rectangle (8, -0.3);\n    \\draw [dashed] (5.5, -1.3) rectangle (8, -0.3);\n    \\node [left] at (-0.7, 0) {$\\text{period}~T$};\n    \\node [left] at (-0.7, -0.8) {$\\text{period}~T'$};\n    \\node [left] at (-0.7, -1.6) {$\\text{period}~T''$};\n    \\node [above] at (3, 0) {State};\n    \\node [above] at (5, 0) {Input};\n    \\node [above] at (7, 0) {Output};\n    \\node [below] at (1.5, 0.3) {\\scriptsize $x_{t_0}$};\n    \\node [below] at (5.5, 0.3) {\\scriptsize $u_{t_0 +1}$};\n    \\draw [fill=orange, fill opacity=0.5] (1.2, -0.2) rectangle (1.8, 0.2);\n    \\draw [fill=orange, fill opacity=0.5] (5.2, -0.2) rectangle (5.8, 0.2);\n    \\draw [fill=orange, fill opacity=0.5] (1.2, -0.9) rectangle (1.8, -0.5);\n    \\draw [fill=orange, fill opacity=0.5] (5.2, -0.9) rectangle (5.8, -0.5);\n    \\node [right] at (1.8, 0.1) {$\\vdots$};\n    \\node [right] at (5.8, 0.1) {$\\vdots$};\n    \\node [right] at (1.8, -0.8) {$\\vdots$};\n    \\node [right] at (5.8, -0.8) {$\\vdots$};\n    \\draw [fill=red, fill opacity=0.5] (1.2, -1.2) rectangle (1.8, -0.8);\n    \\draw [fill=red, fill opacity=0.5] (5.2, -1.2) rectangle (5.8, -0.8);\n    \\draw [fill=red, fill opacity=0.5] (1.2, -1.9) rectangle (1.8, -1.5);\n    \\draw [fill=red, fill opacity=0.5] (5.2, -1.9) rectangle (5.8, -1.5);\n    \\node [right] at (1.8, -0.6) {$\\vdots$};\n    \\node [right] at (5.8, -0.6) {$\\vdots$};\n    \\node [right] at (1.8, -1.5) {$\\vdots$};\n    \\node [right] at (5.8, -1.5) {$\\vdots$};\n    \\node [right] at (1.8, -1.2) {\\tiny $x_{t_0 + 1}$};\n    \\node [right] at (5.8, -1.2) {\\tiny $u_{t_0 + 1}$};\n    \\node [right] at (1.8, -1.9) {\\tiny $x_{t_0 + 2}$};\n    \\node [right] at (5.8, -1.9) {\\tiny $u_{t_0 + 1}$};\n    \\draw [fill=green, fill opacity=0.5] (1.2, -2.3) rectangle (1.8, -1.9);\n    \\draw [fill=green, fill opacity=0.5] (5.2, -2.3) rectangle (5.8, -1.9);\n    \\draw [fill=green, fill opacity=0.5] (1.2, -3) rectangle (1.8, -2.6);\n    \\draw [fill=green, fill opacity=0.5] (5.2, -3) rectangle (5.8, -2.6);\n    \\node [right] at (1.8, -1.7) {\\tiny $x_{t_0 + 2}$};\n    \\node [right] at (5.8, -1.7) {\\tiny $u_{t_0 + 1}$};\n    \\node [right] at (1.8, -2.4) {\\tiny $\\vdots$};\n    \\node [right] at (5.8, -2.4) {\\tiny $\\vdots$};\n    \\node [right] at (1.8, -2.8) {\\tiny $x_{t_0 + 2}$};\n    \\node [right] at (5.8, -2.8) {\\tiny $u_{t_0 + 1}$};\n    \\draw [dashed] (0.5, -2.8) rectangle (8, -3.6);\n    \\draw [fill=blue, fill opacity=0.5] (0.5, -3.2) rectangle (1.5, -2.8);\n    \\draw [fill=blue, fill opacity=0.5] (1.5, -3.2) rectangle (2.5, -2.8);\n    \\draw [fill=blue, fill opacity=0.5] (2.5, -3.2) rectangle (3.5, -2.8);\n    \\draw [fill=blue, fill opacity=0.5] (3.5, -3.2) rectangle (4.5, -2.8);\n    \\draw [fill=blue, fill opacity=0.5] (4.5, -3.2) rectangle (5.5, -2.8);\n    \\draw [fill=blue, fill opacity=0.5] (5.5, -3.2) rectangle (6.5, -2.8);\n    \\draw [fill=blue, fill opacity=0.5] (6.5, -3.2) rectangle (7.5, -2.8);\n    \\draw [fill=blue, fill opacity=0.5] (7.5, -3.2) rectangle (8, -2.8);\n    \\node [right] at (8.2, 0) {$\\text{period}~T$};\n    \\node [right] at (8.2, -0.8) {$\\text{period}~T'$};\n    \\node [right] at (8.2, -1.6) {$\\text{period}~T''$};\n  \\end{tikzpicture}\n\n\\end"
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        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\fill [orange!30, rotate=30, opacity=0.5] (0,0) ellipse (2cm and 1cm);\n\\fill [blue!30, rotate=10, opacity=0.5] (2.5,1) ellipse (0.8cm and 0.5cm);\n\\fill [green!30, rotate=-10, opacity=0.5] (1.4,1) ellipse (0.6cm and 0.3cm);\n\\node (a) at (0,0) {$L^2_x:=0$ in $\\Omega$};\n\\node (b) at (4,0.7) {$\\Lambda_{i,j}^fW_2$};\n\\node (c) at (4.2,0) {$f\\in C^\\infty(W_1)$};\n\\node (d) at (3,0) {$\\mathcal{C}\\subset W_1$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage[utf8]{inputenc}\n\\usepackage{color}\n\\usetikzlibrary{arrows,decorations.pathreplacing,backgrounds,fit,decorations.pathreplacing,decorations.pathreplacing,calc,shapes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\t\t\\node at (0,3) {$[0]$};\n\t\t\\node at (0,2.5) {$[0]$};\n\t\t\\node at (0,2) {$[0]$};\n\t\t\\node at (0,1) {$[0]$};\n\t\t\n\t\t\\node at (2,3) {$X$};\n\t\t\\node at (2,2.5) {$X$};\n\t\t\\node at (2,2) {$X$};\n\t\t\\node at (2,1) {$X$};\n\t\t\n\t\t\\draw (0.5,0) rectangle (2.5,1.5);\n\t\t\\draw (1,1.5) rectangle (3,3);\n\t\t\\draw (2.5,0.5) rectangle (3.5,3);\n\t\t\n\t\t\\draw (0,3) -- (2.5,3);\n\t\t\\draw (0,2.5) -- (2.5,2.5);\n\t\t\\draw (0,2) -- (3,2);\n\t\t\\draw (0,1) -- (3.5,1);\n\t\t\n\t\t\\draw[dashed] (3.5,1) -- (4.5,1);\n\t\t\\draw[dashed] (3.5,2) -- (4.5,2);\n\t\t\\draw[dashed] (3.5,3) -- (4.5,3);\n\t\t\n\t\t\\node at (4.75,2.5) {$\\dots$};\n\t\t\\node at (4.75,2) {$\\dots$};\n\t\t\\node at (4.75,1) {$\\dots$};\n\t\t\n\t\t\\draw (0.5,-0.5) rectangle (2.5,-1);\n\t\t\\draw (1,-1.5) rectangle (3,-2);\n\t\t\\draw (2.5,-0.5) rectangle (3.5,-2);\n\t\t\n\t\t\\draw (0,-0.5) -- (2.5,-0.5);\n\t\t\\draw (0,-1) -- (3,-1);\n\t\t\\draw (0,-1.5) -- (3.5,-1.5);\n\t\t\\draw (0,-2) -- (3.5,-2);\n\t\t\n\t\t\\draw[dashed] (3.5,-1) -- (4.5,-1);\n\t\t\\draw[dashed] (3.5,-2) -- (4.5,-2);\n\t\t\\draw[dashed] (3.5,-3) -- (4.5,-3);\n\t\t\n\t\t\\node at (4.75,-1.5) {$\\dots$};\n\t\t\\node at (4.75,-2) {$\\dots$};\n\t\t\n\t\t\\draw (1,-3.5) rectangle (3,-4);\n\t\t\\draw (2.5,-3.5) rectangle (3.5,-4);\n\t\t\n\t\t\\draw (0,-3.5) -- (2.5,-3.5);\n\t\t\\draw (0,-4) -- (3,-4);\n\t\t\\draw (0,-4.5) -- (3.5,-4.5);\n\t\t\\draw (0,-5) -- (3.5,-5);\n\t\t\n\t\t\\draw[dashed] (3.5,-4) -- (4.5,-4);\n\t\t\\draw[dashed] (3.5,-5) -- (4.5,-5);\n\t\t\\draw[dashed] (3.5,-6) -- (4.5,-6);\n\t\t\n\t\t\\node at (4.75,-4.5) {$\\dots$};\n\t\t\\node at (4.75,-5) {$\\dots$};\n\t\t\n\t\t\\node at (0,-5.5) {$[0]$};\n\t\t\\node at (0,-5) {$[0]$};\n\t\t\n\t\t\\node at (2,-5.5) {$U$};\n\t\t\\node at (2,-5) {$U$};\n\t\t\\node at (2,-4.5) {$U$};\n\t\t\\node at (2,-4) {$U$};\n\t\t\n\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 561,
        "tikz_code": "\\documentclass[a4paper,10pt,twoside]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage[T1]{fontenc}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[->] (0,0) -- (12,0) node[anchor=north] {$r$};\n\\draw\t(0,2) node[anchor=east] {$J_{0,0}$}\n\t\t(0,4) node[anchor=east] {$J_{0,1}$}\n\t\t(0,6) node[anchor=east] {$J_{0,2}$}\n\t\t(0,8) node[anchor=east] {$J_{0,3}$}\n\t\t(0,10) node[anchor=east] {$J_{0,4}$}\n\t\t(0,12) node[anchor=east] {$J_{0,5}$};\n\\draw\t(0,0) node[anchor=north] {$I_0$}\n\t\t(2,0) node[anchor=north] {$I_1$}\n\t\t(4,0) node[anchor=north] {$I_2$}\n\t\t(6,0) node[anchor=north] {$I_3$}\n\t\t(8,0) node[anchor=north] {$I_4$}\n\t\t(10,0) node[anchor=north] {$I_5$}\n\t\t(12,0) node[anchor=north] {$I_6$};\n\\draw[->] (0,0) -- (0,12) ;\n\n\\draw[dashed] (0,0) -- (12,2);\n\\draw[dashed] (0,4) -- (12,6);\n\\draw[dashed] (0,8) -- (12,10);\n\\draw[dashed] (0,12) -- (12,14);\n\\draw[dashed] (2,0) -- (12,8);\n\\draw[dashed] (4,0) -- (12,12);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 562,
        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amssymb,amsthm,bbm}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{shapes,arrows}\n\\usetikzlibrary{calc}\n\\tikzset{\n  block/.style    = {draw, thick, rectangle, minimum height = 3em,\n    minimum width = 3em},\n  sum/.style      = {draw, circle, node distance = 2cm}, % Adder\n  input/.style    = {coordinate}, % Input\n  output/.style   = {coordinate} % Output\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n  font=\\sffamily\\footnotesize,\n  every node/.style={inner sep=1pt,outer sep=0,scale=0.8},\n  block/.style={draw, thick, rectangle, minimum height=4em,\n    minimum width=5em,fill=gray!10},\n  bigblock/.style={draw, thick, rectangle, minimum height=11em,\n    minimum width=12em,fill=gray!10},\n  state/.style={draw, thick, rectangle, minimum height=1em,\n    minimum width=1em},\n  arr/.style={->,>=latex,thick},\n  vcont/.style={<-,>=latex,thick,blue}\n  ]\n\n  % Draw the blocks\n  \\draw node at (2.5,0) [name=y2,bigblock] {};\n  \\draw node at (9.5,0) [name=y1,bigblock] {};\n  \\draw node at (2.5,-2) [name=x2,bigblock] {};\n  \\draw node at (9.5,-2) [name=x1,bigblock] {};\n\n  \\draw node at (3,-0.5) [state] (x3) {$r=x_n$};\n  \\draw node at (4,-0.5) [state] (x4) {$\\dots$};\n  \\draw node at (5,-0.5) [state] (x5) {$x_1$};\n  \\draw node at (6,-0.5) [state] (x6) {$\\dots$};\n  \\draw node at (7,-0.5) [state] (x7) {$x_n$};\n  \\draw node at (8,-0.5) [state] (x8) {$\\dots$};\n  \\draw node at (9,-0.5) [state] (x9) {$x_{n+1}$};\n  \\draw node at (10,-0.5) [state] (x10) {$\\dots$};\n  \\draw node at (11,-0.5) [state] (x11) {$x_{2n-1}$};\n\n  \\draw node at (3,-1.5) [state] (x12) {$y_n$};\n  \\draw node at (4,-1.5) [state] (x13) {$\\dots$};\n  \\draw node at (5,-1.5) [state] (x14) {$y_1$};\n  \\draw node at (6,-1.5) [state] (x15) {$\\dots$};\n  \\draw node at (7,-1.5) [state] (x16) {$y_{n}$};\n  \\draw node at (8,-1.5) [state] (x17) {$\\dots$};\n  \\draw node at (9,-1.5) [state] (x18) {$y_{n+1}$};\n  \\draw node at (10,-1.5) [state] (x19) {$\\dots$};\n  \\draw node at (11,-1.5) [state] (x20) {$y_{2n-1}$};\n\n  \\draw node at (2.5,2) [state,inner sep=0.25cm] (C) {$C=\\mathbb{C}^{n+1}$};\n  \\draw node at (9.5,2) [state,inner sep=0.25cm] (B) {$B=\\mathbb{C}^{n+1}\\setminus C$};\n  \\draw node at (2.5,-3) [state,inner sep=0.25cm] (F) {$F=\\mathbb{C}^{n+1}\\setminus B$};\n  \\draw node at (9.5,-3) [state,inner sep=0.25cm] (G) {$G=\\mathbb{C}^{n+1}\\setminus F$};\n\n  % Connect input\n  \\path[arr,vcont] (y1.135) |- node[pos=0.25,below] {loops of colour 1} (x3);\n  \\path[arr,vcont] (y2.45) |- node[pos=0.25,above] {loops of colour 2} (x4);\n  \\path[arr,red] (x3) -- node[pos=0.35,below] {loops of colour 2} (x5);\n  \\path[arr,red] (x4) -- node[pos=0.35,below] {loops of colour 2} (x6);\n  \\path[arr,vcont] (x5) -- node[pos=0.35,above] {loops of colour 0} (x7);\n  \\path[arr,red] (x6) -- node[pos=0.35,below] {loops of colour 0} (x8);\n  \\path[arr,red] (x7) -- node[pos=0.35,above] {loops of colour 0} (x9);\n  \\path[arr,vcont] (x8) -- node[pos=0.35,below] {loops of colour 1} (x10);\n  \\path[arr,vcont] (x9) -- node[pos=0.35,above] {loops of colour 1} (x11);\n  \\path[arr,vcont] (x12) -- node[pos=0.35,above] {loops of colour 2} (x13);\n  \\path[arr,red] (x13) -- node[pos=0.35,below] {loops of colour 2} (x14);\n  \\path[arr,red] (x14) -- node[pos=0.35,below] {loops of colour 2} (x15);\n  \\path[arr,vcont] (x15) -- node[pos=0.35,above] {loops of colour"
    },
    {
        "index": 563,
        "tikz_code": "\\documentclass[reqno,12pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[T1]{fontenc}\n\\usepackage{tikz-network}\n\n\\begin{document}\n\n\\begin{tikzpicture}[thick,scale=0.8, every node/.style={scale=0.8}]\n\\Vertex[x=0,y=0,IdAsLabel]{A}\n\\Vertex[x=0,y=2,IdAsLabel]{B}\n\\Vertex[x=1,y=4,IdAsLabel]{C}\n\\Vertex[x=3,y=4,IdAsLabel]{D}\n\\Vertex[x=4,y=2,IdAsLabel]{E}\n\\Vertex[x=4,y=0,IdAsLabel]{F}\n\\Vertex[x=2,y=2,IdAsLabel]{G}\n\\Vertex[x=2,y=5,IdAsLabel]{H}\n\\Vertex[x=3.5,y=3,IdAsLabel]{I}\n\\Vertex[x=1.5,y=3,IdAsLabel]{J}\n\\Vertex[x=3.2,y=0.8,IdAsLabel]{K}\n\\Vertex[x=0.8,y=0.8,IdAsLabel]{L}\n\\Vertex[x=0.8,y=2.2,IdAsLabel]{M}\n\\Vertex[x=2.2,y=2.2,IdAsLabel]{N}\n\\Edge[color=red,label=1,position=left](A)(B)\n\\Edge[color=red,label=2,position=above](B)(C)\n\\Edge[color=red,label=3,position=above](C)(D)\n\\Edge[color=red,label=1,position=above](D)(E)\n\\Edge[color=red,label=2,position=right](E)(F)\n\\Edge[color=green,label=1,position=left](A)(L)\n\\Edge[color=green,label=2,position=right](L)(M)\n\\Edge[color=black,label=2,position=above](G)(J)\n\\Edge[color=black,label=3,position=left](J)(I)\n\\Edge[color=black,label=1,position=above](A)(N)\n\\Edge[color=black,label=2,position=right](N)(I)\n\\Edge[color=black,label=3,position=left](A)(G)\n\\Edge[color=black,label=4,position=above](G)(M)\n\\Edge[color=black,label=3,position=above](K)(L)\n\\Edge[color=black,label=3,position=right](M)(K)\n\\Edge[color=black,label=4,position=right](M)(N)\n\\Edge[color=black,label=1,position=right](G)(F)\n\\Edge[color=black,label=2,position=above](N)(E)\n\\Edge[color=black,label=2,position=left](L)(D)\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 564,
        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes.geometric}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\tikzstyle{databox} = [circle, fill=white, draw, minimum size=1cm]\n\\tikzstyle{residual} = [circle, fill=cyan!50, draw, minimum size=1cm]\n\\tikzstyle{residualbox} = [rectangle, fill=cyan!50, draw, minimum width=1.5cm, minimum height=3cm]\n\\tikzstyle{inputbox} = [rectangle, fill=gray!20, draw, minimum width=2.5cm, minimum height=3cm]\n\n\\node[inputbox] (Box0) at (0, 0){};\n\\node[inputbox] (Box1) at (3, 0){};\n\\node[inputbox] (Box2) at (6, 0){};\n\\node[inputbox] (Box3) at (9, 0){};\n\n\\node[residualbox] (Res0) at (0, -3){};\n\\node[residualbox] (Res1) at (3, -3){};\n\\node[residualbox] (Res2) at (6, -3){};\n\\node[residualbox] (Res3) at (9, -3){};\n\n\\foreach \\x in {0,...,3}\n{\n  \\foreach \\y in {0,...,3}\n  {\n    \\node[databox] at (2.5*\\x, 1.5*\\y){$X_\\y$};\n  }\n}\n\n\\node[residualbox] (Res0) at (0, -6){};\n\\node[residualbox] (Res1) at (3, -6){};\n\\node[residualbox] (Res2) at (6, -6){};\n\\node[residualbox] (Res3) at (9, -6){};\n\n\\foreach \\x in {0,...,3}\n{\n  \\foreach \\y in {0,...,3}\n  {\n    \\node[databox] at (2.5*\\x, 1.5*\\y){$X_\\y$};\n  }\n}\n\n\\node[residualbox] (Res0) at (0, -9){};\n\\node[residualbox] (Res1) at (3, -9){};\n\\node[residualbox] (Res2) at (6, -9){};\n\\node[residualbox] (Res3) at (9, -9){};\n\n\\node[residualbox] (Res0) at (0, -12){};\n\\node[residualbox] (Res1) at (3, -12){};\n\\node[residualbox] (Res2) at (6, -12){};\n\\node[residualbox] (Res3) at (9, -12){};\n\n\\node at (-1, 1.5) {Particle 1};\n\\node at (4.5, 1.5) {Particle 2};\n\\node at (8, 1.5) {Particle 3};\n\\node at (11.5, 1.5) {Particle 4};\n\n\\draw[dashed] (Box0.north east) -- (Res0.south west);\n\\draw[dashed] (Box0.north west) -- (Res0.south east);\n\\draw[dashed] (Box0.south east) -- (Res0.north west);\n\\draw[dashed] (Box0.south west) -- (Res0.north east);\n\n\\draw[dashed] (Box1.north east) -- (Res1.south west);\n\\draw[dashed] (Box1.north west) -- (Res1.south east);\n\\draw[dashed] (Box1.south east) -- (Res1.north west);\n\\draw[dashed] (Box1.south west) -- (Res1.north east);\n\n\\draw[dashed] (Box2.north east) -- (Res2.south west);\n\\draw[dashed] (Box2.north west) -- (Res2.south east);\n\\draw[dashed] (Box2.south east) -- (Res2.north west);\n\\draw[dashed] (Box2.south west) -- (Res2.north east);\n\n\\draw[dashed] (Box3.north east) -- (Res3.south west);\n\\draw[dashed] (Box3.north west) -- (Res3.south east);\n\\draw[dashed] (Box3.south east) -- (Res3.north west);\n\\draw[dashed] (Box3.south west) -- (Res3.north east);\n\n\\draw[ultra thick, ->] (2.5, 1.5) -- (2.5, -2.25);\n\\node[circle, draw, fill=cyan!50, inner sep=0, minimum width=1cm] (Weights) at (-2, -2.25) {\\Large Weights};\n\\node[circle, draw, fill=cyan!50, inner sep=0, minimum width=1cm] (Resamplings) at (-2, -5.5) {\\Large Resamplings};\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 565,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{amssymb,amsmath,amsthm, euscript}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{calc}\n\n\\newcommand{\\calA}{\\mathcal{A}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[>=latex,scale=2.5,>=latex,very thick,decoration={\n    markings,\n    mark= at position 0.5 with {\\arrow{>}}}]\n\t\n\t\t\\coordinate (A) at (0,0);\n\t\t\\coordinate (B) at (0,1.2);\n\t\t\\coordinate (C) at (1.2,0);\n\t\t\\coordinate (D) at (0,1.2);\n\t\t\\coordinate (E) at (1.2,0);\n\t\t\\coordinate (F) at (1.2,1.2);\n\t\t\\coordinate (G) at (0,0);\n\t\t\\coordinate (H) at (0.6,0.6);\n\t\t\\coordinate (I) at (0,0.6);\n\t\t\\coordinate (J) at (0.6,0);\n\t\t\\coordinate (K) at (1.2,1.2);\n\t\t\\coordinate (L) at (0,1.2);\n\t\t\\coordinate (M) at (1.2,0.6);\n\t\t\\coordinate (N) at (1.2,0);\n\t\t\\coordinate (P) at (0.6,0);\n\t\t\\coordinate (Q) at (1.2,0.6);\n\t\t\\coordinate (R) at (0,0.6);\n\t\t\\coordinate (S) at (0.6,1.2);\n\t\t\\coordinate (T) at (0.6,0);\n\t\t\\coordinate (U) at (0.6,1.2);\n\t\t\\coordinate (V) at (1.2,0.6);\n\t\t\\coordinate (W) at (1.2,0);\n\t\t\\coordinate (X) at (0,1.2);\n\t\t\n\t\t\n\t\t\\draw[fill,color=black!10] (A)--(B)--(C)--(D)--(E)--(F)--(G);\n\t\t\\draw[fill,color=black!5] (A)--(B)--(C)--(D)--(E)--(F)--(G);\n\t\t\\draw[fill,color=black!10] (A)--(I)--(B)--(D)--(E)--(F)--(G);\n\t\t\\draw[fill,color=black!20] (A)--(I)--(J)--(D)--(E)--(F)--(G);\n\t\t\\draw[fill,color=black!30] (A)--(I)--(J)--(K)--(D)--(E)--(F)--(G);\n\t\t\\draw[fill,color=black!20] (A)--(I)--(J)--(K)--(L)--(D)--(E)--(F)--(G);\n\t\t\\draw[fill,color=black!40] (A)--(I)--(J)--(K)--(L)--(M)--(D)--(E)--(F)--(G);\n\t\t\\draw[fill,color=black!50] (A)--(I)--(J)--(K)--(L)--(M)--(N)--(D)--(E)--(F)--(G);\n\t\t\\draw[fill,color=black!70] (A)--(I)--(J)--(K)--(L)--(M)--(N)--(O)--(P)--(Q);\n\t\t\n\t\t\\draw[dashed,color=blue] (A)--(N);\n\t\t\\draw[dashed,color=blue] (O)--(W);\n\t\t\\draw[dashed,color=blue] (P)--(V);\n\t\t\n\t\t\\draw (0.6,0.35) node[anchor=west] {$I_1 = D_2 + D_3$};\n\t\t\\draw (1.1,0.8) node[anchor=west] {$E_1 = S_1$};\n\t\t\\draw (0.8,0) node[anchor=north] {$I_2 = D_2$};\n\t\t\n\t\t\\draw[very thick,color=red] (0.6,0.6) -- (1.2,1.2);\n\t\t\\draw[very thick,color=red] (0.6,0.6) -- (0,1.2);\n\t\t\n\t\t\\draw[very thick,color=red] (0,1.2) -- (0,0.6);\n\t\t\\draw[very thick,color=red] (0,0.6) -- (0.6,0);\n\t\t\n\t\t\\draw (0.5,-0.15) node[anchor=north] {$\\calA$};\n\t\t\\draw (-0.15,0.5) node[anchor=east] {$\\calA^*$};\n\t\t\\draw (-0.15,1.2) node[anchor=east] {$\\calA^*$};\n\t\t\\draw (1.2,-0.15) node[anchor=north] {$q$};\n\t\t\\draw (-0.15,1.2) node[anchor=east] {$p$};\n\t\t\\draw (1.2,0) node[anchor=north] {$q$};\n\t\t\n\t\t\\draw (0.5,1.15) node[anchor=east] {$p^*$};\n\t\t\\draw (0.5,0.5) node[anchor=east] {$p$};\n\t\t\\draw (-0.15,0.5) node[anchor=east] {$p^*$};\n\t\t\n\t\t\n\t\t\\draw[fill,color=blue!20,decorate,decoration={zigzag,segment length=6,amplitude=.4,post=lineto,post length=10}] (0,1.2)--(0,0.6);\n\t\t\\draw[fill,color=blue!20,decorate,decoration={zigzag,segment length=6,amplitude=.4,post=lineto,post length=10}] (0.6,0.6)--(1.2,0.6);\n\t\t\\draw[fill,color=blue!20,decorate,decoration={zigzag,segment length=6,amplitude=.4,post=lineto,post length=10}] (0,0.6)--(0,1.2);\n\t\t\\draw[fill,color=blue!20,decorate,decoration={zigzag,segment length=6,amplitude=.4,post=lineto,post length=10}] (0.6,0.6)--(1.2,1.2);\n\t\t\n\t\t\\draw[fill,color=blue!20,decorate,decoration={zigzag,segment length=6,amplitude=.4,post=lineto,post length=10}] (0,0)--(0,0.6);\n\t\t\\draw[fill,color=blue!20,decorate,decoration={zigzag,segment length=6,amplitude=.4,"
    },
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        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts,amssymb,stmaryrd}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{decorations.pathreplacing,calc,tikzmark}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5]\n\\draw (-1,-0.4) node {$(h_0^*)(\\frac{\\mathrm{H}^0_\\alpha(\\mathcal{O}_0) \\star \\mathfrak{h}^\\pm_\\alpha(\\mathcal{O}_0)}{\\mathfrak{h}^0_\\alpha(\\mathcal{O}_0)})$};\n\\draw (6,-0.4) node {$\\scriptstyle\\mathbb{P}^1$};\n\\draw (1.5,1.5) node {$t_1$};\n\\draw (4.5,1.5) node {$t_2$};\n\\draw (0,0) -- (5,0) node[pos=0.35,above] {$I$} node[pos=0.5,above] {$III$} node[pos=0.65,above] {$II$} node[pos=0.85,above] {$\\bar{II}$};\n\\draw[red] (1,1.5) -- (1,0) node[below] {$\\scriptstyle-\\frac{d}{2c}$} node[above] {$\\scriptstyle\\tau$};\n\\draw[red] (3,1.5) -- (3,0) node[below] {$\\scriptstyle-1$} node[above] {$\\scriptstyle\\tau\\to 0$};\n\\draw[red] (5,1.5) -- (5,0) node[below] {$\\scriptstyle-1+\\frac{d}{2c}$} node[above] {$\\scriptstyle\\tau\\to 0$};\n\\draw (2,0.5) node {$\\scriptstyle S=0$};\n\\draw (4,0.5) node {$\\scriptstyle S=0$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[tikz,border=3mm]{standalone}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.16}\n\\begin{document}\n\\begin{tikzpicture}[\n    declare function={\n        xmin=0;\n        xmax=8;\n        ymin=-1;\n        ymax=3;\n    }\n]\n    \\begin{axis}[\n        xmin=xmin,\n        xmax=xmax,\n        ymin=ymin,\n        ymax=ymax,\n        axis lines=middle,\n        axis equal image,\n        xlabel=$\\rho$,\n        ylabel=$\\beta$,\n        clip=false,\n    ]\n        \\draw[dotted] (0,1) -- (8,1);\n        \\node[below] at (0,1) {$\\rho=0$};\n        \\node[below] at (8,1) {$\\rho=1$};\n\n        \\addplot[only marks, mark=square*, mark size=3pt] coordinates {\n            (1,1) (1.5,0.7) (2.5,1.5) (2.25,1.25)\n        };\n        \\addplot[only marks, mark=square*, mark size=3pt] coordinates {\n            (5,0.5) (4,2.2) (6.25,1.25) (5.5,2)\n        };\n\n        \\draw[dashed] (1,1) -- (1,0);\n        \\draw[dashed] (5,0.5) -- (5,0);\n        \\node[below] at (1,0) {$\\rho=\\frac{1}{p-1}$};\n        \\node[below] at (5,0) {$\\rho=\\frac{1}{2}$};\n\n        \\addplot[domain=1:5]{0.3*x + 1};\n        \\addplot[only marks, mark=x, mark size=3pt] coordinates {\n            (3.75,2.25) (4.25,2.25) (3.75,2.75) (4.25,2.75)\n        };\n    \\end{axis}\n\\end{tikzpicture}\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[svgnames]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw [ultra thick] (-5,0) -- (5,0);\n\\fill (0,0) circle (3pt);\n\\node at (0,-.5) {$\\bar{c}_{i_1}$};\n\\fill (-3,-2) circle (3pt);\n\\node at (-3.2,-2.5) {$\\bar{c}_{i_2}$};\n\\fill (-1,-2) circle (3pt);\n\\node at (-1.2,-2.5) {$\\bar{c}_{i_3}$};\n\\fill (1,-2) circle (3pt);\n\\node at (1.2,-2.5) {$\\bar{c}_{i_4}$};\n\\fill (3,-2) circle (3pt);\n\\node at (3.2,-2.5) {$\\bar{c}_{i_5}$};\n\\fill (0,-4) circle (3pt);\n\\node at (0,-4.5) {$\\bar{c}_{i_6}$};\n\\draw [ultra thick] (-5,-5) -- (5,-5);\n\\node at (0,-5) {$\\bar{C}_{i_1}$};\n\\draw [ultra thick] (-5,-6) -- (5,-6);\n\\node at (0,-6) {$\\bar{C}_{i_2}$};\n\\draw [ultra thick] (-5,-7) -- (5,-7);\n\\node at (0,-7) {$\\bar{C}_{i_3}$};\n\\draw [ultra thick] (-5,-8) -- (5,-8);\n\\node at (0,-8) {$\\bar{C}_{i_4}$};\n\\draw [ultra thick] (-5,-9) -- (5,-9);\n\\node at (0,-9) {$\\bar{C}_{i_5}$};\n\\draw [ultra thick] (-3,-2) -- (-3,-4);\n\\node at (-3.5,-3) {$\\bar{C}_{i_6}$};\n\\draw [ultra thick] (-1,-2) -- (-1,-4);\n\\node at (-1.5,-3) {$\\bar{C}_{i_6}$};\n\\draw [ultra thick] (1,-2) -- (1,-4);\n\\node at (1.5,-3) {$\\bar{C}_{i_6}$};\n\\draw [ultra thick] (3,-2) -- (3,-4);\n\\node at (3.5,-3) {$\\bar{C}_{i_6}$};\n\\draw [ultra thick] (0,-4) -- (0,-6);\n\\draw [ultra thick] (0,-6) -- (0,-8);\n\\draw [ultra thick] (0,-8) -- (0,-10);\n\\draw [ultra thick] (0,-10) -- (0,-12);\n\\draw [ultra thick] (0,-4) -- (-1.5,-6);\n\\draw [ultra thick] (0,-6) -- (-1,-8);\n\\draw [ultra thick] (0,-8) -- (-0.5,-10);\n\\draw [ultra thick] (0,-10) -- (0.5,-12);\n\\draw [ultra thick] (0,-4) -- (1.5,-6);\n\\draw [ultra thick] (0,-6) -- (1,-8);\n\\draw [ultra thick] (0,-8) -- (1.5,-10);\n\\draw [ultra thick] (0,-10) -- (2.5,-12);\n\\draw [ultra thick] (0,-4) -- (3.5,-6);\n\\draw [ultra thick] (0,-6) -- (3,-8);\n\\draw [ultra thick] (0,-8) -- (3.5,-10);\n\\draw [ultra thick] (0,-10) -- (4.5,-12);\n\\node at (15,-5) {$\\cdots\\cdots$};\n\\node at (15,-7) {$\\cdots\\cdots$};\n\\draw [dotted] (-2,-4.5) -- (-2,1);\n\\draw [dashed] (2,-4.5) -- (2,1);\n\\draw [dotted] (-4,-6.5) -- (-4,1);\n\\draw [dashed] (4,-6.5) -- (4,1);\n\\node at (10,1) {$\\bar{G}=\\bar{S}^5$};\n\\draw [->] (10.5,1) -- (10.5,0);\n\\draw [dotted] (3,2) -- (3,1);\n\\draw [dashed] (1,2) -- (1,1);\n\\node at (1,2) {$\\bar{L}^{\\frac{1}{2}}(1)\\vee\\bar{L}^{\\frac{1}{3}}(1)$};\n\\draw [dashed] (-3,2) -- (-3,1);\n\\node at (-3,2) {$\\bar{L}^{\\frac{1}{2}}(1)\\vee\\bar{L}^{\\frac{1}{3}}(1)$};\n\\draw [dashed] (-1,2) -- (-1,1);\n\\node at (-1,2) {$\\bar{L}^{\\frac{1}{2}}(1)\\vee\\bar{L}^{\\frac{1}{3}}(1)$};\n\\draw [dashed] (1,2) -- (1,1);\n\\node at (1,2) {$\\bar{L}^{\\frac{1}{2}}(1)\\vee\\bar{L}^{\\frac{1}{3}}(1)$};\n\\draw [dashed] (3,2) -- (3,1);\n\\node at (3,2) {$\\bar{L}^{\\frac{1}{2}}(1)\\vee\\bar{L}^{\\frac{1}{3}}(1)$};\n\\draw [->] (10.5,0) -- (10.5,-5);\n\\node at (15,-1) {$\\bar{C}_{\\bar{G}}$};\n\\draw [->] (10.5,-5) -- (10.5,-6);\n\\node at (15,-6) {$\\bar{C}_{\\bar{G}}$};\n\\draw [->] (10.5,-6) -- (10.5,-7);\n\\node at (15,-7) {$\\bar{C}_{\\bar{G}}$};\n\\draw [<->] (15,-8.5) -- (15"
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        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{xcolor}\n\\usepackage{amssymb}\n\\usepackage[colorlinks=true,\nlinkcolor=blue,\nurlcolor=red,\ncitecolor=green]{hyperref}\n\\usepackage{pgf,tikz,pgfplots}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{patterns}\n\\pgfplotsset{compat=1.14}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n\t\t\t\t\\draw [color=black] (-3,0) node {$X_1$};\n\t\t\t\t\\draw [color=black] (2,0) node {$X_2$};\n\t\t\t\t\\draw[densely dotted,blue]  (1.5,0) ellipse (3cm and 2cm);\n\t\t\t\t\\draw[densely dotted,blue]  (1.5,0) ellipse (1cm and 1cm);\n\t\t\t\t\\draw[densely dotted,blue]  (-3,0) ellipse (4cm and 4cm);\n\t\t\t\t\\draw[densely dotted,blue]  (1.5,0) ellipse (1cm and 2cm);\n\t\t\t\t\\draw[densely dotted,blue]  (1.5,0) ellipse (2cm and 2cm);\n\t\t\t\t\\draw[densely dotted,blue]  (1.5,0) ellipse (3cm and 2cm);\n\t\t\t\t\n\t\t\t\t\\draw[dashed,red] (2,0) to (6,0);\n\t\t\t\t\n\t\t\t\t\\draw[color=black] (8.5,0) node {$\\bullet$};\n\t\t\t\t\\draw[color=black] (9.3,-0.5) node {Extremal cases, not belonging to the parameter space};\n\t\t\t\t\n\t\t\t\t\\draw[dashed,color=red] (5,0) to (9,0);\n\t\t\t\t\n\t\t\t\t\\draw[color=black] (10.5,0) node {$\\bullet$};\n\t\t\t\t\\draw[color=black] (11,0.5) node {Two flat bands};\n\t\t\t\t\n\t\t\t\t\\draw[color=black] (10.5,1.5) node {$\\bullet$};\n\t\t\t\t\\draw[color=black] (11,2) node {One flat band (Case$-$)};\n\t\t\t\t\n\t\t\t\t\\draw[color=black] (10.5,3) node {$\\bullet$};\n\t\t\t\t\\draw[color=black] (11,3.5) node {One flat band (Case$+$)};\n\t\t\t\t\n\t\t\t\t\\draw[color=black] (10.5,4.5) node {$\\bullet$};\n\t\t\t\t\\draw[color=black] (11,5) node {One flat band (Case$++$)};\n\t\t\t\t\n\t\t\t\t\\draw[color=black] (10.5,6) node {$\\bullet$};\n\t\t\t\t\\draw[color=black] (11,6.5) node {Monomerial edge weights:};\n\t\t\t\t\n\t\t\t\t\\draw[color=black] (10.5,7.5) node {$\\bullet$};\n\t\t\t\t\\draw[color=black] (11,8) node {One flat band (Case$--$)};\n\t\t\t\t\n\t\t\t\t\\draw[color=black] (10.5,9) node {$\\bullet$};\n\t\t\t\t\\draw[color=black] (11,9.5) node {One flat band (Case$-++$)};\n\t\t\t\t\n\t\t\t\t\n\t\t\t\t\\end{tikzpicture}\n\n\\end{document}"
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        "index": 598,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsthm,amssymb}\n\\usepackage[leqno]{amsmath}\n\\usepackage{tcolorbox}\n\\usepackage{epsfig,graphicx,graphics,color}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,arrows.meta,positioning,calc}\n\n\\newcommand{\\mbf}[1]{\\mathbf{#1}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.3,>=latex,shorten >=1.5pt, shorten <=1.5pt]\n    \\tikzset{\n      set node distance=2cm,>=latex,auto,\n      vertex/.style={circle,minimum size=20pt,draw=black},\n      othervertex/.style={circle,minimum size=20pt,draw=white,fill=white},\n      set/.style={draw=black,inner sep=3pt,fill=gray!20!white,minimum height=40pt},\n      set2/.style={draw=black,inner sep=3pt,fill=gray!75!white,minimum height=40pt},\n      otherset/.style={draw=black,inner sep=3pt,fill=gray!20!white,minimum height=25pt},\n      edge/.style={draw=black},\n    }\n    \n    \\begin{scope}[shift={(-0.3,0.85)}]\n    \\node at (0,-1.5) {$G$};\n    \\node at (-0.35,-1.85) {$H_1$};\n    \\node at (0.35,-1.85) {$H_2$};\n    \\draw[black,fill=white] (-1,-1.5) rectangle (0.4,1.5);\n    \\end{scope}\n    \n    \\begin{scope}\n    \\node[vertex] (1) at (-1,0) {$1$};\n    \\node[vertex] (2) at (-0.5,-0.65) {$2$};\n    \\node[vertex] (3) at (-0.5,0.65) {$3$};\n    \\node[vertex] (4) at (1,0) {$4$};\n    \\node[vertex] (5) at (1,-0.65) {$5$};\n    \\node[vertex] (6) at (1,0.65) {$6$};\n    \\node[otherset] at (0,0) {};\n    \\node[otherset] at (0,0.65) {};\n    \\node[otherset] at (0,-0.65) {};\n    \\node[otherset] at (0,-1) {};\n    \\node[otherset] at (0,1) {};\n    \\draw[edge] (1)--(2)--(3)--(4)--(5)--(6)--(3);\n    \\draw[edge] (1)--(4);\n    \\node at (0,-2) {$G_i$};\n    \\node at (0,-2.2) {is a joint of $G_i,H_i$};\n    \\node at (0.35,-2.5) {or};\n    \\node at (0.9,-2.5) {a decomposition of $TS(G_i)$};\n    \\end{scope}\n    \n    \\begin{scope}[shift={(3.5,0.4)}]\n    \\node[vertex] (1) at (-1,0) {$1$};\n    \\node[vertex] (2) at (-0.5,-0.65) {$2$};\n    \\node[vertex] (3) at (-0.5,0.65) {$3$};\n    \\node[vertex] (4) at (1,0) {$4$};\n    \\node[vertex] (5) at (1,-0.65) {$5$};\n    \\node[vertex] (6) at (1,0.65) {$6$};\n    \\node[otherset] at (0,0) {};\n    \\node[otherset] at (0,0.65) {};\n    \\node[otherset] at (0,-0.65) {};\n    \\node[otherset] at (0,-1) {};\n    \\node[otherset] at (0,1) {};\n    \\node[otherset] at (0,-1.5) {};\n    \\node[otherset] at (0,1.5) {};\n    \\node[otherset] at (0.25,-1.5) {};\n    \\node[otherset] at (0.25,1.5) {};\n    \\node[otherset] at (0.75,-1.5) {};\n    \\node[otherset] at (0.75,1.5) {};\n    \\draw[edge] (1)--(2)--(3)--(4)--(5)--(6)--(3);\n    \\draw[edge] (1)--(4);\n    \\node at (0,-1.5) {$TS(G_i)$};\n    \\node at (0,-1.7) {is $\\mbf{TS}(G_i)$};\n    \\node at (0.35,-1.5) {or};\n    \\node at (0.9,-1.5) {$\\mbf{TS}(G_i)\\cap\\mbf{TS}(G_i)$};\n    \\end{scope}\n    \n    \\begin{scope}[shift={(3.5,-0.5)}]\n    \\node[vertex] (1) at (-1,0) {$1$};\n    \\node[vertex] (2) at (-0.5,-0.65) {$2$};\n    \\node[vertex] (3) at (-0.5,0.65) {$3$};\n    \\node[vertex] (4) at (1,0) {$4$};\n    \\node[vertex] (5) at (1,-0.65) {$5$};\n    \\node[vertex] (6) at (1,0.65) {$6$};\n    \\node[otherset] at (0,0) {};\n    \\node[otherset] at (0,0.65) {};\n    \\node[otherset] at (0,-0.65) {};\n    \\node[otherset] at (0,-1) {};\n    \\node[otherset] at (0,1) {};\n    \\node[otherset] at (0,-1.5) {};\n    \\node[otherset] at (0,1.5) {};\n    \\node[otherset] at (0.25,-1.5) {};\n    \\node[otherset] at (0.25,1.5) {};\n    \\node[otherset] at (0.75,-1.5) {};\n    \\node["
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    {
        "index": 599,
        "tikz_code": "\\documentclass[10pt,journal,compsoc]{IEEEtran}\n\\usepackage{xcolor}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{pgfplots}\n\\usepackage{tikz}\n\\usepackage{color}\n\\usepackage{xcolor}\n\\usepackage{pgfplots}\n\\usepackage{pgfplotstable}\n\\usepackage{colortbl}\n\\pgfplotsset{compat=1.14}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\begin{axis}[\n        width=10cm,\n        height=4cm,\n        xmin=0,\n        xmax=1,\n        xtick={0, 0.25, 0.5, 0.75, 1},\n        xticklabels={$k_{b,*^{\\prime}}$, $\\bar{k}_A$, $k_B$, $\\bar{k}_A$, $k_{b,*^{\\prime}}$},\n        ymin=0,\n        ymax=0.6,\n        ytick={0, 0.2, 0.4},\n        legend pos=north west,\n        ymajorgrids=true,\n        grid style=dashed,\n    ]\n    \n    \\addplot[domain=0:1, ultra thick, blue] {(1-x)/(1-x-0.25+0.2)};\n    \\addplot[domain=0:0.25, ultra thick, red, dashed] {(1-x)/(1-x-0.25+0.2)};\n    \\addplot[domain=0.25:0.5, ultra thick, blue] {x/x+0.2};\n    \\addplot[domain=0.5:0.75, ultra thick, red, dashed] {x/x+0.2};\n    \\addplot[domain=0.75:1, ultra thick, blue] {(1-x)/(1-x-0.25+0.2)};\n    \n    \\addlegendentry{Case 1}\n    \\addlegendentry{Case 2}\n    \n    \\draw [decorate,decoration={brace,amplitude=8pt,mirror,raise=8pt},yshift=0pt]\n(0.31,0.05) -- (0.89,0.05) node [black,midway,yshift=-1.2cm] {\\footnotesize $\\mathcal{I}^{1}_{B,D}$};\n    \\end{axis}\n    \\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 600,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{fullpage,amsmath,amssymb,amsthm,enumerate,tikz,graphicx}\n\\usetikzlibrary{decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.75]\n\\filldraw (0,0) circle (0.075);\n\\filldraw (1,0) circle (0.075);\n\\filldraw (5,0) circle (0.075);\n\\filldraw (0.5,-0.5) circle (0.075);\n\\filldraw (5.5,-0.5) circle (0.075);\n\\filldraw (2.5,3.5) circle (0.075);\n\\filldraw (3.5,2.5) circle (0.075);\n\\filldraw (4.5,1.5) circle (0.075);\n\\draw (0,0) -- (1,0) -- (5,0) -- (5.5,-0.5) -- (4.5,1.5) -- (3.5,2.5) -- (2.5,3.5) -- (1,0);\n\\draw (0,0) -- (5,0);\n\\draw (0.5,-0.5) -- (3.5,2.5);\n\\draw[dashed, thick, blue] (0,0) -- (5.5,-0.5) -- (2.5,3.5) -- (0,0);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 601,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix,arrows,backgrounds,shapes.misc,shapes.geometric,patterns,calc,positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[point/.style={shape=circle,fill=black,scale=.3pt,outer sep=3pt},>=latex, baseline=-3,scale=2]  \n\\node[point,label={below:$1$}] (1) at (0,0) {} ; \n\\node[point,label={below:$2$}] (2) at (1,0) {} ; \n\\node[point,label={below:$3$}] (3) at (2,0) {} ; \n\\node[point,label={below:$4$}] (4) at (3,0) {} ; \n\\node[point,label={below:$5$}] (5) at (4,0) {} ; \n\\node[point,label={below:$6$}] (6) at (5,0) {} ; \n\\path[->] (1.30) edge node[above] {$+q$} (2.150) \n(2.-30) edge node[below] {$+q$} (1.-150) \n(3.30) edge node[above] {$-q$} (4.150) \n(4.-30) edge node[below] {$-q$} (3.-150) \n(5.30) edge node[above] {$+1$} (6.150) \n(6.-30) edge node[below] {$+1$} (5.-150) ; \n\\begin{scope}[yshift=-1.3cm]\n\\node[point,label={below:$1$}] (1') at (0,0) {} ; \n\\node[point,label={below:$2$}] (2') at (1,0) {} ; \n\\node[point,label={below:$3$}] (3') at (2,0) {} ; \n\\node[point,label={below:$4$}] (4') at (3,0) {} ; \n\\node[point,label={below:$5$}] (5') at (4,0) {} ; \n\\node[point,label={below:$6$}] (6') at (5,0) {} ; \n\\path[->] (1'.30) edge node[above] {$+q$} (2'.150) \n(2'.30) edge node[above] {$-q$} (3'.150) \n(3'.30) edge node[above] {$-q$} (4'.150) \n(4'.30) edge node[above] {$+1$} (5'.150) \n(5'.30) edge node[above] {$+1$} (6'.150) ; \n\\end{scope}\n\\begin{scope}[yshift=-2.6cm]\n\\node[point,label={below:$1$}] (1'') at (0,0) {} ; \n\\node[point,label={below:$2$}] (2'') at (1,0) {} ; \n\\node[point,label={below:$3$}] (3'') at (2,0) {} ; \n\\node[point,label={below:$4$}] (4'') at (3,0) {} ; \n\\node[point,label={below:$5$}] (5'') at (4,0) {} ; \n\\node[point,label={below:$6$}] (6'') at (5,0) {} ; \n\\path[->] (1''.30) edge node[above] {$+1$} (2''.150) \n(2''.30) edge node[above] {$+q$} (3''.150) \n(3''.30) edge node[above] {$+q$} (4''.150) \n(4''.30) edge node[above] {$+1$} (5''.150) \n(5''.30) edge node[above] {$+1$} (6''.150) ; \n\\end{scope}\n\\path[->] (1) edge node[above] {$\\sigma_1$} (1') (1) edge node[above] {$\\sigma_2$} (1'') (2) edge node[above] {$\\sigma_3$} (2') (2) edge node[above] {$\\sigma_4$} (2'') (3) edge node[above] {$\\sigma_5$} (3') (3) edge node[above] {$\\sigma_6$} (3'') (4) edge node[above] {$\\sigma_7$} (4') (4) edge node[above] {$\\sigma_8$} (4'') (5) edge node[above] {$\\sigma_9$} (5') (5) edge node[above] {$\\sigma_{10}$} (5'') (6) edge node[above] {$\\sigma_{11}$} (6') ; \n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[letterpaper]{amsart}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage[usenames,dvipsnames]{xcolor}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.45]\n\\filldraw[draw=black, fill=green!10] (0,0) rectangle (1,1);\n\\filldraw[draw=black, fill=green!10] (0,2) rectangle (1,3);\n\\filldraw[draw=black, fill=green!10] (2,0) rectangle (3,1);\n\\filldraw[draw=black, fill=green!10] (2,2) rectangle (3,3);\n\\filldraw[draw=black, fill=green!10] (4,0) rectangle (5,1);\n\\filldraw[draw=black, fill=green!10] (4,2) rectangle (5,3);\n\\filldraw[draw=black, fill=green!10] (6,0) rectangle (7,1);\n\\filldraw[draw=black, fill=green!10] (6,2) rectangle (7,3);\n\\filldraw[draw=black, fill=green!10] (8,0) rectangle (9,1);\n\\filldraw[draw=black, fill=green!10] (8,2) rectangle (9,3);\n\\filldraw[draw=black, fill=green!10] (10,0) rectangle (11,1);\n\\filldraw[draw=black, fill=green!10] (10,2) rectangle (11,3);\n\\filldraw[draw=black, fill=green!10] (12,0) rectangle (13,1);\n\\filldraw[draw=black, fill=green!10] (12,2) rectangle (13,3);\n\\filldraw[draw=black, fill=green!10] (14,0) rectangle (15,1);\n\\filldraw[draw=black, fill=green!10] (14,2) rectangle (15,3);\n\\filldraw[draw=black, fill=green!10] (16,0) rectangle (17,1);\n\\filldraw[draw=black, fill=green!10] (16,2) rectangle (17,3);\n\\filldraw[draw=black, fill=green!10] (18,0) rectangle (19,1);\n\\filldraw[draw=black, fill=green!10] (18,2) rectangle (19,3);\n\\filldraw[draw=black, fill=green!10] (20,0) rectangle (21,1);\n\\filldraw[draw=black, fill=green!10] (20,2) rectangle (21,3);\n\\filldraw[draw=black, fill=green!10] (22,0) rectangle (23,1);\n\\filldraw[draw=black, fill=green!10] (22,2) rectangle (23,3);\n\\filldraw[draw=black, fill=green!10] (24,0) rectangle (25,1);\n\\filldraw[draw=black, fill=green!10] (24,2) rectangle (25,3);\n\\draw[step=2cm] (-0.4,-0.4) grid (25.4,3.4);\n\\filldraw[draw=black, fill=blue!10, opacity=0.5] (2,2) -- (4,0) -- (6,2) -- (2,2);\n\\filldraw[draw=blue, fill=blue!10, opacity=0.5] (2,2) circle (0.1cm);\n\\filldraw[draw=blue, fill=blue!10, opacity=0.5] (6,2) circle (0.1cm);\n\\filldraw[draw=blue, fill=blue!10, opacity=0.5] (4,0) circle (0.1cm);\n\\filldraw[draw=blue, fill=blue!10, opacity=0.5] (2,0) circle (0.1cm);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 603,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage[ansinew]{inputenc}\n\\usepackage{amsmath,amssymb}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing,angles,quotes,calligraphy}\n\\usepackage{tikz-3dplot}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8]\n\t\n\t\n\t\\begin{scope}[shift={(0,0)}]\n\t\n\t\\draw[black,thick, fill=gray!20] (-5,0.2) to [out=315,in=225] (-4.5,0.2) to [out=45,in=135] (-3.5,0.2) to [out=45,in=180] (-2.5,0.2) to [out=0,in=225] (-1.5,0.2) to [out=45,in=135] (-1,0.2) to [out=45,in=135] (-0.5,0.2) to [out=45,in=180] (0.5,0.2) to [out=0,in=180] (1,0.2) to [out=0,in=135] (1.5,0.2) to [out=45,in=135] (2.5,0.2) to [out=45,in=315] (3,0.2) to [out=225,in=135] (3.5,0.2) to [out=45,in=225] (4.5,0.2) to [out=45,in=315] (5,0.2) to [out=135,in=45] (5.5,0.2) to [out=225,in=45] (6,0.2) to [out=225,in=45] (6.5,0.2) to [out=225,in=135] (7,0.2) to [out=315,in=135] (7.5,0.2) to [out=315,in=45] (8,0.2) to [out=135,in=315] (8.5,0.2) to [out=135,in=315] (9,0.2) to [out=135,in=315] (9.5,0.2) to [out=135,in=45] (10,0.2) to [out=225,in=315] (10.5,0.2) to [out=135,in=225] (11,0.2) to [out=135,in=225] (11.5,0.2) to [out=135,in=225] (12,0.2) to [out=135,in=225] (12.5,0.2) to [out=135,in=45] (13,0.2) to [out=315,in=45] (13.5,0.2);\n\t\n\t\\draw[black,thick, fill=white] (-5,0.2) to [out=315,in=225] (-4.5,0.2) to [out=45,in=135] (-3.5,0.2) to [out=45,in=180] (-2.5,0.2) to [out=0,in=225] (-1.5,0.2) to [out=45,in=135] (-1,0.2) to [out=45,in=135] (-0.5,0.2) to [out=45,in=180] (0.5,0.2) to [out=0,in=180] (1,0.2) to [out=0,in=135] (1.5,0.2) to [out=45,in=135] (2.5,0.2) to [out=45,in=315] (3,0.2) to [out=225,in=135] (3.5,0.2) to [out=45,in=225] (4.5,0.2) to [out=45,in=315] (5,0.2) to [out=135,in=45] (5.5,0.2) to [out=225,in=45] (6,0.2) to [out=225,in=45] (6.5,0.2) to [out=225,in=135] (7,0.2) to [out=315,in=135] (7.5,0.2) to [out=315,in=45] (8,0.2) to [out=135,in=315] (8.5,0.2) to [out=135,in=315] (9,0.2) to [out=135,in=315] (9.5,0.2) to [out=135,in=45] (10,0.2) to [out=225,in=315] (10.5,0.2) to [out=135,in=225] (11,0.2) to [out=135,in=225] (11.5,0.2) to [out=135,in=225] (12,0.2) to [out=135,in=225] (12.5,0.2) to [out=135,in=45] (13,0.2) to [out=315,in=45] (13.5,0.2);\n\t\n\t\\draw[black,thick] (1,0.2) to [out=0,in=135] (1.5,0.2);\n\t\\draw[black,thick] (4,0.2) to [out=0,in=135] (4.5,0.2);\n\t\\draw[black,thick] (7,0.2) to [out=0,in=135] (7.5,0.2);\n\t\\draw[black,thick] (10,0.2) to [out=0,in=135] (10.5,0.2);"
    },
    {
        "index": 604,
        "tikz_code": "\\documentclass[12pt,reqno]{amsart}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usetikzlibrary{arrows,decorations.markings, matrix}\n\\usepackage[bookmarks=true, bookmarksopen=true,%\nbookmarksdepth=3,bookmarksopenlevel=2,%\ncolorlinks=true,%\nlinkcolor=blue,%\ncitecolor=blue,%\nfilecolor=blue,%\nmenucolor=blue,%\nurlcolor=blue]{hyperref}\n\\usetikzlibrary{decorations.pathreplacing}\n\n\\newcommand{\\exp}{\\operatorname{exp}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale = .7]\n      \\tikzset{->-/.style={decoration={ markings,\n        mark=at position #1 with {\\arrow[scale=1.5,>=stealth]{>}}},postaction={decorate}}}\n         \\tikzset{-<-/.style={decoration={ markings,\n        mark=at position #1 with {\\arrow[scale=1.5,>=stealth]{<}}},postaction={decorate}}}\n         \\draw[black,thick,fill=red!30,opacity=.5] (0,0) circle (1.5);\n         \\draw[black,thick,fill=red!30,opacity=.5] (3,3) circle (1.5);\n         \\node (l1) at (-.7,.7) {$\\bullet$};\n         \\node (l2) at (2.5,1.5) {$\\bullet$};\n         \\draw [black,thick,->-=.7,domain=0:10] plot ({cos(\\x)}, {sin(\\x)});\n         \\node at (1.7,2.2) {$\\theta$};\n         \\node at (-.2,.7) {$0$};\n         \\node at (2.5,1.5) {$\\varepsilon$};\n         \\node at (-1.1,4) {$T_{\\exp,0}M$};\n         \\node at (4.1,1.8) {$T_{\\exp,0}M$};\n         \\draw[dashed,black,thick,opacity=.5] (0.2,-.2) rectangle (2.8,2.8);\n         \\draw[black,opacity=0.5] (0.2,-.2) -- (2.8,-.2);\n         \\draw[black,opacity=0.5] (0.2,-.2) -- (0.2,2.8);\n         \\draw[black,opacity=0.5] (2.8,-.2) -- (2.8,2.8);\n         \\draw[black,opacity=0.5] (0.2,2.8) -- (2.8,2.8);\n         \\node at (1.5,-.7) {$\\psi_{\\exp,0}$};\n         \\node at (3.4,1.2) {$\\psi_{\\exp,0}$};\n         \\draw[black,thick,->-=.5] (2,1)--(3,1);\n         \\node at (2.2,1.2) {$\\overrightarrow{y}$};\n         \\draw[black,thick,->-=.5] (3.5,3)--(4.5,3);\n         \\node at (4.4,3.5) {$\\overrightarrow{y}$};\n         \\draw[black,thick,fill=red!30,opacity=.5] (7,0) circle (1.5);\n         \\draw[black,thick,fill=red!30,opacity=.5] (10,3) circle (1.5);\n         \\node (l1) at (6.7,.7) {$\\bullet$};\n         \\node (l2) at (10.5,1.5) {$\\bullet$};\n         \\draw [black,thick,->-=.7,domain=0:10] plot ({6+cos(\\x)}, {1+sin(\\x)});\n         \\node at (9.3,.7) {$\\bullet$};\n         \\node at (9.6,1.5) {$\\bullet$};\n         \\node at (6.2,.7) {$\\bullet$};\n         \\node at (9.8,1.5) {$\\bullet$};\n         \\node at (7.2,2.2) {$\\theta$};\n         \\node at (6.5,-.7) {$\\psi_{\\exp,0}$};\n         \\node at (10.5,1.8) {$\\psi_{\\exp,0}$};\n         \\draw[dashed,black,thick,opacity=.5] (6.2,-.2) rectangle (10.8,2.8);\n         \\draw[black,opacity=0.5] (6.2,-.2) -- (10.8,-.2);\n         \\draw[black,opacity=0.5] (6.2,-.2) -- (6.2,2.8);\n         \\draw[black,opacity=0.5] (10.8,-.2) -- (10.8,2.8);\n         \\draw[black,opacity=0.5] (6.2,2.8) -- (10.8,2.8);\n         \\node at (9.5,-.7) {$\\psi_{\\exp,-r}$};\n         \\node at (11.4,1.2) {$\\psi_{\\exp,-r}$};\n         \\node at (5.5,-3) {$M$};\n         \\node at (9.5,-3) {$M$};\n         \\node at (3.5,-3) {$T_{\\exp,0}$};\n         \\node at (7.5,-3) {$T_{\\exp,0}$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 605,
        "tikz_code": "\\documentclass{article}\n\\usepackage[table]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{fit}\n\n\\definecolor{color1}{HTML}{FF6666}\n\\definecolor{color2}{HTML}{66B3FF}\n\\definecolor{color3}{HTML}{66A6FF}\n\\definecolor{color4}{HTML}{FFB366}\n\n\\begin{document}\n    \\begin{tikzpicture}\n\\coordinate (top) at (0,3);\n\\node[draw,fit={(top) (current bounding box.north)},inner sep=0,outer sep=0,\n    label={[font=\\sffamily]below:West},label={[font=\\sffamily,color=color1]above:+},\n    fill=color1] {};\n\\node[draw,fit={(top) (current bounding box.north)},inner sep=0,outer sep=0,\n    label={[font=\\sffamily,color=color2]below:South},label={[font=\\sffamily]above:+},\n    fill=color2] {};\n\\node[draw,fit={(top) (current bounding box.north)},inner sep=0,outer sep=0,\n    label={[font=\\sffamily]below:East},label={[font=\\sffamily,color=color3]above:-},\n    fill=color3] {};\n\\node[draw,fit={(top) (current bounding box.north)},inner sep=0,outer sep=0,\n    label={[font=\\sffamily,color=color4]below:North},label={[font=\\sffamily]above:-},\n    fill=color4] {};\n\\end{tikzpicture}\n\\end{document}"
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    {
        "index": 606,
        "tikz_code": "\\documentclass[11pt,leqno]{article}\n\\usepackage{amsthm,amsfonts,amssymb,amsmath,oldgerm}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usetikzlibrary{arrows.meta}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n  \t\t\\begin{scope}[scale=1.25, rotate=270]\n  \t\t\t\\draw[->] (-3,0) -- (3,0);\n  \t\t\t\\draw[->] (0,-3) -- (0,3);\n  \t\t\t\n  \t\t\t\\draw (1.2,0.3) node {Re};\n  \t\t\t\\draw (0.3,1.2) node {Im};\n  \t\t\t\n  \t\t\t\\draw (2,0) node[above] {$\\mathbb{C}$};\n  \t\t\t\n  \t\t\t\\draw (2.5,-2.5) node[below right] {$\\mathbb{R}$};\n  \t\t\t\n  \t\t\t\\draw[domain=1:2,samples=200,thick, smooth] plot (\\x, {0});\n  \t\t\t\\draw[domain=0:2,samples=200,thick, smooth] plot (\\x, {-0.25*(\\x-1)*(\\x-1)});\n  \t\t\t\\draw[domain=-2:-1,samples=200,thick, smooth] plot (\\x, {-0.25*(\\x+1)*(\\x+1)});\n  \t\t\t\\draw[domain=-2:0,samples=200,thick, smooth] plot (\\x, {0});\n  \t\t\t\n  \t\t\t\\foreach \\i in {1,2}{\n  \t\t\t\t\\draw[dotted] (0,0) -- (\\i,0);\n  \t\t\t\t\\draw[dotted] (0,0) -- (0,\\i);\n  \t\t\t}\n  \t\t\t\n  \t\t\t\\draw (0,0) node[below left] {$0$};\n  \t\t\t\\draw[dashed] (0,0) circle (1);\n  \t\t\t\\draw (0,0) circle (2);\n  \t\t\\end{scope}\n  \t\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 607,
        "tikz_code": "\\documentclass[12pt,reqno]{amsart}\n\\usepackage{amsthm,amsfonts,amssymb,epsfig,graphics,amsmath,epstopdf,color}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{axis}[width=8cm, height=8cm, xmin=-1, xmax = 0, ymin=-2, ymax = 2, axis lines = middle, ticks=none]\n\t\\addplot[samples=100, domain=-1:0, color=blue]{(1/x)};\n\t\\addplot[samples=100, domain=0:1, color=red]{(1/(x^2))+(1/(2*x))};\n\t\\addplot[samples=50, domain=1:2, color=red]{(-2/(x^2))+(4/(3*x))};\n\t\\draw[thick, color = purple] (axis cs: 0, 0) -- (axis cs: 0, -3);\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 608,
        "tikz_code": "\\documentclass[table]{amsart}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz-cd}\n\\usepackage{tkz-graph}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7, every node/.style={scale=0.7}]\n\t\\node at (2.5,0) {$T_{2}$};\n\t\\node at (5,0) {$T_{3}$};\n\t\\node at (7.5,0) {$T_{4}$};\n\t\\node at (10,0) {$T_{5}$};\n\t\\node at (12.5,0) {$T_{6}$};\n\t\\node at (15,0) {$T_{7}$};\n\t\\node at (2.5,-1.5) {$S_{1}$};\n\t\\node at (5,-1.5) {$S_{2}$};\n\t\\node at (7.5,-1.5) {$S_{3}$};\n\t\\node at (10,-1.5) {$S_{4}$};\n\t\\node at (12.5,-1.5) {$S_{5}$};\n\t\\node at (15,-1.5) {$S_{6}$};\n\t\\node at (2.5,-3) {$R_{1}$};\n\t\\node at (5,-3) {$R_{2}$};\n\t\\node at (7.5,-3) {$R_{3}$};\n\t\\node at (10,-3) {$R_{4}$};\n\t\\node at (12.5,-3) {$R_{5}$};\n\t\\node at (15,-3) {$R_{6}$};\n\t\\node at (2.5,-4.5) {$S_{1}$};\n\t\\node at (5,-4.5) {$S_{2}$};\n\t\\node at (7.5,-4.5) {$S_{3}$};\n\t\\node at (10,-4.5) {$S_{4}$};\n\t\\node at (12.5,-4.5) {$S_{5}$};\n\t\\node at (15,-4.5) {$S_{6}$};\n\t\\node at (2.5,-6) {$R_{1}$};\n\t\\node at (5,-6) {$R_{2}$};\n\t\\node at (7.5,-6) {$R_{3}$};\n\t\\node at (10,-6) {$R_{4}$};\n\t\\node at (12.5,-6) {$R_{5}$};\n\t\\node at (15,-6) {$R_{6}$};\n\t\\node at (2.5,-7.5) {$S_{1}$};\n\t\\node at (5,-7.5) {$S_{2}$};\n\t\\node at (7.5,-7.5) {$S_{3}$};\n\t\\node at (10,-7.5) {$S_{4}$};\n\t\\node at (12.5,-7.5) {$S_{5}$};\n\t\\node at (15,-7.5) {$S_{6}$};\n\t\\node at (2.5,-9) {$R_{1}$};\n\t\\node at (5,-9) {$R_{2}$};\n\t\\node at (7.5,-9) {$R_{3}$};\n\t\\node at (10,-9) {$R_{4}$};\n\t\\node at (12.5,-9) {$R_{5}$};\n\t\\node at (15,-9) {$R_{6}$};\n\t\\node at (2.5,-10.5) {$S_{1}$};\n\t\\node at (5,-10.5) {$S_{2}$};\n\t\\node at (7.5,-10.5) {$S_{3}$};\n\t\\node at (10,-10.5) {$S_{4}$};\n\t\\node at (12.5,-10.5) {$S_{5}$};\n\t\\node at (15,-10.5) {$S_{6}$};\n\t\\node at (2.5,-12) {$R_{1}$};\n\t\\node at (5,-12) {$R_{2}$};\n\t\\node at (7.5,-12) {$R_{3}$};\n\t\\node at (10,-12) {$R_{4}$};\n\t\\node at (12.5,-12) {$R_{5}$};\n\t\\node at (15,-12) {$R_{6}$};\n\t\\node at (2.5,-13.5) {$S_{1}$};\n\t\\node at (5,-13.5) {$S_{2}$};\n\t\\node at (7.5,-13.5) {$S_{3}$};\n\t\\node at (10,-13.5) {$S_{4}$};\n\t\\node at (12.5,-13.5) {$S_{5}$};\n\t\\node at (15,-13.5) {$S_{6}$};\n\t\\node at (2.5,-15) {$R_{1}$};\n\t\\node at (5,-15) {$R_{2}$};\n\t\\node at (7.5,-15) {$R_{3}$};\n\t\\node at (10,-15) {$R_{4}$};\n\t\\node at (12.5,-15) {$R_{5}$};\n\t\\node at (15,-15) {$R_{6}$};\n\t\n\t\\tikzset{\n\t\tVertexStyle/.style = {shape = circle, draw, \n\t\t\tinner sep = 1pt, outer sep = 1ex, minimum size = 0.15cm,\n\t\t\tfill = gray},\n\t\tEdge/.style = {-,>=latex}}\n\t\t\\SetGraphUnit{1.25} \n\t\t\\Vertex[L=\\scriptsize{$\\tiny\\Gamma$}]{T1}\n\t\t\\EA[L=\\scriptsize{$\\tiny\\Delta$}](T1){T2}\n\t\t\\NOEA[L=\\scriptsize{$\\tiny\\Gamma$}](T2){T3}\n\t\t\\EA[L=\\scriptsize{$\\tiny\\Delta$}](T3){T4}\n\t\t\\NOEA[L=\\scriptsize{$\\tiny\\Delta$}](T4){T5}\n\t\t\\NOEA[L=\\scriptsize{$\\tiny\\Delta$}](T5){T6}\n\t\t\\EA[L=\\scriptsize{$\\tiny\\Gamma$}](T6){T7}\n\t\t\n\t\t\\SetGraphUnit{1.1}"
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        "tikz_code": "\\documentclass[11pt,twocolumn]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[usenames,dvipsnames,svgnames,table]{xcolor}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{shapes}\n\\usetikzlibrary{shapes.misc}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{positioning}\n\\usepackage{tikz-3dplot}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.12}\n\\usepgfplotslibrary{fillbetween}\n\\usetikzlibrary{patterns}\n\\usepackage{colortbl}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{intersections}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usepackage[pagebackref=true,breaklinks=true,colorlinks,bookmarks=false]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.75]\n\n\n\\fill[red!30!white] (0,0) rectangle (1,3);\n\\fill[blue!30!white] (1,0) rectangle (2,3);\n\\fill[red!30!white] (2,0) rectangle (3,3);\n\\fill[blue!30!white] (3,0) rectangle (4,3);\n\\fill[red!30!white] (4,0) rectangle (5,3);\n\\fill[blue!30!white] (5,0) rectangle (6,3);\n\\fill[red!30!white] (6,0) rectangle (7,3);\n\\fill[blue!30!white] (7,0) rectangle (8,3);\n\\fill[red!30!white] (8,0) rectangle (9,3);\n\n\\draw[fill=blue!20!white,draw=none] (0,1) rectangle (1,2);\n\\draw[fill=red!20!white,draw=none] (0,2) rectangle (1,3);\n\n\\draw[fill=blue!20!white,draw=none] (1,1) rectangle (2,2);\n\\draw[fill=red!20!white,draw=none] (1,2) rectangle (2,3);\n\n\\draw[fill=blue!20!white,draw=none] (2,1) rectangle (3,2);\n\\draw[fill=red!20!white,draw=none] (2,2) rectangle (3,3);\n\n\\draw[fill=blue!20!white,draw=none] (3,1) rectangle (4,2);\n\\draw[fill=red!20!white,draw=none] (3,2) rectangle (4,3);\n\n\\draw[fill=blue!20!white,draw=none] (4,1) rectangle (5,2);\n\\draw[fill=red!20!white,draw=none] (4,2) rectangle (5,3);\n\n\\draw[fill=blue!20!white,draw=none] (5,1) rectangle (6,2);\n\\draw[fill=red!20!white,draw=none] (5,2) rectangle (6,3);\n\n\\draw[fill=blue!20!white,draw=none] (6,1) rectangle (7,2);\n\\draw[fill=red!20!white,draw=none] (6,2) rectangle (7,3);\n\n\\draw[fill=blue!20!white,draw=none] (7,1) rectangle (8,2);\n\\draw[fill=red!20!white,draw=none] (7,2) rectangle (8,3);\n\n\\draw[fill=blue!20!white,draw=none] (8,1) rectangle (9,2);\n\\draw[fill=red!20!white,draw=none] (8,2) rectangle (9,3);\n\n\\node at (1,3.5) {$u$};\n\\draw[thick,->] (1.75,3.5) -- (1.75,3);\n\\draw[thick,->] (2.5,3.5) -- (2.5,3);\n\n\\node at (2,3.5) {$j$};\n\\draw[fill=blue!30!white,draw=none] (2.5,4) rectangle (3.5,3);\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[a4paper]{amsart}\n\\usepackage{amssymb, amsfonts, amsmath, amsthm, graphicx, bm, tikz, enumerate}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.5]\n\\draw (-1,-1) node [below] {$(0,0)$};\n\\draw (-1,0)--(3,0);\n\\draw (0,0)--(0,3);\n\\draw [dashed] (0,3)--(0,5);\n\\draw [dashed] (3,0)--(5,0);\n\n\\draw [fill] (0,5) circle [radius=0.05];\n\\draw (-0.4, 5) node [below] {$(0,t)$};\n\\draw [fill] (3,0) circle [radius=0.05];\n\\draw (3, 0) node [below] {$t$};\n\n\\draw (-0.1,-0.1) node [below] {$0$};\n\n\\draw [thick, dashed] (0,0)--(0,1)--(0.5,1.5);\n\\draw [thick] (0,1)--(1.5,2.5)--(2,3)--(2.5,3.5)--(3,4);\n\n\\draw (1.5, 2.5) node [above] {$M=(x_1,s)$};\n\\draw (2, 3) node [below] {$N=(x_2,t)$};\n\n\\draw (2.5,3.5) node [right] {$\\gamma(s)$};\n\\draw (3,4) node [above] {$\\gamma(t)$};\n\\draw [fill] (3, 4) circle [radius=0.1];\n\n\\draw [fill] (0, 1) circle [radius=0.1];\n\\draw (0,1) node [right] {$\\gamma(1)=x_1=2s$};\n\n\\draw [fill] (3,3) circle [radius=0.1];\n\\draw (3, 3) node [right] {$\\gamma(2)=x_2=2t$};\n\n\\draw [thick] (6,6)--(7,6)--(7,7)--(8,7)--(8,8)--(9,8);\n\\draw (7.5, 7.5) node [right] {$x=x_1x_2^{-1}\\frac{s}{dt}=2A\\frac{x_1}{s}dt$};\n\n\\draw (8.5, 8.5) node [above] {$x_1=t$};\n\\draw (9.5, 8.5) node [above] {$x_2=s$};\n\\draw [fill] (8, 8) circle [radius=0.05];\n\\draw [fill] (9, 8) circle [radius=0.05];\n\\draw [fill] (8, 7) circle [radius=0.05];\n\n\\draw (6, 6) node [left] {$E_1=f_1=x_1^{-1}\\frac{t}{s}ds$};\n\\draw (7, 7) node [left] {$E_2=f_2=x_2^{-1}\\frac{s}{t}ds$};\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amssymb,amsmath,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes.geometric,calc}\n\\usetikzlibrary{shapes,arrows,chains}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{shapes.multipart}\n\\tikzset{snake it/.style={decorate, decoration=snake}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n\n\\draw[line width=0.01cm] (-4,0) -- (8,0);\n\n\\draw[line width=0.01cm] (1,-3) -- (1,2);\n\\draw[line width=0.01cm] (3,-3) -- (3,1);\n\n\\node at (0,0) [circle,draw=black,fill=black,scale=0.5] {};\n\\node at (1,0) [circle,draw=black,fill=black,scale=0.5] {};\n\\node at (3,0) [circle,draw=black,fill=black,scale=0.5] {};\n\n\\node at (-1,0) {$v_{i-2}$};\n\\node at (2,0) {$v_{i-1}$};\n\\node at (4,0) {$v_{i}$};\n\n\n\\node at (1,-1) [circle,draw=black,fill=black,scale=0.5] {};\n\\node at (2,-1) {$v_{i+1}$};\n\\node at (3,1) [circle,draw=black,fill=black,scale=0.5] {};\n\\node at (4,1) {$v_{i+2}$};\n\n\n\n\\draw[line width=0.5cm,black] (1,0) -- (3,0);\n\\draw[line width=0.5cm,black] (1,0) -- (3,1);\n\\draw[line width=0.5cm,black] (1,0) -- (3,-3);\n\n\\draw[line width=0.5cm,black] (1,0) -- (-3,0);\n\\draw[line width=0.5cm,black] (1,0) -- (5,2);\n\\draw[line width=0.5cm,black] (1,0) -- (5,-3);\n\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath, amssymb, amsthm}\n\\usepackage{pgfplots}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[thick, smooth, domain = 0: 0.5, scale = 3.5]\n\\draw[->] (-0.1, 0) -- (1.1, 0);\n\\draw[->] (0, -0.1) -- (0, 1.1);\n\\draw[color = blue] plot (\\x, {exp(3 * \\x) - 2});\n\\draw[color = blue] (0.5, 0) node [below] {$\\lambda_*$};\n\\draw (0.5, -0.02) -- (0.5, 0.02);\n\\draw[very thick] (0, 0) -- (0.5, 0) node [below] {$\\lambda$};\n\\draw[very thick] (0.5, 0) -- (1, 0);\n\\draw (0, 0.02) -- (0, -0.02) node [below] {$0$};\n\\draw (0, 1) -- (-0.05, 1) node [left] {$1$};\n\\draw (0, -0.05) -- (0, -0.02) node [left] {$-1$};\n\\draw (1, -0.05) -- (1, -0.02) node [below] {$1$};\n\\draw (0.5, 0.02) -- (0.5, -0.02) node [below] {$\\lambda_*^{\\star}$};\n\\draw (-0.05, 0) node [left] {$-0.5$};\n\\draw (0.5, 0.5) node [right] {$q(v)$};\n\\draw (0.5, 0) node [below] {$\\lambda_*$};\n\\draw (0.5, 0) node [above] {$\\bar{v}$};\n\\draw (1, 0) node [above] {$v$};\n\\draw (1, 0) -- (1, -0.02);\n\\draw (0, 1) -- (-0.02, 1);\n\\draw (-0.02, 1) node [left] {$1$};\n\\draw (1, 0) -- (1, -0.02) node [below] {$\\lambda_*$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\n\\newcommand{\\xvec}{\\mathbf{x}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.5,transform shape,\ncirc/.style={draw,circle,minimum size=10pt,inner sep=0pt,fill=white}]\n\n\\foreach \\j in {1,...,4} {\n\\node at (-10.5,11.2*\\j-2.25) {$a_{\\j}$};\n\\node at (-9.5,11.2*\\j-2.25) {$a_{\\j}$};\n\\node at (-8.5,11.2*\\j-2.25) {$a_{\\j}$};\n\\node at (-7.5,11.2*\\j-2.25) {$a_{\\j}$};\n\\node at (-6.5,11.2*\\j-2.25) {$a_{\\j}$};\n}\n\\foreach \\j in {1,...,4} {\n\\node at (-9.5,11.2*\\j-2.25) {$\\hat{a}_{\\j}$};\n\\node at (-8.5,11.2*\\j-2.25) {$\\hat{a}_{\\j}$};\n\\node at (-7.5,11.2*\\j-2.25) {$\\hat{a}_{\\j}$};\n\\node at (-6.5,11.2*\\j-2.25) {$\\hat{a}_{\\j}$};\n}\n\n\\foreach \\i in {1,2,3} {\n\\node (z\\i) at (2*\\i-9,11) {};\n\\draw (z\\i) circle (4pt);\n\\foreach \\j in {1,...,4} {\n\\node (w\\i\\j) at (2*\\i-9,11.2*\\j-2.25) {};\n\\draw (w\\i\\j) circle (4pt);\n}\n\\foreach \\j in {1,...,4} {\n\\draw[->,densely dotted] (w\\i\\j) -- (z\\i);\n}\n}\n\\draw[->,densely dotted] (z1) -- (z2);\n\\draw[->,densely dotted] (z2) -- (z3);\n\\draw[->,densely dotted] (z3) -- (z1);\n\n\\draw[->,densely dotted] (w22) -- (z2);\n\\draw[->,densely dotted] (w23) -- (z3);\n\\draw[->,densely dotted] (w21) -- (z1);\n\\draw[->,densely dotted] (w32) -- (z2);\n\\draw[->,densely dotted] (w33) -- (z3);\n\\draw[->,densely dotted] (w31) -- (z1);\n\n\\node at (-10.5,5.2) {$\\xvec$};\n\\node at (-9.5,5.2) {$\\xvec$};\n\\node at (-8.5,5.2) {$\\xvec$};\n\\node at (-7.5,5.2) {$\\xvec$};\n\\node at (-6.5,5.2) {$\\xvec$};\n\n\\node at (-10.5,13.7) {$K$};\n\\node at (-9.5,13.7) {$K$};\n\\node at (-8.5,13.7) {$K$};\n\\node at (-7.5,13.7) {$K$};\n\\node at (-6.5,13.7) {$K$};\n\n\\node (F) at (2*1-9,15) {};\n\\node (G) at (2*3-9,15) {};\n\\node at ($(F)!.5!(G)+(-3,0)$) {$F=K\\cup S$};\n\\draw[densely dotted] ($(F)+(0,1)$) rectangle ($(G)+(0,2)$);\n\n\\node at (-10.5,-1) {$K$};\n\\node at (-9.5,-1) {$K$};\n\\node at (-8.5,-1) {$K$};\n\\node at (-7.5,-1) {$K$};\n\\node at (-6.5,-1) {$K$};\n\n\\node (F) at (2*1-9,-1) {};\n\\node (G) at (2*3-9,-1) {};\n\\node at ($(F)!.5!(G)+(-3,0)$) {$G$};\n\\draw[densely dotted] ($(F)+(0,-1)$) rectangle ($(G)+(0,1)$);\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 620,
        "tikz_code": "\\documentclass[10pt]{article}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n    node distance = 1.5cm and 1cm,\n      start chain = going below,\n disc/.style = {shape=circle, draw, minimum size=7mm},\n  alg/.style = {shape=rectangle, rounded corners, draw, minimum width=5.5cm, minimum height=3.5mm, inner xsep=5mm},\nalgr/.style = {alg, minimum width=4.5cm, text width=4.5cm, align=center},\nalgs/.style = {algr, minimum width=5.5cm, text width=5.5cm, align=center},\n                    ]\n  \\node[alg] (1)  {$1 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{0}^{\\mathbb{C}}$};\n  \\node[algr] (2)  {$2 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{1}^{\\mathbb{C}}$};\n  \\node[alg] (3)  {$3 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{2}^{\\mathbb{C}}$};\n  \\node[algr] (4)  {$4 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{3}^{\\mathbb{C}}$};\n  \\node[alg] (5)  {$5 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{4}^{\\mathbb{C}}$};\n  \\node[alg] (6)  {$6 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{5}^{\\mathbb{C}}$};\n  \\node[algr] (7)  {$7 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{6}^{\\mathbb{C}}$};\n  \\node[alg] (8)  {$8 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{7}^{\\mathbb{C}}$};\n  \\node[alg] (9)  {$9 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{8}^{\\mathbb{C}}$};\n  \\node[alg] (10) {$10 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{9}^{\\mathbb{C}}$};\n  \\node[alg] (11) {$11 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{10}^{\\mathbb{C}}$};\n  \\node[algr] (12) {$12 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{11}^{\\mathbb{C}}$};\n  \\node[algr] (13) {$13 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{12}^{\\mathbb{C}}$};\n  \\node[alg] (14) {$14 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{13}^{\\mathbb{C}}$};\n  \\node[alg] (15) {$15 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{14}^{\\mathbb{C}}$};\n  \\node[alg] (16) {$16 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{15}^{\\mathbb{C}}$};\n  \\node[algr] (17) {$17 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{16}^{\\mathbb{C}}$};\n  \\node[alg] (18) {$18 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{17}^{\\mathbb{C}}$};\n  \\node[algr] (19) {$19 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{18}^{\\mathbb{C}}$};\n  \\node[alg] (20) {$20 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{19}^{\\mathbb{C}}$};\n  \\node[algr] (21) {$21 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{20}^{\\mathbb{C}}$};\n  \\node[algr] (22) {$22 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{21}^{\\mathbb{C}}$};\n  \\node[alg] (23) {$23 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{22}^{\\mathbb{C}}$};\n  \\node[algr] (24) {$24 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{23}^{\\mathbb{C}}$};\n  \\node[alg] (25) {$25 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{24}^{\\mathbb{C}}$};\n  \\node[algr] (26) {$26 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{25}^{\\mathbb{C}}$};\n  \\node[alg] (27) {$27 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{26}^{\\mathbb{C}}$};\n  \\node[alg] (28) {$28 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{27}^{\\mathbb{C}}$};\n  \\node[algr] (29) {$29 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{28}^{\\mathbb{C}}$};\n  \\node[algr] (30) {$30 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{29}^{\\mathbb{C}}$};\n  \\node[algr] (31) {$31 \\preceq_{[\\mathbb{C},\\mathbb{C}]} \\mathfrak{S}_{30}^{\\mathbb{C}}$};\n%\n  \\begin{scope}[every node/.style={on chain, join=by -latex}]\n    \\node[alg, above right=of 6.west] (32) {$32 \\preceq_{[\\"
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    {
        "index": 621,
        "tikz_code": "\\documentclass[letterpaper,11pt]{article}\n\\usepackage{amsmath,amssymb, amsthm, dsfont}\n\\usepackage{tikz,color,pbox}\n\\usetikzlibrary{shapes,arrows}\n\\usetikzlibrary{calc}\n\\usepackage{pgfplots}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{intersections, calc}\n\\usepackage{pgfplots}\n\\usepackage{pgfplotstable}\n\\usepackage{tikz}\n\\usetikzlibrary{intersections, calc}\n\\usetikzlibrary{patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=3]\n    \\begin{axis}[\n        xlabel=\\LARGE $\\rho_i$,\n        ylabel=\\LARGE $\\gamma$,\n        ytick=\\empty,\n        xtick=\\empty,\n        ymax=0.4,\n        xmax=1,\n        axis lines = left,\n        xmin=0,\n        ymin=0,\n        width=5cm,\n        height=5cm,\n        clip=false\n    ]\n    \\draw[->,>=latex,line width=0.01mm](0,0) to (1,0);\n    \\draw[->,>=latex,line width=0.01mm](0,0) to (0,0.5);\n    \\node[align=left,text width=0.4cm] (right-1) at (1,0.15) {exotic};\n    \\node[align=left,text width=0.4cm] (right-1) at (1,0.3) {tensor-triangular exotic};\n    \\node[align=left,text width=0.4cm] (right-1) at (1,0.45) {possibly-rigid};\n    \\node[align=left,text width=0.4cm] (right-1) at (1,0.6) {rigid};\n    \\node[align=left,text width=0.4cm] (right-1) at (0.1,0.1) {2.0};\n    \\draw[fill=green!30,line width=0.01mm] (0,0.2) to [out=90,in=180] (0.1,0.37) to [out=0,in=150] (1,0.4);\n    \\draw[fill=blue!30,line width=0.01mm] (0,0) to [out=90,in=180] (0.1,0.3) to [out=0,in=150] (1,0.37);\n    \\draw[fill=orange!30,line width=0.01mm] (0,0) to [out=90,in=180] (0.1,0.25) to [out=0,in=150] (1,0.3);\n    \\draw[fill=red!30,line width=0.01mm] (0,0.2) to [out=90,in=180] (0.1,0.32) to [out=0,in=150] (1,0.37);\n    \\draw[fill=purple!30,line width=0.01mm] (0,0.2) to [out=90,in=180] (0.1,0.28) to [out=0,in=150] (1,0.3);\n    \\end{axis}\n    \\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 622,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amsfonts,bm}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{colortbl}\n\\usepackage{tikz}\n\\usetikzlibrary{fit}\n\\usetikzlibrary{calc,shapes}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n        \\node[inner sep=0pt] (russell) at (0,0)\n            {\\includegraphics[trim=260 90 330 100,clip,height=3.5cm]{example-image}};\n        \\node[inner sep=0pt] (whitehead) at (5.5,0)\n            {\\includegraphics[trim=260 90 330 100,clip,height=3.5cm]{example-image}};\n        \\node[inner sep=0pt] (squirrel) at (11,0)\n            {\\includegraphics[trim=260 90 330 100,clip,height=3.5cm]{example-image}};\n        \\node[inner sep=0pt] (mudskipper) at (5.5,-3)\n            {\\includegraphics[trim=260 90 330 100,clip,height=3.5cm]{example-image}};\n        \\node[draw, align=left] at (0.0,1.8) {Foliate-hard \\\\ MSE: 0.047};\n        \\node[draw, align=left] at (5.5,1.8) {Overlapping Mesh \\\\ MSE: 0.003};\n        \\node[draw, align=left] at (11.0,1.8) {Foliate-soft \\\\ MSE: 0.022};\n        \\node[draw, align=left] at (5.5,-1.5) {MSE: 0.001 \\\\ 0.003};\n        \\end{tikzpicture}\n\n\\end{document}"
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        "index": 623,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amssymb,amsfonts}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n  thick,\n  every node/.style={draw,circle,fill=black,minimum size=4pt,inner sep=0pt},\n  every path/.style={draw,thick},\n  scale=1.5,\n  ]\n  \\node (v1) at (0.1,-0.3) {};\n  \\node (v2) at (0.5,-0.4) {};\n  \\node (v3) at (0,0.2) {};\n  \\node (v4) at (1,0.2) {};\n  \\node (v5) at (0.1,-0.9) {};\n  \\node (v6) at (0.5,-0.8) {};\n  \\path (v1) edge (v2);\n  \\path (v1) edge (v3);\n  \\path (v1) edge (v4);\n  \\path (v2) edge (v3);\n  \\path (v2) edge (v4);\n  \\path (v3) edge (v5);\n  \\path (v3) edge (v6);\n  \\path (v4) edge (v5);\n  \\path (v4) edge (v6);\n  \\path (v5) edge (v6);\n  \\node (v1) at (2.1,-0.3) {};\n  \\node (v2) at (2.5,-0.4) {};\n  \\node (v3) at (2,0.2) {};\n  \\node (v4) at (3,0.2) {};\n  \\node (v5) at (2.1,-0.9) {};\n  \\node (v6) at (2.5,-0.8) {};\n  \\path (v1) edge (v2);\n  \\path (v1) edge (v3);\n  \\path (v1) edge (v4);\n  \\path (v2) edge (v3);\n  \\path (v2) edge (v4);\n  \\path (v3) edge (v5);\n  \\path (v3) edge (v6);\n  \\path (v4) edge (v5);\n  \\path (v4) edge (v6);\n  \\path (v5) edge (v6);\n  \\node (v1) at (4.1,-0.3) {};\n  \\node (v2) at (4.5,-0.4) {};\n  \\node (v3) at (4,0.2) {};\n  \\node (v4) at (5,0.2) {};\n  \\node (v5) at (4.1,-0.9) {};\n  \\node (v6) at (4.5,-0.8) {};\n  \\path (v1) edge (v2);\n  \\path (v1) edge (v3);\n  \\path (v1) edge (v4);\n  \\path (v2) edge (v3);\n  \\path (v2) edge (v4);\n  \\path (v3) edge (v5);\n  \\path (v3) edge (v6);\n  \\path (v4) edge (v5);\n  \\path (v4) edge (v6);\n  \\path (v5) edge (v6);\n  \\node (v1) at (4.25,1.2) {};\n  \\node (v2) at (4.75,1.1) {};\n  \\node (v3) at (4.25,0.2) {};\n  \\node (v4) at (5.25,0.2) {};\n  \\node (v5) at (4.25,-0.3) {};\n  \\node (v6) at (4.75,-0.4) {};\n  \\path (v1) edge (v2);\n  \\path (v1) edge (v3);\n  \\path (v1) edge (v4);\n  \\path (v2) edge (v3);\n  \\path (v2) edge (v4);\n  \\path (v3) edge (v5);\n  \\path (v3) edge (v6);\n  \\path (v4) edge (v5);\n  \\path (v4) edge (v6);\n  \\path (v5) edge (v6);\n  \\path[dashed] (v1) edge (v2);\n  \\path[dashed] (v3) edge (v4);\n  \\end{tikzpicture}\n\n\\end{document}"
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        "index": 624,
        "tikz_code": "\\documentclass[10pt]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage{latexsym, amscd, amsbsy, xypic, color,verbatim}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node at (0.3,0) {\\tiny\\textbullet};\n\\node at (0.3,0.9) {\\tiny\\textbullet};\n\\node at (1.3,0) {\\tiny\\textbullet};\n\\node at (1.3,0.9) {\\tiny\\textbullet};\n\\node at (0.2,0.3) {\\scriptsize$\\frac{1}{z_m}$};\n\\node at (1.4,0.3) {\\scriptsize$z_m$};\n\\node at (0.7,0.6) {\\scriptsize$z_m$};\n\n\\draw (0.8,1.3) --(0,0.9);\n\\draw (0,0) --(0,0.9);\n\\draw (0.8,0) --(0.8,0.9);\n\\draw (2,0.9) --(1.2,0.9);\n\\draw (1.2,0) --(2,0);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 625,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath,amsfonts,amssymb,amsthm}\n\\usepackage{tikz}\n\\usepackage{xcolor}\n\\usepackage[backgroundcolor=gray!10]{todonotes}\n\\usepackage[ocgcolorlinks, linkcolor=red!80!black, citecolor=blue!80!black]{hyperref}\n\\usepackage[colorinlistoftodos,prependcaption,textsize=tiny]{todonotes}\n\\usepackage[setpagesize=false,pagebackref,hypindex,breaklinks,colorlinks,linkcolor=black]{hyperref}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.0]\n            \\draw[fill=gray!20!white] (0,0) rectangle (6,6);\n            \\draw[fill=gray!20!white] (6.5,0) rectangle (12.5,6);\n            \\draw[fill=gray!20!white] (0,6.5) rectangle (6,12.5);\n            \\draw[fill=gray!20!white] (6.5,6.5) rectangle (12.5,12.5);\n\n            \\draw[color=gray!20!white,fill=orange!40!white] (1.5,1.5) rectangle (2.5,2.5);\n            \\draw[color=gray!20!white,fill=orange!40!white] (1.5,5.5) rectangle (2.5,6.5);\n            \\draw[color=gray!20!white,fill=orange!40!white] (5.5,1.5) rectangle (6.5,2.5);\n            \\draw[color=gray!20!white,fill=orange!40!white] (5.5,5.5) rectangle (6.5,6.5);\n\n            \\draw[fill=white] (3.5,3.5) rectangle (4.5,4.5);\n            \\draw[fill=orange!40!white] (3.5,3.5) rectangle (4.5,4.5);\n            \\draw[fill=white] (3.5,6.5) rectangle (4.5,7.5);\n            \\draw[fill=orange!40!white] (3.5,6.5) rectangle (4.5,7.5);\n\n            \\draw[color=gray!20!white,fill=orange!40!white] (8.5,1.5) rectangle (9.5,2.5);\n            \\draw[color=gray!20!white,fill=orange!40!white] (8.5,5.5) rectangle (9.5,6.5);\n            \\draw[color=gray!20!white,fill=orange!40!white] (12.5,1.5) rectangle (13.5,2.5);\n            \\draw[color=gray!20!white,fill=orange!40!white] (12.5,5.5) rectangle (13.5,6.5);\n\n            \\draw[color=gray!20!white,fill=orange!40!white] (10.5,3.5) rectangle (11.5,4.5);\n\n            \\draw[fill=white] (11.5,3.5) rectangle (12.5,4.5);\n            \\draw[fill=white] (11.5,6.5) rectangle (12.5,7.5);\n            \\draw[color=gray!20!white,fill=orange!40!white] (11.5,3.5) rectangle (12.5,4.5);\n            \\draw[color=gray!20!white,fill=orange!40!white] (11.5,6.5) rectangle (12.5,7.5);\n\n            \\draw (0.5,0.5) node {$\\times$};\n            \\draw (1.5,1.5) node {$\\times$};\n            \\draw (2.5,2.5) node {$\\times$};\n            \\draw (5.5,1.5) node {$\\times$};\n            \\draw (6.5,2.5) node {$\\times$};\n            \\draw (3.5,3.5) node {$\\times$};\n            \\draw (3.5,4.5) node {$\\times$};\n            \\draw (3.5,5.5) node {$\\times$};\n            \\draw (4.5,3.5) node {$\\times$};\n            \\draw (4.5,4.5) node {$\\times$};\n            \\draw (4.5,5.5) node {$\\times$};\n            \\draw (11.5,3.5) node {$\\times$};\n            \\draw (11.5,4.5) node {$\\times$};\n            \\draw (11.5,5.5) node {$\\times$};\n\n            \\draw (6.5,3.5) node {$\\times$};\n\n            \\draw[color=gray!20!white] (0.5,0.5) -- (3.5,3.5);\n            \\draw[color=gray!20!white] (6.5,2.5) -- (11.5,3.5);\n\n            \\draw[color=gray!20!white] (5,1) node[anchor=east] {$L_{1\\#2}|_{I_\\rho}$};\n            \\draw[color=gray!20!white] (7,3) node[anchor=east] {C};\n            \\draw[color=gray!20!white] (10,1) node[anchor=east] {$L_{1}$};\n            \\draw[color=gray!20!white] (12,3) node[anchor=east] {$L_{2}$};\n\n            \\draw[color=red!80!black] (6.5,3.5) -- (13,3.5);\n            \\draw[color=red!80!black] (6.5,5.5) -- (13,5.5);\n            \\draw[color=red!80!black] (6.5,4.5) -- (13,4.5);\n\n            \\draw[color=red!80!black] (11,"
    },
    {
        "index": 626,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amssymb,amsfonts,amsthm,mathtools,bm,bbm,mathrsfs}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usepackage{tikz-3dplot}\n\\usepackage{tikz-cd}\n\\usetikzlibrary{snakes}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{intersections,shapes.geometric}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.9]\n\t\t\t% Fibers\n\t\t\t\\draw (-2,0)--(2,0);\n\t\t\t\\draw (2,0)--(2,-10);\n\t\t\t\\draw (-2,-10)--(2,-10);\n\t\t\t\\draw (-2,0)--(-2,-10);\n\t\t\t\\draw (2,0)--(2,-8);\n\t\t\t\\draw (-2,-8)--(2,-8);\n\t\t\t\\draw (-2,-10)--(2,-8);\n\t\t\t\\draw[dashed] (0,0)--(0,-10);\n\t\t\t\\draw[dashed] (0,0)--(0,-8);\n\t\t\t\n\t\t\t% GAP\n\t\t\t\\draw (-1.9,-8.1)--(-1.9,-9.9);\n\t\t\t\\draw[dotted,thick] (-1.9,-9.9)--(0,-9.9);\n\t\t\t\\draw[dotted,thick] (0,-8.1)--(0,-9.9);\n\t\t\t\\draw (0,-8.1)--(1.9,-8.1);\n\t\t\t\\draw (0,-8.1)--(1.9,-9.9);\n\t\t\t\\draw (0,-8.1)--(-1.9,-9.9);\n\t\t\t\n\t\t\t%Fiber lines\n\t\t\t\\draw (-1.8,-2)--(2,-2);\n\t\t\t\\draw (-1.8,-4)--(2,-4);\n\t\t\t\\draw (-1.8,-6)--(2,-6);\n\t\t\t\\draw (-1.8,-8)--(2,-8);\n\t\t\t\\draw[dotted, thick] (-1.8,-8)--(-1.8,-10);\n\t\t\t\\draw[dotted, thick] (2,-8)--(2,-10);\n\t\t\t\n\t\t\t%Points\n\t\t\t\\filldraw (-2,0) circle (2pt);\n\t\t\t\\filldraw (2,0) circle (2pt);\n\t\t\t\\filldraw (2,-10) circle (2pt);\n\t\t\t\\filldraw (-2,-10) circle (2pt);\n\t\t\t\\filldraw (-2,-8) circle (2pt);\n\t\t\t\\filldraw (2,-8) circle (2pt);\n\t\t\t\\filldraw (0,0) circle (2pt);\n\t\t\t\\filldraw (-1.8,-8.1) circle (2pt);\n\t\t\t\\filldraw (-1.8,-9.9) circle (2pt);\n\t\t\t\\filldraw (0,-8.1) circle (2pt);\n\t\t\t\\filldraw (0,-9.9) circle (2pt);\n\t\t\t\n\t\t\t%Labels\n\t\t\t\\node[anchor=east] at (-2,0) {$\\left\\langle n_{1},n_{2},n_{3}\\right\\rangle$};\n\t\t\t\\node[anchor=west] at (2,0) {$\\left\\langle n_{1},n_{2},n_{3}\\right\\rangle$};\n\t\t\t\\node[anchor=west] at (2,-10) {$\\left\\langle n_{1},n_{2},n_{3}\\right\\rangle$};\n\t\t\t\\node[anchor=east] at (-2,-10) {$\\left\\langle n_{1},n_{2},n_{3}\\right\\rangle$};\n\t\t\t\\node[anchor=east] at (-2,-8) {$\\left\\langle n_{1},n_{3}\\right\\rangle$};\n\t\t\t\\node[anchor=west] at (2,-8) {$\\left\\langle n_{2},n_{3}\\right\\rangle$};\n\t\t\t\\node[anchor=south] at (0,0) {$\\left\\langle n_{1},n_{2}\\right\\rangle$};\n\t\t\t\\node[anchor=east] at (-1.8,-8.1) {$F_{n_{1}}$};\n\t\t\t\\node[anchor=east] at (-1.8,-9.9) {$\\left\\langle n_{1}\\right\\rangle$};\n\t\t\t\\node[anchor=west] at (0,-8.1) {$F_{n_{2}}$};\n\t\t\t\\node[anchor=west] at (0,-9.9) {$\\left\\langle n_{2}\\right\\rangle$};\n\t\t\t\n\t\t\t%Boxes\n\t\t\t\\draw (-0.4,-2.1) rectangle (0.4,-1.9);\n\t\t\t\\draw (-0.4,-4.1) rectangle (0.4,-3.9);\n\t\t\t\\draw (-0.4,-6.1) rectangle (0.4,-5.9);\n\t\t\t\\draw (-0.4,-8.1) rectangle (0.4,-7.9);\n\t\t\t\n\t\t\t%Angles\n\t\t\t\\draw (0.5,-2.4) arc (45:-135:0.2);\n\t\t\t\\draw (0.5,-3.6) arc (45:-135:0.2);\n\t\t\t\\draw (0.5,-5.6) arc (45:-135:0.2);\n\t\t\t\\draw (0.5,-7.6) arc (45:-135:0.2);\n\t\t\t\n\t\t\t%Labels\n\t\t\t\\node at (0.3,-1.8) {$\\frac{n_{2}}{-y_2}$};\n\t\t\t\\node at (0.3,-3.8) {$\\frac{n_{3}}{-y_2}$};\n\t\t\t\\node at (0.3,-5.8) {$\\frac{n_{2}}{-y_1}$};\n\t\t\t\\node at (0.3,-7.8) {$\\frac{1}{-y_1}$};\n\t\t\t\n\t\t\t%Fiber\n\t\t\t\\draw[opacity=0.5] (-1.8,-2) rectangle (1.8,-10);\n\t\t\t\\node at (-0.8,-9) {$F_{n_{1},n_{2}}$};\n\t\t\t\n\t\t\t%Boxes\n\t\t\t\\draw (-0.4,-8) rectangle (0.4,-7.8);\n\t\t\t\\draw (-0.4,-10) rectangle (0.4,-9.8);\n\t\t\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 627,
        "tikz_code": "\\documentclass[reqno,11pt]{amsart}\n\\usepackage{amsthm,amsfonts, amssymb, amscd}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix,arrows}\n\\usetikzlibrary{positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.4]\n\\draw (.5,.5) -- ++(6,0) -- ++(0,1) -- ++(-1,0) -- ++(0,1) -- ++(-1,0)\n-- ++(0,3) -- ++(2,0) -- ++(0,2) -- ++(-1,0) -- ++(0,3) -- ++(-2,0)\n-- ++(0,1) -- ++(-1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,1) -- ++(1,0)\n-- ++"
    },
    {
        "index": 628,
        "tikz_code": "\\documentclass[a4paper,11pt]{article}\n\\usepackage{amsmath,amsthm}\n\\usepackage[latin1]{inputenc}\n\\usepackage{amssymb,latexsym}\n\\usepackage{graphicx,color}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usepackage[latin1]{inputenc}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usepackage{color}\n\\usepackage[colorlinks=true,\nlinkcolor=blue,\ncitecolor=blue,\nurlcolor=blue]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.9]\n    \\draw[->] (-1.5,0) -- (5.5,0) node[below] {$n$};\n    \\draw[->] (-.5,-.5) -- (-.5,2.2) node[left] {$y$};\n    \\draw[domain=-1.4:5.4,smooth,variable=\\x,blue] plot ({\\x},{max(1,sqrt(2.2*\\x+1.2))});\n    \\draw (0,0) node[below] {$\\mathbf{n}$};\n    \\draw[dashed] (-1.4,.7) -- (5.4,.7) node[below] {$\\sqrt{T\\mathbf{n}}$};\n    \\draw[dashed] (0,.7) -- (0,2.2) node[above] {$n_2$};\n    \\draw[dashed] (2.2,0) -- (2.2,2.2) node[above] {$n_1$};\n    \\draw (5.4,1.5) node[right] {$\\sqrt{T\\mathbf{n}}+\\sqrt{\\epsilon}$};\n    \\draw[dashed] (2.5,0) -- (2.5,1.5) node[right] {$C\\times \\sqrt{n}$};\n  \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 629,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes.misc}\n\\usetikzlibrary{shapes.symbols}\n\\usetikzlibrary{snakes}\n\\usetikzlibrary{decorations}\n\\tikzset{\n\tdot/.style={circle,fill=black,inner sep=0pt, minimum size=1mm},\n\tgraydot/.style={circle,draw=gray,inner sep=0pt, minimum size=1mm},\n\tloopnode/.style={circle,draw=black,inner sep=0pt, minimum size=1.5mm},\n\ttreenode/.style={circle,fill=black,inner sep=0pt, minimum size=1.5mm},\n\tcharge/.style={circle,draw=black,inner sep=0pt, minimum size=3mm},\n\t%\n\tloopline/.style={->,semithick,shorten >=1pt,shorten <=1pt},\n\ttreeline/.style={semithick, densely dashed, shorten >=1pt,shorten <=1pt},\n\t%\n\thomoge/.style={font=\\scriptsize,draw=black,fill=white,inner sep=2pt},\n\thomo/.style={font=\\scriptsize},\n\tKK/.style={thick,shorten >=1pt,shorten <=1pt, densely dashed, >=latex},\n\t%% KK is used for K(x-y) if without arrow, or K(x-y)-K(x) if with arrow\nkerAlg/.style={thick},\nkerAlg2/.style={semithick,dashed},\nkerP/.style={very thick},\narrow/.style={->,thick,shorten >=3pt,shorten <=3pt},\nrenorm/.style={ultra thick},\n\tkernel/.style={semithick,shorten >=1pt,shorten <=1pt},\n\t}\n\n\\newcommand{\\BKK}{\\operatorname{BKK}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node at (2,2) {$\\cdots$};\n\\node at (3.8,2) {$\\cdots$};\n\\node at (5.2,2) {$\\cdots$};\n\\node at (6.5,2) {$\\cdots$};\n\\node at (7.5,2) {$\\cdots$};\n\\node at (8.8,2) {$\\cdots$};\n\\node at (10,2) {$\\cdots$};\n\n\\node at (2.3,2.5) {$\\scriptstyle 1$};\n\\node at (3.3,2.5) {$\\scriptstyle 2$};\n\\node at (4.5,2.5) {$\\scriptstyle 3$};\n\\node at (5.9,2.5) {$\\scriptstyle 4$};\n\\node at (7.3,2.5) {$\\scriptstyle 5$};\n\\node at (8.6,2.5) {$\\scriptstyle 6$};\n\\node at (9.9,2.5) {$\\scriptstyle 7$};\n\\node at (11.4,2.5) {$\\scriptstyle 8$};\n\\node at (12.3,2.5) {$\\scriptstyle 9$};\n\\node at (13.6,2.5) {$\\scriptstyle 10$};\n\n\\draw[kernel] (0,2) node[dot,label=above:{$1$}] {} -- (1.5,2) node[dot,label=above:{$p$}] {} -- (2.25,2) node[dot,label=above:{$q$}] {} -- (3.5,2) node[dot,label=above:{$p$}] {} -- (5,2) node[dot,label=above:{$q$}] {} -- (6,2) node[dot,label=above:{$p$}] {} -- (7,2) node[dot,label=above:{$q$}] {} -- (8,2) node[dot,label=above:{$p$}] {} -- (10,2) node[dot,label=above:{$q$}] {} -- (12,2) node[dot,label=above:{$p$}] {} -- (13,2) node[dot,label=above:{$q$}] {} -- (14,2) node[dot,label=above:{$p$}] {} ;\n\\draw[kernel] (3.5,2) -- (3.5,2.5);\n\\draw[kernel] (6,2) -- (6,2.5);\n\\draw[kernel] (7,2) -- (7,2.5);\n\\draw[kernel] (10,2) -- (10,2.5);\n\\draw[kernel] (12,2) -- (12,2.5);\n\\draw[kernel] (13,2) -- (13,2.5);\n\\draw[kernel] (0.5,2) node[dot,label=below:{$1$}] {} -- (1.5,2) node[dot,label=below:{$p$}] {} -- (2.25,2) node[dot,label=below:{$q$}] {} -- (3.5,2) node[dot,label=below:{$p$}] {} -- (5,2) node[dot,label=below:{$q$}] {} -- (6,2) node[dot,label=below:{$p$}] {} -- (7,2) node[dot,label=below:{$q$}] {} -- (8,2) node[dot,label=below:{$p$}] {} -- (10,2) node[dot,label=below:{$q$}] {} -- (12,2) node[dot,label=below:{$p$}] {} -- (13,2) node[dot,label=below:{$q$}] {} ;\n\n\\node at (0.5,1.6) {$K$};\n\\draw (0.5,1.6) circle [radius=0.8];\n\\node at (13.6,1.6) {reservoir};\n\n\\node at (13.45,3) {FASP(on)};\n\n\\draw [->,bend left=20] (2.3,2.1) to (4.5,2.1);\n\\draw [->,bend left=20] (5.9,2.1) to (8.6,2.1);\n\\draw [->,bend left=20] (7.3,2.1) to (9.9,2.1);\n\\draw [->,bend left=20] (10.1,2.1) to (12.3,2.1);\n\n\n\\node at (2.3,"
    },
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        "tikz_code": "\\documentclass{standalone}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.9}\n\n\\begin{document}\n\\begin{tikzpicture}\n\\begin{axis}[\n    domain=0:18.8,\n    xmin=0, xmax=18.8,\n    ymin=0, ymax=5,\n    zmin=0, zmax=5,\n    grid=both,\n    minor tick num=1,\n    axis equal\n]\n    \\addplot3 [\n        surf,\n        colormap/hot,\n        shader=flat,\n        fill opacity=.5\n    ] {1/(x^2+y^2)};\n\\end{axis}\n\\end{tikzpicture}\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns,shapes,positioning,backgrounds,calc,scopes}\n\\tikzset{every picture/.style={line width=0.75pt}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node[rounded corners,minimum width=2.25cm,fill=red!35,line width=0.75pt] (a) at (0,0) {\\LARGE A conversation between two persons.};\n\\node[rounded corners,minimum width=2.25cm,fill=green!35,line width=0.75pt] (b) at (0,-1.5) {\\LARGE Person 1 (utterance 1)};\n\\node[rounded corners,minimum width=2.25cm,fill=green!35,line width=0.75pt] (b) at (0,-3) {\\LARGE Person 2 (utterance 1)};\n\\node[rounded corners,minimum width=5.25cm,fill=green!15,line width=0.75pt] (c) at (0,-4.5) {\\LARGE A conversation between two persons.};\n\\node[rounded corners,minimum width=5.25cm,fill=red!15,line width=0.75pt] (c) at (0,-6) {\\LARGE Person 1 (utterance 2)};\n\\node[rounded corners,minimum width=5.25cm,fill=red!15,line width=0.75pt] (c) at (0,-7.5) {\\LARGE Person 2 (utterance 2)};\n\\node[rounded corners,minimum width=2.25cm,fill=green!35,line width=0.75pt] (d) at (0,-9) {\\LARGE A conversation between two persons.};\n\\draw[thick,decorate,decoration={brace,amplitude=7pt,mirror},xshift=0pt,yshift=0pt] (-4.25,0.25) -- (-4.25,-1.75) node[black,midway,xshift=-0.6cm]{\\LARGE Demonstration};\n\\draw[thick,decorate,decoration={brace,amplitude=7pt,mirror},xshift=0pt,yshift=0pt] (-4.25,-2.25) -- (-4.25,-3.75) node[black,midway,xshift=-0.6cm]{\\LARGE Person 1};\n\\draw[thick,decorate,decoration={brace,amplitude=7pt,mirror},xshift=0pt,yshift=0pt] (-4.25,-4.25) -- (-4.25,-5.75) node[black,midway,xshift=-0.6cm]{\\LARGE Person 2};\n\\draw[thick,decorate,decoration={brace,amplitude=7pt,mirror},xshift=0pt,yshift=0pt] (-4.25,-6.25) -- (-4.25,-7.75) node[black,midway,xshift=-0.6cm]{\\LARGE Target Conversation};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 642,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{color}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8]\n\n\\draw[fill] (-5,0) circle (0.05cm);\n\\draw[fill] (0,0) circle (0.05cm);\n\\draw[fill] (5,0) circle (0.05cm);\n\\draw[fill] (0,-2) circle (0.05cm);\n\n\\node at (-5,0) [anchor=east] {\\small $50\\%$};\n\\node at (0,0) [anchor=south] {\\small $\\nu_1$};\n\\node at (5,0) [anchor=west] {\\small $\\nu_2$};\n\\node at (0,-2) [anchor=north] {\\small $\\mu_2$};\n\n\\draw[->] (-4.9,0.1) -- (-0.1,0.1);\n\\draw[->] (-4.9,-0.1) -- (-0.1,-0.1);\n\\draw[->] (-0.1,0) -- (-0.1,-1.9);\n\\draw[->] (-0.1,-2.1) -- (-0.1,-0.1);\n\n\\node at (-2.5,0) [anchor=south] {\\small $1$};\n\\node at (-2.5,-2) [anchor=north] {\\small $2$};\n\\node at (2.5,0) [anchor=south] {\\small $s_1$: the husband recovers};\n\\node at (2.5,-2) [anchor=north] {\\small $s_2$: the husband remains paralyzed};\n\n\\draw[dotted] (-5,0) -- (0,-2);\n\\draw[dotted] (0,0) -- (5,0);\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{shapes}\n\\usepackage{tkz-euclide}\n\\usetikzlibrary{decorations.markings,arrows}\n\\usetikzlibrary{arrows,shapes,backgrounds}\n\\usetikzlibrary{decorations.pathreplacing,decorations.markings}\n\\usetikzlibrary{calc, trees, positioning, arrows, shapes, shapes.multipart, shadows, matrix, decorations.pathreplacing, decorations.pathmorphing}\n\\usetikzlibrary{shapes.misc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.70]\n\\draw (0.4,0) -- (1.8,0);\n\\draw (2.8,0) -- (4.2,0);\n\\draw (0,0) circle (0.4cm);\n\\draw (0,-0.8) node {\\footnotesize{$A_3$}};\n\\draw (1.6,0) -- (1.6,0.4);\n\\draw (2.4,0) -- (2.4,0.4);\n\\draw (1.2,0) circle (0.4cm);\n\\draw (2.04,0) -- (2.04,0.4);\n\\draw (2.84,0) -- (2.84,0.4);\n\\draw (1.2,0.8) node {\\footnotesize{$A_4$}};\n\\draw (2.4,0.8) node {\\footnotesize{$A_4$}};\n\\draw (1.2,1.2) [red,fill=red!30] circle (0.4cm);\n\\draw (1.2,2) node {\\footnotesize{$A_5$}};\n\\draw (0,-0.2) node {\\footnotesize{$A_1$}};\n\\draw (1.2,0.24) [->,>=Latex,red] -- (1.2,0.36);\n\\draw (1.4,0.24) node {\\footnotesize{$$}};\n\\draw (0,0.4) circle (0.4cm);\n\\draw(1.2,0.4) node {\\footnotesize{$A_2$}};\n\\draw (0,0.8) node {\\footnotesize{$$}};\n\\draw (-2.8,0) -- (-1.4,0);\n\\draw (-1.8,0) circle (0.4cm);\n\\draw (-2.8,0.4) [red,fill=red!30] circle (0.4cm);\n\\draw (-2.8,1.2) node {\\footnotesize{$A_1$}};\n\\draw (-2.8,0.8) node {\\footnotesize{$$}};\n\\draw (-2.8,1.6) [orange,fill=orange!30] circle (0.4cm);\n\\draw (-2.8,2.4) node {\\footnotesize{$A_6$}};\n% triple link\n\\draw (-1.4,0.4) .. controls (-1.1,0.7) and (-0.7,0.7) .. (-0.4,0.4);\n\\draw (-0.7,0.5) -- (-0.52,0.32);\n\\draw (-0.28,0.52) -- (-0.4,0.64);\n\\draw (0.28,0.52) -- (-0.08,0.32);\n\\draw (-0.7,1.04) node {\\footnotesize{$$}};\n\\draw (0,1.2) circle (0.4cm);\n\\draw (-0.8,1.2) node {\\footnotesize{$A_3$}};\n\\draw (0.4,1.2) [blue,fill=blue!30] circle (0.4cm);\n\\draw (0,2) node {\\footnotesize{$A_6$}};\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 646,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[very thick] (0,0) -- (10,0);\n\\draw (2,0) -- (2,5);\n\\draw (4,0) -- (4,5);\n\\draw (6,0) -- (6,5);\n\\draw (8,0) -- (8,5);\n\\draw (10,0) -- (10,5);\n\n\\draw (5,0) -- (5,4);\n\\draw (3,0) -- (3,4);\n\\draw (1,0) -- (1,4);\n\n\\draw[thick] (0,1) -- (1,1);\n\\draw[thick] (0,2) -- (3,2);\n\\draw[thick] (0,3) -- (4,3);\n\\draw[thick] (0,4) -- (10,4);\n\n\\draw[dashed] (0,0) -- (1,1);\n\\draw[dashed] (1,1) -- (2,2);\n\\draw[dashed] (2,2) -- (3,3);\n\\draw[dashed] (3,3) -- (4,4);\n\\draw[dashed] (4,4) -- (5,5);\n\\draw[dashed] (5,5) -- (6,4);\n\\draw[dashed] (6,4) -- (7,3);\n\\draw[dashed] (7,3) -- (8,2);\n\\draw[dashed] (8,2) -- (9,1);\n\\draw[dashed] (9,1) -- (10,0);\n\n\\draw[dotted] (0,2) -- (2,2);\n\\draw[dotted] (2,2) -- (2,4);\n\\draw[dotted] (3,2) -- (3,3);\n\\draw[dotted] (3,3) -- (4,3);\n\n\\draw[dotted] (0,4) -- (4,4);\n\\draw[dotted] (4,4) -- (4,5);\n\\draw[dotted] (5,4) -- (5,5);\n\\draw[dotted] (5,5) -- (6,5);\n\\draw[dotted] (6,4) -- (6,5);\n\n\n\\draw[dotted] (6,0) -- (6,2);\n\\draw[dotted] (7,0) -- (7,1);\n\\draw[dotted] (8,0) -- (8,1);\n\\draw[dotted] (9,0) -- (9,1);\n\n\\filldraw[black] (0,0) circle (2pt) node[anchor=north] {$R$};\n\\filldraw[black] (10,0) circle (2pt) node[anchor=north] {$R\\times[0,1]$};\n\\filldraw[black] (0,5) circle (2pt) node[anchor=south] {$R\\times[0,1]$};\n\\filldraw[black] (10,5) circle (2pt) node[anchor=south] {$R\\times[1,2]$};\n\n\\filldraw[black] (1,0) circle (2pt) node[anchor=north] {$X_1$};\n\\filldraw[black] (1,1) circle (2pt) node[anchor=north] {$X_2$};\n\\filldraw[black] (1,2) circle (2pt) node[anchor=north] {$X_3$};\n\\filldraw[black] (1,3) circle (2pt) node[anchor=north] {$X_4$};\n\n\\filldraw[black] (3,4) circle (2pt) node[anchor=west] {$Y_1$};\n\\filldraw[black] (4,4) circle (2pt) node[anchor=west] {$Y_2$};\n\\filldraw[black] (5,5) circle (2pt) node[anchor=west] {$Y_3$};\n\\filldraw[black] (6,4) circle (2pt) node[anchor=west] {$Y_4$};\n\\filldraw[black] (6,5) circle (2pt) node[anchor=west] {$Y_5$};\n\\filldraw[black] (7,3) circle (2pt) node[anchor=west] {$Y_6$};\n\\filldraw[black] (8,2) circle (2pt) node[anchor=west] {$Y_7$};\n\n\\filldraw[black] (5,0) circle (2pt) node[anchor=north] {$f_1$};\n\\filldraw[black] (7,0) circle (2pt) node[anchor=north] {$f_2$};\n\\filldraw[black] (8,0) circle (2pt) node[anchor=north] {$f_3$};\n\\filldraw[black] (9,0) circle (2pt) node[anchor=north] {$f_4$};\n\n\\draw[thick,->] (4.5,0) to [bend right] (3.5,1);\n\\draw[thick,->] (5.5,0) to [bend right] (4.5,2);\n\\draw[thick,->] (6.5,0) to [bend right] (5.5,3);\n\\draw[thick,->] (7.5,0) to [bend right] (6.5,4);\n\\draw[thick,->] (8.5,0) to [bend right] (7.5,5);\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 647,
        "tikz_code": "\\documentclass{article}\n\\usepackage{pgfplots}\n\\usepgfplotslibrary{units}\n\\pgfplotsset{compat=newest}\n\\begin{document}\n\\begin{tikzpicture}\n\\begin{semilogyaxis}[\n  xlabel={$\\log(\\left\\|A-\\hat{A}\\right\\|)$},\n  ylabel={$\\log(\\left\\|A-\\hat{A}\\right\\|)$},\n]\n\\addplot+[only marks,domain=-6:1,samples=1000] {0.1*x^2-0.1*x+0.1};\n\\addplot+[only marks,mark=square*,color=red,domain=-4:4,samples=1000] {0.1*x^2-1};\n\\addplot+[only marks,mark=diamond*,color=blue,domain=-4:4,samples=1000] {0.1*x^2-0.5};\n\\end{semilogyaxis}\n\\end{tikzpicture}\n\\end{document}"
    },
    {
        "index": 648,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage{pgf,tikz}\n\\usetikzlibrary{arrows}\n\\usepackage[colorlinks=true,citecolor=cyan,urlcolor=blue]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1cm,y=1cm, thick, every node/.style={scale=0.7},scale=.3]\n\\draw (0,3)--(0,1)--(2,1)--(2,0)--(3,0)--(3,2)--(2,2)--(2,3)--(1,3)--(1,2);\n\\draw (1,1)--(2,1);\n\\draw (1,2)--(2,2);\n\\draw (1,3)--(2,3);\n\\draw (0.5,0.5) node{$1$};\n\\draw (0.5,1.5) node{$1$};\n\\draw (1.5,1.5) node{$1$};\n\\draw (0.5,2.5) node{$1$};\n\\draw (1.5,2.5) node{$2$};\n\\draw (2.5,2.5) node{$1$};\n\\draw (1.5,3.5) node{$1$};\n\\draw (0.5,3.5) node{$1$};\n\\draw (1,0)--(2,0);\n\\draw (1,1)--(2,1);\n\\draw (1,2)--(2,2);\n\\draw (0.5,-0.5) node{$1$};\n\\draw (1.5,-0.5) node{$1$};\n\\fill[line width=2.8pt,fill=gray,fill opacity=0.3] (0,2) -- (1,2) -- (1,3) -- (2,3) -- (2,1) -- (1,1) -- (1,0) -- (0,0) -- cycle;\n\\fill[line width=2.8pt,fill=gray,fill opacity=0.3] (1,1) -- (2,1) -- (2,2) -- (3,2) -- (3,0) -- (1,0) -- cycle;\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 649,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows, shapes, calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n  \\node[draw, regular polygon, regular polygon sides=4] (int) at (0,0) {0};\n  \\node[draw, regular polygon, regular polygon sides=4] (int2) at (0,-0.75) {0};\n  \\node[draw, regular polygon, regular polygon sides=4] (int3) at (0,-1.5) {0};\n  \\node[draw, regular polygon, regular polygon sides=4] (int4) at (-0.75,-0.75) {1};\n  \\node[draw, regular polygon, regular polygon sides=4] (int5) at (0.75,-0.75) {1};\n  \\node[draw, regular polygon, regular polygon sides=4] (int6) at (0.75,-1.5) {1};\n\n  \\node[draw, regular polygon, regular polygon sides=4] (int12) at (0,-2.25) {0};\n  \\node[draw, regular polygon, regular polygon sides=4] (int13) at (0,-3) {0};\n  \\node[draw, regular polygon, regular polygon sides=4] (int14) at (0,-3.75) {0};\n  \\node[draw, regular polygon, regular polygon sides=4] (int15) at (0.75,-3) {1};\n  \\node[draw, regular polygon, regular polygon sides=4] (int16) at (-0.75,-3) {1};\n\n  \\node[draw, regular polygon, regular polygon sides=4] (int17) at (0,-4.5) {2};\n  \\node[draw, regular polygon, regular polygon sides=4] (int18) at (-0.75,-4.5) {3};\n  \\node[draw, regular polygon, regular polygon sides=4] (int19) at (0.75,-4.5) {4};\n\n  \\node at (-2.75,0) {0.};\n  \\node at (-2.75,-0.75) {1.};\n  \\node at (-2.75,-1.5) {2.};\n  \\node at (-2.75,-2.25) {2.};\n  \\node at (-2.75,-3) {3.};\n  \\node at (-2.75,-3.75) {4.};\n  \\node at (-2.75,-4.5) {5.};\n\n  \\draw (int) -- (int2) -- (int3) -- (int4) -- (int) -- (int5) -- (int6) -- (int3) -- (int15) -- (int13) -- (int14) -- (int12) -- (int17) -- (int16) -- (int15);\n  \\draw[style=->] (int13) -- (int12);\n  \\draw[style=->] (int14) -- (int13);\n  \\draw[style=->] (int16) -- (int17);\n\n  \\draw (int4) -- (int15);\n  \\draw (int5) -- (int16);\n\n  \\draw (int12) -- (int17);\n\n  \\node at (1.25,0) {$\\infty$};\n  \\node at (1.25,-0.75) {$\\infty$};\n  \\node at (1.25,-1.5) {$\\infty$};\n  \\node at (1.25,-2.25) {$\\infty$};\n  \\node at (1.25,-3) {$\\infty$};\n  \\node at (1.25,-3.75) {$\\infty$};\n  \\node at (1.25,-4.5) {$\\infty$};\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 650,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usepackage{color,soul}\n\\usepackage{amsmath}\n\\usetikzlibrary{positioning, automata, chains, arrows.meta}\n\\usetikzlibrary{matrix,positioning,calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[node distance = .35cm, font=\\Huge]\n\\tikzstyle{every node}=[scale=0.35]\n% NODES\n\\node[state] (E) at (1,1) {};\n\\node[state] (F) at (2,1) {};\n\\node[state] (G) at (3,1) {};\n\\node[state] (H) at (4,1) {};\n\\node[state] (A) at (5,1) {};\n\\node[state] (B) at (6,1) {};\n\\node[state] (C) at (7,1) {};\n\\node[state] (D) at (8,1) {};\n\\node[state] (E2) at (1,2) {};\n\\node[state] (F2) at (2,2) {};\n\\node[state] (G2) at (3,2) {};\n\\node[state] (H2) at (4,2) {};\n\\node[state] (A2) at (5,2) {};\n\\node[state] (B2) at (6,2) {};\n\\node[state] (C2) at (7,2) {};\n\\node[state] (D2) at (8,2) {};\n% LETTERS\n\\node[thick] at (0,1) {$R$};\n\\node[thick] at (0,2) {$P$};\n\\node[thick] at (1.5,3) {$I$};\n\\node[thick] at (3.5,3) {$E$};\n\\node[thick] at (5.5,3) {$A$};\n\\node[thick] at (7.5,3) {$C$};\n\\draw[dotted, thick] (2.5,0.5) -- (2.5,2.5);\n% ARROWS\n\\draw[every loop]\n(F) edge[bend left] node {} (E)\n(E) edge[bend left] node [scale=1.2, above=0.1 of C] {} (F);\n\\draw[every loop]\n(E2) edge[bend left] node [scale=1.2, above=0.1 of C2] {} (F2)\n(F2) edge[bend left] node [scale=1.2, above=0.1 of C2] {} (E2);\n\\draw[every loop]\n(E) edge[bend left] node [scale=1.2, above=0.1 of C] {} (F)\n(F) edge[bend left] node [scale=1.2, above=0.1 of C] {} (E);\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 651,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows.meta}\n\\usepackage{amssymb}\n\\usetikzlibrary{external}\n\\tikzexternalize\n\\tikzset{external/mode=graphics if exists}\n\n\\begin{document}\n\n\\begin{tikzpicture}[x=0.5cm,y=0.5cm]\n\\draw[step=1cm,color=gray] (-5,-3) grid (4,4);\n\\fill[blue] (-3,-1) circle(3pt);\n\\fill[blue] (-2,-1) circle(3pt);\n\\fill[blue] (-1,-1) circle(3pt);\n\\fill[blue] (0,-1) circle(3pt);\n\\fill[blue] (1,-1) circle(3pt);\n\\fill[blue] (2,-1) circle(3pt);\n\\fill[blue] (3,-1) circle(3pt);\n\\fill[blue] (-3,0) circle(3pt);\n\\fill[blue] (-2,0) circle(3pt);\n\\fill[blue] (-1,0) circle(3pt);\n\\fill[blue] (0,0) circle(3pt);\n\\fill[blue] (1,0) circle(3pt);\n\\fill[blue] (2,0) circle(3pt);\n\\fill[blue] (3,0) circle(3pt);\n\\fill[blue] (-3,1) circle(3pt);\n\\fill[blue] (-2,1) circle(3pt);\n\\fill[blue] (-1,1) circle(3pt);\n\\fill[blue] (0,1) circle(3pt);\n\\fill[blue] (1,1) circle(3pt);\n\\fill[blue] (2,1) circle(3pt);\n\\fill[blue] (3,1) circle(3pt);\n\\fill[blue] (-3,2) circle(3pt);\n\\fill[blue] (-2,2) circle(3pt);\n\\fill[blue] (-1,2) circle(3pt);\n\\fill[blue] (0,2) circle(3pt);\n\\fill[blue] (1,2) circle(3pt);\n\\fill[blue] (2,2) circle(3pt);\n\\fill[blue] (3,2) circle(3pt);\n\\fill[blue] (-3,3) circle(3pt);\n\\fill[blue] (-2,3) circle(3pt);\n\\fill[blue] (-1,3) circle(3pt);\n\\fill[blue] (0,3) circle(3pt);\n\\fill[blue] (1,3) circle(3pt);\n\\fill[blue] (2,3) circle(3pt);\n\\fill[blue] (3,3) circle(3pt);\n\\draw[very thick] (-4,-1) -- (4,-1);\n\\draw[very thick] (-4,2) -- (4,2);\n\\draw[very thick] (-4,3) -- (4,3);\n\\draw[very thick] (-1,-2) -- (-1,4);\n\\draw[very thick] (0,-2) -- (0,4);\n\\draw[very thick] (1,-2) -- (1,4);\n\\fill[red] (-1.5,-2) circle(3pt);\n\\node at (5.5,0.5) {$x^p$};\n\\fill[red] (5,0.5) circle(3pt);\n\\node at (5.5,1.5) {$x^q$};\n\\fill[red] (5,1.5) circle(3pt);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 652,
        "tikz_code": "\\documentclass[12pt, a4paper]{amsart}\n\\usepackage{color}\n\\usepackage{amssymb,amsmath,amsthm}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[xscale = .5pt, yscale = .5pt]  \n\\draw[step=2,black!10,thin] (0,0) grid (8,8);\n\\draw[thick] (0,0) -- (8,0);\n\\draw[thick] (0,0) -- (0,8);\n\\draw[thick] (8,0) -- (8,8);\n\\draw[thick] (0,8) -- (8,8);\n\\draw[blue, xshift=4pt, yshift=4pt, thick] (0,0) -- (2,1) -- (3,1) -- (4,3) -- (6,5) -- (8,7);\n\\draw[blue, xshift=4pt, yshift=4pt, thick] (0,0) -- (2,1) -- (3,1) -- (4,3) -- (6,5) -- (8,7);\n\\fill[blue] (4,3) circle (3pt);\n\\fill[blue] (6,5) circle (3pt);\n\\fill[blue] (8,7) circle (3pt);\n\n\n\\draw[blue, xshift=4pt, yshift=4pt, thick] (8,1) -- (10,2) -- (11,2) -- (12,4) -- (14,6) -- (16,8);\n\\draw[blue, xshift=4pt, yshift=4pt, thick] (8,1) -- (10,2) -- (11,2) -- (12,4) -- (14,6) -- (16,8);\n\\fill[blue] (12,4) circle (3pt);\n\\fill[blue] (14,6) circle (3pt);\n\\fill[blue] (16,8) circle (3pt);\n\n\\fill[blue] (6,7) circle (3pt);\n\\fill[blue] (8,5) circle (3pt);\n\\fill[blue] (10,3) circle (3pt);\n\\fill[blue] (4,2) circle (3pt);\n\n\\node at (6, -2) {intersection};\n\\node at (6, -3) {$\\nearrow$};\n\\node at (6, -4) {$\\nearrow$};\n\\node at (12, -2) {$\\overset{\\tau}{\\rightarrow}$};\n\\node at (12, -3) {$\\overset{\\tau}{\\rightarrow}$};\n\\node at (18, -2) {$\\overset{\\tau}{\\rightarrow}$};\n\\node at (18, -3) {$\\overset{\\tau}{\\rightarrow}$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 653,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.4]\n\\draw (0,0) -- (0,8);\n\\draw (0,4) -- (3,4);\n\\draw (1,5) -- (4,5);\n\\draw (0,2) -- (1,2);\n\\draw (0,6) -- (1,6);\n\\draw (2,1) -- (2,7);\n\\draw (2,3) -- (3,3);\n\\draw (6,0) -- (6,8);\n\\draw (6,4) -- (9,4);\n\\draw (7,5) -- (10,5);\n\\draw (6,2) -- (7,2);\n\\draw (6,6) -- (7,6);\n\\draw (8,1) -- (8,7);\n\\draw (8,3) -- (9,3);\n\\draw[fill] (0,0) circle (0.2);\n\\draw[fill] (0,2) circle (0.2);\n\\draw[fill] (0,4) circle (0.2);\n\\draw[fill] (0,6) circle (0.2);\n\\draw[fill] (1,2) circle (0.2);\n\\draw[fill] (1,4) circle (0.2);\n\\draw[fill] (1,6) circle (0.2);\n\\draw[fill] (2,1) circle (0.2);\n\\draw[fill] (2,3) circle (0.2);\n\\draw[fill] (2,5) circle (0.2);\n\\draw[fill] (2,7) circle (0.2);\n\\draw[fill] (3,2) circle (0.2);\n\\draw[fill] (3,4) circle (0.2);\n\\draw[fill] (3,6) circle (0.2);\n\\draw[fill] (4,2) circle (0.2);\n\\draw[fill] (4,4) circle (0.2);\n\\draw[fill] (4,6) circle (0.2);\n\\draw[fill] (6,0) circle (0.2);\n\\draw[fill] (6,2) circle (0.2);\n\\draw[fill] (6,4) circle (0.2);\n\\draw[fill] (6,6) circle (0.2);\n\\draw[fill] (7,2) circle (0.2);\n\\draw[fill] (7,4) circle (0.2);\n\\draw[fill] (7,6) circle (0.2);\n\\draw[fill] (8,1) circle (0.2);\n\\draw[fill] (8,3) circle (0.2);\n\\draw[fill] (8,5) circle (0.2);\n\\draw[fill] (8,7) circle (0.2);\n\\draw[fill] (9,2) circle (0.2);\n\\draw[fill] (9,4) circle (0.2);\n\\draw[fill] (9,6) circle (0.2);\n\\draw[fill=gray!20!white] (2,1) circle (0.5);\n\\draw[fill=gray!20!white] (2,3) circle (0.5);\n\\node at (1.5,0.5) {$\\bigcirc$};\n\\draw[thick,->] (1,1.7) -- (1,0.3);\n\\draw[thick,->] (1,2.3) -- (1,3.7);\n\\draw[thick,->] (2,1.3) -- (2,0.7);\n\\draw[thick,->] (2,2.7) -- (2,2.3);\n\\draw[thick,->] (2,3.3) -- (2,4.7);\n\\draw[thick,->] (4,2.3) -- (4,1.7);\n\\node at (11,4) {$\\Rightarrow$};\n\\draw[fill=gray!20!white] (13,1) rectangle (16,5);\n\\draw[thick] (13,1) -- (16,1);\n\\draw[thick] (13,5) -- (16,5);\n\\draw[fill] (13,1) circle (0.2);\n\\draw[fill] (13,3) circle (0.2);\n\\draw[fill] (13,5) circle (0.2);\n\\draw[fill] (14,1) circle (0.2);\n\\draw[fill] (14,3) circle (0.2);\n\\draw[fill] (14,5) circle (0.2);\n\\draw[fill] (15,1) circle (0.2);\n\\draw[fill] (15,3) circle (0.2);\n\\draw[fill] (15,5) circle (0.2);\n\\draw[fill] (16,1) circle (0.2);\n\\draw[fill] (16,3) circle (0.2);\n\\draw[fill] (16,5) circle (0.2);\n\\end{tikzpicture}\n\n\\end{document}"
    },
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        "tikz_code": "\\documentclass[a4paper]{article}\n\\usepackage{amsmath,amssymb,latexsym,times,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\\usepackage{amsmath, amssymb, stmaryrd}\n\\usepackage{xcolor}\n\\usetikzlibrary{backgrounds}\n\n\\begin{document}\n\n\\begin{tikzpicture}[->,>=stealth,shorten >=1pt,auto,node distance=1.5cm,\n main node/.style={circle,draw,minimum size=0.6cm,draw,font=\\sffamily\\bfseries}]\n\n  \\node[main node] (1) {$a$};\n  \\node[main node] (2) [below right of=1] {$b$};\n  \\node[main node] (3) [below of=2] {$c$};\n   \\node[main node, label=below:$G_1$] (4) [below of=3] {$d$};\n\n\\node[main node] (6) [right of=3] {$c$};\n  \\node[main node] (7) [below of=6] {$d$};\n\n  \\node[main node] (8) [right of=6] {$a$};\n  \\node[main node] (9) [below right of=8] {$b$};\n  \\node[main node] (10) [below of=9] {$d$};\n\n  \\node[main node, label=below:$G_2$] (11) [below of=7] {$d$};\n\n \\path[every node/.style={sloped,anchor=south,auto=false}]\n  (2) edge [dashed] node {} (1)\n       edge node {} (3)\n  (1) edge [dashed] node {} (2)\n  (3) edge [dashed] node {} (4)\n  (6) edge node {} (7)\n  (8) edge node {} (9)\n  (9) edge [dashed] node {} (10)\n  (7) edge [dashed] node {} (8)\n  (10) edge node {} (11)\n  (7) edge node {} (11);\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt,a4paper,reqno]{article}\n\\usepackage{amsmath,amssymb,amsthm,mathrsfs,bbm}\n\\usepackage{tikz,pgfplots}\n\\usetikzlibrary{calc,patterns}\n\\pgfplotsset{compat=1.10}\n\n\\begin{document}\n\n\\begin{tikzpicture}[baseline,trim axis right, scale=0.8]\n\\draw[-] (0,0) -- (0,6) -- (6,6) -- (6,0) -- cycle;\n%\n\\node at (-0.2,1) {$0$};\n\\node at (-0.2,5) {$\\frac{1}{q-1}$};\n\\node at (5,6.2) {$1$};\n\\node at (2.25,-0.2) {$\\frac{1}{q_1}$};\n\\node at (4.75,-0.2) {$\\frac{1}{q_1-1}$};\n\\node at (1.5,-0.2) {$1$};\n\\node at (5.5,-0.2) {$1$};\n\\node at (0.85,2.15) {$0$};\n\\node at (0.85,4.25) {$T_{0,q_0}$};\n\\node at (3.65,4.35) {$T_{1,q_1}$};\n%\n\\draw[very thick] (1.5,0) -- (1.5,5);\n\\draw[very thick] (5.5,0) -- (5.5,6);\n%\n\\draw[domain=0:6] plot (\\x, {(5-\\x)/5});\n\\draw[domain=0:1.5] plot (\\x, {0});\n\\draw[domain=1.5:5.5] plot (\\x, {5-\\x});\n\\draw[domain=5.5:6] plot (\\x, {6});\n%\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{color}\n\\usepackage{amsmath,amsthm,amsfonts,amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows.meta}\n\\usetikzlibrary{knots}\n\\usetikzlibrary{hobby}\n\\usetikzlibrary{arrows,decorations.markings}\n\\usetikzlibrary{fadings}\n\n\\begin{document}\n\n\\begin{tikzpicture}[use Hobby shortcut, scale=.6]\n\\begin{knot}[\n%draft mode=crossings,\n  consider self intersections = true,\n  %ignore endpoint intersections = false,\n  clip width=5,\n  flip crossing/.list={5,6,7,8}\n]\n%type 1\n\\draw[stealth-] (-6,1)..(-3,-2)..(-.5,3);\n\\draw[stealth-] (-6,-1)..(-3,2)..(-.5,-3);\n\\draw[stealth-] (-1,-3)..(-1,3);\n\\draw[latex'-latex', thick](-2.5,-3.5)..(-2.5,3.5);\n\\draw[latex'-latex', thick](-7,-2)..(-7,2);\n\\end{knot}\n\\draw[red] (-3,1)..(-1.8,1);\n\\draw[red] (-3,-1)..(-1.8,-1);\n\\draw[red] (-1.8,1)..(-1.3,-.5);\n\\draw[red] (-1.8,-1)..(-1.3,.5);\n\\node[red] at (-3,1) {$\\bullet$};\n\\node[red] at (-3,-1) {$\\bullet$};\n\\node[red] at (-1.8,1) {$\\bullet$};\n\\node[red] at (-1.8,-1) {$\\bullet$};\n\\draw[blue,dashed] (-2.4,-1.7)..(-.2,-.7);\n\\draw[blue,dashed] (-2.4,1.7)..(.2,.7);\n\\draw[blue,dashed] (-7.2,-2)..(-.2,-.7);\n\\draw[blue,dashed] (-7.2,2)..(.2,.7);\n\\draw[blue,dashed] (-.7,3)..(-4.7,-3);\n\\node[draw] at (2,2) {$C_{P_Y}$};\n\\node[draw] at (-1.5,3) {$-C_{P_Y}$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 664,
        "tikz_code": "\\documentclass[onecolumn,groupedaddress,showkeys,showpacs]{revtex4-1}\n\\usepackage{tikz}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}[>=stealth, scale=1.5]\n\t\t\t\n\t\t\t\\draw (0,0) node[]{\\includegraphics[width=1.9in]{example-image}};\n\t\t\t\n\t\t\t% Axis Labels\n\t\t\t\\node at (-3.2,2.34){\\large $33$};\n\t\t\t\\node at (-3.2,0.875){\\large $4$};\n\t\t\t\\node at (-3.2,-0.6875){\\large $1$};\n\t\t\t\\node at (-3.2,-2.0625){\\large $0$};\n\t\t\t\\node at (-3.2,-2.96875){\\large $-1$};\n\t\t\t\\node at (-3.2,-3.94375){\\large $-2$};\n\t\t\t\\node at (-3.2,-4.875){\\large $-3$};\n\t\t\t\n\t\t\t\\node at (-0.5,2.34){\\large $43$};\n\t\t\t\\node at (-0.5,0.875){\\large $3$};\n\t\t\t\\node at (-0.5,-0.6875){\\large $2$};\n\t\t\t\\node at (-0.5,-2.0625){\\large $1$};\n\t\t\t\\node at (-0.5,-2.96875){\\large $0$};\n\t\t\t\\node at (-0.5,-3.94375){\\large $-1$};\n\t\t\t\\node at (-0.5,-4.875){\\large $-2$};\n\t\t\t\n\t\t\t% Axis Lines\n\t\t\t\\draw [->] (-3.7,0) -- (3.2,0);\n\t\t\t\\draw [->] (0,-4.875) -- (0,2.5);\n\t\t\t\n\t\t\t% Help Lines\n\t\t\t\\draw [help lines] (0,0) -- (-1.25,0);\n\t\t\t\\draw [help lines] (0,0) -- (0,1.25);\n\t\t\t\n\t\t\t% Tick Marks\n\t\t\t\\draw [very thick] (-1.25,0) node[below=0.15] {\\large $\\frac{1}{2}$} -- (-1.25,0.125);\n\t\t\t\\draw [very thick] (-1.25,0) node[above=0.15] {\\large $\\frac{1}{2}$} -- (-1.25,-0.125);\n\t\t\t\\draw [very thick] (0,1.25) node[left=0.15] {\\large $\\frac{1}{2}$} -- (0.125,1.25);\n\t\t\t\\draw [very thick] (0,1.25) node[right=0.15] {\\large $\\frac{1}{2}$} -- (-0.125,1.25);\n\t\t\t\n\t\t\t\\draw [very thick, red] (0,2.34) node[left=0.15] {\\large $\\frac{1}{2}$} -- (0.125,2.34);\n\t\t\t\\draw [very thick, red] (0,2.34) node[right=0.15] {\\large $\\frac{1}{2}$} -- (-0.125,2.34);\n\t\t\t\n\t\t\t\\draw [very thick, red] (0,-2.34) node[left=0.15] {\\large $\\frac{1}{2}$} -- (0.125,-2.34);\n\t\t\t\\draw [very thick, red] (0,-2.34) node[right=0.15] {\\large $\\frac{1}{2}$} -- (-0.125,-2.34);\n\t\t\t\n\t\t\t\\draw [very thick, red] (0,-2.0625) node[left=0.15] {\\large $\\frac{1}{2}$} -- (0.125,-2.0625);\n\t\t\t\\draw [very thick, red] (0,-2.0625) node[right=0.15] {\\large $\\frac{1}{2}$} -- (-0.125,-2.0625);\n\t\t\t\n\t\t\t\\draw [very thick, red] (0,-2.96875) node[left=0.15] {\\large $\\frac{1}{2}$} -- (0.125,-2.96875);\n\t\t\t\\draw [very thick, red] (0,-2.96875) node[right=0.15] {\\large $\\frac{1}{2}$} -- (-0.125,-2.96875);\n\t\t\t\n\t\t\t\\draw [very thick, red] (0,-3.94375) node[left=0.15] {\\large $\\frac{1}{2}$} -- (0.125,-3.94375);\n\t\t\t\\draw [very thick, red] (0,-3.94375) node[right=0.15] {\\large $\\frac{1}{2}$} -- (-0.125,-3.94375);\n\t\t\t\n\t\t\t\\draw [very thick, red] (0,-4.875) node[left=0.15] {\\large $\\frac{1}{2}$} -- (0.125,-4.875);\n\t\t\t\\draw [very thick, red] (0,-4.875) node[right=0.15] {\\large $\\frac{1}{2}$} -- (-0.125,-4.875);\n\t\t\t\n\t\t\t\\draw [very thick] (3.2,0) node[below=0.15] {\\large $\\frac{1}{R}$} -- (3.2,-0.125);\n\t\t\t\\draw [very thick] (3.2,0) node[above=0.15] {\\large $\\frac{1}{R}$} -- (3.2,0.125);\n\t\t\t\n\t\t\t\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 665,
        "tikz_code": "\\documentclass[conference]{IEEEtran}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{xcolor}\n\\usepackage{pgf,tikz,pgfplots}\n\\pgfplotsset{compat=1.14}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n  \\begin{axis}[\n    ybar stacked,\n    bar width=25pt,\n    nodes near coords,\n    enlargelimits=0.15,\n    legend style={at={(0.5,-0.20)},\n      anchor=north,legend columns=-1},\n    ylabel={\\#participants},\n    symbolic x coords={VN, EE, NA, Others},\n    xtick=data,\n    x tick label style={rotate=45,anchor=east},\n    ]\n    \\addplot+[ybar] plot coordinates {(VN,1) (EE,1)  (NA,2) (Others,1)};\n    \\addplot+[ybar] plot coordinates {(VN,3) (EE,2)  (NA,2) (Others,1)};\n    \\addplot+[ybar] plot coordinates {(VN,4) (EE,4)  (NA,0) (Others,0)};\n    \\legend{\\strut General student, \\strut Radiologist, \\strut Patient, \\strut AI scientist}\n  \\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 666,
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        "index": 667,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amssymb,amsmath,amsthm,amsfonts,mathrsfs}\n\\usepackage{color}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw (0,0) circle (3cm);\n\\draw (-3,0) arc (180:360:3 and 0.6);\n\\draw[dashed] (-3,0) arc (180:0:3 and 0.6);\n\\draw[fill=white] (2.3,-0.6) rectangle (2.5,-0.4);\n\\draw[fill=white] (2.3,0.4) rectangle (2.5,0.6);\n\\draw (2.3,0.4) -- (2.3,-0.4);\n\\draw (2.5,0.4) -- (2.5,-0.4);\n\\draw (2.3,-0.1) node{$\\Sigma$};\n\\draw (-2.8,-0.1) node{$\\Sigma$};\n\\draw (-2.8,0.4) node{$\\vee$};\n\\draw (2.3,0.6) node{$\\Pi$};\n\\draw (2.3,-0.6) node{$\\Gamma_0$};\n\\draw (2.3,-2.5) node{$\\Gamma_out$};\n\\draw (-2.3,-2.5) node{$\\Gamma_in$};\n\\draw[fill=white] (-2,-2) circle (0.4);\n\\draw[fill=white] (-1,-1) circle (0.4);\n\\draw[fill=white] (-0.7,-1.6) rectangle (-0.9,-1.4);\n\\draw[fill=white] (-1.3,-1.6) rectangle (-1.1,-1.4);\n\\draw[fill=white] (-1.6,-1.2) rectangle (-1.8,-1.4);\n\\draw[fill=white] (-1.2,-1.2) rectangle (-1.4,-1.4);\n\\draw[thick] (-2,-2) -- (-1.8,-2);\n\\draw[thick] (-1.8,-2) -- (-1.6,-1.2);\n\\draw[thick] (-1.6,-1.2) -- (-1.4,-1.2);\n\\draw[thick] (-1.4,-1.2) -- (-0.7,-1.6);\n\\draw[thick] (-0.7,-1.6) -- (-0.9,-1.6);\n\\draw[thick] (-0.9,-1.6) -- (-1,-1);\n\\draw[thick] (-1,-1) -- (-1.2,-1.2);\n\\draw[thick] (-1.2,-1.2) -- (-1.3,-1.2);\n\\draw[thick] (-1.3,-1.2) -- (-1.6,-1.2);\n\\draw[thick] (-1.6,-1.2) -- (-1.8,-2);\n\\draw[thick] (-1.8,-2) -- (-2,-2);\n\\draw[thick] (-1,-2) -- (-1,-1);\n\\draw[thick] (-1,-1) -- (-1.6,-1.2);\n\\draw[thick] (-2,-2) -- (-2,-2.8);\n\\draw[thick] (-1,-1) -- (-1.6,-1.2);\n\\draw[thick] (-1.6,-1.2) -- (-1.8,-2);\n\\draw[thick] (-1.8,-2) -- (-2,-2.8);\n\\draw[thick] (-2,-2.8) -- (-1,-2.8);\n\\draw[thick] (-1,-2.8) -- (-1,-2);\n\\draw[thick] (-1,-2) -- (-1.8,-2);\n\\draw[thick] (-1.8,-2) -- (-2,-2);\n\\draw[thick] (-1,-2) -- (-1,-2.8);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 669,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath, amsthm, amssymb, amsfonts}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{decorations}\n\\usetikzlibrary{decorations.pathreplacing}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.85]\n\\draw[color=red!50, fill=red!10, ultra thick] (0.0,6.0) -- (0.0,0.0) -- (2.0,0.0) -- cycle;\n\\draw[color=red!50, fill=red!10, ultra thick] (0.0,6.0) -- (4.0,6.0) -- (4.0,0.0) -- cycle;\n\\draw[color=blue, fill=blue, very thick] (0.0,0.0) circle (0.1);\n\\draw[color=blue, fill=blue, very thick] (2.0,0.0) circle (0.1);\n\\draw[color=blue, fill=blue, very thick] (4.0,0.0) circle (0.1);\n\\draw[color=blue, fill=blue, very thick] (0.0,6.0) circle (0.1);\n\\draw[color=blue, fill=blue, very thick] (4.0,6.0) circle (0.1);\n\\draw[color=blue, fill=blue, very thick] (1.0,2.0) circle (0.1);\n\\draw[color=blue, fill=blue, very thick] (3.0,2.0) circle (0.1);\n\\draw[color=red, dashed] (0.0,6.0) -- (0.0,0.0);\n\\draw[color=red, dashed] (4.0,6.0) -- (4.0,0.0);\n\\draw[color=red, dashed] (1.0,2.0) -- (0.0,6.0);\n\\draw[color=red, dashed] (3.0,2.0) -- (4.0,6.0);\n\\draw[color=red, thick, <->] (1.0,2.1) -- (3.0,2.1);\n\\draw (2.0,2.1) node[anchor=south] {\\color{red} $\\overline{U}(1^+)$};\n\\draw[color=red, thick, <->] (4.0,6.1) -- (2.0,6.1);\n\\draw (3.0,6.1) node[anchor=south] {\\color{red} $\\overline{U}(1^+)$};\n\\draw[color=red, thick, <->] (0.0,-0.1) -- (1.0,-0.1);\n\\draw (0.5,-0.1) node[anchor=north] {\\color{red} $(-1,-1)$};\n\\draw[color=red, thick, <->] (2.0,-0.1) -- (3.0,-0.1);\n\\draw (2.5,-0.1) node[anchor=north] {\\color{red} $(-1,-1)$};\n\\draw[color=red, thick, <->] (4.0,-0.1) -- (6.0,-0.1);\n\\draw (5.0,-0.1) node[anchor=north] {\\color{red} $(1,-1)$};\n\\draw[color=red, thick, <->] (-0.1,6.0) -- (-0.1,4.0);\n\\draw (-0.1,5.0) node[anchor=east] {\\color{red} $(-1,4)$};\n\\draw[color=red, thick, <->] (-0.1,4.0) -- (-0.1,2.0);\n\\draw (-0.1,3.0) node[anchor=east] {\\color{red} $(-1,4)$};\n\\draw[color=blue, thick, <->] (-0.1,0.0) -- (-0.1,2.0);\n\\draw (-0.1,1.0) node[anchor=east] {\\color{blue} $(-1,1)$};\n\\draw[color=blue, thick, <->] (1.0,2.1) -- (4.0,2.1);\n\\draw (2.5,2.1) node[anchor=south] {\\color{blue} $\\overline{U}(1^+)$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 670,
        "tikz_code": "\\documentclass[reqno, 11pt]{amsart}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{xcolor}\n\\usepackage[T1]{fontenc}\n\\usepackage{tikz}\n\\usetikzlibrary{calc,decorations.pathmorphing}\n\\pgfdeclarelayer{background}\n\\pgfdeclarelayer{foreground}\n\\pgfdeclarelayer{front}\n\\pgfsetlayers{background,main,foreground,front}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\t\\tikzstyle{w}=[circle, draw, inner sep=0pt, minimum width=4pt]\n\t\t\t\\tikzstyle{b}=[circle, draw, fill=black, inner sep=0pt, minimum width=4pt]\n\t\t\t\\tikzstyle{gray}=[circle, draw=gray!50, fill=gray!50, inner sep=0pt, minimum width=4pt]\n\t\t\t\\tikzstyle{edge_w}=[draw, line width=1.2pt, color=black]\n\t\t\t\\tikzstyle{edge_red}=[draw, line width=1.2pt, color=red]\n\t\t\t\\tikzstyle{edge_dotted}=[draw, dashed]\n\t\t\t\n\t\t\t\\foreach \\x in {0,1,2}{\n\t\t\t\t\\node[gray] (x\\x) at (2*\\x, 0) {};\n\t\t\t}\n\t\t\t\n\t\t\t\\foreach \\x in {0,...,6}{\n\t\t\t\t\\node[gray] (y\\x) at (2*\\x+1, 0) {};\n\t\t\t}\n\t\t\t\n\t\t\t\\foreach \\x in {0,...,6}{\n\t\t\t\t\\node[gray] (z\\x) at (2*\\x+1, -1) {};\n\t\t\t}\n\t\t\t\n\t\t\t\\foreach \\x in {0,...,3}{\n\t\t\t\t\\node[gray] (a\\x) at (2*\\x, 2) {};\n\t\t\t}\n\t\t\t\n\t\t\t\\foreach \\x in {0,...,3}{\n\t\t\t\t\\node[gray] (b\\x) at (2*\\x, 3) {};\n\t\t\t}\n\t\t\t\n\t\t\t\\foreach \\x in {0,...,3}{\n\t\t\t\t\\node[gray] (c\\x) at (2*\\x, 5) {};\n\t\t\t}\n\t\t\t\n\t\t\t\\foreach \\x in {0,...,3}{\n\t\t\t\t\\node[gray] (d\\x) at (2*\\x, 6) {};\n\t\t\t}\n\t\t\t\n\t\t\t\\foreach \\x in {0,...,3}{\n\t\t\t\t\\node[gray] (e\\x) at (2*\\x, 7) {};\n\t\t\t}\n\t\t\t\n\t\t\t\\foreach \\x in {0,...,3}{\n\t\t\t\t\\node[gray] (f\\x) at (2*\\x, 9) {};\n\t\t\t}\n\t\t\t\n\t\t\t\\foreach \\x in {0,...,3}{\n\t\t\t\t\\node[gray] (g\\x) at (2*\\x, 10) {};\n\t\t\t}\n\t\t\t\n\t\t\t\\foreach \\x in {0,...,3}{\n\t\t\t\t\\node[gray] (h\\x) at (2*\\x, 12) {};\n\t\t\t}\n\t\t\t\n\t\t\t\\foreach \\x in {0,...,6}{\n\t\t\t\t\\node[gray] (i\\x) at (2*\\x-1, 13) {};\n\t\t\t}\n\t\t\t\n\t\t\t\\foreach \\x in {0,...,6}{\n\t\t\t\t\\node[gray] (j\\x) at (2*\\x-1, 14) {};\n\t\t\t}\n\t\t\t\n\t\t\t\\foreach \\x in {0,...,6}{\n\t\t\t\t\\node[gray] (k\\x) at (2*\\x-1, 15) {};\n\t\t\t}\n\t\t\t\n\t\t\t\\draw[edge_dotted] (x0) -- (x1) -- (x2);\n\t\t\t\\draw[edge_dotted] (y0) -- (y1) -- (y2);\n\t\t\t\\draw[edge_dotted] (z0) -- (z1) -- (z2);\n\t\t\t\\draw[edge_dotted] (a0) -- (a1) -- (a2);\n\t\t\t\\draw[edge_dotted] (b0) -- (b1) -- (b2);\n\t\t\t\\draw[edge_dotted] (c0) -- (c1) -- (c2);\n\t\t\t\\draw[edge_dotted] (d0) -- (d1) -- (d2);\n\t\t\t\\draw[edge_dotted] (e0) -- (e1) -- (e2);\n\t\t\t\\draw[edge_dotted] (f0) -- (f1) -- (f2);\n\t\t\t\\draw[edge_dotted] (g0) -- (g1) -- (g2);\n\t\t\t\\draw[edge_dotted] (h0) -- (h1) -- (h2);\n\t\t\t\\draw[edge_dotted] (i0) -- (i1) -- (i2);\n\t\t\t\\draw[edge_dotted] (j0) -- (j1) -- (j2);\n\t\t\t\\draw[edge_dotted] (k0) -- (k1) -- (k2);\n\t\t\t\n\t\t\t\\node[gray] (x3) at (9, 0) {};\n\t\t\t\\node[gray] (y3) at (9, 13) {};\n\t\t\t\\node[gray] (z3) at (9, -1) {};\n\t\t\t\\node[gray] (a3) at (9, 2) {};\n\t\t\t\\node[gray] (b3) at (9, 3) {};\n\t\t\t\\node[gray] (c3) at (9, 5) {};\n\t\t\t\\node[gray] (d3) at (9, 6) {};\n\t\t\t\\node[gray] (e3) at (9, 7) {};\n\t\t\t\\node[gray] (f3) at (9, 9) {};\n\t\t\t\\node[gray] (g3) at (9, 10) {};\n\t\t\t\\node[gray] (h3) at (9, 12) {};\n\t\t\t\\node[gray] (i3) at (9, 13) {};\n\t\t\t\\node[gray] (j3) at (9, 14) {};\n\t\t\t\\node[gray] (k3) at (9, 15) {};\n\t\t\t\n\t\t\t\\node[w] (x4) at (12, 0) {};\n\t\t\t\\node[w] (y4) at (12, 13) {};\n\t\t\t\\node[w] (z4) at (12, -1) {};\n\t\t\t\\node[w] (a4) at (12, 2) {};\n\t\t\t\\node[w] (b4) at (12, 3) {};\n\t\t\t\\node[w] (c4) at (12, 5) {};\n\t\t\t\\node[w] (d4) at (12, 6) {};\n\t\t\t\\node[w] (e4) at (12, 7) {};\n\t\t\t\\node[w] (f4) at (12, 9) {};\n\t\t\t\\node[w] (g4) at (12, 10"
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        "index": 671,
        "tikz_code": "\\documentclass[a4paper,12pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,shapes, positioning, matrix, patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node (n11) [circle,draw, draw=blue, fill=blue!10, inner sep=0pt,minimum size=5mm] {$X_1$};\n\\node (n21) [circle,draw,draw=blue, fill=blue!10, inner sep=0pt,minimum size=5mm, right=of n11] {$X_2$};\n\\node (n12) [circle,draw,draw=blue, fill=blue!10, inner sep=0pt,minimum size=5mm, above left=of n11] {$X_1$};\n\\node (n13) [circle,draw,draw=blue, fill=blue!10, inner sep=0pt,minimum size=5mm, above right=of n11] {$X_2$};\n\\node (n22) [circle,draw,draw=blue, fill=blue!10, inner sep=0pt,minimum size=5mm, right=of n11] {$Y$};\n\\node (M) [circle,draw] {M};\n\\node (m1) [left=of n12, color=blue] {$\\delta_{\\text{M}}\\delta_{M\\to X_1}$};\n\\node (m2) [right=of n13, color=blue] {$\\delta_{\\text{M}}\\delta_{M\\to X_2}$};\n\n\\draw[->, blue] (m1) to (n12);\n\\draw[->, blue] (m2) to (n13);\n\\draw[->] (n11) to (n21);\n\\draw[->] (n21) to (n13);\n\\draw[->] (n11) to (n12);\n\\draw[->] (n12) to (n22);\n\\draw[->] (n13) to (n22);\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[10pt, DIV=17]{scrartcl}\n\\usepackage{amsmath,amsthm}\n\\usepackage{subcaption,tikz}\n\\usetikzlibrary{decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}[baseline=.875cm, scale=.75]\n\\draw[step=1,gray, very thin] (0,0) grid (8,8);\n\\draw[blue, very thick] (2,2) rectangle (5,5);\n\\draw[blue, very thick] (1,4) rectangle (4,7);\n\\draw[blue, very thick] (6,6) rectangle (7,7);\n\\draw[blue, very thick] (7,1) rectangle (8,2);\n\\draw[blue, very thick] (3,3) rectangle (4,4);\n\\draw[step=.5, black, very thin] (0,0) grid (8,8);\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[a4paper, 11pt]{amsart}\n\\usepackage{amsthm, amsfonts, amsmath, amssymb,amstext}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows, backgrounds}\n\\tikzset{vertex/.style={circle,fill=black,minimum size=0.4pt,inner sep=1.8pt}}\n\\tikzset{emptyvertex/.style={shape=circle, inner sep = 1.8pt, minimum size=0.4pt, draw}}\n\\tikzset{extended line/.style={shorten >=-#1,shorten <=-#1},\n extended line/.default=8cm}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale = .4]\n\t  \\clip (-6,-4) rectangle (6,4);\n\t  \\draw[color = black, extended line] (-5,0) -- (5,0);\n\t  \\draw[color = black, extended line] (0,-3) -- (0,3);\n\t  \\draw[color = black] (-2,2) -- (2,2) -- (2,-2) -- (-2,-2) -- (-2,2);\n\t  \\node[color = black] at (3,0) {$\\to$}; \n\t  \\draw[color = black, extended line] (6,0) -- (10,0);\n\t  \\draw[color = black, extended line] (9,-3) -- (9,3);\n\t  \\draw[color = black] (7,2) -- (11,2) -- (11,-2) -- (7,-2) -- (7,2);\n\t  \\filldraw (5.5,0) circle (4pt);\n\t  \\filldraw (0.5,0) circle (4pt);\n\t  \\filldraw (9.5,0) circle (4pt);\n\t  \\filldraw[fill = white] (7.5,2) circle (4pt);\n\t  \\node[color = black] at (6,-2.5) {res};\n\t  \\begin{scope}[shift = {(0,-6)}]\n\t  \t\\draw[color = black, extended line] (-5,0) -- (5,0);\n\t  \t\\draw[color = black, extended line] (0,-3) -- (0,3);\n\t  \t\\draw[color = black] (-2,2) -- (2,2) -- (2,-2) -- (-2,-2) -- (-2,2);\n\t  \t\\filldraw (0.5,0) circle (4pt);\n\t  \t\\filldraw (5.5,0) circle (4pt);\n\t  \t\\node[color = black] at (2.5,2.5) {res};\n\t  \t\\begin{scope}[shift = {(0,2)}]\n\t  \t\t\\draw[color = black, extended line] (-5,0) -- (5,0);\n\t  \t\t\\draw[color = black, extended line] (0,-3) -- (0,3);\n\t  \t\t\\draw[color = black] (-2,2) -- (2,2) -- (2,-2) -- (-2,-2) -- (-2,2);\n\t  \t\t\\filldraw (0.5,0) circle (4pt);\n\t  \t\t\\filldraw[fill = white] (2.5,2) circle (4pt);\n\t  \t\\end{scope}\n\t  \\end{scope}\n\t\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 674,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,calc,fit,matrix,positioning,shapes,shadows,arrows.meta}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\tikzstyle{label} = [draw=none, node distance=1cm, font={\\small}]\n\\tikzstyle{wires} = [line width=0.5mm, color=red!60!black]\n\\tikzstyle{input} = [draw=none, node distance=1cm, font={\\tiny}]\n\\tikzstyle{output} = [draw=none, node distance=1cm, font={\\tiny}]\n\n\\node [label, left] at (0, 0) {Alice's input:};\n\\node [label, right] at (2, 0) {Bob's input:};\n\\node [input] (input0) at (0, -1) {000};\n\\node [input] (input1) at (0, -0.7) {001};\n\\node [input] (input2) at (0, -0.4) {010};\n\\node [input] (input3) at (0, -0.1) {011};\n\\node [input] (input4) at (0, 0.2) {100};\n\\node [input] (input5) at (0, 0.5) {101};\n\\node [input] (input6) at (0, 0.8) {110};\n\\node [input] (input7) at (0, 1.1) {111};\n\n\\node [label, left] at (2, 1.1) {000};\n\\node [label, left] at (2, 0.8) {001};\n\\node [label, left] at (2, 0.5) {010};\n\\node [label, left] at (2, 0.2) {011};\n\\node [label, left] at (2, -0.1) {100};\n\\node [label, left] at (2, -0.4) {101};\n\\node [label, left] at (2, -0.7) {110};\n\\node [label, left] at (2, -1) {111};\n\n\\node [output] (output0) at (2, -1) {111};\n\\node [output] (output1) at (2, -0.7) {110};\n\\node [output] (output2) at (2, -0.4) {100};\n\\node [output] (output3) at (2, -0.1) {011};\n\\node [output] (output4) at (2, 0.2) {010};\n\\node [output] (output5) at (2, 0.5) {101};\n\\node [output] (output6) at (2, 0.8) {001};\n\\node [output] (output7) at (2, 1.1) {000};\n\n\\draw [wires] (input0) -- (output0);\n\\draw [wires] (input1) -- (output1);\n\\draw [wires] (input2) -- (output2);\n\\draw [wires] (input3) -- (output3);\n\\draw [wires] (input4) -- (output4);\n\\draw [wires] (input5) -- (output5);\n\\draw [wires] (input6) -- (output6);\n\\draw [wires] (input7) -- (output7);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 676,
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{color}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix,positioning}\n\\tikzset{bullet/.style={circle,fill,inner sep=2pt}}\n\\usepackage{pgfplots}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\\begin{semilogyaxis}[\n\txtick={5, 10, 15},\n\tymin=1e-5,\n\tymax=1e0,\n\twidth=0.45\\textwidth,\n\theight=0.3\\textwidth,\n\tlegend cell align=left,\n\tlegend pos=south east\n\t]\n\t\\addplot[green, thick, mark=x] coordinates {\n\t\t(5,  3.21e-04)\n\t\t(10, 3.17e-05)\n\t\t(15, 3.14e-06)\n\t};\n\t\\addplot[blue, thick, mark=+] coordinates {\n\t\t(5,  3.08e-04)\n\t\t(10, 3.03e-05)\n\t\t(15, 2.99e-06)\n\t};\n\t\\addplot[black, thick, mark=o] coordinates {\n\t\t(5,  2.75e-04)\n\t\t(10, 2.68e-05)\n\t\t(15, 2.62e-06)\n\t};\n\t\\addplot[red, thick, mark=triangle] coordinates {\n\t\t(5,  3.10e-04)\n\t\t(10, 3.04e-05)\n\t\t(15, 2.99e-06)\n\t};\n\t\\addplot[black, dashed] coordinates {\n\t\t(5,  3.29e-04)\n\t\t(10, 3.25e-05)\n\t\t(15, 3.21e-06)\n\t};\n\t\\addplot[blue, dashed] coordinates {\n\t\t(5,  3.08e-04)\n\t\t(10, 3.03e-05)\n\t\t(15, 2.99e-06)\n\t};\n\t\\addplot[green, dashed] coordinates {\n\t\t(5,  2.81e-04)\n\t\t(10, 2.76e-05)\n\t\t(15, 2.71e-06)\n\t};\n\t\\addplot[red, dashed] coordinates {\n\t\t(5,  3.08e-04)\n\t\t(10, 3.03e-05)\n\t\t(15, 2.99e-06)\n\t};\n\t\\legend{1e-4, 1e-3, 1e-2, 1e-1, 1, 2, 10, 100}\n\t\\end{semilogyaxis}\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "index": 678,
        "tikz_code": "\\documentclass[10pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath,amsthm,enumerate}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage[color=green!30]{todonotes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n\\path (0,4) node[draw=blue,shape=circle,fill=white,inner sep=1pt] (x0) {$L_0$}\n-- (2,4) node[draw=blue,shape=circle,fill=white,inner sep=1pt] (x1) {$L_1$}\n-- (3,3) node[draw=blue,shape=circle,fill=white,inner sep=1pt] (x2) {$L_2$}\n-- (3,2) node[draw=blue,shape=circle,fill=white,inner sep=1pt] (x3) {$L_3$}\n-- (2,1) node[draw=blue,shape=circle,fill=white,inner sep=1pt] (x4) {$L_4$};\n\\draw[->,blue] (x0) to[bend left=40] node[midway,fill=white,inner sep=1pt] {$L_4$} (x2);\n\\draw[->,blue] (x2) to[bend left=40] node[midway,fill=white,inner sep=1pt] {$L_3$} (x0);\n\\draw[->,blue] (x2) to[bend right=40] node[midway,fill=white,inner sep=1pt] {$R_4$} (x4);\n\\draw[->,blue] (x4) to[bend right=40] node[midway,fill=white,inner sep=1pt] {$R_3$} (x2);\n\\draw[->,blue] (x1) to[bend left=40] node[midway,fill=white,inner sep=1pt] {$L_2$} (x3);\n\\draw[->,blue] (x3) to[bend left=40] node[midway,fill=white,inner sep=1pt] {$L_1$} (x1);\n\\draw[->,blue] (x3) to[bend right=40] node[midway,fill=white,inner sep=1pt] {$R_2$} (x4);\n\\draw[->,blue] (x4) to[bend right=40] node[midway,fill=white,inner sep=1pt] {$R_1$} (x3);\n\\draw[->,blue] (x0) to[bend right=40] node[midway,fill=white,inner sep=1pt] {$R_0$} (x4);\n\\draw[->,blue] (x4) to[bend right=40] node[midway,fill=white,inner sep=1pt] {$L_0$} (x0);\n\\draw[loosely dotted,blue] (4.2,2.5) -- (5,2.5) -- (5,3.5) -- (4.2,3.5) -- cycle;\n\\path (8,4) node[draw=blue,shape=circle,fill=white,inner sep=1pt] (y0) {$L_0$}\n-- (10,4) node[draw=blue,shape=circle,fill=white,inner sep=1pt] (y1) {$L_1$}\n-- (11,3) node[draw=blue,shape=circle,fill=white,inner sep=1pt] (y2) {$L_2$}\n-- (11,2) node[draw=blue,shape=circle,fill=white,inner sep=1pt] (y3) {$L_3$}\n-- (10,1) node[draw=blue,shape=circle,fill=white,inner sep=1pt] (y4) {$L_4$}\n-- (9,1) node[draw=blue,shape=circle,fill=white,inner sep=1pt] (y5) {$L_5$};\n\\draw[->,blue] (y0) to[bend left=40] node[midway,fill=white,inner sep=1pt] {$L_4$} (y2);\n\\draw[->,blue] (y2) to[bend left=40] node[midway,fill=white,inner sep=1pt] {$L_3$} (y0);\n\\draw[->,blue] (y2) to[bend right=40] node[midway,fill=white,inner sep=1pt] {$R_4$} (y4);\n\\draw[->,blue] (y4) to[bend right=40] node[midway,fill=white,inner sep=1pt] {$R_3$} (y2);\n\\draw[->,blue] (y1) to[bend left=40] node[midway,fill=white,inner sep=1pt] {$L_2$} (y3);\n\\draw[->,blue] (y3) to[bend left=40] node[midway,fill=white,inner sep=1pt] {$L_1$} (y1);\n\\draw[->,blue] (y3) to[bend right=40] node[midway,fill=white,inner sep=1pt] {$R_2$} (y4);\n\\draw[->,blue] (y4) to[bend right=40] node[midway,fill=white,inner sep=1pt] {$R_1$} (y3);\n\\draw[->,blue] (y0) to[bend right=40] node[midway,fill=white,inner sep=1pt] {$R_0$} (y4);\n\\draw[->,blue] (y4) to[bend right=40] node[midway,fill=white,inner sep=1pt] {$L_0$} (y0);\n\\draw[->,blue] (y5) to[bend right=40] node[midway,fill=white,inner sep=1pt] {$L_5$} (y4);\n\\draw[->,blue] (y4) to[bend right=40] node[midway,fill=white,inner sep=1pt] {$L_4$} (y5);\n\\draw[loosely dotted,blue] (11.2,2.5) -- (12,2.5) -- (12,3.5) -- (11.2,3.5) -- cycle;\n\\draw (4.5,-1) node {(a)};\n\\draw ("
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    {
        "index": 679,
        "tikz_code": "\\documentclass[runningheads, envcountsame, a4paper]{llncs}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{chains,fit,shapes,patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t% nodes %\n\t\t\\node[draw, circle, inner sep=2pt, fill=black] (A) at (0,0) {};\n\t\t\\node[draw, circle, inner sep=2pt, fill=black] (B) at (0,2) {};\n\t\t\\node[draw, circle, inner sep=2pt, fill=black] (C) at (2,2) {};\n\t\t\\node[draw, circle, inner sep=2pt, fill=black] (D) at (4,1) {};\n\t\t\\node[draw, circle, inner sep=2pt, fill=black] (Y) at (6,0) {};\n\t\t\n\t\t% edges %\n\t\t\\draw[->] (A) -> (B);\n\t\t\\draw[->] (A) -> (C);\n\t\t\\draw[->] (A) -> (D);\n\t\t\\draw[->] (A) -> (Y);\n\t\t\\draw[->] (D) -> (Y);\n\t\t\\draw[->] (B) -> (D);\n\t\t\\draw[->] (B) -> (Y);\n\t\t\\draw[->] (C) -> (Y);\n\t\t\n\t\t% dashed edges %\n\t\t\\draw[dashed] (1.5,3) rectangle (3.5,1);\n\t\t\n\t\t% labels %\n\t\t\\node[label=below:{$A$}] at (2,0) {};\n\t\t\\node[label=above:{$B$}] at (2,2) {};\n\t\t\\node[label=above:{$V_1$}] at (3,2) {};\n\t\t\\node[label=above:{$V_2$}] at (4,2) {};\n\t\t\\node[label=below:{$Y$}] at (6,0) {};\n\t\t\\node at (-1,1) {$(S,U)$};\n\t\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 680,
        "tikz_code": "\\documentclass[11pt,reqno]{amsart}\n\\usepackage{amsfonts,amsmath,amssymb,wasysym,stmaryrd,enumerate}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,matrix,decorations.markings,shapes.geometric}\n\n\\begin{document}\n\n\\begin{tikzpicture}[rotate=45,scale=.5] \n\\draw (0,0) -- (7,0) -- (7.5,0.5);\n\\draw (0,1) -- (2,1) -- (2.5,1.5);\n\\draw (0,2) -- (3,2) -- (3.5,2.5);\n\\draw (0,3) -- (1,3) -- (1.5,3.5);\n\\draw (0,4) -- (4,4) -- (4.5,4.5);\n\\draw (0,5) -- (5,5) -- (5.5,5.5);\n\\draw (0,6) -- (6,6) -- (6.5,6.5);\n\\draw (0,7) -- (7,7) -- (7.5,7.5);\n\\draw[shift={(-0.1,0.1)},color=black] (0,0) -- (0,1) -- (1,1) -- (1,0) -- (0,0) -- cycle;\n\\draw[shift={(-0.1,1.1)},color=black] (0,1) -- (0,2) -- (1,2) -- (1,1) -- (0,1) -- cycle;\n\\draw[shift={(-0.1,2.1)},color=black] (0,2) -- (0,3) -- (1,3) -- (1,2) -- (0,2) -- cycle;\n\\draw[shift={(-0.1,3.1)},color=black] (0,3) -- (0,4) -- (1,4) -- (1,3) -- (0,3) -- cycle;\n\\draw[shift={(-0.1,4.1)},color=black] (0,4) -- (0,5) -- (1,5) -- (1,4) -- (0,4) -- cycle;\n\\draw[shift={(-0.1,5.1)},color=black] (0,5) -- (0,6) -- (1,6) -- (1,5) -- (0,5) -- cycle;\n\\draw[shift={(-0.1,6.1)},color=black] (0,6) -- (0,7) -- (1,7) -- (1,6) -- (0,6) -- cycle;\n\\draw[shift={(-0.1,7.1)},color=black] (0,7) -- (0,8) -- (1,8) -- (1,7) -- (0,7) -- cycle;\n\\foreach \\x in {0,1,2,3,4,5,6,7}\n\\foreach \\y in {0,1,2,3,4,5,6,7}\n\\filldraw [black] (\\x,\\y) circle (2pt);\n\\foreach \\y in {0,1,2,3,4,5,6,7}\n\\filldraw [red] (0,\\y) circle (3pt);\n\\foreach \\y in {0,1,2,3,4,5,6,7}\n\\filldraw [blue] (7,\\y) circle (3pt);\n\\foreach \\y in {0,1,2,3,4,5,6,7}\n\\filldraw [red] (7,\\y) circle (3pt);\n\\foreach \\y in {0,1,2,3,4,5,6,7}\n\\filldraw [blue] (7-0.1,\\y) circle (3pt);\n\\foreach \\y in {0,1,2,3,4,5,6,7}\n\\filldraw [red] (7-0.1,\\y) circle (3pt);\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[a4paper,10pt,reqno]{article}\n\\usepackage[colorinlistoftodos,prependcaption]{todonotes}\n\\usepackage{amsmath}\n\\usepackage{amsthm,xcolor}\n\\usepackage[colorlinks, linkcolor=red]{hyperref}\n\\usepackage{amssymb}\n\\usepackage{tikz-cd}\n\\usepackage{tikz}\n\\usepackage{tkz-tab}\n\\usepackage[T1]{fontenc}\n\\usepackage{xcolor}\n\\usepackage{pgfplots}\n\\usepgfplotslibrary{fillbetween}\n\\usepackage[colorinlistoftodos,prependcaption]{todonotes}\n\\pgfplotsset{width=10cm,compat=1.11}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\\begin{axis}[\n    axis lines = middle,\n    xlabel = $x$,\n    ylabel = {$y$},\n    ymin=0, ymax=4,\n    xmin=0, xmax=10,\n    xtick={0,2,4,6,8,10},\n    ytick={0,2,4},\n    grid = major,\n]\n\n    \\addplot [\n        domain=0:8, \n        samples=100, \n        color=red,\n    ]\n    {2^(-x)};\n    \n    \\addplot [\n        domain=2:8, \n        samples=100, \n        color=blue,\n    ]\n    {3^(-x)};\n    \n    \\addplot [\n        domain=4:8, \n        samples=100, \n        color=green,\n    ]\n    {5^(-x)};\n\n    \\addplot [\n        domain=6:8, \n        samples=100, \n        color=orange,\n    ]\n    {7^(-x)};\n    \n    \\addplot [\n        domain=8:8, \n        samples=100, \n        color=violet,\n    ]\n    {9^(-x)};\n\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,automata}\n\\tikzset{initial text={}}\n\\usepackage{pgfgantt}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\node [fill=red!10, minimum width=3cm, minimum height=2cm,anchor=west] (a) at (0,2) {};\n    \\node [fill=cyan!10, minimum width=3cm, minimum height=2cm,anchor=east] (b) at (3,2) {};\n    \\node [fill=cyan!10, minimum width=3cm, minimum height=2cm,anchor=west] (c) at (3,-2) {};\n    \\node [fill=red!10, minimum width=3cm, minimum height=2cm,anchor=east] (d) at (0,-2) {};\n    \n    \\draw[dotted,->,>=stealth'] (-1.5,2) -- (-0.5,1);\n    \\node at (-0.5,1.75) {\\tiny $(a_k,1+1)$};\n    \\draw[dotted,<-,>=stealth'] (3.5,2) -- (4.5,1);\n    \\node at (4.5,1.75) {\\tiny $(a_k,1+k_a)$};\n    \\draw[dotted,->,>=stealth'] (3.5,-2) -- (4.5,-1);\n    \\node at (4.5,-1.75) {\\tiny $(a_k,1+k_a)$};\n    \\draw[dotted,<-,>=stealth'] (-1.5,-2) -- (-0.5,-1);\n    \\node at (-0.5,-1.75) {\\tiny $(a_k,1+1)$};\n    \n    \\draw[->,>=stealth'] (1,2.25) -- (1.9,1.3);\n    \\draw[->,>=stealth'] (1,-2.25) -- (1.9,-1.3);\n    \\draw[dotted,->,>=stealth'] (2,2.25) -- (2.9,1.3);\n    \\draw[dotted,->,>=stealth'] (2,-2.25) -- (2.9,-1.3);\n    \n    \\draw[<-,>=stealth'] (-1.5,1) -- (-0.5,0.1);\n    \\draw[<-,>=stealth'] (3.5,1) -- (4.5,0.1);\n    \\draw[<-,>=stealth'] (-1.5,-1) -- (-0.5,-0.1);\n    \\draw[<-,>=stealth'] (3.5,-1) -- (4.5,-0.1);\n    \\draw[dotted,<-,>=stealth'] (0.1,1.5) -- (0.9,2);\n    \\draw[dotted,<-,>=stealth'] (0.1,-1.5) -- (0.9,-2);\n    \\draw[dotted,->,>=stealth'] (1.1,1.5) -- (1.9,2);\n    \\draw[dotted,->,>=stealth'] (1.1,-1.5) -- (1.9,-2);\n    \n    \\node at (1,2.75) {\\tiny $\\Sigma_{k+1}$};\n    \\node at (1,-2.75) {\\tiny $\\Sigma_{k+1}$};\n    \\node at (2.3,2.75) {\\tiny $\\Sigma_{k+1}$};\n    \\node at (2.3,-2.75) {\\tiny $\\Sigma_{k+1}$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 695,
        "tikz_code": "\\documentclass{article}\n\\usepackage{pgfplots}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,shadows,arrows,backgrounds}\n\\usepgfplotslibrary{groupplots}\n\\usepackage{color, colortbl}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{axis} [\n    width=10cm,\n    height=6cm,\n    ylabel = difference in utility,\n    xlabel = \\# queries,\n    xmin=0, xmax=500,\n    ymin=-8, ymax=8,\n    xtick={0,100,200,300,400,500},\n    %legend pos=north west,\n    ymajorgrids=true,\n    grid style=dashed,\n    legend columns=2,\n    legend style={at={(0,0)},anchor=north west}]\n\n%query 1\n\\addplot[smooth,color=gray,mark=triangle, thick] coordinates {\n    (0,0)\n    (50,0.013)\n    (100,0.015)\n    (150,0.02)\n    (200,0.026)\n    (250,0.019)\n    (300,0.014)\n    (350,0.014)\n    (400,0.014)\n    (450,0.012)\n    (500,0.011)\n};\n\n\\addplot[smooth,color=blue, mark=*, thick] coordinates {\n    (0,0)\n    (50,0.04)\n    (100,0.038)\n    (150,0.033)\n    (200,0.03)\n    (250,0.035)\n    (300,0.03)\n    (350,0.028)\n    (400,0.027)\n    (450,0.028)\n    (500,0.03)\n};\n\n\\legend{mean, 55\\% CI}\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{pgfplots}\n\\usepackage{amsmath}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{axis}[ybar,ylabel=Blaze, xlabel=Baseline, \nsymbolic x coords={8-1, 8-2, 8-3, 8-4, 8-5, 8-6, 8-7, 8-8, 8-9, 8-10, 8-11, 8-12, 8-13, 8-14, 8-15, 8-16, 8-17, 8-18, 8-19, 8-20, 8-21, 8-22, 8-23, 8-24, 8-25, 8-26, 8-27, 8-28, 8-29, 8-30, 8-31, 8-32, 8-33, 8-34, 8-35, 8-36, 8-37, 8-38, 8-39, 8-40, 8-41, 8-42, 8-43, 8-44, 8-45, 8-46, 8-47, 8-48, 8-49, 8-50, 8-51, 8-52, 8-53, 8-54, 8-55, 8-56, 8-57, 8-58, 8-59, 8-60, 8-61, 8-62, 8-63, 8-64, 8-65, 8-66, 8-67, 8-68, 8-69, 8-70, 8-71, 8-72, 8-73, 8-74, 8-75, 8-76, 8-77, 8-78, 8-79, 8-80, 8-81, 8-82, 8-83, 8-84, 8-85, 8-86, 8-87, 8-88, 8-89, 8-90, 8-91, 8-92, 8-93, 8-94, 8-95, 8-96, 8-97, 8-98, 8-99, 8-100, 8-101, 8-102, 8-103, 8-104, 8-105, 8-106, 8-107, 8-108, 8-109, 8-110, 8-111, 8-112, 8-113, 8-114, 8-115, 8-116, 8-117, 8-118, 8-119, 8-120, 8-121, 8-122, 8-123, 8-124, 8-125, 8-126, 8-127, 8-128, 8-129, 8-130, 8-131, 8-132, 8-133, 8-134, 8-135, 8-136, 8-137, 8-138, 8-139, 8-140, 8-141, 8-142, 8-143, 8-144, 8-145, 8-146, 8-147, 8-148, 8-149, 8-150, 8-151, 8-152, 8-153, 8-154, 8-155, 8-156, 8-157, 8-158, 8-159, 8-160, 8-161, 8-162, 8-163, 8-164, 8-165, 8-166, 8-167, 8-168, 8-169, 8-170, 8-171, 8-172, 8-173, 8-174, 8-175, 8-176, 8-177, 8-178, 8-179, 8-180, 8-181, 8-182, 8-183, 8-184, 8-185, 8-186, 8-187, 8-188, 8-189, 8-190, 8-191, 8-192, 8-193, 8-194, 8-195, 8-196, 8-197, 8-198, 8-199, 8-200, 8-201, 8-202, 8-203, 8-204, 8-205, 8-206, 8-207, 8-208, 8-209, 8-210, 8-211, 8-212, 8-213, 8-214, 8-215, 8-216, 8-217, 8-218, 8-219, 8-220, 8-221, 8-222, 8-223, 8-224, 8-225, 8-226, 8-227, 8-228, 8-229, 8-230, 8-231, 8-232, 8-233, 8-234, 8-235, 8-236, 8-237, 8-238, 8-239, 8-240, 8-241, 8-"
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        "tikz_code": "\\documentclass[11pt,letterpaper]{scrartcl}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage[table]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{fit,shapes.misc,shapes.geometric,decorations.pathreplacing}\n\\pgfdeclarelayer{bg}\n\\pgfsetlayers{bg,main}\n\n\\begin{document}\n\n\\begin{tikzpicture}[thick,\n                  vertex/.style={draw, circle, thick, fill=black, inner sep=0pt, minimum size=4pt},\n                  edge/.style={line width=1.5pt}\n                ]\n                    \\foreach \\i in {1,...,5}\n                    \\foreach \\j in {1,2}\n                    {\n                        \\node[vertex] (u\\i\\j) at (\\i, \\j) {};\n                    }\n                    \\node (d1) at (0, 0) {$T_s$};\n                    \\node (d2) at (5, 0) {$Y$};\n                    \\node (d3) at (1, 2.25) {$X_1$};\n                    \\node (d4) at (2.5, 2.25) {$X_2$};\n                    \\node (d5) at (3.75, 2.25) {$\\dots$};\n                    \\node (d6) at (4, 2.25) {$X_{n-1}$};\n                    \\node (d7) at (5, 2.25) {$X_n$};\n                    \\draw[edge] (d1) -- (u11);\n                    \\draw[edge] (d1) -- (u12);\n                    \\draw[edge] (d2) -- (u11);\n                    \\draw[edge] (d2) -- (u12);\n                    \\draw[edge] (d3) -- (u51);\n                    \\draw[edge] (d3) -- (u52);\n                    \\draw[edge] (d4) -- (u51);\n                    \\draw[edge] (d4) -- (u52);\n                    \\draw[edge] (d6) -- (u51);\n                    \\draw[edge] (d6) -- (u52);\n                    \\draw[edge] (d7) -- (u51);\n                    \\draw[edge] (d7) -- (u52);\n                \\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{calc}\n\\tikzset{b/.style = {circle,draw,inner sep=0pt,fill=black ,minimum size=3.0pt},\n         w/.style = {circle,draw,inner sep=0pt,fill=white,thick,minimum size=3.2pt},\n         i/.style = {circle,     inner sep=0pt,thick,minimum size=3.0pt},\n       stc/.style = {circle,draw,inner sep=0pt,thick,minimum size=7.0mm},\n       tac/.style = {rectangle,draw,inner sep=0pt,thick,rotate=45,minimum size=7mm}\n     }\n\\tikzset{every picture/.style={line width=0.75pt}}\n\\tikzset{empty/.style={rectangle,draw=none,fill=none}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[line width=0.5pt,minimum size=2pt,inner sep=0.9pt,scale=0.9,font=\\small]\n\\draw (-2,-2.5) node[circle,b,label=left:$z_2$] (0) {}\n (0,0) node[b] (1) {}\n (0,-1) node[circle,b,label=left:$x_j$] (2) {} (2,-2) node[circle,b] (3) {} (0,-3) node[circle,b] (4) {}\n (1,-4) node[circle,b,label=left:$x_{j,2}$] (5) {} (3,-4) node[circle,b] (6) {} (1,-5) node[circle,b] (7) {}\n (2,-6) node[circle,b,label=left:$x_{j,3}$] (8) {} (4,-6) node[circle,b] (9) {} (2,-7) node[circle,b] (10) {}\n (3,-8) node[circle,b,label=left:$x_{j,4}$] (11) {};\n \\foreach \\x/\\y in {0/1,1/2,1/3,2/1,2/3,3/4,4/5,5/6,6/3,6/7,7/4,7/8,8/6,8/9,9/10,10/8,11/7}{\n  \\draw (\\x)--(\\y);}\n \\draw[densely dashed] (0)--(5) (1)--(2) (3)--(4) (6)--(9) (10)--(11);\n \\begin{scope}[xshift=5cm]\n \\draw (-2,-2.5) node[circle,b,label=left:$z_2$] (0) {}\n (0,0) node[circle,b,label=left:$x_j$] (1) {}\n (0,-1) node[circle,b,label=left:$x_{j,2}$] (2) {} (2,-2) node[circle,b] (3) {} (0,-3) node[circle,b] (4) {}\n (1,-4) node[circle,b,label=left:$x_{j,3}$] (5) {} (3,-4) node[circle,b] (6) {} (1,-5) node[circle,b] (7) {}\n (2,-6) node[circle,b,label=left:$x_{j,4}$] (8) {} (4,-6) node[circle,b] (9) {} (2,-7) node[circle,b] (10) {}\n (3,-8) node[circle,b,label=left:$x_{j,5}$] (11) {};\n \\foreach \\x/\\y in {0/1,1/2,1/3,2/1,2/3,3/4,4/5,5/6,6/3,6/7,7/4,7/8,8/6,8/9,9/10,10/8,11/7}{\n  \\draw (\\x)--(\\y);}\n \\draw[densely dashed] (0)--(5) (1)--(2) (3)--(4) (6)--(9) (10)--(11);\n \\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usepackage[T1]{fontenc}\n\\usepackage{inputenc}\n\n\\newcommand{\\eps}{\\varepsilon}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw [line width=0.7mm, green!50!black, ->] (0,0) -- (2.5,0);\n\\draw [line width=0.7mm, blue, ->] (2.5,0) -- (10,0);\n\\draw [line width=0.7mm, red, ->] (10,0) -- (13,0);\n\\draw (0,0.1) -- (0,-0.1) node[below]{$0$};\n\\draw (2.5,0.1) -- (2.5,-0.1) node[below]{$1-c$};\n\\draw (10,0.1) -- (10,-0.1) node[below]{$1$};\n\\draw (13,0.1) -- (13,-0.1) node[below]{$\\tau$};\n\\draw [line width=0.4mm, black, ->] (6,2) -- (6,0.5);\n\\draw [line width=0.4mm, black, ->] (6,2) -- (4.5,2);\n\\draw [line width=0.4mm, black, ->] (6,2) -- (7.5,2);\n\\draw (5.2,2) node[above,red]{Lemna ?};\n\\draw (5.2,1) node[above,blue]{Lemna ?};\n\\draw (5.2,0.6) node[above,green!50!black]{$\\eps$};\n\\draw [line width=0.4mm, black, ->] (6,2) -- (6,-1.7);\n\\draw [line width=0.4mm, black, ->] (6,-1.7) to [out=125, in=-125] (8,-1.7);\n\\draw [line width=0.4mm, black, ->] (8,-1.7) to [out=-65, in=65] (9,-1.7);\n\\draw (6,-2) node[above, red]{Lemna ?};\n\\draw (9,-2) node[above, red]{Lemna ?};\n\\draw (6.75,-1.7) node[below, red]{$0.5$};\n\\draw (7.6,-1.7) node[below, red]{$0.5$};\n\\draw (8.5,-1.7) node[below, red]{$0.5$};\n\\draw [line width=0.4mm, black, ->] (4.8,-1.4) -- (4.8,-2.5);\n\\draw [line width=0.4mm, black, ->] (9.2,-1.4) -- (9.2,-2.5);\n\\draw [line width=0.4mm, black, ->] (5.2,-2.5) -- (9.2,-2.5);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 716,
        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usepackage{xcolor}\n\\usepackage[colorlinks=true]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\tikzset{\n    \tblock/.style = {draw, fill=white, rectangle, minimum height=1cm, minimum width=1cm, rounded corners},\n    \ttrapezium/.style = {draw, shape border rotate=270, fill=white, trapezium, trapezium left angle=70, trapezium right angle=110, minimum height=1cm, minimum width=2cm, rounded corners},\n    \tsum/.style = {draw, fill=white, circle, minimum size=1cm, inner sep=0pt, anchor=input}\n    }\n    \\node [trapezium,label={[name=label] \\small $1 - \\frac{1}{N}$}] (S1) at (0,5) {\\scriptsize $\\sigma(\\sum_{i \\in P_k} w_i x_i + b)$};\n    \\node [trapezium,label={[name=label2] \\small $\\frac{1}{N}$}] (S2) at (5,5) {\\scriptsize $\\sigma(\\sum_{i \\in P_k} w_i x_i + b)$};\n    \\node [trapezium] (D1) at (0,2.5) {\\scriptsize $\\sigma(\\sum_{i \\in P_k} w_i x_i + b)$};\n    \\node [trapezium] (D2) at (5,2.5) {\\scriptsize $\\sigma(\\sum_{i \\in P_k} w_i x_i + b)$};\n    \\node (dots1) at (0,1) {\\scriptsize $\\vdots$};\n    \\node (dots2) at (5,1) {\\scriptsize $\\vdots$};\n    \\node (dots3) at (2.5,6) {\\scriptsize $\\dots$};\n    \\node [block, label={[name=male] \\small Male}] (M1) at (-2,8) {\\color{green} 0.9};\n    \\node [block, label={[name=male] \\small Hassas\\-i\\-ng}] (M2) at (-2,6.5) {\\color{green} 0.9};\n    \\node [block, label={[name=male] \\small Mother}] (M3) at (-2,5) {\\color{green} 0.9};\n    \\node [block, label={[name=male] \\small Father}] (M4) at (-2,2.5) {\\color{green} 0.9};\n    \\node [block, label={[name=male] \\small Child}] (M5) at (-2,1) {\\color{green} 0.9};\n    \\node [block, label={[name=female] \\small Male}] (F1) at (7,8) {\\color{red} 0.5};\n    \\node [block, label={[name=female] \\small Hassas\\-i\\-ng}] (F2) at (7,6.5) {\\color{red} 0.5};\n    \\node [block, label={[name=female] \\small Mother}] (F3) at (7,5) {\\color{red} 0.5};\n    \\node [block, label={[name=female] \\small Father}] (F4) at (7,2.5) {\\color{red} 0.5};\n    \\node [block, label={[name=female] \\small Child}] (F5) at (7,1) {\\color{red} 0.5};\n    \\draw [->] (M1) -- (D1);\n    \\draw [->] (M2) -- (D1);\n    \\draw [->] (M3) -- (D1);\n    \\draw [->] (M4) -- (D1);\n    \\draw [->] (M5) -- (D1);\n    \\draw [->] (F1) -- (D2);\n    \\draw [->] (F2) -- (D2);\n    \\draw [->] (F3) -- (D2);\n    \\draw [->] (F4) -- (D2);\n    \\draw [->] (F5) -- (D2);\n    \\draw [->] (D1) -- (S1);\n    \\draw [->] (D2) -- (S2);\n    \\draw [->] (D1) -- (S1);\n    \\draw [->] (D2) -- (S2);\n    \\draw [->] (S1) -- (dots3);\n    \\draw [->] (S2) -- (dots3);\n    \\draw [->] (S1) -- (dots2);\n    \\draw [->] (S2) -- (dots2);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 717,
        "tikz_code": "\\documentclass[12pt,reqno]{amsart}\n\\usepackage{amssymb,amsmath,dsfont}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.14}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{xcolor}\n\\usepackage{pgfplots}\n\\usetikzlibrary{shapes,arrows}\n\\usetikzlibrary{hobby}\n\\usetikzlibrary{bending}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.6]\n\\filldraw[blue!25] (15:1) -- (270:1) -- (315:1) -- cycle;\n\\filldraw[red!25] (0,0) -- (30:1) -- (315:1) -- cycle;\n\\filldraw[red!25] (0,0) -- (30:1) -- (15:1) -- cycle;\n\\filldraw[red!25] (0,0) -- (15:1) -- (270:1) -- cycle;\n\\draw[thick,-latex] (-2,0) -- (14,0);\n\\draw[thick,-latex] (-1,-1.5) -- (-1,3.5);\n\\draw[thick,-latex] (-1,-1.5) -- (14,0);\n\\node[below] at (14,0) {$x_1$};\n\\node[right] at (1,3) {$x_2$};\n\\node[above left] at (-1,-1.5) {$x_1'$};\n\\node at (1.5,0) {$\\bullet$};\n\\node[below] at (1.5,0) {$\\theta$};\n\\draw[thick] (15:1) arc (15:30:1);\n\\draw[thick,-latex] (0,0) -- (15:1);\n\\draw[thick] (15:1) arc (15:315:1);\n\\draw[thick,-latex] (0,0) -- (30:1);\n\\draw[thick] (30:1) arc (30:315:1);\n\\draw[thick,-latex] (0,0) -- (315:1);\n\\draw[thick] (315:1) arc (315:360:1);\n\\node at (1,1.3) {$\\rho$};\n\\node at (1.3,1) {$\\varphi$};\n\\node at (3,1.5) {$\\beta$};\n\\node at (1.6,1.5) {$\\alpha$};\n\\node at (3.8,0.8) {$2\\rho$};\n\\node at (-1.2,-0.5) {$\\beta$};\n\\node at (2.5,0) {$\\bullet$};\n\\node at (2.7,0.3) {$\\alpha$};\n\\node[above left] at (-1,1.3) {Type I};\n\\node[above left] at (-1,-0.2) {Type II};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 718,
        "tikz_code": "\\documentclass[conference]{IEEEtran}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{xcolor}\n\\usepackage{pgf,tikz,pgfplots}\n\\usetikzlibrary{arrows,shapes}\n\\usetikzlibrary{plotmarks}\n\\usepgfplotslibrary{groupplots}\n\\pgfplotsset{compat=newest}\n\\pgfplotsset{plot coordinates/math parser=false}\n\\usetikzlibrary{positioning,spy}\n\\usetikzlibrary{backgrounds}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\tikzstyle{every node}=[font=\\footnotesize]\n\\node[align = center] at (0,0) {\\includegraphics[width=40mm]{example-image}};\n\\node at (0.3,-0.8) {Dimensionality-Free Noise-Free};\n\\node at (0.3,-1.6) {Feature Set};\n\\node[align = center] at (2.5,-2.35) {\\includegraphics[width=20mm]{example-image}};\n\\node at (2.7,-2.8) {$h_1$};\n\\node at (4.3,-2.8) {$h_2$};\n\\node at (5.9,-2.8) {$h_3$};\n\\node at (7.5,-2.8) {$\\ldots$};\n\\node at (9.1,-2.8) {$h_T$};\n\\node[align = center] at (10.5,0) {\\includegraphics[width=40mm]{example-image}};\n\\draw[->, >=latex] (2.5,-1.3) to (2.5,-1.0);\n\\draw[->, >=latex] (5.1,-1.3) to (5.1,-1.0);\n\\draw[->, >=latex] (7.7,-1.3) to (7.7,-1.0);\n\\draw[->, >=latex] (9.5,-1.3) to (9.5,-1.0);\n\\node[align = center] at (5.1,0.1) {DL-Based Feature Representation};\n\\draw[dashed] (-1.4,-1.9) rectangle (8.1,1.5);\n\\draw[<->, >=latex] (10.5,0) to (10.5,-0.6);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 719,
        "tikz_code": "\\documentclass[preprint,12pt]{elsarticle}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usepackage{pgf}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.9, shift={(0,0)}]\n\\tikzstyle{vertex}=[circle,draw=black, fill=white]\n\\tikzstyle{point}=[circle,draw=black, fill=white, inner sep = 0.06cm]\n\n    \\node[vertex] (p11) at (0,0) {};\n\t\\node[vertex] (p21) at (2,0) {};\n\t\\node[vertex] (p31) at (3,0) {};\n\t\\node[vertex] (p10) at (0,-1) {};\n\t\\node[vertex] (p20) at (2,-1) {};\n\t\\node[vertex] (p30) at (3,-1) {};\n\t\\node[vertex] (p13) at (0.5,1.5) {};\n\t\\node[vertex] (p23) at (2.5,1.5) {};\n\t\\node[vertex] (p33) at (3.5,1.5) {};\n\n\t\\node[vertex] (p12) at (0.5,-0.5) {};\n\t\\node[vertex] (p22) at (2.5,-0.5) {};\n\t\\node[vertex] (p32) at (3.5,-0.5) {};\n\t\n\t\\node[point] (p1) at (0.2,-2) {};\n\t\\node[point] (p2) at (2.2,-2) {};\n\t\\node[point] (p3) at (3.2,-2) {};\n\n\n\t\\draw[ultra thick] (p11) -- (p12) -- (p13) -- (p10) -- (p11) -- (p21) -- (p22) -- (p23) -- (p33) -- (p32) -- (p31) -- (p30) -- (p20) -- (p10) -- (p20) -- (p30) -- (p21) -- (p31) -- (p22) -- (p32) -- (p23) -- (p13) -- (p23);\n\t\\draw[ultra thick] (p1) -- (p11);\n\t\\draw[ultra thick] (p2) -- (p21);\n\t\\draw[ultra thick] (p3) -- (p31);\n\t\n\t\\draw (0.5, -1.5) node {$\\tau_2$};\n\n\t\n\t\\draw[<->] (-0.5,1) -- (-0.5,-1.5) node[pos=0.5, left] {$\\tau_1$};\n\t\n\n\t\\node at (0.5,0.2) {$p_{10}$};\n\t\\node at (2.5,0.2) {$p_{20}$};\n\t\\node at (3.5,0.2) {$p_{30}$};\n\t\\node at (-0.5,0.7) {$p_{110}$};\n\t\\node at (-0.5,-0.8) {$p_{100}$};\n\t\\node at (0.5,-0.8) {$p_{210}$};\n\t\\node at (3.5,-0.8) {$p_{001}$};\n\t\\node at (2.5,-0.8) {$p_{310}$};\n\t\\node at (3.5,1.8) {$p_{111}$};\n\t\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 720,
        "tikz_code": "\\documentclass{article}\n\\usepackage[T1]{fontenc}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,shapes,positioning,shadows,trees,calc,decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n  node distance=1em,\n  box/.style={draw,outer sep=0pt,\n  minimum width=2em,minimum height=2em,\n  align=center,node distance=2em},\n  bnode/.style={box,draw=black,thick,fill=white,\n  inner sep=0pt},\n  enode/.style={box,draw=black,thick,fill=white,\n  inner sep=0pt,double=white},\n  tnode/.style={box,draw=black,thick,fill=white,\n  inner sep=0pt,double=white,dashed},\n  ynode/.style={box,draw=black,thick,fill=white,\n  inner sep=0pt,double=white},\n  fnode/.style={box,draw=black,thick,fill=white,\n  inner sep=0pt,double=white},\n  gnode/.style={box,draw=black,thick,fill=white,\n  inner sep=0pt,double=white},\n  gnoded/.style={box,draw=black,thick,fill=white,\n  inner sep=0pt,double=white},\n  gnodef/.style={box,draw=black,thick,fill=white,\n  inner sep=0pt,double=white},\n  gnodeg/.style={box,draw=black,thick,fill=white,\n  inner sep=0pt,double=white}\n  ]\n  \\node[tnode](t6){b};\n  \\node[enode](e6)[below=0pt of t6]{b};\n  \\node[bnode](b6)[below=0pt of e6]{b};\n  \\node[gnode](g6)[below=0pt of b6]{d};\n  \\node[fnode](f6)[below=0pt of g6]{d};\n  \\node[ynode](y6)[below=0pt of f6]{e};\n  \\node[enode](e5)[right=0pt of t6]{b};\n  \\node[bnode](b5)[below=0pt of e5]{b};\n  \\node[gnodef](g5)[below=0pt of b5]{d};\n  \\node[fnode](f5)[below=0pt of g5]{d};\n  \\node[ynode](y5)[below=0pt of f5]{e};\n  \\node[enode](e4)[right=0pt of e5]{b};\n  \\node[bnode](b4)[below=0pt of e4]{b};\n  \\node[gnode](g4)[below=0pt of b4]{d};\n  \\node[fnode](f4)[below=0pt of g4]{d};\n  \\node[ynode](y4)[below=0pt of f4]{e};\n  \\node[enode](e3)[right=0pt of e4]{b};\n  \\node[bnode](b3)[below=0pt of e3]{b};\n  \\node[gnode](g3)[below=0pt of b3]{d};\n  \\node[fnode](f3)[below=0pt of g3]{d};\n  \\node[ynode](y3)[below=0pt of f3]{e};\n  \\node[enode](e2)[right=0pt of e3]{b};\n  \\node[bnode](b2)[below=0pt of e2]{b};\n  \\node[gnode](g2)[below=0pt of b2]{d};\n  \\node[fnode](f2)[below=0pt of g2]{d};\n  \\node[ynode](y2)[below=0pt of f2]{e};\n  \\node[enode](e1)[right=0pt of e2]{b};\n  \\node[bnode](b1)[below=0pt of e1]{b};\n  \\node[gnode](g1)[below=0pt of b1]{d};\n  \\node[fnode](f1)[below=0pt of g1]{d};\n  \\node[ynode](y1)[below=0pt of f1]{e};\n  \\node[enode](e0)[right=0pt of e1]{b};\n  \\node[bnode](b0)[below=0pt of e0]{b};\n  \\node[gnode](g0)[below=0pt of b0]{d};\n  \\node[fnode](f0)[below=0pt of g0]{d};\n  \\node[ynode](y0)[below=0pt of f0]{e};\n  \\node[enode](e-1)[right=0pt of e0]{b};\n  \\node[bnode](b-1)[below=0pt of e-1]{b};\n  \\node[gnode](g-1)[below=0pt of b-1]{d};\n  \\node[fnode](f-1)[below=0pt of g-1]{d};\n  \\node[ynode](y-1)[below=0pt of f-1]{e};\n  \\node[enode](e-2)[right=0pt of e-1]{b};\n  \\node[bnode](b-2)[below=0pt of e-2]{b};\n  \\node[gnode](g-2)[below=0pt of b-2]{d};\n  \\node[fnode](f-2)[below=0pt of g-2]{d};\n  \\node[ynode](y-2)[below=0pt of f-2]{e};\n  \\node[enode](e-3)[right=0pt of e-2]{b};\n  \\node[bnode](b-3)[below=0pt of e-3]{b};\n  \\node[gnode](g-3)[below=0pt of b-3]{d};\n  \\node[fnode](f-3)[below=0pt of g-3]{d};\n  \\node[ynode](y-3)[below=0pt of f-3]{e};\n  \\node[enode](e-4)[right=0pt of e-3]{b};\n  \\node[bnode](b-4)[below=0pt of e-4]{b};\n  \\node[gnode](g-4)[below=0pt of b-4]{d};\n  \\node[fnode](f-4)[below=0pt of g-4]{d};\n  \\node[ynode](y-4)[below=0pt of f-4]{e};\n  \\node[enode](e-5)[right=0pt of e-4]{b};\n  \\node[bnode](b-5)[below=0pt of e-5]{b};\n  \\node[gnode](g-5)[below=0pt"
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        "index": 721,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amsmath,amssymb,amsthm,graphicx,pstricks,comment,amscd,amsfonts,latexsym}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[>=stealth,scale=1] \n\n\\draw[thick,white] (0,0)--(1,0);\n\\draw[thick,white] (0,0)--(-1,0);\n\\draw[thick,white] (0,0)--(0,1);\n\\draw[thick,white] (0,0)--(0,-1);\n\\fill[gray!10](0,0)--(-2,1)--(-2,-1)--(2,-1)--(2,1)--(0,0);\n\n\n\\draw[thick,red](-2,0)--(-1,0); \n\\draw[thick,blue](-1,0)..controls (-0.5,0.5) and (0.5,0.5)..(1,0); \n\\node at (0,0)[circle,inner sep=1pt,draw]{};\n\n\\draw[thick,red](2,0)--(1,0); \n\\draw[thick,blue](1,0)..controls (1.5,0.5) and (2.5,0.5)..(3,0); \n\\node at (2,0)[circle,inner sep=1pt,draw]{};\n\n\n\\draw[dotted,thick](1,0)..controls (0.75,-0.25) and (0.25,-0.25)..(0,0); \n\\draw[dotted,thick](0,0)..controls (-0.75,-0.25) and (-0.25,-0.25)..(0,0); \n\\draw[thick,red](0,0)..controls (-1,1) and (-2,1)..(-3,0); \n\\draw[thick,blue](0,0)..controls (-1,-1) and (-2,-1)..(-3,0); \n\n\n\\draw[thick,red](3,0)--(4,0); \n\\draw[thick,blue](4,0)..controls (4.5,0.5) and (5.5,0.5)..(6,0); \n\\node at (5,0)[circle,inner sep=1pt,draw]{};\n\n\\draw[thick,red](6,0)--(7,0); \n\\draw[thick,blue](7,0)..controls (6.5,0.5) and (5.5,0.5)..(5,0); \n\\node at (6,0)[circle,inner sep=1pt,draw]{};\n\n\\draw[thick,red](-3,0)--(-2,0); \n\\draw[thick,blue](-2,0)..controls (-1.5,0.5) and (-0.5,0.5)..(0,0); \n\\node at (-1,0)[circle,inner sep=1pt,draw]{};\n\n\\draw[thick,red](0,0)--(1,0); \n\\draw[thick,blue](1,0)..controls (1.5,0.5) and (2.5,0.5)..(3,0); \n\\node at (1,0)[circle,inner sep=1pt,draw]{};\n\n\n\\node at (-1,1.5){$R_{\\lambda,r}$};\n\\node at (1,1.5){$R_{\\lambda,r}$};\n\\node at (0,-0.5){$\\gamma$};\n\n\\draw[thick, blue] (0,-1)..controls (1,-3) and (3,-3)..(4,-1);\n\\draw[thick, blue] (-1,-1)..controls (-0.5,-1.5) and (-0.5,-2.5)..(0,-3);\n\\draw[thick, blue] (1,-1)..controls (2,-2.5) and (2,-3.5)..(3,-3.5);\n\\draw[thick, blue] (5,-1)..controls (4.5,-1.5) and (4.5,-2.5)..(5,-3);\n\n\\draw[thick, blue] (-3,-3.5)..controls (-1,-3.5) and (1,-3.5)..(3,-3.5);\n\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 722,
        "tikz_code": "\\documentclass{article}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.16}\n\\begin{document}\n\\begin{tikzpicture}\n\\begin{axis}[domain=0:1, samples=500,\n    restrict y to domain=-3:3, xmin=-1,xmax=1, ymin=-3, ymax=3,\n    axis lines=middle,\n    enlarge y limits=upper,\n    enlarge x limits={0.1,upper},\n    xtick=\\empty, ytick=\\empty,\n    declare function={f(\\x,\\y)= sqrt(4*\\x*\\x+\\y*\\y);}]\n\\addplot [red] (x,{f(x,x)});\n\\addplot [blue] (x,{f(x,x/4)});\n\\addplot [red] (x,{f(x,x/2)});\n\\addplot [blue] (x,{f(x,x/8)});\n\\addplot [red] (x,{f(x,x/16)});\n\\end{axis}\n\\end{tikzpicture}\n\\end{document}"
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    {
        "index": 723,
        "tikz_code": "\\documentclass[a4paper,11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\tikzset{\nblock/.style={\n  rectangle,\n  draw,\n  fill=blue!20,\n  text width=6em,\n  text centered,\n  rounded corners,\n  minimum height=2em},\nline/.style={draw},\nedge/.style={draw}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n[node distance=1cm, auto,font=\\footnotesize,\n% style={\n% draw, rounded corners, align=center,\n% minimum width=0.5cm, minimum height=0.5cm\n% },\nblock/.style={\n  rectangle,\n  draw,\n  fill=blue!20,\n  text width=4.5em,\n  text centered,\n  rounded corners,\n  minimum height=0.5cm\n},\nline/.style={draw},\nedge/.style={draw}]\n\n\\node (Input) [block,draw=none, fill=none] {\\bf Input parameters};\n\\node (RP) [block, below=of Input] {Rendering pipeline};\n\\node (Rec) [block, below=of RP] {Printing \\& recording};\n\\node (Ano) [block, below=of Rec] {Automated Annotation};\n\\node (AR) [block, below=of Ano] {Manual Annotation};\n\\node (SR) [block, below=of AR] {Partly-real Data Set};\n\\node (RRD) [block, below=of SR] {Real Data Set};\n\n\\draw [edge] (Input) -- (RP);\n\\draw [edge] (RP) -- (Rec);\n\\draw [edge] (Rec) -- (Ano);\n\\draw [edge] (Ano) -- (AR);\n\\draw [edge] (AR) -- (SR);\n\\draw [edge] (SR) -- (RRD);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 724,
        "tikz_code": "\\documentclass[12pt,reqno]{amsart}\n\\usepackage{amsthm,amssymb,amsmath,enumerate,graphicx, tikz}\n\\tikzset{node distance=2cm, auto}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n[ultra thick]\n\\coordinate (a) at (-4,0);\n\\coordinate (b) at (-2,2);\n\\coordinate (c) at (2,2);\n\\coordinate (d) at (4,0);\n\\coordinate (e) at (2,-2);\n\\coordinate (f) at (-2,-2);\n\n\\filldraw [black] (a) circle (4pt)\n(b) circle (4pt)\n(c) circle (4pt)\n(d) circle (4pt)\n(e) circle (4pt)\n(f) circle (4pt);\n\n\n\\node (h) at (-2,-4) {$(1)$};\n\n\n\\draw (a) -- (b) node[pos=0.5,above] {$z_1$};\n\\draw (a) -- (f) node[pos=0.5,above] {$z_2$};\n\\draw (b) -- (c) node[pos=0.5,above] {$x_1$};\n\\draw (c) -- (d) node[pos=0.5,above] {$y_1$};\n\\draw (c) -- (e) node[pos=0.5,right] {$w_1$};\n\\draw (e) -- (d) node[pos=0.5,above] {$b_{m-1}$};\n\\draw (f) -- (e) node[pos=0.5,left] {$x_2$};\n\\draw (f) -- (b) node[pos=0.5,left] {$w_2$};\n\n\\draw[dashed] (a) -- (f)\n(b) -- (d)\n(c) -- (e);\n\n\\begin{scope}\n[xshift = 8cm]\n\\coordinate (a) at (-4,0);\n\\coordinate (b) at (-2,2);\n\\coordinate (c) at (2,2);\n\\coordinate (d) at (4,0);\n\\coordinate (e) at (2,-2);\n\\coordinate (f) at (-2,-2);\n\n\\filldraw [black] (a) circle (4pt)\n(b) circle (4pt)\n(c) circle (4pt)\n(d) circle (4pt)\n(e) circle (4pt)\n(f) circle (4pt);\n\n\n\\node (h) at (-2,-4) {$(2)$};\n\n\n\\draw (a) -- (b) node[pos=0.5,above] {$z_1$};\n\\draw (a) -- (f) node[pos=0.5,above] {$z_2$};\n\\draw (b) -- (c) node[pos=0.5,above] {$x_1$};\n\\draw (c) -- (d) node[pos=0.5,above] {$y_1$};\n\\draw (c) -- (e) node[pos=0.5,right] {$w_1$};\n\\draw (e) -- (d) node[pos=0.5,above] {$b_{m-1}$};\n\\draw (f) -- (e) node[pos=0.5,left] {$x_2$};\n\\draw (f) -- (b) node[pos=0.5,left] {$w_2$};\n\n\\draw[dashed] (a) -- (f)\n(b) -- (d)\n(c) -- (e);\n\n\\draw (0,-0.5) node {$N$};\n\\draw (0,1.2) node {$w$};\n\\draw (-1,0.5) node {$b_1$};\n\\draw (1,0.5) node {$b_2$};\n\\draw (-1.1,-0.5) node {$x_1$};\n\\draw (1.1,-0.5) node {$x_2$};\n\\draw (0,0.6) circle (0.7);\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 725,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage[latin1]{inputenc}\n\\usepackage{amssymb, amsmath, tikz}\n\\usetikzlibrary{matrix,arrows, calc}\n\\usetikzlibrary{fit}\n\\usetikzlibrary{positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5]\n\n\n      \\draw[thick] (0,0) -- (0.5,1);\n      \\draw[thick] (0.5,1) -- (1,0);\n      \\draw[thick] (0,0) -- (-1,-1.5);\n      \\draw[thick] (0,0) -- (0.5,-1.5);\n      \\draw[thick] (1,0) -- (1.5,-1.5);\n      \\draw[thick] (0.5,-1.5) -- (1,-2.5);\n      \\draw[thick] (1,-2.5) -- (1.5,-1.5);\n      \\draw[thick] (-1,-1.5) -- (-0.5,-2.5);\n      \\draw[thick] (-0.5,-2.5) -- (0,-1.5);\n\n      \\draw[fill=black] (0,0) circle (0.05);\n      \\draw[fill=black] (0.5,1) circle (0.05);\n      \\draw[fill=black] (1,0) circle (0.05);\n      \\draw[fill=black] (-1,-1.5) circle (0.05);\n      \\draw[fill=black] (0.5,-1.5) circle (0.05);\n      \\draw[fill=black] (1.5,-1.5) circle (0.05);\n      \\draw[fill=black] (1,-2.5) circle (0.05);\n      \\draw[fill=black] (-0.5,-2.5) circle (0.05);\n      \\draw[fill=black] (0,-1.5) circle (0.05);\n\n\n      \\node[right] at (1.5,-0.2) {$x_K$};\n      \\node[right] at (1,-1.7) {$x_k$};\n      \\node[right] at (0.2,-1) {$x_2$};\n      \\node[right] at (-0.2,-1) {$x_1$};\n      \\node[above] at (0.25,0.5) {$r^+$};\n      \\node[below] at (0.25,-1.3) {$\\downarrow x_2$};\n      \\node[below] at (-0.75,-2) {$\\downarrow x_T$};\n      \\node[below] at (0.75,-2) {$x_k^\\uparrow$};\n\n\n\n  \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 726,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,positioning}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.8]\n\\node (0,0) {$\\bullet$};\n\\draw[thick, <-] (0,0) -- (-1.5,2) node [anchor=east] {$\\vec{n}_2$};\n\\node (0,0) {$\\bullet$};\n\\draw[thick, <-] (0,0) -- (0,-1) node [anchor=north] {$\\vec{n}_4$};\n\\node (0,0) {$\\bullet$};\n\\draw[thick, <-] (0,0) -- (-.5,0) node [anchor=north] {$\\vec{n}_3$};\n\\node (0,0) {$\\bullet$};\n\\draw[thick, <-] (0,0) -- (.5,0) node [anchor=north] {$\\vec{n}_1$};\n\\node (0,0) {$\\bullet$};\n\\draw[thick, <-] (0,0) -- (0,3) node [anchor=south] {$\\vec{n}_1$};\n\\node (0,0) {$\\bullet$};\n\\draw[thick, <-] (0,0) -- (1.5,2) node [anchor=west] {$\\vec{n}_1$};\n\\draw (1.5,2) -- (2.5,4) -- (-1.5,2) -- (-2.5,0) -- (1.5,2) -- (-1.5,4);\n\\node at (0.5,-1) {$\\vec{n}_4^+$};\n\\node at (-.5,1) {$\\vec{n}_3^+$};\n\\node at (1,2) {$\\vec{n}_1^-$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 727,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath, amsthm, amssymb, graphics, graphicx}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.4]\n\t\t\t\\filldraw[black] (0,0) circle (4pt) node[anchor=north] {$v_1$};\n\t\t\t\\filldraw[black] (1,2) circle (4pt) node[anchor=south east] {$v_0$};\n\t\t\t\\filldraw[black] (2.5,0) circle (4pt) node[anchor=north west] {$v_{m-1}$};\n\t\t\t\\filldraw[black] (6,4) circle (4pt) node[anchor=south] {$z = v_n$};\n\t\t\t\\filldraw[black] (6,1) circle (4pt) node[anchor=west] {$e_m$};\n\t\t\t\\filldraw[black] (9,2) circle (4pt) node[anchor=west] {$e_0$};\n\t\t\t\\draw[dotted, thick] (0,0) -- (1,2);\n\t\t\t\\draw[dotted, thick] (2.5,0) -- (6,4);\n\t\t\t\\draw[dotted, thick] (6,4) -- (9,2);\n\t\t\t\\draw[dotted, thick] (1,2) -- (6,1);\n\t\t\t\\draw[-stealth, thick] (0.5,0.7) -- (2,1.5);\n\t\t\t\\draw[-stealth, thick] (2,1.5) -- (4.5,3);\n\t\t\t\\draw[-stealth, thick] (4.5,3) -- (5,2.6);\n\t\t\t\\draw[-stealth, thick] (5,2.6) -- (8.5,2);\n\t\t\t\\draw[-stealth, thick] (0.5,0.7) -- (0.5,-1);\n\t\t\t\\draw[-stealth, thick] (2,1.5) -- (2.5,0);\n\t\t\t\\draw[-stealth, thick] (4.5,3) -- (5.5,3.5);\n\t\t\t\\draw[-stealth, thick] (8.5,2) -- (8.9,-0.5);\n\t\t\t\\node at (4.5,1.5) {$\\Delta_{v,z}$};\n\t\t\t\\node at (0.5,-0.5) {$\\bar{\\varepsilon}_{1}$};\n\t\t\t\\node at (2.5,1.5) {$\\bar{\\varepsilon}_{m}$};\n\t\t\t\\node at (6.8,3) {$\\bar{\\varepsilon}_{0}$};\n\t\t\t\\node at (8.5,0.5) {$\\bar{\\varepsilon}_{m-1}$};\n\t\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 728,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{color}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usepackage{pgffor}\n\\usepackage{eqnarray,amsmath}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.6]\n    \\foreach \\i in {0,...,7} {\n        \\draw [very thin,lightgray] (\\i,0) -- (\\i,8);%\n    }\n    \\foreach \\i in {0,...,7} {\n        \\draw [very thin,lightgray] (0,\\i) -- (8,\\i);%\n    }\n\\foreach \\i in {0,...,8} {\n        \\draw [very thin,lightgray] (\\i,8) -- (8,8-\\i);%\n    }\n\\foreach \\i in {0,...,8} {\n        \\draw [very thin,lightgray] (8,8-\\i) -- (8-\\i,0);%\n    }\n\\foreach \\i in {0,...,8} {\n        \\draw [very thin,lightgray] (8-\\i,8) -- (0,8-\\i);%\n    }\n\\foreach \\i in {0,...,7} {\n        \\draw [very thin,lightgray] (8-\\i,8) -- (8,8-\\i);%\n    }\n    \\draw[step=1cm,blue, very thick] (-.5,-.5) grid (7.5,7.5);\n    \\foreach \\i in {0,...,4} {\n        \\draw[step=1cm,blue, very thick] (8-\\i,8) -- (8,8-\\i);%\n    }\n\\foreach \\i in {0,...,5} {\n        \\draw[step=1cm,blue, very thick] (8-\\i,8-\\i) -- (8-\\i,7);%\n    }\n\\foreach \\i in {0,...,6} {\n        \\draw[step=1cm,blue, very thick] (8-\\i,7) -- (7-\\i,7);%\n    }\n    \\foreach \\i in {0,...,6} {\n        \\draw[step=1cm,blue, very thick] (7-\\i,7) -- (7-\\i,6);%\n    }\n\\foreach \\i in {0,...,6} {\n        \\draw[step=1cm,blue, very thick] (7-\\i,6) -- (6,6-\\i);%\n    }\n\\foreach \\i in {0,...,6} {\n        \\draw[step=1cm,blue, very thick] (6,6-\\i) -- (6-\\i,3);%\n    }\n\\foreach \\i in {0,...,6} {\n        \\draw[step=1cm,blue, very thick] (6-\\i,3) -- (3-\\i,3);%\n    }\n\\foreach \\i in {0,...,6} {\n        \\draw[step=1cm,blue, very thick] (3-\\i,3) -- (3,2-\\i);%\n    }\n\\foreach \\i in {0,...,6} {\n        \\draw[step=1cm,blue, very thick] (3,2-\\i) -- (2,2-\\i);%\n    }\n\\foreach \\i in {0,...,6} {\n        \\draw[step=1cm,blue, very thick] (2,2-\\i) -- (2-\\i,1);%\n    }\n\\foreach \\i in {0,...,6} {\n        \\draw[step=1cm,blue, very thick] (2-\\i,1) -- (1,1-\\i);%\n    }\n\\foreach \\i in {0,...,6} {\n        \\draw[step=1cm,blue, very thick] (1,1-\\i) -- (1-\\i,0);%\n    }\n\\foreach \\i in {0,...,6} {\n        \\draw[step=1cm,blue, very thick] (1-\\i,0) -- (0,0-\\i);%\n    }\n\\foreach \\i in {0,...,5} {\n        \\draw[step=1cm,blue, very thick] (0,0-\\i) -- (-1+\\i,0);%\n    }\n\\foreach \\i in {0,...,5} {\n        \\draw[step=1cm,blue, very thick] (-1+\\i,0) -- (-1+\\i,1);%\n    }\n\\foreach \\i in {0,...,4} {\n        \\draw[step=1cm,blue, very thick] (-1+\\i,1) -- (-1+\\i,2);%\n    }\n\\foreach \\i in {0,...,3} {\n        \\draw[step=1cm,blue, very thick] (-1+\\i,2) -- (-1+\\i,3);%\n    }\n\\foreach \\i in {0,...,2} {\n        \\draw[step=1cm,blue, very thick] (-1+\\i,3) -- (-1+\\i,4);%\n    }\n\\foreach \\i in {0,...,1} {\n        \\draw[step=1cm,blue, very thick] (-1+\\i,4) -- (-1+\\i,5);%\n    }\n\\foreach \\i in {0,...,1} {\n        \\draw[step=1cm,blue, very thick] (-1+\\i,5) -- (-1+\\i,6);%\n    }\n\\foreach \\i in {0,...,0} {\n        \\draw[step=1cm,blue, very thick] (-1+\\i,6) -- (-1+\\i,7);%\n    }\n\n\\draw[red, dashed] (-0.5,4.5) -- (4.5,7.5);\n\\draw[red, dashed] (-0.5,4.5) -- (4.5,0.5);\n\\draw[red, dashed] (-0.5,4.5) -- (3.5,4.5);\n\\draw[red, dashed] (4.5,7.5) -- (4.5,0.5);\n\\draw[red, dashed] (4.5,0.5) -- (7.5,3.5);\n\\draw[red, dashed] (4.5,0.5) -- (7.5,0.5);\n\\draw[red, dashed] (7.5,3.5) -- (7.5,0.5);\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 729,
        "tikz_code": "\\documentclass[border=3mm]{standalone}\n\\usepackage{tikz}\n\\usetikzlibrary{lindenmayersystems}\n\\pgfdeclarelindenmayersystem{A}{\n    \\rule{A -> A-Bf+A+Bf}\n    \\rule{B -> A}\n}\n\\begin{document}\n\\begin{tikzpicture}\n    \\filldraw [gray]\n    l-system [l-system={A,axiom=A,order=15,angle=90,step=1pt}]\n    lindenmayer system;\n\\end{tikzpicture}\n\\end{document}"
    },
    {
        "index": 730,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\n\\newcommand{\\bt}{\\alpha}\n\n\\begin{document}\n\n\\begin{tikzpicture} [place/.style={circle,draw=black,fill=white, inner sep=0pt,minimum size=8}] \n\\draw(-1,0)--(0,0);\n\\draw(0,0)--(1,0);\n\\draw[dashed] (-2,0) -- (2,0);\n\\draw(2,0)--(3,0); \n\\draw(-2,0)--(-3,0);\n\\draw (-3,0)--(-4,0);\n\\draw (1,0)--(2,0); \n\\draw[dashed] (-4,0)--(-5,0);\n\\draw (-5,0)--(-6,0); \n\\draw[dashed] (3,0)--(4,0);\n\\draw (4,0)--(5,0); \n\\draw[dashed] (-1,0)--(-2,0);\n\\draw (-6,0)--(-7,0); \n\\draw(-1,0)--(0,0);\n\\draw[dashed] (5,0)--(6,0);\n\\draw (6,0)--(7,0); \n\\draw[dashed] (-7,0)--(-8,0);\n\\draw (-8,0)--(-9,0); \n\\draw (-2,0.05)--(-2,0.5);\n\\draw (-2,-0.05)--(-2,-0.5);\n\\draw (0,0.05)--(0,0.5);\n\\draw (0,-0.05)--(0,-0.5);\n\\draw (1,0.05)--(1,0.5);\n\\draw (1,-0.05)--(1,-0.5);\n\\draw (2,0.05)--(2,0.5);\n\\draw (2,-0.05)--(2,-0.5);\n\\draw (3,0.05)--(3,0.5);\n\\draw (3,-0.05)--(3,-0.5);\n\\draw (-1,0.05)--(-1,0.5);\n\\draw (-1,-0.05)--(-1,-0.5);\n\\draw (-2,0.05)--(-2,0.5);\n\\draw (-2,-0.05)--(-2,-0.5);\n\\draw (-3,0.05)--(-3,0.5);\n\\draw (-3,-0.05)--(-3,-0.5);\n\\draw (-4,0.05)--(-4,0.5);\n\\draw (-4,-0.05)--(-4,-0.5);\n\\draw (-5,0.05)--(-5,0.5);\n\\draw (-5,-0.05)--(-5,-0.5);\n\\draw (-6,0.05)--(-6,0.5);\n\\draw (-6,-0.05)--(-6,-0.5);\n\\draw (-7,0.05)--(-7,0.5);\n\\draw (-7,-0.05)--(-7,-0.5);\n\\draw (-8,0.05)--(-8,0.5);\n\\draw (-8,-0.05)--(-8,-0.5);\n\\draw (-9,0.05)--(-9,0.5);\n\\draw (-9,-0.05)--(-9,-0.5);\n\\draw(-4,0)--(-3,0);\n\\draw(-3,0)--(-2,0);\n\\draw(-2,0)--(-1,0);\n\\draw (-7,0)--(-6,0); \n\\draw (-6,0)--(-5,0); \n\\draw (-5,0)--(-4,0);\n\\draw (-4,0)--(-3,0);\n\\draw (-3,0)--(-2,0);\n\\draw (-2,0)--(-1,0);\n\\draw (-1,0)--(0,0);\n\\draw[dashed] (-6,0)--(-7,0);\n\\draw (-7,0)--(-8,0); \n\\draw(-8,0)--(-9,0); \n\\node at (0,-0.3) {$\\bt$};\n\\node at (-1,-0.3) {$\\bt'$};\n\\node at (-2,-0.3) {$\\bt''$};\n\\node at (-3,-0.3) {$\\bt'''$};\n\\node at (-4,-0.3) {$\\bt'$};\n\\node at (-5,-0.3) {$\\bt$};\n\\node at (-6,-0.3) {$\\bt'''$};\n\\node at (-7,-0.3) {$\\bt'$};\n\\node at (-8,-0.3) {$\\bt$};\n\\node at (-9,-0.3) {$\\bt'''$};\n\\draw[fill=gray] (-1,0) circle (0.1);\n\\draw[fill=gray] (0,0) circle (0.1);\n\\draw[fill=gray] (1,0) circle (0.1);\n\\draw[fill=gray] (2,0) circle (0.1);\n\\draw[fill=gray] (3,0) circle (0.1);\n\\draw[fill=gray] (-2,0) circle (0.1);\n\\draw[fill=gray] (-3,0) circle (0.1);\n\\draw[fill=gray] (-4,0) circle (0.1);\n\\draw[fill=gray] (-5,0) circle (0.1);\n\\draw[fill=gray] (-6,0) circle (0.1);\n\\draw[fill=gray] (-7,0) circle (0.1);\n\\draw[fill=gray] (-8,0) circle (0.1);\n\\draw[fill=gray] (-9,0) circle (0.1);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 731,
        "tikz_code": "\\documentclass{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,calc,through,backgrounds,matrix,positioning,decorations.pathmorphing}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[dotted] (-4.5,0.5) -- (-4.5,3.5);\n\\draw[dotted] (0.5,0.5) -- (0.5,3.5);\n\\draw (-2,1) circle (0.5)\nnode[left=15pt]{$p$};\n\\draw (-3,2) circle (0.5)\nnode[below=15pt]{$p$};\n\\draw (-2,3) circle (0.5)\nnode[below=15pt]{$p$};\n\\draw[fill=black] (-3,1) circle (2pt);\n\\draw[fill=black] (-3,2) circle (2pt);\n\\draw[fill=black] (-3,3) circle (2pt);\n\\draw[fill=black] (0,2) circle (2pt);\n\\draw (0,2) circle (0.5);\n\\draw (0,1.5) node[below=15pt]{$p$};\n\\draw (1.5,2.5) node{$2p$ Ne};\n\\draw (4,2.5) node{$2p$ Ne};\n\n\\draw (0,2) circle (0.5);\n\\draw (0,2) circle (0.5);\n\\draw (2,2) circle (0.5);\n\\draw[fill=black] (0,2) circle (2pt);\n\\draw[fill=black] (2,2) circle (2pt);\n\\draw[fill=black] (2,1) circle (2pt);\n\\draw (2,1) -- (3,0);\n\\draw[dotted] (0,1.5) -- (0,1);\n\\draw (2.1,1.3) node{$p$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 732,
        "tikz_code": "\\documentclass[11pt,reqno]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{arrows,shapes,positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.75]\n\\draw[gray, thick] (0,0) --(4,0);\n\\draw[gray, thick] (0,0) to [bend right=60](4,0);\n\\draw[gray, thick] (0,2) to [bend left=60](4,2);\n\\draw[gray, thick] (2,2) to [bend right=60](2,0);\n\\filldraw[red] (2,0) circle (0.05cm) node[align=right, above]{$x_{2}$} node[align=left, above]{$x_{2}$};\n\\filldraw[red] (2,2) circle (0.05cm) node[align=right, above]{$x_{1}$} node[align=left, above]{$x_{1}$};\n\\filldraw[red] (1.8,1) circle (0.03cm) node[align=left, above]{$x_{2}$};\n\\filldraw[red] (2.2,1) circle (0.03cm) node[align=right, above]{$x_{3}$};\n\\filldraw[red] (1.5,.2) circle (0.03cm) node[align=left, above]{$x_{1}$};\n\\filldraw[red] (2.5,.2) circle (0.03cm) node[align=right, above]{$x_{4}$};\n\\filldraw (6,0) circle (0.03cm) node[align=right, below]{$\\Sigma$};\n\\draw[gray, thick,dashed] (7.2,0) --(7.2,1);\n\\draw[gray, thick,dashed] (9,0) --(9,1);\n\\draw[gray, thick] (6.5,1) to [bend right=60](9.5,1);\n\\draw[gray, thick] (7.2,1) to [bend left=60](9.5,1);\n\\filldraw[red] (7.2,0) circle (0.05cm) node[align=right, above]{$x_{2}$} node[align=left, above]{$x_{2}$};\n\\filldraw[red] (7.2,2) circle (0.05cm) node[align=right, above]{$x_{1}$} node[align=left, above]{$x_{1}$};\n\\filldraw[red] (7.2+1.8,1) circle (0.03cm) node[align=left, above]{$x_{2}$};\n\\filldraw[red] (7.2+2.2,1) circle (0.03cm) node[align=right, above]{$x_{3}$};\n\\filldraw[red] (7.2+1.5,.2) circle (0.03cm) node[align=left, above]{$x_{1}$};\n\\filldraw[red] (7.2+2.5,.2) circle (0.03cm) node[align=right, above]{$x_{4}$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 733,
        "tikz_code": "\\documentclass[twoside,11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{fit,positioning}\n\\usetikzlibrary{shapes.geometric}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{decorations.pathreplacing}\n\n\\begin{document}\n\n\\begin{tikzpicture}[thick, scale=1.0, every node/.style={scale=1.0}]\n\\tikzstyle{main}=[circle, minimum size = 7mm, thick, draw =black!80, node distance = 16mm]\n\\tikzstyle{connect}=[-latex, thick]\n\\tikzstyle{box}=[rectangle, draw=black!100]\n  \\node[main] (T) [] {$T$};\n  \\node[main, fill = black!10] (H) [above=of T] {$H$};\n  \\node[main] (Y) [right=of T] {$Y$};\n  \\node[main] (M) [right=of Y] {$M$};\n  \\path (H) edge [connect] (T)\n        (T) edge [connect] (Y)\n        (M) edge [bend right, connect] (Y);\n        \\node[main, fill = black!10] (Tt) [right=of M, yshift=-12mm] {$T$};\n        \\node[main, fill = black!10] (Ht) [above=of Tt] {$H$};\n        \\node[main] (Yt) [right=of Tt] {$Y$};\n        \\node[main] (Mt) [right=of Yt] {$M$};\n        \\path (Ht) edge [connect] (Tt)\n        (Tt) edge [connect] (Yt)\n        (Mt) edge [bend right, connect] (Yt);\n        \\node[draw=black!100, rounded corners=8pt, inner sep=3pt, fit= (M) (Y)] (M_Y) {};\n        \\node[draw=black!100, rounded corners=8pt, inner sep=3pt, fit= (Mt) (Yt)] (Mt_Yt) {};\n        \\node[draw=black!100, rounded corners=8pt, inner sep=3pt, fit= (M_Y) (Mt_Yt)] (Mt_Y) {};\n        \\node[main, fill = black!10, minimum size = 5mm] (Ft) [below=of Mt_Y] {$F_T$};\n        \\node[main, fill = black!10] (Htt) [above=of Ft] {$H$};\n        \\node[main] (Ytt) [right=of Ft] {$Y$};\n        \\node[main] (Mtt) [right=of Ytt] {$M$};\n        \\path (Htt) edge [connect] (Ft)\n        (Ft) edge [connect] (Ytt)\n        (Mtt) edge [bend right, connect] (Ytt)\n        (Mtt) edge [bend right, connect, line width=0.75mm] (Htt);\n        \\node[main, fill = black!10] (Ttt) [right=of Mtt, yshift=-12mm] {$T$};\n        \\node[main, fill = black!10] (Httt) [above=of Ttt] {$H$};\n        \\node[main] (Yttt) [right=of Ttt] {$Y$};\n        \\node[main] (Mttt) [right=of Yttt] {$M$};\n        \\path (Httt) edge [connect] (Ttt)\n        (Ttt) edge [connect] (Yttt)\n        (Mttt) edge [bend right, connect] (Yttt);\n        \\node[draw=black!100, rounded corners=8pt, inner sep=3pt, fit= (Mtt) (Ytt)] (Mtt_Yt) {};\n        \\node[draw=black!100, rounded corners=8pt, inner sep=3pt, fit= (Mttt) (Mtt_Yt)] (Mttt_Mtt) {};\n        \\node[draw=black!100, rounded corners=8pt, inner sep=3pt, fit= (Mtt_Yt) (Mttt_Mtt)] (Mttt_Yt) {};\n        \\node[main, fill = black!10, minimum size = 5mm] (Ftt) [below=of Mttt_Yt] {$F_T = \\overline{F_T}$};\n        \\node[main, fill = black!10] (Htttt) [above=of Ftt] {$H$};\n        \\node[main] (Ytttt) [right=of Ftt] {$Y$};\n        \\node[main] (Mtttt) [right=of Ytttt] {$M$};\n        \\path (Htttt) edge [connect] (Ftt)\n        (Ftt) edge [connect] (Ytttt)\n        (Mtttt) edge [bend right, connect] (Ytttt);\n        \\node[] (a) [below=of Ttt] {(a)};\n        \\node[] (b) [below=of Tttt] {(b)};\n        \\node[] (c) [below=of Mtttt] {(c)};\n        \\node[] (d) [below=of Mttttt] {(d)};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 734,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n  \\draw[step=1cm,gray,very thin,dotted] (0,0) grid (4,4);\n  \\fill[blue,opacity=0.2] (0,0) rectangle (4,4);\n  \\fill[red,opacity=0.2] (1,1) rectangle (3,3);\n  \\fill[blue,opacity=0.2] (0,3) -- (1,2) -- (0,1) -- (1,0) -- (3,1) -- (4,0) --\n  (3,2) -- (4,3) -- (3,4) -- (2,3) -- (1,4) -- (0,3) -- cycle;\n  \\fill[green,opacity=0.2] (1,0) -- (0,1) -- (1,0);\n  \\fill[green,opacity=0.2] (4,0) -- (3,1) -- (4,0);\n  \\fill[green,opacity=0.2] (1,4) -- (0,3) -- (1,4);\n  \\fill[green,opacity=0.2] (4,4) -- (3,3) -- (4,4);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 735,
        "tikz_code": "\\documentclass[10pt,journal,compsoc]{IEEEtran}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning,arrows,calc,shapes.geometric,shadows,spy}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n% Tiny Vision\n\n\\node[inner sep=0pt] (CIFAR10-Tiny) at (-7,0)\n{\\includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=0.31\\textwidth]{example-image}};\n\\node at (-7,-0.9) {\\scriptsize $3.744 / 6.004 / 4.054$};\n\\node[inner sep=0pt] (CIFAR10-Tiny) at (-5,0)\n{\\includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=0.31\\textwidth]{example-image}};\n\\node at (-5,-0.9) {\\scriptsize $4.342 / 5.728 / 4.312$};\n\\node[inner sep=0pt] (CIFAR10-Tiny) at (-3,0)\n{\\includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=0.31\\textwidth]{example-image}};\n\\node at (-3,-0.9) {\\scriptsize $2.714 / 2.409 / 1.955$};\n\\node[inner sep=0pt] (CIFAR10-Tiny) at (-1,0)\n{\\includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=0.31\\textwidth]{example-image}};\n\\node at (-1,-0.9) {\\scriptsize $1.996 / 2.315 / 1.608$};\n\n% Tiny Vision + RR\n\n\\node[inner sep=0pt] (CIFAR10-TinyRR) at (-7,-3)\n{\\includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=0.31\\textwidth]{example-image}};\n\\node at (-7,-3.9) {\\scriptsize $3.599 / 6.020 / 4.260$};\n\\node[inner sep=0pt] (CIFAR10-TinyRR) at (-5,-3)\n{\\includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=0.31\\textwidth]{example-image}};\n\\node at (-5,-3.9) {\\scriptsize $4.086 / 5.706 / 4.226$};\n\\node[inner sep=0pt] (CIFAR10-TinyRR) at (-3,-3)\n{\\includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=0.31\\textwidth]{example-image}};\n\\node at (-3,-3.9) {\\scriptsize $2.719 / 2.579 / 2.204$};\n\\node[inner sep=0pt] (CIFAR10-TinyRR) at (-1,-3)\n{\\includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=0.31\\textwidth]{example-image}};\n\\node at (-1,-3.9) {\\scriptsize $2.172 / 2.343 / 1.822$};\n\n% Tiny Vision + RR + CP\n\n\\node[inner sep=0pt] (CIFAR10-TinyRRCP) at (-7,-6)\n{\\includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=0.31\\textwidth]{example-image}};\n\\node at (-7,-6.9) {\\scriptsize $3.896 / 6.139 / 4.444$};\n\\node[inner sep=0pt] (CIFAR10-TinyRRCP) at (-5,-6)\n{\\includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=0.31\\textwidth]{example-image}};\n\\node at (-5,-6.9) {\\scriptsize $4.448 / 5.965 / 4.446$};\n\\node[inner sep=0pt] (CIFAR10-TinyRRCP) at (-3,-6)\n{\\includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=0.31\\textwidth]{example-image}};\n\\node at (-3,-6.9) {\\scriptsize $2.834 / 2.637 / 2.354$};\n\\node[inner sep=0pt] (CIFAR10-TinyRRCP) at (-1,-6)\n{\\includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=0.31\\textwidth]{example-image}};\n\\node at (-1,-6.9) {\\scriptsize $2.255 / 2.446 / 1.912$};\n\n% CIFAR10\n\n\\node[inner sep=0pt] (CIFAR10) at (-7,-9)\n{\\includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=0.31\\textwidth]{example-image}};\n\\node at (-7,-9.9) {\\scriptsize $3.870 / 6.020 / 4.241$};\n\\node[inner sep=0pt] (CIFAR10) at (-5,-9)\n{\\includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=0.31\\textwidth]{example-image}};\n\\node at (-5,-9.9) {\\scriptsize $4.436 / 6.010 / 4.441$};\n\\node[inner sep=0pt] (CIFAR10) at (-3,-9)\n{\\includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=0.31\\textwidth]{example-image}};\n\\node at (-3,-9.9) {\\scriptsize $2.849 / 2.676 / 2.389$};\n\\node[inner sep=0pt] (CIFAR10) at (-1,-9)\n{\\includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=0.31\\textwidth]{example-image}};\n\\node at (-1,-9.9) {\\scriptsize $2.266 / 2.479 / 1.922$};\n\n% RT-RCN\n\n\\node[inner"
    },
    {
        "index": 736,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amssymb,amsmath,mathabx, amscd}\n\\usepackage{tikz}\n\\usepackage{tikz-cd, wrapfig}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw (0, 0) ellipse (2 and 1);\n\\node (V) at (0, 0) {$X$};\n\\draw (4, 0) ellipse (2 and 1);\n\\draw (4, 0) ellipse (1.5 and .5);\n\\draw (4,0) ellipse (1.5 and -.5);\n\\draw (4, 0) ellipse (1 and .33);\n\\draw (4, 0) ellipse (.5 and .25);\n\\draw[very thick, ->] (1, 0) -- (3, 0);\n\\node (S) at (4, 0) {Splitting};\n\\draw (0, -3) ellipse (.3 and 1);\n\\draw (0, -3) ellipse (-.3 and 1);\n\\draw (0, -3) ellipse (.5 and .3);\n\\draw (0, -3) ellipse (-.5 and -.3);\n\\draw (0, -3) ellipse (.5 and .2);\n\\draw (0, -3) ellipse (-.5 and -.2);\n\\draw (0, -3) ellipse (.3 and .15);\n\\draw (0, -3) ellipse (-.3 and -.15);\n\\draw[very thick, ->] (1, -3) -- (3, -3);\n\\node (S) at (4, -3) {Splitting};\n\\node (C) at (-.65, -3) {$\\tilde{I}_1$};\n\\node (C) at (5.5, -3) {$\\tilde{I}_2$};\n\\node (C) at (0, -6) {$I_1$};\n\\node (C) at (4, -6) {$I_2$};\n\\node (C) at (4, -6) {$\\tilde{I}_1$};\n\\node (C) at (0, -6) {$I_1$};\n\\draw[fill] (0, -3.33) circle [radius=0.05];\n\\draw[fill] (0, -3.67) circle [radius=0.05];\n\\draw[fill] (0, -4) circle [radius=0.05];\n\\draw[fill] (0, -3.67) circle [radius=0.05];\n\\draw[fill] (0, -3.33) circle [radius=0.05];\n\\draw[fill] (4, -3.33) circle [radius=0.05];\n\\draw[fill] (4, -3.67) circle [radius=0.05];\n\\draw[fill] (4, -4) circle [radius=0.05];\n\\draw[fill] (4, -3.67) circle [radius=0.05];\n\\draw[fill] (4, -3.33) circle [radius=0.05];\n\\draw[fill] (4, -3.33) circle [radius=0.05];\n\\draw[fill] (4, -3.33) circle [radius=0.05];\n\\draw[fill] (0, -4.33) circle [radius=0.05];\n\\draw[fill] (0, -4) circle [radius=0.05];\n\\draw[fill] (0, -3.67) circle [radius=0.05];\n\\draw[fill] (0, -4.33) circle [radius=0.05];\n\\draw[fill] (4, -4.33) circle [radius=0.05];\n\\draw[fill] (4, -4) circle [radius=0.05];\n\\draw[fill] (4, -4.33) circle [radius=0.05];\n\\draw[fill] (4, -4) circle [radius=0.05];\n\\draw[fill] (4, -4.33) circle [radius=0.05];\n\\draw[fill] (4, -4) circle [radius=0.05];\n\\draw[fill] (4, -4.33) circle [radius=0.05];\n\\draw[fill] (4, -3.33) circle [radius=0.05];\n\\draw[fill] (4, -3.33) circle [radius=0.05];\n\\draw[fill] (4, -3.33) circle [radius=0.05];\n\\draw[fill] (4, -3.33) circle [radius=0.05];\n\\draw[fill] (4, -3.33) circle [radius=0.05];\n\\draw[fill] (0, -3.33) circle [radius=0.05];\n\\draw[fill] (0, -3.33) circle [radius=0.05];\n\\draw[fill] (0, -3.33) circle [radius=0.05];\n\\draw[fill] (4, -3.33) circle [radius=0.05];\n\\draw[fill] (4, -3.33) circle [radius=0.05];\n\\draw[fill] (4, -3.33) circle [radius=0.05];\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 737,
        "tikz_code": "\\documentclass[a4paper,11pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\\draw[->] (0,0) node[anchor=north] {$D_\\infty$} -- (5,0);\n\t\\draw (2, 0.1) -- (2, -0.1) node[anchor=north] {$E_1^\\dagger$};\n\t\\draw (3, 0.1) -- (3, -0.1) node[anchor=north] {$E_2^\\dagger$};\n\t\\draw (4, 0.1) -- (4, -0.1) node[anchor=north] {$E_3^\\dagger$};\n\t\\draw[dashed] (2, 0) -- (3, 1.5) -- (4, 1.5);\n\t\\draw[dashed] (3, 0) -- (4, 1.5) -- (5, 1.5);\n\t\\draw[<->] (2, 1.5) -- (3, 1.5) node[anchor=south] {$\\widetilde{E_1}$};\n\t\\draw[<->] (3, 1.5) -- (4, 1.5) node[anchor=south] {$E_2$};\n\t\\draw[<->] (4, 1.5) -- (5, 1.5) node[anchor=south] {$\\widetilde{E_3}$};\n\t\\draw[<->] (2.5, 0) -- (2.5, 1.5);\n\t\\draw (2.5, 0.75) node {$D_1$};\n\t\\draw[<->] (4.5, 0) -- (4.5, 1.5);\n\t\\draw (4.5, 0.75) node {$D_2$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 738,
        "tikz_code": "\\documentclass[tikz, margin=3mm]{standalone}\n\\usetikzlibrary{arrows.meta,\n                positioning,\n                quotes}\n\n\\begin{document}\n    \\begin{tikzpicture}[\nnode distance = 8mm and 12mm,\n     N/.style = {circle, draw, minimum size=12mm, inner sep=2mm},\n   arr/.style = {semithick, -{Straight Barb[scale=0.8]}},\nevery edge quotes/.style = {fill=white, inner sep=1pt, sloped}\n                        ]\n\\node (n0)  [N,label=left:$T_N$]              {$SU(N)_k$};\n\\node (n1)  [N,above left=of n0]              {$SU(N)_k$};\n\\node (n2)  [N,above right=of n1]            {$SU(N)_k$};\n\\node (n3)  [N,above right=of n0]            {$SU(N)_k$};\n\\node (n4)  [N,below right=of n3]            {$SU(N)_{k3}$};\n\\draw[arr]  (n0) edge [\" \"]                 (n1)\n            (n0) edge [\" \"]                 (n2)\n            (n0) edge [\" \"]                 (n3)\n            (n1) edge [\" \"]                 (n4)\n            (n2) edge [\" \"]                 (n4)\n            (n3) edge [\" \"]                 (n4);\n\\path    (n4) edge [ultra thick, shorten <=1pt, \"TN\"']      (n3);\n    \\end{tikzpicture}\n\\end{document}"
    },
    {
        "index": 739,
        "tikz_code": "\\documentclass[a4paper]{amsart}\n\\usepackage[dvipsnames,svgnames,x11names,hyperref]{xcolor}\n\\usepackage{mathtools,url,graphicx,verbatim,amssymb,enumerate,stmaryrd,nicefrac}\n\\usepackage[pagebackref,colorlinks,citecolor=Mahogany,linkcolor=Mahogany,urlcolor=Mahogany,filecolor=Mahogany]{hyperref}\n\\usepackage{tikz, tikz-cd}\n\\usetikzlibrary{matrix,calc,positioning,arrows,decorations.pathreplacing,decorations.markings,patterns}\n\\tikzset{->-/.style={decoration={\n\t\t\tmarkings,\n\t\t\tmark=at position #1 with {\\arrow{>}}},postaction={decorate}}}\n\\tikzset{-<-/.style={decoration={\n\t\t\t\t\tmarkings,\n\t\t\t\t\tmark=at position #1 with {\\arrow{<}}},postaction={decorate}}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\\shade[ball color = gray!40, opacity = 0.4] (0,0) circle (1.4cm);\n\t\t\\draw (0,0) circle (1.4cm);\n\t\t\\draw (-1.4,0) arc (180:360:1.4 and 0.6);\n\t\t\\draw[dashed] (-1.4,0) arc (180:0:1.4 and 0.6);\n\t\t\\draw (1.4,0) arc (0:180:1.4 and 0.6);\n\t\t\n\t\t\\node at (-1,0) {$\\bullet$};\n\t\t\\node at (0,0) {$\\bullet$};\n\t\t\\node at (1,0) {$\\bullet$};\n\t\t\n\t\t\\draw (-1,0) -- (1,0);\n\t\t\\node at (0,-1.5) {\\small $\\mathbb{R}^d\\setminus \\{(0,0)\\}$};\n\t\t\\node at (-3.5,0) {\\small $C_{E,1,n}$};\n\t\t\\node at (0,1.5) {\\small $\\mu$};\n\t\t\n\t\t\\draw (-3, -1.5) -- (3, -1.5);\n\t\t\\draw (-3, 1.5) -- (3, 1.5);\n\t\t\n\t\t\\draw[<->] (4,1.5) -- (4,0.5) -- (4,-0.5) -- (4,-1.5);\n\t\t\\draw[<->] (5,1.5) -- (5,0.5) -- (5,-0.5) -- (5,-1.5);\n\t\t\n\t\t\\node at (5,1.7) {\\small $\\tau = 1$};\n\t\t\\node at (4.7,1.2) {\\small $c_1$};\n\t\t\n\t\t\\node at (5,0.5) {\\small $\\tau = 0$};\n\t\t\\node at (4.7,0) {\\small $c_2$};\n\t\t\n\t\t\\node at (5,-0.5) {\\small $\\tau = 1$};\n\t\t\\node at (4.7,-1.2) {\\small $c_{n-1}$};\n\t\t\n\t\t\\node at (5,-1.5) {\\small $\\tau = 0$};\n\t\t\\node at (4.7,-2) {\\small $c_n$};\n\t\t\n\t\t\\draw (-4.5,-1.5) -- (-0.5, 1.5) -- (4.5, -1.5) -- (0.5, 1.5) -- (-4.5,-1.5);\n\t\t\\node at (-5.5,0) {\\small $H^1_{n+1}$};\n\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 740,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{tikz}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n  \\matrix (m) [matrix of math nodes,row sep=0em,column sep=2em,minimum width=1em]\n  {\n  & \\text{Prop} & \\\\\n  \\text{Prop} && \\text{RRS}\\\\\n  & (\\frac{1}{2},Prop1) & \\\\\n  & (\\frac{1}{2}-Prop1) & \\\\};\n  \\path[-stealth]\n  (m-1-2) edge [dashed, red] node  {} (m-2-2)\n  (m-1-2) edge [dashed, red] node  {} (m-3-2)\n  (m-1-2) edge [dashed, red] node  {} (m-4-2)\n  (m-3-2) edge [blue] node  {} (m-4-2)\n  (m-2-2) edge [dashed, red] node  {} (m-3-2)\n  (m-2-2) edge [dashed, red] node  {} (m-4-2)\n  (m-2-2) edge [dashed, red] node  {} (m-5-2)\n  (m-2-2) edge [dashed, red] node  {} (m-3-2)\n  (m-2-2) edge [dashed, red] node  {} (m-4-2)\n  (m-5-2) edge [dashed, red] node  {} (m-3-2)\n  (m-5-2) edge [blue] node  {} (m-4-2)\n  (m-4-2) edge [blue] node  {} (m-3-2)\n  (m-3-2) edge [blue] node  {} (m-4-2)\n  (m-3-2) edge [blue, bend left=15] node  {} (m-5-2)\n  (m-1-2) edge [bend left=15, dashed, red] node  {} (m-5-2)\n  (m-1-2) edge [bend left=15, dashed, red] node  {} (m-2-2)\n  (m-1-2) edge [bend left=15, dashed, red] node  {} (m-3-2)\n  (m-2-2) edge [bend left=15, dashed, red] node  {} (m-4-2)\n  ;\n  \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 741,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amsthm,amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\n\\newcommand{\\Pbl}{{\\mathcal{P}_{\\mathrm{bl}}}}\n\n\\newcommand{\\Pbm}{{\\mathcal{P}_{\\mathrm{bm}}}}\n\n\\newcommand{\\Pbr}{{\\mathcal{P}_{\\mathrm{br}}}}\n\n\\newcommand{\\Mbl}{\\mathcal{M}_{\\mathrm{bl}}}\n\n\\newcommand{\\Mbm}{\\mathcal{M}_{\\mathrm{bm}}}\n\n\\newcommand{\\Mbr}{\\mathcal{M}_{\\mathrm{br}}}\n\n\\newcommand{\\Tr}{\\mathrm{Tr}}\n\n\\newcommand{\\Pss}{\\mathcal{P}_{\\mathrm{ss}}}\n\n\\newcommand{\\p}{\\mathbf{p}}\n\n\\newcommand{\\B}{\\mathbf{B}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n  back line/.style={dashed,gray},\n  cross line/.style={preaction={draw=white, -,line width=6pt}}]\n  \n\n  \n\n  \\node (1) at (5.5,3) {\\includegraphics[scale=0.15]{example-image}};\n  \\node (2) at (12,3) {\\includegraphics[scale=0.15]{example-image}};\n  \n  \\node at (3,4.2) {\\tiny Pulliary boundary Parameterization};\n  \\node at (10.5,4.2) {\\tiny Pulliary boundary Parameterization};\n  \n  \\draw[->,line width=1pt] (2) to node[midway,above]{} (3.7,3);\n  \n  \\node at (7.5,2.9) {\\tiny Symmetric Boundary Parameterization};\n  \\node at (7.5,2.4) {\\tiny Noise free feature Detection};\n  \n  \\draw[cross line] (1.8,3.75) to [out=180,in=90] (1.55,3.65);\n  \\draw[cross line] (2.2,3.75) to [out=0,in=90] (2.6,3.65);\n  \n  \\node at (6.5,3.6) {\\Large $\\color{red}{\\mathbf{+}}$};\n  \\node at (7.7,3.6) {\\Large $\\color{blue}{\\mathbf{+}}$};\n  \\node at (8.9,3.6) {\\Large $\\color{green}{\\mathbf{+}}$};\n  \n  \\draw[->,line width=1pt] (5.7,3.6) to [out=20,in=150] (8.4,3.6);\n  \n  \\node at (7.5,0) {\\tiny Dimensionless Noise-Free};\n  \\node at (7.5,0.5) {\\tiny Representation};\n  \n  \\draw[->,line width=1pt] (5.7,-0.6) to [out=20,in=150] (8.4,-0.6);\n  \n  \\node at (5,3.3) {\\includegraphics[scale=0.32]{example-image}};\n  \\node at (12.5,3.3) {\\includegraphics[scale=0.32]{example-image}};\n  \n  \\node at (10,3.3) {\\Large $\\color{red}{\\mathbf{+}}$};\n  \n  \\draw[->,line width=1pt] (10,3.3) to [out=20,in=150] (10.5,3.3);\n  \n  \n  \\draw[back line] (4.75,4.7) rectangle (12.25,0.2);\n  \\node at (11,4.4) {\\footnotesize Iris Segmentation Main Tasks};\n  \n  \n  \n  \\node at (1.4,3.6) {$\\Pbl$};\n  \\node at (1.4,2.3) {$\\Pbm$};\n  \\node at (1.4,0.6) {$\\Pbr$};\n  \n  \\node at (1.5,4.7) {$\\Mbl$};\n  \\node at (1.5,2.4) {$\\Mbm$};\n  \\node at (1.5,0.6) {$\\Mbr$};\n  \n  \\node at (0.8,3.2) {\\large $\\Tr$};\n  \n  \\node at (7,3.3) {$\\Pss$};\n  \n  \\draw[->,line width=1pt,dashed] (2.25,2.9) to [out=-80,in=-180] (3.35,2.9);\n  \\draw[->,line width=1pt,dashed] (10.6,2.9) to [out=-80,in=-180] (11.7,2.9);\n  \n  \\node at (5.1,2.2) {$\\p$};\n  \\node at (11.9,2.2) {$\\B$};\n  \n  \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 742,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsthm,amsmath,amssymb,amsfonts,amscd,epsfig}\n\\usepackage{xcolor}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.16}\n\\usetikzlibrary{arrows.meta,matrix}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{scope}[scale=0.5]\n\\draw[step=1cm,gray,very thin] (-3,-3) grid (5,4);\n\\draw[->] (-3,0)--(5,0) node[right]{$x$};\n\\draw[->] (0,-3)--(0,4) node[above]{$y$};\n\\foreach \\x in {-2.5,-1.5,...,4.5} \\draw (\\x cm,1pt)--( \\x cm,-1pt) node[anchor=north] {$\\x$};\n\\foreach \\y in {-2.5,-1.5,...,3.5} \\draw (1pt,\\y cm)--(-1pt,\\y cm) node[anchor=east] {$\\y$};\n\\fill[blue!30!white] (-1.5,-1.5) rectangle (2.5,2.5);\n\\fill[red] (1,1) rectangle (2,2);\n\\draw[thick,green!70!black,densely dashed] (2,2) -- (7,2) node[anchor=west] {$M_K$};\n\\draw[thick,red!70!black,densely dashed] (2,2) -- (2,4) node[anchor=south] {$T_h$};\n\\draw[-{Stealth[scale=1]}] (5,2.5) arc (90:180:1.5cm);\n\\end{scope}\n\\begin{scope}[scale=0.5,shift={(10,0)}]\n\\filldraw[opacity=0.5,fill=blue!30!white] (0,0) -- (0,4) -- (3,4) -- (3,2) -- (5,2) -- (5,0) -- (0,0);\n\\filldraw[opacity=0.5,fill=red] (1,1) rectangle (2,2);\n\\draw[thick,green!70!black,densely dashed] (2,2) -- (7,2) node[anchor=west] {$M_K$};\n\\draw[thick,red!70!black,densely dashed] (2,2) -- (2,4) node[anchor=south] {$T_h$};\n\\filldraw[opacity=0.5,fill=black!30!white] (0,0) -- (0,-2.5) -- (1,-2.5) -- (1,-1) -- (3,-1) -- (3,0) -- (0,0);\n\\draw[thick,blue!70!black,densely dashed] (2,2) -- (7,2) node[anchor=west] {$K$};\n\\node[scale=1.5] at (2,2) {\\includegraphics[scale=0.25]{example-image}};\n\\node[scale=1.5] at (1,1.5) {\\includegraphics[scale=0.1]{example-image}};\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 743,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amsthm,amssymb,amsfonts,enumerate,xcolor,layout,tikz,enumitem,fullpage, verbatim, graphicx, caption, subcaption}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usepackage{tikz-cd}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale = 1.2]\n      \\draw (0,0) -- (1,1) -- (0,2) -- (-1,1) -- cycle;\n      \\draw [dashed] (0,0) -- (0,2);\n      \\node at (0.5,1) {$CFT_r$};\n      \\draw [dashed] (1,1) -- (2,2) -- (1,3) -- (0,2) -- cycle;\n      \\node at (0.5,1.5) {$Ch_z$};\n      \\draw [dashed] (2,2) -- (3,3) -- (2,4) -- (1,3) -- cycle;\n      \\node at (1.5,2.5) {$AdS_r$};\n      \\draw [dashed] (3,3) -- (4,4) -- (3,5) -- (2,4) -- cycle;\n      \\node at (2.5,3.5) {$CFT_r$};\n      \\draw [dashed] (4,4) -- (5,5) -- (4,6) -- (3,5) -- cycle;\n      \\node at (3.5,4.5) {$Ch_z$};\n      \\draw [dashed] (5,5) -- (6,6) -- (5,7) -- (4,6) -- cycle;\n      \\node at (4.5,5.5) {$CFT_r$};\n      \\draw (8,0) -- (9,1) -- (10,2) -- (9,3) -- (8,4) -- cycle;\n      \\draw (9,1) -- (10,0) -- (9,3) -- (8,2) -- cycle;\n      \\draw [dashed] (8,4) -- (7,5) -- (8,6) -- (9,5) -- (8,4) -- cycle;\n      \\draw [dashed] (10,2) -- (11,3) -- (10,4) -- (9,5) -- (9,3) -- (10,2) -- cycle;\n      \\draw [dashed] (11,3) -- (12,4) -- (11,5) -- (10,4) -- cycle;\n      \\draw [dashed] (12,4) -- (13,5) -- (12,6) -- (11,5) -- cycle;\n    \\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 744,
        "tikz_code": "\\documentclass[10pt]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amsmath,arydshln,multirow}\n\\usepackage{amsmath}\n\\usepackage{amsfonts,amsmath,amssymb,amscd,bbm,amsthm,mathrsfs,dsfont}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage[color,matrix,arrow]{xy}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.60]\n  \\node at (0,0) (A) {};\n  \\node at (5,0) (B) {};\n  \\node at (10,0) (C) {};\n  \\node at (15,0) (D) {};\n  \\node at (20,0) (E) {};\n  \\draw (A) node [below] {$-2$};\n  \\draw (B) node [below] {$-1$};\n  \\draw (C) node [below] {$0$};\n  \\draw (D) node [below] {$1$};\n  \\draw (E) node [below] {$2$};\n  \\draw[thick] (A) -- (E) ;\n  \\node at (0,5) (A1) {};\n  \\node at (15,5) (B1) {};\n  \\node at (20,5) (C1) {};\n  \\draw (A1) node [above] {$-2$};\n  \\draw (B1) node [above] {$-1$};\n  \\draw (C1) node [above] {$0$};\n  \\draw[thick] (A1) -- (C1) ;\n  \\draw[dotted] (A) -- (A1) ;\n  \\draw[dotted] (B) -- (B1) ;\n  \\draw[dotted] (C) -- (C1) ;\n  \\draw[dotted] (D) -- (B1) ;\n  \\draw[dotted] (E) -- (C1) ;\n  \\draw (B) -- (A1) ;\n  \\draw (B) -- (B1) ;\n  \\draw (C) -- (B1) ;\n  \\draw (C) -- (C1) ;\n  \\draw (D) -- (C1) ;\n  \\draw (D) -- (D) ;\n  \\draw (E) -- (C1) ;\n  \\draw (A) node [below] {$\\tilde \\ell(0)$};\n  \\draw (B) node [below] {$\\tilde \\ell(1)$};\n  \\draw (C) node [below] {$\\tilde \\ell(2)$};\n  \\draw (D) node [below] {$\\tilde \\ell(3)$};\n  \\draw (E) node [below] {$\\tilde \\ell(4)$};\n  \\draw (17,3) node [below] {$\\tilde \\ell(5)$};\n  \\node at (17,3) (A2) {};\n  \\draw (A2) node [below] {$\\tilde \\ell(6)$};\n  \\node at (17,3) (A3) {};\n  \\draw (A3) node [below] {$\\tilde \\ell(7)$};\n  \\node at (17,3) (A4) {};\n  \\draw (A4) node [below] {$\\tilde \\ell(8)$};\n  \\draw (17,3) node [below] {$\\tilde \\ell(9)$};\n  \\node at (17,3) (A5) {};\n  \\draw (A5) node [below] {$\\tilde \\ell(10)$};\n  \\draw[thick] (A2) -- (A5) ;\n  \\node at (17,0) (A6) {};\n  \\draw (A6) node [below] {$\\tilde \\ell(11)$};\n  \\node at (17,0) (A7) {};\n  \\draw (A7) node [below] {$\\tilde \\ell(12)$};\n  \\draw[thick] (A6) -- (A7) ;\n  \\node at (17,1) (A8) {};\n  \\draw (A8) node [below] {$\\tilde \\ell(13)$};\n  \\node at (17,1) (A9) {};\n  \\draw (A9) node [below] {$\\tilde \\ell(14)$};\n  \\draw[thick] (A8) -- (A9) ;\n  \\node at (17,2) (A10) {};\n  \\draw (A10) node [below] {$\\tilde \\ell(15)$};\n  \\node at (17,2) (A11) {};\n  \\draw (A11) node [below] {$\\tilde \\ell(16)$};\n  \\draw[thick] (A10) -- (A11) ;\n  \\draw[dotted] (A6) -- (A) ;\n  \\draw[dotted] (A7) -- (B) ;\n  \\draw[dotted] (A8) -- (C) ;\n  \\draw[dotted] (A9) -- (D) ;\n  \\draw[dotted] (A10) -- (E) ;\n  \\draw[dotted] (A11) -- (E) ;\n  \\draw[dotted] (A) -- (A3) ;\n  \\draw[dotted] (B) -- (A4) ;\n  \\draw[dotted] (C) -- (A5) ;\n  \\draw[dotted] (D) -- (A6) ;\n  \\draw[dotted] (E) -- (A7) ;\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 745,
        "tikz_code": "\\documentclass{article}\n\\usepackage{pgfplots}\n\\usepackage{filecontents}\n\\usepackage{catchfile}\n\n\\begin{filecontents*}{classindex.csv}\n    class,start,end,\n    1,0,38,\n    2,38,57,\n    3,57,85,\n    4,85,100,\n\\end{filecontents*}\n\n\\newcommand*{\\ReadOutElement}[4]{%\n    \\BODY\n    \\def\\pgfplotspointmeta##1{\\pgfkeysvalueof{/data point/##1}}\n    \\def\\pgfplotspointmeta#1#2{\\def\\pgfplotspointmeta{#2}\\pgfplotspoint#1}%\n    \\immediate\\write\\tempfile{#4}%\n    \\CatchFileDef{\\loadedfile}{classindex.csv}{\\endlinechar=-1}{\\endlinechar=0}%\n    \\def\\endpoint{1}%\n    \\def\\lastendpoint{0}%\n    \\def\\lastclass{0}%\n    \\openout\\tempfile\\normalbaseline\n    \\ifnum#1=1\n        \\loop\n        \\ifnum#2=1\n            \\endloop\n        \\fi\n        \\ifnum#2=0\n            \\endloop\n        \\fi\n        \\ifnum\\value{line}=\\value{numexpr#1-1}\n            \\endloop\n        \\fi\n        \\ifnum\\value{line}=\\value{numexpr#1+1}\n            \\endloop\n        \\fi\n        \\read[space]from\\tempfile to\\loadedfile{%\n            \\ifnum#2=1\n                \\expandafter\\xdef\\csname class#1\\endcsname{\\pgfplotspointmeta}%\n                \\global\\edef\\lastclass{\\csname class#1\\endcsname}%\n            \\else\n                \\ifnum#2=0\n                    \\expandafter\\xdef\\csname class#1\\endcsname{\\pgfplotspointmeta}%\n                    \\global\\edef\\lastclass{\\csname class#1\\endcsname}%\n                \\else\n                    \\xdef\\csname class#1\\endcsname{\\pgfplotspointmeta}%\n                \\fi\n            \\fi\n            \\ifnum#2=\\lastendpoint\n                \\endinput\n            \\fi\n        }%\n    \\fi\n}%\n\n\\newcommand{\\ClassIndex}[1]{%\n    \\edef\\arg{#1}%\n    \\edef\\extracted{\\noexpand\\ReadOutElement{\\arg}{0}{0}{\\arg}}%\n    \\extracted%\n    \\pgfmathsetmacro{\\ClassIndex}{int(\\lastclass)}%\n}%\n\n\\pgfplotsset{\n    Class Index/.code={\\pgfplotscolormappablelistread{\\colormapindexcolors}{ClassIndex}%\n    \\pgfmathsetmacro{\\ClassIndexColor}{\\colormapindexcolors[\\ClassIndex]}%\n    \\def\\ClassIndexColor{\\pgfmathresult}%\n    \\pgfplotsset{color map/uniform,point meta min=0,point meta max=\\ClassIndex,colorbar},\n    Class Index/.append style={\n        colorbar style={\n            width=10cm,\n            ytick=data,\n            yticklabels={\\noexpand\\ClassIndex{\\pgfplotspointmeta},},\n            yticklabel style={text width=2cm,align=right}\n        },\n        colorbar\n    },\n    ClassIndex/.append style={\\ClassIndexColor},\n    },\n    colormap={Class Index}{\\ClassIndexColor},\n}\n\n\\begin{document}\n\n\\pgfplotstableread{classindex.csv}{\\ClassIndexTable}%\n\n\\begin{tikzpicture}\n    \\begin{axis}[\n        height=5cm, width=15cm,\n        xlabel={Class index},\n        ylabel={Samples},\n        yticklabel={%\n            \\pgfmathparse{\\pgfplotspointmeta*100}%\n            \\pgfmathprintnumber[fixed]{\\pgfmathresult}\\,\\%\n        }\n    ]\n\n        \\addplot[Class Index,fill] table[x index=0,y index=1]{\\ClassIndexTable};\n        \\addplot[Class Index,ybar] table[x index=0,y index=2]{\\ClassIndexTable};\n\n    \\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 746,
        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usepackage{tikz-qtree}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8]\n\\draw[dashed] (0.1,1.9) -- (0.1,3.2);\n\\draw[dashed] (0.1,3.2) -- (1.4,3.2);\n\\draw[dashed] (1.4,3.2) -- (1.4,1.9);\n\\draw[dashed] (1.4,1.9) -- (0.1,1.9);\n\n\\draw[dashed] (2.8,1.9) -- (2.8,3.2);\n\\draw[dashed] (2.8,3.2) -- (4.1,3.2);\n\\draw[dashed] (4.1,3.2) -- (4.1,1.9);\n\\draw[dashed] (4.1,1.9) -- (2.8,1.9);\n\n\\draw[dashed] (0.1,1.9) -- (1.4,1.9);\n\\draw[dashed] (1.4,1.9) -- (2.8,1.9);\n\\draw[dashed] (2.8,1.9) -- (4.1,1.9);\n\\draw[dashed] (4.1,1.9) -- (5.4,1.9);\n\n\\draw[dashed] (0.1,3.2) -- (2.8,3.2);\n\\draw[dashed] (2.8,3.2) -- (4.1,3.2);\n\\draw[dashed] (4.1,3.2) -- (5.4,3.2);\n\n\\draw[dashed] (0.1,4.5) -- (0.1,5.8);\n\\draw[dashed] (0.1,5.8) -- (1.4,5.8);\n\\draw[dashed] (1.4,5.8) -- (1.4,4.5);\n\\draw[dashed] (1.4,4.5) -- (0.1,4.5);\n\n\\draw[dashed] (2.8,4.5) -- (2.8,5.8);\n\\draw[dashed] (2.8,5.8) -- (4.1,5.8);\n\\draw[dashed] (4.1,5.8) -- (4.1,4.5);\n\\draw[dashed] (4.1,4.5) -- (2.8,4.5);\n\n\\draw[dashed] (0.1,5.8) -- (1.4,5.8);\n\\draw[dashed] (1.4,5.8) -- (2.8,5.8);\n\\draw[dashed] (2.8,5.8) -- (4.1,5.8);\n\\draw[dashed] (4.1,5.8) -- (5.4,5.8);\n\n\\draw[dashed] (0.1,7.1) -- (0.1,8.4);\n\\draw[dashed] (0.1,8.4) -- (1.4,8.4);\n\\draw[dashed] (1.4,8.4) -- (1.4,7.1);\n\\draw[dashed] (1.4,7.1) -- (0.1,7.1);\n\n\\draw[dashed] (2.8,7.1) -- (2.8,8.4);\n\\draw[dashed] (2.8,8.4) -- (4.1,8.4);\n\\draw[dashed] (4.1,8.4) -- (4.1,7.1);\n\\draw[dashed] (4.1,7.1) -- (2.8,7.1);\n\n\\draw[dashed] (0.1,8.4) -- (1.4,8.4);\n\\draw[dashed] (1.4,8.4) -- (2.8,8.4);\n\\draw[dashed] (2.8,8.4) -- (4.1,8.4);\n\\draw[dashed] (4.1,8.4) -- (5.4,8.4);\n\n\\node[red] at (2.8,1.9) {\\textbullet};\n\\node[red] at (4.1,1.9) {\\textbullet};\n\\node[red] at (2.8,3.2) {\\textbullet};\n\\node[red] at (4.1,3.2) {\\textbullet};\n\\node[red] at (0.1,5.8) {\\textbullet};\n\\node[red] at (2.8,5.8) {\\textbullet};\n\\node[red] at (4.1,5.8) {\\textbullet};\n\\node[red] at (0.1,7.1) {\\textbullet};\n\\node[red] at (2.8,7.1) {\\textbullet};\n\\node[red] at (4.1,7.1) {\\textbullet};\n\n\\draw (1.4,5.8) -- (1.4,7.1);\n\\draw (1.4,7.1) -- (0.1,8.4);\n\\draw (1.4,7.1) -- (2.8,8.4);\n\n\\draw (0.1,5.8) -- (2.8,7.1);\n\\draw (2.8,7.1) -- (4.1,8.4);\n\\draw (2.8,7.1) -- (2.8,8.4);\n\n\\draw[blue, <-] (2.1,5.6) -- (2.5,4.8);\n\\draw[blue, <-] (2.5,4.8) -- (2.1,4.3);\n\\draw[blue, <-] (2.5,4.8) -- (3.3,4.8);\n\\draw[blue, <-] (3.3,4.8) -- (2.9,4.3);\n\\draw[blue, <-] (2.9,4.3) -- (2.9,3.7);\n\\draw[blue, <-] (2.9,3.7) -- (2.5,3.2);\n\\draw[blue, <-] (2.5,3.2) -- (1.7,3.2);\n\\draw[blue, <-] (1.7,3.2) -- (1.7,3.7);\n\\draw[blue, <-] (1.7,3.7) -- (2.5,4.8);\n\\draw[blue, <-] (2.5,4.8) -- (2.1,5.6);\n\n\\draw[blue, <-] (3.4,5.4) -- (4.1,4.5);\n\\draw[blue, <-"
    },
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        "tikz_code": "\\documentclass[tikz,border=10pt,multi]{standalone}\n\\usetikzlibrary{lindenmayersystems}\n\\tikzset{\n  hexagon_top/.style={\n    l-system={\n      rule set={F -> F+F-F-F-FF-F-F-fF},\n      axiom=F++F++F,\n      step=2pt,\n      angle=60,\n      #1\n    }\n  },\n  hexagon_bottom/.style={\n    l-system={\n      rule set={F -> F-F++F-F},\n      axiom=F++F++F,\n      step=2pt,\n      angle=60,\n      #1\n    }\n  },\n  hexagon/.style={\n    hexagon_top=#1,\n    hexagon_bottom=#1\n  }\n}\n\\begin{document}\n\\begin{tikzpicture}\n  \\fill [blue!50] (0,0) -- ++(1,0) -- ++(0,1) -- cycle;\n  \\fill [cyan!50] (0,0) -- ++(1,0) -- ++(1,1) -- cycle;\n  \\fill [yellow!50] (0,0) -- ++(2,0) -- ++(2,2) -- cycle;\n  \\fill [magenta!50] (0,0) -- ++(3,0) -- ++(3,3) -- cycle;\n  \\fill [black] (0,0) -- ++(4,0) -- ++(4,4) -- cycle;\n  \\fill [orange!50] (0,0) -- ++(5,0) -- ++(5,5) -- cycle;\n  \\fill [red!50] (0,0) -- ++(6,0) -- ++(6,6) -- cycle;\n  \\draw [dotted, ultra thick] (0,0) -- ++(0,6) -- ++(6,0) -- cycle;\n  \\draw [dotted, ultra thick, rotate=30] (0,0) -- ++(0,6) -- ++(6,0) -- cycle;\n  \\draw [dotted, ultra thick, rotate=45] (0,0) -- ++(0,6) -- ++(6,0) -- cycle;\n  \\path [hexagon={hexagon_top={fill=cyan, line width=1.5pt, line join=round}}]\n    l-system\n  ;\n  \\path [hexagon={hexagon_top={fill=yellow, line width=1.5pt, line join=round}}]\n    l-system\n  ;\n  \\path [hexagon={hexagon_top={fill=magenta, line width=1.5pt, line join=round}}]\n    l-system\n  ;\n  \\path [hexagon={hexagon_bottom={fill=black, line width=1.5pt, line join=round}}]\n    l-system\n  ;\n  \\path [hexagon={hexagon_bottom={fill=orange, line width=1.5pt, line join=round}}]\n    l-system\n  ;\n  \\path [hexagon={hexagon_bottom={fill=red, line width=1.5pt, line join=round}}]\n    l-system\n  ;\n\\end{tikzpicture}\n\\end{document}"
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        "index": 749,
        "tikz_code": "\\documentclass[runningheads]{llncs}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usepackage{amsmath}\n\\usetikzlibrary{bayesnet}\n\\usetikzlibrary{shapes.gates.logic.US,trees,positioning,arrows}\n\\usetikzlibrary{trees}\n\\usetikzlibrary{\ttrees}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}[x=1.7cm,y=1.8cm]\n\t\t\n\t\t% Nodes for plate GM\n\t\t\\node[obs] (root) {$v_H$} ; %\n\t\t\\node[latent, left=1cm of root] (parent) {$u_1$} ; %\n\t\t\\node[latent, below=0.4cm of parent] (leftchild) {}; %\n\t\t\\node[latent, above=0.4cm of parent] (rightchild) {}; %\n\t\t\\node[latent, right=1cm of root] (child) {$u_4$} ; %\n\t\t\\node[latent, below=0.4cm of child] (leftsibling) {}; %\n\t\t\\node[latent, above=0.4cm of child] (rightsibling) {}; %\n\t\t\\node[latent, left=0.4cm of leftchild] (leftexpl) {}; %\n\t\t\\node[latent, above=0.4cm of leftexpl] (leftuppl) {}; %\n\t\t\\node[latent, right=0.4cm of rightchild] (rightexpl) {}; %\n\t\t\\node[latent, above=0.4cm of rightexpl] (rightuppl) {}; %\n\t\t\\node[latent, above=0.4cm of leftuppl] (leftupright) {}; %\n\t\t\\node[latent, above=0.4cm of rightuppl] (rightupleft) {}; %\n\t\t\\node[latent, left=0.4cm of leftsibling] (leftexpls) {}; %\n\t\t\\node[latent, above=0.4cm of leftexpls] (leftuppls) {}; %\n\t\t\\node[latent, right=0.4cm of rightsibling] (rightexplr) {}; %\n\t\t\\node[latent, above=0.4cm of rightexplr] (rightupplr) {}; %\n\t\t\\node[latent, below=0.4cm of child] (leftexpls2) {}; %\n\t\t\\node[latent, above=0.4cm of leftexpls2] (leftuppls2) {}; %\n\t\t\\node[latent, right=0.4cm of child] (rightexplr2) {}; %\n\t\t\\node[latent, above=0.4cm of rightexplr2] (rightupplr2) {}; %\n\t\t\\node[latent, left=0.4cm of leftsibling] (leftexpls3) {}; %\n\t\t\\node[latent, above=0.4cm of leftexpls3] (leftuppls3) {}; %\n\t\t\\node[latent, right=0.4cm of rightsibling] (rightexplr3) {}; %\n\t\t\\node[latent, above=0.4cm of rightexplr3] (rightupplr3) {}; %\n\t\t\n\t\t\n\t\t\\edge {parent} {root} ; %\n\t\t\\edge {leftchild} {root} ; %\n\t\t\\edge {rightchild} {root} ; %\n\t\t\\edge {child} {root} ; %\n\t\t\\edge {leftsibling} {child} ; %\n\t\t\\edge {rightsibling} {child} ; %\n\t\t\\edge {leftexpl} {leftchild} ; %\n\t\t\\edge {leftuppl} {leftexpl} ; %\n\t\t\\edge {rightexpl} {rightchild} ; %\n\t\t\\edge {rightuppl} {rightchild} ; %\n\t\t\\edge {leftupright} {leftchild} ; %\n\t\t\\edge {rightupleft} {rightchild} ; %\n\t\t\\edge {leftexpls} {leftsibling} ; %\n\t\t\\edge {leftuppls} {leftsibling} ; %\n\t\t\\edge {rightexplr} {rightsibling} ; %\n\t\t\\edge {rightupplr} {rightsibling} ; %\n\t\t\\edge {leftexpls2} {child} ; %\n\t\t\\edge {leftuppls2} {child} ; %\n\t\t\\edge {rightexplr2} {child} ; %\n\t\t\\edge {rightupplr2} {child} ; %\n\t\t\\edge {leftexpls3} {leftsibling} ; %\n\t\t\\edge {leftuppls3} {leftsibling} ; %\n\t\t\\edge {rightexplr3} {rightsibling} ; %\n\t\t\\edge {rightupplr3} {rightsibling} ; %\n\t\t\n\t\t\\plate {} {(root)(parent)(child)(leftexpl)(leftexpls)(leftexpls2)(leftexpls3)(leftchild)(leftsibling)(rightchild)(rightsibling)(rightexpl)(rightexplr)(rightexplr2)(rightexplr3)(rightchild)(rightsibling)(rightexpl)(rightexplr)} {$H_1$} ; %\n\t\t\\plate {} {(root)(parent)(child)(leftexpl)(leftexpls)(leftexpls2)(leftexpls3)(leftchild)(leftsibling)(rightchild)(rightsibling)(rightexpl)(rightexplr)(rightexplr2)(rightexplr3)(rightchild)(rightsibling)(rightexpl)(rightexplr)} {$H_2$} ; %\n\t\t\\plate {} {(root)(parent)(child)(leftexpl)(leftexpls)(leftexpls2)(leftexpls3)(leftchild)(leftsibling)(rightchild)(rightsibling)(rightexpl)(rightexplr)(rightexplr2)(rightexplr3)(rightchild)(rightsibling)(rightexpl)(rightexplr)} {$H_3$} ; %\n\t\t\\plate {} {(root)(parent)(child)(leftexpl)(leftexpls)(leftexpls2)(leftexpls3)(leftchild)(leftsibling)(rightchild)(rightsibling)(rightexpl)(rightexplr)(rightexplr2)(rightexplr3)(rightchild)(rightsibling)(rightexpl)(rightexplr)} {$B$} ; %\n\t\t\\plate {} {(leftchild)(rightchild)(leftsibling)(rightsibling)(leftexpl)(leftexpls)(leftexpls2)(leftexpls3)(leftexpls3)(leftupright)(leftupleft)(leftupright)(leftupleft)(rightupleft)(rightupright)(rightupright)(rightupright)} {$C$} ; %\n\t\t\\plate {} {(root)(parent)(child)(leftexpl)(leftexpls)("
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    {
        "index": 750,
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        "tikz_code": "\\documentclass[border=5pt, tikz]{standalone}\n\\usetikzlibrary{positioning, trees}\n\n\\begin{document}\n\n    \\begin{tikzpicture}[\n    every node/.style = {draw=black, thick, anchor=west},\n    edge from parent/.style = {draw, red, thick, -latex},\n    edge from parent path = {(\\tikzparentnode.south) -- ++(0,-8mm) -| (\\tikzchildnode.north)},\n    edge from parent/.append style = {anchor=south west},\n    level 1/.style = {sibling distance=20em},\n    level 2/.style = {sibling distance=25em},\n    level 3/.style = {sibling distance=25em},\n    level 4/.style = {sibling distance=20em}\n    ]\n    \\node {Mechanics}\n    child { node {Quantum mechanics}\n            child { node {Hamiltonian}}\n            child { node {Quantum mechanics}\n                child { node {$\\text{Q} \\rightarrow \\partial \\mathcal{M} \\rightarrow \\text{time}$}}\n                child { node {QCD}}\n                child { node {other}}\n            }\n            child { node {Classical mechanics}}\n    }\n    child { node {Quantum mechanics}\n            child { node {Observable}}\n            child { node {Classical mechanics}}\n            child { node {Quantum mechanics}}\n            child { node {Quantum mechanics}}\n    };\n    \\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[10pt,a4paper]{article}\n\\usepackage[latin1]{inputenc}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage[T1]{fontenc}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw (0,0) -- (12,0);\n\\draw (0,1) -- (12,1);\n\\draw (1,0) node {$\\bullet$};\n\\draw (1,1) node {$\\bullet$};\n\\draw (1,0.5) node[below] {$x_1$};\n\\draw (1,1.5) node[above] {$z_1$};\n\\draw (2,0) node {$\\bullet$};\n\\draw (2,1) node {$\\bullet$};\n\\draw (2,0.5) node[below] {$x_2$};\n\\draw (2,1.5) node[above] {$z_2$};\n\\draw (3,0) node {$\\bullet$};\n\\draw (3,1) node {$\\bullet$};\n\\draw (3,0.5) node[below] {$x_3$};\n\\draw (3,1.5) node[above] {$z_3$};\n\\draw (4,0) node {$\\bullet$};\n\\draw (4,1) node {$\\bullet$};\n\\draw (4,0.5) node[below] {$x_4$};\n\\draw (4,1.5) node[above] {$z_4$};\n\\draw (5,0) node {$\\bullet$};\n\\draw (5,1) node {$\\bullet$};\n\\draw (5,0.5) node[below] {$x_5$};\n\\draw (5,1.5) node[above] {$z_5$};\n\\draw (6,0) node {$\\bullet$};\n\\draw (6,1) node {$\\bullet$};\n\\draw (6,0.5) node[below] {$x_6$};\n\\draw (6,1.5) node[above] {$z_6$};\n\\draw (7,0) node {$\\bullet$};\n\\draw (7,1) node {$\\bullet$};\n\\draw (7,0.5) node[below] {$x_7$};\n\\draw (7,1.5) node[above] {$z_7$};\n\\draw (8,0) node {$\\bullet$};\n\\draw (8,1) node {$\\bullet$};\n\\draw (8,0.5) node[below] {$x_8$};\n\\draw (8,1.5) node[above] {$z_8$};\n\\draw (9,0) node {$\\bullet$};\n\\draw (9,1) node {$\\bullet$};\n\\draw (9,0.5) node[below] {$x_9$};\n\\draw (9,1.5) node[above] {$z_9$};\n\\draw (10,0) node {$\\bullet$};\n\\draw (10,1) node {$\\bullet$};\n\\draw (10,0.5) node[below] {$x_{10}$};\n\\draw (10,1.5) node[above] {$z_{10}$};\n\\draw (11,0) node {$\\bullet$};\n\\draw (11,1) node {$\\bullet$};\n\\draw (11,0.5) node[below] {$x_{11}$};\n\\draw (11,1.5) node[above] {$z_{11}$};\n\\draw[->] (1.5,1) to [out=45,in=135] (3.5,1);\n\\draw[->] (4.5,0) to [out=45,in=135] (6.5,0);\n\\draw[->] (5.5,1) to [out=45,in=135] (7.5,1);\n\\draw[->] (8.5,1) to [out=45,in=135] (10.5,1);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 755,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amssymb,amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.25]\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\\draw [->] (-6,0) -- (6,0);\n\t\t\\node [above] at (6,0) {$x$};\n\t\t\\draw [->] (0,-2) -- (0,2);\n\t\t\\node [above] at (0,2) {$y$};\n\t\t\n\t\t\\node [above right] at (5.5,0) {$y=R^{-1}(x)^{\\frac{1}{2}}$};\n\t\t\\node [above right] at (-5.5,0) {$y=R^{-1}(x)^{-\\frac{1}{2}}$};\n\t\t\n\t\t\n\t\t\n\t\t\\filldraw [opacity=0.5, pattern=north west lines, pattern color=black] (-6,1.8) -- (6,1.8) -- (6,-1.8) -- (-6,-1.8) -- (-6,1.8);\n\t\t\\filldraw [opacity=0.5, pattern=north east lines, pattern color=black] (-6,-1.8) -- (-6,1.8) -- (6,1.8) -- (6,-1.8) -- (-6,-1.8);\n\t\t\n\t\t\\draw (6,1.8) -- (6,-1.8);\n\t\t\\draw (-6,1.8) -- (-6,-1.8);\n\t\t\n\t\t\\draw (6,1.8) -- (-6,1.8);\n\t\t\\draw (6,-1.8) -- (-6,-1.8);\n\t\t\n\t\t\\draw [opacity=0.5, pattern=north east lines, pattern color=black] (-6,0.5) -- (6,0.5);\n\t\t\\draw [opacity=0.5, pattern=north west lines, pattern color=black] (-6,-0.5) -- (6,-0.5);\n\t\t\n\t\t\n\t\t\n\t\t\\draw [opacity=0.5] (-6,0.5) -- (6,0.5);\n\t\t\\draw [opacity=0.5] (-6,-0.5) -- (6,-0.5);\n\t\t\n\t\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 756,
        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,decorations,arrows,calc,arrows.meta,fit,positioning}\n\\tikzset{\n    -Latex,auto,node distance =1 cm and 1 cm,semithick,\n    state/.style ={ellipse, draw, minimum width = 0.7 cm},\n    point/.style = {circle, draw, inner sep=0.04cm,fill,node contents={}},\n    bidirected/.style={Latex-Latex,dashed},\n    el/.style = {inner sep=2pt, align=left, sloped}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}[>=stealth',shorten >=1pt,auto,node distance=2cm,main node/.style={circle,draw,font=\\sffamily\\small\\bfseries}]\n    \n    % Drawing states\n    \\node[state] (u) at (0,0) {$u$};\n    \\node[state] (v) at (0,-2.5) {$v$};\n    \\node[state] (u1) at (3,-2.5) {$a_{2,1}$};\n    \\node[state] (u2) at (3,0) {$b_{2,1}$};\n    \\node[state] (v1) at (3,2.5) {$a_{1,2}$};\n    \\node[state] (v2) at (3,5) {$b_{1,2}$};\n    \n    \\node[state] (A1) at (-1.5,2.5) {$A_1$};\n    \\node[state] (A2) at (-1.5,-2.5) {$A_2$};\n    \\node[state] (B1) at (5,2.5) {$B_1$};\n    \\node[state] (B2) at (5,-2.5) {$B_2$};\n\n    \\path (u) edge (v);\n    \\path (u) edge (u1);\n    \\path (u) edge (u2);\n    \n    \\path (v) edge (v1);\n    \\path (v) edge (v2);\n    \n    \\path[red] (u) edge (v1);\n    \\path[red] (u) edge (v2);\n    \\path[red] (u1) edge (v2);\n    \\path[red] (u2) edge (v1);\n    \n    \\path[green] (v) edge (u1);\n    \\path[green] (v) edge (u2);\n    \\path[green] (v1) edge (u2);\n    \\path[green] (v2) edge (u1);\n\n    \\path[blue] (v) edge[bend left=15] (u);\n    \\path[blue] (v1) edge[bend right=15] (u);\n    \\path[blue] (v2) edge[bend right=15] (u);\n    \\path[blue] (u1) edge[bend left=15] (u2);\n\n    \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 757,
        "tikz_code": "\\documentclass[letterpaper]{article}\n\\usepackage{amsmath}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usepackage{colortbl}\n\\usetikzlibrary{arrows.meta,calc,decorations.markings,math,arrows.meta, shapes.misc, decorations.pathmorphing}\n\\tikzset{cross/.style={cross out, draw, \n\t\tminimum size=2*(#1-\\pgflinewidth), \n\t\tinner sep=0pt, outer sep=0pt}}\n\n\\begin{document}\n\n\\begin{tikzpicture} [scale=0.8]\n\t\t%\n\t\t\\begin{scope} [xshift=-2.5cm]\n\t\t\\begin{scope}\n\t\t\\draw (0,0) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (a) {};\n\t\t\\draw (0,0.5) node[circle, draw, inner sep=0pt, minimum size=0.5cm, blue] (b) {};\n\t\t\\draw (0,1) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (c) {};\n\t\t\\draw (0.5,0.5) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (d) {};\n\t\t\\draw (0.5,-0.5) node[circle, draw, inner sep=0pt, minimum size=0.5cm, blue] (e) {};\n\t\t\\draw (0.5,-1) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (f) {};\n\t\t\\draw (-0.5,0.5) node[circle, draw, inner sep=0pt, minimum size=0.5cm, blue] (g) {};\n\t\t\\draw (-0.5,-0.5) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (h) {};\n\t\t\\draw (-0.5,-1) node[circle, draw, inner sep=0pt, minimum size=0.5cm, blue] (i) {};\n\t\t\n\t\t\\draw (a) -- (c);\n\t\t\\draw (b) -- (c);\n\t\t\\draw (c) -- (d);\n\t\t\\draw (d) -- (e);\n\t\t\\draw (e) -- (f);\n\t\t\\draw (f) -- (g);\n\t\t\\draw (g) -- (h);\n\t\t\\draw (h) -- (i);\n\t\t\n\t\t\\draw (a) -- (b);\n\t\t\n\t\t\\draw (e) -- (f);\n\t\t\n\t\t\\node[right, blue] at (-0.5,2) {$A^\\prime$};\n\t\t\\node[blue] at (0,1.5) {$A$};\n\t\t\\end{scope}\n\t\t\\draw[blue] (-1.75,-1.5) node {Case 1};\n\t\t\\end{scope}\n\t\t\n\t\t%\n\t\t\\begin{scope}\n\t\t\\draw (0,0) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (a) {};\n\t\t\\draw (0,0.5) node[circle, draw, inner sep=0pt, minimum size=0.5cm, blue] (b) {};\n\t\t\\draw (0,1) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (c) {};\n\t\t\\draw (0.5,0.5) node[circle, draw, inner sep=0pt, minimum size=0.5cm, green] (d) {};\n\t\t\\draw (0.5,-0.5) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (e) {};\n\t\t\\draw (0.5,-1) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (f) {};\n\t\t\\draw (-0.5,0.5) node[circle, draw, inner sep=0pt, minimum size=0.5cm, green] (g) {};\n\t\t\\draw (-0.5,-0.5) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (h) {};\n\t\t\\draw (-0.5,-1) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (i) {};\n\t\t\n\t\t\\draw (a) -- (c);\n\t\t\\draw (b) -- (c);\n\t\t\\draw (c) -- (d);\n\t\t\\draw (d) -- (e);\n\t\t\\draw (e) -- (f);\n\t\t\\draw (f) -- (g);\n\t\t\\draw (g) -- (h);\n\t\t\\draw (h) -- (i);\n\t\t\n\t\t\\draw (a) -- (b);\n\t\t\n\t\t\\draw (e) -- (f);\n\t\t\n\t\t\\node[right, blue] at (-0.5,2) {$A^\\prime$};\n\t\t\\node[blue] at (0,1.5) {$A$};\n\t\t\\end{scope}\n\t\t\\draw[blue] (0,-1.5) node {Case 2};\n\t\t\n\t\t%\n\t\t\\begin{scope} [xshift=2.5cm]\n\t\t\\begin{scope}\n\t\t\\draw (0,0) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (a) {};\n\t\t\\draw (0,0.5) node[circle, draw, inner sep=0pt, minimum size=0.5cm, green] (b) {};\n\t\t\\draw (0,1) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (c) {};\n\t\t\\draw (0.5,0.5) node[circle, draw, inner sep=0pt, minimum size=0.5cm, green] (d) {};\n\t\t\\draw (0.5,-0.5) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (e) {};\n\t\t\\draw (0.5,-1) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (f) {};\n\t\t\\draw (-0.5,0.5) node[circle, draw, inner sep=0pt, minimum size=0.5cm, green] (g) {};\n\t\t\\draw (-0.5,-0.5) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (h) {};\n\t\t\\draw (-0.5,-1) node[circle, draw, inner sep=0pt, minimum size=0.5cm] (i) {};\n\t\t\n\t\t\\draw (a) -- (c);\n\t\t\\draw (b) -- (c);\n\t\t\\draw (c) -- (d);\n\t\t\\draw (d) -- (e);\n\t\t\\draw (e) -- (f);\n\t\t\\draw (f) -- (g);\n\t\t\\draw (g) -- (h);\n\t\t\\draw (h) -- ("
    },
    {
        "index": 758,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{graphicx, amssymb, amsthm, amsfonts, latexsym, epsfig, amsmath, amscd, amsxtra, epsf, xcolor, hyperref, zref}\n\\usepackage{tikz}\n\\usetikzlibrary{backgrounds, decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.85]\n\\draw[thick, dashed, blue] (2,2) -- (2,-2);\n\\draw[thick, dashed, blue] (-2,-2) -- (2,-2);\n\\draw[thick, blue] (2,2) -- (2,-2);\n\\draw[thick, blue] (-2,-2) -- (2,-2);\n\\draw[thick, dashed, blue] (-2,-2) -- (-2,2);\n\\draw[thick, dashed, blue] (-2,2) -- (2,2);\n\\draw[thick, dashed, blue] (-2,2) -- (2,-2);\n\n\\filldraw[color=black!50, fill=blue!5, very thick](2,2) circle (0.1);\n\\filldraw[color=black!50, fill=blue!5, very thick] (2,-2) circle (0.1);\n\\filldraw[color=black!50, fill=blue!5, very thick] (-2,-2) circle (0.1);\n\\filldraw[color=black!50, fill=blue!5, very thick] (0,-2) circle (0.1);\n\\filldraw[color=black!50, fill=blue!5, very thick] (-2,0) circle (0.1);\n\n\\node at (3,2) {$A_1$};\n\\node at (3,-2) {$B_1$};\n\\node at (-3,-2) {$A_2$};\n\\node at (-3,2) {$C$};\n\\node at (-1,-1) {$v$};\n\\node at (-1,1) {$x$};\n\\node at (1,-1) {$y$};\n\\node at (-1,-3) {$\\mathcal{B}$};\n\\node at (3,-3) {$\\mathcal{C}$};\n\\node at (1.5,0.1) {$\\mathcal{B}_1$};\n\\node at (-0.7,-1.5) {$\\mathcal{A}_1$};\n\\node at (0.5,-1.5) {$\\mathcal{Y}_B$};\n\\node at (-0.5,0.5) {$\\mathcal{X}_A$};\n\\node at (1.5,1.5) {$\\mathcal{B}_1\\times \\mathcal{A}_2$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 759,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amsthm,amssymb,latexsym,color}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[xscale=.35,yscale=.3]\n  \\draw[->] (-10,0) -- (11,0) node[below] {$b$};\n  \\draw[->] (-10,0) -- (-10,9) node[left] {$t$};\n  \\foreach \\x in {-10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9} { \\draw (\\x,1pt) -- (\\x,-1pt); }\n  \\foreach \\x/\\xtext in {-10/-2, 0/0, 1/1, 2/2, 3/3, 4/4, 5/5, 6/6, 7/7, 8/8, 9/9}\n    \\draw (\\x,1pt) -- (\\x,-1pt) node[below=2pt,fill=white] {$\\xtext$};\n  \\foreach \\y in {1, 2, 3, 4, 5, 6, 7, 8} { \\draw (-1pt,\\y) -- (1pt,\\y); }\n  \\draw[blue, very thick, rounded corners=2pt] (-10,1) -- (0,0) -- (5,7) -- (9,7);\n  \\draw[red, thick, rounded corners=2pt] (-10,1) -- (0,0) -- (5,7) -- (9,7);\n  \\draw[densely dashed, gray] (-10,8) -- (9,8);\n  \\draw (0,6) node[red] {$\\bullet$} node[red, left=1mm, fill=white] {$\\alpha=0$};\n  \\draw (2,4) node[blue] {$\\bullet$} node[blue, left=1mm, fill=white] {$\\overline{\\alpha}$};\n  \\draw (6,2) node[blue] {$\\bullet$} node[blue, left=1mm, fill=white] {$\\overline{\\beta}$};\n  \\draw (6,7) node[red] {$\\bullet$} node[red, left=1mm, fill=white] {$\\beta$};\n  \\draw (4,2) node[red] {$\\bullet$} node[red, right=1mm, fill=white] {$\\overline{b}=1$};\n  \\draw (7,4) node[green] {$\\bullet$} node[green, right=1mm, fill=white] {$x$};\n  \\draw (3,8) node[green] {$\\bullet$} node[green, right=1mm, fill=white] {$\\overline{x}$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 760,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{tikz}\n\\usepackage{tikz-dependency}\n\\usetikzlibrary{shapes.geometric, arrows}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{colortbl}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node[rectangle, rounded corners,draw,text opacity=0.5, text width=6.5cm, minimum height=0.7cm, align=center] (a) {\\textbf{I'm on a diet to lose weight!}};\n\n\\node[rectangle, rounded corners,draw,text opacity=0.5, text width=7cm, minimum height=0.7cm, align=center, below of=a] (b) {\\textbf{I'm underlyig it, because I have sukvent of the loss weight.}};\n\n\\node[rectangle, rounded corners,draw,text opacity=0.5, text width=7.5cm, minimum height=0.7cm, align=center, below of=b, node distance=2cm] (c) {\\textbf{I'm relaated to food. Has property. Healthy.}};\n\n\\node[rectangle, rounded corners,draw,text opacity=0.5, text width=7cm, minimum height=0.7cm, align=center, right of=a, node distance=6cm] (d) {\\textbf{I'm not forget to eat more healthy.}};\n\n\\node[rectangle, rounded corners,draw,text opacity=0.5, text width=8cm, minimum height=0.7cm, align=center, right of=d, node distance=6cm] (e) {\\textbf{I'm underlyig it, because I have sukvent of the loss weight.}};\n\n\\draw[<-, thick, purple] (a) -- (b) node [midway, below, align=center] (edge1) {};\n\\draw[<-, thick, purple] (b) -- (c) node [midway, below, align=center] (edge2) {};\n\\draw[<-, thick, teal] (e) -- (d) node [midway, below, align=center] (edge3) {};\n\n\\node[align=center] at (edge1) {\\textbf{Underringing Commmonsense Knowledge:}};\n\\node[align=center] at (edge2) {\\textbf{Diet is subevnt of \\dots}};\n\\node[align=center] at (edge3) {\\textbf{Diet Related to \\dots Has Property \\dots}};\n\n\n\\node[align=center] at (edge1) {{\\color{teal} \\textbf{Has sukvent of \\dots}}};\n\\node[align=center] at (edge2) {{\\color{purple} \\textbf{Diet is related to \\dots}}};\n\\node[align=center] at (edge3) {{\\color{teal} \\textbf{Healthy}}};\n\n\\node[align=center] at (edge1) {{\\color{teal} \\textbf{Has sukvent of \\dots}}};\n\\node[align=center] at (edge2) {{\\color{purple} \\textbf{Diet is related to \\dots}}};\n\\node[align=center] at (edge3) {{\\color{teal} \\textbf{Healthy}}};\n\n\\draw[dashed, thick] (1,-3) rectangle (8.2,2);\n\n\\node[align=center] at (1.4, 2) {{\\color{blue} \\textbf{I'm on a diet to lose weight!}}};\n\\node[align=center] at (1.4, 1.8) {\\textbf{Image}};\n\n\\node[align=center] at (1.4, -3) {{\\color{blue} \\textbf{I'm not forget to eat more healthy.}}};\n\\node[align=center] at (1.4, -3.2) {\\textbf{Image}};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 761,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{bayesnet}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n  % Define nodes\n  \\node[obs]                               (X1) {$X_1$};\n  \\node[latent, below=of X1, xshift=-1.0cm] (X2) {$X_2$};\n  \\node[latent, below=of X1, xshift=1.0cm]  (X3) {$X_3$};\n\n  \\node[latent, below=of X2] (X4) {$X_4$};\n  \\node[latent, below=of X4] (X5) {$X_5$};\n\n  \\node[obs, right=of X3, yshift=0.6cm]  (X7) {$X_7$};\n  \\node[obs, right=of X3, yshift=-0.6cm]  (X8) {$X_8$};\n\n  \\node[obs, right=of X7, yshift=0.6cm]  (X9) {$X_9$};\n  \\node[obs, right=of X7, yshift=-0.6cm]  (X10) {$X_{10}$};\n\n  \\node[obs, right=of X9, yshift=0.6cm]  (X11) {$X_{11}$};\n  \\node[obs, right=of X10, yshift=-0.6cm]  (X12) {$X_{12}$};\n\n  % Connect the nodes\n  \\edge {X1} {X2, X3}\n  \\edge {X4} {X2}\n  \\edge {X5} {X2}\n\n  \\edge {X7} {X9, X11}\n  \\edge {X8} {X10}\n  \\edge {X12} {X11}\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 762,
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        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.6, transform shape]\n\\draw [thick](-4,0)--(-4,6);\n\\draw [thick](0,0)--(0,6);\n\\draw [thick](4,0)--(4,6);\n\\draw (-4,0) node[circle, fill=black]{};\n\\draw (0,0) node[circle, fill=black]{};\n\\draw (4,0) node[circle, fill=black]{};\n\\draw [thick,fill=gray] (-2,0)--(-2,3) arc(180:360:1.5 and 0.5) arc(0:180:1.5 and 0.5) --(2,0);\n\\draw (-4,0) node[circle, fill=gray, minimum size=0.3cm, scale=0.6]{};\n\\draw (0,0) node[circle, fill=gray, minimum size=0.3cm, scale=0.6]{};\n\\draw (4,0) node[circle, fill=gray, minimum size=0.3cm, scale=0.6]{};\n\\draw [thick,fill=gray] (-3,0)--(-3,6) arc(180:360:0.75 and 0.25) arc(0:180:0.75 and 0.25) --(3,0);\n\\draw [thick,fill=gray] (-1,0)--(-1,6) arc(180:360:0.5 and 0.25) arc(0:180:0.5 and 0.25) --(1,0);\n\\draw [thick,fill=gray] (-0.5,0)--(-0.5,6) arc(180:360:0.3 and 0.125) arc(0:180:0.3 and 0.125) --(0.5,0);\n\\draw [thick,fill=gray] (0,0) circle (0.2);\n\\draw (-4,0) node[scale=0.7,text width=0.7cm, align=center, text height=0.6cm]{k=$<$ S$\\cap$ S$};\n\\draw (0,0) node[scale=0.7, text width=0.7cm,align=center, text height=0.6cm]{k=$<$ S$\\cap$ N};\n\\draw (4,0) node[scale=0.7,text width=0.7cm, align=center, text height=0.6cm]{k=$>=$ S$\\cap$ S$};\n\\draw (4,0) node[scale=0.7, text width=0.7cm,align=center, text height=0.6cm]{k=$>=$ S$\\cap$ N};\n\\draw (-2.8,1.5) node[scale=0.6]{$k\\leq S\\cap S$};\n\\draw (-2.8,3.5) node[scale=0.6]{$k\\leq S\\cap N$};\n\\draw (-2.8,5.5) node[scale=0.6]{layer};\n\\draw (2.8,1.5) node[scale=0.6]{$k=S\\cap N$};\n\\draw (2.8,3.5) node[scale=0.6]{$k=S\\cap S$};\n\\draw (2.8,5.5) node[scale=0.6]{$k=S\\cap S\\setminus C$};\n\\draw (-1.2,-1) node[scale=0.6]{diference of two large balls centered at $ps_x$};\n\\draw (-1.2,-2) node[scale=0.6]{and twn $ps_x$ resps};\n\\draw (1.2,-1) node[scale=0.6]{equal sized balls centered at $ps_x$};\n\\draw (1.2,-2) node[scale=0.6]{and twn $ps_x$ resps};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usepackage{color}\n\n\\newcommand{\\sP}{\\mathcal{P}}\n\n\\newcommand{\\sG}{\\mathcal{G}}\n\n\\newcommand{\\sR}{\\mathcal{R}}\n\n\\newcommand{\\sH}{\\mathcal{H}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[thick, fill=green] (5,0)--(8,0)--(5,5)--(0,0);\n\\draw[thick, fill=green] (5,0)--(10,0)--(5,10)--(0,0);\n\\draw[thick, fill=green] (5,0)--(15,0)--(5,15)--(0,0);\n\\draw[thick, fill=green] (5,0)--(20,0)--(5,20)--(0,0);\n\\draw[thick, fill=green] (5,0)--(25,0)--(5,25)--(0,0);\n\\draw[thick, fill=green] (5,0)--(30,0)--(5,30)--(0,0);\n\\draw[thick, fill=green] (5,0)--(35,0)--(5,35)--(0,0);\n\\draw[thick, fill=green] (5,0)--(40,0)--(5,40)--(0,0);\n\\draw[thick, fill=green] (5,0)--(45,0)--(5,45)--(0,0);\n\\draw[thick, fill=green] (5,0)--(50,0)--(5,50)--(0,0);\n\\draw[thick, fill=green] (5,0)--(55,0)--(5,55)--(0,0);\n\\draw[thick, fill=green] (5,0)--(60,0)--(5,60)--(0,0);\n\\draw[thick, fill=red] (5,0)--(8,0)--(10,0)--(5,5)--(0,0);\n\\draw[thick, fill=red] (5,0)--(10,0)--(15,0)--(5,5)--(0,0);\n\\draw[thick, fill=red] (5,0)--(15,0)--(20,0)--(5,5)--(0,0);\n\\draw[thick, fill=red] (5,0)--(20,0)--(25,0)--(5,5)--(0,0);\n\\draw[thick, fill=red] (5,0)--(25,0)--(30,0)--(5,5)--(0,0);\n\\draw[thick, fill=red] (5,0)--(30,0)--(35,0)--(5,5)--(0,0);\n\\draw[thick, fill=red] (5,0)--(35,0)--(40,0)--(5,5)--(0,0);\n\\draw[thick, fill=red] (5,0)--(40,0)--(45,0)--(5,5)--(0,0);\n\\draw[thick, fill=red] (5,0)--(45,0)--(50,0)--(5,5)--(0,0);\n\\draw[thick, fill=red] (5,0)--(50,0)--(55,0)--(5,5)--(0,0);\n\\draw[thick, fill=red] (5,0)--(55,0)--(60,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(8,0)--(10,0)--(15,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(10,0)--(15,0)--(20,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(15,0)--(20,0)--(25,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(20,0)--(25,0)--(30,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(25,0)--(30,0)--(35,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(30,0)--(35,0)--(40,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(35,0)--(40,0)--(45,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(40,0)--(45,0)--(50,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(50,0)--(55,0)--(60,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(55,0)--(60,0)--(65,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(60,0)--(65,0)--(70,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(65,0)--(70,0)--(75,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(70,0)--(75,0)--(80,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(75,0)--(80,0)--(85,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(80,0)--(85,0)--(90,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(85,0)--(90,0)--(95,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(90,0)--(95,0)--(100,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(95,0)--(100,0)--(105,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(100,0)--(105,0)--(110,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(110,0)--(115,0)--(120,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(115,0)--(120,0)--(125,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(120,0)--(125,0)--(130,0)--(5,5)--(0,0);\n\\draw[thick, fill=yellow] (5,0)--(125,0)--(130,0)--(135"
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    {
        "index": 766,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amssymb}\n\\usepackage[colorlinks=true, allcolors=blue]{hyperref}\n\\usepackage{tikz}\n\\tikzset{\nevery node/.style={draw, circle, inner sep=2pt}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=3.8]\n% vertices\n\\node (1) at (-1.0, -1.0) {1};\n\\node (2) at (-1, 1.0) {2};\n\\node (3) at (1.0, 1.0) {3};\n\\node (4) at (1.0, -1.0) {4};\n\\node[shape=rectangle, color=white, text=black] (title) at (-1.3,1.55) {$G=(V_{i}, E_{i})$:};\n\\node[shape=rectangle, color=white, text=black] (title) at (1.3,1.55) {$V_{k}$:};\n\\node[shape=rectangle, color=white, text=black] (title) at (-1.3,-1.55) {$V_{j}$: $n=\\pi$};\n\\node[shape=rectangle, color=white, text=black] (title) at (1.3,-1.55) {$V_{l}$: $n=+1$};\n% edges\n\\draw (-0.75,0.1) -- (-0.85,0.1);\n\\draw (-0.75,0.1) -- (-0.85,-0.1);\n\\draw (-0.75,0.1) -- (-0.65,0.05);\n\\draw (-0.75,-0.1) -- (-0.85,0.1);\n\\draw (-0.75,-0.1) -- (-0.85,-0.1);\n\\draw (-0.75,-0.1) -- (-0.65,-0.05);\n\\draw (-0.75,0.1) -- (-0.75,-0.1);\n\\draw (-0.75,0.1) -- (-0.65,0.05);\n\\draw (-0.75,0.1) -- (-0.65,-0.05);\n\\draw (-0.85,0.1) -- (-0.75,-0.1);\n\\draw (-0.85,0.1) -- (-0.65,0.05);\n\\draw (-0.85,0.1) -- (-0.65,-0.05);\n\\draw (-0.85,-0.1) -- (-0.75,-0.1);\n\\draw (-0.85,-0.1) -- (-0.65,-0.05);\n\\draw (-0.85,-0.1) -- (-0.65,0.05);\n\\draw (0.1,0.67) -- (0.1,-0.67);\n\\draw (0.1,0.67) -- (-0.65,0.12);\n\\draw (0.1,0.67) -- (-0.65,-0.05);\n\\draw (0.1,0.67) -- (-0.75,-0.1);\n\\draw (0.1,0.67) -- (-0.85,-0.1);\n\\draw (0.1,0.67) -- (-0.85,0.1);\n\\draw (0.1,0.67) -- (-0.75,0.1);\n\\draw (0.1,0.67) -- (-0.65,0.05);\n\\draw (0.1,0.67) -- (-0.75,0.1);\n\\draw (0.1,0.67) -- (-0.85,0.1);\n\\draw (0.1,-0.67) -- (0.1,0.67);\n\\draw (0.1,-0.67) -- (-0.65,0.05);\n\\draw (0.1,-0.67) -- (-0.75,-0.1);\n\\draw (0.1,-0.67) -- (-0.85,-0.1);\n\\draw (0.1,-0.67) -- (-0.85,0.1);\n\\draw (0.1,-0.67) -- (-0.75,0.1);\n\\draw (0.1,-0.67) -- (-0.65,-0.05);\n\\draw (-0.65,0.05) -- (0.1,0.67);\n\\draw (-0.65,0.05) -- (0.1,-0.67);\n\\draw (-0.65,0.05) -- (0.1,0.25);\n\\draw (-0.65,0.05) -- (0.1,-0.25);\n\\draw (-0.65,0.05) -- (0.05,0.4);\n\\draw (-0.65,0.05) -- (0.05,-0.4);\n\\draw (-0.65,0.05) -- (-0.1,0.45);\n\\draw (-0.65,0.05) -- (-0.1,-0.45);\n\\draw (-0.65,0.05) -- (-0.2,0.5);\n\\draw (-0.65,0.05) -- (-0.2,-0.5);\n\\draw (-0.65,0.05) -- (-0.15,0.45);\n\\draw (-0.65,0.05) -- (-0.15,-0.45);\n\\draw (-0.65,0.05) -- (-0.25,0.5);\n\\draw (-0.65,0.05) -- (-0.25,-0.5);\n\\draw (-0.65,0.05) -- (-0.1,0.6);\n\\draw (-0.65,0.05) -- (-0.1,-0.6);\n\\draw (-0.65,0.05) -- (0.0,0.45);\n\\draw (-0.65,0.05) -- (0.0,-0.45);\n\\draw (-0.65,0.05) -- (0.05,0.55);\n\\draw (-0.65,0.05) -- (0.05,-0.55);\n\\draw (-0.65,0.05) -- (0.2,0.6);\n\\draw (-0.65,0.05) -- (0"
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    {
        "index": 767,
        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,arrows,positioning,calc}\n\n\\tikzset{\nblock/.style = {draw, fill=white, rectangle, minimum height=2.5em, minimum width=3em},\ntmp/.style = {coordinate},\nsum/.style= {draw, fill=white, circle, node distance=1cm},\ninput/.style = {coordinate},\noutput/.style= {coordinate},\npinstyle/.style = {pin edge={to-,thin,black}\n}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}[auto, node distance=2cm,>=latex']\n\\node [input, name=rinput] (rinput) {};\n\\node [block, right of=rinput,text width=1.5cm,align=center] (controller) {$\\Delta c$};\n\\node [block, right of=controller,node distance=3cm,text width=1.5cm,align=center] (system) {$L\\frac{\\mathrm{d}c}{\\mathrm{d}t}$};\n\\node [output, right of=system, node distance=2cm] (output) {};\n\\node [tmp, below of=controller,node distance=0.9cm] (tmp1) {};\n\\draw [->] (rinput) -- node{\\hspace{-0.4cm} } (controller);\n\\draw [->] (controller) -- node [name=v]{} (system);\n\\draw [->] (system) -- node [name=y] {} (output);\n\\draw [->] (output) |- ($(y.center)+(0,-0.5)$) -| (tmp1) |- (controller);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 768,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amssymb, amsthm, amsmath, amsfonts, amsrefs}\n\\usepackage{epstopdf, color}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,decorations.pathmorphing,decorations.footprints,fadings,calc,trees,mindmap,shadows,decorations.text,patterns,positioning,shapes,matrix,fit,through}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.8]\n\t\\node (v0) at (3,0) [circle,draw,fill,label=-45:$v$] {};\n\t\\node (v1) at (4,1) [circle,draw,fill,label=0:$v_1$] {};\n\t\\node (v2) at (6,1) [circle,draw,fill,label=0:$v_2$] {};\n\t\\node (v3) at (4,-1) [circle,draw,fill,label=-135:$v_3$] {};\n\t\\node (v4) at (6,-1) [circle,draw,fill,label=-135:$v_4$] {};\n\t\\node (v5) at (9,1) [circle,draw,fill,label=0:$v_5$] {};\n\t\\node (v6) at (7,0) [circle,draw,fill,label=-45:$v_6$] {};\n\t\\node (v7) at (9,-1) [circle,draw,fill,label=-135:$v_7$] {};\n\t\\node (v8) at (11,1) [circle,draw,fill,label=0:$v_8$] {};\n\t\\node (v9) at (13,0) [circle,draw,fill,label=-45:$v_9$] {};\n\t\\node (v10) at (14,1) [circle,draw,fill,label=0:$v_{10}$] {};\n\t\\node (v11) at (12,-1) [circle,draw,fill,label=-135:$v_{11}$] {};\n\t\\node (v12) at (13,-1) [circle,draw,fill,label=-135:$v_{12}$] {};\n\t\\node (v13) at (15,-1) [circle,draw,fill,label=-135:$v_{13}$] {};\n\t\\node (v14) at (15,1) [circle,draw,fill,label=0:$v_{14}$] {};\n\t\\node (v15) at (17,0) [circle,draw,fill,label=-45:$v_{15}$] {};\n\t\n\t\\node (u) at (18,0) [circle,draw,fill,label=-45:$u$] {};\n\t\n\t\\draw (v1) -- (v0) -- (v3) -- (v0) -- (v4) -- (v2);\n\t\\draw (v6) -- (v5) -- (v8);\n\t\\draw (v11) -- (v6) -- (v9) -- (v10) -- (v12) -- (v11) -- (v7) -- (v9);\n\t\\draw (v12) -- (v13) -- (v15);\n\t\n\t\\draw[dashed] (v0) -- (v1) -- (v2) -- (v3) -- (v4) -- (v6) -- (v7) -- (v8) -- (v9) -- (v10) -- (v11) -- (v12) -- (v13) -- (v14) -- (v15) -- (u);\n\t\n\t\\node (b1) at (4,2) {$b_1$};\n\t\\node (b2) at (6,2) {$b_2$};\n\t\\node (b3) at (9,2) {$b_3$};\n\t\\node (b4) at (13,2) {$b_4$};\n\t\\node (b5) at (15,2) {$b_5$};\n\t\n\t\\node (c1) at (4,-2) {$c_1$};\n\t\\node (c2) at (6,-2) {$c_2$};\n\t\\node (c3) at (9,-2) {$c_3$};\n\t\\node (c4) at (13,-2) {$c_4$};\n\t\\node (c5) at (15,-2) {$c_5$};\n\t\\node (c6) at (17,-2) {$c_6$};\n\t\n\t\\node (a1) at (3,2) {$a_1$};\n\t\\node (a2) at (11,2) {$a_2$};\n\t\\node (a3) at (17,2) {$a_3$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 769,
        "tikz_code": "\\documentclass[conference,10pt]{IEEEtran}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n\tscale=1,\n\taxis/.style={very thick, ->, >=stealth'},\n\timportant line/.style={thick},\n\tdashed line/.style={dashed, thin},\n\tevery node/.style={color=black,}\n\t]\n\t\\draw[axis] (0,0)  -- (11,0) node(xline)[right]{$t$};\n\t\\draw[dashed line] (0,-0.5)  -- (0,0.5) node(yline)[above]{};\n\t\\draw[dashed line] (10,-0.5)  -- (10,0.5) node(yline)[above]{};\n\t\\draw[dashed line] (2,-0.5)  -- (2,0.5) node(yline)[above]{};\n\t\\draw[dashed line] (5.5,-0.5)  -- (5.5,0.5) node(yline)[above]{};\n\t\n\t\\draw[thick, red] (0,-1)  -- (0,1) node(yline)[above]{};\n\t\\draw[thick, red] (10,-1)  -- (10,1) node(yline)[above]{};\n\t\\draw[thick, red] (2,-1)  -- (2,1) node(yline)[above]{};\n\t\\draw[thick, red] (5.5,-1)  -- (5.5,1) node(yline)[above]{};\n\t\n\t\\node[draw,text width=1cm, align=center,  fill=white] (X) at (0,0.75) {Non-disclosure \\\\ disclosure \\\\ $\\kappa$};\n\t\n\t\\node[draw,text width=1cm, align=center,  fill=white] (X) at (2,0.75) {Posted disclosure of \\\\ 2nd stage completion \\\\ and disclosure};\n\t\n\t\\node[draw,text width=1cm, align=center,  fill=white] (X) at (5.5,0.75) {Immediate disclosure of\\\\ 2nd stage completion  \\\\ and intrinsic deadline for 1st stage};\n\t\n\t\\node[draw,text width=1cm, align=center,  fill=white] (X) at (10,0.75) {Non-disclosure \\\\ disclosure $\\kappa^*$};\n\t\n\t\\node[draw=none,fill=none] (X) at (1,-0.35) {$k$};\n\t\\node[draw=none,fill=none] (X) at (3.5,-0.35) {$k'$};\n\t\\node[draw=none,fill=none] (X) at (6,-0.35) {$k''$};\n\t\\node[draw=none,fill=none] (X) at (8.5,-0.35) {$k'''$};\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "index": 770,
        "tikz_code": "\\documentclass[tikz,border=3mm]{standalone}\n\\usetikzlibrary{shapes,arrows,positioning,calc}\n\\begin{document}\n\\begin{tikzpicture}[\n  >=latex,\n  every node/.style={minimum size=8mm, inner sep=0pt, outer sep=0pt},\n  action/.style={draw,fill=white,inner sep=0pt,minimum size=5mm},\n  gain/.style={fill=lightgray, regular polygon, regular polygon sides=3, inner sep=0pt, minimum size=4.5mm},\n  bias/.style={circle,draw,inner sep=0pt,minimum size=4.5mm},\n  output/.style={circle,draw,fill=lightgray,inner sep=0pt,minimum size=4.5mm},\n  data/.style={circle,draw,inner sep=0pt,minimum size=4.5mm},\n  sum/.style={circle,draw,fill=lightgray,inner sep=0pt,minimum size=5mm},\n  argument/.style={circle,draw,fill=white,inner sep=0pt,minimum size=7mm},\n  ]\n\\node[sum] (sum1) at (0,1.5) {};\n\\node[sum] (sum2) at (0,0) {};\n\\node[sum] (sum3) at (0,-1.5) {};\n\\node[data,label=left:{$m$}] (data) at (0,-3) {};\n\\node[action,anchor=south west] (f1) at (sum1.north west) {$F_1(m)$};\n\\node[action,anchor=south east] (f2) at (sum2.north east) {$F_2(m)$};\n\\node[action,anchor=south east] (f3) at (sum3.north east) {};\n\\node[argument,label=below right:{$output$}] (out) at (5,0) {};\n\\draw[->] (f1.east) -- (sum1);\n\\draw[->] (f2.east) -- (sum2);\n\\draw[->] (f3.east) -- (sum3);\n\\draw[->] (data.east) -- (sum3);\n\\draw[<-] (sum1.west) -- node[above] {int rate} ++ (-1,0);\n\\draw[->] (sum1) -- (out);\n\\draw[->] (sum2) -- (out);\n\\draw[->] (sum3) -- (out);\n\\draw[red,->] (data.south) -- ++ (0,-2.5) -| node[pos=0.25,below] {capital} ($(sum3.south east)!0.25!(sum3.south west)$);\n\\foreach \\X in {1,2,3}\n {\\draw[red,->] (sum\\X.south) -- ++ (0,-1.5) -| node[pos=0.25,below] {int rate} ++ (-2,0);}\n\\path (out.north east) -- coordinate[pos=0.25] (aux) (out.north west);\n\\draw[red,->] (aux) |- ++ (-1.5,0) node[left] {$m$};\n\\end{tikzpicture}\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[colorlinks=true,linkcolor=blue,citecolor=blue]{hyperref}\n\\usepackage{a4wide, amsthm, amsmath, amssymb, amsfonts}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{automata,positioning}\n\\tikzset{>=latex}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[baseline=1.5ex,scale=0.15]\n  \\draw (0,3) to (0,0);\n  \\draw (2,0) to [out=90, in=-90] (2,3);\n  \\draw (4,0) to [out=90, in=-90] (4,3);\n  \\draw[red] (0,0) to [out=90, in=-90, looseness=2] (0,3);\n  \\draw[red] (2,0) to [out=90, in=-90, looseness=2] (2,3);\n  \\draw[red] (4,0) to [out=90, in=-90, looseness=2] (4,3);\n  \\end{tikzpicture}\n\n\\end{document}"
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        "index": 772,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath, amssymb, amsthm}\n\\usepackage{color}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{pgf,tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale = 1]\n\\tikzstyle{every node}=[draw,circle,fill=white,minimum size=2pt,inner sep=2pt]\n\\node (x) at (0,0) {$x$};\n\\node [fill=gray] (u) at (0,1) {$u$};\n\\node [fill=gray] (u1) at (-1,0) {$u_1$};\n\\node [fill=gray] (u2) at (-0.5,0) {$u_2$};\n\\node (w2) at (0.5,0) {$w/u_3$};\n\\node [fill=gray] (w3) at (1,0) {$w_3$};\n\\node (y) at (0.5,-1) {$y$};\n\\node (w1) at (0.5,-0.5) {$w_1$};\n\\node (w2) at (1.5,-0.5) {$w_2$};\n\\draw (x) -- (u);\n\\draw (x) -- (u1);\n\\draw (x) -- (u2);\n\\draw (x) -- (w2);\n\\draw (u) -- (w2);\n\\draw (u) -- (y);\n\\draw (y) -- (w1);\n\\draw (y) -- (w3);\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[sigconf]{acmart}\n\\usepackage[utf8]{inputenc}\n\\usepackage[simplified]{pgf-umlcd}\n\\usepackage{amsmath}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n        \\begin{class}[text width=2cm]{gP}{0,0}{1}{}\n            \\attribute{gP}\n            \\operation{gp}\n            \\operation[0]{...}\n            \\operation[2]{...}\n            \\operation[4]{...}\n        \\end{class}\n        \\begin{class}[text width=2cm]{gPr}{4,0}{1}{}\n            \\inherit{gP}\n            \\operation{gp*}\n            \\operation[0]{...}\n            \\operation[2]{...}\n            \\operation[4]{...}\n        \\end{class}\n        \\begin{class}[text width=2cm]{pS}{0,-3}{1}{}\n            \\attribute{pS}\n            \\operation{ps}\n            \\operation[0]{...}\n            \\operation[2]{...}\n            \\operation[4]{...}\n        \\end{class}\n        \\begin{class}[text width=2cm]{pSk}{4,-3}{1}{}\n            \\inherit{pS}\n            \\operation{psk}\n            \\operation[0]{...}\n            \\operation[2]{...}\n            \\operation[4]{...}\n        \\end{class}\n        \\begin{class}[text width=2cm]{pSr}{0,-6}{1}{}\n            \\inherit{gP}\n            \\operation{car}\n            \\operation[0]{...}\n            \\operation[2]{...}\n            \\operation[4]{...}\n        \\end{class}\n        \\begin{class}[text width=2cm]{events}{-3,-6}{1}{}\n            \\attribute{events-}\n            \\operation{weaver}\n        \\end{class}\n        \\begin{class}[text width=2cm]{eventsr}{4,-6}{1}{}\n            \\inherit{gPr}\n            \\operation{events*}\n            \\operation[0]{...}\n            \\operation[2]{...}\n            \\operation[4]{...}\n        \\end{class}\n        \\begin{class}[text width=2cm]{eventt}{8,-6}{1}{}\n            \\attribute{events+}\n            \\operation{event}\n        \\end{class}\n        \n        \\unidirectionalAssociation{gPr}{pSr}{0..*}\n        \\unidirectionalAssociation{pSk}{pSr}{0..*}\n        \\unidirectionalAssociation{gP}{pS}{0..*}\n        \\unidirectionalAssociation{pS}{events}{0..*}\n        \\unidirectionalAssociation{pSk}{eventsr}{0..*}\n        \\unidirectionalAssociation{pSr}{eventt}{0..*}\n    \\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 774,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amsmath,amssymb}\n\\usepackage{tikz-cd}\n\\usepackage{tikz}\n\\usepackage{color}\n\\usepackage{xcolor}\n\\usepackage{amssymb}\n\\usepackage[latin1]{inputenc}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n\\draw[step=2.0,black!15,thin] (-3,-3) grid (3,3);\n\n\n%x-axis\n\\draw [->] (-3,0)--(3,0) node[right] {$x$};\n\n%y-axis\n\\draw [->] (0,-3)--(0,3) node[above] {$y$};\n\n%Fixed point set\n\\draw [thick] (-2,-2)--(-2,2);\n\\draw [thick] (-2,-2)--(2,-2);\n\\draw [thick] (2,-2)--(2,-1);\n\\draw [thick] (2,-1)--(2,1);\n\\draw [thick] (2,1)--(2,2);\n\\draw [thick] (2,2)--(-2,2);\n\\draw [thick] (-2,2)--(-2,1);\n\\draw [thick] (-2,1)--(-2,-1);\n\\draw [thick] (-2,-1)--(-2,-2);\n\n%Fixed point set\n\\draw [thick] (0,0)--(0,2);\n\\draw [thick] (0,2)--(2,2);\n\\draw [thick] (2,2)--(2,0);\n\\draw [thick] (2,0)--(0,0);\n\n%Points of continuity\n\\fill (-1,-1) circle [radius=2pt];\n\\fill (1,1) circle [radius=2pt];\n\\fill (1,-1) circle [radius=2pt];\n\\fill (-1,1) circle [radius=2pt];\n\n%Continuity lines\n\\draw (-3,1)--(3,1);\n\\draw (1,-3)--(1,3);\n\\draw (0,-3)--(0,3);\n\n\n%Labeling the fixed point set\n\\node [above right] at (1,1) {$Q_0$};\n\\node [below left] at (-1,-1) {$Q_1$};\n\\node [above right] at (1,-1) {$Q_1'$};\n\\node [below left] at (-1,1) {$Q_2$};\n\\node [below left] at (0,0) {$Q_2'$};\n\\node [above right] at (-2,-2) {$Q'_1$};\n\\node [above right] at (2,-1) {$Q'_1'$};\n\\node [above right] at (2,1) {$Q'_2$};\n\\node [above right] at (2,2) {$Q'_2'$};\n\n%Marks\n\\node [below left] at (-3,2) {$L$};\n\\node [above right] at (2,-3) {$L'$};\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 775,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz-cd}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\\draw[dashed] (-3.5,0) -- (1,-3);\n\\draw[dashed] (-3.5,0) -- (-1,-3);\n\\draw[dashed] (-3.5,0) -- (0,-3);\n\n\\draw[thick, dotted, color=black!90] (-3.5,0) -- (-3.75,-1);\n\\draw[thick, dotted, color=black!90] (-3.5,0) -- (-3.5,-1);\n\\draw[thick, dotted, color=black!90] (-3.5,0) -- (-3.25,-1);\n\n\\draw[thick, dotted, color=black!90] (-1.5,0) -- (-1.75,-1);\n\\draw[thick, dotted, color=black!90] (-1.5,0) -- (-1.5,-1);\n\\draw[thick, dotted, color=black!90] (-1.5,0) -- (-1.25,-1);\n\n\\draw[thick, dotted, color=black!90] (-0.5,0) -- (-0.75,-1);\n\\draw[thick, dotted, color=black!90] (-0.5,0) -- (-0.5,-1);\n\\draw[thick, dotted, color=black!90] (-0.5,0) -- (-0.25,-1);\n\n\\draw[thick, dotted, color=black!90] (1.5,0) -- (1.75,-1);\n\\draw[thick, dotted, color=black!90] (1.5,0) -- (1.5,-1);\n\\draw[thick, dotted, color=black!90] (1.5,0) -- (1.25,-1);\n\n\\draw[thick, dotted, color=black!90] (3,0) -- (3.25,-1);\n\\draw[thick, dotted, color=black!90] (3,0) -- (3,-1);\n\\draw[thick, dotted, color=black!90] (3,0) -- (2.75,-1);\n\n\\draw[thick, color=black!90] (-3.5,0) .. controls (-3.75,-0.5) and (-3.75,-1) .. (-3.5,-1.5);\n\\draw[thick, color=black!90] (-1.5,0) .. controls (-1.75,-0.5) and (-1.75,-1) .. (-1.5,-1.5);\n\\draw[thick, color=black!90] (-0.5,0) .. controls (-0.25,-0.25) and (-0.25,-0.5) .. (-0.5,-1.5);\n\\draw[thick, color=black!90] (1.5,0) .. controls (1.75,-0.25) and (1.75,-0.5) .. (1.5,-1.5);\n\\draw[thick, color=black!90] (3,0) .. controls (3.25,-0.25) and (3.25,-0.5) .. (3,-1.5);\n\n\\draw[thick, color=black!90] (-3.5,0) .. controls (-3,-1) and (-2,-2) .. (-1,-3);\n\\draw[thick, color=black!90] (-1.5,0) .. controls (-1,-1) and (0,-2) .. (1,-3);\n\\draw[thick, color=black!90] (-0.5,0) .. controls (-0.25,-0.5) and (0,-1) .. (0.75,-1.5);\n\\draw[thick, color=black!90] (1.5,0) .. controls (1,-1) and (2,-2) .. (3,-3);\n\n\n\\draw (-3.5,0) .. controls (-3,-1) and (-2,-2) .. (-1,-3);\n\\draw (-1.5,0) .. controls (-1,-1) and (0,-2) .. (1,-3);\n\\draw (-0.5,0) .. controls (-0.25,-0.5) and (0,-1) .. (0.75,-1.5);\n\\draw (1.5,0) .. controls (1,-1) and (2,-2) .. (3,-3);\n\n\\node[color=black!90] (n1) at (-4.25,-1.75) {$\\mathcal{E}_u$};\n\\node[color=black!90] (n1) at (0.5,-1.75) {$\\mathcal{E}_2$};\n\\node[color=black!90] (n1) at (0.25,-1) {$\\mathcal{E}_3$};\n\\node[color=black!90] (n1) at (1.75,-2) {$\\mathcal{E}_3'$};\n\\node[color=black!90] (n1) at (4,-2) {$\\mathcal{E}_u$};\n\n\\draw[color=red, thick] (-3.5,0) .. controls (-3.25,-0.5) and (-3,-1) .. (-2.25,-1.5);\n\\draw[color=red, thick] (-2.25,-1.5) .. controls (-1.5,-2) and (-1.25,-2.5) .. (-1,-3);\n\\draw[color=red, thick] (-1.5,0) .. controls (-1.25,-0.5) and (-1,-1) .. (-0.5,-1.5);\n\\draw[color=red, thick] (-0.5,-1.5) .. controls (0,-2) and (0.5,-2.5) .. (1.25,-3);\n\\draw[color=red, thick] (0.75,-1.5) .. controls (1,-2) and (1.5,-2.5) .. (2.25,-3);\n\\draw[color=red, thick] (3,0) .. controls (2.75,-0.5) and (2.5,-1) .. (1.5,-1.5);\n\\draw[color=red, thick] (1.5,-1.5) .. controls (1.25,-2) and (0.75,-2.5) .. (0.5,-3);\n\n\\node[color=red, thick] (n1) at (-3.5,-1.25)"
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    {
        "index": 776,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns,arrows,decorations.pathreplacing}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node at (-.5,0) {$\\{c,d\\}$};\n\\node at (2,1) {$\\{a\\}$};\n\\node at (4.5,0) {$\\{b,c\\}$};\n\\node at (2,4) {$\\{a,b\\}$};\n\\node at (5.5,5) {$\\{a,b\\}$};\n\\node at (0,2) {$\\{d\\}$};\n\\node at (5.5,2) {$\\{b\\}$};\n\\node at (0,5) {$\\{a\\}$};\n\\node at (0,0) {$\\{c,d\\}$};\n\n\\draw[->,thick](0,1.5)--(0,2.5);\n\\draw[->,thick](2,0)--(3,0);\n\\draw[->,thick](4,0)--(4,1.5);\n\\draw[->,thick](2,4)--(3,4);\n\\draw[->,thick](5.5,4)--(5.5,3.5);\n\\draw[->,thick](2,0)--(4,0);\n\\draw[->,thick](2,4)--(4,4);\n\\draw[->,thick](5.5,5)--(5.5,4.5);\n\\draw[->,thick](0,2)--(0,3.5);\n\\draw[->,thick](0,0)--(2,0);\n\\draw[->,thick](4,0)--(5.5,0);\n\\draw[->,thick](0,5)--(0,4.5);\n\\draw[->,thick](0,5)--(2,4);\n\\draw[->,thick](2,4)--(4,4);\n\\draw[->,thick](5.5,4)--(4,4);\n\\draw[->,thick](5.5,5)--(4,4);\n\\draw[->,thick](5.5,5)--(2,4);\n\\draw[->,thick](0,2)--(2,2);\n\\draw[->,thick](2,2)--(4,2);\n\\draw[->,thick](4,2)--(5.5,2);\n\\draw[->,thick](0,0)--(2,2);\n\\draw[->,thick](2,2)--(4,2);\n\\draw[->,thick](4,2)--(5.5,2);\n\n\\draw (0,2) .. controls (1,3) and (1,1) .. (0,2);\n\\draw (5.5,2) .. controls (4,3) and (4,1) .. (5.5,2);\n\n\\node at (1.25,2.75) {$\\theta$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 777,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usepackage[framemethod=tikz]{mdframed}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.5}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw [fill=black] (0,0) circle (0.05 cm);\n\\draw [fill=black] (1,1) circle (0.05 cm);\n\\draw [fill=black] (1,2) circle (0.05 cm);\n\\draw [fill=black] (2,3) circle (0.05 cm);\n\\draw (0,0) -- (1,1);\n\\draw (1,2) -- (2,3);\n\\node at (0.5,-0.5) {$a$};\n\\node at (1,0.5) {$l_a^k$};\n\\node at (1.5,2.5) {$b$};\n\\begin{scope}[shift={(5,0)}]\n\\draw [fill=black] (1,1) circle (0.05 cm);\n\\draw [fill=black] (1,2) circle (0.05 cm);\n\\draw [fill=black] (2,3) circle (0.05 cm);\n\\draw (1,1) -- (1,2);\n\\draw (1,2) -- (2,3);\n\\node at (1.5,2.5) {$b$};\n\\node at (1.5,-0.5) {$a$};\n\\draw [fill=black] (0,0) circle (0.05 cm);\n\\draw (0,0) -- (2,3);\n\\node at (0.5,-0.5) {$a$};\n\\node at (2,2.5) {$R_a^k(a)$};\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 778,
        "tikz_code": "\\documentclass[10pt]{amsart}\n\\usepackage{amsmath,amsfonts,array,amscd,amsthm,amssymb,stackrel,verbatim,wrapfig,subfig,float}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,matrix}\n\\usetikzlibrary{shapes.geometric}\n\\usetikzlibrary{decorations.markings}\n\\tikzset{\n  vertice/.style={circle,draw=black},\n  decoration={markings,mark=at position 0.5 with {\\arrow{>}}}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n   \\node[vertice] (a) at (0,0) {$g$};\n   \\node[vertice] (b) at (2,0) {$1$};\n   \\path[->] (a) edge[out=30,in=150] (b);\n   \\path[->] (b) edge[out=210,in=-30] (a);\n   \n   \\node (message) at (-1.5,-0.5) {$r=g$};\n   \n   \\tikzset{\n  vertice/.style={circle,draw=black},\n  decoration={markings,mark=at position 0.5 with {\\arrow{>}}}\n}\n   \n   \\node[vertice] (a) at (5,0) {$g$};\n   \\node[vertice] (b) at (6,1) {$g$};\n   \\node[vertice] (c) at (6,-1) {$g$};\n   \\node[vertice] (d) at (8,1) {$1$};\n   \\node[vertice] (e) at (8,-1) {$g$};\n   \\path[->] (a) edge[out=30,in=150] (b);\n   \\path[->] (b) edge[out=210,in=-30] (a);\n   \\path[->] (a) edge[out=250,in=90] (c);\n   \\path[->] (c) edge[out=210,in=-90] (a);\n   \\path[->] (a) edge[out=320,in=110] (e);\n   \\path[->] (e) edge[out=210,in=-30] (a);\n   \\path[->] (a) edge[out=0,in=140] (d);\n   \\path[->] (d) edge[out=210,in=-30] (a);\n   \n   \\node (message) at (4.5,-1) {$g \\cdot (1+ \\frac{g}{r} \\cdot g^{r-1})$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 779,
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        "index": 780,
        "tikz_code": "\\documentclass[a4paper,twoside,11pt]{amsart}\n\\usepackage{pgf,tikz}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{calc}\n\\usepackage{amsmath, amssymb, amsthm, bm, centernot}\n\\usepackage{color,booktabs}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.75]\n\\tikzstyle{vertex}=[circle, draw=black, thick, fill=black!15!white, inner sep = 0.65mm]\n\\tikzstyle{vertex-phantom}=[circle, draw=black, thick, fill=white, inner sep = 0.65mm]\n\\tikzstyle{edge}=[line width=1.2pt]\n\\tikzstyle{edge-phantom}=[line width=1.2pt,dashed]\n\n% Platzhalter\n\\foreach \\x/\\y in {0/0,2/0,4/0,0/1,2/1,4/1,0/2,2/2,4/2} {\n\\draw[edge-phantom] (\\x+0.5,\\y+0.5) rectangle (\\x+4.5,\\y+4.5);\n\\draw [fill=white,draw=white] (\\x+2.5,\\y+2.5) circle (1.5mm);\n}\n\n% GKZ-Knoten\n\\foreach \\x/\\y in {0/0,2/0,4/0,0/1,2/1,4/1,0/2,2/2,4/2} {\n\\node[vertex] (a\\x\\y) at (\\x+1.5,\\y+1.5) {};\n\\draw [fill=black] (\\x+1.5,\\y+1.5) circle (1.5mm);\n}\n\\node[vertex-phantom] (c01) at (3.5,3.5) {};\n\\node[vertex-phantom] (c00) at (3.5,2.5) {};\n\\node[vertex-phantom] (c10) at (3.5,1.5) {};\n\\node[vertex-phantom] (c11) at (3.5,0.5) {};\n\n% GKZ-Kanten\n\\foreach \\x in {0,2,4} {\n\\foreach \\y in {0,1} {\n\\pgfmathtruncatemacro{\\v}{\\x+1}\n\\draw [edge] (a\\x\\y)--(a\\v\\y);\n\\draw [edge] (a\\x\\y)--(c\\x0);\n\\draw [edge] (a\\x\\y)--(c\\x1);\n}\n}\n\\foreach \\y in {0,2} {\n\\foreach \\x in {0,2,4} {\n\\pgfmathtruncatemacro{\\v}{\\y+1}\n\\draw [edge] (a\\x\\y)--(a\\v\\y);\n\\draw [edge] (a\\x\\y)--(c\\x0);\n\\draw [edge] (a\\x\\y)--(c\\x1);\n}\n}\n\\foreach \\x in {1,3} {\n\\foreach \\y in {0,1} {\n\\pgfmathtruncatemacro{\\v}{\\x+1}\n\\draw [edge] (a\\x\\y)--(a\\v\\y);\n\\draw [edge] (a\\x\\y)--(c\\x0);\n\\draw [edge] (a\\x\\y)--(c\\x1);\n}\n}\n\\draw [edge] (c00)--(a00)--(a40)--(c40)--(c00);\n\\draw [edge] (c10)--(a01)--(a41)--(c41)--(c10);\n\\draw [edge] (c01)--(a02)--(a42)--(c42)--(c01);\n\\draw [edge] (c11)--(a03)--(a43)--(c43)--(c11);\n\n\n% GKZ-Felder\n\\foreach \\x/\\y in {0/0,2/0,4/0,0/1,2/1,4/1,0/2,2/2,4/2} {\n\\draw[edge-phantom] (\\x,\\y) rectangle (\\x+4,\\y+4);\n\\draw [fill=white] (\\x+2,\\y+2) circle (1.5mm);\n}\n\n% GKZ-Pfeil\n\\draw [->,thick,line width=1.5pt] (6,3) -- (8,3);\n\\draw[edge-phantom] (6.5,0.5) -- (6.5,2.5);\n\\draw[edge-phantom] (7,0.5) -- (7,2.5);\n\\draw[edge-phantom] (7.5,0.5) -- (7.5,2.5);\n\\draw[edge-phantom] (6.5,3) -- (7.5,3);\n\\draw (6.5,3) -- (7.5,3);\n\\draw [fill=black] (7.5,3) circle (1.5mm);\n\\draw [fill=white] (7,2.5) circle (1.5mm);\n\\draw [fill=white] (6.5,2.5) circle (1.5mm);\n\\draw [fill=white] (7.5,2.5) circle (1.5mm);\n\\draw [fill=white] (7,2) circle (1.5mm);\n\\draw [fill=white] (6.5,2) circle (1.5mm);\n\\draw [fill=white] (7.5,2) circle (1.5mm);\n\\draw [fill=white] (7,1.5) circle (1.5mm);\n\\draw [fill=white] (6.5,1.5) circle (1.5mm);\n\\draw [fill=white] (7.5,1.5) circle (1.5mm);\n\\draw [fill=white] (7,1) circle (1.5mm);\n\\draw [fill=white] (6.5,1) circle (1.5mm);\n\\draw [fill=white] (7.5,1) circle (1.5mm);\n\\draw [fill=white] (7,0.5) circle (1.5mm);\n\\draw [fill=white] (6.5,0.5) circle (1.5mm);\n\\draw [fill=white] (7.5,0.5) circle (1.5mm);\n\\draw [fill=white] (7,0) circle (1.5mm);\n\\draw [fill=white] (6.5,0) circle (1.5mm);\n\\draw [fill=white] (7.5,0) circle (1.5mm);\n\n% Hilfslinien\n\\node[black] at (0.5,4.5) {"
    },
    {
        "index": 781,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{intersections}\n\\usetikzlibrary{shapes.geometric}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{decorations.pathmorphing, patterns,shapes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8, baseline={(current bounding box.center)}]\n\\draw[thick] (-100pt,10pt) -- (100pt,10pt);\n\\draw[thick] (-100pt,-10pt) -- (100pt,-10pt);\n\\draw[thick,->] (-100pt,-10pt) -- (-100pt,50pt);\n\\draw[thick,->] (-100pt,-10pt) -- (50pt,-10pt);\n\\node at (20pt, -20pt) {$n$};\n\\node at (40pt, 15pt) {$\\hat{\\eta}^+$};\n\\node at (-18pt,55pt) {$E_n^+$};\n\\node at (-50pt, -20pt) {$E_B$};\n\\draw[red,dashed, thick] (-10pt,-10pt) -- (5pt,-10pt);\n\\draw[red,dashed, thick] (5pt,-10pt) .. controls (5pt,-15pt) and (30pt,0pt) .. (30pt,0pt);\n\\draw[red,dashed, thick] (30pt,0pt) .. controls (30pt,0pt) and (55pt,30pt) .. (55pt,30pt);\n\\draw[red,dashed, thick] (55pt,30pt) -- (60pt,30pt);\n\\draw[blue, dotted, thick] (-10pt,-3pt) -- (5pt,-3pt);\n\\draw[blue, dotted, thick] (5pt,-3pt) .. controls (5pt,-5pt) and (20pt,0pt) .. (20pt,0pt);\n\\draw[blue, dotted, thick] (20pt,0pt) .. controls (20pt,0pt) and (40pt,20pt) .. (40pt,20pt);\n\\draw[blue, dotted, thick] (40pt,20pt) -- (60pt,20pt);\n\\node at (70pt, -20pt) {\\scriptsize $\\varepsilon\\times B/2$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 782,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amsthm,amsmath,amssymb, amsaddr,datetime}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.8]\n        \\node[fill=black,circle,inner sep=1pt] (t1) at (0,0) {};\n        \\node[fill=black,circle,inner sep=1pt] (t2) at (2,0) {};\n        \\node[fill=black,circle,inner sep=1pt] (t3) at (4,0) {};\n        \\node[fill=black,circle,inner sep=1pt] (t4) at (6,0) {};\n        \\node[fill=black,circle,inner sep=1pt] (t5) at (8,0) {};\n        \\node[fill=black,circle,inner sep=1pt] (t6) at (10,0) {};\n        \\node[fill=black,circle,inner sep=1pt] (t7) at (4,2) {};\n        \\node[fill=black,circle,inner sep=1pt] (t8) at (6,2) {};\n        \\node[fill=black,circle,inner sep=1pt] (t9) at (8,2) {};\n        \n        \\draw (t1)--(t2);\n        \\draw (t3)--(t2);\n        \\draw (t3)--(t4);\n        \\draw (t5)--(t6);\n        \\draw (t7)--(t3);\n        \\draw (t5)--(t8);\n        \\draw (t8)--(t9);\n        \n        \\node at (0,.4) {$b_{n-1}$};\n        \\node at (2,.4) {$b_{n}$};\n        \\node at (4,.4) {$b_{n+1}$};\n        \\node at (6,.4) {$b_{n+2}$};\n        \\node at (8,.4) {$b_{n+3}$};\n        \\node at (4,2.4) {$a_{n-1}$};\n        \\node at (6,2.4) {$a_n$};\n        \\node at (8,2.4) {$a_{n+1}$};\n        \n        \n        \n        \n    \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 783,
        "tikz_code": "\\documentclass[11pt,letterpaper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node(1){$R_1$};\n\\node(2)[node distance=1.2in, right of=1]{$S_1$};\n\\node(3)[node distance=.8in, below of=1]{$R_2$};\n\\node(4)[node distance=.8in, below of=2]{$S_2$};\n\\node(5)[node distance=.8in, below of=3]{$\\vdots$};\n\\node(6)[node distance=.8in, below of=4]{$\\vdots$};\n\\node(7)[node distance=.8in, below of=5]{$T_{n-1}$};\n\\node(8)[node distance=.8in, below of=6]{$\\vdots$};\n\\node(9)[node distance=.8in, below of=7]{$U_{n-1}$};\n\\node(10)[node distance=.8in, below of=8]{$\\vdots$};\n\\node(11)[node distance=.8in, below of=9]{$\\left\\{0\\right\\}$};\n\\draw[->](1) to node [above]{$$}(2);\n\\draw[->](1) to node [left]{$$}(3);\n\\draw[->](2) to node [right]{$$}(4);\n\\draw[->](3) to node [below]{$$}(4);\n\\draw[->](3) to node [left]{$$}(5);\n\\draw[->](4) to node [right]{$$}(6);\n\\draw[->](5) to node [below]{$$}(7);\n\\draw[->](6) to node [below]{$$}(8);\n\\draw[->](7) to node [below]{$$}(9);\n\\draw[->](8) to node [below]{$$}(10);\n\\draw[->](9) to node [below]{$$}(11);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 784,
        "tikz_code": "\\documentclass[12pt, reqno]{amsart}\n\\usepackage{amsmath,amssymb, amsfonts,amscd,psfrag,graphicx,stmaryrd}\n\\usepackage[table]{xcolor}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,shadows,calc}\n\\usepgflibrary{arrows}\n\\usetikzlibrary{arrows, decorations.markings, calc, fadings, decorations.pathreplacing, patterns, decorations.pathmorphing, positioning}\n\\tikzset{nodc/.style={circle,draw=blue!50,fill=pink!80,inner sep=1.6pt}}\n\\tikzset{nodr/.style={circle,draw=black,fill=green!50!black,inner sep=2pt}}\n\\tikzset{nodel/.style={circle,draw=black,inner sep=2.2pt}}\n\\tikzset{nodinvisible/.style={circle,draw=white,inner sep=2pt}}\n\\tikzset{nodpale/.style={circle,draw=gray,fill=gray,inner sep=1.6pt}}\n\\tikzset{nod1/.style={circle,draw=black,fill=black,inner sep=1pt}}\n\\tikzset{nod2/.style={circle,draw=black,fill=blue!75!black,inner sep=1.6pt}}\n\\tikzset{nod3/.style={circle,draw=black,fill=black,inner sep=1.8pt}}\n\\tikzset{noddiam/.style={diamond,draw=black,inner sep=2pt}}\n\\tikzset{nodw/.style={circle,draw=black,inner sep=1.8pt}}\n\\usepackage[colorlinks, urlcolor=blue, linkcolor=blue, citecolor=blue]{hyperref}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\\node [nodr] at (0,0) (v)  {};\n\\node [nod2] at (2,0) (v2)  {}\n\tedge (v);\n\\node [nod2] at (2,2) (v3)  {}\n\tedge [<-] (v2);\n\\node [nod2] at (2,-2) (v4)  {}\n\tedge [->] (v2);\t\n\\node [nod2] at (0,2) (v5)  {}\n\tedge (v)\n\tedge [<-] (v3);\t\n\\node [nod2] at (-2,0) (v1)  {}\n\tedge (v)\t\n\tedge [<-] (v4)\n\tedge [<-] (v5);\t\n\\node [nod2] at (0,-2) (v6)  {}\n\tedge (v)\n\tedge [->] (v4)\n\tedge [<-] (v2);\n\\node [nod2] at (-2,2) (v7)  {}\n\tedge (v)\n\tedge [<-] (v5)\n\tedge [<-] (v1);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 785,
        "tikz_code": "\\documentclass[a4paper,11pt]{article}\n\\usepackage{amsmath,amssymb,amsfonts,amsxtra, mathrsfs,graphics,graphicx,amsthm,epsfig, youngtab,bm,longtable,float,tikz,empheq,nccmath}\n\\usetikzlibrary{positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[node distance=2cm,cnode/.style={circle,draw,thick,minimum size=8mm},snode/.style={rectangle,draw,thick,minimum size=8mm},pnode/.style={rectangle,red,draw,thick,minimum size=8mm}]\n\\node[cnode] (1) at (-3,-2) {$p_{1}$};\n\\node[cnode] (2) at (-3,-4) {$p_{2}$};\n\\node[cnode] (3) at (-3,-6) {$p_{3}$};\n\\node[cnode] (4) at (-3,-8) {$p_{4}$};\n\\node[cnode] (5) at (-3,-10) {$p_{5}$};\n\\node[cnode] (6) at (-10,-9) {$p_{6}$};\n\\node[cnode] (7) at (-10, -7) {$p_{7}$};\n\\node[cnode] (8) at (-10, -5) {$p_{8}$};\n\\node[cnode] (9) at (-10,-2) {$p_{9}$};\n\\node[cnode] (10) at (-10, 1) {$p_{10}$};\n\\node[cnode] (11) at (-13,3) {$p_{11}$};\n\\node[cnode] (12) at (-13, -1) {$p_{12}$};\n\\node[snode] (13) at (-13, -11) {$Y^{0}$};\n\\node[snode] (14) at (-13,7) {$X^{0}$};\n\\node[snode] (15) at (3,-11) {$Y^{*}$};\n\\node[snode] (16) at (3,7) {$X^{*}$};\n\\node[snode] (17) at (6,-11) {$Z^{0}$};\n\\node[snode] (18) at (6,7) {$Z^{*}$};\n\\node[snode] (19) at (10,-11) {$W^{0}$};\n\\node[snode] (20) at (10,7) {$W^{*}$};\n\\draw[thick] (1) to (2);\n\\draw[thick] (2) to (3);\n\\draw[thick] (3) to (4);\n\\draw[thick] (4) to (5);\n\\draw[thick] (5) to (10);\n\\draw[thick] (10) to (11);\n\\draw[thick] (10) to (12);\n\\draw[thick] (11) to (12);\n\\draw[thick] (13) to (12);\n\\draw[thick] (13) to (2);\n\\draw[thick] (14) to (11);\n\\draw[thick] (14) to (12);\n\\draw[thick] (15) to (5);\n\\draw[thick] (15) to (12);\n\\draw[thick] (16) to (11);\n\\draw[thick] (16) to (12);\n\\draw[thick] (17) to (4);\n\\draw[thick] (17) to (12);\n\\draw[thick] (18) to (11);\n\\draw[thick] (18) to (12);\n\\draw[thick] (19) to (4);\n\\draw[thick] (19) to (12);\n\\draw[thick] (13) to (16);\n\\draw[thick] (13) to (17);\n\\draw[thick] (6) to (2);\n\\draw[thick] (6) to (7);\n\\draw[thick] (7) to (8);\n\\draw[thick] (8) to (9);\n\\draw[thick] (9) to (10);\n\\draw[thick] (10) to (6);\n\\node[text width=1cm](9) at (-2.5, -3) {$2$};\n\\node[text width=1cm](10) at (-2.5, -5) {$3$};\n\\node[text width=1cm](11) at (-2.5, -7) {$5$};\n\\node[text width=1cm](12) at (-2.5, -9) {$7$};\n\\node[text width=1cm](13) at (-2.5, -2) {$1$};\n\\node[text width=1cm](14) at (-2.5, 0.5) {$4$};\n\\node[text width=1cm](15) at (-2.5, 2.5) {$10$};\n\\node[text width=1cm](16) at (-2.5, 4.5) {$11$};\n\\node[text width=1cm](17) at (-2.5, 6.5) {$12$};\n\\node[text width=1cm](18) at (-2.5, 8.5) {$13$};\n\\draw[thick] (20) to (17);\n\\draw[thick] (20) to (18);\n\\draw[thick, dashed] (20) to (15);\n\\draw[thick, dashed] (20) to (16);\n\\draw[thick] (19) to (17);\n\\draw[thick] (19) to (18);\n\\draw[thick, dashed] (19) to (15);\n\\draw[thick, dashed] (19) to (16);\n\\draw[thick] (18) to (15);\n\\draw[thick] (18) to (16);\n\\draw[thick] (17) to (15);\n\\draw[thick] (17) to (16);\n\\draw[thick, dashed] (16) to (15);\n\\node[text width=1cm](21) at (5, -9) {$g_1$};\n\\node[text width=1cm](22) at (5, -3) {$g_2$};\n\\node[text width=1cm](23) at (5, 2) {$g_3$};\n\\node[text width=1cm]("
    },
    {
        "index": 786,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{cd}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8]\n        \\draw (0,0) -- (0,3) -- (-2,3) -- (-2,4) -- (0,4) -- (0,0);\n        \\draw[dashed] (0,2) -- (0,3) -- (-2,2);\n        \\draw[dashed] (-1,0) -- (-2,1);\n        \\node at (-0.5,1.8) {\\small $D^{n_0}_{g_1}(h)$};\n        \\draw (0,0) -- (2,0) -- (2,1) -- (4,1) -- (4,2) -- (2,2) -- (2,0);\n        \\draw[dashed] (2,2) -- (2,3) -- (0,3);\n        \\draw[dashed] (3,0) -- (4,1);\n        \\node at (1.5,0.8) {\\small $D^{n_0}_{g_2}(h)$};\n        \\draw[dashed] (-1,0) -- (-2,0);\n        \\node at (-1.5,-0.3) {\\small $D^{n_0}_{g_2}(h)$};\n        \n        \\node at (5,2) {$\\xRightarrow{}$};\n        \n        \\draw (7,0) -- (7,3) -- (5,3) -- (5,4) -- (7,4) -- (7,0);\n        \\draw[dashed] (7,3) -- (5,3);\n        \\draw[dashed] (8,0) -- (7,1);\n        \\draw[dashed] (8,2) -- (9,3);\n        \\draw (7,0) -- (10,0) -- (10,1) -- (12,1) -- (12,2) -- (10,2) -- (10,0);\n        \\draw[dashed] (10,2) -- (10,3) -- (7,3);\n        \\draw[dashed] (11,0) -- (12,1);\n        \\node at (7.5,0.8) {\\small $D^{n_0}_{g_2}(h)$};\n        \\node at (9.5,0.8) {\\small $D^{n_0}_{g_2}(h)$};\n        \\node at (6.5,-0.3) {\\small $D^{n_0}_{g_1}(h)$};\n    \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 787,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usepackage{xcolor}\n\\usepackage{pgf,tikz}\n\\usetikzlibrary{calc,arrows}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.17}\n\\usepgfplotslibrary{fillbetween}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n\\begin{axis}[\n    xlabel={$x$},\n    ylabel={$f(x)$},\n    xmin=0, xmax=50,\n    ymin=0.2, ymax=1.0,\n    xtick={0,10,20,30,40,50},\n    ytick={0,0.2,0.4,0.6,0.8,1.0},\n    %legend pos=outer north east,\n    ymajorgrids=true,\n    grid style=dashed,\n    legend style={nodes={scale=0.5, transform shape}},\n]\n\n\\addplot [\n    domain=0:50, \n    samples=1000, \n    color=blue,\n    ]\n    {(1/2)*((x+1)^2+1-1/2*((x+1)^2+1-1/2*((x+2)^2+1-1)))};\n\\addlegendentry{$f(x)=\\frac{1}{2}(x+1)^2+1-\\frac{1}{4}x^2$}\n\n\\addplot [\n    domain=0:50, \n    samples=1000, \n    color=red,\n    ]\n    {(1/2)*((2*x+1)^2+1-1/2*((x+1)^2+1-1/2*((x+2)^2+1-1)))};\n\\addlegendentry{$1-\\frac{1}{2}x^2$}\n\n\\addplot [\n    domain=0:50, \n    samples=1000, \n    color=black,\n    ]\n    {(1/2)*((x+2)^2+1-1/2*((x+1)^2+1-1/2*((x+2)^2+1-1)))};\n\\addlegendentry{$1-\\frac{1}{2}x^2$}\n\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 788,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,automata}\n\\tikzset{initial text={}}\n\\usepackage{pgfgantt}\n\n\\begin{document}\n\n\\begin{tikzpicture}[shorten >=1pt,node distance=1.2cm,>=stealth',auto,\n                                    every state/.style={thin,fill=blue!10}]\n\\draw (-0.8,-1.6) rectangle (0.8,0.4);\n\\node at (-0.4,-1.0) {\\tiny $\\rho_-$};\n\\node at (-0.4,-0.2) {\\tiny $\\rho_+$};\n\\node at (-1.0,-0.2) {\\tiny $\\rho_-$};\n\\node at (1.0,-0.2) {\\tiny $\\rho_+$};\n\\draw  [->] (-1.0,-0.2)--(-0.6,-0.7);\n\\draw  [->] (1.0,-0.2)-- (0.6,-0.7);\n\\node at (-0.8,-1.0) {\\tiny $\\bullet$};\n\\node at (-0.8,-0.2) {\\tiny $\\bullet$};\n\\draw  [->] (-0.8,-1.0)--(-0.8,-0.5);\n\\draw  [->] (-0.8,-0.2)--(-0.8,0.2);\n\\node at (-0.8,0.0) {\\tiny $\\bullet$};\n\\draw  [->] (0.8,-0.2)--(0.8,-0.5);\n\\draw  [->] (0.8,-1.0)--(0.8,-0.5);\n\\node at (0.8,-0.2) {\\tiny $\\bullet$};\n\\node at (0.8,-1.0) {\\tiny $\\bullet$};\n\\node at (0.8,0.0) {\\tiny $\\bullet$};\n\\draw  [<-] (0.8,0.0)--(0.8,0.2);\n\\draw  [->] (0.8,-0.7)--(-0.7,-0.7);\n\\node[state,initial above,inner sep=2pt,minimum size=0pt]        (u_0)                           {\\tiny $v_0$};  \n\\node[state,inner sep=2pt,minimum size=0pt]  (u_1)  [below left of=u_0]     {\\tiny $v_-$}; \n\\node[state,inner sep=2pt,minimum size=0pt]  (u_2)  [below right of=u_0]     {\\tiny $v_+$};\n\\path[->]       \n             (u_0)     edge    node{\\tiny $\\lambda_e$}     (u_2)\n                       edge    node{\\tiny $\\lambda_d$}     (u_1)\n             (u_1)     edge    node{\\tiny $\\rho_+$}     (u_2);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 789,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{scope}[xshift=-1.5cm]\n\\node at (0,0) {$\\cdots$};\n\\node at (0,1) {$\\bullet$};\n\\node[left] at (-0.5,1) {$a_1$};\n\\node at (1,1) {$\\bullet$};\n\\node[left] at (1,-0.5) {$a_0$};\n\\node at (0,0) {$\\cdots$};\n\\node at (0,1) {$\\bullet$};\n\\node[left] at (-0.5,1) {$a_1$};\n\\node at (1,1) {$\\bullet$};\n\\node[left] at (1,-0.5) {$a_0$};\n\\node at (2,1) {$\\bullet$};\n\\node[left] at (2,-0.5) {$b_1$};\n\\node at (3,1) {$\\bullet$};\n\\node[left] at (3,-0.5) {$b_0$};\n\\node at (4,0) {$\\cdots$};\n\\node at (4,1) {$\\bullet$};\n\\node[left] at (4.5,1) {$a_2$};\n\\draw (0,0) -- (0,1);\n\\draw (0,0) -- (1,1);\n\\draw (1,1) -- (2,1);\n\\draw (2,1) -- (3,1);\n\\draw (3,1) -- (4,1);\n\\draw (0,1) -- (1,1);\n\\draw (1,0) -- (2,1);\n\\draw (2,0) -- (3,1);\n\\draw (3,0) -- (4,1);\n\\draw (0,0) ellipse (1.5cm and 0.5cm);\n\\end{scope}\n\\begin{scope}[xshift=3.5cm]\n\\node at (0,0) {$\\cdots$};\n\\node at (0,1) {$\\bullet$};\n\\node[left] at (-0.5,1) {$a_2$};\n\\node at (1,1) {$\\bullet$};\n\\node[left] at (1,-0.5) {$a_1$};\n\\node at (0,0) {$\\cdots$};\n\\node at (0,1) {$\\bullet$};\n\\node[left] at (-0.5,1) {$a_1$};\n\\node at (1,1) {$\\bullet$};\n\\node[left] at (1,-0.5) {$a_0$};\n\\node at (2,1) {$\\bullet$};\n\\node[left] at (2,-0.5) {$b_1$};\n\\node at (3,1) {$\\bullet$};\n\\node[left] at (3,-0.5) {$b_0$};\n\\node at (4,0) {$\\cdots$};\n\\node at (4,1) {$\\bullet$};\n\\node[left] at (4.5,1) {$a_3$};\n\\draw (0,0) -- (0,1);\n\\draw (0,0) -- (1,1);\n\\draw (1,1) -- (2,1);\n\\draw (2,1) -- (3,1);\n\\draw (3,1) -- (4,1);\n\\draw (0,1) -- (1,1);\n\\draw (1,0) -- (2,1);\n\\draw (2,0) -- (3,1);\n\\draw (3,0) -- (4,1);\n\\draw (0,0) ellipse (1.5cm and 0.5cm);\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 790,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{tikz}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[->](-1,0)--(7,0)node[right]{$k$};\n\\draw[->](0,-1)--(0,7)node[above]{$\\tau$};\n\\draw(-1,-1)node[below]{$N$};\n\\draw(1,1)--(7,1);\n\\draw(1,2)--(7,2);\n\\draw(1,3)--(7,3);\n\\draw(1,4)--(7,4);\n\\draw(1,5)--(7,5);\n\\draw(1,6)--(7,6);\n\\draw[domain=-0.7:7]plot(\\x,0.1*\\x*\\x*\\x);\n\\draw(1,5.2)node[right]{Both holes open};\n\\draw(2,5)node[right]{Both holes open};\n\\draw(2.5,4.5)node[right]{Right hole only open};\n\\draw(1,1)node[left]{Left hole only open};\n\\draw(1,6)node[left]{Left hole only open};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 791,
        "tikz_code": "\\documentclass[border=5mm]{standalone}\n\\usepackage{tikz}\n\\usetikzlibrary{quotes,angles}\n\\begin{document}\n\\begin{tikzpicture}[>=latex,font=\\small]\n\\coordinate (O) at (0,0);\n\\coordinate (B) at (0,2);\n\\coordinate (H) at (-1.5,0);\n\\coordinate (R) at (3,0);\n\\coordinate (N) at (0,4);\n\\coordinate (M) at ({3*cos(45)},{3*sin(45)});\n\n\\draw[dashed] (O) node[below left] {$x$} -- (M) node[above left] {$y$};\n\\draw[thick,red] (O) -- (R) node[midway,below] {$R$};\n\\draw[dashed] (B) node[left] {$\\theta_0$} -- (M) node[midway,above] {$\\gamma$};\n\\draw[dashed] (H) node[left] {$\\theta_0$} -- (M) node[midway,right] {$H$};\n\\draw[thick,blue] (O) to[out=0,in=45] (B);\n\\draw[thick,green] (O) to[out=0,in=135] (N);\n\\draw[thick,dashed,black] (O) to[out=180,in=90] (H) to[out=-90,in=180] (B);\n\\draw (O) circle (1.5);\n\\draw (B) circle (3);\n\\draw[fill=black] (O) circle (0.06);\n\\draw pic[draw,angle radius=2cm,\"$\\theta$\" shift={(2mm,2mm)}] {angle=R--O--B};\n\\end{tikzpicture}\n\\end{document}"
    },
    {
        "index": 792,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n  \\matrix (m) [matrix of math nodes,row sep=3em,column sep=4em,minimum width=2em]\n  {\n     \\sigma & \\emptyset & \\emptyset & \\emptyset \\\\\n     \\tau & \\sigma & \\sigma & \\tau \\\\};\n  \\path[-stealth]\n    (m-1-1) edge node [left] {$a$} (m-2-1)\n            edge [dashed] node [left] {$a$} (m-2-2)\n    (m-2-1) edge node [left] {$a$} (m-2-2)\n    (m-2-2) edge node [above] {$a$} (m-2-3)\n    (m-2-3) edge node [above] {$a$} (m-2-4)\n    (m-1-4) edge [dashed] node [left] {$a$} (m-2-4);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 793,
        "tikz_code": "\\documentclass[10pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath,amsthm,enumerate}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage[color=green!30]{todonotes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[join=bevel,inner sep=0.6mm]\n\n\\node[draw,shape=circle,draw=black] (x) at (0,0) {};\n\\draw (x)+(0,-0.3) node {$x$};\n\\node[draw,shape=circle,draw=black] (y) at (2,0) {};\n\\draw (y)+(0,-0.3) node {$x-g_1(t)$};\n\\node[draw,shape=circle,draw=black] (z) at (4,0) {};\n\\draw (z)+(0,-0.3) node {$x-g_6(t)$};\n\\node[draw,shape=circle,draw=black] (a) at (1,1.7) {};\n\\draw (a)+(-0.3,0) node {$x-g_5(t)$};\n\\node[draw,shape=circle,draw=black] (b) at (3,1.7) {};\n\\draw (b)+(0.3,0) node {$x-g_4(t)$};\n\\node[draw,shape=circle,draw=black] (c) at (2,3.4) {};\n\\draw (c)+(-0.3,0) node {$f_2(t)-x$};\n\\node[draw,shape=circle,draw=black] (d) at (0.5,0.8) {};\n\\draw (d)+(-0.3,0) node {$x-g_3(t)$};\n\\node[draw,shape=circle,draw=black] (e) at (3.5,0.8) {};\n\\draw (e)+(0.3,0) node {$x-g_2(t)$};\n\n\\draw[-,line width=0.4mm] (x) to (y);\n\\draw[-,line width=0.4mm] (y) to (z);\n\\draw[-,line width=0.4mm] (x) to (d);\n\\draw[-,line width=0.4mm] (d) to (a);\n\\draw[-,line width=0.4mm] (a) to (c);\n\\draw[-,line width=0.4mm] (y) to (e);\n\\draw[-,line width=0.4mm] (e) to (b);\n\\draw[-,line width=0.4mm] (b) to (c);\n\\draw[-,line width=0.4mm] (z) to (e);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 794,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale = 3]\n\\draw[->, very thick] (-0.2,0) -- (2.4,0) node[right]{$\\frac1p$};\n\\draw[->, very thick] (0,-0.2) -- (0,2.4) node[above]{$\\frac1q$};\n\\draw[domain=0:2.4,smooth,variable=\\x,black] plot ({\\x},{(2-\\x)/(1+\\x)});\n\\draw[domain=0:2.4,smooth,variable=\\x,black] plot ({\\x},{2/(1+\\x)});\n\\draw[domain=0:1.4,smooth,variable=\\x,black] plot ({\\x},{2*\\x/(1+\\x)}) node[above,right] {$\\frac{2+d}{2+2d} \\frac{\\frac{2}{1+p}}{1+\\frac{2}{1+p}} = \\frac{2+d}{2+2d} \\frac{p}{1+p}$};\n\\draw[domain=0:1.8,smooth,variable=\\x,black] plot ({\\x},{2*\\x/(1+\\x)}) node[above,right] {$\\frac{2}{1+p}$};\n\\draw[domain=0:1.4,smooth,variable=\\y,black] plot ({1.3},{\\y}) node[above,right] {$\\frac{2+d}{2+2d} \\frac{\\frac{2}{1+q}}{1+\\frac{2}{1+q}} = \\frac{2+d}{2+2d} \\frac{q}{1+q}$};\n\\draw[domain=0:1.8,smooth,variable=\\y,black] plot ({1.3},{\\y}) node[above,right] {$\\frac{2}{1+q}$};\n\\draw[domain=0:2.4,smooth,variable=\\x,black] plot ({\\x},{1/(1+\\x)}) node[below,right] {$\\frac{1}{1+p} = \\frac{n_0}{n_0 + (n_0+1)\\frac{d}{2+d}} = \\frac{1}{1+q}$};\n\\fill[fill=gray!10] (0,0)--(0,2)--(2,0)--(2,2)--(0,0);\n\\draw[->, very thick] (1,0.8) -- (0.8,1);\n\\draw[->, very thick] (1.2,0.9) -- (1.3,0.7);\n\\draw[->, very thick] (1.2,0.9) -- (1.4,0.6);\n\\draw[->, very thick] (1.2,0.9) -- (1.1,0.8);\n\\draw[->, very thick] (1.5,0.3) -- (1.2,0.2);\n\\draw[->, very thick] (1.5,0.3) -- (1.8,0.4);\n\\draw[->, very thick] (1.5,0.3) -- (1.3,0.5);\n\\draw[->, very thick] (1.5,0.3) -- (1.6,0.6);\n\\node[right] at (0.5,1.2) {$\\left( \\begin{matrix} 2-\\frac{2}{1+p} \\\\ \\frac{2}{1+p} \\end{matrix} \\right)$};\n\\node[left] at (0.5,0.8) {$\\left( \\begin{matrix} 2-\\frac{2}{1+q} \\\\ \\frac{2}{1+q} \\end{matrix} \\right)$};\n\\node[right] at (1.2,0.5) {$\\left( \\begin{matrix} 1-\\frac{2}{1+p}n_0 \\\\ 1-\\frac{2}{1+q}n_0 \\end{matrix} \\right)$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 795,
        "tikz_code": "\\documentclass[12pt,a4paper]{amsart}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amssymb, amsthm, amsmath}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usetikzlibrary{calc}\n\\pgfplotsset{ticks=none}\n\\pgfplotsset{compat=1.16}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\t\\draw (-1,0) -- (10,0);\n\t\\draw (0,3) -- (3,1);\n\t\\draw (5,0) -- (1,2);\n\t\n\t\\draw[dashed] (0,3) -- (5,0);\n\t\\draw[dashed] (3,1) -- (1,2);\n\t\n\t\\draw[dashed] (3,1) -- (5,0);\n\t\\draw[dashed] (1,2) -- (3,1);\n\t\\draw[dashed] (1,2) -- (0,3);\n\t\n\t\n\t\\draw (-0.5,2) -- (0.5,2);\n\t\\draw (-0.5,0) -- (-0.1,0);\n\t\\draw (0.1,0) -- (0.5,0);\n\t\\draw (-0.1,2) -- (0.1,2);\n\t\n\t\\draw (5.5,0) -- (6,0);\n\t\\draw (6,0) -- (6.5,0);\n\t\\draw (6.5,0) -- (7,0);\n\t\\draw (5.5,0) -- (6.5,0);\n\t\n\t\\node [above] at (-0.5,2) {$i_1$};\n\t\\node [above] at (5.5,0) {$i_2$};\n\t\\node [above] at (6,0) {$i_3$};\n\t\\node [above] at (1,2) {$j_1$};\n\t\\node [above] at (3,1) {$j_2$};\n\t\\node [above] at (0,3) {$j_3$};\n\t\\node [above] at (2,1.5) {$K$};\n\t\\draw[domain=1:3,smooth,variable=\\x,black] plot ({\\x},{0.8*sqrt(6*(\\x-2)*(\\x-2))});\n\t\\draw[domain=3:4,smooth,variable=\\x,black] plot ({\\x},{0.8*sqrt(3*(\\x-2)*(\\x-2))});\n\t\\draw[domain=4:5,smooth,variable=\\x,black] plot ({\\x},{0.8*sqrt(3*(\\x-2)*(\\x-2))});\n\t\\node [above] at (4,1.75) {$J$};\n\t\\node [below] at (6.5,-0.2) {$a \\wedge b \\cup u_1 \\cup u_2$};\n\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 796,
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[blue] (-6,1) -- (-4,1);\n\\draw[blue] (-6,-1) -- (-4,-1);\n\\draw[cyan] (-6,-1) -- (-6,1);\n\\draw[cyan] (-4,-1) -- (-4,1);\n\\draw[->] (-2.5,0) -- (-1.5,0);\n\\node at (-1.5,0.5) {\\color{blue}{$D_\\theta^{(j)}$}};\n\\node at (-1.5,-0.5) {\\color{cyan}{$D_\\theta^{(k)}$}};\n\\draw (-4,1) -- (-2,1);\n\\draw (-4,-1) -- (-2,-1);\n\\draw (-2,1) -- (-2,-1);\n\\node at (-3,1.4) {$D_\\theta^{(i)}$};\n\\node at (-3,-1.4) {$D_\\theta^{(j)}$};\n\\draw[thick] (-1,0.3) -- (0,0.3);\n\\draw[thick] (-1,-0.3) -- (0,-0.3);\n\\draw[thick] (-1,0.3) -- (-1,-0.3);\n\\draw[thick] (0,0.3) -- (0,-0.3);\n\\draw[->] (1.5,0) -- (2.5,0);\n\\node at (1.5,0.5) {\\color{cyan}{$D_\\theta^{(k)}$}};\n\\node at (1.5,-0.5) {\\color{blue}{$D_\\theta^{(j)}$}};\n\\draw (4,1) -- (6,1);\n\\draw (4,-1) -- (6,-1);\n\\draw (4,1) -- (4,-1);\n\\node at (5,1.4) {$D_\\theta^{(i)}$};\n\\node at (5,-1.4) {$D_\\theta^{(k)\\ast (k_i,k_j,k_s)}$};\n\\draw[->] (6,0.3) -- (7,0.3);\n\\node at (6.5,0.65) {$k$};\n\\draw[->] (6,-0.3) -- (7,-0.3);\n\\node at (6.5,-0.65) {$h(k_i,k_j,k_s)$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{shapes.geometric,calc,arrows, positioning,shapes.misc,decorations.markings}\n\\tikzset{\n  big arrow/.style={\n    decoration={markings,mark=at position 1 with {\\arrow[scale=2,#1]{>}}},\n    postaction={decorate},\n    shorten >=0.4pt},\n  big arrow/.default=black}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.9]\n\\begin{scope}[shift={(0,-0.3)}]\n\\node (v0) at (-0.5,0.25) {$\\hat{\\text{I}}^*_{4}$};\n\\end{scope}\n\\node (v1) at (-0.5,0.25) {$\\hat{\\text{I}}^*_{4}$};\n\\begin{scope}[shift={(1.5,0)}]\n\\node (v2) at (-0.5,0.25) {1};\n\\node at (-0.5,0.6) {\\scriptsize{$e$}};\n\\node at (-0.5,-0.2) {\\scriptsize{$e$-$y,f$-$y$}};\n\\end{scope}\n\\begin{scope}[shift={(0,-1.15)}]\n\\node (w2) at (-0.5,0.25) {1};\n\\node (v10) at (-0.5,0.6) {\\scriptsize{$e$}};\n\\node (v9) at (-0.5,-0.2) {\\scriptsize{$e$-$y,f$-$y$}};\n\\end{scope}\n\\begin{scope}[shift={(1.5,-1.15)}]\n\\node (v3) at (-0.5,0.25) {$\\hat{\\text{I}}^*_{4}$};\n\\node (w4) at (-0.5,0.6) {\\scriptsize{$2h$}};\n\\node (w3) at (-0.5,-0.2) {\\scriptsize{$2h$-$y,f$-$y$}};\n\\end{scope}\n\\begin{scope}[shift={(3,0)}]\n\\node (v5) at (-0.5,0.25) {$\\hat{\\text{I}}^*_{4}$};\n\\end{scope}\n\\begin{scope}[shift={(3,-1.15)}]\n\\node (v6) at (-0.5,0.25) {$\\hat{\\text{I}}^*_{4}$};\n\\end{scope}\n\\begin{scope}[shift={(1.5,0)}]\n\\draw [red] (0.35,0.2) arc (270:90:0.15);\n\\end{scope}\n\\draw  (v1) -- (v2);\n\\draw  (v0) edge (v1);\n\\draw  (v3) edge (v2);\n\\draw  (w3) edge (w4);\n\\draw  (w2) edge (w3);\n\\draw  (v5) edge (v6);\n\\draw  (v4) edge (v5);\n\\draw  (v3) edge (v4);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 800,
        "tikz_code": "\\documentclass[10pt,twocolumn,letterpaper]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n        \\node (agent_0) at (0, 0) {\\includegraphics[width=0.32\\linewidth]{example-image}};\n        \\node (agent_1) at (2.7, 0) {\\includegraphics[width=0.32\\linewidth]{example-image}};\n        \\node (agent_2) at (6.4, 0) {\\includegraphics[width=0.32\\linewidth]{example-image}};\n        \\node (agent_3) at (9.1, 0) {\\includegraphics[width=0.32\\linewidth]{example-image}};\n        \\node (rewards) at (0, -2.7) {\\includegraphics[width=0.48\\linewidth]{example-image}};\n        \\node[] at (0, -1.8) {(a) Agent};\n        \\node[] at (2.7, -1.8) {(b) Agent Target};\n        \\node[] at (6.4, -1.8) {(c) Agent Generation Mechanics};\n        \\node[] at (9.1, -1.8) {(d) Agent Actions};\n        \\draw [-, line width=2pt] (3.7,-2.4) -- (7.9,-2.4);\n        \\draw [-, line width=2pt] (3.7,-2.7) -- (7.9,-2.7);\n        \\draw [-, line width=2pt] (7.9,-2.1) -- (7.9,-2.4);\n    \\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[a4paper,10pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usetikzlibrary{patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n    \\begin{axis}[\n        xlabel={\\small Group size},\n        ylabel={\\small Overhead (s)},\n        xmin=1, xmax=5,\n        ymin=0, ymax=4000,\n        xtick={1,2,3,4,5},\n        xticklabels={1,2,4,8,24},\n        ytick={0,1000,2000,3000,4000},\n        legend pos=south west,\n        ymajorgrids=true,\n        grid style=dashed,\n    ]\n\n    \\addplot[\n        color=blue,\n        mark=square,\n        ]\n        coordinates {\n        (1,947)(2,993)(3,1048)(4,1093)(5,1133)\n        };\n        \\addlegendentry{of processes}\n\n    \\addplot[\n        color=red,\n        mark=square,\n        ]\n        coordinates {\n        (1,173)(2,206)(3,236)(4,267)(5,286)\n        };\n        \\addlegendentry{32}\n        \n    \\addplot[\n        color=green,\n        mark=square,\n        ]\n        coordinates {\n        (1,235)(2,266)(3,299)(4,328)(5,347)\n        };\n        \\addlegendentry{64}\n        \n    \\addplot[\n        color=orange,\n        mark=square,\n        ]\n        coordinates {\n        (1,297)(2,327)(3,356)(4,386)(5,406)\n        };\n        \\addlegendentry{128}\n        \n    \\addplot[\n        color=black,\n        mark=square,\n        ]\n        coordinates {\n        (1,585)(2,630)(3,673)(4,712)(5,731)\n        };\n        \\addlegendentry{256}\n        \n    \\addplot[\n        color=violet,\n        mark=square,\n        ]\n        coordinates {\n        (1,1246)(2,1286)(3,1325)(4,1363)(5,1389)\n        };\n        \\addlegendentry{512}\n\n    \\end{axis}\n    \\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{automata}\n\\usetikzlibrary{positioning}\n\\usepackage{tikz-cd}\n\\usepackage{pgfplots}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{calc}\n\\usepackage{amsmath,bbm}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.3]\n\n%------------------------------------------------------\n%-14----------------------------------------------------\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-14,-1) -- (-14,1)-- (-12,3) -- (-12, 4) -- (-14,6) -- (-14,1);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-14,-1) -- (-14,-5)-- (-12,-3) -- (-12, 0) -- (-14,2) -- (-14,-1);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-14,1) -- (-14,5)-- (-12,7) -- (-12, 4) -- (-14,6) -- (-14,1);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-14,1) -- (-14,5)-- (-12,3) -- (-12, 0) -- (-14,-2) -- (-14,1);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-14,6) -- (-14,10)-- (-12, 8) -- (-12, 4) -- (-14,2) -- (-14,6);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-14,10) -- (-14,14)-- (-12, 12) -- (-12, 8) -- (-14,12) -- (-14,10);\n\n%--12----------------\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-12,3) -- (-12, 4)-- (-10, 6) -- (-10, 7) -- (-12, 9) -- (-12, 3);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-12,3) -- (-12, -1)-- (-10, -3) -- (-10, 0) -- (-12, 2) -- (-12, 3);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-12,3) -- (-12, 9)-- (-10, 7) -- (-10, 6) -- (-12, 10) -- (-12, 3);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-12,3) -- (-12, -1)-- (-10, -3) -- (-10, -5) -- (-12, -7) -- (-12, 3);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-12,9) -- (-12, 13)-- (-10, 11) -- (-10, 7) -- (-12, 10) -- (-12, 9);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-12,13) -- (-12, 17)-- (-10, 15) -- (-10, 11) -- (-12, 14) -- (-12, 13);\n\n%--14----------------\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-14,-1) -- (-14,1)-- (-16,3) -- (-16, 4) -- (-14,6) -- (-14,-1);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-14,-1) -- (-14,-5)-- (-16,-3) -- (-16, 0) -- (-14,2) -- (-14,-1);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-14,-1) -- (-14,5)-- (-16, 3) -- (-16, 0) -- (-14,-2) -- (-14,-1);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-14,-1) -- (-14,5)-- (-16, 7) -- (-16, 4) -- (-14,2) -- (-14,-1);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-14,6) -- (-14,10)-- (-16, 8) -- (-16, 4) -- (-14,2) -- (-14,6);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-14,10) -- (-14,14)-- (-16, 12) -- (-16, 8) -- (-14,12) -- (-14,10);\n\n%--16----------------\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-16,3) -- (-16, 4)-- (-18, 6) -- (-18, 7) -- (-16, 9) -- (-16, 3);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-16,3) -- (-16, -1)-- (-18, -3) -- (-18, 0) -- (-16,2) -- (-16, 3);\n\n\\filldraw[color=gray!30, fill=gray!30, very thin]\n(-16,3) -- (-16, 9)-- (-18, 7) -- (-18, 6) -- (-16,10) -- (-16, 3);\n\n\\filldraw[color=gray!30, fill=gray"
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        "tikz_code": "\\documentclass[10pt,twoside]{article}\n\\usepackage[latin1]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath,amssymb,amsthm,amsfonts,bbm}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{decorations.markings}\n\\usepackage{color}\n\n\\newcommand{\\f}{\\mathfrak}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.6]\n\\draw[-latex](0,0)--(10,0);\n\\draw[-latex](0,0)--(0,5);\n\\draw[brown](3,3)--(6,3);\n\\draw[brown](6,3)--(6,0);\n\\draw[brown](3,3)--(3,0);\n\\draw[brown](6,3)--(3,3);\n\\draw[red](6,3)..controls (4,2) and (1,1)..(3,3);\n\\draw[green](6,3)..controls (8,2) and (9,1)..(3,3);\n\\draw[green](6,3)..controls (8,4) and (9,5)..(3,3);\n\\draw[blue](6,3)..controls (5,3) and (2,2)..(3,3);\n\\draw[blue](6,3)..controls (5,3) and (4,2)..(3,3);\n\\draw[blue](6,3)..controls (7,3) and (8,2)..(3,3);\n\\node[brown] at (4.5,4) {$\\lambda^{1}$};\n\\node[red] at (7.5,2.5) {$\\lambda^{2}$};\n\\node[green] at (8.5,2.5) {$\\lambda^{3}$};\n\\node[blue] at (9,2.5) {$\\lambda^{4}$};\n\\node at (10,4.5) {$\\bar{\\f{X}}^{\\alpha}_{i}$};\n\\node at (2.8,2.5) {$\\bar{\\f{X}}^{\\alpha}_{-i}$};\n\\node at (1.5,-0.5) {$\\rho^{\\alpha}_{i}$};\n\\node at (3.5,-0.5) {$\\rho^{\\alpha}_{-i}$};\n\\node at (8,-0.5) {$w_{i}$};\n\\node at (5,-0.5) {$w_{0}$};\n\\node at (6,-0.5) {$w_{i}$};\n\\node at (1,4.5) {$\\bar{\\f{X}}^{\\alpha}_{i}$};\n\\node at (6.5,4.5) {$\\bar{\\f{X}}^{\\alpha}_{-i}$};\n\\node at (1,0.5) {$\\bar{\\f{U}}$};\n\\draw[densely dotted](1,4)--(1,0);\n\\draw[densely dotted](6,4)--(6,0);\n\\draw[densely dotted](7.5,2.5)--(0,2.5);\n\\draw[densely dotted](7.5,2.5)--(7.5,0);\n\\draw[densely dotted](2,2.5)--(2,0);\n\\draw[densely dotted](8,2.5)--(8,0);\n\\draw[densely dotted](3,3)--(0,3);\n\\draw[densely dotted](6,3)--(0,3);\n\\node[red,scale=0.7] at (9,0.5) {$\\bar{\\f{X}}^{\\alpha}_{i}<1-\\bar{\\f{U}}$ at some fixed point $\\bar{\\f{x}}_{i}$};\n\\node[green,scale=0.7] at (1,0.5) {$\\bar{\\f{X}}^{\\alpha}_{-i}<1-\\bar{\\f{U}}$ at some fixed point $\\bar{\\f{x}}_{i}$};\n\\draw[black](1,0)--(1,0.1);\n\\draw[black](6,0)--(6,0.1);\n\\node[scale=0.7] at (0,-0.5) {$0$};\n\\draw[black](1,0)--(0.9,0.1);\n\\draw[black](1,0)--(0.9,-0.1);\n\\node[scale=0.7] at (1,-0.5) {$\\rho^{\\alpha}_{-i}$};\n\\draw[black](2,0)--(1.9,0.1);\n\\draw[black](2,0)--(1.9,-0.1);\n\\node[scale=0.7] at (2,-0.5) {$\\rho^{\\alpha}_{i}$};\n\\draw[black](8,0)--(7.9,0.1);\n\\draw[black](8,0)--(7.9,-0.1);\n\\node[scale=0.7] at (8,-0.5) {$w_{0}$};\n\\draw[black](3,0)--(2.9,0.1);\n\\draw[black](3,0)--(2.9,-0.1);\n\\node[scale=0.7] at (3,-0.5) {$\\rho^{\\alpha}_{-i}$};\n\\draw[black](0,2.5)--(0.1,2.6);\n\\draw[black](0,2.5)--(0.1,2.4);\n\\node[scale=0.7] at (0,2.8) {$\\rho^{\\alpha}_{i}$};\n\\draw[black](0,3)--(0.1,3);\n\\draw[black](0,3)--(0.1,3.2);\n\\node[scale=0.7] at (0,3.3) {$\\rho^{\\alpha}_{-i}$};\n\\node[scale=0.7] at (-1.5,3) {$\\lambda^{2}(w_{0})=\\lambda^{2}(w_{i})=\\lambda^{2}(w_{0}+c)=\\lambda^{2}(w_{0})+c$};\n\\node[scale=0.7] at (-6,3) {$\\lambda^{1}(w_{0})=\\lambda^{1}(w_{i})=\\lambda^{1}(w_{0}+c)=\\lambda^{1}(w_{0})+c$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 806,
        "tikz_code": "\\documentclass[11pt]{amsart}\n\\usepackage{amsmath,amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\\draw (-5,-1.5) to[in=270,out=90] (-6,-3) to [in=270,out=90] (-7,-1.5);\n\\draw (-5,1.5) to[in=90,out=270] (-6,3) to [in=90,out=270] (-7,1.5);\n\\draw (-5,1.5) to[in=150,out=30] (-5.5,2);\n\\draw (-6,3) to[in=30,out=150] (-5.5,2.5);\n\\draw (-5,-1.5) to[in=330,out=210] (-5.5,-2);\n\\draw (-6,-3) to[in=150,out=330] (-5.5,-2.5);\n\\node at (-4,-4.5) {(a)};\n\n\\draw (1,-1.5) to[in=270,out=90] (0,-3) to [in=270,out=90] (-1,-1.5);\n\\draw (1,1.5) to[in=90,out=270] (0,3) to [in=90,out=270] (-1,1.5);\n\\draw (1,1.5) to[in=150,out=30] (0.5,2);\n\\draw (0,3) to[in=30,out=150] (0.5,2.5);\n\\draw (1,-1.5) to[in=330,out=210] (0.5,-2);\n\\draw (0,-3) to[in=150,out=330] (0.5,-2.5);\n\\draw (0.5,2.5) to [in=90,out=30] (1,1.5);\n\\draw (0.5,-2.5) to [in=270,out=330] (1,-1.5);\n\n\\draw[fill] (1.5,0) circle [radius=0.05];\n\\draw[fill] (2.5,0) circle [radius=0.05];\n\\draw[fill] (0.5,0) circle [radius=0.05];\n\\draw [dashed] (1.5,0) -- (2.5,0);\n\n\\node at (1.5,-4.5) {(b)};\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 807,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amsfonts,bm}\n\\usepackage{tikz}\n\\usetikzlibrary{spy}\n\\usepackage{tikz,pgfplots,pgfplotstable}\n\\pgfplotsset{compat=1.17}\n\\usepgfplotslibrary{groupplots}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n        \\node[anchor=south west,inner sep=0] (image) at (0,0) {\\includegraphics[width=0.7\\textwidth]{example-image}};\n        \\node[anchor=south west,inner sep=0] (image) at (10.8,2.1) {\\includegraphics[width=0.18\\textwidth]{example-image}};\n        \\node[anchor=south west,inner sep=0] (image) at (10.8,4.7) {\\includegraphics[width=0.18\\textwidth]{example-image}};\n        \\node[anchor=south west,inner sep=0] (image) at (10.8,7.3) {\\includegraphics[width=0.18\\textwidth]{example-image}};\n        \\node[anchor=south west,inner sep=0] (image) at (10.8,9.9) {\\includegraphics[width=0.18\\textwidth]{example-image}};\n        \\begin{scope}[x={(image.south east)},y={(image.north west)}]\n        \\node[anchor=south west,inner sep=0] (image) at (10.7,0.38) {\\includegraphics[width=0.18\\textwidth]{example-image}};\n        \\end{scope}\n        \\node[anchor=south west,inner sep=0] (image) at (11.7,10.7) {\\includegraphics[width=0.05\\textwidth]{example-image}};\n        \\node[] at (11.4,10.8) {\\small \\textbf{Taken from:}};\n        \\node[] at (11.4,11) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,11.2) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,11.4) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,11.6) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,11.8) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,12) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,12.2) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,12.4) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,12.6) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,12.8) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,13) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,13.2) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,13.4) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,13.6) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,13.8) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,14) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,14.2) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,14.4) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,14.6) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,14.8) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,15) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,15.2) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,15.4) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,15.6) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,15.8) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,16) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,16.2) {\\small \\textbf{https://arxiv.org/pdf/2006.07419}};\n        \\node[] at (11.4,16.4) {\\small"
    },
    {
        "index": 808,
        "tikz_code": "\\documentclass[12pt,reqno]{amsart}\n\\usepackage[usenames, dvipsnames, svgnames]{xcolor}\n\\usepackage{amsmath, amssymb,graphicx,amsthm,latexsym, amsfonts, enumitem, mathtools, tensor}\n\\usepackage[all, color]{xy}\n\\usepackage{color}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,decorations.pathmorphing,decorations.pathreplacing,positioning,shapes.geometric,shapes.misc,decorations.markings,decorations.fractals,calc,patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=3]\n      \\draw (0,0) circle (1cm);\n      \n      \\draw (-26.7:1) node[label={[shift={(-0.6,-0.6)}]$v_2$}] {$\\bullet$};\n      \\draw (-26.7:1.2) node {$v_3$};\n      \\draw (-22.3:1) node {$\\bullet$};\n      \\draw (-22.3:1.2) node {$v_4$};\n      \\draw (-18:1) node {$\\bullet$};\n      \\draw (-18:1.2) node {$v_5$};\n      \\draw (-13.5:1) node {$\\bullet$};\n      \\draw (-13.5:1.2) node {$v_1$};\n      \\draw (-9:1) node {$\\bullet$};\n      \\draw (-9:1.2) node {$v'_1$};\n      \\draw (-4.5:1) node {$\\bullet$};\n      \\draw (-4.5:1.2) node {$v'$};\n      \\draw (0:1) node {$\\bullet$};\n      \\draw (0:1.2) node {$v'$};\n      \\draw (4.5:1) node {$\\bullet$};\n      \\draw (4.5:1.2) node {$v_2'$};\n      \\draw (9:1) node {$\\bullet$};\n      \\draw (9:1.2) node {$v_3'$};\n      \\draw (13.5:1) node {$\\bullet$};\n      \\draw (13.5:1.2) node {$v_4'$};\n      \\draw (18:1) node {$\\bullet$};\n      \\draw (18:1.2) node {$v_5'$};\n      \\draw (22.3:1) node {$\\bullet$};\n      \\draw (22.3:1.2) node {$v_1'$};\n      \\draw (26.7:1) node {$\\bullet$};\n      \\draw (26.7:1.2) node {$v_2$};\n      \n      \\draw[->,bend left] (-26.7:1) to (-22.3:1);\n      \\draw[->,bend left] (-22.3:1) to (-18:1);\n      \\draw[->,bend left] (-18:1) to (-13.5:1);\n      \\draw[->,bend left] (-13.5:1) to (-9:1);\n      \\draw[->,bend left] (-9:1) to (-4.5:1);\n      \\draw[->,bend left] (-4.5:1) to (0:1);\n      \\draw[->,bend left] (0:1) to (4.5:1);\n      \\draw[->,bend left] (4.5:1) to (9:1);\n      \\draw[->,bend left] (9:1) to (13.5:1);\n      \\draw[->,bend left] (13.5:1) to (18:1);\n      \\draw[->,bend left] (18:1) to (22.3:1);\n      \\draw[->,bend left] (22.3:1) to (26.7:1);\n      \n      \\draw (-27:1.2) node {$k_5$};\n      \\draw (-19.5:1.2) node {$k_4$};\n      \\draw (-10.5:1.2) node {$k_3$};\n      \\draw (-4.5:1.2) node {$k_2$};\n      \\draw (0.5:1.2) node {$k_1$};\n      \\draw (6:1.2) node {$k_5$};\n      \\draw (10.5:1.2) node {$k_4$};\n      \\draw (18:1.2) node {$k_3$};\n      \\draw (24:1.2) node {$k_2$};\n      \\draw (27:1.2) node {$k_1$};\n      \n      \\draw (-18:0.2) node {$e_1$};\n      \\draw (-10.5:0.2) node {$e_2$};\n      \\draw (24:0.2) node {$e_1$};\n      \\draw (0:0.2) node {$e_2$};\n      \\draw (6:0.2) node {$e_3$};\n      \\draw (12:0.3) node {$-e_3$};\n      \n      \\draw (-26.7:0.8) node[label={[shift={(-0.3,-0.3)}]$\\gamma_3$}] {$\\bullet$};\n      \\draw (-18:0.8) node[label={[shift={(0,-0.4)}]$\\gamma_4$}] {$\\bullet$};\n      \\draw (0:0.8) node[label={[shift={(0.3,-0.3)}]$\\gamma_5$}] {$\\bullet$};\n      \\draw (6:0.8) node[label={[shift={(-0.3,-0.3)}]$\\gamma_2$}] {$\\bullet$};\n      \\draw (12:0.8) node[label={[shift={(0.3,-0.3)}]$\\gamma_1$}] {$\\bullet$};\n      \\draw (18:0.8) node[label={[shift={(0.3,-0.3)}]$\\gamma'_1$}] {$\\bullet$};\n      \\draw (24:0.8) node[label={[shift={(0,-0.4)}]$\\gamma'_2$}] {$\\bullet$};\n      \\draw"
    },
    {
        "index": 809,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{intersections}\n\\usepackage{tkz-euclide}\n\\usetikzlibrary{calc,through}\n\\usetikzlibrary{angles,quotes}\n\\usepackage[colorinlistoftodos]{todonotes}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw (0,0) circle (3cm);\n\\draw (0,0) circle (1cm);\n\\filldraw[opacity=0.2] (0,0) -- (30:1) arc (30:150:1) -- cycle;\n\\draw (0,0) -- node[fill=white] {\\(x\\)} (30:3) (0,0) -- node[fill=white] {\\(y\\)} (150:1) (0,0) -- node[fill=white] {\\(a\\)} (-30:3);\n\\draw[dashed] (0,0) -- (45:3);\n\\draw[dashed] (0,0) -- (60:3);\n\\draw pic[draw, angle radius=1cm, \"{\\(\\alpha/2\\)}\"] {angle=30mm--0--150mm};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 810,
        "tikz_code": "\\documentclass[10pt]{article}\n\\usepackage{latexsym,amssymb,amsmath,amsfonts,graphicx,color,fancyvrb,amsthm,enumerate,subfigure,mathrsfs,mathtools}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usetikzlibrary{patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\coordinate (O) at (0,0);\n\\coordinate (P) at (2,0);\n\\coordinate (L) at (1.8,0);\n\\coordinate (L1) at (1.6,0.2);\n\\coordinate (L2) at (1.4,0.4);\n\\coordinate (L3) at (1.2,0.6);\n\\coordinate (R) at (2,1.4);\n\\coordinate (R1) at (2.1,1.2);\n\\coordinate (R2) at (2.3,1);\n\\coordinate (A) at (3,2);\n\\coordinate (B) at (0,-1);\n\\coordinate (B1) at (0.1,-1.1);\n\\coordinate (B2) at (0.2,-1.2);\n\\coordinate (B3) at (0.3,-1.3);\n\\coordinate (C) at (-1,3);\n\\coordinate (C1) at (-1.1,3.1);\n\\coordinate (C2) at (-1.2,3.2);\n\\coordinate (C3) at (-1.3,3.3);\n\\draw[fill=black!10,draw=none] (O) circle [radius=3];\n\\draw (O)--(P);\n\\draw[dashed] (O)--(L);\n\\draw (O)--(R);\n\\draw (R)--(A);\n\\draw (L)--(B);\n\\draw[dashed] (B)--(C);\n\\draw[dashed] (B)--(B1);\n\\draw[dashed] (B)--(B2);\n\\draw[dashed] (B)--(B3);\n\\draw[dashed] (C)--(C1);\n\\draw[dashed] (C)--(C2);\n\\draw[dashed] (C)--(C3);\n\\draw[fill] (O) circle [radius=0.05];\n\\draw[fill] (P) circle [radius=0.05];\n\\draw[fill] (R) circle [radius=0.05];\n\\draw[->,thick] (O)--(L) node[midway,left] {$e_1$};\n\\draw[->,thick] (O)--(R) node[midway,right] {$e_2$};\n\\draw[->,thick] (O)--(P) node[midway,right] {$e_3$};\n\\draw[->,thick] (R)--(A) node[midway,right] {$a_\\phi$};\n\\draw[->,thick] (L)--(B) node[midway,left] {$b_\\phi$};\n\\draw[->,thick] (C)--(B) node[midway,above] {$\\phi$};\n\\draw (0.7,0) arc (0:45:0.7);\n\\node at (1,0.3) {$\\theta$};\n\\draw (2.3,0.7) arc (90:135:0.7);\n\\node at (2.1,0.9) {$\\theta$};\n\\draw[dashed] (0.7,0) arc (0:-45:0.7);\n\\draw[dashed] (2.3,0.7) arc (90:225:0.7);\n\\draw[->,thick] (2,0)--(2,0.7) node[midway,right] {$\\lambda$};\n\\draw[->,thick] (2,0)--(2.6,0.3) node[midway,right] {$a_\\phi(\\lambda)$};\n\\node at (2,2) {$\\eta$};\n\\node at (4,2) {$a_\\phi$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
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        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage{tkz-graph}\n\\usepackage[utf8]{inputenc}\n\\usepackage[colorlinks  = true,\n            citecolor   = blue,\n            linkcolor   = blue,\n            bookmarks   = true,\n            linktocpage = true]{hyperref}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix}\n\n\\begin{document}\n\n\\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=1.5cm,\n\tthick,main node/.style={circle,draw,font=\\small\\bfseries}]\n\t\n\t\\node (0) {};\n\t\\node[main node] (1) [right of=0]{};\n\t\\node[main node] (2) [right of=1] {};\n\t\\node[main node] (3) [above right of=2] {};\n\t\\node[main node] (4) [below right of=2] {};\n\t\n\t\\path\n\t(1) edge node [below]{2} (2)\n\t(2) edge [dashed] node [above]{3} (3)\n\t(2) edge node [below]{4} (4);\n\t\n\t\\node (5) [right of=2] {};\n\t\\node[main node] (6) [right of=5] {};\n\t\\node[main node] (7) [right of=6] {};\n\t\\node[main node] (8) [above of=7] {};\n\t\\node[main node] (9) [below of=7] {};\n\t\n\t\\path\n\t(6) edge node [below]{2} (7)\n\t(7) edge node [above]{1} (8)\n\t(7) edge node [below]{3} (9);\n\t\n\t\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[font=\\sffamily]\n\t\t\\node[draw,fill=white,minimum size=1.5cm] (engine) at (0,0) {\\small Text\\\\\\small Engine};\n\t\t\\node[draw,fill=green!40,minimum size=1.5cm] (mq) at (5,0) {\\small MQA};\n\t\t\\node[draw,fill=green!40,minimum size=1.5cm] (com) at (5,5) {\\small QA};\n\n\t\t\\draw [-latex, line width=1.5pt, dashed] (engine) -- node [midway, fill=white] (120) {} node [midway, fill=white, above, inner sep=0.3cm, outer sep=0] (120label) {\\tiny Open-\\\\\\ \\tiny Composition} (com);\n\n\t\t\\draw [-latex, line width=1.5pt, dashed] (engine) -- node [midway, fill=white] (120) {} node [midway, fill=white, below, inner sep=0.3cm, outer sep=0] (120label) {\\tiny Engine-} (mq);\n\n\t\t\\draw [-latex, line width=1.5pt, dashed] (com) -- node [midway, fill=white] (120) {} node [midway, fill=white, above, inner sep=0.3cm, outer sep=0] (120label) {\\tiny Answers} (mq);\n\n\t\t\\draw [-latex, line width=1.5pt, dashed] (mq) -- node [midway, fill=white] (120) {} node [midway, fill=white, above, inner sep=0.3cm, outer sep=0] (120label) {\\tiny Remove-\\\\ \\tiny Choices} (com);\n\t\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 827,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{graphicx,amssymb,amsmath,empheq}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{intersections}\n\\usetikzlibrary{shapes.geometric}\n\\usetikzlibrary{decorations.pathmorphing, patterns,shapes}\n\n\\begin{document}\n\n\\begin{tikzpicture}[baseline={([yshift=-3pt]current bounding box.center)}]\n\\draw[thick] (-20pt,20pt)--(80pt,20pt);\n\\draw[thick] (-20pt,0pt)--(80pt,0pt);\n\\draw[thick] (-20pt,-20pt)--(80pt,-20pt);\n\\draw[->] (40pt,-20pt)--(40pt,-10pt);\n\\draw (40pt,-10pt)--(40pt,0pt);\n\\draw (40pt,0pt)--(40pt,10pt);\n\\draw[->] (40pt,20pt)--(40pt,10pt);\n\\node at (40pt,-25pt){$A$};\n\\node at (40pt,25pt){$R$};\n\\node at (85pt,-10pt){$t$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 828,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amssymb,amsfonts,amsmath}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=2,\nfouille/.style={blue,thick},\nbarreblanche/.style={red,thick},\nsomm/.style={},\n]\n\\coordinate (o) at (0,0);\n\\coordinate (d) at (2,0);\n\\coordinate (g) at (2,2);\n\\coordinate (ab) at (0,2);\n\\coordinate (a) at (0.5,0.5);\n\\coordinate (b) at (1.5,0.5);\n\\coordinate (c) at (0.5,1.5);\n\\coordinate (ac) at ($(a)!0.5!(c)$);\n\\coordinate (bc) at ($(b)!0.5!(c)$);\n\\coordinate (abc) at ($(a)!0.5!(b)$);\n\\coordinate (abcd) at ($(a)!0.5!(b)$);\n\n\\draw[barreblanche] (c) -- (a) -- (b);\n\n\\draw[somm] (o) -- (d) ;\n\\draw[somm] (g) -- (ab) ;\n\\draw[somm] (g) -- (o) ;\n\n\\draw[somm] (a) -- (ab) ;\n\\draw[somm] (b) -- (g) ;\n\\draw[somm] (c) -- (ab) ;\n\\draw[somm] (ac) -- (abc) ;\n\\draw[somm] (bc) -- (abc) ;\n\\draw[somm] (abc) -- (abcd) ;\n\\draw[somm] (ac) -- (abcd) ;\n\\draw[somm] (bc) -- (abcd) ;\n\n\n\\draw[fouille] (a) -- (c) ;\n\\draw[fouille] (b) -- (c) ;\n\n\\foreach \\j in {o,d,g,ab,a,b,c,ac,bc,abc,abcd}\n\\fill[black] (\\j) circle (0.03 cm) ;\n\n\\node[below] at (0.5,0) {$0$};\n\\node[below] at (1,0) {$0.5$};\n\\node[below] at (1.5,0) {$1$};\n\\node[below] at (0,0) {$0$};\n\\node[below] at (0,0.5) {$0.5$};\n\\node[below] at (0,1) {$1$};\n\n\\node[right] at (2,0.5) {$\\frac{1}{4}$};\n\\node[right] at (2,1) {$\\frac{1}{2}$};\n\\node[right] at (2,1.5) {$\\frac{3}{4}$};\n\\node[right] at (2,2) {$1$};\n\n\\node[below] at (0.5,-0.2) {$v$};\n\\node[below] at (1,-0.2) {$\\nu$};\n\n\\node[left] at (0,1) {$\\Gamma_n^-(v)$};\n\\node[left] at (0,0.5) {$\\Gamma_n^-(0.5)$};\n\\node[left] at (0,0) {$0$};\n\n\\draw[blue] ($(a)+(0.1,0.1)$) -- ($(a)+(0.1,-0.1)$) -- ($(a)+(-0.1,-0.1)$) -- ($(a)+(-0.1,0.1)$) -- ($(a)+(0.1,0.1)$) ;\n\\draw[blue] ($(b)+(0.1,0.1)$) -- ($(b)+(0.1,-0.1)$) -- ($(b)+(-0.1,-0.1)$) -- ($(b)+(-0.1,0.1)$) -- ($(b)+(0.1,0.1)$) ;\n\\draw[blue] ($(ac)+(0.1,0.1)$) -- ($(ac)+(0.1,-0.1)$) -- ($(ac)+(-0.1,-0.1)$) -- ($(ac)+(-0.1,0.1)$) -- ($(ac)+(0.1,0.1)$) ;\n\\draw[blue] ($(bc)+(0.1,0.1)$) -- ($(bc)+(0.1,-0.1)$) -- ($(bc)+(-0.1,-0.1)$) -- ($(bc)+(-0.1,0.1)$) -- ($(bc)+(0.1,0.1)$) ;\n\n\\draw[blue] (0.4,0.8) -- (0.6,0.8) -- (0.6,0.6) -- (0.4,0.6) ;\n\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 829,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amsmath,amssymb,amsthm, amscd, bm}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,calc,matrix,topaths,positioning,scopes,shapes,decorations,decorations.markings}\n\\usepackage{tikz-cd}\n\n\\begin{document}\n\n\\begin{tikzpicture}[baseline=-0.4ex,scale=0.5,>=stealth]\n\\draw [fill=gray!45,gray!45] (-.7,-.75)  rectangle (.4,.75)   ;\n\\draw[->] (-0.7,-0.75) to (-.7,.75);\n\\draw[line width=1.2] (-0.7,-0.3) to (-0.3,-.3);\n\\draw[line width=1.2] (-0.7,0.3) to (-0.3,.3);\n\\draw[line width=1.15] (-.4,0) ++(-90:.3) arc (-90:90:.3);\n\\draw (-0.9,0.3) node {\\scriptsize{$-$}}; \n\\draw (-0.9,-0.3) node {\\scriptsize{$-$}}; \n\\draw[line width=1.2] (0.4,-0.75) to (0.4,.75);\n\\draw (1.2,0) node {$\\cdots$};\n\\draw[line width=1.2] (1.6,-0.75) to (1.6,.75);\n\\draw[<-] (1.7,-0.3) to (2.3,-.3);\n\\draw[<-] (1.7,0.3) to (2.3,.3);\n\\draw (2.6,0) node {$\\cdots$};\n\\draw[line width=1.2] (3,-0.75) to (3,.75);\n\\draw[<-] (2.3,0.3) to (1.7,0.3);\n\\draw[<-] (2.3,-0.3) to (1.7,-0.3);\n\\draw  (-.7,0.3) node {\\scriptsize{$-$}};\n\\draw  (-.7,-0.3) node {\\scriptsize{$-$}};\n\\draw (0.55,0.3) node {\\scriptsize{$-$}};\n\\draw (0.55,-0.3) node {\\scriptsize{$-$}};\n\\draw (1.5,0.3) node {\\scriptsize{$-$}};\n\\draw (1.5,-0.3) node {\\scriptsize{$-$}};\n\\draw (3,0.3) node {\\scriptsize{$-$}};\n\\draw (3,-0.3) node {\\scriptsize{$-$}};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 830,
        "tikz_code": "\\documentclass[conference]{IEEEtran}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{quantikz}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.17}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n        \\node[scale=0.85]{\n        \\begin{quantikz}[thin lines, column sep=0.3cm]\n            \\lstick{$\\ket{0}$} & \\ctrl{1} & \\gate{H} & \\ctrl{1} & \\qw & \\qw & \\qw & \\qw & \\qw & \\gate{H} & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\gate{H} & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\gate{H} & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw & \\qw"
    },
    {
        "index": 831,
        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage[colorlinks=true,citecolor=black,linkcolor=black,urlcolor=blue]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n%grid\n\\def\\xmin{-4.5}\n\\def\\xmax{4.5}\n\\def\\ymin{-1}\n\\def\\ymax{3.5}\n%axes\n\\draw[very thick, <->] (\\xmin,\\ymax+0.5)--(0,\\ymax+0.5) node[right,scale=1]{$\\eta$};\n\\draw[very thick, <->] (\\xmin,\\ymax+0.25)--(\\xmin+2.5,\\ymax+0.25) node[right,scale=1]{$\\frac{u_R}{u_L}$};\n\\draw[very thick, <->] (\\xmin+2.5,\\ymax+0.75)--(\\xmin+4.5,\\ymax+0.75) node[right,scale=1]{$\\frac{u_r}{u_l}$};\n%label\n\\draw (\\xmin+0.25,\\ymax+0.5) node[left,scale=1] {$H$};\n\\draw (\\xmin+0.25,\\ymax+0.25) node[left,scale=1] {$\\Psi_R$};\n\\draw (\\xmin+2.25,\\ymax+0.25) node[left,scale=1] {$\\Psi_L$};\n\\draw (\\xmin+4.25,\\ymax+0.25) node[left,scale=1] {$u_L$};\n\\draw (\\xmin+0.25,\\ymax+0.75) node[left,scale=1] {$\\Psi_U$};\n\\draw (\\xmin+2.25,\\ymax+0.75) node[left,scale=1] {$\\Psi_U$};\n\\draw (\\xmin+4.25,\\ymax+0.75) node[left,scale=1] {$u_r$};\n%arrows\n\\draw[thick,->] (\\xmax-0.5,\\ymax+0.25) -- (\\xmin+0.75,\\ymax+0.25);\n\\draw[thick,->] (\\xmax-0.5,\\ymax+0.75) -- (\\xmin+2.25,\\ymax+0.75);\n\\draw[thick,->] (\\xmax-0.5,\\ymax+0.5) -- (\\xmin+1.25,\\ymax+0.5);\n\\draw[thick,->] (\\xmin+4.5,\\ymax+0.25) -- (\\xmin+4.5-0.5,\\ymax+0.25);\n\\draw[thick,->] (\\xmin+4.5,\\ymax+0.75) -- (\\xmin+4.5-0.5,\\ymax+0.75);\n%dots\n\\filldraw (\\xmin+0.25,\\ymax+0.5) circle (2pt);\n\\filldraw (\\xmin+0.25,\\ymax+0.25) circle (2pt);\n\\filldraw (\\xmin+0.25,\\ymax+0.75) circle (2pt);\n\\filldraw (\\xmin+2.25,\\ymax+0.75) circle (2pt);\n\\filldraw (\\xmin+2.25,\\ymax+0.25) circle (2pt);\n\\filldraw (\\xmin+4.25,\\ymax+0.25) circle (2pt);\n\\filldraw (\\xmin+4.25,\\ymax+0.75) circle (2pt);\n%H\n\\draw[dashed] (\\xmin+0.25,\\ymax+0.5) -- (\\xmin+0.25,\\ymax+0.25);\n\\draw[dashed] (\\xmin+2.25,\\ymax+0.75) -- (\\xmin+2.25,\\ymax+0.25);\n\\draw[dashed] (\\xmin+4.25,\\ymax+0.75) -- (\\xmin+4.25,\\ymax+0.25);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 832,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amsmath,amssymb,latexsym,cancel,rotating}\n\\usepackage{graphicx,amssymb,mathrsfs,amsmath,color,fancyhdr,amsthm}\n\\usepackage{pgfplots}\n\\usepackage{tikz}\n\\usepackage{circuitikz-1.0}\n\\usetikzlibrary{decorations.pathreplacing,decorations.markings}\n\\usetikzlibrary{arrows, decorations.pathmorphing,backgrounds,positioning,fit,petri}\n\\usetikzlibrary{decorations.pathreplacing,decorations.markings}\n\\usetikzlibrary{arrows.meta}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n  \\begin{scope}[very thick,decoration={markings, mark=at position 0.5 with {\\arrow{>}}}] \n    \\draw[line width=0.5pt](-6,0)--(6,0)node[right]{\\footnotesize $x$};\n    \\draw[line width=0.5pt](0,0)--(0,2)node[right]{\\footnotesize $y$};\n    \\draw[line width=0.5pt,postaction={decorate}](-4.5,0)--(4.5,0)node[right]{\\footnotesize $r=\\frac{n}{2\\pi}+i\\frac{1}{2}$};\n    \\draw[line width=0.5pt](-1,0)--(-1,1.7)node[right]{\\footnotesize $\\vec{r}_+=\\sqrt{\\frac{n}{2\\pi}}e^{i\\frac{\\pi}{4}}$};\n    \\draw[line width=0.5pt,postaction={decorate}](1,0)--(1,1.7)node[right]{\\footnotesize $\\vec{r}_+=-\\sqrt{\\frac{n}{2\\pi}}e^{-i\\frac{\\pi}{4}}$};\n    \\draw[dashed](-4.5,2)--(4.5,2);\n    \\node [below] at (4.5,2) {\\footnotesize $r=+\\infty$};\n    \\draw[dashed](-6,1.5)--(6,1.5);\n    \\node [below] at (6,1.5) {\\footnotesize $r=-\\infty$};\n    \\draw[blue,dashed,line width=0.5pt] (4.5,0) circle (3);\n    \\draw[blue,dashed,line width=0.5pt] (1,0) circle (1);\n  \\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 833,
        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{color}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\\node at (0,0) {\\includegraphics[width=0.4\\linewidth]{example-image}};\n\t\t\\node at (-1.9,0.2) {\\textcolor{red}{$W_j$}};\n\t\t\\node at (2.5,0.2) {\\textcolor{red}{$H_j$}};\n\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 834,
        "tikz_code": "\\documentclass[tikz,border=5mm]{standalone}\n\\usetikzlibrary{chains,backgrounds,fit,calc,shadows,shapes}\n\\begin{document}\n\\begin{tikzpicture}[scale=2,\nnode distance=1mm,\n  start chain,\nevery node/.style={on chain,fill=#1,draw,fill opacity=.5,\n    text=white,inner sep=1pt,outer sep=0pt,\n    minimum height=10mm,minimum width=30mm,rounded corners,\n    drop shadow,alias=this},\n  every join/.style={draw=black!50,thick,opacity=.5}\n]\n\n\\node[join] (big1) {Big impact};\n\\node[join] (huge1) {Small tables};\n\n\\begin{scope}[every node/.append style={join},\n    start chain=going below,node distance=1mm]\n\\node {Embedding table};\n\\node {Parameters};\n\\node {Random};\n\\node {Two random functions};\n\\end{scope}\n\n\\node[join] (big2) {Small clustered};\n\\node[join] (huge2) {Big clusters};\n\n\\begin{scope}[every node/.append style={join},\n    start chain=going below,node distance=1mm]\n\\node {Nearest cluster center};\n\\node {Phase 1: Two random points};\n\\node {Phase 2: Single pointer $t$};\n\\node {Phase 3: One random pointer};\n\\end{scope}\n\n\\begin{scope}[on background layer]\n\\node[draw,fill=blue!20,thick,fit=(big1)(huge1),\n    label={[fill=white,inner sep=2pt]center:Phase I}] {};\n\n\\node[draw,fill=red!20,thick,fit=(big2)(huge2),\n    label={[fill=white,inner sep=2pt]center:Phase II}] {};\n\n\\node[draw,fill=green!20,thick,fit=(big1-1)(huge1-1),\n    label={[fill=white,inner sep=2pt]center:Phase III}] {};\n\\end{scope}\n\n\\end{tikzpicture}\n\\end{document}"
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    {
        "index": 835,
        "tikz_code": "\\documentclass[reqno, 11pt]{amsart}\n\\usepackage{calc,graphicx,amsfonts,amsthm,amscd,amsmath,amssymb,enumerate,dsfont,mathrsfs,paralist,bbm,tikz}\n\\usetikzlibrary{patterns,arrows}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[>=latex,scale=1.2]\n\\def\\y{0.1};\n\\draw [thin, ->] (0,0+\\y) -- (7.5,0+\\y);\n\\draw [thin, ->] (0,3+\\y) -- (7.5,3+\\y);\n\\foreach \\x in {0,1,2,4,5,6}\n   \\draw[thick] (\\x,0+\\y) -- (\\x,3+\\y);\n\n\\node at (0,0+\\y) [below] {$U_{m}$};\n\\node at (1,0+\\y) [below] {$U_{m+1}$};\n\\node at (2,0+\\y) [below] {$U_{i-2}$};\n\\node at (4,0+\\y) [below] {$U_{i-1}$};\n\\node at (5,0+\\y) [below] {$U_{i}$};\n\\node at (6,0+\\y) [below] {$U_{i+1}$};\n\\node at (7.5,0+\\y) [below] {$\\bar{t}_{m}$};\n\\node at (0,3+\\y) [above] {$U_{m-1}$};\n\\node at (1,3+\\y) [above] {$U_{m+1}$};\n\\node at (2,3+\\y) [above] {$U_{2}$};\n\\node at (4,3+\\y) [above] {$U_{i-1}$};\n\\node at (5,3+\\y) [above] {$U_{i}$};\n\\node at (6,3+\\y) [above] {$U_{i+1}$};\n\\node at (7.5,3+\\y) [above] {$\\bar{t}_{m-1}$};\n\\node at (3,1.5+\\y) [below] {$\\cdots$};\n\n\\draw [thick, blue, dashed] (4,0+\\y) -- (1,3+\\y);\n\\draw [thick, blue, dashed] (4,0+\\y) -- (2,3+\\y);\n\\draw [thick, blue, dashed] (4,0+\\y) -- (5,3+\\y);\n\\draw [thick, blue, dashed] (4,0+\\y) -- (6,3+\\y);\n\\draw [thick, blue, dashed] (4,0+\\y) -- (7.5,3+\\y);\n\n\\draw [thick, red, dashed] (1,0+\\y) -- (4,3+\\y);\n\\draw [thick, red, dashed] (2,0+\\y) -- (4,3+\\y);\n\\draw [thick, red, dashed] (5,0+\\y) -- (4,3+\\y);\n\\draw [thick, red, dashed] (6,0+\\y) -- (4,3+\\y);\n\\draw [thick, red, dashed] (7.5,0+\\y) -- (4,3+\\y);\n\n\\foreach \\x in {0,1,2,4,5,6}\n  \\node at (\\x,3+\\y) [circle,fill=black, inner sep=1pt]{};\n\\foreach \\x in {0,1,2,4,5,6}\n  \\node at (\\x,0+\\y) [circle,fill=black, inner sep=1pt]{};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.16}\n\\usetikzlibrary{positioning,calc,intersections}\n\\usetikzlibrary{backgrounds}\n\\usetikzlibrary{decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\\begin{axis}[\n    axis lines = left,\n    xlabel = $k$,\n    ylabel = {Profit/Inquality},\n    xmin=0.8, xmax=6.4,\n    ymin=0.758, ymax=0.780,\n]\n\n\n\\coordinate (p1) at (axis cs:1,0.758){};\n\\coordinate (p2) at (axis cs:2,0.758){};\n\\coordinate (p3) at (axis cs:3,0.758){};\n\\coordinate (p4) at (axis cs:4,0.758){};\n\\coordinate (p5) at (axis cs:5,0.758){};\n\\coordinate (p6) at (axis cs:6,0.758){};\n\n\\addplot[\n    dashed,\n    color=black,\n    ]\n    coordinates {(p1)(p2)(p3)(p4)(p5)(p6)};\n\n\\addplot[\n    domain=0.8:6, \n    samples=100, \n    color=black,\n]\n{0.778163 + 0.009080*x - 0.042425*x^2 + 0.003097*x^3 - 0.000124*x^4};\n\n\\addplot [\n    color=black,\n    dashed,\n    mark=*,\n    mark options={solid},\n    ]\n    coordinates {(p1) (p2)};\n\\addplot [\n    color=black,\n    dashed,\n    mark=*,\n    mark options={solid},\n    ]\n    coordinates {(p3) (p4)};\n\\addplot [\n    color=black,\n    dashed,\n    mark=*,\n    mark options={solid},\n    ]\n    coordinates {(p5) (p6)};\n\n\n\\node [right] at (6,0.758) {Best dynamic policy $\\{\\gamma_k\\}$};\n\\node [right] at (6,0.752) {Best static policy $\\{\\sigma_k\\}$};\n\\node [right] at (6,0.745) {This paper};\n\\node [right] at (6,0.738) {Upper bound \\eqref{ubound}};\n\\addlegendentry{Upper bound \\eqref{ubound}}\n\\addlegendentry{Best dynamic policy $\\{\\gamma_k\\}$}\n\\addlegendentry{Best static policy $\\{\\sigma_k\\}$}\n\\addlegendentry{This paper}\n\\addlegendentry{$\\lambda_k$}\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[a4paper,12pt,twoside]{book}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.17}\n\\usepackage{tikz}\n\\usetikzlibrary{automata,positioning}\n\\tikzset{\n    every state/.style={thick, fill=gray!10},\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}[]\n    \\node[state, accepting] (0) {$\\overline{x}$};\n    \\node[draw=none, fill=none] (0-Dots) [right=3em of 0] {\\(\\dots\\)};\n\n    \\node[state, draw=none] (0-1) [below left=of 0] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (0-2) [below=of 0] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (0-3) [below right=of 0] {\\(\\mathbf{\\bullet}\\)};\n\n    \\node[state, draw=none] (1-1) [below left=of 0-1] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (1-2) [below=of 1-1] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (1-3) [below right=of 1-1] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (1-4) [below=of 1-2] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (1-5) [below=of 1-3] {\\(\\mathbf{\\bullet}\\)};\n\n    \\node[state, draw=none] (1-6) [below left=of 1-2] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (1-7) [below=of 1-6] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (1-8) [below right=of 1-6] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (1-9) [below=of 1-7] {\\(\\mathbf{\\bullet}\\)};\n\n    \\node[state, draw=none] (2-1) [below left=of 1-3] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (2-2) [below=of 2-1] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (2-3) [below right=of 2-1] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (2-4) [below=of 2-2] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (2-5) [below=of 2-3] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (2-6) [below=of 2-4] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (2-7) [below=of 2-5] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (2-8) [below=of 2-6] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (2-9) [below=of 2-7] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (2-10) [below=of 2-8] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (2-11) [below=of 2-9] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (2-12) [below=of 2-10] {\\(\\mathbf{\\bullet}\\)};\n\n    \\node[state, draw=none] (3-1) [below left=of 2-3] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (3-2) [below=of 3-1] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (3-3) [below right=of 3-1] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (3-4) [below=of 3-2] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (3-5) [below=of 3-3] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (3-6) [below=of 3-4] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (3-7) [below=of 3-5] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (3-8) [below=of 3-6] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (3-9) [below=of 3-7] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (3-10) [below=of 3-8] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (3-11) [below=of 3-9] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (3-12) [below=of 3-10] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (3-13) [below=of 3-11] {\\(\\mathbf{\\bullet}\\)};\n    \\node[state, draw=none] (3-14) [below=of 3-12] {\\(\\mathbf{\\bullet}\\)};\n\n    \\path[->] (0) edge node[above] {1} (0-1);\n    \\path[->] (0) edge node[above] {2} (0-2);\n    \\path[->] (0) edge node[above] {3} (0-3);\n\n    \\path[->] (0-1) edge node[above] {1} (1-1);\n    \\path[->] (0-1) edge node[above] {2} (1-2);\n    \\path[->] (0-1) edge node[above] {3} (1-3);\n\n    \\path[->] (1-1) edge node[above] {1} (2-1);\n    \\path[->] (1-1) edge node[above] {2} (2-2);\n    \\path[->] (1-1) edge node[above] {3} (2-3);\n\n    \\path[->] (1-2) edge node[above] {1} (2-6"
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    {
        "index": 845,
        "tikz_code": "\\documentclass[tikz,border=3.14mm]{standalone}\n\\usepackage{tikz-3dplot}\n\\begin{document}\n\\tdplotsetmaincoords{70}{110}\n\\begin{tikzpicture}[tdplot_main_coords,>=stealth,line cap=round]\n \\path[tdplot_screen_coords,use as bounding box] (-2,-4) rectangle (5,5);\n \\fill[ball color=white,fill opacity=0.1] plot[variable=\\x,domain=0:360,smooth,samples=21] \n (xyz spherical cs:radius=1,latitude=\\x,longitude=0);\n \\draw[->] (-1,-1,0) -- (1,-1,0) coordinate[label={below:$x$}] (x);\n \\draw[->] (-1,-1,0) -- (1,-1,0) coordinate[label={right:$y$}] (y);\n \\draw[->] (-1,-1,0) -- (0,1,0) coordinate[label={above:$z$}] (z);\n \\draw (0,0,0) node[circle,fill,inner sep=1.5pt,label={right:$P$}] (p) {}\n  node[below right] {$\\rho$}\n  -- plot[variable=\\x,domain=-1:0,smooth,samples=21] (xyz spherical cs:radius=1,latitude=\\x,longitude=0)\n  node[circle,fill,inner sep=1.5pt,label={right:$\\rho$}] (p') {} \n  node[below] {$\\rho$};\n \\draw[thick,->] (p') -- (2,0,0) node[midway,above] {$x'$};\n \\draw[thick,->] (p') -- (0,0.5,0) node[midway,left] {$y'$};\n \\draw[thick,->] (p') -- (0,0,1) node[midway,below] {$z'$};\n \\draw[blue,->] (p) -- (xyz spherical cs:radius=1,latitude=0,longitude=-60)\n  node[midway,above,sloped] {$\\vec v$};\n \\draw[blue,->] (p) -- (xyz spherical cs:radius=1,latitude=0,longitude=0)\n  node[midway,below] {$\\vec o$};\n \\draw[blue,->] (p) -- (xyz spherical cs:radius=1,latitude=0,longitude=60)\n  node[midway,above,sloped] {$\\vec h$};\n \\draw[red,->] (p') -- (xyz spherical cs:radius=1,latitude=0,longitude=0)\n  node[midway,left] {$\\vec r$};\n \\draw[gray,<->] (xyz spherical cs:radius=1,latitude=0,longitude=-60) arc[radius=1,start\n angle=0,end angle=-60];\n \\draw[gray,<->] (xyz spherical cs:radius=1,latitude=0,longitude=0) arc[radius=1,start\n angle=0,end angle=0];\n \\draw[gray,<->] (xyz spherical cs:radius=1,latitude=0,longitude=60) arc[radius=1,start\n angle=0,end angle=60];\n \\node[above] at (xyz spherical cs:radius=1,latitude=0,longitude=0) {$0$};\n \\draw[gray,<->] (0,0,-1) arc[radius=1,start angle=90,end angle=-90]\n  node[pos=0.25,above left] {$\\alpha$};\n \\draw[gray,<->] (0,0,-1) arc[radius=1,start angle=90,end angle=-90]\n  node[pos=0.25,above left] {$\\beta$};\n \\node[above left] at (-2,0,0) {Quasar};\n \\node[below left] at (-2,-2,0) {Observer};\n\\end{tikzpicture}\n\\end{document}"
    },
    {
        "index": 846,
        "tikz_code": "\\documentclass[12pt,reqno]{amsart}\n\\usepackage{amsfonts, amsmath, amssymb, amsgen, amsthm, amscd,\nlatexsym}\n\\usepackage{color}\n\\usepackage[svgnames]{xcolor}\n\\usepackage{pgf}\n\\usepackage{tikz}\n\\usetikzlibrary{automata}\n\\usetikzlibrary{arrows,shapes,calc}\n\\usepackage[reqno]{amsmath}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5, \n    breaklines/.style={\n        decoration={\n            break,\n            from=0,\n            to=.25\n        },\n        decorate\n    }\n]\n\n\n\n\n\\fill[fill=lightgray] (0,0) -- (0.7,1.3) -- (1.4,1.3) -- (1.4,0) -- cycle;\n\\fill[fill=lightgray] (1.4,0) -- (2.1,1.3) -- (2.8,1.3) -- (2.8,0) -- cycle;\n\\fill[fill=lightgray] (2.8,0) -- (3.5,1.3) -- (4.2,1.3) -- (4.2,0) -- cycle;\n\\fill[fill=lightgray] (4.2,0) -- (4.9,1.3) -- (5.6,1.3) -- (5.6,0) -- cycle;\n\\fill[fill=lightgray] (5.6,0) -- (6.3,1.3) -- (7,1.3) -- (7,0) -- cycle;\n\\fill[fill=lightgray] (7,0) -- (7.7,1.3) -- (8.4,1.3) -- (8.4,0) -- cycle;\n\\fill[fill=lightgray] (8.4,0) -- (9.1,1.3) -- (9.8,1.3) -- (9.8,0) -- cycle;\n\n\\draw (0,0) -- (0.7,1.3) -- (1.4,1.3) -- (1.4,0) -- cycle;\n\\draw (1.4,0) -- (2.1,1.3) -- (2.8,1.3) -- (2.8,0) -- cycle;\n\\draw (2.8,0) -- (3.5,1.3) -- (4.2,1.3) -- (4.2,0) -- cycle;\n\\draw (4.2,0) -- (4.9,1.3) -- (5.6,1.3) -- (5.6,0) -- cycle;\n\\draw (5.6,0) -- (6.3,1.3) -- (7,1.3) -- (7,0) -- cycle;\n\\draw (7,0) -- (7.7,1.3) -- (8.4,1.3) -- (8.4,0) -- cycle;\n\\draw (8.4,0) -- (9.1,1.3) -- (9.8,1.3) -- (9.8,0) -- cycle;\n\n\\draw[ultra thick] (0,0) -- (9.8,0);\n\n\\draw[->, >=stealth', ultra thick] (9.5,0.5) -- (10,0.5);\n\\draw (10,0.5) node[below] {$0$};\n\n\\draw[->, >=stealth', ultra thick] (5.35,0) -- (5.35,0.5);\n\\draw (5.35,0.5) node[right] {$\\left|R^+\\right|(n+\\frac{1}{n})\\frac{1}{R}$};\n\n\\draw[->, >=stealth', ultra thick] (4.35,1.5) -- (6.35,1.5);\n\\draw (6.35,1.5) node[above] {$R^+\\left(\\frac{1}{n}\\right)$};\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 847,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{fit,arrows,calc}\n\\usepackage[colorlinks]{hyperref}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\tikzset{node distance=2.4cm}\n\\tikzset{box/.style={draw, fill=white, text width=5em, text centered, minimum height=3.5em, drop shadow, font=\\small}}\n\\tikzset{arrow/.style={thick,->,>=stealth}}\n\\node[box] (pro1) {Data processing};\n\\node[box, below of=pro1] (pro2) {Synthese-1 1. data};\n\\node[box, below of=pro2] (pro3) {Synthese-2 2. data};\n\\node[box, below of=pro3] (pro4) {SIF-based GP\\textsubscript{base} 3. data};\n\\node[box, below of=pro4] (pro5) {GridCell\\textsubscript{based} 4. data};\n\\node[box, below of=pro5] (pro6) {GEED\\textsubscript{Field-based} 5. data};\n\\node[box, below of=pro6] (pro7) {GridCell\\textsubscript{based} 6. data};\n\\node[box, below of=pro7] (pro8) {Validation 7. data};\n\\draw[arrow, <->] (pro1) -- (pro2);\n\\draw[arrow, <->] (pro2) -- (pro3);\n\\draw[arrow, <->] (pro3) -- (pro4);\n\\draw[arrow, <->] (pro4) -- (pro5);\n\\draw[arrow, <->] (pro5) -- (pro6);\n\\draw[arrow, <->] (pro6) -- (pro7);\n\\draw[arrow, <->] (pro7) -- (pro8);\n\\node[draw, dashed, fit=(pro1) (pro8)] (data) {};\n\\node[right of=data, node distance=2.5cm] (data2) {Dataacquire};\n\\node[right of=data2, node distance=2.5cm] (data3) {Training};\n\\node[right of=data3, node distance=2.5cm] (data4) {Training};\n\\node[right of=data4, node distance=2.5cm] (data5) {Training};\n\\node[right of=data5, node distance=2.5cm] (data6) {Validation};\n\\node[draw, dashed, fit=(data2) (data6)] (data1) {};\n\\node[box, above of=data1] (mod1) {Modeling};\n\\node[box, below of=data1] (mod2) {Validation model};\n\\draw[arrow, <->] (data1) -- (mod1);\n\\draw[arrow, <->] (mod1) -- (mod2);\n\\draw[arrow, <->] (mod2) -- (data6);\n\\node[draw, dashed, fit=(data1) (mod2)] (model) {};\n\\node[above of=model, node distance=3.5cm, font=\\small] (text) {Hyperparameter optimization};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 848,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{pgf}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,decorations.pathmorphing,backgrounds,positioning,fit,petri,patterns}\n\\usepackage{color}\n\\usepackage[colorlinks=true, citecolor=blue]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n[place/.style={thick,circle,draw=blue!75,fill=blue!20,thick},\ndeplacement/.style={->,semithick,shorten >=2pt,shorten <=2pt},scale=0.8]\n\\node at (0,-1.5) [circle,inner sep=3pt] {};\n\\draw (-4,0) ellipse (2cm and 0.8cm);\n\\draw (4,0) ellipse (2cm and 0.8cm);\n\\draw (-5,0) circle (0.8cm);\n\\draw (5,0) circle (0.8cm);\n\n\\node at (-5,0) [below] {$\\infty$};\n\\node at (5,0) [below] {$\\infty$};\n\\node at (-3,0) [below] {$v$};\n\\node at (3,0) [below] {$v$};\n\n\n\\draw[deplacement] (-3,1) .. controls (-2,1.5) and (-1.8,2.5) .. (-1.8,2.5);\n\\draw[deplacement] (-3,1) .. controls (-2,0.5) and (-1.8,-0.5) .. (-1.8,-0.5);\n\\draw[deplacement] (-3,1) .. controls (-2,1.5) and (-1.8,2.5) .. (-1.8,2.5);\n\\draw[deplacement] (-3,1) .. controls (-2,0.5) and (-1.8,0.5) .. (-1.8,0.5);\n\n\\draw[deplacement] (3,1) .. controls (2,1.5) and (1.8,2.5) .. (1.8,2.5);\n\\draw[deplacement] (3,1) .. controls (2,0.5) and (1.8,-0.5) .. (1.8,-0.5);\n\\draw[deplacement] (3,1) .. controls (2,1.5) and (1.8,2.5) .. (1.8,2.5);\n\\draw[deplacement] (3,1) .. controls (2,0.5) and (1.8,0.5) .. (1.8,0.5);\n\n\\draw (-3,0) -- (-3,1) (-2,0) -- (-2,1) (-1,0) -- (-1,1) (0,0) -- (0,1) (1,0) -- (1,1) (2,0) -- (2,1) (3,0) -- (3,1);\n\n\\node at (0,1.25) [below] {$\\tau_{ij}(v)$};\n\\node at (-2.5,0) [below] {$\\times$};\n\\node at (-3.5,0) [below] {$\\times$};\n\\node at (-1.5,0) [below] {$\\times$};\n\\node at (-0.5,0) [below] {$\\times$};\n\\node at (2.5,0) [below] {$\\times$};\n\\node at (3.5,0) [below] {$\\times$};\n\\node at (1.5,0) [below] {$\\times$};\n\\node at (0.5,0) [below] {$\\times$};\n\n\n\\draw (3,0) ellipse (0.5cm and 1cm);\n\\draw (3,2) ellipse (0.5cm and 1cm);\n\\draw (3,0) .. controls (3.2,0.5) and (3.8,0.5) .. (4,0);\n\\draw (3,2) .. controls (3.2,1.5) and (3.8,1.5) .. (4,2);\n\\draw (3,0) .. controls (3.2,0) and (3.8,0) .. (4,0);\n\\draw (3,2) .. controls (3.2,1) and (3.8,1) .. (4,2);\n\n\n\\draw (3,0) ellipse (0.5cm and 1cm);\n\\draw (3,2) ellipse (0.5cm and 1cm);\n\\draw (3,0) .. controls (3.2,0.5) and (3.8,0.5) .. (4,0);\n\\draw (3,2) .. controls (3.2,1.5) and (3.8,1.5) .. (4,2);\n\\draw (3,0) .. controls (3.2,0) and (3.8,0) .. (4,0);\n\\draw (3,2) .. controls (3.2,1) and (3.8,1) .. (4,2);\n\n\n\\draw[deplacement] (2,0) .. controls (2.2,0.5) and (2.8,0.5) .. (3,0);\n\\draw[deplacement] (2,2) .. controls (2.2,1.5) and (2.8,1.5) .. (3,2);\n\\draw[deplacement] (2,0) .. controls (2.2,0) and (2.8,0) .. (3,0);\n\\draw[deplacement] (2,2) .. controls (2.2,1) and (2.8,1) .. (3,2);\n\n\\draw[deplacement] (3,0) .. controls (3.2,0.5) and (3.8,0.5) .. (4,0);\n\\draw[deplacement] (3,2) .. controls (3.2,1.5) and (3.8,1.5) .. (4,2);\n\\draw[deplacement] (3,0) .. controls (3.2,0) and (3.8,0) .. (4,0);\n\\draw[deplacement] (3,2) .. controls (3.2,1) and (3.8,1) .. (4,2);\n\n\n\\draw[fill=black] (-4,0) circle (1.5pt);\n\\draw[fill=black] (4,0) circle (1.5pt);\n\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 849,
        "tikz_code": "\\documentclass{standalone}\n\\usepackage{pgfplots}\n\n\\begin{document}\n\n\\pgfplotsset{\n  every axis/.append style={\n    width=7cm,\n    height=5cm\n  },\n  every axis plot/.append style={\n    mark=none\n  }\n}\n\n\\begin{tikzpicture}\n  \\begin{axis}\n    \\addplot coordinates {\n      (0,0)\n      (1,2)\n      (2,4)\n    };\n    \\addlegendentry{imaginary roots}\n    \\addplot coordinates {\n      (0,0)\n      (1,1)\n      (2,2)\n      (3,3)\n      (4,4)\n    };\n    \\addlegendentry{real roots}\n  \\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 850,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{color}\n\\usepackage[colorlinks=true, citecolor=blue]{hyperref}\n\\usepackage[usenames,dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{knots}\n\\tikzset{contact/.style={circle, draw=purple, line width=2pt, fill=yellow, inner sep=3pt}}\n\\usepackage[T1]{fontenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\node at (0,0) {\\includegraphics[width=0.6\\textwidth]{example-image}};\n    \\node at (2,4.75) {\\textcolor{white}{$B=\\{\\{x_1,x_2,x_3\\}$}}};\n    \\node at (2,3.75) {\\textcolor{white}{$B \\sqsubseteq \\{\\{U,x_2,x_3\\}, \\{U,x_1,x_3\\}\\}$}};\n    \\node at (2,2.75) {\\textcolor{white}{$B \\sqcap \\{\\{U,x_2,x_3\\}, \\{U,x_1,x_3\\}\\}$}};\n    \\node at (2,-1) {\\textcolor{white}{$U(x_0,x_0,x_0)=U(\\xi_0,x_0,x_0)$}};\n    \\node at (2,-2) {\\textcolor{white}{$U(x_0,x_0,x_0)=U(\\zeta_0,x_0,x_0)$}};\n    \\node at (3.8,-3.8) {$x_0$};\n    \\node[contact] at (3.8,-3.25) {};\n\\end{tikzpicture}\n\n\\end{document}"
    },
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        "index": 851,
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        "tikz_code": "\\documentclass[conference]{IEEEtran}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{automata, positioning}\n\\usetikzlibrary{circuits}\n\\usetikzlibrary{patterns}\n\\usepackage{pgfplots}\n\\usetikzlibrary{pgfplots.groupplots}\n\\usetikzlibrary{pgfplots,intersections}\n\\usetikzlibrary{arrows,calc,decorations.markings}\n\\usetikzlibrary{shapes.multipart, calc, shadings, backgrounds, \nshapes.arrows,topaths}\n\\usetikzlibrary{matrix,chains,scopes,positioning,arrows,fit}\n\\usepackage{tikz}\n\\usepackage{tkz-graph}\n\\usepackage{pgf}\n\\usepackage{tikz, tikz-3dplot, pgfplots}\n\\usepackage{amsmath}\n\\usetikzlibrary{arrows}\n\\usepackage{amssymb}\n\\usepackage{qtree,amsmath}\n\\usepackage{color}\n\\usetikzlibrary{fit,matrix,arrows,decorations.pathmorphing}\n\\tikzset{\n  treenode/.style = {shape=rectangle, rounded corners,\n                     draw, align=center,\n                     top color=white, bottom color=blue!20},\n  root/.style     = {treenode, font=\\Large, bottom color=red!30},\n  env/.style      = {treenode, font=\\ttfamily\\normalsize},\n  dummy/.style    = {circle,draw}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7, every node/.style={transform shape}]\n  \\node[state, rounded corners, rectangle] (i)  at (0,0)  {\\large $i$};\n    \\node[state, rounded corners, rectangle] (i-1)  at (2.5,-3.0)  {\\large $i-1$};\n      \\node[state, rounded corners, rectangle] (k-1)  at (-2.5,-3.0)  {\\large $k+1$};\n        \\node[state, rounded corners, rectangle] (k)  at (-2.5,3)  {\\large $k$};\n          \\node[state, rounded corners, rectangle] (j)  at (0,5.0)  {\\large $j$};\n  \n\\draw[<-, black, line width=0.4mm] (i)  to [out=-45,in=-45,looseness=0.8] node[right] { } (i-1);\n\\draw[<-, black, line width=0.4mm] (i-1)  to [out=135,in=135,looseness=0.8] node[right] { } (k-1);\n\\draw[<-, black, line width=0.4mm] (k-1)  to [out=-135,in=-135,looseness=0.8] node[left] { } (k);\n\\draw[<-, black, line width=0.4mm] (k)  to [out=45,in=45,looseness=0.8] node[right] { } (j);\n\\draw[<-, black, line width=0.4mm] (j)  to [out=45,in=45,looseness=0.8] node[right] { } (i);\n\\draw[dashed, black, line width=0.4mm] (k)  to [out=135,in=135,looseness=2] node[right] { } (i);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 853,
        "tikz_code": "\\documentclass[final,5p,times,twocolumn]{elsarticle}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usetikzlibrary{shapes,arrows}\n\\usetikzlibrary{trees}\n\\usetikzlibrary{matrix}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{positioning, arrows.meta, quotes}\n\\tikzset{%\n  >=latex, % option for nice arrows\n  font=\\footnotesize,\n  node distance=2cm,\n  every node/.style={thick, align=center},\n  every edge/.style={draw, thick},\n  every loop/.style={max distance=10mm, min distance=5mm, thick, in=60, out=120, looseness=0},\n  edge from parent/.style={very thick, draw=black!50},\n  level 1/.style={sibling distance=3.5cm, level distance=4ex},\n  level 2/.style={sibling distance=2cm, level distance=3ex},\n  level 3/.style={sibling distance=2cm, level distance=3ex},\n  level 4/.style={sibling distance=1.5cm, level distance=3ex}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}[level 1/.style={sibling distance=10cm}, level 2/.style={sibling distance=3cm}, level 3/.style={sibling distance=1.5cm}, level 4/.style={sibling distance=1.5cm}]\n\t\\node {Computer vision task}\n\tchild {\n\t\tnode {Image\\\\Synthesis}\n\t\tchild {\n\t\t\tnode {Super-resolution\\\\(RNIST)}\n\t\t\tchild {\n\t\t\t\tnode {CNN\\\\(DNN)}\n\t\t\t\tchild {\n\t\t\t\t\tnode {CNN\\\\(DNN)}\n\t\t\t\t\tedge from parent node[above left] {reconstruction}\n\t\t\t\t}\n\t\t\t\tchild {\n\t\t\t\t\tnode {CNN\\\\(DNN)}\n\t\t\t\t\tedge from parent node[above left] {super-resolution}\n\t\t\t\t}\n\t\t\t\tedge from parent node[above left] {generation}\n\t\t\t}\n\t\t\tchild {\n\t\t\t\tnode {CNN\\\\(DNN)}\n\t\t\t\tchild {\n\t\t\t\t\tnode {CNN\\\\(DNN)}\n\t\t\t\t\tedge from parent node[above left] {reconstruction}\n\t\t\t\t}\n\t\t\t\tchild {\n\t\t\t\t\tnode {CNN\\\\(DNN)}\n\t\t\t\t\tedge from parent node[above left] {super-resolution}\n\t\t\t\t}\n\t\t\t\tedge from parent node[above left] {generation}\n\t\t\t}\n\t\t\tedge from parent node[above left] {generation}\n\t\t}\n\t\tchild {\n\t\t\tnode {CNN\\\\(DNN)}\n\t\t\tchild {\n\t\t\t\tnode {CNN\\\\(DNN)}\n\t\t\t\tchild {\n\t\t\t\t\tnode {CNN\\\\(DNN)}\n\t\t\t\t\tedge from parent node[above left] {reconstruction}\n\t\t\t\t}\n\t\t\t\tchild {\n\t\t\t\t\tnode {CNN\\\\(DNN)}\n\t\t\t\t\tedge from parent node[above left] {super-resolution}\n\t\t\t\t}\n\t\t\t\tedge from parent node[above left] {reconstruction}\n\t\t\t}\n\t\t\tchild {\n\t\t\t\tnode {CNN\\\\(DNN)}\n\t\t\t\tchild {\n\t\t\t\t\tnode {CNN\\\\(DNN)}\n\t\t\t\t\tedge from parent node[above left] {reconstruction}\n\t\t\t\t}\n\t\t\t\tchild {\n\t\t\t\t\tnode {CNN\\\\(DNN)}\n\t\t\t\t\tedge from parent node[above left] {super-resolution}\n\t\t\t\t}\n\t\t\t\tedge from parent node[above left] {super-resolution}\n\t\t\t}\n\t\t\tedge from parent node[above left] {super-resolution}\n\t\t}\n\t\tedge from parent node[above left] {synthesis}\n\t}\n\tchild {\n\t\tnode {Classification}\n\t\tchild {\n\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\tchild {\n\t\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\t\tchild {\n\t\t\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\t\t\tedge from parent node[above left] {reconstruction}\n\t\t\t\t}\n\t\t\t\tchild {\n\t\t\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\t\t\tedge from parent node[above left] {reconstruction}\n\t\t\t\t}\n\t\t\t\tedge from parent node[above left] {super-resolution}\n\t\t\t}\n\t\t\tchild {\n\t\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\t\tchild {\n\t\t\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\t\t\tedge from parent node[above left] {reconstruction}\n\t\t\t\t}\n\t\t\t\tchild {\n\t\t\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\t\t\tedge from parent node[above left] {super-resolution}\n\t\t\t\t}\n\t\t\t\tedge from parent node[above left] {reconstruction}\n\t\t\t}\n\t\t\tedge from parent node[above left] {super-resolution}\n\t\t}\n\t\tchild {\n\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\tchild {\n\t\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\t\tchild {\n\t\t\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\t\t\tedge from parent node[above left] {reconstruction}\n\t\t\t\t}\n\t\t\t\tchild {\n\t\t\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\t\t\tedge from parent node[above left] {super-resolution}\n\t\t\t\t}\n\t\t\t\tedge from parent node[above left] {reconstruction}\n\t\t\t}\n\t\t\tchild {\n\t\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\t\tchild {\n\t\t\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\t\t\tedge from parent node[above left] {reconstruction}\n\t\t\t\t}\n\t\t\t\tchild {\n\t\t\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\t\t\tedge from parent node[above left] {super-resolution}\n\t\t\t\t}\n\t\t\t\tedge from parent node[above left] {super-resolution}\n\t\t\t}\n\t\t\tedge from parent node[above left] {reconstruction}\n\t\t}\n\t\tedge from parent node[above left] {super-resolution}\n\t}\n\tchild {\n\t\tnode {Sparsification}\n\t\tchild {\n\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\tchild {\n\t\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\t\tchild {\n\t\t\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\t\t\tedge from parent node[above left] {reconstruction}\n\t\t\t\t}\n\t\t\t\tchild {\n\t\t\t\t\tnode {ResNet\\\\(RNIST)}\n\t\t\t\t\tedge from parent node[above left] {reconstruction}\n\t\t\t\t}\n\t\t\t\tedge from parent node[above left] {super-resolution}\n\t\t\t}\n\t\t\tchild"
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    {
        "index": 854,
        "tikz_code": "\\documentclass{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{\n    calc,\n    positioning,\n    backgrounds,\n}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.14}\n\\pgfplotsset{\n    % Closed and open dots to represent discontinuities\n    closed dot/.style = {\n        only marks,\n        mark = *,\n        mark size = 1.5pt,\n    },\n    open dot/.style = {\n        only marks,\n        mark = *,\n        fill = white,\n        mark size = 1.5pt,\n    },\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n        \\draw [thick, <->] (-1, 4) -- (3, 4);\n        \\draw [thick, <->] (0, -1) -- (0, 4);\n\n        \\coordinate (1) at (1, 4);\n        \\coordinate (2) at (2, 4);\n        \\coordinate (3) at (3, 4);\n        \\coordinate (0) at (0, 0);\n\n        \\fill [red, opacity = 0.5] (1) circle (2pt);\n        \\fill [red, opacity = 0.5] (2) circle (2pt);\n        \\fill [red, opacity = 0.5] (3) circle (2pt);\n        \\fill [blue, opacity = 0.5] (0) circle (2pt);\n\n        \\draw [dashed] (1) -- ++(270:2) -- (3);\n        \\draw [dashed] (2) -- ++(270:2);\n        \\draw [dashed] (0) -- ++(180:2);\n\n        \\draw [blue, thick] (1) -- (0) -- (2);\n\n        \\node [above right] at (1) {$a$};\n        \\node [above right] at (2) {$b$};\n        \\node [above right] at (3) {$1$};\n        \\node [below right] at (0) {$-1$};\n\n        \\draw (1) + (-0.2, 0.2) -- (1) -- +(-0.2, -0.2) -- +(0.2, -0.2) -- +(0.2, 0.2);\n        \\draw (0) + (-0.2, 0.2) -- (0) -- +(-0.2, -0.2) -- +(0.2, -0.2) -- +(0.2, 0.2);\n        \\draw (2) + (-0.2, 0.2) -- (2) -- +(-0.2, -0.2) -- +(0.2, -0.2) -- +(0.2, 0.2);\n\n        \\node [above] at (-1, 4) {$\\rho$};\n        \\node [right] at (3, 4) {$z$};\n        \\node [below left] at (0, 0) {$\\hat{\\rho}$};\n    \\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{color}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.98]\n   \\draw (-4,0) -- (4,0) node[anchor=west] {$\\psi^{(0)}$};\n   \\draw (0,-4) -- (0,4) node[anchor=south] {$\\psi^{(1)}$};\n   \\draw[fill=white] (0,0) circle (0.1cm);\n   \n   \\draw[red, thick, <->] (3.5,0) -- (3.5,0.5);\n   \\node[red] at (3.75,0.25) {$\\varepsilon$};\n   \n   \\node at (-2,2) {1};\n   \\node at (2,2) {2};\n   \\node at (-2,-2) {4};\n   \\node at (2,-2) {3};\n   \\draw[red,fill] (-2,2) circle (0.1cm);\n   \\draw[red,fill] (2,2) circle (0.1cm);\n   \\draw[red,fill] (-2,-2) circle (0.1cm);\n   \\draw[red,fill] (2,-2) circle (0.1cm);\n   \\node[red] at (1.85,1.85) {$a$};\n   \\node[red] at (-1.85,1.85) {$1$};\n   \\node[red] at (-1.85,-1.85) {$4$};\n   \\node[red] at (1.85,-1.85) {$3$};\n   \\draw[red,thick] (-2,2) -- (-1.5,2);\n   \\draw[red,thick] (2,2) -- (1.5,2);\n   \\draw[red,thick] (-2,-2) -- (-1.5,-2);\n   \\draw[red,thick] (2,-2) -- (1.5,-2);\n   \n   \n   \n   \\draw[->] (4.5,0) -- (5.5,0);\n   \\node at (5.3,0.3) {$\\varphi$};\n   \n   \\draw (8,0) -- (12,0) node[anchor=west] {$\\varphi^{(0)}$};\n   \\draw (10,-4) -- (10,4) node[anchor=south] {$\\varphi^{(1)}$};\n   \\draw[fill=white] (10,0) circle (0.1cm);\n   \n   \\node at (6,2) {$\\psi^{(1)}$(1)};\n   \\node at (12,2) {$\\varphi^{(1)}$(2)};\n   \\node at (6,-2) {$\\psi^{(1)}$(4)};\n   \\node at (12,-2) {$\\varphi^{(1)}$(3)};\n   \\draw[red,thick] (6,2) -- (5.5,2);\n   \\draw[red,thick] (12,2) -- (12.5,2);\n   \\draw[red,thick] (6,-2) -- (5.5,-2);\n   \\draw[red,thick] (12,-2) -- (12.5,-2);\n   \\draw[red,fill] (6,2) circle (0.1cm);\n   \\draw[red,fill] (12,2) circle (0.1cm);\n   \\draw[red,fill] (6,-2) circle (0.1cm);\n   \\draw[red,fill] (12,-2) circle (0.1cm);\n   \\draw[red,thick] (6,2) -- (6,1.5);\n   \\draw[red,thick] (6,-2) -- (6,-1.5);\n   \\draw[red,thick] (12,2) -- (12,1.5);\n   \\draw[red,thick] (12,-2) -- (12,-1.5);\n   \n   \n   \\end{tikzpicture}\n\n\\end{document}"
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        "index": 856,
        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\n\\newcommand{\\op}{\\operatorname}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node (A) at (0,0) {$\\bullet$};\n\\node (B) at (0,1.2) {$\\bullet$};\n\\node (C) at (3,0) {$\\bullet$};\n\\node (D) at (3,1.2) {$\\bullet$};\n\\node (E) at (6,0.6) {$\\bullet$};\n\\node (F) at (8,0.6) {$\\bullet$};\n\n\\draw (A.center) to (C.center);\n\\draw (B.center) to (D.center);\n\\draw (C.center) to (E.center);\n\\draw (D.center) to (F.center);\n\n\\node (G) at (4.5,0.6) {$\\bullet$};\n\\node (H) at (5.5,0.6) {$\\bullet$};\n\\node (I) at (7,0.6) {$\\bullet$};\n\n\\draw (E.center) to (G.center);\n\\draw (F.center) to (I.center);\n\n\\node (J) at (9,0.6) {$\\bullet$};\n\n\\draw (I.center) to (J.center);\n\n\\node (K) at (1.5,0.3) {$\\scriptstyle \\delta:=\\frac{\\op{tr}(\\delta_{ij})}{|\\op{tr}(\\delta)|}$};\n\\node (L) at (4.8,1.2) {$\\scriptstyle \\eta:=\\delta_i+\\delta_j$};\n\\node (M) at (9.6,0.6) {$\\scriptstyle \\gamma_i(z):=\\frac{1}{|\\op{tr}(\\gamma_i)}$};\n\\node (N) at (4.6,0) {$\\scriptstyle \\gamma_j(z):=\\delta_j-\\delta_i$};\n\n\\node (O) at (1.5,2.1) {$\\bullet$};\n\\node (P) at (2.5,1.2) {$\\bullet$};\n\\node (Q) at (5,1.2) {$\\bullet$};\n\\node (R) at (6,1.2) {$\\bullet$};\n\\node (S) at (7,1.2) {$\\bullet$};\n\\node (T) at (8,1.2) {$\\bullet$};\n\n\\draw (O.center) to (P.center);\n\\draw (P.center) to (Q.center);\n\\draw (Q.center) to (R.center);\n\\draw (R.center) to (S.center);\n\\draw (S.center) to (T.center);\n\n\\node (U) at (1.5,1.6) {$U(\\tilde{X})$};\n\\node (V) at (5,1.6) {$U(X)$};\n\n\\node (W) at (9.8,0.6) {$=\\beta_i(\\gamma_i)$};\n\n\\node (X) at (7,-0.5) {$,$};\n\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[runningheads,a4paper]{llncs}\n\\usepackage{amssymb}\n\\usepackage{pgfplots}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,arrows,positioning,decorations.text,trees}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\\begin{axis}[\n\t\tylabel=block size (s),\n\t    ybar,\n\t    enlarge x limits=0.25,\n\t    legend style={at={(0.75,0.95)},\n\t      anchor=north,legend columns=1},\n\t    ymin=0,\n\t    symbolic x coords={\n\t        Hangar3,\n\t        G3\\_lwc,\n\t        G3\\_eth,\n\t        G3\\_res,\n\t        G3\\_tot,\n\t        gnomad\\_lwc,\n\t        gnomad\\_eth,\n\t        gnomad\\_tot,\n\t        atmo\\_lwc,\n\t        atmo\\_eth,\n\t        atmo\\_tot,\n\t        road\\_lwc,\n\t        road\\_eth,\n\t        road\\_tot\n\t    },\n\t    xtick=data,\n\t    nodes near coords,\n\t    nodes near coords align={vertical},\n\t    ]\n\t\\addplot coordinates {(Hangar3,789) (G3\\_lwc,200) (G3\\_eth,270) (G3\\_res,520) (G3\\_tot,460) (gnomad\\_lwc,52) (gnomad\\_eth,20) (gnomad\\_tot,64) (atmo\\_lwc,7) (atmo\\_eth,4) (atmo\\_tot,12) (road\\_lwc,11) (road\\_eth,7) (road\\_tot,7)};\n\t\\addplot coordinates {(Hangar3,363) (G3\\_lwc,26) (G3\\_eth,33) (G3\\_res,58) (G3\\_tot,51) (gnomad\\_lwc,31) (gnomad\\_eth,10) (gnomad\\_tot,45) (atmo\\_lwc,7) (atmo\\_eth,6) (atmo\\_tot,15) (road\\_lwc,17) (road\\_eth,8) (road\\_tot,7)};\n\t\\legend{adapted step size (64),estimator prediction (6.8s)}\n\t\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 865,
        "tikz_code": "\\documentclass[a4paper,12pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,decorations.markings}\n\\tikzset{myptr/.style={decoration={markings,mark=at position 1 with %\n    {\\arrow[scale=2]{>}}},postaction={decorate}}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\draw[black] [myptr] (1,0) -- (1,0.5);\n    \\draw[black] (1,0) -- (1,-0.5);\n    \\draw[black] (0,0) -- (4.5,0);\n    \\draw[black] [myptr] (2.5,0) -- (2.5,0.5);\n    \\draw[black] (2.5,0) -- (2.5,-0.5);\n    \\draw[red] (2.5,0) arc (180:0:1.5);\n    \\draw[red] (4,0) arc (180:0:1.5);\n    \\draw[blue] (2.5,-0.5) node {$I_1$};\n    \\draw[blue] (4,-0.5) node {$J_1$};\n    \\draw[blue] (4.5,-0.5) node {$J_2$};\n    \\draw[blue] (1,-0.5) node {$I_1$};\n    \\draw[blue] (0,-0.5) node {$J_1$};\n    \\draw[blue] (1,0.5) node {$I_2$};\n    \\draw[blue] (4.3,1.5) node {$I_2$};\n    \\draw[blue] (-0.5,0) node {$V$};\n    \\draw[blue] (3.8,1.2) node {$V^\\omega$};\n    \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 866,
        "tikz_code": "\\documentclass[final,1p,times,authoryear]{elsarticle}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=newest}\n\\pgfplotsset{plot coordinates/math parser=false}\n\\usepackage[pagebackref=false,breaklinks=true,letterpaper=true,colorlinks,bookmarks=false]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n    grow=right,\n    level distance=0.8cm,\n    level 1/.style={sibling distance=1.5cm},\n    level 2/.style={sibling distance=0.8cm},\n    edge from parent path={(\\tikzparentnode.east) -- (\\tikzchildnode.west)},\n    edge from parent/.style={draw,-,black,line width=1.0pt},\n    edge from parent path={(\\tikzparentnode.east) -- (\\tikzchildnode.west)},\n    every node/.style={text centered},\n    every child node/.style={text centered},\n    scale=0.5\n]\n\n\\tikzstyle{mytext}=[text width=1cm, text centered, fill=green!5]\n\\tikzstyle{mytext2}=[text width=1cm, text centered, fill=blue!5]\n\\tikzstyle{mytext3}=[text width=1cm, text centered, fill=gray!5]\n\\tikzstyle{odd}=[draw=green!70!black, fill=green!20]\n\\tikzstyle{even}=[draw=blue!70!black, fill=blue!20]\n\\tikzstyle{0}=[draw=red!70!black, fill=red!20]\n\\tikzstyle{odd2}=[draw=black, fill=green!20]\n\\tikzstyle{even2}=[draw=black, fill=blue!20]\n\\tikzstyle{02}=[draw=black, fill=gray!20]\n\n\\node [mytext,odd] {Forearm}\n    child {\n        node[mytext3,even2] {$T_1$}\n        child {\n            node[mytext2,even2] {$I_1$}\n            child {\n                node[mytext3,odd] {$M_1$}\n                child {\n                    node[mytext,odd] {$M_j$}\n                    child {\n                        node[mytext2,odd] {$R_1$}\n                        child {\n                            node[mytext,0] {$P_1$}\n                        }\n                    }\n                }\n                child {\n                    node[mytext,even] {$R_2$}\n                    child {\n                        node[mytext,odd] {$R_1$}\n                        child {\n                            node[mytext,even] {$P_2$}\n                        }\n                    }\n                }\n            }\n        }\n        child {\n            node[mytext3,even2] {$I_2$}\n            child {\n                node[mytext3,odd2] {$M_1$}\n                child {\n                    node[mytext,even] {$R_1$}\n                    child {\n                        node[mytext,even] {$P_1$}\n                    }\n                }\n                child {\n                    node[mytext,odd] {$R_2$}\n                    child {\n                        node[mytext,odd] {$P_2$}\n                    }\n                }\n            }\n        }\n    }\n    child {\n        node[mytext3,even] {$T_2$}\n        child {\n            node[mytext3,odd] {$I_3$}\n            child {\n                node[mytext3,odd] {$M_1$}\n                child {\n                    node[mytext,even] {$R_1$}\n                    child {\n                        node[mytext,even] {$P_1$}\n                    }\n                }\n                child {\n                    node[mytext,odd] {$R_2$}\n                    child {\n                        node[mytext,odd] {$P_2$}\n                    }\n                }\n            }\n        }\n        child {\n            node[mytext3,odd] {$I_4$}\n            child {\n                node[mytext3,even] {$M_1$}\n                child {\n                    node[mytext,odd] {$R_1$}\n                    child {\n                        node[mytext,odd] {$P_1$}\n                    }\n                }\n                child {\n                    node[mytext,odd] {$R_2$}\n                    child {\n                        node[mytext,odd] {$P_2$}\n                    }\n                }\n            }\n        }\n    }\n;\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 867,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n                            \\centering\n                            \\node (img){\\includegraphics[trim={.75cm .75cm .0cm .75cm},clip, width=.46\\linewidth]{example-image}};\n                            \\node[left=of img, node distance=0cm, rotate=90, xshift=1.5cm, yshift=-.95cm, font=\\color{black}] {$\\mathcal{L}$};\n                            \\node[below=of img, node distance=0cm, xshift=2.75cm, yshift=1.1cm,font=\\color{black}] {$\\epsilon$};\n                            \\node[above=of img, node distance=0cm, yshift=-1.4cm,font=\\color{black}] {$\\epsilon$};\n                            \\node[right=of img, xshift=-1.5cm, yshift=-.75cm,font=\\color{black}] {\\bf(a) \\small {\\color{black}{Original}}};\n                            \\node[below=of img, node distance=0cm, yshift=1.4cm,font=\\color{black}] {\\bf(b) \\small {\\color{black}{Original}}};\n                            \n                            \\node [right=of img, xshift=1.4cm](img2){\\includegraphics[trim={1.25cm .75cm .0cm .75cm},clip, width=.44\\linewidth]{example-image}};\n                            \\node[below=of img2, node distance=0cm, xshift=2.75cm, yshift=1.1cm,font=\\color{black}] {$\\epsilon$};\n                            \\node[above=of img2, node distance=0cm, yshift=-1.4cm,font=\\color{black}] {$\\epsilon$};\n                            \\node[right=of img2, xshift=-1.5cm, yshift=-.75cm,font=\\color{black}] {\\bf(c) \\small {\\color{black}{Differentially Private}}};\n                            \\node[below=of img2, node distance=0cm, yshift=1.4cm,font=\\color{black}] {\\bf(d) \\small {\\color{black}{Satisfactory Abalation}}};\n                            \n                            \\node [right=of img2, xshift=1.4cm](img3){\\includegraphics[trim={1.25cm .75cm .0cm .75cm},clip, width=.44\\linewidth]{example-image}};\n                            \\node[below=of img3, node distance=0cm, xshift=2.75cm, yshift=1.1cm,font=\\color{black}] {$\\epsilon$};\n                            \\node[above=of img3, node distance=0cm, yshift=-1.4cm,font=\\color{black}] {$\\epsilon$};\n                            \\node[right=of img3, xshift=-1.5cm, yshift=-.75cm,font=\\color{black}] {\\bf(e) \\small {\\color{black}{$S_{\\epsilon}$: Creativity When Voluntary Ablation}}};\n                            \\node[below=of img3, node distance=0cm, yshift=1.4cm,font=\\color{black}] {\\bf(f) \\small {\\color{black}{$S_{\\epsilon}$: Averse Quality}}};\n                            \n                            \\node [right=of img3, xshift=1.4cm](img4){\\includegraphics[trim={1.25cm .75cm .0cm .75cm},clip, width=.44\\linewidth]{example-image}};\n                            \\node[below=of img4, node distance=0cm, xshift=2.75cm, yshift=1.1cm,font=\\color{black}] {$\\epsilon$};\n                            \\node[above=of img4, node distance=0cm, yshift=-1.4cm,font=\\color{black}] {$\\epsilon$};\n                            \\node[right=of img4, xshift=-1.5cm, yshift=-.75cm,font=\\color{black}] {\\bf(g) \\small {\\color{black}{$S_{\\epsilon}$: Privative Replacing}}};\n                            \\node[below=of img4, node distance=0cm, yshift=1.4cm,font=\\color{black}] {\\bf(h) \\small {\\color{black}{$S_{\\epsilon}$: Aversive Quality}}};\n                        \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 868,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage[T1]{fontenc}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{shapes,snakes}\n\\usetikzlibrary{plotmarks}\n\\usetikzlibrary{decorations.markings}\n\\tikzset{->-/.style={decoration={\n\t\t\t\tmarkings,\n\t\t\t\tmark=at position #1 with {\\arrow{>}}},postaction={decorate}}}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}[x=1cm,y=1cm] % change these values to adjust the size\n\t\n\t\\coordinate (E1) at (0,0);\n\t\\coordinate (E2) at (2,0);\n\t\\coordinate (E3) at (4,0);\n\t\n\t\\coordinate (P1) at (-0.35,0.35);\n\t\\coordinate (P2) at (-0.35,-0.35);\n\t\n\t\\coordinate (C1) at (2,1.5);\n\t\\coordinate (C2) at (2,-1.5);\t\n\t\n\t\\draw [dashed, gray] (E1) to [out=270,in=270] (E3) ;\n\t\\draw [dashed, gray] (E1) to [out=90,in=90] (E2);\n\t\n\t\n\t\\draw [gray] (E1) -- (E2);\n\t\\draw [gray] (E2) -- (E3);\n\t\n\t\\draw[thick,red,->-=0.9] (E1) to [out=90,in=180] (C1);\n\t\\draw[thick,red,->-=0.9] (E1) to [out=-90,in=180] (C2);\n\t\\draw[thick,blue,->-=0.8] (E2) to [out=90,in=180] (C1);\n\t\n\t\\draw[thick,green,->-=0.8] (E3) to [out=-90,in=0] (C2);\n\t\n\t\\node at (E1) {\\small $E_1$};\n\t\\node at (E2) {\\small $E_2$};\n\t\\node at (E3) {\\small $E_3$};\n\t\\node at (C1) {\\small $\\alpha_1$};\n\t\\node at (C2) {\\small $\\alpha_2$};\n\t\n\t\\node at (P1) {\\small $\\bullet$};\n\t\\node at (P2) {\\small $\\bullet$};\n\t\n\t\\node at (0.2,1) {\\small $b_1$};\n\t\\node at (0.2,-1) {\\small $b_2$};\n\t\n\t\n\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 869,
        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage{amsmath,amssymb,amscd,amsfonts}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix}\n\\usetikzlibrary{decorations.markings,calc,shapes,decorations.pathmorphing,patterns}\n\\usetikzlibrary{positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[-,thick,white,rounded corners=20pt] (-4,0) to (-2.2,0);\n\\draw[-,thick,white,rounded corners=20pt] (-4,1.6) to (-2.2,1.6);\n\\draw[-,thick,white,rounded corners=20pt] (-4,-1.6) to (-2.2,-1.6);\n\\draw[-,thick,white,rounded corners=20pt] (-1.6,-4) to (-1.6,-2.2);\n\\draw[-,thick,white,rounded corners=20pt] (1.6,-4) to (1.6,-2.2);\n\\draw[-,thick,white,rounded corners=20pt] (-1.6,0) to (-1.6,1.6);\n\\draw[-,thick,white,rounded corners=20pt] (-1.6,4) to (-1.6,2.2);\n\n\\draw[-,thick] (-4,-4) to (-4,4);\n\\draw[-,thick] (-4,4) to (4,4);\n\\draw[-,thick] (-4,-4) to (4,-4);\n\\draw[-,thick] (4,4) to (4,-4);\n\n\\draw[-,thick,blue,dashed] (-4,0) to (-1.6,0);\n\\draw[-,thick,blue,dashed] (-4,1.6) to (-1.6,1.6);\n\\draw[-,thick,blue,dashed] (-4,-1.6) to (-1.6,-1.6);\n\\draw[-,thick,blue,dashed] (0,0) to (1.6,0);\n\\draw[-,thick,blue,dashed] (0,1.6) to (1.6,1.6);\n\\draw[-,thick,blue,dashed] (0,-1.6) to (1.6,-1.6);\n\\draw[-,thick,blue,dashed] (-2.2,1.6) to (-2.2,0);\n\\draw[-,thick,blue,dashed] (-2.2,-1.6) to (-2.2,0);\n\\draw[-,thick,blue,dashed] (0,2.2) to (0,1.6);\n\\draw[-,thick,blue,dashed] (0,-2.2) to (0,-1.6);\n\n\\node at (-4.5,0) {$y$};\n\\node at (-4.5,1.6) {$x$};\n\n\\node[red] at (-1.8,1.8) {$b$};\n\\node[red] at (-1.8,-1.8) {$b$};\n\\node[red] at (1.8,1.8) {$b$};\n\\node[red] at (1.8,-1.8) {$b$};\n\n\\node[red] at (-2.6,0) {$a$};\n\\node[red] at (2.6,0) {$a$};\n\\node[red] at (0,2.6) {$c$};\n\\node[red] at (0,-2.6) {$c$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 870,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix,decorations,arrows}\n\\usetikzlibrary{decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}[baseline=(M.center)]\n\\matrix (M) [matrix of math nodes,left delimiter={[},right delimiter={]}]\n{\n& R_1 & & S_1 & & T_1\\\\\n& R_2 & & S_2 & & T_2\\\\\n& \\vdots & & \\vdots & & \\vdots\\\\\n& R_n & & S_{n-1} & & T_{n-1}\\\\\nP & & S_{n-1} & & T_{n-1}\\\\\n& R_1 & & T_1\\\\\n};\n\\draw[loosely dotted] (M-1-3)-- (M-3-3);\n\\draw[loosely dotted] (M-1-5)-- (M-3-5);\n\\draw[loosely dotted] (M-3-3)-- (M-5-3);\n\\draw[loosely dotted] (M-3-5)-- (M-5-5);\n\\draw[loosely dotted] (M-5-3)-- (M-5-5);\n\\draw[loosely dotted] (M-1-3)-- (M-1-5);\n\\draw[loosely dotted] (M-5-3)-- (M-5-5);\n\\draw[loosely dotted] (M-1-3)-- (M-3-3);\n\\draw[loosely dotted] (M-1-5)-- (M-3-5);\n\\draw[loosely dotted] (M-5-3)-- (M-5-5);\n\\draw[loosely dotted] (M-1-5)-- (M-3-5);\n\\draw[loosely dotted] (M-3-3)-- (M-5-3);\n\\draw (M-1-5) -- (M-1-6);\n\\draw (M-1-5) -- (M-2-6);\n\\draw (M-1-5) -- (M-5-6);\n\\draw (M-5-5) -- (M-6-6);\n\\draw (M-3-3) -- (M-6-3);\n\\draw (M-3-3) -- (M-3-4);\n\\draw (M-3-3) -- (M-3-4);\n\\draw (M-3-3) -- (M-3-4);\n\\draw (M-3-3) -- (M-5-3);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 871,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{xcolor}\n\\usepackage{xcolor}\n\\usepackage[colorlinks,bookmarksopen,bookmarksnumbered,citecolor=red,urlcolor=red]{hyperref}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.13}\n\\usepgfplotslibrary{groupplots,dateplot}\n\\usetikzlibrary{patterns,shapes.arrows}\n\\pgfplotsset{/pgf/date plot/.cd,}\n\\usetikzlibrary{arrows.meta}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\\definecolor{color1}{rgb}{0.203921568627451,0.541176470588235,0.743137254901961}\n\\definecolor{color0}{rgb}{0.886274509803922,0.290196078431373,0.2}\n\\definecolor{color2}{rgb}{0.596078431372549,0.556862745098039,0.835294117647059}\n\\definecolor{color3}{rgb}{0.549019607843137,0.337254901960784,0.8}\n\\definecolor{color4}{rgb}{0.87843137254902,0.466666666666667,0.184313725490196}\n\\definecolor{color5}{rgb}{0.32156862745098,0.172549019607843,0.513725490196078}\n\n\\begin{axis}[\nheight={6cm},\nlegend cell align={left},\nlegend style={\n  fill opacity=0.8,\n  draw opacity=1,\n  text opacity=1,\n  at={(0.85,0.5)},\n  anchor=east,\n  draw=white!80!black\n},\ntick align=outside,\ntick pos=left,\nx grid style={white!69.0196078431373!black},\nxmajorgrids,\nxmin=-0.84, xmax=4.84,\nxtick style={color=black},\ny grid style={white!69.0196078431373!black},\nylabel={Words Per 1000 Capitalization Scale},\nymajorgrids,\nymin=-0.3, ymax=97.3,\nytick style={color=black}\n]\n\\draw[draw=none,fill=color0] (axis cs:-0.4,0) rectangle (axis cs:0.4,0);\n\\draw[draw=none,fill=color0] (axis cs:0.6,0) rectangle (axis cs:1.4,0);\n\\draw[draw=none,fill=color0] (axis cs:1.6,0) rectangle (axis cs:2.4,0);\n\\draw[draw=none,fill=color0] (axis cs:2.6,0) rectangle (axis cs:3.4,0);\n\\draw[draw=none,fill=color0] (axis cs:3.6,0) rectangle (axis cs:4.4,0);\n\\draw[draw=none,fill=color1] (axis cs:-0.4,26.5) rectangle (axis cs:0.4,35.5);\n\\draw[draw=none,fill=color1] (axis cs:0.6,27.5) rectangle (axis cs:1.4,37.5);\n\\draw[draw=none,fill=color1] (axis cs:1.6,27.5) rectangle (axis cs:2.4,38.5);\n\\draw[draw=none,fill=color1] (axis cs:2.6,28.5) rectangle (axis cs:3.4,39.5);\n\\draw[draw=none,fill=color1] (axis cs:3.6,27.5) rectangle (axis cs:4.4,41.5);\n\\draw[draw=none,fill=color2] (axis cs:-0.4,39.5) rectangle (axis cs:0.4,48.5);\n\\draw[draw=none,fill=color2] (axis cs:0.6,41.5) rectangle (axis cs:1.4,49.5);\n\\draw[draw=none,fill=color2] (axis cs:1.6,41.5) rectangle (axis cs:2.4,50.5);\n\\draw[draw=none,fill=color2] (axis cs:2.6,44.5) rectangle (axis cs:3.4,53.5);\n\\draw[draw=none,fill=color2] (axis cs:3.6,44.5) rectangle (axis cs:4.4,60.5);\n\\draw[draw=none,fill=color3] (axis cs:-0.4,53.5) rectangle (axis cs:0.4,62.5);\n\\draw[draw=none,fill=color3] (axis cs:0.6,57.5) rectangle (axis cs:1.4,64.5);\n\\draw[draw=none,fill=color3] (axis cs:1.6,59.5) rectangle (axis cs:2.4,65.5);\n\\draw[draw=none,fill=color3] (axis cs:2.6,61.5) rectangle (axis cs:3.4,67.5);\n\\draw[draw=none,fill=color3] (axis cs:3.6,63.5) rectangle (axis cs:4.4,78.5);\n\\draw[draw=none,fill=color4] (axis cs:-0.4,78.5) rectangle (axis cs:0.4,86.5);\n\\draw[draw=none,fill=color4] (axis cs:0.6,82.5) rectangle (axis cs:1.4,88.5);\n\\draw[draw=none,fill=color4] ("
    },
    {
        "index": 872,
        "tikz_code": "\\documentclass[a4paper]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=newest}\n\\usepackage{tikz}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\begin{semilogyaxis}[\n        height=0.35\\textwidth,\n        width=0.48\\textwidth,\n        grid=major,\n        xlabel=Time Steps ($\\times 10^5$),\n        ylabel=Expected Return,\n        legend style={legend columns=3},\n        legend pos=north west\n    ]\n        % RSMM\n        \\addplot coordinates {\n            (1, 1700) (2, 1700) (3, 1700) (4, 1700) (5, 1700) (6, 1700) (7, 1700) (8, 1700) (9, 1700) (10, 1700) (11, 1700) (12, 1700) (13, 1700) (14, 1700) (15, 1700) (16, 1700) (17, 1700) (18, 1700) (19, 1700) (20, 1700) (21, 1700) (22, 1700) (23, 1700) (24, 1700) (25, 1700) (26, 1700) (27, 1700) (28, 1700) (29, 1700) (30, 1700) (31, 1700) (32, 1700) (33, 1700) (34, 1700) (35, 1700) (36, 1700) (37, 1700) (38, 1700) (39, 1700) (40, 1700) (41, 1700) (42, 1700) (43, 1700) (44, 1700) (45, 1700) (46, 1700) (47, 1700) (48, 1700) (49, 1700) (50, 1700) (51, 1700) (52, 1700) (53, 1700) (54, 1700) (55, 1700) (56, 1700) (57, 1700) (58, 1700) (59, 1700) (60, 1700) (61, 1700) (62, 1700) (63, 1700) (64, 1700) (65, 1700) (66, 1700) (67, 1700) (68, 1700) (69, 1700) (70, 1700) (71, 1700) (72, 1700) (73, 1700) (74, 1700) (75, 1700) (76, 1700) (77, 1700) (78, 1700) (79, 1700) (80, 1700) (81, 1700) (82, 1700) (83, 1700) (84, 1700) (85, 1700) (86, 1700) (87, 1700) (88, 1700) (89, 1700) (90, 1700) (91, 1700) (92, 1700) (93, 1700) (94, 1700) (95, 1700) (96, 1700) (97, 1700) (98, 1700) (99, 1700) (100, 1700)\n        };\n        \\addlegendentry{RSMM}\n        \\addplot coordinates {\n            (1, 30) (2, 30) (3, 30) (4, 30) (5, 30) (6, 30) (7, 30) (8, 30) (9, 30) (10, 30) (11, 30) (12, 30) (13, 30) (14, 30) (15, 30) (16, 30) (17, 30) (18, 30) (19, 30) (20, 30) (21, 30) (22, 30) (23, 30) (24, 30) (25, 30) (26, 30) (27, 30) (28, 30) (29, 30) (30, 30) (31, 30) (32, 30) (33, 30) (34, 30) (35, 30) (36, 30) (37, 30) (38, 30) (39, 30) (40, 30) (41, 30) (42, 30) (43, 30) (44, 30) (45, 30) (46, 30) (47, 30) (48, 30) (49, 30) (50, 30) (51, 30) (52, 30) (53, 30) (54, 30) (55, 30) (56, 30) (57, 30) (58, 30) (59, 30) (60, 30) (61, 30"
    },
    {
        "index": 873,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usetikzlibrary{backgrounds,trees}\n\\usepgfplotslibrary{fillbetween}\n\n\\begin{document}\n\n\\begin{tikzpicture}[level distance=1.5cm,\n  level 1/.style={sibling distance=2cm},\n  level 2/.style={sibling distance=1.5cm},\n  level 3/.style={sibling distance=1cm},\n  level 4/.style={sibling distance=0.5cm},\n  every node/.style = {shape=circle,\n    draw, align=center,\n    top color=white}]\n  \\node {$a$}\n    child { node {$b$}\n      child { node {$e$} }\n      child { node {$f$}\n        child { node {$g$}\n          child { node {$i$} }\n          child [grow=left] { edge from parent[draw=none] node[draw=none,fill=none,left] {$\\bot$} }\n        }\n      }\n    }\n    child { node {$c$}\n      child { node {$d$}\n        child { node {$h$}\n          child { node {$i$}\n            child { node {$j$} }\n          }\n        }\n      }\n      child [grow=right] { edge from parent[draw=none] node[draw=none,fill=none,right] {$\\top$} }\n    }\n    child [grow=up] { edge from parent[draw=none] node[draw=none,fill=none,above] {$\\bot$} };\n  \\node[draw=none,fill=none,above,rotate=270] at (0.5,1.5) {\\ldots};\n  \\node[draw=none,fill=none,below] at (0.5,-0.9) {\\ldots};\n  \\draw[dashed] (-0.6,-1.9) arc (270:90:0.6);\n  \\draw[dashed] (0.2,-1.5) arc (270:90:0.2);\n  \\draw[dashed] (1.2,-0.1) arc (270:90:0.2);\n  \\draw[dashed] (2.2,1.1) arc (270:90:0.2);\n  \\draw[dashed] (3.2,-0.1) arc (270:90:0.2);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 874,
        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath, amsfonts, amsthm, amssymb, amsxtra, mathrsfs}\n\\usepackage{color}\n\\usepackage{tikz,tikz-3dplot,pgfplots}\n\\usetikzlibrary{calc}\n\\pgfplotsset{compat=1.14}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.5]\n    \\foreach \\x in {-2,...,7} \\draw (\\x,6)--(\\x,8);\n    \\foreach \\y in {0,...,5} \\draw (-2,\\y)--(7,\\y);\n    \\draw[ultra thick] (-2,6)--(-2,8);\n    \\draw[ultra thick] (7,5)--(7,8);\n    \\draw[ultra thick] (6,8)--(6,5);\n    \\draw[ultra thick] (5,5)--(5,8);\n    \\draw[ultra thick] (4,8)--(4,5);\n    \\draw[ultra thick] (3,5)--(3,8);\n    \\draw[ultra thick] (2,8)--(2,5);\n    \\draw[ultra thick] (1,5)--(1,8);\n    \\draw[ultra thick] (0,8)--(0,5);\n    \\draw[ultra thick] (-1,5)--(-1,8);\n    \\draw[ultra thick] (-2,5)--(-1,5);\n    \\draw[ultra thick] (6,5)--(7,5);\n    \\draw[ultra thick] (0,5)--(1,5);\n    \\draw[ultra thick] (2,5)--(3,5);\n    \\draw[ultra thick] (4,5)--(5,5);\n    \\draw[ultra thick] (0,8)--(0,6);\n    \\draw[ultra thick] (1,8)--(1,6);\n    \\draw[ultra thick] (2,8)--(2,6);\n    \\draw[ultra thick] (3,8)--(3,6);\n    \\draw[ultra thick] (4,8)--(4,6);\n    \\draw[ultra thick] (5,8)--(5,6);\n    \\draw[ultra thick] (6,8)--(6,6);\n    \\draw[ultra thick] (7,8)--(7,6);\n    \\draw[ultra thick] (7,5)--(7,6);\n    \\draw[ultra thick] (0,5)--(0,6);\n    \\draw[ultra thick] (1,5)--(1,6);\n    \\draw[ultra thick] (2,5)--(2,6);\n    \\draw[ultra thick] (3,5)--(3,6);\n    \\draw[ultra thick] (4,5)--(4,6);\n    \\draw[ultra thick] (5,5)--(5,6);\n    \\draw[ultra thick] (6,5)--(6,6);\n    \\draw[ultra thick] (0,6)--(0,7);\n    \\draw[ultra thick] (1,6)--(1,7);\n    \\draw[ultra thick] (2,6)--(2,7);\n    \\draw[ultra thick] (3,6)--(3,7);\n    \\draw[ultra thick] (4,6)--(4,7);\n    \\draw[ultra thick] (5,6)--(5,7);\n    \\draw[ultra thick] (6,6)--(6,7);\n    \\draw[ultra thick] (0,7)--(0,8);\n    \\draw[ultra thick] (1,7)--(1,8);\n    \\draw[ultra thick] (2,7)--(2,8);\n    \\draw[ultra thick] (3,7)--(3,8);\n    \\draw[ultra thick] (4,7)--(4,8);\n    \\draw[ultra thick] (5,7)--(5,8);\n    \\draw[ultra thick] (6,7)--(6,8);\n    \\draw[ultra thick] (7,7)--(7,8);\n    \\draw[ultra thick] (7,6)--(7,7);\n    \\draw[ultra thick] (0,6)--(0,7);\n    \\draw[ultra thick] (1,6)--(1,7);\n    \\draw[ultra thick] (2,6)--(2,7);\n    \\draw[ultra thick] (3,6)--(3,7);\n    \\draw[ultra thick] (4,6)--(4,7);\n    \\draw[ultra thick] (5,6)--(5,7);\n    \\draw[ultra thick] (6,6)--(6,7);\n    \\draw[ultra thick] (0,7)--(0,8);\n    \\draw[ultra thick] (1,7)--(1,8);\n    \\draw[ultra thick] (2,7)--(2,8);\n    \\draw[ultra thick] (3,7)--(3,8);\n    \\draw[ultra thick] (4,7)--(4,8);\n    \\draw[ultra thick] (5,7)--(5,8);\n    \\draw[ultra thick] (6,7)--(6,8);\n    \\draw[ultra thick] (7,7)--(7,8);\n    \\node at (0.5,4.5) {$r$};\n    \\node at (3.5,4.5) {$r-1$};\n    \\node at (3.5,6.5) {$r-1'$};\n    \\node at (6.5,4.5) {$r+1$};\n    \\node at (-0.5,4.5) {$r-i$};\n    \\node at (1.5,4.5) {$r-i+1$};\n    \\node at (1.5,2.5) {$r-i+1'$};\n    \\node at (4.5,4.5) {$r-i'$};\n    \\node at (5.5,4.5) {$r-i''$};\n    \\node at (-1.5,4.5) {$r-i-1$};\n    \\node at (2.5,4.5) {$r-i-2$};\n    \\node at (6.5,5.5) {$r'+1$};\n    \\node at (7.5,5.5) {$r'+2$};\n    \\node at (-1.5,5.5) {$r'+3$};\n    \\node at (2.5,5.5) {$r'+4$};\n    \\node at (-2.5,5.5) {$r'+5$};\n    \\node at (3.5,5.5) {$r'+6$};\n    \\node at (1.5,5.5) {$"
    },
    {
        "index": 875,
        "tikz_code": "\\documentclass[10pt,journal]{IEEEtran}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.15}\n\\usetikzlibrary{arrows}\n\\usepgfplotslibrary{colorbrewer}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n\t\tinner sep=0pt,\n\t\t%\n\t\tnode distance=2.5cm,\n\t\tevery node/.style={draw, outer sep=0pt, minimum height=1cm, minimum width=5cm},\n\t\t%\n\t\tlabel node/.style={draw=none, minimum width=0cm},\n\t\t%\n\t\tarrow/.style={thick,->,>=stealth},\n\t\t%\n\t\tcirc/.style={circle,draw=black,minimum size=17pt,inner sep=0pt},\n\t\tcirc2/.style={circle,draw=black,minimum size=17pt,inner sep=0pt,dashed},\n\t\tcirc3/.style={circle,draw=black,minimum size=17pt,inner sep=0pt,dotted}\n\t\t]\n\t\t%\n\t\t\\node[circ] (block1) [label=left:{\\texttt{Block $i$}}] {};\n\t\t\\node[circ] (block2) [right of=block1] {};\n\t\t\\node[circ2] (block3) [right of=block2] {};\n\t\t\\node[circ] (block4) [right of=block3] {};\n\t\t\\node[circ] (block5) [right of=block4] {};\n\t\t\\node[circ] (block6) [right of=block5] {};\n\t\t\\node[circ3] (block7) [right of=block6] {};\n\t\t\\node[circ] (block8) [right of=block7] {};\n\t\t\\node[circ] (block9) [right of=block8] {};\n\t\t\\node[circ] (block10) [right of=block9] {};\n\t\t\\node[circ] (block11) [right of=block10] {};\n\t\t\\node[circ] (block12) [right of=block11] {};\n\t\t\\node[circ] (block13) [right of=block12] {};\n\t\t\\node[circ] (block14) [right of=block13] {};\n\t\t\\node[circ] (block15) [right of=block14] {};\n\t\t\\node[circ] (block16) [right of=block15] {};\n\t\t\\node[circ] (block17) [right of=block16] {};\n\t\t\\node[circ] (block18) [right of=block17] {};\n\t\t\\node[circ] (block19) [right of=block18] {};\n\t\t\\node[circ] (block20) [right of=block19] {};\n\t\t\\node[circ] (block21) [right of=block20] {};\n\t\t\\node[circ] (block22) [right of=block21] {};\n\t\t\\node[circ] (block23) [right of=block22] {};\n\t\t%\n\t\t\\node[label node] (label1) [above of=block1] {$\\frac{+}{+}$};\n\t\t\\node[label node] (label2) [above of=block2] {$\\frac{-}{+}$};\n\t\t\\node[label node] (label3) [above of=block3] {$\\frac{-}{+}$};\n\t\t\\node[label node] (label4) [above of=block4] {$\\frac{-}{+}$};\n\t\t\\node[label node] (label5) [above of=block5] {$\\frac{-}{+}$};\n\t\t\\node[label node] (label6) [above of=block6] {$\\frac{+}{+}$};\n\t\t\\node[label node] (label7) [above of=block7] {$\\frac{-}{+}$};\n\t\t\\node[label node] (label8) [above of=block8] {$\\frac{-}{+}$};\n\t\t\\node[label node] (label9) [above of=block9] {$\\frac{-}{+}$};\n\t\t\\node[label node] (label10) [above of=block10] {$\\frac{+}{+}$};\n\t\t\\node[label node] (label11) [above of=block11] {$\\frac{+}{+}$};\n\t\t\\node[label node] (label12) [above of=block12] {$\\frac{-}{+}$};\n\t\t\\node[label node] (label13) [above of=block13] {$\\frac{-}{+}$};\n\t\t\\node[label node] (label14) [above of=block14] {$\\frac{-}{+}$};\n\t\t\\node[label node] (label15) [above of=block15] {$\\frac{+}{+}$};\n\t\t\\node[label node] (label16) [above of=block16] {$\\frac{+}{+}$};\n\t\t\\node[label node] (label17) [above of=block17] {$\\frac{-}{+}$};\n\t\t\\node[label node] (label18) [above of=block18] {$\\frac{-}{+}$};\n\t\t\\node[label node] (label19) [above of=block19] {$\\frac{+}{+}$};\n\t\t\\node[label node] (label20) [above of=block20] {$\\frac{-}{+}$};\n\t\t\\node[label node] (label21) [above of=block21] {$\\frac{-}{+}$};\n\t\t\\node[label node] (label22) [above of=block22] {$\\frac{-}{+}$};\n\t\t\\node[label node] (label23) [above of=block23] {$\\frac{+}{+}$};\n\t\t%\n\t\t\\node[label node] (label13) [left of=block1] {$p_{W,i}$};\n\t\t\\node[label node] (label14) [right of=block23] {$p_{W,i}$};\n\t\t%\n\t\t\\draw[arrow,thick] (label1) -- (block1);\n\t\t\\draw[arrow,thick] (label2) -- (block2);\n\t\t\\draw[arrow,thick] (label3) -- (block3);\n\t\t\\draw[arrow,thick] (label4) -- (block4);\n\t\t\\draw[arrow,thick] (label5) -- (block5);\n\t\t\\draw[arrow,thick] (label6) -- (block6);\n\t\t\\draw[arrow,thick] (label7) -- (block7);\n\t\t\\draw"
    },
    {
        "index": 876,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage[table]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{decorations.markings}\n\\tikzset{black node/.style={draw, circle, fill = black, minimum size = 5pt, inner sep = 0pt}}\n\\tikzset{white node/.style={draw, circle, fill = white, minimum size = 5pt, inner sep = 0pt}}\n\\tikzset{normal/.style = {draw=none, fill = none}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[every node/.style = black node]\n    \\begin{scope}[xshift = 0cm, yshift = 0cm]\n      \\draw (0,0) -- (0,2) -- (1,1) -- (1,0) -- cycle;\n      \\draw (0,2) -- (1,1);\n      \\draw (0,0) -- (1,1);\n      \\begin{scope}[xshift = 4cm, yshift = 0cm]\n\t\\draw (0,0) -- (0,2) -- (1,1) -- (1,0) -- cycle;\n\t\\draw (0,2) -- (1,1);\n\t\\draw (0,0) -- (1,1);\n\t\\draw (1,1) -- (0,2);\n      \\end{scope}\n      \\begin{scope}[xshift = 8cm, yshift = 0cm]\n\t\\draw (0,0) -- (0,2) -- (1,1) -- (1,0) -- cycle;\n\t\\draw (0,2) -- (1,1);\n\t\\draw (0,0) -- (1,1);\n\t\\draw (1,1) -- (0,0);\n\t\\draw (1,0) -- (0,2);\n      \\end{scope}\n    \\end{scope}\n  \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 877,
        "tikz_code": "\\documentclass[12pt, a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usepackage{amsmath}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\t\\node (img)  {\\includegraphics[width=1\\textwidth]{example-image}};\n\t\t\t\\node[below=of img, node distance=0cm, yshift=1.3cm,font=\\color{black}] {\\small{$p_1(s)$}};\n\t\t\t\\node[below=of img, node distance=1cm, yshift=2.2cm,font=\\color{black}] {$B$};\n\t\t\t\\node[right=of img, node distance=0cm, yshift=-1cm,font=\\color{black}] {\\small{$p_2(s)$}};\n\t\t\t\\node[right=of img, node distance=0cm, yshift=-2.3cm,font=\\color{black}] {$B$};\n\t\t\t\\node[below=of img, node distance=0cm, yshift=1.3cm,font=\\color{black}] {\\scriptsize{$K_f(s)$}};\n\t\t\t\\node[left=of img, node distance=0cm, yshift=-0.4cm,font=\\color{black}] {\\small{$\\Omega_1$}};\n\t\t\t\\node[right=of img, node distance=0cm, yshift=-0.7cm,font=\\color{black}] {\\scriptsize{$\\Omega_2$}};\n\t\t\t\\node[above=of img, node distance=0cm, xshift=-3.7cm, yshift=-3.5cm,font=\\color{black}] {\\scriptsize{$\\sigma_f(s)=\\sigma(p_1(s)-\\phi)$}};\n\t\t\t\\node[below=of img, node distance=0cm, yshift=-4.5cm,font=\\color{black}] {\\scriptsize{$D_f$}};\n\t\t\t\\node[above=of img, node distance=0cm, xshift=1.4cm, yshift=-0.5cm,font=\\color{black}] {\\scriptsize{$B_f(s)=0.05$}};\n\t\t\t\\node[below=of img, node distance=0cm, yshift=-5.3cm,font=\\color{black}] {\\scriptsize{$\\sigma_f(s)=\\sigma(p_2(s)-\\phi)$}};\n\t\t\t\\node[below=of img, node distance=0cm, yshift=-6.1cm,font=\\color{black}] {\\scriptsize{$D_f$}};\n\t\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 878,
        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{positioning}\n\\usetikzlibrary{shapes.multipart}\n\n\\begin{document}\n\n\\begin{tikzpicture}[every text node part/.style={align=center}]\n  \\pgfmathsetmacro{\\blockwidth}{4.8}\n  \\pgfmathsetmacro{\\blockoffset}{2.7}\n\n  % Hard-coded block positions\n  \\pgfmathsetmacro{\\prevx}{\\blockoffset+0.3}\n  \\pgfmathsetmacro{\\currx}{\\prevx+\\blockwidth}\n  \\pgfmathsetmacro{\\nextx}{\\currx+0.2}\n\n  \\draw [draw=black] (0,0) rectangle (10,\\blockwidth) node[pos=.5] {Hard Soft\\\\Perturb Loss\\\\TAA (1.3ms)};\n  \\draw [draw=black,fill=gray] (0,0) rectangle (10,2.7) node[pos=.5] {Restoration\\\\ Image};\n  \\draw [draw=black,fill=gray] (0,2.7) rectangle (10,3.4) node[pos=.5] {Bistro\\\\ Baked\\\\ Pizza\\\\ Objects};\n  \\draw [draw=black,fill=gray] (0,3.4) rectangle (10,4.2) node[pos=.5] {Bistro\\\\ Mini\\\\ Tacos\\\\ Objects};\n  \\draw [draw=black,fill=gray] (0,4.2) rectangle (10,6.1) node[pos=.5] {Bistro\\\\ Cookies\\\\ Eggs\\\\ Objects};\n  \\draw [draw=black,fill=gray] (0,6.1) rectangle (10,7.6) node[pos=.5] {Dinner\\\\ Salad\\\\ Objects};\n  \\draw [draw=black,fill=gray] (0,7.6) rectangle (10,8.2) node[pos=.5] {Bistro\\\\ Cucumber\\\\ Salad\\\\ Objects};\n  \\draw [draw=black,fill=gray] (0,8.2) rectangle (10,8.8) node[pos=.5] {Bistro\\\\ Spaghetti\\\\ Objects};\n  \\draw [draw=black,fill=gray] (0,8.8) rectangle (10,10) node[pos=.5] {Conf\\\\ Sponza\\\\ Room};\n  \\draw [draw=black,fill=gray] (0,10) rectangle (10,11) node[pos=.5] {Bistro\\\\ Funny\\\\ Dish\\\\ Objects};\n  \\draw [draw=black,fill=gray] (0,11) rectangle (10,11.7) node[pos=.5] {Bistro\\\\ Wine\\\\ Glass\\\\ Objects};\n\n  \\draw [draw=black,fill=gray] (11.5,2.7) rectangle (10,11.7) node[pos=.5] {Sponza\\\\ Room};\n  \\draw [draw=black,fill=gray] (11.5,3.4) rectangle (10,11) node[pos=.5] {Sponza\\\\ Room};\n\n  \\draw [draw=black,fill=gray] (13,2.7) rectangle (10,11) node[pos=.5] {Sponza\\\\ Room};\n  \\draw [draw=black,fill=gray] (13,3.4) rectangle (10,11) node[pos=.5] {Sponza\\\\ Room};\n  \\draw [draw=black,fill=gray] (13,4.2) rectangle (10,11) node[pos=.5] {Sponza\\\\ Room};\n  \\draw [draw=black,fill=gray] (13,6.1) rectangle (10,11) node[pos=.5] {Sponza\\\\ Room};\n  \\draw [draw=black,fill=gray] (13,7.6) rectangle (10,11) node[pos=.5] {Sponza\\\\ Room};\n  \\draw [draw=black,fill=gray] (13,8.2) rectangle (10,11) node[pos=.5] {Sponza\\\\ Room};\n  \\draw [draw=black,fill=gray] (13,8.8) rectangle (10,11) node[pos=.5] {Sponza\\\\ Room};\n  \\draw [draw=black,fill=gray] (13,10) rectangle (10,11) node[pos=.5] {Sponza\\\\ Room};\n  \\draw [draw=black,fill=gray] (13,11) rectangle (10,11.7) node[pos=.5] {Sponza\\\\ Room};\n  \\draw [draw=black,fill=gray] (13,11.7) rectangle (10,11) node[pos=.5] {Sponza\\\\ Room};\n  \\draw [draw=black,fill=gray] (13,11) rectangle (10,11.7) node[pos=.5] {Sponza\\\\ Room};\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 879,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amsmath,amssymb,amsfonts,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usepackage{tikz-qtree}\n\\usetikzlibrary{backgrounds}\n\n\\begin{document}\n\n\\begin{tikzpicture}[baseline=0]\n\\draw (0,0) -- (0,1) -- (2,1) -- (2,0) -- (0,0);\n\\draw[red] (1,0) -- (1,.2) (1,1) -- (1,1.3);\n\\draw (1,.8) node[left]{\\scriptsize$\\pm\\frac1n$};\n\\draw (.5,.5) node[right]{\\scriptsize$\\pm1$};\n\\draw (1.5,.5) node[left]{\\scriptsize$\\pm1$};\n\\draw (1,.8) -- (1,.95) (1,1.15) -- (1,1.3);\n\\draw (1,1.5) node{\\scriptsize$\\vdots$};\n\\draw (1,-.5) node{\\scriptsize$\\eta$};\n\\draw (3,0) -- (3,1) -- (5,1) -- (5,0) -- (3,0);\n\\draw[red] (4,0) -- (4,.2) (4,1) -- (4,1.3);\n\\draw (4,.8) node[left]{\\scriptsize$\\pm\\frac1n$};\n\\draw (3.5,.5) node[right]{\\scriptsize$\\pm1$};\n\\draw (4.5,.5) node[left]{\\scriptsize$\\pm1$};\n\\draw (4,.8) -- (4,.95) (4,1.15) -- (4,1.3);\n\\draw (4,1.5) node{\\scriptsize$\\vdots$};\n\\draw (4,-.5) node{\\scriptsize$\\eta$};\n\\draw (6,0) -- (6,1) -- (8,1) -- (8,0) -- (6,0);\n\\draw[red] (7,0) -- (7,.2) (7,1) -- (7,1.3);\n\\draw (7,.8) node[left]{\\scriptsize$\\pm\\frac1n$};\n\\draw (6.5,.5) node[right]{\\scriptsize$\\pm1$};\n\\draw (7.5,.5) node[left]{\\scriptsize$\\pm1$};\n\\draw (7,.8) -- (7,.95) (7,1.15) -- (7,1.3);\n\\draw (7,1.5) node{\\scriptsize$\\vdots$};\n\\draw (7,-.5) node{\\scriptsize$\\eta$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 880,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture} [>=stealth',shorten >=1pt,auto,node distance=3cm,\n                    thick,main node/.style={draw,font=\\sffamily\\bfseries}]\n \\node (a) at (-2,0) {};\n \\node (u) at (1.5,1.5) {};\n \\node (d) at (-2,-2) {};\n \\node (x) at (-2,1.5) {};\n \\node (y) at (-.5,-2) {};\n \\node (z) at (1.5,-2) {};\n \\node (m) at (1.5,-.5) {};\n \\node (n) at (1.5,.5) {};\n \\node (b) at (1.5,0) {};\n \\node (c) at (-.5,1.5) {};\n \\node (s) at (1.5,-.5) {};\n \\node (r) at (.5,-.5) {};\n \\node (t) at (-.5,.5) {};\n \\node (q) at (-.5,1.5) {};\n \\node (v) at (-.5,-.5) {};\n \\node (w) at (.5,1.5) {};\n \\node (e) at (.5,.5) {};\n \\node (f) at (-.5,-.5) {};\n \\node (j) at (-.5,0) {};\n \\node (k) at (-.5,-1.5) {};\n \\node (l) at (-1.5,0) {};\n \\node (g) at (-1.5,-1.5) {};\n \\node (p) at (-.5,1.5) {};\n \\node (i) at (-1.5,1.5) {};\n \\node (o) at (-1.5,-.5) {};\n \\node (aa) at (2.25,0) {$m=2^N$};\n \\node (bb) at (2.25,-1.25) {$m=2^{N-1}$};\n \\node (cc) at (2.25,1.25) {$m=1$};\n \\node (dd) at (1.5,2.25) {$n=1$};\n \\node (ee) at (2.25,-2.25) {$n=1$};\n \\node (ff) at (0,2.25) {$i$};\n \\node (gg) at (-2.25,-2.25) {$1$};\n \\node (hh) at (-2.25,0) {$j$};\n \\node (ii) at (0,-2.25) {$j$};\n \\node (jj) at (1.25,0) {$N$};\n \\node (kk) at (-.5,0) {$N$};\n \\node (ll) at (-2.25,-.5) {$0$};\n \\node (mm) at (-1.25,-1.25) {$1$};\n \\node (nn) at (.5,-1.25) {$N$};\n \\node (oo) at (-.5,-1.25) {$N$};\n \\node (pp) at (.5,-2.25) {$N$};\n \\node (qq) at (-1.25,-2.25) {$0$};\n \\node (rr) at (-2.25,-.5) {$1$};\n \\draw [->] (a) to (b);\n \\draw [->] (b) to (x);\n \\draw [->] (b) to (y);\n \\draw [->] (b) to (z);\n \\draw [->] (d) to (x);\n \\draw [->] (d) to (y);\n \\draw [->] (d) to (z);\n \\draw [->] (u) to (x);\n \\draw [->] (u) to (y);\n \\draw [->] (u) to (z);\n \\draw [->] (r) to (m);\n \\draw [->] (m) to (s);\n \\draw [->] (m) to (w);\n \\draw [->] (n) to (m);\n \\draw [->] (n) to (v);\n \\draw [->] (n) to (t);\n \\draw [->] (n) to (q);\n \\draw [->] (t) to (c);\n \\draw [->] (t) to (w);\n \\draw [->] (w) to (c);\n \\draw [->] (s) to (r);\n \\draw [->] (r) to (e);\n \\draw [->] (v) to (f);\n \\draw [->] (f) to (q);\n \\draw [->] (e) to (u);\n \\draw [->] (q) to (u);\n \\draw [->] (f) to (u);\n \\draw [->] (g) to (l);\n \\draw [->] (l) to (a);\n \\draw [->] (l) to (g);\n \\draw [->] (g) to (d);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 881,
        "tikz_code": "\\documentclass[preprint,authoryear,12pt]{elsarticle}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows, arrows.meta}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{calc}\n\\usepackage{amsmath,amssymb,amsthm}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.0]\n\t\t\\node (label) at (0,0) {\\includegraphics[width=0.6\\textwidth]{example-image}};\n\t\t\\foreach \\x in {-4.1,-3.1,-2.1,-1.1,0.1,1.1,2.1,3.1,4.1} {\n\t\t\t\\draw[thick] (\\x,-1.4) -- (\\x,1.4);\n\t\t}\n\t\t\\foreach \\y in {-1.4,-0.4,0.4,1.4} {\n\t\t\t\\draw[thick] (-4.7,\\y) -- (4.7,\\y);\n\t\t}\n\t\t\\foreach \\x in {-4,-3,-2,-1,0,1,2,3,4} {\n\t\t\t\\foreach \\y in {-1.4,-0.4,0.4,1.4} {\n\t\t\t\t\\draw[fill=blue] (\\x,\\y) circle (0.1cm);\n\t\t\t\t\\draw[fill=orange] (\\x+0.125,\\y-0.125) circle (0.1cm);\n\t\t\t\t\\draw[fill=green] (\\x-0.125,\\y+0.125) circle (0.1cm);\n\t\t\t\t\\draw[fill=brown] (\\x+0.25,\\y) circle (0.1cm);\n\t\t\t}\n\t\t}\n\t\t\\node at (4.8,0.6) {(a)};\n\t\t\\node at (4.8,0) {(b)};\n\t\t\\node at (4.8,-0.6) {(c)};\n\t\t\n\t\t\\node at (-2.25,-0.3) {\\scriptsize $(x_0,y_0)$};\n\t\t\\node at (-1.55,0.15) {\\scriptsize $(x_0,y_0)$};\n\t\t\\node at (-2.8,-0.6) {\\scriptsize $(x_0,y_0)$};\n\t\t\n\t\t\\node at (-0.15,-1.1) {\\scriptsize $(x,y)$};\n\t\t\\node at (-0.3,0.9) {\\scriptsize $(x,y)$};\n\t\t\\node at (-1.4,-0.9) {\\scriptsize $(x,y)$};\n\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 882,
        "tikz_code": "\\documentclass[twocolumn]{article}\n\\usepackage{amsmath,epsfig}\n\\usepackage{amsmath}\n\\usepackage{tikz, graphicx}\n\\usepackage[T1]{fontenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.25]\n     \\node (img) {\\includegraphics[scale=0.13]{example-image}};\n     \\node (img2) at (12,0) {\\includegraphics[scale=0.13]{example-image}};\n     \\draw[->] [ultra thick](1.5, 7).. controls (2, 1) and (6, -1) ..(11, 7);\n     \\draw[->, dotted] [ultra thick](-5, 4).. controls (-4, 4) and (-2.2, 1) ..(0, 4);\n     \\draw[->, dotted] [ultra thick](-6, -4).. controls (-4, -4) and (-1.5, -1) ..(0, -4);\n     \\draw [thick] (5.3,-3.5)--(7.5,-3.5);\n     \\node [below] at (6.8, -3.5) {$k$};\n     \\node [below] at (7.5, -3.5) {$\\dot{k}$};\n     \\draw [thick] (5.3,-3.5)--(5.3,3);\n     \\draw [thick] (7.5,-3.5)--(7.5,3);\n     \\node [below] at (5.3, -3.5) {$-1$};\n     \\node [below] at (7.5, -3.5) {$1$};\n     \\node [below] at (3, -2) {$h_{k-1}$};\n     \\node [below] at (11, -2) {$h_k$};\n     \\draw [ultra thick, red, dashed] (2.1, 2.1).. controls (2.5, 2) and (2.5, 1.5) ..(2.5, 1.5);\n     \\draw [ultra thick, red, dashed] (11, 2.1).. controls (11.4, 2) and (11.4, 1.5) ..(11.4, 1.5);\n     \\draw [ultra thick, red, dashed] (9, -2.1).. controls (9.3, -2) and (9.3, -1.5) ..(9.3, -1.5);\n     \\draw [ultra thick, red, dashed] (8, -2.1).. controls (8.2, -2) and (8.2, -1.5) ..(8.2, -1.5);\n     \\node [below] at (8.7, -1.5) {$D_0$};\n     \\node [below] at (2.9, -1.5) {$D_0$};\n     \\node [red] (theta) at (7.5, 2.2) {\\rotatebox{23}{\\scalebox{1.5}{$\\theta_{k-1}$}}};\n     \\draw[->,red, ultra thick] (11, 2.1) .. controls (10, 2.6) and (9.2, 1.8) ..(8.2, 1.5);\n     \\draw[->,red, ultra thick] (9, -2.1) .. controls (9.2, -2.6) and (10, -1.8) ..(11, -1.5);\n     \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 883,
        "tikz_code": "\\documentclass[a4paper]{article}\n\\usepackage{amsmath,amsfonts,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,automata}\n\\usepackage{color}\n\n\\newcommand{\\x}{\\mathbf{x}}\n\n\\newcommand{\\y}{\\mathbf{y}}\n\n\\newcommand{\\u}{\\mathbf{u}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n\tscale=0.8,\n\ttransform shape,\n\t>=stealth',\n\tshorten >=1pt,\n\tauto,\n\tnode distance=2.8cm,\n\tevery state/.style={rectangle,rounded corners,draw=blue!40,fill=blue!20,very thick},\n\taccepting/.style={accepting by arrow}\n\t]\n\t\n\t\\node[state] (q0) {$\\overline{q_0}$};\n\t\\node[state,right of=q0] (q1) {$\\overline{q_1}$};\n\t\\node[right of=q1,draw=red] (qd) {$\\dots$};\n\t\\node[state,right of=qd] (qn) {$\\overline{q_n}$};\n\t\\node[state,right of=qn,draw=red] (qf) {$\\dots$};\n\t\\node[state,right of=qf] (qk) {$\\overline{q_k}$};\n\t\\node[state,accepting,above of=qn] (qn1) {$\\overline{q_{n+1}}$};\n\t\\node[state,accepting,below of=qn] (qn2) {$\\overline{q_{n+2}}$};\n\t\\node[above of=qk,draw=red] (qdk) {$\\dots$};\n\t\\node[right of=qdk,draw=red] (qdq) {$\\dots$};\n\t\\node[state,accepting,right of=qdq] (qq) {$\\overline{q_q}$};\n\t\\node[right of=qq] (qq2) {$\\dots$};\n\t\\node[right of=qq2] (qq1) {$\\overline{q_{q-1}}$};\n\t\n\t\\node[below of=qk] (q11) {$W_{0\\rightarrow k}$};\n\t\\node[below of=qn] (q12) {$W_{0\\rightarrow n}$};\n\t\\node[below of=qn1] (q13) {$W_{0\\rightarrow n+1}$};\n\t\\node[below of=qn2] (q14) {$W_{0\\rightarrow n+2}$};\n\t\\node[right of=q11,draw=red] (q15) {$\\dots$};\n\t\\node[right of=q15,draw=red] (q16) {$\\dots$};\n\t\n\t\\node[right of=q16] (q17) {$W_k$};\n\t\n\t\\node[right of=q17] (q18) {$X_{0\\rightarrow k}$};\n\t\\node[right of=q18] (q19) {$Y_{0\\rightarrow k}$};\n\t\\node[right of=q19] (q20) {$\\overline{X_{k+1}}$};\n\t\\node[right of=q20] (q21) {$\\overline{Y_{k+1}}$};\n\t\\node[right of=q21,draw=red] (q22) {$\\dots$};\n\t\\node[right of=q22,draw=red] (q23) {$\\dots$};\n\t\\node[right of=q23] (q24) {$\\overline{X_{q}}$};\n\t\\node[right of=q24] (q25) {$\\overline{Y_{q}}$};\n\t\\node[below of=q20] (q26) {$X_{0\\rightarrow q}$};\n\t\\node[right of=q26] (q27) {$Y_{0\\rightarrow q}$};\n\t\n\t\\node[right of=q21,draw=red] (q28) {$\\dots$};\n\t\\node[right of=q28,draw=red] (q29) {$\\dots$};\n\t\n\t\\path[->,red] (q0) edge[bend left] node[above] {$do(Y_0)$} (qn1);\n\t\\path[->,red] (qn1) edge[bend left] node[below] {$do(Y_0)$} (q0);\n\t\\path[->,red] (q1) edge[bend left] node[above] {$do(Y_1)$} (qn2);\n\t\\path[->,red] (qn2) edge[bend left] node[below] {$do(Y_1)$} (q1);\n\t\n\t\\path[->] (q0) edge[bend right] node[above] {$do(\\x_1)$} (q1);\n\t\\path[->] (q1) edge[bend right] node[above] {$do(\\x_2)$} (q2);\n\t\\path[->] (q2) edge[bend right] node[above] {$do(\\x_3)$} (q3);\n\t\\path[->] (q3) edge[bend right] node[above] {$do(\\x_{q-1})$} (qq);\n\t\\path[->] (qq) edge[bend right] node[above] {$do(\\x_{q})$} (qq1);\n\t\\path[->] (qq1) edge[bend right] node[above] {$do(\\x_{q+1})$} (qq2);\n\t\n\t\\path[->] (qn1) edge[bend left] node[above] {$do(\\x_n)$} (qn);\n\t\\path[->] (qn) edge[bend left] node[above] {$do(\\x_{n+1})$} (qn1);\n\t\\path[->] (qn) edge[bend right] node[above] {$do(\\x_{n+2})$} (qk);\n\t\\path[->] (qk) edge[bend right] node[above] {$do(\\x_{k+1})$} (qk1);\n\t\\path[->] (qk1) edge[bend right] node[above] {$do(\\x_{k+2})$} (qk2);\n\t\n\t\\path[->] (qk) edge[bend right] node[above] {$do(\\y_k)$} (q1);\n\t\\path[->] (qn) edge[bend right] node[above] {$do(\\y_{n})$} (q1);\n\t\\path"
    },
    {
        "index": 884,
        "tikz_code": "\\documentclass[tikz, border=2mm]{standalone}\n\\usepackage{tikz}\n\\usetikzlibrary{backgrounds,calc}\n\n\\newcommand{\\number}[1]{\n  \\pgfmathsetmacro{\\x}{1.5*#1}\n  \\pgfmathsetmacro{\\y}{sin(deg(#1))*2}\n  \\pgfmathsetmacro{\\color}{int(mod(#1, 3)-1)}\n  \\pgfmathsetmacro{\\fillcolor}{int(mod(#1, 3))}\n  \\pgfmathsetmacro{\\fill}{int(mod(#1, 3)-1)}\n  \\node[inner sep=1.2pt, circle, draw=black] at (\\x, \\y) {};\n  \\begin{scope}[on background layer]\n    \\node[inner sep=1.3pt, circle, draw=black, fill=white,] at (\\x, \\y) {};\n    \\fill (\\x-0.05, \\y) circle [x radius=0.1cm, y radius=0.1cm];\n    \\fill (\\x+0.05, \\y) circle [x radius=0.1cm, y radius=0.1cm];\n  \\end{scope}\n  \\pgfmathsetmacro{\\myfillcolor}{{\\color==0 ? \"magenta\" : \\color==1 ? \"cyan\" : \"black\"}}\n  \\fill[\\myfillcolor] (\\x, \\y) circle [x radius=0.1cm, y radius=0.1cm];\n  \\pgfmathsetmacro{\\myfillcolor}{int(mod(\\color,3)-1)}\n  \\fill[\\myfillcolor] (\\x, \\y) circle [x radius=0.1cm, y radius=0.1cm];\n  \\fill (\\x, \\y) circle [x radius=0.1cm, y radius=0.1cm];\n}\n\n\\begin{document}\n\\begin{tikzpicture}\n  \\foreach \\i in {0, 0.5, ..., 2} {\n    \\foreach \\j in {0, 0.5, ..., 2} {\n      \\number{\\i + \\j}\n    }\n  }\n\\end{tikzpicture}\n\\begin{tikzpicture}\n  \\foreach \\i in {0, 0.5, ..., 2} {\n    \\foreach \\j in {0, 0.5, ..., 2} {\n      \\number{\\i - \\j}\n    }\n  }\n\\end{tikzpicture}\n\\begin{tikzpicture}\n  \\foreach \\i in {0, 0.5, ..., 2} {\n    \\foreach \\j in {0, 0.5, ..., 2} {\n      \\number{\\j - \\i}\n    }\n  }\n\\end{tikzpicture}\n\\end{document}"
    },
    {
        "index": 885,
        "tikz_code": "\\documentclass[a4paper]{article}\n\\usepackage{tikz}\n\\usetikzlibrary{automata,positioning,decorations.text,topaths,arrows.meta,decorations.pathmorphing,quotes,bending}\n\\usepackage{amssymb}\n\\usepackage{xcolor}\n\\usepackage{amsmath}\n\n\\begin{document}\n\n\\begin{tikzpicture}[shorten >=1pt,node distance=0.4cm,on grid,auto]\n  \\tikzstyle{every state}+=[inner sep=0pt]\n\n  \\node[state, initial, rectangle, inner sep=0.3mm, minimum size=0.4cm] (q_0) {$a$};\n  \\node[state, rectangle, inner sep=0.3mm, minimum size=0.4cm] (q_1) [right=of q_0] {$a$};\n  \\node[state, rectangle, inner sep=0.3mm, minimum size=0.4cm] (q_2) [right=of q_1] {$b$};\n  \\node[state, rectangle, inner sep=0.3mm, minimum size=0.4cm] (q_3) [right=of q_2] {$c$};\n  \\node[state, rectangle, inner sep=0.3mm, minimum size=0.4cm] (q_4) [right=of q_3] {$a$};\n  \\node[state, rectangle, inner sep=0.3mm, minimum size=0.4cm] (q_5) [right=of q_4] {$c$};\n  \\node[state, rectangle, inner sep=0.3mm, minimum size=0.4cm] (q_6) [right=of q_5] {$b$};\n  \\node[state, rectangle, inner sep=0.3mm, minimum size=0.4cm] (q_7) [right=of q_6] {$c$};\n  \\node[state, rectangle, inner sep=0.3mm, minimum size=0.4cm] (q_8) [right=of q_7] {$a$};\n  \\node[state, rectangle, inner sep=0.3mm, minimum size=0.4cm] (q_9) [right=of q_8] {$b$};\n\n  \\path[->]\n  (q_0) edge [in=120,out=120,loop] node [pos=0.05, above] {\\footnotesize$0$} (q_0)\n  (q_0) edge [bend left,out=240,in=120] node [pos=0.05, above] {\\footnotesize$1$} (q_1)\n  (q_1) edge [bend left,out=240,in=120] node [pos=0.05, above] {\\footnotesize$2$} (q_2)\n  (q_2) edge [bend left,out=240,in=120] node [pos=0.05, above] {\\footnotesize$3$} (q_3)\n  (q_3) edge [bend left,out=240,in=120] node [pos=0.05, above] {\\footnotesize$4$} (q_4)\n  (q_4) edge [bend left,out=240,in=120] node [pos=0.05, above] {\\footnotesize$5$} (q_5)\n  (q_5) edge [bend left,out=240,in=120] node [pos=0.05, above] {\\footnotesize$6$} (q_6)\n  (q_6) edge [bend left,out=240,in=120] node [pos=0.05, above] {\\footnotesize$7$} (q_7)\n  (q_7) edge [bend left,out=240,in=120] node [pos=0.05, above] {\\footnotesize$8$} (q_8)\n  (q_8) edge [bend left,out=240,in=120] node [pos=0.05, above] {\\footnotesize$9$} (q_9)\n  (q_9) edge [bend left,out=240,in=120] node [pos=0.05, below] {\\footnotesize$\\bot$} (q_0)\n  (q_9) edge [bend left,out=240,in=120] node [pos=0.05, below] {\\footnotesize$\\bot$} (q_1)\n  (q_8) edge [bend left,out=240,in=120] node [pos=0.05, below] {\\footnotesize$\\bot$} (q_2)\n  (q_7) edge [bend left,out=240,in=120] node [pos=0.05, below] {\\footnotesize$\\bot$} (q_3)\n  (q_6) edge [bend left,out=240,in=120] node [pos=0.05, below] {\\footnotesize$\\bot$} (q_4)\n  (q_5) edge [bend left,out=240,in=120] node [pos=0.05, below] {\\footnotesize$\\bot$} (q_5)\n  (q_4) edge [bend left,out=240,in=120] node [pos=0.05, below] {\\footnotesize$\\bot$} (q_6)\n  (q_3) edge [bend left,out=240,in=120] node [pos=0.05, below] {\\footnotesize$\\bot$} (q_7)\n  (q_2) edge [bend left,out=240,in=120] node [pos=0.05, below] {\\footnotesize$\\bot$} (q_8)\n  (q_1) edge [bend left,out=240,in=120] node [pos=0.05, below] {\\footnotesize$\\bot$} (q_9);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 886,
        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage{tikz-3dplot}\n\\usetikzlibrary{shapes,shadows,arrows,trees}\n\\usetikzlibrary{trees}\n\\usetikzlibrary{automata,positioning}\n\\usepackage{amsmath}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n\\begin{scope}\n\\draw (0,0) ellipse (0.5 and 1);\n\\draw (0,-1) -- (8,-1);\n\\draw (0,1) -- (8,1);\n\\draw (8,-1) arc (270:90:0.5 and 1);\n\\draw[dashed] (8,1) arc (90:-90:0.5 and 1);\n\\draw (8,-1.5) node {\\footnotesize{likes on zero section}};\n\\draw (-1.5,-0.5) node {\\footnotesize{orbit of $\\mathcal{X}_i$}};\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
    },
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        "index": 887,
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amssymb, amsmath, amsthm, fullpage, color, tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.2]\n%%%%%%%%%%% horizontal axis\n\\draw[latex-latex] (-3,0) -- (4,0) ;   -\t\n\\draw (3.5,0) node[below]{$x$};\n\\draw[dotted] (0,0) -- (-3,0);\n\\draw[dotted] (4,0) -- (3,0);\n\\draw[dotted] (3,0) -- (3.8,1);\n\\draw[dotted] (3.8,1) -- (0,1);\n\\draw[dotted] (0,1) -- (-3,1);\n\\draw[dotted] (3,0) -- (4,1);\n\\draw (3.8,1) node[right]{$\\xi$};\n\\draw (-1.5,1) node[right]{$\\xi^\\prime$};\n\\draw[dashed, blue] (0,0) -- (0,1);\n\\draw[dashed, red] (0,0) -- (3.8,1);\n\\draw (0,0) node[below]{$0$};\n\\draw (0,0.8) node[left]{$\\varepsilon$};\n\\draw (1.5,-0.4) node[below]{$-\\tfrac{1}{u(1-\\xi)}$};\n\\draw[latex-latex] (0,0.6) -- (1.5,-0.4) ;   -\t\n\\draw (1.5,-0.2) node[below]{$u(1-\\xi)$};\n\\draw[dashed, blue] (3.8,1) -- (3,0);\n\\draw[dashed, red] (3.8,1) -- (4,0);\n\\draw (3,0) node[below]{$u^\\prime(1-\\xi)$};\n\\draw (4,0) node[below]{$1$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\newcommand{\\SO}{\\mathrm{SO}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\fill (0,0) circle (1.5pt);\n\\draw[dashed] (0,0) -- (0.4,1.7);\n\\draw (0,0) -- (1,1.5);\n\\draw[dashed] (0,0) -- (2,1.7);\n\\draw[dashed] (0,0) -- (2,1.3);\n\\draw (0,0) -- (2,1);\n\\draw[dashed] (0,0) -- (0.4,-1.7);\n\\draw (0,0) -- (1,-1.5);\n\\draw[dashed] (0,0) -- (2,-1.7);\n\\draw (0,0) -- (2,-1.3);\n\\draw (0.4,1.7) node [anchor=south east]{$\\SO(3)$};\n\\draw (0.4,-1.7) node [anchor=north east]{$\\mathcal{J}$};\n\\draw (1,1.5) node [anchor=south west]{$(R_4,R_2,R_1)$};\n\\draw (2,1.7) node [anchor=south west]{$(R_5,R_2,R_1)$};\n\\draw (2,1.3) node [anchor=south east]{$(R_2,R_2,R_1)$};\n\\draw (2,1) node [anchor=south east]{$(R_2,R_3,R_1)$};\n\\draw (1,-1.5) node [anchor=north west]{$(R_2,R_2,R_2)$};\n\\draw (2,-1.7) node [anchor=north west]{$(R_5,R_3,R_1)$};\n\\draw (2,-1.3) node [anchor=north east]{$(R_4,R_3,R_1)$};\n\\fill (1,1.5) circle (1.5pt);\n\\fill (2,1.7) circle (1.5pt);\n\\fill (2,1.3) circle (1.5pt);\n\\fill (2,1) circle (1.5pt);\n\\fill (1,-1.5) circle (1.5pt);\n\\fill (2,-1.7) circle (1.5pt);\n\\fill (2,-1.3) circle (1.5pt);\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{tikz}\n\\usepackage{amsmath}\n\\usetikzlibrary{shapes,positioning}\n\\tikzset{\n\trect/.style={\n\t\trectangle,\n\t\trounded corners,\n\t\tdraw=black, \n\t\tthick,\n\t\ttext centered},\n\trectw/.style={\n\t\trectangle,\n\t\trounded corners,\n\t\tdraw=white, \n\t\tthick,\n\t\ttext centered},\n\trectn/.style={\n\t\trectangle,\n\t\trounded corners,\n\t\tdraw=none, \n\t\tthick,\n\t\ttext centered},\n\tarrow/.style={\n\t\t->,\n\t\tthick,\n\t\tshorten <=2pt,\n\t\tshorten >=2pt},\n\tdash/.style={\n\t\t-,\n\t\tdashed,\n\t\tthick,\n\t\tshorten <=2pt,\n\t\tshorten >=2pt},\n\tpipe/.style={\n\t\t-|,\n\t\tthick,\n\t\tshorten <=2pt,\n\t\tshorten >=2pt,}\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\\node at (3,1.5) {\\includegraphics[scale=.5]{example-image}};\n\t\\node at (8,1.5) {\\includegraphics[scale=.5]{example-image}};\n\t\\node at (3,-1.5) {\\includegraphics[scale=.5]{example-image}};\n\t\\node at (8,-1.5) {\\includegraphics[scale=.5]{example-image}};\n\t\\node at (0,5) {\\includegraphics[scale=.7]{example-image}};\n\t\\node at (10,5) {\\includegraphics[scale=.7]{example-image}};\n\t\\node[rectw] (t1) at (3,4.5) {$f_x$};\n\t\\node[rectw] (t2) at (8,4.5) {$f_y$};\n\t\\node[rectw] (s1) at (3,2.5) {$h_x$};\n\t\\node[rectw] (s2) at (8,2.5) {$h_y$};\n\t\\node[rectw] (q1) at (3,-0.5) {$D_x(\\vec{x})$};\n\t\\node[rectw] (q2) at (8,-0.5) {$D_y(\\vec{y})$};\n\t\\node[rectw] (s3) at (3,-3) {$t_x(\\vec{x})$};\n\t\\node[rectw] (s4) at (8,-3) {$t_y(\\vec{y})$};\n\t\\node[rectw] (s5) at (5.5,0) {$p_x(\\vec{x}, \\vec{w})$};\n\t\\node[rectw] (s6) at (5.5,-2.5) {$p_y(\\vec{y}, \\vec{w})$};\n\t\\node[rectw] (t3) at (0,0.5) {$u(x)$};\n\t\\node[rectw] (t4) at (10,0.5) {$u(y)$};\n\t\\node[rectw] (t5) at (5.5,-5) {$q_x(\\vec{x})$};\n\t\\node[rectw] (t6) at (5.5,-6.5) {$q_y(\\vec{y})$};\n\t\\node[rectw] (t7) at (2.5,-8.5) {quantized label map};\n\t\\draw[arrow] (0,4.5) -- (t1.north);\n\t\\draw[arrow] (t1.south) -- (0,3);\n\t\\draw[arrow] (s1.south) -- (s3.north);\n\t\\draw[arrow] (s2.south) -- (s4.north);\n\t\\draw[arrow] (0,0) -- (t3.north);\n\t\\draw[arrow] (t3.south) -- (0,1.5);\n\t\\draw[arrow] (t4) -- (t1.east);\n\t\\draw[arrow] (t1.east) -- (t5.west);\n\t\\draw[arrow] (t4.south) -- (t6.north);\n\t\\draw[arrow] (t5.south) -- (s3.west);\n\t\\draw[arrow] (t6.south) -- (s4.west);\n\t\\draw[arrow] (s1.north) -- (s2.south);\n\t\\draw[arrow] (s2.west) -- (s5.north);\n\t\\draw[arrow] (s5.south) -- (s6.north);\n\t\\draw[arrow] (s6.west) -- (s4.east);\n\t\\draw[arrow] (s5.east) -- (10,2.5);\n\t\\draw[arrow] (s6.east) -- (10,-0.5);\n\t\\draw[arrow] (10,-2.5) -- (t5.south);\n\t\\draw[arrow] (t5.south) -- (10,-3.5);\n\t\\draw[arrow] (q1.north) -- (s3.south);\n\t\\draw[arrow] (q2.north) -- (s4.south);\n\t\\draw[arrow] (10,-5) -- (t6.south);\n\t\\draw[arrow] (t6.south) -- (t7.north);\n\t\\node[rectw] at (10,-7) {reconstructed $\\vec{x}$};\n\t\\node[rectw] at (3,5.5) {$\\vec{x}$};\n\t\\node[rectw] at (8,5.5) {$\\vec{y}$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 900,
        "tikz_code": "\\documentclass[12pt,a4paper,reqno]{article}\n\\usepackage{amsmath,amssymb,amsthm,mathrsfs,comment}\n\\usepackage{pgfplots}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{axis}[\n    axis lines = left,\n    xlabel = $\\lambda$,\n    ylabel = {$r$},\n    legend pos= north west,\n    grid=both,\n    clip=false,\n    width=10cm,\n    height=10cm,\n    %ymajorgrids=false,\n    %xmajorgrids=false,\n    %xtick = data,\n    %ytick = data,\n    %xmin=0,     %start of diagram, can be used to shift diagram\n    %xmax=10,\n    %ymin=0,\n    %ymax=100,\n    %axis background/.style={fill=white},\n]\n\n\n\\addplot [\n    domain=0:10, \n    samples=100, \n    color=red,\n]\n{exp(-x)};\n\\addlegendentry{$r = \\exp(- \\lambda )$}\n\n\\addplot [\n    domain=0:10, \n    samples=100, \n    color=blue,\n    dash pattern=on 4pt off 3pt on 1pt off 3pt,\n    ]\n    {exp(-2*x)};\n\\addlegendentry{$r = \\exp(- 2\\lambda )$ and \\eqref{eq:Hilbert-space-bound-II}}\n\n\\addplot [\n    domain=0:10, \n    samples=100, \n    color=orange,\n    style={very thick},\n    ]\n    {exp(-0.5*x)};\n\\addlegendentry{\\eqref{eq:Hilbert-space-bound-I}}\n\n\\addplot [\n    domain=0:10, \n    samples=100, \n    color=black,\n    style={very thick},\n    ]\n    {exp(-3*x)};\n\\addplot [\n    domain=0:10, \n    samples=100, \n    color=black,\n    style={very thick},\n    ]\n    {exp(-1*x)};\n\\addplot [\n    domain=0:10, \n    samples=100, \n    color=black,\n    style={very thick},\n    ]\n    {exp(-2.5*x)};\n\\addplot [\n    domain=0:10, \n    samples=100, \n    color=black,\n    style={very thick},\n    ]\n    {exp(-4*x)};\n\\addplot [\n    domain=0:10, \n    samples=100, \n    color=black,\n    style={very thick},\n    ]\n    {exp(-5*x)};\n\\addplot [\n    domain=0:10, \n    samples=100, \n    color=black,\n    style={very thick},\n    ]\n    {exp(-6*x)};\n\\addplot [\n    domain=0:10, \n    samples=100, \n    color=black,\n    style={very thick},\n    ]\n    {exp(-7*x)};\n\\addplot [\n    domain=0:10, \n    samples=100, \n    color=black,\n    style={very thick},\n    ]\n    {exp(-8*x)};\n\\addplot [\n    domain=0:10, \n    samples=100, \n    color=black,\n    style={very thick},\n    ]\n    {exp(-9*x)};\n\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 901,
        "tikz_code": "\\documentclass[10pt,a4paper,oneside]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix, arrows, calc}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\\tikzstyle{every node}=[draw,rectangle,fill=black]\n\n\\node[fill=white] at (0,0) (0) {};\n\n\\node[fill=white] at (1,0) (1) {};\n\\node[fill=white] at (0,1) (2) {};\n\n\\node[fill=white] at (2,0) (3) {};\n\\node[fill=white] at (1,1) (4) {};\n\\node[fill=white] at (0,2) (5) {};\n\n\\node[fill=white] at (3,0) (6) {};\n\\node[fill=white] at (2,1) (7) {};\n\\node[fill=white] at (1,2) (8) {};\n\\node[fill=white] at (0,3) (9) {};\n\n\\node[fill=white] at (4,0) (10) {};\n\\node[fill=white] at (3,1) (11) {};\n\\node[fill=white] at (2,2) (12) {};\n\\node[fill=white] at (1,3) (13) {};\n\\node[fill=white] at (0,4) (14) {};\n\\node[fill=white] at (5,0) (15) {};\n\\node[fill=white] at (4,1) (16) {};\n\\node[fill=white] at (3,2) (17) {};\n\\node[fill=white] at (2,3) (18) {};\n\n\\draw[line width=1] (0.north east) -- (3.north east) -- (3.south east) -- (0.south east) -- (0.north east);\n\\draw[line width=1] (1.north east) -- (4.north east) -- (4.south east) -- (1.south east) -- (1.north east);\n\\draw[line width=1] (2.north east) -- (5.north east) -- (5.south east) -- (2.south east) -- (2.north east);\n\\draw[line width=1] (3.north east) -- (6.north east) -- (6.south east) -- (3.south east) -- (3.north east);\n\\draw[line width=1] (4.north east) -- (7.north east) -- (7.south east) -- (4.south east) -- (4.north east);\n\\draw[line width=1] (5.north east) -- (8.north east) -- (8.south east) -- (5.south east) -- (5.north east);\n\\draw[line width=1] (6.north east) -- (9.north east) -- (9.south east) -- (6.south east) -- (6.north east);\n\\draw[line width=1] (7.north east) -- (10.north east) -- (10.south east) -- (7.south east) -- (7.north east);\n\\draw[line width=1] (8.north east) -- (11.north east) -- (11.south east) -- (8.south east) -- (8.north east);\n\\draw[line width=1] (9.north east) -- (12.north east) -- (12.south east) -- (9.south east) -- (9.north east);\n\\draw[line width=1] (10.north east) -- (13.north east) -- (13.south east) -- (10.south east) -- (10.north east);\n\\draw[line width=1] (11.north east) -- (14.north east) -- (14.south east) -- (11.south east) -- (11.north east);\n\\draw[line width=1] (12.north east) -- (15.north east) -- (15.south east) -- (12.south east) -- (12.north east);\n\\draw[line width=1] (13.north east) -- (16.north east) -- (16.south east) -- (13.south east) -- (13.north east);\n\\draw[line width=1] (14.north east) -- (17.north east) -- (17.south east) -- (14.south east) -- (14.north east);\n\\draw[line width=1] (15.north east) -- (18.north east) -- (18.south east) -- (15.south east) -- (15.north east);\n\\draw[line width=1] (16.north east) -- (18.north east) -- (18.south east) -- (16.south east) -- (16.north east);\n\\draw[line width=1] (17.north east) -- (18.north east) -- (18.south east) -- (17.south east) -- (17.north east);\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[tikz,border=3.14mm]{standalone}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.16}\n\\begin{document}\n\\begin{tikzpicture}\n\\begin{axis}[axis lines=middle,axis on top,xlabel=$x$,ylabel=$w$,\n  xmin=-3,xmax=3,ymin=-3,ymax=3,\n  domain=-2.9:2.9,samples=101,smooth,\n  xtick=\\empty,ytick=\\empty,\n  every axis plot post/.append style={very thick},\n  clip=false,\n  ]\n  \\addplot[variable=\\t,domain=0:2,red] ({t^2},{t});\n  \\addplot[variable=\\t,domain=-2:0,red] ({t^2},{-t});\n  \\addplot[red] coordinates {(0,0) (2,0)};\n  \\addplot[red] coordinates {(0,0) (0,2)};\n  \\addplot[red] coordinates {(0,0) (-2,0)};\n  \\addplot[red] coordinates {(0,0) (0,-2)};\n  \\node at (axis cs:0,0) [anchor=north west,text=red]{$N=(N/2)^2$};\n  \\node at (axis cs:0,2) [anchor=south,text=red]{$D$};\n\\end{axis}\n\\end{tikzpicture}\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz,xcolor}\n\\usepackage{pgf}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{arrows,automata}\n\\usetikzlibrary{positioning}\n\\usepackage{amssymb}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\n\\draw[fill=cyan] (0,0) circle (0.1);\n\\draw[fill=cyan] (-2,-1) circle (0.1);\n\\draw[fill=cyan] (0,-1) circle (0.1);\n\\draw[fill=cyan] (2,-1) circle (0.1);\n\\draw[fill=cyan] (0,1) circle (0.1);\n\\draw[thick,orange] (0,0) -- (-2,-1);\n\\draw[thick,orange] (0,0) -- (0,-1);\n\\draw[thick,orange] (0,0) -- (2,-1);\n\\draw[thick,orange] (0,0) -- (0,1);\n\\draw[thick,cyan,dashed] (-2,-1) -- (2,-1);\n\n\\draw[fill=cyan] (4,0) circle (0.1);\n\\draw[fill=cyan] (3,-1) circle (0.1);\n\\draw[fill=cyan] (5,-1) circle (0.1);\n\\draw[fill=cyan] (4,1) circle (0.1);\n\\draw[thick,orange] (4,0) -- (3,-1);\n\\draw[thick,orange] (4,0) -- (5,-1);\n\\draw[thick,orange] (4,0) -- (4,1);\n\\draw[thick,orange] (3,-1) -- (5,-1);\n\\draw[thick,orange] (4,1) -- (5,-1);\n\\draw[thick,orange] (3,-1) arc (150:100:2);\n\\draw[thick,orange] (4,1) arc (30:80:2);\n\\draw[thick,cyan,dashed] (3,-1) -- (5,-1);\n\n\\draw[fill=cyan] (8,0) circle (0.1);\n\\draw[fill=cyan] (6,-1) circle (0.1);\n\\draw[fill=cyan] (8,-1) circle (0.1);\n\\draw[fill=cyan] (8,1) circle (0.1);\n\\draw[thick,orange] (8,0) -- (6,-1);\n\\draw[thick,orange] (8,0) -- (8,-1);\n\\draw[thick,orange] (8,0) -- (8,1);\n\\draw[thick,orange] (8,0) arc (60:120:1);\n\\draw[thick,orange] (8,1) arc (120:240:1);\n\\draw[thick,orange] (6,-1) arc (210:240:1);\n\\draw[thick,orange] (8,-1) arc (300:330:1);\n\\draw[thick,cyan,dashed] (8,0) -- (6,-1);\n\\draw[thick,cyan,dashed] (8,0) -- (8,-1);\n\\draw[thick,cyan,dashed] (8,0) -- (8,1);\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amsthm,amsfonts,latexsym,amsopn,verbatim,amscd,amssymb}\n\\usepackage{pgfplots}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{axis}\n[\nxlabel={houses \\ build},\nylabel={worker utility},\nxmin=1, xmax=11000,\nymin=0, ymax=1100,\ngrid = both,\nminor tick num = 1,\nmajor grid style = {lightgray},\nminor grid style = {lightgray!25},\nwidth=.5\\textwidth,\nheight=.5\\textwidth,\nlegend style={legend pos=north west},\n ]\n\\addplot[domain=1:2000,samples=100,color=red,style=dashed]{(1.1*x^0.46+30*x^0.35+2.2*10^(-4)*x^1.9)};\n\\tiny\n\\addlegendentry{$s=1$}\n\\addplot[domain=1:2000,samples=100,color=green,style=dashed]{(1.1*x^0.46+50*x^0.25+2.2*10^(-4)*x^1.1)};\n\\tiny\n\\addlegendentry{$s=2$}\n\\addplot[domain=1:2000,samples=100,color=blue,style=dashed]{(1.1*x^0.46+80*x^0.08+2.2*10^(-4)*x^1.0)};\n\\tiny\n\\addlegendentry{$s=3$}\n\\addplot[domain=1:2000,samples=100,color=black]{(1.1*x^0.46+150*x^-0.1+2.2*10^(-4)*x^1.1)};\n\\tiny\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 905,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.6]\n  \\draw [gray] (0, 2.8) -- (0,3);\n  \\draw [gray] (0, -3.2) -- (0,-3);\n  \\foreach \\x in {0,...,7}\n  {\n    \\draw [gray] (2*\\x,3) -- (2*\\x,2.8) -- (2*\\x+2,3) -- (2*\\x+2,0) -- (2*\\x+1,1) -- (2*\\x,1) -- (2*\\x,0);\n    \\draw [gray] (2*\\x+1,1) -- (2*\\x+1,0) -- (2*\\x+1.5,2.8/3) -- (2*\\x+0.5,0) -- (2*\\x,1);\n    \\draw [gray] (2*\\x,2.8) -- (2*\\x+1,2.8) -- (2*\\x+0.5,2.8/3) -- (2*\\x+0.5,0);\n  }\n  \\draw (7.5,0) node[below] {$n_4=18$};\n  \\draw (7.5,1) node[below] {$n_3=16$};\n  \\draw (7.5,2.8/3) node[below] {$n_2=6$};\n  \\draw (7.5,3) node[below] {$n_1=4$};\n\n  \\draw (1.5,-1) node[below] {$2n_3+n_4=30$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 906,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{amsmath, amsfonts,amssymb,mathtools,nicefrac,nccmath,cases}\n\\usepackage[usenames,dvipsnames,table]{xcolor}\n\\usepackage{colortbl}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,arrows}\n\\usetikzlibrary{calc,shapes.callouts,shapes.arrows,bending,intersections}\n\\usetikzlibrary{shapes.geometric}\n\\usetikzlibrary{arrows.meta,arrows}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{shapes.multipart}\n\\usetikzlibrary{tikzmark}\n\\usepackage{colortbl}\n\\usepackage{xcolor}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\node[inner sep=0pt, draw, circle, line width=0.45pt] (plus) at (0, 0) {\\Large $+$};\n    \\node[inner sep=0pt, draw, rectangle split, rectangle split horizontal, rectangle split parts=5, line width=0.45pt] (image) at (0, -1) {\\includegraphics[width=0.15\\textwidth]{example-image}\\nodepart{two}\\includegraphics[width=0.15\\textwidth]{example-image}\\nodepart{three}\\includegraphics[width=0.15\\textwidth]{example-image}\\nodepart{four}\\includegraphics[width=0.15\\textwidth]{example-image}\\nodepart{five}\\includegraphics[width=0.15\\textwidth]{example-image}};\n    \\node[inner sep=0pt, draw, rectangle, line width=0.45pt] (input) at (0, -4) {\\includegraphics[width=0.35\\textwidth]{example-image}};\n    \\draw[-{stealth[length=3mm, width=2mm]}, line width=0.45pt] (image) -- (plus);\n    \\draw[-{stealth[length=3mm, width=2mm]}, line width=0.45pt] (input) -- (plus);\n    \\draw[-{stealth[length=3mm, width=2mm]}, line width=0.45pt] (plus) -- (4, 1) node[above, midway] {\\footnotesize 0.25};\n    \\draw[-{stealth[length=3mm, width=2mm]}, line width=0.45pt] (plus) -- (4, -0) node[above, midway] {\\footnotesize 0.34};\n    \\draw[-{stealth[length=3mm, width=2mm]}, line width=0.45pt] (plus) -- (4, -2) node[above, midway] {\\footnotesize 0.06};\n    \\draw[-{stealth[length=3mm, width=2mm]}, line width=0.45pt] (plus) -- (4, -3) node[above, midway] {\\footnotesize 0.03};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 907,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{cd}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{decorations.text}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{arrows.meta}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[yshift=1cm] (270:1)--(330:1)--(30:1)--(-90:1)--(150:1)--(90:1);\n\\draw[yshift=1cm,dotted] (270:1)--(30:1);\n\\draw[yshift=1cm,dotted] (-90:1)--(330:1);\n\\draw[yshift=1cm,dotted] (150:1)--(90:1);\n\\draw[yshift=1cm] (-90:1)--(-30:1);\n\\draw[yshift=1cm] (330:1)--(150:1);\n\\draw[xshift=1cm,dotted] (270:1)--(30:1);\n\\draw[xshift=1cm,dotted] (-90:1)--(330:1);\n\\draw[xshift=1cm,dotted] (150:1)--(90:1);\n\\draw[xshift=1cm] (-90:1)--(-30:1);\n\\draw[xshift=1cm] (330:1)--(150:1);\n\\draw[xshift=1cm,dotted] (270:1)--(90:1);\n\\draw[xshift=1cm,dotted] (30:1)--(150:1);\n\\draw[yshift=1cm,dotted] (270:1)--(90:1);\n\\draw[yshift=1cm,dotted] (330:1)--(30:1);\n\\draw[yshift=1cm,dotted] (-90:1)--(-30:1);\n\\draw[dotted] (0,0) circle(1cm);\n\\draw[fill=black] (0:1) circle(0.05);\n\\draw[fill=black] (30:1) circle(0.05);\n\\draw[fill=black] (60:1) circle(0.05);\n\\draw[fill=black] (90:1) circle(0.05);\n\\draw[fill=black] (120:1) circle(0.05);\n\\draw[fill=black] (150:1) circle(0.05);\n\\draw[fill=black] (180:1) circle(0.05);\n\\draw[fill=black] (210:1) circle(0.05);\n\\draw[fill=black] (240:1) circle(0.05);\n\\draw[fill=black] (270:1) circle(0.05);\n\\draw[yshift=1cm,fill=black] (0:1) circle(0.05);\n\\draw[yshift=1cm,fill=black] (30:1) circle(0.05);\n\\draw[yshift=1cm,fill=black] (60:1) circle(0.05);\n\\draw[yshift=1cm,fill=black] (90:1) circle(0.05);\n\\draw[yshift=1cm,fill=black] (120:1) circle(0.05);\n\\draw[yshift=1cm,fill=black] (150:1) circle(0.05);\n\\draw[yshift=1cm,fill=black] (180:1) circle(0.05);\n\\draw[yshift=1cm,fill=black] (210:1) circle(0.05);\n\\draw[yshift=1cm,fill=black] (240:1) circle(0.05);\n\\draw[yshift=1cm,fill=black] (270:1) circle(0.05);\n\\draw[yshift=1cm,dotted] (30:1)--(90:1);\n\\draw[yshift=1cm,dotted] (60:1)--(150:1);\n\\draw[yshift=1cm,dotted] (210:1)--(270:1);\n\\draw (0,.7) node{$M$};\n\\draw (0,1.5) node{$\\scriptscriptstyle{\\bullet}$};\n\\draw (.15,.7) node{$\\scriptscriptstyle{\\bullet}$};\n\\draw (0,2) node{$\\scriptscriptstyle{\\bullet}$};\n\\draw (0.35,.7) node{$\\scriptscriptstyle{\\bullet}$};\n\\draw (0,3) node{$\\scriptscriptstyle{\\bullet}$};\n\\draw (-.15,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (-.3,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (-.45,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (.15,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (.3,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (.45,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (.6,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (.75,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (1.25,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (1.5,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (1.65,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (1.8,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (1.95,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (2.1,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (2.25,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (2.4,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (2.55,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (2.7,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (2.85,.7) node{$\\scriptscriptstyle{\\circ}$};\n\\draw (3,.7) node{$\\scriptscriptstyle{\\bullet}$};\n\\draw (2.8,1.5) node{$\\scriptscriptstyle{\\bullet"
    },
    {
        "index": 908,
        "tikz_code": "\\documentclass[reqno,a4paper,11pt]{article}\n\\usepackage{amsmath,amsthm,dsfont,amsfonts,amssymb,fancyhdr}\n\\usepackage[usenames,dvipsnames]{color}\n\\usepackage{tikz}\n\\usetikzlibrary[trees]\n\\usepackage[colorlinks=true, allcolors=blue]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\draw (0,0) circle [x radius=1.5, y radius=1];\n    \\draw (0.5,0.6) circle [x radius=0.4, y radius=0.4];\n    \\draw (3.25,0.8) circle [x radius=0.4, y radius=0.4];\n    \\draw (6,0.6) circle [x radius=0.4, y radius=0.4];\n    \\draw (9.75,0.8) circle [x radius=0.4, y radius=0.4];\n    \\draw (1.5,1.2) ellipse (0.6 and 0.6);\n    \\draw (1.5,-1.2) ellipse (0.6 and 0.6);\n    \\draw (5.5,1.2) ellipse (0.6 and 0.6);\n    \\draw (5.5,-1.2) ellipse (0.6 and 0.6);\n    \\draw (9.5,1.2) ellipse (0.6 and 0.6);\n    \\draw (9.5,-1.2) ellipse (0.6 and 0.6);\n\n    \\draw [red, thick] (1.5,0.8) .. controls (1,1.5) and (1,0.5) .. (1.5,-0.8);\n    \\draw [red, thick] (4,0.8) .. controls (3.5,1.5) and (3.5,0.5) .. (4,-0.8);\n    \\draw [red, thick] (6.5,0.8) .. controls (6,1.5) and (6,0.5) .. (6.5,-0.8);\n    \\draw [red, thick] (9,0.8) .. controls (8.5,1.5) and (8.5,0.5) .. (9,-0.8);\n\n    \\draw [blue, thick] (2.25,1.2) .. controls (2.5,0.8) and (2.5,1.2) .. (2.75,1.2);\n    \\draw [blue, thick] (2.75,0) .. controls (2.5,-0.2) and (2.5,0.2) .. (2.75,0);\n    \\draw [blue, thick] (3.75,0) .. controls (3.5,-0.2) and (3.5,0.2) .. (3.75,0);\n    \\draw [blue, thick] (6.25,0) .. controls (6.5,-0.2) and (6.5,0.2) .. (6.25,0);\n    \\draw [blue, thick] (7.25,0) .. controls (7.5,-0.2) and (7.5,0.2) .. (7.25,0);\n    \\draw [blue, thick] (8.25,0) .. controls (8.5,-0.2) and (8.5,0.2) .. (8.25,0);\n    \\draw [blue, thick] (1.75,1.2) .. controls (1.5,0.8) and (1.5,1.2) .. (1.75,1.2);\n\n    \\draw [dashed] (2,2.5) -- (2,2.7);\n    \\draw [dashed] (10,2.5) -- (10,2.7);\n    \\draw [dashed] (0.5,-1.7) -- (0.5,-2.7);\n    \\draw [dashed] (6.5,-1.7) -- (6.5,-2.7);\n    \\draw [dashed] (12,-1.7) -- (12,-2.7);\n\n    \\draw (1.7,0.6) node {$1$};\n    \\draw (5.7,0.6) node {$2$};\n    \\draw (9.7,0.6) node {$3$};\n    \\draw (1.8,1.4) node {$1$};\n    \\draw (5.8,1.4) node {$2$};\n    \\draw (9.8,1.4) node {$3$};\n\n    \\draw (0,0) node {$1$};\n    \\draw (1.5,0) node {$2$};\n    \\draw (3.25,0) node {$3$};\n    \\draw (5.5,0) node {$1$};\n    \\draw (6.5,0) node {$2$};\n    \\draw (7.5,0) node {$3$};\n    \\draw (9,0) node {$1$};\n\n    \\draw (3.25,-2) node {$S_4$};\n    \\draw (6,-2) node {$S_5$};\n    \\draw (9,-2) node {$S_6$};\n    \\draw (10,-2) node {$S_7$};\n    \\draw (1,-2) node {$S_8$};\n\n    \\draw (1.5,-0.8) node {$1$};\n    \\draw (4,-0.8) node {$2$};\n    \\draw (6.5,-0.8) node {$3$};\n    \\draw (9,-0.8) node {$1$};\n\n    \\draw (0,0) .. controls (1.5,1.5) and (1.5,0.5) .. (0.5,0.6);\n    \\draw (1.5,0.8) .. controls (0.5,1.5) and (0.5,0.5) .. (1.5,-0.8);\n    \\draw (0.5,0) .. controls (2.25,1.2) and (2.25,0) .. (0.5,0);\n    \\draw (3.25,0.8) .. controls (2.75,1.2) and (2.75,0) .. (3.25,0.8);\n    \\draw (6,0.6) .. controls (5.5,1.5) and (5.5,0.5) .. (6.5,0.6);\n    \\draw (6.5,0) .. controls (5.5,"
    },
    {
        "index": 909,
        "tikz_code": "\\documentclass[a4paper,11pt,oneside]{amsart}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amssymb}\n\\usepackage[dvipsnames]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix,arrows,decorations.pathmorphing}\n\\usetikzlibrary{patterns}\n\\usepackage[\n\tocgcolorlinks, % cf tex.stackexchange.com/questions/4425/\n\tlinkcolor=BlueViolet, citecolor=OliveGreen, urlcolor=RawSienna, filecolor=Sepia,\n\thyperfootnotes=false,\n\t% hidelinks % TURN OFF FOR DIGITAL VERSION\n\t]{hyperref}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\fill[pattern=north west lines, pattern color=blue!50]\n\t(0,0) -- (0,3) -- (4,0) -- cycle;\n\\node[rotate=45] at (3,2.3)\n\t{implementable with unobservable type};\n\\node[rotate=45] at (2.7,1.4)\n\t{implementable outcome};\n\\node[rotate=-45] at (3.1,0.7)\n\t{no additional information};\n\\draw[thin]\n\t(0,0) node[below] {$0$} -- (0,3)\n\t(0,0) -- (4,0) node[below] {$W=1/4$};\n\\draw[thin]\n\t(0,0) -- (0,3.5)\n\t(4,0) -- (0,3.5) node[left] {$3/2=W$};\n\\draw[ultra thick]\n\t(0,3) -- (4,0);\n\\node at (3.2,2) {implementable outcome with\\\\observable type};\n\\node at (0,-0.7) {$5s=0$};\n\\node at (4.2,-0.7) {$W$};\n\\node at (4.2,2.5) {$U$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 910,
        "tikz_code": "\\documentclass{amsart}\n\\usepackage{amsmath,amssymb,amsthm,amsfonts,mathrsfs,textcomp,mathtools,accents}\n\\usepackage{graphicx,color}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,calc,positioning,spy}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5]\n\n\\fill[fill=gray!20] (-2,0) -- (0,1) -- (-2,1) -- cycle;\n\\fill[fill=gray!20] (-2,0) -- (0,-1) -- (-2,-1) -- cycle;\n\n\\draw[fill] (-2,0) circle (0.05);\n\\draw[fill] (0,1) circle (0.05);\n\\draw[fill] (0,-1) circle (0.05);\n\\draw[thick,dashed] (-2,0) -- (0,1);\n\\draw[thick,dashed] (-2,0) -- (0,-1);\n\\draw[thick,dashed] (-2,0) -- (-4,0);\n\n\\node at (-1.5,0.35) {$(-1,-1)$};\n\\node at (-1.5,-0.2) {$(-1,0)$};\n\\node at (-2.5,1.1) {$(-1,+\\omega_2)$};\n\n\\node at (-0.85,-0.1) {$C_3$};\n\\node at (-2.25,0.25) {$C_2$};\n\\node at (-2.25,0.75) {$C_1$};\n\n\\draw[ultra thick] (-2,0) -- (0,1);\n\\draw[ultra thick] (-2,0) -- (0,-1);\n\n\\begin{scope}[xshift=5cm]\n\\fill[fill=gray!20] (-1,0) -- (1,1) -- (-1,1) -- cycle;\n\\fill[fill=gray!20] (-1,0) -- (1,-1) -- (-1,-1) -- cycle;\n\n\\draw[fill] (-1,0) circle (0.05);\n\\draw[fill] (1,1) circle (0.05);\n\\draw[fill] (1,-1) circle (0.05);\n\\draw[thick,dashed] (-1,0) -- (1,1);\n\\draw[thick,dashed] (-1,0) -- (1,-1);\n\\draw[thick,dashed] (-1,0) -- (-2,0);\n\n\\node at (-0.45,-0.35) {$(-1,n_1)$};\n\\node at (-0.3,-0.3) {$(-1,n_1+1)$};\n\\node at (-2.2,1.1) {$(-1,+\\omega_1)$};\n\n\\node at (-1.8,0.25) {$C_3$};\n\\node at (-1.35,0.25) {$C_2$};\n\\node at (-1.35,0.75) {$C_1$};\n\n\\draw[ultra thick] (-1,0) -- (1,1);\n\\draw[ultra thick] (-1,0) -- (1,-1);\n\\end{scope}\n\n\\begin{scope}[xshift=10cm]\n\\fill[fill=gray!20] (-1,0) -- (1,1) -- (0,1) -- cycle;\n\\fill[fill=gray!20] (-1,0) -- (1,-1) -- (0,-1) -- cycle;\n\n\\draw[fill] (-1,0) circle (0.05);\n\\draw[fill] (1,1) circle (0.05);\n\\draw[fill] (1,-1) circle (0.05);\n\\draw[thick,dashed] (-1,0) -- (1,1);\n\\draw[thick,dashed] (-1,0) -- (1,-1);\n\\draw[thick,dashed] (-1,0) -- (-2,0);\n\n\\node at (-0.45,-0.35) {$(-1,n_1)$};\n\\node at (-0.3,-0.3) {$(-1,n_1+1)$};\n\\node at (-2.2,1.1) {$(-1,+\\omega_1)$};\n\n\\node at (-1.8,0.25) {$C_3$};\n\\node at (-1.35,0.25) {$C_2$};\n\\node at (-1.35,0.75) {$C_1$};\n\n\\draw[ultra thick] (-1,0) -- (1,1);\n\\draw[ultra thick] (-1,0) -- (1,-1);\n\\draw[ultra thick] (0,1) -- (0,-1);\n\\end{scope}\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 911,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amssymb,amsmath,amsthm,enumitem,mathrsfs,mathabx,accents,xy}\n\\usepackage{tikz}\n\\usetikzlibrary{cd}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw (0,0) node [draw,solid,inner sep=2pt,fill=white,rounded corners=5pt] (A) {$B_0$};\n\\draw (1,0.5) node [draw,dashed,inner sep=2pt,fill=white,rounded corners=5pt] (B) {$B_1$};\n\\draw (2,1) node [draw,solid,inner sep=2pt,fill=white,rounded corners=5pt] (C) {$B_2$};\n\\draw (4,0.5) node [draw,dashed,inner sep=2pt,fill=white,rounded corners=5pt] (D) {$B_3$};\n\\draw (6,0.5) node [draw,solid,inner sep=2pt,fill=white,rounded corners=5pt] (E) {$B_{n_3}$};\n\\draw [thick,double,->] (3,0.25) -- (4,0.25);\n\\draw (5,0) node {$\\longrightarrow$};\n\\draw (9,0) node [draw,solid,inner sep=2pt,fill=white,rounded corners=5pt] (F) {$B_0$};\n\\draw (10,1) node [draw,dashed,inner sep=2pt,fill=white,rounded corners=5pt] (G) {$B_1$};\n\\draw (11,0.5) node [draw,dashed,inner sep=2pt,fill=white,rounded corners=5pt] (H) {$B_2$};\n\\draw (13,0.5) node [draw,solid,inner sep=2pt,fill=white,rounded corners=5pt] (I) {$B_{n_3}$};\n\\draw (10,0) node [draw,dashed,inner sep=2pt,fill=white,rounded corners=5pt] (J) {$B_3$};\n\\draw (9,1) node [draw,solid,inner sep=2pt,fill=white,rounded corners=5pt] (K) {$B_{n_3+1}$};\n\\draw (F) -- (G) -- (H) -- (I);\n\\draw (F) -- (J);\n\\draw (H) -- (K);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 912,
        "tikz_code": "\\documentclass[runningheads, a4paper]{llncs}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[final,colorlinks=true,linktocpage=true,hyperfootnotes]{hyperref}\n\\usepackage{pgf}\n\\usepackage{tikz}\n\\usepackage[version=3,arrows=pgf]{mhchem}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{arrows,automata}\n\n\\begin{document}\n\n\\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=2cm,\n                    semithick]\n  \\tikzstyle{every state}=[fill=blue!50,draw=none,text=white]\n\n  \\node[state]  (1) {$x_0$};\n  \\node[state]  (2) [right of = 1] {$x_1$};\n  \\node[state]  (3) [right of = 2] {$x_2$};\n  \\path (1) edge [bend right] node {$E_1$} (2)\n        (2) edge [bend right] node {$E_2$} (3)\n        (3) edge [bend right] node {$E_1$} (2)\n        (2) edge [bend right] node {$E_2$} (1)\n        (1) edge [loop left] node {$E_0$} (1);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 913,
        "tikz_code": "\\documentclass[a4paper,12pt]{article}\n\\usepackage{amsmath, amssymb, amsthm}\n\\usepackage{graphicx,color}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.9, transform shape]\n\\begin{scope}\n \\clip (-2.5,-2.5) rectangle (2.5,2.5);\n \\draw[fill=yellow,fill opacity=0.5, rotate=135] (0,0) rectangle (2.5,2.5);\n \\draw[fill=red,fill opacity=0.5] (0,0) rectangle (-2.5,2.5);\n \\draw[fill=yellow,fill opacity=0.5, rotate=45] (0,0) rectangle (2.5,2.5);\n \\draw[fill=red,fill opacity=0.5] (0,0) rectangle (-2.5,-2.5);\n\\end{scope}\n\\draw[thick,color=black,->, >=stealth](-3,0)--(3,0)node[left,below,font=\\small]{$\\mu_1+\\mu_2=-\\lambda$};\n\\draw[thick,color=black,->, >=stealth](0,-2.8)--(0,3)node[right,font=\\small]{$\\mu_2=\\lambda_2$};\n\\draw[thick,color=black](-2.5,-2.5)--(2.5,2.5)node[right,font=\\small]{$\\lambda_1=0$};\n\\draw[thick,color=black](-2.5,2.5)--(2.5,-2.5)node[right,font=\\small]{$\\lambda_1=-\\lambda$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 914,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing}\n\\usetikzlibrary{patterns}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\t\\draw (0,0) -- (5,0);\n\t\t\t\\draw (0,-0.2) -- (0,0.2);\n\t\t\t\\draw (5,-0.2) -- (5,0.2);\n\t\t\t\\draw (1.8, -0.2) -- (1.8, 0.2);\n\t\t\t\\draw (3.4, -0.2) -- (3.4, 0.2);\n\t\t\t\\draw (4.2, -0.2) -- (4.2, 0.2);\n\t\t\t\\draw [<->] (0,-0.3) -- (5,-0.3);\n\t\t\t\\draw [<->] (1.8,-0.3) -- (3.4,-0.3);\n\t\t\t\\draw [<->] (4.2,-0.3) -- (5,-0.3);\n\t\t\t\\node [below] at (2.5,-0.3) {$d_i$};\n\t\t\t\\node [below] at (3.75, -0.3) {$r_i$};\n\t\t\t\\node [below] at (4.9, -0.3) {$a_i$};\n\t\t\t\\node [above] at (2.5, 0.3) {$t_i$};\n\t\t\t\\node [above] at (3.75, 0.3) {$r_i$};\n\t\t\t\\node [above] at (4.9, 0.3) {$t_i$};\n\t\t\t\\draw [decorate, decoration={brace, mirror}] (1.8, 0.4) -- (3.4, 0.4);\n\t\t\t\\node [above] at (2.5, 0.7) {$\\omega$};\n\t\t\t\\draw [decorate, decoration={brace, mirror}] (4.2, 0.4) -- (5, 0.4);\n\t\t\t\\node [above] at (4.9, 0.7) {$T_i / \\omega$};\n\n\t\t\t\\draw (7,0) -- (12,0);\n\t\t\t\\draw (7,-0.2) -- (7,0.2);\n\t\t\t\\draw (12,-0.2) -- (12,0.2);\n\t\t\t\\draw (9.4, -0.2) -- (9.4, 0.2);\n\t\t\t\\draw (11.8, -0.2) -- (11.8, 0.2);\n\t\t\t\\draw [<->] (7,-0.3) -- (12,-0.3);\n\t\t\t\\draw [<->] (9.4,-0.3) -- (11.8,-0.3);\n\t\t\t\\draw [<->] (7,0.3) -- (9.4,0.3);\n\t\t\t\\node [below] at (8.75,0.3) {$d_i$};\n\t\t\t\\node [below] at (10.5, 0.3) {$r_i$};\n\t\t\t\\node [below] at (11.75, -0.3) {$a_i$};\n\t\t\t\\node [above] at (8.75, -0.3) {$\\omega$};\n\t\t\t\\node [above] at (10.5, 0.3) {$r_i$};\n\t\t\t\\node [above] at (11.75, 0.3) {$a_i$};\n\t\t\t\\draw [decorate, decoration={brace, mirror}] (9.4, 0.4) -- (11.8, 0.4);\n\t\t\t\\node [above] at (10.5, 0.7) {$\\omega$};\n\t\t\t\\draw [decorate, decoration={brace, mirror}] (7, 0.4) -- (12, 0.4);\n\t\t\t\\node [above] at (8.75, 0.7) {$T_i / \\omega$};\n\t\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 915,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathmorphing}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8]\n    \\node (j0) at (0,0) {$j_0 = 0$};\n\n    \\node (j1) at (-4,-1.5) {$j_1 = 0$};\n    \\node (p1) at (-2,-1.5) {$p^0 = 0$};\n    \\node (p2) at (0,-1.5) {$p^1 = 0$};\n    \\node (p3) at (2,-1.5) {$p^2 = 0$};\n    \\node (j2) at (4,-1.5) {$j_2 = 0$};\n\n    \\node (p12) at (-3,-3) {$p^0 = 0$};\n    \\node (p23) at (-1,-3) {$p^1 = 0$};\n    \\node (p13) at (1,-3) {$p^2 = 0$};\n    \\node (p22) at (3,-3) {$p^3 = 0$};\n    \\node (p11) at (0,-3) {$p^0 = 0$};\n\n    \\node (p32) at (1.5,-4.5) {$p^2 = 0$};\n    \\node (p33) at (3.5,-4.5) {$p^3 = 0$};\n    \\node (p31) at (-1.5,-4.5) {$p^2 = 0$};\n    \\node (p31) at (-3.5,-4.5) {$p^3 = 0$};\n    \\node (p30) at (-0.5,-4.5) {$p^2 = 0$};\n\n    \\node (p312) at (2,-6) {$p^3 = 0$};\n    \\node (p322) at (4,-6) {$p^3 = 0$};\n    \\node (p301) at (-2,-6) {$p^3 = 0$};\n    \\node (p311) at (-4,-6) {$p^3 = 0$};\n\n    \\draw (j0) -- (p1) -- (p12);\n    \\draw (p1) -- (p2) -- (p23);\n    \\draw (p2) -- (p3) -- (p33);\n    \\draw (p2) -- (p22);\n    \\draw (p3) -- (p32);\n\n    \\draw (j1) -- (p12) -- (p11) -- (p31) -- (p312);\n    \\draw (p12) -- (p30) -- (p301);\n\n    \\draw (j2) -- (p3) -- (p33);\n    \\draw (p3) -- (p32);\n\n    \\draw (j0) -- (p2) -- (p22);\n    \\draw (p2) -- (p3) -- (p32);\n\n    \\node[text width=0.5cm] at (-4,-5) {$p = 0$};\n    \\node[text width=0.5cm] at (-2,-5) {$(11,2)$};\n    \\node[text width=0.5cm] at (0,-5) {$(12,1)$};\n    \\node[text width=0.5cm] at (2,-5) {$(2,1)$};\n    \\node[text width=0.5cm] at (4,-5) {$(2,2)$};\n\n    \\node[text width=0.5cm] at (1.5,-7) {$v = 0$};\n    \\node[text width=0.5cm] at (3.5,-7) {$(3,3)$};\n    \\node[text width=0.5cm] at (-1.5,-7) {$(4,1)$};\n    \\node[text width=0.5cm] at (-3.5,-7) {$(4,1)$};\n    \\node[text width=0.5cm] at (-0.5,-7) {$(3,3)$};\n\n    \\node[text width=0.5cm] at (2,-9) {$M = 0$};\n    \\node[text width=0.5cm] at (-2,-9) {$M = 0$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 916,
        "tikz_code": "\\documentclass[twocolumn,aps,prb,superscriptaddress,showpacs,floatfix]{revtex4-1}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.markings}\n\\usetikzlibrary{decorations.pathmorphing,patterns,calc=1cm,decorations.pathreplacing}\n\\usetikzlibrary{arrows,decorations,calc,fit,shapes,positioning,shadows,shapes.geometric,arrows.meta}\n\\tikzset{>=stealth}\n\n\\begin{document}\n\n\\begin{tikzpicture}[\n    scale=1.5,\n    level/.style={thick},\n    virtual/.style={thick,densely dashed},\n    trans/.style={thick,->,shorten >=2pt,shorten <=2pt,>=stealth},\n    classical/.style={thin,double,<->,shorten >=4pt,shorten <=4pt,>=stealth}\n    ]\n    % Draw the energy levels.\n    \\draw[level] (0,0) -- (1,0) ;\n    \\draw[level] (1,0) -- (2,0) ;\n    \\draw[level] (1,1) -- (2,1) ;\n    \\draw[level] (0,1) -- (1,1) ;\n    \\draw[level] (2,0) -- (3,0) ;\n    \\draw[level] (2,1) -- (3,1) ;\n    \\draw[level] (3,0) -- (4,0) ;\n    \\draw[level] (3,1) -- (4,1) ;\n    \\draw[level] (4,0) -- (5,0) ;\n    \\draw[level] (4,1) -- (5,1) ;\n    \\draw[level] (5,0) -- (6,0) ;\n    \\draw[level] (5,1) -- (6,1) ;\n    % Draw the transitions.\n    \\draw[trans] (0,1) -- (0,0) ;\n    \\draw[trans] (1,1) -- (1,0) ;\n    \\draw[trans] (2,1) -- (2,0) ;\n    \\draw[trans] (3,1) -- (3,0) ;\n    \\draw[trans] (4,1) -- (4,0) ;\n    \\draw[trans] (5,1) -- (5,0) ;\n    \\draw[trans] (6,1) -- (6,0) ;\n    % Draw the labels.\n    \\node[left] at (0,1) {$p=\\textcolor{black}{p_1}$};\n    \\node[left] at (0,0) {$p=\\textcolor{black}{p_2}$};\n    \\node[left] at (2,0) {$p'=\\textcolor{black}{p_2}$};\n    \\node[left] at (1,1) {$p_3$};\n    \\node[left] at (1,0) {$p_3$};\n    \\node[right] at (3,1) {$p_4=\\textcolor{black}{p_1}$};\n    \\node[right] at (3,0) {$p_4=\\textcolor{black}{p_1}$};\n    \\node[right] at (4,1) {$p_5=\\textcolor{black}{p_2}$};\n    \\node[right] at (4,0) {$p_5=\\textcolor{black}{p_2}$};\n    \\node[right] at (6,1) {$p_6=\\textcolor{black}{p_3}$};\n    \\node[right] at (6,0) {$p_6=\\textcolor{black}{p_3}$};\n    \\node[below] at (2.5,0) {$\\textcolor{black}{\\overrightarrow{p_3}}$};\n    \\node[below] at (3.5,0) {$\\textcolor{black}{\\overrightarrow{p_3}}$};\n    \\node[below] at (4.5,0) {$\\textcolor{black}{\\overrightarrow{p_3}}$};\n    \\node[above] at (2.5,1) {$\\textcolor{black}{\\overrightarrow{p_4}}$};\n    \\node[above] at (3.5,1) {$\\textcolor{black}{\\overrightarrow{p_4}}$};\n    \\node[above] at (4.5,1) {$\\textcolor{black}{\\overrightarrow{p_4}}$};\n    \\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 917,
        "tikz_code": "\\documentclass[a4paper,10pt]{article}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usepackage{tikz-qtree}\n\n\\begin{document}\n\n\\begin{tikzpicture}[every tree node/.style={draw,circle},\n   level distance=1.2cm,sibling distance=0.6cm,scale=0.8,\n   edge from parent path={(\\tikzparentnode) -- (\\tikzchildnode)}]\n\\Tree [.\\node[rectangle,draw,inner sep=2.5pt]{AND};\n    \\edge node[auto=right,draw=none,scale=0.8]{$\\vee$};\n    [.\\node[rectangle,draw,inner sep=2.5pt]{OR};\n      \\edge node[auto=right,draw=none,scale=0.8]{$\\wedge$};\n      [.\\node[rectangle,draw,inner sep=2.5pt]{AGE};\n        \\edge node[auto=right,draw=none,scale=0.8]{$\\sim$};\n        [.\\node[rectangle,draw,inner sep=2.5pt]{BloodType}; \\node[rectangle,draw,inner sep=2.5pt]{\\texttt{=}}; \\node[rectangle,draw,inner sep=2.5pt]{\\texttt{$\\varepsilon$}}; ]\n      ]\n      [.\\node[rectangle,draw,inner sep=2.5pt]{LI}; \\node[rectangle,draw,inner sep=2.5pt]{\\texttt{=}}; \\node[rectangle,draw,inner sep=2.5pt]{$1$}; ]\n    ]\n    [.\\node[rectangle,draw,inner sep=2.5pt]{OR};\n      \\edge node[auto=right,draw=none,scale=0.8]{$\\wedge$};\n      [.\\node[rectangle,draw,inner sep=2.5pt]{WEIGHT};\n        \\edge node[auto=right,draw=none,scale=0.8]{$\\sim$};\n        [.\\node[rectangle,draw,inner sep=2.5pt]{Weight}; \\node[rectangle,draw,inner sep=2.5pt]{\\texttt{:}}; \\node[rectangle,draw,inner sep=2.5pt]{$\\varepsilon$}; ]\n      ]\n      [.\\node[rectangle,draw,inner sep=2.5pt]{LI}; \\node[rectangle,draw,inner sep=2.5pt]{\\texttt{>}}; \\node[rectangle,draw,inner sep=2.5pt]{$50$}; ]\n    ]\n  ]\n  [.\\node[rectangle,draw,inner sep=2.5pt]{AND};\n    \\edge node[auto=right,draw=none,scale=0.8]{$\\vee$};\n    [.\\node[rectangle,draw,inner sep=2.5pt]{OR};\n      \\edge node[auto=right,draw=none,scale=0.8]{$\\wedge$};\n      [.\\node[rectangle,draw,inner sep=2.5pt]{AGE};\n        \\edge node[auto=right,draw=none,scale=0.8]{$\\sim$};\n        [.\\node[rectangle,draw,inner sep=2.5pt]{BloodType}; \\node[rectangle,draw,inner sep=2.5pt]{\\texttt{=}}; \\node[rectangle,draw,inner sep=2.5pt]{\\texttt{$\\varepsilon$}}; ]\n      ]\n      [.\\node[rectangle,draw,inner sep=2.5pt]{LI}; \\node[rectangle,draw,inner sep=2.5pt]{\\texttt{=}}; \\node[rectangle,draw,inner sep=2.5pt]{$100$}; ]\n    ]\n    [.\\node[rectangle,draw,inner sep=2.5pt]{OR};\n      \\edge node[auto=right,draw=none,scale=0.8]{$\\wedge$};\n      [.\\node[rectangle,draw,inner sep=2.5pt]{WEIGHT};\n        \\edge node[auto=right,draw=none,scale=0.8]{$\\sim$};\n        [.\\node[rectangle,draw,inner sep=2.5pt]{Weight}; \\node[rectangle,draw,inner sep=2.5pt]{\\texttt{:}}; \\node[rectangle,draw,inner sep=2.5pt]{$100$}; ]\n      ]\n      [.\\node[rectangle,draw,inner sep=2.5pt]{LI}; \\node[rectangle,draw,inner sep=2.5pt]{\\texttt{<}}; \\node[rectangle,draw,inner sep=2.5pt]{$105$}; ]\n    ]\n  ]\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 918,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amssymb,amsthm,mathtools}\n\\usepackage{tikz,graphicx}\n\\usetikzlibrary{arrows.meta}\n\\usetikzlibrary{decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\\draw (-2.5,2) node {\\small{longest bar}};\n\t\t\\draw (-2.5,0) node {\\small{$q=0$}};\n\t\t\\draw (0,0) node {\\small{$q=1$}};\n\t\t\\draw[dotted] (0,0)--(0,2);\n\t\t\\draw[dotted] (2,0)--(2,2);\n\t\t\\draw (0,0)--(2,0);\n\t\t\\draw (0,2)--(2,2);\n\t\t\\draw[very thick]\n\t\t(2,1.5)--(1.5,2)\n\t\t(2,1.5)--(2.5,2)\n\t\t(2,1.5)--(2.5,1)\n\t\t(2,1.5)--(2.5,0)\n\t\t(2,1.5)--(1.5,0)\n\t\t(2,1.5)--(2.5,1);\n\t\t\\draw[smooth,samples=100,domain=1.3:2] plot(\\x,{1.5+1.7*sin(4*pi*\\x r)});\n\t\t\\draw[smooth,samples=100,domain=1.3:2] plot(\\x,{1.5-1.7*sin(4*pi*\\x r)});\n\t\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 919,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath,amssymb,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{math}\n\\usetikzlibrary{shapes.geometric}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{arrows.meta}\n\\providecommand{\\tikzpicture}{\\comment}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1, every node/.style={scale=0.6}]\n\\node(root) at (0,0) {$11$};\n\\node(c1) at (0,-1){$\\dfrac{9}{10}$};\n\\node(c2) at (1,-2){$7$};\n\\node(c3) at (-1,-2){$3$};\n\\node(c1c2) at (0,-3){$8$};\n\\node(c1c3) at (-2,-4){$3$};\n\\node(c2c3) at (2,-4){$4$};\n\\node(c1c2c3) at (0,-5){$6$};\n\\node(t) at (0,-6){$\\mathbf{1}$};\n\n\\draw(root)--(c1)--(c2)--(c1c2)--(c2c3)--(c1c2c3)--(t);\n\\draw(root)--(c1)--(c3)--(c1c3)--(c1c2c3);\n\\draw(c2)--(c1c3);\n\\draw(c3)--(c2c3);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 920,
        "tikz_code": "\\documentclass[11pt,reqno,a4paper]{amsart}\n\\usepackage[backgroundcolor=yellow!40,textsize=scriptsize]{todonotes}\n\\usepackage{amsfonts,amstext,amsmath,amssymb,stmaryrd,mathrsfs,calc,amsthm,mathtools,bold-extra}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\\fill[blue!10] (-2,2) -- (2,2) -- (3,3) -- (1,3) -- (-2,2);\n\\fill[blue!10] (-2,4) -- (2,4) -- (3,5) -- (1,5) -- (-2,4);\n\\fill[blue!10] (-2,6) -- (2,6) -- (3,7) -- (1,7) -- (-2,6);\n\\fill[blue!10] (-2,8) -- (2,8) -- (3,9) -- (1,9) -- (-2,8);\n\\draw[thick,->] (-2,0) -- (3,0);\n\\draw[thick,->] (-2,0) -- (-2,10);\n\\draw (-2,2) -- (2,2);\n\\draw (-2,4) -- (2,4);\n\\draw (-2,6) -- (2,6);\n\\draw (-2,8) -- (2,8);\n\\draw[thick] (1,1) -- (1,9);\n\\draw[thick] (1,5) -- (1,7);\n\\draw[thick] (1,3) -- (1,9);\n\\draw[thick] (1,3) -- (1,5);\n\\draw[fill] (1,3) circle (2pt);\n\\draw[fill] (1,5) circle (2pt);\n\\draw (1,1) node[above] {\\small $L$};\n\\draw (1,7) node[above] {\\small $g^{-h_1 -h_k - h}L$};\n\\draw (1,9) node[above] {\\small $g^{-h^\\prime -h_1 -h_k -1}L$};\n\\draw (2.2,2) node[right] {\\small $U_9$};\n\\draw (2.2,4) node[right] {\\small $U_{h^\\prime}$};\n\\draw (2.2,6) node[right] {\\small $U_{h}$};\n\\draw (2.2,8) node[right] {\\small $U_{h^\\prime - 1}U_{h}$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 921,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amssymb, amsmath, amsthm}\n\\usepackage{tikz}\n\n\\newcommand{\\dbrd}[2]{\n\\begin{scope}[xshift = #1 cm, yshift = #2 cm]\n\\draw[blue, thick] (45:0.75) -- (-135:0.75);\n\\draw[blue, thick] (45:0.75) arc (45:-45:0.75);\n\\draw[blue, thick] (-45:0.75) -- (135:0.75);\n\\end{scope}\n}\n\n\\newcommand{\\sdot}[2]{\n\\draw[black, fill=black] (#1, #2) circle [radius = 0.05]\n}\n\n\\newcommand{\\ddot}[2]{\n\\draw[black, fill=black] (#1, #2) circle [radius = 0.1]\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw [->] (0,1) -- (1,1);\n\\draw [->] (0,2) -- (1,2);\n\\draw [->] (0,3) -- (1,3);\n\\draw [->] (14,1) -- (15,1);\n\\draw [->] (14,2) -- (15,2);\n\\draw [->] (14,3) -- (15,3);\n\\node [left] at (0,1) {$L_0$};\n\\node [left] at (0,2) {$L_1$};\n\\node [left] at (0,3) {$L_2$};\n\\node [right] at (15,1) {$L_2$};\n\\node [right] at (15,2) {$L_1$};\n\\node [right] at (15,3) {$L_0$};\n\\dbrd{14}{2}; \\sdot{14}{2}; \\ddot{14}{2};\n\\node [above] at (7.5,2) {$D_{D_1\\setminus\\{a\\}}^{(0)}$};\n\\node [below] at (7.5,1) {$\\Pi$};\n\\node [below] at (14,1) {$a$};\n\\node [above] at (14,2) {$o$};\n\\node [left] at (0,-0.5) {$\\pi_{6,6}(g) \\times L_4$};\n\n\\begin{scope}[xshift = 6cm]\n\\draw [->] (0,1) -- (1,1);\n\\draw [->] (0,2) -- (1,2);\n\\draw [->] (0,3) -- (1,3);\n\\draw [->] (14,1) -- (15,1);\n\\draw [->] (14,2) -- (15,2);\n\\draw [->] (14,3) -- (15,3);\n\\node [left] at (0,1) {$L_0$};\n\\node [left] at (0,2) {$L_1$};\n\\node [left] at (0,3) {$L_2$};\n\\node [right] at (15,1) {$L_0$};\n\\node [right] at (15,2) {$L_2$};\n\\node [right] at (15,3) {$L_1$};\n\\dbrd{14}{2}; \\sdot{14}{2}; \\ddot{14}{2};\n\\node [above] at (7.5,2) {$L_2$};\n\\node [below] at (7.5,1) {$D_{D_2\\setminus\\{a\\}}^{(0)}$};\n\\node [below] at (14,1) {$a$};\n\\node [above] at (14,2) {$o$};\n\\node [left] at (0,-0.5) {$\\pi_{6,9}(g) \\times L_4$};\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 922,
        "tikz_code": "\\documentclass[twocolumn,aps,showpacs,prb,usenames,superscriptaddress]{revtex4-1}\n\\usepackage{tikz}\n\\usetikzlibrary{calc,positioning}\n\\usepackage{amsmath,amssymb}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usepackage{amsmath,amssymb}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node (img1a) {\\includegraphics[width=.85\\textwidth]{example-image}};\n\\node[left=of img1a,node distance=0cm,rotate=90,anchor=center,yshift=-1.1cm]{\\large{ $c)$}};\n\\node (img1b) [below=of img1a,yshift=1.55cm]{\\includegraphics[width=.85\\textwidth]{example-image}};\n\\node[left=of img1b,node distance=0cm,rotate=90,anchor=center,yshift=-1.1cm]{\\large{$d)$}};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 923,
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        "index": 927,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usepackage{amsthm,amsmath, amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.5]\n    \\begin{axis}[ymin=-5,ymax=16,\n      xlabel={$\\log_{10}$ of the time step},\n      ylabel={$\\log_{10}$ of the error}]\n      \\addplot[color=black,mark=*] coordinates {\n          (-0.5,   15.5)\n          (0.0,    13.6)\n          (0.5,    12.5)\n          (1.0,    11.8)\n          (1.5,    11.1)\n          (2.0,    10.5)\n          (2.5,    10.0)\n          (3.0,    9.5)\n          (3.5,    9.1)\n          (4.0,    8.8)\n          (4.5,    8.5)\n          (5.0,    8.2)\n          (5.5,    8.0)\n          (6.0,    7.8)\n          (6.5,    7.6)\n          (7.0,    7.5)\n          (7.5,    7.4)\n      }; \\addlegendentry{regular steps}\n      \\addplot[color=orange,mark=star] coordinates {\n          (-0.5,   13.5)\n          (0.0,    12.2)\n          (0.5,    11.6)\n          (1.0,    11.1)\n          (1.5,    10.7)\n          (2.0,    10.4)\n          (2.5,    10.1)\n          (3.0,    9.8)\n          (3.5,    9.5)\n          (4.0,    9.3)\n          (4.5,    9.1)\n          (5.0,    8.8)\n          (5.5,    8.6)\n          (6.0,    8.4)\n          (6.5,    8.3)\n          (7.0,    8.2)\n          (7.5,    8.0)\n      }; \\addlegendentry{slope 5}\n      \\addplot[color=green,mark=*] coordinates {\n          (-0.5,    8.3)\n          (0.0,    8.1)\n          (0.5,    8.1)\n          (1.0,    8.1)\n          (1.5,    8.1)\n          (2.0,    8.1)\n          (2.5,    8.1)\n          (3.0,    8.1)\n          (3.5,    8.1)\n          (4.0,    8.1)\n          (4.5,    8.1)\n          (5.0,    8.1)\n          (5.5,    8.1)\n          (6.0,    8.1)\n          (6.5,    8.1)\n          (7.0,    8.1)\n          (7.5,    8.1)\n      }; \\addlegendentry{resonant steps}\n    \\end{axis}\n  \\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{latexsym,amssymb,amsmath}\n\\usepackage{tikz,verbatim,cancel}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n      % graph G\n\n      \\draw (0,0) -- (4,0);\n      \\draw (0,0) -- (-1,1);\n      \\draw (0,0) -- (-1,-1);\n      \\draw (0,0) -- (-1,0.5);\n      \\draw (0,0) -- (-1,-0.5);\n      \\draw (0,0) -- (-1,0);\n\n      \\fill[fill=white,draw=black] (0,0) circle (.1);\n      \\fill[fill=black,draw=black] (1,0) circle (.1);\n      \\fill[fill=black,draw=black] (2,0) circle (.1);\n      \\fill[fill=black,draw=black] (3,0) circle (.1);\n      \\fill[fill=black,draw=black] (4,0) circle (.1);\n      \\fill[fill=black,draw=black] (-1,1) circle (.1);\n      \\fill[fill=black,draw=black] (-1,-1) circle (.1);\n      \\fill[fill=black,draw=black] (-1,0.5) circle (.1);\n      \\fill[fill=black,draw=black] (-1,-0.5) circle (.1);\n      \\fill[fill=black,draw=black] (-1,0) circle (.1);\n\n      \\draw (-1,0) node[anchor=north east] {$*$};\n      \\draw (-1,-0.5) node[anchor=north east] {$2$};\n\n\n    \\end{tikzpicture}\n\n\\end{document}"
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        "index": 929,
        "tikz_code": "\\documentclass[a4paper,12pt]{amsart}\n\\usepackage{amsmath,amsfonts,amssymb}\n\\usepackage[usenames]{color}\n\\usepackage{tikz}\n\\usepackage{xcolor}\n\\usepackage{color}\n\\usetikzlibrary{arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[-stealth] (-1.5,0)--(1.5,0);\n\\draw[-stealth] (0,-1.5)--(0,1.5);\n\\draw (1.4,1.4)node[anchor=south west]{$(3,4)$};\n\\draw (-1.4,1.4)node[anchor=south east]{$(2,3)b$};\n\\draw (1.4,-1.4)node[anchor=north west]{$(4,5)$};\n\\draw (-1.4,-1.4)node[anchor=north east]{$(2,5)$};\n\\draw (3,-0.1)node[anchor=south]{$x^{2}(-d)^{1/2}$};\n\\draw (-3,-0.1)node[anchor=south]{$x^{2}(-d)^{1/2}$};\n\\draw (0.1,3)node[anchor=west]{$x^{2}(-c)^{1/2}$};\n\\draw (0.1,-3)node[anchor=west]{$x^{2}(-c)^{1/2}$};\n\\draw (0,0)--(0,2)--(2,2)--(3,0)--(2,-2)--(0,-2)--(-2,0)--cycle;\n\\draw (0,1)--(2,1)--(2,-1)--(0,-1)--cycle;\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 930,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath}\n\\usepackage{pgfplots}\n\\usepackage{pgfplotstable}\n\\pgfplotsset{width=7cm,compat=1.8}\n\\usepackage{color,xcolor,framed}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\selectcolormodel{RGB}\n\\begin{axis}[\ntitle={\\huge 3D Laplace, $\\gamma_{min}=32$},\nxlabel={},xlabel style = {font=\\footnotesize},\nylabel={Percentage of time},ylabel style = {font=\\footnotesize},\nxmin=-4.5, xmax=4.5,\nymin=0, ymax=55,\nxtick={-3,-2,-1,0,1,2,3},\nytick={0,10,20,30,40,50},\nwidth=\\linewidth,\nlegend pos=south east\n]\n%Density\n\\addplot+[ybar,bar width=3pt]\ncoordinates\n{(-3, 37.5) (-2, 18.75) (-1, 4.375) (0, 2.5625) (1, 3.515625) (2, 3.90625) (3, 1.40625)}; %Density\n\n%FEM\n\\addplot+[ybar,bar width=3pt]\ncoordinates\n{(-3, 4.375) (-2, 1.15625) (-1, 0.09375) (0, 0.046875) (1, 0.046875) (2, 0.046875) (3, 0.046875)};\n\n%SCOT\n\\addplot+[ybar,bar width=3pt]\ncoordinates\n{(-3, 25.625) (-2, 4.375) (-1, 0.046875) (0, 0.046875) (1, 0.046875) (2, 0.046875) (3, 0.046875)};\n\n%TIMES\n\\addplot+[ybar,bar width=3pt]\ncoordinates\n{(-3, 27.5) (-2, 12.5) (-1, 18.75) (0, 11.25) (1, 25) (2, 25) (3, 25)};\n\n\\legend{Density, FEM, SCOT, TIMES};\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathreplacing,calc,tikzmark}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.9]\n    \\draw[black, very thick] (-2.5,-2) arc (-90:270:0.25 and 2);\n    \\draw[black, very thick] (-1,0) arc (0:360:1 and 1);\n    \\draw[black, very thick] (0,-1) arc (180:360:1 and 1);\n    \\draw[black, very thick] (0,-1) arc (-180:-360:1 and 1);\n    \\draw[black, very thick] (2.5,2) arc (270:450:0.25 and 2);\n    \\draw[black, very thick] (-0.75,0) to [out=270, in=180] (0,-1);\n    \\draw[black, very thick] (-2.5,-2) to [out=0, in=180] (-0.75,0);\n    \\draw[black, very thick] (-0.75,0) to [out=0, in=180] (0,1);\n    \\draw[black, very thick] (-2.5,-2) to [out=90, in=180] (0,1);\n    \\draw[black, very thick] (0,-1) to [out=0, in=180] (2.5,2);\n    \\draw[black, very thick] (2.5,2) to [out=180, in=90] (0,1);\n    \n    \\draw[black, very thick, ->] (-2.5,-2) arc (-90:270:0.25 and 2);\n    \\draw[black, very thick, ->] (-1,0) arc (0:360:1 and 1);\n    \\draw[black, very thick, ->] (0,-1) arc (180:360:1 and 1);\n    \\draw[black, very thick, ->] (0,-1) arc (-180:-360:1 and 1);\n    \\draw[black, very thick, ->] (2.5,2) arc (270:450:0.25 and 2);\n    \\draw[black, very thick, ->] (-0.75,0) to [out=270, in=180] (0,-1);\n    \\draw[black, very thick, ->] (-2.5,-2) to [out=0, in=180] (-0.75,0);\n    \\draw[black, very thick, ->] (-0.75,0) to [out=0, in=180] (0,1);\n    \\draw[black, very thick, ->] (-2.5,-2) to [out=90, in=180] (0,1);\n    \\draw[black, very thick, ->] (0,-1) to [out=0, in=180] (2.5,2);\n    \\draw[black, very thick, ->] (2.5,2) to [out=180, in=90] (0,1);\n    \n    \\draw [fill=black] (-2.5,-2) circle [radius=0.05];\n    \\draw [fill=black] (-1,0) circle [radius=0.05];\n    \\draw [fill=black] (0,-1) circle [radius=0.05];\n    \\draw [fill=black] (0,1) circle [radius=0.05];\n    \\draw [fill=black] (2.5,2) circle [radius=0.05];\n    \\draw [fill=black] (-0.75,0) circle [radius=0.05];\n    \\node [below] at (0,-3) {$D$};\n    \n    \\draw[black, very thick] (6,0) arc (0:360:1 and 1);\n    \\draw[black, very thick] (5.5,0.8) arc (90:-180:0.4 and 0.8);\n    \\draw[black, very thick] (6,1.6) arc (90:180:0.4 and 0.8);\n    \\draw[black, very thick] (5,0) arc (270:450:1 and 0.8);\n    \\draw[black, very thick] (4,1.6) arc (180:270:1 and 0.8);\n    \\draw[black, very thick] (4.5,0.8) arc (-90:0:0.4 and 0.8);\n    \\draw[black, very thick] (5,0) arc (-90:-270:1 and 0.8);\n    \\draw[black, very thick] (5.5,0.8) arc (90:180:0.4 and 0.8);\n    \\draw[black, very thick] (5.5,0.8) to [out=0,in=180] (6,1.6);\n    \\draw[black, very thick] (6,0) to [out=0,in=180] (6,1.6);\n    \\draw[black, very thick] (5.5,0.8) to [out=180,in=0] (4,1.6);\n    \\draw[black, very thick] (4.5,0.8) to [out=180,in=0] (4,1.6);\n    \\draw[black, very thick] (4,1.6) to [out=180,in=0] (4.5,0.8);\n    \\draw[black, very thick] (5,0) to [out=180,in=0] (4.5,0.8);\n    \\draw[black, very thick] (5,0) to [out=180,in=0] (5.5,0.8);\n    \n    \\draw[black, very thick, ->] (5.5,0.8) arc (90:180:0.4 and 0.8);\n    \\draw[black, very thick, ->] (6,1.6) arc (90:180:0.4 and 0.8);\n    \\draw[black, very thick, ->] (4,1.6) arc (180:270:1 and 0.8);\n   "
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        "index": 932,
        "tikz_code": "\\documentclass[10pt, conference, compsocconf]{IEEEtran}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.13}\n\\usetikzlibrary{intersections}\n\\usetikzlibrary{pgfplots.groupplots}\n\\usetikzlibrary{decorations.pathmorphing}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{axis}[\n    xlabel={$R_{\\text{sum}}$ (bits/channel use)},\n    ylabel={CDF},\n    xmin=0, xmax=45,\n    ymin=0, ymax=1,\n    xtick={0,10,20,30,40},\n    ytick={0,0.2,0.4,0.6,0.8,1},\n    legend pos=north west,\n    ymajorgrids=true,\n    grid style=dashed,\n    width=8.75cm,\n    height=6.75cm,\n    % ylabel near ticks,\n    % xlabel near ticks,\n    % axis y line*=left,\n    % axis x line*=bottom,\n    legend style={nodes={scale=0.7, transform shape}}\n]\n\n\\addplot[\n    color=blue,\n    style=dashed,\n    mark=none,\n    ]\n    coordinates {\n    (1,0)(1,0.10)(5,0.10)(5,0.35)(10,0.35)(10,0.77)(20,0.77)(20,0.94)(30,0.94)(30,1)(40,1)(40,1)};\n\n\\addplot[\n    color=red,\n    style=dashed,\n    mark=none,\n    ]\n    coordinates {\n    (1,0)(1,0.05)(5,0.05)(5,0.35)(10,0.35)(10,0.73)(20,0.73)(20,0.99)(30,0.99)(30,1)(40,1)(40,1)};\n\n\n\\addplot[\n    color=blue,\n    mark=none,\n    ]\n    coordinates {\n    (1,0)(1,0.10)(5,0.10)(5,0.30)(10,0.30)(10,0.70)(20,0.70)(20,0.94)(30,0.94)(30,1)(40,1)(40,1)};\n\n\n\\addplot[\n    color=red,\n    mark=none,\n    ]\n    coordinates {\n    (1,0)(1,0.05)(5,0.05)(5,0.29)(10,0.29)(10,0.66)(20,0.66)(20,0.99)(30,0.99)(30,1)(40,1)(40,1)};\n    \n\\legend{NN, ZF}\n\\end{axis}\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 933,
        "tikz_code": "\\documentclass[a4paper,12pt]{amsart}\n\\usepackage{amsmath, amssymb}\n\\usepackage{tikz}\n\n\\newcommand{\\fD}{\\mathfrak{D}}\n\n\\newcommand{\\fP}{\\mathfrak{P}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n % figure\n \\node [inner sep=0pt] at (6,0)\n {\\includegraphics[width=.8\\textwidth]{example-image}};\n % gamma\n \\draw [-,thick,red] (5,1) to (5.5,-1);\n \\node at (4.6,-0.7) {\\large $\\gamma$};\n % P0\n \\fill (3.6,1.7) circle (2pt) node [above] {\\large $P_0$};\n \\draw [->,thick] (3.6,1.7) to (5.7,0.7);\n % P1\n \\fill (7.6,-0.7) circle (2pt) node [below] {\\large $P_1$};\n \\draw [->,thick] (3.7,1.9) to [out=30, in=180] (7.6,-0.7);\n % P2\n \\fill (9.6,-1.6) circle (2pt) node [below] {\\large $P_2$};\n \\draw [->,thick] (7.6,-0.7) to [out=30, in=160] (9.6,-1.6);\n % D\n \\draw [-,thick,black!20] (7.9,0) to [out=-20,in=110] (8.8,0.1);\n \\fill (7.9,0) circle (2pt) node [below] {\\large $\\fD(P_0,P_1)$};\n \\draw [->,thick,black!20] (7.9,0) to [out=-30,in=110] (8.8,0.1);\n % P\n \\fill (8.6,0.4) circle (2pt) node [above] {\\large $P$};\n \\draw [->,thick] (8.6,0.4) to [out=-20,in=120] (8.8,0.1);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 934,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[colorlinks=true, linkcolor=red, citecolor=blue]{hyperref}\n\\usepackage{tikz}\n\\usetikzlibrary{shapes,graphs,graphs.standard}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\begin{scope}[every node/.style={circle,thick,draw,minimum size=1pt,inner sep=2}]\n    \\node[fill] (0) at (0:0) {};\n    \\node[fill] (1) at (30:1) {};\n    \\node[fill] (2) at (90:1) {};\n    \\node[fill] (3) at (150:1) {};\n    \\node[fill] (4) at (210:1) {};\n    \\node[fill] (5) at (270:1) {};\n    \\node[fill] (6) at (330:1) {};\n    \n    \\node[fill] (10) at (30:2) {};\n    \\node[fill] (11) at (90:2) {};\n    \\node[fill] (12) at (150:2) {};\n    \\node[fill] (13) at (210:2) {};\n    \\node[fill] (14) at (270:2) {};\n    \\node[fill] (15) at (330:2) {};\n    \n    \\node[fill] (20) at (30:3) {};\n    \\node[fill] (21) at (90:3) {};\n    \\node[fill] (22) at (150:3) {};\n    \\node[fill] (23) at (210:3) {};\n    \\node[fill] (24) at (270:3) {};\n    \\node[fill] (25) at (330:3) {};\n\\end{scope}\n\n\\begin{scope}[every edge/.style={draw=black,thick}]\n    \\path (0) edge (1);\n    \\path (1) edge (2);\n    \\path (2) edge (3);\n    \\path (3) edge (4);\n    \\path (4) edge (5);\n    \\path (5) edge (6);\n    \\path (6) edge (0);\n    \\path (0) edge (10);\n    \\path (10) edge (11);\n    \\path (11) edge (12);\n    \\path (12) edge (13);\n    \\path (13) edge (14);\n    \\path (14) edge (15);\n    \\path (15) edge (0);\n    \\path (10) edge (12);\n    \\path (12) edge (14);\n    \\path (14) edge (11);\n    \\path (11) edge (13);\n    \\path (13) edge (15);\n    \\path (20) edge (21);\n    \\path (21) edge (22);\n    \\path (22) edge (23);\n    \\path (23) edge (24);\n    \\path (24) edge (25);\n    \\path (25) edge (20);\n    \\path (20) edge[bend left=45] (21);\n    \\path (21) edge[bend left=45] (22);\n    \\path (22) edge[bend left=45] (23);\n    \\path (23) edge[bend left=45] (24);\n    \\path (24) edge[bend left=45] (25);\n    \\path (25) edge[bend left=45] (20);\n\\end{scope}\n\\node at (0,-3) {$G$};\n\n\\begin{scope}[xshift=7cm,yshift=0.25cm,every node/.style={circle,thick,draw,minimum size=1pt,inner sep=2}]\n    \\node[fill] (0) at (0:0) {};\n    \\node[fill] (1) at (30:1) {};\n    \\node[fill] (2) at (90:1) {};\n    \\node[fill] (3) at (150:1) {};\n    \\node[fill] (4) at (210:1) {};\n    \\node[fill] (5) at (270:1) {};\n    \\node[fill] (6) at (330:1) {};\n    \n    \\node[fill] (10) at (30:2) {};\n    \\node[fill] (11) at (90:2) {};\n    \\node[fill] (12) at (150:2) {};\n    \\node[fill] (13) at (210:2) {};\n    \\node[fill] (14) at (270:2) {};\n    \\node[fill] (15) at (330:2) {};\n    \n    \\node[fill] (20) at (30:3) {};\n    \\node[fill] (21) at (90:3) {};\n    \\node[fill] (22) at (150:3) {};\n    \\node[fill] (23) at (210:3) {};\n    \\node[fill] (24) at (270:3) {};\n    \\node[fill] (25) at (330:3) {};\n\\end{scope}\n\n\\begin{scope}[yshift=0.25cm,every edge/.style={draw=black,thick}]\n    \\path (0) edge[bend left=45] (1);\n    \\path (1) edge[bend left=45] (2);\n    \\path (2) edge[bend left=45] (3);\n    \\path (3) edge[bend left=45] (4);\n    \\path (4) edge[bend left=45] (5);\n    \\path (5) edge[bend left=45] (6);\n    \\path (6) edge[bend left=45] (0);\n    \n    \\path (0) edge (10);\n    \\path (10) edge (11);\n    \\path (11) edge (12);\n    \\path (12) edge (13);\n    \\path (13) edge (14);\n    \\path (14) edge (15);\n    \\path (15) edge (0);\n    \n    \\path"
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    {
        "index": 935,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usetikzlibrary{arrows.meta}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\t\n\t\t\t% draw the axes\n\t\t\t\\draw[black,-{Latex[scale=2.0]}] (1.2,2.2) -- (-0.5,2.2) node[below] {$x$};\n\t\t\t\\draw[black,-{Latex[scale=2.0]}] (1.2,2.2) -- (1.2,-0.5) node[right] {$y$};\n\t\t\t\n\t\t\t% draw the lines\n\t\t\t\\draw[blue] (-2,1) -- (1.2,3.2) node[above right] {$w$};\n\t\t\t\\draw[blue] (2,1) -- (1.2,3.2);\n\t\t\t\\draw[blue] (-2,0) -- (1.2,2.2);\n\t\t\t\\draw[blue] (2,0) -- (1.2,2.2);\n\t\t\t\\draw[red,dashed] (-2,1) -- (1.2,1);\n\t\t\t\\draw[red,dashed] (2,1) -- (1.2,1);\n\t\t\t\n\t\t\t\\draw[black] (-2,1) circle (0.5 and 0.25);\n\t\t\t\\draw[black] (-2,0) circle (0.5 and 0.25);\n\t\t\t\\draw[black] (-0.5,2.5) circle (0.5 and 0.25);\n\t\t\t\\draw[black] (-0.5,2.2) circle (0.5 and 0.25);\n\t\t\t\\draw[black] (0.5,2.5) circle (0.5 and 0.25);\n\t\t\t\\draw[black] (0.5,2.2) circle (0.5 and 0.25);\n\t\t\t\\draw[black] (2,1) circle (0.5 and 0.25);\n\t\t\t\\draw[black] (2,0) circle (0.5 and 0.25);\n\t\t\t\n\t\t\t\\filldraw[fill=black, draw=black] (1.2,3.2) circle (1.5pt);\n\t\t\t\\filldraw[fill=black, draw=black] (1.2,2.2) circle (1.5pt);\n\t\t\t\\filldraw[fill=black, draw=black] (1.2,1) circle (1.5pt);\n\t\t\t\n\t\t\t\\draw[blue] (1.2,3.2) -- (5,3.2);\n\t\t\t\\draw[blue] (1.2,3.2) -- (5.5,4.4);\n\t\t\t\\draw[blue] (1.2,3.2) -- (6.5,4.4);\n\t\t\t\\draw[blue] (1.2,3.2) -- (7,3.2);\n\t\t\t\\draw[blue] (1.2,2.2) -- (5,2.2);\n\t\t\t\\draw[blue] (1.2,2.2) -- (5.5,0.8);\n\t\t\t\\draw[blue] (1.2,2.2) -- (6.5,0.8);\n\t\t\t\\draw[blue] (1.2,2.2) -- (7,2.2);\n\t\t\t\\draw[blue] (1.2,1) -- (5,1);\n\t\t\t\\draw[blue] (1.2,1) -- (5.5,-0.2);\n\t\t\t\\draw[blue] (1.2,1) -- (6.5,-0.2);\n\t\t\t\\draw[blue] (1.2,1) -- (7,1);\n\t\t\t\n\t\t\t\\draw[black] (5,3.2) circle (0.5 and 0.25);\n\t\t\t\\draw[black] (5,2.2) circle (0.5 and 0.25);\n\t\t\t\\draw[black] (5,1) circle (0.5 and 0.25);\n\t\t\t\\draw[black] (7,3.2) circle (0.5 and 0.25);\n\t\t\t\\draw[black] (7,2.2) circle (0.5 and 0.25);\n\t\t\t\\draw[black] (7,1) circle (0.5 and 0.25);\n\t\t\t\n\t\t\t\\filldraw[fill=black, draw=black] (5,3.2) circle (1.5pt);\n\t\t\t\\filldraw[fill=black, draw=black] (5,2.2) circle (1.5pt);\n\t\t\t\\filldraw[fill=black, draw=black] (5,1) circle (1.5pt);\n\t\t\t\\filldraw[fill=black, draw=black] (7,3.2) circle (1.5pt);\n\t\t\t\\filldraw[fill=black, draw=black] (7,2.2) circle (1.5pt);\n\t\t\t\\filldraw[fill=black, draw=black] (7,1) circle (1.5pt);\n\t\t\t\n\t\t\t\\filldraw[fill=black, draw=black] (1.2,2.2) circle (1.5pt);\n\t\t\t\n\t\t\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 936,
        "tikz_code": "\\documentclass[12pt,a4paper,oneside,headings=small]{scrartcl}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage[x11names]{xcolor}\n\\usepackage{tikz}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\\node (nl) at (-3.5,-4) {\\includegraphics[width=4cm]{example-image}};\n\\node (nl1) at (0,-4) {\\includegraphics[width=4cm]{example-image}};\n\\node (nl2) at (3.5,-4) {\\includegraphics[width=4cm]{example-image}};\n\\node at (-2,-4.5) {$\\mathbf{Image}$};\n\\node at (-2,-1.5) {$\\mathbf{Image}$};\n\\node at (1,-4.5) {$\\mathbf{Image}$};\n\\node at (1,-1.5) {$\\mathbf{Image}$};\n\n\\node at (0,-2.5) {$\\mathbf{Input} \\text{ data}$};\n\\node at (0,-5.5) {$\\mathbf{Neural} \\text{ network}$};\n\n\\node at (1.5,-8) {$\\mathbf{Neural} \\text{ network}$};\n\\node at (3.5,-7.8) {\\includegraphics[width=3cm]{example-image}};\n\\node at (4.5,-8.2) {\\includegraphics[width=3cm]{example-image}};\n\\node at (1.5,-10.5) {$\\mathbf{Neural} \\text{ network}$};\n\n\\node (nl3) at (6,-4) {\\includegraphics[width=4cm]{example-image}};\n\\node (nl4) at (9,-4) {\\includegraphics[width=4cm]{example-image}};\n\n\\node (nl5) at (6,-10) {\\includegraphics[width=4cm]{example-image}};\n\\node (nl6) at (9,-10) {\\includegraphics[width=4cm]{example-image}};\n\n\\node at (6,-6.5) {$\\mathbf{Relation} \\text{ graph}$};\n\\node at (9,-6.5) {$\\mathbf{Clean} \\text{ graph}$};\n\\node at (8.5,-9.2) {\\includegraphics[width=3cm]{example-image}};\n\\node at (9.5,-9.6) {\\includegraphics[width=3cm]{example-image}};\n\\node at (8.5,-11.2) {\\includegraphics[width=3cm]{example-image}};\n\\node at (9.5,-11.6) {\\includegraphics[width=3cm]{example-image}};\n\\node at (8.5,-13) {\\includegraphics[width=3cm]{example-image}};\n\\node at (9.5,-13.4) {\\includegraphics[width=3cm]{example-image}};\n\\node at (8.5,-14.6) {\\includegraphics[width=3cm]{example-image}};\n\\node at (9.5,-15) {\\includegraphics[width=3cm]{example-image}};\n\\node at (8.5,-16.2) {\\includegraphics[width=3cm]{example-image}};\n\\node at (9.5,-16.6) {\\includegraphics[width=3cm]{example-image}};\n\n\\node[rectangle,draw,fill=white!50!gray] at (nl.north) {\\textbf{Label set}};\n\n\\node[rectangle,draw,fill=white!50!gray] at (nl1.north) {\\textbf{Score}};\n\n\\node[rectangle,draw,fill=white!50!gray] at (nl2.north) {\\textbf{Clean noise}};\n\n\\node[rectangle,draw,fill=white!50!gray] at (nl3.north) {\\textbf{Score}};\n\n\\node[rectangle,draw,fill=white!50!gray] at (nl4.north) {\\textbf{Clean noise}};\n\n\\node[rectangle,draw,fill=white!50!gray] at (nl5.north) {\\textbf{Score}};\n\n\\node[rectangle,draw,fill=white!50!gray] at (nl6.north) {\\textbf{Clean noise}};\n\n\\draw[->,shorten >=2pt,shorten <=2pt] (nl.south) .. controls +(down:1) and +(left:1) .. (nl1.south);\n\\draw[->,shorten >=2pt,shorten <=2pt] (nl1.south) .. controls +(down:1) and +(left:1) .. (nl2.south);\n\\draw[->,shorten >=2pt,shorten <=2pt] (nl2.south) .. controls +(down:1) and +(left:1) .. (nl3.north);\n\\draw[->,shorten >=2pt,shorten <=2pt] (nl3.north) .. controls +(up:1) and +(right:1) .. (nl2.north);\n\\draw[->,shorten >=2pt,shorten <=2pt] (nl3.north) .. controls +(up:1) and +(right:1) .. (nl4.south);\n\\draw[->,shorten >=2pt,shorten <=2pt] (nl4.south) .. controls +(down:1) and +(right:1) .. (nl3.south);\n\\draw[->,shorten >=2pt,shorten <=2pt] (nl5.south) .. controls +(down:1) and +(left:1) .. (nl6.north);\n\\draw[->,shorten >=2pt,shorten <=2pt] (nl6.north) .. controls +(up:1) and +(right:1) .. (nl5.south);\n\n\\node[circle,draw,fill=white] at (10,-3.7) {};\n\\node[circle,draw,fill=white] at (10,-5.7) {};\n\\node[circle,draw,fill=white] at (9,-8.7) {};\n\\node[circle,draw,fill=white] at (10,-8.7) {};\n\\node[circle,draw,fill=white] at (10,-9.7) {};\n\\node[circle,draw,fill=white] at (9,-12.7) {};\n\\node[circle,draw,fill=white] at (10,-12.7) {};\n\\node[circle,draw,fill=white] at (10,-13.7) {};\n\\node[circle,draw,fill=white] at (9,-16.7) {};\n\\node[circle,draw,fill="
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    {
        "index": 937,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{fullpage,amsthm,amssymb,amsmath,amsfonts,rotate}\n\\usepackage{tikz}\n\\usetikzlibrary{calc,3d}\n\\usetikzlibrary{intersections,decorations.pathmorphing,shapes,decorations.pathreplacing,fit}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath,ifthen,color,eurosym}\n\\usepackage{latexsym,amsthm,amsmath,amssymb,url}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{backgrounds}\n\\usetikzlibrary{decorations.pathreplacing}\n\\tikzset{black node/.style={draw, circle, fill = black, minimum size = 4pt, inner sep = 0pt}}\n\\tikzset{hblack node/.style={draw, circle, fill = black, minimum size = 5pt, inner sep = 0pt}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[every node/.style = black node, scale = 0.7]\n\t\t\\begin{scope}\n\t\t\\draw[rotate = 90] (-1.3,0) node[hblack node] (u1) {}\n\t\t-- (0,0) node[hblack node] (u0) {}\n\t\t-- (1.3,0) node[hblack node] (u2) {}\n\t\t-- (0,1.3) node[hblack node] (u3) {}\n\t\t-- (0,-1.3) node[hblack node] (u4) {}\n\t\t-- cycle;\n\t\t\n\t\t\\draw[rotate = 0] (-1.3,0) node[hblack node] (u5) {}\n\t\t-- (0,0) node[hblack node] (u6) {}\n\t\t-- (1.3,0) node[hblack node] (u7) {}\n\t\t-- (0,1.3) node[hblack node] (u8) {}\n\t\t-- (0,-1.3) node[hblack node] (u9) {}\n\t\t-- cycle;\n\t\t\n\t\t\\draw[rotate = -90] (-1.3,0) node[hblack node] (u10) {}\n\t\t-- (0,0) node[hblack node] (u11) {}\n\t\t-- (1.3,0) node[hblack node] (u12) {}\n\t\t-- (0,1.3) node[hblack node] (u13) {}\n\t\t-- (0,-1.3) node[hblack node] (u14) {}\n\t\t-- cycle;\n\t\t\n\t\t\\draw (0,-1.5) node {$\\overline{K}_6$};\n\t\t\n\t\t\\draw (0,0) circle (0.75);\n\t\t\n\t\t\\draw (u0) -- (u1) node[pos = 0.3, right] {$u_1$} node[pos = 0.55, right] {$u_2$} node[pos = 0.8, right] {$u_3$}\n\t\t-- (u2) node[pos = 0.5, right] {$u_4$}\n\t\t-- (u3) node[pos = 0.5, above] {$\\overline{K}_3$};\n\t\t\n\t\t\\draw (u3) -- (u4) node[pos = 0.5, right] {$u_5$} node[pos = 0.5, above] {$\\overline{K}_4$}\n\t\t-- (u6) node[pos = 0.5, right] {$u_6$}\n\t\t-- (u7) node[pos = 0.5, right] {$u_7$} node[pos = 0.5, above] {$\\overline{K}_5$};\n\t\t\n\t\t\\draw (u9) -- (u10) node[pos = 0.5, left] {$u_8$} node[pos = 0.5, above] {$\\overline{K}_1$}\n\t\t-- (u11) node[pos = 0.5, left] {$u_9$}\n\t\t-- (u12) node[pos = 0.5, left] {$u_{10}$} node[pos = 0.5, above] {$\\overline{K}_2$};\n\t\t\n\t\t\\draw (u13) -- (u14) node[pos = 0.5, left] {$u_{11}$} node[pos = 0.5, below] {$\\overline{K}_7$}\n\t\t-- (u12) node[pos = 0.5, left] {$u_{12}$}\n\t\t-- (u11) node[pos = 0.5, left] {$u_{13}$} node[pos = 0.5, below] {$\\overline{K}_8$};\n\t\t\n\t\t\\draw (u4) -- (u9) node[pos = 0.5, below] {$\\overline{K}_9$}\n\t\t-- (u5) node[pos = 0.5, below] {$\\overline{K}_{10}$}\n\t\t-- (u0) node[pos = 0.5, below] {$\\overline{K}_{11}$};\n\t\t\n\t\t\\draw (u10) -- (u13) node[pos = 0.5, above] {$\\overline{K}_{12}$}\n\t\t-- (u14) node[pos = 0.5, above] {$\\overline{K}_{14}$}\n\t\t-- (u8) node[pos = 0.5, above] {$\\overline{K}_{15}$};\n\t\t\n\t\t\\end{scope}\n\t\t\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 938,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows.meta,arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.8]\n\\draw[thick,double] (0,-0.5) -- (0,1);\n\\draw[thick,double] (0,0.5) -- (0,2);\n\\draw (0,1) node {$\\vdots$};\n\\draw[thick,double] (1.5,-0.5) -- (1.5,0.5);\n\\draw[thick,double] (1.5,1) -- (1.5,2);\n\\draw (1.5,0.5) node {$\\vdots$};\n\\draw (1.5,1) node {$\\vdots$};\n\\draw[thick,double] (3,-0.5) -- (3,1);\n\\draw[thick,double] (3,0.5) -- (3,2);\n\\draw (3,0.5) node {$\\vdots$};\n\\draw (3,1) node {$\\vdots$};\n\\draw[->,very thick] (1.8,0) -- (2.8,0);\n\\draw[->,very thick] (4,0) -- (5,0);\n\\draw[thick,double] (6.5,-0.5) -- (6.5,0.5);\n\\draw[thick,double] (6.5,1) -- (6.5,2);\n\\draw (6.5,1) node {$\\vdots$};\n\\draw[thick,double] (8,0.5) -- (8,2);\n\\draw[thick,double] (8,-0.5) -- (8,-2);\n\\draw (8,-0.5) node {$\\vdots$};\n\\draw (8,1) node {$\\vdots$};\n\\draw[->,very thick] (6.8,0) -- (7.8,0);\n\\draw[->,very thick] (9,0) -- (10,0);\n\\draw[thick,double,-{Latex[length=1.5mm,width=1.5mm]}] (8.2,0) -- (7.8,0);\n\\draw[thick,double,-{Latex[length=1.5mm,width=1.5mm]}] (9.2,0) -- (8.8,0);\n\\draw[thick,double] (8.8,2) -- (8.8,0.5);\n\\draw[thick,double] (9.2,2) -- (9.2,0.5);\n\\draw[thick,double] (9.2,2) -- (9.2,1.5);\n\\draw[thick,double] (8.8,2) -- (8.8,1.5);\n\\draw (10,0) node {$\\big\\downarrow$};\n\\draw (10,-0.5) node {$\\frac{1}{q}$};\n\\draw[thick,double] (10.5,0.5) -- (10.5,1);\n\\draw[thick,double] (10.5,1.5) -- (10.5,2);\n\\draw (10.5,1) node {$\\vdots$};\n\\draw[thick,double,-{Latex[length=1.5mm,width=1.5mm]}] (11,0) -- (10.6,0);\n\\draw[thick,double,-{Latex[length=1.5mm,width=1.5mm]}] (10.4,0) -- (11,0);\n\\draw[thick,double] (11,0) -- (11,0.5);\n\\draw (10.5,0.5) node {$\\big\\downarrow$};\n\\draw (10.5,0.5) node {$\\frac{1}{p}$};\n\\draw[thick,double] (11,0.5) -- (11,1);\n\\draw[thick,double] (11,1) -- (11,2);\n\\draw (11,1) node {$\\vdots$};\n\\draw (10.5,1.5) node {$\\big\\uparrow$};\n\\draw (10.5,1.5) node {$\\frac{1}{q}$};\n\\draw[thick,double,-{Latex[length=1.5mm,width=1.5mm]}] (10.7,1.5) -- (11.3,1.5);\n\\draw[thick,double,-{Latex[length=1.5mm,width=1.5mm]}] (10.3,1.5) -- (10.7,1.5);\n\\draw[thick,double] (10.3,1.5) -- (10.3,2);\n\\draw[thick,double] (11.3,1.5) -- (11.3,2);\n\\draw[->,very thick] (11.3,1.5) -- (12.3,1.5);\n\\draw (12.3,1.5) node {$\\big\\downarrow$};\n\\draw (12.3,1.5) node {$\\frac{1}{p}$};\n\\draw[thick,double,-{Latex[length=1.5mm,width=1.5mm]}] (12.5,1.5) -- (13.1,1.5);\n\\draw[thick,double,-{Latex[length=1.5mm,width=1.5mm]}] (12.9,1.5) -- (12.5,1.5);\n\\draw[thick,double] (12.9,1.5) -- (12.9,2);\n\\draw[thick,double] (13.1,1.5) -- (13.1,2);\n\\draw[thick,double] (13.1,1.5) -- (13.1,0.5);\n\\draw (12.9,1.5) node {$\\big\\uparrow$};\n\\draw (12.9,1.5) node {$\\frac{1}{q}$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 939,
        "tikz_code": "\\documentclass[10pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amssymb, amsmath, amsfonts, amscd, amsthm, amsbsy}\n\\usepackage{tikz}\n\\usepackage{tikz-cd}\n\\usepackage{tikz-3dplot}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=newest}\n\\usetikzlibrary{matrix,arrows,automata,shapes,calc,patterns,decorations.markings,decorations.pathmorphing}\n\\tikzset{compass/.style={decorate, decoration={markings, mark=at position .5 with {\\arrow[scale=1.5,black]{>}}}}}\n\\usepackage{color}\n\\usepackage{color}\n\n\\newcommand{\\gw}{\\mathrm{GW}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw [blue, dashed] (1, 5) -- (1, 2);\n\\draw [blue, dashed] (2, 5) -- (2, 2);\n\\draw [blue, dashed] (3, 5) -- (3, 2);\n\\draw [blue, dashed] (4, 5) -- (4, 2);\n\\draw [blue, dashed] (5, 5) -- (5, 2);\n\\draw [blue, dashed] (6, 5) -- (6, 2);\n\\draw [blue, dashed] (7, 5) -- (7, 2);\n\\draw [black, thick] (0.5, 3.5) to[out=0, in=180] (2.5, 2.5) to[out=0, in=180] (5, 3.5);\n\\draw [black, thick] (0.5, 3.5) to[out=180, in=0] (1.5, 3.5) to[out=180, in=0] (2.5, 3.5);\n\\draw [black, thick] (6, 3.5) to[out=0, in=180] (7.5, 3.5);\n\\node [blue, above] at (1, 5) {Cosmic inflation, radiation};\n\\node [blue, above] at (2, 5) {matter};\n\\node [blue, above] at (5, 5) {A};\n\\node [blue, above] at (7, 5) {B};\n\\node [blue, right] at (5.5, 3.5) {$\\gamma$};\n\\node [blue, right] at (7.5, 3.5) {$\\gamma$};\n\\node [blue, right] at (6.5, 3.5) {CBM};\n\\node [blue, right] at (7.5, 2.5) {$\\gw$};\n\\node [below] at (0.5, 2.5) {$\\frac{\\pi}{2}$};\n\\node [below] at (1.5, 2.5) {$\\gamma / 2$};\n\\node [below] at (2.5, 2.5) {$e^{-}$};\n\\node [below] at (4.5, 2.5) {$\\gw / 2$};\n\\node [below] at (5.5, 2.5) {$m_e$};\n\\node [below] at (7.5, 2.5) {$\\frac{ln(t)}{n(t)} / \\frac{1}{2}$};\n\\draw [black, very thick] (0,2.5) -- (8,2.5);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 940,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath,amsthm,amssymb,amsfonts,amscd}\n\\usepackage{color}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usepackage{tcolorbox}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5]\n\\tikzstyle{myarrows}=[line width=1mm, draw=black]\n\n% Dijkstra's Algo\n\\draw[thick] (-4,0) -- (-6,1) -- (-8,0);\n\\draw[thick] (-4,0) -- (-6,-1) -- (-8,0);\n\\draw[thick] (-4,0) -- (-6,1) -- (-8,2);\n\\draw[thick] (-4,0) -- (-6,-1) -- (-8,2);\n\\draw[thick] (-4,0) -- (-6,1) -- (-8,-1);\n\\draw[thick] (-4,0) -- (-6,-1) -- (-8,-1);\n\\draw[thick] (-4,0) -- (-6,1) -- (-8,-2);\n\\draw[thick] (-4,0) -- (-6,-1) -- (-8,-2);\n\\draw[thick] (-4,0) -- (-6,1) -- (-8,2);\n\\draw[thick] (-4,0) -- (-6,-1) -- (-8,2);\n\\draw[thick] (-4,0) -- (-6,1) -- (-8,1);\n\\draw[thick] (-4,0) -- (-6,-1) -- (-8,1);\n\\draw[thick] (-4,0) -- (-6,1) -- (-8,0);\n\\draw[thick] (-4,0) -- (-6,-1) -- (-8,0);\n\\draw[thick] (-4,0) -- (-6,1) -- (-8,1);\n\\draw[thick] (-4,0) -- (-6,-1) -- (-8,1);\n\n% Outer circle\n\\draw[thick] (-4,0) circle (0.5cm);\n\\draw[thick] (-8,0) circle (0.5cm);\n\\draw[thick] (-8,2) circle (0.5cm);\n\\draw[thick] (-8,-1) circle (0.5cm);\n\\draw[thick] (-8,-2) circle (0.5cm);\n\\draw[thick] (-6,1) circle (0.5cm);\n\\draw[thick] (-6,-1) circle (0.5cm);\n\\draw[thick] (-8,1) circle (0.5cm);\n\n\n% Neighbors of outer circle\n\\draw[thick] (-5.2,1.1) -- (-3.8,1.1);\n\\draw[thick] (-5.2,-0.9) -- (-3.8,-0.9);\n\\draw[thick] (-5.2,0.9) -- (-3.8,0.9);\n\n\\draw[thick] (-5.2,1.5) -- (-3.8,1.5);\n\\draw[thick] (-5.2,-0.5) -- (-3.8,-0.5);\n\\draw[thick] (-5.2,0.5) -- (-3.8,0.5);\n\n\\draw[thick] (-5.2,1.9) -- (-3.8,1.9);\n\\draw[thick] (-5.2,-0.1) -- (-3.8,-0.1);\n\\draw[thick] (-5.2,0.1) -- (-3.8,0.1);\n\n% Outer dots\n\\fill (-4,0) circle (1mm);\n\\fill (-8,0) circle (1mm);\n\\fill (-8,2) circle (1mm);\n\\fill (-8,-1) circle (1mm);\n\\fill (-8,-2) circle (1mm);\n\\fill (-6,1) circle (1mm);\n\\fill (-6,-1) circle (1mm);\n\\fill (-8,1) circle (1mm);\n\n% Inner dots\n\\fill[red] (-3.8,1.1) circle (1mm);\n\\fill[red] (-3.8,-0.9) circle (1mm);\n\\fill[red] (-3.8,0.9) circle (1mm);\n\\fill[red] (-3.8,1.5) circle (1mm);\n\\fill[red] (-3.8,-0.5) circle (1mm);\n\\fill[red] (-3.8,0.5) circle (1mm);\n\\fill[red] (-3.8,1.9) circle (1mm);\n\\fill[red] (-3.8,-0.1) circle (1mm);\n\\fill[red] (-3.8,0.1) circle (1mm);\n\n% Labels\n\\node at (-4,0) {$x_0$};\n\\node at (-8,0) {$x_1$};\n\\node at (-8,2) {$x_2$};\n\\node at (-8,-1) {$x_3$};\n\\node at (-8,-2) {$x_4$};\n\\node at (-6,1) {$x_5$};\n\\node at (-6,-1) {$x_6$};\n\\node at (-8,1) {$x_7$};\n\\node at (-8.5,0) {$\\cdots$};\n\\node at (-8,-2.5) {$\\cdots$};\n\\node at (-8,2.5) {$\\cdots$};\n\\node at (-9,0) {$\\lambda$};\n\\node at (-9,2) {$\\mu$};\n\\node at (-9,-1) {$\\rho$};\n\\node at (-9,1) {$\\tau$};\n\n%Inner circle\n\n% Labels\n\\node at (-2,-1) {$\\sqrt{2}R'$};\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 941,
        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\begin{document}\n\\begin{tikzpicture}\n\\draw[step=.5cm,gray,very thin] (-2.5,-2.5) grid (2.5,2.5);\n\\draw[latex-latex] (-2.5,0) -- (2.5,0);\n\\draw[latex-latex] (0,-2.5) -- (0,2.5);\n\\end{tikzpicture}\n\\begin{tikzpicture}\n\\draw[step=.5cm,gray,very thin] (-2.5,-2.5) grid (2.5,2.5);\n\\draw[latex-latex] (-2.5,0) -- (2.5,0);\n\\draw[latex-latex] (0,-2.5) -- (0,2.5);\n\\end{tikzpicture}\n\\begin{tikzpicture}\n\\draw[step=.5cm,gray,very thin] (-2.5,-2.5) grid (2.5,2.5);\n\\draw[latex-latex] (-2.5,0) -- (2.5,0);\n\\draw[latex-latex] (0,-2.5) -- (0,2.5);\n\\end{tikzpicture}\n\\end{document}"
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    {
        "index": 942,
        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{tikz}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usetikzlibrary{arrows,positioning,matrix,backgrounds}\n\\usepackage{pgfplots}\n\\tikzset{\n    table/.style={\n        matrix of nodes,\n        row sep=-\\pgflinewidth,\n        column sep=-\\pgflinewidth,\n        nodes={\n            rectangle,\n            draw=black,\n            align=center,\n            minimum height=1.5em,\n            text depth=0.5ex,\n            text height=1ex,\n            fill=white,\n            text width=1.5em,\n        },\n        minimum width=2em,\n        row 1/.style={\n            nodes={\n                fill=black,\n                text=white,\n                font=\\bfseries,\n            }\n        },\n    }\n}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n    \\matrix[table,inner sep=0pt] (A)\n    {\n        & & & & & & & & & & & & & & & & & & & \\\\\n        & & & & & & & & & & & & & & & & & & & \\\\\n        & & & & & & & & & & & & & & & & & & & \\\\\n        & & & & & & & & & & & & & & & & & & & \\\\\n        & & & & & & & & & & & & & & & & & & & \\\\\n        & & & & & & & & & & & & & & & & & & & \\\\\n        & & & & & & & & & & & & & & & & & & & \\\\\n        & & & & & & & & & & & & & & & & & & & \\\\\n        & & & & & & & & & & & & & & & & & & & \\\\\n        & & & & & & & & & & & & & & & & & & & \\\\\n        & & & & & & & & & & & & & & & & & & & \\\\\n        & & & & & & & & & & & & & & & & & & & \\\\\n    };\n    \n    \\node[left=0.2em of A] (D) {$\\mathbf{G}$};\n    \\node[left=0.2em of A-1-1] (G1) {$\\mathbf{G_1}$};\n    \\node[left=0.2em of A-2-1] (G2) {$\\mathbf{G_2}$};\n    \\node[left=0.2em of A-3-1] (G3) {$\\mathbf{G_3}$};\n    \\node[left=0.2em of A-4-1] (G4) {$\\mathbf{G_4}$};\n    \n    \\draw[dashed,draw=black!50] (A-5-1.south west) -- (A-5-1.north west);\n    \\draw[dashed,draw=black!50] (A-6-1.south west) -- (A-6-1.north west);\n    \\draw[dashed,draw=black!50] (A-7-1.south west) -- (A-7-1.north west);\n    \\draw[dashed,draw=black!50] (A-8-1.south west) -- (A-8-1.north west);\n    \\draw[dashed,draw=black!50] (A-9-1.south west) -- (A-9-1.north west);\n    \n    \\node[below=0.1em of A-1-25] (D) {$\\mathbf{D_0}$};\n    \\node[below=0.1em of A-2-25] (D) {$\\mathbf{D_1}$};\n    \\node[below=0.1em of A-3-25] (D) {$\\mathbf{D_2}$};\n    \\node[below=0.1em of A-4-25] (D) {$\\mathbf{D_3}$};\n    \n    \\draw[dashed,draw=black!50] (A-1-22.south west) -- (A-1-22.north west);\n    \\draw[dashed,draw=black!50] (A-1-23.south west) -- (A-1-23.north west);\n    \\draw[dashed,draw=black!50] (A-1-24.south west) -- (A-1-24.north west);\n    \n    \\foreach \\x in {1,...,24}\n    {\n        \\draw[-latex] (A-1-\\x.north) -- (A-2-\\x.south);\n        \\draw[-latex] (A-2-\\x.north) -- (A-3-\\x.south);\n        \\draw[-latex] (A-3-\\x.north) -- (A-4-\\x.south);\n    }\n    \n    \\foreach \\x in {1,...,24}\n    {\n        \\draw[-latex] (A-2-\\x.north) -- (A-3-\\x.south);\n        \\draw[-latex] (A-3-\\x.north) -- (A-4-\\x.south);\n        \\draw[-latex] (A-4-\\x.north) -- (A-5-\\x.south);\n    }\n    \n    \\foreach \\x in {1,...,24}\n    {\n        \\draw[-latex] (A-3-\\x.north) -- (A-4-\\x.south);\n        \\draw[-latex] (A-4-\\x.north) -- (A-5-\\x.south);\n        \\draw[-latex] (A-5-\\x.north) -- (A-6-\\x.south);\n    }\n    \n    \\foreach \\x in {1,...,24}\n    {\n        \\draw[-latex] (A-4-\\x.north) -- (A-5-\\x.south);\n        \\draw[-latex] (A-5-\\x.north) -- (A-6-\\x.south);\n        \\draw[-latex] (A-6-\\x.north) -- (A-7-\\x.south);\n    }\n    \n    \\foreach \\x in {1,...,24}\n    {\n        \\draw[-latex] (A-5-\\x.north) -- (A-6-\\x.south);\n        \\draw[-latex] (A-6-\\x.north) -- (A-7-\\x.south);\n        \\draw[-latex] (A-7-\\x.north) -- (A-8"
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        "index": 943,
        "tikz_code": "\\documentclass[12pt,reqno]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usepackage{xcolor}\n\\usepackage{pgfplots}\n\\usepackage{pgfplotstable}\n\\usepackage{color}\n\\usetikzlibrary{arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale = 0.8]\n\t\t\t\\draw[->, line width=0.6] (-3.5,0) -- (6.5,0)  node at (7,-0.3) {$b = 0$};\n\t\t\t\\draw[->,line width=0.6] (0,-3.5) -- (0,5) node at (0.8,6) {$a = 0$};\n\t\t\t\\draw[red] (-0.4,-3.5) -- (-0.4,3.5);\n\t\t\t\\draw[red] (-0.4,3.5) -- (3.3,3.5);\n\t\t\t\\draw[red] (3.3,3.5) -- (3.3,-3.5);\n\t\t\t\\draw[red] (3.3,-3.5) -- (-0.4,-3.5);\n\t\t\t\\draw[blue, line width=0.3] (-0.4,-3.5) -- (-0.4,3.5);\n\t\t\t\\draw[blue, line width=0.3] (-0.4,3.5) -- (3.3,3.5);\n\t\t\t\\draw[blue, line width=0.3] (3.3,3.5) -- (3.3,-3.5);\n\t\t\t\\draw[blue, line width=0.3] (3.3,-3.5) -- (-0.4,-3.5);\n\t\t\t\\draw[fill=blue, opacity = 0.1] (3.3,3.5) -- (3.3,-3.5) -- (-0.4,-3.5) -- (-0.4,3.5) -- (3.3,3.5);\n\t\t\t\\draw[fill=red, opacity = 0.1] (-0.4,3.5) -- (3.3,3.5) -- (3.3,-3.5) -- (-0.4,-3.5);\n\t\t\t\\node[red] at (5.4,-2.4) {$H^1 = H^1_0 = H^1_2 = H^1_1 = 0$};\n\t\t\t\\node[blue] at (5.4,-0.7) {$H^0_1$};\n\t\t\t\\node[blue] at (-1.4,-0.7) {$H^0_2$};\n\t\t\t\\node[blue] at (-1.4,1.8) {$H^0_1$};\n\t\t\t\\node[blue] at (-1.4,4.4) {$H^0_2$};\n\t\t\t\\foreach \\x in {-3,-2,...,3}{\n\t\t\t\t\\foreach \\y in {-3,-2,...,3}{\n\t\t\t\t\t\\node[draw,circle,inner sep=1pt,fill] at (\\x,\\y) {};\n\t\t\t\t}\n\t\t\t}\n\t\t\t\\end{tikzpicture}\n\n\\end{document}"
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        "index": 944,
        "tikz_code": "\\documentclass[a4paper]{amsart}\n\\usepackage{amsmath,amssymb,amsfonts,amsthm}\n\\usepackage[T1]{fontenc}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix,positioning,calc,decorations.markings}\n\\usetikzlibrary{arrows}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale = .4]\n\n\t\\fill[green!40] (1,1) -- (3,1) -- (6,4) -- (6,6) -- (3,9) -- (1,6) -- cycle;\n\n\t\\draw[line width=1pt] (0,2) -- (1,1) -- (6,4) -- (6,6) -- (3,9) -- (0,6) -- cycle;\n\n\t\\draw[line width = 1.5pt, black!40] (1,1) -- (6,4);\n\t\\draw[line width = 1.5pt, black!40] (0,6) -- (6,6);\n\n\t\\draw[line width = 1.5pt, ->] (3,6) -- (3,9);\n\t\\draw[line width = 1.5pt, ->] (3,6) -- (0,6);\n\t\n\t\\draw (3.3,6) node[right] {$k_+$};\n\t\\draw (3.3,9) node[right] {$k_-$};\n\t\\draw (0,6) node[left] {$t=t_0$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\tikzstyle{level 1}=[sibling distance=30mm]\n\\tikzstyle{level 2}=[sibling distance=15mm]\n\\tikzstyle{level 3}=[sibling distance=5mm]\n\\node [circle,draw] (root){}\nchild {node [circle,draw] {}\n\tchild {node [circle,draw,label=below:{$(2,0)$}] {}\n\t\tchild {node [circle,draw,label=below:{$(3,0)$}] {}\n\t\t\tchild {node [circle,draw,label=below:{$(4,0)$}] {} }\n\t\t\tchild {node [circle,draw,label=below:{$(2,1)$}] {} }\n\t\t}\n\t\tchild {node [circle,draw,label=below:{$(1,1)$}] {} }\n\t}\n\tchild {node [circle,draw,label=below:{$(3,2)$}] {}\n\t\tchild {node [circle,draw,label=below:{$(4,3)$}] {} }\n\t\tchild {node [circle,draw,label=below:{$(3,3)$}] {} }\n\t}\n}\nchild {node [circle,draw] {}\n\tchild {node [circle,draw,label=below:{$(2,2)$}] {}\n\t\tchild {node [circle,draw,label=below:{$(3,2)$}] {}\n\t\t\tchild {node [circle,draw,label=below:{$(4,2)$}] {} }\n\t\t\tchild {node [circle,draw,label=below:{$(3,1)$}] {} }\n\t\t}\n\t\tchild {node [circle,draw,label=below:{$(1,3)$}] {} }\n\t}\n\tchild {node [circle,draw,label=below:{$(1,1)$}] {} }\n};\n\\node at (root)[above] {$\\mathbf{R}=(0,0)$};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 946,
        "tikz_code": "\\documentclass[conference,10pt]{IEEEtran}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{xcolor}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.15}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\\begin{axis}[\naxis line style={white!80!black},\nlegend cell align={left},\nlegend style={fill opacity=0.8, draw opacity=1, text opacity=1, at={(0.99,0.01)}, anchor=south east, draw=white!80!black},\nlog basis y={10},\ntick align=outside,\ntick pos=left,\nx grid style={white!80!black},\nxlabel={\\large Time in s},\nxmajorgrids,\nxmin=-3.25, xmax=72.25,\nxtick style={color=white!15!black},\ny grid style={white!80!black},\nylabel={\\large Client sin $\\omega_{\\mathrm{ch},t}$ [mV]},\nymajorgrids,\nymin=0.00070310027338148, ymax=300.14536680206,\nymode=log,\nytick style={color=white!15!black},\nytick={0.0001,0.001,0.01,0.1,1,10,100,1000,10000},\nyticklabels={\n  \\(\\displaystyle {10^{-3}}\\),\n  \\(\\displaystyle {10^{-2}}\\),\n  \\(\\displaystyle {10^{-1}}\\),\n  \\(\\displaystyle {10^{0}}\\),\n  \\(\\displaystyle {10^{1}}\\),\n  \\(\\displaystyle {10^{2}}\\),\n  \\(\\displaystyle {10^{3}}\\),\n  \\(\\displaystyle {10^{4}}\\),\n  \\(\\displaystyle {10^{5}}\\)\n}\n]\n\\addplot [thick, red, opacity=0.55]\ntable {%\n0 0.02010434\n25 0.019424933\n50 0.018886171\n75 0.025647012\n100 0.031485443\n125 0.029025771\n150 0.028870428\n175 0.03005679\n200 0.032911543\n225 0.035471674\n250 0.029197866\n275 0.029995961\n300 0.029084447\n325 0.031598671\n350 0.026149471\n375 0.032282243\n400 0.027487205\n425 0.024479054\n450 0.030045106\n475 0.023291208\n500 0.028171267\n525 0.029410674\n550 0.026918799\n575 0.028191596\n600 0.031931872\n625 0.028718224\n650 0.029114424\n675 0.030571528\n700 0.033354474\n};\n\\addlegendentry{$\\mathbf{V_{\\mathrm{tot}}}$}\n\\addplot [thick, blue, opacity=0.55]\ntable {%\n0 0.00064524201019595\n25 0.0006287661105782\n50 0.00055847520167154\n75 0.00047605933320765\n100 0.00038234322061277\n125 0.0003035812920614\n150 0.00025679180657879\n175 0.00023974642003938\n200 0.00024889604521891\n225 0.0002489118096052\n250 0.00026130316063222\n275 0.00032717340612264\n300 0.00038180813484841\n325 0.00040096340928203\n350 0.00040340792695116\n375 0.00041714788447636\n400 0.00044568286450097\n425 0.00046791371750111\n450 0.00049651647820918\n475 0.00053298669189871\n500 0.00054261391996455\n525 0.00054967623477816\n550 0.0005754301398132\n575 0.00058515758980286\n600 0.00059048530645358\n625 0.00060180919561245\n650 0.000604825989660"
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        "tikz_code": "\\documentclass[11pt, oneside]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{tikz}\n\\usetikzlibrary{matrix,arrows,decorations.pathmorphing}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=4]\n\\fill[gray!40!white] (0,0) rectangle (1,1);\n\\node at (0.5,0.5) {$\\circ$};\n\\node at (-1.5,0.5) {$\\circ$};\n\\node at (1.5,0.5) {$\\circ$};\n\\node at (1.5,-0.5) {$\\circ$};\n\\node at (-1.5,-0.5) {$\\circ$};\n\\node at (-1.5,1.5) {$\\circ$};\n\\node at (1.5,1.5) {$\\circ$};\n\\node at (0.5,-1.5) {$\\circ$};\n\\node at (1.5,1) {$\\circ$};\n\\node at (-1.5,1) {$\\circ$};\n\\node at (-1.5,-1.5) {$\\circ$};\n\\node at (1.5,-1.5) {$\\circ$};\n\\node at (-1.5,1.25) {$(g_x,u_1^1+\\delta_1^1)$};\n\\node at (-0.5,1.25) {$(g_x,u_1^1+\\delta_1^1)$};\n\\node at (1.25,1.25) {$(u_1^2,u_1^2+\\delta_2^2)$};\n\\node at (-1.5,0.25) {$(g_x,u_1^1+\\delta_1^1)$};\n\\node at (1.25,0.25) {$(g_x,u_1^2+\\delta_2^2)$};\n\\node at (-1.5,-0.25) {$(u_1^2,u_1^2+\\delta_2^2)$};\n\\node at (1.25,-0.25) {$(u_1^2,u_1^2+\\delta_2^2)$};\n\\node at (0.25,1.5) {$(u_1^2,u_1^2+\\delta_2^2)$};\n\\node at (1.25,-1.25) {$(u_1^2,u_1^2+\\delta_2^2)$};\n\\node at (-0.25,1.5) {$(g_x,u_1^1+\\delta_1^1)$};\n\\node at (-1.25,1.5) {$(g_x,u_1^1+\\delta_1^1)$};\n\\node at (-0.25,-1.25) {$(g_x,u_1^1+\\delta_1^1)$};\n\\node at (-1.25,-1.25) {$(g_x,u_1^1+\\delta_1^1)$};\n\\path[font=\\large, >=angle 90,thick]\n(0.5,0.5) edge (1.5,0.5)\n(1.5,0.5) edge (1.5,-0.5)\n(1.5,-0.5) edge (-1.5,-0.5)\n(-1.5,-0.5) edge (-1.5,1.5)\n(-1.5,1.5) edge (1.5,1.5)\n(1.5,1.5) edge (0.5,-1.5)\n(0.5,-1.5) edge (1.5,-1.5)\n(1.5,1) edge (1.5,1.5)\n(1.5,1) edge (1,1);\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 948,
        "tikz_code": "\\documentclass[12pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathmorphing}\n\\usetikzlibrary{decorations.markings}\n\\usepgflibrary{shapes.geometric}\n\n\\newcommand{\\R}{\\mathbb{R}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.7]\n\\draw[thick,->] (-8,0) -- (8,0) node[right]{$k_1$};\n\\draw[thick,->] (0,-2) -- (0,4.5) node[right]{$k_2$};\n\\filldraw [black] (0,0) circle (2pt) node[anchor=north] {$h(k_1)$};\n\\draw[red, thick] (-7.8,4) -- (7.8,4);\n\\draw[red, thick] (-7.8,4) node[anchor=south] {\\begin{tabular}{c}$\\lambda^\\pm=\\frac{\\pm\\sqrt{p}}{2\\pi}$ \\\\ $\\lambda^-=\\frac{-\\sqrt{p}}{2\\pi}$ \\end{tabular}};\n\\draw[red, thick] (7.8,4) node[anchor=south] {$\\lambda_+=\\frac{\\sqrt{p}}{2\\pi}$};\n\\draw [thick,dotted] (4,0) node[anchor=north] {$K_2$} -- (4,4);\n\\draw [thick,dotted] (-4,0) node[anchor=north] {$-K_2$} -- (-4,4);\n\\draw[blue, thick,dashed] (0,0) -- (0,4);\n\\draw[blue, thick] plot [smooth, tension=1] coordinates { (4,3.5) (3,2.5) (2,1.5) (1,1) (0,0.5) (-1,1) (-2,1.5) (-3,2.5) (-4,3.5)};\n\\draw[blue, thick] plot [smooth, tension=1] coordinates { (7.8,3.5) (7,2.5) (6,1.5) (5,1) (4,0.5) (3,1) (2,1.5) (1,2.5) (0,3.5)};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 949,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{color}\n\\usepackage{amsmath, amsthm, amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node[anchor=south west,inner sep=0] (image) at (0,0)\n{\\includegraphics[width=12cm]{example-image}};\n\\node at (2.25,0) {$x$};\n\\node at (10,0) {$y$};\n\\node at (6.25,0) {$y$};\n\\node at (10,3.75) {$\\lambda$};\n\\node at (5.5,3.75) {$\\lambda-1$};\n\\node at (10,-0.25) {$0$};\n\\node at (6.25,-0.25) {$0$};\n\\node at (10,2.5) {$y=1$};\n\\node at (5.5,2.5) {$y=\\frac{n}{2}-1$};\n\\node at (10,-0.5) {$x$};\n\\node at (6.25,-0.5) {$x$};\n\\draw[thick,<->] (6.25,2.25) -- (6.25,3);\n\\node at (6.75,2.75) {$r$};\n\\draw[dashed,thick] (0,2.5) -- (10,2.5);\n\\draw[dashed,thick] (0,0) -- (10,0);\n\\draw[<->] (0,0.5) -- (0,1.5);\n\\draw[<->] (0,4.5) -- (0,5.5);\n\\node at (-0.5,4.5) {$y$};\n\\node at (-0.5,0.5) {$y=-n(x)$};\n\\node at (2.5,-0.5) {$\\rho_x=1$};\n\\node at (2.5,1) {$\\rho_x=\\frac{n}{2}-1$};\n\\draw[thick,->] (7.5,4.5) -- (7.5,4);\n\\draw[thick,->] (7.5,0.5) -- (7.5,1);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 950,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amsmath,amsfonts,amssymb,amsthm}\n\\usepackage{tikz}\n\\usetikzlibrary{decorations.pathmorphing}\n\\tikzset{meter/.append style={draw, inner sep=10, rectangle, font=\\vphantom{A}, minimum width=30, line width=.8,\n path picture={\\draw[black] ([shift={(.1,.3)}]path picture bounding box.south west) to[bend left=50] ([shift={(-.1,.3)}]path picture bounding box.south east);\\draw[black,-latex] ([shift={(0,.1)}]path picture bounding box.south) -- ([shift={(.3,-.1)}]path picture bounding box.north);}}}\n\\usetikzlibrary{decorations.pathmorphing}\n\n\\begin{document}\n\n\\begin{tikzpicture}[baseline=-1mm,scale=0.8]\n\\draw[thick] (-1,0) -- (0,0.5) -- (1,0) -- (2,0.5) -- (3,0) -- (4,0.5) -- (5,0);\n\\draw[thick] (0,0.5) -- (2,0.5);\n\\draw[thick,densely dotted] (2,0.5) -- (2,-0.5);\n\\draw[thick] (2,-0.5) -- (2,-1);\n\\draw[thick] (2,-0.5) -- (3,-1) -- (4,-0.5);\n\\draw[thick] (0,0.5) -- (-1,1) -- (0,1.5) -- (1,1) -- (0,1.5);\n\\draw[thick] (3,0) -- (5,1) -- (4,1.5) -- (3,1) -- (4,1.5);\n\\draw[fill=white] (-1,0) circle (0.25);\n\\draw[fill=white] (0,0.5) circle (0.25);\n\\draw[fill=white] (1,0) circle (0.25);\n\\draw[fill=white] (2,0.5) circle (0.25);\n\\draw[fill=white] (3,0) circle (0.25);\n\\draw[fill=white] (4,0.5) circle (0.25);\n\\draw[fill=white] (5,0) circle (0.25);\n\\draw[fill=white] (0,1.5) circle (0.25);\n\\draw[fill=white] (2,1.5) circle (0.25);\n\\draw[fill=white] (3,1) circle (0.25);\n\\draw[fill=white] (4,1.5) circle (0.25);\n\\draw[fill=white] (2,-0.5) circle (0.25);\n\\draw[fill=white] (2,-1) circle (0.25);\n\\draw[fill=white] (4,-0.5) circle (0.25);\n\\draw[fill=white] (4,-1) circle (0.25);\n\\draw[fill=white] (5,1) circle (0.25);\n\\node[anchor=east] at (-1,0) {$s$};\n\\node[anchor=south] at (0,1.5) {$a_1$};\n\\node[anchor=south] at (2,1.5) {$B_1$};\n\\node[anchor=south] at (4,1.5) {$c_1$};\n\\node[anchor=west] at (0,0.5) {$a_2$};\n\\node[anchor=west] at (2,0.5) {$B_2$};\n\\node[anchor=west] at (4,0.5) {$c_2$};\n\\node at (2,-1.5) {$\\vdots$};\n\\node[anchor=north] at (0,-0.5) {$a_k$};\n\\node[anchor=north] at (2,-0.5) {$B_k$};\n\\node[anchor=north] at (4,-0.5) {$c_k$};\n\\node[anchor=west] at (5,0) {$t$};\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 951,
        "tikz_code": "\\documentclass{article}\n\\usepackage{amsmath,amssymb,amsthm,amsfonts}\n\\usepackage{tikz}\n\\usetikzlibrary{tikzmark}\n\\usetikzlibrary{automata,positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[level distance=1cm,\n  level 1/.style={sibling distance=3.2cm},\n  level 2/.style={sibling distance=2cm},\n  level 3/.style={sibling distance=1.7cm},\n  level 4/.style={sibling distance=1.4cm},\n  level 5/.style={sibling distance=1.2cm},\n  level 6/.style={sibling distance=1cm},\n  every text node part/.style={font=\\small}\n  ]\n  \\node[circle,draw] (z){12}\n    child {node[circle,draw] {8}\n      child {node[circle,draw] {6}\n        child {node[circle,draw] {4}\n          child {node[circle,draw] {3}\n            child {node[circle,draw] {1}}\n          }\n          child {node[circle,draw] {5}\n            child {node[circle,draw] {2}}\n          }\n        }\n        child {node[circle,draw] {7}\n          child {node[circle,draw] {10}\n            child {node[circle,draw] {9}}\n            child {node[circle,draw] {11}}\n          }\n        }\n      }\n      child {node[circle,draw] {11}\n        child {node[circle,draw] {13}\n          child {node[circle,draw] {14}\n            child {node[circle,draw] {15}\n              child {node[circle,draw] {16}\n                child {node[circle,draw] {17}\n                  child {node[circle,draw] {18}\n                    child {node[circle,draw] {19}}\n                    child {node[circle,draw] {1}}\n                  }\n                }\n                child {node[circle,draw] {10}}\n              }\n            }\n          }\n          child {node[circle,draw] {12}}\n        }\n        child {node[circle,draw] {14}}\n      }\n    }\n    child {node[circle,draw] {11}\n      child {node[circle,draw] {13}\n        child {node[circle,draw] {15}\n          child {node[circle,draw] {17}\n            child {node[circle,draw] {18}\n              child {node[circle,draw] {19}}\n              child {node[circle,draw] {1}}\n            }\n          }\n          child {node[circle,draw] {10}}\n        }\n      }\n      child {node[circle,draw] {14}}\n    };\n  \\end{tikzpicture}\n\n\\end{document}"
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        "index": 952,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{amssymb,latexsym,amsmath,amsthm,amsfonts, enumerate}\n\\usepackage{color}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning,shapes,shadows,arrows,snakes}\n\\usepackage[colorlinks=true,\npagebackref,hyperindex]{hyperref}\n\n\\newcommand{\\vv}{{\\bf v}}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\usetikzlibrary{positioning,shapes,shadows,arrows,snakes}\n\\node at (0,0) {$R$};\n\\node at (4,0) {$P$};\n\\node at (2,2) {$Q$};\n\\draw[-latex](4,0)to node[below right,midway]{$Y_3$}(2,2);\n\\draw[-latex](0,0)to node[above,midway]{$L$}(2,2);\n\\draw[-latex](0,0)to node[below,midway]{$B$}(4,0);\n\\begin{scope}[shift={(8,-1)}]\n\\node at (0,-.5) {$Y_1$};\n\\node at (2,-.5) {$Y_2$};\n\\node at (4,-.5) {$Y_3$};\n\\node at (0,2.5) {$Q$};\n\\node[left] at (2,4) {$Y_1(x,y,c)=x+y-\\frac{ab}{2}$};\n\\node[left] at (4,3) {$Y_2(x,y,z)=x-y$};\n\\node[left] at (4,-1) {$Y_3(x,y,z)=x+y$};\n\\node[right] at (0,-1) {$L=(X_1,Y_1,Y_3)=(T_1,T_3,T_4)$};\n\\node[right] at (2,-1) {$B=(X_1,Y_1,X_2)=(T_1,T_3,T_2)$};\n\\node[right] at (4,-1) {$Y_3=(X_1,X_2,Y_3)=(T_1,T_2,T_3)$};\n\\draw[-latex](0,0)--(2,0);\n\\draw[-latex](2,0)--(2,2);\n\\draw[-latex](2,2)--(4,0);\n\\draw[-latex](0,0)--(0,2);\n\\draw[-latex](0,2)--(2,2);\n\\draw[-latex](4,0)--(2,0);\n\\end{scope}\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 966,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.35]\n    \\draw[->] (0,0) -- (0,3);\n    \\draw[->] (0,0) -- (5,0);\n    \\draw (0,2.8) -- (0.2,2.8) node [left] {$\\alpha=\\frac{i}{2}$};\n    \\draw (0,0) node [left] {$0$};\n    \\draw (2.5,0) node [below] {$\\frac{1}{4}$} -- (2.5,2.8);\n    \\draw (0,2.8) node [left] {$\\frac{i}{2}$} -- (2.5,0);\n    \\draw (0,0) node [below] {$\\frac{i}{2}$};\n    \\fill[fill=red,opacity=0.2] (0,0) -- (2.5,0) -- (2.5,2.8) -- (0,2.8) -- (0,0);\n    \\draw (2,1.4) node {$I_1$};\n    \\draw (4.3,1.4) node {$I_2$};\n    \\fill[fill=red,opacity=0.2] (5,0) -- (5,3) -- (3,3) -- (3,0) -- (5,0);\n    \\draw[dashed,color=red] (5,0) -- (3,3);\n    \\draw (3,0) node [below] {$\\frac{3}{4}$};\n    \\draw[dashed,color=red] (5,3) -- (3,0);\n    \\draw (4.8,1.4) node {$\\sigma(A_\\lambda)$};\n    \\draw (3,-0.8) node {Flat ban};\n    \\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 967,
        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usepackage{color}\n\\usepackage{amsmath}\n\\usetikzlibrary{shapes,snakes,arrows,positioning,backgrounds,calc,patterns,fit,decorations.pathreplacing,matrix}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.9, every node/.style={scale=0.9}]\n\\definecolor{yellow}{RGB}{255,255,153}\n\\definecolor{olive}{RGB}{153,204,0}\n\\definecolor{orange}{RGB}{255,153,0}\n\\fill [yellow] (2,2) ellipse (2.6cm and 2.6cm);\n\\fill [yellow] (2,2) ellipse (1.5cm and 1.5cm);\n\\fill [yellow] (-0.4,-1.6) ellipse (2.6cm and 2.6cm);\n\\fill [yellow] (-0.4,-1.6) ellipse (1.5cm and 1.5cm);\n\\fill [yellow] (5.2,-1.6) ellipse (2.6cm and 2.6cm);\n\\fill [yellow] (5.2,-1.6) ellipse (1.5cm and 1.5cm);\n\\draw (0.9,1.1) node {\\color{olive} SpotBugs};\n\\draw (0.9,0) node {\\color{orange} Aster};\n\\draw (0.9,-1.9) node {\\color{olive} This Work};\n\\draw (3.9,0) node {\\color{orange} Astre};\n\\draw (3.9,-1.9) node {\\color{olive} Coq};\n\\draw (1.8,2.9) node {\\color{olive} Automated};\n\\draw (1.8,1.7) node {\\color{orange} Correct};\n\\draw (1.8,-0.7) node {\\color{olive} Interactive};\n\\draw (1.8,-2.3) node {\\color{orange} Coq};\n\\end{tikzpicture}\n\n\\end{document}"
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        "index": 968,
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        "tikz_code": "\\documentclass[tikz,border=5mm]{standalone}\n\\begin{document}\n\\begin{tikzpicture}[z={(-.3cm,-.2cm)},line cap=round,line join=round]\n\\draw[dashed,thin] (0,0,0)--(0,0,1) node[left]{$W$};\n\\draw[thin] (-3,-3,0)--(3,3,0) node[below right]{$n$};\n\\draw[thin] (0,0,0)--(0,0,5) node[above]{$k$};\n\n\\fill[gray,opacity=.25] (-3,-3,5)--(3,3,5)--(3,3,0)--(-3,-3,0)--cycle;\n\\fill[gray,opacity=.25] (-3,-3,5)--(-3,-3,0)--(3,3,0)--(3,3,5)--cycle;\n\\fill[gray,opacity=.25] (-3,-3,5)--(-3,-3,0)--(3,3,0)--(3,3,5)--cycle;\n\n\\draw[red,ultra thick] (-3,-3,0)--(-3,-3,5)--(3,3,5)--(3,3,0)--cycle;\n\\draw[red,ultra thick] (0,0,1)--(0,0,5);\n\n\\node[red] at (-1,-1,-1) {$W$};\n\\node[red] at (1,1,1) {$W$};\n\\node[red] at (0,.5,5) {$T$};\n\\node[red] at (0,-1.5,1) {$T$};\n\n\\draw[-latex] (-3,0,0) -- (-3,0,5) node[below left]{$\\mathrm{h}$};\n\\draw[-latex] (0,0,0) -- (0,5,0) node[right]{$\\mathrm{i}$};\n\\draw[-latex] (0,0,0) -- (5,0,0) node[above]{$\\mathrm{j}$};\n\\end{tikzpicture}\n\\end{document}"
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        "index": 970,
        "tikz_code": "\\documentclass[tikz]{standalone}\n\\usetikzlibrary{positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}[>=stealth,every node/.style={rectangle,draw,minimum width=2cm,minimum height=1cm},node distance=1.5cm]\n\\node (box1) [minimum height=2cm] {PE samples};\n\\node (box2) [below=of box1, minimum height=2cm] {C. AP\\textsuperscript{-1}C.};\n\\node (box3) [below=of box2, minimum height=2cm] {Compile};\n\\node (box4) [below left=of box3.north, minimum width=1.2cm, minimum height=0.3cm] {};\n\\node (box5) [below right=of box3.north, minimum width=1.2cm, minimum height=0.3cm] {};\n\\node (box6) [below=of box3, minimum height=0.3cm] {DataSet};\n\\draw[->] (box1) edge (box2);\n\\draw[->] (box2) edge (box3);\n\\draw[->] (box3) edge (box4);\n\\draw[->] (box3) edge (box5);\n\\draw[->] (box4) edge (box6);\n\\draw[->] (box5) edge (box6);\n\\end{tikzpicture}\n\n\\end{document}"
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    {
        "index": 971,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{xcolor}\n\n\\newcommand{\\tree}[3]{\\footnotesize\\begin{tabular}{c} #1 \\\\ #2 \\\\ #3 \\end{tabular}}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.9, every node/.style={align=center, scale=0.8}]\n\t\t\\node[draw,  text width=5.4cm,  minimum height=1cm] at (0,0)  {\\tree{Is there any internal edge?}{Rate $\\geq3/4$ achievable (Theorem~\\ref{th:NfR})}{Theorem~\\ref{th:fR}}};\n\t\t\\node[draw, text width=5.4cm,  minimum height=1cm] at (-3,-2)  {\\tree{Yes}{Rate $\\geq3/4$ achievable (Theorem~\\ref{th:NfR})}{Theorem~\\ref{th:fR}}};\n\t\t\\node[draw, text width=5.4cm,  minimum height=1cm] at (3,-2)  {\\tree{No}{ Rate $\\geq3/4$ achievable (Theorem~\\ref{th:NfR})}{Theorem~\\ref{th:fR}}};\n\t\t\\node[draw,  text width=6cm,  minimum height=1cm] at (-6,-4) {\\tree{\\textbf{Rate $\\geq4/3$ achievable,} \\\\ \\textbf{Theorem~\\ref{th:fR}}}{Theorem~\\ref{th:NfR}}{Theorem~\\ref{th:NfR}}};\n\t\t\\node[draw,  text width=6cm,  minimum height=1cm] at (-2,-4) {\\tree{\\textbf{Rate $\\geq4/3$ achievable} \\\\ \\textbf{Theorem~\\ref{th:NfR}}}{Theorem~\\ref{th:fR}}{Theorem~\\ref{th:NfR}}};\n\t\t\\node[draw, text width=6cm,  minimum height=1cm] at (2,-4) {\\tree{\\textbf{No} \\\\ \\textbf{Theorem~\\ref{th:NfR}}}{Theorem~\\ref{th:fR}}{Theorem~\\ref{th:NfR}}};\n\t\t\\node[draw, text width=6cm,  minimum height=1cm] at (5,-4) {\\tree{\\textbf{Rate $\\geq4/3$ achievable} \\\\ \\textbf{Theorem~\\ref{th:NfR}}}{Theorem~\\ref{th:fR}}{Theorem~\\ref{th:NfR}}};\n\t\t\\node[draw, text width=5.4cm,  minimum height=1cm] at (-6,-6) {\\tree{\\textbf{Rate $\\geq4/3$ cannot be achieved} \\\\ \\textbf{Theorem~\\ref{th:fR}}}{Theorem~\\ref{th:NfR}}{Theorem~\\ref{th:fR}}};\n\t\t\\node[draw, text width=5.4cm,  minimum height=1cm] at (5,-6) {\\tree{\\textbf{Rate $\\geq4/3$ achievable,} \\\\ \\textbf{one example where rate $\\geq3$ (Theorem~\\ref{th:fR})} \\\\ \\textbf{can not be achieved (Theorem~\\ref{th:NfR})}}}{Theorem~\\ref{th:NfR}}{Theorem~\\ref{th:NfR}};\n\t\t\\draw [->] (0,-0.75) -- (-3,-1.25);\n\t\t\\draw [->] (0,-0.75) -- (3,-1.25);\n\t\t\\draw [->] (-3,-2.75) -- (-6,-3.25);\n\t\t\\draw [->] (-3,-2.75) -- (-2,-3.25);\n\t\t\\draw [->] (3,-2.75) -- (2,-3.25);\n\t\t\\draw [->] (3,-2.75) -- (5,-3.25);\n\t\t\\draw [->] (-6,-4.75) -- (-6,-5.25);\n\t\t\\draw [->] (-6,-4.75) -- (-2,-5.25);\n\t\t\\draw [->] (-2,-4.75) -- (-2,-5.25);\n\t\t\\draw [->] (2,-4.75) -- (2,-5.25);\n\t\t\\draw [->] (2,-4.75) -- (5,-5.25);\n\t\t\\draw [->] (5,-4.75) -- (5,-5.25);\n\t\t\\draw [->] (5,-4.75) -- (2,-5.25);\n\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 972,
        "tikz_code": "\\documentclass[11pt]{article}\n\\usepackage{amssymb,amsmath,amsthm}\n\\usepackage{tikz,pgf, amsmath,amsthm,verbatim,amssymb,amsfonts,amscd, graphicx, tabu, multirow, tabulary, enumitem}\n\\usepackage{graphics, scrextend, pgfplots, float}\n\\usetikzlibrary{arrows.meta}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n[\n\tscale=1.2,\n\taction/.style={circle, draw=black, fill=white, minimum size=2mm},\n\tobservation/.style={circle, draw=black, fill=white, minimum size=2mm}\n\t]\n\t\\node[action] (a) at (0,0) {$a$};\n\t\\node[action] (b) at (0,-1) {$b$};\n\t\\node[action] (c) at (0,-2) {$c$};\n\t\\node[action] (d) at (1,-1) {$d$};\n\t\\node[action] (e) at (1,-2) {$e$};\n\t\\node[action] (f) at (1.5,-2) {$f$};\n\t\\node[action] (g) at (2,-1) {$g$};\n\t\\node[action] (h) at (2,-2) {$h$};\n\t\n\t\\node[observation] (o) at (3,0) {$o$};\n\t\\node[observation] (y) at (3,-1) {$y$};\n\t\\node[observation] (z) at (3,-2) {$z$};\n\t\n\t\\draw[-Latex] (a) to (b);\n\t\\draw[-Latex] (b) to (c);\n\t\\draw[-Latex] (a) to [out=20, in=160] (o);\n\t\\draw[-Latex] (b) to [out=20, in=160] (y);\n\t\\draw[-Latex] (c) to [out=20, in=160] (z);\n\t\\draw[-Latex] (d) to (b);\n\t\\draw[-Latex] (e) to (c);\n\t\\draw[-Latex] (f) to (c);\n\t\\draw[-Latex] (g) to (d);\n\t\\draw[-Latex] (h) to (d);\n\t\n\t\\draw[dashed] (a) to (d);\n\t\\draw[dashed] (b) to (g);\n\t\\draw[dashed] (c) to (e);\n\t\\draw[dashed] (d) to (y);\n\t\\draw[dashed] (e) to (z);\n\t\\draw[dashed] (f) to (y);\n\t\\draw[dashed] (g) to (h);\n\t\n\t\\draw[dotted] (o) to (y);\n\t\\draw[dotted] (y) to (z);\n\t\n\t\\node at (4,-1) {$\\kappa=1$};\n\t\n\t\\node at (3.5,1) {Induced graph $H_2$};\n\t\n\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 973,
        "tikz_code": "\\documentclass[a4paper,12pt]{amsart}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=.9]\n\\fill[fill=black!10] (1.5,0) .. controls (1.5,1) and (3.5,1) .. (3.5,0);\n\\fill[fill=black!10] (4.5,0) .. controls (4.5,1) and (6.5,1) .. (6.5,0);\n\n\\fill[fill=black!20] (7,0) .. controls (7,1) and (9,1) .. (9,0) .. controls (9,.5) and (8.5,.5) .. (8.5,0);\n\\fill[fill=black!20] (10,0) .. controls (10,1) and (12,1) .. (12,0) .. controls (12,-.5) and (11.5,-.5) .. (11.5,0);\n\n\\fill[fill=black!10] (9.5,0) .. controls (9.5,.5) and (9,1) .. (9,2) .. controls (9,2.5) and (8.5,2.5) .. (8.5,2);\n\\fill[fill=black!10] (11.5,0) .. controls (11.5,.5) and (11,1) .. (11,2) .. controls (11,2.5) and (11.5,2.5) .. (11.5,2);\n\n\\draw[line width=1mm] (1.5,0) .. controls (1.5,1) and (3.5,1) .. (3.5,0);\n\\draw[line width=1mm] (4.5,0) .. controls (4.5,1) and (6.5,1) .. (6.5,0);\n\n\\draw[line width=1mm] (7,0) .. controls (7,1) and (9,1) .. (9,0) .. controls (9,.5) and (8.5,.5) .. (8.5,0);\n\\draw[line width=1mm] (10,0) .. controls (10,1) and (12,1) .. (12,0) .. controls (12,-.5) and (11.5,-.5) .. (11.5,0);\n\n\\draw[line width=1mm] (9.5,0) .. controls (9.5,.5) and (9,1) .. (9,2) .. controls (9,2.5) and (8.5,2.5) .. (8.5,2);\n\\draw[line width=1mm] (11.5,0) .. controls (11.5,.5) and (11,1) .. (11,2) .. controls (11,2.5) and (11.5,2.5) .. (11.5,2);\n\n\\draw[line width=.5mm] (0,1) .. controls (0,1.5) and (1,2) .. (1.5,2) .. controls (2,2) and (2,1) .. (3,1) .. controls (3.5,1) and (3.5,2) .. (4,2);\n\\draw[line width=.5mm] (4,2) .. controls (4.5,2) and (4.5,1) .. (5,1) .. controls (5.5,1) and (5.5,2) .. (6,2);\n\\draw[line width=.5mm] (6,2) .. controls (6.5,2) and (6.5,1) .. (7,1) .. controls (7.5,1) and (7.5,2) .. (8,2);\n\\draw[line width=.5mm] (8,2) .. controls (8.5,2) and (8.5,1) .. (9,1) .. controls (9.5,1) and (9.5,2) .. (10,2);\n\\draw[line width=.5mm] (10,2) .. controls (10.5,2) and (10.5,1) .. (11,1) .. controls (11.5,1) and (11.5,2) .. (12,2);\n\\draw[line width=.5mm] (12,2) .. controls (12.5,2) and (12.5,1) .. (13,1) .. controls (13.5,1) and (13.5,2) .. (14,2);\n\\draw[line width=.5mm] (14,2) .. controls (14.5,2) and (14.5,1) .. (15,1) .. controls (15.5,1) and (15.5,2) .. (16,2);\n\\draw[line width=.5mm] (16,2) .. controls (16.5,2) and (16.5,1) .. (17,1) .. controls (17.5,1) and (17.5,2) .. (18,2);\n\\draw[line width=.5mm] (18,2) .. controls (18.5,2) and (18.5,1) .. (19,1) .. controls (19.5,1) and (19.5,2) .. (20,2);\n\n\\draw[line width=.5mm] (0,0) .. controls (0,-.5) and (1,-.5) .. (1.5,0);\n\\draw[line width=.5mm] (1.5,0) .. controls (2,-.5) and (3,-.5) .. (3.5,0);\n\\draw[line width=.5mm] (4.5,0) .. controls (5,-.5) and (6,-.5) .. (6.5,0);\n\\draw[line width=.5mm] (7,0) .. controls (7,-.5) and (8,-.5) .. (8.5,0);\n\\draw[line width=.5mm] (9,0) .. controls (9,-.5) and (10,-.5) .. (10.5,0);\n\\draw[line width=.5mm] (11,0) .. controls (11,-.5) and (12,-.5) .. (12.5,0);\n\\draw[line width=.5mm] (13.5,0) .. controls (14,-.5) and (15,-.5) .. (15.5,0);\n\\draw[line width=.5mm] (16.5"
    },
    {
        "index": 974,
        "tikz_code": "\\documentclass[a4paper,11pt]{article}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{color,soul}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{decorations.markings}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1.5]\n\t\t\\draw[very thick, black,->] (0,-2) -- (0,1); \n\t\t\\draw[very thick, black,->] (0,0) -- (3.3,0); \n\t\t\\draw[thick, red,->] (-2.5,0) -- (0,0);\n\t\t\\draw[thick, black] (0,0) -- (1.5,1.5);\n\t\t\\draw[thick, red] (1.5,1.5) -- (3,0);\n\t\t\\draw[thick, blue] (0,0) -- (1.5,-1.5);\n\t\t\\draw[thick, black] (1.5,-1.5) -- (3,0);\n\t\t\\draw[thick, blue] (1.5,1.5) -- (1.5,-1.5);\n\t\t\n\t\t\\draw[thick, blue] (1.8,-1.5) -- (3.8,1.5);\n\t\t\n\t\t\\draw[thick, red] (0.4,1.3) -- (1.1,0.4);\n\t\t\\draw[thick, red] (0.9,-1.2) -- (1.6,0.1);\n\t\t\n\t\t\\node at (0.8,0.45) {$\\textcolor{red}{\\mathcal{R}R_{\\Delta}}$};\n\t\t\\node at (0.8,-0.45) {$\\textcolor{red}{\\mathcal{R}O_{\\Delta}}$};\n\t\t\\node at (0.8,-1.1) {$\\mathcal{O}$};\n\t\t\\node at (1.5,1.5) {$\\mathcal{R}_1$};\n\t\t\\node at (1.5,-1.5) {$\\mathcal{R}_2$};\n\t\t\n\t\t\\node at (1.5,-2.5) {$\\mathcal{R}_2\\subset\\mathcal{R}_1$};\n\t\t\\node at (3,-2.5) {$\\mathcal{R}_2\\supset\\mathcal{R}_1$};\n\t\t\\node at (-2.5,0.4) {$\\mathcal{T}_1\\times\\mathcal{T}_2$};\n\t\t\\node at (-2.5,-0.4) {$0$};\n\t\t\\node at (3.5,0.4) {$\\mathcal{R}_2\\times(-1)$};\n\t\t\\node at (3.5,-0.4) {$\\mathcal{X}_2\\times\\mathcal{X}_1$};\n\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 975,
        "tikz_code": "\\documentclass[11pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz-feynman}\n\\usepackage{xcolor}\n\\tikzfeynmanset{compat=1.1.0}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n  \\begin{feynman}\n    \\vertex(a1){$p_1$};\n    \\vertex[below=4cm of a1](a2){$q$};\n    \\vertex[right=4.5cm of a1](a3){$p_2$};\n    \\vertex[right=4.5cm of a2](a4){$q$};\n    \\vertex at ($(a1)!0.5!(a2) -(0,1.5cm)$) (c1);\n    \\vertex at ($(a3)!0.5!(a4) -(0,1.5cm)$) (c2);\n    \\vertex at ($(a1)!0.5!(a2) +(0,1.5cm)$) (c3);\n    \\vertex at ($(a3)!0.5!(a4) +(0,1.5cm)$) (c4);\n    \\vertex at ($(c1)!0.5!(c2)$) (d12);\n    \\vertex at ($(d12)!0.5!(c3)$) (d34);\n    \\vertex at ($(d12)!0.5!(c4)$) (d14);\n    \\diagram*{\n    (a1)--[fermion](c1)--[scalar,edge label=$p_2$](c3)--[anti fermion](a3),\n    (a2)--[fermion](c2)--[scalar,edge label'=$p_1$](c4)--[anti fermion](a4),\n    (c1)--[scalar](c2),\n    (d12)--[fermion](d34)--[fermion](d14)--[scalar](d12),\n    };\n  \\end{feynman}\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 976,
        "tikz_code": "\\documentclass[conference]{IEEEtran}\n\\usepackage[utf8]{inputenc}\n\\usepackage{amsmath,amssymb,amsfonts, amsthm}\n\\usepackage{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\\usepackage[T1]{fontenc}\n\\usepackage{pgfplots}\n\\pgfplotsset{compat=1.14}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node[draw, circle] (v1) {$v_1$};\n\\node[draw, circle, right=0.75 of v1] (v2) {$v_2$};\n\\node[draw, circle, right=0.75 of v2] (v3) {$v_3$};\n\\node[draw, circle, right=0.75 of v3] (v4) {$v_4$};\n\\node[draw, circle, right=0.75 of v4] (v5) {$v_5$};\n\\node[draw, circle, above right=0.5 of v5] (v6) {$v_6$};\n\\node[draw, circle, below right=0.5 of v5] (v7) {$v_7$};\n\\node[draw, circle, above right=0.5 of v7] (v8) {$v_8$};\n\\node[draw, circle, below right=0.5 of v7] (v9) {$v_9$};\n\\node[draw, circle, above left=0.5 of v1] (v10) {$v_{10}$};\n\\node[draw, circle, left=0.75 of v10] (v11) {$v_{11}$};\n\\node[draw, circle, left=0.75 of v11] (v12) {$v_{12}$};\n\\node at (2.25, 0.5) {$\\mathcal{G}^*$};\n\\node at (2.25, -0.5) {$\\mathcal{G}$};\n\\node at (4.75, 0.5) {$\\widetilde{\\mathcal{G}}^*$};\n\\node at (4.75, -0.5) {$\\widetilde{\\mathcal{G}} = \\{|\\mathcal{V}|\\}$};\n\n\\draw (v1) -- (v2);\n\\draw (v2) -- (v3);\n\\draw (v3) -- (v4);\n\\draw (v4) -- (v5);\n\\draw (v5) -- (v6);\n\\draw (v5) -- (v7);\n\\draw (v7) -- (v8);\n\\draw (v7) -- (v9);\n\\draw (v10) -- (v11);\n\\draw (v11) -- (v12);\n\n\\node at (3.5, 0) {$\\dots$};\n\n\\node at (0.5, 0) {$\\dots$};\n\\node at (1, -1) {$\\vdots$};\n\n\\node at (6.5, 0) {$\\dots$};\n\\node at (7, -1) {$\\vdots$};\n\n\\draw[->,>=stealth] (v6) to (v2);\n\\draw[->,>=stealth] (v6) to (v3);\n\\draw[->,>=stealth] (v7) to (v2);\n\\draw[->,>=stealth] (v7) to (v3);\n\\draw[->,>=stealth] (v8) to (v1);\n\\draw[->,>=stealth] (v9) to (v1);\n\\draw[->,>=stealth] (v10) to (v4);\n\\draw[->,>=stealth] (v11) to (v4);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 977,
        "tikz_code": "\\documentclass[10pt, conference]{IEEEtran}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{color}\n\\usepackage[usenames,x11names]{xcolor}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,shapes,calc,positioning}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\\tikzstyle{arrow} = [->,>=stealth',shorten >=1pt,thick,draw]\n\t\\tikzstyle{darrow} = [dotted,->,>=stealth',shorten >=1pt,draw]\n\t\\tikzstyle{box} = [rectangle,rounded corners,minimum width=1.5cm,minimum height=1cm,text centered,draw=black,fill=black!20]\n\t\\tikzstyle{dbox} = [rectangle,rounded corners,minimum width=2.5cm,minimum height=1.5cm,text centered,draw=black,fill=black!20]\n\t\\tikzstyle{cross} = [cross out,-,draw=black,inner sep=0,minimum size=1.3mm]\n\t\n\t\\node at (0,0) (init) {\\textbf{$\\bullet$}};\n\t\\node at (-1,-1.8) (train) {$\\bullet$};\n\t\\node at (1,-1.8) (nontrain) {$\\bullet$};\n\t\\node[dbox,text width=2.6cm,text height=0.5cm] at (0,2.3) (qua) {\\textbf{Quantization Policy ($\\alpha_t$)}};\n\t\\node[dbox,text width=2.6cm,text height=0.5cm] at (0,4.7) (train_model) {\\textbf{Train model ($\\beta_t$)}};\n\t\\node[dbox,text width=2.6cm,text height=0.5cm] at (0,7.1) (qua_update) {\\textbf{Quantization aware \\\\ DNN ($\\boldsymbol{D_t}$)}};\n\t\\node[dbox,text width=2.6cm,text height=0.5cm] at (0,9.5) (train_model_update) {\\textbf{Train model ($\\boldsymbol{\\beta_t}$)}};\n\t\\node[dbox,text width=2.6cm,text height=0.5cm] at (0,12) (update) {\\textbf{Update model}};\n\t\\node[dbox,text width=2.6cm,text height=0.5cm] at (0,14) (sr) {\\textbf{Synthesize model ($\\boldsymbol{\\mu_t}$)}};\n\t\n\t\\node[dbox,text width=1.9cm,text height=0.5cm] at (0,-2.7) (final) {\\textbf{Final training \\\\ ? ($\\boldsymbol{r_t}$)}};\n\t\\node[text width=1.9cm,text height=0.5cm] at (-3.25,12) (search) {Search space ($\\boldsymbol{\\mathcal{S}}$)};\n\t\\node[text width=1.9cm,text height=0.5cm] at (0,15) (train_search) {Trial space ($\\boldsymbol{\\mathcal{T}}$)};\n\t\\node[text width=1.9cm,text height=0.5cm] at (0,17.5) (nontrain_search) {Max trial ?};\n\t\\node[text width=1.9cm,text height=0.5cm] at (-3.25,16) (nontrain_search) {No trial ?};\n\t\n\t\\node[circle,text width=0.5cm,text height=0.5cm] at (4.15,12) (max_trial) {No};\n\t\\node[circle,text width=0.5cm,text height=0.5cm] at (4.15,15) (max_trial) {Yes};\n\t\n\t\\draw[arrow] (init) to (train);\n\t\\draw[arrow] (train) to (qua);\n\t\\draw[arrow] (qua) to (train_model);\n\t\\draw[arrow] (train_model) to (qua_update);\n\t\\draw[arrow] (qua_update) to (train_model_update);\n\t\\draw[arrow] (train_model_update) to (update);\n\t\\draw[arrow] (update) to (sr);\n\t\n\t\\draw[arrow] (train) to (nontrain);\n\t\\draw[arrow] (nontrain) to (qua);\n\t\\draw[arrow] (final) to (train);\n\t\\draw[arrow] (max_trial) to (sr);\n\t\n\t\\draw[darrow] (train) to [out=180,in=180,looseness=0.6] (0,-4.5) to (0,-4.5) to [out=0,in=0,looseness=0.6] (train);\n\t\\draw[darrow] (nontrain) to [out=0,in=0,looseness=0.6] (4.15,7.1) to (4.15,7.1) to [out=180,in=180,looseness=0.6] (nontrain);\n\t\n\t\\draw[arrow] (-4.5,16) to (sr);\n\t\\draw[arrow] (sr) to (train_search);\n\t\\draw[arrow] (train_search) to (nontrain_search);\n\t\\draw[arrow] (nontrain_search) to (max_trial);\n\t\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 978,
        "tikz_code": "\\documentclass[12pt,reqno]{amsart}\n\\usepackage{amsmath,amssymb,amscd,amsthm,amscd,amsthm,amsfonts,mathrsfs,array}\n\\usepackage{graphicx,color}\n\\usepackage{tikz}\n\\usetikzlibrary{intersections,calc,arrows.meta}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[dashed](0,0)-- node[auto=right]{$P_2$} (6,0)--  (6,2) -- node[auto=right]{$P_4$} (3,4)node[above=20pt,right=1pt]{$\\longmapsto$}--  (0,3)--  cycle;\n\\draw[ultra thick] (0,3) -- (3,4);\n\\draw[ultra thick] (6,0) -- (6,2);\n\\fill[black](0,3)circle(0.06) node[right]{$p_1$};\n\\fill[black](6,0)circle(0.06) node[below]{$p_3$};\n\\fill[black](6,2)circle(0.06) node[right]{$p_4$};\n\\fill[black](3,4)circle(0.06) node[right]{$p_2$};\n\\draw[ultra thick, dotted](0,0) -- (6,0);\n\\draw[ultra thick, dotted](0,2) -- (6,2);\n\\draw[ultra thick, dotted](0,4) -- (3,4);\n\\draw[ultra thick, dotted](3,0) -- (3,4);\n\\draw[ultra thick, dotted](2,0) -- (2,4);\n\\draw[ultra thick, dotted](1,0) -- (1,4);\n\\draw[ultra thick, dotted](4,0) -- (4,2);\n\\draw[ultra thick, dotted](5,0) -- (5,2);\n\\draw[ultra thick](0,3) -- (3,4);\n\\draw[ultra thick](0,3) -- (6,0);\n\\draw[ultra thick](6,2) -- (3,4);\n\\draw[ultra thick](6,0) -- (3,4);\n\\draw [fill=gray, opacity=0.2](0,3)--(3,4)--(4,3)--(4,2)--node[auto=right]{$P$} (3,0)--(0,0)--cycle;\n\\draw [fill=gray, opacity=0.2](0,3)--(3,4)--(6,2)--(3,0)--cycle;\n\\fill[black](3,0)circle(0.06);\n\\fill[black](0,3)circle(0.06);\n\\fill[black](3,4)circle(0.06);\n\\fill[black](6,2)circle(0.06);\n\\fill[black](0,0)circle(0.06);\n\\draw (0,3) -- (3,4);\n\\draw [dashed,thick] (0,0) -- (6,0);\n\\draw [dashed,thick] (0,2) -- (6,2);\n\\draw [dashed,thick] (0,4) -- (3,4);\n\\draw [dashed,thick] (3,0) -- (3,4);\n\\draw [dashed,thick] (2,0) -- (2,4);\n\\draw [dashed,thick] (1,0) -- (1,4);\n\\draw [dashed,thick] (4,0) -- (4,2);\n\\draw [dashed,thick] (5,0) -- (5,2);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 979,
        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usetikzlibrary{3d,calc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[x  = {(0.5cm,0.5cm)},\n                    y  = {(0.95cm,-0.25cm)},\n                    z  = {(0cm,0.9cm)}]\n\\begin{scope}[canvas is yz plane at x=-1]\n  \\draw[red] (0,0) rectangle (1,1);\n  \\draw[blue] (0,1) rectangle (1,2);\n  \\draw[green] (1,1) rectangle (2,2);\n\\end{scope}\n\\begin{scope}[canvas is xz plane at y=0]\n  \\draw[red,densely dotted] (0,0) rectangle (1,1);\n  \\draw[blue,densely dotted] (0,1) rectangle (1,2);\n  \\draw[green,densely dotted] (1,1) rectangle (2,2);\n\\end{scope}\n\\begin{scope}[canvas is yx plane at z=2]\n  \\draw[red,densely dotted] (0,0) rectangle (1,1);\n  \\draw[blue,densely dotted] (0,1) rectangle (1,2);\n  \\draw[green,densely dotted] (1,1) rectangle (2,2);\n\\end{scope}\n\\begin{scope}[canvas is xy plane at z=1]\n  \\fill[yellow] (0,0) rectangle (1,1);\n\\end{scope}\n\\begin{scope}[canvas is yx plane at z=0]\n  \\draw[red,densely dotted] (0,0) rectangle (1,1);\n  \\draw[blue,densely dotted] (0,1) rectangle (1,2);\n  \\draw[green,densely dotted] (1,1) rectangle (2,2);\n\\end{scope}\n\\begin{scope}[canvas is yz plane at x=1]\n  \\draw[red] (0,0) rectangle (1,1);\n  \\draw[blue] (0,1) rectangle (1,2);\n  \\draw[green] (1,1) rectangle (2,2);\n\\end{scope}\n\\begin{scope}[canvas is xz plane at y=1]\n  \\draw[red,densely dotted] (0,0) rectangle (1,1);\n  \\draw[blue,densely dotted] (0,1) rectangle (1,2);\n  \\draw[green,densely dotted] (1,1) rectangle (2,2);\n\\end{scope}\n\\begin{scope}[canvas is yx plane at z=1]\n  \\draw[red,densely dotted] (0,0) rectangle (1,1);\n  \\draw[blue,densely dotted] (0,1) rectangle (1,2);\n  \\draw[green,densely dotted] (1,1) rectangle (2,2);\n\\end{scope}\n\\node[draw] at (1.5,2.5,1.5) {seed};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 980,
        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,calc}\n\\begin{document}\n\\begin{tikzpicture}\n\\draw[->](-5,0)--(5,0)node[right]{$x$};\n\\draw[->](0,-2)--(0,2)node[right]{$y$};\n\\foreach \\y in {-2,-1.5,...,2}{\n\\draw[-,red](-4.5,\\y)--(4.5,\\y-1)node[above]{$\\textcolor{black}{\\text{$y$}\\text{$x$}=\\pgfmathparse{int(\\y+1)}\\pgfmathresult}$};\n}\n\\node[red,fill=white] at (0.1,1.5) {$\\mathbf r$};\n\\draw[fill=blue](2,-1) circle(1mm)node[right,blue]{$-I\\mathbf x+\\mathbf v$};\n\\draw[->,blue](2,-1)--(4,1)node[above]{$\\mathbf v$};\n\\end{tikzpicture}\n\\end{document}"
    },
    {
        "index": 981,
        "tikz_code": "\\documentclass[12pt]{article}\n\\usepackage{color,amsmath,mathtools,setspace,hyperref,\narray,tabu,stackengine,imakeidx,amssymb,graphicx,amsfonts,\nxcolor,soul,slashed,subcaption}\n\\usepackage{colortbl}\n\\usepackage{xcolor}\n\\usepackage{amsmath,lipsum}\n\\usepackage{amssymb,tikz,pgfplots}\n\\usetikzlibrary{shapes,arrows,snakes}\n\\usepackage[utf8]{inputenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n \n  \\shade[top color=red!40, bottom color=white,opacity=0.8] (-5,2) rectangle (5,0.2);\n   \\draw[fill=blue!20,opacity=0.5](-4,2.2)--(4,2.2)--(4,-2.2)--(-4,-2.2)--cycle;\n     \\draw[ultra thick,blue!60,fill=blue!20,opacity=0.5](-0.7,1.5)--(-0.7,1.5)--(0.7,1.5)--(0.7,1.5)--cycle;\n     \\draw[ultra thick,green!60,fill=green!20,opacity=0.5](-0.7,1.2)--(-0.7,1.2)--(-1.5,0.5)--(-1.5,0.5)--cycle;\n     \\draw[ultra thick,orange!60,fill=orange!20,opacity=0.5](-0.7,1)--(-0.7,1)--(1,0.2)--(1,0.2)--cycle;\n        \\draw[ultra thick,red!60,fill=red!20,opacity=0.5](-0.7,0.7)--(-0.7,0.7)--(-3,0.2)--(-3,0.2)--cycle;\n        \n         \n     \\draw[ultra thick,black!80](-4,2)--(4,2);\n     \\draw[ultra thick,black!80](-4,-2)--(4,-2);\n     \n     \\draw[<->](-4,0)--(4,0);\n     \\draw[<->](0,-2)--(0,2);\n     \\draw[ultra thick,blue!60,fill=blue!20,opacity=0.5](-0.7,1.5)--(-0.7,1.5)--(0.7,1.5)--(0.7,1.5)--cycle;\n      \\draw[ultra thick,green!60,fill=green!20,opacity=0.5](-0.7,1.2)--(-0.7,1.2)--(-1.5,0.5)--(-1.5,0.5)--cycle;\n       \\draw[ultra thick,orange!60,fill=orange!20,opacity=0.5](-0.7,1)--(-0.7,1)--(1,0.2)--(1,0.2)--cycle;\n        \\draw[ultra thick,red!60,fill=red!20,opacity=0.5](-0.7,0.7)--(-0.7,0.7)--(-3,0.2)--(-3,0.2)--cycle;\n        \n        \n      \\draw[<-](0.7,0.2)--(0.7,0.9);\n       \\draw[<-](-0.7,0.2)--(-0.7,0.9);\n        \\draw[<-](-1.5,0.2)--(-1.5,0.9);\n          \\draw[<-](-3,0.2)--(-3,0.9);\n          \n          \\node[above] at (0.7,0.9) {$(x_{i},y_{i})$};\n          \\node[above] at (-0.7,0.9) {$(x_{j},y_{j})$};\n          \\node[above] at (-1.5,0.9) {$(x_{k},y_{k})$};\n          \\node[above] at (-3,0.9) {$(x_{l},y_{l})$};\n          \n          \\node[right] at (4,0) {$x$};\n          \\node[right] at (0,2) {$E$};\n       \n         \\draw[ultra thick,fill=gray!20,opacity=0.5] (0,0) ellipse (1.6 and 1.3);\n         \\draw[ultra thick,red,fill=red!20,opacity=0.5] (-3.5,0.9) arc (-130:130:2);\n         \\draw[ultra thick,red,fill=red!20,opacity=0.5] (3.5,0.9) arc (40:320:2);\n         \n         \\draw[red,<->] (-1.5,0)--(1,0);\n         \\node[above,red] at (0.75,0) {$U_{2}$};\n         \\draw[red,<->] (1.5,0)--(4,0);\n         \\node[above,red] at (3,0) {$U_{1}$};\n         \\draw[red,<->] (-4,0)--(-1.5,0);\n         \\node[above,red] at (-2.75,0) {$supp(g_{ij})$};\n         \\draw[red,<->] (-3.6,0.9)--(-3,0.9);\n         \\node[above,red] at (-3.3,1) {$supp(g_{ij})$};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 982,
        "tikz_code": "\\documentclass{article}\n\\usepackage{tikz}\n\\usepackage{amsmath,amssymb,amsfonts,amsthm}\n\\usepackage{tikz,xcolor}\n\\usetikzlibrary{shapes,arrows}\n\n\\begin{document}\n\n\\begin{tikzpicture}[x=1.2cm, y=1.2cm]\n\\begin{scope}[shift={(0,0)},scale=0.8]\n\\draw [red,thick] (0,0) -- (0,2);\n\\draw [thick] (0.5,2.3) -- (0.5,2.5);\n\\draw [thick] (0.5,0.3) -- (0.5,-0.3);\n\\draw [red,thick] (1,0) -- (1,2);\n\\draw [thick] (1.5,2.3) -- (1.5,2.5);\n\\draw [thick] (1.5,0.3) -- (1.5,-0.3);\n\\draw [red,thick] (2,0) -- (2,2);\n\\draw [thick] (2.5,2.3) -- (2.5,2.5);\n\\draw [thick] (2.5,0.3) -- (2.5,-0.3);\n\\draw [thick] (0.5,2.3) -- (0.5,2.5);\n\\draw [thick] (0.5,0.3) -- (0.5,-0.3);\n\\draw [thick] (0.5,0.3) -- (0.5,-0.3);\n\\draw [fill=red] (0.5,2.3) circle [radius=0.06];\n\\draw [fill=red] (0.5,2) circle [radius=0.06];\n\\draw [fill=red] (0.5,1.5) circle [radius=0.06];\n\\draw [fill=red] (0.5,1.2) circle [radius=0.06];\n\\draw [fill=red] (0.5,0.3) circle [radius=0.06];\n\\draw [fill=red] (0.5,-0.3) circle [radius=0.06];\n\\draw [fill=red] (0.5,0) circle [radius=0.06];\n\\draw [fill=yellow] (0.5,-0.3) circle [radius=0.06];\n\\draw [fill=yellow] (0.5,0) circle [radius=0.06];\n\\draw [fill=yellow] (0.5,0.3) circle [radius=0.06];\n\\draw [fill=yellow] (0.5,1.2) circle [radius=0.06];\n\\draw [fill=yellow] (0.5,1.5) circle [radius=0.06];\n\\draw [fill=yellow] (0.5,2) circle [radius=0.06];\n\\draw [fill=yellow] (0.5,2.3) circle [radius=0.06];\n\\draw [fill=green] (0.5,-0.3) circle [radius=0.06];\n\\draw [fill=green] (0.5,0) circle [radius=0.06];\n\\draw [fill=green] (0.5,0.3) circle [radius=0.06];\n\\draw [fill=green] (0.5,1.2) circle [radius=0.06];\n\\draw [fill=green] (0.5,1.5) circle [radius=0.06];\n\\draw [fill=green] (0.5,2) circle [radius=0.06];\n\\draw [fill=green] (0.5,2.3) circle [radius=0.06];\n\\draw [fill=black] (0.5,0.5) circle [radius=0.04];\n\\draw [fill=black] (0.5,1) circle [radius=0.04];\n\\draw [fill=black] (0.5,1.75) circle [radius=0.04];\n\\draw [fill=black] (0.5,2.15) circle [radius=0.04];\n\\draw [fill=black] (0.5,-0.5) circle [radius=0.04];\n\\draw [fill=black] (0.5,-0.1) circle [radius=0.04];\n\\draw [fill=black] (0.5,2.9) circle [radius=0.04];\n\\draw [fill=black] (0.5,2.55) circle [radius=0.04];\n\\node [scale=0.8] at (0.5,3) {$\\nu_1$};\n\\node [scale=0.8] at (0.5,-0.9) {$\\nu_1$};\n\\node [scale=0.8] at (0.5,1) {$\\nu_1$};\n\\node [scale=0.8] at (0.5,1.5) {$\\nu_2$};\n\\node [scale=0.8] at (0.5,2.5) {$\\nu_3$};\n\\node [scale=0.8] at (0.5,0) {$\\nu_2$};\n\\node [scale=0.8] at (0.5,-1) {$\\nu_2$};\n\\node [scale=0.8] at (0.5,2.1) {$\\nu_3$};\n\\node [scale=0.8] at (0.5,0.25) {$\\nu_4$};\n\\node [scale=0.8] at (0.5,1.4) {$\\nu_4$};\n\\node [scale=0.8] at (0.5,1.85) {$\\nu_4$};\n\\node [scale=0.8] at (0.5,2.35) {$\\nu_4$};\n\\node [scale=0.8] at (0.5,2.85) {$\\nu_5$};\n\\node [scale=0.8] at (0.5,-1.4) {$\\nu_2$};\n\\node [scale=0.8] at (0.5,-1.05) {$\\nu_2$};\n\\node [scale=0.8] at (0.5,2.95) {$\\nu_4$};\n\\node [scale=0.8] at (0.5,0.7) {$\\nu_4$};\n\\node [scale=0.8] at (0.5,1.7) {$\\nu_4$};\n\\node [scale=0.8] at (0.5,2.6) {$\\nu_5$};\n\\draw [red,thick] (0,0) -- (0,2"
    },
    {
        "index": 983,
        "tikz_code": "\\documentclass[11pt,letterpaper]{article}\n\\usepackage{xcolor}\n\\usepackage{amsmath, amssymb}\n\\usepackage{tikz}\n\\usetikzlibrary{external,positioning,decorations.pathreplacing,shapes,arrows,patterns}\n\\usepackage{tikz-3dplot}\n\\usepackage{pgfplots}\n\\usepackage{color}\n\\usetikzlibrary{calc}\n\\usetikzlibrary{shapes.misc}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\n\\node[inner sep=0pt, draw=none] at (0,0)\n    {\\includegraphics[width=0.5\\textwidth]{example-image}};\n\n\\node[inner sep=0pt, draw=none] at (6.5,0)\n    {\\includegraphics[width=0.5\\textwidth]{example-image}};\n    \n\\node[inner sep=0pt, draw=none] at (0,-5.7)\n    {\\includegraphics[width=0.5\\textwidth]{example-image}};\n\n\\node[inner sep=0pt, draw=none] at (6.5,-5.7)\n    {\\includegraphics[width=0.5\\textwidth]{example-image}};\n\n\\node[inner sep=0pt, draw=none] at (0,-11.5)\n    {\\includegraphics[width=0.5\\textwidth]{example-image}};\n\n\\node[inner sep=0pt, draw=none] at (6.5,-11.5)\n    {\\includegraphics[width=0.5\\textwidth]{example-image}};\n\n\\node[inner sep=0pt, draw=none] at (0,-17.3)\n    {\\includegraphics[width=0.5\\textwidth]{example-image}};\n\n\\node[inner sep=0pt, draw=none] at (6.5,-17.3)\n    {\\includegraphics[width=0.5\\textwidth]{example-image}};\n    \n\\node[anchor=west] at (0,1.75) {$t=1$};\n\\node[anchor=west] at (6.5,1.75) {$t=1$};\n\\node[anchor=west] at (0,-3.75) {$t=1$};\n\\node[anchor=west] at (6.5,-3.75) {$t=1$};\n\\node[anchor=west] at (0,-9) {$t=1$};\n\\node[anchor=west] at (6.5,-9) {$t=1$};\n\\node[anchor=west] at (0,-14.85) {$t=1$};\n\\node[anchor=west] at (6.5,-14.85) {$t=1$};\n\\node[anchor=west] at (0,-20.75) {$t=1$};\n\\node[anchor=west] at (6.5,-20.75) {$t=1$};\n\n\\node[anchor=west] at (0,-10.25) {$\\log(N)$};\n\\node[anchor=west] at (6.5,-10.25) {$\\log(N)$};\n\\node[anchor=west] at (0,-16.1) {$\\log(N)$};\n\\node[anchor=west] at (6.5,-16.1) {$\\log(N)$};\n\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 984,
        "tikz_code": "\\documentclass[12pt]{amsart}\n\\usepackage{tikz}\n\\usetikzlibrary{arrows,shapes,automata,snakes,backgrounds,petri,positioning}\n\\usepackage[utf8]{inputenc}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw [rounded corners, fill=lightgray] (-1.25,-1) rectangle (3.25,1.5);\n\\draw [rounded corners, fill=lightgray] (0.25,-2) rectangle (5.25,-0.5);\n\\draw [rounded corners, fill=lightgray] (1.75,-2) rectangle (4.75,-0.5);\n\\draw (2,1.75) node {$P$};\n\\draw (0,-1.75) node {$P_u$};\n\\draw (4,-1.75) node {$P_v$};\n\\tikzstyle{wn}=[inner sep =3, fill=white, draw=black, circle];\n\\tikzstyle{bn}=[inner sep =3, fill=black, draw=black, circle];\n\\draw (0,0) node [wn] {};\n\\draw (1,0) node [bn] {};\n\\draw (2,0) node [wn] {};\n\\draw (3,0) node [bn] {};\n\\draw (4,0) node [wn] {};\n\\draw (0,0) node[above] {$a_1$};\n\\draw (2,0) node[above] {$b$};\n\\draw (4,0) node[above] {$a_2$};\n\\draw (0,0) edge[out=45, in=135] (2,0);\n\\draw (1,0) edge (2,0);\n\\draw (2,0) edge (3,0);\n\\draw (3,0) edge (4,0);\n\\draw (1, -1) node [wn] {};\n\\draw (3, -1) node [bn] {};\n\\draw (1,-1) node[below] {$a_4$};\n\\draw (3,-1) node[below] {$a_6$};\n\\draw (1,-1) edge[out=45, in=135] (3,-1);\n\\draw (1,-2.5) node [wn] {};\n\\draw (3,-2.5) node [bn] {};\n\\draw (1,-2.5) node[below] {$a_5$};\n\\draw (3,-2.5) node[below] {$a_5$};\n\\draw (1,-2.5) edge (2,-2.5);\n\\draw (3,-2.5) edge (4,-2.5);\n\\draw (2,-2.5) edge (2,0);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 985,
        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=1]\n\t\\node[inner sep=0pt] (cusp) at (0,0)\n\t{\\includegraphics[width=.45\\textwidth]{example-image}};\n\t% Sparsity pattern\n\t\\foreach \\i in {-0.15, -0.10, -0.05, 0, 0.05, 0.10, 0.15}{\n\t\t\\draw[opacity=0.5,green,fill] (3.2,\\i) circle [radius=2pt];\n\t\t\\draw[opacity=0.5,red,fill] (-2.1,\\i) circle [radius=2pt];\n\t\t\\foreach \\j in {-0.05,-0.02,0.02,0.05}{\n\t\t\t\\draw[opacity=0.5,green,fill] (2.4+\\j,0.85*\\i) circle [radius=2pt];\n\t\t\t\\draw[opacity=0.5,red,fill] (-2.1+\\j,0.85*\\i) circle [radius=2pt];\n\t\t}\n\t}\n\t% Draw the projection\n\t\\draw[thick,red,->] (1.9,0.4) -- (-0.6,0.4);\n\t\\draw[thick,red,->] (1.9,0.4) -- (-0.6,0.2);\n\t\\draw[thick,red,->] (1.9,0.4) -- (-0.6,-0.2);\n\t\\draw[thick,red,->] (1.9,0.4) -- (-0.6,-0.4);\n\t% Draw the plot of the projection\n\t\\draw[thick,green,->] (0.7,2.8) -- (1.9,1.55);\n\t\\draw[thick,green,->] (0.7,2.8) -- (1.9,0.4);\n\t\\draw[thick,green,->] (0.7,2.8) -- (1.9,-0.55);\n\t% Draw the plot of the projection\n\t\\draw[thick,red,->] (-1.9,0.4) -- (-0.6,0.4);\n\t\\draw[thick,red,->] (-1.9,0.4) -- (-0.6,0.2);\n\t\\draw[thick,red,->] (-1.9,0.4) -- (-0.6,-0.2);\n\t\\draw[thick,red,->] (-1.9,0.4) -- (-0.6,-0.4);\n\t% Draw the plot of the projection\n\t\\draw[thick,green,->] (-0.7,2.8) -- (-1.9,1.55);\n\t\\draw[thick,green,->] (-0.7,2.8) -- (-1.9,0.4);\n\t\\draw[thick,green,->] (-0.7,2.8) -- (-1.9,-0.55);\n\t% Draw the plot of the projection\n\t\\draw[thick,red,->] (1.9,0.4) -- (-0.6,0.4);\n\t\\draw[thick,red,->] (1.9,0.4) -- (-0.6,0.2);\n\t\\draw[thick,red,->] (1.9,0.4) -- (-0.6,-0.2);\n\t\\draw[thick,red,->] (1.9,0.4) -- (-0.6,-0.4);\n\t% Draw the plot of the projection\n\t\\draw[thick,green,->] (-1.9,0.4) -- (-0.6,0.4);\n\t\\draw[thick,green,->] (-1.9,0.4) -- (-0.6,0.2);\n\t\\draw[thick,green,->] (-1.9,0.4) -- (-0.6,-0.2);\n\t\\draw[thick,green,->] (-1.9,0.4) -- (-0.6,-0.4);\n\t% Draw the plot of the projection\n\t\\draw[thick,red,->] (-0.7,2.8) -- (1.9,1.55);\n\t\\draw[thick,red,->] (-0.7,2.8) -- (1.9,0.4);\n\t\\draw[thick,red,->] (-0.7,2.8) -- (1.9,-0.55);\n\t% Draw the plot of the projection\n\t\\draw[thick,green,->] (0.7,2.8) -- (-1.9,1.55);\n\t\\draw[thick,green,->] (0.7,2.8) -- (-1.9,0.4);\n\t\\draw[thick,green,->] (0.7,2.8) -- (-1.9,-0.55);\n\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 986,
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        "tikz_code": "\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage{tikz}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[black, thick] (0,0) rectangle (5,5);\n\\draw[blue, thick] (2.5,0) -- (2.5,5);\n\\draw[blue, thick] (0,2.5) -- (5,2.5);\n\\node[] at (2.5,-.8) {$g^{-1}$};\n\\node[] at (-.5,2.5) {$g$};\n\\node[below] at (2.5,0) {$g$-discontinuous};\n\\node[below] at (2.5,-1) {The action of $\\mathcal{T}$};\n\\node[below] at (2.5,-2) {on the right discontinuous};\n\\node[below] at (2.5,-3) {and hence};\n\\node[below] at (2.5,-4) {the action of $\\mathcal{T}$ on the};\n\\node[below] at (2.5,-5) {right discontinuous space and hence};\n\\node[below] at (2.5,-6) {$g^{-1}$-discontinuous};\n\n\\draw[black, thick] (7,0) rectangle (12,5);\n\\draw[blue, thick] (9.5,0) -- (9.5,5);\n\\draw[blue, thick] (7,2.5) -- (12,2.5);\n\\node[] at (9.5,-.8) {$g^{-1}$};\n\\node[] at (6.5,2.5) {$g$};\n\\node[below] at (9.5,0) {$g^{-1}$-discontinuous};\n\\node[below] at (9.5,-1) {The action of $\\mathcal{T}$ is fixed};\n\\node[below] at (9.5,-2) {in time, the arrow discontinuous};\n\\node[below] at (9.5,-3) {it from $g^{-1}$};\n\n\\draw[black, thick] (0,-7) rectangle (5,-2);\n\\draw[blue, thick] (2.5,-7) -- (2.5,-2);\n\\draw[blue, thick] (0,-2.5) -- (5,-2.5);\n\\node[] at (2.5,-6.2) {$g^{-1}$};\n\\node[] at (-.5,-2.5) {$g$};\n\\node[below] at (2.5,-7) {$g^{-1}$-discontinuous};\n\\node[below] at (2.5,-8) {A non defect, no operator is};\n\\node[below] at (2.5,-9) {inspected};\n\\node[below] at (2.5,-10) {A defect, no operator is};\n\\node[below] at (2.5,-11) {inspected};\n\n\\draw[black, thick] (7,-7) rectangle (12,-2);\n\\draw[blue, thick] (9.5,-7) -- (9.5,-2);\n\\draw[blue, thick] (7,-2.5) -- (12,-2.5);\n\\node[] at (9.5,-6.2) {$g^{-1}$};\n\\node[] at (6.5,-2.5) {$g$};\n\\node[below] at (9.5,-7) {$g^{-1}$-discontinuous};\n\\node[below] at (9.5,-8) {The action of $\\mathcal{T}$};\n\\node[below] at (9.5,-9) {on the left discontinuous};\n\\node[below] at (9.5,-10) {and hence};\n\\node[below] at (9.5,-11) {the action of $\\mathcal{T}$ on the};\n\\node[below] at (9.5,-12) {left discontinuous space and hence};\n\\node[below] at (9.5,-13) {$g^{-1}$-discontinuous};\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 997,
        "tikz_code": "\\documentclass[11pt,a4paper,oneside,reqno]{amsart}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath,amsthm,amssymb,amsfonts,float}\n\\usepackage{tikz}\n\\usetikzlibrary{patterns}\n\\usetikzlibrary{arrows.meta}\n\\usetikzlibrary{decorations.markings}\n\\usepackage{color}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\node at (-0.5, 4.5) {\\tiny parametric manifold $\\Omega$};\n\\node at (2.5, -0.5) {\\includegraphics[scale=0.5]{example-image}};\n\\node at (6.5, 4.5) {\\tiny $m_\\Omega(x)$};\n\\node at (6.5, -0.5) {\\includegraphics[scale=0.4]{example-image}};\n\\node at (10, -0.5) {\\tiny $m_\\Omega(x')$};\n\\node at (10, 4.5) {\\tiny $m(x)$};\n\\node at (10, 0.75) {\\includegraphics[scale=0.4]{example-image}};\n\\node at (10, -2.25) {\\tiny $T^i_\\Omega$};\n\\node at (4, -3.5) {\\includegraphics[scale=0.3]{example-image}};\n\\node at (4.5, -4) {\\tiny spherical complex $\\Sigma$};\n\\node at (0.5, -4) {\\tiny $\\gamma_\\pi$};\n\\draw (0.5, -3.5) -- (2.5, -3.5) -- (2.25, -2) -- (3, -0.5) -- (2.75, -2) -- (0.25, -2) -- (0.5, -3.5);\n\\draw[-{Latex[length=1.5mm]}] (0.75, -2.25) to [out=45, in=-90] (5.5, -0.5);\n\\draw[-{Latex[length=1.5mm]}] (1.5, 0.5) -- (2.25, 0.25);\n\\draw[-{Latex[length=1.5mm]}] (5.5, 2) -- (4, 2.25);\n\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 998,
        "tikz_code": "\\documentclass[12pt,reqno]{amsart}\n\\usepackage{amsfonts,amsmath,amssymb}\n\\usepackage[latin1]{inputenc}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}[scale=0.45]\n\t\t\t\t\t\\draw[step=1.cm,black] (-0.0,-0.0) grid (5.0,5.0);\n\t\t\t\t\t\\draw[ultra thick] (0,0) to (1,0) to (1,1)to (2,1) to (2,2)to (3,2)to (3,3)to (4,3)to (4,4)to (5,4)to (5,5);\n\t\t\t\t\t\\draw[ultra thick,red] (-0.0,-0.5)to (5.0,5.5);\n\t\t\t\t\t\\draw[thick] (4.5,0)to (5.5,1);\n\t\t\t\t\t\\node at (0.5,0.5) {$s_{4}$};\\node at (0.5,1.5) {$s_{3}$};\\node at (0.5,2.5) {$s_{2}$};\\node at (0.5,3.5) {$s_{1}$};\n\t\t\t\t\t\\node at (1.5,1.5) {$\\uparrow$};\\node at (1.5,2.5) {$\\uparrow$};\\node at (1.5,3.5) {$\\uparrow$};\n\t\t\t\t\t\\node at (2.5,2.5) {$\\uparrow$};\\node at (2.5,3.5) {$\\uparrow$};\n\t\t\t\t\t\\node at (3.5,3.5) {$\\uparrow$};\n\t\t\t\t\t\\node at (4.5,4.5) {$\\uparrow$};\n\t\t\t\t\t\\draw[thick,red] (0.5,-0.5)to (5.5,5.5);\n\t\t\t\t\t\\node at (3.5,0.5) {$1$};\\node at (2.5,1.5) {$1$};\\node at (1.5,2.5) {$1$};\\node at (0.5,3.5) {$1$};\n\t\t\t\t\t\\node at (3.5,1.5) {$2$};\\node at (2.5,2.5) {$2$};\\node at (1.5,3.5) {$2$};\\node at (0.5,4.5) {$3$};\n\t\t\t\t\t\\node at (3.5,2.5) {$3$};\\node at (2.5,3.5) {$3$};\\node at (1.5,4.5) {$4$};\\node at (0.5,5.5) {$4$};\n\t\t\t\t\t\\node at (2.5,-1.5) {$(0,0)$};\n\t\t\t\t\t\\filldraw[red] (2,-1) circle (4pt)node[anchor=west]{};\n\t\t\t\t\t\\node at (4,6.5) {$E_3$};\\node at (6,6.5) {$E_2E_1$};\\node at (6,4) {$E_1$};\n\t\t\t\t\t\\node at (3,6.5) {$E_4$};\n\t\t\t\t\\end{tikzpicture}\n\n\\end{document}"
    },
    {
        "index": 999,
        "tikz_code": "\\documentclass[aps,prd,11pt,notitlepage,longbibliography,nofootinbib,tightenlines,preprintnumbers,superscriptaddress]{revtex4-1}\n\\usepackage{amsmath,amssymb,amsfonts}\n\\usepackage{color}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\t\t\\node at (0,0.1) {\\includegraphics[width=0.46\\linewidth]{example-image}};\n\t\t\\node at (-0.4,2.3) {\\footnotesize (a)};\n\t\t\\node at (4.9,2.3) {\\footnotesize (b)};\n\t\\end{tikzpicture}\n\n\\end{document}"
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]