Datasets:

JosselinSom

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Latex-VLM

like 0

\begin{tikzpicture} \begin{axis}[ axis y line = left, axis x line = bottom, tickwidth = 5pt, enlarge y limits = 0.2, xmin = 0, xmax = 5, width = 1.5\columnwidth, height =0.8\textheight, yticklabels={ Foot Motion\\Controller, Handheld VR\\Controller, Desk\\Joystick, Pedals, Sensorized\\Shoes, Gaming Console\\Controller }, ytick = data, xtick = data, bar width = 45pt, xlabel = Number of Teams, xlabel style={ font =\large, align=center }, major grid style = { line width = 0.2pt, draw=gray!50 }, ymajorgrids=false, xmajorgrids=true, xminorgrids=false, major tick length=3mm, minor tick length=2mm, y tick label style={ font =\large, align=center }, x tick label style={ font =\large, align=center }, ] \addplot[xbar,fill=blue] coordinates { (5,5) (4,4) (3,3) (2,2) (2,1) (1,0) }; \end{axis} \node[font=\small, text=white, align=center] at (5,13.5) {Cyberselves $\vert$ Touchlab, i-Botics,\\ NimbRo, Team Northeastern, Team UNIST}; \node[font=\small, text=white, align=center] at (4,11.3) {AlterEgo, AvaDynamics, AVATRINA,\\ Pollen Robotics}; \node[font=\small, text=white, align=center] at (3,9) {Dragon Tree Labs,\\ Last Mile, Tangible}; \node[font=\small, text=black, align=center] at (6.1,6.7) {INBIODROID, Team SNU}; \node[font=\small, text=black, align=center] at (5,4.5) {iCub, Janus}; \node[font=\small, text=black, align=center] at (3.1,2.2) {Avatar-Hubo}; \end{tikzpicture}

plot

cs

\begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-1,xscale=1,baseline=(current bounding box.center)] \draw (228.91,104.46) -- (228.96,190.26) ; \draw [color={rgb, 255:red, 47; green, 157; blue, 175 } ,draw opacity=1 ] [dash pattern={on 4.5pt off 4.5pt}] (228.96,190.26) -- (314.77,190.22) ; \draw (314.41,121.72) -- (228.6,121.78) ; \draw (314.72,104.41) -- (314.77,190.22) ; \draw (314.41,141.68) -- (228.6,141.74) ; \draw [dash pattern={on 0.84pt off 2.51pt}] (314.72,159.29) -- (228.91,159.3) ; \draw [dash pattern={on 0.84pt off 2.51pt}] (315.03,177.07) -- (229.22,177.07) ; \draw [color={rgb, 255:red, 177; green, 0; blue, 0 } ,draw opacity=1 ] [dash pattern={on 4.5pt off 4.5pt}] (206.2,190.58) -- (228.96,190.26) ; \draw [color={rgb, 255:red, 177; green, 0; blue, 0 } ,draw opacity=1 ] [dash pattern={on 4.5pt off 4.5pt}] (314.77,190.22) -- (337.53,189.91) ; \draw (338.63,128.05) -- (314.36,128.11) ; \draw (339.41,148.47) -- (315.14,148.53) ; \draw [dash pattern={on 0.84pt off 2.51pt}] (338.33,167.76) -- (314.05,167.76) ; \draw (228.71,128.44) -- (204.43,128.5) ; \draw (229.1,149.25) -- (204.82,149.31) ; \draw [dash pattern={on 0.84pt off 2.51pt}] (228.4,168.15) -- (204.13,168.15) ; \draw (448.5,147.2) .. controls (448.5,141.13) and (453.43,136.2) .. (459.5,136.2) .. controls (465.58,136.2) and (470.51,141.12) .. (470.51,147.2) .. controls (470.51,153.27) and (465.59,158.2) .. (459.51,158.2) .. controls (453.44,158.21) and (448.51,153.28) .. (448.5,147.2) -- cycle ; \draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (550.25,156.32) -- (530.81,156.32) -- (530.81,136.88) -- (550.25,136.88) -- cycle ; \draw (530.43,147.07) -- (470.51,147.2) ; \draw (214.38,87.99) node [anchor=north west][inner sep=0.75pt] [align=left] {NS5}; \draw (256.77,194.32) node [anchor=north west][inner sep=0.75pt] [align=left] {O4$\displaystyle ^{-}$}; \draw (300.44,87.36) node [anchor=north west][inner sep=0.75pt] [align=left] {NS5}; \draw (195.65,193.54) node [anchor=north west][inner sep=0.75pt] [align=left] {O4$\displaystyle ^{+}$}; \draw (318.2,193.22) node [anchor=north west][inner sep=0.75pt] [align=left] {O4$\displaystyle ^{+}$}; \draw (339.75,127.76) node [anchor=north west][inner sep=0.75pt] [align=left] {D4$\displaystyle ^{+}$}; \draw (339.75,160.51) node [anchor=north west][inner sep=0.75pt] [align=left] {D4$\displaystyle ^{-}$}; \draw (417,172.9) node [anchor=north west][inner sep=0.75pt] {$\mathrm{OSp}( n_{0} |n_{1})$}; \draw (510.5,169) node [anchor=north west][inner sep=0.75pt] [align=left] {SpO$\displaystyle \left( n_{0}^{\mathrm{f}} |n_{1}^{\mathrm{f}}\right)$}; \draw (391,140.9) node [anchor=north west][inner sep=0.75pt] {$\leadsto $}; \end{tikzpicture}

plot

physics

\begin{tikzpicture} \begin{axis}[ colorbar, colormap/jet, % Choose the colormap you prefer enlargelimits=false, point meta max=0.002166748046875, point meta min=0, axis line style = {draw=none}, tick style = {draw=none}, xtick = \empty, ytick = \empty, colorbar style={ ylabel = {$|T_\text{NL} - T_\text{L}|$}, height=0.7*\pgfkeysvalueof{/pgfplots/parent axis height}, at={(1.05,0.5)}, % Adjust the position to center vertically anchor=west, % Adjust the anchor point }, width=0.8\textwidth ] \addplot graphics [includegraphics cmd=\pgfimage, xmin=0, xmax=1, ymin=0, ymax=1] {fig/eye/results/linearization/normInf.png}; \end{axis} \end{tikzpicture}

plot

math

\begin{tikzpicture} \definecolor{crimson2143940}{RGB}{214,39,40} \definecolor{darkgray176}{RGB}{176,176,176} \definecolor{darkorange25512714}{RGB}{255,127,14} \definecolor{forestgreen4416044}{RGB}{44,160,44} \definecolor{lightgray204}{RGB}{204,204,204} \definecolor{mediumpurple148103189}{RGB}{148,103,189} \definecolor{steelblue31119180}{RGB}{31,119,180} \begin{axis}[ enlargelimits=0.05, legend style={ fill opacity=0.8, draw opacity=1, text opacity=1, at={(0.97,0.97)}, anchor=north east, draw=lightgray204}, ybar, legend image code/.code={ \draw [#1] (0cm,-0.1cm) rectangle (0.2cm,0.25cm); }, height=5cm, width=\linewidth, y grid style={darkgray176}, ylabel={maximum SER}, xlabel={number of frames $K$}, ymajorgrids, xtick={0,1,2}, ymin=16.5, ymax=17.15, xmin=-0.5, xmax=2.5, xticklabels={225, 450, 900} ] \addplot [fill=steelblue31119180, steelblue31119180] coordinates { (0, 17.1) (1, 16.64) (2, 16.60)}; \addplot [fill=darkorange25512714, darkorange25512714] coordinates { (0, 17.05) (1, 16.64) (2, 16.60)}; \legend{t-DIP, FMLP} \end{axis} \end{tikzpicture}

plot

eess

\begin{tikzpicture}[overlay, remember picture] \path (current page.north east) ++(-3.5,-0.4) node[below left] { M. Abate, A Schwartz, X Iuan Wong, W Luo, R Littman, M Klinger, L Kuhnert, D Blue, L Carlone }; \end{tikzpicture}

plot

cs

\begin{tikzpicture} \draw[line width=1] (0,0) -- (0.,-0.25); \draw[line width=1] (0.25,0) -- (0.25,-0.25); \draw[line width=1] (0.5,0) -- (0.5,-0.25); \draw[line width=1] (0.75,0) -- (0.75,-0.25); \end{tikzpicture}

plot

physics

\begin{tikzpicture} [sibling distance=10em,level distance=5em] \node {EXPLOIT-UCB$(B)$} child { node {EXPLOIT-UCB$(\textcolor{blue}{nB^2})$} child { node {EXPLOIT-UCB$(\textcolor{brown}{2nB^2})$} child { node {EXPLOIT-UCB$(\textcolor{orange}{3nB^2})$} child { node {} edge from parent [dashed]} child { node {} edge from parent [dashed]} edge from parent node [left] {if $B_t$ reaches $\textcolor{orange}{3nB^2}$ for some $t_3\leq T$}} child { node {ruin with high proba} edge from parent node [right] {else}} edge from parent node [left] {if $B_t$ reaches $\textcolor{brown}{2nB^2}$ for some $t_2\leq T$}} child { node {ruin with high proba} edge from parent node [right] {else}} edge from parent node [left] {if $B_t$ reaches $\textcolor{blue}{nB^2}$ for some $t_1\leq T$}} child { node {ruin with high proba} edge from parent node [right] {else}}; \end{tikzpicture}

plot

cs

\begin{tikzpicture}[scale = 0.6] \draw[color=blue] (6, 3.5) to[out=0, in=180] (8, 0.5); \draw[color=magenta] (6, 2.5) to[out=0, in=180] (8, 3.5); \draw[color=red] (6, 1.5) to[out=0, in=180] (8, 2.5); \draw[color=cyan] (6, 0.5) to[out=0, in=180] (8, 1.5); \draw[color=red] (8,2.5) to[out=0, in=180] (10,0.5); \draw[color=magenta] (8,3.5) to[out=0, in=180] (10, 3.5); \draw[color=cyan] (8, 1.5) to[out=0, in=180] (10,2.5); \draw[color=blue] (8, 0.5) to [out=0, in=180] (10,1.5); \draw[color=red] (10,0.5) to[out=0, in=180] (12, 3.5); \draw[color=blue] (10,1.5) to[out=0, in=180] (12, 0.5); \draw[color=cyan] (10, 2.5) to [out=0, in=180] (12, 2.5); \draw[color=magenta] (10, 3.5) to [out=-20, in=180] (12, 1.5); \end{tikzpicture}

plot

math

\begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-1,xscale=1] \draw [color={rgb, 255:red, 58; green, 246; blue, 25 } ,draw opacity=1 ][fill={rgb, 255:red, 225; green, 250; blue, 210 } ,fill opacity=1 ][line width=1.5] (261.75,164.88) .. controls (261.75,157.63) and (267.63,151.75) .. (274.88,151.75) .. controls (282.12,151.75) and (288,157.63) .. (288,164.88) .. controls (288,172.12) and (282.12,178) .. (274.88,178) .. controls (267.63,178) and (261.75,172.12) .. (261.75,164.88) -- cycle ; \draw [color={rgb, 255:red, 59; green, 255; blue, 70 } ,draw opacity=1 ][fill={rgb, 255:red, 234; green, 254; blue, 213 } ,fill opacity=1 ][line width=1.5] (374,165) .. controls (374,158.1) and (379.6,152.5) .. (386.5,152.5) .. controls (393.4,152.5) and (399,158.1) .. (399,165) .. controls (399,171.9) and (393.4,177.5) .. (386.5,177.5) .. controls (379.6,177.5) and (374,171.9) .. (374,165) -- cycle ; \draw [color={rgb, 255:red, 208; green, 2; blue, 27 } ,draw opacity=1 ][fill={rgb, 255:red, 255; green, 225; blue, 215 } ,fill opacity=1 ][line width=1.5] (318,58) -- (344,58) -- (344,82) -- (318,82) -- cycle ; \draw (278,150) -- (316.99,83.72) ; \draw [shift={(318,82)}, rotate = 120.47] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (6.56,-1.97) .. controls (4.17,-0.84) and (1.99,-0.18) .. (0,0) .. controls (1.99,0.18) and (4.17,0.84) .. (6.56,1.97) ; \draw (288,166) -- (372,165.02) ; \draw [shift={(374,165)}, rotate = 179.33] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (6.56,-1.97) .. controls (4.17,-0.84) and (1.99,-0.18) .. (0,0) .. controls (1.99,0.18) and (4.17,0.84) .. (6.56,1.97) ; \draw (373,160) -- (289,160) ; \draw [shift={(287,160)}, rotate = 360] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (6.56,-1.97) .. controls (4.17,-0.84) and (1.99,-0.18) .. (0,0) .. controls (1.99,0.18) and (4.17,0.84) .. (6.56,1.97); \draw (324,84) -- (284.03,150.29) ; \draw [shift={(283,152)}, rotate = 301.09] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (6.56,-1.97) .. controls (4.17,-0.84) and (1.99,-0.18) .. (0,0) .. controls (1.99,0.18) and (4.17,0.84) .. (6.56,1.97); \draw (339,84) -- (378.01,152.26) ; \draw [shift={(379,154)}, rotate = 240.26] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (6.56,-1.97) .. controls (4.17,-0.84) and (1.99,-0.18) .. (0,0) .. controls (1.99,0.18) and (4.17,0.84) .. (6.56,1.97); \draw (382,149) -- (344.99,83.74) ; \draw [shift={(344,82)}, rotate = 60.44] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (6.56,-1.97) .. controls (4.17,-0.84) and (1.99,-0.18) .. (0,0) .. controls (1.99,0.18) and (4.17,0.84) .. (6.56,1.97); \draw (344,58) .. controls (346.93,31.67) and (316.58,31.97) .. (317.84,56.1) ; \draw [shift={(318,58)}, rotate = 263.42] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (6.56,-1.97) .. controls (4.17,-0.84) and (1.99,-0.18) .. (0,0) .. controls (1.99,0.18) and (4.17,0.84) .. (6.56,1.97); \draw (399,165) .. controls (414.6,179.63) and (409.29,188.55) .. (388.16,178.32) ; \draw [shift={(386.5,177.5)}, rotate = 27.07] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (6.56,-1.97) .. controls (4.17,-0.84) and (1.99,-0.18) .. (0,0) .. controls (1.99,0.18) and (4.17,0.84) .. (6.56,1.97); \draw (261.75,164.88) .. controls (244.69,175.11) and (250.68,188.32) .. (273.12,178.78) ; \draw [shift={(274.88,178)}, rotate = 155.26] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (6.56,-1.97) .. controls (4.17,-0.84) and (1.99,-0.18) .. (0,0) .. controls (1.99,0.18) and (4.17,0.84) .. (6.56,1.97); \draw (326,21) node [anchor=north west][inner sep=0.75pt] [align=left] {0}; \draw (367,97) node [anchor=north west][inner sep=0.75pt] [align=left] {9}; \draw (330,142) node [anchor=north west][inner sep=0.75pt] [align=left] {6}; \draw (330,169) node [anchor=north west][inner sep=0.75pt] [align=left] {5}; \draw (305,114) node [anchor=north west][inner sep=0.75pt] [align=left] {4}; \draw (285,99) node [anchor=north west][inner sep=0.75pt] [align=left] {3}; \draw (407,186) node [anchor=north west][inner sep=0.75pt] [align=left] {2}; \draw (240,185) node [anchor=north west][inner sep=0.75pt] [align=left] {1}; \draw (342,114) node [anchor=north west][inner sep=0.75pt] [align=left] {8}; \draw (326,61) node [anchor=north west][inner sep=0.75pt] [align=left] {1}; \draw (269,156) node [anchor=north west][inner sep=0.75pt] [align=left] {2}; \draw (381,157) node [anchor=north west][inner sep=0.75pt] [align=left] {3}; \end{tikzpicture}

plot

math

\begin{tikzpicture} \draw[->] (-5,0) -- (-1,0); \draw (-1,0) node[right]{$x$}; \draw (-4,1) node[above]{$y$}; \draw (-2,1) node[above]{time $0$}; \draw[->] (-4,-1) -- (-4,1); \fill[opacity=0.5,black] (-5,0.5) circle(0.3); \fill[opacity=0.8,black] (-3.5,-0.5) circle(0.2); \draw[color=red] (-4.25,-1) -- (-4.25,1); \draw[color=red] (-4.25,-1) node[below]{$x=m(0)$}; \draw[->] (1,0) -- (5,0); \draw[->] (2,-1) -- (2,1); \draw (5,0) node[right]{$x$}; \draw (2,1) node[above]{$y$}; \draw (5,1) node[above]{time $t_0>0$}; \fill[opacity=0.5,black] (2,0.5) circle(0.3); \fill[opacity=0.8,black] (4.5,-0.5) circle(0.2); \draw[color=red] (3.25,-1) -- (3.25,1); \draw[color=red] (3.25,-1) node[below]{$x=m(t_0)$}; \end{tikzpicture}

plot

math

\begin{tikzpicture}[domain=0:6] \draw[-] (-0.6,0.0) -- (-2.0, -1.6); \draw[-] (-0.6,3.2) -- (-2.0, 1.6); \draw[-] (-2.0, -1.6) -- (-2.0, 1.6); \draw[-] (-0.6,3.2) -- (-0.6,0.0); \draw[dashed] (-3.6,0.0) -- (-5.0, -1.6); \draw[-] (-3.6,3.2) -- (-5.0, 1.6); \draw[-] (-5.0, -1.6) -- (-5.0, 1.6); \draw[dashed] (-3.6,3.2) -- (-3.6,0.0); \draw[dashed] (-0.6,0.0) -- (-3.6, 0.0); \draw[-] (-0.6,3.2) -- (-3.6, 3.2); \draw[-] (-2.0, -1.6) -- (-5.0, -1.6)node[pos=0.5,below] {$ds=\upsilon dt$}; \draw[-] (-2.0,1.6) -- (-5.0,1.6); \fill (-2.5,0.7) circle (3.6pt); \draw[->, line width=0.5mm] (-2.5,0.7) -- (2.5,0.7) node[pos=0.8,below] {$\vec{F}- \nabla \mu(1)$}; \draw[->, line width=0.5mm] (-2.5,0.7) -- (0.4,1.7) node[pos=0.98,sloped,below] {$- \nabla \mu(1)$}; \draw[->, line width=0.5mm] (-2.5,0.7) -- (0.4,-0.3) node[pos=0.98,below] {$\vec{F}$}; \draw[] (-0.9,1.7) -- (0.4,2.7) node[right] {$dS$}; \draw[->] (-6.5,0.7)--(-2.7,0.5) node[above,pos=0] {$\mu(1)$}; \end{tikzpicture}

plot

physics

\begin{tikzpicture}[scale=0.92] \begin{axis}[ title={Engagement vs Inference Speed}, xlabel={Relative Inference Speed (1/FLOPs)}, ylabel={Improvement Over Baseline}, ylabel style={yshift=-5pt, inner sep=-1pt}, xmin=0, xmax=1., ymin=0.1, ymax=1.4, grid=both, scatter/classes={ a={mark=*,draw=black} } ] \addplot[ scatter, only marks, scatter src=explicit symbolic, mark options={scale=1.3} ]table[meta=label] { x y label 0.1 0.82 a 0.72 1.15 a 0.35 0.25 a 1.0 0.25 a }; \addplot[smooth, thick, gray, line width=2pt] coordinates { (0 , 0.7) (0.2, 0.64) (0.4, 0.58) (0.6, 0.52) (1.0, 0.4) }; \node at (axis cs:0.2,0.85) [above] {GPT3.5 (175B)}; \node at (axis cs:0.72,1.2) [above] {Blend (13,6,6B)}; \node at (axis cs:0.35,0.25) [above] {Vicuna+ (13B)}; \node at (axis cs:0.825, 0.25) [above] {ChaiLLM (6B)}; \end{axis} \end{tikzpicture}

plot

cs

\begin{tikzpicture} \draw [thick] (0,0) to[out=55,in=180] (2.5,1.3) to[out=0,in=125] (5,0); \draw [thick] (0,0) -- (2.5,0) -- (5,0); \draw [thick] (0,0) to[out=-55,in=180] (2.5,-1.3) to[out=0,in=-125] (5,0); \begin{scope}[shift={(0,0)}] \draw [thick,fill=white] (0,0) circle (0.45); \node [] at (0,0) {$V^{s'*}$}; \end{scope} \begin{scope}[shift={(5,0)}] \draw [thick,fill=white] (0,0) circle (0.45); \node [] at (0,0) {$V^{s}$}; \end{scope} \begin{scope}[shift={(2.5,1.3)}] \draw [thick,fill=white] (-0.3,-0.3) -- (0.3,-0.3) -- (0.3,0.3) -- (-0.3,0.3) -- cycle; \node [] at (0,0) {$g_1$}; \end{scope} \begin{scope}[shift={(2.5,0)}] \draw [thick,fill=white] (-0.3,-0.3) -- (0.3,-0.3) -- (0.3,0.3) -- (-0.3,0.3) -- cycle; \node [] at (0,0) {$g_2$}; \end{scope} \begin{scope}[shift={(2.5,-1.3)}] \draw [thick,fill=white] (-0.3,-0.3) -- (0.3,-0.3) -- (0.3,0.3) -- (-0.3,0.3) -- cycle; \node [] at (0,0) {$g_3$}; \end{scope} \end{tikzpicture}

plot

physics

\begin{tikzpicture} \draw (0,0)--(4,2); \filldraw[black] (0,0) circle (2pt) node[anchor=north west]{\(x_1\)}; \filldraw[black] (0.6,0.3) circle (2pt) node[anchor=north west]{\(x_2\)}; \filldraw[black] (1.2,0.6) circle (2pt) node[anchor=north west]{\(x_3\)}; \filldraw[black] (1.6,0.8) circle (2pt) node[anchor=west]{\hspace{1em}\(\cdots\)}; \filldraw[black] (2.0,1.0) circle (2pt); \filldraw[black] (2.2,1.1) circle (2pt); \filldraw[black] (2.6,1.3) circle (2pt); \filldraw[black] (3.0,1.5) circle (2pt); \filldraw[black] (3.2,1.6) circle (2pt); \filldraw[black] (3.6,1.8) circle (2pt); \filldraw[black] (4,2) circle (2pt) node[anchor=north west]{\(x_{n-2}\)}; \filldraw[red] (0.5,2.5) circle (2pt) node[anchor=south east]{\(u\)}; \filldraw[red] (2.5,2.5) circle (2pt) node[anchor=south west]{\(v\)}; \draw[red] (3.5,0.5) circle (2pt); \draw[red,dashed] (0.5,2.5)--(2.5,2.5); \draw (6,0)--(10,2); \filldraw[black] (6,0) circle (2pt) node[anchor=north west]{\(x_1\)}; \filldraw[black] (6.6,0.3) circle (2pt) node[anchor=west]{\hspace{1em}\(\cdots\)}; \filldraw[black] (7.2,0.6) circle (2pt); \filldraw[black] (7.6,0.8) circle (2pt); \filldraw[black] (8.0,1.0) circle (2pt); \filldraw[black] (8.2,1.1) circle (2pt); \filldraw[black] (8.6,1.3) circle (2pt); \filldraw[black] (9.0,1.5) circle (2pt); \filldraw[black] (9.2,1.6) circle (2pt); \filldraw[black] (9.6,1.8) circle (2pt); \filldraw[black] (10,2) circle (2pt) node[anchor=north west]{\(x_{n-2}\)}; \filldraw[red] (6.5,2.5) circle (2pt) node[anchor=south east]{\(u\)}; \draw[red] (8.5,2.5) circle (2pt); \filldraw[red] (9.5,0.5) circle (2pt) node[anchor=north west]{\(v\)}; \draw[red,dashed] (6.5,2.5)--(9.5,0.5); ; \end{tikzpicture}

plot

math

\begin{tikzpicture}[baseline={([yshift=-1ex]current bounding box.center)},vertex/.style={anchor=base, circle,fill=black!25,minimum size=18pt,inner sep=2pt},scale=1] \draw[cyan, thick] (0,0) -- (0,3) -- (2,4) -- (2,1) -- (0,0); \draw[cyan, thick, fill = cyan, opacity = 0.1] (0,0) -- (0,3) -- (2,4) -- (2,1) -- (0,0); \fill[yellow, opacity = 0.2] (0,0) -- (4,0) -- (4,1) -- (2,1) -- (0,0); \fill[yellow, opacity = 0.2] (2,1) -- (4,1) -- (4,3) -- (2,3) -- (2,1); \fill[yellow, opacity = 0.2] (2,3) -- (4,3) -- (6,4) -- (2,4) -- (2,3); \draw[black, thick, dashed] (0,0) -- (4,0); \draw[black, thick, dashed] (2,1) -- (6,1); \draw[black, thick, dashed] (0,3) -- (4,3); \draw[black, thick, dashed] (2,4) -- (6,4); \draw[orange, thick] (4,0) -- (4,3) -- (6,4) -- (6,1) -- (4,0); \draw[fill = orange, opacity = 0.15] (4,0) -- (4,3) -- (6,4) -- (6,1) -- (4,0); \node[below] at (5,0) {$|N_B\rangle$}; \node[below] at (0,0) {$\langle {\rm QFT}'|$}; \node[above] at (6.5,2) {glue}; \draw[orange, thick] (7,0) -- (7,3) -- (9,4) -- (9,1) -- (7,0); \draw[orange, thick, fill = orange, opacity = 0.1] (7,0) -- (7,3) -- (9,4) -- (9,1) -- (7,0); \node[below] at (7,0) {$\langle N_B|$}; \fill[yellow, opacity = 0.2] (7,0) -- (9.5,0) -- (9.5,1) -- (9,1) -- (7,0); \fill[yellow, opacity = 0.2] (9,1) -- (9.5,1) -- (9.5,3) -- (9,3) -- (9,1); \fill[yellow, opacity = 0.2] (9,3) -- (9.5,3) -- (11.5,4) -- (9,4) -- (9,3); \draw[black, thick, dashed] (7,0) -- (9.5,0); \draw[black, thick, dashed] (9,1) -- (11.5,1); \draw[black, thick, dashed] (7,3) -- (9.5,3); \draw[black, thick, dashed] (9,4) -- (11.5,4); \draw[orange, thick] (9.5,0) -- (9.5,3) -- (11.5,4) -- (11.5,1) -- (9.5,0); \draw[orange, thick, fill = orange, opacity = 0.1] (9.5,0) -- (9.5,3) -- (11.5,4) -- (11.5,1) -- (9.5,0); \draw[black, thick, stealth-] (5,2) -- (7,2); \draw[black, thick, dashed, -stealth] (7,2) -- (8,2); \node[below] at (9.5,0) {$| D_A\rangle$}; \end{tikzpicture}

plot

math

\begin{tikzpicture}[scale=.33] \draw[-] (0,0) -| (1,1); \end{tikzpicture}

plot

math

\begin{tikzpicture} \definecolor{crimson2143940}{RGB}{214,39,40} \definecolor{darkgray176}{RGB}{176,176,176} \definecolor{darkorange25512714}{RGB}{255,127,14} \definecolor{forestgreen4416044}{RGB}{44,160,44} \definecolor{lightgray204}{RGB}{204,204,204} \definecolor{mediumpurple148103189}{RGB}{148,103,189} \definecolor{steelblue31119180}{RGB}{31,119,180} \begin{axis}[ legend cell align={left}, legend style={ fill opacity=0.8, draw opacity=1, text opacity=1, at={(0.97,0.97)}, anchor=north east, draw=lightgray204 }, log basis x={10}, tick align=outside, tick pos=left, x grid style={darkgray176}, xlabel={$s_{\text{x}} = s_{\text{y}}$}, xmin=3, xmax=100000, xmode=log, xtick style={color=black}, y grid style={darkgray176}, ylabel={SER}, ymin=8, ymax=13, xmajorgrids, ymajorgrids, ytick style={color=black} ] \addplot [semithick, mediumpurple148103189, mark=*] table {% 3 12.04 10 12.44 100 11.02 }; \addlegendentry{$s_{\text{out}} = 100$} \addplot [semithick, steelblue31119180, mark=square*] table {% 3 12 10 12.43 30 10.9 100 8.35 1000 8.35 }; \addlegendentry{$s_{\text{out}} = 1000$} \addplot [semithick, darkorange25512714, mark=triangle*] table {% 3 11.87 10 12.4 30 10.94 }; \addlegendentry{$s_{\text{out}} = 3000$} \addplot [semithick, forestgreen4416044, mark=diamond*] table {% 100 8.43 1000 8.36 10000 8.32 100000 8.34 }; \addlegendentry{$s_{\text{out}} = 3600$} \end{axis} \end{tikzpicture}

plot

eess

\begin{tikzpicture} \begin{axis}[ width=0.8\textwidth, height=0.6\textwidth, xlabel={Frequency (Hz)}, ylabel={Hearing Threshold (dB)}, title={Noise-notch Hearing Loss Audiogram}, grid=major, ymin=-100, ymax=0, % Adjust the y-axis limits as needed ] \addplot[blue, line width=1.5pt] coordinates { (250, -30) (4000, -30) (6000, -80) (8000, -30) }; \end{axis} \end{tikzpicture}

plot

eess

\begin{tikzpicture}[scale=0.9] \draw[help lines,step=1] (0,0) grid (3,3); \draw[-latex] (-1,0) -- (4,0); \draw[-latex] (0,-1) -- (0,4); \draw (4,0)coordinate (A)node[below] {$i$}; \draw (0,4)coordinate (A)node[left] {$j$}; \draw (0,0)coordinate (A)node[above right] {$s_{11}$}; \draw (0,1)coordinate (B)node[above right] {$s_{21}$}; \draw (0,2)coordinate (B)node[above right] {$s_{31}$}; \draw (0,3)coordinate (B)node[above right] {$s_{41}$}; \draw (1,0)coordinate (A)node[above right] {$s_{12}$}; \draw (2,0)coordinate (A)node[above right] {$s_{13}$}; \draw (3,0)coordinate (A)node[above right] {$s_{14}$}; \draw (1,1)coordinate (B)node[above right] {$s_{22}$}; \draw (1,2)coordinate (B)node[above right] {$s_{32}$}; \draw (1,3)coordinate (B)node[above right] {$s_{42}$}; \draw (2,1)coordinate (B)node[above right] {$s_{23}$}; \draw (2,2)coordinate (B)node[above right] {$s_{33}$}; \draw (2,3)coordinate (B)node[above right] {$s_{43}$}; \draw (3,1)coordinate (B)node[above right] {$s_{24}$}; \draw (3,2)coordinate (B)node[above right] {$s_{34}$}; \draw (3,3)coordinate (B)node[above right] {$s_{44}$}; \node (1) at(6.5,1.5) {$\to \mathsf{Spin}=\begin{bmatrix} s_{11} & s_{12} & s_{13} & s_{14} & \cdots\\ s_{21} & s_{22} & s_{23} & s_{24} &\cdots\\ s_{31} & s_{32} & s_{33} & s_{34} &\cdots\\ s_{41} & s_{42} & s_{43} & s_{44} &\cdots\\ \vdots & \vdots & \vdots & \vdots &\ddots\\ \end{bmatrix}$}; \end{tikzpicture}

plot

physics

\begin{tikzpicture}[scale=1.3] \begin{scope} \draw[fill=cyan!60, opacity=1] (0,0) -- (-1,0) -- (-1,1) -- (1,1) -- (1,-1) -- (0,-1) -- (0,0); \draw[fill=cyan!20,opacity=1] (0,-1)--(1,-1)--(1,0)--(0,0)--(0,-1); \draw[fill=blue!10,opacity=1] (-1,0)--(-1,1)--(0,1)--(0,0)--(-1,0); \node at (-0.5,0.5) {$U_1$}; \node at (0.5,-0.5) {$U_2$}; \node at (0.5,0.5) {$U_{1,2}$}; {\footnotesize \draw[->,gray] (-1,-1) -- (-0.7,-1) node[right] {$x$}; \draw[->,gray] (-1,-1) -- (-1,-0.7) node[above] {$y$};} \end{scope} \end{tikzpicture}

plot

math

\begin{tikzpicture}[baseline={([yshift=-1ex]current bounding box.center)},vertex/.style={anchor=base, circle,fill=black!25,minimum size=18pt,inner sep=2pt},scale=1] \draw[orange, thick] (5,0) -- (5,3) -- (7,4) -- (7,1) -- (5,0); \draw[fill = brown, opacity = 0.5, thick] (5,0) -- (5,3) -- (7,4) -- (7,1) -- (5,0); \node[teal, right] at (7,4) {\scriptsize $e^{i\int_{X_d} d\varphi \wedge (h_{d-1} - db_{d-2})}$}; \draw[teal, thick] (3,2) -- (6,2); \filldraw[teal] (6,2) circle (1pt); \node[teal, above] at (3.5,2) {$W_{n_2}$}; \node[below, teal] at (6,2) {\scriptsize $x_2$}; \draw[teal, thick] (3.5,2.8) -- (6.5,2.8); \filldraw[teal] (6.5,2.8) circle (1pt); \node[teal, above] at (4,2.8) {$W_{n_3}$}; \node[below, teal] at (6.5,2.8) {\scriptsize $x_3$}; \draw[teal, thick] (2.5,1) -- (5.5,1); \filldraw[teal] (5.5,1) circle (1pt); \node[teal, above] at (3,1) {$W_{n_1}$}; \node[below, teal] at (5.5,1) {\scriptsize $x_1$}; \node[black] at (8,2) {$=$}; \draw[orange, thick] (5+7,0) -- (5+7,3) -- (7+7,4) -- (7+7,1) -- (5+7,0); \draw[fill = orange, opacity = 0.15, thick] (5+7,0) -- (5+7,3) -- (7+7,4) -- (7+7,1) -- (5+7,0); \draw[teal, thick] (3+7,2) -- (6+7,2); \filldraw[teal] (6+7,2) circle (1pt); \node[teal, above] at (3.5+7,2) {$W_{n_2}$}; \node[below, teal] at (6+7,2) {\scriptsize $x_2$}; \node[above, teal] at (6+7,2) {\scriptsize $e^{i \varphi(x_2)}$}; \draw[teal, thick] (3.5+7,2.8) -- (6.5+7,2.8); \filldraw[teal] (6.5+7,2.8) circle (1pt); \node[teal, above] at (4+7,2.8) {$W_{n_3}$}; \node[below, teal] at (6.5+7,2.8) {\scriptsize $x_3$}; \node[above, teal] at (6.5+7,2.8) {\scriptsize $e^{i \varphi(x_3)}$}; \draw[teal, thick] (2.5+7,1) -- (5.5+7,1); \filldraw[teal] (5.5+7,1) circle (1pt); \node[teal, above] at (3+7,1) {$W_{n_1}$}; \node[below, teal] at (5.5+7,1) {\scriptsize $x_1$}; \node[above, teal] at (5.5+7,1) {\scriptsize $e^{i \varphi(x_1)}$}; \end{tikzpicture}

plot

math

\begin{tikzpicture}[baseline=0] \draw [blue] (0, -0.5) -- node [right] {$\gamma'$} (0, 0.5); \foreach \i in {0,1} { \draw [blue] (135-90*\i:1) -- (0,0.5); \draw [blue] (-45-90*\i:1) -- (0,-0.5); } \end{tikzpicture}

plot

math

\begin{tikzpicture} \draw[line width=1,black,->] (-3,0)--(10,0); \draw[line width=1,black,->] (2,0)--(2,4); \filldraw [red] (2, 0) circle [radius = 0.05]; \filldraw [red] (-3, 0) circle [radius = 0.05]; \node[] at (10,-0.5){$R$}; \node[] at (2.7,4){$R_{orb.}$}; \node[] at (2,-0.5){$R=2$}; \node[] at (2,-1.){KT pt.}; \node[] at (-3,-0.5){$R=1$}; \node[] at (-3,-1.){$SU(2)_1$ pt.}; \end{tikzpicture}

plot

physics

\begin{tikzpicture}[scale = 1.5] \node (a) at (0,1) {}; \node (b) at (0,0.5) {}; \node (c) at (0,0) {}; \node (ap) at (1,1) {}; \node (bp) at (1,0.5) {}; \node (cp) at (1,0) {}; \node at (0,1) [left] {$ p_1$}; \node at (0,0.5) [left] {$p_2$}; \node at (0,0) [left] {$p_3$}; \node at (1,1) [right] {$q_1$}; \node at (1,0.5) [right] {$q_2$}; \node at (1,0) [right] {$q_3$}; \draw[black, fill] (a) circle (.035); \draw[black, fill] (b) circle (.035); \draw[black, fill] (c) circle (.035); \draw[black, fill] (ap) circle (.035); \draw[black, fill] (bp) circle (.035); \draw[black, fill] (cp) circle (.035); \draw[orange] (a) -- (ap); \draw[orange] (a) -- (bp); \draw[orange] (a) -- (cp); \draw[white, fill] (0.5,0.5) circle (.035); \draw[orange] (b) -- (bp); \draw[orange] (b) -- (cp); \draw[orange] (c) -- (cp); \end{tikzpicture}

plot

math

\begin{tikzpicture}[baseline=.9cm] \draw[very thick] (-3,0) -- (-3,2); \draw[->,>=stealth,thick] (-1.2, 0.2) -- (-2.2, 0.7); \draw[<-,>=stealth,thick] (-1.2, 1.8) -- (-2.2, 1.3); \draw[decorate, decoration={snake,amplitude=.6mm}] (-3,1) -- (-2.2, 1.3); \foreach \x in {0,...,12} \draw (-3-.2,.15*\x+.04) -- (.2-3-.2,.15*\x+.1+.04); \foreach \x in {-1,...,11} \draw (-3-.1,.15*\x+.09+.075) -- (.2-3-.2,.15*\x+.1+.04+.075); \node at (-.1, 1.9) {$\tilde{\psi}_0 +\tilde{\psi}_5 + T$}; \node at (-1.7+1,.1) {$\psi_3$}; \filldraw (-1.2, 0.2) circle (1pt); \filldraw (-2.2, 1.3) circle (1pt); \end{tikzpicture}

plot

physics

\begin{tikzpicture} \tikzset{enclosed/.style={draw, circle, inner sep=0pt, minimum size=.2cm}} \node[enclosed, label={left, yshift=0cm: $u$}] (w_1) at (0.5,1.8) {}; \node[enclosed, label={left, yshift=0cm: $v$}] (w_2) at (0.5,3.2) {}; \node[enclosed, fill=black] (w_3) at (1.5,2.5) {}; \node[enclosed, fill=black] (w_4) at (3,2.5) {}; \node[enclosed, fill=black] (w_6) at (5,2.5) {}; \draw (w_1) -- (w_3); \draw (w_2) -- (w_3); \draw (w_4) -- (w_3); \draw (w_4) -- node[below] {$\underbrace{}_{n-2\ \text{vertices}}$} (w_6)[dashed]; \end{tikzpicture}

plot

physics

\begin{tikzpicture}[node distance=2cm, auto] \node (prior) [align=center] {Uniform prior \\ $f(\phi)$}; \node (likelihood) [below of=prior, align=center] {Likelihood function\\ $f(t|\phi, n,a, b)$}; \node (posterior) [below of=likelihood, align=center] {Posterior distribution \\ $f(\phi|t, n, a, b)$}; \draw[->] (prior) -- (likelihood) node[midway, right] {Bayes' Rule}; \draw[->] (likelihood) -- (posterior) node[midway, right] {Normalization}; \end{tikzpicture}

plot

stat

\begin{tikzpicture}[every node/.style={draw,circle,inner sep=1pt,fill=black}] \clip (-3.5,-2.5) rectangle (3.5,3.5); \foreach \s in {0,1,2} \fill[fill=green!30] (90 + 120 * \s : 2) -- + (60 + 120 * \s : 3) -- + (120 + 120 * \s : 3) -- cycle; \fill[fill=green!30] (0,2) node[label={[right]{$e_1$}}] {} -- (-1.732,-1) node[label={[above left]{$e_2$}}] {} -- (1.732,-1) node[label={[above right]{$e_3$}}] {} -- cycle; \end{tikzpicture}

plot

stat

\begin{tikzpicture}[scale=.9] \draw[->] (0, 0) -- (10, 0) node[right] {\scriptsize $l$}; \draw[->] (0, 0) -- (0, 7); \node[circle,inner sep=0pt,fill=black,label=left:{\tiny $ATT(d'|d')$}] at (0,3.497*1.5) {}; \node[circle,inner sep=0pt,fill=black,label=left:{\tiny $ATT(d|d')$}] at (0,2.197*1.5) {}; \node[circle,inner sep=0pt,fill=black,label=left:{\tiny $ATT(d|d)$}] at (0,0.693*1.5) {}; \node[circle,inner sep=0pt,fill=black,label=below:{\tiny $d'=d+1$}] at (4*1.5,0) {}; \node[circle,inner sep=0pt,fill=black,label=below:{\tiny $d=1$}] at (1*1.5,0) {}; \draw[scale=1.5, domain=0:5, smooth, variable=\d, black] plot ({\d}, {ln(1+\d)}); \draw[scale=1.5, domain=0:5, smooth, variable=\d, black] plot ({\d}, {ln(1+8*\d)}); \node[circle,inner sep=0pt,fill=white,label=below right:{\tiny $ATT(l|d)$}] at (5*1.5,1.7*1.75) {}; \node[circle,inner sep=0pt,label=below right:{\tiny $ATT(l|d')$}] at (4*1.9,4.1*1.45) {}; \draw[line width=.3mm] (1*1.5,2.197*1.5) -- (4*1.5,3.497*1.5); \draw (1.5*1.5, 2.41*1.5) -- (1.5*1.5,2.7*1.5); \draw (2.18*1.5, 2.7*1.5) -- (1.5*1.5,2.7*1.5); \node[circle,inner sep=0pt,fill=white,label=above left:{\tiny $ACRT(d'|d')$}] at (1.5*1.6,2.7*1.5) {}; \draw[line width=.3mm] (1*1.5, 0.693*1.5)-- (4*1.5,3.497*1.5); \draw (3*1.5, 2.56*1.5) -- (3.5*1.5,2.56*1.5); \draw (3.5*1.5, 2.56*1.5) -- (3.5*1.5,3.027*1.5); \node[circle,draw,line width=1pt,inner sep=0pt,minimum size=6pt,label=below right:{}] at (4*1.5,3.497*1.5) {}; \node[circle,draw,line width=1pt,inner sep=0pt,minimum size=6pt,label=below right:{}] at (1*1.5,0.693*1.5) {}; \node[circle,inner sep=0pt,fill=white,label=right:{ \tiny \begin{tabular}{l c} $=ACRT(d'|d')+ ATT(d|d') -ATT(d|d)$ \end{tabular}}] at (1.5*3.3,2.66*1.5) {}; \draw[densely dotted] (4*1.5,0) -- (4*1.5,3.497*1.5); \draw[densely dotted] (0,1.5*3.497) -- (4*1.5,3.497*1.5); \draw[densely dotted] (1*1.5,0) -- (1*1.5,0.693*1.5); \draw[densely dotted] (0,0.693*1.5) -- (1*1.5,0.693*1.5); \draw[densely dotted] (1*1.5, 0.693*1.5)-- (1*1.5,2.197*1.5); \draw[densely dotted] (0, 2.197*1.5)-- (1*1.5,2.197*1.5); \end{tikzpicture}

plot

econ

\begin{tikzpicture}[baseline=0] \tikzset{>=latex} \draw [help lines,line width=2pt,-] (-3,-3) -- (3,3); \draw [help lines,line width=2pt,-] (-3,3) -- (3,-3); \draw [->,line width=3pt,red] (0,0)--(1,1) node[right,scale=2,red] {$p_4$}; \draw [->,line width=3pt,red] (0,0)--(-1,1) node[left,scale=2,red] {$p_3$}; \draw [->,line width=3pt,blue] (0,0)--(-2,-2) node[xshift=-0.5cm,yshift=0.6cm,scale=2,blue] {$-p_1$}; \draw [->,line width=3pt,blue] (0,0)--(2,-2) node[xshift=0.4cm,yshift=0.6cm,scale=2,blue] {$-p_2$}; \draw [->,line width=5pt,black] (0,0)--(0,-2) node[yshift=-.4cm,scale=2,black] {$Q$}; \end{tikzpicture}

plot

physics

\begin{tikzpicture} \begin{scope}[scale=1.6,yshift=0cm] \foreach \x in {-3,...,3}{ \fill[blue] (\x,0) circle [radius=3pt]; \fill[red] (\x,0.7) circle [radius=3pt]; \draw[<->,brown,very thick] (\x+0.92,0.09)--(\x+0.09,0.64); } \draw[<->,brown,very thick] (-4+0.92,0.09)--(-4+0.09,0.64); \node at (-4.5,0.35) {$\ldots$}; \node at (4.5,0.35) {$\ldots$}; \end{scope} \end{tikzpicture}

plot

physics

\begin{tikzpicture}[ scale=0.95, arr/.style={->,thick}, varr/.style={->,ultra thick}, dot/.style={radius=0.7mm}, node distance=50mm ] \draw[arr] (0,0,0) -- (0,0,5); \draw[arr] (0,0,0) -- (5,0,0); \draw[arr] (0,0,0) -- (0,5,0); \node[below right] at (0,0,4) {$b_1$}; \node[above] at (4,0,0) {$b_2$}; \node[left] at (0,4,0) {$b_3$}; \draw[fill] (0,0,0) circle[dot]; \node[above left] at (0,0,0) {$r^1 = o$}; \draw[fill] (0,0,3) circle[dot]; \node[above left] at (0,0,3) {$r^2$}; \draw[varr] (0,0,0) -- (0,0,3); \node[below right] at (0,0,1.5) {$v_1$}; \draw[fill] (3,0,2) circle[dot]; \node[below right] at (3,0,2) {$r^3$}; \draw[varr] (0,0,0) -- (3,0,2); \node[below left] at (1.5,0,1) {$v_2$}; \draw[varr] (0,0,0) -- (3,0,0); \node[above] at (1.5,0,0) {$v_{2,\bot}$}; \draw[dotted] (3,0,0) -- (3,0,2); \draw[fill] (4.5,5,3.5) circle[dot]; \node[above right] at (4.5,5,3.5) {$x^i$}; \draw[dashed] (4.5,5,3.5) -- (4.5,0,3.5); \draw[dashed] (4.5,0,3.5) -- (0,0,3.5); \draw[dashed] (4.5,0,3.5) -- (4.5,0,0); \node[below] at (2.25,0,3.5) {$\left(x^i\right)_1$}; \node[below right] at (4.5,0,1.75) {$\left(x^i\right)_2$}; \node[below right] at (4.5,3.5,3.5) {$\left(x^i\right)_3$}; \end{tikzpicture}%

plot

cs

\begin{tikzpicture} \draw[lime, fill=lime] (0,0) circle [radius=0.16] node[white] {{\fontfamily{qag}\selectfont \tiny $\dot{\mathsf I}$D}}; \draw[white, fill=white] (-0.0625,0.095) circle [radius=0.007]; \end{tikzpicture}

plot

cs

\begin{tikzpicture} \begin{axis}[ xlabel=dimension $d$ (in terms of $n$), x label style={at={(axis description cs:0.5,-0.06)},anchor=north,anchor=north, below=5mm}, ylabel=Frobenius error $\alpha$, y label style={at={(axis description cs:-0.2,0.5)},anchor=north,anchor=north, below=5mm}, xmin=0, xmax=120, ymin=0, ymax=54, xticklabels={$1^{\textcolor{white}{1}}$, $n^{1/2}$, $n^{2/3}$, $n^{\textcolor{white}{1}}$, $n^{4/3}$, $n^2$}, yticklabels={$n^{-1}$, $n^{-1/2}$, $n^{-1/3}$, $1$}, xtick={0,30,40,60,80,120}, ytick={0,27,36,54}, legend style={at={(0.61,0.2)},anchor=west}, axis equal image ] \addplot[mark=*,blue,densely dashed,very thick] plot coordinates { (0,0) (40,36) (120,54) }; \addlegendentry{Prev. Upper Bound} \addplot[mark=*,orange,dashed,very thick] plot coordinates { (0,0) (30,27) (60,27) (120,54) }; \addlegendentry{Prev. Lower Bound} \addplot[mark=*,red,very thick] plot coordinates { (30,27) (40,36) (80,36) }; \addlegendentry{Our Lower Bound} \end{axis} \end{tikzpicture}

plot

math

\begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-1,xscale=1] \draw [fill={rgb, 255:red, 238; green, 228; blue, 137 } ,fill opacity=1 ] (28.14,40) -- (43.83,40) -- (43.83,87.35) -- (28.14,87.35) -- cycle ; \draw [fill={rgb, 255:red, 241; green, 191; blue, 115 } ,fill opacity=1 ] (67.38,52.63) .. controls (67.38,45.65) and (73.03,40) .. (80,40) -- (141.07,40) .. controls (148.04,40) and (153.7,45.65) .. (153.7,52.63) -- (153.7,90.51) .. controls (153.7,97.48) and (148.04,103.13) .. (141.07,103.13) -- (80,103.13) .. controls (73.03,103.13) and (67.38,97.48) .. (67.38,90.51) -- cycle ; \draw (43.83,63.67) -- (65.38,63.67) ; \draw [shift={(67.38,63.67)}, rotate = 180] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; \draw (47.76,99.19) -- (65.97,80.88) ; \draw [shift={(67.38,79.46)}, rotate = 134.84] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; \draw (208.63,71.57) node {\includegraphics[width=47.08pt,height=47.35pt]{2791_sec_Images_ButterImg.jpg}}; \draw (153.7,64.07) -- (175.63,64.07) ; \draw [shift={(177.63,64.07)}, rotate = 180] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; \draw (177.24,79.46) -- (156.09,80.18) ; \draw [shift={(154.09,80.25)}, rotate = 358.05] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; \draw (338.11,71.57) node {\includegraphics[width=47.08pt,height=47.35pt]{2791_sec_Images_ButterImg.jpg}}; \draw [dash pattern={on 7.5pt off 2.25pt}] (306.72,71.57) -- (242.02,71.57) ; \draw [shift={(240.02,71.57)}, rotate = 360] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; \draw [dash pattern={on 7.5pt off 3.75pt}] (339,40) -- (339,16) -- (37,15) -- (37,37) ; \draw [shift={(37,39)}, rotate = 270] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; \draw (27,93) node [anchor=north west][inner sep=0.75pt] [align=left] {$c_s$}; \draw (247,60) node [anchor=north west][inner sep=0.75pt] [align=left] {\begin{minipage}[lt]{38.76pt}\setlength\topsep{0pt} \begin{center} {\tiny Reconstruction }\\{\tiny Loss} \end{center} \end{minipage}}; \draw (72.32,49) node [anchor=north west][inner sep=0.75pt] [align=left] {\begin{minipage}[lt]{54.4pt}\setlength\topsep{0pt} \begin{center} {\scriptsize Pre-trained }\\{\scriptsize Stable Diffusion}\\{\scriptsize Model} \end{center} \end{minipage}}; \draw (32,75) node [anchor=north west][inner sep=0.75pt] [rotate=-270] [align=left] {{\tiny Noise}}; \end{tikzpicture}

plot

cs

assets/cs/2791_sec_Images_ButterImg.jpg

assets/cs/2791_sec_Images_ButterImg.jpg

\begin{tikzpicture} \begin{axis}[ xlabel=dimension $d$ (in terms of $n$), x label style={at={(axis description cs:0.5,-0.06)},anchor=north,anchor=north, below=5mm}, ylabel=Frobenius error $\alpha$, y label style={at={(axis description cs:-0.2,0.5)},anchor=north,anchor=north, below=5mm}, xmin=0, xmax=120, ymin=0, ymax=54, xticklabels={$1^{\textcolor{white}{1}}$, $n^{1/2}$, $n^{2/3}$, $n^{\textcolor{white}{1}}$, $n^{4/3}$, $n^2$}, yticklabels={$n^{-1}$, $n^{-1/2}$, $n^{-1/3}$, $1$}, xtick={0,30,40,60,80,120}, ytick={0,27,36,54}, legend style={at={(0.61,0.2)},anchor=west}, axis equal image ] \addplot[mark=*,blue,densely dashed,very thick] plot coordinates { (0,0) (40,36) (120,54) }; \addlegendentry{Prev. Upper Bound} \addplot[mark=*,orange,dashed,very thick] plot coordinates { (0,0) (30,27) (60,27) (120,54) }; \addlegendentry{Prev. Lower Bound} \addplot[mark=*,red,very thick] plot coordinates { (30,27) (40,36) (80,36) }; \addlegendentry{Our Lower Bound} \end{axis} \end{tikzpicture}

plot

stat

\begin{tikzpicture}[scale = 0.9, baseline = -2,every node/.style={scale=1}] \def\s{0.5}; \foreach \x in {-5,...,3,6,7,11,12} { \draw[fill=black] (\x*\s,0) circle (0.025); } \foreach \count/\valone/\valtwo/\valthree/\valfour/\valfive in {0/\overline{1}/\overline{1}/2/1/\overline{1},1/\overline{3}/\overline{2}/\overline{3}/1/\overline{2}}{ \node (a) at (4*\s,0 + \count*\s) {$\valone$}; \node (b) at (5*\s,0 + \count*\s) {$\valtwo$}; \node (c) at (8*\s,0 + \count*\s) {$\valthree$}; \node (d) at (9*\s,0 + \count*\s) {$\valfour$}; \node (d) at (10*\s,0 + \count*\s) {$\valfive$}; } \end{tikzpicture}

plot

physics

\begin{tikzpicture} \draw (-6,0) -- (9,0); \filldraw (-4,0) circle (1pt) node[below] {$U_t(m_1\mid z_{st})$}; \filldraw (-4.2,-0.5) node[below] {$=L_t(m_K\mid z_{st})$}; \filldraw (-1,0) circle (1pt); \filldraw (1.0,0) circle (1pt) node[below] {$U_t(m_{K-1}\mid z_{st})$}; \draw[red, thick, -latex] (4.0,0) -- (4.0,0.6); \node[above] at (4.0,0.5) {$\tilde{L}(m_K \mid z_{st})$}; \filldraw (6,0) circle (1pt) node[below] {$U_t(m_K\mid z_{st})$}; \end{tikzpicture}

plot

econ

\begin{tikzpicture} \draw (0,0)--(0,3)--(2,3)--(2,0)--(0,0); \draw (0,4)--(2,4)--(3,1); \draw [line width=3,color=blue] (0,4)--(2,4)--(2.5,2.5)--(3,3); \draw (2,3)--(3,4); \draw (2,2)--(3,3); \draw (2,1)--(3,2); \draw (3.7,4) node {$1$}; \draw (3.7,3.5) node {$\vdots$}; \draw (3.7,3) node {\small $d$\normalsize}; \draw (3.7,2) node {$\vdots$}; \draw (3.7,1) node {\small$\lambda_{n-k}^t+1$\normalsize}; \draw[<->,dashed] (-0.2,-0.2)--(3.2,-0.2); \draw (1.5,-0.5) node {$w^*$}; \draw [line width=3,color=blue] (4.5,3)--(6,0); \draw (6.2,0) node {$n$}; \draw[<->,dashed] (3.9,-0.2)--(6.2,-0.2); \draw (4.7,-0.5) node {$u^{-1}w_0$}; \draw[<->,dashed] (6.5,-0.2)--(9.2,-0.2); \draw (7.5,-0.5) node {$\Delta_n$}; \draw [line width=3,color=blue] (6.5,0)--(9,4); \draw (1,1.5) node {$\widetilde{w}$}; \draw (-0.2,-0.2)--(-0.2,-0.8); \draw (-0.2,-1) node {$x=0$}; \draw (3.7,-0.2)--(3.7,-0.8); \draw (3.7,-1) node {$x=1$}; \draw (6.2,-0.2)--(6.2,-0.8); \draw (6.2,-1) node {$x=2$}; \end{tikzpicture}

plot

math

\begin{tikzpicture}[scale=1.5, every node/.style={scale=.7}] \draw[->] (0,0) -- (4.5,0) node[below right] {$x$}; \draw[->] (0,0) -- (0,6) node[above left] {$y$}; \draw[domain=0.25:4,smooth,variable=\x,blue] plot ({\x},{1/\x}) ; \draw[dashed] (0,2+.5*4)-- (.5,2) --(2/4+.5,0); \draw[dotted] (0,.5)node[left]{DAI} -- (2,.5) -- (2,0) node[below]{ETH}; \draw(2-.08,0) arc[start angle=0, end angle=-40, radius=-.5]; \node at (2-.4,.2) {$-p(x)$}; \draw(.8,{(2+.5*4)/(2/4+.5)*(2.13-.8)})--(2.13,0); \draw[blue, ->](3,.4)--(3.3,1.3); \draw[blue, ->](1.1,1.1)--(2,2); \draw[blue, ->](.5,3)--(1.2,3.2); \draw[domain=.8:4,smooth,variable=\x,blue] plot ({\x},{4.55/\x}) ; \end{tikzpicture}

plot

cs

\begin{tikzpicture} \draw[gray, thick] (-12,-2) -- (-8,-2); \draw[gray, thick] (-15,-1) -- (-10,-1); \filldraw[black] (-15,-1) circle (2pt) node[anchor=south] {$i_{1}$}; \filldraw[black] (-10,-1) circle (2pt) node[anchor=south] {$j_{1}$}; \filldraw[black] (-12,-2) circle (2pt) node[anchor=south] {$i_{2}$}; \filldraw[black] (-8,-2) circle (2pt) node[anchor=south] {$j_{2}$}; \filldraw[black] (-11,-2) circle (2pt) node[anchor=south] {$i_{2}+1$}; \end{tikzpicture}

plot

math

\begin{tikzpicture}[font = \footnotesize, scale =0.75] \fill [cyan, opacity=0.2] (0,0)--(3,0)--(3,3)--(0,3)--(0,0); \draw[->] (0,0)--(3,0) node[below] {$\mathcal{Q}_4=(m_- n_-,0) \, , \mathcal{Q}_2=(m_+ n_-,0)$}; \draw[->] (0,0)--(0,3) node[above ] {$\,\,\,\qquad \mathcal{Q}_3=(0,n_-)$}; \draw[->] (0,0)--(-3,3) node[above ] {$\mathcal{Q}_1=(-t,n_+)$}; \draw[->] (0,0)--(1.5,1.5) node[above] {$(t_1,t_2)$}; \end{tikzpicture}

plot

math

\begin{tikzpicture}[scale=.6] \draw [ultra thick, red] (0,0)--(1.5, 0) -- (1.5,2.5) -- (2.5,2.5) --(2.5,1.5) -- (3.5, 1.5)--(3.5, 4.5)-- (6.5, 4.5)--(6.5, 2.5)--(7.5,2.5)--(7.5, 3.5) -- (8.5, 3.5) --(8.5, 1.5)--(9.5, 1.5)--(9.5, 2.5)--(10.5, 2.5)-- (11.5, 2.5)--(11.5, 0.5)--(12, 0.5); \foreach \i in {0,...,8}{ \foreach \j in {0,...,12}{ \node[draw,circle,inner sep=1pt,fill] at (\j,\i) {}; } \fill[white] (4.5,0.5)--(4.5,2.5)--(6.5,2.5)--(6.5,0.5)--(4.5,0.5); \node at (5.5, 1.5) {$+$}; \fill[white] (8.5,5.5)--(8.5,7.5)--(10.5,7.5)--(10.5,5.5)--(8.5,5.5); \node at (9.5, 6.5) {$-$}; } \end{tikzpicture}

plot

physics

\begin{tikzpicture} \draw[->] (-3, 0) -- (3, 0); \draw[->] (0, -3) -- (0, 3); \fill[draw,gray, opacity=.5] (1, -.3) -- (1, .3) -- (2.5, .6) -- (2.5, -.6) -- cycle; \fill[draw,gray, opacity=.5] (-1, -.3) -- (-1, .3) -- (-2.5, .6) -- (-2.5, -.6) -- cycle; \fill[draw,gray!20!black, opacity=.5] (1, .3) -- (1, .9) -- (2.5, 1.8) -- (2.5, .6) -- cycle; \fill[draw,gray!20!black, opacity=.5] (-1, -.3) -- (-1, -.9) -- (-2.5, -1.8) -- (-2.5, -.6) -- cycle; \end{tikzpicture}

plot

eess

\begin{tikzpicture}[scale=4.6] \draw[line width = 0.3mm, color = black] (0,0) -- (1,0) -- (1,1) -- (0,1) -- cycle; \foreach \i in {0,...,2}{ \draw[line width=0.15mm,color=gray!50] (1/4,\i/16) -- (5/8,\i/16); \draw[line width=0.15mm,color=gray!50] (1/4+\i/16,0) -- (1/4+\i/16,1/8); \draw[line width=0.15mm,color=gray!50] (3/8+\i/16,0) -- (3/8+\i/16,1/8); \draw[line width=0.15mm,color=gray!50] (1/2+\i/16,0) -- (1/2+\i/16,1/8); } \foreach \i in {0,...,6}{ \draw[line width=0.15mm,color=gray!50] (11/16,\i/32+11/16) -- (14/16,\i/32+11/16); \draw[line width=0.15mm,color=gray!50] (\i/32+11/16,11/16) -- (\i/32+11/16,14/16); } \foreach \i in {0,...,12}{ \draw[line width=0.15mm,color=gray!50] (0,\i/32+20/32) -- (3/8,\i/32+20/32); \draw[line width=0.15mm,color=gray!50] (\i/32,5/8) -- (\i/32,1); } \foreach \i in {0,...,8}{ \draw[line width=0.3mm] (0,\i/8) -- (1,\i/8); \draw[line width=0.3mm] (\i/8,0) -- (\i/8,1); } \foreach \i in {0,...,6}{ \draw[line width=0.3mm] (0,\i/16) -- (3/8,\i/16); \draw[line width=0.3mm] (\i/16,0) -- (\i/16,3/8); } \foreach \i in {8,...,16}{ \draw[line width=0.3mm] (1/2,\i/16) -- (1,\i/16); \draw[line width=0.3mm] (\i/16,1/2) -- (\i/16,1); } \foreach \i in {0,...,2}{ \draw[line width=0.3mm] (0,\i/16+14/16) -- (1/8,\i/16+14/16); \draw[line width=0.3mm] (0,\i/16+12/16) -- (1/8,\i/16+12/16); \draw[line width=0.3mm] (\i/16,3/4) -- (\i/16,1); } \foreach \i in {0,...,2}{ \draw[line width=0.3mm] (0,\i/16+6/16) -- (1/8,\i/16+6/16); \draw[line width=0.3mm] (\i/16,3/8) -- (\i/16,4/8); } \foreach \i in {0,...,2}{ \draw[line width=0.3mm] (0,\i/32) -- (1/16,\i/32); \draw[line width=0.3mm] (0,\i/32+2/32) -- (1/16,\i/32+2/32); \draw[line width=0.3mm] (\i/32,0) -- (\i/32,2/16); } \foreach \i in {26,...,32}{ \draw[line width=0.3mm] (13/16,\i/32) -- (1,\i/32); \draw[line width=0.3mm] (\i/32,13/16) -- (\i/32,1); } \foreach \i in {0,...,2}{ \draw[line width=0.3mm] (0,\i/32+30/32) -- (1/16,\i/32+30/32); \draw[line width=0.3mm] (\i/32,15/16) -- (\i/32,1); } \foreach \i in {62,...,64}{ \draw[line width=0.3mm] (62/64,\i/64) -- (1,\i/64); \draw[line width=0.3mm] (\i/64,62/64) -- (\i/64,1); } \draw[line width=1.0mm,color = blue] (5/8,0) -- (5/8,1/8) -- (2/8,1/8) -- (2/8,0) -- cycle; \draw[line width=1.0mm,color = blue] (5/8+1/16,5/8+1/16) -- (14/16,5/8+1/16) -- (14/16,14/16) -- (5/8+1/16,14/16) -- cycle; \draw[line width=1.0mm,color = blue] (0,5/8) -- (3/8,5/8) -- (3/8,1) -- (0,1) -- cycle; \end{tikzpicture}

plot

cs

\begin{tikzpicture}[scale=0.5] \node[label=right:{$o$},draw, circle] at (0,4) {}; \foreach \i in {1,...,4} \foreach \j in {1,...,7}{ \node[draw, circle] at (0,\j) {}; } \foreach \i in {1,...,1} \foreach \j in {1,...,6}{ \draw (0,\j) edge (0, \j+1); } \end{tikzpicture}

plot

physics

\begin{tikzpicture}[scale=1.0] \node (Ep) at (+4.63,-0.55) {$E^*$}; \node (E) at (+3.37,-0.55) {$E$}; \node (EpS) at (-1.7,0) {$E + S$}; \node (ES) at (0,0) {$ES$}; \node (EpP) at (1.7,0) {$E + P$}; \node (EppS) at (0,-1.1) {$E^* + S$}; \draw[arrows={-stealth},transform canvas={yshift=2pt}, shorten <=0.2em, shorten >=0.2em] (EpS) to node[above] {$k_1$} (ES); \draw[arrows={-stealth},transform canvas={yshift=-2pt}, shorten <=0.2em, shorten >=0.2em] (ES) to node[below] {$k_2$} (EpS); \draw[arrows={-stealth},transform canvas={yshift=2pt}, shorten <=0.2em, shorten >=0.2em] (ES) to node[above] {$k_3$} (EpP); \draw[arrows={-stealth},transform canvas={yshift=-2pt}, shorten <=0.2em, shorten >=0.2em] (EpP) to node[below] {$k_4$} (ES); \draw[arrows={-stealth},transform canvas={yshift=2pt}, shorten <=0.2em, shorten >=0.2em] (E) to node[above] {$k_5$} (Ep); \draw[arrows={-stealth},transform canvas={yshift=-2pt}, shorten <=0.2em, shorten >=0.2em] (Ep) to node[below] {$k_6$} (E); \draw[arrows={-stealth},transform canvas={yshift=2pt}, shorten <=0.2em, shorten >=0.2em] (ES) to node[right] {$k_5$} (EppS); \end{tikzpicture}

plot

math

\begin{tikzpicture} \draw[green!50!black, ultra thick] (-4,0) -- node[above=2pt]{\begin{large}$A_-$\end{large}} (-2,0); \draw[green!50!black, ultra thick] (-2,0) -- node[above=2pt]{\begin{large}$A_+$\end{large}} (2,0); \draw[green!50!black, ultra thick] (2,0) -- node[above=2pt]{\begin{large}$A_-$\end{large}} (4,0); \filldraw [red] (-4,0) circle (2pt) node[anchor=north]{$-\infty$}; \filldraw [red] (4,0) circle (2pt) node[anchor=north]{$+\infty$}; \filldraw [blue] (-2,0) circle (2pt) node[anchor=north]{$0$}; \filldraw [blue] (2,0) circle (2pt) node[anchor=north]{$1$}; \filldraw [black] (0,0) circle (2pt) node[anchor=north]{$\frac{1}{2}$}; \end{tikzpicture}

plot

stat

\begin{tikzpicture} \draw[-] (-5,0) -- (5,0); \foreach \i in {1,4,6,10,11} {\draw[-] (-6+\i,0)--(-6+\i,0.2);} \node at (-5,-0.3) {$x_0$}; \node at (-2,-0.3) {$x_{i_1}$}; \node at (0,-0.3) {$x_{i_2}$}; \node at (4,-0.3) {$x_{i_3}$}; \node at (5,-0.23) {$x_I(x_{i_4})$}; \fill[fill=black,opacity=0.2](-2,0) rectangle (0,0.7); \fill[fill=black,opacity=0.2](4,0) rectangle (5,0.7); \end{tikzpicture}

plot

math

\begin{tikzpicture}[scale=0.8] \def\r{0.4}; \node [above] at (0, 0) {$G$}; \draw (0, 0) -- (-1.5, -0.5); \draw (0, 0) -- (1.5, -0.5); \draw (-1.5, -0.5) -- (-2.5, -1.5); \draw (-1.5, -0.5) -- (-1.5, -1.5); \draw (-1.5, -0.5) -- (-0.5, -1.5); \draw (-2.5, -1.5-\r) circle (\r) node {$1$}; \draw (-1.5, -1.5-\r) circle (\r) node {$1$}; \draw (-0.5, -1.5-\r) circle (\r) node {$1$}; \draw (1.5, -0.5) -- (1, -1.5); \draw (1.5, -0.5) -- (2, -1.5); \draw (1, -1.5-\r) circle (\r) node {$0$}; \draw (2, -1.5-\r) circle (\r) node {$0$}; \draw (6, -1.1) -- (6.6, -1.1) -- (6.6, -1.25) -- (7, -1) -- (6.6, -0.75) -- (6.6, -0.9) -- (6, -0.9) -- cycle; \def\x{10}; \node [above] at (\x, 0) {$G$}; \draw (0+\x, 0) -- (-1+\x, -0.5); \draw (0+\x, 0) -- (1+\x, -0.5); \draw (-1+\x, -0.5-\r) circle (\r) node {$1$}; \draw (1+\x, -0.5-\r) circle (\r) node {$0$}; \def\y{-4}; \node [above] at (0, 0+\y) {$G$}; \draw (0, 0+\y) -- (-1, -1+\y); \draw (0, 0+\y) -- (1, -1+\y); \draw (-1, -1+\y-\r) circle (\r) node {$0$}; \draw (1, -1+\y) -- (0, -2+\y); \draw (1, -1+\y) -- (1, -2+\y); \draw (1, -1+\y) -- (2.5, -2+\y); \draw (0, -2+\y-\r) circle (\r) node {$1$}; \draw (1, -2+\y-\r) circle (\r) node {$1$}; \draw (2.5, -2+\y) -- (1.5, -3+\y); \draw (2.5, -2+\y) -- (3.5, -3+\y); \draw (1.5, -3+\y-\r) circle (\r) node {$1$}; \draw (3.5, -3+\y) -- (2.5, -4+\y); \draw (3.5, -3+\y) -- (3.5, -4+\y); \draw (3.5, -3+\y) -- (4.5, -4+\y); \draw (3.5, -4+\y-\r) circle (\r) node {$1$}; \draw (4.5, -4+\y-\r) circle (\r) node {$1$}; \draw (2.5, -4+\y) -- (2, -5+\y); \draw (2.5, -4+\y) -- (2.5, -5+\y) node [below] {$\vdots$}; \draw (2.5, -4+\y) -- (3, -5+\y); \draw (6, -1.1+\y) -- (6.6, -1.1+\y) -- (6.6, -1.25+\y) -- (7, -1+\y) -- (6.6, -0.75+\y) -- (6.6, -0.9+\y) -- (6, -0.9+\y) -- cycle; \node [above] at (\x, \y) {$G$}; \draw (0+\x, 0+\y) -- (-1+\x, -0.5+\y); \draw (0+\x, 0+\y) -- (1+\x, -0.5+\y); \draw (-1+\x, -0.5+\y-\r) circle (\r) node {$0$}; \draw (1+\x, -0.5+\y-\r) circle (\r) node {$1$}; \end{tikzpicture}

plot

math

\begin{tikzpicture} \begin{axis}[ width=0.7\linewidth, height=0.5\linewidth, ybar, bar width=7pt, enlarge x limits=0.15, legend style={at={(0.5,-0.3)}, anchor=north, legend columns=-1}, % Adjusted y-coordinate ylabel={Score}, symbolic x coords={Factuality, Completeness, Hallucinations}, xtick=data, nodes near coords align={vertical}, x tick label style={rotate=45, anchor=east, font=\small}, y tick label style={font=\small}, ] \addplot[fill=violet] coordinates {(Factuality,97.5) (Completeness,95) (Hallucinations,0)}; \addplot[fill=teal] coordinates {(Factuality,95) (Completeness,92.5) (Hallucinations,7.5)}; \addplot coordinates {(Factuality,90) (Completeness,90) (Hallucinations,5)}; \addplot coordinates {(Factuality,75) (Completeness,82.5) (Hallucinations,10.5)}; \addplot[fill=pink] coordinates {(Factuality,55) (Completeness,39.5) (Hallucinations,65)}; \addplot[fill=cyan] coordinates {(Factuality,27.5) (Completeness,27.5) (Hallucinations,65.6)}; \legend{GPT-4, StableBeluga2, GPT-3.5, Llama2, Guanaco-65B, Guanaco-33B} \end{axis} \end{tikzpicture}

plot

cs

\begin{tikzpicture} \draw (0,0) grid (5,1); \foreach \x in {0,...,4} \draw (\x,0)--++(1,1); \foreach \x in {1,...,5} \draw[dotted] (\x,0)--++(-1,1); \draw (0,0) node [below]{$N$}; \foreach \x in {0,...,4} \draw (\x+1,0) node [below] {$\x$}; \foreach \x in {0,...,5} \draw (\x,1) node [above] {$\x$}; \end{tikzpicture}

plot

cs

\begin{tikzpicture} [->,shorten >=1pt,scale=.75,inner sep=1pt, minimum size=12pt, auto=center, node distance=3cm, thick, node/.style={circle, draw=black, thick},] \tikzstyle{block1} = [rectangle, draw, fill=red!10, text width=8em, text centered, rounded corners, minimum height=0.8cm, minimum width=1cm]; \node (rect) at (0,0) (A) [draw, rounded corners, minimum width= 1.5cm, minimum height=1cm] {Worker}; \node (rect) at (6,0) (S) [draw, rounded corners, minimum width= 1.5cm, minimum height=1cm] {Server}; \coordinate (a1) at (1, 0.4); \coordinate (s1) at (5,0.4); \draw[->,thick] (s1) -- node[pos=.5,above]{Iterate $x_t$} (a1); \coordinate (a2) at (1,-0.4); \coordinate (s2) at (5,-0.4); \draw[->,thick] (a2) -- node[pos=.5,below] {$\bar{B}$-bit symbol $\sigma_t$} node[pos=.5,above] {Channel} (s2); \node at (0,-1.6) {Encode $\nabla f(x_t)$}; \node at (8, -1.6) {Perform update: $x_{t+1}=x_{t}-\alpha g_t$}; \end{tikzpicture}

plot

eess

\begin{tikzpicture}[scale=0.90] \definecolor{darkgray176}{RGB}{176,176,176} \definecolor{darkorange25512714}{RGB}{255,127,14} \definecolor{forestgreen4416044}{RGB}{44,160,44} \definecolor{steelblue31119180}{RGB}{31,119,180} \definecolor{red}{RGB}{255,0,60} \definecolor{blue}{RGB}{0,0,255} \definecolor{lightgray204}{RGB}{255,255,255} \begin{axis}[ legend cell align={left}, legend style={ fill opacity=0.8, draw opacity=1, text opacity=1, at={(0.0,0.7)}, anchor=south west, draw=lightgray204 }, tick align=outside, tick pos=left, ylabel = {Time(ms)}, x grid style={darkgray176}, xmajorgrids, xmin=42.5, xmax=207.5, xtick style={color=black}, y grid style={darkgray176}, xlabel = {Number of subnetworks}, ymajorgrids, ymin=1.34199541807175, ymax=43.8010907769203, ytick style={color=black} ] \addplot [dashed, red, mark=o, mark size=3, mark options={solid}] table {% 50 3.60772442817688 60 4.00972652435303 70 4.32450103759766 80 4.34334278106689 90 4.72414207458496 100 5.00572490692139 110 5.31423425674438 120 5.65466403961182 130 5.91401290893555 140 6.02741861343384 150 6.31173086166382 160 6.58063745498657 170 6.9404935836792 180 7.24755191802979 190 7.54800128936768 200 7.85946798324585 }; \addlegendentry{GGNN} \addplot [dashed, teal, mark=triangle, mark size=3, mark options={solid}] table {% 50 3.27195429801941 60 4.36027574539185 70 4.93752956390381 80 5.5459098815918 90 6.5501708984375 100 7.63566970825195 110 8.77511024475098 120 9.74986553192139 130 10.8464908599854 140 11.9308700561523 150 13.2322483062744 160 14.4715852737427 170 16.3326377868652 180 17.7110958099365 190 19.4075908660889 200 21.0409393310547 };\addlegendentry{CGC} \addplot [dashed, blue, mark=+, mark size=3, mark options={solid}] table {% 50 9.76164817810059 60 11.6957693099976 70 13.9707870483398 80 15.6113710403442 90 17.4726963043213 100 19.5271015167236 110 21.3734550476074 120 23.5450477600098 130 25.7252159118652 140 27.6036434173584 150 29.5222969055176 160 31.8150978088379 170 34.9156913757324 180 37.2278022766113 190 40.1598892211914 200 41.8711318969727 };\addlegendentry{SISA} \end{axis} \end{tikzpicture}

plot

eess

\scalebox{0.7}{\begin{tikzpicture} \node[circle, name=a] at (0,0) {$A$}; \node[circle, name=az] at (2,2) {$A_Z$}; \node[circle, name=am] at (2,0) {$A_M$}; \node[circle, name=ay] at (2,-2) {$A_Y$}; \node[circle, name=lz] at (4,2) {$L_Z$}; \node[circle, name=lm] at (4,0) {$L_M$}; \node[circle, name=ly] at (4,-2) {$L_Y$}; \node[circle, name=z] at (6,2) {$Z$}; \node[circle, name=m] at (6,0) {$M$}; \node[circle, name=y] at (10,0) {$Y$}; \draw[->](az) to (lz); \draw[->](am) to (lm); \draw[->](ay) to (ly); \draw[->](lz) to (z); \draw[->](lm) to (m); \draw[->](ly) to (y); \draw[->](z) to (m); \draw[->](z) to (y); \draw[->](m) to (y); \draw[->](a) to (lz); \draw[->](a) to[out=20,in=150] (lm); \draw[->](a) to (ly); \end{tikzpicture}}

plot

stat

\begin{tikzpicture} \filldraw[fill=red,draw=green] circle (3pt); \end{tikzpicture}

plot

cs

\centerline{\begin{tikzpicture}[scale=0.8] \draw[->][dashed][thick](-8,0)--(8,0); \draw[fill] (8.5,0) node{$Rez$}; \draw[fill] [blue](-3,0) circle [radius=0.05]; \draw[fill][blue] (-3,-0.3) node{$z_{2}$}; \draw[->][thick](-6,1.5)--(-4,0.5); \draw[-][thick](-4,0.5)--(-3,0); \draw[fill] (-4.5,0.3) node{$\Omega_{21}$}; \draw[fill] (-3,0.5) node{$\Omega_{22}$}; \draw[fill] (-1.5,0.3) node{$\Omega_{23}$}; \draw[fill] (-1.5,-0.3) node{$\Omega_{24}$}; \draw[fill] (-3,-0.8) node{$\Omega_{25}$}; \draw[fill] (-4.5,-0.3) node{$\Omega_{26}$}; \draw[fill] (-6.5,1.7) node{$\Sigma_{21}$}; \draw[fill] (-6.5,-1.7) node{$\Sigma_{24}$}; \draw[fill] (-1.5,1.2) node{$\Sigma_{22}$}; \draw[fill] (-1.5,-1.2) node{$\Sigma_{23}$}; \draw[->][thick](-6,-1.5)--(-4,-0.5); \draw[-][thick](-4,-0.5)--(-3,0); \draw[->][thick](-3,0)--(-1.5,0.75); \draw[-][thick](-1.5,0.75)--(-0,1.5); \draw[->][thick](-3,0)--(-1.5,-0.75); \draw[-][thick](-1.5,-0.75)--(0,-1.5); \draw[fill][red] (0,0) circle [radius=0.05]; \draw[fill][red] (0,-0.3) node{$0$}; \draw[->][dashed][thick](0,-3)--(0,3); \draw[fill] (0.6,3) node{$Imz$}; \draw[fill] [blue](-3,0) circle [radius=0.05]; \draw[fill][blue] (-3,-0.3) node{$z_{2}$}; \draw[-][thick](6,1.5)--(4,0.5); \draw[<-][thick](4,0.5)--(3,0); \draw[fill] (4.5,0.3) node{$\Omega_{11}$}; \draw[fill] (3,0.5) node{$\Omega_{12}$}; \draw[fill] (1.5,0.3) node{$\Omega_{13}$}; \draw[fill] (1.5,-0.3) node{$\Omega_{14}$}; \draw[fill] (3,-0.8) node{$\Omega_{15}$}; \draw[fill] (4.5,-0.3) node{$\Omega_{16}$}; \draw[fill] (6.5,1.7) node{$\Sigma_{11}$}; \draw[fill] (6.5,-1.7) node{$\Sigma_{14}$}; \draw[fill] (1.5,1.2) node{$\Sigma_{12}$}; \draw[fill] (1.5,-1.2) node{$\Sigma_{13}$}; \draw[-][thick](6,-1.5)--(4,-0.5); \draw[<-][thick](4,-0.5)--(3,0); \draw[-][thick](3,0)--(1.5,0.75); \draw[<-][thick](1.5,0.75)--(0,1.5); \draw[-][thick](3,0)--(1.5,-0.75); \draw[<-][thick](1.5,-0.75)--(0,-1.5); \draw[fill][blue] (3,-0.3) node{$z_{1}$}; \end{tikzpicture}}

plot

physics

\begin{tikzpicture} [->,shorten >=1pt,scale=.75,inner sep=1pt, minimum size=12pt, auto=center, node distance=3cm, thick, node/.style={circle, draw=black, thick},] \tikzstyle{block1} = [rectangle, draw, fill=red!10, text width=8em, text centered, rounded corners, minimum height=0.8cm, minimum width=1cm]; \node (rect) at (0,0) (A) [draw, rounded corners, minimum width= 1.5cm, minimum height=1cm] {Worker}; \node (rect) at (6,0) (S) [draw, rounded corners, minimum width= 1.5cm, minimum height=1cm] {Server}; \coordinate (a1) at (1, 0.4); \coordinate (s1) at (5,0.4); \draw[->,thick] (s1) -- node[pos=.5,above]{Iterate $x_t$} (a1); \coordinate (a2) at (1,-0.4); \coordinate (s2) at (5,-0.4); \draw[->,thick] (a2) -- node[pos=.5,below] {$B$-bit symbol $\sigma_t$} node[pos=.5,above] {Channel} (s2); \node at (0,-1.6) {Encode $\nabla f(x_t)$}; \node at (8, -1.6) {Perform update: $x_{t+1}=x_{t}-\alpha g_t$}; \end{tikzpicture}

plot

eess

\begin{tikzpicture}[scale=1.25] \begin{scope}[scale=0.9] \draw [->](-1.5,0)--(-1.5,3); \draw [->](-1.5,0)--(3,0); \draw [rotate=45](1.5,-1) rectangle (3.5,0.5); \draw [fill=gray,rotate=45](1.7,-1.15) rectangle (2.1,-1); \draw [fill=gray,rotate=45](3,-1.15) rectangle (3.4,-1); \draw [fill=gray,rotate=45](1.7,0.5) rectangle (2.1,0.65); \draw [fill=gray,rotate=45](3,0.5) rectangle (3.4,0.65); \draw [->,thick](2,1.75)--(1,2.75); \draw (1.0,2.25)node [rotate=45]{\tiny{$V_y(t)$}}; \draw [->,dashed](2,1.75)--(0.5,3.25); \draw [->,thick](2.0,1.75)--(3,2.75); \draw (3.25,2.5)node [rotate=45]{\tiny{$V_x(t)$}}; \draw [->,dashed](2.0,1.75)--(3.25,3); \draw[dashed](2,0)--(2,1.75); \draw[dashed](-1.5,1.75)--(3.5,1.75); \draw (2.5,1.75) arc (0:45:0.5); \draw (2.7,2)node {\small{$\theta$}}; \draw (-1.6,3)node{\small{Y}}; \draw (3.25,0)node{\small{X}}; \draw (2,-0.1)node{\tiny{$x$}}; \draw (-1.6,1.75)node{\tiny{$y$}}; \draw (-0.25,3)circle (1mm); \draw [<->](2.2,0.5)--(-0.25,3); \draw [<->](1,0.75)--(-0.75,2.5); \draw[dashed](2,1.75)--(0.5,0.25); \draw (-0.75,2.9)node {\small{ICC}}; \draw (-0.0,1.25)node {\small{R}}; \draw (1.5,1) node [rotate=135]{\small{\textsl{l}}}; \end{scope} \end{tikzpicture}

plot

eess

\begin{tikzpicture} [ level 1/.style = {sibling distance = 3cm}, level 2/.style = {sibling distance = 1cm}, level 3/.style = {sibling distance = 3cm} ] \node {$X'$} child { node { $A$}} child { node{$B$}} ; \end{tikzpicture}

plot

cs

\begin{tikzpicture}[scale=.2] \begin{scope} \draw[thin, scale=2] (0, 0) grid (2, 2); \draw[very thick ] (0,0) -- (0,-4); \draw[very thick] (4,0) -- (4,-4); \draw[very thick] (0,-2) -- (4,-2); \draw[very thick] (0,-4) -- (4,-4); \draw[very thick] (4,-4) -- (8,-4); \draw[very thick] (4,4) -- (8,4); \draw[very thick] (6,-4) -- (6,4); \draw[very thick] (8,-4) -- (8,4); \end{scope} \end{tikzpicture}

plot

physics

\begin{tikzpicture}[scale = 0.5] \draw[step=1cm,black,very thin] (3, 0) grid (11,6); \fill[blue!40!white] (3,0) rectangle (4,1); \fill[blue!40!white] (3,1) rectangle (4,2); \fill[blue!40!white] (4,1) rectangle (5,2); \fill[blue!40!white] (4,2) rectangle (5,3); \fill[blue!40!white] (4,3) rectangle (5,4); \fill[blue!40!white] (4,4) rectangle (5,5); \fill[blue!40!white] (4,5) rectangle (5,6); \fill[blue!40!white] (5,1) rectangle (6,2); \fill[blue!40!white] (5,2) rectangle (6,3); \fill[blue!40!white] (5,3) rectangle (6,4); \fill[blue!40!white] (5,4) rectangle (6,5); \fill[blue!40!white] (5,5) rectangle (6,6); \fill[blue!40!white] (6,1) rectangle (7,2); \fill[blue!40!white] (7,1) rectangle (8,2); \fill[blue!40!white] (8,1) rectangle (9,2); \fill[blue!40!white] (8,2) rectangle (9,3); \fill[blue!40!white] (8,3) rectangle (9,4); \fill[blue!40!white] (8,4) rectangle (9,5); \fill[blue!40!white] (8,5) rectangle (9,6); \fill[blue!40!white] (9,1) rectangle (10,2); \fill[blue!40!white] (9,2) rectangle (10,3); \fill[blue!40!white] (9,3) rectangle (10,4); \fill[blue!40!white] (9,4) rectangle (10,5); \fill[blue!40!white] (9,5) rectangle (10,6); \fill[blue!40!white] (10,0) rectangle (11,1); \fill[blue!40!white] (10,1) rectangle (11,2); \draw[step=1cm,black,very thin] (3, 0) grid (11,6); \end{tikzpicture}

plot

math

\begin{tikzpicture}[scale=1.5] \draw[->] (0,-0.3) -- (0,3.5); \draw[->] (-0.3,0) -- (5,0); \node[below] at (4.9,0) {\small $r$}; \node[left] at (0,3.4) {\small $t$}; \draw [domain=0:3.5] plot(\x, \x); \node[right] at (3.4,3.4) {\tiny $t=r$}; \draw[dashed] [domain=0:5] plot (\x, 1.5); \node[left] at (0,1.5) {\small $T$}; \draw[dashed] [domain=0:5.3] plot (\x, 3); \node[left] at (0,3) {\small $2T$}; \draw[red, thick] [domain=0.5:2] plot(\x+.5, \x+1); \draw[red, thick] [domain=.5:2] plot(\x, \x+1); \draw[red, thick] [domain=0:0.5] plot(\x+.5, 1.5); \draw[red, thick] [domain=1.5:2] plot(\x+.5, 3); \node[red,thick] at (0.9, 2.4) {\tiny $C^+_{TS}$}; \draw[red, thick] [domain=2.5:4] plot(\x-.5, \x-1); \draw[red, thick] [domain=3.5:5] plot(\x-1, \x-2); \draw[red, thick] [domain=2.5:3] plot(\x-.5, 1.5); \draw[red, thick] [domain=4:4.5] plot(\x-.5, 3); \node[red,thick] at (3.9, 2.4) {\tiny $C^{-}_{TS}$}; \fill[red!40,nearly transparent] (2,1.5) -- (2.5,1.5) -- (4,3) -- (3.5,3) -- cycle; \fill[red!40,nearly transparent] (0.5,1.5) -- (1,1.5) -- (2.5,3) -- (2, 3) -- cycle; \end{tikzpicture}

plot

math

\begin{tikzpicture} \draw (0,0) grid (5,1); \foreach \x in {0,...,4} \draw (\x,0)--++(1,1); \foreach \x in {1,...,5} \draw[dotted] (\x,0)--++(-1,1); \draw (0,0) node [below]{$N$}; \foreach \x in {0,...,4} \draw (\x+1,0) node [below] {$\x$}; \foreach \x in {0,...,5} \draw (\x,1) node [above] {$\x$}; \end{tikzpicture}

plot

math

\begin{tikzpicture}%[>=Stealth] \draw (-2,0) -- (2,0); \draw (-1.5,2) -- (1.2,-1.6); \draw (-1.2,-1.6) -- (1.5,2); \filldraw (0,0) circle [radius=1.5pt] (0.5,2) circle [radius=1.5pt] (1.78,1.025) circle [radius=1.5pt] (1.78,-1.025) circle [radius=1.5pt] (1.14,0.4875) circle [radius=1.5pt]; \draw (-0.5,0.25) node {$x^*$} (0.9,2.1) node {$x^k$} (3.05,1.125) node {$y^k=R_{C_1}(x^k)$} (3.05,-1.025) node {$z^k=R_{C_2}(y^k)$} (0.75,0.3) node {$x^{k+1}$}; \draw (-1.5,0.25) node {$C_2$} (-1.1,-1.05) node {$C_1$}; \draw [-stealth] (0.5,2) -- (1.7,1.085); \draw [-stealth] (1.78,1.025) -- (1.78,-0.925); \draw [dash pattern=on 3pt off 2pt] (0.5,2) -- (1.78,-1.025); \end{tikzpicture}

plot

math

\begin{tikzpicture}[scale=.7, transform shape] \tikzstyle{session1arrow}=[<->,semithick] \tikzstyle{session2arrow}=[->, semithick, dashed] \node (proximity) at (0,0) [circle, draw=black, very thick, minimum width=4cm]{}; \node (verifier) at (-1,0){\includegraphics[scale=.03]{16172_images_honest.png}}; \node (ghost) at (-1,-2.5){}; \node (device) at (1,0) {\includegraphics[scale=.03]{16173_images_attacker.png}}; \draw [session1arrow] (device) to node [above] [near start] {} (verifier); \node [above of =device, node distance=0.5cm] {Device}; \node [above of =verifier, node distance=0.5cm] {Verifier}; \end{tikzpicture}

plot

cs

assets/cs/16172_images_honest.png

assets/cs/16173_images_attacker.png

\begin{tikzpicture}[scale=1.6, every node/.style={scale=.8}] \def\t{.5}; %fee \def\QUSD{1.15}; %initial DAI pool \def\QE{1.15}; % initial ETH pool \draw[->] (0,0) -- (6.5,0) node[below right] {ETH}; \draw[->] (0,0) -- (0,6) node[above left] {DAI}; \draw[dotted] (0,\QUSD)node[left]{$Y$} -- (\QE,\QUSD) -- (\QE,0) node[below]{$X$}; \draw[domain=.8:2.6,smooth,variable=\x, blue] plot ({\x},{5.1/\x-(\t/(1-\t))*\QUSD}) ; \draw[dotted,domain=2.6:4,smooth,variable=\x, blue] plot ({\x},{5.1/\x-(\t/(1-\t))*\QUSD}) ; \draw[domain=2.6:6.5,smooth,variable=\x, blue] plot ({\x},{(3.1/(\x+\QE*(\t/(1-\t)))}) ; \draw[dotted,domain=0.4:2.6,smooth,variable=\x, blue] plot ({\x},{(3.1/(\x+\QE*(\t/(1-\t)))}) ; \draw (0,1.4) --(6.25,0); \draw(5,0) arc[start angle=0, end angle=-30, radius=-.5]; \node at (4.45,0.15) {$-\tilde p( x, x_{i''},\tau)$}; \draw (0,2.8) --(3.65,0); \draw(3.25,0) arc[start angle=0, end angle=-30, radius=-.5]; \node at (2.7,0.15) {$-\tilde p( x, x_{i'},\tau)$}; \end{tikzpicture}

plot

cs

\begin{tikzpicture} \node[draw, circle, inner sep=0pt, minimum size=14pt] (v0) at (0,0) {$v_0$}; \node[draw, circle, inner sep=0pt, minimum size=14pt] (v1) at (1,-1) {$v_1$}; \node[draw, circle, inner sep=0pt, minimum size=14pt] (vj1) at (-1,-1) {\scriptsize $v_{j+2}$}; \node[draw, circle, inner sep=0pt, minimum size=14pt] (vj2) at (4,-1) {\scriptsize $v_{j-1}$}; \node[draw, circle, inner sep=0pt, minimum size=14pt] (vl0) at (3,0) {$v_\lambda$}; \node[draw, circle, inner sep=0pt, minimum size=14pt] (vl1) at (2,-1) {\scriptsize $v_{\lambda-1}$}; \draw[thick] (v0)--(v1) (v0) -- (vj1) (vl0)--(vl1) (vl0) -- (vj2) (v0) edge[dashed] (vl0); \draw[thick,dashdotted] plot [smooth, tension=2] coordinates { (v1.south) (2.5,-2) (vj2.south) }; \draw[thick,dashdotted] plot [smooth, tension=2] coordinates { (vl1.south) (0.5,-2) (vj1.south) }; \end{tikzpicture}

plot

cs

\begin{tikzpicture} \node[circle, draw, minimum size = 4em]{Root}[sibling distance= 5 cm, level distance = 3 cm] child {node[circle, draw, minimum size = 4em] {$N_1$} [sibling distance = 2.5 cm] child{node[circle, draw, minimum size = 4em] {AQ1} edge from parent node[left, xshift=-0.2cm] {\Large 11.6}} child {node[circle, draw, minimum size = 4em] {OQ} edge from parent node[right, xshift=0.2cm] {\Large 10.3}} edge from parent node[left, xshift=-0.2cm] {\Large 8.1} } child {node[circle, draw, minimum size = 4em] {$N_2$} [sibling distance = 2.5 cm] child {node[circle, draw, minimum size = 4em] {AQ2} edge from parent node[left, xshift=-0.2cm] {\Large 5.6}} child{node[circle, draw, minimum size = 4em] {TQ} edge from parent node[right, xshift=0.2cm] {\Large 9.2}} edge from parent node[right, xshift=0.2cm] {\Large 11.2} }; \end{tikzpicture}

plot

stat

\begin{tikzpicture}[scale=0.8] \draw[thick,dashed,->] (-0.5,0)--(3,0); \draw[thick,dashed,->] (0,-0.5)--(0,2); \draw[thick,gray] (1,-0.5) -- (1,2); \node at (0,0) {$\bullet$}; \node at (1,0) {\color{gray}$\bullet$}; \node at (1,1.5) {\color{gray}$\bullet$}; \node at (-0.3,1.8) {e${}_2$}; \node at (2.8,-0.3) {e${}_1$}; \end{tikzpicture}

plot

q-fin

\begin{tikzpicture} \node[circle, draw, fill=black, inner sep=1.5pt, label=above:1] (v1) at (-4/3,0) {}; \node[circle, draw, fill=black, inner sep=1.5pt,label=right:2] (v2) at (0,0) {}; \node[circle, draw, fill=black, inner sep=1.5pt, label= right :3] (v3) at (3/4,1) {}; \node[circle, draw, fill=black, inner sep=1.5pt, label= right:4] (v4) at (3/4,-1) {}; \fill[color=lightgray] (v1.center) -- (v2.center) -- (v3.center) -- cycle; \fill[color=lightgray] (v1.center) -- (v2.center) -- (v4.center) -- cycle; \draw (v1) -- (v2); \draw (v1) -- (v3); \draw (v1) -- (v4); \draw (v2) -- (v3); \draw (v2) -- (v4); \draw (v3) -- (v4); \node[circle, draw, fill=black, inner sep=1.5pt] at (-4/3,0) {}; \node[circle, draw, fill=black, inner sep=1.5pt] at (0,0) {}; \node[circle, draw, fill=black, inner sep=1.5pt] at (3/4,1) {}; \node[circle, draw, fill=black, inner sep=1.5pt] at (3/4,-1) {}; \end{tikzpicture}

plot

stat

\begin{tikzpicture} \begin{axis}[% width=4.5in, height=3.5in, scale only axis, xmin=0.1, xmax=0.5, xlabel style={font=\color{white!15!black}, at={(axis cs: 0.3,0.1)}}, xlabel={Bit per pixel (BPP)}, ymode=log, ymin=0.1, ymax=0.5, yminorticks=true, ytick = {0.1,0.15,0.2, 0.25, 0.3, 0.35, 0.4, .45, .5}, yticklabels = {0.1,0.15,0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5}, ylabel style={font=\color{white!15!black}, at={(axis cs: 0.1,0.25)}}, ylabel={SSIM}, axis background/.style={fill=white}, xmajorgrids, ymajorgrids, yminorgrids, legend style={at={(axis cs: 0.5,0.1)}, anchor=south east, legend cell align=left, align=left, draw=white!15!black} ] \addplot [color=red, line width=1.0pt] table[row sep=crcr]{% 0.26616974914966 0.216819795287559\\ 0.266302614795918 0.217076911094681\\ 0.278984640731293 0.249056392831938\\ 0.303139615221088 0.301838144106932\\ 0.328636532738095 0.347287831829525\\ 0.566931069302721 0.557600654247583\\ }; \addlegendentry{JPEG} \addplot [color=black, line width=1.0pt] table[row sep=crcr]{% 0.131384194302721 0.0957299056703332\\ 0.143541400935374 0.149210727406744\\ 0.158814306972789 0.179399724771426\\ 0.17784731079932 0.208815158187379\\ 0.188436702806122 0.230824914521954\\ 0.219334608843537 0.2776170957478\\ 0.258576477465986 0.324522948655854\\ 0.296463116496599 0.365897396562047\\ 0.34402237457483 0.409028052413993\\ 0.442017431972789 0.464381009398488\\ 0.484634088010204 0.480418601139433\\ 0.561330782312925 0.503685930965175\\ }; \addlegendentry{JPEG-TMAE (Optimized)} \addplot [color=green, line width=1.0pt] table[row sep=crcr]{% 0.15583462185329858 0.10005479852202352\\ 0.1617889404296875 0.13439492852385929\\ 0.16532474093967017 0.15059053639389894\\ 0.16795010036892366 0.15883068032018086\\ 0.16986423068576387 0.16415489353010065\\ 0.17078823513454863 0.16656789836941904\\ 0.17131720648871526 0.16811935272638226\\ 0.17161220974392363 0.16865256504237\\ 0.17186652289496526 0.16927173673077942\\ 0.17205047607421875 0.16978527558660705\\ 0.1721369425455729 0.17018323184257259\\ 0.17225731743706596 0.1701982345665436\\ 0.17243872748480904 0.17030083823028472\\ 0.17266591389973954 0.17049914467515284\\ 0.2577395968967014 0.26311950422145176\\ 0.3071738349066841 0.32328938829565285\\ 0.33673434787326384 0.3824002583473112\\ 0.3608957926432292 0.4207165501303598\\ 0.3771396213107639 0.4428826127495627\\ 0.38805389404296875 0.45852518054993957\\ 0.3957095675998265 0.46985682074589286\\ 0.4020572238498264 0.47701610728861965\\ 0.40517340766059035 0.4811334995592545\\ 0.4079615275065105 0.4845167843088319\\ 0.40952131483289916 0.48739381847968577\\ 0.4108784993489584 0.4903266787751413\\ 0.412324693467882 0.4924518318067699\\ 0.4134462144639757 0.49421304458665083\\ }; \addlegendentry{ConvLSTM (CNN-LSTM Based)\cite{ConvLSTM}} \addplot [color=brown, line width=1.0pt] table[row sep=crcr]{% 0.17167522 0.16625049\\ 0.21742701 0.27015172\\ 0.27555805 0.34790647\\ 0.31232452 0.38280889\\ 0.39392401 0.43696703\\ 0.46371333 0.46766172\\ 0.58388265 0.50097406\\ 0.77102294 0.53066724\\ 1.01181511 0.54945989\\ }; \addlegendentry{cheng2020-anchor(CNN based)\cite{cheng2020image}} \addplot [color=blue, line width=1.0pt] table[row sep=crcr]{% 0.17003716 0.16144037\\ 0.21402232 0.25665099\\ 0.26508416 0.31950167\\ 0.29616631 0.34490801\\ 0.36334144 0.38455074\\ 0.45891232 0.46451866\\ 0.57301500 0.49298646\\ 0.74923282 0.52114487\\ 0.86121707 0.53466851\\ }; \addlegendentry{mbt2018(CNN Based)\cite{minnenbt18}} \end{axis} \end{tikzpicture}%

plot

cs

\begin{tikzpicture} \draw [decorate, decoration={brace,amplitude=5pt},line width=0.5pt] (0,0) -- (5,0); \node at (2.5,0.4) {\tiny Theorems~\ref{thm:nonparam_dis_cont_a}~\&~\ref{thm:nonparam_dis_disc_a}}; \end{tikzpicture}

plot

stat

\begin{tikzpicture}[scale=1.0,pin distance=0.5cm] \draw[step=0.125in,gray,very thin] (0,0) grid (2.0in,1.5in); \draw[thick,->] (-0.1in,0) -- (2.1in,0) node[below left] {FPR}; \draw[thick,->] (0,-0.1in) -- (0,1.6in) node[below left] {TPR}; \foreach \y/\l in {0.25,0.5,0.75} \draw (1pt,3*\y/2) -- (-1pt,3*\y/2) node[left] {\y}; \definecolor{c0}{RGB}{51,34,136} \definecolor{c1}{RGB}{68,170,153} \definecolor{c2}{RGB}{136,204,238} \definecolor{c3}{RGB}{17,119,51} \definecolor{c4}{RGB}{153,153,51} \draw (1.3333333333333333,1pt) -- (1.3333333333333333,-1pt) node[below] {$10^{-1}$}; \draw (0.6666666666666666,1pt) -- (0.6666666666666666,-1pt) node[below] {$10^{-2}$}; \draw[c1,ultra thick] (0.054,0.003) -- (1.073,0.215) -- (1.134,0.275) -- (1.175,0.329) -- (1.205,0.367) -- (1.237,0.403) -- node[pin=320:RoBERTa]{} (1.264,0.430) -- (1.289,0.464) -- (1.311,0.491) -- (1.330,0.517) -- (1.347,0.541) -- (1.364,0.567) -- (1.380,0.586) -- (1.395,0.610) -- (1.405,0.630) -- (1.415,0.649) -- (1.426,0.666) -- (1.437,0.685) -- (1.447,0.698) -- (1.457,0.709) -- (1.468,0.723) -- (1.479,0.735) -- (1.489,0.748) -- (1.497,0.762) -- (1.506,0.777) -- (1.515,0.794) -- (1.525,0.809) -- (1.533,0.823) -- (1.543,0.835) -- (1.553,0.846) -- (1.562,0.857) -- (1.570,0.870) -- (1.578,0.883) -- (1.587,0.895) -- (1.595,0.907) -- (1.604,0.919) -- (1.612,0.933) -- (1.620,0.945) -- (1.627,0.954) -- (1.635,0.964) -- (1.641,0.975) -- (1.649,0.991) -- (1.655,1.002) -- (1.662,1.014) -- (1.668,1.027) -- (1.675,1.036) -- (1.682,1.047) -- (1.689,1.057) -- (1.696,1.067) -- (1.702,1.079) -- (1.709,1.089) -- (1.719,1.099) -- (1.726,1.109) -- (1.732,1.118) -- (1.738,1.128) -- (1.744,1.137) -- (1.749,1.148) -- (1.756,1.156) -- (1.763,1.165) -- (1.769,1.173) -- (1.776,1.182) -- (1.781,1.191) -- (1.787,1.200) -- (1.792,1.210) -- (1.797,1.217) -- (1.802,1.223) -- (1.808,1.232) -- (1.814,1.240) -- (1.819,1.249) -- (1.824,1.257) -- (1.829,1.266) -- (1.834,1.276) -- (1.838,1.285) -- (1.844,1.292) -- (1.850,1.301) -- (1.855,1.308) -- (1.861,1.316) -- (1.866,1.324) -- (1.872,1.332) -- (1.877,1.339) -- (1.883,1.347) -- (1.889,1.356) -- (1.895,1.363) -- (1.901,1.370) -- (1.906,1.377) -- (1.912,1.385) -- (1.916,1.392) -- (1.923,1.400) -- (1.927,1.407) -- (1.934,1.414) -- (1.940,1.421) -- (1.947,1.429) -- (1.952,1.435) -- (1.958,1.442) -- (1.963,1.448) -- (1.968,1.456) -- (1.972,1.461) -- (1.977,1.468) -- (1.982,1.474) -- (1.988,1.482); \draw[c0,ultra thick] (0.000,0.051) -- (0.478,0.139) -- (0.645,0.194) -- (0.760,0.253) -- (0.841,0.280) -- (0.906,0.303) -- (0.967,0.334) -- (1.006,0.358) -- (1.042,0.381) node[pin=120:UAR]{}-- (1.076,0.404) -- (1.106,0.424) -- (1.134,0.446) -- (1.156,0.474) -- (1.176,0.505) -- (1.197,0.528) -- (1.218,0.548) -- (1.235,0.569) -- (1.252,0.591) -- (1.269,0.609) -- (1.285,0.630) -- (1.299,0.654) -- (1.315,0.671) -- (1.329,0.693) -- (1.342,0.712) -- (1.356,0.731) -- (1.371,0.748) -- (1.385,0.762) -- (1.397,0.778) -- (1.409,0.796) -- (1.420,0.813) -- (1.430,0.829) -- (1.439,0.843) -- (1.448,0.858) -- (1.458,0.871) -- (1.467,0.883) -- (1.476,0.894) -- (1.486,0.907) -- (1.498,0.920) -- (1.508,0.932) -- (1.517,0.944) -- (1.526,0.955) -- (1.533,0.967) -- (1.542,0.980) -- (1.551,0.993) -- (1.563,1.010) -- (1.576,1.030) -- (1.591,1.049) -- (1.605,1.067) -- (1.612,1.077) -- (1.619,1.087) -- (1.626,1.097) -- (1.632,1.108) -- (1.640,1.117) -- (1.648,1.129) -- (1.654,1.139) -- (1.660,1.149) -- (1.667,1.158) -- (1.674,1.169) -- (1.681,1.177) -- (1.688,1.186) -- (1.696,1.194) -- (1.703,1.204) -- (1.710,1.211) -- (1.717,1.219) -- (1.724,1.228) -- (1.730,1.236) -- (1.735,1.245) -- (1.742,1.252) -- (1.749,1.260) -- (1.755,1.268) -- (1.761,1.278) -- (1.768,1.286) -- (1.773,1.295) -- (1.779,1.302) -- (1.785,1.311) -- (1.790,1.319) -- (1.796,1.326) -- (1.802,1.334) -- (1.809,1.342) -- (1.814,1.352) -- (1.820,1.360) -- (1.827,1.368) -- (1.834,1.376) -- (1.841,1.383) -- (1.850,1.395) -- (1.867,1.412) -- (1.877,1.420) -- (1.882,1.427) -- (1.889,1.433) -- (1.895,1.439) -- (1.903,1.445) -- (1.909,1.451) -- (1.915,1.457) -- (1.923,1.463) -- (1.932,1.469) -- (1.942,1.476) -- (1.954,1.480) -- (1.963,1.486) -- (1.972,1.492) -- (1.983,1.495); \end{tikzpicture}

plot

cs

\begin{tikzpicture}[baseline={(0, +0.3cm)}] \draw[thick] (-2.5,-0.05) -- (2.5,-0.05); \draw[thick] (-1.5,0) -- (1.5,0); \draw[thick] (1.5,0) -- (1.5,1); \draw[thick] (-1.5,0) -- (-1.5,1); \draw[thick] (.5,0.05) -- (0.5,1); \draw[thick] (-.5,0.05) -- (-.5,1); \draw[thick] (-.5,0.05) -- (.5,0.05); \node at (-2.6,-0.1) {$1$}; \node at (-1.5,1.2) {$2$}; \node at (-.5,1.2) {$3$}; \node at (.5,1.2) {$4$}; \node at (1.5,1.2) {$5$}; \node at (2.6,-0.1) {$6$}; \end{tikzpicture}

plot

physics

\begin{tikzpicture} \node[circle,draw, minimum width=0.25in] at (0,0) (a) {$a$}; \node[circle,draw,minimum width=0.25in] at (3,0) (c) {$c$}; \node[circle,draw,minimum width=0.25in, fill=gray!75] at (1.5,1.5) (b) {$b$}; \node[circle,draw,minimum width=0.25in, fill=gray!75] at (1.5,-1.5) (d) {$d$}; \path[->,draw,thick] (a) to[pos=.7] node[fill=white] {$6$} (c); \path[->,draw,thick] (b) to node[fill=white] {$5$} (a); \path[->,draw,thick] (a) to node[fill=white] {$2$} (d); \path[->,draw,thick] (c) to node[fill=white] {$1$} (d); \path[->,draw,thick] (b) to[pos=.7] node[fill=white] {$3$} (d); \path[->,draw,thick] (c) to node[fill=white] {$4$} (b); \end{tikzpicture}

plot

econ

\begin{tikzpicture}[baseline] \begin{scope}[shift={(0,3)}] \node at (0,-2.5) {$\text{Ising}^e_0\oplus(\text{Ising}^m_1)_{\sqrt2}\oplus(\text{Ising}^m_2)_{\sqrt2}$}; \begin{scope}[shift={(-1.9,0)}] \draw [stealth-stealth](1.3,-2.2) .. controls (1.1,-1.9) and (0.2,-1.9) .. (0,-2.2); \end{scope} \draw [stealth-stealth](-2,-2.2) .. controls (-1.6,-1.3) and (0.9,-1.3) .. (1.3,-2.2); \node at (-0.3,-1.3) {$S$}; \draw [-stealth](-2.2,-2.8) .. controls (-2.6,-3.3) and (-1.6,-3.3) .. (-2,-2.8); \node at (-2.1,-3.5) {$A$}; \begin{scope}[shift={(-0.4,-1.2)}] \draw [stealth-stealth](2,-1.6) .. controls (1.8,-2.1) and (0.2,-2.1) .. (0,-1.6); \node at (1,-2.3) {$A$}; \end{scope} \end{scope} \end{tikzpicture}

plot

math

\begin{tikzpicture} \node[anchor=south west,inner sep=0] at (0,0) { \includegraphics[width=.99\textwidth]{6763_imgs_levir_changeformer_gt_1771.jpg}}; \end{tikzpicture}

plot

cs

assets/cs/6763_imgs_levir_changeformer_gt_1771.jpg

\begin{tikzpicture}[>=stealth, node distance=1.5cm] \tikzstyle{square} = [draw, thick, minimum size=1.0mm, inner sep=3pt] \begin{scope} \path[->, thick] node[] (a) {$A$} node[right of=a] (y) {$Y$} node[above of=a, xshift=0.75cm] (u) {$U$} node[left of=u] (age) {Age} node[right of=u] (gen) {Gender} (a) edge[black] (y) (u) edge[black] (a) (u) edge[black] (y) (age) edge[black] (a) (age) edge[black] (y) (gen) edge[black] (a) (gen) edge[black] (y) ; \end{scope} \end{tikzpicture}

plot

stat

\begin{tikzpicture} \begin{axis} [xbar, grid=major, bar width =25, symbolic y coords={device\_off,weather,wind\_speed,BPM,location}, ytick=data, nodes near coords] \addplot [draw=black,fill=gray] coordinates { (0.2,device\_off) (0.15,weather) (0.14,wind\_speed) (0.12,BPM) (0.1,location) }; \end{axis} \end{tikzpicture}

plot

cs

\begin{tikzpicture}[scale=0.4,style=thick,x=1cm,y=1cm] \def\vr{6pt} \begin{scope} %mutual \coordinate(a) at (0,14); \coordinate(b) at (2,14); \coordinate(c) at (2,12); \coordinate(d) at (0,12); \draw (a) -- (b) -- (c) -- (d) -- (a) -- (c) -- (b) -- (d); \draw(a)[fill=black] circle(\vr); \draw(b)[fill=black] circle(\vr); \draw(c)[fill=black] circle(\vr); \draw(d)[fill=black] circle(\vr); \node at (-6,13) {Mutual-visibility}; \end{scope} \begin{scope} %outer \coordinate(a) at (0,10); \coordinate(b) at (2,10); \coordinate(c) at (2,8); \coordinate(d) at (0,8); \coordinate(e) at (4,10); \coordinate(f) at (6,10); \coordinate(g) at (6,8); \coordinate(h) at (4,8); \draw (a) -- (b) -- (c) -- (d) -- (a) -- (c) -- (b) -- (d); \draw (e) -- (h) -- (g) -- (e) -- (f) -- (h); \draw(a)[fill=black] circle(\vr); \draw(b)[fill=black] circle(\vr); \draw(c)[fill=black] circle(\vr); \draw(d)[fill=black] circle(\vr); \draw(e)[fill=black] circle(\vr); \draw(f)[fill=black] circle(\vr); \draw(g)[fill=black] circle(\vr); \draw(h)[fill=black] circle(\vr); \node at (-7.3,9) {Outer mutual-visibility}; \end{scope} \begin{scope} %dual \coordinate(a) at (0,6); \coordinate(b) at (2,6); \coordinate(c) at (2,4); \coordinate(d) at (0,4); \coordinate(e) at (4,6); \coordinate(f) at (6,6); \coordinate(g) at (6,4); \coordinate(h) at (4,4); \draw (a) -- (b) -- (c) -- (d) -- (a) -- (c) -- (b) -- (d); \draw (e) -- (f) -- (g) -- (h) -- (e); \draw(a)[fill=black] circle(\vr); \draw(b)[fill=black] circle(\vr); \draw(c)[fill=black] circle(\vr); \draw(d)[fill=black] circle(\vr); \draw(e)[fill=black] circle(\vr); \draw(f)[fill=black] circle(\vr); \draw(g)[fill=black] circle(\vr); \draw(h)[fill=black] circle(\vr); \node at (-7.1,5) {Dual mutual-visibility}; \end{scope} \begin{scope} %total \coordinate(a) at (0,2); \coordinate(b) at (2,2); \coordinate(c) at (2,0); \coordinate(d) at (0,0); \coordinate(e) at (4,2); \coordinate(f) at (6,2); \coordinate(g) at (6,0); \coordinate(h) at (4,0); \coordinate(i) at (8,2); \coordinate(l) at (10,2); \coordinate(m) at (10,0); \coordinate(n) at (8,0); \draw (a) -- (b) -- (c) -- (d) -- (a) -- (c) -- (b) -- (d); \draw (e) -- (h) -- (g) -- (e) -- (f) -- (h); \draw (i) -- (l) -- (m) -- (n) -- (i); \draw(a)[fill=black] circle(\vr); \draw(b)[fill=black] circle(\vr); \draw(c)[fill=black] circle(\vr); \draw(d)[fill=black] circle(\vr); \draw(e)[fill=black] circle(\vr); \draw(f)[fill=black] circle(\vr); \draw(g)[fill=black] circle(\vr); \draw(h)[fill=black] circle(\vr); \draw(i)[fill=black] circle(\vr); \draw(l)[fill=black] circle(\vr); \draw(m)[fill=black] circle(\vr); \draw(n)[fill=black] circle(\vr); \node at (-7.3,1) {Total mutual-visibility}; \end{scope} \end{tikzpicture}

plot

math

\begin{tikzpicture}[scale=1.3] \draw[thick,domain = -90:180] plot({cos(\x)},{sin(\x)}); \draw[thick,domain =0:90] plot ({0.35*cos(\x)},{0.35*sin(\x)}); \node[] at (0.5,0.15) {$\frac{\pi}{4}$}; \draw[thick,green] (1,0)--(0,0)--(-1,0); \draw[thick,blue] (0,1)--(0,0)--(0,-1); \filldraw[black] (0,0) circle (0.1); \end{tikzpicture}

plot

math

\begin{tikzpicture} \node[inner sep=0pt] at (-0,5) {\includegraphics[width=1\textwidth]{9419_figures_Corr_CovarianceReconstructedLambda.pdf}}; \node at (-8,10) {\textbf{(a)}}; \node[inner sep=0pt] at (-0,-4) {\includegraphics[width=0.8\textwidth]{9420_figures_error_weights.pdf}}; \node at (-8,-1) {\textbf{(b)}}; \end{tikzpicture}

plot

physics

assets/physics/9419_figures_Corr_CovarianceReconstructedLambda.pdf

assets/physics/9420_figures_error_weights.pdf

\begin{tikzpicture} \begin{axis}[ width=0.49\textwidth, height=150pt, xlabel={\footnotesize Epoch}, ylabel={\footnotesize WER (\%)}, xmin=0, xmax=62, ymin=0, ymax=100, xtick={0,10,20,30,40,50,60}, ytick={0,20,40,60,80,100}, legend style={at={(0.45,-0.45)}, anchor=north west, legend columns=6, anchor=north}, ymajorgrids=true, xmajorgrids=true, major grid style={line width=0.6pt,dotted,green!10!black} ] \addplot[ mark=+, mark size=1pt, smooth, line width=1pt ] coordinates { (1,71.93)(10,46.18)(20,36.80)(30,32.96)(40,31.66)(50,29.93)(60,28.78) }; \addlegendentry{ \texttt{TeLeS}}; \node (mark) [draw, green, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 1,71.93) {}; \node (mark) [draw, green, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 10,46.18) {}; \node (mark) [draw, green, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 20,36.80) {}; \node (mark) [draw, green, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 30,32.96) {}; \node (mark) [draw, red, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 40,31.66) {}; \node (mark) [draw, red, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 50,29.93) {}; \node (mark) [draw, red, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 60,28.78) {}; \addplot[ mark=square, mark size=1pt, smooth, line width=1pt ] coordinates { (1,95.43)(10,84.8)(20,65.94)(30,43.53)(40,39.29)(50,34.74)(60,31.71) }; \addlegendentry{Path Probability}; \node (mark) [draw, green, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 1,95.43) {}; \node (mark) [draw, green, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 10,84.8) {}; \node (mark) [draw, green, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 20,65.94) {}; \node (mark) [draw, green, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 30,43.53) {}; \node (mark) [draw, red, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 40,39.29) {}; \node (mark) [draw, red, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 50,34.74) {}; \node (mark) [draw, red, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 60,31.71) {}; \addplot[ mark=*, mark size=1pt, smooth, line width=1pt ] coordinates { (1,92.48)(10,80.5)(20,64.75)(30,59.97)(40,52.49)(50,38.02)(60,33.09) }; \addlegendentry{Dropout}; \node (mark) [draw, green, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 1,92.48) {}; \node (mark) [draw, green, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 10,80.5) {}; \node (mark) [draw, green, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 20,64.75) {}; \node (mark) [draw, green, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 30,59.97) {}; \node (mark) [draw, red, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 40,52.49) {}; \node (mark) [draw, red, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 50,38.02) {}; \node (mark) [draw, red, circle, minimum size = 5pt, inner sep=1pt, thick] at (axis cs: 60,33.09) {}; \end{axis} \end{tikzpicture}

plot

eess

\begin{tikzpicture} \node[anchor=mid] at (-2.9,5.8){\textbf{(a)} Single-degree-of-freedom system}; \node at (-3.1,3.2){\includegraphics[width=0.36\textwidth]{6226_figs_1dof_BW_cs1.pdf}}; \node[anchor=mid] at (5.5,5.8){\textbf{(b)} System response}; \node at (5.2,3){\includegraphics{6227_figs_orig_resp.pdf}}; \node[anchor=mid] at (5.5,.3){\textbf{(c)} Noisy data}; \node at (5.2,-2.5){\includegraphics{6228_figs_noisy_data.pdf}}; \end{tikzpicture}

plot

stat

assets/stat/6226_figs_1dof_BW_cs1.pdf

assets/stat/6227_figs_orig_resp.pdf

assets/stat/6228_figs_noisy_data.pdf

\begin{tikzpicture} \def \n {12} \def \radius {1.7cm} \def \margin {1} % margin in angles, depends on the radius \node[label=right:{$o$},draw, circle] at ({0}:\radius) {}; \foreach \s in {1,...,\n} { \node[draw, circle] at ({360/\n * (\s - 1)}:\radius) { }; \draw ({360/\n * (\s - 1)+\margin}:\radius) edge ({360/\n * (\s)-\margin}:\radius); } \end{tikzpicture}

plot

physics

\begin{tikzpicture}[scale=0.8\columnwidth/10cm,font=\footnotesize] \begin{axis}[% width=8 cm, height=4 cm, at={(1.011in,0.642in)}, scale only axis, xmin=15, xmax=35, xlabel style={font=\color{white!15!black}}, xlabel={Transmit Power (dBm)}, ymode=log, ymin=0.01, ymax=1000, yminorticks=true, ylabel style={font=\color{white!15!black}}, ylabel={RMSE (m/s)}, axis background/.style={fill=white}, xmajorgrids, ymajorgrids, yminorgrids, legend pos=south west, legend style={legend cell align=left, align=left, draw=white!15!black} ] \addplot [color=red, line width=2.0pt, mark=o, mark options={solid, red}] table[row sep=crcr]{% 15 199.243780158084\\ 17.5000000000000 194.163167940730\\ 20 174.228060997417\\ 22.5000000000000 91.3895720013635\\ 25 3.65264668570572\\ 27.5000000000000 1.22272600933260\\ 30 0.427381773468185\\ 32.5000000000000 0.0439498826946753\\ 35 0.0334928255770541\\ }; \addlegendentry{Joint, $M/L=2$} \addplot [color=blue, line width=2.0pt, mark=triangle, mark options={solid, blue}] table[row sep=crcr]{% 15 190.855917549964\\ 17.5000000000000 195.664218994481\\ 20 178.050278183231\\ 22.5000000000000 123.834231220601\\ 25 12.1888612815114\\ 27.5000000000000 0.283925327056736\\ 30 0.0577413244336539\\ 32.5000000000000 0.0421210208191051\\ 35 0.0327317648156685\\ }; \addlegendentry{Joint, $M/L=5$} \addplot [color=red, dashdotted, line width=2.0pt] table[row sep=crcr]{% 15 0.336285841175641\\ 17.5000000000000 0.252178804979125\\ 20 0.189107425571529\\ 22.5000000000000 0.141810563378049\\ 25 0.106342920299630\\ 27.5000000000000 0.0797459401357261\\ 30 0.0598010187254517\\ 32.5000000000000 0.0448444376542461\\ 35 0.0336285841178686\\ }; \addlegendentry{CRB, $M/L=2$} \addplot [color=blue, dashed, line width=2.0pt] table[row sep=crcr]{% 15 0.327917487523110\\ 17.5000000000000 0.245903425032826\\ 20 0.184401554487220\\ 22.5000000000000 0.138281657902165\\ 25 0.103696614517354\\ 27.5000000000000 0.0777614907540377\\ 30 0.0583128916254873\\ 32.5000000000000 0.0437284997595780\\ 35 0.0327917487524856\\ }; \addlegendentry{CRB, $M/L=5$} \end{axis} \end{tikzpicture}%

plot

eess

\begin{tikzpicture}[x = {(0.75cm,0.25cm)}, y={(0.6cm,-0.15cm)}, z={(0cm,1cm)},] \draw [color=orange, mark=*, mark size=1] plot coordinates{(-0.81684757298044, 0.63369514596088, -0.7745966692414834)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(0.63369514596088, -0.81684757298044, -0.7745966692414834)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(-0.81684757298044, -0.81684757298044, -0.7745966692414834)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(-0.108103018168072, -0.783793963663856, -0.7745966692414834)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(-0.783793963663856, -0.108103018168072, -0.7745966692414834)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(-0.108103018168072, -0.108103018168072, -0.7745966692414834)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(-0.81684757298044, 0.63369514596088, 0.0)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(0.63369514596088, -0.81684757298044, 0.0)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(-0.81684757298044, -0.81684757298044, 0.0)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(-0.108103018168072, -0.783793963663856, 0.0)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(-0.783793963663856, -0.108103018168072, 0.0)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(-0.108103018168072, -0.108103018168072, 0.0)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(-0.81684757298044, 0.63369514596088, 0.7745966692414834)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(0.63369514596088, -0.81684757298044, 0.7745966692414834)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(-0.81684757298044, -0.81684757298044, 0.7745966692414834)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(-0.108103018168072, -0.783793963663856, 0.7745966692414834)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(-0.783793963663856, -0.108103018168072, 0.7745966692414834)}; \draw [color=orange, mark=*, mark size=1] plot coordinates{(-0.108103018168072, -0.108103018168072, 0.7745966692414834)}; \path (-1,-1,-1) coordinate (A) (1,-1,-1) coordinate (B) (-1,1,-1) coordinate (C); % (0,0,0) coordinate (D) (0,\z,\y) coordinate (E) (\x,\z,\y) coordinate (F) (\x,\z,0) coordinate (G) (0,\z,0) coordinate (H); \path (-1,-1,1) coordinate (D) (1,-1,1) coordinate (E) (-1,1,1) coordinate (F); \draw (A)--(B)--(C)--(A)--(D)--(E)--(F)--(D); \draw (B)--(E); \draw (C)--(F); \foreach \z in {-0.7745966692414834,0,0.7745966692414834}{ \draw [dashed, black, fill=black, fill opacity=0.075] (-1,-1,\z)--(1,-1,\z)--(-1,1,\z)--(-1,-1,\z); } \end{tikzpicture}

plot

math

\begin{tikzpicture}[scale = 1.3] \draw[thick,fill=gray!8] (-1,0) rectangle (1,1); \draw[thick,fill=gray!8] (0,-1) rectangle (1,1); \filldraw (0,0) circle (0.1); \end{tikzpicture}\hspace{0.8cm}

plot

math

\begin{tikzpicture}[baseline] \begin{scope}[shift={(0,3)}] \node at (1.5,-3) {$\text{Ising}_e\oplus\text{Ising}_m$}; \node at (3.5,-2.9) {$P$}; \draw [-stealth](2.7,-3.1) .. controls (3.2,-3.4) and (3.2,-2.5) .. (2.7,-2.8); \draw [-stealth,rotate=180](-0.2,2.8) .. controls (0.3,2.5) and (0.3,3.4) .. (-0.2,3.1); \node at (-0.5,-3) {$P$}; \draw [stealth-stealth](0.7,-3.3) .. controls (0.9,-3.7) and (1.9,-3.7) .. (2.1,-3.3); \node at (1.4,-3.9) {$S$}; \end{scope} \end{tikzpicture}

plot

math

\begin{tikzpicture}[font = \footnotesize] \draw (-4,0)--(-2,1.5) node[above] {$v^{a+1}$} --(0,2) node[above] {$v^{a}$}--(2,1) node[above right] {$v^{a-1}$}--(4,-1); \draw (-1,-1) node[below] {$\bar v$}--(0,2); \draw (-1,-1) node[below] {$\bar v$}--(-2,1.5); \draw (-1,-1) node[below] {$\bar v$}--(2,1); \filldraw (0,2) circle (2pt); \filldraw (-2,1.5) circle (2pt); \filldraw (2,1) circle (2pt); \filldraw (-1,-1) circle (2pt); \node[draw=none] at (0.2, 0.8) {I}; \node[draw=none] at (-1, 0.8) {II}; \end{tikzpicture}

plot

math

\begin{tikzpicture}[scale=.6] \draw [fill=gray!100] (-4,0) to (0,0) to (0,-4) to (-4,-4); \draw [fill=gray!25] (-4,-4) to (0,-4) to (0,-8) to (-4,-8); \draw [ultra thick][-] (-4,0) -- (4,0); \draw [dashed, ultra thick][-] (-4,-4) -- (0,-4); \draw [ultra thick][-] (-4,-8) -- (4,-8); \draw [ultra thick][-] (-4,0) -- (-4,-8); \draw [ultra thick][-] (0,0) -- (0,-8); \draw [ultra thick][-] (4,0) -- (4,-8); \node[align=center, above] at (-2,0) {$Z=1$}; \node[align=center] at (-2,-2) {$D=1$}; \node[align=center] at (-2,-6) {$D=0$}; \node[align=center] at (2,-4) {$D=0$}; \node[align=center, above] at (2,0) {$Z=0$}; \end{tikzpicture}

plot

econ

\begin{tikzpicture} \node[inner sep=0pt] at (-0,6.5) {\includegraphics[width=\textwidth]{9417_figures_scExtract.pdf}}; \node at (-8.5,11) {\textbf{(a)}}; \node[inner sep=0pt] at (0,-1) {\includegraphics[width=\textwidth]{9418_figures_circuitExtract.pdf}}; \node at (-8.5,1) {\textbf{(b)}}; \end{tikzpicture}

plot

physics

assets/physics/9417_figures_scExtract.pdf

assets/physics/9418_figures_circuitExtract.pdf

\begin{tikzpicture} \node[circle, draw, fill=black, inner sep=1.5pt, label=above:1] (v1) at (-4/3,0) {}; \node[circle, draw, fill=black, inner sep=1.5pt,label=right:2] (v2) at (0,0) {}; \node[circle, draw, fill=black, inner sep=1.5pt, label= right :3] (v3) at (3/4,1) {}; \node[circle, draw, fill=black, inner sep=1.5pt, label= right:4] (v4) at (3/4,-1) {}; \fill[color=lightgray] (v1.center) -- (v2.center) -- (v3.center) -- cycle; \fill[color=lightgray] (v1.center) -- (v2.center) -- (v4.center) -- cycle; \draw (v1) -- (v2); \draw (v1) -- (v3); \draw (v1) -- (v4); \draw (v2) -- (v3); \draw (v2) -- (v4); \draw (v3) -- (v4); \node[circle, draw, fill=black, inner sep=1.5pt] at (-4/3,0) {}; \node[circle, draw, fill=black, inner sep=1.5pt] at (0,0) {}; \node[circle, draw, fill=black, inner sep=1.5pt] at (3/4,1) {}; \node[circle, draw, fill=black, inner sep=1.5pt] at (3/4,-1) {}; \end{tikzpicture}

plot

math

\begin{tikzpicture} \def\psize{1.5cm} \def\msize{1.35cm} \def\w{.8cm} % block size \foreach \b in {0,1}{ \draw[fill=gray!30,xshift=-\msize+\b*\w,yshift=\msize-\b*\w] (0,0)--(\w,0)--(\w,-\w)--(0,-\w)--cycle; \draw[xshift=-\msize+\b*\w,yshift=\msize-\b*\w-.2cm, <->] (0,-.4)--(\w,-.4); \draw[xshift=-\msize+\b*\w,yshift=\msize-\b*\w, <->] (.2,-\w)--(.2,0); \node at (-\msize+\b*\w+.35cm,\msize-\b*\w-.4cm) {$d$}; } \node at (.2,0) [below right] {$\ddots$}; \node at (-\psize,0) {$\left(\vphantom{\rule{\psize}{\psize}}\right.$}; \node at (\psize,0) {$\left.\vphantom{\rule{\psize}{\psize}}\right)$}; \end{tikzpicture}

plot

math

\begin{tikzpicture}[scale=1.15] \filldraw[fill=none, very thick, fill=gray!20!white] (0,0) circle [radius=2.25cm]; \draw (0,-0.1) -- ++ (0,0.2); \draw (-0.1,0) -- ++ (0.2,0); \node[anchor=west] (M2) at (2.5, 1.9) {MISP 2}; \node[circle, fill=black, inner sep=1.75pt] (M2tc) at (0.4,1.9) {}; \draw (M2) -- (M2tc); \node[anchor=east] (M3) at (-2.5, 1.9) {MISP 3}; \node[circle, fill=black, inner sep=1.75pt] (M3tc) at (-0.4,1.9) {}; \draw (M3) -- (M3tc); \node[anchor=west] (M6) at (2.5, 1.25) {MISP 6}; \node[circle, fill=black, inner sep=1.75pt] (M6tc) at (0,1.25) {}; \draw (M6) -- (M6tc); \node[anchor=east] (M7) at (-2.5, 0.5) {MISP 7}; \node[circle, fill=black, inner sep=1.75pt] (M7tc) at (0,0.5) {}; \draw (M7) -- (M7tc); \node[anchor=west] (M5) at (2.5, 0.2) {MISP 5}; \node[circle, fill=black, inner sep=1.75pt] (M5tc) at (0,0.2) {}; \draw (M5) -- (M5tc); \node[anchor=east] (M4) at (-2.5, -1.4) {MISP 4}; \node[circle, fill=black, inner sep=1.75pt] (M4tc) at (0,-1.4) {}; \draw (M4) -- (M4tc); \node[anchor=west] (M1) at (2.5, -0.8) {MISP 1}; \node[circle, fill=black, inner sep=1.75pt] (M1tc) at (0,-0.8) {}; \draw (M1) -- (M1tc); \end{tikzpicture}

plot

stat

\begin{tikzpicture} \begin{scope}[scale=1.6,yshift=0cm] \foreach \x in {-3,...,3}{ \fill[blue] (\x,0) circle [radius=3pt]; \fill[red] (\x,0.7) circle [radius=3pt]; } \foreach \x in {1,...,3}{ \draw[<->,orange,very thick] (\x,0.1)--(\x,0.6); } \foreach \x in {0,...,3}{ \draw[<->,brown,very thick] (\x+0.92,0.09)--(\x+0.09,0.64); } \node at (-4,0.35) {$\ldots$}; \node at (4.5,0.35) {$\ldots$}; \end{scope} \end{tikzpicture}

plot

physics

\begin{tikzpicture} \draw[gray, thick] (-15,-1) -- (-16,-1); \draw[gray, thick] (-13,-2) -- (-18,-2); \filldraw[black] (-15,-1) circle (2pt) node[anchor=south] {$i+1$}; \filldraw[black] (-16,-1) circle (2pt) node[anchor=south] {$i$}; \filldraw[black] (-13,-2) circle (2pt) node[anchor=south] {$j'$}; \filldraw[black] (-18,-2) circle (2pt) node[anchor=south] {$j$}; \end{tikzpicture}

plot

math

\begin{tikzpicture} \draw[lime, fill=lime] (0,0) circle [radius=0.13] node[white] {{\fontfamily{qag}\selectfont \tiny ID}}; \draw[white, fill=white] (-0.0625,0.095) circle [radius=0.007]; \end{tikzpicture}

plot

physics

\begin{tikzpicture}[scale = 0.5] \draw[step=1cm,black,very thin] (-1, -1) grid (5,8); \fill[blue!40!white] (-1,-1) rectangle (0,0); \fill[blue!40!white] (-1,0) rectangle (0,1); \fill[blue!40!white] (-1,1) rectangle (0,2); \fill[blue!40!white] (-1,2) rectangle (0,3); \fill[blue!40!white] (-1,3) rectangle (0,4); \fill[blue!40!white] (-1,4) rectangle (0,5); \fill[blue!40!white] (-1,5) rectangle (0,6); \fill[blue!40!white] (-1,6) rectangle (0,7); \fill[blue!40!white] (-1,7) rectangle (0,8); \fill[blue!40!white] (0,-1) rectangle (1,0); \fill[blue!40!white] (0,0) rectangle (1,1); \fill[blue!40!white] (0,2) rectangle (1,3); \fill[blue!40!white] (0,4) rectangle (1,5); \fill[blue!40!white] (0,6) rectangle (1,7); \fill[blue!40!white] (1,-1) rectangle (2,0); \fill[blue!40!white] (1,1) rectangle (2,2); \fill[blue!40!white] (1,3) rectangle (2,4); \fill[blue!40!white] (1,5) rectangle (2,6); \fill[blue!40!white] (1,7) rectangle (2,8); \fill[blue!40!white] (2,-1) rectangle (3,0); \fill[blue!40!white] (2,0) rectangle (3,1); \fill[blue!40!white] (2,2) rectangle (3,3); \fill[blue!40!white] (2,4) rectangle (3,5); \fill[blue!40!white] (2,6) rectangle (3,7); \fill[blue!40!white] (3,-1) rectangle (4,0); \fill[blue!40!white] (3,1) rectangle (4,2); \fill[blue!40!white] (3,3) rectangle (4,4); \fill[blue!40!white] (3,5) rectangle (4,6); \fill[blue!40!white] (3,7) rectangle (4,8); \fill[blue!40!white] (4,-1) rectangle (5,0); \fill[blue!40!white] (4,0) rectangle (5,1); \fill[blue!40!white] (4,1) rectangle (5,2); \fill[blue!40!white] (4,2) rectangle (5,3); \fill[blue!40!white] (4,3) rectangle (5,4); \fill[blue!40!white] (4,4) rectangle (5,5); \fill[blue!40!white] (4,5) rectangle (5,6); \fill[blue!40!white] (4,6) rectangle (5,7); \fill[blue!40!white] (4,7) rectangle (5,8); \draw[step=1cm,black,very thin] (-1, -1) grid (5,8); \end{tikzpicture}

plot

math